Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), 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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(3.72311 + 6.44862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.z.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −5.22311 | − | 9.04669i | −0.467169 | − | 0.809161i | 0.532127 | − | 0.846664i | \(-0.321393\pi\) |
−0.999296 | + | 0.0375035i | \(0.988059\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.4462 | + | 18.0934i | −0.330339 | + | 0.572163i | ||||
\(11\) | −30.5618 | + | 52.9346i | −0.837702 | + | 1.45094i | 0.0541093 | + | 0.998535i | \(0.482768\pi\) |
−0.891811 | + | 0.452407i | \(0.850565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.2311 | 1.26367 | 0.631837 | − | 0.775102i | \(-0.282301\pi\) | ||||
0.631837 | + | 0.775102i | \(0.282301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 10.2311 | − | 17.7208i | 0.145965 | − | 0.252819i | −0.783767 | − | 0.621054i | \(-0.786705\pi\) |
0.929733 | + | 0.368235i | \(0.120038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.1693 | − | 69.5753i | −0.485025 | − | 0.840088i | 0.514827 | − | 0.857294i | \(-0.327856\pi\) |
−0.999852 | + | 0.0172061i | \(0.994523\pi\) | |||||||
\(20\) | 41.7849 | 0.467169 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 122.247 | 1.18469 | ||||||||
\(23\) | 79.1236 | + | 137.046i | 0.717322 | + | 1.24244i | 0.962057 | + | 0.272848i | \(0.0879656\pi\) |
−0.244735 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.93822 | − | 13.7494i | 0.0635058 | − | 0.109995i | ||||
\(26\) | −59.2311 | − | 102.591i | −0.446776 | − | 0.773839i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −85.1236 | −0.545071 | −0.272535 | − | 0.962146i | \(-0.587862\pi\) | ||||
−0.272535 | + | 0.962146i | \(0.587862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 121.747 | − | 210.872i | 0.705369 | − | 1.22173i | −0.261190 | − | 0.965287i | \(-0.584115\pi\) |
0.966558 | − | 0.256447i | \(-0.0825518\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −40.9244 | −0.206426 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −145.185 | − | 251.468i | −0.645090 | − | 1.11733i | −0.984281 | − | 0.176611i | \(-0.943487\pi\) |
0.339191 | − | 0.940718i | \(-0.389847\pi\) | |||||||
\(38\) | −80.3387 | + | 139.151i | −0.342965 | + | 0.594032i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −41.7849 | − | 72.3735i | −0.165169 | − | 0.286082i | ||||
\(41\) | 168.000 | 0.639932 | 0.319966 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319966 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.62934 | 0.0270573 | 0.0135286 | − | 0.999908i | \(-0.495694\pi\) | ||||
0.0135286 | + | 0.999908i | \(0.495694\pi\) | |||||||
\(44\) | −122.247 | − | 211.738i | −0.418851 | − | 0.725471i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 158.247 | − | 274.092i | 0.507223 | − | 0.878536i | ||||
\(47\) | −84.6453 | − | 146.610i | −0.262698 | − | 0.455006i | 0.704260 | − | 0.709942i | \(-0.251279\pi\) |
−0.966958 | + | 0.254936i | \(0.917946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −31.7529 | −0.0898107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −118.462 | + | 205.183i | −0.315918 | + | 0.547187i | ||||
\(53\) | 125.056 | − | 216.603i | 0.324109 | − | 0.561373i | −0.657223 | − | 0.753696i | \(-0.728269\pi\) |
0.981332 | + | 0.192324i | \(0.0616023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 638.510 | 1.56539 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 85.1236 | + | 147.438i | 0.192712 | + | 0.333786i | ||||
\(59\) | −402.610 | + | 697.341i | −0.888395 | + | 1.53875i | −0.0466235 | + | 0.998913i | \(0.514846\pi\) |
−0.841772 | + | 0.539833i | \(0.818487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16.5858 | + | 28.7274i | 0.0348130 | + | 0.0602978i | 0.882907 | − | 0.469548i | \(-0.155583\pi\) |
−0.848094 | + | 0.529846i | \(0.822250\pi\) | |||||||
\(62\) | −486.988 | −0.997542 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −309.371 | − | 535.846i | −0.590349 | − | 1.02252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 138.691 | − | 240.220i | 0.252893 | − | 0.438023i | −0.711428 | − | 0.702759i | \(-0.751951\pi\) |
0.964321 | + | 0.264736i | \(0.0852847\pi\) | |||||||
\(68\) | 40.9244 | + | 70.8832i | 0.0729826 | + | 0.126410i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −631.506 | −1.05558 | −0.527788 | − | 0.849376i | \(-0.676979\pi\) | ||||
−0.527788 | + | 0.849376i | \(0.676979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −384.142 | + | 665.353i | −0.615896 | + | 1.06676i | 0.374331 | + | 0.927295i | \(0.377872\pi\) |
−0.990227 | + | 0.139468i | \(0.955461\pi\) | |||||||
\(74\) | −290.371 | + | 502.937i | −0.456147 | + | 0.790070i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 321.355 | 0.485025 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 209.365 | + | 362.631i | 0.298169 | + | 0.516445i | 0.975717 | − | 0.219034i | \(-0.0702906\pi\) |
−0.677548 | + | 0.735479i | \(0.736957\pi\) | |||||||
\(80\) | −83.5698 | + | 144.747i | −0.116792 | + | 0.202290i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −168.000 | − | 290.985i | −0.226250 | − | 0.391876i | ||||
\(83\) | 761.714 | 1.00734 | 0.503668 | − | 0.863897i | \(-0.331983\pi\) | ||||
0.503668 | + | 0.863897i | \(0.331983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −213.753 | −0.272762 | ||||||||
\(86\) | −7.62934 | − | 13.2144i | −0.00956619 | − | 0.0165691i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −244.494 | + | 423.476i | −0.296172 | + | 0.512986i | ||||
\(89\) | −786.048 | − | 1361.48i | −0.936190 | − | 1.62153i | −0.772498 | − | 0.635017i | \(-0.780993\pi\) |
−0.163692 | − | 0.986511i | \(-0.552340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −632.988 | −0.717322 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −169.291 | + | 293.220i | −0.185755 | + | 0.321738i | ||||
\(95\) | −419.618 | + | 726.799i | −0.453178 | + | 0.784927i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1045.16 | −1.09402 | −0.547012 | − | 0.837125i | \(-0.684235\pi\) | ||||
−0.547012 | + | 0.837125i | \(0.684235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 31.7529 | + | 54.9976i | 0.0317529 | + | 0.0549976i | ||||
\(101\) | 487.961 | − | 845.173i | 0.480732 | − | 0.832652i | −0.519024 | − | 0.854760i | \(-0.673704\pi\) |
0.999756 | + | 0.0221078i | \(0.00703770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −321.572 | − | 556.979i | −0.307626 | − | 0.532823i | 0.670217 | − | 0.742165i | \(-0.266201\pi\) |
−0.977842 | + | 0.209342i | \(0.932868\pi\) | |||||||
\(104\) | 473.849 | 0.446776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −500.224 | −0.458359 | ||||||||
\(107\) | 155.797 | + | 269.849i | 0.140762 | + | 0.243806i | 0.927784 | − | 0.373119i | \(-0.121712\pi\) |
−0.787022 | + | 0.616925i | \(0.788378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 932.915 | − | 1615.86i | 0.819790 | − | 1.41992i | −0.0860476 | − | 0.996291i | \(-0.527424\pi\) |
0.905837 | − | 0.423626i | \(-0.139243\pi\) | |||||||
\(110\) | −638.510 | − | 1105.93i | −0.553451 | − | 0.958604i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1720.49 | −1.43231 | −0.716153 | − | 0.697944i | \(-0.754099\pi\) | ||||
−0.716153 | + | 0.697944i | \(0.754099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 826.542 | − | 1431.61i | 0.670221 | − | 1.16086i | ||||
\(116\) | 170.247 | − | 294.877i | 0.136268 | − | 0.236022i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1610.44 | 1.25638 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1202.54 | − | 2082.87i | −0.903489 | − | 1.56489i | ||||
\(122\) | 33.1715 | − | 57.4548i | 0.0246165 | − | 0.0426370i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 486.988 | + | 843.489i | 0.352684 | + | 0.610867i | ||||
\(125\) | −1471.63 | −1.05301 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142.236 | 0.0993808 | 0.0496904 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496904 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −618.741 | + | 1071.69i | −0.417440 | + | 0.723027i | ||||
\(131\) | −1243.26 | − | 2153.38i | −0.829189 | − | 1.43620i | −0.898676 | − | 0.438614i | \(-0.855470\pi\) |
0.0694870 | − | 0.997583i | \(-0.477864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −554.764 | −0.357644 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 81.8489 | − | 141.766i | 0.0516065 | − | 0.0893851i | ||||
\(137\) | −1298.61 | + | 2249.25i | −0.809835 | + | 1.40268i | 0.103143 | + | 0.994667i | \(0.467110\pi\) |
−0.912978 | + | 0.408009i | \(0.866223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1600.52 | −0.976651 | −0.488325 | − | 0.872662i | \(-0.662392\pi\) | ||||
−0.488325 | + | 0.872662i | \(0.662392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 631.506 | + | 1093.80i | 0.373203 | + | 0.646406i | ||||
\(143\) | −1810.21 | + | 3135.37i | −1.05858 | + | 1.83352i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 444.610 | + | 770.087i | 0.254640 | + | 0.441050i | ||||
\(146\) | 1536.57 | 0.871008 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1161.48 | 0.645090 | ||||||||
\(149\) | −1468.85 | − | 2544.13i | −0.807605 | − | 1.39881i | −0.914518 | − | 0.404545i | \(-0.867430\pi\) |
0.106913 | − | 0.994268i | \(-0.465903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −911.662 | + | 1579.05i | −0.491325 | + | 0.850999i | −0.999950 | − | 0.00998867i | \(-0.996820\pi\) |
0.508625 | + | 0.860988i | \(0.330154\pi\) | |||||||
\(152\) | −321.355 | − | 556.603i | −0.171482 | − | 0.297016i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2543.59 | −1.31811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 316.824 | − | 548.755i | 0.161053 | − | 0.278952i | −0.774194 | − | 0.632949i | \(-0.781844\pi\) |
0.935247 | + | 0.353997i | \(0.115178\pi\) | |||||||
\(158\) | 418.730 | − | 725.261i | 0.210838 | − | 0.365182i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 334.279 | 0.165169 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 672.853 | + | 1165.42i | 0.323325 | + | 0.560015i | 0.981172 | − | 0.193137i | \(-0.0618660\pi\) |
−0.657847 | + | 0.753151i | \(0.728533\pi\) | |||||||
\(164\) | −336.000 | + | 581.969i | −0.159983 | + | 0.277098i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −761.714 | − | 1319.33i | −0.356147 | − | 0.616865i | ||||
\(167\) | −387.922 | −0.179750 | −0.0898751 | − | 0.995953i | \(-0.528647\pi\) | ||||
−0.0898751 | + | 0.995953i | \(0.528647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1311.32 | 0.596870 | ||||||||
\(170\) | 213.753 | + | 370.231i | 0.0964359 | + | 0.167032i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.2587 | + | 26.4288i | −0.00676432 | + | 0.0117161i | ||||
\(173\) | −311.330 | − | 539.239i | −0.136821 | − | 0.236980i | 0.789471 | − | 0.613788i | \(-0.210355\pi\) |
−0.926291 | + | 0.376808i | \(0.877022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 977.977 | 0.418851 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1572.10 | + | 2722.95i | −0.661986 | + | 1.14659i | ||||
\(179\) | 224.965 | − | 389.651i | 0.0939368 | − | 0.162703i | −0.815228 | − | 0.579141i | \(-0.803388\pi\) |
0.909164 | + | 0.416437i | \(0.136721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −184.353 | −0.0757063 | −0.0378532 | − | 0.999283i | \(-0.512052\pi\) | ||||
−0.0378532 | + | 0.999283i | \(0.512052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 632.988 | + | 1096.37i | 0.253612 | + | 0.439268i | ||||
\(185\) | −1516.64 | + | 2626.89i | −0.602732 | + | 1.04396i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 625.362 | + | 1083.16i | 0.244551 | + | 0.423574i | ||||
\(188\) | 677.163 | 0.262698 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1678.47 | 0.640890 | ||||||||
\(191\) | −175.483 | − | 303.945i | −0.0664789 | − | 0.115145i | 0.830870 | − | 0.556466i | \(-0.187843\pi\) |
−0.897349 | + | 0.441321i | \(0.854510\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −764.129 | + | 1323.51i | −0.284991 | + | 0.493619i | −0.972607 | − | 0.232456i | \(-0.925324\pi\) |
0.687616 | + | 0.726074i | \(0.258657\pi\) | |||||||
\(194\) | 1045.16 | + | 1810.28i | 0.386796 | + | 0.669950i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2874.65 | 1.03965 | 0.519823 | − | 0.854274i | \(-0.325998\pi\) | ||||
0.519823 | + | 0.854274i | \(0.325998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2474.35 | − | 4285.70i | 0.881418 | − | 1.52666i | 0.0316529 | − | 0.999499i | \(-0.489923\pi\) |
0.849765 | − | 0.527162i | \(-0.176744\pi\) | |||||||
\(200\) | 63.5058 | − | 109.995i | 0.0224527 | − | 0.0388892i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1951.84 | −0.679858 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −877.483 | − | 1519.84i | −0.298956 | − | 0.517808i | ||||
\(206\) | −643.144 | + | 1113.96i | −0.217524 | + | 0.376763i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −473.849 | − | 820.730i | −0.157959 | − | 0.273593i | ||||
\(209\) | 4910.58 | 1.62523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5280.90 | −1.72299 | −0.861497 | − | 0.507762i | \(-0.830473\pi\) | ||||
−0.861497 | + | 0.507762i | \(0.830473\pi\) | |||||||
\(212\) | 500.224 | + | 866.413i | 0.162054 | + | 0.280686i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 311.595 | − | 539.698i | 0.0995335 | − | 0.172397i | ||||
\(215\) | −39.8489 | − | 69.0203i | −0.0126403 | − | 0.0218937i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3731.66 | −1.15936 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1277.02 | + | 2211.86i | −0.391349 | + | 0.677836i | ||||
\(221\) | 606.000 | − | 1049.62i | 0.184452 | − | 0.319481i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3996.57 | −1.20013 | −0.600067 | − | 0.799950i | \(-0.704859\pi\) | ||||
−0.600067 | + | 0.799950i | \(0.704859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1720.49 | + | 2979.98i | 0.506396 | + | 0.877104i | ||||
\(227\) | 269.296 | − | 466.434i | 0.0787392 | − | 0.136380i | −0.823967 | − | 0.566638i | \(-0.808244\pi\) |
0.902706 | + | 0.430257i | \(0.141577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2085.80 | + | 3612.72i | 0.601895 | + | 1.04251i | 0.992534 | + | 0.121968i | \(0.0389206\pi\) |
−0.390639 | + | 0.920544i | \(0.627746\pi\) | |||||||
\(230\) | −3306.17 | −0.947836 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −680.988 | −0.192712 | ||||||||
\(233\) | 769.865 | + | 1333.45i | 0.216461 | + | 0.374922i | 0.953724 | − | 0.300684i | \(-0.0972151\pi\) |
−0.737262 | + | 0.675607i | \(0.763882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −884.224 | + | 1531.52i | −0.245449 | + | 0.425129i | ||||
\(236\) | −1610.44 | − | 2789.36i | −0.444198 | − | 0.769373i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3132.67 | −0.847848 | −0.423924 | − | 0.905698i | \(-0.639348\pi\) | ||||
−0.423924 | + | 0.905698i | \(0.639348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1303.35 | − | 2257.46i | 0.348365 | − | 0.603386i | −0.637594 | − | 0.770372i | \(-0.720070\pi\) |
0.985959 | + | 0.166987i | \(0.0534037\pi\) | |||||||
\(242\) | −2405.09 | + | 4165.74i | −0.638863 | + | 1.10654i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −132.686 | −0.0348130 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2379.27 | − | 4121.02i | −0.612913 | − | 1.06160i | ||||
\(248\) | 973.977 | − | 1686.98i | 0.249385 | − | 0.431948i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1471.63 | + | 2548.93i | 0.372295 | + | 0.644834i | ||||
\(251\) | −3426.24 | −0.861603 | −0.430801 | − | 0.902447i | \(-0.641769\pi\) | ||||
−0.430801 | + | 0.902447i | \(0.641769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9672.63 | −2.40361 | ||||||||
\(254\) | −142.236 | − | 246.359i | −0.0351364 | − | 0.0608581i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2928.72 | − | 5072.69i | −0.710850 | − | 1.23123i | −0.964538 | − | 0.263943i | \(-0.914977\pi\) |
0.253688 | − | 0.967286i | \(-0.418356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2474.97 | 0.590349 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2486.51 | + | 4306.76i | −0.586325 | + | 1.01554i | ||||
\(263\) | −542.965 | + | 940.443i | −0.127303 | + | 0.220495i | −0.922631 | − | 0.385684i | \(-0.873965\pi\) |
0.795328 | + | 0.606180i | \(0.207299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2612.73 | −0.605654 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 554.764 | + | 960.880i | 0.126446 | + | 0.219012i | ||||
\(269\) | 2789.73 | − | 4831.95i | 0.632315 | − | 1.09520i | −0.354763 | − | 0.934956i | \(-0.615438\pi\) |
0.987077 | − | 0.160245i | \(-0.0512283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −280.164 | − | 485.258i | −0.0627997 | − | 0.108772i | 0.832916 | − | 0.553399i | \(-0.186670\pi\) |
−0.895716 | + | 0.444627i | \(0.853336\pi\) | |||||||
\(272\) | −327.396 | −0.0729826 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5194.42 | 1.14528 | ||||||||
\(275\) | 485.212 | + | 840.413i | 0.106398 | + | 0.184286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2254.04 | − | 3904.11i | 0.488924 | − | 0.846842i | −0.510994 | − | 0.859584i | \(-0.670723\pi\) |
0.999919 | + | 0.0127421i | \(0.00405606\pi\) | |||||||
\(278\) | 1600.52 | + | 2772.19i | 0.345298 | + | 0.598074i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4329.75 | 0.919186 | 0.459593 | − | 0.888130i | \(-0.347995\pi\) | ||||
0.459593 | + | 0.888130i | \(0.347995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −435.526 | + | 754.353i | −0.0914817 | + | 0.158451i | −0.908135 | − | 0.418678i | \(-0.862494\pi\) |
0.816653 | + | 0.577129i | \(0.195827\pi\) | |||||||
\(284\) | 1263.01 | − | 2187.60i | 0.263894 | − | 0.457078i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7240.83 | 1.49706 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2247.15 | + | 3892.18i | 0.457388 | + | 0.792220i | ||||
\(290\) | 889.220 | − | 1540.17i | 0.180058 | − | 0.311869i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1536.57 | − | 2661.41i | −0.307948 | − | 0.533381i | ||||
\(293\) | 1651.91 | 0.329372 | 0.164686 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164686 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8411.50 | 1.66012 | ||||||||
\(296\) | −1161.48 | − | 2011.75i | −0.228074 | − | 0.395035i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2937.71 | + | 5088.26i | −0.571063 | + | 0.989110i | ||||
\(299\) | 4686.58 | + | 8117.39i | 0.906460 | + | 1.57004i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3646.65 | 0.694838 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −642.709 | + | 1113.21i | −0.121256 | + | 0.210022i | ||||
\(305\) | 173.259 | − | 300.093i | 0.0325271 | − | 0.0563386i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1016.42 | −0.188958 | −0.0944791 | − | 0.995527i | \(-0.530119\pi\) | ||||
−0.0944791 | + | 0.995527i | \(0.530119\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2543.59 | + | 4405.64i | 0.466021 | + | 0.807172i | ||||
\(311\) | 4596.53 | − | 7961.42i | 0.838087 | − | 1.45161i | −0.0534049 | − | 0.998573i | \(-0.517007\pi\) |
0.891492 | − | 0.453037i | \(-0.149659\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3346.30 | − | 5795.97i | −0.604295 | − | 1.04667i | −0.992162 | − | 0.124954i | \(-0.960122\pi\) |
0.387868 | − | 0.921715i | \(-0.373212\pi\) | |||||||
\(314\) | −1267.30 | −0.227763 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1674.92 | −0.298169 | ||||||||
\(317\) | 3526.25 | + | 6107.64i | 0.624775 | + | 1.08214i | 0.988584 | + | 0.150669i | \(0.0481426\pi\) |
−0.363809 | + | 0.931473i | \(0.618524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2601.53 | − | 4505.98i | 0.456607 | − | 0.790866i | ||||
\(320\) | −334.279 | − | 578.988i | −0.0583962 | − | 0.101145i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1643.91 | −0.283187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 470.190 | − | 814.393i | 0.0802506 | − | 0.138998i | ||||
\(326\) | 1345.71 | − | 2330.83i | 0.228625 | − | 0.395990i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1344.00 | 0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1570.19 | − | 2719.64i | −0.260741 | − | 0.451616i | 0.705698 | − | 0.708513i | \(-0.250633\pi\) |
−0.966439 | + | 0.256896i | \(0.917300\pi\) | |||||||
\(332\) | −1523.43 | + | 2638.65i | −0.251834 | + | 0.436190i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 387.922 | + | 671.900i | 0.0635513 | + | 0.110074i | ||||
\(335\) | −2897.60 | −0.472575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2743.87 | 0.443526 | 0.221763 | − | 0.975101i | \(-0.428819\pi\) | ||||
0.221763 | + | 0.975101i | \(0.428819\pi\) | |||||||
\(338\) | −1311.32 | − | 2271.28i | −0.211026 | − | 0.365507i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 427.506 | − | 740.462i | 0.0681905 | − | 0.118109i | ||||
\(341\) | 7441.62 | + | 12889.3i | 1.18178 | + | 2.04690i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 61.0347 | 0.00956619 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −622.660 | + | 1078.48i | −0.0967468 | + | 0.167570i | ||||
\(347\) | 5218.45 | − | 9038.62i | 0.807323 | − | 1.39832i | −0.107389 | − | 0.994217i | \(-0.534249\pi\) |
0.914712 | − | 0.404107i | \(-0.132418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2257.01 | 0.346175 | 0.173087 | − | 0.984906i | \(-0.444626\pi\) | ||||
0.173087 | + | 0.984906i | \(0.444626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −977.977 | − | 1693.91i | −0.148086 | − | 0.256493i | ||||
\(353\) | −2808.22 | + | 4863.98i | −0.423418 | + | 0.733381i | −0.996271 | − | 0.0862770i | \(-0.972503\pi\) |
0.572854 | + | 0.819658i | \(0.305836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3298.42 | + | 5713.04i | 0.493133 | + | 0.854131i | ||||
\(356\) | 6288.38 | 0.936190 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −899.861 | −0.132847 | ||||||||
\(359\) | −397.795 | − | 689.002i | −0.0584815 | − | 0.101293i | 0.835302 | − | 0.549791i | \(-0.185293\pi\) |
−0.893784 | + | 0.448498i | \(0.851959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 202.349 | − | 350.479i | 0.0295013 | − | 0.0510977i | ||||
\(362\) | 184.353 | + | 319.309i | 0.0267662 | + | 0.0463605i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8025.66 | 1.15091 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4096.99 | − | 7096.19i | 0.582727 | − | 1.00931i | −0.412427 | − | 0.910990i | \(-0.635319\pi\) |
0.995155 | − | 0.0983227i | \(-0.0313477\pi\) | |||||||
\(368\) | 1265.98 | − | 2192.74i | 0.179330 | − | 0.310609i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6066.55 | 0.852392 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7038.69 | − | 12191.4i | −0.977076 | − | 1.69235i | −0.672906 | − | 0.739728i | \(-0.734954\pi\) |
−0.304170 | − | 0.952618i | \(-0.598379\pi\) | |||||||
\(374\) | 1250.72 | − | 2166.32i | 0.172923 | − | 0.299512i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −677.163 | − | 1172.88i | −0.0928777 | − | 0.160869i | ||||
\(377\) | −5041.96 | −0.688791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6221.22 | 0.843173 | 0.421587 | − | 0.906788i | \(-0.361473\pi\) | ||||
0.421587 | + | 0.906788i | \(0.361473\pi\) | |||||||
\(380\) | −1678.47 | − | 2907.20i | −0.226589 | − | 0.392463i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −350.965 | + | 607.890i | −0.0470077 | + | 0.0814197i | ||||
\(383\) | 5350.71 | + | 9267.70i | 0.713860 | + | 1.23644i | 0.963397 | + | 0.268077i | \(0.0863883\pi\) |
−0.249537 | + | 0.968365i | \(0.580278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3056.52 | 0.403038 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2090.33 | − | 3620.56i | 0.273506 | − | 0.473726i | ||||
\(389\) | 2110.81 | − | 3656.03i | 0.275121 | − | 0.476524i | −0.695044 | − | 0.718967i | \(-0.744615\pi\) |
0.970166 | + | 0.242443i | \(0.0779487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3238.09 | 0.418816 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2874.65 | − | 4979.04i | −0.367570 | − | 0.636651i | ||||
\(395\) | 2187.07 | − | 3788.12i | 0.278591 | − | 0.482534i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6037.87 | − | 10457.9i | −0.763305 | − | 1.32208i | −0.941138 | − | 0.338023i | \(-0.890242\pi\) |
0.177833 | − | 0.984061i | \(-0.443091\pi\) | |||||||
\(398\) | −9897.41 | −1.24651 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −254.023 | −0.0317529 | ||||||||
\(401\) | −2753.19 | − | 4768.66i | −0.342862 | − | 0.593855i | 0.642101 | − | 0.766620i | \(-0.278063\pi\) |
−0.984963 | + | 0.172766i | \(0.944730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7211.22 | − | 12490.2i | 0.891356 | − | 1.54387i | ||||
\(404\) | 1951.84 | + | 3380.69i | 0.240366 | + | 0.416326i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17748.5 | 2.16157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 714.089 | − | 1236.84i | 0.0863311 | − | 0.149530i | −0.819627 | − | 0.572898i | \(-0.805819\pi\) |
0.905958 | + | 0.423368i | \(0.139152\pi\) | |||||||
\(410\) | −1754.97 | + | 3039.69i | −0.211394 | + | 0.366145i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2572.58 | 0.307626 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3978.52 | − | 6890.99i | −0.470597 | − | 0.815097i | ||||
\(416\) | −947.698 | + | 1641.46i | −0.111694 | + | 0.193460i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4910.58 | − | 8505.38i | −0.574604 | − | 0.995244i | ||||
\(419\) | 264.960 | 0.0308929 | 0.0154465 | − | 0.999881i | \(-0.495083\pi\) | ||||
0.0154465 | + | 0.999881i | \(0.495083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −281.066 | −0.0325375 | −0.0162688 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162688 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(422\) | 5280.90 | + | 9146.78i | 0.609171 | + | 1.05511i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1000.45 | − | 1732.83i | 0.114590 | − | 0.198475i | ||||
\(425\) | −162.434 | − | 281.343i | −0.0185393 | − | 0.0321110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1246.38 | −0.140762 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −79.6978 | + | 138.041i | −0.00893806 | + | 0.0154812i | ||||
\(431\) | −893.189 | + | 1547.05i | −0.0998223 | + | 0.172897i | −0.911611 | − | 0.411054i | \(-0.865161\pi\) |
0.811789 | + | 0.583951i | \(0.198494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −184.621 | −0.0204904 | −0.0102452 | − | 0.999948i | \(-0.503261\pi\) | ||||
−0.0102452 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3731.66 | + | 6463.43i | 0.409895 | + | 0.709959i | ||||
\(437\) | 6356.68 | − | 11010.1i | 0.695838 | − | 1.20523i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5637.32 | + | 9764.12i | 0.612881 | + | 1.06154i | 0.990752 | + | 0.135682i | \(0.0433227\pi\) |
−0.377872 | + | 0.925858i | \(0.623344\pi\) | |||||||
\(440\) | 5108.08 | 0.553451 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2424.00 | −0.260855 | ||||||||
\(443\) | 3984.92 | + | 6902.09i | 0.427380 | + | 0.740244i | 0.996639 | − | 0.0819142i | \(-0.0261033\pi\) |
−0.569259 | + | 0.822158i | \(0.692770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8211.23 | + | 14222.3i | −0.874718 | + | 1.51506i | ||||
\(446\) | 3996.57 | + | 6922.25i | 0.424311 | + | 0.734929i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8850.37 | −0.930233 | −0.465117 | − | 0.885249i | \(-0.653988\pi\) | ||||
−0.465117 | + | 0.885249i | \(0.653988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5134.38 | + | 8893.00i | −0.536072 | + | 0.928504i | ||||
\(452\) | 3440.99 | − | 5959.97i | 0.358076 | − | 0.620206i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1077.18 | −0.111354 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6513.65 | + | 11282.0i | 0.666730 | + | 1.15481i | 0.978813 | + | 0.204756i | \(0.0656400\pi\) |
−0.312083 | + | 0.950055i | \(0.601027\pi\) | |||||||
\(458\) | 4171.61 | − | 7225.44i | 0.425604 | − | 0.737167i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3306.17 | + | 5726.45i | 0.335111 | + | 0.580429i | ||||
\(461\) | 1261.05 | 0.127403 | 0.0637016 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637016 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4005.47 | −0.402052 | −0.201026 | − | 0.979586i | \(-0.564427\pi\) | ||||
−0.201026 | + | 0.979586i | \(0.564427\pi\) | |||||||
\(464\) | 680.988 | + | 1179.51i | 0.0681338 | + | 0.118011i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1539.73 | − | 2666.89i | 0.153061 | − | 0.265110i | ||||
\(467\) | −8548.91 | − | 14807.1i | −0.847101 | − | 1.46722i | −0.883784 | − | 0.467895i | \(-0.845012\pi\) |
0.0366825 | − | 0.999327i | \(-0.488321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3536.90 | 0.347117 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3220.88 | + | 5578.72i | −0.314095 | + | 0.544029i | ||||
\(473\) | −233.166 | + | 403.856i | −0.0226659 | + | 0.0392586i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1275.49 | −0.123208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3132.67 | + | 5425.95i | 0.299760 | + | 0.519199i | ||||
\(479\) | −5844.26 | + | 10122.6i | −0.557477 | + | 0.965578i | 0.440230 | + | 0.897885i | \(0.354897\pi\) |
−0.997706 | + | 0.0676925i | \(0.978436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8599.49 | − | 14894.8i | −0.815183 | − | 1.41194i | ||||
\(482\) | −5213.39 | −0.492662 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9620.36 | 0.903489 | ||||||||
\(485\) | 5459.01 | + | 9455.28i | 0.511095 | + | 0.885242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4812.40 | − | 8335.31i | 0.447783 | − | 0.775583i | −0.550458 | − | 0.834863i | \(-0.685547\pi\) |
0.998241 | + | 0.0592793i | \(0.0188803\pi\) | |||||||
\(488\) | 132.686 | + | 229.819i | 0.0123082 | + | 0.0213185i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6320.63 | 0.580949 | 0.290475 | − | 0.956883i | \(-0.406187\pi\) | ||||
0.290475 | + | 0.956883i | \(0.406187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −870.908 | + | 1508.46i | −0.0795613 | + | 0.137804i | ||||
\(494\) | −4758.55 | + | 8242.05i | −0.433395 | + | 0.750662i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3895.91 | −0.352684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7527.29 | + | 13037.6i | 0.675286 | + | 1.16963i | 0.976385 | + | 0.216037i | \(0.0693130\pi\) |
−0.301100 | + | 0.953593i | \(0.597354\pi\) | |||||||
\(500\) | 2943.25 | − | 5097.86i | 0.263253 | − | 0.455967i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3426.24 | + | 5934.42i | 0.304623 | + | 0.527622i | ||||
\(503\) | 16559.1 | 1.46786 | 0.733930 | − | 0.679225i | \(-0.237684\pi\) | ||||
0.733930 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10194.7 | −0.898333 | ||||||||
\(506\) | 9672.63 | + | 16753.5i | 0.849804 | + | 1.47190i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −284.471 | + | 492.718i | −0.0248452 | + | 0.0430332i | ||||
\(509\) | 6669.48 | + | 11551.9i | 0.580785 | + | 1.00595i | 0.995387 | + | 0.0959462i | \(0.0305877\pi\) |
−0.414601 | + | 0.910003i | \(0.636079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5857.44 | + | 10145.4i | −0.502647 | + | 0.870610i | ||||
\(515\) | −3359.21 | + | 5818.33i | −0.287426 | + | 0.497837i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10347.6 | 0.880250 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2474.97 | − | 4286.77i | −0.208720 | − | 0.361514i | ||||
\(521\) | 3591.35 | − | 6220.40i | 0.301996 | − | 0.523072i | −0.674592 | − | 0.738191i | \(-0.735680\pi\) |
0.976588 | + | 0.215118i | \(0.0690138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4815.07 | + | 8339.94i | 0.402578 | + | 0.697285i | 0.994036 | − | 0.109050i | \(-0.0347810\pi\) |
−0.591459 | + | 0.806335i | \(0.701448\pi\) | |||||||
\(524\) | 9946.04 | 0.829189 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2171.86 | 0.180034 | ||||||||
\(527\) | −2491.22 | − | 4314.91i | −0.205919 | − | 0.356661i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6437.57 | + | 11150.2i | −0.529101 | + | 0.916430i | ||||
\(530\) | 2612.73 | + | 4525.37i | 0.214131 | + | 0.370886i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9950.83 | 0.808664 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1627.49 | − | 2818.90i | 0.131519 | − | 0.227798i | ||||
\(536\) | 1109.53 | − | 1921.76i | 0.0894111 | − | 0.154865i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11158.9 | −0.894228 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7774.74 | − | 13466.2i | −0.617860 | − | 1.07016i | −0.989875 | − | 0.141938i | \(-0.954667\pi\) |
0.372016 | − | 0.928227i | \(-0.378667\pi\) | |||||||
\(542\) | −560.327 | + | 970.515i | −0.0444061 | + | 0.0769136i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 327.396 | + | 567.066i | 0.0258032 | + | 0.0446925i | ||||
\(545\) | −19490.9 | −1.53192 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5917.38 | −0.462539 | −0.231270 | − | 0.972890i | \(-0.574288\pi\) | ||||
−0.231270 | + | 0.972890i | \(0.574288\pi\) | |||||||
\(548\) | −5194.42 | − | 8997.01i | −0.404918 | − | 0.701338i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 970.425 | − | 1680.83i | 0.0752346 | − | 0.130310i | ||||
\(551\) | 3419.36 | + | 5922.50i | 0.264373 | + | 0.457907i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9016.15 | −0.691444 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3201.04 | − | 5544.37i | 0.244163 | − | 0.422902i | ||||
\(557\) | 1065.93 | − | 1846.25i | 0.0810862 | − | 0.140445i | −0.822631 | − | 0.568576i | \(-0.807494\pi\) |
0.903717 | + | 0.428131i | \(0.140828\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 451.894 | 0.0341916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4329.75 | − | 7499.35i | −0.324981 | − | 0.562884i | ||||
\(563\) | 3687.95 | − | 6387.72i | 0.276072 | − | 0.478171i | −0.694333 | − | 0.719654i | \(-0.744300\pi\) |
0.970405 | + | 0.241483i | \(0.0776337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8986.33 | + | 15564.8i | 0.669129 | + | 1.15897i | ||||
\(566\) | 1742.10 | 0.129375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5052.05 | −0.373203 | ||||||||
\(569\) | −6350.42 | − | 10999.3i | −0.467880 | − | 0.810391i | 0.531447 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0367005i | \(0.988315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3845.06 | − | 6659.84i | 0.281805 | − | 0.488101i | −0.690024 | − | 0.723786i | \(-0.742400\pi\) |
0.971829 | + | 0.235686i | \(0.0757335\pi\) | |||||||
\(572\) | −7240.83 | − | 12541.5i | −0.529291 | − | 0.916759i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2512.40 | 0.182216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1547.43 | − | 2680.23i | 0.111647 | − | 0.193379i | −0.804787 | − | 0.593563i | \(-0.797721\pi\) |
0.916435 | + | 0.400185i | \(0.131054\pi\) | |||||||
\(578\) | 4494.30 | − | 7784.35i | 0.323422 | − | 0.560184i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3556.88 | −0.254640 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7643.87 | + | 13239.6i | 0.543013 | + | 0.940526i | ||||
\(584\) | −3073.13 | + | 5322.82i | −0.217752 | + | 0.377158i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1651.91 | − | 2861.20i | −0.116450 | − | 0.201698i | ||||
\(587\) | −9967.83 | −0.700880 | −0.350440 | − | 0.936585i | \(-0.613968\pi\) | ||||
−0.350440 | + | 0.936585i | \(0.613968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19562.0 | −1.36849 | ||||||||
\(590\) | −8411.50 | − | 14569.1i | −0.586942 | − | 1.01661i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2322.97 | + | 4023.49i | −0.161272 | + | 0.279332i | ||||
\(593\) | −884.864 | − | 1532.63i | −0.0612766 | − | 0.106134i | 0.833760 | − | 0.552127i | \(-0.186184\pi\) |
−0.895036 | + | 0.445993i | \(0.852851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11750.8 | 0.807605 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9373.15 | − | 16234.8i | 0.640964 | − | 1.11018i | ||||
\(599\) | −3173.66 | + | 5496.95i | −0.216481 | + | 0.374957i | −0.953730 | − | 0.300665i | \(-0.902791\pi\) |
0.737248 | + | 0.675622i | \(0.236125\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22005.7 | −1.49356 | −0.746781 | − | 0.665070i | \(-0.768401\pi\) | ||||
−0.746781 | + | 0.665070i | \(0.768401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3646.65 | − | 6316.18i | −0.245662 | − | 0.425500i | ||||
\(605\) | −12562.0 | + | 21758.1i | −0.844165 | + | 1.46214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8853.55 | + | 15334.8i | 0.592017 | + | 1.02540i | 0.993960 | + | 0.109740i | \(0.0350017\pi\) |
−0.401943 | + | 0.915665i | \(0.631665\pi\) | |||||||
\(608\) | 2570.84 | 0.171482 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −693.035 | −0.0460003 | ||||||||
\(611\) | −5013.64 | − | 8683.87i | −0.331964 | − | 0.574979i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7923.32 | + | 13723.6i | −0.522055 | + | 0.904226i | 0.477616 | + | 0.878569i | \(0.341501\pi\) |
−0.999671 | + | 0.0256570i | \(0.991832\pi\) | |||||||
\(614\) | 1016.42 | + | 1760.49i | 0.0668068 | + | 0.115713i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29473.4 | −1.92311 | −0.961553 | − | 0.274621i | \(-0.911448\pi\) | ||||
−0.961553 | + | 0.274621i | \(0.911448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5763.74 | − | 9983.08i | 0.374255 | − | 0.648229i | −0.615960 | − | 0.787778i | \(-0.711232\pi\) |
0.990215 | + | 0.139548i | \(0.0445650\pi\) | |||||||
\(620\) | 5087.19 | − | 8811.27i | 0.329527 | − | 0.570757i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18386.1 | −1.18523 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6694.19 | + | 11594.7i | 0.428428 | + | 0.742059i | ||||
\(626\) | −6692.61 | + | 11591.9i | −0.427301 | + | 0.740107i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1267.30 | + | 2195.02i | 0.0805265 | + | 0.139476i | ||||
\(629\) | −5941.63 | −0.376643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25846.1 | 1.63062 | 0.815308 | − | 0.579027i | \(-0.196568\pi\) | ||||
0.815308 | + | 0.579027i | \(0.196568\pi\) | |||||||
\(632\) | 1674.92 | + | 2901.04i | 0.105419 | + | 0.182591i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7052.49 | − | 12215.3i | 0.441783 | − | 0.765190i | ||||
\(635\) | −742.912 | − | 1286.76i | −0.0464277 | − | 0.0804151i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10406.1 | −0.645739 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −668.558 | + | 1157.98i | −0.0412923 | + | 0.0715204i | ||||
\(641\) | 2767.39 | − | 4793.26i | 0.170523 | − | 0.295355i | −0.768080 | − | 0.640354i | \(-0.778788\pi\) |
0.938603 | + | 0.344999i | \(0.112121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1634.56 | −0.100250 | −0.0501251 | − | 0.998743i | \(-0.515962\pi\) | ||||
−0.0501251 | + | 0.998743i | \(0.515962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1643.91 | + | 2847.33i | 0.100122 | + | 0.173416i | ||||
\(647\) | −3769.00 | + | 6528.10i | −0.229018 | + | 0.396671i | −0.957517 | − | 0.288375i | \(-0.906885\pi\) |
0.728499 | + | 0.685047i | \(0.240218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24608.9 | − | 42623.9i | −1.48842 | − | 2.57802i | ||||
\(650\) | −1880.76 | −0.113491 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5382.83 | −0.323325 | ||||||||
\(653\) | −6656.09 | − | 11528.7i | −0.398887 | − | 0.690892i | 0.594702 | − | 0.803946i | \(-0.297270\pi\) |
−0.993589 | + | 0.113054i | \(0.963937\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12987.3 | + | 22494.7i | −0.774743 | + | 1.34189i | ||||
\(656\) | −1344.00 | − | 2327.88i | −0.0799914 | − | 0.138549i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10962.0 | −0.647981 | −0.323991 | − | 0.946060i | \(-0.605025\pi\) | ||||
−0.323991 | + | 0.946060i | \(0.605025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11816.3 | + | 20466.4i | −0.695309 | + | 1.20431i | 0.274767 | + | 0.961511i | \(0.411399\pi\) |
−0.970076 | + | 0.242800i | \(0.921934\pi\) | |||||||
\(662\) | −3140.37 | + | 5439.28i | −0.184372 | + | 0.319341i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6093.71 | 0.356147 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6735.28 | − | 11665.8i | −0.390991 | − | 0.677216i | ||||
\(668\) | 775.843 | − | 1343.80i | 0.0449376 | − | 0.0778341i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2897.60 | + | 5018.78i | 0.167080 | + | 0.289392i | ||||
\(671\) | −2027.56 | −0.116652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23483.0 | 1.34503 | 0.672513 | − | 0.740085i | \(-0.265215\pi\) | ||||
0.672513 | + | 0.740085i | \(0.265215\pi\) | |||||||
\(674\) | −2743.87 | − | 4752.53i | −0.156810 | − | 0.271603i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2622.65 | + | 4542.56i | −0.149218 | + | 0.258452i | ||||
\(677\) | −12336.2 | − | 21367.0i | −0.700325 | − | 1.21300i | −0.968352 | − | 0.249587i | \(-0.919705\pi\) |
0.268028 | − | 0.963411i | \(-0.413628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1710.02 | −0.0964359 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14883.2 | − | 25778.5i | 0.835643 | − | 1.44738i | ||||
\(683\) | 4469.73 | − | 7741.80i | 0.250409 | − | 0.433721i | −0.713229 | − | 0.700931i | \(-0.752768\pi\) |
0.963638 | + | 0.267209i | \(0.0861016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27131.1 | 1.51332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −61.0347 | − | 105.715i | −0.00338216 | − | 0.00585807i | ||||
\(689\) | 7407.21 | − | 12829.7i | 0.409568 | − | 0.709392i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7555.03 | + | 13085.7i | 0.415929 | + | 0.720410i | 0.995525 | − | 0.0944937i | \(-0.0301232\pi\) |
−0.579597 | + | 0.814904i | \(0.696790\pi\) | |||||||
\(692\) | 2490.64 | 0.136821 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20873.8 | −1.14173 | ||||||||
\(695\) | 8359.70 | + | 14479.4i | 0.456261 | + | 0.790268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1718.83 | − | 2977.09i | 0.0934077 | − | 0.161787i | ||||
\(698\) | −2257.01 | − | 3909.26i | −0.122391 | − | 0.211988i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18353.3 | −0.988865 | −0.494432 | − | 0.869216i | \(-0.664624\pi\) | ||||
−0.494432 | + | 0.869216i | \(0.664624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11664.0 | + | 20202.6i | −0.625769 | + | 1.08386i | ||||
\(704\) | −1955.95 | + | 3387.81i | −0.104713 | + | 0.181368i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11232.9 | 0.598803 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5036.85 | + | 8724.07i | 0.266802 | + | 0.462115i | 0.968034 | − | 0.250818i | \(-0.0806997\pi\) |
−0.701232 | + | 0.712933i | \(0.747366\pi\) | |||||||
\(710\) | 6596.85 | − | 11426.1i | 0.348698 | − | 0.603962i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6288.38 | − | 10891.8i | −0.330993 | − | 0.573297i | ||||
\(713\) | 38532.3 | 2.02391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37819.7 | 1.97815 | ||||||||
\(716\) | 899.861 | + | 1558.61i | 0.0469684 | + | 0.0813517i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −795.591 | + | 1378.00i | −0.0413526 | + | 0.0716249i | ||||
\(719\) | −9944.63 | − | 17224.6i | −0.515817 | − | 0.893420i | −0.999831 | − | 0.0183607i | \(-0.994155\pi\) |
0.484015 | − | 0.875060i | \(-0.339178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −809.397 | −0.0417211 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 368.706 | − | 638.617i | 0.0189266 | − | 0.0327818i | ||||
\(725\) | −675.730 | + | 1170.40i | −0.0346151 | + | 0.0599552i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13403.5 | −0.683780 | −0.341890 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341890 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8025.66 | − | 13900.9i | −0.406908 | − | 0.704786i | ||||
\(731\) | 78.0566 | − | 135.198i | 0.00394942 | − | 0.00684060i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6627.50 | + | 11479.2i | 0.333960 | + | 0.578435i | 0.983284 | − | 0.182076i | \(-0.0582817\pi\) |
−0.649325 | + | 0.760511i | \(0.724948\pi\) | |||||||
\(734\) | −16387.9 | −0.824101 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5063.91 | −0.253612 | ||||||||
\(737\) | 8477.29 | + | 14683.1i | 0.423698 | + | 0.733866i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7710.19 | + | 13354.4i | −0.383794 | + | 0.664751i | −0.991601 | − | 0.129334i | \(-0.958716\pi\) |
0.607807 | + | 0.794085i | \(0.292049\pi\) | |||||||
\(740\) | −6066.55 | − | 10507.6i | −0.301366 | − | 0.521981i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −943.019 | −0.0465626 | −0.0232813 | − | 0.999729i | \(-0.507411\pi\) | ||||
−0.0232813 | + | 0.999729i | \(0.507411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15344.0 | + | 26576.5i | −0.754576 | + | 1.30696i | ||||
\(746\) | −14077.4 | + | 24382.7i | −0.690897 | + | 1.19667i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5002.89 | −0.244551 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14297.9 | + | 24764.7i | 0.694726 | + | 1.20330i | 0.970273 | + | 0.242013i | \(0.0778076\pi\) |
−0.275547 | + | 0.961287i | \(0.588859\pi\) | |||||||
\(752\) | −1354.33 | + | 2345.76i | −0.0656744 | + | 0.113751i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5041.96 | + | 8732.94i | 0.243524 | + | 0.421797i | ||||
\(755\) | 19046.9 | 0.918127 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28984.4 | −1.39162 | −0.695810 | − | 0.718226i | \(-0.744955\pi\) | ||||
−0.695810 | + | 0.718226i | \(0.744955\pi\) | |||||||
\(758\) | −6221.22 | − | 10775.5i | −0.298107 | − | 0.516336i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3356.94 | + | 5814.39i | −0.160222 | + | 0.277513i | ||||
\(761\) | −4465.05 | − | 7733.70i | −0.212691 | − | 0.368392i | 0.739865 | − | 0.672756i | \(-0.234890\pi\) |
−0.952556 | + | 0.304364i | \(0.901556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1403.86 | 0.0664789 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10701.4 | − | 18535.4i | 0.504776 | − | 0.874297i | ||||
\(767\) | −23847.0 | + | 41304.3i | −1.12264 | + | 1.94447i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2373.15 | −0.111285 | −0.0556424 | − | 0.998451i | \(-0.517721\pi\) | ||||
−0.0556424 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3056.52 | − | 5294.04i | −0.142495 | − | 0.246809i | ||||
\(773\) | −13988.5 | + | 24228.8i | −0.650881 | + | 1.12736i | 0.332029 | + | 0.943269i | \(0.392267\pi\) |
−0.982909 | + | 0.184089i | \(0.941066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1932.91 | − | 3347.90i | −0.0895900 | − | 0.155174i | ||||
\(776\) | −8361.32 | −0.386796 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8443.23 | −0.389080 | ||||||||
\(779\) | −6748.45 | − | 11688.7i | −0.310383 | − | 0.537599i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19299.9 | − | 33428.5i | 0.884259 | − | 1.53158i | ||||
\(782\) | −3238.09 | − | 5608.53i | −0.148074 | − | 0.256471i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6619.23 | −0.300956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17180.5 | − | 29757.4i | 0.778167 | − | 1.34782i | −0.154831 | − | 0.987941i | \(-0.549483\pi\) |
0.932997 | − | 0.359883i | \(-0.117183\pi\) | |||||||
\(788\) | −5749.30 | + | 9958.08i | −0.259911 | + | 0.450180i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8748.29 | −0.393987 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 982.394 | + | 1701.56i | 0.0439922 | + | 0.0761968i | ||||
\(794\) | −12075.7 | + | 20915.8i | −0.539738 | + | 0.934854i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9897.41 | + | 17142.8i | 0.440709 | + | 0.763330i | ||||
\(797\) | −10399.5 | −0.462196 | −0.231098 | − | 0.972930i | \(-0.574232\pi\) | ||||
−0.231098 | + | 0.972930i | \(0.574232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3464.06 | −0.153379 | ||||||||
\(800\) | 254.023 | + | 439.981i | 0.0112263 | + | 0.0194446i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5506.38 | + | 9537.33i | −0.242440 | + | 0.419919i | ||||
\(803\) | −23480.1 | − | 40668.7i | −1.03187 | − | 1.78726i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28844.9 | −1.26057 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3903.69 | − | 6761.38i | 0.169964 | − | 0.294387i | ||||
\(809\) | −8971.53 | + | 15539.1i | −0.389891 | + | 0.675312i | −0.992435 | − | 0.122775i | \(-0.960821\pi\) |
0.602543 | + | 0.798086i | \(0.294154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 571.663 | 0.0247519 | 0.0123760 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123760 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17748.5 | − | 30741.3i | −0.764231 | − | 1.32369i | ||||
\(815\) | 7028.78 | − | 12174.2i | 0.302095 | − | 0.523244i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −306.465 | − | 530.814i | −0.0131235 | − | 0.0227305i | ||||
\(818\) | −2856.36 | −0.122091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7019.86 | 0.298956 | ||||||||
\(821\) | 6947.84 | + | 12034.0i | 0.295349 | + | 0.511559i | 0.975066 | − | 0.221915i | \(-0.0712308\pi\) |
−0.679717 | + | 0.733474i | \(0.737897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10814.6 | − | 18731.5i | 0.458049 | − | 0.793364i | −0.540809 | − | 0.841145i | \(-0.681882\pi\) |
0.998858 | + | 0.0477816i | \(0.0152152\pi\) | |||||||
\(824\) | −2572.58 | − | 4455.83i | −0.108762 | − | 0.188381i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4700.10 | −0.197628 | −0.0988140 | − | 0.995106i | \(-0.531505\pi\) | ||||
−0.0988140 | + | 0.995106i | \(0.531505\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19055.4 | + | 33004.9i | −0.798337 | + | 1.38276i | 0.122361 | + | 0.992486i | \(0.460953\pi\) |
−0.920698 | + | 0.390275i | \(0.872380\pi\) | |||||||
\(830\) | −7957.03 | + | 13782.0i | −0.332762 | + | 0.576361i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3790.79 | 0.157959 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2026.16 | + | 3509.41i | 0.0839738 | + | 0.145447i | ||||
\(836\) | −9821.17 | + | 17010.8i | −0.406307 | + | 0.703744i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −264.960 | − | 458.924i | −0.0109223 | − | 0.0189180i | ||||
\(839\) | 20080.2 | 0.826277 | 0.413138 | − | 0.910668i | \(-0.364433\pi\) | ||||
0.413138 | + | 0.910668i | \(0.364433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17143.0 | −0.702898 | ||||||||
\(842\) | 281.066 | + | 486.820i | 0.0115038 | + | 0.0199251i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10561.8 | − | 18293.6i | 0.430749 | − | 0.746079i | ||||
\(845\) | −6849.19 | − | 11863.1i | −0.278840 | − | 0.482964i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4001.79 | −0.162054 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −324.867 | + | 562.687i | −0.0131092 | + | 0.0227059i | ||||
\(851\) | 22975.2 | − | 39794.1i | 0.925474 | − | 1.60297i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34906.8 | 1.40116 | 0.700578 | − | 0.713576i | \(-0.252926\pi\) | ||||
0.700578 | + | 0.713576i | \(0.252926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1246.38 | + | 2158.79i | 0.0497668 | + | 0.0861985i | ||||
\(857\) | −24023.4 | + | 41609.7i | −0.957553 | + | 1.65853i | −0.229139 | + | 0.973394i | \(0.573591\pi\) |
−0.728414 | + | 0.685137i | \(0.759742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17603.1 | − | 30489.5i | −0.699198 | − | 1.21105i | −0.968745 | − | 0.248059i | \(-0.920207\pi\) |
0.269547 | − | 0.962987i | \(-0.413126\pi\) | |||||||
\(860\) | 318.791 | 0.0126403 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3572.76 | 0.141170 | ||||||||
\(863\) | −17928.8 | − | 31053.7i | −0.707190 | − | 1.22489i | −0.965895 | − | 0.258933i | \(-0.916629\pi\) |
0.258705 | − | 0.965956i | \(-0.416704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3252.22 | + | 5633.01i | −0.127837 | + | 0.221420i | ||||
\(866\) | 184.621 | + | 319.773i | 0.00724444 | + | 0.0125477i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25594.3 | −0.999109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8214.83 | − | 14228.5i | 0.319574 | − | 0.553518i | ||||
\(872\) | 7463.32 | − | 12926.9i | 0.289839 | − | 0.502017i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25426.7 | −0.984064 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3683.09 | − | 6379.30i | −0.141812 | − | 0.245625i | 0.786367 | − | 0.617760i | \(-0.211959\pi\) |
−0.928179 | + | 0.372134i | \(0.878626\pi\) | |||||||
\(878\) | 11274.6 | − | 19528.2i | 0.433372 | − | 0.750622i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5108.08 | − | 8847.46i | −0.195674 | − | 0.338918i | ||||
\(881\) | 3628.00 | 0.138741 | 0.0693703 | − | 0.997591i | \(-0.477901\pi\) | ||||
0.0693703 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25123.0 | 0.957483 | 0.478741 | − | 0.877956i | \(-0.341093\pi\) | ||||
0.478741 | + | 0.877956i | \(0.341093\pi\) | |||||||
\(884\) | 2424.00 | + | 4198.49i | 0.0922262 | + | 0.159740i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7969.84 | − | 13804.2i | 0.302203 | − | 0.523431i | ||||
\(887\) | 7887.38 | + | 13661.3i | 0.298571 | + | 0.517140i | 0.975809 | − | 0.218624i | \(-0.0701568\pi\) |
−0.677238 | + | 0.735764i | \(0.736823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32844.9 | 1.23704 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7993.13 | − | 13844.5i | 0.300033 | − | 0.519673i | ||||
\(893\) | −6800.29 | + | 11778.5i | −0.254830 | + | 0.441378i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4700.07 | −0.175538 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8850.37 | + | 15329.3i | 0.328887 | + | 0.569649i | ||||
\(899\) | −10363.5 | + | 17950.2i | −0.384476 | + | 0.665931i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2558.92 | − | 4432.19i | −0.0946172 | − | 0.163882i | ||||
\(902\) | 20537.5 | 0.758120 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13764.0 | −0.506396 | ||||||||
\(905\) | 962.896 | + | 1667.78i | 0.0353677 | + | 0.0612586i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2556.99 | − | 4428.84i | 0.0936092 | − | 0.162136i | −0.815418 | − | 0.578872i | \(-0.803493\pi\) |
0.909027 | + | 0.416737i | \(0.136826\pi\) | |||||||
\(908\) | 1077.18 | + | 1865.74i | 0.0393696 | + | 0.0681902i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10279.1 | −0.373834 | −0.186917 | − | 0.982376i | \(-0.559850\pi\) | ||||
−0.186917 | + | 0.982376i | \(0.559850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23279.3 | + | 40321.0i | −0.843848 | + | 1.46159i | ||||
\(914\) | 13027.3 | − | 22563.9i | 0.471449 | − | 0.816574i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16686.4 | −0.601895 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19461.0 | + | 33707.4i | 0.698540 | + | 1.20991i | 0.968973 | + | 0.247168i | \(0.0794999\pi\) |
−0.270433 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(920\) | 6612.34 | − | 11452.9i | 0.236959 | − | 0.410425i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1261.05 | − | 2184.20i | −0.0450439 | − | 0.0780182i | ||||
\(923\) | −37404.8 | −1.33390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4610.05 | −0.163868 | ||||||||
\(926\) | 4005.47 | + | 6937.67i | 0.142147 | + | 0.246205i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1361.98 | − | 2359.01i | 0.0481779 | − | 0.0834466i | ||||
\(929\) | 7483.82 | + | 12962.4i | 0.264302 | + | 0.457784i | 0.967380 | − | 0.253328i | \(-0.0815252\pi\) |
−0.703079 | + | 0.711112i | \(0.748192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6158.92 | −0.216461 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17097.8 | + | 29614.3i | −0.598991 | + | 1.03748i | ||||
\(935\) | 6532.67 | − | 11314.9i | 0.228493 | − | 0.395762i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22353.0 | 0.779339 | 0.389669 | − | 0.920955i | \(-0.372589\pi\) | ||||
0.389669 | + | 0.920955i | \(0.372589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3536.90 | − | 6126.08i | −0.122724 | − | 0.212565i | ||||
\(941\) | 6690.77 | − | 11588.7i | 0.231788 | − | 0.401469i | −0.726546 | − | 0.687118i | \(-0.758876\pi\) |
0.958334 | + | 0.285649i | \(0.0922090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13292.8 | + | 23023.7i | 0.459037 | + | 0.795075i | ||||
\(944\) | 12883.5 | 0.444198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 932.665 | 0.0320545 | ||||||||
\(947\) | −316.888 | − | 548.867i | −0.0108738 | − | 0.0188340i | 0.860537 | − | 0.509387i | \(-0.170128\pi\) |
−0.871411 | + | 0.490553i | \(0.836795\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22753.1 | + | 39409.6i | −0.778291 | + | 1.34804i | ||||
\(950\) | 1275.49 | + | 2209.22i | 0.0435605 | + | 0.0754489i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49340.0 | 1.67710 | 0.838551 | − | 0.544823i | \(-0.183403\pi\) | ||||
0.838551 | + | 0.544823i | \(0.183403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1833.13 | + | 3175.08i | −0.0621138 | + | 0.107584i | ||||
\(956\) | 6265.34 | − | 10851.9i | 0.211962 | − | 0.367129i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23377.1 | 0.788391 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14749.2 | − | 25546.4i | −0.495090 | − | 0.857520i | ||||
\(962\) | −17199.0 | + | 29789.5i | −0.576421 | + | 0.998391i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5213.39 | + | 9029.85i | 0.174182 | + | 0.301693i | ||||
\(965\) | 15964.5 | 0.532556 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3340.71 | −0.111096 | −0.0555480 | − | 0.998456i | \(-0.517691\pi\) | ||||
−0.0555480 | + | 0.998456i | \(0.517691\pi\) | |||||||
\(968\) | −9620.36 | − | 16662.9i | −0.319432 | − | 0.553272i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10918.0 | − | 18910.6i | 0.361398 | − | 0.625960i | ||||
\(971\) | 2435.20 | + | 4217.89i | 0.0804833 | + | 0.139401i | 0.903458 | − | 0.428677i | \(-0.141020\pi\) |
−0.822974 | + | 0.568079i | \(0.807687\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19249.6 | −0.633261 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 265.372 | − | 459.638i | 0.00870324 | − | 0.0150745i | ||||
\(977\) | −3420.67 | + | 5924.78i | −0.112013 | + | 0.194013i | −0.916582 | − | 0.399847i | \(-0.869063\pi\) |
0.804569 | + | 0.593860i | \(0.202397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 96092.1 | 3.13699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6320.63 | − | 10947.7i | −0.205397 | − | 0.355757i | ||||
\(983\) | −5344.94 | + | 9257.71i | −0.173425 | + | 0.300382i | −0.939615 | − | 0.342233i | \(-0.888817\pi\) |
0.766190 | + | 0.642614i | \(0.222150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15014.6 | − | 26006.1i | −0.485691 | − | 0.841241i | ||||
\(986\) | 3483.63 | 0.112517 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19034.2 | 0.612913 | ||||||||
\(989\) | 603.660 | + | 1045.57i | 0.0194088 | + | 0.0336170i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3732.84 | + | 6465.48i | −0.119655 | + | 0.207248i | −0.919631 | − | 0.392784i | \(-0.871512\pi\) |
0.799976 | + | 0.600032i | \(0.204845\pi\) | |||||||
\(992\) | 3895.91 | + | 6747.91i | 0.124693 | + | 0.215974i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51695.3 | −1.64709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8677.41 | + | 15029.7i | −0.275643 | + | 0.477428i | −0.970297 | − | 0.241916i | \(-0.922224\pi\) |
0.694654 | + | 0.719344i | \(0.255557\pi\) | |||||||
\(998\) | 15054.6 | − | 26075.3i | 0.477499 | − | 0.827053i | ||||
\(999\) | 0 | 0 |
(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 | 882.4.g.z.361.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.bj.361.2 | 4 | |||
7.2 | even | 3 | inner | 882.4.g.z.667.1 | 4 | ||
7.3 | odd | 6 | 882.4.a.bd.1.1 | 2 | |||
7.4 | even | 3 | 882.4.a.bh.1.2 | 2 | |||
7.5 | odd | 6 | 126.4.g.e.37.2 | ✓ | 4 | ||
7.6 | odd | 2 | 126.4.g.e.109.2 | yes | 4 | ||
21.2 | odd | 6 | 882.4.g.bj.667.2 | 4 | |||
21.5 | even | 6 | 126.4.g.f.37.1 | yes | 4 | ||
21.11 | odd | 6 | 882.4.a.u.1.1 | 2 | |||
21.17 | even | 6 | 882.4.a.ba.1.2 | 2 | |||
21.20 | even | 2 | 126.4.g.f.109.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.g.e.37.2 | ✓ | 4 | 7.5 | odd | 6 | ||
126.4.g.e.109.2 | yes | 4 | 7.6 | odd | 2 | ||
126.4.g.f.37.1 | yes | 4 | 21.5 | even | 6 | ||
126.4.g.f.109.1 | yes | 4 | 21.20 | even | 2 | ||
882.4.a.u.1.1 | 2 | 21.11 | odd | 6 | |||
882.4.a.ba.1.2 | 2 | 21.17 | even | 6 | |||
882.4.a.bd.1.1 | 2 | 7.3 | odd | 6 | |||
882.4.a.bh.1.2 | 2 | 7.4 | even | 3 | |||
882.4.g.z.361.1 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.z.667.1 | 4 | 7.2 | even | 3 | inner | ||
882.4.g.bj.361.2 | 4 | 3.2 | odd | 2 | |||
882.4.g.bj.667.2 | 4 | 21.2 | odd | 6 |