Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.21 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.20 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | − | 3.95881i | − | 0.565544i | −0.959187 | − | 0.282772i | \(-0.908746\pi\) | ||
0.959187 | − | 0.282772i | \(-0.0912540\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | 5.67111i | 0.515556i | 0.966204 | + | 0.257778i | \(0.0829903\pi\) | ||||
−0.966204 | + | 0.257778i | \(0.917010\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | 11.1376 | 0.856742 | 0.428371 | − | 0.903603i | \(-0.359088\pi\) | ||||
0.428371 | + | 0.903603i | \(0.359088\pi\) | |||||||
\(14\) | − | 5.59860i | − | 0.399900i | ||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 2.12953i | − | 0.125266i | −0.998037 | − | 0.0626332i | \(-0.980050\pi\) | ||
0.998037 | − | 0.0626332i | \(-0.0199498\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 20.9865i | 1.10455i | 0.833661 | + | 0.552277i | \(0.186241\pi\) | ||||
−0.833661 | + | 0.552277i | \(0.813759\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 6.85686i | 0.326517i | ||||||||
\(22\) | 8.02016i | 0.364553i | ||||||||
\(23\) | −10.6801 | − | 20.3700i | −0.464350 | − | 0.885652i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 15.7510 | 0.605808 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 7.91762i | − | 0.282772i | ||||||
\(29\) | 36.0592 | 1.24342 | 0.621710 | − | 0.783248i | \(-0.286438\pi\) | ||||
0.621710 | + | 0.783248i | \(0.286438\pi\) | |||||||
\(30\) | − | 5.47723i | − | 0.182574i | ||||||
\(31\) | 39.7941 | 1.28368 | 0.641840 | − | 0.766838i | \(-0.278171\pi\) | ||||
0.641840 | + | 0.766838i | \(0.278171\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 9.82265i | − | 0.297656i | ||||||
\(34\) | − | 3.01161i | − | 0.0885767i | ||||||
\(35\) | 8.85217 | 0.252919 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 50.2613i | 1.35841i | 0.733946 | + | 0.679207i | \(0.237676\pi\) | ||||
−0.733946 | + | 0.679207i | \(0.762324\pi\) | |||||||
\(38\) | 29.6794i | 0.781037i | ||||||||
\(39\) | −19.2910 | −0.494640 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 41.6563 | 1.01601 | 0.508003 | − | 0.861355i | \(-0.330384\pi\) | ||||
0.508003 | + | 0.861355i | \(0.330384\pi\) | |||||||
\(42\) | 9.69706i | 0.230882i | ||||||||
\(43\) | 41.3234i | 0.961009i | 0.876992 | + | 0.480505i | \(0.159547\pi\) | ||||
−0.876992 | + | 0.480505i | \(0.840453\pi\) | |||||||
\(44\) | 11.3422i | 0.257778i | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | −15.1039 | − | 28.8075i | −0.328345 | − | 0.626250i | ||||
\(47\) | 60.1764 | 1.28035 | 0.640175 | − | 0.768229i | \(-0.278862\pi\) | ||||
0.640175 | + | 0.768229i | \(0.278862\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 33.3278 | 0.680160 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 3.68845i | 0.0723226i | ||||||||
\(52\) | 22.2753 | 0.428371 | ||||||||
\(53\) | 3.29435i | 0.0621575i | 0.999517 | + | 0.0310787i | \(0.00989427\pi\) | ||||
−0.999517 | + | 0.0310787i | \(0.990106\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | −12.6810 | −0.230563 | ||||||||
\(56\) | − | 11.1972i | − | 0.199950i | ||||||
\(57\) | − | 36.3497i | − | 0.637714i | ||||||
\(58\) | 50.9954 | 0.879231 | ||||||||
\(59\) | −83.2918 | −1.41173 | −0.705863 | − | 0.708349i | \(-0.749440\pi\) | ||||
−0.705863 | + | 0.708349i | \(0.749440\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | 37.8857i | 0.621077i | 0.950561 | + | 0.310538i | \(0.100509\pi\) | ||||
−0.950561 | + | 0.310538i | \(0.899491\pi\) | |||||||
\(62\) | 56.2773 | 0.907699 | ||||||||
\(63\) | − | 11.8764i | − | 0.188515i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 24.9045i | 0.383147i | ||||||||
\(66\) | − | 13.8913i | − | 0.210475i | ||||||
\(67\) | − | 61.1024i | − | 0.911975i | −0.889986 | − | 0.455988i | \(-0.849286\pi\) | ||
0.889986 | − | 0.455988i | \(-0.150714\pi\) | |||||||
\(68\) | − | 4.25906i | − | 0.0626332i | ||||||
\(69\) | 18.4984 | + | 35.2819i | 0.268093 | + | 0.511331i | ||||
\(70\) | 12.5189 | 0.178841 | ||||||||
\(71\) | −0.572102 | −0.00805777 | −0.00402888 | − | 0.999992i | \(-0.501282\pi\) | ||||
−0.00402888 | + | 0.999992i | \(0.501282\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | 40.8795 | 0.559994 | 0.279997 | − | 0.960001i | \(-0.409667\pi\) | ||||
0.279997 | + | 0.960001i | \(0.409667\pi\) | |||||||
\(74\) | 71.0803i | 0.960544i | ||||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | 41.9730i | 0.552277i | ||||||||
\(77\) | 22.4509 | 0.291570 | ||||||||
\(78\) | −27.2815 | −0.349763 | ||||||||
\(79\) | 86.8569i | 1.09945i | 0.835344 | + | 0.549727i | \(0.185268\pi\) | ||||
−0.835344 | + | 0.549727i | \(0.814732\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 58.9109 | 0.718425 | ||||||||
\(83\) | 84.6886i | 1.02034i | 0.860072 | + | 0.510172i | \(0.170418\pi\) | ||||
−0.860072 | + | 0.510172i | \(0.829582\pi\) | |||||||
\(84\) | 13.7137i | 0.163259i | ||||||||
\(85\) | 4.76177 | 0.0560208 | ||||||||
\(86\) | 58.4401i | 0.679536i | ||||||||
\(87\) | −62.4563 | −0.717889 | ||||||||
\(88\) | 16.0403i | 0.182276i | ||||||||
\(89\) | − | 94.7533i | − | 1.06464i | −0.846542 | − | 0.532322i | \(-0.821320\pi\) | ||
0.846542 | − | 0.532322i | \(-0.178680\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | − | 44.0918i | − | 0.484525i | ||||||
\(92\) | −21.3601 | − | 40.7400i | −0.232175 | − | 0.442826i | ||||
\(93\) | −68.9254 | −0.741133 | ||||||||
\(94\) | 85.1023 | 0.905344 | ||||||||
\(95\) | −46.9273 | −0.493971 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | − | 171.701i | − | 1.77011i | −0.465485 | − | 0.885056i | \(-0.654120\pi\) | ||
0.465485 | − | 0.885056i | \(-0.345880\pi\) | |||||||
\(98\) | 47.1327 | 0.480946 | ||||||||
\(99\) | 17.0133i | 0.171852i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −48.8836 | −0.483997 | −0.241998 | − | 0.970277i | \(-0.577803\pi\) | ||||
−0.241998 | + | 0.970277i | \(0.577803\pi\) | |||||||
\(102\) | 5.21626i | 0.0511398i | ||||||||
\(103\) | 3.88018i | 0.0376716i | 0.999823 | + | 0.0188358i | \(0.00599598\pi\) | ||||
−0.999823 | + | 0.0188358i | \(0.994004\pi\) | |||||||
\(104\) | 31.5020 | 0.302904 | ||||||||
\(105\) | −15.3324 | −0.146023 | ||||||||
\(106\) | 4.65891i | 0.0439520i | ||||||||
\(107\) | − | 121.583i | − | 1.13629i | −0.822927 | − | 0.568147i | \(-0.807661\pi\) | ||
0.822927 | − | 0.568147i | \(-0.192339\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | 140.035i | 1.28473i | 0.766401 | + | 0.642363i | \(0.222046\pi\) | ||||
−0.766401 | + | 0.642363i | \(0.777954\pi\) | |||||||
\(110\) | −17.9336 | −0.163033 | ||||||||
\(111\) | − | 87.0552i | − | 0.784281i | ||||||
\(112\) | − | 15.8352i | − | 0.141386i | ||||||
\(113\) | − | 3.73201i | − | 0.0330267i | −0.999864 | − | 0.0165133i | \(-0.994743\pi\) | ||
0.999864 | − | 0.0165133i | \(-0.00525660\pi\) | |||||||
\(114\) | − | 51.4063i | − | 0.450932i | ||||||
\(115\) | 45.5487 | − | 23.8813i | 0.396075 | − | 0.207664i | ||||
\(116\) | 72.1184 | 0.621710 | ||||||||
\(117\) | 33.4129 | 0.285581 | ||||||||
\(118\) | −117.792 | −0.998240 | ||||||||
\(119\) | −8.43040 | −0.0708437 | ||||||||
\(120\) | − | 10.9545i | − | 0.0912871i | ||||||
\(121\) | 88.8385 | 0.734202 | ||||||||
\(122\) | 53.5784i | 0.439167i | ||||||||
\(123\) | −72.1508 | −0.586592 | ||||||||
\(124\) | 79.5882 | 0.641840 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | − | 16.7958i | − | 0.133300i | ||||||
\(127\) | 189.032 | 1.48844 | 0.744221 | − | 0.667933i | \(-0.232821\pi\) | ||||
0.744221 | + | 0.667933i | \(0.232821\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 71.5742i | − | 0.554839i | ||||||
\(130\) | 35.2203i | 0.270926i | ||||||||
\(131\) | −102.753 | −0.784374 | −0.392187 | − | 0.919885i | \(-0.628281\pi\) | ||||
−0.392187 | + | 0.919885i | \(0.628281\pi\) | |||||||
\(132\) | − | 19.6453i | − | 0.148828i | ||||||
\(133\) | 83.0816 | 0.624674 | ||||||||
\(134\) | − | 86.4118i | − | 0.644864i | ||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | − | 6.02322i | − | 0.0442884i | ||||||
\(137\) | − | 53.0102i | − | 0.386936i | −0.981107 | − | 0.193468i | \(-0.938026\pi\) | ||
0.981107 | − | 0.193468i | \(-0.0619736\pi\) | |||||||
\(138\) | 26.1607 | + | 49.8961i | 0.189570 | + | 0.361566i | ||||
\(139\) | −230.317 | −1.65696 | −0.828478 | − | 0.560022i | \(-0.810793\pi\) | ||||
−0.828478 | + | 0.560022i | \(0.810793\pi\) | |||||||
\(140\) | 17.7043 | 0.126460 | ||||||||
\(141\) | −104.229 | −0.739210 | ||||||||
\(142\) | −0.809074 | −0.00569770 | ||||||||
\(143\) | 63.1628i | 0.441698i | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 80.6308i | 0.556074i | ||||||||
\(146\) | 57.8124 | 0.395975 | ||||||||
\(147\) | −57.7255 | −0.392690 | ||||||||
\(148\) | 100.523i | 0.679207i | ||||||||
\(149\) | − | 34.0099i | − | 0.228254i | −0.993466 | − | 0.114127i | \(-0.963593\pi\) | ||
0.993466 | − | 0.114127i | \(-0.0364071\pi\) | |||||||
\(150\) | 12.2474 | 0.0816497 | ||||||||
\(151\) | −273.426 | −1.81077 | −0.905383 | − | 0.424596i | \(-0.860416\pi\) | ||||
−0.905383 | + | 0.424596i | \(0.860416\pi\) | |||||||
\(152\) | 59.3588i | 0.390519i | ||||||||
\(153\) | − | 6.38859i | − | 0.0417555i | ||||||
\(154\) | 31.7503 | 0.206171 | ||||||||
\(155\) | 88.9823i | 0.574079i | ||||||||
\(156\) | −38.5819 | −0.247320 | ||||||||
\(157\) | − | 302.701i | − | 1.92803i | −0.265841 | − | 0.964017i | \(-0.585650\pi\) | ||
0.265841 | − | 0.964017i | \(-0.414350\pi\) | |||||||
\(158\) | 122.834i | 0.777431i | ||||||||
\(159\) | − | 5.70598i | − | 0.0358866i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −80.6409 | + | 42.2803i | −0.500875 | + | 0.262611i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −101.769 | −0.624352 | −0.312176 | − | 0.950024i | \(-0.601058\pi\) | ||||
−0.312176 | + | 0.950024i | \(0.601058\pi\) | |||||||
\(164\) | 83.3126 | 0.508003 | ||||||||
\(165\) | 21.9641 | 0.133116 | ||||||||
\(166\) | 119.768i | 0.721493i | ||||||||
\(167\) | −124.606 | −0.746143 | −0.373071 | − | 0.927803i | \(-0.621695\pi\) | ||||
−0.373071 | + | 0.927803i | \(0.621695\pi\) | |||||||
\(168\) | 19.3941i | 0.115441i | ||||||||
\(169\) | −44.9529 | −0.265994 | ||||||||
\(170\) | 6.73416 | 0.0396127 | ||||||||
\(171\) | 62.9595i | 0.368184i | ||||||||
\(172\) | 82.6468i | 0.480505i | ||||||||
\(173\) | −278.331 | −1.60885 | −0.804425 | − | 0.594054i | \(-0.797526\pi\) | ||||
−0.804425 | + | 0.594054i | \(0.797526\pi\) | |||||||
\(174\) | −88.3266 | −0.507624 | ||||||||
\(175\) | 19.7940i | 0.113109i | ||||||||
\(176\) | 22.6844i | 0.128889i | ||||||||
\(177\) | 144.266 | 0.815060 | ||||||||
\(178\) | − | 134.001i | − | 0.752817i | ||||||
\(179\) | −22.7044 | −0.126840 | −0.0634202 | − | 0.997987i | \(-0.520201\pi\) | ||||
−0.0634202 | + | 0.997987i | \(0.520201\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | 151.385i | 0.836379i | 0.908360 | + | 0.418189i | \(0.137335\pi\) | ||||
−0.908360 | + | 0.418189i | \(0.862665\pi\) | |||||||
\(182\) | − | 62.3552i | − | 0.342611i | ||||||
\(183\) | − | 65.6199i | − | 0.358579i | ||||||
\(184\) | −30.2078 | − | 57.6150i | −0.164173 | − | 0.313125i | ||||
\(185\) | −112.388 | −0.607502 | ||||||||
\(186\) | −97.4752 | −0.524060 | ||||||||
\(187\) | 12.0768 | 0.0645818 | ||||||||
\(188\) | 120.353 | 0.640175 | ||||||||
\(189\) | 20.5706i | 0.108839i | ||||||||
\(190\) | −66.3652 | −0.349290 | ||||||||
\(191\) | − | 68.1039i | − | 0.356565i | −0.983979 | − | 0.178282i | \(-0.942946\pi\) | ||
0.983979 | − | 0.178282i | \(-0.0570541\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | 243.269 | 1.26046 | 0.630230 | − | 0.776408i | \(-0.282961\pi\) | ||||
0.630230 | + | 0.776408i | \(0.282961\pi\) | |||||||
\(194\) | − | 242.822i | − | 1.25166i | ||||||
\(195\) | − | 43.1359i | − | 0.221210i | ||||||
\(196\) | 66.6556 | 0.340080 | ||||||||
\(197\) | −131.358 | −0.666790 | −0.333395 | − | 0.942787i | \(-0.608194\pi\) | ||||
−0.333395 | + | 0.942787i | \(0.608194\pi\) | |||||||
\(198\) | 24.0605i | 0.121518i | ||||||||
\(199\) | − | 313.700i | − | 1.57638i | −0.615432 | − | 0.788190i | \(-0.711018\pi\) | ||
0.615432 | − | 0.788190i | \(-0.288982\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 105.832i | 0.526529i | ||||||||
\(202\) | −69.1319 | −0.342237 | ||||||||
\(203\) | − | 142.751i | − | 0.703209i | ||||||
\(204\) | 7.37690i | 0.0361613i | ||||||||
\(205\) | 93.1463i | 0.454372i | ||||||||
\(206\) | 5.48740i | 0.0266379i | ||||||||
\(207\) | −32.0402 | − | 61.1100i | −0.154783 | − | 0.295217i | ||||
\(208\) | 44.5506 | 0.214185 | ||||||||
\(209\) | −119.017 | −0.569459 | ||||||||
\(210\) | −21.6833 | −0.103254 | ||||||||
\(211\) | 75.8630 | 0.359540 | 0.179770 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179770 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(212\) | 6.58869i | 0.0310787i | ||||||||
\(213\) | 0.990909 | 0.00465216 | ||||||||
\(214\) | − | 171.945i | − | 0.803481i | ||||||
\(215\) | −92.4019 | −0.429777 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | − | 157.537i | − | 0.725978i | ||||||
\(218\) | 198.040i | 0.908438i | ||||||||
\(219\) | −70.8054 | −0.323313 | ||||||||
\(220\) | −25.3620 | −0.115282 | ||||||||
\(221\) | − | 23.7179i | − | 0.107321i | ||||||
\(222\) | − | 123.115i | − | 0.554571i | ||||||
\(223\) | −165.794 | −0.743472 | −0.371736 | − | 0.928338i | \(-0.621237\pi\) | ||||
−0.371736 | + | 0.928338i | \(0.621237\pi\) | |||||||
\(224\) | − | 22.3944i | − | 0.0999750i | ||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | − | 5.27786i | − | 0.0233534i | ||||||
\(227\) | − | 405.393i | − | 1.78587i | −0.450183 | − | 0.892937i | \(-0.648641\pi\) | ||
0.450183 | − | 0.892937i | \(-0.351359\pi\) | |||||||
\(228\) | − | 72.6994i | − | 0.318857i | ||||||
\(229\) | 382.310i | 1.66947i | 0.550649 | + | 0.834737i | \(0.314380\pi\) | ||||
−0.550649 | + | 0.834737i | \(0.685620\pi\) | |||||||
\(230\) | 64.4156 | − | 33.7733i | 0.280068 | − | 0.146840i | ||||
\(231\) | −38.8860 | −0.168338 | ||||||||
\(232\) | 101.991 | 0.439615 | ||||||||
\(233\) | −125.133 | −0.537050 | −0.268525 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268525 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(234\) | 47.2530 | 0.201936 | ||||||||
\(235\) | 134.559i | 0.572590i | ||||||||
\(236\) | −166.584 | −0.705863 | ||||||||
\(237\) | − | 150.441i | − | 0.634770i | ||||||
\(238\) | −11.9224 | −0.0500941 | ||||||||
\(239\) | −129.207 | −0.540616 | −0.270308 | − | 0.962774i | \(-0.587126\pi\) | ||||
−0.270308 | + | 0.962774i | \(0.587126\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | 313.373i | 1.30030i | 0.759805 | + | 0.650151i | \(0.225295\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774705\pi\) | |||||||
\(242\) | 125.637 | 0.519160 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 75.7713i | 0.310538i | ||||||||
\(245\) | 74.5233i | 0.304177i | ||||||||
\(246\) | −102.037 | −0.414783 | ||||||||
\(247\) | 233.740i | 0.946317i | ||||||||
\(248\) | 112.555 | 0.453850 | ||||||||
\(249\) | − | 146.685i | − | 0.589096i | ||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | − | 152.125i | − | 0.606075i | −0.952979 | − | 0.303037i | \(-0.901999\pi\) | ||
0.952979 | − | 0.303037i | \(-0.0980007\pi\) | |||||||
\(252\) | − | 23.7529i | − | 0.0942574i | ||||||
\(253\) | 115.520 | − | 60.5678i | 0.456603 | − | 0.239398i | ||||
\(254\) | 267.332 | 1.05249 | ||||||||
\(255\) | −8.24763 | −0.0323436 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 19.5904 | 0.0762272 | 0.0381136 | − | 0.999273i | \(-0.487865\pi\) | ||||
0.0381136 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(258\) | − | 101.221i | − | 0.392330i | ||||||
\(259\) | 198.975 | 0.768244 | ||||||||
\(260\) | 49.8090i | 0.191573i | ||||||||
\(261\) | 108.178 | 0.414473 | ||||||||
\(262\) | −145.315 | −0.554636 | ||||||||
\(263\) | 127.348i | 0.484212i | 0.970250 | + | 0.242106i | \(0.0778381\pi\) | ||||
−0.970250 | + | 0.242106i | \(0.922162\pi\) | |||||||
\(264\) | − | 27.7827i | − | 0.105237i | ||||||
\(265\) | −7.36638 | −0.0277977 | ||||||||
\(266\) | 117.495 | 0.441711 | ||||||||
\(267\) | 164.118i | 0.614672i | ||||||||
\(268\) | − | 122.205i | − | 0.455988i | ||||||
\(269\) | 142.959 | 0.531448 | 0.265724 | − | 0.964049i | \(-0.414389\pi\) | ||||
0.265724 | + | 0.964049i | \(0.414389\pi\) | |||||||
\(270\) | − | 16.4317i | − | 0.0608581i | ||||||
\(271\) | −63.7008 | −0.235058 | −0.117529 | − | 0.993069i | \(-0.537497\pi\) | ||||
−0.117529 | + | 0.993069i | \(0.537497\pi\) | |||||||
\(272\) | − | 8.51812i | − | 0.0313166i | ||||||
\(273\) | 76.3692i | 0.279741i | ||||||||
\(274\) | − | 74.9678i | − | 0.273605i | ||||||
\(275\) | − | 28.3556i | − | 0.103111i | ||||||
\(276\) | 36.9968 | + | 70.5637i | 0.134046 | + | 0.255666i | ||||
\(277\) | 448.470 | 1.61903 | 0.809513 | − | 0.587101i | \(-0.199731\pi\) | ||||
0.809513 | + | 0.587101i | \(0.199731\pi\) | |||||||
\(278\) | −325.717 | −1.17164 | ||||||||
\(279\) | 119.382 | 0.427893 | ||||||||
\(280\) | 25.0377 | 0.0894204 | ||||||||
\(281\) | − | 154.698i | − | 0.550525i | −0.961369 | − | 0.275263i | \(-0.911235\pi\) | ||
0.961369 | − | 0.275263i | \(-0.0887648\pi\) | |||||||
\(282\) | −147.402 | −0.522701 | ||||||||
\(283\) | 19.1545i | 0.0676837i | 0.999427 | + | 0.0338418i | \(0.0107742\pi\) | ||||
−0.999427 | + | 0.0338418i | \(0.989226\pi\) | |||||||
\(284\) | −1.14420 | −0.00402888 | ||||||||
\(285\) | 81.2804 | 0.285194 | ||||||||
\(286\) | 89.3257i | 0.312328i | ||||||||
\(287\) | − | 164.909i | − | 0.574597i | ||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 284.465 | 0.984308 | ||||||||
\(290\) | 114.029i | 0.393204i | ||||||||
\(291\) | 297.395i | 1.02197i | ||||||||
\(292\) | 81.7591 | 0.279997 | ||||||||
\(293\) | 269.403i | 0.919463i | 0.888058 | + | 0.459732i | \(0.152054\pi\) | ||||
−0.888058 | + | 0.459732i | \(0.847946\pi\) | |||||||
\(294\) | −81.6362 | −0.277674 | ||||||||
\(295\) | − | 186.246i | − | 0.631343i | ||||||
\(296\) | 142.161i | 0.480272i | ||||||||
\(297\) | − | 29.4680i | − | 0.0992187i | ||||||
\(298\) | − | 48.0972i | − | 0.161400i | ||||||
\(299\) | −118.951 | − | 226.874i | −0.397828 | − | 0.758775i | ||||
\(300\) | 17.3205 | 0.0577350 | ||||||||
\(301\) | 163.592 | 0.543493 | ||||||||
\(302\) | −386.682 | −1.28040 | ||||||||
\(303\) | 84.6690 | 0.279436 | ||||||||
\(304\) | 83.9461i | 0.276138i | ||||||||
\(305\) | −84.7149 | −0.277754 | ||||||||
\(306\) | − | 9.03483i | − | 0.0295256i | ||||||
\(307\) | 331.722 | 1.08053 | 0.540263 | − | 0.841496i | \(-0.318325\pi\) | ||||
0.540263 | + | 0.841496i | \(0.318325\pi\) | |||||||
\(308\) | 44.9017 | 0.145785 | ||||||||
\(309\) | − | 6.72067i | − | 0.0217497i | ||||||
\(310\) | 125.840i | 0.405935i | ||||||||
\(311\) | −397.584 | −1.27840 | −0.639202 | − | 0.769039i | \(-0.720735\pi\) | ||||
−0.639202 | + | 0.769039i | \(0.720735\pi\) | |||||||
\(312\) | −54.5631 | −0.174882 | ||||||||
\(313\) | 124.944i | 0.399181i | 0.979879 | + | 0.199590i | \(0.0639611\pi\) | ||||
−0.979879 | + | 0.199590i | \(0.936039\pi\) | |||||||
\(314\) | − | 428.084i | − | 1.36333i | ||||||
\(315\) | 26.5565 | 0.0843064 | ||||||||
\(316\) | 173.714i | 0.549727i | ||||||||
\(317\) | 272.823 | 0.860642 | 0.430321 | − | 0.902676i | \(-0.358400\pi\) | ||||
0.430321 | + | 0.902676i | \(0.358400\pi\) | |||||||
\(318\) | − | 8.06947i | − | 0.0253757i | ||||||
\(319\) | 204.496i | 0.641052i | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | 210.589i | 0.656039i | ||||||||
\(322\) | −114.043 | + | 59.7934i | −0.354172 | + | 0.185694i | ||||
\(323\) | 44.6914 | 0.138363 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −55.6882 | −0.171348 | ||||||||
\(326\) | −143.924 | −0.441483 | ||||||||
\(327\) | − | 242.548i | − | 0.741737i | ||||||
\(328\) | 117.822 | 0.359213 | ||||||||
\(329\) | − | 238.227i | − | 0.724094i | ||||||
\(330\) | 31.0620 | 0.0941271 | ||||||||
\(331\) | 158.093 | 0.477621 | 0.238811 | − | 0.971066i | \(-0.423243\pi\) | ||||
0.238811 | + | 0.971066i | \(0.423243\pi\) | |||||||
\(332\) | 169.377i | 0.510172i | ||||||||
\(333\) | 150.784i | 0.452805i | ||||||||
\(334\) | −176.219 | −0.527603 | ||||||||
\(335\) | 136.629 | 0.407848 | ||||||||
\(336\) | 27.4274i | 0.0816293i | ||||||||
\(337\) | 187.915i | 0.557610i | 0.960348 | + | 0.278805i | \(0.0899383\pi\) | ||||
−0.960348 | + | 0.278805i | \(0.910062\pi\) | |||||||
\(338\) | −63.5730 | −0.188086 | ||||||||
\(339\) | 6.46404i | 0.0190680i | ||||||||
\(340\) | 9.52354 | 0.0280104 | ||||||||
\(341\) | 225.677i | 0.661809i | ||||||||
\(342\) | 89.0382i | 0.260346i | ||||||||
\(343\) | − | 325.920i | − | 0.950205i | ||||||
\(344\) | 116.880i | 0.339768i | ||||||||
\(345\) | −78.8926 | + | 41.3637i | −0.228674 | + | 0.119895i | ||||
\(346\) | −393.620 | −1.13763 | ||||||||
\(347\) | −313.436 | −0.903274 | −0.451637 | − | 0.892202i | \(-0.649160\pi\) | ||||
−0.451637 | + | 0.892202i | \(0.649160\pi\) | |||||||
\(348\) | −124.913 | −0.358944 | ||||||||
\(349\) | 363.470 | 1.04146 | 0.520730 | − | 0.853721i | \(-0.325660\pi\) | ||||
0.520730 | + | 0.853721i | \(0.325660\pi\) | |||||||
\(350\) | 27.9930i | 0.0799800i | ||||||||
\(351\) | −57.8729 | −0.164880 | ||||||||
\(352\) | 32.0807i | 0.0911382i | ||||||||
\(353\) | −524.725 | −1.48647 | −0.743236 | − | 0.669029i | \(-0.766710\pi\) | ||||
−0.743236 | + | 0.669029i | \(0.766710\pi\) | |||||||
\(354\) | 204.022 | 0.576334 | ||||||||
\(355\) | − | 1.27926i | − | 0.00360354i | ||||||
\(356\) | − | 189.507i | − | 0.532322i | ||||||
\(357\) | 14.6019 | 0.0409016 | ||||||||
\(358\) | −32.1089 | −0.0896897 | ||||||||
\(359\) | − | 311.701i | − | 0.868249i | −0.900853 | − | 0.434124i | \(-0.857058\pi\) | ||
0.900853 | − | 0.434124i | \(-0.142942\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | −79.4338 | −0.220038 | ||||||||
\(362\) | 214.090i | 0.591409i | ||||||||
\(363\) | −153.873 | −0.423892 | ||||||||
\(364\) | − | 88.1836i | − | 0.242263i | ||||||
\(365\) | 91.4094i | 0.250437i | ||||||||
\(366\) | − | 92.8006i | − | 0.253553i | ||||||
\(367\) | − | 468.490i | − | 1.27654i | −0.769813 | − | 0.638269i | \(-0.779651\pi\) | ||
0.769813 | − | 0.638269i | \(-0.220349\pi\) | |||||||
\(368\) | −42.7202 | − | 81.4799i | −0.116088 | − | 0.221413i | ||||
\(369\) | 124.969 | 0.338669 | ||||||||
\(370\) | −158.940 | −0.429568 | ||||||||
\(371\) | 13.0417 | 0.0351528 | ||||||||
\(372\) | −137.851 | −0.370567 | ||||||||
\(373\) | − | 7.45302i | − | 0.0199813i | −0.999950 | − | 0.00999064i | \(-0.996820\pi\) | ||
0.999950 | − | 0.00999064i | \(-0.00318017\pi\) | |||||||
\(374\) | 17.0792 | 0.0456662 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | 170.205 | 0.452672 | ||||||||
\(377\) | 401.614 | 1.06529 | ||||||||
\(378\) | 29.0912i | 0.0769608i | ||||||||
\(379\) | 444.034i | 1.17159i | 0.810458 | + | 0.585796i | \(0.199218\pi\) | ||||
−0.810458 | + | 0.585796i | \(0.800782\pi\) | |||||||
\(380\) | −93.8545 | −0.246986 | ||||||||
\(381\) | −327.413 | −0.859353 | ||||||||
\(382\) | − | 96.3134i | − | 0.252129i | ||||||
\(383\) | − | 315.599i | − | 0.824017i | −0.911180 | − | 0.412009i | \(-0.864827\pi\) | ||
0.911180 | − | 0.412009i | \(-0.135173\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | 50.2016i | 0.130394i | ||||||||
\(386\) | 344.034 | 0.891280 | ||||||||
\(387\) | 123.970i | 0.320336i | ||||||||
\(388\) | − | 343.402i | − | 0.885056i | ||||||
\(389\) | − | 126.333i | − | 0.324763i | −0.986728 | − | 0.162381i | \(-0.948083\pi\) | ||
0.986728 | − | 0.162381i | \(-0.0519175\pi\) | |||||||
\(390\) | − | 61.0034i | − | 0.156419i | ||||||
\(391\) | −43.3785 | + | 22.7435i | −0.110942 | + | 0.0581675i | ||||
\(392\) | 94.2653 | 0.240473 | ||||||||
\(393\) | 177.974 | 0.452859 | ||||||||
\(394\) | −185.768 | −0.471492 | ||||||||
\(395\) | −194.218 | −0.491691 | ||||||||
\(396\) | 34.0267i | 0.0859259i | ||||||||
\(397\) | −165.211 | −0.416148 | −0.208074 | − | 0.978113i | \(-0.566719\pi\) | ||||
−0.208074 | + | 0.978113i | \(0.566719\pi\) | |||||||
\(398\) | − | 443.638i | − | 1.11467i | ||||||
\(399\) | −143.902 | −0.360656 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 298.998i | 0.745630i | 0.927906 | + | 0.372815i | \(0.121607\pi\) | ||||
−0.927906 | + | 0.372815i | \(0.878393\pi\) | |||||||
\(402\) | 149.670i | 0.372312i | ||||||||
\(403\) | 443.212 | 1.09978 | ||||||||
\(404\) | −97.7673 | −0.241998 | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | − | 201.881i | − | 0.497244i | ||||||
\(407\) | −285.038 | −0.700338 | ||||||||
\(408\) | 10.4325i | 0.0255699i | ||||||||
\(409\) | −55.5554 | −0.135832 | −0.0679162 | − | 0.997691i | \(-0.521635\pi\) | ||||
−0.0679162 | + | 0.997691i | \(0.521635\pi\) | |||||||
\(410\) | 131.729i | 0.321290i | ||||||||
\(411\) | 91.8164i | 0.223398i | ||||||||
\(412\) | 7.76036i | 0.0188358i | ||||||||
\(413\) | 329.736i | 0.798393i | ||||||||
\(414\) | −45.3117 | − | 86.4225i | −0.109448 | − | 0.208750i | ||||
\(415\) | −189.369 | −0.456312 | ||||||||
\(416\) | 63.0040 | 0.151452 | ||||||||
\(417\) | 398.920 | 0.956644 | ||||||||
\(418\) | −168.315 | −0.402668 | ||||||||
\(419\) | 422.645i | 1.00870i | 0.863500 | + | 0.504349i | \(0.168268\pi\) | ||||
−0.863500 | + | 0.504349i | \(0.831732\pi\) | |||||||
\(420\) | −30.6648 | −0.0730114 | ||||||||
\(421\) | − | 106.651i | − | 0.253328i | −0.991946 | − | 0.126664i | \(-0.959573\pi\) | ||
0.991946 | − | 0.126664i | \(-0.0404269\pi\) | |||||||
\(422\) | 107.287 | 0.254233 | ||||||||
\(423\) | 180.529 | 0.426783 | ||||||||
\(424\) | 9.31782i | 0.0219760i | ||||||||
\(425\) | 10.6476i | 0.0250533i | ||||||||
\(426\) | 1.40136 | 0.00328957 | ||||||||
\(427\) | 149.982 | 0.351246 | ||||||||
\(428\) | − | 243.167i | − | 0.568147i | ||||||
\(429\) | − | 109.401i | − | 0.255014i | ||||||
\(430\) | −130.676 | −0.303898 | ||||||||
\(431\) | 305.614i | 0.709080i | 0.935041 | + | 0.354540i | \(0.115363\pi\) | ||||
−0.935041 | + | 0.354540i | \(0.884637\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | − | 285.890i | − | 0.660254i | −0.943936 | − | 0.330127i | \(-0.892908\pi\) | ||
0.943936 | − | 0.330127i | \(-0.107092\pi\) | |||||||
\(434\) | − | 222.791i | − | 0.513344i | ||||||
\(435\) | − | 139.657i | − | 0.321050i | ||||||
\(436\) | 280.070i | 0.642363i | ||||||||
\(437\) | 427.495 | − | 224.137i | 0.978249 | − | 0.512900i | ||||
\(438\) | −100.134 | −0.228616 | ||||||||
\(439\) | −461.780 | −1.05189 | −0.525945 | − | 0.850519i | \(-0.676288\pi\) | ||||
−0.525945 | + | 0.850519i | \(0.676288\pi\) | |||||||
\(440\) | −35.8673 | −0.0815165 | ||||||||
\(441\) | 99.9835 | 0.226720 | ||||||||
\(442\) | − | 33.5422i | − | 0.0758874i | ||||||
\(443\) | −65.0709 | −0.146887 | −0.0734434 | − | 0.997299i | \(-0.523399\pi\) | ||||
−0.0734434 | + | 0.997299i | \(0.523399\pi\) | |||||||
\(444\) | − | 174.110i | − | 0.392141i | ||||||
\(445\) | 211.875 | 0.476123 | ||||||||
\(446\) | −234.469 | −0.525714 | ||||||||
\(447\) | 58.9068i | 0.131783i | ||||||||
\(448\) | − | 31.6705i | − | 0.0706930i | ||||||
\(449\) | 547.308 | 1.21895 | 0.609475 | − | 0.792806i | \(-0.291380\pi\) | ||||
0.609475 | + | 0.792806i | \(0.291380\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | 236.237i | 0.523808i | ||||||||
\(452\) | − | 7.46403i | − | 0.0165133i | ||||||
\(453\) | 473.587 | 1.04545 | ||||||||
\(454\) | − | 573.313i | − | 1.26280i | ||||||
\(455\) | 98.5923 | 0.216686 | ||||||||
\(456\) | − | 102.813i | − | 0.225466i | ||||||
\(457\) | 334.369i | 0.731660i | 0.930682 | + | 0.365830i | \(0.119215\pi\) | ||||
−0.930682 | + | 0.365830i | \(0.880785\pi\) | |||||||
\(458\) | 540.667i | 1.18050i | ||||||||
\(459\) | 11.0654i | 0.0241075i | ||||||||
\(460\) | 91.0973 | − | 47.7627i | 0.198038 | − | 0.103832i | ||||
\(461\) | −384.546 | −0.834156 | −0.417078 | − | 0.908871i | \(-0.636946\pi\) | ||||
−0.417078 | + | 0.908871i | \(0.636946\pi\) | |||||||
\(462\) | −54.9931 | −0.119033 | ||||||||
\(463\) | 741.501 | 1.60151 | 0.800757 | − | 0.598990i | \(-0.204431\pi\) | ||||
0.800757 | + | 0.598990i | \(0.204431\pi\) | |||||||
\(464\) | 144.237 | 0.310855 | ||||||||
\(465\) | − | 154.122i | − | 0.331445i | ||||||
\(466\) | −176.964 | −0.379752 | ||||||||
\(467\) | − | 183.855i | − | 0.393695i | −0.980434 | − | 0.196847i | \(-0.936930\pi\) | ||
0.980434 | − | 0.196847i | \(-0.0630704\pi\) | |||||||
\(468\) | 66.8259 | 0.142790 | ||||||||
\(469\) | −241.893 | −0.515763 | ||||||||
\(470\) | 190.295i | 0.404882i | ||||||||
\(471\) | 524.294i | 1.11315i | ||||||||
\(472\) | −235.585 | −0.499120 | ||||||||
\(473\) | −234.350 | −0.495454 | ||||||||
\(474\) | − | 212.755i | − | 0.448850i | ||||||
\(475\) | − | 104.933i | − | 0.220911i | ||||||
\(476\) | −16.8608 | −0.0354218 | ||||||||
\(477\) | 9.88304i | 0.0207192i | ||||||||
\(478\) | −182.727 | −0.382273 | ||||||||
\(479\) | − | 643.670i | − | 1.34378i | −0.740652 | − | 0.671889i | \(-0.765483\pi\) | ||
0.740652 | − | 0.671889i | \(-0.234517\pi\) | |||||||
\(480\) | − | 21.9089i | − | 0.0456435i | ||||||
\(481\) | 559.793i | 1.16381i | ||||||||
\(482\) | 443.176i | 0.919453i | ||||||||
\(483\) | 139.674 | − | 73.2317i | 0.289180 | − | 0.151618i | ||||
\(484\) | 177.677 | 0.367101 | ||||||||
\(485\) | 383.935 | 0.791618 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −404.712 | −0.831031 | −0.415516 | − | 0.909586i | \(-0.636399\pi\) | ||||
−0.415516 | + | 0.909586i | \(0.636399\pi\) | |||||||
\(488\) | 107.157i | 0.219584i | ||||||||
\(489\) | 176.270 | 0.360470 | ||||||||
\(490\) | 105.392i | 0.215085i | ||||||||
\(491\) | 173.587 | 0.353537 | 0.176769 | − | 0.984252i | \(-0.443436\pi\) | ||||
0.176769 | + | 0.984252i | \(0.443436\pi\) | |||||||
\(492\) | −144.302 | −0.293296 | ||||||||
\(493\) | − | 76.7891i | − | 0.155759i | ||||||
\(494\) | 330.559i | 0.669147i | ||||||||
\(495\) | −38.0430 | −0.0768545 | ||||||||
\(496\) | 159.176 | 0.320920 | ||||||||
\(497\) | 2.26484i | 0.00455703i | ||||||||
\(498\) | − | 207.444i | − | 0.416554i | ||||||
\(499\) | 6.44061 | 0.0129070 | 0.00645352 | − | 0.999979i | \(-0.497946\pi\) | ||||
0.00645352 | + | 0.999979i | \(0.497946\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | 215.824 | 0.430786 | ||||||||
\(502\) | − | 215.137i | − | 0.428559i | ||||||
\(503\) | 617.629i | 1.22789i | 0.789348 | + | 0.613945i | \(0.210419\pi\) | ||||
−0.789348 | + | 0.613945i | \(0.789581\pi\) | |||||||
\(504\) | − | 33.5916i | − | 0.0666500i | ||||||
\(505\) | − | 109.307i | − | 0.216450i | ||||||
\(506\) | 163.371 | − | 85.6558i | 0.322867 | − | 0.169280i | ||||
\(507\) | 77.8608 | 0.153572 | ||||||||
\(508\) | 378.064 | 0.744221 | ||||||||
\(509\) | 200.449 | 0.393809 | 0.196904 | − | 0.980423i | \(-0.436911\pi\) | ||||
0.196904 | + | 0.980423i | \(0.436911\pi\) | |||||||
\(510\) | −11.6639 | −0.0228704 | ||||||||
\(511\) | − | 161.834i | − | 0.316701i | ||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 109.049i | − | 0.212571i | ||||||
\(514\) | 27.7050 | 0.0539008 | ||||||||
\(515\) | −8.67634 | −0.0168473 | ||||||||
\(516\) | − | 143.148i | − | 0.277420i | ||||||
\(517\) | 341.267i | 0.660091i | ||||||||
\(518\) | 281.393 | 0.543230 | ||||||||
\(519\) | 482.083 | 0.928870 | ||||||||
\(520\) | 70.4406i | 0.135463i | ||||||||
\(521\) | − | 201.610i | − | 0.386968i | −0.981103 | − | 0.193484i | \(-0.938021\pi\) | ||
0.981103 | − | 0.193484i | \(-0.0619787\pi\) | |||||||
\(522\) | 152.986 | 0.293077 | ||||||||
\(523\) | − | 678.779i | − | 1.29786i | −0.760850 | − | 0.648928i | \(-0.775218\pi\) | ||
0.760850 | − | 0.648928i | \(-0.224782\pi\) | |||||||
\(524\) | −205.506 | −0.392187 | ||||||||
\(525\) | − | 34.2843i | − | 0.0653034i | ||||||
\(526\) | 180.097i | 0.342389i | ||||||||
\(527\) | − | 84.7427i | − | 0.160802i | ||||||
\(528\) | − | 39.2906i | − | 0.0744140i | ||||||
\(529\) | −300.873 | + | 435.105i | −0.568757 | + | 0.822505i | ||||
\(530\) | −10.4176 | −0.0196559 | ||||||||
\(531\) | −249.875 | −0.470575 | ||||||||
\(532\) | 166.163 | 0.312337 | ||||||||
\(533\) | 463.953 | 0.870455 | ||||||||
\(534\) | 232.097i | 0.434639i | ||||||||
\(535\) | 271.869 | 0.508166 | ||||||||
\(536\) | − | 172.824i | − | 0.322432i | ||||||
\(537\) | 39.3252 | 0.0732313 | ||||||||
\(538\) | 202.175 | 0.375790 | ||||||||
\(539\) | 189.006i | 0.350660i | ||||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | 465.332 | 0.860133 | 0.430067 | − | 0.902797i | \(-0.358490\pi\) | ||||
0.430067 | + | 0.902797i | \(0.358490\pi\) | |||||||
\(542\) | −90.0865 | −0.166211 | ||||||||
\(543\) | − | 262.206i | − | 0.482884i | ||||||
\(544\) | − | 12.0464i | − | 0.0221442i | ||||||
\(545\) | −313.128 | −0.574547 | ||||||||
\(546\) | 108.002i | 0.197807i | ||||||||
\(547\) | −309.522 | −0.565853 | −0.282926 | − | 0.959142i | \(-0.591305\pi\) | ||||
−0.282926 | + | 0.959142i | \(0.591305\pi\) | |||||||
\(548\) | − | 106.020i | − | 0.193468i | ||||||
\(549\) | 113.657i | 0.207026i | ||||||||
\(550\) | − | 40.1008i | − | 0.0729106i | ||||||
\(551\) | 756.756i | 1.37342i | ||||||||
\(552\) | 52.3214 | + | 99.7921i | 0.0947851 | + | 0.180783i | ||||
\(553\) | 343.850 | 0.621790 | ||||||||
\(554\) | 634.233 | 1.14482 | ||||||||
\(555\) | 194.661 | 0.350741 | ||||||||
\(556\) | −460.634 | −0.828478 | ||||||||
\(557\) | − | 826.642i | − | 1.48410i | −0.670346 | − | 0.742049i | \(-0.733854\pi\) | ||
0.670346 | − | 0.742049i | \(-0.266146\pi\) | |||||||
\(558\) | 168.832 | 0.302566 | ||||||||
\(559\) | 460.245i | 0.823337i | ||||||||
\(560\) | 35.4087 | 0.0632298 | ||||||||
\(561\) | −20.9176 | −0.0372863 | ||||||||
\(562\) | − | 218.775i | − | 0.389280i | ||||||
\(563\) | 1018.64i | 1.80931i | 0.426140 | + | 0.904657i | \(0.359873\pi\) | ||||
−0.426140 | + | 0.904657i | \(0.640127\pi\) | |||||||
\(564\) | −208.457 | −0.369605 | ||||||||
\(565\) | 8.34503 | 0.0147700 | ||||||||
\(566\) | 27.0885i | 0.0478596i | ||||||||
\(567\) | − | 35.6293i | − | 0.0628383i | ||||||
\(568\) | −1.61815 | −0.00284885 | ||||||||
\(569\) | 766.176i | 1.34653i | 0.739401 | + | 0.673266i | \(0.235109\pi\) | ||||
−0.739401 | + | 0.673266i | \(0.764891\pi\) | |||||||
\(570\) | 114.948 | 0.201663 | ||||||||
\(571\) | 119.265i | 0.208870i | 0.994532 | + | 0.104435i | \(0.0333035\pi\) | ||||
−0.994532 | + | 0.104435i | \(0.966697\pi\) | |||||||
\(572\) | 126.326i | 0.220849i | ||||||||
\(573\) | 117.959i | 0.205863i | ||||||||
\(574\) | − | 233.217i | − | 0.406301i | ||||||
\(575\) | 53.4003 | + | 101.850i | 0.0928701 | + | 0.177130i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | −73.2216 | −0.126901 | −0.0634503 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634503 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(578\) | 402.294 | 0.696011 | ||||||||
\(579\) | −421.354 | −0.727727 | ||||||||
\(580\) | 161.262i | 0.278037i | ||||||||
\(581\) | 335.266 | 0.577050 | ||||||||
\(582\) | 420.579i | 0.722645i | ||||||||
\(583\) | −18.6826 | −0.0320456 | ||||||||
\(584\) | 115.625 | 0.197988 | ||||||||
\(585\) | 74.7136i | 0.127716i | ||||||||
\(586\) | 380.993i | 0.650159i | ||||||||
\(587\) | 829.222 | 1.41264 | 0.706322 | − | 0.707891i | \(-0.250353\pi\) | ||||
0.706322 | + | 0.707891i | \(0.250353\pi\) | |||||||
\(588\) | −115.451 | −0.196345 | ||||||||
\(589\) | 835.139i | 1.41789i | ||||||||
\(590\) | − | 263.392i | − | 0.446427i | ||||||
\(591\) | 227.518 | 0.384972 | ||||||||
\(592\) | 201.045i | 0.339604i | ||||||||
\(593\) | 82.6719 | 0.139413 | 0.0697065 | − | 0.997568i | \(-0.477794\pi\) | ||||
0.0697065 | + | 0.997568i | \(0.477794\pi\) | |||||||
\(594\) | − | 41.6740i | − | 0.0701582i | ||||||
\(595\) | − | 18.8509i | − | 0.0316823i | ||||||
\(596\) | − | 68.0198i | − | 0.114127i | ||||||
\(597\) | 543.344i | 0.910123i | ||||||||
\(598\) | −168.222 | − | 320.848i | −0.281307 | − | 0.536535i | ||||
\(599\) | 390.672 | 0.652208 | 0.326104 | − | 0.945334i | \(-0.394264\pi\) | ||||
0.326104 | + | 0.945334i | \(0.394264\pi\) | |||||||
\(600\) | 24.4949 | 0.0408248 | ||||||||
\(601\) | −726.400 | −1.20865 | −0.604326 | − | 0.796737i | \(-0.706558\pi\) | ||||
−0.604326 | + | 0.796737i | \(0.706558\pi\) | |||||||
\(602\) | 231.353 | 0.384308 | ||||||||
\(603\) | − | 183.307i | − | 0.303992i | ||||||
\(604\) | −546.851 | −0.905383 | ||||||||
\(605\) | 198.649i | 0.328345i | ||||||||
\(606\) | 119.740 | 0.197591 | ||||||||
\(607\) | −289.612 | −0.477120 | −0.238560 | − | 0.971128i | \(-0.576675\pi\) | ||||
−0.238560 | + | 0.971128i | \(0.576675\pi\) | |||||||
\(608\) | 118.718i | 0.195259i | ||||||||
\(609\) | 247.253i | 0.405998i | ||||||||
\(610\) | −119.805 | −0.196402 | ||||||||
\(611\) | 670.224 | 1.09693 | ||||||||
\(612\) | − | 12.7772i | − | 0.0208777i | ||||||
\(613\) | − | 457.354i | − | 0.746091i | −0.927813 | − | 0.373045i | \(-0.878314\pi\) | ||
0.927813 | − | 0.373045i | \(-0.121686\pi\) | |||||||
\(614\) | 469.125 | 0.764048 | ||||||||
\(615\) | − | 161.334i | − | 0.262332i | ||||||
\(616\) | 63.5006 | 0.103085 | ||||||||
\(617\) | − | 934.894i | − | 1.51523i | −0.652705 | − | 0.757613i | \(-0.726366\pi\) | ||
0.652705 | − | 0.757613i | \(-0.273634\pi\) | |||||||
\(618\) | − | 9.50446i | − | 0.0153794i | ||||||
\(619\) | 79.2136i | 0.127970i | 0.997951 | + | 0.0639851i | \(0.0203810\pi\) | ||||
−0.997951 | + | 0.0639851i | \(0.979619\pi\) | |||||||
\(620\) | 177.965i | 0.287040i | ||||||||
\(621\) | 55.4952 | + | 105.846i | 0.0893643 | + | 0.170444i | ||||
\(622\) | −562.268 | −0.903968 | ||||||||
\(623\) | −375.110 | −0.602103 | ||||||||
\(624\) | −77.1638 | −0.123660 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 176.697i | 0.282263i | ||||||||
\(627\) | 206.143 | 0.328777 | ||||||||
\(628\) | − | 605.403i | − | 0.964017i | ||||||
\(629\) | 107.033 | 0.170164 | ||||||||
\(630\) | 37.5566 | 0.0596136 | ||||||||
\(631\) | − | 405.115i | − | 0.642021i | −0.947076 | − | 0.321011i | \(-0.895977\pi\) | ||
0.947076 | − | 0.321011i | \(-0.104023\pi\) | |||||||
\(632\) | 245.668i | 0.388716i | ||||||||
\(633\) | −131.399 | −0.207581 | ||||||||
\(634\) | 385.831 | 0.608566 | ||||||||
\(635\) | 422.689i | 0.665652i | ||||||||
\(636\) | − | 11.4120i | − | 0.0179433i | ||||||
\(637\) | 371.193 | 0.582721 | ||||||||
\(638\) | 289.200i | 0.453292i | ||||||||
\(639\) | −1.71630 | −0.00268592 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | − | 984.727i | − | 1.53623i | −0.640309 | − | 0.768117i | \(-0.721194\pi\) | ||
0.640309 | − | 0.768117i | \(-0.278806\pi\) | |||||||
\(642\) | 297.817i | 0.463890i | ||||||||
\(643\) | − | 330.197i | − | 0.513526i | −0.966474 | − | 0.256763i | \(-0.917344\pi\) | ||
0.966474 | − | 0.256763i | \(-0.0826560\pi\) | |||||||
\(644\) | −161.282 | + | 84.5606i | −0.250438 | + | 0.131305i | ||||
\(645\) | 160.045 | 0.248132 | ||||||||
\(646\) | 63.2032 | 0.0978377 | ||||||||
\(647\) | 948.869 | 1.46657 | 0.733284 | − | 0.679923i | \(-0.237987\pi\) | ||||
0.733284 | + | 0.679923i | \(0.237987\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − | 472.357i | − | 0.727823i | ||||||
\(650\) | −78.7550 | −0.121162 | ||||||||
\(651\) | 272.863i | 0.419144i | ||||||||
\(652\) | −203.539 | −0.312176 | ||||||||
\(653\) | −378.498 | −0.579630 | −0.289815 | − | 0.957083i | \(-0.593594\pi\) | ||||
−0.289815 | + | 0.957083i | \(0.593594\pi\) | |||||||
\(654\) | − | 343.014i | − | 0.524487i | ||||||
\(655\) | − | 229.763i | − | 0.350783i | ||||||
\(656\) | 166.625 | 0.254002 | ||||||||
\(657\) | 122.639 | 0.186665 | ||||||||
\(658\) | − | 336.904i | − | 0.512012i | ||||||
\(659\) | 470.040i | 0.713262i | 0.934245 | + | 0.356631i | \(0.116075\pi\) | ||||
−0.934245 | + | 0.356631i | \(0.883925\pi\) | |||||||
\(660\) | 43.9282 | 0.0665579 | ||||||||
\(661\) | 244.609i | 0.370058i | 0.982733 | + | 0.185029i | \(0.0592380\pi\) | ||||
−0.982733 | + | 0.185029i | \(0.940762\pi\) | |||||||
\(662\) | 223.577 | 0.337729 | ||||||||
\(663\) | 41.0807i | 0.0619618i | ||||||||
\(664\) | 239.536i | 0.360746i | ||||||||
\(665\) | 185.776i | 0.279363i | ||||||||
\(666\) | 213.241i | 0.320181i | ||||||||
\(667\) | −385.114 | − | 734.525i | −0.577383 | − | 1.10124i | ||||
\(668\) | −249.212 | −0.373071 | ||||||||
\(669\) | 287.164 | 0.429244 | ||||||||
\(670\) | 193.223 | 0.288392 | ||||||||
\(671\) | −214.854 | −0.320199 | ||||||||
\(672\) | 38.7883i | 0.0577206i | ||||||||
\(673\) | 297.873 | 0.442605 | 0.221302 | − | 0.975205i | \(-0.428969\pi\) | ||||
0.221302 | + | 0.975205i | \(0.428969\pi\) | |||||||
\(674\) | 265.751i | 0.394290i | ||||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | −89.9059 | −0.132997 | ||||||||
\(677\) | − | 306.899i | − | 0.453322i | −0.973974 | − | 0.226661i | \(-0.927219\pi\) | ||
0.973974 | − | 0.226661i | \(-0.0727809\pi\) | |||||||
\(678\) | 9.14153i | 0.0134831i | ||||||||
\(679\) | −679.731 | −1.00108 | ||||||||
\(680\) | 13.4683 | 0.0198064 | ||||||||
\(681\) | 702.162i | 1.03107i | ||||||||
\(682\) | 319.155i | 0.467969i | ||||||||
\(683\) | 270.473 | 0.396007 | 0.198003 | − | 0.980201i | \(-0.436554\pi\) | ||||
0.198003 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(684\) | 125.919i | 0.184092i | ||||||||
\(685\) | 118.534 | 0.173043 | ||||||||
\(686\) | − | 460.921i | − | 0.671896i | ||||||
\(687\) | − | 662.180i | − | 0.963871i | ||||||
\(688\) | 165.294i | 0.240252i | ||||||||
\(689\) | 36.6913i | 0.0532529i | ||||||||
\(690\) | −111.571 | + | 58.4971i | −0.161697 | + | 0.0847784i | ||||
\(691\) | −994.734 | −1.43956 | −0.719779 | − | 0.694204i | \(-0.755757\pi\) | ||||
−0.719779 | + | 0.694204i | \(0.755757\pi\) | |||||||
\(692\) | −556.662 | −0.804425 | ||||||||
\(693\) | 67.3526 | 0.0971898 | ||||||||
\(694\) | −443.266 | −0.638711 | ||||||||
\(695\) | − | 515.004i | − | 0.741013i | ||||||
\(696\) | −176.653 | −0.253812 | ||||||||
\(697\) | − | 88.7082i | − | 0.127272i | ||||||
\(698\) | 514.024 | 0.736424 | ||||||||
\(699\) | 216.736 | 0.310066 | ||||||||
\(700\) | 39.5881i | 0.0565544i | ||||||||
\(701\) | 615.121i | 0.877490i | 0.898612 | + | 0.438745i | \(0.144577\pi\) | ||||
−0.898612 | + | 0.438745i | \(0.855423\pi\) | |||||||
\(702\) | −81.8446 | −0.116588 | ||||||||
\(703\) | −1054.81 | −1.50044 | ||||||||
\(704\) | 45.3689i | 0.0644444i | ||||||||
\(705\) | − | 233.062i | − | 0.330585i | ||||||
\(706\) | −742.073 | −1.05109 | ||||||||
\(707\) | 193.521i | 0.273721i | ||||||||
\(708\) | 288.531 | 0.407530 | ||||||||
\(709\) | − | 768.270i | − | 1.08360i | −0.840509 | − | 0.541798i | \(-0.817744\pi\) | ||
0.840509 | − | 0.541798i | \(-0.182256\pi\) | |||||||
\(710\) | − | 1.80914i | − | 0.00254809i | ||||||
\(711\) | 260.571i | 0.366485i | ||||||||
\(712\) | − | 268.003i | − | 0.376408i | ||||||
\(713\) | −425.003 | − | 810.605i | −0.596078 | − | 1.13689i | ||||
\(714\) | 20.6502 | 0.0289218 | ||||||||
\(715\) | −141.236 | −0.197533 | ||||||||
\(716\) | −45.4088 | −0.0634202 | ||||||||
\(717\) | 223.793 | 0.312125 | ||||||||
\(718\) | − | 440.812i | − | 0.613944i | ||||||
\(719\) | −613.243 | −0.852910 | −0.426455 | − | 0.904509i | \(-0.640238\pi\) | ||||
−0.426455 | + | 0.904509i | \(0.640238\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 15.3609 | 0.0213050 | ||||||||
\(722\) | −112.336 | −0.155590 | ||||||||
\(723\) | − | 542.778i | − | 0.750730i | ||||||
\(724\) | 302.769i | 0.418189i | ||||||||
\(725\) | −180.296 | −0.248684 | ||||||||
\(726\) | −217.609 | −0.299737 | ||||||||
\(727\) | 1148.29i | 1.57949i | 0.613436 | + | 0.789744i | \(0.289787\pi\) | ||||
−0.613436 | + | 0.789744i | \(0.710213\pi\) | |||||||
\(728\) | − | 124.710i | − | 0.171306i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 129.272i | 0.177086i | ||||||||
\(731\) | 87.9994 | 0.120382 | ||||||||
\(732\) | − | 131.240i | − | 0.179289i | ||||||
\(733\) | − | 570.538i | − | 0.778361i | −0.921162 | − | 0.389180i | \(-0.872758\pi\) | ||
0.921162 | − | 0.389180i | \(-0.127242\pi\) | |||||||
\(734\) | − | 662.544i | − | 0.902649i | ||||||
\(735\) | − | 129.078i | − | 0.175616i | ||||||
\(736\) | −60.4155 | − | 115.230i | −0.0820863 | − | 0.156563i | ||||
\(737\) | 346.518 | 0.470174 | ||||||||
\(738\) | 176.733 | 0.239475 | ||||||||
\(739\) | −1062.30 | −1.43749 | −0.718744 | − | 0.695275i | \(-0.755283\pi\) | ||||
−0.718744 | + | 0.695275i | \(0.755283\pi\) | |||||||
\(740\) | −224.776 | −0.303751 | ||||||||
\(741\) | − | 404.850i | − | 0.546356i | ||||||
\(742\) | 18.4437 | 0.0248568 | ||||||||
\(743\) | 166.131i | 0.223595i | 0.993731 | + | 0.111797i | \(0.0356608\pi\) | ||||
−0.993731 | + | 0.111797i | \(0.964339\pi\) | |||||||
\(744\) | −194.950 | −0.262030 | ||||||||
\(745\) | 76.0484 | 0.102078 | ||||||||
\(746\) | − | 10.5402i | − | 0.0141289i | ||||||
\(747\) | 254.066i | 0.340115i | ||||||||
\(748\) | 24.1536 | 0.0322909 | ||||||||
\(749\) | −481.325 | −0.642624 | ||||||||
\(750\) | 27.3861i | 0.0365148i | ||||||||
\(751\) | − | 1210.26i | − | 1.61153i | −0.592236 | − | 0.805765i | \(-0.701755\pi\) | ||
0.592236 | − | 0.805765i | \(-0.298245\pi\) | |||||||
\(752\) | 240.706 | 0.320087 | ||||||||
\(753\) | 263.488i | 0.349917i | ||||||||
\(754\) | 567.968 | 0.753274 | ||||||||
\(755\) | − | 611.398i | − | 0.809799i | ||||||
\(756\) | 41.1412i | 0.0544195i | ||||||||
\(757\) | − | 500.893i | − | 0.661681i | −0.943687 | − | 0.330841i | \(-0.892668\pi\) | ||
0.943687 | − | 0.330841i | \(-0.107332\pi\) | |||||||
\(758\) | 627.958i | 0.828441i | ||||||||
\(759\) | −200.087 | + | 104.907i | −0.263620 | + | 0.138217i | ||||
\(760\) | −132.730 | −0.174645 | ||||||||
\(761\) | 788.375 | 1.03597 | 0.517987 | − | 0.855389i | \(-0.326682\pi\) | ||||
0.517987 | + | 0.855389i | \(0.326682\pi\) | |||||||
\(762\) | −463.032 | −0.607654 | ||||||||
\(763\) | 554.372 | 0.726569 | ||||||||
\(764\) | − | 136.208i | − | 0.178282i | ||||||
\(765\) | 14.2853 | 0.0186736 | ||||||||
\(766\) | − | 446.324i | − | 0.582668i | ||||||
\(767\) | −927.674 | −1.20948 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 115.079i | 0.149647i | 0.997197 | + | 0.0748237i | \(0.0238394\pi\) | ||||
−0.997197 | + | 0.0748237i | \(0.976161\pi\) | |||||||
\(770\) | 70.9958i | 0.0922024i | ||||||||
\(771\) | −33.9315 | −0.0440098 | ||||||||
\(772\) | 486.538 | 0.630230 | ||||||||
\(773\) | 1396.31i | 1.80635i | 0.429272 | + | 0.903175i | \(0.358770\pi\) | ||||
−0.429272 | + | 0.903175i | \(0.641230\pi\) | |||||||
\(774\) | 175.320i | 0.226512i | ||||||||
\(775\) | −198.970 | −0.256736 | ||||||||
\(776\) | − | 485.643i | − | 0.625829i | ||||||
\(777\) | −344.635 | −0.443546 | ||||||||
\(778\) | − | 178.661i | − | 0.229642i | ||||||
\(779\) | 874.220i | 1.12223i | ||||||||
\(780\) | − | 86.2718i | − | 0.110605i | ||||||
\(781\) | − | 3.24445i | − | 0.00415423i | ||||||
\(782\) | −61.3464 | + | 32.1642i | −0.0784481 | + | 0.0411306i | ||||
\(783\) | −187.369 | −0.239296 | ||||||||
\(784\) | 133.311 | 0.170040 | ||||||||
\(785\) | 676.861 | 0.862243 | ||||||||
\(786\) | 251.693 | 0.320220 | ||||||||
\(787\) | − | 608.869i | − | 0.773659i | −0.922151 | − | 0.386829i | \(-0.873570\pi\) | ||
0.922151 | − | 0.386829i | \(-0.126430\pi\) | |||||||
\(788\) | −262.715 | −0.333395 | ||||||||
\(789\) | − | 220.573i | − | 0.279560i | ||||||
\(790\) | −274.666 | −0.347678 | ||||||||
\(791\) | −14.7743 | −0.0186780 | ||||||||
\(792\) | 48.1210i | 0.0607588i | ||||||||
\(793\) | 421.957i | 0.532102i | ||||||||
\(794\) | −233.643 | −0.294261 | ||||||||
\(795\) | 12.7590 | 0.0160490 | ||||||||
\(796\) | − | 627.399i | − | 0.788190i | ||||||
\(797\) | − | 651.157i | − | 0.817009i | −0.912756 | − | 0.408505i | \(-0.866050\pi\) | ||
0.912756 | − | 0.408505i | \(-0.133950\pi\) | |||||||
\(798\) | −203.508 | −0.255022 | ||||||||
\(799\) | − | 128.147i | − | 0.160385i | ||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | − | 284.260i | − | 0.354881i | ||||||
\(802\) | 422.847i | 0.527240i | ||||||||
\(803\) | 231.832i | 0.288708i | ||||||||
\(804\) | 211.665i | 0.263265i | ||||||||
\(805\) | −94.5417 | − | 180.319i | −0.117443 | − | 0.223998i | ||||
\(806\) | 626.797 | 0.777664 | ||||||||
\(807\) | −247.613 | −0.306832 | ||||||||
\(808\) | −138.264 | −0.171119 | ||||||||
\(809\) | −521.791 | −0.644983 | −0.322492 | − | 0.946572i | \(-0.604520\pi\) | ||||
−0.322492 | + | 0.946572i | \(0.604520\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | −1004.88 | −1.23907 | −0.619533 | − | 0.784971i | \(-0.712678\pi\) | ||||
−0.619533 | + | 0.784971i | \(0.712678\pi\) | |||||||
\(812\) | − | 285.503i | − | 0.351604i | ||||||
\(813\) | 110.333 | 0.135711 | ||||||||
\(814\) | −403.104 | −0.495214 | ||||||||
\(815\) | − | 227.563i | − | 0.279219i | ||||||
\(816\) | 14.7538i | 0.0180806i | ||||||||
\(817\) | −867.234 | −1.06149 | ||||||||
\(818\) | −78.5673 | −0.0960480 | ||||||||
\(819\) | − | 132.275i | − | 0.161508i | ||||||
\(820\) | 186.293i | 0.227186i | ||||||||
\(821\) | −752.571 | −0.916652 | −0.458326 | − | 0.888784i | \(-0.651551\pi\) | ||||
−0.458326 | + | 0.888784i | \(0.651551\pi\) | |||||||
\(822\) | 129.848i | 0.157966i | ||||||||
\(823\) | −1119.05 | −1.35972 | −0.679858 | − | 0.733343i | \(-0.737959\pi\) | ||||
−0.679858 | + | 0.733343i | \(0.737959\pi\) | |||||||
\(824\) | 10.9748i | 0.0133189i | ||||||||
\(825\) | 49.1133i | 0.0595312i | ||||||||
\(826\) | 466.318i | 0.564549i | ||||||||
\(827\) | 305.110i | 0.368936i | 0.982839 | + | 0.184468i | \(0.0590562\pi\) | ||||
−0.982839 | + | 0.184468i | \(0.940944\pi\) | |||||||
\(828\) | −64.0804 | − | 122.220i | −0.0773917 | − | 0.147609i | ||||
\(829\) | −1139.25 | −1.37424 | −0.687121 | − | 0.726543i | \(-0.741126\pi\) | ||||
−0.687121 | + | 0.726543i | \(0.741126\pi\) | |||||||
\(830\) | −267.809 | −0.322661 | ||||||||
\(831\) | −776.774 | −0.934746 | ||||||||
\(832\) | 89.1011 | 0.107093 | ||||||||
\(833\) | − | 70.9726i | − | 0.0852012i | ||||||
\(834\) | 564.159 | 0.676449 | ||||||||
\(835\) | − | 278.627i | − | 0.333685i | ||||||
\(836\) | −238.034 | −0.284729 | ||||||||
\(837\) | −206.776 | −0.247044 | ||||||||
\(838\) | 597.710i | 0.713258i | ||||||||
\(839\) | − | 811.707i | − | 0.967470i | −0.875215 | − | 0.483735i | \(-0.839280\pi\) | ||
0.875215 | − | 0.483735i | \(-0.160720\pi\) | |||||||
\(840\) | −43.3666 | −0.0516269 | ||||||||
\(841\) | 459.264 | 0.546093 | ||||||||
\(842\) | − | 150.827i | − | 0.179130i | ||||||
\(843\) | 267.944i | 0.317846i | ||||||||
\(844\) | 151.726 | 0.179770 | ||||||||
\(845\) | − | 100.518i | − | 0.118956i | ||||||
\(846\) | 255.307 | 0.301781 | ||||||||
\(847\) | − | 351.695i | − | 0.415224i | ||||||
\(848\) | 13.1774i | 0.0155394i | ||||||||
\(849\) | − | 33.1765i | − | 0.0390772i | ||||||
\(850\) | 15.0580i | 0.0177153i | ||||||||
\(851\) | 1023.82 | − | 536.794i | 1.20308 | − | 0.630781i | ||||
\(852\) | 1.98182 | 0.00232608 | ||||||||
\(853\) | −336.775 | −0.394812 | −0.197406 | − | 0.980322i | \(-0.563252\pi\) | ||||
−0.197406 | + | 0.980322i | \(0.563252\pi\) | |||||||
\(854\) | 212.107 | 0.248369 | ||||||||
\(855\) | −140.782 | −0.164657 | ||||||||
\(856\) | − | 343.890i | − | 0.401740i | ||||||
\(857\) | −764.331 | −0.891869 | −0.445934 | − | 0.895066i | \(-0.647129\pi\) | ||||
−0.445934 | + | 0.895066i | \(0.647129\pi\) | |||||||
\(858\) | − | 154.717i | − | 0.180322i | ||||||
\(859\) | −368.659 | −0.429172 | −0.214586 | − | 0.976705i | \(-0.568840\pi\) | ||||
−0.214586 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(860\) | −184.804 | −0.214888 | ||||||||
\(861\) | 285.631i | 0.331744i | ||||||||
\(862\) | 432.203i | 0.501395i | ||||||||
\(863\) | −731.744 | −0.847907 | −0.423954 | − | 0.905684i | \(-0.639358\pi\) | ||||
−0.423954 | + | 0.905684i | \(0.639358\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | − | 622.367i | − | 0.719500i | ||||||
\(866\) | − | 404.310i | − | 0.466870i | ||||||
\(867\) | −492.708 | −0.568291 | ||||||||
\(868\) | − | 315.074i | − | 0.362989i | ||||||
\(869\) | −492.575 | −0.566830 | ||||||||
\(870\) | − | 197.504i | − | 0.227016i | ||||||
\(871\) | − | 680.536i | − | 0.781327i | ||||||
\(872\) | 396.079i | 0.454219i | ||||||||
\(873\) | − | 515.102i | − | 0.590037i | ||||||
\(874\) | 604.569 | − | 316.978i | 0.691727 | − | 0.362675i | ||||
\(875\) | −44.2608 | −0.0505838 | ||||||||
\(876\) | −141.611 | −0.161656 | ||||||||
\(877\) | −53.7425 | −0.0612799 | −0.0306400 | − | 0.999530i | \(-0.509755\pi\) | ||||
−0.0306400 | + | 0.999530i | \(0.509755\pi\) | |||||||
\(878\) | −653.055 | −0.743799 | ||||||||
\(879\) | − | 466.619i | − | 0.530852i | ||||||
\(880\) | −50.7240 | −0.0576409 | ||||||||
\(881\) | − | 860.235i | − | 0.976430i | −0.872723 | − | 0.488215i | \(-0.837648\pi\) | ||
0.872723 | − | 0.488215i | \(-0.162352\pi\) | |||||||
\(882\) | 141.398 | 0.160315 | ||||||||
\(883\) | −445.282 | −0.504283 | −0.252142 | − | 0.967690i | \(-0.581135\pi\) | ||||
−0.252142 | + | 0.967690i | \(0.581135\pi\) | |||||||
\(884\) | − | 47.4359i | − | 0.0536605i | ||||||
\(885\) | 322.588i | 0.364506i | ||||||||
\(886\) | −92.0241 | −0.103865 | ||||||||
\(887\) | 121.682 | 0.137184 | 0.0685921 | − | 0.997645i | \(-0.478149\pi\) | ||||
0.0685921 | + | 0.997645i | \(0.478149\pi\) | |||||||
\(888\) | − | 246.229i | − | 0.277285i | ||||||
\(889\) | − | 748.343i | − | 0.841780i | ||||||
\(890\) | 299.636 | 0.336670 | ||||||||
\(891\) | 51.0400i | 0.0572840i | ||||||||
\(892\) | −331.589 | −0.371736 | ||||||||
\(893\) | 1262.89i | 1.41421i | ||||||||
\(894\) | 83.3069i | 0.0931844i | ||||||||
\(895\) | − | 50.7686i | − | 0.0567247i | ||||||
\(896\) | − | 44.7888i | − | 0.0499875i | ||||||
\(897\) | 206.029 | + | 392.957i | 0.229686 | + | 0.438079i | ||||
\(898\) | 774.011 | 0.861927 | ||||||||
\(899\) | 1434.94 | 1.59615 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 7.01541 | 0.00778625 | ||||||||
\(902\) | 334.090i | 0.370388i | ||||||||
\(903\) | −283.349 | −0.313786 | ||||||||
\(904\) | − | 10.5557i | − | 0.0116767i | ||||||
\(905\) | −338.506 | −0.374040 | ||||||||
\(906\) | 669.753 | 0.739242 | ||||||||
\(907\) | 914.181i | 1.00792i | 0.863728 | + | 0.503959i | \(0.168124\pi\) | ||||
−0.863728 | + | 0.503959i | \(0.831876\pi\) | |||||||
\(908\) | − | 810.786i | − | 0.892937i | ||||||
\(909\) | −146.651 | −0.161332 | ||||||||
\(910\) | 139.431 | 0.153220 | ||||||||
\(911\) | 936.862i | 1.02839i | 0.857674 | + | 0.514195i | \(0.171909\pi\) | ||||
−0.857674 | + | 0.514195i | \(0.828091\pi\) | |||||||
\(912\) | − | 145.399i | − | 0.159429i | ||||||
\(913\) | −480.278 | −0.526044 | ||||||||
\(914\) | 472.869i | 0.517362i | ||||||||
\(915\) | 146.731 | 0.160361 | ||||||||
\(916\) | 764.619i | 0.834737i | ||||||||
\(917\) | 406.780i | 0.443598i | ||||||||
\(918\) | 15.6488i | 0.0170466i | ||||||||
\(919\) | 1272.45i | 1.38460i | 0.721610 | + | 0.692300i | \(0.243403\pi\) | ||||
−0.721610 | + | 0.692300i | \(0.756597\pi\) | |||||||
\(920\) | 128.831 | − | 67.5466i | 0.140034 | − | 0.0734202i | ||||
\(921\) | −574.559 | −0.623842 | ||||||||
\(922\) | −543.830 | −0.589838 | ||||||||
\(923\) | −6.37186 | −0.00690343 | ||||||||
\(924\) | −77.7720 | −0.0841689 | ||||||||
\(925\) | − | 251.307i | − | 0.271683i | ||||||
\(926\) | 1048.64 | 1.13244 | ||||||||
\(927\) | 11.6405i | 0.0125572i | ||||||||
\(928\) | 203.981 | 0.219808 | ||||||||
\(929\) | −1343.27 | −1.44593 | −0.722967 | − | 0.690882i | \(-0.757222\pi\) | ||||
−0.722967 | + | 0.690882i | \(0.757222\pi\) | |||||||
\(930\) | − | 217.961i | − | 0.234367i | ||||||
\(931\) | 699.435i | 0.751273i | ||||||||
\(932\) | −250.265 | −0.268525 | ||||||||
\(933\) | 688.635 | 0.738087 | ||||||||
\(934\) | − | 260.011i | − | 0.278384i | ||||||
\(935\) | 27.0045i | 0.0288819i | ||||||||
\(936\) | 94.5060 | 0.100968 | ||||||||
\(937\) | − | 850.505i | − | 0.907690i | −0.891081 | − | 0.453845i | \(-0.850052\pi\) | ||
0.891081 | − | 0.453845i | \(-0.149948\pi\) | |||||||
\(938\) | −342.088 | −0.364699 | ||||||||
\(939\) | − | 216.409i | − | 0.230467i | ||||||
\(940\) | 269.117i | 0.286295i | ||||||||
\(941\) | − | 1778.92i | − | 1.89045i | −0.326417 | − | 0.945226i | \(-0.605841\pi\) | ||
0.326417 | − | 0.945226i | \(-0.394159\pi\) | |||||||
\(942\) | 741.464i | 0.787116i | ||||||||
\(943\) | −444.892 | − | 848.538i | −0.471783 | − | 0.899828i | ||||
\(944\) | −333.167 | −0.352931 | ||||||||
\(945\) | −45.9972 | −0.0486743 | ||||||||
\(946\) | −331.420 | −0.350339 | ||||||||
\(947\) | 121.252 | 0.128038 | 0.0640190 | − | 0.997949i | \(-0.479608\pi\) | ||||
0.0640190 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(948\) | − | 300.881i | − | 0.317385i | ||||||
\(949\) | 455.302 | 0.479770 | ||||||||
\(950\) | − | 148.397i | − | 0.156207i | ||||||
\(951\) | −472.544 | −0.496892 | ||||||||
\(952\) | −23.8448 | −0.0250470 | ||||||||
\(953\) | 1183.70i | 1.24207i | 0.783781 | + | 0.621037i | \(0.213288\pi\) | ||||
−0.783781 | + | 0.621037i | \(0.786712\pi\) | |||||||
\(954\) | 13.9767i | 0.0146507i | ||||||||
\(955\) | 152.285 | 0.159461 | ||||||||
\(956\) | −258.414 | −0.270308 | ||||||||
\(957\) | − | 354.197i | − | 0.370112i | ||||||
\(958\) | − | 910.286i | − | 0.950195i | ||||||
\(959\) | −209.857 | −0.218829 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | 622.570 | 0.647835 | ||||||||
\(962\) | 791.667i | 0.822938i | ||||||||
\(963\) | − | 364.750i | − | 0.378764i | ||||||
\(964\) | 626.746i | 0.650151i | ||||||||
\(965\) | 543.966i | 0.563695i | ||||||||
\(966\) | 197.529 | − | 103.565i | 0.204481 | − | 0.107210i | ||||
\(967\) | 1135.29 | 1.17403 | 0.587015 | − | 0.809576i | \(-0.300303\pi\) | ||||
0.587015 | + | 0.809576i | \(0.300303\pi\) | |||||||
\(968\) | 251.273 | 0.259580 | ||||||||
\(969\) | −77.4078 | −0.0798842 | ||||||||
\(970\) | 542.966 | 0.559758 | ||||||||
\(971\) | − | 1446.26i | − | 1.48945i | −0.667369 | − | 0.744727i | \(-0.732579\pi\) | ||
0.667369 | − | 0.744727i | \(-0.267421\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | 911.780i | 0.937082i | ||||||||
\(974\) | −572.349 | −0.587628 | ||||||||
\(975\) | 96.4548 | 0.0989280 | ||||||||
\(976\) | 151.543i | 0.155269i | ||||||||
\(977\) | 77.0844i | 0.0788991i | 0.999222 | + | 0.0394496i | \(0.0125604\pi\) | ||||
−0.999222 | + | 0.0394496i | \(0.987440\pi\) | |||||||
\(978\) | 249.283 | 0.254890 | ||||||||
\(979\) | 537.356 | 0.548883 | ||||||||
\(980\) | 149.047i | 0.152088i | ||||||||
\(981\) | 420.105i | 0.428242i | ||||||||
\(982\) | 245.489 | 0.249989 | ||||||||
\(983\) | − | 496.933i | − | 0.505527i | −0.967528 | − | 0.252763i | \(-0.918661\pi\) | ||
0.967528 | − | 0.252763i | \(-0.0813394\pi\) | |||||||
\(984\) | −204.073 | −0.207392 | ||||||||
\(985\) | − | 293.725i | − | 0.298198i | ||||||
\(986\) | − | 108.596i | − | 0.110138i | ||||||
\(987\) | 412.621i | 0.418056i | ||||||||
\(988\) | 467.481i | 0.473158i | ||||||||
\(989\) | 841.757 | − | 441.336i | 0.851120 | − | 0.446245i | ||||
\(990\) | −53.8009 | −0.0543443 | ||||||||
\(991\) | 290.841 | 0.293482 | 0.146741 | − | 0.989175i | \(-0.453122\pi\) | ||||
0.146741 | + | 0.989175i | \(0.453122\pi\) | |||||||
\(992\) | 225.109 | 0.226925 | ||||||||
\(993\) | −273.824 | −0.275755 | ||||||||
\(994\) | 3.20297i | 0.00322230i | ||||||||
\(995\) | 701.454 | 0.704978 | ||||||||
\(996\) | − | 293.370i | − | 0.294548i | ||||||
\(997\) | −1034.44 | −1.03756 | −0.518778 | − | 0.854909i | \(-0.673613\pi\) | ||||
−0.518778 | + | 0.854909i | \(0.673613\pi\) | |||||||
\(998\) | 9.10840 | 0.00912665 | ||||||||
\(999\) | − | 261.166i | − | 0.261427i |
(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 | 690.3.c.a.91.21 | yes | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.2 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.20 | ✓ | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.15 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.20 | ✓ | 32 | 23.22 | odd | 2 | inner | |
690.3.c.a.91.21 | yes | 32 | 1.1 | even | 1 | trivial | |
2070.3.c.b.91.2 | 32 | 3.2 | odd | 2 | |||
2070.3.c.b.91.15 | 32 | 69.68 | even | 2 |