Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Character | \(\chi\) | \(=\) | 76.5 |
Dual form | 76.4.i.a.61.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.42726 | − | 8.09439i | 0.274676 | − | 1.55777i | −0.465312 | − | 0.885147i | \(-0.654058\pi\) |
0.739989 | − | 0.672619i | \(-0.234831\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.74894 | − | 5.66304i | −0.603644 | − | 0.506517i | 0.288971 | − | 0.957338i | \(-0.406687\pi\) |
−0.892615 | + | 0.450821i | \(0.851131\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.266189 | + | 0.461053i | 0.0143729 | + | 0.0248945i | 0.873122 | − | 0.487501i | \(-0.162091\pi\) |
−0.858750 | + | 0.512396i | \(0.828758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −38.1104 | − | 13.8710i | −1.41150 | − | 0.513742i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.3647 | + | 31.8086i | −0.503379 | + | 0.871879i | 0.496613 | + | 0.867972i | \(0.334577\pi\) |
−0.999992 | + | 0.00390668i | \(0.998756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.11500 | − | 46.0225i | −0.173131 | − | 0.981872i | −0.940280 | − | 0.340403i | \(-0.889436\pi\) |
0.767149 | − | 0.641469i | \(-0.221675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −55.4713 | + | 46.5460i | −0.954842 | + | 0.801208i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 92.4595 | − | 33.6525i | 1.31910 | − | 0.480114i | 0.415931 | − | 0.909396i | \(-0.363456\pi\) |
0.903170 | + | 0.429282i | \(0.141233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −51.1181 | − | 65.1609i | −0.617227 | − | 0.786786i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.11186 | − | 1.49660i | 0.0427277 | − | 0.0155516i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 81.4195 | − | 68.3191i | 0.738137 | − | 0.619370i | −0.194200 | − | 0.980962i | \(-0.562211\pi\) |
0.932337 | + | 0.361592i | \(0.117767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.22776 | − | 46.6620i | −0.0658221 | − | 0.373296i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −55.7110 | + | 96.4943i | −0.397096 | + | 0.687790i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 81.7536 | + | 29.7559i | 0.523492 | + | 0.190535i | 0.590230 | − | 0.807235i | \(-0.299037\pi\) |
−0.0667383 | + | 0.997771i | \(0.521259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 121.465 | + | 210.384i | 0.703736 | + | 1.21891i | 0.967146 | + | 0.254223i | \(0.0818196\pi\) |
−0.263410 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 231.260 | + | 194.050i | 1.21992 | + | 1.02363i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.814465 | − | 4.61906i | 0.00393342 | − | 0.0223075i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 120.346 | 0.534721 | 0.267361 | − | 0.963597i | \(-0.413849\pi\) | ||||
0.267361 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −384.106 | −1.57708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −56.4094 | + | 319.913i | −0.214870 | + | 1.21859i | 0.666263 | + | 0.745717i | \(0.267893\pi\) |
−0.881132 | + | 0.472870i | \(0.843218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −217.204 | − | 182.256i | −0.770310 | − | 0.646367i | 0.170478 | − | 0.985361i | \(-0.445469\pi\) |
−0.940788 | + | 0.338994i | \(0.889913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 178.653 | + | 309.435i | 0.591821 | + | 1.02506i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 231.156 | + | 84.1337i | 0.717394 | + | 0.261110i | 0.674819 | − | 0.737983i | \(-0.264222\pi\) |
0.0425747 | + | 0.999093i | \(0.486444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 171.358 | − | 296.801i | 0.499587 | − | 0.865310i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −140.433 | − | 796.434i | −0.385579 | − | 2.18673i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 363.284 | − | 304.832i | 0.941527 | − | 0.790035i | −0.0363232 | − | 0.999340i | \(-0.511565\pi\) |
0.977850 | + | 0.209305i | \(0.0671201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 304.076 | − | 110.675i | 0.745484 | − | 0.271334i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −600.396 | + | 320.769i | −1.39517 | + | 0.745383i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −500.026 | + | 181.995i | −1.10335 | + | 0.401588i | −0.828552 | − | 0.559913i | \(-0.810835\pi\) |
−0.274802 | + | 0.961501i | \(0.588612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 418.648 | − | 351.287i | 0.878727 | − | 0.737339i | −0.0871901 | − | 0.996192i | \(-0.527789\pi\) |
0.965917 | + | 0.258852i | \(0.0833443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.74928 | − | 21.2632i | −0.00749785 | − | 0.0425224i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −205.859 | + | 356.559i | −0.392826 | + | 0.680395i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −885.145 | − | 322.166i | −1.61399 | − | 0.587446i | −0.631770 | − | 0.775156i | \(-0.717671\pi\) |
−0.982225 | + | 0.187710i | \(0.939894\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −436.795 | − | 756.551i | −0.762085 | − | 1.31997i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 355.291 | + | 298.124i | 0.593876 | + | 0.498322i | 0.889471 | − | 0.456992i | \(-0.151073\pi\) |
−0.295594 | + | 0.955314i | \(0.595518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −81.3097 | + | 461.130i | −0.130364 | + | 0.739332i | 0.847612 | + | 0.530616i | \(0.178039\pi\) |
−0.977976 | + | 0.208716i | \(0.933072\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −389.443 | −0.599587 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.5540 | −0.0289400 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −139.607 | + | 791.751i | −0.198823 | + | 1.12758i | 0.708045 | + | 0.706167i | \(0.249577\pi\) |
−0.906868 | + | 0.421415i | \(0.861534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −137.284 | − | 115.195i | −0.188318 | − | 0.158018i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 466.579 | + | 808.139i | 0.617033 | + | 1.06873i | 0.990024 | + | 0.140897i | \(0.0449987\pi\) |
−0.372991 | + | 0.927835i | \(0.621668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −814.579 | − | 296.483i | −1.03945 | − | 0.378330i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 357.539 | − | 619.276i | 0.440600 | − | 0.763142i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −192.936 | − | 1094.19i | −0.229788 | − | 1.30319i | −0.853317 | − | 0.521393i | \(-0.825413\pi\) |
0.623529 | − | 0.781800i | \(-0.285698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.0587 | − | 15.9921i | 0.0219549 | − | 0.0184223i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1876.29 | − | 682.915i | 2.09207 | − | 0.761452i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.0149 | + | 729.251i | −0.0259355 | + | 0.787574i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 899.137 | − | 327.259i | 0.941170 | − | 0.342558i | 0.174542 | − | 0.984650i | \(-0.444155\pi\) |
0.766628 | + | 0.642092i | \(0.221933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1141.11 | − | 957.501i | 1.15844 | − | 0.972046i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 278.121 | + | 1577.30i | 0.274001 | + | 1.55393i | 0.742119 | + | 0.670269i | \(0.233821\pi\) |
−0.468118 | + | 0.883666i | \(0.655068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −419.331 | + | 726.302i | −0.401144 | + | 0.694802i | −0.993864 | − | 0.110606i | \(-0.964721\pi\) |
0.592720 | + | 0.805409i | \(0.298054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −36.2260 | − | 13.1852i | −0.0336695 | − | 0.0122547i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 935.751 | + | 1620.77i | 0.845444 | + | 1.46435i | 0.885235 | + | 0.465144i | \(0.153997\pi\) |
−0.0397911 | + | 0.999208i | \(0.512669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1006.92 | − | 844.904i | −0.884819 | − | 0.742451i | 0.0823454 | − | 0.996604i | \(-0.473759\pi\) |
−0.967164 | + | 0.254153i | \(0.918203\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 171.764 | − | 974.124i | 0.146875 | − | 0.832971i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −375.620 | −0.312702 | −0.156351 | − | 0.987702i | \(-0.549973\pi\) | ||||
−0.156351 | + | 0.987702i | \(0.549973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −936.389 | −0.759294 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −329.114 | + | 1866.50i | −0.260056 | + | 1.47485i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40.1273 | + | 33.6708i | 0.0309115 | + | 0.0259378i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.02654 | − | 15.6344i | −0.00678177 | − | 0.0117464i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2508.99 | + | 913.199i | 1.83925 | + | 0.669434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −759.352 | + | 1315.24i | −0.543348 | + | 0.941107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −156.370 | − | 886.816i | −0.109256 | − | 0.619624i | −0.989435 | − | 0.144980i | \(-0.953688\pi\) |
0.880178 | − | 0.474643i | \(-0.157423\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1785.26 | + | 1498.01i | −1.21847 | + | 1.02242i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 850.037 | − | 309.388i | 0.566932 | − | 0.206346i | −0.0426216 | − | 0.999091i | \(-0.513571\pi\) |
0.609553 | + | 0.792745i | \(0.291349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.4355 | − | 40.9133i | 0.0107153 | − | 0.0266739i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 922.441 | − | 335.741i | 0.588082 | − | 0.214044i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −939.827 | + | 788.609i | −0.586094 | + | 0.491791i | −0.886942 | − | 0.461881i | \(-0.847175\pi\) |
0.300848 | + | 0.953672i | \(0.402730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −231.255 | − | 1311.51i | −0.141114 | − | 0.800296i | −0.970406 | − | 0.241480i | \(-0.922367\pi\) |
0.829292 | − | 0.558816i | \(-0.188744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1010.93 | − | 1750.98i | 0.603799 | − | 1.04581i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1612.94 | + | 587.063i | 0.943224 | + | 0.343305i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −383.242 | − | 663.794i | −0.219493 | − | 0.380173i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2157.85 | − | 1810.65i | −1.21073 | − | 1.01592i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 211.662 | − | 1200.40i | 0.116376 | − | 0.660002i | −0.869684 | − | 0.493610i | \(-0.835677\pi\) |
0.986060 | − | 0.166392i | \(-0.0532117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −26.0819 | −0.0140564 | −0.00702820 | − | 0.999975i | \(-0.502237\pi\) | ||||
−0.00702820 | + | 0.999975i | \(0.502237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3990.46 | −2.10856 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 371.650 | − | 2107.73i | 0.192591 | − | 1.09224i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1689.12 | + | 1417.34i | 0.858637 | + | 0.720482i | 0.961674 | − | 0.274195i | \(-0.0884114\pi\) |
−0.103037 | + | 0.994678i | \(0.532856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1948.93 | − | 3375.64i | −0.972075 | − | 1.68368i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 53.1717 | + | 19.3529i | 0.0260281 | + | 0.00947344i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 81.7353 | − | 141.570i | 0.0392761 | − | 0.0680282i | −0.845719 | − | 0.533628i | \(-0.820828\pi\) |
0.884995 | + | 0.465600i | \(0.154161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −461.848 | − | 2619.27i | −0.217908 | − | 1.23582i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1398.72 | + | 1173.66i | −0.648119 | + | 0.543837i | −0.906500 | − | 0.422207i | \(-0.861256\pi\) |
0.258380 | + | 0.966043i | \(0.416811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2899 | − | 4.47317i | 0.00559396 | − | 0.00203604i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1044.28 | + | 3192.37i | 0.467007 | + | 1.42764i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3417.90 | − | 1244.01i | 1.50207 | − | 0.546708i | 0.545473 | − | 0.838128i | \(-0.316350\pi\) |
0.956595 | + | 0.291420i | \(0.0941277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.3235 | − | 16.2143i | 0.00834696 | − | 0.00700393i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 759.469 | + | 4307.16i | 0.322515 | + | 1.82907i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1154.54 | + | 1999.73i | −0.482092 | + | 0.835009i | −0.999789 | − | 0.0205559i | \(-0.993456\pi\) |
0.517696 | + | 0.855564i | \(0.326790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2914.95 | − | 1060.96i | −1.19705 | − | 0.435692i | −0.334858 | − | 0.942268i | \(-0.608688\pi\) |
−0.862195 | + | 0.506577i | \(0.830911\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2245.94 | − | 3890.07i | −0.907237 | − | 1.57138i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −812.205 | − | 681.521i | −0.322781 | − | 0.270846i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −627.553 | + | 3559.03i | −0.245408 | + | 1.39178i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59.3186 | −0.0228296 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 39.7562 | 0.0150610 | 0.00753051 | − | 0.999972i | \(-0.497603\pi\) | ||||
0.00753051 | + | 0.999972i | \(0.497603\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 339.425 | − | 1924.98i | 0.126593 | − | 0.717942i | −0.853757 | − | 0.520672i | \(-0.825681\pi\) |
0.980349 | − | 0.197270i | \(-0.0632076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2592.31 | + | 2175.21i | 0.951996 | + | 0.798819i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1277.51 | − | 2212.71i | −0.462024 | − | 0.800249i | 0.537038 | − | 0.843558i | \(-0.319543\pi\) |
−0.999062 | + | 0.0433090i | \(0.986210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4978.66 | + | 1812.08i | 1.77351 | + | 0.645504i | 0.999930 | + | 0.0118012i | \(0.00375653\pi\) |
0.773577 | + | 0.633703i | \(0.218466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3871.07 | + | 6704.89i | −1.35843 | + | 2.35287i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.04288 | + | 45.6134i | 0.00278078 | + | 0.0157706i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2192.38 | − | 1839.63i | 0.746940 | − | 0.626757i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4050.59 | + | 1474.29i | −1.36007 | + | 0.495026i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3011.45 | − | 429.337i | 0.996681 | − | 0.142095i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4238.15 | − | 1542.56i | 1.38278 | − | 0.503290i | 0.459759 | − | 0.888043i | \(-0.347936\pi\) |
0.923020 | + | 0.384753i | \(0.125713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2920.22 | − | 2450.36i | 0.939392 | − | 0.788243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 433.777 | + | 2460.07i | 0.137597 | + | 0.780351i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −64.6655 | + | 112.004i | −0.0202294 | + | 0.0350383i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3616.52 | + | 1316.31i | 1.11590 | + | 0.406154i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2299.08 | − | 3982.13i | −0.699787 | − | 1.21207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3384.38 | − | 2839.83i | −1.01630 | − | 0.852778i | −0.0271425 | − | 0.999632i | \(-0.508641\pi\) |
−0.989158 | + | 0.146854i | \(0.953085\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −333.687 | + | 1892.43i | −0.0988702 | + | 0.560721i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 777.194 | 0.227243 | 0.113621 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5918.88 | 1.70799 | 0.853997 | − | 0.520277i | \(-0.174171\pi\) | ||||
0.853997 | + | 0.520277i | \(0.174171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −27.9086 | + | 158.277i | −0.00794913 | + | 0.0450817i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2069.04 | − | 1736.13i | −0.581749 | − | 0.488146i | 0.303772 | − | 0.952745i | \(-0.401754\pi\) |
−0.885521 | + | 0.464599i | \(0.846198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1083.60 | − | 1876.86i | −0.300794 | − | 0.520990i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6209.49 | + | 2260.07i | 1.70190 | + | 0.619440i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1058.53 | − | 1833.42i | 0.286487 | − | 0.496210i | −0.686482 | − | 0.727147i | \(-0.740846\pi\) |
0.972969 | + | 0.230937i | \(0.0741792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 630.358 | + | 3574.94i | 0.168485 | + | 0.955528i | 0.945398 | + | 0.325919i | \(0.105674\pi\) |
−0.776912 | + | 0.629609i | \(0.783215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3432.94 | + | 2880.58i | −0.906267 | + | 0.760448i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2837.28 | + | 1032.69i | −0.739867 | + | 0.269290i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2584.04 | + | 2881.36i | −0.665662 | + | 0.742254i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7207.32 | − | 2623.25i | 1.83432 | − | 0.667637i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3044.21 | − | 2554.40i | 0.765533 | − | 0.642359i | −0.174028 | − | 0.984741i | \(-0.555678\pi\) |
0.939561 | + | 0.342382i | \(0.111234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 677.890 | + | 3844.51i | 0.168453 | + | 0.955344i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3562.46 | + | 6170.37i | −0.874863 | + | 1.51531i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1207.97 | − | 439.665i | −0.293195 | − | 0.106714i | 0.191235 | − | 0.981544i | \(-0.438751\pi\) |
−0.484430 | + | 0.874830i | \(0.660973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.0347 | + | 55.4857i | 0.00768547 | + | 0.0133116i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2702.91 | − | 2268.01i | −0.641020 | − | 0.537880i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 231.574 | − | 1313.32i | 0.0542946 | − | 0.307920i | −0.945551 | − | 0.325473i | \(-0.894476\pi\) |
0.999846 | + | 0.0175529i | \(0.00558756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4178.06 | −0.968514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9132.19 | −2.09319 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0699 | − | 68.4517i | 0.00273574 | − | 0.0155151i | −0.983409 | − | 0.181400i | \(-0.941937\pi\) |
0.986145 | + | 0.165885i | \(0.0530481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2411.95 | − | 2023.87i | −0.540648 | − | 0.453658i | 0.331111 | − | 0.943592i | \(-0.392576\pi\) |
−0.871760 | + | 0.489934i | \(0.837021\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −102.245 | − | 177.093i | −0.0226672 | − | 0.0392607i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1635.35 | + | 595.220i | 0.358602 | + | 0.130520i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1997.82 | + | 3460.32i | −0.433347 | + | 0.750579i | −0.997159 | − | 0.0753239i | \(-0.976001\pi\) |
0.563812 | + | 0.825903i | \(0.309334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1710.84 | − | 9702.67i | −0.367116 | − | 2.08202i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2105.00 | + | 1766.31i | −0.446883 | + | 0.374979i | −0.838278 | − | 0.545244i | \(-0.816437\pi\) |
0.391395 | + | 0.920223i | \(0.371993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5683.81 | + | 2068.74i | −1.19388 | + | 0.434536i | −0.861084 | − | 0.508463i | \(-0.830214\pi\) |
−0.332795 | + | 0.942999i | \(0.607992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5868.56 | + | 1235.22i | 1.21973 | + | 0.256729i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −162.513 | + | 59.1497i | −0.0334244 | + | 0.0121655i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3652.70 | − | 3064.98i | 0.743476 | − | 0.623850i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1365.66 | − | 7745.05i | −0.275108 | − | 1.56022i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 367.726 | − | 636.921i | 0.0733202 | − | 0.126994i | −0.827034 | − | 0.562151i | \(-0.809974\pi\) |
0.900355 | + | 0.435157i | \(0.143307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4405.29 | + | 1603.40i | 0.869444 | + | 0.316452i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2046.23 | − | 3544.18i | −0.399780 | − | 0.692439i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3804.93 | − | 3192.72i | −0.735937 | − | 0.617524i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.2123 | − | 148.657i | 0.00501944 | − | 0.0284666i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13164.2 | 2.49593 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4814.78 | −0.903913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 432.394 | − | 2452.23i | 0.0803844 | − | 0.455883i | −0.917873 | − | 0.396874i | \(-0.870095\pi\) |
0.998257 | − | 0.0590087i | \(-0.0187940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5280.48 | + | 4430.85i | 0.972155 | + | 0.815735i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3468.76 | − | 6008.06i | −0.632460 | − | 1.09545i | −0.987047 | − | 0.160430i | \(-0.948712\pi\) |
0.354587 | − | 0.935023i | \(-0.384622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4478.14 | − | 1629.91i | −0.808688 | − | 0.294338i | −0.0956064 | − | 0.995419i | \(-0.530479\pi\) |
−0.713082 | + | 0.701081i | \(0.752701\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −95.1107 | + | 164.737i | −0.0170123 | + | 0.0294662i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −478.848 | − | 2715.68i | −0.0848416 | − | 0.481160i | −0.997391 | − | 0.0721932i | \(-0.977000\pi\) |
0.912549 | − | 0.408967i | \(-0.134111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2447.88 | + | 2054.01i | −0.429639 | + | 0.360510i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14454.7 | − | 5261.08i | 2.51334 | − | 0.914781i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6919.18 | − | 4304.49i | −1.19193 | − | 0.741511i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2080.73 | + | 757.324i | −0.355133 | + | 0.129258i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8276.12 | + | 6944.49i | −1.39960 | + | 1.17441i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.7410 | + | 128.970i | 0.00381079 | + | 0.0216121i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −685.049 | + | 1186.54i | −0.113757 | + | 0.197034i | −0.917282 | − | 0.398237i | \(-0.869622\pi\) |
0.803525 | + | 0.595271i | \(0.202955\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4586.41 | − | 1669.32i | −0.754756 | − | 0.274709i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4149.35 | + | 7186.89i | 0.676726 | + | 1.17212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5256.71 | + | 4410.90i | 0.849706 | + | 0.712988i | 0.959725 | − | 0.280941i | \(-0.0906466\pi\) |
−0.110019 | + | 0.993930i | \(0.535091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −536.107 | + | 3040.41i | −0.0858919 | + | 0.487117i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8922.71 | −1.41699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 365.060 | 0.0574677 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1336.47 | + | 7579.50i | −0.208560 | + | 1.18280i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 483.123 | + | 405.388i | 0.0747418 | + | 0.0627158i | 0.679393 | − | 0.733774i | \(-0.262243\pi\) |
−0.604651 | + | 0.796490i | \(0.706688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3958.82 | + | 6856.88i | 0.607194 | + | 1.05169i | 0.991701 | + | 0.128569i | \(0.0410384\pi\) |
−0.384506 | + | 0.923122i | \(0.625628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4893.00 | + | 1780.91i | 0.744071 | + | 0.270820i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2341.51 | + | 4055.62i | −0.353048 | + | 0.611498i | −0.986782 | − | 0.162054i | \(-0.948188\pi\) |
0.633734 | + | 0.773551i | \(0.281522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −709.548 | − | 4024.05i | −0.106081 | − | 0.601617i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 329.817 | − | 276.749i | 0.0488957 | − | 0.0410283i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9258.89 | − | 3369.96i | 1.36119 | − | 0.495431i | 0.444765 | − | 0.895647i | \(-0.353287\pi\) |
0.916421 | + | 0.400216i | \(0.131065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1632.87 | + | 6661.80i | −0.238063 | + | 0.971250i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −139.434 | + | 50.7500i | −0.0201609 | + | 0.00733797i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3160.15 | − | 2651.68i | 0.453178 | − | 0.380262i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2206.46 | + | 12513.5i | 0.313832 | + | 1.77983i | 0.578695 | + | 0.815544i | \(0.303562\pi\) |
−0.264863 | + | 0.964286i | \(0.585327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6587.31 | − | 11409.6i | 0.929327 | − | 1.60964i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 237.246 | + | 86.3504i | 0.0332000 | + | 0.0120838i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −567.039 | − | 982.141i | −0.0787136 | − | 0.136336i | 0.823982 | − | 0.566617i | \(-0.191748\pi\) |
−0.902695 | + | 0.430281i | \(0.858415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9562.24 | + | 8023.68i | 1.31678 | + | 1.10491i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 706.008 | − | 4003.97i | 0.0964490 | − | 0.546989i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2663.99 | −0.361055 | −0.180528 | − | 0.983570i | \(-0.557781\pi\) | ||||
−0.180528 | + | 0.983570i | \(0.557781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7401.41 | −0.995239 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −484.525 | + | 2747.88i | −0.0646425 | + | 0.366606i | 0.935277 | + | 0.353917i | \(0.115150\pi\) |
−0.999919 | + | 0.0126892i | \(0.995961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 131.969 | + | 110.735i | 0.0174695 | + | 0.0146586i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5749.65 | + | 9958.69i | 0.755223 | + | 1.30808i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7299.03 | − | 2656.63i | −0.951351 | − | 0.346264i | −0.180713 | − | 0.983536i | \(-0.557840\pi\) |
−0.770639 | + | 0.637272i | \(0.780063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5228.90 | − | 9056.72i | 0.676309 | − | 1.17140i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1291.09 | − | 7322.11i | −0.165717 | − | 0.939826i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5425.92 | − | 4552.88i | 0.691158 | − | 0.579951i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7106.69 | − | 2586.62i | 0.898425 | − | 0.327000i | 0.148803 | − | 0.988867i | \(-0.452458\pi\) |
0.749621 | + | 0.661867i | \(0.230236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −307.710 | − | 191.429i | −0.0386085 | − | 0.0240187i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2600.31 | + | 946.436i | −0.323824 | + | 0.117862i | −0.498817 | − | 0.866707i | \(-0.666232\pi\) |
0.174993 | + | 0.984570i | \(0.444010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8696.71 | − | 7297.40i | 1.07497 | − | 0.902009i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 274.169 | + | 1554.89i | 0.0336384 | + | 0.190773i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2210.11 | + | 3828.03i | −0.269168 | + | 0.466212i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4310.73 | − | 1568.98i | −0.521153 | − | 0.189684i | 0.0680307 | − | 0.997683i | \(-0.478328\pi\) |
−0.589184 | + | 0.807999i | \(0.700551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5041.93 | + | 8732.88i | 0.605110 | + | 1.04808i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −217.011 | − | 182.094i | −0.0258557 | − | 0.0216955i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1427.60 | − | 8096.34i | 0.168863 | − | 0.957671i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10946.0 | −1.28543 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4970.33 | 0.579514 | 0.289757 | − | 0.957100i | \(-0.406425\pi\) | ||||
0.289757 | + | 0.957100i | \(0.406425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1247.62 | + | 7075.59i | −0.144430 | + | 0.819105i | 0.823392 | + | 0.567472i | \(0.192079\pi\) |
−0.967823 | + | 0.251633i | \(0.919032\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7642.40 | − | 6412.74i | −0.878454 | − | 0.737111i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2331.03 | − | 4037.46i | −0.266050 | − | 0.460813i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 273.401 | + | 99.5099i | 0.0309855 | + | 0.0112778i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7054.00 | − | 12217.9i | 0.793871 | − | 1.37502i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1780.70 | + | 10098.9i | 0.199010 | + | 1.12864i | 0.906591 | + | 0.422010i | \(0.138675\pi\) |
−0.707581 | + | 0.706632i | \(0.750214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3021.76 | − | 2535.56i | 0.335373 | − | 0.281411i | −0.459512 | − | 0.888172i | \(-0.651976\pi\) |
0.794885 | + | 0.606760i | \(0.207531\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5919.99 | + | 2154.70i | −0.652510 | + | 0.237494i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8613.75 | − | 1813.02i | −0.942909 | − | 0.198464i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10816.0 | + | 3936.69i | −1.17590 | + | 0.427991i | −0.854751 | − | 0.519038i | \(-0.826290\pi\) |
−0.321146 | + | 0.947030i | \(0.604068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10647.5 | + | 8934.29i | −1.14971 | + | 0.964722i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1353.88 | − | 7678.26i | −0.145203 | − | 0.823488i | −0.967204 | − | 0.254001i | \(-0.918253\pi\) |
0.822001 | − | 0.569486i | \(-0.192858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4894.34 | + | 8477.24i | −0.521380 | + | 0.903056i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9414.37 | − | 3426.55i | −0.996162 | − | 0.362573i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4095.48 | + | 7093.59i | 0.430463 | + | 0.745584i | 0.996913 | − | 0.0785124i | \(-0.0250170\pi\) |
−0.566450 | + | 0.824096i | \(0.691684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9140.07 | − | 7669.43i | −0.954299 | − | 0.800752i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.2257 | + | 211.117i | −0.00386096 | + | 0.0218966i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −219.190 | −0.0225841 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17554.1 | 1.79682 | 0.898409 | − | 0.439159i | \(-0.144724\pi\) | ||||
0.898409 | + | 0.439159i | \(0.144724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1903.74 | + | 10796.6i | −0.193592 | + | 1.09792i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1482.79 | − | 1244.21i | −0.149805 | − | 0.125702i | 0.564805 | − | 0.825225i | \(-0.308951\pi\) |
−0.714610 | + | 0.699523i | \(0.753396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5715.70 | + | 9899.89i | 0.573718 | + | 0.993708i | 0.996180 | + | 0.0873274i | \(0.0278326\pi\) |
−0.422462 | + | 0.906381i | \(0.638834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16530.4 | − | 6016.56i | −1.64855 | − | 0.600025i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4742.62 | − | 8214.46i | 0.469941 | − | 0.813962i | −0.529468 | − | 0.848330i | \(-0.677609\pi\) |
0.999409 | + | 0.0343682i | \(0.0109419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −87.0801 | − | 493.856i | −0.00857353 | − | 0.0486229i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13883.3 | − | 11649.5i | 1.35819 | − | 1.13966i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9786.21 | − | 3561.89i | 0.951312 | − | 0.346249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2619.94 | + | 2921.40i | −0.253076 | + | 0.282196i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18073.2 | + | 6578.12i | −1.73484 | + | 0.631429i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9693.22 | − | 8133.58i | 0.924623 | − | 0.775851i | −0.0502211 | − | 0.998738i | \(-0.515993\pi\) |
0.974844 | + | 0.222887i | \(0.0715482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −976.605 | − | 5538.60i | −0.0925766 | − | 0.525028i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 232.540 | − | 402.771i | 0.0219067 | − | 0.0379435i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7921.50 | − | 2883.19i | −0.741643 | − | 0.269936i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7300.56 | − | 12644.9i | −0.679301 | − | 1.17658i | −0.975192 | − | 0.221362i | \(-0.928950\pi\) |
0.295890 | − | 0.955222i | \(-0.404384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1029.26 | − | 863.655i | −0.0951838 | − | 0.0798687i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −946.574 | + | 5368.29i | −0.0870026 | + | 0.493416i | 0.909904 | + | 0.414819i | \(0.136155\pi\) |
−0.996906 | + | 0.0785970i | \(0.974956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8560.26 | 0.782018 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13123.6 | −1.19164 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.8766 | + | 243.165i | −0.00386977 | + | 0.0219466i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10667.1 | − | 8950.76i | −0.956964 | − | 0.802988i | 0.0234929 | − | 0.999724i | \(-0.492521\pi\) |
−0.980456 | + | 0.196736i | \(0.936966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7503.75 | + | 12996.9i | 0.669147 | + | 1.15900i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7275.70 | + | 2648.14i | 0.644945 | + | 0.234741i | 0.643723 | − | 0.765258i | \(-0.277389\pi\) |
0.00122202 | + | 0.999999i | \(0.499611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7055.29 | − | 12220.1i | 0.621696 | − | 1.07681i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.6667 | − | 105.864i | −0.00163514 | − | 0.00927333i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14923.4 | + | 12522.3i | −1.29955 | + | 1.09045i | −0.309326 | + | 0.950956i | \(0.600103\pi\) |
−0.990223 | + | 0.139494i | \(0.955452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −234.249 | + | 85.2598i | −0.0202790 | + | 0.00738096i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9135.49 | − | 1302.43i | 0.786241 | − | 0.112093i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6943.11 | − | 2527.09i | 0.594078 | − | 0.216227i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6921.29 | + | 5807.65i | −0.588777 | + | 0.494043i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5191.30 | − | 29441.3i | −0.439061 | − | 2.49004i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5234.99 | − | 9067.26i | 0.440209 | − | 0.762464i | −0.557496 | − | 0.830180i | \(-0.688238\pi\) |
0.997705 | + | 0.0677155i | \(0.0215710\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5454.79 | + | 1985.38i | 0.456064 | + | 0.165994i | 0.559829 | − | 0.828608i | \(-0.310867\pi\) |
−0.103765 | + | 0.994602i | \(0.533089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −103.665 | − | 179.554i | −0.00861778 | − | 0.0149264i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18310.6 | + | 15364.4i | 1.51351 | + | 1.26999i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −151.136 | + | 857.136i | −0.0124218 | + | 0.0704476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21580.6 | 1.76369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15181.0 | 1.23370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2863.14 | − | 16237.7i | 0.231373 | − | 1.31218i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14538.7 | + | 12199.4i | 1.16833 | + | 0.980344i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6293.90 | + | 10901.3i | 0.502964 | + | 0.871158i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15227.2 | − | 5542.23i | −1.21011 | − | 0.440442i | −0.343365 | − | 0.939202i | \(-0.611567\pi\) |
−0.866740 | + | 0.498760i | \(0.833789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12748.2 | + | 22080.5i | −1.00751 | + | 1.74505i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2010.91 | + | 11404.4i | 0.158051 | + | 0.896352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −157.642 | + | 132.278i | −0.0123223 | + | 0.0103396i | −0.648928 | − | 0.760850i | \(-0.724782\pi\) |
0.636606 | + | 0.771189i | \(0.280338\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20827.5 | + | 7580.60i | −1.61912 | + | 0.589312i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2240.17 | − | 6848.20i | −0.173202 | − | 0.529479i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −402.201 | + | 146.389i | −0.0309283 | + | 0.0112570i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6675.72 | + | 5601.60i | −0.510574 | + | 0.428423i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3982.46 | + | 22585.6i | 0.302948 | + | 1.71811i | 0.633008 | + | 0.774145i | \(0.281820\pi\) |
−0.330060 | + | 0.943960i | \(0.607069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6625.26 | + | 11475.3i | −0.501285 | + | 0.868252i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27912.5 | + | 10159.3i | 2.10065 | + | 0.764576i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5298.64 | + | 9177.51i | 0.396645 | + | 0.687009i | 0.993310 | − | 0.115482i | \(-0.0368411\pi\) |
−0.596665 | + | 0.802491i | \(0.703508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2535.04 | + | 2127.15i | 0.188761 | + | 0.158389i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.5675 | − | 93.9588i | 0.00122710 | − | 0.00695925i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10436.4 | −0.768925 | −0.384463 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384463 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10195.1 | 0.747200 | 0.373600 | − | 0.927590i | \(-0.378123\pi\) | ||||
0.373600 | + | 0.927590i | \(0.378123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 56.7424 | − | 321.802i | 0.00413690 | − | 0.0234615i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3857.80 | − | 3237.08i | −0.279794 | − | 0.234775i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9760.95 | − | 16906.5i | −0.704252 | − | 1.21980i | −0.966961 | − | 0.254926i | \(-0.917949\pi\) |
0.262708 | − | 0.964875i | \(-0.415384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15097.1 | − | 5494.88i | −1.08361 | − | 0.394403i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −248.397 | + | 430.235i | −0.0177370 | + | 0.0307215i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3024.67 | + | 17153.7i | 0.214869 | + | 1.21859i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12791.2 | − | 10733.1i | 0.904020 | − | 0.758563i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14354.6 | + | 5224.63i | −1.00933 | + | 0.367366i | −0.793175 | − | 0.608994i | \(-0.791573\pi\) |
−0.216154 | + | 0.976359i | \(0.569351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7499.73 | − | 18669.2i | 0.524654 | − | 1.30603i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19733.9 | + | 7182.54i | −1.37351 | + | 0.499916i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11373.9 | + | 9543.81i | −0.787637 | + | 0.660906i | −0.945159 | − | 0.326609i | \(-0.894094\pi\) |
0.157522 | + | 0.987515i | \(0.449649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −80.1379 | − | 454.485i | −0.00552157 | − | 0.0313144i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21773.6 | − | 37712.9i | 1.49268 | − | 2.58540i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5053.44 | + | 1839.30i | 0.344705 | + | 0.125462i | 0.508570 | − | 0.861020i | \(-0.330174\pi\) |
−0.163866 | + | 0.986483i | \(0.552396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6933.22 | + | 12008.7i | 0.470569 | + | 0.815049i | 0.999433 | − | 0.0336573i | \(-0.0107155\pi\) |
−0.528865 | + | 0.848706i | \(0.677382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29264.4 | + | 24555.8i | 1.97635 | + | 1.65835i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.6187 | + | 156.633i | −0.00185597 | + | 0.0105257i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13443.5 | −0.898940 | −0.449470 | − | 0.893295i | \(-0.648387\pi\) | ||||
−0.449470 | + | 0.893295i | \(0.648387\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 380.692 | 0.0253307 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1996.21 | − | 11321.1i | 0.132174 | − | 0.749595i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 217.601 | + | 182.589i | 0.0143374 | + | 0.0120305i | 0.649928 | − | 0.759996i | \(-0.274799\pi\) |
−0.635591 | + | 0.772026i | \(0.719243\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11761.6 | − | 20371.6i | −0.771175 | − | 1.33571i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21426.3 | + | 7798.54i | 1.39804 | + | 0.508845i | 0.927596 | − | 0.373585i | \(-0.121872\pi\) |
0.470444 | + | 0.882430i | \(0.344094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12269.2 | + | 21250.9i | −0.796673 | + | 1.37988i | 0.125099 | + | 0.992144i | \(0.460075\pi\) |
−0.921772 | + | 0.387733i | \(0.873258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2056.44 | + | 11662.6i | 0.132886 | + | 0.753633i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 453.123 | − | 380.216i | 0.0291396 | − | 0.0244511i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7007.52 | − | 2550.53i | 0.448481 | − | 0.163234i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 822.897 | − | 24988.6i | 0.0524136 | − | 1.59163i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11127.1 | − | 4049.93i | 0.705352 | − | 0.256727i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4454.15 | − | 3737.47i | 0.281009 | − | 0.235795i | −0.491378 | − | 0.870946i | \(-0.663507\pi\) |
0.772388 | + | 0.635152i | \(0.219062\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6437.15 | − | 36506.9i | −0.404192 | − | 2.29229i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3966.74 | + | 6870.60i | −0.247898 | + | 0.429372i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15050.1 | − | 5477.79i | −0.936117 | − | 0.340719i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9404.96 | − | 16289.9i | −0.582245 | − | 1.00848i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17383.6 | − | 14586.6i | −1.07116 | − | 0.898809i | −0.0760014 | − | 0.997108i | \(-0.524215\pi\) |
−0.995157 | + | 0.0982991i | \(0.968660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −775.919 | + | 4400.45i | −0.0475883 | + | 0.269886i | −0.999313 | − | 0.0370670i | \(-0.988198\pi\) |
0.951725 | + | 0.306953i | \(0.0993096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20531.9 | 1.25340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2668.71 | −0.162161 | −0.0810804 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810804 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3393.84 | − | 19247.4i | 0.205270 | − | 1.16414i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 814.309 | + | 683.286i | 0.0490250 | + | 0.0411369i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8339.53 | − | 14444.5i | −0.499772 | − | 0.865631i | 0.500228 | − | 0.865894i | \(-0.333250\pi\) |
−1.00000 | 0.000263124i | \(0.999916\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7488.93 | − | 2725.75i | −0.446743 | − | 0.162601i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9495.10 | − | 16446.0i | 0.563835 | − | 0.976590i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3317.12 | + | 18812.4i | 0.196080 | + | 1.11203i | 0.910872 | + | 0.412689i | \(0.135410\pi\) |
−0.714792 | + | 0.699337i | \(0.753479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2932.65 | + | 2460.79i | −0.172567 | + | 0.144801i | −0.724981 | − | 0.688769i | \(-0.758151\pi\) |
0.552413 | + | 0.833570i | \(0.313707\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −35514.3 | + | 12926.1i | −2.08033 | + | 0.757179i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −342.616 | + | 183.046i | −0.0199790 | + | 0.0106740i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8689.23 | − | 3162.62i | 0.504421 | − | 0.183594i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27817.1 | + | 23341.3i | −1.60758 | + | 1.34892i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3485.61 | + | 19767.9i | 0.200538 | + | 1.13730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14243.5 | + | 24670.5i | −0.815822 | + | 1.41305i | 0.0929140 | + | 0.995674i | \(0.470382\pi\) |
−0.908736 | + | 0.417371i | \(0.862951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4960.99 | + | 1805.65i | 0.282887 | + | 0.102962i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15257.8 | + | 26427.3i | 0.866181 | + | 1.50027i | 0.865869 | + | 0.500270i | \(0.166766\pi\) |
0.000312116 | 1.00000i | \(0.499901\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 390.224 | + | 327.437i | 0.0220551 | + | 0.0185064i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1109.26 | − | 6290.91i | 0.0624182 | − | 0.353991i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7906.32 | −0.442938 | −0.221469 | − | 0.975167i | \(-0.571085\pi\) | ||||
−0.221469 | + | 0.975167i | \(0.571085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10808.8 | 0.602893 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8447.78 | − | 47909.7i | 0.469145 | − | 2.66066i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16977.2 | − | 14245.5i | −0.938721 | − | 0.787680i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15436.6 | − | 26737.0i | −0.849836 | − | 1.47196i | −0.881354 | − | 0.472456i | \(-0.843368\pi\) |
0.0315186 | − | 0.999503i | \(-0.489966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 745.209 | + | 271.234i | 0.0408487 | + | 0.0148677i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5866.42 | + | 10160.9i | −0.320181 | + | 0.554570i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5550.31 | + | 31477.4i | 0.301625 | + | 1.71060i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17006.0 | + | 14269.7i | −0.920209 | + | 0.772147i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32180.3 | + | 11712.7i | −1.73386 | + | 0.631072i | −0.998893 | − | 0.0470366i | \(-0.985022\pi\) |
−0.734962 | + | 0.678108i | \(0.762800\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6151.84 | − | 7841.82i | −0.330044 | − | 0.420711i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16738.6 | + | 6092.35i | −0.894201 | + | 0.325462i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −653.187 | + | 548.089i | −0.0347463 | + | 0.0291556i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2020.41 | + | 11458.3i | 0.107021 | + | 0.606948i | 0.990394 | + | 0.138276i | \(0.0441562\pi\) |
−0.883372 | + | 0.468672i | \(0.844733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16302.9 | − | 28237.4i | 0.859924 | − | 1.48943i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24262.9 | + | 8830.98i | 1.27441 | + | 0.463847i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7561.10 | − | 13096.2i | −0.395481 | − | 0.684993i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13329.6 | − | 11184.9i | −0.694288 | − | 0.582577i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −237.869 | + | 1349.02i | −0.0123380 | + | 0.0699724i | −0.990355 | − | 0.138552i | \(-0.955755\pi\) |
0.978017 | + | 0.208525i | \(0.0668662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −446.485 | −0.0230624 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29836.6 | 1.53477 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 715.818 | − | 4059.61i | 0.0366687 | − | 0.207959i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15601.0 | + | 13090.8i | 0.795884 | + | 0.667826i | 0.947194 | − | 0.320661i | \(-0.103905\pi\) |
−0.151310 | + | 0.988486i | \(0.548349\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15997.5 | + | 27708.4i | 0.812755 | + | 1.40773i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26216.0 | − | 9541.83i | −1.32645 | − | 0.482787i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13283.0 | − | 23006.8i | 0.669330 | − | 1.15931i | −0.308762 | − | 0.951139i | \(-0.599915\pi\) |
0.978092 | − | 0.208174i | \(-0.0667520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4309.43 | + | 24440.0i | 0.216266 | + | 1.22651i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26503.1 | − | 22238.8i | 1.32463 | − | 1.11150i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5877.58 | + | 2139.26i | −0.292571 | + | 0.106487i | −0.484136 | − | 0.874993i | \(-0.660866\pi\) |
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19634.8 | + | 25028.7i | 0.973417 | + | 1.24083i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2905.50 | + | 1057.52i | −0.143462 | + | 0.0522160i | −0.412753 | − | 0.910843i | \(-0.635433\pi\) |
0.269291 | + | 0.963059i | \(0.413211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8226.38 | + | 6902.75i | −0.404552 | + | 0.339459i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6571.78 | − | 37270.4i | −0.321886 | − | 1.82551i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −498.173 | + | 862.862i | −0.0243029 | + | 0.0420938i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2007.09 | + | 730.521i | 0.0975229 | + | 0.0354954i | 0.390321 | − | 0.920679i | \(-0.372364\pi\) |
−0.292798 | + | 0.956174i | \(0.594586\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16331.4 | − | 28286.8i | −0.790371 | − | 1.36896i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 176.025 | + | 147.703i | 0.00848506 | + | 0.00711981i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2248.44 | − | 12751.5i | 0.107954 | − | 0.612236i | −0.882046 | − | 0.471164i | \(-0.843834\pi\) |
0.989999 | − | 0.141072i | \(-0.0450549\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32086.5 | 1.53447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31461.5 | 1.49866 | 0.749329 | − | 0.662198i | \(-0.230376\pi\) | ||||
0.749329 | + | 0.662198i | \(0.230376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 121.515 | − | 689.147i | 0.00576559 | − | 0.0326983i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26931.4 | + | 22598.1i | 1.27282 | + | 1.06802i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12433.6 | + | 21535.6i | 0.585332 | + | 1.01383i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8870.73 | + | 3228.68i | 0.415978 | + | 0.151403i | 0.541526 | − | 0.840684i | \(-0.317847\pi\) |
−0.125548 | + | 0.992088i | \(0.540069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5282.91 | + | 9150.27i | −0.246770 | + | 0.427418i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2460.15 | + | 13952.2i | 0.114470 | + | 0.649192i | 0.987011 | + | 0.160652i | \(0.0513596\pi\) |
−0.872541 | + | 0.488541i | \(0.837529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8817.55 | − | 7398.80i | 0.408691 | − | 0.342933i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 494.844 | − | 180.109i | 0.0228474 | − | 0.00831578i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23729.4 | − | 12677.7i | 1.09139 | − | 0.583088i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16007.7 | + | 5826.34i | −0.733421 | + | 0.266943i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7425.85 | + | 6231.03i | −0.338925 | + | 0.284392i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3373.32 | − | 19131.0i | −0.153374 | − | 0.869830i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 761.140 | − | 1318.33i | 0.0344748 | − | 0.0597122i | −0.848273 | − | 0.529559i | \(-0.822357\pi\) |
0.882748 | + | 0.469847i | \(0.155691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10300.0 | − | 3748.91i | −0.464754 | − | 0.169157i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −99.9859 | − | 173.181i | −0.00449442 | − | 0.00778457i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19564.4 | − | 16416.5i | −0.876107 | − | 0.735141i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5963.17 | + | 33818.8i | −0.266028 | + | 1.50872i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22894.6 | −1.01753 | −0.508764 | − | 0.860906i | \(-0.669897\pi\) | ||||
−0.508764 | + | 0.860906i | \(0.669897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24203.8 | 1.07168 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7824.74 | + | 44376.3i | −0.345160 | + | 1.95750i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13174.7 | − | 11054.9i | −0.578985 | − | 0.485826i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −249.257 | − | 431.725i | −0.0109132 | − | 0.0189022i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −536.848 | − | 195.397i | −0.0234175 | − | 0.00852328i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4454.63 | + | 7715.65i | −0.193593 | + | 0.335312i | −0.946438 | − | 0.322885i | \(-0.895347\pi\) |
0.752846 | + | 0.658197i | \(0.228681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3986.15 | − | 22606.6i | −0.172593 | − | 0.978823i | −0.940886 | − | 0.338724i | \(-0.890005\pi\) |
0.768293 | − | 0.640098i | \(-0.221106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19824.5 | + | 16634.7i | −0.855196 | + | 0.717594i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1353.34 | + | 492.576i | −0.0581663 | + | 0.0211708i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −772.881 | + | 23469.8i | −0.0330963 | + | 1.00502i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −948.160 | + | 345.102i | −0.0404535 | + | 0.0147239i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12939.7 | − | 10857.7i | 0.550061 | − | 0.461556i | −0.324901 | − | 0.945748i | \(-0.605331\pi\) |
0.874962 | + | 0.484192i | \(0.160887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4495.45 | + | 25494.9i | 0.190403 | + | 1.07983i | 0.918815 | + | 0.394688i | \(0.129147\pi\) |
−0.728412 | + | 0.685139i | \(0.759741\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7152.02 | − | 12387.7i | 0.301820 | − | 0.522767i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3873.96 | − | 1410.00i | −0.162891 | − | 0.0592874i | 0.259288 | − | 0.965800i | \(-0.416512\pi\) |
−0.422178 | + | 0.906513i | \(0.638734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16132.1 | + | 27941.6i | 0.675864 | + | 1.17063i | 0.976215 | + | 0.216803i | \(0.0695628\pi\) |
−0.300351 | + | 0.953829i | \(0.597104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25157.8 | + | 21109.9i | 1.05020 | + | 0.881220i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5855.60 | − | 33208.7i | 0.243559 | − | 1.38129i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16086.3 | 0.666696 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27067.8 | −1.11780 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5326.50 | + | 30208.1i | −0.219179 | + | 1.24303i | 0.654327 | + | 0.756212i | \(0.272952\pi\) |
−0.873506 | + | 0.486814i | \(0.838159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12884.8 | − | 10811.6i | −0.528305 | − | 0.443300i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11292.8 | + | 19559.7i | 0.461382 | + | 0.799136i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −108.276 | − | 39.4092i | −0.00440805 | − | 0.00160440i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.80553 | − | 8.32342i | 0.000194947 | − | 0.000337658i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8632.90 | + | 48959.6i | 0.348976 | + | 1.97914i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9798.48 | − | 8221.90i | 0.394697 | − | 0.331190i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15883.2 | − | 5781.01i | 0.637550 | − | 0.232049i | −0.00296407 | − | 0.999996i | \(-0.500943\pi\) |
0.640514 | + | 0.767946i | \(0.278721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11030.7 | − | 27458.9i | 0.441218 | − | 1.09833i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14641.4 | − | 5329.04i | 0.583596 | − | 0.212411i | −0.0333147 | − | 0.999445i | \(-0.510606\pi\) |
0.616910 | + | 0.787033i | \(0.288384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 589.608 | − | 494.740i | 0.0234193 | − | 0.0196511i | −0.631003 | − | 0.775780i | \(-0.717356\pi\) |
0.654422 | + | 0.756129i | \(0.272912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 246.833 | + | 1399.86i | 0.00977010 | + | 0.0554090i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 663.275 | − | 1148.83i | 0.0261624 | − | 0.0453146i | −0.852648 | − | 0.522486i | \(-0.825005\pi\) |
0.878810 | + | 0.477172i | \(0.158338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30112.1 | − | 10959.9i | −1.18363 | − | 0.430807i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19595.8 | − | 33940.9i | −0.767597 | − | 1.32952i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22620.7 | − | 18981.0i | −0.883031 | − | 0.740951i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7643.94 | + | 43350.9i | −0.297365 | + | 1.68644i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38805.9 | −1.50444 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −808.525 | −0.0312379 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6156.67 | − | 34916.2i | 0.237054 | − | 1.34440i | −0.601192 | − | 0.799105i | \(-0.705307\pi\) |
0.838245 | − | 0.545293i | \(-0.183582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4630.64 | − | 3885.57i | −0.177688 | − | 0.149098i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16247.0 | − | 28140.6i | −0.621311 | − | 1.07614i | −0.989242 | − | 0.146289i | \(-0.953267\pi\) |
0.367930 | − | 0.929853i | \(-0.380066\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23145.7 | − | 8424.36i | −0.882125 | − | 0.321067i | −0.139058 | − | 0.990284i | \(-0.544407\pi\) |
−0.743067 | + | 0.669217i | \(0.766630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19266.0 | − | 33369.7i | 0.731773 | − | 1.26747i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6915.72 | − | 39221.0i | −0.261789 | − | 1.48468i | −0.778024 | − | 0.628235i | \(-0.783778\pi\) |
0.516235 | − | 0.856447i | \(-0.327333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 367.245 | − | 308.155i | 0.0138549 | − | 0.0116256i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6185.38 | − | 2251.29i | 0.232568 | − | 0.0846477i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6334.01 | − | 19363.1i | −0.237357 | − | 0.725599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19116.5 | − | 6957.82i | 0.713958 | − | 0.259860i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31273.7 | + | 26241.8i | −1.16410 | + | 0.976798i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3670.06 | + | 20814.0i | 0.136155 | + | 0.772174i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23330.7 | − | 40410.0i | 0.862663 | − | 1.49418i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1165.88 | − | 424.345i | −0.0429656 | − | 0.0156382i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13664.6 | + | 23667.8i | 0.501908 | + | 0.869331i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31913.9 | + | 26778.9i | 1.16834 | + | 0.980352i | 0.999986 | − | 0.00537469i | \(-0.00171083\pi\) |
0.168353 | + | 0.985727i | \(0.446155\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11279.5 | − | 63969.4i | 0.411571 | − | 2.33414i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29821.5 | −1.08455 | −0.542277 | − | 0.840200i | \(-0.682438\pi\) | ||||
−0.542277 | + | 0.840200i | \(0.682438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34274.4 | −1.24241 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6871.94 | + | 38972.7i | −0.248283 | + | 1.40809i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 368.915 | + | 309.556i | 0.0132853 | + | 0.0111477i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8810.07 | + | 15259.5i | 0.316232 | + | 0.547730i | 0.979699 | − | 0.200476i | \(-0.0642488\pi\) |
−0.663467 | + | 0.748206i | \(0.730916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19232.1 | − | 6999.93i | −0.688079 | − | 0.250440i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10837.2 | − | 18770.6i | 0.386470 | − | 0.669385i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −990.174 | − | 5615.56i | −0.0351965 | − | 0.199609i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26055.4 | − | 21863.1i | 0.923163 | − | 0.774625i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30747.5 | − | 11191.2i | 1.08589 | − | 0.395232i | 0.263793 | − | 0.964579i | \(-0.415026\pi\) |
0.822097 | + | 0.569348i | \(0.192804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28099.3 | + | 4006.07i | −0.989171 | + | 0.141024i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −53582.4 | + | 19502.4i | −1.88018 | + | 0.684330i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24390.2 | − | 20465.8i | 0.853098 | − | 0.715834i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6534.42 | − | 37058.6i | −0.227823 | − | 1.29205i | −0.857214 | − | 0.514960i | \(-0.827807\pi\) |
0.629391 | − | 0.777089i | \(-0.283305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19584.6 | + | 33921.5i | −0.680638 | + | 1.17890i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11394.5 | − | 4147.26i | −0.394740 | − | 0.143674i | 0.137021 | − | 0.990568i | \(-0.456247\pi\) |
−0.531761 | + | 0.846894i | \(0.678470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17263.4 | + | 29901.0i | 0.596153 | + | 1.03257i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 400.338 | + | 335.924i | 0.0137809 | + | 0.0115636i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6684.28 | − | 37908.4i | 0.229366 | − | 1.30080i | −0.624794 | − | 0.780790i | \(-0.714817\pi\) |
0.854160 | − | 0.520011i | \(-0.174072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21882.2 | 0.748500 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22665.2 | −0.772839 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2043.83 | − | 11591.1i | 0.0694713 | − | 0.393992i | −0.930168 | − | 0.367134i | \(-0.880339\pi\) |
0.999639 | − | 0.0268572i | \(-0.00854995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −268.312 | − | 225.141i | −0.00909149 | − | 0.00762867i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13132.2 | + | 22745.7i | 0.443578 | + | 0.768300i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −613.762 | − | 223.391i | −0.0206667 | − | 0.00752208i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14612.2 | + | 25309.0i | −0.490489 | + | 0.849552i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13180.1 | − | 74748.0i | −0.441041 | − | 2.50127i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13192.0 | + | 11069.4i | −0.440067 | + | 0.369260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32805.5 | − | 11940.2i | 1.09095 | − | 0.397075i | 0.266980 | − | 0.963702i | \(-0.413974\pi\) |
0.823974 | + | 0.566627i | \(0.191752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44717.7 | + | 49863.0i | −1.48250 | + | 1.65307i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25214.5 | + | 9177.33i | −0.833339 | + | 0.303311i | −0.723229 | − | 0.690609i | \(-0.757343\pi\) |
−0.110111 | + | 0.993919i | \(0.535120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 543.120 | − | 455.732i | 0.0178948 | − | 0.0150155i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3160.33 | + | 17923.1i | 0.103807 | + | 0.588718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19774.5 | + | 34250.4i | −0.647536 | + | 1.12156i | 0.336174 | + | 0.941800i | \(0.390867\pi\) |
−0.983710 | + | 0.179765i | \(0.942466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38348.0 | + | 13957.5i | 1.25190 | + | 0.455653i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26654.3 | + | 46166.6i | 0.867489 | + | 1.50253i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15096.8 | + | 12667.8i | 0.489842 | + | 0.411026i | 0.853970 | − | 0.520323i | \(-0.174188\pi\) |
−0.364128 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3908.82 | + | 22168.0i | −0.126442 | + | 0.717089i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1076.39 | 0.0347133 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30136.2 | −0.968935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1956.42 | − | 11095.4i | 0.0627121 | − | 0.355658i | −0.937263 | − | 0.348623i | \(-0.886649\pi\) |
0.999975 | − | 0.00703523i | \(-0.00223940\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8626.57 | + | 7238.56i | 0.275686 | + | 0.231328i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23338.8 | − | 40424.0i | −0.743608 | − | 1.28797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27936.4 | + | 10168.0i | 0.887418 | + | 0.322994i | 0.745199 | − | 0.666842i | \(-0.232354\pi\) |
0.142218 | + | 0.989835i | \(0.454577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6704.57 | + | 11612.7i | −0.212336 | + | 0.367776i |
(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 | 76.4.i.a.5.5 | ✓ | 30 | |
19.2 | odd | 18 | 1444.4.a.k.1.2 | 15 | |||
19.4 | even | 9 | inner | 76.4.i.a.61.5 | yes | 30 | |
19.17 | even | 9 | 1444.4.a.j.1.14 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.i.a.5.5 | ✓ | 30 | 1.1 | even | 1 | trivial | |
76.4.i.a.61.5 | yes | 30 | 19.4 | even | 9 | inner | |
1444.4.a.j.1.14 | 15 | 19.17 | even | 9 | |||
1444.4.a.k.1.2 | 15 | 19.2 | odd | 18 |