Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(323,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.323");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.b (of order \(2\), degree \(1\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Character | \(\chi\) | \(=\) | 324.323 |
Dual form | 324.4.b.c.323.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82820 | − | 0.0360939i | −0.999919 | − | 0.0127611i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.99739 | + | 0.204161i | 0.999674 | + | 0.0255202i | ||||
\(5\) | 16.9163i | 1.51304i | 0.653972 | + | 0.756519i | \(0.273101\pi\) | ||||
−0.653972 | + | 0.756519i | \(0.726899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.56763i | − | 0.192634i | −0.995351 | − | 0.0963170i | \(-0.969294\pi\) | ||
0.995351 | − | 0.0963170i | \(-0.0307062\pi\) | |||||||
\(8\) | −22.6108 | − | 0.866066i | −0.999267 | − | 0.0382750i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.610574 | − | 47.8425i | 0.0193080 | − | 1.51291i | ||||
\(11\) | 50.1376 | 1.37428 | 0.687139 | − | 0.726526i | \(-0.258866\pi\) | ||||
0.687139 | + | 0.726526i | \(0.258866\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.9933 | 0.810573 | 0.405286 | − | 0.914190i | \(-0.367172\pi\) | ||||
0.405286 | + | 0.914190i | \(0.367172\pi\) | |||||||
\(14\) | −0.128770 | + | 10.0900i | −0.00245822 | + | 0.192618i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 63.9166 | + | 3.26552i | 0.998697 | + | 0.0510237i | ||||
\(17\) | 84.3819i | 1.20386i | 0.798549 | + | 0.601930i | \(0.205601\pi\) | ||||
−0.798549 | + | 0.601930i | \(0.794399\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 62.9237i | − | 0.759773i | −0.925033 | − | 0.379887i | \(-0.875963\pi\) | ||
0.925033 | − | 0.379887i | \(-0.124037\pi\) | |||||||
\(20\) | −3.45365 | + | 135.286i | −0.0386130 | + | 1.51254i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −141.799 | − | 1.80966i | −1.37417 | − | 0.0175373i | ||||
\(23\) | 75.2133 | 0.681872 | 0.340936 | − | 0.940087i | \(-0.389256\pi\) | ||||
0.340936 | + | 0.940087i | \(0.389256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −161.160 | −1.28928 | ||||||||
\(26\) | −107.453 | − | 1.37133i | −0.810507 | − | 0.0103438i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.728372 | − | 28.5317i | 0.00491605 | − | 0.192571i | ||||
\(29\) | − | 121.988i | − | 0.781122i | −0.920577 | − | 0.390561i | \(-0.872281\pi\) | ||
0.920577 | − | 0.390561i | \(-0.127719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.9532i | 0.115603i | 0.998328 | + | 0.0578016i | \(0.0184091\pi\) | ||||
−0.998328 | + | 0.0578016i | \(0.981591\pi\) | |||||||
\(32\) | −180.651 | − | 11.5425i | −0.997965 | − | 0.0637640i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.04567 | − | 238.649i | 0.0153626 | − | 1.20376i | ||||
\(35\) | 60.3510 | 0.291462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.7622 | 0.0789211 | 0.0394606 | − | 0.999221i | \(-0.487436\pi\) | ||||
0.0394606 | + | 0.999221i | \(0.487436\pi\) | |||||||
\(38\) | −2.27116 | + | 177.961i | −0.00969556 | + | 0.759712i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.6506 | − | 382.491i | 0.0579116 | − | 1.51193i | ||||
\(41\) | 345.339i | 1.31544i | 0.753264 | + | 0.657718i | \(0.228478\pi\) | ||||
−0.753264 | + | 0.657718i | \(0.771522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 130.719i | 0.463593i | 0.972764 | + | 0.231796i | \(0.0744603\pi\) | ||||
−0.972764 | + | 0.231796i | \(0.925540\pi\) | |||||||
\(44\) | 400.970 | + | 10.2362i | 1.37383 | + | 0.0350718i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −212.718 | − | 2.71474i | −0.681816 | − | 0.00870145i | ||||
\(47\) | −306.165 | −0.950188 | −0.475094 | − | 0.879935i | \(-0.657586\pi\) | ||||
−0.475094 | + | 0.879935i | \(0.657586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 330.272 | 0.962892 | ||||||||
\(50\) | 455.793 | + | 5.81690i | 1.28918 | + | 0.0164527i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 303.847 | + | 7.75676i | 0.810309 | + | 0.0206859i | ||||
\(53\) | 479.464i | 1.24263i | 0.783561 | + | 0.621315i | \(0.213401\pi\) | ||||
−0.783561 | + | 0.621315i | \(0.786599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 848.142i | 2.07933i | ||||||||
\(56\) | −3.08980 | + | 80.6671i | −0.00737307 | + | 0.192493i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.40301 | + | 345.005i | −0.00996799 | + | 0.781058i | ||||
\(59\) | −491.548 | −1.08465 | −0.542323 | − | 0.840170i | \(-0.682455\pi\) | ||||
−0.542323 | + | 0.840170i | \(0.682455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 99.8337 | 0.209547 | 0.104774 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104774 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(62\) | 0.720188 | − | 56.4315i | 0.00147523 | − | 0.115594i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 510.500 | + | 39.1649i | 0.997070 | + | 0.0764940i | ||||
\(65\) | 642.705i | 1.22643i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 619.691i | 1.12996i | 0.825104 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825104 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(68\) | −17.2275 | + | 674.836i | −0.0307227 | + | 1.20347i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −170.684 | − | 2.17830i | −0.291439 | − | 0.00371939i | ||||
\(71\) | −254.455 | −0.425327 | −0.212663 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212663 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 100.485 | 0.161108 | 0.0805541 | − | 0.996750i | \(-0.474331\pi\) | ||||
0.0805541 | + | 0.996750i | \(0.474331\pi\) | |||||||
\(74\) | −50.2349 | − | 0.641106i | −0.0789147 | − | 0.00100712i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.8466 | − | 503.226i | 0.0193895 | − | 0.759526i | ||||
\(77\) | − | 178.873i | − | 0.264733i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 988.765i | 1.40816i | 0.710120 | + | 0.704080i | \(0.248641\pi\) | ||||
−0.710120 | + | 0.704080i | \(0.751359\pi\) | |||||||
\(80\) | −55.2404 | + | 1081.23i | −0.0772008 | + | 1.51107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.4646 | − | 976.687i | 0.0167864 | − | 1.31533i | ||||
\(83\) | 503.510 | 0.665873 | 0.332936 | − | 0.942949i | \(-0.391961\pi\) | ||||
0.332936 | + | 0.942949i | \(0.391961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1427.43 | −1.82149 | ||||||||
\(86\) | 4.71816 | − | 369.700i | 0.00591596 | − | 0.463555i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1133.65 | − | 43.4225i | −1.37327 | − | 0.0526006i | ||||
\(89\) | − | 1019.86i | − | 1.21467i | −0.794448 | − | 0.607333i | \(-0.792239\pi\) | ||
0.794448 | − | 0.607333i | \(-0.207761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 135.546i | − | 0.156144i | ||||||
\(92\) | 601.510 | + | 15.3556i | 0.681650 | + | 0.0174015i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 865.896 | + | 11.0507i | 0.950110 | + | 0.0121255i | ||||
\(95\) | 1064.43 | 1.14957 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1007.18 | 1.05426 | 0.527131 | − | 0.849784i | \(-0.323268\pi\) | ||||
0.527131 | + | 0.849784i | \(0.323268\pi\) | |||||||
\(98\) | −934.074 | − | 11.9208i | −0.962814 | − | 0.0122876i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1288.86 | − | 32.9027i | −1.28886 | − | 0.0329027i | ||||
\(101\) | 420.983i | 0.414747i | 0.978262 | + | 0.207373i | \(0.0664915\pi\) | ||||
−0.978262 | + | 0.207373i | \(0.933509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1728.13i | 1.65318i | 0.562803 | + | 0.826591i | \(0.309723\pi\) | ||||
−0.562803 | + | 0.826591i | \(0.690277\pi\) | |||||||
\(104\) | −859.060 | − | 32.9047i | −0.809979 | − | 0.0310247i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.3057 | − | 1356.02i | 0.0158574 | − | 1.24253i | ||||
\(107\) | −63.1607 | −0.0570652 | −0.0285326 | − | 0.999593i | \(-0.509083\pi\) | ||||
−0.0285326 | + | 0.999593i | \(0.509083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −835.373 | −0.734076 | −0.367038 | − | 0.930206i | \(-0.619628\pi\) | ||||
−0.367038 | + | 0.930206i | \(0.619628\pi\) | |||||||
\(110\) | 30.6127 | − | 2398.71i | 0.0265346 | − | 2.07917i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.6502 | − | 228.031i | 0.00982890 | − | 0.192383i | ||||
\(113\) | − | 1029.89i | − | 0.857384i | −0.903451 | − | 0.428692i | \(-0.858975\pi\) | ||
0.903451 | − | 0.428692i | \(-0.141025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1272.33i | 1.03170i | ||||||||
\(116\) | 24.9051 | − | 975.583i | 0.0199343 | − | 0.780867i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1390.19 | + | 17.7419i | 1.08456 | + | 0.0138413i | ||||
\(119\) | 301.044 | 0.231904 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1182.78 | 0.888642 | ||||||||
\(122\) | −282.349 | − | 3.60339i | −0.209530 | − | 0.00267406i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.07367 | + | 159.573i | −0.00295021 | + | 0.115565i | ||||
\(125\) | − | 611.695i | − | 0.437693i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 794.523i | 0.555138i | 0.960706 | + | 0.277569i | \(0.0895287\pi\) | ||||
−0.960706 | + | 0.277569i | \(0.910471\pi\) | |||||||
\(128\) | −1442.38 | − | 129.192i | −0.996013 | − | 0.0892115i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 23.1977 | − | 1817.70i | 0.0156506 | − | 1.22633i | ||||
\(131\) | −222.078 | −0.148115 | −0.0740575 | − | 0.997254i | \(-0.523595\pi\) | ||||
−0.0740575 | + | 0.997254i | \(0.523595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −224.489 | −0.146358 | ||||||||
\(134\) | 22.3671 | − | 1752.61i | 0.0144196 | − | 1.12987i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.0803 | − | 1907.95i | 0.0460778 | − | 1.20298i | ||||
\(137\) | − | 1217.38i | − | 0.759181i | −0.925155 | − | 0.379591i | \(-0.876065\pi\) | ||
0.925155 | − | 0.379591i | \(-0.123935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2204.42i | − | 1.34516i | −0.740026 | − | 0.672578i | \(-0.765187\pi\) | ||
0.740026 | − | 0.672578i | \(-0.234813\pi\) | |||||||
\(140\) | 482.651 | + | 12.3213i | 0.291367 | + | 0.00743817i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 719.648 | + | 9.18426i | 0.425292 | + | 0.00542765i | ||||
\(143\) | 1904.89 | 1.11395 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2063.57 | 1.18187 | ||||||||
\(146\) | −284.192 | − | 3.62690i | −0.161095 | − | 0.00205592i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 142.051 | + | 3.62635i | 0.0788954 | + | 0.00201408i | ||||
\(149\) | − | 406.594i | − | 0.223553i | −0.993733 | − | 0.111777i | \(-0.964346\pi\) | ||
0.993733 | − | 0.111777i | \(-0.0356541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3452.75i | − | 1.86080i | −0.366549 | − | 0.930399i | \(-0.619461\pi\) | ||
0.366549 | − | 0.930399i | \(-0.380539\pi\) | |||||||
\(152\) | −54.4961 | + | 1422.76i | −0.0290804 | + | 0.759217i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.45621 | + | 505.887i | −0.00337829 | + | 0.264711i | ||||
\(155\) | −337.533 | −0.174912 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −880.574 | −0.447627 | −0.223813 | − | 0.974632i | \(-0.571851\pi\) | ||||
−0.223813 | + | 0.974632i | \(0.571851\pi\) | |||||||
\(158\) | 35.6884 | − | 2796.42i | 0.0179697 | − | 1.40805i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 195.256 | − | 3055.94i | 0.0964774 | − | 1.50996i | ||||
\(161\) | − | 268.333i | − | 0.131352i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1693.56i | 0.813802i | 0.913472 | + | 0.406901i | \(0.133391\pi\) | ||||
−0.913472 | + | 0.406901i | \(0.866609\pi\) | |||||||
\(164\) | −70.5049 | + | 2761.81i | −0.0335702 | + | 1.31501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1424.03 | − | 18.1737i | −0.665818 | − | 0.00849728i | ||||
\(167\) | −1640.10 | −0.759970 | −0.379985 | − | 0.924993i | \(-0.624071\pi\) | ||||
−0.379985 | + | 0.924993i | \(0.624071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.509 | −0.342972 | ||||||||
\(170\) | 4037.05 | + | 51.5214i | 1.82134 | + | 0.0232442i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −26.6878 | + | 1045.41i | −0.0118310 | + | 0.463442i | ||||
\(173\) | − | 2181.42i | − | 0.958672i | −0.877631 | − | 0.479336i | \(-0.840877\pi\) | ||
0.877631 | − | 0.479336i | \(-0.159123\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 574.960i | 0.248359i | ||||||||
\(176\) | 3204.63 | + | 163.725i | 1.37249 | + | 0.0701208i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −36.8108 | + | 2884.37i | −0.0155005 | + | 1.21457i | ||||
\(179\) | −2350.24 | −0.981370 | −0.490685 | − | 0.871337i | \(-0.663253\pi\) | ||||
−0.490685 | + | 0.871337i | \(0.663253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2280.14 | −0.936362 | −0.468181 | − | 0.883633i | \(-0.655090\pi\) | ||||
−0.468181 | + | 0.883633i | \(0.655090\pi\) | |||||||
\(182\) | −4.89239 | + | 383.351i | −0.00199257 | + | 0.156131i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1700.64 | − | 65.1396i | −0.681372 | − | 0.0260987i | ||||
\(185\) | 300.470i | 0.119411i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4230.71i | 1.65444i | ||||||||
\(188\) | −2448.53 | − | 62.5071i | −0.949878 | − | 0.0242489i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3010.43 | − | 38.4196i | −1.14947 | − | 0.0146697i | ||||
\(191\) | −3932.95 | −1.48994 | −0.744970 | − | 0.667098i | \(-0.767536\pi\) | ||||
−0.744970 | + | 0.667098i | \(0.767536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2713.19 | 1.01192 | 0.505958 | − | 0.862558i | \(-0.331139\pi\) | ||||
0.505958 | + | 0.862558i | \(0.331139\pi\) | |||||||
\(194\) | −2848.50 | − | 36.3530i | −1.05418 | − | 0.0134536i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2641.32 | + | 67.4288i | 0.962579 | + | 0.0245732i | ||||
\(197\) | 1997.91i | 0.722565i | 0.932456 | + | 0.361282i | \(0.117661\pi\) | ||||
−0.932456 | + | 0.361282i | \(0.882339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2409.09i | − | 0.858170i | −0.903264 | − | 0.429085i | \(-0.858836\pi\) | ||
0.903264 | − | 0.429085i | \(-0.141164\pi\) | |||||||
\(200\) | 3643.97 | + | 139.575i | 1.28834 | + | 0.0493473i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.1949 | − | 1190.62i | 0.00529263 | − | 0.414713i | ||||
\(203\) | −435.207 | −0.150471 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5841.85 | −1.99030 | ||||||||
\(206\) | 62.3750 | − | 4887.49i | 0.0210965 | − | 1.65305i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2428.40 | + | 124.068i | 0.809517 | + | 0.0413584i | ||||
\(209\) | − | 3154.85i | − | 1.04414i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1819.43i | 0.593626i | 0.954936 | + | 0.296813i | \(0.0959238\pi\) | ||||
−0.954936 | + | 0.296813i | \(0.904076\pi\) | |||||||
\(212\) | −97.8880 | + | 3834.46i | −0.0317121 | + | 1.24223i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 178.631 | + | 2.27971i | 0.0570605 | + | 0.000728215i | ||||
\(215\) | −2211.28 | −0.701433 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 71.1856 | 0.0222691 | ||||||||
\(218\) | 2362.60 | + | 30.1519i | 0.734016 | + | 0.00936763i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −173.158 | + | 6782.92i | −0.0530650 | + | 2.07866i | ||||
\(221\) | 3205.95i | 0.975816i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2674.44i | − | 0.803110i | −0.915835 | − | 0.401555i | \(-0.868470\pi\) | ||
0.915835 | − | 0.401555i | \(-0.131530\pi\) | |||||||
\(224\) | −41.1795 | + | 644.496i | −0.0122831 | + | 0.192242i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.1729 | + | 2912.74i | −0.0109412 | + | 0.857314i | ||||
\(227\) | 5899.16 | 1.72485 | 0.862425 | − | 0.506184i | \(-0.168944\pi\) | ||||
0.862425 | + | 0.506184i | \(0.168944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3032.75 | 0.875152 | 0.437576 | − | 0.899181i | \(-0.355837\pi\) | ||||
0.437576 | + | 0.899181i | \(0.355837\pi\) | |||||||
\(230\) | 45.9233 | − | 3598.39i | 0.0131656 | − | 1.03161i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −105.649 | + | 2758.24i | −0.0298975 | + | 0.780549i | ||||
\(233\) | 1294.13i | 0.363867i | 0.983311 | + | 0.181934i | \(0.0582356\pi\) | ||||
−0.983311 | + | 0.181934i | \(0.941764\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5179.18i | − | 1.43767i | ||||||
\(236\) | −3931.10 | − | 100.355i | −1.08429 | − | 0.0276803i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −851.410 | − | 10.8658i | −0.231885 | − | 0.00295936i | ||||
\(239\) | 5750.29 | 1.55630 | 0.778149 | − | 0.628080i | \(-0.216159\pi\) | ||||
0.778149 | + | 0.628080i | \(0.216159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6017.64 | 1.60842 | 0.804212 | − | 0.594343i | \(-0.202588\pi\) | ||||
0.804212 | + | 0.594343i | \(0.202588\pi\) | |||||||
\(242\) | −3345.14 | − | 42.6912i | −0.888570 | − | 0.0113401i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 798.409 | + | 20.3822i | 0.209479 | + | 0.00534769i | ||||
\(245\) | 5586.97i | 1.45689i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2390.68i | − | 0.615852i | ||||||
\(248\) | 17.2808 | − | 451.158i | 0.00442472 | − | 0.115518i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.0785 | + | 1729.99i | −0.00558546 | + | 0.437658i | ||||
\(251\) | 3207.28 | 0.806541 | 0.403270 | − | 0.915081i | \(-0.367873\pi\) | ||||
0.403270 | + | 0.915081i | \(0.367873\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3771.02 | 0.937082 | ||||||||
\(254\) | 28.6774 | − | 2247.07i | 0.00708418 | − | 0.555093i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4074.67 | + | 417.442i | 0.994793 | + | 0.101914i | ||||
\(257\) | − | 2907.84i | − | 0.705784i | −0.935664 | − | 0.352892i | \(-0.885198\pi\) | ||
0.935664 | − | 0.352892i | \(-0.114802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 63.3688i | − | 0.0152029i | ||||||
\(260\) | −131.215 | + | 5139.96i | −0.0312986 | + | 1.22603i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 628.081 | + | 8.01567i | 0.148103 | + | 0.00189011i | ||||
\(263\) | −312.106 | −0.0731761 | −0.0365880 | − | 0.999330i | \(-0.511649\pi\) | ||||
−0.0365880 | + | 0.999330i | \(0.511649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8110.74 | −1.88015 | ||||||||
\(266\) | 634.898 | + | 8.10267i | 0.146346 | + | 0.00186769i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −126.517 | + | 4955.92i | −0.0288368 | + | 1.12959i | ||||
\(269\) | − | 1826.27i | − | 0.413939i | −0.978347 | − | 0.206969i | \(-0.933640\pi\) | ||
0.978347 | − | 0.206969i | \(-0.0663600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4987.26i | 1.11791i | 0.829197 | + | 0.558956i | \(0.188798\pi\) | ||||
−0.829197 | + | 0.558956i | \(0.811202\pi\) | |||||||
\(272\) | −275.551 | + | 5393.41i | −0.0614254 | + | 1.20229i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −43.9400 | + | 3442.99i | −0.00968800 | + | 0.759119i | ||||
\(275\) | −8080.19 | −1.77183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4251.84 | 0.922268 | 0.461134 | − | 0.887330i | \(-0.347443\pi\) | ||||
0.461134 | + | 0.887330i | \(0.347443\pi\) | |||||||
\(278\) | −79.5662 | + | 6234.54i | −0.0171657 | + | 1.34505i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1364.59 | − | 52.2679i | −0.291249 | − | 0.0111557i | ||||
\(281\) | 2934.87i | 0.623059i | 0.950237 | + | 0.311529i | \(0.100841\pi\) | ||||
−0.950237 | + | 0.311529i | \(0.899159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4003.62i | − | 0.840956i | −0.907303 | − | 0.420478i | \(-0.861862\pi\) | ||
0.907303 | − | 0.420478i | \(-0.138138\pi\) | |||||||
\(284\) | −2034.97 | − | 51.9498i | −0.425188 | − | 0.0108544i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5387.42 | − | 68.7551i | −1.11386 | − | 0.0142153i | ||||
\(287\) | 1232.04 | 0.253398 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2207.31 | −0.449280 | ||||||||
\(290\) | −5836.20 | − | 74.4825i | −1.18177 | − | 0.0150819i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 803.620 | + | 20.5152i | 0.161056 | + | 0.00411151i | ||||
\(293\) | 2695.37i | 0.537424i | 0.963221 | + | 0.268712i | \(0.0865980\pi\) | ||||
−0.963221 | + | 0.268712i | \(0.913402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8315.16i | − | 1.64111i | ||||||
\(296\) | −401.617 | − | 15.3832i | −0.0788633 | − | 0.00302071i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.6755 | + | 1149.93i | −0.00285279 | + | 0.223535i | ||||
\(299\) | 2857.60 | 0.552707 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 466.358 | 0.0893037 | ||||||||
\(302\) | −124.623 | + | 9765.04i | −0.0237459 | + | 1.86065i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 205.479 | − | 4021.87i | 0.0387665 | − | 0.758784i | ||||
\(305\) | 1688.81i | 0.317053i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4575.16i | − | 0.850547i | −0.905065 | − | 0.425274i | \(-0.860178\pi\) | ||
0.905065 | − | 0.425274i | \(-0.139822\pi\) | |||||||
\(308\) | 36.5189 | − | 1430.51i | 0.00675602 | − | 0.264647i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 954.611 | + | 12.1829i | 0.174898 | + | 0.00223207i | ||||
\(311\) | 8238.91 | 1.50221 | 0.751103 | − | 0.660185i | \(-0.229522\pi\) | ||||
0.751103 | + | 0.660185i | \(0.229522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5319.81 | −0.960682 | −0.480341 | − | 0.877082i | \(-0.659487\pi\) | ||||
−0.480341 | + | 0.877082i | \(0.659487\pi\) | |||||||
\(314\) | 2490.44 | + | 31.7833i | 0.447591 | + | 0.00571222i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −201.867 | + | 7907.54i | −0.0359365 | + | 1.40770i | ||||
\(317\) | 8823.47i | 1.56333i | 0.623699 | + | 0.781665i | \(0.285629\pi\) | ||||
−0.623699 | + | 0.781665i | \(0.714371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6116.17i | − | 1.07348i | ||||||
\(320\) | −662.525 | + | 8635.75i | −0.115738 | + | 1.50860i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.68519 | + | 758.899i | −0.00167619 | + | 0.131341i | ||||
\(323\) | 5309.63 | 0.914661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6123.01 | −1.04506 | ||||||||
\(326\) | 61.1271 | − | 4789.72i | 0.0103850 | − | 0.813736i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 299.086 | − | 7808.41i | 0.0503484 | − | 1.31447i | ||||
\(329\) | 1092.29i | 0.183038i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2374.33i | − | 0.394275i | −0.980376 | − | 0.197138i | \(-0.936835\pi\) | ||
0.980376 | − | 0.197138i | \(-0.0631645\pi\) | |||||||
\(332\) | 4026.77 | + | 102.797i | 0.665656 | + | 0.0169932i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4638.53 | + | 59.1977i | 0.759908 | + | 0.00969806i | ||||
\(335\) | −10482.9 | −1.70967 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −643.776 | −0.104062 | −0.0520308 | − | 0.998645i | \(-0.516569\pi\) | ||||
−0.0520308 | + | 0.998645i | \(0.516569\pi\) | |||||||
\(338\) | 2131.07 | + | 27.1971i | 0.342944 | + | 0.00437671i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11415.7 | − | 291.425i | −1.82089 | − | 0.0464846i | ||||
\(341\) | 1000.41i | 0.158871i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2401.99i | − | 0.378120i | ||||||
\(344\) | 113.211 | − | 2955.67i | 0.0177440 | − | 0.463253i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −78.7360 | + | 6169.49i | −0.0122337 | + | 0.958594i | ||||
\(347\) | −1536.53 | −0.237710 | −0.118855 | − | 0.992912i | \(-0.537922\pi\) | ||||
−0.118855 | + | 0.992912i | \(0.537922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6865.30 | 1.05298 | 0.526492 | − | 0.850180i | \(-0.323507\pi\) | ||||
0.526492 | + | 0.850180i | \(0.323507\pi\) | |||||||
\(350\) | 20.7525 | − | 1626.10i | 0.00316934 | − | 0.248339i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9057.41 | − | 578.715i | −1.37148 | − | 0.0876296i | ||||
\(353\) | − | 124.671i | − | 0.0187976i | −0.999956 | − | 0.00939881i | \(-0.997008\pi\) | ||
0.999956 | − | 0.00939881i | \(-0.00299178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4304.42i | − | 0.643535i | ||||||
\(356\) | 208.216 | − | 8156.24i | 0.0309985 | − | 1.21427i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6646.94 | + | 84.8293i | 0.981290 | + | 0.0125234i | ||||
\(359\) | −4489.49 | −0.660017 | −0.330009 | − | 0.943978i | \(-0.607052\pi\) | ||||
−0.330009 | + | 0.943978i | \(0.607052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2899.60 | 0.422744 | ||||||||
\(362\) | 6448.68 | + | 82.2991i | 0.936285 | + | 0.0119490i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.6733 | − | 1084.02i | 0.00398482 | − | 0.156093i | ||||
\(365\) | 1699.83i | 0.243763i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 867.177i | − | 0.123341i | −0.998097 | − | 0.0616707i | \(-0.980357\pi\) | ||
0.998097 | − | 0.0616707i | \(-0.0196429\pi\) | |||||||
\(368\) | 4807.38 | + | 245.610i | 0.680984 | + | 0.0347916i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.8451 | − | 849.787i | 0.00152381 | − | 0.119401i | ||||
\(371\) | 1710.55 | 0.239373 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4339.15 | −0.602340 | −0.301170 | − | 0.953570i | \(-0.597377\pi\) | ||||
−0.301170 | + | 0.953570i | \(0.597377\pi\) | |||||||
\(374\) | 152.703 | − | 11965.3i | 0.0211125 | − | 1.65430i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6922.66 | + | 265.159i | 0.949491 | + | 0.0363685i | ||||
\(377\) | − | 4634.71i | − | 0.633156i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14096.9i | − | 1.91058i | −0.295677 | − | 0.955288i | \(-0.595545\pi\) | ||
0.295677 | − | 0.955288i | \(-0.404455\pi\) | |||||||
\(380\) | 8512.71 | + | 217.316i | 1.14919 | + | 0.0293371i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11123.2 | + | 141.956i | 1.48982 | + | 0.0190133i | ||||
\(383\) | −8268.91 | −1.10319 | −0.551594 | − | 0.834112i | \(-0.685980\pi\) | ||||
−0.551594 | + | 0.834112i | \(0.685980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3025.86 | 0.400550 | ||||||||
\(386\) | −7673.45 | − | 97.9297i | −1.01183 | − | 0.0129132i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8054.80 | + | 205.627i | 1.05392 | + | 0.0269050i | ||||
\(389\) | − | 5742.29i | − | 0.748446i | −0.927339 | − | 0.374223i | \(-0.877909\pi\) | ||
0.927339 | − | 0.374223i | \(-0.122091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6346.64i | 0.820878i | ||||||||
\(392\) | −7467.73 | − | 286.037i | −0.962187 | − | 0.0368547i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 72.1124 | − | 5650.48i | 0.00922073 | − | 0.722506i | ||||
\(395\) | −16726.2 | −2.13060 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10494.4 | 1.32670 | 0.663349 | − | 0.748310i | \(-0.269134\pi\) | ||||
0.663349 | + | 0.748310i | \(0.269134\pi\) | |||||||
\(398\) | −86.9535 | + | 6813.38i | −0.0109512 | + | 0.858100i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10300.8 | − | 526.271i | −1.28760 | − | 0.0657839i | ||||
\(401\) | − | 8163.95i | − | 1.01668i | −0.861157 | − | 0.508339i | \(-0.830260\pi\) | ||
0.861157 | − | 0.508339i | \(-0.169740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 758.087i | 0.0937047i | ||||||||
\(404\) | −85.9485 | + | 3366.77i | −0.0105844 | + | 0.414611i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1230.85 | + | 15.7083i | 0.150458 | + | 0.00192017i | ||||
\(407\) | 890.553 | 0.108460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4074.86 | 0.492638 | 0.246319 | − | 0.969189i | \(-0.420779\pi\) | ||||
0.246319 | + | 0.969189i | \(0.420779\pi\) | |||||||
\(410\) | 16521.9 | + | 210.855i | 1.99014 | + | 0.0253985i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −352.817 | + | 13820.5i | −0.0421895 | + | 1.65264i | ||||
\(413\) | 1753.66i | 0.208940i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8517.52i | 1.00749i | ||||||||
\(416\) | −6863.53 | − | 438.539i | −0.808923 | − | 0.0516854i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −113.871 | + | 8922.53i | −0.0133244 | + | 1.04406i | ||||
\(419\) | 693.073 | 0.0808086 | 0.0404043 | − | 0.999183i | \(-0.487135\pi\) | ||||
0.0404043 | + | 0.999183i | \(0.487135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10725.4 | −1.24162 | −0.620810 | − | 0.783961i | \(-0.713196\pi\) | ||||
−0.620810 | + | 0.783961i | \(0.713196\pi\) | |||||||
\(422\) | 65.6705 | − | 5145.72i | 0.00757533 | − | 0.593577i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 415.247 | − | 10841.1i | 0.0475618 | − | 1.24172i | ||||
\(425\) | − | 13599.0i | − | 1.55211i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 356.170i | − | 0.0403660i | ||||||
\(428\) | −505.121 | − | 12.8950i | −0.0570466 | − | 0.00145631i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6253.94 | + | 79.8137i | 0.701376 | + | 0.00895107i | ||||
\(431\) | 10013.8 | 1.11914 | 0.559569 | − | 0.828784i | \(-0.310967\pi\) | ||||
0.559569 | + | 0.828784i | \(0.310967\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9726.02 | −1.07945 | −0.539726 | − | 0.841841i | \(-0.681472\pi\) | ||||
−0.539726 | + | 0.841841i | \(0.681472\pi\) | |||||||
\(434\) | −201.327 | − | 2.56936i | −0.0222673 | − | 0.000284178i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6680.81 | − | 170.551i | −0.733836 | − | 0.0187337i | ||||
\(437\) | − | 4732.70i | − | 0.518068i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6554.02i | 0.712542i | 0.934383 | + | 0.356271i | \(0.115952\pi\) | ||||
−0.934383 | + | 0.356271i | \(0.884048\pi\) | |||||||
\(440\) | 734.546 | − | 19177.2i | 0.0795866 | − | 2.07781i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 115.715 | − | 9067.05i | 0.0124525 | − | 0.975737i | ||||
\(443\) | 5879.21 | 0.630542 | 0.315271 | − | 0.949002i | \(-0.397905\pi\) | ||||
0.315271 | + | 0.949002i | \(0.397905\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17252.3 | 1.83783 | ||||||||
\(446\) | −96.5309 | + | 7563.84i | −0.0102486 | + | 0.803045i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 139.726 | − | 1821.27i | 0.0147353 | − | 0.192070i | ||||
\(449\) | − | 6761.00i | − | 0.710627i | −0.934747 | − | 0.355313i | \(-0.884374\pi\) | ||
0.934747 | − | 0.355313i | \(-0.115626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17314.5i | 1.80778i | ||||||||
\(452\) | 210.265 | − | 8236.47i | 0.0218806 | − | 0.857104i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16684.0 | − | 212.924i | −1.72471 | − | 0.0220110i | ||||
\(455\) | 2292.93 | 0.236251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15240.3 | −1.55998 | −0.779992 | − | 0.625790i | \(-0.784777\pi\) | ||||
−0.779992 | + | 0.625790i | \(0.784777\pi\) | |||||||
\(458\) | −8577.22 | − | 109.464i | −0.875081 | − | 0.0111679i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −259.760 | + | 10175.3i | −0.0263291 | + | 1.03136i | ||||
\(461\) | − | 13741.4i | − | 1.38828i | −0.719838 | − | 0.694142i | \(-0.755784\pi\) | ||
0.719838 | − | 0.694142i | \(-0.244216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17657.3i | 1.77237i | 0.463336 | + | 0.886183i | \(0.346652\pi\) | ||||
−0.463336 | + | 0.886183i | \(0.653348\pi\) | |||||||
\(464\) | 398.352 | − | 7797.04i | 0.0398557 | − | 0.780104i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 46.7101 | − | 3660.05i | 0.00464335 | − | 0.363838i | ||||
\(467\) | 6165.12 | 0.610895 | 0.305447 | − | 0.952209i | \(-0.401194\pi\) | ||||
0.305447 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2210.83 | 0.217669 | ||||||||
\(470\) | −186.937 | + | 14647.7i | −0.0183463 | + | 1.43755i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11114.3 | + | 425.713i | 1.08385 | + | 0.0415149i | ||||
\(473\) | 6553.95i | 0.637106i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10140.8i | 0.979562i | ||||||||
\(476\) | 2407.56 | + | 61.4614i | 0.231829 | + | 0.00591824i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16262.9 | − | 207.550i | −1.55617 | − | 0.0198601i | ||||
\(479\) | 17318.1 | 1.65195 | 0.825976 | − | 0.563705i | \(-0.190624\pi\) | ||||
0.825976 | + | 0.563705i | \(0.190624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 674.843 | 0.0639713 | ||||||||
\(482\) | −17019.1 | − | 217.200i | −1.60829 | − | 0.0205253i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9459.18 | + | 241.478i | 0.888353 | + | 0.0226783i | ||||
\(485\) | 17037.7i | 1.59514i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7352.14i | − | 0.684101i | −0.939682 | − | 0.342050i | \(-0.888879\pi\) | ||
0.939682 | − | 0.342050i | \(-0.111121\pi\) | |||||||
\(488\) | −2257.32 | − | 86.4625i | −0.209394 | − | 0.00802044i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 201.656 | − | 15801.1i | 0.0185916 | − | 1.45677i | ||||
\(491\) | 8442.54 | 0.775981 | 0.387991 | − | 0.921663i | \(-0.373169\pi\) | ||||
0.387991 | + | 0.921663i | \(0.373169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10293.5 | 0.940361 | ||||||||
\(494\) | −86.2890 | + | 6761.31i | −0.00785896 | + | 0.615801i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −65.1574 | + | 1275.34i | −0.00589850 | + | 0.115453i | ||||
\(497\) | 907.800i | 0.0819324i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7554.44i | − | 0.677722i | −0.940837 | − | 0.338861i | \(-0.889958\pi\) | ||
0.940837 | − | 0.338861i | \(-0.110042\pi\) | |||||||
\(500\) | 124.884 | − | 4891.97i | 0.0111700 | − | 0.437551i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9070.82 | − | 115.763i | −0.806475 | − | 0.0102924i | ||||
\(503\) | 604.632 | 0.0535968 | 0.0267984 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267984 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7121.47 | −0.627527 | ||||||||
\(506\) | −10665.2 | − | 136.111i | −0.937006 | − | 0.0119582i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −162.211 | + | 6354.11i | −0.0141672 | + | 0.554957i | ||||
\(509\) | 10232.6i | 0.891061i | 0.895267 | + | 0.445531i | \(0.146985\pi\) | ||||
−0.895267 | + | 0.445531i | \(0.853015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 358.494i | − | 0.0310349i | ||||||
\(512\) | −11508.9 | − | 1327.68i | −0.993412 | − | 0.114601i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −104.955 | + | 8223.96i | −0.00900659 | + | 0.705726i | ||||
\(515\) | −29233.5 | −2.50133 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15350.4 | −1.30582 | ||||||||
\(518\) | −2.28723 | + | 179.220i | −0.000194006 | + | 0.0152017i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 556.624 | − | 14532.1i | 0.0469415 | − | 1.22553i | ||||
\(521\) | − | 18465.3i | − | 1.55274i | −0.630276 | − | 0.776371i | \(-0.717058\pi\) | ||
0.630276 | − | 0.776371i | \(-0.282942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15941.5i | 1.33284i | 0.745579 | + | 0.666418i | \(0.232173\pi\) | ||||
−0.745579 | + | 0.666418i | \(0.767827\pi\) | |||||||
\(524\) | −1776.05 | − | 45.3398i | −0.148067 | − | 0.00377992i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 882.698 | + | 11.2651i | 0.0731701 | + | 0.000933809i | ||||
\(527\) | −1683.69 | −0.139170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6509.96 | −0.535051 | ||||||||
\(530\) | 22938.8 | + | 292.748i | 1.87999 | + | 0.0239928i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1795.32 | − | 45.8319i | −0.146310 | − | 0.00373508i | ||||
\(533\) | 13120.6i | 1.06626i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1068.44i | − | 0.0863417i | ||||||
\(536\) | 536.693 | − | 14011.7i | 0.0432493 | − | 1.12913i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −65.9171 | + | 5165.04i | −0.00528232 | + | 0.413905i | ||||
\(539\) | 16559.1 | 1.32328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7256.04 | 0.576638 | 0.288319 | − | 0.957534i | \(-0.406904\pi\) | ||||
0.288319 | + | 0.957534i | \(0.406904\pi\) | |||||||
\(542\) | 180.010 | − | 14104.9i | 0.0142658 | − | 1.11782i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 973.981 | − | 15243.7i | 0.0767630 | − | 1.20141i | ||||
\(545\) | − | 14131.4i | − | 1.11068i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 433.011i | − | 0.0338468i | −0.999857 | − | 0.0169234i | \(-0.994613\pi\) | ||
0.999857 | − | 0.0169234i | \(-0.00538715\pi\) | |||||||
\(548\) | 248.542 | − | 9735.87i | 0.0193744 | − | 0.758934i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 22852.4 | + | 291.646i | 1.77169 | + | 0.0226106i | ||||
\(551\) | −7675.91 | −0.593475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3527.55 | 0.271260 | ||||||||
\(554\) | −12025.0 | − | 153.466i | −0.922193 | − | 0.0117692i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 450.058 | − | 17629.6i | 0.0343286 | − | 1.34472i | ||||
\(557\) | 9185.88i | 0.698776i | 0.936978 | + | 0.349388i | \(0.113610\pi\) | ||||
−0.936978 | + | 0.349388i | \(0.886390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4966.45i | 0.375776i | ||||||||
\(560\) | 3857.43 | + | 197.077i | 0.291083 | + | 0.0148715i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 105.931 | − | 8300.38i | 0.00795093 | − | 0.623008i | ||||
\(563\) | 12998.2 | 0.973019 | 0.486510 | − | 0.873675i | \(-0.338270\pi\) | ||||
0.486510 | + | 0.873675i | \(0.338270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17422.0 | 1.29725 | ||||||||
\(566\) | −144.506 | + | 11323.0i | −0.0107315 | + | 0.840888i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5753.43 | + | 220.374i | 0.425015 | + | 0.0162794i | ||||
\(569\) | − | 6263.58i | − | 0.461482i | −0.973015 | − | 0.230741i | \(-0.925885\pi\) | ||
0.973015 | − | 0.230741i | \(-0.0741149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25216.1i | 1.84809i | 0.382278 | + | 0.924047i | \(0.375140\pi\) | ||||
−0.382278 | + | 0.924047i | \(0.624860\pi\) | |||||||
\(572\) | 15234.2 | + | 388.906i | 1.11359 | + | 0.0284283i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3484.46 | − | 44.4692i | −0.253377 | − | 0.00323364i | ||||
\(575\) | −12121.4 | −0.879125 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18112.2 | 1.30680 | 0.653398 | − | 0.757014i | \(-0.273343\pi\) | ||||
0.653398 | + | 0.757014i | \(0.273343\pi\) | |||||||
\(578\) | 6242.71 | + | 79.6705i | 0.449243 | + | 0.00573331i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16503.2 | + | 421.302i | 1.18148 | + | 0.0301614i | ||||
\(581\) | − | 1796.34i | − | 0.128270i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24039.2i | 1.70772i | ||||||||
\(584\) | −2272.05 | − | 87.0268i | −0.160990 | − | 0.00616643i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 97.2865 | − | 7623.04i | 0.00685813 | − | 0.537380i | ||||
\(587\) | 26344.3 | 1.85238 | 0.926189 | − | 0.377060i | \(-0.123065\pi\) | ||||
0.926189 | + | 0.377060i | \(0.123065\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1255.53 | 0.0878322 | ||||||||
\(590\) | −300.126 | + | 23516.9i | −0.0209424 | + | 1.64098i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1135.30 | + | 58.0027i | 0.0788183 | + | 0.00402685i | ||||
\(593\) | − | 11633.4i | − | 0.805609i | −0.915286 | − | 0.402804i | \(-0.868035\pi\) | ||
0.915286 | − | 0.402804i | \(-0.131965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5092.53i | 0.350880i | ||||||||
\(596\) | 83.0107 | − | 3251.69i | 0.00570512 | − | 0.223481i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8081.86 | − | 103.142i | −0.552662 | − | 0.00705316i | ||||
\(599\) | −22120.9 | −1.50891 | −0.754454 | − | 0.656353i | \(-0.772098\pi\) | ||||
−0.754454 | + | 0.656353i | \(0.772098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1693.85 | −0.114964 | −0.0574820 | − | 0.998347i | \(-0.518307\pi\) | ||||
−0.0574820 | + | 0.998347i | \(0.518307\pi\) | |||||||
\(602\) | −1318.95 | − | 16.8327i | −0.0892964 | − | 0.00113962i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 704.917 | − | 27613.0i | 0.0474879 | − | 1.86019i | ||||
\(605\) | 20008.3i | 1.34455i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13184.9i | − | 0.881642i | −0.897595 | − | 0.440821i | \(-0.854687\pi\) | ||
0.897595 | − | 0.440821i | \(-0.145313\pi\) | |||||||
\(608\) | −726.299 | + | 11367.2i | −0.0484462 | + | 0.758227i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 60.9559 | − | 4776.30i | 0.00404595 | − | 0.317027i | ||||
\(611\) | −11632.2 | −0.770196 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18052.3 | −1.18944 | −0.594719 | − | 0.803934i | \(-0.702737\pi\) | ||||
−0.594719 | + | 0.803934i | \(0.702737\pi\) | |||||||
\(614\) | −165.135 | + | 12939.4i | −0.0108539 | + | 0.850478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −154.915 | + | 4044.46i | −0.0101327 | + | 0.264539i | ||||
\(617\) | − | 21820.6i | − | 1.42377i | −0.702297 | − | 0.711884i | \(-0.747842\pi\) | ||
0.702297 | − | 0.711884i | \(-0.252158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18059.5i | − | 1.17265i | −0.810075 | − | 0.586326i | \(-0.800574\pi\) | ||
0.810075 | − | 0.586326i | \(-0.199426\pi\) | |||||||
\(620\) | −2699.39 | − | 68.9112i | −0.174855 | − | 0.00446378i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23301.3 | − | 297.374i | −1.50208 | − | 0.0191698i | ||||
\(623\) | −3638.49 | −0.233986 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9797.42 | −0.627035 | ||||||||
\(626\) | 15045.5 | + | 192.013i | 0.960604 | + | 0.0122594i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7042.30 | − | 179.779i | −0.447481 | − | 0.0114235i | ||||
\(629\) | 1498.81i | 0.0950100i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7301.94i | − | 0.460674i | −0.973111 | − | 0.230337i | \(-0.926017\pi\) | ||
0.973111 | − | 0.230337i | \(-0.0739829\pi\) | |||||||
\(632\) | 856.335 | − | 22356.8i | 0.0538974 | − | 1.40713i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 318.473 | − | 24954.5i | 0.0199498 | − | 1.56320i | ||||
\(635\) | −13440.4 | −0.839944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12548.1 | 0.780494 | ||||||||
\(638\) | −220.756 | + | 17297.7i | −0.0136988 | + | 1.07339i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2185.45 | − | 24399.7i | 0.134980 | − | 1.50700i | ||||
\(641\) | − | 849.848i | − | 0.0523666i | −0.999657 | − | 0.0261833i | \(-0.991665\pi\) | ||
0.999657 | − | 0.0261833i | \(-0.00833535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1136.85i | 0.0697245i | 0.999392 | + | 0.0348622i | \(0.0110992\pi\) | ||||
−0.999392 | + | 0.0348622i | \(0.988901\pi\) | |||||||
\(644\) | 54.7833 | − | 2145.97i | 0.00335212 | − | 0.131309i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15016.7 | − | 191.645i | −0.914587 | − | 0.0116721i | ||||
\(647\) | −995.889 | −0.0605138 | −0.0302569 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302569 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24645.0 | −1.49061 | ||||||||
\(650\) | 17317.1 | + | 221.003i | 1.04497 | + | 0.0133361i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −345.759 | + | 13544.1i | −0.0207684 | + | 0.813537i | ||||
\(653\) | 28285.8i | 1.69511i | 0.530704 | + | 0.847557i | \(0.321928\pi\) | ||||
−0.530704 | + | 0.847557i | \(0.678072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3756.74i | − | 0.224104i | ||||||
\(656\) | −1127.71 | + | 22072.9i | −0.0671185 | + | 1.31372i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 39.4248 | − | 3089.20i | 0.00233577 | − | 0.183023i | ||||
\(659\) | −25443.9 | −1.50403 | −0.752014 | − | 0.659147i | \(-0.770917\pi\) | ||||
−0.752014 | + | 0.659147i | \(0.770917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4218.61 | −0.248237 | −0.124119 | − | 0.992267i | \(-0.539610\pi\) | ||||
−0.124119 | + | 0.992267i | \(0.539610\pi\) | |||||||
\(662\) | −85.6989 | + | 6715.08i | −0.00503139 | + | 0.394243i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11384.8 | − | 436.073i | −0.665385 | − | 0.0254863i | ||||
\(665\) | − | 3797.51i | − | 0.221445i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9175.09i | − | 0.532625i | ||||||
\(668\) | −13116.5 | − | 334.845i | −0.759722 | − | 0.0193945i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29647.6 | + | 378.368i | 1.70953 | + | 0.0218173i | ||||
\(671\) | 5005.43 | 0.287977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14425.7 | 0.826257 | 0.413129 | − | 0.910673i | \(-0.364436\pi\) | ||||
0.413129 | + | 0.910673i | \(0.364436\pi\) | |||||||
\(674\) | 1820.73 | + | 23.2364i | 0.104053 | + | 0.00132794i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6026.11 | − | 153.837i | −0.342860 | − | 0.00875270i | ||||
\(677\) | 32182.1i | 1.82697i | 0.406871 | + | 0.913486i | \(0.366620\pi\) | ||||
−0.406871 | + | 0.913486i | \(0.633380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3593.24i | − | 0.203087i | ||||||
\(680\) | 32275.3 | + | 1236.25i | 1.82015 | + | 0.0697174i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 36.1085 | − | 2829.34i | 0.00202737 | − | 0.158858i | ||||
\(683\) | −28383.3 | −1.59012 | −0.795062 | − | 0.606528i | \(-0.792562\pi\) | ||||
−0.795062 | + | 0.606528i | \(0.792562\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20593.5 | 1.14867 | ||||||||
\(686\) | −86.6970 | + | 6793.29i | −0.00482523 | + | 0.378089i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −426.866 | + | 8355.13i | −0.0236542 | + | 0.462989i | ||||
\(689\) | 18216.4i | 1.00724i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5303.09i | 0.291952i | 0.989288 | + | 0.145976i | \(0.0466323\pi\) | ||||
−0.989288 | + | 0.145976i | \(0.953368\pi\) | |||||||
\(692\) | 445.362 | − | 17445.7i | 0.0244655 | − | 0.958360i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4345.61 | + | 55.4594i | 0.237690 | + | 0.00303344i | ||||
\(695\) | 37290.6 | 2.03527 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29140.4 | −1.58360 | ||||||||
\(698\) | −19416.4 | − | 247.796i | −1.05290 | − | 0.0134372i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −117.385 | + | 4598.18i | −0.00633817 | + | 0.248278i | ||||
\(701\) | 10087.7i | 0.543519i | 0.962365 | + | 0.271760i | \(0.0876056\pi\) | ||||
−0.962365 | + | 0.271760i | \(0.912394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1117.66i | − | 0.0599622i | ||||||
\(704\) | 25595.3 | + | 1963.64i | 1.37025 | + | 0.105124i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.49986 | + | 352.594i | −0.000239879 | + | 0.0187961i | ||||
\(707\) | 1501.91 | 0.0798943 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25739.3 | −1.36341 | −0.681706 | − | 0.731626i | \(-0.738762\pi\) | ||||
−0.681706 | + | 0.731626i | \(0.738762\pi\) | |||||||
\(710\) | −155.363 | + | 12173.8i | −0.00821223 | + | 0.643483i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −883.268 | + | 23059.9i | −0.0464914 | + | 1.21378i | ||||
\(713\) | 1500.74i | 0.0788265i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32223.7i | 1.68545i | ||||||||
\(716\) | −18795.8 | − | 479.828i | −0.981050 | − | 0.0250447i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12697.2 | + | 162.043i | 0.659964 | + | 0.00842256i | ||||
\(719\) | 7178.86 | 0.372359 | 0.186180 | − | 0.982516i | \(-0.440389\pi\) | ||||
0.186180 | + | 0.982516i | \(0.440389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6165.33 | 0.318459 | ||||||||
\(722\) | −8200.65 | − | 104.658i | −0.422710 | − | 0.00539469i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18235.2 | − | 465.516i | −0.936057 | − | 0.0238961i | ||||
\(725\) | 19659.5i | 1.00709i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21074.1i | 1.07510i | 0.843233 | + | 0.537548i | \(0.180649\pi\) | ||||
−0.843233 | + | 0.537548i | \(0.819351\pi\) | |||||||
\(728\) | −117.392 | + | 3064.81i | −0.00597641 | + | 0.156029i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 61.3537 | − | 4807.47i | 0.00311069 | − | 0.243743i | ||||
\(731\) | −11030.3 | −0.558101 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20228.0 | 1.01929 | 0.509645 | − | 0.860385i | \(-0.329777\pi\) | ||||
0.509645 | + | 0.860385i | \(0.329777\pi\) | |||||||
\(734\) | −31.2998 | + | 2452.55i | −0.00157397 | + | 0.123331i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13587.4 | − | 868.151i | −0.680484 | − | 0.0434789i | ||||
\(737\) | 31069.9i | 1.55288i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8782.55i | 0.437173i | 0.975818 | + | 0.218587i | \(0.0701447\pi\) | ||||
−0.975818 | + | 0.218587i | \(0.929855\pi\) | |||||||
\(740\) | −61.3443 | + | 2402.97i | −0.00304738 | + | 0.119372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4837.77 | − | 61.7404i | −0.239353 | − | 0.00305467i | ||||
\(743\) | 23353.5 | 1.15311 | 0.576553 | − | 0.817060i | \(-0.304397\pi\) | ||||
0.576553 | + | 0.817060i | \(0.304397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6878.05 | 0.338245 | ||||||||
\(746\) | 12272.0 | + | 156.617i | 0.602291 | + | 0.00768654i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −863.747 | + | 33834.7i | −0.0422216 | + | 1.65390i | ||||
\(749\) | 225.334i | 0.0109927i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16887.9i | − | 0.820569i | −0.911957 | − | 0.410285i | \(-0.865429\pi\) | ||
0.911957 | − | 0.410285i | \(-0.134571\pi\) | |||||||
\(752\) | −19569.1 | − | 999.788i | −0.948950 | − | 0.0484821i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −167.285 | + | 13107.9i | −0.00807978 | + | 0.633104i | ||||
\(755\) | 58407.6 | 2.81546 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6838.01 | 0.328311 | 0.164156 | − | 0.986434i | \(-0.447510\pi\) | ||||
0.164156 | + | 0.986434i | \(0.447510\pi\) | |||||||
\(758\) | −508.811 | + | 39868.8i | −0.0243811 | + | 1.91042i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24067.8 | − | 921.870i | −1.14872 | − | 0.0439997i | ||||
\(761\) | − | 23675.9i | − | 1.12779i | −0.825846 | − | 0.563896i | \(-0.809302\pi\) | ||
0.825846 | − | 0.563896i | \(-0.190698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2980.30i | 0.141408i | ||||||||
\(764\) | −31453.4 | − | 802.957i | −1.48945 | − | 0.0380235i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23386.1 | + | 298.457i | 1.10310 | + | 0.0140779i | ||||
\(767\) | −18675.5 | −0.879184 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36837.3 | 1.72742 | 0.863711 | − | 0.503988i | \(-0.168134\pi\) | ||||
0.863711 | + | 0.503988i | \(0.168134\pi\) | |||||||
\(770\) | −8557.72 | − | 109.215i | −0.400518 | − | 0.00511147i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21698.5 | + | 553.929i | 1.01159 | + | 0.0258243i | ||||
\(773\) | 7505.51i | 0.349230i | 0.984637 | + | 0.174615i | \(0.0558680\pi\) | ||||
−0.984637 | + | 0.174615i | \(0.944132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3215.66i | − | 0.149045i | ||||||
\(776\) | −22773.1 | − | 872.282i | −1.05349 | − | 0.0403520i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −207.261 | + | 16240.3i | −0.00955101 | + | 0.748385i | ||||
\(779\) | 21730.0 | 0.999434 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12757.8 | −0.584518 | ||||||||
\(782\) | 229.075 | − | 17949.6i | 0.0104753 | − | 0.820812i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21109.9 | + | 1078.51i | 0.961638 | + | 0.0491303i | ||||
\(785\) | − | 14896.0i | − | 0.677276i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19472.8i | − | 0.881997i | −0.897508 | − | 0.440998i | \(-0.854624\pi\) | ||
0.897508 | − | 0.440998i | \(-0.145376\pi\) | |||||||
\(788\) | −407.896 | + | 15978.1i | −0.0184400 | + | 0.722329i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 47305.0 | + | 603.714i | 2.13043 | + | 0.0271888i | ||||
\(791\) | −3674.28 | −0.165161 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3793.01 | 0.169853 | ||||||||
\(794\) | −29680.2 | − | 378.784i | −1.32659 | − | 0.0169302i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 491.843 | − | 19266.4i | 0.0219006 | − | 0.857891i | ||||
\(797\) | − | 35777.2i | − | 1.59008i | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||
0.606557 | − | 0.795040i | \(-0.292550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 25834.8i | − | 1.14389i | ||||||
\(800\) | 29113.7 | + | 1860.20i | 1.28666 | + | 0.0822098i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −294.669 | + | 23089.3i | −0.0129740 | + | 1.01660i | ||||
\(803\) | 5038.09 | 0.221408 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4539.20 | 0.198740 | ||||||||
\(806\) | 27.3623 | − | 2144.02i | 0.00119578 | − | 0.0936971i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 364.599 | − | 9518.78i | 0.0158744 | − | 0.414443i | ||||
\(809\) | − | 16519.8i | − | 0.717932i | −0.933351 | − | 0.358966i | \(-0.883129\pi\) | ||
0.933351 | − | 0.358966i | \(-0.116871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18594.4i | 0.805103i | 0.915397 | + | 0.402552i | \(0.131877\pi\) | ||||
−0.915397 | + | 0.402552i | \(0.868123\pi\) | |||||||
\(812\) | −3480.52 | − | 88.8523i | −0.150422 | − | 0.00384003i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2518.66 | − | 32.1435i | −0.108451 | − | 0.00138407i | ||||
\(815\) | −28648.7 | −1.23131 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8225.34 | 0.352225 | ||||||||
\(818\) | −11524.5 | − | 147.078i | −0.492598 | − | 0.00628661i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46719.6 | − | 1192.68i | −1.98966 | − | 0.0507929i | ||||
\(821\) | − | 41224.9i | − | 1.75244i | −0.481907 | − | 0.876222i | \(-0.660056\pi\) | ||
0.481907 | − | 0.876222i | \(-0.339944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4287.73i | − | 0.181605i | −0.995869 | − | 0.0908025i | \(-0.971057\pi\) | ||
0.995869 | − | 0.0908025i | \(-0.0289432\pi\) | |||||||
\(824\) | 1496.67 | − | 39074.5i | 0.0632756 | − | 1.65197i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 63.2965 | − | 4959.70i | 0.00266630 | − | 0.208922i | ||||
\(827\) | −24944.4 | −1.04885 | −0.524426 | − | 0.851456i | \(-0.675720\pi\) | ||||
−0.524426 | + | 0.851456i | \(0.675720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31040.8 | −1.30047 | −0.650235 | − | 0.759733i | \(-0.725330\pi\) | ||||
−0.650235 | + | 0.759733i | \(0.725330\pi\) | |||||||
\(830\) | 307.430 | − | 24089.2i | 0.0128567 | − | 1.00741i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19395.6 | + | 1488.00i | 0.808198 | + | 0.0620040i | ||||
\(833\) | 27869.0i | 1.15919i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 27744.4i | − | 1.14986i | ||||||
\(836\) | 644.098 | − | 25230.6i | 0.0266466 | − | 1.04380i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1960.15 | − | 25.0157i | −0.0808021 | − | 0.00103121i | ||||
\(839\) | 12787.2 | 0.526178 | 0.263089 | − | 0.964772i | \(-0.415259\pi\) | ||||
0.263089 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9508.03 | 0.389849 | ||||||||
\(842\) | 30333.4 | + | 387.120i | 1.24152 | + | 0.0158445i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −371.458 | + | 14550.7i | −0.0151494 | + | 0.593432i | ||||
\(845\) | − | 12746.6i | − | 0.518929i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4219.73i | − | 0.171183i | ||||||
\(848\) | −1565.70 | + | 30645.7i | −0.0634036 | + | 1.24101i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −490.841 | + | 38460.7i | −0.0198067 | + | 1.55199i | ||||
\(851\) | 1335.95 | 0.0538141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46982.9 | −1.88589 | −0.942946 | − | 0.332947i | \(-0.891957\pi\) | ||||
−0.942946 | + | 0.332947i | \(0.891957\pi\) | |||||||
\(854\) | −12.8556 | + | 1007.32i | −0.000515115 | + | 0.0403627i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1428.12 | + | 54.7013i | 0.0570234 | + | 0.00218417i | ||||
\(857\) | − | 46178.0i | − | 1.84062i | −0.391189 | − | 0.920310i | \(-0.627936\pi\) | ||
0.391189 | − | 0.920310i | \(-0.372064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6548.05i | 0.260089i | 0.991508 | + | 0.130045i | \(0.0415120\pi\) | ||||
−0.991508 | + | 0.130045i | \(0.958488\pi\) | |||||||
\(860\) | −17684.5 | − | 451.458i | −0.701205 | − | 0.0179007i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28321.1 | − | 361.438i | −1.11905 | − | 0.0142815i | ||||
\(863\) | 29442.2 | 1.16133 | 0.580663 | − | 0.814144i | \(-0.302793\pi\) | ||||
0.580663 | + | 0.814144i | \(0.302793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36901.5 | 1.45051 | ||||||||
\(866\) | 27507.1 | + | 351.050i | 1.07936 | + | 0.0137750i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 569.299 | + | 14.5333i | 0.0222618 | + | 0.000568311i | ||||
\(869\) | 49574.3i | 1.93521i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23544.1i | 0.915915i | ||||||||
\(872\) | 18888.5 | + | 723.488i | 0.733538 | + | 0.0280968i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −170.822 | + | 13385.0i | −0.00661113 | + | 0.518026i | ||||
\(875\) | −2182.30 | −0.0843146 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32768.6 | −1.26171 | −0.630853 | − | 0.775903i | \(-0.717295\pi\) | ||||
−0.630853 | + | 0.775903i | \(0.717295\pi\) | |||||||
\(878\) | 236.560 | − | 18536.0i | 0.00909284 | − | 0.712484i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2769.62 | + | 54210.4i | −0.106095 | + | 2.07663i | ||||
\(881\) | − | 15082.2i | − | 0.576769i | −0.957515 | − | 0.288384i | \(-0.906882\pi\) | ||
0.957515 | − | 0.288384i | \(-0.0931181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 425.340i | − | 0.0162105i | −0.999967 | − | 0.00810523i | \(-0.997420\pi\) | ||
0.999967 | − | 0.00810523i | \(-0.00258000\pi\) | |||||||
\(884\) | −654.531 | + | 25639.2i | −0.0249030 | + | 0.975498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16627.6 | − | 212.204i | −0.630490 | − | 0.00804642i | ||||
\(887\) | −12156.8 | −0.460188 | −0.230094 | − | 0.973168i | \(-0.573903\pi\) | ||||
−0.230094 | + | 0.973168i | \(0.573903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2834.56 | 0.106938 | ||||||||
\(890\) | −48792.8 | − | 622.702i | −1.83768 | − | 0.0234528i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 546.017 | − | 21388.5i | 0.0204955 | − | 0.802849i | ||||
\(893\) | 19265.1i | 0.721927i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 39757.3i | − | 1.48485i | ||||||
\(896\) | −460.910 | + | 5145.88i | −0.0171852 | + | 0.191866i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −244.031 | + | 19121.4i | −0.00906839 | + | 0.710569i | ||||
\(899\) | 2434.04 | 0.0903001 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40458.1 | −1.49595 | ||||||||
\(902\) | 624.947 | − | 48968.8i | 0.0230693 | − | 1.80763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −891.956 | + | 23286.8i | −0.0328164 | + | 0.856755i | ||||
\(905\) | − | 38571.5i | − | 1.41675i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45812.3i | − | 1.67715i | −0.544788 | − | 0.838574i | \(-0.683390\pi\) | ||
0.544788 | − | 0.838574i | \(-0.316610\pi\) | |||||||
\(908\) | 47177.9 | + | 1204.38i | 1.72429 | + | 0.0440185i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6484.87 | − | 82.7609i | −0.236232 | − | 0.00301483i | ||||
\(911\) | 28823.7 | 1.04827 | 0.524134 | − | 0.851636i | \(-0.324389\pi\) | ||||
0.524134 | + | 0.851636i | \(0.324389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25244.8 | 0.915095 | ||||||||
\(914\) | 43102.6 | + | 550.083i | 1.55986 | + | 0.0199071i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24254.1 | + | 619.171i | 0.874867 | + | 0.0223340i | ||||
\(917\) | 792.293i | 0.0285320i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41488.4i | − | 1.48920i | −0.667511 | − | 0.744600i | \(-0.732640\pi\) | ||
0.667511 | − | 0.744600i | \(-0.267360\pi\) | |||||||
\(920\) | 1101.92 | − | 28768.4i | 0.0394883 | − | 1.03094i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −495.980 | + | 38863.3i | −0.0177161 | + | 1.38817i | ||||
\(923\) | −9667.57 | −0.344758 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2862.55 | −0.101752 | ||||||||
\(926\) | 637.321 | − | 49938.4i | 0.0226174 | − | 1.77222i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1408.04 | + | 22037.2i | −0.0498075 | + | 0.779532i | ||||
\(929\) | − | 4226.17i | − | 0.149253i | −0.997212 | − | 0.0746266i | \(-0.976224\pi\) | ||
0.997212 | − | 0.0746266i | \(-0.0237765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20782.0i | − | 0.731580i | ||||||
\(932\) | −264.211 | + | 10349.6i | −0.00928595 | + | 0.363749i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17436.2 | − | 222.523i | −0.610845 | − | 0.00779570i | ||||
\(935\) | −71567.8 | −2.50323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31514.2 | 1.09875 | 0.549373 | − | 0.835577i | \(-0.314867\pi\) | ||||
0.549373 | + | 0.835577i | \(0.314867\pi\) | |||||||
\(938\) | −6252.66 | − | 79.7975i | −0.217651 | − | 0.00277770i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1057.39 | − | 41419.9i | 0.0366895 | − | 1.43720i | ||||
\(941\) | − | 26604.6i | − | 0.921664i | −0.887487 | − | 0.460832i | \(-0.847551\pi\) | ||
0.887487 | − | 0.460832i | \(-0.152449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25974.1i | 0.896959i | ||||||||
\(944\) | −31418.1 | − | 1605.16i | −1.08323 | − | 0.0553426i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 236.558 | − | 18535.9i | 0.00813018 | − | 0.637054i | ||||
\(947\) | −51629.3 | −1.77162 | −0.885811 | − | 0.464046i | \(-0.846397\pi\) | ||||
−0.885811 | + | 0.464046i | \(0.846397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3817.76 | 0.130590 | ||||||||
\(950\) | 366.021 | − | 28680.2i | 0.0125003 | − | 0.979482i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6806.85 | − | 260.723i | −0.231734 | − | 0.00887615i | ||||
\(953\) | 25766.7i | 0.875829i | 0.899017 | + | 0.437915i | \(0.144283\pi\) | ||||
−0.899017 | + | 0.437915i | \(0.855717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 66530.9i | − | 2.25433i | ||||||
\(956\) | 45987.3 | + | 1173.99i | 1.55579 | + | 0.0397170i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48979.1 | − | 625.079i | −1.65182 | − | 0.0210808i | ||||
\(959\) | −4343.16 | −0.146244 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29392.9 | 0.986636 | ||||||||
\(962\) | −1908.59 | − | 24.3577i | −0.0639661 | − | 0.000816346i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48125.4 | + | 1228.57i | 1.60790 | + | 0.0410472i | ||||
\(965\) | 45897.1i | 1.53107i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45989.7i | 1.52940i | 0.644387 | + | 0.764700i | \(0.277113\pi\) | ||||
−0.644387 | + | 0.764700i | \(0.722887\pi\) | |||||||
\(968\) | −26743.7 | − | 1024.37i | −0.887991 | − | 0.0340128i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 614.957 | − | 48186.0i | 0.0203558 | − | 1.59501i | ||||
\(971\) | −22109.4 | −0.730714 | −0.365357 | − | 0.930867i | \(-0.619053\pi\) | ||||
−0.365357 | + | 0.930867i | \(0.619053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7864.57 | −0.259123 | ||||||||
\(974\) | −265.367 | + | 20793.3i | −0.00872989 | + | 0.684045i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6381.03 | + | 326.009i | 0.209275 | + | 0.0106919i | ||||
\(977\) | − | 50634.6i | − | 1.65808i | −0.559189 | − | 0.829040i | \(-0.688887\pi\) | ||
0.559189 | − | 0.829040i | \(-0.311113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 51133.5i | − | 1.66929i | ||||||
\(980\) | −1140.64 | + | 44681.2i | −0.0371801 | + | 1.45642i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23877.2 | − | 304.724i | −0.775918 | − | 0.00990239i | ||||
\(983\) | 13979.6 | 0.453590 | 0.226795 | − | 0.973943i | \(-0.427175\pi\) | ||||
0.226795 | + | 0.973943i | \(0.427175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33797.2 | −1.09327 | ||||||||
\(986\) | −29112.2 | − | 371.534i | −0.940285 | − | 0.0120001i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 488.084 | − | 19119.2i | 0.0157166 | − | 0.615651i | ||||
\(989\) | 9831.82i | 0.316111i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29526.4i | − | 0.946456i | −0.880940 | − | 0.473228i | \(-0.843089\pi\) | ||
0.880940 | − | 0.473228i | \(-0.156911\pi\) | |||||||
\(992\) | 230.310 | − | 3604.56i | 0.00737132 | − | 0.115368i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.7661 | − | 2567.44i | 0.00104555 | − | 0.0819257i | ||||
\(995\) | 40752.8 | 1.29844 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5027.73 | 0.159709 | 0.0798545 | − | 0.996807i | \(-0.474554\pi\) | ||||
0.0798545 | + | 0.996807i | \(0.474554\pi\) | |||||||
\(998\) | −272.669 | + | 21365.4i | −0.00864849 | + | 0.677667i | ||||
\(999\) | 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 | 324.4.b.c.323.1 | 24 | ||
3.2 | odd | 2 | inner | 324.4.b.c.323.24 | 24 | ||
4.3 | odd | 2 | inner | 324.4.b.c.323.23 | 24 | ||
9.2 | odd | 6 | 36.4.h.b.23.5 | yes | 24 | ||
9.4 | even | 3 | 36.4.h.b.11.9 | yes | 24 | ||
9.5 | odd | 6 | 108.4.h.b.35.4 | 24 | |||
9.7 | even | 3 | 108.4.h.b.71.8 | 24 | |||
12.11 | even | 2 | inner | 324.4.b.c.323.2 | 24 | ||
36.7 | odd | 6 | 108.4.h.b.71.4 | 24 | |||
36.11 | even | 6 | 36.4.h.b.23.9 | yes | 24 | ||
36.23 | even | 6 | 108.4.h.b.35.8 | 24 | |||
36.31 | odd | 6 | 36.4.h.b.11.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.5 | ✓ | 24 | 36.31 | odd | 6 | ||
36.4.h.b.11.9 | yes | 24 | 9.4 | even | 3 | ||
36.4.h.b.23.5 | yes | 24 | 9.2 | odd | 6 | ||
36.4.h.b.23.9 | yes | 24 | 36.11 | even | 6 | ||
108.4.h.b.35.4 | 24 | 9.5 | odd | 6 | |||
108.4.h.b.35.8 | 24 | 36.23 | even | 6 | |||
108.4.h.b.71.4 | 24 | 36.7 | odd | 6 | |||
108.4.h.b.71.8 | 24 | 9.7 | even | 3 | |||
324.4.b.c.323.1 | 24 | 1.1 | even | 1 | trivial | ||
324.4.b.c.323.2 | 24 | 12.11 | even | 2 | inner | ||
324.4.b.c.323.23 | 24 | 4.3 | odd | 2 | inner | ||
324.4.b.c.323.24 | 24 | 3.2 | odd | 2 | inner |