Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, 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("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.14 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.13 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.75802 | −0.879012 | −0.439506 | − | 0.898240i | \(-0.644846\pi\) | ||||
−0.439506 | + | 0.898240i | \(0.644846\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −0.909354 | −0.227339 | ||||||||
\(5\) | − | 0.711109i | − | 0.142222i | −0.997468 | − | 0.0711109i | \(-0.977346\pi\) | ||
0.997468 | − | 0.0711109i | \(-0.0226544\pi\) | |||||||
\(6\) | 3.04499 | 0.507498 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 8.63076 | 1.07884 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 1.25015i | 0.125015i | ||||||||
\(11\) | − | 8.01603i | − | 0.728730i | −0.931256 | − | 0.364365i | \(-0.881286\pi\) | ||
0.931256 | − | 0.364365i | \(-0.118714\pi\) | |||||||
\(12\) | 1.57505 | 0.131254 | ||||||||
\(13\) | −19.1112 | −1.47009 | −0.735047 | − | 0.678017i | \(-0.762840\pi\) | ||||
−0.735047 | + | 0.678017i | \(0.762840\pi\) | |||||||
\(14\) | − | 4.65129i | − | 0.332235i | ||||||
\(15\) | 1.23168i | 0.0821118i | ||||||||
\(16\) | −11.5357 | −0.720979 | ||||||||
\(17\) | 25.4247i | 1.49557i | 0.663940 | + | 0.747786i | \(0.268883\pi\) | ||||
−0.663940 | + | 0.747786i | \(0.731117\pi\) | |||||||
\(18\) | −5.27407 | −0.293004 | ||||||||
\(19\) | 5.80334i | 0.305439i | 0.988270 | + | 0.152719i | \(0.0488031\pi\) | ||||
−0.988270 | + | 0.152719i | \(0.951197\pi\) | |||||||
\(20\) | 0.646650i | 0.0323325i | ||||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | 14.0924i | 0.640562i | ||||||||
\(23\) | −19.3326 | + | 12.4600i | −0.840547 | + | 0.541739i | ||||
\(24\) | −14.9489 | −0.622871 | ||||||||
\(25\) | 24.4943 | 0.979773 | ||||||||
\(26\) | 33.5979 | 1.29223 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 2.40593i | − | 0.0859259i | ||||||
\(29\) | −13.4076 | −0.462332 | −0.231166 | − | 0.972914i | \(-0.574254\pi\) | ||||
−0.231166 | + | 0.972914i | \(0.574254\pi\) | |||||||
\(30\) | − | 2.16532i | − | 0.0721772i | ||||||
\(31\) | 49.8044 | 1.60659 | 0.803297 | − | 0.595579i | \(-0.203077\pi\) | ||||
0.803297 | + | 0.595579i | \(0.203077\pi\) | |||||||
\(32\) | −14.2431 | −0.445096 | ||||||||
\(33\) | 13.8842i | 0.420733i | ||||||||
\(34\) | − | 44.6973i | − | 1.31463i | ||||||
\(35\) | 1.88142 | 0.0537548 | ||||||||
\(36\) | −2.72806 | −0.0757795 | ||||||||
\(37\) | − | 61.8720i | − | 1.67222i | −0.548566 | − | 0.836108i | \(-0.684826\pi\) | ||
0.548566 | − | 0.836108i | \(-0.315174\pi\) | |||||||
\(38\) | − | 10.2024i | − | 0.268484i | ||||||
\(39\) | 33.1016 | 0.848759 | ||||||||
\(40\) | − | 6.13741i | − | 0.153435i | ||||||
\(41\) | 11.2387 | 0.274115 | 0.137057 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137057 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(42\) | 8.05627i | 0.191816i | ||||||||
\(43\) | − | 69.0959i | − | 1.60688i | −0.595385 | − | 0.803441i | \(-0.703000\pi\) | ||
0.595385 | − | 0.803441i | \(-0.297000\pi\) | |||||||
\(44\) | 7.28941i | 0.165669i | ||||||||
\(45\) | − | 2.13333i | − | 0.0474073i | ||||||
\(46\) | 33.9871 | − | 21.9050i | 0.738850 | − | 0.476195i | ||||
\(47\) | −8.79613 | −0.187152 | −0.0935758 | − | 0.995612i | \(-0.529830\pi\) | ||||
−0.0935758 | + | 0.995612i | \(0.529830\pi\) | |||||||
\(48\) | 19.9803 | 0.416257 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | −43.0616 | −0.861232 | ||||||||
\(51\) | − | 44.0369i | − | 0.863469i | ||||||
\(52\) | 17.3789 | 0.334209 | ||||||||
\(53\) | − | 63.7575i | − | 1.20297i | −0.798884 | − | 0.601485i | \(-0.794576\pi\) | ||
0.798884 | − | 0.601485i | \(-0.205424\pi\) | |||||||
\(54\) | 9.13496 | 0.169166 | ||||||||
\(55\) | −5.70027 | −0.103641 | ||||||||
\(56\) | 22.8348i | 0.407765i | ||||||||
\(57\) | − | 10.0517i | − | 0.176345i | ||||||
\(58\) | 23.5709 | 0.406395 | ||||||||
\(59\) | 54.3128 | 0.920556 | 0.460278 | − | 0.887775i | \(-0.347750\pi\) | ||||
0.460278 | + | 0.887775i | \(0.347750\pi\) | |||||||
\(60\) | − | 1.12003i | − | 0.0186672i | ||||||
\(61\) | − | 65.2892i | − | 1.07031i | −0.844753 | − | 0.535157i | \(-0.820252\pi\) | ||
0.844753 | − | 0.535157i | \(-0.179748\pi\) | |||||||
\(62\) | −87.5573 | −1.41221 | ||||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | 71.1823 | 1.11222 | ||||||||
\(65\) | 13.5902i | 0.209079i | ||||||||
\(66\) | − | 24.4087i | − | 0.369829i | ||||||
\(67\) | 102.088i | 1.52370i | 0.647751 | + | 0.761852i | \(0.275710\pi\) | ||||
−0.647751 | + | 0.761852i | \(0.724290\pi\) | |||||||
\(68\) | − | 23.1201i | − | 0.340001i | ||||||
\(69\) | 33.4850 | − | 21.5813i | 0.485290 | − | 0.312773i | ||||
\(70\) | −3.30758 | −0.0472511 | ||||||||
\(71\) | 14.5341 | 0.204705 | 0.102353 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102353 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(72\) | 25.8923 | 0.359615 | ||||||||
\(73\) | 74.1461 | 1.01570 | 0.507850 | − | 0.861446i | \(-0.330441\pi\) | ||||
0.507850 | + | 0.861446i | \(0.330441\pi\) | |||||||
\(74\) | 108.772i | 1.46990i | ||||||||
\(75\) | −42.4254 | −0.565672 | ||||||||
\(76\) | − | 5.27729i | − | 0.0694380i | ||||||
\(77\) | 21.2084 | 0.275434 | ||||||||
\(78\) | −58.1934 | −0.746069 | ||||||||
\(79\) | − | 70.0342i | − | 0.886509i | −0.896396 | − | 0.443255i | \(-0.853824\pi\) | ||
0.896396 | − | 0.443255i | \(-0.146176\pi\) | |||||||
\(80\) | 8.20311i | 0.102539i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −19.7579 | −0.240950 | ||||||||
\(83\) | − | 68.9881i | − | 0.831181i | −0.909552 | − | 0.415591i | \(-0.863575\pi\) | ||
0.909552 | − | 0.415591i | \(-0.136425\pi\) | |||||||
\(84\) | 4.16719i | 0.0496093i | ||||||||
\(85\) | 18.0798 | 0.212703 | ||||||||
\(86\) | 121.472i | 1.41247i | ||||||||
\(87\) | 23.2227 | 0.266928 | ||||||||
\(88\) | − | 69.1844i | − | 0.786187i | ||||||
\(89\) | 12.2196i | 0.137299i | 0.997641 | + | 0.0686497i | \(0.0218691\pi\) | ||||
−0.997641 | + | 0.0686497i | \(0.978131\pi\) | |||||||
\(90\) | 3.75044i | 0.0416715i | ||||||||
\(91\) | − | 50.5635i | − | 0.555643i | ||||||
\(92\) | 17.5802 | − | 11.3306i | 0.191089 | − | 0.123158i | ||||
\(93\) | −86.2638 | −0.927568 | ||||||||
\(94\) | 15.4638 | 0.164508 | ||||||||
\(95\) | 4.12681 | 0.0434401 | ||||||||
\(96\) | 24.6697 | 0.256976 | ||||||||
\(97\) | − | 135.825i | − | 1.40026i | −0.714016 | − | 0.700130i | \(-0.753125\pi\) | ||
0.714016 | − | 0.700130i | \(-0.246875\pi\) | |||||||
\(98\) | 12.3062 | 0.125573 | ||||||||
\(99\) | − | 24.0481i | − | 0.242910i | ||||||
\(100\) | −22.2740 | −0.222740 | ||||||||
\(101\) | 86.7443 | 0.858854 | 0.429427 | − | 0.903102i | \(-0.358716\pi\) | ||||
0.429427 | + | 0.903102i | \(0.358716\pi\) | |||||||
\(102\) | 77.4179i | 0.758999i | ||||||||
\(103\) | − | 15.5070i | − | 0.150554i | −0.997163 | − | 0.0752769i | \(-0.976016\pi\) | ||
0.997163 | − | 0.0752769i | \(-0.0239841\pi\) | |||||||
\(104\) | −164.944 | −1.58600 | ||||||||
\(105\) | −3.25871 | −0.0310353 | ||||||||
\(106\) | 112.087i | 1.05743i | ||||||||
\(107\) | − | 39.3116i | − | 0.367398i | −0.982982 | − | 0.183699i | \(-0.941193\pi\) | ||
0.982982 | − | 0.183699i | \(-0.0588072\pi\) | |||||||
\(108\) | 4.72514 | 0.0437513 | ||||||||
\(109\) | − | 119.619i | − | 1.09742i | −0.836012 | − | 0.548711i | \(-0.815119\pi\) | ||
0.836012 | − | 0.548711i | \(-0.184881\pi\) | |||||||
\(110\) | 10.0212 | 0.0911020 | ||||||||
\(111\) | 107.165i | 0.965454i | ||||||||
\(112\) | − | 30.5205i | − | 0.272504i | ||||||
\(113\) | 188.364i | 1.66694i | 0.552565 | + | 0.833470i | \(0.313649\pi\) | ||||
−0.552565 | + | 0.833470i | \(0.686351\pi\) | |||||||
\(114\) | 17.6711i | 0.155009i | ||||||||
\(115\) | 8.86042 | + | 13.7476i | 0.0770471 | + | 0.119544i | ||||
\(116\) | 12.1923 | 0.105106 | ||||||||
\(117\) | −57.3336 | −0.490031 | ||||||||
\(118\) | −95.4832 | −0.809180 | ||||||||
\(119\) | −67.2675 | −0.565273 | ||||||||
\(120\) | 10.6303i | 0.0885859i | ||||||||
\(121\) | 56.7432 | 0.468952 | ||||||||
\(122\) | 114.780i | 0.940818i | ||||||||
\(123\) | −19.4660 | −0.158260 | ||||||||
\(124\) | −45.2899 | −0.365241 | ||||||||
\(125\) | − | 35.1959i | − | 0.281567i | ||||||
\(126\) | − | 13.9539i | − | 0.110745i | ||||||
\(127\) | 77.7836 | 0.612469 | 0.306235 | − | 0.951956i | \(-0.400931\pi\) | ||||
0.306235 | + | 0.951956i | \(0.400931\pi\) | |||||||
\(128\) | −68.1678 | −0.532561 | ||||||||
\(129\) | 119.678i | 0.927733i | ||||||||
\(130\) | − | 23.8918i | − | 0.183783i | ||||||
\(131\) | −79.4552 | −0.606528 | −0.303264 | − | 0.952907i | \(-0.598076\pi\) | ||||
−0.303264 | + | 0.952907i | \(0.598076\pi\) | |||||||
\(132\) | − | 12.6256i | − | 0.0956488i | ||||||
\(133\) | −15.3542 | −0.115445 | ||||||||
\(134\) | − | 179.473i | − | 1.33935i | ||||||
\(135\) | 3.69503i | 0.0273706i | ||||||||
\(136\) | 219.435i | 1.61349i | ||||||||
\(137\) | 113.187i | 0.826184i | 0.910689 | + | 0.413092i | \(0.135551\pi\) | ||||
−0.910689 | + | 0.413092i | \(0.864449\pi\) | |||||||
\(138\) | −58.8674 | + | 37.9405i | −0.426575 | + | 0.274931i | ||||
\(139\) | 121.495 | 0.874067 | 0.437033 | − | 0.899445i | \(-0.356029\pi\) | ||||
0.437033 | + | 0.899445i | \(0.356029\pi\) | |||||||
\(140\) | −1.71088 | −0.0122205 | ||||||||
\(141\) | 15.2353 | 0.108052 | ||||||||
\(142\) | −25.5512 | −0.179938 | ||||||||
\(143\) | 153.196i | 1.07130i | ||||||||
\(144\) | −34.6070 | −0.240326 | ||||||||
\(145\) | 9.53429i | 0.0657537i | ||||||||
\(146\) | −130.350 | −0.892812 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | 56.2635i | 0.380159i | ||||||||
\(149\) | − | 21.8043i | − | 0.146338i | −0.997320 | − | 0.0731688i | \(-0.976689\pi\) | ||
0.997320 | − | 0.0731688i | \(-0.0233112\pi\) | |||||||
\(150\) | 74.5849 | 0.497232 | ||||||||
\(151\) | 44.0474 | 0.291704 | 0.145852 | − | 0.989306i | \(-0.453408\pi\) | ||||
0.145852 | + | 0.989306i | \(0.453408\pi\) | |||||||
\(152\) | 50.0872i | 0.329521i | ||||||||
\(153\) | 76.2742i | 0.498524i | ||||||||
\(154\) | −37.2849 | −0.242110 | ||||||||
\(155\) | − | 35.4164i | − | 0.228493i | ||||||
\(156\) | −30.1011 | −0.192956 | ||||||||
\(157\) | − | 282.497i | − | 1.79934i | −0.436569 | − | 0.899671i | \(-0.643807\pi\) | ||
0.436569 | − | 0.899671i | \(-0.356193\pi\) | |||||||
\(158\) | 123.122i | 0.779252i | ||||||||
\(159\) | 110.431i | 0.694536i | ||||||||
\(160\) | 10.1284i | 0.0633024i | ||||||||
\(161\) | −32.9660 | − | 51.1492i | −0.204758 | − | 0.317697i | ||||
\(162\) | −15.8222 | −0.0976680 | ||||||||
\(163\) | −318.274 | −1.95260 | −0.976299 | − | 0.216426i | \(-0.930560\pi\) | ||||
−0.976299 | + | 0.216426i | \(0.930560\pi\) | |||||||
\(164\) | −10.2200 | −0.0623169 | ||||||||
\(165\) | 9.87316 | 0.0598374 | ||||||||
\(166\) | 121.283i | 0.730618i | ||||||||
\(167\) | −40.9876 | −0.245435 | −0.122717 | − | 0.992442i | \(-0.539161\pi\) | ||||
−0.122717 | + | 0.992442i | \(0.539161\pi\) | |||||||
\(168\) | − | 39.5511i | − | 0.235423i | ||||||
\(169\) | 196.238 | 1.16117 | ||||||||
\(170\) | −31.7846 | −0.186968 | ||||||||
\(171\) | 17.4100i | 0.101813i | ||||||||
\(172\) | 62.8327i | 0.365306i | ||||||||
\(173\) | 205.900 | 1.19017 | 0.595086 | − | 0.803662i | \(-0.297118\pi\) | ||||
0.595086 | + | 0.803662i | \(0.297118\pi\) | |||||||
\(174\) | −40.8260 | −0.234632 | ||||||||
\(175\) | 64.8059i | 0.370319i | ||||||||
\(176\) | 92.4702i | 0.525399i | ||||||||
\(177\) | −94.0726 | −0.531484 | ||||||||
\(178\) | − | 21.4824i | − | 0.120688i | ||||||
\(179\) | −250.038 | −1.39686 | −0.698430 | − | 0.715678i | \(-0.746118\pi\) | ||||
−0.698430 | + | 0.715678i | \(0.746118\pi\) | |||||||
\(180\) | 1.93995i | 0.0107775i | ||||||||
\(181\) | 31.4840i | 0.173945i | 0.996211 | + | 0.0869724i | \(0.0277192\pi\) | ||||
−0.996211 | + | 0.0869724i | \(0.972281\pi\) | |||||||
\(182\) | 88.8918i | 0.488417i | ||||||||
\(183\) | 113.084i | 0.617946i | ||||||||
\(184\) | −166.855 | + | 107.539i | −0.906820 | + | 0.584452i | ||||
\(185\) | −43.9977 | −0.237825 | ||||||||
\(186\) | 151.654 | 0.815343 | ||||||||
\(187\) | 203.805 | 1.08987 | ||||||||
\(188\) | 7.99880 | 0.0425468 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | −7.25502 | −0.0381843 | ||||||||
\(191\) | − | 356.198i | − | 1.86491i | −0.361288 | − | 0.932454i | \(-0.617663\pi\) | ||
0.361288 | − | 0.932454i | \(-0.382337\pi\) | |||||||
\(192\) | −123.291 | −0.642142 | ||||||||
\(193\) | −17.4493 | −0.0904107 | −0.0452053 | − | 0.998978i | \(-0.514394\pi\) | ||||
−0.0452053 | + | 0.998978i | \(0.514394\pi\) | |||||||
\(194\) | 238.784i | 1.23084i | ||||||||
\(195\) | − | 23.5388i | − | 0.120712i | ||||||
\(196\) | 6.36548 | 0.0324769 | ||||||||
\(197\) | 216.442 | 1.09869 | 0.549346 | − | 0.835595i | \(-0.314877\pi\) | ||||
0.549346 | + | 0.835595i | \(0.314877\pi\) | |||||||
\(198\) | 42.2771i | 0.213521i | ||||||||
\(199\) | 79.5233i | 0.399615i | 0.979835 | + | 0.199807i | \(0.0640316\pi\) | ||||
−0.979835 | + | 0.199807i | \(0.935968\pi\) | |||||||
\(200\) | 211.405 | 1.05702 | ||||||||
\(201\) | − | 176.822i | − | 0.879711i | ||||||
\(202\) | −152.498 | −0.754943 | ||||||||
\(203\) | − | 35.4733i | − | 0.174745i | ||||||
\(204\) | 40.0452i | 0.196300i | ||||||||
\(205\) | − | 7.99195i | − | 0.0389851i | ||||||
\(206\) | 27.2617i | 0.132338i | ||||||||
\(207\) | −57.9977 | + | 37.3800i | −0.280182 | + | 0.180580i | ||||
\(208\) | 220.460 | 1.05991 | ||||||||
\(209\) | 46.5197 | 0.222582 | ||||||||
\(210\) | 5.72889 | 0.0272804 | ||||||||
\(211\) | −137.441 | −0.651378 | −0.325689 | − | 0.945477i | \(-0.605596\pi\) | ||||
−0.325689 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(212\) | 57.9781i | 0.273482i | ||||||||
\(213\) | −25.1737 | −0.118187 | ||||||||
\(214\) | 69.1108i | 0.322948i | ||||||||
\(215\) | −49.1347 | −0.228534 | ||||||||
\(216\) | −44.8467 | −0.207624 | ||||||||
\(217\) | 131.770i | 0.607236i | ||||||||
\(218\) | 210.293i | 0.964646i | ||||||||
\(219\) | −128.425 | −0.586414 | ||||||||
\(220\) | 5.18357 | 0.0235617 | ||||||||
\(221\) | − | 485.897i | − | 2.19863i | ||||||
\(222\) | − | 188.399i | − | 0.848645i | ||||||
\(223\) | −206.967 | −0.928105 | −0.464052 | − | 0.885808i | \(-0.653605\pi\) | ||||
−0.464052 | + | 0.885808i | \(0.653605\pi\) | |||||||
\(224\) | − | 37.6837i | − | 0.168231i | ||||||
\(225\) | 73.4830 | 0.326591 | ||||||||
\(226\) | − | 331.149i | − | 1.46526i | ||||||
\(227\) | 332.026i | 1.46267i | 0.682019 | + | 0.731335i | \(0.261102\pi\) | ||||
−0.682019 | + | 0.731335i | \(0.738898\pi\) | |||||||
\(228\) | 9.14053i | 0.0400901i | ||||||||
\(229\) | − | 1.54210i | − | 0.00673406i | −0.999994 | − | 0.00336703i | \(-0.998928\pi\) | ||
0.999994 | − | 0.00336703i | \(-0.00107176\pi\) | |||||||
\(230\) | −15.5768 | − | 24.1685i | −0.0677253 | − | 0.105081i | ||||
\(231\) | −36.7341 | −0.159022 | ||||||||
\(232\) | −115.718 | −0.498785 | ||||||||
\(233\) | 78.1284 | 0.335315 | 0.167658 | − | 0.985845i | \(-0.446380\pi\) | ||||
0.167658 | + | 0.985845i | \(0.446380\pi\) | |||||||
\(234\) | 100.794 | 0.430743 | ||||||||
\(235\) | 6.25501i | 0.0266170i | ||||||||
\(236\) | −49.3896 | −0.209278 | ||||||||
\(237\) | 121.303i | 0.511826i | ||||||||
\(238\) | 118.258 | 0.496882 | ||||||||
\(239\) | −292.092 | −1.22214 | −0.611072 | − | 0.791575i | \(-0.709261\pi\) | ||||
−0.611072 | + | 0.791575i | \(0.709261\pi\) | |||||||
\(240\) | − | 14.2082i | − | 0.0592009i | ||||||
\(241\) | − | 394.307i | − | 1.63613i | −0.575126 | − | 0.818065i | \(-0.695047\pi\) | ||
0.575126 | − | 0.818065i | \(-0.304953\pi\) | |||||||
\(242\) | −99.7559 | −0.412214 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 59.3710i | 0.243324i | ||||||||
\(245\) | 4.97776i | 0.0203174i | ||||||||
\(246\) | 34.2217 | 0.139113 | ||||||||
\(247\) | − | 110.909i | − | 0.449023i | ||||||
\(248\) | 429.850 | 1.73327 | ||||||||
\(249\) | 119.491i | 0.479883i | ||||||||
\(250\) | 61.8751i | 0.247501i | ||||||||
\(251\) | 107.173i | 0.426984i | 0.976945 | + | 0.213492i | \(0.0684838\pi\) | ||||
−0.976945 | + | 0.213492i | \(0.931516\pi\) | |||||||
\(252\) | − | 7.21778i | − | 0.0286420i | ||||||
\(253\) | 99.8797 | + | 154.971i | 0.394782 | + | 0.612532i | ||||
\(254\) | −136.745 | −0.538368 | ||||||||
\(255\) | −31.3151 | −0.122804 | ||||||||
\(256\) | −164.889 | −0.644096 | ||||||||
\(257\) | −42.3722 | −0.164872 | −0.0824362 | − | 0.996596i | \(-0.526270\pi\) | ||||
−0.0824362 | + | 0.996596i | \(0.526270\pi\) | |||||||
\(258\) | − | 210.396i | − | 0.815488i | ||||||
\(259\) | 163.698 | 0.632038 | ||||||||
\(260\) | − | 12.3583i | − | 0.0475318i | ||||||
\(261\) | −40.2229 | −0.154111 | ||||||||
\(262\) | 139.684 | 0.533145 | ||||||||
\(263\) | 40.5143i | 0.154047i | 0.997029 | + | 0.0770234i | \(0.0245416\pi\) | ||||
−0.997029 | + | 0.0770234i | \(0.975458\pi\) | |||||||
\(264\) | 119.831i | 0.453905i | ||||||||
\(265\) | −45.3385 | −0.171089 | ||||||||
\(266\) | 26.9930 | 0.101478 | ||||||||
\(267\) | − | 21.1651i | − | 0.0792699i | ||||||
\(268\) | − | 92.8343i | − | 0.346397i | ||||||
\(269\) | 517.952 | 1.92547 | 0.962737 | − | 0.270440i | \(-0.0871690\pi\) | ||||
0.962737 | + | 0.270440i | \(0.0871690\pi\) | |||||||
\(270\) | − | 6.49595i | − | 0.0240591i | ||||||
\(271\) | 265.958 | 0.981395 | 0.490697 | − | 0.871330i | \(-0.336742\pi\) | ||||
0.490697 | + | 0.871330i | \(0.336742\pi\) | |||||||
\(272\) | − | 293.291i | − | 1.07828i | ||||||
\(273\) | 87.5786i | 0.320801i | ||||||||
\(274\) | − | 198.986i | − | 0.726225i | ||||||
\(275\) | − | 196.347i | − | 0.713990i | ||||||
\(276\) | −30.4497 | + | 19.6251i | −0.110325 | + | 0.0711054i | ||||
\(277\) | 426.483 | 1.53965 | 0.769824 | − | 0.638256i | \(-0.220344\pi\) | ||||
0.769824 | + | 0.638256i | \(0.220344\pi\) | |||||||
\(278\) | −213.591 | −0.768315 | ||||||||
\(279\) | 149.413 | 0.535531 | ||||||||
\(280\) | 16.2381 | 0.0579931 | ||||||||
\(281\) | − | 365.313i | − | 1.30005i | −0.759914 | − | 0.650024i | \(-0.774759\pi\) | ||
0.759914 | − | 0.650024i | \(-0.225241\pi\) | |||||||
\(282\) | −26.7841 | −0.0949790 | ||||||||
\(283\) | 517.783i | 1.82962i | 0.403882 | + | 0.914811i | \(0.367660\pi\) | ||||
−0.403882 | + | 0.914811i | \(0.632340\pi\) | |||||||
\(284\) | −13.2166 | −0.0465374 | ||||||||
\(285\) | −7.14784 | −0.0250801 | ||||||||
\(286\) | − | 269.322i | − | 0.941686i | ||||||
\(287\) | 29.7348i | 0.103606i | ||||||||
\(288\) | −42.7292 | −0.148365 | ||||||||
\(289\) | −357.417 | −1.23674 | ||||||||
\(290\) | − | 16.7615i | − | 0.0577983i | ||||||
\(291\) | 235.256i | 0.808440i | ||||||||
\(292\) | −67.4250 | −0.230908 | ||||||||
\(293\) | − | 478.496i | − | 1.63309i | −0.577280 | − | 0.816546i | \(-0.695886\pi\) | ||
0.577280 | − | 0.816546i | \(-0.304114\pi\) | |||||||
\(294\) | −21.3149 | −0.0724997 | ||||||||
\(295\) | − | 38.6223i | − | 0.130923i | ||||||
\(296\) | − | 534.002i | − | 1.80406i | ||||||
\(297\) | 41.6525i | 0.140244i | ||||||||
\(298\) | 38.3325i | 0.128632i | ||||||||
\(299\) | 369.469 | − | 238.126i | 1.23568 | − | 0.796407i | ||||
\(300\) | 38.5797 | 0.128599 | ||||||||
\(301\) | 182.811 | 0.607344 | ||||||||
\(302\) | −77.4363 | −0.256411 | ||||||||
\(303\) | −150.245 | −0.495860 | ||||||||
\(304\) | − | 66.9453i | − | 0.220215i | ||||||
\(305\) | −46.4277 | −0.152222 | ||||||||
\(306\) | − | 134.092i | − | 0.438208i | ||||||
\(307\) | −395.306 | −1.28764 | −0.643821 | − | 0.765176i | \(-0.722652\pi\) | ||||
−0.643821 | + | 0.765176i | \(0.722652\pi\) | |||||||
\(308\) | −19.2860 | −0.0626168 | ||||||||
\(309\) | 26.8590i | 0.0869222i | ||||||||
\(310\) | 62.2628i | 0.200848i | ||||||||
\(311\) | 584.020 | 1.87788 | 0.938939 | − | 0.344084i | \(-0.111810\pi\) | ||||
0.938939 | + | 0.344084i | \(0.111810\pi\) | |||||||
\(312\) | 285.692 | 0.915679 | ||||||||
\(313\) | 121.168i | 0.387118i | 0.981089 | + | 0.193559i | \(0.0620031\pi\) | ||||
−0.981089 | + | 0.193559i | \(0.937997\pi\) | |||||||
\(314\) | 496.636i | 1.58164i | ||||||||
\(315\) | 5.64425 | 0.0179183 | ||||||||
\(316\) | 63.6859i | 0.201538i | ||||||||
\(317\) | −557.796 | −1.75961 | −0.879805 | − | 0.475335i | \(-0.842327\pi\) | ||||
−0.879805 | + | 0.475335i | \(0.842327\pi\) | |||||||
\(318\) | − | 194.141i | − | 0.610505i | ||||||
\(319\) | 107.476i | 0.336915i | ||||||||
\(320\) | − | 50.6184i | − | 0.158182i | ||||||
\(321\) | 68.0898i | 0.212118i | ||||||||
\(322\) | 57.9551 | + | 89.9215i | 0.179985 | + | 0.279259i | ||||
\(323\) | −147.548 | −0.456806 | ||||||||
\(324\) | −8.18419 | −0.0252598 | ||||||||
\(325\) | −468.116 | −1.44036 | ||||||||
\(326\) | 559.532 | 1.71636 | ||||||||
\(327\) | 207.186i | 0.633596i | ||||||||
\(328\) | 96.9986 | 0.295727 | ||||||||
\(329\) | − | 23.2724i | − | 0.0707367i | ||||||
\(330\) | −17.3573 | −0.0525977 | ||||||||
\(331\) | 511.085 | 1.54406 | 0.772031 | − | 0.635585i | \(-0.219241\pi\) | ||||
0.772031 | + | 0.635585i | \(0.219241\pi\) | |||||||
\(332\) | 62.7346i | 0.188960i | ||||||||
\(333\) | − | 185.616i | − | 0.557405i | ||||||
\(334\) | 72.0572 | 0.215740 | ||||||||
\(335\) | 72.5958 | 0.216704 | ||||||||
\(336\) | 52.8630i | 0.157330i | ||||||||
\(337\) | − | 486.160i | − | 1.44261i | −0.692617 | − | 0.721305i | \(-0.743542\pi\) | ||
0.692617 | − | 0.721305i | \(-0.256458\pi\) | |||||||
\(338\) | −344.992 | −1.02069 | ||||||||
\(339\) | − | 326.256i | − | 0.962408i | ||||||
\(340\) | −16.4409 | −0.0483556 | ||||||||
\(341\) | − | 399.234i | − | 1.17077i | ||||||
\(342\) | − | 30.6072i | − | 0.0894947i | ||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | − | 596.350i | − | 1.73358i | ||||||
\(345\) | −15.3467 | − | 23.8115i | −0.0444832 | − | 0.0690188i | ||||
\(346\) | −361.976 | −1.04617 | ||||||||
\(347\) | 237.184 | 0.683528 | 0.341764 | − | 0.939786i | \(-0.388976\pi\) | ||||
0.341764 | + | 0.939786i | \(0.388976\pi\) | |||||||
\(348\) | −21.1177 | −0.0606829 | ||||||||
\(349\) | 132.541 | 0.379775 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(350\) | − | 113.930i | − | 0.325515i | ||||||
\(351\) | 99.3048 | 0.282920 | ||||||||
\(352\) | 114.173i | 0.324355i | ||||||||
\(353\) | 183.098 | 0.518691 | 0.259346 | − | 0.965785i | \(-0.416493\pi\) | ||||
0.259346 | + | 0.965785i | \(0.416493\pi\) | |||||||
\(354\) | 165.382 | 0.467180 | ||||||||
\(355\) | − | 10.3353i | − | 0.0291135i | ||||||
\(356\) | − | 11.1120i | − | 0.0312135i | ||||||
\(357\) | 116.511 | 0.326361 | ||||||||
\(358\) | 439.573 | 1.22786 | ||||||||
\(359\) | 299.975i | 0.835584i | 0.908543 | + | 0.417792i | \(0.137196\pi\) | ||||
−0.908543 | + | 0.417792i | \(0.862804\pi\) | |||||||
\(360\) | − | 18.4122i | − | 0.0511451i | ||||||
\(361\) | 327.321 | 0.906707 | ||||||||
\(362\) | − | 55.3496i | − | 0.152899i | ||||||
\(363\) | −98.2821 | −0.270750 | ||||||||
\(364\) | 45.9801i | 0.126319i | ||||||||
\(365\) | − | 52.7259i | − | 0.144455i | ||||||
\(366\) | − | 198.805i | − | 0.543182i | ||||||
\(367\) | − | 135.980i | − | 0.370517i | −0.982690 | − | 0.185259i | \(-0.940688\pi\) | ||
0.982690 | − | 0.185259i | \(-0.0593123\pi\) | |||||||
\(368\) | 223.014 | − | 143.734i | 0.606016 | − | 0.390582i | ||||
\(369\) | 33.7161 | 0.0913716 | ||||||||
\(370\) | 77.3490 | 0.209051 | ||||||||
\(371\) | 168.686 | 0.454680 | ||||||||
\(372\) | 78.4444 | 0.210872 | ||||||||
\(373\) | 4.36491i | 0.0117022i | 0.999983 | + | 0.00585109i | \(0.00186247\pi\) | ||||
−0.999983 | + | 0.00585109i | \(0.998138\pi\) | |||||||
\(374\) | −358.295 | −0.958007 | ||||||||
\(375\) | 60.9610i | 0.162563i | ||||||||
\(376\) | −75.9172 | −0.201908 | ||||||||
\(377\) | 256.236 | 0.679671 | ||||||||
\(378\) | 24.1688i | 0.0639387i | ||||||||
\(379\) | 152.822i | 0.403225i | 0.979465 | + | 0.201612i | \(0.0646182\pi\) | ||||
−0.979465 | + | 0.201612i | \(0.935382\pi\) | |||||||
\(380\) | −3.75273 | −0.00987560 | ||||||||
\(381\) | −134.725 | −0.353609 | ||||||||
\(382\) | 626.204i | 1.63928i | ||||||||
\(383\) | 408.302i | 1.06606i | 0.846096 | + | 0.533031i | \(0.178947\pi\) | ||||
−0.846096 | + | 0.533031i | \(0.821053\pi\) | |||||||
\(384\) | 118.070 | 0.307474 | ||||||||
\(385\) | − | 15.0815i | − | 0.0391727i | ||||||
\(386\) | 30.6762 | 0.0794720 | ||||||||
\(387\) | − | 207.288i | − | 0.535627i | ||||||
\(388\) | 123.513i | 0.318333i | ||||||||
\(389\) | 653.238i | 1.67928i | 0.543146 | + | 0.839638i | \(0.317233\pi\) | ||||
−0.543146 | + | 0.839638i | \(0.682767\pi\) | |||||||
\(390\) | 41.3818i | 0.106107i | ||||||||
\(391\) | −316.792 | − | 491.525i | −0.810210 | − | 1.25710i | ||||
\(392\) | −60.4153 | −0.154121 | ||||||||
\(393\) | 137.620 | 0.350179 | ||||||||
\(394\) | −380.510 | −0.965762 | ||||||||
\(395\) | −49.8020 | −0.126081 | ||||||||
\(396\) | 21.8682i | 0.0552228i | ||||||||
\(397\) | −347.048 | −0.874176 | −0.437088 | − | 0.899419i | \(-0.643990\pi\) | ||||
−0.437088 | + | 0.899419i | \(0.643990\pi\) | |||||||
\(398\) | − | 139.804i | − | 0.351266i | ||||||
\(399\) | 26.5942 | 0.0666522 | ||||||||
\(400\) | −282.558 | −0.706395 | ||||||||
\(401\) | 75.2554i | 0.187669i | 0.995588 | + | 0.0938347i | \(0.0299125\pi\) | ||||
−0.995588 | + | 0.0938347i | \(0.970087\pi\) | |||||||
\(402\) | 310.857i | 0.773276i | ||||||||
\(403\) | −951.823 | −2.36184 | ||||||||
\(404\) | −78.8813 | −0.195251 | ||||||||
\(405\) | − | 6.39998i | − | 0.0158024i | ||||||
\(406\) | 62.3628i | 0.153603i | ||||||||
\(407\) | −495.968 | −1.21859 | ||||||||
\(408\) | − | 380.072i | − | 0.931549i | ||||||
\(409\) | −120.274 | −0.294068 | −0.147034 | − | 0.989131i | \(-0.546973\pi\) | ||||
−0.147034 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(410\) | 14.0500i | 0.0342684i | ||||||||
\(411\) | − | 196.046i | − | 0.476998i | ||||||
\(412\) | 14.1014i | 0.0342267i | ||||||||
\(413\) | 143.698i | 0.347938i | ||||||||
\(414\) | 101.961 | − | 65.7149i | 0.246283 | − | 0.158732i | ||||
\(415\) | −49.0580 | −0.118212 | ||||||||
\(416\) | 272.203 | 0.654333 | ||||||||
\(417\) | −210.436 | −0.504643 | ||||||||
\(418\) | −81.7828 | −0.195653 | ||||||||
\(419\) | 223.088i | 0.532430i | 0.963914 | + | 0.266215i | \(0.0857731\pi\) | ||||
−0.963914 | + | 0.266215i | \(0.914227\pi\) | |||||||
\(420\) | 2.96332 | 0.00705553 | ||||||||
\(421\) | 475.998i | 1.13064i | 0.824873 | + | 0.565318i | \(0.191247\pi\) | ||||
−0.824873 | + | 0.565318i | \(0.808753\pi\) | |||||||
\(422\) | 241.624 | 0.572569 | ||||||||
\(423\) | −26.3884 | −0.0623839 | ||||||||
\(424\) | − | 550.275i | − | 1.29782i | ||||||
\(425\) | 622.761i | 1.46532i | ||||||||
\(426\) | 44.2560 | 0.103887 | ||||||||
\(427\) | 172.739 | 0.404541 | ||||||||
\(428\) | 35.7482i | 0.0835239i | ||||||||
\(429\) | − | 265.343i | − | 0.618516i | ||||||
\(430\) | 86.3800 | 0.200884 | ||||||||
\(431\) | − | 589.612i | − | 1.36801i | −0.729477 | − | 0.684005i | \(-0.760237\pi\) | ||
0.729477 | − | 0.684005i | \(-0.239763\pi\) | |||||||
\(432\) | 59.9410 | 0.138752 | ||||||||
\(433\) | − | 28.3248i | − | 0.0654153i | −0.999465 | − | 0.0327077i | \(-0.989587\pi\) | ||
0.999465 | − | 0.0327077i | \(-0.0104130\pi\) | |||||||
\(434\) | − | 231.655i | − | 0.533767i | ||||||
\(435\) | − | 16.5139i | − | 0.0379629i | ||||||
\(436\) | 108.776i | 0.249486i | ||||||||
\(437\) | −72.3095 | − | 112.193i | −0.165468 | − | 0.256736i | ||||
\(438\) | 225.774 | 0.515465 | ||||||||
\(439\) | 770.570 | 1.75528 | 0.877642 | − | 0.479316i | \(-0.159115\pi\) | ||||
0.877642 | + | 0.479316i | \(0.159115\pi\) | |||||||
\(440\) | −49.1977 | −0.111813 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 854.219i | 1.93262i | ||||||||
\(443\) | −192.079 | −0.433588 | −0.216794 | − | 0.976217i | \(-0.569560\pi\) | ||||
−0.216794 | + | 0.976217i | \(0.569560\pi\) | |||||||
\(444\) | − | 97.4513i | − | 0.219485i | ||||||
\(445\) | 8.68950 | 0.0195270 | ||||||||
\(446\) | 363.853 | 0.815815 | ||||||||
\(447\) | 37.7662i | 0.0844880i | ||||||||
\(448\) | 188.331i | 0.420381i | ||||||||
\(449\) | −810.000 | −1.80401 | −0.902004 | − | 0.431727i | \(-0.857904\pi\) | ||||
−0.902004 | + | 0.431727i | \(0.857904\pi\) | |||||||
\(450\) | −129.185 | −0.287077 | ||||||||
\(451\) | − | 90.0899i | − | 0.199756i | ||||||
\(452\) | − | 171.290i | − | 0.378960i | ||||||
\(453\) | −76.2923 | −0.168416 | ||||||||
\(454\) | − | 583.709i | − | 1.28570i | ||||||
\(455\) | −35.9562 | −0.0790246 | ||||||||
\(456\) | − | 86.7536i | − | 0.190249i | ||||||
\(457\) | − | 84.0185i | − | 0.183848i | −0.995766 | − | 0.0919239i | \(-0.970698\pi\) | ||
0.995766 | − | 0.0919239i | \(-0.0293017\pi\) | |||||||
\(458\) | 2.71105i | 0.00591931i | ||||||||
\(459\) | − | 132.111i | − | 0.287823i | ||||||
\(460\) | −8.05726 | − | 12.5014i | −0.0175158 | − | 0.0271770i | ||||
\(461\) | 156.389 | 0.339240 | 0.169620 | − | 0.985510i | \(-0.445746\pi\) | ||||
0.169620 | + | 0.985510i | \(0.445746\pi\) | |||||||
\(462\) | 64.5794 | 0.139782 | ||||||||
\(463\) | 729.911 | 1.57648 | 0.788241 | − | 0.615366i | \(-0.210992\pi\) | ||||
0.788241 | + | 0.615366i | \(0.210992\pi\) | |||||||
\(464\) | 154.666 | 0.333332 | ||||||||
\(465\) | 61.3430i | 0.131920i | ||||||||
\(466\) | −137.352 | −0.294746 | ||||||||
\(467\) | 278.356i | 0.596051i | 0.954558 | + | 0.298026i | \(0.0963281\pi\) | ||||
−0.954558 | + | 0.298026i | \(0.903672\pi\) | |||||||
\(468\) | 52.1366 | 0.111403 | ||||||||
\(469\) | −270.100 | −0.575906 | ||||||||
\(470\) | − | 10.9964i | − | 0.0233967i | ||||||
\(471\) | 489.298i | 1.03885i | ||||||||
\(472\) | 468.761 | 0.993138 | ||||||||
\(473\) | −553.875 | −1.17098 | ||||||||
\(474\) | − | 213.253i | − | 0.449901i | ||||||
\(475\) | 142.149i | 0.299261i | ||||||||
\(476\) | 61.1700 | 0.128508 | ||||||||
\(477\) | − | 191.272i | − | 0.400990i | ||||||
\(478\) | 513.505 | 1.07428 | ||||||||
\(479\) | 195.302i | 0.407728i | 0.978999 | + | 0.203864i | \(0.0653501\pi\) | ||||
−0.978999 | + | 0.203864i | \(0.934650\pi\) | |||||||
\(480\) | − | 17.5429i | − | 0.0365477i | ||||||
\(481\) | 1182.45i | 2.45831i | ||||||||
\(482\) | 693.201i | 1.43818i | ||||||||
\(483\) | 57.0989 | + | 88.5930i | 0.118217 | + | 0.183422i | ||||
\(484\) | −51.5997 | −0.106611 | ||||||||
\(485\) | −96.5865 | −0.199147 | ||||||||
\(486\) | 27.4049 | 0.0563886 | ||||||||
\(487\) | −356.792 | −0.732632 | −0.366316 | − | 0.930491i | \(-0.619381\pi\) | ||||
−0.366316 | + | 0.930491i | \(0.619381\pi\) | |||||||
\(488\) | − | 563.495i | − | 1.15470i | ||||||
\(489\) | 551.266 | 1.12733 | ||||||||
\(490\) | − | 8.75102i | − | 0.0178592i | ||||||
\(491\) | −336.651 | −0.685644 | −0.342822 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342822 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(492\) | 17.7015 | 0.0359787 | ||||||||
\(493\) | − | 340.885i | − | 0.691451i | ||||||
\(494\) | 194.980i | 0.394697i | ||||||||
\(495\) | −17.1008 | −0.0345471 | ||||||||
\(496\) | −574.527 | −1.15832 | ||||||||
\(497\) | 38.4535i | 0.0773713i | ||||||||
\(498\) | − | 210.068i | − | 0.421823i | ||||||
\(499\) | −168.599 | −0.337873 | −0.168936 | − | 0.985627i | \(-0.554033\pi\) | ||||
−0.168936 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(500\) | 32.0055i | 0.0640110i | ||||||||
\(501\) | 70.9927 | 0.141702 | ||||||||
\(502\) | − | 188.413i | − | 0.375324i | ||||||
\(503\) | 804.464i | 1.59933i | 0.600445 | + | 0.799666i | \(0.294990\pi\) | ||||
−0.600445 | + | 0.799666i | \(0.705010\pi\) | |||||||
\(504\) | 68.5045i | 0.135922i | ||||||||
\(505\) | − | 61.6846i | − | 0.122148i | ||||||
\(506\) | −175.591 | − | 272.442i | −0.347018 | − | 0.538423i | ||||
\(507\) | −339.895 | −0.670404 | ||||||||
\(508\) | −70.7329 | −0.139238 | ||||||||
\(509\) | 62.7242 | 0.123230 | 0.0616152 | − | 0.998100i | \(-0.480375\pi\) | ||||
0.0616152 | + | 0.998100i | \(0.480375\pi\) | |||||||
\(510\) | 55.0526 | 0.107946 | ||||||||
\(511\) | 196.172i | 0.383898i | ||||||||
\(512\) | 562.549 | 1.09873 | ||||||||
\(513\) | − | 30.1550i | − | 0.0587817i | ||||||
\(514\) | 74.4913 | 0.144925 | ||||||||
\(515\) | −11.0272 | −0.0214120 | ||||||||
\(516\) | − | 108.829i | − | 0.210910i | ||||||
\(517\) | 70.5100i | 0.136383i | ||||||||
\(518\) | −287.785 | −0.555569 | ||||||||
\(519\) | −356.629 | −0.687146 | ||||||||
\(520\) | 117.293i | 0.225564i | ||||||||
\(521\) | − | 497.634i | − | 0.955152i | −0.878590 | − | 0.477576i | \(-0.841515\pi\) | ||
0.878590 | − | 0.477576i | \(-0.158485\pi\) | |||||||
\(522\) | 70.7128 | 0.135465 | ||||||||
\(523\) | 84.1903i | 0.160976i | 0.996756 | + | 0.0804878i | \(0.0256478\pi\) | ||||
−0.996756 | + | 0.0804878i | \(0.974352\pi\) | |||||||
\(524\) | 72.2529 | 0.137887 | ||||||||
\(525\) | − | 112.247i | − | 0.213804i | ||||||
\(526\) | − | 71.2251i | − | 0.135409i | ||||||
\(527\) | 1266.26i | 2.40278i | ||||||||
\(528\) | − | 160.163i | − | 0.303339i | ||||||
\(529\) | 218.497 | − | 481.768i | 0.413038 | − | 0.910714i | ||||
\(530\) | 79.7062 | 0.150389 | ||||||||
\(531\) | 162.938 | 0.306852 | ||||||||
\(532\) | 13.9624 | 0.0262451 | ||||||||
\(533\) | −214.785 | −0.402974 | ||||||||
\(534\) | 37.2087i | 0.0696791i | ||||||||
\(535\) | −27.9549 | −0.0522521 | ||||||||
\(536\) | 881.098i | 1.64384i | ||||||||
\(537\) | 433.079 | 0.806478 | ||||||||
\(538\) | −910.572 | −1.69251 | ||||||||
\(539\) | 56.1122i | 0.104104i | ||||||||
\(540\) | − | 3.36009i | − | 0.00622239i | ||||||
\(541\) | 71.2344 | 0.131672 | 0.0658359 | − | 0.997830i | \(-0.479029\pi\) | ||||
0.0658359 | + | 0.997830i | \(0.479029\pi\) | |||||||
\(542\) | −467.560 | −0.862657 | ||||||||
\(543\) | − | 54.5319i | − | 0.100427i | ||||||
\(544\) | − | 362.126i | − | 0.665674i | ||||||
\(545\) | −85.0621 | −0.156077 | ||||||||
\(546\) | − | 153.965i | − | 0.281987i | ||||||
\(547\) | −504.297 | −0.921933 | −0.460966 | − | 0.887418i | \(-0.652497\pi\) | ||||
−0.460966 | + | 0.887418i | \(0.652497\pi\) | |||||||
\(548\) | − | 102.927i | − | 0.187823i | ||||||
\(549\) | − | 195.867i | − | 0.356771i | ||||||
\(550\) | 345.183i | 0.627606i | ||||||||
\(551\) | − | 77.8090i | − | 0.141214i | ||||||
\(552\) | 289.001 | − | 186.263i | 0.523553 | − | 0.337434i | ||||
\(553\) | 185.293 | 0.335069 | ||||||||
\(554\) | −749.766 | −1.35337 | ||||||||
\(555\) | 76.2063 | 0.137309 | ||||||||
\(556\) | −110.482 | −0.198709 | ||||||||
\(557\) | 243.692i | 0.437507i | 0.975780 | + | 0.218754i | \(0.0701991\pi\) | ||||
−0.975780 | + | 0.218754i | \(0.929801\pi\) | |||||||
\(558\) | −262.672 | −0.470738 | ||||||||
\(559\) | 1320.51i | 2.36227i | ||||||||
\(560\) | −21.7034 | −0.0387561 | ||||||||
\(561\) | −353.001 | −0.629236 | ||||||||
\(562\) | 642.230i | 1.14276i | ||||||||
\(563\) | 790.151i | 1.40346i | 0.712441 | + | 0.701732i | \(0.247590\pi\) | ||||
−0.712441 | + | 0.701732i | \(0.752410\pi\) | |||||||
\(564\) | −13.8543 | −0.0245644 | ||||||||
\(565\) | 133.948 | 0.237075 | ||||||||
\(566\) | − | 910.274i | − | 1.60826i | ||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | 125.440 | 0.220845 | ||||||||
\(569\) | − | 739.643i | − | 1.29990i | −0.759977 | − | 0.649950i | \(-0.774790\pi\) | ||
0.759977 | − | 0.649950i | \(-0.225210\pi\) | |||||||
\(570\) | 12.5661 | 0.0220457 | ||||||||
\(571\) | − | 692.965i | − | 1.21360i | −0.794855 | − | 0.606799i | \(-0.792453\pi\) | ||
0.794855 | − | 0.606799i | \(-0.207547\pi\) | |||||||
\(572\) | − | 139.310i | − | 0.243548i | ||||||
\(573\) | 616.952i | 1.07671i | ||||||||
\(574\) | − | 52.2745i | − | 0.0910706i | ||||||
\(575\) | −473.538 | + | 305.199i | −0.823545 | + | 0.530781i | ||||
\(576\) | 213.547 | 0.370741 | ||||||||
\(577\) | −932.406 | −1.61596 | −0.807978 | − | 0.589213i | \(-0.799438\pi\) | ||||
−0.807978 | + | 0.589213i | \(0.799438\pi\) | |||||||
\(578\) | 628.347 | 1.08711 | ||||||||
\(579\) | 30.2230 | 0.0521986 | ||||||||
\(580\) | − | 8.67005i | − | 0.0149484i | ||||||
\(581\) | 182.525 | 0.314157 | ||||||||
\(582\) | − | 413.586i | − | 0.710628i | ||||||
\(583\) | −511.082 | −0.876641 | ||||||||
\(584\) | 639.937 | 1.09578 | ||||||||
\(585\) | 40.7705i | 0.0696931i | ||||||||
\(586\) | 841.207i | 1.43551i | ||||||||
\(587\) | 253.018 | 0.431035 | 0.215518 | − | 0.976500i | \(-0.430856\pi\) | ||||
0.215518 | + | 0.976500i | \(0.430856\pi\) | |||||||
\(588\) | −11.0253 | −0.0187506 | ||||||||
\(589\) | 289.032i | 0.490716i | ||||||||
\(590\) | 67.8990i | 0.115083i | ||||||||
\(591\) | −374.889 | −0.634330 | ||||||||
\(592\) | 713.734i | 1.20563i | ||||||||
\(593\) | 91.0966 | 0.153620 | 0.0768100 | − | 0.997046i | \(-0.475527\pi\) | ||||
0.0768100 | + | 0.997046i | \(0.475527\pi\) | |||||||
\(594\) | − | 73.2261i | − | 0.123276i | ||||||
\(595\) | 47.8345i | 0.0803942i | ||||||||
\(596\) | 19.8278i | 0.0332682i | ||||||||
\(597\) | − | 137.738i | − | 0.230718i | ||||||
\(598\) | −649.535 | + | 418.630i | −1.08618 | + | 0.700051i | ||||
\(599\) | −426.693 | −0.712342 | −0.356171 | − | 0.934421i | \(-0.615918\pi\) | ||||
−0.356171 | + | 0.934421i | \(0.615918\pi\) | |||||||
\(600\) | −366.164 | −0.610273 | ||||||||
\(601\) | 243.004 | 0.404332 | 0.202166 | − | 0.979351i | \(-0.435202\pi\) | ||||
0.202166 | + | 0.979351i | \(0.435202\pi\) | |||||||
\(602\) | −321.385 | −0.533862 | ||||||||
\(603\) | 306.265i | 0.507901i | ||||||||
\(604\) | −40.0547 | −0.0663156 | ||||||||
\(605\) | − | 40.3506i | − | 0.0666952i | ||||||
\(606\) | 264.135 | 0.435866 | ||||||||
\(607\) | 242.034 | 0.398738 | 0.199369 | − | 0.979924i | \(-0.436111\pi\) | ||||
0.199369 | + | 0.979924i | \(0.436111\pi\) | |||||||
\(608\) | − | 82.6574i | − | 0.135950i | ||||||
\(609\) | 61.4415i | 0.100889i | ||||||||
\(610\) | 81.6210 | 0.133805 | ||||||||
\(611\) | 168.105 | 0.275130 | ||||||||
\(612\) | − | 69.3603i | − | 0.113334i | ||||||
\(613\) | − | 118.345i | − | 0.193058i | −0.995330 | − | 0.0965291i | \(-0.969226\pi\) | ||
0.995330 | − | 0.0965291i | \(-0.0307741\pi\) | |||||||
\(614\) | 694.957 | 1.13185 | ||||||||
\(615\) | 13.8425i | 0.0225081i | ||||||||
\(616\) | 183.045 | 0.297151 | ||||||||
\(617\) | − | 1152.80i | − | 1.86840i | −0.356749 | − | 0.934200i | \(-0.616115\pi\) | ||
0.356749 | − | 0.934200i | \(-0.383885\pi\) | |||||||
\(618\) | − | 47.2187i | − | 0.0764057i | ||||||
\(619\) | − | 12.3379i | − | 0.0199319i | −0.999950 | − | 0.00996596i | \(-0.996828\pi\) | ||
0.999950 | − | 0.00996596i | \(-0.00317232\pi\) | |||||||
\(620\) | 32.2060i | 0.0519452i | ||||||||
\(621\) | 100.455 | − | 64.7440i | 0.161763 | − | 0.104258i | ||||
\(622\) | −1026.72 | −1.65068 | ||||||||
\(623\) | −32.3302 | −0.0518943 | ||||||||
\(624\) | −381.849 | −0.611937 | ||||||||
\(625\) | 587.330 | 0.939728 | ||||||||
\(626\) | − | 213.016i | − | 0.340281i | ||||||
\(627\) | −80.5746 | −0.128508 | ||||||||
\(628\) | 256.890i | 0.409060i | ||||||||
\(629\) | 1573.08 | 2.50092 | ||||||||
\(630\) | −9.92273 | −0.0157504 | ||||||||
\(631\) | − | 51.6407i | − | 0.0818395i | −0.999162 | − | 0.0409198i | \(-0.986971\pi\) | ||
0.999162 | − | 0.0409198i | \(-0.0130288\pi\) | |||||||
\(632\) | − | 604.448i | − | 0.956406i | ||||||
\(633\) | 238.054 | 0.376073 | ||||||||
\(634\) | 980.619 | 1.54672 | ||||||||
\(635\) | − | 55.3126i | − | 0.0871065i | ||||||
\(636\) | − | 100.421i | − | 0.157895i | ||||||
\(637\) | 133.778 | 0.210013 | ||||||||
\(638\) | − | 188.945i | − | 0.296153i | ||||||
\(639\) | 43.6022 | 0.0682350 | ||||||||
\(640\) | 48.4747i | 0.0757418i | ||||||||
\(641\) | − | 700.130i | − | 1.09225i | −0.837705 | − | 0.546123i | \(-0.816103\pi\) | ||
0.837705 | − | 0.546123i | \(-0.183897\pi\) | |||||||
\(642\) | − | 119.703i | − | 0.186454i | ||||||
\(643\) | − | 839.673i | − | 1.30587i | −0.757415 | − | 0.652934i | \(-0.773538\pi\) | ||
0.757415 | − | 0.652934i | \(-0.226462\pi\) | |||||||
\(644\) | 29.9778 | + | 46.5127i | 0.0465494 | + | 0.0722248i | ||||
\(645\) | 85.1038 | 0.131944 | ||||||||
\(646\) | 259.393 | 0.401538 | ||||||||
\(647\) | −790.982 | −1.22254 | −0.611269 | − | 0.791423i | \(-0.709341\pi\) | ||||
−0.611269 | + | 0.791423i | \(0.709341\pi\) | |||||||
\(648\) | 77.6768 | 0.119872 | ||||||||
\(649\) | − | 435.373i | − | 0.670837i | ||||||
\(650\) | 822.959 | 1.26609 | ||||||||
\(651\) | − | 228.233i | − | 0.350588i | ||||||
\(652\) | 289.423 | 0.443901 | ||||||||
\(653\) | 341.232 | 0.522561 | 0.261280 | − | 0.965263i | \(-0.415855\pi\) | ||||
0.261280 | + | 0.965263i | \(0.415855\pi\) | |||||||
\(654\) | − | 364.238i | − | 0.556939i | ||||||
\(655\) | 56.5013i | 0.0862615i | ||||||||
\(656\) | −129.646 | −0.197631 | ||||||||
\(657\) | 222.438 | 0.338566 | ||||||||
\(658\) | 40.9134i | 0.0621783i | ||||||||
\(659\) | − | 682.936i | − | 1.03632i | −0.855283 | − | 0.518161i | \(-0.826617\pi\) | ||
0.855283 | − | 0.518161i | \(-0.173383\pi\) | |||||||
\(660\) | −8.97821 | −0.0136033 | ||||||||
\(661\) | − | 562.849i | − | 0.851511i | −0.904838 | − | 0.425755i | \(-0.860008\pi\) | ||
0.904838 | − | 0.425755i | \(-0.139992\pi\) | |||||||
\(662\) | −898.499 | −1.35725 | ||||||||
\(663\) | 841.599i | 1.26938i | ||||||||
\(664\) | − | 595.419i | − | 0.896716i | ||||||
\(665\) | 10.9185i | 0.0164188i | ||||||||
\(666\) | 326.317i | 0.489965i | ||||||||
\(667\) | 259.204 | − | 167.059i | 0.388612 | − | 0.250463i | ||||
\(668\) | 37.2723 | 0.0557968 | ||||||||
\(669\) | 358.478 | 0.535842 | ||||||||
\(670\) | −127.625 | −0.190485 | ||||||||
\(671\) | −523.360 | −0.779970 | ||||||||
\(672\) | 65.2700i | 0.0971280i | ||||||||
\(673\) | 28.5552 | 0.0424297 | 0.0212149 | − | 0.999775i | \(-0.493247\pi\) | ||||
0.0212149 | + | 0.999775i | \(0.493247\pi\) | |||||||
\(674\) | 854.680i | 1.26807i | ||||||||
\(675\) | −127.276 | −0.188557 | ||||||||
\(676\) | −178.450 | −0.263980 | ||||||||
\(677\) | 663.295i | 0.979757i | 0.871791 | + | 0.489878i | \(0.162959\pi\) | ||||
−0.871791 | + | 0.489878i | \(0.837041\pi\) | |||||||
\(678\) | 573.566i | 0.845968i | ||||||||
\(679\) | 359.360 | 0.529248 | ||||||||
\(680\) | 156.042 | 0.229474 | ||||||||
\(681\) | − | 575.086i | − | 0.844473i | ||||||
\(682\) | 701.862i | 1.02912i | ||||||||
\(683\) | −24.5205 | −0.0359012 | −0.0179506 | − | 0.999839i | \(-0.505714\pi\) | ||||
−0.0179506 | + | 0.999839i | \(0.505714\pi\) | |||||||
\(684\) | − | 15.8319i | − | 0.0231460i | ||||||
\(685\) | 80.4885 | 0.117501 | ||||||||
\(686\) | 32.5590i | 0.0474622i | ||||||||
\(687\) | 2.67099i | 0.00388791i | ||||||||
\(688\) | 797.067i | 1.15853i | ||||||||
\(689\) | 1218.48i | 1.76848i | ||||||||
\(690\) | 26.9798 | + | 41.8612i | 0.0391012 | + | 0.0606683i | ||||
\(691\) | −421.109 | −0.609419 | −0.304710 | − | 0.952445i | \(-0.598559\pi\) | ||||
−0.304710 | + | 0.952445i | \(0.598559\pi\) | |||||||
\(692\) | −187.236 | −0.270572 | ||||||||
\(693\) | 63.6253 | 0.0918114 | ||||||||
\(694\) | −416.976 | −0.600829 | ||||||||
\(695\) | − | 86.3964i | − | 0.124311i | ||||||
\(696\) | 200.430 | 0.287973 | ||||||||
\(697\) | 285.741i | 0.409959i | ||||||||
\(698\) | −233.011 | −0.333826 | ||||||||
\(699\) | −135.322 | −0.193594 | ||||||||
\(700\) | − | 58.9315i | − | 0.0841879i | ||||||
\(701\) | − | 1159.54i | − | 1.65413i | −0.562109 | − | 0.827063i | \(-0.690010\pi\) | ||
0.562109 | − | 0.827063i | \(-0.309990\pi\) | |||||||
\(702\) | −174.580 | −0.248690 | ||||||||
\(703\) | 359.064 | 0.510759 | ||||||||
\(704\) | − | 570.600i | − | 0.810511i | ||||||
\(705\) | − | 10.8340i | − | 0.0153674i | ||||||
\(706\) | −321.891 | −0.455936 | ||||||||
\(707\) | 229.504i | 0.324616i | ||||||||
\(708\) | 85.5453 | 0.120827 | ||||||||
\(709\) | − | 156.174i | − | 0.220273i | −0.993916 | − | 0.110137i | \(-0.964871\pi\) | ||
0.993916 | − | 0.110137i | \(-0.0351289\pi\) | |||||||
\(710\) | 18.1697i | 0.0255911i | ||||||||
\(711\) | − | 210.103i | − | 0.295503i | ||||||
\(712\) | 105.465i | 0.148125i | ||||||||
\(713\) | −962.848 | + | 620.563i | −1.35042 | + | 0.870355i | ||||
\(714\) | −204.829 | −0.286875 | ||||||||
\(715\) | 108.939 | 0.152362 | ||||||||
\(716\) | 227.373 | 0.317560 | ||||||||
\(717\) | 505.919 | 0.705605 | ||||||||
\(718\) | − | 527.362i | − | 0.734488i | ||||||
\(719\) | −498.495 | −0.693317 | −0.346659 | − | 0.937991i | \(-0.612684\pi\) | ||||
−0.346659 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(720\) | 24.6093i | 0.0341796i | ||||||||
\(721\) | 41.0278 | 0.0569040 | ||||||||
\(722\) | −575.438 | −0.797006 | ||||||||
\(723\) | 682.960i | 0.944620i | ||||||||
\(724\) | − | 28.6301i | − | 0.0395444i | ||||||
\(725\) | −328.411 | −0.452980 | ||||||||
\(726\) | 172.782 | 0.237992 | ||||||||
\(727\) | − | 1060.14i | − | 1.45824i | −0.684385 | − | 0.729121i | \(-0.739929\pi\) | ||
0.684385 | − | 0.729121i | \(-0.260071\pi\) | |||||||
\(728\) | − | 436.401i | − | 0.599453i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 92.6934i | 0.126977i | ||||||||
\(731\) | 1756.74 | 2.40321 | ||||||||
\(732\) | − | 102.834i | − | 0.140483i | ||||||
\(733\) | − | 807.046i | − | 1.10102i | −0.834829 | − | 0.550509i | \(-0.814434\pi\) | ||
0.834829 | − | 0.550509i | \(-0.185566\pi\) | |||||||
\(734\) | 239.056i | 0.325689i | ||||||||
\(735\) | − | 8.62174i | − | 0.0117303i | ||||||
\(736\) | 275.355 | − | 177.469i | 0.374124 | − | 0.241126i | ||||
\(737\) | 818.342 | 1.11037 | ||||||||
\(738\) | −59.2737 | −0.0803167 | ||||||||
\(739\) | −603.367 | −0.816463 | −0.408232 | − | 0.912878i | \(-0.633854\pi\) | ||||
−0.408232 | + | 0.912878i | \(0.633854\pi\) | |||||||
\(740\) | 40.0095 | 0.0540669 | ||||||||
\(741\) | 192.100i | 0.259244i | ||||||||
\(742\) | −296.555 | −0.399669 | ||||||||
\(743\) | 578.041i | 0.777982i | 0.921241 | + | 0.388991i | \(0.127176\pi\) | ||||
−0.921241 | + | 0.388991i | \(0.872824\pi\) | |||||||
\(744\) | −744.522 | −1.00070 | ||||||||
\(745\) | −15.5052 | −0.0208124 | ||||||||
\(746\) | − | 7.67362i | − | 0.0102864i | ||||||
\(747\) | − | 206.964i | − | 0.277060i | ||||||
\(748\) | −185.331 | −0.247769 | ||||||||
\(749\) | 104.009 | 0.138864 | ||||||||
\(750\) | − | 107.171i | − | 0.142895i | ||||||
\(751\) | − | 138.968i | − | 0.185044i | −0.995711 | − | 0.0925222i | \(-0.970507\pi\) | ||
0.995711 | − | 0.0925222i | \(-0.0294929\pi\) | |||||||
\(752\) | 101.469 | 0.134932 | ||||||||
\(753\) | − | 185.629i | − | 0.246519i | ||||||
\(754\) | −450.469 | −0.597439 | ||||||||
\(755\) | − | 31.3225i | − | 0.0414867i | ||||||
\(756\) | 12.5016i | 0.0165364i | ||||||||
\(757\) | 804.571i | 1.06284i | 0.847108 | + | 0.531421i | \(0.178342\pi\) | ||||
−0.847108 | + | 0.531421i | \(0.821658\pi\) | |||||||
\(758\) | − | 268.665i | − | 0.354439i | ||||||
\(759\) | −172.997 | − | 268.417i | −0.227927 | − | 0.353645i | ||||
\(760\) | 35.6175 | 0.0468651 | ||||||||
\(761\) | 142.923 | 0.187810 | 0.0939049 | − | 0.995581i | \(-0.470065\pi\) | ||||
0.0939049 | + | 0.995581i | \(0.470065\pi\) | |||||||
\(762\) | 236.850 | 0.310827 | ||||||||
\(763\) | 316.482 | 0.414786 | ||||||||
\(764\) | 323.910i | 0.423966i | ||||||||
\(765\) | 54.2393 | 0.0709010 | ||||||||
\(766\) | − | 717.804i | − | 0.937080i | ||||||
\(767\) | −1037.98 | −1.35330 | ||||||||
\(768\) | 285.595 | 0.371869 | ||||||||
\(769\) | 544.852i | 0.708520i | 0.935147 | + | 0.354260i | \(0.115267\pi\) | ||||
−0.935147 | + | 0.354260i | \(0.884733\pi\) | |||||||
\(770\) | 26.5136i | 0.0344333i | ||||||||
\(771\) | 73.3908 | 0.0951891 | ||||||||
\(772\) | 15.8676 | 0.0205538 | ||||||||
\(773\) | − | 221.017i | − | 0.285921i | −0.989728 | − | 0.142961i | \(-0.954338\pi\) | ||
0.989728 | − | 0.142961i | \(-0.0456622\pi\) | |||||||
\(774\) | 364.417i | 0.470822i | ||||||||
\(775\) | 1219.93 | 1.57410 | ||||||||
\(776\) | − | 1172.27i | − | 1.51066i | ||||||
\(777\) | −283.533 | −0.364907 | ||||||||
\(778\) | − | 1148.41i | − | 1.47610i | ||||||
\(779\) | 65.2220i | 0.0837253i | ||||||||
\(780\) | 21.4051i | 0.0274425i | ||||||||
\(781\) | − | 116.506i | − | 0.149175i | ||||||
\(782\) | 556.928 | + | 864.113i | 0.712184 | + | 1.10500i | ||||
\(783\) | 69.6681 | 0.0889759 | ||||||||
\(784\) | 80.7496 | 0.102997 | ||||||||
\(785\) | −200.886 | −0.255906 | ||||||||
\(786\) | −241.940 | −0.307812 | ||||||||
\(787\) | 533.056i | 0.677327i | 0.940908 | + | 0.338663i | \(0.109975\pi\) | ||||
−0.940908 | + | 0.338663i | \(0.890025\pi\) | |||||||
\(788\) | −196.823 | −0.249775 | ||||||||
\(789\) | − | 70.1729i | − | 0.0889390i | ||||||
\(790\) | 87.5530 | 0.110827 | ||||||||
\(791\) | −498.365 | −0.630044 | ||||||||
\(792\) | − | 207.553i | − | 0.262062i | ||||||
\(793\) | 1247.75i | 1.57346i | ||||||||
\(794\) | 610.118 | 0.768410 | ||||||||
\(795\) | 78.5286 | 0.0987781 | ||||||||
\(796\) | − | 72.3149i | − | 0.0908478i | ||||||
\(797\) | − | 126.679i | − | 0.158945i | −0.996837 | − | 0.0794723i | \(-0.974676\pi\) | ||
0.996837 | − | 0.0794723i | \(-0.0253235\pi\) | |||||||
\(798\) | −46.7533 | −0.0585881 | ||||||||
\(799\) | − | 223.639i | − | 0.279899i | ||||||
\(800\) | −348.875 | −0.436093 | ||||||||
\(801\) | 36.6589i | 0.0457665i | ||||||||
\(802\) | − | 132.301i | − | 0.164964i | ||||||
\(803\) | − | 594.357i | − | 0.740171i | ||||||
\(804\) | 160.794i | 0.199992i | ||||||||
\(805\) | −36.3727 | + | 23.4425i | −0.0451834 | + | 0.0291211i | ||||
\(806\) | 1673.33 | 2.07609 | ||||||||
\(807\) | −897.120 | −1.11167 | ||||||||
\(808\) | 748.669 | 0.926570 | ||||||||
\(809\) | −15.3007 | −0.0189131 | −0.00945656 | − | 0.999955i | \(-0.503010\pi\) | ||||
−0.00945656 | + | 0.999955i | \(0.503010\pi\) | |||||||
\(810\) | 11.2513i | 0.0138905i | ||||||||
\(811\) | 1102.85 | 1.35987 | 0.679933 | − | 0.733275i | \(-0.262009\pi\) | ||||
0.679933 | + | 0.733275i | \(0.262009\pi\) | |||||||
\(812\) | 32.2578i | 0.0397263i | ||||||||
\(813\) | −460.653 | −0.566609 | ||||||||
\(814\) | 871.923 | 1.07116 | ||||||||
\(815\) | 226.327i | 0.277702i | ||||||||
\(816\) | 507.995i | 0.622543i | ||||||||
\(817\) | 400.987 | 0.490804 | ||||||||
\(818\) | 211.444 | 0.258489 | ||||||||
\(819\) | − | 151.691i | − | 0.185214i | ||||||
\(820\) | 7.26751i | 0.00886282i | ||||||||
\(821\) | −818.210 | −0.996602 | −0.498301 | − | 0.867004i | \(-0.666043\pi\) | ||||
−0.498301 | + | 0.867004i | \(0.666043\pi\) | |||||||
\(822\) | 344.653i | 0.419286i | ||||||||
\(823\) | −972.988 | −1.18225 | −0.591123 | − | 0.806582i | \(-0.701315\pi\) | ||||
−0.591123 | + | 0.806582i | \(0.701315\pi\) | |||||||
\(824\) | − | 133.837i | − | 0.162424i | ||||||
\(825\) | 340.084i | 0.412222i | ||||||||
\(826\) | − | 252.625i | − | 0.305841i | ||||||
\(827\) | 479.613i | 0.579944i | 0.957035 | + | 0.289972i | \(0.0936459\pi\) | ||||
−0.957035 | + | 0.289972i | \(0.906354\pi\) | |||||||
\(828\) | 52.7405 | − | 33.9917i | 0.0636962 | − | 0.0410527i | ||||
\(829\) | −1279.03 | −1.54286 | −0.771431 | − | 0.636313i | \(-0.780459\pi\) | ||||
−0.771431 | + | 0.636313i | \(0.780459\pi\) | |||||||
\(830\) | 86.2452 | 0.103910 | ||||||||
\(831\) | −738.690 | −0.888917 | ||||||||
\(832\) | −1360.38 | −1.63507 | ||||||||
\(833\) | − | 177.973i | − | 0.213653i | ||||||
\(834\) | 369.951 | 0.443587 | ||||||||
\(835\) | 29.1467i | 0.0349062i | ||||||||
\(836\) | −42.3029 | −0.0506016 | ||||||||
\(837\) | −258.791 | −0.309189 | ||||||||
\(838\) | − | 392.194i | − | 0.468012i | ||||||
\(839\) | 448.957i | 0.535110i | 0.963543 | + | 0.267555i | \(0.0862157\pi\) | ||||
−0.963543 | + | 0.267555i | \(0.913784\pi\) | |||||||
\(840\) | −28.1252 | −0.0334823 | ||||||||
\(841\) | −661.235 | −0.786249 | ||||||||
\(842\) | − | 836.816i | − | 0.993843i | ||||||
\(843\) | 632.741i | 0.750583i | ||||||||
\(844\) | 124.982 | 0.148083 | ||||||||
\(845\) | − | 139.547i | − | 0.165144i | ||||||
\(846\) | 46.3914 | 0.0548362 | ||||||||
\(847\) | 150.128i | 0.177247i | ||||||||
\(848\) | 735.484i | 0.867316i | ||||||||
\(849\) | − | 896.826i | − | 1.05633i | ||||||
\(850\) | − | 1094.83i | − | 1.28803i | ||||||
\(851\) | 770.924 | + | 1196.14i | 0.905904 | + | 1.40558i | ||||
\(852\) | 22.8918 | 0.0268684 | ||||||||
\(853\) | 861.052 | 1.00944 | 0.504720 | − | 0.863283i | \(-0.331596\pi\) | ||||
0.504720 | + | 0.863283i | \(0.331596\pi\) | |||||||
\(854\) | −303.679 | −0.355596 | ||||||||
\(855\) | 12.3804 | 0.0144800 | ||||||||
\(856\) | − | 339.289i | − | 0.396366i | ||||||
\(857\) | 791.635 | 0.923728 | 0.461864 | − | 0.886951i | \(-0.347181\pi\) | ||||
0.461864 | + | 0.886951i | \(0.347181\pi\) | |||||||
\(858\) | 466.480i | 0.543683i | ||||||||
\(859\) | −1239.94 | −1.44347 | −0.721736 | − | 0.692169i | \(-0.756655\pi\) | ||||
−0.721736 | + | 0.692169i | \(0.756655\pi\) | |||||||
\(860\) | 44.6809 | 0.0519545 | ||||||||
\(861\) | − | 51.5022i | − | 0.0598168i | ||||||
\(862\) | 1036.55i | 1.20250i | ||||||||
\(863\) | 1478.24 | 1.71291 | 0.856454 | − | 0.516223i | \(-0.172663\pi\) | ||||
0.856454 | + | 0.516223i | \(0.172663\pi\) | |||||||
\(864\) | 74.0092 | 0.0856588 | ||||||||
\(865\) | − | 146.417i | − | 0.169268i | ||||||
\(866\) | 49.7957i | 0.0575008i | ||||||||
\(867\) | 619.064 | 0.714030 | ||||||||
\(868\) | − | 119.826i | − | 0.138048i | ||||||
\(869\) | −561.397 | −0.646026 | ||||||||
\(870\) | 29.0318i | 0.0333699i | ||||||||
\(871\) | − | 1951.03i | − | 2.23999i | ||||||
\(872\) | − | 1032.40i | − | 1.18395i | ||||||
\(873\) | − | 407.476i | − | 0.466753i | ||||||
\(874\) | 127.122 | + | 197.239i | 0.145448 | + | 0.225674i | ||||
\(875\) | 93.1195 | 0.106422 | ||||||||
\(876\) | 116.784 | 0.133315 | ||||||||
\(877\) | 765.506 | 0.872869 | 0.436434 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436434 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(878\) | −1354.68 | −1.54292 | ||||||||
\(879\) | 828.779i | 0.942866i | ||||||||
\(880\) | 65.7564 | 0.0747232 | ||||||||
\(881\) | − | 1228.09i | − | 1.39398i | −0.717083 | − | 0.696988i | \(-0.754523\pi\) | ||
0.717083 | − | 0.696988i | \(-0.245477\pi\) | |||||||
\(882\) | 36.9185 | 0.0418577 | ||||||||
\(883\) | 665.576 | 0.753767 | 0.376883 | − | 0.926261i | \(-0.376996\pi\) | ||||
0.376883 | + | 0.926261i | \(0.376996\pi\) | |||||||
\(884\) | 441.853i | 0.499833i | ||||||||
\(885\) | 66.8959i | 0.0755886i | ||||||||
\(886\) | 337.680 | 0.381129 | ||||||||
\(887\) | −4.28591 | −0.00483192 | −0.00241596 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241596 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(888\) | 924.919i | 1.04157i | ||||||||
\(889\) | 205.796i | 0.231492i | ||||||||
\(890\) | −15.2763 | −0.0171644 | ||||||||
\(891\) | − | 72.1443i | − | 0.0809700i | ||||||
\(892\) | 188.207 | 0.210994 | ||||||||
\(893\) | − | 51.0469i | − | 0.0571634i | ||||||
\(894\) | − | 66.3938i | − | 0.0742660i | ||||||
\(895\) | 177.804i | 0.198664i | ||||||||
\(896\) | − | 180.355i | − | 0.201289i | ||||||
\(897\) | −639.939 | + | 412.446i | −0.713421 | + | 0.459806i | ||||
\(898\) | 1424.00 | 1.58574 | ||||||||
\(899\) | −667.759 | −0.742780 | ||||||||
\(900\) | −66.8221 | −0.0742467 | ||||||||
\(901\) | 1621.02 | 1.79913 | ||||||||
\(902\) | 158.380i | 0.175588i | ||||||||
\(903\) | −316.637 | −0.350650 | ||||||||
\(904\) | 1625.73i | 1.79837i | ||||||||
\(905\) | 22.3886 | 0.0247387 | ||||||||
\(906\) | 134.124 | 0.148039 | ||||||||
\(907\) | − | 812.413i | − | 0.895714i | −0.894105 | − | 0.447857i | \(-0.852187\pi\) | ||
0.894105 | − | 0.447857i | \(-0.147813\pi\) | |||||||
\(908\) | − | 301.929i | − | 0.332521i | ||||||
\(909\) | 260.233 | 0.286285 | ||||||||
\(910\) | 63.2118 | 0.0694635 | ||||||||
\(911\) | − | 551.157i | − | 0.605002i | −0.953149 | − | 0.302501i | \(-0.902178\pi\) | ||
0.953149 | − | 0.302501i | \(-0.0978215\pi\) | |||||||
\(912\) | 115.953i | 0.127141i | ||||||||
\(913\) | −553.011 | −0.605707 | ||||||||
\(914\) | 147.706i | 0.161604i | ||||||||
\(915\) | 80.4152 | 0.0878854 | ||||||||
\(916\) | 1.40231i | 0.00153091i | ||||||||
\(917\) | − | 210.219i | − | 0.229246i | ||||||
\(918\) | 232.254i | 0.253000i | ||||||||
\(919\) | − | 899.360i | − | 0.978629i | −0.872107 | − | 0.489314i | \(-0.837247\pi\) | ||
0.872107 | − | 0.489314i | \(-0.162753\pi\) | |||||||
\(920\) | 76.4721 | + | 118.652i | 0.0831219 | + | 0.128970i | ||||
\(921\) | 684.690 | 0.743420 | ||||||||
\(922\) | −274.936 | −0.298196 | ||||||||
\(923\) | −277.763 | −0.300936 | ||||||||
\(924\) | 33.4043 | 0.0361518 | ||||||||
\(925\) | − | 1515.51i | − | 1.63839i | ||||||
\(926\) | −1283.20 | −1.38575 | ||||||||
\(927\) | − | 46.5211i | − | 0.0501846i | ||||||
\(928\) | 190.966 | 0.205782 | ||||||||
\(929\) | −426.862 | −0.459485 | −0.229743 | − | 0.973251i | \(-0.573788\pi\) | ||||
−0.229743 | + | 0.973251i | \(0.573788\pi\) | |||||||
\(930\) | − | 107.842i | − | 0.115960i | ||||||
\(931\) | − | 40.6234i | − | 0.0436341i | ||||||
\(932\) | −71.0464 | −0.0762301 | ||||||||
\(933\) | −1011.55 | −1.08419 | ||||||||
\(934\) | − | 489.356i | − | 0.523936i | ||||||
\(935\) | − | 144.928i | − | 0.155003i | ||||||
\(936\) | −494.833 | −0.528667 | ||||||||
\(937\) | 425.634i | 0.454252i | 0.973865 | + | 0.227126i | \(0.0729329\pi\) | ||||
−0.973865 | + | 0.227126i | \(0.927067\pi\) | |||||||
\(938\) | 474.842 | 0.506228 | ||||||||
\(939\) | − | 209.869i | − | 0.223503i | ||||||
\(940\) | − | 5.68802i | − | 0.00605108i | ||||||
\(941\) | 1307.90i | 1.38991i | 0.719055 | + | 0.694953i | \(0.244575\pi\) | ||||
−0.719055 | + | 0.694953i | \(0.755425\pi\) | |||||||
\(942\) | − | 860.198i | − | 0.913161i | ||||||
\(943\) | −217.273 | + | 140.034i | −0.230406 | + | 0.148499i | ||||
\(944\) | −626.534 | −0.663701 | ||||||||
\(945\) | −9.77613 | −0.0103451 | ||||||||
\(946\) | 973.725 | 1.02931 | ||||||||
\(947\) | 660.525 | 0.697492 | 0.348746 | − | 0.937217i | \(-0.386608\pi\) | ||||
0.348746 | + | 0.937217i | \(0.386608\pi\) | |||||||
\(948\) | − | 110.307i | − | 0.116358i | ||||||
\(949\) | −1417.02 | −1.49317 | ||||||||
\(950\) | − | 249.901i | − | 0.263054i | ||||||
\(951\) | 966.131 | 1.01591 | ||||||||
\(952\) | −580.570 | −0.609842 | ||||||||
\(953\) | − | 143.346i | − | 0.150416i | −0.997168 | − | 0.0752078i | \(-0.976038\pi\) | ||
0.997168 | − | 0.0752078i | \(-0.0239620\pi\) | |||||||
\(954\) | 336.261i | 0.352475i | ||||||||
\(955\) | −253.295 | −0.265231 | ||||||||
\(956\) | 265.615 | 0.277840 | ||||||||
\(957\) | − | 186.154i | − | 0.194518i | ||||||
\(958\) | − | 343.345i | − | 0.358398i | ||||||
\(959\) | −299.465 | −0.312268 | ||||||||
\(960\) | 87.6736i | 0.0913267i | ||||||||
\(961\) | 1519.48 | 1.58114 | ||||||||
\(962\) | − | 2078.77i | − | 2.16088i | ||||||
\(963\) | − | 117.935i | − | 0.122466i | ||||||
\(964\) | 358.565i | 0.371955i | ||||||||
\(965\) | 12.4083i | 0.0128584i | ||||||||
\(966\) | −100.381 | − | 155.749i | −0.103914 | − | 0.161230i | ||||
\(967\) | 681.391 | 0.704644 | 0.352322 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352322 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(968\) | 489.737 | 0.505927 | ||||||||
\(969\) | 255.561 | 0.263737 | ||||||||
\(970\) | 169.801 | 0.175053 | ||||||||
\(971\) | − | 812.942i | − | 0.837221i | −0.908166 | − | 0.418611i | \(-0.862517\pi\) | ||
0.908166 | − | 0.418611i | \(-0.137483\pi\) | |||||||
\(972\) | 14.1754 | 0.0145838 | ||||||||
\(973\) | 321.446i | 0.330366i | ||||||||
\(974\) | 627.248 | 0.643992 | ||||||||
\(975\) | 810.801 | 0.831591 | ||||||||
\(976\) | 753.153i | 0.771673i | ||||||||
\(977\) | − | 654.475i | − | 0.669882i | −0.942239 | − | 0.334941i | \(-0.891284\pi\) | ||
0.942239 | − | 0.334941i | \(-0.108716\pi\) | |||||||
\(978\) | −969.138 | −0.990939 | ||||||||
\(979\) | 97.9531 | 0.100054 | ||||||||
\(980\) | − | 4.52655i | − | 0.00461893i | ||||||
\(981\) | − | 358.857i | − | 0.365807i | ||||||
\(982\) | 591.841 | 0.602689 | ||||||||
\(983\) | − | 1694.86i | − | 1.72417i | −0.506760 | − | 0.862087i | \(-0.669157\pi\) | ||
0.506760 | − | 0.862087i | \(-0.330843\pi\) | |||||||
\(984\) | −168.007 | −0.170738 | ||||||||
\(985\) | − | 153.914i | − | 0.156258i | ||||||
\(986\) | 599.284i | 0.607793i | ||||||||
\(987\) | 40.3089i | 0.0408398i | ||||||||
\(988\) | 100.855i | 0.102080i | ||||||||
\(989\) | 860.935 | + | 1335.80i | 0.870510 | + | 1.35066i | ||||
\(990\) | 30.0636 | 0.0303673 | ||||||||
\(991\) | −995.227 | −1.00427 | −0.502133 | − | 0.864791i | \(-0.667451\pi\) | ||||
−0.502133 | + | 0.864791i | \(0.667451\pi\) | |||||||
\(992\) | −709.368 | −0.715089 | ||||||||
\(993\) | −885.224 | −0.891465 | ||||||||
\(994\) | − | 67.6022i | − | 0.0680102i | ||||||
\(995\) | 56.5498 | 0.0568339 | ||||||||
\(996\) | − | 108.659i | − | 0.109096i | ||||||
\(997\) | 27.1125 | 0.0271941 | 0.0135970 | − | 0.999908i | \(-0.495672\pi\) | ||||
0.0135970 | + | 0.999908i | \(0.495672\pi\) | |||||||
\(998\) | 296.400 | 0.296994 | ||||||||
\(999\) | 321.496i | 0.321818i |
(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 | 483.3.f.a.22.14 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.13 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.13 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.14 | yes | 48 | 1.1 | even | 1 | trivial |