Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.395900\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.395900 | 0.228573 | 0.114287 | − | 0.993448i | \(-0.463542\pi\) | ||||
0.114287 | + | 0.993448i | \(0.463542\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.151677 | 0.0678319 | 0.0339160 | − | 0.999425i | \(-0.489202\pi\) | ||||
0.0339160 | + | 0.999425i | \(0.489202\pi\) | |||||||
\(6\) | 0.395900 | 0.161626 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.84326 | −0.947754 | ||||||||
\(10\) | 0.151677 | 0.0479644 | ||||||||
\(11\) | 2.85030 | 0.859398 | 0.429699 | − | 0.902972i | \(-0.358620\pi\) | ||||
0.429699 | + | 0.902972i | \(0.358620\pi\) | |||||||
\(12\) | 0.395900 | 0.114287 | ||||||||
\(13\) | −2.70854 | −0.751214 | −0.375607 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375607 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.0600489 | 0.0155046 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00368 | −0.243428 | −0.121714 | − | 0.992565i | \(-0.538839\pi\) | ||||
−0.121714 | + | 0.992565i | \(0.538839\pi\) | |||||||
\(18\) | −2.84326 | −0.670164 | ||||||||
\(19\) | 2.34557 | 0.538112 | 0.269056 | − | 0.963125i | \(-0.413288\pi\) | ||||
0.269056 | + | 0.963125i | \(0.413288\pi\) | |||||||
\(20\) | 0.151677 | 0.0339160 | ||||||||
\(21\) | −0.395900 | −0.0863925 | ||||||||
\(22\) | 2.85030 | 0.607686 | ||||||||
\(23\) | −0.830286 | −0.173127 | −0.0865633 | − | 0.996246i | \(-0.527588\pi\) | ||||
−0.0865633 | + | 0.996246i | \(0.527588\pi\) | |||||||
\(24\) | 0.395900 | 0.0808128 | ||||||||
\(25\) | −4.97699 | −0.995399 | ||||||||
\(26\) | −2.70854 | −0.531188 | ||||||||
\(27\) | −2.31335 | −0.445204 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.14114 | 0.583296 | 0.291648 | − | 0.956526i | \(-0.405796\pi\) | ||||
0.291648 | + | 0.956526i | \(0.405796\pi\) | |||||||
\(30\) | 0.0600489 | 0.0109634 | ||||||||
\(31\) | −4.76935 | −0.856601 | −0.428301 | − | 0.903636i | \(-0.640888\pi\) | ||||
−0.428301 | + | 0.903636i | \(0.640888\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.12843 | 0.196435 | ||||||||
\(34\) | −1.00368 | −0.172130 | ||||||||
\(35\) | −0.151677 | −0.0256381 | ||||||||
\(36\) | −2.84326 | −0.473877 | ||||||||
\(37\) | 2.32662 | 0.382494 | 0.191247 | − | 0.981542i | \(-0.438747\pi\) | ||||
0.191247 | + | 0.981542i | \(0.438747\pi\) | |||||||
\(38\) | 2.34557 | 0.380502 | ||||||||
\(39\) | −1.07231 | −0.171707 | ||||||||
\(40\) | 0.151677 | 0.0239822 | ||||||||
\(41\) | −3.35096 | −0.523332 | −0.261666 | − | 0.965158i | \(-0.584272\pi\) | ||||
−0.261666 | + | 0.965158i | \(0.584272\pi\) | |||||||
\(42\) | −0.395900 | −0.0610887 | ||||||||
\(43\) | −11.1914 | −1.70668 | −0.853339 | − | 0.521356i | \(-0.825426\pi\) | ||||
−0.853339 | + | 0.521356i | \(0.825426\pi\) | |||||||
\(44\) | 2.85030 | 0.429699 | ||||||||
\(45\) | −0.431257 | −0.0642880 | ||||||||
\(46\) | −0.830286 | −0.122419 | ||||||||
\(47\) | −9.19342 | −1.34100 | −0.670499 | − | 0.741910i | \(-0.733920\pi\) | ||||
−0.670499 | + | 0.741910i | \(0.733920\pi\) | |||||||
\(48\) | 0.395900 | 0.0571433 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.97699 | −0.703853 | ||||||||
\(51\) | −0.397357 | −0.0556411 | ||||||||
\(52\) | −2.70854 | −0.375607 | ||||||||
\(53\) | 0.902309 | 0.123942 | 0.0619708 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619708 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(54\) | −2.31335 | −0.314807 | ||||||||
\(55\) | 0.432324 | 0.0582946 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0.928613 | 0.122998 | ||||||||
\(58\) | 3.14114 | 0.412453 | ||||||||
\(59\) | −0.539748 | −0.0702692 | −0.0351346 | − | 0.999383i | \(-0.511186\pi\) | ||||
−0.0351346 | + | 0.999383i | \(0.511186\pi\) | |||||||
\(60\) | 0.0600489 | 0.00775228 | ||||||||
\(61\) | −3.28025 | −0.419992 | −0.209996 | − | 0.977702i | \(-0.567345\pi\) | ||||
−0.209996 | + | 0.977702i | \(0.567345\pi\) | |||||||
\(62\) | −4.76935 | −0.605708 | ||||||||
\(63\) | 2.84326 | 0.358217 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.410823 | −0.0509563 | ||||||||
\(66\) | 1.12843 | 0.138901 | ||||||||
\(67\) | −8.88542 | −1.08553 | −0.542764 | − | 0.839885i | \(-0.682622\pi\) | ||||
−0.542764 | + | 0.839885i | \(0.682622\pi\) | |||||||
\(68\) | −1.00368 | −0.121714 | ||||||||
\(69\) | −0.328710 | −0.0395721 | ||||||||
\(70\) | −0.151677 | −0.0181288 | ||||||||
\(71\) | 9.68947 | 1.14993 | 0.574964 | − | 0.818178i | \(-0.305016\pi\) | ||||
0.574964 | + | 0.818178i | \(0.305016\pi\) | |||||||
\(72\) | −2.84326 | −0.335082 | ||||||||
\(73\) | 1.66771 | 0.195191 | 0.0975953 | − | 0.995226i | \(-0.468885\pi\) | ||||
0.0975953 | + | 0.995226i | \(0.468885\pi\) | |||||||
\(74\) | 2.32662 | 0.270464 | ||||||||
\(75\) | −1.97039 | −0.227521 | ||||||||
\(76\) | 2.34557 | 0.269056 | ||||||||
\(77\) | −2.85030 | −0.324822 | ||||||||
\(78\) | −1.07231 | −0.121415 | ||||||||
\(79\) | 4.67827 | 0.526346 | 0.263173 | − | 0.964749i | \(-0.415231\pi\) | ||||
0.263173 | + | 0.964749i | \(0.415231\pi\) | |||||||
\(80\) | 0.151677 | 0.0169580 | ||||||||
\(81\) | 7.61393 | 0.845993 | ||||||||
\(82\) | −3.35096 | −0.370052 | ||||||||
\(83\) | 13.9915 | 1.53577 | 0.767886 | − | 0.640587i | \(-0.221309\pi\) | ||||
0.767886 | + | 0.640587i | \(0.221309\pi\) | |||||||
\(84\) | −0.395900 | −0.0431962 | ||||||||
\(85\) | −0.152235 | −0.0165122 | ||||||||
\(86\) | −11.1914 | −1.20680 | ||||||||
\(87\) | 1.24358 | 0.133326 | ||||||||
\(88\) | 2.85030 | 0.303843 | ||||||||
\(89\) | −1.06964 | −0.113382 | −0.0566910 | − | 0.998392i | \(-0.518055\pi\) | ||||
−0.0566910 | + | 0.998392i | \(0.518055\pi\) | |||||||
\(90\) | −0.431257 | −0.0454585 | ||||||||
\(91\) | 2.70854 | 0.283932 | ||||||||
\(92\) | −0.830286 | −0.0865633 | ||||||||
\(93\) | −1.88819 | −0.195796 | ||||||||
\(94\) | −9.19342 | −0.948229 | ||||||||
\(95\) | 0.355769 | 0.0365011 | ||||||||
\(96\) | 0.395900 | 0.0404064 | ||||||||
\(97\) | −6.33555 | −0.643277 | −0.321639 | − | 0.946863i | \(-0.604234\pi\) | ||||
−0.321639 | + | 0.946863i | \(0.604234\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −8.10415 | −0.814498 | ||||||||
\(100\) | −4.97699 | −0.497699 | ||||||||
\(101\) | −2.64274 | −0.262963 | −0.131481 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131481 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(102\) | −0.397357 | −0.0393442 | ||||||||
\(103\) | −7.36597 | −0.725791 | −0.362895 | − | 0.931830i | \(-0.618212\pi\) | ||||
−0.362895 | + | 0.931830i | \(0.618212\pi\) | |||||||
\(104\) | −2.70854 | −0.265594 | ||||||||
\(105\) | −0.0600489 | −0.00586017 | ||||||||
\(106\) | 0.902309 | 0.0876400 | ||||||||
\(107\) | 2.57808 | 0.249232 | 0.124616 | − | 0.992205i | \(-0.460230\pi\) | ||||
0.124616 | + | 0.992205i | \(0.460230\pi\) | |||||||
\(108\) | −2.31335 | −0.222602 | ||||||||
\(109\) | −17.7365 | −1.69885 | −0.849425 | − | 0.527710i | \(-0.823051\pi\) | ||||
−0.849425 | + | 0.527710i | \(0.823051\pi\) | |||||||
\(110\) | 0.432324 | 0.0412205 | ||||||||
\(111\) | 0.921109 | 0.0874278 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.6543 | −1.66077 | −0.830387 | − | 0.557187i | \(-0.811881\pi\) | ||||
−0.830387 | + | 0.557187i | \(0.811881\pi\) | |||||||
\(114\) | 0.928613 | 0.0869726 | ||||||||
\(115\) | −0.125935 | −0.0117435 | ||||||||
\(116\) | 3.14114 | 0.291648 | ||||||||
\(117\) | 7.70109 | 0.711966 | ||||||||
\(118\) | −0.539748 | −0.0496878 | ||||||||
\(119\) | 1.00368 | 0.0920071 | ||||||||
\(120\) | 0.0600489 | 0.00548169 | ||||||||
\(121\) | −2.87579 | −0.261435 | ||||||||
\(122\) | −3.28025 | −0.296979 | ||||||||
\(123\) | −1.32665 | −0.119620 | ||||||||
\(124\) | −4.76935 | −0.428301 | ||||||||
\(125\) | −1.51328 | −0.135352 | ||||||||
\(126\) | 2.84326 | 0.253298 | ||||||||
\(127\) | −1.89718 | −0.168348 | −0.0841738 | − | 0.996451i | \(-0.526825\pi\) | ||||
−0.0841738 | + | 0.996451i | \(0.526825\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.43069 | −0.390101 | ||||||||
\(130\) | −0.410823 | −0.0360315 | ||||||||
\(131\) | −18.4798 | −1.61459 | −0.807295 | − | 0.590148i | \(-0.799069\pi\) | ||||
−0.807295 | + | 0.590148i | \(0.799069\pi\) | |||||||
\(132\) | 1.12843 | 0.0982176 | ||||||||
\(133\) | −2.34557 | −0.203387 | ||||||||
\(134\) | −8.88542 | −0.767584 | ||||||||
\(135\) | −0.350881 | −0.0301991 | ||||||||
\(136\) | −1.00368 | −0.0860648 | ||||||||
\(137\) | 7.37889 | 0.630421 | 0.315211 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315211 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(138\) | −0.328710 | −0.0279817 | ||||||||
\(139\) | −12.3861 | −1.05058 | −0.525288 | − | 0.850924i | \(-0.676042\pi\) | ||||
−0.525288 | + | 0.850924i | \(0.676042\pi\) | |||||||
\(140\) | −0.151677 | −0.0128190 | ||||||||
\(141\) | −3.63968 | −0.306516 | ||||||||
\(142\) | 9.68947 | 0.813122 | ||||||||
\(143\) | −7.72015 | −0.645592 | ||||||||
\(144\) | −2.84326 | −0.236939 | ||||||||
\(145\) | 0.476439 | 0.0395661 | ||||||||
\(146\) | 1.66771 | 0.138021 | ||||||||
\(147\) | 0.395900 | 0.0326533 | ||||||||
\(148\) | 2.32662 | 0.191247 | ||||||||
\(149\) | 15.5998 | 1.27798 | 0.638992 | − | 0.769214i | \(-0.279352\pi\) | ||||
0.638992 | + | 0.769214i | \(0.279352\pi\) | |||||||
\(150\) | −1.97039 | −0.160882 | ||||||||
\(151\) | −7.65766 | −0.623171 | −0.311586 | − | 0.950218i | \(-0.600860\pi\) | ||||
−0.311586 | + | 0.950218i | \(0.600860\pi\) | |||||||
\(152\) | 2.34557 | 0.190251 | ||||||||
\(153\) | 2.85372 | 0.230710 | ||||||||
\(154\) | −2.85030 | −0.229684 | ||||||||
\(155\) | −0.723400 | −0.0581049 | ||||||||
\(156\) | −1.07231 | −0.0858536 | ||||||||
\(157\) | 3.84490 | 0.306856 | 0.153428 | − | 0.988160i | \(-0.450969\pi\) | ||||
0.153428 | + | 0.988160i | \(0.450969\pi\) | |||||||
\(158\) | 4.67827 | 0.372183 | ||||||||
\(159\) | 0.357224 | 0.0283297 | ||||||||
\(160\) | 0.151677 | 0.0119911 | ||||||||
\(161\) | 0.830286 | 0.0654357 | ||||||||
\(162\) | 7.61393 | 0.598207 | ||||||||
\(163\) | 21.9243 | 1.71725 | 0.858623 | − | 0.512607i | \(-0.171320\pi\) | ||||
0.858623 | + | 0.512607i | \(0.171320\pi\) | |||||||
\(164\) | −3.35096 | −0.261666 | ||||||||
\(165\) | 0.171157 | 0.0133246 | ||||||||
\(166\) | 13.9915 | 1.08595 | ||||||||
\(167\) | −9.30474 | −0.720022 | −0.360011 | − | 0.932948i | \(-0.617227\pi\) | ||||
−0.360011 | + | 0.932948i | \(0.617227\pi\) | |||||||
\(168\) | −0.395900 | −0.0305444 | ||||||||
\(169\) | −5.66381 | −0.435678 | ||||||||
\(170\) | −0.152235 | −0.0116759 | ||||||||
\(171\) | −6.66908 | −0.509998 | ||||||||
\(172\) | −11.1914 | −0.853339 | ||||||||
\(173\) | −13.3146 | −1.01229 | −0.506144 | − | 0.862449i | \(-0.668930\pi\) | ||||
−0.506144 | + | 0.862449i | \(0.668930\pi\) | |||||||
\(174\) | 1.24358 | 0.0942755 | ||||||||
\(175\) | 4.97699 | 0.376225 | ||||||||
\(176\) | 2.85030 | 0.214849 | ||||||||
\(177\) | −0.213686 | −0.0160617 | ||||||||
\(178\) | −1.06964 | −0.0801732 | ||||||||
\(179\) | 2.54428 | 0.190169 | 0.0950843 | − | 0.995469i | \(-0.469688\pi\) | ||||
0.0950843 | + | 0.995469i | \(0.469688\pi\) | |||||||
\(180\) | −0.431257 | −0.0321440 | ||||||||
\(181\) | 4.36483 | 0.324435 | 0.162218 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162218 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(182\) | 2.70854 | 0.200770 | ||||||||
\(183\) | −1.29865 | −0.0959989 | ||||||||
\(184\) | −0.830286 | −0.0612095 | ||||||||
\(185\) | 0.352894 | 0.0259453 | ||||||||
\(186\) | −1.88819 | −0.138449 | ||||||||
\(187\) | −2.86079 | −0.209202 | ||||||||
\(188\) | −9.19342 | −0.670499 | ||||||||
\(189\) | 2.31335 | 0.168271 | ||||||||
\(190\) | 0.355769 | 0.0258102 | ||||||||
\(191\) | −20.2581 | −1.46582 | −0.732911 | − | 0.680324i | \(-0.761839\pi\) | ||||
−0.732911 | + | 0.680324i | \(0.761839\pi\) | |||||||
\(192\) | 0.395900 | 0.0285716 | ||||||||
\(193\) | 25.3832 | 1.82712 | 0.913562 | − | 0.406699i | \(-0.133320\pi\) | ||||
0.913562 | + | 0.406699i | \(0.133320\pi\) | |||||||
\(194\) | −6.33555 | −0.454866 | ||||||||
\(195\) | −0.162645 | −0.0116472 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.58473 | 0.397896 | 0.198948 | − | 0.980010i | \(-0.436248\pi\) | ||||
0.198948 | + | 0.980010i | \(0.436248\pi\) | |||||||
\(198\) | −8.10415 | −0.575937 | ||||||||
\(199\) | −19.5254 | −1.38412 | −0.692058 | − | 0.721842i | \(-0.743296\pi\) | ||||
−0.692058 | + | 0.721842i | \(0.743296\pi\) | |||||||
\(200\) | −4.97699 | −0.351927 | ||||||||
\(201\) | −3.51774 | −0.248122 | ||||||||
\(202\) | −2.64274 | −0.185943 | ||||||||
\(203\) | −3.14114 | −0.220465 | ||||||||
\(204\) | −0.397357 | −0.0278205 | ||||||||
\(205\) | −0.508263 | −0.0354986 | ||||||||
\(206\) | −7.36597 | −0.513212 | ||||||||
\(207\) | 2.36072 | 0.164081 | ||||||||
\(208\) | −2.70854 | −0.187803 | ||||||||
\(209\) | 6.68559 | 0.462452 | ||||||||
\(210\) | −0.0600489 | −0.00414377 | ||||||||
\(211\) | −12.8303 | −0.883273 | −0.441637 | − | 0.897194i | \(-0.645602\pi\) | ||||
−0.441637 | + | 0.897194i | \(0.645602\pi\) | |||||||
\(212\) | 0.902309 | 0.0619708 | ||||||||
\(213\) | 3.83606 | 0.262843 | ||||||||
\(214\) | 2.57808 | 0.176234 | ||||||||
\(215\) | −1.69748 | −0.115767 | ||||||||
\(216\) | −2.31335 | −0.157403 | ||||||||
\(217\) | 4.76935 | 0.323765 | ||||||||
\(218\) | −17.7365 | −1.20127 | ||||||||
\(219\) | 0.660247 | 0.0446153 | ||||||||
\(220\) | 0.432324 | 0.0291473 | ||||||||
\(221\) | 2.71851 | 0.182866 | ||||||||
\(222\) | 0.921109 | 0.0618208 | ||||||||
\(223\) | 21.9733 | 1.47144 | 0.735722 | − | 0.677284i | \(-0.236843\pi\) | ||||
0.735722 | + | 0.677284i | \(0.236843\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 14.1509 | 0.943394 | ||||||||
\(226\) | −17.6543 | −1.17434 | ||||||||
\(227\) | 28.8717 | 1.91628 | 0.958140 | − | 0.286302i | \(-0.0924259\pi\) | ||||
0.958140 | + | 0.286302i | \(0.0924259\pi\) | |||||||
\(228\) | 0.928613 | 0.0614989 | ||||||||
\(229\) | −25.3652 | −1.67618 | −0.838089 | − | 0.545534i | \(-0.816327\pi\) | ||||
−0.838089 | + | 0.545534i | \(0.816327\pi\) | |||||||
\(230\) | −0.125935 | −0.00830391 | ||||||||
\(231\) | −1.12843 | −0.0742455 | ||||||||
\(232\) | 3.14114 | 0.206226 | ||||||||
\(233\) | −5.57673 | −0.365344 | −0.182672 | − | 0.983174i | \(-0.558475\pi\) | ||||
−0.182672 | + | 0.983174i | \(0.558475\pi\) | |||||||
\(234\) | 7.70109 | 0.503436 | ||||||||
\(235\) | −1.39443 | −0.0909625 | ||||||||
\(236\) | −0.539748 | −0.0351346 | ||||||||
\(237\) | 1.85213 | 0.120309 | ||||||||
\(238\) | 1.00368 | 0.0650589 | ||||||||
\(239\) | −29.2351 | −1.89106 | −0.945530 | − | 0.325535i | \(-0.894456\pi\) | ||||
−0.945530 | + | 0.325535i | \(0.894456\pi\) | |||||||
\(240\) | 0.0600489 | 0.00387614 | ||||||||
\(241\) | 0.626558 | 0.0403602 | 0.0201801 | − | 0.999796i | \(-0.493576\pi\) | ||||
0.0201801 | + | 0.999796i | \(0.493576\pi\) | |||||||
\(242\) | −2.87579 | −0.184863 | ||||||||
\(243\) | 9.95440 | 0.638575 | ||||||||
\(244\) | −3.28025 | −0.209996 | ||||||||
\(245\) | 0.151677 | 0.00969028 | ||||||||
\(246\) | −1.32665 | −0.0845839 | ||||||||
\(247\) | −6.35308 | −0.404237 | ||||||||
\(248\) | −4.76935 | −0.302854 | ||||||||
\(249\) | 5.53925 | 0.351036 | ||||||||
\(250\) | −1.51328 | −0.0957081 | ||||||||
\(251\) | 10.7106 | 0.676050 | 0.338025 | − | 0.941137i | \(-0.390241\pi\) | ||||
0.338025 | + | 0.941137i | \(0.390241\pi\) | |||||||
\(252\) | 2.84326 | 0.179109 | ||||||||
\(253\) | −2.36656 | −0.148785 | ||||||||
\(254\) | −1.89718 | −0.119040 | ||||||||
\(255\) | −0.0602698 | −0.00377424 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.7103 | 0.792845 | 0.396422 | − | 0.918068i | \(-0.370252\pi\) | ||||
0.396422 | + | 0.918068i | \(0.370252\pi\) | |||||||
\(258\) | −4.43069 | −0.275843 | ||||||||
\(259\) | −2.32662 | −0.144569 | ||||||||
\(260\) | −0.410823 | −0.0254781 | ||||||||
\(261\) | −8.93110 | −0.552821 | ||||||||
\(262\) | −18.4798 | −1.14169 | ||||||||
\(263\) | −5.36770 | −0.330986 | −0.165493 | − | 0.986211i | \(-0.552922\pi\) | ||||
−0.165493 | + | 0.986211i | \(0.552922\pi\) | |||||||
\(264\) | 1.12843 | 0.0694503 | ||||||||
\(265\) | 0.136859 | 0.00840720 | ||||||||
\(266\) | −2.34557 | −0.143816 | ||||||||
\(267\) | −0.423472 | −0.0259161 | ||||||||
\(268\) | −8.88542 | −0.542764 | ||||||||
\(269\) | 26.7652 | 1.63190 | 0.815952 | − | 0.578119i | \(-0.196213\pi\) | ||||
0.815952 | + | 0.578119i | \(0.196213\pi\) | |||||||
\(270\) | −0.350881 | −0.0213540 | ||||||||
\(271\) | −26.7417 | −1.62444 | −0.812222 | − | 0.583349i | \(-0.801742\pi\) | ||||
−0.812222 | + | 0.583349i | \(0.801742\pi\) | |||||||
\(272\) | −1.00368 | −0.0608570 | ||||||||
\(273\) | 1.07231 | 0.0648992 | ||||||||
\(274\) | 7.37889 | 0.445775 | ||||||||
\(275\) | −14.1859 | −0.855444 | ||||||||
\(276\) | −0.328710 | −0.0197860 | ||||||||
\(277\) | 0.0718655 | 0.00431798 | 0.00215899 | − | 0.999998i | \(-0.499313\pi\) | ||||
0.00215899 | + | 0.999998i | \(0.499313\pi\) | |||||||
\(278\) | −12.3861 | −0.742869 | ||||||||
\(279\) | 13.5605 | 0.811847 | ||||||||
\(280\) | −0.151677 | −0.00906442 | ||||||||
\(281\) | 16.4509 | 0.981378 | 0.490689 | − | 0.871335i | \(-0.336745\pi\) | ||||
0.490689 | + | 0.871335i | \(0.336745\pi\) | |||||||
\(282\) | −3.63968 | −0.216740 | ||||||||
\(283\) | −19.2773 | −1.14592 | −0.572959 | − | 0.819584i | \(-0.694205\pi\) | ||||
−0.572959 | + | 0.819584i | \(0.694205\pi\) | |||||||
\(284\) | 9.68947 | 0.574964 | ||||||||
\(285\) | 0.140849 | 0.00834318 | ||||||||
\(286\) | −7.72015 | −0.456502 | ||||||||
\(287\) | 3.35096 | 0.197801 | ||||||||
\(288\) | −2.84326 | −0.167541 | ||||||||
\(289\) | −15.9926 | −0.940743 | ||||||||
\(290\) | 0.476439 | 0.0279774 | ||||||||
\(291\) | −2.50824 | −0.147036 | ||||||||
\(292\) | 1.66771 | 0.0975953 | ||||||||
\(293\) | 31.6786 | 1.85068 | 0.925340 | − | 0.379137i | \(-0.123779\pi\) | ||||
0.925340 | + | 0.379137i | \(0.123779\pi\) | |||||||
\(294\) | 0.395900 | 0.0230894 | ||||||||
\(295\) | −0.0818673 | −0.00476650 | ||||||||
\(296\) | 2.32662 | 0.135232 | ||||||||
\(297\) | −6.59374 | −0.382608 | ||||||||
\(298\) | 15.5998 | 0.903671 | ||||||||
\(299\) | 2.24886 | 0.130055 | ||||||||
\(300\) | −1.97039 | −0.113761 | ||||||||
\(301\) | 11.1914 | 0.645064 | ||||||||
\(302\) | −7.65766 | −0.440649 | ||||||||
\(303\) | −1.04626 | −0.0601061 | ||||||||
\(304\) | 2.34557 | 0.134528 | ||||||||
\(305\) | −0.497537 | −0.0284889 | ||||||||
\(306\) | 2.85372 | 0.163137 | ||||||||
\(307\) | −12.1393 | −0.692829 | −0.346415 | − | 0.938082i | \(-0.612601\pi\) | ||||
−0.346415 | + | 0.938082i | \(0.612601\pi\) | |||||||
\(308\) | −2.85030 | −0.162411 | ||||||||
\(309\) | −2.91619 | −0.165896 | ||||||||
\(310\) | −0.723400 | −0.0410864 | ||||||||
\(311\) | −1.46226 | −0.0829174 | −0.0414587 | − | 0.999140i | \(-0.513200\pi\) | ||||
−0.0414587 | + | 0.999140i | \(0.513200\pi\) | |||||||
\(312\) | −1.07231 | −0.0607077 | ||||||||
\(313\) | −7.45357 | −0.421300 | −0.210650 | − | 0.977562i | \(-0.567558\pi\) | ||||
−0.210650 | + | 0.977562i | \(0.567558\pi\) | |||||||
\(314\) | 3.84490 | 0.216980 | ||||||||
\(315\) | 0.431257 | 0.0242986 | ||||||||
\(316\) | 4.67827 | 0.263173 | ||||||||
\(317\) | 8.92427 | 0.501237 | 0.250619 | − | 0.968086i | \(-0.419366\pi\) | ||||
0.250619 | + | 0.968086i | \(0.419366\pi\) | |||||||
\(318\) | 0.357224 | 0.0200321 | ||||||||
\(319\) | 8.95321 | 0.501283 | ||||||||
\(320\) | 0.151677 | 0.00847899 | ||||||||
\(321\) | 1.02066 | 0.0569677 | ||||||||
\(322\) | 0.830286 | 0.0462700 | ||||||||
\(323\) | −2.35420 | −0.130991 | ||||||||
\(324\) | 7.61393 | 0.422996 | ||||||||
\(325\) | 13.4804 | 0.747757 | ||||||||
\(326\) | 21.9243 | 1.21428 | ||||||||
\(327\) | −7.02189 | −0.388311 | ||||||||
\(328\) | −3.35096 | −0.185026 | ||||||||
\(329\) | 9.19342 | 0.506850 | ||||||||
\(330\) | 0.171157 | 0.00942190 | ||||||||
\(331\) | 26.5579 | 1.45975 | 0.729877 | − | 0.683578i | \(-0.239577\pi\) | ||||
0.729877 | + | 0.683578i | \(0.239577\pi\) | |||||||
\(332\) | 13.9915 | 0.767886 | ||||||||
\(333\) | −6.61519 | −0.362510 | ||||||||
\(334\) | −9.30474 | −0.509133 | ||||||||
\(335\) | −1.34771 | −0.0736334 | ||||||||
\(336\) | −0.395900 | −0.0215981 | ||||||||
\(337\) | 22.4767 | 1.22439 | 0.612193 | − | 0.790708i | \(-0.290288\pi\) | ||||
0.612193 | + | 0.790708i | \(0.290288\pi\) | |||||||
\(338\) | −5.66381 | −0.308071 | ||||||||
\(339\) | −6.98933 | −0.379608 | ||||||||
\(340\) | −0.152235 | −0.00825610 | ||||||||
\(341\) | −13.5941 | −0.736161 | ||||||||
\(342\) | −6.66908 | −0.360623 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.1914 | −0.603402 | ||||||||
\(345\) | −0.0498577 | −0.00268425 | ||||||||
\(346\) | −13.3146 | −0.715796 | ||||||||
\(347\) | −8.23114 | −0.441871 | −0.220935 | − | 0.975288i | \(-0.570911\pi\) | ||||
−0.220935 | + | 0.975288i | \(0.570911\pi\) | |||||||
\(348\) | 1.24358 | 0.0666629 | ||||||||
\(349\) | −16.0146 | −0.857240 | −0.428620 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428620 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(350\) | 4.97699 | 0.266032 | ||||||||
\(351\) | 6.26580 | 0.334443 | ||||||||
\(352\) | 2.85030 | 0.151922 | ||||||||
\(353\) | −17.9707 | −0.956486 | −0.478243 | − | 0.878227i | \(-0.658726\pi\) | ||||
−0.478243 | + | 0.878227i | \(0.658726\pi\) | |||||||
\(354\) | −0.213686 | −0.0113573 | ||||||||
\(355\) | 1.46967 | 0.0780019 | ||||||||
\(356\) | −1.06964 | −0.0566910 | ||||||||
\(357\) | 0.397357 | 0.0210304 | ||||||||
\(358\) | 2.54428 | 0.134470 | ||||||||
\(359\) | −7.87372 | −0.415559 | −0.207780 | − | 0.978176i | \(-0.566624\pi\) | ||||
−0.207780 | + | 0.978176i | \(0.566624\pi\) | |||||||
\(360\) | −0.431257 | −0.0227292 | ||||||||
\(361\) | −13.4983 | −0.710436 | ||||||||
\(362\) | 4.36483 | 0.229410 | ||||||||
\(363\) | −1.13852 | −0.0597570 | ||||||||
\(364\) | 2.70854 | 0.141966 | ||||||||
\(365\) | 0.252953 | 0.0132402 | ||||||||
\(366\) | −1.29865 | −0.0678815 | ||||||||
\(367\) | 6.21171 | 0.324249 | 0.162124 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162124 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(368\) | −0.830286 | −0.0432816 | ||||||||
\(369\) | 9.52766 | 0.495990 | ||||||||
\(370\) | 0.352894 | 0.0183461 | ||||||||
\(371\) | −0.902309 | −0.0468456 | ||||||||
\(372\) | −1.88819 | −0.0978980 | ||||||||
\(373\) | 23.3144 | 1.20718 | 0.603588 | − | 0.797297i | \(-0.293737\pi\) | ||||
0.603588 | + | 0.797297i | \(0.293737\pi\) | |||||||
\(374\) | −2.86079 | −0.147928 | ||||||||
\(375\) | −0.599107 | −0.0309378 | ||||||||
\(376\) | −9.19342 | −0.474114 | ||||||||
\(377\) | −8.50791 | −0.438180 | ||||||||
\(378\) | 2.31335 | 0.118986 | ||||||||
\(379\) | 13.6025 | 0.698713 | 0.349357 | − | 0.936990i | \(-0.386400\pi\) | ||||
0.349357 | + | 0.936990i | \(0.386400\pi\) | |||||||
\(380\) | 0.355769 | 0.0182506 | ||||||||
\(381\) | −0.751094 | −0.0384797 | ||||||||
\(382\) | −20.2581 | −1.03649 | ||||||||
\(383\) | −27.4489 | −1.40257 | −0.701287 | − | 0.712879i | \(-0.747391\pi\) | ||||
−0.701287 | + | 0.712879i | \(0.747391\pi\) | |||||||
\(384\) | 0.395900 | 0.0202032 | ||||||||
\(385\) | −0.432324 | −0.0220333 | ||||||||
\(386\) | 25.3832 | 1.29197 | ||||||||
\(387\) | 31.8202 | 1.61751 | ||||||||
\(388\) | −6.33555 | −0.321639 | ||||||||
\(389\) | 29.7462 | 1.50819 | 0.754096 | − | 0.656764i | \(-0.228075\pi\) | ||||
0.754096 | + | 0.656764i | \(0.228075\pi\) | |||||||
\(390\) | −0.162645 | −0.00823584 | ||||||||
\(391\) | 0.833341 | 0.0421439 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −7.31617 | −0.369052 | ||||||||
\(394\) | 5.58473 | 0.281355 | ||||||||
\(395\) | 0.709585 | 0.0357031 | ||||||||
\(396\) | −8.10415 | −0.407249 | ||||||||
\(397\) | 8.96900 | 0.450141 | 0.225071 | − | 0.974342i | \(-0.427739\pi\) | ||||
0.225071 | + | 0.974342i | \(0.427739\pi\) | |||||||
\(398\) | −19.5254 | −0.978718 | ||||||||
\(399\) | −0.928613 | −0.0464888 | ||||||||
\(400\) | −4.97699 | −0.248850 | ||||||||
\(401\) | −31.8397 | −1.59000 | −0.795000 | − | 0.606609i | \(-0.792529\pi\) | ||||
−0.795000 | + | 0.606609i | \(0.792529\pi\) | |||||||
\(402\) | −3.51774 | −0.175449 | ||||||||
\(403\) | 12.9180 | 0.643490 | ||||||||
\(404\) | −2.64274 | −0.131481 | ||||||||
\(405\) | 1.15486 | 0.0573853 | ||||||||
\(406\) | −3.14114 | −0.155892 | ||||||||
\(407\) | 6.63156 | 0.328714 | ||||||||
\(408\) | −0.397357 | −0.0196721 | ||||||||
\(409\) | −10.4532 | −0.516879 | −0.258440 | − | 0.966027i | \(-0.583208\pi\) | ||||
−0.258440 | + | 0.966027i | \(0.583208\pi\) | |||||||
\(410\) | −0.508263 | −0.0251013 | ||||||||
\(411\) | 2.92130 | 0.144097 | ||||||||
\(412\) | −7.36597 | −0.362895 | ||||||||
\(413\) | 0.539748 | 0.0265593 | ||||||||
\(414\) | 2.36072 | 0.116023 | ||||||||
\(415\) | 2.12219 | 0.104174 | ||||||||
\(416\) | −2.70854 | −0.132797 | ||||||||
\(417\) | −4.90366 | −0.240133 | ||||||||
\(418\) | 6.68559 | 0.327003 | ||||||||
\(419\) | −17.1744 | −0.839022 | −0.419511 | − | 0.907750i | \(-0.637799\pi\) | ||||
−0.419511 | + | 0.907750i | \(0.637799\pi\) | |||||||
\(420\) | −0.0600489 | −0.00293008 | ||||||||
\(421\) | 29.5853 | 1.44190 | 0.720949 | − | 0.692988i | \(-0.243706\pi\) | ||||
0.720949 | + | 0.692988i | \(0.243706\pi\) | |||||||
\(422\) | −12.8303 | −0.624569 | ||||||||
\(423\) | 26.1393 | 1.27094 | ||||||||
\(424\) | 0.902309 | 0.0438200 | ||||||||
\(425\) | 4.99531 | 0.242308 | ||||||||
\(426\) | 3.83606 | 0.185858 | ||||||||
\(427\) | 3.28025 | 0.158742 | ||||||||
\(428\) | 2.57808 | 0.124616 | ||||||||
\(429\) | −3.05641 | −0.147565 | ||||||||
\(430\) | −1.69748 | −0.0818598 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −2.31335 | −0.111301 | ||||||||
\(433\) | −26.4582 | −1.27150 | −0.635749 | − | 0.771896i | \(-0.719309\pi\) | ||||
−0.635749 | + | 0.771896i | \(0.719309\pi\) | |||||||
\(434\) | 4.76935 | 0.228936 | ||||||||
\(435\) | 0.188622 | 0.00904374 | ||||||||
\(436\) | −17.7365 | −0.849425 | ||||||||
\(437\) | −1.94750 | −0.0931614 | ||||||||
\(438\) | 0.660247 | 0.0315478 | ||||||||
\(439\) | 34.8667 | 1.66410 | 0.832049 | − | 0.554702i | \(-0.187168\pi\) | ||||
0.832049 | + | 0.554702i | \(0.187168\pi\) | |||||||
\(440\) | 0.432324 | 0.0206103 | ||||||||
\(441\) | −2.84326 | −0.135393 | ||||||||
\(442\) | 2.71851 | 0.129306 | ||||||||
\(443\) | 21.3817 | 1.01588 | 0.507938 | − | 0.861394i | \(-0.330408\pi\) | ||||
0.507938 | + | 0.861394i | \(0.330408\pi\) | |||||||
\(444\) | 0.921109 | 0.0437139 | ||||||||
\(445\) | −0.162240 | −0.00769093 | ||||||||
\(446\) | 21.9733 | 1.04047 | ||||||||
\(447\) | 6.17595 | 0.292113 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −1.49850 | −0.0707186 | −0.0353593 | − | 0.999375i | \(-0.511258\pi\) | ||||
−0.0353593 | + | 0.999375i | \(0.511258\pi\) | |||||||
\(450\) | 14.1509 | 0.667080 | ||||||||
\(451\) | −9.55125 | −0.449751 | ||||||||
\(452\) | −17.6543 | −0.830387 | ||||||||
\(453\) | −3.03167 | −0.142440 | ||||||||
\(454\) | 28.8717 | 1.35501 | ||||||||
\(455\) | 0.410823 | 0.0192597 | ||||||||
\(456\) | 0.928613 | 0.0434863 | ||||||||
\(457\) | 7.11181 | 0.332677 | 0.166338 | − | 0.986069i | \(-0.446806\pi\) | ||||
0.166338 | + | 0.986069i | \(0.446806\pi\) | |||||||
\(458\) | −25.3652 | −1.18524 | ||||||||
\(459\) | 2.32186 | 0.108375 | ||||||||
\(460\) | −0.125935 | −0.00587175 | ||||||||
\(461\) | 5.48316 | 0.255376 | 0.127688 | − | 0.991814i | \(-0.459244\pi\) | ||||
0.127688 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(462\) | −1.12843 | −0.0524995 | ||||||||
\(463\) | 12.5409 | 0.582824 | 0.291412 | − | 0.956598i | \(-0.405875\pi\) | ||||
0.291412 | + | 0.956598i | \(0.405875\pi\) | |||||||
\(464\) | 3.14114 | 0.145824 | ||||||||
\(465\) | −0.286394 | −0.0132812 | ||||||||
\(466\) | −5.57673 | −0.258337 | ||||||||
\(467\) | −12.2467 | −0.566708 | −0.283354 | − | 0.959015i | \(-0.591447\pi\) | ||||
−0.283354 | + | 0.959015i | \(0.591447\pi\) | |||||||
\(468\) | 7.70109 | 0.355983 | ||||||||
\(469\) | 8.88542 | 0.410291 | ||||||||
\(470\) | −1.39443 | −0.0643202 | ||||||||
\(471\) | 1.52220 | 0.0701391 | ||||||||
\(472\) | −0.539748 | −0.0248439 | ||||||||
\(473\) | −31.8990 | −1.46672 | ||||||||
\(474\) | 1.85213 | 0.0850710 | ||||||||
\(475\) | −11.6739 | −0.535636 | ||||||||
\(476\) | 1.00368 | 0.0460036 | ||||||||
\(477\) | −2.56550 | −0.117466 | ||||||||
\(478\) | −29.2351 | −1.33718 | ||||||||
\(479\) | 30.2923 | 1.38409 | 0.692045 | − | 0.721854i | \(-0.256710\pi\) | ||||
0.692045 | + | 0.721854i | \(0.256710\pi\) | |||||||
\(480\) | 0.0600489 | 0.00274084 | ||||||||
\(481\) | −6.30174 | −0.287335 | ||||||||
\(482\) | 0.626558 | 0.0285389 | ||||||||
\(483\) | 0.328710 | 0.0149568 | ||||||||
\(484\) | −2.87579 | −0.130718 | ||||||||
\(485\) | −0.960955 | −0.0436347 | ||||||||
\(486\) | 9.95440 | 0.451541 | ||||||||
\(487\) | 28.9776 | 1.31310 | 0.656549 | − | 0.754283i | \(-0.272015\pi\) | ||||
0.656549 | + | 0.754283i | \(0.272015\pi\) | |||||||
\(488\) | −3.28025 | −0.148490 | ||||||||
\(489\) | 8.67985 | 0.392516 | ||||||||
\(490\) | 0.151677 | 0.00685206 | ||||||||
\(491\) | −0.484813 | −0.0218793 | −0.0109396 | − | 0.999940i | \(-0.503482\pi\) | ||||
−0.0109396 | + | 0.999940i | \(0.503482\pi\) | |||||||
\(492\) | −1.32665 | −0.0598098 | ||||||||
\(493\) | −3.15270 | −0.141991 | ||||||||
\(494\) | −6.35308 | −0.285839 | ||||||||
\(495\) | −1.22921 | −0.0552490 | ||||||||
\(496\) | −4.76935 | −0.214150 | ||||||||
\(497\) | −9.68947 | −0.434632 | ||||||||
\(498\) | 5.53925 | 0.248220 | ||||||||
\(499\) | 9.87310 | 0.441981 | 0.220990 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220990 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(500\) | −1.51328 | −0.0676759 | ||||||||
\(501\) | −3.68375 | −0.164578 | ||||||||
\(502\) | 10.7106 | 0.478040 | ||||||||
\(503\) | 2.07393 | 0.0924719 | 0.0462360 | − | 0.998931i | \(-0.485277\pi\) | ||||
0.0462360 | + | 0.998931i | \(0.485277\pi\) | |||||||
\(504\) | 2.84326 | 0.126649 | ||||||||
\(505\) | −0.400842 | −0.0178373 | ||||||||
\(506\) | −2.36656 | −0.105207 | ||||||||
\(507\) | −2.24230 | −0.0995842 | ||||||||
\(508\) | −1.89718 | −0.0841738 | ||||||||
\(509\) | −3.03420 | −0.134489 | −0.0672443 | − | 0.997737i | \(-0.521421\pi\) | ||||
−0.0672443 | + | 0.997737i | \(0.521421\pi\) | |||||||
\(510\) | −0.0602698 | −0.00266879 | ||||||||
\(511\) | −1.66771 | −0.0737751 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.42613 | −0.239570 | ||||||||
\(514\) | 12.7103 | 0.560626 | ||||||||
\(515\) | −1.11725 | −0.0492318 | ||||||||
\(516\) | −4.43069 | −0.195050 | ||||||||
\(517\) | −26.2040 | −1.15245 | ||||||||
\(518\) | −2.32662 | −0.102226 | ||||||||
\(519\) | −5.27124 | −0.231382 | ||||||||
\(520\) | −0.410823 | −0.0180158 | ||||||||
\(521\) | −30.2969 | −1.32733 | −0.663667 | − | 0.748028i | \(-0.731001\pi\) | ||||
−0.663667 | + | 0.748028i | \(0.731001\pi\) | |||||||
\(522\) | −8.93110 | −0.390904 | ||||||||
\(523\) | −18.2395 | −0.797557 | −0.398778 | − | 0.917047i | \(-0.630566\pi\) | ||||
−0.398778 | + | 0.917047i | \(0.630566\pi\) | |||||||
\(524\) | −18.4798 | −0.807295 | ||||||||
\(525\) | 1.97039 | 0.0859950 | ||||||||
\(526\) | −5.36770 | −0.234043 | ||||||||
\(527\) | 4.78690 | 0.208521 | ||||||||
\(528\) | 1.12843 | 0.0491088 | ||||||||
\(529\) | −22.3106 | −0.970027 | ||||||||
\(530\) | 0.136859 | 0.00594479 | ||||||||
\(531\) | 1.53465 | 0.0665980 | ||||||||
\(532\) | −2.34557 | −0.101694 | ||||||||
\(533\) | 9.07621 | 0.393134 | ||||||||
\(534\) | −0.423472 | −0.0183254 | ||||||||
\(535\) | 0.391034 | 0.0169059 | ||||||||
\(536\) | −8.88542 | −0.383792 | ||||||||
\(537\) | 1.00728 | 0.0434674 | ||||||||
\(538\) | 26.7652 | 1.15393 | ||||||||
\(539\) | 2.85030 | 0.122771 | ||||||||
\(540\) | −0.350881 | −0.0150995 | ||||||||
\(541\) | −22.6644 | −0.974419 | −0.487210 | − | 0.873285i | \(-0.661985\pi\) | ||||
−0.487210 | + | 0.873285i | \(0.661985\pi\) | |||||||
\(542\) | −26.7417 | −1.14866 | ||||||||
\(543\) | 1.72804 | 0.0741571 | ||||||||
\(544\) | −1.00368 | −0.0430324 | ||||||||
\(545\) | −2.69022 | −0.115236 | ||||||||
\(546\) | 1.07231 | 0.0458907 | ||||||||
\(547\) | 12.6896 | 0.542569 | 0.271285 | − | 0.962499i | \(-0.412552\pi\) | ||||
0.271285 | + | 0.962499i | \(0.412552\pi\) | |||||||
\(548\) | 7.37889 | 0.315211 | ||||||||
\(549\) | 9.32660 | 0.398050 | ||||||||
\(550\) | −14.1859 | −0.604890 | ||||||||
\(551\) | 7.36779 | 0.313878 | ||||||||
\(552\) | −0.328710 | −0.0139908 | ||||||||
\(553\) | −4.67827 | −0.198940 | ||||||||
\(554\) | 0.0718655 | 0.00305327 | ||||||||
\(555\) | 0.139711 | 0.00593039 | ||||||||
\(556\) | −12.3861 | −0.525288 | ||||||||
\(557\) | 37.7129 | 1.59795 | 0.798974 | − | 0.601366i | \(-0.205377\pi\) | ||||
0.798974 | + | 0.601366i | \(0.205377\pi\) | |||||||
\(558\) | 13.5605 | 0.574063 | ||||||||
\(559\) | 30.3125 | 1.28208 | ||||||||
\(560\) | −0.151677 | −0.00640951 | ||||||||
\(561\) | −1.13259 | −0.0478178 | ||||||||
\(562\) | 16.4509 | 0.693939 | ||||||||
\(563\) | 29.4977 | 1.24318 | 0.621591 | − | 0.783342i | \(-0.286487\pi\) | ||||
0.621591 | + | 0.783342i | \(0.286487\pi\) | |||||||
\(564\) | −3.63968 | −0.153258 | ||||||||
\(565\) | −2.67774 | −0.112654 | ||||||||
\(566\) | −19.2773 | −0.810286 | ||||||||
\(567\) | −7.61393 | −0.319755 | ||||||||
\(568\) | 9.68947 | 0.406561 | ||||||||
\(569\) | −10.3836 | −0.435301 | −0.217651 | − | 0.976027i | \(-0.569839\pi\) | ||||
−0.217651 | + | 0.976027i | \(0.569839\pi\) | |||||||
\(570\) | 0.140849 | 0.00589952 | ||||||||
\(571\) | −15.1532 | −0.634142 | −0.317071 | − | 0.948402i | \(-0.602699\pi\) | ||||
−0.317071 | + | 0.948402i | \(0.602699\pi\) | |||||||
\(572\) | −7.72015 | −0.322796 | ||||||||
\(573\) | −8.02017 | −0.335047 | ||||||||
\(574\) | 3.35096 | 0.139866 | ||||||||
\(575\) | 4.13233 | 0.172330 | ||||||||
\(576\) | −2.84326 | −0.118469 | ||||||||
\(577\) | −26.9099 | −1.12027 | −0.560137 | − | 0.828400i | \(-0.689252\pi\) | ||||
−0.560137 | + | 0.828400i | \(0.689252\pi\) | |||||||
\(578\) | −15.9926 | −0.665206 | ||||||||
\(579\) | 10.0492 | 0.417632 | ||||||||
\(580\) | 0.476439 | 0.0197830 | ||||||||
\(581\) | −13.9915 | −0.580467 | ||||||||
\(582\) | −2.50824 | −0.103970 | ||||||||
\(583\) | 2.57185 | 0.106515 | ||||||||
\(584\) | 1.66771 | 0.0690103 | ||||||||
\(585\) | 1.16808 | 0.0482940 | ||||||||
\(586\) | 31.6786 | 1.30863 | ||||||||
\(587\) | −24.0191 | −0.991375 | −0.495687 | − | 0.868501i | \(-0.665084\pi\) | ||||
−0.495687 | + | 0.868501i | \(0.665084\pi\) | |||||||
\(588\) | 0.395900 | 0.0163266 | ||||||||
\(589\) | −11.1869 | −0.460947 | ||||||||
\(590\) | −0.0818673 | −0.00337042 | ||||||||
\(591\) | 2.21100 | 0.0909482 | ||||||||
\(592\) | 2.32662 | 0.0956234 | ||||||||
\(593\) | 46.5065 | 1.90979 | 0.954897 | − | 0.296938i | \(-0.0959656\pi\) | ||||
0.954897 | + | 0.296938i | \(0.0959656\pi\) | |||||||
\(594\) | −6.59374 | −0.270544 | ||||||||
\(595\) | 0.152235 | 0.00624102 | ||||||||
\(596\) | 15.5998 | 0.638992 | ||||||||
\(597\) | −7.73009 | −0.316372 | ||||||||
\(598\) | 2.24886 | 0.0919628 | ||||||||
\(599\) | 28.6066 | 1.16883 | 0.584417 | − | 0.811453i | \(-0.301323\pi\) | ||||
0.584417 | + | 0.811453i | \(0.301323\pi\) | |||||||
\(600\) | −1.97039 | −0.0804409 | ||||||||
\(601\) | 1.96721 | 0.0802441 | 0.0401220 | − | 0.999195i | \(-0.487225\pi\) | ||||
0.0401220 | + | 0.999195i | \(0.487225\pi\) | |||||||
\(602\) | 11.1914 | 0.456129 | ||||||||
\(603\) | 25.2636 | 1.02881 | ||||||||
\(604\) | −7.65766 | −0.311586 | ||||||||
\(605\) | −0.436190 | −0.0177336 | ||||||||
\(606\) | −1.04626 | −0.0425015 | ||||||||
\(607\) | −37.0758 | −1.50486 | −0.752430 | − | 0.658673i | \(-0.771118\pi\) | ||||
−0.752430 | + | 0.658673i | \(0.771118\pi\) | |||||||
\(608\) | 2.34557 | 0.0951256 | ||||||||
\(609\) | −1.24358 | −0.0503924 | ||||||||
\(610\) | −0.497537 | −0.0201447 | ||||||||
\(611\) | 24.9007 | 1.00738 | ||||||||
\(612\) | 2.85372 | 0.115355 | ||||||||
\(613\) | 5.14413 | 0.207770 | 0.103885 | − | 0.994589i | \(-0.466873\pi\) | ||||
0.103885 | + | 0.994589i | \(0.466873\pi\) | |||||||
\(614\) | −12.1393 | −0.489904 | ||||||||
\(615\) | −0.201221 | −0.00811403 | ||||||||
\(616\) | −2.85030 | −0.114842 | ||||||||
\(617\) | 17.9122 | 0.721119 | 0.360559 | − | 0.932736i | \(-0.382586\pi\) | ||||
0.360559 | + | 0.932736i | \(0.382586\pi\) | |||||||
\(618\) | −2.91619 | −0.117306 | ||||||||
\(619\) | 32.9535 | 1.32451 | 0.662256 | − | 0.749278i | \(-0.269599\pi\) | ||||
0.662256 | + | 0.749278i | \(0.269599\pi\) | |||||||
\(620\) | −0.723400 | −0.0290525 | ||||||||
\(621\) | 1.92074 | 0.0770767 | ||||||||
\(622\) | −1.46226 | −0.0586314 | ||||||||
\(623\) | 1.06964 | 0.0428544 | ||||||||
\(624\) | −1.07231 | −0.0429268 | ||||||||
\(625\) | 24.6554 | 0.986218 | ||||||||
\(626\) | −7.45357 | −0.297904 | ||||||||
\(627\) | 2.64683 | 0.105704 | ||||||||
\(628\) | 3.84490 | 0.153428 | ||||||||
\(629\) | −2.33518 | −0.0931097 | ||||||||
\(630\) | 0.431257 | 0.0171817 | ||||||||
\(631\) | −40.1058 | −1.59659 | −0.798293 | − | 0.602270i | \(-0.794263\pi\) | ||||
−0.798293 | + | 0.602270i | \(0.794263\pi\) | |||||||
\(632\) | 4.67827 | 0.186092 | ||||||||
\(633\) | −5.07951 | −0.201892 | ||||||||
\(634\) | 8.92427 | 0.354428 | ||||||||
\(635\) | −0.287758 | −0.0114193 | ||||||||
\(636\) | 0.357224 | 0.0141649 | ||||||||
\(637\) | −2.70854 | −0.107316 | ||||||||
\(638\) | 8.95321 | 0.354461 | ||||||||
\(639\) | −27.5497 | −1.08985 | ||||||||
\(640\) | 0.151677 | 0.00599555 | ||||||||
\(641\) | −7.94400 | −0.313769 | −0.156885 | − | 0.987617i | \(-0.550145\pi\) | ||||
−0.156885 | + | 0.987617i | \(0.550145\pi\) | |||||||
\(642\) | 1.02066 | 0.0402823 | ||||||||
\(643\) | 31.7676 | 1.25279 | 0.626397 | − | 0.779504i | \(-0.284529\pi\) | ||||
0.626397 | + | 0.779504i | \(0.284529\pi\) | |||||||
\(644\) | 0.830286 | 0.0327178 | ||||||||
\(645\) | −0.672033 | −0.0264613 | ||||||||
\(646\) | −2.35420 | −0.0926249 | ||||||||
\(647\) | 34.6495 | 1.36221 | 0.681106 | − | 0.732185i | \(-0.261499\pi\) | ||||
0.681106 | + | 0.732185i | \(0.261499\pi\) | |||||||
\(648\) | 7.61393 | 0.299104 | ||||||||
\(649\) | −1.53844 | −0.0603892 | ||||||||
\(650\) | 13.4804 | 0.528744 | ||||||||
\(651\) | 1.88819 | 0.0740039 | ||||||||
\(652\) | 21.9243 | 0.858623 | ||||||||
\(653\) | −15.9056 | −0.622433 | −0.311216 | − | 0.950339i | \(-0.600736\pi\) | ||||
−0.311216 | + | 0.950339i | \(0.600736\pi\) | |||||||
\(654\) | −7.02189 | −0.274578 | ||||||||
\(655\) | −2.80296 | −0.109521 | ||||||||
\(656\) | −3.35096 | −0.130833 | ||||||||
\(657\) | −4.74174 | −0.184993 | ||||||||
\(658\) | 9.19342 | 0.358397 | ||||||||
\(659\) | 36.1413 | 1.40787 | 0.703933 | − | 0.710266i | \(-0.251425\pi\) | ||||
0.703933 | + | 0.710266i | \(0.251425\pi\) | |||||||
\(660\) | 0.171157 | 0.00666229 | ||||||||
\(661\) | 5.86031 | 0.227940 | 0.113970 | − | 0.993484i | \(-0.463643\pi\) | ||||
0.113970 | + | 0.993484i | \(0.463643\pi\) | |||||||
\(662\) | 26.5579 | 1.03220 | ||||||||
\(663\) | 1.07626 | 0.0417983 | ||||||||
\(664\) | 13.9915 | 0.542977 | ||||||||
\(665\) | −0.355769 | −0.0137961 | ||||||||
\(666\) | −6.61519 | −0.256333 | ||||||||
\(667\) | −2.60805 | −0.100984 | ||||||||
\(668\) | −9.30474 | −0.360011 | ||||||||
\(669\) | 8.69925 | 0.336332 | ||||||||
\(670\) | −1.34771 | −0.0520667 | ||||||||
\(671\) | −9.34969 | −0.360941 | ||||||||
\(672\) | −0.395900 | −0.0152722 | ||||||||
\(673\) | 0.806263 | 0.0310791 | 0.0155396 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155396 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(674\) | 22.4767 | 0.865772 | ||||||||
\(675\) | 11.5135 | 0.443156 | ||||||||
\(676\) | −5.66381 | −0.217839 | ||||||||
\(677\) | 18.4218 | 0.708009 | 0.354005 | − | 0.935244i | \(-0.384820\pi\) | ||||
0.354005 | + | 0.935244i | \(0.384820\pi\) | |||||||
\(678\) | −6.98933 | −0.268424 | ||||||||
\(679\) | 6.33555 | 0.243136 | ||||||||
\(680\) | −0.152235 | −0.00583794 | ||||||||
\(681\) | 11.4303 | 0.438010 | ||||||||
\(682\) | −13.5941 | −0.520545 | ||||||||
\(683\) | 26.7634 | 1.02407 | 0.512036 | − | 0.858964i | \(-0.328892\pi\) | ||||
0.512036 | + | 0.858964i | \(0.328892\pi\) | |||||||
\(684\) | −6.66908 | −0.254999 | ||||||||
\(685\) | 1.11921 | 0.0427627 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −10.0421 | −0.383129 | ||||||||
\(688\) | −11.1914 | −0.426670 | ||||||||
\(689\) | −2.44394 | −0.0931067 | ||||||||
\(690\) | −0.0498577 | −0.00189805 | ||||||||
\(691\) | 1.30138 | 0.0495068 | 0.0247534 | − | 0.999694i | \(-0.492120\pi\) | ||||
0.0247534 | + | 0.999694i | \(0.492120\pi\) | |||||||
\(692\) | −13.3146 | −0.506144 | ||||||||
\(693\) | 8.10415 | 0.307851 | ||||||||
\(694\) | −8.23114 | −0.312450 | ||||||||
\(695\) | −1.87869 | −0.0712626 | ||||||||
\(696\) | 1.24358 | 0.0471378 | ||||||||
\(697\) | 3.36329 | 0.127394 | ||||||||
\(698\) | −16.0146 | −0.606161 | ||||||||
\(699\) | −2.20783 | −0.0835078 | ||||||||
\(700\) | 4.97699 | 0.188113 | ||||||||
\(701\) | −37.9923 | −1.43495 | −0.717474 | − | 0.696585i | \(-0.754702\pi\) | ||||
−0.717474 | + | 0.696585i | \(0.754702\pi\) | |||||||
\(702\) | 6.26580 | 0.236487 | ||||||||
\(703\) | 5.45726 | 0.205824 | ||||||||
\(704\) | 2.85030 | 0.107425 | ||||||||
\(705\) | −0.552055 | −0.0207916 | ||||||||
\(706\) | −17.9707 | −0.676338 | ||||||||
\(707\) | 2.64274 | 0.0993905 | ||||||||
\(708\) | −0.213686 | −0.00803083 | ||||||||
\(709\) | 34.7336 | 1.30445 | 0.652224 | − | 0.758026i | \(-0.273836\pi\) | ||||
0.652224 | + | 0.758026i | \(0.273836\pi\) | |||||||
\(710\) | 1.46967 | 0.0551557 | ||||||||
\(711\) | −13.3015 | −0.498847 | ||||||||
\(712\) | −1.06964 | −0.0400866 | ||||||||
\(713\) | 3.95993 | 0.148300 | ||||||||
\(714\) | 0.397357 | 0.0148707 | ||||||||
\(715\) | −1.17097 | −0.0437917 | ||||||||
\(716\) | 2.54428 | 0.0950843 | ||||||||
\(717\) | −11.5742 | −0.432245 | ||||||||
\(718\) | −7.87372 | −0.293845 | ||||||||
\(719\) | 2.02151 | 0.0753896 | 0.0376948 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376948 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(720\) | −0.431257 | −0.0160720 | ||||||||
\(721\) | 7.36597 | 0.274323 | ||||||||
\(722\) | −13.4983 | −0.502354 | ||||||||
\(723\) | 0.248054 | 0.00922525 | ||||||||
\(724\) | 4.36483 | 0.162218 | ||||||||
\(725\) | −15.6335 | −0.580612 | ||||||||
\(726\) | −1.13852 | −0.0422546 | ||||||||
\(727\) | −23.2705 | −0.863054 | −0.431527 | − | 0.902100i | \(-0.642025\pi\) | ||||
−0.431527 | + | 0.902100i | \(0.642025\pi\) | |||||||
\(728\) | 2.70854 | 0.100385 | ||||||||
\(729\) | −18.9009 | −0.700032 | ||||||||
\(730\) | 0.252953 | 0.00936221 | ||||||||
\(731\) | 11.2326 | 0.415453 | ||||||||
\(732\) | −1.29865 | −0.0479995 | ||||||||
\(733\) | −7.55748 | −0.279142 | −0.139571 | − | 0.990212i | \(-0.544572\pi\) | ||||
−0.139571 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(734\) | 6.21171 | 0.229278 | ||||||||
\(735\) | 0.0600489 | 0.00221494 | ||||||||
\(736\) | −0.830286 | −0.0306047 | ||||||||
\(737\) | −25.3261 | −0.932900 | ||||||||
\(738\) | 9.52766 | 0.350718 | ||||||||
\(739\) | 27.3338 | 1.00549 | 0.502745 | − | 0.864435i | \(-0.332323\pi\) | ||||
0.502745 | + | 0.864435i | \(0.332323\pi\) | |||||||
\(740\) | 0.352894 | 0.0129726 | ||||||||
\(741\) | −2.51519 | −0.0923976 | ||||||||
\(742\) | −0.902309 | −0.0331248 | ||||||||
\(743\) | −27.0621 | −0.992812 | −0.496406 | − | 0.868091i | \(-0.665347\pi\) | ||||
−0.496406 | + | 0.868091i | \(0.665347\pi\) | |||||||
\(744\) | −1.88819 | −0.0692243 | ||||||||
\(745\) | 2.36612 | 0.0866881 | ||||||||
\(746\) | 23.3144 | 0.853602 | ||||||||
\(747\) | −39.7816 | −1.45553 | ||||||||
\(748\) | −2.86079 | −0.104601 | ||||||||
\(749\) | −2.57808 | −0.0942008 | ||||||||
\(750\) | −0.599107 | −0.0218763 | ||||||||
\(751\) | 37.4171 | 1.36537 | 0.682684 | − | 0.730713i | \(-0.260812\pi\) | ||||
0.682684 | + | 0.730713i | \(0.260812\pi\) | |||||||
\(752\) | −9.19342 | −0.335250 | ||||||||
\(753\) | 4.24035 | 0.154527 | ||||||||
\(754\) | −8.50791 | −0.309840 | ||||||||
\(755\) | −1.16149 | −0.0422709 | ||||||||
\(756\) | 2.31335 | 0.0841357 | ||||||||
\(757\) | −38.6902 | −1.40622 | −0.703109 | − | 0.711082i | \(-0.748205\pi\) | ||||
−0.703109 | + | 0.711082i | \(0.748205\pi\) | |||||||
\(758\) | 13.6025 | 0.494065 | ||||||||
\(759\) | −0.936923 | −0.0340082 | ||||||||
\(760\) | 0.355769 | 0.0129051 | ||||||||
\(761\) | −18.6624 | −0.676510 | −0.338255 | − | 0.941055i | \(-0.609837\pi\) | ||||
−0.338255 | + | 0.941055i | \(0.609837\pi\) | |||||||
\(762\) | −0.751094 | −0.0272093 | ||||||||
\(763\) | 17.7365 | 0.642105 | ||||||||
\(764\) | −20.2581 | −0.732911 | ||||||||
\(765\) | 0.432844 | 0.0156495 | ||||||||
\(766\) | −27.4489 | −0.991770 | ||||||||
\(767\) | 1.46193 | 0.0527872 | ||||||||
\(768\) | 0.395900 | 0.0142858 | ||||||||
\(769\) | −3.03393 | −0.109406 | −0.0547032 | − | 0.998503i | \(-0.517421\pi\) | ||||
−0.0547032 | + | 0.998503i | \(0.517421\pi\) | |||||||
\(770\) | −0.432324 | −0.0155799 | ||||||||
\(771\) | 5.03200 | 0.181223 | ||||||||
\(772\) | 25.3832 | 0.913562 | ||||||||
\(773\) | 27.8610 | 1.00209 | 0.501046 | − | 0.865421i | \(-0.332949\pi\) | ||||
0.501046 | + | 0.865421i | \(0.332949\pi\) | |||||||
\(774\) | 31.8202 | 1.14375 | ||||||||
\(775\) | 23.7370 | 0.852660 | ||||||||
\(776\) | −6.33555 | −0.227433 | ||||||||
\(777\) | −0.921109 | −0.0330446 | ||||||||
\(778\) | 29.7462 | 1.06645 | ||||||||
\(779\) | −7.85993 | −0.281611 | ||||||||
\(780\) | −0.162645 | −0.00582362 | ||||||||
\(781\) | 27.6179 | 0.988246 | ||||||||
\(782\) | 0.833341 | 0.0298002 | ||||||||
\(783\) | −7.26656 | −0.259686 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0.583182 | 0.0208147 | ||||||||
\(786\) | −7.31617 | −0.260959 | ||||||||
\(787\) | 6.10093 | 0.217475 | 0.108737 | − | 0.994071i | \(-0.465319\pi\) | ||||
0.108737 | + | 0.994071i | \(0.465319\pi\) | |||||||
\(788\) | 5.58473 | 0.198948 | ||||||||
\(789\) | −2.12507 | −0.0756545 | ||||||||
\(790\) | 0.709585 | 0.0252459 | ||||||||
\(791\) | 17.6543 | 0.627714 | ||||||||
\(792\) | −8.10415 | −0.287969 | ||||||||
\(793\) | 8.88467 | 0.315504 | ||||||||
\(794\) | 8.96900 | 0.318298 | ||||||||
\(795\) | 0.0541826 | 0.00192166 | ||||||||
\(796\) | −19.5254 | −0.692058 | ||||||||
\(797\) | 24.3675 | 0.863140 | 0.431570 | − | 0.902079i | \(-0.357960\pi\) | ||||
0.431570 | + | 0.902079i | \(0.357960\pi\) | |||||||
\(798\) | −0.928613 | −0.0328725 | ||||||||
\(799\) | 9.22725 | 0.326437 | ||||||||
\(800\) | −4.97699 | −0.175963 | ||||||||
\(801\) | 3.04128 | 0.107458 | ||||||||
\(802\) | −31.8397 | −1.12430 | ||||||||
\(803\) | 4.75347 | 0.167746 | ||||||||
\(804\) | −3.51774 | −0.124061 | ||||||||
\(805\) | 0.125935 | 0.00443863 | ||||||||
\(806\) | 12.9180 | 0.455016 | ||||||||
\(807\) | 10.5964 | 0.373009 | ||||||||
\(808\) | −2.64274 | −0.0929713 | ||||||||
\(809\) | −49.8699 | −1.75333 | −0.876665 | − | 0.481100i | \(-0.840237\pi\) | ||||
−0.876665 | + | 0.481100i | \(0.840237\pi\) | |||||||
\(810\) | 1.15486 | 0.0405775 | ||||||||
\(811\) | −39.7231 | −1.39487 | −0.697434 | − | 0.716649i | \(-0.745675\pi\) | ||||
−0.697434 | + | 0.716649i | \(0.745675\pi\) | |||||||
\(812\) | −3.14114 | −0.110233 | ||||||||
\(813\) | −10.5871 | −0.371304 | ||||||||
\(814\) | 6.63156 | 0.232436 | ||||||||
\(815\) | 3.32541 | 0.116484 | ||||||||
\(816\) | −0.397357 | −0.0139103 | ||||||||
\(817\) | −26.2503 | −0.918383 | ||||||||
\(818\) | −10.4532 | −0.365489 | ||||||||
\(819\) | −7.70109 | −0.269098 | ||||||||
\(820\) | −0.508263 | −0.0177493 | ||||||||
\(821\) | −5.74872 | −0.200632 | −0.100316 | − | 0.994956i | \(-0.531985\pi\) | ||||
−0.100316 | + | 0.994956i | \(0.531985\pi\) | |||||||
\(822\) | 2.92130 | 0.101892 | ||||||||
\(823\) | −10.5288 | −0.367012 | −0.183506 | − | 0.983019i | \(-0.558745\pi\) | ||||
−0.183506 | + | 0.983019i | \(0.558745\pi\) | |||||||
\(824\) | −7.36597 | −0.256606 | ||||||||
\(825\) | −5.61621 | −0.195531 | ||||||||
\(826\) | 0.539748 | 0.0187802 | ||||||||
\(827\) | 2.75411 | 0.0957699 | 0.0478849 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478849 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(828\) | 2.36072 | 0.0820407 | ||||||||
\(829\) | 13.2129 | 0.458903 | 0.229451 | − | 0.973320i | \(-0.426307\pi\) | ||||
0.229451 | + | 0.973320i | \(0.426307\pi\) | |||||||
\(830\) | 2.12219 | 0.0736624 | ||||||||
\(831\) | 0.0284516 | 0.000986974 0 | ||||||||
\(832\) | −2.70854 | −0.0939017 | ||||||||
\(833\) | −1.00368 | −0.0347754 | ||||||||
\(834\) | −4.90366 | −0.169800 | ||||||||
\(835\) | −1.41131 | −0.0488405 | ||||||||
\(836\) | 6.68559 | 0.231226 | ||||||||
\(837\) | 11.0332 | 0.381362 | ||||||||
\(838\) | −17.1744 | −0.593278 | ||||||||
\(839\) | −35.9953 | −1.24270 | −0.621348 | − | 0.783535i | \(-0.713415\pi\) | ||||
−0.621348 | + | 0.783535i | \(0.713415\pi\) | |||||||
\(840\) | −0.0600489 | −0.00207188 | ||||||||
\(841\) | −19.1332 | −0.659766 | ||||||||
\(842\) | 29.5853 | 1.01958 | ||||||||
\(843\) | 6.51291 | 0.224317 | ||||||||
\(844\) | −12.8303 | −0.441637 | ||||||||
\(845\) | −0.859069 | −0.0295529 | ||||||||
\(846\) | 26.1393 | 0.898688 | ||||||||
\(847\) | 2.87579 | 0.0988132 | ||||||||
\(848\) | 0.902309 | 0.0309854 | ||||||||
\(849\) | −7.63190 | −0.261926 | ||||||||
\(850\) | 4.99531 | 0.171338 | ||||||||
\(851\) | −1.93176 | −0.0662198 | ||||||||
\(852\) | 3.83606 | 0.131421 | ||||||||
\(853\) | −24.2029 | −0.828691 | −0.414346 | − | 0.910120i | \(-0.635990\pi\) | ||||
−0.414346 | + | 0.910120i | \(0.635990\pi\) | |||||||
\(854\) | 3.28025 | 0.112248 | ||||||||
\(855\) | −1.01155 | −0.0345941 | ||||||||
\(856\) | 2.57808 | 0.0881168 | ||||||||
\(857\) | −31.6458 | −1.08100 | −0.540501 | − | 0.841344i | \(-0.681765\pi\) | ||||
−0.540501 | + | 0.841344i | \(0.681765\pi\) | |||||||
\(858\) | −3.05641 | −0.104344 | ||||||||
\(859\) | 23.9937 | 0.818656 | 0.409328 | − | 0.912387i | \(-0.365763\pi\) | ||||
0.409328 | + | 0.912387i | \(0.365763\pi\) | |||||||
\(860\) | −1.69748 | −0.0578836 | ||||||||
\(861\) | 1.32665 | 0.0452120 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | 38.5603 | 1.31261 | 0.656304 | − | 0.754496i | \(-0.272119\pi\) | ||||
0.656304 | + | 0.754496i | \(0.272119\pi\) | |||||||
\(864\) | −2.31335 | −0.0787017 | ||||||||
\(865\) | −2.01951 | −0.0686655 | ||||||||
\(866\) | −26.4582 | −0.899085 | ||||||||
\(867\) | −6.33148 | −0.215028 | ||||||||
\(868\) | 4.76935 | 0.161882 | ||||||||
\(869\) | 13.3345 | 0.452341 | ||||||||
\(870\) | 0.188622 | 0.00639489 | ||||||||
\(871\) | 24.0665 | 0.815463 | ||||||||
\(872\) | −17.7365 | −0.600634 | ||||||||
\(873\) | 18.0136 | 0.609669 | ||||||||
\(874\) | −1.94750 | −0.0658751 | ||||||||
\(875\) | 1.51328 | 0.0511582 | ||||||||
\(876\) | 0.660247 | 0.0223077 | ||||||||
\(877\) | −17.9125 | −0.604864 | −0.302432 | − | 0.953171i | \(-0.597798\pi\) | ||||
−0.302432 | + | 0.953171i | \(0.597798\pi\) | |||||||
\(878\) | 34.8667 | 1.17670 | ||||||||
\(879\) | 12.5415 | 0.423016 | ||||||||
\(880\) | 0.432324 | 0.0145737 | ||||||||
\(881\) | −39.4006 | −1.32744 | −0.663720 | − | 0.747981i | \(-0.731023\pi\) | ||||
−0.663720 | + | 0.747981i | \(0.731023\pi\) | |||||||
\(882\) | −2.84326 | −0.0957376 | ||||||||
\(883\) | −7.44940 | −0.250692 | −0.125346 | − | 0.992113i | \(-0.540004\pi\) | ||||
−0.125346 | + | 0.992113i | \(0.540004\pi\) | |||||||
\(884\) | 2.71851 | 0.0914332 | ||||||||
\(885\) | −0.0324113 | −0.00108949 | ||||||||
\(886\) | 21.3817 | 0.718333 | ||||||||
\(887\) | −56.6982 | −1.90374 | −0.951869 | − | 0.306505i | \(-0.900840\pi\) | ||||
−0.951869 | + | 0.306505i | \(0.900840\pi\) | |||||||
\(888\) | 0.921109 | 0.0309104 | ||||||||
\(889\) | 1.89718 | 0.0636294 | ||||||||
\(890\) | −0.162240 | −0.00543831 | ||||||||
\(891\) | 21.7020 | 0.727044 | ||||||||
\(892\) | 21.9733 | 0.735722 | ||||||||
\(893\) | −21.5638 | −0.721607 | ||||||||
\(894\) | 6.17595 | 0.206555 | ||||||||
\(895\) | 0.385909 | 0.0128995 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0.890325 | 0.0297271 | ||||||||
\(898\) | −1.49850 | −0.0500056 | ||||||||
\(899\) | −14.9812 | −0.499652 | ||||||||
\(900\) | 14.1509 | 0.471697 | ||||||||
\(901\) | −0.905629 | −0.0301709 | ||||||||
\(902\) | −9.55125 | −0.318022 | ||||||||
\(903\) | 4.43069 | 0.147444 | ||||||||
\(904\) | −17.6543 | −0.587172 | ||||||||
\(905\) | 0.662043 | 0.0220071 | ||||||||
\(906\) | −3.03167 | −0.100720 | ||||||||
\(907\) | −14.2665 | −0.473711 | −0.236856 | − | 0.971545i | \(-0.576117\pi\) | ||||
−0.236856 | + | 0.971545i | \(0.576117\pi\) | |||||||
\(908\) | 28.8717 | 0.958140 | ||||||||
\(909\) | 7.51401 | 0.249224 | ||||||||
\(910\) | 0.410823 | 0.0136186 | ||||||||
\(911\) | 15.5405 | 0.514880 | 0.257440 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257440 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(912\) | 0.928613 | 0.0307495 | ||||||||
\(913\) | 39.8801 | 1.31984 | ||||||||
\(914\) | 7.11181 | 0.235238 | ||||||||
\(915\) | −0.196975 | −0.00651179 | ||||||||
\(916\) | −25.3652 | −0.838089 | ||||||||
\(917\) | 18.4798 | 0.610258 | ||||||||
\(918\) | 2.32186 | 0.0766328 | ||||||||
\(919\) | 0.128723 | 0.00424617 | 0.00212308 | − | 0.999998i | \(-0.499324\pi\) | ||||
0.00212308 | + | 0.999998i | \(0.499324\pi\) | |||||||
\(920\) | −0.125935 | −0.00415196 | ||||||||
\(921\) | −4.80597 | −0.158362 | ||||||||
\(922\) | 5.48316 | 0.180578 | ||||||||
\(923\) | −26.2443 | −0.863842 | ||||||||
\(924\) | −1.12843 | −0.0371228 | ||||||||
\(925\) | −11.5796 | −0.380734 | ||||||||
\(926\) | 12.5409 | 0.412119 | ||||||||
\(927\) | 20.9434 | 0.687871 | ||||||||
\(928\) | 3.14114 | 0.103113 | ||||||||
\(929\) | −50.4325 | −1.65464 | −0.827319 | − | 0.561732i | \(-0.810135\pi\) | ||||
−0.827319 | + | 0.561732i | \(0.810135\pi\) | |||||||
\(930\) | −0.286394 | −0.00939124 | ||||||||
\(931\) | 2.34557 | 0.0768731 | ||||||||
\(932\) | −5.57673 | −0.182672 | ||||||||
\(933\) | −0.578911 | −0.0189527 | ||||||||
\(934\) | −12.2467 | −0.400723 | ||||||||
\(935\) | −0.433915 | −0.0141905 | ||||||||
\(936\) | 7.70109 | 0.251718 | ||||||||
\(937\) | −5.71367 | −0.186657 | −0.0933287 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933287 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(938\) | 8.88542 | 0.290119 | ||||||||
\(939\) | −2.95087 | −0.0962979 | ||||||||
\(940\) | −1.39443 | −0.0454812 | ||||||||
\(941\) | 0.0891990 | 0.00290780 | 0.00145390 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145390 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(942\) | 1.52220 | 0.0495958 | ||||||||
\(943\) | 2.78226 | 0.0906027 | ||||||||
\(944\) | −0.539748 | −0.0175673 | ||||||||
\(945\) | 0.350881 | 0.0114142 | ||||||||
\(946\) | −31.8990 | −1.03712 | ||||||||
\(947\) | 29.5625 | 0.960652 | 0.480326 | − | 0.877090i | \(-0.340518\pi\) | ||||
0.480326 | + | 0.877090i | \(0.340518\pi\) | |||||||
\(948\) | 1.85213 | 0.0601543 | ||||||||
\(949\) | −4.51706 | −0.146630 | ||||||||
\(950\) | −11.6739 | −0.378752 | ||||||||
\(951\) | 3.53312 | 0.114569 | ||||||||
\(952\) | 1.00368 | 0.0325294 | ||||||||
\(953\) | 24.1278 | 0.781577 | 0.390788 | − | 0.920481i | \(-0.372202\pi\) | ||||
0.390788 | + | 0.920481i | \(0.372202\pi\) | |||||||
\(954\) | −2.56550 | −0.0830612 | ||||||||
\(955\) | −3.07268 | −0.0994295 | ||||||||
\(956\) | −29.2351 | −0.945530 | ||||||||
\(957\) | 3.54458 | 0.114580 | ||||||||
\(958\) | 30.2923 | 0.978700 | ||||||||
\(959\) | −7.37889 | −0.238277 | ||||||||
\(960\) | 0.0600489 | 0.00193807 | ||||||||
\(961\) | −8.25327 | −0.266235 | ||||||||
\(962\) | −6.30174 | −0.203176 | ||||||||
\(963\) | −7.33015 | −0.236211 | ||||||||
\(964\) | 0.626558 | 0.0201801 | ||||||||
\(965\) | 3.85005 | 0.123937 | ||||||||
\(966\) | 0.328710 | 0.0105761 | ||||||||
\(967\) | −10.9786 | −0.353048 | −0.176524 | − | 0.984296i | \(-0.556485\pi\) | ||||
−0.176524 | + | 0.984296i | \(0.556485\pi\) | |||||||
\(968\) | −2.87579 | −0.0924313 | ||||||||
\(969\) | −0.932030 | −0.0299411 | ||||||||
\(970\) | −0.960955 | −0.0308544 | ||||||||
\(971\) | −0.692288 | −0.0222166 | −0.0111083 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111083 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(972\) | 9.95440 | 0.319288 | ||||||||
\(973\) | 12.3861 | 0.397080 | ||||||||
\(974\) | 28.9776 | 0.928501 | ||||||||
\(975\) | 5.33689 | 0.170917 | ||||||||
\(976\) | −3.28025 | −0.104998 | ||||||||
\(977\) | 22.0437 | 0.705240 | 0.352620 | − | 0.935767i | \(-0.385291\pi\) | ||||
0.352620 | + | 0.935767i | \(0.385291\pi\) | |||||||
\(978\) | 8.67985 | 0.277551 | ||||||||
\(979\) | −3.04881 | −0.0974403 | ||||||||
\(980\) | 0.151677 | 0.00484514 | ||||||||
\(981\) | 50.4296 | 1.61009 | ||||||||
\(982\) | −0.484813 | −0.0154710 | ||||||||
\(983\) | 53.9526 | 1.72082 | 0.860410 | − | 0.509603i | \(-0.170208\pi\) | ||||
0.860410 | + | 0.509603i | \(0.170208\pi\) | |||||||
\(984\) | −1.32665 | −0.0422919 | ||||||||
\(985\) | 0.847074 | 0.0269900 | ||||||||
\(986\) | −3.15270 | −0.100402 | ||||||||
\(987\) | 3.63968 | 0.115852 | ||||||||
\(988\) | −6.35308 | −0.202118 | ||||||||
\(989\) | 9.29209 | 0.295471 | ||||||||
\(990\) | −1.22921 | −0.0390669 | ||||||||
\(991\) | 19.2823 | 0.612522 | 0.306261 | − | 0.951948i | \(-0.400922\pi\) | ||||
0.306261 | + | 0.951948i | \(0.400922\pi\) | |||||||
\(992\) | −4.76935 | −0.151427 | ||||||||
\(993\) | 10.5143 | 0.333661 | ||||||||
\(994\) | −9.68947 | −0.307331 | ||||||||
\(995\) | −2.96154 | −0.0938872 | ||||||||
\(996\) | 5.53925 | 0.175518 | ||||||||
\(997\) | −17.2621 | −0.546696 | −0.273348 | − | 0.961915i | \(-0.588131\pi\) | ||||
−0.273348 | + | 0.961915i | \(0.588131\pi\) | |||||||
\(998\) | 9.87310 | 0.312527 | ||||||||
\(999\) | −5.38228 | −0.170288 |
(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 | 6034.2.a.l.1.10 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.l.1.10 | ✓ | 20 | 1.1 | even | 1 | trivial |