Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,4,Mod(49,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("176.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.m (of order \(5\), degree \(4\), 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: | \(10.3843361610\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(2.22300 - 6.84169i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.97 |
Dual form | 176.4.m.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | −6.31989 | + | 4.59167i | −1.21626 | + | 0.883667i | −0.995784 | − | 0.0917244i | \(-0.970762\pi\) |
−0.220479 | + | 0.975392i | \(0.570762\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.60996 | + | 14.1880i | 0.412327 | + | 1.26901i | 0.914620 | + | 0.404315i | \(0.132490\pi\) |
−0.502293 | + | 0.864698i | \(0.667510\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.6106 | + | 12.7948i | 0.950881 | + | 0.690856i | 0.951015 | − | 0.309144i | \(-0.100043\pi\) |
−0.000134039 | 1.00000i | \(0.500043\pi\) | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.5141 | − | 32.3592i | 0.389412 | − | 1.19849i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 29.3767 | + | 21.6335i | 0.805219 | + | 0.592978i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.6056 | + | 41.8736i | −0.290270 | + | 0.893358i | 0.694500 | + | 0.719493i | \(0.255626\pi\) |
−0.984769 | + | 0.173865i | \(0.944374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −94.2810 | − | 68.4992i | −1.62288 | − | 1.17909i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.69900 | − | 23.6951i | −0.109840 | − | 0.338053i | 0.880996 | − | 0.473124i | \(-0.156874\pi\) |
−0.990836 | + | 0.135071i | \(0.956874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.7638 | − | 12.9061i | 0.214489 | − | 0.155835i | −0.475353 | − | 0.879795i | \(-0.657680\pi\) |
0.689842 | + | 0.723960i | \(0.257680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −170.046 | −1.76701 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −177.749 | −1.61145 | −0.805723 | − | 0.592293i | \(-0.798223\pi\) | ||||
−0.805723 | + | 0.592293i | \(0.798223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −78.9203 | + | 57.3389i | −0.631362 | + | 0.458711i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.9569 | + | 52.1881i | 0.120865 | + | 0.371985i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 120.864 | + | 87.8130i | 0.773928 | + | 0.562292i | 0.903151 | − | 0.429324i | \(-0.141248\pi\) |
−0.129223 | + | 0.991616i | \(0.541248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.2207 | + | 71.4658i | −0.134534 | + | 0.414053i | −0.995517 | − | 0.0945803i | \(-0.969849\pi\) |
0.860983 | + | 0.508633i | \(0.169849\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −284.992 | − | 1.83359i | −1.50335 | − | 0.00967232i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −100.349 | + | 308.842i | −0.484630 | + | 1.49154i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −179.874 | − | 130.686i | −0.799219 | − | 0.580667i | 0.111466 | − | 0.993768i | \(-0.464445\pi\) |
−0.910685 | + | 0.413102i | \(0.864445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −106.284 | − | 327.109i | −0.436387 | − | 1.34306i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 204.779 | − | 148.781i | 0.780029 | − | 0.566724i | −0.124959 | − | 0.992162i | \(-0.539880\pi\) |
0.904988 | + | 0.425438i | \(0.139880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −130.623 | −0.463253 | −0.231626 | − | 0.972805i | \(-0.574405\pi\) | ||||
−0.231626 | + | 0.972805i | \(0.574405\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 507.582 | 1.68146 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 403.775 | − | 293.360i | 1.25312 | − | 0.910445i | 0.254722 | − | 0.967014i | \(-0.418016\pi\) |
0.998399 | + | 0.0565693i | \(0.0180162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.4316 | + | 124.436i | 0.117876 | + | 0.362786i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 157.457 | + | 114.399i | 0.432321 | + | 0.314100i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.99933 | − | 12.3087i | 0.0103651 | − | 0.0319005i | −0.945740 | − | 0.324924i | \(-0.894661\pi\) |
0.956105 | + | 0.293023i | \(0.0946613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −171.511 | + | 516.526i | −0.420483 | + | 1.26633i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −53.0044 | + | 163.131i | −0.123169 | + | 0.379074i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28.7697 | + | 20.9024i | 0.0634831 | + | 0.0461232i | 0.619074 | − | 0.785332i | \(-0.287508\pi\) |
−0.555591 | + | 0.831456i | \(0.687508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 166.357 | + | 511.995i | 0.349178 | + | 1.07466i | 0.959309 | + | 0.282359i | \(0.0911169\pi\) |
−0.610131 | + | 0.792301i | \(0.708883\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 599.190 | − | 435.337i | 1.19827 | − | 0.870592i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −656.824 | −1.25337 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 519.621 | 0.947491 | 0.473745 | − | 0.880662i | \(-0.342902\pi\) | ||||
0.473745 | + | 0.880662i | \(0.342902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1123.35 | − | 816.165i | 1.95994 | − | 1.42398i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24.2420 | − | 74.6091i | −0.0405210 | − | 0.124711i | 0.928750 | − | 0.370708i | \(-0.120885\pi\) |
−0.969271 | + | 0.245997i | \(0.920885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −925.571 | − | 672.467i | −1.48397 | − | 1.07817i | −0.976250 | − | 0.216648i | \(-0.930488\pi\) |
−0.507722 | − | 0.861521i | \(-0.669512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 235.486 | − | 724.752i | 0.362555 | − | 1.11583i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 240.543 | + | 756.848i | 0.356005 | + | 1.12014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −238.730 | + | 734.735i | −0.339990 | + | 1.04638i | 0.624222 | + | 0.781247i | \(0.285416\pi\) |
−0.964212 | + | 0.265134i | \(0.914584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 396.416 | + | 288.013i | 0.543780 | + | 0.395079i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −166.017 | − | 510.947i | −0.219551 | − | 0.675708i | −0.998799 | − | 0.0489926i | \(-0.984399\pi\) |
0.779248 | − | 0.626715i | \(-0.215601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 300.694 | − | 218.467i | 0.383704 | − | 0.278777i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1167.06 | −1.43818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 667.089 | 0.794509 | 0.397255 | − | 0.917708i | \(-0.369963\pi\) | ||||
0.397255 | + | 0.917708i | \(0.369963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −775.368 | + | 563.338i | −0.893194 | + | 0.648943i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −181.395 | − | 558.278i | −0.202256 | − | 0.622481i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 265.003 | + | 192.536i | 0.286197 | + | 0.207934i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −55.5161 | + | 170.861i | −0.0581114 | + | 0.178848i | −0.975899 | − | 0.218224i | \(-0.929974\pi\) |
0.917787 | + | 0.397072i | \(0.129974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1008.91 | − | 723.148i | 1.02424 | − | 0.734132i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −126.924 | + | 390.633i | −0.125044 | + | 0.384846i | −0.993909 | − | 0.110203i | \(-0.964850\pi\) |
0.868865 | + | 0.495049i | \(0.164850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1106.46 | + | 803.890i | 1.05847 | + | 0.769026i | 0.973805 | − | 0.227383i | \(-0.0730171\pi\) |
0.0846679 | + | 0.996409i | \(0.473017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −783.907 | − | 2412.62i | −0.728586 | − | 2.24236i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −319.756 | + | 232.317i | −0.288897 | + | 0.209896i | −0.722789 | − | 0.691069i | \(-0.757140\pi\) |
0.433892 | + | 0.900965i | \(0.357140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 505.826 | 0.444490 | 0.222245 | − | 0.974991i | \(-0.428662\pi\) | ||||
0.222245 | + | 0.974991i | \(0.428662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1736.85 | 1.48518 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1243.96 | + | 903.793i | −1.03560 | + | 0.752404i | −0.969421 | − | 0.245404i | \(-0.921079\pi\) |
−0.0661744 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −819.416 | − | 2521.90i | −0.664443 | − | 2.04494i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1211.95 | + | 880.530i | 0.957645 | + | 0.695770i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 167.591 | − | 515.791i | 0.129101 | − | 0.397332i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 394.980 | + | 1271.04i | 0.296754 | + | 0.954954i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −611.031 | + | 1880.56i | −0.447925 | + | 1.37857i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 331.285 | + | 240.693i | 0.237048 | + | 0.172226i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 215.487 | + | 663.202i | 0.150562 | + | 0.463383i | 0.997684 | − | 0.0680154i | \(-0.0216667\pi\) |
−0.847122 | + | 0.531399i | \(0.821667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 825.525 | − | 599.779i | 0.563437 | − | 0.409361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 259.910 | 0.173347 | 0.0866735 | − | 0.996237i | \(-0.472376\pi\) | ||||
0.0866735 | + | 0.996237i | \(0.472376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 477.962 | 0.311613 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −662.273 | + | 481.170i | −0.422218 | + | 0.306759i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −643.856 | − | 1981.58i | −0.401520 | − | 1.23575i | −0.923766 | − | 0.382958i | \(-0.874906\pi\) |
0.522245 | − | 0.852795i | \(-0.325094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 140.307 | + | 101.939i | 0.0856163 | + | 0.0622039i | 0.629770 | − | 0.776782i | \(-0.283149\pi\) |
−0.544154 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1204.80 | + | 3708.00i | −0.719594 | + | 2.21468i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1305.56 | + | 935.772i | −0.763473 | + | 0.547225i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −688.711 | + | 2119.63i | −0.394444 | + | 1.21397i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −826.891 | − | 600.772i | −0.463951 | − | 0.337080i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −138.766 | − | 427.077i | −0.0762961 | − | 0.234815i | 0.905634 | − | 0.424061i | \(-0.139396\pi\) |
−0.981930 | + | 0.189246i | \(0.939396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0859 | − | 16.7729i | 0.0124418 | − | 0.00903947i | −0.581547 | − | 0.813513i | \(-0.697552\pi\) |
0.593989 | + | 0.804473i | \(0.297552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −847.702 | −0.447926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1121.00 | −0.580910 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1394.63 | + | 1013.26i | −0.708941 | + | 0.515076i | −0.882832 | − | 0.469689i | \(-0.844366\pi\) |
0.173891 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.2420 | + | 96.1531i | 0.0155827 | + | 0.0479587i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3130.26 | − | 2274.27i | −1.53229 | − | 1.11328i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1025.39 | + | 3155.82i | −0.492727 | + | 1.51646i | 0.327743 | + | 0.944767i | \(0.393712\pi\) |
−0.820470 | + | 0.571690i | \(0.806288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1287.78 | − | 4051.91i | −0.607599 | − | 1.91176i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 931.871 | − | 2868.00i | 0.431799 | − | 1.32894i | −0.464533 | − | 0.885556i | \(-0.653778\pi\) |
0.896332 | − | 0.443384i | \(-0.146222\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 209.120 | + | 151.934i | 0.0951842 | + | 0.0691554i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −230.862 | − | 710.519i | −0.103242 | − | 0.317747i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1787.45 | − | 1298.66i | 0.785534 | − | 0.570724i | −0.121101 | − | 0.992640i | \(-0.538643\pi\) |
0.906635 | + | 0.421917i | \(0.138643\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2123.47 | −0.917254 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −277.799 | −0.117970 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1837.95 | + | 1335.35i | −0.767457 | + | 0.557590i | −0.901189 | − | 0.433427i | \(-0.857304\pi\) |
0.133731 | + | 0.991018i | \(0.457304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −192.961 | − | 593.873i | −0.0792413 | − | 0.243880i | 0.903586 | − | 0.428406i | \(-0.140925\pi\) |
−0.982828 | + | 0.184527i | \(0.940925\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3402.27 | − | 2471.89i | −1.37433 | − | 0.998512i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1024.96 | − | 3154.51i | 0.407333 | − | 1.25364i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 286.438 | − | 862.640i | 0.112013 | − | 0.337340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −369.116 | + | 1136.02i | −0.142059 | + | 0.437214i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1087.48 | − | 790.100i | −0.411975 | − | 0.299317i | 0.362426 | − | 0.932013i | \(-0.381949\pi\) |
−0.774401 | + | 0.632695i | \(0.781949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1428.82 | + | 4397.46i | 0.532895 | + | 1.64008i | 0.748154 | + | 0.663526i | \(0.230941\pi\) |
−0.215258 | + | 0.976557i | \(0.569059\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4151.06 | − | 3015.92i | 1.52443 | − | 1.10756i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 664.691 | 0.240392 | 0.120196 | − | 0.992750i | \(-0.461648\pi\) | ||||
0.120196 | + | 0.992750i | \(0.461648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3042.82 | 1.08392 | 0.541959 | − | 0.840405i | \(-0.317683\pi\) | ||||
0.541959 | + | 0.840405i | \(0.317683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3283.95 | + | 2385.93i | −1.15240 | + | 0.837266i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1004.93 | + | 3092.87i | 0.347451 | + | 1.06934i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3054.93 | + | 2219.53i | 1.04081 | + | 0.756190i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1868.88 | + | 5751.81i | −0.627517 | + | 1.93130i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 801.047 | + | 5.15380i | 0.265118 | + | 0.00170572i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −800.851 | + | 2464.77i | −0.261293 | + | 0.804178i | 0.731231 | + | 0.682130i | \(0.238946\pi\) |
−0.992524 | + | 0.122048i | \(0.961054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 495.787 | + | 360.210i | 0.159487 | + | 0.115874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −602.168 | − | 1853.28i | −0.191012 | − | 0.587873i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1323.32 | + | 961.449i | −0.413977 | + | 0.300772i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8937.26 | 2.75764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1096.95 | 0.333886 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2133.54 | − | 1550.11i | 0.640684 | − | 0.465484i | −0.219401 | − | 0.975635i | \(-0.570410\pi\) |
0.860085 | + | 0.510150i | \(0.170410\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1025.66 | + | 3156.66i | 0.303900 | + | 0.935308i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 202.796 | + | 147.340i | 0.0592954 | + | 0.0430806i | 0.617038 | − | 0.786933i | \(-0.288332\pi\) |
−0.557743 | + | 0.830014i | \(0.688332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 556.018 | − | 1711.25i | 0.160449 | − | 0.493810i | −0.838224 | − | 0.545327i | \(-0.816406\pi\) |
0.998672 | + | 0.0515169i | \(0.0164056\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4995.40 | − | 3678.71i | −1.42283 | − | 1.04780i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 982.821 | − | 3024.81i | 0.276338 | − | 0.850481i | −0.712524 | − | 0.701647i | \(-0.752448\pi\) |
0.988862 | − | 0.148833i | \(-0.0475518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6023.57 | + | 4376.38i | 1.67206 | + | 1.21482i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1864.91 | − | 5739.61i | −0.511135 | − | 1.57311i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4056.25 | − | 2947.04i | 1.09781 | − | 0.797608i | 0.117111 | − | 0.993119i | \(-0.462637\pi\) |
0.980701 | + | 0.195511i | \(0.0626366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6074.13 | 1.62352 | 0.811761 | − | 0.583990i | \(-0.198509\pi\) | ||||
0.811761 | + | 0.583990i | \(0.198509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5309.35 | −1.40163 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1579.10 | + | 1147.29i | −0.411777 | + | 0.299173i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 298.741 | + | 919.430i | 0.0769572 | + | 0.236850i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3395.31 | + | 2466.84i | 0.864132 | + | 0.627829i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1721.13 | − | 5297.09i | 0.432816 | − | 1.33207i | −0.462493 | − | 0.886623i | \(-0.653045\pi\) |
0.895309 | − | 0.445447i | \(-0.146955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5221.68 | − | 3845.34i | −1.29757 | − | 0.955552i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −897.224 | + | 2761.37i | −0.220339 | + | 0.678133i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4778.90 | + | 3472.08i | 1.15992 | + | 0.842732i | 0.989768 | − | 0.142685i | \(-0.0455737\pi\) |
0.170153 | + | 0.985418i | \(0.445574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1495.58 | − | 4602.91i | −0.358805 | − | 1.10429i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4112.34 | − | 2987.79i | 0.975277 | − | 0.708580i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6853.74 | 1.60692 | 0.803459 | − | 0.595360i | \(-0.202991\pi\) | ||||
0.803459 | + | 0.595360i | \(0.202991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 193.072 | 0.0447559 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4215.93 | + | 3063.05i | −0.966333 | + | 0.702082i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 340.340 | + | 1047.46i | 0.0771409 | + | 0.237415i | 0.982190 | − | 0.187893i | \(-0.0601657\pi\) |
−0.905049 | + | 0.425308i | \(0.860166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2080.54 | − | 1511.60i | −0.466362 | − | 0.338832i | 0.329660 | − | 0.944100i | \(-0.393066\pi\) |
−0.796022 | + | 0.605268i | \(0.793066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2313.58 | − | 7120.46i | 0.512909 | − | 1.57857i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3558.86 | − | 22.8971i | −0.780390 | − | 0.00502090i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2268.22 | + | 6980.85i | −0.492000 | + | 1.51422i | 0.329581 | + | 0.944127i | \(0.393092\pi\) |
−0.821581 | + | 0.570092i | \(0.806908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2068.43 | + | 1502.80i | 0.443848 | + | 0.322475i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2315.45 | − | 7126.21i | −0.491559 | − | 1.51286i | −0.822252 | − | 0.569124i | \(-0.807282\pi\) |
0.330693 | − | 0.943738i | \(-0.392718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5253.84 | + | 3817.14i | −1.10356 | + | 0.801785i | −0.981638 | − | 0.190754i | \(-0.938907\pi\) |
−0.121925 | + | 0.992539i | \(0.538907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2558.85 | −0.531835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5509.91 | 1.13324 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3472.52 | − | 2522.93i | 0.706802 | − | 0.513522i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −433.681 | − | 1334.73i | −0.0873638 | − | 0.268878i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2172.11 | + | 1578.13i | 0.433092 | + | 0.314660i | 0.782884 | − | 0.622168i | \(-0.213748\pi\) |
−0.349792 | + | 0.936827i | \(0.613748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −163.936 | + | 504.544i | −0.0323551 | + | 0.0995787i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −630.874 | + | 1899.95i | −0.123256 | + | 0.371200i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2418.38 | − | 7443.00i | 0.467754 | − | 1.43960i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2300.35 | − | 1671.30i | −0.440498 | − | 0.320041i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −991.509 | − | 3051.55i | −0.187989 | − | 0.578571i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6497.28 | + | 4720.55i | −1.21978 | + | 0.886223i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8331.66 | −1.54890 | −0.774451 | − | 0.632633i | \(-0.781974\pi\) | ||||
−0.774451 | + | 0.632633i | \(0.781974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10683.9 | −1.96695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4061.55 | + | 2950.89i | −0.740545 | + | 0.538037i | −0.892882 | − | 0.450292i | \(-0.851320\pi\) |
0.152337 | + | 0.988329i | \(0.451320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 933.873 | + | 2874.16i | 0.168644 | + | 0.519033i | 0.999286 | − | 0.0377733i | \(-0.0120265\pi\) |
−0.830642 | + | 0.556807i | \(0.812026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8938.80 | + | 6494.42i | 1.59887 | + | 1.16165i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3257.08 | + | 10024.3i | −0.577085 | + | 1.77609i | 0.0518809 | + | 0.998653i | \(0.483478\pi\) |
−0.628966 | + | 0.777433i | \(0.716522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1650.88 | + | 5194.37i | 0.289755 | + | 0.911690i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 954.104 | − | 2936.43i | 0.165897 | − | 0.510578i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −442.576 | − | 321.550i | −0.0762402 | − | 0.0553917i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1327.23 | − | 4084.81i | −0.226528 | − | 0.697183i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3196.77 | + | 2322.59i | −0.540617 | + | 0.392781i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10864.2 | 1.82055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −309.871 | −0.0514563 | −0.0257281 | − | 0.999669i | \(-0.508190\pi\) | ||||
−0.0257281 | + | 0.999669i | \(0.508190\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6120.11 | + | 4446.52i | −1.00715 | + | 0.731736i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2395.43 | + | 7372.39i | 0.390676 | + | 1.20238i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9032.40 | − | 6562.42i | −1.46002 | − | 1.06076i | −0.983358 | − | 0.181677i | \(-0.941848\pi\) |
−0.476659 | − | 0.879088i | \(-0.658152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3711.80 | − | 11423.7i | 0.594682 | − | 1.83024i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2228.20 | + | 1597.08i | −0.353854 | + | 0.253627i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1427.13 | − | 4392.25i | 0.224658 | − | 0.691425i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16758.4 | + | 12175.7i | 2.61519 | + | 1.90005i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −777.327 | − | 2392.37i | −0.120257 | − | 0.370112i | 0.872750 | − | 0.488167i | \(-0.162334\pi\) |
−0.993007 | + | 0.118055i | \(0.962334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9203.85 | − | 6686.99i | 1.41166 | − | 1.02563i | 0.418587 | − | 0.908177i | \(-0.362526\pi\) |
0.993078 | − | 0.117457i | \(-0.0374744\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2416.01 | −0.367400 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6210.08 | 0.936343 | 0.468172 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 946.799 | − | 687.889i | 0.141552 | − | 0.102843i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1309.19 | + | 4029.27i | 0.194088 | + | 0.597343i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2012.43 | − | 1462.12i | −0.295856 | − | 0.214952i | 0.429948 | − | 0.902854i | \(-0.358532\pi\) |
−0.725804 | + | 0.687902i | \(0.758532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1970.56 | + | 6064.77i | −0.287296 | + | 0.884207i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8332.44 | − | 6219.24i | −1.20479 | − | 0.899244i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5274.11 | − | 16232.0i | 0.756328 | − | 2.32774i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5436.21 | + | 3949.64i | 0.773209 | + | 0.561770i | 0.902933 | − | 0.429781i | \(-0.141409\pi\) |
−0.129724 | + | 0.991550i | \(0.541409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2661.35 | − | 8190.80i | −0.375459 | − | 1.15554i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 227.918 | − | 165.592i | 0.0318946 | − | 0.0231728i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8614.37 | −1.19580 | −0.597902 | − | 0.801569i | \(-0.703999\pi\) | ||||
−0.597902 | + | 0.801569i | \(0.703999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3198.87 | −0.440503 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5321.47 | + | 3866.28i | −0.726976 | + | 0.528179i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2474.95 | + | 7617.10i | 0.335434 | + | 1.03236i | 0.966508 | + | 0.256637i | \(0.0826144\pi\) |
−0.631074 | + | 0.775723i | \(0.717386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4407.06 | − | 3201.92i | −0.592600 | − | 0.430549i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2475.83 | + | 7619.82i | −0.330310 | + | 1.01659i | 0.638676 | + | 0.769476i | \(0.279483\pi\) |
−0.968986 | + | 0.247115i | \(0.920517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9629.27 | + | 6901.86i | −1.27468 | + | 0.913639i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1373.39 | + | 4226.86i | −0.180396 | + | 0.555203i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6496.09 | − | 4719.68i | −0.846696 | − | 0.615160i | 0.0775373 | − | 0.996989i | \(-0.475294\pi\) |
−0.924233 | + | 0.381829i | \(0.875294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1368.49 | + | 4211.78i | 0.177001 | + | 0.544754i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1642.60 | + | 1193.42i | −0.210836 | + | 0.153181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11524.9 | −1.46806 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4435.00 | 0.560670 | 0.280335 | − | 0.959902i | \(-0.409554\pi\) | ||||
0.280335 | + | 0.959902i | \(0.409554\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3020.67 | + | 2194.64i | −0.379004 | + | 0.275363i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1214.19 | − | 3736.90i | −0.151207 | − | 0.465366i | 0.846550 | − | 0.532309i | \(-0.178675\pi\) |
−0.997757 | + | 0.0669429i | \(0.978675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2676.60 | − | 1944.67i | −0.330847 | − | 0.240374i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2258.86 | + | 6952.07i | −0.277145 | + | 0.852965i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2456.90 | − | 7730.44i | −0.299223 | − | 0.941483i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4500.59 | + | 13851.4i | −0.544107 | + | 1.67459i | 0.178996 | + | 0.983850i | \(0.442715\pi\) |
−0.723103 | + | 0.690740i | \(0.757285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13167.9 | + | 9567.02i | 1.58035 | + | 1.14819i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 239.208 | + | 736.208i | 0.0285004 | + | 0.0877153i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6483.98 | − | 4710.89i | 0.766955 | − | 0.557225i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1354.79 | −0.159099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4028.77 | −0.469734 | −0.234867 | − | 0.972028i | \(-0.575465\pi\) | ||||
−0.234867 | + | 0.972028i | \(0.575465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6898.98 | − | 5012.40i | 0.798659 | − | 0.580260i | −0.111861 | − | 0.993724i | \(-0.535681\pi\) |
0.910521 | + | 0.413464i | \(0.135681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5247.54 | − | 16150.3i | −0.603177 | − | 1.85639i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1966.26 | + | 1428.57i | 0.224418 | + | 0.163049i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3621.24 | + | 11145.0i | −0.410408 | + | 1.26310i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3954.25 | − | 11908.7i | 0.445019 | − | 1.34023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4145.53 | + | 12758.6i | −0.463302 | + | 1.42590i | 0.397803 | + | 0.917471i | \(0.369773\pi\) |
−0.861105 | + | 0.508427i | \(0.830227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3343.11 | − | 2428.91i | −0.371038 | − | 0.269575i | 0.386603 | − | 0.922246i | \(-0.373648\pi\) |
−0.757641 | + | 0.652671i | \(0.773648\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5380.08 | − | 16558.2i | −0.593000 | − | 1.82507i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3157.50 | + | 2294.06i | −0.345637 | + | 0.251120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3358.46 | −0.365126 | −0.182563 | − | 0.983194i | \(-0.558439\pi\) | ||||
−0.182563 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4451.74 | 0.480698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −357.383 | + | 259.654i | −0.0383290 | + | 0.0278477i | −0.606785 | − | 0.794866i | \(-0.707541\pi\) |
0.568456 | + | 0.822714i | \(0.307541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3075.25 | + | 9464.66i | 0.327598 | + | 1.00824i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2837.98 | + | 2061.91i | 0.300295 | + | 0.218177i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −126.227 | + | 388.486i | −0.0132673 | + | 0.0408325i | −0.957471 | − | 0.288530i | \(-0.906834\pi\) |
0.944204 | + | 0.329362i | \(0.106834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9234.40 | + | 59.4126i | 0.964148 | + | 0.00620317i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −68.8849 | + | 212.006i | −0.00714458 | + | 0.0219888i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11567.0 | − | 8403.95i | −1.19181 | − | 0.865897i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 470.585 | + | 1448.31i | 0.0481686 | + | 0.148248i | 0.972248 | − | 0.233953i | \(-0.0751663\pi\) |
−0.924079 | + | 0.382201i | \(0.875166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1106.05 | − | 803.592i | 0.112475 | − | 0.0817178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13861.4 | −1.40041 | −0.700203 | − | 0.713944i | \(-0.746907\pi\) | ||||
−0.700203 | + | 0.713944i | \(0.746907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6502.26 | 0.652669 | 0.326334 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326334 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7084.62 | − | 5147.27i | 0.706540 | − | 0.513331i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −131.015 | − | 403.223i | −0.0129821 | − | 0.0399548i | 0.944356 | − | 0.328926i | \(-0.106687\pi\) |
−0.957338 | + | 0.288971i | \(0.906687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9150.83 | + | 6648.46i | 0.900951 | + | 0.654579i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4161.37 | − | 12807.4i | 0.407104 | − | 1.25294i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3837.28 | − | 2825.84i | −0.373020 | − | 0.274699i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −661.898 | + | 2037.11i | −0.0639368 | + | 0.196777i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −356.249 | − | 258.830i | −0.0341961 | − | 0.0248449i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1408.29 | − | 4334.29i | −0.134335 | − | 0.413442i | 0.861151 | − | 0.508350i | \(-0.169744\pi\) |
−0.995486 | + | 0.0949081i | \(0.969744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7919.59 | − | 5753.92i | 0.750732 | − | 0.545439i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30225.6 | 2.84744 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2680.10 | −0.250922 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5427.63 | + | 3943.41i | −0.505030 | + | 0.366926i | −0.810935 | − | 0.585136i | \(-0.801041\pi\) |
0.305905 | + | 0.952062i | \(0.401041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8010.13 | − | 24652.6i | −0.740758 | − | 2.27982i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11753.1 | + | 8539.14i | 1.08027 | + | 0.784859i | 0.977729 | − | 0.209870i | \(-0.0673040\pi\) |
0.102537 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1150.20 | − | 3539.96i | 0.105076 | − | 0.323391i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14911.1 | + | 10980.8i | 1.35394 | + | 0.997070i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 527.695 | − | 1624.08i | 0.0476265 | − | 0.146579i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7847.09 | − | 5701.24i | −0.703976 | − | 0.511468i | 0.177249 | − | 0.984166i | \(-0.443280\pi\) |
−0.881225 | + | 0.472698i | \(0.843280\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7279.61 | + | 22404.3i | 0.649159 | + | 1.99791i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12707.4 | − | 9232.43i | 1.12643 | − | 0.818397i | 0.141256 | − | 0.989973i | \(-0.454886\pi\) |
0.985171 | + | 0.171576i | \(0.0548859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6127.41 | −0.539933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2019.25 | −0.176879 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1192.56 | − | 866.443i | 0.103849 | − | 0.0754507i | −0.534649 | − | 0.845074i | \(-0.679556\pi\) |
0.638498 | + | 0.769624i | \(0.279556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7695.74 | − | 23685.0i | −0.666222 | − | 2.05042i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 974.766 | + | 708.209i | 0.0838928 | + | 0.0609517i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6304.85 | + | 19404.3i | −0.539466 | + | 1.66031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18208.0 | + | 117.147i | 1.54891 | + | 0.00996542i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5333.48 | + | 16414.8i | −0.451086 | + | 1.38830i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7501.89 | + | 5450.44i | 0.630832 | + | 0.458326i | 0.856688 | − | 0.515834i | \(-0.172518\pi\) |
−0.225856 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1311.01 | + | 4034.86i | 0.109610 | + | 0.337346i | 0.990785 | − | 0.135445i | \(-0.0432464\pi\) |
−0.881174 | + | 0.472791i | \(0.843246\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13420.1 | − | 9750.28i | 1.11562 | − | 0.810547i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1872.17 | 0.154749 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19427.7 | 1.59676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 978.875 | − | 711.194i | 0.0799992 | − | 0.0581228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3443.86 | + | 10599.1i | 0.279869 | + | 0.861348i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4770.17 | − | 3465.73i | −0.385481 | − | 0.280068i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5484.16 | − | 16878.5i | 0.440706 | − | 1.35635i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1504.24 | + | 4530.19i | −0.120208 | + | 0.362020i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2014.87 | + | 6201.13i | −0.160122 | + | 0.492805i | −0.998644 | − | 0.0520633i | \(-0.983420\pi\) |
0.838522 | + | 0.544868i | \(0.183420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3946.36 | + | 2867.20i | 0.311887 | + | 0.226599i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2331.84 | + | 7176.66i | 0.183275 | + | 0.564063i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5154.07 | − | 3744.65i | 0.402874 | − | 0.292705i | −0.367836 | − | 0.929890i | \(-0.619901\pi\) |
0.770711 | + | 0.637185i | \(0.219901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18316.8 | 1.42394 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3280.33 | 0.253624 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13605.0 | + | 9884.59i | −1.04619 | + | 0.760100i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8006.81 | + | 24642.4i | 0.612379 | + | 1.88471i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4938.23 | − | 3587.84i | −0.375655 | − | 0.272929i | 0.383897 | − | 0.923376i | \(-0.374582\pi\) |
−0.759552 | + | 0.650447i | \(0.774582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1777.20 | − | 5469.67i | 0.134468 | − | 0.413851i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2150.70 | + | 6767.02i | 0.161859 | + | 0.509276i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4200.34 | − | 12927.3i | 0.314429 | − | 0.967711i | −0.661561 | − | 0.749892i | \(-0.730106\pi\) |
0.975989 | − | 0.217820i | \(-0.0698945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18557.6 | − | 13482.9i | −1.38181 | − | 1.00395i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3296.03 | + | 10144.1i | 0.244127 | + | 0.751347i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13913.1 | + | 10108.5i | −1.02508 | + | 0.744761i | −0.967317 | − | 0.253569i | \(-0.918395\pi\) |
−0.0577589 | + | 0.998331i | \(0.518395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2475.65 | −0.181441 | −0.0907203 | − | 0.995876i | \(-0.528917\pi\) | ||||
−0.0907203 | + | 0.995876i | \(0.528917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10500.6 | 0.765567 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14028.0 | − | 10191.9i | 1.01741 | − | 0.739188i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6285.32 | − | 19344.2i | −0.453485 | − | 1.39568i | −0.872904 | − | 0.487892i | \(-0.837766\pi\) |
0.419419 | − | 0.907793i | \(-0.362234\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29221.7 | − | 21230.8i | −2.09743 | − | 1.52387i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3613.83 | − | 11122.2i | 0.258050 | − | 0.794196i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 383.767 | − | 275.068i | 0.0272625 | − | 0.0195406i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6905.94 | + | 21254.3i | −0.488078 | + | 1.50215i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11988.4 | − | 8710.07i | −0.842953 | − | 0.612441i | 0.0802411 | − | 0.996775i | \(-0.474431\pi\) |
−0.923194 | + | 0.384334i | \(0.874431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 509.862 | + | 1569.19i | 0.0356681 | + | 0.109775i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4200.77 | + | 3052.04i | −0.292380 | + | 0.212427i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11123.2 | 0.770281 | 0.385140 | − | 0.922858i | \(-0.374153\pi\) | ||||
0.385140 | + | 0.922858i | \(0.374153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8090.63 | 0.557451 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19230.3 | + | 13971.6i | −1.31833 | + | 0.957824i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2560.26 | − | 7879.67i | −0.174640 | − | 0.537487i | 0.824977 | − | 0.565167i | \(-0.191188\pi\) |
−0.999617 | + | 0.0276796i | \(0.991188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22101.0 | − | 16057.3i | −1.50003 | − | 1.08984i | −0.970370 | − | 0.241625i | \(-0.922320\pi\) |
−0.529660 | − | 0.848210i | \(-0.677680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5463.37 | − | 16814.5i | 0.368965 | − | 1.13556i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16212.7 | + | 11463.4i | −1.08949 | + | 0.770338i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5045.53 | + | 15528.6i | −0.337384 | + | 1.03836i | 0.628152 | + | 0.778091i | \(0.283812\pi\) |
−0.965536 | + | 0.260270i | \(0.916188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20552.5 | − | 14932.3i | −1.36754 | − | 0.993574i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6790.45 | + | 20898.9i | 0.449611 | + | 1.38376i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17009.8 | − | 12358.4i | 1.12075 | − | 0.814274i | 0.136429 | − | 0.990650i | \(-0.456437\pi\) |
0.984323 | + | 0.176376i | \(0.0564374\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −29498.2 | −1.93412 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 871.824 | 0.0568854 | 0.0284427 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284427 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7602.75 | − | 5523.72i | 0.493668 | − | 0.358671i | −0.312925 | − | 0.949778i | \(-0.601309\pi\) |
0.806593 | + | 0.591107i | \(0.201309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3014.08 | − | 9276.38i | −0.194768 | − | 0.599434i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11747.8 | + | 8535.29i | 0.755484 | + | 0.548891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5655.84 | + | 17406.9i | −0.361974 | + | 1.11404i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5086.19 | + | 3645.57i | −0.323960 | + | 0.232201i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1711.77 | + | 5268.28i | −0.108510 | + | 0.333959i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11759.8 | − | 8544.01i | −0.741919 | − | 0.539036i | 0.151393 | − | 0.988474i | \(-0.451624\pi\) |
−0.893311 | + | 0.449438i | \(0.851624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6256.10 | − | 19254.3i | −0.392824 | − | 1.20899i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8416.12 | + | 6114.67i | −0.525958 | + | 0.382131i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5760.67 | −0.358314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2669.17 | −0.165244 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9238.70 | − | 6712.31i | 0.569277 | − | 0.413604i | −0.265565 | − | 0.964093i | \(-0.585559\pi\) |
0.834843 | + | 0.550489i | \(0.185559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7407.11 | − | 22796.7i | −0.454289 | − | 1.39816i | −0.871968 | − | 0.489563i | \(-0.837156\pi\) |
0.417679 | − | 0.908595i | \(-0.362844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12315.3 | + | 8947.58i | 0.751805 | + | 0.546218i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2569.24 | + | 7907.32i | −0.156117 | + | 0.480478i | −0.998272 | − | 0.0587569i | \(-0.981286\pi\) |
0.842156 | + | 0.539234i | \(0.181286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 392.966 | + | 1236.44i | 0.0237677 | + | 0.0747833i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3948.59 | − | 12152.5i | 0.237723 | − | 0.731635i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24334.7 | + | 17680.2i | 1.45833 | + | 1.05954i | 0.983794 | + | 0.179303i | \(0.0573843\pi\) |
0.474536 | + | 0.880236i | \(0.342616\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1198.17 | + | 3687.60i | 0.0714757 | + | 0.219980i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31492.1 | + | 22880.3i | −1.87005 | + | 1.35867i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10041.6 | 0.593572 | 0.296786 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296786 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1402.50 | 0.0825281 | 0.0412640 | − | 0.999148i | \(-0.486862\pi\) | ||||
0.0412640 | + | 0.999148i | \(0.486862\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6932.60 | + | 5036.83i | −0.406093 | + | 0.295044i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2203.39 | + | 6781.32i | 0.128487 | + | 0.395441i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21483.5 | − | 15608.7i | −1.24714 | − | 0.906102i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6366.17 | + | 19593.1i | −0.367908 | + | 1.13230i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6189.24 | + | 18639.6i | −0.356085 | + | 1.07239i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6299.43 | − | 19387.7i | 0.360810 | − | 1.11046i | −0.591753 | − | 0.806119i | \(-0.701564\pi\) |
0.952563 | − | 0.304341i | \(-0.0984361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4330.65 | − | 3146.40i | −0.246944 | − | 0.179415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2282.09 | − | 7023.55i | −0.129554 | − | 0.398725i | 0.865149 | − | 0.501514i | \(-0.167223\pi\) |
−0.994703 | + | 0.102789i | \(0.967223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3163.81 | + | 2298.64i | −0.178815 | + | 0.129917i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1958.19 | −0.110188 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25844.0 | 1.44787 | 0.723935 | − | 0.689868i | \(-0.242332\pi\) | ||||
0.723935 | + | 0.689868i | \(0.242332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25146.5 | − | 18270.0i | 1.40263 | − | 1.01907i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4343.51 | + | 13368.0i | 0.241216 | + | 0.742386i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 460.996 | + | 334.933i | 0.0254899 | + | 0.0185195i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2607.73 | + | 8025.78i | −0.143564 | + | 0.441845i | −0.996824 | − | 0.0796417i | \(-0.974622\pi\) |
0.853259 | + | 0.521487i | \(0.174622\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27020.1 | + | 173.843i | 1.48111 | + | 0.00952920i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −799.499 | + | 2460.60i | −0.0436356 | + | 0.134296i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5101.98 | − | 3706.80i | −0.277261 | − | 0.201442i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7677.62 | + | 23629.3i | 0.415442 | + | 1.27860i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10503.8 | − | 7631.43i | 0.565937 | − | 0.411177i | −0.267690 | − | 0.963505i | \(-0.586260\pi\) |
0.833627 | + | 0.552328i | \(0.186260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4881.90 | −0.261912 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −58163.2 | −3.10717 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7233.28 | + | 5255.29i | −0.384775 | + | 0.279555i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5537.15 | − | 17041.6i | −0.293303 | − | 0.902695i | −0.983786 | − | 0.179346i | \(-0.942602\pi\) |
0.690483 | − | 0.723349i | \(-0.257398\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21265.4 | + | 15450.2i | 1.12168 | + | 0.814948i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4127.45 | − | 12703.0i | 0.216794 | − | 0.667224i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19295.3 | − | 14209.4i | −1.00924 | − | 0.743220i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12103.2 | + | 37250.0i | −0.630410 | + | 1.94020i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2845.59 | + | 2067.45i | 0.147598 | + | 0.107236i | 0.659133 | − | 0.752026i | \(-0.270923\pi\) |
−0.511536 | + | 0.859262i | \(0.670923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9199.75 | + | 28313.9i | 0.475196 | + | 1.46250i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38387.8 | + | 27890.4i | −1.97463 | + | 1.43465i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14573.7 | −0.746559 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29438.9 | 1.50183 | 0.750913 | − | 0.660401i | \(-0.229614\pi\) | ||||
0.750913 | + | 0.660401i | \(0.229614\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22851.3 | − | 16602.5i | 1.16097 | − | 0.843492i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1005.67 | + | 3095.13i | 0.0508837 | + | 0.156604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2779.70 | − | 2019.57i | −0.140069 | − | 0.101766i | 0.515544 | − | 0.856863i | \(-0.327590\pi\) |
−0.655613 | + | 0.755097i | \(0.727590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4711.81 | − | 14501.5i | 0.236459 | − | 0.727747i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15264.8 | + | 11241.3i | 0.762937 | + | 0.561841i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10383.5 | − | 31957.2i | 0.516866 | − | 1.59075i | −0.262995 | − | 0.964797i | \(-0.584710\pi\) |
0.779861 | − | 0.625953i | \(-0.215290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6109.73 | − | 4438.98i | −0.302897 | − | 0.220067i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 368.875 | + | 1135.28i | 0.0182136 | + | 0.0560557i | 0.959750 | − | 0.280855i | \(-0.0906180\pi\) |
−0.941537 | + | 0.336911i | \(0.890618\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5419.66 | − | 3937.61i | 0.266525 | − | 0.193641i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18279.4 | −0.895324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8603.54 | −0.419715 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19828.5 | − | 14406.2i | 0.963451 | − | 0.699988i | 0.00950152 | − | 0.999955i | \(-0.496976\pi\) |
0.953950 | + | 0.299967i | \(0.0969755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13445.1 | + | 41379.9i | 0.650688 | + | 2.00261i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 344.399 | + | 250.221i | 0.0166013 | + | 0.0120615i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3338.57 | − | 10275.0i | 0.160294 | − | 0.493333i | −0.838365 | − | 0.545109i | \(-0.816488\pi\) |
0.998659 | + | 0.0517762i | \(0.0164882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 50657.0 | + | 325.918i | 2.42257 | + | 0.0155864i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2526.49 | − | 7775.75i | 0.120349 | − | 0.370395i | −0.872676 | − | 0.488299i | \(-0.837617\pi\) |
0.993025 | + | 0.117904i | \(0.0376175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8907.88 | + | 6471.96i | 0.422657 | + | 0.307078i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3907.87 | − | 12027.2i | −0.184692 | − | 0.568424i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1266.69 | + | 920.304i | −0.0596317 | + | 0.0433250i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28895.9 | −1.35502 | −0.677511 | − | 0.735513i | \(-0.736941\pi\) | ||||
−0.677511 | + | 0.735513i | \(0.736941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46144.8 | −2.15547 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14559.7 | − | 10578.3i | 0.677460 | − | 0.492203i | −0.195054 | − | 0.980792i | \(-0.562488\pi\) |
0.872514 | + | 0.488589i | \(0.162488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2265.19 | − | 6971.55i | −0.104991 | − | 0.323130i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30586.9 | + | 22222.7i | 1.41223 | + | 1.02604i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1717.47 | − | 5285.83i | 0.0789919 | − | 0.243112i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 901.910 | − | 2716.21i | 0.0413225 | − | 0.124448i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2533.30 | + | 7796.71i | −0.115623 | + | 0.355851i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20805.3 | − | 15115.9i | −0.945954 | − | 0.687276i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4906.17 | + | 15099.6i | 0.222219 | + | 0.683918i | 0.998562 | + | 0.0536084i | \(0.0170723\pi\) |
−0.776343 | + | 0.630310i | \(0.782928\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43314.9 | + | 31470.1i | −1.95444 | + | 1.41998i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33470.8 | −1.50453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23702.5 | −1.06141 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1220.19 | + | 886.523i | −0.0544350 | + | 0.0395494i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5098.07 | + | 15690.2i | 0.226578 | + | 0.697336i | 0.998128 | + | 0.0611668i | \(0.0194822\pi\) |
−0.771549 | + | 0.636170i | \(0.780518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10059.9 | − | 7308.91i | −0.445422 | − | 0.323618i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7013.87 | − | 21586.5i | 0.309392 | − | 0.952210i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12642.4 | − | 39778.2i | −0.555591 | − | 1.74812i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17836.9 | − | 54896.4i | 0.780955 | − | 2.40353i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6960.50 | − | 5057.10i | −0.303620 | − | 0.220593i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2812.97 | − | 8657.42i | −0.122248 | − | 0.376241i | 0.871142 | − | 0.491032i | \(-0.163380\pi\) |
−0.993390 | + | 0.114791i | \(0.963380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29590.8 | − | 21499.0i | 1.28123 | − | 0.930865i | 0.281636 | − | 0.959521i | \(-0.409123\pi\) |
0.999589 | + | 0.0286567i | \(0.00912297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20089.6 | 0.866633 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49501.7 | −2.12757 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2320.36 | + | 1685.84i | −0.0993626 | + | 0.0721912i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10076.8 | + | 31013.3i | 0.429930 | + | 1.32319i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2948.23 | + | 2142.01i | 0.125328 | + | 0.0910558i | 0.648683 | − | 0.761059i | \(-0.275320\pi\) |
−0.523356 | + | 0.852114i | \(0.675320\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5221.12 | − | 16068.9i | 0.221138 | − | 0.680593i | −0.777523 | − | 0.628855i | \(-0.783524\pi\) |
0.998661 | − | 0.0517380i | \(-0.0164761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22596.7 | − | 16196.4i | 0.953597 | − | 0.683499i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11983.1 | − | 36880.1i | 0.503860 | − | 1.55072i | −0.298817 | − | 0.954310i | \(-0.596592\pi\) |
0.802678 | − | 0.596413i | \(-0.203408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10027.2 | + | 7285.20i | 0.420096 | + | 0.305218i | 0.777677 | − | 0.628665i | \(-0.216398\pi\) |
−0.357580 | + | 0.933882i | \(0.616398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17718.9 | − | 54533.1i | −0.739665 | − | 2.27645i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2637.23 | − | 1916.06i | 0.109694 | − | 0.0796970i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44987.1 | 1.86448 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4123.41 | −0.170282 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19872.6 | − | 14438.3i | 0.817732 | − | 0.594117i | −0.0983299 | − | 0.995154i | \(-0.531350\pi\) |
0.916062 | + | 0.401037i | \(0.131350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −639.584 | − | 1968.44i | −0.0262243 | − | 0.0807100i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47354.6 | + | 34405.1i | 1.93473 | + | 1.40566i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1191.61 | + | 3667.40i | −0.0485120 | + | 0.149305i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9306.97 | + | 27437.5i | −0.377557 | + | 1.11306i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15676.7 | − | 48247.8i | 0.633712 | − | 1.95036i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31972.4 | + | 23229.3i | 1.28790 | + | 0.935712i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3772.37 | − | 11610.1i | −0.151422 | − | 0.466030i | 0.846358 | − | 0.532614i | \(-0.178790\pi\) |
−0.997781 | + | 0.0665834i | \(0.978790\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9016.57 | − | 6550.92i | 0.360655 | − | 0.262031i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7281.72 | 0.290244 | 0.145122 | − | 0.989414i | \(-0.453643\pi\) | ||||
0.145122 | + | 0.989414i | \(0.453643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5927.39 | −0.235437 | −0.117718 | − | 0.993047i | \(-0.537558\pi\) | ||||
−0.117718 | + | 0.993047i | \(0.537558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34822.0 | + | 25299.7i | −1.37832 | + | 1.00141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11916.3 | + | 36674.5i | 0.470028 | + | 1.44660i | 0.852547 | + | 0.522651i | \(0.175057\pi\) |
−0.382518 | + | 0.923948i | \(0.624943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26665.4 | + | 19373.6i | 1.04815 | + | 0.761527i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10361.5 | + | 31889.3i | −0.405875 | + | 1.24916i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22908.0 | + | 16419.5i | −0.894247 | + | 0.640959i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7069.75 | + | 21758.4i | −0.275028 | + | 0.846449i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4945.22 | + | 3592.91i | 0.191719 | + | 0.139292i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2754.49 | + | 8477.46i | 0.106422 | + | 0.327532i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23067.2 | + | 16759.3i | −0.888170 | + | 0.645293i | −0.935400 | − | 0.353591i | \(-0.884961\pi\) |
0.0472301 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20973.7 | −0.804809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40747.6 | 1.55826 | 0.779128 | − | 0.626865i | \(-0.215662\pi\) | ||||
0.779128 | + | 0.626865i | \(0.215662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2908.89 | + | 2113.43i | −0.110863 | + | 0.0805467i | −0.641835 | − | 0.766842i | \(-0.721827\pi\) |
0.530972 | + | 0.847389i | \(0.321827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1280.64 | − | 3941.41i | −0.0486421 | − | 0.149705i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6241.81 | − | 4534.94i | −0.236279 | − | 0.171667i | 0.463345 | − | 0.886178i | \(-0.346649\pi\) |
−0.699624 | + | 0.714511i | \(0.746649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4690.70 | + | 14436.5i | −0.176964 | + | 0.544639i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5414.64 | + | 17036.7i | 0.203588 | + | 0.640575i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3386.43 | − | 10422.4i | 0.126901 | − | 0.390561i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27418.8 | − | 19920.9i | −1.02403 | − | 0.744003i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18891.9 | + | 58143.4i | 0.703214 | + | 2.16427i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9082.17 | + | 6598.58i | −0.336938 | + | 0.244800i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −322.446 | −0.0119226 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22212.0 | 0.818571 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7536.32 | − | 5475.46i | 0.276813 | − | 0.201117i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10418.1 | + | 32063.6i | 0.381398 | + | 1.17382i | 0.939060 | + | 0.343753i | \(0.111698\pi\) |
−0.557662 | + | 0.830068i | \(0.688302\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11306.1 | + | 8214.33i | 0.412539 | + | 0.299727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4644.75 | + | 14295.1i | −0.168922 | + | 0.519887i | −0.999304 | − | 0.0373070i | \(-0.988122\pi\) |
0.830382 | + | 0.557194i | \(0.188122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6176.57 | − | 18601.5i | 0.223894 | − | 0.674281i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19386.9 | − | 59666.7i | 0.700449 | − | 2.15576i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4577.16 | + | 3325.50i | 0.164832 | + | 0.119758i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5281.31 | + | 16254.2i | 0.189570 | + | 0.583435i | 0.999997 | − | 0.00240379i | \(-0.000765151\pi\) |
−0.810428 | + | 0.585839i | \(0.800765\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 52655.2 | − | 38256.3i | 1.88387 | − | 1.36871i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3453.98 | 0.123173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21689.1 | 0.770955 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37646.7 | − | 27351.9i | 1.33385 | − | 0.969099i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4066.74 | + | 12516.1i | 0.143623 | + | 0.442025i | 0.996831 | − | 0.0795446i | \(-0.0253466\pi\) |
−0.853209 | + | 0.521570i | \(0.825347\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2324.20 | + | 1688.63i | 0.0818182 | + | 0.0594444i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12119.0 | − | 37298.6i | 0.425252 | − | 1.30879i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13559.6 | + | 87.2401i | 0.474274 | + | 0.00305140i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1253.46 | − | 3857.76i | 0.0437021 | − | 0.134501i | −0.926825 | − | 0.375494i | \(-0.877473\pi\) |
0.970527 | + | 0.240993i | \(0.0774731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19099.2 | − | 13876.4i | −0.663768 | − | 0.482256i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10320.4 | + | 31763.0i | 0.357531 | + | 1.10037i | 0.954527 | + | 0.298123i | \(0.0963607\pi\) |
−0.596996 | + | 0.802244i | \(0.703639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36399.3 | + | 26445.7i | −1.25697 | + | 0.913245i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17819.5 | −0.613405 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25660.8 | −0.880533 | −0.440267 | − | 0.897867i | \(-0.645116\pi\) | ||||
−0.440267 | + | 0.897867i | \(0.645116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40751.6 | − | 29607.8i | 1.39394 | − | 1.01276i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25443.7 | − | 78307.8i | −0.867581 | − | 2.67014i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39522.7 | − | 28714.9i | −1.34341 | − | 0.976042i | −0.999311 | − | 0.0371079i | \(-0.988185\pi\) |
−0.344096 | − | 0.938935i | \(-0.611815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6196.70 | − | 19071.5i | 0.209969 | − | 0.646218i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34284.3 | − | 25247.6i | −1.15805 | − | 0.852809i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14015.4 | − | 43134.8i | 0.471929 | − | 1.45245i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19533.3 | + | 14191.7i | 0.655677 | + | 0.476377i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4155.61 | + | 12789.7i | 0.139058 | + | 0.427976i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −55804.3 | + | 40544.2i | −1.86156 | + | 1.35250i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48861.8 | 1.62491 | 0.812456 | − | 0.583023i | \(-0.198130\pi\) | ||||
0.812456 | + | 0.583023i | \(0.198130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4273.48 | 0.141676 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28224.6 | − | 20506.4i | 0.932822 | − | 0.677735i | −0.0138603 | − | 0.999904i | \(-0.504412\pi\) |
0.946682 | + | 0.322169i | \(0.104412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1166.59 | + | 3590.40i | 0.0384370 | + | 0.118297i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27144.1 | + | 19721.3i | 0.891596 | + | 0.647782i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5875.16 | + | 18081.9i | −0.192388 | + | 0.592109i | 0.807609 | + | 0.589718i | \(0.200761\pi\) |
−0.999997 | + | 0.00239112i | \(0.999239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19596.9 | + | 14431.5i | 0.639754 | + | 0.471126i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5318.33 | − | 16368.1i | 0.173090 | − | 0.532716i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6025.47 | − | 4377.76i | −0.195506 | − | 0.142044i | 0.485726 | − | 0.874111i | \(-0.338555\pi\) |
−0.681232 | + | 0.732068i | \(0.738555\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3064.20 | + | 9430.63i | 0.0991202 | + | 0.305061i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −68660.5 | + | 49884.8i | −2.21427 | + | 1.60876i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23218.2 | 0.746506 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5313.37 | −0.170318 | −0.0851588 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851588 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1958.35 | − | 1422.82i | 0.0625844 | − | 0.0454702i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14027.3 | + | 43171.5i | 0.446929 | + | 1.37551i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43301.8 | − | 31460.6i | −1.37551 | − | 0.999365i | −0.997284 | − | 0.0736504i | \(-0.976535\pi\) |
−0.378223 | − | 0.925714i | \(-0.623465\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3770.14 | − | 11603.3i | 0.119401 | − | 0.367480i |
(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 | 176.4.m.b.97.1 | 8 | ||
4.3 | odd | 2 | 22.4.c.b.9.2 | yes | 8 | ||
11.4 | even | 5 | 1936.4.a.bn.1.4 | 4 | |||
11.5 | even | 5 | inner | 176.4.m.b.49.1 | 8 | ||
11.7 | odd | 10 | 1936.4.a.bm.1.4 | 4 | |||
12.11 | even | 2 | 198.4.f.d.163.1 | 8 | |||
44.3 | odd | 10 | 242.4.c.r.81.1 | 8 | |||
44.7 | even | 10 | 242.4.a.o.1.1 | 4 | |||
44.15 | odd | 10 | 242.4.a.n.1.1 | 4 | |||
44.19 | even | 10 | 242.4.c.n.81.1 | 8 | |||
44.27 | odd | 10 | 22.4.c.b.5.2 | ✓ | 8 | ||
44.31 | odd | 10 | 242.4.c.r.3.1 | 8 | |||
44.35 | even | 10 | 242.4.c.n.3.1 | 8 | |||
44.39 | even | 10 | 242.4.c.q.27.2 | 8 | |||
44.43 | even | 2 | 242.4.c.q.9.2 | 8 | |||
132.59 | even | 10 | 2178.4.a.by.1.1 | 4 | |||
132.71 | even | 10 | 198.4.f.d.181.1 | 8 | |||
132.95 | odd | 10 | 2178.4.a.bt.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.5.2 | ✓ | 8 | 44.27 | odd | 10 | ||
22.4.c.b.9.2 | yes | 8 | 4.3 | odd | 2 | ||
176.4.m.b.49.1 | 8 | 11.5 | even | 5 | inner | ||
176.4.m.b.97.1 | 8 | 1.1 | even | 1 | trivial | ||
198.4.f.d.163.1 | 8 | 12.11 | even | 2 | |||
198.4.f.d.181.1 | 8 | 132.71 | even | 10 | |||
242.4.a.n.1.1 | 4 | 44.15 | odd | 10 | |||
242.4.a.o.1.1 | 4 | 44.7 | even | 10 | |||
242.4.c.n.3.1 | 8 | 44.35 | even | 10 | |||
242.4.c.n.81.1 | 8 | 44.19 | even | 10 | |||
242.4.c.q.9.2 | 8 | 44.43 | even | 2 | |||
242.4.c.q.27.2 | 8 | 44.39 | even | 10 | |||
242.4.c.r.3.1 | 8 | 44.31 | odd | 10 | |||
242.4.c.r.81.1 | 8 | 44.3 | odd | 10 | |||
1936.4.a.bm.1.4 | 4 | 11.7 | odd | 10 | |||
1936.4.a.bn.1.4 | 4 | 11.4 | even | 5 | |||
2178.4.a.bt.1.1 | 4 | 132.95 | odd | 10 | |||
2178.4.a.by.1.1 | 4 | 132.59 | even | 10 |