Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(123,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.123");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.e (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: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 123.10 | ||
Character | \(\chi\) | \(=\) | 349.123 |
Dual form | 349.2.e.a.227.10 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.03662 | + | 0.598491i | −0.732999 | + | 0.423197i | −0.819518 | − | 0.573053i | \(-0.805759\pi\) |
0.0865193 | + | 0.996250i | \(0.472426\pi\) | |||||||
\(3\) | 0.00513702 | − | 0.00889758i | 0.00296586 | − | 0.00513702i | −0.864539 | − | 0.502566i | \(-0.832389\pi\) |
0.867505 | + | 0.497429i | \(0.165723\pi\) | |||||||
\(4\) | −0.283617 | + | 0.491238i | −0.141808 | + | 0.245619i | ||||
\(5\) | −0.193021 | + | 0.334323i | −0.0863217 | + | 0.149514i | −0.905954 | − | 0.423377i | \(-0.860845\pi\) |
0.819632 | + | 0.572890i | \(0.194178\pi\) | |||||||
\(6\) | 0.0122978i | 0.00502057i | ||||||||
\(7\) | 3.23720 | − | 1.86900i | 1.22355 | − | 0.706415i | 0.257875 | − | 0.966178i | \(-0.416978\pi\) |
0.965672 | + | 0.259763i | \(0.0836444\pi\) | |||||||
\(8\) | − | 3.07293i | − | 1.08645i | ||||||
\(9\) | 1.49995 | + | 2.59798i | 0.499982 | + | 0.865995i | ||||
\(10\) | − | 0.462086i | − | 0.146124i | ||||||
\(11\) | − | 4.48490i | − | 1.35225i | −0.736788 | − | 0.676124i | \(-0.763658\pi\) | ||
0.736788 | − | 0.676124i | \(-0.236342\pi\) | |||||||
\(12\) | 0.00291389 | + | 0.00504700i | 0.000841167 | + | 0.00145694i | ||||
\(13\) | −1.35467 | + | 0.782122i | −0.375719 | + | 0.216921i | −0.675954 | − | 0.736944i | \(-0.736268\pi\) |
0.300235 | + | 0.953865i | \(0.402935\pi\) | |||||||
\(14\) | −2.23716 | + | 3.87487i | −0.597906 | + | 1.03560i | ||||
\(15\) | 0.00198311 | + | 0.00343484i | 0.000512036 | + | 0.000886873i | ||||
\(16\) | 1.27189 | + | 2.20298i | 0.317973 | + | 0.550745i | ||||
\(17\) | 6.40967 | 1.55457 | 0.777287 | − | 0.629146i | \(-0.216595\pi\) | ||||
0.777287 | + | 0.629146i | \(0.216595\pi\) | |||||||
\(18\) | −3.10974 | − | 1.79541i | −0.732973 | − | 0.423182i | ||||
\(19\) | −2.90902 | + | 5.03856i | −0.667374 | + | 1.15593i | 0.311262 | + | 0.950324i | \(0.399248\pi\) |
−0.978636 | + | 0.205602i | \(0.934085\pi\) | |||||||
\(20\) | −0.109488 | − | 0.189639i | −0.0244823 | − | 0.0424045i | ||||
\(21\) | − | 0.0384043i | − | 0.00838051i | ||||||
\(22\) | 2.68417 | + | 4.64912i | 0.572267 | + | 0.991196i | ||||
\(23\) | 2.27143 | + | 3.93424i | 0.473626 | + | 0.820345i | 0.999544 | − | 0.0301904i | \(-0.00961138\pi\) |
−0.525918 | + | 0.850535i | \(0.676278\pi\) | |||||||
\(24\) | −0.0273417 | − | 0.0157857i | −0.00558109 | − | 0.00322225i | ||||
\(25\) | 2.42549 | + | 4.20106i | 0.485097 | + | 0.840213i | ||||
\(26\) | 0.936186 | − | 1.62152i | 0.183601 | − | 0.318006i | ||||
\(27\) | 0.0616432 | 0.0118632 | ||||||||
\(28\) | 2.12032i | 0.400702i | ||||||||
\(29\) | 3.46755 | − | 6.00597i | 0.643908 | − | 1.11528i | −0.340645 | − | 0.940192i | \(-0.610645\pi\) |
0.984553 | − | 0.175089i | \(-0.0560213\pi\) | |||||||
\(30\) | −0.00411145 | − | 0.00237375i | −0.000750644 | − | 0.000433385i | ||||
\(31\) | −2.15649 | −0.387317 | −0.193659 | − | 0.981069i | \(-0.562035\pi\) | ||||
−0.193659 | + | 0.981069i | \(0.562035\pi\) | |||||||
\(32\) | 2.68555 | + | 1.55050i | 0.474743 | + | 0.274093i | ||||
\(33\) | −0.0399047 | − | 0.0230390i | −0.00694652 | − | 0.00401058i | ||||
\(34\) | −6.64438 | + | 3.83613i | −1.13950 | + | 0.657891i | ||||
\(35\) | 1.44303i | 0.243916i | ||||||||
\(36\) | −1.70164 | −0.283607 | ||||||||
\(37\) | 4.45227 | 0.731949 | 0.365975 | − | 0.930625i | \(-0.380736\pi\) | ||||
0.365975 | + | 0.930625i | \(0.380736\pi\) | |||||||
\(38\) | − | 6.96408i | − | 1.12972i | ||||||
\(39\) | 0.0160711i | 0.00257343i | ||||||||
\(40\) | 1.02735 | + | 0.593141i | 0.162438 | + | 0.0937839i | ||||
\(41\) | 5.24919 | 0.819785 | 0.409893 | − | 0.912134i | \(-0.365566\pi\) | ||||
0.409893 | + | 0.912134i | \(0.365566\pi\) | |||||||
\(42\) | 0.0229847 | + | 0.0398106i | 0.00354661 | + | 0.00614291i | ||||
\(43\) | −7.50306 | − | 4.33190i | −1.14421 | − | 0.660608i | −0.196738 | − | 0.980456i | \(-0.563035\pi\) |
−0.947469 | + | 0.319848i | \(0.896368\pi\) | |||||||
\(44\) | 2.20315 | + | 1.27199i | 0.332138 | + | 0.191760i | ||||
\(45\) | −1.15809 | −0.172637 | ||||||||
\(46\) | −4.70921 | − | 2.71886i | −0.694335 | − | 0.400875i | ||||
\(47\) | 2.22995i | 0.325272i | 0.986686 | + | 0.162636i | \(0.0519996\pi\) | ||||
−0.986686 | + | 0.162636i | \(0.948000\pi\) | |||||||
\(48\) | 0.0261349 | 0.00377225 | ||||||||
\(49\) | 3.48632 | − | 6.03848i | 0.498045 | − | 0.862640i | ||||
\(50\) | −5.02860 | − | 2.90326i | −0.711151 | − | 0.410583i | ||||
\(51\) | 0.0329266 | − | 0.0570306i | 0.00461065 | − | 0.00798588i | ||||
\(52\) | − | 0.887291i | − | 0.123045i | ||||||
\(53\) | 6.90943i | 0.949083i | 0.880233 | + | 0.474542i | \(0.157386\pi\) | ||||
−0.880233 | + | 0.474542i | \(0.842614\pi\) | |||||||
\(54\) | −0.0639003 | + | 0.0368929i | −0.00869574 | + | 0.00502049i | ||||
\(55\) | 1.49940 | + | 0.865681i | 0.202179 | + | 0.116728i | ||||
\(56\) | −5.74331 | − | 9.94770i | −0.767482 | − | 1.32932i | ||||
\(57\) | 0.0298874 | + | 0.0517664i | 0.00395868 | + | 0.00685663i | ||||
\(58\) | 8.30119i | 1.09000i | ||||||||
\(59\) | −7.74318 | − | 4.47053i | −1.00808 | − | 0.582013i | −0.0974488 | − | 0.995241i | \(-0.531068\pi\) |
−0.910628 | + | 0.413227i | \(0.864402\pi\) | |||||||
\(60\) | −0.00224977 | −0.000290444 | ||||||||
\(61\) | 4.16196i | 0.532884i | 0.963851 | + | 0.266442i | \(0.0858481\pi\) | ||||
−0.963851 | + | 0.266442i | \(0.914152\pi\) | |||||||
\(62\) | 2.23545 | − | 1.29064i | 0.283903 | − | 0.163911i | ||||
\(63\) | 9.71126 | + | 5.60680i | 1.22350 | + | 0.706390i | ||||
\(64\) | −8.79941 | −1.09993 | ||||||||
\(65\) | − | 0.603864i | − | 0.0749002i | ||||||
\(66\) | 0.0551546 | 0.00678906 | ||||||||
\(67\) | 1.09453 | 0.133718 | 0.0668591 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668591 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(68\) | −1.81789 | + | 3.14868i | −0.220451 | + | 0.381833i | ||||
\(69\) | 0.0466736 | 0.00561884 | ||||||||
\(70\) | −0.863639 | − | 1.49587i | −0.103225 | − | 0.178790i | ||||
\(71\) | 5.25715 | − | 3.03521i | 0.623908 | − | 0.360214i | −0.154481 | − | 0.987996i | \(-0.549370\pi\) |
0.778389 | + | 0.627782i | \(0.216037\pi\) | |||||||
\(72\) | 7.98343 | − | 4.60924i | 0.940857 | − | 0.543204i | ||||
\(73\) | 1.25178 | − | 2.16815i | 0.146510 | − | 0.253763i | −0.783425 | − | 0.621486i | \(-0.786529\pi\) |
0.929935 | + | 0.367723i | \(0.119863\pi\) | |||||||
\(74\) | −4.61530 | + | 2.66465i | −0.536518 | + | 0.309759i | ||||
\(75\) | 0.0498391 | 0.00575492 | ||||||||
\(76\) | −1.65009 | − | 2.85804i | −0.189278 | − | 0.327840i | ||||
\(77\) | −8.38227 | − | 14.5185i | −0.955248 | − | 1.65454i | ||||
\(78\) | −0.00961841 | − | 0.0166596i | −0.00108907 | − | 0.00188633i | ||||
\(79\) | − | 7.81600i | − | 0.879369i | −0.898152 | − | 0.439685i | \(-0.855090\pi\) | ||
0.898152 | − | 0.439685i | \(-0.144910\pi\) | |||||||
\(80\) | −0.982007 | −0.109792 | ||||||||
\(81\) | −4.49953 | + | 7.79341i | −0.499947 | + | 0.865934i | ||||
\(82\) | −5.44140 | + | 3.14159i | −0.600902 | + | 0.346931i | ||||
\(83\) | −6.53928 | − | 11.3264i | −0.717779 | − | 1.24323i | −0.961878 | − | 0.273480i | \(-0.911825\pi\) |
0.244098 | − | 0.969750i | \(-0.421508\pi\) | |||||||
\(84\) | 0.0188657 | + | 0.0108921i | 0.00205842 | + | 0.00118843i | ||||
\(85\) | −1.23720 | + | 2.14290i | −0.134194 | + | 0.232430i | ||||
\(86\) | 10.3704 | 1.11827 | ||||||||
\(87\) | −0.0356257 | − | 0.0617056i | −0.00381948 | − | 0.00661553i | ||||
\(88\) | −13.7818 | −1.46914 | ||||||||
\(89\) | −1.83741 | − | 1.06083i | −0.194765 | − | 0.112448i | 0.399446 | − | 0.916757i | \(-0.369202\pi\) |
−0.594212 | + | 0.804309i | \(0.702536\pi\) | |||||||
\(90\) | 1.20049 | − | 0.693105i | 0.126543 | − | 0.0730597i | ||||
\(91\) | −2.92357 | + | 5.06377i | −0.306473 | + | 0.530827i | ||||
\(92\) | −2.57686 | −0.268657 | ||||||||
\(93\) | −0.0110779 | + | 0.0191875i | −0.00114873 | + | 0.00198966i | ||||
\(94\) | −1.33461 | − | 2.31161i | −0.137654 | − | 0.238424i | ||||
\(95\) | −1.12300 | − | 1.94510i | −0.115218 | − | 0.199563i | ||||
\(96\) | 0.0275914 | − | 0.0159299i | 0.00281604 | − | 0.00162584i | ||||
\(97\) | −7.79942 | + | 4.50300i | −0.791911 | + | 0.457210i | −0.840635 | − | 0.541602i | \(-0.817818\pi\) |
0.0487239 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(98\) | 8.34612i | 0.843085i | ||||||||
\(99\) | 11.6517 | − | 6.72711i | 1.17104 | − | 0.676100i | ||||
\(100\) | −2.75163 | −0.275163 | ||||||||
\(101\) | − | 5.16963i | − | 0.514397i | −0.966359 | − | 0.257199i | \(-0.917201\pi\) | ||
0.966359 | − | 0.257199i | \(-0.0827995\pi\) | |||||||
\(102\) | 0.0788252i | 0.00780485i | ||||||||
\(103\) | − | 9.73136i | − | 0.958860i | −0.877580 | − | 0.479430i | \(-0.840843\pi\) | ||
0.877580 | − | 0.479430i | \(-0.159157\pi\) | |||||||
\(104\) | 2.40341 | + | 4.16282i | 0.235673 | + | 0.408198i | ||||
\(105\) | 0.0128394 | + | 0.00741286i | 0.00125300 | + | 0.000723421i | ||||
\(106\) | −4.13523 | − | 7.16244i | −0.401649 | − | 0.695677i | ||||
\(107\) | 3.62358 | − | 2.09207i | 0.350305 | − | 0.202248i | −0.314515 | − | 0.949253i | \(-0.601842\pi\) |
0.664819 | + | 0.747004i | \(0.268508\pi\) | |||||||
\(108\) | −0.0174830 | + | 0.0302815i | −0.00168230 | + | 0.00291384i | ||||
\(109\) | 8.25160 | − | 14.2922i | 0.790360 | − | 1.36894i | −0.135385 | − | 0.990793i | \(-0.543227\pi\) |
0.925744 | − | 0.378150i | \(-0.123440\pi\) | |||||||
\(110\) | −2.07241 | −0.197596 | ||||||||
\(111\) | 0.0228714 | − | 0.0396145i | 0.00217086 | − | 0.00376004i | ||||
\(112\) | 8.23473 | + | 4.75432i | 0.778109 | + | 0.449241i | ||||
\(113\) | −2.42839 | + | 1.40203i | −0.228444 | + | 0.131892i | −0.609854 | − | 0.792514i | \(-0.708772\pi\) |
0.381410 | + | 0.924406i | \(0.375439\pi\) | |||||||
\(114\) | −0.0619635 | − | 0.0357746i | −0.00580341 | − | 0.00335060i | ||||
\(115\) | −1.75374 | −0.163537 | ||||||||
\(116\) | 1.96691 | + | 3.40679i | 0.182623 | + | 0.316312i | ||||
\(117\) | −4.06388 | − | 2.34628i | −0.375706 | − | 0.216914i | ||||
\(118\) | 10.7023 | 0.985226 | ||||||||
\(119\) | 20.7494 | − | 11.9797i | 1.90209 | − | 1.09817i | ||||
\(120\) | 0.0105550 | − | 0.00609396i | 0.000963539 | − | 0.000556300i | ||||
\(121\) | −9.11430 | −0.828573 | ||||||||
\(122\) | −2.49090 | − | 4.31436i | −0.225515 | − | 0.390604i | ||||
\(123\) | 0.0269652 | − | 0.0467051i | 0.00243137 | − | 0.00421125i | ||||
\(124\) | 0.611616 | − | 1.05935i | 0.0549248 | − | 0.0951325i | ||||
\(125\) | −3.80289 | −0.340141 | ||||||||
\(126\) | −13.4225 | −1.19577 | ||||||||
\(127\) | 15.5408i | 1.37902i | 0.724276 | + | 0.689510i | \(0.242174\pi\) | ||||
−0.724276 | + | 0.689510i | \(0.757826\pi\) | |||||||
\(128\) | 3.75052 | − | 2.16536i | 0.331502 | − | 0.191393i | ||||
\(129\) | −0.0770868 | + | 0.0445061i | −0.00678711 | + | 0.00391854i | ||||
\(130\) | 0.361408 | + | 0.625976i | 0.0316975 | + | 0.0549017i | ||||
\(131\) | 6.38883i | 0.558194i | 0.960263 | + | 0.279097i | \(0.0900352\pi\) | ||||
−0.960263 | + | 0.279097i | \(0.909965\pi\) | |||||||
\(132\) | 0.0226353 | − | 0.0130685i | 0.00197015 | − | 0.00113747i | ||||
\(133\) | 21.7478i | 1.88577i | ||||||||
\(134\) | −1.13461 | + | 0.655066i | −0.0980152 | + | 0.0565891i | ||||
\(135\) | −0.0118984 | + | 0.0206087i | −0.00102405 | + | 0.00177371i | ||||
\(136\) | − | 19.6965i | − | 1.68896i | ||||||
\(137\) | −11.2718 | − | 6.50781i | −0.963019 | − | 0.555999i | −0.0659181 | − | 0.997825i | \(-0.520998\pi\) |
−0.897101 | + | 0.441826i | \(0.854331\pi\) | |||||||
\(138\) | −0.0483826 | + | 0.0279337i | −0.00411860 | + | 0.00237788i | ||||
\(139\) | 12.6754 | 1.07511 | 0.537556 | − | 0.843228i | \(-0.319348\pi\) | ||||
0.537556 | + | 0.843228i | \(0.319348\pi\) | |||||||
\(140\) | −0.708870 | − | 0.409266i | −0.0599104 | − | 0.0345893i | ||||
\(141\) | 0.0198412 | + | 0.0114553i | 0.00167093 | + | 0.000964711i | ||||
\(142\) | −3.63310 | + | 6.29271i | −0.304883 | + | 0.528073i | ||||
\(143\) | 3.50773 | + | 6.07558i | 0.293332 | + | 0.508065i | ||||
\(144\) | −3.81554 | + | 6.60870i | −0.317961 | + | 0.550725i | ||||
\(145\) | 1.33862 | + | 2.31856i | 0.111166 | + | 0.192546i | ||||
\(146\) | 2.99672i | 0.248011i | ||||||||
\(147\) | −0.0358186 | − | 0.0620396i | −0.00295426 | − | 0.00511694i | ||||
\(148\) | −1.26274 | + | 2.18713i | −0.103797 | + | 0.179781i | ||||
\(149\) | −11.0183 | + | 6.36139i | −0.902650 | + | 0.521145i | −0.878059 | − | 0.478552i | \(-0.841162\pi\) |
−0.0245913 | + | 0.999698i | \(0.507828\pi\) | |||||||
\(150\) | −0.0516640 | + | 0.0298282i | −0.00421835 | + | 0.00243547i | ||||
\(151\) | 0.00348899 | − | 0.00604311i | 0.000283930 | − | 0.000491781i | −0.865883 | − | 0.500246i | \(-0.833243\pi\) |
0.866167 | + | 0.499754i | \(0.166576\pi\) | |||||||
\(152\) | 15.4832 | + | 8.93921i | 1.25585 | + | 0.725066i | ||||
\(153\) | 9.61417 | + | 16.6522i | 0.777260 | + | 1.34625i | ||||
\(154\) | 17.3784 | + | 10.0334i | 1.40039 | + | 0.808517i | ||||
\(155\) | 0.416248 | − | 0.720963i | 0.0334339 | − | 0.0579092i | ||||
\(156\) | −0.00789474 | − | 0.00455803i | −0.000632085 | − | 0.000364934i | ||||
\(157\) | −9.64158 | + | 16.6997i | −0.769482 | + | 1.33278i | 0.168362 | + | 0.985725i | \(0.446152\pi\) |
−0.937844 | + | 0.347057i | \(0.887181\pi\) | |||||||
\(158\) | 4.67781 | + | 8.10220i | 0.372147 | + | 0.644577i | ||||
\(159\) | 0.0614772 | + | 0.0354939i | 0.00487546 | + | 0.00281485i | ||||
\(160\) | −1.03674 | + | 0.598560i | −0.0819612 | + | 0.0473203i | ||||
\(161\) | 14.7062 | + | 8.49061i | 1.15901 | + | 0.669154i | ||||
\(162\) | − | 10.7717i | − | 0.846305i | ||||||
\(163\) | 19.0217i | 1.48989i | 0.667125 | + | 0.744945i | \(0.267524\pi\) | ||||
−0.667125 | + | 0.744945i | \(0.732476\pi\) | |||||||
\(164\) | −1.48876 | + | 2.57860i | −0.116252 | + | 0.201355i | ||||
\(165\) | 0.0154049 | − | 0.00889404i | 0.00119927 | − | 0.000692400i | ||||
\(166\) | 13.5575 | + | 7.82740i | 1.05226 | + | 0.607524i | ||||
\(167\) | − | 20.4590i | − | 1.58317i | −0.611062 | − | 0.791583i | \(-0.709258\pi\) | ||
0.611062 | − | 0.791583i | \(-0.290742\pi\) | |||||||
\(168\) | −0.118014 | −0.00910498 | ||||||||
\(169\) | −5.27657 | + | 9.13929i | −0.405890 | + | 0.703022i | ||||
\(170\) | − | 2.96182i | − | 0.227161i | ||||||
\(171\) | −17.4535 | −1.33470 | ||||||||
\(172\) | 4.25599 | − | 2.45720i | 0.324516 | − | 0.187359i | ||||
\(173\) | −11.9421 | + | 6.89475i | −0.907938 | + | 0.524198i | −0.879767 | − | 0.475405i | \(-0.842302\pi\) |
−0.0281708 | + | 0.999603i | \(0.508968\pi\) | |||||||
\(174\) | 0.0738605 | + | 0.0426434i | 0.00559935 | + | 0.00323279i | ||||
\(175\) | 15.7036 | + | 9.06646i | 1.18708 | + | 0.685360i | ||||
\(176\) | 9.88013 | − | 5.70430i | 0.744743 | − | 0.429977i | ||||
\(177\) | −0.0795538 | + | 0.0459304i | −0.00597963 | + | 0.00345234i | ||||
\(178\) | 2.53959 | 0.190350 | ||||||||
\(179\) | − | 22.2533i | − | 1.66329i | −0.555306 | − | 0.831646i | \(-0.687399\pi\) | ||
0.555306 | − | 0.831646i | \(-0.312601\pi\) | |||||||
\(180\) | 0.328453 | − | 0.568897i | 0.0244814 | − | 0.0424031i | ||||
\(181\) | 0.730722 | 0.0543141 | 0.0271571 | − | 0.999631i | \(-0.491355\pi\) | ||||
0.0271571 | + | 0.999631i | \(0.491355\pi\) | |||||||
\(182\) | − | 6.99892i | − | 0.518795i | ||||||
\(183\) | 0.0370314 | + | 0.0213801i | 0.00273744 | + | 0.00158046i | ||||
\(184\) | 12.0896 | − | 6.97996i | 0.891260 | − | 0.514569i | ||||
\(185\) | −0.859384 | + | 1.48850i | −0.0631831 | + | 0.109436i | ||||
\(186\) | − | 0.0265202i | − | 0.00194455i | ||||||
\(187\) | − | 28.7467i | − | 2.10217i | ||||||
\(188\) | −1.09544 | − | 0.632451i | −0.0798930 | − | 0.0461262i | ||||
\(189\) | 0.199551 | − | 0.115211i | 0.0145152 | − | 0.00838037i | ||||
\(190\) | 2.32825 | + | 1.34422i | 0.168909 | + | 0.0975197i | ||||
\(191\) | 7.60086 | + | 13.1651i | 0.549979 | + | 0.952591i | 0.998275 | + | 0.0587061i | \(0.0186975\pi\) |
−0.448297 | + | 0.893885i | \(0.647969\pi\) | |||||||
\(192\) | −0.0452027 | + | 0.0782934i | −0.00326223 | + | 0.00565034i | ||||
\(193\) | 4.21991 | + | 2.43637i | 0.303756 | + | 0.175374i | 0.644129 | − | 0.764917i | \(-0.277220\pi\) |
−0.340373 | + | 0.940291i | \(0.610553\pi\) | |||||||
\(194\) | 5.39001 | − | 9.33577i | 0.386980 | − | 0.670269i | ||||
\(195\) | −0.00537293 | − | 0.00310206i | −0.000384764 | − | 0.000222143i | ||||
\(196\) | 1.97755 | + | 3.42523i | 0.141254 | + | 0.244659i | ||||
\(197\) | −14.5646 | − | 8.40887i | −1.03768 | − | 0.599107i | −0.118507 | − | 0.992953i | \(-0.537811\pi\) |
−0.919176 | + | 0.393846i | \(0.871144\pi\) | |||||||
\(198\) | −8.05223 | + | 13.9469i | −0.572247 | + | 0.991161i | ||||
\(199\) | −15.6891 | + | 9.05809i | −1.11217 | + | 0.642111i | −0.939390 | − | 0.342850i | \(-0.888608\pi\) |
−0.172778 | + | 0.984961i | \(0.555274\pi\) | |||||||
\(200\) | 12.9096 | − | 7.45335i | 0.912846 | − | 0.527032i | ||||
\(201\) | 0.00562262 | − | 0.00973867i | 0.000396589 | − | 0.000686913i | ||||
\(202\) | 3.09398 | + | 5.35893i | 0.217692 | + | 0.377053i | ||||
\(203\) | − | 25.9234i | − | 1.81947i | ||||||
\(204\) | 0.0186771 | + | 0.0323496i | 0.00130766 | + | 0.00226493i | ||||
\(205\) | −1.01320 | + | 1.75492i | −0.0707653 | + | 0.122569i | ||||
\(206\) | 5.82414 | + | 10.0877i | 0.405787 | + | 0.702843i | ||||
\(207\) | −6.81406 | + | 11.8023i | −0.473610 | + | 0.820316i | ||||
\(208\) | −3.44599 | − | 1.98955i | −0.238937 | − | 0.137950i | ||||
\(209\) | 22.5974 | + | 13.0466i | 1.56310 | + | 0.902455i | ||||
\(210\) | −0.0177461 | −0.00122460 | ||||||||
\(211\) | 6.90557 | − | 3.98693i | 0.475399 | − | 0.274472i | −0.243098 | − | 0.970002i | \(-0.578164\pi\) |
0.718497 | + | 0.695530i | \(0.244830\pi\) | |||||||
\(212\) | −3.39418 | − | 1.95963i | −0.233113 | − | 0.134588i | ||||
\(213\) | − | 0.0623678i | − | 0.00427337i | ||||||
\(214\) | −2.50418 | + | 4.33736i | −0.171182 | + | 0.296496i | ||||
\(215\) | 2.89650 | − | 1.67230i | 0.197540 | − | 0.114050i | ||||
\(216\) | − | 0.189425i | − | 0.0128888i | ||||||
\(217\) | −6.98099 | + | 4.03048i | −0.473901 | + | 0.273607i | ||||
\(218\) | 19.7540i | 1.33791i | ||||||||
\(219\) | −0.0128609 | − | 0.0222757i | −0.000869056 | − | 0.00150525i | ||||
\(220\) | −0.850511 | + | 0.491043i | −0.0573414 | + | 0.0331061i | ||||
\(221\) | −8.68302 | + | 5.01314i | −0.584083 | + | 0.337221i | ||||
\(222\) | 0.0547534i | 0.00367481i | ||||||||
\(223\) | 0.0439219 | 0.00294123 | 0.00147062 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00147062 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(224\) | 11.5916 | 0.774493 | ||||||||
\(225\) | −7.27620 | + | 12.6027i | −0.485080 | + | 0.840183i | ||||
\(226\) | 1.67821 | − | 2.90675i | 0.111633 | − | 0.193354i | ||||
\(227\) | 3.00631 | + | 5.20708i | 0.199536 | + | 0.345606i | 0.948378 | − | 0.317142i | \(-0.102723\pi\) |
−0.748842 | + | 0.662748i | \(0.769390\pi\) | |||||||
\(228\) | −0.0339062 | −0.00224549 | ||||||||
\(229\) | 6.55402 | − | 3.78397i | 0.433102 | − | 0.250052i | −0.267565 | − | 0.963540i | \(-0.586219\pi\) |
0.700667 | + | 0.713488i | \(0.252886\pi\) | |||||||
\(230\) | 1.81796 | − | 1.04960i | 0.119872 | − | 0.0692084i | ||||
\(231\) | −0.172240 | −0.0113325 | ||||||||
\(232\) | −18.4559 | − | 10.6555i | −1.21169 | − | 0.699571i | ||||
\(233\) | −5.94303 | − | 10.2936i | −0.389341 | − | 0.674358i | 0.603020 | − | 0.797726i | \(-0.293964\pi\) |
−0.992361 | + | 0.123368i | \(0.960630\pi\) | |||||||
\(234\) | 5.61692 | 0.367189 | ||||||||
\(235\) | −0.745523 | − | 0.430428i | −0.0486326 | − | 0.0280780i | ||||
\(236\) | 4.39219 | − | 2.53583i | 0.285907 | − | 0.165069i | ||||
\(237\) | −0.0695435 | − | 0.0401510i | −0.00451734 | − | 0.00260809i | ||||
\(238\) | −14.3395 | + | 24.8367i | −0.929489 | + | 1.60992i | ||||
\(239\) | −25.4355 | −1.64528 | −0.822642 | − | 0.568560i | \(-0.807501\pi\) | ||||
−0.822642 | + | 0.568560i | \(0.807501\pi\) | |||||||
\(240\) | −0.00504459 | + | 0.00873749i | −0.000325627 | + | 0.000564002i | ||||
\(241\) | −0.919176 | + | 1.59206i | −0.0592093 | + | 0.102554i | −0.894111 | − | 0.447846i | \(-0.852191\pi\) |
0.834901 | + | 0.550400i | \(0.185525\pi\) | |||||||
\(242\) | 9.44804 | − | 5.45483i | 0.607343 | − | 0.350650i | ||||
\(243\) | 0.138693 | + | 0.240223i | 0.00889716 | + | 0.0154103i | ||||
\(244\) | −2.04451 | − | 1.18040i | −0.130887 | − | 0.0755674i | ||||
\(245\) | 1.34587 | + | 2.33111i | 0.0859843 | + | 0.148929i | ||||
\(246\) | 0.0645537i | 0.00411579i | ||||||||
\(247\) | − | 9.10082i | − | 0.579071i | ||||||
\(248\) | 6.62675i | 0.420799i | ||||||||
\(249\) | −0.134370 | −0.00851533 | ||||||||
\(250\) | 3.94214 | − | 2.27600i | 0.249323 | − | 0.143947i | ||||
\(251\) | − | 1.24886i | − | 0.0788271i | −0.999223 | − | 0.0394135i | \(-0.987451\pi\) | ||
0.999223 | − | 0.0394135i | \(-0.0125490\pi\) | |||||||
\(252\) | −5.50855 | + | 3.18036i | −0.347006 | + | 0.200344i | ||||
\(253\) | 17.6446 | − | 10.1871i | 1.10931 | − | 0.640460i | ||||
\(254\) | −9.30101 | − | 16.1098i | −0.583597 | − | 1.01082i | ||||
\(255\) | 0.0127111 | + | 0.0220162i | 0.000795998 | + | 0.00137871i | ||||
\(256\) | 6.20751 | − | 10.7517i | 0.387969 | − | 0.671982i | ||||
\(257\) | −18.9213 | −1.18028 | −0.590140 | − | 0.807301i | \(-0.700928\pi\) | ||||
−0.590140 | + | 0.807301i | \(0.700928\pi\) | |||||||
\(258\) | 0.0532730 | − | 0.0922715i | 0.00331663 | − | 0.00574457i | ||||
\(259\) | 14.4129 | − | 8.32130i | 0.895575 | − | 0.517060i | ||||
\(260\) | 0.296641 | + | 0.171266i | 0.0183969 | + | 0.0106215i | ||||
\(261\) | 20.8046 | 1.28777 | ||||||||
\(262\) | −3.82366 | − | 6.62277i | −0.236226 | − | 0.409156i | ||||
\(263\) | −20.7894 | −1.28193 | −0.640966 | − | 0.767569i | \(-0.721466\pi\) | ||||
−0.640966 | + | 0.767569i | \(0.721466\pi\) | |||||||
\(264\) | −0.0707973 | + | 0.122625i | −0.00435727 | + | 0.00754702i | ||||
\(265\) | −2.30998 | − | 1.33367i | −0.141901 | − | 0.0819265i | ||||
\(266\) | −13.0159 | − | 22.5441i | −0.798054 | − | 1.38227i | ||||
\(267\) | −0.0188777 | + | 0.0108990i | −0.00115529 | + | 0.000667009i | ||||
\(268\) | −0.310427 | + | 0.537675i | −0.0189623 | + | 0.0328437i | ||||
\(269\) | −12.8324 | −0.782406 | −0.391203 | − | 0.920304i | \(-0.627941\pi\) | ||||
−0.391203 | + | 0.920304i | \(0.627941\pi\) | |||||||
\(270\) | − | 0.0284844i | − | 0.00173351i | ||||||
\(271\) | −8.80236 | − | 15.2461i | −0.534706 | − | 0.926137i | −0.999178 | − | 0.0405493i | \(-0.987089\pi\) |
0.464472 | − | 0.885588i | \(-0.346244\pi\) | |||||||
\(272\) | 8.15240 | + | 14.1204i | 0.494312 | + | 0.856173i | ||||
\(273\) | 0.0300369 | + | 0.0520254i | 0.00181791 | + | 0.00314872i | ||||
\(274\) | 15.5795 | 0.941189 | ||||||||
\(275\) | 18.8413 | − | 10.8781i | 1.13618 | − | 0.655971i | ||||
\(276\) | −0.0132374 | + | 0.0229278i | −0.000796798 | + | 0.00138009i | ||||
\(277\) | 13.9067 | − | 8.02903i | 0.835572 | − | 0.482418i | −0.0201844 | − | 0.999796i | \(-0.506425\pi\) |
0.855757 | + | 0.517378i | \(0.173092\pi\) | |||||||
\(278\) | −13.1395 | + | 7.58611i | −0.788056 | + | 0.454984i | ||||
\(279\) | −3.23462 | − | 5.60253i | −0.193652 | − | 0.335415i | ||||
\(280\) | 4.43432 | 0.265002 | ||||||||
\(281\) | 14.0882 | − | 24.4015i | 0.840431 | − | 1.45567i | −0.0490990 | − | 0.998794i | \(-0.515635\pi\) |
0.889530 | − | 0.456876i | \(-0.151032\pi\) | |||||||
\(282\) | −0.0274236 | −0.00163305 | ||||||||
\(283\) | −31.8724 | −1.89462 | −0.947308 | − | 0.320325i | \(-0.896208\pi\) | ||||
−0.947308 | + | 0.320325i | \(0.896208\pi\) | |||||||
\(284\) | 3.44335i | 0.204325i | ||||||||
\(285\) | −0.0230756 | −0.00136688 | ||||||||
\(286\) | −7.27236 | − | 4.19870i | −0.430023 | − | 0.248274i | ||||
\(287\) | 16.9927 | − | 9.81073i | 1.00305 | − | 0.579109i | ||||
\(288\) | 9.30269i | 0.548166i | ||||||||
\(289\) | 24.0839 | 1.41670 | ||||||||
\(290\) | −2.77528 | − | 1.60231i | −0.162970 | − | 0.0940907i | ||||
\(291\) | 0.0925279i | 0.00542408i | ||||||||
\(292\) | 0.710053 | + | 1.22985i | 0.0415527 | + | 0.0719714i | ||||
\(293\) | 12.9482 | + | 22.4270i | 0.756442 | + | 1.31020i | 0.944654 | + | 0.328068i | \(0.106398\pi\) |
−0.188212 | + | 0.982128i | \(0.560269\pi\) | |||||||
\(294\) | 0.0742603 | + | 0.0428742i | 0.00433095 | + | 0.00250047i | ||||
\(295\) | 2.98920 | − | 1.72581i | 0.174038 | − | 0.100481i | ||||
\(296\) | − | 13.6815i | − | 0.795223i | ||||||
\(297\) | − | 0.276463i | − | 0.0160420i | ||||||
\(298\) | 7.61447 | − | 13.1887i | 0.441095 | − | 0.763998i | ||||
\(299\) | −6.15410 | − | 3.55307i | −0.355901 | − | 0.205479i | ||||
\(300\) | −0.0141352 | + | 0.0244829i | −0.000816095 | + | 0.00141352i | ||||
\(301\) | −32.3852 | −1.86665 | ||||||||
\(302\) | 0.00835252i | 0.000480633i | ||||||||
\(303\) | −0.0459972 | − | 0.0265565i | −0.00264247 | − | 0.00152563i | ||||
\(304\) | −14.7998 | −0.848827 | ||||||||
\(305\) | −1.39144 | − | 0.803347i | −0.0796735 | − | 0.0459995i | ||||
\(306\) | −19.9324 | − | 11.5080i | −1.13946 | − | 0.657868i | ||||
\(307\) | 12.3017 | + | 21.3072i | 0.702097 | + | 1.21607i | 0.967729 | + | 0.251994i | \(0.0810862\pi\) |
−0.265632 | + | 0.964075i | \(0.585580\pi\) | |||||||
\(308\) | 9.50940 | 0.541849 | ||||||||
\(309\) | −0.0865856 | − | 0.0499902i | −0.00492568 | − | 0.00284384i | ||||
\(310\) | 0.996484i | 0.0565965i | ||||||||
\(311\) | 13.7005i | 0.776882i | 0.921474 | + | 0.388441i | \(0.126986\pi\) | ||||
−0.921474 | + | 0.388441i | \(0.873014\pi\) | |||||||
\(312\) | 0.0493854 | 0.00279590 | ||||||||
\(313\) | −26.3292 | −1.48822 | −0.744108 | − | 0.668059i | \(-0.767125\pi\) | ||||
−0.744108 | + | 0.668059i | \(0.767125\pi\) | |||||||
\(314\) | − | 23.0816i | − | 1.30257i | ||||||
\(315\) | −3.74896 | + | 2.16446i | −0.211230 | + | 0.121954i | ||||
\(316\) | 3.83952 | + | 2.21675i | 0.215990 | + | 0.124702i | ||||
\(317\) | 15.9446 | + | 9.20559i | 0.895535 | + | 0.517037i | 0.875749 | − | 0.482767i | \(-0.160368\pi\) |
0.0197862 | + | 0.999804i | \(0.493701\pi\) | |||||||
\(318\) | −0.0849711 | −0.00476494 | ||||||||
\(319\) | −26.9362 | − | 15.5516i | −1.50814 | − | 0.870722i | ||||
\(320\) | 1.69847 | − | 2.94184i | 0.0949475 | − | 0.164454i | ||||
\(321\) | − | 0.0429881i | − | 0.00239936i | ||||||
\(322\) | −20.3262 | −1.13274 | ||||||||
\(323\) | −18.6458 | + | 32.2956i | −1.03748 | + | 1.79697i | ||||
\(324\) | −2.55228 | − | 4.42068i | −0.141793 | − | 0.245593i | ||||
\(325\) | −6.57149 | − | 3.79405i | −0.364520 | − | 0.210456i | ||||
\(326\) | −11.3843 | − | 19.7182i | −0.630518 | − | 1.09209i | ||||
\(327\) | −0.0847772 | − | 0.146838i | −0.00468819 | − | 0.00812019i | ||||
\(328\) | − | 16.1304i | − | 0.890652i | ||||||
\(329\) | 4.16778 | + | 7.21880i | 0.229777 | + | 0.397985i | ||||
\(330\) | −0.0106460 | + | 0.0184394i | −0.000586043 | + | 0.00101506i | ||||
\(331\) | −12.1878 | − | 7.03665i | −0.669904 | − | 0.386770i | 0.126136 | − | 0.992013i | \(-0.459742\pi\) |
−0.796040 | + | 0.605243i | \(0.793076\pi\) | |||||||
\(332\) | 7.41860 | 0.407148 | ||||||||
\(333\) | 6.67818 | + | 11.5669i | 0.365962 | + | 0.633865i | ||||
\(334\) | 12.2445 | + | 21.2082i | 0.669991 | + | 1.16046i | ||||
\(335\) | −0.211268 | + | 0.365926i | −0.0115428 | + | 0.0199927i | ||||
\(336\) | 0.0846039 | − | 0.0488461i | 0.00461552 | − | 0.00266477i | ||||
\(337\) | −1.85401 | − | 3.21123i | −0.100994 | − | 0.174927i | 0.811100 | − | 0.584907i | \(-0.198869\pi\) |
−0.912095 | + | 0.409980i | \(0.865536\pi\) | |||||||
\(338\) | − | 12.6319i | − | 0.687086i | ||||||
\(339\) | 0.0288091i | 0.00156470i | ||||||||
\(340\) | −0.701783 | − | 1.21552i | −0.0380595 | − | 0.0659210i | ||||
\(341\) | 9.67164i | 0.523748i | ||||||||
\(342\) | 18.0926 | − | 10.4458i | 0.978335 | − | 0.564842i | ||||
\(343\) | 0.102295i | 0.00552342i | ||||||||
\(344\) | −13.3116 | + | 23.0564i | −0.717715 | + | 1.24312i | ||||
\(345\) | −0.00900899 | + | 0.0156040i | −0.000485028 | + | 0.000840093i | ||||
\(346\) | 8.25290 | − | 14.2944i | 0.443678 | − | 0.768474i | ||||
\(347\) | −15.6017 | + | 9.00766i | −0.837545 | + | 0.483557i | −0.856429 | − | 0.516265i | \(-0.827322\pi\) |
0.0188843 | + | 0.999822i | \(0.493989\pi\) | |||||||
\(348\) | 0.0404162 | 0.00216654 | ||||||||
\(349\) | −5.77011 | − | 17.7681i | −0.308867 | − | 0.951105i | ||||
\(350\) | −21.7048 | −1.16017 | ||||||||
\(351\) | −0.0835064 | + | 0.0482124i | −0.00445724 | + | 0.00257339i | ||||
\(352\) | 6.95385 | − | 12.0444i | 0.370641 | − | 0.641969i | ||||
\(353\) | −12.9162 | + | 22.3715i | −0.687460 | + | 1.19072i | 0.285197 | + | 0.958469i | \(0.407941\pi\) |
−0.972657 | + | 0.232247i | \(0.925392\pi\) | |||||||
\(354\) | 0.0549779 | − | 0.0952245i | 0.00292204 | − | 0.00506112i | ||||
\(355\) | 2.34344i | 0.124377i | ||||||||
\(356\) | 1.04224 | − | 0.601738i | 0.0552387 | − | 0.0318921i | ||||
\(357\) | − | 0.246159i | − | 0.0130281i | ||||||
\(358\) | 13.3184 | + | 23.0682i | 0.703900 | + | 1.21919i | ||||
\(359\) | − | 18.0925i | − | 0.954883i | −0.878663 | − | 0.477442i | \(-0.841564\pi\) | ||
0.878663 | − | 0.477442i | \(-0.158436\pi\) | |||||||
\(360\) | 3.55872i | 0.187561i | ||||||||
\(361\) | −7.42476 | − | 12.8601i | −0.390777 | − | 0.676845i | ||||
\(362\) | −0.757479 | + | 0.437330i | −0.0398122 | + | 0.0229856i | ||||
\(363\) | −0.0468204 | + | 0.0810952i | −0.00245743 | + | 0.00425640i | ||||
\(364\) | −1.65835 | − | 2.87234i | −0.0869209 | − | 0.150551i | ||||
\(365\) | 0.483241 | + | 0.836998i | 0.0252940 | + | 0.0438105i | ||||
\(366\) | −0.0511831 | −0.00267538 | ||||||||
\(367\) | 20.5388 | + | 11.8581i | 1.07212 | + | 0.618987i | 0.928759 | − | 0.370684i | \(-0.120877\pi\) |
0.143358 | + | 0.989671i | \(0.454210\pi\) | |||||||
\(368\) | −5.77802 | + | 10.0078i | −0.301200 | + | 0.521694i | ||||
\(369\) | 7.87350 | + | 13.6373i | 0.409878 | + | 0.709930i | ||||
\(370\) | − | 2.05733i | − | 0.106956i | ||||||
\(371\) | 12.9137 | + | 22.3672i | 0.670447 | + | 1.16125i | ||||
\(372\) | −0.00628377 | − | 0.0108838i | −0.000325798 | − | 0.000564299i | ||||
\(373\) | 14.7945 | + | 8.54161i | 0.766031 | + | 0.442268i | 0.831457 | − | 0.555589i | \(-0.187507\pi\) |
−0.0654261 | + | 0.997857i | \(0.520841\pi\) | |||||||
\(374\) | 17.2047 | + | 29.7993i | 0.889632 | + | 1.54089i | ||||
\(375\) | −0.0195355 | + | 0.0338365i | −0.00100881 | + | 0.00174731i | ||||
\(376\) | 6.85249 | 0.353390 | ||||||||
\(377\) | 10.8482i | 0.558710i | ||||||||
\(378\) | −0.137906 | + | 0.238859i | −0.00709310 | + | 0.0122856i | ||||
\(379\) | −21.5009 | − | 12.4135i | −1.10443 | − | 0.637641i | −0.167046 | − | 0.985949i | \(-0.553423\pi\) |
−0.937380 | + | 0.348308i | \(0.886756\pi\) | |||||||
\(380\) | 1.27401 | 0.0653554 | ||||||||
\(381\) | 0.138275 | + | 0.0798332i | 0.00708405 | + | 0.00408998i | ||||
\(382\) | −15.7584 | − | 9.09809i | −0.806268 | − | 0.465499i | ||||
\(383\) | 25.9973 | − | 15.0096i | 1.32840 | − | 0.766953i | 0.343349 | − | 0.939208i | \(-0.388439\pi\) |
0.985052 | + | 0.172255i | \(0.0551053\pi\) | |||||||
\(384\) | − | 0.0444940i | − | 0.00227058i | ||||||
\(385\) | 6.47183 | 0.329835 | ||||||||
\(386\) | −5.83258 | −0.296871 | ||||||||
\(387\) | − | 25.9905i | − | 1.32117i | ||||||
\(388\) | − | 5.10850i | − | 0.259345i | ||||||
\(389\) | −1.67396 | − | 0.966464i | −0.0848733 | − | 0.0490016i | 0.456963 | − | 0.889486i | \(-0.348937\pi\) |
−0.541836 | + | 0.840484i | \(0.682271\pi\) | |||||||
\(390\) | 0.00742623 | 0.000376042 | ||||||||
\(391\) | 14.5591 | + | 25.2172i | 0.736287 | + | 1.27529i | ||||
\(392\) | −18.5558 | − | 10.7132i | −0.937211 | − | 0.541099i | ||||
\(393\) | 0.0568451 | + | 0.0328195i | 0.00286746 | + | 0.00165553i | ||||
\(394\) | 20.1305 | 1.01416 | ||||||||
\(395\) | 2.61307 | + | 1.50866i | 0.131478 | + | 0.0759087i | ||||
\(396\) | 7.63168i | 0.383506i | ||||||||
\(397\) | 26.9666 | 1.35341 | 0.676706 | − | 0.736253i | \(-0.263407\pi\) | ||||
0.676706 | + | 0.736253i | \(0.263407\pi\) | |||||||
\(398\) | 10.8424 | − | 18.7795i | 0.543479 | − | 0.941333i | ||||
\(399\) | 0.193503 | + | 0.111719i | 0.00968726 | + | 0.00559294i | ||||
\(400\) | −6.16990 | + | 10.6866i | −0.308495 | + | 0.534329i | ||||
\(401\) | − | 30.0144i | − | 1.49885i | −0.662092 | − | 0.749423i | \(-0.730331\pi\) | ||
0.662092 | − | 0.749423i | \(-0.269669\pi\) | |||||||
\(402\) | 0.0134604i | 0.000671342i | ||||||||
\(403\) | 2.92134 | − | 1.68664i | 0.145522 | − | 0.0840174i | ||||
\(404\) | 2.53952 | + | 1.46619i | 0.126346 | + | 0.0729458i | ||||
\(405\) | −1.73701 | − | 3.00859i | −0.0863126 | − | 0.149498i | ||||
\(406\) | 15.5149 | + | 26.8726i | 0.769992 | + | 1.33367i | ||||
\(407\) | − | 19.9680i | − | 0.989777i | ||||||
\(408\) | −0.175251 | − | 0.101181i | −0.00867622 | − | 0.00500922i | ||||
\(409\) | −31.4182 | −1.55353 | −0.776766 | − | 0.629789i | \(-0.783141\pi\) | ||||
−0.776766 | + | 0.629789i | \(0.783141\pi\) | |||||||
\(410\) | − | 2.42558i | − | 0.119791i | ||||||
\(411\) | −0.115807 | + | 0.0668614i | −0.00571236 | + | 0.00329803i | ||||
\(412\) | 4.78042 | + | 2.75998i | 0.235514 | + | 0.135974i | ||||
\(413\) | −33.4217 | −1.64457 | ||||||||
\(414\) | − | 16.3126i | − | 0.801721i | ||||||
\(415\) | 5.04888 | 0.247840 | ||||||||
\(416\) | −4.85073 | −0.237826 | ||||||||
\(417\) | 0.0651137 | − | 0.112780i | 0.00318863 | − | 0.00552287i | ||||
\(418\) | −31.2332 | −1.52767 | ||||||||
\(419\) | −1.10991 | − | 1.92242i | −0.0542227 | − | 0.0939165i | 0.837640 | − | 0.546223i | \(-0.183935\pi\) |
−0.891863 | + | 0.452306i | \(0.850601\pi\) | |||||||
\(420\) | −0.00728296 | + | 0.00420482i | −0.000355372 | + | 0.000205174i | ||||
\(421\) | 31.0765 | − | 17.9421i | 1.51458 | − | 0.874442i | 0.514724 | − | 0.857356i | \(-0.327894\pi\) |
0.999854 | − | 0.0170864i | \(-0.00543902\pi\) | |||||||
\(422\) | −4.77229 | + | 8.26584i | −0.232311 | + | 0.402375i | ||||
\(423\) | −5.79338 | + | 3.34481i | −0.281684 | + | 0.162630i | ||||
\(424\) | 21.2322 | 1.03113 | ||||||||
\(425\) | 15.5466 | + | 26.9274i | 0.754119 | + | 1.30617i | ||||
\(426\) | 0.0373266 | + | 0.0646516i | 0.00180848 | + | 0.00313238i | ||||
\(427\) | 7.77870 | + | 13.4731i | 0.376438 | + | 0.652009i | ||||
\(428\) | 2.37339i | 0.114722i | ||||||||
\(429\) | 0.0720772 | 0.00347992 | ||||||||
\(430\) | −2.00171 | + | 3.46706i | −0.0965310 | + | 0.167197i | ||||
\(431\) | −28.0274 | + | 16.1816i | −1.35003 | + | 0.779441i | −0.988253 | − | 0.152824i | \(-0.951163\pi\) |
−0.361778 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(432\) | 0.0784033 | + | 0.135799i | 0.00377218 | + | 0.00653361i | ||||
\(433\) | −19.9728 | − | 11.5313i | −0.959834 | − | 0.554160i | −0.0637118 | − | 0.997968i | \(-0.520294\pi\) |
−0.896122 | + | 0.443808i | \(0.853627\pi\) | |||||||
\(434\) | 4.82441 | − | 8.35613i | 0.231579 | − | 0.401107i | ||||
\(435\) | 0.0275061 | 0.00131882 | ||||||||
\(436\) | 4.68058 | + | 8.10700i | 0.224159 | + | 0.388255i | ||||
\(437\) | −26.4305 | −1.26434 | ||||||||
\(438\) | 0.0266636 | + | 0.0153942i | 0.00127403 | + | 0.000735564i | ||||
\(439\) | 21.4683 | − | 12.3947i | 1.02462 | − | 0.591567i | 0.109184 | − | 0.994022i | \(-0.465176\pi\) |
0.915440 | + | 0.402454i | \(0.131843\pi\) | |||||||
\(440\) | 2.66018 | − | 4.60756i | 0.126819 | − | 0.219657i | ||||
\(441\) | 20.9172 | 0.996055 | ||||||||
\(442\) | 6.00064 | − | 10.3934i | 0.285422 | − | 0.494365i | ||||
\(443\) | 10.8643 | + | 18.8175i | 0.516179 | + | 0.894048i | 0.999824 | + | 0.0187834i | \(0.00597929\pi\) |
−0.483645 | + | 0.875264i | \(0.660687\pi\) | |||||||
\(444\) | 0.0129734 | + | 0.0224706i | 0.000615692 | + | 0.00106641i | ||||
\(445\) | 0.709320 | − | 0.409526i | 0.0336250 | − | 0.0194134i | ||||
\(446\) | −0.0455302 | + | 0.0262869i | −0.00215592 | + | 0.00124472i | ||||
\(447\) | 0.130714i | 0.00618258i | ||||||||
\(448\) | −28.4855 | + | 16.4461i | −1.34581 | + | 0.777005i | ||||
\(449\) | −24.1741 | −1.14085 | −0.570423 | − | 0.821351i | \(-0.693221\pi\) | ||||
−0.570423 | + | 0.821351i | \(0.693221\pi\) | |||||||
\(450\) | − | 17.4190i | − | 0.821138i | ||||||
\(451\) | − | 23.5421i | − | 1.10855i | ||||||
\(452\) | − | 1.59056i | − | 0.0748137i | ||||||
\(453\) | −3.58460e−5 | 0 | 6.20871e-5i | −1.68419e−6 | 0 | 2.91711e-6i | ||||
\(454\) | −6.23278 | − | 3.59850i | −0.292519 | − | 0.168886i | ||||
\(455\) | −1.12862 | − | 1.95483i | −0.0529106 | − | 0.0916439i | ||||
\(456\) | 0.159075 | − | 0.0918418i | 0.00744936 | − | 0.00430089i | ||||
\(457\) | −2.95967 | + | 5.12630i | −0.138448 | + | 0.239798i | −0.926909 | − | 0.375286i | \(-0.877545\pi\) |
0.788462 | + | 0.615084i | \(0.210878\pi\) | |||||||
\(458\) | −4.52934 | + | 7.84505i | −0.211642 | + | 0.366575i | ||||
\(459\) | 0.395112 | 0.0184423 | ||||||||
\(460\) | 0.497390 | − | 0.861504i | 0.0231909 | − | 0.0401678i | ||||
\(461\) | 30.8723 | + | 17.8241i | 1.43787 | + | 0.830152i | 0.997701 | − | 0.0677652i | \(-0.0215869\pi\) |
0.440164 | + | 0.897917i | \(0.354920\pi\) | |||||||
\(462\) | 0.178546 | − | 0.103084i | 0.00830673 | − | 0.00479589i | ||||
\(463\) | −3.52986 | − | 2.03797i | −0.164047 | − | 0.0947124i | 0.415729 | − | 0.909489i | \(-0.363526\pi\) |
−0.579776 | + | 0.814776i | \(0.696860\pi\) | |||||||
\(464\) | 17.6414 | 0.818980 | ||||||||
\(465\) | −0.00427655 | − | 0.00740721i | −0.000198320 | − | 0.000343501i | ||||
\(466\) | 12.3213 | + | 7.11370i | 0.570773 | + | 0.329536i | ||||
\(467\) | −14.6924 | −0.679884 | −0.339942 | − | 0.940446i | \(-0.610407\pi\) | ||||
−0.339942 | + | 0.940446i | \(0.610407\pi\) | |||||||
\(468\) | 2.30517 | − | 1.33089i | 0.106556 | − | 0.0615204i | ||||
\(469\) | 3.54321 | − | 2.04568i | 0.163610 | − | 0.0944605i | ||||
\(470\) | 1.03043 | 0.0475302 | ||||||||
\(471\) | 0.0990580 | + | 0.171574i | 0.00456435 | + | 0.00790569i | ||||
\(472\) | −13.7376 | + | 23.7943i | −0.632326 | + | 1.09522i | ||||
\(473\) | −19.4281 | + | 33.6505i | −0.893305 | + | 1.54725i | ||||
\(474\) | 0.0961200 | 0.00441494 | ||||||||
\(475\) | −28.2231 | −1.29497 | ||||||||
\(476\) | 13.5905i | 0.622921i | ||||||||
\(477\) | −17.9506 | + | 10.3638i | −0.821901 | + | 0.474525i | ||||
\(478\) | 26.3668 | − | 15.2229i | 1.20599 | − | 0.696279i | ||||
\(479\) | 3.42434 | + | 5.93112i | 0.156462 | + | 0.271000i | 0.933590 | − | 0.358342i | \(-0.116658\pi\) |
−0.777128 | + | 0.629342i | \(0.783324\pi\) | |||||||
\(480\) | 0.0122993i | 0.000561382i | ||||||||
\(481\) | −6.03138 | + | 3.48222i | −0.275007 | + | 0.158776i | ||||
\(482\) | − | 2.20047i | − | 0.100229i | ||||||
\(483\) | 0.151092 | − | 0.0872329i | 0.00687491 | − | 0.00396923i | ||||
\(484\) | 2.58497 | − | 4.47730i | 0.117499 | − | 0.203513i | ||||
\(485\) | − | 3.47670i | − | 0.157869i | ||||||
\(486\) | −0.287543 | − | 0.166013i | −0.0130432 | − | 0.00753051i | ||||
\(487\) | 16.6995 | − | 9.64144i | 0.756725 | − | 0.436896i | −0.0713935 | − | 0.997448i | \(-0.522745\pi\) |
0.828119 | + | 0.560553i | \(0.189411\pi\) | |||||||
\(488\) | 12.7894 | 0.578950 | ||||||||
\(489\) | 0.169247 | + | 0.0977146i | 0.00765360 | + | 0.00441881i | ||||
\(490\) | −2.79030 | − | 1.61098i | −0.126053 | − | 0.0727766i | ||||
\(491\) | 1.74217 | − | 3.01753i | 0.0786231 | − | 0.136179i | −0.824033 | − | 0.566542i | \(-0.808281\pi\) |
0.902656 | + | 0.430363i | \(0.141614\pi\) | |||||||
\(492\) | 0.0152955 | + | 0.0264927i | 0.000689576 | + | 0.00119438i | ||||
\(493\) | 22.2259 | − | 38.4963i | 1.00100 | − | 1.73379i | ||||
\(494\) | 5.44676 | + | 9.43407i | 0.245061 | + | 0.424459i | ||||
\(495\) | 5.19390i | 0.233448i | ||||||||
\(496\) | −2.74282 | − | 4.75070i | −0.123156 | − | 0.213313i | ||||
\(497\) | 11.3456 | − | 19.6512i | 0.508921 | − | 0.881477i | ||||
\(498\) | 0.139290 | − | 0.0804191i | 0.00624173 | − | 0.00360366i | ||||
\(499\) | 31.5288 | − | 18.2032i | 1.41142 | − | 0.814886i | 0.415901 | − | 0.909410i | \(-0.363466\pi\) |
0.995523 | + | 0.0945245i | \(0.0301331\pi\) | |||||||
\(500\) | 1.07856 | − | 1.86813i | 0.0482348 | − | 0.0835452i | ||||
\(501\) | −0.182036 | − | 0.105098i | −0.00813275 | − | 0.00469545i | ||||
\(502\) | 0.747429 | + | 1.29459i | 0.0333594 | + | 0.0577802i | ||||
\(503\) | 19.5961 | + | 11.3138i | 0.873749 | + | 0.504459i | 0.868592 | − | 0.495527i | \(-0.165025\pi\) |
0.00515674 | + | 0.999987i | \(0.498359\pi\) | |||||||
\(504\) | 17.2293 | − | 29.8421i | 0.767455 | − | 1.32927i | ||||
\(505\) | 1.72832 | + | 0.997849i | 0.0769094 | + | 0.0444037i | ||||
\(506\) | −12.1938 | + | 21.1203i | −0.542082 | + | 0.938913i | ||||
\(507\) | 0.0542117 | + | 0.0938974i | 0.00240763 | + | 0.00417013i | ||||
\(508\) | −7.63422 | − | 4.40762i | −0.338714 | − | 0.195556i | ||||
\(509\) | −19.9810 | + | 11.5360i | −0.885641 | + | 0.511325i | −0.872514 | − | 0.488589i | \(-0.837512\pi\) |
−0.0131265 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(510\) | −0.0263530 | − | 0.0152149i | −0.00116693 | − | 0.000673728i | ||||
\(511\) | − | 9.35832i | − | 0.413988i | ||||||
\(512\) | 23.5220i | 1.03954i | ||||||||
\(513\) | −0.179321 | + | 0.310593i | −0.00791721 | + | 0.0137130i | ||||
\(514\) | 19.6142 | − | 11.3243i | 0.865145 | − | 0.499491i | ||||
\(515\) | 3.25342 | + | 1.87836i | 0.143363 | + | 0.0827704i | ||||
\(516\) | − | 0.0504906i | − | 0.00222273i | ||||||
\(517\) | 10.0011 | 0.439848 | ||||||||
\(518\) | −9.96045 | + | 17.2520i | −0.437637 | + | 0.758009i | ||||
\(519\) | 0.141674i | 0.00621879i | ||||||||
\(520\) | −1.85563 | −0.0813750 | ||||||||
\(521\) | 13.4284 | − | 7.75290i | 0.588309 | − | 0.339661i | −0.176119 | − | 0.984369i | \(-0.556354\pi\) |
0.764429 | + | 0.644708i | \(0.223021\pi\) | |||||||
\(522\) | −21.5664 | + | 12.4513i | −0.943934 | + | 0.544981i | ||||
\(523\) | 32.0015 | + | 18.4761i | 1.39933 | + | 0.807902i | 0.994322 | − | 0.106412i | \(-0.0339362\pi\) |
0.405006 | + | 0.914314i | \(0.367269\pi\) | |||||||
\(524\) | −3.13844 | − | 1.81198i | −0.137103 | − | 0.0791566i | ||||
\(525\) | 0.161339 | − | 0.0931492i | 0.00704142 | − | 0.00406536i | ||||
\(526\) | 21.5507 | − | 12.4423i | 0.939655 | − | 0.542510i | ||||
\(527\) | −13.8224 | −0.602113 | ||||||||
\(528\) | − | 0.117212i | − | 0.00510101i | ||||||
\(529\) | 1.18119 | − | 2.04588i | 0.0513561 | − | 0.0889513i | ||||
\(530\) | 3.19275 | 0.138684 | ||||||||
\(531\) | − | 26.8222i | − | 1.16399i | ||||||
\(532\) | −10.6834 | − | 6.16804i | −0.463182 | − | 0.267418i | ||||
\(533\) | −7.11094 | + | 4.10550i | −0.308009 | + | 0.177829i | ||||
\(534\) | 0.0130459 | − | 0.0225962i | 0.000564553 | − | 0.000977834i | ||||
\(535\) | 1.61526i | 0.0698338i | ||||||||
\(536\) | − | 3.36342i | − | 0.145277i | ||||||
\(537\) | −0.198001 | − | 0.114316i | −0.00854436 | − | 0.00493309i | ||||
\(538\) | 13.3023 | − | 7.68009i | 0.573503 | − | 0.331112i | ||||
\(539\) | −27.0820 | − | 15.6358i | −1.16650 | − | 0.673480i | ||||
\(540\) | −0.00674919 | − | 0.0116899i | −0.000290439 | − | 0.000503055i | ||||
\(541\) | −8.69714 | + | 15.0639i | −0.373919 | + | 0.647647i | −0.990165 | − | 0.139907i | \(-0.955320\pi\) |
0.616245 | + | 0.787554i | \(0.288653\pi\) | |||||||
\(542\) | 18.2494 | + | 10.5363i | 0.783877 | + | 0.452572i | ||||
\(543\) | 0.00375373 | − | 0.00650165i | 0.000161088 | − | 0.000279013i | ||||
\(544\) | 17.2135 | + | 9.93822i | 0.738023 | + | 0.426098i | ||||
\(545\) | 3.18547 | + | 5.51739i | 0.136450 | + | 0.236339i | ||||
\(546\) | −0.0622735 | − | 0.0359536i | −0.00266506 | − | 0.00153867i | ||||
\(547\) | −3.21255 | + | 5.56430i | −0.137359 | + | 0.237912i | −0.926496 | − | 0.376305i | \(-0.877195\pi\) |
0.789137 | + | 0.614217i | \(0.210528\pi\) | |||||||
\(548\) | 6.39377 | − | 3.69144i | 0.273128 | − | 0.157691i | ||||
\(549\) | −10.8127 | + | 6.24272i | −0.461475 | + | 0.266433i | ||||
\(550\) | −13.0208 | + | 22.5528i | −0.555210 | + | 0.961653i | ||||
\(551\) | 20.1743 | + | 34.9429i | 0.859455 | + | 1.48862i | ||||
\(552\) | − | 0.143425i | − | 0.00610456i | ||||||
\(553\) | −14.6081 | − | 25.3020i | −0.621200 | − | 1.07595i | ||||
\(554\) | −9.61061 | + | 16.6461i | −0.408316 | + | 0.707224i | ||||
\(555\) | 0.00882934 | + | 0.0152929i | 0.000374785 | + | 0.000649146i | ||||
\(556\) | −3.59495 | + | 6.22664i | −0.152460 | + | 0.264068i | ||||
\(557\) | 6.68880 | + | 3.86178i | 0.283414 | + | 0.163629i | 0.634968 | − | 0.772539i | \(-0.281013\pi\) |
−0.351554 | + | 0.936168i | \(0.614347\pi\) | |||||||
\(558\) | 6.70613 | + | 3.87178i | 0.283893 | + | 0.163906i | ||||
\(559\) | 13.5523 | 0.573200 | ||||||||
\(560\) | −3.17896 | + | 1.83537i | −0.134335 | + | 0.0775586i | ||||
\(561\) | −0.255776 | − | 0.147672i | −0.0107989 | − | 0.00623474i | ||||
\(562\) | 33.7266i | 1.42267i | ||||||||
\(563\) | 6.74649 | − | 11.6853i | 0.284331 | − | 0.492475i | −0.688116 | − | 0.725601i | \(-0.741562\pi\) |
0.972447 | + | 0.233126i | \(0.0748953\pi\) | |||||||
\(564\) | −0.0112546 | + | 0.00649783i | −0.000473903 | + | 0.000273608i | ||||
\(565\) | − | 1.08249i | − | 0.0455407i | ||||||
\(566\) | 33.0394 | − | 19.0753i | 1.38875 | − | 0.801796i | ||||
\(567\) | 33.6384i | 1.41268i | ||||||||
\(568\) | −9.32701 | − | 16.1549i | −0.391353 | − | 0.677843i | ||||
\(569\) | 27.4730 | − | 15.8615i | 1.15173 | − | 0.664950i | 0.202420 | − | 0.979299i | \(-0.435119\pi\) |
0.949308 | + | 0.314349i | \(0.101786\pi\) | |||||||
\(570\) | 0.0239205 | − | 0.0138105i | 0.00100192 | − | 0.000578459i | ||||
\(571\) | − | 28.5921i | − | 1.19654i | −0.801293 | − | 0.598272i | \(-0.795854\pi\) | ||
0.801293 | − | 0.598272i | \(-0.204146\pi\) | |||||||
\(572\) | −3.97941 | −0.166387 | ||||||||
\(573\) | 0.156183 | 0.00652464 | ||||||||
\(574\) | −11.7433 | + | 20.3399i | −0.490155 | + | 0.848973i | ||||
\(575\) | −11.0187 | + | 19.0849i | −0.459510 | + | 0.795894i | ||||
\(576\) | −13.1986 | − | 22.8607i | −0.549944 | − | 0.952531i | ||||
\(577\) | 38.1470 | 1.58808 | 0.794041 | − | 0.607864i | \(-0.207974\pi\) | ||||
0.794041 | + | 0.607864i | \(0.207974\pi\) | |||||||
\(578\) | −24.9658 | + | 14.4140i | −1.03844 | + | 0.599544i | ||||
\(579\) | 0.0433556 | − | 0.0250313i | 0.00180180 | − | 0.00104027i | ||||
\(580\) | −1.51862 | −0.0630573 | ||||||||
\(581\) | −42.3379 | − | 24.4438i | −1.75647 | − | 1.01410i | ||||
\(582\) | −0.0553771 | − | 0.0959160i | −0.00229546 | − | 0.00397585i | ||||
\(583\) | 30.9881 | 1.28340 | ||||||||
\(584\) | −6.66258 | − | 3.84664i | −0.275700 | − | 0.159175i | ||||
\(585\) | 1.56883 | − | 0.905765i | 0.0648632 | − | 0.0374488i | ||||
\(586\) | −26.8447 | − | 15.4988i | −1.10894 | − | 0.640249i | ||||
\(587\) | 10.4336 | − | 18.0715i | 0.430640 | − | 0.745891i | −0.566288 | − | 0.824207i | \(-0.691621\pi\) |
0.996929 | + | 0.0783166i | \(0.0249545\pi\) | |||||||
\(588\) | 0.0406349 | 0.00167576 | ||||||||
\(589\) | 6.27327 | − | 10.8656i | 0.258485 | − | 0.447710i | ||||
\(590\) | −2.06577 | + | 3.57802i | −0.0850464 | + | 0.147305i | ||||
\(591\) | −0.149637 | + | 0.0863930i | −0.00615525 | + | 0.00355373i | ||||
\(592\) | 5.66280 | + | 9.80826i | 0.232740 | + | 0.403117i | ||||
\(593\) | −0.680726 | − | 0.393017i | −0.0279540 | − | 0.0161393i | 0.485958 | − | 0.873982i | \(-0.338471\pi\) |
−0.513912 | + | 0.857843i | \(0.671804\pi\) | |||||||
\(594\) | 0.165461 | + | 0.286586i | 0.00678894 | + | 0.0117588i | ||||
\(595\) | 9.24933i | 0.379185i | ||||||||
\(596\) | − | 7.21678i | − | 0.295611i | ||||||
\(597\) | 0.186126i | 0.00761764i | ||||||||
\(598\) | 8.50593 | 0.347833 | ||||||||
\(599\) | −23.4092 | + | 13.5153i | −0.956473 | + | 0.552220i | −0.895086 | − | 0.445894i | \(-0.852886\pi\) |
−0.0613871 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(600\) | − | 0.153152i | − | 0.00625241i | ||||||
\(601\) | −23.6632 | + | 13.6619i | −0.965241 | + | 0.557282i | −0.897782 | − | 0.440440i | \(-0.854822\pi\) |
−0.0674587 | + | 0.997722i | \(0.521489\pi\) | |||||||
\(602\) | 33.5711 | − | 19.3823i | 1.36826 | − | 0.789963i | ||||
\(603\) | 1.64174 | + | 2.84357i | 0.0668567 | + | 0.115799i | ||||
\(604\) | 0.00197907 | + | 0.00342785i | 8.05272e−5 | + | 0.000139477i | ||||
\(605\) | 1.75925 | − | 3.04712i | 0.0715239 | − | 0.123883i | ||||
\(606\) | 0.0635753 | 0.00258257 | ||||||||
\(607\) | 10.7731 | − | 18.6596i | 0.437268 | − | 0.757371i | −0.560209 | − | 0.828351i | \(-0.689279\pi\) |
0.997478 | + | 0.0709800i | \(0.0226126\pi\) | |||||||
\(608\) | −15.6246 | + | 9.02088i | −0.633662 | + | 0.365845i | ||||
\(609\) | −0.230655 | − | 0.133169i | −0.00934663 | − | 0.00539628i | ||||
\(610\) | 1.92318 | 0.0778674 | ||||||||
\(611\) | −1.74409 | − | 3.02086i | −0.0705584 | − | 0.122211i | ||||
\(612\) | −10.9070 | −0.440887 | ||||||||
\(613\) | −11.1478 | + | 19.3086i | −0.450257 | + | 0.779869i | −0.998402 | − | 0.0565151i | \(-0.982001\pi\) |
0.548144 | + | 0.836384i | \(0.315334\pi\) | |||||||
\(614\) | −25.5044 | − | 14.7250i | −1.02927 | − | 0.594251i | ||||
\(615\) | 0.0104097 | + | 0.0180301i | 0.000419760 | + | 0.000727045i | ||||
\(616\) | −44.6144 | + | 25.7582i | −1.79757 | + | 1.03783i | ||||
\(617\) | 20.8234 | − | 36.0673i | 0.838320 | − | 1.45201i | −0.0529779 | − | 0.998596i | \(-0.516871\pi\) |
0.891298 | − | 0.453418i | \(-0.149795\pi\) | |||||||
\(618\) | 0.119675 | 0.00481403 | ||||||||
\(619\) | 28.1954i | 1.13327i | 0.823970 | + | 0.566634i | \(0.191755\pi\) | ||||
−0.823970 | + | 0.566634i | \(0.808245\pi\) | |||||||
\(620\) | 0.236110 | + | 0.408954i | 0.00948240 | + | 0.0164240i | ||||
\(621\) | 0.140018 | + | 0.242519i | 0.00561874 | + | 0.00973194i | ||||
\(622\) | −8.19960 | − | 14.2021i | −0.328774 | − | 0.569453i | ||||
\(623\) | −7.93077 | −0.317740 | ||||||||
\(624\) | −0.0354043 | + | 0.0204407i | −0.00141731 | + | 0.000818282i | ||||
\(625\) | −11.3934 | + | 19.7339i | −0.455736 | + | 0.789357i | ||||
\(626\) | 27.2933 | − | 15.7578i | 1.09086 | − | 0.629809i | ||||
\(627\) | 0.232167 | − | 0.134042i | 0.00927186 | − | 0.00535311i | ||||
\(628\) | −5.46903 | − | 9.47263i | −0.218238 | − | 0.377999i | ||||
\(629\) | 28.5376 | 1.13787 | ||||||||
\(630\) | 2.59082 | − | 4.48744i | 0.103221 | − | 0.178784i | ||||
\(631\) | −2.26897 | −0.0903263 | −0.0451632 | − | 0.998980i | \(-0.514381\pi\) | ||||
−0.0451632 | + | 0.998980i | \(0.514381\pi\) | |||||||
\(632\) | −24.0181 | −0.955387 | ||||||||
\(633\) | − | 0.0819238i | − | 0.00325618i | ||||||
\(634\) | −22.0379 | −0.875235 | ||||||||
\(635\) | −5.19563 | − | 2.99970i | −0.206182 | − | 0.119039i | ||||
\(636\) | −0.0348719 | + | 0.0201333i | −0.00138276 | + | 0.000798338i | ||||
\(637\) | 10.9069i | 0.432147i | ||||||||
\(638\) | 37.2300 | 1.47395 | ||||||||
\(639\) | 15.7709 | + | 9.10532i | 0.623886 | + | 0.360201i | ||||
\(640\) | 1.67184i | 0.0660855i | ||||||||
\(641\) | 8.55626 | + | 14.8199i | 0.337952 | + | 0.585350i | 0.984047 | − | 0.177907i | \(-0.0569325\pi\) |
−0.646095 | + | 0.763257i | \(0.723599\pi\) | |||||||
\(642\) | 0.0257280 | + | 0.0445622i | 0.00101540 | + | 0.00175873i | ||||
\(643\) | −21.9744 | − | 12.6870i | −0.866588 | − | 0.500325i | −0.000374786 | − | 1.00000i | \(-0.500119\pi\) |
−0.866213 | + | 0.499675i | \(0.833453\pi\) | |||||||
\(644\) | −8.34183 | + | 4.81616i | −0.328714 | + | 0.189783i | ||||
\(645\) | − | 0.0343625i | − | 0.00135302i | ||||||
\(646\) | − | 44.6375i | − | 1.75624i | ||||||
\(647\) | −6.32499 | + | 10.9552i | −0.248661 | + | 0.430694i | −0.963155 | − | 0.268948i | \(-0.913324\pi\) |
0.714493 | + | 0.699642i | \(0.246657\pi\) | |||||||
\(648\) | 23.9486 | + | 13.8267i | 0.940790 | + | 0.543166i | ||||
\(649\) | −20.0499 | + | 34.7274i | −0.787026 | + | 1.36317i | ||||
\(650\) | 9.08282 | 0.356258 | ||||||||
\(651\) | 0.0828186i | 0.00324592i | ||||||||
\(652\) | −9.34417 | − | 5.39486i | −0.365946 | − | 0.211279i | ||||
\(653\) | 28.6343 | 1.12055 | 0.560274 | − | 0.828308i | \(-0.310696\pi\) | ||||
0.560274 | + | 0.828308i | \(0.310696\pi\) | |||||||
\(654\) | 0.175763 | + | 0.101477i | 0.00687288 | + | 0.00396806i | ||||
\(655\) | −2.13593 | − | 1.23318i | −0.0834577 | − | 0.0481843i | ||||
\(656\) | 6.67639 | + | 11.5638i | 0.260669 | + | 0.451492i | ||||
\(657\) | 7.51043 | 0.293010 | ||||||||
\(658\) | −8.64078 | − | 4.98876i | −0.336853 | − | 0.194482i | ||||
\(659\) | 22.4849i | 0.875887i | 0.899002 | + | 0.437944i | \(0.144293\pi\) | ||||
−0.899002 | + | 0.437944i | \(0.855707\pi\) | |||||||
\(660\) | 0.0100900i | 0.000392752i | ||||||||
\(661\) | 11.9641 | 0.465349 | 0.232675 | − | 0.972555i | \(-0.425252\pi\) | ||||
0.232675 | + | 0.972555i | \(0.425252\pi\) | |||||||
\(662\) | 16.8455 | 0.654719 | ||||||||
\(663\) | 0.103010i | 0.00400059i | ||||||||
\(664\) | −34.8052 | + | 20.0948i | −1.35070 | + | 0.779828i | ||||
\(665\) | −7.27078 | − | 4.19779i | −0.281949 | − | 0.162783i | ||||
\(666\) | −13.8454 | − | 7.99366i | −0.536499 | − | 0.309748i | ||||
\(667\) | 31.5052 | 1.21989 | ||||||||
\(668\) | 10.0502 | + | 5.80251i | 0.388856 | + | 0.224506i | ||||
\(669\) | 0.000225628 | 0 | 0.000390799i | 8.72328e−6 | 0 | 1.51092e-5i | ||||
\(670\) | − | 0.505767i | − | 0.0195395i | ||||||
\(671\) | 18.6660 | 0.720591 | ||||||||
\(672\) | 0.0595460 | − | 0.103137i | 0.00229704 | − | 0.00397859i | ||||
\(673\) | 3.36883 | + | 5.83499i | 0.129859 | + | 0.224922i | 0.923622 | − | 0.383305i | \(-0.125214\pi\) |
−0.793763 | + | 0.608227i | \(0.791881\pi\) | |||||||
\(674\) | 3.84379 | + | 2.21921i | 0.148057 | + | 0.0854809i | ||||
\(675\) | 0.149515 | + | 0.258967i | 0.00575482 | + | 0.00996764i | ||||
\(676\) | −2.99305 | − | 5.18411i | −0.115117 | − | 0.199389i | ||||
\(677\) | 2.38709i | 0.0917434i | 0.998947 | + | 0.0458717i | \(0.0146065\pi\) | ||||
−0.998947 | + | 0.0458717i | \(0.985393\pi\) | |||||||
\(678\) | −0.0172420 | − | 0.0298640i | −0.000662175 | − | 0.00114692i | ||||
\(679\) | −16.8322 | + | 29.1542i | −0.645960 | + | 1.11884i | ||||
\(680\) | 6.58498 | + | 3.80184i | 0.252523 | + | 0.145794i | ||||
\(681\) | 0.0617739 | 0.00236718 | ||||||||
\(682\) | −5.78839 | − | 10.0258i | −0.221649 | − | 0.383907i | ||||
\(683\) | −17.3319 | − | 30.0197i | −0.663186 | − | 1.14867i | −0.979774 | − | 0.200109i | \(-0.935871\pi\) |
0.316588 | − | 0.948563i | \(-0.397463\pi\) | |||||||
\(684\) | 4.95010 | − | 8.57382i | 0.189272 | − | 0.327828i | ||||
\(685\) | 4.35141 | − | 2.51229i | 0.166259 | − | 0.0959897i | ||||
\(686\) | −0.0612227 | − | 0.106041i | −0.00233749 | − | 0.00404866i | ||||
\(687\) | − | 0.0777532i | − | 0.00296647i | ||||||
\(688\) | − | 22.0388i | − | 0.840221i | ||||||
\(689\) | −5.40402 | − | 9.36003i | −0.205877 | − | 0.356589i | ||||
\(690\) | − | 0.0215672i | − | 0.000821050i | ||||||
\(691\) | −16.7177 | + | 9.65196i | −0.635971 | + | 0.367178i | −0.783061 | − | 0.621945i | \(-0.786343\pi\) |
0.147090 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(692\) | − | 7.82186i | − | 0.297343i | ||||||
\(693\) | 25.1459 | − | 43.5540i | 0.955215 | − | 1.65448i | ||||
\(694\) | 10.7820 | − | 18.6750i | 0.409280 | − | 0.708893i | ||||
\(695\) | −2.44662 | + | 4.23767i | −0.0928055 | + | 0.160744i | ||||
\(696\) | −0.189617 | + | 0.109475i | −0.00718742 | + | 0.00414966i | ||||
\(697\) | 33.6456 | 1.27442 | ||||||||
\(698\) | 16.6155 | + | 14.9654i | 0.628904 | + | 0.566448i | ||||
\(699\) | −0.122118 | −0.00461892 | ||||||||
\(700\) | −8.90759 | + | 5.14280i | −0.336675 | + | 0.194380i | ||||
\(701\) | −2.97024 | + | 5.14460i | −0.112184 | + | 0.194309i | −0.916651 | − | 0.399689i | \(-0.869118\pi\) |
0.804466 | + | 0.593998i | \(0.202451\pi\) | |||||||
\(702\) | 0.0577094 | − | 0.0999557i | 0.00217810 | − | 0.00377258i | ||||
\(703\) | −12.9517 | + | 22.4331i | −0.488484 | + | 0.846079i | ||||
\(704\) | 39.4644i | 1.48737i | ||||||||
\(705\) | −0.00765953 | + | 0.00442223i | −0.000288475 | + | 0.000166551i | ||||
\(706\) | − | 30.9209i | − | 1.16372i | ||||||
\(707\) | −9.66204 | − | 16.7351i | −0.363378 | − | 0.629390i | ||||
\(708\) | − | 0.0521065i | − | 0.00195828i | ||||||
\(709\) | 21.9809i | 0.825508i | 0.910842 | + | 0.412754i | \(0.135433\pi\) | ||||
−0.910842 | + | 0.412754i | \(0.864567\pi\) | |||||||
\(710\) | −1.40253 | − | 2.42925i | −0.0526360 | − | 0.0911683i | ||||
\(711\) | 20.3059 | − | 11.7236i | 0.761529 | − | 0.439669i | ||||
\(712\) | −3.25986 | + | 5.64625i | −0.122168 | + | 0.211602i | ||||
\(713\) | −4.89832 | − | 8.48414i | −0.183444 | − | 0.317734i | ||||
\(714\) | 0.147324 | + | 0.255173i | 0.00551347 | + | 0.00954961i | ||||
\(715\) | −2.70827 | −0.101284 | ||||||||
\(716\) | 10.9317 | + | 6.31141i | 0.408536 | + | 0.235869i | ||||
\(717\) | −0.130663 | + | 0.226314i | −0.00487968 | + | 0.00845186i | ||||
\(718\) | 10.8282 | + | 18.7550i | 0.404104 | + | 0.699929i | ||||
\(719\) | 23.5988i | 0.880087i | 0.897977 | + | 0.440043i | \(0.145037\pi\) | ||||
−0.897977 | + | 0.440043i | \(0.854963\pi\) | |||||||
\(720\) | −1.47296 | − | 2.55124i | −0.0548939 | − | 0.0950791i | ||||
\(721\) | −18.1879 | − | 31.5024i | −0.677353 | − | 1.17321i | ||||
\(722\) | 15.3933 | + | 8.88730i | 0.572878 | + | 0.330751i | ||||
\(723\) | 0.00944365 | + | 0.0163569i | 0.000351213 | + | 0.000608319i | ||||
\(724\) | −0.207245 | + | 0.358958i | −0.00770219 | + | 0.0133406i | ||||
\(725\) | 33.6420 | 1.24943 | ||||||||
\(726\) | − | 0.112086i | − | 0.00415991i | ||||||
\(727\) | −2.72134 | + | 4.71350i | −0.100929 | + | 0.174814i | −0.912068 | − | 0.410040i | \(-0.865515\pi\) |
0.811139 | + | 0.584854i | \(0.198848\pi\) | |||||||
\(728\) | 15.5606 | + | 8.98393i | 0.576715 | + | 0.332967i | ||||
\(729\) | −26.9943 | −0.999789 | ||||||||
\(730\) | −1.00187 | − | 0.578431i | −0.0370810 | − | 0.0214087i | ||||
\(731\) | −48.0922 | − | 27.7660i | −1.77875 | − | 1.02696i | ||||
\(732\) | −0.0210054 | + | 0.0121275i | −0.000776382 | + | 0.000448245i | ||||
\(733\) | 39.5799i | 1.46192i | 0.682423 | + | 0.730958i | \(0.260926\pi\) | ||||
−0.682423 | + | 0.730958i | \(0.739074\pi\) | |||||||
\(734\) | −28.3878 | −1.04781 | ||||||||
\(735\) | 0.0276550 | 0.00102007 | ||||||||
\(736\) | 14.0875i | 0.519270i | ||||||||
\(737\) | − | 4.90885i | − | 0.180820i | ||||||
\(738\) | −16.3236 | − | 9.42445i | −0.600881 | − | 0.346919i | ||||
\(739\) | −17.0571 | −0.627457 | −0.313728 | − | 0.949513i | \(-0.601578\pi\) | ||||
−0.313728 | + | 0.949513i | \(0.601578\pi\) | |||||||
\(740\) | −0.487471 | − | 0.844325i | −0.0179198 | − | 0.0310380i | ||||
\(741\) | −0.0809753 | − | 0.0467511i | −0.00297470 | − | 0.00171744i | ||||
\(742\) | −26.7732 | − | 15.4575i | −0.982874 | − | 0.567463i | ||||
\(743\) | −19.8934 | −0.729818 | −0.364909 | − | 0.931043i | \(-0.618900\pi\) | ||||
−0.364909 | + | 0.931043i | \(0.618900\pi\) | |||||||
\(744\) | 0.0589620 | + | 0.0340417i | 0.00216165 | + | 0.00124803i | ||||
\(745\) | − | 4.91154i | − | 0.179945i | ||||||
\(746\) | −20.4483 | −0.748666 | ||||||||
\(747\) | 19.6172 | − | 33.9779i | 0.717754 | − | 1.24319i | ||||
\(748\) | 14.1215 | + | 8.15305i | 0.516333 | + | 0.298105i | ||||
\(749\) | 7.82017 | − | 13.5449i | 0.285743 | − | 0.494921i | ||||
\(750\) | − | 0.0467674i | − | 0.00170770i | ||||||
\(751\) | 8.00054i | 0.291944i | 0.989289 | + | 0.145972i | \(0.0466309\pi\) | ||||
−0.989289 | + | 0.145972i | \(0.953369\pi\) | |||||||
\(752\) | −4.91253 | + | 2.83625i | −0.179142 | + | 0.103427i | ||||
\(753\) | −0.0111118 | − | 0.00641540i | −0.000404936 | − | 0.000233790i | ||||
\(754\) | −6.49254 | − | 11.2454i | −0.236444 | − | 0.409534i | ||||
\(755\) | 0.00134690 | + | 0.00233290i | 4.90186e−5 | + | 8.49028e-5i | ||||
\(756\) | 0.130703i | 0.00475362i | ||||||||
\(757\) | −26.5533 | − | 15.3306i | −0.965097 | − | 0.557199i | −0.0673588 | − | 0.997729i | \(-0.521457\pi\) |
−0.897738 | + | 0.440530i | \(0.854791\pi\) | |||||||
\(758\) | 29.7176 | 1.07939 | ||||||||
\(759\) | − | 0.209326i | − | 0.00759806i | ||||||
\(760\) | −5.97716 | + | 3.45092i | −0.216814 | + | 0.125178i | ||||
\(761\) | −40.2958 | − | 23.2648i | −1.46072 | − | 0.843348i | −0.461678 | − | 0.887048i | \(-0.652752\pi\) |
−0.999045 | + | 0.0436993i | \(0.986086\pi\) | |||||||
\(762\) | −0.191118 | −0.00692347 | ||||||||
\(763\) | − | 61.6889i | − | 2.23329i | ||||||
\(764\) | −8.62292 | −0.311966 | ||||||||
\(765\) | −7.42296 | −0.268378 | ||||||||
\(766\) | −17.9662 | + | 31.1183i | −0.649145 | + | 1.12435i | ||||
\(767\) | 13.9860 | 0.505005 | ||||||||
\(768\) | −0.0637762 | − | 0.110464i | −0.00230132 | − | 0.00398601i | ||||
\(769\) | −13.6794 | + | 7.89779i | −0.493291 | + | 0.284802i | −0.725939 | − | 0.687759i | \(-0.758594\pi\) |
0.232648 | + | 0.972561i | \(0.425261\pi\) | |||||||
\(770\) | −6.70881 | + | 3.87333i | −0.241769 | + | 0.139585i | ||||
\(771\) | −0.0971993 | + | 0.168354i | −0.00350055 | + | 0.00606312i | ||||
\(772\) | −2.39368 | + | 1.38199i | −0.0861503 | + | 0.0497389i | ||||
\(773\) | 15.6634 | 0.563372 | 0.281686 | − | 0.959507i | \(-0.409106\pi\) | ||||
0.281686 | + | 0.959507i | \(0.409106\pi\) | |||||||
\(774\) | 15.5551 | + | 26.9422i | 0.559115 | + | 0.968416i | ||||
\(775\) | −5.23054 | − | 9.05955i | −0.187886 | − | 0.325429i | ||||
\(776\) | 13.8374 | + | 23.9671i | 0.496734 | + | 0.860368i | ||||
\(777\) | − | 0.170987i | − | 0.00613411i | ||||||
\(778\) | 2.31368 | 0.0829494 | ||||||||
\(779\) | −15.2700 | + | 26.4484i | −0.547104 | + | 0.947611i | ||||
\(780\) | 0.00304771 | − | 0.00175959i | 0.000109125 | − | 6.30035e-5i | ||||
\(781\) | −13.6126 | − | 23.5778i | −0.487098 | − | 0.843679i | ||||
\(782\) | −30.1845 | − | 17.4270i | −1.07940 | − | 0.623189i | ||||
\(783\) | 0.213751 | − | 0.370227i | 0.00763882 | − | 0.0132308i | ||||
\(784\) | 17.7368 | 0.633459 | ||||||||
\(785\) | −3.72206 | − | 6.44680i | −0.132846 | − | 0.230096i | ||||
\(786\) | −0.0785688 | −0.00280246 | ||||||||
\(787\) | −25.9330 | − | 14.9725i | −0.924413 | − | 0.533710i | −0.0393729 | − | 0.999225i | \(-0.512536\pi\) |
−0.885040 | + | 0.465514i | \(0.845869\pi\) | |||||||
\(788\) | 8.26152 | − | 4.76979i | 0.294304 | − | 0.169917i | ||||
\(789\) | −0.106796 | + | 0.184976i | −0.00380203 | + | 0.00658531i | ||||
\(790\) | −3.61167 | −0.128497 | ||||||||
\(791\) | −5.24080 | + | 9.07734i | −0.186341 | + | 0.322753i | ||||
\(792\) | −20.6720 | − | 35.8049i | −0.734546 | − | 1.27227i | ||||
\(793\) | −3.25516 | − | 5.63810i | −0.115594 | − | 0.200215i | ||||
\(794\) | −27.9540 | + | 16.1392i | −0.992050 | + | 0.572760i | ||||
\(795\) | −0.0237328 | + | 0.0137022i | −0.000841716 | + | 0.000485965i | ||||
\(796\) | − | 10.2761i | − | 0.364227i | ||||||
\(797\) | −34.6941 | + | 20.0307i | −1.22893 | + | 0.709523i | −0.966806 | − | 0.255511i | \(-0.917756\pi\) |
−0.262124 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(798\) | −0.267451 | −0.00946766 | ||||||||
\(799\) | 14.2933i | 0.505659i | ||||||||
\(800\) | 15.0429i | 0.531846i | ||||||||
\(801\) | − | 6.36476i | − | 0.224888i | ||||||
\(802\) | 17.9633 | + | 31.1134i | 0.634307 | + | 1.09865i | ||||
\(803\) | −9.72393 | − | 5.61412i | −0.343150 | − | 0.198118i | ||||
\(804\) | 0.00318934 | + | 0.00552409i | 0.000112479 | + | 0.000194820i | ||||
\(805\) | −5.67721 | + | 3.27774i | −0.200095 | + | 0.115525i | ||||
\(806\) | −2.01888 | + | 3.49679i | −0.0711118 | + | 0.123169i | ||||
\(807\) | −0.0659204 | + | 0.114177i | −0.00232051 | + | 0.00401924i | ||||
\(808\) | −15.8859 | −0.558865 | ||||||||
\(809\) | 21.5225 | − | 37.2781i | 0.756692 | − | 1.31063i | −0.187836 | − | 0.982200i | \(-0.560147\pi\) |
0.944529 | − | 0.328429i | \(-0.106519\pi\) | |||||||
\(810\) | 3.60122 | + | 2.07917i | 0.126534 | + | 0.0730545i | ||||
\(811\) | 25.6539 | − | 14.8113i | 0.900831 | − | 0.520095i | 0.0233611 | − | 0.999727i | \(-0.492563\pi\) |
0.877470 | + | 0.479632i | \(0.159230\pi\) | |||||||
\(812\) | 12.7346 | + | 7.35230i | 0.446896 | + | 0.258015i | ||||
\(813\) | −0.180872 | −0.00634345 | ||||||||
\(814\) | 11.9507 | + | 20.6992i | 0.418871 | + | 0.725505i | ||||
\(815\) | −6.35937 | − | 3.67158i | −0.222759 | − | 0.128610i | ||||
\(816\) | 0.167516 | 0.00586424 | ||||||||
\(817\) | 43.6531 | − | 25.2031i | 1.52723 | − | 0.881745i | ||||
\(818\) | 32.5687 | − | 18.8035i | 1.13874 | − | 0.657450i | ||||
\(819\) | −17.5408 | −0.612925 | ||||||||
\(820\) | −0.574723 | − | 0.995450i | −0.0200702 | − | 0.0347626i | ||||
\(821\) | 14.6818 | − | 25.4297i | 0.512399 | − | 0.887501i | −0.487497 | − | 0.873124i | \(-0.662090\pi\) |
0.999897 | − | 0.0143770i | \(-0.00457650\pi\) | |||||||
\(822\) | 0.0800320 | − | 0.138619i | 0.00279144 | − | 0.00483491i | ||||
\(823\) | 51.0307 | 1.77882 | 0.889409 | − | 0.457113i | \(-0.151116\pi\) | ||||
0.889409 | + | 0.457113i | \(0.151116\pi\) | |||||||
\(824\) | −29.9038 | −1.04175 | ||||||||
\(825\) | − | 0.223523i | − | 0.00778208i | ||||||
\(826\) | 34.6455 | − | 20.0026i | 1.20547 | − | 0.695979i | ||||
\(827\) | 27.7314 | − | 16.0107i | 0.964315 | − | 0.556747i | 0.0668164 | − | 0.997765i | \(-0.478716\pi\) |
0.897498 | + | 0.441018i | \(0.145382\pi\) | |||||||
\(828\) | −3.86516 | − | 6.69465i | −0.134324 | − | 0.232655i | ||||
\(829\) | − | 34.6149i | − | 1.20223i | −0.799164 | − | 0.601113i | \(-0.794724\pi\) | ||
0.799164 | − | 0.601113i | \(-0.205276\pi\) | |||||||
\(830\) | −5.23376 | + | 3.02171i | −0.181666 | + | 0.104885i | ||||
\(831\) | − | 0.164981i | − | 0.00572314i | ||||||
\(832\) | 11.9203 | − | 6.88221i | 0.413263 | − | 0.238598i | ||||
\(833\) | 22.3461 | − | 38.7047i | 0.774248 | − | 1.34104i | ||||
\(834\) | 0.155880i | 0.00539768i | ||||||||
\(835\) | 6.83991 | + | 3.94902i | 0.236705 | + | 0.136662i | ||||
\(836\) | −12.8180 | + | 7.40049i | −0.443321 | + | 0.255951i | ||||
\(837\) | −0.132933 | −0.00459483 | ||||||||
\(838\) | 2.30111 | + | 1.32854i | 0.0794904 | + | 0.0458938i | ||||
\(839\) | 14.9132 | + | 8.61011i | 0.514859 | + | 0.297254i | 0.734829 | − | 0.678253i | \(-0.237262\pi\) |
−0.219970 | + | 0.975507i | \(0.570596\pi\) | |||||||
\(840\) | 0.0227792 | − | 0.0394547i | 0.000785957 | − | 0.00136132i | ||||
\(841\) | −9.54779 | − | 16.5373i | −0.329234 | − | 0.570250i | ||||
\(842\) | −21.4763 | + | 37.1981i | −0.740123 | + | 1.28193i | ||||
\(843\) | −0.144743 | − | 0.250702i | −0.00498520 | − | 0.00863462i | ||||
\(844\) | 4.52304i | 0.155689i | ||||||||
\(845\) | −2.03698 | − | 3.52815i | −0.0700743 | − | 0.121372i | ||||
\(846\) | 4.00368 | − | 6.93457i | 0.137649 | − | 0.238416i | ||||
\(847\) | −29.5048 | + | 17.0346i | −1.01380 | + | 0.585317i | ||||
\(848\) | −15.2213 | + | 8.78804i | −0.522703 | + | 0.301782i | ||||
\(849\) | −0.163729 | + | 0.283587i | −0.00561916 | + | 0.00973267i | ||||
\(850\) | −32.2317 | − | 18.6090i | −1.10554 | − | 0.638282i | ||||
\(851\) | 10.1130 | + | 17.5163i | 0.346671 | + | 0.600451i | ||||
\(852\) | 0.0306375 | + | 0.0176886i | 0.00104962 | + | 0.000606000i | ||||
\(853\) | −20.1938 | + | 34.9767i | −0.691423 | + | 1.19758i | 0.279949 | + | 0.960015i | \(0.409683\pi\) |
−0.971372 | + | 0.237565i | \(0.923651\pi\) | |||||||
\(854\) | −16.1271 | − | 9.31096i | −0.551857 | − | 0.318615i | ||||
\(855\) | 3.36889 | − | 5.83510i | 0.115214 | − | 0.199556i | ||||
\(856\) | −6.42880 | − | 11.1350i | −0.219732 | − | 0.380587i | ||||
\(857\) | −17.4603 | − | 10.0807i | −0.596434 | − | 0.344351i | 0.171204 | − | 0.985236i | \(-0.445234\pi\) |
−0.767637 | + | 0.640885i | \(0.778568\pi\) | |||||||
\(858\) | −0.0747165 | + | 0.0431376i | −0.00255078 | + | 0.00147269i | ||||
\(859\) | −46.7776 | − | 27.0071i | −1.59603 | − | 0.921469i | −0.992242 | − | 0.124325i | \(-0.960323\pi\) |
−0.603790 | − | 0.797144i | \(-0.706343\pi\) | |||||||
\(860\) | 1.89716i | 0.0646927i | ||||||||
\(861\) | − | 0.201592i | − | 0.00687022i | ||||||
\(862\) | 19.3691 | − | 33.5483i | 0.659714 | − | 1.14266i | ||||
\(863\) | 37.2304 | − | 21.4950i | 1.26734 | − | 0.731697i | 0.292854 | − | 0.956157i | \(-0.405395\pi\) |
0.974483 | + | 0.224460i | \(0.0720618\pi\) | |||||||
\(864\) | 0.165546 | + | 0.0955779i | 0.00563198 | + | 0.00325163i | ||||
\(865\) | − | 5.32333i | − | 0.180999i | ||||||
\(866\) | 27.6056 | 0.938076 | ||||||||
\(867\) | 0.123719 | − | 0.214288i | 0.00420173 | − | 0.00727762i | ||||
\(868\) | − | 4.57244i | − | 0.155199i | ||||||
\(869\) | −35.0540 | −1.18912 | ||||||||
\(870\) | −0.0285133 | + | 0.0164622i | −0.000966691 | + | 0.000558119i | ||||
\(871\) | −1.48273 | + | 0.856055i | −0.0502404 | + | 0.0290063i | ||||
\(872\) | −43.9189 | − | 25.3566i | −1.48728 | − | 0.858683i | ||||
\(873\) | −23.3974 | − | 13.5085i | −0.791883 | − | 0.457194i | ||||
\(874\) | 27.3983 | − | 15.8184i | 0.926763 | − | 0.535067i | ||||
\(875\) | −12.3107 | + | 7.10761i | −0.416179 | + | 0.240281i | ||||
\(876\) | 0.0145902 | 0.000492958 | ||||||||
\(877\) | 44.9084i | 1.51645i | 0.651994 | + | 0.758224i | \(0.273933\pi\) | ||||
−0.651994 | + | 0.758224i | \(0.726067\pi\) | |||||||
\(878\) | −14.8363 | + | 25.6971i | −0.500699 | + | 0.867236i | ||||
\(879\) | 0.266061 | 0.00897401 | ||||||||
\(880\) | 4.40420i | 0.148466i | ||||||||
\(881\) | 46.6606 | + | 26.9395i | 1.57203 | + | 0.907614i | 0.995920 | + | 0.0902455i | \(0.0287652\pi\) |
0.576115 | + | 0.817369i | \(0.304568\pi\) | |||||||
\(882\) | −21.6831 | + | 12.5187i | −0.730108 | + | 0.421528i | ||||
\(883\) | 14.1846 | − | 24.5685i | 0.477351 | − | 0.826796i | −0.522312 | − | 0.852754i | \(-0.674930\pi\) |
0.999663 | + | 0.0259583i | \(0.00826370\pi\) | |||||||
\(884\) | − | 5.68724i | − | 0.191283i | ||||||
\(885\) | − | 0.0354622i | − | 0.00119205i | ||||||
\(886\) | −22.5242 | − | 13.0044i | −0.756717 | − | 0.436891i | ||||
\(887\) | −10.5481 | + | 6.08997i | −0.354172 | + | 0.204481i | −0.666521 | − | 0.745486i | \(-0.732217\pi\) |
0.312349 | + | 0.949967i | \(0.398884\pi\) | |||||||
\(888\) | −0.121733 | − | 0.0702823i | −0.00408508 | − | 0.00235852i | ||||
\(889\) | 29.0457 | + | 50.3086i | 0.974161 | + | 1.68730i | ||||
\(890\) | −0.490195 | + | 0.849043i | −0.0164314 | + | 0.0284600i | ||||
\(891\) | 34.9526 | + | 20.1799i | 1.17096 | + | 0.676052i | ||||
\(892\) | −0.0124570 | + | 0.0215761i | −0.000417091 | + | 0.000722423i | ||||
\(893\) | −11.2358 | − | 6.48697i | −0.375990 | − | 0.217078i | ||||
\(894\) | −0.0782314 | − | 0.135501i | −0.00261645 | − | 0.00453182i | ||||
\(895\) | 7.43979 | + | 4.29537i | 0.248685 | + | 0.143578i | ||||
\(896\) | 8.09412 | − | 14.0194i | 0.270406 | − | 0.468356i | ||||
\(897\) | −0.0632275 | + | 0.0365044i | −0.00211110 | + | 0.00121885i | ||||
\(898\) | 25.0593 | − | 14.4680i | 0.836239 | − | 0.482803i | ||||
\(899\) | −7.47773 | + | 12.9518i | −0.249396 | + | 0.431967i | ||||
\(900\) | −4.12730 | − | 7.14870i | −0.137577 | − | 0.238290i | ||||
\(901\) | 44.2872i | 1.47542i | ||||||||
\(902\) | 14.0897 | + | 24.4041i | 0.469136 | + | 0.812568i | ||||
\(903\) | −0.166364 | + | 0.288150i | −0.00553623 | + | 0.00958904i | ||||
\(904\) | 4.30836 | + | 7.46229i | 0.143294 | + | 0.248192i | ||||
\(905\) | −0.141045 | + | 0.244297i | −0.00468849 | + | 0.00812070i | ||||
\(906\) | 7.43172e−5 | 0 | 4.29070e-5i | 2.46902e−6 | 0 | 1.42549e-6i | ||||
\(907\) | 20.1596 | + | 11.6392i | 0.669389 | + | 0.386472i | 0.795845 | − | 0.605500i | \(-0.207027\pi\) |
−0.126456 | + | 0.991972i | \(0.540360\pi\) | |||||||
\(908\) | −3.41056 | −0.113183 | ||||||||
\(909\) | 13.4306 | − | 7.75417i | 0.445466 | − | 0.257190i | ||||
\(910\) | 2.33990 | + | 1.35094i | 0.0775669 | + | 0.0447833i | ||||
\(911\) | − | 17.9360i | − | 0.594245i | −0.954839 | − | 0.297122i | \(-0.903973\pi\) | ||
0.954839 | − | 0.297122i | \(-0.0960269\pi\) | |||||||
\(912\) | −0.0760268 | + | 0.131682i | −0.00251750 | + | 0.00436044i | ||||
\(913\) | −50.7976 | + | 29.3280i | −1.68116 | + | 0.970615i | ||||
\(914\) | − | 7.08535i | − | 0.234362i | ||||||
\(915\) | −0.0142957 | + | 0.00825361i | −0.000472601 | + | 0.000272856i | ||||
\(916\) | 4.29278i | 0.141838i | ||||||||
\(917\) | 11.9407 | + | 20.6819i | 0.394317 | + | 0.682977i | ||||
\(918\) | −0.409580 | + | 0.236471i | −0.0135182 | + | 0.00780472i | ||||
\(919\) | 35.0733 | − | 20.2496i | 1.15696 | − | 0.667972i | 0.206387 | − | 0.978470i | \(-0.433829\pi\) |
0.950574 | + | 0.310499i | \(0.100496\pi\) | |||||||
\(920\) | 5.38912i | 0.177674i | ||||||||
\(921\) | 0.252777 | 0.00832929 | ||||||||
\(922\) | −42.6703 | −1.40527 | ||||||||
\(923\) | −4.74781 | + | 8.22345i | −0.156276 | + | 0.270678i | ||||
\(924\) | 0.0488500 | − | 0.0846107i | 0.00160705 | − | 0.00278349i | ||||
\(925\) | 10.7989 | + | 18.7043i | 0.355067 | + | 0.614993i | ||||
\(926\) | 4.87882 | 0.160328 | ||||||||
\(927\) | 25.2819 | − | 14.5965i | 0.830368 | − | 0.479413i | ||||
\(928\) | 18.6246 | − | 10.7529i | 0.611381 | − | 0.352981i | ||||
\(929\) | 21.0065 | 0.689199 | 0.344600 | − | 0.938750i | \(-0.388015\pi\) | ||||
0.344600 | + | 0.938750i | \(0.388015\pi\) | |||||||
\(930\) | 0.00886630 | + | 0.00511896i | 0.000290737 | + | 0.000167857i | ||||
\(931\) | 20.2835 | + | 35.1321i | 0.664765 | + | 1.15141i | ||||
\(932\) | 6.74216 | 0.220847 | ||||||||
\(933\) | 0.121901 | + | 0.0703795i | 0.00399086 | + | 0.00230412i | ||||
\(934\) | 15.2304 | − | 8.79328i | 0.498354 | − | 0.287725i | ||||
\(935\) | 9.61068 | + | 5.54873i | 0.314303 | + | 0.181463i | ||||
\(936\) | −7.20997 | + | 12.4880i | −0.235665 | + | 0.408184i | ||||
\(937\) | −0.206878 | −0.00675842 | −0.00337921 | − | 0.999994i | \(-0.501076\pi\) | ||||
−0.00337921 | + | 0.999994i | \(0.501076\pi\) | |||||||
\(938\) | −2.44864 | + | 4.24116i | −0.0799508 | + | 0.138479i | ||||
\(939\) | −0.135254 | + | 0.234266i | −0.00441384 | + | 0.00764500i | ||||
\(940\) | 0.422886 | − | 0.244153i | 0.0137930 | − | 0.00796340i | ||||
\(941\) | −3.22485 | − | 5.58560i | −0.105127 | − | 0.182085i | 0.808663 | − | 0.588272i | \(-0.200192\pi\) |
−0.913790 | + | 0.406187i | \(0.866858\pi\) | |||||||
\(942\) | −0.205370 | − | 0.118571i | −0.00669133 | − | 0.00386324i | ||||
\(943\) | 11.9232 | + | 20.6515i | 0.388272 | + | 0.672507i | ||||
\(944\) | − | 22.7441i | − | 0.740257i | ||||||
\(945\) | 0.0889527i | 0.00289363i | ||||||||
\(946\) | − | 46.5102i | − | 1.51218i | ||||||
\(947\) | −15.1114 | −0.491054 | −0.245527 | − | 0.969390i | \(-0.578961\pi\) | ||||
−0.245527 | + | 0.969390i | \(0.578961\pi\) | |||||||
\(948\) | 0.0394474 | − | 0.0227750i | 0.00128119 | − | 0.000739696i | ||||
\(949\) | 3.91618i | 0.127125i | ||||||||
\(950\) | 29.2566 | − | 16.8913i | 0.949208 | − | 0.548026i | ||||
\(951\) | 0.163815 | − | 0.0945786i | 0.00531206 | − | 0.00306692i | ||||
\(952\) | −36.8127 | − | 63.7615i | −1.19311 | − | 2.06652i | ||||
\(953\) | −0.170556 | − | 0.295412i | −0.00552485 | − | 0.00956933i | 0.863250 | − | 0.504777i | \(-0.168425\pi\) |
−0.868775 | + | 0.495208i | \(0.835092\pi\) | |||||||
\(954\) | 12.4053 | − | 21.4866i | 0.401635 | − | 0.695653i | ||||
\(955\) | −5.86851 | −0.189900 | ||||||||
\(956\) | 7.21392 | − | 12.4949i | 0.233315 | − | 0.404113i | ||||
\(957\) | −0.276743 | + | 0.159778i | −0.00894584 | + | 0.00516488i | ||||
\(958\) | −7.09945 | − | 4.09887i | −0.229373 | − | 0.132428i | ||||
\(959\) | −48.6523 | −1.57107 | ||||||||
\(960\) | −0.0174502 | − | 0.0302246i | −0.000563202 | − | 0.000975495i | ||||
\(961\) | −26.3496 | −0.849986 | ||||||||
\(962\) | 4.16816 | − | 7.21946i | 0.134387 | − | 0.232765i | ||||
\(963\) | 10.8704 | + | 6.27600i | 0.350292 | + | 0.202241i | ||||
\(964\) | −0.521387 | − | 0.903069i | −0.0167927 | − | 0.0290859i | ||||
\(965\) | −1.62907 | + | 0.940542i | −0.0524415 | + | 0.0302771i | ||||
\(966\) | −0.104416 | + | 0.180854i | −0.00335954 | + | 0.00581889i | ||||
\(967\) | 3.23101 | 0.103902 | 0.0519511 | − | 0.998650i | \(-0.483456\pi\) | ||||
0.0519511 | + | 0.998650i | \(0.483456\pi\) | |||||||
\(968\) | 28.0076i | 0.900200i | ||||||||
\(969\) | 0.191568 | + | 0.331806i | 0.00615406 | + | 0.0106591i | ||||
\(970\) | 2.08077 | + | 3.60400i | 0.0668096 | + | 0.115718i | ||||
\(971\) | 3.17576 | + | 5.50057i | 0.101915 | + | 0.176522i | 0.912474 | − | 0.409136i | \(-0.134170\pi\) |
−0.810559 | + | 0.585657i | \(0.800836\pi\) | |||||||
\(972\) | −0.157343 | −0.00504677 | ||||||||
\(973\) | 41.0328 | − | 23.6903i | 1.31545 | − | 0.759476i | ||||
\(974\) | −11.5406 | + | 19.9890i | −0.369786 | + | 0.640488i | ||||
\(975\) | −0.0675157 | + | 0.0389802i | −0.00216223 | + | 0.00124837i | ||||
\(976\) | −9.16870 | + | 5.29355i | −0.293483 | + | 0.169443i | ||||
\(977\) | 7.07374 | + | 12.2521i | 0.226309 | + | 0.391979i | 0.956711 | − | 0.291038i | \(-0.0940007\pi\) |
−0.730402 | + | 0.683017i | \(0.760667\pi\) | |||||||
\(978\) | −0.233925 | −0.00748011 | ||||||||
\(979\) | −4.75772 | + | 8.24061i | −0.152057 | + | 0.263371i | ||||
\(980\) | −1.52684 | −0.0487731 | ||||||||
\(981\) | 49.5078 | 1.58066 | ||||||||
\(982\) | 4.17069i | 0.133092i | ||||||||
\(983\) | 30.5549 | 0.974548 | 0.487274 | − | 0.873249i | \(-0.337991\pi\) | ||||
0.487274 | + | 0.873249i | \(0.337991\pi\) | |||||||
\(984\) | −0.143522 | − | 0.0828622i | −0.00457530 | − | 0.00264155i | ||||
\(985\) | 5.62255 | − | 3.24618i | 0.179149 | − | 0.103432i | ||||
\(986\) | 53.2079i | 1.69449i | ||||||||
\(987\) | 0.0856398 | 0.00272595 | ||||||||
\(988\) | 4.47067 | + | 2.58114i | 0.142231 | + | 0.0821171i | ||||
\(989\) | − | 39.3584i | − | 1.25153i | ||||||
\(990\) | −3.10850 | − | 5.38409i | −0.0987947 | − | 0.171117i | ||||
\(991\) | −21.1574 | − | 36.6457i | −0.672087 | − | 1.16409i | −0.977311 | − | 0.211808i | \(-0.932065\pi\) |
0.305225 | − | 0.952280i | \(-0.401268\pi\) | |||||||
\(992\) | −5.79136 | − | 3.34364i | −0.183876 | − | 0.106161i | ||||
\(993\) | −0.125218 | + | 0.0722949i | −0.00397369 | + | 0.00229421i | ||||
\(994\) | 27.1610i | 0.861496i | ||||||||
\(995\) | − | 6.99361i | − | 0.221712i | ||||||
\(996\) | 0.0381095 | − | 0.0660075i | 0.00120754 | − | 0.00209153i | ||||
\(997\) | 1.90676 | + | 1.10087i | 0.0603876 | + | 0.0348648i | 0.529890 | − | 0.848067i | \(-0.322233\pi\) |
−0.469502 | + | 0.882931i | \(0.655567\pi\) | |||||||
\(998\) | −21.7889 | + | 37.7394i | −0.689715 | + | 1.19462i | ||||
\(999\) | 0.274452 | 0.00868328 |
(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 | 349.2.e.a.123.10 | ✓ | 58 | |
349.227 | even | 6 | inner | 349.2.e.a.227.10 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.e.a.123.10 | ✓ | 58 | 1.1 | even | 1 | trivial | |
349.2.e.a.227.10 | yes | 58 | 349.227 | even | 6 | inner |