Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(5.36472\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.36472 | 1.89672 | 0.948358 | − | 0.317201i | \(-0.102743\pi\) | ||||
0.948358 | + | 0.317201i | \(0.102743\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 20.7803 | 2.59753 | ||||||||
\(5\) | −2.69631 | −0.241165 | −0.120583 | − | 0.992703i | \(-0.538476\pi\) | ||||
−0.120583 | + | 0.992703i | \(0.538476\pi\) | |||||||
\(6\) | 16.0942 | 1.09507 | ||||||||
\(7\) | −15.2025 | −0.820856 | −0.410428 | − | 0.911893i | \(-0.634621\pi\) | ||||
−0.410428 | + | 0.911893i | \(0.634621\pi\) | |||||||
\(8\) | 68.5626 | 3.03007 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −14.4650 | −0.457423 | ||||||||
\(11\) | 66.8848 | 1.83332 | 0.916661 | − | 0.399666i | \(-0.130874\pi\) | ||||
0.916661 | + | 0.399666i | \(0.130874\pi\) | |||||||
\(12\) | 62.3408 | 1.49969 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −81.5570 | −1.55693 | ||||||||
\(15\) | −8.08894 | −0.139237 | ||||||||
\(16\) | 201.577 | 3.14965 | ||||||||
\(17\) | 4.16354 | 0.0594004 | 0.0297002 | − | 0.999559i | \(-0.490545\pi\) | ||||
0.0297002 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(18\) | 48.2825 | 0.632239 | ||||||||
\(19\) | −26.0850 | −0.314963 | −0.157482 | − | 0.987522i | \(-0.550338\pi\) | ||||
−0.157482 | + | 0.987522i | \(0.550338\pi\) | |||||||
\(20\) | −56.0301 | −0.626436 | ||||||||
\(21\) | −45.6074 | −0.473921 | ||||||||
\(22\) | 358.819 | 3.47729 | ||||||||
\(23\) | 47.3242 | 0.429034 | 0.214517 | − | 0.976720i | \(-0.431182\pi\) | ||||
0.214517 | + | 0.976720i | \(0.431182\pi\) | |||||||
\(24\) | 205.688 | 1.74941 | ||||||||
\(25\) | −117.730 | −0.941839 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −315.911 | −2.13220 | ||||||||
\(29\) | 257.007 | 1.64569 | 0.822845 | − | 0.568266i | \(-0.192386\pi\) | ||||
0.822845 | + | 0.568266i | \(0.192386\pi\) | |||||||
\(30\) | −43.3949 | −0.264093 | ||||||||
\(31\) | −206.242 | −1.19491 | −0.597455 | − | 0.801903i | \(-0.703821\pi\) | ||||
−0.597455 | + | 0.801903i | \(0.703821\pi\) | |||||||
\(32\) | 532.906 | 2.94392 | ||||||||
\(33\) | 200.655 | 1.05847 | ||||||||
\(34\) | 22.3362 | 0.112666 | ||||||||
\(35\) | 40.9906 | 0.197962 | ||||||||
\(36\) | 187.022 | 0.865845 | ||||||||
\(37\) | −175.686 | −0.780611 | −0.390305 | − | 0.920685i | \(-0.627631\pi\) | ||||
−0.390305 | + | 0.920685i | \(0.627631\pi\) | |||||||
\(38\) | −139.939 | −0.597396 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −184.866 | −0.730748 | ||||||||
\(41\) | −156.463 | −0.595984 | −0.297992 | − | 0.954568i | \(-0.596317\pi\) | ||||
−0.297992 | + | 0.954568i | \(0.596317\pi\) | |||||||
\(42\) | −244.671 | −0.898895 | ||||||||
\(43\) | 51.9845 | 0.184362 | 0.0921809 | − | 0.995742i | \(-0.470616\pi\) | ||||
0.0921809 | + | 0.995742i | \(0.470616\pi\) | |||||||
\(44\) | 1389.88 | 4.76211 | ||||||||
\(45\) | −24.2668 | −0.0803885 | ||||||||
\(46\) | 253.881 | 0.813755 | ||||||||
\(47\) | 354.222 | 1.09933 | 0.549666 | − | 0.835384i | \(-0.314755\pi\) | ||||
0.549666 | + | 0.835384i | \(0.314755\pi\) | |||||||
\(48\) | 604.732 | 1.81845 | ||||||||
\(49\) | −111.885 | −0.326196 | ||||||||
\(50\) | −631.588 | −1.78640 | ||||||||
\(51\) | 12.4906 | 0.0342948 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4723 | −0.0271412 | −0.0135706 | − | 0.999908i | \(-0.504320\pi\) | ||||
−0.0135706 | + | 0.999908i | \(0.504320\pi\) | |||||||
\(54\) | 144.848 | 0.365023 | ||||||||
\(55\) | −180.342 | −0.442134 | ||||||||
\(56\) | −1042.32 | −2.48725 | ||||||||
\(57\) | −78.2550 | −0.181844 | ||||||||
\(58\) | 1378.77 | 3.12141 | ||||||||
\(59\) | −445.114 | −0.982185 | −0.491092 | − | 0.871107i | \(-0.663402\pi\) | ||||
−0.491092 | + | 0.871107i | \(0.663402\pi\) | |||||||
\(60\) | −168.090 | −0.361673 | ||||||||
\(61\) | 119.696 | 0.251238 | 0.125619 | − | 0.992079i | \(-0.459908\pi\) | ||||
0.125619 | + | 0.992079i | \(0.459908\pi\) | |||||||
\(62\) | −1106.43 | −2.26640 | ||||||||
\(63\) | −136.822 | −0.273619 | ||||||||
\(64\) | 1246.28 | 2.43413 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1076.46 | 2.00761 | ||||||||
\(67\) | 22.4078 | 0.0408589 | 0.0204294 | − | 0.999791i | \(-0.493497\pi\) | ||||
0.0204294 | + | 0.999791i | \(0.493497\pi\) | |||||||
\(68\) | 86.5195 | 0.154295 | ||||||||
\(69\) | 141.973 | 0.247703 | ||||||||
\(70\) | 219.903 | 0.375478 | ||||||||
\(71\) | −285.207 | −0.476731 | −0.238365 | − | 0.971176i | \(-0.576612\pi\) | ||||
−0.238365 | + | 0.971176i | \(0.576612\pi\) | |||||||
\(72\) | 617.064 | 1.01002 | ||||||||
\(73\) | −740.989 | −1.18803 | −0.594015 | − | 0.804454i | \(-0.702458\pi\) | ||||
−0.594015 | + | 0.804454i | \(0.702458\pi\) | |||||||
\(74\) | −942.507 | −1.48060 | ||||||||
\(75\) | −353.190 | −0.543771 | ||||||||
\(76\) | −542.053 | −0.818128 | ||||||||
\(77\) | −1016.81 | −1.50489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −547.679 | −0.779983 | −0.389992 | − | 0.920818i | \(-0.627522\pi\) | ||||
−0.389992 | + | 0.920818i | \(0.627522\pi\) | |||||||
\(80\) | −543.516 | −0.759586 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −839.378 | −1.13041 | ||||||||
\(83\) | −603.056 | −0.797518 | −0.398759 | − | 0.917056i | \(-0.630559\pi\) | ||||
−0.398759 | + | 0.917056i | \(0.630559\pi\) | |||||||
\(84\) | −947.734 | −1.23103 | ||||||||
\(85\) | −11.2262 | −0.0143253 | ||||||||
\(86\) | 278.882 | 0.349682 | ||||||||
\(87\) | 771.021 | 0.950139 | ||||||||
\(88\) | 4585.80 | 5.55509 | ||||||||
\(89\) | −215.668 | −0.256863 | −0.128431 | − | 0.991718i | \(-0.540994\pi\) | ||||
−0.128431 | + | 0.991718i | \(0.540994\pi\) | |||||||
\(90\) | −130.185 | −0.152474 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 983.409 | 1.11443 | ||||||||
\(93\) | −618.726 | −0.689881 | ||||||||
\(94\) | 1900.31 | 2.08512 | ||||||||
\(95\) | 70.3333 | 0.0759583 | ||||||||
\(96\) | 1598.72 | 1.69967 | ||||||||
\(97\) | −1447.50 | −1.51517 | −0.757586 | − | 0.652735i | \(-0.773622\pi\) | ||||
−0.757586 | + | 0.652735i | \(0.773622\pi\) | |||||||
\(98\) | −600.233 | −0.618700 | ||||||||
\(99\) | 601.964 | 0.611107 | ||||||||
\(100\) | −2446.46 | −2.44646 | ||||||||
\(101\) | −883.450 | −0.870362 | −0.435181 | − | 0.900343i | \(-0.643316\pi\) | ||||
−0.435181 | + | 0.900343i | \(0.643316\pi\) | |||||||
\(102\) | 67.0087 | 0.0650476 | ||||||||
\(103\) | 1251.74 | 1.19745 | 0.598726 | − | 0.800954i | \(-0.295674\pi\) | ||||
0.598726 | + | 0.800954i | \(0.295674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 122.972 | 0.114293 | ||||||||
\(106\) | −56.1812 | −0.0514792 | ||||||||
\(107\) | −341.614 | −0.308645 | −0.154323 | − | 0.988021i | \(-0.549319\pi\) | ||||
−0.154323 | + | 0.988021i | \(0.549319\pi\) | |||||||
\(108\) | 561.067 | 0.499896 | ||||||||
\(109\) | −775.177 | −0.681179 | −0.340589 | − | 0.940212i | \(-0.610627\pi\) | ||||
−0.340589 | + | 0.940212i | \(0.610627\pi\) | |||||||
\(110\) | −967.487 | −0.838603 | ||||||||
\(111\) | −527.058 | −0.450686 | ||||||||
\(112\) | −3064.47 | −2.58541 | ||||||||
\(113\) | 1279.05 | 1.06480 | 0.532402 | − | 0.846492i | \(-0.321290\pi\) | ||||
0.532402 | + | 0.846492i | \(0.321290\pi\) | |||||||
\(114\) | −419.816 | −0.344907 | ||||||||
\(115\) | −127.601 | −0.103468 | ||||||||
\(116\) | 5340.67 | 4.27473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2387.91 | −1.86293 | ||||||||
\(119\) | −63.2961 | −0.0487592 | ||||||||
\(120\) | −554.599 | −0.421898 | ||||||||
\(121\) | 3142.58 | 2.36107 | ||||||||
\(122\) | 642.137 | 0.476528 | ||||||||
\(123\) | −469.388 | −0.344091 | ||||||||
\(124\) | −4285.77 | −3.10382 | ||||||||
\(125\) | 654.476 | 0.468305 | ||||||||
\(126\) | −734.013 | −0.518977 | ||||||||
\(127\) | −1113.82 | −0.778233 | −0.389117 | − | 0.921188i | \(-0.627220\pi\) | ||||
−0.389117 | + | 0.921188i | \(0.627220\pi\) | |||||||
\(128\) | 2422.68 | 1.67294 | ||||||||
\(129\) | 155.953 | 0.106441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2100.12 | 1.40068 | 0.700339 | − | 0.713811i | \(-0.253032\pi\) | ||||
0.700339 | + | 0.713811i | \(0.253032\pi\) | |||||||
\(132\) | 4169.65 | 2.74941 | ||||||||
\(133\) | 396.556 | 0.258540 | ||||||||
\(134\) | 120.211 | 0.0774977 | ||||||||
\(135\) | −72.8004 | −0.0464123 | ||||||||
\(136\) | 285.463 | 0.179987 | ||||||||
\(137\) | 1205.02 | 0.751471 | 0.375736 | − | 0.926727i | \(-0.377390\pi\) | ||||
0.375736 | + | 0.926727i | \(0.377390\pi\) | |||||||
\(138\) | 761.643 | 0.469822 | ||||||||
\(139\) | 322.890 | 0.197030 | 0.0985149 | − | 0.995136i | \(-0.468591\pi\) | ||||
0.0985149 | + | 0.995136i | \(0.468591\pi\) | |||||||
\(140\) | 851.796 | 0.514213 | ||||||||
\(141\) | 1062.67 | 0.634700 | ||||||||
\(142\) | −1530.06 | −0.904223 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1814.20 | 1.04988 | ||||||||
\(145\) | −692.971 | −0.396884 | ||||||||
\(146\) | −3975.20 | −2.25336 | ||||||||
\(147\) | −335.655 | −0.188329 | ||||||||
\(148\) | −3650.80 | −2.02766 | ||||||||
\(149\) | −1128.86 | −0.620669 | −0.310335 | − | 0.950627i | \(-0.600441\pi\) | ||||
−0.310335 | + | 0.950627i | \(0.600441\pi\) | |||||||
\(150\) | −1894.77 | −1.03138 | ||||||||
\(151\) | 2940.44 | 1.58470 | 0.792350 | − | 0.610066i | \(-0.208857\pi\) | ||||
0.792350 | + | 0.610066i | \(0.208857\pi\) | |||||||
\(152\) | −1788.46 | −0.954361 | ||||||||
\(153\) | 37.4719 | 0.0198001 | ||||||||
\(154\) | −5454.93 | −2.85436 | ||||||||
\(155\) | 556.093 | 0.288171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 629.388 | 0.319940 | 0.159970 | − | 0.987122i | \(-0.448860\pi\) | ||||
0.159970 | + | 0.987122i | \(0.448860\pi\) | |||||||
\(158\) | −2938.15 | −1.47941 | ||||||||
\(159\) | −31.4170 | −0.0156700 | ||||||||
\(160\) | −1436.88 | −0.709972 | ||||||||
\(161\) | −719.444 | −0.352175 | ||||||||
\(162\) | 434.543 | 0.210746 | ||||||||
\(163\) | 394.912 | 0.189766 | 0.0948832 | − | 0.995488i | \(-0.469752\pi\) | ||||
0.0948832 | + | 0.995488i | \(0.469752\pi\) | |||||||
\(164\) | −3251.33 | −1.54809 | ||||||||
\(165\) | −541.027 | −0.255266 | ||||||||
\(166\) | −3235.23 | −1.51267 | ||||||||
\(167\) | 151.860 | 0.0703669 | 0.0351834 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351834 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(168\) | −3126.96 | −1.43601 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −60.2255 | −0.0271711 | ||||||||
\(171\) | −234.765 | −0.104988 | ||||||||
\(172\) | 1080.25 | 0.478886 | ||||||||
\(173\) | 538.813 | 0.236793 | 0.118397 | − | 0.992966i | \(-0.462225\pi\) | ||||
0.118397 | + | 0.992966i | \(0.462225\pi\) | |||||||
\(174\) | 4136.31 | 1.80214 | ||||||||
\(175\) | 1789.78 | 0.773114 | ||||||||
\(176\) | 13482.5 | 5.77432 | ||||||||
\(177\) | −1335.34 | −0.567065 | ||||||||
\(178\) | −1157.00 | −0.487196 | ||||||||
\(179\) | −2220.80 | −0.927319 | −0.463659 | − | 0.886014i | \(-0.653464\pi\) | ||||
−0.463659 | + | 0.886014i | \(0.653464\pi\) | |||||||
\(180\) | −504.271 | −0.208812 | ||||||||
\(181\) | −3822.78 | −1.56986 | −0.784932 | − | 0.619582i | \(-0.787302\pi\) | ||||
−0.784932 | + | 0.619582i | \(0.787302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 359.089 | 0.145052 | ||||||||
\(184\) | 3244.67 | 1.30000 | ||||||||
\(185\) | 473.704 | 0.188256 | ||||||||
\(186\) | −3319.30 | −1.30851 | ||||||||
\(187\) | 278.478 | 0.108900 | ||||||||
\(188\) | 7360.84 | 2.85555 | ||||||||
\(189\) | −410.467 | −0.157974 | ||||||||
\(190\) | 377.319 | 0.144071 | ||||||||
\(191\) | 3464.19 | 1.31236 | 0.656178 | − | 0.754606i | \(-0.272172\pi\) | ||||
0.656178 | + | 0.754606i | \(0.272172\pi\) | |||||||
\(192\) | 3738.83 | 1.40535 | ||||||||
\(193\) | −4697.40 | −1.75195 | −0.875975 | − | 0.482357i | \(-0.839781\pi\) | ||||
−0.875975 | + | 0.482357i | \(0.839781\pi\) | |||||||
\(194\) | −7765.46 | −2.87385 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2325.00 | −0.847304 | ||||||||
\(197\) | 2887.89 | 1.04443 | 0.522217 | − | 0.852813i | \(-0.325105\pi\) | ||||
0.522217 | + | 0.852813i | \(0.325105\pi\) | |||||||
\(198\) | 3229.37 | 1.15910 | ||||||||
\(199\) | 63.0092 | 0.0224453 | 0.0112226 | − | 0.999937i | \(-0.496428\pi\) | ||||
0.0112226 | + | 0.999937i | \(0.496428\pi\) | |||||||
\(200\) | −8071.87 | −2.85384 | ||||||||
\(201\) | 67.2233 | 0.0235899 | ||||||||
\(202\) | −4739.47 | −1.65083 | ||||||||
\(203\) | −3907.14 | −1.35087 | ||||||||
\(204\) | 259.558 | 0.0890820 | ||||||||
\(205\) | 421.872 | 0.143731 | ||||||||
\(206\) | 6715.24 | 2.27123 | ||||||||
\(207\) | 425.918 | 0.143011 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1744.69 | −0.577429 | ||||||||
\(210\) | 659.710 | 0.216782 | ||||||||
\(211\) | −1049.70 | −0.342484 | −0.171242 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171242 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(212\) | −217.618 | −0.0705002 | ||||||||
\(213\) | −855.622 | −0.275241 | ||||||||
\(214\) | −1832.66 | −0.585412 | ||||||||
\(215\) | −140.166 | −0.0444617 | ||||||||
\(216\) | 1851.19 | 0.583137 | ||||||||
\(217\) | 3135.39 | 0.980848 | ||||||||
\(218\) | −4158.61 | −1.29200 | ||||||||
\(219\) | −2222.97 | −0.685909 | ||||||||
\(220\) | −3747.56 | −1.14846 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2827.52 | −0.854823 | ||||||||
\(223\) | −2313.49 | −0.694722 | −0.347361 | − | 0.937732i | \(-0.612922\pi\) | ||||
−0.347361 | + | 0.937732i | \(0.612922\pi\) | |||||||
\(224\) | −8101.49 | −2.41653 | ||||||||
\(225\) | −1059.57 | −0.313946 | ||||||||
\(226\) | 6861.74 | 2.01963 | ||||||||
\(227\) | −3799.46 | −1.11092 | −0.555460 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555460 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(228\) | −1626.16 | −0.472347 | ||||||||
\(229\) | 4321.07 | 1.24692 | 0.623459 | − | 0.781856i | \(-0.285727\pi\) | ||||
0.623459 | + | 0.781856i | \(0.285727\pi\) | |||||||
\(230\) | −684.543 | −0.196250 | ||||||||
\(231\) | −3050.44 | −0.868850 | ||||||||
\(232\) | 17621.1 | 4.98655 | ||||||||
\(233\) | 5279.77 | 1.48450 | 0.742251 | − | 0.670122i | \(-0.233758\pi\) | ||||
0.742251 | + | 0.670122i | \(0.233758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −955.094 | −0.265121 | ||||||||
\(236\) | −9249.59 | −2.55126 | ||||||||
\(237\) | −1643.04 | −0.450323 | ||||||||
\(238\) | −339.566 | −0.0924823 | ||||||||
\(239\) | −1547.92 | −0.418939 | −0.209469 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209469 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(240\) | −1630.55 | −0.438547 | ||||||||
\(241\) | 4918.01 | 1.31451 | 0.657255 | − | 0.753669i | \(-0.271718\pi\) | ||||
0.657255 | + | 0.753669i | \(0.271718\pi\) | |||||||
\(242\) | 16859.1 | 4.47828 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2487.32 | 0.652600 | ||||||||
\(245\) | 301.677 | 0.0786671 | ||||||||
\(246\) | −2518.14 | −0.652644 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −14140.5 | −3.62066 | ||||||||
\(249\) | −1809.17 | −0.460447 | ||||||||
\(250\) | 3511.08 | 0.888241 | ||||||||
\(251\) | 1155.78 | 0.290646 | 0.145323 | − | 0.989384i | \(-0.453578\pi\) | ||||
0.145323 | + | 0.989384i | \(0.453578\pi\) | |||||||
\(252\) | −2843.20 | −0.710734 | ||||||||
\(253\) | 3165.27 | 0.786556 | ||||||||
\(254\) | −5975.34 | −1.47609 | ||||||||
\(255\) | −33.6786 | −0.00827073 | ||||||||
\(256\) | 3026.80 | 0.738965 | ||||||||
\(257\) | 2351.95 | 0.570859 | 0.285429 | − | 0.958400i | \(-0.407864\pi\) | ||||
0.285429 | + | 0.958400i | \(0.407864\pi\) | |||||||
\(258\) | 836.647 | 0.201889 | ||||||||
\(259\) | 2670.86 | 0.640769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2313.06 | 0.548563 | ||||||||
\(262\) | 11266.6 | 2.65669 | ||||||||
\(263\) | 5521.88 | 1.29465 | 0.647326 | − | 0.762213i | \(-0.275887\pi\) | ||||
0.647326 | + | 0.762213i | \(0.275887\pi\) | |||||||
\(264\) | 13757.4 | 3.20723 | ||||||||
\(265\) | 28.2367 | 0.00654553 | ||||||||
\(266\) | 2127.41 | 0.490376 | ||||||||
\(267\) | −647.004 | −0.148300 | ||||||||
\(268\) | 465.639 | 0.106132 | ||||||||
\(269\) | 3916.95 | 0.887810 | 0.443905 | − | 0.896074i | \(-0.353593\pi\) | ||||
0.443905 | + | 0.896074i | \(0.353593\pi\) | |||||||
\(270\) | −390.554 | −0.0880310 | ||||||||
\(271\) | 2777.53 | 0.622593 | 0.311297 | − | 0.950313i | \(-0.399237\pi\) | ||||
0.311297 | + | 0.950313i | \(0.399237\pi\) | |||||||
\(272\) | 839.276 | 0.187090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6464.58 | 1.42533 | ||||||||
\(275\) | −7874.34 | −1.72669 | ||||||||
\(276\) | 2950.23 | 0.643416 | ||||||||
\(277\) | 6583.08 | 1.42794 | 0.713969 | − | 0.700177i | \(-0.246896\pi\) | ||||
0.713969 | + | 0.700177i | \(0.246896\pi\) | |||||||
\(278\) | 1732.21 | 0.373710 | ||||||||
\(279\) | −1856.18 | −0.398303 | ||||||||
\(280\) | 2810.42 | 0.599839 | ||||||||
\(281\) | −2871.66 | −0.609640 | −0.304820 | − | 0.952410i | \(-0.598596\pi\) | ||||
−0.304820 | + | 0.952410i | \(0.598596\pi\) | |||||||
\(282\) | 5700.92 | 1.20385 | ||||||||
\(283\) | 7518.04 | 1.57916 | 0.789578 | − | 0.613651i | \(-0.210300\pi\) | ||||
0.789578 | + | 0.613651i | \(0.210300\pi\) | |||||||
\(284\) | −5926.69 | −1.23832 | ||||||||
\(285\) | 211.000 | 0.0438546 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2378.62 | 0.489217 | ||||||||
\(288\) | 4796.16 | 0.981307 | ||||||||
\(289\) | −4895.66 | −0.996472 | ||||||||
\(290\) | −3717.60 | −0.752776 | ||||||||
\(291\) | −4342.51 | −0.874785 | ||||||||
\(292\) | −15397.9 | −3.08595 | ||||||||
\(293\) | −4506.57 | −0.898555 | −0.449278 | − | 0.893392i | \(-0.648319\pi\) | ||||
−0.449278 | + | 0.893392i | \(0.648319\pi\) | |||||||
\(294\) | −1800.70 | −0.357207 | ||||||||
\(295\) | 1200.17 | 0.236869 | ||||||||
\(296\) | −12045.5 | −2.36530 | ||||||||
\(297\) | 1805.89 | 0.352823 | ||||||||
\(298\) | −6056.02 | −1.17723 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7339.38 | −1.41246 | ||||||||
\(301\) | −790.292 | −0.151335 | ||||||||
\(302\) | 15774.7 | 3.00573 | ||||||||
\(303\) | −2650.35 | −0.502504 | ||||||||
\(304\) | −5258.15 | −0.992024 | ||||||||
\(305\) | −322.738 | −0.0605900 | ||||||||
\(306\) | 201.026 | 0.0375552 | ||||||||
\(307\) | −9538.89 | −1.77333 | −0.886667 | − | 0.462409i | \(-0.846985\pi\) | ||||
−0.886667 | + | 0.462409i | \(0.846985\pi\) | |||||||
\(308\) | −21129.7 | −3.90901 | ||||||||
\(309\) | 3755.22 | 0.691350 | ||||||||
\(310\) | 2983.29 | 0.546578 | ||||||||
\(311\) | −7466.28 | −1.36133 | −0.680666 | − | 0.732594i | \(-0.738309\pi\) | ||||
−0.680666 | + | 0.732594i | \(0.738309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1821.65 | −0.328964 | −0.164482 | − | 0.986380i | \(-0.552595\pi\) | ||||
−0.164482 | + | 0.986380i | \(0.552595\pi\) | |||||||
\(314\) | 3376.49 | 0.606836 | ||||||||
\(315\) | 368.915 | 0.0659874 | ||||||||
\(316\) | −11380.9 | −2.02603 | ||||||||
\(317\) | −3125.14 | −0.553708 | −0.276854 | − | 0.960912i | \(-0.589292\pi\) | ||||
−0.276854 | + | 0.960912i | \(0.589292\pi\) | |||||||
\(318\) | −168.543 | −0.0297215 | ||||||||
\(319\) | 17189.9 | 3.01708 | ||||||||
\(320\) | −3360.35 | −0.587029 | ||||||||
\(321\) | −1024.84 | −0.178196 | ||||||||
\(322\) | −3859.62 | −0.667976 | ||||||||
\(323\) | −108.606 | −0.0187090 | ||||||||
\(324\) | 1683.20 | 0.288615 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2118.60 | 0.359933 | ||||||||
\(327\) | −2325.53 | −0.393279 | ||||||||
\(328\) | −10727.5 | −1.80587 | ||||||||
\(329\) | −5385.05 | −0.902394 | ||||||||
\(330\) | −2902.46 | −0.484167 | ||||||||
\(331\) | 1553.67 | 0.257999 | 0.128999 | − | 0.991645i | \(-0.458823\pi\) | ||||
0.128999 | + | 0.991645i | \(0.458823\pi\) | |||||||
\(332\) | −12531.7 | −2.07158 | ||||||||
\(333\) | −1581.17 | −0.260204 | ||||||||
\(334\) | 814.686 | 0.133466 | ||||||||
\(335\) | −60.4183 | −0.00985375 | ||||||||
\(336\) | −9193.42 | −1.49269 | ||||||||
\(337\) | −3190.43 | −0.515709 | −0.257855 | − | 0.966184i | \(-0.583016\pi\) | ||||
−0.257855 | + | 0.966184i | \(0.583016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3837.15 | 0.614764 | ||||||||
\(340\) | −233.283 | −0.0372105 | ||||||||
\(341\) | −13794.5 | −2.19065 | ||||||||
\(342\) | −1259.45 | −0.199132 | ||||||||
\(343\) | 6915.37 | 1.08862 | ||||||||
\(344\) | 3564.19 | 0.558629 | ||||||||
\(345\) | −382.802 | −0.0597373 | ||||||||
\(346\) | 2890.59 | 0.449130 | ||||||||
\(347\) | −5718.68 | −0.884712 | −0.442356 | − | 0.896840i | \(-0.645857\pi\) | ||||
−0.442356 | + | 0.896840i | \(0.645857\pi\) | |||||||
\(348\) | 16022.0 | 2.46802 | ||||||||
\(349\) | 3328.46 | 0.510511 | 0.255256 | − | 0.966874i | \(-0.417840\pi\) | ||||
0.255256 | + | 0.966874i | \(0.417840\pi\) | |||||||
\(350\) | 9601.70 | 1.46638 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 35643.4 | 5.39715 | ||||||||
\(353\) | 12306.5 | 1.85555 | 0.927774 | − | 0.373142i | \(-0.121719\pi\) | ||||
0.927774 | + | 0.373142i | \(0.121719\pi\) | |||||||
\(354\) | −7163.74 | −1.07556 | ||||||||
\(355\) | 769.008 | 0.114971 | ||||||||
\(356\) | −4481.64 | −0.667210 | ||||||||
\(357\) | −189.888 | −0.0281511 | ||||||||
\(358\) | −11914.0 | −1.75886 | ||||||||
\(359\) | −8539.97 | −1.25549 | −0.627747 | − | 0.778418i | \(-0.716023\pi\) | ||||
−0.627747 | + | 0.778418i | \(0.716023\pi\) | |||||||
\(360\) | −1663.80 | −0.243583 | ||||||||
\(361\) | −6178.57 | −0.900798 | ||||||||
\(362\) | −20508.2 | −2.97759 | ||||||||
\(363\) | 9427.74 | 1.36316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1997.94 | 0.286512 | ||||||||
\(366\) | 1926.41 | 0.275123 | ||||||||
\(367\) | 2496.65 | 0.355107 | 0.177553 | − | 0.984111i | \(-0.443182\pi\) | ||||
0.177553 | + | 0.984111i | \(0.443182\pi\) | |||||||
\(368\) | 9539.49 | 1.35130 | ||||||||
\(369\) | −1408.16 | −0.198661 | ||||||||
\(370\) | 2541.29 | 0.357069 | ||||||||
\(371\) | 159.205 | 0.0222790 | ||||||||
\(372\) | −12857.3 | −1.79199 | ||||||||
\(373\) | −1142.91 | −0.158653 | −0.0793264 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793264 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(374\) | 1493.96 | 0.206552 | ||||||||
\(375\) | 1963.43 | 0.270376 | ||||||||
\(376\) | 24286.4 | 3.33105 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2202.04 | −0.299632 | ||||||||
\(379\) | 12181.8 | 1.65102 | 0.825512 | − | 0.564384i | \(-0.190886\pi\) | ||||
0.825512 | + | 0.564384i | \(0.190886\pi\) | |||||||
\(380\) | 1461.54 | 0.197304 | ||||||||
\(381\) | −3341.46 | −0.449313 | ||||||||
\(382\) | 18584.4 | 2.48917 | ||||||||
\(383\) | 10180.6 | 1.35824 | 0.679118 | − | 0.734029i | \(-0.262362\pi\) | ||||
0.679118 | + | 0.734029i | \(0.262362\pi\) | |||||||
\(384\) | 7268.04 | 0.965874 | ||||||||
\(385\) | 2741.65 | 0.362928 | ||||||||
\(386\) | −25200.3 | −3.32295 | ||||||||
\(387\) | 467.860 | 0.0614539 | ||||||||
\(388\) | −30079.5 | −3.93571 | ||||||||
\(389\) | 5845.83 | 0.761941 | 0.380971 | − | 0.924587i | \(-0.375590\pi\) | ||||
0.380971 | + | 0.924587i | \(0.375590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 197.036 | 0.0254848 | ||||||||
\(392\) | −7671.13 | −0.988395 | ||||||||
\(393\) | 6300.37 | 0.808681 | ||||||||
\(394\) | 15492.7 | 1.98100 | ||||||||
\(395\) | 1476.71 | 0.188105 | ||||||||
\(396\) | 12509.0 | 1.58737 | ||||||||
\(397\) | 2500.92 | 0.316166 | 0.158083 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158083 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(398\) | 338.027 | 0.0425723 | ||||||||
\(399\) | 1189.67 | 0.149268 | ||||||||
\(400\) | −23731.7 | −2.96646 | ||||||||
\(401\) | 9189.25 | 1.14436 | 0.572181 | − | 0.820127i | \(-0.306098\pi\) | ||||
0.572181 | + | 0.820127i | \(0.306098\pi\) | |||||||
\(402\) | 360.634 | 0.0447433 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −18358.3 | −2.26080 | ||||||||
\(405\) | −218.401 | −0.0267962 | ||||||||
\(406\) | −20960.7 | −2.56223 | ||||||||
\(407\) | −11750.7 | −1.43111 | ||||||||
\(408\) | 856.390 | 0.103916 | ||||||||
\(409\) | −9214.38 | −1.11399 | −0.556995 | − | 0.830516i | \(-0.688046\pi\) | ||||
−0.556995 | + | 0.830516i | \(0.688046\pi\) | |||||||
\(410\) | 2263.23 | 0.272617 | ||||||||
\(411\) | 3615.05 | 0.433862 | ||||||||
\(412\) | 26011.5 | 3.11042 | ||||||||
\(413\) | 6766.83 | 0.806232 | ||||||||
\(414\) | 2284.93 | 0.271252 | ||||||||
\(415\) | 1626.03 | 0.192334 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 968.669 | 0.113755 | ||||||||
\(418\) | −9359.78 | −1.09522 | ||||||||
\(419\) | −6494.41 | −0.757214 | −0.378607 | − | 0.925558i | \(-0.623597\pi\) | ||||
−0.378607 | + | 0.925558i | \(0.623597\pi\) | |||||||
\(420\) | 2555.39 | 0.296881 | ||||||||
\(421\) | −3059.56 | −0.354190 | −0.177095 | − | 0.984194i | \(-0.556670\pi\) | ||||
−0.177095 | + | 0.984194i | \(0.556670\pi\) | |||||||
\(422\) | −5631.33 | −0.649595 | ||||||||
\(423\) | 3188.00 | 0.366444 | ||||||||
\(424\) | −718.010 | −0.0822398 | ||||||||
\(425\) | −490.173 | −0.0559456 | ||||||||
\(426\) | −4590.18 | −0.522054 | ||||||||
\(427\) | −1819.68 | −0.206230 | ||||||||
\(428\) | −7098.82 | −0.801716 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −751.954 | −0.0843313 | ||||||||
\(431\) | −7937.05 | −0.887040 | −0.443520 | − | 0.896264i | \(-0.646271\pi\) | ||||
−0.443520 | + | 0.896264i | \(0.646271\pi\) | |||||||
\(432\) | 5442.59 | 0.606150 | ||||||||
\(433\) | 7294.37 | 0.809573 | 0.404786 | − | 0.914411i | \(-0.367346\pi\) | ||||
0.404786 | + | 0.914411i | \(0.367346\pi\) | |||||||
\(434\) | 16820.5 | 1.86039 | ||||||||
\(435\) | −2078.91 | −0.229141 | ||||||||
\(436\) | −16108.4 | −1.76938 | ||||||||
\(437\) | −1234.45 | −0.135130 | ||||||||
\(438\) | −11925.6 | −1.30098 | ||||||||
\(439\) | 15214.7 | 1.65412 | 0.827059 | − | 0.562115i | \(-0.190012\pi\) | ||||
0.827059 | + | 0.562115i | \(0.190012\pi\) | |||||||
\(440\) | −12364.7 | −1.33970 | ||||||||
\(441\) | −1006.97 | −0.108732 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1517.05 | 0.162703 | 0.0813515 | − | 0.996685i | \(-0.474076\pi\) | ||||
0.0813515 | + | 0.996685i | \(0.474076\pi\) | |||||||
\(444\) | −10952.4 | −1.17067 | ||||||||
\(445\) | 581.509 | 0.0619464 | ||||||||
\(446\) | −12411.3 | −1.31769 | ||||||||
\(447\) | −3386.58 | −0.358343 | ||||||||
\(448\) | −18946.5 | −1.99807 | ||||||||
\(449\) | 705.247 | 0.0741262 | 0.0370631 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370631 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(450\) | −5684.30 | −0.595467 | ||||||||
\(451\) | −10465.0 | −1.09263 | ||||||||
\(452\) | 26579.0 | 2.76586 | ||||||||
\(453\) | 8821.33 | 0.914927 | ||||||||
\(454\) | −20383.1 | −2.10710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5365.37 | −0.551001 | ||||||||
\(457\) | 7277.73 | 0.744940 | 0.372470 | − | 0.928044i | \(-0.378511\pi\) | ||||
0.372470 | + | 0.928044i | \(0.378511\pi\) | |||||||
\(458\) | 23181.4 | 2.36505 | ||||||||
\(459\) | 112.416 | 0.0114316 | ||||||||
\(460\) | −2651.58 | −0.268762 | ||||||||
\(461\) | −1961.88 | −0.198208 | −0.0991041 | − | 0.995077i | \(-0.531598\pi\) | ||||
−0.0991041 | + | 0.995077i | \(0.531598\pi\) | |||||||
\(462\) | −16364.8 | −1.64796 | ||||||||
\(463\) | 10374.1 | 1.04131 | 0.520653 | − | 0.853768i | \(-0.325689\pi\) | ||||
0.520653 | + | 0.853768i | \(0.325689\pi\) | |||||||
\(464\) | 51806.8 | 5.18334 | ||||||||
\(465\) | 1668.28 | 0.166376 | ||||||||
\(466\) | 28324.5 | 2.81568 | ||||||||
\(467\) | 8788.92 | 0.870883 | 0.435442 | − | 0.900217i | \(-0.356592\pi\) | ||||
0.435442 | + | 0.900217i | \(0.356592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −340.653 | −0.0335392 | ||||||||
\(470\) | −5123.82 | −0.502860 | ||||||||
\(471\) | 1888.16 | 0.184718 | ||||||||
\(472\) | −30518.2 | −2.97609 | ||||||||
\(473\) | 3476.97 | 0.337995 | ||||||||
\(474\) | −8814.44 | −0.854136 | ||||||||
\(475\) | 3070.98 | 0.296645 | ||||||||
\(476\) | −1315.31 | −0.126654 | ||||||||
\(477\) | −94.2510 | −0.00904707 | ||||||||
\(478\) | −8304.14 | −0.794608 | ||||||||
\(479\) | 11141.7 | 1.06279 | 0.531394 | − | 0.847125i | \(-0.321668\pi\) | ||||
0.531394 | + | 0.847125i | \(0.321668\pi\) | |||||||
\(480\) | −4310.65 | −0.409903 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26383.8 | 2.49325 | ||||||||
\(483\) | −2158.33 | −0.203328 | ||||||||
\(484\) | 65303.7 | 6.13295 | ||||||||
\(485\) | 3902.92 | 0.365407 | ||||||||
\(486\) | 1303.63 | 0.121674 | ||||||||
\(487\) | 19640.5 | 1.82750 | 0.913752 | − | 0.406273i | \(-0.133172\pi\) | ||||
0.913752 | + | 0.406273i | \(0.133172\pi\) | |||||||
\(488\) | 8206.69 | 0.761269 | ||||||||
\(489\) | 1184.74 | 0.109562 | ||||||||
\(490\) | 1618.41 | 0.149209 | ||||||||
\(491\) | −3410.31 | −0.313453 | −0.156726 | − | 0.987642i | \(-0.550094\pi\) | ||||
−0.156726 | + | 0.987642i | \(0.550094\pi\) | |||||||
\(492\) | −9754.00 | −0.893789 | ||||||||
\(493\) | 1070.06 | 0.0977546 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1623.08 | −0.147378 | ||||||||
\(496\) | −41573.8 | −3.76354 | ||||||||
\(497\) | 4335.86 | 0.391327 | ||||||||
\(498\) | −9705.68 | −0.873338 | ||||||||
\(499\) | 5032.44 | 0.451469 | 0.225735 | − | 0.974189i | \(-0.427522\pi\) | ||||
0.225735 | + | 0.974189i | \(0.427522\pi\) | |||||||
\(500\) | 13600.2 | 1.21644 | ||||||||
\(501\) | 455.580 | 0.0406263 | ||||||||
\(502\) | 6200.44 | 0.551274 | ||||||||
\(503\) | 17189.4 | 1.52373 | 0.761866 | − | 0.647735i | \(-0.224284\pi\) | ||||
0.761866 | + | 0.647735i | \(0.224284\pi\) | |||||||
\(504\) | −9380.89 | −0.829083 | ||||||||
\(505\) | 2382.06 | 0.209901 | ||||||||
\(506\) | 16980.8 | 1.49187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23145.5 | −2.02149 | ||||||||
\(509\) | 930.560 | 0.0810341 | 0.0405170 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405170 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(510\) | −180.676 | −0.0156872 | ||||||||
\(511\) | 11264.9 | 0.975201 | ||||||||
\(512\) | −3143.50 | −0.271337 | ||||||||
\(513\) | −704.295 | −0.0606148 | ||||||||
\(514\) | 12617.6 | 1.08276 | ||||||||
\(515\) | −3375.08 | −0.288784 | ||||||||
\(516\) | 3240.75 | 0.276485 | ||||||||
\(517\) | 23692.1 | 2.01543 | ||||||||
\(518\) | 14328.4 | 1.21536 | ||||||||
\(519\) | 1616.44 | 0.136713 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9869.60 | −0.829933 | −0.414966 | − | 0.909837i | \(-0.636207\pi\) | ||||
−0.414966 | + | 0.909837i | \(0.636207\pi\) | |||||||
\(522\) | 12408.9 | 1.04047 | ||||||||
\(523\) | −21420.6 | −1.79093 | −0.895466 | − | 0.445129i | \(-0.853158\pi\) | ||||
−0.895466 | + | 0.445129i | \(0.853158\pi\) | |||||||
\(524\) | 43641.1 | 3.63831 | ||||||||
\(525\) | 5369.35 | 0.446358 | ||||||||
\(526\) | 29623.4 | 2.45559 | ||||||||
\(527\) | −858.697 | −0.0709781 | ||||||||
\(528\) | 40447.4 | 3.33380 | ||||||||
\(529\) | −9927.42 | −0.815930 | ||||||||
\(530\) | 151.482 | 0.0124150 | ||||||||
\(531\) | −4006.03 | −0.327395 | ||||||||
\(532\) | 8240.54 | 0.671565 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3471.00 | −0.281283 | ||||||||
\(535\) | 921.097 | 0.0744345 | ||||||||
\(536\) | 1536.34 | 0.123805 | ||||||||
\(537\) | −6662.39 | −0.535388 | ||||||||
\(538\) | 21013.4 | 1.68392 | ||||||||
\(539\) | −7483.41 | −0.598021 | ||||||||
\(540\) | −1512.81 | −0.120558 | ||||||||
\(541\) | −7771.50 | −0.617602 | −0.308801 | − | 0.951127i | \(-0.599928\pi\) | ||||
−0.308801 | + | 0.951127i | \(0.599928\pi\) | |||||||
\(542\) | 14900.7 | 1.18088 | ||||||||
\(543\) | −11468.3 | −0.906361 | ||||||||
\(544\) | 2218.78 | 0.174870 | ||||||||
\(545\) | 2090.12 | 0.164277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15577.5 | −1.21763 | −0.608817 | − | 0.793310i | \(-0.708356\pi\) | ||||
−0.608817 | + | 0.793310i | \(0.708356\pi\) | |||||||
\(548\) | 25040.6 | 1.95197 | ||||||||
\(549\) | 1077.27 | 0.0837461 | ||||||||
\(550\) | −42243.7 | −3.27505 | ||||||||
\(551\) | −6704.02 | −0.518332 | ||||||||
\(552\) | 9734.01 | 0.750556 | ||||||||
\(553\) | 8326.07 | 0.640254 | ||||||||
\(554\) | 35316.4 | 2.70840 | ||||||||
\(555\) | 1421.11 | 0.108690 | ||||||||
\(556\) | 6709.74 | 0.511792 | ||||||||
\(557\) | 22804.5 | 1.73475 | 0.867377 | − | 0.497652i | \(-0.165804\pi\) | ||||
0.867377 | + | 0.497652i | \(0.165804\pi\) | |||||||
\(558\) | −9957.89 | −0.755468 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8262.78 | 0.623511 | ||||||||
\(561\) | 835.433 | 0.0628734 | ||||||||
\(562\) | −15405.7 | −1.15631 | ||||||||
\(563\) | −3517.41 | −0.263306 | −0.131653 | − | 0.991296i | \(-0.542028\pi\) | ||||
−0.131653 | + | 0.991296i | \(0.542028\pi\) | |||||||
\(564\) | 22082.5 | 1.64865 | ||||||||
\(565\) | −3448.71 | −0.256794 | ||||||||
\(566\) | 40332.2 | 2.99521 | ||||||||
\(567\) | −1231.40 | −0.0912062 | ||||||||
\(568\) | −19554.6 | −1.44453 | ||||||||
\(569\) | −6093.44 | −0.448946 | −0.224473 | − | 0.974480i | \(-0.572066\pi\) | ||||
−0.224473 | + | 0.974480i | \(0.572066\pi\) | |||||||
\(570\) | 1131.96 | 0.0831797 | ||||||||
\(571\) | 10460.2 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10392.6 | 0.757689 | ||||||||
\(574\) | 12760.6 | 0.927906 | ||||||||
\(575\) | −5571.47 | −0.404081 | ||||||||
\(576\) | 11216.5 | 0.811378 | ||||||||
\(577\) | 9648.19 | 0.696117 | 0.348058 | − | 0.937473i | \(-0.386841\pi\) | ||||
0.348058 | + | 0.937473i | \(0.386841\pi\) | |||||||
\(578\) | −26263.9 | −1.89002 | ||||||||
\(579\) | −14092.2 | −1.01149 | ||||||||
\(580\) | −14400.1 | −1.03092 | ||||||||
\(581\) | 9167.93 | 0.654647 | ||||||||
\(582\) | −23296.4 | −1.65922 | ||||||||
\(583\) | −700.440 | −0.0497586 | ||||||||
\(584\) | −50804.1 | −3.59981 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24176.5 | −1.70430 | ||||||||
\(587\) | −2170.73 | −0.152633 | −0.0763166 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763166 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(588\) | −6975.01 | −0.489191 | ||||||||
\(589\) | 5379.82 | 0.376353 | ||||||||
\(590\) | 6438.56 | 0.449274 | ||||||||
\(591\) | 8663.66 | 0.603004 | ||||||||
\(592\) | −35414.3 | −2.45865 | ||||||||
\(593\) | −22885.9 | −1.58484 | −0.792421 | − | 0.609975i | \(-0.791180\pi\) | ||||
−0.792421 | + | 0.609975i | \(0.791180\pi\) | |||||||
\(594\) | 9688.11 | 0.669205 | ||||||||
\(595\) | 170.666 | 0.0117590 | ||||||||
\(596\) | −23458.0 | −1.61221 | ||||||||
\(597\) | 189.028 | 0.0129588 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23978.7 | −1.63563 | −0.817815 | − | 0.575482i | \(-0.804815\pi\) | ||||
−0.817815 | + | 0.575482i | \(0.804815\pi\) | |||||||
\(600\) | −24215.6 | −1.64766 | ||||||||
\(601\) | 12873.2 | 0.873728 | 0.436864 | − | 0.899528i | \(-0.356089\pi\) | ||||
0.436864 | + | 0.899528i | \(0.356089\pi\) | |||||||
\(602\) | −4239.70 | −0.287039 | ||||||||
\(603\) | 201.670 | 0.0136196 | ||||||||
\(604\) | 61103.2 | 4.11631 | ||||||||
\(605\) | −8473.38 | −0.569408 | ||||||||
\(606\) | −14218.4 | −0.953107 | ||||||||
\(607\) | −7117.15 | −0.475908 | −0.237954 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237954 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(608\) | −13900.9 | −0.927227 | ||||||||
\(609\) | −11721.4 | −0.779927 | ||||||||
\(610\) | −1731.40 | −0.114922 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 778.675 | 0.0514315 | ||||||||
\(613\) | −173.297 | −0.0114183 | −0.00570913 | − | 0.999984i | \(-0.501817\pi\) | ||||
−0.00570913 | + | 0.999984i | \(0.501817\pi\) | |||||||
\(614\) | −51173.5 | −3.36351 | ||||||||
\(615\) | 1265.62 | 0.0829830 | ||||||||
\(616\) | −69715.5 | −4.55993 | ||||||||
\(617\) | 6102.75 | 0.398197 | 0.199099 | − | 0.979979i | \(-0.436199\pi\) | ||||
0.199099 | + | 0.979979i | \(0.436199\pi\) | |||||||
\(618\) | 20145.7 | 1.31129 | ||||||||
\(619\) | 14867.8 | 0.965409 | 0.482705 | − | 0.875783i | \(-0.339654\pi\) | ||||
0.482705 | + | 0.875783i | \(0.339654\pi\) | |||||||
\(620\) | 11555.8 | 0.748534 | ||||||||
\(621\) | 1277.75 | 0.0825676 | ||||||||
\(622\) | −40054.6 | −2.58206 | ||||||||
\(623\) | 3278.69 | 0.210847 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12951.6 | 0.828900 | ||||||||
\(626\) | −9772.64 | −0.623951 | ||||||||
\(627\) | −5234.07 | −0.333379 | ||||||||
\(628\) | 13078.9 | 0.831056 | ||||||||
\(629\) | −731.475 | −0.0463686 | ||||||||
\(630\) | 1979.13 | 0.125159 | ||||||||
\(631\) | 17210.6 | 1.08580 | 0.542902 | − | 0.839796i | \(-0.317325\pi\) | ||||
0.542902 | + | 0.839796i | \(0.317325\pi\) | |||||||
\(632\) | −37550.3 | −2.36340 | ||||||||
\(633\) | −3149.09 | −0.197733 | ||||||||
\(634\) | −16765.5 | −1.05023 | ||||||||
\(635\) | 3003.21 | 0.187683 | ||||||||
\(636\) | −652.853 | −0.0407033 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 92218.9 | 5.72254 | ||||||||
\(639\) | −2566.87 | −0.158910 | ||||||||
\(640\) | −6532.30 | −0.403456 | ||||||||
\(641\) | −12636.0 | −0.778616 | −0.389308 | − | 0.921108i | \(-0.627286\pi\) | ||||
−0.389308 | + | 0.921108i | \(0.627286\pi\) | |||||||
\(642\) | −5497.99 | −0.337988 | ||||||||
\(643\) | 9586.37 | 0.587947 | 0.293973 | − | 0.955814i | \(-0.405022\pi\) | ||||
0.293973 | + | 0.955814i | \(0.405022\pi\) | |||||||
\(644\) | −14950.2 | −0.914786 | ||||||||
\(645\) | −420.499 | −0.0256700 | ||||||||
\(646\) | −582.641 | −0.0354856 | ||||||||
\(647\) | 5244.32 | 0.318664 | 0.159332 | − | 0.987225i | \(-0.449066\pi\) | ||||
0.159332 | + | 0.987225i | \(0.449066\pi\) | |||||||
\(648\) | 5553.57 | 0.336674 | ||||||||
\(649\) | −29771.4 | −1.80066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9406.17 | 0.566293 | ||||||||
\(652\) | 8206.39 | 0.492925 | ||||||||
\(653\) | 18869.0 | 1.13078 | 0.565392 | − | 0.824822i | \(-0.308725\pi\) | ||||
0.565392 | + | 0.824822i | \(0.308725\pi\) | |||||||
\(654\) | −12475.8 | −0.745938 | ||||||||
\(655\) | −5662.59 | −0.337795 | ||||||||
\(656\) | −31539.3 | −1.87714 | ||||||||
\(657\) | −6668.90 | −0.396010 | ||||||||
\(658\) | −28889.3 | −1.71159 | ||||||||
\(659\) | −24299.8 | −1.43639 | −0.718197 | − | 0.695839i | \(-0.755033\pi\) | ||||
−0.718197 | + | 0.695839i | \(0.755033\pi\) | |||||||
\(660\) | −11242.7 | −0.663062 | ||||||||
\(661\) | −29915.0 | −1.76030 | −0.880151 | − | 0.474694i | \(-0.842559\pi\) | ||||
−0.880151 | + | 0.474694i | \(0.842559\pi\) | |||||||
\(662\) | 8335.03 | 0.489350 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41347.1 | −2.41653 | ||||||||
\(665\) | −1069.24 | −0.0623508 | ||||||||
\(666\) | −8482.56 | −0.493532 | ||||||||
\(667\) | 12162.6 | 0.706056 | ||||||||
\(668\) | 3155.69 | 0.182780 | ||||||||
\(669\) | −6940.48 | −0.401098 | ||||||||
\(670\) | −324.128 | −0.0186898 | ||||||||
\(671\) | 8005.86 | 0.460600 | ||||||||
\(672\) | −24304.5 | −1.39519 | ||||||||
\(673\) | 15493.7 | 0.887426 | 0.443713 | − | 0.896169i | \(-0.353661\pi\) | ||||
0.443713 | + | 0.896169i | \(0.353661\pi\) | |||||||
\(674\) | −17115.8 | −0.978154 | ||||||||
\(675\) | −3178.71 | −0.181257 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11729.7 | 0.665891 | 0.332945 | − | 0.942946i | \(-0.391958\pi\) | ||||
0.332945 | + | 0.942946i | \(0.391958\pi\) | |||||||
\(678\) | 20585.2 | 1.16603 | ||||||||
\(679\) | 22005.6 | 1.24374 | ||||||||
\(680\) | −769.698 | −0.0434067 | ||||||||
\(681\) | −11398.4 | −0.641390 | ||||||||
\(682\) | −74003.5 | −4.15505 | ||||||||
\(683\) | 1168.42 | 0.0654587 | 0.0327294 | − | 0.999464i | \(-0.489580\pi\) | ||||
0.0327294 | + | 0.999464i | \(0.489580\pi\) | |||||||
\(684\) | −4878.48 | −0.272709 | ||||||||
\(685\) | −3249.10 | −0.181229 | ||||||||
\(686\) | 37099.1 | 2.06480 | ||||||||
\(687\) | 12963.2 | 0.719909 | ||||||||
\(688\) | 10478.9 | 0.580675 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2053.63 | −0.113305 | ||||||||
\(691\) | −32992.9 | −1.81637 | −0.908183 | − | 0.418574i | \(-0.862530\pi\) | ||||
−0.908183 | + | 0.418574i | \(0.862530\pi\) | |||||||
\(692\) | 11196.7 | 0.615078 | ||||||||
\(693\) | −9151.33 | −0.501631 | ||||||||
\(694\) | −30679.2 | −1.67805 | ||||||||
\(695\) | −870.612 | −0.0475168 | ||||||||
\(696\) | 52863.2 | 2.87899 | ||||||||
\(697\) | −651.438 | −0.0354017 | ||||||||
\(698\) | 17856.3 | 0.968295 | ||||||||
\(699\) | 15839.3 | 0.857078 | ||||||||
\(700\) | 37192.2 | 2.00819 | ||||||||
\(701\) | −14785.8 | −0.796651 | −0.398326 | − | 0.917244i | \(-0.630409\pi\) | ||||
−0.398326 | + | 0.917244i | \(0.630409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4582.77 | 0.245864 | ||||||||
\(704\) | 83357.0 | 4.46255 | ||||||||
\(705\) | −2865.28 | −0.153068 | ||||||||
\(706\) | 66021.0 | 3.51945 | ||||||||
\(707\) | 13430.6 | 0.714442 | ||||||||
\(708\) | −27748.8 | −1.47297 | ||||||||
\(709\) | −12634.0 | −0.669225 | −0.334612 | − | 0.942356i | \(-0.608605\pi\) | ||||
−0.334612 | + | 0.942356i | \(0.608605\pi\) | |||||||
\(710\) | 4125.52 | 0.218067 | ||||||||
\(711\) | −4929.11 | −0.259994 | ||||||||
\(712\) | −14786.8 | −0.778312 | ||||||||
\(713\) | −9760.24 | −0.512656 | ||||||||
\(714\) | −1018.70 | −0.0533947 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46148.7 | −2.40874 | ||||||||
\(717\) | −4643.75 | −0.241874 | ||||||||
\(718\) | −45814.6 | −2.38132 | ||||||||
\(719\) | −27296.5 | −1.41584 | −0.707920 | − | 0.706292i | \(-0.750366\pi\) | ||||
−0.707920 | + | 0.706292i | \(0.750366\pi\) | |||||||
\(720\) | −4891.64 | −0.253195 | ||||||||
\(721\) | −19029.5 | −0.982936 | ||||||||
\(722\) | −33146.3 | −1.70856 | ||||||||
\(723\) | 14754.0 | 0.758932 | ||||||||
\(724\) | −79438.5 | −4.07777 | ||||||||
\(725\) | −30257.4 | −1.54997 | ||||||||
\(726\) | 50577.2 | 2.58553 | ||||||||
\(727\) | 4658.21 | 0.237639 | 0.118819 | − | 0.992916i | \(-0.462089\pi\) | ||||
0.118819 | + | 0.992916i | \(0.462089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 10718.4 | 0.543432 | ||||||||
\(731\) | 216.439 | 0.0109512 | ||||||||
\(732\) | 7461.96 | 0.376779 | ||||||||
\(733\) | 166.474 | 0.00838864 | 0.00419432 | − | 0.999991i | \(-0.498665\pi\) | ||||
0.00419432 | + | 0.999991i | \(0.498665\pi\) | |||||||
\(734\) | 13393.9 | 0.673537 | ||||||||
\(735\) | 905.031 | 0.0454185 | ||||||||
\(736\) | 25219.4 | 1.26304 | ||||||||
\(737\) | 1498.74 | 0.0749074 | ||||||||
\(738\) | −7554.41 | −0.376804 | ||||||||
\(739\) | −12738.1 | −0.634069 | −0.317035 | − | 0.948414i | \(-0.602687\pi\) | ||||
−0.317035 | + | 0.948414i | \(0.602687\pi\) | |||||||
\(740\) | 9843.70 | 0.489002 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 854.092 | 0.0422570 | ||||||||
\(743\) | 30724.5 | 1.51705 | 0.758527 | − | 0.651641i | \(-0.225919\pi\) | ||||
0.758527 | + | 0.651641i | \(0.225919\pi\) | |||||||
\(744\) | −42421.5 | −2.09039 | ||||||||
\(745\) | 3043.76 | 0.149684 | ||||||||
\(746\) | −6131.38 | −0.300919 | ||||||||
\(747\) | −5427.50 | −0.265839 | ||||||||
\(748\) | 5786.84 | 0.282871 | ||||||||
\(749\) | 5193.37 | 0.253353 | ||||||||
\(750\) | 10533.2 | 0.512826 | ||||||||
\(751\) | −39538.6 | −1.92115 | −0.960575 | − | 0.278021i | \(-0.910322\pi\) | ||||
−0.960575 | + | 0.278021i | \(0.910322\pi\) | |||||||
\(752\) | 71403.2 | 3.46251 | ||||||||
\(753\) | 3467.34 | 0.167805 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7928.35 | −0.382175 | ||||||||
\(756\) | −8529.61 | −0.410342 | ||||||||
\(757\) | 23035.1 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(758\) | 65352.1 | 3.13153 | ||||||||
\(759\) | 9495.81 | 0.454119 | ||||||||
\(760\) | 4822.23 | 0.230159 | ||||||||
\(761\) | −32454.0 | −1.54594 | −0.772968 | − | 0.634445i | \(-0.781229\pi\) | ||||
−0.772968 | + | 0.634445i | \(0.781229\pi\) | |||||||
\(762\) | −17926.0 | −0.852220 | ||||||||
\(763\) | 11784.6 | 0.559150 | ||||||||
\(764\) | 71986.8 | 3.40889 | ||||||||
\(765\) | −101.036 | −0.00477511 | ||||||||
\(766\) | 54616.1 | 2.57619 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9080.40 | 0.426641 | ||||||||
\(769\) | 32216.2 | 1.51072 | 0.755362 | − | 0.655307i | \(-0.227461\pi\) | ||||
0.755362 | + | 0.655307i | \(0.227461\pi\) | |||||||
\(770\) | 14708.2 | 0.688372 | ||||||||
\(771\) | 7055.86 | 0.329586 | ||||||||
\(772\) | −97613.2 | −4.55075 | ||||||||
\(773\) | −2924.60 | −0.136081 | −0.0680404 | − | 0.997683i | \(-0.521675\pi\) | ||||
−0.0680404 | + | 0.997683i | \(0.521675\pi\) | |||||||
\(774\) | 2509.94 | 0.116561 | ||||||||
\(775\) | 24280.9 | 1.12541 | ||||||||
\(776\) | −99244.7 | −4.59108 | ||||||||
\(777\) | 8012.58 | 0.369948 | ||||||||
\(778\) | 31361.2 | 1.44519 | ||||||||
\(779\) | 4081.32 | 0.187713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19076.1 | −0.874001 | ||||||||
\(782\) | 1057.04 | 0.0483374 | ||||||||
\(783\) | 6939.19 | 0.316713 | ||||||||
\(784\) | −22553.5 | −1.02740 | ||||||||
\(785\) | −1697.03 | −0.0771586 | ||||||||
\(786\) | 33799.8 | 1.53384 | ||||||||
\(787\) | −25507.1 | −1.15531 | −0.577656 | − | 0.816280i | \(-0.696033\pi\) | ||||
−0.577656 | + | 0.816280i | \(0.696033\pi\) | |||||||
\(788\) | 60011.1 | 2.71295 | ||||||||
\(789\) | 16565.6 | 0.747468 | ||||||||
\(790\) | 7922.16 | 0.356782 | ||||||||
\(791\) | −19444.7 | −0.874050 | ||||||||
\(792\) | 41272.2 | 1.85170 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13416.8 | 0.599677 | ||||||||
\(795\) | 84.7100 | 0.00377906 | ||||||||
\(796\) | 1309.35 | 0.0583023 | ||||||||
\(797\) | 5448.98 | 0.242174 | 0.121087 | − | 0.992642i | \(-0.461362\pi\) | ||||
0.121087 | + | 0.992642i | \(0.461362\pi\) | |||||||
\(798\) | 6382.24 | 0.283119 | ||||||||
\(799\) | 1474.82 | 0.0653008 | ||||||||
\(800\) | −62739.0 | −2.77270 | ||||||||
\(801\) | −1941.01 | −0.0856209 | ||||||||
\(802\) | 49297.8 | 2.17053 | ||||||||
\(803\) | −49560.9 | −2.17804 | ||||||||
\(804\) | 1396.92 | 0.0612755 | ||||||||
\(805\) | 1939.85 | 0.0849324 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11750.9 | 0.512577 | ||||||||
\(808\) | −60571.7 | −2.63726 | ||||||||
\(809\) | −2453.12 | −0.106610 | −0.0533048 | − | 0.998578i | \(-0.516975\pi\) | ||||
−0.0533048 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(810\) | −1171.66 | −0.0508247 | ||||||||
\(811\) | 5133.85 | 0.222286 | 0.111143 | − | 0.993804i | \(-0.464549\pi\) | ||||
0.111143 | + | 0.993804i | \(0.464549\pi\) | |||||||
\(812\) | −81191.4 | −3.50894 | ||||||||
\(813\) | 8332.58 | 0.359454 | ||||||||
\(814\) | −63039.4 | −2.71441 | ||||||||
\(815\) | −1064.81 | −0.0457651 | ||||||||
\(816\) | 2517.83 | 0.108017 | ||||||||
\(817\) | −1356.01 | −0.0580673 | ||||||||
\(818\) | −49432.6 | −2.11292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8766.61 | 0.373345 | ||||||||
\(821\) | 23854.0 | 1.01402 | 0.507009 | − | 0.861941i | \(-0.330751\pi\) | ||||
0.507009 | + | 0.861941i | \(0.330751\pi\) | |||||||
\(822\) | 19393.8 | 0.822913 | ||||||||
\(823\) | 757.156 | 0.0320690 | 0.0160345 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160345 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(824\) | 85822.6 | 3.62836 | ||||||||
\(825\) | −23623.0 | −0.996907 | ||||||||
\(826\) | 36302.2 | 1.52919 | ||||||||
\(827\) | −28621.2 | −1.20345 | −0.601726 | − | 0.798702i | \(-0.705520\pi\) | ||||
−0.601726 | + | 0.798702i | \(0.705520\pi\) | |||||||
\(828\) | 8850.68 | 0.371476 | ||||||||
\(829\) | 27429.2 | 1.14916 | 0.574582 | − | 0.818447i | \(-0.305165\pi\) | ||||
0.574582 | + | 0.818447i | \(0.305165\pi\) | |||||||
\(830\) | 8723.19 | 0.364803 | ||||||||
\(831\) | 19749.2 | 0.824421 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −465.838 | −0.0193761 | ||||||||
\(834\) | 5196.64 | 0.215761 | ||||||||
\(835\) | −409.462 | −0.0169701 | ||||||||
\(836\) | −36255.1 | −1.49989 | ||||||||
\(837\) | −5568.54 | −0.229960 | ||||||||
\(838\) | −34840.7 | −1.43622 | ||||||||
\(839\) | 4633.62 | 0.190668 | 0.0953339 | − | 0.995445i | \(-0.469608\pi\) | ||||
0.0953339 | + | 0.995445i | \(0.469608\pi\) | |||||||
\(840\) | 8431.27 | 0.346317 | ||||||||
\(841\) | 41663.6 | 1.70829 | ||||||||
\(842\) | −16413.7 | −0.671798 | ||||||||
\(843\) | −8614.98 | −0.351976 | ||||||||
\(844\) | −21813.0 | −0.889614 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17102.7 | 0.695041 | ||||||||
\(847\) | −47775.0 | −1.93810 | ||||||||
\(848\) | −2110.99 | −0.0854853 | ||||||||
\(849\) | 22554.1 | 0.911726 | ||||||||
\(850\) | −2629.64 | −0.106113 | ||||||||
\(851\) | −8314.19 | −0.334908 | ||||||||
\(852\) | −17780.1 | −0.714947 | ||||||||
\(853\) | 14854.6 | 0.596261 | 0.298131 | − | 0.954525i | \(-0.403637\pi\) | ||||
0.298131 | + | 0.954525i | \(0.403637\pi\) | |||||||
\(854\) | −9762.07 | −0.391161 | ||||||||
\(855\) | 632.999 | 0.0253194 | ||||||||
\(856\) | −23421.9 | −0.935216 | ||||||||
\(857\) | −42799.5 | −1.70595 | −0.852977 | − | 0.521948i | \(-0.825206\pi\) | ||||
−0.852977 | + | 0.521948i | \(0.825206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8246.47 | −0.327551 | −0.163775 | − | 0.986498i | \(-0.552367\pi\) | ||||
−0.163775 | + | 0.986498i | \(0.552367\pi\) | |||||||
\(860\) | −2912.70 | −0.115491 | ||||||||
\(861\) | 7135.85 | 0.282450 | ||||||||
\(862\) | −42580.1 | −1.68246 | ||||||||
\(863\) | −17695.4 | −0.697983 | −0.348991 | − | 0.937126i | \(-0.613476\pi\) | ||||
−0.348991 | + | 0.937126i | \(0.613476\pi\) | |||||||
\(864\) | 14388.5 | 0.566558 | ||||||||
\(865\) | −1452.81 | −0.0571064 | ||||||||
\(866\) | 39132.3 | 1.53553 | ||||||||
\(867\) | −14687.0 | −0.575313 | ||||||||
\(868\) | 65154.2 | 2.54779 | ||||||||
\(869\) | −36631.4 | −1.42996 | ||||||||
\(870\) | −11152.8 | −0.434615 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −53148.2 | −2.06402 | ||||||||
\(873\) | −13027.5 | −0.505058 | ||||||||
\(874\) | −6622.49 | −0.256303 | ||||||||
\(875\) | −9949.64 | −0.384411 | ||||||||
\(876\) | −46193.8 | −1.78167 | ||||||||
\(877\) | 14346.8 | 0.552401 | 0.276200 | − | 0.961100i | \(-0.410925\pi\) | ||||
0.276200 | + | 0.961100i | \(0.410925\pi\) | |||||||
\(878\) | 81622.7 | 3.13739 | ||||||||
\(879\) | −13519.7 | −0.518781 | ||||||||
\(880\) | −36353.0 | −1.39257 | ||||||||
\(881\) | −2063.51 | −0.0789121 | −0.0394560 | − | 0.999221i | \(-0.512563\pi\) | ||||
−0.0394560 | + | 0.999221i | \(0.512563\pi\) | |||||||
\(882\) | −5402.09 | −0.206233 | ||||||||
\(883\) | −34137.1 | −1.30103 | −0.650513 | − | 0.759495i | \(-0.725446\pi\) | ||||
−0.650513 | + | 0.759495i | \(0.725446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3600.50 | 0.136756 | ||||||||
\(886\) | 8138.58 | 0.308602 | ||||||||
\(887\) | −22238.5 | −0.841821 | −0.420910 | − | 0.907102i | \(-0.638289\pi\) | ||||
−0.420910 | + | 0.907102i | \(0.638289\pi\) | |||||||
\(888\) | −36136.5 | −1.36561 | ||||||||
\(889\) | 16932.8 | 0.638817 | ||||||||
\(890\) | 3119.63 | 0.117495 | ||||||||
\(891\) | 5417.67 | 0.203702 | ||||||||
\(892\) | −48075.0 | −1.80456 | ||||||||
\(893\) | −9239.89 | −0.346250 | ||||||||
\(894\) | −18168.0 | −0.679676 | ||||||||
\(895\) | 5987.96 | 0.223637 | ||||||||
\(896\) | −36830.7 | −1.37325 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3783.45 | 0.140596 | ||||||||
\(899\) | −53005.7 | −1.96645 | ||||||||
\(900\) | −22018.1 | −0.815486 | ||||||||
\(901\) | −43.6019 | −0.00161220 | ||||||||
\(902\) | −56141.7 | −2.07241 | ||||||||
\(903\) | −2370.88 | −0.0873730 | ||||||||
\(904\) | 87694.9 | 3.22643 | ||||||||
\(905\) | 10307.4 | 0.378597 | ||||||||
\(906\) | 47324.0 | 1.73536 | ||||||||
\(907\) | −44160.3 | −1.61667 | −0.808335 | − | 0.588723i | \(-0.799631\pi\) | ||||
−0.808335 | + | 0.588723i | \(0.799631\pi\) | |||||||
\(908\) | −78953.8 | −2.88565 | ||||||||
\(909\) | −7951.05 | −0.290121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11916.3 | 0.433376 | 0.216688 | − | 0.976241i | \(-0.430475\pi\) | ||||
0.216688 | + | 0.976241i | \(0.430475\pi\) | |||||||
\(912\) | −15774.4 | −0.572745 | ||||||||
\(913\) | −40335.3 | −1.46211 | ||||||||
\(914\) | 39043.0 | 1.41294 | ||||||||
\(915\) | −968.215 | −0.0349816 | ||||||||
\(916\) | 89793.0 | 3.23891 | ||||||||
\(917\) | −31927.1 | −1.14975 | ||||||||
\(918\) | 603.078 | 0.0216825 | ||||||||
\(919\) | −20128.9 | −0.722516 | −0.361258 | − | 0.932466i | \(-0.617653\pi\) | ||||
−0.361258 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(920\) | −8748.64 | −0.313515 | ||||||||
\(921\) | −28616.7 | −1.02383 | ||||||||
\(922\) | −10525.0 | −0.375945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −63389.0 | −2.25687 | ||||||||
\(925\) | 20683.5 | 0.735210 | ||||||||
\(926\) | 55654.1 | 1.97506 | ||||||||
\(927\) | 11265.7 | 0.399151 | ||||||||
\(928\) | 136961. | 4.84478 | ||||||||
\(929\) | 31428.4 | 1.10994 | 0.554969 | − | 0.831871i | \(-0.312730\pi\) | ||||
0.554969 | + | 0.831871i | \(0.312730\pi\) | |||||||
\(930\) | 8949.86 | 0.315567 | ||||||||
\(931\) | 2918.52 | 0.102740 | ||||||||
\(932\) | 109715. | 3.85605 | ||||||||
\(933\) | −22398.9 | −0.785965 | ||||||||
\(934\) | 47150.1 | 1.65182 | ||||||||
\(935\) | −750.863 | −0.0262629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42473.2 | 1.48083 | 0.740416 | − | 0.672149i | \(-0.234629\pi\) | ||||
0.740416 | + | 0.672149i | \(0.234629\pi\) | |||||||
\(938\) | −1827.51 | −0.0636144 | ||||||||
\(939\) | −5464.94 | −0.189927 | ||||||||
\(940\) | −19847.1 | −0.688661 | ||||||||
\(941\) | 42644.0 | 1.47732 | 0.738659 | − | 0.674079i | \(-0.235459\pi\) | ||||
0.738659 | + | 0.674079i | \(0.235459\pi\) | |||||||
\(942\) | 10129.5 | 0.350357 | ||||||||
\(943\) | −7404.46 | −0.255697 | ||||||||
\(944\) | −89725.0 | −3.09354 | ||||||||
\(945\) | 1106.75 | 0.0380978 | ||||||||
\(946\) | 18653.0 | 0.641080 | ||||||||
\(947\) | −4282.95 | −0.146966 | −0.0734831 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734831 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(948\) | −34142.7 | −1.16973 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 16475.0 | 0.562651 | ||||||||
\(951\) | −9375.42 | −0.319683 | ||||||||
\(952\) | −4339.74 | −0.147744 | ||||||||
\(953\) | 40593.9 | 1.37982 | 0.689908 | − | 0.723897i | \(-0.257651\pi\) | ||||
0.689908 | + | 0.723897i | \(0.257651\pi\) | |||||||
\(954\) | −505.630 | −0.0171597 | ||||||||
\(955\) | −9340.54 | −0.316495 | ||||||||
\(956\) | −32166.1 | −1.08821 | ||||||||
\(957\) | 51569.6 | 1.74191 | ||||||||
\(958\) | 59771.9 | 2.01581 | ||||||||
\(959\) | −18319.2 | −0.616850 | ||||||||
\(960\) | −10081.1 | −0.338922 | ||||||||
\(961\) | 12744.8 | 0.427808 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3074.52 | −0.102882 | ||||||||
\(964\) | 102198. | 3.41448 | ||||||||
\(965\) | 12665.7 | 0.422510 | ||||||||
\(966\) | −11578.9 | −0.385656 | ||||||||
\(967\) | −17709.4 | −0.588931 | −0.294466 | − | 0.955662i | \(-0.595142\pi\) | ||||
−0.294466 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(968\) | 215464. | 7.15420 | ||||||||
\(969\) | −325.818 | −0.0108016 | ||||||||
\(970\) | 20938.1 | 0.693074 | ||||||||
\(971\) | 4038.97 | 0.133488 | 0.0667440 | − | 0.997770i | \(-0.478739\pi\) | ||||
0.0667440 | + | 0.997770i | \(0.478739\pi\) | |||||||
\(972\) | 5049.61 | 0.166632 | ||||||||
\(973\) | −4908.72 | −0.161733 | ||||||||
\(974\) | 105366. | 3.46626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24128.1 | 0.791312 | ||||||||
\(977\) | 2764.30 | 0.0905197 | 0.0452598 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452598 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(978\) | 6355.79 | 0.207807 | ||||||||
\(979\) | −14424.9 | −0.470912 | ||||||||
\(980\) | 6268.93 | 0.204340 | ||||||||
\(981\) | −6976.59 | −0.227060 | ||||||||
\(982\) | −18295.4 | −0.594531 | ||||||||
\(983\) | 17804.5 | 0.577695 | 0.288848 | − | 0.957375i | \(-0.406728\pi\) | ||||
0.288848 | + | 0.957375i | \(0.406728\pi\) | |||||||
\(984\) | −32182.4 | −1.04262 | ||||||||
\(985\) | −7786.65 | −0.251881 | ||||||||
\(986\) | 5740.57 | 0.185413 | ||||||||
\(987\) | −16155.2 | −0.520997 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2460.12 | 0.0790974 | ||||||||
\(990\) | −8707.39 | −0.279534 | ||||||||
\(991\) | −8129.69 | −0.260593 | −0.130297 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130297 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(992\) | −109908. | −3.51772 | ||||||||
\(993\) | 4661.02 | 0.148956 | ||||||||
\(994\) | 23260.7 | 0.742237 | ||||||||
\(995\) | −169.893 | −0.00541302 | ||||||||
\(996\) | −37595.0 | −1.19603 | ||||||||
\(997\) | −29452.9 | −0.935589 | −0.467795 | − | 0.883837i | \(-0.654951\pi\) | ||||
−0.467795 | + | 0.883837i | \(0.654951\pi\) | |||||||
\(998\) | 26997.7 | 0.856309 | ||||||||
\(999\) | −4743.52 | −0.150229 |
(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 | 507.4.a.r.1.10 | 10 | ||
3.2 | odd | 2 | 1521.4.a.bk.1.1 | 10 | |||
13.5 | odd | 4 | 507.4.b.i.337.1 | 10 | |||
13.6 | odd | 12 | 39.4.j.c.10.1 | yes | 10 | ||
13.8 | odd | 4 | 507.4.b.i.337.10 | 10 | |||
13.11 | odd | 12 | 39.4.j.c.4.1 | ✓ | 10 | ||
13.12 | even | 2 | inner | 507.4.a.r.1.1 | 10 | ||
39.11 | even | 12 | 117.4.q.e.82.5 | 10 | |||
39.32 | even | 12 | 117.4.q.e.10.5 | 10 | |||
39.38 | odd | 2 | 1521.4.a.bk.1.10 | 10 | |||
52.11 | even | 12 | 624.4.bv.h.433.3 | 10 | |||
52.19 | even | 12 | 624.4.bv.h.49.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.1 | ✓ | 10 | 13.11 | odd | 12 | ||
39.4.j.c.10.1 | yes | 10 | 13.6 | odd | 12 | ||
117.4.q.e.10.5 | 10 | 39.32 | even | 12 | |||
117.4.q.e.82.5 | 10 | 39.11 | even | 12 | |||
507.4.a.r.1.1 | 10 | 13.12 | even | 2 | inner | ||
507.4.a.r.1.10 | 10 | 1.1 | even | 1 | trivial | ||
507.4.b.i.337.1 | 10 | 13.5 | odd | 4 | |||
507.4.b.i.337.10 | 10 | 13.8 | odd | 4 | |||
624.4.bv.h.49.3 | 10 | 52.19 | even | 12 | |||
624.4.bv.h.433.3 | 10 | 52.11 | even | 12 | |||
1521.4.a.bk.1.1 | 10 | 3.2 | odd | 2 | |||
1521.4.a.bk.1.10 | 10 | 39.38 | odd | 2 |