Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,4,Mod(129,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.e (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: | \(30.2089779229\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.129 |
Dual form | 512.4.e.n.385.2 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 4.47214 | + | 4.47214i | 0.860663 | + | 0.860663i | 0.991415 | − | 0.130752i | \(-0.0417392\pi\) |
−0.130752 | + | 0.991415i | \(0.541739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.0000 | − | 11.0000i | 0.983870 | − | 0.983870i | −0.0160020 | − | 0.999872i | \(-0.505094\pi\) |
0.999872 | + | 0.0160020i | \(0.00509383\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 26.8328i | − | 1.44884i | −0.689361 | − | 0.724418i | \(-0.742109\pi\) | ||
0.689361 | − | 0.724418i | \(-0.257891\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.0000i | 0.481481i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.3050 | + | 31.3050i | −0.858073 | + | 0.858073i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) |
0.133038 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.0000 | − | 23.0000i | −0.490696 | − | 0.490696i | 0.417829 | − | 0.908526i | \(-0.362791\pi\) |
−0.908526 | + | 0.417829i | \(0.862791\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 98.3870 | 1.69356 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 96.0000 | 1.36961 | 0.684806 | − | 0.728725i | \(-0.259887\pi\) | ||||
0.684806 | + | 0.728725i | \(0.259887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.0263 | − | 76.0263i | −0.917981 | − | 0.917981i | 0.0789018 | − | 0.996882i | \(-0.474859\pi\) |
−0.996882 | + | 0.0789018i | \(0.974859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 120.000 | − | 120.000i | 1.24696 | − | 1.24696i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 116.276i | − | 1.05414i | −0.849823 | − | 0.527068i | \(-0.823291\pi\) | ||
0.849823 | − | 0.527068i | \(-0.176709\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 117.000i | − | 0.936000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 62.6099 | − | 62.6099i | 0.446270 | − | 0.446270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 103.000 | + | 103.000i | 0.659539 | + | 0.659539i | 0.955271 | − | 0.295732i | \(-0.0955636\pi\) |
−0.295732 | + | 0.955271i | \(0.595564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −196.774 | −1.14005 | −0.570027 | − | 0.821626i | \(-0.693067\pi\) | ||||
−0.570027 | + | 0.821626i | \(0.693067\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −280.000 | −1.47702 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −295.161 | − | 295.161i | −1.42547 | − | 1.42547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −75.0000 | + | 75.0000i | −0.333241 | + | 0.333241i | −0.853816 | − | 0.520575i | \(-0.825718\pi\) |
0.520575 | + | 0.853816i | \(0.325718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 205.718i | − | 0.844648i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 312.000i | − | 1.18844i | −0.804301 | − | 0.594222i | \(-0.797460\pi\) | ||
0.804301 | − | 0.594222i | \(-0.202540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −254.912 | + | 254.912i | −0.904039 | + | 0.904039i | −0.995783 | − | 0.0917437i | \(-0.970756\pi\) |
0.0917437 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 143.000 | + | 143.000i | 0.473715 | + | 0.473715i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 89.4427 | 0.277586 | 0.138793 | − | 0.990321i | \(-0.455678\pi\) | ||||
0.138793 | + | 0.990321i | \(0.455678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −377.000 | −1.09913 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 429.325 | + | 429.325i | 1.17878 | + | 1.17878i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 325.000 | − | 325.000i | 0.842305 | − | 0.842305i | −0.146853 | − | 0.989158i | \(-0.546914\pi\) |
0.989158 | + | 0.146853i | \(0.0469144\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 688.709i | 1.68846i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 680.000i | − | 1.58014i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 263.856 | − | 263.856i | 0.582223 | − | 0.582223i | −0.353291 | − | 0.935513i | \(-0.614937\pi\) |
0.935513 | + | 0.353291i | \(0.114937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.0000 | − | 39.0000i | −0.0818596 | − | 0.0818596i | 0.664991 | − | 0.746851i | \(-0.268435\pi\) |
−0.746851 | + | 0.664991i | \(0.768435\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 348.827 | 0.697588 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −506.000 | −0.965563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 424.853 | + | 424.853i | 0.774687 | + | 0.774687i | 0.978922 | − | 0.204235i | \(-0.0654706\pi\) |
−0.204235 | + | 0.978922i | \(0.565471\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 520.000 | − | 520.000i | 0.907256 | − | 0.907256i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 366.715i | − | 0.612973i | −0.951875 | − | 0.306486i | \(-0.900847\pi\) | ||
0.951875 | − | 0.306486i | \(-0.0991534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1138.00i | − | 1.82456i | −0.409568 | − | 0.912280i | \(-0.634321\pi\) | ||
0.409568 | − | 0.912280i | \(-0.365679\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 523.240 | − | 523.240i | 0.805581 | − | 0.805581i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 840.000 | + | 840.000i | 1.24321 | + | 1.24321i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 911.000 | 1.24966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 523.240 | + | 523.240i | 0.691964 | + | 0.691964i | 0.962664 | − | 0.270700i | \(-0.0872550\pi\) |
−0.270700 | + | 0.962664i | \(0.587255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1056.00 | − | 1056.00i | 1.34752 | − | 1.34752i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 921.260i | 1.13528i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1410.00i | 1.67932i | 0.543110 | + | 0.839661i | \(0.317246\pi\) | ||||
−0.543110 | + | 0.839661i | \(0.682754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −617.155 | + | 617.155i | −0.710938 | + | 0.710938i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −880.000 | − | 880.000i | −0.981202 | − | 0.981202i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1672.58 | −1.80635 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 464.000 | 0.485691 | 0.242846 | − | 0.970065i | \(-0.421919\pi\) | ||||
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −406.964 | − | 406.964i | −0.413146 | − | 0.413146i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 949.000 | − | 949.000i | 0.934941 | − | 0.934941i | −0.0630683 | − | 0.998009i | \(-0.520089\pi\) |
0.998009 | + | 0.0630683i | \(0.0200886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1744.13i | 1.66849i | 0.551393 | + | 0.834245i | \(0.314096\pi\) | ||||
−0.551393 | + | 0.834245i | \(0.685904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2640.00i | − | 2.45369i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −174.413 | + | 174.413i | −0.157581 | + | 0.157581i | −0.781494 | − | 0.623913i | \(-0.785542\pi\) |
0.623913 | + | 0.781494i | \(0.285542\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 583.000 | + | 583.000i | 0.512305 | + | 0.512305i | 0.915232 | − | 0.402927i | \(-0.132007\pi\) |
−0.402927 | + | 0.915232i | \(0.632007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −670.820 | −0.573617 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1118.00 | −0.930731 | −0.465365 | − | 0.885119i | \(-0.654077\pi\) | ||||
−0.465365 | + | 0.885119i | \(0.654077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1279.03 | − | 1279.03i | −1.03713 | − | 1.03713i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 299.000 | − | 299.000i | 0.236261 | − | 0.236261i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2575.95i | − | 1.98434i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 629.000i | − | 0.472577i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1395.31 | − | 1395.31i | 1.02285 | − | 1.02285i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 88.0000 | + | 88.0000i | 0.0629677 | + | 0.0629677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2092.96 | 1.46236 | 0.731182 | − | 0.682183i | \(-0.238969\pi\) | ||||
0.731182 | + | 0.682183i | \(0.238969\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2280.00 | −1.55615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 693.181 | + | 693.181i | 0.462317 | + | 0.462317i | 0.899414 | − | 0.437097i | \(-0.143993\pi\) |
−0.437097 | + | 0.899414i | \(0.643993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2040.00 | + | 2040.00i | −1.33000 | + | 1.33000i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1377.42i | − | 0.878143i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1144.00i | 0.713420i | 0.934215 | + | 0.356710i | \(0.116102\pi\) | ||||
−0.934215 | + | 0.356710i | \(0.883898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −809.457 | + | 809.457i | −0.493937 | + | 0.493937i | −0.909544 | − | 0.415607i | \(-0.863569\pi\) |
0.415607 | + | 0.909544i | \(0.363569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 400.000 | + | 400.000i | 0.238908 | + | 0.238908i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1440.03 | 0.842106 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2266.00 | 1.29780 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1686.00 | − | 1686.00i | −0.945976 | − | 0.945976i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 507.000 | − | 507.000i | 0.278759 | − | 0.278759i | −0.553855 | − | 0.832613i | \(-0.686844\pi\) |
0.832613 | + | 0.553855i | \(0.186844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2298.68i | − | 1.23883i | −0.785063 | − | 0.619416i | \(-0.787369\pi\) | ||
0.785063 | − | 0.619416i | \(-0.212631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1248.00i | 0.659443i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2164.51 | + | 2164.51i | −1.12166 | + | 1.12166i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −519.000 | − | 519.000i | −0.263826 | − | 0.263826i | 0.562780 | − | 0.826606i | \(-0.309732\pi\) |
−0.826606 | + | 0.562780i | \(0.809732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2906.89 | 1.44988 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3120.00 | −1.52727 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 988.342 | + | 988.342i | 0.474926 | + | 0.474926i | 0.903505 | − | 0.428579i | \(-0.140985\pi\) |
−0.428579 | + | 0.903505i | \(0.640985\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3080.00 | + | 3080.00i | −1.45320 | + | 1.45320i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1976.68i | 0.915931i | 0.888970 | + | 0.457965i | \(0.151422\pi\) | ||||
−0.888970 | + | 0.457965i | \(0.848578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1139.00i | − | 0.518434i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 988.342 | − | 988.342i | 0.441991 | − | 0.441991i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1625.00 | + | 1625.00i | 0.714141 | + | 0.714141i | 0.967399 | − | 0.253258i | \(-0.0815020\pi\) |
−0.253258 | + | 0.967399i | \(0.581502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3139.44 | −1.35611 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2360.00 | 1.00219 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 326.466 | + | 326.466i | 0.136320 | + | 0.136320i | 0.771974 | − | 0.635654i | \(-0.219270\pi\) |
−0.635654 | + | 0.771974i | \(0.719270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 299.000 | − | 299.000i | 0.122787 | − | 0.122787i | −0.643043 | − | 0.765830i | \(-0.722328\pi\) |
0.765830 | + | 0.643043i | \(0.222328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 348.827i | − | 0.140907i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1650.00i | 0.655732i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3005.28 | + | 3005.28i | −1.17523 | + | 1.17523i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1680.00 | − | 1680.00i | −0.646572 | − | 0.646572i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1735.19 | −0.657350 | −0.328675 | − | 0.944443i | \(-0.606602\pi\) | ||||
−0.328675 | + | 0.944443i | \(0.606602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1872.00 | 0.698184 | 0.349092 | − | 0.937088i | \(-0.386490\pi\) | ||||
0.349092 | + | 0.937088i | \(0.386490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2262.90 | − | 2262.90i | −0.831024 | − | 0.831024i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1029.00 | + | 1029.00i | −0.372148 | + | 0.372148i | −0.868259 | − | 0.496111i | \(-0.834761\pi\) |
0.496111 | + | 0.868259i | \(0.334761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4606.30i | − | 1.64086i | −0.571744 | − | 0.820432i | \(-0.693733\pi\) | ||
0.571744 | − | 0.820432i | \(-0.306267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3800.00i | 1.33349i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2763.78 | − | 2763.78i | 0.955563 | − | 0.955563i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3432.00 | − | 3432.00i | −1.16927 | − | 1.16927i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1511.58 | 0.507547 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4760.00 | 1.57539 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 809.457 | + | 809.457i | 0.264101 | + | 0.264101i | 0.826718 | − | 0.562617i | \(-0.190205\pi\) |
−0.562617 | + | 0.826718i | \(0.690205\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1640.00 | − | 1640.00i | 0.527563 | − | 0.527563i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5608.06i | 1.77891i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5280.00i | 1.65175i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5089.29 | − | 5089.29i | 1.57033 | − | 1.57033i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2208.00 | − | 2208.00i | −0.672064 | − | 0.672064i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5134.01 | −1.54170 | −0.770850 | − | 0.637017i | \(-0.780168\pi\) | ||||
−0.770850 | + | 0.637017i | \(0.780168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1521.00 | 0.450667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 755.791 | + | 755.791i | 0.220985 | + | 0.220985i | 0.808913 | − | 0.587928i | \(-0.200056\pi\) |
−0.587928 | + | 0.808913i | \(0.700056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1557.00 | + | 1557.00i | −0.449299 | + | 0.449299i | −0.895121 | − | 0.445822i | \(-0.852911\pi\) |
0.445822 | + | 0.895121i | \(0.352911\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7513.19i | 2.13996i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4558.00i | 1.28156i | 0.767723 | + | 0.640782i | \(0.221390\pi\) | ||||
−0.767723 | + | 0.640782i | \(0.778610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 983.870 | − | 983.870i | 0.273109 | − | 0.273109i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3041.05 | −0.823052 | −0.411526 | − | 0.911398i | \(-0.635004\pi\) | ||||
−0.411526 | + | 0.911398i | \(0.635004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1632.00 | 0.436209 | 0.218104 | − | 0.975925i | \(-0.430013\pi\) | ||||
0.218104 | + | 0.975925i | \(0.430013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2383.65 | + | 2383.65i | 0.629264 | + | 0.629264i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4147.00 | + | 4147.00i | −1.08140 | + | 1.08140i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3497.21i | 0.900899i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4680.00i | 1.19110i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3009.75 | + | 3009.75i | −0.756867 | + | 0.756867i | −0.975751 | − | 0.218884i | \(-0.929758\pi\) |
0.218884 | + | 0.975751i | \(0.429758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3640.00 | + | 3640.00i | 0.904525 | + | 0.904525i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9445.15 | 2.31952 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −814.000 | −0.197572 | −0.0987858 | − | 0.995109i | \(-0.531496\pi\) | ||||
−0.0987858 | + | 0.995109i | \(0.531496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2012.46 | + | 2012.46i | 0.482812 | + | 0.482812i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1339.00 | + | 1339.00i | −0.317556 | + | 0.317556i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2441.79i | − | 0.572498i | −0.958155 | − | 0.286249i | \(-0.907592\pi\) | ||
0.958155 | − | 0.286249i | \(-0.0924085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7150.00i | − | 1.65744i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6305.71 | + | 6305.71i | −1.44533 | + | 1.44533i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 247.000 | + | 247.000i | 0.0559846 | + | 0.0559846i | 0.734545 | − | 0.678560i | \(-0.237396\pi\) |
−0.678560 | + | 0.734545i | \(0.737396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 89.4427 | 0.0200489 | 0.0100245 | − | 0.999950i | \(-0.496809\pi\) | ||||
0.0100245 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5520.00 | −1.22376 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3662.68 | + | 3662.68i | 0.803156 | + | 0.803156i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2795.00 | + | 2795.00i | −0.606265 | + | 0.606265i | −0.941968 | − | 0.335703i | \(-0.891026\pi\) |
0.335703 | + | 0.941968i | \(0.391026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2558.06i | − | 0.548915i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 930.000i | − | 0.197435i | −0.995116 | − | 0.0987173i | \(-0.968526\pi\) | ||
0.995116 | − | 0.0987173i | \(-0.0314740\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5871.91 | − | 5871.91i | 1.23339 | − | 1.23339i | 0.270735 | − | 0.962654i | \(-0.412733\pi\) |
0.962654 | − | 0.270735i | \(-0.0872668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7480.00 | − | 7480.00i | −1.55466 | − | 1.55466i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8371.84 | −1.72186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4303.00 | 0.875840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2075.07 | + | 2075.07i | 0.418017 | + | 0.418017i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 283.000 | − | 283.000i | 0.0564267 | − | 0.0564267i | −0.678330 | − | 0.734757i | \(-0.737296\pi\) |
0.734757 | + | 0.678330i | \(0.237296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5804.83i | − | 1.14566i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3920.00i | 0.765864i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2674.34 | + | 2674.34i | −0.517261 | + | 0.517261i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6840.00 | + | 6840.00i | 1.30980 | + | 1.30980i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8488.11 | 1.60934 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −858.000 | −0.161078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 84.9706 | + | 84.9706i | 0.0157965 | + | 0.0157965i | 0.714961 | − | 0.699164i | \(-0.246444\pi\) |
−0.699164 | + | 0.714961i | \(0.746444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7800.00 | + | 7800.00i | −1.43601 | + | 1.43601i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2745.89i | − | 0.500660i | −0.968161 | − | 0.250330i | \(-0.919461\pi\) | ||
0.968161 | − | 0.250330i | \(-0.0805391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4408.00i | 0.796022i | 0.917381 | + | 0.398011i | \(0.130299\pi\) | ||||
−0.917381 | + | 0.398011i | \(0.869701\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3837.09 | − | 3837.09i | 0.686335 | − | 0.686335i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −585.000 | − | 585.000i | −0.103649 | − | 0.103649i | 0.653380 | − | 0.757030i | \(-0.273350\pi\) |
−0.757030 | + | 0.653380i | \(0.773350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6448.82 | −1.13186 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1560.00 | −0.271248 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7298.53 | − | 7298.53i | −1.25728 | − | 1.25728i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2691.00 | + | 2691.00i | −0.459292 | + | 0.459292i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5214.51i | 0.881844i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2400.00i | − | 0.402177i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58.1378 | − | 58.1378i | 0.00965420 | − | 0.00965420i | −0.702263 | − | 0.711917i | \(-0.747827\pi\) |
0.711917 | + | 0.702263i | \(0.247827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −975.000 | − | 975.000i | −0.160449 | − | 0.160449i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9346.76 | 1.52438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9394.00 | −1.51847 | −0.759234 | − | 0.650818i | \(-0.774426\pi\) | ||||
−0.759234 | + | 0.650818i | \(0.774426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4999.85 | − | 4999.85i | −0.801046 | − | 0.801046i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6160.00 | − | 6160.00i | 0.978248 | − | 0.978248i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 912.316i | 0.143616i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 11440.0i | − | 1.78524i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6623.23 | + | 6623.23i | −1.02465 | + | 1.02465i | −0.0249623 | + | 0.999688i | \(0.507947\pi\) |
−0.999688 | + | 0.0249623i | \(0.992053\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7127.00 | + | 7127.00i | 1.09312 | + | 1.09312i | 0.995193 | + | 0.0979285i | \(0.0312217\pi\) |
0.0979285 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2880.06 | −0.437966 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2418.00 | −0.364581 | −0.182291 | − | 0.983245i | \(-0.558351\pi\) | ||||
−0.182291 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4033.87 | − | 4033.87i | −0.603086 | − | 0.603086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11520.0 | − | 11520.0i | 1.70785 | − | 1.70785i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6162.60i | − | 0.905988i | −0.891514 | − | 0.452994i | \(-0.850356\pi\) | ||
0.891514 | − | 0.452994i | \(-0.149644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4701.00i | 0.685377i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2812.97 | − | 2812.97i | 0.406730 | − | 0.406730i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12518.0 | − | 12518.0i | −1.79513 | − | 1.79513i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1055.42 | −0.150116 | −0.0750582 | − | 0.997179i | \(-0.523914\pi\) | ||||
−0.0750582 | + | 0.997179i | \(0.523914\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4056.00 | 0.572214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8720.67 | − | 8720.67i | −1.22036 | − | 1.22036i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2613.00 | − | 2613.00i | 0.362724 | − | 0.362724i | −0.502091 | − | 0.864815i | \(-0.667436\pi\) |
0.864815 | + | 0.502091i | \(0.167436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 787.096i | 0.108388i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4738.00i | − | 0.647266i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 639.515 | − | 639.515i | 0.0866747 | − | 0.0866747i | −0.662440 | − | 0.749115i | \(-0.730479\pi\) |
0.749115 | + | 0.662440i | \(0.230479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9360.00 | + | 9360.00i | 1.25860 | + | 1.25860i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6296.77 | 0.840078 | 0.420039 | − | 0.907506i | \(-0.362016\pi\) | ||||
0.420039 | + | 0.907506i | \(0.362016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18480.0 | 2.44631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3313.85 | − | 3313.85i | −0.435278 | − | 0.435278i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6037.00 | − | 6037.00i | 0.786859 | − | 0.786859i | −0.194119 | − | 0.980978i | \(-0.562185\pi\) |
0.980978 | + | 0.194119i | \(0.0621849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11162.5i | − | 1.44376i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6200.00i | 0.795798i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −585.000 | − | 585.000i | −0.0739554 | − | 0.0739554i | 0.669162 | − | 0.743117i | \(-0.266653\pi\) |
−0.743117 | + | 0.669162i | \(0.766653\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18246.3 | −2.28937 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2080.00 | −0.259028 | −0.129514 | − | 0.991578i | \(-0.541342\pi\) | ||||
−0.129514 | + | 0.991578i | \(0.541342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4525.80 | + | 4525.80i | 0.559420 | + | 0.559420i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10021.0 | − | 10021.0i | 1.22950 | − | 1.22950i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4695.74i | − | 0.571890i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13000.0i | − | 1.57166i | −0.618443 | − | 0.785830i | \(-0.712236\pi\) | ||
0.618443 | − | 0.785830i | \(-0.287764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5116.12 | + | 5116.12i | −0.614014 | + | 0.614014i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7080.00 | − | 7080.00i | −0.843545 | − | 0.843545i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11511.3 | 1.36161 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7240.00 | −0.850226 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8599.92 | + | 8599.92i | 1.00271 | + | 1.00271i | 0.999996 | + | 0.00270882i | \(0.000862246\pi\) |
0.00270882 | + | 0.999996i | \(0.499138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1029.00 | + | 1029.00i | −0.119122 | + | 0.119122i | −0.764155 | − | 0.645033i | \(-0.776844\pi\) |
0.645033 | + | 0.764155i | \(0.276844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1162.76i | 0.133653i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 11232.0i | − | 1.28196i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1046.48 | + | 1046.48i | −0.118601 | + | 0.118601i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6440.00 | + | 6440.00i | 0.724770 | + | 0.724770i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5330.79 | −0.595765 | −0.297883 | − | 0.954602i | \(-0.596280\pi\) | ||||
−0.297883 | + | 0.954602i | \(0.596280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7808.00 | 0.866579 | 0.433289 | − | 0.901255i | \(-0.357353\pi\) | ||||
0.433289 | + | 0.901255i | \(0.357353\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10133.9 | + | 10133.9i | 1.11697 | + | 1.11697i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8840.00 | + | 8840.00i | −0.967676 | + | 0.967676i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4695.74i | 0.510514i | 0.966873 | + | 0.255257i | \(0.0821601\pi\) | ||||
−0.966873 | + | 0.255257i | \(0.917840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 4901.00i | − | 0.529209i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3027.64 | − | 3027.64i | 0.324712 | − | 0.324712i | −0.525860 | − | 0.850571i | \(-0.676256\pi\) |
0.850571 | + | 0.525860i | \(0.176256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15510.0 | + | 15510.0i | 1.65223 | + | 1.65223i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4534.75 | 0.479835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12720.0 | −1.33696 | −0.668479 | − | 0.743731i | \(-0.733054\pi\) | ||||
−0.668479 | + | 0.743731i | \(0.733054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9767.14 | + | 9767.14i | 1.01977 | + | 1.01977i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10280.0 | − | 10280.0i | 1.06622 | − | 1.06622i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13577.4i | 1.39894i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 56.0000i | − | 0.00573210i | −0.999996 | − | 0.00286605i | \(-0.999088\pi\) | ||
0.999996 | − | 0.00286605i | \(-0.000912293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6010.55 | − | 6010.55i | 0.611217 | − | 0.611217i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12729.0 | − | 12729.0i | −1.28601 | − | 1.28601i | −0.937192 | − | 0.348814i | \(-0.886585\pi\) |
−0.348814 | − | 0.937192i | \(-0.613415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13953.1 | 1.40055 | 0.700274 | − | 0.713874i | \(-0.253061\pi\) | ||||
0.700274 | + | 0.713874i | \(0.253061\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19360.0 | −1.93075 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1220.89 | − | 1220.89i | −0.120977 | − | 0.120977i | 0.644026 | − | 0.765003i | \(-0.277263\pi\) |
−0.765003 | + | 0.644026i | \(0.777263\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11400.0 | − | 11400.0i | 1.12239 | − | 1.12239i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4642.08i | − | 0.454131i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 15960.0i | − | 1.55146i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8895.08 | + | 8895.08i | −0.859230 | + | 0.859230i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4225.00 | + | 4225.00i | 0.405554 | + | 0.405554i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14507.6 | 1.38386 | 0.691931 | − | 0.721964i | \(-0.256760\pi\) | ||||
0.691931 | + | 0.721964i | \(0.256760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3450.00 | 0.327040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13953.1 | − | 13953.1i | −1.31446 | − | 1.31446i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5104.00 | − | 5104.00i | 0.477857 | − | 0.477857i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16394.9i | 1.52551i | 0.646690 | + | 0.762753i | \(0.276153\pi\) | ||||
−0.646690 | + | 0.762753i | \(0.723847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8840.00i | 0.817502i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2929.25 | − | 2929.25i | 0.269237 | − | 0.269237i | −0.559556 | − | 0.828793i | \(-0.689028\pi\) |
0.828793 | + | 0.559556i | \(0.189028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9888.00 | + | 9888.00i | 0.903313 | + | 0.903313i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8953.22 | −0.812964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9840.00 | −0.888097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2499.92 | − | 2499.92i | −0.224272 | − | 0.224272i | 0.586022 | − | 0.810295i | \(-0.300693\pi\) |
−0.810295 | + | 0.586022i | \(0.800693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8840.00 | + | 8840.00i | −0.788308 | + | 0.788308i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3962.31i | 0.351234i | 0.984459 | + | 0.175617i | \(0.0561921\pi\) | ||||
−0.984459 | + | 0.175617i | \(0.943808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 20878.0i | − | 1.83972i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5093.76 | − | 5093.76i | 0.446197 | − | 0.446197i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10313.0 | + | 10313.0i | 0.898066 | + | 0.898066i | 0.995265 | − | 0.0971988i | \(-0.0309883\pi\) |
−0.0971988 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30535.7 | −2.64349 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9520.00 | −0.819334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19185.5 | + | 19185.5i | 1.64158 | + | 1.64158i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2800.00 | + | 2800.00i | −0.238189 | + | 0.238189i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14534.4i | 1.22927i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4200.00i | − | 0.353177i | −0.984285 | − | 0.176589i | \(-0.943494\pi\) | ||
0.984285 | − | 0.176589i | \(-0.0565062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11453.1 | − | 11453.1i | 0.957573 | − | 0.957573i | −0.0415626 | − | 0.999136i | \(-0.513234\pi\) |
0.999136 | + | 0.0415626i | \(0.0132336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14040.0 | − | 14040.0i | −1.16715 | − | 1.16715i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18890.3 | −1.56143 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1353.00 | −0.111202 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3430.13 | + | 3430.13i | 0.280329 | + | 0.280329i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7176.00 | + | 7176.00i | −0.583165 | + | 0.583165i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3837.09i | 0.310078i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2920.00i | 0.234650i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11802.0 | − | 11802.0i | 0.943129 | − | 0.943129i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6471.00 | − | 6471.00i | −0.514251 | − | 0.514251i | 0.401575 | − | 0.915826i | \(-0.368463\pi\) |
−0.915826 | + | 0.401575i | \(0.868463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2674.34 | 0.211357 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12826.0 | 1.00808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 353.299 | + | 353.299i | 0.0276160 | + | 0.0276160i | 0.720780 | − | 0.693164i | \(-0.243784\pi\) |
−0.693164 | + | 0.720780i | \(0.743784\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 507.000 | − | 507.000i | 0.0394139 | − | 0.0394139i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15661.4i | − | 1.21089i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7379.02 | + | 7379.02i | −0.564364 | + | 0.564364i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6809.00 | + | 6809.00i | 0.517965 | + | 0.517965i | 0.916955 | − | 0.398990i | \(-0.130639\pi\) |
−0.398990 | + | 0.916955i | \(0.630639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11725.9 | 0.887217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26880.0 | −2.02295 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11954.0 | − | 11954.0i | −0.894852 | − | 0.894852i | 0.100123 | − | 0.994975i | \(-0.468076\pi\) |
−0.994975 | + | 0.100123i | \(0.968076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12298.0 | + | 12298.0i | −0.915718 | + | 0.915718i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 24444.7i | − | 1.81055i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11240.0i | 0.828129i | 0.910248 | + | 0.414064i | \(0.135891\pi\) | ||||
−0.910248 | + | 0.414064i | \(0.864109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17580.0 | + | 17580.0i | −1.28844 | + | 1.28844i | −0.352704 | + | 0.935735i | \(0.614738\pi\) |
−0.935735 | + | 0.352704i | \(0.885262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7760.00 | − | 7760.00i | −0.565757 | − | 0.565757i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13604.2 | −0.986671 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26654.0 | 1.92309 | 0.961543 | − | 0.274655i | \(-0.0885635\pi\) | ||||
0.961543 | + | 0.274655i | \(0.0885635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8371.84 | + | 8371.84i | 0.600901 | + | 0.600901i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14040.0 | − | 14040.0i | 1.00254 | − | 1.00254i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20348.2i | 1.44552i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6578.00i | − | 0.464901i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 988.342 | − | 988.342i | 0.0694944 | − | 0.0694944i | −0.671505 | − | 0.741000i | \(-0.734352\pi\) |
0.741000 | + | 0.671505i | \(0.234352\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14960.0 | + | 14960.0i | 1.04655 | + | 1.04655i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9203.66 | −0.640589 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11538.0 | 0.799003 | 0.399502 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399502 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28335.5 | − | 28335.5i | −1.95234 | − | 1.95234i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20600.0 | − | 20600.0i | 1.41223 | − | 1.41223i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18362.6i | 1.25255i | 0.779604 | + | 0.626273i | \(0.215420\pi\) | ||||
−0.779604 | + | 0.626273i | \(0.784580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14210.0i | 0.964456i | 0.876046 | + | 0.482228i | \(0.160172\pi\) | ||||
−0.876046 | + | 0.482228i | \(0.839828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5523.09 | + | 5523.09i | −0.372998 | + | 0.372998i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6919.00 | − | 6919.00i | −0.464954 | − | 0.464954i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21752.5 | 1.45454 | 0.727270 | − | 0.686352i | \(-0.240789\pi\) | ||||
0.727270 | + | 0.686352i | \(0.240789\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24720.0 | 1.64484 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2057.18 | − | 2057.18i | −0.136211 | − | 0.136211i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12315.0 | − | 12315.0i | 0.811416 | − | 0.811416i | −0.173430 | − | 0.984846i | \(-0.555485\pi\) |
0.984846 | + | 0.173430i | \(0.0554850\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 30696.7i | − | 2.01270i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1586.00i | 0.103485i | 0.998660 | + | 0.0517423i | \(0.0164774\pi\) | ||||
−0.998660 | + | 0.0517423i | \(0.983523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12732.2 | + | 12732.2i | −0.826735 | + | 0.826735i | −0.987064 | − | 0.160328i | \(-0.948745\pi\) |
0.160328 | + | 0.987064i | \(0.448745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7280.00 | − | 7280.00i | −0.470429 | − | 0.470429i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37834.3 | 2.43306 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16561.0 | 1.05990 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21287.4 | + | 21287.4i | 1.35588 | + | 1.35588i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7200.00 | + | 7200.00i | −0.456411 | + | 0.456411i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2119.79i | − | 0.133736i | −0.997762 | − | 0.0668681i | \(-0.978699\pi\) | ||
0.997762 | − | 0.0668681i | \(-0.0213007\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7240.00i | 0.454604i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23022.6 | − | 23022.6i | 1.43878 | − | 1.43878i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8671.00 | + | 8671.00i | 0.539337 | + | 0.539337i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4767.30 | 0.295135 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14992.0 | −0.923788 | −0.461894 | − | 0.886935i | \(-0.652830\pi\) | ||||
−0.461894 | + | 0.886935i | \(0.652830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20504.7 | − | 20504.7i | −1.25759 | − | 1.25759i | −0.952242 | − | 0.305345i | \(-0.901228\pi\) |
−0.305345 | − | 0.952242i | \(-0.598772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25080.0 | + | 25080.0i | −1.53105 | + | 1.53105i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 19257.0i | − | 1.17013i | −0.810988 | − | 0.585063i | \(-0.801070\pi\) | ||
0.810988 | − | 0.585063i | \(-0.198930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16520.0i | 0.999178i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23612.9 | + | 23612.9i | −1.42160 | + | 1.42160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18473.0 | − | 18473.0i | −1.10705 | − | 1.10705i | −0.993536 | − | 0.113515i | \(-0.963789\pi\) |
−0.113515 | − | 0.993536i | \(-0.536211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15250.0 | 0.909719 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14794.0 | 0.878491 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14476.3 | + | 14476.3i | 0.855716 | + | 0.855716i | 0.990830 | − | 0.135114i | \(-0.0431401\pi\) |
−0.135114 | + | 0.990830i | \(0.543140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16341.0 | + | 16341.0i | −0.961560 | + | 0.961560i | −0.999288 | − | 0.0377279i | \(-0.987988\pi\) |
0.0377279 | + | 0.999288i | \(0.487988\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 19749.0i | − | 1.15684i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44880.0i | 2.61710i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11976.4 | − | 11976.4i | 0.695243 | − | 0.695243i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22960.0 | − | 22960.0i | −1.32688 | − | 1.32688i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2441.79 | 0.140483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17168.0 | −0.983325 | −0.491663 | − | 0.870786i | \(-0.663611\pi\) | ||||
−0.491663 | + | 0.870786i | \(0.663611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7325.36 | − | 7325.36i | −0.417708 | − | 0.417708i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3029.00 | − | 3029.00i | 0.171956 | − | 0.171956i | −0.615882 | − | 0.787838i | \(-0.711200\pi\) |
0.787838 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12450.4i | − | 0.703687i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6760.00i | 0.380387i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16220.4 | − | 16220.4i | 0.908723 | − | 0.908723i | −0.0874463 | − | 0.996169i | \(-0.527871\pi\) |
0.996169 | + | 0.0874463i | \(0.0278706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12584.0 | + | 12584.0i | 0.701912 | + | 0.701912i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13926.2 | −0.773390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14950.0 | −0.826632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11220.6 | + | 11220.6i | 0.617730 | + | 0.617730i | 0.944949 | − | 0.327219i | \(-0.106111\pi\) |
−0.327219 | + | 0.944949i | \(0.606111\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10920.0 | + | 10920.0i | −0.598581 | + | 0.598581i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17808.0i | 0.971939i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 29952.0i | − | 1.62771i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20384.0 | + | 20384.0i | −1.10300 | + | 1.10300i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10569.0 | + | 10569.0i | 0.569452 | + | 0.569452i | 0.931975 | − | 0.362523i | \(-0.118085\pi\) |
−0.362523 | + | 0.931975i | \(0.618085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11403.9 | 0.611818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8800.00 | 0.470109 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25464.3 | − | 25464.3i | −1.35458 | − | 1.35458i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21307.0 | + | 21307.0i | −1.12863 | + | 1.12863i | −0.138234 | + | 0.990400i | \(0.544143\pi\) |
−0.990400 | + | 0.138234i | \(0.955857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22880.0i | 1.20177i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15840.3 | − | 15840.3i | 0.828523 | − | 0.828523i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13600.0 | − | 13600.0i | −0.708370 | − | 0.708370i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21788.2 | −1.13013 | −0.565066 | − | 0.825046i | \(-0.691149\pi\) | ||||
−0.565066 | + | 0.825046i | \(0.691149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46800.0 | 2.41737 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7298.53 | + | 7298.53i | 0.375429 | + | 0.375429i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12051.0 | − | 12051.0i | 0.617328 | − | 0.617328i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15160.5i | − | 0.773416i | −0.922202 | − | 0.386708i | \(-0.873612\pi\) | ||
0.922202 | − | 0.386708i | \(-0.126388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 3277.00i | − | 0.166489i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24471.5 | + | 24471.5i | −1.23818 | + | 1.23818i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12105.0 | − | 12105.0i | −0.609971 | − | 0.609971i | 0.332968 | − | 0.942938i | \(-0.391950\pi\) |
−0.942938 | + | 0.332968i | \(0.891950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37091.9 | −1.86144 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26600.0 | −1.32948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6453.29 | − | 6453.29i | −0.321229 | − | 0.321229i | 0.528010 | − | 0.849238i | \(-0.322939\pi\) |
−0.849238 | + | 0.528010i | \(0.822939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15640.0 | + | 15640.0i | −0.775371 | + | 0.775371i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7074.92i | − | 0.349332i | −0.984628 | − | 0.174666i | \(-0.944115\pi\) | ||
0.984628 | − | 0.174666i | \(-0.0558846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 11154.0i | − | 0.548525i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6802.12 | + | 6802.12i | −0.333168 | + | 0.333168i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4680.00 | + | 4680.00i | 0.228309 | + | 0.228309i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6511.43 | −0.316385 | −0.158193 | − | 0.987408i | \(-0.550567\pi\) | ||||
−0.158193 | + | 0.987408i | \(0.550567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26920.0 | −1.30281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25285.5 | − | 25285.5i | −1.21885 | − | 1.21885i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27365.0 | + | 27365.0i | −1.31387 | + | 1.31387i | −0.395327 | + | 0.918540i | \(0.629369\pi\) |
−0.918540 | + | 0.395327i | \(0.870631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32557.1i | 1.55698i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29400.0i | 1.40046i | 0.713918 | + | 0.700229i | \(0.246919\pi\) | ||||
−0.713918 | + | 0.700229i | \(0.753081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15643.5 | − | 15643.5i | 0.742246 | − | 0.742246i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13728.0 | + | 13728.0i | 0.648806 | + | 0.648806i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12137.4 | −0.571389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8944.00 | 0.419413 | 0.209707 | − | 0.977764i | \(-0.432749\pi\) | ||||
0.209707 | + | 0.977764i | \(0.432749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3640.32 | − | 3640.32i | −0.170043 | − | 0.170043i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17275.0 | + | 17275.0i | −0.803802 | + | 0.803802i | −0.983687 | − | 0.179886i | \(-0.942427\pi\) |
0.179886 | + | 0.983687i | \(0.442427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23022.6i | 1.06709i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18000.0i | 0.831076i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23720.2 | + | 23720.2i | −1.09097 | + | 1.09097i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11480.0 | + | 11480.0i | 0.525975 | + | 0.525975i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12897.6 | 0.588664 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11418.0 | −0.519141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24010.9 | + | 24010.9i | 1.08754 | + | 1.08754i | 0.995781 | + | 0.0917617i | \(0.0292498\pi\) |
0.0917617 | + | 0.995781i | \(0.470750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10920.0 | − | 10920.0i | 0.492728 | − | 0.492728i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29999.1i | 1.34848i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1794.00i | 0.0803365i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31975.8 | − | 31975.8i | 1.42650 | − | 1.42650i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1175.00 | − | 1175.00i | −0.0522216 | − | 0.0522216i | 0.680514 | − | 0.732735i | \(-0.261757\pi\) |
−0.732735 | + | 0.680514i | \(0.761757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8586.50 | 0.380186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18330.0 | −0.808563 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35625.0 | + | 35625.0i | 1.56560 | + | 1.56560i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34320.0 | + | 34320.0i | −1.50263 | + | 1.50263i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2209.24i | 0.0963677i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17304.0i | − | 0.752010i | −0.926618 | − | 0.376005i | \(-0.877298\pi\) | ||
0.926618 | − | 0.376005i | \(-0.122702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20522.6 | − | 20522.6i | 0.888591 | − | 0.888591i | −0.105797 | − | 0.994388i | \(-0.533739\pi\) |
0.994388 | + | 0.105797i | \(0.0337394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 400.000 | + | 400.000i | 0.0172554 | + | 0.0172554i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21743.5 | 0.934531 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38760.0 | 1.65978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8023.01 | − | 8023.01i | −0.342304 | − | 0.342304i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10229.0 | − | 10229.0i | 0.434829 | − | 0.434829i | −0.455438 | − | 0.890267i | \(-0.650517\pi\) |
0.890267 | + | 0.455438i | \(0.150517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34140.3i | 1.44600i | 0.690850 | + | 0.722999i | \(0.257237\pi\) | ||||
−0.690850 | + | 0.722999i | \(0.742763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32760.0i | 1.38249i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9735.84 | − | 9735.84i | 0.409369 | − | 0.409369i | −0.472149 | − | 0.881519i | \(-0.656522\pi\) |
0.881519 | + | 0.472149i | \(0.156522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2647.00 | − | 2647.00i | −0.110898 | − | 0.110898i | 0.649481 | − | 0.760378i | \(-0.274986\pi\) |
−0.760378 | + | 0.649481i | \(0.774986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24999.2 | −1.04358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36192.0 | −1.50538 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21743.5 | + | 21743.5i | 0.901157 | + | 0.901157i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12320.0 | + | 12320.0i | −0.508771 | + | 0.508771i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 8255.56i | − | 0.339706i | −0.985469 | − | 0.169853i | \(-0.945671\pi\) | ||
0.985469 | − | 0.169853i | \(-0.0543294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 3171.00i | − | 0.130018i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4159.09 | − | 4159.09i | 0.169925 | − | 0.169925i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12529.0 | − | 12529.0i | −0.510072 | − | 0.510072i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16877.8 | −0.684687 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52520.0 | 2.12306 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8720.67 | + | 8720.67i | 0.351281 | + | 0.351281i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28005.0 | − | 28005.0i | 1.12412 | − | 1.12412i | 0.133003 | − | 0.991116i | \(-0.457538\pi\) |
0.991116 | − | 0.133003i | \(-0.0424619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 21743.5i | − | 0.869723i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30056.0i | 1.19801i | 0.800746 | + | 0.599004i | \(0.204437\pi\) | ||||
−0.800746 | + | 0.599004i | \(0.795563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6220.74 | − | 6220.74i | 0.247088 | − | 0.247088i | −0.572686 | − | 0.819775i | \(-0.694099\pi\) |
0.819775 | + | 0.572686i | \(0.194099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37440.0 | − | 37440.0i | −1.48194 | − | 1.48194i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27458.9 | 1.08310 | 0.541548 | − | 0.840670i | \(-0.317838\pi\) | ||||
0.541548 | + | 0.840670i | \(0.317838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35750.0 | 1.40524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19243.6 | + | 19243.6i | 0.753803 | + | 0.753803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 19543.2i | − | 0.760272i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6032.00i | 0.233851i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2361.29 | − | 2361.29i | 0.0912298 | − | 0.0912298i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13479.0 | + | 13479.0i | 0.518989 | + | 0.518989i | 0.917265 | − | 0.398276i | \(-0.130391\pi\) |
−0.398276 | + | 0.917265i | \(0.630391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2531.23 | 0.0971288 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30350.0 | 1.16063 | 0.580316 | − | 0.814391i | \(-0.302929\pi\) | ||||
0.580316 | + | 0.814391i | \(0.302929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1140.39 | + | 1140.39i | 0.0434624 | + | 0.0434624i | 0.728504 | − | 0.685042i | \(-0.240216\pi\) |
−0.685042 | + | 0.728504i | \(0.740216\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25960.0 | − | 25960.0i | 0.986029 | − | 0.986029i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 43603.3i | − | 1.65057i | −0.564716 | − | 0.825285i | \(-0.691014\pi\) | ||
0.564716 | − | 0.825285i | \(-0.308986\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 56160.0i | − | 2.11872i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28518.8 | + | 28518.8i | −1.07230 | + | 1.07230i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6800.00 | − | 6800.00i | −0.254819 | − | 0.254819i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7182.25 | 0.268242 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23920.0 | −0.890374 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20267.7 | − | 20267.7i | −0.751909 | − | 0.751909i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31200.0 | − | 31200.0i | 1.15363 | − | 1.15363i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 61178.8i | 2.25460i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6578.00i | − | 0.241613i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11721.5 | + | 11721.5i | −0.429112 | + | 0.429112i | −0.888326 | − | 0.459214i | \(-0.848131\pi\) |
0.459214 | + | 0.888326i | \(0.348131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12337.0 | + | 12337.0i | 0.450157 | + | 0.450157i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41734.0 | 1.51779 | 0.758896 | − | 0.651212i | \(-0.225739\pi\) | ||||
0.758896 | + | 0.651212i | \(0.225739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32760.0 | −1.18751 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3837.09 | − | 3837.09i | −0.138634 | − | 0.138634i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18600.0 | − | 18600.0i | 0.669821 | − | 0.669821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14999.5i | − | 0.538400i | −0.963084 | − | 0.269200i | \(-0.913241\pi\) | ||
0.963084 | − | 0.269200i | \(-0.0867592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 760.000i | 0.0271909i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8434.45 | + | 8434.45i | −0.300784 | + | 0.300784i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8775.00 | + | 8775.00i | 0.311914 | + | 0.311914i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22673.7 | −0.803347 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11440.0 | 0.404020 | 0.202010 | − | 0.979383i | \(-0.435253\pi\) | ||||
0.202010 | + | 0.979383i | \(0.435253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28661.9 | + | 28661.9i | 1.00898 | + | 1.00898i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12280.0 | − | 12280.0i | 0.430899 | − | 0.430899i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 66116.1i | 2.31254i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9906.00i | − | 0.345373i | −0.984977 | − | 0.172687i | \(-0.944755\pi\) | ||
0.984977 | − | 0.172687i | \(-0.0552448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19713.2 | + | 19713.2i | −0.685107 | + | 0.685107i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1159.00 | + | 1159.00i | 0.0401512 | + | 0.0401512i | 0.726897 | − | 0.686746i | \(-0.240962\pi\) |
−0.686746 | + | 0.726897i | \(0.740962\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36278.0 | −1.25278 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36960.0 | −1.27228 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16077.3 | + | 16077.3i | 0.551682 | + | 0.551682i | 0.926926 | − | 0.375244i | \(-0.122441\pi\) |
−0.375244 | + | 0.926926i | \(0.622441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26174.0 | + | 26174.0i | −0.895305 | + | 0.895305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 5232.40i | − | 0.178414i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49512.0i | 1.68295i | 0.540296 | + | 0.841475i | \(0.318312\pi\) | ||||
−0.540296 | + | 0.841475i | \(0.681688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19087.1 | + | 19087.1i | −0.646747 | + | 0.646747i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28840.0 | − | 28840.0i | −0.974153 | − | 0.974153i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30696.7 | 1.03363 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8929.00 | 0.299721 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2267.37 | − | 2267.37i | −0.0758723 | − | 0.0758723i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20592.0 | − | 20592.0i | 0.686922 | − | 0.686922i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52225.6i | − | 1.73678i | −0.495886 | − | 0.868388i | \(-0.665156\pi\) | ||
0.495886 | − | 0.868388i | \(-0.334844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 65280.0i | − | 2.16419i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24538.6 | − | 24538.6i | 0.811000 | − | 0.811000i | −0.173783 | − | 0.984784i | \(-0.555599\pi\) |
0.984784 | + | 0.173783i | \(0.0555993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21720.0 | + | 21720.0i | 0.715633 | + | 0.715633i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24069.0 | −0.790591 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3584.00 | −0.117362 | −0.0586808 | − | 0.998277i | \(-0.518689\pi\) | ||||
−0.0586808 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44140.0 | − | 44140.0i | −1.44098 | − | 1.44098i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7579.00 | + | 7579.00i | −0.246665 | + | 0.246665i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 32584.0i | − | 1.05724i | −0.848858 | − | 0.528620i | \(-0.822710\pi\) | ||
0.848858 | − | 0.528620i | \(-0.177290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22638.0i | 0.732291i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10733.1 | − | 10733.1i | 0.346139 | − | 0.346139i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29640.0 | + | 29640.0i | 0.952980 | + | 0.952980i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19641.6 | −0.629603 | −0.314802 | − | 0.949158i | \(-0.601938\pi\) | ||||
−0.314802 | + | 0.949158i | \(0.601938\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 520.000 | 0.0166180 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50669.3 | − | 50669.3i | −1.61440 | − | 1.61440i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3301.00 | − | 3301.00i | 0.104858 | − | 0.104858i | −0.652731 | − | 0.757590i | \(-0.726377\pi\) |
0.757590 | + | 0.652731i | \(0.226377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9391.49i | 0.297431i |
(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 | 512.4.e.n.129.2 | yes | 4 | |
4.3 | odd | 2 | inner | 512.4.e.n.129.1 | yes | 4 | |
8.3 | odd | 2 | 512.4.e.k.129.2 | yes | 4 | ||
8.5 | even | 2 | 512.4.e.k.129.1 | ✓ | 4 | ||
16.3 | odd | 4 | 512.4.e.k.385.2 | yes | 4 | ||
16.5 | even | 4 | inner | 512.4.e.n.385.2 | yes | 4 | |
16.11 | odd | 4 | inner | 512.4.e.n.385.1 | yes | 4 | |
16.13 | even | 4 | 512.4.e.k.385.1 | yes | 4 | ||
32.3 | odd | 8 | 1024.4.b.f.513.2 | 4 | |||
32.5 | even | 8 | 1024.4.a.g.1.2 | 4 | |||
32.11 | odd | 8 | 1024.4.a.g.1.1 | 4 | |||
32.13 | even | 8 | 1024.4.b.f.513.1 | 4 | |||
32.19 | odd | 8 | 1024.4.b.f.513.3 | 4 | |||
32.21 | even | 8 | 1024.4.a.g.1.3 | 4 | |||
32.27 | odd | 8 | 1024.4.a.g.1.4 | 4 | |||
32.29 | even | 8 | 1024.4.b.f.513.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.4.e.k.129.1 | ✓ | 4 | 8.5 | even | 2 | ||
512.4.e.k.129.2 | yes | 4 | 8.3 | odd | 2 | ||
512.4.e.k.385.1 | yes | 4 | 16.13 | even | 4 | ||
512.4.e.k.385.2 | yes | 4 | 16.3 | odd | 4 | ||
512.4.e.n.129.1 | yes | 4 | 4.3 | odd | 2 | inner | |
512.4.e.n.129.2 | yes | 4 | 1.1 | even | 1 | trivial | |
512.4.e.n.385.1 | yes | 4 | 16.11 | odd | 4 | inner | |
512.4.e.n.385.2 | yes | 4 | 16.5 | even | 4 | inner | |
1024.4.a.g.1.1 | 4 | 32.11 | odd | 8 | |||
1024.4.a.g.1.2 | 4 | 32.5 | even | 8 | |||
1024.4.a.g.1.3 | 4 | 32.21 | even | 8 | |||
1024.4.a.g.1.4 | 4 | 32.27 | odd | 8 | |||
1024.4.b.f.513.1 | 4 | 32.13 | even | 8 | |||
1024.4.b.f.513.2 | 4 | 32.3 | odd | 8 | |||
1024.4.b.f.513.3 | 4 | 32.19 | odd | 8 | |||
1024.4.b.f.513.4 | 4 | 32.29 | even | 8 |