Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 19x^{2} + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(2.17945 + 3.77492i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.r.226.2 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17945 | + | 3.77492i | 0.770552 | + | 1.33463i | 0.937261 | + | 0.348629i | \(0.113353\pi\) |
−0.166709 | + | 0.986006i | \(0.553314\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.50000 | + | 9.52628i | −0.687500 | + | 1.19078i | ||||
\(5\) | 4.35890 | + | 7.54983i | 0.389872 | + | 0.675278i | 0.992432 | − | 0.122796i | \(-0.0391860\pi\) |
−0.602560 | + | 0.798073i | \(0.705853\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −13.0767 | −0.577914 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −19.0000 | + | 32.9090i | −0.600833 | + | 1.04067i | ||||
\(11\) | −21.7945 | + | 37.7492i | −0.597390 | + | 1.03471i | 0.395815 | + | 0.918330i | \(0.370462\pi\) |
−0.993205 | + | 0.116379i | \(0.962871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 82.0000 | 1.74944 | 0.874720 | − | 0.484629i | \(-0.161046\pi\) | ||||
0.874720 | + | 0.484629i | \(0.161046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5000 | + | 26.8468i | 0.242188 | + | 0.419481i | ||||
\(17\) | −39.2301 | + | 67.9485i | −0.559688 | + | 0.969408i | 0.437834 | + | 0.899056i | \(0.355746\pi\) |
−0.997522 | + | 0.0703522i | \(0.977588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.0000 | + | 17.3205i | 0.120745 | + | 0.209137i | 0.920062 | − | 0.391773i | \(-0.128138\pi\) |
−0.799317 | + | 0.600910i | \(0.794805\pi\) | |||||||
\(20\) | −95.8958 | −1.07215 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −190.000 | −1.84128 | ||||||||
\(23\) | −65.3835 | − | 113.248i | −0.592756 | − | 1.02668i | −0.993859 | − | 0.110651i | \(-0.964706\pi\) |
0.401103 | − | 0.916033i | \(-0.368627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.5000 | − | 42.4352i | 0.196000 | − | 0.339482i | ||||
\(26\) | 178.715 | + | 309.543i | 1.34803 | + | 2.33486i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −244.098 | −1.56303 | −0.781516 | − | 0.623885i | \(-0.785553\pi\) | ||||
−0.781516 | + | 0.623885i | \(0.785553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −78.0000 | + | 135.100i | −0.451910 | + | 0.782731i | −0.998505 | − | 0.0546661i | \(-0.982591\pi\) |
0.546595 | + | 0.837397i | \(0.315924\pi\) | |||||||
\(32\) | −119.870 | + | 207.620i | −0.662193 | + | 1.14695i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −342.000 | −1.72507 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −93.0000 | − | 161.081i | −0.413219 | − | 0.715716i | 0.582021 | − | 0.813174i | \(-0.302262\pi\) |
−0.995240 | + | 0.0974576i | \(0.968929\pi\) | |||||||
\(38\) | −43.5890 | + | 75.4983i | −0.186081 | + | 0.322301i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −57.0000 | − | 98.7269i | −0.225312 | − | 0.390252i | ||||
\(41\) | 165.638 | 0.630935 | 0.315467 | − | 0.948936i | \(-0.397839\pi\) | ||||
0.315467 | + | 0.948936i | \(0.397839\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | −239.739 | − | 415.241i | −0.821411 | − | 1.42273i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 285.000 | − | 493.634i | 0.913499 | − | 1.58223i | ||||
\(47\) | 235.381 | + | 407.691i | 0.730506 | + | 1.26527i | 0.956667 | + | 0.291184i | \(0.0940490\pi\) |
−0.226161 | + | 0.974090i | \(0.572618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 213.586 | 0.604113 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −451.000 | + | 781.155i | −1.20274 | + | 2.08321i | ||||
\(53\) | −78.4602 | + | 135.897i | −0.203346 | + | 0.352205i | −0.949604 | − | 0.313451i | \(-0.898515\pi\) |
0.746259 | + | 0.665656i | \(0.231848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −380.000 | −0.931622 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −532.000 | − | 921.451i | −1.20440 | − | 2.08608i | ||||
\(59\) | 78.4602 | − | 135.897i | 0.173130 | − | 0.299869i | −0.766383 | − | 0.642384i | \(-0.777945\pi\) |
0.939512 | + | 0.342515i | \(0.111279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −395.000 | − | 684.160i | −0.829091 | − | 1.43603i | −0.898752 | − | 0.438457i | \(-0.855525\pi\) |
0.0696607 | − | 0.997571i | \(-0.477808\pi\) | |||||||
\(62\) | −679.988 | −1.39288 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −797.000 | −1.55664 | ||||||||
\(65\) | 357.430 | + | 619.086i | 0.682057 | + | 1.18136i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22.0000 | − | 38.1051i | 0.0401153 | − | 0.0694818i | −0.845271 | − | 0.534338i | \(-0.820561\pi\) |
0.885386 | + | 0.464857i | \(0.153894\pi\) | |||||||
\(68\) | −431.531 | − | 747.434i | −0.769571 | − | 1.33294i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −444.608 | −0.743172 | −0.371586 | − | 0.928398i | \(-0.621186\pi\) | ||||
−0.371586 | + | 0.928398i | \(0.621186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63.0000 | + | 109.119i | −0.101008 | + | 0.174951i | −0.912100 | − | 0.409967i | \(-0.865540\pi\) |
0.811092 | + | 0.584918i | \(0.198873\pi\) | |||||||
\(74\) | 405.378 | − | 702.135i | 0.636813 | − | 1.10299i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −220.000 | −0.332049 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 356.000 | + | 616.610i | 0.507002 | + | 0.878153i | 0.999967 | + | 0.00810375i | \(0.00257953\pi\) |
−0.492966 | + | 0.870049i | \(0.664087\pi\) | |||||||
\(80\) | −135.126 | + | 234.045i | −0.188844 | + | 0.327088i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 361.000 | + | 625.270i | 0.486168 | + | 0.842068i | ||||
\(83\) | 1464.59 | 1.93686 | 0.968432 | − | 0.249280i | \(-0.0801938\pi\) | ||||
0.968432 | + | 0.249280i | \(0.0801938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −684.000 | −0.872826 | ||||||||
\(86\) | 357.430 | + | 619.086i | 0.448170 | + | 0.776254i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 285.000 | − | 493.634i | 0.345240 | − | 0.597973i | ||||
\(89\) | −727.936 | − | 1260.82i | −0.866978 | − | 1.50165i | −0.865069 | − | 0.501652i | \(-0.832726\pi\) |
−0.00190909 | − | 0.999998i | \(-0.500608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1438.44 | 1.63008 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1026.00 | + | 1777.08i | −1.12579 | + | 1.94992i | ||||
\(95\) | −87.1780 | + | 150.997i | −0.0941502 | + | 0.163073i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 798.000 | 0.835305 | 0.417653 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417653 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 269.500 | + | 466.788i | 0.269500 | + | 0.466788i | ||||
\(101\) | 204.868 | − | 354.842i | 0.201833 | − | 0.349585i | −0.747286 | − | 0.664503i | \(-0.768643\pi\) |
0.949119 | + | 0.314917i | \(0.101977\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 458.000 | + | 793.279i | 0.438137 | + | 0.758875i | 0.997546 | − | 0.0700167i | \(-0.0223052\pi\) |
−0.559409 | + | 0.828892i | \(0.688972\pi\) | |||||||
\(104\) | −1072.29 | −1.01103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −684.000 | −0.626754 | ||||||||
\(107\) | 448.967 | + | 777.633i | 0.405638 | + | 0.702585i | 0.994395 | − | 0.105724i | \(-0.0337161\pi\) |
−0.588758 | + | 0.808310i | \(0.700383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.000 | − | 296.181i | 0.150264 | − | 0.260266i | −0.781060 | − | 0.624456i | \(-0.785321\pi\) |
0.931325 | + | 0.364190i | \(0.118654\pi\) | |||||||
\(110\) | −828.191 | − | 1434.47i | −0.717863 | − | 1.24337i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 488.197 | 0.406422 | 0.203211 | − | 0.979135i | \(-0.434862\pi\) | ||||
0.203211 | + | 0.979135i | \(0.434862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 570.000 | − | 987.269i | 0.462198 | − | 0.800550i | ||||
\(116\) | 1342.54 | − | 2325.35i | 1.07458 | − | 1.86123i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 684.000 | 0.533621 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −284.500 | − | 492.768i | −0.213749 | − | 0.370224i | ||||
\(122\) | 1721.77 | − | 2982.18i | 1.27772 | − | 2.21307i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −858.000 | − | 1486.10i | −0.621376 | − | 1.07626i | ||||
\(125\) | 1516.90 | 1.08540 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 456.000 | 0.318610 | 0.159305 | − | 0.987229i | \(-0.449075\pi\) | ||||
0.159305 | + | 0.987229i | \(0.449075\pi\) | |||||||
\(128\) | −778.063 | − | 1347.65i | −0.537279 | − | 0.930595i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1558.00 | + | 2698.54i | −1.05112 | + | 1.82059i | ||||
\(131\) | 749.731 | + | 1298.57i | 0.500033 | + | 0.866082i | 1.00000 | 3.76230e-5i | \(1.19758e-5\pi\) | |
−0.499967 | + | 0.866044i | \(0.666655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 191.792 | 0.123644 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 513.000 | − | 888.542i | 0.323451 | − | 0.560234i | ||||
\(137\) | −444.608 | + | 770.083i | −0.277266 | + | 0.480238i | −0.970704 | − | 0.240278i | \(-0.922762\pi\) |
0.693439 | + | 0.720516i | \(0.256095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −768.000 | −0.468640 | −0.234320 | − | 0.972160i | \(-0.575286\pi\) | ||||
−0.234320 | + | 0.972160i | \(0.575286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −969.000 | − | 1678.36i | −0.572653 | − | 0.991863i | ||||
\(143\) | −1787.15 | + | 3095.43i | −1.04510 | + | 1.81016i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1064.00 | − | 1842.90i | −0.609382 | − | 1.05548i | ||||
\(146\) | −549.221 | −0.311328 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2046.00 | 1.13635 | ||||||||
\(149\) | 496.914 | + | 860.681i | 0.273214 | + | 0.473220i | 0.969683 | − | 0.244367i | \(-0.0785801\pi\) |
−0.696469 | + | 0.717587i | \(0.745247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1748.00 | − | 3027.62i | 0.942054 | − | 1.63169i | 0.180510 | − | 0.983573i | \(-0.442225\pi\) |
0.761544 | − | 0.648113i | \(-0.224442\pi\) | |||||||
\(152\) | −130.767 | − | 226.495i | −0.0697803 | − | 0.120863i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1359.98 | −0.704748 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 253.000 | − | 438.209i | 0.128609 | − | 0.222757i | −0.794529 | − | 0.607226i | \(-0.792282\pi\) |
0.923138 | + | 0.384469i | \(0.125615\pi\) | |||||||
\(158\) | −1551.77 | + | 2687.74i | −0.781342 | + | 1.35332i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2090.00 | −1.03268 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1282.00 | + | 2220.49i | 0.616037 | + | 1.06701i | 0.990202 | + | 0.139645i | \(0.0445961\pi\) |
−0.374165 | + | 0.927362i | \(0.622071\pi\) | |||||||
\(164\) | −911.010 | + | 1577.92i | −0.433768 | + | 0.751308i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3192.00 | + | 5528.71i | 1.49245 | + | 2.58500i | ||||
\(167\) | 645.117 | 0.298926 | 0.149463 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149463 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4527.00 | 2.06054 | ||||||||
\(170\) | −1490.74 | − | 2582.04i | −0.672558 | − | 1.16490i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −902.000 | + | 1562.31i | −0.399865 | + | 0.692587i | ||||
\(173\) | 1930.99 | + | 3344.58i | 0.848616 | + | 1.46985i | 0.882443 | + | 0.470419i | \(0.155897\pi\) |
−0.0338270 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1351.26 | −0.578721 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3173.00 | − | 5495.80i | 1.33610 | − | 2.31420i | ||||
\(179\) | −135.126 | + | 234.045i | −0.0564234 | + | 0.0977281i | −0.892857 | − | 0.450339i | \(-0.851303\pi\) |
0.836434 | + | 0.548068i | \(0.184636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 418.000 | 0.171656 | 0.0858279 | − | 0.996310i | \(-0.472646\pi\) | ||||
0.0858279 | + | 0.996310i | \(0.472646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 855.000 | + | 1480.90i | 0.342562 | + | 0.593335i | ||||
\(185\) | 810.755 | − | 1404.27i | 0.322205 | − | 0.558075i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1710.00 | − | 2961.81i | −0.668704 | − | 1.15823i | ||||
\(188\) | −5178.37 | −2.00889 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −760.000 | −0.290191 | ||||||||
\(191\) | 762.807 | + | 1321.22i | 0.288978 | + | 0.500525i | 0.973566 | − | 0.228406i | \(-0.0733512\pi\) |
−0.684588 | + | 0.728930i | \(0.740018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −679.000 | + | 1176.06i | −0.253241 | + | 0.438626i | −0.964416 | − | 0.264389i | \(-0.914830\pi\) |
0.711175 | + | 0.703015i | \(0.248163\pi\) | |||||||
\(194\) | 1739.20 | + | 3012.38i | 0.643646 | + | 1.11483i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3748.65 | −1.35574 | −0.677869 | − | 0.735183i | \(-0.737096\pi\) | ||||
−0.677869 | + | 0.735183i | \(0.737096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 528.000 | − | 914.523i | 0.188085 | − | 0.325773i | −0.756527 | − | 0.653963i | \(-0.773105\pi\) |
0.944612 | + | 0.328190i | \(0.106439\pi\) | |||||||
\(200\) | −320.379 | + | 554.913i | −0.113271 | + | 0.196191i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1786.00 | 0.622092 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 722.000 | + | 1250.54i | 0.245984 | + | 0.426056i | ||||
\(206\) | −1996.38 | + | 3457.82i | −0.675214 | + | 1.16950i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1271.00 | + | 2201.44i | 0.423692 | + | 0.733857i | ||||
\(209\) | −871.780 | −0.288528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3620.00 | −1.18110 | −0.590548 | − | 0.807003i | \(-0.701088\pi\) | ||||
−0.590548 | + | 0.807003i | \(0.701088\pi\) | |||||||
\(212\) | −863.062 | − | 1494.87i | −0.279601 | − | 0.484283i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1957.00 | + | 3389.62i | −0.625130 | + | 1.08276i | ||||
\(215\) | 714.859 | + | 1238.17i | 0.226758 | + | 0.392757i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1490.74 | 0.463146 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2090.00 | − | 3619.99i | 0.640490 | − | 1.10936i | ||||
\(221\) | −3216.87 | + | 5571.78i | −0.979140 | + | 1.69592i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5368.00 | 1.61196 | 0.805982 | − | 0.591940i | \(-0.201638\pi\) | ||||
0.805982 | + | 0.591940i | \(0.201638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1064.00 | + | 1842.90i | 0.313169 | + | 0.542425i | ||||
\(227\) | 810.755 | − | 1404.27i | 0.237056 | − | 0.410593i | −0.722812 | − | 0.691045i | \(-0.757151\pi\) |
0.959868 | + | 0.280451i | \(0.0904842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1093.00 | − | 1893.13i | −0.315404 | − | 0.546295i | 0.664119 | − | 0.747626i | \(-0.268807\pi\) |
−0.979523 | + | 0.201331i | \(0.935473\pi\) | |||||||
\(230\) | 4969.14 | 1.42459 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3192.00 | 0.903298 | ||||||||
\(233\) | −2066.12 | − | 3578.62i | −0.580927 | − | 1.00619i | −0.995370 | − | 0.0961192i | \(-0.969357\pi\) |
0.414443 | − | 0.910075i | \(-0.363976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2052.00 | + | 3554.17i | −0.569607 | + | 0.986589i | ||||
\(236\) | 863.062 | + | 1494.87i | 0.238053 | + | 0.412320i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4838.38 | 1.30949 | 0.654746 | − | 0.755849i | \(-0.272776\pi\) | ||||
0.654746 | + | 0.755849i | \(0.272776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −643.000 | + | 1113.71i | −0.171864 | + | 0.297678i | −0.939072 | − | 0.343722i | \(-0.888312\pi\) |
0.767207 | + | 0.641399i | \(0.221646\pi\) | |||||||
\(242\) | 1240.11 | − | 2147.93i | 0.329409 | − | 0.570554i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8690.00 | 2.28000 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 820.000 | + | 1420.28i | 0.211236 | + | 0.365872i | ||||
\(248\) | 1019.98 | − | 1766.66i | 0.261165 | − | 0.452351i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3306.00 | + | 5726.16i | 0.836359 | + | 1.44862i | ||||
\(251\) | 1795.87 | 0.451610 | 0.225805 | − | 0.974173i | \(-0.427499\pi\) | ||||
0.225805 | + | 0.974173i | \(0.427499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5700.00 | 1.41643 | ||||||||
\(254\) | 993.829 | + | 1721.36i | 0.245505 | + | 0.425228i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 203.500 | − | 352.472i | 0.0496826 | − | 0.0860528i | ||||
\(257\) | −972.034 | − | 1683.61i | −0.235929 | − | 0.408642i | 0.723613 | − | 0.690206i | \(-0.242480\pi\) |
−0.959542 | + | 0.281564i | \(0.909147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7863.45 | −1.87566 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3268.00 | + | 5660.34i | −0.770602 | + | 1.33472i | ||||
\(263\) | 2672.01 | − | 4628.05i | 0.626475 | − | 1.08509i | −0.361779 | − | 0.932264i | \(-0.617830\pi\) |
0.988254 | − | 0.152822i | \(-0.0488362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1368.00 | −0.317115 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 242.000 | + | 419.156i | 0.0551586 | + | 0.0955375i | ||||
\(269\) | −2000.73 | + | 3465.37i | −0.453483 | + | 0.785456i | −0.998600 | − | 0.0529046i | \(-0.983152\pi\) |
0.545117 | + | 0.838360i | \(0.316485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1394.00 | − | 2414.48i | −0.312470 | − | 0.541215i | 0.666426 | − | 0.745571i | \(-0.267823\pi\) |
−0.978897 | + | 0.204356i | \(0.934490\pi\) | |||||||
\(272\) | −2432.27 | −0.542198 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3876.00 | −0.854590 | ||||||||
\(275\) | 1067.93 | + | 1849.71i | 0.234177 | + | 0.405606i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2281.00 | − | 3950.81i | 0.494773 | − | 0.856971i | −0.505209 | − | 0.862997i | \(-0.668585\pi\) |
0.999982 | + | 0.00602561i | \(0.00191802\pi\) | |||||||
\(278\) | −1673.82 | − | 2899.14i | −0.361111 | − | 0.625463i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1551.77 | 0.329433 | 0.164717 | − | 0.986341i | \(-0.447329\pi\) | ||||
0.164717 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3394.00 | − | 5878.58i | 0.712906 | − | 1.23479i | −0.250856 | − | 0.968024i | \(-0.580712\pi\) |
0.963762 | − | 0.266765i | \(-0.0859547\pi\) | |||||||
\(284\) | 2445.34 | − | 4235.46i | 0.510931 | − | 0.884958i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15580.0 | −3.22121 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −621.500 | − | 1076.47i | −0.126501 | − | 0.219106i | ||||
\(290\) | 4637.87 | − | 8033.02i | 0.939121 | − | 1.62660i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −693.000 | − | 1200.31i | −0.138886 | − | 0.240558i | ||||
\(293\) | −1142.03 | −0.227707 | −0.113854 | − | 0.993498i | \(-0.536319\pi\) | ||||
−0.113854 | + | 0.993498i | \(0.536319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1368.00 | 0.269993 | ||||||||
\(296\) | 1216.13 | + | 2106.40i | 0.238805 | + | 0.413622i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2166.00 | + | 3751.62i | −0.421050 | + | 0.729281i | ||||
\(299\) | −5361.45 | − | 9286.30i | −1.03699 | − | 1.79612i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15238.7 | 2.90361 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −310.000 | + | 536.936i | −0.0584859 | + | 0.101301i | ||||
\(305\) | 3443.53 | − | 5964.37i | 0.646479 | − | 1.11973i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 532.000 | 0.0989018 | 0.0494509 | − | 0.998777i | \(-0.484253\pi\) | ||||
0.0494509 | + | 0.998777i | \(0.484253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2964.00 | − | 5133.80i | −0.543045 | − | 0.940581i | ||||
\(311\) | 3269.17 | − | 5662.38i | 0.596070 | − | 1.03242i | −0.397325 | − | 0.917678i | \(-0.630061\pi\) |
0.993395 | − | 0.114746i | \(-0.0366054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2497.00 | − | 4324.93i | −0.450923 | − | 0.781021i | 0.547521 | − | 0.836792i | \(-0.315572\pi\) |
−0.998444 | + | 0.0557711i | \(0.982238\pi\) | |||||||
\(314\) | 2205.60 | 0.396399 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7832.00 | −1.39425 | ||||||||
\(317\) | −235.381 | − | 407.691i | −0.0417044 | − | 0.0722341i | 0.844420 | − | 0.535682i | \(-0.179945\pi\) |
−0.886124 | + | 0.463448i | \(0.846612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5320.00 | − | 9214.51i | 0.933739 | − | 1.61728i | ||||
\(320\) | −3474.04 | − | 6017.22i | −0.606890 | − | 1.05116i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1569.20 | −0.270318 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2009.00 | − | 3479.69i | 0.342890 | − | 0.593903i | ||||
\(326\) | −5588.11 | + | 9678.89i | −0.949376 | + | 1.64437i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2166.00 | −0.364626 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1294.00 | − | 2241.27i | −0.214878 | − | 0.372180i | 0.738357 | − | 0.674410i | \(-0.235602\pi\) |
−0.953235 | + | 0.302230i | \(0.902269\pi\) | |||||||
\(332\) | −8055.25 | + | 13952.1i | −1.33159 | + | 2.30639i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1406.00 | + | 2435.26i | 0.230338 | + | 0.398957i | ||||
\(335\) | 383.583 | 0.0625594 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 238.000 | 0.0384709 | 0.0192354 | − | 0.999815i | \(-0.493877\pi\) | ||||
0.0192354 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(338\) | 9866.37 | + | 17089.1i | 1.58775 | + | 2.75006i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3762.00 | − | 6515.98i | 0.600068 | − | 1.03935i | ||||
\(341\) | −3399.94 | − | 5888.87i | −0.539933 | − | 0.935191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2144.58 | −0.336128 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8417.00 | + | 14578.7i | −1.30781 | + | 2.26519i | ||||
\(347\) | 3526.35 | − | 6107.82i | 0.545546 | − | 0.944913i | −0.453027 | − | 0.891497i | \(-0.649656\pi\) |
0.998572 | − | 0.0534159i | \(-0.0170109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10850.0 | −1.66415 | −0.832073 | − | 0.554666i | \(-0.812846\pi\) | ||||
−0.832073 | + | 0.554666i | \(0.812846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5225.00 | − | 9049.97i | −0.791175 | − | 1.37035i | ||||
\(353\) | 2645.85 | − | 4582.75i | 0.398936 | − | 0.690978i | −0.594659 | − | 0.803978i | \(-0.702713\pi\) |
0.993595 | + | 0.113000i | \(0.0360462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1938.00 | − | 3356.71i | −0.289742 | − | 0.501848i | ||||
\(356\) | 16014.6 | 2.38419 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1178.00 | −0.173908 | ||||||||
\(359\) | −2410.47 | − | 4175.06i | −0.354373 | − | 0.613792i | 0.632638 | − | 0.774448i | \(-0.281972\pi\) |
−0.987010 | + | 0.160656i | \(0.948639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3229.50 | − | 5593.66i | 0.470841 | − | 0.815521i | ||||
\(362\) | 911.010 | + | 1577.92i | 0.132270 | + | 0.229098i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1098.44 | −0.157521 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5856.00 | + | 10142.9i | −0.832917 | + | 1.44266i | 0.0627973 | + | 0.998026i | \(0.479998\pi\) |
−0.895715 | + | 0.444629i | \(0.853336\pi\) | |||||||
\(368\) | 2026.89 | − | 3510.67i | 0.287116 | − | 0.497300i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7068.00 | 0.993102 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5225.00 | + | 9049.97i | 0.725309 | + | 1.25627i | 0.958847 | + | 0.283924i | \(0.0916364\pi\) |
−0.233538 | + | 0.972348i | \(0.575030\pi\) | |||||||
\(374\) | 7453.72 | − | 12910.2i | 1.03054 | − | 1.78495i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3078.00 | − | 5331.25i | −0.422169 | − | 0.731219i | ||||
\(377\) | −20016.1 | −2.73443 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −756.000 | −0.102462 | −0.0512310 | − | 0.998687i | \(-0.516314\pi\) | ||||
−0.0512310 | + | 0.998687i | \(0.516314\pi\) | |||||||
\(380\) | −958.958 | − | 1660.96i | −0.129457 | − | 0.224225i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3325.00 | + | 5759.07i | −0.445345 | + | 0.771360i | ||||
\(383\) | 3190.71 | + | 5526.48i | 0.425686 | + | 0.737310i | 0.996484 | − | 0.0837802i | \(-0.0266994\pi\) |
−0.570798 | + | 0.821091i | \(0.693366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5919.38 | −0.780541 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4389.00 | + | 7601.97i | −0.574272 | + | 0.994669i | ||||
\(389\) | −209.227 | + | 362.392i | −0.0272705 | + | 0.0472339i | −0.879339 | − | 0.476197i | \(-0.842015\pi\) |
0.852068 | + | 0.523431i | \(0.175348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10260.0 | 1.32703 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8170.00 | − | 14150.9i | −1.04467 | − | 1.80942i | ||||
\(395\) | −3103.54 | + | 5375.48i | −0.395331 | + | 0.684734i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2901.00 | + | 5024.68i | 0.366743 | + | 0.635218i | 0.989054 | − | 0.147552i | \(-0.0471395\pi\) |
−0.622311 | + | 0.782770i | \(0.713806\pi\) | |||||||
\(398\) | 4603.00 | 0.579717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1519.00 | 0.189875 | ||||||||
\(401\) | −2066.12 | − | 3578.62i | −0.257299 | − | 0.445655i | 0.708218 | − | 0.705994i | \(-0.249499\pi\) |
−0.965517 | + | 0.260338i | \(0.916166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6396.00 | + | 11078.2i | −0.790589 | + | 1.36934i | ||||
\(404\) | 2253.55 | + | 3903.26i | 0.277521 | + | 0.480680i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8107.55 | 0.987411 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 665.000 | − | 1151.81i | 0.0803964 | − | 0.139251i | −0.823024 | − | 0.568007i | \(-0.807715\pi\) |
0.903420 | + | 0.428756i | \(0.141048\pi\) | |||||||
\(410\) | −3147.13 | + | 5450.98i | −0.379086 | + | 0.656597i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10076.0 | −1.20488 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6384.00 | + | 11057.4i | 0.755128 | + | 1.30792i | ||||
\(416\) | −9829.32 | + | 17024.9i | −1.15847 | + | 2.00652i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1900.00 | − | 3290.90i | −0.222325 | − | 0.385079i | ||||
\(419\) | −10409.1 | −1.21364 | −0.606820 | − | 0.794839i | \(-0.707555\pi\) | ||||
−0.606820 | + | 0.794839i | \(0.707555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12274.0 | −1.42090 | −0.710449 | − | 0.703749i | \(-0.751508\pi\) | ||||
−0.710449 | + | 0.703749i | \(0.751508\pi\) | |||||||
\(422\) | −7889.61 | − | 13665.2i | −0.910095 | − | 1.57633i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1026.00 | − | 1777.08i | 0.117516 | − | 0.203544i | ||||
\(425\) | 1922.27 | + | 3329.48i | 0.219398 | + | 0.380008i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9877.27 | −1.11550 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3116.00 | + | 5397.07i | −0.349458 | + | 0.605279i | ||||
\(431\) | −2340.73 | + | 4054.26i | −0.261598 | + | 0.453102i | −0.966667 | − | 0.256037i | \(-0.917583\pi\) |
0.705068 | + | 0.709139i | \(0.250916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5770.00 | 0.640389 | 0.320195 | − | 0.947352i | \(-0.396252\pi\) | ||||
0.320195 | + | 0.947352i | \(0.396252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1881.00 | + | 3257.99i | 0.206614 | + | 0.357865i | ||||
\(437\) | 1307.67 | − | 2264.95i | 0.143145 | − | 0.247934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 936.000 | + | 1621.20i | 0.101760 | + | 0.176254i | 0.912410 | − | 0.409277i | \(-0.134219\pi\) |
−0.810650 | + | 0.585532i | \(0.800886\pi\) | |||||||
\(440\) | 4969.14 | 0.538397 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28044.0 | −3.01791 | ||||||||
\(443\) | −5557.60 | − | 9626.04i | −0.596048 | − | 1.03239i | −0.993398 | − | 0.114719i | \(-0.963403\pi\) |
0.397350 | − | 0.917667i | \(-0.369930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6346.00 | − | 10991.6i | 0.676021 | − | 1.17090i | ||||
\(446\) | 11699.3 | + | 20263.8i | 1.24210 | + | 2.15138i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7636.79 | 0.802678 | 0.401339 | − | 0.915930i | \(-0.368545\pi\) | ||||
0.401339 | + | 0.915930i | \(0.368545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3610.00 | + | 6252.70i | −0.376914 | + | 0.652834i | ||||
\(452\) | −2685.08 | + | 4650.70i | −0.279415 | + | 0.483961i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7068.00 | 0.730656 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7571.00 | − | 13113.4i | −0.774959 | − | 1.34227i | −0.934817 | − | 0.355129i | \(-0.884437\pi\) |
0.159858 | − | 0.987140i | \(-0.448896\pi\) | |||||||
\(458\) | 4764.28 | − | 8251.97i | 0.486070 | − | 0.841898i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6270.00 | + | 10860.0i | 0.635522 | + | 1.10076i | ||||
\(461\) | 13190.0 | 1.33258 | 0.666292 | − | 0.745691i | \(-0.267881\pi\) | ||||
0.666292 | + | 0.745691i | \(0.267881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9328.00 | 0.936304 | 0.468152 | − | 0.883648i | \(-0.344920\pi\) | ||||
0.468152 | + | 0.883648i | \(0.344920\pi\) | |||||||
\(464\) | −3783.52 | − | 6553.26i | −0.378547 | − | 0.655662i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9006.00 | − | 15598.8i | 0.895268 | − | 1.55065i | ||||
\(467\) | 1699.97 | + | 2944.44i | 0.168448 | + | 0.291761i | 0.937874 | − | 0.346975i | \(-0.112791\pi\) |
−0.769426 | + | 0.638736i | \(0.779458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17888.9 | −1.75565 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1026.00 | + | 1777.08i | −0.100054 | + | 0.173299i | ||||
\(473\) | −3574.30 | + | 6190.86i | −0.347455 | + | 0.601810i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 980.000 | 0.0946642 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10545.0 | + | 18264.5i | 1.00903 | + | 1.74769i | ||||
\(479\) | 1787.15 | − | 3095.43i | 0.170474 | − | 0.295269i | −0.768112 | − | 0.640316i | \(-0.778804\pi\) |
0.938586 | + | 0.345047i | \(0.112137\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7626.00 | − | 13208.6i | −0.722902 | − | 1.25210i | ||||
\(482\) | −5605.54 | −0.529721 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6259.00 | 0.587810 | ||||||||
\(485\) | 3478.40 | + | 6024.77i | 0.325662 | + | 0.564063i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4484.00 | + | 7766.52i | −0.417227 | + | 0.722658i | −0.995659 | − | 0.0930722i | \(-0.970331\pi\) |
0.578433 | + | 0.815730i | \(0.303665\pi\) | |||||||
\(488\) | 5165.30 | + | 8946.55i | 0.479143 | + | 0.829901i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5169.65 | −0.475159 | −0.237580 | − | 0.971368i | \(-0.576354\pi\) | ||||
−0.237580 | + | 0.971368i | \(0.576354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9576.00 | − | 16586.1i | 0.874810 | − | 1.51522i | ||||
\(494\) | −3574.30 | + | 6190.86i | −0.325537 | + | 0.563846i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4836.00 | −0.437788 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1970.00 | − | 3412.14i | −0.176732 | − | 0.306109i | 0.764027 | − | 0.645184i | \(-0.223219\pi\) |
−0.940759 | + | 0.339075i | \(0.889886\pi\) | |||||||
\(500\) | −8342.93 | + | 14450.4i | −0.746215 | + | 1.29248i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3914.00 | + | 6779.25i | 0.347989 | + | 0.602734i | ||||
\(503\) | −10252.1 | −0.908787 | −0.454394 | − | 0.890801i | \(-0.650144\pi\) | ||||
−0.454394 | + | 0.890801i | \(0.650144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3572.00 | 0.314756 | ||||||||
\(506\) | 12422.9 | + | 21517.0i | 1.09143 | + | 1.89041i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2508.00 | + | 4343.98i | −0.219044 | + | 0.379396i | ||||
\(509\) | 4886.33 | + | 8463.36i | 0.425506 | + | 0.736998i | 0.996468 | − | 0.0839787i | \(-0.0267628\pi\) |
−0.570961 | + | 0.820977i | \(0.693429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10674.9 | −0.921426 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4237.00 | − | 7338.70i | 0.363592 | − | 0.629759i | ||||
\(515\) | −3992.75 | + | 6915.65i | −0.341634 | + | 0.591728i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20520.0 | −1.74559 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4674.00 | − | 8095.61i | −0.394170 | − | 0.682723i | ||||
\(521\) | −3700.71 | + | 6409.81i | −0.311192 | + | 0.539000i | −0.978621 | − | 0.205674i | \(-0.934061\pi\) |
0.667429 | + | 0.744673i | \(0.267395\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1384.00 | + | 2397.16i | 0.115713 | + | 0.200421i | 0.918065 | − | 0.396431i | \(-0.129751\pi\) |
−0.802351 | + | 0.596852i | \(0.796418\pi\) | |||||||
\(524\) | −16494.1 | −1.37509 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23294.0 | 1.93093 | ||||||||
\(527\) | −6119.89 | − | 10600.0i | −0.505857 | − | 0.876170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2466.50 | + | 4272.10i | −0.202720 | + | 0.351122i | ||||
\(530\) | −2981.49 | − | 5164.09i | −0.244354 | − | 0.423233i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13582.3 | 1.10378 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3914.00 | + | 6779.25i | −0.316293 | + | 0.547836i | ||||
\(536\) | −287.687 | + | 498.289i | −0.0231832 | + | 0.0401545i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17442.0 | −1.39773 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8155.00 | − | 14124.9i | −0.648079 | − | 1.12251i | −0.983581 | − | 0.180467i | \(-0.942239\pi\) |
0.335502 | − | 0.942040i | \(-0.391094\pi\) | |||||||
\(542\) | 6076.31 | − | 10524.5i | 0.481549 | − | 0.834068i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9405.00 | − | 16289.9i | −0.741243 | − | 1.28387i | ||||
\(545\) | 2981.49 | 0.234336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11140.0 | 0.870771 | 0.435386 | − | 0.900244i | \(-0.356612\pi\) | ||||
0.435386 | + | 0.900244i | \(0.356612\pi\) | |||||||
\(548\) | −4890.68 | − | 8470.91i | −0.381240 | − | 0.660328i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4655.00 | + | 8062.70i | −0.360891 | + | 0.625081i | ||||
\(551\) | −2440.98 | − | 4227.91i | −0.188728 | − | 0.326887i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19885.3 | 1.52499 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4224.00 | − | 7316.18i | 0.322190 | − | 0.558049i | ||||
\(557\) | 11394.2 | − | 19735.3i | 0.866761 | − | 1.50127i | 0.00147399 | − | 0.999999i | \(-0.499531\pi\) |
0.865287 | − | 0.501276i | \(-0.167136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13448.0 | 1.01751 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3382.00 | + | 5857.80i | 0.253845 | + | 0.439673i | ||||
\(563\) | −5762.46 | + | 9980.88i | −0.431366 | + | 0.747147i | −0.996991 | − | 0.0775149i | \(-0.975301\pi\) |
0.565625 | + | 0.824662i | \(0.308635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2128.00 | + | 3685.80i | 0.158452 | + | 0.274448i | ||||
\(566\) | 29588.2 | 2.19732 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5814.00 | 0.429489 | ||||||||
\(569\) | −845.626 | − | 1464.67i | −0.0623032 | − | 0.107912i | 0.833191 | − | 0.552985i | \(-0.186511\pi\) |
−0.895495 | + | 0.445073i | \(0.853178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5614.00 | + | 9723.73i | −0.411451 | + | 0.712654i | −0.995049 | − | 0.0993888i | \(-0.968311\pi\) |
0.583598 | + | 0.812043i | \(0.301645\pi\) | |||||||
\(572\) | −19658.6 | − | 34049.8i | −1.43701 | − | 2.48897i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6407.58 | −0.464721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1025.00 | + | 1775.35i | −0.0739537 | + | 0.128092i | −0.900631 | − | 0.434585i | \(-0.856895\pi\) |
0.826677 | + | 0.562677i | \(0.190228\pi\) | |||||||
\(578\) | 2709.06 | − | 4692.22i | 0.194951 | − | 0.337666i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23408.0 | 1.67580 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3420.00 | − | 5923.61i | −0.242954 | − | 0.420808i | ||||
\(584\) | 823.832 | − | 1426.92i | 0.0583740 | − | 0.101107i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2489.00 | − | 4311.07i | −0.175460 | − | 0.303906i | ||||
\(587\) | −18394.6 | −1.29340 | −0.646699 | − | 0.762745i | \(-0.723851\pi\) | ||||
−0.646699 | + | 0.762745i | \(0.723851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3120.00 | −0.218264 | ||||||||
\(590\) | 2981.49 | + | 5164.09i | 0.208044 | + | 0.360343i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2883.00 | − | 4993.50i | 0.200153 | − | 0.346675i | ||||
\(593\) | −6316.04 | − | 10939.7i | −0.437384 | − | 0.757572i | 0.560103 | − | 0.828423i | \(-0.310762\pi\) |
−0.997487 | + | 0.0708515i | \(0.977428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10932.1 | −0.751337 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23370.0 | − | 40478.0i | 1.59811 | − | 2.76801i | ||||
\(599\) | −4799.15 | + | 8312.37i | −0.327359 | + | 0.567002i | −0.981987 | − | 0.188949i | \(-0.939492\pi\) |
0.654628 | + | 0.755951i | \(0.272825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10758.0 | −0.730163 | −0.365082 | − | 0.930976i | \(-0.618959\pi\) | ||||
−0.365082 | + | 0.930976i | \(0.618959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19228.0 | + | 33303.9i | 1.29532 | + | 2.24357i | ||||
\(605\) | 2480.21 | − | 4295.86i | 0.166669 | − | 0.288680i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10676.0 | + | 18491.4i | 0.713881 | + | 1.23648i | 0.963390 | + | 0.268105i | \(0.0863974\pi\) |
−0.249509 | + | 0.968372i | \(0.580269\pi\) | |||||||
\(608\) | −4794.79 | −0.319826 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30020.0 | 1.99258 | ||||||||
\(611\) | 19301.2 | + | 33430.7i | 1.27798 | + | 2.21352i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2857.00 | − | 4948.47i | 0.188243 | − | 0.326047i | −0.756421 | − | 0.654085i | \(-0.773054\pi\) |
0.944665 | + | 0.328038i | \(0.106387\pi\) | |||||||
\(614\) | 1159.47 | + | 2008.26i | 0.0762089 | + | 0.131998i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6747.58 | −0.440271 | −0.220135 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220135 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 940.000 | − | 1628.13i | 0.0610368 | − | 0.105719i | −0.833892 | − | 0.551927i | \(-0.813893\pi\) |
0.894929 | + | 0.446208i | \(0.147226\pi\) | |||||||
\(620\) | 7479.87 | − | 12955.5i | 0.484514 | − | 0.839203i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28500.0 | 1.83721 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3549.50 | + | 6147.91i | 0.227168 | + | 0.393467i | ||||
\(626\) | 10884.2 | − | 18851.9i | 0.694918 | − | 1.20363i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2783.00 | + | 4820.30i | 0.176837 | + | 0.306291i | ||||
\(629\) | 14593.6 | 0.925095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28888.0 | −1.82252 | −0.911262 | − | 0.411826i | \(-0.864891\pi\) | ||||
−0.911262 | + | 0.411826i | \(0.864891\pi\) | |||||||
\(632\) | −4655.30 | − | 8063.22i | −0.293003 | − | 0.507497i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1026.00 | − | 1777.08i | 0.0642708 | − | 0.111320i | ||||
\(635\) | 1987.66 | + | 3442.72i | 0.124217 | + | 0.215150i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 46378.7 | 2.87798 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6783.00 | − | 11748.5i | 0.418940 | − | 0.725625i | ||||
\(641\) | 12998.2 | − | 22513.6i | 0.800935 | − | 1.38726i | −0.118066 | − | 0.993006i | \(-0.537669\pi\) |
0.919001 | − | 0.394255i | \(-0.128997\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24788.0 | 1.52029 | 0.760143 | − | 0.649756i | \(-0.225129\pi\) | ||||
0.760143 | + | 0.649756i | \(0.225129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3420.00 | − | 5923.61i | −0.208294 | − | 0.360776i | ||||
\(647\) | 14236.2 | − | 24657.8i | 0.865041 | − | 1.49829i | −0.00196599 | − | 0.999998i | \(-0.500626\pi\) |
0.867007 | − | 0.498296i | \(-0.166041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3420.00 | + | 5923.61i | 0.206852 | + | 0.358278i | ||||
\(650\) | 17514.1 | 1.05686 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28204.0 | −1.69410 | ||||||||
\(653\) | 1621.51 | + | 2808.54i | 0.0971740 | + | 0.168310i | 0.910514 | − | 0.413479i | \(-0.135686\pi\) |
−0.813340 | + | 0.581789i | \(0.802353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6536.00 | + | 11320.7i | −0.389897 | + | 0.675322i | ||||
\(656\) | 2567.39 | + | 4446.85i | 0.152805 | + | 0.264665i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1176.90 | −0.0695685 | −0.0347842 | − | 0.999395i | \(-0.511074\pi\) | ||||
−0.0347842 | + | 0.999395i | \(0.511074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5795.00 | + | 10037.2i | −0.340998 | + | 0.590625i | −0.984618 | − | 0.174720i | \(-0.944098\pi\) |
0.643621 | + | 0.765345i | \(0.277431\pi\) | |||||||
\(662\) | 5640.42 | − | 9769.49i | 0.331149 | − | 0.573568i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19152.0 | −1.11934 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15960.0 | + | 27643.5i | 0.926497 | + | 1.60474i | ||||
\(668\) | −3548.14 | + | 6145.57i | −0.205512 | + | 0.355957i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 836.000 | + | 1447.99i | 0.0482052 | + | 0.0834939i | ||||
\(671\) | 34435.3 | 1.98116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23062.0 | 1.32091 | 0.660457 | − | 0.750864i | \(-0.270363\pi\) | ||||
0.660457 | + | 0.750864i | \(0.270363\pi\) | |||||||
\(674\) | 518.709 | + | 898.430i | 0.0296438 | + | 0.0513446i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24898.5 | + | 43125.5i | −1.41662 | + | 2.45366i | ||||
\(677\) | −11442.1 | − | 19818.3i | −0.649566 | − | 1.12508i | −0.983227 | − | 0.182388i | \(-0.941617\pi\) |
0.333661 | − | 0.942693i | \(-0.391716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8944.46 | 0.504418 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14820.0 | − | 25669.0i | 0.832093 | − | 1.44123i | ||||
\(683\) | −12357.5 | + | 21403.8i | −0.692307 | + | 1.19911i | 0.278773 | + | 0.960357i | \(0.410072\pi\) |
−0.971080 | + | 0.238754i | \(0.923261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7752.00 | −0.432392 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2542.00 | + | 4402.87i | 0.140862 | + | 0.243980i | ||||
\(689\) | −6433.73 | + | 11143.6i | −0.355741 | + | 0.616162i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5300.00 | + | 9179.87i | 0.291782 | + | 0.505382i | 0.974231 | − | 0.225552i | \(-0.0724184\pi\) |
−0.682449 | + | 0.730933i | \(0.739085\pi\) | |||||||
\(692\) | −42481.8 | −2.33369 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30742.0 | 1.68148 | ||||||||
\(695\) | −3347.63 | − | 5798.27i | −0.182709 | − | 0.316462i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6498.00 | + | 11254.9i | −0.353127 | + | 0.611633i | ||||
\(698\) | −23647.0 | − | 40957.9i | −1.28231 | − | 2.22103i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12449.0 | −0.670746 | −0.335373 | − | 0.942085i | \(-0.608862\pi\) | ||||
−0.335373 | + | 0.942085i | \(0.608862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1860.00 | − | 3221.61i | 0.0997884 | − | 0.172839i | ||||
\(704\) | 17370.2 | − | 30086.1i | 0.929921 | − | 1.61067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23066.0 | 1.22960 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6855.00 | + | 11873.2i | 0.363110 | + | 0.628925i | 0.988471 | − | 0.151411i | \(-0.0483816\pi\) |
−0.625361 | + | 0.780336i | \(0.715048\pi\) | |||||||
\(710\) | 8447.55 | − | 14631.6i | 0.446522 | − | 0.773399i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9519.00 | + | 16487.4i | 0.501039 | + | 0.867825i | ||||
\(713\) | 20399.6 | 1.07149 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31160.0 | −1.62982 | ||||||||
\(716\) | −1486.38 | − | 2574.49i | −0.0775821 | − | 0.134376i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10507.0 | − | 18198.7i | 0.546125 | − | 0.945916i | ||||
\(719\) | −1255.36 | − | 2174.35i | −0.0651142 | − | 0.112781i | 0.831630 | − | 0.555329i | \(-0.187408\pi\) |
−0.896745 | + | 0.442548i | \(0.854075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 28154.1 | 1.45123 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2299.00 | + | 3981.98i | −0.118013 | + | 0.204405i | ||||
\(725\) | −5980.41 | + | 10358.4i | −0.306354 | + | 0.530621i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 620.000 | 0.0316293 | 0.0158147 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158147 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2394.00 | − | 4146.53i | −0.121378 | − | 0.210233i | ||||
\(731\) | −6433.73 | + | 11143.6i | −0.325527 | + | 0.563829i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10107.0 | + | 17505.8i | 0.509291 | + | 0.882119i | 0.999942 | + | 0.0107622i | \(0.00342577\pi\) |
−0.490651 | + | 0.871356i | \(0.663241\pi\) | |||||||
\(734\) | −51051.4 | −2.56722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31350.0 | 1.57008 | ||||||||
\(737\) | 958.958 | + | 1660.96i | 0.0479290 | + | 0.0830154i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6162.00 | − | 10672.9i | 0.306729 | − | 0.531270i | −0.670916 | − | 0.741534i | \(-0.734099\pi\) |
0.977645 | + | 0.210263i | \(0.0674321\pi\) | |||||||
\(740\) | 8918.31 | + | 15447.0i | 0.443032 | + | 0.767353i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29736.4 | −1.46827 | −0.734134 | − | 0.679005i | \(-0.762412\pi\) | ||||
−0.734134 | + | 0.679005i | \(0.762412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4332.00 | + | 7503.24i | −0.213037 | + | 0.368990i | ||||
\(746\) | −22775.2 | + | 39447.9i | −1.11778 | + | 1.93605i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 37620.0 | 1.83894 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9668.00 | − | 16745.5i | −0.469761 | − | 0.813650i | 0.529641 | − | 0.848222i | \(-0.322326\pi\) |
−0.999402 | + | 0.0345721i | \(0.988993\pi\) | |||||||
\(752\) | −7296.80 | + | 12638.4i | −0.353839 | + | 0.612867i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −43624.0 | − | 75559.0i | −2.10702 | − | 3.64946i | ||||
\(755\) | 30477.4 | 1.46912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15986.0 | 0.767531 | 0.383766 | − | 0.923431i | \(-0.374627\pi\) | ||||
0.383766 | + | 0.923431i | \(0.374627\pi\) | |||||||
\(758\) | −1647.66 | − | 2853.84i | −0.0789523 | − | 0.136749i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1140.00 | − | 1974.54i | 0.0544107 | − | 0.0942421i | ||||
\(761\) | 18503.5 | + | 32049.0i | 0.881409 | + | 1.52665i | 0.849775 | + | 0.527146i | \(0.176738\pi\) |
0.0316342 | + | 0.999500i | \(0.489929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16781.8 | −0.794690 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13908.0 | + | 24089.4i | −0.656027 | + | 1.13627i | ||||
\(767\) | 6433.73 | − | 11143.6i | 0.302880 | − | 0.524603i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36070.0 | −1.69144 | −0.845720 | − | 0.533627i | \(-0.820829\pi\) | ||||
−0.845720 | + | 0.533627i | \(0.820829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7469.00 | − | 12936.7i | −0.348206 | − | 0.603111i | ||||
\(773\) | −265.893 | + | 460.540i | −0.0123719 | + | 0.0214288i | −0.872145 | − | 0.489247i | \(-0.837272\pi\) |
0.859773 | + | 0.510676i | \(0.170605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3822.00 | + | 6619.90i | 0.177149 | + | 0.306831i | ||||
\(776\) | −10435.2 | −0.482735 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1824.00 | −0.0840534 | ||||||||
\(779\) | 1656.38 | + | 2868.94i | 0.0761823 | + | 0.131952i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9690.00 | − | 16783.6i | 0.443963 | − | 0.768967i | ||||
\(782\) | 22361.2 | + | 38730.7i | 1.02255 | + | 1.77111i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4411.21 | 0.200564 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 568.000 | − | 983.805i | 0.0257268 | − | 0.0445602i | −0.852875 | − | 0.522115i | \(-0.825143\pi\) |
0.878602 | + | 0.477554i | \(0.158477\pi\) | |||||||
\(788\) | 20617.6 | − | 35710.7i | 0.932070 | − | 1.61439i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27056.0 | −1.21849 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32390.0 | − | 56101.1i | −1.45044 | − | 2.51224i | ||||
\(794\) | −12645.2 | + | 21902.1i | −0.565189 | + | 0.978936i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5808.00 | + | 10059.8i | 0.258617 | + | 0.447938i | ||||
\(797\) | −18054.6 | −0.802416 | −0.401208 | − | 0.915987i | \(-0.631409\pi\) | ||||
−0.401208 | + | 0.915987i | \(0.631409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36936.0 | −1.63542 | ||||||||
\(800\) | 5873.62 | + | 10173.4i | 0.259580 | + | 0.449605i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9006.00 | − | 15598.8i | 0.396525 | − | 0.686801i | ||||
\(803\) | −2746.11 | − | 4756.40i | −0.120682 | − | 0.209028i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55759.0 | −2.43676 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2679.00 | + | 4640.16i | −0.116642 | + | 0.202030i | ||||
\(809\) | −19353.5 | + | 33521.3i | −0.841079 | + | 1.45679i | 0.0479036 | + | 0.998852i | \(0.484746\pi\) |
−0.888983 | + | 0.457940i | \(0.848587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17936.0 | 0.776595 | 0.388297 | − | 0.921534i | \(-0.373063\pi\) | ||||
0.388297 | + | 0.921534i | \(0.373063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17670.0 | + | 30605.3i | 0.760852 | + | 1.31783i | ||||
\(815\) | −11176.2 | + | 19357.8i | −0.480351 | + | 0.831992i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1640.00 | + | 2840.56i | 0.0702281 | + | 0.121639i | ||||
\(818\) | 5797.34 | 0.247798 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15884.0 | −0.676455 | ||||||||
\(821\) | 12457.7 | + | 21577.4i | 0.529571 | + | 0.917244i | 0.999405 | + | 0.0344893i | \(0.0109805\pi\) |
−0.469834 | + | 0.882755i | \(0.655686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11712.0 | + | 20285.8i | −0.496057 | + | 0.859195i | −0.999990 | − | 0.00454737i | \(-0.998553\pi\) |
0.503933 | + | 0.863743i | \(0.331886\pi\) | |||||||
\(824\) | −5989.13 | − | 10373.5i | −0.253205 | − | 0.438564i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26650.3 | 1.12058 | 0.560291 | − | 0.828296i | \(-0.310689\pi\) | ||||
0.560291 | + | 0.828296i | \(0.310689\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13127.0 | − | 22736.6i | 0.549963 | − | 0.952564i | −0.448313 | − | 0.893877i | \(-0.647975\pi\) |
0.998276 | − | 0.0586877i | \(-0.0186916\pi\) | |||||||
\(830\) | −27827.2 | + | 48198.1i | −1.16373 | + | 2.01564i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −65354.0 | −2.72325 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2812.00 | + | 4870.53i | 0.116543 | + | 0.201858i | ||||
\(836\) | 4794.79 | − | 8304.82i | 0.198363 | − | 0.343574i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22686.0 | − | 39293.3i | −0.935173 | − | 1.61977i | ||||
\(839\) | 6189.64 | 0.254696 | 0.127348 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127348 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35195.0 | 1.44307 | ||||||||
\(842\) | −26750.6 | − | 46333.3i | −1.09488 | − | 1.89638i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19910.0 | − | 34485.1i | 0.812003 | − | 1.40643i | ||||
\(845\) | 19732.7 | + | 34178.1i | 0.803345 | + | 1.39143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4864.53 | −0.196991 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8379.00 | + | 14512.9i | −0.338115 | + | 0.585632i | ||||
\(851\) | −12161.3 | + | 21064.0i | −0.489877 | + | 0.848491i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45322.0 | −1.81922 | −0.909611 | − | 0.415462i | \(-0.863620\pi\) | ||||
−0.909611 | + | 0.415462i | \(0.863620\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5871.00 | − | 10168.9i | −0.234424 | − | 0.406034i | ||||
\(857\) | 4345.82 | − | 7527.18i | 0.173221 | − | 0.300028i | −0.766323 | − | 0.642455i | \(-0.777916\pi\) |
0.939544 | + | 0.342428i | \(0.111249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21626.0 | + | 37457.3i | 0.858987 | + | 1.48781i | 0.872897 | + | 0.487905i | \(0.162239\pi\) |
−0.0139098 | + | 0.999903i | \(0.504428\pi\) | |||||||
\(860\) | −15726.9 | −0.623585 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20406.0 | −0.806301 | ||||||||
\(863\) | −14659.0 | − | 25390.1i | −0.578212 | − | 1.00149i | −0.995684 | − | 0.0928036i | \(-0.970417\pi\) |
0.417472 | − | 0.908690i | \(-0.362916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16834.0 | + | 29157.3i | −0.661703 | + | 1.14610i | ||||
\(866\) | 12575.4 | + | 21781.3i | 0.493453 | + | 0.854686i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31035.4 | −1.21151 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1804.00 | − | 3124.62i | 0.0701793 | − | 0.121554i | ||||
\(872\) | −2236.12 | + | 3873.07i | −0.0868399 | + | 0.150411i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11400.0 | 0.441202 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23555.0 | − | 40798.5i | −0.906951 | − | 1.57088i | −0.818277 | − | 0.574824i | \(-0.805070\pi\) |
−0.0886738 | − | 0.996061i | \(-0.528263\pi\) | |||||||
\(878\) | −4079.93 | + | 7066.65i | −0.156823 | + | 0.271626i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5890.00 | − | 10201.8i | −0.225627 | − | 0.390798i | ||||
\(881\) | 42133.1 | 1.61124 | 0.805619 | − | 0.592434i | \(-0.201833\pi\) | ||||
0.805619 | + | 0.592434i | \(0.201833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22732.0 | −0.866356 | −0.433178 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433178 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(884\) | −35385.5 | − | 61289.6i | −1.34632 | − | 2.33189i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24225.0 | − | 41958.9i | 0.918572 | − | 1.59101i | ||||
\(887\) | 10731.6 | + | 18587.7i | 0.406237 | + | 0.703623i | 0.994465 | − | 0.105072i | \(-0.0335074\pi\) |
−0.588228 | + | 0.808695i | \(0.700174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 55323.1 | 2.08364 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29524.0 | + | 51137.1i | −1.10822 | + | 1.91950i | ||||
\(893\) | −4707.61 | + | 8153.82i | −0.176410 | + | 0.305551i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2356.00 | −0.0879915 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16644.0 | + | 28828.3i | 0.618505 | + | 1.07128i | ||||
\(899\) | 19039.7 | − | 32977.7i | 0.706350 | − | 1.22343i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6156.00 | − | 10662.5i | −0.227621 | − | 0.394250i | ||||
\(902\) | −31471.3 | −1.16173 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6384.00 | −0.234877 | ||||||||
\(905\) | 1822.02 | + | 3155.83i | 0.0669237 | + | 0.115915i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3458.00 | − | 5989.43i | 0.126594 | − | 0.219268i | −0.795761 | − | 0.605611i | \(-0.792929\pi\) |
0.922355 | + | 0.386343i | \(0.126262\pi\) | |||||||
\(908\) | 8918.31 | + | 15447.0i | 0.325952 | + | 0.564565i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38210.1 | −1.38963 | −0.694817 | − | 0.719186i | \(-0.744515\pi\) | ||||
−0.694817 | + | 0.719186i | \(0.744515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31920.0 | + | 55287.1i | −1.15706 | + | 2.00409i | ||||
\(914\) | 33001.2 | − | 57159.8i | 1.19429 | − | 2.06858i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24046.0 | 0.867360 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23816.0 | + | 41250.5i | 0.854861 | + | 1.48066i | 0.876774 | + | 0.480903i | \(0.159691\pi\) |
−0.0219127 | + | 0.999760i | \(0.506976\pi\) | |||||||
\(920\) | −7453.72 | + | 12910.2i | −0.267111 | + | 0.462649i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28747.0 | + | 49791.3i | 1.02682 | + | 1.77851i | ||||
\(923\) | −36457.8 | −1.30013 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9114.00 | −0.323964 | ||||||||
\(926\) | 20329.9 | + | 35212.4i | 0.721471 | + | 1.24962i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29260.0 | − | 50679.8i | 1.03503 | − | 1.79272i | ||||
\(929\) | −1652.02 | − | 2861.39i | −0.0583435 | − | 0.101054i | 0.835378 | − | 0.549675i | \(-0.185249\pi\) |
−0.893722 | + | 0.448621i | \(0.851915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 45454.6 | 1.59755 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7410.00 | + | 12834.5i | −0.259596 | + | 0.449633i | ||||
\(935\) | 14907.4 | − | 25820.4i | 0.521417 | − | 0.903121i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21858.0 | 0.762081 | 0.381040 | − | 0.924558i | \(-0.375566\pi\) | ||||
0.381040 | + | 0.924558i | \(0.375566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −22572.0 | − | 39095.9i | −0.783210 | − | 1.35656i | ||||
\(941\) | −25190.1 | + | 43630.5i | −0.872660 | + | 1.51149i | −0.0134252 | + | 0.999910i | \(0.504274\pi\) |
−0.859235 | + | 0.511582i | \(0.829060\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10830.0 | − | 18758.1i | −0.373991 | − | 0.647771i | ||||
\(944\) | 4864.53 | 0.167719 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31160.0 | −1.07093 | ||||||||
\(947\) | 15530.8 | + | 26900.1i | 0.532927 | + | 0.923056i | 0.999261 | + | 0.0384476i | \(0.0122413\pi\) |
−0.466334 | + | 0.884609i | \(0.654425\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5166.00 | + | 8947.77i | −0.176708 | + | 0.306066i | ||||
\(950\) | 2135.86 | + | 3699.42i | 0.0729436 | + | 0.126342i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22770.9 | −0.773999 | −0.387000 | − | 0.922080i | \(-0.626489\pi\) | ||||
−0.387000 | + | 0.922080i | \(0.626489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6650.00 | + | 11518.1i | −0.225329 | + | 0.390281i | ||||
\(956\) | −26611.1 | + | 46091.7i | −0.900276 | + | 1.55932i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15580.0 | 0.525435 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2727.50 | + | 4724.17i | 0.0915545 | + | 0.158577i | ||||
\(962\) | 33241.0 | − | 57575.0i | 1.11407 | − | 1.92962i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7073.00 | − | 12250.8i | −0.236313 | − | 0.409307i | ||||
\(965\) | −11838.8 | −0.394926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36416.0 | −1.21102 | −0.605512 | − | 0.795836i | \(-0.707032\pi\) | ||||
−0.605512 | + | 0.795836i | \(0.707032\pi\) | |||||||
\(968\) | 3720.32 | + | 6443.78i | 0.123529 | + | 0.213958i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15162.0 | + | 26261.4i | −0.501879 | + | 0.869280i | ||||
\(971\) | −9310.61 | − | 16126.4i | −0.307715 | − | 0.532979i | 0.670147 | − | 0.742229i | \(-0.266231\pi\) |
−0.977862 | + | 0.209250i | \(0.932898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −39090.6 | −1.28598 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12245.0 | − | 21209.0i | 0.401591 | − | 0.695576i | ||||
\(977\) | −2903.03 | + | 5028.19i | −0.0950625 | + | 0.164653i | −0.909635 | − | 0.415409i | \(-0.863638\pi\) |
0.814572 | + | 0.580062i | \(0.196972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63460.0 | 2.07170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11267.0 | − | 19515.0i | −0.366135 | − | 0.634164i | ||||
\(983\) | −1621.51 | + | 2808.54i | −0.0526126 | + | 0.0911276i | −0.891132 | − | 0.453744i | \(-0.850088\pi\) |
0.838520 | + | 0.544871i | \(0.183422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16340.0 | − | 28301.7i | −0.528564 | − | 0.915500i | ||||
\(986\) | 83481.6 | 2.69635 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18040.0 | −0.580900 | ||||||||
\(989\) | −10722.9 | − | 18572.6i | −0.344760 | − | 0.597143i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24724.0 | + | 42823.2i | −0.792516 | + | 1.37268i | 0.131888 | + | 0.991265i | \(0.457896\pi\) |
−0.924404 | + | 0.381414i | \(0.875437\pi\) | |||||||
\(992\) | −18699.7 | − | 32388.8i | −0.598503 | − | 1.03664i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9205.99 | 0.293316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8147.00 | + | 14111.0i | −0.258794 | + | 0.448245i | −0.965919 | − | 0.258844i | \(-0.916659\pi\) |
0.707125 | + | 0.707089i | \(0.249992\pi\) | |||||||
\(998\) | 8587.03 | − | 14873.2i | 0.272362 | − | 0.471746i | ||||
\(999\) | 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 | 441.4.e.r.361.2 | 4 | ||
3.2 | odd | 2 | inner | 441.4.e.r.361.1 | 4 | ||
7.2 | even | 3 | inner | 441.4.e.r.226.2 | 4 | ||
7.3 | odd | 6 | 441.4.a.q.1.1 | 2 | |||
7.4 | even | 3 | 63.4.a.d.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 441.4.e.s.226.2 | 4 | |||
7.6 | odd | 2 | 441.4.e.s.361.2 | 4 | |||
21.2 | odd | 6 | inner | 441.4.e.r.226.1 | 4 | ||
21.5 | even | 6 | 441.4.e.s.226.1 | 4 | |||
21.11 | odd | 6 | 63.4.a.d.1.2 | yes | 2 | ||
21.17 | even | 6 | 441.4.a.q.1.2 | 2 | |||
21.20 | even | 2 | 441.4.e.s.361.1 | 4 | |||
28.11 | odd | 6 | 1008.4.a.be.1.1 | 2 | |||
35.4 | even | 6 | 1575.4.a.t.1.2 | 2 | |||
84.11 | even | 6 | 1008.4.a.be.1.2 | 2 | |||
105.74 | odd | 6 | 1575.4.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.a.d.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
63.4.a.d.1.2 | yes | 2 | 21.11 | odd | 6 | ||
441.4.a.q.1.1 | 2 | 7.3 | odd | 6 | |||
441.4.a.q.1.2 | 2 | 21.17 | even | 6 | |||
441.4.e.r.226.1 | 4 | 21.2 | odd | 6 | inner | ||
441.4.e.r.226.2 | 4 | 7.2 | even | 3 | inner | ||
441.4.e.r.361.1 | 4 | 3.2 | odd | 2 | inner | ||
441.4.e.r.361.2 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.s.226.1 | 4 | 21.5 | even | 6 | |||
441.4.e.s.226.2 | 4 | 7.5 | odd | 6 | |||
441.4.e.s.361.1 | 4 | 21.20 | even | 2 | |||
441.4.e.s.361.2 | 4 | 7.6 | odd | 2 | |||
1008.4.a.be.1.1 | 2 | 28.11 | odd | 6 | |||
1008.4.a.be.1.2 | 2 | 84.11 | even | 6 | |||
1575.4.a.t.1.1 | 2 | 105.74 | odd | 6 | |||
1575.4.a.t.1.2 | 2 | 35.4 | even | 6 |