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: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.ba.361.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | 9.89949 | − | 17.1464i | 0.885438 | − | 1.53362i | 0.0402266 | − | 0.999191i | \(-0.487192\pi\) |
0.845211 | − | 0.534433i | \(-0.179475\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 19.7990 | + | 34.2929i | 0.626099 | + | 1.08444i | ||||
\(11\) | −7.00000 | − | 12.1244i | −0.191871 | − | 0.332330i | 0.753999 | − | 0.656875i | \(-0.228122\pi\) |
−0.945870 | + | 0.324545i | \(0.894789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.9117 | −1.08618 | −0.543091 | − | 0.839674i | \(-0.682746\pi\) | ||||
−0.543091 | + | 0.839674i | \(0.682746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.707107 | − | 1.22474i | −0.0100882 | − | 0.0174732i | 0.860937 | − | 0.508711i | \(-0.169878\pi\) |
−0.871025 | + | 0.491238i | \(0.836545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.707107 | + | 1.22474i | −0.00853797 | + | 0.0147882i | −0.870263 | − | 0.492588i | \(-0.836051\pi\) |
0.861725 | + | 0.507376i | \(0.169384\pi\) | |||||||
\(20\) | −79.1960 | −0.885438 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.0000 | 0.271346 | ||||||||
\(23\) | 70.0000 | − | 121.244i | 0.634609 | − | 1.09918i | −0.351989 | − | 0.936004i | \(-0.614494\pi\) |
0.986598 | − | 0.163171i | \(-0.0521722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −133.500 | − | 231.229i | −1.06800 | − | 1.84983i | ||||
\(26\) | 50.9117 | − | 88.1816i | 0.384023 | − | 0.665148i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 286.000 | 1.83134 | 0.915670 | − | 0.401931i | \(-0.131661\pi\) | ||||
0.915670 | + | 0.401931i | \(0.131661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.6690 | − | 80.8332i | −0.270387 | − | 0.468325i | 0.698574 | − | 0.715538i | \(-0.253818\pi\) |
−0.968961 | + | 0.247213i | \(0.920485\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.82843 | 0.0142668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.0000 | − | 32.9090i | 0.0844211 | − | 0.146222i | −0.820723 | − | 0.571326i | \(-0.806429\pi\) |
0.905144 | + | 0.425104i | \(0.139763\pi\) | |||||||
\(38\) | −1.41421 | − | 2.44949i | −0.00603726 | − | 0.0104568i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 79.1960 | − | 137.171i | 0.313050 | − | 0.542218i | ||||
\(41\) | −125.865 | −0.479434 | −0.239717 | − | 0.970843i | \(-0.577055\pi\) | ||||
−0.239717 | + | 0.970843i | \(0.577055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.120580 | −0.0602901 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602901 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(44\) | −28.0000 | + | 48.4974i | −0.0959354 | + | 0.166165i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 140.000 | + | 242.487i | 0.448736 | + | 0.777234i | ||||
\(47\) | −261.630 | + | 453.156i | −0.811970 | + | 1.40637i | 0.0995134 | + | 0.995036i | \(0.468271\pi\) |
−0.911483 | + | 0.411337i | \(0.865062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 534.000 | 1.51038 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 101.823 | + | 176.363i | 0.271545 | + | 0.470330i | ||||
\(53\) | −37.0000 | − | 64.0859i | −0.0958932 | − | 0.166092i | 0.814088 | − | 0.580742i | \(-0.197237\pi\) |
−0.909981 | + | 0.414650i | \(0.863904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −277.186 | −0.679559 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −286.000 | + | 495.367i | −0.647477 | + | 1.12146i | ||||
\(59\) | −217.082 | − | 375.997i | −0.479011 | − | 0.829671i | 0.520699 | − | 0.853740i | \(-0.325671\pi\) |
−0.999710 | + | 0.0240689i | \(0.992338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.07107 | − | 12.2474i | 0.0148419 | − | 0.0257070i | −0.858509 | − | 0.512798i | \(-0.828609\pi\) |
0.873351 | + | 0.487091i | \(0.161942\pi\) | |||||||
\(62\) | 186.676 | 0.382385 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −504.000 | + | 872.954i | −0.961746 | + | 1.66579i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −342.000 | − | 592.361i | −0.623611 | − | 1.08013i | −0.988808 | − | 0.149196i | \(-0.952332\pi\) |
0.365196 | − | 0.930930i | \(-0.381002\pi\) | |||||||
\(68\) | −2.82843 | + | 4.89898i | −0.00504408 | + | 0.00873660i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −588.000 | −0.982856 | −0.491428 | − | 0.870918i | \(-0.663525\pi\) | ||||
−0.491428 | + | 0.870918i | \(0.663525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −135.057 | − | 233.926i | −0.216538 | − | 0.375055i | 0.737209 | − | 0.675664i | \(-0.236143\pi\) |
−0.953747 | + | 0.300610i | \(0.902810\pi\) | |||||||
\(74\) | 38.0000 | + | 65.8179i | 0.0596947 | + | 0.103394i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.65685 | 0.00853797 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −610.000 | + | 1056.55i | −0.868739 | + | 1.50470i | −0.00545246 | + | 0.999985i | \(0.501736\pi\) |
−0.863286 | + | 0.504715i | \(0.831598\pi\) | |||||||
\(80\) | 158.392 | + | 274.343i | 0.221359 | + | 0.383406i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 125.865 | − | 218.005i | 0.169506 | − | 0.293592i | ||||
\(83\) | 422.850 | 0.559202 | 0.279601 | − | 0.960116i | \(-0.409798\pi\) | ||||
0.279601 | + | 0.960116i | \(0.409798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.0000 | −0.0357297 | ||||||||
\(86\) | 34.0000 | − | 58.8897i | 0.0426316 | − | 0.0738400i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −56.0000 | − | 96.9948i | −0.0678366 | − | 0.117496i | ||||
\(89\) | −309.006 | + | 535.214i | −0.368028 | + | 0.637444i | −0.989257 | − | 0.146185i | \(-0.953300\pi\) |
0.621229 | + | 0.783629i | \(0.286634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −560.000 | −0.634609 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −523.259 | − | 906.311i | −0.574149 | − | 0.994456i | ||||
\(95\) | 14.0000 | + | 24.2487i | 0.0151197 | + | 0.0261881i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1483.51 | −1.55286 | −0.776431 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776431 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −534.000 | + | 924.915i | −0.534000 | + | 0.924915i | ||||
\(101\) | −564.271 | − | 977.346i | −0.555912 | − | 0.962867i | −0.997832 | − | 0.0658130i | \(-0.979036\pi\) |
0.441920 | − | 0.897054i | \(-0.354297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −434.164 | + | 751.993i | −0.415334 | + | 0.719380i | −0.995463 | − | 0.0951446i | \(-0.969669\pi\) |
0.580129 | + | 0.814524i | \(0.303002\pi\) | |||||||
\(104\) | −407.294 | −0.384023 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 148.000 | 0.135613 | ||||||||
\(107\) | −842.000 | + | 1458.39i | −0.760740 | + | 1.31764i | 0.181729 | + | 0.983349i | \(0.441831\pi\) |
−0.942469 | + | 0.334292i | \(0.891503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 409.000 | + | 708.409i | 0.359405 | + | 0.622507i | 0.987861 | − | 0.155337i | \(-0.0496465\pi\) |
−0.628457 | + | 0.777844i | \(0.716313\pi\) | |||||||
\(110\) | 277.186 | − | 480.100i | 0.240260 | − | 0.416143i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 540.000 | 0.449548 | 0.224774 | − | 0.974411i | \(-0.427836\pi\) | ||||
0.224774 | + | 0.974411i | \(0.427836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1385.93 | − | 2400.50i | −1.12381 | − | 1.94650i | ||||
\(116\) | −572.000 | − | 990.733i | −0.457835 | − | 0.792994i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 868.327 | 0.677424 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 567.500 | − | 982.939i | 0.426371 | − | 0.738496i | ||||
\(122\) | 14.1421 | + | 24.4949i | 0.0104948 | + | 0.0181776i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −186.676 | + | 323.333i | −0.135194 | + | 0.234162i | ||||
\(125\) | −2811.46 | −2.01171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1720.00 | 1.20177 | 0.600887 | − | 0.799334i | \(-0.294814\pi\) | ||||
0.600887 | + | 0.799334i | \(0.294814\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1008.00 | − | 1745.91i | −0.680057 | − | 1.17789i | ||||
\(131\) | 867.620 | − | 1502.76i | 0.578659 | − | 1.00227i | −0.416975 | − | 0.908918i | \(-0.636910\pi\) |
0.995634 | − | 0.0933484i | \(-0.0297571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1368.00 | 0.881919 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.65685 | − | 9.79796i | −0.00356670 | − | 0.00617771i | ||||
\(137\) | 414.000 | + | 717.069i | 0.258178 | + | 0.447178i | 0.965754 | − | 0.259460i | \(-0.0835445\pi\) |
−0.707576 | + | 0.706638i | \(0.750211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 425.678 | 0.259752 | 0.129876 | − | 0.991530i | \(-0.458542\pi\) | ||||
0.129876 | + | 0.991530i | \(0.458542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 588.000 | − | 1018.45i | 0.347492 | − | 0.601874i | ||||
\(143\) | 356.382 | + | 617.271i | 0.208407 | + | 0.360971i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2831.26 | − | 4903.88i | 1.62154 | − | 2.80859i | ||||
\(146\) | 540.230 | 0.306231 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −152.000 | −0.0844211 | ||||||||
\(149\) | 1025.00 | − | 1775.35i | 0.563566 | − | 0.976124i | −0.433616 | − | 0.901098i | \(-0.642763\pi\) |
0.997182 | − | 0.0750264i | \(-0.0239041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 236.000 | + | 408.764i | 0.127188 | + | 0.220296i | 0.922586 | − | 0.385791i | \(-0.126071\pi\) |
−0.795398 | + | 0.606087i | \(0.792738\pi\) | |||||||
\(152\) | −5.65685 | + | 9.79796i | −0.00301863 | + | 0.00522842i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1848.00 | −0.957645 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1105.92 | − | 1915.50i | −0.562176 | − | 0.973717i | −0.997306 | − | 0.0733498i | \(-0.976631\pi\) |
0.435130 | − | 0.900367i | \(-0.356702\pi\) | |||||||
\(158\) | −1220.00 | − | 2113.10i | −0.614291 | − | 1.06398i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −633.568 | −0.313050 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1643.00 | + | 2845.76i | −0.789507 | + | 1.36747i | 0.136762 | + | 0.990604i | \(0.456331\pi\) |
−0.926269 | + | 0.376863i | \(0.877003\pi\) | |||||||
\(164\) | 251.730 | + | 436.009i | 0.119859 | + | 0.207601i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −422.850 | + | 732.397i | −0.197708 | + | 0.342440i | ||||
\(167\) | −1490.58 | −0.690686 | −0.345343 | − | 0.938476i | \(-0.612237\pi\) | ||||
−0.345343 | + | 0.938476i | \(0.612237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 395.000 | 0.179791 | ||||||||
\(170\) | 28.0000 | − | 48.4974i | 0.0126324 | − | 0.0218799i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 68.0000 | + | 117.779i | 0.0301451 | + | 0.0522128i | ||||
\(173\) | 1035.20 | − | 1793.03i | 0.454943 | − | 0.787984i | −0.543742 | − | 0.839252i | \(-0.682993\pi\) |
0.998685 | + | 0.0512682i | \(0.0163263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 224.000 | 0.0959354 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −618.011 | − | 1070.43i | −0.260235 | − | 0.450741i | ||||
\(179\) | 270.000 | + | 467.654i | 0.112742 | + | 0.195274i | 0.916875 | − | 0.399175i | \(-0.130703\pi\) |
−0.804133 | + | 0.594449i | \(0.797370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3784.44 | −1.55412 | −0.777058 | − | 0.629429i | \(-0.783289\pi\) | ||||
−0.777058 | + | 0.629429i | \(0.783289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 560.000 | − | 969.948i | 0.224368 | − | 0.388617i | ||||
\(185\) | −376.181 | − | 651.564i | −0.149499 | − | 0.258940i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.89949 | + | 17.1464i | −0.00387124 | + | 0.00670519i | ||||
\(188\) | 2093.04 | 0.811970 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −56.0000 | −0.0213825 | ||||||||
\(191\) | 514.000 | − | 890.274i | 0.194721 | − | 0.337267i | −0.752088 | − | 0.659063i | \(-0.770953\pi\) |
0.946809 | + | 0.321796i | \(0.104286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2296.00 | − | 3976.79i | −0.856320 | − | 1.48319i | −0.875415 | − | 0.483372i | \(-0.839412\pi\) |
0.0190956 | − | 0.999818i | \(-0.493921\pi\) | |||||||
\(194\) | 1483.51 | − | 2569.51i | 0.549020 | − | 0.950930i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −794.000 | −0.287158 | −0.143579 | − | 0.989639i | \(-0.545861\pi\) | ||||
−0.143579 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1243.09 | + | 2153.10i | 0.442817 | + | 0.766981i | 0.997897 | − | 0.0648153i | \(-0.0206458\pi\) |
−0.555080 | + | 0.831797i | \(0.687312\pi\) | |||||||
\(200\) | −1068.00 | − | 1849.83i | −0.377595 | − | 0.654014i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2257.08 | 0.786178 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1246.00 | + | 2158.14i | −0.424509 | + | 0.735272i | ||||
\(206\) | −868.327 | − | 1503.99i | −0.293686 | − | 0.508678i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 407.294 | − | 705.453i | 0.135773 | − | 0.235165i | ||||
\(209\) | 19.7990 | 0.00655275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2748.00 | −0.896588 | −0.448294 | − | 0.893886i | \(-0.647968\pi\) | ||||
−0.448294 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(212\) | −148.000 | + | 256.344i | −0.0479466 | + | 0.0830460i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1684.00 | − | 2916.77i | −0.537925 | − | 0.931713i | ||||
\(215\) | −336.583 | + | 582.979i | −0.106766 | + | 0.184925i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1636.00 | −0.508275 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 554.372 | + | 960.200i | 0.169890 | + | 0.294258i | ||||
\(221\) | 36.0000 | + | 62.3538i | 0.0109576 | + | 0.0189791i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3428.05 | 1.02941 | 0.514707 | − | 0.857366i | \(-0.327901\pi\) | ||||
0.514707 | + | 0.857366i | \(0.327901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −540.000 | + | 935.307i | −0.158939 | + | 0.275291i | ||||
\(227\) | −2645.29 | − | 4581.77i | −0.773453 | − | 1.33966i | −0.935660 | − | 0.352903i | \(-0.885195\pi\) |
0.162207 | − | 0.986757i | \(-0.448139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1374.62 | + | 2380.90i | −0.396669 | + | 0.687051i | −0.993313 | − | 0.115456i | \(-0.963167\pi\) |
0.596644 | + | 0.802506i | \(0.296501\pi\) | |||||||
\(230\) | 5543.72 | 1.58931 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2288.00 | 0.647477 | ||||||||
\(233\) | 36.0000 | − | 62.3538i | 0.0101221 | − | 0.0175319i | −0.860920 | − | 0.508740i | \(-0.830111\pi\) |
0.871042 | + | 0.491208i | \(0.163445\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5180.00 | + | 8972.02i | 1.43790 | + | 2.49051i | ||||
\(236\) | −868.327 | + | 1503.99i | −0.239505 | + | 0.414836i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4308.00 | −1.16595 | −0.582974 | − | 0.812491i | \(-0.698111\pi\) | ||||
−0.582974 | + | 0.812491i | \(0.698111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −770.039 | − | 1333.75i | −0.205820 | − | 0.356490i | 0.744574 | − | 0.667540i | \(-0.232653\pi\) |
−0.950394 | + | 0.311050i | \(0.899319\pi\) | |||||||
\(242\) | 1135.00 | + | 1965.88i | 0.301490 | + | 0.522196i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −56.5685 | −0.0148419 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.0000 | − | 62.3538i | 0.00927379 | − | 0.0160627i | ||||
\(248\) | −373.352 | − | 646.665i | −0.0955964 | − | 0.165578i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2811.46 | − | 4869.59i | 0.711249 | − | 1.23192i | ||||
\(251\) | 931.967 | 0.234363 | 0.117182 | − | 0.993110i | \(-0.462614\pi\) | ||||
0.117182 | + | 0.993110i | \(0.462614\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1960.00 | −0.487052 | ||||||||
\(254\) | −1720.00 | + | 2979.13i | −0.424891 | + | 0.735933i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −468.812 | + | 812.006i | −0.113789 | + | 0.197088i | −0.917295 | − | 0.398209i | \(-0.869632\pi\) |
0.803506 | + | 0.595296i | \(0.202965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4032.00 | 0.961746 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1735.24 | + | 3005.52i | 0.409174 | + | 0.708709i | ||||
\(263\) | 3570.00 | + | 6183.42i | 0.837018 | + | 1.44976i | 0.892377 | + | 0.451291i | \(0.149036\pi\) |
−0.0553595 | + | 0.998466i | \(0.517630\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1465.13 | −0.339630 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1368.00 | + | 2369.45i | −0.311806 | + | 0.540063i | ||||
\(269\) | −2305.17 | − | 3992.67i | −0.522485 | − | 0.904971i | −0.999658 | − | 0.0261615i | \(-0.991672\pi\) |
0.477172 | − | 0.878810i | \(-0.341662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1182.28 | + | 2047.77i | −0.265013 | + | 0.459016i | −0.967567 | − | 0.252614i | \(-0.918710\pi\) |
0.702554 | + | 0.711630i | \(0.252043\pi\) | |||||||
\(272\) | 22.6274 | 0.00504408 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1656.00 | −0.365119 | ||||||||
\(275\) | −1869.00 | + | 3237.20i | −0.409836 | + | 0.709857i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2003.00 | − | 3469.30i | −0.434472 | − | 0.752527i | 0.562781 | − | 0.826606i | \(-0.309731\pi\) |
−0.997252 | + | 0.0740794i | \(0.976398\pi\) | |||||||
\(278\) | −425.678 | + | 737.296i | −0.0918363 | + | 0.159065i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5984.00 | 1.27038 | 0.635188 | − | 0.772358i | \(-0.280923\pi\) | ||||
0.635188 | + | 0.772358i | \(0.280923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2464.27 | − | 4268.24i | −0.517617 | − | 0.896538i | −0.999791 | − | 0.0204627i | \(-0.993486\pi\) |
0.482174 | − | 0.876075i | \(-0.339847\pi\) | |||||||
\(284\) | 1176.00 | + | 2036.89i | 0.245714 | + | 0.425589i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1425.53 | −0.294731 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2455.50 | − | 4253.05i | 0.499796 | − | 0.865673i | ||||
\(290\) | 5662.51 | + | 9807.76i | 1.14660 | + | 1.98597i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −540.230 | + | 935.705i | −0.108269 | + | 0.187527i | ||||
\(293\) | 1971.41 | 0.393076 | 0.196538 | − | 0.980496i | \(-0.437030\pi\) | ||||
0.196538 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8596.00 | −1.69654 | ||||||||
\(296\) | 152.000 | − | 263.272i | 0.0298474 | − | 0.0516972i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2050.00 | + | 3550.70i | 0.398501 | + | 0.690224i | ||||
\(299\) | −3563.82 | + | 6172.71i | −0.689301 | + | 1.19390i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −944.000 | −0.179871 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.3137 | − | 19.5959i | −0.00213449 | − | 0.00369705i | ||||
\(305\) | −140.000 | − | 242.487i | −0.0262832 | − | 0.0455238i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4767.31 | 0.886270 | 0.443135 | − | 0.896455i | \(-0.353866\pi\) | ||||
0.443135 | + | 0.896455i | \(0.353866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1848.00 | − | 3200.83i | 0.338579 | − | 0.586435i | ||||
\(311\) | 3388.46 | + | 5868.98i | 0.617819 | + | 1.07009i | 0.989883 | + | 0.141887i | \(0.0453169\pi\) |
−0.372064 | + | 0.928207i | \(0.621350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3095.01 | + | 5360.71i | −0.558914 | + | 0.968068i | 0.438673 | + | 0.898647i | \(0.355449\pi\) |
−0.997587 | + | 0.0694210i | \(0.977885\pi\) | |||||||
\(314\) | 4423.66 | 0.795037 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4880.00 | 0.868739 | ||||||||
\(317\) | 4913.00 | − | 8509.57i | 0.870478 | − | 1.50771i | 0.00897524 | − | 0.999960i | \(-0.497143\pi\) |
0.861503 | − | 0.507753i | \(-0.169524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2002.00 | − | 3467.57i | −0.351381 | − | 0.608609i | ||||
\(320\) | 633.568 | − | 1097.37i | 0.110680 | − | 0.191703i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.000344529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6796.71 | + | 11772.2i | 1.16004 | + | 2.00925i | ||||
\(326\) | −3286.00 | − | 5691.52i | −0.558266 | − | 0.966945i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1006.92 | −0.169506 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2869.00 | − | 4969.25i | 0.476418 | − | 0.825181i | −0.523216 | − | 0.852200i | \(-0.675268\pi\) |
0.999635 | + | 0.0270189i | \(0.00860142\pi\) | |||||||
\(332\) | −845.700 | − | 1464.79i | −0.139801 | − | 0.242142i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1490.58 | − | 2581.76i | 0.244195 | − | 0.422957i | ||||
\(335\) | −13542.5 | −2.20868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2254.00 | −0.364342 | −0.182171 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182171 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(338\) | −395.000 | + | 684.160i | −0.0635656 | + | 0.110099i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 56.0000 | + | 96.9948i | 0.00893243 | + | 0.0154714i | ||||
\(341\) | −653.367 | + | 1131.66i | −0.103759 | + | 0.179716i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −272.000 | −0.0426316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2070.41 | + | 3586.05i | 0.321693 | + | 0.557189i | ||||
\(347\) | −993.000 | − | 1719.93i | −0.153623 | − | 0.266082i | 0.778934 | − | 0.627106i | \(-0.215761\pi\) |
−0.932557 | + | 0.361024i | \(0.882427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6771.25 | −1.03856 | −0.519279 | − | 0.854605i | \(-0.673800\pi\) | ||||
−0.519279 | + | 0.854605i | \(0.673800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −224.000 | + | 387.979i | −0.0339183 | + | 0.0587482i | ||||
\(353\) | −3496.64 | − | 6056.36i | −0.527217 | − | 0.913166i | −0.999497 | − | 0.0317177i | \(-0.989902\pi\) |
0.472280 | − | 0.881449i | \(-0.343431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5820.90 | + | 10082.1i | −0.870258 | + | 1.50733i | ||||
\(356\) | 2472.05 | 0.368028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1080.00 | −0.159441 | ||||||||
\(359\) | 2972.00 | − | 5147.66i | 0.436925 | − | 0.756777i | −0.560525 | − | 0.828137i | \(-0.689401\pi\) |
0.997451 | + | 0.0713606i | \(0.0227341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3428.50 | + | 5938.34i | 0.499854 | + | 0.865773i | ||||
\(362\) | 3784.44 | − | 6554.83i | 0.549463 | − | 0.951697i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5348.00 | −0.766924 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −421.436 | − | 729.948i | −0.0599421 | − | 0.103823i | 0.834497 | − | 0.551012i | \(-0.185758\pi\) |
−0.894439 | + | 0.447190i | \(0.852425\pi\) | |||||||
\(368\) | 1120.00 | + | 1939.90i | 0.158652 | + | 0.274794i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1504.72 | 0.211424 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2863.00 | − | 4958.86i | 0.397428 | − | 0.688365i | −0.595980 | − | 0.802999i | \(-0.703236\pi\) |
0.993408 | + | 0.114634i | \(0.0365696\pi\) | |||||||
\(374\) | −19.7990 | − | 34.2929i | −0.00273738 | − | 0.00474129i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2093.04 | + | 3625.24i | −0.287075 | + | 0.497228i | ||||
\(377\) | −14560.7 | −1.98917 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10330.0 | 1.40004 | 0.700022 | − | 0.714122i | \(-0.253174\pi\) | ||||
0.700022 | + | 0.714122i | \(0.253174\pi\) | |||||||
\(380\) | 56.0000 | − | 96.9948i | 0.00755984 | − | 0.0130940i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1028.00 | + | 1780.55i | 0.137689 | + | 0.238484i | ||||
\(383\) | −502.046 | + | 869.569i | −0.0669800 | + | 0.116013i | −0.897571 | − | 0.440871i | \(-0.854670\pi\) |
0.830591 | + | 0.556884i | \(0.188003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9184.00 | 1.21102 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2967.02 | + | 5139.03i | 0.388216 | + | 0.672409i | ||||
\(389\) | 2605.00 | + | 4511.99i | 0.339534 | + | 0.588090i | 0.984345 | − | 0.176252i | \(-0.0563973\pi\) |
−0.644811 | + | 0.764342i | \(0.723064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −197.990 | −0.0256081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 794.000 | − | 1375.25i | 0.101526 | − | 0.175848i | ||||
\(395\) | 12077.4 | + | 20918.6i | 1.53843 | + | 2.66464i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.7696 | + | 63.6867i | −0.00464839 | + | 0.00805125i | −0.868340 | − | 0.495969i | \(-0.834813\pi\) |
0.863692 | + | 0.504020i | \(0.168146\pi\) | |||||||
\(398\) | −4972.37 | −0.626238 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4272.00 | 0.534000 | ||||||||
\(401\) | −249.000 | + | 431.281i | −0.0310086 | + | 0.0537085i | −0.881113 | − | 0.472905i | \(-0.843205\pi\) |
0.850105 | + | 0.526614i | \(0.176539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2376.00 | + | 4115.35i | 0.293690 | + | 0.508686i | ||||
\(404\) | −2257.08 | + | 3909.39i | −0.277956 | + | 0.481434i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −532.000 | −0.0647918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1677.96 | + | 2906.32i | 0.202861 | + | 0.351365i | 0.949449 | − | 0.313921i | \(-0.101643\pi\) |
−0.746588 | + | 0.665286i | \(0.768309\pi\) | |||||||
\(410\) | −2492.00 | − | 4316.27i | −0.300173 | − | 0.519916i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3473.31 | 0.415334 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4186.00 | − | 7250.36i | 0.495139 | − | 0.857606i | ||||
\(416\) | 814.587 | + | 1410.91i | 0.0960058 | + | 0.166287i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −19.7990 | + | 34.2929i | −0.00231675 | + | 0.00401272i | ||||
\(419\) | 14545.2 | 1.69589 | 0.847946 | − | 0.530082i | \(-0.177839\pi\) | ||||
0.847946 | + | 0.530082i | \(0.177839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10854.0 | 1.25651 | 0.628256 | − | 0.778007i | \(-0.283769\pi\) | ||||
0.628256 | + | 0.778007i | \(0.283769\pi\) | |||||||
\(422\) | 2748.00 | − | 4759.68i | 0.316992 | − | 0.549046i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −296.000 | − | 512.687i | −0.0339034 | − | 0.0587224i | ||||
\(425\) | −188.798 | + | 327.007i | −0.0215483 | + | 0.0373227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6736.00 | 0.760740 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −673.166 | − | 1165.96i | −0.0754952 | − | 0.130762i | ||||
\(431\) | −2682.00 | − | 4645.36i | −0.299739 | − | 0.519163i | 0.676337 | − | 0.736592i | \(-0.263566\pi\) |
−0.976076 | + | 0.217429i | \(0.930233\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6487.00 | 0.719966 | 0.359983 | − | 0.932959i | \(-0.382783\pi\) | ||||
0.359983 | + | 0.932959i | \(0.382783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1636.00 | − | 2833.64i | 0.179702 | − | 0.311253i | ||||
\(437\) | 98.9949 | + | 171.464i | 0.0108365 | + | 0.0187694i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6966.42 | − | 12066.2i | 0.757378 | − | 1.31182i | −0.186806 | − | 0.982397i | \(-0.559813\pi\) |
0.944183 | − | 0.329420i | \(-0.106853\pi\) | |||||||
\(440\) | −2217.49 | −0.240260 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −144.000 | −0.0154963 | ||||||||
\(443\) | 2998.00 | − | 5192.69i | 0.321533 | − | 0.556912i | −0.659271 | − | 0.751905i | \(-0.729135\pi\) |
0.980805 | + | 0.194993i | \(0.0624684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6118.00 | + | 10596.7i | 0.651733 | + | 1.12883i | ||||
\(446\) | −3428.05 | + | 5937.56i | −0.363953 | + | 0.630385i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2622.00 | −0.275590 | −0.137795 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137795 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 881.055 | + | 1526.03i | 0.0919895 | + | 0.159330i | ||||
\(452\) | −1080.00 | − | 1870.61i | −0.112387 | − | 0.194660i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10581.1 | 1.09383 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5604.00 | + | 9706.41i | −0.573619 | + | 0.993538i | 0.422571 | + | 0.906330i | \(0.361128\pi\) |
−0.996190 | + | 0.0872080i | \(0.972206\pi\) | |||||||
\(458\) | −2749.23 | − | 4761.81i | −0.280487 | − | 0.485818i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5543.72 | + | 9602.00i | −0.561907 | + | 0.973251i | ||||
\(461\) | 9786.36 | 0.988712 | 0.494356 | − | 0.869260i | \(-0.335404\pi\) | ||||
0.494356 | + | 0.869260i | \(0.335404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3952.00 | 0.396685 | 0.198342 | − | 0.980133i | \(-0.436444\pi\) | ||||
0.198342 | + | 0.980133i | \(0.436444\pi\) | |||||||
\(464\) | −2288.00 | + | 3962.93i | −0.228918 | + | 0.396497i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 72.0000 | + | 124.708i | 0.00715737 | + | 0.0123969i | ||||
\(467\) | −8753.27 | + | 15161.1i | −0.867352 | + | 1.50230i | −0.00265876 | + | 0.999996i | \(0.500846\pi\) |
−0.864693 | + | 0.502301i | \(0.832487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −20720.0 | −2.03349 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1736.65 | − | 3007.97i | −0.169356 | − | 0.293333i | ||||
\(473\) | 238.000 | + | 412.228i | 0.0231358 | + | 0.0400724i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 377.595 | 0.0364742 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4308.00 | − | 7461.67i | 0.412225 | − | 0.713994i | ||||
\(479\) | −1144.10 | − | 1981.64i | −0.109134 | − | 0.189026i | 0.806286 | − | 0.591526i | \(-0.201474\pi\) |
−0.915420 | + | 0.402501i | \(0.868141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −967.322 | + | 1675.45i | −0.0916967 | + | 0.158823i | ||||
\(482\) | 3080.16 | 0.291073 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4540.00 | −0.426371 | ||||||||
\(485\) | −14686.0 | + | 25436.9i | −1.37496 | + | 2.38151i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −486.000 | − | 841.777i | −0.0452213 | − | 0.0783256i | 0.842529 | − | 0.538651i | \(-0.181066\pi\) |
−0.887750 | + | 0.460326i | \(0.847733\pi\) | |||||||
\(488\) | 56.5685 | − | 97.9796i | 0.00524741 | − | 0.00908879i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7404.00 | 0.680525 | 0.340263 | − | 0.940330i | \(-0.389484\pi\) | ||||
0.340263 | + | 0.940330i | \(0.389484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −202.233 | − | 350.277i | −0.0184748 | − | 0.0319994i | ||||
\(494\) | 72.0000 | + | 124.708i | 0.00655756 | + | 0.0113580i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1493.41 | 0.135194 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6122.00 | − | 10603.6i | 0.549215 | − | 0.951269i | −0.449113 | − | 0.893475i | \(-0.648260\pi\) |
0.998329 | − | 0.0577938i | \(-0.0184066\pi\) | |||||||
\(500\) | 5622.91 | + | 9739.17i | 0.502929 | + | 0.871098i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −931.967 | + | 1614.21i | −0.0828600 | + | 0.143518i | ||||
\(503\) | −2415.48 | −0.214117 | −0.107058 | − | 0.994253i | \(-0.534143\pi\) | ||||
−0.107058 | + | 0.994253i | \(0.534143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22344.0 | −1.96890 | ||||||||
\(506\) | 1960.00 | − | 3394.82i | 0.172199 | − | 0.298257i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3440.00 | − | 5958.25i | −0.300444 | − | 0.520383i | ||||
\(509\) | 2853.88 | − | 4943.07i | 0.248519 | − | 0.430447i | −0.714596 | − | 0.699537i | \(-0.753390\pi\) |
0.963115 | + | 0.269090i | \(0.0867228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −937.624 | − | 1624.01i | −0.0804607 | − | 0.139362i | ||||
\(515\) | 8596.00 | + | 14888.7i | 0.735505 | + | 1.27393i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7325.63 | 0.623173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4032.00 | + | 6983.63i | −0.340029 | + | 0.588947i | ||||
\(521\) | −0.707107 | − | 1.22474i | −5.94605e−5 | − | 0.000102989i | 0.865996 | − | 0.500051i | \(-0.166686\pi\) |
−0.866055 | + | 0.499949i | \(0.833352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6128.49 | + | 10614.9i | −0.512391 | + | 0.887487i | 0.487506 | + | 0.873120i | \(0.337907\pi\) |
−0.999897 | + | 0.0143672i | \(0.995427\pi\) | |||||||
\(524\) | −6940.96 | −0.578659 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14280.0 | −1.18372 | ||||||||
\(527\) | −66.0000 | + | 114.315i | −0.00545542 | + | 0.00944906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3716.50 | − | 6437.17i | −0.305457 | − | 0.529068i | ||||
\(530\) | 1465.13 | − | 2537.67i | 0.120077 | − | 0.207980i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6408.00 | 0.520753 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16670.7 | + | 28874.6i | 1.34718 | + | 2.33338i | ||||
\(536\) | −2736.00 | − | 4738.89i | −0.220480 | − | 0.381882i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9220.67 | 0.738906 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1025.00 | + | 1775.35i | −0.0814569 | + | 0.141088i | −0.903876 | − | 0.427795i | \(-0.859291\pi\) |
0.822419 | + | 0.568882i | \(0.192624\pi\) | |||||||
\(542\) | −2364.57 | − | 4095.55i | −0.187393 | − | 0.324573i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22.6274 | + | 39.1918i | −0.00178335 | + | 0.00308885i | ||||
\(545\) | 16195.6 | 1.27292 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14554.0 | 1.13763 | 0.568815 | − | 0.822465i | \(-0.307402\pi\) | ||||
0.568815 | + | 0.822465i | \(0.307402\pi\) | |||||||
\(548\) | 1656.00 | − | 2868.28i | 0.129089 | − | 0.223589i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3738.00 | − | 6474.41i | −0.289798 | − | 0.501945i | ||||
\(551\) | −202.233 | + | 350.277i | −0.0156359 | + | 0.0270822i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8012.00 | 0.614435 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −851.357 | − | 1474.59i | −0.0649381 | − | 0.112476i | ||||
\(557\) | 3477.00 | + | 6022.34i | 0.264498 | + | 0.458123i | 0.967432 | − | 0.253131i | \(-0.0814605\pi\) |
−0.702934 | + | 0.711255i | \(0.748127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1731.00 | 0.130972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5984.00 | + | 10364.6i | −0.449146 | + | 0.777943i | ||||
\(563\) | 818.123 | + | 1417.03i | 0.0612429 | + | 0.106076i | 0.895021 | − | 0.446024i | \(-0.147160\pi\) |
−0.833778 | + | 0.552099i | \(0.813827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5345.73 | − | 9259.07i | 0.398047 | − | 0.689437i | ||||
\(566\) | 9857.07 | 0.732020 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4704.00 | −0.347492 | ||||||||
\(569\) | −3571.00 | + | 6185.15i | −0.263100 | + | 0.455703i | −0.967064 | − | 0.254533i | \(-0.918078\pi\) |
0.703964 | + | 0.710236i | \(0.251412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10303.0 | + | 17845.3i | 0.755109 | + | 1.30789i | 0.945320 | + | 0.326144i | \(0.105749\pi\) |
−0.190211 | + | 0.981743i | \(0.560917\pi\) | |||||||
\(572\) | 1425.53 | − | 2469.09i | 0.104203 | − | 0.180485i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37380.0 | −2.71105 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4401.74 | − | 7624.04i | −0.317585 | − | 0.550074i | 0.662398 | − | 0.749152i | \(-0.269539\pi\) |
−0.979984 | + | 0.199078i | \(0.936205\pi\) | |||||||
\(578\) | 4911.00 | + | 8506.10i | 0.353409 | + | 0.612123i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −22650.0 | −1.62154 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −518.000 | + | 897.202i | −0.0367982 | + | 0.0637364i | ||||
\(584\) | −1080.46 | − | 1871.41i | −0.0765577 | − | 0.132602i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1971.41 | + | 3414.59i | −0.138973 | + | 0.240709i | ||||
\(587\) | 6503.97 | 0.457321 | 0.228661 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228661 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 132.000 | 0.00923424 | ||||||||
\(590\) | 8596.00 | − | 14888.7i | 0.599816 | − | 1.03891i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 304.000 | + | 526.543i | 0.0211053 | + | 0.0365554i | ||||
\(593\) | 11570.4 | − | 20040.5i | 0.801246 | − | 1.38780i | −0.117550 | − | 0.993067i | \(-0.537504\pi\) |
0.918796 | − | 0.394732i | \(-0.129163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8200.00 | −0.563566 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7127.64 | − | 12345.4i | −0.487409 | − | 0.844218i | ||||
\(599\) | −5648.00 | − | 9782.62i | −0.385260 | − | 0.667291i | 0.606545 | − | 0.795049i | \(-0.292555\pi\) |
−0.991805 | + | 0.127759i | \(0.959222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8727.11 | −0.592323 | −0.296162 | − | 0.955138i | \(-0.595707\pi\) | ||||
−0.296162 | + | 0.955138i | \(0.595707\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 944.000 | − | 1635.06i | 0.0635941 | − | 0.110148i | ||||
\(605\) | −11235.9 | − | 19461.2i | −0.755050 | − | 1.30779i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9868.38 | − | 17092.5i | 0.659877 | − | 1.14294i | −0.320770 | − | 0.947157i | \(-0.603942\pi\) |
0.980647 | − | 0.195783i | \(-0.0627249\pi\) | |||||||
\(608\) | 45.2548 | 0.00301863 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 560.000 | 0.0371701 | ||||||||
\(611\) | 13320.0 | − | 23070.9i | 0.881947 | − | 1.52758i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8481.00 | − | 14689.5i | −0.558800 | − | 0.967870i | −0.997597 | − | 0.0692837i | \(-0.977929\pi\) |
0.438797 | − | 0.898586i | \(-0.355405\pi\) | |||||||
\(614\) | −4767.31 | + | 8257.23i | −0.313344 | + | 0.542727i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19034.0 | 1.24194 | 0.620972 | − | 0.783832i | \(-0.286738\pi\) | ||||
0.620972 | + | 0.783832i | \(0.286738\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9338.76 | − | 16175.2i | −0.606392 | − | 1.05030i | −0.991830 | − | 0.127568i | \(-0.959283\pi\) |
0.385438 | − | 0.922734i | \(-0.374050\pi\) | |||||||
\(620\) | 3696.00 | + | 6401.66i | 0.239411 | + | 0.414672i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13553.8 | −0.873728 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11144.5 | + | 19302.8i | −0.713248 | + | 1.23538i | ||||
\(626\) | −6190.01 | − | 10721.4i | −0.395212 | − | 0.684527i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4423.66 | + | 7662.00i | −0.281088 | + | 0.486859i | ||||
\(629\) | −53.7401 | −0.00340661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14716.0 | −0.928423 | −0.464211 | − | 0.885724i | \(-0.653662\pi\) | ||||
−0.464211 | + | 0.885724i | \(0.653662\pi\) | |||||||
\(632\) | −4880.00 | + | 8452.41i | −0.307146 | + | 0.531992i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9826.00 | + | 17019.1i | 0.615521 | + | 1.06611i | ||||
\(635\) | 17027.1 | − | 29491.9i | 1.06410 | − | 1.84307i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8008.00 | 0.496928 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1267.14 | + | 2194.74i | 0.0782624 | + | 0.135554i | ||||
\(641\) | 2365.00 | + | 4096.30i | 0.145728 | + | 0.252409i | 0.929644 | − | 0.368458i | \(-0.120114\pi\) |
−0.783916 | + | 0.620867i | \(0.786781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19056.5 | −1.16877 | −0.584383 | − | 0.811478i | \(-0.698663\pi\) | ||||
−0.584383 | + | 0.811478i | \(0.698663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.00000 | + | 3.46410i | −0.000121810 | + | 0.000210980i | ||||
\(647\) | −4671.15 | − | 8090.66i | −0.283836 | − | 0.491618i | 0.688490 | − | 0.725245i | \(-0.258274\pi\) |
−0.972326 | + | 0.233627i | \(0.924940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3039.14 | + | 5263.95i | −0.183816 | + | 0.318379i | ||||
\(650\) | −27186.8 | −1.64055 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13144.0 | 0.789507 | ||||||||
\(653\) | 1887.00 | − | 3268.38i | 0.113084 | − | 0.195868i | −0.803928 | − | 0.594727i | \(-0.797260\pi\) |
0.917012 | + | 0.398859i | \(0.130594\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17178.0 | − | 29753.2i | −1.02473 | − | 1.77489i | ||||
\(656\) | 1006.92 | − | 1744.04i | 0.0599293 | − | 0.103801i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21150.0 | 1.25021 | 0.625104 | − | 0.780541i | \(-0.285057\pi\) | ||||
0.625104 | + | 0.780541i | \(0.285057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5188.75 | − | 8987.18i | −0.305324 | − | 0.528836i | 0.672010 | − | 0.740542i | \(-0.265431\pi\) |
−0.977333 | + | 0.211706i | \(0.932098\pi\) | |||||||
\(662\) | 5738.00 | + | 9938.51i | 0.336879 | + | 0.583491i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3382.80 | 0.197708 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20020.0 | − | 34675.7i | 1.16219 | − | 2.01296i | ||||
\(668\) | 2981.16 | + | 5163.52i | 0.172672 | + | 0.299076i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13542.5 | − | 23456.3i | 0.780885 | − | 1.35253i | ||||
\(671\) | −197.990 | −0.0113909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1164.00 | −0.0666700 | −0.0333350 | − | 0.999444i | \(-0.510613\pi\) | ||||
−0.0333350 | + | 0.999444i | \(0.510613\pi\) | |||||||
\(674\) | 2254.00 | − | 3904.04i | 0.128814 | − | 0.223113i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −790.000 | − | 1368.32i | −0.0449477 | − | 0.0778516i | ||||
\(677\) | −13576.5 | + | 23515.1i | −0.770732 | + | 1.33495i | 0.166431 | + | 0.986053i | \(0.446776\pi\) |
−0.937162 | + | 0.348893i | \(0.886558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −224.000 | −0.0126324 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1306.73 | − | 2263.33i | −0.0733686 | − | 0.127078i | ||||
\(683\) | −8298.00 | − | 14372.6i | −0.464882 | − | 0.805199i | 0.534315 | − | 0.845286i | \(-0.320570\pi\) |
−0.999196 | + | 0.0400871i | \(0.987236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16393.6 | 0.914403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 272.000 | − | 471.118i | 0.0150725 | − | 0.0261064i | ||||
\(689\) | 1883.73 | + | 3262.72i | 0.104157 | + | 0.180406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5649.08 | − | 9784.49i | 0.311000 | − | 0.538668i | −0.667579 | − | 0.744539i | \(-0.732669\pi\) |
0.978579 | + | 0.205871i | \(0.0660028\pi\) | |||||||
\(692\) | −8281.63 | −0.454943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3972.00 | 0.217255 | ||||||||
\(695\) | 4214.00 | − | 7298.86i | 0.229994 | − | 0.398362i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 89.0000 | + | 154.153i | 0.00483661 | + | 0.00837725i | ||||
\(698\) | 6771.25 | − | 11728.2i | 0.367186 | − | 0.635985i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2754.00 | 0.148384 | 0.0741920 | − | 0.997244i | \(-0.476362\pi\) | ||||
0.0741920 | + | 0.997244i | \(0.476362\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.8701 | + | 46.5403i | 0.00144157 | + | 0.00249687i | ||||
\(704\) | −448.000 | − | 775.959i | −0.0239839 | − | 0.0415413i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13986.6 | 0.745597 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14717.0 | + | 25490.6i | −0.779561 | + | 1.35024i | 0.152634 | + | 0.988283i | \(0.451224\pi\) |
−0.932195 | + | 0.361956i | \(0.882109\pi\) | |||||||
\(710\) | −11641.8 | − | 20164.2i | −0.615365 | − | 1.06584i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2472.05 | + | 4281.71i | −0.130118 | + | 0.225370i | ||||
\(713\) | −13067.3 | −0.686361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14112.0 | 0.738124 | ||||||||
\(716\) | 1080.00 | − | 1870.61i | 0.0563708 | − | 0.0976371i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5944.00 | + | 10295.3i | 0.308953 | + | 0.535122i | ||||
\(719\) | 8834.59 | − | 15302.0i | 0.458240 | − | 0.793695i | −0.540628 | − | 0.841262i | \(-0.681813\pi\) |
0.998868 | + | 0.0475666i | \(0.0151466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13714.0 | −0.706901 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7568.87 | + | 13109.7i | 0.388529 | + | 0.672952i | ||||
\(725\) | −38181.0 | − | 66131.4i | −1.95587 | − | 3.38767i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28445.5 | −1.45115 | −0.725574 | − | 0.688144i | \(-0.758426\pi\) | ||||
−0.725574 | + | 0.688144i | \(0.758426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5348.00 | − | 9263.01i | 0.271148 | − | 0.469643i | ||||
\(731\) | 24.0416 | + | 41.6413i | 0.00121643 | + | 0.00210692i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11170.9 | − | 19348.5i | 0.562900 | − | 0.974971i | −0.434342 | − | 0.900748i | \(-0.643019\pi\) |
0.997242 | − | 0.0742230i | \(-0.0236477\pi\) | |||||||
\(734\) | 1685.74 | 0.0847710 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4480.00 | −0.224368 | ||||||||
\(737\) | −4788.00 | + | 8293.06i | −0.239306 | + | 0.414490i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10335.0 | − | 17900.7i | −0.514451 | − | 0.891055i | −0.999859 | − | 0.0167675i | \(-0.994662\pi\) |
0.485409 | − | 0.874287i | \(-0.338671\pi\) | |||||||
\(740\) | −1504.72 | + | 2606.26i | −0.0747496 | + | 0.129470i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25400.0 | 1.25415 | 0.627076 | − | 0.778958i | \(-0.284251\pi\) | ||||
0.627076 | + | 0.778958i | \(0.284251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20294.0 | − | 35150.2i | −0.998004 | − | 1.72859i | ||||
\(746\) | 5726.00 | + | 9917.72i | 0.281024 | + | 0.486748i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 79.1960 | 0.00387124 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14590.0 | + | 25270.6i | −0.708917 | + | 1.22788i | 0.256342 | + | 0.966586i | \(0.417483\pi\) |
−0.965259 | + | 0.261294i | \(0.915851\pi\) | |||||||
\(752\) | −4186.07 | − | 7250.49i | −0.202992 | − | 0.351593i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14560.7 | − | 25219.9i | 0.703277 | − | 1.21811i | ||||
\(755\) | 9345.12 | 0.450469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26206.0 | −1.25822 | −0.629110 | − | 0.777316i | \(-0.716581\pi\) | ||||
−0.629110 | + | 0.777316i | \(0.716581\pi\) | |||||||
\(758\) | −10330.0 | + | 17892.1i | −0.494990 | + | 0.857348i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 112.000 | + | 193.990i | 0.00534561 | + | 0.00925888i | ||||
\(761\) | −3431.59 | + | 5943.69i | −0.163463 | + | 0.283125i | −0.936108 | − | 0.351712i | \(-0.885600\pi\) |
0.772646 | + | 0.634838i | \(0.218933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4112.00 | −0.194721 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1004.09 | − | 1739.14i | −0.0473620 | − | 0.0820334i | ||||
\(767\) | 11052.0 | + | 19142.6i | 0.520293 | + | 0.901174i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9058.04 | 0.424761 | 0.212380 | − | 0.977187i | \(-0.431878\pi\) | ||||
0.212380 | + | 0.977187i | \(0.431878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9184.00 | + | 15907.2i | −0.428160 | + | 0.741595i | ||||
\(773\) | 66.4680 | + | 115.126i | 0.00309274 | + | 0.00535679i | 0.867568 | − | 0.497319i | \(-0.165682\pi\) |
−0.864475 | + | 0.502676i | \(0.832349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12460.6 | + | 21582.5i | −0.577547 | + | 1.00034i | ||||
\(776\) | −11868.1 | −0.549020 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10420.0 | −0.480174 | ||||||||
\(779\) | 89.0000 | − | 154.153i | 0.00409340 | − | 0.00708997i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4116.00 | + | 7129.12i | 0.188581 | + | 0.326633i | ||||
\(782\) | 197.990 | − | 342.929i | 0.00905384 | − | 0.0156817i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43792.0 | −1.99109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4364.97 | − | 7560.35i | −0.197706 | − | 0.342436i | 0.750078 | − | 0.661349i | \(-0.230016\pi\) |
−0.947784 | + | 0.318913i | \(0.896682\pi\) | |||||||
\(788\) | 1588.00 | + | 2750.50i | 0.0717895 | + | 0.124343i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −48309.5 | −2.17567 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −360.000 | + | 623.538i | −0.0161210 | + | 0.0279224i | ||||
\(794\) | −73.5391 | − | 127.373i | −0.00328691 | − | 0.00569309i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4972.37 | − | 8612.41i | 0.221408 | − | 0.383491i | ||||
\(797\) | 7517.96 | 0.334128 | 0.167064 | − | 0.985946i | \(-0.446571\pi\) | ||||
0.167064 | + | 0.985946i | \(0.446571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 740.000 | 0.0327651 | ||||||||
\(800\) | −4272.00 | + | 7399.32i | −0.188798 | + | 0.327007i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −498.000 | − | 862.561i | −0.0219264 | − | 0.0379777i | ||||
\(803\) | −1890.80 | + | 3274.97i | −0.0830947 | + | 0.143924i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9504.00 | −0.415340 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4514.17 | − | 7818.77i | −0.196544 | − | 0.340425i | ||||
\(809\) | 1888.00 | + | 3270.11i | 0.0820501 | + | 0.142115i | 0.904130 | − | 0.427257i | \(-0.140520\pi\) |
−0.822080 | + | 0.569372i | \(0.807187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36227.9 | 1.56860 | 0.784300 | − | 0.620382i | \(-0.213023\pi\) | ||||
0.784300 | + | 0.620382i | \(0.213023\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 532.000 | − | 921.451i | 0.0229074 | − | 0.0396767i | ||||
\(815\) | 32529.7 | + | 56343.2i | 1.39812 | + | 2.42161i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0416 | − | 41.6413i | 0.00102951 | − | 0.00178316i | ||||
\(818\) | −6711.86 | −0.286888 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9968.00 | 0.424509 | ||||||||
\(821\) | −8205.00 | + | 14211.5i | −0.348790 | + | 0.604122i | −0.986035 | − | 0.166540i | \(-0.946741\pi\) |
0.637245 | + | 0.770661i | \(0.280074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11036.0 | − | 19114.9i | −0.467425 | − | 0.809604i | 0.531882 | − | 0.846818i | \(-0.321485\pi\) |
−0.999307 | + | 0.0372144i | \(0.988152\pi\) | |||||||
\(824\) | −3473.31 | + | 6015.95i | −0.146843 | + | 0.254339i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11628.0 | 0.488930 | 0.244465 | − | 0.969658i | \(-0.421388\pi\) | ||||
0.244465 | + | 0.969658i | \(0.421388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15453.1 | − | 26765.6i | −0.647417 | − | 1.12136i | −0.983738 | − | 0.179612i | \(-0.942516\pi\) |
0.336321 | − | 0.941748i | \(-0.390817\pi\) | |||||||
\(830\) | 8372.00 | + | 14500.7i | 0.350116 | + | 0.606419i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3258.35 | −0.135773 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14756.0 | + | 25558.1i | −0.611560 | + | 1.05925i | ||||
\(836\) | −39.5980 | − | 68.5857i | −0.00163819 | − | 0.00283742i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14545.2 | + | 25193.0i | −0.599588 | + | 1.03852i | ||||
\(839\) | 17884.1 | 0.735911 | 0.367955 | − | 0.929843i | \(-0.380058\pi\) | ||||
0.367955 | + | 0.929843i | \(0.380058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57407.0 | 2.35381 | ||||||||
\(842\) | −10854.0 | + | 18799.7i | −0.444244 | + | 0.769453i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5496.00 | + | 9519.35i | 0.224147 | + | 0.388234i | ||||
\(845\) | 3910.30 | − | 6772.84i | 0.159193 | − | 0.275731i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1184.00 | 0.0479466 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −377.595 | − | 654.014i | −0.0152369 | − | 0.0263912i | ||||
\(851\) | −2660.00 | − | 4607.26i | −0.107149 | − | 0.185587i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20755.0 | 0.833104 | 0.416552 | − | 0.909112i | \(-0.363238\pi\) | ||||
0.416552 | + | 0.909112i | \(0.363238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6736.00 | + | 11667.1i | −0.268962 | + | 0.465856i | ||||
\(857\) | −22459.8 | − | 38901.6i | −0.895231 | − | 1.55059i | −0.833518 | − | 0.552492i | \(-0.813677\pi\) |
−0.0617133 | − | 0.998094i | \(-0.519656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.6482 | − | 60.0125i | 0.00137623 | − | 0.00238370i | −0.865336 | − | 0.501191i | \(-0.832895\pi\) |
0.866713 | + | 0.498808i | \(0.166229\pi\) | |||||||
\(860\) | 2692.66 | 0.106766 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10728.0 | 0.423895 | ||||||||
\(863\) | −2726.00 | + | 4721.57i | −0.107525 | + | 0.186239i | −0.914767 | − | 0.403982i | \(-0.867626\pi\) |
0.807242 | + | 0.590221i | \(0.200959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20496.0 | − | 35500.1i | −0.805647 | − | 1.39542i | ||||
\(866\) | −6487.00 | + | 11235.8i | −0.254546 | + | 0.440887i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17080.0 | 0.666743 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17411.8 | + | 30158.1i | 0.677355 | + | 1.17321i | ||||
\(872\) | 3272.00 | + | 5667.27i | 0.127069 | + | 0.220089i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −395.980 | −0.0153252 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15553.0 | + | 26938.6i | −0.598845 | + | 1.03723i | 0.394146 | + | 0.919048i | \(0.371040\pi\) |
−0.992992 | + | 0.118183i | \(0.962293\pi\) | |||||||
\(878\) | 13932.8 | + | 24132.4i | 0.535547 | + | 0.927595i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2217.49 | − | 3840.80i | 0.0849448 | − | 0.147129i | ||||
\(881\) | 5943.94 | 0.227306 | 0.113653 | − | 0.993521i | \(-0.463745\pi\) | ||||
0.113653 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34796.0 | 1.32614 | 0.663068 | − | 0.748559i | \(-0.269254\pi\) | ||||
0.663068 | + | 0.748559i | \(0.269254\pi\) | |||||||
\(884\) | 144.000 | − | 249.415i | 0.00547878 | − | 0.00948953i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5996.00 | + | 10385.4i | 0.227358 | + | 0.393796i | ||||
\(887\) | −4982.27 | + | 8629.55i | −0.188600 | + | 0.326665i | −0.944784 | − | 0.327694i | \(-0.893728\pi\) |
0.756184 | + | 0.654360i | \(0.227062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24472.0 | −0.921689 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6856.11 | − | 11875.1i | −0.257354 | − | 0.445750i | ||||
\(893\) | −370.000 | − | 640.859i | −0.0138651 | − | 0.0240151i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10691.5 | 0.399303 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2622.00 | − | 4541.44i | 0.0974357 | − | 0.168764i | ||||
\(899\) | −13347.3 | − | 23118.3i | −0.495171 | − | 0.857662i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.3259 | + | 90.6311i | −0.00193477 | + | 0.00335112i | ||||
\(902\) | −3524.22 | −0.130093 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4320.00 | 0.158939 | ||||||||
\(905\) | −37464.0 | + | 64889.6i | −1.37607 | + | 2.38343i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14878.0 | + | 25769.5i | 0.544670 | + | 0.943396i | 0.998628 | + | 0.0523731i | \(0.0166785\pi\) |
−0.453957 | + | 0.891023i | \(0.649988\pi\) | |||||||
\(908\) | −10581.1 | + | 18327.1i | −0.386726 | + | 0.669830i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21440.0 | −0.779735 | −0.389868 | − | 0.920871i | \(-0.627479\pi\) | ||||
−0.389868 | + | 0.920871i | \(0.627479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2959.95 | − | 5126.78i | −0.107295 | − | 0.185840i | ||||
\(914\) | −11208.0 | − | 19412.8i | −0.405610 | − | 0.702537i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10996.9 | 0.396669 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4144.00 | − | 7177.62i | 0.148746 | − | 0.257636i | −0.782018 | − | 0.623256i | \(-0.785810\pi\) |
0.930764 | + | 0.365620i | \(0.119143\pi\) | |||||||
\(920\) | −11087.4 | − | 19204.0i | −0.397328 | − | 0.688193i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9786.36 | + | 16950.5i | −0.349562 | + | 0.605460i | ||||
\(923\) | 29936.1 | 1.06756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10146.0 | −0.360647 | ||||||||
\(926\) | −3952.00 | + | 6845.06i | −0.140249 | + | 0.242919i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4576.00 | − | 7925.86i | −0.161869 | − | 0.280366i | ||||
\(929\) | 22790.8 | − | 39474.8i | 0.804888 | − | 1.39411i | −0.111479 | − | 0.993767i | \(-0.535559\pi\) |
0.916367 | − | 0.400339i | \(-0.131108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −288.000 | −0.0101221 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17506.5 | − | 30322.2i | −0.613310 | − | 1.06228i | ||||
\(935\) | 196.000 | + | 339.482i | 0.00685549 | + | 0.0118741i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11665.8 | −0.406731 | −0.203365 | − | 0.979103i | \(-0.565188\pi\) | ||||
−0.203365 | + | 0.979103i | \(0.565188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20720.0 | − | 35888.1i | 0.718949 | − | 1.24526i | ||||
\(941\) | −7.07107 | − | 12.2474i | −0.000244963 | − | 0.000424288i | 0.865903 | − | 0.500212i | \(-0.166745\pi\) |
−0.866148 | + | 0.499788i | \(0.833411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8810.55 | + | 15260.3i | −0.304253 | + | 0.526982i | ||||
\(944\) | 6946.62 | 0.239505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −952.000 | −0.0327190 | ||||||||
\(947\) | 7017.00 | − | 12153.8i | 0.240783 | − | 0.417049i | −0.720154 | − | 0.693814i | \(-0.755929\pi\) |
0.960938 | + | 0.276765i | \(0.0892623\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6876.00 | + | 11909.6i | 0.235200 | + | 0.407378i | ||||
\(950\) | −377.595 | + | 654.014i | −0.0128956 | + | 0.0223358i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42698.0 | 1.45134 | 0.725668 | − | 0.688045i | \(-0.241531\pi\) | ||||
0.725668 | + | 0.688045i | \(0.241531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10176.7 | − | 17626.5i | −0.344827 | − | 0.597258i | ||||
\(956\) | 8616.00 | + | 14923.3i | 0.291487 | + | 0.504870i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4576.40 | 0.154339 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10539.5 | − | 18254.9i | 0.353781 | − | 0.612767i | ||||
\(962\) | −1934.64 | − | 3350.90i | −0.0648393 | − | 0.112305i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3080.16 | + | 5334.99i | −0.102910 | + | 0.178245i | ||||
\(965\) | −90917.0 | −3.03287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48492.0 | −1.61261 | −0.806307 | − | 0.591497i | \(-0.798537\pi\) | ||||
−0.806307 | + | 0.591497i | \(0.798537\pi\) | |||||||
\(968\) | 4540.00 | − | 7863.51i | 0.150745 | − | 0.261098i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29372.0 | − | 50873.8i | −0.972245 | − | 1.68398i | ||||
\(971\) | −26334.8 | + | 45613.2i | −0.870364 | + | 1.50751i | −0.00874297 | + | 0.999962i | \(0.502783\pi\) |
−0.861621 | + | 0.507553i | \(0.830550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1944.00 | 0.0639525 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 113.137 | + | 195.959i | 0.00371048 | + | 0.00642674i | ||||
\(977\) | −27690.0 | − | 47960.5i | −0.906737 | − | 1.57051i | −0.818569 | − | 0.574408i | \(-0.805232\pi\) |
−0.0881674 | − | 0.996106i | \(-0.528101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8652.16 | 0.282456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7404.00 | + | 12824.1i | −0.240602 | + | 0.416735i | ||||
\(983\) | 25267.8 | + | 43765.0i | 0.819854 | + | 1.42003i | 0.905790 | + | 0.423728i | \(0.139279\pi\) |
−0.0859360 | + | 0.996301i | \(0.527388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7860.20 | + | 13614.3i | −0.254261 | + | 0.440392i | ||||
\(986\) | 808.930 | 0.0261274 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −288.000 | −0.00927379 | ||||||||
\(989\) | −2380.00 | + | 4122.28i | −0.0765213 | + | 0.132539i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19856.0 | + | 34391.6i | 0.636475 | + | 1.10241i | 0.986201 | + | 0.165555i | \(0.0529415\pi\) |
−0.349726 | + | 0.936852i | \(0.613725\pi\) | |||||||
\(992\) | −1493.41 | + | 2586.66i | −0.0477982 | + | 0.0827889i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49224.0 | 1.56835 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1093.19 | + | 1893.46i | 0.0347258 | + | 0.0601468i | 0.882866 | − | 0.469625i | \(-0.155611\pi\) |
−0.848140 | + | 0.529772i | \(0.822278\pi\) | |||||||
\(998\) | 12244.0 | + | 21207.2i | 0.388354 | + | 0.672648i | ||||
\(999\) | 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.ba.667.2 | 4 | ||
3.2 | odd | 2 | 98.4.c.h.79.1 | 4 | |||
7.2 | even | 3 | 882.4.a.bg.1.1 | 2 | |||
7.3 | odd | 6 | inner | 882.4.g.ba.361.1 | 4 | ||
7.4 | even | 3 | inner | 882.4.g.ba.361.2 | 4 | ||
7.5 | odd | 6 | 882.4.a.bg.1.2 | 2 | |||
7.6 | odd | 2 | inner | 882.4.g.ba.667.1 | 4 | ||
21.2 | odd | 6 | 98.4.a.g.1.2 | yes | 2 | ||
21.5 | even | 6 | 98.4.a.g.1.1 | ✓ | 2 | ||
21.11 | odd | 6 | 98.4.c.h.67.1 | 4 | |||
21.17 | even | 6 | 98.4.c.h.67.2 | 4 | |||
21.20 | even | 2 | 98.4.c.h.79.2 | 4 | |||
84.23 | even | 6 | 784.4.a.y.1.1 | 2 | |||
84.47 | odd | 6 | 784.4.a.y.1.2 | 2 | |||
105.44 | odd | 6 | 2450.4.a.bx.1.1 | 2 | |||
105.89 | even | 6 | 2450.4.a.bx.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.4.a.g.1.1 | ✓ | 2 | 21.5 | even | 6 | ||
98.4.a.g.1.2 | yes | 2 | 21.2 | odd | 6 | ||
98.4.c.h.67.1 | 4 | 21.11 | odd | 6 | |||
98.4.c.h.67.2 | 4 | 21.17 | even | 6 | |||
98.4.c.h.79.1 | 4 | 3.2 | odd | 2 | |||
98.4.c.h.79.2 | 4 | 21.20 | even | 2 | |||
784.4.a.y.1.1 | 2 | 84.23 | even | 6 | |||
784.4.a.y.1.2 | 2 | 84.47 | odd | 6 | |||
882.4.a.bg.1.1 | 2 | 7.2 | even | 3 | |||
882.4.a.bg.1.2 | 2 | 7.5 | odd | 6 | |||
882.4.g.ba.361.1 | 4 | 7.3 | odd | 6 | inner | ||
882.4.g.ba.361.2 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.ba.667.1 | 4 | 7.6 | odd | 2 | inner | ||
882.4.g.ba.667.2 | 4 | 1.1 | even | 1 | trivial | ||
2450.4.a.bx.1.1 | 2 | 105.44 | odd | 6 | |||
2450.4.a.bx.1.2 | 2 | 105.89 | even | 6 |