Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.1 | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.h.683.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.73016 | + | 0.0809240i | −0.998908 | + | 0.0467215i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.662050 | − | 2.13581i | −0.296078 | − | 0.955164i | ||||
\(6\) | 1.16619 | − | 1.28063i | 0.476093 | − | 0.522815i | ||||
\(7\) | 2.89525 | + | 2.89525i | 1.09430 | + | 1.09430i | 0.995064 | + | 0.0992373i | \(0.0316403\pi\) |
0.0992373 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.98690 | − | 0.280023i | 0.995634 | − | 0.0933409i | ||||
\(10\) | 1.97839 | + | 1.04211i | 0.625621 | + | 0.329543i | ||||
\(11\) | − | 1.62335i | − | 0.489460i | −0.969591 | − | 0.244730i | \(-0.921301\pi\) | ||
0.969591 | − | 0.244730i | \(-0.0786993\pi\) | |||||||
\(12\) | 0.0809240 | + | 1.73016i | 0.0233607 | + | 0.499454i | ||||
\(13\) | −1.74736 | + | 1.74736i | −0.484631 | + | 0.484631i | −0.906607 | − | 0.421976i | \(-0.861337\pi\) |
0.421976 | + | 0.906607i | \(0.361337\pi\) | |||||||
\(14\) | −4.09450 | −1.09430 | ||||||||
\(15\) | 1.31829 | + | 3.64172i | 0.340381 | + | 0.940288i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.396012 | + | 0.396012i | −0.0960470 | + | 0.0960470i | −0.753498 | − | 0.657451i | \(-0.771635\pi\) |
0.657451 | + | 0.753498i | \(0.271635\pi\) | |||||||
\(18\) | −1.91405 | + | 2.31007i | −0.451147 | + | 0.544488i | ||||
\(19\) | − | 4.55776i | − | 1.04562i | −0.852449 | − | 0.522811i | \(-0.824883\pi\) | ||
0.852449 | − | 0.522811i | \(-0.175117\pi\) | |||||||
\(20\) | −2.13581 | + | 0.662050i | −0.477582 | + | 0.148039i | ||||
\(21\) | −5.24354 | − | 4.77495i | −1.14423 | − | 1.04198i | ||||
\(22\) | 1.14789 | + | 1.14789i | 0.244730 | + | 0.244730i | ||||
\(23\) | 0.0718525 | + | 0.0718525i | 0.0149823 | + | 0.0149823i | 0.714558 | − | 0.699576i | \(-0.246628\pi\) |
−0.699576 | + | 0.714558i | \(0.746628\pi\) | |||||||
\(24\) | −1.28063 | − | 1.16619i | −0.261407 | − | 0.238047i | ||||
\(25\) | −4.12338 | + | 2.82803i | −0.824676 | + | 0.565605i | ||||
\(26\) | − | 2.47114i | − | 0.484631i | ||||||
\(27\) | −5.14516 | + | 0.726196i | −0.990186 | + | 0.139756i | ||||
\(28\) | 2.89525 | − | 2.89525i | 0.547151 | − | 0.547151i | ||||
\(29\) | 3.20334 | 0.594845 | 0.297422 | − | 0.954746i | \(-0.403873\pi\) | ||||
0.297422 | + | 0.954746i | \(0.403873\pi\) | |||||||
\(30\) | −3.50726 | − | 1.64291i | −0.640334 | − | 0.299953i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.131368 | + | 2.80866i | 0.0228683 | + | 0.488925i | ||||
\(34\) | − | 0.560046i | − | 0.0960470i | ||||||
\(35\) | 4.26691 | − | 8.10050i | 0.721239 | − | 1.36923i | ||||
\(36\) | −0.280023 | − | 2.98690i | −0.0466705 | − | 0.497817i | ||||
\(37\) | 5.51900 | + | 5.51900i | 0.907319 | + | 0.907319i | 0.996055 | − | 0.0887366i | \(-0.0282829\pi\) |
−0.0887366 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(38\) | 3.22282 | + | 3.22282i | 0.522811 | + | 0.522811i | ||||
\(39\) | 2.88181 | − | 3.16462i | 0.461459 | − | 0.506745i | ||||
\(40\) | 1.04211 | − | 1.97839i | 0.164772 | − | 0.312810i | ||||
\(41\) | 4.20851i | 0.657258i | 0.944459 | + | 0.328629i | \(0.106587\pi\) | ||||
−0.944459 | + | 0.328629i | \(0.893413\pi\) | |||||||
\(42\) | 7.08414 | − | 0.331343i | 1.09311 | − | 0.0511274i | ||||
\(43\) | 7.67725 | − | 7.67725i | 1.17077 | − | 1.17077i | 0.188744 | − | 0.982026i | \(-0.439558\pi\) |
0.982026 | − | 0.188744i | \(-0.0604417\pi\) | |||||||
\(44\) | −1.62335 | −0.244730 | ||||||||
\(45\) | −2.57555 | − | 6.19407i | −0.383941 | − | 0.923358i | ||||
\(46\) | −0.101615 | −0.0149823 | ||||||||
\(47\) | 6.63515 | − | 6.63515i | 0.967835 | − | 0.967835i | −0.0316631 | − | 0.999499i | \(-0.510080\pi\) |
0.999499 | + | 0.0316631i | \(0.0100804\pi\) | |||||||
\(48\) | 1.73016 | − | 0.0809240i | 0.249727 | − | 0.0116804i | ||||
\(49\) | 9.76493i | 1.39499i | ||||||||
\(50\) | 0.915953 | − | 4.91539i | 0.129535 | − | 0.695141i | ||||
\(51\) | 0.653117 | − | 0.717211i | 0.0914547 | − | 0.100430i | ||||
\(52\) | 1.74736 | + | 1.74736i | 0.242316 | + | 0.242316i | ||||
\(53\) | −2.49463 | − | 2.49463i | −0.342664 | − | 0.342664i | 0.514704 | − | 0.857368i | \(-0.327902\pi\) |
−0.857368 | + | 0.514704i | \(0.827902\pi\) | |||||||
\(54\) | 3.12468 | − | 4.15167i | 0.425215 | − | 0.564971i | ||||
\(55\) | −3.46718 | + | 1.07474i | −0.467514 | + | 0.144918i | ||||
\(56\) | 4.09450i | 0.547151i | ||||||||
\(57\) | 0.368832 | + | 7.88565i | 0.0488530 | + | 1.04448i | ||||
\(58\) | −2.26510 | + | 2.26510i | −0.297422 | + | 0.297422i | ||||
\(59\) | 6.90534 | 0.898998 | 0.449499 | − | 0.893281i | \(-0.351602\pi\) | ||||
0.449499 | + | 0.893281i | \(0.351602\pi\) | |||||||
\(60\) | 3.64172 | − | 1.31829i | 0.470144 | − | 0.170191i | ||||
\(61\) | 8.74025 | 1.11907 | 0.559537 | − | 0.828805i | \(-0.310979\pi\) | ||||
0.559537 | + | 0.828805i | \(0.310979\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | 9.45856 | + | 7.83709i | 1.19167 | + | 0.987381i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 4.88888 | + | 2.57520i | 0.606391 | + | 0.319414i | ||||
\(66\) | −2.07892 | − | 1.89313i | −0.255897 | − | 0.233029i | ||||
\(67\) | 7.82013 | + | 7.82013i | 0.955381 | + | 0.955381i | 0.999046 | − | 0.0436654i | \(-0.0139036\pi\) |
−0.0436654 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(68\) | 0.396012 | + | 0.396012i | 0.0480235 | + | 0.0480235i | ||||
\(69\) | −0.130131 | − | 0.118502i | −0.0156659 | − | 0.0142659i | ||||
\(70\) | 2.71076 | + | 8.74508i | 0.323998 | + | 1.04524i | ||||
\(71\) | − | 7.38175i | − | 0.876053i | −0.898962 | − | 0.438026i | \(-0.855678\pi\) | ||
0.898962 | − | 0.438026i | \(-0.144322\pi\) | |||||||
\(72\) | 2.31007 | + | 1.91405i | 0.272244 | + | 0.225573i | ||||
\(73\) | 7.37382 | − | 7.37382i | 0.863040 | − | 0.863040i | −0.128650 | − | 0.991690i | \(-0.541064\pi\) |
0.991690 | + | 0.128650i | \(0.0410643\pi\) | |||||||
\(74\) | −7.80505 | −0.907319 | ||||||||
\(75\) | 6.90525 | − | 5.22662i | 0.797350 | − | 0.603518i | ||||
\(76\) | −4.55776 | −0.522811 | ||||||||
\(77\) | 4.70002 | − | 4.70002i | 0.535617 | − | 0.535617i | ||||
\(78\) | 0.199975 | + | 4.27547i | 0.0226427 | + | 0.484102i | ||||
\(79\) | − | 0.229093i | − | 0.0257750i | −0.999917 | − | 0.0128875i | \(-0.995898\pi\) | ||
0.999917 | − | 0.0128875i | \(-0.00410233\pi\) | |||||||
\(80\) | 0.662050 | + | 2.13581i | 0.0740194 | + | 0.238791i | ||||
\(81\) | 8.84317 | − | 1.67280i | 0.982575 | − | 0.185867i | ||||
\(82\) | −2.97586 | − | 2.97586i | −0.328629 | − | 0.328629i | ||||
\(83\) | −0.833196 | − | 0.833196i | −0.0914551 | − | 0.0914551i | 0.659899 | − | 0.751354i | \(-0.270599\pi\) |
−0.751354 | + | 0.659899i | \(0.770599\pi\) | |||||||
\(84\) | −4.77495 | + | 5.24354i | −0.520989 | + | 0.572117i | ||||
\(85\) | 1.10799 | + | 0.583627i | 0.120178 | + | 0.0633033i | ||||
\(86\) | 10.8573i | 1.17077i | ||||||||
\(87\) | −5.54228 | + | 0.259227i | −0.594195 | + | 0.0277920i | ||||
\(88\) | 1.14789 | − | 1.14789i | 0.122365 | − | 0.122365i | ||||
\(89\) | −10.4607 | −1.10883 | −0.554415 | − | 0.832241i | \(-0.687058\pi\) | ||||
−0.554415 | + | 0.832241i | \(0.687058\pi\) | |||||||
\(90\) | 6.20106 | + | 2.55868i | 0.653649 | + | 0.269708i | ||||
\(91\) | −10.1181 | −1.06067 | ||||||||
\(92\) | 0.0718525 | − | 0.0718525i | 0.00749115 | − | 0.00749115i | ||||
\(93\) | 1.73016 | − | 0.0809240i | 0.179409 | − | 0.00839143i | ||||
\(94\) | 9.38351i | 0.967835i | ||||||||
\(95\) | −9.73452 | + | 3.01746i | −0.998740 | + | 0.309585i | ||||
\(96\) | −1.16619 | + | 1.28063i | −0.119023 | + | 0.130704i | ||||
\(97\) | 7.96436 | + | 7.96436i | 0.808658 | + | 0.808658i | 0.984431 | − | 0.175772i | \(-0.0562423\pi\) |
−0.175772 | + | 0.984431i | \(0.556242\pi\) | |||||||
\(98\) | −6.90485 | − | 6.90485i | −0.697495 | − | 0.697495i | ||||
\(99\) | −0.454576 | − | 4.84880i | −0.0456866 | − | 0.487323i | ||||
\(100\) | 2.82803 | + | 4.12338i | 0.282803 | + | 0.412338i | ||||
\(101\) | − | 13.5753i | − | 1.35079i | −0.737456 | − | 0.675395i | \(-0.763973\pi\) | ||
0.737456 | − | 0.675395i | \(-0.236027\pi\) | |||||||
\(102\) | 0.0453211 | + | 0.968968i | 0.00448746 | + | 0.0959421i | ||||
\(103\) | −1.42399 | + | 1.42399i | −0.140310 | + | 0.140310i | −0.773773 | − | 0.633463i | \(-0.781633\pi\) |
0.633463 | + | 0.773773i | \(0.281633\pi\) | |||||||
\(104\) | −2.47114 | −0.242316 | ||||||||
\(105\) | −6.72690 | + | 14.3605i | −0.656478 | + | 1.40144i | ||||
\(106\) | 3.52794 | 0.342664 | ||||||||
\(107\) | −3.00041 | + | 3.00041i | −0.290061 | + | 0.290061i | −0.837104 | − | 0.547044i | \(-0.815753\pi\) |
0.547044 | + | 0.837104i | \(0.315753\pi\) | |||||||
\(108\) | 0.726196 | + | 5.14516i | 0.0698782 | + | 0.495093i | ||||
\(109\) | − | 7.90833i | − | 0.757481i | −0.925503 | − | 0.378740i | \(-0.876357\pi\) | ||
0.925503 | − | 0.378740i | \(-0.123643\pi\) | |||||||
\(110\) | 1.69171 | − | 3.21162i | 0.161298 | − | 0.306216i | ||||
\(111\) | −9.99537 | − | 9.10214i | −0.948719 | − | 0.863936i | ||||
\(112\) | −2.89525 | − | 2.89525i | −0.273575 | − | 0.273575i | ||||
\(113\) | 13.5684 | + | 13.5684i | 1.27641 | + | 1.27641i | 0.942663 | + | 0.333747i | \(0.108313\pi\) |
0.333747 | + | 0.942663i | \(0.391687\pi\) | |||||||
\(114\) | −5.83680 | − | 5.31519i | −0.546667 | − | 0.497814i | ||||
\(115\) | 0.105894 | − | 0.201033i | 0.00987462 | − | 0.0187465i | ||||
\(116\) | − | 3.20334i | − | 0.297422i | ||||||
\(117\) | −4.72990 | + | 5.70851i | −0.437280 | + | 0.527751i | ||||
\(118\) | −4.88281 | + | 4.88281i | −0.449499 | + | 0.449499i | ||||
\(119\) | −2.29311 | −0.210209 | ||||||||
\(120\) | −1.64291 | + | 3.50726i | −0.149977 | + | 0.320167i | ||||
\(121\) | 8.36472 | 0.760429 | ||||||||
\(122\) | −6.18029 | + | 6.18029i | −0.559537 | + | 0.559537i | ||||
\(123\) | −0.340569 | − | 7.28139i | −0.0307081 | − | 0.656541i | ||||
\(124\) | 1.00000i | 0.0898027i | ||||||||
\(125\) | 8.77002 | + | 6.93447i | 0.784414 | + | 0.620238i | ||||
\(126\) | −12.2299 | + | 1.14655i | −1.08952 | + | 0.102143i | ||||
\(127\) | −1.53100 | − | 1.53100i | −0.135854 | − | 0.135854i | 0.635910 | − | 0.771764i | \(-0.280625\pi\) |
−0.771764 | + | 0.635910i | \(0.780625\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −12.6616 | + | 13.9041i | −1.11479 | + | 1.22419i | ||||
\(130\) | −5.27790 | + | 1.63602i | −0.462902 | + | 0.143489i | ||||
\(131\) | 1.63084i | 0.142487i | 0.997459 | + | 0.0712437i | \(0.0226968\pi\) | ||||
−0.997459 | + | 0.0712437i | \(0.977303\pi\) | |||||||
\(132\) | 2.80866 | − | 0.131368i | 0.244463 | − | 0.0114341i | ||||
\(133\) | 13.1959 | − | 13.1959i | 1.14423 | − | 1.14423i | ||||
\(134\) | −11.0593 | −0.955381 | ||||||||
\(135\) | 4.95737 | + | 10.5083i | 0.426662 | + | 0.904411i | ||||
\(136\) | −0.560046 | −0.0480235 | ||||||||
\(137\) | −10.3702 | + | 10.3702i | −0.885989 | + | 0.885989i | −0.994135 | − | 0.108146i | \(-0.965509\pi\) |
0.108146 | + | 0.994135i | \(0.465509\pi\) | |||||||
\(138\) | 0.175810 | − | 0.00822308i | 0.0149659 | − | 0.000699995i | ||||
\(139\) | − | 15.9812i | − | 1.35551i | −0.735289 | − | 0.677754i | \(-0.762954\pi\) | ||
0.735289 | − | 0.677754i | \(-0.237046\pi\) | |||||||
\(140\) | −8.10050 | − | 4.26691i | −0.684617 | − | 0.360619i | ||||
\(141\) | −10.9429 | + | 12.0168i | −0.921560 | + | 1.01200i | ||||
\(142\) | 5.21969 | + | 5.21969i | 0.438026 | + | 0.438026i | ||||
\(143\) | 2.83659 | + | 2.83659i | 0.237208 | + | 0.237208i | ||||
\(144\) | −2.98690 | + | 0.280023i | −0.248909 | + | 0.0233352i | ||||
\(145\) | −2.12077 | − | 6.84172i | −0.176120 | − | 0.568174i | ||||
\(146\) | 10.4282i | 0.863040i | ||||||||
\(147\) | −0.790217 | − | 16.8949i | −0.0651760 | − | 1.39347i | ||||
\(148\) | 5.51900 | − | 5.51900i | 0.453659 | − | 0.453659i | ||||
\(149\) | 17.6969 | 1.44979 | 0.724894 | − | 0.688860i | \(-0.241889\pi\) | ||||
0.724894 | + | 0.688860i | \(0.241889\pi\) | |||||||
\(150\) | −1.18697 | + | 8.57853i | −0.0969158 | + | 0.700434i | ||||
\(151\) | −7.84423 | −0.638354 | −0.319177 | − | 0.947695i | \(-0.603406\pi\) | ||||
−0.319177 | + | 0.947695i | \(0.603406\pi\) | |||||||
\(152\) | 3.22282 | − | 3.22282i | 0.261406 | − | 0.261406i | ||||
\(153\) | −1.07196 | + | 1.29374i | −0.0866626 | + | 0.104593i | ||||
\(154\) | 6.64683i | 0.535617i | ||||||||
\(155\) | 0.662050 | + | 2.13581i | 0.0531771 | + | 0.171552i | ||||
\(156\) | −3.16462 | − | 2.88181i | −0.253372 | − | 0.230730i | ||||
\(157\) | −15.3315 | − | 15.3315i | −1.22359 | − | 1.22359i | −0.966347 | − | 0.257241i | \(-0.917186\pi\) |
−0.257241 | − | 0.966347i | \(-0.582814\pi\) | |||||||
\(158\) | 0.161993 | + | 0.161993i | 0.0128875 | + | 0.0128875i | ||||
\(159\) | 4.51798 | + | 4.11423i | 0.358299 | + | 0.326280i | ||||
\(160\) | −1.97839 | − | 1.04211i | −0.156405 | − | 0.0823858i | ||||
\(161\) | 0.416062i | 0.0327903i | ||||||||
\(162\) | −5.07022 | + | 7.43592i | −0.398354 | + | 0.584221i | ||||
\(163\) | 13.3507 | − | 13.3507i | 1.04571 | − | 1.04571i | 0.0468022 | − | 0.998904i | \(-0.485097\pi\) |
0.998904 | − | 0.0468022i | \(-0.0149030\pi\) | |||||||
\(164\) | 4.20851 | 0.328629 | ||||||||
\(165\) | 5.91180 | − | 2.14005i | 0.460233 | − | 0.166603i | ||||
\(166\) | 1.17832 | 0.0914551 | ||||||||
\(167\) | 3.74931 | − | 3.74931i | 0.290130 | − | 0.290130i | −0.547002 | − | 0.837132i | \(-0.684231\pi\) |
0.837132 | + | 0.547002i | \(0.184231\pi\) | |||||||
\(168\) | −0.331343 | − | 7.08414i | −0.0255637 | − | 0.546553i | ||||
\(169\) | 6.89344i | 0.530265i | ||||||||
\(170\) | −1.19615 | + | 0.370778i | −0.0917406 | + | 0.0284374i | ||||
\(171\) | −1.27628 | − | 13.6136i | −0.0975993 | − | 1.04106i | ||||
\(172\) | −7.67725 | − | 7.67725i | −0.585385 | − | 0.585385i | ||||
\(173\) | 0.496896 | + | 0.496896i | 0.0377783 | + | 0.0377783i | 0.725744 | − | 0.687965i | \(-0.241496\pi\) |
−0.687965 | + | 0.725744i | \(0.741496\pi\) | |||||||
\(174\) | 3.73569 | − | 4.10229i | 0.283202 | − | 0.310994i | ||||
\(175\) | −20.1261 | − | 3.75037i | −1.52139 | − | 0.283501i | ||||
\(176\) | 1.62335i | 0.122365i | ||||||||
\(177\) | −11.9473 | + | 0.558807i | −0.898017 | + | 0.0420025i | ||||
\(178\) | 7.39681 | − | 7.39681i | 0.554415 | − | 0.554415i | ||||
\(179\) | −5.69409 | −0.425596 | −0.212798 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212798 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(180\) | −6.19407 | + | 2.57555i | −0.461679 | + | 0.191970i | ||||
\(181\) | 16.1019 | 1.19684 | 0.598422 | − | 0.801181i | \(-0.295795\pi\) | ||||
0.598422 | + | 0.801181i | \(0.295795\pi\) | |||||||
\(182\) | 7.15458 | − | 7.15458i | 0.530333 | − | 0.530333i | ||||
\(183\) | −15.1220 | + | 0.707296i | −1.11785 | + | 0.0522848i | ||||
\(184\) | 0.101615i | 0.00749115i | ||||||||
\(185\) | 8.13369 | − | 15.4414i | 0.598001 | − | 1.13527i | ||||
\(186\) | −1.16619 | + | 1.28063i | −0.0855089 | + | 0.0939003i | ||||
\(187\) | 0.642868 | + | 0.642868i | 0.0470112 | + | 0.0470112i | ||||
\(188\) | −6.63515 | − | 6.63515i | −0.483918 | − | 0.483918i | ||||
\(189\) | −16.9990 | − | 12.7940i | −1.23650 | − | 0.930626i | ||||
\(190\) | 4.74967 | − | 9.01701i | 0.344578 | − | 0.654163i | ||||
\(191\) | − | 13.8091i | − | 0.999191i | −0.866259 | − | 0.499595i | \(-0.833482\pi\) | ||
0.866259 | − | 0.499595i | \(-0.166518\pi\) | |||||||
\(192\) | −0.0809240 | − | 1.73016i | −0.00584019 | − | 0.124863i | ||||
\(193\) | 9.32773 | − | 9.32773i | 0.671425 | − | 0.671425i | −0.286620 | − | 0.958044i | \(-0.592532\pi\) |
0.958044 | + | 0.286620i | \(0.0925317\pi\) | |||||||
\(194\) | −11.2633 | −0.808658 | ||||||||
\(195\) | −8.66694 | − | 4.05987i | −0.620652 | − | 0.290734i | ||||
\(196\) | 9.76493 | 0.697495 | ||||||||
\(197\) | −17.6217 | + | 17.6217i | −1.25549 | + | 1.25549i | −0.302269 | + | 0.953223i | \(0.597744\pi\) |
−0.953223 | + | 0.302269i | \(0.902256\pi\) | |||||||
\(198\) | 3.75006 | + | 3.10719i | 0.266505 | + | 0.220818i | ||||
\(199\) | − | 4.43694i | − | 0.314527i | −0.987557 | − | 0.157263i | \(-0.949733\pi\) | ||
0.987557 | − | 0.157263i | \(-0.0502671\pi\) | |||||||
\(200\) | −4.91539 | − | 0.915953i | −0.347570 | − | 0.0647677i | ||||
\(201\) | −14.1629 | − | 12.8972i | −0.998974 | − | 0.909701i | ||||
\(202\) | 9.59917 | + | 9.59917i | 0.675395 | + | 0.675395i | ||||
\(203\) | 9.27446 | + | 9.27446i | 0.650939 | + | 0.650939i | ||||
\(204\) | −0.717211 | − | 0.653117i | −0.0502148 | − | 0.0457273i | ||||
\(205\) | 8.98858 | − | 2.78624i | 0.627789 | − | 0.194600i | ||||
\(206\) | − | 2.01383i | − | 0.140310i | ||||||
\(207\) | 0.234737 | + | 0.194496i | 0.0163153 | + | 0.0135184i | ||||
\(208\) | 1.74736 | − | 1.74736i | 0.121158 | − | 0.121158i | ||||
\(209\) | −7.39886 | −0.511790 | ||||||||
\(210\) | −5.39774 | − | 14.9110i | −0.372479 | − | 1.02896i | ||||
\(211\) | 14.6718 | 1.01005 | 0.505023 | − | 0.863106i | \(-0.331484\pi\) | ||||
0.505023 | + | 0.863106i | \(0.331484\pi\) | |||||||
\(212\) | −2.49463 | + | 2.49463i | −0.171332 | + | 0.171332i | ||||
\(213\) | 0.597361 | + | 12.7716i | 0.0409305 | + | 0.875096i | ||||
\(214\) | − | 4.24322i | − | 0.290061i | ||||||
\(215\) | −21.4799 | − | 11.3144i | −1.46492 | − | 0.771639i | ||||
\(216\) | −4.15167 | − | 3.12468i | −0.282486 | − | 0.212607i | ||||
\(217\) | −2.89525 | − | 2.89525i | −0.196542 | − | 0.196542i | ||||
\(218\) | 5.59204 | + | 5.59204i | 0.378740 | + | 0.378740i | ||||
\(219\) | −12.1612 | + | 13.3546i | −0.821775 | + | 0.902420i | ||||
\(220\) | 1.07474 | + | 3.46718i | 0.0724591 | + | 0.233757i | ||||
\(221\) | − | 1.38395i | − | 0.0930948i | ||||||
\(222\) | 13.5040 | − | 0.631616i | 0.906328 | − | 0.0423913i | ||||
\(223\) | −20.1771 | + | 20.1771i | −1.35116 | + | 1.35116i | −0.466793 | + | 0.884367i | \(0.654591\pi\) |
−0.884367 | + | 0.466793i | \(0.845409\pi\) | |||||||
\(224\) | 4.09450 | 0.273575 | ||||||||
\(225\) | −11.5242 | + | 9.60168i | −0.768282 | + | 0.640112i | ||||
\(226\) | −19.1886 | −1.27641 | ||||||||
\(227\) | 14.0570 | − | 14.0570i | 0.932999 | − | 0.932999i | −0.0648933 | − | 0.997892i | \(-0.520671\pi\) |
0.997892 | + | 0.0648933i | \(0.0206707\pi\) | |||||||
\(228\) | 7.88565 | − | 0.368832i | 0.522240 | − | 0.0244265i | ||||
\(229\) | 9.05951i | 0.598669i | 0.954148 | + | 0.299335i | \(0.0967647\pi\) | ||||
−0.954148 | + | 0.299335i | \(0.903235\pi\) | |||||||
\(230\) | 0.0672741 | + | 0.217030i | 0.00443592 | + | 0.0143105i | ||||
\(231\) | −7.75143 | + | 8.51212i | −0.510007 | + | 0.560056i | ||||
\(232\) | 2.26510 | + | 2.26510i | 0.148711 | + | 0.148711i | ||||
\(233\) | 1.24516 | + | 1.24516i | 0.0815733 | + | 0.0815733i | 0.746716 | − | 0.665143i | \(-0.231629\pi\) |
−0.665143 | + | 0.746716i | \(0.731629\pi\) | |||||||
\(234\) | −0.691977 | − | 7.38107i | −0.0452359 | − | 0.482516i | ||||
\(235\) | −18.5642 | − | 9.77862i | −1.21100 | − | 0.637887i | ||||
\(236\) | − | 6.90534i | − | 0.449499i | ||||||
\(237\) | 0.0185391 | + | 0.396368i | 0.00120425 | + | 0.0257468i | ||||
\(238\) | 1.62147 | − | 1.62147i | 0.105104 | − | 0.105104i | ||||
\(239\) | −15.7892 | −1.02132 | −0.510659 | − | 0.859784i | \(-0.670598\pi\) | ||||
−0.510659 | + | 0.859784i | \(0.670598\pi\) | |||||||
\(240\) | −1.31829 | − | 3.64172i | −0.0850953 | − | 0.235072i | ||||
\(241\) | 9.56070 | 0.615859 | 0.307929 | − | 0.951409i | \(-0.400364\pi\) | ||||
0.307929 | + | 0.951409i | \(0.400364\pi\) | |||||||
\(242\) | −5.91475 | + | 5.91475i | −0.380214 | + | 0.380214i | ||||
\(243\) | −15.1647 | + | 3.60984i | −0.972818 | + | 0.231571i | ||||
\(244\) | − | 8.74025i | − | 0.559537i | ||||||
\(245\) | 20.8560 | − | 6.46487i | 1.33244 | − | 0.413025i | ||||
\(246\) | 5.38954 | + | 4.90790i | 0.343624 | + | 0.312916i | ||||
\(247\) | 7.96406 | + | 7.96406i | 0.506741 | + | 0.506741i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | 1.50899 | + | 1.37414i | 0.0956281 | + | 0.0870823i | ||||
\(250\) | −11.1047 | + | 1.29793i | −0.702326 | + | 0.0820882i | ||||
\(251\) | 8.18335i | 0.516529i | 0.966074 | + | 0.258264i | \(0.0831505\pi\) | ||||
−0.966074 | + | 0.258264i | \(0.916849\pi\) | |||||||
\(252\) | 7.83709 | − | 9.45856i | 0.493690 | − | 0.595833i | ||||
\(253\) | 0.116642 | − | 0.116642i | 0.00733323 | − | 0.00733323i | ||||
\(254\) | 2.16516 | 0.135854 | ||||||||
\(255\) | −1.96422 | − | 0.920105i | −0.123004 | − | 0.0576192i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.02526 | + | 4.02526i | −0.251089 | + | 0.251089i | −0.821417 | − | 0.570328i | \(-0.806816\pi\) |
0.570328 | + | 0.821417i | \(0.306816\pi\) | |||||||
\(258\) | −0.878614 | − | 18.7848i | −0.0547001 | − | 1.16949i | ||||
\(259\) | 31.9578i | 1.98576i | ||||||||
\(260\) | 2.57520 | − | 4.88888i | 0.159707 | − | 0.303195i | ||||
\(261\) | 9.56806 | − | 0.897007i | 0.592248 | − | 0.0555234i | ||||
\(262\) | −1.15318 | − | 1.15318i | −0.0712437 | − | 0.0712437i | ||||
\(263\) | 15.2841 | + | 15.2841i | 0.942457 | + | 0.942457i | 0.998432 | − | 0.0559749i | \(-0.0178267\pi\) |
−0.0559749 | + | 0.998432i | \(0.517827\pi\) | |||||||
\(264\) | −1.89313 | + | 2.07892i | −0.116514 | + | 0.127948i | ||||
\(265\) | −3.67649 | + | 6.97963i | −0.225845 | + | 0.428755i | ||||
\(266\) | 18.6618i | 1.14423i | ||||||||
\(267\) | 18.0986 | − | 0.846519i | 1.10762 | − | 0.0518061i | ||||
\(268\) | 7.82013 | − | 7.82013i | 0.477690 | − | 0.477690i | ||||
\(269\) | −15.0385 | −0.916912 | −0.458456 | − | 0.888717i | \(-0.651597\pi\) | ||||
−0.458456 | + | 0.888717i | \(0.651597\pi\) | |||||||
\(270\) | −10.9359 | − | 3.92511i | −0.665537 | − | 0.238874i | ||||
\(271\) | −12.6980 | −0.771349 | −0.385674 | − | 0.922635i | \(-0.626031\pi\) | ||||
−0.385674 | + | 0.922635i | \(0.626031\pi\) | |||||||
\(272\) | 0.396012 | − | 0.396012i | 0.0240118 | − | 0.0240118i | ||||
\(273\) | 17.5059 | − | 0.818797i | 1.05951 | − | 0.0495558i | ||||
\(274\) | − | 14.6657i | − | 0.885989i | ||||||
\(275\) | 4.59089 | + | 6.69371i | 0.276841 | + | 0.403646i | ||||
\(276\) | −0.118502 | + | 0.130131i | −0.00713297 | + | 0.00783296i | ||||
\(277\) | −11.3481 | − | 11.3481i | −0.681838 | − | 0.681838i | 0.278576 | − | 0.960414i | \(-0.410138\pi\) |
−0.960414 | + | 0.278576i | \(0.910138\pi\) | |||||||
\(278\) | 11.3004 | + | 11.3004i | 0.677754 | + | 0.677754i | ||||
\(279\) | −2.98690 | + | 0.280023i | −0.178821 | + | 0.0167645i | ||||
\(280\) | 8.74508 | − | 2.71076i | 0.522618 | − | 0.161999i | ||||
\(281\) | 28.4115i | 1.69489i | 0.530884 | + | 0.847444i | \(0.321860\pi\) | ||||
−0.530884 | + | 0.847444i | \(0.678140\pi\) | |||||||
\(282\) | −0.759351 | − | 16.2350i | −0.0452187 | − | 0.966779i | ||||
\(283\) | −7.62439 | + | 7.62439i | −0.453223 | + | 0.453223i | −0.896423 | − | 0.443200i | \(-0.853843\pi\) |
0.443200 | + | 0.896423i | \(0.353843\pi\) | |||||||
\(284\) | −7.38175 | −0.438026 | ||||||||
\(285\) | 16.5981 | − | 6.00845i | 0.983185 | − | 0.355910i | ||||
\(286\) | −4.01154 | −0.237208 | ||||||||
\(287\) | −12.1847 | + | 12.1847i | −0.719239 | + | 0.719239i | ||||
\(288\) | 1.91405 | − | 2.31007i | 0.112787 | − | 0.136122i | ||||
\(289\) | 16.6863i | 0.981550i | ||||||||
\(290\) | 6.33744 | + | 3.33822i | 0.372147 | + | 0.196027i | ||||
\(291\) | −14.4241 | − | 13.1351i | −0.845557 | − | 0.769994i | ||||
\(292\) | −7.37382 | − | 7.37382i | −0.431520 | − | 0.431520i | ||||
\(293\) | −5.08033 | − | 5.08033i | −0.296796 | − | 0.296796i | 0.542962 | − | 0.839758i | \(-0.317303\pi\) |
−0.839758 | + | 0.542962i | \(0.817303\pi\) | |||||||
\(294\) | 12.5053 | + | 11.3877i | 0.729321 | + | 0.664145i | ||||
\(295\) | −4.57168 | − | 14.7485i | −0.266173 | − | 0.858691i | ||||
\(296\) | 7.80505i | 0.453659i | ||||||||
\(297\) | 1.17887 | + | 8.35242i | 0.0684052 | + | 0.484656i | ||||
\(298\) | −12.5136 | + | 12.5136i | −0.724894 | + | 0.724894i | ||||
\(299\) | −0.251105 | −0.0145218 | ||||||||
\(300\) | −5.22662 | − | 6.90525i | −0.301759 | − | 0.398675i | ||||
\(301\) | 44.4551 | 2.56235 | ||||||||
\(302\) | 5.54671 | − | 5.54671i | 0.319177 | − | 0.319177i | ||||
\(303\) | 1.09857 | + | 23.4874i | 0.0631109 | + | 1.34931i | ||||
\(304\) | 4.55776i | 0.261406i | ||||||||
\(305\) | −5.78648 | − | 18.6675i | −0.331333 | − | 1.06890i | ||||
\(306\) | −0.156825 | − | 1.67280i | −0.00896512 | − | 0.0956277i | ||||
\(307\) | −19.6876 | − | 19.6876i | −1.12363 | − | 1.12363i | −0.991191 | − | 0.132439i | \(-0.957719\pi\) |
−0.132439 | − | 0.991191i | \(-0.542281\pi\) | |||||||
\(308\) | −4.70002 | − | 4.70002i | −0.267808 | − | 0.267808i | ||||
\(309\) | 2.34850 | − | 2.57897i | 0.133601 | − | 0.146713i | ||||
\(310\) | −1.97839 | − | 1.04211i | −0.112365 | − | 0.0591877i | ||||
\(311\) | 6.92495i | 0.392678i | 0.980536 | + | 0.196339i | \(0.0629053\pi\) | ||||
−0.980536 | + | 0.196339i | \(0.937095\pi\) | |||||||
\(312\) | 4.27547 | − | 0.199975i | 0.242051 | − | 0.0113213i | ||||
\(313\) | −10.5189 | + | 10.5189i | −0.594565 | + | 0.594565i | −0.938861 | − | 0.344296i | \(-0.888118\pi\) |
0.344296 | + | 0.938861i | \(0.388118\pi\) | |||||||
\(314\) | 21.6820 | 1.22359 | ||||||||
\(315\) | 10.4765 | − | 25.3902i | 0.590284 | − | 1.43058i | ||||
\(316\) | −0.229093 | −0.0128875 | ||||||||
\(317\) | −17.5631 | + | 17.5631i | −0.986441 | + | 0.986441i | −0.999909 | − | 0.0134684i | \(-0.995713\pi\) |
0.0134684 | + | 0.999909i | \(0.495713\pi\) | |||||||
\(318\) | −6.10390 | + | 0.285495i | −0.342290 | + | 0.0160098i | ||||
\(319\) | − | 5.20015i | − | 0.291153i | ||||||
\(320\) | 2.13581 | − | 0.662050i | 0.119395 | − | 0.0370097i | ||||
\(321\) | 4.94838 | − | 5.43399i | 0.276192 | − | 0.303296i | ||||
\(322\) | −0.294200 | − | 0.294200i | −0.0163951 | − | 0.0163951i | ||||
\(323\) | 1.80493 | + | 1.80493i | 0.100429 | + | 0.100429i | ||||
\(324\) | −1.67280 | − | 8.84317i | −0.0929334 | − | 0.491287i | ||||
\(325\) | 2.26345 | − | 12.1466i | 0.125554 | − | 0.673774i | ||||
\(326\) | 18.8807i | 1.04571i | ||||||||
\(327\) | 0.639974 | + | 13.6827i | 0.0353906 | + | 0.756654i | ||||
\(328\) | −2.97586 | + | 2.97586i | −0.164315 | + | 0.164315i | ||||
\(329\) | 38.4208 | 2.11821 | ||||||||
\(330\) | −2.66703 | + | 5.69352i | −0.146815 | + | 0.313418i | ||||
\(331\) | −19.1502 | −1.05259 | −0.526295 | − | 0.850302i | \(-0.676419\pi\) | ||||
−0.526295 | + | 0.850302i | \(0.676419\pi\) | |||||||
\(332\) | −0.833196 | + | 0.833196i | −0.0457276 | + | 0.0457276i | ||||
\(333\) | 18.0302 | + | 14.9393i | 0.988047 | + | 0.818667i | ||||
\(334\) | 5.30232i | 0.290130i | ||||||||
\(335\) | 11.5250 | − | 21.8796i | 0.629678 | − | 1.19541i | ||||
\(336\) | 5.24354 | + | 4.77495i | 0.286058 | + | 0.260495i | ||||
\(337\) | 0.640755 | + | 0.640755i | 0.0349041 | + | 0.0349041i | 0.724343 | − | 0.689439i | \(-0.242143\pi\) |
−0.689439 | + | 0.724343i | \(0.742143\pi\) | |||||||
\(338\) | −4.87440 | − | 4.87440i | −0.265132 | − | 0.265132i | ||||
\(339\) | −24.5735 | − | 22.3775i | −1.33465 | − | 1.21538i | ||||
\(340\) | 0.583627 | − | 1.10799i | 0.0316516 | − | 0.0600890i | ||||
\(341\) | 1.62335i | 0.0879096i | ||||||||
\(342\) | 10.5287 | + | 8.72380i | 0.569328 | + | 0.471729i | ||||
\(343\) | −8.00515 | + | 8.00515i | −0.432238 | + | 0.432238i | ||||
\(344\) | 10.8573 | 0.585385 | ||||||||
\(345\) | −0.166944 | + | 0.356389i | −0.00898797 | + | 0.0191873i | ||||
\(346\) | −0.702717 | −0.0377783 | ||||||||
\(347\) | −11.8865 | + | 11.8865i | −0.638103 | + | 0.638103i | −0.950087 | − | 0.311984i | \(-0.899006\pi\) |
0.311984 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(348\) | 0.259227 | + | 5.54228i | 0.0138960 | + | 0.297098i | ||||
\(349\) | 9.01900i | 0.482776i | 0.970429 | + | 0.241388i | \(0.0776026\pi\) | ||||
−0.970429 | + | 0.241388i | \(0.922397\pi\) | |||||||
\(350\) | 16.8832 | − | 11.5794i | 0.902444 | − | 0.618943i | ||||
\(351\) | 7.72153 | − | 10.2594i | 0.412145 | − | 0.547605i | ||||
\(352\) | −1.14789 | − | 1.14789i | −0.0611825 | − | 0.0611825i | ||||
\(353\) | −20.0852 | − | 20.0852i | −1.06903 | − | 1.06903i | −0.997434 | − | 0.0715963i | \(-0.977191\pi\) |
−0.0715963 | − | 0.997434i | \(-0.522809\pi\) | |||||||
\(354\) | 8.05291 | − | 8.84318i | 0.428007 | − | 0.470010i | ||||
\(355\) | −15.7660 | + | 4.88709i | −0.836774 | + | 0.259380i | ||||
\(356\) | 10.4607i | 0.554415i | ||||||||
\(357\) | 3.96744 | − | 0.185567i | 0.209979 | − | 0.00982126i | ||||
\(358\) | 4.02633 | − | 4.02633i | 0.212798 | − | 0.212798i | ||||
\(359\) | 26.3374 | 1.39003 | 0.695017 | − | 0.718993i | \(-0.255397\pi\) | ||||
0.695017 | + | 0.718993i | \(0.255397\pi\) | |||||||
\(360\) | 2.55868 | − | 6.20106i | 0.134854 | − | 0.326825i | ||||
\(361\) | −1.77319 | −0.0933256 | ||||||||
\(362\) | −11.3858 | + | 11.3858i | −0.598422 | + | 0.598422i | ||||
\(363\) | −14.4723 | + | 0.676906i | −0.759599 | + | 0.0355284i | ||||
\(364\) | 10.1181i | 0.530333i | ||||||||
\(365\) | −20.6309 | − | 10.8673i | −1.07987 | − | 0.568818i | ||||
\(366\) | 10.1928 | − | 11.1930i | 0.532784 | − | 0.585069i | ||||
\(367\) | 6.04081 | + | 6.04081i | 0.315328 | + | 0.315328i | 0.846969 | − | 0.531642i | \(-0.178425\pi\) |
−0.531642 | + | 0.846969i | \(0.678425\pi\) | |||||||
\(368\) | −0.0718525 | − | 0.0718525i | −0.00374557 | − | 0.00374557i | ||||
\(369\) | 1.17848 | + | 12.5704i | 0.0613491 | + | 0.654389i | ||||
\(370\) | 5.16733 | + | 16.6701i | 0.268637 | + | 0.866638i | ||||
\(371\) | − | 14.4452i | − | 0.749955i | ||||||
\(372\) | −0.0809240 | − | 1.73016i | −0.00419571 | − | 0.0897046i | ||||
\(373\) | −10.5024 | + | 10.5024i | −0.543796 | + | 0.543796i | −0.924639 | − | 0.380844i | \(-0.875634\pi\) |
0.380844 | + | 0.924639i | \(0.375634\pi\) | |||||||
\(374\) | −0.909153 | −0.0470112 | ||||||||
\(375\) | −15.7347 | − | 11.2880i | −0.812536 | − | 0.582911i | ||||
\(376\) | 9.38351 | 0.483918 | ||||||||
\(377\) | −5.59739 | + | 5.59739i | −0.288280 | + | 0.288280i | ||||
\(378\) | 21.0668 | − | 2.97341i | 1.08356 | − | 0.152936i | ||||
\(379\) | − | 1.55688i | − | 0.0799714i | −0.999200 | − | 0.0399857i | \(-0.987269\pi\) | ||
0.999200 | − | 0.0399857i | \(-0.0127312\pi\) | |||||||
\(380\) | 3.01746 | + | 9.73452i | 0.154793 | + | 0.499370i | ||||
\(381\) | 2.77276 | + | 2.52497i | 0.142053 | + | 0.129358i | ||||
\(382\) | 9.76450 | + | 9.76450i | 0.499595 | + | 0.499595i | ||||
\(383\) | −3.53739 | − | 3.53739i | −0.180752 | − | 0.180752i | 0.610931 | − | 0.791684i | \(-0.290795\pi\) |
−0.791684 | + | 0.610931i | \(0.790795\pi\) | |||||||
\(384\) | 1.28063 | + | 1.16619i | 0.0653518 | + | 0.0595117i | ||||
\(385\) | −13.1500 | − | 6.92670i | −0.670186 | − | 0.353017i | ||||
\(386\) | 13.1914i | 0.671425i | ||||||||
\(387\) | 20.7814 | − | 25.0810i | 1.05638 | − | 1.27494i | ||||
\(388\) | 7.96436 | − | 7.96436i | 0.404329 | − | 0.404329i | ||||
\(389\) | 32.6543 | 1.65564 | 0.827819 | − | 0.560995i | \(-0.189581\pi\) | ||||
0.827819 | + | 0.560995i | \(0.189581\pi\) | |||||||
\(390\) | 8.99921 | − | 3.25769i | 0.455693 | − | 0.164959i | ||||
\(391\) | −0.0569089 | −0.00287801 | ||||||||
\(392\) | −6.90485 | + | 6.90485i | −0.348747 | + | 0.348747i | ||||
\(393\) | −0.131974 | − | 2.82162i | −0.00665722 | − | 0.142332i | ||||
\(394\) | − | 24.9208i | − | 1.25549i | ||||||
\(395\) | −0.489300 | + | 0.151671i | −0.0246193 | + | 0.00763140i | ||||
\(396\) | −4.84880 | + | 0.454576i | −0.243662 | + | 0.0228433i | ||||
\(397\) | −8.53863 | − | 8.53863i | −0.428542 | − | 0.428542i | 0.459590 | − | 0.888131i | \(-0.347996\pi\) |
−0.888131 | + | 0.459590i | \(0.847996\pi\) | |||||||
\(398\) | 3.13739 | + | 3.13739i | 0.157263 | + | 0.157263i | ||||
\(399\) | −21.7631 | + | 23.8988i | −1.08952 | + | 1.19644i | ||||
\(400\) | 4.12338 | − | 2.82803i | 0.206169 | − | 0.141401i | ||||
\(401\) | − | 31.6949i | − | 1.58277i | −0.611321 | − | 0.791383i | \(-0.709362\pi\) | ||
0.611321 | − | 0.791383i | \(-0.290638\pi\) | |||||||
\(402\) | 19.1344 | − | 0.894965i | 0.954337 | − | 0.0446368i | ||||
\(403\) | 1.74736 | − | 1.74736i | 0.0870424 | − | 0.0870424i | ||||
\(404\) | −13.5753 | −0.675395 | ||||||||
\(405\) | −9.42741 | − | 17.7799i | −0.468452 | − | 0.883489i | ||||
\(406\) | −13.1161 | −0.650939 | ||||||||
\(407\) | 8.95930 | − | 8.95930i | 0.444096 | − | 0.444096i | ||||
\(408\) | 0.968968 | − | 0.0453211i | 0.0479711 | − | 0.00224373i | ||||
\(409\) | 18.9112i | 0.935098i | 0.883967 | + | 0.467549i | \(0.154863\pi\) | ||||
−0.883967 | + | 0.467549i | \(0.845137\pi\) | |||||||
\(410\) | −4.38571 | + | 8.32605i | −0.216595 | + | 0.411195i | ||||
\(411\) | 17.1030 | − | 18.7814i | 0.843627 | − | 0.926416i | ||||
\(412\) | 1.42399 | + | 1.42399i | 0.0701551 | + | 0.0701551i | ||||
\(413\) | 19.9927 | + | 19.9927i | 0.983775 | + | 0.983775i | ||||
\(414\) | −0.303514 | + | 0.0284545i | −0.0149169 | + | 0.00139846i | ||||
\(415\) | −1.22793 | + | 2.33117i | −0.0602768 | + | 0.114432i | ||||
\(416\) | 2.47114i | 0.121158i | ||||||||
\(417\) | 1.29326 | + | 27.6500i | 0.0633313 | + | 1.35403i | ||||
\(418\) | 5.23179 | − | 5.23179i | 0.255895 | − | 0.255895i | ||||
\(419\) | 7.06832 | 0.345310 | 0.172655 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172655 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(420\) | 14.3605 | + | 6.72690i | 0.700719 | + | 0.328239i | ||||
\(421\) | 29.7297 | 1.44894 | 0.724468 | − | 0.689308i | \(-0.242085\pi\) | ||||
0.724468 | + | 0.689308i | \(0.242085\pi\) | |||||||
\(422\) | −10.3745 | + | 10.3745i | −0.505023 | + | 0.505023i | ||||
\(423\) | 17.9605 | − | 21.6765i | 0.873271 | − | 1.05395i | ||||
\(424\) | − | 3.52794i | − | 0.171332i | ||||||
\(425\) | 0.512975 | − | 2.75284i | 0.0248830 | − | 0.133532i | ||||
\(426\) | −9.45329 | − | 8.60849i | −0.458013 | − | 0.417083i | ||||
\(427\) | 25.3052 | + | 25.3052i | 1.22460 | + | 1.22460i | ||||
\(428\) | 3.00041 | + | 3.00041i | 0.145030 | + | 0.145030i | ||||
\(429\) | −5.13730 | − | 4.67821i | −0.248031 | − | 0.225866i | ||||
\(430\) | 23.1891 | − | 7.18806i | 1.11828 | − | 0.346639i | ||||
\(431\) | − | 27.1832i | − | 1.30937i | −0.755903 | − | 0.654684i | \(-0.772802\pi\) | ||
0.755903 | − | 0.654684i | \(-0.227198\pi\) | |||||||
\(432\) | 5.14516 | − | 0.726196i | 0.247546 | − | 0.0349391i | ||||
\(433\) | 12.0553 | − | 12.0553i | 0.579342 | − | 0.579342i | −0.355380 | − | 0.934722i | \(-0.615648\pi\) |
0.934722 | + | 0.355380i | \(0.115648\pi\) | |||||||
\(434\) | 4.09450 | 0.196542 | ||||||||
\(435\) | 4.22293 | + | 11.6657i | 0.202474 | + | 0.559325i | ||||
\(436\) | −7.90833 | −0.378740 | ||||||||
\(437\) | 0.327487 | − | 0.327487i | 0.0156658 | − | 0.0156658i | ||||
\(438\) | −0.843888 | − | 18.0424i | −0.0403225 | − | 0.862098i | ||||
\(439\) | 4.38472i | 0.209271i | 0.994511 | + | 0.104636i | \(0.0333676\pi\) | ||||
−0.994511 | + | 0.104636i | \(0.966632\pi\) | |||||||
\(440\) | −3.21162 | − | 1.69171i | −0.153108 | − | 0.0806491i | ||||
\(441\) | 2.73440 | + | 29.1669i | 0.130210 | + | 1.38890i | ||||
\(442\) | 0.978603 | + | 0.978603i | 0.0465474 | + | 0.0465474i | ||||
\(443\) | −18.6578 | − | 18.6578i | −0.886457 | − | 0.886457i | 0.107724 | − | 0.994181i | \(-0.465644\pi\) |
−0.994181 | + | 0.107724i | \(0.965644\pi\) | |||||||
\(444\) | −9.10214 | + | 9.99537i | −0.431968 | + | 0.474359i | ||||
\(445\) | 6.92549 | + | 22.3420i | 0.328300 | + | 1.05911i | ||||
\(446\) | − | 28.5347i | − | 1.35116i | ||||||
\(447\) | −30.6185 | + | 1.43211i | −1.44820 | + | 0.0677362i | ||||
\(448\) | −2.89525 | + | 2.89525i | −0.136788 | + | 0.136788i | ||||
\(449\) | 10.1528 | 0.479142 | 0.239571 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239571 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(450\) | 1.35944 | − | 14.9383i | 0.0640847 | − | 0.704197i | ||||
\(451\) | 6.83190 | 0.321702 | ||||||||
\(452\) | 13.5684 | − | 13.5684i | 0.638205 | − | 0.638205i | ||||
\(453\) | 13.5718 | − | 0.634786i | 0.637657 | − | 0.0298249i | ||||
\(454\) | 19.8797i | 0.932999i | ||||||||
\(455\) | 6.69869 | + | 21.6104i | 0.314039 | + | 1.01311i | ||||
\(456\) | −5.31519 | + | 5.83680i | −0.248907 | + | 0.273333i | ||||
\(457\) | −6.23308 | − | 6.23308i | −0.291571 | − | 0.291571i | 0.546130 | − | 0.837701i | \(-0.316101\pi\) |
−0.837701 | + | 0.546130i | \(0.816101\pi\) | |||||||
\(458\) | −6.40604 | − | 6.40604i | −0.299335 | − | 0.299335i | ||||
\(459\) | 1.74996 | − | 2.32513i | 0.0816812 | − | 0.108528i | ||||
\(460\) | −0.201033 | − | 0.105894i | −0.00937323 | − | 0.00493731i | ||||
\(461\) | 7.19713i | 0.335204i | 0.985855 | + | 0.167602i | \(0.0536023\pi\) | ||||
−0.985855 | + | 0.167602i | \(0.946398\pi\) | |||||||
\(462\) | −0.537888 | − | 11.5001i | −0.0250248 | − | 0.535032i | ||||
\(463\) | −15.5749 | + | 15.5749i | −0.723826 | + | 0.723826i | −0.969382 | − | 0.245557i | \(-0.921029\pi\) |
0.245557 | + | 0.969382i | \(0.421029\pi\) | |||||||
\(464\) | −3.20334 | −0.148711 | ||||||||
\(465\) | −1.31829 | − | 3.64172i | −0.0611342 | − | 0.168881i | ||||
\(466\) | −1.76092 | −0.0815733 | ||||||||
\(467\) | −27.0181 | + | 27.0181i | −1.25025 | + | 1.25025i | −0.294640 | + | 0.955608i | \(0.595200\pi\) |
−0.955608 | + | 0.294640i | \(0.904800\pi\) | |||||||
\(468\) | 5.70851 | + | 4.72990i | 0.263876 | + | 0.218640i | ||||
\(469\) | 45.2824i | 2.09095i | ||||||||
\(470\) | 20.0414 | − | 6.21235i | 0.924441 | − | 0.286554i | ||||
\(471\) | 27.7667 | + | 25.2853i | 1.27942 | + | 1.16508i | ||||
\(472\) | 4.88281 | + | 4.88281i | 0.224750 | + | 0.224750i | ||||
\(473\) | −12.4629 | − | 12.4629i | −0.573045 | − | 0.573045i | ||||
\(474\) | −0.293383 | − | 0.267165i | −0.0134755 | − | 0.0122713i | ||||
\(475\) | 12.8895 | + | 18.7934i | 0.591410 | + | 0.862299i | ||||
\(476\) | 2.29311i | 0.105104i | ||||||||
\(477\) | −8.14977 | − | 6.75267i | −0.373152 | − | 0.309183i | ||||
\(478\) | 11.1646 | − | 11.1646i | 0.510659 | − | 0.510659i | ||||
\(479\) | 20.0787 | 0.917419 | 0.458710 | − | 0.888586i | \(-0.348312\pi\) | ||||
0.458710 | + | 0.888586i | \(0.348312\pi\) | |||||||
\(480\) | 3.50726 | + | 1.64291i | 0.160084 | + | 0.0749883i | ||||
\(481\) | −19.2874 | −0.879430 | ||||||||
\(482\) | −6.76044 | + | 6.76044i | −0.307929 | + | 0.307929i | ||||
\(483\) | −0.0336694 | − | 0.719853i | −0.00153201 | − | 0.0327545i | ||||
\(484\) | − | 8.36472i | − | 0.380214i | ||||||
\(485\) | 11.7376 | − | 22.2832i | 0.532976 | − | 1.01183i | ||||
\(486\) | 8.17054 | − | 13.2756i | 0.370623 | − | 0.602195i | ||||
\(487\) | 1.10651 | + | 1.10651i | 0.0501406 | + | 0.0501406i | 0.731733 | − | 0.681592i | \(-0.238712\pi\) |
−0.681592 | + | 0.731733i | \(0.738712\pi\) | |||||||
\(488\) | 6.18029 | + | 6.18029i | 0.279769 | + | 0.279769i | ||||
\(489\) | −22.0184 | + | 24.1792i | −0.995707 | + | 1.09342i | ||||
\(490\) | −10.1761 | + | 19.3188i | −0.459709 | + | 0.872734i | ||||
\(491\) | 39.8508i | 1.79844i | 0.437496 | + | 0.899220i | \(0.355865\pi\) | ||||
−0.437496 | + | 0.899220i | \(0.644135\pi\) | |||||||
\(492\) | −7.28139 | + | 0.340569i | −0.328270 | + | 0.0153540i | ||||
\(493\) | −1.26856 | + | 1.26856i | −0.0571331 | + | 0.0571331i | ||||
\(494\) | −11.2629 | −0.506741 | ||||||||
\(495\) | −10.0552 | + | 4.18104i | −0.451947 | + | 0.187924i | ||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 21.3720 | − | 21.3720i | 0.958666 | − | 0.958666i | ||||
\(498\) | −2.03868 | + | 0.0953541i | −0.0913552 | + | 0.00427292i | ||||
\(499\) | − | 1.93331i | − | 0.0865468i | −0.999063 | − | 0.0432734i | \(-0.986221\pi\) | ||
0.999063 | − | 0.0432734i | \(-0.0137787\pi\) | |||||||
\(500\) | 6.93447 | − | 8.77002i | 0.310119 | − | 0.392207i | ||||
\(501\) | −6.18349 | + | 6.79031i | −0.276258 | + | 0.303369i | ||||
\(502\) | −5.78650 | − | 5.78650i | −0.258264 | − | 0.258264i | ||||
\(503\) | −1.63114 | − | 1.63114i | −0.0727289 | − | 0.0727289i | 0.669807 | − | 0.742536i | \(-0.266377\pi\) |
−0.742536 | + | 0.669807i | \(0.766377\pi\) | |||||||
\(504\) | 1.14655 | + | 12.2299i | 0.0510715 | + | 0.544762i | ||||
\(505\) | −28.9942 | + | 8.98751i | −1.29023 | + | 0.399939i | ||||
\(506\) | 0.164957i | 0.00733323i | ||||||||
\(507\) | −0.557845 | − | 11.9268i | −0.0247748 | − | 0.529686i | ||||
\(508\) | −1.53100 | + | 1.53100i | −0.0679270 | + | 0.0679270i | ||||
\(509\) | −40.9970 | −1.81716 | −0.908581 | − | 0.417709i | \(-0.862833\pi\) | ||||
−0.908581 | + | 0.417709i | \(0.862833\pi\) | |||||||
\(510\) | 2.03953 | − | 0.738302i | 0.0903118 | − | 0.0326926i | ||||
\(511\) | 42.6981 | 1.88885 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 3.30983 | + | 23.4504i | 0.146132 | + | 1.03536i | ||||
\(514\) | − | 5.69257i | − | 0.251089i | ||||||
\(515\) | 3.98414 | + | 2.09863i | 0.175562 | + | 0.0924765i | ||||
\(516\) | 13.9041 | + | 12.6616i | 0.612096 | + | 0.557396i | ||||
\(517\) | −10.7712 | − | 10.7712i | −0.473717 | − | 0.473717i | ||||
\(518\) | −22.5976 | − | 22.5976i | −0.992880 | − | 0.992880i | ||||
\(519\) | −0.899920 | − | 0.819498i | −0.0395021 | − | 0.0359720i | ||||
\(520\) | 1.63602 | + | 5.27790i | 0.0717443 | + | 0.231451i | ||||
\(521\) | − | 33.9332i | − | 1.48664i | −0.668936 | − | 0.743320i | \(-0.733250\pi\) | ||
0.668936 | − | 0.743320i | \(-0.266750\pi\) | |||||||
\(522\) | −6.13136 | + | 7.39992i | −0.268362 | + | 0.323886i | ||||
\(523\) | 27.3843 | − | 27.3843i | 1.19743 | − | 1.19743i | 0.222500 | − | 0.974933i | \(-0.428578\pi\) |
0.974933 | − | 0.222500i | \(-0.0714217\pi\) | |||||||
\(524\) | 1.63084 | 0.0712437 | ||||||||
\(525\) | 35.1248 | + | 4.86006i | 1.53297 | + | 0.212110i | ||||
\(526\) | −21.6150 | −0.942457 | ||||||||
\(527\) | 0.396012 | − | 0.396012i | 0.0172506 | − | 0.0172506i | ||||
\(528\) | −0.131368 | − | 2.80866i | −0.00571707 | − | 0.122231i | ||||
\(529\) | − | 22.9897i | − | 0.999551i | ||||||
\(530\) | −2.33567 | − | 7.53501i | −0.101455 | − | 0.327300i | ||||
\(531\) | 20.6256 | − | 1.93365i | 0.895074 | − | 0.0839133i | ||||
\(532\) | −13.1959 | − | 13.1959i | −0.572113 | − | 0.572113i | ||||
\(533\) | −7.35379 | − | 7.35379i | −0.318528 | − | 0.318528i | ||||
\(534\) | −12.1991 | + | 13.3962i | −0.527906 | + | 0.579712i | ||||
\(535\) | 8.39473 | + | 4.42189i | 0.362936 | + | 0.191175i | ||||
\(536\) | 11.0593i | 0.477690i | ||||||||
\(537\) | 9.85169 | − | 0.460789i | 0.425132 | − | 0.0198845i | ||||
\(538\) | 10.6338 | − | 10.6338i | 0.458456 | − | 0.458456i | ||||
\(539\) | 15.8519 | 0.682792 | ||||||||
\(540\) | 10.5083 | − | 4.95737i | 0.452206 | − | 0.213331i | ||||
\(541\) | −24.7593 | −1.06449 | −0.532243 | − | 0.846592i | \(-0.678651\pi\) | ||||
−0.532243 | + | 0.846592i | \(0.678651\pi\) | |||||||
\(542\) | 8.97885 | − | 8.97885i | 0.385674 | − | 0.385674i | ||||
\(543\) | −27.8588 | + | 1.30303i | −1.19554 | + | 0.0559183i | ||||
\(544\) | 0.560046i | 0.0240118i | ||||||||
\(545\) | −16.8907 | + | 5.23571i | −0.723518 | + | 0.224273i | ||||
\(546\) | −11.7996 | + | 12.9575i | −0.504976 | + | 0.554531i | ||||
\(547\) | −16.5080 | − | 16.5080i | −0.705831 | − | 0.705831i | 0.259825 | − | 0.965656i | \(-0.416335\pi\) |
−0.965656 | + | 0.259825i | \(0.916335\pi\) | |||||||
\(548\) | 10.3702 | + | 10.3702i | 0.442995 | + | 0.442995i | ||||
\(549\) | 26.1063 | − | 2.44747i | 1.11419 | − | 0.104455i | ||||
\(550\) | −7.97942 | − | 1.48692i | −0.340244 | − | 0.0634023i | ||||
\(551\) | − | 14.6000i | − | 0.621983i | ||||||
\(552\) | −0.00822308 | − | 0.175810i | −0.000349997 | − | 0.00748296i | ||||
\(553\) | 0.663281 | − | 0.663281i | 0.0282056 | − | 0.0282056i | ||||
\(554\) | 16.0486 | 0.681838 | ||||||||
\(555\) | −12.8230 | + | 27.3743i | −0.544306 | + | 1.16197i | ||||
\(556\) | −15.9812 | −0.677754 | ||||||||
\(557\) | −32.1980 | + | 32.1980i | −1.36427 | + | 1.36427i | −0.495887 | + | 0.868387i | \(0.665157\pi\) |
−0.868387 | + | 0.495887i | \(0.834843\pi\) | |||||||
\(558\) | 1.91405 | − | 2.31007i | 0.0810283 | − | 0.0977929i | ||||
\(559\) | 26.8299i | 1.13478i | ||||||||
\(560\) | −4.26691 | + | 8.10050i | −0.180310 | + | 0.342309i | ||||
\(561\) | −1.16429 | − | 1.06024i | −0.0491563 | − | 0.0447634i | ||||
\(562\) | −20.0900 | − | 20.0900i | −0.847444 | − | 0.847444i | ||||
\(563\) | 6.51375 | + | 6.51375i | 0.274522 | + | 0.274522i | 0.830917 | − | 0.556396i | \(-0.187816\pi\) |
−0.556396 | + | 0.830917i | \(0.687816\pi\) | |||||||
\(564\) | 12.0168 | + | 10.9429i | 0.505999 | + | 0.460780i | ||||
\(565\) | 19.9966 | − | 37.9626i | 0.841264 | − | 1.59710i | ||||
\(566\) | − | 10.7825i | − | 0.453223i | ||||||
\(567\) | 30.4464 | + | 20.7600i | 1.27863 | + | 0.871839i | ||||
\(568\) | 5.21969 | − | 5.21969i | 0.219013 | − | 0.219013i | ||||
\(569\) | 1.99748 | 0.0837389 | 0.0418694 | − | 0.999123i | \(-0.486669\pi\) | ||||
0.0418694 | + | 0.999123i | \(0.486669\pi\) | |||||||
\(570\) | −7.48800 | + | 15.9852i | −0.313638 | + | 0.669548i | ||||
\(571\) | −10.3526 | −0.433244 | −0.216622 | − | 0.976256i | \(-0.569504\pi\) | ||||
−0.216622 | + | 0.976256i | \(0.569504\pi\) | |||||||
\(572\) | 2.83659 | − | 2.83659i | 0.118604 | − | 0.118604i | ||||
\(573\) | 1.11749 | + | 23.8919i | 0.0466837 | + | 0.998100i | ||||
\(574\) | − | 17.2317i | − | 0.719239i | ||||||
\(575\) | −0.499476 | − | 0.0930744i | −0.0208296 | − | 0.00388147i | ||||
\(576\) | 0.280023 | + | 2.98690i | 0.0116676 | + | 0.124454i | ||||
\(577\) | 31.4080 | + | 31.4080i | 1.30753 | + | 1.30753i | 0.923190 | + | 0.384344i | \(0.125572\pi\) |
0.384344 | + | 0.923190i | \(0.374428\pi\) | |||||||
\(578\) | −11.7990 | − | 11.7990i | −0.490775 | − | 0.490775i | ||||
\(579\) | −15.3836 | + | 16.8933i | −0.639321 | + | 0.702061i | ||||
\(580\) | −6.84172 | + | 2.12077i | −0.284087 | + | 0.0880601i | ||||
\(581\) | − | 4.82462i | − | 0.200159i | ||||||
\(582\) | 19.4873 | − | 0.911472i | 0.807775 | − | 0.0377817i | ||||
\(583\) | −4.04967 | + | 4.04967i | −0.167720 | + | 0.167720i | ||||
\(584\) | 10.4282 | 0.431520 | ||||||||
\(585\) | 15.3237 | + | 6.32286i | 0.633558 | + | 0.261418i | ||||
\(586\) | 7.18467 | 0.296796 | ||||||||
\(587\) | 29.2278 | − | 29.2278i | 1.20636 | − | 1.20636i | 0.234162 | − | 0.972198i | \(-0.424765\pi\) |
0.972198 | − | 0.234162i | \(-0.0752345\pi\) | |||||||
\(588\) | −16.8949 | + | 0.790217i | −0.696733 | + | 0.0325880i | ||||
\(589\) | 4.55776i | 0.187799i | ||||||||
\(590\) | 13.6614 | + | 7.19610i | 0.562432 | + | 0.296259i | ||||
\(591\) | 29.0623 | − | 31.9143i | 1.19546 | − | 1.31278i | ||||
\(592\) | −5.51900 | − | 5.51900i | −0.226830 | − | 0.226830i | ||||
\(593\) | 10.4703 | + | 10.4703i | 0.429964 | + | 0.429964i | 0.888616 | − | 0.458652i | \(-0.151667\pi\) |
−0.458652 | + | 0.888616i | \(0.651667\pi\) | |||||||
\(594\) | −6.73964 | − | 5.07246i | −0.276531 | − | 0.208126i | ||||
\(595\) | 1.51815 | + | 4.89764i | 0.0622381 | + | 0.200784i | ||||
\(596\) | − | 17.6969i | − | 0.724894i | ||||||
\(597\) | 0.359055 | + | 7.67662i | 0.0146951 | + | 0.314183i | ||||
\(598\) | 0.177558 | − | 0.177558i | 0.00726089 | − | 0.00726089i | ||||
\(599\) | 10.7834 | 0.440598 | 0.220299 | − | 0.975432i | \(-0.429297\pi\) | ||||
0.220299 | + | 0.975432i | \(0.429297\pi\) | |||||||
\(600\) | 8.57853 | + | 1.18697i | 0.350217 | + | 0.0484579i | ||||
\(601\) | −38.9612 | −1.58926 | −0.794630 | − | 0.607094i | \(-0.792335\pi\) | ||||
−0.794630 | + | 0.607094i | \(0.792335\pi\) | |||||||
\(602\) | −31.4345 | + | 31.4345i | −1.28118 | + | 1.28118i | ||||
\(603\) | 25.5478 | + | 21.1681i | 1.04039 | + | 0.862034i | ||||
\(604\) | 7.84423i | 0.319177i | ||||||||
\(605\) | −5.53786 | − | 17.8655i | −0.225146 | − | 0.726334i | ||||
\(606\) | −17.3849 | − | 15.8313i | −0.706213 | − | 0.643102i | ||||
\(607\) | 8.11174 | + | 8.11174i | 0.329245 | + | 0.329245i | 0.852300 | − | 0.523054i | \(-0.175207\pi\) |
−0.523054 | + | 0.852300i | \(0.675207\pi\) | |||||||
\(608\) | −3.22282 | − | 3.22282i | −0.130703 | − | 0.130703i | ||||
\(609\) | −16.7968 | − | 15.2958i | −0.680641 | − | 0.619816i | ||||
\(610\) | 17.2916 | + | 9.10828i | 0.700117 | + | 0.368783i | ||||
\(611\) | 23.1880i | 0.938087i | ||||||||
\(612\) | 1.29374 | + | 1.07196i | 0.0522964 | + | 0.0433313i | ||||
\(613\) | 27.0043 | − | 27.0043i | 1.09069 | − | 1.09069i | 0.0952399 | − | 0.995454i | \(-0.469638\pi\) |
0.995454 | − | 0.0952399i | \(-0.0303618\pi\) | |||||||
\(614\) | 27.8425 | 1.12363 | ||||||||
\(615\) | −15.3262 | + | 5.54803i | −0.618012 | + | 0.223718i | ||||
\(616\) | 6.64683 | 0.267808 | ||||||||
\(617\) | −7.33375 | + | 7.33375i | −0.295246 | + | 0.295246i | −0.839148 | − | 0.543903i | \(-0.816946\pi\) |
0.543903 | + | 0.839148i | \(0.316946\pi\) | |||||||
\(618\) | 0.162967 | + | 3.48425i | 0.00655550 | + | 0.140157i | ||||
\(619\) | − | 34.5763i | − | 1.38974i | −0.719137 | − | 0.694869i | \(-0.755463\pi\) | ||
0.719137 | − | 0.694869i | \(-0.244537\pi\) | |||||||
\(620\) | 2.13581 | − | 0.662050i | 0.0857762 | − | 0.0265886i | ||||
\(621\) | −0.421872 | − | 0.317514i | −0.0169291 | − | 0.0127414i | ||||
\(622\) | −4.89668 | − | 4.89668i | −0.196339 | − | 0.196339i | ||||
\(623\) | −30.2863 | − | 30.2863i | −1.21339 | − | 1.21339i | ||||
\(624\) | −2.88181 | + | 3.16462i | −0.115365 | + | 0.126686i | ||||
\(625\) | 9.00453 | − | 23.3221i | 0.360181 | − | 0.932882i | ||||
\(626\) | − | 14.8760i | − | 0.594565i | ||||||
\(627\) | 12.8012 | − | 0.598746i | 0.511231 | − | 0.0239116i | ||||
\(628\) | −15.3315 | + | 15.3315i | −0.611794 | + | 0.611794i | ||||
\(629\) | −4.37118 | −0.174290 | ||||||||
\(630\) | 10.5456 | + | 25.3616i | 0.420147 | + | 1.01043i | ||||
\(631\) | −12.9099 | −0.513935 | −0.256968 | − | 0.966420i | \(-0.582723\pi\) | ||||
−0.256968 | + | 0.966420i | \(0.582723\pi\) | |||||||
\(632\) | 0.161993 | − | 0.161993i | 0.00644375 | − | 0.00644375i | ||||
\(633\) | −25.3845 | + | 1.18730i | −1.00894 | + | 0.0471909i | ||||
\(634\) | − | 24.8379i | − | 0.986441i | ||||||
\(635\) | −2.25632 | + | 4.28352i | −0.0895395 | + | 0.169986i | ||||
\(636\) | 4.11423 | − | 4.51798i | 0.163140 | − | 0.179150i | ||||
\(637\) | −17.0629 | − | 17.0629i | −0.676056 | − | 0.676056i | ||||
\(638\) | 3.67706 | + | 3.67706i | 0.145576 | + | 0.145576i | ||||
\(639\) | −2.06706 | − | 22.0486i | −0.0817716 | − | 0.872228i | ||||
\(640\) | −1.04211 | + | 1.97839i | −0.0411929 | + | 0.0782026i | ||||
\(641\) | 24.4580i | 0.966032i | 0.875611 | + | 0.483016i | \(0.160459\pi\) | ||||
−0.875611 | + | 0.483016i | \(0.839541\pi\) | |||||||
\(642\) | 0.343378 | + | 7.34145i | 0.0135521 | + | 0.289744i | ||||
\(643\) | −25.1274 | + | 25.1274i | −0.990929 | + | 0.990929i | −0.999959 | − | 0.00903042i | \(-0.997125\pi\) |
0.00903042 | + | 0.999959i | \(0.497125\pi\) | |||||||
\(644\) | 0.416062 | 0.0163951 | ||||||||
\(645\) | 38.0792 | + | 17.8375i | 1.49937 | + | 0.702353i | ||||
\(646\) | −2.55255 | −0.100429 | ||||||||
\(647\) | 34.1529 | − | 34.1529i | 1.34269 | − | 1.34269i | 0.449317 | − | 0.893372i | \(-0.351667\pi\) |
0.893372 | − | 0.449317i | \(-0.148333\pi\) | |||||||
\(648\) | 7.43592 | + | 5.07022i | 0.292110 | + | 0.199177i | ||||
\(649\) | − | 11.2098i | − | 0.440024i | ||||||
\(650\) | 6.98846 | + | 10.1895i | 0.274110 | + | 0.399664i | ||||
\(651\) | 5.24354 | + | 4.77495i | 0.205510 | + | 0.187145i | ||||
\(652\) | −13.3507 | − | 13.3507i | −0.522853 | − | 0.522853i | ||||
\(653\) | −17.7976 | − | 17.7976i | −0.696473 | − | 0.696473i | 0.267175 | − | 0.963648i | \(-0.413910\pi\) |
−0.963648 | + | 0.267175i | \(0.913910\pi\) | |||||||
\(654\) | −10.1276 | − | 9.22258i | −0.396022 | − | 0.360632i | ||||
\(655\) | 3.48317 | − | 1.07970i | 0.136099 | − | 0.0421873i | ||||
\(656\) | − | 4.20851i | − | 0.164315i | ||||||
\(657\) | 19.9600 | − | 24.0897i | 0.778716 | − | 0.939829i | ||||
\(658\) | −27.1676 | + | 27.1676i | −1.05910 | + | 1.05910i | ||||
\(659\) | 39.0933 | 1.52286 | 0.761428 | − | 0.648249i | \(-0.224498\pi\) | ||||
0.761428 | + | 0.648249i | \(0.224498\pi\) | |||||||
\(660\) | −2.14005 | − | 5.91180i | −0.0833014 | − | 0.230117i | ||||
\(661\) | −19.6035 | −0.762488 | −0.381244 | − | 0.924474i | \(-0.624504\pi\) | ||||
−0.381244 | + | 0.924474i | \(0.624504\pi\) | |||||||
\(662\) | 13.5412 | − | 13.5412i | 0.526295 | − | 0.526295i | ||||
\(663\) | 0.111995 | + | 2.39446i | 0.00434953 | + | 0.0929931i | ||||
\(664\) | − | 1.17832i | − | 0.0457276i | ||||||
\(665\) | −36.9202 | − | 19.4475i | −1.43170 | − | 0.754143i | ||||
\(666\) | −23.3129 | + | 2.18559i | −0.903357 | + | 0.0846899i | ||||
\(667\) | 0.230168 | + | 0.230168i | 0.00891214 | + | 0.00891214i | ||||
\(668\) | −3.74931 | − | 3.74931i | −0.145065 | − | 0.145065i | ||||
\(669\) | 33.2768 | − | 36.5424i | 1.28656 | − | 1.41281i | ||||
\(670\) | 7.32183 | + | 23.6206i | 0.282867 | + | 0.912545i | ||||
\(671\) | − | 14.1885i | − | 0.547742i | ||||||
\(672\) | −7.08414 | + | 0.331343i | −0.273277 | + | 0.0127818i | ||||
\(673\) | 1.80880 | − | 1.80880i | 0.0697242 | − | 0.0697242i | −0.671385 | − | 0.741109i | \(-0.734300\pi\) |
0.741109 | + | 0.671385i | \(0.234300\pi\) | |||||||
\(674\) | −0.906164 | −0.0349041 | ||||||||
\(675\) | 19.1617 | − | 17.5450i | 0.737536 | − | 0.675308i | ||||
\(676\) | 6.89344 | 0.265132 | ||||||||
\(677\) | −21.5329 | + | 21.5329i | −0.827578 | + | 0.827578i | −0.987181 | − | 0.159603i | \(-0.948979\pi\) |
0.159603 | + | 0.987181i | \(0.448979\pi\) | |||||||
\(678\) | 33.1994 | − | 1.55282i | 1.27502 | − | 0.0596357i | ||||
\(679\) | 46.1176i | 1.76983i | ||||||||
\(680\) | 0.370778 | + | 1.19615i | 0.0142187 | + | 0.0458703i | ||||
\(681\) | −23.1834 | + | 25.4585i | −0.888389 | + | 0.975571i | ||||
\(682\) | −1.14789 | − | 1.14789i | −0.0439548 | − | 0.0439548i | ||||
\(683\) | −4.74586 | − | 4.74586i | −0.181595 | − | 0.181595i | 0.610455 | − | 0.792051i | \(-0.290987\pi\) |
−0.792051 | + | 0.610455i | \(0.790987\pi\) | |||||||
\(684\) | −13.6136 | + | 1.27628i | −0.520529 | + | 0.0487997i | ||||
\(685\) | 29.0145 | + | 15.2833i | 1.10859 | + | 0.583943i | ||||
\(686\) | − | 11.3210i | − | 0.432238i | ||||||
\(687\) | −0.733132 | − | 15.6744i | −0.0279707 | − | 0.598016i | ||||
\(688\) | −7.67725 | + | 7.67725i | −0.292693 | + | 0.292693i | ||||
\(689\) | 8.71805 | 0.332131 | ||||||||
\(690\) | −0.133958 | − | 0.370053i | −0.00509969 | − | 0.0140877i | ||||
\(691\) | −39.0929 | −1.48716 | −0.743582 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743582 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(692\) | 0.496896 | − | 0.496896i | 0.0188891 | − | 0.0188891i | ||||
\(693\) | 12.7224 | − | 15.3546i | 0.483283 | − | 0.583273i | ||||
\(694\) | − | 16.8101i | − | 0.638103i | ||||||
\(695\) | −34.1328 | + | 10.5804i | −1.29473 | + | 0.401336i | ||||
\(696\) | −4.10229 | − | 3.73569i | −0.155497 | − | 0.141601i | ||||
\(697\) | −1.66662 | − | 1.66662i | −0.0631277 | − | 0.0631277i | ||||
\(698\) | −6.37740 | − | 6.37740i | −0.241388 | − | 0.241388i | ||||
\(699\) | −2.25509 | − | 2.05357i | −0.0852954 | − | 0.0776730i | ||||
\(700\) | −3.75037 | + | 20.1261i | −0.141751 | + | 0.760693i | ||||
\(701\) | 5.93509i | 0.224165i | 0.993699 | + | 0.112083i | \(0.0357521\pi\) | ||||
−0.993699 | + | 0.112083i | \(0.964248\pi\) | |||||||
\(702\) | 1.79454 | + | 12.7144i | 0.0677304 | + | 0.479875i | ||||
\(703\) | 25.1543 | − | 25.1543i | 0.948712 | − | 0.948712i | ||||
\(704\) | 1.62335 | 0.0611825 | ||||||||
\(705\) | 32.9104 | + | 15.4163i | 1.23948 | + | 0.580611i | ||||
\(706\) | 28.4048 | 1.06903 | ||||||||
\(707\) | 39.3038 | − | 39.3038i | 1.47817 | − | 1.47817i | ||||
\(708\) | 0.558807 | + | 11.9473i | 0.0210013 | + | 0.449008i | ||||
\(709\) | 39.1504i | 1.47032i | 0.677891 | + | 0.735162i | \(0.262894\pi\) | ||||
−0.677891 | + | 0.735162i | \(0.737106\pi\) | |||||||
\(710\) | 7.69257 | − | 14.6040i | 0.288697 | − | 0.548077i | ||||
\(711\) | −0.0641513 | − | 0.684279i | −0.00240586 | − | 0.0256625i | ||||
\(712\) | −7.39681 | − | 7.39681i | −0.277207 | − | 0.277207i | ||||
\(713\) | −0.0718525 | − | 0.0718525i | −0.00269090 | − | 0.00269090i | ||||
\(714\) | −2.67419 | + | 2.93662i | −0.100079 | + | 0.109900i | ||||
\(715\) | 4.18046 | − | 7.93639i | 0.156340 | − | 0.296804i | ||||
\(716\) | 5.69409i | 0.212798i | ||||||||
\(717\) | 27.3178 | − | 1.27772i | 1.02020 | − | 0.0477174i | ||||
\(718\) | −18.6233 | + | 18.6233i | −0.695017 | + | 0.695017i | ||||
\(719\) | 40.4594 | 1.50888 | 0.754441 | − | 0.656368i | \(-0.227908\pi\) | ||||
0.754441 | + | 0.656368i | \(0.227908\pi\) | |||||||
\(720\) | 2.57555 | + | 6.19407i | 0.0959852 | + | 0.230839i | ||||
\(721\) | −8.24563 | −0.307083 | ||||||||
\(722\) | 1.25383 | − | 1.25383i | 0.0466628 | − | 0.0466628i | ||||
\(723\) | −16.5415 | + | 0.773690i | −0.615186 | + | 0.0287738i | ||||
\(724\) | − | 16.1019i | − | 0.598422i | ||||||
\(725\) | −13.2086 | + | 9.05912i | −0.490554 | + | 0.336447i | ||||
\(726\) | 9.75481 | − | 10.7121i | 0.362035 | − | 0.397563i | ||||
\(727\) | −7.03815 | − | 7.03815i | −0.261031 | − | 0.261031i | 0.564442 | − | 0.825473i | \(-0.309091\pi\) |
−0.825473 | + | 0.564442i | \(0.809091\pi\) | |||||||
\(728\) | −7.15458 | − | 7.15458i | −0.265166 | − | 0.265166i | ||||
\(729\) | 25.9453 | − | 7.47278i | 0.960936 | − | 0.276770i | ||||
\(730\) | 22.2726 | − | 6.90396i | 0.824345 | − | 0.255527i | ||||
\(731\) | 6.08057i | 0.224898i | ||||||||
\(732\) | 0.707296 | + | 15.1220i | 0.0261424 | + | 0.558926i | ||||
\(733\) | −25.0986 | + | 25.0986i | −0.927040 | + | 0.927040i | −0.997514 | − | 0.0704741i | \(-0.977549\pi\) |
0.0704741 | + | 0.997514i | \(0.477549\pi\) | |||||||
\(734\) | −8.54300 | −0.315328 | ||||||||
\(735\) | −35.5611 | + | 12.8730i | −1.31169 | + | 0.474828i | ||||
\(736\) | 0.101615 | 0.00374557 | ||||||||
\(737\) | 12.6948 | − | 12.6948i | 0.467621 | − | 0.467621i | ||||
\(738\) | −9.72193 | − | 8.05531i | −0.357869 | − | 0.296520i | ||||
\(739\) | − | 27.0688i | − | 0.995740i | −0.867252 | − | 0.497870i | \(-0.834116\pi\) | ||
0.867252 | − | 0.497870i | \(-0.165884\pi\) | |||||||
\(740\) | −15.4414 | − | 8.13369i | −0.567637 | − | 0.299001i | ||||
\(741\) | −14.4236 | − | 13.1346i | −0.529864 | − | 0.482512i | ||||
\(742\) | 10.2143 | + | 10.2143i | 0.374977 | + | 0.374977i | ||||
\(743\) | 17.7922 | + | 17.7922i | 0.652731 | + | 0.652731i | 0.953650 | − | 0.300919i | \(-0.0972933\pi\) |
−0.300919 | + | 0.953650i | \(0.597293\pi\) | |||||||
\(744\) | 1.28063 | + | 1.16619i | 0.0469501 | + | 0.0427544i | ||||
\(745\) | −11.7162 | − | 37.7973i | −0.429250 | − | 1.38479i | ||||
\(746\) | − | 14.8527i | − | 0.543796i | ||||||
\(747\) | −2.72199 | − | 2.25536i | −0.0995923 | − | 0.0825193i | ||||
\(748\) | 0.642868 | − | 0.642868i | 0.0235056 | − | 0.0235056i | ||||
\(749\) | −17.3739 | −0.634827 | ||||||||
\(750\) | 19.1079 | − | 3.14426i | 0.697724 | − | 0.114812i | ||||
\(751\) | −17.7423 | −0.647424 | −0.323712 | − | 0.946156i | \(-0.604931\pi\) | ||||
−0.323712 | + | 0.946156i | \(0.604931\pi\) | |||||||
\(752\) | −6.63515 | + | 6.63515i | −0.241959 | + | 0.241959i | ||||
\(753\) | −0.662229 | − | 14.1585i | −0.0241330 | − | 0.515964i | ||||
\(754\) | − | 7.91591i | − | 0.288280i | ||||||
\(755\) | 5.19327 | + | 16.7538i | 0.189002 | + | 0.609733i | ||||
\(756\) | −12.7940 | + | 16.9990i | −0.465313 | + | 0.618249i | ||||
\(757\) | −23.0320 | − | 23.0320i | −0.837113 | − | 0.837113i | 0.151365 | − | 0.988478i | \(-0.451633\pi\) |
−0.988478 | + | 0.151365i | \(0.951633\pi\) | |||||||
\(758\) | 1.10088 | + | 1.10088i | 0.0399857 | + | 0.0399857i | ||||
\(759\) | −0.192370 | + | 0.211249i | −0.00698260 | + | 0.00766784i | ||||
\(760\) | −9.01701 | − | 4.74967i | −0.327081 | − | 0.172289i | ||||
\(761\) | − | 0.261797i | − | 0.00949014i | −0.999989 | − | 0.00474507i | \(-0.998490\pi\) | ||
0.999989 | − | 0.00474507i | \(-0.00151041\pi\) | |||||||
\(762\) | −3.74607 | + | 0.175213i | −0.135706 | + | 0.00634730i | ||||
\(763\) | 22.8966 | − | 22.8966i | 0.828912 | − | 0.828912i | ||||
\(764\) | −13.8091 | −0.499595 | ||||||||
\(765\) | 3.47288 | + | 1.43298i | 0.125562 | + | 0.0518094i | ||||
\(766\) | 5.00263 | 0.180752 | ||||||||
\(767\) | −12.0661 | + | 12.0661i | −0.435683 | + | 0.435683i | ||||
\(768\) | −1.73016 | + | 0.0809240i | −0.0624317 | + | 0.00292009i | ||||
\(769\) | − | 7.62321i | − | 0.274900i | −0.990509 | − | 0.137450i | \(-0.956109\pi\) | ||
0.990509 | − | 0.137450i | \(-0.0438906\pi\) | |||||||
\(770\) | 14.1964 | − | 4.40053i | 0.511602 | − | 0.158584i | ||||
\(771\) | 6.63860 | − | 7.29008i | 0.239083 | − | 0.262546i | ||||
\(772\) | −9.32773 | − | 9.32773i | −0.335712 | − | 0.335712i | ||||
\(773\) | 20.6595 | + | 20.6595i | 0.743070 | + | 0.743070i | 0.973168 | − | 0.230097i | \(-0.0739045\pi\) |
−0.230097 | + | 0.973168i | \(0.573904\pi\) | |||||||
\(774\) | 3.04028 | + | 32.4296i | 0.109281 | + | 1.16566i | ||||
\(775\) | 4.12338 | − | 2.82803i | 0.148116 | − | 0.101586i | ||||
\(776\) | 11.2633i | 0.404329i | ||||||||
\(777\) | −2.58615 | − | 55.2920i | −0.0927776 | − | 1.98359i | ||||
\(778\) | −23.0901 | + | 23.0901i | −0.827819 | + | 0.827819i | ||||
\(779\) | 19.1814 | 0.687244 | ||||||||
\(780\) | −4.05987 | + | 8.66694i | −0.145367 | + | 0.310326i | ||||
\(781\) | −11.9832 | −0.428793 | ||||||||
\(782\) | 0.0402407 | − | 0.0402407i | 0.00143900 | − | 0.00143900i | ||||
\(783\) | −16.4817 | + | 2.32625i | −0.589007 | + | 0.0831334i | ||||
\(784\) | − | 9.76493i | − | 0.348747i | ||||||
\(785\) | −22.5950 | + | 42.8955i | −0.806450 | + | 1.53100i | ||||
\(786\) | 2.08851 | + | 1.90187i | 0.0744945 | + | 0.0678373i | ||||
\(787\) | −1.98539 | − | 1.98539i | −0.0707716 | − | 0.0707716i | 0.670835 | − | 0.741607i | \(-0.265936\pi\) |
−0.741607 | + | 0.670835i | \(0.765936\pi\) | |||||||
\(788\) | 17.6217 | + | 17.6217i | 0.627746 | + | 0.627746i | ||||
\(789\) | −27.6808 | − | 25.2071i | −0.985461 | − | 0.897395i | ||||
\(790\) | 0.238739 | − | 0.453235i | 0.00849397 | − | 0.0161254i | ||||
\(791\) | 78.5679i | 2.79355i | ||||||||
\(792\) | 3.10719 | − | 3.75006i | 0.110409 | − | 0.133252i | ||||
\(793\) | −15.2724 | + | 15.2724i | −0.542339 | + | 0.542339i | ||||
\(794\) | 12.0754 | 0.428542 | ||||||||
\(795\) | 5.79609 | − | 12.3734i | 0.205566 | − | 0.438839i | ||||
\(796\) | −4.43694 | −0.157263 | ||||||||
\(797\) | −32.7775 | + | 32.7775i | −1.16104 | + | 1.16104i | −0.176790 | + | 0.984249i | \(0.556571\pi\) |
−0.984249 | + | 0.176790i | \(0.943429\pi\) | |||||||
\(798\) | −1.51018 | − | 32.2878i | −0.0534599 | − | 1.14298i | ||||
\(799\) | 5.25519i | 0.185915i | ||||||||
\(800\) | −0.915953 | + | 4.91539i | −0.0323838 | + | 0.173785i | ||||
\(801\) | −31.2450 | + | 2.92923i | −1.10399 | + | 0.103499i | ||||
\(802\) | 22.4116 | + | 22.4116i | 0.791383 | + | 0.791383i | ||||
\(803\) | −11.9703 | − | 11.9703i | −0.422424 | − | 0.422424i | ||||
\(804\) | −12.8972 | + | 14.1629i | −0.454850 | + | 0.499487i | ||||
\(805\) | 0.888630 | − | 0.275454i | 0.0313201 | − | 0.00970847i | ||||
\(806\) | 2.47114i | 0.0870424i | ||||||||
\(807\) | 26.0190 | − | 1.21697i | 0.915911 | − | 0.0428395i | ||||
\(808\) | 9.59917 | − | 9.59917i | 0.337698 | − | 0.337698i | ||||
\(809\) | −11.4242 | −0.401655 | −0.200827 | − | 0.979627i | \(-0.564363\pi\) | ||||
−0.200827 | + | 0.979627i | \(0.564363\pi\) | |||||||
\(810\) | 19.2385 | + | 5.90608i | 0.675970 | + | 0.207519i | ||||
\(811\) | −30.9776 | −1.08777 | −0.543886 | − | 0.839159i | \(-0.683048\pi\) | ||||
−0.543886 | + | 0.839159i | \(0.683048\pi\) | |||||||
\(812\) | 9.27446 | − | 9.27446i | 0.325470 | − | 0.325470i | ||||
\(813\) | 21.9696 | − | 1.02757i | 0.770507 | − | 0.0360386i | ||||
\(814\) | 12.6704i | 0.444096i | ||||||||
\(815\) | −37.3534 | − | 19.6757i | −1.30843 | − | 0.689211i | ||||
\(816\) | −0.653117 | + | 0.717211i | −0.0228637 | + | 0.0251074i | ||||
\(817\) | −34.9911 | − | 34.9911i | −1.22418 | − | 1.22418i | ||||
\(818\) | −13.3722 | − | 13.3722i | −0.467549 | − | 0.467549i | ||||
\(819\) | −30.2218 | + | 2.83330i | −1.05603 | + | 0.0990035i | ||||
\(820\) | −2.78624 | − | 8.98858i | −0.0972998 | − | 0.313895i | ||||
\(821\) | − | 1.02880i | − | 0.0359054i | −0.999839 | − | 0.0179527i | \(-0.994285\pi\) | ||
0.999839 | − | 0.0179527i | \(-0.00571482\pi\) | |||||||
\(822\) | 1.18681 | + | 25.3741i | 0.0413947 | + | 0.885022i | ||||
\(823\) | 24.6895 | − | 24.6895i | 0.860621 | − | 0.860621i | −0.130789 | − | 0.991410i | \(-0.541751\pi\) |
0.991410 | + | 0.130789i | \(0.0417511\pi\) | |||||||
\(824\) | −2.01383 | −0.0701551 | ||||||||
\(825\) | −8.48466 | − | 11.2097i | −0.295398 | − | 0.390271i | ||||
\(826\) | −28.2739 | −0.983775 | ||||||||
\(827\) | 6.48529 | − | 6.48529i | 0.225516 | − | 0.225516i | −0.585301 | − | 0.810816i | \(-0.699024\pi\) |
0.810816 | + | 0.585301i | \(0.199024\pi\) | |||||||
\(828\) | 0.194496 | − | 0.234737i | 0.00675921 | − | 0.00815767i | ||||
\(829\) | − | 17.3145i | − | 0.601356i | −0.953726 | − | 0.300678i | \(-0.902787\pi\) | ||
0.953726 | − | 0.300678i | \(-0.0972129\pi\) | |||||||
\(830\) | −0.780104 | − | 2.51666i | −0.0270778 | − | 0.0873546i | ||||
\(831\) | 20.5523 | + | 18.7156i | 0.712950 | + | 0.649237i | ||||
\(832\) | −1.74736 | − | 1.74736i | −0.0605789 | − | 0.0605789i | ||||
\(833\) | −3.86703 | − | 3.86703i | −0.133985 | − | 0.133985i | ||||
\(834\) | −20.4660 | − | 18.6370i | −0.708679 | − | 0.645348i | ||||
\(835\) | −10.4900 | − | 5.52558i | −0.363023 | − | 0.191221i | ||||
\(836\) | 7.39886i | 0.255895i | ||||||||
\(837\) | 5.14516 | − | 0.726196i | 0.177843 | − | 0.0251010i | ||||
\(838\) | −4.99806 | + | 4.99806i | −0.172655 | + | 0.172655i | ||||
\(839\) | 13.9786 | 0.482594 | 0.241297 | − | 0.970451i | \(-0.422427\pi\) | ||||
0.241297 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(840\) | −14.9110 | + | 5.39774i | −0.514479 | + | 0.186240i | ||||
\(841\) | −18.7386 | −0.646160 | ||||||||
\(842\) | −21.0221 | + | 21.0221i | −0.724468 | + | 0.724468i | ||||
\(843\) | −2.29917 | − | 49.1564i | −0.0791877 | − | 1.69304i | ||||
\(844\) | − | 14.6718i | − | 0.505023i | ||||||
\(845\) | 14.7231 | − | 4.56380i | 0.506490 | − | 0.157000i | ||||
\(846\) | 2.62760 | + | 28.0276i | 0.0903386 | + | 0.963610i | ||||
\(847\) | 24.2179 | + | 24.2179i | 0.832138 | + | 0.832138i | ||||
\(848\) | 2.49463 | + | 2.49463i | 0.0856660 | + | 0.0856660i | ||||
\(849\) | 12.5744 | − | 13.8084i | 0.431552 | − | 0.473903i | ||||
\(850\) | 1.58382 | + | 2.30928i | 0.0543247 | + | 0.0792077i | ||||
\(851\) | 0.793109i | 0.0271874i | ||||||||
\(852\) | 12.7716 | − | 0.597361i | 0.437548 | − | 0.0204652i | ||||
\(853\) | −37.6051 | + | 37.6051i | −1.28757 | + | 1.28757i | −0.351319 | + | 0.936256i | \(0.614267\pi\) |
−0.936256 | + | 0.351319i | \(0.885733\pi\) | |||||||
\(854\) | −35.7870 | −1.22460 | ||||||||
\(855\) | −28.2311 | + | 11.7388i | −0.965483 | + | 0.401457i | ||||
\(856\) | −4.24322 | −0.145030 | ||||||||
\(857\) | −10.2076 | + | 10.2076i | −0.348686 | + | 0.348686i | −0.859620 | − | 0.510934i | \(-0.829300\pi\) |
0.510934 | + | 0.859620i | \(0.329300\pi\) | |||||||
\(858\) | 6.94061 | − | 0.324630i | 0.236949 | − | 0.0110827i | ||||
\(859\) | − | 42.2900i | − | 1.44292i | −0.692458 | − | 0.721458i | \(-0.743472\pi\) | ||
0.692458 | − | 0.721458i | \(-0.256528\pi\) | |||||||
\(860\) | −11.3144 | + | 21.4799i | −0.385819 | + | 0.732458i | ||||
\(861\) | 20.0954 | − | 22.0675i | 0.684849 | − | 0.752057i | ||||
\(862\) | 19.2214 | + | 19.2214i | 0.654684 | + | 0.654684i | ||||
\(863\) | −2.70566 | − | 2.70566i | −0.0921017 | − | 0.0921017i | 0.659555 | − | 0.751656i | \(-0.270745\pi\) |
−0.751656 | + | 0.659555i | \(0.770745\pi\) | |||||||
\(864\) | −3.12468 | + | 4.15167i | −0.106304 | + | 0.141243i | ||||
\(865\) | 0.732306 | − | 1.39025i | 0.0248991 | − | 0.0472698i | ||||
\(866\) | 17.0488i | 0.579342i | ||||||||
\(867\) | −1.35033 | − | 28.8700i | −0.0458595 | − | 0.980478i | ||||
\(868\) | −2.89525 | + | 2.89525i | −0.0982711 | + | 0.0982711i | ||||
\(869\) | −0.371899 | −0.0126158 | ||||||||
\(870\) | −11.2349 | − | 5.26280i | −0.380899 | − | 0.178426i | ||||
\(871\) | −27.3292 | −0.926015 | ||||||||
\(872\) | 5.59204 | − | 5.59204i | 0.189370 | − | 0.189370i | ||||
\(873\) | 26.0190 | + | 21.5586i | 0.880609 | + | 0.729647i | ||||
\(874\) | 0.463136i | 0.0156658i | ||||||||
\(875\) | 5.31437 | + | 45.4684i | 0.179658 | + | 1.53711i | ||||
\(876\) | 13.3546 | + | 12.1612i | 0.451210 | + | 0.410888i | ||||
\(877\) | 27.0903 | + | 27.0903i | 0.914774 | + | 0.914774i | 0.996643 | − | 0.0818686i | \(-0.0260888\pi\) |
−0.0818686 | + | 0.996643i | \(0.526089\pi\) | |||||||
\(878\) | −3.10046 | − | 3.10046i | −0.104636 | − | 0.104636i | ||||
\(879\) | 9.20090 | + | 8.37866i | 0.310339 | + | 0.282605i | ||||
\(880\) | 3.46718 | − | 1.07474i | 0.116879 | − | 0.0362295i | ||||
\(881\) | 14.3326i | 0.482878i | 0.970416 | + | 0.241439i | \(0.0776193\pi\) | ||||
−0.970416 | + | 0.241439i | \(0.922381\pi\) | |||||||
\(882\) | −22.5576 | − | 18.6906i | −0.759554 | − | 0.629345i | ||||
\(883\) | −3.56870 | + | 3.56870i | −0.120096 | + | 0.120096i | −0.764601 | − | 0.644504i | \(-0.777064\pi\) |
0.644504 | + | 0.764601i | \(0.277064\pi\) | |||||||
\(884\) | −1.38395 | −0.0465474 | ||||||||
\(885\) | 9.10324 | + | 25.1473i | 0.306002 | + | 0.845317i | ||||
\(886\) | 26.3861 | 0.886457 | ||||||||
\(887\) | −29.8263 | + | 29.8263i | −1.00147 | + | 1.00147i | −0.00147171 | + | 0.999999i | \(0.500468\pi\) |
−0.999999 | + | 0.00147171i | \(0.999532\pi\) | |||||||
\(888\) | −0.631616 | − | 13.5040i | −0.0211956 | − | 0.453164i | ||||
\(889\) | − | 8.86524i | − | 0.297330i | ||||||
\(890\) | −20.6953 | − | 10.9011i | −0.693707 | − | 0.365407i | ||||
\(891\) | −2.71555 | − | 14.3556i | −0.0909744 | − | 0.480931i | ||||
\(892\) | 20.1771 | + | 20.1771i | 0.675580 | + | 0.675580i | ||||
\(893\) | −30.2414 | − | 30.2414i | −1.01199 | − | 1.01199i | ||||
\(894\) | 20.6379 | − | 22.6632i | 0.690234 | − | 0.757971i | ||||
\(895\) | 3.76977 | + | 12.1615i | 0.126010 | + | 0.406514i | ||||
\(896\) | − | 4.09450i | − | 0.136788i | ||||||
\(897\) | 0.434452 | − | 0.0203204i | 0.0145059 | − | 0.000678479i | ||||
\(898\) | −7.17914 | + | 7.17914i | −0.239571 | + | 0.239571i | ||||
\(899\) | −3.20334 | −0.106837 | ||||||||
\(900\) | 9.60168 | + | 11.5242i | 0.320056 | + | 0.384141i | ||||
\(901\) | 1.97581 | 0.0658237 | ||||||||
\(902\) | −4.83088 | + | 4.83088i | −0.160851 | + | 0.160851i | ||||
\(903\) | −76.9144 | + | 3.59749i | −2.55955 | + | 0.119717i | ||||
\(904\) | 19.1886i | 0.638205i | ||||||||
\(905\) | −10.6603 | − | 34.3906i | −0.354359 | − | 1.14318i | ||||
\(906\) | −9.14782 | + | 10.0455i | −0.303916 | + | 0.333741i | ||||
\(907\) | −12.9671 | − | 12.9671i | −0.430564 | − | 0.430564i | 0.458256 | − | 0.888820i | \(-0.348474\pi\) |
−0.888820 | + | 0.458256i | \(0.848474\pi\) | |||||||
\(908\) | −14.0570 | − | 14.0570i | −0.466499 | − | 0.466499i | ||||
\(909\) | −3.80139 | − | 40.5480i | −0.126084 | − | 1.34489i | ||||
\(910\) | −20.0175 | − | 10.5441i | −0.663574 | − | 0.349535i | ||||
\(911\) | − | 10.4211i | − | 0.345266i | −0.984986 | − | 0.172633i | \(-0.944773\pi\) | ||
0.984986 | − | 0.172633i | \(-0.0552275\pi\) | |||||||
\(912\) | −0.368832 | − | 7.88565i | −0.0122133 | − | 0.261120i | ||||
\(913\) | −1.35257 | + | 1.35257i | −0.0447636 | + | 0.0447636i | ||||
\(914\) | 8.81490 | 0.291571 | ||||||||
\(915\) | 11.5222 | + | 31.8295i | 0.380912 | + | 1.05225i | ||||
\(916\) | 9.05951 | 0.299335 | ||||||||
\(917\) | −4.72170 | + | 4.72170i | −0.155924 | + | 0.155924i | ||||
\(918\) | 0.406703 | + | 2.88152i | 0.0134232 | + | 0.0951044i | ||||
\(919\) | − | 6.66283i | − | 0.219787i | −0.993943 | − | 0.109893i | \(-0.964949\pi\) | ||
0.993943 | − | 0.109893i | \(-0.0350509\pi\) | |||||||
\(920\) | 0.217030 | − | 0.0672741i | 0.00715527 | − | 0.00221796i | ||||
\(921\) | 35.6559 | + | 32.4695i | 1.17490 | + | 1.06991i | ||||
\(922\) | −5.08914 | − | 5.08914i | −0.167602 | − | 0.167602i | ||||
\(923\) | 12.8986 | + | 12.8986i | 0.424563 | + | 0.424563i | ||||
\(924\) | 8.51212 | + | 7.75143i | 0.280028 | + | 0.255003i | ||||
\(925\) | −38.3648 | − | 7.14906i | −1.26143 | − | 0.235060i | ||||
\(926\) | − | 22.0262i | − | 0.723826i | ||||||
\(927\) | −3.85458 | + | 4.65208i | −0.126601 | + | 0.152794i | ||||
\(928\) | 2.26510 | − | 2.26510i | 0.0743556 | − | 0.0743556i | ||||
\(929\) | −7.60114 | −0.249385 | −0.124693 | − | 0.992195i | \(-0.539795\pi\) | ||||
−0.124693 | + | 0.992195i | \(0.539795\pi\) | |||||||
\(930\) | 3.50726 | + | 1.64291i | 0.115007 | + | 0.0538732i | ||||
\(931\) | 44.5062 | 1.45863 | ||||||||
\(932\) | 1.24516 | − | 1.24516i | 0.0407866 | − | 0.0407866i | ||||
\(933\) | −0.560395 | − | 11.9813i | −0.0183465 | − | 0.392249i | ||||
\(934\) | − | 38.2093i | − | 1.25025i | ||||||
\(935\) | 0.947434 | − | 1.79866i | 0.0309844 | − | 0.0588223i | ||||
\(936\) | −7.38107 | + | 0.691977i | −0.241258 | + | 0.0226180i | ||||
\(937\) | −34.7274 | − | 34.7274i | −1.13449 | − | 1.13449i | −0.989421 | − | 0.145073i | \(-0.953658\pi\) |
−0.145073 | − | 0.989421i | \(-0.546342\pi\) | |||||||
\(938\) | −32.0195 | − | 32.0195i | −1.04547 | − | 1.04547i | ||||
\(939\) | 17.3482 | − | 19.0507i | 0.566137 | − | 0.621695i | ||||
\(940\) | −9.77862 | + | 18.5642i | −0.318943 | + | 0.605498i | ||||
\(941\) | − | 11.3755i | − | 0.370832i | −0.982660 | − | 0.185416i | \(-0.940637\pi\) | ||
0.982660 | − | 0.185416i | \(-0.0593632\pi\) | |||||||
\(942\) | −37.5134 | + | 1.75460i | −1.22225 | + | 0.0571679i | ||||
\(943\) | −0.302392 | + | 0.302392i | −0.00984724 | + | 0.00984724i | ||||
\(944\) | −6.90534 | −0.224750 | ||||||||
\(945\) | −16.0713 | + | 44.7770i | −0.522801 | + | 1.45659i | ||||
\(946\) | 17.6252 | 0.573045 | ||||||||
\(947\) | −2.49401 | + | 2.49401i | −0.0810444 | + | 0.0810444i | −0.746467 | − | 0.665423i | \(-0.768251\pi\) |
0.665423 | + | 0.746467i | \(0.268251\pi\) | |||||||
\(948\) | 0.396368 | − | 0.0185391i | 0.0128734 | − | 0.000602123i | ||||
\(949\) | 25.7695i | 0.836513i | ||||||||
\(950\) | −22.4032 | − | 4.17469i | −0.726854 | − | 0.135445i | ||||
\(951\) | 28.9657 | − | 31.8082i | 0.939276 | − | 1.03145i | ||||
\(952\) | −1.62147 | − | 1.62147i | −0.0525522 | − | 0.0525522i | ||||
\(953\) | 20.1590 | + | 20.1590i | 0.653013 | + | 0.653013i | 0.953717 | − | 0.300704i | \(-0.0972217\pi\) |
−0.300704 | + | 0.953717i | \(0.597222\pi\) | |||||||
\(954\) | 10.5376 | − | 0.987904i | 0.341168 | − | 0.0319846i | ||||
\(955\) | −29.4936 | + | 9.14231i | −0.954391 | + | 0.295838i | ||||
\(956\) | 15.7892i | 0.510659i | ||||||||
\(957\) | 0.420817 | + | 8.99709i | 0.0136031 | + | 0.290835i | ||||
\(958\) | −14.1978 | + | 14.1978i | −0.458710 | + | 0.458710i | ||||
\(959\) | −60.0488 | −1.93908 | ||||||||
\(960\) | −3.64172 | + | 1.31829i | −0.117536 | + | 0.0425476i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 13.6383 | − | 13.6383i | 0.439715 | − | 0.439715i | ||||
\(963\) | −8.12175 | + | 9.80211i | −0.261720 | + | 0.315869i | ||||
\(964\) | − | 9.56070i | − | 0.307929i | ||||||
\(965\) | −26.0977 | − | 13.7468i | −0.840114 | − | 0.442527i | ||||
\(966\) | 0.532821 | + | 0.485205i | 0.0171432 | + | 0.0156112i | ||||
\(967\) | 42.9073 | + | 42.9073i | 1.37981 | + | 1.37981i | 0.844930 | + | 0.534877i | \(0.179642\pi\) |
0.534877 | + | 0.844930i | \(0.320358\pi\) | |||||||
\(968\) | 5.91475 | + | 5.91475i | 0.190107 | + | 0.190107i | ||||
\(969\) | −3.26887 | − | 2.97675i | −0.105011 | − | 0.0956270i | ||||
\(970\) | 7.45687 | + | 24.0563i | 0.239426 | + | 0.772401i | ||||
\(971\) | − | 13.1853i | − | 0.423137i | −0.977363 | − | 0.211568i | \(-0.932143\pi\) | ||
0.977363 | − | 0.211568i | \(-0.0678571\pi\) | |||||||
\(972\) | 3.60984 | + | 15.1647i | 0.115786 | + | 0.486409i | ||||
\(973\) | 46.2695 | − | 46.2695i | 1.48333 | − | 1.48333i | ||||
\(974\) | −1.56484 | −0.0501406 | ||||||||
\(975\) | −2.93318 | + | 21.1988i | −0.0939369 | + | 0.678904i | ||||
\(976\) | −8.74025 | −0.279769 | ||||||||
\(977\) | 13.9002 | − | 13.9002i | 0.444706 | − | 0.444706i | −0.448884 | − | 0.893590i | \(-0.648178\pi\) |
0.893590 | + | 0.448884i | \(0.148178\pi\) | |||||||
\(978\) | −1.52790 | − | 32.6667i | −0.0488569 | − | 1.04456i | ||||
\(979\) | 16.9814i | 0.542728i | ||||||||
\(980\) | −6.46487 | − | 20.8560i | −0.206513 | − | 0.666222i | ||||
\(981\) | −2.21451 | − | 23.6214i | −0.0707040 | − | 0.754174i | ||||
\(982\) | −28.1788 | − | 28.1788i | −0.899220 | − | 0.899220i | ||||
\(983\) | −30.0974 | − | 30.0974i | −0.959958 | − | 0.959958i | 0.0392708 | − | 0.999229i | \(-0.487496\pi\) |
−0.999229 | + | 0.0392708i | \(0.987496\pi\) | |||||||
\(984\) | 4.90790 | − | 5.38954i | 0.156458 | − | 0.171812i | ||||
\(985\) | 49.3030 | + | 25.9701i | 1.57092 | + | 0.827477i | ||||
\(986\) | − | 1.79401i | − | 0.0571331i | ||||||
\(987\) | −66.4741 | + | 3.10916i | −2.11589 | + | 0.0989658i | ||||
\(988\) | 7.96406 | − | 7.96406i | 0.253371 | − | 0.253371i | ||||
\(989\) | 1.10326 | 0.0350816 | ||||||||
\(990\) | 4.15364 | − | 10.0665i | 0.132011 | − | 0.319935i | ||||
\(991\) | 42.9669 | 1.36489 | 0.682444 | − | 0.730937i | \(-0.260917\pi\) | ||||
0.682444 | + | 0.730937i | \(0.260917\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | 33.1329 | − | 1.54971i | 1.05144 | − | 0.0491786i | ||||
\(994\) | 30.2246i | 0.958666i | ||||||||
\(995\) | −9.47647 | + | 2.93748i | −0.300424 | + | 0.0931243i | ||||
\(996\) | 1.37414 | − | 1.50899i | 0.0435412 | − | 0.0478141i | ||||
\(997\) | −26.5138 | − | 26.5138i | −0.839701 | − | 0.839701i | 0.149118 | − | 0.988819i | \(-0.452357\pi\) |
−0.988819 | + | 0.149118i | \(0.952357\pi\) | |||||||
\(998\) | 1.36706 | + | 1.36706i | 0.0432734 | + | 0.0432734i | ||||
\(999\) | −32.4040 | − | 24.3883i | −1.02522 | − | 0.771610i |
(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 | 930.2.j.h.497.1 | ✓ | 40 | |
3.2 | odd | 2 | inner | 930.2.j.h.497.16 | yes | 40 | |
5.3 | odd | 4 | inner | 930.2.j.h.683.16 | yes | 40 | |
15.8 | even | 4 | inner | 930.2.j.h.683.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.h.497.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
930.2.j.h.497.16 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.j.h.683.1 | yes | 40 | 15.8 | even | 4 | inner | |
930.2.j.h.683.16 | yes | 40 | 5.3 | odd | 4 | inner |