Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.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: | \(64.1198728231\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 6 x^{13} + 136 x^{12} - 149 x^{11} - 876 x^{10} + 1631 x^{9} + 2142 x^{8} - 5473 x^{7} - 1914 x^{6} + 7517 x^{5} + 392 x^{4} - 3966 x^{3} - 79 x^{2} + 491 x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.35747\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-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 | ||||||||
\(3\) | 1.35747 | 0.783737 | 0.391869 | − | 0.920021i | \(-0.371829\pi\) | ||||
0.391869 | + | 0.920021i | \(0.371829\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.35747 | 0.554186 | ||||||||
\(7\) | 0.608019 | 0.229809 | 0.114905 | − | 0.993377i | \(-0.463344\pi\) | ||||
0.114905 | + | 0.993377i | \(0.463344\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.15727 | −0.385756 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.35747 | 0.391869 | ||||||||
\(13\) | −1.27461 | −0.353514 | −0.176757 | − | 0.984254i | \(-0.556561\pi\) | ||||
−0.176757 | + | 0.984254i | \(0.556561\pi\) | |||||||
\(14\) | 0.608019 | 0.162500 | ||||||||
\(15\) | −1.35747 | −0.350498 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.40721 | 1.31144 | 0.655721 | − | 0.755004i | \(-0.272365\pi\) | ||||
0.655721 | + | 0.755004i | \(0.272365\pi\) | |||||||
\(18\) | −1.15727 | −0.272771 | ||||||||
\(19\) | −5.57690 | −1.27943 | −0.639715 | − | 0.768612i | \(-0.720948\pi\) | ||||
−0.639715 | + | 0.768612i | \(0.720948\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.825369 | 0.180110 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 6.46978 | 1.34904 | 0.674521 | − | 0.738255i | \(-0.264350\pi\) | ||||
0.674521 | + | 0.738255i | \(0.264350\pi\) | |||||||
\(24\) | 1.35747 | 0.277093 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.27461 | −0.249972 | ||||||||
\(27\) | −5.64338 | −1.08607 | ||||||||
\(28\) | 0.608019 | 0.114905 | ||||||||
\(29\) | 5.96812 | 1.10825 | 0.554126 | − | 0.832433i | \(-0.313053\pi\) | ||||
0.554126 | + | 0.832433i | \(0.313053\pi\) | |||||||
\(30\) | −1.35747 | −0.247839 | ||||||||
\(31\) | 3.61424 | 0.649137 | 0.324569 | − | 0.945862i | \(-0.394781\pi\) | ||||
0.324569 | + | 0.945862i | \(0.394781\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.35747 | −0.236306 | ||||||||
\(34\) | 5.40721 | 0.927329 | ||||||||
\(35\) | −0.608019 | −0.102774 | ||||||||
\(36\) | −1.15727 | −0.192878 | ||||||||
\(37\) | 3.57853 | 0.588306 | 0.294153 | − | 0.955758i | \(-0.404962\pi\) | ||||
0.294153 | + | 0.955758i | \(0.404962\pi\) | |||||||
\(38\) | −5.57690 | −0.904693 | ||||||||
\(39\) | −1.73025 | −0.277062 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 4.81019 | 0.751226 | 0.375613 | − | 0.926777i | \(-0.377432\pi\) | ||||
0.375613 | + | 0.926777i | \(0.377432\pi\) | |||||||
\(42\) | 0.825369 | 0.127357 | ||||||||
\(43\) | 4.63923 | 0.707476 | 0.353738 | − | 0.935344i | \(-0.384910\pi\) | ||||
0.353738 | + | 0.935344i | \(0.384910\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.15727 | 0.172515 | ||||||||
\(46\) | 6.46978 | 0.953917 | ||||||||
\(47\) | −3.42434 | −0.499491 | −0.249746 | − | 0.968312i | \(-0.580347\pi\) | ||||
−0.249746 | + | 0.968312i | \(0.580347\pi\) | |||||||
\(48\) | 1.35747 | 0.195934 | ||||||||
\(49\) | −6.63031 | −0.947188 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 7.34014 | 1.02783 | ||||||||
\(52\) | −1.27461 | −0.176757 | ||||||||
\(53\) | 6.33551 | 0.870250 | 0.435125 | − | 0.900370i | \(-0.356704\pi\) | ||||
0.435125 | + | 0.900370i | \(0.356704\pi\) | |||||||
\(54\) | −5.64338 | −0.767966 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0.608019 | 0.0812499 | ||||||||
\(57\) | −7.57049 | −1.00274 | ||||||||
\(58\) | 5.96812 | 0.783653 | ||||||||
\(59\) | 8.43549 | 1.09821 | 0.549104 | − | 0.835754i | \(-0.314969\pi\) | ||||
0.549104 | + | 0.835754i | \(0.314969\pi\) | |||||||
\(60\) | −1.35747 | −0.175249 | ||||||||
\(61\) | −11.5083 | −1.47348 | −0.736740 | − | 0.676176i | \(-0.763636\pi\) | ||||
−0.736740 | + | 0.676176i | \(0.763636\pi\) | |||||||
\(62\) | 3.61424 | 0.459009 | ||||||||
\(63\) | −0.703640 | −0.0886503 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.27461 | 0.158096 | ||||||||
\(66\) | −1.35747 | −0.167093 | ||||||||
\(67\) | 3.72409 | 0.454970 | 0.227485 | − | 0.973782i | \(-0.426950\pi\) | ||||
0.227485 | + | 0.973782i | \(0.426950\pi\) | |||||||
\(68\) | 5.40721 | 0.655721 | ||||||||
\(69\) | 8.78255 | 1.05730 | ||||||||
\(70\) | −0.608019 | −0.0726721 | ||||||||
\(71\) | −10.2186 | −1.21272 | −0.606362 | − | 0.795189i | \(-0.707372\pi\) | ||||
−0.606362 | + | 0.795189i | \(0.707372\pi\) | |||||||
\(72\) | −1.15727 | −0.136385 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | 3.57853 | 0.415995 | ||||||||
\(75\) | 1.35747 | 0.156747 | ||||||||
\(76\) | −5.57690 | −0.639715 | ||||||||
\(77\) | −0.608019 | −0.0692902 | ||||||||
\(78\) | −1.73025 | −0.195913 | ||||||||
\(79\) | 1.90817 | 0.214685 | 0.107343 | − | 0.994222i | \(-0.465766\pi\) | ||||
0.107343 | + | 0.994222i | \(0.465766\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −4.18893 | −0.465436 | ||||||||
\(82\) | 4.81019 | 0.531197 | ||||||||
\(83\) | 1.16567 | 0.127949 | 0.0639745 | − | 0.997952i | \(-0.479622\pi\) | ||||
0.0639745 | + | 0.997952i | \(0.479622\pi\) | |||||||
\(84\) | 0.825369 | 0.0900551 | ||||||||
\(85\) | −5.40721 | −0.586494 | ||||||||
\(86\) | 4.63923 | 0.500261 | ||||||||
\(87\) | 8.10156 | 0.868579 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 14.1616 | 1.50112 | 0.750561 | − | 0.660801i | \(-0.229783\pi\) | ||||
0.750561 | + | 0.660801i | \(0.229783\pi\) | |||||||
\(90\) | 1.15727 | 0.121987 | ||||||||
\(91\) | −0.774989 | −0.0812409 | ||||||||
\(92\) | 6.46978 | 0.674521 | ||||||||
\(93\) | 4.90624 | 0.508753 | ||||||||
\(94\) | −3.42434 | −0.353193 | ||||||||
\(95\) | 5.57690 | 0.572178 | ||||||||
\(96\) | 1.35747 | 0.138546 | ||||||||
\(97\) | −4.84035 | −0.491464 | −0.245732 | − | 0.969338i | \(-0.579028\pi\) | ||||
−0.245732 | + | 0.969338i | \(0.579028\pi\) | |||||||
\(98\) | −6.63031 | −0.669763 | ||||||||
\(99\) | 1.15727 | 0.116310 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.27870 | 0.326243 | 0.163122 | − | 0.986606i | \(-0.447844\pi\) | ||||
0.163122 | + | 0.986606i | \(0.447844\pi\) | |||||||
\(102\) | 7.34014 | 0.726782 | ||||||||
\(103\) | 6.53669 | 0.644080 | 0.322040 | − | 0.946726i | \(-0.395632\pi\) | ||||
0.322040 | + | 0.946726i | \(0.395632\pi\) | |||||||
\(104\) | −1.27461 | −0.124986 | ||||||||
\(105\) | −0.825369 | −0.0805477 | ||||||||
\(106\) | 6.33551 | 0.615359 | ||||||||
\(107\) | 13.5564 | 1.31055 | 0.655275 | − | 0.755390i | \(-0.272553\pi\) | ||||
0.655275 | + | 0.755390i | \(0.272553\pi\) | |||||||
\(108\) | −5.64338 | −0.543034 | ||||||||
\(109\) | −2.59741 | −0.248786 | −0.124393 | − | 0.992233i | \(-0.539698\pi\) | ||||
−0.124393 | + | 0.992233i | \(0.539698\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 4.85775 | 0.461078 | ||||||||
\(112\) | 0.608019 | 0.0574524 | ||||||||
\(113\) | 19.6270 | 1.84636 | 0.923178 | − | 0.384373i | \(-0.125582\pi\) | ||||
0.923178 | + | 0.384373i | \(0.125582\pi\) | |||||||
\(114\) | −7.57049 | −0.709042 | ||||||||
\(115\) | −6.46978 | −0.603310 | ||||||||
\(116\) | 5.96812 | 0.554126 | ||||||||
\(117\) | 1.47507 | 0.136370 | ||||||||
\(118\) | 8.43549 | 0.776550 | ||||||||
\(119\) | 3.28768 | 0.301382 | ||||||||
\(120\) | −1.35747 | −0.123920 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.5083 | −1.04191 | ||||||||
\(123\) | 6.52971 | 0.588764 | ||||||||
\(124\) | 3.61424 | 0.324569 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.703640 | −0.0626853 | ||||||||
\(127\) | 4.68487 | 0.415715 | 0.207858 | − | 0.978159i | \(-0.433351\pi\) | ||||
0.207858 | + | 0.978159i | \(0.433351\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.29763 | 0.554476 | ||||||||
\(130\) | 1.27461 | 0.111791 | ||||||||
\(131\) | 2.46553 | 0.215414 | 0.107707 | − | 0.994183i | \(-0.465649\pi\) | ||||
0.107707 | + | 0.994183i | \(0.465649\pi\) | |||||||
\(132\) | −1.35747 | −0.118153 | ||||||||
\(133\) | −3.39086 | −0.294025 | ||||||||
\(134\) | 3.72409 | 0.321713 | ||||||||
\(135\) | 5.64338 | 0.485705 | ||||||||
\(136\) | 5.40721 | 0.463664 | ||||||||
\(137\) | −8.44166 | −0.721220 | −0.360610 | − | 0.932717i | \(-0.617431\pi\) | ||||
−0.360610 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(138\) | 8.78255 | 0.747620 | ||||||||
\(139\) | 20.5520 | 1.74320 | 0.871600 | − | 0.490218i | \(-0.163083\pi\) | ||||
0.871600 | + | 0.490218i | \(0.163083\pi\) | |||||||
\(140\) | −0.608019 | −0.0513870 | ||||||||
\(141\) | −4.64845 | −0.391470 | ||||||||
\(142\) | −10.2186 | −0.857525 | ||||||||
\(143\) | 1.27461 | 0.106589 | ||||||||
\(144\) | −1.15727 | −0.0964390 | ||||||||
\(145\) | −5.96812 | −0.495625 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | −9.00047 | −0.742346 | ||||||||
\(148\) | 3.57853 | 0.294153 | ||||||||
\(149\) | −1.05695 | −0.0865883 | −0.0432942 | − | 0.999062i | \(-0.513785\pi\) | ||||
−0.0432942 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(150\) | 1.35747 | 0.110837 | ||||||||
\(151\) | 10.2067 | 0.830607 | 0.415304 | − | 0.909683i | \(-0.363675\pi\) | ||||
0.415304 | + | 0.909683i | \(0.363675\pi\) | |||||||
\(152\) | −5.57690 | −0.452347 | ||||||||
\(153\) | −6.25759 | −0.505896 | ||||||||
\(154\) | −0.608019 | −0.0489955 | ||||||||
\(155\) | −3.61424 | −0.290303 | ||||||||
\(156\) | −1.73025 | −0.138531 | ||||||||
\(157\) | 7.28511 | 0.581415 | 0.290707 | − | 0.956812i | \(-0.406109\pi\) | ||||
0.290707 | + | 0.956812i | \(0.406109\pi\) | |||||||
\(158\) | 1.90817 | 0.151806 | ||||||||
\(159\) | 8.60029 | 0.682047 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.93375 | 0.310023 | ||||||||
\(162\) | −4.18893 | −0.329113 | ||||||||
\(163\) | 3.70131 | 0.289909 | 0.144955 | − | 0.989438i | \(-0.453696\pi\) | ||||
0.144955 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(164\) | 4.81019 | 0.375613 | ||||||||
\(165\) | 1.35747 | 0.105679 | ||||||||
\(166\) | 1.16567 | 0.0904736 | ||||||||
\(167\) | 14.8922 | 1.15239 | 0.576197 | − | 0.817311i | \(-0.304536\pi\) | ||||
0.576197 | + | 0.817311i | \(0.304536\pi\) | |||||||
\(168\) | 0.825369 | 0.0636786 | ||||||||
\(169\) | −11.3754 | −0.875028 | ||||||||
\(170\) | −5.40721 | −0.414714 | ||||||||
\(171\) | 6.45397 | 0.493547 | ||||||||
\(172\) | 4.63923 | 0.353738 | ||||||||
\(173\) | 4.99951 | 0.380106 | 0.190053 | − | 0.981774i | \(-0.439134\pi\) | ||||
0.190053 | + | 0.981774i | \(0.439134\pi\) | |||||||
\(174\) | 8.10156 | 0.614178 | ||||||||
\(175\) | 0.608019 | 0.0459619 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 11.4510 | 0.860706 | ||||||||
\(178\) | 14.1616 | 1.06145 | ||||||||
\(179\) | −20.3087 | −1.51794 | −0.758970 | − | 0.651126i | \(-0.774297\pi\) | ||||
−0.758970 | + | 0.651126i | \(0.774297\pi\) | |||||||
\(180\) | 1.15727 | 0.0862576 | ||||||||
\(181\) | −12.2620 | −0.911425 | −0.455713 | − | 0.890127i | \(-0.650615\pi\) | ||||
−0.455713 | + | 0.890127i | \(0.650615\pi\) | |||||||
\(182\) | −0.774989 | −0.0574460 | ||||||||
\(183\) | −15.6221 | −1.15482 | ||||||||
\(184\) | 6.46978 | 0.476959 | ||||||||
\(185\) | −3.57853 | −0.263099 | ||||||||
\(186\) | 4.90624 | 0.359743 | ||||||||
\(187\) | −5.40721 | −0.395414 | ||||||||
\(188\) | −3.42434 | −0.249746 | ||||||||
\(189\) | −3.43128 | −0.249589 | ||||||||
\(190\) | 5.57690 | 0.404591 | ||||||||
\(191\) | −18.4536 | −1.33526 | −0.667628 | − | 0.744495i | \(-0.732690\pi\) | ||||
−0.667628 | + | 0.744495i | \(0.732690\pi\) | |||||||
\(192\) | 1.35747 | 0.0979672 | ||||||||
\(193\) | 18.2662 | 1.31483 | 0.657415 | − | 0.753529i | \(-0.271650\pi\) | ||||
0.657415 | + | 0.753529i | \(0.271650\pi\) | |||||||
\(194\) | −4.84035 | −0.347517 | ||||||||
\(195\) | 1.73025 | 0.123906 | ||||||||
\(196\) | −6.63031 | −0.473594 | ||||||||
\(197\) | 12.1870 | 0.868288 | 0.434144 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434144 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(198\) | 1.15727 | 0.0822434 | ||||||||
\(199\) | 18.6779 | 1.32404 | 0.662021 | − | 0.749485i | \(-0.269699\pi\) | ||||
0.662021 | + | 0.749485i | \(0.269699\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 5.05535 | 0.356577 | ||||||||
\(202\) | 3.27870 | 0.230689 | ||||||||
\(203\) | 3.62873 | 0.254687 | ||||||||
\(204\) | 7.34014 | 0.513913 | ||||||||
\(205\) | −4.81019 | −0.335959 | ||||||||
\(206\) | 6.53669 | 0.455433 | ||||||||
\(207\) | −7.48727 | −0.520401 | ||||||||
\(208\) | −1.27461 | −0.0883786 | ||||||||
\(209\) | 5.57690 | 0.385762 | ||||||||
\(210\) | −0.825369 | −0.0569559 | ||||||||
\(211\) | −5.62682 | −0.387366 | −0.193683 | − | 0.981064i | \(-0.562043\pi\) | ||||
−0.193683 | + | 0.981064i | \(0.562043\pi\) | |||||||
\(212\) | 6.33551 | 0.435125 | ||||||||
\(213\) | −13.8715 | −0.950457 | ||||||||
\(214\) | 13.5564 | 0.926699 | ||||||||
\(215\) | −4.63923 | −0.316393 | ||||||||
\(216\) | −5.64338 | −0.383983 | ||||||||
\(217\) | 2.19753 | 0.149178 | ||||||||
\(218\) | −2.59741 | −0.175919 | ||||||||
\(219\) | −1.35747 | −0.0917295 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −6.89210 | −0.463613 | ||||||||
\(222\) | 4.85775 | 0.326031 | ||||||||
\(223\) | 15.6774 | 1.04983 | 0.524917 | − | 0.851153i | \(-0.324096\pi\) | ||||
0.524917 | + | 0.851153i | \(0.324096\pi\) | |||||||
\(224\) | 0.608019 | 0.0406250 | ||||||||
\(225\) | −1.15727 | −0.0771512 | ||||||||
\(226\) | 19.6270 | 1.30557 | ||||||||
\(227\) | 15.5410 | 1.03149 | 0.515746 | − | 0.856741i | \(-0.327515\pi\) | ||||
0.515746 | + | 0.856741i | \(0.327515\pi\) | |||||||
\(228\) | −7.57049 | −0.501368 | ||||||||
\(229\) | 10.7970 | 0.713486 | 0.356743 | − | 0.934203i | \(-0.383887\pi\) | ||||
0.356743 | + | 0.934203i | \(0.383887\pi\) | |||||||
\(230\) | −6.46978 | −0.426605 | ||||||||
\(231\) | −0.825369 | −0.0543053 | ||||||||
\(232\) | 5.96812 | 0.391826 | ||||||||
\(233\) | −11.7711 | −0.771150 | −0.385575 | − | 0.922676i | \(-0.625997\pi\) | ||||
−0.385575 | + | 0.922676i | \(0.625997\pi\) | |||||||
\(234\) | 1.47507 | 0.0964283 | ||||||||
\(235\) | 3.42434 | 0.223379 | ||||||||
\(236\) | 8.43549 | 0.549104 | ||||||||
\(237\) | 2.59028 | 0.168257 | ||||||||
\(238\) | 3.28768 | 0.213109 | ||||||||
\(239\) | −26.9077 | −1.74052 | −0.870259 | − | 0.492595i | \(-0.836048\pi\) | ||||
−0.870259 | + | 0.492595i | \(0.836048\pi\) | |||||||
\(240\) | −1.35747 | −0.0876245 | ||||||||
\(241\) | −28.4825 | −1.83472 | −0.917360 | − | 0.398059i | \(-0.869684\pi\) | ||||
−0.917360 | + | 0.398059i | \(0.869684\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 11.2438 | 0.721289 | ||||||||
\(244\) | −11.5083 | −0.736740 | ||||||||
\(245\) | 6.63031 | 0.423595 | ||||||||
\(246\) | 6.52971 | 0.416319 | ||||||||
\(247\) | 7.10840 | 0.452297 | ||||||||
\(248\) | 3.61424 | 0.229505 | ||||||||
\(249\) | 1.58237 | 0.100278 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.7900 | 0.744176 | 0.372088 | − | 0.928197i | \(-0.378642\pi\) | ||||
0.372088 | + | 0.928197i | \(0.378642\pi\) | |||||||
\(252\) | −0.703640 | −0.0443252 | ||||||||
\(253\) | −6.46978 | −0.406752 | ||||||||
\(254\) | 4.68487 | 0.293955 | ||||||||
\(255\) | −7.34014 | −0.459657 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.6820 | 1.53962 | 0.769810 | − | 0.638273i | \(-0.220351\pi\) | ||||
0.769810 | + | 0.638273i | \(0.220351\pi\) | |||||||
\(258\) | 6.29763 | 0.392074 | ||||||||
\(259\) | 2.17581 | 0.135198 | ||||||||
\(260\) | 1.27461 | 0.0790482 | ||||||||
\(261\) | −6.90671 | −0.427515 | ||||||||
\(262\) | 2.46553 | 0.152321 | ||||||||
\(263\) | −2.79278 | −0.172210 | −0.0861051 | − | 0.996286i | \(-0.527442\pi\) | ||||
−0.0861051 | + | 0.996286i | \(0.527442\pi\) | |||||||
\(264\) | −1.35747 | −0.0835467 | ||||||||
\(265\) | −6.33551 | −0.389187 | ||||||||
\(266\) | −3.39086 | −0.207907 | ||||||||
\(267\) | 19.2239 | 1.17648 | ||||||||
\(268\) | 3.72409 | 0.227485 | ||||||||
\(269\) | 6.34426 | 0.386817 | 0.193408 | − | 0.981118i | \(-0.438046\pi\) | ||||
0.193408 | + | 0.981118i | \(0.438046\pi\) | |||||||
\(270\) | 5.64338 | 0.343445 | ||||||||
\(271\) | −20.0684 | −1.21907 | −0.609534 | − | 0.792760i | \(-0.708644\pi\) | ||||
−0.609534 | + | 0.792760i | \(0.708644\pi\) | |||||||
\(272\) | 5.40721 | 0.327860 | ||||||||
\(273\) | −1.05203 | −0.0636715 | ||||||||
\(274\) | −8.44166 | −0.509979 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 8.78255 | 0.528648 | ||||||||
\(277\) | −10.7700 | −0.647105 | −0.323552 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323552 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(278\) | 20.5520 | 1.23263 | ||||||||
\(279\) | −4.18265 | −0.250409 | ||||||||
\(280\) | −0.608019 | −0.0363361 | ||||||||
\(281\) | −18.2462 | −1.08848 | −0.544239 | − | 0.838930i | \(-0.683181\pi\) | ||||
−0.544239 | + | 0.838930i | \(0.683181\pi\) | |||||||
\(282\) | −4.64845 | −0.276811 | ||||||||
\(283\) | −1.64455 | −0.0977581 | −0.0488790 | − | 0.998805i | \(-0.515565\pi\) | ||||
−0.0488790 | + | 0.998805i | \(0.515565\pi\) | |||||||
\(284\) | −10.2186 | −0.606362 | ||||||||
\(285\) | 7.57049 | 0.448437 | ||||||||
\(286\) | 1.27461 | 0.0753695 | ||||||||
\(287\) | 2.92469 | 0.172639 | ||||||||
\(288\) | −1.15727 | −0.0681927 | ||||||||
\(289\) | 12.2379 | 0.719878 | ||||||||
\(290\) | −5.96812 | −0.350460 | ||||||||
\(291\) | −6.57065 | −0.385178 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | 14.0979 | 0.823609 | 0.411805 | − | 0.911272i | \(-0.364899\pi\) | ||||
0.411805 | + | 0.911272i | \(0.364899\pi\) | |||||||
\(294\) | −9.00047 | −0.524918 | ||||||||
\(295\) | −8.43549 | −0.491133 | ||||||||
\(296\) | 3.57853 | 0.207998 | ||||||||
\(297\) | 5.64338 | 0.327462 | ||||||||
\(298\) | −1.05695 | −0.0612272 | ||||||||
\(299\) | −8.24647 | −0.476906 | ||||||||
\(300\) | 1.35747 | 0.0783737 | ||||||||
\(301\) | 2.82074 | 0.162585 | ||||||||
\(302\) | 10.2067 | 0.587328 | ||||||||
\(303\) | 4.45075 | 0.255689 | ||||||||
\(304\) | −5.57690 | −0.319857 | ||||||||
\(305\) | 11.5083 | 0.658961 | ||||||||
\(306\) | −6.25759 | −0.357723 | ||||||||
\(307\) | −10.1607 | −0.579902 | −0.289951 | − | 0.957041i | \(-0.593639\pi\) | ||||
−0.289951 | + | 0.957041i | \(0.593639\pi\) | |||||||
\(308\) | −0.608019 | −0.0346451 | ||||||||
\(309\) | 8.87338 | 0.504789 | ||||||||
\(310\) | −3.61424 | −0.205275 | ||||||||
\(311\) | −8.66290 | −0.491228 | −0.245614 | − | 0.969368i | \(-0.578990\pi\) | ||||
−0.245614 | + | 0.969368i | \(0.578990\pi\) | |||||||
\(312\) | −1.73025 | −0.0979563 | ||||||||
\(313\) | 4.68241 | 0.264666 | 0.132333 | − | 0.991205i | \(-0.457753\pi\) | ||||
0.132333 | + | 0.991205i | \(0.457753\pi\) | |||||||
\(314\) | 7.28511 | 0.411122 | ||||||||
\(315\) | 0.703640 | 0.0396456 | ||||||||
\(316\) | 1.90817 | 0.107343 | ||||||||
\(317\) | −14.1539 | −0.794963 | −0.397482 | − | 0.917610i | \(-0.630116\pi\) | ||||
−0.397482 | + | 0.917610i | \(0.630116\pi\) | |||||||
\(318\) | 8.60029 | 0.482280 | ||||||||
\(319\) | −5.96812 | −0.334151 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 18.4025 | 1.02713 | ||||||||
\(322\) | 3.93375 | 0.219219 | ||||||||
\(323\) | −30.1555 | −1.67790 | ||||||||
\(324\) | −4.18893 | −0.232718 | ||||||||
\(325\) | −1.27461 | −0.0707029 | ||||||||
\(326\) | 3.70131 | 0.204997 | ||||||||
\(327\) | −3.52591 | −0.194983 | ||||||||
\(328\) | 4.81019 | 0.265599 | ||||||||
\(329\) | −2.08206 | −0.114788 | ||||||||
\(330\) | 1.35747 | 0.0747264 | ||||||||
\(331\) | −4.41687 | −0.242773 | −0.121387 | − | 0.992605i | \(-0.538734\pi\) | ||||
−0.121387 | + | 0.992605i | \(0.538734\pi\) | |||||||
\(332\) | 1.16567 | 0.0639745 | ||||||||
\(333\) | −4.14132 | −0.226943 | ||||||||
\(334\) | 14.8922 | 0.814866 | ||||||||
\(335\) | −3.72409 | −0.203469 | ||||||||
\(336\) | 0.825369 | 0.0450276 | ||||||||
\(337\) | −20.8916 | −1.13804 | −0.569020 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569020 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(338\) | −11.3754 | −0.618738 | ||||||||
\(339\) | 26.6432 | 1.44706 | ||||||||
\(340\) | −5.40721 | −0.293247 | ||||||||
\(341\) | −3.61424 | −0.195722 | ||||||||
\(342\) | 6.45397 | 0.348991 | ||||||||
\(343\) | −8.28748 | −0.447482 | ||||||||
\(344\) | 4.63923 | 0.250131 | ||||||||
\(345\) | −8.78255 | −0.472837 | ||||||||
\(346\) | 4.99951 | 0.268776 | ||||||||
\(347\) | 32.1610 | 1.72649 | 0.863247 | − | 0.504781i | \(-0.168427\pi\) | ||||
0.863247 | + | 0.504781i | \(0.168427\pi\) | |||||||
\(348\) | 8.10156 | 0.434289 | ||||||||
\(349\) | 8.52683 | 0.456431 | 0.228215 | − | 0.973611i | \(-0.426711\pi\) | ||||
0.228215 | + | 0.973611i | \(0.426711\pi\) | |||||||
\(350\) | 0.608019 | 0.0325000 | ||||||||
\(351\) | 7.19313 | 0.383941 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −12.2726 | −0.653206 | −0.326603 | − | 0.945162i | \(-0.605904\pi\) | ||||
−0.326603 | + | 0.945162i | \(0.605904\pi\) | |||||||
\(354\) | 11.4510 | 0.608611 | ||||||||
\(355\) | 10.2186 | 0.542346 | ||||||||
\(356\) | 14.1616 | 0.750561 | ||||||||
\(357\) | 4.46294 | 0.236204 | ||||||||
\(358\) | −20.3087 | −1.07335 | ||||||||
\(359\) | −5.96357 | −0.314745 | −0.157373 | − | 0.987539i | \(-0.550302\pi\) | ||||
−0.157373 | + | 0.987539i | \(0.550302\pi\) | |||||||
\(360\) | 1.15727 | 0.0609934 | ||||||||
\(361\) | 12.1019 | 0.636940 | ||||||||
\(362\) | −12.2620 | −0.644475 | ||||||||
\(363\) | 1.35747 | 0.0712488 | ||||||||
\(364\) | −0.774989 | −0.0406205 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −15.6221 | −0.816582 | ||||||||
\(367\) | −15.5688 | −0.812684 | −0.406342 | − | 0.913721i | \(-0.633196\pi\) | ||||
−0.406342 | + | 0.913721i | \(0.633196\pi\) | |||||||
\(368\) | 6.46978 | 0.337261 | ||||||||
\(369\) | −5.56668 | −0.289790 | ||||||||
\(370\) | −3.57853 | −0.186039 | ||||||||
\(371\) | 3.85211 | 0.199992 | ||||||||
\(372\) | 4.90624 | 0.254377 | ||||||||
\(373\) | −6.58501 | −0.340959 | −0.170479 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170479 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(374\) | −5.40721 | −0.279600 | ||||||||
\(375\) | −1.35747 | −0.0700996 | ||||||||
\(376\) | −3.42434 | −0.176597 | ||||||||
\(377\) | −7.60705 | −0.391783 | ||||||||
\(378\) | −3.43128 | −0.176486 | ||||||||
\(379\) | −18.6144 | −0.956159 | −0.478080 | − | 0.878316i | \(-0.658667\pi\) | ||||
−0.478080 | + | 0.878316i | \(0.658667\pi\) | |||||||
\(380\) | 5.57690 | 0.286089 | ||||||||
\(381\) | 6.35959 | 0.325811 | ||||||||
\(382\) | −18.4536 | −0.944168 | ||||||||
\(383\) | 0.874732 | 0.0446967 | 0.0223484 | − | 0.999750i | \(-0.492886\pi\) | ||||
0.0223484 | + | 0.999750i | \(0.492886\pi\) | |||||||
\(384\) | 1.35747 | 0.0692732 | ||||||||
\(385\) | 0.608019 | 0.0309875 | ||||||||
\(386\) | 18.2662 | 0.929725 | ||||||||
\(387\) | −5.36884 | −0.272913 | ||||||||
\(388\) | −4.84035 | −0.245732 | ||||||||
\(389\) | −2.34683 | −0.118989 | −0.0594946 | − | 0.998229i | \(-0.518949\pi\) | ||||
−0.0594946 | + | 0.998229i | \(0.518949\pi\) | |||||||
\(390\) | 1.73025 | 0.0876148 | ||||||||
\(391\) | 34.9835 | 1.76919 | ||||||||
\(392\) | −6.63031 | −0.334881 | ||||||||
\(393\) | 3.34689 | 0.168828 | ||||||||
\(394\) | 12.1870 | 0.613972 | ||||||||
\(395\) | −1.90817 | −0.0960102 | ||||||||
\(396\) | 1.15727 | 0.0581549 | ||||||||
\(397\) | −10.1299 | −0.508405 | −0.254203 | − | 0.967151i | \(-0.581813\pi\) | ||||
−0.254203 | + | 0.967151i | \(0.581813\pi\) | |||||||
\(398\) | 18.6779 | 0.936239 | ||||||||
\(399\) | −4.60300 | −0.230438 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 25.3431 | 1.26558 | 0.632788 | − | 0.774325i | \(-0.281911\pi\) | ||||
0.632788 | + | 0.774325i | \(0.281911\pi\) | |||||||
\(402\) | 5.05535 | 0.252138 | ||||||||
\(403\) | −4.60677 | −0.229479 | ||||||||
\(404\) | 3.27870 | 0.163122 | ||||||||
\(405\) | 4.18893 | 0.208150 | ||||||||
\(406\) | 3.62873 | 0.180091 | ||||||||
\(407\) | −3.57853 | −0.177381 | ||||||||
\(408\) | 7.34014 | 0.363391 | ||||||||
\(409\) | −27.1863 | −1.34427 | −0.672137 | − | 0.740426i | \(-0.734624\pi\) | ||||
−0.672137 | + | 0.740426i | \(0.734624\pi\) | |||||||
\(410\) | −4.81019 | −0.237559 | ||||||||
\(411\) | −11.4593 | −0.565247 | ||||||||
\(412\) | 6.53669 | 0.322040 | ||||||||
\(413\) | 5.12894 | 0.252379 | ||||||||
\(414\) | −7.48727 | −0.367979 | ||||||||
\(415\) | −1.16567 | −0.0572205 | ||||||||
\(416\) | −1.27461 | −0.0624931 | ||||||||
\(417\) | 27.8988 | 1.36621 | ||||||||
\(418\) | 5.57690 | 0.272775 | ||||||||
\(419\) | −13.2670 | −0.648136 | −0.324068 | − | 0.946034i | \(-0.605051\pi\) | ||||
−0.324068 | + | 0.946034i | \(0.605051\pi\) | |||||||
\(420\) | −0.825369 | −0.0402739 | ||||||||
\(421\) | −32.3904 | −1.57861 | −0.789305 | − | 0.614002i | \(-0.789559\pi\) | ||||
−0.789305 | + | 0.614002i | \(0.789559\pi\) | |||||||
\(422\) | −5.62682 | −0.273909 | ||||||||
\(423\) | 3.96288 | 0.192682 | ||||||||
\(424\) | 6.33551 | 0.307680 | ||||||||
\(425\) | 5.40721 | 0.262288 | ||||||||
\(426\) | −13.8715 | −0.672074 | ||||||||
\(427\) | −6.99723 | −0.338620 | ||||||||
\(428\) | 13.5564 | 0.655275 | ||||||||
\(429\) | 1.73025 | 0.0835374 | ||||||||
\(430\) | −4.63923 | −0.223724 | ||||||||
\(431\) | 7.86742 | 0.378960 | 0.189480 | − | 0.981885i | \(-0.439320\pi\) | ||||
0.189480 | + | 0.981885i | \(0.439320\pi\) | |||||||
\(432\) | −5.64338 | −0.271517 | ||||||||
\(433\) | 34.1919 | 1.64316 | 0.821578 | − | 0.570096i | \(-0.193094\pi\) | ||||
0.821578 | + | 0.570096i | \(0.193094\pi\) | |||||||
\(434\) | 2.19753 | 0.105485 | ||||||||
\(435\) | −8.10156 | −0.388440 | ||||||||
\(436\) | −2.59741 | −0.124393 | ||||||||
\(437\) | −36.0813 | −1.72600 | ||||||||
\(438\) | −1.35747 | −0.0648626 | ||||||||
\(439\) | 12.0906 | 0.577052 | 0.288526 | − | 0.957472i | \(-0.406835\pi\) | ||||
0.288526 | + | 0.957472i | \(0.406835\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 7.67305 | 0.365383 | ||||||||
\(442\) | −6.89210 | −0.327824 | ||||||||
\(443\) | 23.9911 | 1.13985 | 0.569926 | − | 0.821696i | \(-0.306972\pi\) | ||||
0.569926 | + | 0.821696i | \(0.306972\pi\) | |||||||
\(444\) | 4.85775 | 0.230539 | ||||||||
\(445\) | −14.1616 | −0.671322 | ||||||||
\(446\) | 15.6774 | 0.742345 | ||||||||
\(447\) | −1.43477 | −0.0678625 | ||||||||
\(448\) | 0.608019 | 0.0287262 | ||||||||
\(449\) | −23.0951 | −1.08993 | −0.544964 | − | 0.838460i | \(-0.683457\pi\) | ||||
−0.544964 | + | 0.838460i | \(0.683457\pi\) | |||||||
\(450\) | −1.15727 | −0.0545541 | ||||||||
\(451\) | −4.81019 | −0.226503 | ||||||||
\(452\) | 19.6270 | 0.923178 | ||||||||
\(453\) | 13.8553 | 0.650978 | ||||||||
\(454\) | 15.5410 | 0.729375 | ||||||||
\(455\) | 0.774989 | 0.0363320 | ||||||||
\(456\) | −7.57049 | −0.354521 | ||||||||
\(457\) | −24.6058 | −1.15101 | −0.575505 | − | 0.817798i | \(-0.695194\pi\) | ||||
−0.575505 | + | 0.817798i | \(0.695194\pi\) | |||||||
\(458\) | 10.7970 | 0.504511 | ||||||||
\(459\) | −30.5149 | −1.42431 | ||||||||
\(460\) | −6.46978 | −0.301655 | ||||||||
\(461\) | 20.7783 | 0.967740 | 0.483870 | − | 0.875140i | \(-0.339231\pi\) | ||||
0.483870 | + | 0.875140i | \(0.339231\pi\) | |||||||
\(462\) | −0.825369 | −0.0383996 | ||||||||
\(463\) | 18.1764 | 0.844729 | 0.422364 | − | 0.906426i | \(-0.361200\pi\) | ||||
0.422364 | + | 0.906426i | \(0.361200\pi\) | |||||||
\(464\) | 5.96812 | 0.277063 | ||||||||
\(465\) | −4.90624 | −0.227521 | ||||||||
\(466\) | −11.7711 | −0.545285 | ||||||||
\(467\) | −5.88706 | −0.272421 | −0.136210 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136210 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(468\) | 1.47507 | 0.0681851 | ||||||||
\(469\) | 2.26432 | 0.104556 | ||||||||
\(470\) | 3.42434 | 0.157953 | ||||||||
\(471\) | 9.88933 | 0.455676 | ||||||||
\(472\) | 8.43549 | 0.388275 | ||||||||
\(473\) | −4.63923 | −0.213312 | ||||||||
\(474\) | 2.59028 | 0.118976 | ||||||||
\(475\) | −5.57690 | −0.255886 | ||||||||
\(476\) | 3.28768 | 0.150691 | ||||||||
\(477\) | −7.33188 | −0.335704 | ||||||||
\(478\) | −26.9077 | −1.23073 | ||||||||
\(479\) | −8.58515 | −0.392266 | −0.196133 | − | 0.980577i | \(-0.562838\pi\) | ||||
−0.196133 | + | 0.980577i | \(0.562838\pi\) | |||||||
\(480\) | −1.35747 | −0.0619599 | ||||||||
\(481\) | −4.56124 | −0.207975 | ||||||||
\(482\) | −28.4825 | −1.29734 | ||||||||
\(483\) | 5.33995 | 0.242976 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 4.84035 | 0.219789 | ||||||||
\(486\) | 11.2438 | 0.510028 | ||||||||
\(487\) | −21.4531 | −0.972132 | −0.486066 | − | 0.873922i | \(-0.661568\pi\) | ||||
−0.486066 | + | 0.873922i | \(0.661568\pi\) | |||||||
\(488\) | −11.5083 | −0.520954 | ||||||||
\(489\) | 5.02443 | 0.227213 | ||||||||
\(490\) | 6.63031 | 0.299527 | ||||||||
\(491\) | −21.0332 | −0.949215 | −0.474608 | − | 0.880197i | \(-0.657410\pi\) | ||||
−0.474608 | + | 0.880197i | \(0.657410\pi\) | |||||||
\(492\) | 6.52971 | 0.294382 | ||||||||
\(493\) | 32.2709 | 1.45341 | ||||||||
\(494\) | 7.10840 | 0.319822 | ||||||||
\(495\) | −1.15727 | −0.0520153 | ||||||||
\(496\) | 3.61424 | 0.162284 | ||||||||
\(497\) | −6.21309 | −0.278695 | ||||||||
\(498\) | 1.58237 | 0.0709075 | ||||||||
\(499\) | −21.7241 | −0.972505 | −0.486253 | − | 0.873818i | \(-0.661637\pi\) | ||||
−0.486253 | + | 0.873818i | \(0.661637\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 20.2158 | 0.903175 | ||||||||
\(502\) | 11.7900 | 0.526212 | ||||||||
\(503\) | −38.2583 | −1.70585 | −0.852926 | − | 0.522031i | \(-0.825174\pi\) | ||||
−0.852926 | + | 0.522031i | \(0.825174\pi\) | |||||||
\(504\) | −0.703640 | −0.0313426 | ||||||||
\(505\) | −3.27870 | −0.145900 | ||||||||
\(506\) | −6.46978 | −0.287617 | ||||||||
\(507\) | −15.4417 | −0.685792 | ||||||||
\(508\) | 4.68487 | 0.207858 | ||||||||
\(509\) | 43.3695 | 1.92232 | 0.961161 | − | 0.275989i | \(-0.0890054\pi\) | ||||
0.961161 | + | 0.275989i | \(0.0890054\pi\) | |||||||
\(510\) | −7.34014 | −0.325027 | ||||||||
\(511\) | −0.608019 | −0.0268972 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 31.4726 | 1.38955 | ||||||||
\(514\) | 24.6820 | 1.08868 | ||||||||
\(515\) | −6.53669 | −0.288041 | ||||||||
\(516\) | 6.29763 | 0.277238 | ||||||||
\(517\) | 3.42434 | 0.150602 | ||||||||
\(518\) | 2.17581 | 0.0955997 | ||||||||
\(519\) | 6.78671 | 0.297903 | ||||||||
\(520\) | 1.27461 | 0.0558955 | ||||||||
\(521\) | 0.164537 | 0.00720849 | 0.00360424 | − | 0.999994i | \(-0.498853\pi\) | ||||
0.00360424 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(522\) | −6.90671 | −0.302299 | ||||||||
\(523\) | 4.84807 | 0.211991 | 0.105996 | − | 0.994367i | \(-0.466197\pi\) | ||||
0.105996 | + | 0.994367i | \(0.466197\pi\) | |||||||
\(524\) | 2.46553 | 0.107707 | ||||||||
\(525\) | 0.825369 | 0.0360220 | ||||||||
\(526\) | −2.79278 | −0.121771 | ||||||||
\(527\) | 19.5430 | 0.851305 | ||||||||
\(528\) | −1.35747 | −0.0590764 | ||||||||
\(529\) | 18.8581 | 0.819916 | ||||||||
\(530\) | −6.33551 | −0.275197 | ||||||||
\(531\) | −9.76213 | −0.423640 | ||||||||
\(532\) | −3.39086 | −0.147012 | ||||||||
\(533\) | −6.13114 | −0.265569 | ||||||||
\(534\) | 19.2239 | 0.831900 | ||||||||
\(535\) | −13.5564 | −0.586096 | ||||||||
\(536\) | 3.72409 | 0.160856 | ||||||||
\(537\) | −27.5684 | −1.18967 | ||||||||
\(538\) | 6.34426 | 0.273521 | ||||||||
\(539\) | 6.63031 | 0.285588 | ||||||||
\(540\) | 5.64338 | 0.242852 | ||||||||
\(541\) | 1.68555 | 0.0724673 | 0.0362336 | − | 0.999343i | \(-0.488464\pi\) | ||||
0.0362336 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(542\) | −20.0684 | −0.862012 | ||||||||
\(543\) | −16.6453 | −0.714318 | ||||||||
\(544\) | 5.40721 | 0.231832 | ||||||||
\(545\) | 2.59741 | 0.111261 | ||||||||
\(546\) | −1.05203 | −0.0450226 | ||||||||
\(547\) | 0.160774 | 0.00687418 | 0.00343709 | − | 0.999994i | \(-0.498906\pi\) | ||||
0.00343709 | + | 0.999994i | \(0.498906\pi\) | |||||||
\(548\) | −8.44166 | −0.360610 | ||||||||
\(549\) | 13.3181 | 0.568404 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −33.2836 | −1.41793 | ||||||||
\(552\) | 8.78255 | 0.373810 | ||||||||
\(553\) | 1.16020 | 0.0493367 | ||||||||
\(554\) | −10.7700 | −0.457572 | ||||||||
\(555\) | −4.85775 | −0.206200 | ||||||||
\(556\) | 20.5520 | 0.871600 | ||||||||
\(557\) | −22.6746 | −0.960753 | −0.480376 | − | 0.877062i | \(-0.659500\pi\) | ||||
−0.480376 | + | 0.877062i | \(0.659500\pi\) | |||||||
\(558\) | −4.18265 | −0.177066 | ||||||||
\(559\) | −5.91323 | −0.250103 | ||||||||
\(560\) | −0.608019 | −0.0256935 | ||||||||
\(561\) | −7.34014 | −0.309901 | ||||||||
\(562\) | −18.2462 | −0.769670 | ||||||||
\(563\) | −7.53055 | −0.317375 | −0.158687 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158687 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(564\) | −4.64845 | −0.195735 | ||||||||
\(565\) | −19.6270 | −0.825715 | ||||||||
\(566\) | −1.64455 | −0.0691254 | ||||||||
\(567\) | −2.54695 | −0.106962 | ||||||||
\(568\) | −10.2186 | −0.428763 | ||||||||
\(569\) | 39.3562 | 1.64990 | 0.824948 | − | 0.565208i | \(-0.191204\pi\) | ||||
0.824948 | + | 0.565208i | \(0.191204\pi\) | |||||||
\(570\) | 7.57049 | 0.317093 | ||||||||
\(571\) | 12.9036 | 0.540000 | 0.270000 | − | 0.962860i | \(-0.412976\pi\) | ||||
0.270000 | + | 0.962860i | \(0.412976\pi\) | |||||||
\(572\) | 1.27461 | 0.0532943 | ||||||||
\(573\) | −25.0503 | −1.04649 | ||||||||
\(574\) | 2.92469 | 0.122074 | ||||||||
\(575\) | 6.46978 | 0.269809 | ||||||||
\(576\) | −1.15727 | −0.0482195 | ||||||||
\(577\) | 3.42560 | 0.142609 | 0.0713047 | − | 0.997455i | \(-0.477284\pi\) | ||||
0.0713047 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(578\) | 12.2379 | 0.509031 | ||||||||
\(579\) | 24.7959 | 1.03048 | ||||||||
\(580\) | −5.96812 | −0.247813 | ||||||||
\(581\) | 0.708750 | 0.0294039 | ||||||||
\(582\) | −6.57065 | −0.272362 | ||||||||
\(583\) | −6.33551 | −0.262390 | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | −1.47507 | −0.0609866 | ||||||||
\(586\) | 14.0979 | 0.582380 | ||||||||
\(587\) | 11.8855 | 0.490565 | 0.245283 | − | 0.969452i | \(-0.421119\pi\) | ||||
0.245283 | + | 0.969452i | \(0.421119\pi\) | |||||||
\(588\) | −9.00047 | −0.371173 | ||||||||
\(589\) | −20.1563 | −0.830525 | ||||||||
\(590\) | −8.43549 | −0.347284 | ||||||||
\(591\) | 16.5435 | 0.680510 | ||||||||
\(592\) | 3.57853 | 0.147077 | ||||||||
\(593\) | −45.6647 | −1.87523 | −0.937613 | − | 0.347682i | \(-0.886969\pi\) | ||||
−0.937613 | + | 0.347682i | \(0.886969\pi\) | |||||||
\(594\) | 5.64338 | 0.231551 | ||||||||
\(595\) | −3.28768 | −0.134782 | ||||||||
\(596\) | −1.05695 | −0.0432942 | ||||||||
\(597\) | 25.3548 | 1.03770 | ||||||||
\(598\) | −8.24647 | −0.337223 | ||||||||
\(599\) | −24.0849 | −0.984081 | −0.492040 | − | 0.870572i | \(-0.663749\pi\) | ||||
−0.492040 | + | 0.870572i | \(0.663749\pi\) | |||||||
\(600\) | 1.35747 | 0.0554186 | ||||||||
\(601\) | −4.20692 | −0.171604 | −0.0858019 | − | 0.996312i | \(-0.527345\pi\) | ||||
−0.0858019 | + | 0.996312i | \(0.527345\pi\) | |||||||
\(602\) | 2.82074 | 0.114965 | ||||||||
\(603\) | −4.30977 | −0.175507 | ||||||||
\(604\) | 10.2067 | 0.415304 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 4.45075 | 0.180799 | ||||||||
\(607\) | 20.4287 | 0.829174 | 0.414587 | − | 0.910010i | \(-0.363926\pi\) | ||||
0.414587 | + | 0.910010i | \(0.363926\pi\) | |||||||
\(608\) | −5.57690 | −0.226173 | ||||||||
\(609\) | 4.92590 | 0.199608 | ||||||||
\(610\) | 11.5083 | 0.465956 | ||||||||
\(611\) | 4.36471 | 0.176577 | ||||||||
\(612\) | −6.25759 | −0.252948 | ||||||||
\(613\) | 45.2149 | 1.82621 | 0.913105 | − | 0.407724i | \(-0.133677\pi\) | ||||
0.913105 | + | 0.407724i | \(0.133677\pi\) | |||||||
\(614\) | −10.1607 | −0.410053 | ||||||||
\(615\) | −6.52971 | −0.263303 | ||||||||
\(616\) | −0.608019 | −0.0244978 | ||||||||
\(617\) | −26.7362 | −1.07636 | −0.538180 | − | 0.842830i | \(-0.680888\pi\) | ||||
−0.538180 | + | 0.842830i | \(0.680888\pi\) | |||||||
\(618\) | 8.87338 | 0.356940 | ||||||||
\(619\) | −18.2248 | −0.732516 | −0.366258 | − | 0.930513i | \(-0.619361\pi\) | ||||
−0.366258 | + | 0.930513i | \(0.619361\pi\) | |||||||
\(620\) | −3.61424 | −0.145152 | ||||||||
\(621\) | −36.5114 | −1.46515 | ||||||||
\(622\) | −8.66290 | −0.347351 | ||||||||
\(623\) | 8.61049 | 0.344972 | ||||||||
\(624\) | −1.73025 | −0.0692656 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.68241 | 0.187147 | ||||||||
\(627\) | 7.57049 | 0.302336 | ||||||||
\(628\) | 7.28511 | 0.290707 | ||||||||
\(629\) | 19.3499 | 0.771529 | ||||||||
\(630\) | 0.703640 | 0.0280337 | ||||||||
\(631\) | 5.40052 | 0.214991 | 0.107496 | − | 0.994206i | \(-0.465717\pi\) | ||||
0.107496 | + | 0.994206i | \(0.465717\pi\) | |||||||
\(632\) | 1.90817 | 0.0759028 | ||||||||
\(633\) | −7.63825 | −0.303593 | ||||||||
\(634\) | −14.1539 | −0.562124 | ||||||||
\(635\) | −4.68487 | −0.185913 | ||||||||
\(636\) | 8.60029 | 0.341023 | ||||||||
\(637\) | 8.45109 | 0.334844 | ||||||||
\(638\) | −5.96812 | −0.236280 | ||||||||
\(639\) | 11.8256 | 0.467815 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 3.87647 | 0.153111 | 0.0765557 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765557 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(642\) | 18.4025 | 0.726289 | ||||||||
\(643\) | 30.2728 | 1.19384 | 0.596922 | − | 0.802299i | \(-0.296390\pi\) | ||||
0.596922 | + | 0.802299i | \(0.296390\pi\) | |||||||
\(644\) | 3.93375 | 0.155011 | ||||||||
\(645\) | −6.29763 | −0.247969 | ||||||||
\(646\) | −30.1555 | −1.18645 | ||||||||
\(647\) | −31.9670 | −1.25675 | −0.628376 | − | 0.777910i | \(-0.716280\pi\) | ||||
−0.628376 | + | 0.777910i | \(0.716280\pi\) | |||||||
\(648\) | −4.18893 | −0.164557 | ||||||||
\(649\) | −8.43549 | −0.331122 | ||||||||
\(650\) | −1.27461 | −0.0499945 | ||||||||
\(651\) | 2.98308 | 0.116916 | ||||||||
\(652\) | 3.70131 | 0.144955 | ||||||||
\(653\) | 0.256173 | 0.0100248 | 0.00501241 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501241 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(654\) | −3.52591 | −0.137874 | ||||||||
\(655\) | −2.46553 | −0.0963363 | ||||||||
\(656\) | 4.81019 | 0.187807 | ||||||||
\(657\) | 1.15727 | 0.0451493 | ||||||||
\(658\) | −2.08206 | −0.0811672 | ||||||||
\(659\) | −8.16400 | −0.318024 | −0.159012 | − | 0.987277i | \(-0.550831\pi\) | ||||
−0.159012 | + | 0.987277i | \(0.550831\pi\) | |||||||
\(660\) | 1.35747 | 0.0528396 | ||||||||
\(661\) | 1.39542 | 0.0542756 | 0.0271378 | − | 0.999632i | \(-0.491361\pi\) | ||||
0.0271378 | + | 0.999632i | \(0.491361\pi\) | |||||||
\(662\) | −4.41687 | −0.171667 | ||||||||
\(663\) | −9.35584 | −0.363351 | ||||||||
\(664\) | 1.16567 | 0.0452368 | ||||||||
\(665\) | 3.39086 | 0.131492 | ||||||||
\(666\) | −4.14132 | −0.160473 | ||||||||
\(667\) | 38.6124 | 1.49508 | ||||||||
\(668\) | 14.8922 | 0.576197 | ||||||||
\(669\) | 21.2816 | 0.822794 | ||||||||
\(670\) | −3.72409 | −0.143874 | ||||||||
\(671\) | 11.5083 | 0.444271 | ||||||||
\(672\) | 0.825369 | 0.0318393 | ||||||||
\(673\) | −12.5908 | −0.485339 | −0.242670 | − | 0.970109i | \(-0.578023\pi\) | ||||
−0.242670 | + | 0.970109i | \(0.578023\pi\) | |||||||
\(674\) | −20.8916 | −0.804715 | ||||||||
\(675\) | −5.64338 | −0.217214 | ||||||||
\(676\) | −11.3754 | −0.437514 | ||||||||
\(677\) | 3.86811 | 0.148663 | 0.0743317 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743317 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(678\) | 26.6432 | 1.02322 | ||||||||
\(679\) | −2.94303 | −0.112943 | ||||||||
\(680\) | −5.40721 | −0.207357 | ||||||||
\(681\) | 21.0965 | 0.808419 | ||||||||
\(682\) | −3.61424 | −0.138397 | ||||||||
\(683\) | −31.9618 | −1.22298 | −0.611492 | − | 0.791251i | \(-0.709430\pi\) | ||||
−0.611492 | + | 0.791251i | \(0.709430\pi\) | |||||||
\(684\) | 6.45397 | 0.246774 | ||||||||
\(685\) | 8.44166 | 0.322539 | ||||||||
\(686\) | −8.28748 | −0.316418 | ||||||||
\(687\) | 14.6566 | 0.559186 | ||||||||
\(688\) | 4.63923 | 0.176869 | ||||||||
\(689\) | −8.07533 | −0.307646 | ||||||||
\(690\) | −8.78255 | −0.334346 | ||||||||
\(691\) | 36.2225 | 1.37797 | 0.688984 | − | 0.724777i | \(-0.258057\pi\) | ||||
0.688984 | + | 0.724777i | \(0.258057\pi\) | |||||||
\(692\) | 4.99951 | 0.190053 | ||||||||
\(693\) | 0.703640 | 0.0267291 | ||||||||
\(694\) | 32.1610 | 1.22082 | ||||||||
\(695\) | −20.5520 | −0.779583 | ||||||||
\(696\) | 8.10156 | 0.307089 | ||||||||
\(697\) | 26.0097 | 0.985189 | ||||||||
\(698\) | 8.52683 | 0.322745 | ||||||||
\(699\) | −15.9789 | −0.604379 | ||||||||
\(700\) | 0.608019 | 0.0229809 | ||||||||
\(701\) | −33.0030 | −1.24651 | −0.623253 | − | 0.782020i | \(-0.714189\pi\) | ||||
−0.623253 | + | 0.782020i | \(0.714189\pi\) | |||||||
\(702\) | 7.19313 | 0.271487 | ||||||||
\(703\) | −19.9571 | −0.752697 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 4.64845 | 0.175071 | ||||||||
\(706\) | −12.2726 | −0.461887 | ||||||||
\(707\) | 1.99351 | 0.0749737 | ||||||||
\(708\) | 11.4510 | 0.430353 | ||||||||
\(709\) | −0.716856 | −0.0269221 | −0.0134610 | − | 0.999909i | \(-0.504285\pi\) | ||||
−0.0134610 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(710\) | 10.2186 | 0.383497 | ||||||||
\(711\) | −2.20826 | −0.0828162 | ||||||||
\(712\) | 14.1616 | 0.530727 | ||||||||
\(713\) | 23.3834 | 0.875714 | ||||||||
\(714\) | 4.46294 | 0.167021 | ||||||||
\(715\) | −1.27461 | −0.0476679 | ||||||||
\(716\) | −20.3087 | −0.758970 | ||||||||
\(717\) | −36.5265 | −1.36411 | ||||||||
\(718\) | −5.96357 | −0.222558 | ||||||||
\(719\) | −3.29324 | −0.122817 | −0.0614086 | − | 0.998113i | \(-0.519559\pi\) | ||||
−0.0614086 | + | 0.998113i | \(0.519559\pi\) | |||||||
\(720\) | 1.15727 | 0.0431288 | ||||||||
\(721\) | 3.97443 | 0.148016 | ||||||||
\(722\) | 12.1019 | 0.450384 | ||||||||
\(723\) | −38.6642 | −1.43794 | ||||||||
\(724\) | −12.2620 | −0.455713 | ||||||||
\(725\) | 5.96812 | 0.221650 | ||||||||
\(726\) | 1.35747 | 0.0503805 | ||||||||
\(727\) | −38.4438 | −1.42580 | −0.712901 | − | 0.701265i | \(-0.752619\pi\) | ||||
−0.712901 | + | 0.701265i | \(0.752619\pi\) | |||||||
\(728\) | −0.774989 | −0.0287230 | ||||||||
\(729\) | 27.8299 | 1.03074 | ||||||||
\(730\) | 1.00000 | 0.0370117 | ||||||||
\(731\) | 25.0853 | 0.927814 | ||||||||
\(732\) | −15.6221 | −0.577411 | ||||||||
\(733\) | 49.9850 | 1.84624 | 0.923119 | − | 0.384515i | \(-0.125631\pi\) | ||||
0.923119 | + | 0.384515i | \(0.125631\pi\) | |||||||
\(734\) | −15.5688 | −0.574655 | ||||||||
\(735\) | 9.00047 | 0.331987 | ||||||||
\(736\) | 6.46978 | 0.238479 | ||||||||
\(737\) | −3.72409 | −0.137179 | ||||||||
\(738\) | −5.56668 | −0.204912 | ||||||||
\(739\) | −8.94290 | −0.328970 | −0.164485 | − | 0.986380i | \(-0.552596\pi\) | ||||
−0.164485 | + | 0.986380i | \(0.552596\pi\) | |||||||
\(740\) | −3.57853 | −0.131549 | ||||||||
\(741\) | 9.64946 | 0.354482 | ||||||||
\(742\) | 3.85211 | 0.141415 | ||||||||
\(743\) | −47.5663 | −1.74504 | −0.872520 | − | 0.488578i | \(-0.837516\pi\) | ||||
−0.872520 | + | 0.488578i | \(0.837516\pi\) | |||||||
\(744\) | 4.90624 | 0.179871 | ||||||||
\(745\) | 1.05695 | 0.0387235 | ||||||||
\(746\) | −6.58501 | −0.241094 | ||||||||
\(747\) | −1.34899 | −0.0493571 | ||||||||
\(748\) | −5.40721 | −0.197707 | ||||||||
\(749\) | 8.24257 | 0.301177 | ||||||||
\(750\) | −1.35747 | −0.0495679 | ||||||||
\(751\) | −45.0276 | −1.64308 | −0.821540 | − | 0.570151i | \(-0.806885\pi\) | ||||
−0.821540 | + | 0.570151i | \(0.806885\pi\) | |||||||
\(752\) | −3.42434 | −0.124873 | ||||||||
\(753\) | 16.0046 | 0.583239 | ||||||||
\(754\) | −7.60705 | −0.277032 | ||||||||
\(755\) | −10.2067 | −0.371459 | ||||||||
\(756\) | −3.43128 | −0.124794 | ||||||||
\(757\) | 15.4036 | 0.559853 | 0.279926 | − | 0.960021i | \(-0.409690\pi\) | ||||
0.279926 | + | 0.960021i | \(0.409690\pi\) | |||||||
\(758\) | −18.6144 | −0.676107 | ||||||||
\(759\) | −8.78255 | −0.318786 | ||||||||
\(760\) | 5.57690 | 0.202296 | ||||||||
\(761\) | −28.9539 | −1.04958 | −0.524790 | − | 0.851232i | \(-0.675856\pi\) | ||||
−0.524790 | + | 0.851232i | \(0.675856\pi\) | |||||||
\(762\) | 6.35959 | 0.230383 | ||||||||
\(763\) | −1.57927 | −0.0571735 | ||||||||
\(764\) | −18.4536 | −0.667628 | ||||||||
\(765\) | 6.25759 | 0.226244 | ||||||||
\(766\) | 0.874732 | 0.0316053 | ||||||||
\(767\) | −10.7520 | −0.388232 | ||||||||
\(768\) | 1.35747 | 0.0489836 | ||||||||
\(769\) | 4.98586 | 0.179795 | 0.0898973 | − | 0.995951i | \(-0.471346\pi\) | ||||
0.0898973 | + | 0.995951i | \(0.471346\pi\) | |||||||
\(770\) | 0.608019 | 0.0219115 | ||||||||
\(771\) | 33.5051 | 1.20666 | ||||||||
\(772\) | 18.2662 | 0.657415 | ||||||||
\(773\) | −8.43430 | −0.303361 | −0.151680 | − | 0.988430i | \(-0.548468\pi\) | ||||
−0.151680 | + | 0.988430i | \(0.548468\pi\) | |||||||
\(774\) | −5.36884 | −0.192979 | ||||||||
\(775\) | 3.61424 | 0.129827 | ||||||||
\(776\) | −4.84035 | −0.173759 | ||||||||
\(777\) | 2.95361 | 0.105960 | ||||||||
\(778\) | −2.34683 | −0.0841380 | ||||||||
\(779\) | −26.8260 | −0.961141 | ||||||||
\(780\) | 1.73025 | 0.0619530 | ||||||||
\(781\) | 10.2186 | 0.365650 | ||||||||
\(782\) | 34.9835 | 1.25101 | ||||||||
\(783\) | −33.6804 | −1.20364 | ||||||||
\(784\) | −6.63031 | −0.236797 | ||||||||
\(785\) | −7.28511 | −0.260017 | ||||||||
\(786\) | 3.34689 | 0.119380 | ||||||||
\(787\) | −11.9511 | −0.426012 | −0.213006 | − | 0.977051i | \(-0.568325\pi\) | ||||
−0.213006 | + | 0.977051i | \(0.568325\pi\) | |||||||
\(788\) | 12.1870 | 0.434144 | ||||||||
\(789\) | −3.79112 | −0.134968 | ||||||||
\(790\) | −1.90817 | −0.0678895 | ||||||||
\(791\) | 11.9336 | 0.424310 | ||||||||
\(792\) | 1.15727 | 0.0411217 | ||||||||
\(793\) | 14.6686 | 0.520896 | ||||||||
\(794\) | −10.1299 | −0.359497 | ||||||||
\(795\) | −8.60029 | −0.305021 | ||||||||
\(796\) | 18.6779 | 0.662021 | ||||||||
\(797\) | 9.14504 | 0.323934 | 0.161967 | − | 0.986796i | \(-0.448216\pi\) | ||||
0.161967 | + | 0.986796i | \(0.448216\pi\) | |||||||
\(798\) | −4.60300 | −0.162944 | ||||||||
\(799\) | −18.5161 | −0.655053 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −16.3887 | −0.579066 | ||||||||
\(802\) | 25.3431 | 0.894897 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 5.05535 | 0.178289 | ||||||||
\(805\) | −3.93375 | −0.138646 | ||||||||
\(806\) | −4.60677 | −0.162266 | ||||||||
\(807\) | 8.61217 | 0.303163 | ||||||||
\(808\) | 3.27870 | 0.115344 | ||||||||
\(809\) | 39.5390 | 1.39012 | 0.695058 | − | 0.718953i | \(-0.255379\pi\) | ||||
0.695058 | + | 0.718953i | \(0.255379\pi\) | |||||||
\(810\) | 4.18893 | 0.147184 | ||||||||
\(811\) | 19.4631 | 0.683443 | 0.341721 | − | 0.939801i | \(-0.388990\pi\) | ||||
0.341721 | + | 0.939801i | \(0.388990\pi\) | |||||||
\(812\) | 3.62873 | 0.127343 | ||||||||
\(813\) | −27.2423 | −0.955430 | ||||||||
\(814\) | −3.57853 | −0.125427 | ||||||||
\(815\) | −3.70131 | −0.129651 | ||||||||
\(816\) | 7.34014 | 0.256956 | ||||||||
\(817\) | −25.8726 | −0.905166 | ||||||||
\(818\) | −27.1863 | −0.950546 | ||||||||
\(819\) | 0.896870 | 0.0313392 | ||||||||
\(820\) | −4.81019 | −0.167979 | ||||||||
\(821\) | 41.6945 | 1.45515 | 0.727574 | − | 0.686029i | \(-0.240648\pi\) | ||||
0.727574 | + | 0.686029i | \(0.240648\pi\) | |||||||
\(822\) | −11.4593 | −0.399690 | ||||||||
\(823\) | −2.79126 | −0.0972970 | −0.0486485 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486485 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(824\) | 6.53669 | 0.227717 | ||||||||
\(825\) | −1.35747 | −0.0472611 | ||||||||
\(826\) | 5.12894 | 0.178459 | ||||||||
\(827\) | 32.9618 | 1.14619 | 0.573097 | − | 0.819488i | \(-0.305742\pi\) | ||||
0.573097 | + | 0.819488i | \(0.305742\pi\) | |||||||
\(828\) | −7.48727 | −0.260201 | ||||||||
\(829\) | 27.4543 | 0.953528 | 0.476764 | − | 0.879031i | \(-0.341810\pi\) | ||||
0.476764 | + | 0.879031i | \(0.341810\pi\) | |||||||
\(830\) | −1.16567 | −0.0404610 | ||||||||
\(831\) | −14.6199 | −0.507160 | ||||||||
\(832\) | −1.27461 | −0.0441893 | ||||||||
\(833\) | −35.8515 | −1.24218 | ||||||||
\(834\) | 27.8988 | 0.966057 | ||||||||
\(835\) | −14.8922 | −0.515367 | ||||||||
\(836\) | 5.57690 | 0.192881 | ||||||||
\(837\) | −20.3965 | −0.705008 | ||||||||
\(838\) | −13.2670 | −0.458302 | ||||||||
\(839\) | 11.2227 | 0.387452 | 0.193726 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193726 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(840\) | −0.825369 | −0.0284779 | ||||||||
\(841\) | 6.61847 | 0.228223 | ||||||||
\(842\) | −32.3904 | −1.11625 | ||||||||
\(843\) | −24.7687 | −0.853080 | ||||||||
\(844\) | −5.62682 | −0.193683 | ||||||||
\(845\) | 11.3754 | 0.391324 | ||||||||
\(846\) | 3.96288 | 0.136246 | ||||||||
\(847\) | 0.608019 | 0.0208918 | ||||||||
\(848\) | 6.33551 | 0.217562 | ||||||||
\(849\) | −2.23243 | −0.0766167 | ||||||||
\(850\) | 5.40721 | 0.185466 | ||||||||
\(851\) | 23.1523 | 0.793650 | ||||||||
\(852\) | −13.8715 | −0.475228 | ||||||||
\(853\) | 7.82241 | 0.267834 | 0.133917 | − | 0.990993i | \(-0.457244\pi\) | ||||
0.133917 | + | 0.990993i | \(0.457244\pi\) | |||||||
\(854\) | −6.99723 | −0.239440 | ||||||||
\(855\) | −6.45397 | −0.220721 | ||||||||
\(856\) | 13.5564 | 0.463350 | ||||||||
\(857\) | −7.54594 | −0.257764 | −0.128882 | − | 0.991660i | \(-0.541139\pi\) | ||||
−0.128882 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(858\) | 1.73025 | 0.0590699 | ||||||||
\(859\) | 21.5268 | 0.734486 | 0.367243 | − | 0.930125i | \(-0.380302\pi\) | ||||
0.367243 | + | 0.930125i | \(0.380302\pi\) | |||||||
\(860\) | −4.63923 | −0.158197 | ||||||||
\(861\) | 3.97018 | 0.135303 | ||||||||
\(862\) | 7.86742 | 0.267965 | ||||||||
\(863\) | −2.00484 | −0.0682455 | −0.0341228 | − | 0.999418i | \(-0.510864\pi\) | ||||
−0.0341228 | + | 0.999418i | \(0.510864\pi\) | |||||||
\(864\) | −5.64338 | −0.191992 | ||||||||
\(865\) | −4.99951 | −0.169989 | ||||||||
\(866\) | 34.1919 | 1.16189 | ||||||||
\(867\) | 16.6126 | 0.564195 | ||||||||
\(868\) | 2.19753 | 0.0745889 | ||||||||
\(869\) | −1.90817 | −0.0647301 | ||||||||
\(870\) | −8.10156 | −0.274669 | ||||||||
\(871\) | −4.74678 | −0.160838 | ||||||||
\(872\) | −2.59741 | −0.0879593 | ||||||||
\(873\) | 5.60159 | 0.189585 | ||||||||
\(874\) | −36.0813 | −1.22047 | ||||||||
\(875\) | −0.608019 | −0.0205548 | ||||||||
\(876\) | −1.35747 | −0.0458648 | ||||||||
\(877\) | −6.29155 | −0.212451 | −0.106225 | − | 0.994342i | \(-0.533876\pi\) | ||||
−0.106225 | + | 0.994342i | \(0.533876\pi\) | |||||||
\(878\) | 12.0906 | 0.408037 | ||||||||
\(879\) | 19.1375 | 0.645493 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −18.7614 | −0.632087 | −0.316043 | − | 0.948745i | \(-0.602355\pi\) | ||||
−0.316043 | + | 0.948745i | \(0.602355\pi\) | |||||||
\(882\) | 7.67305 | 0.258365 | ||||||||
\(883\) | 20.2339 | 0.680924 | 0.340462 | − | 0.940258i | \(-0.389416\pi\) | ||||
0.340462 | + | 0.940258i | \(0.389416\pi\) | |||||||
\(884\) | −6.89210 | −0.231807 | ||||||||
\(885\) | −11.4510 | −0.384920 | ||||||||
\(886\) | 23.9911 | 0.805998 | ||||||||
\(887\) | −16.1549 | −0.542429 | −0.271215 | − | 0.962519i | \(-0.587425\pi\) | ||||
−0.271215 | + | 0.962519i | \(0.587425\pi\) | |||||||
\(888\) | 4.85775 | 0.163016 | ||||||||
\(889\) | 2.84849 | 0.0955353 | ||||||||
\(890\) | −14.1616 | −0.474696 | ||||||||
\(891\) | 4.18893 | 0.140334 | ||||||||
\(892\) | 15.6774 | 0.524917 | ||||||||
\(893\) | 19.0972 | 0.639064 | ||||||||
\(894\) | −1.43477 | −0.0479860 | ||||||||
\(895\) | 20.3087 | 0.678843 | ||||||||
\(896\) | 0.608019 | 0.0203125 | ||||||||
\(897\) | −11.1944 | −0.373769 | ||||||||
\(898\) | −23.0951 | −0.770695 | ||||||||
\(899\) | 21.5702 | 0.719408 | ||||||||
\(900\) | −1.15727 | −0.0385756 | ||||||||
\(901\) | 34.2574 | 1.14128 | ||||||||
\(902\) | −4.81019 | −0.160162 | ||||||||
\(903\) | 3.82908 | 0.127424 | ||||||||
\(904\) | 19.6270 | 0.652785 | ||||||||
\(905\) | 12.2620 | 0.407602 | ||||||||
\(906\) | 13.8553 | 0.460311 | ||||||||
\(907\) | −1.37058 | −0.0455094 | −0.0227547 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227547 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(908\) | 15.5410 | 0.515746 | ||||||||
\(909\) | −3.79434 | −0.125850 | ||||||||
\(910\) | 0.774989 | 0.0256906 | ||||||||
\(911\) | −39.1208 | −1.29613 | −0.648064 | − | 0.761586i | \(-0.724421\pi\) | ||||
−0.648064 | + | 0.761586i | \(0.724421\pi\) | |||||||
\(912\) | −7.57049 | −0.250684 | ||||||||
\(913\) | −1.16567 | −0.0385781 | ||||||||
\(914\) | −24.6058 | −0.813887 | ||||||||
\(915\) | 15.6221 | 0.516452 | ||||||||
\(916\) | 10.7970 | 0.356743 | ||||||||
\(917\) | 1.49909 | 0.0495043 | ||||||||
\(918\) | −30.5149 | −1.00714 | ||||||||
\(919\) | −45.9131 | −1.51453 | −0.757266 | − | 0.653106i | \(-0.773466\pi\) | ||||
−0.757266 | + | 0.653106i | \(0.773466\pi\) | |||||||
\(920\) | −6.46978 | −0.213302 | ||||||||
\(921\) | −13.7929 | −0.454491 | ||||||||
\(922\) | 20.7783 | 0.684295 | ||||||||
\(923\) | 13.0248 | 0.428715 | ||||||||
\(924\) | −0.825369 | −0.0271526 | ||||||||
\(925\) | 3.57853 | 0.117661 | ||||||||
\(926\) | 18.1764 | 0.597314 | ||||||||
\(927\) | −7.56470 | −0.248458 | ||||||||
\(928\) | 5.96812 | 0.195913 | ||||||||
\(929\) | −48.6547 | −1.59631 | −0.798155 | − | 0.602452i | \(-0.794190\pi\) | ||||
−0.798155 | + | 0.602452i | \(0.794190\pi\) | |||||||
\(930\) | −4.90624 | −0.160882 | ||||||||
\(931\) | 36.9766 | 1.21186 | ||||||||
\(932\) | −11.7711 | −0.385575 | ||||||||
\(933\) | −11.7597 | −0.384994 | ||||||||
\(934\) | −5.88706 | −0.192630 | ||||||||
\(935\) | 5.40721 | 0.176835 | ||||||||
\(936\) | 1.47507 | 0.0482142 | ||||||||
\(937\) | −12.3082 | −0.402090 | −0.201045 | − | 0.979582i | \(-0.564434\pi\) | ||||
−0.201045 | + | 0.979582i | \(0.564434\pi\) | |||||||
\(938\) | 2.26432 | 0.0739326 | ||||||||
\(939\) | 6.35625 | 0.207428 | ||||||||
\(940\) | 3.42434 | 0.111690 | ||||||||
\(941\) | −22.9424 | −0.747900 | −0.373950 | − | 0.927449i | \(-0.621997\pi\) | ||||
−0.373950 | + | 0.927449i | \(0.621997\pi\) | |||||||
\(942\) | 9.88933 | 0.322212 | ||||||||
\(943\) | 31.1209 | 1.01344 | ||||||||
\(944\) | 8.43549 | 0.274552 | ||||||||
\(945\) | 3.43128 | 0.111620 | ||||||||
\(946\) | −4.63923 | −0.150834 | ||||||||
\(947\) | 59.1141 | 1.92095 | 0.960475 | − | 0.278368i | \(-0.0897934\pi\) | ||||
0.960475 | + | 0.278368i | \(0.0897934\pi\) | |||||||
\(948\) | 2.59028 | 0.0841285 | ||||||||
\(949\) | 1.27461 | 0.0413757 | ||||||||
\(950\) | −5.57690 | −0.180939 | ||||||||
\(951\) | −19.2136 | −0.623043 | ||||||||
\(952\) | 3.28768 | 0.106554 | ||||||||
\(953\) | −1.33413 | −0.0432166 | −0.0216083 | − | 0.999767i | \(-0.506879\pi\) | ||||
−0.0216083 | + | 0.999767i | \(0.506879\pi\) | |||||||
\(954\) | −7.33188 | −0.237378 | ||||||||
\(955\) | 18.4536 | 0.597144 | ||||||||
\(956\) | −26.9077 | −0.870259 | ||||||||
\(957\) | −8.10156 | −0.261886 | ||||||||
\(958\) | −8.58515 | −0.277374 | ||||||||
\(959\) | −5.13269 | −0.165743 | ||||||||
\(960\) | −1.35747 | −0.0438122 | ||||||||
\(961\) | −17.9372 | −0.578621 | ||||||||
\(962\) | −4.56124 | −0.147060 | ||||||||
\(963\) | −15.6884 | −0.505553 | ||||||||
\(964\) | −28.4825 | −0.917360 | ||||||||
\(965\) | −18.2662 | −0.588010 | ||||||||
\(966\) | 5.33995 | 0.171810 | ||||||||
\(967\) | 50.0088 | 1.60817 | 0.804087 | − | 0.594512i | \(-0.202655\pi\) | ||||
0.804087 | + | 0.594512i | \(0.202655\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −40.9353 | −1.31503 | ||||||||
\(970\) | 4.84035 | 0.155414 | ||||||||
\(971\) | −0.494504 | −0.0158694 | −0.00793469 | − | 0.999969i | \(-0.502526\pi\) | ||||
−0.00793469 | + | 0.999969i | \(0.502526\pi\) | |||||||
\(972\) | 11.2438 | 0.360644 | ||||||||
\(973\) | 12.4960 | 0.400604 | ||||||||
\(974\) | −21.4531 | −0.687401 | ||||||||
\(975\) | −1.73025 | −0.0554125 | ||||||||
\(976\) | −11.5083 | −0.368370 | ||||||||
\(977\) | −54.3441 | −1.73862 | −0.869310 | − | 0.494267i | \(-0.835437\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(978\) | 5.02443 | 0.160664 | ||||||||
\(979\) | −14.1616 | −0.452605 | ||||||||
\(980\) | 6.63031 | 0.211798 | ||||||||
\(981\) | 3.00589 | 0.0959708 | ||||||||
\(982\) | −21.0332 | −0.671197 | ||||||||
\(983\) | −32.8799 | −1.04871 | −0.524353 | − | 0.851501i | \(-0.675693\pi\) | ||||
−0.524353 | + | 0.851501i | \(0.675693\pi\) | |||||||
\(984\) | 6.52971 | 0.208159 | ||||||||
\(985\) | −12.1870 | −0.388310 | ||||||||
\(986\) | 32.2709 | 1.02771 | ||||||||
\(987\) | −2.82634 | −0.0899634 | ||||||||
\(988\) | 7.10840 | 0.226148 | ||||||||
\(989\) | 30.0148 | 0.954416 | ||||||||
\(990\) | −1.15727 | −0.0367804 | ||||||||
\(991\) | −9.97742 | −0.316943 | −0.158472 | − | 0.987364i | \(-0.550657\pi\) | ||||
−0.158472 | + | 0.987364i | \(0.550657\pi\) | |||||||
\(992\) | 3.61424 | 0.114752 | ||||||||
\(993\) | −5.99578 | −0.190270 | ||||||||
\(994\) | −6.21309 | −0.197067 | ||||||||
\(995\) | −18.6779 | −0.592130 | ||||||||
\(996\) | 1.58237 | 0.0501392 | ||||||||
\(997\) | −4.82352 | −0.152762 | −0.0763812 | − | 0.997079i | \(-0.524337\pi\) | ||||
−0.0763812 | + | 0.997079i | \(0.524337\pi\) | |||||||
\(998\) | −21.7241 | −0.687665 | ||||||||
\(999\) | −20.1950 | −0.638941 |
(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 | 8030.2.a.bg.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.bg.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |