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 | 1457.10 | ||
Character | \(\chi\) | \(=\) | 2100.1457 |
Dual form | 2100.2.s.b.1793.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.38370 | − | 1.04182i | 0.798877 | − | 0.601494i | ||||
\(4\) | 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 | −0.500152 | − | 0.865938i | \(-0.666723\pi\) |
0.865938 | + | 0.500152i | \(0.166723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.79377 | + | 4.79377i | −1.16266 | + | 1.16266i | −0.178770 | + | 0.983891i | \(0.557212\pi\) |
−0.983891 | + | 0.178770i | \(0.942788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.66781i | − | 0.841454i | −0.907187 | − | 0.420727i | \(-0.861775\pi\) | ||
0.907187 | − | 0.420727i | \(-0.138225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71510 | − | 0.241744i | −0.374265 | − | 0.0527528i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.15405 | − | 6.15405i | −1.28321 | − | 1.28321i | −0.938832 | − | 0.344376i | \(-0.888091\pi\) |
−0.344376 | − | 0.938832i | \(-0.611909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.85629 | − | 4.85327i | −0.357243 | − | 0.934011i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.65350 | 1.23552 | 0.617762 | − | 0.786365i | \(-0.288040\pi\) | ||||
0.617762 | + | 0.786365i | \(0.288040\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.677592 | 0.121699 | 0.0608495 | − | 0.998147i | \(-0.480619\pi\) | ||||
0.0608495 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.26122 | − | 1.67509i | −0.219550 | − | 0.291596i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.16682 | − | 5.16682i | −0.849419 | − | 0.849419i | 0.140641 | − | 0.990061i | \(-0.455084\pi\) |
−0.990061 | + | 0.140641i | \(0.955084\pi\) | |||||||
\(38\) | 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 | −0.504116 | − | 0.863636i | \(-0.668182\pi\) |
0.863636 | + | 0.504116i | \(0.168182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.91004 | + | 1.91004i | −0.278608 | + | 0.278608i | −0.832553 | − | 0.553945i | \(-0.813122\pi\) |
0.553945 | + | 0.832553i | \(0.313122\pi\) | |||||||
\(48\) | 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 | 0.977771 | + | 0.209678i | \(0.0672415\pi\) |
0.209678 | + | 0.977771i | \(0.432759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.82120 | − | 5.07514i | −0.506130 | − | 0.672219i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.62929 | −0.863061 | −0.431530 | − | 0.902098i | \(-0.642026\pi\) | ||||
−0.431530 | + | 0.902098i | \(0.642026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07370 | −0.905695 | −0.452847 | − | 0.891588i | \(-0.649592\pi\) | ||||
−0.452847 | + | 0.891588i | \(0.649592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.62503 | + | 1.45232i | −0.330722 | + | 0.182975i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94717 | − | 4.94717i | −0.604394 | − | 0.604394i | 0.337082 | − | 0.941475i | \(-0.390560\pi\) |
−0.941475 | + | 0.337082i | \(0.890560\pi\) | |||||||
\(68\) | 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 | −0.0684701 | − | 0.997653i | \(-0.521812\pi\) |
0.997653 | + | 0.0684701i | \(0.0218118\pi\) | |||||||
\(74\) | 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 | \(-0.795748\pi\) | ||
0.801093 | − | 0.598539i | \(-0.204252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.62476 | − | 4.78153i | −0.847196 | − | 0.531281i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.69039 | + | 9.69039i | 1.06366 | + | 1.06366i | 0.997831 | + | 0.0658277i | \(0.0209688\pi\) |
0.0658277 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.20642 | − | 6.93174i | 0.987032 | − | 0.743161i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.84828 | −0.301917 | −0.150958 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150958 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.86515 | −0.195520 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.937581 | − | 0.705928i | 0.0972226 | − | 0.0732013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.90018 | − | 3.90018i | −0.396003 | − | 0.396003i | 0.480817 | − | 0.876821i | \(-0.340340\pi\) |
−0.876821 | + | 0.480817i | \(0.840340\pi\) | |||||||
\(98\) | 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 | −0.507423 | − | 0.861697i | \(-0.669402\pi\) |
0.861697 | + | 0.507423i | \(0.169402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.72919 | − | 1.72919i | 0.167167 | − | 0.167167i | −0.618566 | − | 0.785733i | \(-0.712286\pi\) |
0.785733 | + | 0.618566i | \(0.212286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.6004i | 1.87738i | 0.344766 | + | 0.938688i | \(0.387958\pi\) | ||||
−0.344766 | + | 0.938688i | \(0.612042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.5322 | − | 1.76642i | −1.18950 | − | 0.167661i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9813 | − | 11.9813i | −1.12711 | − | 1.12711i | −0.990645 | − | 0.136465i | \(-0.956426\pi\) |
−0.136465 | − | 0.990645i | \(-0.543574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.70879 | − | 4.89606i | −0.250428 | − | 0.452641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.77942 | 0.621468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53447 | 0.866770 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.85135 | − | 6.44334i | −0.437432 | − | 0.580977i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.34817 | − | 2.34817i | −0.208366 | − | 0.208366i | 0.595207 | − | 0.803573i | \(-0.297070\pi\) |
−0.803573 | + | 0.595207i | \(0.797070\pi\) | |||||||
\(128\) | 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 | \(-0.592067\pi\) |
0.958461 | + | 0.285222i | \(0.0920675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.15820i | − | 0.437513i | −0.975779 | − | 0.218756i | \(-0.929800\pi\) | ||
0.975779 | − | 0.218756i | \(-0.0702000\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 1.04182 | + | 1.38370i | 0.0859278 | + | 0.114125i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16856 | 0.751118 | 0.375559 | − | 0.926798i | \(-0.377451\pi\) | ||||
0.375559 | + | 0.926798i | \(0.377451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.55639 | −0.370794 | −0.185397 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185397 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.84589 | + | 17.7961i | 0.795993 | + | 1.43873i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5673 | + | 12.5673i | 1.00298 | + | 1.00298i | 0.999996 | + | 0.00298395i | \(0.000949822\pi\) |
0.00298395 | + | 0.999996i | \(0.499050\pi\) | |||||||
\(158\) | 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 | 0.579444 | − | 0.815012i | \(-0.303270\pi\) |
0.815012 | − | 0.579444i | \(-0.196730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.53053 | + | 8.53053i | −0.660112 | + | 0.660112i | −0.955406 | − | 0.295294i | \(-0.904582\pi\) |
0.295294 | + | 0.955406i | \(0.404582\pi\) | |||||||
\(168\) | 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 | \(-0.309692\pi\) |
−0.826536 | + | 0.562884i | \(0.809692\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.17293 | + | 6.90652i | −0.689479 | + | 0.519126i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.3729 | −1.52274 | −0.761370 | − | 0.648318i | \(-0.775473\pi\) | ||||
−0.761370 | + | 0.648318i | \(0.775473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.23245 | 0.240266 | 0.120133 | − | 0.992758i | \(-0.461668\pi\) | ||||
0.120133 | + | 0.992758i | \(0.461668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.78785 | + | 7.36952i | −0.723539 | + | 0.544770i | ||||
\(184\) | 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 | −0.956465 | − | 0.291848i | \(-0.905730\pi\) |
0.291848 | + | 0.956465i | \(0.405730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.73126 | + | 6.73126i | −0.479583 | + | 0.479583i | −0.904998 | − | 0.425415i | \(-0.860128\pi\) |
0.425415 | + | 0.904998i | \(0.360128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.77719i | 0.267758i | 0.990998 | + | 0.133879i | \(0.0427434\pi\) | ||||
−0.990998 | + | 0.133879i | \(0.957257\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | −22.8460 | + | 12.6398i | −1.58790 | + | 0.878523i | ||||
\(208\) | 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 | ||||||||
\(213\) | 1.94835 | + | 2.58770i | 0.133499 | + | 0.177307i | ||||
\(214\) | 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 | −0.597064 | − | 0.802193i | \(-0.703666\pi\) |
0.802193 | + | 0.597064i | \(0.203666\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6081 | − | 13.6081i | 0.903204 | − | 0.903204i | −0.0925080 | − | 0.995712i | \(-0.529488\pi\) |
0.995712 | + | 0.0925080i | \(0.0294884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3847i | 1.14882i | 0.818569 | + | 0.574408i | \(0.194768\pi\) | ||||
−0.818569 | + | 0.574408i | \(0.805232\pi\) | |||||||
\(230\) | 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 | \(-0.285126\pi\) |
−0.780678 | + | 0.624934i | \(0.785126\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0848 | − | 14.7223i | −0.720036 | − | 0.956319i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2026 | 0.983376 | 0.491688 | − | 0.870771i | \(-0.336380\pi\) | ||||
0.491688 | + | 0.870771i | \(0.336380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5037 | 0.741021 | 0.370511 | − | 0.928828i | \(-0.379183\pi\) | ||||
0.370511 | + | 0.928828i | \(0.379183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5318 | + | 1.32744i | −0.996368 | + | 0.0851555i | ||||
\(244\) | 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 | \(-0.637332\pi\) |
0.908363 | + | 0.418182i | \(0.137332\pi\) | |||||||
\(258\) | 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 | \(-0.0966737\pi\) |
−0.299062 | + | 0.954234i | \(0.596674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.94115 | + | 2.96739i | −0.241194 | + | 0.181601i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.5570 | 1.13144 | 0.565720 | − | 0.824598i | \(-0.308598\pi\) | ||||
0.565720 | + | 0.824598i | \(0.308598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7027 | 1.19685 | 0.598427 | − | 0.801177i | \(-0.295792\pi\) | ||||
0.598427 | + | 0.801177i | \(0.295792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.58080 | + | 1.94314i | −0.156197 | + | 0.117604i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3407 | + | 16.3407i | 0.981815 | + | 0.981815i | 0.999838 | − | 0.0180230i | \(-0.00573721\pi\) |
−0.0180230 | + | 0.999838i | \(0.505737\pi\) | |||||||
\(278\) | 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 | −0.243761 | − | 0.969835i | \(-0.578381\pi\) |
0.969835 | + | 0.243761i | \(0.0783812\pi\) | |||||||
\(284\) | 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 | \(-0.421638\pi\) |
−0.969850 | + | 0.243702i | \(0.921638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.87532 | + | 2.24721i | −0.340921 | + | 0.130396i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2326 | −0.938757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.33405 | −0.192171 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.01401 | − | 10.6438i | −0.460393 | − | 0.611472i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.76706 | + | 6.76706i | 0.386217 | + | 0.386217i | 0.873336 | − | 0.487119i | \(-0.161952\pi\) |
−0.487119 | + | 0.873336i | \(0.661952\pi\) | |||||||
\(308\) | 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 | −0.775227 | − | 0.631683i | \(-0.782364\pi\) |
0.631683 | + | 0.775227i | \(0.282364\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.68000 | − | 4.68000i | 0.262855 | − | 0.262855i | −0.563358 | − | 0.826213i | \(-0.690491\pi\) |
0.826213 | + | 0.563358i | \(0.190491\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 20.4201 | + | 27.1210i | 1.12923 | + | 1.49979i | ||||
\(328\) | 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 | ||||||||
\(333\) | −19.1810 | + | 10.6121i | −1.05111 | + | 0.581539i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6095 | − | 17.6095i | −0.959250 | − | 0.959250i | 0.0399517 | − | 0.999202i | \(-0.487280\pi\) |
−0.999202 | + | 0.0399517i | \(0.987280\pi\) | |||||||
\(338\) | 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 | \(-0.592378\pi\) |
0.958182 | + | 0.286159i | \(0.0923785\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7929i | 0.952429i | 0.879329 | + | 0.476215i | \(0.157992\pi\) | ||||
−0.879329 | + | 0.476215i | \(0.842008\pi\) | |||||||
\(350\) | 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 | \(-0.294098\pi\) |
−0.797980 | + | 0.602684i | \(0.794098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.38065 | − | 7.06292i | 0.496477 | − | 0.373810i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.5503 | −1.55960 | −0.779802 | − | 0.626026i | \(-0.784680\pi\) | ||||
−0.779802 | + | 0.626026i | \(0.784680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.54713 | 0.291954 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.1928 | − | 9.93319i | 0.692443 | − | 0.521357i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5412 | + | 21.5412i | 1.12444 | + | 1.12444i | 0.991065 | + | 0.133377i | \(0.0425823\pi\) |
0.133377 | + | 0.991065i | \(0.457418\pi\) | |||||||
\(368\) | 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 | −0.307590 | − | 0.951519i | \(-0.599523\pi\) |
0.951519 | + | 0.307590i | \(0.0995225\pi\) | |||||||
\(374\) | 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 | \(-0.887324\pi\) | ||
0.938000 | − | 0.346635i | \(-0.112676\pi\) | |||||||
\(380\) | 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 | \(-0.171131\pi\) |
−0.512096 | + | 0.858928i | \(0.671131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.84211 | − | 8.75197i | −0.246138 | − | 0.444887i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.3012 | −1.58703 | −0.793517 | − | 0.608548i | \(-0.791752\pi\) | ||||
−0.793517 | + | 0.608548i | \(0.791752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.0022 | 2.98387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4014 | + | 16.4709i | 0.625567 | + | 0.830849i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.83384 | + | 1.83384i | 0.0920379 | + | 0.0920379i | 0.751627 | − | 0.659589i | \(-0.229270\pi\) |
−0.659589 | + | 0.751627i | \(0.729270\pi\) | |||||||
\(398\) | 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 | \(0.184750\pi\) | ||||
−0.836238 | + | 0.548366i | \(0.815250\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | −5.37391 | − | 7.13738i | −0.263162 | − | 0.349519i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.0297 | 0.783102 | 0.391551 | − | 0.920156i | \(-0.371939\pi\) | ||||
0.391551 | + | 0.920156i | \(0.371939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.809448 | 0.0394501 | 0.0197250 | − | 0.999805i | \(-0.493721\pi\) | ||||
0.0197250 | + | 0.999805i | \(0.493721\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.92301 | + | 7.09073i | 0.190743 | + | 0.344763i | ||||
\(424\) | 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 | −0.911269 | − | 0.411811i | \(-0.864896\pi\) |
0.411811 | + | 0.911269i | \(0.364896\pi\) | |||||||
\(434\) | 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 | \(0.226769\pi\) | ||||
−0.756786 | + | 0.653663i | \(0.773231\pi\) | |||||||
\(440\) | 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 | \(-0.0876700\pi\) |
−0.271954 | + | 0.962310i | \(0.587670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6865 | − | 9.55198i | 0.600051 | − | 0.451793i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.2047 | −1.28387 | −0.641935 | − | 0.766759i | \(-0.721868\pi\) | ||||
−0.641935 | + | 0.766759i | \(0.721868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.63726 | −0.265448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.30466 | + | 4.74693i | −0.296219 | + | 0.223030i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.74086 | − | 5.74086i | −0.268546 | − | 0.268546i | 0.559968 | − | 0.828514i | \(-0.310813\pi\) |
−0.828514 | + | 0.559968i | \(0.810813\pi\) | |||||||
\(458\) | 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 | −0.751871 | − | 0.659310i | \(-0.770848\pi\) |
0.659310 | + | 0.751871i | \(0.270848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9386 | − | 14.9386i | 0.691278 | − | 0.691278i | −0.271236 | − | 0.962513i | \(-0.587432\pi\) |
0.962513 | + | 0.271236i | \(0.0874322\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 32.0923 | − | 17.7554i | 1.46941 | − | 0.812964i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.1482 | 0.966286 | 0.483143 | − | 0.875541i | \(-0.339495\pi\) | ||||
0.483143 | + | 0.875541i | \(0.339495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6286 | −0.621410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.06709 | + | 12.0425i | 0.412567 | + | 0.547952i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6516 | + | 15.6516i | 0.709241 | + | 0.709241i | 0.966376 | − | 0.257135i | \(-0.0827785\pi\) |
−0.257135 | + | 0.966376i | \(0.582778\pi\) | |||||||
\(488\) | 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 | \(-0.755144\pi\) | ||
0.718440 | − | 0.695588i | \(-0.244856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.91639 | + | 20.6909i | −0.130295 | + | 0.924402i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.5230 | − | 25.5230i | −1.13802 | − | 1.13802i | −0.988805 | − | 0.149211i | \(-0.952327\pi\) |
−0.149211 | − | 0.988805i | \(-0.547673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.91939 | + | 13.1745i | 0.440536 | + | 0.585099i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0369 | 1.24271 | 0.621356 | − | 0.783528i | \(-0.286582\pi\) | ||||
0.621356 | + | 0.783528i | \(0.286582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2274 | −0.496669 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.8009 | + | 6.80853i | −0.785928 | + | 0.300604i | ||||
\(514\) | 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 | −0.369948 | − | 0.929053i | \(-0.620624\pi\) |
0.929053 | + | 0.369948i | \(0.120624\pi\) | |||||||
\(524\) | 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 | ||||||||
\(537\) | −28.1899 | + | 21.2248i | −1.21648 | + | 0.915919i | ||||
\(538\) | 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 | ||||||||
\(543\) | 4.47273 | − | 3.36763i | 0.191943 | − | 0.144519i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.60733 | + | 4.60733i | 0.196995 | + | 0.196995i | 0.798711 | − | 0.601715i | \(-0.205516\pi\) |
−0.601715 | + | 0.798711i | \(0.705516\pi\) | |||||||
\(548\) | 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 | \(-0.707779\pi\) |
0.794412 | + | 0.607380i | \(0.207779\pi\) | |||||||
\(558\) | 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 | \(-0.454033\pi\) |
−0.989591 | + | 0.143908i | \(0.954033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.01047 | + | 8.77257i | 0.0844319 | + | 0.368413i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.35737 | −0.350359 | −0.175180 | − | 0.984537i | \(-0.556051\pi\) | ||||
−0.175180 | + | 0.984537i | \(0.556051\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5864 | 0.443026 | 0.221513 | − | 0.975157i | \(-0.428900\pi\) | ||||
0.221513 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2151 | − | 16.2236i | −0.510294 | − | 0.677749i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8642 | + | 21.8642i | 0.910217 | + | 0.910217i | 0.996289 | − | 0.0860719i | \(-0.0274315\pi\) |
−0.0860719 | + | 0.996289i | \(0.527431\pi\) | |||||||
\(578\) | 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 | −0.224392 | + | 0.974499i | \(0.572040\pi\) |
−0.974499 | + | 0.224392i | \(0.927960\pi\) | |||||||
\(588\) | 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 | \(-0.0133177\pi\) |
−0.0418264 | + | 0.999125i | \(0.513318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.93515 | + | 5.22649i | 0.161055 | + | 0.213906i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.2640 | 1.68600 | 0.843000 | − | 0.537914i | \(-0.180787\pi\) | ||||
0.843000 | + | 0.537914i | \(0.180787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.93221 | −0.282771 | −0.141385 | − | 0.989955i | \(-0.545156\pi\) | ||||
−0.141385 | + | 0.989955i | \(0.545156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.3656 | + | 10.1610i | −0.747906 | + | 0.413786i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1329 | + | 24.1329i | 0.979523 | + | 0.979523i | 0.999795 | − | 0.0202711i | \(-0.00645293\pi\) |
−0.0202711 | + | 0.999795i | \(0.506453\pi\) | |||||||
\(608\) | 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 | −0.946340 | − | 0.323173i | \(-0.895250\pi\) |
0.323173 | + | 0.946340i | \(0.395250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.98976 | − | 3.98976i | 0.160622 | − | 0.160622i | −0.622220 | − | 0.782842i | \(-0.713769\pi\) |
0.782842 | + | 0.622220i | \(0.213769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4604i | 0.741985i | 0.928636 | + | 0.370993i | \(0.120982\pi\) | ||||
−0.928636 | + | 0.370993i | \(0.879018\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −6.14392 | + | 4.62591i | −0.245365 | + | 0.184741i | ||||
\(628\) | 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 | ||||||||
\(633\) | −4.58408 | + | 3.45146i | −0.182201 | + | 0.137183i | ||||
\(634\) | 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 | −0.856928 | − | 0.515437i | \(-0.827630\pi\) |
0.515437 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.2705 | − | 11.2705i | 0.443088 | − | 0.443088i | −0.449961 | − | 0.893048i | \(-0.648562\pi\) |
0.893048 | + | 0.449961i | \(0.148562\pi\) | |||||||
\(648\) | 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 | \(-0.0979965\pi\) |
−0.303025 | + | 0.952983i | \(0.597997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.3057 | − | 29.4721i | −0.636147 | − | 1.14982i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.99323 | 0.194509 | 0.0972543 | − | 0.995260i | \(-0.468994\pi\) | ||||
0.0972543 | + | 0.995260i | \(0.468994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.6925 | −1.07711 | −0.538556 | − | 0.842589i | \(-0.681030\pi\) | ||||
−0.538556 | + | 0.842589i | \(0.681030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.1734 | + | 17.4963i | 0.511612 | + | 0.679500i | ||||
\(664\) | 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 | 0.211344 | − | 0.977412i | \(-0.432216\pi\) |
0.977412 | − | 0.211344i | \(-0.0677841\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.2980 | + | 15.2980i | −0.587952 | + | 0.587952i | −0.937076 | − | 0.349125i | \(-0.886479\pi\) |
0.349125 | + | 0.937076i | \(0.386479\pi\) | |||||||
\(678\) | 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 | \(-0.369793\pi\) |
−0.917497 | + | 0.397743i | \(0.869793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.1117 | + | 24.0552i | 0.691006 | + | 0.917763i | ||||
\(688\) | 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 | ||||||||
\(693\) | 1.75817 | + | 3.17783i | 0.0667873 | + | 0.120716i | ||||
\(694\) | 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 | \(-0.945675\pi\) | ||
0.985471 | − | 0.169841i | \(-0.0543255\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | 21.0358 | − | 15.8384i | 0.785596 | − | 0.591495i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9027 | −1.22706 | −0.613531 | − | 0.789670i | \(-0.710252\pi\) | ||||
−0.613531 | + | 0.789670i | \(0.710252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.08479 | −0.189367 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.9177 | − | 11.9848i | 0.591985 | − | 0.445720i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.5266 | + | 30.5266i | 1.13217 | + | 1.13217i | 0.989816 | + | 0.142351i | \(0.0454663\pi\) |
0.142351 | + | 0.989816i | \(0.454534\pi\) | |||||||
\(728\) | 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 | −0.956614 | − | 0.291358i | \(-0.905893\pi\) |
0.291358 | + | 0.956614i | \(0.405893\pi\) | |||||||
\(734\) | 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 | \(-0.858445\pi\) | ||
0.902736 | − | 0.430195i | \(-0.141555\pi\) | |||||||
\(740\) | 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 | \(-0.339901\pi\) |
−0.876156 | + | 0.482027i | \(0.839901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.9741 | − | 19.9030i | 1.31622 | − | 0.728214i | ||||
\(748\) | 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 | ||||||||
\(753\) | −17.8076 | − | 23.6513i | −0.648947 | − | 0.861901i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.00745 | − | 4.00745i | −0.145653 | − | 0.145653i | 0.630520 | − | 0.776173i | \(-0.282842\pi\) |
−0.776173 | + | 0.630520i | \(0.782842\pi\) | |||||||
\(758\) | 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 | \(-0.761919\pi\) | ||
0.733082 | − | 0.680140i | \(-0.238081\pi\) | |||||||
\(770\) | 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 | \(-0.0929771\pi\) |
−0.287960 | + | 0.957642i | \(0.592977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.61255 | + | 10.1106i | 0.273099 | + | 0.362717i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.0796 | −0.611941 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.26398 | 0.0810114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3508 | − | 32.2912i | −0.441382 | − | 1.15399i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.9229 | − | 38.9229i | −1.38745 | − | 1.38745i | −0.830636 | − | 0.556816i | \(-0.812023\pi\) |
−0.556816 | − | 0.830636i | \(-0.687977\pi\) | |||||||
\(788\) | 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 | \(-0.890056\pi\) |
0.338573 | + | 0.940940i | \(0.390056\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | 25.6772 | − | 19.3330i | 0.903881 | − | 0.680554i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.65158 | −0.269015 | −0.134508 | − | 0.990913i | \(-0.542945\pi\) | ||||
−0.134508 | + | 0.990913i | \(0.542945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4460 | 0.472152 | 0.236076 | − | 0.971735i | \(-0.424139\pi\) | ||||
0.236076 | + | 0.971735i | \(0.424139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.2626 | − | 20.5267i | 0.956140 | − | 0.719901i | ||||
\(814\) | 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 | −0.396961 | − | 0.917836i | \(-0.629935\pi\) |
0.917836 | + | 0.396961i | \(0.129935\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.4905 | + | 16.4905i | −0.573430 | + | 0.573430i | −0.933085 | − | 0.359655i | \(-0.882894\pi\) |
0.359655 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.7459i | 1.93614i | 0.250689 | + | 0.968068i | \(0.419343\pi\) | ||||
−0.250689 | + | 0.968068i | \(0.580657\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | −1.25781 | − | 3.28853i | −0.0434762 | − | 0.113668i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.77729 | 0.0613588 | 0.0306794 | − | 0.999529i | \(-0.490233\pi\) | ||||
0.0306794 | + | 0.999529i | \(0.490233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.2691 | 0.526520 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.2257 | + | 14.9095i | 0.386634 | + | 0.513509i | ||||
\(844\) | 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 | −0.853411 | − | 0.521239i | \(-0.825470\pi\) |
0.521239 | + | 0.853411i | \(0.325470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.21818 | + | 4.21818i | −0.144090 | + | 0.144090i | −0.775472 | − | 0.631382i | \(-0.782488\pi\) |
0.631382 | + | 0.775472i | \(0.282488\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.26158i | 0.0771642i | 0.999255 | + | 0.0385821i | \(0.0122841\pi\) | ||||
−0.999255 | + | 0.0385821i | \(0.987716\pi\) | |||||||
\(860\) | 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 | \(-0.0922909\pi\) |
−0.285895 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.1716 | − | 40.0725i | −1.02468 | − | 1.36093i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8805 | −0.436942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0492 | −0.442157 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.4788 | + | 8.01055i | −0.490034 | + | 0.271116i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.4841 | − | 23.4841i | −0.793003 | − | 0.793003i | 0.188978 | − | 0.981981i | \(-0.439482\pi\) |
−0.981981 | + | 0.188978i | \(0.939482\pi\) | |||||||
\(878\) | 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 | −0.104591 | − | 0.994515i | \(-0.533353\pi\) |
0.994515 | + | 0.104591i | \(0.0333533\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.6576 | − | 29.6576i | 0.995806 | − | 0.995806i | −0.00418537 | − | 0.999991i | \(-0.501332\pi\) |
0.999991 | + | 0.00418537i | \(0.00133225\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | −22.4610 | + | 16.9115i | −0.749951 | + | 0.564657i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.50836 | 0.150362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.8820 | −2.76120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.61331 | + | 3.47347i | −0.153521 | + | 0.115590i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.87348 | − | 8.87348i | −0.294639 | − | 0.294639i | 0.544271 | − | 0.838910i | \(-0.316806\pi\) |
−0.838910 | + | 0.544271i | \(0.816806\pi\) | |||||||
\(908\) | 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 | \(-0.764685\pi\) | ||
0.738965 | − | 0.673743i | \(-0.235315\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −7.38475 | − | 13.3477i | −0.242547 | − | 0.438396i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.5171 | −0.705954 | −0.352977 | − | 0.935632i | \(-0.614831\pi\) | ||||
−0.352977 | + | 0.935632i | \(0.614831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66781 | 0.120208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.8824 | + | 34.3759i | 0.847353 | + | 1.12541i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0454 | − | 14.0454i | −0.458842 | − | 0.458842i | 0.439433 | − | 0.898275i | \(-0.355179\pi\) |
−0.898275 | + | 0.439433i | \(0.855179\pi\) | |||||||
\(938\) | 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 | \(-0.823171\pi\) |
0.527389 | + | 0.849624i | \(0.323171\pi\) | |||||||
\(948\) | 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 | 0.958537 | + | 0.284967i | \(0.0919827\pi\) |
0.284967 | + | 0.958537i | \(0.408017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.39151 | − | 11.1452i | −0.271259 | − | 0.360274i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1441 | −0.359861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5409 | −0.985189 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.55157 | − | 6.41935i | −0.114448 | − | 0.206861i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.8316 | − | 20.8316i | −0.669898 | − | 0.669898i | 0.287794 | − | 0.957692i | \(-0.407078\pi\) |
−0.957692 | + | 0.287794i | \(0.907078\pi\) | |||||||
\(968\) | 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 | \(-0.577825\pi\) |
0.970260 | + | 0.242065i | \(0.0778247\pi\) | |||||||
\(978\) | 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 | \(-0.321828\pi\) |
−0.847390 | + | 0.530970i | \(0.821828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.73764 | − | 2.81416i | 0.118970 | − | 0.0895758i | ||||
\(988\) | 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 | ||||||||
\(993\) | 44.8713 | − | 33.7847i | 1.42395 | − | 1.07212i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.49889 | + | 8.49889i | 0.269163 | + | 0.269163i | 0.828763 | − | 0.559600i | \(-0.189045\pi\) |
−0.559600 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(998\) | 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.1457.10 | 24 | ||
3.2 | odd | 2 | inner | 2100.2.s.b.1457.8 | 24 | ||
5.2 | odd | 4 | 420.2.s.a.113.5 | yes | 24 | ||
5.3 | odd | 4 | inner | 2100.2.s.b.1793.8 | 24 | ||
5.4 | even | 2 | 420.2.s.a.197.3 | yes | 24 | ||
15.2 | even | 4 | 420.2.s.a.113.3 | ✓ | 24 | ||
15.8 | even | 4 | inner | 2100.2.s.b.1793.10 | 24 | ||
15.14 | odd | 2 | 420.2.s.a.197.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.s.a.113.3 | ✓ | 24 | 15.2 | even | 4 | ||
420.2.s.a.113.5 | yes | 24 | 5.2 | odd | 4 | ||
420.2.s.a.197.3 | yes | 24 | 5.4 | even | 2 | ||
420.2.s.a.197.5 | yes | 24 | 15.14 | odd | 2 | ||
2100.2.s.b.1457.8 | 24 | 3.2 | odd | 2 | inner | ||
2100.2.s.b.1457.10 | 24 | 1.1 | even | 1 | trivial | ||
2100.2.s.b.1793.8 | 24 | 5.3 | odd | 4 | inner | ||
2100.2.s.b.1793.10 | 24 | 15.8 | even | 4 | inner |