Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.a (trivial) |
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: | yes |
Analytic conductor: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{22}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 156) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.69042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.38083 | −0.839047 | −0.419524 | − | 0.907744i | \(-0.637803\pi\) | ||||
−0.419524 | + | 0.907744i | \(0.637803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.1425 | −1.73553 | −0.867766 | − | 0.496973i | \(-0.834445\pi\) | ||||
−0.867766 | + | 0.496973i | \(0.834445\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.7617 | 1.33656 | 0.668282 | − | 0.743908i | \(-0.267030\pi\) | ||||
0.668282 | + | 0.743908i | \(0.267030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28.1425 | −0.484424 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −110.285 | −1.57341 | −0.786707 | − | 0.617327i | \(-0.788216\pi\) | ||||
−0.786707 | + | 0.617327i | \(0.788216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 136.142 | 1.64385 | 0.821927 | − | 0.569593i | \(-0.192899\pi\) | ||||
0.821927 | + | 0.569593i | \(0.192899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.4275 | −1.00201 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 32.9533 | 0.298750 | 0.149375 | − | 0.988781i | \(-0.452274\pi\) | ||||
0.149375 | + | 0.988781i | \(0.452274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −37.0000 | −0.296000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 133.617 | 0.855586 | 0.427793 | − | 0.903877i | \(-0.359291\pi\) | ||||
0.427793 | + | 0.903877i | \(0.359291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −180.712 | −1.04700 | −0.523499 | − | 0.852026i | \(-0.675374\pi\) | ||||
−0.523499 | + | 0.852026i | \(0.675374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 146.285 | 0.771665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 301.523 | 1.45619 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −114.855 | −0.510325 | −0.255163 | − | 0.966898i | \(-0.582129\pi\) | ||||
−0.255163 | + | 0.966898i | \(0.582129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 116.712 | 0.444571 | 0.222286 | − | 0.974982i | \(-0.428648\pi\) | ||||
0.222286 | + | 0.974982i | \(0.428648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 502.565 | 1.78234 | 0.891168 | − | 0.453674i | \(-0.149887\pi\) | ||||
0.891168 | + | 0.453674i | \(0.149887\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −84.4275 | −0.279682 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 526.757 | 1.63479 | 0.817397 | − | 0.576074i | \(-0.195416\pi\) | ||||
0.817397 | + | 0.576074i | \(0.195416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 690.140 | 2.01207 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −330.855 | −0.908411 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 382.570 | 0.991510 | 0.495755 | − | 0.868462i | \(-0.334891\pi\) | ||||
0.495755 | + | 0.868462i | \(0.334891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −457.425 | −1.12144 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 408.427 | 0.949080 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 801.233 | 1.76799 | 0.883997 | − | 0.467492i | \(-0.154842\pi\) | ||||
0.883997 | + | 0.467492i | \(0.154842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 266.570 | 0.559521 | 0.279761 | − | 0.960070i | \(-0.409745\pi\) | ||||
0.279761 | + | 0.960070i | \(0.409745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −289.282 | −0.578511 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 121.951 | 0.232710 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −213.852 | −0.389944 | −0.194972 | − | 0.980809i | \(-0.562462\pi\) | ||||
−0.194972 | + | 0.980809i | \(0.562462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 98.8600 | 0.172483 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −655.228 | −1.09523 | −0.547615 | − | 0.836731i | \(-0.684464\pi\) | ||||
−0.547615 | + | 0.836731i | \(0.684464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 766.285 | 1.22859 | 0.614294 | − | 0.789077i | \(-0.289441\pi\) | ||||
0.614294 | + | 0.789077i | \(0.289441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −111.000 | −0.170896 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1567.32 | −2.31965 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 314.850 | 0.448397 | 0.224199 | − | 0.974543i | \(-0.428024\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −730.570 | −0.966150 | −0.483075 | − | 0.875579i | \(-0.660480\pi\) | ||||
−0.483075 | + | 0.875579i | \(0.660480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1034.56 | 1.32017 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 400.850 | 0.493973 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1298.99 | −1.54711 | −0.773556 | − | 0.633728i | \(-0.781524\pi\) | ||||
−0.773556 | + | 0.633728i | \(0.781524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 417.852 | 0.481350 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −542.137 | −0.604484 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1277.13 | −1.37927 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 20.5751 | 0.0215369 | 0.0107685 | − | 0.999942i | \(-0.496572\pi\) | ||||
0.0107685 | + | 0.999942i | \(0.496572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 438.855 | 0.445521 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −273.902 | −0.269844 | −0.134922 | − | 0.990856i | \(-0.543078\pi\) | ||||
−0.134922 | + | 0.990856i | \(0.543078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 760.285 | 0.727312 | 0.363656 | − | 0.931533i | \(-0.381528\pi\) | ||||
0.363656 | + | 0.931533i | \(0.381528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 904.570 | 0.840733 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −728.176 | −0.657902 | −0.328951 | − | 0.944347i | \(-0.606695\pi\) | ||||
−0.328951 | + | 0.944347i | \(0.606695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1058.57 | 0.930207 | 0.465104 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465104 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −344.565 | −0.294637 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 845.036 | 0.703490 | 0.351745 | − | 0.936096i | \(-0.385588\pi\) | ||||
0.351745 | + | 0.936096i | \(0.385588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −309.130 | −0.250665 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3544.83 | 2.73071 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1046.70 | 0.786401 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 350.137 | 0.256673 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1519.69 | 1.08741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1071.69 | 0.748799 | 0.374400 | − | 0.927267i | \(-0.377849\pi\) | ||||
0.374400 | + | 0.927267i | \(0.377849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1507.69 | 1.02903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 777.513 | 0.518562 | 0.259281 | − | 0.965802i | \(-0.416514\pi\) | ||||
0.259281 | + | 0.965802i | \(0.416514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4375.96 | −2.85296 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −253.282 | −0.161475 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1558.69 | −0.972026 | −0.486013 | − | 0.873951i | \(-0.661549\pi\) | ||||
−0.486013 | + | 0.873951i | \(0.661549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2514.29 | 1.53424 | 0.767120 | − | 0.641504i | \(-0.221689\pi\) | ||||
0.767120 | + | 0.641504i | \(0.221689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1580.27 | 0.943849 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −633.902 | −0.370696 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1253.44 | −0.717877 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2070.42 | 1.16167 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1172.15 | −0.644473 | −0.322237 | − | 0.946659i | \(-0.604435\pi\) | ||||
−0.322237 | + | 0.946659i | \(0.604435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −446.137 | −0.240438 | −0.120219 | − | 0.992747i | \(-0.538360\pi\) | ||||
−0.120219 | + | 0.992747i | \(0.538360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −992.565 | −0.524471 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1695.23 | 0.878480 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2258.56 | 1.14811 | 0.574053 | − | 0.818818i | \(-0.305370\pi\) | ||||
0.574053 | + | 0.818818i | \(0.305370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1147.71 | 0.572449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1059.20 | −0.518490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2290.40 | −1.10060 | −0.550301 | − | 0.834966i | \(-0.685487\pi\) | ||||
−0.550301 | + | 0.834966i | \(0.685487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1372.27 | −0.647463 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3323.13 | −1.53983 | −0.769915 | − | 0.638147i | \(-0.779701\pi\) | ||||
−0.769915 | + | 0.638147i | \(0.779701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1225.28 | 0.547951 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1691.58 | 0.743402 | 0.371701 | − | 0.928353i | \(-0.378775\pi\) | ||||
0.371701 | + | 0.928353i | \(0.378775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1189.27 | 0.513717 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2403.70 | 1.02075 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2490.84 | −1.04008 | −0.520039 | − | 0.854142i | \(-0.674083\pi\) | ||||
−0.520039 | + | 0.854142i | \(0.674083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −776.860 | −0.319025 | −0.159513 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159513 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 799.710 | 0.323040 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1077.44 | 0.428187 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5377.68 | −2.10297 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −867.847 | −0.334003 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 283.026 | 0.107220 | 0.0536101 | − | 0.998562i | \(-0.482927\pi\) | ||||
0.0536101 | + | 0.998562i | \(0.482927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1747.11 | −0.651605 | −0.325802 | − | 0.945438i | \(-0.605634\pi\) | ||||
−0.325802 | + | 0.945438i | \(0.605634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 365.852 | 0.134355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 328.702 | 0.118879 | 0.0594393 | − | 0.998232i | \(-0.481069\pi\) | ||||
0.0594393 | + | 0.998232i | \(0.481069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5205.39 | 1.85427 | 0.927137 | − | 0.374722i | \(-0.122262\pi\) | ||||
0.927137 | + | 0.374722i | \(0.122262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −641.557 | −0.225134 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4294.77 | −1.48490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1094.86 | −0.373016 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 296.580 | 0.0995833 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6638.53 | 2.19711 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3763.98 | 1.22807 | 0.614036 | − | 0.789278i | \(-0.289545\pi\) | ||||
0.614036 | + | 0.789278i | \(0.289545\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1965.68 | −0.632331 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4714.48 | −1.49546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5808.55 | 1.81710 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2298.85 | 0.709325 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1433.70 | 0.436387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −900.102 | −0.270293 | −0.135146 | − | 0.990826i | \(-0.543150\pi\) | ||||
−0.135146 | + | 0.990826i | \(0.543150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −333.000 | −0.0986667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3193.73 | −0.933811 | −0.466905 | − | 0.884307i | \(-0.654631\pi\) | ||||
−0.466905 | + | 0.884307i | \(0.654631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1261.43 | −0.364007 | −0.182004 | − | 0.983298i | \(-0.558258\pi\) | ||||
−0.182004 | + | 0.983298i | \(0.558258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4701.96 | −1.33925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4125.90 | −1.16007 | −0.580036 | − | 0.814591i | \(-0.696962\pi\) | ||||
−0.580036 | + | 0.814591i | \(0.696962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4941.41 | −1.37167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 944.550 | 0.258882 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3282.30 | −0.888343 | −0.444172 | − | 0.895942i | \(-0.646502\pi\) | ||||
−0.444172 | + | 0.895942i | \(0.646502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1768.59 | 0.472716 | 0.236358 | − | 0.971666i | \(-0.424046\pi\) | ||||
0.236358 | + | 0.971666i | \(0.424046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6474.09 | −1.68822 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1769.85 | −0.455923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2191.71 | −0.557807 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6097.65 | 1.53339 | 0.766694 | − | 0.642013i | \(-0.221901\pi\) | ||||
0.766694 | + | 0.642013i | \(0.221901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1606.86 | 0.399298 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3103.69 | 0.762200 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1612.59 | −0.391402 | −0.195701 | − | 0.980664i | \(-0.562698\pi\) | ||||
−0.195701 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3691.73 | 0.885686 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1202.55 | 0.285195 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3219.39 | −0.754814 | −0.377407 | − | 0.926048i | \(-0.623184\pi\) | ||||
−0.377407 | + | 0.926048i | \(0.623184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3588.82 | −0.831924 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3896.98 | −0.893225 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2235.17 | −0.506620 | −0.253310 | − | 0.967385i | \(-0.581519\pi\) | ||||
−0.253310 | + | 0.967385i | \(0.581519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2652.38 | 0.594540 | 0.297270 | − | 0.954793i | \(-0.403924\pi\) | ||||
0.297270 | + | 0.954793i | \(0.403924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1253.56 | 0.277907 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1804.18 | −0.395623 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2450.02 | −0.531435 | −0.265717 | − | 0.964051i | \(-0.585609\pi\) | ||||
−0.265717 | + | 0.964051i | \(0.585609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1626.41 | −0.348999 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1999.41 | 0.424465 | 0.212232 | − | 0.977219i | \(-0.431927\pi\) | ||||
0.212232 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2846.54 | 0.597913 | 0.298957 | − | 0.954267i | \(-0.403361\pi\) | ||||
0.298957 | + | 0.954267i | \(0.403361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3831.39 | −0.796323 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3751.43 | −0.771568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7249.78 | 1.47563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 61.7252 | 0.0124343 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1737.35 | 0.346406 | 0.173203 | − | 0.984886i | \(-0.444588\pi\) | ||||
0.173203 | + | 0.984886i | \(0.444588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7516.23 | −1.48343 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1316.56 | 0.257222 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −428.394 | −0.0828583 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16153.7 | −3.09330 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −821.705 | −0.155794 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2500.65 | −0.469465 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2523.51 | 0.469135 | 0.234567 | − | 0.972100i | \(-0.424633\pi\) | ||||
0.234567 | + | 0.972100i | \(0.424633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2280.85 | 0.419914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2697.76 | 0.491884 | 0.245942 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245942 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2589.38 | −0.467605 | −0.233803 | − | 0.972284i | \(-0.575117\pi\) | ||||
−0.233803 | + | 0.972284i | \(0.575117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2713.71 | 0.485398 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3692.06 | 0.654154 | 0.327077 | − | 0.944998i | \(-0.393936\pi\) | ||||
0.327077 | + | 0.944998i | \(0.393936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6515.37 | 1.14354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2184.53 | −0.379840 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15014.5 | −2.58646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 481.000 | 0.0820956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3175.71 | 0.537056 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16931.3 | −2.83724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6100.12 | −1.01297 | −0.506485 | − | 0.862249i | \(-0.669055\pi\) | ||||
−0.506485 | + | 0.862249i | \(0.669055\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1033.69 | −0.170108 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2006.11 | 0.327181 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1105.39 | −0.178678 | −0.0893389 | − | 0.996001i | \(-0.528475\pi\) | ||||
−0.0893389 | + | 0.996001i | \(0.528475\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2535.11 | 0.406160 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8811.84 | −1.39938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11157.9 | −1.75648 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −927.389 | −0.144722 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11014.7 | 1.70404 | 0.852020 | − | 0.523510i | \(-0.175378\pi\) | ||||
0.852020 | + | 0.523510i | \(0.175378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1450.35 | −0.222451 | −0.111225 | − | 0.993795i | \(-0.535478\pi\) | ||||
−0.111225 | + | 0.993795i | \(0.535478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4589.21 | −0.691953 | −0.345976 | − | 0.938243i | \(-0.612452\pi\) | ||||
−0.345976 | + | 0.938243i | \(0.612452\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6146.59 | 0.918949 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10634.5 | 1.57658 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 879.170 | 0.129250 | 0.0646251 | − | 0.997910i | \(-0.479415\pi\) | ||||
0.0646251 | + | 0.997910i | \(0.479415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11675.8 | 1.70226 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3140.10 | 0.454029 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7188.39 | −1.03084 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9883.42 | 1.40575 | 0.702875 | − | 0.711313i | \(-0.251899\pi\) | ||||
0.702875 | + | 0.711313i | \(0.251899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1050.41 | 0.148190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12296.8 | −1.72080 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4981.98 | −0.691574 | −0.345787 | − | 0.938313i | \(-0.612388\pi\) | ||||
−0.345787 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4559.08 | 0.627814 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1737.02 | −0.237297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2095.29 | −0.283978 | −0.141989 | − | 0.989868i | \(-0.545350\pi\) | ||||
−0.141989 | + | 0.989868i | \(0.545350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3215.08 | 0.432320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11211.7 | 1.49580 | 0.747900 | − | 0.663812i | \(-0.231062\pi\) | ||||
0.747900 | + | 0.663812i | \(0.231062\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14702.8 | 1.94629 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4523.08 | 0.594112 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7697.74 | −1.00332 | −0.501659 | − | 0.865065i | \(-0.667277\pi\) | ||||
−0.501659 | + | 0.865065i | \(0.667277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3634.26 | −0.470057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2332.54 | 0.299392 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2953.55 | −0.376226 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9240.59 | 1.16819 | 0.584095 | − | 0.811685i | \(-0.301449\pi\) | ||||
0.584095 | + | 0.811685i | \(0.301449\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13127.9 | −1.64716 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12268.3 | 1.52781 | 0.763903 | − | 0.645331i | \(-0.223280\pi\) | ||||
0.763903 | + | 0.645331i | \(0.223280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2349.26 | 0.290385 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −759.847 | −0.0932275 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5600.52 | −0.682082 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7748.49 | 0.936769 | 0.468384 | − | 0.883525i | \(-0.344836\pi\) | ||||
0.468384 | + | 0.883525i | \(0.344836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4676.06 | −0.561200 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25753.6 | −3.06841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6853.35 | 0.810646 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7542.87 | 0.885794 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6153.08 | 0.717417 | 0.358708 | − | 0.933450i | \(-0.383217\pi\) | ||||
0.358708 | + | 0.933450i | \(0.383217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1163.77 | 0.134724 | 0.0673619 | − | 0.997729i | \(-0.478542\pi\) | ||||
0.0673619 | + | 0.997729i | \(0.478542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4740.81 | 0.544932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4080.54 | 0.465731 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8568.22 | −0.971067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1901.70 | −0.214021 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8945.32 | 0.999723 | 0.499862 | − | 0.866105i | \(-0.333384\pi\) | ||||
0.499862 | + | 0.866105i | \(0.333384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3602.01 | 0.399773 | 0.199886 | − | 0.979819i | \(-0.435943\pi\) | ||||
0.199886 | + | 0.979819i | \(0.435943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3760.31 | −0.414466 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4486.35 | 0.491101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9684.72 | 1.05291 | 0.526454 | − | 0.850204i | \(-0.323521\pi\) | ||||
0.526454 | + | 0.850204i | \(0.323521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6211.26 | 0.670690 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2294.27 | 0.246059 | 0.123029 | − | 0.992403i | \(-0.460739\pi\) | ||||
0.123029 | + | 0.992403i | \(0.460739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12185.6 | 1.29810 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3516.46 | −0.372087 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12453.3 | 1.30893 | 0.654464 | − | 0.756093i | \(-0.272894\pi\) | ||||
0.654464 | + | 0.756093i | \(0.272894\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5691.09 | 0.594198 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1338.41 | −0.138817 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3919.80 | −0.403875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13922.7 | −1.42511 | −0.712555 | − | 0.701616i | \(-0.752462\pi\) | ||||
−0.712555 | + | 0.701616i | \(0.752462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2977.69 | −0.302804 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14345.0 | −1.44927 | −0.724633 | − | 0.689135i | \(-0.757991\pi\) | ||||
−0.724633 | + | 0.689135i | \(0.757991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −125.252 | −0.0125723 | −0.00628613 | − | 0.999980i | \(-0.502001\pi\) | ||||
−0.00628613 | + | 0.999980i | \(0.502001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5085.70 | 0.507191 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12764.6 | −1.26482 | −0.632412 | − | 0.774632i | \(-0.717935\pi\) | ||||
−0.632412 | + | 0.774632i | \(0.717935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6873.75 | 0.676760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6775.68 | 0.662860 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24505.9 | 2.38220 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5037.27 | −0.486581 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3443.13 | 0.330503 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5904.54 | 0.563227 | 0.281613 | − | 0.959528i | \(-0.409130\pi\) | ||||
0.281613 | + | 0.959528i | \(0.409130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1493.11 | 0.141539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3177.61 | −0.299350 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −193.011 | −0.0180705 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20385.3 | −1.89680 | −0.948402 | − | 0.317069i | \(-0.897301\pi\) | ||||
−0.948402 | + | 0.317069i | \(0.897301\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6871.21 | −0.635433 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9155.16 | −0.841480 | −0.420740 | − | 0.907181i | \(-0.638230\pi\) | ||||
−0.420740 | + | 0.907181i | \(0.638230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14735.9 | −1.34619 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4116.82 | −0.373813 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21060.7 | 1.90081 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20308.9 | 1.82195 | 0.910974 | − | 0.412464i | \(-0.135332\pi\) | ||||
0.910974 | + | 0.412464i | \(0.135332\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9969.39 | −0.889021 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5341.99 | 0.473534 | 0.236767 | − | 0.971566i | \(-0.423912\pi\) | ||||
0.236767 | + | 0.971566i | \(0.423912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2569.42 | 0.226412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8142.10 | 0.709022 | 0.354511 | − | 0.935052i | \(-0.384647\pi\) | ||||
0.354511 | + | 0.935052i | \(0.384647\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24630.3 | −2.13225 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3675.85 | 0.316360 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7132.11 | −0.610249 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25685.5 | 2.18501 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5074.74 | 0.429203 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3103.65 | 0.260985 | 0.130493 | − | 0.991449i | \(-0.458344\pi\) | ||||
0.130493 | + | 0.991449i | \(0.458344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17409.0 | 1.45553 | 0.727767 | − | 0.685824i | \(-0.240558\pi\) | ||||
0.727767 | + | 0.685824i | \(0.240558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3567.82 | 0.296595 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19929.9 | 1.64736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11081.1 | −0.910748 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7211.10 | 0.589332 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1517.26 | −0.123302 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6830.90 | 0.552010 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7472.52 | −0.600490 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33652.4 | 2.68926 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8794.50 | −0.698900 | −0.349450 | − | 0.936955i | \(-0.613632\pi\) | ||||
−0.349450 | + | 0.936955i | \(0.613632\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2330.58 | −0.184189 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9930.27 | −0.780488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3153.07 | −0.246463 | −0.123232 | − | 0.992378i | \(-0.539326\pi\) | ||||
−0.123232 | + | 0.992378i | \(0.539326\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2399.13 | 0.186507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18190.9 | 1.40646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10120.1 | −0.778208 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3232.31 | 0.247214 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15234.8 | −1.15892 | −0.579460 | − | 0.815000i | \(-0.696737\pi\) | ||||
−0.579460 | + | 0.815000i | \(0.696737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6533.34 | −0.494331 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16133.0 | −1.21415 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3473.44 | 0.260014 | 0.130007 | − | 0.991513i | \(-0.458500\pi\) | ||||
0.130007 | + | 0.991513i | \(0.458500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7927.15 | −0.590261 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2603.54 | −0.192837 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15167.6 | −1.11750 | −0.558752 | − | 0.829335i | \(-0.688719\pi\) | ||||
−0.558752 | + | 0.829335i | \(0.688719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16058.9 | −1.17696 | −0.588479 | − | 0.808512i | \(-0.700273\pi\) | ||||
−0.588479 | + | 0.808512i | \(0.700273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 849.079 | 0.0619036 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1219.27 | −0.0884300 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9238.39 | −0.666550 | −0.333275 | − | 0.942830i | \(-0.608154\pi\) | ||||
−0.333275 | + | 0.942830i | \(0.608154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5241.33 | −0.376204 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23482.3 | 1.67678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18654.7 | 1.32522 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1097.56 | 0.0775699 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25895.9 | −1.82085 | −0.910424 | − | 0.413677i | \(-0.864244\pi\) | ||||
−0.910424 | + | 0.413677i | \(0.864244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24602.6 | −1.72111 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 986.107 | 0.0686346 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17572.0 | 1.21686 | 0.608428 | − | 0.793609i | \(-0.291800\pi\) | ||||
0.608428 | + | 0.793609i | \(0.291800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33253.5 | −2.29119 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15616.2 | 1.07057 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12752.8 | −0.869894 | −0.434947 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434947 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −951.801 | −0.0646003 | −0.0323002 | − | 0.999478i | \(-0.510283\pi\) | ||||
−0.0323002 | + | 0.999478i | \(0.510283\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1924.67 | −0.129981 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9818.91 | −0.659827 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18701.1 | 1.25050 | 0.625252 | − | 0.780423i | \(-0.284996\pi\) | ||||
0.625252 | + | 0.780423i | \(0.284996\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12884.3 | −0.857305 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6847.84 | −0.453410 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25600.3 | 1.68676 | 0.843381 | − | 0.537316i | \(-0.180562\pi\) | ||||
0.843381 | + | 0.537316i | \(0.180562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3284.58 | −0.215361 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7742.12 | 0.505164 | 0.252582 | − | 0.967575i | \(-0.418720\pi\) | ||||
0.252582 | + | 0.967575i | \(0.418720\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17409.3 | 1.13044 | 0.565218 | − | 0.824942i | \(-0.308792\pi\) | ||||
0.565218 | + | 0.824942i | \(0.308792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 889.740 | 0.0574944 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41752.9 | 2.68506 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9631.00 | −0.616384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19915.6 | 1.26850 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12666.8 | 0.802953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4994.82 | 0.315120 | 0.157560 | − | 0.987509i | \(-0.449637\pi\) | ||||
0.157560 | + | 0.987509i | \(0.449637\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11291.9 | 0.709027 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10053.4 | −0.628278 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8971.82 | −0.558048 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5897.05 | −0.365076 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14610.1 | 0.900257 | 0.450128 | − | 0.892964i | \(-0.351378\pi\) | ||||
0.450128 | + | 0.892964i | \(0.351378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23102.5 | 1.41691 | 0.708456 | − | 0.705755i | \(-0.249392\pi\) | ||||
0.708456 | + | 0.705755i | \(0.249392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14143.4 | −0.863406 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1830.50 | −0.111228 | −0.0556139 | − | 0.998452i | \(-0.517712\pi\) | ||||
−0.0556139 | + | 0.998452i | \(0.517712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39069.5 | 2.36304 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17425.6 | 1.04910 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2834.46 | −0.169864 | −0.0849318 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849318 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7293.72 | −0.435098 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6896.56 | 0.409529 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24787.3 | 1.46521 | 0.732607 | − | 0.680652i | \(-0.238303\pi\) | ||||
0.732607 | + | 0.680652i | \(0.238303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9370.39 | −0.551385 | −0.275693 | − | 0.961246i | \(-0.588907\pi\) | ||||
−0.275693 | + | 0.961246i | \(0.588907\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4301.11 | 0.251948 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41050.1 | 2.39377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4403.12 | 0.255606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2700.31 | −0.156054 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12998.4 | 0.747835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19925.8 | −1.14128 | −0.570641 | − | 0.821200i | \(-0.693305\pi\) | ||||
−0.570641 | + | 0.821200i | \(0.693305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −999.000 | −0.0569652 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10634.5 | 0.603719 | 0.301860 | − | 0.953352i | \(-0.402393\pi\) | ||||
0.301860 | + | 0.953352i | \(0.402393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −661.334 | −0.0373780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9581.18 | −0.539136 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8250.11 | −0.462199 | −0.231099 | − | 0.972930i | \(-0.574232\pi\) | ||||
−0.231099 | + | 0.972930i | \(0.574232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14621.8 | 0.815576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3784.29 | −0.210160 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4973.41 | −0.274995 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33965.8 | 1.86993 | 0.934964 | − | 0.354744i | \(-0.115432\pi\) | ||||
0.934964 | + | 0.354744i | \(0.115432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14105.9 | −0.773216 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23586.1 | −1.28730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12871.6 | −0.699495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12377.7 | −0.669768 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25354.8 | 1.36610 | 0.683051 | − | 0.730371i | \(-0.260653\pi\) | ||||
0.683051 | + | 0.730371i | \(0.260653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15636.6 | −0.838901 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14824.2 | −0.791934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8803.88 | 0.468323 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6783.28 | −0.359311 | −0.179656 | − | 0.983730i | \(-0.557498\pi\) | ||||
−0.179656 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2833.65 | 0.149466 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5955.08 | −0.312790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5946.52 | 0.311031 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9846.89 | −0.512885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21704.4 | −1.12578 | −0.562892 | − | 0.826530i | \(-0.690311\pi\) | ||||
−0.562892 | + | 0.826530i | \(0.690311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24437.5 | −1.26227 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5305.76 | 0.272923 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4943.82 | −0.253253 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30734.0 | −1.56790 | −0.783949 | − | 0.620825i | \(-0.786798\pi\) | ||||
−0.783949 | + | 0.620825i | \(0.786798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55425.4 | −2.80435 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1005.22 | 0.0506528 | 0.0253264 | − | 0.999679i | \(-0.491937\pi\) | ||||
0.0253264 | + | 0.999679i | \(0.491937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19422.3 | −0.974695 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10427.8 | −0.521184 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5216.68 | 0.259674 | 0.129837 | − | 0.991535i | \(-0.458555\pi\) | ||||
0.129837 | + | 0.991535i | \(0.458555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5309.56 | −0.263227 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26994.7 | −1.33289 | −0.666447 | − | 0.745552i | \(-0.732186\pi\) | ||||
−0.666447 | + | 0.745552i | \(0.732186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10995.8 | 0.540743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6575.13 | −0.322050 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23405.4 | 1.14181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14488.7 | 0.703996 | 0.351998 | − | 0.936001i | \(-0.385502\pi\) | ||||
0.351998 | + | 0.936001i | \(0.385502\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18292.9 | 0.885302 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4185.14 | 0.201739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21724.8 | 1.04307 | 0.521534 | − | 0.853230i | \(-0.325360\pi\) | ||||
0.521534 | + | 0.853230i | \(0.325360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4820.58 | 0.230535 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11449.5 | −0.545391 | −0.272695 | − | 0.962100i | \(-0.587915\pi\) | ||||
−0.272695 | + | 0.962100i | \(0.587915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34025.1 | −1.61440 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9311.08 | 0.440056 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10416.0 | −0.490353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19602.4 | −0.919220 | −0.459610 | − | 0.888121i | \(-0.652011\pi\) | ||||
−0.459610 | + | 0.888121i | \(0.652011\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4837.76 | −0.225976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31311.3 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6686.36 | 0.309911 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11075.2 | 0.511351 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15889.5 | 0.730811 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31950.0 | −1.46384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3607.65 | 0.164658 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21187.2 | −0.963315 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1739.06 | 0.0787686 | 0.0393843 | − | 0.999224i | \(-0.487460\pi\) | ||||
0.0393843 | + | 0.999224i | \(0.487460\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9658.17 | −0.435792 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27161.6 | −1.22093 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3465.41 | −0.155183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10766.5 | −0.480311 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34119.8 | 1.51642 | 0.758209 | − | 0.652011i | \(-0.226074\pi\) | ||||
0.758209 | + | 0.652011i | \(0.226074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58093.3 | −2.57221 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11690.9 | −0.515704 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37365.3 | 1.64208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9936.20 | 0.435037 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6705.51 | −0.292497 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26108.4 | 1.13464 | 0.567319 | − | 0.823498i | \(-0.307981\pi\) | ||||
0.567319 | + | 0.823498i | \(0.307981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13917.9 | −0.602620 | −0.301310 | − | 0.953526i | \(-0.597424\pi\) | ||||
−0.301310 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7957.13 | 0.343258 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21485.9 | 0.923457 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68420.4 | 2.92990 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3760.67 | 0.160450 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1594.62 | 0.0677863 | 0.0338932 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338932 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17656.3 | −0.747825 | −0.373913 | − | 0.927464i | \(-0.621984\pi\) | ||||
−0.373913 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5412.54 | −0.228413 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3246.70 | −0.136516 | −0.0682581 | − | 0.997668i | \(-0.521744\pi\) | ||||
−0.0682581 | + | 0.997668i | \(0.521744\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6464.17 | 0.270820 | 0.135410 | − | 0.990790i | \(-0.456765\pi\) | ||||
0.135410 | + | 0.990790i | \(0.456765\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7350.06 | −0.306824 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −76112.1 | −3.16582 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31173.7 | 1.29199 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4879.24 | −0.201495 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38238.9 | 1.57348 | 0.786741 | − | 0.617283i | \(-0.211767\pi\) | ||||
0.786741 | + | 0.617283i | \(0.211767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6535.60 | −0.267973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5998.22 | 0.245065 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1585.36 | −0.0645421 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33643.5 | −1.36482 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8539.63 | 0.345206 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3784.86 | −0.152460 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32957.3 | 1.32290 | 0.661451 | − | 0.749988i | \(-0.269941\pi\) | ||||
0.661451 | + | 0.749988i | \(0.269941\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11494.2 | −0.459757 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46853.1 | −1.86753 | −0.933765 | − | 0.357887i | \(-0.883497\pi\) | ||||
−0.933765 | + | 0.357887i | \(0.883497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44005.5 | 1.74790 | 0.873951 | − | 0.486014i | \(-0.161550\pi\) | ||||
0.873951 | + | 0.486014i | \(0.161550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11254.3 | −0.445465 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27483.9 | 1.08408 | 0.542041 | − | 0.840352i | \(-0.317652\pi\) | ||||
0.542041 | + | 0.840352i | \(0.317652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15868.4 | −0.623749 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21749.3 | 0.851956 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15352.6 | 0.599311 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2780.08 | 0.108151 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 185.175 | 0.00717897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48846.8 | −1.88723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23933.7 | 0.921531 | 0.460766 | − | 0.887522i | \(-0.347575\pi\) | ||||
0.460766 | + | 0.887522i | \(0.347575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5212.05 | 0.199998 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4109.49 | 0.157154 | 0.0785768 | − | 0.996908i | \(-0.474962\pi\) | ||||
0.0785768 | + | 0.996908i | \(0.474962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30422.0 | −1.15944 | −0.579718 | − | 0.814817i | \(-0.696837\pi\) | ||||
−0.579718 | + | 0.814817i | \(0.696837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22548.7 | −0.856459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32471.3 | −1.22918 | −0.614588 | − | 0.788848i | \(-0.710678\pi\) | ||||
−0.614588 | + | 0.788848i | \(0.710678\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34446.9 | −1.29957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3949.69 | 0.148507 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 71714.0 | 2.68736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23366.1 | 0.872675 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1285.18 | −0.0478383 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24146.2 | −0.895796 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42191.7 | −1.56006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48461.1 | −1.78592 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7287.59 | 0.267677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37788.4 | 1.38340 | 0.691699 | − | 0.722186i | \(-0.256862\pi\) | ||||
0.691699 | + | 0.722186i | \(0.256862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2465.11 | −0.0899480 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47254.0 | 1.71855 | 0.859274 | − | 0.511516i | \(-0.170916\pi\) | ||||
0.859274 | + | 0.511516i | \(0.170916\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35623.8 | −1.29132 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7501.94 | −0.271045 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24991.2 | −0.899981 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27178.7 | −0.975562 | −0.487781 | − | 0.872966i | \(-0.662194\pi\) | ||||
−0.487781 | + | 0.872966i | \(0.662194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7570.53 | 0.270855 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8517.97 | 0.303762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4249.63 | 0.151056 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6842.56 | 0.242437 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32561.1 | −1.14994 | −0.574971 | − | 0.818174i | \(-0.694987\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 93957.4 | 3.30755 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8093.28 | 0.283989 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50447.1 | 1.76449 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38995.8 | 1.35959 | 0.679797 | − | 0.733401i | \(-0.262068\pi\) | ||||
0.679797 | + | 0.733401i | \(0.262068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7768.14 | −0.269972 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8625.11 | −0.298800 | −0.149400 | − | 0.988777i | \(-0.547734\pi\) | ||||
−0.149400 | + | 0.988777i | \(0.547734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3846.07 | 0.132816 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8141.13 | 0.280244 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5147.81 | 0.176644 | 0.0883218 | − | 0.996092i | \(-0.471850\pi\) | ||||
0.0883218 | + | 0.996092i | \(0.471850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9961.70 | −0.340749 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11076.2 | 0.377676 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33910.8 | −1.15265 | −0.576326 | − | 0.817220i | \(-0.695514\pi\) | ||||
−0.576326 | + | 0.817220i | \(0.695514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2655.02 | −0.0899628 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19546.1 | 0.660226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50100.1 | 1.68698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2866.00 | 0.0962035 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6553.59 | −0.219301 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16389.3 | 0.546727 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12891.9 | −0.428725 | −0.214362 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214362 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45043.4 | −1.49330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19035.1 | 0.629109 | 0.314555 | − | 0.949239i | \(-0.398145\pi\) | ||||
0.314555 | + | 0.949239i | \(0.398145\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −80815.6 | −2.66272 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1443.00 | 0.0473979 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7411.48 | 0.242696 | 0.121348 | − | 0.992610i | \(-0.461278\pi\) | ||||
0.121348 | + | 0.992610i | \(0.461278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63341.0 | −2.06781 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9527.13 | 0.310069 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43006.5 | 1.39542 | 0.697708 | − | 0.716382i | \(-0.254203\pi\) | ||||
0.697708 | + | 0.716382i | \(0.254203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3083.50 | −0.0997447 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −50793.8 | −1.63808 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16561.2 | 0.532473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49948.6 | −1.60108 | −0.800539 | − | 0.599280i | \(-0.795454\pi\) | ||||
−0.800539 | + | 0.599280i | \(0.795454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18300.4 | −0.584838 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48830.9 | −1.55582 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10657.9 | −0.338555 | −0.169278 | − | 0.985568i | \(-0.554143\pi\) | ||||
−0.169278 | + | 0.985568i | \(0.554143\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3101.08 | −0.0982122 |
(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 | 624.4.a.p.1.1 | 2 | ||
3.2 | odd | 2 | 1872.4.a.y.1.2 | 2 | |||
4.3 | odd | 2 | 156.4.a.c.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 2496.4.a.bf.1.2 | 2 | |||
8.5 | even | 2 | 2496.4.a.w.1.2 | 2 | |||
12.11 | even | 2 | 468.4.a.g.1.2 | 2 | |||
52.31 | even | 4 | 2028.4.b.e.337.4 | 4 | |||
52.47 | even | 4 | 2028.4.b.e.337.1 | 4 | |||
52.51 | odd | 2 | 2028.4.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.4.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
468.4.a.g.1.2 | 2 | 12.11 | even | 2 | |||
624.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1872.4.a.y.1.2 | 2 | 3.2 | odd | 2 | |||
2028.4.a.d.1.2 | 2 | 52.51 | odd | 2 | |||
2028.4.b.e.337.1 | 4 | 52.47 | even | 4 | |||
2028.4.b.e.337.4 | 4 | 52.31 | even | 4 | |||
2496.4.a.w.1.2 | 2 | 8.5 | even | 2 | |||
2496.4.a.bf.1.2 | 2 | 8.3 | odd | 2 |