Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,5,Mod(17,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.9818314355\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 41.3 | ||
Character | \(\chi\) | \(=\) | 232.41 |
Dual form | 232.5.j.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/232\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(117\) | \(175\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.45823 | − | 9.45823i | −1.05091 | − | 1.05091i | −0.998632 | − | 0.0522823i | \(-0.983350\pi\) |
−0.0522823 | − | 0.998632i | \(-0.516650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 40.7263i | 1.62905i | 0.580127 | + | 0.814526i | \(0.303003\pi\) | ||||
−0.580127 | + | 0.814526i | \(0.696997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.09414 | −0.144778 | −0.0723892 | − | 0.997376i | \(-0.523062\pi\) | ||||
−0.0723892 | + | 0.997376i | \(0.523062\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 97.9163i | 1.20884i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 127.843 | + | 127.843i | 1.05655 | + | 1.05655i | 0.998302 | + | 0.0582509i | \(0.0185523\pi\) |
0.0582509 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 129.421i | − | 0.765803i | −0.923789 | − | 0.382902i | \(-0.874925\pi\) | ||
0.923789 | − | 0.382902i | \(-0.125075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 385.199 | − | 385.199i | 1.71200 | − | 1.71200i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −375.293 | − | 375.293i | −1.29859 | − | 1.29859i | −0.929323 | − | 0.369269i | \(-0.879608\pi\) |
−0.369269 | − | 0.929323i | \(-0.620392\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49.5930 | + | 49.5930i | 0.137377 | + | 0.137377i | 0.772451 | − | 0.635074i | \(-0.219031\pi\) |
−0.635074 | + | 0.772451i | \(0.719031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 67.0980 | + | 67.0980i | 0.152150 | + | 0.152150i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 490.923 | 0.928021 | 0.464010 | − | 0.885830i | \(-0.346410\pi\) | ||||
0.464010 | + | 0.885830i | \(0.346410\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1033.63 | −1.65381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 159.998 | − | 159.998i | 0.219476 | − | 0.219476i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −541.690 | + | 643.314i | −0.644102 | + | 0.764939i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 154.628 | + | 154.628i | 0.160904 | + | 0.160904i | 0.782967 | − | 0.622063i | \(-0.213705\pi\) |
−0.622063 | + | 0.782967i | \(0.713705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2418.34i | − | 2.22069i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 288.918i | − | 0.235852i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 409.322 | − | 409.322i | 0.298993 | − | 0.298993i | −0.541626 | − | 0.840619i | \(-0.682191\pi\) |
0.840619 | + | 0.541626i | \(0.182191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1224.09 | + | 1224.09i | −0.804794 | + | 0.804794i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1509.38 | + | 1509.38i | −0.897908 | + | 0.897908i | −0.995251 | − | 0.0973426i | \(-0.968966\pi\) |
0.0973426 | + | 0.995251i | \(0.468966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2266.20 | − | 2266.20i | −1.22564 | − | 1.22564i | −0.965598 | − | 0.260038i | \(-0.916265\pi\) |
−0.260038 | − | 0.965598i | \(-0.583735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3987.77 | −1.96927 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 120.559 | − | 120.559i | 0.0545761 | − | 0.0545761i | −0.679292 | − | 0.733868i | \(-0.737713\pi\) |
0.733868 | + | 0.679292i | \(0.237713\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2350.67 | −0.979039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7099.22i | 2.72942i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 871.941 | 0.310410 | 0.155205 | − | 0.987882i | \(-0.450396\pi\) | ||||
0.155205 | + | 0.987882i | \(0.450396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5206.57 | + | 5206.57i | −1.72118 | + | 1.72118i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 938.124i | − | 0.288742i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 43.7251 | 0.0125611 | 0.00628054 | − | 0.999980i | \(-0.498001\pi\) | ||||
0.00628054 | + | 0.999980i | \(0.498001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3300.32 | − | 3300.32i | −0.886945 | − | 0.886945i | 0.107283 | − | 0.994229i | \(-0.465785\pi\) |
−0.994229 | + | 0.107283i | \(0.965785\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 694.632i | − | 0.175014i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5270.83 | 1.24753 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7321.19i | − | 1.63092i | −0.578815 | − | 0.815459i | \(-0.696485\pi\) | ||
0.578815 | − | 0.815459i | \(-0.303515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4643.26 | − | 4643.26i | −0.975270 | − | 0.975270i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6686.16i | − | 1.32636i | −0.748462 | − | 0.663178i | \(-0.769207\pi\) | ||
0.748462 | − | 0.663178i | \(-0.230793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2411.68 | + | 2411.68i | −0.452557 | + | 0.452557i | −0.896202 | − | 0.443645i | \(-0.853685\pi\) |
0.443645 | + | 0.896202i | \(0.353685\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9776.34 | + | 9776.34i | 1.73802 | + | 1.73802i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −906.935 | − | 906.935i | −0.152966 | − | 0.152966i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7494.79 | − | 7494.79i | −1.20090 | − | 1.20090i | −0.973895 | − | 0.227001i | \(-0.927108\pi\) |
−0.227001 | − | 0.973895i | \(-0.572892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4904.62 | 0.747542 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −296.718 | −0.0430713 | −0.0215356 | − | 0.999768i | \(-0.506856\pi\) | ||||
−0.0215356 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15284.3 | − | 15284.3i | 2.11547 | − | 2.11547i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11208.0 | − | 961.185i | 1.48078 | − | 0.126990i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 412.162 | + | 412.162i | 0.0520341 | + | 0.0520341i | 0.732645 | − | 0.680611i | \(-0.238286\pi\) |
−0.680611 | + | 0.732645i | \(0.738286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 918.129i | 0.110872i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2925.02i | − | 0.338192i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2019.74 | + | 2019.74i | −0.223794 | + | 0.223794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4463.03 | + | 4463.03i | −0.474336 | + | 0.474336i | −0.903315 | − | 0.428978i | \(-0.858874\pi\) |
0.428978 | + | 0.903315i | \(0.358874\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12517.9 | + | 12517.9i | −1.27721 | + | 1.27721i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2165.71 | − | 2165.71i | −0.212304 | − | 0.212304i | 0.592942 | − | 0.805245i | \(-0.297966\pi\) |
−0.805245 | + | 0.592942i | \(0.797966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 102.720 | 0.00968230 | 0.00484115 | − | 0.999988i | \(-0.498459\pi\) | ||||
0.00484115 | + | 0.999988i | \(0.498459\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2732.66 | + | 2732.66i | −0.247860 | + | 0.247860i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17072.5 | 1.49117 | 0.745587 | − | 0.666408i | \(-0.232169\pi\) | ||||
0.745587 | + | 0.666408i | \(0.232169\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1220.10i | 0.102693i | 0.998681 | + | 0.0513466i | \(0.0163513\pi\) | ||||
−0.998681 | + | 0.0513466i | \(0.983649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7742.92 | −0.628433 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6473.89 | + | 6473.89i | −0.507000 | + | 0.507000i | −0.913604 | − | 0.406604i | \(-0.866713\pi\) |
0.406604 | + | 0.913604i | \(0.366713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19993.5i | 1.51179i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12672.4 | 0.925736 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2662.38 | + | 2662.38i | 0.188008 | + | 0.188008i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18046.6i | 1.23261i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28552.2 | 1.88725 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 16642.1i | − | 1.06510i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10713.8 | − | 10713.8i | −0.664254 | − | 0.664254i | 0.292126 | − | 0.956380i | \(-0.405638\pi\) |
−0.956380 | + | 0.292126i | \(0.905638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 42868.5i | 2.57608i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4061.23 | + | 4061.23i | −0.236655 | + | 0.236655i | −0.815463 | − | 0.578809i | \(-0.803518\pi\) |
0.578809 | + | 0.815463i | \(0.303518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −351.820 | − | 351.820i | −0.0198892 | − | 0.0198892i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6516.14 | + | 6516.14i | 0.357538 | + | 0.357538i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24908.6 | − | 24908.6i | −1.32711 | − | 1.32711i | −0.907877 | − | 0.419237i | \(-0.862298\pi\) |
−0.419237 | − | 0.907877i | \(-0.637702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 978.274 | 0.0506327 | 0.0253164 | − | 0.999679i | \(-0.491941\pi\) | ||||
0.0253164 | + | 0.999679i | \(0.491941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2280.54 | −0.114710 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16545.5 | − | 16545.5i | 0.809112 | − | 0.809112i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26199.8 | − | 22061.0i | −1.24613 | − | 1.04928i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22233.2 | + | 22233.2i | 1.02889 | + | 1.02889i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 35641.8i | − | 1.60542i | −0.596373 | − | 0.802708i | \(-0.703392\pi\) | ||
0.596373 | − | 0.802708i | \(-0.296608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 31500.6i | 1.38155i | 0.723072 | + | 0.690773i | \(0.242730\pi\) | ||||
−0.723072 | + | 0.690773i | \(0.757270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36747.3 | − | 36747.3i | 1.56979 | − | 1.56979i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6297.45 | + | 6297.45i | −0.262121 | + | 0.262121i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −32944.9 | + | 32944.9i | −1.33656 | + | 1.33656i | −0.437191 | + | 0.899369i | \(0.644026\pi\) |
−0.899369 | + | 0.437191i | \(0.855974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8247.02 | − | 8247.02i | −0.326214 | − | 0.326214i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3482.68 | −0.134357 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23341.5 | − | 23341.5i | 0.878525 | − | 0.878525i | −0.114857 | − | 0.993382i | \(-0.536641\pi\) |
0.993382 | + | 0.114857i | \(0.0366410\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 98489.9 | 3.61763 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 35118.9i | 1.25924i | 0.776904 | + | 0.629619i | \(0.216789\pi\) | ||||
−0.776904 | + | 0.629619i | \(0.783211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11811.3 | 0.413545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4855.96 | + | 4855.96i | −0.166067 | + | 0.166067i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 44917.1i | − | 1.50079i | −0.660991 | − | 0.750394i | \(-0.729864\pi\) | ||
0.660991 | − | 0.750394i | \(-0.270136\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7332.74 | 0.239436 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −413.563 | − | 413.563i | −0.0132006 | − | 0.0132006i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 81.2940i | − | 0.00253719i | −0.999999 | − | 0.00126859i | \(-0.999596\pi\) | ||
0.999999 | − | 0.00126859i | \(-0.000403806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1340.50 | −0.0409177 | −0.0204588 | − | 0.999791i | \(-0.506513\pi\) | ||||
−0.0204588 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 62430.4i | 1.86421i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16670.2 | + | 16670.2i | 0.487076 | + | 0.487076i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 95957.1i | − | 2.74406i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1135.05 | + | 1135.05i | −0.0317754 | + | 0.0317754i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 31040.6 | + | 31040.6i | 0.850870 | + | 0.850870i | 0.990240 | − | 0.139370i | \(-0.0445078\pi\) |
−0.139370 | + | 0.990240i | \(0.544508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 44020.7 | + | 44020.7i | 1.18180 | + | 1.18180i | 0.979279 | + | 0.202517i | \(0.0649121\pi\) |
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −49852.7 | − | 49852.7i | −1.31105 | − | 1.31105i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20207.4 | −0.520688 | −0.260344 | − | 0.965516i | \(-0.583836\pi\) | ||||
−0.260344 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18474.7 | −0.466520 | −0.233260 | − | 0.972414i | \(-0.574939\pi\) | ||||
−0.233260 | + | 0.972414i | \(0.574939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −69245.5 | + | 69245.5i | −1.71396 | + | 1.71396i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3842.82 | − | 4563.76i | 0.0932521 | − | 0.110747i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −61471.7 | − | 61471.7i | −1.46274 | − | 1.46274i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 48069.3i | 1.12183i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12680.2i | 0.290292i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33395.8 | − | 33395.8i | 0.750113 | − | 0.750113i | −0.224387 | − | 0.974500i | \(-0.572038\pi\) |
0.974500 | + | 0.224387i | \(0.0720380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −63239.3 | + | 63239.3i | −1.39389 | + | 1.39389i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 92294.1 | − | 92294.1i | 1.99663 | − | 1.99663i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1096.96 | − | 1096.96i | −0.0232954 | − | 0.0232954i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45620.4 | 0.951198 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −48570.7 | + | 48570.7i | −0.994466 | + | 0.994466i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −37362.6 | −0.751324 | −0.375662 | − | 0.926757i | \(-0.622585\pi\) | ||||
−0.375662 | + | 0.926757i | \(0.622585\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 101210.i | − | 1.99920i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −50545.2 | −0.980908 | −0.490454 | − | 0.871467i | \(-0.663169\pi\) | ||||
−0.490454 | + | 0.871467i | \(0.663169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 40586.2 | − | 40586.2i | 0.773940 | − | 0.773940i | −0.204853 | − | 0.978793i | \(-0.565672\pi\) |
0.978793 | + | 0.204853i | \(0.0656717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17156.0i | 0.321508i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 60054.0 | 1.10619 | 0.553095 | − | 0.833118i | \(-0.313446\pi\) | ||||
0.553095 | + | 0.833118i | \(0.313446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4909.91 | + | 4909.91i | 0.0889074 | + | 0.0889074i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 141775.i | 2.52408i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −47752.4 | −0.835986 | −0.417993 | − | 0.908450i | \(-0.637266\pi\) | ||||
−0.417993 | + | 0.908450i | \(0.637266\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21146.1i | 0.364079i | 0.983291 | + | 0.182040i | \(0.0582699\pi\) | ||||
−0.983291 | + | 0.182040i | \(0.941730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59348.9 | − | 59348.9i | −1.00508 | − | 1.00508i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 95734.3i | − | 1.59491i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6418.36 | − | 6418.36i | 0.105204 | − | 0.105204i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2806.43 | + | 2806.43i | 0.0452642 | + | 0.0452642i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3327.03 | − | 3327.03i | −0.0528092 | − | 0.0528092i | 0.680209 | − | 0.733018i | \(-0.261889\pi\) |
−0.733018 | + | 0.680209i | \(0.761889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 62761.0 | + | 62761.0i | 0.980503 | + | 0.980503i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −289125. | −4.44637 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −120640. | −1.82652 | −0.913259 | − | 0.407379i | \(-0.866443\pi\) | ||||
−0.913259 | + | 0.407379i | \(0.866443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2903.78 | + | 2903.78i | −0.0432877 | + | 0.0432877i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −62990.9 | − | 53040.3i | −0.924692 | − | 0.778618i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −53908.3 | − | 53908.3i | −0.779371 | − | 0.779371i | 0.200353 | − | 0.979724i | \(-0.435791\pi\) |
−0.979724 | + | 0.200353i | \(0.935791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35510.9i | 0.505674i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7796.66i | − | 0.109367i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2654.79 | + | 2654.79i | −0.0366882 | + | 0.0366882i | −0.725213 | − | 0.688525i | \(-0.758259\pi\) |
0.688525 | + | 0.725213i | \(0.258259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20233.1 | + | 20233.1i | −0.275501 | + | 0.275501i | −0.831310 | − | 0.555809i | \(-0.812409\pi\) |
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8683.88 | − | 8683.88i | 0.116517 | − | 0.116517i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −132143. | − | 132143.i | −1.74734 | − | 1.74734i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 128929. | 1.68031 | 0.840157 | − | 0.542343i | \(-0.182463\pi\) | ||||
0.840157 | + | 0.542343i | \(0.182463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15140.6 | + | 15140.6i | −0.194507 | + | 0.194507i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10319.2 | 0.130687 | 0.0653436 | − | 0.997863i | \(-0.479186\pi\) | ||||
0.0653436 | + | 0.997863i | \(0.479186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 76103.8i | 0.950240i | 0.879921 | + | 0.475120i | \(0.157595\pi\) | ||||
−0.879921 | + | 0.475120i | \(0.842405\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38206.3 | 0.470377 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10707.8 | − | 10707.8i | 0.129998 | − | 0.129998i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 198169.i | 2.37268i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 84424.7 | 0.996974 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20822.9 | + | 20822.9i | 0.242553 | + | 0.242553i | 0.817905 | − | 0.575353i | \(-0.195135\pi\) |
−0.575353 | + | 0.817905i | \(0.695135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1780.76i | 0.0204627i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40909.3 | 0.463776 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 63535.6i | − | 0.710681i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16076.8 | + | 16076.8i | 0.177446 | + | 0.177446i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 40967.5i | 0.446226i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 134410. | − | 134410.i | 1.44488 | − | 1.44488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17004.9 | − | 17004.9i | −0.180426 | − | 0.180426i | 0.611116 | − | 0.791541i | \(-0.290721\pi\) |
−0.791541 | + | 0.611116i | \(0.790721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −971.545 | − | 971.545i | −0.0101753 | − | 0.0101753i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3650.36 | − | 3650.36i | −0.0377411 | − | 0.0377411i | 0.687984 | − | 0.725725i | \(-0.258496\pi\) |
−0.725725 | + | 0.687984i | \(0.758496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75535.1 | 0.771010 | 0.385505 | − | 0.922706i | \(-0.374027\pi\) | ||||
0.385505 | + | 0.922706i | \(0.374027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 28289.8 | 0.285108 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −49235.3 | + | 49235.3i | −0.489957 | + | 0.489957i | −0.908292 | − | 0.418336i | \(-0.862614\pi\) |
0.418336 | + | 0.908292i | \(0.362614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −151494. | + | 12991.9i | −1.48873 | + | 0.127671i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −161475. | − | 161475.i | −1.56710 | − | 1.56710i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 37223.8i | − | 0.356793i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 133774.i | 1.26650i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11540.0 | − | 11540.0i | 0.107922 | − | 0.107922i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −855.260 | + | 855.260i | −0.00790144 | + | 0.00790144i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −72078.4 | + | 72078.4i | −0.657884 | + | 0.657884i | −0.954879 | − | 0.296995i | \(-0.904015\pi\) |
0.296995 | + | 0.954879i | \(0.404015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 40079.3 | + | 40079.3i | 0.361436 | + | 0.361436i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 298165. | 2.65685 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −100550. | + | 100550.i | −0.885369 | + | 0.885369i | −0.994074 | − | 0.108705i | \(-0.965330\pi\) |
0.108705 | + | 0.994074i | \(0.465330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 122463. | 1.06563 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39536.3i | 0.340007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 33709.0 | 0.286522 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 189103. | − | 189103.i | 1.58877 | − | 1.58877i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152683.i | 1.26803i | 0.773319 | + | 0.634017i | \(0.218595\pi\) | ||||
−0.773319 | + | 0.634017i | \(0.781405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 169599. | 1.39242 | 0.696212 | − | 0.717836i | \(-0.254867\pi\) | ||||
0.696212 | + | 0.717836i | \(0.254867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20707.1 | − | 20707.1i | −0.168076 | − | 0.168076i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 97996.9i | 0.786435i | 0.919445 | + | 0.393218i | \(0.128638\pi\) | ||||
−0.919445 | + | 0.393218i | \(0.871362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 272303. | 2.16070 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 50362.8i | − | 0.395161i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −96368.6 | − | 96368.6i | −0.747733 | − | 0.747733i | 0.226320 | − | 0.974053i | \(-0.427330\pi\) |
−0.974053 | + | 0.226320i | \(0.927330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 125402.i | − | 0.962255i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 170689. | − | 170689.i | 1.29537 | − | 1.29537i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −98218.7 | − | 98218.7i | −0.737239 | − | 0.737239i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29088.3 | − | 29088.3i | −0.215966 | − | 0.215966i | 0.590830 | − | 0.806796i | \(-0.298800\pi\) |
−0.806796 | + | 0.590830i | \(0.798800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −147793. | − | 147793.i | −1.08543 | − | 1.08543i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6185.67 | −0.0449406 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −69556.5 | −0.499942 | −0.249971 | − | 0.968253i | \(-0.580421\pi\) | ||||
−0.249971 | + | 0.968253i | \(0.580421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −157405. | + | 157405.i | −1.11932 | + | 1.11932i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 83258.2 | + | 70105.9i | 0.585793 | + | 0.493256i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 189492. | + | 189492.i | 1.31920 | + | 1.31920i | 0.914405 | + | 0.404800i | \(0.132659\pi\) |
0.404800 | + | 0.914405i | \(0.367341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 202666.i | 1.39615i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17421.9i | 0.118768i | 0.998235 | + | 0.0593839i | \(0.0189136\pi\) | ||||
−0.998235 | + | 0.0593839i | \(0.981086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36936.1 | − | 36936.1i | 0.249190 | − | 0.249190i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 221898. | − | 221898.i | 1.48160 | − | 1.48160i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13862.8 | + | 13862.8i | −0.0916116 | + | 0.0916116i | −0.751427 | − | 0.659816i | \(-0.770634\pi\) |
0.659816 | + | 0.751427i | \(0.270634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −184240. | − | 184240.i | −1.20512 | − | 1.20512i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 76824.1 | 0.497408 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 305235. | − | 305235.i | 1.95632 | − | 1.95632i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −232731. | −1.47664 | −0.738318 | − | 0.674453i | \(-0.764380\pi\) | ||||
−0.738318 | + | 0.674453i | \(0.764380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6655.18i | 0.0418037i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33759.5 | 0.209946 | 0.104973 | − | 0.994475i | \(-0.466524\pi\) | ||||
0.104973 | + | 0.994475i | \(0.466524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20012.1 | − | 20012.1i | 0.123221 | − | 0.123221i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 199747.i | 1.21778i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 104658. | 0.631804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −191407. | − | 191407.i | −1.14422 | − | 1.14422i | −0.987669 | − | 0.156554i | \(-0.949962\pi\) |
−0.156554 | − | 0.987669i | \(-0.550038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 471183.i | 2.78937i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −310.192 | −0.00181857 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12084.2i | − | 0.0701654i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9252.75 | − | 9252.75i | −0.0532106 | − | 0.0532106i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 86465.1i | 0.492507i | 0.969205 | + | 0.246254i | \(0.0791996\pi\) | ||||
−0.969205 | + | 0.246254i | \(0.920800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −198891. | + | 198891.i | −1.12215 | + | 1.12215i | −0.130734 | + | 0.991417i | \(0.541733\pi\) |
−0.991417 | + | 0.130734i | \(0.958267\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11804.7 | + | 11804.7i | 0.0659740 | + | 0.0659740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 387915. | + | 387915.i | 2.14763 | + | 2.14763i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23413.0 | + | 23413.0i | 0.128410 | + | 0.128410i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −312983. | −1.70061 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −153604. | −0.826892 | −0.413446 | − | 0.910529i | \(-0.635675\pi\) | ||||
−0.413446 | + | 0.910529i | \(0.635675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38181.3 | − | 38181.3i | 0.203646 | − | 0.203646i | −0.597914 | − | 0.801560i | \(-0.704004\pi\) |
0.801560 | + | 0.597914i | \(0.204004\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39145.5 | + | 456462.i | 0.206873 | + | 2.41227i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24346.3 | + | 24346.3i | 0.127488 | + | 0.127488i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 240456.i | 1.24769i | 0.781549 | + | 0.623844i | \(0.214430\pi\) | ||||
−0.781549 | + | 0.623844i | \(0.785570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 230169.i | − | 1.18350i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 106757. | − | 106757.i | 0.543986 | − | 0.543986i | −0.380709 | − | 0.924695i | \(-0.624320\pi\) |
0.924695 | + | 0.380709i | \(0.124320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16785.9 | + | 16785.9i | −0.0847664 | + | 0.0847664i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −337109. | + | 337109.i | −1.68715 | + | 1.68715i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38020.7 | + | 38020.7i | 0.188594 | + | 0.188594i | 0.795088 | − | 0.606494i | \(-0.207425\pi\) |
−0.606494 | + | 0.795088i | \(0.707425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −385928. | −1.89738 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 297940. | − | 297940.i | 1.45189 | − | 1.45189i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −37392.0 | −0.180616 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14157.9i | − | 0.0677899i | −0.999425 | − | 0.0338950i | \(-0.989209\pi\) | ||
0.999425 | − | 0.0338950i | \(-0.0107912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −120092. | −0.570020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −135949. | + | 135949.i | −0.639698 | + | 0.639698i | −0.950481 | − | 0.310783i | \(-0.899409\pi\) |
0.310783 | + | 0.950481i | \(0.399409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 169569.i | 0.791015i | 0.918463 | + | 0.395507i | \(0.129431\pi\) | ||||
−0.918463 | + | 0.395507i | \(0.870569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 119125. | 0.550933 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 60089.7 | + | 60089.7i | 0.275528 | + | 0.275528i | 0.831321 | − | 0.555793i | \(-0.187585\pi\) |
−0.555793 | + | 0.831321i | \(0.687585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51937.5i | 0.236122i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 623200. | 2.80922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 579436.i | − | 2.58990i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51261.0 | − | 51261.0i | −0.227195 | − | 0.227195i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 85377.2i | 0.375237i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 261533. | − | 261533.i | 1.13987 | − | 1.13987i | 0.151395 | − | 0.988473i | \(-0.451623\pi\) |
0.988473 | − | 0.151395i | \(-0.0483766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52974.7 | − | 52974.7i | −0.228970 | − | 0.228970i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 32940.0 | + | 32940.0i | 0.141198 | + | 0.141198i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −181763. | − | 181763.i | −0.772719 | − | 0.772719i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −238103. | −1.00394 | −0.501969 | − | 0.864886i | \(-0.667391\pi\) | ||||
−0.501969 | + | 0.864886i | \(0.667391\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −441539. | −1.84651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 264900. | − | 264900.i | 1.09880 | − | 1.09880i | 0.104248 | − | 0.994551i | \(-0.466756\pi\) |
0.994551 | − | 0.104248i | \(-0.0332435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 444724. | − | 38138.8i | 1.82977 | − | 0.156918i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −509808. | − | 509808.i | −2.08064 | − | 2.08064i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47432.6i | 0.192028i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11964.6i | 0.0480505i | 0.999711 | + | 0.0240252i | \(0.00764821\pi\) | ||||
−0.999711 | + | 0.0240252i | \(0.992352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 332163. | − | 332163.i | 1.32335 | − | 1.32335i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 242260. | − | 242260.i | 0.957514 | − | 0.957514i | −0.0416196 | − | 0.999134i | \(-0.513252\pi\) |
0.999134 | + | 0.0416196i | \(0.0132518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 88201.3 | − | 88201.3i | 0.345854 | − | 0.345854i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −111714. | − | 111714.i | −0.434601 | − | 0.434601i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 302988. | 1.16947 | 0.584736 | − | 0.811224i | \(-0.301198\pi\) | ||||
0.584736 | + | 0.811224i | \(0.301198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17108.8 | − | 17108.8i | 0.0655205 | − | 0.0655205i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15869.6 | 0.0603018 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4183.39i | 0.0157730i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30825.1 | 0.115325 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −424836. | + | 424836.i | −1.57720 | + | 1.57720i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 120775.i | 0.444939i | 0.974940 | + | 0.222469i | \(0.0714118\pi\) | ||||
−0.974940 | + | 0.222469i | \(0.928588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 540405. | 1.97568 | 0.987838 | − | 0.155485i | \(-0.0496940\pi\) | ||||
0.987838 | + | 0.155485i | \(0.0496940\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −69354.7 | − | 69354.7i | −0.251627 | − | 0.251627i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 116062.i | − | 0.417896i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −38835.7 | −0.138778 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4281.40i | 0.0151844i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 195346. | + | 195346.i | 0.687621 | + | 0.687621i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 695298.i | 2.42920i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −768.897 | + | 768.897i | −0.00266637 | + | 0.00266637i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −300517. | − | 300517.i | −1.03441 | − | 1.03441i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −200272. | − | 200272.i | −0.684268 | − | 0.684268i | 0.276691 | − | 0.960959i | \(-0.410762\pi\) |
−0.960959 | + | 0.276691i | \(0.910762\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12678.8 | + | 12678.8i | 0.0430010 | + | 0.0430010i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −49690.1 | −0.167293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −405571. | −1.35548 | −0.677738 | − | 0.735303i | \(-0.737040\pi\) | ||||
−0.677738 | + | 0.735303i | \(0.737040\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 323155. | − | 323155.i | 1.07218 | − | 1.07218i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58767.9 | + | 5039.85i | −0.193570 | + | 0.0166002i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 53169.1 | + | 53169.1i | 0.173864 | + | 0.173864i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 315341.i | − | 1.02375i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 214148.i | − | 0.690245i | −0.938558 | − | 0.345122i | \(-0.887837\pi\) | ||
0.938558 | − | 0.345122i | \(-0.112163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −293294. | + | 293294.i | −0.938597 | + | 0.938597i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −907584. | + | 907584.i | −2.88377 | + | 2.88377i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −431981. | + | 431981.i | −1.36285 | + | 1.36285i | −0.492583 | + | 0.870265i | \(0.663947\pi\) |
−0.870265 | + | 0.492583i | \(0.836053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −263658. | − | 263658.i | −0.825930 | − | 0.825930i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34794.1 | −0.108228 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25660.6 | + | 25660.6i | −0.0792579 | + | 0.0792579i | −0.745624 | − | 0.666366i | \(-0.767849\pi\) |
0.666366 | + | 0.745624i | \(0.267849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 293162. | 0.899156 | 0.449578 | − | 0.893241i | \(-0.351574\pi\) | ||||
0.449578 | + | 0.893241i | \(0.351574\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 587178.i | − | 1.78838i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −507434. | −1.53477 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 262662. | − | 262662.i | 0.788944 | − | 0.788944i | −0.192377 | − | 0.981321i | \(-0.561620\pi\) |
0.981321 | + | 0.192377i | \(0.0616196\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 832716.i | − | 2.48393i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2104.96 | 0.00623579 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 111471. | + | 111471.i | 0.327964 | + | 0.327964i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 516100.i | 1.50807i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −229034. | −0.664697 | −0.332349 | − | 0.943157i | \(-0.607841\pi\) | ||||
−0.332349 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15337.0i | 0.0442089i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 191126. | + | 191126.i | 0.547199 | + | 0.547199i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 530121.i | − | 1.50753i | −0.657145 | − | 0.753765i | \(-0.728236\pi\) | ||
0.657145 | − | 0.753765i | \(-0.271764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −108429. | + | 108429.i | −0.306275 | + | 0.306275i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 174738. | + | 174738.i | 0.490273 | + | 0.490273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 103657. | + | 103657.i | 0.288899 | + | 0.288899i | 0.836645 | − | 0.547746i | \(-0.184514\pi\) |
−0.547746 | + | 0.836645i | \(0.684514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −81135.9 | − | 81135.9i | −0.224628 | − | 0.224628i | 0.585816 | − | 0.810444i | \(-0.300774\pi\) |
−0.810444 | + | 0.585816i | \(0.800774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 716864. | 1.97152 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −734972. | −2.00798 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −127958. | + | 127958.i | −0.347289 | + | 0.347289i | −0.859099 | − | 0.511810i | \(-0.828975\pi\) |
0.511810 | + | 0.859099i | \(0.328975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −79511.4 | + | 6818.78i | −0.214385 | + | 0.0183854i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15602.8 | − | 15602.8i | −0.0417946 | − | 0.0417946i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 395876.i | 1.05351i | 0.850018 | + | 0.526754i | \(0.176591\pi\) | ||||
−0.850018 | + | 0.526754i | \(0.823409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.16283e6i | 3.07443i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −293540. | + | 293540.i | −0.771075 | + | 0.771075i | −0.978294 | − | 0.207219i | \(-0.933559\pi\) |
0.207219 | + | 0.978294i | \(0.433559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −344693. | + | 344693.i | −0.899604 | + | 0.899604i | −0.995401 | − | 0.0957965i | \(-0.969460\pi\) |
0.0957965 | + | 0.995401i | \(0.469460\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 78546.8 | − | 78546.8i | 0.203678 | − | 0.203678i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2923.94 | − | 2923.94i | −0.00753342 | − | 0.00753342i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31751.7 | 0.0812843 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 119933. | − | 119933.i | 0.305072 | − | 0.305072i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −307231. | −0.776540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4114.51i | 0.0103338i | 0.999987 | + | 0.00516690i | \(0.00164468\pi\) | ||||
−0.999987 | + | 0.00516690i | \(0.998355\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −631730. | −1.57661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 436332. | − | 436332.i | 1.08211 | − | 1.08211i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 304226.i | 0.749751i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 654684. | 1.60336 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 172115. | + | 172115.i | 0.418893 | + | 0.418893i | 0.884822 | − | 0.465929i | \(-0.154280\pi\) |
−0.465929 | + | 0.884822i | \(0.654280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 691844.i | − | 1.67335i | −0.547701 | − | 0.836674i | \(-0.684497\pi\) | ||
0.547701 | − | 0.836674i | \(-0.315503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.74588e6 | −4.19657 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 330415.i | − | 0.789317i | −0.918828 | − | 0.394658i | \(-0.870863\pi\) | ||
0.918828 | − | 0.394658i | \(-0.129137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5589.95 | + | 5589.95i | 0.0132715 | + | 0.0132715i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20750.5i | 0.0489629i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −262278. | + | 262278.i | −0.615086 | + | 0.615086i | −0.944267 | − | 0.329181i | \(-0.893228\pi\) |
0.329181 | + | 0.944267i | \(0.393228\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −165399. | − | 165399.i | −0.385523 | − | 0.385523i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −236142. | − | 236142.i | −0.547070 | − | 0.547070i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −76977.1 | − | 76977.1i | −0.177252 | − | 0.177252i | 0.612905 | − | 0.790157i | \(-0.290001\pi\) |
−0.790157 | + | 0.612905i | \(0.790001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −630040. | −1.44200 | −0.721000 | − | 0.692936i | \(-0.756317\pi\) | ||||
−0.721000 | + | 0.692936i | \(0.756317\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 918786. | 2.09020 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14328.3 | − | 14328.3i | 0.0324005 | − | 0.0324005i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −265928. | + | 315818.i | −0.597740 | + | 0.709880i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 353384. | + | 353384.i | 0.789577 | + | 0.789577i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 843846.i | − | 1.87421i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 651683.i | 1.43882i | 0.694586 | + | 0.719410i | \(0.255588\pi\) | ||||
−0.694586 | + | 0.719410i | \(0.744412\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −165379. | + | 165379.i | −0.362973 | + | 0.362973i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 628871. | − | 628871.i | 1.37210 | − | 1.37210i | 0.514764 | − | 0.857332i | \(-0.327880\pi\) |
0.857332 | − | 0.514764i | \(-0.172120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31661.4 | − | 31661.4i | 0.0686736 | − | 0.0686736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 478068. | + | 478068.i | 1.03085 | + | 1.03085i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 817192. | 1.75179 | 0.875897 | − | 0.482498i | \(-0.160271\pi\) | ||||
0.875897 | + | 0.482498i | \(0.160271\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.01444e6 | − | 1.01444e6i | 2.16194 | − | 2.16194i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −767747. | −1.62669 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 112847.i | − | 0.237713i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 85525.8 | 0.179119 | 0.0895594 | − | 0.995981i | \(-0.471454\pi\) | ||||
0.0895594 | + | 0.995981i | \(0.471454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 88803.7 | − | 88803.7i | 0.184912 | − | 0.184912i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39841.5i | 0.0824833i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.13292e6 | 2.33203 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −568005. | − | 568005.i | −1.16251 | − | 1.16251i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37523.5i | 0.0763602i | 0.999271 | + | 0.0381801i | \(0.0121561\pi\) | ||||
−0.999271 | + | 0.0381801i | \(0.987844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40599.0 | 0.0821494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 92878.1i | − | 0.186868i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15363.8 | + | 15363.8i | 0.0307370 | + | 0.0307370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 451762.i | − | 0.898705i | −0.893354 | − | 0.449353i | \(-0.851655\pi\) | ||
0.893354 | − | 0.449353i | \(-0.148345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 733862. | − | 733862.i | 1.45169 | − | 1.45169i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 75910.7 | + | 75910.7i | 0.149322 | + | 0.149322i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 673838. | + | 673838.i | 1.31809 | + | 1.31809i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 451653. | + | 451653.i | 0.878550 | + | 0.878550i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 57862.6 | 0.111928 | 0.0559642 | − | 0.998433i | \(-0.482177\pi\) | ||||
0.0559642 | + | 0.998433i | \(0.482177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −728.707 | −0.00140179 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 200005. | − | 200005.i | 0.382616 | − | 0.382616i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 559909. | − | 664951.i | 1.06522 | − | 1.26507i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39425.0 | − | 39425.0i | −0.0745938 | − | 0.0745938i | 0.668826 | − | 0.743419i | \(-0.266797\pi\) |
−0.743419 | + | 0.668826i | \(0.766797\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 725397.i | 1.36496i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.70098e6i | 3.18320i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −126137. | + | 126137.i | −0.234766 | + | 0.234766i | −0.814679 | − | 0.579912i | \(-0.803087\pi\) |
0.579912 | + | 0.814679i | \(0.303087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −905477. | + | 905477.i | −1.67611 | + | 1.67611i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 935962. | − | 935962.i | 1.72315 | − | 1.72315i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −580797. | − | 580797.i | −1.06350 | − | 1.06350i | −0.997843 | − | 0.0656532i | \(-0.979087\pi\) |
−0.0656532 | − | 0.997843i | \(-0.520913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −121413. | −0.221120 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 551049. | − | 551049.i | 0.998188 | − | 0.998188i | −0.00181018 | − | 0.999998i | \(-0.500576\pi\) |
0.999998 | + | 0.00181018i | \(0.000576200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.45156e6 | 2.61531 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 29053.5i | − | 0.0520664i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −121114. | −0.215890 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 82212.0 | − | 82212.0i | 0.145766 | − | 0.145766i | −0.630458 | − | 0.776223i | \(-0.717133\pi\) |
0.776223 | + | 0.630458i | \(0.217133\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62935.7i | 0.110996i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.28290e6 | −2.25061 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 334338. | + | 334338.i | 0.583438 | + | 0.583438i | 0.935846 | − | 0.352409i | \(-0.114637\pi\) |
−0.352409 | + | 0.935846i | \(0.614637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.18722e6i | − | 2.06085i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −341996. | −0.590543 | −0.295272 | − | 0.955413i | \(-0.595410\pi\) | ||||
−0.295272 | + | 0.955413i | \(0.595410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8655.55i | − | 0.0148678i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.49658e6 | + | 1.49658e6i | 2.55728 | + | 2.55728i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5658.94i | − | 0.00961932i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −535764. | + | 535764.i | −0.905984 | + | 0.905984i | −0.995945 | − | 0.0899608i | \(-0.971326\pi\) |
0.0899608 | + | 0.995945i | \(0.471326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.14104e6 | + | 1.14104e6i | 1.91951 | + | 1.91951i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −319054. | − | 319054.i | −0.533955 | − | 0.533955i | 0.387792 | − | 0.921747i | \(-0.373238\pi\) |
−0.921747 | + | 0.387792i | \(0.873238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −159829. | − | 159829.i | −0.266105 | − | 0.266105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54929.3 | 0.0909834 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −149710. | −0.246703 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 854778. | − | 854778.i | 1.40137 | − | 1.40137i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16259.7 | + | 189598.i | 0.0265209 | + | 0.309251i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.34172e6 | − | 1.34172e6i | −2.17733 | − | 2.17733i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 570876.i | − | 0.921706i | −0.887476 | − | 0.460853i | \(-0.847543\pi\) | ||
0.887476 | − | 0.460853i | \(-0.152457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.01976e6i | 1.63811i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45926.7 | − | 45926.7i | 0.0734027 | − | 0.0734027i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −427130. | + | 427130.i | −0.679226 | + | 0.679226i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 335871. | − | 335871.i | 0.531420 | − | 0.531420i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 473963. | + | 473963.i | 0.746152 | + | 0.746152i | 0.973754 | − | 0.227602i | \(-0.0730885\pi\) |
−0.227602 | + | 0.973754i | \(0.573088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −90489.6 | −0.141744 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40357.4 | + | 40357.4i | −0.0629011 | + | 0.0629011i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −616631. | −0.956301 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 141837.i | − | 0.218875i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50219.3 | 0.0771123 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −594352. | + | 594352.i | −0.908127 | + | 0.908127i | −0.996121 | − | 0.0879938i | \(-0.971954\pi\) |
0.0879938 | + | 0.996121i | \(0.471954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 213751.i | − | 0.324987i | −0.986710 | − | 0.162494i | \(-0.948046\pi\) | ||
0.986710 | − | 0.162494i | \(-0.0519537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 382738. | 0.579056 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 950615. | + | 950615.i | 1.43116 | + | 1.43116i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 224776.i | − | 0.336748i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −89899.8 | −0.134027 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00384e6i | 1.48929i | 0.667463 | + | 0.744643i | \(0.267380\pi\) | ||||
−0.667463 | + | 0.744643i | \(0.732620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 456517. | + | 456517.i | 0.673996 | + | 0.673996i | 0.958635 | − | 0.284639i | \(-0.0918738\pi\) |
−0.284639 | + | 0.958635i | \(0.591874\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.49967e6i | 3.67261i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31375.3 | − | 31375.3i | 0.0458751 | − | 0.0458751i | −0.683797 | − | 0.729672i | \(-0.739673\pi\) |
0.729672 | + | 0.683797i | \(0.239673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −172264. | − | 172264.i | −0.250660 | − | 0.250660i | 0.570581 | − | 0.821241i | \(-0.306718\pi\) |
−0.821241 | + | 0.570581i | \(0.806718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.21944e6 | − | 1.21944e6i | −1.76587 | − | 1.76587i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 882191. | + | 882191.i | 1.27137 | + | 1.27137i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.43026e6 | −2.05137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49480.5 | 0.0706291 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −362834. | + | 362834.i | −0.515447 | + | 0.515447i | −0.916190 | − | 0.400743i | \(-0.868752\pi\) |
0.400743 | + | 0.916190i | \(0.368752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −120425. | − | 696954.i | −0.170265 | − | 0.985398i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −97601.3 | − | 97601.3i | −0.137341 | − | 0.137341i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 481029.i | 0.673687i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 128025.i | − | 0.178455i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 719807. | − | 719807.i | 0.998621 | − | 0.998621i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 200945. | − | 200945.i | 0.277472 | − | 0.277472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −169818. | + | 169818.i | −0.233392 | + | 0.233392i | −0.814107 | − | 0.580715i | \(-0.802773\pi\) |
0.580715 | + | 0.814107i | \(0.302773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −197765. | − | 197765.i | −0.270532 | − | 0.270532i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −759638. | −1.03430 | −0.517148 | − | 0.855896i | \(-0.673006\pi\) | ||||
−0.517148 | + | 0.855896i | \(0.673006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 553536. | − | 553536.i | 0.750170 | − | 0.750170i | −0.224341 | − | 0.974511i | \(-0.572023\pi\) |
0.974511 | + | 0.224341i | \(0.0720228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −202553. | −0.273233 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 154706.i | 0.207723i | 0.994592 | + | 0.103862i | \(0.0331199\pi\) | ||||
−0.994592 | + | 0.103862i | \(0.966880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.82931e6 | 2.44486 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.87432e6 | − | 1.87432e6i | 2.49348 | − | 2.49348i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.91631e6i | − | 2.53762i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −947514. | −1.24896 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −437003. | − | 437003.i | −0.573398 | − | 0.573398i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 118062.i | 0.154203i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −922498. | −1.19941 | −0.599703 | − | 0.800222i | \(-0.704715\pi\) | ||||
−0.599703 | + | 0.800222i | \(0.704715\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 393896.i | − | 0.509804i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −326153. | − | 326153.i | −0.420213 | − | 0.420213i | 0.465064 | − | 0.885277i | \(-0.346031\pi\) |
−0.885277 | + | 0.465064i | \(0.846031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 598316.i | 0.767378i | 0.923462 | + | 0.383689i | \(0.125347\pi\) | ||||
−0.923462 | + | 0.383689i | \(0.874653\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16842.9 | − | 16842.9i | 0.0215045 | − | 0.0215045i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −813195. | − | 813195.i | −1.03359 | − | 1.03359i | −0.999416 | − | 0.0341727i | \(-0.989120\pi\) |
−0.0341727 | − | 0.999416i | \(-0.510880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 76004.9 | + | 76004.9i | 0.0961697 | + | 0.0961697i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 627021. | + | 627021.i | 0.789817 | + | 0.789817i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11957.7 | 0.0149950 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3310.80 | 0.00413321 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −600935. | + | 600935.i | −0.746865 | + | 0.746865i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −183235. | + | 15714.0i | −0.226720 | + | 0.0194432i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −327233. | − | 327233.i | −0.403095 | − | 0.403095i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 304115.i | − | 0.372960i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 54593.8i | − | 0.0666570i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −474402. | + | 474402.i | −0.576676 | + | 0.576676i | −0.933986 | − | 0.357310i | \(-0.883694\pi\) |
0.357310 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 212058. | − | 212058.i | 0.256642 | − | 0.256642i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 350774. | − | 350774.i | 0.422660 | − | 0.422660i | −0.463459 | − | 0.886119i | \(-0.653392\pi\) |
0.886119 | + | 0.463459i | \(0.153392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37933.3 | − | 37933.3i | −0.0455071 | − | 0.0455071i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.54256e6 | −3.03689 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28810.9 | − | 28810.9i | 0.0342625 | − | 0.0342625i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −972483. | −1.15147 | −0.575733 | − | 0.817638i | \(-0.695283\pi\) | ||||
−0.575733 | + | 0.817638i | \(0.695283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 321673.i | 0.379224i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −865328. | −1.01573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −423088. | + | 423088.i | −0.494479 | + | 0.494479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10057.9i | 0.0117044i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −359756. | −0.416847 | −0.208424 | − | 0.978039i | \(-0.566833\pi\) | ||||
−0.208424 | + | 0.978039i | \(0.566833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −116577. | − | 116577.i | −0.134497 | − | 0.134497i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 69051.9i | 0.0793254i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.90798e6 | 4.47022 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 729562.i | − | 0.830966i | −0.909601 | − | 0.415483i | \(-0.863613\pi\) | ||
0.909601 | − | 0.415483i | \(-0.136387\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −714428. | − | 714428.i | −0.810266 | − | 0.810266i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 644663.i | 0.728037i | 0.931392 | + | 0.364018i | \(0.118595\pi\) | ||||
−0.931392 | + | 0.364018i | \(0.881405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −740991. | + | 740991.i | −0.833277 | + | 0.833277i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46226.4 | − | 46226.4i | −0.0517638 | − | 0.0517638i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 316196. | + | 316196.i | 0.352579 | + | 0.352579i | 0.861068 | − | 0.508489i | \(-0.169796\pi\) |
−0.508489 | + | 0.861068i | \(0.669796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 312121. | + | 312121.i | 0.346570 | + | 0.346570i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 931357. | 1.02981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.75063e6 | −1.92757 | −0.963784 | − | 0.266685i | \(-0.914072\pi\) | ||||
−0.963784 | + | 0.266685i | \(0.914072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.26417e6 | + | 1.26417e6i | −1.38611 | + | 1.38611i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.55575e6 | + | 1.30999e6i | 1.69870 | + | 1.43035i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 176705. | + | 176705.i | 0.192137 | + | 0.192137i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 875701.i | − | 0.948220i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.67167e6i | 1.80260i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.79280e6 | + | 1.79280e6i | −1.92521 | + | 1.92521i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 614157. | − | 614157.i | 0.656790 | − | 0.656790i | −0.297829 | − | 0.954619i | \(-0.596263\pi\) |
0.954619 | + | 0.297829i | \(0.0962626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −352071. | + | 352071.i | −0.374959 | + | 0.374959i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 711809. | + | 711809.i | 0.754962 | + | 0.754962i | 0.975401 | − | 0.220439i | \(-0.0707489\pi\) |
−0.220439 | + | 0.975401i | \(0.570749\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6940.02 | −0.00733052 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.26526e6 | − | 1.26526e6i | 1.33098 | − | 1.33098i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 906813. | 0.950011 | 0.475005 | − | 0.879983i | \(-0.342446\pi\) | ||||
0.475005 | + | 0.879983i | \(0.342446\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 105384.i | 0.109954i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −119468. | −0.124140 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.31463e6 | + | 1.31463e6i | −1.36049 | + | 1.36049i | −0.487196 | + | 0.873293i | \(0.661980\pi\) |
−0.873293 | + | 0.487196i | \(0.838020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 822973.i | − | 0.848229i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16178.5 | 0.0166075 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.11253e6 | − | 1.11253e6i | −1.13742 | − | 1.13742i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.36793e6i | − | 1.39289i | −0.717610 | − | 0.696445i | \(-0.754764\pi\) | ||
0.717610 | − | 0.696445i | \(-0.245236\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.36347e6 | 1.38276 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 752406.i | − | 0.759986i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −361820. | − | 361820.i | −0.364000 | − | 0.364000i | 0.501283 | − | 0.865283i | \(-0.332862\pi\) |
−0.865283 | + | 0.501283i | \(0.832862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 130981.i | − | 0.131244i |
(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 | 232.5.j.a.41.3 | yes | 30 | |
29.17 | odd | 4 | inner | 232.5.j.a.17.3 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.5.j.a.17.3 | ✓ | 30 | 29.17 | odd | 4 | inner | |
232.5.j.a.41.3 | yes | 30 | 1.1 | even | 1 | trivial |