Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(111,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.111");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.r (of order \(4\), degree \(2\), not 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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 271.9 | ||
Character | \(\chi\) | \(=\) | 320.271 |
Dual form | 320.3.r.a.111.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.374900 | + | 0.374900i | 0.124967 | + | 0.124967i | 0.766824 | − | 0.641857i | \(-0.221836\pi\) |
−0.641857 | + | 0.766824i | \(0.721836\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | − | 1.58114i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.42442 | −0.346345 | −0.173173 | − | 0.984891i | \(-0.555402\pi\) | ||||
−0.173173 | + | 0.984891i | \(0.555402\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 8.71890i | − | 0.968767i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.8058 | + | 13.8058i | −1.25507 | + | 1.25507i | −0.301658 | + | 0.953416i | \(0.597540\pi\) |
−0.953416 | + | 0.301658i | \(0.902460\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.90470 | − | 8.90470i | 0.684977 | − | 0.684977i | −0.276141 | − | 0.961117i | \(-0.589056\pi\) |
0.961117 | + | 0.276141i | \(0.0890556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.18554i | − | 0.0790358i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −27.7570 | −1.63276 | −0.816382 | − | 0.577512i | \(-0.804024\pi\) | ||||
−0.816382 | + | 0.577512i | \(0.804024\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.49556 | − | 7.49556i | −0.394503 | − | 0.394503i | 0.481786 | − | 0.876289i | \(-0.339988\pi\) |
−0.876289 | + | 0.481786i | \(0.839988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.908914 | − | 0.908914i | −0.0432816 | − | 0.0432816i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.5071 | −0.587266 | −0.293633 | − | 0.955918i | \(-0.594864\pi\) | ||||
−0.293633 | + | 0.955918i | \(0.594864\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.64281 | − | 6.64281i | 0.246030 | − | 0.246030i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.5369 | + | 10.5369i | −0.363343 | + | 0.363343i | −0.865042 | − | 0.501699i | \(-0.832708\pi\) |
0.501699 | + | 0.865042i | \(0.332708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 46.4696i | − | 1.49902i | −0.661993 | − | 0.749510i | \(-0.730289\pi\) | ||
0.661993 | − | 0.749510i | \(-0.269711\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.3516 | −0.313685 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.83334 | + | 3.83334i | 0.109524 | + | 0.109524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.68607 | − | 4.68607i | −0.126650 | − | 0.126650i | 0.640940 | − | 0.767591i | \(-0.278545\pi\) |
−0.767591 | + | 0.640940i | \(0.778545\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.67674 | 0.171198 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 38.6588i | − | 0.942897i | −0.881894 | − | 0.471449i | \(-0.843731\pi\) | ||
0.881894 | − | 0.471449i | \(-0.156269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45.6877 | + | 45.6877i | −1.06251 | + | 1.06251i | −0.0645935 | + | 0.997912i | \(0.520575\pi\) |
−0.997912 | + | 0.0645935i | \(0.979425\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.7858 | + | 13.7858i | −0.306351 | + | 0.306351i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 35.3503i | − | 0.752134i | −0.926592 | − | 0.376067i | \(-0.877276\pi\) | ||
0.926592 | − | 0.376067i | \(-0.122724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −43.1222 | −0.880045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4061 | − | 10.4061i | −0.204041 | − | 0.204041i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 61.0885 | + | 61.0885i | 1.15261 | + | 1.15261i | 0.986027 | + | 0.166586i | \(0.0532745\pi\) |
0.166586 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.6578 | 0.793779 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.62017i | − | 0.0985994i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.21882 | − | 9.21882i | 0.156251 | − | 0.156251i | −0.624652 | − | 0.780903i | \(-0.714759\pi\) |
0.780903 | + | 0.624652i | \(0.214759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 20.3084 | − | 20.3084i | 0.332925 | − | 0.332925i | −0.520771 | − | 0.853696i | \(-0.674356\pi\) |
0.853696 | + | 0.520771i | \(0.174356\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.1383i | 0.335528i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −28.1591 | −0.433217 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.47945 | − | 3.47945i | −0.0519320 | − | 0.0519320i | 0.680664 | − | 0.732596i | \(-0.261691\pi\) |
−0.732596 | + | 0.680664i | \(0.761691\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.06382 | − | 5.06382i | −0.0733887 | − | 0.0733887i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.72384 | 0.122871 | 0.0614355 | − | 0.998111i | \(-0.480432\pi\) | ||||
0.0614355 | + | 0.998111i | \(0.480432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 23.1038i | 0.316490i | 0.987400 | + | 0.158245i | \(0.0505836\pi\) | ||||
−0.987400 | + | 0.158245i | \(0.949416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.87450 | + | 1.87450i | −0.0249933 | + | 0.0249933i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.4711 | − | 33.4711i | 0.434689 | − | 0.434689i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 73.9752i | − | 0.936394i | −0.883624 | − | 0.468197i | \(-0.844904\pi\) | ||
0.883624 | − | 0.468197i | \(-0.155096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73.4893 | −0.907276 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 50.7301 | + | 50.7301i | 0.611206 | + | 0.611206i | 0.943260 | − | 0.332055i | \(-0.107742\pi\) |
−0.332055 | + | 0.943260i | \(0.607742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.8877 | + | 43.8877i | 0.516325 | + | 0.516325i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.90060 | −0.0908115 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 51.4759i | 0.578381i | 0.957272 | + | 0.289191i | \(0.0933861\pi\) | ||||
−0.957272 | + | 0.289191i | \(0.906614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.5887 | + | 21.5887i | −0.237238 | + | 0.237238i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.4215 | − | 17.4215i | 0.187328 | − | 0.187328i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.7030i | 0.249506i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82.8950 | 0.854588 | 0.427294 | − | 0.904113i | \(-0.359467\pi\) | ||||
0.427294 | + | 0.904113i | \(0.359467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 120.372 | + | 120.372i | 1.21587 | + | 1.21587i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.9079 | + | 90.9079i | 0.900078 | + | 0.900078i | 0.995442 | − | 0.0953644i | \(-0.0304016\pi\) |
−0.0953644 | + | 0.995442i | \(0.530402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 32.2822 | 0.313419 | 0.156710 | − | 0.987645i | \(-0.449911\pi\) | ||||
0.156710 | + | 0.987645i | \(0.449911\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.87424i | 0.0273737i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −39.5799 | + | 39.5799i | −0.369906 | + | 0.369906i | −0.867443 | − | 0.497537i | \(-0.834238\pi\) |
0.497537 | + | 0.867443i | \(0.334238\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.28042 | + | 1.28042i | −0.0117469 | + | 0.0117469i | −0.712956 | − | 0.701209i | \(-0.752644\pi\) |
0.701209 | + | 0.712956i | \(0.252644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.51361i | − | 0.0316542i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 181.626 | 1.60731 | 0.803654 | − | 0.595096i | \(-0.202886\pi\) | ||||
0.803654 | + | 0.595096i | \(0.202886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.3566 | + | 21.3566i | 0.185710 | + | 0.185710i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −77.6392 | − | 77.6392i | −0.663582 | − | 0.663582i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 67.2945 | 0.565500 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 260.201i | − | 2.15042i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.4932 | − | 14.4932i | 0.117831 | − | 0.117831i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | − | 7.90569i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.6769i | 0.351787i | 0.984409 | + | 0.175893i | \(0.0562814\pi\) | ||||
−0.984409 | + | 0.175893i | \(0.943719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −34.2566 | −0.265555 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −151.968 | − | 151.968i | −1.16006 | − | 1.16006i | −0.984461 | − | 0.175602i | \(-0.943813\pi\) |
−0.175602 | − | 0.984461i | \(-0.556187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.1724 | + | 18.1724i | 0.136634 | + | 0.136634i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.0064 | −0.155603 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 106.085i | 0.774342i | 0.922008 | + | 0.387171i | \(0.126548\pi\) | ||||
−0.922008 | + | 0.387171i | \(0.873452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 111.976 | − | 111.976i | 0.805586 | − | 0.805586i | −0.178376 | − | 0.983962i | \(-0.557084\pi\) |
0.983962 | + | 0.178376i | \(0.0570844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.2528 | − | 13.2528i | 0.0939917 | − | 0.0939917i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 245.873i | 1.71939i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.3208 | 0.229798 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.1665 | − | 16.1665i | −0.109976 | − | 0.109976i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −67.4923 | − | 67.4923i | −0.452969 | − | 0.452969i | 0.443370 | − | 0.896339i | \(-0.353783\pi\) |
−0.896339 | + | 0.443370i | \(0.853783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 154.364 | 1.02228 | 0.511140 | − | 0.859498i | \(-0.329223\pi\) | ||||
0.511140 | + | 0.859498i | \(0.329223\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 242.010i | 1.58177i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −73.4749 | + | 73.4749i | −0.474032 | + | 0.474032i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 85.0691 | − | 85.0691i | 0.541842 | − | 0.541842i | −0.382227 | − | 0.924069i | \(-0.624843\pi\) |
0.924069 | + | 0.382227i | \(0.124843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 45.8041i | 0.288076i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.7469 | 0.203397 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 114.693 | + | 114.693i | 0.703636 | + | 0.703636i | 0.965189 | − | 0.261553i | \(-0.0842346\pi\) |
−0.261553 | + | 0.965189i | \(0.584235\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.3673 | + | 16.3673i | 0.0991958 | + | 0.0991958i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −279.035 | −1.67087 | −0.835435 | − | 0.549590i | \(-0.814784\pi\) | ||||
−0.835435 | + | 0.549590i | \(0.814784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4128i | 0.0616142i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −65.3530 | + | 65.3530i | −0.382182 | + | 0.382182i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −217.656 | + | 217.656i | −1.25813 | + | 1.25813i | −0.306145 | + | 0.951985i | \(0.599039\pi\) |
−0.951985 | + | 0.306145i | \(0.900961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12.1221i | − | 0.0692691i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.91227 | 0.0390523 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −203.712 | − | 203.712i | −1.13805 | − | 1.13805i | −0.988799 | − | 0.149256i | \(-0.952312\pi\) |
−0.149256 | − | 0.988799i | \(-0.547688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −175.707 | − | 175.707i | −0.970755 | − | 0.970755i | 0.0288295 | − | 0.999584i | \(-0.490822\pi\) |
−0.999584 | + | 0.0288295i | \(0.990822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.2272 | 0.0832090 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.8186i | 0.0801008i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 383.208 | − | 383.208i | 2.04924 | − | 2.04924i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.1050 | + | 16.1050i | −0.0852114 | + | 0.0852114i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 350.356i | − | 1.83433i | −0.398512 | − | 0.917163i | \(-0.630473\pi\) | ||
0.398512 | − | 0.917163i | \(-0.369527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −134.033 | −0.694470 | −0.347235 | − | 0.937778i | \(-0.612879\pi\) | ||||
−0.347235 | + | 0.937778i | \(0.612879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.5568 | − | 10.5568i | −0.0541377 | − | 0.0541377i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −149.471 | − | 149.471i | −0.758736 | − | 0.758736i | 0.217356 | − | 0.976092i | \(-0.430257\pi\) |
−0.976092 | + | 0.217356i | \(0.930257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −307.365 | −1.54455 | −0.772274 | − | 0.635290i | \(-0.780881\pi\) | ||||
−0.772274 | + | 0.635290i | \(0.780881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.60889i | − | 0.0129795i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.5460 | − | 25.5460i | 0.125842 | − | 0.125842i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −61.1249 | + | 61.1249i | −0.298170 | + | 0.298170i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 117.767i | 0.568924i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 206.965 | 0.990262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −76.7992 | − | 76.7992i | −0.363977 | − | 0.363977i | 0.501298 | − | 0.865275i | \(-0.332856\pi\) |
−0.865275 | + | 0.501298i | \(0.832856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.27056 | + | 3.27056i | 0.0153548 | + | 0.0153548i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 144.477 | 0.671987 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 112.662i | 0.519179i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.66161 | + | 8.66161i | −0.0395507 | + | 0.0395507i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −247.168 | + | 247.168i | −1.11841 | + | 1.11841i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 108.117i | − | 0.484830i | −0.970173 | − | 0.242415i | \(-0.922060\pi\) | ||
0.970173 | − | 0.242415i | \(-0.0779396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 43.5945 | 0.193753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.15669 | − | 6.15669i | −0.0271220 | − | 0.0271220i | 0.693416 | − | 0.720538i | \(-0.256105\pi\) |
−0.720538 | + | 0.693416i | \(0.756105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −110.025 | − | 110.025i | −0.480459 | − | 0.480459i | 0.424819 | − | 0.905278i | \(-0.360338\pi\) |
−0.905278 | + | 0.424819i | \(0.860338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.0966 | 0.108643 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 109.457i | − | 0.469772i | −0.972023 | − | 0.234886i | \(-0.924528\pi\) | ||
0.972023 | − | 0.234886i | \(-0.0754717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −55.8938 | + | 55.8938i | −0.237846 | + | 0.237846i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.7333 | − | 27.7333i | 0.117018 | − | 0.117018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 418.232i | 1.74992i | 0.484192 | + | 0.874962i | \(0.339114\pi\) | ||||
−0.484192 | + | 0.874962i | \(0.660886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −240.522 | −0.998015 | −0.499007 | − | 0.866598i | \(-0.666302\pi\) | ||||
−0.499007 | + | 0.866598i | \(0.666302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −87.3364 | − | 87.3364i | −0.359409 | − | 0.359409i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 68.1822 | + | 68.1822i | 0.278295 | + | 0.278295i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −133.491 | −0.540451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.0374i | 0.152761i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −55.0912 | + | 55.0912i | −0.219487 | + | 0.219487i | −0.808282 | − | 0.588795i | \(-0.799602\pi\) |
0.588795 | + | 0.808282i | \(0.299602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 186.477 | − | 186.477i | 0.737063 | − | 0.737063i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.9070i | 0.129047i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.417209 | 0.00162338 | 0.000811690 | − | 1.00000i | \(-0.499742\pi\) | ||||
0.000811690 | 1.00000i | \(0.499742\pi\) | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3610 | + | 11.3610i | 0.0438648 | + | 0.0438648i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 91.8706 | + | 91.8706i | 0.351995 | + | 0.351995i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −53.6800 | −0.204106 | −0.102053 | − | 0.994779i | \(-0.532541\pi\) | ||||
−0.102053 | + | 0.994779i | \(0.532541\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 193.179i | − | 0.728977i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.2983 | + | 19.2983i | −0.0722783 | + | 0.0722783i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 229.835 | − | 229.835i | 0.854404 | − | 0.854404i | −0.136268 | − | 0.990672i | \(-0.543511\pi\) |
0.990672 | + | 0.136268i | \(0.0435110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 180.605i | 0.666439i | 0.942849 | + | 0.333220i | \(0.108135\pi\) | ||||
−0.942849 | + | 0.333220i | \(0.891865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.1872 | −0.0592938 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −69.0291 | − | 69.0291i | −0.251015 | − | 0.251015i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −255.348 | − | 255.348i | −0.921834 | − | 0.921834i | 0.0753246 | − | 0.997159i | \(-0.476001\pi\) |
−0.997159 | + | 0.0753246i | \(0.976001\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −405.164 | −1.45220 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 397.276i | − | 1.41379i | −0.707317 | − | 0.706897i | \(-0.750095\pi\) | ||
0.707317 | − | 0.706897i | \(-0.249905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 130.023 | − | 130.023i | 0.459444 | − | 0.459444i | −0.439029 | − | 0.898473i | \(-0.644678\pi\) |
0.898473 | + | 0.439029i | \(0.144678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.88627 | + | 8.88627i | −0.0311799 | + | 0.0311799i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 93.7250i | 0.326568i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 481.451 | 1.66592 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.0773 | + | 31.0773i | 0.106795 | + | 0.106795i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −170.949 | − | 170.949i | −0.583443 | − | 0.583443i | 0.352405 | − | 0.935848i | \(-0.385364\pi\) |
−0.935848 | + | 0.352405i | \(0.885364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.1525 | −0.0988219 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 183.419i | 0.617572i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −120.277 | + | 120.277i | −0.402264 | + | 0.402264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110.766 | − | 110.766i | 0.367994 | − | 0.367994i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 68.1627i | 0.224959i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −64.2208 | −0.210560 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 108.448 | + | 108.448i | 0.353251 | + | 0.353251i | 0.861318 | − | 0.508066i | \(-0.169640\pi\) |
−0.508066 | + | 0.861318i | \(0.669640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1026 | + | 12.1026i | 0.0391669 | + | 0.0391669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 436.855 | 1.40468 | 0.702340 | − | 0.711842i | \(-0.252139\pi\) | ||||
0.702340 | + | 0.711842i | \(0.252139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 328.972i | 1.05103i | 0.850785 | + | 0.525514i | \(0.176127\pi\) | ||||
−0.850785 | + | 0.525514i | \(0.823873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 33.4225 | − | 33.4225i | 0.106103 | − | 0.106103i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −306.697 | + | 306.697i | −0.967498 | + | 0.967498i | −0.999488 | − | 0.0319904i | \(-0.989815\pi\) |
0.0319904 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 290.942i | − | 0.912045i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.6770 | −0.0924517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 208.054 | + | 208.054i | 0.644131 | + | 0.644131i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44.5235 | + | 44.5235i | 0.136995 | + | 0.136995i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.960056 | −0.00293595 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 85.7039i | 0.260498i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −245.686 | + | 245.686i | −0.742253 | + | 0.742253i | −0.973011 | − | 0.230758i | \(-0.925879\pi\) |
0.230758 | + | 0.973011i | \(0.425879\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.8574 | + | 40.8574i | −0.122695 | + | 0.122695i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0030i | 0.0328447i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 205.265 | 0.609095 | 0.304548 | − | 0.952497i | \(-0.401495\pi\) | ||||
0.304548 | + | 0.952497i | \(0.401495\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 68.0915 | + | 68.0915i | 0.200860 | + | 0.200860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 641.551 | + | 641.551i | 1.88138 | + | 1.88138i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 223.343 | 0.651145 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0132i | 0.0464151i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 82.7836 | − | 82.7836i | 0.238570 | − | 0.238570i | −0.577688 | − | 0.816258i | \(-0.696045\pi\) |
0.816258 | + | 0.577688i | \(0.196045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 89.8282 | − | 89.8282i | 0.257387 | − | 0.257387i | −0.566603 | − | 0.823991i | \(-0.691743\pi\) |
0.823991 | + | 0.566603i | \(0.191743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 118.304i | − | 0.337050i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −104.126 | −0.294974 | −0.147487 | − | 0.989064i | \(-0.547119\pi\) | ||||
−0.147487 | + | 0.989064i | \(0.547119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7936 | − | 13.7936i | −0.0388552 | − | 0.0388552i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.2287 | + | 25.2287i | 0.0706687 | + | 0.0706687i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 372.933 | 1.03881 | 0.519405 | − | 0.854528i | \(-0.326154\pi\) | ||||
0.519405 | + | 0.854528i | \(0.326154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 248.633i | − | 0.688735i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 97.5494 | − | 97.5494i | 0.268731 | − | 0.268731i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.5303 | − | 36.5303i | 0.100083 | − | 0.100083i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 283.076i | − | 0.771325i | −0.922640 | − | 0.385663i | \(-0.873973\pi\) | ||
0.922640 | − | 0.385663i | \(-0.126027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −337.062 | −0.913447 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −148.104 | − | 148.104i | −0.399202 | − | 0.399202i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 48.6420 | + | 48.6420i | 0.130407 | + | 0.130407i | 0.769298 | − | 0.638890i | \(-0.220606\pi\) |
−0.638890 | + | 0.769298i | \(0.720606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.92769 | 0.0158072 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 187.657i | 0.497763i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 120.242 | − | 120.242i | 0.317262 | − | 0.317262i | −0.530453 | − | 0.847715i | \(-0.677978\pi\) |
0.847715 | + | 0.530453i | \(0.177978\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7494 | + | 16.7494i | −0.0439616 | + | 0.0439616i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 46.9823i | − | 0.122669i | −0.998117 | − | 0.0613346i | \(-0.980464\pi\) | ||
0.998117 | − | 0.0613346i | \(-0.0195357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −105.845 | −0.274922 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 398.347 | + | 398.347i | 1.02932 | + | 1.02932i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 103.685 | + | 103.685i | 0.266542 | + | 0.266542i | 0.827705 | − | 0.561163i | \(-0.189646\pi\) |
−0.561163 | + | 0.827705i | \(0.689646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 374.917 | 0.958867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 113.946i | − | 0.289938i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −116.965 | + | 116.965i | −0.296114 | + | 0.296114i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 290.747 | − | 290.747i | 0.732361 | − | 0.732361i | −0.238726 | − | 0.971087i | \(-0.576730\pi\) |
0.971087 | + | 0.238726i | \(0.0767299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.6256i | 0.0341495i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.07753 | −0.0126622 | −0.00633108 | − | 0.999980i | \(-0.502015\pi\) | ||||
−0.00633108 | + | 0.999980i | \(0.502015\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −413.798 | − | 413.798i | −1.02679 | − | 1.02679i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 116.197 | + | 116.197i | 0.286906 | + | 0.286906i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 129.390 | 0.317912 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 254.647i | 0.622610i | 0.950310 | + | 0.311305i | \(0.100766\pi\) | ||||
−0.950310 | + | 0.311305i | \(0.899234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.7712 | + | 39.7712i | −0.0967669 | + | 0.0967669i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.3503 | + | 22.3503i | −0.0541169 | + | 0.0541169i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 160.423i | − | 0.386560i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 83.9599 | 0.201343 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 257.710 | + | 257.710i | 0.615059 | + | 0.615059i | 0.944260 | − | 0.329201i | \(-0.106779\pi\) |
−0.329201 | + | 0.944260i | \(0.606779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 280.397 | + | 280.397i | 0.666026 | + | 0.666026i | 0.956794 | − | 0.290768i | \(-0.0939108\pi\) |
−0.290768 | + | 0.956794i | \(0.593911\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −308.216 | −0.728643 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 138.785i | − | 0.326553i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −49.2361 | + | 49.2361i | −0.115307 | + | 0.115307i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −92.1778 | + | 92.1778i | −0.214867 | + | 0.214867i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 203.154i | 0.471355i | 0.971831 | + | 0.235677i | \(0.0757308\pi\) | ||||
−0.971831 | + | 0.235677i | \(0.924269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3904 | 0.0447816 | 0.0223908 | − | 0.999749i | \(-0.492872\pi\) | ||||
0.0223908 | + | 0.999749i | \(0.492872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.4919 | + | 12.4919i | 0.0287171 | + | 0.0287171i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 101.243 | + | 101.243i | 0.231678 | + | 0.231678i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 286.595 | 0.652835 | 0.326418 | − | 0.945226i | \(-0.394158\pi\) | ||||
0.326418 | + | 0.945226i | \(0.394158\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 375.978i | 0.852558i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −234.141 | + | 234.141i | −0.528535 | + | 0.528535i | −0.920136 | − | 0.391600i | \(-0.871922\pi\) |
0.391600 | + | 0.920136i | \(0.371922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 81.3906 | − | 81.3906i | 0.182900 | − | 0.182900i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 50.6057i | − | 0.113212i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −586.663 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 533.716 | + | 533.716i | 1.18341 | + | 1.18341i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.8711 | + | 57.8711i | 0.127751 | + | 0.127751i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 68.2695 | 0.150043 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 284.950i | 0.623524i | 0.950160 | + | 0.311762i | \(0.100919\pi\) | ||||
−0.950160 | + | 0.311762i | \(0.899081\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −184.385 | + | 184.385i | −0.401709 | + | 0.401709i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −443.411 | + | 443.411i | −0.961845 | + | 0.961845i | −0.999298 | − | 0.0374533i | \(-0.988075\pi\) |
0.0374533 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 725.563i | − | 1.56709i | −0.621335 | − | 0.783545i | \(-0.713409\pi\) | ||
0.621335 | − | 0.783545i | \(-0.286591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −55.0915 | −0.118476 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −105.560 | − | 105.560i | −0.226039 | − | 0.226039i | 0.584997 | − | 0.811036i | \(-0.301096\pi\) |
−0.811036 | + | 0.584997i | \(0.801096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.43563 | + | 8.43563i | 0.0179864 | + | 0.0179864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 63.7848 | 0.135424 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1261.51i | − | 2.66705i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.4778 | − | 37.4778i | 0.0789006 | − | 0.0789006i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 532.625 | − | 532.625i | 1.11661 | − | 1.11661i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 606.909i | − | 1.26703i | −0.773729 | − | 0.633516i | \(-0.781611\pi\) | ||
0.773729 | − | 0.633516i | \(-0.218389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −83.4560 | −0.173505 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.2768 | + | 12.2768i | 0.0254178 | + | 0.0254178i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −131.068 | − | 131.068i | −0.270244 | − | 0.270244i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −961.389 | −1.97411 | −0.987053 | − | 0.160396i | \(-0.948723\pi\) | ||||
−0.987053 | + | 0.160396i | \(0.948723\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 85.9966i | 0.175862i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −564.547 | + | 564.547i | −1.14979 | + | 1.14979i | −0.163197 | + | 0.986594i | \(0.552181\pi\) |
−0.986594 | + | 0.163197i | \(0.947819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 292.474 | − | 292.474i | 0.593254 | − | 0.593254i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 380.648i | − | 0.768986i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.1502 | −0.0425558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.48141 | − | 5.48141i | −0.0109848 | − | 0.0109848i | 0.701593 | − | 0.712578i | \(-0.252472\pi\) |
−0.712578 | + | 0.701593i | \(0.752472\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −104.610 | − | 104.610i | −0.208803 | − | 0.208803i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 558.604 | 1.11054 | 0.555272 | − | 0.831669i | \(-0.312614\pi\) | ||||
0.555272 | + | 0.831669i | \(0.312614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 287.476i | − | 0.569259i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.90376 | + | 3.90376i | −0.00769972 | + | 0.00769972i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −170.507 | + | 170.507i | −0.334985 | + | 0.334985i | −0.854476 | − | 0.519491i | \(-0.826122\pi\) |
0.519491 | + | 0.854476i | \(0.326122\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 56.0132i | − | 0.109615i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −99.5832 | −0.194119 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −51.0426 | − | 51.0426i | −0.0991118 | − | 0.0991118i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 488.040 | + | 488.040i | 0.943985 | + | 0.943985i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −163.199 | −0.314448 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 248.276i | 0.476537i | 0.971199 | + | 0.238269i | \(0.0765798\pi\) | ||||
−0.971199 | + | 0.238269i | \(0.923420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −53.5442 | + | 53.5442i | −0.102379 | + | 0.102379i | −0.756441 | − | 0.654062i | \(-0.773064\pi\) |
0.654062 | + | 0.756441i | \(0.273064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.54457 | − | 4.54457i | 0.00865632 | − | 0.00865632i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1289.86i | 2.44755i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −346.558 | −0.655118 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −80.3779 | − | 80.3779i | −0.151371 | − | 0.151371i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −344.245 | − | 344.245i | −0.645862 | − | 0.645862i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 125.163 | 0.233949 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 152.743i | − | 0.284438i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 595.337 | − | 595.337i | 1.10452 | − | 1.10452i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 356.241 | − | 356.241i | 0.658486 | − | 0.658486i | −0.296536 | − | 0.955022i | \(-0.595831\pi\) |
0.955022 | + | 0.296536i | \(0.0958314\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 131.745i | − | 0.242624i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.04903 | 0.00742942 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −205.888 | − | 205.888i | −0.376394 | − | 0.376394i | 0.493405 | − | 0.869799i | \(-0.335752\pi\) |
−0.869799 | + | 0.493405i | \(0.835752\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −177.067 | − | 177.067i | −0.322526 | − | 0.322526i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 157.961 | 0.286680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 179.347i | 0.324316i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.55551 | + | 5.55551i | −0.0100099 | + | 0.0100099i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −378.558 | + | 378.558i | −0.679638 | + | 0.679638i | −0.959918 | − | 0.280280i | \(-0.909573\pi\) |
0.280280 | + | 0.959918i | \(0.409573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 813.670i | 1.45558i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 287.329 | 0.512173 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −600.937 | − | 600.937i | −1.06738 | − | 1.06738i | −0.997559 | − | 0.0698249i | \(-0.977756\pi\) |
−0.0698249 | − | 0.997559i | \(-0.522244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −287.176 | − | 287.176i | −0.508276 | − | 0.508276i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 178.169 | 0.314231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 394.322i | − | 0.693009i | −0.938048 | − | 0.346504i | \(-0.887369\pi\) | ||
0.938048 | − | 0.346504i | \(-0.112631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −86.9337 | + | 86.9337i | −0.152248 | + | 0.152248i | −0.779121 | − | 0.626873i | \(-0.784334\pi\) |
0.626873 | + | 0.779121i | \(0.284334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 131.349 | − | 131.349i | 0.229230 | − | 0.229230i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 67.5356i | − | 0.117453i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −398.959 | −0.691436 | −0.345718 | − | 0.938338i | \(-0.612365\pi\) | ||||
−0.345718 | + | 0.938338i | \(0.612365\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −50.2488 | − | 50.2488i | −0.0867855 | − | 0.0867855i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −122.991 | − | 122.991i | −0.211688 | − | 0.211688i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1686.75 | −2.89323 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 245.517i | 0.419686i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −332.530 | + | 332.530i | −0.566490 | + | 0.566490i | −0.931143 | − | 0.364653i | \(-0.881188\pi\) |
0.364653 | + | 0.931143i | \(0.381188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −348.316 | + | 348.316i | −0.591368 | + | 0.591368i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 112.073i | − | 0.189633i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −154.212 | −0.260054 | −0.130027 | − | 0.991510i | \(-0.541506\pi\) | ||||
−0.130027 | + | 0.991510i | \(0.541506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −106.402 | − | 106.402i | −0.178827 | − | 0.178827i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −115.231 | − | 115.231i | −0.193017 | − | 0.193017i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 382.295 | 0.638223 | 0.319111 | − | 0.947717i | \(-0.396616\pi\) | ||||
0.319111 | + | 0.947717i | \(0.396616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 84.1090i | − | 0.139948i | −0.997549 | − | 0.0699742i | \(-0.977708\pi\) | ||
0.997549 | − | 0.0699742i | \(-0.0222917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.3369 | + | 30.3369i | −0.0503100 | + | 0.0503100i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −411.414 | + | 411.414i | −0.680024 | + | 0.680024i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 848.304i | − | 1.39754i | −0.715348 | − | 0.698768i | \(-0.753732\pi\) | ||
0.715348 | − | 0.698768i | \(-0.246268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1544 | 0.0314521 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −314.784 | − | 314.784i | −0.515194 | − | 0.515194i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −216.458 | − | 216.458i | −0.353112 | − | 0.353112i | 0.508154 | − | 0.861266i | \(-0.330328\pi\) |
−0.861266 | + | 0.508154i | \(0.830328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −45.8314 | −0.0745226 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 654.303i | − | 1.06046i | −0.847854 | − | 0.530229i | \(-0.822106\pi\) | ||
0.847854 | − | 0.530229i | \(-0.177894\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −61.5563 | + | 61.5563i | −0.0994448 | + | 0.0994448i | −0.755079 | − | 0.655634i | \(-0.772401\pi\) |
0.655634 | + | 0.755079i | \(0.272401\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −89.7253 | + | 89.7253i | −0.144485 | + | 0.144485i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 124.799i | − | 0.200320i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 77.5910 | + | 77.5910i | 0.123750 | + | 0.123750i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 130.071 | + | 130.071i | 0.206790 | + | 0.206790i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −532.078 | −0.843230 | −0.421615 | − | 0.906775i | \(-0.638537\pi\) | ||||
−0.421615 | + | 0.906775i | \(0.638537\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 57.5840i | − | 0.0909700i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 70.6404 | − | 70.6404i | 0.111245 | − | 0.111245i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −383.990 | + | 383.990i | −0.602810 | + | 0.602810i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 76.0623i | − | 0.119033i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 85.5372 | 0.133443 | 0.0667217 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667217 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 405.524 | + | 405.524i | 0.630675 | + | 0.630675i | 0.948237 | − | 0.317562i | \(-0.102864\pi\) |
−0.317562 | + | 0.948237i | \(0.602864\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 54.1645 | + | 54.1645i | 0.0839760 | + | 0.0839760i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 778.109 | 1.20264 | 0.601321 | − | 0.799008i | \(-0.294641\pi\) | ||||
0.601321 | + | 0.799008i | \(0.294641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 254.547i | 0.392214i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.2369 | + | 42.2369i | −0.0648800 | + | 0.0648800i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 561.135 | − | 561.135i | 0.859319 | − | 0.859319i | −0.131939 | − | 0.991258i | \(-0.542120\pi\) |
0.991258 | + | 0.131939i | \(0.0421204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 480.566i | 0.733689i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 201.440 | 0.306605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 212.956 | + | 212.956i | 0.323150 | + | 0.323150i | 0.849974 | − | 0.526824i | \(-0.176617\pi\) |
−0.526824 | + | 0.849974i | \(0.676617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 250.037 | + | 250.037i | 0.378270 | + | 0.378270i | 0.870478 | − | 0.492208i | \(-0.163810\pi\) |
−0.492208 | + | 0.870478i | \(0.663810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −185.326 | −0.279527 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 57.4661i | − | 0.0864151i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 142.324 | − | 142.324i | 0.213379 | − | 0.213379i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.5331 | − | 40.5331i | 0.0605876 | − | 0.0605876i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 560.749i | 0.835691i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 363.444 | 0.540036 | 0.270018 | − | 0.962855i | \(-0.412970\pi\) | ||||
0.270018 | + | 0.962855i | \(0.412970\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.2141 | + | 33.2141i | 0.0492060 | + | 0.0492060i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −628.852 | − | 628.852i | −0.928880 | − | 0.928880i | 0.0687532 | − | 0.997634i | \(-0.478098\pi\) |
−0.997634 | + | 0.0687532i | \(0.978098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −200.972 | −0.295982 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.61628i | − | 0.00677869i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 321.108 | − | 321.108i | 0.470144 | − | 0.470144i | −0.431817 | − | 0.901961i | \(-0.642128\pi\) |
0.901961 | + | 0.431817i | \(0.142128\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 167.735 | − | 167.735i | 0.244868 | − | 0.244868i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 82.4969i | − | 0.120083i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1087.95 | 1.57903 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 451.940 | + | 451.940i | 0.654038 | + | 0.654038i | 0.953963 | − | 0.299925i | \(-0.0969615\pi\) |
−0.299925 | + | 0.953963i | \(0.596962\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −291.831 | − | 291.831i | −0.421112 | − | 0.421112i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −354.101 | −0.509497 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1073.05i | 1.53953i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.0354 | − | 41.0354i | 0.0587059 | − | 0.0587059i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 252.343 | − | 252.343i | 0.359976 | − | 0.359976i | −0.503828 | − | 0.863804i | \(-0.668075\pi\) |
0.863804 | + | 0.503828i | \(0.168075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 70.2494i | 0.0999280i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.9091 | −0.0594456 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −220.399 | − | 220.399i | −0.311738 | − | 0.311738i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −401.245 | − | 401.245i | −0.565931 | − | 0.565931i | 0.365055 | − | 0.930986i | \(-0.381050\pi\) |
−0.930986 | + | 0.365055i | \(0.881050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −644.982 | −0.907148 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 627.671i | 0.880324i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 388.760 | − | 388.760i | 0.543720 | − | 0.543720i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −156.795 | + | 156.795i | −0.218682 | + | 0.218682i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 518.286i | − | 0.720843i | −0.932790 | − | 0.360422i | \(-0.882633\pi\) | ||
0.932790 | − | 0.360422i | \(-0.117367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −78.2654 | −0.108551 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −90.1715 | − | 90.1715i | −0.124719 | − | 0.124719i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −52.6847 | − | 52.6847i | −0.0726686 | − | 0.0726686i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1097.86 | 1.51012 | 0.755059 | − | 0.655657i | \(-0.227608\pi\) | ||||
0.755059 | + | 0.655657i | \(0.227608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 595.919i | 0.817447i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1268.15 | − | 1268.15i | 1.73482 | − | 1.73482i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −749.818 | + | 749.818i | −1.02294 | + | 1.02294i | −0.0232137 | + | 0.999731i | \(0.507390\pi\) |
−0.999731 | + | 0.0232137i | \(0.992610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 51.1230i | 0.0695551i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 96.0732 | 0.130357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −687.419 | − | 687.419i | −0.930201 | − | 0.930201i | 0.0675168 | − | 0.997718i | \(-0.478492\pi\) |
−0.997718 | + | 0.0675168i | \(0.978492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.0459 | − | 50.0459i | −0.0675383 | − | 0.0675383i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 825.630 | 1.11121 | 0.555605 | − | 0.831446i | \(-0.312487\pi\) | ||||
0.555605 | + | 0.831446i | \(0.312487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 213.429i | 0.286482i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 442.310 | − | 442.310i | 0.592116 | − | 0.592116i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 95.9582 | − | 95.9582i | 0.128115 | − | 0.128115i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1237.27i | 1.64749i | 0.566958 | + | 0.823747i | \(0.308120\pi\) | ||||
−0.566958 | + | 0.823747i | \(0.691880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −41.3073 | −0.0548570 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −244.071 | − | 244.071i | −0.323273 | − | 0.323273i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 606.680 | + | 606.680i | 0.801427 | + | 0.801427i | 0.983319 | − | 0.181892i | \(-0.0582220\pi\) |
−0.181892 | + | 0.983319i | \(0.558222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 139.820 | 0.184216 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1024.72i | 1.34655i | 0.739393 | + | 0.673274i | \(0.235113\pi\) | ||||
−0.739393 | + | 0.673274i | \(0.764887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.10426 | − | 3.10426i | 0.00406850 | − | 0.00406850i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 382.652 | − | 382.652i | 0.500199 | − | 0.500199i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 164.182i | − | 0.214057i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 161.299 | 0.209752 | 0.104876 | − | 0.994485i | \(-0.466555\pi\) | ||||
0.104876 | + | 0.994485i | \(0.466555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.156411 | + | 0.156411i | 0.000202868 | + | 0.000202868i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 679.758 | + | 679.758i | 0.879377 | + | 0.879377i | 0.993470 | − | 0.114093i | \(-0.0363963\pi\) |
−0.114093 | + | 0.993470i | \(0.536396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 232.348 | 0.299804 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.51846i | 0.0109633i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −289.769 | + | 289.769i | −0.371976 | + | 0.371976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −120.440 | + | 120.440i | −0.154212 | + | 0.154212i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 139.990i | 0.178787i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −269.012 | −0.342691 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 441.767 | + | 441.767i | 0.561331 | + | 0.561331i | 0.929685 | − | 0.368355i | \(-0.120079\pi\) |
−0.368355 | + | 0.929685i | \(0.620079\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.1246 | − | 20.1246i | −0.0255065 | − | 0.0255065i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −440.337 | −0.556684 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 361.681i | − | 0.456091i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.4227 | − | 72.4227i | 0.0910977 | − | 0.0910977i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −99.4692 | + | 99.4692i | −0.124804 | + | 0.124804i | −0.766750 | − | 0.641946i | \(-0.778127\pi\) |
0.641946 | + | 0.766750i | \(0.278127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 981.219i | 1.22806i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 448.814 | 0.560317 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −318.967 | − | 318.967i | −0.397219 | − | 0.397219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51.7774 | − | 51.7774i | −0.0643198 | − | 0.0643198i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 172.330 | 0.213544 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1353.26i | − | 1.67276i | −0.548153 | − | 0.836378i | \(-0.684669\pi\) | ||
0.548153 | − | 0.836378i | \(-0.315331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 78.4824 | − | 78.4824i | 0.0967724 | − | 0.0967724i | −0.657063 | − | 0.753836i | \(-0.728202\pi\) |
0.753836 | + | 0.657063i | \(0.228202\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −67.7088 | + | 67.7088i | −0.0832826 | + | 0.0832826i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 362.690i | − | 0.445019i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 684.910 | 0.838323 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 188.230 | + | 188.230i | 0.229829 | + | 0.229829i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −574.440 | − | 574.440i | −0.699684 | − | 0.699684i | 0.264659 | − | 0.964342i | \(-0.414741\pi\) |
−0.964342 | + | 0.264659i | \(0.914741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 918.417 | 1.11594 | 0.557969 | − | 0.829862i | \(-0.311581\pi\) | ||||
0.557969 | + | 0.829862i | \(0.311581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 51.7580i | − | 0.0627370i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −675.019 | + | 675.019i | −0.816226 | + | 0.816226i | −0.985559 | − | 0.169333i | \(-0.945839\pi\) |
0.169333 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −312.622 | + | 312.622i | −0.377107 | + | 0.377107i | −0.870057 | − | 0.492950i | \(-0.835918\pi\) |
0.492950 | + | 0.870057i | \(0.335918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 191.460i | − | 0.230397i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1196.94 | 1.43691 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 441.193 | + | 441.193i | 0.528375 | + | 0.528375i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −308.689 | − | 308.689i | −0.368804 | − | 0.368804i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −612.003 | −0.729443 | −0.364722 | − | 0.931117i | \(-0.618836\pi\) | ||||
−0.364722 | + | 0.931117i | \(0.618836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 618.945i | 0.735964i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 148.939 | − | 148.939i | 0.176677 | − | 0.176677i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.4641 | − | 16.4641i | 0.0194841 | − | 0.0194841i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 630.837i | 0.744789i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 97.4909 | 0.114830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.2953 | + | 63.2953i | 0.0743775 | + | 0.0743775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −184.397 | − | 184.397i | −0.216175 | − | 0.216175i | 0.590709 | − | 0.806884i | \(-0.298848\pi\) |
−0.806884 | + | 0.590709i | \(0.798848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 206.664 | 0.241713 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 602.644i | − | 0.703202i | −0.936150 | − | 0.351601i | \(-0.885637\pi\) | ||
0.936150 | − | 0.351601i | \(-0.114363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −628.796 | + | 628.796i | −0.732009 | + | 0.732009i | −0.971018 | − | 0.239008i | \(-0.923178\pi\) |
0.239008 | + | 0.971018i | \(0.423178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.1375 | + | 35.1375i | −0.0408101 | + | 0.0408101i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1015.61i | 1.17684i | 0.808555 | + | 0.588420i | \(0.200250\pi\) | ||||
−0.808555 | + | 0.588420i | \(0.799750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 688.290 | 0.795711 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 180.496 | + | 180.496i | 0.208184 | + | 0.208184i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1021.29 | + | 1021.29i | 1.17524 | + | 1.17524i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.9668 | −0.0711445 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 722.753i | − | 0.827896i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.1667 | + | 19.1667i | −0.0219048 | + | 0.0219048i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 395.253 | − | 395.253i | 0.450687 | − | 0.450687i | −0.444895 | − | 0.895583i | \(-0.646759\pi\) |
0.895583 | + | 0.444895i | \(0.146759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 128.177i | − | 0.145822i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1316.34 | 1.49415 | 0.747073 | − | 0.664742i | \(-0.231459\pi\) | ||||
0.747073 | + | 0.664742i | \(0.231459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 433.169 | + | 433.169i | 0.490565 | + | 0.490565i | 0.908484 | − | 0.417919i | \(-0.137241\pi\) |
−0.417919 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.9293 | − | 10.9293i | −0.0123494 | − | 0.0123494i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1519.98 | −1.71362 | −0.856810 | − | 0.515633i | \(-0.827557\pi\) | ||||
−0.856810 | + | 0.515633i | \(0.827557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 108.315i | − | 0.121840i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1014.58 | − | 1014.58i | 1.13870 | − | 1.13870i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −264.970 | + | 264.970i | −0.296719 | + | 0.296719i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 644.193i | 0.719769i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −90.1835 | −0.100539 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 489.648 | + | 489.648i | 0.544659 | + | 0.544659i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1695.63 | − | 1695.63i | −1.88195 | − | 1.88195i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 83.0524 | 0.0919739 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 555.633i | 0.613959i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −183.726 | + | 183.726i | −0.202564 | + | 0.202564i | −0.801098 | − | 0.598534i | \(-0.795750\pi\) |
0.598534 | + | 0.801098i | \(0.295750\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 792.617 | − | 792.617i | 0.871966 | − | 0.871966i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 194.108i | − | 0.213071i | −0.994309 | − | 0.106535i | \(-0.966024\pi\) | ||
0.994309 | − | 0.106535i | \(-0.0339758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1400.74 | −1.53422 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.0764 | − | 24.0764i | −0.0263130 | − | 0.0263130i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 368.435 | + | 368.435i | 0.401783 | + | 0.401783i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 100.398 | 0.109247 | 0.0546237 | − | 0.998507i | \(-0.482604\pi\) | ||||
0.0546237 | + | 0.998507i | \(0.482604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 81.3144i | 0.0882893i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 77.6831 | − | 77.6831i | 0.0841637 | − | 0.0841637i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.4303 | − | 23.4303i | 0.0253301 | − | 0.0253301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 281.465i | − | 0.303630i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 546.652 | 0.588430 | 0.294215 | − | 0.955739i | \(-0.404942\pi\) | ||||
0.294215 | + | 0.955739i | \(0.404942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 323.225 | + | 323.225i | 0.347180 | + | 0.347180i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 163.777 | + | 163.777i | 0.175538 | + | 0.175538i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1211.81 | −1.29605 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1158.63i | − | 1.23653i | −0.785971 | − | 0.618264i | \(-0.787836\pi\) | ||
0.785971 | − | 0.618264i | \(-0.212164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −123.331 | + | 123.331i | −0.131343 | + | 0.131343i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 218.412 | − | 218.412i | 0.232106 | − | 0.232106i | −0.581465 | − | 0.813571i | \(-0.697520\pi\) |
0.813571 | + | 0.581465i | \(0.197520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 522.169i | 0.553732i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 50.9283 | 0.0538924 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1323.25 | − | 1323.25i | −1.39731 | − | 1.39731i | −0.807665 | − | 0.589642i | \(-0.799269\pi\) |
−0.589642 | − | 0.807665i | \(-0.700731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 205.732 | + | 205.732i | 0.216788 | + | 0.216788i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −229.961 | −0.241810 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1435.67i | 1.50647i | 0.657751 | + | 0.753235i | \(0.271508\pi\) | ||||
−0.657751 | + | 0.753235i | \(0.728492\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −553.962 | + | 553.962i | −0.580065 | + | 0.580065i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 109.074 | − | 109.074i | 0.113975 | − | 0.113975i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 257.194i | − | 0.268190i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1198.43 | −1.24706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 345.093 | + | 345.093i | 0.358352 | + | 0.358352i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 211.924 | + | 211.924i | 0.219611 | + | 0.219611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1507.98 | 1.55945 | 0.779723 | − | 0.626125i | \(-0.215360\pi\) | ||||
0.779723 | + | 0.626125i | \(0.215360\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 155.999i | 0.160990i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 137.835 | − | 137.835i | 0.141951 | − | 0.141951i | −0.632560 | − | 0.774511i | \(-0.717996\pi\) |
0.774511 | + | 0.632560i | \(0.217996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −271.478 | + | 271.478i | −0.279011 | + | 0.279011i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33.3837i | 0.0342397i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1819.85 | −1.86269 | −0.931346 | − | 0.364137i | \(-0.881364\pi\) | ||||
−0.931346 | + | 0.364137i | \(0.881364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −710.667 | − | 710.667i | −0.725912 | − | 0.725912i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.1638 | + | 11.1638i | 0.0113800 | + | 0.0113800i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 644.917 | 0.656070 | 0.328035 | − | 0.944666i | \(-0.393614\pi\) | ||||
0.328035 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 472.669i | 0.479867i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.1304 | + | 32.1304i | −0.0325536 | + | 0.0325536i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 617.110 | − | 617.110i | 0.623973 | − | 0.623973i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1660.16i | − | 1.67524i | −0.546252 | − | 0.837621i | \(-0.683946\pi\) | ||
0.546252 | − | 0.837621i | \(-0.316054\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −184.215 | −0.185514 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 485.987 | + | 485.987i | 0.488429 | + | 0.488429i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1038.21 | + | 1038.21i | 1.04134 | + | 1.04134i | 0.999108 | + | 0.0422293i | \(0.0134460\pi\) |
0.0422293 | + | 0.999108i | \(0.486554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −62.2573 | −0.0623197 |
(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 | 320.3.r.a.271.9 | 32 | ||
4.3 | odd | 2 | 80.3.r.a.11.1 | ✓ | 32 | ||
8.3 | odd | 2 | 640.3.r.a.31.9 | 32 | |||
8.5 | even | 2 | 640.3.r.b.31.8 | 32 | |||
16.3 | odd | 4 | inner | 320.3.r.a.111.9 | 32 | ||
16.5 | even | 4 | 640.3.r.a.351.9 | 32 | |||
16.11 | odd | 4 | 640.3.r.b.351.8 | 32 | |||
16.13 | even | 4 | 80.3.r.a.51.1 | yes | 32 | ||
20.3 | even | 4 | 400.3.k.g.299.10 | 32 | |||
20.7 | even | 4 | 400.3.k.h.299.7 | 32 | |||
20.19 | odd | 2 | 400.3.r.f.251.16 | 32 | |||
80.13 | odd | 4 | 400.3.k.h.99.7 | 32 | |||
80.29 | even | 4 | 400.3.r.f.51.16 | 32 | |||
80.77 | odd | 4 | 400.3.k.g.99.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.r.a.11.1 | ✓ | 32 | 4.3 | odd | 2 | ||
80.3.r.a.51.1 | yes | 32 | 16.13 | even | 4 | ||
320.3.r.a.111.9 | 32 | 16.3 | odd | 4 | inner | ||
320.3.r.a.271.9 | 32 | 1.1 | even | 1 | trivial | ||
400.3.k.g.99.10 | 32 | 80.77 | odd | 4 | |||
400.3.k.g.299.10 | 32 | 20.3 | even | 4 | |||
400.3.k.h.99.7 | 32 | 80.13 | odd | 4 | |||
400.3.k.h.299.7 | 32 | 20.7 | even | 4 | |||
400.3.r.f.51.16 | 32 | 80.29 | even | 4 | |||
400.3.r.f.251.16 | 32 | 20.19 | odd | 2 | |||
640.3.r.a.31.9 | 32 | 8.3 | odd | 2 | |||
640.3.r.a.351.9 | 32 | 16.5 | even | 4 | |||
640.3.r.b.31.8 | 32 | 8.5 | even | 2 | |||
640.3.r.b.351.8 | 32 | 16.11 | odd | 4 |