Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,3,Mod(7,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.980928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.4 | ||
Root | \(0.186266 - 1.99131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.7 |
Dual form | 36.3.f.c.31.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.186266 | + | 1.99131i | −0.0931330 | + | 0.995654i | ||||
\(3\) | −2.67178 | + | 1.36441i | −0.890592 | + | 0.454803i | ||||
\(4\) | −3.93061 | − | 0.741826i | −0.982652 | − | 0.185456i | ||||
\(5\) | 3.07403 | + | 5.32438i | 0.614806 | + | 1.06488i | 0.990418 | + | 0.138099i | \(0.0440991\pi\) |
−0.375612 | + | 0.926777i | \(0.622568\pi\) | |||||||
\(6\) | −2.21930 | − | 5.57447i | −0.369883 | − | 0.929078i | ||||
\(7\) | 0.511543 | + | 0.295340i | 0.0730776 | + | 0.0421914i | 0.536094 | − | 0.844159i | \(-0.319899\pi\) |
−0.463016 | + | 0.886350i | \(0.653233\pi\) | |||||||
\(8\) | 2.20934 | − | 7.68888i | 0.276168 | − | 0.961109i | ||||
\(9\) | 5.27677 | − | 7.29079i | 0.586308 | − | 0.810088i | ||||
\(10\) | −11.1751 | + | 5.12959i | −1.11751 | + | 0.512959i | ||||
\(11\) | 15.1205 | + | 8.72982i | 1.37459 | + | 0.793620i | 0.991502 | − | 0.130092i | \(-0.0415274\pi\) |
0.383088 | + | 0.923712i | \(0.374861\pi\) | |||||||
\(12\) | 11.5139 | − | 3.38097i | 0.959489 | − | 0.281748i | ||||
\(13\) | −0.892255 | − | 1.54543i | −0.0686350 | − | 0.118879i | 0.829666 | − | 0.558261i | \(-0.188531\pi\) |
−0.898301 | + | 0.439381i | \(0.855198\pi\) | |||||||
\(14\) | −0.683395 | + | 0.963628i | −0.0488140 | + | 0.0688306i | ||||
\(15\) | −15.4778 | − | 10.0313i | −1.03185 | − | 0.668754i | ||||
\(16\) | 14.8994 | + | 5.83166i | 0.931212 | + | 0.364479i | ||||
\(17\) | −16.9171 | −0.995123 | −0.497562 | − | 0.867429i | \(-0.665771\pi\) | ||||
−0.497562 | + | 0.867429i | \(0.665771\pi\) | |||||||
\(18\) | 13.5353 | + | 11.8657i | 0.751963 | + | 0.659206i | ||||
\(19\) | − | 19.5058i | − | 1.02662i | −0.858203 | − | 0.513310i | \(-0.828419\pi\) | ||
0.858203 | − | 0.513310i | \(-0.171581\pi\) | |||||||
\(20\) | −8.13306 | − | 23.2084i | −0.406653 | − | 1.16042i | ||||
\(21\) | −1.76969 | − | 0.0911265i | −0.0842711 | − | 0.00433936i | ||||
\(22\) | −20.2002 | + | 28.4835i | −0.918190 | + | 1.29470i | ||||
\(23\) | −6.86778 | + | 3.96511i | −0.298599 | + | 0.172396i | −0.641813 | − | 0.766861i | \(-0.721818\pi\) |
0.343214 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(24\) | 4.58791 | + | 23.5574i | 0.191163 | + | 0.981558i | ||||
\(25\) | −6.39933 | + | 11.0840i | −0.255973 | + | 0.443359i | ||||
\(26\) | 3.24362 | − | 1.48889i | 0.124755 | − | 0.0572651i | ||||
\(27\) | −4.15071 | + | 26.6790i | −0.153730 | + | 0.988113i | ||||
\(28\) | −1.79159 | − | 1.54034i | −0.0639852 | − | 0.0550122i | ||||
\(29\) | 3.17517 | − | 5.49956i | 0.109489 | − | 0.189640i | −0.806075 | − | 0.591814i | \(-0.798412\pi\) |
0.915563 | + | 0.402174i | \(0.131745\pi\) | |||||||
\(30\) | 22.8584 | − | 28.9525i | 0.761946 | − | 0.965083i | ||||
\(31\) | 27.6558 | − | 15.9671i | 0.892124 | − | 0.515068i | 0.0174873 | − | 0.999847i | \(-0.494433\pi\) |
0.874637 | + | 0.484779i | \(0.161100\pi\) | |||||||
\(32\) | −14.3879 | + | 28.5830i | −0.449621 | + | 0.893219i | ||||
\(33\) | −52.3096 | − | 2.69357i | −1.58514 | − | 0.0816233i | ||||
\(34\) | 3.15108 | − | 33.6871i | 0.0926788 | − | 0.990798i | ||||
\(35\) | 3.63153i | 0.103758i | ||||||||
\(36\) | −26.1494 | + | 24.7428i | −0.726373 | + | 0.687301i | ||||
\(37\) | 58.2834 | 1.57523 | 0.787614 | − | 0.616169i | \(-0.211316\pi\) | ||||
0.787614 | + | 0.616169i | \(0.211316\pi\) | |||||||
\(38\) | 38.8420 | + | 3.63326i | 1.02216 | + | 0.0956122i | ||||
\(39\) | 4.49251 | + | 2.91164i | 0.115192 | + | 0.0746575i | ||||
\(40\) | 47.7301 | − | 11.8725i | 1.19325 | − | 0.296812i | ||||
\(41\) | −2.66948 | − | 4.62368i | −0.0651093 | − | 0.112773i | 0.831633 | − | 0.555325i | \(-0.187406\pi\) |
−0.896742 | + | 0.442553i | \(0.854073\pi\) | |||||||
\(42\) | 0.511095 | − | 3.50703i | 0.0121689 | − | 0.0835007i | ||||
\(43\) | −33.9324 | − | 19.5909i | −0.789126 | − | 0.455602i | 0.0505290 | − | 0.998723i | \(-0.483909\pi\) |
−0.839655 | + | 0.543121i | \(0.817243\pi\) | |||||||
\(44\) | −52.9567 | − | 45.5303i | −1.20356 | − | 1.03478i | ||||
\(45\) | 55.0399 | + | 5.68339i | 1.22311 | + | 0.126298i | ||||
\(46\) | −6.61653 | − | 14.4144i | −0.143838 | − | 0.313357i | ||||
\(47\) | −9.64117 | − | 5.56633i | −0.205131 | − | 0.118433i | 0.393915 | − | 0.919147i | \(-0.371120\pi\) |
−0.599047 | + | 0.800714i | \(0.704454\pi\) | |||||||
\(48\) | −47.7646 | + | 4.74800i | −0.995096 | + | 0.0989166i | ||||
\(49\) | −24.3255 | − | 42.1331i | −0.496440 | − | 0.859859i | ||||
\(50\) | −20.8796 | − | 14.8076i | −0.417592 | − | 0.296152i | ||||
\(51\) | 45.1987 | − | 23.0819i | 0.886249 | − | 0.452585i | ||||
\(52\) | 2.36067 | + | 6.73638i | 0.0453974 | + | 0.129546i | ||||
\(53\) | 35.8770 | 0.676925 | 0.338462 | − | 0.940980i | \(-0.390093\pi\) | ||||
0.338462 | + | 0.940980i | \(0.390093\pi\) | |||||||
\(54\) | −52.3530 | − | 13.2347i | −0.969501 | − | 0.245088i | ||||
\(55\) | 107.343i | 1.95169i | ||||||||
\(56\) | 3.40100 | − | 3.28069i | 0.0607322 | − | 0.0585837i | ||||
\(57\) | 26.6139 | + | 52.1151i | 0.466910 | + | 0.914299i | ||||
\(58\) | 10.3599 | + | 7.34713i | 0.178619 | + | 0.126675i | ||||
\(59\) | −20.8974 | + | 12.0651i | −0.354194 | + | 0.204494i | −0.666531 | − | 0.745477i | \(-0.732222\pi\) |
0.312337 | + | 0.949971i | \(0.398888\pi\) | |||||||
\(60\) | 53.3955 | + | 50.9109i | 0.889926 | + | 0.848516i | ||||
\(61\) | −37.9460 | + | 65.7244i | −0.622066 | + | 1.07745i | 0.367034 | + | 0.930207i | \(0.380373\pi\) |
−0.989100 | + | 0.147243i | \(0.952960\pi\) | |||||||
\(62\) | 26.6441 | + | 58.0454i | 0.429743 | + | 0.936216i | ||||
\(63\) | 4.85256 | − | 2.17112i | 0.0770247 | − | 0.0344622i | ||||
\(64\) | −54.2376 | − | 33.9747i | −0.847463 | − | 0.530855i | ||||
\(65\) | 5.48564 | − | 9.50141i | 0.0843944 | − | 0.146175i | ||||
\(66\) | 15.1072 | − | 103.663i | 0.228897 | − | 1.57065i | ||||
\(67\) | −31.8200 | + | 18.3713i | −0.474925 | + | 0.274198i | −0.718299 | − | 0.695734i | \(-0.755079\pi\) |
0.243374 | + | 0.969933i | \(0.421746\pi\) | |||||||
\(68\) | 66.4945 | + | 12.5495i | 0.977860 | + | 0.184552i | ||||
\(69\) | 12.9391 | − | 19.9644i | 0.187524 | − | 0.289339i | ||||
\(70\) | −7.23150 | − | 0.676431i | −0.103307 | − | 0.00966331i | ||||
\(71\) | − | 87.8370i | − | 1.23714i | −0.785730 | − | 0.618570i | \(-0.787712\pi\) | ||
0.785730 | − | 0.618570i | \(-0.212288\pi\) | |||||||
\(72\) | −44.3998 | − | 56.6803i | −0.616664 | − | 0.787226i | ||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | −10.8562 | + | 116.060i | −0.146706 | + | 1.56838i | ||||
\(75\) | 1.97450 | − | 38.3452i | 0.0263267 | − | 0.511269i | ||||
\(76\) | −14.4699 | + | 76.6696i | −0.190393 | + | 1.00881i | ||||
\(77\) | 5.15652 | + | 8.93136i | 0.0669678 | + | 0.115992i | ||||
\(78\) | −6.63478 | + | 8.40362i | −0.0850613 | + | 0.107739i | ||||
\(79\) | 32.1841 | + | 18.5815i | 0.407394 | + | 0.235209i | 0.689669 | − | 0.724124i | \(-0.257756\pi\) |
−0.282275 | + | 0.959333i | \(0.591089\pi\) | |||||||
\(80\) | 14.7512 | + | 97.2567i | 0.184391 | + | 1.21571i | ||||
\(81\) | −25.3114 | − | 76.9437i | −0.312486 | − | 0.949922i | ||||
\(82\) | 9.70439 | − | 4.45452i | 0.118346 | − | 0.0543234i | ||||
\(83\) | −66.0281 | − | 38.1214i | −0.795520 | − | 0.459294i | 0.0463824 | − | 0.998924i | \(-0.485231\pi\) |
−0.841902 | + | 0.539630i | \(0.818564\pi\) | |||||||
\(84\) | 6.88838 | + | 1.67099i | 0.0820045 | + | 0.0198927i | ||||
\(85\) | −52.0037 | − | 90.0730i | −0.611808 | − | 1.05968i | ||||
\(86\) | 45.3319 | − | 63.9207i | 0.527115 | − | 0.743264i | ||||
\(87\) | −0.979694 | + | 19.0258i | −0.0112609 | + | 0.218688i | ||||
\(88\) | 100.529 | − | 96.9724i | 1.14237 | − | 1.10196i | ||||
\(89\) | −27.5873 | −0.309969 | −0.154985 | − | 0.987917i | \(-0.549533\pi\) | ||||
−0.154985 | + | 0.987917i | \(0.549533\pi\) | |||||||
\(90\) | −21.5694 | + | 108.543i | −0.239660 | + | 1.20603i | ||||
\(91\) | − | 1.05407i | − | 0.0115832i | ||||||
\(92\) | 29.9360 | − | 10.4906i | 0.325391 | − | 0.114028i | ||||
\(93\) | −52.1045 | + | 80.3944i | −0.560264 | + | 0.864456i | ||||
\(94\) | 12.8801 | − | 18.1617i | 0.137022 | − | 0.193210i | ||||
\(95\) | 103.856 | − | 59.9614i | 1.09322 | − | 0.631172i | ||||
\(96\) | −0.557801 | − | 95.9984i | −0.00581043 | − | 0.999983i | ||||
\(97\) | 13.0585 | − | 22.6180i | 0.134624 | − | 0.233176i | −0.790830 | − | 0.612036i | \(-0.790351\pi\) |
0.925454 | + | 0.378861i | \(0.123684\pi\) | |||||||
\(98\) | 88.4309 | − | 40.5917i | 0.902357 | − | 0.414201i | ||||
\(99\) | 143.435 | − | 64.1751i | 1.44883 | − | 0.648234i | ||||
\(100\) | 33.3757 | − | 38.8196i | 0.333757 | − | 0.388196i | ||||
\(101\) | −12.8831 | + | 22.3142i | −0.127556 | + | 0.220933i | −0.922729 | − | 0.385449i | \(-0.874047\pi\) |
0.795173 | + | 0.606382i | \(0.207380\pi\) | |||||||
\(102\) | 37.5441 | + | 94.3038i | 0.368079 | + | 0.924547i | ||||
\(103\) | −16.9947 | + | 9.81187i | −0.164997 | + | 0.0952609i | −0.580225 | − | 0.814457i | \(-0.697035\pi\) |
0.415228 | + | 0.909717i | \(0.363702\pi\) | |||||||
\(104\) | −13.8539 | + | 3.44605i | −0.133211 | + | 0.0331351i | ||||
\(105\) | −4.95490 | − | 9.70264i | −0.0471895 | − | 0.0924061i | ||||
\(106\) | −6.68267 | + | 71.4422i | −0.0630441 | + | 0.673983i | ||||
\(107\) | 183.200i | 1.71215i | 0.516850 | + | 0.856076i | \(0.327105\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672895\pi\) | |||||||
\(108\) | 36.1060 | − | 101.786i | 0.334315 | − | 0.942461i | ||||
\(109\) | 100.841 | 0.925147 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(110\) | −213.753 | − | 19.9943i | −1.94321 | − | 0.181767i | ||||
\(111\) | −155.720 | + | 79.5225i | −1.40288 | + | 0.716419i | ||||
\(112\) | 5.89936 | + | 7.38353i | 0.0526729 | + | 0.0659243i | ||||
\(113\) | −9.12484 | − | 15.8047i | −0.0807508 | − | 0.139865i | 0.822822 | − | 0.568299i | \(-0.192398\pi\) |
−0.903573 | + | 0.428435i | \(0.859065\pi\) | |||||||
\(114\) | −108.734 | + | 43.2891i | −0.953810 | + | 0.379729i | ||||
\(115\) | −42.2235 | − | 24.3778i | −0.367161 | − | 0.211981i | ||||
\(116\) | −16.5601 | + | 19.2612i | −0.142759 | + | 0.166045i | ||||
\(117\) | −15.9756 | − | 1.64964i | −0.136544 | − | 0.0140995i | ||||
\(118\) | −20.1329 | − | 43.8606i | −0.170618 | − | 0.371700i | ||||
\(119\) | −8.65383 | − | 4.99629i | −0.0727212 | − | 0.0419856i | ||||
\(120\) | −111.325 | + | 96.8439i | −0.927709 | + | 0.807033i | ||||
\(121\) | 91.9194 | + | 159.209i | 0.759664 | + | 1.31578i | ||||
\(122\) | −123.810 | − | 87.8044i | −1.01483 | − | 0.719708i | ||||
\(123\) | 13.4408 | + | 8.71116i | 0.109275 | + | 0.0708224i | ||||
\(124\) | −120.549 | + | 42.2447i | −0.972170 | + | 0.340683i | ||||
\(125\) | 75.0146 | 0.600117 | ||||||||
\(126\) | 3.41950 | + | 10.0673i | 0.0271389 | + | 0.0798995i | ||||
\(127\) | − | 164.386i | − | 1.29438i | −0.762331 | − | 0.647188i | \(-0.775945\pi\) | ||
0.762331 | − | 0.647188i | \(-0.224055\pi\) | |||||||
\(128\) | 77.7567 | − | 101.675i | 0.607474 | − | 0.794339i | ||||
\(129\) | 117.390 | + | 6.04473i | 0.909998 | + | 0.0468584i | ||||
\(130\) | 17.8984 | + | 12.6934i | 0.137680 | + | 0.0976414i | ||||
\(131\) | −123.421 | + | 71.2570i | −0.942143 | + | 0.543947i | −0.890631 | − | 0.454726i | \(-0.849737\pi\) |
−0.0515116 | + | 0.998672i | \(0.516404\pi\) | |||||||
\(132\) | 203.610 | + | 49.3920i | 1.54250 | + | 0.374182i | ||||
\(133\) | 5.76083 | − | 9.97805i | 0.0433145 | − | 0.0750229i | ||||
\(134\) | −30.6559 | − | 66.7853i | −0.228775 | − | 0.498398i | ||||
\(135\) | −154.809 | + | 59.9122i | −1.14673 | + | 0.443794i | ||||
\(136\) | −37.3757 | + | 130.073i | −0.274821 | + | 0.956422i | ||||
\(137\) | −3.08176 | + | 5.33777i | −0.0224946 | + | 0.0389618i | −0.877054 | − | 0.480393i | \(-0.840494\pi\) |
0.854559 | + | 0.519354i | \(0.173828\pi\) | |||||||
\(138\) | 37.3451 | + | 29.4845i | 0.270616 | + | 0.213655i | ||||
\(139\) | 103.168 | − | 59.5642i | 0.742218 | − | 0.428519i | −0.0806575 | − | 0.996742i | \(-0.525702\pi\) |
0.822875 | + | 0.568222i | \(0.192369\pi\) | |||||||
\(140\) | 2.69397 | − | 14.2741i | 0.0192426 | − | 0.101958i | ||||
\(141\) | 33.3538 | + | 1.71748i | 0.236552 | + | 0.0121807i | ||||
\(142\) | 174.910 | + | 16.3610i | 1.23176 | + | 0.115219i | ||||
\(143\) | − | 31.1569i | − | 0.217880i | ||||||
\(144\) | 121.138 | − | 77.8561i | 0.841237 | − | 0.540667i | ||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | 11.1838 | − | 119.563i | 0.0766017 | − | 0.818923i | ||||
\(147\) | 122.479 | + | 79.3801i | 0.833192 | + | 0.540001i | ||||
\(148\) | −229.089 | − | 43.2361i | −1.54790 | − | 0.292136i | ||||
\(149\) | −103.365 | − | 179.034i | −0.693726 | − | 1.20157i | −0.970608 | − | 0.240665i | \(-0.922634\pi\) |
0.276882 | − | 0.960904i | \(-0.410699\pi\) | |||||||
\(150\) | 75.9893 | + | 11.0742i | 0.506595 | + | 0.0738283i | ||||
\(151\) | 127.422 | + | 73.5670i | 0.843853 | + | 0.487199i | 0.858572 | − | 0.512693i | \(-0.171352\pi\) |
−0.0147190 | + | 0.999892i | \(0.504685\pi\) | |||||||
\(152\) | −149.977 | − | 43.0949i | −0.986694 | − | 0.283519i | ||||
\(153\) | −89.2676 | + | 123.339i | −0.583449 | + | 0.806138i | ||||
\(154\) | −18.7456 | + | 8.60461i | −0.121724 | + | 0.0558741i | ||||
\(155\) | 170.030 | + | 98.1668i | 1.09697 | + | 0.633334i | ||||
\(156\) | −15.4984 | − | 14.7772i | −0.0993485 | − | 0.0947256i | ||||
\(157\) | 31.4395 | + | 54.4548i | 0.200251 | + | 0.346846i | 0.948609 | − | 0.316449i | \(-0.102491\pi\) |
−0.748358 | + | 0.663295i | \(0.769157\pi\) | |||||||
\(158\) | −42.9963 | + | 60.6274i | −0.272129 | + | 0.383718i | ||||
\(159\) | −95.8554 | + | 48.9510i | −0.602864 | + | 0.307868i | ||||
\(160\) | −196.416 | + | 11.2586i | −1.22760 | + | 0.0703665i | ||||
\(161\) | −4.68422 | −0.0290946 | ||||||||
\(162\) | 157.933 | − | 36.0707i | 0.974896 | − | 0.222659i | ||||
\(163\) | − | 143.325i | − | 0.879292i | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||
0.898171 | − | 0.439646i | \(-0.144896\pi\) | |||||||
\(164\) | 7.06272 | + | 20.1542i | 0.0430654 | + | 0.122891i | ||||
\(165\) | −146.460 | − | 286.796i | −0.887635 | − | 1.73816i | ||||
\(166\) | 88.2102 | − | 124.382i | 0.531386 | − | 0.749287i | ||||
\(167\) | 150.531 | − | 86.9089i | 0.901381 | − | 0.520413i | 0.0237332 | − | 0.999718i | \(-0.492445\pi\) |
0.877648 | + | 0.479306i | \(0.159111\pi\) | |||||||
\(168\) | −4.61052 | + | 13.4056i | −0.0274436 | + | 0.0797954i | ||||
\(169\) | 82.9078 | − | 143.600i | 0.490578 | − | 0.849707i | ||||
\(170\) | 189.050 | − | 86.7777i | 1.11206 | − | 0.510457i | ||||
\(171\) | −142.213 | − | 102.927i | −0.831653 | − | 0.601915i | ||||
\(172\) | 118.842 | + | 102.176i | 0.690942 | + | 0.594047i | ||||
\(173\) | −125.806 | + | 217.902i | −0.727201 | + | 1.25955i | 0.230861 | + | 0.972987i | \(0.425846\pi\) |
−0.958062 | + | 0.286562i | \(0.907488\pi\) | |||||||
\(174\) | −37.7038 | − | 5.49474i | −0.216688 | − | 0.0315790i | ||||
\(175\) | −6.54707 | + | 3.77995i | −0.0374118 | + | 0.0215997i | ||||
\(176\) | 174.377 | + | 218.246i | 0.990777 | + | 1.24004i | ||||
\(177\) | 39.3715 | − | 60.7480i | 0.222438 | − | 0.343209i | ||||
\(178\) | 5.13857 | − | 54.9347i | 0.0288684 | − | 0.308622i | ||||
\(179\) | 96.0059i | 0.536346i | 0.963371 | + | 0.268173i | \(0.0864199\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(180\) | −212.124 | − | 63.1692i | −1.17847 | − | 0.350940i | ||||
\(181\) | −328.757 | −1.81634 | −0.908170 | − | 0.418603i | \(-0.862520\pi\) | ||||
−0.908170 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(182\) | 2.09898 | + | 0.196338i | 0.0115329 | + | 0.00107878i | ||||
\(183\) | 11.7082 | − | 227.375i | 0.0639791 | − | 1.24249i | ||||
\(184\) | 15.3140 | + | 61.5658i | 0.0832282 | + | 0.334597i | ||||
\(185\) | 179.165 | + | 310.323i | 0.968460 | + | 1.67742i | ||||
\(186\) | −150.385 | − | 118.731i | −0.808520 | − | 0.638338i | ||||
\(187\) | −255.795 | − | 147.683i | −1.36789 | − | 0.789749i | ||||
\(188\) | 33.7664 | + | 29.0312i | 0.179609 | + | 0.154421i | ||||
\(189\) | −10.0027 | + | 12.4216i | −0.0529241 | + | 0.0657229i | ||||
\(190\) | 100.057 | + | 217.978i | 0.526614 | + | 1.14725i | ||||
\(191\) | −0.351914 | − | 0.203178i | −0.00184248 | − | 0.00106376i | 0.499078 | − | 0.866557i | \(-0.333672\pi\) |
−0.500921 | + | 0.865493i | \(0.667005\pi\) | |||||||
\(192\) | 191.266 | + | 16.7705i | 0.996178 | + | 0.0873463i | ||||
\(193\) | −31.2230 | − | 54.0798i | −0.161777 | − | 0.280206i | 0.773729 | − | 0.633517i | \(-0.218389\pi\) |
−0.935506 | + | 0.353311i | \(0.885056\pi\) | |||||||
\(194\) | 42.6071 | + | 30.2165i | 0.219624 | + | 0.155755i | ||||
\(195\) | −1.69258 | + | 32.8703i | −0.00867992 | + | 0.168566i | ||||
\(196\) | 64.3588 | + | 183.654i | 0.328361 | + | 0.937010i | ||||
\(197\) | −207.861 | −1.05513 | −0.527566 | − | 0.849514i | \(-0.676895\pi\) | ||||
−0.527566 | + | 0.849514i | \(0.676895\pi\) | |||||||
\(198\) | 101.075 | + | 297.576i | 0.510482 | + | 1.50291i | ||||
\(199\) | 299.128i | 1.50316i | 0.659643 | + | 0.751579i | \(0.270707\pi\) | ||||
−0.659643 | + | 0.751579i | \(0.729293\pi\) | |||||||
\(200\) | 71.0849 | + | 73.6919i | 0.355425 | + | 0.368460i | ||||
\(201\) | 59.9499 | − | 92.4995i | 0.298258 | − | 0.460196i | ||||
\(202\) | −42.0348 | − | 29.8107i | −0.208093 | − | 0.147578i | ||||
\(203\) | 3.24848 | − | 1.87551i | 0.0160024 | − | 0.00923896i | ||||
\(204\) | −194.781 | + | 57.1962i | −0.954809 | + | 0.280374i | ||||
\(205\) | 16.4121 | − | 28.4266i | 0.0800592 | − | 0.138667i | ||||
\(206\) | −16.3729 | − | 35.6692i | −0.0794802 | − | 0.173152i | ||||
\(207\) | −7.33086 | + | 70.9946i | −0.0354148 | + | 0.342969i | ||||
\(208\) | −4.28163 | − | 28.2293i | −0.0205848 | − | 0.135718i | ||||
\(209\) | 170.282 | − | 294.937i | 0.814746 | − | 1.41118i | ||||
\(210\) | 20.2439 | − | 8.05946i | 0.0963994 | − | 0.0383784i | ||||
\(211\) | −141.744 | + | 81.8360i | −0.671773 | + | 0.387848i | −0.796748 | − | 0.604311i | \(-0.793448\pi\) |
0.124975 | + | 0.992160i | \(0.460115\pi\) | |||||||
\(212\) | −141.019 | − | 26.6145i | −0.665182 | − | 0.125540i | ||||
\(213\) | 119.846 | + | 234.681i | 0.562656 | + | 1.10179i | ||||
\(214\) | −364.808 | − | 34.1240i | −1.70471 | − | 0.159458i | ||||
\(215\) | − | 240.892i | − | 1.12043i | ||||||
\(216\) | 195.962 | + | 90.8575i | 0.907229 | + | 0.420636i | ||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | −18.7833 | + | 200.805i | −0.0861617 | + | 0.921126i | ||||
\(219\) | 160.420 | − | 81.9223i | 0.732510 | − | 0.374075i | ||||
\(220\) | 79.6297 | − | 421.923i | 0.361953 | − | 1.91783i | ||||
\(221\) | 15.0944 | + | 26.1442i | 0.0683003 | + | 0.118300i | ||||
\(222\) | −129.348 | − | 324.899i | −0.582650 | − | 1.46351i | ||||
\(223\) | 330.681 | + | 190.919i | 1.48287 | + | 0.856138i | 0.999811 | − | 0.0194478i | \(-0.00619081\pi\) |
0.483063 | + | 0.875586i | \(0.339524\pi\) | |||||||
\(224\) | −15.8017 | + | 10.3721i | −0.0705434 | + | 0.0463042i | ||||
\(225\) | 47.0431 | + | 105.144i | 0.209081 | + | 0.467306i | ||||
\(226\) | 33.1717 | − | 15.2265i | 0.146777 | − | 0.0673739i | ||||
\(227\) | −51.5472 | − | 29.7608i | −0.227080 | − | 0.131105i | 0.382144 | − | 0.924103i | \(-0.375186\pi\) |
−0.609224 | + | 0.792998i | \(0.708519\pi\) | |||||||
\(228\) | −65.9485 | − | 224.587i | −0.289248 | − | 0.985030i | ||||
\(229\) | 64.4366 | + | 111.608i | 0.281383 | + | 0.487369i | 0.971726 | − | 0.236113i | \(-0.0758736\pi\) |
−0.690343 | + | 0.723482i | \(0.742540\pi\) | |||||||
\(230\) | 56.4084 | − | 79.5393i | 0.245254 | − | 0.345823i | ||||
\(231\) | −25.9631 | − | 16.8270i | −0.112394 | − | 0.0728441i | ||||
\(232\) | −35.2704 | − | 36.5639i | −0.152028 | − | 0.157603i | ||||
\(233\) | 14.9939 | 0.0643513 | 0.0321757 | − | 0.999482i | \(-0.489756\pi\) | ||||
0.0321757 | + | 0.999482i | \(0.489756\pi\) | |||||||
\(234\) | 6.26065 | − | 31.5051i | 0.0267549 | − | 0.134637i | ||||
\(235\) | − | 68.4443i | − | 0.291252i | ||||||
\(236\) | 91.0899 | − | 31.9211i | 0.385974 | − | 0.135259i | ||||
\(237\) | −111.342 | − | 5.73329i | −0.469796 | − | 0.0241911i | ||||
\(238\) | 11.5611 | − | 16.3018i | 0.0485759 | − | 0.0684949i | ||||
\(239\) | −315.244 | + | 182.006i | −1.31901 | + | 0.761532i | −0.983570 | − | 0.180529i | \(-0.942219\pi\) |
−0.335442 | + | 0.942061i | \(0.608886\pi\) | |||||||
\(240\) | −172.110 | − | 239.721i | −0.717125 | − | 0.998839i | ||||
\(241\) | −40.5235 | + | 70.1888i | −0.168147 | + | 0.291240i | −0.937769 | − | 0.347261i | \(-0.887112\pi\) |
0.769621 | + | 0.638501i | \(0.220445\pi\) | |||||||
\(242\) | −334.156 | + | 153.385i | −1.38081 | + | 0.633820i | ||||
\(243\) | 172.609 | + | 171.041i | 0.710326 | + | 0.703873i | ||||
\(244\) | 197.907 | − | 230.188i | 0.811095 | − | 0.943393i | ||||
\(245\) | 149.555 | − | 259.037i | 0.610428 | − | 1.05729i | ||||
\(246\) | −19.8502 | + | 25.1423i | −0.0806917 | + | 0.102204i | ||||
\(247\) | −30.1448 | + | 17.4041i | −0.122044 | + | 0.0704620i | ||||
\(248\) | −61.6679 | − | 247.919i | −0.248661 | − | 0.999674i | ||||
\(249\) | 228.426 | + | 11.7623i | 0.917372 | + | 0.0472381i | ||||
\(250\) | −13.9727 | + | 149.377i | −0.0558907 | + | 0.597508i | ||||
\(251\) | − | 281.883i | − | 1.12304i | −0.827463 | − | 0.561520i | \(-0.810217\pi\) | ||
0.827463 | − | 0.561520i | \(-0.189783\pi\) | |||||||
\(252\) | −20.6841 | + | 4.93406i | −0.0820798 | + | 0.0195796i | ||||
\(253\) | −138.459 | −0.547268 | ||||||||
\(254\) | 327.342 | + | 30.6195i | 1.28875 | + | 0.120549i | ||||
\(255\) | 261.839 | + | 169.701i | 1.02682 | + | 0.665492i | ||||
\(256\) | 187.984 | + | 173.776i | 0.734311 | + | 0.678813i | ||||
\(257\) | −37.6564 | − | 65.2227i | −0.146523 | − | 0.253785i | 0.783417 | − | 0.621496i | \(-0.213475\pi\) |
−0.929940 | + | 0.367711i | \(0.880142\pi\) | |||||||
\(258\) | −33.9026 | + | 232.633i | −0.131406 | + | 0.901679i | ||||
\(259\) | 29.8145 | + | 17.2134i | 0.115114 | + | 0.0664610i | ||||
\(260\) | −28.6103 | + | 33.2769i | −0.110040 | + | 0.127988i | ||||
\(261\) | −23.3415 | − | 52.1695i | −0.0894311 | − | 0.199883i | ||||
\(262\) | −118.905 | − | 259.041i | −0.453838 | − | 0.988708i | ||||
\(263\) | −105.914 | − | 61.1497i | −0.402716 | − | 0.232508i | 0.284939 | − | 0.958546i | \(-0.408027\pi\) |
−0.687655 | + | 0.726037i | \(0.741360\pi\) | |||||||
\(264\) | −136.280 | + | 396.251i | −0.516213 | + | 1.50095i | ||||
\(265\) | 110.287 | + | 191.023i | 0.416178 | + | 0.720841i | ||||
\(266\) | 18.7963 | + | 13.3302i | 0.0706628 | + | 0.0501134i | ||||
\(267\) | 73.7070 | − | 37.6403i | 0.276056 | − | 0.140975i | ||||
\(268\) | 138.700 | − | 48.6054i | 0.517538 | − | 0.181364i | ||||
\(269\) | 280.452 | 1.04257 | 0.521287 | − | 0.853382i | \(-0.325452\pi\) | ||||
0.521287 | + | 0.853382i | \(0.325452\pi\) | |||||||
\(270\) | −90.4681 | − | 319.431i | −0.335067 | − | 1.18308i | ||||
\(271\) | 81.4468i | 0.300542i | 0.988645 | + | 0.150271i | \(0.0480146\pi\) | ||||
−0.988645 | + | 0.150271i | \(0.951985\pi\) | |||||||
\(272\) | −252.054 | − | 98.6547i | −0.926670 | − | 0.362701i | ||||
\(273\) | 1.43819 | + | 2.81625i | 0.00526809 | + | 0.0103159i | ||||
\(274\) | −10.0551 | − | 7.13098i | −0.0366975 | − | 0.0260255i | ||||
\(275\) | −193.522 | + | 111.730i | −0.703716 | + | 0.406291i | ||||
\(276\) | −65.6687 | + | 68.8735i | −0.237930 | + | 0.249542i | ||||
\(277\) | 224.861 | − | 389.471i | 0.811774 | − | 1.40603i | −0.0998479 | − | 0.995003i | \(-0.531836\pi\) |
0.911622 | − | 0.411031i | \(-0.134831\pi\) | |||||||
\(278\) | 99.3939 | + | 216.534i | 0.357532 | + | 0.778901i | ||||
\(279\) | 29.5206 | − | 285.888i | 0.105809 | − | 1.02469i | ||||
\(280\) | 27.9224 | + | 8.02330i | 0.0997229 | + | 0.0286546i | ||||
\(281\) | −37.8649 | + | 65.5838i | −0.134750 | + | 0.233394i | −0.925502 | − | 0.378743i | \(-0.876357\pi\) |
0.790752 | + | 0.612137i | \(0.209690\pi\) | |||||||
\(282\) | −9.63272 | + | 66.0978i | −0.0341586 | + | 0.234389i | ||||
\(283\) | −322.061 | + | 185.942i | −1.13803 | + | 0.657039i | −0.945941 | − | 0.324339i | \(-0.894858\pi\) |
−0.192084 | + | 0.981378i | \(0.561525\pi\) | |||||||
\(284\) | −65.1597 | + | 345.253i | −0.229436 | + | 1.21568i | ||||
\(285\) | −195.668 | + | 301.906i | −0.686556 | + | 1.05932i | ||||
\(286\) | 62.0429 | + | 5.80347i | 0.216933 | + | 0.0202919i | ||||
\(287\) | − | 3.15361i | − | 0.0109882i | ||||||
\(288\) | 132.471 | + | 255.725i | 0.459970 | + | 0.887934i | ||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | −7.27226 | + | 77.7453i | −0.0250768 | + | 0.268087i | ||||
\(291\) | −4.02919 | + | 78.2475i | −0.0138460 | + | 0.268892i | ||||
\(292\) | 236.003 | + | 44.5409i | 0.808229 | + | 0.152537i | ||||
\(293\) | −66.3946 | − | 114.999i | −0.226603 | − | 0.392488i | 0.730196 | − | 0.683237i | \(-0.239429\pi\) |
−0.956799 | + | 0.290750i | \(0.906095\pi\) | |||||||
\(294\) | −180.884 | + | 229.108i | −0.615252 | + | 0.779279i | ||||
\(295\) | −128.479 | − | 74.1772i | −0.435521 | − | 0.251448i | ||||
\(296\) | 128.768 | − | 448.134i | 0.435027 | − | 1.51397i | ||||
\(297\) | −295.664 | + | 367.165i | −0.995502 | + | 1.23625i | ||||
\(298\) | 375.765 | − | 172.484i | 1.26096 | − | 0.578806i | ||||
\(299\) | 12.2556 | + | 7.07579i | 0.0409887 | + | 0.0236648i | ||||
\(300\) | −36.2065 | + | 149.255i | −0.120688 | + | 0.497517i | ||||
\(301\) | −11.5719 | − | 20.0432i | −0.0384450 | − | 0.0665886i | ||||
\(302\) | −170.229 | + | 240.033i | −0.563672 | + | 0.794811i | ||||
\(303\) | 3.97507 | − | 77.1965i | 0.0131190 | − | 0.254774i | ||||
\(304\) | 113.751 | − | 290.624i | 0.374181 | − | 0.956000i | ||||
\(305\) | −466.589 | −1.52980 | ||||||||
\(306\) | −228.978 | − | 200.733i | −0.748296 | − | 0.655991i | ||||
\(307\) | − | 336.514i | − | 1.09614i | −0.836434 | − | 0.548068i | \(-0.815363\pi\) | ||
0.836434 | − | 0.548068i | \(-0.184637\pi\) | |||||||
\(308\) | −13.6428 | − | 38.9309i | −0.0442947 | − | 0.126399i | ||||
\(309\) | 32.0185 | − | 49.4028i | 0.103620 | − | 0.159880i | ||||
\(310\) | −227.151 | + | 320.296i | −0.732745 | + | 1.03321i | ||||
\(311\) | 304.206 | − | 175.634i | 0.978156 | − | 0.564738i | 0.0764428 | − | 0.997074i | \(-0.475644\pi\) |
0.901713 | + | 0.432336i | \(0.142310\pi\) | |||||||
\(312\) | 32.3127 | − | 28.1095i | 0.103567 | − | 0.0900946i | ||||
\(313\) | −95.4299 | + | 165.289i | −0.304888 | + | 0.528081i | −0.977236 | − | 0.212154i | \(-0.931952\pi\) |
0.672349 | + | 0.740235i | \(0.265286\pi\) | |||||||
\(314\) | −114.292 | + | 52.4626i | −0.363988 | + | 0.167078i | ||||
\(315\) | 26.4768 | + | 19.1628i | 0.0840532 | + | 0.0608342i | ||||
\(316\) | −112.719 | − | 96.9117i | −0.356706 | − | 0.306683i | ||||
\(317\) | −202.797 | + | 351.255i | −0.639738 | + | 1.10806i | 0.345752 | + | 0.938326i | \(0.387624\pi\) |
−0.985490 | + | 0.169733i | \(0.945709\pi\) | |||||||
\(318\) | −79.6218 | − | 199.995i | −0.250383 | − | 0.628916i | ||||
\(319\) | 96.0203 | − | 55.4374i | 0.301004 | − | 0.173785i | ||||
\(320\) | 14.1661 | − | 393.221i | 0.0442692 | − | 1.22882i | ||||
\(321\) | −249.960 | − | 489.470i | −0.778693 | − | 1.52483i | ||||
\(322\) | 0.872512 | − | 9.32773i | 0.00270966 | − | 0.0289681i | ||||
\(323\) | 329.981i | 1.02161i | ||||||||
\(324\) | 42.4103 | + | 321.212i | 0.130896 | + | 0.991396i | ||||
\(325\) | 22.8393 | 0.0702749 | ||||||||
\(326\) | 285.403 | + | 26.6965i | 0.875470 | + | 0.0818911i | ||||
\(327\) | −269.424 | + | 137.588i | −0.823928 | + | 0.420760i | ||||
\(328\) | −41.4487 | + | 10.3100i | −0.126368 | + | 0.0314330i | ||||
\(329\) | −3.28792 | − | 5.69484i | −0.00999368 | − | 0.0173096i | ||||
\(330\) | 598.380 | − | 238.226i | 1.81327 | − | 0.721897i | ||||
\(331\) | 384.104 | + | 221.763i | 1.16044 | + | 0.669978i | 0.951408 | − | 0.307932i | \(-0.0996370\pi\) |
0.209027 | + | 0.977910i | \(0.432970\pi\) | |||||||
\(332\) | 231.251 | + | 198.822i | 0.696541 | + | 0.598860i | ||||
\(333\) | 307.548 | − | 424.932i | 0.923568 | − | 1.27607i | ||||
\(334\) | 145.024 | + | 315.941i | 0.434203 | + | 0.945931i | ||||
\(335\) | −195.631 | − | 112.948i | −0.583974 | − | 0.337158i | ||||
\(336\) | −25.8359 | − | 11.6780i | −0.0768927 | − | 0.0347559i | ||||
\(337\) | −254.239 | − | 440.356i | −0.754420 | − | 1.30669i | −0.945662 | − | 0.325150i | \(-0.894585\pi\) |
0.191243 | − | 0.981543i | \(-0.438748\pi\) | |||||||
\(338\) | 270.510 | + | 191.843i | 0.800325 | + | 0.567582i | ||||
\(339\) | 45.9436 | + | 29.7766i | 0.135527 | + | 0.0878365i | ||||
\(340\) | 137.588 | + | 392.619i | 0.404670 | + | 1.15476i | ||||
\(341\) | 557.560 | 1.63507 | ||||||||
\(342\) | 231.450 | − | 264.017i | 0.676753 | − | 0.771980i | ||||
\(343\) | − | 57.6805i | − | 0.168165i | ||||||
\(344\) | −225.600 | + | 217.619i | −0.655814 | + | 0.632614i | ||||
\(345\) | 146.073 | + | 7.52172i | 0.423400 | + | 0.0218021i | ||||
\(346\) | −410.476 | − | 291.106i | −1.18635 | − | 0.841346i | ||||
\(347\) | 492.773 | − | 284.503i | 1.42010 | − | 0.819893i | 0.423790 | − | 0.905761i | \(-0.360700\pi\) |
0.996307 | + | 0.0858678i | \(0.0273663\pi\) | |||||||
\(348\) | 17.9646 | − | 74.0564i | 0.0516226 | − | 0.212806i | ||||
\(349\) | −206.901 | + | 358.363i | −0.592840 | + | 1.02683i | 0.401008 | + | 0.916074i | \(0.368660\pi\) |
−0.993848 | + | 0.110754i | \(0.964673\pi\) | |||||||
\(350\) | −6.30755 | − | 13.7413i | −0.0180216 | − | 0.0392609i | ||||
\(351\) | 44.9341 | − | 17.3899i | 0.128017 | − | 0.0495438i | ||||
\(352\) | −467.076 | + | 306.586i | −1.32692 | + | 0.870982i | ||||
\(353\) | 62.3070 | − | 107.919i | 0.176507 | − | 0.305719i | −0.764175 | − | 0.645009i | \(-0.776853\pi\) |
0.940682 | + | 0.339290i | \(0.110187\pi\) | |||||||
\(354\) | 113.634 | + | 89.7160i | 0.321001 | + | 0.253435i | ||||
\(355\) | 467.677 | − | 270.014i | 1.31740 | − | 0.760602i | ||||
\(356\) | 108.435 | + | 20.4649i | 0.304592 | + | 0.0574858i | ||||
\(357\) | 29.9381 | + | 1.54160i | 0.0838601 | + | 0.00431820i | ||||
\(358\) | −191.177 | − | 17.8826i | −0.534015 | − | 0.0499515i | ||||
\(359\) | 303.196i | 0.844557i | 0.906466 | + | 0.422278i | \(0.138770\pi\) | ||||
−0.906466 | + | 0.422278i | \(0.861230\pi\) | |||||||
\(360\) | 165.301 | − | 410.638i | 0.459169 | − | 1.14066i | ||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | 61.2363 | − | 654.657i | 0.169161 | − | 1.80844i | ||||
\(363\) | −462.814 | − | 299.955i | −1.27497 | − | 0.826323i | ||||
\(364\) | −0.781939 | + | 4.14315i | −0.00214818 | + | 0.0113823i | ||||
\(365\) | −184.572 | − | 319.688i | −0.505677 | − | 0.875858i | ||||
\(366\) | 450.592 | + | 65.6668i | 1.23113 | + | 0.179418i | ||||
\(367\) | −615.571 | − | 355.400i | −1.67730 | − | 0.968392i | −0.963369 | − | 0.268181i | \(-0.913578\pi\) |
−0.713936 | − | 0.700211i | \(-0.753089\pi\) | |||||||
\(368\) | −125.449 | + | 19.0273i | −0.340894 | + | 0.0517045i | ||||
\(369\) | −47.7965 | − | 4.93544i | −0.129530 | − | 0.0133752i | ||||
\(370\) | −651.321 | + | 298.970i | −1.76033 | + | 0.808027i | ||||
\(371\) | 18.3527 | + | 10.5959i | 0.0494681 | + | 0.0285604i | ||||
\(372\) | 264.441 | − | 277.347i | 0.710864 | − | 0.745556i | ||||
\(373\) | 166.740 | + | 288.803i | 0.447025 | + | 0.774271i | 0.998191 | − | 0.0601254i | \(-0.0191501\pi\) |
−0.551166 | + | 0.834396i | \(0.685817\pi\) | |||||||
\(374\) | 341.728 | − | 481.857i | 0.913712 | − | 1.28839i | ||||
\(375\) | −200.422 | + | 102.351i | −0.534459 | + | 0.272935i | ||||
\(376\) | −64.0995 | + | 61.8318i | −0.170477 | + | 0.164446i | ||||
\(377\) | −11.3323 | −0.0300590 | ||||||||
\(378\) | −22.8721 | − | 22.2321i | −0.0605082 | − | 0.0588150i | ||||
\(379\) | 662.686i | 1.74851i | 0.485465 | + | 0.874256i | \(0.338650\pi\) | ||||
−0.485465 | + | 0.874256i | \(0.661350\pi\) | |||||||
\(380\) | −452.699 | + | 158.642i | −1.19131 | + | 0.417478i | ||||
\(381\) | 224.289 | + | 439.202i | 0.588686 | + | 1.15276i | ||||
\(382\) | 0.470139 | − | 0.662924i | 0.00123073 | − | 0.00173540i | ||||
\(383\) | −69.9008 | + | 40.3572i | −0.182509 | + | 0.105371i | −0.588471 | − | 0.808518i | \(-0.700270\pi\) |
0.405962 | + | 0.913890i | \(0.366936\pi\) | |||||||
\(384\) | −69.0216 | + | 377.746i | −0.179744 | + | 0.983713i | ||||
\(385\) | −31.7026 | + | 54.9106i | −0.0823445 | + | 0.142625i | ||||
\(386\) | 113.505 | − | 52.1013i | 0.294055 | − | 0.134977i | ||||
\(387\) | −321.887 | + | 144.018i | −0.831748 | + | 0.372139i | ||||
\(388\) | −68.1066 | + | 79.2155i | −0.175533 | + | 0.204164i | ||||
\(389\) | −346.006 | + | 599.301i | −0.889476 | + | 1.54062i | −0.0489809 | + | 0.998800i | \(0.515597\pi\) |
−0.840495 | + | 0.541819i | \(0.817736\pi\) | |||||||
\(390\) | −65.1396 | − | 9.49307i | −0.167025 | − | 0.0243412i | ||||
\(391\) | 116.183 | − | 67.0782i | 0.297143 | − | 0.171556i | ||||
\(392\) | −377.700 | + | 93.9497i | −0.963519 | + | 0.239668i | ||||
\(393\) | 232.529 | − | 358.779i | 0.591676 | − | 0.912924i | ||||
\(394\) | 38.7174 | − | 413.915i | 0.0982675 | − | 1.05055i | ||||
\(395\) | 228.481i | 0.578432i | ||||||||
\(396\) | −611.392 | + | 145.844i | −1.54392 | + | 0.368293i | ||||
\(397\) | 657.713 | 1.65671 | 0.828354 | − | 0.560206i | \(-0.189278\pi\) | ||||
0.828354 | + | 0.560206i | \(0.189278\pi\) | |||||||
\(398\) | −595.657 | − | 55.7175i | −1.49662 | − | 0.139994i | ||||
\(399\) | −1.77749 | + | 34.5192i | −0.00445487 | + | 0.0865144i | ||||
\(400\) | −159.984 | + | 127.826i | −0.399960 | + | 0.319564i | ||||
\(401\) | 296.433 | + | 513.437i | 0.739235 | + | 1.28039i | 0.952840 | + | 0.303472i | \(0.0981459\pi\) |
−0.213606 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(402\) | 173.028 | + | 136.608i | 0.430418 | + | 0.339821i | ||||
\(403\) | −49.3521 | − | 28.4935i | −0.122462 | − | 0.0707034i | ||||
\(404\) | 67.1918 | − | 78.1515i | 0.166316 | − | 0.193444i | ||||
\(405\) | 331.869 | − | 371.295i | 0.819431 | − | 0.916777i | ||||
\(406\) | 3.12963 | + | 6.81806i | 0.00770846 | + | 0.0167933i | ||||
\(407\) | 881.274 | + | 508.804i | 2.16529 | + | 1.25013i | ||||
\(408\) | −77.6141 | − | 398.523i | −0.190231 | − | 0.976771i | ||||
\(409\) | −161.594 | − | 279.889i | −0.395095 | − | 0.684325i | 0.598018 | − | 0.801483i | \(-0.295955\pi\) |
−0.993113 | + | 0.117157i | \(0.962622\pi\) | |||||||
\(410\) | 53.5492 | + | 37.9765i | 0.130608 | + | 0.0926257i | ||||
\(411\) | 0.950872 | − | 18.4661i | 0.00231356 | − | 0.0449297i | ||||
\(412\) | 74.0781 | − | 25.9596i | 0.179801 | − | 0.0630086i | ||||
\(413\) | −14.2533 | −0.0345115 | ||||||||
\(414\) | −140.007 | − | 27.8219i | −0.338180 | − | 0.0672026i | ||||
\(415\) | − | 468.745i | − | 1.12951i | ||||||
\(416\) | 57.0107 | − | 3.26788i | 0.137045 | − | 0.00785549i | ||||
\(417\) | −194.372 | + | 299.906i | −0.466121 | + | 0.719199i | ||||
\(418\) | 555.592 | + | 394.020i | 1.32917 | + | 0.942632i | ||||
\(419\) | −222.744 | + | 128.601i | −0.531608 | + | 0.306924i | −0.741671 | − | 0.670764i | \(-0.765967\pi\) |
0.210063 | + | 0.977688i | \(0.432633\pi\) | |||||||
\(420\) | 12.2781 | + | 41.8130i | 0.0292336 | + | 0.0995547i | ||||
\(421\) | 41.9905 | − | 72.7297i | 0.0997400 | − | 0.172755i | −0.811837 | − | 0.583884i | \(-0.801532\pi\) |
0.911577 | + | 0.411129i | \(0.134866\pi\) | |||||||
\(422\) | −136.559 | − | 297.499i | −0.323598 | − | 0.704975i | ||||
\(423\) | −91.4573 | + | 40.9196i | −0.216211 | + | 0.0967365i | ||||
\(424\) | 79.2646 | − | 275.854i | 0.186945 | − | 0.650599i | ||||
\(425\) | 108.258 | − | 187.509i | 0.254725 | − | 0.441197i | ||||
\(426\) | −489.645 | + | 194.936i | −1.14940 | + | 0.457597i | ||||
\(427\) | −38.8221 | + | 22.4139i | −0.0909182 | + | 0.0524917i | ||||
\(428\) | 135.903 | − | 720.089i | 0.317530 | − | 1.68245i | ||||
\(429\) | 42.5108 | + | 83.2442i | 0.0990927 | + | 0.194042i | ||||
\(430\) | 479.690 | + | 44.8700i | 1.11556 | + | 0.104349i | ||||
\(431\) | 144.348i | 0.334914i | 0.985879 | + | 0.167457i | \(0.0535555\pi\) | ||||
−0.985879 | + | 0.167457i | \(0.946445\pi\) | |||||||
\(432\) | −217.426 | + | 373.296i | −0.503301 | + | 0.864111i | ||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | −3.51351 | + | 37.5618i | −0.00809566 | + | 0.0865479i | ||||
\(435\) | −104.312 | + | 53.2697i | −0.239798 | + | 0.122459i | ||||
\(436\) | −396.367 | − | 74.8065i | −0.909098 | − | 0.171574i | ||||
\(437\) | 77.3426 | + | 133.961i | 0.176985 | + | 0.306548i | ||||
\(438\) | 133.252 | + | 334.704i | 0.304228 | + | 0.764165i | ||||
\(439\) | −194.776 | − | 112.454i | −0.443682 | − | 0.256160i | 0.261476 | − | 0.965210i | \(-0.415791\pi\) |
−0.705158 | + | 0.709050i | \(0.749124\pi\) | |||||||
\(440\) | 825.346 | + | 237.157i | 1.87579 | + | 0.538994i | ||||
\(441\) | −435.544 | − | 44.9740i | −0.987628 | − | 0.101982i | ||||
\(442\) | −54.8727 | + | 25.1877i | −0.124146 | + | 0.0569858i | ||||
\(443\) | −369.184 | − | 213.148i | −0.833373 | − | 0.481148i | 0.0216335 | − | 0.999766i | \(-0.493113\pi\) |
−0.855006 | + | 0.518618i | \(0.826447\pi\) | |||||||
\(444\) | 671.067 | − | 197.055i | 1.51141 | − | 0.443817i | ||||
\(445\) | −84.8041 | − | 146.885i | −0.190571 | − | 0.330079i | ||||
\(446\) | −441.772 | + | 622.926i | −0.990521 | + | 1.39669i | ||||
\(447\) | 520.444 | + | 337.306i | 1.16430 | + | 0.754599i | ||||
\(448\) | −17.7108 | − | 33.3981i | −0.0395331 | − | 0.0745493i | ||||
\(449\) | −406.744 | −0.905888 | −0.452944 | − | 0.891539i | \(-0.649626\pi\) | ||||
−0.452944 | + | 0.891539i | \(0.649626\pi\) | |||||||
\(450\) | −218.136 | + | 74.0926i | −0.484747 | + | 0.164650i | ||||
\(451\) | − | 93.2163i | − | 0.206688i | ||||||
\(452\) | 24.1419 | + | 68.8911i | 0.0534112 | + | 0.152414i | ||||
\(453\) | −440.818 | − | 22.6990i | −0.973108 | − | 0.0501081i | ||||
\(454\) | 68.8644 | − | 97.1029i | 0.151684 | − | 0.213883i | ||||
\(455\) | 5.61228 | − | 3.24025i | 0.0123347 | − | 0.00712144i | ||||
\(456\) | 459.505 | − | 89.4908i | 1.00769 | − | 0.196252i | ||||
\(457\) | −159.600 | + | 276.435i | −0.349234 | + | 0.604891i | −0.986114 | − | 0.166072i | \(-0.946892\pi\) |
0.636879 | + | 0.770963i | \(0.280225\pi\) | |||||||
\(458\) | −234.247 | + | 107.524i | −0.511457 | + | 0.234770i | ||||
\(459\) | 70.2180 | − | 451.332i | 0.152980 | − | 0.983294i | ||||
\(460\) | 147.880 | + | 127.142i | 0.321479 | + | 0.276396i | ||||
\(461\) | 293.888 | − | 509.029i | 0.637501 | − | 1.10418i | −0.348478 | − | 0.937317i | \(-0.613302\pi\) |
0.985979 | − | 0.166867i | \(-0.0533652\pi\) | |||||||
\(462\) | 38.3437 | − | 48.5662i | 0.0829951 | − | 0.105122i | ||||
\(463\) | 230.088 | − | 132.841i | 0.496950 | − | 0.286914i | −0.230503 | − | 0.973072i | \(-0.574037\pi\) |
0.727453 | + | 0.686157i | \(0.240704\pi\) | |||||||
\(464\) | 79.3797 | − | 63.4236i | 0.171077 | − | 0.136689i | ||||
\(465\) | −588.221 | − | 30.2892i | −1.26499 | − | 0.0651380i | ||||
\(466\) | −2.79285 | + | 29.8574i | −0.00599323 | + | 0.0640716i | ||||
\(467\) | − | 794.598i | − | 1.70149i | −0.525575 | − | 0.850747i | \(-0.676150\pi\) | ||
0.525575 | − | 0.850747i | \(-0.323850\pi\) | |||||||
\(468\) | 61.5703 | + | 18.3352i | 0.131560 | + | 0.0391778i | ||||
\(469\) | −21.7031 | −0.0462752 | ||||||||
\(470\) | 136.294 | + | 12.7489i | 0.289987 | + | 0.0271252i | ||||
\(471\) | −158.298 | − | 102.595i | −0.336089 | − | 0.217823i | ||||
\(472\) | 46.5978 | + | 187.334i | 0.0987241 | + | 0.396894i | ||||
\(473\) | −342.050 | − | 592.447i | −0.723149 | − | 1.25253i | ||||
\(474\) | 32.1559 | − | 220.647i | 0.0678395 | − | 0.465501i | ||||
\(475\) | 216.201 | + | 124.824i | 0.455161 | + | 0.262787i | ||||
\(476\) | 30.3084 | + | 26.0581i | 0.0636732 | + | 0.0547439i | ||||
\(477\) | 189.315 | − | 261.572i | 0.396886 | − | 0.548369i | ||||
\(478\) | −303.711 | − | 661.649i | −0.635378 | − | 1.38420i | ||||
\(479\) | −572.964 | − | 330.801i | −1.19617 | − | 0.690607i | −0.236468 | − | 0.971639i | \(-0.575990\pi\) |
−0.959698 | + | 0.281033i | \(0.909323\pi\) | |||||||
\(480\) | 509.417 | − | 298.072i | 1.06129 | − | 0.620983i | ||||
\(481\) | −52.0037 | − | 90.0730i | −0.108116 | − | 0.187262i | ||||
\(482\) | −132.219 | − | 93.7686i | −0.274314 | − | 0.194541i | ||||
\(483\) | 12.5152 | − | 6.39120i | 0.0259114 | − | 0.0132323i | ||||
\(484\) | −243.194 | − | 693.977i | −0.502467 | − | 1.43384i | ||||
\(485\) | 160.569 | 0.331071 | ||||||||
\(486\) | −372.747 | + | 311.859i | −0.766969 | + | 0.641684i | ||||
\(487\) | − | 57.1525i | − | 0.117356i | −0.998277 | − | 0.0586781i | \(-0.981311\pi\) | ||
0.998277 | − | 0.0586781i | \(-0.0186886\pi\) | |||||||
\(488\) | 421.511 | + | 436.970i | 0.863753 | + | 0.895430i | ||||
\(489\) | 195.553 | + | 382.931i | 0.399905 | + | 0.783090i | ||||
\(490\) | 487.965 | + | 346.060i | 0.995847 | + | 0.706244i | ||||
\(491\) | 48.6600 | − | 28.0939i | 0.0991040 | − | 0.0572177i | −0.449629 | − | 0.893215i | \(-0.648444\pi\) |
0.548733 | + | 0.835998i | \(0.315110\pi\) | |||||||
\(492\) | −46.3686 | − | 44.2109i | −0.0942450 | − | 0.0898596i | ||||
\(493\) | −53.7147 | + | 93.0366i | −0.108955 | + | 0.188715i | ||||
\(494\) | −29.0420 | − | 63.2694i | −0.0587895 | − | 0.128076i | ||||
\(495\) | 782.615 | + | 566.424i | 1.58104 | + | 1.14429i | ||||
\(496\) | 505.170 | − | 76.6208i | 1.01849 | − | 0.154477i | ||||
\(497\) | 25.9417 | − | 44.9324i | 0.0521967 | − | 0.0904073i | ||||
\(498\) | −65.9702 | + | 452.675i | −0.132470 | + | 0.908985i | ||||
\(499\) | 522.225 | − | 301.507i | 1.04654 | − | 0.604222i | 0.124863 | − | 0.992174i | \(-0.460151\pi\) |
0.921679 | + | 0.387952i | \(0.126817\pi\) | |||||||
\(500\) | −294.853 | − | 55.6477i | −0.589706 | − | 0.111295i | ||||
\(501\) | −283.605 | + | 437.587i | −0.566077 | + | 0.873427i | ||||
\(502\) | 561.316 | + | 52.5052i | 1.11816 | + | 0.104592i | ||||
\(503\) | 549.354i | 1.09216i | 0.837734 | + | 0.546078i | \(0.183880\pi\) | ||||
−0.837734 | + | 0.546078i | \(0.816120\pi\) | |||||||
\(504\) | −5.97249 | − | 42.1075i | −0.0118502 | − | 0.0835466i | ||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | 25.7902 | − | 275.714i | 0.0509687 | − | 0.544890i | ||||
\(507\) | −25.5810 | + | 496.788i | −0.0504557 | + | 0.979859i | ||||
\(508\) | −121.946 | + | 646.136i | −0.240050 | + | 1.27192i | ||||
\(509\) | −119.464 | − | 206.918i | −0.234704 | − | 0.406519i | 0.724483 | − | 0.689293i | \(-0.242079\pi\) |
−0.959187 | + | 0.282774i | \(0.908745\pi\) | |||||||
\(510\) | −386.698 | + | 489.792i | −0.758230 | + | 0.960376i | ||||
\(511\) | −30.7143 | − | 17.7329i | −0.0601062 | − | 0.0347023i | ||||
\(512\) | −381.057 | + | 341.964i | −0.744252 | + | 0.667899i | ||||
\(513\) | 520.395 | + | 80.9629i | 1.01442 | + | 0.157822i | ||||
\(514\) | 136.893 | − | 62.8366i | 0.266328 | − | 0.122250i | ||||
\(515\) | −104.484 | − | 60.3240i | −0.202882 | − | 0.117134i | ||||
\(516\) | −456.929 | − | 110.842i | −0.885522 | − | 0.214811i | ||||
\(517\) | −97.1862 | − | 168.331i | −0.187981 | − | 0.325593i | ||||
\(518\) | −39.8306 | + | 56.1636i | −0.0768931 | + | 0.108424i | ||||
\(519\) | 38.8171 | − | 753.836i | 0.0747922 | − | 1.45248i | ||||
\(520\) | −60.9355 | − | 63.1703i | −0.117184 | − | 0.121481i | ||||
\(521\) | −567.711 | −1.08966 | −0.544828 | − | 0.838548i | \(-0.683405\pi\) | ||||
−0.544828 | + | 0.838548i | \(0.683405\pi\) | |||||||
\(522\) | 108.233 | − | 36.7627i | 0.207343 | − | 0.0704267i | ||||
\(523\) | 941.999i | 1.80114i | 0.434706 | + | 0.900572i | \(0.356852\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(524\) | 537.979 | − | 188.527i | 1.02668 | − | 0.359784i | ||||
\(525\) | 12.3349 | − | 19.0321i | 0.0234950 | − | 0.0362516i | ||||
\(526\) | 141.496 | − | 199.518i | 0.269004 | − | 0.379312i | ||||
\(527\) | −467.856 | + | 270.117i | −0.887773 | + | 0.512556i | ||||
\(528\) | −763.673 | − | 345.184i | −1.44635 | − | 0.653758i | ||||
\(529\) | −233.056 | + | 403.664i | −0.440559 | + | 0.763071i | ||||
\(530\) | −400.928 | + | 184.034i | −0.756468 | + | 0.347235i | ||||
\(531\) | −22.3065 | + | 216.024i | −0.0420085 | + | 0.406825i | ||||
\(532\) | −30.0456 | + | 34.9463i | −0.0564766 | + | 0.0656885i | ||||
\(533\) | −4.76372 | + | 8.25100i | −0.00893755 | + | 0.0154803i | ||||
\(534\) | 61.2244 | + | 153.784i | 0.114652 | + | 0.287986i | ||||
\(535\) | −975.428 | + | 563.163i | −1.82323 | + | 1.05264i | ||||
\(536\) | 70.9532 | + | 285.248i | 0.132375 | + | 0.532180i | ||||
\(537\) | −130.991 | − | 256.506i | −0.243932 | − | 0.477665i | ||||
\(538\) | −52.2387 | + | 558.467i | −0.0970980 | + | 1.03804i | ||||
\(539\) | − | 849.430i | − | 1.57594i | ||||||
\(540\) | 652.937 | − | 120.651i | 1.20914 | − | 0.223427i | ||||
\(541\) | −242.245 | −0.447772 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(542\) | −162.186 | − | 15.1708i | −0.299235 | − | 0.0279904i | ||||
\(543\) | 878.366 | − | 448.560i | 1.61762 | − | 0.826077i | ||||
\(544\) | 243.401 | − | 483.542i | 0.447428 | − | 0.888863i | ||||
\(545\) | 309.988 | + | 536.915i | 0.568786 | + | 0.985166i | ||||
\(546\) | −5.87590 | + | 2.33930i | −0.0107617 | + | 0.00428444i | ||||
\(547\) | −170.503 | − | 98.4402i | −0.311706 | − | 0.179964i | 0.335983 | − | 0.941868i | \(-0.390931\pi\) |
−0.647690 | + | 0.761904i | \(0.724265\pi\) | |||||||
\(548\) | 16.0729 | − | 18.6945i | 0.0293301 | − | 0.0341141i | ||||
\(549\) | 278.951 | + | 623.470i | 0.508107 | + | 1.13565i | ||||
\(550\) | −186.442 | − | 406.173i | −0.338986 | − | 0.738497i | ||||
\(551\) | −107.273 | − | 61.9342i | −0.194688 | − | 0.112403i | ||||
\(552\) | −124.917 | − | 143.595i | −0.226298 | − | 0.260137i | ||||
\(553\) | 10.9757 | + | 19.0105i | 0.0198476 | + | 0.0343770i | ||||
\(554\) | 733.673 | + | 520.313i | 1.32432 | + | 0.939194i | ||||
\(555\) | −902.096 | − | 584.659i | −1.62540 | − | 1.05344i | ||||
\(556\) | −449.700 | + | 157.591i | −0.808814 | + | 0.283437i | ||||
\(557\) | 958.121 | 1.72015 | 0.860073 | − | 0.510171i | \(-0.170418\pi\) | ||||
0.860073 | + | 0.510171i | \(0.170418\pi\) | |||||||
\(558\) | 563.792 | + | 112.036i | 1.01038 | + | 0.200781i | ||||
\(559\) | 69.9202i | 0.125081i | ||||||||
\(560\) | −21.1779 | + | 54.1076i | −0.0378176 | + | 0.0966208i | ||||
\(561\) | 884.926 | + | 45.5674i | 1.57741 | + | 0.0812253i | ||||
\(562\) | −123.545 | − | 87.6166i | −0.219830 | − | 0.155901i | ||||
\(563\) | 165.774 | − | 95.7097i | 0.294448 | − | 0.169999i | −0.345498 | − | 0.938419i | \(-0.612290\pi\) |
0.639946 | + | 0.768420i | \(0.278957\pi\) | |||||||
\(564\) | −129.827 | − | 31.4935i | −0.230189 | − | 0.0558395i | ||||
\(565\) | 56.1001 | − | 97.1682i | 0.0992922 | − | 0.171979i | ||||
\(566\) | −310.279 | − | 675.957i | −0.548196 | − | 1.19427i | ||||
\(567\) | 9.77666 | − | 46.8355i | 0.0172428 | − | 0.0826023i | ||||
\(568\) | −675.368 | − | 194.062i | −1.18903 | − | 0.341658i | ||||
\(569\) | 228.215 | − | 395.280i | 0.401081 | − | 0.694693i | −0.592775 | − | 0.805368i | \(-0.701968\pi\) |
0.993857 | + | 0.110675i | \(0.0353012\pi\) | |||||||
\(570\) | −564.740 | − | 445.871i | −0.990773 | − | 0.782229i | ||||
\(571\) | −842.764 | + | 486.570i | −1.47594 | + | 0.852136i | −0.999632 | − | 0.0271399i | \(-0.991360\pi\) |
−0.476312 | + | 0.879276i | \(0.658027\pi\) | |||||||
\(572\) | −23.1130 | + | 122.466i | −0.0404073 | + | 0.214101i | ||||
\(573\) | 1.21745 | + | 0.0626902i | 0.00212470 | + | 0.000109407i | ||||
\(574\) | 6.27982 | + | 0.587411i | 0.0109404 | + | 0.00102336i | ||||
\(575\) | − | 101.496i | − | 0.176515i | ||||||
\(576\) | −533.902 | + | 216.159i | −0.926913 | + | 0.375275i | ||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | 0.523773 | − | 5.59948i | 0.000906181 | − | 0.00968768i | ||||
\(579\) | 157.208 | + | 101.888i | 0.271516 | + | 0.175972i | ||||
\(580\) | −153.460 | − | 28.9626i | −0.264586 | − | 0.0499355i | ||||
\(581\) | −22.5175 | − | 39.0015i | −0.0387565 | − | 0.0671282i | ||||
\(582\) | −155.064 | − | 22.5982i | −0.266434 | − | 0.0388285i | ||||
\(583\) | 542.478 | + | 313.200i | 0.930494 | + | 0.537221i | ||||
\(584\) | −132.654 | + | 461.658i | −0.227147 | + | 0.790510i | ||||
\(585\) | −40.3263 | − | 90.1314i | −0.0689339 | − | 0.154071i | ||||
\(586\) | 241.365 | − | 110.792i | 0.411886 | − | 0.189064i | ||||
\(587\) | 620.808 | + | 358.424i | 1.05759 | + | 0.610602i | 0.924766 | − | 0.380537i | \(-0.124261\pi\) |
0.132829 | + | 0.991139i | \(0.457594\pi\) | |||||||
\(588\) | −422.532 | − | 402.871i | −0.718591 | − | 0.685154i | ||||
\(589\) | −311.451 | − | 539.449i | −0.528779 | − | 0.915872i | ||||
\(590\) | 171.641 | − | 242.024i | 0.290917 | − | 0.410210i | ||||
\(591\) | 555.358 | − | 283.607i | 0.939691 | − | 0.479877i | ||||
\(592\) | 868.387 | + | 339.889i | 1.46687 | + | 0.574137i | ||||
\(593\) | 542.129 | 0.914214 | 0.457107 | − | 0.889412i | \(-0.348886\pi\) | ||||
0.457107 | + | 0.889412i | \(0.348886\pi\) | |||||||
\(594\) | −676.067 | − | 657.148i | −1.13816 | − | 1.10631i | ||||
\(595\) | − | 61.4350i | − | 0.103252i | ||||||
\(596\) | 273.477 | + | 780.391i | 0.458853 | + | 1.30938i | ||||
\(597\) | −408.134 | − | 799.204i | −0.683641 | − | 1.33870i | ||||
\(598\) | −16.3729 | + | 23.0867i | −0.0273794 | + | 0.0386066i | ||||
\(599\) | −245.527 | + | 141.755i | −0.409895 | + | 0.236653i | −0.690744 | − | 0.723099i | \(-0.742717\pi\) |
0.280850 | + | 0.959752i | \(0.409384\pi\) | |||||||
\(600\) | −290.469 | − | 99.8994i | −0.484115 | − | 0.166499i | ||||
\(601\) | 377.424 | − | 653.717i | 0.627993 | − | 1.08772i | −0.359961 | − | 0.932967i | \(-0.617210\pi\) |
0.987954 | − | 0.154748i | \(-0.0494567\pi\) | |||||||
\(602\) | 42.0676 | − | 19.3099i | 0.0698797 | − | 0.0320763i | ||||
\(603\) | −33.9656 | + | 328.934i | −0.0563276 | + | 0.545496i | ||||
\(604\) | −446.272 | − | 383.688i | −0.738860 | − | 0.635245i | ||||
\(605\) | −565.126 | + | 978.827i | −0.934093 | + | 1.61790i | ||||
\(606\) | 152.982 | + | 22.2947i | 0.252445 | + | 0.0367899i | ||||
\(607\) | 77.2227 | − | 44.5845i | 0.127220 | − | 0.0734506i | −0.435039 | − | 0.900411i | \(-0.643266\pi\) |
0.562260 | + | 0.826961i | \(0.309932\pi\) | |||||||
\(608\) | 557.534 | + | 280.647i | 0.916997 | + | 0.461590i | ||||
\(609\) | −6.12024 | + | 9.44320i | −0.0100497 | + | 0.0155061i | ||||
\(610\) | 86.9097 | − | 929.122i | 0.142475 | − | 1.52315i | ||||
\(611\) | 19.8664i | 0.0325145i | ||||||||
\(612\) | 442.372 | − | 418.577i | 0.722831 | − | 0.683949i | ||||
\(613\) | −316.779 | −0.516769 | −0.258385 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258385 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(614\) | 670.103 | + | 62.6811i | 1.09137 | + | 0.102087i | ||||
\(615\) | −5.06393 | + | 98.3425i | −0.00823404 | + | 0.159907i | ||||
\(616\) | 80.0646 | − | 19.9154i | 0.129975 | − | 0.0323302i | ||||
\(617\) | 534.934 | + | 926.533i | 0.866992 | + | 1.50167i | 0.865056 | + | 0.501675i | \(0.167283\pi\) |
0.00193565 | + | 0.999998i | \(0.499384\pi\) | |||||||
\(618\) | 92.4122 | + | 72.9608i | 0.149534 | + | 0.118059i | ||||
\(619\) | 578.542 | + | 334.021i | 0.934640 | + | 0.539615i | 0.888276 | − | 0.459310i | \(-0.151903\pi\) |
0.0463638 | + | 0.998925i | \(0.485237\pi\) | |||||||
\(620\) | −595.498 | − | 511.988i | −0.960481 | − | 0.825787i | ||||
\(621\) | −77.2793 | − | 199.684i | −0.124443 | − | 0.321552i | ||||
\(622\) | 293.077 | + | 638.483i | 0.471185 | + | 1.02650i | ||||
\(623\) | −14.1121 | − | 8.14762i | −0.0226518 | − | 0.0130780i | ||||
\(624\) | 49.9559 | + | 69.5805i | 0.0800575 | + | 0.111507i | ||||
\(625\) | 390.580 | + | 676.505i | 0.624929 | + | 1.08241i | ||||
\(626\) | −311.367 | − | 220.818i | −0.497391 | − | 0.352744i | ||||
\(627\) | −52.5402 | + | 1020.34i | −0.0837961 | + | 1.62734i | ||||
\(628\) | −83.1804 | − | 237.363i | −0.132453 | − | 0.377967i | ||||
\(629\) | −985.986 | −1.56755 | ||||||||
\(630\) | −43.0907 | + | 49.1540i | −0.0683979 | + | 0.0780222i | ||||
\(631\) | − | 150.631i | − | 0.238718i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) | ||
0.992851 | − | 0.119359i | \(-0.0380839\pi\) | |||||||
\(632\) | 213.977 | − | 206.407i | 0.338571 | − | 0.326593i | ||||
\(633\) | 267.051 | − | 412.045i | 0.421881 | − | 0.650939i | ||||
\(634\) | −661.682 | − | 469.258i | −1.04366 | − | 0.740155i | ||||
\(635\) | 875.252 | − | 505.327i | 1.37835 | − | 0.795790i | ||||
\(636\) | 413.083 | − | 121.299i | 0.649502 | − | 0.190722i | ||||
\(637\) | −43.4092 | + | 75.1869i | −0.0681463 | + | 0.118033i | ||||
\(638\) | 92.5075 | + | 201.532i | 0.144996 | + | 0.315881i | ||||
\(639\) | −640.401 | − | 463.496i | −1.00219 | − | 0.725345i | ||||
\(640\) | 780.385 | + | 101.453i | 1.21935 | + | 0.158520i | ||||
\(641\) | 351.521 | − | 608.852i | 0.548395 | − | 0.949847i | −0.449990 | − | 0.893034i | \(-0.648573\pi\) |
0.998385 | − | 0.0568139i | \(-0.0180942\pi\) | |||||||
\(642\) | 1021.24 | − | 406.576i | 1.59072 | − | 0.633296i | ||||
\(643\) | 742.057 | − | 428.427i | 1.15405 | − | 0.666293i | 0.204182 | − | 0.978933i | \(-0.434546\pi\) |
0.949872 | + | 0.312639i | \(0.101213\pi\) | |||||||
\(644\) | 18.4119 | + | 3.47488i | 0.0285898 | + | 0.00539577i | ||||
\(645\) | 328.675 | + | 643.609i | 0.509574 | + | 0.997844i | ||||
\(646\) | −657.094 | − | 61.4643i | −1.01717 | − | 0.0951459i | ||||
\(647\) | − | 156.257i | − | 0.241510i | −0.992682 | − | 0.120755i | \(-0.961468\pi\) | ||
0.992682 | − | 0.120755i | \(-0.0385316\pi\) | |||||||
\(648\) | −647.532 | + | 24.6211i | −0.999278 | + | 0.0379955i | ||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | −4.25419 | + | 45.4802i | −0.00654491 | + | 0.0699695i | ||||
\(651\) | −50.3974 | + | 25.7367i | −0.0774154 | + | 0.0395341i | ||||
\(652\) | −106.322 | + | 563.353i | −0.163070 | + | 0.864038i | ||||
\(653\) | −441.773 | − | 765.173i | −0.676528 | − | 1.17178i | −0.976020 | − | 0.217682i | \(-0.930151\pi\) |
0.299492 | − | 0.954099i | \(-0.403183\pi\) | |||||||
\(654\) | −223.796 | − | 562.135i | −0.342196 | − | 0.859534i | ||||
\(655\) | −758.798 | − | 438.092i | −1.15847 | − | 0.668843i | ||||
\(656\) | −12.8099 | − | 84.4574i | −0.0195273 | − | 0.128746i | ||||
\(657\) | −316.830 | + | 437.756i | −0.482237 | + | 0.666296i | ||||
\(658\) | 11.9526 | − | 5.48650i | 0.0181651 | − | 0.00833815i | ||||
\(659\) | −379.533 | − | 219.123i | −0.575922 | − | 0.332509i | 0.183589 | − | 0.983003i | \(-0.441228\pi\) |
−0.759511 | + | 0.650494i | \(0.774562\pi\) | |||||||
\(660\) | 362.923 | + | 1235.93i | 0.549884 | + | 1.87262i | ||||
\(661\) | 233.924 | + | 405.168i | 0.353894 | + | 0.612963i | 0.986928 | − | 0.161161i | \(-0.0515239\pi\) |
−0.633034 | + | 0.774124i | \(0.718191\pi\) | |||||||
\(662\) | −513.143 | + | 723.562i | −0.775140 | + | 1.09299i | ||||
\(663\) | −76.0002 | − | 49.2565i | −0.114631 | − | 0.0742934i | ||||
\(664\) | −438.989 | + | 423.459i | −0.661128 | + | 0.637739i | ||||
\(665\) | 70.8359 | 0.106520 | ||||||||
\(666\) | 788.885 | + | 691.573i | 1.18451 | + | 1.03840i | ||||
\(667\) | 50.3597i | 0.0755018i | ||||||||
\(668\) | −656.149 | + | 229.938i | −0.982259 | + | 0.344218i | ||||
\(669\) | −1144.00 | − | 58.9076i | −1.71001 | − | 0.0880533i | ||||
\(670\) | 261.353 | − | 368.524i | 0.390079 | − | 0.550035i | ||||
\(671\) | −1147.52 | + | 662.524i | −1.71017 | + | 0.987368i | ||||
\(672\) | 28.0668 | − | 49.2721i | 0.0417661 | − | 0.0733215i | ||||
\(673\) | 273.302 | − | 473.372i | 0.406094 | − | 0.703376i | −0.588354 | − | 0.808604i | \(-0.700224\pi\) |
0.994448 | + | 0.105227i | \(0.0335571\pi\) | |||||||
\(674\) | 924.240 | − | 424.246i | 1.37128 | − | 0.629444i | ||||
\(675\) | −269.148 | − | 216.734i | −0.398738 | − | 0.321088i | ||||
\(676\) | −432.405 | + | 502.934i | −0.639652 | + | 0.743986i | ||||
\(677\) | 227.606 | − | 394.225i | 0.336198 | − | 0.582312i | −0.647516 | − | 0.762052i | \(-0.724192\pi\) |
0.983714 | + | 0.179740i | \(0.0575255\pi\) | |||||||
\(678\) | −67.8520 | + | 85.9415i | −0.100077 | + | 0.126757i | ||||
\(679\) | 13.3600 | − | 7.71341i | 0.0196760 | − | 0.0113600i | ||||
\(680\) | −807.454 | + | 200.848i | −1.18743 | + | 0.295364i | ||||
\(681\) | 178.329 | + | 9.18264i | 0.261863 | + | 0.0134841i | ||||
\(682\) | −103.854 | + | 1110.27i | −0.152279 | + | 1.62797i | ||||
\(683\) | − | 123.214i | − | 0.180400i | −0.995924 | − | 0.0902002i | \(-0.971249\pi\) | ||
0.995924 | − | 0.0902002i | \(-0.0287507\pi\) | |||||||
\(684\) | 482.628 | + | 510.065i | 0.705596 | + | 0.745709i | ||||
\(685\) | −37.8937 | −0.0553193 | ||||||||
\(686\) | 114.860 | + | 10.7439i | 0.167434 | + | 0.0156617i | ||||
\(687\) | −324.439 | − | 210.272i | −0.472254 | − | 0.306073i | ||||
\(688\) | −391.325 | − | 489.774i | −0.568786 | − | 0.711881i | ||||
\(689\) | −32.0115 | − | 55.4455i | −0.0464607 | − | 0.0804724i | ||||
\(690\) | −42.1865 | + | 289.475i | −0.0611399 | + | 0.419529i | ||||
\(691\) | −163.326 | − | 94.2965i | −0.236362 | − | 0.136464i | 0.377141 | − | 0.926156i | \(-0.376907\pi\) |
−0.613504 | + | 0.789692i | \(0.710240\pi\) | |||||||
\(692\) | 656.139 | − | 763.162i | 0.948177 | − | 1.10283i | ||||
\(693\) | 92.3265 | + | 9.53359i | 0.133227 | + | 0.0137570i | ||||
\(694\) | 474.746 | + | 1034.26i | 0.684071 | + | 1.49028i | ||||
\(695\) | 634.285 | + | 366.204i | 0.912640 | + | 0.526913i | ||||
\(696\) | 144.123 | + | 49.5673i | 0.207073 | + | 0.0712174i | ||||
\(697\) | 45.1599 | + | 78.2192i | 0.0647918 | + | 0.112223i | ||||
\(698\) | −675.073 | − | 478.754i | −0.967153 | − | 0.685895i | ||||
\(699\) | −40.0602 | + | 20.4578i | −0.0573107 | + | 0.0292672i | ||||
\(700\) | 28.5381 | − | 10.0007i | 0.0407686 | − | 0.0142868i | ||||
\(701\) | −810.064 | −1.15558 | −0.577792 | − | 0.816184i | \(-0.696085\pi\) | ||||
−0.577792 | + | 0.816184i | \(0.696085\pi\) | |||||||
\(702\) | 26.2589 | + | 92.7168i | 0.0374058 | + | 0.132075i | ||||
\(703\) | − | 1136.86i | − | 1.61716i | ||||||
\(704\) | −523.506 | − | 987.199i | −0.743616 | − | 1.40227i | ||||
\(705\) | 93.3861 | + | 182.868i | 0.132463 | + | 0.259387i | ||||
\(706\) | 203.294 | + | 144.174i | 0.287952 | + | 0.204212i | ||||
\(707\) | −13.1806 | + | 7.60980i | −0.0186429 | + | 0.0107635i | ||||
\(708\) | −199.818 | + | 209.570i | −0.282229 | + | 0.296003i | ||||
\(709\) | −651.819 | + | 1128.98i | −0.919349 | + | 1.59236i | −0.118944 | + | 0.992901i | \(0.537951\pi\) |
−0.800406 | + | 0.599459i | \(0.795382\pi\) | |||||||
\(710\) | 450.568 | + | 981.583i | 0.634602 | + | 1.38251i | ||||
\(711\) | 305.302 | − | 136.597i | 0.429398 | − | 0.192120i | ||||
\(712\) | −60.9497 | + | 212.115i | −0.0856035 | + | 0.297914i | ||||
\(713\) | −126.623 | + | 219.317i | −0.177592 | + | 0.307598i | ||||
\(714\) | −8.64624 | + | 59.3288i | −0.0121096 | + | 0.0830935i | ||||
\(715\) | 165.891 | − | 95.7772i | 0.232015 | − | 0.133954i | ||||
\(716\) | 71.2197 | − | 377.362i | 0.0994688 | − | 0.527042i | ||||
\(717\) | 593.930 | − | 916.401i | 0.828354 | − | 1.27810i | ||||
\(718\) | −603.756 | − | 56.4751i | −0.840886 | − | 0.0786561i | ||||
\(719\) | 788.981i | 1.09733i | 0.836042 | + | 0.548666i | \(0.184864\pi\) | ||||
−0.836042 | + | 0.548666i | \(0.815136\pi\) | |||||||
\(720\) | 786.917 | + | 405.653i | 1.09294 | + | 0.563407i | ||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | 3.62757 | − | 38.7812i | 0.00502434 | − | 0.0537135i | ||||
\(723\) | 12.5035 | − | 242.820i | 0.0172939 | − | 0.335850i | ||||
\(724\) | 1292.22 | + | 243.881i | 1.78483 | + | 0.336852i | ||||
\(725\) | 40.6380 | + | 70.3870i | 0.0560524 | + | 0.0970856i | ||||
\(726\) | 683.510 | − | 865.734i | 0.941473 | − | 1.19247i | ||||
\(727\) | −232.676 | − | 134.335i | −0.320049 | − | 0.184780i | 0.331365 | − | 0.943502i | \(-0.392491\pi\) |
−0.651414 | + | 0.758722i | \(0.725824\pi\) | |||||||
\(728\) | −8.10464 | − | 2.32881i | −0.0111327 | − | 0.00319891i | ||||
\(729\) | −694.543 | − | 221.474i | −0.952734 | − | 0.303805i | ||||
\(730\) | 670.977 | − | 307.992i | 0.919146 | − | 0.421907i | ||||
\(731\) | 574.038 | + | 331.421i | 0.785277 | + | 0.453380i | ||||
\(732\) | −214.693 | + | 885.037i | −0.293296 | + | 1.20907i | ||||
\(733\) | −36.8343 | − | 63.7989i | −0.0502514 | − | 0.0870380i | 0.839806 | − | 0.542887i | \(-0.182669\pi\) |
−0.890057 | + | 0.455849i | \(0.849336\pi\) | |||||||
\(734\) | 822.370 | − | 1159.59i | 1.12040 | − | 1.57982i | ||||
\(735\) | −46.1449 | + | 896.143i | −0.0627822 | + | 1.21924i | ||||
\(736\) | −14.5222 | − | 253.351i | −0.0197313 | − | 0.344227i | ||||
\(737\) | −641.512 | −0.870437 | ||||||||
\(738\) | 18.7309 | − | 94.2582i | 0.0253806 | − | 0.127721i | ||||
\(739\) | − | 448.249i | − | 0.606562i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) | ||
0.952901 | − | 0.303281i | \(-0.0980820\pi\) | |||||||
\(740\) | −474.022 | − | 1352.67i | −0.640571 | − | 1.82793i | ||||
\(741\) | 56.7939 | − | 87.6298i | 0.0766449 | − | 0.118259i | ||||
\(742\) | −24.5182 | + | 34.5721i | −0.0330434 | + | 0.0465932i | ||||
\(743\) | 656.602 | − | 379.089i | 0.883718 | − | 0.510215i | 0.0118352 | − | 0.999930i | \(-0.496233\pi\) |
0.871882 | + | 0.489715i | \(0.162899\pi\) | |||||||
\(744\) | 503.026 | + | 578.244i | 0.676110 | + | 0.777210i | ||||
\(745\) | 635.496 | − | 1100.71i | 0.853015 | − | 1.47746i | ||||
\(746\) | −606.153 | + | 278.237i | −0.812538 | + | 0.372972i | ||||
\(747\) | −626.350 | + | 280.240i | −0.838488 | + | 0.375154i | ||||
\(748\) | 895.874 | + | 770.240i | 1.19769 | + | 1.02973i | ||||
\(749\) | −54.1063 | + | 93.7149i | −0.0722381 | + | 0.125120i | ||||
\(750\) | −166.480 | − | 418.166i | −0.221973 | − | 0.557555i | ||||
\(751\) | 1141.58 | − | 659.091i | 1.52008 | − | 0.877618i | 0.520358 | − | 0.853948i | \(-0.325798\pi\) |
0.999720 | − | 0.0236697i | \(-0.00753501\pi\) | |||||||
\(752\) | −111.187 | − | 139.159i | −0.147855 | − | 0.185052i | ||||
\(753\) | 384.604 | + | 753.128i | 0.510762 | + | 1.00017i | ||||
\(754\) | 2.11081 | − | 22.5660i | 0.00279949 | − | 0.0299284i | ||||
\(755\) | 904.589i | 1.19813i | ||||||||
\(756\) | 48.5312 | − | 41.4043i | 0.0641947 | − | 0.0547676i | ||||
\(757\) | 587.874 | 0.776583 | 0.388292 | − | 0.921537i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921537i | \(0.373065\pi\) | |||||||
\(758\) | −1319.61 | − | 123.436i | −1.74091 | − | 0.162844i | ||||
\(759\) | 369.931 | − | 188.915i | 0.487393 | − | 0.248899i | ||||
\(760\) | −231.582 | − | 931.012i | −0.304713 | − | 1.22502i | ||||
\(761\) | −188.496 | − | 326.485i | −0.247695 | − | 0.429021i | 0.715191 | − | 0.698929i | \(-0.246340\pi\) |
−0.962886 | + | 0.269908i | \(0.913007\pi\) | |||||||
\(762\) | −916.363 | + | 364.821i | −1.20258 | + | 0.478768i | ||||
\(763\) | 51.5845 | + | 29.7823i | 0.0676075 | + | 0.0390332i | ||||
\(764\) | 1.23252 | + | 1.05967i | 0.00161324 | + | 0.00138701i | ||||
\(765\) | −931.115 | − | 96.1465i | −1.21714 | − | 0.125682i | ||||
\(766\) | −67.3435 | − | 146.711i | −0.0879158 | − | 0.191529i | ||||
\(767\) | 37.2917 | + | 21.5304i | 0.0486202 | + | 0.0280709i | ||||
\(768\) | −739.352 | − | 207.804i | −0.962698 | − | 0.270579i | ||||
\(769\) | 643.939 | + | 1115.34i | 0.837372 | + | 1.45037i | 0.892084 | + | 0.451869i | \(0.149243\pi\) |
−0.0547122 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(770\) | −103.439 | − | 73.3576i | −0.134336 | − | 0.0952697i | ||||
\(771\) | 189.600 | + | 122.882i | 0.245914 | + | 0.159380i | ||||
\(772\) | 82.6075 | + | 235.728i | 0.107005 | + | 0.305348i | ||||
\(773\) | 778.578 | 1.00722 | 0.503608 | − | 0.863932i | \(-0.332006\pi\) | ||||
0.503608 | + | 0.863932i | \(0.332006\pi\) | |||||||
\(774\) | −226.827 | − | 667.801i | −0.293058 | − | 0.862792i | ||||
\(775\) | 408.715i | 0.527375i | ||||||||
\(776\) | −145.057 | − | 150.376i | −0.186929 | − | 0.193784i | ||||
\(777\) | −103.144 | − | 5.31117i | −0.132746 | − | 0.00683548i | ||||
\(778\) | −1128.94 | − | 800.634i | −1.45108 | − | 1.02909i | ||||
\(779\) | −90.1884 | + | 52.0703i | −0.115775 | + | 0.0668425i | ||||
\(780\) | 31.0369 | − | 127.945i | 0.0397909 | − | 0.164032i | ||||
\(781\) | 766.801 | − | 1328.14i | 0.981819 | − | 1.70056i | ||||
\(782\) | 111.932 | + | 243.850i | 0.143136 | + | 0.311829i | ||||
\(783\) | 133.544 | + | 107.538i | 0.170554 | + | 0.137341i | ||||
\(784\) | −116.730 | − | 769.615i | −0.148890 | − | 0.981652i | ||||
\(785\) | −193.292 | + | 334.791i | −0.246232 | + | 0.426486i | ||||
\(786\) | 671.127 | + | 529.865i | 0.853852 | + | 0.674128i | ||||
\(787\) | −390.283 | + | 225.330i | −0.495913 | + | 0.286315i | −0.727024 | − | 0.686612i | \(-0.759097\pi\) |
0.231111 | + | 0.972927i | \(0.425764\pi\) | |||||||
\(788\) | 817.020 | + | 154.197i | 1.03683 | + | 0.195681i | ||||
\(789\) | 366.413 | + | 18.8676i | 0.464402 | + | 0.0239134i | ||||
\(790\) | −454.975 | − | 42.5582i | −0.575918 | − | 0.0538711i | ||||
\(791\) | − | 10.7797i | − | 0.0136280i | ||||||
\(792\) | −176.538 | − | 1244.64i | −0.222902 | − | 1.57151i | ||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | −122.510 | + | 1309.71i | −0.154294 | + | 1.64951i | ||||
\(795\) | −555.296 | − | 359.893i | −0.698485 | − | 0.452696i | ||||
\(796\) | 221.901 | − | 1175.76i | 0.278770 | − | 1.47708i | ||||
\(797\) | −182.891 | − | 316.776i | −0.229474 | − | 0.397461i | 0.728178 | − | 0.685388i | \(-0.240367\pi\) |
−0.957652 | + | 0.287927i | \(0.907034\pi\) | |||||||
\(798\) | −68.4073 | − | 9.96930i | −0.0857235 | − | 0.0124929i | ||||
\(799\) | 163.101 | + | 94.1662i | 0.204131 | + | 0.117855i | ||||
\(800\) | −224.741 | − | 342.387i | −0.280926 | − | 0.427984i | ||||
\(801\) | −145.572 | + | 201.133i | −0.181737 | + | 0.251103i | ||||
\(802\) | −1077.63 | + | 494.653i | −1.34367 | + | 0.616775i | ||||
\(803\) | −907.869 | − | 524.158i | −1.13060 | − | 0.652750i | ||||
\(804\) | −304.258 | + | 319.107i | −0.378431 | + | 0.396899i | ||||
\(805\) | −14.3994 | − | 24.9406i | −0.0178875 | − | 0.0309821i | ||||
\(806\) | 65.9319 | − | 92.9679i | 0.0818013 | − | 0.115345i | ||||
\(807\) | −749.305 | + | 382.652i | −0.928507 | + | 0.474166i | ||||
\(808\) | 143.108 | + | 148.357i | 0.177114 | + | 0.183610i | ||||
\(809\) | 1167.70 | 1.44339 | 0.721695 | − | 0.692212i | \(-0.243364\pi\) | ||||
0.721695 | + | 0.692212i | \(0.243364\pi\) | |||||||
\(810\) | 677.546 | + | 730.014i | 0.836476 | + | 0.901251i | ||||
\(811\) | − | 810.121i | − | 0.998916i | −0.866338 | − | 0.499458i | \(-0.833533\pi\) | ||
0.866338 | − | 0.499458i | \(-0.166467\pi\) | |||||||
\(812\) | −14.1598 | + | 4.96209i | −0.0174382 | + | 0.00611095i | ||||
\(813\) | −111.127 | − | 217.608i | −0.136687 | − | 0.267660i | ||||
\(814\) | −1177.34 | + | 1660.11i | −1.44636 | + | 2.03945i | ||||
\(815\) | 763.114 | − | 440.584i | 0.936336 | − | 0.540594i | ||||
\(816\) | 808.038 | − | 80.3223i | 0.990243 | − | 0.0984342i | ||||
\(817\) | −382.135 | + | 661.878i | −0.467730 | + | 0.810132i | ||||
\(818\) | 587.445 | − | 269.650i | 0.718148 | − | 0.329645i | ||||
\(819\) | −7.68503 | − | 5.56210i | −0.00938343 | − | 0.00679134i | ||||
\(820\) | −85.5973 | + | 99.5591i | −0.104387 | + | 0.121414i | ||||
\(821\) | −280.513 | + | 485.862i | −0.341672 | + | 0.591793i | −0.984743 | − | 0.174013i | \(-0.944327\pi\) |
0.643071 | + | 0.765806i | \(0.277660\pi\) | |||||||
\(822\) | 36.5946 | + | 5.33308i | 0.0445189 | + | 0.00648794i | ||||
\(823\) | −1016.04 | + | 586.612i | −1.23456 | + | 0.712773i | −0.967977 | − | 0.251039i | \(-0.919228\pi\) |
−0.266583 | + | 0.963812i | \(0.585895\pi\) | |||||||
\(824\) | 37.8952 | + | 152.348i | 0.0459894 | + | 0.184888i | ||||
\(825\) | 364.602 | − | 562.561i | 0.441942 | − | 0.681892i | ||||
\(826\) | 2.65490 | − | 28.3826i | 0.00321416 | − | 0.0343615i | ||||
\(827\) | − | 267.739i | − | 0.323747i | −0.986811 | − | 0.161874i | \(-0.948246\pi\) | ||
0.986811 | − | 0.161874i | \(-0.0517537\pi\) | |||||||
\(828\) | 81.4804 | − | 273.614i | 0.0984062 | − | 0.330451i | ||||
\(829\) | −432.474 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(830\) | 933.415 | + | 87.3113i | 1.12460 | + | 0.105194i | ||||
\(831\) | −69.3806 | + | 1347.38i | −0.0834904 | + | 1.62140i | ||||
\(832\) | −4.11180 | + | 114.135i | −0.00494207 | + | 0.137181i | ||||
\(833\) | 411.518 | + | 712.769i | 0.494019 | + | 0.855665i | ||||
\(834\) | −561.000 | − | 442.917i | −0.672662 | − | 0.531076i | ||||
\(835\) | 925.472 | + | 534.321i | 1.10835 | + | 0.639906i | ||||
\(836\) | −888.103 | + | 1032.96i | −1.06232 | + | 1.23560i | ||||
\(837\) | 311.196 | + | 804.106i | 0.371799 | + | 0.960701i | ||||
\(838\) | −214.595 | − | 467.506i | −0.256080 | − | 0.557883i | ||||
\(839\) | −459.103 | − | 265.063i | −0.547202 | − | 0.315927i | 0.200790 | − | 0.979634i | \(-0.435649\pi\) |
−0.747993 | + | 0.663707i | \(0.768982\pi\) | |||||||
\(840\) | −85.5495 | + | 16.6612i | −0.101845 | + | 0.0198347i | ||||
\(841\) | 400.337 | + | 693.403i | 0.476024 | + | 0.824499i | ||||
\(842\) | 137.006 | + | 97.1632i | 0.162715 | + | 0.115396i | ||||
\(843\) | 11.6831 | − | 226.889i | 0.0138590 | − | 0.269144i | ||||
\(844\) | 617.849 | − | 216.516i | 0.732049 | − | 0.256536i | ||||
\(845\) | 1019.44 | 1.20644 | ||||||||
\(846\) | −64.4480 | − | 189.741i | −0.0761797 | − | 0.224281i | ||||
\(847\) | 108.590i | 0.128205i | ||||||||
\(848\) | 534.546 | + | 209.222i | 0.630361 | + | 0.246725i | ||||
\(849\) | 606.774 | − | 936.219i | 0.714692 | − | 1.10273i | ||||
\(850\) | 353.222 | + | 250.502i | 0.415556 | + | 0.294708i | ||||
\(851\) | −400.278 | + | 231.100i | −0.470361 | + | 0.271563i | ||||
\(852\) | −296.974 | − | 1011.34i | −0.348561 | − | 1.18702i | ||||
\(853\) | 88.3868 | − | 153.090i | 0.103619 | − | 0.179473i | −0.809554 | − | 0.587045i | \(-0.800291\pi\) |
0.913173 | + | 0.407572i | \(0.133624\pi\) | |||||||
\(854\) | −37.4018 | − | 81.4816i | −0.0437960 | − | 0.0954118i | ||||
\(855\) | 110.859 | − | 1073.60i | 0.129660 | − | 1.25567i | ||||
\(856\) | 1408.60 | + | 404.752i | 1.64557 | + | 0.472841i | ||||
\(857\) | −194.859 | + | 337.505i | −0.227373 | + | 0.393821i | −0.957029 | − | 0.289993i | \(-0.906347\pi\) |
0.729656 | + | 0.683815i | \(0.239680\pi\) | |||||||
\(858\) | −173.683 | + | 69.1464i | −0.202428 | + | 0.0805903i | ||||
\(859\) | −503.279 | + | 290.568i | −0.585889 | + | 0.338263i | −0.763470 | − | 0.645843i | \(-0.776506\pi\) |
0.177581 | + | 0.984106i | \(0.443173\pi\) | |||||||
\(860\) | −178.700 | + | 946.852i | −0.207791 | + | 1.10099i | ||||
\(861\) | 4.30282 | + | 8.42575i | 0.00499747 | + | 0.00978601i | ||||
\(862\) | −287.441 | − | 26.8871i | −0.333458 | − | 0.0311915i | ||||
\(863\) | 827.326i | 0.958663i | 0.877634 | + | 0.479331i | \(0.159121\pi\) | ||||
−0.877634 | + | 0.479331i | \(0.840879\pi\) | |||||||
\(864\) | −702.848 | − | 502.495i | −0.813481 | − | 0.581591i | ||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | −73.6409 | + | 787.270i | −0.0850357 | + | 0.909088i | ||||
\(867\) | 7.51293 | − | 3.83667i | 0.00866543 | − | 0.00442522i | ||||
\(868\) | −74.1426 | − | 13.9930i | −0.0854178 | − | 0.0161209i | ||||
\(869\) | 324.426 | + | 561.923i | 0.373333 | + | 0.646632i | ||||
\(870\) | −86.6466 | − | 217.640i | −0.0995938 | − | 0.250161i | ||||
\(871\) | 56.7831 | + | 32.7837i | 0.0651930 | + | 0.0376392i | ||||
\(872\) | 222.792 | − | 775.354i | 0.255496 | − | 0.889167i | ||||
\(873\) | −95.9966 | − | 214.557i | −0.109962 | − | 0.245770i | ||||
\(874\) | −281.165 | + | 129.060i | −0.321699 | + | 0.147666i | ||||
\(875\) | 38.3732 | + | 22.1548i | 0.0438551 | + | 0.0253198i | ||||
\(876\) | −691.319 | + | 203.001i | −0.789177 | + | 0.231737i | ||||
\(877\) | −279.815 | − | 484.653i | −0.319059 | − | 0.552626i | 0.661233 | − | 0.750181i | \(-0.270033\pi\) |
−0.980292 | + | 0.197554i | \(0.936700\pi\) | |||||||
\(878\) | 260.211 | − | 366.913i | 0.296368 | − | 0.417897i | ||||
\(879\) | 334.297 | + | 216.662i | 0.380315 | + | 0.246487i | ||||
\(880\) | −625.987 | + | 1599.34i | −0.711349 | + | 1.81744i | ||||
\(881\) | −957.127 | −1.08641 | −0.543205 | − | 0.839600i | \(-0.682789\pi\) | ||||
−0.543205 | + | 0.839600i | \(0.682789\pi\) | |||||||
\(882\) | 170.684 | − | 858.925i | 0.193520 | − | 0.973838i | ||||
\(883\) | 625.252i | 0.708100i | 0.935227 | + | 0.354050i | \(0.115196\pi\) | ||||
−0.935227 | + | 0.354050i | \(0.884804\pi\) | |||||||
\(884\) | −39.9356 | − | 113.960i | −0.0451760 | − | 0.128914i | ||||
\(885\) | 444.475 | + | 22.8873i | 0.502231 | + | 0.0258613i | ||||
\(886\) | 493.211 | − | 695.457i | 0.556671 | − | 0.784940i | ||||
\(887\) | 921.187 | − | 531.847i | 1.03854 | − | 0.599602i | 0.119122 | − | 0.992880i | \(-0.461992\pi\) |
0.919420 | + | 0.393277i | \(0.128659\pi\) | |||||||
\(888\) | 267.399 | + | 1373.01i | 0.301125 | + | 1.54618i | ||||
\(889\) | 48.5496 | − | 84.0904i | 0.0546115 | − | 0.0945899i | ||||
\(890\) | 308.289 | − | 141.511i | 0.346393 | − | 0.159002i | ||||
\(891\) | 288.984 | − | 1384.39i | 0.324337 | − | 1.55375i | ||||
\(892\) | −1158.15 | − | 995.735i | −1.29837 | − | 1.11629i | ||||
\(893\) | −108.576 | + | 188.059i | −0.121585 | + | 0.210592i | ||||
\(894\) | −768.620 | + | 973.536i | −0.859754 | + | 1.08897i | ||||
\(895\) | −511.172 | + | 295.125i | −0.571142 | + | 0.329749i | ||||
\(896\) | 69.8047 | − | 29.0467i | 0.0779071 | − | 0.0324182i | ||||
\(897\) | −42.3985 | − | 2.18322i | −0.0472670 | − | 0.00243391i | ||||
\(898\) | 75.7625 | − | 809.951i | 0.0843681 | − | 0.901950i | ||||
\(899\) | − | 202.793i | − | 0.225577i | ||||||
\(900\) | −106.910 | − | 448.177i | −0.118789 | − | 0.497974i | ||||
\(901\) | −606.935 | −0.673624 | ||||||||
\(902\) | 185.622 | + | 17.3630i | 0.205790 | + | 0.0192495i | ||||
\(903\) | 58.2647 | + | 37.7620i | 0.0645235 | + | 0.0418184i | ||||
\(904\) | −141.680 | + | 35.2418i | −0.156726 | + | 0.0389843i | ||||
\(905\) | −1010.61 | − | 1750.43i | −1.11670 | − | 1.93418i | ||||
\(906\) | 127.310 | − | 873.576i | 0.140519 | − | 0.964212i | ||||
\(907\) | 207.207 | + | 119.631i | 0.228453 | + | 0.131898i | 0.609858 | − | 0.792510i | \(-0.291226\pi\) |
−0.381405 | + | 0.924408i | \(0.624560\pi\) | |||||||
\(908\) | 180.535 | + | 155.217i | 0.198827 | + | 0.170944i | ||||
\(909\) | 94.7072 | + | 211.675i | 0.104188 | + | 0.232866i | ||||
\(910\) | 5.40696 | + | 11.7793i | 0.00594172 | + | 0.0129443i | ||||
\(911\) | 175.804 | + | 101.501i | 0.192980 | + | 0.111417i | 0.593377 | − | 0.804925i | \(-0.297794\pi\) |
−0.400397 | + | 0.916342i | \(0.631128\pi\) | |||||||
\(912\) | 92.6134 | + | 931.685i | 0.101550 | + | 1.02158i | ||||
\(913\) | −665.585 | − | 1152.83i | −0.729009 | − | 1.26268i | ||||
\(914\) | −520.740 | − | 369.303i | −0.569737 | − | 0.404052i | ||||
\(915\) | 1246.62 | − | 636.619i | 1.36243 | − | 0.695758i | ||||
\(916\) | −170.482 | − | 486.486i | −0.186116 | − | 0.531099i | ||||
\(917\) | −84.1801 | −0.0917994 | ||||||||
\(918\) | 885.661 | + | 223.893i | 0.964773 | + | 0.243893i | ||||
\(919\) | 878.708i | 0.956156i | 0.878317 | + | 0.478078i | \(0.158666\pi\) | ||||
−0.878317 | + | 0.478078i | \(0.841334\pi\) | |||||||
\(920\) | −280.724 | + | 270.793i | −0.305135 | + | 0.294340i | ||||
\(921\) | 459.143 | + | 899.090i | 0.498527 | + | 0.976210i | ||||
\(922\) | 958.892 | + | 680.036i | 1.04001 | + | 0.737566i | ||||
\(923\) | −135.746 | + | 78.3730i | −0.147070 | + | 0.0849111i | ||||
\(924\) | 89.5682 | + | 85.4004i | 0.0969353 | + | 0.0924247i | ||||
\(925\) | −372.975 | + | 646.011i | −0.403216 | + | 0.698391i | ||||
\(926\) | 221.670 | + | 482.920i | 0.239385 | + | 0.521512i | ||||
\(927\) | −18.1406 | + | 175.680i | −0.0195691 | + | 0.189514i | ||||
\(928\) | 111.510 | + | 169.883i | 0.120162 | + | 0.183064i | ||||
\(929\) | 300.259 | − | 520.064i | 0.323207 | − | 0.559810i | −0.657941 | − | 0.753069i | \(-0.728572\pi\) |
0.981148 | + | 0.193259i | \(0.0619058\pi\) | |||||||
\(930\) | 169.881 | − | 1165.69i | 0.182667 | − | 1.25343i | ||||
\(931\) | −821.838 | + | 474.489i | −0.882748 | + | 0.509655i | ||||
\(932\) | −58.9350 | − | 11.1228i | −0.0632350 | − | 0.0119344i | ||||
\(933\) | −573.135 | + | 884.316i | −0.614293 | + | 0.947820i | ||||
\(934\) | 1582.29 | + | 148.007i | 1.69410 | + | 0.158465i | ||||
\(935\) | − | 1815.93i | − | 1.94217i | ||||||
\(936\) | −47.9795 | + | 119.190i | −0.0512602 | + | 0.127340i | ||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | 4.04255 | − | 43.2175i | 0.00430975 | − | 0.0460741i | ||||
\(939\) | 29.4447 | − | 571.822i | 0.0313575 | − | 0.608969i | ||||
\(940\) | −50.7738 | + | 269.028i | −0.0540147 | + | 0.286200i | ||||
\(941\) | −377.587 | − | 653.999i | −0.401261 | − | 0.695005i | 0.592617 | − | 0.805484i | \(-0.298095\pi\) |
−0.993878 | + | 0.110479i | \(0.964761\pi\) | |||||||
\(942\) | 233.783 | − | 296.110i | 0.248177 | − | 0.314342i | ||||
\(943\) | 36.6668 | + | 21.1696i | 0.0388831 | + | 0.0224492i | ||||
\(944\) | −381.719 | + | 57.8966i | −0.404363 | + | 0.0613311i | ||||
\(945\) | −96.8859 | − | 15.0735i | −0.102525 | − | 0.0159507i | ||||
\(946\) | 1243.46 | − | 570.773i | 1.31444 | − | 0.603354i | ||||
\(947\) | −769.965 | − | 444.539i | −0.813057 | − | 0.469419i | 0.0349595 | − | 0.999389i | \(-0.488870\pi\) |
−0.848016 | + | 0.529970i | \(0.822203\pi\) | |||||||
\(948\) | 433.387 | + | 105.131i | 0.457159 | + | 0.110898i | ||||
\(949\) | 53.5731 | + | 92.7913i | 0.0564521 | + | 0.0977779i | ||||
\(950\) | −288.834 | + | 407.273i | −0.304036 | + | 0.428708i | ||||
\(951\) | 62.5727 | − | 1215.17i | 0.0657967 | − | 1.27778i | ||||
\(952\) | −57.5351 | + | 55.4997i | −0.0604360 | + | 0.0582980i | ||||
\(953\) | 15.5920 | 0.0163610 | 0.00818050 | − | 0.999967i | \(-0.497396\pi\) | ||||
0.00818050 | + | 0.999967i | \(0.497396\pi\) | |||||||
\(954\) | 485.607 | + | 425.706i | 0.509022 | + | 0.446233i | ||||
\(955\) | − | 2.49830i | − | 0.00261602i | ||||||
\(956\) | 1374.12 | − | 481.539i | 1.43736 | − | 0.503702i | ||||
\(957\) | −180.905 | + | 279.127i | −0.189034 | + | 0.291669i | ||||
\(958\) | 765.449 | − | 1079.33i | 0.799008 | − | 1.12665i | ||||
\(959\) | −3.15291 | + | 1.82033i | −0.00328770 | + | 0.00189816i | ||||
\(960\) | 498.666 | + | 1069.93i | 0.519443 | + | 1.11451i | ||||
\(961\) | 29.3970 | − | 50.9172i | 0.0305900 | − | 0.0529835i | ||||
\(962\) | 189.050 | − | 86.7777i | 0.196517 | − | 0.0902056i | ||||
\(963\) | 1335.68 | + | 966.706i | 1.38699 | + | 1.00385i | ||||
\(964\) | 211.350 | − | 245.824i | 0.219243 | − | 0.255004i | ||||
\(965\) | 191.961 | − | 332.486i | 0.198923 | − | 0.344545i | ||||
\(966\) | 10.3957 | + | 26.1121i | 0.0107616 | + | 0.0270311i | ||||
\(967\) | 847.921 | − | 489.548i | 0.876858 | − | 0.506254i | 0.00723669 | − | 0.999974i | \(-0.497696\pi\) |
0.869621 | + | 0.493720i | \(0.164363\pi\) | |||||||
\(968\) | 1427.22 | − | 355.009i | 1.47440 | − | 0.366745i | ||||
\(969\) | −450.229 | − | 881.635i | −0.464633 | − | 0.909840i | ||||
\(970\) | −29.9086 | + | 319.743i | −0.0308336 | + | 0.329632i | ||||
\(971\) | 67.3838i | 0.0693963i | 0.999398 | + | 0.0346982i | \(0.0110470\pi\) | ||||
−0.999398 | + | 0.0346982i | \(0.988953\pi\) | |||||||
\(972\) | −551.576 | − | 800.342i | −0.567465 | − | 0.823397i | ||||
\(973\) | 70.3667 | 0.0723193 | ||||||||
\(974\) | 113.808 | + | 10.6456i | 0.116846 | + | 0.0109297i | ||||
\(975\) | −61.0216 | + | 31.1622i | −0.0625863 | + | 0.0319613i | ||||
\(976\) | −948.655 | + | 757.966i | −0.971983 | + | 0.776604i | ||||
\(977\) | 353.710 | + | 612.644i | 0.362037 | + | 0.627067i | 0.988296 | − | 0.152549i | \(-0.0487480\pi\) |
−0.626259 | + | 0.779615i | \(0.715415\pi\) | |||||||
\(978\) | −798.959 | + | 318.080i | −0.816931 | + | 0.325235i | ||||
\(979\) | −417.133 | − | 240.832i | −0.426081 | − | 0.245998i | ||||
\(980\) | −780.002 | + | 907.229i | −0.795921 | + | 0.925744i | ||||
\(981\) | 532.115 | − | 735.211i | 0.542421 | − | 0.749451i | ||||
\(982\) | 46.8799 | + | 102.130i | 0.0477392 | + | 0.104002i | ||||
\(983\) | −338.829 | − | 195.623i | −0.344689 | − | 0.199006i | 0.317655 | − | 0.948206i | \(-0.397105\pi\) |
−0.662343 | + | 0.749200i | \(0.730438\pi\) | |||||||
\(984\) | 96.6744 | − | 84.0990i | 0.0982464 | − | 0.0854665i | ||||
\(985\) | −638.971 | − | 1106.73i | −0.648701 | − | 1.12358i | ||||
\(986\) | −175.259 | − | 124.292i | −0.177748 | − | 0.126057i | ||||
\(987\) | 16.5547 | + | 10.7293i | 0.0167727 | + | 0.0108706i | ||||
\(988\) | 131.398 | − | 46.0466i | 0.132994 | − | 0.0466059i | ||||
\(989\) | 310.720 | 0.314176 | ||||||||
\(990\) | −1273.70 | + | 1452.92i | −1.28656 | + | 1.46760i | ||||
\(991\) | 104.988i | 0.105941i | 0.998596 | + | 0.0529706i | \(0.0168690\pi\) | ||||
−0.998596 | + | 0.0529706i | \(0.983131\pi\) | |||||||
\(992\) | 58.4795 | + | 1020.22i | 0.0589512 | + | 1.02845i | ||||
\(993\) | −1328.81 | − | 68.4244i | −1.33818 | − | 0.0689068i | ||||
\(994\) | 84.6422 | + | 60.0274i | 0.0851531 | + | 0.0603897i | ||||
\(995\) | −1592.67 | + | 919.530i | −1.60068 | + | 0.924151i | ||||
\(996\) | −889.126 | − | 215.685i | −0.892697 | − | 0.216551i | ||||
\(997\) | −39.0028 | + | 67.5547i | −0.0391201 | + | 0.0677580i | −0.884923 | − | 0.465738i | \(-0.845789\pi\) |
0.845802 | + | 0.533496i | \(0.179122\pi\) | |||||||
\(998\) | 503.120 | + | 1096.07i | 0.504128 | + | 1.09827i | ||||
\(999\) | −241.918 | + | 1554.95i | −0.242160 | + | 1.55650i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 36.3.f.c.7.4 | yes | 16 | |
3.2 | odd | 2 | 108.3.f.c.19.5 | 16 | |||
4.3 | odd | 2 | inner | 36.3.f.c.7.3 | ✓ | 16 | |
8.3 | odd | 2 | 576.3.o.g.511.2 | 16 | |||
8.5 | even | 2 | 576.3.o.g.511.7 | 16 | |||
9.2 | odd | 6 | 324.3.d.g.163.2 | 8 | |||
9.4 | even | 3 | inner | 36.3.f.c.31.3 | yes | 16 | |
9.5 | odd | 6 | 108.3.f.c.91.6 | 16 | |||
9.7 | even | 3 | 324.3.d.i.163.7 | 8 | |||
12.11 | even | 2 | 108.3.f.c.19.6 | 16 | |||
24.5 | odd | 2 | 1728.3.o.g.127.8 | 16 | |||
24.11 | even | 2 | 1728.3.o.g.127.7 | 16 | |||
36.7 | odd | 6 | 324.3.d.i.163.8 | 8 | |||
36.11 | even | 6 | 324.3.d.g.163.1 | 8 | |||
36.23 | even | 6 | 108.3.f.c.91.5 | 16 | |||
36.31 | odd | 6 | inner | 36.3.f.c.31.4 | yes | 16 | |
72.5 | odd | 6 | 1728.3.o.g.1279.7 | 16 | |||
72.13 | even | 6 | 576.3.o.g.319.2 | 16 | |||
72.59 | even | 6 | 1728.3.o.g.1279.8 | 16 | |||
72.67 | odd | 6 | 576.3.o.g.319.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
36.3.f.c.7.4 | yes | 16 | 1.1 | even | 1 | trivial | |
36.3.f.c.31.3 | yes | 16 | 9.4 | even | 3 | inner | |
36.3.f.c.31.4 | yes | 16 | 36.31 | odd | 6 | inner | |
108.3.f.c.19.5 | 16 | 3.2 | odd | 2 | |||
108.3.f.c.19.6 | 16 | 12.11 | even | 2 | |||
108.3.f.c.91.5 | 16 | 36.23 | even | 6 | |||
108.3.f.c.91.6 | 16 | 9.5 | odd | 6 | |||
324.3.d.g.163.1 | 8 | 36.11 | even | 6 | |||
324.3.d.g.163.2 | 8 | 9.2 | odd | 6 | |||
324.3.d.i.163.7 | 8 | 9.7 | even | 3 | |||
324.3.d.i.163.8 | 8 | 36.7 | odd | 6 | |||
576.3.o.g.319.2 | 16 | 72.13 | even | 6 | |||
576.3.o.g.319.7 | 16 | 72.67 | odd | 6 | |||
576.3.o.g.511.2 | 16 | 8.3 | odd | 2 | |||
576.3.o.g.511.7 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.127.7 | 16 | 24.11 | even | 2 | |||
1728.3.o.g.127.8 | 16 | 24.5 | odd | 2 | |||
1728.3.o.g.1279.7 | 16 | 72.5 | odd | 6 | |||
1728.3.o.g.1279.8 | 16 | 72.59 | even | 6 |