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 | 169.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.169 |
Dual form | 210.4.g.a.169.4 |
$q$-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 | \(-0.599607\pi\) | ||
0.307843 | − | 0.951437i | \(-0.400393\pi\) | |||||||
\(14\) | −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 | \(-0.957211\pi\) | ||
0.990979 | − | 0.134021i | \(-0.0427888\pi\) | |||||||
\(18\) | 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 | \(-0.743026\pi\) | ||
0.691447 | − | 0.722428i | \(-0.256974\pi\) | |||||||
\(24\) | 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 | \(-0.783609\pi\) | ||
0.777691 | − | 0.628647i | \(-0.216391\pi\) | |||||||
\(38\) | − | 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 | \(0.196839\pi\) | ||||
−0.814814 | + | 0.579723i | \(0.803161\pi\) | |||||||
\(44\) | −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 | \(0.0583315\pi\) | ||||
−0.983256 | + | 0.182230i | \(0.941668\pi\) | |||||||
\(48\) | − | 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 | \(-0.692733\pi\) | ||
0.569163 | − | 0.822225i | \(-0.307267\pi\) | |||||||
\(54\) | 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 | \(0.278634\pi\) | ||||
−0.640724 | + | 0.767772i | \(0.721366\pi\) | |||||||
\(68\) | 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 | \(-0.921856\pi\) | ||
0.970017 | − | 0.243038i | \(-0.0781439\pi\) | |||||||
\(74\) | −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 | \(-0.834041\pi\) | ||
0.867135 | − | 0.498074i | \(-0.165959\pi\) | |||||||
\(84\) | 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 | \(0.216557\pi\) | ||||
−0.777362 | + | 0.629053i | \(0.783443\pi\) | |||||||
\(98\) | 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 | \(0.0388017\pi\) | ||||
−0.992579 | + | 0.121597i | \(0.961198\pi\) | |||||||
\(104\) | 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 | \(0.172642\pi\) | ||||
−0.856487 | + | 0.516168i | \(0.827358\pi\) | |||||||
\(108\) | − | 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 | \(0.120918\pi\) | ||||
−0.928711 | + | 0.370805i | \(0.879082\pi\) | |||||||
\(114\) | −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 | \(0.297816\pi\) | ||||
−0.593323 | + | 0.804965i | \(0.702184\pi\) | |||||||
\(128\) | 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 | \(-0.846252\pi\) | ||
0.885599 | − | 0.464450i | \(-0.153748\pi\) | |||||||
\(138\) | 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 | \(0.0286364\pi\) | ||||
−0.995956 | + | 0.0898426i | \(0.971364\pi\) | |||||||
\(158\) | 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 | \(-0.931778\pi\) | ||
0.977120 | − | 0.212689i | \(-0.0682221\pi\) | |||||||
\(164\) | 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 | \(0.268067\pi\) | ||||
−0.665855 | + | 0.746081i | \(0.731933\pi\) | |||||||
\(168\) | − | 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 | \(-0.687919\pi\) | ||
0.556663 | − | 0.830738i | \(-0.312081\pi\) | |||||||
\(174\) | 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 | \(0.174908\pi\) | ||||
−0.852792 | + | 0.522251i | \(0.825092\pi\) | |||||||
\(194\) | 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 | \(0.200145\pi\) | ||||
−0.808749 | + | 0.588154i | \(0.799855\pi\) | |||||||
\(198\) | 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 | \(0.183270\pi\) | ||||
−0.838778 | + | 0.544473i | \(0.816730\pi\) | |||||||
\(224\) | −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 | \(-0.896288\pi\) | ||
0.947389 | − | 0.320086i | \(-0.103712\pi\) | |||||||
\(228\) | 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 | \(-0.813798\pi\) | ||
0.833729 | − | 0.552174i | \(-0.186202\pi\) | |||||||
\(234\) | 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 | \(0.110839\pi\) | ||||
−0.939985 | + | 0.341216i | \(0.889161\pi\) | |||||||
\(258\) | − | 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 | \(0.118513\pi\) | ||||
−0.931486 | + | 0.363778i | \(0.881487\pi\) | |||||||
\(264\) | 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 | \(0.171031\pi\) | ||||
−0.859089 | + | 0.511826i | \(0.828969\pi\) | |||||||
\(278\) | − | 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 | \(0.317288\pi\) | ||||
−0.543002 | + | 0.839732i | \(0.682712\pi\) | |||||||
\(284\) | −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 | \(0.349537\pi\) | ||||
−0.455286 | + | 0.890345i | \(0.650463\pi\) | |||||||
\(294\) | 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 | \(0.0751324\pi\) | ||||
−0.972273 | + | 0.233850i | \(0.924868\pi\) | |||||||
\(308\) | 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 | \(-0.788618\pi\) | ||
0.787487 | − | 0.616331i | \(-0.211382\pi\) | |||||||
\(314\) | 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 | \(-0.929927\pi\) | ||
0.975867 | − | 0.218367i | \(-0.0700730\pi\) | |||||||
\(318\) | 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 | \(0.0494485\pi\) | ||||
−0.987958 | + | 0.154723i | \(0.950551\pi\) | |||||||
\(338\) | 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 | \(-0.750779\pi\) | ||
0.708835 | − | 0.705375i | \(-0.249221\pi\) | |||||||
\(348\) | − | 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 | \(-0.932138\pi\) | ||
0.977360 | − | 0.211585i | \(-0.0678625\pi\) | |||||||
\(354\) | −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 | \(0.00830922\pi\) | ||||
−0.999659 | + | 0.0261012i | \(0.991691\pi\) | |||||||
\(368\) | − | 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 | \(0.0288613\pi\) | ||||
−0.995892 | + | 0.0905461i | \(0.971139\pi\) | |||||||
\(374\) | −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 | \(-0.853410\pi\) | ||
0.895818 | − | 0.444420i | \(-0.146590\pi\) | |||||||
\(384\) | 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 | \(-0.644841\pi\) | ||
0.439490 | − | 0.898248i | \(-0.355159\pi\) | |||||||
\(398\) | − | 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 | \(-0.702838\pi\) | ||
0.594974 | − | 0.803745i | \(-0.297162\pi\) | |||||||
\(434\) | 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 | \(0.371087\pi\) | ||||
−0.394013 | + | 0.919105i | \(0.628913\pi\) | |||||||
\(444\) | 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 | \(-0.608778\pi\) | ||
0.335124 | − | 0.942174i | \(-0.391222\pi\) | |||||||
\(458\) | − | 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 | \(-0.781970\pi\) | ||
0.774443 | − | 0.632644i | \(-0.218030\pi\) | |||||||
\(464\) | −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 | \(-0.701006\pi\) | ||
0.590340 | − | 0.807155i | \(-0.298994\pi\) | |||||||
\(468\) | − | 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 | \(-0.721361\pi\) | ||
0.640714 | − | 0.767780i | \(-0.278639\pi\) | |||||||
\(488\) | 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 | \(-0.743036\pi\) | ||
0.691469 | − | 0.722406i | \(-0.256964\pi\) | |||||||
\(504\) | −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 | \(0.223169\pi\) | ||||
−0.764129 | + | 0.645064i | \(0.776831\pi\) | |||||||
\(524\) | −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 | \(0.0437496\pi\) | ||||
−0.990569 | + | 0.137011i | \(0.956250\pi\) | |||||||
\(548\) | 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 | \(-0.815109\pi\) | ||
0.835995 | − | 0.548737i | \(-0.184891\pi\) | |||||||
\(558\) | − | 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 | \(0.121760\pi\) | ||||
−0.927727 | + | 0.373259i | \(0.878240\pi\) | |||||||
\(564\) | −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 | \(0.151952\pi\) | ||||
−0.888205 | + | 0.459447i | \(0.848048\pi\) | |||||||
\(578\) | − | 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 | \(0.153915\pi\) | ||||
−0.885355 | + | 0.464915i | \(0.846085\pi\) | |||||||
\(588\) | − | 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 | \(0.0275766\pi\) | ||||
−0.996250 | + | 0.0865261i | \(0.972423\pi\) | |||||||
\(594\) | 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 | \(0.319841\pi\) | ||||
−0.536248 | + | 0.844060i | \(0.680159\pi\) | |||||||
\(608\) | − | 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 | \(0.0421513\pi\) | ||||
−0.991245 | + | 0.132036i | \(0.957849\pi\) | |||||||
\(614\) | 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 | \(-0.844927\pi\) | ||
0.883658 | − | 0.468133i | \(-0.155073\pi\) | |||||||
\(618\) | − | 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 | \(0.188592\pi\) | ||||
−0.829559 | + | 0.558419i | \(0.811408\pi\) | |||||||
\(644\) | 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 | \(-0.866504\pi\) | ||
0.913338 | − | 0.407203i | \(-0.133496\pi\) | |||||||
\(648\) | 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 | \(0.0183449\pi\) | ||||
−0.998340 | + | 0.0576003i | \(0.981655\pi\) | |||||||
\(654\) | −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 | \(-0.843259\pi\) | ||
0.881193 | − | 0.472757i | \(-0.156741\pi\) | |||||||
\(674\) | 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 | \(-0.858813\pi\) | ||
0.903234 | − | 0.429149i | \(-0.141187\pi\) | |||||||
\(678\) | − | 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 | \(0.000612195\pi\) | ||||
−0.999998 | + | 0.00192327i | \(0.999388\pi\) | |||||||
\(684\) | 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 | \(-0.975131\pi\) | ||
0.996950 | − | 0.0780489i | \(-0.0248690\pi\) | |||||||
\(728\) | − | 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 | \(0.00387465\pi\) | ||||
−0.999926 | + | 0.0121723i | \(0.996125\pi\) | |||||||
\(734\) | 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 | \(0.0102966\pi\) | ||||
−0.999477 | + | 0.0323420i | \(0.989703\pi\) | |||||||
\(744\) | −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 | \(0.0301110\pi\) | ||||
−0.995529 | + | 0.0944555i | \(0.969889\pi\) | |||||||
\(758\) | 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 | \(0.148469\pi\) | ||||
−0.893180 | + | 0.449699i | \(0.851531\pi\) | |||||||
\(774\) | −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 | \(0.0292379\pi\) | ||||
−0.995784 | + | 0.0917244i | \(0.970762\pi\) | |||||||
\(788\) | − | 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 | \(0.240580\pi\) | ||||
−0.727720 | + | 0.685874i | \(0.759420\pi\) | |||||||
\(798\) | 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 | \(0.0808697\pi\) | ||||
−0.967900 | + | 0.251335i | \(0.919130\pi\) | |||||||
\(824\) | −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 | \(0.0616123\pi\) | ||||
−0.981326 | + | 0.192354i | \(0.938388\pi\) | |||||||
\(828\) | − | 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 | \(0.0664516\pi\) | ||||
−0.978288 | + | 0.207251i | \(0.933548\pi\) | |||||||
\(854\) | −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 | \(0.112557\pi\) | ||||
−0.938129 | + | 0.346285i | \(0.887443\pi\) | |||||||
\(858\) | 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 | \(0.145491\pi\) | ||||
−0.897348 | + | 0.441324i | \(0.854509\pi\) | |||||||
\(864\) | 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 | \(0.141021\pi\) | ||||
−0.903456 | + | 0.428681i | \(0.858979\pi\) | |||||||
\(878\) | − | 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 | \(-0.689470\pi\) | ||
0.560705 | − | 0.828016i | \(-0.310530\pi\) | |||||||
\(884\) | 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 | \(-0.775846\pi\) | ||
0.762130 | − | 0.647424i | \(-0.224154\pi\) | |||||||
\(888\) | − | 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 | \(0.150788\pi\) | ||||
−0.889880 | + | 0.456196i | \(0.849212\pi\) | |||||||
\(908\) | 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 | \(-0.978882\pi\) | ||
0.997800 | − | 0.0662951i | \(-0.0211179\pi\) | |||||||
\(938\) | − | 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 | \(0.243270\pi\) | ||||
−0.721899 | + | 0.691998i | \(0.756730\pi\) | |||||||
\(948\) | − | 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 | \(0.235028\pi\) | ||||
−0.739573 | + | 0.673077i | \(0.764972\pi\) | |||||||
\(954\) | 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 | \(0.0219276\pi\) | ||||
−0.997628 | + | 0.0688332i | \(0.978072\pi\) | |||||||
\(968\) | − | 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 | \(0.225800\pi\) | ||||
−0.758772 | + | 0.651357i | \(0.774200\pi\) | |||||||
\(978\) | 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 | \(0.0196353\pi\) | ||||
−0.998098 | + | 0.0616471i | \(0.980365\pi\) | |||||||
\(984\) | −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 | \(-0.775504\pi\) | ||
0.761432 | − | 0.648244i | \(-0.224496\pi\) | |||||||
\(998\) | 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.169.2 | ✓ | 4 | |
3.2 | odd | 2 | 630.4.g.e.379.3 | 4 | |||
5.2 | odd | 4 | 1050.4.a.bg.1.2 | 2 | |||
5.3 | odd | 4 | 1050.4.a.bc.1.2 | 2 | |||
5.4 | even | 2 | inner | 210.4.g.a.169.4 | yes | 4 | |
15.14 | odd | 2 | 630.4.g.e.379.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.4.g.a.169.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
210.4.g.a.169.4 | yes | 4 | 5.4 | even | 2 | inner | |
630.4.g.e.379.1 | 4 | 15.14 | odd | 2 | |||
630.4.g.e.379.3 | 4 | 3.2 | odd | 2 | |||
1050.4.a.bc.1.2 | 2 | 5.3 | odd | 4 | |||
1050.4.a.bg.1.2 | 2 | 5.2 | odd | 4 |