Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.38 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.9 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.27623i | 1.31418i | 0.753811 | + | 0.657091i | \(0.228213\pi\) | ||||
−0.753811 | + | 0.657091i | \(0.771787\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.55864i | − | 1.14426i | −0.820163 | − | 0.572129i | \(-0.806118\pi\) | ||
0.820163 | − | 0.572129i | \(-0.193882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00518i | 0.379923i | 0.981792 | + | 0.189962i | \(0.0608363\pi\) | ||||
−0.981792 | + | 0.189962i | \(0.939164\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.18122 | −0.727073 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.20954i | − | 1.26922i | −0.772831 | − | 0.634612i | \(-0.781160\pi\) | ||
0.772831 | − | 0.634612i | \(-0.218840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.65655 | −1.84619 | −0.923097 | − | 0.384568i | \(-0.874350\pi\) | ||||
−0.923097 | + | 0.384568i | \(0.874350\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.82405 | 1.50376 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.10815 | + | 3.54340i | 0.511301 | + | 0.859402i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96359 | 0.450478 | 0.225239 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225239 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.28803 | −0.499288 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.06438i | 1.47302i | 0.676424 | + | 0.736512i | \(0.263529\pi\) | ||||
−0.676424 | + | 0.736512i | \(0.736471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.54664 | −0.309328 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.86373i | 0.358675i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.50313i | − | 0.464820i | −0.972618 | − | 0.232410i | \(-0.925339\pi\) | ||
0.972618 | − | 0.232410i | \(-0.0746611\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.19153i | − | 1.29164i | −0.763491 | − | 0.645818i | \(-0.776516\pi\) | ||
0.763491 | − | 0.645818i | \(-0.223484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.58187 | 1.66799 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.57190 | 0.434730 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.03511i | − | 0.827767i | −0.910330 | − | 0.413884i | \(-0.864172\pi\) | ||
0.910330 | − | 0.413884i | \(-0.135828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 15.1518i | − | 2.42623i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6991i | 1.82709i | 0.406736 | + | 0.913546i | \(0.366667\pi\) | ||||
−0.406736 | + | 0.913546i | \(0.633333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35785 | 0.359569 | 0.179785 | − | 0.983706i | \(-0.442460\pi\) | ||||
0.179785 | + | 0.983706i | \(0.442460\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.58095i | 0.831960i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.91253 | −1.44589 | −0.722946 | − | 0.690905i | \(-0.757212\pi\) | ||||
−0.722946 | + | 0.690905i | \(0.757212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.98961 | 0.855658 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.06560 | + | 4.79863i | −1.12941 | + | 0.671943i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.260490 | 0.0357811 | 0.0178905 | − | 0.999840i | \(-0.494305\pi\) | ||||
0.0178905 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.7707 | −1.45232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.46958i | 0.592010i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4088i | 1.33271i | 0.745634 | + | 0.666355i | \(0.232147\pi\) | ||||
−0.745634 | + | 0.666355i | \(0.767853\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.19252i | − | 0.276232i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.0317i | 2.11252i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.87736 | 0.473695 | 0.236848 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236848 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.0801 | −1.93582 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.64239i | − | 0.669629i | −0.942284 | − | 0.334814i | \(-0.891326\pi\) | ||
0.942284 | − | 0.334814i | \(-0.108674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.82479i | 1.03286i | 0.856328 | + | 0.516432i | \(0.172740\pi\) | ||||
−0.856328 | + | 0.516432i | \(0.827260\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3.52050i | − | 0.406513i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.23135 | 0.482207 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6738i | 1.53842i | 0.638994 | + | 0.769212i | \(0.279351\pi\) | ||||
−0.638994 | + | 0.769212i | \(0.720649\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7859 | −1.19844 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.15593 | 0.236644 | 0.118322 | − | 0.992975i | \(-0.462248\pi\) | ||||
0.118322 | + | 0.992975i | \(0.462248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.06629 | − | 5.39399i | 0.983378 | − | 0.585061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.69770 | 0.610857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.88983 | 0.518321 | 0.259161 | − | 0.965834i | \(-0.416554\pi\) | ||||
0.259161 | + | 0.965834i | \(0.416554\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.69104i | − | 0.701412i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.3696 | 1.69744 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.02412i | − | 0.515464i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2137i | 1.24012i | 0.784556 | + | 0.620058i | \(0.212891\pi\) | ||||
−0.784556 | + | 0.620058i | \(0.787109\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.18192i | 0.922818i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.57122 | 0.454853 | 0.227427 | − | 0.973795i | \(-0.426969\pi\) | ||||
0.227427 | + | 0.973795i | \(0.426969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.37882 | 0.628524 | 0.314262 | − | 0.949336i | \(-0.398243\pi\) | ||||
0.314262 | + | 0.949336i | \(0.398243\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.85423i | 0.571315i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2575i | 1.28165i | 0.767685 | + | 0.640827i | \(0.221408\pi\) | ||||
−0.767685 | + | 0.640827i | \(0.778592\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6707i | 1.69255i | 0.532748 | + | 0.846274i | \(0.321159\pi\) | ||||
−0.532748 | + | 0.846274i | \(0.678841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.4611 | 1.08784 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8665i | 1.11630i | 0.829739 | + | 0.558152i | \(0.188489\pi\) | ||||
−0.829739 | + | 0.558152i | \(0.811511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0752 | 1.68552 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5194 | 1.34232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.56177 | + | 2.11907i | −0.326507 | + | 0.194255i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.72020 | −0.610927 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.6298 | −2.40113 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 8.83591i | − | 0.790308i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7130 | −1.12810 | −0.564048 | − | 0.825742i | \(-0.690757\pi\) | ||||
−0.564048 | + | 0.825742i | \(0.690757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.36701i | 0.472539i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.992715i | − | 0.0867339i | −0.999059 | − | 0.0433670i | \(-0.986192\pi\) | ||
0.999059 | − | 0.0433670i | \(-0.0138085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.97377i | 0.171147i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.76862 | 0.410417 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.80553 | 0.837743 | 0.418871 | − | 0.908046i | \(-0.362426\pi\) | ||||
0.418871 | + | 0.908046i | \(0.362426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.2279i | − | 1.20680i | −0.797440 | − | 0.603398i | \(-0.793813\pi\) | ||
0.797440 | − | 0.603398i | \(-0.206187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 22.5632i | − | 1.90016i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.0210i | 2.34323i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.40461 | −0.531874 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.6337i | 1.12449i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.7986 | −1.62197 | −0.810983 | − | 0.585070i | \(-0.801067\pi\) | ||||
−0.810983 | + | 0.585070i | \(0.801067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6733 | −1.51961 | −0.759804 | − | 0.650152i | \(-0.774705\pi\) | ||||
−0.759804 | + | 0.650152i | \(0.774705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.59833 | − | 7.72894i | −0.371753 | − | 0.624848i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.4005 | −1.47797 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.00844362 | −0.000673874 | −0.000336937 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000336937 | 1.00000i | \(0.500107\pi\) | ||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.592936i | 0.0470229i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.10099 | −0.559636 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.81580i | − | 0.220550i | −0.993901 | − | 0.110275i | \(-0.964827\pi\) | ||
0.993901 | − | 0.110275i | \(-0.0351732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 24.5166i | − | 1.90861i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8605i | 1.22732i | 0.789569 | + | 0.613661i | \(0.210304\pi\) | ||||
−0.789569 | + | 0.613661i | \(0.789696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.3096 | 2.40843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.28302 | −0.327531 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4777i | 1.17675i | 0.808589 | + | 0.588374i | \(0.200232\pi\) | ||||
−0.808589 | + | 0.588374i | \(0.799768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.55465i | − | 0.117521i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.27623i | 0.171092i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.06073 | 0.677231 | 0.338616 | − | 0.940925i | \(-0.390041\pi\) | ||||
0.338616 | + | 0.940925i | \(0.390041\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.64116i | 0.196316i | 0.995171 | + | 0.0981579i | \(0.0312950\pi\) | ||||
−0.995171 | + | 0.0981579i | \(0.968705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.6928 | −1.75142 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.8830 | −0.947180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9161 | − | 8.87433i | 1.09077 | − | 0.648955i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.87339 | −0.136269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8146 | −0.999592 | −0.499796 | − | 0.866143i | \(-0.666592\pi\) | ||||
−0.499796 | + | 0.866143i | \(0.666592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.45032i | 0.392322i | 0.980572 | + | 0.196161i | \(0.0628476\pi\) | ||||
−0.980572 | + | 0.196161i | \(0.937152\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −38.7681 | −2.77624 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.1005i | − | 1.57459i | −0.616574 | − | 0.787297i | \(-0.711480\pi\) | ||
0.616574 | − | 0.787297i | \(-0.288520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8021i | 0.836629i | 0.908302 | + | 0.418315i | \(0.137379\pi\) | ||||
−0.908302 | + | 0.418315i | \(0.862621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.82576i | 0.622521i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.51610 | 0.176596 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.9338 | 2.09066 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 15.4090i | − | 1.07100i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.26580i | − | 0.571758i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.7529i | 1.97943i | 0.143060 | + | 0.989714i | \(0.454306\pi\) | ||||
−0.143060 | + | 0.989714i | \(0.545694\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.8434 | 0.880014 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.03289i | − | 0.411440i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.22879 | 0.490722 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.0872 | −1.35737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.0330 | − | 23.5868i | −0.943961 | − | 1.58662i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4175 | 1.30029 | 0.650147 | − | 0.759808i | \(-0.274707\pi\) | ||||
0.650147 | + | 0.759808i | \(0.274707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.37356 | 0.224904 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 21.4500i | − | 1.42368i | −0.702339 | − | 0.711842i | \(-0.747861\pi\) | ||
0.702339 | − | 0.711842i | \(-0.252139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6539 | 0.704032 | 0.352016 | − | 0.935994i | \(-0.385496\pi\) | ||||
0.352016 | + | 0.935994i | \(0.385496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.63153i | 0.633708i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.7340i | − | 1.62038i | −0.586166 | − | 0.810191i | \(-0.699364\pi\) | ||
0.586166 | − | 0.810191i | \(-0.300636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.3626i | 1.65447i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.1247 | −2.02177 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.6967 | −1.53282 | −0.766408 | − | 0.642355i | \(-0.777958\pi\) | ||||
−0.766408 | + | 0.642355i | \(0.777958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.04958i | − | 0.389688i | −0.980834 | − | 0.194844i | \(-0.937580\pi\) | ||
0.980834 | − | 0.194844i | \(-0.0624200\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 18.9601i | − | 1.21629i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 15.3253i | − | 0.979094i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.0707 | −0.831670 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.90739i | 0.310994i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.14423 | −0.261581 | −0.130791 | − | 0.991410i | \(-0.541752\pi\) | ||||
−0.130791 | + | 0.991410i | \(0.541752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.7378 | 1.86960 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.2780 | + | 20.6370i | 0.768876 | + | 1.29234i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.4226 | 1.83533 | 0.917664 | − | 0.397357i | \(-0.130072\pi\) | ||||
0.917664 | + | 0.397357i | \(0.130072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.06120 | 0.314488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.45988i | 0.337958i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.77247 | −0.479271 | −0.239636 | − | 0.970863i | \(-0.577028\pi\) | ||||
−0.239636 | + | 0.970863i | \(0.577028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.666501i | − | 0.0409428i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.1304i | 0.681168i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.48426i | − | 0.212439i | −0.994343 | − | 0.106220i | \(-0.966125\pi\) | ||
0.994343 | − | 0.106220i | \(-0.0338747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.3356 | 1.96425 | 0.982124 | − | 0.188233i | \(-0.0602760\pi\) | ||||
0.982124 | + | 0.188233i | \(0.0602760\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.2303 | 0.921782 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.51063i | 0.392606i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.1946i | 1.69405i | 0.531553 | + | 0.847025i | \(0.321609\pi\) | ||||
−0.531553 | + | 0.847025i | \(0.678391\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.6863i | 0.939114i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6074 | −0.752092 | −0.376046 | − | 0.926601i | \(-0.622717\pi\) | ||||
−0.376046 | + | 0.926601i | \(0.622717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 31.0152i | − | 1.84366i | −0.387594 | − | 0.921830i | \(-0.626694\pi\) | ||
0.387594 | − | 0.921830i | \(-0.373306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.4360 | 0.677413 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.7597 | −0.694154 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.11142 | + | 14.9400i | −0.477142 | + | 0.878826i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.8013 | −1.62974 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.10723 | −0.181527 | −0.0907633 | − | 0.995872i | \(-0.528931\pi\) | ||||
−0.0907633 | + | 0.995872i | \(0.528931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.55864i | − | 0.148970i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.84545 | 0.455239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 47.0243i | − | 2.71949i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.37007i | 0.136609i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.4051i | 0.597760i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.6324 | 1.52497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4347 | −1.62285 | −0.811426 | − | 0.584455i | \(-0.801308\pi\) | ||||
−0.811426 | + | 0.584455i | \(0.801308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.5197i | 0.825995i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.6607i | 1.90873i | 0.298651 | + | 0.954363i | \(0.403463\pi\) | ||||
−0.298651 | + | 0.954363i | \(0.596537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.3042i | − | 0.695474i | −0.937592 | − | 0.347737i | \(-0.886950\pi\) | ||
0.937592 | − | 0.347737i | \(-0.113050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.60988 | −0.316081 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.4950i | 1.71277i | 0.516339 | + | 0.856384i | \(0.327294\pi\) | ||||
−0.516339 | + | 0.856384i | \(0.672706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.5370 | −0.589960 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.1772 | −1.68433 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.13954 | + | 6.95779i | 0.230330 | + | 0.387142i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.2953 | 0.571079 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −40.2226 | −2.22431 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.96390i | − | 0.549328i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.55529 | −0.140451 | −0.0702256 | − | 0.997531i | \(-0.522372\pi\) | ||||
−0.0702256 | + | 0.997531i | \(0.522372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.9827i | 0.601847i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.92077i | − | 0.542030i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8364i | 0.590297i | 0.955451 | + | 0.295149i | \(0.0953692\pi\) | ||||
−0.955451 | + | 0.295149i | \(0.904631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.0108 | −1.46703 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.2730 | −1.63937 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0569i | 0.705008i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 41.1433i | 2.21508i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.510915i | − | 0.0274273i | −0.999906 | − | 0.0137137i | \(-0.995635\pi\) | ||
0.999906 | − | 0.0137137i | \(-0.00436533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3955 | −0.931157 | −0.465579 | − | 0.885007i | \(-0.654154\pi\) | ||||
−0.465579 | + | 0.885007i | \(0.654154\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 12.4060i | − | 0.662184i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8410 | 1.58827 | 0.794137 | − | 0.607739i | \(-0.207923\pi\) | ||||
0.794137 | + | 0.607739i | \(0.207923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4369 | −0.766229 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.82350 | − | 8.10740i | −0.255287 | − | 0.429089i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.4112 | −1.55226 | −0.776131 | − | 0.630571i | \(-0.782821\pi\) | ||||
−0.776131 | + | 0.630571i | \(0.782821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1443 | −0.797069 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.2967i | − | 0.802870i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.5794 | 1.18186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.6869i | 0.871049i | 0.900177 | + | 0.435525i | \(0.143437\pi\) | ||||
−0.900177 | + | 0.435525i | \(0.856563\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 25.5183i | − | 1.32843i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.261840i | 0.0135941i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.46715 | 0.438413 | 0.219206 | − | 0.975679i | \(-0.429653\pi\) | ||||
0.219206 | + | 0.975679i | \(0.429653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.1126 | 1.03861 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6622i | 0.858147i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.6790i | − | 1.31904i | −0.751686 | − | 0.659521i | \(-0.770759\pi\) | ||
0.751686 | − | 0.659521i | \(-0.229241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 28.9377i | − | 1.48252i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0159 | 0.920569 | 0.460284 | − | 0.887771i | \(-0.347747\pi\) | ||||
0.460284 | + | 0.887771i | \(0.347747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 10.8265i | − | 0.551770i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.14299 | −0.261433 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5210 | −0.837649 | −0.418825 | − | 0.908067i | \(-0.637558\pi\) | ||||
−0.418825 | + | 0.908067i | \(0.637558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0319 | + | 14.8928i | −1.26592 | + | 0.753159i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.25965 | 0.113984 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.9864 | 1.76035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7.10777i | − | 0.356729i | −0.983965 | − | 0.178364i | \(-0.942919\pi\) | ||
0.983965 | − | 0.178364i | \(-0.0570806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.49274 | −0.224918 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 23.7556i | − | 1.18630i | −0.805093 | − | 0.593148i | \(-0.797885\pi\) | ||
0.805093 | − | 0.593148i | \(-0.202115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.8707i | 2.38461i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.5973i | 1.37132i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1955 | −1.05062 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.3537 | −1.74813 | −0.874063 | − | 0.485813i | \(-0.838524\pi\) | ||||
−0.874063 | + | 0.485813i | \(0.838524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.3196i | 1.10095i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.00518i | 0.0494618i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.51625i | − | 0.270782i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.3860 | 1.58595 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.19866i | − | 0.0585585i | −0.999571 | − | 0.0292792i | \(-0.990679\pi\) | ||
0.999571 | − | 0.0292792i | \(-0.00932120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8949 | 0.530983 | 0.265492 | − | 0.964113i | \(-0.414466\pi\) | ||||
0.265492 | + | 0.964113i | \(0.414466\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.6214 | 1.05127 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.26054 | − | 5.48036i | −0.158160 | − | 0.265837i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.4627 | −0.506328 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −63.7822 | −3.07943 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.595134i | − | 0.0286666i | −0.999897 | − | 0.0143333i | \(-0.995437\pi\) | ||
0.999897 | − | 0.0143333i | \(-0.00456259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6870 | 0.994154 | 0.497077 | − | 0.867706i | \(-0.334407\pi\) | ||||
0.497077 | + | 0.867706i | \(0.334407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 14.5784i | − | 0.698979i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8715i | 0.663566i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.10626i | 0.386891i | 0.981111 | + | 0.193445i | \(0.0619662\pi\) | ||||
−0.981111 | + | 0.193445i | \(0.938034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.0647 | −0.622126 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.07515 | 0.288639 | 0.144320 | − | 0.989531i | \(-0.453901\pi\) | ||||
0.144320 | + | 0.989531i | \(0.453901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.5113i | − | 0.593094i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 45.0662i | − | 2.13156i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.9914i | − | 1.13222i | −0.824329 | − | 0.566111i | \(-0.808447\pi\) | ||
0.824329 | − | 0.566111i | \(-0.191553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49.2478 | 2.31899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 42.5046i | − | 1.99704i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.1200 | −0.802596 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.45563 | 0.161647 | 0.0808237 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808237 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.60396 | + | 3.92903i | −0.308246 | + | 0.183391i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.5005 | 1.93287 | 0.966436 | − | 0.256906i | \(-0.0827032\pi\) | ||||
0.966436 | + | 0.256906i | \(0.0827032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.955366 | 0.0443996 | 0.0221998 | − | 0.999754i | \(-0.492933\pi\) | ||||
0.0221998 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 41.8838i | − | 1.94232i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.3197 | −1.31048 | −0.655240 | − | 0.755421i | \(-0.727432\pi\) | ||||
−0.655240 | + | 0.755421i | \(0.727432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.89746i | 0.179968i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 0.0192196i | − | 0.000885593i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.92547i | − | 0.456373i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.03696 | −0.139345 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.568186 | −0.0260155 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.0796i | − | 0.826079i | −0.910713 | − | 0.413039i | \(-0.864467\pi\) | ||
0.910713 | − | 0.413039i | \(-0.135533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.5164i | 1.52822i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 16.1635i | − | 0.735463i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.2505 | 1.41901 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.7402i | − | 0.939828i | −0.882712 | − | 0.469914i | \(-0.844285\pi\) | ||
0.882712 | − | 0.469914i | \(-0.155715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.40940 | 0.289843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.46942 | 0.427349 | 0.213674 | − | 0.976905i | \(-0.431457\pi\) | ||||
0.213674 | + | 0.976905i | \(0.431457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.86960 | − | 5.27697i | 0.399467 | − | 0.237663i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.4932 | 1.05594 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.67163 | 0.254408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.8318i | 1.38022i | 0.723705 | + | 0.690110i | \(0.242438\pi\) | ||||
−0.723705 | + | 0.690110i | \(0.757562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.1021 | −1.61292 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0282i | 0.937603i | 0.883303 | + | 0.468802i | \(0.155314\pi\) | ||||
−0.883303 | + | 0.468802i | \(0.844686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 11.6961i | − | 0.520470i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 71.2678i | 3.16511i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.87582 | −0.349090 | −0.174545 | − | 0.984649i | \(-0.555845\pi\) | ||||
−0.174545 | + | 0.984649i | \(0.555845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.87052 | −0.392409 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.65961i | 0.161576i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 16.3211i | − | 0.719194i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.7272i | 1.83516i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.2308 | −1.54646 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.28579i | 0.187764i | 0.995583 | + | 0.0938820i | \(0.0299276\pi\) | ||||
−0.995583 | + | 0.0938820i | \(0.970072\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.03467 | 0.395058 | 0.197529 | − | 0.980297i | \(-0.436708\pi\) | ||||
0.197529 | + | 0.980297i | \(0.436708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.53875 | 0.154444 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4825 | − | 15.1608i | 1.11003 | − | 0.660415i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.9054 | −1.16980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.18122 | −0.0946569 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 77.8755i | − | 3.37316i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.9212 | 1.46654 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.6243i | 0.890005i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 25.2135i | − | 1.08602i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.7720i | − | 1.19401i | −0.802237 | − | 0.597006i | \(-0.796357\pi\) | ||
0.802237 | − | 0.597006i | \(-0.203643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.01189 | −0.257995 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45.2130 | 1.93671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.2621i | − | 0.524289i | −0.965029 | − | 0.262144i | \(-0.915570\pi\) | ||
0.965029 | − | 0.262144i | \(-0.0844297\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 22.7039i | − | 0.968978i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.91512i | − | 0.209391i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.7447 | −0.584483 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 29.3247i | − | 1.24477i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.41588 | −0.314221 | −0.157111 | − | 0.987581i | \(-0.550218\pi\) | ||||
−0.157111 | + | 0.987581i | \(0.550218\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.6951 | −0.663834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.2000 | + | 33.9524i | 0.852845 | + | 1.43347i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.04178 | −0.0860509 | −0.0430255 | − | 0.999074i | \(-0.513700\pi\) | ||||
−0.0430255 | + | 0.999074i | \(0.513700\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.3620 | 1.27734 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 10.8418i | − | 0.455314i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.6366 | −1.24243 | −0.621216 | − | 0.783639i | \(-0.713361\pi\) | ||||
−0.621216 | + | 0.783639i | \(0.713361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.3519i | − | 1.22834i | −0.789174 | − | 0.614169i | \(-0.789491\pi\) | ||
0.789174 | − | 0.614169i | \(-0.210509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 31.4453i | − | 1.31364i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.9260i | − | 0.455647i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.38873 | −0.141075 | −0.0705374 | − | 0.997509i | \(-0.522471\pi\) | ||||
−0.0705374 | + | 0.997509i | \(0.522471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.4062 | −0.515583 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.16710i | 0.0899066i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.09654i | − | 0.0454142i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 37.1499i | − | 1.53596i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.9740 | −1.27844 | −0.639218 | − | 0.769026i | \(-0.720742\pi\) | ||||
−0.639218 | + | 0.769026i | \(0.720742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.1212i | − | 0.581854i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.3057 | 2.06930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5290 | 0.925155 | 0.462577 | − | 0.886579i | \(-0.346925\pi\) | ||||
0.462577 | + | 0.886579i | \(0.346925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.42195 | + | 9.11328i | 0.222278 | + | 0.373608i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.8643 | −1.09948 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.2890 | 1.48273 | 0.741364 | − | 0.671103i | \(-0.234179\pi\) | ||||
0.741364 | + | 0.671103i | \(0.234179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5.37020i | − | 0.219055i | −0.993984 | − | 0.109527i | \(-0.965066\pi\) | ||
0.993984 | − | 0.109527i | \(-0.0349338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.45738 | −0.344411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.1946i | 0.699059i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 29.1625i | − | 1.18367i | −0.806059 | − | 0.591835i | \(-0.798404\pi\) | ||
0.806059 | − | 0.591835i | \(-0.201596\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.72722i | 0.232079i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 65.9832 | 2.66940 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.7291 | −1.20075 | −0.600374 | − | 0.799719i | \(-0.704982\pi\) | ||||
−0.600374 | + | 0.799719i | \(0.704982\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 68.1361i | 2.74751i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.474131i | − | 0.0190878i | −0.999954 | − | 0.00954391i | \(-0.996962\pi\) | ||
0.999954 | − | 0.00954391i | \(-0.00303797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.5114i | 1.66848i | 0.551399 | + | 0.834242i | \(0.314094\pi\) | ||||
−0.551399 | + | 0.834242i | \(0.685906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.1661 | −0.528338 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.91517i | 0.196922i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3411 | −1.21364 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.8149 | 0.751393 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.8414 | − | 10.6148i | 0.711384 | − | 0.423238i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.42025 | −0.136158 | −0.0680791 | − | 0.997680i | \(-0.521687\pi\) | ||||
−0.0680791 | + | 0.997680i | \(0.521687\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −65.4481 | −2.60133 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.5280i | 1.29083i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.8701 | −1.57971 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.3073i | 0.486869i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.25740i | 0.0496643i | 0.999692 | + | 0.0248322i | \(0.00790514\pi\) | ||||
−0.999692 | + | 0.0248322i | \(0.992095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.0990i | 1.69966i | 0.527059 | + | 0.849829i | \(0.323295\pi\) | ||||
−0.527059 | + | 0.849829i | \(0.676705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.7323 | 0.540707 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.97098 | 0.274058 | 0.137029 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137029 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.20954i | − | 0.165239i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.4544i | 0.644898i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.9941i | 1.17376i | 0.809674 | + | 0.586880i | \(0.199644\pi\) | ||||
−0.809674 | + | 0.586880i | \(0.800356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.54000 | −0.0992460 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 19.2488i | − | 0.750967i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.2812 | 1.33541 | 0.667703 | − | 0.744428i | \(-0.267278\pi\) | ||||
0.667703 | + | 0.744428i | \(0.267278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.6709 | 1.23186 | 0.615928 | − | 0.787803i | \(-0.288781\pi\) | ||||
0.615928 | + | 0.787803i | \(0.288781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 53.6890 | − | 31.9423i | 2.08511 | − | 1.24054i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.05015 | 0.195837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.6831 | 0.684691 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.1988i | 1.70882i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.8162 | 1.69151 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9400i | 1.15410i | 0.816708 | + | 0.577051i | \(0.195797\pi\) | ||||
−0.816708 | + | 0.577051i | \(0.804203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.88252i | − | 0.110948i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.31186i | 0.127285i | 0.997973 | + | 0.0636426i | \(0.0202718\pi\) | ||||
−0.997973 | + | 0.0636426i | \(0.979728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2770 | −0.471149 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.8250 | 1.87098 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.80915i | 0.184017i | 0.995758 | + | 0.0920085i | \(0.0293287\pi\) | ||||
−0.995758 | + | 0.0920085i | \(0.970671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.0888i | − | 0.958594i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2508i | 0.925226i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.73397 | −0.0660588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.1889i | − | 0.539772i | −0.962892 | − | 0.269886i | \(-0.913014\pi\) | ||
0.962892 | − | 0.269886i | \(-0.0869861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.22951 | −0.350600 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.4041 | −1.38089 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.4546 | + | 24.6634i | −1.57021 | + | 0.934194i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 56.3004 | 2.12948 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.33659 | −0.0882517 | −0.0441258 | − | 0.999026i | \(-0.514050\pi\) | ||||
−0.0441258 | + | 0.999026i | \(0.514050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.88689i | − | 0.372891i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −57.7311 | −2.17428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.59491i | 0.172809i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.65401i | 0.212341i | 0.994348 | + | 0.106170i | \(0.0338589\pi\) | ||||
−0.994348 | + | 0.106170i | \(0.966141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 29.8256i | − | 1.11855i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.8036 | 1.90261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 71.6956 | 2.68126 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 53.9392i | − | 2.01440i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 27.2950i | − | 1.01793i | −0.860787 | − | 0.508966i | \(-0.830028\pi\) | ||
0.860787 | − | 0.508966i | \(-0.169972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.41188i | 0.238791i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.7702 | 0.512120 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.87144i | 0.143782i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.29246 | 0.270462 | 0.135231 | − | 0.990814i | \(-0.456822\pi\) | ||||
0.135231 | + | 0.990814i | \(0.456822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.7997 | 0.399987 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.97070 | + | 8.35482i | 0.183848 | + | 0.309014i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.4584 | 1.64211 | 0.821055 | − | 0.570850i | \(-0.193386\pi\) | ||||
0.821055 | + | 0.570850i | \(0.193386\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.8838 | 1.28671 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.3219i | − | 0.601225i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.3561 | 1.44774 | 0.723868 | − | 0.689939i | \(-0.242362\pi\) | ||||
0.723868 | + | 0.689939i | \(0.242362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 29.7520i | − | 1.09297i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 35.7207i | − | 1.31047i | −0.755426 | − | 0.655234i | \(-0.772570\pi\) | ||
0.755426 | − | 0.655234i | \(-0.227430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.6575i | 1.85595i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.70256 | −0.172058 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.3262 | −0.486930 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 37.7059i | − | 1.37591i | −0.725754 | − | 0.687954i | \(-0.758509\pi\) | ||
0.725754 | − | 0.687954i | \(-0.241491\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9.43321i | − | 0.343765i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.7782i | 1.73883i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.21403 | 0.116816 | 0.0584080 | − | 0.998293i | \(-0.481398\pi\) | ||||
0.0584080 | + | 0.998293i | \(0.481398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 67.6900i | 2.45699i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.2104 | −0.732627 | −0.366313 | − | 0.930492i | \(-0.619380\pi\) | ||||
−0.366313 | + | 0.930492i | \(0.619380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.7623 | −0.643038 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.7756 | + | 11.7655i | −0.714987 | + | 0.425382i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.65655 | −0.240354 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.75506 | 0.315716 | 0.157858 | − | 0.987462i | \(-0.449541\pi\) | ||||
0.157858 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 66.9725i | 2.41195i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.8172 | 1.75583 | 0.877916 | − | 0.478814i | \(-0.158933\pi\) | ||||
0.877916 | + | 0.478814i | \(0.158933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1227i | 0.399539i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.5205i | 0.413294i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.9722i | 0.823065i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.7519 | −0.849909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.66517 | 0.166719 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0216042i | 0.000771086i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.5500i | − | 0.732527i | −0.930511 | − | 0.366264i | \(-0.880637\pi\) | ||
0.930511 | − | 0.366264i | \(-0.119363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 17.6919i | − | 0.629849i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9280 | −0.424110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 69.2867i | − | 2.46044i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.51711 | 0.0538063 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.49022 | 0.0527864 | 0.0263932 | − | 0.999652i | \(-0.491598\pi\) | ||||
0.0263932 | + | 0.999652i | \(0.491598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.8971 | − | 35.1241i | −0.739286 | − | 1.24260i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6658 | −0.376858 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.1483 | 1.31093 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.1689i | 0.640368i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.93098 | 0.279184 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.0847i | − | 0.530351i | −0.964200 | − | 0.265175i | \(-0.914570\pi\) | ||
0.964200 | − | 0.265175i | \(-0.0854298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.2886i | − | 0.536857i | −0.963300 | − | 0.268429i | \(-0.913496\pi\) | ||
0.963300 | − | 0.268429i | \(-0.0865043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 73.6033i | 2.58138i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.20461 | −0.252367 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.62985 | 0.161978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.5946i | 0.509978i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24.2068i | − | 0.844823i | −0.906404 | − | 0.422412i | \(-0.861184\pi\) | ||
0.906404 | − | 0.422412i | \(-0.138816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.7573i | 1.24642i | 0.782054 | + | 0.623211i | \(0.214172\pi\) | ||||
−0.782054 | + | 0.623211i | \(0.785828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.8197 | −0.515955 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.32093i | − | 0.254574i | −0.991866 | − | 0.127287i | \(-0.959373\pi\) | ||
0.991866 | − | 0.127287i | \(-0.0406269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.26753 | 0.217680 | 0.108840 | − | 0.994059i | \(-0.465286\pi\) | ||||
0.108840 | + | 0.994059i | \(0.465286\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.1774 | −2.22629 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.6270 | + | 21.2236i | 0.437499 | + | 0.735354i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.5813 | 1.40437 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.4031 | 0.463278 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.79735i | 0.165623i | 0.996565 | + | 0.0828115i | \(0.0263899\pi\) | ||||
−0.996565 | + | 0.0828115i | \(0.973610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7343 | 0.783943 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 28.6972i | − | 0.988385i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 80.1100i | − | 2.75587i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.75503i | − | 0.232105i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 70.5976 | 2.42290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5699 | 1.21932 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.1214i | − | 0.346552i | −0.984873 | − | 0.173276i | \(-0.944565\pi\) | ||
0.984873 | − | 0.173276i | \(-0.0554352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9587i | 0.374780i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.759286i | − | 0.0259367i | −0.999916 | − | 0.0129684i | \(-0.995872\pi\) | ||
0.999916 | − | 0.0129684i | \(-0.00412807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7082 | 0.979512 | 0.489756 | − | 0.871859i | \(-0.337086\pi\) | ||||
0.489756 | + | 0.871859i | \(0.337086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 26.7678i | − | 0.912245i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.5354 | 1.10752 | 0.553759 | − | 0.832677i | \(-0.313193\pi\) | ||||
0.553759 | + | 0.832677i | \(0.313193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.6018 | 1.34650 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.0070 | − | 18.4634i | −1.15494 | − | 0.627051i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.5604 | 1.95260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.8098 | −0.874533 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 26.6408i | − | 0.901655i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.88170 | 0.300256 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.0504i | 1.48748i | 0.668472 | + | 0.743738i | \(0.266949\pi\) | ||||
−0.668472 | + | 0.743738i | \(0.733051\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7.07278i | − | 0.238559i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.31272i | 0.280063i | 0.990147 | + | 0.140031i | \(0.0447203\pi\) | ||||
−0.990147 | + | 0.140031i | \(0.955280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.5567 | 0.523526 | 0.261763 | − | 0.965132i | \(-0.415696\pi\) | ||||
0.261763 | + | 0.965132i | \(0.415696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.82405 | 0.195773 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 21.0174i | − | 0.705694i | −0.935681 | − | 0.352847i | \(-0.885214\pi\) | ||
0.935681 | − | 0.352847i | \(-0.114786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.7789i | − | 0.428590i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.4038i | 1.52109i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.4642 | −0.651343 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 23.1832i | − | 0.774927i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 107.038 | 3.57390 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0013 | −0.600378 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.549152 | + | 0.923022i | 0.0182949 | + | 0.0307503i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.39482 | −0.179529 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.75778 | 0.224636 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.9651i | 1.62586i | 0.582363 | + | 0.812929i | \(0.302128\pi\) | ||||
−0.582363 | + | 0.812929i | \(0.697872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.97083 | −0.330711 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.64946i | − | 0.187175i | −0.995611 | − | 0.0935875i | \(-0.970167\pi\) | ||
0.995611 | − | 0.0935875i | \(-0.0298335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.07547i | − | 0.300354i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 60.6214i | 2.00408i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.997860 | 0.0329522 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.7510 | −0.651527 | −0.325763 | − | 0.945451i | \(-0.605621\pi\) | ||||
−0.325763 | + | 0.945451i | \(0.605621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 64.7238i | − | 2.13272i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.5588i | 1.23626i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.78750i | 0.256051i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.9136 | −0.456983 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 13.6660i | − | 0.448367i | −0.974547 | − | 0.224183i | \(-0.928029\pi\) | ||
0.974547 | − | 0.224183i | \(-0.0719715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.7611 | 0.385456 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −76.6195 | −2.50841 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.7062 | − | 38.1649i | −0.742573 | − | 1.24813i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7283 | 1.68989 | 0.844945 | − | 0.534853i | \(-0.179633\pi\) | ||||
0.844945 | + | 0.534853i | \(0.179633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.0072 | 0.913979 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7528i | 0.709120i | 0.935033 | + | 0.354560i | \(0.115369\pi\) | ||||
−0.935033 | + | 0.354560i | \(0.884631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −82.6468 | −2.69135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.79333i | 0.155927i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.9877i | − | 0.422044i | −0.977481 | − | 0.211022i | \(-0.932321\pi\) | ||
0.977481 | − | 0.211022i | \(-0.0676791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 58.7426i | − | 1.90686i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −69.4135 | −2.25089 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.8930 | 1.55141 | 0.775704 | − | 0.631097i | \(-0.217395\pi\) | ||||
0.775704 | + | 0.631097i | \(0.217395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.3467i | 1.14379i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 23.9847i | − | 0.775314i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.85634i | 0.318278i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7180 | −0.668324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 28.9176i | − | 0.931856i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.9454 | 0.448918 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.36657 | 0.236893 | 0.118447 | − | 0.992960i | \(-0.462209\pi\) | ||||
0.118447 | + | 0.992960i | \(0.462209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.8375 | + | 9.42254i | −0.508775 | + | 0.302696i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0629 | −0.515484 | −0.257742 | − | 0.966214i | \(-0.582979\pi\) | ||||
−0.257742 | + | 0.966214i | \(0.582979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.3016 | 0.458490 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.4344i | 0.750501i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.6732 | 0.373459 | 0.186730 | − | 0.982411i | \(-0.440211\pi\) | ||||
0.186730 | + | 0.982411i | \(0.440211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20.5839i | − | 0.657866i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 38.5437i | − | 1.23061i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.6125i | − | 0.976386i | −0.872736 | − | 0.488193i | \(-0.837656\pi\) | ||
0.872736 | − | 0.488193i | \(-0.162344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.5472 | −1.80174 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.6801 | 0.721916 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.6568i | 0.529654i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.3755i | − | 0.393122i | −0.980492 | − | 0.196561i | \(-0.937023\pi\) | ||
0.980492 | − | 0.196561i | \(-0.0629773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.81642i | − | 0.184578i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.1973 | 0.957320 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.64552i | 0.273806i | 0.990584 | + | 0.136903i | \(0.0437149\pi\) | ||||
−0.990584 | + | 0.136903i | \(0.956285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.38410 | 0.296900 |
(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 | 4012.2.b.b.237.38 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.9 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.9 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.38 | yes | 46 | 1.1 | even | 1 | trivial |