Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(323,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.j (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.16 | ||
Character | \(\chi\) | \(=\) | 552.323 |
Dual form | 552.2.j.d.323.15 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.734855 | + | 1.20830i | −0.519621 | + | 0.854397i | ||||
\(3\) | −1.73179 | + | 0.0302019i | −0.999848 | + | 0.0174371i | ||||
\(4\) | −0.919975 | − | 1.77585i | −0.459988 | − | 0.887925i | ||||
\(5\) | −0.871841 | −0.389899 | −0.194950 | − | 0.980813i | \(-0.562454\pi\) | ||||
−0.194950 | + | 0.980813i | \(0.562454\pi\) | |||||||
\(6\) | 1.23612 | − | 2.11471i | 0.504644 | − | 0.863328i | ||||
\(7\) | − | 3.09231i | − | 1.16878i | −0.811472 | − | 0.584392i | \(-0.801333\pi\) | ||
0.811472 | − | 0.584392i | \(-0.198667\pi\) | |||||||
\(8\) | 2.82181 | + | 0.193388i | 0.997660 | + | 0.0683728i | ||||
\(9\) | 2.99818 | − | 0.104607i | 0.999392 | − | 0.0348688i | ||||
\(10\) | 0.640677 | − | 1.05344i | 0.202600 | − | 0.333129i | ||||
\(11\) | 1.90350i | 0.573926i | 0.957942 | + | 0.286963i | \(0.0926456\pi\) | ||||
−0.957942 | + | 0.286963i | \(0.907354\pi\) | |||||||
\(12\) | 1.64684 | + | 3.04761i | 0.475401 | + | 0.879769i | ||||
\(13\) | 1.23856i | 0.343514i | 0.985139 | + | 0.171757i | \(0.0549444\pi\) | ||||
−0.985139 | + | 0.171757i | \(0.945056\pi\) | |||||||
\(14\) | 3.73644 | + | 2.27240i | 0.998605 | + | 0.607325i | ||||
\(15\) | 1.50984 | − | 0.0263313i | 0.389840 | − | 0.00679870i | ||||
\(16\) | −2.30729 | + | 3.26748i | −0.576823 | + | 0.816869i | ||||
\(17\) | 1.98300i | 0.480949i | 0.970655 | + | 0.240474i | \(0.0773030\pi\) | ||||
−0.970655 | + | 0.240474i | \(0.922697\pi\) | |||||||
\(18\) | −2.07683 | + | 3.69956i | −0.489513 | + | 0.871996i | ||||
\(19\) | −4.96848 | −1.13985 | −0.569924 | − | 0.821697i | \(-0.693027\pi\) | ||||
−0.569924 | + | 0.821697i | \(0.693027\pi\) | |||||||
\(20\) | 0.802072 | + | 1.54826i | 0.179349 | + | 0.346201i | ||||
\(21\) | 0.0933936 | + | 5.35522i | 0.0203802 | + | 1.16861i | ||||
\(22\) | −2.29999 | − | 1.39879i | −0.490360 | − | 0.298224i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −4.89261 | − | 0.249682i | −0.998700 | − | 0.0509662i | ||||
\(25\) | −4.23989 | −0.847979 | ||||||||
\(26\) | −1.49655 | − | 0.910161i | −0.293498 | − | 0.178497i | ||||
\(27\) | −5.18904 | + | 0.271707i | −0.998632 | + | 0.0522900i | ||||
\(28\) | −5.49148 | + | 2.84485i | −1.03779 | + | 0.537626i | ||||
\(29\) | 2.31109 | 0.429159 | 0.214580 | − | 0.976706i | \(-0.431162\pi\) | ||||
0.214580 | + | 0.976706i | \(0.431162\pi\) | |||||||
\(30\) | −1.07770 | + | 1.84369i | −0.196760 | + | 0.336611i | ||||
\(31\) | − | 3.48492i | − | 0.625909i | −0.949768 | − | 0.312955i | \(-0.898681\pi\) | ||
0.949768 | − | 0.312955i | \(-0.101319\pi\) | |||||||
\(32\) | −2.25257 | − | 5.18902i | −0.398201 | − | 0.917298i | ||||
\(33\) | −0.0574892 | − | 3.29645i | −0.0100076 | − | 0.573838i | ||||
\(34\) | −2.39606 | − | 1.45722i | −0.410921 | − | 0.249911i | ||||
\(35\) | 2.69600i | 0.455708i | ||||||||
\(36\) | −2.94401 | − | 5.22808i | −0.490669 | − | 0.871346i | ||||
\(37\) | 4.56655i | 0.750735i | 0.926876 | + | 0.375368i | \(0.122484\pi\) | ||||
−0.926876 | + | 0.375368i | \(0.877516\pi\) | |||||||
\(38\) | 3.65112 | − | 6.00341i | 0.592289 | − | 0.973882i | ||||
\(39\) | −0.0374068 | − | 2.14492i | −0.00598989 | − | 0.343462i | ||||
\(40\) | −2.46017 | − | 0.168603i | −0.388987 | − | 0.0266585i | ||||
\(41\) | 8.71457i | 1.36099i | 0.732754 | + | 0.680493i | \(0.238234\pi\) | ||||
−0.732754 | + | 0.680493i | \(0.761766\pi\) | |||||||
\(42\) | −6.53934 | − | 3.82247i | −1.00904 | − | 0.589819i | ||||
\(43\) | −3.26780 | −0.498336 | −0.249168 | − | 0.968460i | \(-0.580157\pi\) | ||||
−0.249168 | + | 0.968460i | \(0.580157\pi\) | |||||||
\(44\) | 3.38032 | − | 1.75117i | 0.509603 | − | 0.263999i | ||||
\(45\) | −2.61393 | + | 0.0912003i | −0.389662 | + | 0.0135953i | ||||
\(46\) | −0.734855 | + | 1.20830i | −0.108349 | + | 0.178154i | ||||
\(47\) | −7.68114 | −1.12041 | −0.560205 | − | 0.828354i | \(-0.689277\pi\) | ||||
−0.560205 | + | 0.828354i | \(0.689277\pi\) | |||||||
\(48\) | 3.89705 | − | 5.72826i | 0.562491 | − | 0.826803i | ||||
\(49\) | −2.56238 | −0.366054 | ||||||||
\(50\) | 3.11571 | − | 5.12306i | 0.440628 | − | 0.724510i | ||||
\(51\) | −0.0598904 | − | 3.43414i | −0.00838634 | − | 0.480876i | ||||
\(52\) | 2.19950 | − | 1.13944i | 0.305015 | − | 0.158012i | ||||
\(53\) | −7.53051 | −1.03439 | −0.517197 | − | 0.855866i | \(-0.673025\pi\) | ||||
−0.517197 | + | 0.855866i | \(0.673025\pi\) | |||||||
\(54\) | 3.48489 | − | 6.46958i | 0.474234 | − | 0.880399i | ||||
\(55\) | − | 1.65955i | − | 0.223773i | ||||||
\(56\) | 0.598014 | − | 8.72591i | 0.0799130 | − | 1.16605i | ||||
\(57\) | 8.60435 | − | 0.150058i | 1.13967 | − | 0.0198756i | ||||
\(58\) | −1.69832 | + | 2.79249i | −0.223000 | + | 0.366672i | ||||
\(59\) | 12.2120i | 1.58986i | 0.606698 | + | 0.794932i | \(0.292494\pi\) | ||||
−0.606698 | + | 0.794932i | \(0.707506\pi\) | |||||||
\(60\) | −1.43578 | − | 2.65703i | −0.185358 | − | 0.343021i | ||||
\(61\) | 10.7975i | 1.38248i | 0.722623 | + | 0.691242i | \(0.242936\pi\) | ||||
−0.722623 | + | 0.691242i | \(0.757064\pi\) | |||||||
\(62\) | 4.21082 | + | 2.56091i | 0.534775 | + | 0.325236i | ||||
\(63\) | −0.323476 | − | 9.27129i | −0.0407541 | − | 1.16807i | ||||
\(64\) | 7.92520 | + | 1.09141i | 0.990650 | + | 0.136426i | ||||
\(65\) | − | 1.07983i | − | 0.133936i | ||||||
\(66\) | 4.02535 | + | 2.35295i | 0.495486 | + | 0.289628i | ||||
\(67\) | −0.0562647 | −0.00687383 | −0.00343692 | − | 0.999994i | \(-0.501094\pi\) | ||||
−0.00343692 | + | 0.999994i | \(0.501094\pi\) | |||||||
\(68\) | 3.52152 | − | 1.82431i | 0.427047 | − | 0.221231i | ||||
\(69\) | −1.73179 | + | 0.0302019i | −0.208483 | + | 0.00363588i | ||||
\(70\) | −3.25758 | − | 1.98117i | −0.389355 | − | 0.236795i | ||||
\(71\) | −7.84847 | −0.931442 | −0.465721 | − | 0.884932i | \(-0.654205\pi\) | ||||
−0.465721 | + | 0.884932i | \(0.654205\pi\) | |||||||
\(72\) | 8.48051 | + | 0.284630i | 0.999437 | + | 0.0335440i | ||||
\(73\) | −7.04796 | −0.824902 | −0.412451 | − | 0.910980i | \(-0.635327\pi\) | ||||
−0.412451 | + | 0.910980i | \(0.635327\pi\) | |||||||
\(74\) | −5.51775 | − | 3.35575i | −0.641426 | − | 0.390098i | ||||
\(75\) | 7.34259 | − | 0.128053i | 0.847850 | − | 0.0147863i | ||||
\(76\) | 4.57088 | + | 8.82328i | 0.524316 | + | 1.01210i | ||||
\(77\) | 5.88620 | 0.670795 | ||||||||
\(78\) | 2.61919 | + | 1.53101i | 0.296565 | + | 0.173352i | ||||
\(79\) | − | 5.10654i | − | 0.574531i | −0.957851 | − | 0.287265i | \(-0.907254\pi\) | ||
0.957851 | − | 0.287265i | \(-0.0927462\pi\) | |||||||
\(80\) | 2.01159 | − | 2.84872i | 0.224903 | − | 0.318497i | ||||
\(81\) | 8.97811 | − | 0.627258i | 0.997568 | − | 0.0696953i | ||||
\(82\) | −10.5298 | − | 6.40395i | −1.16282 | − | 0.707198i | ||||
\(83\) | 0.795490i | 0.0873163i | 0.999047 | + | 0.0436582i | \(0.0139012\pi\) | ||||
−0.999047 | + | 0.0436582i | \(0.986099\pi\) | |||||||
\(84\) | 9.42416 | − | 5.09253i | 1.02826 | − | 0.555640i | ||||
\(85\) | − | 1.72886i | − | 0.187522i | ||||||
\(86\) | 2.40136 | − | 3.94849i | 0.258946 | − | 0.425776i | ||||
\(87\) | −4.00232 | + | 0.0697994i | −0.429094 | + | 0.00748329i | ||||
\(88\) | −0.368112 | + | 5.37130i | −0.0392409 | + | 0.572582i | ||||
\(89\) | 17.3867i | 1.84298i | 0.388399 | + | 0.921491i | \(0.373028\pi\) | ||||
−0.388399 | + | 0.921491i | \(0.626972\pi\) | |||||||
\(90\) | 1.81066 | − | 3.22543i | 0.190861 | − | 0.339990i | ||||
\(91\) | 3.83001 | 0.401494 | ||||||||
\(92\) | −0.919975 | − | 1.77585i | −0.0959141 | − | 0.185145i | ||||
\(93\) | 0.105251 | + | 6.03513i | 0.0109140 | + | 0.625814i | ||||
\(94\) | 5.64452 | − | 9.28111i | 0.582188 | − | 0.957274i | ||||
\(95\) | 4.33173 | 0.444426 | ||||||||
\(96\) | 4.05768 | + | 8.91825i | 0.414136 | + | 0.910215i | ||||
\(97\) | 9.05221 | 0.919113 | 0.459557 | − | 0.888149i | \(-0.348008\pi\) | ||||
0.459557 | + | 0.888149i | \(0.348008\pi\) | |||||||
\(98\) | 1.88298 | − | 3.09612i | 0.190210 | − | 0.312756i | ||||
\(99\) | 0.199118 | + | 5.70701i | 0.0200121 | + | 0.573577i | ||||
\(100\) | 3.90060 | + | 7.52942i | 0.390060 | + | 0.752942i | ||||
\(101\) | −19.5806 | −1.94835 | −0.974173 | − | 0.225803i | \(-0.927500\pi\) | ||||
−0.974173 | + | 0.225803i | \(0.927500\pi\) | |||||||
\(102\) | 4.19348 | + | 2.45123i | 0.415216 | + | 0.242708i | ||||
\(103\) | − | 2.96013i | − | 0.291670i | −0.989309 | − | 0.145835i | \(-0.953413\pi\) | ||
0.989309 | − | 0.145835i | \(-0.0465869\pi\) | |||||||
\(104\) | −0.239522 | + | 3.49497i | −0.0234870 | + | 0.342710i | ||||
\(105\) | −0.0814244 | − | 4.66890i | −0.00794621 | − | 0.455638i | ||||
\(106\) | 5.53383 | − | 9.09911i | 0.537494 | − | 0.883784i | ||||
\(107\) | − | 8.95826i | − | 0.866028i | −0.901387 | − | 0.433014i | \(-0.857450\pi\) | ||
0.901387 | − | 0.433014i | \(-0.142550\pi\) | |||||||
\(108\) | 5.25630 | + | 8.96500i | 0.505788 | + | 0.862658i | ||||
\(109\) | − | 9.35024i | − | 0.895591i | −0.894136 | − | 0.447795i | \(-0.852209\pi\) | ||
0.894136 | − | 0.447795i | \(-0.147791\pi\) | |||||||
\(110\) | 2.00523 | + | 1.21953i | 0.191191 | + | 0.116277i | ||||
\(111\) | −0.137918 | − | 7.90829i | −0.0130906 | − | 0.750621i | ||||
\(112\) | 10.1041 | + | 7.13486i | 0.954743 | + | 0.674181i | ||||
\(113\) | 1.47151i | 0.138428i | 0.997602 | + | 0.0692140i | \(0.0220491\pi\) | ||||
−0.997602 | + | 0.0692140i | \(0.977951\pi\) | |||||||
\(114\) | −6.14164 | + | 10.5069i | −0.575217 | + | 0.984062i | ||||
\(115\) | −0.871841 | −0.0812996 | ||||||||
\(116\) | −2.12615 | − | 4.10416i | −0.197408 | − | 0.381062i | ||||
\(117\) | 0.129561 | + | 3.71342i | 0.0119779 | + | 0.343305i | ||||
\(118\) | −14.7557 | − | 8.97404i | −1.35838 | − | 0.826127i | ||||
\(119\) | 6.13206 | 0.562125 | ||||||||
\(120\) | 4.26558 | + | 0.217683i | 0.389392 | + | 0.0198717i | ||||
\(121\) | 7.37670 | 0.670609 | ||||||||
\(122\) | −13.0467 | − | 7.93463i | −1.18119 | − | 0.718368i | ||||
\(123\) | −0.263196 | − | 15.0918i | −0.0237316 | − | 1.36078i | ||||
\(124\) | −6.18869 | + | 3.20604i | −0.555761 | + | 0.287911i | ||||
\(125\) | 8.05572 | 0.720525 | ||||||||
\(126\) | 11.4402 | + | 6.42220i | 1.01917 | + | 0.572135i | ||||
\(127\) | 6.90921i | 0.613093i | 0.951856 | + | 0.306547i | \(0.0991735\pi\) | ||||
−0.951856 | + | 0.306547i | \(0.900826\pi\) | |||||||
\(128\) | −7.14262 | + | 8.77399i | −0.631325 | + | 0.775519i | ||||
\(129\) | 5.65914 | − | 0.0986939i | 0.498260 | − | 0.00868951i | ||||
\(130\) | 1.30475 | + | 0.793516i | 0.114434 | + | 0.0695959i | ||||
\(131\) | 12.5716i | 1.09839i | 0.835695 | + | 0.549193i | \(0.185065\pi\) | ||||
−0.835695 | + | 0.549193i | \(0.814935\pi\) | |||||||
\(132\) | −5.80111 | + | 3.13474i | −0.504922 | + | 0.272845i | ||||
\(133\) | 15.3641i | 1.33224i | ||||||||
\(134\) | 0.0413464 | − | 0.0679846i | 0.00357179 | − | 0.00587298i | ||||
\(135\) | 4.52402 | − | 0.236885i | 0.389366 | − | 0.0203878i | ||||
\(136\) | −0.383488 | + | 5.59565i | −0.0328838 | + | 0.479823i | ||||
\(137\) | − | 1.78484i | − | 0.152490i | −0.997089 | − | 0.0762448i | \(-0.975707\pi\) | ||
0.997089 | − | 0.0762448i | \(-0.0242930\pi\) | |||||||
\(138\) | 1.23612 | − | 2.11471i | 0.105226 | − | 0.180016i | ||||
\(139\) | 5.90847 | 0.501150 | 0.250575 | − | 0.968097i | \(-0.419380\pi\) | ||||
0.250575 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(140\) | 4.78770 | − | 2.48026i | 0.404634 | − | 0.209620i | ||||
\(141\) | 13.3021 | − | 0.231985i | 1.12024 | − | 0.0195367i | ||||
\(142\) | 5.76749 | − | 9.48330i | 0.483997 | − | 0.795821i | ||||
\(143\) | −2.35759 | −0.197152 | ||||||||
\(144\) | −6.57586 | + | 10.0378i | −0.547989 | + | 0.836486i | ||||
\(145\) | −2.01491 | −0.167329 | ||||||||
\(146\) | 5.17923 | − | 8.51605i | 0.428636 | − | 0.704793i | ||||
\(147\) | 4.43750 | − | 0.0773888i | 0.365999 | − | 0.00638292i | ||||
\(148\) | 8.10950 | − | 4.20111i | 0.666597 | − | 0.345329i | ||||
\(149\) | 18.3640 | 1.50444 | 0.752219 | − | 0.658914i | \(-0.228984\pi\) | ||||
0.752219 | + | 0.658914i | \(0.228984\pi\) | |||||||
\(150\) | −5.24102 | + | 8.96615i | −0.427927 | + | 0.732083i | ||||
\(151\) | 5.65286i | 0.460023i | 0.973188 | + | 0.230012i | \(0.0738764\pi\) | ||||
−0.973188 | + | 0.230012i | \(0.926124\pi\) | |||||||
\(152\) | −14.0201 | − | 0.960843i | −1.13718 | − | 0.0779346i | ||||
\(153\) | 0.207435 | + | 5.94539i | 0.0167701 | + | 0.480656i | ||||
\(154\) | −4.32550 | + | 7.11229i | −0.348559 | + | 0.573125i | ||||
\(155\) | 3.03829i | 0.244041i | ||||||||
\(156\) | −3.77464 | + | 2.03970i | −0.302213 | + | 0.163307i | ||||
\(157\) | − | 17.6786i | − | 1.41090i | −0.708758 | − | 0.705451i | \(-0.750744\pi\) | ||
0.708758 | − | 0.705451i | \(-0.249256\pi\) | |||||||
\(158\) | 6.17023 | + | 3.75257i | 0.490877 | + | 0.298538i | ||||
\(159\) | 13.0412 | − | 0.227436i | 1.03424 | − | 0.0180368i | ||||
\(160\) | 1.96388 | + | 4.52400i | 0.155258 | + | 0.357654i | ||||
\(161\) | − | 3.09231i | − | 0.243708i | ||||||
\(162\) | −5.83970 | + | 11.3092i | −0.458810 | + | 0.888534i | ||||
\(163\) | −15.4158 | −1.20746 | −0.603728 | − | 0.797191i | \(-0.706319\pi\) | ||||
−0.603728 | + | 0.797191i | \(0.706319\pi\) | |||||||
\(164\) | 15.4758 | − | 8.01719i | 1.20845 | − | 0.626037i | ||||
\(165\) | 0.0501214 | + | 2.87398i | 0.00390195 | + | 0.223739i | ||||
\(166\) | −0.961190 | − | 0.584570i | −0.0746028 | − | 0.0453714i | ||||
\(167\) | 9.04899 | 0.700232 | 0.350116 | − | 0.936706i | \(-0.386142\pi\) | ||||
0.350116 | + | 0.936706i | \(0.386142\pi\) | |||||||
\(168\) | −0.772095 | + | 15.1295i | −0.0595684 | + | 1.16726i | ||||
\(169\) | 11.4660 | 0.881998 | ||||||||
\(170\) | 2.08898 | + | 1.27046i | 0.160218 | + | 0.0974401i | ||||
\(171\) | −14.8964 | + | 0.519736i | −1.13915 | + | 0.0397452i | ||||
\(172\) | 3.00630 | + | 5.80313i | 0.229228 | + | 0.442485i | ||||
\(173\) | 2.83727 | 0.215714 | 0.107857 | − | 0.994166i | \(-0.465601\pi\) | ||||
0.107857 | + | 0.994166i | \(0.465601\pi\) | |||||||
\(174\) | 2.85679 | − | 4.88730i | 0.216573 | − | 0.370505i | ||||
\(175\) | 13.1111i | 0.991103i | ||||||||
\(176\) | −6.21963 | − | 4.39192i | −0.468822 | − | 0.331053i | ||||
\(177\) | −0.368825 | − | 21.1486i | −0.0277226 | − | 1.58962i | ||||
\(178\) | −21.0083 | − | 12.7767i | −1.57464 | − | 0.957653i | ||||
\(179\) | − | 10.5834i | − | 0.791043i | −0.918457 | − | 0.395521i | \(-0.870564\pi\) | ||
0.918457 | − | 0.395521i | \(-0.129436\pi\) | |||||||
\(180\) | 2.56671 | + | 4.55805i | 0.191311 | + | 0.339737i | ||||
\(181\) | − | 8.60505i | − | 0.639608i | −0.947484 | − | 0.319804i | \(-0.896383\pi\) | ||
0.947484 | − | 0.319804i | \(-0.103617\pi\) | |||||||
\(182\) | −2.81450 | + | 4.62780i | −0.208625 | + | 0.343035i | ||||
\(183\) | −0.326106 | − | 18.6991i | −0.0241065 | − | 1.38227i | ||||
\(184\) | 2.82181 | + | 0.193388i | 0.208026 | + | 0.0142567i | ||||
\(185\) | − | 3.98130i | − | 0.292711i | ||||||
\(186\) | −7.36959 | − | 4.30778i | −0.540365 | − | 0.315861i | ||||
\(187\) | −3.77464 | −0.276029 | ||||||||
\(188\) | 7.06646 | + | 13.6406i | 0.515374 | + | 0.994840i | ||||
\(189\) | 0.840202 | + | 16.0461i | 0.0611157 | + | 1.16718i | ||||
\(190\) | −3.18319 | + | 5.23402i | −0.230933 | + | 0.379716i | ||||
\(191\) | −14.6068 | −1.05691 | −0.528454 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528454 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(192\) | −13.7577 | − | 1.65073i | −0.992879 | − | 0.119131i | ||||
\(193\) | −5.48507 | −0.394824 | −0.197412 | − | 0.980321i | \(-0.563254\pi\) | ||||
−0.197412 | + | 0.980321i | \(0.563254\pi\) | |||||||
\(194\) | −6.65207 | + | 10.9378i | −0.477591 | + | 0.785287i | ||||
\(195\) | 0.0326128 | + | 1.87003i | 0.00233545 | + | 0.133916i | ||||
\(196\) | 2.35733 | + | 4.55040i | 0.168380 | + | 0.325029i | ||||
\(197\) | −21.8619 | −1.55760 | −0.778798 | − | 0.627274i | \(-0.784170\pi\) | ||||
−0.778798 | + | 0.627274i | \(0.784170\pi\) | |||||||
\(198\) | −7.04211 | − | 3.95324i | −0.500461 | − | 0.280944i | ||||
\(199\) | 19.5960i | 1.38912i | 0.719435 | + | 0.694560i | \(0.244401\pi\) | ||||
−0.719435 | + | 0.694560i | \(0.755599\pi\) | |||||||
\(200\) | −11.9642 | − | 0.819943i | −0.845994 | − | 0.0579787i | ||||
\(201\) | 0.0974385 | − | 0.00169930i | 0.00687279 | − | 0.000119859i | ||||
\(202\) | 14.3889 | − | 23.6593i | 1.01240 | − | 1.66466i | ||||
\(203\) | − | 7.14662i | − | 0.501594i | ||||||
\(204\) | −6.04342 | + | 3.26568i | −0.423124 | + | 0.228643i | ||||
\(205\) | − | 7.59772i | − | 0.530647i | ||||||
\(206\) | 3.57672 | + | 2.17527i | 0.249202 | + | 0.151558i | ||||
\(207\) | 2.99818 | − | 0.104607i | 0.208388 | − | 0.00727066i | ||||
\(208\) | −4.04696 | − | 2.85771i | −0.280606 | − | 0.198147i | ||||
\(209\) | − | 9.45748i | − | 0.654188i | ||||||
\(210\) | 5.70127 | + | 3.33258i | 0.393425 | + | 0.229970i | ||||
\(211\) | 9.82214 | 0.676184 | 0.338092 | − | 0.941113i | \(-0.390218\pi\) | ||||
0.338092 | + | 0.941113i | \(0.390218\pi\) | |||||||
\(212\) | 6.92788 | + | 13.3731i | 0.475809 | + | 0.918465i | ||||
\(213\) | 13.5919 | − | 0.237039i | 0.931300 | − | 0.0162416i | ||||
\(214\) | 10.8243 | + | 6.58302i | 0.739931 | + | 0.450006i | ||||
\(215\) | 2.84901 | 0.194301 | ||||||||
\(216\) | −14.6950 | − | 0.236792i | −0.999870 | − | 0.0161116i | ||||
\(217\) | −10.7764 | −0.731552 | ||||||||
\(218\) | 11.2979 | + | 6.87107i | 0.765190 | + | 0.465368i | ||||
\(219\) | 12.2056 | − | 0.212862i | 0.824776 | − | 0.0143839i | ||||
\(220\) | −2.94710 | + | 1.52674i | −0.198694 | + | 0.102933i | ||||
\(221\) | −2.45607 | −0.165213 | ||||||||
\(222\) | 9.65693 | + | 5.64480i | 0.648131 | + | 0.378854i | ||||
\(223\) | − | 5.37339i | − | 0.359829i | −0.983682 | − | 0.179914i | \(-0.942418\pi\) | ||
0.983682 | − | 0.179914i | \(-0.0575821\pi\) | |||||||
\(224\) | −16.0461 | + | 6.96563i | −1.07212 | + | 0.465411i | ||||
\(225\) | −12.7119 | + | 0.443521i | −0.847463 | + | 0.0295680i | ||||
\(226\) | −1.77802 | − | 1.08135i | −0.118272 | − | 0.0719301i | ||||
\(227\) | − | 23.0536i | − | 1.53012i | −0.643957 | − | 0.765061i | \(-0.722709\pi\) | ||
0.643957 | − | 0.765061i | \(-0.277291\pi\) | |||||||
\(228\) | −8.18227 | − | 15.1420i | −0.541884 | − | 1.00280i | ||||
\(229\) | − | 27.2263i | − | 1.79916i | −0.436752 | − | 0.899582i | \(-0.643871\pi\) | ||
0.436752 | − | 0.899582i | \(-0.356129\pi\) | |||||||
\(230\) | 0.640677 | − | 1.05344i | 0.0422450 | − | 0.0694621i | ||||
\(231\) | −10.1936 | + | 0.177774i | −0.670693 | + | 0.0116967i | ||||
\(232\) | 6.52147 | + | 0.446937i | 0.428155 | + | 0.0293428i | ||||
\(233\) | − | 21.6173i | − | 1.41620i | −0.706114 | − | 0.708098i | \(-0.749553\pi\) | ||
0.706114 | − | 0.708098i | \(-0.250447\pi\) | |||||||
\(234\) | −4.58213 | − | 2.57227i | −0.299543 | − | 0.168155i | ||||
\(235\) | 6.69673 | 0.436846 | ||||||||
\(236\) | 21.6867 | − | 11.2347i | 1.41168 | − | 0.731318i | ||||
\(237\) | 0.154227 | + | 8.84345i | 0.0100181 | + | 0.574444i | ||||
\(238\) | −4.50618 | + | 7.40936i | −0.292092 | + | 0.480278i | ||||
\(239\) | 17.6777 | 1.14348 | 0.571738 | − | 0.820436i | \(-0.306270\pi\) | ||||
0.571738 | + | 0.820436i | \(0.306270\pi\) | |||||||
\(240\) | −3.39761 | + | 4.99413i | −0.219315 | + | 0.322370i | ||||
\(241\) | −16.3445 | −1.05284 | −0.526419 | − | 0.850225i | \(-0.676466\pi\) | ||||
−0.526419 | + | 0.850225i | \(0.676466\pi\) | |||||||
\(242\) | −5.42081 | + | 8.91327i | −0.348463 | + | 0.572967i | ||||
\(243\) | −15.5292 | + | 1.35743i | −0.996201 | + | 0.0870794i | ||||
\(244\) | 19.1748 | − | 9.93348i | 1.22754 | − | 0.635926i | ||||
\(245\) | 2.23399 | 0.142724 | ||||||||
\(246\) | 18.4288 | + | 10.7723i | 1.17498 | + | 0.686814i | ||||
\(247\) | − | 6.15376i | − | 0.391554i | ||||||
\(248\) | 0.673939 | − | 9.83376i | 0.0427952 | − | 0.624445i | ||||
\(249\) | −0.0240253 | − | 1.37762i | −0.00152254 | − | 0.0873030i | ||||
\(250\) | −5.91979 | + | 9.73372i | −0.374400 | + | 0.615614i | ||||
\(251\) | 14.1286i | 0.891791i | 0.895085 | + | 0.445896i | \(0.147115\pi\) | ||||
−0.895085 | + | 0.445896i | \(0.852885\pi\) | |||||||
\(252\) | −16.1668 | + | 9.10380i | −1.01841 | + | 0.573486i | ||||
\(253\) | 1.90350i | 0.119672i | ||||||||
\(254\) | −8.34839 | − | 5.07727i | −0.523825 | − | 0.318576i | ||||
\(255\) | 0.0522149 | + | 2.99402i | 0.00326983 | + | 0.187493i | ||||
\(256\) | −5.35282 | − | 15.0780i | −0.334551 | − | 0.942378i | ||||
\(257\) | − | 13.2937i | − | 0.829238i | −0.909995 | − | 0.414619i | \(-0.863915\pi\) | ||
0.909995 | − | 0.414619i | \(-0.136085\pi\) | |||||||
\(258\) | −4.03940 | + | 6.91047i | −0.251482 | + | 0.430227i | ||||
\(259\) | 14.1212 | 0.877447 | ||||||||
\(260\) | −1.91761 | + | 0.993413i | −0.118925 | + | 0.0616089i | ||||
\(261\) | 6.92907 | − | 0.241756i | 0.428898 | − | 0.0149643i | ||||
\(262\) | −15.1903 | − | 9.23832i | −0.938458 | − | 0.570745i | ||||
\(263\) | −25.3919 | −1.56573 | −0.782865 | − | 0.622192i | \(-0.786242\pi\) | ||||
−0.782865 | + | 0.622192i | \(0.786242\pi\) | |||||||
\(264\) | 0.475269 | − | 9.31307i | 0.0292508 | − | 0.573180i | ||||
\(265\) | 6.56541 | 0.403310 | ||||||||
\(266\) | −18.5644 | − | 11.2904i | −1.13826 | − | 0.692258i | ||||
\(267\) | −0.525110 | − | 30.1100i | −0.0321362 | − | 1.84270i | ||||
\(268\) | 0.0517622 | + | 0.0999177i | 0.00316188 | + | 0.00610345i | ||||
\(269\) | −2.58876 | −0.157840 | −0.0789198 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789198 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(270\) | −3.03827 | + | 5.64045i | −0.184903 | + | 0.343267i | ||||
\(271\) | 29.5135i | 1.79282i | 0.443226 | + | 0.896410i | \(0.353834\pi\) | ||||
−0.443226 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(272\) | −6.47942 | − | 4.57536i | −0.392872 | − | 0.277422i | ||||
\(273\) | −6.63276 | + | 0.115673i | −0.401433 | + | 0.00700088i | ||||
\(274\) | 2.15663 | + | 1.31160i | 0.130287 | + | 0.0792368i | ||||
\(275\) | − | 8.07062i | − | 0.486677i | ||||||
\(276\) | 1.64684 | + | 3.04761i | 0.0991279 | + | 0.183445i | ||||
\(277\) | − | 1.08750i | − | 0.0653413i | −0.999466 | − | 0.0326707i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326707i | \(-0.0104012\pi\) | |||||||
\(278\) | −4.34187 | + | 7.13920i | −0.260408 | + | 0.428181i | ||||
\(279\) | −0.364545 | − | 10.4484i | −0.0218247 | − | 0.625529i | ||||
\(280\) | −0.521373 | + | 7.60760i | −0.0311580 | + | 0.454641i | ||||
\(281\) | − | 3.26761i | − | 0.194929i | −0.995239 | − | 0.0974647i | \(-0.968927\pi\) | ||
0.995239 | − | 0.0974647i | \(-0.0310733\pi\) | |||||||
\(282\) | −9.49481 | + | 16.2434i | −0.565408 | + | 0.967280i | ||||
\(283\) | 6.37119 | 0.378728 | 0.189364 | − | 0.981907i | \(-0.439357\pi\) | ||||
0.189364 | + | 0.981907i | \(0.439357\pi\) | |||||||
\(284\) | 7.22040 | + | 13.9377i | 0.428452 | + | 0.827051i | ||||
\(285\) | −7.50163 | + | 0.130826i | −0.444358 | + | 0.00774948i | ||||
\(286\) | 1.73249 | − | 2.84868i | 0.102444 | − | 0.168446i | ||||
\(287\) | 26.9481 | 1.59070 | ||||||||
\(288\) | −7.29640 | − | 15.3220i | −0.429944 | − | 0.902855i | ||||
\(289\) | 13.0677 | 0.768688 | ||||||||
\(290\) | 1.48066 | − | 2.43461i | 0.0869476 | − | 0.142965i | ||||
\(291\) | −15.6765 | + | 0.273394i | −0.918973 | + | 0.0160266i | ||||
\(292\) | 6.48395 | + | 12.5161i | 0.379445 | + | 0.732451i | ||||
\(293\) | −24.5319 | −1.43317 | −0.716584 | − | 0.697501i | \(-0.754295\pi\) | ||||
−0.716584 | + | 0.697501i | \(0.754295\pi\) | |||||||
\(294\) | −3.16741 | + | 5.41870i | −0.184727 | + | 0.316025i | ||||
\(295\) | − | 10.6469i | − | 0.619887i | ||||||
\(296\) | −0.883113 | + | 12.8859i | −0.0513299 | + | 0.748979i | ||||
\(297\) | −0.517193 | − | 9.87732i | −0.0300106 | − | 0.573140i | ||||
\(298\) | −13.4949 | + | 22.1892i | −0.781738 | + | 1.28539i | ||||
\(299\) | 1.23856i | 0.0716277i | ||||||||
\(300\) | −6.98241 | − | 12.9215i | −0.403130 | − | 0.746026i | ||||
\(301\) | 10.1051i | 0.582446i | ||||||||
\(302\) | −6.83035 | − | 4.15403i | −0.393042 | − | 0.239038i | ||||
\(303\) | 33.9095 | − | 0.591372i | 1.94805 | − | 0.0339735i | ||||
\(304\) | 11.4637 | − | 16.2344i | 0.657490 | − | 0.931107i | ||||
\(305\) | − | 9.41374i | − | 0.539029i | ||||||
\(306\) | −7.33625 | − | 4.11836i | −0.419385 | − | 0.235431i | ||||
\(307\) | 6.49267 | 0.370556 | 0.185278 | − | 0.982686i | \(-0.440681\pi\) | ||||
0.185278 | + | 0.982686i | \(0.440681\pi\) | |||||||
\(308\) | −5.41516 | − | 10.4530i | −0.308557 | − | 0.595615i | ||||
\(309\) | 0.0894015 | + | 5.12631i | 0.00508587 | + | 0.291626i | ||||
\(310\) | −3.67117 | − | 2.23271i | −0.208508 | − | 0.126809i | ||||
\(311\) | −26.3522 | −1.49430 | −0.747149 | − | 0.664657i | \(-0.768578\pi\) | ||||
−0.747149 | + | 0.664657i | \(0.768578\pi\) | |||||||
\(312\) | 0.309246 | − | 6.05979i | 0.0175076 | − | 0.343068i | ||||
\(313\) | −33.2164 | −1.87750 | −0.938750 | − | 0.344599i | \(-0.888015\pi\) | ||||
−0.938750 | + | 0.344599i | \(0.888015\pi\) | |||||||
\(314\) | 21.3610 | + | 12.9912i | 1.20547 | + | 0.733135i | ||||
\(315\) | 0.282019 | + | 8.08309i | 0.0158900 | + | 0.455430i | ||||
\(316\) | −9.06846 | + | 4.69789i | −0.510141 | + | 0.264277i | ||||
\(317\) | 21.3265 | 1.19782 | 0.598908 | − | 0.800818i | \(-0.295601\pi\) | ||||
0.598908 | + | 0.800818i | \(0.295601\pi\) | |||||||
\(318\) | −9.30861 | + | 15.9249i | −0.522001 | + | 0.893022i | ||||
\(319\) | 4.39916i | 0.246306i | ||||||||
\(320\) | −6.90952 | − | 0.951532i | −0.386254 | − | 0.0531922i | ||||
\(321\) | 0.270556 | + | 15.5138i | 0.0151010 | + | 0.865896i | ||||
\(322\) | 3.73644 | + | 2.27240i | 0.208223 | + | 0.126636i | ||||
\(323\) | − | 9.85251i | − | 0.548208i | ||||||
\(324\) | −9.37356 | − | 15.3667i | −0.520753 | − | 0.853707i | ||||
\(325\) | − | 5.25136i | − | 0.291293i | ||||||
\(326\) | 11.3284 | − | 18.6269i | 0.627419 | − | 1.03165i | ||||
\(327\) | 0.282395 | + | 16.1926i | 0.0156165 | + | 0.895454i | ||||
\(328\) | −1.68529 | + | 24.5908i | −0.0930545 | + | 1.35780i | ||||
\(329\) | 23.7525i | 1.30952i | ||||||||
\(330\) | −3.50946 | − | 2.05140i | −0.193189 | − | 0.112926i | ||||
\(331\) | −7.14989 | −0.392994 | −0.196497 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196497 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(332\) | 1.41267 | − | 0.731831i | 0.0775304 | − | 0.0401644i | ||||
\(333\) | 0.477691 | + | 13.6913i | 0.0261773 | + | 0.750279i | ||||
\(334\) | −6.64970 | + | 10.9339i | −0.363855 | + | 0.598276i | ||||
\(335\) | 0.0490539 | 0.00268010 | ||||||||
\(336\) | −17.7136 | − | 12.0509i | −0.966354 | − | 0.657430i | ||||
\(337\) | 7.67027 | 0.417826 | 0.208913 | − | 0.977934i | \(-0.433007\pi\) | ||||
0.208913 | + | 0.977934i | \(0.433007\pi\) | |||||||
\(338\) | −8.42583 | + | 13.8543i | −0.458305 | + | 0.753576i | ||||
\(339\) | −0.0444424 | − | 2.54834i | −0.00241378 | − | 0.138407i | ||||
\(340\) | −3.07020 | + | 1.59051i | −0.166505 | + | 0.0862576i | ||||
\(341\) | 6.63352 | 0.359225 | ||||||||
\(342\) | 10.3187 | − | 18.3812i | 0.557971 | − | 0.993943i | ||||
\(343\) | − | 13.7225i | − | 0.740945i | ||||||
\(344\) | −9.22112 | − | 0.631953i | −0.497169 | − | 0.0340726i | ||||
\(345\) | 1.50984 | − | 0.0263313i | 0.0812872 | − | 0.00141763i | ||||
\(346\) | −2.08498 | + | 3.42827i | −0.112089 | + | 0.184305i | ||||
\(347\) | 27.3593i | 1.46872i | 0.678759 | + | 0.734361i | \(0.262518\pi\) | ||||
−0.678759 | + | 0.734361i | \(0.737482\pi\) | |||||||
\(348\) | 3.80599 | + | 7.04332i | 0.204023 | + | 0.377561i | ||||
\(349\) | 6.07938i | 0.325422i | 0.986674 | + | 0.162711i | \(0.0520238\pi\) | ||||
−0.986674 | + | 0.162711i | \(0.947976\pi\) | |||||||
\(350\) | −15.8421 | − | 9.63474i | −0.846795 | − | 0.514998i | ||||
\(351\) | −0.336525 | − | 6.42693i | −0.0179624 | − | 0.343044i | ||||
\(352\) | 9.87728 | − | 4.28775i | 0.526461 | − | 0.228538i | ||||
\(353\) | 25.6872i | 1.36719i | 0.729861 | + | 0.683595i | \(0.239585\pi\) | ||||
−0.729861 | + | 0.683595i | \(0.760415\pi\) | |||||||
\(354\) | 25.8248 | + | 15.0955i | 1.37257 | + | 0.802316i | ||||
\(355\) | 6.84262 | 0.363168 | ||||||||
\(356\) | 30.8761 | − | 15.9953i | 1.63643 | − | 0.847749i | ||||
\(357\) | −10.6194 | + | 0.185200i | −0.562039 | + | 0.00980181i | ||||
\(358\) | 12.7880 | + | 7.77729i | 0.675864 | + | 0.411042i | ||||
\(359\) | −17.9590 | −0.947838 | −0.473919 | − | 0.880568i | \(-0.657161\pi\) | ||||
−0.473919 | + | 0.880568i | \(0.657161\pi\) | |||||||
\(360\) | −7.39365 | − | 0.248152i | −0.389680 | − | 0.0130788i | ||||
\(361\) | 5.68581 | 0.299253 | ||||||||
\(362\) | 10.3975 | + | 6.32347i | 0.546479 | + | 0.332354i | ||||
\(363\) | −12.7749 | + | 0.222790i | −0.670508 | + | 0.0116935i | ||||
\(364\) | −3.52351 | − | 6.80152i | −0.184682 | − | 0.356497i | ||||
\(365\) | 6.14470 | 0.321628 | ||||||||
\(366\) | 22.8337 | + | 13.3471i | 1.19354 | + | 0.697662i | ||||
\(367\) | − | 22.5647i | − | 1.17787i | −0.808180 | − | 0.588935i | \(-0.799547\pi\) | ||
0.808180 | − | 0.588935i | \(-0.200453\pi\) | |||||||
\(368\) | −2.30729 | + | 3.26748i | −0.120276 | + | 0.170329i | ||||
\(369\) | 0.911601 | + | 26.1278i | 0.0474560 | + | 1.36016i | ||||
\(370\) | 4.81060 | + | 2.92568i | 0.250091 | + | 0.152099i | ||||
\(371\) | 23.2867i | 1.20898i | ||||||||
\(372\) | 10.6207 | − | 5.73908i | 0.550656 | − | 0.297558i | ||||
\(373\) | 19.6359i | 1.01671i | 0.861147 | + | 0.508355i | \(0.169746\pi\) | ||||
−0.861147 | + | 0.508355i | \(0.830254\pi\) | |||||||
\(374\) | 2.77381 | − | 4.56089i | 0.143430 | − | 0.235838i | ||||
\(375\) | −13.9508 | + | 0.243298i | −0.720416 | + | 0.0125639i | ||||
\(376\) | −21.6747 | − | 1.48544i | −1.11779 | − | 0.0766055i | ||||
\(377\) | 2.86243i | 0.147422i | ||||||||
\(378\) | −20.0060 | − | 10.7764i | −1.02900 | − | 0.554277i | ||||
\(379\) | −13.9167 | −0.714855 | −0.357428 | − | 0.933941i | \(-0.616346\pi\) | ||||
−0.357428 | + | 0.933941i | \(0.616346\pi\) | |||||||
\(380\) | −3.98508 | − | 7.69250i | −0.204430 | − | 0.394617i | ||||
\(381\) | −0.208671 | − | 11.9653i | −0.0106905 | − | 0.613000i | ||||
\(382\) | 10.7339 | − | 17.6493i | 0.549192 | − | 0.903019i | ||||
\(383\) | 27.2328 | 1.39153 | 0.695766 | − | 0.718269i | \(-0.255065\pi\) | ||||
0.695766 | + | 0.718269i | \(0.255065\pi\) | |||||||
\(384\) | 12.1045 | − | 15.4104i | 0.617706 | − | 0.786409i | ||||
\(385\) | −5.13183 | −0.261542 | ||||||||
\(386\) | 4.03073 | − | 6.62761i | 0.205159 | − | 0.337336i | ||||
\(387\) | −9.79745 | + | 0.341834i | −0.498032 | + | 0.0173764i | ||||
\(388\) | −8.32781 | − | 16.0754i | −0.422781 | − | 0.816104i | ||||
\(389\) | 0.198260 | 0.0100522 | 0.00502608 | − | 0.999987i | \(-0.498400\pi\) | ||||
0.00502608 | + | 0.999987i | \(0.498400\pi\) | |||||||
\(390\) | −2.28352 | − | 1.33479i | −0.115631 | − | 0.0675900i | ||||
\(391\) | 1.98300i | 0.100285i | ||||||||
\(392\) | −7.23055 | − | 0.495532i | −0.365198 | − | 0.0250282i | ||||
\(393\) | −0.379687 | − | 21.7714i | −0.0191527 | − | 1.09822i | ||||
\(394\) | 16.0653 | − | 26.4157i | 0.809360 | − | 1.33081i | ||||
\(395\) | 4.45209i | 0.224009i | ||||||||
\(396\) | 9.95162 | − | 5.60392i | 0.500088 | − | 0.281607i | ||||
\(397\) | − | 12.8510i | − | 0.644971i | −0.946574 | − | 0.322485i | \(-0.895482\pi\) | ||
0.946574 | − | 0.322485i | \(-0.104518\pi\) | |||||||
\(398\) | −23.6778 | − | 14.4002i | −1.18686 | − | 0.721816i | ||||
\(399\) | −0.464025 | − | 26.6073i | −0.0232303 | − | 1.33203i | ||||
\(400\) | 9.78267 | − | 13.8538i | 0.489133 | − | 0.692688i | ||||
\(401\) | 23.3200i | 1.16454i | 0.812994 | + | 0.582272i | \(0.197836\pi\) | ||||
−0.812994 | + | 0.582272i | \(0.802164\pi\) | |||||||
\(402\) | −0.0695500 | + | 0.118984i | −0.00346884 | + | 0.00593437i | ||||
\(403\) | 4.31627 | 0.215009 | ||||||||
\(404\) | 18.0137 | + | 34.7723i | 0.896215 | + | 1.72999i | ||||
\(405\) | −7.82749 | + | 0.546869i | −0.388951 | + | 0.0271741i | ||||
\(406\) | 8.63526 | + | 5.25173i | 0.428561 | + | 0.260639i | ||||
\(407\) | −8.69240 | −0.430866 | ||||||||
\(408\) | 0.495120 | − | 9.70206i | 0.0245121 | − | 0.480324i | ||||
\(409\) | 2.90989 | 0.143885 | 0.0719425 | − | 0.997409i | \(-0.477080\pi\) | ||||
0.0719425 | + | 0.997409i | \(0.477080\pi\) | |||||||
\(410\) | 9.18032 | + | 5.58322i | 0.453383 | + | 0.275736i | ||||
\(411\) | 0.0539057 | + | 3.09097i | 0.00265897 | + | 0.152466i | ||||
\(412\) | −5.25674 | + | 2.72324i | −0.258981 | + | 0.134165i | ||||
\(413\) | 37.7632 | 1.85821 | ||||||||
\(414\) | −2.07683 | + | 3.69956i | −0.102071 | + | 0.181824i | ||||
\(415\) | − | 0.693540i | − | 0.0340446i | ||||||
\(416\) | 6.42691 | − | 2.78994i | 0.315105 | − | 0.136788i | ||||
\(417\) | −10.2322 | + | 0.178447i | −0.501074 | + | 0.00873859i | ||||
\(418\) | 11.4275 | + | 6.94988i | 0.558936 | + | 0.339930i | ||||
\(419\) | 15.9445i | 0.778941i | 0.921039 | + | 0.389470i | \(0.127342\pi\) | ||||
−0.921039 | + | 0.389470i | \(0.872658\pi\) | |||||||
\(420\) | −8.21637 | + | 4.43987i | −0.400918 | + | 0.216644i | ||||
\(421\) | − | 30.6791i | − | 1.49521i | −0.664144 | − | 0.747604i | \(-0.731204\pi\) | ||
0.664144 | − | 0.747604i | \(-0.268796\pi\) | |||||||
\(422\) | −7.21785 | + | 11.8681i | −0.351360 | + | 0.577730i | ||||
\(423\) | −23.0294 | + | 0.803497i | −1.11973 | + | 0.0390674i | ||||
\(424\) | −21.2497 | − | 1.45631i | −1.03197 | − | 0.0707245i | ||||
\(425\) | − | 8.40772i | − | 0.407834i | ||||||
\(426\) | −9.70165 | + | 16.5972i | −0.470047 | + | 0.804139i | ||||
\(427\) | 33.3894 | 1.61582 | ||||||||
\(428\) | −15.9085 | + | 8.24138i | −0.768968 | + | 0.398362i | ||||
\(429\) | 4.08285 | − | 0.0712037i | 0.197122 | − | 0.00343775i | ||||
\(430\) | −2.09361 | + | 3.44245i | −0.100963 | + | 0.166010i | ||||
\(431\) | 35.6205 | 1.71578 | 0.857890 | − | 0.513833i | \(-0.171775\pi\) | ||||
0.857890 | + | 0.513833i | \(0.171775\pi\) | |||||||
\(432\) | 11.0848 | − | 17.5820i | 0.533319 | − | 0.845914i | ||||
\(433\) | 3.15606 | 0.151670 | 0.0758352 | − | 0.997120i | \(-0.475838\pi\) | ||||
0.0758352 | + | 0.997120i | \(0.475838\pi\) | |||||||
\(434\) | 7.91912 | − | 13.0212i | 0.380130 | − | 0.625036i | ||||
\(435\) | 3.48939 | − | 0.0608540i | 0.167303 | − | 0.00291773i | ||||
\(436\) | −16.6046 | + | 8.60199i | −0.795218 | + | 0.411961i | ||||
\(437\) | −4.96848 | −0.237675 | ||||||||
\(438\) | −8.71213 | + | 14.9044i | −0.416282 | + | 0.712160i | ||||
\(439\) | 27.8197i | 1.32776i | 0.747839 | + | 0.663880i | \(0.231092\pi\) | ||||
−0.747839 | + | 0.663880i | \(0.768908\pi\) | |||||||
\(440\) | 0.320935 | − | 4.68292i | 0.0153000 | − | 0.223249i | ||||
\(441\) | −7.68247 | + | 0.268042i | −0.365832 | + | 0.0127639i | ||||
\(442\) | 1.80485 | − | 2.96766i | 0.0858481 | − | 0.141157i | ||||
\(443\) | 6.53287i | 0.310386i | 0.987884 | + | 0.155193i | \(0.0496000\pi\) | ||||
−0.987884 | + | 0.155193i | \(0.950400\pi\) | |||||||
\(444\) | −13.9171 | + | 7.52035i | −0.660474 | + | 0.356900i | ||||
\(445\) | − | 15.1584i | − | 0.718577i | ||||||
\(446\) | 6.49267 | + | 3.94867i | 0.307437 | + | 0.186975i | ||||
\(447\) | −31.8025 | + | 0.554628i | −1.50421 | + | 0.0262330i | ||||
\(448\) | 3.37496 | − | 24.5072i | 0.159452 | − | 1.15786i | ||||
\(449\) | − | 25.4871i | − | 1.20281i | −0.798943 | − | 0.601406i | \(-0.794607\pi\) | ||
0.798943 | − | 0.601406i | \(-0.205393\pi\) | |||||||
\(450\) | 8.80554 | − | 15.6858i | 0.415097 | − | 0.739434i | ||||
\(451\) | −16.5881 | −0.781105 | ||||||||
\(452\) | 2.61318 | − | 1.35375i | 0.122914 | − | 0.0636752i | ||||
\(453\) | −0.170727 | − | 9.78955i | −0.00802146 | − | 0.459953i | ||||
\(454\) | 27.8557 | + | 16.9411i | 1.30733 | + | 0.795084i | ||||
\(455\) | −3.33916 | −0.156542 | ||||||||
\(456\) | 24.3089 | + | 1.24054i | 1.13837 | + | 0.0580937i | ||||
\(457\) | 2.40286 | 0.112401 | 0.0562004 | − | 0.998420i | \(-0.482101\pi\) | ||||
0.0562004 | + | 0.998420i | \(0.482101\pi\) | |||||||
\(458\) | 32.8975 | + | 20.0074i | 1.53720 | + | 0.934884i | ||||
\(459\) | −0.538796 | − | 10.2899i | −0.0251488 | − | 0.480291i | ||||
\(460\) | 0.802072 | + | 1.54826i | 0.0373968 | + | 0.0721880i | ||||
\(461\) | −14.0637 | −0.655013 | −0.327506 | − | 0.944849i | \(-0.606208\pi\) | ||||
−0.327506 | + | 0.944849i | \(0.606208\pi\) | |||||||
\(462\) | 7.27605 | − | 12.4476i | 0.338512 | − | 0.579115i | ||||
\(463\) | 35.7689i | 1.66232i | 0.556031 | + | 0.831161i | \(0.312323\pi\) | ||||
−0.556031 | + | 0.831161i | \(0.687677\pi\) | |||||||
\(464\) | −5.33237 | + | 7.55145i | −0.247549 | + | 0.350567i | ||||
\(465\) | −0.0917622 | − | 5.26168i | −0.00425537 | − | 0.244004i | ||||
\(466\) | 26.1202 | + | 15.8856i | 1.20999 | + | 0.735886i | ||||
\(467\) | − | 39.3360i | − | 1.82025i | −0.414331 | − | 0.910126i | \(-0.635985\pi\) | ||
0.414331 | − | 0.910126i | \(-0.364015\pi\) | |||||||
\(468\) | 6.47528 | − | 3.64633i | 0.299320 | − | 0.168552i | ||||
\(469\) | 0.173988i | 0.00803402i | ||||||||
\(470\) | −4.92113 | + | 8.09165i | −0.226995 | + | 0.373240i | ||||
\(471\) | 0.533926 | + | 30.6155i | 0.0246020 | + | 1.41069i | ||||
\(472\) | −2.36165 | + | 34.4599i | −0.108704 | + | 1.58614i | ||||
\(473\) | − | 6.22025i | − | 0.286007i | ||||||
\(474\) | −10.7989 | − | 6.31230i | −0.496008 | − | 0.289934i | ||||
\(475\) | 21.0658 | 0.966567 | ||||||||
\(476\) | −5.64134 | − | 10.8896i | −0.258571 | − | 0.499125i | ||||
\(477\) | −22.5778 | + | 0.787740i | −1.03377 | + | 0.0360682i | ||||
\(478\) | −12.9906 | + | 21.3600i | −0.594174 | + | 0.976982i | ||||
\(479\) | 2.16149 | 0.0987611 | 0.0493805 | − | 0.998780i | \(-0.484275\pi\) | ||||
0.0493805 | + | 0.998780i | \(0.484275\pi\) | |||||||
\(480\) | −3.53766 | − | 7.77530i | −0.161471 | − | 0.354892i | ||||
\(481\) | −5.65593 | −0.257888 | ||||||||
\(482\) | 12.0108 | − | 19.7490i | 0.547077 | − | 0.899542i | ||||
\(483\) | 0.0933936 | + | 5.35522i | 0.00424956 | + | 0.243671i | ||||
\(484\) | −6.78639 | − | 13.0999i | −0.308472 | − | 0.595451i | ||||
\(485\) | −7.89209 | −0.358361 | ||||||||
\(486\) | 9.77156 | − | 19.7615i | 0.443247 | − | 0.896400i | ||||
\(487\) | 28.2115i | 1.27839i | 0.769046 | + | 0.639193i | \(0.220732\pi\) | ||||
−0.769046 | + | 0.639193i | \(0.779268\pi\) | |||||||
\(488\) | −2.08811 | + | 30.4686i | −0.0945244 | + | 1.37925i | ||||
\(489\) | 26.6968 | − | 0.465585i | 1.20727 | − | 0.0210545i | ||||
\(490\) | −1.64166 | + | 2.69933i | −0.0741625 | + | 0.121943i | ||||
\(491\) | − | 5.65453i | − | 0.255185i | −0.991827 | − | 0.127593i | \(-0.959275\pi\) | ||
0.991827 | − | 0.127593i | \(-0.0407250\pi\) | |||||||
\(492\) | −26.5586 | + | 14.3515i | −1.19735 | + | 0.647014i | ||||
\(493\) | 4.58291i | 0.206404i | ||||||||
\(494\) | 7.43558 | + | 4.52212i | 0.334543 | + | 0.203460i | ||||
\(495\) | −0.173599 | − | 4.97561i | −0.00780271 | − | 0.223637i | ||||
\(496\) | 11.3869 | + | 8.04071i | 0.511286 | + | 0.361039i | ||||
\(497\) | 24.2699i | 1.08865i | ||||||||
\(498\) | 1.68223 | + | 0.983321i | 0.0753826 | + | 0.0440637i | ||||
\(499\) | 31.1605 | 1.39494 | 0.697468 | − | 0.716616i | \(-0.254310\pi\) | ||||
0.697468 | + | 0.716616i | \(0.254310\pi\) | |||||||
\(500\) | −7.41106 | − | 14.3057i | −0.331433 | − | 0.639773i | ||||
\(501\) | −15.6709 | + | 0.273297i | −0.700125 | + | 0.0122100i | ||||
\(502\) | −17.0716 | − | 10.3825i | −0.761944 | − | 0.463394i | ||||
\(503\) | −0.784770 | −0.0349912 | −0.0174956 | − | 0.999847i | \(-0.505569\pi\) | ||||
−0.0174956 | + | 0.999847i | \(0.505569\pi\) | |||||||
\(504\) | 0.880165 | − | 26.2244i | 0.0392057 | − | 1.16813i | ||||
\(505\) | 17.0712 | 0.759658 | ||||||||
\(506\) | −2.29999 | − | 1.39879i | −0.102247 | − | 0.0621840i | ||||
\(507\) | −19.8566 | + | 0.346294i | −0.881864 | + | 0.0153795i | ||||
\(508\) | 12.2697 | − | 6.35630i | 0.544381 | − | 0.282015i | ||||
\(509\) | 1.62618 | 0.0720790 | 0.0360395 | − | 0.999350i | \(-0.488526\pi\) | ||||
0.0360395 | + | 0.999350i | \(0.488526\pi\) | |||||||
\(510\) | −3.65605 | − | 2.13708i | −0.161892 | − | 0.0946316i | ||||
\(511\) | 21.7945i | 0.964131i | ||||||||
\(512\) | 22.1523 | + | 4.61237i | 0.979004 | + | 0.203840i | ||||
\(513\) | 25.7817 | − | 1.34997i | 1.13829 | − | 0.0596027i | ||||
\(514\) | 16.0628 | + | 9.76895i | 0.708499 | + | 0.430890i | ||||
\(515\) | 2.58076i | 0.113722i | ||||||||
\(516\) | −5.38154 | − | 9.95900i | −0.236909 | − | 0.438420i | ||||
\(517\) | − | 14.6210i | − | 0.643031i | ||||||
\(518\) | −10.3770 | + | 17.0626i | −0.455940 | + | 0.749688i | ||||
\(519\) | −4.91355 | + | 0.0856910i | −0.215681 | + | 0.00376142i | ||||
\(520\) | 0.208825 | − | 3.04706i | 0.00915758 | − | 0.133623i | ||||
\(521\) | 22.0363i | 0.965429i | 0.875778 | + | 0.482715i | \(0.160349\pi\) | ||||
−0.875778 | + | 0.482715i | \(0.839651\pi\) | |||||||
\(522\) | −4.79975 | + | 8.55004i | −0.210079 | + | 0.374225i | ||||
\(523\) | −0.873026 | −0.0381748 | −0.0190874 | − | 0.999818i | \(-0.506076\pi\) | ||||
−0.0190874 | + | 0.999818i | \(0.506076\pi\) | |||||||
\(524\) | 22.3253 | − | 11.5656i | 0.975286 | − | 0.505244i | ||||
\(525\) | −0.395979 | − | 22.7056i | −0.0172819 | − | 0.990953i | ||||
\(526\) | 18.6593 | − | 30.6810i | 0.813586 | − | 1.33775i | ||||
\(527\) | 6.91060 | 0.301030 | ||||||||
\(528\) | 10.9037 | + | 7.41802i | 0.474524 | + | 0.322828i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.82462 | + | 7.93298i | −0.209568 | + | 0.344586i | ||||
\(531\) | 1.27745 | + | 36.6137i | 0.0554368 | + | 1.58890i | ||||
\(532\) | 27.2843 | − | 14.1346i | 1.18293 | − | 0.612812i | ||||
\(533\) | −10.7935 | −0.467518 | ||||||||
\(534\) | 36.7678 | + | 21.4920i | 1.59110 | + | 0.930050i | ||||
\(535\) | 7.81018i | 0.337663i | ||||||||
\(536\) | −0.158768 | − | 0.0108809i | −0.00685774 | − | 0.000469983i | ||||
\(537\) | 0.319640 | + | 18.3282i | 0.0137935 | + | 0.790922i | ||||
\(538\) | 1.90236 | − | 3.12800i | 0.0820168 | − | 0.134858i | ||||
\(539\) | − | 4.87748i | − | 0.210088i | ||||||
\(540\) | −4.58266 | − | 7.81606i | −0.197206 | − | 0.336350i | ||||
\(541\) | − | 40.4127i | − | 1.73748i | −0.495269 | − | 0.868739i | \(-0.664931\pi\) | ||
0.495269 | − | 0.868739i | \(-0.335069\pi\) | |||||||
\(542\) | −35.6612 | − | 21.6882i | −1.53178 | − | 0.931587i | ||||
\(543\) | 0.259889 | + | 14.9021i | 0.0111529 | + | 0.639511i | ||||
\(544\) | 10.2898 | − | 4.46685i | 0.441173 | − | 0.191514i | ||||
\(545\) | 8.15192i | 0.349190i | ||||||||
\(546\) | 4.73435 | − | 8.09936i | 0.202611 | − | 0.346621i | ||||
\(547\) | 26.3268 | 1.12565 | 0.562825 | − | 0.826576i | \(-0.309714\pi\) | ||||
0.562825 | + | 0.826576i | \(0.309714\pi\) | |||||||
\(548\) | −3.16962 | + | 1.64201i | −0.135399 | + | 0.0701433i | ||||
\(549\) | 1.12949 | + | 32.3729i | 0.0482056 | + | 1.38164i | ||||
\(550\) | 9.75172 | + | 5.93074i | 0.415815 | + | 0.252887i | ||||
\(551\) | −11.4826 | −0.489176 | ||||||||
\(552\) | −4.89261 | − | 0.249682i | −0.208243 | − | 0.0106272i | ||||
\(553\) | −15.7910 | −0.671502 | ||||||||
\(554\) | 1.31402 | + | 0.799152i | 0.0558274 | + | 0.0339527i | ||||
\(555\) | 0.120243 | + | 6.89477i | 0.00510402 | + | 0.292667i | ||||
\(556\) | −5.43565 | − | 10.4926i | −0.230523 | − | 0.444984i | ||||
\(557\) | 26.7166 | 1.13202 | 0.566009 | − | 0.824399i | \(-0.308487\pi\) | ||||
0.566009 | + | 0.824399i | \(0.308487\pi\) | |||||||
\(558\) | 12.8927 | + | 7.23758i | 0.545790 | + | 0.306391i | ||||
\(559\) | − | 4.04737i | − | 0.171185i | ||||||
\(560\) | −8.80913 | − | 6.22046i | −0.372254 | − | 0.262862i | ||||
\(561\) | 6.53687 | − | 0.114001i | 0.275987 | − | 0.00481313i | ||||
\(562\) | 3.94825 | + | 2.40122i | 0.166547 | + | 0.101289i | ||||
\(563\) | − | 13.0343i | − | 0.549330i | −0.961540 | − | 0.274665i | \(-0.911433\pi\) | ||
0.961540 | − | 0.274665i | \(-0.0885669\pi\) | |||||||
\(564\) | −12.6496 | − | 23.4091i | −0.532643 | − | 0.985702i | ||||
\(565\) | − | 1.28292i | − | 0.0539729i | ||||||
\(566\) | −4.68191 | + | 7.69831i | −0.196795 | + | 0.323584i | ||||
\(567\) | −1.93967 | − | 27.7631i | −0.0814587 | − | 1.16594i | ||||
\(568\) | −22.1469 | − | 1.51780i | −0.929262 | − | 0.0636853i | ||||
\(569\) | − | 38.2253i | − | 1.60249i | −0.598338 | − | 0.801244i | \(-0.704172\pi\) | ||
0.598338 | − | 0.801244i | \(-0.295828\pi\) | |||||||
\(570\) | 5.35453 | − | 9.16035i | 0.224277 | − | 0.383685i | ||||
\(571\) | 25.1413 | 1.05213 | 0.526066 | − | 0.850444i | \(-0.323667\pi\) | ||||
0.526066 | + | 0.850444i | \(0.323667\pi\) | |||||||
\(572\) | 2.16893 | + | 4.18673i | 0.0906873 | + | 0.175056i | ||||
\(573\) | 25.2958 | − | 0.441152i | 1.05675 | − | 0.0184294i | ||||
\(574\) | −19.8030 | + | 32.5614i | −0.826561 | + | 1.35909i | ||||
\(575\) | −4.23989 | −0.176816 | ||||||||
\(576\) | 23.8753 | + | 2.44320i | 0.994805 | + | 0.101800i | ||||
\(577\) | −20.3082 | −0.845442 | −0.422721 | − | 0.906260i | \(-0.638925\pi\) | ||||
−0.422721 | + | 0.906260i | \(0.638925\pi\) | |||||||
\(578\) | −9.60287 | + | 15.7897i | −0.399427 | + | 0.656765i | ||||
\(579\) | 9.49898 | − | 0.165660i | 0.394764 | − | 0.00688458i | ||||
\(580\) | 1.85366 | + | 3.57817i | 0.0769692 | + | 0.148576i | ||||
\(581\) | 2.45990 | 0.102054 | ||||||||
\(582\) | 11.1896 | − | 19.1428i | 0.463825 | − | 0.793496i | ||||
\(583\) | − | 14.3343i | − | 0.593666i | ||||||
\(584\) | −19.8880 | − | 1.36299i | −0.822971 | − | 0.0564009i | ||||
\(585\) | −0.112957 | − | 3.23751i | −0.00467019 | − | 0.133854i | ||||
\(586\) | 18.0274 | − | 29.6419i | 0.744705 | − | 1.22449i | ||||
\(587\) | 15.5366i | 0.641263i | 0.947204 | + | 0.320631i | \(0.103895\pi\) | ||||
−0.947204 | + | 0.320631i | \(0.896105\pi\) | |||||||
\(588\) | −4.21982 | − | 7.80914i | −0.174022 | − | 0.322043i | ||||
\(589\) | 17.3147i | 0.713441i | ||||||||
\(590\) | 12.8647 | + | 7.82394i | 0.529629 | + | 0.322106i | ||||
\(591\) | 37.8602 | − | 0.660271i | 1.55736 | − | 0.0271599i | ||||
\(592\) | −14.9211 | − | 10.5363i | −0.613253 | − | 0.433041i | ||||
\(593\) | − | 6.77501i | − | 0.278216i | −0.990277 | − | 0.139108i | \(-0.955576\pi\) | ||
0.990277 | − | 0.139108i | \(-0.0444236\pi\) | |||||||
\(594\) | 12.3148 | + | 6.63348i | 0.505283 | + | 0.272175i | ||||
\(595\) | −5.34618 | −0.219172 | ||||||||
\(596\) | −16.8944 | − | 32.6117i | −0.692023 | − | 1.33583i | ||||
\(597\) | −0.591835 | − | 33.9360i | −0.0242222 | − | 1.38891i | ||||
\(598\) | −1.49655 | − | 0.910161i | −0.0611985 | − | 0.0372193i | ||||
\(599\) | −32.7522 | −1.33822 | −0.669109 | − | 0.743164i | \(-0.733324\pi\) | ||||
−0.669109 | + | 0.743164i | \(0.733324\pi\) | |||||||
\(600\) | 20.7442 | + | 1.05863i | 0.846877 | + | 0.0432182i | ||||
\(601\) | −7.83996 | −0.319799 | −0.159899 | − | 0.987133i | \(-0.551117\pi\) | ||||
−0.159899 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(602\) | −12.2099 | − | 7.42576i | −0.497640 | − | 0.302651i | ||||
\(603\) | −0.168692 | + | 0.00588566i | −0.00686965 | + | 0.000239683i | ||||
\(604\) | 10.0386 | − | 5.20049i | 0.408466 | − | 0.211605i | ||||
\(605\) | −6.43131 | −0.261470 | ||||||||
\(606\) | −24.2040 | + | 41.4074i | −0.983221 | + | 1.68206i | ||||
\(607\) | 11.1151i | 0.451147i | 0.974226 | + | 0.225574i | \(0.0724256\pi\) | ||||
−0.974226 | + | 0.225574i | \(0.927574\pi\) | |||||||
\(608\) | 11.1918 | + | 25.7816i | 0.453889 | + | 1.04558i | ||||
\(609\) | 0.215841 | + | 12.3764i | 0.00874634 | + | 0.501518i | ||||
\(610\) | 11.3746 | + | 6.91774i | 0.460545 | + | 0.280091i | ||||
\(611\) | − | 9.51354i | − | 0.384877i | ||||||
\(612\) | 10.3673 | − | 5.83799i | 0.419073 | − | 0.235987i | ||||
\(613\) | − | 2.83979i | − | 0.114698i | −0.998354 | − | 0.0573490i | \(-0.981735\pi\) | ||
0.998354 | − | 0.0573490i | \(-0.0182648\pi\) | |||||||
\(614\) | −4.77117 | + | 7.84509i | −0.192549 | + | 0.316602i | ||||
\(615\) | 0.229465 | + | 13.1576i | 0.00925294 | + | 0.530567i | ||||
\(616\) | 16.6097 | + | 1.13832i | 0.669225 | + | 0.0458641i | ||||
\(617\) | − | 2.11914i | − | 0.0853133i | −0.999090 | − | 0.0426566i | \(-0.986418\pi\) | ||
0.999090 | − | 0.0426566i | \(-0.0135822\pi\) | |||||||
\(618\) | −6.25982 | − | 3.65907i | −0.251807 | − | 0.147190i | ||||
\(619\) | −19.2856 | −0.775154 | −0.387577 | − | 0.921837i | \(-0.626688\pi\) | ||||
−0.387577 | + | 0.921837i | \(0.626688\pi\) | |||||||
\(620\) | 5.39555 | − | 2.79515i | 0.216691 | − | 0.112256i | ||||
\(621\) | −5.18904 | + | 0.271707i | −0.208229 | + | 0.0109032i | ||||
\(622\) | 19.3651 | − | 31.8414i | 0.776469 | − | 1.27672i | ||||
\(623\) | 53.7649 | 2.15405 | ||||||||
\(624\) | 7.09479 | + | 4.82673i | 0.284019 | + | 0.193224i | ||||
\(625\) | 14.1762 | 0.567047 | ||||||||
\(626\) | 24.4092 | − | 40.1353i | 0.975589 | − | 1.60413i | ||||
\(627\) | 0.285634 | + | 16.3784i | 0.0114071 | + | 0.654088i | ||||
\(628\) | −31.3945 | + | 16.2638i | −1.25278 | + | 0.648998i | ||||
\(629\) | −9.05547 | −0.361065 | ||||||||
\(630\) | −9.97403 | − | 5.59914i | −0.397375 | − | 0.223075i | ||||
\(631\) | 12.4518i | 0.495696i | 0.968799 | + | 0.247848i | \(0.0797234\pi\) | ||||
−0.968799 | + | 0.247848i | \(0.920277\pi\) | |||||||
\(632\) | 0.987542 | − | 14.4097i | 0.0392823 | − | 0.573186i | ||||
\(633\) | −17.0099 | + | 0.296647i | −0.676081 | + | 0.0117907i | ||||
\(634\) | −15.6719 | + | 25.7688i | −0.622411 | + | 1.02341i | ||||
\(635\) | − | 6.02373i | − | 0.239044i | ||||||
\(636\) | −12.4015 | − | 22.9501i | −0.491752 | − | 0.910029i | ||||
\(637\) | − | 3.17366i | − | 0.125745i | ||||||
\(638\) | −5.31550 | − | 3.23274i | −0.210443 | − | 0.127986i | ||||
\(639\) | −23.5311 | + | 0.821001i | −0.930875 | + | 0.0324783i | ||||
\(640\) | 6.22723 | − | 7.64953i | 0.246153 | − | 0.302374i | ||||
\(641\) | 18.3406i | 0.724411i | 0.932098 | + | 0.362205i | \(0.117976\pi\) | ||||
−0.932098 | + | 0.362205i | \(0.882024\pi\) | |||||||
\(642\) | −18.9441 | − | 11.0735i | −0.747665 | − | 0.437036i | ||||
\(643\) | 42.8115 | 1.68832 | 0.844160 | − | 0.536091i | \(-0.180100\pi\) | ||||
0.844160 | + | 0.536091i | \(0.180100\pi\) | |||||||
\(644\) | −5.49148 | + | 2.84485i | −0.216395 | + | 0.112103i | ||||
\(645\) | −4.93387 | + | 0.0860454i | −0.194271 | + | 0.00338803i | ||||
\(646\) | 11.9048 | + | 7.24017i | 0.468388 | + | 0.284861i | ||||
\(647\) | −24.2136 | −0.951935 | −0.475968 | − | 0.879463i | \(-0.657902\pi\) | ||||
−0.475968 | + | 0.879463i | \(0.657902\pi\) | |||||||
\(648\) | 25.4558 | − | 0.0337447i | 0.999999 | − | 0.00132562i | ||||
\(649\) | −23.2455 | −0.912464 | ||||||||
\(650\) | 6.34521 | + | 3.85899i | 0.248880 | + | 0.151362i | ||||
\(651\) | 18.6625 | − | 0.325469i | 0.731441 | − | 0.0127561i | ||||
\(652\) | 14.1821 | + | 27.3761i | 0.555415 | + | 1.07213i | ||||
\(653\) | −37.6716 | −1.47420 | −0.737101 | − | 0.675782i | \(-0.763806\pi\) | ||||
−0.737101 | + | 0.675782i | \(0.763806\pi\) | |||||||
\(654\) | −19.7731 | − | 11.5580i | −0.773188 | − | 0.451954i | ||||
\(655\) | − | 10.9604i | − | 0.428260i | ||||||
\(656\) | −28.4747 | − | 20.1070i | −1.11175 | − | 0.785048i | ||||
\(657\) | −21.1310 | + | 0.737263i | −0.824400 | + | 0.0287634i | ||||
\(658\) | −28.7001 | − | 17.4546i | −1.11885 | − | 0.680452i | ||||
\(659\) | − | 24.6271i | − | 0.959337i | −0.877450 | − | 0.479669i | \(-0.840757\pi\) | ||
0.877450 | − | 0.479669i | \(-0.159243\pi\) | |||||||
\(660\) | 5.05765 | − | 2.73300i | 0.196869 | − | 0.106382i | ||||
\(661\) | − | 43.8276i | − | 1.70470i | −0.522976 | − | 0.852348i | \(-0.675178\pi\) | ||
0.522976 | − | 0.852348i | \(-0.324822\pi\) | |||||||
\(662\) | 5.25414 | − | 8.63921i | 0.204208 | − | 0.335773i | ||||
\(663\) | 4.25338 | − | 0.0741778i | 0.165188 | − | 0.00288083i | ||||
\(664\) | −0.153838 | + | 2.24472i | −0.00597006 | + | 0.0871120i | ||||
\(665\) | − | 13.3950i | − | 0.519437i | ||||||
\(666\) | −16.8942 | − | 9.48394i | −0.654638 | − | 0.367495i | ||||
\(667\) | 2.31109 | 0.0894859 | ||||||||
\(668\) | −8.32484 | − | 16.0696i | −0.322098 | − | 0.621753i | ||||
\(669\) | 0.162287 | + | 9.30557i | 0.00627436 | + | 0.359774i | ||||
\(670\) | −0.0360475 | + | 0.0592718i | −0.00139264 | + | 0.00228987i | ||||
\(671\) | −20.5531 | −0.793443 | ||||||||
\(672\) | 27.5780 | − | 12.5476i | 1.06384 | − | 0.484035i | ||||
\(673\) | −33.5022 | −1.29142 | −0.645708 | − | 0.763584i | \(-0.723438\pi\) | ||||
−0.645708 | + | 0.763584i | \(0.723438\pi\) | |||||||
\(674\) | −5.63654 | + | 9.26799i | −0.217111 | + | 0.356989i | ||||
\(675\) | 22.0010 | − | 1.15201i | 0.846819 | − | 0.0443408i | ||||
\(676\) | −10.5484 | − | 20.3619i | −0.405708 | − | 0.783148i | ||||
\(677\) | −14.9572 | −0.574850 | −0.287425 | − | 0.957803i | \(-0.592799\pi\) | ||||
−0.287425 | + | 0.957803i | \(0.592799\pi\) | |||||||
\(678\) | 3.11182 | + | 1.81896i | 0.119509 | + | 0.0698568i | ||||
\(679\) | − | 27.9923i | − | 1.07424i | ||||||
\(680\) | 0.334341 | − | 4.87852i | 0.0128214 | − | 0.187083i | ||||
\(681\) | 0.696263 | + | 39.9240i | 0.0266809 | + | 1.52989i | ||||
\(682\) | −4.87468 | + | 8.01528i | −0.186661 | + | 0.306921i | ||||
\(683\) | − | 4.05767i | − | 0.155262i | −0.996982 | − | 0.0776312i | \(-0.975264\pi\) | ||
0.996982 | − | 0.0776312i | \(-0.0247357\pi\) | |||||||
\(684\) | 14.6273 | + | 25.9756i | 0.559288 | + | 0.993202i | ||||
\(685\) | 1.55610i | 0.0594555i | ||||||||
\(686\) | 16.5809 | + | 10.0840i | 0.633061 | + | 0.385011i | ||||
\(687\) | 0.822286 | + | 47.1502i | 0.0313722 | + | 1.79889i | ||||
\(688\) | 7.53978 | − | 10.6775i | 0.287451 | − | 0.407075i | ||||
\(689\) | − | 9.32698i | − | 0.355329i | ||||||
\(690\) | −1.07770 | + | 1.84369i | −0.0410273 | + | 0.0701882i | ||||
\(691\) | −23.0400 | −0.876485 | −0.438242 | − | 0.898857i | \(-0.644399\pi\) | ||||
−0.438242 | + | 0.898857i | \(0.644399\pi\) | |||||||
\(692\) | −2.61022 | − | 5.03857i | −0.0992257 | − | 0.191538i | ||||
\(693\) | 17.6479 | − | 0.615735i | 0.670387 | − | 0.0233898i | ||||
\(694\) | −33.0582 | − | 20.1051i | −1.25487 | − | 0.763179i | ||||
\(695\) | −5.15125 | −0.195398 | ||||||||
\(696\) | −11.3073 | − | 0.577039i | −0.428602 | − | 0.0218726i | ||||
\(697\) | −17.2810 | −0.654565 | ||||||||
\(698\) | −7.34572 | − | 4.46747i | −0.278040 | − | 0.169096i | ||||
\(699\) | 0.652884 | + | 37.4366i | 0.0246943 | + | 1.41598i | ||||
\(700\) | 23.2833 | − | 12.0619i | 0.880026 | − | 0.455895i | ||||
\(701\) | 22.3112 | 0.842683 | 0.421342 | − | 0.906902i | \(-0.361559\pi\) | ||||
0.421342 | + | 0.906902i | \(0.361559\pi\) | |||||||
\(702\) | 8.01296 | + | 4.31624i | 0.302430 | + | 0.162906i | ||||
\(703\) | − | 22.6888i | − | 0.855724i | ||||||
\(704\) | −2.07749 | + | 15.0856i | −0.0782982 | + | 0.568560i | ||||
\(705\) | −11.5973 | + | 0.202254i | −0.436780 | + | 0.00761732i | ||||
\(706\) | −31.0378 | − | 18.8764i | −1.16812 | − | 0.710421i | ||||
\(707\) | 60.5494i | 2.27719i | ||||||||
\(708\) | −37.2174 | + | 20.1111i | −1.39871 | + | 0.755823i | ||||
\(709\) | 17.9668i | 0.674758i | 0.941369 | + | 0.337379i | \(0.109540\pi\) | ||||
−0.941369 | + | 0.337379i | \(0.890460\pi\) | |||||||
\(710\) | −5.02833 | + | 8.26793i | −0.188710 | + | 0.310290i | ||||
\(711\) | −0.534178 | − | 15.3103i | −0.0200332 | − | 0.574182i | ||||
\(712\) | −3.36236 | + | 49.0618i | −0.126010 | + | 1.83867i | ||||
\(713\) | − | 3.48492i | − | 0.130511i | ||||||
\(714\) | 7.57996 | − | 12.9675i | 0.283673 | − | 0.485298i | ||||
\(715\) | 2.05544 | 0.0768693 | ||||||||
\(716\) | −18.7946 | + | 9.73649i | −0.702387 | + | 0.363870i | ||||
\(717\) | −30.6140 | + | 0.533900i | −1.14330 | + | 0.0199389i | ||||
\(718\) | 13.1972 | − | 21.6998i | 0.492517 | − | 0.809830i | ||||
\(719\) | 34.2271 | 1.27646 | 0.638228 | − | 0.769848i | \(-0.279668\pi\) | ||||
0.638228 | + | 0.769848i | \(0.279668\pi\) | |||||||
\(720\) | 5.73311 | − | 8.75139i | 0.213660 | − | 0.326145i | ||||
\(721\) | −9.15363 | −0.340899 | ||||||||
\(722\) | −4.17825 | + | 6.87016i | −0.155498 | + | 0.255681i | ||||
\(723\) | 28.3051 | − | 0.493634i | 1.05268 | − | 0.0183584i | ||||
\(724\) | −15.2813 | + | 7.91644i | −0.567925 | + | 0.294212i | ||||
\(725\) | −9.79879 | −0.363918 | ||||||||
\(726\) | 9.11849 | − | 15.5996i | 0.338419 | − | 0.578956i | ||||
\(727\) | 19.2864i | 0.715293i | 0.933857 | + | 0.357646i | \(0.116421\pi\) | ||||
−0.933857 | + | 0.357646i | \(0.883579\pi\) | |||||||
\(728\) | 10.8075 | + | 0.740676i | 0.400554 | + | 0.0274513i | ||||
\(729\) | 26.8524 | − | 2.81980i | 0.994532 | − | 0.104437i | ||||
\(730\) | −4.51547 | + | 7.42464i | −0.167125 | + | 0.274798i | ||||
\(731\) | − | 6.48007i | − | 0.239674i | ||||||
\(732\) | −32.9067 | + | 17.7818i | −1.21627 | + | 0.657234i | ||||
\(733\) | 13.7227i | 0.506860i | 0.967354 | + | 0.253430i | \(0.0815587\pi\) | ||||
−0.967354 | + | 0.253430i | \(0.918441\pi\) | |||||||
\(734\) | 27.2650 | + | 16.5818i | 1.00637 | + | 0.612046i | ||||
\(735\) | −3.86879 | + | 0.0674707i | −0.142703 | + | 0.00248869i | ||||
\(736\) | −2.25257 | − | 5.18902i | −0.0830307 | − | 0.191270i | ||||
\(737\) | − | 0.107100i | − | 0.00394507i | ||||||
\(738\) | −32.2401 | − | 18.0987i | −1.18677 | − | 0.666221i | ||||
\(739\) | −21.1541 | −0.778167 | −0.389083 | − | 0.921203i | \(-0.627208\pi\) | ||||
−0.389083 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(740\) | −7.07020 | + | 3.66270i | −0.259906 | + | 0.134643i | ||||
\(741\) | 0.185855 | + | 10.6570i | 0.00682756 | + | 0.391495i | ||||
\(742\) | −28.1373 | − | 17.1123i | −1.03295 | − | 0.628213i | ||||
\(743\) | −26.8675 | −0.985673 | −0.492837 | − | 0.870122i | \(-0.664040\pi\) | ||||
−0.492837 | + | 0.870122i | \(0.664040\pi\) | |||||||
\(744\) | −0.870121 | + | 17.0503i | −0.0319002 | + | 0.625096i | ||||
\(745\) | −16.0105 | −0.586579 | ||||||||
\(746\) | −23.7261 | − | 14.4296i | −0.868674 | − | 0.528304i | ||||
\(747\) | 0.0832134 | + | 2.38502i | 0.00304462 | + | 0.0872632i | ||||
\(748\) | 3.47257 | + | 6.70319i | 0.126970 | + | 0.245093i | ||||
\(749\) | −27.7017 | −1.01220 | ||||||||
\(750\) | 9.95784 | − | 17.0355i | 0.363609 | − | 0.622049i | ||||
\(751\) | 6.80908i | 0.248467i | 0.992253 | + | 0.124233i | \(0.0396472\pi\) | ||||
−0.992253 | + | 0.124233i | \(0.960353\pi\) | |||||||
\(752\) | 17.7226 | − | 25.0979i | 0.646277 | − | 0.915228i | ||||
\(753\) | −0.426711 | − | 24.4678i | −0.0155502 | − | 0.891656i | ||||
\(754\) | −3.45867 | − | 2.10347i | −0.125957 | − | 0.0766038i | ||||
\(755\) | − | 4.92839i | − | 0.179363i | ||||||
\(756\) | 27.7226 | − | 16.2541i | 1.00826 | − | 0.591157i | ||||
\(757\) | − | 5.76958i | − | 0.209699i | −0.994488 | − | 0.104849i | \(-0.966564\pi\) | ||
0.994488 | − | 0.104849i | \(-0.0334361\pi\) | |||||||
\(758\) | 10.2268 | − | 16.8156i | 0.371454 | − | 0.610770i | ||||
\(759\) | −0.0574892 | − | 3.29645i | −0.00208673 | − | 0.119654i | ||||
\(760\) | 12.2233 | + | 0.837702i | 0.443386 | + | 0.0303866i | ||||
\(761\) | − | 39.7502i | − | 1.44095i | −0.693483 | − | 0.720473i | \(-0.743925\pi\) | ||
0.693483 | − | 0.720473i | \(-0.256075\pi\) | |||||||
\(762\) | 14.6110 | + | 8.54061i | 0.529300 | + | 0.309394i | ||||
\(763\) | −28.9138 | −1.04675 | ||||||||
\(764\) | 13.4379 | + | 25.9394i | 0.486165 | + | 0.938455i | ||||
\(765\) | −0.180850 | − | 5.18343i | −0.00653866 | − | 0.187407i | ||||
\(766\) | −20.0122 | + | 32.9054i | −0.723069 | + | 1.18892i | ||||
\(767\) | −15.1253 | −0.546141 | ||||||||
\(768\) | 9.72533 | + | 25.9503i | 0.350933 | + | 0.936401i | ||||
\(769\) | 44.3637 | 1.59980 | 0.799898 | − | 0.600136i | \(-0.204887\pi\) | ||||
0.799898 | + | 0.600136i | \(0.204887\pi\) | |||||||
\(770\) | 3.77115 | − | 6.20079i | 0.135903 | − | 0.223461i | ||||
\(771\) | 0.401495 | + | 23.0219i | 0.0144595 | + | 0.829112i | ||||
\(772\) | 5.04613 | + | 9.74067i | 0.181614 | + | 0.350574i | ||||
\(773\) | 20.9167 | 0.752321 | 0.376161 | − | 0.926554i | \(-0.377244\pi\) | ||||
0.376161 | + | 0.926554i | \(0.377244\pi\) | |||||||
\(774\) | 6.78667 | − | 12.0895i | 0.243942 | − | 0.434546i | ||||
\(775\) | 14.7757i | 0.530758i | ||||||||
\(776\) | 25.5436 | + | 1.75059i | 0.916962 | + | 0.0628424i | ||||
\(777\) | −24.4549 | + | 0.426486i | −0.877314 | + | 0.0153001i | ||||
\(778\) | −0.145692 | + | 0.239557i | −0.00522332 | + | 0.00858854i | ||||
\(779\) | − | 43.2982i | − | 1.55132i | ||||||
\(780\) | 3.29089 | − | 1.77830i | 0.117833 | − | 0.0636732i | ||||
\(781\) | − | 14.9395i | − | 0.534578i | ||||||
\(782\) | −2.39606 | − | 1.45722i | −0.0856830 | − | 0.0521101i | ||||
\(783\) | −11.9924 | + | 0.627940i | −0.428572 | + | 0.0224408i | ||||
\(784\) | 5.91216 | − | 8.37252i | 0.211148 | − | 0.299019i | ||||
\(785\) | 15.4129i | 0.550110i | ||||||||
\(786\) | 26.5853 | + | 15.5400i | 0.948268 | + | 0.554294i | ||||
\(787\) | −52.1207 | −1.85790 | −0.928951 | − | 0.370202i | \(-0.879289\pi\) | ||||
−0.928951 | + | 0.370202i | \(0.879289\pi\) | |||||||
\(788\) | 20.1124 | + | 38.8235i | 0.716475 | + | 1.38303i | ||||
\(789\) | 43.9733 | − | 0.766883i | 1.56549 | − | 0.0273017i | ||||
\(790\) | −5.37946 | − | 3.27164i | −0.191393 | − | 0.116400i | ||||
\(791\) | 4.55036 | 0.161792 | ||||||||
\(792\) | −0.541793 | + | 16.1426i | −0.0192518 | + | 0.573603i | ||||
\(793\) | −13.3734 | −0.474903 | ||||||||
\(794\) | 15.5278 | + | 9.44359i | 0.551061 | + | 0.335140i | ||||
\(795\) | −11.3699 | + | 0.198288i | −0.403248 | + | 0.00703254i | ||||
\(796\) | 34.7995 | − | 18.0278i | 1.23343 | − | 0.638978i | ||||
\(797\) | 35.1231 | 1.24412 | 0.622062 | − | 0.782968i | \(-0.286295\pi\) | ||||
0.622062 | + | 0.782968i | \(0.286295\pi\) | |||||||
\(798\) | 32.4906 | + | 18.9919i | 1.15016 | + | 0.672304i | ||||
\(799\) | − | 15.2317i | − | 0.538859i | ||||||
\(800\) | 9.55064 | + | 22.0009i | 0.337666 | + | 0.777849i | ||||
\(801\) | 1.81876 | + | 52.1283i | 0.0642627 | + | 1.84186i | ||||
\(802\) | −28.1775 | − | 17.1368i | −0.994983 | − | 0.605122i | ||||
\(803\) | − | 13.4158i | − | 0.473432i | ||||||
\(804\) | −0.0926588 | − | 0.171473i | −0.00326782 | − | 0.00604739i | ||||
\(805\) | 2.69600i | 0.0950216i | ||||||||
\(806\) | −3.17184 | + | 5.21535i | −0.111723 | + | 0.183703i | ||||
\(807\) | 4.48318 | − | 0.0781855i | 0.157816 | − | 0.00275226i | ||||
\(808\) | −55.2528 | − | 3.78665i | −1.94379 | − | 0.133214i | ||||
\(809\) | − | 11.2110i | − | 0.394157i | −0.980388 | − | 0.197078i | \(-0.936855\pi\) | ||
0.980388 | − | 0.197078i | \(-0.0631454\pi\) | |||||||
\(810\) | 5.09129 | − | 9.85982i | 0.178890 | − | 0.346439i | ||||
\(811\) | −23.2309 | −0.815746 | −0.407873 | − | 0.913039i | \(-0.633729\pi\) | ||||
−0.407873 | + | 0.913039i | \(0.633729\pi\) | |||||||
\(812\) | −12.6913 | + | 6.57471i | −0.445378 | + | 0.230727i | ||||
\(813\) | −0.891365 | − | 51.1112i | −0.0312615 | − | 1.79255i | ||||
\(814\) | 6.38766 | − | 10.5030i | 0.223887 | − | 0.368131i | ||||
\(815\) | 13.4401 | 0.470786 | ||||||||
\(816\) | 11.3592 | + | 7.72787i | 0.397650 | + | 0.270529i | ||||
\(817\) | 16.2360 | 0.568027 | ||||||||
\(818\) | −2.13835 | + | 3.51602i | −0.0747657 | + | 0.122935i | ||||
\(819\) | 11.4830 | − | 0.400644i | 0.401250 | − | 0.0139996i | ||||
\(820\) | −13.4924 | + | 6.98971i | −0.471175 | + | 0.244091i | ||||
\(821\) | −8.28219 | −0.289050 | −0.144525 | − | 0.989501i | \(-0.546165\pi\) | ||||
−0.144525 | + | 0.989501i | \(0.546165\pi\) | |||||||
\(822\) | −3.77443 | − | 2.20628i | −0.131648 | − | 0.0769529i | ||||
\(823\) | 17.0583i | 0.594616i | 0.954782 | + | 0.297308i | \(0.0960889\pi\) | ||||
−0.954782 | + | 0.297308i | \(0.903911\pi\) | |||||||
\(824\) | 0.572452 | − | 8.35291i | 0.0199423 | − | 0.290987i | ||||
\(825\) | 0.243748 | + | 13.9766i | 0.00848622 | + | 0.486603i | ||||
\(826\) | −27.7505 | + | 45.6293i | −0.965564 | + | 1.58765i | ||||
\(827\) | 11.3622i | 0.395101i | 0.980293 | + | 0.197551i | \(0.0632987\pi\) | ||||
−0.980293 | + | 0.197551i | \(0.936701\pi\) | |||||||
\(828\) | −2.94401 | − | 5.22808i | −0.102312 | − | 0.181688i | ||||
\(829\) | 33.5403i | 1.16490i | 0.812865 | + | 0.582452i | \(0.197906\pi\) | ||||
−0.812865 | + | 0.582452i | \(0.802094\pi\) | |||||||
\(830\) | 0.838004 | + | 0.509652i | 0.0290876 | + | 0.0176903i | ||||
\(831\) | 0.0328444 | + | 1.88331i | 0.00113936 | + | 0.0653314i | ||||
\(832\) | −1.35177 | + | 9.81583i | −0.0468642 | + | 0.340303i | ||||
\(833\) | − | 5.08121i | − | 0.176053i | ||||||
\(834\) | 7.30358 | − | 12.4947i | 0.252902 | − | 0.432657i | ||||
\(835\) | −7.88928 | −0.273020 | ||||||||
\(836\) | −16.7951 | + | 8.70065i | −0.580870 | + | 0.300918i | ||||
\(837\) | 0.946876 | + | 18.0834i | 0.0327288 | + | 0.625053i | ||||
\(838\) | −19.2658 | − | 11.7169i | −0.665524 | − | 0.404754i | ||||
\(839\) | −0.880528 | −0.0303992 | −0.0151996 | − | 0.999884i | \(-0.504838\pi\) | ||||
−0.0151996 | + | 0.999884i | \(0.504838\pi\) | |||||||
\(840\) | 0.673144 | − | 13.1905i | 0.0232257 | − | 0.455115i | ||||
\(841\) | −23.6588 | −0.815822 | ||||||||
\(842\) | 37.0696 | + | 22.5447i | 1.27750 | + | 0.776942i | ||||
\(843\) | 0.0986881 | + | 5.65881i | 0.00339900 | + | 0.194900i | ||||
\(844\) | −9.03613 | − | 17.4427i | −0.311036 | − | 0.600401i | ||||
\(845\) | −9.99650 | −0.343890 | ||||||||
\(846\) | 15.9524 | − | 28.4169i | 0.548455 | − | 0.976992i | ||||
\(847\) | − | 22.8111i | − | 0.783797i | ||||||
\(848\) | 17.3751 | − | 24.6058i | 0.596662 | − | 0.844966i | ||||
\(849\) | −11.0336 | + | 0.192422i | −0.378671 | + | 0.00660391i | ||||
\(850\) | 10.1590 | + | 6.17846i | 0.348452 | + | 0.211919i | ||||
\(851\) | 4.56655i | 0.156539i | ||||||||
\(852\) | −12.9251 | − | 23.9191i | −0.442808 | − | 0.819454i | ||||
\(853\) | 51.3054i | 1.75666i | 0.478052 | + | 0.878331i | \(0.341343\pi\) | ||||
−0.478052 | + | 0.878331i | \(0.658657\pi\) | |||||||
\(854\) | −24.5363 | + | 40.3443i | −0.839617 | + | 1.38056i | ||||
\(855\) | 12.9873 | − | 0.453127i | 0.444155 | − | 0.0154966i | ||||
\(856\) | 1.73242 | − | 25.2785i | 0.0592128 | − | 0.864001i | ||||
\(857\) | 20.2353i | 0.691224i | 0.938378 | + | 0.345612i | \(0.112329\pi\) | ||||
−0.938378 | + | 0.345612i | \(0.887671\pi\) | |||||||
\(858\) | −2.91427 | + | 4.98563i | −0.0994914 | + | 0.170206i | ||||
\(859\) | −23.4886 | −0.801421 | −0.400710 | − | 0.916205i | \(-0.631237\pi\) | ||||
−0.400710 | + | 0.916205i | \(0.631237\pi\) | |||||||
\(860\) | −2.62101 | − | 5.05941i | −0.0893759 | − | 0.172524i | ||||
\(861\) | −46.6685 | + | 0.813885i | −1.59046 | + | 0.0277371i | ||||
\(862\) | −26.1759 | + | 43.0403i | −0.891556 | + | 1.46596i | ||||
\(863\) | 4.02794 | 0.137113 | 0.0685563 | − | 0.997647i | \(-0.478161\pi\) | ||||
0.0685563 | + | 0.997647i | \(0.478161\pi\) | |||||||
\(864\) | 13.0986 | + | 26.3140i | 0.445622 | + | 0.895221i | ||||
\(865\) | −2.47365 | −0.0841066 | ||||||||
\(866\) | −2.31924 | + | 3.81346i | −0.0788111 | + | 0.129587i | ||||
\(867\) | −22.6305 | + | 0.394669i | −0.768571 | + | 0.0134037i | ||||
\(868\) | 9.91406 | + | 19.1373i | 0.336505 | + | 0.649564i | ||||
\(869\) | 9.72028 | 0.329738 | ||||||||
\(870\) | −2.49067 | + | 4.26095i | −0.0844415 | + | 0.144460i | ||||
\(871\) | − | 0.0696872i | − | 0.00236126i | ||||||
\(872\) | 1.80822 | − | 26.3846i | 0.0612341 | − | 0.893495i | ||||
\(873\) | 27.1401 | − | 0.946921i | 0.918554 | − | 0.0320484i | ||||
\(874\) | 3.65112 | − | 6.00341i | 0.123501 | − | 0.203068i | ||||
\(875\) | − | 24.9108i | − | 0.842138i | ||||||
\(876\) | −11.6068 | − | 21.4794i | −0.392159 | − | 0.725723i | ||||
\(877\) | 37.8678i | 1.27870i | 0.768914 | + | 0.639352i | \(0.220798\pi\) | ||||
−0.768914 | + | 0.639352i | \(0.779202\pi\) | |||||||
\(878\) | −33.6145 | − | 20.4434i | −1.13443 | − | 0.689933i | ||||
\(879\) | 42.4840 | − | 0.740910i | 1.43295 | − | 0.0249903i | ||||
\(880\) | 5.42253 | + | 3.82905i | 0.182793 | + | 0.129077i | ||||
\(881\) | 48.6628i | 1.63949i | 0.572727 | + | 0.819746i | \(0.305885\pi\) | ||||
−0.572727 | + | 0.819746i | \(0.694115\pi\) | |||||||
\(882\) | 5.32163 | − | 9.47969i | 0.179188 | − | 0.319198i | ||||
\(883\) | −6.80087 | −0.228868 | −0.114434 | − | 0.993431i | \(-0.536505\pi\) | ||||
−0.114434 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(884\) | 2.25952 | + | 4.36160i | 0.0759959 | + | 0.146697i | ||||
\(885\) | 0.321557 | + | 18.4382i | 0.0108090 | + | 0.619793i | ||||
\(886\) | −7.89367 | − | 4.80072i | −0.265193 | − | 0.161283i | ||||
\(887\) | −2.86430 | −0.0961737 | −0.0480869 | − | 0.998843i | \(-0.515312\pi\) | ||||
−0.0480869 | + | 0.998843i | \(0.515312\pi\) | |||||||
\(888\) | 1.14019 | − | 22.3423i | 0.0382621 | − | 0.749760i | ||||
\(889\) | 21.3654 | 0.716573 | ||||||||
\(890\) | 18.3159 | + | 11.1392i | 0.613950 | + | 0.373388i | ||||
\(891\) | 1.19398 | + | 17.0898i | 0.0399999 | + | 0.572530i | ||||
\(892\) | −9.54234 | + | 4.94339i | −0.319501 | + | 0.165517i | ||||
\(893\) | 38.1636 | 1.27710 | ||||||||
\(894\) | 22.7001 | − | 38.8346i | 0.759205 | − | 1.29882i | ||||
\(895\) | 9.22707i | 0.308427i | ||||||||
\(896\) | 27.1319 | + | 22.0872i | 0.906413 | + | 0.737882i | ||||
\(897\) | −0.0374068 | − | 2.14492i | −0.00124898 | − | 0.0716168i | ||||
\(898\) | 30.7961 | + | 18.7294i | 1.02768 | + | 0.625007i | ||||
\(899\) | − | 8.05397i | − | 0.268615i | ||||||
\(900\) | 12.4823 | + | 22.1665i | 0.416077 | + | 0.738883i | ||||
\(901\) | − | 14.9330i | − | 0.497491i | ||||||
\(902\) | 12.1899 | − | 20.0434i | 0.405879 | − | 0.667374i | ||||
\(903\) | −0.305192 | − | 17.4998i | −0.0101562 | − | 0.582358i | ||||
\(904\) | −0.284572 | + | 4.15232i | −0.00946471 | + | 0.138104i | ||||
\(905\) | 7.50224i | 0.249383i | ||||||||
\(906\) | 11.9542 | + | 6.98761i | 0.397151 | + | 0.232148i | ||||
\(907\) | −19.3695 | −0.643153 | −0.321576 | − | 0.946884i | \(-0.604213\pi\) | ||||
−0.321576 | + | 0.946884i | \(0.604213\pi\) | |||||||
\(908\) | −40.9398 | + | 21.2088i | −1.35863 | + | 0.703838i | ||||
\(909\) | −58.7062 | + | 2.04826i | −1.94716 | + | 0.0679366i | ||||
\(910\) | 2.45380 | − | 4.03470i | 0.0813426 | − | 0.133749i | ||||
\(911\) | −22.5365 | −0.746668 | −0.373334 | − | 0.927697i | \(-0.621785\pi\) | ||||
−0.373334 | + | 0.927697i | \(0.621785\pi\) | |||||||
\(912\) | −19.3624 | + | 28.4608i | −0.641154 | + | 0.942430i | ||||
\(913\) | −1.51421 | −0.0501131 | ||||||||
\(914\) | −1.76575 | + | 2.90337i | −0.0584059 | + | 0.0960349i | ||||
\(915\) | 0.284313 | + | 16.3026i | 0.00939909 | + | 0.538947i | ||||
\(916\) | −48.3498 | + | 25.0475i | −1.59752 | + | 0.827593i | ||||
\(917\) | 38.8753 | 1.28378 | ||||||||
\(918\) | 12.8292 | + | 6.91055i | 0.423427 | + | 0.228082i | ||||
\(919\) | − | 47.7774i | − | 1.57603i | −0.615656 | − | 0.788015i | \(-0.711109\pi\) | ||
0.615656 | − | 0.788015i | \(-0.288891\pi\) | |||||||
\(920\) | −2.46017 | − | 0.168603i | −0.0811093 | − | 0.00555868i | ||||
\(921\) | −11.2439 | + | 0.196091i | −0.370500 | + | 0.00646142i | ||||
\(922\) | 10.3348 | − | 16.9932i | 0.340359 | − | 0.559641i | ||||
\(923\) | − | 9.72079i | − | 0.319964i | ||||||
\(924\) | 9.69360 | + | 17.9388i | 0.318896 | + | 0.590145i | ||||
\(925\) | − | 19.3617i | − | 0.636608i | ||||||
\(926\) | −43.2196 | − | 26.2850i | −1.42028 | − | 0.863778i | ||||
\(927\) | −0.309649 | − | 8.87498i | −0.0101702 | − | 0.291493i | ||||
\(928\) | −5.20589 | − | 11.9923i | −0.170892 | − | 0.393667i | ||||
\(929\) | − | 40.9144i | − | 1.34236i | −0.741295 | − | 0.671179i | \(-0.765788\pi\) | ||
0.741295 | − | 0.671179i | \(-0.234212\pi\) | |||||||
\(930\) | 6.42511 | + | 3.75569i | 0.210688 | + | 0.123154i | ||||
\(931\) | 12.7311 | 0.417246 | ||||||||
\(932\) | −38.3891 | + | 19.8874i | −1.25748 | + | 0.651433i | ||||
\(933\) | 45.6365 | − | 0.795887i | 1.49407 | − | 0.0260562i | ||||
\(934\) | 47.5296 | + | 28.9063i | 1.55522 | + | 0.945842i | ||||
\(935\) | 3.29088 | 0.107623 | ||||||||
\(936\) | −0.352531 | + | 10.5036i | −0.0115228 | + | 0.343321i | ||||
\(937\) | 27.6662 | 0.903814 | 0.451907 | − | 0.892065i | \(-0.350744\pi\) | ||||
0.451907 | + | 0.892065i | \(0.350744\pi\) | |||||||
\(938\) | −0.210230 | − | 0.127856i | −0.00686424 | − | 0.00417465i | ||||
\(939\) | 57.5237 | − | 1.00320i | 1.87721 | − | 0.0327381i | ||||
\(940\) | −6.16083 | − | 11.8924i | −0.200944 | − | 0.387887i | ||||
\(941\) | −6.59325 | −0.214934 | −0.107467 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107467 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(942\) | −37.3851 | − | 21.8528i | −1.21807 | − | 0.712004i | ||||
\(943\) | 8.71457i | 0.283785i | ||||||||
\(944\) | −39.9024 | − | 28.1766i | −1.29871 | − | 0.917070i | ||||
\(945\) | −0.732522 | − | 13.9897i | −0.0238290 | − | 0.455084i | ||||
\(946\) | 7.51593 | + | 4.57099i | 0.244364 | + | 0.148616i | ||||
\(947\) | 48.2638i | 1.56836i | 0.620531 | + | 0.784182i | \(0.286917\pi\) | ||||
−0.620531 | + | 0.784182i | \(0.713083\pi\) | |||||||
\(948\) | 15.5628 | − | 8.40964i | 0.505455 | − | 0.273132i | ||||
\(949\) | − | 8.72931i | − | 0.283366i | ||||||
\(950\) | −15.4803 | + | 25.4538i | −0.502249 | + | 0.825831i | ||||
\(951\) | −36.9330 | + | 0.644101i | −1.19763 | + | 0.0208864i | ||||
\(952\) | 17.3035 | + | 1.18586i | 0.560809 | + | 0.0384341i | ||||
\(953\) | − | 48.2640i | − | 1.56342i | −0.623640 | − | 0.781712i | \(-0.714347\pi\) | ||
0.623640 | − | 0.781712i | \(-0.285653\pi\) | |||||||
\(954\) | 15.6396 | − | 27.8596i | 0.506350 | − | 0.901988i | ||||
\(955\) | 12.7348 | 0.412087 | ||||||||
\(956\) | −16.2630 | − | 31.3930i | −0.525985 | − | 1.01532i | ||||
\(957\) | −0.132863 | − | 7.61841i | −0.00429485 | − | 0.246268i | ||||
\(958\) | −1.58838 | + | 2.61173i | −0.0513184 | + | 0.0843812i | ||||
\(959\) | −5.51929 | −0.178227 | ||||||||
\(960\) | 11.9946 | + | 1.43917i | 0.387122 | + | 0.0464490i | ||||
\(961\) | 18.8554 | 0.608237 | ||||||||
\(962\) | 4.15629 | − | 6.83406i | 0.134004 | − | 0.220339i | ||||
\(963\) | −0.937092 | − | 26.8584i | −0.0301974 | − | 0.865501i | ||||
\(964\) | 15.0365 | + | 29.0253i | 0.484293 | + | 0.934842i | ||||
\(965\) | 4.78211 | 0.153942 | ||||||||
\(966\) | −6.53934 | − | 3.82247i | −0.210400 | − | 0.122986i | ||||
\(967\) | 51.1796i | 1.64583i | 0.568168 | + | 0.822913i | \(0.307652\pi\) | ||||
−0.568168 | + | 0.822913i | \(0.692348\pi\) | |||||||
\(968\) | 20.8156 | + | 1.42656i | 0.669040 | + | 0.0458515i | ||||
\(969\) | 0.297565 | + | 17.0625i | 0.00955915 | + | 0.548125i | ||||
\(970\) | 5.79954 | − | 9.53601i | 0.186212 | − | 0.306183i | ||||
\(971\) | − | 31.6471i | − | 1.01560i | −0.861474 | − | 0.507802i | \(-0.830458\pi\) | ||
0.861474 | − | 0.507802i | \(-0.169542\pi\) | |||||||
\(972\) | 16.6971 | + | 26.3288i | 0.535560 | + | 0.844497i | ||||
\(973\) | − | 18.2708i | − | 0.585736i | ||||||
\(974\) | −34.0880 | − | 20.7314i | −1.09225 | − | 0.664277i | ||||
\(975\) | 0.158601 | + | 9.09423i | 0.00507929 | + | 0.291249i | ||||
\(976\) | −35.2807 | − | 24.9131i | −1.12931 | − | 0.797448i | ||||
\(977\) | − | 25.9886i | − | 0.831448i | −0.909491 | − | 0.415724i | \(-0.863528\pi\) | ||
0.909491 | − | 0.415724i | \(-0.136472\pi\) | |||||||
\(978\) | −19.0557 | + | 32.5999i | −0.609335 | + | 1.04243i | ||||
\(979\) | −33.0954 | −1.05773 | ||||||||
\(980\) | −2.05521 | − | 3.96723i | −0.0656514 | − | 0.126728i | ||||
\(981\) | −0.978096 | − | 28.0337i | −0.0312282 | − | 0.895046i | ||||
\(982\) | 6.83236 | + | 4.15526i | 0.218029 | + | 0.132600i | ||||
\(983\) | 39.6637 | 1.26507 | 0.632537 | − | 0.774530i | \(-0.282014\pi\) | ||||
0.632537 | + | 0.774530i | \(0.282014\pi\) | |||||||
\(984\) | 2.17587 | − | 42.6370i | 0.0693643 | − | 1.35922i | ||||
\(985\) | 19.0601 | 0.607305 | ||||||||
\(986\) | −5.53752 | − | 3.36777i | −0.176351 | − | 0.107252i | ||||
\(987\) | −0.717369 | − | 41.1342i | −0.0228341 | − | 1.30932i | ||||
\(988\) | −10.9282 | + | 5.66130i | −0.347671 | + | 0.180110i | ||||
\(989\) | −3.26780 | −0.103910 | ||||||||
\(990\) | 6.13960 | + | 3.44659i | 0.195129 | + | 0.109540i | ||||
\(991\) | 13.4539i | 0.427378i | 0.976902 | + | 0.213689i | \(0.0685480\pi\) | ||||
−0.976902 | + | 0.213689i | \(0.931452\pi\) | |||||||
\(992\) | −18.0833 | + | 7.85000i | −0.574145 | + | 0.249238i | ||||
\(993\) | 12.3821 | − | 0.215940i | 0.392934 | − | 0.00685266i | ||||
\(994\) | −29.3253 | − | 17.8349i | −0.930142 | − | 0.565687i | ||||
\(995\) | − | 17.0846i | − | 0.541617i | ||||||
\(996\) | −2.42434 | + | 1.31004i | −0.0768182 | + | 0.0415102i | ||||
\(997\) | 57.2452i | 1.81297i | 0.422234 | + | 0.906487i | \(0.361246\pi\) | ||||
−0.422234 | + | 0.906487i | \(0.638754\pi\) | |||||||
\(998\) | −22.8985 | + | 37.6512i | −0.724838 | + | 1.19183i | ||||
\(999\) | −1.24076 | − | 23.6960i | −0.0392560 | − | 0.749708i |
(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 | 552.2.j.d.323.16 | yes | 42 | |
3.2 | odd | 2 | 552.2.j.c.323.27 | ✓ | 42 | ||
4.3 | odd | 2 | 2208.2.j.d.47.41 | 42 | |||
8.3 | odd | 2 | 552.2.j.c.323.28 | yes | 42 | ||
8.5 | even | 2 | 2208.2.j.c.47.41 | 42 | |||
12.11 | even | 2 | 2208.2.j.c.47.42 | 42 | |||
24.5 | odd | 2 | 2208.2.j.d.47.42 | 42 | |||
24.11 | even | 2 | inner | 552.2.j.d.323.15 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.j.c.323.27 | ✓ | 42 | 3.2 | odd | 2 | ||
552.2.j.c.323.28 | yes | 42 | 8.3 | odd | 2 | ||
552.2.j.d.323.15 | yes | 42 | 24.11 | even | 2 | inner | |
552.2.j.d.323.16 | yes | 42 | 1.1 | even | 1 | trivial | |
2208.2.j.c.47.41 | 42 | 8.5 | even | 2 | |||
2208.2.j.c.47.42 | 42 | 12.11 | even | 2 | |||
2208.2.j.d.47.41 | 42 | 4.3 | odd | 2 | |||
2208.2.j.d.47.42 | 42 | 24.5 | odd | 2 |