Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1793.8 | ||
Character | \(\chi\) | \(=\) | 2100.1793 |
Dual form | 2100.2.s.b.1457.8 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.04182 | + | 1.38370i | 0.601494 | + | 0.798877i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.829228 | + | 2.88312i | −0.276409 | + | 0.961040i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.21059i | − | 0.365007i | −0.983205 | − | 0.182504i | \(-0.941580\pi\) | ||
0.983205 | − | 0.182504i | \(-0.0584201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.31886 | + | 1.31886i | 0.365785 | + | 0.365785i | 0.865938 | − | 0.500152i | \(-0.166723\pi\) |
−0.500152 | + | 0.865938i | \(0.666723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.79377 | + | 4.79377i | 1.16266 | + | 1.16266i | 0.983891 | + | 0.178770i | \(0.0572117\pi\) |
0.178770 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.66781i | 0.841454i | 0.907187 | + | 0.420727i | \(0.138225\pi\) | ||||
−0.907187 | + | 0.420727i | \(0.861775\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71510 | − | 0.241744i | −0.374265 | − | 0.0527528i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.15405 | − | 6.15405i | 1.28321 | − | 1.28321i | 0.344376 | − | 0.938832i | \(-0.388091\pi\) |
0.938832 | − | 0.344376i | \(-0.111909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.85327 | + | 1.85629i | −0.934011 | + | 0.357243i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.65350 | −1.23552 | −0.617762 | − | 0.786365i | \(-0.711960\pi\) | ||||
−0.617762 | + | 0.786365i | \(0.711960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.677592 | 0.121699 | 0.0608495 | − | 0.998147i | \(-0.480619\pi\) | ||||
0.0608495 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.67509 | − | 1.26122i | 0.291596 | − | 0.219550i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.16682 | + | 5.16682i | −0.849419 | + | 0.849419i | −0.990061 | − | 0.140641i | \(-0.955084\pi\) |
0.140641 | + | 0.990061i | \(0.455084\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.450887 | + | 3.19891i | −0.0721997 | + | 0.512235i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.65662i | − | 0.727242i | −0.931547 | − | 0.363621i | \(-0.881540\pi\) | ||
0.931547 | − | 0.363621i | \(-0.118460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35753 | + | 2.35753i | 0.359520 | + | 0.359520i | 0.863636 | − | 0.504116i | \(-0.168182\pi\) |
−0.504116 | + | 0.863636i | \(0.668182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.91004 | + | 1.91004i | 0.278608 | + | 0.278608i | 0.832553 | − | 0.553945i | \(-0.186878\pi\) |
−0.553945 | + | 0.832553i | \(0.686878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.63888 | + | 11.6274i | −0.229489 | + | 1.62816i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.64475 | + | 8.64475i | −1.18745 | + | 1.18745i | −0.209678 | + | 0.977771i | \(0.567241\pi\) |
−0.977771 | + | 0.209678i | \(0.932759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.07514 | + | 3.82120i | −0.672219 | + | 0.506130i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.62929 | 0.863061 | 0.431530 | − | 0.902098i | \(-0.357974\pi\) | ||||
0.431530 | + | 0.902098i | \(0.357974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07370 | −0.905695 | −0.452847 | − | 0.891588i | \(-0.649592\pi\) | ||||
−0.452847 | + | 0.891588i | \(0.649592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.45232 | − | 2.62503i | −0.182975 | − | 0.330722i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94717 | + | 4.94717i | −0.604394 | + | 0.604394i | −0.941475 | − | 0.337082i | \(-0.890560\pi\) |
0.337082 | + | 0.941475i | \(0.390560\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.9267 | + | 2.10393i | 1.79697 | + | 0.253283i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.87014i | 0.221945i | 0.993823 | + | 0.110972i | \(0.0353965\pi\) | ||||
−0.993823 | + | 0.110972i | \(0.964603\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.93894 | + | 7.93894i | 0.929183 | + | 0.929183i | 0.997653 | − | 0.0684701i | \(-0.0218118\pi\) |
−0.0684701 | + | 0.997653i | \(0.521812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.856017 | + | 0.856017i | 0.0975522 | + | 0.0975522i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6399i | 1.19708i | 0.801093 | + | 0.598539i | \(0.204252\pi\) | ||||
−0.801093 | + | 0.598539i | \(0.795748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.62476 | − | 4.78153i | −0.847196 | − | 0.531281i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.69039 | + | 9.69039i | −1.06366 | + | 1.06366i | −0.0658277 | + | 0.997831i | \(0.520969\pi\) |
−0.997831 | + | 0.0658277i | \(0.979031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.93174 | − | 9.20642i | −0.743161 | − | 0.987032i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.84828 | 0.301917 | 0.150958 | − | 0.988540i | \(-0.451764\pi\) | ||||
0.150958 | + | 0.988540i | \(0.451764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.86515 | −0.195520 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.705928 | + | 0.937581i | 0.0732013 | + | 0.0972226i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.90018 | + | 3.90018i | −0.396003 | + | 0.396003i | −0.876821 | − | 0.480817i | \(-0.840340\pi\) |
0.480817 | + | 0.876821i | \(0.340340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.49028 | + | 1.00386i | 0.350786 | + | 0.100891i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.69232i | − | 0.765415i | −0.923870 | − | 0.382707i | \(-0.874992\pi\) | ||
0.923870 | − | 0.382707i | \(-0.125008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.59549 | + | 3.59549i | 0.354274 | + | 0.354274i | 0.861697 | − | 0.507423i | \(-0.169402\pi\) |
−0.507423 | + | 0.861697i | \(0.669402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.72919 | − | 1.72919i | −0.167167 | − | 0.167167i | 0.618566 | − | 0.785733i | \(-0.287714\pi\) |
−0.785733 | + | 0.618566i | \(0.787714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.6004i | − | 1.87738i | −0.344766 | − | 0.938688i | \(-0.612042\pi\) | ||
0.344766 | − | 0.938688i | \(-0.387958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.5322 | − | 1.76642i | −1.18950 | − | 0.167661i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9813 | − | 11.9813i | 1.12711 | − | 1.12711i | 0.136465 | − | 0.990645i | \(-0.456426\pi\) |
0.990645 | − | 0.136465i | \(-0.0435742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.89606 | + | 2.70879i | −0.452641 | + | 0.250428i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.77942 | −0.621468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53447 | 0.866770 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.44334 | − | 4.85135i | 0.580977 | − | 0.437432i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.34817 | + | 2.34817i | −0.208366 | + | 0.208366i | −0.803573 | − | 0.595207i | \(-0.797070\pi\) |
0.595207 | + | 0.803573i | \(0.297070\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.805985 | + | 5.71822i | −0.0709630 | + | 0.503461i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.9036i | 1.04002i | 0.854160 | + | 0.520010i | \(0.174072\pi\) | ||||
−0.854160 | + | 0.520010i | \(0.825928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59354 | − | 2.59354i | −0.224888 | − | 0.224888i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.88006 | − | 7.88006i | −0.673239 | − | 0.673239i | 0.285222 | − | 0.958461i | \(-0.407933\pi\) |
−0.958461 | + | 0.285222i | \(0.907933\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.15820i | 0.437513i | 0.975779 | + | 0.218756i | \(0.0702000\pi\) | ||||
−0.975779 | + | 0.218756i | \(0.929800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.652998 | + | 4.63283i | −0.0549924 | + | 0.390154i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.59660 | − | 1.59660i | 0.133514 | − | 0.133514i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.38370 | − | 1.04182i | 0.114125 | − | 0.0859278i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.16856 | −0.751118 | −0.375559 | − | 0.926798i | \(-0.622549\pi\) | ||||
−0.375559 | + | 0.926798i | \(0.622549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.55639 | −0.370794 | −0.185397 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185397 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.7961 | + | 9.84589i | −1.43873 | + | 0.795993i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5673 | − | 12.5673i | 1.00298 | − | 1.00298i | 0.00298395 | − | 0.999996i | \(-0.499050\pi\) |
0.999996 | − | 0.00298395i | \(-0.000949822\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.9680 | − | 2.95544i | −1.66287 | − | 0.234382i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.70314i | 0.685903i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8032 | + | 17.8032i | 1.39446 | + | 1.39446i | 0.815012 | + | 0.579444i | \(0.196730\pi\) |
0.579444 | + | 0.815012i | \(0.303270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.53053 | + | 8.53053i | 0.660112 | + | 0.660112i | 0.955406 | − | 0.295294i | \(-0.0954177\pi\) |
−0.295294 | + | 0.955406i | \(0.595418\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.52123i | − | 0.732402i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5748 | − | 3.04145i | −0.808671 | − | 0.232586i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.46780 | − | 3.46780i | 0.263652 | − | 0.263652i | −0.562884 | − | 0.826536i | \(-0.690308\pi\) |
0.826536 | + | 0.562884i | \(0.190308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.90652 | + | 9.17293i | 0.519126 | + | 0.689479i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3729 | 1.52274 | 0.761370 | − | 0.648318i | \(-0.224527\pi\) | ||||
0.761370 | + | 0.648318i | \(0.224527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.23245 | 0.240266 | 0.120133 | − | 0.992758i | \(-0.461668\pi\) | ||||
0.120133 | + | 0.992758i | \(0.461668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.36952 | − | 9.78785i | −0.544770 | − | 0.723539i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.80330 | − | 5.80330i | 0.424379 | − | 0.424379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.11918 | − | 4.74437i | 0.154148 | − | 0.345102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.7248i | − | 0.848377i | −0.905574 | − | 0.424189i | \(-0.860559\pi\) | ||
0.905574 | − | 0.424189i | \(-0.139441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.23315 | − | 9.23315i | −0.664617 | − | 0.664617i | 0.291848 | − | 0.956465i | \(-0.405730\pi\) |
−0.956465 | + | 0.291848i | \(0.905730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.73126 | + | 6.73126i | 0.479583 | + | 0.479583i | 0.904998 | − | 0.425415i | \(-0.139872\pi\) |
−0.425415 | + | 0.904998i | \(0.639872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.77719i | − | 0.267758i | −0.990998 | − | 0.133879i | \(-0.957257\pi\) | ||
0.990998 | − | 0.133879i | \(-0.0427434\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9994 | − | 1.69133i | −0.846376 | − | 0.119297i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.70474 | − | 4.70474i | 0.330208 | − | 0.330208i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6398 | + | 22.8460i | 0.878523 | + | 1.58790i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.44023 | 0.307137 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.31292 | −0.228071 | −0.114035 | − | 0.993477i | \(-0.536378\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536378\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.58770 | + | 1.94835i | −0.177307 | + | 0.133499i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.479130 | + | 0.479130i | −0.0325254 | + | 0.0325254i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.71414 | + | 19.2560i | −0.183405 | + | 1.30120i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6446i | 0.850568i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.06323 | + | 3.06323i | 0.205129 | + | 0.205129i | 0.802193 | − | 0.597064i | \(-0.203666\pi\) |
−0.597064 | + | 0.802193i | \(0.703666\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6081 | − | 13.6081i | −0.903204 | − | 0.903204i | 0.0925080 | − | 0.995712i | \(-0.470512\pi\) |
−0.995712 | + | 0.0925080i | \(0.970512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.3847i | − | 1.14882i | −0.818569 | − | 0.574408i | \(-0.805232\pi\) | ||
0.818569 | − | 0.574408i | \(-0.194768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.292653 | + | 2.07628i | −0.0192551 | + | 0.136609i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.37732 | − | 2.37732i | 0.155743 | − | 0.155743i | −0.624934 | − | 0.780678i | \(-0.714874\pi\) |
0.780678 | + | 0.624934i | \(0.214874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7223 | + | 11.0848i | −0.956319 | + | 0.720036i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2026 | −0.983376 | −0.491688 | − | 0.870771i | \(-0.663620\pi\) | ||||
−0.491688 | + | 0.870771i | \(0.663620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5037 | 0.741021 | 0.370511 | − | 0.928828i | \(-0.379183\pi\) | ||||
0.370511 | + | 0.928828i | \(0.379183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.32744 | − | 15.5318i | −0.0851555 | − | 0.996368i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.83733 | + | 4.83733i | −0.307792 | + | 0.307792i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.5042 | − | 3.31292i | −1.48952 | − | 0.209948i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.0928i | − | 1.07889i | −0.842021 | − | 0.539445i | \(-0.818634\pi\) | ||
0.842021 | − | 0.539445i | \(-0.181366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.45004 | − | 7.45004i | −0.468380 | − | 0.468380i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.85821 | − | 7.85821i | −0.490182 | − | 0.490182i | 0.418182 | − | 0.908363i | \(-0.362668\pi\) |
−0.908363 | + | 0.418182i | \(0.862668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.30698i | − | 0.454034i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.51727 | − | 19.1828i | 0.341510 | − | 1.18739i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6251 | + | 10.6251i | −0.655172 | + | 0.655172i | −0.954234 | − | 0.299062i | \(-0.903326\pi\) |
0.299062 | + | 0.954234i | \(0.403326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96739 | + | 3.94115i | 0.181601 | + | 0.241194i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.5570 | −1.13144 | −0.565720 | − | 0.824598i | \(-0.691402\pi\) | ||||
−0.565720 | + | 0.824598i | \(0.691402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7027 | 1.19685 | 0.598427 | − | 0.801177i | \(-0.295792\pi\) | ||||
0.598427 | + | 0.801177i | \(0.295792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.94314 | − | 2.58080i | −0.117604 | − | 0.156197i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3407 | − | 16.3407i | 0.981815 | − | 0.981815i | −0.0180230 | − | 0.999838i | \(-0.505737\pi\) |
0.999838 | + | 0.0180230i | \(0.00573721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.561878 | + | 1.95358i | −0.0336387 | + | 0.116958i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7751i | 0.642788i | 0.946945 | + | 0.321394i | \(0.104151\pi\) | ||||
−0.946945 | + | 0.321394i | \(0.895849\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2145 | + | 12.2145i | 0.726074 | + | 0.726074i | 0.969835 | − | 0.243761i | \(-0.0783812\pi\) |
−0.243761 | + | 0.969835i | \(0.578381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.29273 | + | 3.29273i | 0.194364 | + | 0.194364i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.9605i | 1.70356i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.45994 | − | 1.33338i | −0.554552 | − | 0.0781642i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.4296 | − | 12.4296i | 0.726148 | − | 0.726148i | −0.243702 | − | 0.969850i | \(-0.578362\pi\) |
0.969850 | + | 0.243702i | \(0.0783620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.24721 | + | 5.87532i | 0.130396 | + | 0.340921i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.2326 | 0.938757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.33405 | −0.192171 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.6438 | − | 8.01401i | 0.611472 | − | 0.460393i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.76706 | − | 6.76706i | 0.386217 | − | 0.386217i | −0.487119 | − | 0.873336i | \(-0.661952\pi\) |
0.873336 | + | 0.487119i | \(0.161952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.22921 | + | 8.72091i | −0.0699276 | + | 0.496115i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.8435i | 1.40875i | 0.709830 | + | 0.704373i | \(0.248772\pi\) | ||||
−0.709830 | + | 0.704373i | \(0.751228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.53954 | − | 2.53954i | −0.143543 | − | 0.143543i | 0.631683 | − | 0.775227i | \(-0.282364\pi\) |
−0.775227 | + | 0.631683i | \(0.782364\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.68000 | − | 4.68000i | −0.262855 | − | 0.262855i | 0.563358 | − | 0.826213i | \(-0.309509\pi\) |
−0.826213 | + | 0.563358i | \(0.809509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.05467i | 0.450975i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.591170 | − | 4.19417i | 0.0329959 | − | 0.234096i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.5827 | + | 17.5827i | −0.978326 | + | 0.978326i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.1210 | − | 20.4201i | 1.49979 | − | 1.12923i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.70120 | −0.148922 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.4286 | 1.78244 | 0.891218 | − | 0.453576i | \(-0.149852\pi\) | ||||
0.891218 | + | 0.453576i | \(0.149852\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.6121 | − | 19.1810i | −0.581539 | − | 1.05111i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6095 | + | 17.6095i | −0.959250 | + | 0.959250i | −0.999202 | − | 0.0399517i | \(-0.987280\pi\) |
0.0399517 | + | 0.999202i | \(0.487280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.0609 | + | 4.09615i | 1.57837 | + | 0.222472i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.820287i | − | 0.0444210i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5184 | − | 12.5184i | −0.672023 | − | 0.672023i | 0.286159 | − | 0.958182i | \(-0.407622\pi\) |
−0.958182 | + | 0.286159i | \(0.907622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 17.7929i | − | 0.952429i | −0.879329 | − | 0.476215i | \(-0.842008\pi\) | ||
0.879329 | − | 0.476215i | \(-0.157992\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.84895 | − | 3.95259i | −0.472322 | − | 0.210973i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.66929 | − | 3.66929i | 0.195297 | − | 0.195297i | −0.602684 | − | 0.797980i | \(-0.705902\pi\) |
0.797980 | + | 0.602684i | \(0.205902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.06292 | − | 9.38065i | −0.373810 | − | 0.496477i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.5503 | 1.55960 | 0.779802 | − | 0.626026i | \(-0.215320\pi\) | ||||
0.779802 | + | 0.626026i | \(0.215320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.54713 | 0.291954 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.93319 | + | 13.1928i | 0.521357 | + | 0.692443i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5412 | − | 21.5412i | 1.12444 | − | 1.12444i | 0.133377 | − | 0.991065i | \(-0.457418\pi\) |
0.991065 | − | 0.133377i | \(-0.0425823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.4256 | + | 3.86140i | 0.698909 | + | 0.201016i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 12.2255i | − | 0.634718i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.4363 | + | 12.4363i | 0.643929 | + | 0.643929i | 0.951519 | − | 0.307590i | \(-0.0995225\pi\) |
−0.307590 | + | 0.951519i | \(0.599523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.77502 | − | 8.77502i | −0.451937 | − | 0.451937i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4965i | 0.693270i | 0.938000 | + | 0.346635i | \(0.112676\pi\) | ||||
−0.938000 | + | 0.346635i | \(0.887324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.69551 | − | 0.802784i | −0.291790 | − | 0.0411279i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.78763 | + | 6.78763i | −0.346832 | + | 0.346832i | −0.858928 | − | 0.512096i | \(-0.828869\pi\) |
0.512096 | + | 0.858928i | \(0.328869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.75197 | + | 4.84211i | −0.444887 | + | 0.246138i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.3012 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.0022 | 2.98387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.4709 | + | 12.4014i | −0.830849 | + | 0.625567i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.83384 | − | 1.83384i | 0.0920379 | − | 0.0920379i | −0.659589 | − | 0.751627i | \(-0.729270\pi\) |
0.751627 | + | 0.659589i | \(0.229270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.886671 | − | 6.29066i | 0.0443891 | − | 0.314927i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.1431i | 1.10577i | 0.833257 | + | 0.552886i | \(0.186474\pi\) | ||||
−0.833257 | + | 0.552886i | \(0.813526\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.893647 | + | 0.893647i | 0.0445157 | + | 0.0445157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.25490 | + | 6.25490i | 0.310044 | + | 0.310044i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.1801i | − | 1.09673i | −0.836238 | − | 0.548366i | \(-0.815250\pi\) | ||
0.836238 | − | 0.548366i | \(-0.184750\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.69401 | − | 19.1132i | 0.132886 | − | 0.942784i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.68762 | + | 4.68762i | −0.230663 | + | 0.230663i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.13738 | + | 5.37391i | −0.349519 | + | 0.263162i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0297 | −0.783102 | −0.391551 | − | 0.920156i | \(-0.628061\pi\) | ||||
−0.391551 | + | 0.920156i | \(0.628061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.809448 | 0.0394501 | 0.0197250 | − | 0.999805i | \(-0.493721\pi\) | ||||
0.0197250 | + | 0.999805i | \(0.493721\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.09073 | + | 3.92301i | −0.344763 | + | 0.190743i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00186 | − | 5.00186i | 0.242057 | − | 0.242057i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.87257 | + | 0.545840i | 0.186969 | + | 0.0263534i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27.5870i | − | 1.32882i | −0.747369 | − | 0.664409i | \(-0.768683\pi\) | ||
0.747369 | − | 0.664409i | \(-0.231317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.3930 | − | 10.3930i | −0.499458 | − | 0.499458i | 0.411811 | − | 0.911269i | \(-0.364896\pi\) |
−0.911269 | + | 0.411811i | \(0.864896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.5719 | + | 22.5719i | 1.07976 | + | 1.07976i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.3915i | − | 1.30733i | −0.756786 | − | 0.653663i | \(-0.773231\pi\) | ||
0.756786 | − | 0.653663i | \(-0.226769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.88312 | + | 0.829228i | 0.137291 | + | 0.0394870i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5303 | + | 14.5303i | −0.690356 | + | 0.690356i | −0.962310 | − | 0.271954i | \(-0.912330\pi\) |
0.271954 | + | 0.962310i | \(0.412330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.55198 | − | 12.6865i | −0.451793 | − | 0.600051i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.2047 | 1.28387 | 0.641935 | − | 0.766759i | \(-0.278132\pi\) | ||||
0.641935 | + | 0.766759i | \(0.278132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.63726 | −0.265448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.74693 | − | 6.30466i | −0.223030 | − | 0.296219i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.74086 | + | 5.74086i | −0.268546 | + | 0.268546i | −0.828514 | − | 0.559968i | \(-0.810813\pi\) |
0.559968 | + | 0.828514i | \(0.310813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.1641 | − | 14.3668i | −1.50129 | − | 0.670586i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.0803i | 1.49413i | 0.664751 | + | 0.747065i | \(0.268538\pi\) | ||||
−0.664751 | + | 0.747065i | \(0.731462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.99168 | − | 1.99168i | −0.0925610 | − | 0.0925610i | 0.659310 | − | 0.751871i | \(-0.270848\pi\) |
−0.751871 | + | 0.659310i | \(0.770848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9386 | − | 14.9386i | −0.691278 | − | 0.691278i | 0.271236 | − | 0.962513i | \(-0.412568\pi\) |
−0.962513 | + | 0.271236i | \(0.912568\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.99636i | − | 0.323062i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.4822 | + | 4.29647i | 1.40454 | + | 0.197971i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.85400 | − | 2.85400i | 0.131227 | − | 0.131227i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.7554 | − | 32.0923i | −0.812964 | − | 1.46941i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.1482 | −0.966286 | −0.483143 | − | 0.875541i | \(-0.660505\pi\) | ||||
−0.483143 | + | 0.875541i | \(0.660505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6286 | −0.621410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0425 | + | 9.06709i | −0.547952 | + | 0.412567i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6516 | − | 15.6516i | 0.709241 | − | 0.709241i | −0.257135 | − | 0.966376i | \(-0.582778\pi\) |
0.966376 | + | 0.257135i | \(0.0827785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.08651 | + | 43.1820i | −0.275242 | + | 1.95276i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17.3816i | − | 0.784420i | −0.919876 | − | 0.392210i | \(-0.871711\pi\) | ||
0.919876 | − | 0.392210i | \(-0.128289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.8954 | − | 31.8954i | −1.43650 | − | 1.43650i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.32239 | − | 1.32239i | −0.0593172 | − | 0.0593172i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.0765i | 1.39118i | 0.718440 | + | 0.695588i | \(0.244856\pi\) | ||||
−0.718440 | + | 0.695588i | \(0.755144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.91639 | + | 20.6909i | −0.130295 | + | 0.924402i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.5230 | − | 25.5230i | 1.13802 | − | 1.13802i | 0.149211 | − | 0.988805i | \(-0.452327\pi\) |
0.988805 | − | 0.149211i | \(-0.0476733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.1745 | − | 9.91939i | 0.585099 | − | 0.440536i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.0369 | −1.24271 | −0.621356 | − | 0.783528i | \(-0.713418\pi\) | ||||
−0.621356 | + | 0.783528i | \(0.713418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2274 | −0.496669 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.80853 | − | 17.8009i | −0.300604 | − | 0.785928i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.31228 | − | 2.31228i | 0.101694 | − | 0.101694i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.41121 | + | 1.18556i | 0.369211 | + | 0.0520404i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.5908i | − | 1.55926i | −0.626241 | − | 0.779630i | \(-0.715407\pi\) | ||
0.626241 | − | 0.779630i | \(-0.284593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7863 | + | 12.7863i | 0.559105 | + | 0.559105i | 0.929053 | − | 0.369948i | \(-0.120624\pi\) |
−0.369948 | + | 0.929053i | \(0.620624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.24822 | + | 3.24822i | 0.141495 | + | 0.141495i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 52.7446i | − | 2.29324i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.49719 | + | 19.1131i | −0.238558 | + | 0.829436i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.14142 | − | 6.14142i | 0.266014 | − | 0.266014i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.2248 | + | 28.1899i | 0.915919 | + | 1.21648i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.21059 | −0.0521439 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.50612 | 0.193733 | 0.0968667 | − | 0.995297i | \(-0.469118\pi\) | ||||
0.0968667 | + | 0.995297i | \(0.469118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.36763 | + | 4.47273i | 0.144519 | + | 0.191943i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.60733 | − | 4.60733i | 0.196995 | − | 0.196995i | −0.601715 | − | 0.798711i | \(-0.705516\pi\) |
0.798711 | + | 0.601715i | \(0.205516\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.86571 | − | 20.3943i | 0.250342 | − | 0.870409i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.4038i | − | 1.03964i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.52352 | − | 7.52352i | −0.319933 | − | 0.319933i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.41412 | − | 4.41412i | −0.187032 | − | 0.187032i | 0.607380 | − | 0.794412i | \(-0.292221\pi\) |
−0.794412 | + | 0.607380i | \(0.792221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.21849i | 0.263014i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.0760 | + | 1.98401i | 0.594289 | + | 0.0837652i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0660 | − | 20.0660i | 0.845683 | − | 0.845683i | −0.143908 | − | 0.989591i | \(-0.545967\pi\) |
0.989591 | + | 0.143908i | \(0.0459671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.77257 | − | 2.01047i | 0.368413 | − | 0.0844319i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.35737 | 0.350359 | 0.175180 | − | 0.984537i | \(-0.443949\pi\) | ||||
0.175180 | + | 0.984537i | \(0.443949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5864 | 0.443026 | 0.221513 | − | 0.975157i | \(-0.428900\pi\) | ||||
0.221513 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2236 | − | 12.2151i | 0.677749 | − | 0.510294i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8642 | − | 21.8642i | 0.910217 | − | 0.910217i | −0.0860719 | − | 0.996289i | \(-0.527431\pi\) |
0.996289 | + | 0.0860719i | \(0.0274315\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.15660 | − | 22.3952i | 0.131184 | − | 0.930711i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 13.7043i | − | 0.568549i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4653 | + | 10.4653i | 0.433427 | + | 0.433427i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0468 | + | 29.0468i | 1.19889 | + | 1.19889i | 0.974499 | + | 0.224392i | \(0.0720397\pi\) |
0.224392 | + | 0.974499i | \(0.427960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.48528i | 0.102404i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.30126 | + | 16.3268i | −0.0946614 | + | 0.671594i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.3117 | + | 23.3117i | −0.957298 | + | 0.957298i | −0.999125 | − | 0.0418264i | \(-0.986682\pi\) |
0.0418264 | + | 0.999125i | \(0.486682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.22649 | − | 3.93515i | 0.213906 | − | 0.161055i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.2640 | −1.68600 | −0.843000 | − | 0.537914i | \(-0.819213\pi\) | ||||
−0.843000 | + | 0.537914i | \(0.819213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.93221 | −0.282771 | −0.141385 | − | 0.989955i | \(-0.545156\pi\) | ||||
−0.141385 | + | 0.989955i | \(0.545156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.1610 | − | 18.3656i | −0.413786 | − | 0.747906i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1329 | − | 24.1329i | 0.979523 | − | 0.979523i | −0.0202711 | − | 0.999795i | \(-0.506453\pi\) |
0.999795 | + | 0.0202711i | \(0.00645293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.4114 | + | 1.60844i | 0.462413 | + | 0.0651773i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.03814i | 0.203821i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.4289 | − | 15.4289i | −0.623167 | − | 0.623167i | 0.323173 | − | 0.946340i | \(-0.395250\pi\) |
−0.946340 | + | 0.323173i | \(0.895250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.98976 | − | 3.98976i | −0.160622 | − | 0.160622i | 0.622220 | − | 0.782842i | \(-0.286231\pi\) |
−0.782842 | + | 0.622220i | \(0.786231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.4604i | − | 0.741985i | −0.928636 | − | 0.370993i | \(-0.879018\pi\) | ||
0.928636 | − | 0.370993i | \(-0.120982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4435 | + | 41.2909i | −0.740113 | + | 1.65695i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.01404 | + | 2.01404i | −0.0806906 | + | 0.0806906i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.62591 | + | 6.14392i | 0.184741 | + | 0.245365i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.5371 | −1.97517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.4925 | 0.855603 | 0.427802 | − | 0.903873i | \(-0.359288\pi\) | ||||
0.427802 | + | 0.903873i | \(0.359288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.45146 | − | 4.58408i | −0.137183 | − | 0.182201i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.31886 | − | 1.31886i | 0.0522550 | − | 0.0522550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.39184 | − | 1.55077i | −0.213298 | − | 0.0613476i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.3498i | 0.566784i | 0.959004 | + | 0.283392i | \(0.0914598\pi\) | ||||
−0.959004 | + | 0.283392i | \(0.908540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.65934 | − | 8.65934i | −0.341491 | − | 0.341491i | 0.515437 | − | 0.856928i | \(-0.327630\pi\) |
−0.856928 | + | 0.515437i | \(0.827630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.2705 | − | 11.2705i | −0.443088 | − | 0.443088i | 0.449961 | − | 0.893048i | \(-0.351438\pi\) |
−0.893048 | + | 0.449961i | \(0.851438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.02537i | − | 0.315023i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.16214 | − | 0.163803i | −0.0455477 | − | 0.00641996i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.6089 | + | 16.6089i | −0.649958 | + | 0.649958i | −0.952983 | − | 0.303025i | \(-0.902003\pi\) |
0.303025 | + | 0.952983i | \(0.402003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.4721 | + | 16.3057i | −1.14982 | + | 0.636147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.99323 | −0.194509 | −0.0972543 | − | 0.995260i | \(-0.531006\pi\) | ||||
−0.0972543 | + | 0.995260i | \(0.531006\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.6925 | −1.07711 | −0.538556 | − | 0.842589i | \(-0.681030\pi\) | ||||
−0.538556 | + | 0.842589i | \(0.681030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.4963 | + | 13.1734i | −0.679500 | + | 0.511612i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.9460 | + | 40.9460i | −1.58543 | + | 1.58543i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.04725 | + | 7.42991i | −0.0404889 | + | 0.287257i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.56337i | 0.330585i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.8390 | + | 30.8390i | 1.18876 | + | 1.18876i | 0.977412 | + | 0.211344i | \(0.0677841\pi\) |
0.211344 | + | 0.977412i | \(0.432216\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2980 | + | 15.2980i | 0.587952 | + | 0.587952i | 0.937076 | − | 0.349125i | \(-0.113521\pi\) |
−0.349125 | + | 0.937076i | \(0.613521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.51569i | − | 0.211673i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.65231 | − | 33.0067i | 0.178277 | − | 1.26482i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.5834 | − | 13.5834i | 0.519753 | − | 0.519753i | −0.397743 | − | 0.917497i | \(-0.630207\pi\) |
0.917497 | + | 0.397743i | \(0.130207\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0552 | − | 18.1117i | 0.917763 | − | 0.691006i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.8024 | −0.868702 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.91319 | −0.377116 | −0.188558 | − | 0.982062i | \(-0.560381\pi\) | ||||
−0.188558 | + | 0.982062i | \(0.560381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.17783 | + | 1.75817i | −0.120716 | + | 0.0667873i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.3228 | − | 22.3228i | 0.845535 | − | 0.845535i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.76622 | + | 0.812751i | 0.218099 | + | 0.0307411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.1977i | − | 0.913936i | −0.889483 | − | 0.456968i | \(-0.848935\pi\) | ||
0.889483 | − | 0.456968i | \(-0.151065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9509 | − | 18.9509i | −0.714748 | − | 0.714748i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.43929 | + | 5.43929i | 0.204566 | + | 0.204566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.04474i | 0.339683i | 0.985471 | + | 0.169841i | \(0.0543255\pi\) | ||||
−0.985471 | + | 0.169841i | \(0.945675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.6760 | − | 8.82288i | −1.15044 | − | 0.330884i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.16993 | − | 4.16993i | 0.156165 | − | 0.156165i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.8384 | − | 21.0358i | −0.591495 | − | 0.785596i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.9027 | 1.22706 | 0.613531 | − | 0.789670i | \(-0.289748\pi\) | ||||
0.613531 | + | 0.789670i | \(0.289748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.08479 | −0.189367 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.9848 | + | 15.9177i | 0.445720 | + | 0.591985i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.5266 | − | 30.5266i | 1.13217 | − | 1.13217i | 0.142351 | − | 0.989816i | \(-0.454534\pi\) |
0.989816 | − | 0.142351i | \(-0.0454663\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1084 | − | 18.0181i | 0.744755 | − | 0.667338i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6029i | 0.835999i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0111 | − | 18.0111i | −0.665257 | − | 0.665257i | 0.291358 | − | 0.956614i | \(-0.405893\pi\) |
−0.956614 | + | 0.291358i | \(0.905893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.98901 | + | 5.98901i | 0.220608 | + | 0.220608i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3893i | 0.860391i | 0.902736 | + | 0.430195i | \(0.141555\pi\) | ||||
−0.902736 | + | 0.430195i | \(0.858445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.7330 | − | 1.65377i | −0.431023 | − | 0.0607528i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7432 | − | 10.7432i | 0.394129 | − | 0.394129i | −0.482027 | − | 0.876156i | \(-0.660099\pi\) |
0.876156 | + | 0.482027i | \(0.160099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.9030 | − | 35.9741i | −0.728214 | − | 1.31622i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.44544 | 0.0893545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.66315 | 0.0971798 | 0.0485899 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485899 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6513 | − | 17.8076i | 0.861901 | − | 0.648947i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.00745 | + | 4.00745i | −0.145653 | + | 0.145653i | −0.776173 | − | 0.630520i | \(-0.782842\pi\) |
0.630520 | + | 0.776173i | \(0.282842\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.54700 | − | 18.0702i | 0.0924501 | − | 0.655906i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.2284i | − | 0.914530i | −0.889330 | − | 0.457265i | \(-0.848829\pi\) | ||
0.889330 | − | 0.457265i | \(-0.151171\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8596 | + | 13.8596i | 0.501750 | + | 0.501750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.74310 | + | 8.74310i | 0.315695 | + | 0.315695i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.7217i | 1.36028i | 0.733082 | + | 0.680140i | \(0.238081\pi\) | ||||
−0.733082 | + | 0.680140i | \(0.761919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.68654 | − | 19.0602i | 0.0967534 | − | 0.686437i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.6191 | + | 18.6191i | −0.669682 | + | 0.669682i | −0.957642 | − | 0.287960i | \(-0.907023\pi\) |
0.287960 | + | 0.957642i | \(0.407023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.1106 | − | 7.61255i | 0.362717 | − | 0.273099i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0796 | 0.611941 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.26398 | 0.0810114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.2912 | − | 12.3508i | 1.15399 | − | 0.441382i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.9229 | + | 38.9229i | −1.38745 | + | 1.38745i | −0.556816 | + | 0.830636i | \(0.687977\pi\) |
−0.830636 | + | 0.556816i | \(0.812023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.7713 | − | 3.63248i | −0.917484 | − | 0.129320i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.9442i | 0.602466i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.32921 | − | 9.32921i | −0.331290 | − | 0.331290i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0056 | + | 17.0056i | 0.602368 | + | 0.602368i | 0.940940 | − | 0.338573i | \(-0.109944\pi\) |
−0.338573 | + | 0.940940i | \(0.609944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3126i | 0.647853i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.36187 | + | 8.21192i | −0.0834526 | + | 0.290154i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.61082 | − | 9.61082i | 0.339158 | − | 0.339158i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.3330 | − | 25.6772i | −0.680554 | − | 0.903881i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.65158 | 0.269015 | 0.134508 | − | 0.990913i | \(-0.457055\pi\) | ||||
0.134508 | + | 0.990913i | \(0.457055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4460 | 0.472152 | 0.236076 | − | 0.971735i | \(-0.424139\pi\) | ||||
0.236076 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.5267 | + | 27.2626i | 0.719901 | + | 0.956140i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.64698 | + | 8.64698i | −0.302520 | + | 0.302520i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.54663 | − | 5.37744i | 0.0540437 | − | 0.187903i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 43.2148i | − | 1.50821i | −0.656755 | − | 0.754104i | \(-0.728072\pi\) | ||
0.656755 | − | 0.754104i | \(-0.271928\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.9428 | + | 14.9428i | 0.520875 | + | 0.520875i | 0.917836 | − | 0.396961i | \(-0.129935\pi\) |
−0.396961 | + | 0.917836i | \(0.629935\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.4905 | + | 16.4905i | 0.573430 | + | 0.573430i | 0.933085 | − | 0.359655i | \(-0.117106\pi\) |
−0.359655 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 55.7459i | − | 1.93614i | −0.250689 | − | 0.968068i | \(-0.580657\pi\) | ||
0.250689 | − | 0.968068i | \(-0.419343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.6345 | + | 5.58649i | 1.37491 | + | 0.193793i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.79377 | − | 4.79377i | 0.166094 | − | 0.166094i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.28853 | + | 1.25781i | −0.113668 | + | 0.0434762i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.77729 | −0.0613588 | −0.0306794 | − | 0.999529i | \(-0.509767\pi\) | ||||
−0.0306794 | + | 0.999529i | \(0.509767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.2691 | 0.526520 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.9095 | + | 11.2257i | −0.513509 | + | 0.386634i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.74189 | + | 6.74189i | −0.231654 | + | 0.231654i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.17584 | + | 29.6264i | −0.143315 | + | 1.01677i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.5937i | 2.17996i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.70145 | − | 9.70145i | −0.332171 | − | 0.332171i | 0.521239 | − | 0.853411i | \(-0.325470\pi\) |
−0.853411 | + | 0.521239i | \(0.825470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.21818 | + | 4.21818i | 0.144090 | + | 0.144090i | 0.775472 | − | 0.631382i | \(-0.217512\pi\) |
−0.631382 | + | 0.775472i | \(0.717512\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.26158i | − | 0.0771642i | −0.999255 | − | 0.0385821i | \(-0.987716\pi\) | ||
0.999255 | − | 0.0385821i | \(-0.0122841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.12571 | + | 7.98656i | −0.0383640 | + | 0.272181i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.7520 | + | 19.7520i | −0.672366 | + | 0.672366i | −0.958261 | − | 0.285895i | \(-0.907709\pi\) |
0.285895 | + | 0.958261i | \(0.407709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.0725 | + | 30.1716i | −1.36093 | + | 1.02468i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.8805 | 0.436942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0492 | −0.442157 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.01055 | − | 14.4788i | −0.271116 | − | 0.490034i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.4841 | + | 23.4841i | −0.793003 | + | 0.793003i | −0.981981 | − | 0.188978i | \(-0.939482\pi\) |
0.188978 | + | 0.981981i | \(0.439482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.1483 | + | 4.24941i | 1.01688 | + | 0.143329i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3754i | 0.518009i | 0.965876 | + | 0.259004i | \(0.0833944\pi\) | ||||
−0.965876 | + | 0.259004i | \(0.916606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4444 | + | 26.4444i | 0.889925 | + | 0.889925i | 0.994515 | − | 0.104591i | \(-0.0333533\pi\) |
−0.104591 | + | 0.994515i | \(0.533353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.6576 | − | 29.6576i | −0.995806 | − | 0.995806i | 0.00418537 | − | 0.999991i | \(-0.498668\pi\) |
−0.999991 | + | 0.00418537i | \(0.998668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.32081i | − | 0.111376i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.78847 | + | 9.23047i | −0.193921 | + | 0.309232i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.00567 | + | 7.00567i | −0.234436 | + | 0.234436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.9115 | + | 22.4610i | 0.564657 | + | 0.749951i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.50836 | −0.150362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.8820 | −2.76120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.47347 | − | 4.61331i | −0.115590 | − | 0.153521i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.87348 | + | 8.87348i | −0.294639 | + | 0.294639i | −0.838910 | − | 0.544271i | \(-0.816806\pi\) |
0.544271 | + | 0.838910i | \(0.316806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.1779 | + | 6.37869i | 0.735594 | + | 0.211568i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.64169i | 0.153786i | 0.997039 | + | 0.0768930i | \(0.0245000\pi\) | ||||
−0.997039 | + | 0.0768930i | \(0.975500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7311 | + | 11.7311i | 0.388243 | + | 0.388243i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.41710 | − | 8.41710i | −0.277957 | − | 0.277957i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8491i | 1.34749i | 0.738965 | + | 0.673743i | \(0.235315\pi\) | ||||
−0.738965 | + | 0.673743i | \(0.764685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.4136 | + | 2.31350i | 0.540847 | + | 0.0762325i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.46645 | + | 2.46645i | −0.0811841 | + | 0.0811841i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.3477 | + | 7.38475i | −0.438396 | + | 0.242547i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.5171 | 0.705954 | 0.352977 | − | 0.935632i | \(-0.385169\pi\) | ||||
0.352977 | + | 0.935632i | \(0.385169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66781 | 0.120208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.3759 | + | 25.8824i | −1.12541 | + | 0.847353i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0454 | + | 14.0454i | −0.458842 | + | 0.458842i | −0.898275 | − | 0.439433i | \(-0.855179\pi\) |
0.439433 | + | 0.898275i | \(0.355179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.868209 | − | 6.15968i | 0.0283329 | − | 0.201014i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 18.0981i | − | 0.589983i | −0.955500 | − | 0.294991i | \(-0.904683\pi\) | ||
0.955500 | − | 0.294991i | \(-0.0953167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.6571 | − | 28.6571i | −0.933202 | − | 0.933202i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.91624 | + | 9.91624i | 0.322235 | + | 0.322235i | 0.849624 | − | 0.527389i | \(-0.176829\pi\) |
−0.527389 | + | 0.849624i | \(0.676829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9407i | 0.679763i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.59998 | − | 11.3514i | 0.0518831 | − | 0.368095i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.3878 | + | 38.3878i | −1.24350 | + | 1.24350i | −0.284967 | + | 0.958537i | \(0.591983\pi\) |
−0.958537 | + | 0.284967i | \(0.908017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1452 | + | 8.39151i | −0.360274 | + | 0.271259i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1441 | 0.359861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5409 | −0.985189 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.41935 | − | 3.55157i | 0.206861 | − | 0.114448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.8316 | + | 20.8316i | −0.669898 | + | 0.669898i | −0.957692 | − | 0.287794i | \(-0.907078\pi\) |
0.287794 | + | 0.957692i | \(0.407078\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.6470 | − | 6.01111i | −1.37002 | − | 0.193105i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.8127i | 1.59856i | 0.600956 | + | 0.799282i | \(0.294787\pi\) | ||||
−0.600956 | + | 0.799282i | \(0.705213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.64740 | − | 3.64740i | −0.116930 | − | 0.116930i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.7612 | − | 22.7612i | −0.728195 | − | 0.728195i | 0.242065 | − | 0.970260i | \(-0.422175\pi\) |
−0.970260 | + | 0.242065i | \(0.922175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.44810i | − | 0.110202i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.5103 | + | 16.2532i | 1.80423 | + | 0.518924i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.92066 | − | 9.92066i | 0.316420 | − | 0.316420i | −0.530970 | − | 0.847390i | \(-0.678172\pi\) |
0.847390 | + | 0.530970i | \(0.178172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.81416 | − | 3.73764i | −0.0895758 | − | 0.118970i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.0167 | 0.922677 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.717293 | −0.0227856 | −0.0113928 | − | 0.999935i | \(-0.503627\pi\) | ||||
−0.0113928 | + | 0.999935i | \(0.503627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.7847 | + | 44.8713i | 1.07212 | + | 1.42395i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.49889 | − | 8.49889i | 0.269163 | − | 0.269163i | −0.559600 | − | 0.828763i | \(-0.689045\pi\) |
0.828763 | + | 0.559600i | \(0.189045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.4848 | − | 34.6670i | 0.489918 | − | 1.09682i |
(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 | 2100.2.s.b.1793.8 | 24 | ||
3.2 | odd | 2 | inner | 2100.2.s.b.1793.10 | 24 | ||
5.2 | odd | 4 | inner | 2100.2.s.b.1457.10 | 24 | ||
5.3 | odd | 4 | 420.2.s.a.197.3 | yes | 24 | ||
5.4 | even | 2 | 420.2.s.a.113.5 | yes | 24 | ||
15.2 | even | 4 | inner | 2100.2.s.b.1457.8 | 24 | ||
15.8 | even | 4 | 420.2.s.a.197.5 | yes | 24 | ||
15.14 | odd | 2 | 420.2.s.a.113.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.s.a.113.3 | ✓ | 24 | 15.14 | odd | 2 | ||
420.2.s.a.113.5 | yes | 24 | 5.4 | even | 2 | ||
420.2.s.a.197.3 | yes | 24 | 5.3 | odd | 4 | ||
420.2.s.a.197.5 | yes | 24 | 15.8 | even | 4 | ||
2100.2.s.b.1457.8 | 24 | 15.2 | even | 4 | inner | ||
2100.2.s.b.1457.10 | 24 | 5.2 | odd | 4 | inner | ||
2100.2.s.b.1793.8 | 24 | 1.1 | even | 1 | trivial | ||
2100.2.s.b.1793.10 | 24 | 3.2 | odd | 2 | inner |