Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(229,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.c (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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.11 | ||
Character | \(\chi\) | \(=\) | 230.229 |
Dual form | 230.3.c.a.229.13 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 5.56886i | 1.85629i | 0.372223 | + | 0.928143i | \(0.378596\pi\) | ||||
−0.372223 | + | 0.928143i | \(0.621404\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −0.637273 | + | 4.95922i | −0.127455 | + | 0.991844i | ||||
\(6\) | 7.87556 | 1.31259 | ||||||||
\(7\) | 10.0249 | 1.43213 | 0.716066 | − | 0.698033i | \(-0.245941\pi\) | ||||
0.716066 | + | 0.698033i | \(0.245941\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −22.0122 | −2.44580 | ||||||||
\(10\) | 7.01340 | + | 0.901240i | 0.701340 | + | 0.0901240i | ||||
\(11\) | 9.80810i | 0.891646i | 0.895121 | + | 0.445823i | \(0.147089\pi\) | ||||
−0.895121 | + | 0.445823i | \(0.852911\pi\) | |||||||
\(12\) | − | 11.1377i | − | 0.928143i | ||||||
\(13\) | − | 14.3185i | − | 1.10142i | −0.834696 | − | 0.550712i | \(-0.814356\pi\) | ||
0.834696 | − | 0.550712i | \(-0.185644\pi\) | |||||||
\(14\) | − | 14.1774i | − | 1.01267i | ||||||
\(15\) | −27.6172 | − | 3.54888i | −1.84115 | − | 0.236592i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −17.3824 | −1.02250 | −0.511248 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511248 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(18\) | 31.1300i | 1.72944i | ||||||||
\(19\) | 8.38799i | 0.441473i | 0.975333 | + | 0.220737i | \(0.0708461\pi\) | ||||
−0.975333 | + | 0.220737i | \(0.929154\pi\) | |||||||
\(20\) | 1.27455 | − | 9.91844i | 0.0637273 | − | 0.495922i | ||||
\(21\) | 55.8274i | 2.65845i | ||||||||
\(22\) | 13.8708 | 0.630489 | ||||||||
\(23\) | 14.5930 | + | 17.7777i | 0.634477 | + | 0.772942i | ||||
\(24\) | −15.7511 | −0.656296 | ||||||||
\(25\) | −24.1878 | − | 6.32076i | −0.967511 | − | 0.252830i | ||||
\(26\) | −20.2494 | −0.778824 | ||||||||
\(27\) | − | 72.4631i | − | 2.68382i | ||||||
\(28\) | −20.0498 | −0.716066 | ||||||||
\(29\) | −26.9909 | −0.930719 | −0.465360 | − | 0.885122i | \(-0.654075\pi\) | ||||
−0.465360 | + | 0.885122i | \(0.654075\pi\) | |||||||
\(30\) | −5.01888 | + | 39.0566i | −0.167296 | + | 1.30189i | ||||
\(31\) | 4.24200 | 0.136839 | 0.0684194 | − | 0.997657i | \(-0.478204\pi\) | ||||
0.0684194 | + | 0.997657i | \(0.478204\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −54.6200 | −1.65515 | ||||||||
\(34\) | 24.5825i | 0.723013i | ||||||||
\(35\) | −6.38862 | + | 49.7158i | −0.182532 | + | 1.42045i | ||||
\(36\) | 44.0244 | 1.22290 | ||||||||
\(37\) | 73.2769 | 1.98046 | 0.990229 | − | 0.139454i | \(-0.0445346\pi\) | ||||
0.990229 | + | 0.139454i | \(0.0445346\pi\) | |||||||
\(38\) | 11.8624 | 0.312169 | ||||||||
\(39\) | 79.7377 | 2.04456 | ||||||||
\(40\) | −14.0268 | − | 1.80248i | −0.350670 | − | 0.0450620i | ||||
\(41\) | −19.8591 | −0.484369 | −0.242184 | − | 0.970230i | \(-0.577864\pi\) | ||||
−0.242184 | + | 0.970230i | \(0.577864\pi\) | |||||||
\(42\) | 78.9519 | 1.87981 | ||||||||
\(43\) | −18.1666 | −0.422480 | −0.211240 | − | 0.977434i | \(-0.567750\pi\) | ||||
−0.211240 | + | 0.977434i | \(0.567750\pi\) | |||||||
\(44\) | − | 19.6162i | − | 0.445823i | ||||||
\(45\) | 14.0278 | − | 109.163i | 0.311729 | − | 2.42585i | ||||
\(46\) | 25.1414 | − | 20.6376i | 0.546553 | − | 0.448643i | ||||
\(47\) | 10.2217i | 0.217482i | 0.994070 | + | 0.108741i | \(0.0346820\pi\) | ||||
−0.994070 | + | 0.108741i | \(0.965318\pi\) | |||||||
\(48\) | 22.2754i | 0.464072i | ||||||||
\(49\) | 51.4991 | 1.05100 | ||||||||
\(50\) | −8.93890 | + | 34.2067i | −0.178778 | + | 0.684133i | ||||
\(51\) | − | 96.8003i | − | 1.89804i | ||||||
\(52\) | 28.6370i | 0.550712i | ||||||||
\(53\) | 90.6584 | 1.71053 | 0.855267 | − | 0.518187i | \(-0.173393\pi\) | ||||
0.855267 | + | 0.518187i | \(0.173393\pi\) | |||||||
\(54\) | −102.478 | −1.89775 | ||||||||
\(55\) | −48.6406 | − | 6.25044i | −0.884374 | − | 0.113644i | ||||
\(56\) | 28.3548i | 0.506335i | ||||||||
\(57\) | −46.7115 | −0.819501 | ||||||||
\(58\) | 38.1708i | 0.658118i | ||||||||
\(59\) | 92.9752 | 1.57585 | 0.787926 | − | 0.615770i | \(-0.211155\pi\) | ||||
0.787926 | + | 0.615770i | \(0.211155\pi\) | |||||||
\(60\) | 55.2344 | + | 7.09777i | 0.920574 | + | 0.118296i | ||||
\(61\) | 36.3479i | 0.595867i | 0.954587 | + | 0.297934i | \(0.0962974\pi\) | ||||
−0.954587 | + | 0.297934i | \(0.903703\pi\) | |||||||
\(62\) | − | 5.99909i | − | 0.0967596i | ||||||
\(63\) | −220.671 | −3.50271 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 71.0086 | + | 9.12480i | 1.09244 | + | 0.140381i | ||||
\(66\) | 77.2443i | 1.17037i | ||||||||
\(67\) | −41.4414 | −0.618528 | −0.309264 | − | 0.950976i | \(-0.600083\pi\) | ||||
−0.309264 | + | 0.950976i | \(0.600083\pi\) | |||||||
\(68\) | 34.7648 | 0.511248 | ||||||||
\(69\) | −99.0013 | + | 81.2661i | −1.43480 | + | 1.17777i | ||||
\(70\) | 70.3088 | + | 9.03487i | 1.00441 | + | 0.129070i | ||||
\(71\) | −22.7302 | −0.320143 | −0.160072 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160072 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(72\) | − | 62.2599i | − | 0.864721i | ||||||
\(73\) | 45.3166i | 0.620775i | 0.950610 | + | 0.310388i | \(0.100459\pi\) | ||||
−0.950610 | + | 0.310388i | \(0.899541\pi\) | |||||||
\(74\) | − | 103.629i | − | 1.40039i | ||||||
\(75\) | 35.1994 | − | 134.698i | 0.469326 | − | 1.79598i | ||||
\(76\) | − | 16.7760i | − | 0.220737i | ||||||
\(77\) | 98.3255i | 1.27695i | ||||||||
\(78\) | − | 112.766i | − | 1.44572i | ||||||
\(79\) | − | 65.6145i | − | 0.830563i | −0.909693 | − | 0.415281i | \(-0.863683\pi\) | ||
0.909693 | − | 0.415281i | \(-0.136317\pi\) | |||||||
\(80\) | −2.54909 | + | 19.8369i | −0.0318637 | + | 0.247961i | ||||
\(81\) | 205.427 | 2.53614 | ||||||||
\(82\) | 28.0850i | 0.342500i | ||||||||
\(83\) | −4.65260 | −0.0560554 | −0.0280277 | − | 0.999607i | \(-0.508923\pi\) | ||||
−0.0280277 | + | 0.999607i | \(0.508923\pi\) | |||||||
\(84\) | − | 111.655i | − | 1.32922i | ||||||
\(85\) | 11.0774 | − | 86.2033i | 0.130322 | − | 1.01416i | ||||
\(86\) | 25.6915i | 0.298739i | ||||||||
\(87\) | − | 150.308i | − | 1.72768i | ||||||
\(88\) | −27.7415 | −0.315244 | ||||||||
\(89\) | 121.117i | 1.36086i | 0.732812 | + | 0.680431i | \(0.238207\pi\) | ||||
−0.732812 | + | 0.680431i | \(0.761793\pi\) | |||||||
\(90\) | −154.380 | − | 19.8383i | −1.71534 | − | 0.220425i | ||||
\(91\) | − | 143.542i | − | 1.57738i | ||||||
\(92\) | −29.1859 | − | 35.5553i | −0.317238 | − | 0.386471i | ||||
\(93\) | 23.6231i | 0.254012i | ||||||||
\(94\) | 14.4556 | 0.153783 | ||||||||
\(95\) | −41.5979 | − | 5.34544i | −0.437873 | − | 0.0562678i | ||||
\(96\) | 31.5022 | 0.328148 | ||||||||
\(97\) | −99.8370 | −1.02925 | −0.514624 | − | 0.857416i | \(-0.672068\pi\) | ||||
−0.514624 | + | 0.857416i | \(0.672068\pi\) | |||||||
\(98\) | − | 72.8308i | − | 0.743171i | ||||||
\(99\) | − | 215.898i | − | 2.18079i | ||||||
\(100\) | 48.3755 | + | 12.6415i | 0.483755 | + | 0.126415i | ||||
\(101\) | 144.610 | 1.43178 | 0.715890 | − | 0.698213i | \(-0.246021\pi\) | ||||
0.715890 | + | 0.698213i | \(0.246021\pi\) | |||||||
\(102\) | −136.896 | −1.34212 | ||||||||
\(103\) | 113.571 | 1.10263 | 0.551315 | − | 0.834297i | \(-0.314126\pi\) | ||||
0.551315 | + | 0.834297i | \(0.314126\pi\) | |||||||
\(104\) | 40.4988 | 0.389412 | ||||||||
\(105\) | −276.860 | − | 35.5773i | −2.63677 | − | 0.338831i | ||||
\(106\) | − | 128.210i | − | 1.20953i | ||||||
\(107\) | 20.2694 | 0.189433 | 0.0947166 | − | 0.995504i | \(-0.469805\pi\) | ||||
0.0947166 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(108\) | 144.926i | 1.34191i | ||||||||
\(109\) | 54.8745i | 0.503436i | 0.967801 | + | 0.251718i | \(0.0809955\pi\) | ||||
−0.967801 | + | 0.251718i | \(0.919004\pi\) | |||||||
\(110\) | −8.83946 | + | 68.7881i | −0.0803587 | + | 0.625347i | ||||
\(111\) | 408.069i | 3.67630i | ||||||||
\(112\) | 40.0997 | 0.358033 | ||||||||
\(113\) | 154.079 | 1.36353 | 0.681765 | − | 0.731571i | \(-0.261213\pi\) | ||||
0.681765 | + | 0.731571i | \(0.261213\pi\) | |||||||
\(114\) | 66.0601i | 0.579475i | ||||||||
\(115\) | −97.4631 | + | 61.0405i | −0.847505 | + | 0.530787i | ||||
\(116\) | 53.9817 | 0.465360 | ||||||||
\(117\) | 315.182i | 2.69386i | ||||||||
\(118\) | − | 131.487i | − | 1.11430i | ||||||
\(119\) | −174.257 | −1.46435 | ||||||||
\(120\) | 10.0378 | − | 78.1133i | 0.0836480 | − | 0.650944i | ||||
\(121\) | 24.8011 | 0.204968 | ||||||||
\(122\) | 51.4037 | 0.421342 | ||||||||
\(123\) | − | 110.593i | − | 0.899127i | ||||||
\(124\) | −8.48400 | −0.0684194 | ||||||||
\(125\) | 46.7603 | − | 115.924i | 0.374082 | − | 0.927396i | ||||
\(126\) | 312.075i | 2.47679i | ||||||||
\(127\) | 50.5842i | 0.398301i | 0.979969 | + | 0.199150i | \(0.0638182\pi\) | ||||
−0.979969 | + | 0.199150i | \(0.936182\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 101.167i | − | 0.784244i | ||||||
\(130\) | 12.9044 | − | 100.421i | 0.0992647 | − | 0.772472i | ||||
\(131\) | −190.024 | −1.45056 | −0.725281 | − | 0.688453i | \(-0.758290\pi\) | ||||
−0.725281 | + | 0.688453i | \(0.758290\pi\) | |||||||
\(132\) | 109.240 | 0.827575 | ||||||||
\(133\) | 84.0890i | 0.632248i | ||||||||
\(134\) | 58.6070i | 0.437366i | ||||||||
\(135\) | 359.361 | + | 46.1788i | 2.66193 | + | 0.342065i | ||||
\(136\) | − | 49.1649i | − | 0.361507i | ||||||
\(137\) | −181.592 | −1.32549 | −0.662744 | − | 0.748846i | \(-0.730608\pi\) | ||||
−0.662744 | + | 0.748846i | \(0.730608\pi\) | |||||||
\(138\) | 114.928 | + | 140.009i | 0.832809 | + | 1.01456i | ||||
\(139\) | 85.0630 | 0.611964 | 0.305982 | − | 0.952037i | \(-0.401015\pi\) | ||||
0.305982 | + | 0.952037i | \(0.401015\pi\) | |||||||
\(140\) | 12.7772 | − | 99.4317i | 0.0912659 | − | 0.710226i | ||||
\(141\) | −56.9231 | −0.403710 | ||||||||
\(142\) | 32.1453i | 0.226375i | ||||||||
\(143\) | 140.437 | 0.982079 | ||||||||
\(144\) | −88.0488 | −0.611450 | ||||||||
\(145\) | 17.2006 | − | 133.854i | 0.118624 | − | 0.923129i | ||||
\(146\) | 64.0873 | 0.438954 | ||||||||
\(147\) | 286.791i | 1.95096i | ||||||||
\(148\) | −146.554 | −0.990229 | ||||||||
\(149\) | 100.742i | 0.676119i | 0.941125 | + | 0.338060i | \(0.109771\pi\) | ||||
−0.941125 | + | 0.338060i | \(0.890229\pi\) | |||||||
\(150\) | −190.492 | − | 49.7795i | −1.26995 | − | 0.331863i | ||||
\(151\) | 191.818 | 1.27032 | 0.635160 | − | 0.772381i | \(-0.280934\pi\) | ||||
0.635160 | + | 0.772381i | \(0.280934\pi\) | |||||||
\(152\) | −23.7248 | −0.156084 | ||||||||
\(153\) | 382.625 | 2.50082 | ||||||||
\(154\) | 139.053 | 0.902943 | ||||||||
\(155\) | −2.70331 | + | 21.0370i | −0.0174407 | + | 0.135723i | ||||
\(156\) | −159.475 | −1.02228 | ||||||||
\(157\) | −45.4351 | −0.289395 | −0.144698 | − | 0.989476i | \(-0.546221\pi\) | ||||
−0.144698 | + | 0.989476i | \(0.546221\pi\) | |||||||
\(158\) | −92.7929 | −0.587297 | ||||||||
\(159\) | 504.864i | 3.17524i | ||||||||
\(160\) | 28.0536 | + | 3.60496i | 0.175335 | + | 0.0225310i | ||||
\(161\) | 146.293 | + | 178.220i | 0.908654 | + | 1.10696i | ||||
\(162\) | − | 290.518i | − | 1.79332i | ||||||
\(163\) | − | 182.925i | − | 1.12224i | −0.827734 | − | 0.561121i | \(-0.810370\pi\) | ||
0.827734 | − | 0.561121i | \(-0.189630\pi\) | |||||||
\(164\) | 39.7182 | 0.242184 | ||||||||
\(165\) | 34.8078 | − | 270.872i | 0.210957 | − | 1.64165i | ||||
\(166\) | 6.57976i | 0.0396371i | ||||||||
\(167\) | 255.235i | 1.52835i | 0.645007 | + | 0.764177i | \(0.276855\pi\) | ||||
−0.645007 | + | 0.764177i | \(0.723145\pi\) | |||||||
\(168\) | −157.904 | −0.939903 | ||||||||
\(169\) | −36.0195 | −0.213133 | ||||||||
\(170\) | −121.910 | − | 15.6657i | −0.717117 | − | 0.0921514i | ||||
\(171\) | − | 184.638i | − | 1.07976i | ||||||
\(172\) | 36.3333 | 0.211240 | ||||||||
\(173\) | − | 168.860i | − | 0.976072i | −0.872823 | − | 0.488036i | \(-0.837713\pi\) | ||
0.872823 | − | 0.488036i | \(-0.162287\pi\) | |||||||
\(174\) | −212.568 | −1.22166 | ||||||||
\(175\) | −242.481 | − | 63.3651i | −1.38560 | − | 0.362086i | ||||
\(176\) | 39.2324i | 0.222911i | ||||||||
\(177\) | 517.766i | 2.92523i | ||||||||
\(178\) | 171.285 | 0.962274 | ||||||||
\(179\) | −7.59730 | −0.0424430 | −0.0212215 | − | 0.999775i | \(-0.506756\pi\) | ||||
−0.0212215 | + | 0.999775i | \(0.506756\pi\) | |||||||
\(180\) | −28.0556 | + | 218.327i | −0.155864 | + | 1.21293i | ||||
\(181\) | 40.4613i | 0.223543i | 0.993734 | + | 0.111772i | \(0.0356525\pi\) | ||||
−0.993734 | + | 0.111772i | \(0.964348\pi\) | |||||||
\(182\) | −202.999 | −1.11538 | ||||||||
\(183\) | −202.416 | −1.10610 | ||||||||
\(184\) | −50.2828 | + | 41.2751i | −0.273276 | + | 0.224321i | ||||
\(185\) | −46.6974 | + | 363.397i | −0.252418 | + | 1.96431i | ||||
\(186\) | 33.4081 | 0.179613 | ||||||||
\(187\) | − | 170.489i | − | 0.911704i | ||||||
\(188\) | − | 20.4433i | − | 0.108741i | ||||||
\(189\) | − | 726.437i | − | 3.84358i | ||||||
\(190\) | −7.55960 | + | 58.8283i | −0.0397874 | + | 0.309623i | ||||
\(191\) | 48.7133i | 0.255043i | 0.991836 | + | 0.127522i | \(0.0407022\pi\) | ||||
−0.991836 | + | 0.127522i | \(0.959298\pi\) | |||||||
\(192\) | − | 44.5509i | − | 0.232036i | ||||||
\(193\) | − | 189.753i | − | 0.983178i | −0.870827 | − | 0.491589i | \(-0.836416\pi\) | ||
0.870827 | − | 0.491589i | \(-0.163584\pi\) | |||||||
\(194\) | 141.191i | 0.727788i | ||||||||
\(195\) | −50.8147 | + | 395.437i | −0.260588 | + | 2.02788i | ||||
\(196\) | −102.998 | −0.525501 | ||||||||
\(197\) | − | 338.960i | − | 1.72061i | −0.509779 | − | 0.860305i | \(-0.670273\pi\) | ||
0.509779 | − | 0.860305i | \(-0.329727\pi\) | |||||||
\(198\) | −305.326 | −1.54205 | ||||||||
\(199\) | − | 42.5881i | − | 0.214011i | −0.994258 | − | 0.107005i | \(-0.965874\pi\) | ||
0.994258 | − | 0.107005i | \(-0.0341262\pi\) | |||||||
\(200\) | 17.8778 | − | 68.4133i | 0.0893890 | − | 0.342067i | ||||
\(201\) | − | 230.781i | − | 1.14817i | ||||||
\(202\) | − | 204.509i | − | 1.01242i | ||||||
\(203\) | −270.581 | −1.33291 | ||||||||
\(204\) | 193.601i | 0.949022i | ||||||||
\(205\) | 12.6557 | − | 98.4857i | 0.0617350 | − | 0.480418i | ||||
\(206\) | − | 160.613i | − | 0.779677i | ||||||
\(207\) | −321.223 | − | 391.326i | −1.55180 | − | 1.89046i | ||||
\(208\) | − | 57.2740i | − | 0.275356i | ||||||
\(209\) | −82.2703 | −0.393638 | ||||||||
\(210\) | −50.3139 | + | 391.540i | −0.239590 | + | 1.86448i | ||||
\(211\) | 33.7084 | 0.159755 | 0.0798777 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798777 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(212\) | −181.317 | −0.855267 | ||||||||
\(213\) | − | 126.581i | − | 0.594278i | ||||||
\(214\) | − | 28.6652i | − | 0.133950i | ||||||
\(215\) | 11.5771 | − | 90.0924i | 0.0538470 | − | 0.419034i | ||||
\(216\) | 204.957 | 0.948873 | ||||||||
\(217\) | 42.5257 | 0.195971 | ||||||||
\(218\) | 77.6043 | 0.355983 | ||||||||
\(219\) | −252.362 | −1.15234 | ||||||||
\(220\) | 97.2811 | + | 12.5009i | 0.442187 | + | 0.0568222i | ||||
\(221\) | 248.890i | 1.12620i | ||||||||
\(222\) | 577.097 | 2.59953 | ||||||||
\(223\) | − | 355.037i | − | 1.59209i | −0.605236 | − | 0.796046i | \(-0.706921\pi\) | ||
0.605236 | − | 0.796046i | \(-0.293079\pi\) | |||||||
\(224\) | − | 56.7095i | − | 0.253168i | ||||||
\(225\) | 532.426 | + | 139.134i | 2.36634 | + | 0.618372i | ||||
\(226\) | − | 217.900i | − | 0.964161i | ||||||
\(227\) | 280.641 | 1.23630 | 0.618151 | − | 0.786059i | \(-0.287882\pi\) | ||||
0.618151 | + | 0.786059i | \(0.287882\pi\) | |||||||
\(228\) | 93.4231 | 0.409750 | ||||||||
\(229\) | − | 294.263i | − | 1.28499i | −0.766290 | − | 0.642495i | \(-0.777899\pi\) | ||
0.766290 | − | 0.642495i | \(-0.222101\pi\) | |||||||
\(230\) | 86.3243 | + | 137.834i | 0.375323 | + | 0.599277i | ||||
\(231\) | −547.561 | −2.37039 | ||||||||
\(232\) | − | 76.3417i | − | 0.329059i | ||||||
\(233\) | 73.8157i | 0.316805i | 0.987375 | + | 0.158403i | \(0.0506344\pi\) | ||||
−0.987375 | + | 0.158403i | \(0.949366\pi\) | |||||||
\(234\) | 445.734 | 1.90485 | ||||||||
\(235\) | −50.6915 | − | 6.51400i | −0.215709 | − | 0.0277191i | ||||
\(236\) | −185.950 | −0.787926 | ||||||||
\(237\) | 365.398 | 1.54176 | ||||||||
\(238\) | 246.437i | 1.03545i | ||||||||
\(239\) | −371.921 | −1.55616 | −0.778078 | − | 0.628168i | \(-0.783805\pi\) | ||||
−0.778078 | + | 0.628168i | \(0.783805\pi\) | |||||||
\(240\) | −110.469 | − | 14.1955i | −0.460287 | − | 0.0591481i | ||||
\(241\) | 193.519i | 0.802983i | 0.915863 | + | 0.401492i | \(0.131508\pi\) | ||||
−0.915863 | + | 0.401492i | \(0.868492\pi\) | |||||||
\(242\) | − | 35.0741i | − | 0.144934i | ||||||
\(243\) | 491.827i | 2.02398i | ||||||||
\(244\) | − | 72.6958i | − | 0.297934i | ||||||
\(245\) | −32.8190 | + | 255.396i | −0.133955 | + | 1.04243i | ||||
\(246\) | −156.402 | −0.635779 | ||||||||
\(247\) | 120.103 | 0.486249 | ||||||||
\(248\) | 11.9982i | 0.0483798i | ||||||||
\(249\) | − | 25.9097i | − | 0.104055i | ||||||
\(250\) | −163.942 | − | 66.1290i | −0.655768 | − | 0.264516i | ||||
\(251\) | 7.30977i | 0.0291226i | 0.999894 | + | 0.0145613i | \(0.00463517\pi\) | ||||
−0.999894 | + | 0.0145613i | \(0.995365\pi\) | |||||||
\(252\) | 441.341 | 1.75135 | ||||||||
\(253\) | −174.365 | + | 143.129i | −0.689191 | + | 0.565728i | ||||
\(254\) | 71.5368 | 0.281641 | ||||||||
\(255\) | 480.054 | + | 61.6882i | 1.88256 | + | 0.241915i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 34.2768i | − | 0.133373i | −0.997774 | − | 0.0666864i | \(-0.978757\pi\) | ||
0.997774 | − | 0.0666864i | \(-0.0212427\pi\) | |||||||
\(258\) | −143.072 | −0.554544 | ||||||||
\(259\) | 734.596 | 2.83628 | ||||||||
\(260\) | −142.017 | − | 18.2496i | −0.546220 | − | 0.0701907i | ||||
\(261\) | 594.128 | 2.27635 | ||||||||
\(262\) | 268.734i | 1.02570i | ||||||||
\(263\) | 209.565 | 0.796826 | 0.398413 | − | 0.917206i | \(-0.369561\pi\) | ||||
0.398413 | + | 0.917206i | \(0.369561\pi\) | |||||||
\(264\) | − | 154.489i | − | 0.585184i | ||||||
\(265\) | −57.7741 | + | 449.595i | −0.218016 | + | 1.69658i | ||||
\(266\) | 118.920 | 0.447067 | ||||||||
\(267\) | −674.482 | −2.52615 | ||||||||
\(268\) | 82.8828 | 0.309264 | ||||||||
\(269\) | −369.879 | −1.37501 | −0.687507 | − | 0.726178i | \(-0.741295\pi\) | ||||
−0.687507 | + | 0.726178i | \(0.741295\pi\) | |||||||
\(270\) | 65.3067 | − | 508.213i | 0.241877 | − | 1.88227i | ||||
\(271\) | −313.530 | −1.15694 | −0.578470 | − | 0.815704i | \(-0.696350\pi\) | ||||
−0.578470 | + | 0.815704i | \(0.696350\pi\) | |||||||
\(272\) | −69.5297 | −0.255624 | ||||||||
\(273\) | 799.365 | 2.92808 | ||||||||
\(274\) | 256.810i | 0.937262i | ||||||||
\(275\) | 61.9946 | − | 237.236i | 0.225435 | − | 0.862677i | ||||
\(276\) | 198.003 | − | 162.532i | 0.717401 | − | 0.588885i | ||||
\(277\) | − | 296.723i | − | 1.07120i | −0.844472 | − | 0.535600i | \(-0.820085\pi\) | ||
0.844472 | − | 0.535600i | \(-0.179915\pi\) | |||||||
\(278\) | − | 120.297i | − | 0.432724i | ||||||
\(279\) | −93.3757 | −0.334680 | ||||||||
\(280\) | −140.618 | − | 18.0697i | −0.502206 | − | 0.0645348i | ||||
\(281\) | − | 352.294i | − | 1.25372i | −0.779134 | − | 0.626858i | \(-0.784341\pi\) | ||
0.779134 | − | 0.626858i | \(-0.215659\pi\) | |||||||
\(282\) | 80.5014i | 0.285466i | ||||||||
\(283\) | 71.8786 | 0.253988 | 0.126994 | − | 0.991903i | \(-0.459467\pi\) | ||||
0.126994 | + | 0.991903i | \(0.459467\pi\) | |||||||
\(284\) | 45.4603 | 0.160072 | ||||||||
\(285\) | 29.7680 | − | 231.653i | 0.104449 | − | 0.812817i | ||||
\(286\) | − | 198.608i | − | 0.694435i | ||||||
\(287\) | −199.086 | −0.693680 | ||||||||
\(288\) | 124.520i | 0.432360i | ||||||||
\(289\) | 13.1486 | 0.0454967 | ||||||||
\(290\) | −189.298 | − | 24.3253i | −0.652751 | − | 0.0838802i | ||||
\(291\) | − | 555.978i | − | 1.91058i | ||||||
\(292\) | − | 90.6332i | − | 0.310388i | ||||||
\(293\) | −302.565 | −1.03264 | −0.516322 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516322 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(294\) | 405.584 | 1.37954 | ||||||||
\(295\) | −59.2506 | + | 461.085i | −0.200850 | + | 1.56300i | ||||
\(296\) | 207.258i | 0.700197i | ||||||||
\(297\) | 710.726 | 2.39302 | ||||||||
\(298\) | 142.470 | 0.478088 | ||||||||
\(299\) | 254.550 | − | 208.949i | 0.851336 | − | 0.698827i | ||||
\(300\) | −70.3988 | + | 269.397i | −0.234663 | + | 0.897989i | ||||
\(301\) | −182.119 | −0.605047 | ||||||||
\(302\) | − | 271.272i | − | 0.898251i | ||||||
\(303\) | 805.311i | 2.65779i | ||||||||
\(304\) | 33.5520i | 0.110368i | ||||||||
\(305\) | −180.257 | − | 23.1635i | −0.591008 | − | 0.0759460i | ||||
\(306\) | − | 541.114i | − | 1.76835i | ||||||
\(307\) | − | 17.8780i | − | 0.0582345i | −0.999576 | − | 0.0291173i | \(-0.990730\pi\) | ||
0.999576 | − | 0.0291173i | \(-0.00926962\pi\) | |||||||
\(308\) | − | 196.651i | − | 0.638477i | ||||||
\(309\) | 632.460i | 2.04680i | ||||||||
\(310\) | 29.7508 | + | 3.82306i | 0.0959704 | + | 0.0123325i | ||||
\(311\) | −135.270 | −0.434951 | −0.217475 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217475 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(312\) | 225.532i | 0.722860i | ||||||||
\(313\) | −127.874 | −0.408544 | −0.204272 | − | 0.978914i | \(-0.565483\pi\) | ||||
−0.204272 | + | 0.978914i | \(0.565483\pi\) | |||||||
\(314\) | 64.2549i | 0.204633i | ||||||||
\(315\) | 140.627 | − | 1094.35i | 0.446436 | − | 3.47414i | ||||
\(316\) | 131.229i | 0.415281i | ||||||||
\(317\) | − | 116.383i | − | 0.367138i | −0.983007 | − | 0.183569i | \(-0.941235\pi\) | ||
0.983007 | − | 0.183569i | \(-0.0587652\pi\) | |||||||
\(318\) | 713.985 | 2.24524 | ||||||||
\(319\) | − | 264.729i | − | 0.829872i | ||||||
\(320\) | 5.09819 | − | 39.6738i | 0.0159318 | − | 0.123981i | ||||
\(321\) | 112.877i | 0.351642i | ||||||||
\(322\) | 252.041 | − | 206.890i | 0.782736 | − | 0.642516i | ||||
\(323\) | − | 145.804i | − | 0.451404i | ||||||
\(324\) | −410.854 | −1.26807 | ||||||||
\(325\) | −90.5038 | + | 346.333i | −0.278473 | + | 1.06564i | ||||
\(326\) | −258.696 | −0.793545 | ||||||||
\(327\) | −305.589 | −0.934522 | ||||||||
\(328\) | − | 56.1701i | − | 0.171250i | ||||||
\(329\) | 102.472i | 0.311464i | ||||||||
\(330\) | −383.072 | − | 49.2257i | −1.16082 | − | 0.149169i | ||||
\(331\) | 204.670 | 0.618337 | 0.309169 | − | 0.951007i | \(-0.399949\pi\) | ||||
0.309169 | + | 0.951007i | \(0.399949\pi\) | |||||||
\(332\) | 9.30519 | 0.0280277 | ||||||||
\(333\) | −1612.99 | −4.84380 | ||||||||
\(334\) | 360.957 | 1.08071 | ||||||||
\(335\) | 26.4095 | − | 205.517i | 0.0788343 | − | 0.613484i | ||||
\(336\) | 223.310i | 0.664612i | ||||||||
\(337\) | −470.134 | −1.39506 | −0.697528 | − | 0.716557i | \(-0.745717\pi\) | ||||
−0.697528 | + | 0.716557i | \(0.745717\pi\) | |||||||
\(338\) | 50.9393i | 0.150708i | ||||||||
\(339\) | 858.044i | 2.53110i | ||||||||
\(340\) | −22.1547 | + | 172.407i | −0.0651609 | + | 0.507078i | ||||
\(341\) | 41.6060i | 0.122012i | ||||||||
\(342\) | −261.118 | −0.763502 | ||||||||
\(343\) | 25.0535 | 0.0730422 | ||||||||
\(344\) | − | 51.3830i | − | 0.149369i | ||||||
\(345\) | −339.926 | − | 542.758i | −0.985293 | − | 1.57321i | ||||
\(346\) | −238.805 | −0.690187 | ||||||||
\(347\) | 157.548i | 0.454030i | 0.973891 | + | 0.227015i | \(0.0728966\pi\) | ||||
−0.973891 | + | 0.227015i | \(0.927103\pi\) | |||||||
\(348\) | 300.617i | 0.863841i | ||||||||
\(349\) | 240.406 | 0.688844 | 0.344422 | − | 0.938815i | \(-0.388075\pi\) | ||||
0.344422 | + | 0.938815i | \(0.388075\pi\) | |||||||
\(350\) | −89.6118 | + | 342.919i | −0.256034 | + | 0.979769i | ||||
\(351\) | −1037.56 | −2.95602 | ||||||||
\(352\) | 55.4830 | 0.157622 | ||||||||
\(353\) | − | 155.151i | − | 0.439520i | −0.975554 | − | 0.219760i | \(-0.929473\pi\) | ||
0.975554 | − | 0.219760i | \(-0.0705274\pi\) | |||||||
\(354\) | 732.232 | 2.06845 | ||||||||
\(355\) | 14.4853 | − | 112.724i | 0.0408037 | − | 0.317532i | ||||
\(356\) | − | 242.233i | − | 0.680431i | ||||||
\(357\) | − | 970.415i | − | 2.71825i | ||||||
\(358\) | 10.7442i | 0.0300117i | ||||||||
\(359\) | − | 435.157i | − | 1.21214i | −0.795413 | − | 0.606068i | \(-0.792746\pi\) | ||
0.795413 | − | 0.606068i | \(-0.207254\pi\) | |||||||
\(360\) | 308.761 | + | 39.6766i | 0.857669 | + | 0.110213i | ||||
\(361\) | 290.642 | 0.805101 | ||||||||
\(362\) | 57.2209 | 0.158069 | ||||||||
\(363\) | 138.114i | 0.380479i | ||||||||
\(364\) | 287.084i | 0.788692i | ||||||||
\(365\) | −224.735 | − | 28.8790i | −0.615712 | − | 0.0791207i | ||||
\(366\) | 286.260i | 0.782131i | ||||||||
\(367\) | 176.265 | 0.480287 | 0.240144 | − | 0.970737i | \(-0.422805\pi\) | ||||
0.240144 | + | 0.970737i | \(0.422805\pi\) | |||||||
\(368\) | 58.3718 | + | 71.1107i | 0.158619 | + | 0.193236i | ||||
\(369\) | 437.143 | 1.18467 | ||||||||
\(370\) | 513.920 | + | 66.0401i | 1.38897 | + | 0.178487i | ||||
\(371\) | 908.843 | 2.44971 | ||||||||
\(372\) | − | 47.2462i | − | 0.127006i | ||||||
\(373\) | −157.008 | −0.420932 | −0.210466 | − | 0.977601i | \(-0.567498\pi\) | ||||
−0.210466 | + | 0.977601i | \(0.567498\pi\) | |||||||
\(374\) | −241.107 | −0.644672 | ||||||||
\(375\) | 645.567 | + | 260.401i | 1.72151 | + | 0.694404i | ||||
\(376\) | −28.9113 | −0.0768916 | ||||||||
\(377\) | 386.469i | 1.02512i | ||||||||
\(378\) | −1027.34 | −2.71782 | ||||||||
\(379\) | − | 142.008i | − | 0.374692i | −0.982294 | − | 0.187346i | \(-0.940011\pi\) | ||
0.982294 | − | 0.187346i | \(-0.0599885\pi\) | |||||||
\(380\) | 83.1958 | + | 10.6909i | 0.218936 | + | 0.0281339i | ||||
\(381\) | −281.696 | −0.739360 | ||||||||
\(382\) | 68.8909 | 0.180343 | ||||||||
\(383\) | 37.1634 | 0.0970324 | 0.0485162 | − | 0.998822i | \(-0.484551\pi\) | ||||
0.0485162 | + | 0.998822i | \(0.484551\pi\) | |||||||
\(384\) | −63.0045 | −0.164074 | ||||||||
\(385\) | −487.618 | − | 62.6602i | −1.26654 | − | 0.162754i | ||||
\(386\) | −268.352 | −0.695212 | ||||||||
\(387\) | 399.888 | 1.03330 | ||||||||
\(388\) | 199.674 | 0.514624 | ||||||||
\(389\) | − | 484.710i | − | 1.24604i | −0.782206 | − | 0.623020i | \(-0.785906\pi\) | ||
0.782206 | − | 0.623020i | \(-0.214094\pi\) | |||||||
\(390\) | 559.233 | + | 71.8629i | 1.43393 | + | 0.184264i | ||||
\(391\) | −253.661 | − | 309.019i | −0.648749 | − | 0.790330i | ||||
\(392\) | 145.662i | 0.371585i | ||||||||
\(393\) | − | 1058.21i | − | 2.69266i | ||||||
\(394\) | −479.362 | −1.21666 | ||||||||
\(395\) | 325.397 | + | 41.8143i | 0.823789 | + | 0.105859i | ||||
\(396\) | 431.796i | 1.09039i | ||||||||
\(397\) | 468.421i | 1.17990i | 0.807439 | + | 0.589951i | \(0.200853\pi\) | ||||
−0.807439 | + | 0.589951i | \(0.799147\pi\) | |||||||
\(398\) | −60.2287 | −0.151328 | ||||||||
\(399\) | −468.280 | −1.17363 | ||||||||
\(400\) | −96.7511 | − | 25.2830i | −0.241878 | − | 0.0632076i | ||||
\(401\) | 557.589i | 1.39050i | 0.718770 | + | 0.695248i | \(0.244705\pi\) | ||||
−0.718770 | + | 0.695248i | \(0.755295\pi\) | |||||||
\(402\) | −326.374 | −0.811876 | ||||||||
\(403\) | − | 60.7391i | − | 0.150717i | ||||||
\(404\) | −289.219 | −0.715890 | ||||||||
\(405\) | −130.913 | + | 1018.76i | −0.323242 | + | 2.51545i | ||||
\(406\) | 382.660i | 0.942512i | ||||||||
\(407\) | 718.708i | 1.76587i | ||||||||
\(408\) | 273.792 | 0.671060 | ||||||||
\(409\) | −295.128 | −0.721585 | −0.360793 | − | 0.932646i | \(-0.617494\pi\) | ||||
−0.360793 | + | 0.932646i | \(0.617494\pi\) | |||||||
\(410\) | −139.280 | − | 17.8978i | −0.339707 | − | 0.0436533i | ||||
\(411\) | − | 1011.26i | − | 2.46049i | ||||||
\(412\) | −227.142 | −0.551315 | ||||||||
\(413\) | 932.070 | 2.25683 | ||||||||
\(414\) | −553.418 | + | 454.278i | −1.33676 | + | 1.09729i | ||||
\(415\) | 2.96497 | − | 23.0733i | 0.00714452 | − | 0.0555982i | ||||
\(416\) | −80.9977 | −0.194706 | ||||||||
\(417\) | 473.704i | 1.13598i | ||||||||
\(418\) | 116.348i | 0.278344i | ||||||||
\(419\) | 148.452i | 0.354300i | 0.984184 | + | 0.177150i | \(0.0566878\pi\) | ||||
−0.984184 | + | 0.177150i | \(0.943312\pi\) | |||||||
\(420\) | 553.721 | + | 71.1546i | 1.31838 | + | 0.169416i | ||||
\(421\) | 384.346i | 0.912937i | 0.889740 | + | 0.456468i | \(0.150886\pi\) | ||||
−0.889740 | + | 0.456468i | \(0.849114\pi\) | |||||||
\(422\) | − | 47.6708i | − | 0.112964i | ||||||
\(423\) | − | 225.002i | − | 0.531918i | ||||||
\(424\) | 256.421i | 0.604765i | ||||||||
\(425\) | 420.442 | + | 109.870i | 0.989275 | + | 0.258518i | ||||
\(426\) | −179.013 | −0.420218 | ||||||||
\(427\) | 364.385i | 0.853361i | ||||||||
\(428\) | −40.5387 | −0.0947166 | ||||||||
\(429\) | 782.076i | 1.82302i | ||||||||
\(430\) | −127.410 | − | 16.3725i | −0.296302 | − | 0.0380756i | ||||
\(431\) | − | 138.478i | − | 0.321295i | −0.987012 | − | 0.160647i | \(-0.948642\pi\) | ||
0.987012 | − | 0.160647i | \(-0.0513582\pi\) | |||||||
\(432\) | − | 289.852i | − | 0.670955i | ||||||
\(433\) | 720.106 | 1.66306 | 0.831532 | − | 0.555477i | \(-0.187464\pi\) | ||||
0.831532 | + | 0.555477i | \(0.187464\pi\) | |||||||
\(434\) | − | 60.1405i | − | 0.138572i | ||||||
\(435\) | 745.412 | + | 95.7875i | 1.71359 | + | 0.220201i | ||||
\(436\) | − | 109.749i | − | 0.251718i | ||||||
\(437\) | −149.119 | + | 122.406i | −0.341233 | + | 0.280104i | ||||
\(438\) | 356.893i | 0.814825i | ||||||||
\(439\) | 386.990 | 0.881525 | 0.440763 | − | 0.897624i | \(-0.354708\pi\) | ||||
0.440763 | + | 0.897624i | \(0.354708\pi\) | |||||||
\(440\) | 17.6789 | − | 137.576i | 0.0401794 | − | 0.312673i | ||||
\(441\) | −1133.61 | −2.57054 | ||||||||
\(442\) | 351.984 | 0.796344 | ||||||||
\(443\) | − | 320.366i | − | 0.723174i | −0.932338 | − | 0.361587i | \(-0.882235\pi\) | ||
0.932338 | − | 0.361587i | \(-0.117765\pi\) | |||||||
\(444\) | − | 816.138i | − | 1.83815i | ||||||
\(445\) | −600.644 | − | 77.1844i | −1.34976 | − | 0.173448i | ||||
\(446\) | −502.098 | −1.12578 | ||||||||
\(447\) | −561.017 | −1.25507 | ||||||||
\(448\) | −80.1994 | −0.179017 | ||||||||
\(449\) | −408.120 | −0.908954 | −0.454477 | − | 0.890759i | \(-0.650174\pi\) | ||||
−0.454477 | + | 0.890759i | \(0.650174\pi\) | |||||||
\(450\) | 196.765 | − | 752.964i | 0.437255 | − | 1.67325i | ||||
\(451\) | − | 194.780i | − | 0.431885i | ||||||
\(452\) | −308.158 | −0.681765 | ||||||||
\(453\) | 1068.21i | 2.35808i | ||||||||
\(454\) | − | 396.886i | − | 0.874198i | ||||||
\(455\) | 711.856 | + | 91.4754i | 1.56452 | + | 0.201045i | ||||
\(456\) | − | 132.120i | − | 0.289737i | ||||||
\(457\) | 628.660 | 1.37562 | 0.687812 | − | 0.725889i | \(-0.258571\pi\) | ||||
0.687812 | + | 0.725889i | \(0.258571\pi\) | |||||||
\(458\) | −416.150 | −0.908625 | ||||||||
\(459\) | 1259.58i | 2.74419i | ||||||||
\(460\) | 194.926 | − | 122.081i | 0.423753 | − | 0.265393i | ||||
\(461\) | 468.319 | 1.01588 | 0.507938 | − | 0.861394i | \(-0.330408\pi\) | ||||
0.507938 | + | 0.861394i | \(0.330408\pi\) | |||||||
\(462\) | 774.368i | 1.67612i | ||||||||
\(463\) | − | 489.151i | − | 1.05648i | −0.849095 | − | 0.528240i | \(-0.822852\pi\) | ||
0.849095 | − | 0.528240i | \(-0.177148\pi\) | |||||||
\(464\) | −107.963 | −0.232680 | ||||||||
\(465\) | −117.152 | − | 15.0544i | −0.251940 | − | 0.0323750i | ||||
\(466\) | 104.391 | 0.224015 | ||||||||
\(467\) | 638.769 | 1.36781 | 0.683907 | − | 0.729569i | \(-0.260279\pi\) | ||||
0.683907 | + | 0.729569i | \(0.260279\pi\) | |||||||
\(468\) | − | 630.363i | − | 1.34693i | ||||||
\(469\) | −415.447 | −0.885814 | ||||||||
\(470\) | −9.21218 | + | 71.6887i | −0.0196004 | + | 0.152529i | ||||
\(471\) | − | 253.022i | − | 0.537201i | ||||||
\(472\) | 262.974i | 0.557148i | ||||||||
\(473\) | − | 178.180i | − | 0.376703i | ||||||
\(474\) | − | 516.750i | − | 1.09019i | ||||||
\(475\) | 53.0185 | − | 202.887i | 0.111618 | − | 0.427130i | ||||
\(476\) | 348.515 | 0.732174 | ||||||||
\(477\) | −1995.59 | −4.18363 | ||||||||
\(478\) | 525.976i | 1.10037i | ||||||||
\(479\) | − | 780.804i | − | 1.63007i | −0.579411 | − | 0.815035i | \(-0.696717\pi\) | ||
0.579411 | − | 0.815035i | \(-0.303283\pi\) | |||||||
\(480\) | −20.0755 | + | 156.227i | −0.0418240 | + | 0.325472i | ||||
\(481\) | − | 1049.22i | − | 2.18132i | ||||||
\(482\) | 273.677 | 0.567795 | ||||||||
\(483\) | −992.481 | + | 814.687i | −2.05483 | + | 1.68672i | ||||
\(484\) | −49.6022 | −0.102484 | ||||||||
\(485\) | 63.6234 | − | 495.114i | 0.131182 | − | 1.02085i | ||||
\(486\) | 695.548 | 1.43117 | ||||||||
\(487\) | − | 308.473i | − | 0.633414i | −0.948523 | − | 0.316707i | \(-0.897423\pi\) | ||
0.948523 | − | 0.316707i | \(-0.102577\pi\) | |||||||
\(488\) | −102.807 | −0.210671 | ||||||||
\(489\) | 1018.69 | 2.08320 | ||||||||
\(490\) | 361.184 | + | 46.4131i | 0.737110 | + | 0.0947206i | ||||
\(491\) | 503.424 | 1.02530 | 0.512651 | − | 0.858597i | \(-0.328663\pi\) | ||||
0.512651 | + | 0.858597i | \(0.328663\pi\) | |||||||
\(492\) | 221.185i | 0.449563i | ||||||||
\(493\) | 469.166 | 0.951656 | ||||||||
\(494\) | − | 169.852i | − | 0.343830i | ||||||
\(495\) | 1070.69 | + | 137.586i | 2.16300 | + | 0.277951i | ||||
\(496\) | 16.9680 | 0.0342097 | ||||||||
\(497\) | −227.868 | −0.458487 | ||||||||
\(498\) | −36.6418 | −0.0735779 | ||||||||
\(499\) | −262.884 | −0.526821 | −0.263411 | − | 0.964684i | \(-0.584847\pi\) | ||||
−0.263411 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(500\) | −93.5205 | + | 231.849i | −0.187041 | + | 0.463698i | ||||
\(501\) | −1421.37 | −2.83706 | ||||||||
\(502\) | 10.3376 | 0.0205928 | ||||||||
\(503\) | −162.810 | −0.323677 | −0.161839 | − | 0.986817i | \(-0.551742\pi\) | ||||
−0.161839 | + | 0.986817i | \(0.551742\pi\) | |||||||
\(504\) | − | 624.151i | − | 1.23839i | ||||||
\(505\) | −92.1559 | + | 717.152i | −0.182487 | + | 1.42010i | ||||
\(506\) | 202.415 | + | 246.590i | 0.400030 | + | 0.487331i | ||||
\(507\) | − | 200.588i | − | 0.395636i | ||||||
\(508\) | − | 101.168i | − | 0.199150i | ||||||
\(509\) | 577.023 | 1.13364 | 0.566820 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566820 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(510\) | 87.2403 | − | 678.899i | 0.171059 | − | 1.33117i | ||||
\(511\) | 454.295i | 0.889032i | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 607.820 | 1.18483 | ||||||||
\(514\) | −48.4747 | −0.0943088 | ||||||||
\(515\) | −72.3757 | + | 563.223i | −0.140535 | + | 1.09364i | ||||
\(516\) | 202.335i | 0.392122i | ||||||||
\(517\) | −100.255 | −0.193917 | ||||||||
\(518\) | − | 1038.88i | − | 2.00555i | ||||||
\(519\) | 940.360 | 1.81187 | ||||||||
\(520\) | −25.8088 | + | 200.843i | −0.0496324 | + | 0.386236i | ||||
\(521\) | 971.255i | 1.86421i | 0.362185 | + | 0.932106i | \(0.382031\pi\) | ||||
−0.362185 | + | 0.932106i | \(0.617969\pi\) | |||||||
\(522\) | − | 840.224i | − | 1.60962i | ||||||
\(523\) | 170.780 | 0.326539 | 0.163269 | − | 0.986582i | \(-0.447796\pi\) | ||||
0.163269 | + | 0.986582i | \(0.447796\pi\) | |||||||
\(524\) | 380.047 | 0.725281 | ||||||||
\(525\) | 352.872 | − | 1350.34i | 0.672136 | − | 2.57208i | ||||
\(526\) | − | 296.370i | − | 0.563441i | ||||||
\(527\) | −73.7362 | −0.139917 | ||||||||
\(528\) | −218.480 | −0.413788 | ||||||||
\(529\) | −103.091 | + | 518.858i | −0.194879 | + | 0.980827i | ||||
\(530\) | 635.823 | + | 81.7050i | 1.19967 | + | 0.154160i | ||||
\(531\) | −2046.59 | −3.85422 | ||||||||
\(532\) | − | 168.178i | − | 0.316124i | ||||||
\(533\) | 284.353i | 0.533495i | ||||||||
\(534\) | 953.861i | 1.78626i | ||||||||
\(535\) | −12.9171 | + | 100.520i | −0.0241441 | + | 0.187888i | ||||
\(536\) | − | 117.214i | − | 0.218683i | ||||||
\(537\) | − | 42.3083i | − | 0.0787864i | ||||||
\(538\) | 523.088i | 0.972282i | ||||||||
\(539\) | 505.109i | 0.937122i | ||||||||
\(540\) | −718.721 | − | 92.3576i | −1.33097 | − | 0.171033i | ||||
\(541\) | 314.463 | 0.581263 | 0.290631 | − | 0.956835i | \(-0.406135\pi\) | ||||
0.290631 | + | 0.956835i | \(0.406135\pi\) | |||||||
\(542\) | 443.399i | 0.818079i | ||||||||
\(543\) | −225.323 | −0.414960 | ||||||||
\(544\) | 98.3298i | 0.180753i | ||||||||
\(545\) | −272.135 | − | 34.9701i | −0.499330 | − | 0.0641653i | ||||
\(546\) | − | 1130.47i | − | 2.07046i | ||||||
\(547\) | − | 526.082i | − | 0.961759i | −0.876787 | − | 0.480879i | \(-0.840318\pi\) | ||
0.876787 | − | 0.480879i | \(-0.159682\pi\) | |||||||
\(548\) | 363.184 | 0.662744 | ||||||||
\(549\) | − | 800.097i | − | 1.45737i | ||||||
\(550\) | −335.503 | − | 87.6737i | −0.610005 | − | 0.159407i | ||||
\(551\) | − | 226.399i | − | 0.410888i | ||||||
\(552\) | −229.855 | − | 280.018i | −0.416405 | − | 0.507279i | ||||
\(553\) | − | 657.780i | − | 1.18948i | ||||||
\(554\) | −419.629 | −0.757453 | ||||||||
\(555\) | −2023.70 | − | 260.051i | −3.64631 | − | 0.468561i | ||||
\(556\) | −170.126 | −0.305982 | ||||||||
\(557\) | 709.862 | 1.27444 | 0.637219 | − | 0.770683i | \(-0.280085\pi\) | ||||
0.637219 | + | 0.770683i | \(0.280085\pi\) | |||||||
\(558\) | 132.053i | 0.236655i | ||||||||
\(559\) | 260.119i | 0.465329i | ||||||||
\(560\) | −25.5545 | + | 198.863i | −0.0456330 | + | 0.355113i | ||||
\(561\) | 949.427 | 1.69238 | ||||||||
\(562\) | −498.219 | −0.886511 | ||||||||
\(563\) | 404.353 | 0.718212 | 0.359106 | − | 0.933297i | \(-0.383082\pi\) | ||||
0.359106 | + | 0.933297i | \(0.383082\pi\) | |||||||
\(564\) | 113.846 | 0.201855 | ||||||||
\(565\) | −98.1903 | + | 764.111i | −0.173788 | + | 1.35241i | ||||
\(566\) | − | 101.652i | − | 0.179597i | ||||||
\(567\) | 2059.39 | 3.63208 | ||||||||
\(568\) | − | 64.2906i | − | 0.113188i | ||||||
\(569\) | − | 47.5931i | − | 0.0836433i | −0.999125 | − | 0.0418217i | \(-0.986684\pi\) | ||
0.999125 | − | 0.0418217i | \(-0.0133161\pi\) | |||||||
\(570\) | −327.607 | − | 42.0983i | −0.574749 | − | 0.0738567i | ||||
\(571\) | 178.905i | 0.313319i | 0.987653 | + | 0.156660i | \(0.0500725\pi\) | ||||
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(572\) | −280.875 | −0.491040 | ||||||||
\(573\) | −271.277 | −0.473433 | ||||||||
\(574\) | 281.550i | 0.490506i | ||||||||
\(575\) | −240.603 | − | 522.241i | −0.418440 | − | 0.908245i | ||||
\(576\) | 176.098 | 0.305725 | ||||||||
\(577\) | 463.415i | 0.803146i | 0.915827 | + | 0.401573i | \(0.131536\pi\) | ||||
−0.915827 | + | 0.401573i | \(0.868464\pi\) | |||||||
\(578\) | − | 18.5949i | − | 0.0321710i | ||||||
\(579\) | 1056.71 | 1.82506 | ||||||||
\(580\) | −34.4011 | + | 267.707i | −0.0593122 | + | 0.461564i | ||||
\(581\) | −46.6419 | −0.0802787 | ||||||||
\(582\) | −786.272 | −1.35098 | ||||||||
\(583\) | 889.186i | 1.52519i | ||||||||
\(584\) | −128.175 | −0.219477 | ||||||||
\(585\) | −1563.06 | − | 200.857i | −2.67189 | − | 0.343345i | ||||
\(586\) | 427.891i | 0.730189i | ||||||||
\(587\) | 627.786i | 1.06948i | 0.845016 | + | 0.534741i | \(0.179591\pi\) | ||||
−0.845016 | + | 0.534741i | \(0.820409\pi\) | |||||||
\(588\) | − | 573.583i | − | 0.975481i | ||||||
\(589\) | 35.5819i | 0.0604106i | ||||||||
\(590\) | 652.072 | + | 83.7930i | 1.10521 | + | 0.142022i | ||||
\(591\) | 1887.62 | 3.19395 | ||||||||
\(592\) | 293.108 | 0.495114 | ||||||||
\(593\) | 60.2309i | 0.101570i | 0.998710 | + | 0.0507849i | \(0.0161723\pi\) | ||||
−0.998710 | + | 0.0507849i | \(0.983828\pi\) | |||||||
\(594\) | − | 1005.12i | − | 1.69212i | ||||||
\(595\) | 111.050 | − | 864.181i | 0.186638 | − | 1.45241i | ||||
\(596\) | − | 201.484i | − | 0.338060i | ||||||
\(597\) | 237.167 | 0.397265 | ||||||||
\(598\) | −295.499 | − | 359.987i | −0.494145 | − | 0.601986i | ||||
\(599\) | −434.361 | −0.725143 | −0.362572 | − | 0.931956i | \(-0.618101\pi\) | ||||
−0.362572 | + | 0.931956i | \(0.618101\pi\) | |||||||
\(600\) | 380.984 | + | 99.5590i | 0.634974 | + | 0.165932i | ||||
\(601\) | −121.753 | −0.202583 | −0.101292 | − | 0.994857i | \(-0.532298\pi\) | ||||
−0.101292 | + | 0.994857i | \(0.532298\pi\) | |||||||
\(602\) | 257.555i | 0.427833i | ||||||||
\(603\) | 912.216 | 1.51280 | ||||||||
\(604\) | −383.636 | −0.635160 | ||||||||
\(605\) | −15.8051 | + | 122.994i | −0.0261241 | + | 0.203296i | ||||
\(606\) | 1138.88 | 1.87934 | ||||||||
\(607\) | − | 962.161i | − | 1.58511i | −0.609801 | − | 0.792554i | \(-0.708751\pi\) | ||
0.609801 | − | 0.792554i | \(-0.291249\pi\) | |||||||
\(608\) | 47.4496 | 0.0780422 | ||||||||
\(609\) | − | 1506.83i | − | 2.47427i | ||||||
\(610\) | −32.7582 | + | 254.922i | −0.0537020 | + | 0.417905i | ||||
\(611\) | 146.359 | 0.239540 | ||||||||
\(612\) | −765.251 | −1.25041 | ||||||||
\(613\) | 261.958 | 0.427338 | 0.213669 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213669 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(614\) | −25.2833 | −0.0411780 | ||||||||
\(615\) | 548.453 | + | 70.4777i | 0.891794 | + | 0.114598i | ||||
\(616\) | −278.107 | −0.451472 | ||||||||
\(617\) | −315.081 | −0.510666 | −0.255333 | − | 0.966853i | \(-0.582185\pi\) | ||||
−0.255333 | + | 0.966853i | \(0.582185\pi\) | |||||||
\(618\) | 894.434 | 1.44730 | ||||||||
\(619\) | 465.857i | 0.752596i | 0.926499 | + | 0.376298i | \(0.122803\pi\) | ||||
−0.926499 | + | 0.376298i | \(0.877197\pi\) | |||||||
\(620\) | 5.40663 | − | 42.0740i | 0.00872036 | − | 0.0678614i | ||||
\(621\) | 1288.23 | − | 1057.45i | 2.07444 | − | 1.70282i | ||||
\(622\) | 191.300i | 0.307557i | ||||||||
\(623\) | 1214.19i | 1.94893i | ||||||||
\(624\) | 318.951 | 0.511139 | ||||||||
\(625\) | 545.096 | + | 305.770i | 0.872154 | + | 0.489232i | ||||
\(626\) | 180.842i | 0.288884i | ||||||||
\(627\) | − | 458.152i | − | 0.730704i | ||||||
\(628\) | 90.8701 | 0.144698 | ||||||||
\(629\) | −1273.73 | −2.02501 | ||||||||
\(630\) | −1547.65 | − | 198.877i | −2.45659 | − | 0.315678i | ||||
\(631\) | 15.6603i | 0.0248182i | 0.999923 | + | 0.0124091i | \(0.00395003\pi\) | ||||
−0.999923 | + | 0.0124091i | \(0.996050\pi\) | |||||||
\(632\) | 185.586 | 0.293648 | ||||||||
\(633\) | 187.717i | 0.296552i | ||||||||
\(634\) | −164.590 | −0.259606 | ||||||||
\(635\) | −250.858 | − | 32.2359i | −0.395052 | − | 0.0507653i | ||||
\(636\) | − | 1009.73i | − | 1.58762i | ||||||
\(637\) | − | 737.390i | − | 1.15760i | ||||||
\(638\) | −374.384 | −0.586808 | ||||||||
\(639\) | 500.341 | 0.783006 | ||||||||
\(640\) | −56.1072 | − | 7.20992i | −0.0876675 | − | 0.0112655i | ||||
\(641\) | − | 553.144i | − | 0.862939i | −0.902128 | − | 0.431469i | \(-0.857995\pi\) | ||
0.902128 | − | 0.431469i | \(-0.142005\pi\) | |||||||
\(642\) | 159.632 | 0.248649 | ||||||||
\(643\) | −583.117 | −0.906870 | −0.453435 | − | 0.891289i | \(-0.649802\pi\) | ||||
−0.453435 | + | 0.891289i | \(0.649802\pi\) | |||||||
\(644\) | −292.587 | − | 356.440i | −0.454327 | − | 0.553478i | ||||
\(645\) | 501.712 | + | 64.4713i | 0.777848 | + | 0.0999555i | ||||
\(646\) | −206.197 | −0.319191 | ||||||||
\(647\) | 868.461i | 1.34229i | 0.741326 | + | 0.671145i | \(0.234197\pi\) | ||||
−0.741326 | + | 0.671145i | \(0.765803\pi\) | |||||||
\(648\) | 581.036i | 0.896660i | ||||||||
\(649\) | 911.911i | 1.40510i | ||||||||
\(650\) | 489.788 | + | 127.992i | 0.753520 | + | 0.196910i | ||||
\(651\) | 236.820i | 0.363779i | ||||||||
\(652\) | 365.851i | 0.561121i | ||||||||
\(653\) | − | 381.114i | − | 0.583635i | −0.956474 | − | 0.291817i | \(-0.905740\pi\) | ||
0.956474 | − | 0.291817i | \(-0.0942600\pi\) | |||||||
\(654\) | 432.167i | 0.660806i | ||||||||
\(655\) | 121.097 | − | 942.369i | 0.184881 | − | 1.43873i | ||||
\(656\) | −79.4365 | −0.121092 | ||||||||
\(657\) | − | 997.518i | − | 1.51829i | ||||||
\(658\) | 144.917 | 0.220238 | ||||||||
\(659\) | − | 1117.10i | − | 1.69514i | −0.530683 | − | 0.847571i | \(-0.678064\pi\) | ||
0.530683 | − | 0.847571i | \(-0.321936\pi\) | |||||||
\(660\) | −69.6157 | + | 541.745i | −0.105478 | + | 0.820826i | ||||
\(661\) | 1079.84i | 1.63365i | 0.576889 | + | 0.816823i | \(0.304267\pi\) | ||||
−0.576889 | + | 0.816823i | \(0.695733\pi\) | |||||||
\(662\) | − | 289.447i | − | 0.437230i | ||||||
\(663\) | −1386.03 | −2.09055 | ||||||||
\(664\) | − | 13.1595i | − | 0.0198186i | ||||||
\(665\) | −417.016 | − | 53.5877i | −0.627092 | − | 0.0805829i | ||||
\(666\) | 2281.11i | 3.42509i | ||||||||
\(667\) | −393.877 | − | 479.835i | −0.590520 | − | 0.719392i | ||||
\(668\) | − | 510.470i | − | 0.764177i | ||||||
\(669\) | 1977.15 | 2.95538 | ||||||||
\(670\) | −290.645 | − | 37.3487i | −0.433799 | − | 0.0557443i | ||||
\(671\) | −356.504 | −0.531302 | ||||||||
\(672\) | 315.807 | 0.469952 | ||||||||
\(673\) | − | 750.860i | − | 1.11569i | −0.829945 | − | 0.557845i | \(-0.811628\pi\) | ||
0.829945 | − | 0.557845i | \(-0.188372\pi\) | |||||||
\(674\) | 664.870i | 0.986454i | ||||||||
\(675\) | −458.022 | + | 1752.72i | −0.678551 | + | 2.59662i | ||||
\(676\) | 72.0390 | 0.106567 | ||||||||
\(677\) | −505.958 | −0.747353 | −0.373676 | − | 0.927559i | \(-0.621903\pi\) | ||||
−0.373676 | + | 0.927559i | \(0.621903\pi\) | |||||||
\(678\) | 1213.46 | 1.78976 | ||||||||
\(679\) | −1000.86 | −1.47402 | ||||||||
\(680\) | 243.820 | + | 31.3315i | 0.358558 | + | 0.0460757i | ||||
\(681\) | 1562.85i | 2.29493i | ||||||||
\(682\) | 58.8397 | 0.0862753 | ||||||||
\(683\) | 336.348i | 0.492457i | 0.969212 | + | 0.246229i | \(0.0791914\pi\) | ||||
−0.969212 | + | 0.246229i | \(0.920809\pi\) | |||||||
\(684\) | 369.276i | 0.539878i | ||||||||
\(685\) | 115.724 | − | 900.555i | 0.168940 | − | 1.31468i | ||||
\(686\) | − | 35.4310i | − | 0.0516486i | ||||||
\(687\) | 1638.71 | 2.38531 | ||||||||
\(688\) | −72.6666 | −0.105620 | ||||||||
\(689\) | − | 1298.09i | − | 1.88402i | ||||||
\(690\) | −767.576 | + | 480.728i | −1.11243 | + | 0.696707i | ||||
\(691\) | −331.910 | −0.480333 | −0.240167 | − | 0.970732i | \(-0.577202\pi\) | ||||
−0.240167 | + | 0.970732i | \(0.577202\pi\) | |||||||
\(692\) | 337.721i | 0.488036i | ||||||||
\(693\) | − | 2164.36i | − | 3.12318i | ||||||
\(694\) | 222.807 | 0.321047 | ||||||||
\(695\) | −54.2084 | + | 421.846i | −0.0779976 | + | 0.606973i | ||||
\(696\) | 425.136 | 0.610828 | ||||||||
\(697\) | 345.199 | 0.495265 | ||||||||
\(698\) | − | 339.986i | − | 0.487086i | ||||||
\(699\) | −411.069 | −0.588082 | ||||||||
\(700\) | 484.961 | + | 126.730i | 0.692802 | + | 0.181043i | ||||
\(701\) | − | 1083.72i | − | 1.54596i | −0.634429 | − | 0.772981i | \(-0.718765\pi\) | ||
0.634429 | − | 0.772981i | \(-0.281235\pi\) | |||||||
\(702\) | 1467.34i | 2.09022i | ||||||||
\(703\) | 614.646i | 0.874319i | ||||||||
\(704\) | − | 78.4648i | − | 0.111456i | ||||||
\(705\) | 36.2755 | − | 282.294i | 0.0514547 | − | 0.400417i | ||||
\(706\) | −219.416 | −0.310788 | ||||||||
\(707\) | 1449.70 | 2.05050 | ||||||||
\(708\) | − | 1035.53i | − | 1.46262i | ||||||
\(709\) | 526.644i | 0.742799i | 0.928473 | + | 0.371400i | \(0.121122\pi\) | ||||
−0.928473 | + | 0.371400i | \(0.878878\pi\) | |||||||
\(710\) | −159.416 | − | 20.4853i | −0.224529 | − | 0.0288526i | ||||
\(711\) | 1444.32i | 2.03139i | ||||||||
\(712\) | −342.570 | −0.481137 | ||||||||
\(713\) | 61.9033 | + | 75.4129i | 0.0868209 | + | 0.105768i | ||||
\(714\) | −1372.37 | −1.92209 | ||||||||
\(715\) | −89.4970 | + | 696.460i | −0.125171 | + | 0.974070i | ||||
\(716\) | 15.1946 | 0.0212215 | ||||||||
\(717\) | − | 2071.18i | − | 2.88867i | ||||||
\(718\) | −615.405 | −0.857110 | ||||||||
\(719\) | −975.723 | −1.35706 | −0.678528 | − | 0.734575i | \(-0.737382\pi\) | ||||
−0.678528 | + | 0.734575i | \(0.737382\pi\) | |||||||
\(720\) | 56.1111 | − | 436.654i | 0.0779321 | − | 0.606463i | ||||
\(721\) | 1138.54 | 1.57911 | ||||||||
\(722\) | − | 411.029i | − | 0.569293i | ||||||
\(723\) | −1077.68 | −1.49057 | ||||||||
\(724\) | − | 80.9226i | − | 0.111772i | ||||||
\(725\) | 652.849 | + | 170.603i | 0.900481 | + | 0.235314i | ||||
\(726\) | 195.323 | 0.269039 | ||||||||
\(727\) | −578.127 | −0.795223 | −0.397612 | − | 0.917554i | \(-0.630161\pi\) | ||||
−0.397612 | + | 0.917554i | \(0.630161\pi\) | |||||||
\(728\) | 405.998 | 0.557689 | ||||||||
\(729\) | −890.070 | −1.22095 | ||||||||
\(730\) | −40.8411 | + | 317.823i | −0.0559468 | + | 0.435374i | ||||
\(731\) | 315.780 | 0.431984 | ||||||||
\(732\) | 404.833 | 0.553050 | ||||||||
\(733\) | −1179.77 | −1.60952 | −0.804758 | − | 0.593604i | \(-0.797705\pi\) | ||||
−0.804758 | + | 0.593604i | \(0.797705\pi\) | |||||||
\(734\) | − | 249.277i | − | 0.339614i | ||||||
\(735\) | −1422.26 | − | 182.764i | −1.93505 | − | 0.248659i | ||||
\(736\) | 100.566 | − | 82.5502i | 0.136638 | − | 0.112161i | ||||
\(737\) | − | 406.462i | − | 0.551508i | ||||||
\(738\) | − | 618.213i | − | 0.837687i | ||||||
\(739\) | −532.708 | −0.720850 | −0.360425 | − | 0.932788i | \(-0.617368\pi\) | ||||
−0.360425 | + | 0.932788i | \(0.617368\pi\) | |||||||
\(740\) | 93.3948 | − | 726.793i | 0.126209 | − | 0.982153i | ||||
\(741\) | 668.839i | 0.902617i | ||||||||
\(742\) | − | 1285.30i | − | 1.73221i | ||||||
\(743\) | 930.836 | 1.25281 | 0.626404 | − | 0.779499i | \(-0.284526\pi\) | ||||
0.626404 | + | 0.779499i | \(0.284526\pi\) | |||||||
\(744\) | −66.8162 | −0.0898067 | ||||||||
\(745\) | −499.601 | − | 64.2000i | −0.670605 | − | 0.0861745i | ||||
\(746\) | 222.042i | 0.297644i | ||||||||
\(747\) | 102.414 | 0.137100 | ||||||||
\(748\) | 340.977i | 0.455852i | ||||||||
\(749\) | 203.199 | 0.271293 | ||||||||
\(750\) | 368.263 | − | 912.970i | 0.491017 | − | 1.21729i | ||||
\(751\) | 1425.78i | 1.89851i | 0.314512 | + | 0.949254i | \(0.398159\pi\) | ||||
−0.314512 | + | 0.949254i | \(0.601841\pi\) | |||||||
\(752\) | 40.8867i | 0.0543706i | ||||||||
\(753\) | −40.7071 | −0.0540599 | ||||||||
\(754\) | 546.549 | 0.724866 | ||||||||
\(755\) | −122.241 | + | 951.269i | −0.161908 | + | 1.25996i | ||||
\(756\) | 1452.87i | 1.92179i | ||||||||
\(757\) | −715.631 | −0.945351 | −0.472676 | − | 0.881236i | \(-0.656712\pi\) | ||||
−0.472676 | + | 0.881236i | \(0.656712\pi\) | |||||||
\(758\) | −200.830 | −0.264947 | ||||||||
\(759\) | −797.067 | − | 971.015i | −1.05015 | − | 1.27934i | ||||
\(760\) | 15.1192 | − | 117.657i | 0.0198937 | − | 0.154811i | ||||
\(761\) | −1406.78 | −1.84859 | −0.924297 | − | 0.381674i | \(-0.875348\pi\) | ||||
−0.924297 | + | 0.381674i | \(0.875348\pi\) | |||||||
\(762\) | 398.379i | 0.522806i | ||||||||
\(763\) | 550.113i | 0.720987i | ||||||||
\(764\) | − | 97.4265i | − | 0.127522i | ||||||
\(765\) | −243.837 | + | 1897.52i | −0.318741 | + | 2.48042i | ||||
\(766\) | − | 52.5570i | − | 0.0686123i | ||||||
\(767\) | − | 1331.27i | − | 1.73568i | ||||||
\(768\) | 89.1018i | 0.116018i | ||||||||
\(769\) | 409.262i | 0.532200i | 0.963945 | + | 0.266100i | \(0.0857352\pi\) | ||||
−0.963945 | + | 0.266100i | \(0.914265\pi\) | |||||||
\(770\) | −88.6149 | + | 689.596i | −0.115084 | + | 0.895579i | ||||
\(771\) | 190.883 | 0.247578 | ||||||||
\(772\) | 379.507i | 0.491589i | ||||||||
\(773\) | −346.261 | −0.447944 | −0.223972 | − | 0.974596i | \(-0.571902\pi\) | ||||
−0.223972 | + | 0.974596i | \(0.571902\pi\) | |||||||
\(774\) | − | 565.527i | − | 0.730655i | ||||||
\(775\) | −102.604 | − | 26.8127i | −0.132393 | − | 0.0345970i | ||||
\(776\) | − | 282.382i | − | 0.363894i | ||||||
\(777\) | 4090.86i | 5.26494i | ||||||||
\(778\) | −685.483 | −0.881083 | ||||||||
\(779\) | − | 166.578i | − | 0.213836i | ||||||
\(780\) | 101.629 | − | 790.874i | 0.130294 | − | 1.01394i | ||||
\(781\) | − | 222.940i | − | 0.285454i | ||||||
\(782\) | −437.019 | + | 358.731i | −0.558848 | + | 0.458735i | ||||
\(783\) | 1955.84i | 2.49788i | ||||||||
\(784\) | 205.996 | 0.262751 | ||||||||
\(785\) | 28.9545 | − | 225.323i | 0.0368848 | − | 0.287035i | ||||
\(786\) | −1496.54 | −1.90400 | ||||||||
\(787\) | 620.806 | 0.788826 | 0.394413 | − | 0.918933i | \(-0.370948\pi\) | ||||
0.394413 | + | 0.918933i | \(0.370948\pi\) | |||||||
\(788\) | 677.921i | 0.860305i | ||||||||
\(789\) | 1167.04i | 1.47914i | ||||||||
\(790\) | 59.1344 | − | 460.180i | 0.0748537 | − | 0.582507i | ||||
\(791\) | 1544.63 | 1.95275 | ||||||||
\(792\) | 610.652 | 0.771025 | ||||||||
\(793\) | 520.448 | 0.656302 | ||||||||
\(794\) | 662.448 | 0.834317 | ||||||||
\(795\) | −2503.73 | − | 321.736i | −3.14935 | − | 0.404699i | ||||
\(796\) | 85.1762i | 0.107005i | ||||||||
\(797\) | −379.000 | −0.475533 | −0.237767 | − | 0.971322i | \(-0.576415\pi\) | ||||
−0.237767 | + | 0.971322i | \(0.576415\pi\) | |||||||
\(798\) | 662.248i | 0.829884i | ||||||||
\(799\) | − | 177.677i | − | 0.222375i | ||||||
\(800\) | −35.7556 | + | 136.827i | −0.0446945 | + | 0.171033i | ||||
\(801\) | − | 2666.04i | − | 3.32840i | ||||||
\(802\) | 788.549 | 0.983229 | ||||||||
\(803\) | −444.470 | −0.553512 | ||||||||
\(804\) | 461.563i | 0.574083i | ||||||||
\(805\) | −977.060 | + | 611.926i | −1.21374 | + | 0.760157i | ||||
\(806\) | −85.8980 | −0.106573 | ||||||||
\(807\) | − | 2059.80i | − | 2.55242i | ||||||
\(808\) | 409.018i | 0.506210i | ||||||||
\(809\) | −110.128 | −0.136128 | −0.0680642 | − | 0.997681i | \(-0.521682\pi\) | ||||
−0.0680642 | + | 0.997681i | \(0.521682\pi\) | |||||||
\(810\) | 1440.74 | + | 185.139i | 1.77869 | + | 0.228567i | ||||
\(811\) | −1115.03 | −1.37488 | −0.687439 | − | 0.726242i | \(-0.741265\pi\) | ||||
−0.687439 | + | 0.726242i | \(0.741265\pi\) | |||||||
\(812\) | 541.163 | 0.666457 | ||||||||
\(813\) | − | 1746.01i | − | 2.14761i | ||||||
\(814\) | 1016.41 | 1.24866 | ||||||||
\(815\) | 907.168 | + | 116.573i | 1.11309 | + | 0.143035i | ||||
\(816\) | − | 387.201i | − | 0.474511i | ||||||
\(817\) | − | 152.382i | − | 0.186514i | ||||||
\(818\) | 417.375i | 0.510238i | ||||||||
\(819\) | 3159.67i | 3.85796i | ||||||||
\(820\) | −25.3114 | + | 196.971i | −0.0308675 | + | 0.240209i | ||||
\(821\) | −297.005 | −0.361760 | −0.180880 | − | 0.983505i | \(-0.557895\pi\) | ||||
−0.180880 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(822\) | −1430.14 | −1.73983 | ||||||||
\(823\) | − | 1245.37i | − | 1.51321i | −0.653872 | − | 0.756605i | \(-0.726857\pi\) | ||
0.653872 | − | 0.756605i | \(-0.273143\pi\) | |||||||
\(824\) | 321.227i | 0.389839i | ||||||||
\(825\) | 1321.13 | + | 345.240i | 1.60138 | + | 0.418472i | ||||
\(826\) | − | 1318.15i | − | 1.59582i | ||||||
\(827\) | −162.409 | −0.196384 | −0.0981918 | − | 0.995168i | \(-0.531306\pi\) | ||||
−0.0981918 | + | 0.995168i | \(0.531306\pi\) | |||||||
\(828\) | 642.446 | + | 782.651i | 0.775901 | + | 0.945231i | ||||
\(829\) | 58.6874 | 0.0707930 | 0.0353965 | − | 0.999373i | \(-0.488731\pi\) | ||||
0.0353965 | + | 0.999373i | \(0.488731\pi\) | |||||||
\(830\) | −32.6305 | − | 4.19311i | −0.0393139 | − | 0.00505194i | ||||
\(831\) | 1652.41 | 1.98845 | ||||||||
\(832\) | 114.548i | 0.137678i | ||||||||
\(833\) | −895.179 | −1.07465 | ||||||||
\(834\) | 669.918 | 0.803259 | ||||||||
\(835\) | −1265.77 | − | 162.654i | −1.51589 | − | 0.194796i | ||||
\(836\) | 164.541 | 0.196819 | ||||||||
\(837\) | − | 307.388i | − | 0.367250i | ||||||
\(838\) | 209.942 | 0.250528 | ||||||||
\(839\) | − | 666.002i | − | 0.793805i | −0.917861 | − | 0.396902i | \(-0.870085\pi\) | ||
0.917861 | − | 0.396902i | \(-0.129915\pi\) | |||||||
\(840\) | 100.628 | − | 783.080i | 0.119795 | − | 0.932238i | ||||
\(841\) | −112.493 | −0.133762 | ||||||||
\(842\) | 543.548 | 0.645544 | ||||||||
\(843\) | 1961.88 | 2.32726 | ||||||||
\(844\) | −67.4168 | −0.0798777 | ||||||||
\(845\) | 22.9543 | − | 178.629i | 0.0271648 | − | 0.211395i | ||||
\(846\) | −318.200 | −0.376123 | ||||||||
\(847\) | 248.629 | 0.293541 | ||||||||
\(848\) | 362.633 | 0.427634 | ||||||||
\(849\) | 400.282i | 0.471475i | ||||||||
\(850\) | 155.380 | − | 594.595i | 0.182800 | − | 0.699523i | ||||
\(851\) | 1069.33 | + | 1302.69i | 1.25655 | + | 1.53078i | ||||
\(852\) | 253.162i | 0.297139i | ||||||||
\(853\) | 920.684i | 1.07935i | 0.841874 | + | 0.539674i | \(0.181453\pi\) | ||||
−0.841874 | + | 0.539674i | \(0.818547\pi\) | |||||||
\(854\) | 515.318 | 0.603417 | ||||||||
\(855\) | 915.662 | + | 117.665i | 1.07095 | + | 0.137620i | ||||
\(856\) | 57.3304i | 0.0669748i | ||||||||
\(857\) | − | 628.758i | − | 0.733673i | −0.930285 | − | 0.366836i | \(-0.880441\pi\) | ||
0.930285 | − | 0.366836i | \(-0.119559\pi\) | |||||||
\(858\) | 1106.02 | 1.28907 | ||||||||
\(859\) | 908.763 | 1.05793 | 0.528965 | − | 0.848643i | \(-0.322580\pi\) | ||||
0.528965 | + | 0.848643i | \(0.322580\pi\) | |||||||
\(860\) | −23.1542 | + | 180.185i | −0.0269235 | + | 0.209517i | ||||
\(861\) | − | 1108.68i | − | 1.28767i | ||||||
\(862\) | −195.837 | −0.227190 | ||||||||
\(863\) | 12.6014i | 0.0146019i | 0.999973 | + | 0.00730093i | \(0.00232398\pi\) | ||||
−0.999973 | + | 0.00730093i | \(0.997676\pi\) | |||||||
\(864\) | −409.913 | −0.474437 | ||||||||
\(865\) | 837.417 | + | 107.610i | 0.968112 | + | 0.124405i | ||||
\(866\) | − | 1018.38i | − | 1.17596i | ||||||
\(867\) | 73.2225i | 0.0844550i | ||||||||
\(868\) | −85.0515 | −0.0979855 | ||||||||
\(869\) | 643.553 | 0.740568 | ||||||||
\(870\) | 135.464 | − | 1054.17i | 0.155706 | − | 1.21169i | ||||
\(871\) | 593.379i | 0.681262i | ||||||||
\(872\) | −155.209 | −0.177992 | ||||||||
\(873\) | 2197.63 | 2.51733 | ||||||||
\(874\) | 173.108 | + | 210.886i | 0.198064 | + | 0.241288i | ||||
\(875\) | 468.768 | − | 1162.13i | 0.535735 | − | 1.32815i | ||||
\(876\) | 504.723 | 0.576168 | ||||||||
\(877\) | 1224.19i | 1.39588i | 0.716156 | + | 0.697940i | \(0.245900\pi\) | ||||
−0.716156 | + | 0.697940i | \(0.754100\pi\) | |||||||
\(878\) | − | 547.286i | − | 0.623333i | ||||||
\(879\) | − | 1684.94i | − | 1.91688i | ||||||
\(880\) | −194.562 | − | 25.0018i | −0.221093 | − | 0.0284111i | ||||
\(881\) | 710.448i | 0.806411i | 0.915110 | + | 0.403205i | \(0.132104\pi\) | ||||
−0.915110 | + | 0.403205i | \(0.867896\pi\) | |||||||
\(882\) | 1603.16i | 1.81765i | ||||||||
\(883\) | 231.686i | 0.262385i | 0.991357 | + | 0.131193i | \(0.0418806\pi\) | ||||
−0.991357 | + | 0.131193i | \(0.958119\pi\) | |||||||
\(884\) | − | 497.780i | − | 0.563100i | ||||||
\(885\) | −2567.72 | − | 329.958i | −2.90137 | − | 0.372834i | ||||
\(886\) | −453.066 | −0.511361 | ||||||||
\(887\) | − | 530.453i | − | 0.598030i | −0.954248 | − | 0.299015i | \(-0.903342\pi\) | ||
0.954248 | − | 0.299015i | \(-0.0966581\pi\) | |||||||
\(888\) | −1154.19 | −1.29977 | ||||||||
\(889\) | 507.103i | 0.570419i | ||||||||
\(890\) | −109.155 | + | 849.440i | −0.122646 | + | 0.954427i | ||||
\(891\) | 2014.85i | 2.26134i | ||||||||
\(892\) | 710.073i | 0.796046i | ||||||||
\(893\) | −85.7393 | −0.0960127 | ||||||||
\(894\) | 793.397i | 0.887469i | ||||||||
\(895\) | 4.84155 | − | 37.6767i | 0.00540956 | − | 0.0420968i | ||||
\(896\) | 113.419i | 0.126584i | ||||||||
\(897\) | 1163.61 | + | 1417.55i | 1.29722 | + | 1.58032i | ||||
\(898\) | 577.169i | 0.642727i | ||||||||
\(899\) | −114.495 | −0.127358 | ||||||||
\(900\) | −1064.85 | − | 278.268i | −1.18317 | − | 0.309186i | ||||
\(901\) | −1575.86 | −1.74901 | ||||||||
\(902\) | −275.461 | −0.305389 | ||||||||
\(903\) | − | 1014.20i | − | 1.12314i | ||||||
\(904\) | 435.801i | 0.482081i | ||||||||
\(905\) | −200.657 | − | 25.7849i | −0.221720 | − | 0.0284916i | ||||
\(906\) | 1510.68 | 1.66741 | ||||||||
\(907\) | −262.781 | −0.289725 | −0.144863 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144863 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(908\) | −561.281 | −0.618151 | ||||||||
\(909\) | −3183.18 | −3.50185 | ||||||||
\(910\) | 129.366 | − | 1006.72i | 0.142160 | − | 1.10628i | ||||
\(911\) | − | 1223.98i | − | 1.34355i | −0.740755 | − | 0.671776i | \(-0.765532\pi\) | ||
0.740755 | − | 0.671776i | \(-0.234468\pi\) | |||||||
\(912\) | −186.846 | −0.204875 | ||||||||
\(913\) | − | 45.6331i | − | 0.0499815i | ||||||
\(914\) | − | 889.059i | − | 0.972713i | ||||||
\(915\) | 128.995 | − | 1003.83i | 0.140978 | − | 1.09708i | ||||
\(916\) | 588.525i | 0.642495i | ||||||||
\(917\) | −1904.97 | −2.07740 | ||||||||
\(918\) | 1781.32 | 1.94044 | ||||||||
\(919\) | − | 502.048i | − | 0.546298i | −0.961972 | − | 0.273149i | \(-0.911935\pi\) | ||
0.961972 | − | 0.273149i | \(-0.0880651\pi\) | |||||||
\(920\) | −172.649 | − | 275.667i | −0.187662 | − | 0.299638i | ||||
\(921\) | 99.5600 | 0.108100 | ||||||||
\(922\) | − | 662.302i | − | 0.718332i | ||||||
\(923\) | 325.462i | 0.352613i | ||||||||
\(924\) | 1095.12 | 1.18520 | ||||||||
\(925\) | −1772.40 | − | 463.166i | −1.91611 | − | 0.500720i | ||||
\(926\) | −691.763 | −0.747045 | ||||||||
\(927\) | −2499.94 | −2.69681 | ||||||||
\(928\) | 152.683i | 0.164529i | ||||||||
\(929\) | 12.5466 | 0.0135055 | 0.00675273 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675273 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(930\) | −21.2901 | + | 165.678i | −0.0228926 | + | 0.178149i | ||||
\(931\) | 431.974i | 0.463989i | ||||||||
\(932\) | − | 147.631i | − | 0.158403i | ||||||
\(933\) | − | 753.298i | − | 0.807393i | ||||||
\(934\) | − | 903.356i | − | 0.967191i | ||||||
\(935\) | 845.491 | + | 108.648i | 0.904268 | + | 0.116201i | ||||
\(936\) | −891.469 | −0.952424 | ||||||||
\(937\) | 789.304 | 0.842374 | 0.421187 | − | 0.906974i | \(-0.361614\pi\) | ||||
0.421187 | + | 0.906974i | \(0.361614\pi\) | |||||||
\(938\) | 587.531i | 0.626365i | ||||||||
\(939\) | − | 712.114i | − | 0.758375i | ||||||
\(940\) | 101.383 | + | 13.0280i | 0.107854 | + | 0.0138596i | ||||
\(941\) | 851.539i | 0.904929i | 0.891782 | + | 0.452465i | \(0.149455\pi\) | ||||
−0.891782 | + | 0.452465i | \(0.850545\pi\) | |||||||
\(942\) | −357.826 | −0.379858 | ||||||||
\(943\) | −289.803 | − | 353.049i | −0.307321 | − | 0.374389i | ||||
\(944\) | 371.901 | 0.393963 | ||||||||
\(945\) | 3602.56 | + | 462.939i | 3.81224 | + | 0.489882i | ||||
\(946\) | −251.985 | −0.266369 | ||||||||
\(947\) | − | 990.158i | − | 1.04557i | −0.852464 | − | 0.522787i | \(-0.824892\pi\) | ||
0.852464 | − | 0.522787i | \(-0.175108\pi\) | |||||||
\(948\) | −730.796 | −0.770881 | ||||||||
\(949\) | 648.866 | 0.683736 | ||||||||
\(950\) | −286.925 | − | 74.9794i | −0.302027 | − | 0.0789257i | ||||
\(951\) | 648.120 | 0.681514 | ||||||||
\(952\) | − | 492.875i | − | 0.517725i | ||||||
\(953\) | −88.4608 | −0.0928235 | −0.0464118 | − | 0.998922i | \(-0.514779\pi\) | ||||
−0.0464118 | + | 0.998922i | \(0.514779\pi\) | |||||||
\(954\) | 2822.19i | 2.95827i | ||||||||
\(955\) | −241.580 | − | 31.0436i | −0.252963 | − | 0.0325064i | ||||
\(956\) | 743.842 | 0.778078 | ||||||||
\(957\) | 1474.24 | 1.54048 | ||||||||
\(958\) | −1104.22 | −1.15263 | ||||||||
\(959\) | −1820.45 | −1.89827 | ||||||||
\(960\) | 220.938 | + | 28.3911i | 0.230143 | + | 0.0295740i | ||||
\(961\) | −943.005 | −0.981275 | ||||||||
\(962\) | −1483.82 | −1.54243 | ||||||||
\(963\) | −446.173 | −0.463316 | ||||||||
\(964\) | − | 387.038i | − | 0.401492i | ||||||
\(965\) | 941.029 | + | 120.925i | 0.975160 | + | 0.125311i | ||||
\(966\) | 1152.14 | + | 1403.58i | 1.19269 | + | 1.45298i | ||||
\(967\) | 1463.10i | 1.51303i | 0.653976 | + | 0.756515i | \(0.273100\pi\) | ||||
−0.653976 | + | 0.756515i | \(0.726900\pi\) | |||||||
\(968\) | 70.1481i | 0.0724671i | ||||||||
\(969\) | 811.960 | 0.837936 | ||||||||
\(970\) | −700.197 | − | 89.9771i | −0.721852 | − | 0.0927599i | ||||
\(971\) | 301.283i | 0.310281i | 0.987892 | + | 0.155140i | \(0.0495830\pi\) | ||||
−0.987892 | + | 0.155140i | \(0.950417\pi\) | |||||||
\(972\) | − | 983.654i | − | 1.01199i | ||||||
\(973\) | 852.750 | 0.876413 | ||||||||
\(974\) | −436.246 | −0.447891 | ||||||||
\(975\) | −1928.68 | − | 504.003i | −1.97813 | − | 0.516926i | ||||
\(976\) | 145.392i | 0.148967i | ||||||||
\(977\) | −1083.35 | −1.10886 | −0.554429 | − | 0.832231i | \(-0.687063\pi\) | ||||
−0.554429 | + | 0.832231i | \(0.687063\pi\) | |||||||
\(978\) | − | 1440.64i | − | 1.47305i | ||||||
\(979\) | −1187.92 | −1.21341 | ||||||||
\(980\) | 65.6380 | − | 510.791i | 0.0669776 | − | 0.521215i | ||||
\(981\) | − | 1207.91i | − | 1.23130i | ||||||
\(982\) | − | 711.949i | − | 0.724999i | ||||||
\(983\) | −1143.57 | −1.16335 | −0.581673 | − | 0.813423i | \(-0.697602\pi\) | ||||
−0.581673 | + | 0.813423i | \(0.697602\pi\) | |||||||
\(984\) | 312.803 | 0.317889 | ||||||||
\(985\) | 1680.98 | + | 216.010i | 1.70658 | + | 0.219300i | ||||
\(986\) | − | 663.502i | − | 0.672923i | ||||||
\(987\) | −570.649 | −0.578166 | ||||||||
\(988\) | −240.207 | −0.243124 | ||||||||
\(989\) | −265.105 | − | 322.961i | −0.268054 | − | 0.326553i | ||||
\(990\) | 194.576 | − | 1514.18i | 0.196541 | − | 1.52947i | ||||
\(991\) | 1358.12 | 1.37046 | 0.685229 | − | 0.728328i | \(-0.259702\pi\) | ||||
0.685229 | + | 0.728328i | \(0.259702\pi\) | |||||||
\(992\) | − | 23.9964i | − | 0.0241899i | ||||||
\(993\) | 1139.78i | 1.14781i | ||||||||
\(994\) | 322.254i | 0.324200i | ||||||||
\(995\) | 211.204 | + | 27.1403i | 0.212265 | + | 0.0272766i | ||||
\(996\) | 51.8193i | 0.0520274i | ||||||||
\(997\) | − | 635.885i | − | 0.637798i | −0.947789 | − | 0.318899i | \(-0.896687\pi\) | ||
0.947789 | − | 0.318899i | \(-0.103313\pi\) | |||||||
\(998\) | 371.774i | 0.372519i | ||||||||
\(999\) | − | 5309.87i | − | 5.31519i |
(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 | 230.3.c.a.229.11 | ✓ | 24 | |
5.2 | odd | 4 | 1150.3.d.e.551.13 | 24 | |||
5.3 | odd | 4 | 1150.3.d.e.551.12 | 24 | |||
5.4 | even | 2 | inner | 230.3.c.a.229.14 | yes | 24 | |
23.22 | odd | 2 | inner | 230.3.c.a.229.12 | yes | 24 | |
115.22 | even | 4 | 1150.3.d.e.551.24 | 24 | |||
115.68 | even | 4 | 1150.3.d.e.551.1 | 24 | |||
115.114 | odd | 2 | inner | 230.3.c.a.229.13 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.c.a.229.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.c.a.229.12 | yes | 24 | 23.22 | odd | 2 | inner | |
230.3.c.a.229.13 | yes | 24 | 115.114 | odd | 2 | inner | |
230.3.c.a.229.14 | yes | 24 | 5.4 | even | 2 | inner | |
1150.3.d.e.551.1 | 24 | 115.68 | even | 4 | |||
1150.3.d.e.551.12 | 24 | 5.3 | odd | 4 | |||
1150.3.d.e.551.13 | 24 | 5.2 | odd | 4 | |||
1150.3.d.e.551.24 | 24 | 115.22 | even | 4 |