Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), 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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 386x^{10} + 54793x^{8} + 3447408x^{6} + 90154296x^{4} + 707138208x^{2} + 525876624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.9 | ||
Root | \(-11.2296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.e.673.4 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 6.85537i | − 0.613163i | −0.951844 | − | 0.306581i | \(-0.900815\pi\) | ||||
0.951844 | − | 0.306581i | \(-0.0991852\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 30.4375i | − 0.834295i | −0.908839 | − | 0.417147i | \(-0.863030\pi\) | ||||
0.908839 | − | 0.417147i | \(-0.136970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.1351i | 0.962941i | 0.876462 | + | 0.481470i | \(0.159897\pi\) | ||||
−0.876462 | + | 0.481470i | \(0.840103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.5661 | 0.354010 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −99.4408 | −1.41870 | −0.709351 | − | 0.704855i | \(-0.751012\pi\) | ||||
−0.709351 | + | 0.704855i | \(0.751012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33.9662i | 0.410125i | 0.978749 | + | 0.205063i | \(0.0657398\pi\) | ||||
−0.978749 | + | 0.205063i | \(0.934260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −108.378 | −0.982539 | −0.491270 | − | 0.871008i | \(-0.663467\pi\) | ||||
−0.491270 | + | 0.871008i | \(0.663467\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 78.0039 | 0.624031 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 187.588i | − 1.20118i | −0.799557 | − | 0.600590i | \(-0.794932\pi\) | ||||
0.799557 | − | 0.600590i | \(-0.205068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 174.390 | 1.01037 | 0.505183 | − | 0.863012i | \(-0.331425\pi\) | ||||
0.505183 | + | 0.863012i | \(0.331425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 91.3124 | 0.481680 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 47.9876i | 0.231754i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 241.634i | 1.07363i | 0.843699 | + | 0.536817i | \(0.180373\pi\) | ||||
−0.843699 | + | 0.536817i | \(0.819627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −135.405 | −0.555954 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 474.707 | 1.80821 | 0.904107 | − | 0.427307i | \(-0.140538\pi\) | ||||
0.904107 | + | 0.427307i | \(0.140538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 480.979i | 1.70578i | 0.522090 | + | 0.852890i | \(0.325153\pi\) | ||||
−0.522090 | + | 0.852890i | \(0.674847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 61.6983i | 0.204388i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −516.624 | −1.60335 | −0.801673 | − | 0.597762i | \(-0.796057\pi\) | ||||
−0.801673 | + | 0.597762i | \(0.796057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 298.322i | − 0.819088i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 179.948i | 0.466374i | 0.972432 | + | 0.233187i | \(0.0749154\pi\) | ||||
−0.972432 | + | 0.233187i | \(0.925085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −208.660 | −0.511558 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −101.899 | −0.236786 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 22.3098i | − 0.0492287i | −0.999697 | − | 0.0246143i | \(-0.992164\pi\) | ||||
0.999697 | − | 0.0246143i | \(-0.00783578\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 932.621i | − 1.95754i | −0.204963 | − | 0.978770i | \(-0.565708\pi\) | ||||
0.204963 | − | 0.978770i | \(-0.434292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 309.418 | 0.590439 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 665.460i | − 1.21342i | −0.794925 | − | 0.606708i | \(-0.792490\pi\) | ||||
0.794925 | − | 0.606708i | \(-0.207510\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 325.134i | − 0.567269i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 129.571 | 0.216581 | 0.108291 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108291 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1089.47 | 1.74675 | 0.873377 | − | 0.487044i | \(-0.161925\pi\) | ||||
0.873377 | + | 0.487044i | \(0.161925\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 234.012i | 0.360285i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 213.062i | 0.315334i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 739.469 | 1.05312 | 0.526562 | − | 0.850137i | \(-0.323481\pi\) | ||||
0.526562 | + | 0.850137i | \(0.323481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 81.6835i | − 0.108023i | −0.998540 | − | 0.0540116i | \(-0.982799\pi\) | ||||
0.998540 | − | 0.0540116i | \(-0.0172008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 681.703i | 0.869895i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 562.765 | 0.693502 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1010.60 | −1.20363 | −0.601817 | − | 0.798634i | \(-0.705556\pi\) | ||||
−0.601817 | + | 0.798634i | \(0.705556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 315.946i | − 0.363957i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 523.169i | 0.583335i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 232.851 | 0.251474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 610.737 | 0.639288 | 0.319644 | − | 0.947538i | \(-0.396437\pi\) | ||||
0.319644 | + | 0.947538i | \(0.396437\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 273.937i | 0.278098i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1306.93i | − 1.28757i | −0.765206 | − | 0.643786i | \(-0.777363\pi\) | ||||
0.765206 | − | 0.643786i | \(-0.222637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1547.43 | 1.48032 | 0.740159 | − | 0.672432i | \(-0.234750\pi\) | ||||
0.740159 | + | 0.672432i | \(0.234750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −143.963 | −0.133803 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1830.60i | 1.65393i | 0.562251 | + | 0.826967i | \(0.309935\pi\) | ||||
−0.562251 | + | 0.826967i | \(0.690065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 967.351i | − 0.850050i | −0.905182 | − | 0.425025i | \(-0.860265\pi\) | ||||
0.905182 | − | 0.425025i | \(-0.139735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −724.903 | −0.619863 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1885.99 | 1.57008 | 0.785039 | − | 0.619447i | \(-0.212643\pi\) | ||||
0.785039 | + | 0.619447i | \(0.212643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 742.972i | 0.602456i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 406.216i | − 0.320980i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 696.086 | 0.536219 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 404.560 | 0.303952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1424.12i | 1.04397i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1391.67i | − 0.995796i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −646.747 | −0.451886 | −0.225943 | − | 0.974141i | \(-0.572546\pi\) | ||||
−0.225943 | + | 0.974141i | \(0.572546\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1442.94 | −0.984833 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 256.204i | 0.170875i | 0.996344 | + | 0.0854375i | \(0.0272288\pi\) | ||||
−0.996344 | + | 0.0854375i | \(0.972771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 237.763i | − 0.155013i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −185.095 | −0.118003 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1886.18 | 1.17626 | 0.588130 | − | 0.808767i | \(-0.299864\pi\) | ||||
0.588130 | + | 0.808767i | \(0.299864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 611.918i | − 0.373397i | −0.982417 | − | 0.186699i | \(-0.940221\pi\) | ||||
0.982417 | − | 0.186699i | \(-0.0597788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1549.87i | − 0.925693i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1373.80 | 0.803377 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1285.99 | −0.736519 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1251.17i | 0.687916i | 0.938985 | + | 0.343958i | \(0.111768\pi\) | ||||
−0.938985 | + | 0.343958i | \(0.888232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 428.764 | 0.231075 | 0.115537 | − | 0.993303i | \(-0.463141\pi\) | ||||
0.115537 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 894.967 | 0.472901 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1195.51i | − 0.619519i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1699.44i | 0.863887i | 0.901901 | + | 0.431944i | \(0.142172\pi\) | ||||
−0.901901 | + | 0.431944i | \(0.857828\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −539.845 | −0.269261 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 758.647 | 0.371365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2865.29i | 1.37685i | 0.725308 | + | 0.688425i | \(0.241697\pi\) | ||||
−0.725308 | + | 0.688425i | \(0.758303\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 625.980i | − 0.295348i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.12650 | −0.000521985 0 | −0.000260992 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000260992 | 1.00000i | \(0.500083\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159.820 | 0.0727448 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 305.696i | − 0.136708i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 140.487i | − 0.0617401i | −0.999523 | − | 0.0308701i | \(-0.990172\pi\) | ||||
0.999523 | − | 0.0308701i | \(-0.00982781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −546.028 | −0.235862 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 66.9295 | 0.0284222 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 120.665i | 0.0503850i | 0.999683 | + | 0.0251925i | \(0.00801987\pi\) | ||||
−0.999683 | + | 0.0251925i | \(0.991980\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1440.25i | 0.591451i | 0.955273 | + | 0.295725i | \(0.0955613\pi\) | ||||
−0.955273 | + | 0.295725i | \(0.904439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2797.86 | 1.13019 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1656.49 | 0.658312 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3026.73i | 1.18362i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2921.14 | −1.10663 | −0.553316 | − | 0.832972i | \(-0.686638\pi\) | ||||
−0.553316 | + | 0.832972i | \(0.686638\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2889.35 | 1.07761 | 0.538807 | − | 0.842429i | \(-0.318875\pi\) | ||||
0.538807 | + | 0.842429i | \(0.318875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 928.254i | 0.340890i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1935.70i | − 0.700067i | −0.936737 | − | 0.350033i | \(-0.886170\pi\) | ||||
0.936737 | − | 0.350033i | \(-0.113830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1431.80 | 0.510040 | 0.255020 | − | 0.966936i | \(-0.417918\pi\) | ||||
0.255020 | + | 0.966936i | \(0.417918\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1996.38 | 0.700566 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1313.12i | 0.454004i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3254.29i | − 1.10873i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 975.403 | 0.327513 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1033.85 | 0.342165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2117.07i | 0.690735i | 0.938468 | + | 0.345367i | \(0.112246\pi\) | ||||
−0.938468 | + | 0.345367i | \(0.887754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 388.713i | 0.125043i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3297.29 | 1.04592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1220.73 | −0.381882 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3268.42i | 1.00849i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4488.27i | − 1.36613i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4992.28 | 1.49914 | 0.749570 | − | 0.661925i | \(-0.230260\pi\) | ||||
0.749570 | + | 0.661925i | \(0.230260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −702.035 | −0.208010 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3430.04i | 1.00291i | 0.865185 | + | 0.501453i | \(0.167201\pi\) | ||||
−0.865185 | + | 0.501453i | \(0.832799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2303.45i | − 0.664699i | −0.943156 | − | 0.332349i | \(-0.892159\pi\) | ||||
0.943156 | − | 0.332349i | \(-0.107841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −639.187 | −0.182058 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1087.30 | −0.305713 | −0.152857 | − | 0.988248i | \(-0.548847\pi\) | ||||
−0.152857 | + | 0.988248i | \(0.548847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3541.64i | 0.983112i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2218.41i | 0.608021i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2738.86 | 0.741263 | 0.370632 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2115.29 | −0.565386 | −0.282693 | − | 0.959210i | \(-0.591228\pi\) | ||||
−0.282693 | + | 0.959210i | \(0.591228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 335.913i | − 0.0875947i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1533.07 | −0.394926 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 245.051 | 0.0623673 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3874.74i | 0.974389i | 0.873294 | + | 0.487194i | \(0.161980\pi\) | ||||
−0.873294 | + | 0.487194i | \(0.838020\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3298.76i | 0.819727i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2045.11 | −0.502234 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7877.72 | 1.91206 | 0.956029 | − | 0.293272i | \(-0.0947441\pi\) | ||||
0.956029 | + | 0.293272i | \(0.0947441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1691.44i | − 0.405795i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1688.29i | 0.400394i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4426.08 | −1.03773 | −0.518867 | − | 0.854855i | \(-0.673646\pi\) | ||||
−0.518867 | + | 0.854855i | \(0.673646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1233.61 | 0.285963 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3031.80i | − 0.694918i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3411.18i | 0.773171i | 0.922254 | + | 0.386586i | \(0.126346\pi\) | ||||
−0.922254 | + | 0.386586i | \(0.873654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5417.43 | 1.21434 | 0.607169 | − | 0.794573i | \(-0.292305\pi\) | ||||
0.607169 | + | 0.794573i | \(0.292305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 947.838 | 0.210131 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2374.24i | − 0.520626i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5249.20i | 1.13860i | 0.822128 | + | 0.569302i | \(0.192787\pi\) | ||||
−0.822128 | + | 0.569302i | \(0.807213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1569.51 | −0.336789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4172.91 | 0.885889 | 0.442944 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442944 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7600.93i | 1.59657i | 0.602282 | + | 0.798284i | \(0.294258\pi\) | ||||
−0.602282 | + | 0.798284i | \(0.705742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 698.552i | 0.145188i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3322.95 | −0.683440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4975.47 | 1.01272 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1832.21i | 0.369093i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5751.98i | − 1.14687i | −0.819250 | − | 0.573437i | \(-0.805610\pi\) | ||||
0.819250 | − | 0.573437i | \(-0.194390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −152.942 | −0.0301852 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −821.812 | −0.160560 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4891.66i | − 0.946127i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3366.85i | − 0.644725i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3920.80 | 0.743380 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6393.46 | −1.20029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 948.107i | − 0.176258i | −0.996109 | − | 0.0881292i | \(-0.971911\pi\) | ||||
0.996109 | − | 0.0881292i | \(-0.0280888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4642.29i | 0.854662i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4726.33 | 0.861754 | 0.430877 | − | 0.902411i | \(-0.358204\pi\) | ||||
0.430877 | + | 0.902411i | \(0.358204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5594.30 | −1.01025 | −0.505126 | − | 0.863046i | \(-0.668554\pi\) | ||||
−0.505126 | + | 0.863046i | \(0.668554\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 431.888i | − 0.0772512i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 726.746i | − 0.128764i | −0.997925 | − | 0.0643819i | \(-0.979492\pi\) | ||||
0.997925 | − | 0.0643819i | \(-0.0205076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5709.71 | −1.00214 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5491.80 | −0.954899 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3377.63i | − 0.581846i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3520.72i | 0.600905i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2902.05 | 0.490776 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3616.37 | 0.606008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1398.69i | 0.232263i | 0.993234 | + | 0.116132i | \(0.0370495\pi\) | ||||
−0.993234 | + | 0.116132i | \(0.962951\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2174.71i | − 0.357878i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4561.97 | −0.744021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6562.34 | 1.06075 | 0.530376 | − | 0.847763i | \(-0.322051\pi\) | ||||
0.530376 | + | 0.847763i | \(0.322051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5657.96i | 0.906484i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5307.98i | − 0.842943i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2228.92 | −0.347828 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9993.55i | − 1.54606i | −0.634371 | − | 0.773029i | \(-0.718741\pi\) | ||||
0.634371 | − | 0.773029i | \(-0.281259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8816.69i | − 1.35228i | −0.736772 | − | 0.676141i | \(-0.763651\pi\) | ||||
0.736772 | − | 0.676141i | \(-0.236349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1218.65 | 0.185318 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3670.85 | 0.553483 | 0.276742 | − | 0.960944i | \(-0.410745\pi\) | ||||
0.276742 | + | 0.960944i | \(0.410745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 888.258i | − 0.132800i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2088.26i | 0.309586i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3848.87 | 0.565837 | 0.282919 | − | 0.959144i | \(-0.408697\pi\) | ||||
0.282919 | + | 0.959144i | \(0.408697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5705.30 | 0.831797 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1213.68i | 0.175487i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 7468.73i | − 1.07104i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8050.78 | −1.14509 | −0.572544 | − | 0.819874i | \(-0.694043\pi\) | ||||
−0.572544 | + | 0.819874i | \(0.694043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4272.36 | −0.602738 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1259.64i | − 0.176273i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6135.41i | − 0.851687i | −0.904797 | − | 0.425844i | \(-0.859977\pi\) | ||||
0.904797 | − | 0.425844i | \(-0.140023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4175.00 | 0.574923 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8466.82 | 1.15667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6362.25i | − 0.862287i | −0.902283 | − | 0.431143i | \(-0.858110\pi\) | ||||
0.902283 | − | 0.431143i | \(-0.141890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1940.24i | − 0.260897i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7858.77 | −1.04847 | −0.524235 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524235 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1460.62 | 0.193351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4328.81i | − 0.568594i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12766.7i | 1.66400i | 0.554775 | + | 0.832000i | \(0.312804\pi\) | ||||
−0.554775 | + | 0.832000i | \(0.687196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10777.2 | 1.39393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −768.611 | −0.0986547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 5069.33i | − 0.645736i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5851.29i | − 0.739718i | −0.929088 | − | 0.369859i | \(-0.879406\pi\) | ||||
0.929088 | − | 0.369859i | \(-0.120594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 713.290 | 0.0894967 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6575.76 | 0.818897 | 0.409449 | − | 0.912333i | \(-0.365721\pi\) | ||||
0.409449 | + | 0.912333i | \(0.365721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7871.11i | 0.972922i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 555.285i | − 0.0681292i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7354.74 | 0.895727 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6998.06 | −0.846043 | −0.423022 | − | 0.906120i | \(-0.639031\pi\) | ||||
−0.423022 | + | 0.906120i | \(0.639031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5658.55i | 0.679114i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 156.169i | 0.0186067i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −559.970 | −0.0662358 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1835.75 | 0.215581 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2137.83i | − 0.249260i | −0.992203 | − | 0.124630i | \(-0.960226\pi\) | ||||
0.992203 | − | 0.124630i | \(-0.0397744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 8455.41i | − 0.978840i | −0.872048 | − | 0.489420i | \(-0.837208\pi\) | ||||
0.872048 | − | 0.489420i | \(-0.162792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4649.61 | 0.534449 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7756.77 | −0.885315 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6528.35i | 0.739880i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4121.40i | 0.463830i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5623.37 | −0.628464 | −0.314232 | − | 0.949346i | \(-0.601747\pi\) | ||||
−0.314232 | + | 0.949346i | \(0.601747\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11800.5 | −1.30969 | −0.654846 | − | 0.755763i | \(-0.727266\pi\) | ||||
−0.654846 | + | 0.755763i | \(0.727266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3857.96i | − 0.425230i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3681.19i | − 0.402964i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13405.3 | −1.45740 | −0.728702 | − | 0.684831i | \(-0.759876\pi\) | ||||
−0.728702 | + | 0.684831i | \(0.759876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9275.61i | − 0.994803i | −0.867520 | − | 0.497401i | \(-0.834288\pi\) | ||||
0.867520 | − | 0.497401i | \(-0.165712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6928.04i | 0.738024i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3753.50 | −0.397168 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3033.99 | 0.318893 | 0.159446 | − | 0.987207i | \(-0.449029\pi\) | ||||
0.159446 | + | 0.987207i | \(0.449029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 14448.9i | − 1.50858i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1286.29i | 0.133411i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2165.93 | −0.223165 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18937.3 | −1.93841 | −0.969203 | − | 0.246264i | \(-0.920797\pi\) | ||||
−0.969203 | + | 0.246264i | \(0.920797\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2684.90i | 0.273029i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1583.51i | − 0.159981i | −0.996796 | − | 0.0799906i | \(-0.974511\pi\) | ||||
0.996796 | − | 0.0799906i | \(-0.0254890\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1288.77 | −0.129361 | −0.0646807 | − | 0.997906i | \(-0.520603\pi\) | ||||
−0.0646807 | + | 0.997906i | \(0.520603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3586.52 | 0.357679 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 5756.85i | − 0.570439i | −0.958462 | − | 0.285220i | \(-0.907933\pi\) | ||||
0.958462 | − | 0.285220i | \(-0.0920666\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4658.22i | 0.458628i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5098.33 | −0.498766 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14639.8 | 1.42312 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2649.50i | 0.255931i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1619.53i | − 0.155458i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4549.67 | −0.433987 | −0.216993 | − | 0.976173i | \(-0.569625\pi\) | ||||
−0.216993 | + | 0.976173i | \(0.569625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10906.2 | −1.03385 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2275.94i | 0.214408i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4186.82i | − 0.391987i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17106.0 | 1.59168 | 0.795840 | − | 0.605507i | \(-0.207030\pi\) | ||||
0.795840 | + | 0.605507i | \(0.207030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8595.86 | −0.794925 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 13113.2i | − 1.20528i | −0.798013 | − | 0.602640i | \(-0.794116\pi\) | ||||
0.798013 | − | 0.602640i | \(-0.205884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18653.9i | 1.70412i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1877.94 | 0.170519 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −906.998 | −0.0818600 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16356.0i | 1.46733i | 0.679513 | + | 0.733663i | \(0.262191\pi\) | ||||
−0.679513 | + | 0.733663i | \(0.737809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.37951i | 0 0.000301368i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9257.49 | −0.820618 | −0.410309 | − | 0.911947i | \(-0.634579\pi\) | ||||
−0.410309 | + | 0.911947i | \(0.634579\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8959.50 | −0.789491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 479.461i | 0.0419992i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7477.03i | − 0.651107i | −0.945524 | − | 0.325554i | \(-0.894449\pi\) | ||||
0.945524 | − | 0.325554i | \(-0.105551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7626.31 | −0.660211 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 917.087 | 0.0789286 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 10608.2i | − 0.907676i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15724.7i | 1.33766i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 421.462 | 0.0356457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13165.9 | 1.10711 | 0.553557 | − | 0.832811i | \(-0.313270\pi\) | ||||
0.553557 | + | 0.832811i | \(0.313270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6182.33i | − 0.516892i | −0.966026 | − | 0.258446i | \(-0.916790\pi\) | ||||
0.966026 | − | 0.258446i | \(-0.0832103\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1638.08i | − 0.136175i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17341.5 | −1.43341 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −421.185 | −0.0346170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 200.788i | 0.0164096i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21426.0i | 1.74120i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12549.4 | 1.01413 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −361.994 | −0.0290898 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1491.44i | − 0.119185i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16381.3i | 1.30183i | 0.759152 | + | 0.650913i | \(0.225614\pi\) | ||||
−0.759152 | + | 0.650913i | \(0.774386\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4320.74 | −0.341474 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6631.55 | −0.521219 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7397.09i | 0.578203i | 0.957298 | + | 0.289101i | \(0.0933565\pi\) | ||||
−0.957298 | + | 0.289101i | \(0.906644\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8393.59i | 0.652513i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6371.66 | 0.492635 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5176.28 | −0.398043 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4969.48i | 0.380077i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7579.32i | 0.576564i | 0.957546 | + | 0.288282i | \(0.0930841\pi\) | ||||
−0.957546 | + | 0.288282i | \(0.906916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21709.0 | −1.64257 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9080.18 | −0.683361 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10639.0i | 0.796412i | 0.917296 | + | 0.398206i | \(0.130367\pi\) | ||||
−0.917296 | + | 0.398206i | \(0.869633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 12929.1i | − 0.962713i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 923.880 | 0.0680687 | 0.0340343 | − | 0.999421i | \(-0.489164\pi\) | ||||
0.0340343 | + | 0.999421i | \(0.489164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 25831.9i | − 1.89323i | −0.322370 | − | 0.946614i | \(-0.604480\pi\) | ||||
0.322370 | − | 0.946614i | \(-0.395520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8763.43i | − 0.638914i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8453.92 | −0.613135 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6598.83 | −0.476106 | −0.238053 | − | 0.971252i | \(-0.576509\pi\) | ||||
−0.238053 | + | 0.971252i | \(0.576509\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8668.04i | 0.622161i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 571.785i | 0.0408289i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5477.17 | 0.389093 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2784.76 | −0.196813 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21144.3i | − 1.48674i | −0.668879 | − | 0.743371i | \(-0.733226\pi\) | ||||
0.668879 | − | 0.743371i | \(-0.266774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5923.36i | 0.414376i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5807.11 | 0.404184 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12893.9 | −0.892896 | −0.446448 | − | 0.894810i | \(-0.647311\pi\) | ||||
−0.446448 | + | 0.894810i | \(0.647311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4771.92i | − 0.328790i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4295.41i | 0.294472i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12097.1 | −0.825165 | −0.412582 | − | 0.910920i | \(-0.635373\pi\) | ||||
−0.412582 | + | 0.910920i | \(0.635373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1802.44 | 0.122335 | 0.0611673 | − | 0.998128i | \(-0.480518\pi\) | ||||
0.0611673 | + | 0.998128i | \(0.480518\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5989.14i | 0.404472i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2773.41i | − 0.186372i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5092.87 | −0.340549 | −0.170275 | − | 0.985397i | \(-0.554465\pi\) | ||||
−0.170275 | + | 0.985397i | \(0.554465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3939.35 | −0.262119 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 23317.9i | − 1.54393i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4763.25i | 0.313843i | 0.987611 | + | 0.156922i | \(0.0501570\pi\) | ||||
−0.987611 | + | 0.156922i | \(0.949843\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9762.87 | 0.640125 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2643.13 | 0.172461 | 0.0862304 | − | 0.996275i | \(-0.472518\pi\) | ||||
0.0862304 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 13166.7i | − 0.854952i | −0.904027 | − | 0.427476i | \(-0.859403\pi\) | ||||
0.904027 | − | 0.427476i | \(-0.140597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2926.21i | 0.189090i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7074.20 | 0.454931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 210.106 | 0.0134468 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3101.54i | 0.197549i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 24028.3i | − 1.52317i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28012.9 | 1.76732 | 0.883659 | − | 0.468131i | \(-0.155072\pi\) | ||||
0.883659 | + | 0.468131i | \(0.155072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6351.21 | −0.398796 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4433.69i | 0.277080i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2211.62i | 0.137563i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1166.14 | −0.0721937 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16283.5 | 1.00337 | 0.501685 | − | 0.865050i | \(-0.332714\pi\) | ||||
0.501685 | + | 0.865050i | \(0.332714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1292.91i | 0.0792961i | 0.999214 | + | 0.0396481i | \(0.0126237\pi\) | ||||
−0.999214 | + | 0.0396481i | \(0.987376\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9891.86i | 0.603863i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18335.5 | −1.11413 | −0.557067 | − | 0.830468i | \(-0.688073\pi\) | ||||
−0.557067 | + | 0.830468i | \(0.688073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −679.055 | −0.0410712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3662.19i | − 0.220480i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2508.06i | 0.150303i | 0.997172 | + | 0.0751515i | \(0.0239440\pi\) | ||||
−0.997172 | + | 0.0751515i | \(0.976056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1756.37 | 0.104774 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9805.25 | −0.582252 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 10689.3i | − 0.631859i | −0.948783 | − | 0.315929i | \(-0.897684\pi\) | ||||
0.948783 | − | 0.315929i | \(-0.102316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18520.0i | 1.08978i | 0.838508 | + | 0.544889i | \(0.183428\pi\) | ||||
−0.838508 | + | 0.544889i | \(0.816572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13464.8 | 0.788733 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1629.96 | −0.0950481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20330.5i | 1.18021i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14976.9i | 0.865529i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28386.6 | −1.63316 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4841.15 | −0.277285 | −0.138642 | − | 0.990343i | \(-0.544274\pi\) | ||||
−0.138642 | + | 0.990343i | \(0.544274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2106.11i | − 0.120095i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 29003.8i | − 1.64654i | −0.567652 | − | 0.823269i | \(-0.692148\pi\) | ||||
0.567652 | − | 0.823269i | \(-0.307852\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4275.16 | −0.241628 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10290.1 | −0.579028 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23852.8i | 1.33631i | 0.744021 | + | 0.668156i | \(0.232916\pi\) | ||||
−0.744021 | + | 0.668156i | \(0.767084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12930.5i | − 0.721238i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6910.34 | 0.383764 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8121.99 | −0.449090 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 11568.5i | − 0.636883i | −0.947943 | − | 0.318441i | \(-0.896841\pi\) | ||||
0.947943 | − | 0.318441i | \(-0.103159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1917.56i | − 0.105111i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4194.92 | −0.228953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47205.2 | −2.56532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 3261.89i | − 0.176504i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30210.5i | 1.62773i | 0.581057 | + | 0.813863i | \(0.302639\pi\) | ||||
−0.581057 | + | 0.813863i | \(0.697361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8207.40 | −0.440324 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10624.9 | −0.567600 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9148.53i | 0.486656i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1281.57i | 0.0678850i | 0.999424 | + | 0.0339425i | \(0.0108063\pi\) | ||||
−0.999424 | + | 0.0339425i | \(0.989194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6655.22 | −0.351041 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18900.0 | −0.992724 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 9417.90i | − 0.492601i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8216.57i | 0.427969i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9878.96 | −0.512410 | −0.256205 | − | 0.966622i | \(-0.582472\pi\) | ||||
−0.256205 | + | 0.966622i | \(0.582472\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10832.0 | −0.559508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6345.88i | − 0.326426i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 14632.6i | − 0.749575i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1362.29 | −0.0694971 | −0.0347485 | − | 0.999396i | \(-0.511063\pi\) | ||||
−0.0347485 | + | 0.999396i | \(0.511063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 47828.9i | − 2.42000i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28003.3i | 1.41109i | 0.708667 | + | 0.705543i | \(0.249297\pi\) | ||||
−0.708667 | + | 0.705543i | \(0.750703\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1007.74 | 0.0505728 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20254.9 | −1.01235 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16192.5i | 0.806023i | 0.915195 | + | 0.403012i | \(0.132037\pi\) | ||||
−0.915195 | + | 0.403012i | \(0.867963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4599.21i | − 0.228011i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35041.7 | 1.73022 | 0.865111 | − | 0.501580i | \(-0.167248\pi\) | ||||
0.865111 | + | 0.501580i | \(0.167248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8577.20 | 0.421804 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 735.152i | 0.0360077i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 12814.2i | − 0.625128i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36577.3 | −1.77726 | −0.888631 | − | 0.458624i | \(-0.848343\pi\) | ||||
−0.888631 | + | 0.458624i | \(0.848343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11624.2 | −0.562564 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2939.33i | − 0.141687i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24770.0i | 1.18928i | 0.803994 | + | 0.594638i | \(0.202704\pi\) | ||||
−0.803994 | + | 0.594638i | \(0.797296\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9896.27 | −0.473270 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4300.59 | 0.204857 | 0.102429 | − | 0.994740i | \(-0.467339\pi\) | ||||
0.102429 | + | 0.994740i | \(0.467339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6771.46i | 0.321289i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6135.33i | − 0.289965i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1006.96 | 0.0474043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30850.0 | 1.44666 | 0.723328 | − | 0.690505i | \(-0.242612\pi\) | ||||
0.723328 | + | 0.690505i | \(0.242612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23633.2i | 1.10393i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 23898.4i | − 1.11199i | −0.831186 | − | 0.555994i | \(-0.812338\pi\) | ||||
0.831186 | − | 0.555994i | \(-0.187662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13603.1 | 0.630500 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5074.32 | 0.234286 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16124.0i | 0.741594i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3943.82i | − 0.180693i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5064.88 | −0.231167 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11650.3 | 0.529703 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2774.72i | 0.125678i | 0.998024 | + | 0.0628388i | \(0.0200154\pi\) | ||||
−0.998024 | + | 0.0628388i | \(0.979985\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 13278.2i | − 0.599135i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13201.9 | −0.593433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42094.0 | 1.88499 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3700.84i | 0.165101i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34888.8i | 1.55060i | 0.631596 | + | 0.775298i | \(0.282400\pi\) | ||||
−0.631596 | + | 0.775298i | \(0.717600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51373.5 | 2.27467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9095.40 | 0.401211 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 33160.8i | − 1.45731i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 5200.80i | − 0.227707i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10233.5 | −0.446391 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 647.431 | 0.0281366 | 0.0140683 | − | 0.999901i | \(-0.495522\pi\) | ||||
0.0140683 | + | 0.999901i | \(0.495522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24867.7i | 1.07672i | 0.842714 | + | 0.538362i | \(0.180956\pi\) | ||||
−0.842714 | + | 0.538362i | \(0.819044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16252.3i | 0.701098i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19642.6 | 0.844233 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16337.0 | −0.699584 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2843.51i | 0.121319i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5572.42i | 0.236881i | 0.992961 | + | 0.118440i | \(0.0377894\pi\) | ||||
−0.992961 | + | 0.118440i | \(0.962211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8210.96 | 0.347772 | 0.173886 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173886 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7122.73 | 0.300584 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 26176.4i | − 1.10065i | −0.834949 | − | 0.550327i | \(-0.814503\pi\) | ||||
0.834949 | − | 0.550327i | \(-0.185497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 31756.2i | − 1.33045i | −0.746645 | − | 0.665223i | \(-0.768337\pi\) | ||||
0.746645 | − | 0.665223i | \(-0.231663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15747.6 | −0.657374 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4872.60 | −0.202672 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.72260i | 0 0.000320062i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4708.52i | − 0.194445i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23226.2 | 0.955728 | 0.477864 | − | 0.878434i | \(-0.341411\pi\) | ||||
0.477864 | + | 0.878434i | \(0.341411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10800.3 | −0.442836 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12518.7i | 0.511468i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1095.63i | − 0.0446044i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2831.92 | −0.114883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22802.8 | −0.921779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 26187.9i | − 1.05489i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1169.93i | − 0.0469609i | −0.999724 | − | 0.0234804i | \(-0.992525\pi\) | ||||
0.999724 | − | 0.0234804i | \(-0.00747474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2095.66 | −0.0838245 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28011.2 | 1.11650 | 0.558252 | − | 0.829671i | \(-0.311472\pi\) | ||||
0.558252 | + | 0.829671i | \(0.311472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22305.6i | 0.885981i | 0.896526 | + | 0.442991i | \(0.146083\pi\) | ||||
−0.896526 | + | 0.442991i | \(0.853917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 9968.84i | − 0.394585i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32165.3 | −1.26874 | −0.634368 | − | 0.773031i | \(-0.718739\pi\) | ||||
−0.634368 | + | 0.773031i | \(0.718739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −963.091 | −0.0378567 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14926.4i | 0.584692i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 22507.6i | − 0.878615i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30035.6 | 1.16845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5496.63 | −0.213096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9741.67i | 0.376375i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35803.0i | − 1.37854i | −0.724503 | − | 0.689271i | \(-0.757931\pi\) | ||||
0.724503 | − | 0.689271i | \(-0.242069\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17255.9 | 0.662148 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14860.3 | 0.568282 | 0.284141 | − | 0.958782i | \(-0.408292\pi\) | ||||
0.284141 | + | 0.958782i | \(0.408292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52005.7i | − 1.98203i | −0.133761 | − | 0.991014i | \(-0.542706\pi\) | ||||
0.133761 | − | 0.991014i | \(-0.457294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 458.826i | − 0.0174274i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18483.4 | −0.699676 | −0.349838 | − | 0.936810i | \(-0.613763\pi\) | ||||
−0.349838 | + | 0.936810i | \(0.613763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4527.23 | 0.170797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2465.44i | − 0.0926994i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 17547.7i | − 0.657573i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 827.202 | 0.0308942 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14675.0 | 0.546247 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 32713.5i | − 1.21363i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 17894.2i | − 0.661645i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10100.6 | 0.372232 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9873.41 | 0.362656 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 26109.9i | − 0.955861i | −0.878398 | − | 0.477930i | \(-0.841387\pi\) | ||||
0.878398 | − | 0.477930i | \(-0.158613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11762.4i | 0.429190i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42877.1 | −1.55937 | −0.779683 | − | 0.626174i | \(-0.784620\pi\) | ||||
−0.779683 | + | 0.626174i | \(0.784620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2486.24 | −0.0901232 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 19180.4i | − 0.692988i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1793.43i | − 0.0645847i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3299.71 | 0.118441 | 0.0592205 | − | 0.998245i | \(-0.481138\pi\) | ||||
0.0592205 | + | 0.998245i | \(0.481138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2844.32 | 0.101763 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5848.21i | 0.208555i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18848.4i | 0.669981i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13926.9 | −0.493440 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8109.49 | 0.286398 | 0.143199 | − | 0.989694i | \(-0.454261\pi\) | ||||
0.143199 | + | 0.989694i | \(0.454261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1664.34i | 0.0585893i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14179.0i | 0.497534i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20749.3 | 0.725749 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50079.2 | −1.74601 | −0.873007 | − | 0.487708i | \(-0.837833\pi\) | ||||
−0.873007 | + | 0.487708i | \(0.837833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 16782.9i | − 0.583269i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34701.5i | 1.20216i | 0.799188 | + | 0.601082i | \(0.205263\pi\) | ||||
−0.799188 | + | 0.601082i | \(0.794737\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51447.8 | −1.77664 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1295.66 | 0.0446010 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5170.49i | 0.177422i | 0.996057 | + | 0.0887109i | \(0.0282747\pi\) | ||||
−0.996057 | + | 0.0887109i | \(0.971725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49173.5i | 1.68202i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2180.24 | 0.0743418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53973.9 | 1.83461 | 0.917306 | − | 0.398183i | \(-0.130359\pi\) | ||||
0.917306 | + | 0.398183i | \(0.130359\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20025.5i | 0.678545i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 17129.1i | − 0.578585i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13203.3 | −0.444584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 620.803 | 0.0208386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 16475.4i | − 0.551311i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 19807.5i | − 0.660753i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34514.5 | 1.14779 | 0.573894 | − | 0.818929i | \(-0.305432\pi\) | ||||
0.573894 | + | 0.818929i | \(0.305432\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10132.9 | 0.335929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38224.1i | 1.26331i | 0.775251 | + | 0.631653i | \(0.217623\pi\) | ||||
−0.775251 | + | 0.631653i | \(0.782377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4283.43i | 0.141131i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10562.2 | −0.346933 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27748.4 | 0.908648 | 0.454324 | − | 0.890837i | \(-0.349881\pi\) | ||||
0.454324 | + | 0.890837i | \(0.349881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30760.1i | 1.00419i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8706.16i | 0.283350i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37180.6 | 1.20639 | 0.603193 | − | 0.797595i | \(-0.293895\pi\) | ||||
0.603193 | + | 0.797595i | \(0.293895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13270.0 | −0.429255 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10849.1i | 0.349879i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 52127.6i | − 1.67600i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52211.9 | −1.67363 | −0.836814 | − | 0.547487i | \(-0.815585\pi\) | ||||
−0.836814 | + | 0.547487i | \(0.815585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4196.08 | −0.134097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 9815.55i | − 0.312737i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11220.8i | 0.356436i | 0.983991 | + | 0.178218i | \(0.0570332\pi\) | ||||
−0.983991 | + | 0.178218i | \(0.942967\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6524.13 | 0.206621 |
(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 | 1344.4.c.e.673.9 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.h.673.3 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.h.673.10 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.e.673.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.e.673.4 | ✓ | 12 | 8.5 | even | 2 | inner | |
1344.4.c.e.673.9 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.h.673.3 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.h.673.10 | yes | 12 | 8.3 | odd | 2 |