Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,4,Mod(24,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.24");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.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: | \(6.78521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.9 | ||
Character | \(\chi\) | \(=\) | 115.24 |
Dual form | 115.4.b.a.24.26 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.13266i | − | 1.10756i | −0.832662 | − | 0.553781i | \(-0.813184\pi\) | ||
0.832662 | − | 0.553781i | \(-0.186816\pi\) | |||||||
\(3\) | − | 8.19196i | − | 1.57654i | −0.615328 | − | 0.788272i | \(-0.710976\pi\) | ||
0.615328 | − | 0.788272i | \(-0.289024\pi\) | |||||||
\(4\) | −1.81356 | −0.226694 | ||||||||
\(5\) | −9.71296 | + | 5.53701i | −0.868753 | + | 0.495245i | ||||
\(6\) | −25.6626 | −1.74612 | ||||||||
\(7\) | 13.4923i | 0.728517i | 0.931298 | + | 0.364259i | \(0.118678\pi\) | ||||
−0.931298 | + | 0.364259i | \(0.881322\pi\) | |||||||
\(8\) | − | 19.3800i | − | 0.856484i | ||||||
\(9\) | −40.1082 | −1.48549 | ||||||||
\(10\) | 17.3456 | + | 30.4274i | 0.548515 | + | 0.962199i | ||||
\(11\) | −51.7973 | −1.41977 | −0.709885 | − | 0.704318i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704318i | \(0.751253\pi\) | |||||||
\(12\) | 14.8566i | 0.357394i | ||||||||
\(13\) | − | 3.31182i | − | 0.0706565i | −0.999376 | − | 0.0353283i | \(-0.988752\pi\) | ||
0.999376 | − | 0.0353283i | \(-0.0112477\pi\) | |||||||
\(14\) | 42.2669 | 0.806879 | ||||||||
\(15\) | 45.3589 | + | 79.5681i | 0.780775 | + | 1.36963i | ||||
\(16\) | −75.2195 | −1.17530 | ||||||||
\(17\) | − | 95.2632i | − | 1.35910i | −0.733629 | − | 0.679551i | \(-0.762175\pi\) | ||
0.733629 | − | 0.679551i | \(-0.237825\pi\) | |||||||
\(18\) | 125.645i | 1.64527i | ||||||||
\(19\) | 144.212 | 1.74129 | 0.870647 | − | 0.491909i | \(-0.163701\pi\) | ||||
0.870647 | + | 0.491909i | \(0.163701\pi\) | |||||||
\(20\) | 17.6150 | − | 10.0417i | 0.196942 | − | 0.112269i | ||||
\(21\) | 110.529 | 1.14854 | ||||||||
\(22\) | 162.263i | 1.57248i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | −158.760 | −1.35028 | ||||||||
\(25\) | 63.6831 | − | 107.561i | 0.509465 | − | 0.860491i | ||||
\(26\) | −10.3748 | −0.0782565 | ||||||||
\(27\) | 107.382i | 0.765393i | ||||||||
\(28\) | − | 24.4691i | − | 0.165151i | ||||||
\(29\) | −161.482 | −1.03402 | −0.517008 | − | 0.855980i | \(-0.672954\pi\) | ||||
−0.517008 | + | 0.855980i | \(0.672954\pi\) | |||||||
\(30\) | 249.260 | − | 142.094i | 1.51695 | − | 0.864757i | ||||
\(31\) | −226.933 | −1.31479 | −0.657393 | − | 0.753548i | \(-0.728341\pi\) | ||||
−0.657393 | + | 0.753548i | \(0.728341\pi\) | |||||||
\(32\) | 80.5968i | 0.445238i | ||||||||
\(33\) | 424.321i | 2.23833i | ||||||||
\(34\) | −298.427 | −1.50529 | ||||||||
\(35\) | −74.7071 | − | 131.050i | −0.360795 | − | 0.632902i | ||||
\(36\) | 72.7384 | 0.336752 | ||||||||
\(37\) | − | 187.053i | − | 0.831116i | −0.909567 | − | 0.415558i | \(-0.863586\pi\) | ||
0.909567 | − | 0.415558i | \(-0.136414\pi\) | |||||||
\(38\) | − | 451.768i | − | 1.92859i | ||||||
\(39\) | −27.1303 | −0.111393 | ||||||||
\(40\) | 107.307 | + | 188.237i | 0.424169 | + | 0.744074i | ||||
\(41\) | 205.405 | 0.782413 | 0.391206 | − | 0.920303i | \(-0.372058\pi\) | ||||
0.391206 | + | 0.920303i | \(0.372058\pi\) | |||||||
\(42\) | − | 346.249i | − | 1.27208i | ||||||
\(43\) | − | 232.530i | − | 0.824661i | −0.911034 | − | 0.412331i | \(-0.864715\pi\) | ||
0.911034 | − | 0.412331i | \(-0.135285\pi\) | |||||||
\(44\) | 93.9372 | 0.321854 | ||||||||
\(45\) | 389.569 | − | 222.079i | 1.29052 | − | 0.735680i | ||||
\(46\) | 72.0512 | 0.230943 | ||||||||
\(47\) | − | 322.333i | − | 1.00036i | −0.865920 | − | 0.500182i | \(-0.833266\pi\) | ||
0.865920 | − | 0.500182i | \(-0.166734\pi\) | |||||||
\(48\) | 616.195i | 1.85292i | ||||||||
\(49\) | 160.957 | 0.469262 | ||||||||
\(50\) | −336.953 | − | 199.498i | −0.953048 | − | 0.564264i | ||||
\(51\) | −780.392 | −2.14268 | ||||||||
\(52\) | 6.00618i | 0.0160174i | ||||||||
\(53\) | 553.632i | 1.43485i | 0.696635 | + | 0.717426i | \(0.254680\pi\) | ||||
−0.696635 | + | 0.717426i | \(0.745320\pi\) | |||||||
\(54\) | 336.390 | 0.847721 | ||||||||
\(55\) | 503.105 | − | 286.802i | 1.23343 | − | 0.703133i | ||||
\(56\) | 261.482 | 0.623964 | ||||||||
\(57\) | − | 1181.38i | − | 2.74522i | ||||||
\(58\) | 505.868i | 1.14524i | ||||||||
\(59\) | −531.694 | −1.17323 | −0.586616 | − | 0.809866i | \(-0.699540\pi\) | ||||
−0.586616 | + | 0.809866i | \(0.699540\pi\) | |||||||
\(60\) | −82.2609 | − | 144.301i | −0.176997 | − | 0.310487i | ||||
\(61\) | 97.5357 | 0.204724 | 0.102362 | − | 0.994747i | \(-0.467360\pi\) | ||||
0.102362 | + | 0.994747i | \(0.467360\pi\) | |||||||
\(62\) | 710.904i | 1.45621i | ||||||||
\(63\) | − | 541.153i | − | 1.08220i | ||||||
\(64\) | −349.273 | −0.682175 | ||||||||
\(65\) | 18.3376 | + | 32.1676i | 0.0349923 | + | 0.0613831i | ||||
\(66\) | 1329.25 | 2.47909 | ||||||||
\(67\) | 97.6135i | 0.177991i | 0.996032 | + | 0.0889954i | \(0.0283656\pi\) | ||||
−0.996032 | + | 0.0889954i | \(0.971634\pi\) | |||||||
\(68\) | 172.765i | 0.308101i | ||||||||
\(69\) | 188.415 | 0.328732 | ||||||||
\(70\) | −410.536 | + | 234.032i | −0.700978 | + | 0.399602i | ||||
\(71\) | 583.010 | 0.974514 | 0.487257 | − | 0.873259i | \(-0.337997\pi\) | ||||
0.487257 | + | 0.873259i | \(0.337997\pi\) | |||||||
\(72\) | 777.298i | 1.27230i | ||||||||
\(73\) | − | 58.9911i | − | 0.0945806i | −0.998881 | − | 0.0472903i | \(-0.984941\pi\) | ||
0.998881 | − | 0.0472903i | \(-0.0150586\pi\) | |||||||
\(74\) | −585.973 | −0.920513 | ||||||||
\(75\) | −881.139 | − | 521.689i | −1.35660 | − | 0.803193i | ||||
\(76\) | −261.537 | −0.394741 | ||||||||
\(77\) | − | 698.866i | − | 1.03433i | ||||||
\(78\) | 84.9901i | 0.123375i | ||||||||
\(79\) | 242.740 | 0.345701 | 0.172851 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172851 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(80\) | 730.603 | − | 416.491i | 1.02105 | − | 0.582063i | ||||
\(81\) | −203.255 | −0.278813 | ||||||||
\(82\) | − | 643.465i | − | 0.866571i | ||||||
\(83\) | − | 1117.40i | − | 1.47772i | −0.673859 | − | 0.738860i | \(-0.735365\pi\) | ||
0.673859 | − | 0.738860i | \(-0.264635\pi\) | |||||||
\(84\) | −200.450 | −0.260367 | ||||||||
\(85\) | 527.473 | + | 925.287i | 0.673088 | + | 1.18072i | ||||
\(86\) | −728.436 | −0.913364 | ||||||||
\(87\) | 1322.85i | 1.63017i | ||||||||
\(88\) | 1003.83i | 1.21601i | ||||||||
\(89\) | 455.487 | 0.542489 | 0.271244 | − | 0.962510i | \(-0.412565\pi\) | ||||
0.271244 | + | 0.962510i | \(0.412565\pi\) | |||||||
\(90\) | −695.699 | − | 1220.39i | −0.814812 | − | 1.42933i | ||||
\(91\) | 44.6842 | 0.0514745 | ||||||||
\(92\) | − | 41.7118i | − | 0.0472691i | ||||||
\(93\) | 1859.03i | 2.07282i | ||||||||
\(94\) | −1009.76 | −1.10797 | ||||||||
\(95\) | −1400.73 | + | 798.505i | −1.51275 | + | 0.862367i | ||||
\(96\) | 660.245 | 0.701937 | ||||||||
\(97\) | 431.300i | 0.451463i | 0.974190 | + | 0.225731i | \(0.0724772\pi\) | ||||
−0.974190 | + | 0.225731i | \(0.927523\pi\) | |||||||
\(98\) | − | 504.223i | − | 0.519737i | ||||||
\(99\) | 2077.49 | 2.10905 | ||||||||
\(100\) | −115.493 | + | 195.069i | −0.115493 | + | 0.195069i | ||||
\(101\) | 484.213 | 0.477039 | 0.238520 | − | 0.971138i | \(-0.423338\pi\) | ||||
0.238520 | + | 0.971138i | \(0.423338\pi\) | |||||||
\(102\) | 2444.70i | 2.37315i | ||||||||
\(103\) | 1715.24i | 1.64085i | 0.571756 | + | 0.820424i | \(0.306262\pi\) | ||||
−0.571756 | + | 0.820424i | \(0.693738\pi\) | |||||||
\(104\) | −64.1832 | −0.0605162 | ||||||||
\(105\) | −1073.56 | + | 611.998i | −0.997797 | + | 0.568808i | ||||
\(106\) | 1734.34 | 1.58919 | ||||||||
\(107\) | − | 1595.48i | − | 1.44150i | −0.693193 | − | 0.720752i | \(-0.743797\pi\) | ||
0.693193 | − | 0.720752i | \(-0.256203\pi\) | |||||||
\(108\) | − | 194.743i | − | 0.173510i | ||||||
\(109\) | 1533.25 | 1.34733 | 0.673663 | − | 0.739039i | \(-0.264720\pi\) | ||||
0.673663 | + | 0.739039i | \(0.264720\pi\) | |||||||
\(110\) | −898.452 | − | 1576.06i | −0.778764 | − | 1.36610i | ||||
\(111\) | −1532.33 | −1.31029 | ||||||||
\(112\) | − | 1014.89i | − | 0.856230i | ||||||
\(113\) | − | 966.953i | − | 0.804985i | −0.915423 | − | 0.402492i | \(-0.868144\pi\) | ||
0.915423 | − | 0.402492i | \(-0.131856\pi\) | |||||||
\(114\) | −3700.87 | −3.04051 | ||||||||
\(115\) | −127.351 | − | 223.398i | −0.103266 | − | 0.181148i | ||||
\(116\) | 292.857 | 0.234406 | ||||||||
\(117\) | 132.831i | 0.104959i | ||||||||
\(118\) | 1665.62i | 1.29943i | ||||||||
\(119\) | 1285.32 | 0.990129 | ||||||||
\(120\) | 1542.03 | − | 879.057i | 1.17306 | − | 0.668721i | ||||
\(121\) | 1351.96 | 1.01574 | ||||||||
\(122\) | − | 305.546i | − | 0.226745i | ||||||
\(123\) | − | 1682.67i | − | 1.23351i | ||||||
\(124\) | 411.556 | 0.298055 | ||||||||
\(125\) | −22.9830 | + | 1397.35i | −0.0164453 | + | 0.999865i | ||||
\(126\) | −1695.25 | −1.19861 | ||||||||
\(127\) | − | 1049.29i | − | 0.733147i | −0.930389 | − | 0.366573i | \(-0.880531\pi\) | ||
0.930389 | − | 0.366573i | \(-0.119469\pi\) | |||||||
\(128\) | 1738.93i | 1.20079i | ||||||||
\(129\) | −1904.87 | −1.30011 | ||||||||
\(130\) | 100.770 | − | 57.4454i | 0.0679856 | − | 0.0387561i | ||||
\(131\) | −648.199 | −0.432316 | −0.216158 | − | 0.976358i | \(-0.569353\pi\) | ||||
−0.216158 | + | 0.976358i | \(0.569353\pi\) | |||||||
\(132\) | − | 769.529i | − | 0.507416i | ||||||
\(133\) | 1945.76i | 1.26856i | ||||||||
\(134\) | 305.790 | 0.197136 | ||||||||
\(135\) | −594.573 | − | 1042.99i | −0.379057 | − | 0.664938i | ||||
\(136\) | −1846.20 | −1.16405 | ||||||||
\(137\) | 158.366i | 0.0987599i | 0.998780 | + | 0.0493799i | \(0.0157245\pi\) | ||||
−0.998780 | + | 0.0493799i | \(0.984275\pi\) | |||||||
\(138\) | − | 590.240i | − | 0.364091i | ||||||
\(139\) | −272.315 | −0.166169 | −0.0830843 | − | 0.996543i | \(-0.526477\pi\) | ||||
−0.0830843 | + | 0.996543i | \(0.526477\pi\) | |||||||
\(140\) | 135.486 | + | 237.667i | 0.0817901 | + | 0.143475i | ||||
\(141\) | −2640.54 | −1.57712 | ||||||||
\(142\) | − | 1826.37i | − | 1.07934i | ||||||
\(143\) | 171.543i | 0.100316i | ||||||||
\(144\) | 3016.92 | 1.74590 | ||||||||
\(145\) | 1568.47 | − | 894.128i | 0.898305 | − | 0.512091i | ||||
\(146\) | −184.799 | −0.104754 | ||||||||
\(147\) | − | 1318.55i | − | 0.739812i | ||||||
\(148\) | 339.231i | 0.188409i | ||||||||
\(149\) | 2826.23 | 1.55392 | 0.776958 | − | 0.629552i | \(-0.216762\pi\) | ||||
0.776958 | + | 0.629552i | \(0.216762\pi\) | |||||||
\(150\) | −1634.28 | + | 2760.31i | −0.889587 | + | 1.50252i | ||||
\(151\) | 2065.22 | 1.11302 | 0.556508 | − | 0.830842i | \(-0.312141\pi\) | ||||
0.556508 | + | 0.830842i | \(0.312141\pi\) | |||||||
\(152\) | − | 2794.84i | − | 1.49139i | ||||||
\(153\) | 3820.83i | 2.01893i | ||||||||
\(154\) | −2189.31 | −1.14558 | ||||||||
\(155\) | 2204.19 | − | 1256.53i | 1.14223 | − | 0.651142i | ||||
\(156\) | 49.2023 | 0.0252522 | ||||||||
\(157\) | 137.317i | 0.0698031i | 0.999391 | + | 0.0349015i | \(0.0111118\pi\) | ||||
−0.999391 | + | 0.0349015i | \(0.988888\pi\) | |||||||
\(158\) | − | 760.422i | − | 0.382886i | ||||||
\(159\) | 4535.33 | 2.26211 | ||||||||
\(160\) | −446.265 | − | 782.833i | −0.220502 | − | 0.386802i | ||||
\(161\) | −310.324 | −0.151906 | ||||||||
\(162\) | 636.728i | 0.308803i | ||||||||
\(163\) | − | 3089.75i | − | 1.48471i | −0.670007 | − | 0.742355i | \(-0.733709\pi\) | ||
0.670007 | − | 0.742355i | \(-0.266291\pi\) | |||||||
\(164\) | −372.514 | −0.177369 | ||||||||
\(165\) | −2349.47 | − | 4121.41i | −1.10852 | − | 1.94455i | ||||
\(166\) | −3500.44 | −1.63667 | ||||||||
\(167\) | 199.002i | 0.0922108i | 0.998937 | + | 0.0461054i | \(0.0146810\pi\) | ||||
−0.998937 | + | 0.0461054i | \(0.985319\pi\) | |||||||
\(168\) | − | 2142.05i | − | 0.983706i | ||||||
\(169\) | 2186.03 | 0.995008 | ||||||||
\(170\) | 2898.61 | − | 1652.39i | 1.30773 | − | 0.745487i | ||||
\(171\) | −5784.09 | −2.58667 | ||||||||
\(172\) | 421.705i | 0.186946i | ||||||||
\(173\) | 29.5998i | 0.0130083i | 0.999979 | + | 0.00650413i | \(0.00207034\pi\) | ||||
−0.999979 | + | 0.00650413i | \(0.997930\pi\) | |||||||
\(174\) | 4144.05 | 1.80552 | ||||||||
\(175\) | 1451.25 | + | 859.234i | 0.626883 | + | 0.371154i | ||||
\(176\) | 3896.16 | 1.66866 | ||||||||
\(177\) | 4355.61i | 1.84965i | ||||||||
\(178\) | − | 1426.89i | − | 0.600840i | ||||||
\(179\) | 329.858 | 0.137736 | 0.0688681 | − | 0.997626i | \(-0.478061\pi\) | ||||
0.0688681 | + | 0.997626i | \(0.478061\pi\) | |||||||
\(180\) | −706.505 | + | 402.753i | −0.292554 | + | 0.166775i | ||||
\(181\) | −3600.84 | −1.47872 | −0.739360 | − | 0.673310i | \(-0.764872\pi\) | ||||
−0.739360 | + | 0.673310i | \(0.764872\pi\) | |||||||
\(182\) | − | 139.980i | − | 0.0570112i | ||||||
\(183\) | − | 799.009i | − | 0.322756i | ||||||
\(184\) | 445.741 | 0.178589 | ||||||||
\(185\) | 1035.71 | + | 1816.84i | 0.411606 | + | 0.722035i | ||||
\(186\) | 5823.70 | 2.29578 | ||||||||
\(187\) | 4934.37i | 1.92961i | ||||||||
\(188\) | 584.569i | 0.226777i | ||||||||
\(189\) | −1448.83 | −0.557602 | ||||||||
\(190\) | 2501.44 | + | 4388.00i | 0.955125 | + | 1.67547i | ||||
\(191\) | 2766.29 | 1.04797 | 0.523984 | − | 0.851728i | \(-0.324445\pi\) | ||||
0.523984 | + | 0.851728i | \(0.324445\pi\) | |||||||
\(192\) | 2861.23i | 1.07548i | ||||||||
\(193\) | 342.533i | 0.127752i | 0.997958 | + | 0.0638758i | \(0.0203462\pi\) | ||||
−0.997958 | + | 0.0638758i | \(0.979654\pi\) | |||||||
\(194\) | 1351.12 | 0.500023 | ||||||||
\(195\) | 263.516 | − | 150.221i | 0.0967731 | − | 0.0551668i | ||||
\(196\) | −291.904 | −0.106379 | ||||||||
\(197\) | − | 390.005i | − | 0.141049i | −0.997510 | − | 0.0705246i | \(-0.977533\pi\) | ||
0.997510 | − | 0.0705246i | \(-0.0224673\pi\) | |||||||
\(198\) | − | 6508.08i | − | 2.33590i | ||||||
\(199\) | −3859.22 | −1.37474 | −0.687368 | − | 0.726309i | \(-0.741234\pi\) | ||||
−0.687368 | + | 0.726309i | \(0.741234\pi\) | |||||||
\(200\) | −2084.54 | − | 1234.18i | −0.736997 | − | 0.436349i | ||||
\(201\) | 799.646 | 0.280610 | ||||||||
\(202\) | − | 1516.87i | − | 0.528351i | ||||||
\(203\) | − | 2178.77i | − | 0.753299i | ||||||
\(204\) | 1415.28 | 0.485734 | ||||||||
\(205\) | −1995.09 | + | 1137.33i | −0.679724 | + | 0.387486i | ||||
\(206\) | 5373.25 | 1.81734 | ||||||||
\(207\) | − | 922.488i | − | 0.309746i | ||||||
\(208\) | 249.114i | 0.0830429i | ||||||||
\(209\) | −7469.80 | −2.47223 | ||||||||
\(210\) | 1917.18 | + | 3363.10i | 0.629991 | + | 1.10512i | ||||
\(211\) | −5016.57 | −1.63675 | −0.818376 | − | 0.574683i | \(-0.805125\pi\) | ||||
−0.818376 | + | 0.574683i | \(0.805125\pi\) | |||||||
\(212\) | − | 1004.04i | − | 0.325273i | ||||||
\(213\) | − | 4775.99i | − | 1.53636i | ||||||
\(214\) | −4998.10 | −1.59656 | ||||||||
\(215\) | 1287.52 | + | 2258.55i | 0.408409 | + | 0.716427i | ||||
\(216\) | 2081.06 | 0.655547 | ||||||||
\(217\) | − | 3061.86i | − | 0.957845i | ||||||
\(218\) | − | 4803.14i | − | 1.49225i | ||||||
\(219\) | −483.252 | −0.149110 | ||||||||
\(220\) | −912.408 | + | 520.131i | −0.279612 | + | 0.159396i | ||||
\(221\) | −315.495 | −0.0960293 | ||||||||
\(222\) | 4800.27i | 1.45123i | ||||||||
\(223\) | 429.979i | 0.129119i | 0.997914 | + | 0.0645595i | \(0.0205642\pi\) | ||||
−0.997914 | + | 0.0645595i | \(0.979436\pi\) | |||||||
\(224\) | −1087.44 | −0.324364 | ||||||||
\(225\) | −2554.21 | + | 4314.09i | −0.756804 | + | 1.27825i | ||||
\(226\) | −3029.13 | −0.891571 | ||||||||
\(227\) | − | 699.886i | − | 0.204639i | −0.994752 | − | 0.102320i | \(-0.967374\pi\) | ||
0.994752 | − | 0.102320i | \(-0.0326264\pi\) | |||||||
\(228\) | 2142.50i | 0.622327i | ||||||||
\(229\) | −934.970 | −0.269802 | −0.134901 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134901 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(230\) | −699.830 | + | 398.948i | −0.200632 | + | 0.114373i | ||||
\(231\) | −5725.08 | −1.63066 | ||||||||
\(232\) | 3129.53i | 0.885619i | ||||||||
\(233\) | 852.267i | 0.239630i | 0.992796 | + | 0.119815i | \(0.0382302\pi\) | ||||
−0.992796 | + | 0.119815i | \(0.961770\pi\) | |||||||
\(234\) | 416.115 | 0.116249 | ||||||||
\(235\) | 1784.76 | + | 3130.81i | 0.495425 | + | 0.869070i | ||||
\(236\) | 964.256 | 0.265965 | ||||||||
\(237\) | − | 1988.52i | − | 0.545013i | ||||||
\(238\) | − | 4026.48i | − | 1.09663i | ||||||
\(239\) | −2397.28 | −0.648816 | −0.324408 | − | 0.945917i | \(-0.605165\pi\) | ||||
−0.324408 | + | 0.945917i | \(0.605165\pi\) | |||||||
\(240\) | −3411.87 | − | 5985.07i | −0.917648 | − | 1.60973i | ||||
\(241\) | −1284.37 | −0.343293 | −0.171646 | − | 0.985159i | \(-0.554909\pi\) | ||||
−0.171646 | + | 0.985159i | \(0.554909\pi\) | |||||||
\(242\) | − | 4235.22i | − | 1.12500i | ||||||
\(243\) | 4564.36i | 1.20495i | ||||||||
\(244\) | −176.886 | −0.0464098 | ||||||||
\(245\) | −1563.37 | + | 891.220i | −0.407673 | + | 0.232400i | ||||
\(246\) | −5271.24 | −1.36619 | ||||||||
\(247\) | − | 477.606i | − | 0.123034i | ||||||
\(248\) | 4397.97i | 1.12609i | ||||||||
\(249\) | −9153.70 | −2.32969 | ||||||||
\(250\) | 4377.43 | + | 71.9981i | 1.10741 | + | 0.0182142i | ||||
\(251\) | 5446.42 | 1.36962 | 0.684810 | − | 0.728722i | \(-0.259885\pi\) | ||||
0.684810 | + | 0.728722i | \(0.259885\pi\) | |||||||
\(252\) | 981.411i | 0.245330i | ||||||||
\(253\) | − | 1191.34i | − | 0.296042i | ||||||
\(254\) | −3287.07 | −0.812006 | ||||||||
\(255\) | 7579.92 | − | 4321.04i | 1.86146 | − | 1.06115i | ||||
\(256\) | 2653.28 | 0.647774 | ||||||||
\(257\) | 4124.52i | 1.00109i | 0.865710 | + | 0.500546i | \(0.166867\pi\) | ||||
−0.865710 | + | 0.500546i | \(0.833133\pi\) | |||||||
\(258\) | 5967.32i | 1.43996i | ||||||||
\(259\) | 2523.78 | 0.605483 | ||||||||
\(260\) | −33.2562 | − | 58.3377i | −0.00793255 | − | 0.0139152i | ||||
\(261\) | 6476.75 | 1.53602 | ||||||||
\(262\) | 2030.59i | 0.478817i | ||||||||
\(263\) | 3653.14i | 0.856512i | 0.903658 | + | 0.428256i | \(0.140872\pi\) | ||||
−0.903658 | + | 0.428256i | \(0.859128\pi\) | |||||||
\(264\) | 8223.35 | 1.91709 | ||||||||
\(265\) | −3065.46 | − | 5377.40i | −0.710603 | − | 1.24653i | ||||
\(266\) | 6095.41 | 1.40501 | ||||||||
\(267\) | − | 3731.33i | − | 0.855257i | ||||||
\(268\) | − | 177.027i | − | 0.0403495i | ||||||
\(269\) | −7453.46 | −1.68939 | −0.844694 | − | 0.535250i | \(-0.820217\pi\) | ||||
−0.844694 | + | 0.535250i | \(0.820217\pi\) | |||||||
\(270\) | −3267.34 | + | 1862.59i | −0.736460 | + | 0.419829i | ||||
\(271\) | 7506.57 | 1.68263 | 0.841313 | − | 0.540548i | \(-0.181783\pi\) | ||||
0.841313 | + | 0.540548i | \(0.181783\pi\) | |||||||
\(272\) | 7165.65i | 1.59736i | ||||||||
\(273\) | − | 366.051i | − | 0.0811518i | ||||||
\(274\) | 496.106 | 0.109383 | ||||||||
\(275\) | −3298.61 | + | 5571.39i | −0.723323 | + | 1.22170i | ||||
\(276\) | −341.701 | −0.0745217 | ||||||||
\(277\) | − | 4672.32i | − | 1.01347i | −0.862101 | − | 0.506737i | \(-0.830852\pi\) | ||
0.862101 | − | 0.506737i | \(-0.169148\pi\) | |||||||
\(278\) | 853.069i | 0.184042i | ||||||||
\(279\) | 9101.87 | 1.95310 | ||||||||
\(280\) | −2539.76 | + | 1447.83i | −0.542071 | + | 0.309015i | ||||
\(281\) | 1695.47 | 0.359941 | 0.179970 | − | 0.983672i | \(-0.442400\pi\) | ||||
0.179970 | + | 0.983672i | \(0.442400\pi\) | |||||||
\(282\) | 8271.91i | 1.74676i | ||||||||
\(283\) | 2210.76i | 0.464369i | 0.972672 | + | 0.232184i | \(0.0745872\pi\) | ||||
−0.972672 | + | 0.232184i | \(0.925413\pi\) | |||||||
\(284\) | −1057.32 | −0.220917 | ||||||||
\(285\) | 6541.32 | + | 11474.7i | 1.35956 | + | 2.38492i | ||||
\(286\) | 537.387 | 0.111106 | ||||||||
\(287\) | 2771.40i | 0.570002i | ||||||||
\(288\) | − | 3232.59i | − | 0.661396i | ||||||
\(289\) | −4162.08 | −0.847156 | ||||||||
\(290\) | −2801.00 | − | 4913.48i | −0.567173 | − | 0.994929i | ||||
\(291\) | 3533.19 | 0.711750 | ||||||||
\(292\) | 106.984i | 0.0214409i | ||||||||
\(293\) | − | 944.327i | − | 0.188287i | −0.995559 | − | 0.0941436i | \(-0.969989\pi\) | ||
0.995559 | − | 0.0941436i | \(-0.0300113\pi\) | |||||||
\(294\) | −4130.58 | −0.819388 | ||||||||
\(295\) | 5164.32 | − | 2943.99i | 1.01925 | − | 0.581037i | ||||
\(296\) | −3625.09 | −0.711838 | ||||||||
\(297\) | − | 5562.08i | − | 1.08668i | ||||||
\(298\) | − | 8853.60i | − | 1.72106i | ||||||
\(299\) | 76.1719 | 0.0147329 | ||||||||
\(300\) | 1597.99 | + | 946.113i | 0.307534 | + | 0.182079i | ||||
\(301\) | 3137.37 | 0.600780 | ||||||||
\(302\) | − | 6469.64i | − | 1.23274i | ||||||
\(303\) | − | 3966.65i | − | 0.752073i | ||||||
\(304\) | −10847.6 | −2.04655 | ||||||||
\(305\) | −947.360 | + | 540.056i | −0.177855 | + | 0.101389i | ||||
\(306\) | 11969.4 | 2.23609 | ||||||||
\(307\) | − | 4124.18i | − | 0.766708i | −0.923601 | − | 0.383354i | \(-0.874769\pi\) | ||
0.923601 | − | 0.383354i | \(-0.125231\pi\) | |||||||
\(308\) | 1267.43i | 0.234476i | ||||||||
\(309\) | 14051.1 | 2.58687 | ||||||||
\(310\) | −3936.28 | − | 6904.98i | −0.721180 | − | 1.26509i | ||||
\(311\) | −1043.49 | −0.190260 | −0.0951299 | − | 0.995465i | \(-0.530327\pi\) | ||||
−0.0951299 | + | 0.995465i | \(0.530327\pi\) | |||||||
\(312\) | 525.786i | 0.0954064i | ||||||||
\(313\) | 10692.6i | 1.93093i | 0.260540 | + | 0.965463i | \(0.416099\pi\) | ||||
−0.260540 | + | 0.965463i | \(0.583901\pi\) | |||||||
\(314\) | 430.167 | 0.0773113 | ||||||||
\(315\) | 2996.37 | + | 5256.20i | 0.535956 | + | 0.940168i | ||||
\(316\) | −440.223 | −0.0783686 | ||||||||
\(317\) | 5607.47i | 0.993524i | 0.867887 | + | 0.496762i | \(0.165478\pi\) | ||||
−0.867887 | + | 0.496762i | \(0.834522\pi\) | |||||||
\(318\) | − | 14207.6i | − | 2.50542i | ||||||
\(319\) | 8364.33 | 1.46806 | ||||||||
\(320\) | 3392.48 | − | 1933.93i | 0.592642 | − | 0.337844i | ||||
\(321\) | −13070.1 | −2.27259 | ||||||||
\(322\) | 972.138i | 0.168246i | ||||||||
\(323\) | − | 13738.1i | − | 2.36659i | ||||||
\(324\) | 368.614 | 0.0632054 | ||||||||
\(325\) | −356.225 | − | 210.907i | −0.0607993 | − | 0.0359970i | ||||
\(326\) | −9679.13 | −1.64441 | ||||||||
\(327\) | − | 12560.3i | − | 2.12412i | ||||||
\(328\) | − | 3980.76i | − | 0.670124i | ||||||
\(329\) | 4349.03 | 0.728783 | ||||||||
\(330\) | −12911.0 | + | 7360.08i | −2.15372 | + | 1.22776i | ||||
\(331\) | −5714.38 | −0.948914 | −0.474457 | − | 0.880279i | \(-0.657356\pi\) | ||||
−0.474457 | + | 0.880279i | \(0.657356\pi\) | |||||||
\(332\) | 2026.47i | 0.334991i | ||||||||
\(333\) | 7502.35i | 1.23461i | ||||||||
\(334\) | 623.404 | 0.102129 | ||||||||
\(335\) | −540.486 | − | 948.116i | −0.0881490 | − | 0.154630i | ||||
\(336\) | −8313.90 | −1.34988 | ||||||||
\(337\) | 6359.17i | 1.02791i | 0.857817 | + | 0.513956i | \(0.171820\pi\) | ||||
−0.857817 | + | 0.513956i | \(0.828180\pi\) | |||||||
\(338\) | − | 6848.09i | − | 1.10203i | ||||||
\(339\) | −7921.24 | −1.26909 | ||||||||
\(340\) | −956.601 | − | 1678.06i | −0.152585 | − | 0.267663i | ||||
\(341\) | 11754.5 | 1.86669 | ||||||||
\(342\) | 18119.6i | 2.86490i | ||||||||
\(343\) | 6799.55i | 1.07038i | ||||||||
\(344\) | −4506.43 | −0.706309 | ||||||||
\(345\) | −1830.07 | + | 1043.26i | −0.285587 | + | 0.162803i | ||||
\(346\) | 92.7259 | 0.0144074 | ||||||||
\(347\) | − | 8649.58i | − | 1.33814i | −0.743200 | − | 0.669069i | \(-0.766693\pi\) | ||
0.743200 | − | 0.669069i | \(-0.233307\pi\) | |||||||
\(348\) | − | 2399.07i | − | 0.369551i | ||||||
\(349\) | −6134.27 | −0.940859 | −0.470429 | − | 0.882438i | \(-0.655901\pi\) | ||||
−0.470429 | + | 0.882438i | \(0.655901\pi\) | |||||||
\(350\) | 2691.69 | − | 4546.29i | 0.411076 | − | 0.694312i | ||||
\(351\) | 355.629 | 0.0540800 | ||||||||
\(352\) | − | 4174.69i | − | 0.632136i | ||||||
\(353\) | − | 3494.07i | − | 0.526828i | −0.964683 | − | 0.263414i | \(-0.915151\pi\) | ||
0.964683 | − | 0.263414i | \(-0.0848485\pi\) | |||||||
\(354\) | 13644.7 | 2.04860 | ||||||||
\(355\) | −5662.75 | + | 3228.13i | −0.846613 | + | 0.482623i | ||||
\(356\) | −826.051 | −0.122979 | ||||||||
\(357\) | − | 10529.3i | − | 1.56098i | ||||||
\(358\) | − | 1033.33i | − | 0.152551i | ||||||
\(359\) | −11003.2 | −1.61763 | −0.808814 | − | 0.588064i | \(-0.799890\pi\) | ||||
−0.808814 | + | 0.588064i | \(0.799890\pi\) | |||||||
\(360\) | −4303.90 | − | 7549.86i | −0.630099 | − | 1.10531i | ||||
\(361\) | 13938.2 | 2.03210 | ||||||||
\(362\) | 11280.2i | 1.63777i | ||||||||
\(363\) | − | 11075.2i | − | 1.60136i | ||||||
\(364\) | −81.0373 | −0.0116690 | ||||||||
\(365\) | 326.634 | + | 572.978i | 0.0468405 | + | 0.0821672i | ||||
\(366\) | −2503.02 | −0.357473 | ||||||||
\(367\) | − | 6441.75i | − | 0.916231i | −0.888893 | − | 0.458115i | \(-0.848525\pi\) | ||
0.888893 | − | 0.458115i | \(-0.151475\pi\) | |||||||
\(368\) | − | 1730.05i | − | 0.245068i | ||||||
\(369\) | −8238.44 | −1.16227 | ||||||||
\(370\) | 5691.53 | − | 3244.54i | 0.799699 | − | 0.455879i | ||||
\(371\) | −7469.78 | −1.04531 | ||||||||
\(372\) | − | 3371.45i | − | 0.469896i | ||||||
\(373\) | − | 7432.01i | − | 1.03168i | −0.856686 | − | 0.515838i | \(-0.827481\pi\) | ||
0.856686 | − | 0.515838i | \(-0.172519\pi\) | |||||||
\(374\) | 15457.7 | 2.13716 | ||||||||
\(375\) | 11447.1 | + | 188.276i | 1.57633 | + | 0.0259268i | ||||
\(376\) | −6246.82 | −0.856796 | ||||||||
\(377\) | 534.800i | 0.0730600i | ||||||||
\(378\) | 4538.69i | 0.617579i | ||||||||
\(379\) | 7399.24 | 1.00283 | 0.501416 | − | 0.865206i | \(-0.332813\pi\) | ||||
0.501416 | + | 0.865206i | \(0.332813\pi\) | |||||||
\(380\) | 2540.30 | − | 1448.13i | 0.342933 | − | 0.195494i | ||||
\(381\) | −8595.76 | −1.15584 | ||||||||
\(382\) | − | 8665.84i | − | 1.16069i | ||||||
\(383\) | 5510.66i | 0.735200i | 0.929984 | + | 0.367600i | \(0.119820\pi\) | ||||
−0.929984 | + | 0.367600i | \(0.880180\pi\) | |||||||
\(384\) | 14245.2 | 1.89310 | ||||||||
\(385\) | 3869.62 | + | 6788.05i | 0.512245 | + | 0.898575i | ||||
\(386\) | 1073.04 | 0.141493 | ||||||||
\(387\) | 9326.34i | 1.22502i | ||||||||
\(388\) | − | 782.186i | − | 0.102344i | ||||||
\(389\) | −7779.10 | −1.01392 | −0.506962 | − | 0.861969i | \(-0.669231\pi\) | ||||
−0.506962 | + | 0.861969i | \(0.669231\pi\) | |||||||
\(390\) | −470.591 | − | 825.505i | −0.0611007 | − | 0.107182i | ||||
\(391\) | 2191.05 | 0.283392 | ||||||||
\(392\) | − | 3119.35i | − | 0.401916i | ||||||
\(393\) | 5310.02i | 0.681565i | ||||||||
\(394\) | −1221.75 | −0.156221 | ||||||||
\(395\) | −2357.73 | + | 1344.05i | −0.300329 | + | 0.171207i | ||||
\(396\) | −3767.65 | −0.478110 | ||||||||
\(397\) | − | 4722.18i | − | 0.596976i | −0.954413 | − | 0.298488i | \(-0.903518\pi\) | ||
0.954413 | − | 0.298488i | \(-0.0964823\pi\) | |||||||
\(398\) | 12089.6i | 1.52261i | ||||||||
\(399\) | 15939.6 | 1.99994 | ||||||||
\(400\) | −4790.21 | + | 8090.71i | −0.598776 | + | 1.01134i | ||||
\(401\) | 10838.3 | 1.34972 | 0.674862 | − | 0.737944i | \(-0.264203\pi\) | ||||
0.674862 | + | 0.737944i | \(0.264203\pi\) | |||||||
\(402\) | − | 2505.02i | − | 0.310793i | ||||||
\(403\) | 751.562i | 0.0928982i | ||||||||
\(404\) | −878.146 | −0.108142 | ||||||||
\(405\) | 1974.20 | − | 1125.42i | 0.242220 | − | 0.138081i | ||||
\(406\) | −6825.35 | −0.834326 | ||||||||
\(407\) | 9688.82i | 1.17999i | ||||||||
\(408\) | 15124.0i | 1.83517i | ||||||||
\(409\) | 8904.96 | 1.07658 | 0.538291 | − | 0.842759i | \(-0.319070\pi\) | ||||
0.538291 | + | 0.842759i | \(0.319070\pi\) | |||||||
\(410\) | 3562.87 | + | 6249.95i | 0.429165 | + | 0.752837i | ||||
\(411\) | 1297.33 | 0.155699 | ||||||||
\(412\) | − | 3110.68i | − | 0.371971i | ||||||
\(413\) | − | 7173.79i | − | 0.854719i | ||||||
\(414\) | −2889.84 | −0.343063 | ||||||||
\(415\) | 6187.06 | + | 10853.3i | 0.731833 | + | 1.28377i | ||||
\(416\) | 266.922 | 0.0314590 | ||||||||
\(417\) | 2230.79i | 0.261972i | ||||||||
\(418\) | 23400.3i | 2.73815i | ||||||||
\(419\) | −15917.0 | −1.85584 | −0.927919 | − | 0.372781i | \(-0.878404\pi\) | ||||
−0.927919 | + | 0.372781i | \(0.878404\pi\) | |||||||
\(420\) | 1946.96 | − | 1109.89i | 0.226195 | − | 0.128946i | ||||
\(421\) | −1869.26 | −0.216395 | −0.108197 | − | 0.994129i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994129i | \(0.534508\pi\) | |||||||
\(422\) | 15715.2i | 1.81281i | ||||||||
\(423\) | 12928.2i | 1.48603i | ||||||||
\(424\) | 10729.4 | 1.22893 | ||||||||
\(425\) | −10246.6 | − | 6066.66i | −1.16949 | − | 0.692414i | ||||
\(426\) | −14961.6 | −1.70162 | ||||||||
\(427\) | 1315.98i | 0.149145i | ||||||||
\(428\) | 2893.49i | 0.326781i | ||||||||
\(429\) | 1405.28 | 0.158152 | ||||||||
\(430\) | 7075.27 | − | 4033.35i | 0.793488 | − | 0.452339i | ||||
\(431\) | −6903.88 | −0.771573 | −0.385787 | − | 0.922588i | \(-0.626070\pi\) | ||||
−0.385787 | + | 0.922588i | \(0.626070\pi\) | |||||||
\(432\) | − | 8077.19i | − | 0.899570i | ||||||
\(433\) | 1991.39i | 0.221016i | 0.993875 | + | 0.110508i | \(0.0352478\pi\) | ||||
−0.993875 | + | 0.110508i | \(0.964752\pi\) | |||||||
\(434\) | −9591.75 | −1.06087 | ||||||||
\(435\) | −7324.66 | − | 12848.8i | −0.807334 | − | 1.41622i | ||||
\(436\) | −2780.63 | −0.305431 | ||||||||
\(437\) | 3316.88i | 0.363085i | ||||||||
\(438\) | 1513.86i | 0.165149i | ||||||||
\(439\) | 7051.99 | 0.766681 | 0.383341 | − | 0.923607i | \(-0.374774\pi\) | ||||
0.383341 | + | 0.923607i | \(0.374774\pi\) | |||||||
\(440\) | −5558.23 | − | 9750.18i | −0.602223 | − | 1.05641i | ||||
\(441\) | −6455.69 | −0.697084 | ||||||||
\(442\) | 988.338i | 0.106358i | ||||||||
\(443\) | 241.640i | 0.0259157i | 0.999916 | + | 0.0129579i | \(0.00412473\pi\) | ||||
−0.999916 | + | 0.0129579i | \(0.995875\pi\) | |||||||
\(444\) | 2778.96 | 0.297036 | ||||||||
\(445\) | −4424.13 | + | 2522.03i | −0.471289 | + | 0.268665i | ||||
\(446\) | 1346.98 | 0.143007 | ||||||||
\(447\) | − | 23152.3i | − | 2.44982i | ||||||
\(448\) | − | 4712.51i | − | 0.496976i | ||||||
\(449\) | 12453.4 | 1.30894 | 0.654468 | − | 0.756089i | \(-0.272893\pi\) | ||||
0.654468 | + | 0.756089i | \(0.272893\pi\) | |||||||
\(450\) | 13514.6 | + | 8001.48i | 1.41574 | + | 0.838208i | ||||
\(451\) | −10639.4 | −1.11085 | ||||||||
\(452\) | 1753.62i | 0.182486i | ||||||||
\(453\) | − | 16918.2i | − | 1.75472i | ||||||
\(454\) | −2192.50 | −0.226650 | ||||||||
\(455\) | −434.016 | + | 247.417i | −0.0447186 | + | 0.0254925i | ||||
\(456\) | −22895.2 | −2.35124 | ||||||||
\(457\) | 4700.39i | 0.481127i | 0.970633 | + | 0.240564i | \(0.0773323\pi\) | ||||
−0.970633 | + | 0.240564i | \(0.922668\pi\) | |||||||
\(458\) | 2928.94i | 0.298822i | ||||||||
\(459\) | 10229.5 | 1.04025 | ||||||||
\(460\) | 230.958 | + | 405.145i | 0.0234098 | + | 0.0410651i | ||||
\(461\) | 9555.28 | 0.965366 | 0.482683 | − | 0.875795i | \(-0.339662\pi\) | ||||
0.482683 | + | 0.875795i | \(0.339662\pi\) | |||||||
\(462\) | 17934.7i | 1.80606i | ||||||||
\(463\) | − | 16057.0i | − | 1.61173i | −0.592098 | − | 0.805866i | \(-0.701700\pi\) | ||
0.592098 | − | 0.805866i | \(-0.298300\pi\) | |||||||
\(464\) | 12146.6 | 1.21528 | ||||||||
\(465\) | −10293.4 | − | 18056.6i | −1.02655 | − | 1.80077i | ||||
\(466\) | 2669.86 | 0.265406 | ||||||||
\(467\) | 18657.5i | 1.84875i | 0.381484 | + | 0.924375i | \(0.375413\pi\) | ||||
−0.381484 | + | 0.924375i | \(0.624587\pi\) | |||||||
\(468\) | − | 240.897i | − | 0.0237937i | ||||||
\(469\) | −1317.03 | −0.129669 | ||||||||
\(470\) | 9807.76 | − | 5591.05i | 0.962549 | − | 0.548714i | ||||
\(471\) | 1124.89 | 0.110048 | ||||||||
\(472\) | 10304.2i | 1.00485i | ||||||||
\(473\) | 12044.4i | 1.17083i | ||||||||
\(474\) | −6229.35 | −0.603636 | ||||||||
\(475\) | 9183.89 | − | 15511.7i | 0.887128 | − | 1.49837i | ||||
\(476\) | −2331.00 | −0.224457 | ||||||||
\(477\) | − | 22205.2i | − | 2.13146i | ||||||
\(478\) | 7509.85i | 0.718604i | ||||||||
\(479\) | −12059.8 | −1.15037 | −0.575184 | − | 0.818024i | \(-0.695069\pi\) | ||||
−0.575184 | + | 0.818024i | \(0.695069\pi\) | |||||||
\(480\) | −6412.93 | + | 3655.78i | −0.609811 | + | 0.347631i | ||||
\(481\) | −619.486 | −0.0587238 | ||||||||
\(482\) | 4023.50i | 0.380218i | ||||||||
\(483\) | 2542.16i | 0.239487i | ||||||||
\(484\) | −2451.85 | −0.230264 | ||||||||
\(485\) | −2388.11 | − | 4189.20i | −0.223585 | − | 0.392210i | ||||
\(486\) | 14298.6 | 1.33456 | ||||||||
\(487\) | − | 19826.9i | − | 1.84485i | −0.386178 | − | 0.922424i | \(-0.626205\pi\) | ||
0.386178 | − | 0.922424i | \(-0.373795\pi\) | |||||||
\(488\) | − | 1890.24i | − | 0.175343i | ||||||
\(489\) | −25311.1 | −2.34071 | ||||||||
\(490\) | 2791.89 | + | 4897.50i | 0.257397 | + | 0.451524i | ||||
\(491\) | −1218.93 | −0.112036 | −0.0560178 | − | 0.998430i | \(-0.517840\pi\) | ||||
−0.0560178 | + | 0.998430i | \(0.517840\pi\) | |||||||
\(492\) | 3051.62i | 0.279629i | ||||||||
\(493\) | 15383.3i | 1.40533i | ||||||||
\(494\) | −1496.18 | −0.136268 | ||||||||
\(495\) | −20178.6 | + | 11503.1i | −1.83224 | + | 1.04450i | ||||
\(496\) | 17069.8 | 1.54527 | ||||||||
\(497\) | 7866.16i | 0.709951i | ||||||||
\(498\) | 28675.4i | 2.58028i | ||||||||
\(499\) | −10445.2 | −0.937061 | −0.468531 | − | 0.883447i | \(-0.655216\pi\) | ||||
−0.468531 | + | 0.883447i | \(0.655216\pi\) | |||||||
\(500\) | 41.6810 | − | 2534.18i | 0.00372806 | − | 0.226664i | ||||
\(501\) | 1630.21 | 0.145374 | ||||||||
\(502\) | − | 17061.8i | − | 1.51694i | ||||||
\(503\) | 6597.00i | 0.584783i | 0.956299 | + | 0.292391i | \(0.0944510\pi\) | ||||
−0.956299 | + | 0.292391i | \(0.905549\pi\) | |||||||
\(504\) | −10487.6 | −0.926891 | ||||||||
\(505\) | −4703.14 | + | 2681.09i | −0.414429 | + | 0.236251i | ||||
\(506\) | −3732.05 | −0.327885 | ||||||||
\(507\) | − | 17907.9i | − | 1.56867i | ||||||
\(508\) | 1902.95i | 0.166200i | ||||||||
\(509\) | 20547.8 | 1.78932 | 0.894662 | − | 0.446744i | \(-0.147417\pi\) | ||||
0.894662 | + | 0.446744i | \(0.147417\pi\) | |||||||
\(510\) | −13536.3 | − | 23745.3i | −1.17529 | − | 2.06169i | ||||
\(511\) | 795.927 | 0.0689036 | ||||||||
\(512\) | 5599.60i | 0.483339i | ||||||||
\(513\) | 15485.8i | 1.33277i | ||||||||
\(514\) | 12920.7 | 1.10877 | ||||||||
\(515\) | −9497.28 | − | 16660.0i | −0.812621 | − | 1.42549i | ||||
\(516\) | 3454.59 | 0.294729 | ||||||||
\(517\) | 16696.0i | 1.42029i | ||||||||
\(518\) | − | 7906.14i | − | 0.670610i | ||||||
\(519\) | 242.480 | 0.0205081 | ||||||||
\(520\) | 623.409 | − | 355.383i | 0.0525736 | − | 0.0299703i | ||||
\(521\) | 7024.25 | 0.590668 | 0.295334 | − | 0.955394i | \(-0.404569\pi\) | ||||
0.295334 | + | 0.955394i | \(0.404569\pi\) | |||||||
\(522\) | − | 20289.5i | − | 1.70124i | ||||||
\(523\) | − | 8773.19i | − | 0.733508i | −0.930318 | − | 0.366754i | \(-0.880469\pi\) | ||
0.930318 | − | 0.366754i | \(-0.119531\pi\) | |||||||
\(524\) | 1175.54 | 0.0980036 | ||||||||
\(525\) | 7038.81 | − | 11888.6i | 0.585140 | − | 0.988308i | ||||
\(526\) | 11444.1 | 0.948640 | ||||||||
\(527\) | 21618.4i | 1.78693i | ||||||||
\(528\) | − | 31917.2i | − | 2.63072i | ||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | −16845.6 | + | 9603.05i | −1.38061 | + | 0.787037i | ||||
\(531\) | 21325.3 | 1.74282 | ||||||||
\(532\) | − | 3528.74i | − | 0.287576i | ||||||
\(533\) | − | 680.266i | − | 0.0552826i | ||||||
\(534\) | −11689.0 | −0.947251 | ||||||||
\(535\) | 8834.19 | + | 15496.8i | 0.713897 | + | 1.25231i | ||||
\(536\) | 1891.75 | 0.152446 | ||||||||
\(537\) | − | 2702.19i | − | 0.217147i | ||||||
\(538\) | 23349.1i | 1.87110i | ||||||||
\(539\) | −8337.13 | −0.666244 | ||||||||
\(540\) | 1078.29 | + | 1891.53i | 0.0859301 | + | 0.150738i | ||||
\(541\) | 1418.43 | 0.112723 | 0.0563615 | − | 0.998410i | \(-0.482050\pi\) | ||||
0.0563615 | + | 0.998410i | \(0.482050\pi\) | |||||||
\(542\) | − | 23515.5i | − | 1.86361i | ||||||
\(543\) | 29497.9i | 2.33127i | ||||||||
\(544\) | 7677.90 | 0.605124 | ||||||||
\(545\) | −14892.4 | + | 8489.61i | −1.17049 | + | 0.667256i | ||||
\(546\) | −1146.71 | −0.0898806 | ||||||||
\(547\) | − | 9882.41i | − | 0.772470i | −0.922400 | − | 0.386235i | \(-0.873775\pi\) | ||
0.922400 | − | 0.386235i | \(-0.126225\pi\) | |||||||
\(548\) | − | 287.205i | − | 0.0223883i | ||||||
\(549\) | −3911.98 | −0.304115 | ||||||||
\(550\) | 17453.3 | + | 10333.4i | 1.35311 | + | 0.801125i | ||||
\(551\) | −23287.7 | −1.80053 | ||||||||
\(552\) | − | 3651.49i | − | 0.281554i | ||||||
\(553\) | 3275.13i | 0.251849i | ||||||||
\(554\) | −14636.8 | −1.12249 | ||||||||
\(555\) | 14883.4 | − | 8484.52i | 1.13832 | − | 0.648915i | ||||
\(556\) | 493.858 | 0.0376695 | ||||||||
\(557\) | 5932.82i | 0.451313i | 0.974207 | + | 0.225657i | \(0.0724527\pi\) | ||||
−0.974207 | + | 0.225657i | \(0.927547\pi\) | |||||||
\(558\) | − | 28513.1i | − | 2.16318i | ||||||
\(559\) | −770.097 | −0.0582677 | ||||||||
\(560\) | 5619.43 | + | 9857.54i | 0.424043 | + | 0.743852i | ||||
\(561\) | 40422.2 | 3.04211 | ||||||||
\(562\) | − | 5311.34i | − | 0.398657i | ||||||
\(563\) | 5347.11i | 0.400273i | 0.979768 | + | 0.200137i | \(0.0641386\pi\) | ||||
−0.979768 | + | 0.200137i | \(0.935861\pi\) | |||||||
\(564\) | 4788.76 | 0.357524 | ||||||||
\(565\) | 5354.02 | + | 9391.97i | 0.398665 | + | 0.699333i | ||||
\(566\) | 6925.57 | 0.514317 | ||||||||
\(567\) | − | 2742.38i | − | 0.203120i | ||||||
\(568\) | − | 11298.7i | − | 0.834656i | ||||||
\(569\) | 13568.8 | 0.999709 | 0.499854 | − | 0.866109i | \(-0.333387\pi\) | ||||
0.499854 | + | 0.866109i | \(0.333387\pi\) | |||||||
\(570\) | 35946.4 | − | 20491.7i | 2.64145 | − | 1.50580i | ||||
\(571\) | 5528.45 | 0.405181 | 0.202590 | − | 0.979264i | \(-0.435064\pi\) | ||||
0.202590 | + | 0.979264i | \(0.435064\pi\) | |||||||
\(572\) | − | 311.103i | − | 0.0227411i | ||||||
\(573\) | − | 22661.3i | − | 1.65217i | ||||||
\(574\) | 8681.85 | 0.631312 | ||||||||
\(575\) | 2473.91 | + | 1464.71i | 0.179425 | + | 0.106231i | ||||
\(576\) | 14008.7 | 1.01336 | ||||||||
\(577\) | − | 13634.6i | − | 0.983734i | −0.870670 | − | 0.491867i | \(-0.836315\pi\) | ||
0.870670 | − | 0.491867i | \(-0.163685\pi\) | |||||||
\(578\) | 13038.4i | 0.938278i | ||||||||
\(579\) | 2806.02 | 0.201406 | ||||||||
\(580\) | −2844.51 | + | 1621.55i | −0.203641 | + | 0.116088i | ||||
\(581\) | 15076.3 | 1.07654 | ||||||||
\(582\) | − | 11068.3i | − | 0.788308i | ||||||
\(583\) | − | 28676.6i | − | 2.03716i | ||||||
\(584\) | −1143.25 | −0.0810068 | ||||||||
\(585\) | −735.487 | − | 1290.18i | −0.0519806 | − | 0.0911838i | ||||
\(586\) | −2958.25 | −0.208540 | ||||||||
\(587\) | − | 25831.5i | − | 1.81632i | −0.418622 | − | 0.908160i | \(-0.637487\pi\) | ||
0.418622 | − | 0.908160i | \(-0.362513\pi\) | |||||||
\(588\) | 2391.27i | 0.167711i | ||||||||
\(589\) | −32726.6 | −2.28943 | ||||||||
\(590\) | −9222.53 | − | 16178.1i | −0.643534 | − | 1.12888i | ||||
\(591\) | −3194.90 | −0.222370 | ||||||||
\(592\) | 14070.0i | 0.976814i | ||||||||
\(593\) | 19241.9i | 1.33250i | 0.745731 | + | 0.666248i | \(0.232101\pi\) | ||||
−0.745731 | + | 0.666248i | \(0.767899\pi\) | |||||||
\(594\) | −17424.1 | −1.20357 | ||||||||
\(595\) | −12484.3 | + | 7116.84i | −0.860178 | + | 0.490356i | ||||
\(596\) | −5125.52 | −0.352264 | ||||||||
\(597\) | 31614.5i | 2.16733i | ||||||||
\(598\) | − | 238.621i | − | 0.0163176i | ||||||
\(599\) | 5609.23 | 0.382616 | 0.191308 | − | 0.981530i | \(-0.438727\pi\) | ||||
0.191308 | + | 0.981530i | \(0.438727\pi\) | |||||||
\(600\) | −10110.4 | + | 17076.5i | −0.687922 | + | 1.16191i | ||||
\(601\) | 6750.84 | 0.458191 | 0.229095 | − | 0.973404i | \(-0.426423\pi\) | ||||
0.229095 | + | 0.973404i | \(0.426423\pi\) | |||||||
\(602\) | − | 9828.30i | − | 0.665401i | ||||||
\(603\) | − | 3915.10i | − | 0.264403i | ||||||
\(604\) | −3745.40 | −0.252315 | ||||||||
\(605\) | −13131.5 | + | 7485.79i | −0.882431 | + | 0.503042i | ||||
\(606\) | −12426.2 | −0.832967 | ||||||||
\(607\) | − | 11132.1i | − | 0.744378i | −0.928157 | − | 0.372189i | \(-0.878607\pi\) | ||
0.928157 | − | 0.372189i | \(-0.121393\pi\) | |||||||
\(608\) | 11623.0i | 0.775291i | ||||||||
\(609\) | −17848.4 | −1.18761 | ||||||||
\(610\) | 1691.81 | + | 2967.76i | 0.112294 | + | 0.196985i | ||||
\(611\) | −1067.51 | −0.0706822 | ||||||||
\(612\) | − | 6929.29i | − | 0.457680i | ||||||
\(613\) | − | 8300.26i | − | 0.546891i | −0.961888 | − | 0.273445i | \(-0.911837\pi\) | ||
0.961888 | − | 0.273445i | \(-0.0881633\pi\) | |||||||
\(614\) | −12919.7 | −0.849177 | ||||||||
\(615\) | 9316.97 | + | 16343.7i | 0.610889 | + | 1.07161i | ||||
\(616\) | −13544.0 | −0.885884 | ||||||||
\(617\) | − | 6597.54i | − | 0.430482i | −0.976561 | − | 0.215241i | \(-0.930946\pi\) | ||
0.976561 | − | 0.215241i | \(-0.0690536\pi\) | |||||||
\(618\) | − | 44017.5i | − | 2.86512i | ||||||
\(619\) | 27992.2 | 1.81761 | 0.908805 | − | 0.417221i | \(-0.136996\pi\) | ||||
0.908805 | + | 0.417221i | \(0.136996\pi\) | |||||||
\(620\) | −3997.42 | + | 2278.79i | −0.258936 | + | 0.147610i | ||||
\(621\) | −2469.78 | −0.159595 | ||||||||
\(622\) | 3268.90i | 0.210725i | ||||||||
\(623\) | 6145.58i | 0.395213i | ||||||||
\(624\) | 2040.73 | 0.130921 | ||||||||
\(625\) | −7513.92 | − | 13699.7i | −0.480891 | − | 0.876780i | ||||
\(626\) | 33496.2 | 2.13862 | ||||||||
\(627\) | 61192.3i | 3.89758i | ||||||||
\(628\) | − | 249.032i | − | 0.0158240i | ||||||
\(629\) | −17819.3 | −1.12957 | ||||||||
\(630\) | 16465.9 | − | 9386.60i | 1.04130 | − | 0.593605i | ||||
\(631\) | −447.361 | −0.0282237 | −0.0141119 | − | 0.999900i | \(-0.504492\pi\) | ||||
−0.0141119 | + | 0.999900i | \(0.504492\pi\) | |||||||
\(632\) | − | 4704.31i | − | 0.296088i | ||||||
\(633\) | 41095.5i | 2.58041i | ||||||||
\(634\) | 17566.3 | 1.10039 | ||||||||
\(635\) | 5809.94 | + | 10191.7i | 0.363087 | + | 0.636924i | ||||
\(636\) | −8225.06 | −0.512807 | ||||||||
\(637\) | − | 533.061i | − | 0.0331564i | ||||||
\(638\) | − | 26202.6i | − | 1.62597i | ||||||
\(639\) | −23383.5 | −1.44763 | ||||||||
\(640\) | −9628.46 | − | 16890.1i | −0.594685 | − | 1.04319i | ||||
\(641\) | 20751.5 | 1.27868 | 0.639341 | − | 0.768924i | \(-0.279207\pi\) | ||||
0.639341 | + | 0.768924i | \(0.279207\pi\) | |||||||
\(642\) | 40944.2i | 2.51704i | ||||||||
\(643\) | 3579.70i | 0.219549i | 0.993957 | + | 0.109774i | \(0.0350128\pi\) | ||||
−0.993957 | + | 0.109774i | \(0.964987\pi\) | |||||||
\(644\) | 562.789 | 0.0344363 | ||||||||
\(645\) | 18501.9 | − | 10547.3i | 1.12948 | − | 0.643875i | ||||
\(646\) | −43036.9 | −2.62115 | ||||||||
\(647\) | 547.886i | 0.0332916i | 0.999861 | + | 0.0166458i | \(0.00529876\pi\) | ||||
−0.999861 | + | 0.0166458i | \(0.994701\pi\) | |||||||
\(648\) | 3939.08i | 0.238799i | ||||||||
\(649\) | 27540.3 | 1.66572 | ||||||||
\(650\) | −660.701 | + | 1115.93i | −0.0398689 | + | 0.0673390i | ||||
\(651\) | −25082.6 | −1.51008 | ||||||||
\(652\) | 5603.43i | 0.336575i | ||||||||
\(653\) | 6388.75i | 0.382866i | 0.981506 | + | 0.191433i | \(0.0613134\pi\) | ||||
−0.981506 | + | 0.191433i | \(0.938687\pi\) | |||||||
\(654\) | −39347.2 | −2.35259 | ||||||||
\(655\) | 6295.93 | − | 3589.08i | 0.375576 | − | 0.214102i | ||||
\(656\) | −15450.5 | −0.919573 | ||||||||
\(657\) | 2366.02i | 0.140498i | ||||||||
\(658\) | − | 13624.0i | − | 0.807172i | ||||||
\(659\) | 10862.4 | 0.642092 | 0.321046 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321046 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(660\) | 4260.89 | + | 7474.41i | 0.251295 | + | 0.440820i | ||||
\(661\) | 7995.73 | 0.470496 | 0.235248 | − | 0.971935i | \(-0.424410\pi\) | ||||
0.235248 | + | 0.971935i | \(0.424410\pi\) | |||||||
\(662\) | 17901.2i | 1.05098i | ||||||||
\(663\) | 2584.52i | 0.151394i | ||||||||
\(664\) | −21655.3 | −1.26564 | ||||||||
\(665\) | −10773.7 | − | 18899.1i | −0.628249 | − | 1.10207i | ||||
\(666\) | 23502.3 | 1.36741 | ||||||||
\(667\) | − | 3714.09i | − | 0.215607i | ||||||
\(668\) | − | 360.901i | − | 0.0209037i | ||||||
\(669\) | 3522.37 | 0.203562 | ||||||||
\(670\) | −2970.12 | + | 1693.16i | −0.171263 | + | 0.0976306i | ||||
\(671\) | −5052.08 | −0.290661 | ||||||||
\(672\) | 8908.25i | 0.511374i | ||||||||
\(673\) | 16061.3i | 0.919935i | 0.887936 | + | 0.459967i | \(0.152139\pi\) | ||||
−0.887936 | + | 0.459967i | \(0.847861\pi\) | |||||||
\(674\) | 19921.1 | 1.13848 | ||||||||
\(675\) | 11550.1 | + | 6838.40i | 0.658614 | + | 0.389941i | ||||
\(676\) | −3964.49 | −0.225563 | ||||||||
\(677\) | − | 12848.3i | − | 0.729393i | −0.931127 | − | 0.364696i | \(-0.881173\pi\) | ||
0.931127 | − | 0.364696i | \(-0.118827\pi\) | |||||||
\(678\) | 24814.5i | 1.40560i | ||||||||
\(679\) | −5819.24 | −0.328898 | ||||||||
\(680\) | 17932.1 | − | 10222.4i | 1.01127 | − | 0.576489i | ||||
\(681\) | −5733.44 | −0.322622 | ||||||||
\(682\) | − | 36822.9i | − | 2.06748i | ||||||
\(683\) | − | 31534.0i | − | 1.76664i | −0.468770 | − | 0.883320i | \(-0.655303\pi\) | ||
0.468770 | − | 0.883320i | \(-0.344697\pi\) | |||||||
\(684\) | 10489.8 | 0.586384 | ||||||||
\(685\) | −876.872 | − | 1538.20i | −0.0489103 | − | 0.0857980i | ||||
\(686\) | 21300.7 | 1.18552 | ||||||||
\(687\) | 7659.24i | 0.425354i | ||||||||
\(688\) | 17490.7i | 0.969227i | ||||||||
\(689\) | 1833.53 | 0.101382 | ||||||||
\(690\) | 3268.16 | + | 5732.98i | 0.180314 | + | 0.316305i | ||||
\(691\) | −11002.1 | −0.605702 | −0.302851 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302851 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(692\) | − | 53.6808i | − | 0.00294890i | ||||||
\(693\) | 28030.2i | 1.53648i | ||||||||
\(694\) | −27096.2 | −1.48207 | ||||||||
\(695\) | 2644.98 | − | 1507.81i | 0.144359 | − | 0.0822941i | ||||
\(696\) | 25637.0 | 1.39622 | ||||||||
\(697\) | − | 19567.6i | − | 1.06338i | ||||||
\(698\) | 19216.6i | 1.04206i | ||||||||
\(699\) | 6981.74 | 0.377788 | ||||||||
\(700\) | −2631.93 | − | 1558.27i | −0.142111 | − | 0.0841386i | ||||
\(701\) | −21688.3 | −1.16855 | −0.584277 | − | 0.811554i | \(-0.698622\pi\) | ||||
−0.584277 | + | 0.811554i | \(0.698622\pi\) | |||||||
\(702\) | − | 1114.07i | − | 0.0598970i | ||||||
\(703\) | − | 26975.3i | − | 1.44722i | ||||||
\(704\) | 18091.4 | 0.968531 | ||||||||
\(705\) | 25647.4 | − | 14620.7i | 1.37013 | − | 0.781059i | ||||
\(706\) | −10945.7 | −0.583495 | ||||||||
\(707\) | 6533.16i | 0.347531i | ||||||||
\(708\) | − | 7899.15i | − | 0.419305i | ||||||
\(709\) | 21156.7 | 1.12067 | 0.560335 | − | 0.828266i | \(-0.310672\pi\) | ||||
0.560335 | + | 0.828266i | \(0.310672\pi\) | |||||||
\(710\) | 10112.6 | + | 17739.5i | 0.534535 | + | 0.937676i | ||||
\(711\) | −9735.87 | −0.513535 | ||||||||
\(712\) | − | 8827.35i | − | 0.464633i | ||||||
\(713\) | − | 5219.46i | − | 0.274152i | ||||||
\(714\) | −32984.7 | −1.72888 | ||||||||
\(715\) | −949.837 | − | 1666.19i | −0.0496810 | − | 0.0871498i | ||||
\(716\) | −598.216 | −0.0312240 | ||||||||
\(717\) | 19638.4i | 1.02289i | ||||||||
\(718\) | 34469.4i | 1.79162i | ||||||||
\(719\) | 3485.09 | 0.180767 | 0.0903837 | − | 0.995907i | \(-0.471191\pi\) | ||||
0.0903837 | + | 0.995907i | \(0.471191\pi\) | |||||||
\(720\) | −29303.2 | + | 16704.7i | −1.51676 | + | 0.864648i | ||||
\(721\) | −23142.5 | −1.19539 | ||||||||
\(722\) | − | 43663.6i | − | 2.25068i | ||||||
\(723\) | 10521.5i | 0.541216i | ||||||||
\(724\) | 6530.32 | 0.335218 | ||||||||
\(725\) | −10283.7 | + | 17369.2i | −0.526795 | + | 0.889762i | ||||
\(726\) | −34694.7 | −1.77361 | ||||||||
\(727\) | − | 11214.0i | − | 0.572082i | −0.958217 | − | 0.286041i | \(-0.907661\pi\) | ||
0.958217 | − | 0.286041i | \(-0.0923393\pi\) | |||||||
\(728\) | − | 865.981i | − | 0.0440871i | ||||||
\(729\) | 31903.2 | 1.62085 | ||||||||
\(730\) | 1794.94 | − | 1023.23i | 0.0910053 | − | 0.0518788i | ||||
\(731\) | −22151.5 | −1.12080 | ||||||||
\(732\) | 1449.05i | 0.0731671i | ||||||||
\(733\) | − | 33463.9i | − | 1.68624i | −0.537723 | − | 0.843122i | \(-0.680715\pi\) | ||
0.537723 | − | 0.843122i | \(-0.319285\pi\) | |||||||
\(734\) | −20179.8 | −1.01478 | ||||||||
\(735\) | 7300.84 | + | 12807.0i | 0.366388 | + | 0.642714i | ||||
\(736\) | −1853.73 | −0.0928386 | ||||||||
\(737\) | − | 5056.11i | − | 0.252706i | ||||||
\(738\) | 25808.2i | 1.28728i | ||||||||
\(739\) | −32656.2 | −1.62555 | −0.812773 | − | 0.582581i | \(-0.802043\pi\) | ||||
−0.812773 | + | 0.582581i | \(0.802043\pi\) | |||||||
\(740\) | −1878.32 | − | 3294.93i | −0.0933088 | − | 0.163681i | ||||
\(741\) | −3912.53 | −0.193968 | ||||||||
\(742\) | 23400.3i | 1.15775i | ||||||||
\(743\) | 16670.6i | 0.823129i | 0.911381 | + | 0.411564i | \(0.135017\pi\) | ||||
−0.911381 | + | 0.411564i | \(0.864983\pi\) | |||||||
\(744\) | 36028.0 | 1.77534 | ||||||||
\(745\) | −27451.0 | + | 15648.8i | −1.34997 | + | 0.769569i | ||||
\(746\) | −23282.0 | −1.14264 | ||||||||
\(747\) | 44816.9i | 2.19513i | ||||||||
\(748\) | − | 8948.76i | − | 0.437432i | ||||||
\(749\) | 21526.8 | 1.05016 | ||||||||
\(750\) | 589.805 | − | 35859.7i | 0.0287155 | − | 1.74588i | ||||
\(751\) | 1939.32 | 0.0942303 | 0.0471152 | − | 0.998889i | \(-0.484997\pi\) | ||||
0.0471152 | + | 0.998889i | \(0.484997\pi\) | |||||||
\(752\) | 24245.7i | 1.17573i | ||||||||
\(753\) | − | 44616.8i | − | 2.15927i | ||||||
\(754\) | 1675.35 | 0.0809185 | ||||||||
\(755\) | −20059.4 | + | 11435.2i | −0.966937 | + | 0.551216i | ||||
\(756\) | 2627.53 | 0.126405 | ||||||||
\(757\) | 3445.40i | 0.165423i | 0.996574 | + | 0.0827114i | \(0.0263580\pi\) | ||||
−0.996574 | + | 0.0827114i | \(0.973642\pi\) | |||||||
\(758\) | − | 23179.3i | − | 1.11070i | ||||||
\(759\) | −9759.38 | −0.466723 | ||||||||
\(760\) | 15475.0 | + | 27146.1i | 0.738604 | + | 1.29565i | ||||
\(761\) | −32261.4 | −1.53676 | −0.768381 | − | 0.639993i | \(-0.778937\pi\) | ||||
−0.768381 | + | 0.639993i | \(0.778937\pi\) | |||||||
\(762\) | 26927.6i | 1.28016i | ||||||||
\(763\) | 20687.1i | 0.981551i | ||||||||
\(764\) | −5016.82 | −0.237568 | ||||||||
\(765\) | −21156.0 | − | 37111.6i | −0.999864 | − | 1.75395i | ||||
\(766\) | 17263.0 | 0.814280 | ||||||||
\(767\) | 1760.88i | 0.0828964i | ||||||||
\(768\) | − | 21735.6i | − | 1.02124i | ||||||
\(769\) | 8322.06 | 0.390249 | 0.195124 | − | 0.980779i | \(-0.437489\pi\) | ||||
0.195124 | + | 0.980779i | \(0.437489\pi\) | |||||||
\(770\) | 21264.7 | − | 12122.2i | 0.995228 | − | 0.567343i | ||||
\(771\) | 33787.9 | 1.57827 | ||||||||
\(772\) | − | 621.203i | − | 0.0289606i | ||||||
\(773\) | 11057.9i | 0.514519i | 0.966342 | + | 0.257260i | \(0.0828196\pi\) | ||||
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(774\) | 29216.2 | 1.35679 | ||||||||
\(775\) | −14451.8 | + | 24409.3i | −0.669838 | + | 1.13136i | ||||
\(776\) | 8358.61 | 0.386671 | ||||||||
\(777\) | − | 20674.7i | − | 0.954570i | ||||||
\(778\) | 24369.3i | 1.12298i | ||||||||
\(779\) | 29622.0 | 1.36241 | ||||||||
\(780\) | −477.900 | + | 272.434i | −0.0219379 | + | 0.0125060i | ||||
\(781\) | −30198.3 | −1.38359 | ||||||||
\(782\) | − | 6863.82i | − | 0.313875i | ||||||
\(783\) | − | 17340.2i | − | 0.791429i | ||||||
\(784\) | −12107.1 | −0.551526 | ||||||||
\(785\) | −760.325 | − | 1333.75i | −0.0345696 | − | 0.0606417i | ||||
\(786\) | 16634.5 | 0.754875 | ||||||||
\(787\) | − | 9092.33i | − | 0.411826i | −0.978570 | − | 0.205913i | \(-0.933984\pi\) | ||
0.978570 | − | 0.205913i | \(-0.0660163\pi\) | |||||||
\(788\) | 707.295i | 0.0319751i | ||||||||
\(789\) | 29926.4 | 1.35033 | ||||||||
\(790\) | 4210.46 | + | 7385.95i | 0.189622 | + | 0.332633i | ||||
\(791\) | 13046.4 | 0.586445 | ||||||||
\(792\) | − | 40261.9i | − | 1.80637i | ||||||
\(793\) | − | 323.021i | − | 0.0144651i | ||||||
\(794\) | −14793.0 | −0.661188 | ||||||||
\(795\) | −44051.4 | + | 25112.1i | −1.96521 | + | 1.12030i | ||||
\(796\) | 6998.90 | 0.311645 | ||||||||
\(797\) | − | 11969.9i | − | 0.531988i | −0.963975 | − | 0.265994i | \(-0.914300\pi\) | ||
0.963975 | − | 0.265994i | \(-0.0857002\pi\) | |||||||
\(798\) | − | 49933.3i | − | 2.21506i | ||||||
\(799\) | −30706.5 | −1.35960 | ||||||||
\(800\) | 8669.10 | + | 5132.65i | 0.383124 | + | 0.226833i | ||||
\(801\) | −18268.8 | −0.805861 | ||||||||
\(802\) | − | 33952.7i | − | 1.49490i | ||||||
\(803\) | 3055.58i | 0.134283i | ||||||||
\(804\) | −1450.20 | −0.0636128 | ||||||||
\(805\) | 3014.16 | − | 1718.26i | 0.131969 | − | 0.0752309i | ||||
\(806\) | 2354.39 | 0.102891 | ||||||||
\(807\) | 61058.4i | 2.66339i | ||||||||
\(808\) | − | 9384.05i | − | 0.408576i | ||||||
\(809\) | 29216.4 | 1.26971 | 0.634854 | − | 0.772632i | \(-0.281060\pi\) | ||||
0.634854 | + | 0.772632i | \(0.281060\pi\) | |||||||
\(810\) | −3525.57 | − | 6184.51i | −0.152933 | − | 0.268274i | ||||
\(811\) | −6747.86 | −0.292169 | −0.146085 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146085 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(812\) | 3951.32i | 0.170769i | ||||||||
\(813\) | − | 61493.5i | − | 2.65273i | ||||||
\(814\) | 30351.8 | 1.30692 | ||||||||
\(815\) | 17108.0 | + | 30010.6i | 0.735295 | + | 1.28985i | ||||
\(816\) | 58700.7 | 2.51830 | ||||||||
\(817\) | − | 33533.6i | − | 1.43598i | ||||||
\(818\) | − | 27896.2i | − | 1.19238i | ||||||
\(819\) | −1792.20 | −0.0764648 | ||||||||
\(820\) | 3618.21 | − | 2062.61i | 0.154090 | − | 0.0878409i | ||||
\(821\) | 28219.7 | 1.19960 | 0.599801 | − | 0.800149i | \(-0.295247\pi\) | ||||
0.599801 | + | 0.800149i | \(0.295247\pi\) | |||||||
\(822\) | − | 4064.08i | − | 0.172447i | ||||||
\(823\) | − | 13238.6i | − | 0.560714i | −0.959896 | − | 0.280357i | \(-0.909547\pi\) | ||
0.959896 | − | 0.280357i | \(-0.0904529\pi\) | |||||||
\(824\) | 33241.3 | 1.40536 | ||||||||
\(825\) | 45640.6 | + | 27022.1i | 1.92606 | + | 1.14035i | ||||
\(826\) | −22473.0 | −0.946655 | ||||||||
\(827\) | 26369.9i | 1.10879i | 0.832252 | + | 0.554397i | \(0.187051\pi\) | ||||
−0.832252 | + | 0.554397i | \(0.812949\pi\) | |||||||
\(828\) | 1672.98i | 0.0702176i | ||||||||
\(829\) | −2281.90 | −0.0956013 | −0.0478007 | − | 0.998857i | \(-0.515221\pi\) | ||||
−0.0478007 | + | 0.998857i | \(0.515221\pi\) | |||||||
\(830\) | 33999.6 | − | 19381.9i | 1.42186 | − | 0.810551i | ||||
\(831\) | −38275.4 | −1.59779 | ||||||||
\(832\) | 1156.73i | 0.0482001i | ||||||||
\(833\) | − | 15333.3i | − | 0.637775i | ||||||
\(834\) | 6988.31 | 0.290150 | ||||||||
\(835\) | −1101.87 | − | 1932.89i | −0.0456670 | − | 0.0801085i | ||||
\(836\) | 13546.9 | 0.560442 | ||||||||
\(837\) | − | 24368.5i | − | 1.00633i | ||||||
\(838\) | 49862.5i | 2.05546i | ||||||||
\(839\) | −19587.9 | −0.806019 | −0.403010 | − | 0.915196i | \(-0.632036\pi\) | ||||
−0.403010 | + | 0.915196i | \(0.632036\pi\) | |||||||
\(840\) | 11860.5 | + | 20805.6i | 0.487175 | + | 0.854598i | ||||
\(841\) | 1687.47 | 0.0691899 | ||||||||
\(842\) | 5855.76i | 0.239671i | ||||||||
\(843\) | − | 13889.2i | − | 0.567462i | ||||||
\(844\) | 9097.82 | 0.371043 | ||||||||
\(845\) | −21232.8 | + | 12104.1i | −0.864416 | + | 0.492773i | ||||
\(846\) | 40499.6 | 1.64587 | ||||||||
\(847\) | 18241.0i | 0.739987i | ||||||||
\(848\) | − | 41643.9i | − | 1.68639i | ||||||
\(849\) | 18110.5 | 0.732097 | ||||||||
\(850\) | −19004.8 | + | 32099.3i | −0.766892 | + | 1.29529i | ||||
\(851\) | 4302.22 | 0.173300 | ||||||||
\(852\) | 8661.52i | 0.348285i | ||||||||
\(853\) | 45899.7i | 1.84241i | 0.389078 | + | 0.921205i | \(0.372794\pi\) | ||||
−0.389078 | + | 0.921205i | \(0.627206\pi\) | |||||||
\(854\) | 4122.53 | 0.165187 | ||||||||
\(855\) | 56180.7 | − | 32026.6i | 2.24718 | − | 1.28104i | ||||
\(856\) | −30920.4 | −1.23463 | ||||||||
\(857\) | − | 6236.58i | − | 0.248585i | −0.992246 | − | 0.124293i | \(-0.960334\pi\) | ||
0.992246 | − | 0.124293i | \(-0.0396661\pi\) | |||||||
\(858\) | − | 4402.25i | − | 0.175164i | ||||||
\(859\) | −30799.6 | −1.22336 | −0.611681 | − | 0.791104i | \(-0.709506\pi\) | ||||
−0.611681 | + | 0.791104i | \(0.709506\pi\) | |||||||
\(860\) | −2334.98 | − | 4096.00i | −0.0925841 | − | 0.162410i | ||||
\(861\) | 22703.2 | 0.898632 | ||||||||
\(862\) | 21627.5i | 0.854565i | ||||||||
\(863\) | − | 36472.2i | − | 1.43862i | −0.694689 | − | 0.719310i | \(-0.744458\pi\) | ||
0.694689 | − | 0.719310i | \(-0.255542\pi\) | |||||||
\(864\) | −8654.61 | −0.340782 | ||||||||
\(865\) | −163.894 | − | 287.501i | −0.00644227 | − | 0.0113010i | ||||
\(866\) | 6238.34 | 0.244789 | ||||||||
\(867\) | 34095.6i | 1.33558i | ||||||||
\(868\) | 5552.85i | 0.217138i | ||||||||
\(869\) | −12573.3 | −0.490816 | ||||||||
\(870\) | −40251.0 | + | 22945.7i | −1.56855 | + | 0.894173i | ||||
\(871\) | 323.279 | 0.0125762 | ||||||||
\(872\) | − | 29714.4i | − | 1.15396i | ||||||
\(873\) | − | 17298.7i | − | 0.670643i | ||||||
\(874\) | 10390.7 | 0.402139 | ||||||||
\(875\) | −18853.6 | − | 310.095i | −0.728419 | − | 0.0119807i | ||||
\(876\) | 876.405 | 0.0338025 | ||||||||
\(877\) | − | 2516.40i | − | 0.0968903i | −0.998826 | − | 0.0484451i | \(-0.984573\pi\) | ||
0.998826 | − | 0.0484451i | \(-0.0154266\pi\) | |||||||
\(878\) | − | 22091.5i | − | 0.849147i | ||||||
\(879\) | −7735.88 | −0.296843 | ||||||||
\(880\) | −37843.3 | + | 21573.1i | −1.44965 | + | 0.826396i | ||||
\(881\) | −25947.3 | −0.992266 | −0.496133 | − | 0.868246i | \(-0.665247\pi\) | ||||
−0.496133 | + | 0.868246i | \(0.665247\pi\) | |||||||
\(882\) | 20223.5i | 0.772064i | ||||||||
\(883\) | − | 30869.7i | − | 1.17650i | −0.808680 | − | 0.588249i | \(-0.799818\pi\) | ||
0.808680 | − | 0.588249i | \(-0.200182\pi\) | |||||||
\(884\) | 572.167 | 0.0217693 | ||||||||
\(885\) | −24117.1 | − | 42305.9i | −0.916030 | − | 1.60689i | ||||
\(886\) | 756.975 | 0.0287033 | ||||||||
\(887\) | 13920.9i | 0.526965i | 0.964664 | + | 0.263483i | \(0.0848711\pi\) | ||||
−0.964664 | + | 0.263483i | \(0.915129\pi\) | |||||||
\(888\) | 29696.6i | 1.12224i | ||||||||
\(889\) | 14157.4 | 0.534110 | ||||||||
\(890\) | 7900.67 | + | 13859.3i | 0.297563 | + | 0.521982i | ||||
\(891\) | 10528.0 | 0.395850 | ||||||||
\(892\) | − | 779.791i | − | 0.0292705i | ||||||
\(893\) | − | 46484.4i | − | 1.74193i | ||||||
\(894\) | −72528.4 | −2.71332 | ||||||||
\(895\) | −3203.90 | + | 1826.43i | −0.119659 | + | 0.0682131i | ||||
\(896\) | −23462.2 | −0.874796 | ||||||||
\(897\) | − | 623.997i | − | 0.0232271i | ||||||
\(898\) | − | 39012.3i | − | 1.44973i | ||||||
\(899\) | 36645.6 | 1.35951 | ||||||||
\(900\) | 4632.21 | − | 7823.85i | 0.171563 | − | 0.289772i | ||||
\(901\) | 52740.7 | 1.95011 | ||||||||
\(902\) | 33329.7i | 1.23033i | ||||||||
\(903\) | − | 25701.2i | − | 0.947156i | ||||||
\(904\) | −18739.6 | −0.689457 | ||||||||
\(905\) | 34974.8 | − | 19937.9i | 1.28464 | − | 0.732328i | ||||
\(906\) | −52999.0 | −1.94346 | ||||||||
\(907\) | − | 16652.6i | − | 0.609637i | −0.952410 | − | 0.304818i | \(-0.901404\pi\) | ||
0.952410 | − | 0.304818i | \(-0.0985958\pi\) | |||||||
\(908\) | 1269.28i | 0.0463905i | ||||||||
\(909\) | −19420.9 | −0.708636 | ||||||||
\(910\) | 775.073 | + | 1359.62i | 0.0282345 | + | 0.0495287i | ||||
\(911\) | −3907.51 | −0.142109 | −0.0710547 | − | 0.997472i | \(-0.522636\pi\) | ||||
−0.0710547 | + | 0.997472i | \(0.522636\pi\) | |||||||
\(912\) | 88862.9i | 3.22647i | ||||||||
\(913\) | 57878.3i | 2.09802i | ||||||||
\(914\) | 14724.7 | 0.532879 | ||||||||
\(915\) | 4424.12 | + | 7760.74i | 0.159843 | + | 0.280396i | ||||
\(916\) | 1695.62 | 0.0611625 | ||||||||
\(917\) | − | 8745.71i | − | 0.314950i | ||||||
\(918\) | − | 32045.6i | − | 1.15214i | ||||||
\(919\) | 41052.1 | 1.47354 | 0.736770 | − | 0.676143i | \(-0.236350\pi\) | ||||
0.736770 | + | 0.676143i | \(0.236350\pi\) | |||||||
\(920\) | −4329.46 | + | 2468.07i | −0.155150 | + | 0.0884454i | ||||
\(921\) | −33785.1 | −1.20875 | ||||||||
\(922\) | − | 29933.4i | − | 1.06920i | ||||||
\(923\) | − | 1930.83i | − | 0.0688558i | ||||||
\(924\) | 10382.7 | 0.369662 | ||||||||
\(925\) | −20119.7 | − | 11912.1i | −0.715168 | − | 0.423425i | ||||
\(926\) | −50301.1 | −1.78509 | ||||||||
\(927\) | − | 68795.0i | − | 2.43746i | ||||||
\(928\) | − | 13014.9i | − | 0.460384i | ||||||
\(929\) | −53877.6 | −1.90276 | −0.951382 | − | 0.308014i | \(-0.900336\pi\) | ||||
−0.951382 | + | 0.308014i | \(0.900336\pi\) | |||||||
\(930\) | −56565.3 | + | 32245.9i | −1.99446 | + | 1.13697i | ||||
\(931\) | 23212.0 | 0.817123 | ||||||||
\(932\) | − | 1545.63i | − | 0.0543229i | ||||||
\(933\) | 8548.22i | 0.299953i | ||||||||
\(934\) | 58447.6 | 2.04761 | ||||||||
\(935\) | −27321.7 | − | 47927.4i | −0.955630 | − | 1.67636i | ||||
\(936\) | 2574.27 | 0.0898961 | ||||||||
\(937\) | − | 22558.8i | − | 0.786515i | −0.919428 | − | 0.393257i | \(-0.871348\pi\) | ||
0.919428 | − | 0.393257i | \(-0.128652\pi\) | |||||||
\(938\) | 4125.82i | 0.143617i | ||||||||
\(939\) | 87593.1 | 3.04419 | ||||||||
\(940\) | −3236.76 | − | 5677.89i | −0.112310 | − | 0.197013i | ||||
\(941\) | 54423.8 | 1.88540 | 0.942702 | − | 0.333637i | \(-0.108276\pi\) | ||||
0.942702 | + | 0.333637i | \(0.108276\pi\) | |||||||
\(942\) | − | 3523.91i | − | 0.121885i | ||||||
\(943\) | 4724.32i | 0.163144i | ||||||||
\(944\) | 39993.7 | 1.37890 | ||||||||
\(945\) | 14072.4 | − | 8022.18i | 0.484419 | − | 0.276150i | ||||
\(946\) | 37731.0 | 1.29677 | ||||||||
\(947\) | 20381.8i | 0.699387i | 0.936864 | + | 0.349693i | \(0.113714\pi\) | ||||
−0.936864 | + | 0.349693i | \(0.886286\pi\) | |||||||
\(948\) | 3606.29i | 0.123551i | ||||||||
\(949\) | −195.368 | −0.00668273 | ||||||||
\(950\) | −48592.8 | − | 28770.0i | −1.65954 | − | 0.982549i | ||||
\(951\) | 45936.2 | 1.56633 | ||||||||
\(952\) | − | 24909.6i | − | 0.848030i | ||||||
\(953\) | 28702.1i | 0.975605i | 0.872954 | + | 0.487803i | \(0.162201\pi\) | ||||
−0.872954 | + | 0.487803i | \(0.837799\pi\) | |||||||
\(954\) | −69561.2 | −2.36072 | ||||||||
\(955\) | −26868.9 | + | 15317.0i | −0.910425 | + | 0.519000i | ||||
\(956\) | 4347.59 | 0.147083 | ||||||||
\(957\) | − | 68520.2i | − | 2.31447i | ||||||
\(958\) | 37779.2i | 1.27410i | ||||||||
\(959\) | −2136.72 | −0.0719483 | ||||||||
\(960\) | −15842.7 | − | 27791.0i | −0.532625 | − | 0.934325i | ||||
\(961\) | 21707.6 | 0.728664 | ||||||||
\(962\) | 1940.64i | 0.0650402i | ||||||||
\(963\) | 63991.8i | 2.14134i | ||||||||
\(964\) | 2329.28 | 0.0778226 | ||||||||
\(965\) | −1896.61 | − | 3327.01i | −0.0632684 | − | 0.110985i | ||||
\(966\) | 7963.72 | 0.265247 | ||||||||
\(967\) | − | 5788.98i | − | 0.192514i | −0.995357 | − | 0.0962571i | \(-0.969313\pi\) | ||
0.995357 | − | 0.0962571i | \(-0.0306871\pi\) | |||||||
\(968\) | − | 26200.9i | − | 0.869969i | ||||||
\(969\) | −112542. | −3.73104 | ||||||||
\(970\) | −13123.3 | + | 7481.14i | −0.434397 | + | 0.247634i | ||||
\(971\) | −34807.9 | −1.15040 | −0.575200 | − | 0.818013i | \(-0.695076\pi\) | ||||
−0.575200 | + | 0.818013i | \(0.695076\pi\) | |||||||
\(972\) | − | 8277.72i | − | 0.273156i | ||||||
\(973\) | − | 3674.16i | − | 0.121057i | ||||||
\(974\) | −62110.8 | −2.04329 | ||||||||
\(975\) | −1727.74 | + | 2918.18i | −0.0567508 | + | 0.0958528i | ||||
\(976\) | −7336.58 | −0.240613 | ||||||||
\(977\) | 32169.4i | 1.05342i | 0.850045 | + | 0.526710i | \(0.176575\pi\) | ||||
−0.850045 | + | 0.526710i | \(0.823425\pi\) | |||||||
\(978\) | 79291.0i | 2.59248i | ||||||||
\(979\) | −23593.0 | −0.770209 | ||||||||
\(980\) | 2835.25 | − | 1616.28i | 0.0924172 | − | 0.0526837i | ||||
\(981\) | −61495.8 | −2.00144 | ||||||||
\(982\) | 3818.49i | 0.124086i | ||||||||
\(983\) | 30095.0i | 0.976481i | 0.872709 | + | 0.488240i | \(0.162361\pi\) | ||||
−0.872709 | + | 0.488240i | \(0.837639\pi\) | |||||||
\(984\) | −32610.2 | −1.05648 | ||||||||
\(985\) | 2159.46 | + | 3788.10i | 0.0698539 | + | 0.122537i | ||||
\(986\) | 48190.6 | 1.55649 | ||||||||
\(987\) | − | 35627.0i | − | 1.14896i | ||||||
\(988\) | 866.165i | 0.0278911i | ||||||||
\(989\) | 5348.18 | 0.171954 | ||||||||
\(990\) | 36035.3 | + | 63212.7i | 1.15684 | + | 2.02933i | ||||
\(991\) | 40627.1 | 1.30228 | 0.651141 | − | 0.758957i | \(-0.274291\pi\) | ||||
0.651141 | + | 0.758957i | \(0.274291\pi\) | |||||||
\(992\) | − | 18290.1i | − | 0.585394i | ||||||
\(993\) | 46811.9i | 1.49600i | ||||||||
\(994\) | 24642.0 | 0.786315 | ||||||||
\(995\) | 37484.4 | − | 21368.5i | 1.19431 | − | 0.680831i | ||||
\(996\) | 16600.7 | 0.528127 | ||||||||
\(997\) | − | 5694.87i | − | 0.180901i | −0.995901 | − | 0.0904505i | \(-0.971169\pi\) | ||
0.995901 | − | 0.0904505i | \(-0.0288307\pi\) | |||||||
\(998\) | 32721.4i | 1.03785i | ||||||||
\(999\) | 20086.0 | 0.636131 |
(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 | 115.4.b.a.24.9 | ✓ | 34 | |
5.2 | odd | 4 | 575.4.a.r.1.13 | 17 | |||
5.3 | odd | 4 | 575.4.a.q.1.5 | 17 | |||
5.4 | even | 2 | inner | 115.4.b.a.24.26 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.4.b.a.24.9 | ✓ | 34 | 1.1 | even | 1 | trivial | |
115.4.b.a.24.26 | yes | 34 | 5.4 | even | 2 | inner | |
575.4.a.q.1.5 | 17 | 5.3 | odd | 4 | |||
575.4.a.r.1.13 | 17 | 5.2 | odd | 4 |