Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + \cdots + 48312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.8 | ||
Root | \(-1.59440 - 0.311973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.n.122.5 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89788i | 0.948941i | 0.880271 | + | 0.474471i | \(0.157360\pi\) | ||||
−0.880271 | + | 0.474471i | \(0.842640\pi\) | |||||||
\(3\) | −2.98373 | + | 0.311973i | −0.994578 | + | 0.103991i | ||||
\(4\) | 0.398042 | 0.0995104 | ||||||||
\(5\) | − | 8.25850i | − | 1.65170i | −0.563890 | − | 0.825850i | \(-0.690696\pi\) | ||
0.563890 | − | 0.825850i | \(-0.309304\pi\) | |||||||
\(6\) | −0.592088 | − | 5.66278i | −0.0986814 | − | 0.943796i | ||||
\(7\) | −3.60566 | −0.515094 | −0.257547 | − | 0.966266i | \(-0.582914\pi\) | ||||
−0.257547 | + | 0.966266i | \(0.582914\pi\) | |||||||
\(8\) | 8.34697i | 1.04337i | ||||||||
\(9\) | 8.80535 | − | 1.86169i | 0.978372 | − | 0.206854i | ||||
\(10\) | 15.6737 | 1.56737 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.18765 | + | 0.124178i | −0.0989709 | + | 0.0103482i | ||||
\(13\) | −13.1106 | −1.00851 | −0.504255 | − | 0.863555i | \(-0.668233\pi\) | ||||
−0.504255 | + | 0.863555i | \(0.668233\pi\) | |||||||
\(14\) | − | 6.84311i | − | 0.488794i | ||||||
\(15\) | 2.57643 | + | 24.6412i | 0.171762 | + | 1.64275i | ||||
\(16\) | −14.2494 | −0.890587 | ||||||||
\(17\) | 25.6297i | 1.50763i | 0.657087 | + | 0.753815i | \(0.271788\pi\) | ||||
−0.657087 | + | 0.753815i | \(0.728212\pi\) | |||||||
\(18\) | 3.53327 | + | 16.7115i | 0.196293 | + | 0.928417i | ||||
\(19\) | −12.5064 | −0.658232 | −0.329116 | − | 0.944289i | \(-0.606751\pi\) | ||||
−0.329116 | + | 0.944289i | \(0.606751\pi\) | |||||||
\(20\) | − | 3.28723i | − | 0.164361i | ||||||
\(21\) | 10.7583 | − | 1.12487i | 0.512301 | − | 0.0535651i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.7941i | 1.20844i | 0.796818 | + | 0.604219i | \(0.206515\pi\) | ||||
−0.796818 | + | 0.604219i | \(0.793485\pi\) | |||||||
\(24\) | −2.60403 | − | 24.9051i | −0.108501 | − | 1.03771i | ||||
\(25\) | −43.2029 | −1.72811 | ||||||||
\(26\) | − | 24.8824i | − | 0.957017i | ||||||
\(27\) | −25.6920 | + | 8.30182i | −0.951556 | + | 0.307475i | ||||
\(28\) | −1.43520 | −0.0512572 | ||||||||
\(29\) | 9.48941i | 0.327221i | 0.986525 | + | 0.163611i | \(0.0523140\pi\) | ||||
−0.986525 | + | 0.163611i | \(0.947686\pi\) | |||||||
\(30\) | −46.7661 | + | 4.88976i | −1.55887 | + | 0.162992i | ||||
\(31\) | −5.08780 | −0.164123 | −0.0820613 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820613 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(32\) | 6.34419i | 0.198256i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −48.6422 | −1.43065 | ||||||||
\(35\) | 29.7773i | 0.850781i | ||||||||
\(36\) | 3.50490 | − | 0.741031i | 0.0973582 | − | 0.0205842i | ||||
\(37\) | −34.6432 | −0.936303 | −0.468152 | − | 0.883648i | \(-0.655080\pi\) | ||||
−0.468152 | + | 0.883648i | \(0.655080\pi\) | |||||||
\(38\) | − | 23.7357i | − | 0.624624i | ||||||
\(39\) | 39.1187 | − | 4.09017i | 1.00304 | − | 0.104876i | ||||
\(40\) | 68.9334 | 1.72334 | ||||||||
\(41\) | − | 34.2402i | − | 0.835127i | −0.908648 | − | 0.417563i | \(-0.862884\pi\) | ||
0.908648 | − | 0.417563i | \(-0.137116\pi\) | |||||||
\(42\) | 2.13487 | + | 20.4180i | 0.0508302 | + | 0.486144i | ||||
\(43\) | 39.5371 | 0.919467 | 0.459734 | − | 0.888057i | \(-0.347945\pi\) | ||||
0.459734 | + | 0.888057i | \(0.347945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15.3748 | − | 72.7190i | −0.341662 | − | 1.61598i | ||||
\(46\) | −52.7499 | −1.14674 | ||||||||
\(47\) | 19.4547i | 0.413930i | 0.978348 | + | 0.206965i | \(0.0663587\pi\) | ||||
−0.978348 | + | 0.206965i | \(0.933641\pi\) | |||||||
\(48\) | 42.5164 | − | 4.44543i | 0.885759 | − | 0.0926131i | ||||
\(49\) | −35.9992 | −0.734678 | ||||||||
\(50\) | − | 81.9940i | − | 1.63988i | ||||||
\(51\) | −7.99578 | − | 76.4722i | −0.156780 | − | 1.49946i | ||||
\(52\) | −5.21858 | −0.100357 | ||||||||
\(53\) | − | 17.2882i | − | 0.326192i | −0.986610 | − | 0.163096i | \(-0.947852\pi\) | ||
0.986610 | − | 0.163096i | \(-0.0521480\pi\) | |||||||
\(54\) | −15.7559 | − | 48.7604i | −0.291776 | − | 0.902971i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 30.0963i | − | 0.537434i | ||||||
\(57\) | 37.3158 | − | 3.90167i | 0.654664 | − | 0.0684503i | ||||
\(58\) | −18.0098 | −0.310514 | ||||||||
\(59\) | − | 27.1498i | − | 0.460167i | −0.973171 | − | 0.230083i | \(-0.926100\pi\) | ||
0.973171 | − | 0.230083i | \(-0.0738999\pi\) | |||||||
\(60\) | 1.02553 | + | 9.80822i | 0.0170921 | + | 0.163470i | ||||
\(61\) | −43.7397 | −0.717044 | −0.358522 | − | 0.933521i | \(-0.616719\pi\) | ||||
−0.358522 | + | 0.933521i | \(0.616719\pi\) | |||||||
\(62\) | − | 9.65605i | − | 0.155743i | ||||||
\(63\) | −31.7490 | + | 6.71262i | −0.503953 | + | 0.106549i | ||||
\(64\) | −69.0381 | −1.07872 | ||||||||
\(65\) | 108.274i | 1.66576i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 82.0860 | 1.22516 | 0.612582 | − | 0.790407i | \(-0.290131\pi\) | ||||
0.612582 | + | 0.790407i | \(0.290131\pi\) | |||||||
\(68\) | 10.2017i | 0.150025i | ||||||||
\(69\) | −8.67101 | − | 82.9302i | −0.125667 | − | 1.20189i | ||||
\(70\) | −56.5139 | −0.807341 | ||||||||
\(71\) | 117.008i | 1.64800i | 0.566586 | + | 0.824002i | \(0.308264\pi\) | ||||
−0.566586 | + | 0.824002i | \(0.691736\pi\) | |||||||
\(72\) | 15.5395 | + | 73.4979i | 0.215826 | + | 1.02080i | ||||
\(73\) | −107.556 | −1.47337 | −0.736683 | − | 0.676238i | \(-0.763609\pi\) | ||||
−0.736683 | + | 0.676238i | \(0.763609\pi\) | |||||||
\(74\) | − | 65.7488i | − | 0.888497i | ||||||
\(75\) | 128.906 | − | 13.4781i | 1.71874 | − | 0.179708i | ||||
\(76\) | −4.97808 | −0.0655010 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.76265 | + | 74.2426i | 0.0995212 | + | 0.951828i | ||||
\(79\) | −62.8893 | −0.796068 | −0.398034 | − | 0.917371i | \(-0.630307\pi\) | ||||
−0.398034 | + | 0.917371i | \(0.630307\pi\) | |||||||
\(80\) | 117.679i | 1.47098i | ||||||||
\(81\) | 74.0682 | − | 32.7857i | 0.914422 | − | 0.404761i | ||||
\(82\) | 64.9839 | 0.792486 | ||||||||
\(83\) | 49.1246i | 0.591862i | 0.955209 | + | 0.295931i | \(0.0956299\pi\) | ||||
−0.955209 | + | 0.295931i | \(0.904370\pi\) | |||||||
\(84\) | 4.28226 | − | 0.447744i | 0.0509793 | − | 0.00533029i | ||||
\(85\) | 211.663 | 2.49015 | ||||||||
\(86\) | 75.0368i | 0.872521i | ||||||||
\(87\) | −2.96044 | − | 28.3139i | −0.0340281 | − | 0.325447i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 69.1475i | 0.776938i | 0.921462 | + | 0.388469i | \(0.126996\pi\) | ||||
−0.921462 | + | 0.388469i | \(0.873004\pi\) | |||||||
\(90\) | 138.012 | − | 29.1795i | 1.53347 | − | 0.324217i | ||||
\(91\) | 47.2724 | 0.519477 | ||||||||
\(92\) | 11.0632i | 0.120252i | ||||||||
\(93\) | 15.1806 | − | 1.58726i | 0.163233 | − | 0.0170673i | ||||
\(94\) | −36.9228 | −0.392795 | ||||||||
\(95\) | 103.284i | 1.08720i | ||||||||
\(96\) | −1.97922 | − | 18.9294i | −0.0206168 | − | 0.197181i | ||||
\(97\) | −16.0182 | −0.165136 | −0.0825682 | − | 0.996585i | \(-0.526312\pi\) | ||||
−0.0825682 | + | 0.996585i | \(0.526312\pi\) | |||||||
\(98\) | − | 68.3223i | − | 0.697167i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.1965 | −0.171965 | ||||||||
\(101\) | − | 79.5876i | − | 0.787996i | −0.919111 | − | 0.393998i | \(-0.871092\pi\) | ||
0.919111 | − | 0.393998i | \(-0.128908\pi\) | |||||||
\(102\) | 145.135 | − | 15.1750i | 1.42290 | − | 0.148775i | ||||
\(103\) | 22.1291 | 0.214845 | 0.107423 | − | 0.994213i | \(-0.465740\pi\) | ||||
0.107423 | + | 0.994213i | \(0.465740\pi\) | |||||||
\(104\) | − | 109.434i | − | 1.05225i | ||||||
\(105\) | −9.28972 | − | 88.8476i | −0.0884736 | − | 0.846168i | ||||
\(106\) | 32.8109 | 0.309537 | ||||||||
\(107\) | 200.970i | 1.87823i | 0.343607 | + | 0.939114i | \(0.388351\pi\) | ||||
−0.343607 | + | 0.939114i | \(0.611649\pi\) | |||||||
\(108\) | −10.2265 | + | 3.30447i | −0.0946898 | + | 0.0305970i | ||||
\(109\) | −31.8118 | −0.291852 | −0.145926 | − | 0.989296i | \(-0.546616\pi\) | ||||
−0.145926 | + | 0.989296i | \(0.546616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 103.366 | − | 10.8078i | 0.931227 | − | 0.0973672i | ||||
\(112\) | 51.3784 | 0.458736 | ||||||||
\(113\) | − | 95.2227i | − | 0.842679i | −0.906903 | − | 0.421339i | \(-0.861560\pi\) | ||
0.906903 | − | 0.421339i | \(-0.138440\pi\) | |||||||
\(114\) | 7.40490 | + | 70.8210i | 0.0649553 | + | 0.621237i | ||||
\(115\) | 229.537 | 1.99598 | ||||||||
\(116\) | 3.77718i | 0.0325619i | ||||||||
\(117\) | −115.444 | + | 24.4079i | −0.986698 | + | 0.208615i | ||||
\(118\) | 51.5272 | 0.436671 | ||||||||
\(119\) | − | 92.4119i | − | 0.776571i | ||||||
\(120\) | −205.679 | + | 21.5054i | −1.71399 | + | 0.179212i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 83.0128i | − | 0.680432i | ||||||
\(123\) | 10.6820 | + | 102.164i | 0.0868457 | + | 0.830599i | ||||
\(124\) | −2.02516 | −0.0163319 | ||||||||
\(125\) | 150.328i | 1.20263i | ||||||||
\(126\) | −12.7398 | − | 60.2560i | −0.101109 | − | 0.478222i | ||||
\(127\) | −94.9399 | −0.747558 | −0.373779 | − | 0.927518i | \(-0.621938\pi\) | ||||
−0.373779 | + | 0.927518i | \(0.621938\pi\) | |||||||
\(128\) | − | 105.649i | − | 0.825386i | ||||||
\(129\) | −117.968 | + | 12.3345i | −0.914482 | + | 0.0956164i | ||||
\(130\) | −205.492 | −1.58071 | ||||||||
\(131\) | − | 143.710i | − | 1.09702i | −0.836143 | − | 0.548511i | \(-0.815195\pi\) | ||
0.836143 | − | 0.548511i | \(-0.184805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.0938 | 0.339051 | ||||||||
\(134\) | 155.790i | 1.16261i | ||||||||
\(135\) | 68.5606 | + | 212.178i | 0.507856 | + | 1.57169i | ||||
\(136\) | −213.930 | −1.57302 | ||||||||
\(137\) | − | 208.513i | − | 1.52200i | −0.648754 | − | 0.760998i | \(-0.724710\pi\) | ||
0.648754 | − | 0.760998i | \(-0.275290\pi\) | |||||||
\(138\) | 157.392 | − | 16.4566i | 1.14052 | − | 0.119250i | ||||
\(139\) | 80.0972 | 0.576239 | 0.288119 | − | 0.957595i | \(-0.406970\pi\) | ||||
0.288119 | + | 0.957595i | \(0.406970\pi\) | |||||||
\(140\) | 11.8526i | 0.0846616i | ||||||||
\(141\) | −6.06935 | − | 58.0477i | −0.0430450 | − | 0.411686i | ||||
\(142\) | −222.068 | −1.56386 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −125.471 | + | 26.5280i | −0.871325 | + | 0.184222i | ||||
\(145\) | 78.3683 | 0.540471 | ||||||||
\(146\) | − | 204.128i | − | 1.39814i | ||||||
\(147\) | 107.412 | − | 11.2308i | 0.730695 | − | 0.0764000i | ||||
\(148\) | −13.7895 | −0.0931720 | ||||||||
\(149\) | 94.4891i | 0.634155i | 0.948400 | + | 0.317078i | \(0.102702\pi\) | ||||
−0.948400 | + | 0.317078i | \(0.897298\pi\) | |||||||
\(150\) | 25.5799 | + | 244.648i | 0.170533 | + | 1.63099i | ||||
\(151\) | 182.072 | 1.20577 | 0.602887 | − | 0.797826i | \(-0.294017\pi\) | ||||
0.602887 | + | 0.797826i | \(0.294017\pi\) | |||||||
\(152\) | − | 104.391i | − | 0.686780i | ||||||
\(153\) | 47.7146 | + | 225.678i | 0.311860 | + | 1.47502i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0176i | 0.271081i | ||||||||
\(156\) | 15.5709 | − | 1.62806i | 0.0998132 | − | 0.0104363i | ||||
\(157\) | 144.073 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(158\) | − | 119.357i | − | 0.755422i | ||||||
\(159\) | 5.39344 | + | 51.5833i | 0.0339210 | + | 0.324423i | ||||
\(160\) | 52.3935 | 0.327459 | ||||||||
\(161\) | − | 100.216i | − | 0.622459i | ||||||
\(162\) | 62.2233 | + | 140.573i | 0.384095 | + | 0.867733i | ||||
\(163\) | 56.5652 | 0.347026 | 0.173513 | − | 0.984832i | \(-0.444488\pi\) | ||||
0.173513 | + | 0.984832i | \(0.444488\pi\) | |||||||
\(164\) | − | 13.6290i | − | 0.0831038i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −93.2327 | −0.561643 | ||||||||
\(167\) | − | 131.092i | − | 0.784982i | −0.919756 | − | 0.392491i | \(-0.871613\pi\) | ||
0.919756 | − | 0.392491i | \(-0.128387\pi\) | |||||||
\(168\) | 9.38924 | + | 89.7994i | 0.0558883 | + | 0.534520i | ||||
\(169\) | 2.88870 | 0.0170929 | ||||||||
\(170\) | 401.711i | 2.36301i | ||||||||
\(171\) | −110.123 | + | 23.2831i | −0.643996 | + | 0.136158i | ||||
\(172\) | 15.7374 | 0.0914966 | ||||||||
\(173\) | − | 181.736i | − | 1.05050i | −0.850949 | − | 0.525248i | \(-0.823972\pi\) | ||
0.850949 | − | 0.525248i | \(-0.176028\pi\) | |||||||
\(174\) | 53.7364 | − | 5.61857i | 0.308830 | − | 0.0322906i | ||||
\(175\) | 155.775 | 0.890141 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.47002 | + | 81.0079i | 0.0478532 | + | 0.457672i | ||||
\(178\) | −131.234 | −0.737269 | ||||||||
\(179\) | − | 11.9126i | − | 0.0665507i | −0.999446 | − | 0.0332754i | \(-0.989406\pi\) | ||
0.999446 | − | 0.0332754i | \(-0.0105938\pi\) | |||||||
\(180\) | −6.11980 | − | 28.9452i | −0.0339989 | − | 0.160807i | ||||
\(181\) | −84.7596 | −0.468285 | −0.234143 | − | 0.972202i | \(-0.575228\pi\) | ||||
−0.234143 | + | 0.972202i | \(0.575228\pi\) | |||||||
\(182\) | 89.7175i | 0.492953i | ||||||||
\(183\) | 130.508 | − | 13.6456i | 0.713156 | − | 0.0745661i | ||||
\(184\) | −231.996 | −1.26085 | ||||||||
\(185\) | 286.101i | 1.54649i | ||||||||
\(186\) | 3.01243 | + | 28.8111i | 0.0161958 | + | 0.154898i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.74379i | 0.0411904i | ||||||||
\(189\) | 92.6366 | − | 29.9335i | 0.490141 | − | 0.158378i | ||||
\(190\) | −196.021 | −1.03169 | ||||||||
\(191\) | 69.0031i | 0.361273i | 0.983550 | + | 0.180636i | \(0.0578157\pi\) | ||||
−0.983550 | + | 0.180636i | \(0.942184\pi\) | |||||||
\(192\) | 205.991 | − | 21.5380i | 1.07287 | − | 0.112177i | ||||
\(193\) | −118.824 | −0.615670 | −0.307835 | − | 0.951440i | \(-0.599604\pi\) | ||||
−0.307835 | + | 0.951440i | \(0.599604\pi\) | |||||||
\(194\) | − | 30.4007i | − | 0.156705i | ||||||
\(195\) | −33.7786 | − | 323.061i | −0.173224 | − | 1.65673i | ||||
\(196\) | −14.3292 | −0.0731082 | ||||||||
\(197\) | − | 305.098i | − | 1.54872i | −0.632744 | − | 0.774361i | \(-0.718071\pi\) | ||
0.632744 | − | 0.774361i | \(-0.281929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 125.117 | 0.628727 | 0.314364 | − | 0.949303i | \(-0.398209\pi\) | ||||
0.314364 | + | 0.949303i | \(0.398209\pi\) | |||||||
\(200\) | − | 360.613i | − | 1.80306i | ||||||
\(201\) | −244.923 | + | 25.6086i | −1.21852 | + | 0.127406i | ||||
\(202\) | 151.048 | 0.747762 | ||||||||
\(203\) | − | 34.2156i | − | 0.168550i | ||||||
\(204\) | −3.18265 | − | 30.4391i | −0.0156012 | − | 0.149211i | ||||
\(205\) | −282.773 | −1.37938 | ||||||||
\(206\) | 41.9984i | 0.203876i | ||||||||
\(207\) | 51.7440 | + | 244.736i | 0.249971 | + | 1.18230i | ||||
\(208\) | 186.819 | 0.898166 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 168.622 | − | 17.6308i | 0.802964 | − | 0.0839562i | ||||
\(211\) | −206.404 | −0.978218 | −0.489109 | − | 0.872223i | \(-0.662678\pi\) | ||||
−0.489109 | + | 0.872223i | \(0.662678\pi\) | |||||||
\(212\) | − | 6.88141i | − | 0.0324595i | ||||||
\(213\) | −36.5035 | − | 349.122i | −0.171378 | − | 1.63907i | ||||
\(214\) | −381.418 | −1.78233 | ||||||||
\(215\) | − | 326.517i | − | 1.51868i | ||||||
\(216\) | −69.2950 | − | 214.450i | −0.320810 | − | 0.992826i | ||||
\(217\) | 18.3449 | 0.0845385 | ||||||||
\(218\) | − | 60.3751i | − | 0.276950i | ||||||
\(219\) | 320.918 | − | 33.5545i | 1.46538 | − | 0.153217i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 336.022i | − | 1.52046i | ||||||
\(222\) | 20.5119 | + | 196.177i | 0.0923957 | + | 0.883680i | ||||
\(223\) | −69.1464 | −0.310073 | −0.155037 | − | 0.987909i | \(-0.549550\pi\) | ||||
−0.155037 | + | 0.987909i | \(0.549550\pi\) | |||||||
\(224\) | − | 22.8750i | − | 0.102120i | ||||||
\(225\) | −380.416 | + | 80.4303i | −1.69074 | + | 0.357468i | ||||
\(226\) | 180.722 | 0.799653 | ||||||||
\(227\) | − | 99.6917i | − | 0.439171i | −0.975593 | − | 0.219585i | \(-0.929530\pi\) | ||
0.975593 | − | 0.219585i | \(-0.0704704\pi\) | |||||||
\(228\) | 14.8533 | − | 1.55303i | 0.0651459 | − | 0.00681152i | ||||
\(229\) | 248.362 | 1.08455 | 0.542276 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542276 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(230\) | 435.635i | 1.89407i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −79.2078 | −0.341413 | ||||||||
\(233\) | 290.908i | 1.24853i | 0.781212 | + | 0.624265i | \(0.214602\pi\) | ||||
−0.781212 | + | 0.624265i | \(0.785398\pi\) | |||||||
\(234\) | −46.3234 | − | 219.098i | −0.197963 | − | 0.936318i | ||||
\(235\) | 160.667 | 0.683689 | ||||||||
\(236\) | − | 10.8068i | − | 0.0457914i | ||||||
\(237\) | 187.645 | − | 19.6198i | 0.791752 | − | 0.0827839i | ||||
\(238\) | 175.387 | 0.736920 | ||||||||
\(239\) | 104.939i | 0.439074i | 0.975604 | + | 0.219537i | \(0.0704546\pi\) | ||||
−0.975604 | + | 0.219537i | \(0.929545\pi\) | |||||||
\(240\) | −36.7126 | − | 351.122i | −0.152969 | − | 1.46301i | ||||
\(241\) | 88.3764 | 0.366707 | 0.183354 | − | 0.983047i | \(-0.441305\pi\) | ||||
0.183354 | + | 0.983047i | \(0.441305\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −210.772 | + | 120.931i | −0.867373 | + | 0.497658i | ||||
\(244\) | −17.4102 | −0.0713534 | ||||||||
\(245\) | 297.300i | 1.21347i | ||||||||
\(246\) | −193.895 | + | 20.2732i | −0.788190 | + | 0.0824115i | ||||
\(247\) | 163.967 | 0.663834 | ||||||||
\(248\) | − | 42.4677i | − | 0.171241i | ||||||
\(249\) | −15.3255 | − | 146.575i | −0.0615484 | − | 0.588653i | ||||
\(250\) | −285.306 | −1.14122 | ||||||||
\(251\) | 6.34574i | 0.0252818i | 0.999920 | + | 0.0126409i | \(0.00402383\pi\) | ||||
−0.999920 | + | 0.0126409i | \(0.995976\pi\) | |||||||
\(252\) | −12.6374 | + | 2.67190i | −0.0501486 | + | 0.0106028i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 180.185i | − | 0.709389i | ||||||
\(255\) | −631.546 | + | 66.0332i | −2.47665 | + | 0.258954i | ||||
\(256\) | −75.6421 | −0.295477 | ||||||||
\(257\) | 179.734i | 0.699355i | 0.936870 | + | 0.349678i | \(0.113709\pi\) | ||||
−0.936870 | + | 0.349678i | \(0.886291\pi\) | |||||||
\(258\) | −23.4095 | − | 223.890i | −0.0907343 | − | 0.867790i | ||||
\(259\) | 124.912 | 0.482284 | ||||||||
\(260\) | 43.0977i | 0.165760i | ||||||||
\(261\) | 17.6663 | + | 83.5576i | 0.0676872 | + | 0.320144i | ||||
\(262\) | 272.745 | 1.04101 | ||||||||
\(263\) | 289.307i | 1.10003i | 0.835156 | + | 0.550013i | \(0.185377\pi\) | ||||
−0.835156 | + | 0.550013i | \(0.814623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −142.774 | −0.538771 | ||||||||
\(266\) | 85.5828i | 0.321740i | ||||||||
\(267\) | −21.5722 | − | 206.318i | −0.0807946 | − | 0.772726i | ||||
\(268\) | 32.6737 | 0.121917 | ||||||||
\(269\) | − | 89.4021i | − | 0.332350i | −0.986096 | − | 0.166175i | \(-0.946858\pi\) | ||
0.986096 | − | 0.166175i | \(-0.0531416\pi\) | |||||||
\(270\) | −402.688 | + | 130.120i | −1.49144 | + | 0.481926i | ||||
\(271\) | 272.104 | 1.00407 | 0.502037 | − | 0.864846i | \(-0.332584\pi\) | ||||
0.502037 | + | 0.864846i | \(0.332584\pi\) | |||||||
\(272\) | − | 365.208i | − | 1.34268i | ||||||
\(273\) | −141.048 | + | 14.7477i | −0.516661 | + | 0.0540210i | ||||
\(274\) | 395.734 | 1.44428 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.45142 | − | 33.0097i | −0.0125052 | − | 0.119600i | ||||
\(277\) | 457.600 | 1.65199 | 0.825994 | − | 0.563679i | \(-0.190615\pi\) | ||||
0.825994 | + | 0.563679i | \(0.190615\pi\) | |||||||
\(278\) | 152.015i | 0.546817i | ||||||||
\(279\) | −44.7998 | + | 9.47191i | −0.160573 | + | 0.0339495i | ||||
\(280\) | −248.550 | −0.887680 | ||||||||
\(281\) | − | 20.0841i | − | 0.0714737i | −0.999361 | − | 0.0357368i | \(-0.988622\pi\) | ||
0.999361 | − | 0.0357368i | \(-0.0113778\pi\) | |||||||
\(282\) | 110.168 | − | 11.5189i | 0.390666 | − | 0.0408472i | ||||
\(283\) | −511.601 | −1.80778 | −0.903888 | − | 0.427769i | \(-0.859300\pi\) | ||||
−0.903888 | + | 0.427769i | \(0.859300\pi\) | |||||||
\(284\) | 46.5742i | 0.163994i | ||||||||
\(285\) | −32.2219 | − | 308.173i | −0.113059 | − | 1.08131i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 123.458i | 0.430169i | ||||||||
\(288\) | 11.8109 | + | 55.8628i | 0.0410101 | + | 0.193968i | ||||
\(289\) | −367.882 | −1.27295 | ||||||||
\(290\) | 148.734i | 0.512876i | ||||||||
\(291\) | 47.7941 | − | 4.99726i | 0.164241 | − | 0.0171727i | ||||
\(292\) | −42.8117 | −0.146615 | ||||||||
\(293\) | 493.954i | 1.68585i | 0.538031 | + | 0.842925i | \(0.319168\pi\) | ||||
−0.538031 | + | 0.842925i | \(0.680832\pi\) | |||||||
\(294\) | 21.3147 | + | 203.856i | 0.0724991 | + | 0.693387i | ||||
\(295\) | −224.217 | −0.760058 | ||||||||
\(296\) | − | 289.166i | − | 0.976912i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −179.329 | −0.601776 | ||||||||
\(299\) | − | 364.398i | − | 1.21872i | ||||||
\(300\) | 51.3099 | − | 5.36486i | 0.171033 | − | 0.0178829i | ||||
\(301\) | −142.557 | −0.473612 | ||||||||
\(302\) | 345.551i | 1.14421i | ||||||||
\(303\) | 24.8292 | + | 237.468i | 0.0819445 | + | 0.783724i | ||||
\(304\) | 178.209 | 0.586213 | ||||||||
\(305\) | 361.224i | 1.18434i | ||||||||
\(306\) | −428.311 | + | 90.5566i | −1.39971 | + | 0.295937i | ||||
\(307\) | −560.423 | −1.82548 | −0.912741 | − | 0.408540i | \(-0.866038\pi\) | ||||
−0.912741 | + | 0.408540i | \(0.866038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −66.0273 | + | 6.90367i | −0.213680 | + | 0.0223420i | ||||
\(310\) | −79.7445 | −0.257240 | ||||||||
\(311\) | − | 432.081i | − | 1.38933i | −0.719334 | − | 0.694665i | \(-0.755553\pi\) | ||
0.719334 | − | 0.694665i | \(-0.244447\pi\) | |||||||
\(312\) | 34.1405 | + | 326.522i | 0.109425 | + | 1.04655i | ||||
\(313\) | −156.126 | −0.498805 | −0.249403 | − | 0.968400i | \(-0.580234\pi\) | ||||
−0.249403 | + | 0.968400i | \(0.580234\pi\) | |||||||
\(314\) | 273.434i | 0.870808i | ||||||||
\(315\) | 55.4361 | + | 262.200i | 0.175988 | + | 0.832380i | ||||
\(316\) | −25.0326 | −0.0792171 | ||||||||
\(317\) | − | 338.492i | − | 1.06780i | −0.845549 | − | 0.533898i | \(-0.820727\pi\) | ||
0.845549 | − | 0.533898i | \(-0.179273\pi\) | |||||||
\(318\) | −97.8990 | + | 10.2361i | −0.307858 | + | 0.0321890i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 570.151i | 1.78172i | ||||||||
\(321\) | −62.6973 | − | 599.642i | −0.195319 | − | 1.86804i | ||||
\(322\) | 190.198 | 0.590677 | ||||||||
\(323\) | − | 320.536i | − | 0.992370i | ||||||
\(324\) | 29.4822 | − | 13.0501i | 0.0909946 | − | 0.0402780i | ||||
\(325\) | 566.417 | 1.74282 | ||||||||
\(326\) | 107.354i | 0.329307i | ||||||||
\(327\) | 94.9181 | − | 9.92444i | 0.290269 | − | 0.0303500i | ||||
\(328\) | 285.802 | 0.871347 | ||||||||
\(329\) | − | 70.1470i | − | 0.213213i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2867 | 0.0794161 | 0.0397081 | − | 0.999211i | \(-0.487357\pi\) | ||||
0.0397081 | + | 0.999211i | \(0.487357\pi\) | |||||||
\(332\) | 19.5536i | 0.0588965i | ||||||||
\(333\) | −305.046 | + | 64.4949i | −0.916053 | + | 0.193679i | ||||
\(334\) | 248.797 | 0.744902 | ||||||||
\(335\) | − | 677.907i | − | 2.02360i | ||||||
\(336\) | −153.300 | + | 16.0287i | −0.456249 | + | 0.0477044i | ||||
\(337\) | −309.314 | −0.917847 | −0.458923 | − | 0.888476i | \(-0.651765\pi\) | ||||
−0.458923 | + | 0.888476i | \(0.651765\pi\) | |||||||
\(338\) | 5.48242i | 0.0162202i | ||||||||
\(339\) | 29.7069 | + | 284.119i | 0.0876311 | + | 0.838110i | ||||
\(340\) | 84.2507 | 0.247796 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −44.1885 | − | 209.001i | −0.129206 | − | 0.611114i | ||||
\(343\) | 306.478 | 0.893522 | ||||||||
\(344\) | 330.015i | 0.959346i | ||||||||
\(345\) | −684.879 | + | 71.6095i | −1.98516 | + | 0.207564i | ||||
\(346\) | 344.914 | 0.996860 | ||||||||
\(347\) | 27.1134i | 0.0781367i | 0.999237 | + | 0.0390683i | \(0.0124390\pi\) | ||||
−0.999237 | + | 0.0390683i | \(0.987561\pi\) | |||||||
\(348\) | −1.17838 | − | 11.2701i | −0.00338615 | − | 0.0323854i | ||||
\(349\) | −3.94875 | −0.0113145 | −0.00565723 | − | 0.999984i | \(-0.501801\pi\) | ||||
−0.00565723 | + | 0.999984i | \(0.501801\pi\) | |||||||
\(350\) | 295.642i | 0.844691i | ||||||||
\(351\) | 336.839 | − | 108.842i | 0.959654 | − | 0.310092i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 580.275i | 1.64384i | 0.569603 | + | 0.821920i | \(0.307097\pi\) | ||||
−0.569603 | + | 0.821920i | \(0.692903\pi\) | |||||||
\(354\) | −153.744 | + | 16.0751i | −0.434304 | + | 0.0454099i | ||||
\(355\) | 966.314 | 2.72201 | ||||||||
\(356\) | 27.5236i | 0.0773135i | ||||||||
\(357\) | 28.8300 | + | 275.733i | 0.0807564 | + | 0.772360i | ||||
\(358\) | 22.6087 | 0.0631527 | ||||||||
\(359\) | 73.2374i | 0.204004i | 0.994784 | + | 0.102002i | \(0.0325248\pi\) | ||||
−0.994784 | + | 0.102002i | \(0.967475\pi\) | |||||||
\(360\) | 606.983 | − | 128.333i | 1.68606 | − | 0.356480i | ||||
\(361\) | −204.590 | −0.566730 | ||||||||
\(362\) | − | 160.864i | − | 0.444375i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.8164 | 0.0516934 | ||||||||
\(365\) | 888.249i | 2.43356i | ||||||||
\(366\) | 25.8978 | + | 247.688i | 0.0707589 | + | 0.676743i | ||||
\(367\) | 326.075 | 0.888489 | 0.444244 | − | 0.895906i | \(-0.353472\pi\) | ||||
0.444244 | + | 0.895906i | \(0.353472\pi\) | |||||||
\(368\) | − | 396.049i | − | 1.07622i | ||||||
\(369\) | −63.7446 | − | 301.497i | −0.172750 | − | 0.817064i | ||||
\(370\) | −542.986 | −1.46753 | ||||||||
\(371\) | 62.3351i | 0.168019i | ||||||||
\(372\) | 6.04253 | − | 0.631795i | 0.0162434 | − | 0.00169837i | ||||
\(373\) | −599.517 | −1.60728 | −0.803642 | − | 0.595113i | \(-0.797107\pi\) | ||||
−0.803642 | + | 0.595113i | \(0.797107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −46.8984 | − | 448.540i | −0.125062 | − | 1.19611i | ||||
\(376\) | −162.388 | −0.431883 | ||||||||
\(377\) | − | 124.412i | − | 0.330006i | ||||||
\(378\) | 56.8103 | + | 175.813i | 0.150292 | + | 0.465115i | ||||
\(379\) | 14.8149 | 0.0390895 | 0.0195447 | − | 0.999809i | \(-0.493778\pi\) | ||||
0.0195447 | + | 0.999809i | \(0.493778\pi\) | |||||||
\(380\) | 41.1114i | 0.108188i | ||||||||
\(381\) | 283.275 | − | 29.6187i | 0.743505 | − | 0.0777393i | ||||
\(382\) | −130.960 | −0.342827 | ||||||||
\(383\) | − | 457.401i | − | 1.19426i | −0.802145 | − | 0.597129i | \(-0.796308\pi\) | ||
0.802145 | − | 0.597129i | \(-0.203692\pi\) | |||||||
\(384\) | 32.9598 | + | 315.230i | 0.0858328 | + | 0.820911i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 225.515i | − | 0.584235i | ||||||
\(387\) | 348.138 | − | 73.6058i | 0.899581 | − | 0.190196i | ||||
\(388\) | −6.37592 | −0.0164328 | ||||||||
\(389\) | − | 275.688i | − | 0.708710i | −0.935111 | − | 0.354355i | \(-0.884700\pi\) | ||
0.935111 | − | 0.354355i | \(-0.115300\pi\) | |||||||
\(390\) | 613.133 | − | 64.1079i | 1.57214 | − | 0.164379i | ||||
\(391\) | −712.354 | −1.82188 | ||||||||
\(392\) | − | 300.484i | − | 0.766542i | ||||||
\(393\) | 44.8337 | + | 428.793i | 0.114081 | + | 1.09108i | ||||
\(394\) | 579.041 | 1.46965 | ||||||||
\(395\) | 519.372i | 1.31487i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 582.127 | 1.46632 | 0.733158 | − | 0.680059i | \(-0.238046\pi\) | ||||
0.733158 | + | 0.680059i | \(0.238046\pi\) | |||||||
\(398\) | 237.457i | 0.596625i | ||||||||
\(399\) | −134.548 | + | 14.0681i | −0.337213 | + | 0.0352583i | ||||
\(400\) | 615.615 | 1.53904 | ||||||||
\(401\) | 436.175i | 1.08772i | 0.839177 | + | 0.543859i | \(0.183037\pi\) | ||||
−0.839177 | + | 0.543859i | \(0.816963\pi\) | |||||||
\(402\) | −48.6022 | − | 464.835i | −0.120901 | − | 1.15631i | ||||
\(403\) | 66.7043 | 0.165519 | ||||||||
\(404\) | − | 31.6792i | − | 0.0784138i | ||||||
\(405\) | −270.760 | − | 611.693i | −0.668544 | − | 1.51035i | ||||
\(406\) | 64.9371 | 0.159944 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 638.311 | − | 66.7405i | 1.56449 | − | 0.163580i | ||||
\(409\) | 293.978 | 0.718773 | 0.359386 | − | 0.933189i | \(-0.382986\pi\) | ||||
0.359386 | + | 0.933189i | \(0.382986\pi\) | |||||||
\(410\) | − | 536.669i | − | 1.30895i | ||||||
\(411\) | 65.0506 | + | 622.149i | 0.158274 | + | 1.51374i | ||||
\(412\) | 8.80829 | 0.0213794 | ||||||||
\(413\) | 97.8930i | 0.237029i | ||||||||
\(414\) | −464.481 | + | 98.2040i | −1.12194 | + | 0.237208i | ||||
\(415\) | 405.695 | 0.977579 | ||||||||
\(416\) | − | 83.1763i | − | 0.199943i | ||||||
\(417\) | −238.989 | + | 24.9882i | −0.573114 | + | 0.0599237i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 484.652i | − | 1.15669i | −0.815793 | − | 0.578344i | \(-0.803699\pi\) | ||
0.815793 | − | 0.578344i | \(-0.196301\pi\) | |||||||
\(420\) | −3.69770 | − | 35.3651i | −0.00880404 | − | 0.0842025i | ||||
\(421\) | −52.2706 | −0.124158 | −0.0620791 | − | 0.998071i | \(-0.519773\pi\) | ||||
−0.0620791 | + | 0.998071i | \(0.519773\pi\) | |||||||
\(422\) | − | 391.731i | − | 0.928271i | ||||||
\(423\) | 36.2187 | + | 171.306i | 0.0856233 | + | 0.404978i | ||||
\(424\) | 144.304 | 0.340339 | ||||||||
\(425\) | − | 1107.28i | − | 2.60536i | ||||||
\(426\) | 662.592 | − | 69.2793i | 1.55538 | − | 0.162627i | ||||
\(427\) | 157.710 | 0.369345 | ||||||||
\(428\) | 79.9946i | 0.186903i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 619.691 | 1.44114 | ||||||||
\(431\) | − | 209.726i | − | 0.486603i | −0.969951 | − | 0.243302i | \(-0.921770\pi\) | ||
0.969951 | − | 0.243302i | \(-0.0782305\pi\) | |||||||
\(432\) | 366.096 | − | 118.296i | 0.847444 | − | 0.273833i | ||||
\(433\) | −362.262 | −0.836634 | −0.418317 | − | 0.908301i | \(-0.637380\pi\) | ||||
−0.418317 | + | 0.908301i | \(0.637380\pi\) | |||||||
\(434\) | 34.8164i | 0.0802221i | ||||||||
\(435\) | −233.830 | + | 24.4488i | −0.537541 | + | 0.0562042i | ||||
\(436\) | −12.6624 | −0.0290423 | ||||||||
\(437\) | − | 347.604i | − | 0.795433i | ||||||
\(438\) | 63.6825 | + | 609.064i | 0.145394 | + | 1.39056i | ||||
\(439\) | −414.518 | −0.944233 | −0.472116 | − | 0.881536i | \(-0.656510\pi\) | ||||
−0.472116 | + | 0.881536i | \(0.656510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −316.986 | + | 67.0194i | −0.718789 | + | 0.151972i | ||||
\(442\) | 637.730 | 1.44283 | ||||||||
\(443\) | 772.276i | 1.74329i | 0.490142 | + | 0.871643i | \(0.336945\pi\) | ||||
−0.490142 | + | 0.871643i | \(0.663055\pi\) | |||||||
\(444\) | 41.1441 | − | 4.30194i | 0.0926668 | − | 0.00968905i | ||||
\(445\) | 571.055 | 1.28327 | ||||||||
\(446\) | − | 131.232i | − | 0.294241i | ||||||
\(447\) | −29.4781 | − | 281.930i | −0.0659465 | − | 0.630717i | ||||
\(448\) | 248.928 | 0.555642 | ||||||||
\(449\) | 674.192i | 1.50154i | 0.660563 | + | 0.750771i | \(0.270318\pi\) | ||||
−0.660563 | + | 0.750771i | \(0.729682\pi\) | |||||||
\(450\) | −152.647 | − | 721.985i | −0.339216 | − | 1.60441i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 37.9026i | − | 0.0838553i | ||||||
\(453\) | −543.254 | + | 56.8016i | −1.19924 | + | 0.125390i | ||||
\(454\) | 189.203 | 0.416747 | ||||||||
\(455\) | − | 390.400i | − | 0.858021i | ||||||
\(456\) | 32.5671 | + | 311.474i | 0.0714190 | + | 0.683057i | ||||
\(457\) | 844.966 | 1.84894 | 0.924470 | − | 0.381255i | \(-0.124508\pi\) | ||||
0.924470 | + | 0.381255i | \(0.124508\pi\) | |||||||
\(458\) | 471.363i | 1.02918i | ||||||||
\(459\) | −212.773 | − | 658.479i | −0.463558 | − | 1.43459i | ||||
\(460\) | 91.3655 | 0.198621 | ||||||||
\(461\) | − | 282.181i | − | 0.612107i | −0.952014 | − | 0.306054i | \(-0.900991\pi\) | ||
0.952014 | − | 0.306054i | \(-0.0990087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −732.770 | −1.58266 | −0.791329 | − | 0.611391i | \(-0.790610\pi\) | ||||
−0.791329 | + | 0.611391i | \(0.790610\pi\) | |||||||
\(464\) | − | 135.218i | − | 0.291419i | ||||||
\(465\) | −13.1084 | − | 125.369i | −0.0281900 | − | 0.269612i | ||||
\(466\) | −552.109 | −1.18478 | ||||||||
\(467\) | 459.059i | 0.982996i | 0.870879 | + | 0.491498i | \(0.163551\pi\) | ||||
−0.870879 | + | 0.491498i | \(0.836449\pi\) | |||||||
\(468\) | −45.9514 | + | 9.71538i | −0.0981868 | + | 0.0207594i | ||||
\(469\) | −295.974 | −0.631074 | ||||||||
\(470\) | 304.927i | 0.648780i | ||||||||
\(471\) | −429.876 | + | 44.9469i | −0.912687 | + | 0.0954287i | ||||
\(472\) | 226.619 | 0.480125 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 37.2361 | + | 356.128i | 0.0785571 | + | 0.751326i | ||||
\(475\) | 540.313 | 1.13750 | ||||||||
\(476\) | − | 36.7838i | − | 0.0772769i | ||||||
\(477\) | −32.1852 | − | 152.228i | −0.0674742 | − | 0.319137i | ||||
\(478\) | −199.161 | −0.416655 | ||||||||
\(479\) | 285.861i | 0.596787i | 0.954443 | + | 0.298393i | \(0.0964507\pi\) | ||||
−0.954443 | + | 0.298393i | \(0.903549\pi\) | |||||||
\(480\) | −156.328 | + | 16.3454i | −0.325684 | + | 0.0340528i | ||||
\(481\) | 454.195 | 0.944271 | ||||||||
\(482\) | 167.728i | 0.347983i | ||||||||
\(483\) | 31.2647 | + | 299.018i | 0.0647302 | + | 0.619084i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 132.287i | 0.272756i | ||||||||
\(486\) | −229.513 | − | 400.020i | −0.472249 | − | 0.823086i | ||||
\(487\) | 724.781 | 1.48826 | 0.744128 | − | 0.668037i | \(-0.232865\pi\) | ||||
0.744128 | + | 0.668037i | \(0.232865\pi\) | |||||||
\(488\) | − | 365.094i | − | 0.748143i | ||||||
\(489\) | −168.776 | + | 17.6468i | −0.345144 | + | 0.0360876i | ||||
\(490\) | −564.240 | −1.15151 | ||||||||
\(491\) | 615.334i | 1.25323i | 0.779330 | + | 0.626613i | \(0.215559\pi\) | ||||
−0.779330 | + | 0.626613i | \(0.784441\pi\) | |||||||
\(492\) | 4.25189 | + | 40.6654i | 0.00864206 | + | 0.0826533i | ||||
\(493\) | −243.211 | −0.493328 | ||||||||
\(494\) | 311.190i | 0.629940i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 72.4981 | 0.146165 | ||||||||
\(497\) | − | 421.892i | − | 0.848877i | ||||||
\(498\) | 278.182 | − | 29.0861i | 0.558597 | − | 0.0584058i | ||||
\(499\) | 737.017 | 1.47699 | 0.738494 | − | 0.674260i | \(-0.235537\pi\) | ||||
0.738494 | + | 0.674260i | \(0.235537\pi\) | |||||||
\(500\) | 59.8370i | 0.119674i | ||||||||
\(501\) | 40.8972 | + | 391.144i | 0.0816311 | + | 0.780726i | ||||
\(502\) | −12.0435 | −0.0239910 | ||||||||
\(503\) | − | 800.853i | − | 1.59215i | −0.605196 | − | 0.796076i | \(-0.706905\pi\) | ||
0.605196 | − | 0.796076i | \(-0.293095\pi\) | |||||||
\(504\) | −56.0300 | − | 265.008i | −0.111171 | − | 0.525810i | ||||
\(505\) | −657.274 | −1.30153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.61912 | + | 0.901198i | −0.0170002 | + | 0.00177751i | ||||
\(508\) | −37.7900 | −0.0743898 | ||||||||
\(509\) | 372.727i | 0.732273i | 0.930561 | + | 0.366137i | \(0.119320\pi\) | ||||
−0.930561 | + | 0.366137i | \(0.880680\pi\) | |||||||
\(510\) | −125.323 | − | 1198.60i | −0.245732 | − | 2.35020i | ||||
\(511\) | 387.809 | 0.758922 | ||||||||
\(512\) | − | 566.158i | − | 1.10578i | ||||||
\(513\) | 321.315 | − | 103.826i | 0.626345 | − | 0.202390i | ||||
\(514\) | −341.115 | −0.663647 | ||||||||
\(515\) | − | 182.753i | − | 0.354860i | ||||||
\(516\) | −46.9563 | + | 4.90965i | −0.0910005 | + | 0.00951483i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 237.067i | 0.457659i | ||||||||
\(519\) | 56.6967 | + | 542.252i | 0.109242 | + | 1.04480i | ||||
\(520\) | −903.761 | −1.73800 | ||||||||
\(521\) | 758.547i | 1.45595i | 0.685606 | + | 0.727973i | \(0.259537\pi\) | ||||
−0.685606 | + | 0.727973i | \(0.740463\pi\) | |||||||
\(522\) | −158.582 | + | 33.5287i | −0.303798 | + | 0.0642311i | ||||
\(523\) | −129.733 | −0.248055 | −0.124028 | − | 0.992279i | \(-0.539581\pi\) | ||||
−0.124028 | + | 0.992279i | \(0.539581\pi\) | |||||||
\(524\) | − | 57.2026i | − | 0.109165i | ||||||
\(525\) | −464.790 | + | 48.5975i | −0.885315 | + | 0.0925667i | ||||
\(526\) | −549.071 | −1.04386 | ||||||||
\(527\) | − | 130.399i | − | 0.247436i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −243.511 | −0.460323 | ||||||||
\(530\) | − | 270.969i | − | 0.511262i | ||||||
\(531\) | −50.5446 | − | 239.064i | −0.0951875 | − | 0.450214i | ||||
\(532\) | 17.9492 | 0.0337392 | ||||||||
\(533\) | 448.911i | 0.842234i | ||||||||
\(534\) | 391.567 | − | 40.9414i | 0.733271 | − | 0.0766693i | ||||
\(535\) | 1659.71 | 3.10227 | ||||||||
\(536\) | 685.169i | 1.27830i | ||||||||
\(537\) | 3.71641 | + | 35.5440i | 0.00692068 | + | 0.0661899i | ||||
\(538\) | 169.675 | 0.315380 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 27.2900 | + | 84.4555i | 0.0505370 | + | 0.156399i | ||||
\(541\) | −787.477 | −1.45560 | −0.727798 | − | 0.685792i | \(-0.759456\pi\) | ||||
−0.727798 | + | 0.685792i | \(0.759456\pi\) | |||||||
\(542\) | 516.421i | 0.952807i | ||||||||
\(543\) | 252.900 | − | 26.4427i | 0.465746 | − | 0.0486975i | ||||
\(544\) | −162.600 | −0.298896 | ||||||||
\(545\) | 262.718i | 0.482052i | ||||||||
\(546\) | −27.9895 | − | 267.693i | −0.0512628 | − | 0.490281i | ||||
\(547\) | −721.547 | −1.31910 | −0.659549 | − | 0.751661i | \(-0.729253\pi\) | ||||
−0.659549 | + | 0.751661i | \(0.729253\pi\) | |||||||
\(548\) | − | 82.9971i | − | 0.151455i | ||||||
\(549\) | −385.143 | + | 81.4297i | −0.701535 | + | 0.148324i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 118.679i | − | 0.215388i | ||||||
\(552\) | 692.215 | − | 72.3766i | 1.25401 | − | 0.131117i | ||||
\(553\) | 226.757 | 0.410050 | ||||||||
\(554\) | 868.472i | 1.56764i | ||||||||
\(555\) | −89.2559 | − | 853.650i | −0.160821 | − | 1.53811i | ||||
\(556\) | 31.8820 | 0.0573418 | ||||||||
\(557\) | 546.419i | 0.981003i | 0.871440 | + | 0.490501i | \(0.163186\pi\) | ||||
−0.871440 | + | 0.490501i | \(0.836814\pi\) | |||||||
\(558\) | −17.9766 | − | 85.0248i | −0.0322161 | − | 0.152374i | ||||
\(559\) | −518.356 | −0.927292 | ||||||||
\(560\) | − | 424.309i | − | 0.757694i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.1173 | 0.0678243 | ||||||||
\(563\) | 509.933i | 0.905742i | 0.891576 | + | 0.452871i | \(0.149600\pi\) | ||||
−0.891576 | + | 0.452871i | \(0.850400\pi\) | |||||||
\(564\) | −2.41586 | − | 23.1054i | −0.00428343 | − | 0.0409671i | ||||
\(565\) | −786.397 | −1.39185 | ||||||||
\(566\) | − | 970.958i | − | 1.71547i | ||||||
\(567\) | −267.065 | + | 118.214i | −0.471013 | + | 0.208490i | ||||
\(568\) | −976.665 | −1.71948 | ||||||||
\(569\) | 86.6541i | 0.152292i | 0.997097 | + | 0.0761459i | \(0.0242615\pi\) | ||||
−0.997097 | + | 0.0761459i | \(0.975739\pi\) | |||||||
\(570\) | 584.876 | − | 61.1534i | 1.02610 | − | 0.107287i | ||||
\(571\) | 773.591 | 1.35480 | 0.677400 | − | 0.735615i | \(-0.263107\pi\) | ||||
0.677400 | + | 0.735615i | \(0.263107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.5271 | − | 205.887i | −0.0375691 | − | 0.359314i | ||||
\(574\) | −234.310 | −0.408205 | ||||||||
\(575\) | − | 1200.78i | − | 2.08832i | ||||||
\(576\) | −607.904 | + | 128.528i | −1.05539 | + | 0.223138i | ||||
\(577\) | −307.315 | −0.532609 | −0.266304 | − | 0.963889i | \(-0.585803\pi\) | ||||
−0.266304 | + | 0.963889i | \(0.585803\pi\) | |||||||
\(578\) | − | 698.196i | − | 1.20795i | ||||||
\(579\) | 354.540 | − | 37.0700i | 0.612332 | − | 0.0640242i | ||||
\(580\) | 31.1939 | 0.0537825 | ||||||||
\(581\) | − | 177.126i | − | 0.304865i | ||||||
\(582\) | 9.48420 | + | 90.7076i | 0.0162959 | + | 0.155855i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 897.764i | − | 1.53727i | ||||||
\(585\) | 201.573 | + | 953.392i | 0.344569 | + | 1.62973i | ||||
\(586\) | −937.467 | −1.59977 | ||||||||
\(587\) | 1025.95i | 1.74779i | 0.486113 | + | 0.873896i | \(0.338414\pi\) | ||||
−0.486113 | + | 0.873896i | \(0.661586\pi\) | |||||||
\(588\) | 42.7545 | − | 4.47033i | 0.0727118 | − | 0.00760260i | ||||
\(589\) | 63.6301 | 0.108031 | ||||||||
\(590\) | − | 425.538i | − | 0.721250i | ||||||
\(591\) | 95.1825 | + | 910.332i | 0.161053 | + | 1.54033i | ||||
\(592\) | 493.645 | 0.833860 | ||||||||
\(593\) | 570.008i | 0.961227i | 0.876933 | + | 0.480613i | \(0.159586\pi\) | ||||
−0.876933 | + | 0.480613i | \(0.840414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −763.184 | −1.28266 | ||||||||
\(596\) | 37.6106i | 0.0631051i | ||||||||
\(597\) | −373.315 | + | 39.0331i | −0.625318 | + | 0.0653820i | ||||
\(598\) | 691.585 | 1.15650 | ||||||||
\(599\) | 539.056i | 0.899927i | 0.893047 | + | 0.449963i | \(0.148563\pi\) | ||||
−0.893047 | + | 0.449963i | \(0.851437\pi\) | |||||||
\(600\) | 112.502 | + | 1075.97i | 0.187503 | + | 1.79329i | ||||
\(601\) | −597.502 | −0.994179 | −0.497090 | − | 0.867699i | \(-0.665598\pi\) | ||||
−0.497090 | + | 0.867699i | \(0.665598\pi\) | |||||||
\(602\) | − | 270.557i | − | 0.449430i | ||||||
\(603\) | 722.795 | − | 152.819i | 1.19867 | − | 0.253431i | ||||
\(604\) | 72.4722 | 0.119987 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −450.687 | + | 47.1229i | −0.743708 | + | 0.0777605i | ||||
\(607\) | −626.939 | −1.03285 | −0.516424 | − | 0.856333i | \(-0.672737\pi\) | ||||
−0.516424 | + | 0.856333i | \(0.672737\pi\) | |||||||
\(608\) | − | 79.3430i | − | 0.130498i | ||||||
\(609\) | 10.6743 | + | 102.090i | 0.0175276 | + | 0.167636i | ||||
\(610\) | −685.561 | −1.12387 | ||||||||
\(611\) | − | 255.064i | − | 0.417453i | ||||||
\(612\) | 18.9924 | + | 89.8294i | 0.0310333 | + | 0.146780i | ||||
\(613\) | −180.077 | −0.293763 | −0.146881 | − | 0.989154i | \(-0.546924\pi\) | ||||
−0.146881 | + | 0.989154i | \(0.546924\pi\) | |||||||
\(614\) | − | 1063.62i | − | 1.73227i | ||||||
\(615\) | 843.719 | − | 88.2175i | 1.37190 | − | 0.143443i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 466.729i | − | 0.756449i | −0.925714 | − | 0.378225i | \(-0.876535\pi\) | ||
0.925714 | − | 0.378225i | \(-0.123465\pi\) | |||||||
\(618\) | −13.1024 | − | 125.312i | −0.0212012 | − | 0.202770i | ||||
\(619\) | 350.279 | 0.565878 | 0.282939 | − | 0.959138i | \(-0.408691\pi\) | ||||
0.282939 | + | 0.959138i | \(0.408691\pi\) | |||||||
\(620\) | 16.7248i | 0.0269754i | ||||||||
\(621\) | −230.741 | − | 714.086i | −0.371564 | − | 1.14990i | ||||
\(622\) | 820.040 | 1.31839 | ||||||||
\(623\) | − | 249.322i | − | 0.400196i | ||||||
\(624\) | −557.417 | + | 58.2824i | −0.893297 | + | 0.0934013i | ||||
\(625\) | 161.415 | 0.258265 | ||||||||
\(626\) | − | 296.309i | − | 0.473337i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 57.3471 | 0.0913170 | ||||||||
\(629\) | − | 887.895i | − | 1.41160i | ||||||
\(630\) | −497.624 | + | 105.211i | −0.789879 | + | 0.167002i | ||||
\(631\) | −1043.41 | −1.65358 | −0.826790 | − | 0.562511i | \(-0.809836\pi\) | ||||
−0.826790 | + | 0.562511i | \(0.809836\pi\) | |||||||
\(632\) | − | 524.935i | − | 0.830594i | ||||||
\(633\) | 615.855 | − | 64.3925i | 0.972914 | − | 0.101726i | ||||
\(634\) | 642.417 | 1.01328 | ||||||||
\(635\) | 784.061i | 1.23474i | ||||||||
\(636\) | 2.14681 | + | 20.5323i | 0.00337549 | + | 0.0322835i | ||||
\(637\) | 471.973 | 0.740931 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 217.833 | + | 1030.30i | 0.340897 | + | 1.61236i | ||||
\(640\) | −872.506 | −1.36329 | ||||||||
\(641\) | − | 84.2580i | − | 0.131448i | −0.997838 | − | 0.0657239i | \(-0.979064\pi\) | ||
0.997838 | − | 0.0657239i | \(-0.0209356\pi\) | |||||||
\(642\) | 1138.05 | − | 118.992i | 1.77266 | − | 0.185346i | ||||
\(643\) | −398.321 | −0.619473 | −0.309737 | − | 0.950822i | \(-0.600241\pi\) | ||||
−0.309737 | + | 0.950822i | \(0.600241\pi\) | |||||||
\(644\) | − | 39.8901i | − | 0.0619412i | ||||||
\(645\) | 101.865 | + | 974.241i | 0.157930 | + | 1.51045i | ||||
\(646\) | 608.339 | 0.941701 | ||||||||
\(647\) | 429.581i | 0.663959i | 0.943287 | + | 0.331979i | \(0.107716\pi\) | ||||
−0.943287 | + | 0.331979i | \(0.892284\pi\) | |||||||
\(648\) | 273.661 | + | 618.245i | 0.422316 | + | 0.954082i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1074.99i | 1.65383i | ||||||||
\(651\) | −54.7362 | + | 5.72310i | −0.0840802 | + | 0.00879125i | ||||
\(652\) | 22.5153 | 0.0345327 | ||||||||
\(653\) | − | 541.731i | − | 0.829604i | −0.909912 | − | 0.414802i | \(-0.863851\pi\) | ||
0.909912 | − | 0.414802i | \(-0.136149\pi\) | |||||||
\(654\) | 18.8354 | + | 180.143i | 0.0288003 | + | 0.275449i | ||||
\(655\) | −1186.83 | −1.81195 | ||||||||
\(656\) | 487.902i | 0.743753i | ||||||||
\(657\) | −947.065 | + | 200.235i | −1.44150 | + | 0.304772i | ||||
\(658\) | 133.131 | 0.202326 | ||||||||
\(659\) | − | 742.491i | − | 1.12669i | −0.826221 | − | 0.563347i | \(-0.809514\pi\) | ||
0.826221 | − | 0.563347i | \(-0.190486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1145.01 | 1.73224 | 0.866118 | − | 0.499839i | \(-0.166607\pi\) | ||||
0.866118 | + | 0.499839i | \(0.166607\pi\) | |||||||
\(662\) | 49.8892i | 0.0753613i | ||||||||
\(663\) | 104.830 | + | 1002.60i | 0.158114 | + | 1.51222i | ||||
\(664\) | −410.041 | −0.617532 | ||||||||
\(665\) | − | 372.408i | − | 0.560011i | ||||||
\(666\) | −122.404 | − | 578.941i | −0.183790 | − | 0.869280i | ||||
\(667\) | −263.750 | −0.395427 | ||||||||
\(668\) | − | 52.1801i | − | 0.0781139i | ||||||
\(669\) | 206.314 | − | 21.5718i | 0.308392 | − | 0.0322449i | ||||
\(670\) | 1286.59 | 1.92028 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 7.13637 | + | 68.2528i | 0.0106196 | + | 0.101567i | ||||
\(673\) | 252.175 | 0.374702 | 0.187351 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187351 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(674\) | − | 587.042i | − | 0.870983i | ||||||
\(675\) | 1109.97 | − | 358.662i | 1.64440 | − | 0.531352i | ||||
\(676\) | 1.14982 | 0.00170092 | ||||||||
\(677\) | 631.491i | 0.932779i | 0.884580 | + | 0.466389i | \(0.154445\pi\) | ||||
−0.884580 | + | 0.466389i | \(0.845555\pi\) | |||||||
\(678\) | −539.225 | + | 56.3803i | −0.795317 | + | 0.0831567i | ||||
\(679\) | 57.7562 | 0.0850607 | ||||||||
\(680\) | 1766.74i | 2.59815i | ||||||||
\(681\) | 31.1011 | + | 297.454i | 0.0456698 | + | 0.436789i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 465.998i | 0.682281i | 0.940012 | + | 0.341141i | \(0.110813\pi\) | ||||
−0.940012 | + | 0.341141i | \(0.889187\pi\) | |||||||
\(684\) | −43.8337 | + | 9.26764i | −0.0640843 | + | 0.0135492i | ||||
\(685\) | −1722.01 | −2.51388 | ||||||||
\(686\) | 581.659i | 0.847900i | ||||||||
\(687\) | −741.047 | + | 77.4824i | −1.07867 | + | 0.112784i | ||||
\(688\) | −563.380 | −0.818866 | ||||||||
\(689\) | 226.659i | 0.328967i | ||||||||
\(690\) | −135.906 | − | 1299.82i | −0.196966 | − | 1.88380i | ||||
\(691\) | −610.944 | −0.884144 | −0.442072 | − | 0.896980i | \(-0.645756\pi\) | ||||
−0.442072 | + | 0.896980i | \(0.645756\pi\) | |||||||
\(692\) | − | 72.3385i | − | 0.104535i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −51.4581 | −0.0741471 | ||||||||
\(695\) | − | 661.483i | − | 0.951774i | ||||||
\(696\) | 236.335 | − | 24.7107i | 0.339562 | − | 0.0355039i | ||||
\(697\) | 877.566 | 1.25906 | ||||||||
\(698\) | − | 7.49426i | − | 0.0107368i | ||||||
\(699\) | −90.7554 | − | 867.991i | −0.129836 | − | 1.24176i | ||||
\(700\) | 62.0048 | 0.0885783 | ||||||||
\(701\) | − | 681.303i | − | 0.971901i | −0.873986 | − | 0.485951i | \(-0.838474\pi\) | ||
0.873986 | − | 0.485951i | \(-0.161526\pi\) | |||||||
\(702\) | 206.570 | + | 639.280i | 0.294259 | + | 0.910655i | ||||
\(703\) | 433.262 | 0.616305 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −479.387 | + | 50.1237i | −0.679982 | + | 0.0710975i | ||||
\(706\) | −1101.29 | −1.55991 | ||||||||
\(707\) | 286.965i | 0.405892i | ||||||||
\(708\) | 3.37142 | + | 32.2445i | 0.00476190 | + | 0.0455431i | ||||
\(709\) | 91.6430 | 0.129257 | 0.0646284 | − | 0.997909i | \(-0.479414\pi\) | ||||
0.0646284 | + | 0.997909i | \(0.479414\pi\) | |||||||
\(710\) | 1833.95i | 2.58303i | ||||||||
\(711\) | −553.762 | + | 117.080i | −0.778850 | + | 0.164670i | ||||
\(712\) | −577.172 | −0.810634 | ||||||||
\(713\) | − | 141.411i | − | 0.198332i | ||||||
\(714\) | −523.308 | + | 54.7160i | −0.732924 | + | 0.0766331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4.74171i | − | 0.00662249i | ||||||
\(717\) | −32.7380 | − | 313.109i | −0.0456597 | − | 0.436693i | ||||
\(718\) | −138.996 | −0.193588 | ||||||||
\(719\) | − | 659.916i | − | 0.917824i | −0.888482 | − | 0.458912i | \(-0.848239\pi\) | ||
0.888482 | − | 0.458912i | \(-0.151761\pi\) | |||||||
\(720\) | 219.081 | + | 1036.20i | 0.304279 | + | 1.43917i | ||||
\(721\) | −79.7898 | −0.110665 | ||||||||
\(722\) | − | 388.287i | − | 0.537794i | ||||||
\(723\) | −263.692 | + | 27.5711i | −0.364719 | + | 0.0381343i | ||||
\(724\) | −33.7379 | −0.0465993 | ||||||||
\(725\) | − | 409.970i | − | 0.565476i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −718.942 | −0.988915 | −0.494458 | − | 0.869202i | \(-0.664633\pi\) | ||||
−0.494458 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(728\) | 394.581i | 0.542007i | ||||||||
\(729\) | 591.160 | − | 426.581i | 0.810918 | − | 0.585159i | ||||
\(730\) | −1685.79 | −2.30931 | ||||||||
\(731\) | 1013.32i | 1.38622i | ||||||||
\(732\) | 51.9475 | − | 5.43152i | 0.0709665 | − | 0.00742011i | ||||
\(733\) | 727.430 | 0.992400 | 0.496200 | − | 0.868208i | \(-0.334728\pi\) | ||||
0.496200 | + | 0.868208i | \(0.334728\pi\) | |||||||
\(734\) | 618.853i | 0.843123i | ||||||||
\(735\) | −92.7496 | − | 887.064i | −0.126190 | − | 1.20689i | ||||
\(736\) | −176.331 | −0.239580 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 572.205 | − | 120.980i | 0.775346 | − | 0.163929i | ||||
\(739\) | 603.503 | 0.816648 | 0.408324 | − | 0.912837i | \(-0.366113\pi\) | ||||
0.408324 | + | 0.912837i | \(0.366113\pi\) | |||||||
\(740\) | 113.880i | 0.153892i | ||||||||
\(741\) | −489.234 | + | 51.1533i | −0.660235 | + | 0.0690328i | ||||
\(742\) | −118.305 | −0.159440 | ||||||||
\(743\) | − | 434.637i | − | 0.584976i | −0.956269 | − | 0.292488i | \(-0.905517\pi\) | ||
0.956269 | − | 0.292488i | \(-0.0944831\pi\) | |||||||
\(744\) | 13.2488 | + | 126.712i | 0.0178075 | + | 0.170312i | ||||
\(745\) | 780.339 | 1.04743 | ||||||||
\(746\) | − | 1137.81i | − | 1.52522i | ||||||
\(747\) | 91.4547 | + | 432.559i | 0.122429 | + | 0.579061i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 724.630i | − | 0.967463i | ||||||
\(750\) | 851.276 | − | 89.0077i | 1.13503 | − | 0.118677i | ||||
\(751\) | −319.705 | −0.425705 | −0.212853 | − | 0.977084i | \(-0.568275\pi\) | ||||
−0.212853 | + | 0.977084i | \(0.568275\pi\) | |||||||
\(752\) | − | 277.218i | − | 0.368641i | ||||||
\(753\) | −1.97970 | − | 18.9340i | −0.00262908 | − | 0.0251448i | ||||
\(754\) | 236.120 | 0.313156 | ||||||||
\(755\) | − | 1503.64i | − | 1.99158i | ||||||
\(756\) | 36.8732 | − | 11.9148i | 0.0487741 | − | 0.0157603i | ||||
\(757\) | 910.980 | 1.20341 | 0.601704 | − | 0.798719i | \(-0.294489\pi\) | ||||
0.601704 | + | 0.798719i | \(0.294489\pi\) | |||||||
\(758\) | 28.1170i | 0.0370936i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −862.110 | −1.13436 | ||||||||
\(761\) | − | 645.430i | − | 0.848134i | −0.905631 | − | 0.424067i | \(-0.860602\pi\) | ||
0.905631 | − | 0.424067i | \(-0.139398\pi\) | |||||||
\(762\) | 56.2128 | + | 537.623i | 0.0737701 | + | 0.705542i | ||||
\(763\) | 114.703 | 0.150331 | ||||||||
\(764\) | 27.4661i | 0.0359504i | ||||||||
\(765\) | 1863.77 | − | 394.051i | 2.43629 | − | 0.515099i | ||||
\(766\) | 868.093 | 1.13328 | ||||||||
\(767\) | 355.952i | 0.464083i | ||||||||
\(768\) | 225.696 | − | 23.5983i | 0.293875 | − | 0.0307270i | ||||
\(769\) | −212.256 | −0.276016 | −0.138008 | − | 0.990431i | \(-0.544070\pi\) | ||||
−0.138008 | + | 0.990431i | \(0.544070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −56.0723 | − | 536.280i | −0.0727267 | − | 0.695564i | ||||
\(772\) | −47.2970 | −0.0612656 | ||||||||
\(773\) | − | 1123.99i | − | 1.45406i | −0.686605 | − | 0.727030i | \(-0.740900\pi\) | ||
0.686605 | − | 0.727030i | \(-0.259100\pi\) | |||||||
\(774\) | 139.695 | + | 660.725i | 0.180485 | + | 0.853650i | ||||
\(775\) | 219.808 | 0.283623 | ||||||||
\(776\) | − | 133.704i | − | 0.172298i | ||||||
\(777\) | −372.703 | + | 38.9691i | −0.479669 | + | 0.0501532i | ||||
\(778\) | 523.224 | 0.672524 | ||||||||
\(779\) | 428.222i | 0.549707i | ||||||||
\(780\) | −13.4453 | − | 128.592i | −0.0172376 | − | 0.164861i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 1351.96i | − | 1.72885i | ||||||
\(783\) | −78.7794 | − | 243.802i | −0.100612 | − | 0.311369i | ||||
\(784\) | 512.967 | 0.654295 | ||||||||
\(785\) | − | 1189.83i | − | 1.51570i | ||||||
\(786\) | −813.798 | + | 85.0890i | −1.03537 | + | 0.108256i | ||||
\(787\) | −240.124 | −0.305113 | −0.152556 | − | 0.988295i | \(-0.548751\pi\) | ||||
−0.152556 | + | 0.988295i | \(0.548751\pi\) | |||||||
\(788\) | − | 121.442i | − | 0.154114i | ||||||
\(789\) | −90.2560 | − | 863.215i | −0.114393 | − | 1.09406i | ||||
\(790\) | −985.707 | −1.24773 | ||||||||
\(791\) | 343.340i | 0.434059i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 573.455 | 0.723146 | ||||||||
\(794\) | 1104.81i | 1.39145i | ||||||||
\(795\) | 426.000 | − | 44.5417i | 0.535850 | − | 0.0560273i | ||||
\(796\) | 49.8017 | 0.0625649 | ||||||||
\(797\) | − | 591.993i | − | 0.742777i | −0.928478 | − | 0.371388i | \(-0.878882\pi\) | ||
0.928478 | − | 0.371388i | \(-0.121118\pi\) | |||||||
\(798\) | −26.6995 | − | 255.356i | −0.0334581 | − | 0.319995i | ||||
\(799\) | −498.619 | −0.624053 | ||||||||
\(800\) | − | 274.087i | − | 0.342609i | ||||||
\(801\) | 128.731 | + | 608.867i | 0.160713 | + | 0.760134i | ||||
\(802\) | −827.808 | −1.03218 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −97.4895 | + | 10.1933i | −0.121256 | + | 0.0126782i | ||||
\(805\) | −827.633 | −1.02812 | ||||||||
\(806\) | 126.597i | 0.157068i | ||||||||
\(807\) | 27.8910 | + | 266.752i | 0.0345614 | + | 0.330548i | ||||
\(808\) | 664.315 | 0.822172 | ||||||||
\(809\) | − | 891.236i | − | 1.10165i | −0.834620 | − | 0.550826i | \(-0.814313\pi\) | ||
0.834620 | − | 0.550826i | \(-0.185687\pi\) | |||||||
\(810\) | 1160.92 | − | 513.871i | 1.43324 | − | 0.634409i | ||||
\(811\) | 968.274 | 1.19393 | 0.596963 | − | 0.802269i | \(-0.296374\pi\) | ||||
0.596963 | + | 0.802269i | \(0.296374\pi\) | |||||||
\(812\) | − | 13.6192i | − | 0.0167724i | ||||||
\(813\) | −811.886 | + | 84.8891i | −0.998629 | + | 0.104415i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 467.144i | − | 0.573183i | ||||||
\(816\) | 113.935 | + | 1089.68i | 0.139626 | + | 1.33540i | ||||
\(817\) | −494.467 | −0.605223 | ||||||||
\(818\) | 557.936i | 0.682073i | ||||||||
\(819\) | 416.250 | − | 88.0066i | 0.508242 | − | 0.107456i | ||||
\(820\) | −112.555 | −0.137263 | ||||||||
\(821\) | − | 905.042i | − | 1.10237i | −0.834385 | − | 0.551183i | \(-0.814177\pi\) | ||
0.834385 | − | 0.551183i | \(-0.185823\pi\) | |||||||
\(822\) | −1180.77 | + | 123.458i | −1.43645 | + | 0.150193i | ||||
\(823\) | −1343.44 | −1.63237 | −0.816186 | − | 0.577789i | \(-0.803915\pi\) | ||||
−0.816186 | + | 0.577789i | \(0.803915\pi\) | |||||||
\(824\) | 184.711i | 0.224163i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −185.789 | −0.224927 | ||||||||
\(827\) | 1178.20i | 1.42467i | 0.701840 | + | 0.712334i | \(0.252362\pi\) | ||||
−0.701840 | + | 0.712334i | \(0.747638\pi\) | |||||||
\(828\) | 20.5963 | + | 97.4154i | 0.0248747 | + | 0.117651i | ||||
\(829\) | −424.381 | −0.511919 | −0.255959 | − | 0.966688i | \(-0.582391\pi\) | ||||
−0.255959 | + | 0.966688i | \(0.582391\pi\) | |||||||
\(830\) | 769.962i | 0.927665i | ||||||||
\(831\) | −1365.36 | + | 142.759i | −1.64303 | + | 0.171792i | ||||
\(832\) | 905.133 | 1.08790 | ||||||||
\(833\) | − | 922.650i | − | 1.10762i | ||||||
\(834\) | −47.4246 | − | 453.572i | −0.0568640 | − | 0.543852i | ||||
\(835\) | −1082.62 | −1.29655 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 130.716 | − | 42.2380i | 0.156172 | − | 0.0504636i | ||||
\(838\) | 919.813 | 1.09763 | ||||||||
\(839\) | 1582.29i | 1.88593i | 0.332899 | + | 0.942963i | \(0.391973\pi\) | ||||
−0.332899 | + | 0.942963i | \(0.608027\pi\) | |||||||
\(840\) | 741.608 | − | 77.5410i | 0.882867 | − | 0.0923107i | ||||
\(841\) | 750.951 | 0.892926 | ||||||||
\(842\) | − | 99.2035i | − | 0.117819i | ||||||
\(843\) | 6.26570 | + | 59.9256i | 0.00743262 | + | 0.0710862i | ||||
\(844\) | −82.1574 | −0.0973429 | ||||||||
\(845\) | − | 23.8564i | − | 0.0282324i | ||||||
\(846\) | −325.118 | + | 68.7388i | −0.384300 | + | 0.0812515i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 246.346i | 0.290502i | ||||||||
\(849\) | 1526.48 | − | 159.606i | 1.79797 | − | 0.187993i | ||||
\(850\) | 2101.48 | 2.47233 | ||||||||
\(851\) | − | 962.877i | − | 1.13146i | ||||||
\(852\) | −14.5299 | − | 138.965i | −0.0170539 | − | 0.163105i | ||||
\(853\) | 500.571 | 0.586836 | 0.293418 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293418 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(854\) | 299.315i | 0.350487i | ||||||||
\(855\) | 192.283 | + | 909.454i | 0.224893 | + | 1.06369i | ||||
\(856\) | −1677.49 | −1.95969 | ||||||||
\(857\) | 432.247i | 0.504373i | 0.967679 | + | 0.252186i | \(0.0811496\pi\) | ||||
−0.967679 | + | 0.252186i | \(0.918850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 383.432 | 0.446370 | 0.223185 | − | 0.974776i | \(-0.428355\pi\) | ||||
0.223185 | + | 0.974776i | \(0.428355\pi\) | |||||||
\(860\) | − | 129.968i | − | 0.151125i | ||||||
\(861\) | −38.5157 | − | 368.367i | −0.0447337 | − | 0.427836i | ||||
\(862\) | 398.035 | 0.461758 | ||||||||
\(863\) | − | 395.738i | − | 0.458561i | −0.973360 | − | 0.229280i | \(-0.926363\pi\) | ||
0.973360 | − | 0.229280i | \(-0.0736373\pi\) | |||||||
\(864\) | −52.6683 | − | 162.995i | −0.0609587 | − | 0.188652i | ||||
\(865\) | −1500.87 | −1.73511 | ||||||||
\(866\) | − | 687.532i | − | 0.793916i | ||||||
\(867\) | 1097.66 | − | 114.769i | 1.26605 | − | 0.132375i | ||||
\(868\) | 7.30202 | 0.00841247 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −46.4010 | − | 443.782i | −0.0533345 | − | 0.510095i | ||||
\(871\) | −1076.20 | −1.23559 | ||||||||
\(872\) | − | 265.532i | − | 0.304510i | ||||||
\(873\) | −141.046 | + | 29.8210i | −0.161565 | + | 0.0341592i | ||||
\(874\) | 659.712 | 0.754819 | ||||||||
\(875\) | − | 542.032i | − | 0.619466i | ||||||
\(876\) | 127.739 | − | 13.3561i | 0.145820 | − | 0.0152467i | ||||
\(877\) | −246.001 | −0.280503 | −0.140251 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140251 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(878\) | − | 786.707i | − | 0.896021i | ||||||
\(879\) | −154.100 | − | 1473.83i | −0.175313 | − | 1.67671i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1110.60i | 1.26061i | 0.776346 | + | 0.630307i | \(0.217071\pi\) | ||||
−0.776346 | + | 0.630307i | \(0.782929\pi\) | |||||||
\(882\) | −127.195 | − | 601.602i | −0.144212 | − | 0.682088i | ||||
\(883\) | −114.392 | −0.129549 | −0.0647744 | − | 0.997900i | \(-0.520633\pi\) | ||||
−0.0647744 | + | 0.997900i | \(0.520633\pi\) | |||||||
\(884\) | − | 133.751i | − | 0.151302i | ||||||
\(885\) | 669.004 | − | 69.9497i | 0.755937 | − | 0.0790392i | ||||
\(886\) | −1465.69 | −1.65428 | ||||||||
\(887\) | 985.799i | 1.11139i | 0.831388 | + | 0.555693i | \(0.187547\pi\) | ||||
−0.831388 | + | 0.555693i | \(0.812453\pi\) | |||||||
\(888\) | 90.2120 | + | 862.794i | 0.101590 | + | 0.971615i | ||||
\(889\) | 342.320 | 0.385062 | ||||||||
\(890\) | 1083.79i | 1.21775i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.5231 | −0.0308555 | ||||||||
\(893\) | − | 243.309i | − | 0.272462i | ||||||
\(894\) | 535.071 | − | 55.9459i | 0.598513 | − | 0.0625793i | ||||
\(895\) | −98.3801 | −0.109922 | ||||||||
\(896\) | 380.936i | 0.425151i | ||||||||
\(897\) | 113.682 | + | 1087.27i | 0.126736 | + | 1.21211i | ||||
\(898\) | −1279.54 | −1.42488 | ||||||||
\(899\) | − | 48.2802i | − | 0.0537044i | ||||||
\(900\) | −151.422 | + | 32.0146i | −0.168246 | + | 0.0355718i | ||||
\(901\) | 443.090 | 0.491776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 425.353 | − | 44.4740i | 0.471044 | − | 0.0492514i | ||||
\(904\) | 794.821 | 0.879227 | ||||||||
\(905\) | 699.988i | 0.773467i | ||||||||
\(906\) | −107.803 | − | 1031.03i | −0.118988 | − | 1.13801i | ||||
\(907\) | −485.815 | −0.535628 | −0.267814 | − | 0.963471i | \(-0.586301\pi\) | ||||
−0.267814 | + | 0.963471i | \(0.586301\pi\) | |||||||
\(908\) | − | 39.6815i | − | 0.0437021i | ||||||
\(909\) | −148.167 | − | 700.796i | −0.163000 | − | 0.770953i | ||||
\(910\) | 740.932 | 0.814211 | ||||||||
\(911\) | 1063.16i | 1.16703i | 0.812103 | + | 0.583515i | \(0.198323\pi\) | ||||
−0.812103 | + | 0.583515i | \(0.801677\pi\) | |||||||
\(912\) | −531.728 | + | 55.5964i | −0.583035 | + | 0.0609609i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1603.65i | 1.75454i | ||||||||
\(915\) | −112.692 | − | 1077.80i | −0.123161 | − | 1.17792i | ||||
\(916\) | 98.8586 | 0.107924 | ||||||||
\(917\) | 518.169i | 0.565070i | ||||||||
\(918\) | 1249.72 | − | 403.819i | 1.36135 | − | 0.439889i | ||||
\(919\) | 1366.68 | 1.48714 | 0.743571 | − | 0.668657i | \(-0.233130\pi\) | ||||
0.743571 | + | 0.668657i | \(0.233130\pi\) | |||||||
\(920\) | 1915.94i | 2.08255i | ||||||||
\(921\) | 1672.15 | − | 174.837i | 1.81558 | − | 0.189834i | ||||
\(922\) | 535.547 | 0.580854 | ||||||||
\(923\) | − | 1534.05i | − | 1.66203i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1496.69 | 1.61804 | ||||||||
\(926\) | − | 1390.71i | − | 1.50185i | ||||||
\(927\) | 194.854 | − | 41.1975i | 0.210199 | − | 0.0444417i | ||||
\(928\) | −60.2026 | −0.0648735 | ||||||||
\(929\) | − | 659.675i | − | 0.710092i | −0.934849 | − | 0.355046i | \(-0.884465\pi\) | ||
0.934849 | − | 0.355046i | \(-0.115535\pi\) | |||||||
\(930\) | 237.936 | − | 24.8781i | 0.255846 | − | 0.0267507i | ||||
\(931\) | 450.221 | 0.483589 | ||||||||
\(932\) | 115.793i | 0.124242i | ||||||||
\(933\) | 134.798 | + | 1289.22i | 0.144478 | + | 1.38180i | ||||
\(934\) | −871.241 | −0.932806 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −203.732 | − | 963.604i | −0.217663 | − | 1.02949i | ||||
\(937\) | 1122.73 | 1.19821 | 0.599107 | − | 0.800669i | \(-0.295523\pi\) | ||||
0.599107 | + | 0.800669i | \(0.295523\pi\) | |||||||
\(938\) | − | 561.724i | − | 0.598852i | ||||||
\(939\) | 465.839 | − | 48.7071i | 0.496101 | − | 0.0518713i | ||||
\(940\) | 63.9521 | 0.0680342 | ||||||||
\(941\) | − | 552.721i | − | 0.587376i | −0.955901 | − | 0.293688i | \(-0.905117\pi\) | ||
0.955901 | − | 0.293688i | \(-0.0948827\pi\) | |||||||
\(942\) | −85.3040 | − | 815.854i | −0.0905562 | − | 0.866087i | ||||
\(943\) | 951.675 | 1.00920 | ||||||||
\(944\) | 386.869i | 0.409819i | ||||||||
\(945\) | −247.206 | − | 765.039i | −0.261594 | − | 0.809566i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 903.931i | 0.954520i | 0.878762 | + | 0.477260i | \(0.158370\pi\) | ||||
−0.878762 | + | 0.477260i | \(0.841630\pi\) | |||||||
\(948\) | 74.6906 | − | 7.80950i | 0.0787876 | − | 0.00823786i | ||||
\(949\) | 1410.12 | 1.48590 | ||||||||
\(950\) | 1025.45i | 1.07942i | ||||||||
\(951\) | 105.600 | + | 1009.97i | 0.111041 | + | 1.06201i | ||||
\(952\) | 771.359 | 0.810251 | ||||||||
\(953\) | 904.813i | 0.949437i | 0.880138 | + | 0.474719i | \(0.157450\pi\) | ||||
−0.880138 | + | 0.474719i | \(0.842550\pi\) | |||||||
\(954\) | 288.911 | − | 61.0837i | 0.302842 | − | 0.0640290i | ||||
\(955\) | 569.862 | 0.596714 | ||||||||
\(956\) | 41.7700i | 0.0436924i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −542.530 | −0.566316 | ||||||||
\(959\) | 751.828i | 0.783971i | ||||||||
\(960\) | −177.872 | − | 1701.18i | −0.185283 | − | 1.77206i | ||||
\(961\) | −935.114 | −0.973064 | ||||||||
\(962\) | 862.008i | 0.896058i | ||||||||
\(963\) | 374.144 | + | 1769.61i | 0.388520 | + | 1.83760i | ||||
\(964\) | 35.1775 | 0.0364912 | ||||||||
\(965\) | 981.311i | 1.01690i | ||||||||
\(966\) | −567.500 | + | 59.3367i | −0.587475 | + | 0.0614251i | ||||
\(967\) | 1145.53 | 1.18462 | 0.592310 | − | 0.805710i | \(-0.298216\pi\) | ||||
0.592310 | + | 0.805710i | \(0.298216\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 99.9985 | + | 956.393i | 0.103198 | + | 0.986990i | ||||
\(970\) | −251.064 | −0.258829 | ||||||||
\(971\) | 1108.03i | 1.14112i | 0.821256 | + | 0.570560i | \(0.193274\pi\) | ||||
−0.821256 | + | 0.570560i | \(0.806726\pi\) | |||||||
\(972\) | −83.8959 | + | 48.1356i | −0.0863127 | + | 0.0495222i | ||||
\(973\) | −288.803 | −0.296817 | ||||||||
\(974\) | 1375.55i | 1.41227i | ||||||||
\(975\) | −1690.04 | + | 176.707i | −1.73337 | + | 0.181238i | ||||
\(976\) | 623.264 | 0.638590 | ||||||||
\(977\) | − | 766.291i | − | 0.784330i | −0.919895 | − | 0.392165i | \(-0.871726\pi\) | ||
0.919895 | − | 0.392165i | \(-0.128274\pi\) | |||||||
\(978\) | −33.4916 | − | 320.316i | −0.0342450 | − | 0.327522i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 118.338i | 0.120753i | ||||||||
\(981\) | −280.114 | + | 59.2238i | −0.285539 | + | 0.0603708i | ||||
\(982\) | −1167.83 | −1.18924 | ||||||||
\(983\) | 1747.89i | 1.77812i | 0.457791 | + | 0.889060i | \(0.348641\pi\) | ||||
−0.457791 | + | 0.889060i | \(0.651359\pi\) | |||||||
\(984\) | −852.757 | + | 89.1625i | −0.866623 | + | 0.0906123i | ||||
\(985\) | −2519.66 | −2.55803 | ||||||||
\(986\) | − | 461.586i | − | 0.468140i | ||||||
\(987\) | 21.8840 | + | 209.300i | 0.0221722 | + | 0.212057i | ||||
\(988\) | 65.2657 | 0.0660584 | ||||||||
\(989\) | 1098.90i | 1.11112i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 616.298 | 0.621895 | 0.310948 | − | 0.950427i | \(-0.399354\pi\) | ||||
0.310948 | + | 0.950427i | \(0.399354\pi\) | |||||||
\(992\) | − | 32.2780i | − | 0.0325383i | ||||||
\(993\) | −78.4327 | + | 8.20076i | −0.0789856 | + | 0.00825857i | ||||
\(994\) | 800.701 | 0.805534 | ||||||||
\(995\) | − | 1033.28i | − | 1.03847i | ||||||
\(996\) | −6.10021 | − | 58.3429i | −0.00612471 | − | 0.0585772i | ||||
\(997\) | −744.618 | −0.746859 | −0.373429 | − | 0.927659i | \(-0.621818\pi\) | ||||
−0.373429 | + | 0.927659i | \(0.621818\pi\) | |||||||
\(998\) | 1398.77i | 1.40158i | ||||||||
\(999\) | 890.054 | − | 287.602i | 0.890945 | − | 0.287890i |
(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 | 363.3.b.n.122.8 | yes | 12 | |
3.2 | odd | 2 | inner | 363.3.b.n.122.5 | ✓ | 12 | |
11.2 | odd | 10 | 363.3.h.r.323.6 | 48 | |||
11.3 | even | 5 | 363.3.h.r.251.7 | 48 | |||
11.4 | even | 5 | 363.3.h.r.269.6 | 48 | |||
11.5 | even | 5 | 363.3.h.r.245.5 | 48 | |||
11.6 | odd | 10 | 363.3.h.r.245.7 | 48 | |||
11.7 | odd | 10 | 363.3.h.r.269.8 | 48 | |||
11.8 | odd | 10 | 363.3.h.r.251.5 | 48 | |||
11.9 | even | 5 | 363.3.h.r.323.8 | 48 | |||
11.10 | odd | 2 | inner | 363.3.b.n.122.6 | yes | 12 | |
33.2 | even | 10 | 363.3.h.r.323.7 | 48 | |||
33.5 | odd | 10 | 363.3.h.r.245.8 | 48 | |||
33.8 | even | 10 | 363.3.h.r.251.8 | 48 | |||
33.14 | odd | 10 | 363.3.h.r.251.6 | 48 | |||
33.17 | even | 10 | 363.3.h.r.245.6 | 48 | |||
33.20 | odd | 10 | 363.3.h.r.323.5 | 48 | |||
33.26 | odd | 10 | 363.3.h.r.269.7 | 48 | |||
33.29 | even | 10 | 363.3.h.r.269.5 | 48 | |||
33.32 | even | 2 | inner | 363.3.b.n.122.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.n.122.5 | ✓ | 12 | 3.2 | odd | 2 | inner | |
363.3.b.n.122.6 | yes | 12 | 11.10 | odd | 2 | inner | |
363.3.b.n.122.7 | yes | 12 | 33.32 | even | 2 | inner | |
363.3.b.n.122.8 | yes | 12 | 1.1 | even | 1 | trivial | |
363.3.h.r.245.5 | 48 | 11.5 | even | 5 | |||
363.3.h.r.245.6 | 48 | 33.17 | even | 10 | |||
363.3.h.r.245.7 | 48 | 11.6 | odd | 10 | |||
363.3.h.r.245.8 | 48 | 33.5 | odd | 10 | |||
363.3.h.r.251.5 | 48 | 11.8 | odd | 10 | |||
363.3.h.r.251.6 | 48 | 33.14 | odd | 10 | |||
363.3.h.r.251.7 | 48 | 11.3 | even | 5 | |||
363.3.h.r.251.8 | 48 | 33.8 | even | 10 | |||
363.3.h.r.269.5 | 48 | 33.29 | even | 10 | |||
363.3.h.r.269.6 | 48 | 11.4 | even | 5 | |||
363.3.h.r.269.7 | 48 | 33.26 | odd | 10 | |||
363.3.h.r.269.8 | 48 | 11.7 | odd | 10 | |||
363.3.h.r.323.5 | 48 | 33.20 | odd | 10 | |||
363.3.h.r.323.6 | 48 | 11.2 | odd | 10 | |||
363.3.h.r.323.7 | 48 | 33.2 | even | 10 | |||
363.3.h.r.323.8 | 48 | 11.9 | even | 5 |