Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,4,Mod(169,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("210.169");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.g (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: | \(12.3904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 169.4 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.169 |
Dual form | 210.4.g.a.169.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 8.79796 | − | 6.89898i | 0.786913 | − | 0.617063i | ||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 13.7980 | + | 17.5959i | 0.436330 | + | 0.556432i | ||||
\(11\) | 25.5959 | 0.701587 | 0.350794 | − | 0.936453i | \(-0.385912\pi\) | ||||
0.350794 | + | 0.936453i | \(0.385912\pi\) | |||||||
\(12\) | − | 12.0000i | − | 0.288675i | ||||||
\(13\) | 89.1918i | 1.90287i | 0.307843 | + | 0.951437i | \(0.400393\pi\) | ||||
−0.307843 | + | 0.951437i | \(0.599607\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 20.6969 | + | 26.3939i | 0.356262 | + | 0.454325i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 18.7878i | 0.268041i | 0.990979 | + | 0.134021i | \(0.0427888\pi\) | ||||
−0.990979 | + | 0.134021i | \(0.957211\pi\) | |||||||
\(18\) | − | 18.0000i | − | 0.235702i | ||||||
\(19\) | 11.7980 | 0.142455 | 0.0712273 | − | 0.997460i | \(-0.477308\pi\) | ||||
0.0712273 | + | 0.997460i | \(0.477308\pi\) | |||||||
\(20\) | −35.1918 | + | 27.5959i | −0.393457 | + | 0.308532i | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 51.1918i | 0.496097i | ||||||||
\(23\) | 159.373i | 1.44486i | 0.691447 | + | 0.722428i | \(0.256974\pi\) | ||||
−0.691447 | + | 0.722428i | \(0.743026\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 29.8082 | − | 121.394i | 0.238465 | − | 0.971151i | ||||
\(26\) | −178.384 | −1.34554 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | − | 28.0000i | − | 0.188982i | ||||||
\(29\) | −19.7980 | −0.126772 | −0.0633860 | − | 0.997989i | \(-0.520190\pi\) | ||||
−0.0633860 | + | 0.997989i | \(0.520190\pi\) | |||||||
\(30\) | −52.7878 | + | 41.3939i | −0.321256 | + | 0.251915i | ||||
\(31\) | −126.404 | −0.732350 | −0.366175 | − | 0.930546i | \(-0.619333\pi\) | ||||
−0.366175 | + | 0.930546i | \(0.619333\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 76.7878i | 0.405062i | ||||||||
\(34\) | −37.5755 | −0.189534 | ||||||||
\(35\) | 48.2929 | + | 61.5857i | 0.233228 | + | 0.297425i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 282.969i | 1.25729i | 0.777691 | + | 0.628647i | \(0.216391\pi\) | ||||
−0.777691 | + | 0.628647i | \(0.783609\pi\) | |||||||
\(38\) | 23.5959i | 0.100731i | ||||||||
\(39\) | −267.576 | −1.09862 | ||||||||
\(40\) | −55.1918 | − | 70.3837i | −0.218165 | − | 0.278216i | ||||
\(41\) | −144.384 | −0.549974 | −0.274987 | − | 0.961448i | \(-0.588674\pi\) | ||||
−0.274987 | + | 0.961448i | \(0.588674\pi\) | |||||||
\(42\) | − | 42.0000i | − | 0.154303i | ||||||
\(43\) | − | 326.929i | − | 1.15945i | −0.814814 | − | 0.579723i | \(-0.803161\pi\) | ||
0.814814 | − | 0.579723i | \(-0.196839\pi\) | |||||||
\(44\) | −102.384 | −0.350794 | ||||||||
\(45\) | −79.1816 | + | 62.0908i | −0.262304 | + | 0.205688i | ||||
\(46\) | −318.747 | −1.02167 | ||||||||
\(47\) | − | 117.435i | − | 0.364460i | −0.983256 | − | 0.182230i | \(-0.941668\pi\) | ||
0.983256 | − | 0.182230i | \(-0.0583315\pi\) | |||||||
\(48\) | 48.0000i | 0.144338i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 242.788 | + | 59.6163i | 0.686707 | + | 0.168620i | ||||
\(51\) | −56.3633 | −0.154754 | ||||||||
\(52\) | − | 356.767i | − | 0.951437i | ||||||
\(53\) | 634.504i | 1.64445i | 0.569163 | + | 0.822225i | \(0.307267\pi\) | ||||
−0.569163 | + | 0.822225i | \(0.692733\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 225.192 | − | 176.586i | 0.552088 | − | 0.432924i | ||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 35.3939i | 0.0822462i | ||||||||
\(58\) | − | 39.5959i | − | 0.0896414i | ||||||
\(59\) | 515.069 | 1.13655 | 0.568274 | − | 0.822839i | \(-0.307611\pi\) | ||||
0.568274 | + | 0.822839i | \(0.307611\pi\) | |||||||
\(60\) | −82.7878 | − | 105.576i | −0.178131 | − | 0.227162i | ||||
\(61\) | 395.716 | 0.830595 | 0.415297 | − | 0.909686i | \(-0.363678\pi\) | ||||
0.415297 | + | 0.909686i | \(0.363678\pi\) | |||||||
\(62\) | − | 252.808i | − | 0.517849i | ||||||
\(63\) | − | 63.0000i | − | 0.125988i | ||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 615.333 | + | 784.706i | 1.17419 | + | 1.49740i | ||||
\(66\) | −153.576 | −0.286422 | ||||||||
\(67\) | − | 842.120i | − | 1.53554i | −0.640724 | − | 0.767772i | \(-0.721366\pi\) | ||
0.640724 | − | 0.767772i | \(-0.278634\pi\) | |||||||
\(68\) | − | 75.1510i | − | 0.134021i | ||||||
\(69\) | −478.120 | −0.834187 | ||||||||
\(70\) | −123.171 | + | 96.5857i | −0.210311 | + | 0.164917i | ||||
\(71\) | 402.100 | 0.672120 | 0.336060 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336060 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(72\) | 72.0000i | 0.117851i | ||||||||
\(73\) | 303.171i | 0.486076i | 0.970017 | + | 0.243038i | \(0.0781439\pi\) | ||||
−0.970017 | + | 0.243038i | \(0.921856\pi\) | |||||||
\(74\) | −565.939 | −0.889041 | ||||||||
\(75\) | 364.182 | + | 89.4245i | 0.560694 | + | 0.137678i | ||||
\(76\) | −47.1918 | −0.0712273 | ||||||||
\(77\) | 179.171i | 0.265175i | ||||||||
\(78\) | − | 535.151i | − | 0.776845i | ||||||
\(79\) | −266.384 | −0.379373 | −0.189687 | − | 0.981845i | \(-0.560747\pi\) | ||||
−0.189687 | + | 0.981845i | \(0.560747\pi\) | |||||||
\(80\) | 140.767 | − | 110.384i | 0.196728 | − | 0.154266i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − | 288.767i | − | 0.388890i | ||||||
\(83\) | 753.253i | 0.996148i | 0.867135 | + | 0.498074i | \(0.165959\pi\) | ||||
−0.867135 | + | 0.498074i | \(0.834041\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | 129.616 | + | 165.294i | 0.165398 | + | 0.210925i | ||||
\(86\) | 653.857 | 0.819851 | ||||||||
\(87\) | − | 59.3939i | − | 0.0731919i | ||||||
\(88\) | − | 204.767i | − | 0.248049i | ||||||
\(89\) | 842.967 | 1.00398 | 0.501991 | − | 0.864873i | \(-0.332601\pi\) | ||||
0.501991 | + | 0.864873i | \(0.332601\pi\) | |||||||
\(90\) | −124.182 | − | 158.363i | −0.145443 | − | 0.185477i | ||||
\(91\) | −624.343 | −0.719219 | ||||||||
\(92\) | − | 637.494i | − | 0.722428i | ||||||
\(93\) | − | 379.212i | − | 0.422822i | ||||||
\(94\) | 234.869 | 0.257712 | ||||||||
\(95\) | 103.798 | − | 81.3939i | 0.112099 | − | 0.0879035i | ||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | − | 1201.92i | − | 1.25811i | −0.777362 | − | 0.629053i | \(-0.783443\pi\) | ||
0.777362 | − | 0.629053i | \(-0.216557\pi\) | |||||||
\(98\) | − | 98.0000i | − | 0.101015i | ||||||
\(99\) | −230.363 | −0.233862 | ||||||||
\(100\) | −119.233 | + | 485.576i | −0.119233 | + | 0.485576i | ||||
\(101\) | 575.371 | 0.566847 | 0.283424 | − | 0.958995i | \(-0.408530\pi\) | ||||
0.283424 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(102\) | − | 112.727i | − | 0.109427i | ||||||
\(103\) | − | 254.220i | − | 0.243195i | −0.992579 | − | 0.121597i | \(-0.961198\pi\) | ||
0.992579 | − | 0.121597i | \(-0.0388017\pi\) | |||||||
\(104\) | 713.535 | 0.672768 | ||||||||
\(105\) | −184.757 | + | 144.879i | −0.171719 | + | 0.134654i | ||||
\(106\) | −1269.01 | −1.16280 | ||||||||
\(107\) | − | 1142.61i | − | 1.03234i | −0.856487 | − | 0.516168i | \(-0.827358\pi\) | ||
0.856487 | − | 0.516168i | \(-0.172642\pi\) | |||||||
\(108\) | 108.000i | 0.0962250i | ||||||||
\(109\) | 2054.28 | 1.80518 | 0.902589 | − | 0.430502i | \(-0.141664\pi\) | ||||
0.902589 | + | 0.430502i | \(0.141664\pi\) | |||||||
\(110\) | 353.171 | + | 450.384i | 0.306123 | + | 0.390385i | ||||
\(111\) | −848.908 | −0.725899 | ||||||||
\(112\) | 112.000i | 0.0944911i | ||||||||
\(113\) | − | 890.827i | − | 0.741610i | −0.928711 | − | 0.370805i | \(-0.879082\pi\) | ||
0.928711 | − | 0.370805i | \(-0.120918\pi\) | |||||||
\(114\) | −70.7878 | −0.0581568 | ||||||||
\(115\) | 1099.51 | + | 1402.16i | 0.891567 | + | 1.13698i | ||||
\(116\) | 79.1918 | 0.0633860 | ||||||||
\(117\) | − | 802.727i | − | 0.634291i | ||||||
\(118\) | 1030.14i | 0.803661i | ||||||||
\(119\) | −131.514 | −0.101310 | ||||||||
\(120\) | 211.151 | − | 165.576i | 0.160628 | − | 0.125958i | ||||
\(121\) | −675.849 | −0.507775 | ||||||||
\(122\) | 791.433i | 0.587319i | ||||||||
\(123\) | − | 433.151i | − | 0.317528i | ||||||
\(124\) | 505.616 | 0.366175 | ||||||||
\(125\) | −575.243 | − | 1273.66i | −0.411610 | − | 0.911360i | ||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | − | 2304.16i | − | 1.60993i | −0.593323 | − | 0.804965i | \(-0.702184\pi\) | ||
0.593323 | − | 0.804965i | \(-0.297816\pi\) | |||||||
\(128\) | − | 128.000i | − | 0.0883883i | ||||||
\(129\) | 980.786 | 0.669406 | ||||||||
\(130\) | −1569.41 | + | 1230.67i | −1.05882 | + | 0.830281i | ||||
\(131\) | 955.192 | 0.637065 | 0.318532 | − | 0.947912i | \(-0.396810\pi\) | ||||
0.318532 | + | 0.947912i | \(0.396810\pi\) | |||||||
\(132\) | − | 307.151i | − | 0.202531i | ||||||
\(133\) | 82.5857i | 0.0538428i | ||||||||
\(134\) | 1684.24 | 1.08579 | ||||||||
\(135\) | −186.272 | − | 237.545i | −0.118754 | − | 0.151442i | ||||
\(136\) | 150.302 | 0.0947669 | ||||||||
\(137\) | 1489.53i | 0.928900i | 0.885599 | + | 0.464450i | \(0.153748\pi\) | ||||
−0.885599 | + | 0.464450i | \(0.846252\pi\) | |||||||
\(138\) | − | 956.241i | − | 0.589860i | ||||||
\(139\) | 752.284 | 0.459049 | 0.229525 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229525 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(140\) | −193.171 | − | 246.343i | −0.116614 | − | 0.148713i | ||||
\(141\) | 352.304 | 0.210421 | ||||||||
\(142\) | 804.200i | 0.475260i | ||||||||
\(143\) | 2282.95i | 1.33503i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | −174.182 | + | 136.586i | −0.0997586 | + | 0.0782264i | ||||
\(146\) | −606.343 | −0.343707 | ||||||||
\(147\) | − | 147.000i | − | 0.0824786i | ||||||
\(148\) | − | 1131.88i | − | 0.628647i | ||||||
\(149\) | −1709.01 | −0.939648 | −0.469824 | − | 0.882760i | \(-0.655683\pi\) | ||||
−0.469824 | + | 0.882760i | \(0.655683\pi\) | |||||||
\(150\) | −178.849 | + | 728.363i | −0.0973531 | + | 0.396471i | ||||
\(151\) | −2773.61 | −1.49479 | −0.747395 | − | 0.664380i | \(-0.768696\pi\) | ||||
−0.747395 | + | 0.664380i | \(0.768696\pi\) | |||||||
\(152\) | − | 94.3837i | − | 0.0503653i | ||||||
\(153\) | − | 169.090i | − | 0.0893471i | ||||||
\(154\) | −358.343 | −0.187507 | ||||||||
\(155\) | −1112.10 | + | 872.059i | −0.576296 | + | 0.451906i | ||||
\(156\) | 1070.30 | 0.549312 | ||||||||
\(157\) | − | 353.478i | − | 0.179685i | −0.995956 | − | 0.0898426i | \(-0.971364\pi\) | ||
0.995956 | − | 0.0898426i | \(-0.0286364\pi\) | |||||||
\(158\) | − | 532.767i | − | 0.268258i | ||||||
\(159\) | −1903.51 | −0.949424 | ||||||||
\(160\) | 220.767 | + | 281.535i | 0.109082 | + | 0.139108i | ||||
\(161\) | −1115.61 | −0.546104 | ||||||||
\(162\) | 162.000i | 0.0785674i | ||||||||
\(163\) | 885.231i | 0.425378i | 0.977120 | + | 0.212689i | \(0.0682221\pi\) | ||||
−0.977120 | + | 0.212689i | \(0.931778\pi\) | |||||||
\(164\) | 577.535 | 0.274987 | ||||||||
\(165\) | 529.757 | + | 675.576i | 0.249949 | + | 0.318748i | ||||
\(166\) | −1506.51 | −0.704383 | ||||||||
\(167\) | − | 3220.26i | − | 1.49216i | −0.665855 | − | 0.746081i | \(-0.731933\pi\) | ||
0.665855 | − | 0.746081i | \(-0.268067\pi\) | |||||||
\(168\) | 168.000i | 0.0771517i | ||||||||
\(169\) | −5758.18 | −2.62093 | ||||||||
\(170\) | −330.588 | + | 259.233i | −0.149147 | + | 0.116954i | ||||
\(171\) | −106.182 | −0.0474849 | ||||||||
\(172\) | 1307.71i | 0.579723i | ||||||||
\(173\) | 3780.62i | 1.66148i | 0.556663 | + | 0.830738i | \(0.312081\pi\) | ||||
−0.556663 | + | 0.830738i | \(0.687919\pi\) | |||||||
\(174\) | 118.788 | 0.0517545 | ||||||||
\(175\) | 849.757 | + | 208.657i | 0.367061 | + | 0.0901314i | ||||
\(176\) | 409.535 | 0.175397 | ||||||||
\(177\) | 1545.21i | 0.656186i | ||||||||
\(178\) | 1685.93i | 0.709922i | ||||||||
\(179\) | −4534.07 | −1.89325 | −0.946627 | − | 0.322330i | \(-0.895534\pi\) | ||||
−0.946627 | + | 0.322330i | \(0.895534\pi\) | |||||||
\(180\) | 316.727 | − | 248.363i | 0.131152 | − | 0.102844i | ||||
\(181\) | 1805.49 | 0.741443 | 0.370721 | − | 0.928744i | \(-0.379110\pi\) | ||||
0.370721 | + | 0.928744i | \(0.379110\pi\) | |||||||
\(182\) | − | 1248.69i | − | 0.508565i | ||||||
\(183\) | 1187.15i | 0.479544i | ||||||||
\(184\) | 1274.99 | 0.510833 | ||||||||
\(185\) | 1952.20 | + | 2489.55i | 0.775830 | + | 0.989382i | ||||
\(186\) | 758.424 | 0.298981 | ||||||||
\(187\) | 480.890i | 0.188054i | ||||||||
\(188\) | 469.739i | 0.182230i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 162.788 | + | 207.596i | 0.0621572 | + | 0.0792663i | ||||
\(191\) | 3359.15 | 1.27256 | 0.636282 | − | 0.771456i | \(-0.280471\pi\) | ||||
0.636282 | + | 0.771456i | \(0.280471\pi\) | |||||||
\(192\) | − | 192.000i | − | 0.0721688i | ||||||
\(193\) | − | 2800.56i | − | 1.04450i | −0.852792 | − | 0.522251i | \(-0.825092\pi\) | ||
0.852792 | − | 0.522251i | \(-0.174908\pi\) | |||||||
\(194\) | 2403.84 | 0.889616 | ||||||||
\(195\) | −2354.12 | + | 1846.00i | −0.864523 | + | 0.677921i | ||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | − | 3252.52i | − | 1.17631i | −0.808749 | − | 0.588154i | \(-0.799855\pi\) | ||
0.808749 | − | 0.588154i | \(-0.200145\pi\) | |||||||
\(198\) | − | 460.727i | − | 0.165366i | ||||||
\(199\) | 1525.31 | 0.543347 | 0.271674 | − | 0.962389i | \(-0.412423\pi\) | ||||
0.271674 | + | 0.962389i | \(0.412423\pi\) | |||||||
\(200\) | −971.151 | − | 238.465i | −0.343354 | − | 0.0843102i | ||||
\(201\) | 2526.36 | 0.886546 | ||||||||
\(202\) | 1150.74i | 0.400822i | ||||||||
\(203\) | − | 138.586i | − | 0.0479153i | ||||||
\(204\) | 225.453 | 0.0773768 | ||||||||
\(205\) | −1270.28 | + | 996.100i | −0.432782 | + | 0.339369i | ||||
\(206\) | 508.441 | 0.171965 | ||||||||
\(207\) | − | 1434.36i | − | 0.481618i | ||||||
\(208\) | 1427.07i | 0.475719i | ||||||||
\(209\) | 301.980 | 0.0999443 | ||||||||
\(210\) | −289.757 | − | 369.514i | −0.0952150 | − | 0.121423i | ||||
\(211\) | −2934.29 | −0.957370 | −0.478685 | − | 0.877987i | \(-0.658886\pi\) | ||||
−0.478685 | + | 0.877987i | \(0.658886\pi\) | |||||||
\(212\) | − | 2538.02i | − | 0.822225i | ||||||
\(213\) | 1206.30i | 0.388048i | ||||||||
\(214\) | 2285.21 | 0.729971 | ||||||||
\(215\) | −2255.47 | − | 2876.30i | −0.715451 | − | 0.912383i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | − | 884.829i | − | 0.276802i | ||||||
\(218\) | 4108.56i | 1.27645i | ||||||||
\(219\) | −909.514 | −0.280636 | ||||||||
\(220\) | −900.767 | + | 706.343i | −0.276044 | + | 0.216462i | ||||
\(221\) | −1675.71 | −0.510049 | ||||||||
\(222\) | − | 1697.82i | − | 0.513288i | ||||||
\(223\) | − | 3626.30i | − | 1.08895i | −0.838778 | − | 0.544473i | \(-0.816730\pi\) | ||
0.838778 | − | 0.544473i | \(-0.183270\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −268.273 | + | 1092.54i | −0.0794884 | + | 0.323717i | ||||
\(226\) | 1781.65 | 0.524397 | ||||||||
\(227\) | 2189.45i | 0.640171i | 0.947389 | + | 0.320086i | \(0.103712\pi\) | ||||
−0.947389 | + | 0.320086i | \(0.896288\pi\) | |||||||
\(228\) | − | 141.576i | − | 0.0411231i | ||||||
\(229\) | 5501.00 | 1.58741 | 0.793704 | − | 0.608304i | \(-0.208150\pi\) | ||||
0.793704 | + | 0.608304i | \(0.208150\pi\) | |||||||
\(230\) | −2804.32 | + | 2199.03i | −0.803963 | + | 0.630433i | ||||
\(231\) | −537.514 | −0.153099 | ||||||||
\(232\) | 158.384i | 0.0448207i | ||||||||
\(233\) | 3927.72i | 1.10435i | 0.833729 | + | 0.552174i | \(0.186202\pi\) | ||||
−0.833729 | + | 0.552174i | \(0.813798\pi\) | |||||||
\(234\) | 1605.45 | 0.448512 | ||||||||
\(235\) | −810.180 | − | 1033.19i | −0.224895 | − | 0.286798i | ||||
\(236\) | −2060.28 | −0.568274 | ||||||||
\(237\) | − | 799.151i | − | 0.219031i | ||||||
\(238\) | − | 263.029i | − | 0.0716370i | ||||||
\(239\) | −4435.11 | −1.20035 | −0.600174 | − | 0.799869i | \(-0.704902\pi\) | ||||
−0.600174 | + | 0.799869i | \(0.704902\pi\) | |||||||
\(240\) | 331.151 | + | 422.302i | 0.0890654 | + | 0.113581i | ||||
\(241\) | 4575.81 | 1.22304 | 0.611522 | − | 0.791227i | \(-0.290557\pi\) | ||||
0.611522 | + | 0.791227i | \(0.290557\pi\) | |||||||
\(242\) | − | 1351.70i | − | 0.359051i | ||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −1582.87 | −0.415297 | ||||||||
\(245\) | −431.100 | + | 338.050i | −0.112416 | + | 0.0881519i | ||||
\(246\) | 866.302 | 0.224526 | ||||||||
\(247\) | 1052.28i | 0.271073i | ||||||||
\(248\) | 1011.23i | 0.258925i | ||||||||
\(249\) | −2259.76 | −0.575126 | ||||||||
\(250\) | 2547.33 | − | 1150.49i | 0.644429 | − | 0.291052i | ||||
\(251\) | 1646.96 | 0.414163 | 0.207081 | − | 0.978324i | \(-0.433603\pi\) | ||||
0.207081 | + | 0.978324i | \(0.433603\pi\) | |||||||
\(252\) | 252.000i | 0.0629941i | ||||||||
\(253\) | 4079.31i | 1.01369i | ||||||||
\(254\) | 4608.32 | 1.13839 | ||||||||
\(255\) | −495.882 | + | 388.849i | −0.121778 | + | 0.0954928i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 2811.64i | − | 0.682432i | −0.939985 | − | 0.341216i | \(-0.889161\pi\) | ||
0.939985 | − | 0.341216i | \(-0.110839\pi\) | |||||||
\(258\) | 1961.57i | 0.473341i | ||||||||
\(259\) | −1980.79 | −0.475212 | ||||||||
\(260\) | −2461.33 | − | 3138.82i | −0.587097 | − | 0.748699i | ||||
\(261\) | 178.182 | 0.0422573 | ||||||||
\(262\) | 1910.38i | 0.450473i | ||||||||
\(263\) | − | 3103.13i | − | 0.727556i | −0.931486 | − | 0.363778i | \(-0.881487\pi\) | ||
0.931486 | − | 0.363778i | \(-0.118513\pi\) | |||||||
\(264\) | 614.302 | 0.143211 | ||||||||
\(265\) | 4377.43 | + | 5582.34i | 1.01473 | + | 1.29404i | ||||
\(266\) | −165.171 | −0.0380726 | ||||||||
\(267\) | 2528.90i | 0.579649i | ||||||||
\(268\) | 3368.48i | 0.767772i | ||||||||
\(269\) | 61.1877 | 0.0138687 | 0.00693435 | − | 0.999976i | \(-0.497793\pi\) | ||||
0.00693435 | + | 0.999976i | \(0.497793\pi\) | |||||||
\(270\) | 475.090 | − | 372.545i | 0.107085 | − | 0.0839717i | ||||
\(271\) | 97.6285 | 0.0218838 | 0.0109419 | − | 0.999940i | \(-0.496517\pi\) | ||||
0.0109419 | + | 0.999940i | \(0.496517\pi\) | |||||||
\(272\) | 300.604i | 0.0670103i | ||||||||
\(273\) | − | 1873.03i | − | 0.415241i | ||||||
\(274\) | −2979.07 | −0.656832 | ||||||||
\(275\) | 762.967 | − | 3107.19i | 0.167304 | − | 0.681347i | ||||
\(276\) | 1912.48 | 0.417094 | ||||||||
\(277\) | − | 4719.24i | − | 1.02365i | −0.859089 | − | 0.511826i | \(-0.828969\pi\) | ||
0.859089 | − | 0.511826i | \(-0.171031\pi\) | |||||||
\(278\) | 1504.57i | 0.324597i | ||||||||
\(279\) | 1137.64 | 0.244117 | ||||||||
\(280\) | 492.686 | − | 386.343i | 0.105156 | − | 0.0824586i | ||||
\(281\) | 995.094 | 0.211254 | 0.105627 | − | 0.994406i | \(-0.466315\pi\) | ||||
0.105627 | + | 0.994406i | \(0.466315\pi\) | |||||||
\(282\) | 704.608i | 0.148790i | ||||||||
\(283\) | − | 7995.58i | − | 1.67946i | −0.543002 | − | 0.839732i | \(-0.682712\pi\) | ||
0.543002 | − | 0.839732i | \(-0.317288\pi\) | |||||||
\(284\) | −1608.40 | −0.336060 | ||||||||
\(285\) | 244.182 | + | 311.394i | 0.0507511 | + | 0.0647206i | ||||
\(286\) | −4565.89 | −0.944010 | ||||||||
\(287\) | − | 1010.69i | − | 0.207871i | ||||||
\(288\) | − | 288.000i | − | 0.0589256i | ||||||
\(289\) | 4560.02 | 0.928154 | ||||||||
\(290\) | −273.171 | − | 348.363i | −0.0553144 | − | 0.0705400i | ||||
\(291\) | 3605.76 | 0.726368 | ||||||||
\(292\) | − | 1212.69i | − | 0.243038i | ||||||
\(293\) | − | 8930.79i | − | 1.78069i | −0.455286 | − | 0.890345i | \(-0.650463\pi\) | ||
0.455286 | − | 0.890345i | \(-0.349537\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 4531.56 | − | 3553.45i | 0.894365 | − | 0.701322i | ||||
\(296\) | 2263.76 | 0.444521 | ||||||||
\(297\) | − | 691.090i | − | 0.135021i | ||||||
\(298\) | − | 3418.02i | − | 0.664432i | ||||||
\(299\) | −14214.8 | −2.74938 | ||||||||
\(300\) | −1456.73 | − | 357.698i | −0.280347 | − | 0.0688390i | ||||
\(301\) | 2288.50 | 0.438229 | ||||||||
\(302\) | − | 5547.22i | − | 1.05698i | ||||||
\(303\) | 1726.11i | 0.327270i | ||||||||
\(304\) | 188.767 | 0.0356137 | ||||||||
\(305\) | 3481.50 | − | 2730.04i | 0.653606 | − | 0.512530i | ||||
\(306\) | 338.180 | 0.0631779 | ||||||||
\(307\) | − | 2515.79i | − | 0.467700i | −0.972273 | − | 0.233850i | \(-0.924868\pi\) | ||
0.972273 | − | 0.233850i | \(-0.0751324\pi\) | |||||||
\(308\) | − | 716.686i | − | 0.132588i | ||||||
\(309\) | 762.661 | 0.140409 | ||||||||
\(310\) | −1744.12 | − | 2224.20i | −0.319546 | − | 0.407503i | ||||
\(311\) | 3759.39 | 0.685452 | 0.342726 | − | 0.939435i | \(-0.388650\pi\) | ||||
0.342726 | + | 0.939435i | \(0.388650\pi\) | |||||||
\(312\) | 2140.60i | 0.388423i | ||||||||
\(313\) | 6825.91i | 1.23266i | 0.787487 | + | 0.616331i | \(0.211382\pi\) | ||||
−0.787487 | + | 0.616331i | \(0.788618\pi\) | |||||||
\(314\) | 706.955 | 0.127057 | ||||||||
\(315\) | −434.636 | − | 554.271i | −0.0777427 | − | 0.0991418i | ||||
\(316\) | 1065.53 | 0.189687 | ||||||||
\(317\) | 2464.94i | 0.436734i | 0.975867 | + | 0.218367i | \(0.0700730\pi\) | ||||
−0.975867 | + | 0.218367i | \(0.929927\pi\) | |||||||
\(318\) | − | 3807.02i | − | 0.671344i | ||||||
\(319\) | −506.747 | −0.0889416 | ||||||||
\(320\) | −563.069 | + | 441.535i | −0.0983642 | + | 0.0771329i | ||||
\(321\) | 3427.82 | 0.596019 | ||||||||
\(322\) | − | 2231.23i | − | 0.386154i | ||||||
\(323\) | 221.657i | 0.0381837i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 10827.3 | + | 2658.64i | 1.84798 | + | 0.453769i | ||||
\(326\) | −1770.46 | −0.300788 | ||||||||
\(327\) | 6162.84i | 1.04222i | ||||||||
\(328\) | 1155.07i | 0.194445i | ||||||||
\(329\) | 822.043 | 0.137753 | ||||||||
\(330\) | −1351.15 | + | 1059.51i | −0.225389 | + | 0.176740i | ||||
\(331\) | 3780.36 | 0.627756 | 0.313878 | − | 0.949463i | \(-0.398372\pi\) | ||||
0.313878 | + | 0.949463i | \(0.398372\pi\) | |||||||
\(332\) | − | 3013.01i | − | 0.498074i | ||||||
\(333\) | − | 2546.72i | − | 0.419098i | ||||||
\(334\) | 6440.52 | 1.05512 | ||||||||
\(335\) | −5809.77 | − | 7408.94i | −0.947528 | − | 1.20834i | ||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | − | 1914.39i | − | 0.309446i | −0.987958 | − | 0.154723i | \(-0.950551\pi\) | ||
0.987958 | − | 0.154723i | \(-0.0494485\pi\) | |||||||
\(338\) | − | 11516.4i | − | 1.85328i | ||||||
\(339\) | 2672.48 | 0.428169 | ||||||||
\(340\) | −518.465 | − | 661.176i | −0.0826992 | − | 0.105463i | ||||
\(341\) | −3235.43 | −0.513807 | ||||||||
\(342\) | − | 212.363i | − | 0.0335769i | ||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | −2615.43 | −0.409926 | ||||||||
\(345\) | −4206.48 | + | 3298.54i | −0.656433 | + | 0.514747i | ||||
\(346\) | −7561.24 | −1.17484 | ||||||||
\(347\) | 9118.93i | 1.41075i | 0.708835 | + | 0.705375i | \(0.249221\pi\) | ||||
−0.708835 | + | 0.705375i | \(0.750779\pi\) | |||||||
\(348\) | 237.576i | 0.0365959i | ||||||||
\(349\) | −4832.45 | −0.741189 | −0.370594 | − | 0.928795i | \(-0.620846\pi\) | ||||
−0.370594 | + | 0.928795i | \(0.620846\pi\) | |||||||
\(350\) | −417.314 | + | 1699.51i | −0.0637325 | + | 0.259551i | ||||
\(351\) | 2408.18 | 0.366208 | ||||||||
\(352\) | 819.069i | 0.124024i | ||||||||
\(353\) | 2806.58i | 0.423170i | 0.977360 | + | 0.211585i | \(0.0678625\pi\) | ||||
−0.977360 | + | 0.211585i | \(0.932138\pi\) | |||||||
\(354\) | −3090.42 | −0.463994 | ||||||||
\(355\) | 3537.66 | − | 2774.08i | 0.528900 | − | 0.414740i | ||||
\(356\) | −3371.87 | −0.501991 | ||||||||
\(357\) | − | 394.543i | − | 0.0584914i | ||||||
\(358\) | − | 9068.15i | − | 1.33873i | ||||||
\(359\) | 1075.06 | 0.158049 | 0.0790246 | − | 0.996873i | \(-0.474819\pi\) | ||||
0.0790246 | + | 0.996873i | \(0.474819\pi\) | |||||||
\(360\) | 496.727 | + | 633.453i | 0.0727216 | + | 0.0927386i | ||||
\(361\) | −6719.81 | −0.979707 | ||||||||
\(362\) | 3610.98i | 0.524279i | ||||||||
\(363\) | − | 2027.55i | − | 0.293164i | ||||||
\(364\) | 2497.37 | 0.359609 | ||||||||
\(365\) | 2091.57 | + | 2667.29i | 0.299940 | + | 0.382500i | ||||
\(366\) | −2374.30 | −0.339089 | ||||||||
\(367\) | − | 367.020i | − | 0.0522025i | −0.999659 | − | 0.0261012i | \(-0.991691\pi\) | ||
0.999659 | − | 0.0261012i | \(-0.00830922\pi\) | |||||||
\(368\) | 2549.98i | 0.361214i | ||||||||
\(369\) | 1299.45 | 0.183325 | ||||||||
\(370\) | −4979.11 | + | 3904.40i | −0.699598 | + | 0.548595i | ||||
\(371\) | −4441.53 | −0.621544 | ||||||||
\(372\) | 1516.85i | 0.211411i | ||||||||
\(373\) | − | 1304.56i | − | 0.181092i | −0.995892 | − | 0.0905461i | \(-0.971139\pi\) | ||
0.995892 | − | 0.0905461i | \(-0.0288613\pi\) | |||||||
\(374\) | −961.780 | −0.132974 | ||||||||
\(375\) | 3820.99 | − | 1725.73i | 0.526174 | − | 0.237643i | ||||
\(376\) | −939.478 | −0.128856 | ||||||||
\(377\) | − | 1765.82i | − | 0.241231i | ||||||
\(378\) | 378.000i | 0.0514344i | ||||||||
\(379\) | −5340.61 | −0.723822 | −0.361911 | − | 0.932213i | \(-0.617876\pi\) | ||||
−0.361911 | + | 0.932213i | \(0.617876\pi\) | |||||||
\(380\) | −415.192 | + | 325.576i | −0.0560497 | + | 0.0439518i | ||||
\(381\) | 6912.48 | 0.929493 | ||||||||
\(382\) | 6718.31i | 0.899839i | ||||||||
\(383\) | 6662.27i | 0.888841i | 0.895818 | + | 0.444420i | \(0.146590\pi\) | ||||
−0.895818 | + | 0.444420i | \(0.853410\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 1236.10 | + | 1576.34i | 0.163630 | + | 0.208670i | ||||
\(386\) | 5601.13 | 0.738575 | ||||||||
\(387\) | 2942.36i | 0.386482i | ||||||||
\(388\) | 4807.67i | 0.629053i | ||||||||
\(389\) | 6313.48 | 0.822895 | 0.411448 | − | 0.911433i | \(-0.365023\pi\) | ||||
0.411448 | + | 0.911433i | \(0.365023\pi\) | |||||||
\(390\) | −3692.00 | − | 4708.24i | −0.479363 | − | 0.611310i | ||||
\(391\) | −2994.27 | −0.387281 | ||||||||
\(392\) | 392.000i | 0.0505076i | ||||||||
\(393\) | 2865.58i | 0.367810i | ||||||||
\(394\) | 6505.05 | 0.831776 | ||||||||
\(395\) | −2343.63 | + | 1837.78i | −0.298534 | + | 0.234098i | ||||
\(396\) | 921.453 | 0.116931 | ||||||||
\(397\) | 14210.6i | 1.79650i | 0.439490 | + | 0.898248i | \(0.355159\pi\) | ||||
−0.439490 | + | 0.898248i | \(0.644841\pi\) | |||||||
\(398\) | 3050.61i | 0.384204i | ||||||||
\(399\) | −247.757 | −0.0310861 | ||||||||
\(400\) | 476.931 | − | 1942.30i | 0.0596163 | − | 0.242788i | ||||
\(401\) | 5578.59 | 0.694717 | 0.347359 | − | 0.937732i | \(-0.387079\pi\) | ||||
0.347359 | + | 0.937732i | \(0.387079\pi\) | |||||||
\(402\) | 5052.72i | 0.626883i | ||||||||
\(403\) | − | 11274.2i | − | 1.39357i | ||||||
\(404\) | −2301.49 | −0.283424 | ||||||||
\(405\) | 712.635 | − | 558.817i | 0.0874348 | − | 0.0685626i | ||||
\(406\) | 277.171 | 0.0338812 | ||||||||
\(407\) | 7242.86i | 0.882101i | ||||||||
\(408\) | 450.906i | 0.0547137i | ||||||||
\(409\) | −11914.0 | −1.44037 | −0.720184 | − | 0.693783i | \(-0.755943\pi\) | ||||
−0.720184 | + | 0.693783i | \(0.755943\pi\) | |||||||
\(410\) | −1992.20 | − | 2540.56i | −0.239970 | − | 0.306023i | ||||
\(411\) | −4468.60 | −0.536301 | ||||||||
\(412\) | 1016.88i | 0.121597i | ||||||||
\(413\) | 3605.49i | 0.429575i | ||||||||
\(414\) | 2868.72 | 0.340556 | ||||||||
\(415\) | 5196.68 | + | 6627.09i | 0.614686 | + | 0.783882i | ||||
\(416\) | −2854.14 | −0.336384 | ||||||||
\(417\) | 2256.85i | 0.265032i | ||||||||
\(418\) | 603.959i | 0.0706713i | ||||||||
\(419\) | 12093.0 | 1.40998 | 0.704990 | − | 0.709217i | \(-0.250951\pi\) | ||||
0.704990 | + | 0.709217i | \(0.250951\pi\) | |||||||
\(420\) | 739.029 | − | 579.514i | 0.0858593 | − | 0.0673271i | ||||
\(421\) | −12188.5 | −1.41100 | −0.705500 | − | 0.708710i | \(-0.749277\pi\) | ||||
−0.705500 | + | 0.708710i | \(0.749277\pi\) | |||||||
\(422\) | − | 5868.59i | − | 0.676963i | ||||||
\(423\) | 1056.91i | 0.121487i | ||||||||
\(424\) | 5076.03 | 0.581401 | ||||||||
\(425\) | 2280.72 | + | 560.028i | 0.260308 | + | 0.0639185i | ||||
\(426\) | −2412.60 | −0.274392 | ||||||||
\(427\) | 2770.01i | 0.313935i | ||||||||
\(428\) | 4570.42i | 0.516168i | ||||||||
\(429\) | −6848.84 | −0.770781 | ||||||||
\(430\) | 5752.61 | − | 4510.95i | 0.645152 | − | 0.505900i | ||||
\(431\) | 4968.16 | 0.555238 | 0.277619 | − | 0.960691i | \(-0.410455\pi\) | ||||
0.277619 | + | 0.960691i | \(0.410455\pi\) | |||||||
\(432\) | − | 432.000i | − | 0.0481125i | ||||||
\(433\) | 14483.7i | 1.60749i | 0.594974 | + | 0.803745i | \(0.297162\pi\) | ||||
−0.594974 | + | 0.803745i | \(0.702838\pi\) | |||||||
\(434\) | 1769.66 | 0.195729 | ||||||||
\(435\) | −409.757 | − | 522.545i | −0.0451640 | − | 0.0575957i | ||||
\(436\) | −8217.13 | −0.902589 | ||||||||
\(437\) | 1880.28i | 0.205826i | ||||||||
\(438\) | − | 1819.03i | − | 0.198440i | ||||||
\(439\) | 9937.64 | 1.08040 | 0.540202 | − | 0.841535i | \(-0.318348\pi\) | ||||
0.540202 | + | 0.841535i | \(0.318348\pi\) | |||||||
\(440\) | −1412.69 | − | 1801.53i | −0.153062 | − | 0.195193i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − | 3351.43i | − | 0.360659i | ||||||
\(443\) | − | 17139.6i | − | 1.83821i | −0.394013 | − | 0.919105i | \(-0.628913\pi\) | ||
0.394013 | − | 0.919105i | \(-0.371087\pi\) | |||||||
\(444\) | 3395.63 | 0.362950 | ||||||||
\(445\) | 7416.39 | − | 5815.61i | 0.790047 | − | 0.619520i | ||||
\(446\) | 7252.60 | 0.770001 | ||||||||
\(447\) | − | 5127.03i | − | 0.542506i | ||||||
\(448\) | − | 448.000i | − | 0.0472456i | ||||||
\(449\) | −1555.34 | −0.163477 | −0.0817385 | − | 0.996654i | \(-0.526047\pi\) | ||||
−0.0817385 | + | 0.996654i | \(0.526047\pi\) | |||||||
\(450\) | −2185.09 | − | 536.547i | −0.228902 | − | 0.0562068i | ||||
\(451\) | −3695.63 | −0.385855 | ||||||||
\(452\) | 3563.31i | 0.370805i | ||||||||
\(453\) | − | 8320.84i | − | 0.863018i | ||||||
\(454\) | −4378.90 | −0.452669 | ||||||||
\(455\) | −5492.94 | + | 4307.33i | −0.565963 | + | 0.443804i | ||||
\(456\) | 283.151 | 0.0290784 | ||||||||
\(457\) | 18409.2i | 1.88435i | 0.335124 | + | 0.942174i | \(0.391222\pi\) | ||||
−0.335124 | + | 0.942174i | \(0.608778\pi\) | |||||||
\(458\) | 11002.0i | 1.12247i | ||||||||
\(459\) | 507.269 | 0.0515845 | ||||||||
\(460\) | −4398.06 | − | 5608.64i | −0.445784 | − | 0.568488i | ||||
\(461\) | 6616.52 | 0.668465 | 0.334232 | − | 0.942491i | \(-0.391523\pi\) | ||||
0.334232 | + | 0.942491i | \(0.391523\pi\) | |||||||
\(462\) | − | 1075.03i | − | 0.108257i | ||||||
\(463\) | 12605.5i | 1.26529i | 0.774443 | + | 0.632644i | \(0.218030\pi\) | ||||
−0.774443 | + | 0.632644i | \(0.781970\pi\) | |||||||
\(464\) | −316.767 | −0.0316930 | ||||||||
\(465\) | −2616.18 | − | 3336.29i | −0.260908 | − | 0.332725i | ||||
\(466\) | −7855.43 | −0.780892 | ||||||||
\(467\) | 16291.5i | 1.61431i | 0.590340 | + | 0.807155i | \(0.298994\pi\) | ||||
−0.590340 | + | 0.807155i | \(0.701006\pi\) | |||||||
\(468\) | 3210.91i | 0.317146i | ||||||||
\(469\) | 5894.84 | 0.580381 | ||||||||
\(470\) | 2066.37 | − | 1620.36i | 0.202797 | − | 0.159025i | ||||
\(471\) | 1060.43 | 0.103741 | ||||||||
\(472\) | − | 4120.55i | − | 0.401830i | ||||||
\(473\) | − | 8368.04i | − | 0.813452i | ||||||
\(474\) | 1598.30 | 0.154879 | ||||||||
\(475\) | 351.675 | − | 1432.20i | 0.0339705 | − | 0.138345i | ||||
\(476\) | 526.057 | 0.0506550 | ||||||||
\(477\) | − | 5710.54i | − | 0.548150i | ||||||
\(478\) | − | 8870.22i | − | 0.848775i | ||||||
\(479\) | −11506.3 | −1.09757 | −0.548785 | − | 0.835963i | \(-0.684909\pi\) | ||||
−0.548785 | + | 0.835963i | \(0.684909\pi\) | |||||||
\(480\) | −844.604 | + | 662.302i | −0.0803140 | + | 0.0629788i | ||||
\(481\) | −25238.6 | −2.39247 | ||||||||
\(482\) | 9151.62i | 0.864823i | ||||||||
\(483\) | − | 3346.84i | − | 0.315293i | ||||||
\(484\) | 2703.40 | 0.253888 | ||||||||
\(485\) | −8292.01 | − | 10574.4i | −0.776332 | − | 0.990021i | ||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 16502.9i | 1.53556i | 0.640714 | + | 0.767780i | \(0.278639\pi\) | ||||
−0.640714 | + | 0.767780i | \(0.721361\pi\) | |||||||
\(488\) | − | 3165.73i | − | 0.293660i | ||||||
\(489\) | −2655.69 | −0.245592 | ||||||||
\(490\) | −676.100 | − | 862.200i | −0.0623328 | − | 0.0794903i | ||||
\(491\) | 9269.67 | 0.852004 | 0.426002 | − | 0.904722i | \(-0.359922\pi\) | ||||
0.426002 | + | 0.904722i | \(0.359922\pi\) | |||||||
\(492\) | 1732.60i | 0.158764i | ||||||||
\(493\) | − | 371.959i | − | 0.0339801i | ||||||
\(494\) | −2104.56 | −0.191678 | ||||||||
\(495\) | −2026.73 | + | 1589.27i | −0.184029 | + | 0.144308i | ||||
\(496\) | −2022.47 | −0.183087 | ||||||||
\(497\) | 2814.70i | 0.254037i | ||||||||
\(498\) | − | 4519.52i | − | 0.406676i | ||||||
\(499\) | −13167.3 | −1.18126 | −0.590631 | − | 0.806941i | \(-0.701121\pi\) | ||||
−0.590631 | + | 0.806941i | \(0.701121\pi\) | |||||||
\(500\) | 2300.97 | + | 5094.66i | 0.205805 | + | 0.455680i | ||||
\(501\) | 9660.78 | 0.861500 | ||||||||
\(502\) | 3293.91i | 0.292857i | ||||||||
\(503\) | 16299.1i | 1.44481i | 0.691469 | + | 0.722406i | \(0.256964\pi\) | ||||
−0.691469 | + | 0.722406i | \(0.743036\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | 5062.09 | − | 3969.48i | 0.446060 | − | 0.349781i | ||||
\(506\) | −8158.62 | −0.716788 | ||||||||
\(507\) | − | 17274.6i | − | 1.51319i | ||||||
\(508\) | 9216.64i | 0.804965i | ||||||||
\(509\) | 10595.4 | 0.922656 | 0.461328 | − | 0.887230i | \(-0.347373\pi\) | ||||
0.461328 | + | 0.887230i | \(0.347373\pi\) | |||||||
\(510\) | −777.698 | − | 991.763i | −0.0675236 | − | 0.0861098i | ||||
\(511\) | −2122.20 | −0.183719 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | − | 318.545i | − | 0.0274154i | ||||||
\(514\) | 5623.27 | 0.482552 | ||||||||
\(515\) | −1753.86 | − | 2236.62i | −0.150067 | − | 0.191373i | ||||
\(516\) | −3923.14 | −0.334703 | ||||||||
\(517\) | − | 3005.85i | − | 0.255700i | ||||||
\(518\) | − | 3961.57i | − | 0.336026i | ||||||
\(519\) | −11341.9 | −0.959254 | ||||||||
\(520\) | 6277.65 | − | 4922.66i | 0.529410 | − | 0.415140i | ||||
\(521\) | −3930.10 | −0.330481 | −0.165241 | − | 0.986253i | \(-0.552840\pi\) | ||||
−0.165241 | + | 0.986253i | \(0.552840\pi\) | |||||||
\(522\) | 356.363i | 0.0298805i | ||||||||
\(523\) | − | 15430.7i | − | 1.29013i | −0.764129 | − | 0.645064i | \(-0.776831\pi\) | ||
0.764129 | − | 0.645064i | \(-0.223169\pi\) | |||||||
\(524\) | −3820.77 | −0.318532 | ||||||||
\(525\) | −625.971 | + | 2549.27i | −0.0520374 | + | 0.211923i | ||||
\(526\) | 6206.26 | 0.514459 | ||||||||
\(527\) | − | 2374.85i | − | 0.196300i | ||||||
\(528\) | 1228.60i | 0.101265i | ||||||||
\(529\) | −13232.9 | −1.08761 | ||||||||
\(530\) | −11164.7 | + | 8754.86i | −0.915024 | + | 0.717522i | ||||
\(531\) | −4635.62 | −0.378849 | ||||||||
\(532\) | − | 330.343i | − | 0.0269214i | ||||||
\(533\) | − | 12877.8i | − | 1.04653i | ||||||
\(534\) | −5057.80 | −0.409874 | ||||||||
\(535\) | −7882.82 | − | 10052.6i | −0.637017 | − | 0.812359i | ||||
\(536\) | −6736.96 | −0.542896 | ||||||||
\(537\) | − | 13602.2i | − | 1.09307i | ||||||
\(538\) | 122.375i | 0.00980665i | ||||||||
\(539\) | −1254.20 | −0.100227 | ||||||||
\(540\) | 745.090 | + | 950.180i | 0.0593770 | + | 0.0757208i | ||||
\(541\) | −24132.0 | −1.91777 | −0.958885 | − | 0.283794i | \(-0.908407\pi\) | ||||
−0.958885 | + | 0.283794i | \(0.908407\pi\) | |||||||
\(542\) | 195.257i | 0.0154742i | ||||||||
\(543\) | 5416.48i | 0.428072i | ||||||||
\(544\) | −601.208 | −0.0473834 | ||||||||
\(545\) | 18073.5 | − | 14172.4i | 1.42052 | − | 1.11391i | ||||
\(546\) | 3746.06 | 0.293620 | ||||||||
\(547\) | − | 3505.64i | − | 0.274022i | −0.990569 | − | 0.137011i | \(-0.956250\pi\) | ||
0.990569 | − | 0.137011i | \(-0.0437496\pi\) | |||||||
\(548\) | − | 5958.13i | − | 0.464450i | ||||||
\(549\) | −3561.45 | −0.276865 | ||||||||
\(550\) | 6214.38 | + | 1525.93i | 0.481785 | + | 0.118302i | ||||
\(551\) | −233.576 | −0.0180593 | ||||||||
\(552\) | 3824.96i | 0.294930i | ||||||||
\(553\) | − | 1864.69i | − | 0.143390i | ||||||
\(554\) | 9438.48 | 0.723831 | ||||||||
\(555\) | −7468.66 | + | 5856.60i | −0.571220 | + | 0.447926i | ||||
\(556\) | −3009.13 | −0.229525 | ||||||||
\(557\) | 14427.0i | 1.09747i | 0.835995 | + | 0.548737i | \(0.184891\pi\) | ||||
−0.835995 | + | 0.548737i | \(0.815109\pi\) | |||||||
\(558\) | 2275.27i | 0.172616i | ||||||||
\(559\) | 29159.4 | 2.20628 | ||||||||
\(560\) | 772.686 | + | 985.371i | 0.0583070 | + | 0.0743563i | ||||
\(561\) | −1442.67 | −0.108573 | ||||||||
\(562\) | 1990.19i | 0.149379i | ||||||||
\(563\) | − | 9972.47i | − | 0.746518i | −0.927727 | − | 0.373259i | \(-0.878240\pi\) | ||
0.927727 | − | 0.373259i | \(-0.121760\pi\) | |||||||
\(564\) | −1409.22 | −0.105210 | ||||||||
\(565\) | −6145.79 | − | 7837.46i | −0.457620 | − | 0.583583i | ||||
\(566\) | 15991.2 | 1.18756 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − | 3216.80i | − | 0.237630i | ||||||
\(569\) | 25180.3 | 1.85521 | 0.927605 | − | 0.373563i | \(-0.121864\pi\) | ||||
0.927605 | + | 0.373563i | \(0.121864\pi\) | |||||||
\(570\) | −622.788 | + | 488.363i | −0.0457644 | + | 0.0358865i | ||||
\(571\) | 6146.38 | 0.450470 | 0.225235 | − | 0.974305i | \(-0.427685\pi\) | ||||
0.225235 | + | 0.974305i | \(0.427685\pi\) | |||||||
\(572\) | − | 9131.79i | − | 0.667516i | ||||||
\(573\) | 10077.5i | 0.734715i | ||||||||
\(574\) | 2021.37 | 0.146987 | ||||||||
\(575\) | 19347.0 | + | 4750.63i | 1.40317 | + | 0.344548i | ||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | − | 12735.9i | − | 0.918895i | −0.888205 | − | 0.459447i | \(-0.848048\pi\) | ||
0.888205 | − | 0.459447i | \(-0.151952\pi\) | |||||||
\(578\) | 9120.04i | 0.656304i | ||||||||
\(579\) | 8401.69 | 0.603044 | ||||||||
\(580\) | 696.727 | − | 546.343i | 0.0498793 | − | 0.0391132i | ||||
\(581\) | −5272.77 | −0.376508 | ||||||||
\(582\) | 7211.51i | 0.513620i | ||||||||
\(583\) | 16240.7i | 1.15372i | ||||||||
\(584\) | 2425.37 | 0.171854 | ||||||||
\(585\) | −5537.99 | − | 7062.36i | −0.391398 | − | 0.499132i | ||||
\(586\) | 17861.6 | 1.25914 | ||||||||
\(587\) | − | 13223.9i | − | 0.929829i | −0.885355 | − | 0.464915i | \(-0.846085\pi\) | ||
0.885355 | − | 0.464915i | \(-0.153915\pi\) | |||||||
\(588\) | 588.000i | 0.0412393i | ||||||||
\(589\) | −1491.31 | −0.104327 | ||||||||
\(590\) | 7106.91 | + | 9063.12i | 0.495910 | + | 0.632411i | ||||
\(591\) | 9757.57 | 0.679142 | ||||||||
\(592\) | 4527.51i | 0.314324i | ||||||||
\(593\) | − | 2498.96i | − | 0.173052i | −0.996250 | − | 0.0865261i | \(-0.972423\pi\) | ||
0.996250 | − | 0.0865261i | \(-0.0275766\pi\) | |||||||
\(594\) | 1382.18 | 0.0954739 | ||||||||
\(595\) | −1157.06 | + | 907.314i | −0.0797222 | + | 0.0625147i | ||||
\(596\) | 6836.04 | 0.469824 | ||||||||
\(597\) | 4575.92i | 0.313702i | ||||||||
\(598\) | − | 28429.6i | − | 1.94410i | ||||||
\(599\) | 9468.29 | 0.645850 | 0.322925 | − | 0.946425i | \(-0.395334\pi\) | ||||
0.322925 | + | 0.946425i | \(0.395334\pi\) | |||||||
\(600\) | 715.396 | − | 2913.45i | 0.0486765 | − | 0.198235i | ||||
\(601\) | −12334.1 | −0.837137 | −0.418569 | − | 0.908185i | \(-0.637468\pi\) | ||||
−0.418569 | + | 0.908185i | \(0.637468\pi\) | |||||||
\(602\) | 4577.00i | 0.309875i | ||||||||
\(603\) | 7579.08i | 0.511848i | ||||||||
\(604\) | 11094.4 | 0.747395 | ||||||||
\(605\) | −5946.09 | + | 4662.67i | −0.399575 | + | 0.313330i | ||||
\(606\) | −3452.23 | −0.231415 | ||||||||
\(607\) | − | 25245.6i | − | 1.68812i | −0.536248 | − | 0.844060i | \(-0.680159\pi\) | ||
0.536248 | − | 0.844060i | \(-0.319841\pi\) | |||||||
\(608\) | 377.535i | 0.0251827i | ||||||||
\(609\) | 415.757 | 0.0276639 | ||||||||
\(610\) | 5460.08 | + | 6962.99i | 0.362413 | + | 0.462169i | ||||
\(611\) | 10474.2 | 0.693521 | ||||||||
\(612\) | 676.359i | 0.0446735i | ||||||||
\(613\) | − | 4007.86i | − | 0.264071i | −0.991245 | − | 0.132036i | \(-0.957849\pi\) | ||
0.991245 | − | 0.132036i | \(-0.0421513\pi\) | |||||||
\(614\) | 5031.58 | 0.330714 | ||||||||
\(615\) | −2988.30 | − | 3810.84i | −0.195935 | − | 0.249867i | ||||
\(616\) | 1433.37 | 0.0937535 | ||||||||
\(617\) | 14349.2i | 0.936266i | 0.883658 | + | 0.468133i | \(0.155073\pi\) | ||||
−0.883658 | + | 0.468133i | \(0.844927\pi\) | |||||||
\(618\) | 1525.32i | 0.0992839i | ||||||||
\(619\) | 6004.19 | 0.389869 | 0.194934 | − | 0.980816i | \(-0.437551\pi\) | ||||
0.194934 | + | 0.980816i | \(0.437551\pi\) | |||||||
\(620\) | 4448.39 | − | 3488.24i | 0.288148 | − | 0.225953i | ||||
\(621\) | 4303.08 | 0.278062 | ||||||||
\(622\) | 7518.78i | 0.484688i | ||||||||
\(623\) | 5900.77i | 0.379469i | ||||||||
\(624\) | −4281.21 | −0.274656 | ||||||||
\(625\) | −13847.9 | − | 7237.06i | −0.886269 | − | 0.463172i | ||||
\(626\) | −13651.8 | −0.871624 | ||||||||
\(627\) | 905.939i | 0.0577029i | ||||||||
\(628\) | 1413.91i | 0.0898426i | ||||||||
\(629\) | −5316.36 | −0.337007 | ||||||||
\(630\) | 1108.54 | − | 869.271i | 0.0701038 | − | 0.0549724i | ||||
\(631\) | 17130.6 | 1.08076 | 0.540378 | − | 0.841422i | \(-0.318281\pi\) | ||||
0.540378 | + | 0.841422i | \(0.318281\pi\) | |||||||
\(632\) | 2131.07i | 0.134129i | ||||||||
\(633\) | − | 8802.88i | − | 0.552738i | ||||||
\(634\) | −4929.87 | −0.308817 | ||||||||
\(635\) | −15896.3 | − | 20271.9i | −0.993429 | − | 1.26688i | ||||
\(636\) | 7614.05 | 0.474712 | ||||||||
\(637\) | − | 4370.40i | − | 0.271839i | ||||||
\(638\) | − | 1013.49i | − | 0.0628912i | ||||||
\(639\) | −3618.90 | −0.224040 | ||||||||
\(640\) | −883.069 | − | 1126.14i | −0.0545412 | − | 0.0695540i | ||||
\(641\) | 13484.7 | 0.830911 | 0.415456 | − | 0.909613i | \(-0.363622\pi\) | ||||
0.415456 | + | 0.909613i | \(0.363622\pi\) | |||||||
\(642\) | 6855.64i | 0.421449i | ||||||||
\(643\) | − | 18209.9i | − | 1.11684i | −0.829559 | − | 0.558419i | \(-0.811408\pi\) | ||
0.829559 | − | 0.558419i | \(-0.188592\pi\) | |||||||
\(644\) | 4462.46 | 0.273052 | ||||||||
\(645\) | 8628.91 | − | 6766.42i | 0.526764 | − | 0.413066i | ||||
\(646\) | −443.314 | −0.0270000 | ||||||||
\(647\) | 13402.9i | 0.814406i | 0.913338 | + | 0.407203i | \(0.133496\pi\) | ||||
−0.913338 | + | 0.407203i | \(0.866504\pi\) | |||||||
\(648\) | − | 648.000i | − | 0.0392837i | ||||||
\(649\) | 13183.7 | 0.797387 | ||||||||
\(650\) | −5317.29 | + | 21654.7i | −0.320863 | + | 1.30672i | ||||
\(651\) | 2654.49 | 0.159812 | ||||||||
\(652\) | − | 3540.92i | − | 0.212689i | ||||||
\(653\) | − | 1922.32i | − | 0.115201i | −0.998340 | − | 0.0576003i | \(-0.981655\pi\) | ||
0.998340 | − | 0.0576003i | \(-0.0183449\pi\) | |||||||
\(654\) | −12325.7 | −0.736961 | ||||||||
\(655\) | 8403.74 | − | 6589.85i | 0.501315 | − | 0.393109i | ||||
\(656\) | −2310.14 | −0.137494 | ||||||||
\(657\) | − | 2728.54i | − | 0.162025i | ||||||
\(658\) | 1644.09i | 0.0974060i | ||||||||
\(659\) | −22722.3 | −1.34315 | −0.671574 | − | 0.740937i | \(-0.734382\pi\) | ||||
−0.671574 | + | 0.740937i | \(0.734382\pi\) | |||||||
\(660\) | −2119.03 | − | 2702.30i | −0.124974 | − | 0.159374i | ||||
\(661\) | −16049.3 | −0.944393 | −0.472196 | − | 0.881493i | \(-0.656539\pi\) | ||||
−0.472196 | + | 0.881493i | \(0.656539\pi\) | |||||||
\(662\) | 7560.72i | 0.443891i | ||||||||
\(663\) | − | 5027.14i | − | 0.294477i | ||||||
\(664\) | 6026.02 | 0.352191 | ||||||||
\(665\) | 569.757 | + | 726.586i | 0.0332244 | + | 0.0423696i | ||||
\(666\) | 5093.45 | 0.296347 | ||||||||
\(667\) | − | 3155.27i | − | 0.183167i | ||||||
\(668\) | 12881.0i | 0.746081i | ||||||||
\(669\) | 10878.9 | 0.628703 | ||||||||
\(670\) | 14817.9 | − | 11619.5i | 0.854425 | − | 0.670003i | ||||
\(671\) | 10128.7 | 0.582735 | ||||||||
\(672\) | − | 672.000i | − | 0.0385758i | ||||||
\(673\) | 16507.8i | 0.945513i | 0.881193 | + | 0.472757i | \(0.156741\pi\) | ||||
−0.881193 | + | 0.472757i | \(0.843259\pi\) | |||||||
\(674\) | 3828.78 | 0.218811 | ||||||||
\(675\) | −3277.63 | − | 804.820i | −0.186898 | − | 0.0458927i | ||||
\(676\) | 23032.7 | 1.31047 | ||||||||
\(677\) | 15118.9i | 0.858298i | 0.903234 | + | 0.429149i | \(0.141187\pi\) | ||||
−0.903234 | + | 0.429149i | \(0.858813\pi\) | |||||||
\(678\) | 5344.96i | 0.302761i | ||||||||
\(679\) | 8413.43 | 0.475520 | ||||||||
\(680\) | 1322.35 | − | 1036.93i | 0.0745733 | − | 0.0584772i | ||||
\(681\) | −6568.35 | −0.369603 | ||||||||
\(682\) | − | 6470.86i | − | 0.363317i | ||||||
\(683\) | − | 68.6595i | − | 0.00384654i | −0.999998 | − | 0.00192327i | \(-0.999388\pi\) | ||
0.999998 | − | 0.00192327i | \(-0.000612195\pi\) | |||||||
\(684\) | 424.727 | 0.0237424 | ||||||||
\(685\) | 10276.3 | + | 13104.8i | 0.573191 | + | 0.730964i | ||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 16503.0i | 0.916490i | ||||||||
\(688\) | − | 5230.86i | − | 0.289861i | ||||||
\(689\) | −56592.6 | −3.12918 | ||||||||
\(690\) | −6597.09 | − | 8412.97i | −0.363981 | − | 0.464168i | ||||
\(691\) | −3167.95 | −0.174406 | −0.0872030 | − | 0.996191i | \(-0.527793\pi\) | ||||
−0.0872030 | + | 0.996191i | \(0.527793\pi\) | |||||||
\(692\) | − | 15122.5i | − | 0.830738i | ||||||
\(693\) | − | 1612.54i | − | 0.0883917i | ||||||
\(694\) | −18237.9 | −0.997550 | ||||||||
\(695\) | 6618.56 | − | 5189.99i | 0.361232 | − | 0.283263i | ||||
\(696\) | −475.151 | −0.0258772 | ||||||||
\(697\) | − | 2712.64i | − | 0.147416i | ||||||
\(698\) | − | 9664.89i | − | 0.524100i | ||||||
\(699\) | −11783.1 | −0.637596 | ||||||||
\(700\) | −3399.03 | − | 834.629i | −0.183530 | − | 0.0450657i | ||||
\(701\) | 6930.44 | 0.373408 | 0.186704 | − | 0.982416i | \(-0.440219\pi\) | ||||
0.186704 | + | 0.982416i | \(0.440219\pi\) | |||||||
\(702\) | 4816.36i | 0.258948i | ||||||||
\(703\) | 3338.46i | 0.179107i | ||||||||
\(704\) | −1638.14 | −0.0876984 | ||||||||
\(705\) | 3099.56 | − | 2430.54i | 0.165583 | − | 0.129843i | ||||
\(706\) | −5613.15 | −0.299226 | ||||||||
\(707\) | 4027.60i | 0.214248i | ||||||||
\(708\) | − | 6180.83i | − | 0.328093i | ||||||
\(709\) | −20689.6 | −1.09593 | −0.547966 | − | 0.836501i | \(-0.684598\pi\) | ||||
−0.547966 | + | 0.836501i | \(0.684598\pi\) | |||||||
\(710\) | 5548.16 | + | 7075.32i | 0.293266 | + | 0.373989i | ||||
\(711\) | 2397.45 | 0.126458 | ||||||||
\(712\) | − | 6743.74i | − | 0.354961i | ||||||
\(713\) | − | 20145.5i | − | 1.05814i | ||||||
\(714\) | 789.086 | 0.0413596 | ||||||||
\(715\) | 15750.0 | + | 20085.3i | 0.823800 | + | 1.05055i | ||||
\(716\) | 18136.3 | 0.946627 | ||||||||
\(717\) | − | 13305.3i | − | 0.693022i | ||||||
\(718\) | 2150.13i | 0.111758i | ||||||||
\(719\) | 2807.47 | 0.145620 | 0.0728101 | − | 0.997346i | \(-0.476803\pi\) | ||||
0.0728101 | + | 0.997346i | \(0.476803\pi\) | |||||||
\(720\) | −1266.91 | + | 993.453i | −0.0655761 | + | 0.0514220i | ||||
\(721\) | 1779.54 | 0.0919190 | ||||||||
\(722\) | − | 13439.6i | − | 0.692757i | ||||||
\(723\) | 13727.4i | 0.706125i | ||||||||
\(724\) | −7221.97 | −0.370721 | ||||||||
\(725\) | −590.141 | + | 2403.35i | −0.0302307 | + | 0.123115i | ||||
\(726\) | 4055.09 | 0.207298 | ||||||||
\(727\) | 3059.84i | 0.156098i | 0.996950 | + | 0.0780489i | \(0.0248690\pi\) | ||||
−0.996950 | + | 0.0780489i | \(0.975131\pi\) | |||||||
\(728\) | 4994.74i | 0.254282i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −5334.58 | + | 4183.15i | −0.270468 | + | 0.212089i | ||||
\(731\) | 6142.25 | 0.310779 | ||||||||
\(732\) | − | 4748.60i | − | 0.239772i | ||||||
\(733\) | − | 483.122i | − | 0.0243445i | −0.999926 | − | 0.0121723i | \(-0.996125\pi\) | ||
0.999926 | − | 0.0121723i | \(-0.00387465\pi\) | |||||||
\(734\) | 734.041 | 0.0369127 | ||||||||
\(735\) | −1014.15 | − | 1293.30i | −0.0508945 | − | 0.0649035i | ||||
\(736\) | −5099.95 | −0.255417 | ||||||||
\(737\) | − | 21554.8i | − | 1.07732i | ||||||
\(738\) | 2598.91i | 0.129630i | ||||||||
\(739\) | −15972.4 | −0.795066 | −0.397533 | − | 0.917588i | \(-0.630134\pi\) | ||||
−0.397533 | + | 0.917588i | \(0.630134\pi\) | |||||||
\(740\) | −7808.80 | − | 9958.21i | −0.387915 | − | 0.494691i | ||||
\(741\) | −3156.84 | −0.156504 | ||||||||
\(742\) | − | 8883.06i | − | 0.439498i | ||||||
\(743\) | − | 1310.03i | − | 0.0646840i | −0.999477 | − | 0.0323420i | \(-0.989703\pi\) | ||
0.999477 | − | 0.0323420i | \(-0.0102966\pi\) | |||||||
\(744\) | −3033.70 | −0.149490 | ||||||||
\(745\) | −15035.8 | + | 11790.4i | −0.739422 | + | 0.579823i | ||||
\(746\) | 2609.11 | 0.128052 | ||||||||
\(747\) | − | 6779.28i | − | 0.332049i | ||||||
\(748\) | − | 1923.56i | − | 0.0940271i | ||||||
\(749\) | 7998.24 | 0.390186 | ||||||||
\(750\) | 3451.46 | + | 7641.99i | 0.168039 | + | 0.372061i | ||||
\(751\) | −14752.9 | −0.716830 | −0.358415 | − | 0.933562i | \(-0.616683\pi\) | ||||
−0.358415 | + | 0.933562i | \(0.616683\pi\) | |||||||
\(752\) | − | 1878.96i | − | 0.0911150i | ||||||
\(753\) | 4940.87i | 0.239117i | ||||||||
\(754\) | 3531.63 | 0.170576 | ||||||||
\(755\) | −24402.1 | + | 19135.1i | −1.17627 | + | 0.922381i | ||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | − | 3934.60i | − | 0.188911i | −0.995529 | − | 0.0944555i | \(-0.969889\pi\) | ||
0.995529 | − | 0.0944555i | \(-0.0301110\pi\) | |||||||
\(758\) | − | 10681.2i | − | 0.511820i | ||||||
\(759\) | −12237.9 | −0.585255 | ||||||||
\(760\) | −651.151 | − | 830.384i | −0.0310786 | − | 0.0396331i | ||||
\(761\) | 17102.3 | 0.814662 | 0.407331 | − | 0.913281i | \(-0.366460\pi\) | ||||
0.407331 | + | 0.913281i | \(0.366460\pi\) | |||||||
\(762\) | 13825.0i | 0.657251i | ||||||||
\(763\) | 14380.0i | 0.682293i | ||||||||
\(764\) | −13436.6 | −0.636282 | ||||||||
\(765\) | −1166.55 | − | 1487.64i | −0.0551328 | − | 0.0703084i | ||||
\(766\) | −13324.5 | −0.628505 | ||||||||
\(767\) | 45940.0i | 2.16271i | ||||||||
\(768\) | 768.000i | 0.0360844i | ||||||||
\(769\) | 32173.5 | 1.50872 | 0.754361 | − | 0.656460i | \(-0.227947\pi\) | ||||
0.754361 | + | 0.656460i | \(0.227947\pi\) | |||||||
\(770\) | −3152.69 | + | 2472.20i | −0.147552 | + | 0.115704i | ||||
\(771\) | 8434.91 | 0.394002 | ||||||||
\(772\) | 11202.3i | 0.522251i | ||||||||
\(773\) | − | 19329.5i | − | 0.899398i | −0.893180 | − | 0.449699i | \(-0.851531\pi\) | ||
0.893180 | − | 0.449699i | \(-0.148469\pi\) | |||||||
\(774\) | −5884.71 | −0.273284 | ||||||||
\(775\) | −3767.87 | + | 15344.7i | −0.174640 | + | 0.711222i | ||||
\(776\) | −9615.35 | −0.444808 | ||||||||
\(777\) | − | 5942.36i | − | 0.274364i | ||||||
\(778\) | 12627.0i | 0.581875i | ||||||||
\(779\) | −1703.43 | −0.0783464 | ||||||||
\(780\) | 9416.47 | − | 7383.99i | 0.432261 | − | 0.338961i | ||||
\(781\) | 10292.1 | 0.471551 | ||||||||
\(782\) | − | 5988.54i | − | 0.273849i | ||||||
\(783\) | 534.545i | 0.0243973i | ||||||||
\(784\) | −784.000 | −0.0357143 | ||||||||
\(785\) | −2438.63 | − | 3109.88i | −0.110877 | − | 0.141397i | ||||
\(786\) | −5731.15 | −0.260081 | ||||||||
\(787\) | − | 4050.20i | − | 0.183449i | −0.995784 | − | 0.0917244i | \(-0.970762\pi\) | ||
0.995784 | − | 0.0917244i | \(-0.0292379\pi\) | |||||||
\(788\) | 13010.1i | 0.588154i | ||||||||
\(789\) | 9309.39 | 0.420054 | ||||||||
\(790\) | −3675.55 | − | 4687.27i | −0.165532 | − | 0.211095i | ||||
\(791\) | 6235.79 | 0.280302 | ||||||||
\(792\) | 1842.91i | 0.0826828i | ||||||||
\(793\) | 35294.7i | 1.58052i | ||||||||
\(794\) | −28421.2 | −1.27031 | ||||||||
\(795\) | −16747.0 | + | 13132.3i | −0.747114 | + | 0.585855i | ||||
\(796\) | −6101.22 | −0.271674 | ||||||||
\(797\) | − | 30864.7i | − | 1.37175i | −0.727720 | − | 0.685874i | \(-0.759420\pi\) | ||
0.727720 | − | 0.685874i | \(-0.240580\pi\) | |||||||
\(798\) | − | 495.514i | − | 0.0219812i | ||||||
\(799\) | 2206.33 | 0.0976902 | ||||||||
\(800\) | 3884.60 | + | 953.861i | 0.171677 | + | 0.0421551i | ||||
\(801\) | −7586.71 | −0.334661 | ||||||||
\(802\) | 11157.2i | 0.491239i | ||||||||
\(803\) | 7759.95i | 0.341025i | ||||||||
\(804\) | −10105.4 | −0.443273 | ||||||||
\(805\) | −9815.13 | + | 7696.60i | −0.429736 | + | 0.336981i | ||||
\(806\) | 22548.4 | 0.985402 | ||||||||
\(807\) | 183.563i | 0.00800710i | ||||||||
\(808\) | − | 4602.97i | − | 0.200411i | ||||||
\(809\) | −14213.1 | −0.617682 | −0.308841 | − | 0.951114i | \(-0.599941\pi\) | ||||
−0.308841 | + | 0.951114i | \(0.599941\pi\) | |||||||
\(810\) | 1117.63 | + | 1425.27i | 0.0484811 | + | 0.0618258i | ||||
\(811\) | 1619.57 | 0.0701242 | 0.0350621 | − | 0.999385i | \(-0.488837\pi\) | ||||
0.0350621 | + | 0.999385i | \(0.488837\pi\) | |||||||
\(812\) | 554.343i | 0.0239577i | ||||||||
\(813\) | 292.885i | 0.0126346i | ||||||||
\(814\) | −14485.7 | −0.623740 | ||||||||
\(815\) | 6107.19 | + | 7788.22i | 0.262485 | + | 0.334736i | ||||
\(816\) | −901.812 | −0.0386884 | ||||||||
\(817\) | − | 3857.09i | − | 0.165168i | ||||||
\(818\) | − | 23828.0i | − | 1.01849i | ||||||
\(819\) | 5619.09 | 0.239740 | ||||||||
\(820\) | 5081.13 | − | 3984.40i | 0.216391 | − | 0.169684i | ||||
\(821\) | −20628.1 | −0.876888 | −0.438444 | − | 0.898758i | \(-0.644470\pi\) | ||||
−0.438444 | + | 0.898758i | \(0.644470\pi\) | |||||||
\(822\) | − | 8937.20i | − | 0.379222i | ||||||
\(823\) | − | 11868.2i | − | 0.502671i | −0.967900 | − | 0.251335i | \(-0.919130\pi\) | ||
0.967900 | − | 0.251335i | \(-0.0808697\pi\) | |||||||
\(824\) | −2033.76 | −0.0859824 | ||||||||
\(825\) | 9321.56 | + | 2288.90i | 0.393376 | + | 0.0965931i | ||||
\(826\) | −7210.97 | −0.303755 | ||||||||
\(827\) | − | 9149.35i | − | 0.384709i | −0.981326 | − | 0.192354i | \(-0.938388\pi\) | ||
0.981326 | − | 0.192354i | \(-0.0616123\pi\) | |||||||
\(828\) | 5737.44i | 0.240809i | ||||||||
\(829\) | 11693.7 | 0.489916 | 0.244958 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244958 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(830\) | −13254.2 | + | 10393.4i | −0.554288 | + | 0.434649i | ||||
\(831\) | 14157.7 | 0.591006 | ||||||||
\(832\) | − | 5708.28i | − | 0.237859i | ||||||
\(833\) | − | 920.600i | − | 0.0382916i | ||||||
\(834\) | −4513.70 | −0.187406 | ||||||||
\(835\) | −22216.5 | − | 28331.7i | −0.920759 | − | 1.17420i | ||||
\(836\) | −1207.92 | −0.0499722 | ||||||||
\(837\) | 3412.91i | 0.140941i | ||||||||
\(838\) | 24186.0i | 0.997007i | ||||||||
\(839\) | 41472.3 | 1.70654 | 0.853268 | − | 0.521473i | \(-0.174617\pi\) | ||||
0.853268 | + | 0.521473i | \(0.174617\pi\) | |||||||
\(840\) | 1159.03 | + | 1478.06i | 0.0476075 | + | 0.0607117i | ||||
\(841\) | −23997.0 | −0.983929 | ||||||||
\(842\) | − | 24377.0i | − | 0.997727i | ||||||
\(843\) | 2985.28i | 0.121967i | ||||||||
\(844\) | 11737.2 | 0.478685 | ||||||||
\(845\) | −50660.3 | + | 39725.6i | −2.06245 | + | 1.61728i | ||||
\(846\) | −2113.82 | −0.0859040 | ||||||||
\(847\) | − | 4730.94i | − | 0.191921i | ||||||
\(848\) | 10152.1i | 0.411112i | ||||||||
\(849\) | 23986.8 | 0.969639 | ||||||||
\(850\) | −1120.06 | + | 4561.44i | −0.0451972 | + | 0.184066i | ||||
\(851\) | −45097.8 | −1.81661 | ||||||||
\(852\) | − | 4825.20i | − | 0.194024i | ||||||
\(853\) | − | 10326.4i | − | 0.414501i | −0.978288 | − | 0.207251i | \(-0.933548\pi\) | ||
0.978288 | − | 0.207251i | \(-0.0664516\pi\) | |||||||
\(854\) | −5540.03 | −0.221986 | ||||||||
\(855\) | −934.182 | + | 732.545i | −0.0373665 | + | 0.0293012i | ||||
\(856\) | −9140.85 | −0.364986 | ||||||||
\(857\) | − | 17375.4i | − | 0.692571i | −0.938129 | − | 0.346285i | \(-0.887443\pi\) | ||
0.938129 | − | 0.346285i | \(-0.112557\pi\) | |||||||
\(858\) | − | 13697.7i | − | 0.545025i | ||||||
\(859\) | −10624.9 | −0.422022 | −0.211011 | − | 0.977484i | \(-0.567676\pi\) | ||||
−0.211011 | + | 0.977484i | \(0.567676\pi\) | |||||||
\(860\) | 9021.89 | + | 11505.2i | 0.357726 | + | 0.456191i | ||||
\(861\) | 3032.06 | 0.120014 | ||||||||
\(862\) | 9936.31i | 0.392613i | ||||||||
\(863\) | − | 22377.1i | − | 0.882648i | −0.897348 | − | 0.441324i | \(-0.854509\pi\) | ||
0.897348 | − | 0.441324i | \(-0.145491\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 26082.4 | + | 33261.8i | 1.02524 | + | 1.30744i | ||||
\(866\) | −28967.4 | −1.13667 | ||||||||
\(867\) | 13680.1i | 0.535870i | ||||||||
\(868\) | 3539.31i | 0.138401i | ||||||||
\(869\) | −6818.33 | −0.266164 | ||||||||
\(870\) | 1045.09 | − | 819.514i | 0.0407263 | − | 0.0319358i | ||||
\(871\) | 75110.3 | 2.92195 | ||||||||
\(872\) | − | 16434.3i | − | 0.638227i | ||||||
\(873\) | 10817.3i | 0.419369i | ||||||||
\(874\) | −3760.56 | −0.145541 | ||||||||
\(875\) | 8915.65 | − | 4026.70i | 0.344462 | − | 0.155574i | ||||
\(876\) | 3638.06 | 0.140318 | ||||||||
\(877\) | − | 22267.1i | − | 0.857362i | −0.903456 | − | 0.428681i | \(-0.858979\pi\) | ||
0.903456 | − | 0.428681i | \(-0.141021\pi\) | |||||||
\(878\) | 19875.3i | 0.763961i | ||||||||
\(879\) | 26792.4 | 1.02808 | ||||||||
\(880\) | 3603.07 | − | 2825.37i | 0.138022 | − | 0.108231i | ||||
\(881\) | −7273.13 | −0.278136 | −0.139068 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139068 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(882\) | 882.000i | 0.0336718i | ||||||||
\(883\) | 43452.0i | 1.65603i | 0.560705 | + | 0.828016i | \(0.310530\pi\) | ||||
−0.560705 | + | 0.828016i | \(0.689470\pi\) | |||||||
\(884\) | 6702.86 | 0.255024 | ||||||||
\(885\) | 10660.4 | + | 13594.7i | 0.404909 | + | 0.516362i | ||||
\(886\) | 34279.2 | 1.29981 | ||||||||
\(887\) | 34206.2i | 1.29485i | 0.762130 | + | 0.647424i | \(0.224154\pi\) | ||||
−0.762130 | + | 0.647424i | \(0.775846\pi\) | |||||||
\(888\) | 6791.27i | 0.256644i | ||||||||
\(889\) | 16129.1 | 0.608496 | ||||||||
\(890\) | 11631.2 | + | 14832.8i | 0.438067 | + | 0.558647i | ||||
\(891\) | 2073.27 | 0.0779541 | ||||||||
\(892\) | 14505.2i | 0.544473i | ||||||||
\(893\) | − | 1385.49i | − | 0.0519190i | ||||||
\(894\) | 10254.1 | 0.383610 | ||||||||
\(895\) | −39890.6 | + | 31280.5i | −1.48983 | + | 1.16826i | ||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | − | 42644.4i | − | 1.58735i | ||||||
\(898\) | − | 3110.69i | − | 0.115596i | ||||||
\(899\) | 2502.54 | 0.0928415 | ||||||||
\(900\) | 1073.09 | − | 4370.18i | 0.0397442 | − | 0.161859i | ||||
\(901\) | −11920.9 | −0.440780 | ||||||||
\(902\) | − | 7391.27i | − | 0.272841i | ||||||
\(903\) | 6865.50i | 0.253012i | ||||||||
\(904\) | −7126.61 | −0.262199 | ||||||||
\(905\) | 15884.6 | − | 12456.1i | 0.583451 | − | 0.457517i | ||||
\(906\) | 16641.7 | 0.610246 | ||||||||
\(907\) | − | 24922.5i | − | 0.912391i | −0.889880 | − | 0.456196i | \(-0.849212\pi\) | ||
0.889880 | − | 0.456196i | \(-0.150788\pi\) | |||||||
\(908\) | − | 8757.80i | − | 0.320086i | ||||||
\(909\) | −5178.34 | −0.188949 | ||||||||
\(910\) | −8614.66 | − | 10985.9i | −0.313817 | − | 0.400196i | ||||
\(911\) | 29200.7 | 1.06198 | 0.530989 | − | 0.847379i | \(-0.321821\pi\) | ||||
0.530989 | + | 0.847379i | \(0.321821\pi\) | |||||||
\(912\) | 566.302i | 0.0205616i | ||||||||
\(913\) | 19280.2i | 0.698885i | ||||||||
\(914\) | −36818.4 | −1.33244 | ||||||||
\(915\) | 8190.12 | + | 10444.5i | 0.295909 | + | 0.377360i | ||||
\(916\) | −22004.0 | −0.793704 | ||||||||
\(917\) | 6686.34i | 0.240788i | ||||||||
\(918\) | 1014.54i | 0.0364758i | ||||||||
\(919\) | 31961.7 | 1.14725 | 0.573623 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573623 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(920\) | 11217.3 | − | 8796.11i | 0.401982 | − | 0.315217i | ||||
\(921\) | 7547.38 | 0.270027 | ||||||||
\(922\) | 13233.0i | 0.472676i | ||||||||
\(923\) | 35864.0i | 1.27896i | ||||||||
\(924\) | 2150.06 | 0.0765494 | ||||||||
\(925\) | 34350.8 | + | 8434.80i | 1.22102 | + | 0.299821i | ||||
\(926\) | −25211.0 | −0.894693 | ||||||||
\(927\) | 2287.98i | 0.0810650i | ||||||||
\(928\) | − | 633.535i | − | 0.0224103i | ||||||
\(929\) | 21349.4 | 0.753985 | 0.376993 | − | 0.926216i | \(-0.376958\pi\) | ||||
0.376993 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(930\) | 6672.59 | − | 5232.36i | 0.235272 | − | 0.184490i | ||||
\(931\) | −578.100 | −0.0203507 | ||||||||
\(932\) | − | 15710.9i | − | 0.552174i | ||||||
\(933\) | 11278.2i | 0.395746i | ||||||||
\(934\) | −32583.1 | −1.14149 | ||||||||
\(935\) | 3317.65 | + | 4230.85i | 0.116041 | + | 0.147982i | ||||
\(936\) | −6421.81 | −0.224256 | ||||||||
\(937\) | 3802.95i | 0.132590i | 0.997800 | + | 0.0662951i | \(0.0211179\pi\) | ||||
−0.997800 | + | 0.0662951i | \(0.978882\pi\) | |||||||
\(938\) | 11789.7i | 0.410391i | ||||||||
\(939\) | −20477.7 | −0.711678 | ||||||||
\(940\) | 3240.72 | + | 4132.74i | 0.112447 | + | 0.143399i | ||||
\(941\) | −42690.8 | −1.47894 | −0.739470 | − | 0.673190i | \(-0.764924\pi\) | ||||
−0.739470 | + | 0.673190i | \(0.764924\pi\) | |||||||
\(942\) | 2120.87i | 0.0733562i | ||||||||
\(943\) | − | 23010.9i | − | 0.794633i | ||||||
\(944\) | 8241.11 | 0.284137 | ||||||||
\(945\) | 1662.81 | − | 1303.91i | 0.0572395 | − | 0.0448848i | ||||
\(946\) | 16736.1 | 0.575197 | ||||||||
\(947\) | − | 40333.0i | − | 1.38400i | −0.721899 | − | 0.691998i | \(-0.756730\pi\) | ||
0.721899 | − | 0.691998i | \(-0.243270\pi\) | |||||||
\(948\) | 3196.60i | 0.109516i | ||||||||
\(949\) | −27040.4 | −0.924941 | ||||||||
\(950\) | 2864.40 | + | 703.351i | 0.0978246 | + | 0.0240208i | ||||
\(951\) | −7394.81 | −0.252148 | ||||||||
\(952\) | 1052.11i | 0.0358185i | ||||||||
\(953\) | − | 39603.5i | − | 1.34615i | −0.739573 | − | 0.673077i | \(-0.764972\pi\) | ||
0.739573 | − | 0.673077i | \(-0.235028\pi\) | |||||||
\(954\) | 11421.1 | 0.387601 | ||||||||
\(955\) | 29553.7 | − | 23174.7i | 1.00140 | − | 0.785253i | ||||
\(956\) | 17740.4 | 0.600174 | ||||||||
\(957\) | − | 1520.24i | − | 0.0513505i | ||||||
\(958\) | − | 23012.6i | − | 0.776099i | ||||||
\(959\) | −10426.7 | −0.351091 | ||||||||
\(960\) | −1324.60 | − | 1689.21i | −0.0445327 | − | 0.0567906i | ||||
\(961\) | −13813.0 | −0.463664 | ||||||||
\(962\) | − | 50477.1i | − | 1.69173i | ||||||
\(963\) | 10283.5i | 0.344112i | ||||||||
\(964\) | −18303.2 | −0.611522 | ||||||||
\(965\) | −19321.0 | − | 24639.2i | −0.644524 | − | 0.821933i | ||||
\(966\) | 6693.69 | 0.222946 | ||||||||
\(967\) | − | 4139.69i | − | 0.137666i | −0.997628 | − | 0.0688332i | \(-0.978072\pi\) | ||
0.997628 | − | 0.0688332i | \(-0.0219276\pi\) | |||||||
\(968\) | 5406.79i | 0.179526i | ||||||||
\(969\) | −664.971 | −0.0220454 | ||||||||
\(970\) | 21148.9 | − | 16584.0i | 0.700050 | − | 0.548949i | ||||
\(971\) | 42137.2 | 1.39263 | 0.696316 | − | 0.717735i | \(-0.254821\pi\) | ||||
0.696316 | + | 0.717735i | \(0.254821\pi\) | |||||||
\(972\) | − | 972.000i | − | 0.0320750i | ||||||
\(973\) | 5265.99i | 0.173504i | ||||||||
\(974\) | −33005.8 | −1.08580 | ||||||||
\(975\) | −7975.93 | + | 32482.0i | −0.261984 | + | 1.06693i | ||||
\(976\) | 6331.46 | 0.207649 | ||||||||
\(977\) | − | 39782.4i | − | 1.30271i | −0.758772 | − | 0.651357i | \(-0.774200\pi\) | ||
0.758772 | − | 0.651357i | \(-0.225800\pi\) | |||||||
\(978\) | − | 5311.38i | − | 0.173660i | ||||||
\(979\) | 21576.5 | 0.704381 | ||||||||
\(980\) | 1724.40 | − | 1352.20i | 0.0562081 | − | 0.0440760i | ||||
\(981\) | −18488.5 | −0.601726 | ||||||||
\(982\) | 18539.3i | 0.602458i | ||||||||
\(983\) | − | 3799.91i | − | 0.123294i | −0.998098 | − | 0.0616471i | \(-0.980365\pi\) | ||
0.998098 | − | 0.0616471i | \(-0.0196353\pi\) | |||||||
\(984\) | −3465.21 | −0.112263 | ||||||||
\(985\) | −22439.1 | − | 28615.6i | −0.725857 | − | 0.925653i | ||||
\(986\) | 743.918 | 0.0240276 | ||||||||
\(987\) | 2466.13i | 0.0795317i | ||||||||
\(988\) | − | 4209.13i | − | 0.135537i | ||||||
\(989\) | 52103.7 | 1.67523 | ||||||||
\(990\) | −3178.54 | − | 4053.45i | −0.102041 | − | 0.130128i | ||||
\(991\) | 20113.7 | 0.644735 | 0.322367 | − | 0.946615i | \(-0.395521\pi\) | ||||
0.322367 | + | 0.946615i | \(0.395521\pi\) | |||||||
\(992\) | − | 4044.93i | − | 0.129462i | ||||||
\(993\) | 11341.1i | 0.362435i | ||||||||
\(994\) | −5629.40 | −0.179632 | ||||||||
\(995\) | 13419.6 | − | 10523.1i | 0.427567 | − | 0.335280i | ||||
\(996\) | 9039.04 | 0.287563 | ||||||||
\(997\) | 40814.2i | 1.29649i | 0.761432 | + | 0.648244i | \(0.224496\pi\) | ||||
−0.761432 | + | 0.648244i | \(0.775504\pi\) | |||||||
\(998\) | − | 26334.6i | − | 0.835279i | ||||||
\(999\) | 7640.17 | 0.241966 |
(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 | 210.4.g.a.169.4 | yes | 4 | |
3.2 | odd | 2 | 630.4.g.e.379.1 | 4 | |||
5.2 | odd | 4 | 1050.4.a.bc.1.2 | 2 | |||
5.3 | odd | 4 | 1050.4.a.bg.1.2 | 2 | |||
5.4 | even | 2 | inner | 210.4.g.a.169.2 | ✓ | 4 | |
15.14 | odd | 2 | 630.4.g.e.379.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.g.a.169.2 | ✓ | 4 | 5.4 | even | 2 | inner | |
210.4.g.a.169.4 | yes | 4 | 1.1 | even | 1 | trivial | |
630.4.g.e.379.1 | 4 | 3.2 | odd | 2 | |||
630.4.g.e.379.3 | 4 | 15.14 | odd | 2 | |||
1050.4.a.bc.1.2 | 2 | 5.2 | odd | 4 | |||
1050.4.a.bg.1.2 | 2 | 5.3 | odd | 4 |