Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
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: | \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} - 3723 x^{12} - 14776 x^{11} + 14837 x^{10} + 21886 x^{9} - 28084 x^{8} - 14682 x^{7} + \cdots - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-1.29878\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | 1.29878 | 0.749852 | 0.374926 | − | 0.927055i | \(-0.377668\pi\) | ||||
0.374926 | + | 0.927055i | \(0.377668\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.87965 | 1.28782 | 0.643910 | − | 0.765101i | \(-0.277311\pi\) | ||||
0.643910 | + | 0.765101i | \(0.277311\pi\) | |||||||
\(6\) | 1.29878 | 0.530226 | ||||||||
\(7\) | −3.57798 | −1.35235 | −0.676174 | − | 0.736742i | \(-0.736363\pi\) | ||||
−0.676174 | + | 0.736742i | \(0.736363\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.31316 | −0.437721 | ||||||||
\(10\) | 2.87965 | 0.910626 | ||||||||
\(11\) | −1.21143 | −0.365259 | −0.182630 | − | 0.983182i | \(-0.558461\pi\) | ||||
−0.182630 | + | 0.983182i | \(0.558461\pi\) | |||||||
\(12\) | 1.29878 | 0.374926 | ||||||||
\(13\) | −1.04790 | −0.290635 | −0.145318 | − | 0.989385i | \(-0.546420\pi\) | ||||
−0.145318 | + | 0.989385i | \(0.546420\pi\) | |||||||
\(14\) | −3.57798 | −0.956254 | ||||||||
\(15\) | 3.74004 | 0.965675 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.73345 | −1.63310 | −0.816551 | − | 0.577273i | \(-0.804117\pi\) | ||||
−0.816551 | + | 0.577273i | \(0.804117\pi\) | |||||||
\(18\) | −1.31316 | −0.309516 | ||||||||
\(19\) | −2.53015 | −0.580457 | −0.290229 | − | 0.956957i | \(-0.593731\pi\) | ||||
−0.290229 | + | 0.956957i | \(0.593731\pi\) | |||||||
\(20\) | 2.87965 | 0.643910 | ||||||||
\(21\) | −4.64701 | −1.01406 | ||||||||
\(22\) | −1.21143 | −0.258277 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.29878 | 0.265113 | ||||||||
\(25\) | 3.29240 | 0.658479 | ||||||||
\(26\) | −1.04790 | −0.205510 | ||||||||
\(27\) | −5.60186 | −1.07808 | ||||||||
\(28\) | −3.57798 | −0.676174 | ||||||||
\(29\) | −2.36709 | −0.439558 | −0.219779 | − | 0.975550i | \(-0.570534\pi\) | ||||
−0.219779 | + | 0.975550i | \(0.570534\pi\) | |||||||
\(30\) | 3.74004 | 0.682835 | ||||||||
\(31\) | −4.49280 | −0.806931 | −0.403466 | − | 0.914995i | \(-0.632194\pi\) | ||||
−0.403466 | + | 0.914995i | \(0.632194\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.57338 | −0.273890 | ||||||||
\(34\) | −6.73345 | −1.15478 | ||||||||
\(35\) | −10.3033 | −1.74158 | ||||||||
\(36\) | −1.31316 | −0.218861 | ||||||||
\(37\) | 3.59289 | 0.590668 | 0.295334 | − | 0.955394i | \(-0.404569\pi\) | ||||
0.295334 | + | 0.955394i | \(0.404569\pi\) | |||||||
\(38\) | −2.53015 | −0.410445 | ||||||||
\(39\) | −1.36099 | −0.217933 | ||||||||
\(40\) | 2.87965 | 0.455313 | ||||||||
\(41\) | −4.03401 | −0.630006 | −0.315003 | − | 0.949091i | \(-0.602006\pi\) | ||||
−0.315003 | + | 0.949091i | \(0.602006\pi\) | |||||||
\(42\) | −4.64701 | −0.717049 | ||||||||
\(43\) | −1.35679 | −0.206908 | −0.103454 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103454 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(44\) | −1.21143 | −0.182630 | ||||||||
\(45\) | −3.78146 | −0.563706 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 8.78952 | 1.28208 | 0.641042 | − | 0.767506i | \(-0.278503\pi\) | ||||
0.641042 | + | 0.767506i | \(0.278503\pi\) | |||||||
\(48\) | 1.29878 | 0.187463 | ||||||||
\(49\) | 5.80191 | 0.828844 | ||||||||
\(50\) | 3.29240 | 0.465615 | ||||||||
\(51\) | −8.74529 | −1.22459 | ||||||||
\(52\) | −1.04790 | −0.145318 | ||||||||
\(53\) | 3.01840 | 0.414609 | 0.207304 | − | 0.978277i | \(-0.433531\pi\) | ||||
0.207304 | + | 0.978277i | \(0.433531\pi\) | |||||||
\(54\) | −5.60186 | −0.762317 | ||||||||
\(55\) | −3.48849 | −0.470388 | ||||||||
\(56\) | −3.57798 | −0.478127 | ||||||||
\(57\) | −3.28612 | −0.435257 | ||||||||
\(58\) | −2.36709 | −0.310815 | ||||||||
\(59\) | −2.93882 | −0.382602 | −0.191301 | − | 0.981531i | \(-0.561271\pi\) | ||||
−0.191301 | + | 0.981531i | \(0.561271\pi\) | |||||||
\(60\) | 3.74004 | 0.482837 | ||||||||
\(61\) | −0.722314 | −0.0924828 | −0.0462414 | − | 0.998930i | \(-0.514724\pi\) | ||||
−0.0462414 | + | 0.998930i | \(0.514724\pi\) | |||||||
\(62\) | −4.49280 | −0.570586 | ||||||||
\(63\) | 4.69847 | 0.591951 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.01759 | −0.374286 | ||||||||
\(66\) | −1.57338 | −0.193670 | ||||||||
\(67\) | −12.0647 | −1.47394 | −0.736970 | − | 0.675925i | \(-0.763744\pi\) | ||||
−0.736970 | + | 0.675925i | \(0.763744\pi\) | |||||||
\(68\) | −6.73345 | −0.816551 | ||||||||
\(69\) | 1.29878 | 0.156355 | ||||||||
\(70\) | −10.3033 | −1.23148 | ||||||||
\(71\) | −1.34627 | −0.159773 | −0.0798864 | − | 0.996804i | \(-0.525456\pi\) | ||||
−0.0798864 | + | 0.996804i | \(0.525456\pi\) | |||||||
\(72\) | −1.31316 | −0.154758 | ||||||||
\(73\) | −14.3307 | −1.67728 | −0.838641 | − | 0.544685i | \(-0.816649\pi\) | ||||
−0.838641 | + | 0.544685i | \(0.816649\pi\) | |||||||
\(74\) | 3.59289 | 0.417665 | ||||||||
\(75\) | 4.27611 | 0.493762 | ||||||||
\(76\) | −2.53015 | −0.290229 | ||||||||
\(77\) | 4.33446 | 0.493957 | ||||||||
\(78\) | −1.36099 | −0.154102 | ||||||||
\(79\) | 8.17446 | 0.919699 | 0.459849 | − | 0.887997i | \(-0.347903\pi\) | ||||
0.459849 | + | 0.887997i | \(0.347903\pi\) | |||||||
\(80\) | 2.87965 | 0.321955 | ||||||||
\(81\) | −3.33611 | −0.370679 | ||||||||
\(82\) | −4.03401 | −0.445482 | ||||||||
\(83\) | −2.57120 | −0.282226 | −0.141113 | − | 0.989994i | \(-0.545068\pi\) | ||||
−0.141113 | + | 0.989994i | \(0.545068\pi\) | |||||||
\(84\) | −4.64701 | −0.507031 | ||||||||
\(85\) | −19.3900 | −2.10314 | ||||||||
\(86\) | −1.35679 | −0.146306 | ||||||||
\(87\) | −3.07434 | −0.329604 | ||||||||
\(88\) | −1.21143 | −0.129139 | ||||||||
\(89\) | −8.39887 | −0.890279 | −0.445139 | − | 0.895461i | \(-0.646846\pi\) | ||||
−0.445139 | + | 0.895461i | \(0.646846\pi\) | |||||||
\(90\) | −3.78146 | −0.398600 | ||||||||
\(91\) | 3.74936 | 0.393040 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −5.83517 | −0.605079 | ||||||||
\(94\) | 8.78952 | 0.906570 | ||||||||
\(95\) | −7.28596 | −0.747524 | ||||||||
\(96\) | 1.29878 | 0.132556 | ||||||||
\(97\) | −1.82015 | −0.184808 | −0.0924041 | − | 0.995722i | \(-0.529455\pi\) | ||||
−0.0924041 | + | 0.995722i | \(0.529455\pi\) | |||||||
\(98\) | 5.80191 | 0.586081 | ||||||||
\(99\) | 1.59080 | 0.159882 | ||||||||
\(100\) | 3.29240 | 0.329240 | ||||||||
\(101\) | 5.20144 | 0.517562 | 0.258781 | − | 0.965936i | \(-0.416679\pi\) | ||||
0.258781 | + | 0.965936i | \(0.416679\pi\) | |||||||
\(102\) | −8.74529 | −0.865913 | ||||||||
\(103\) | 17.7702 | 1.75095 | 0.875473 | − | 0.483267i | \(-0.160550\pi\) | ||||
0.875473 | + | 0.483267i | \(0.160550\pi\) | |||||||
\(104\) | −1.04790 | −0.102755 | ||||||||
\(105\) | −13.3818 | −1.30593 | ||||||||
\(106\) | 3.01840 | 0.293173 | ||||||||
\(107\) | 6.79008 | 0.656422 | 0.328211 | − | 0.944604i | \(-0.393554\pi\) | ||||
0.328211 | + | 0.944604i | \(0.393554\pi\) | |||||||
\(108\) | −5.60186 | −0.539039 | ||||||||
\(109\) | 8.16821 | 0.782373 | 0.391186 | − | 0.920311i | \(-0.372065\pi\) | ||||
0.391186 | + | 0.920311i | \(0.372065\pi\) | |||||||
\(110\) | −3.48849 | −0.332614 | ||||||||
\(111\) | 4.66639 | 0.442914 | ||||||||
\(112\) | −3.57798 | −0.338087 | ||||||||
\(113\) | −3.26557 | −0.307199 | −0.153600 | − | 0.988133i | \(-0.549087\pi\) | ||||
−0.153600 | + | 0.988133i | \(0.549087\pi\) | |||||||
\(114\) | −3.28612 | −0.307773 | ||||||||
\(115\) | 2.87965 | 0.268529 | ||||||||
\(116\) | −2.36709 | −0.219779 | ||||||||
\(117\) | 1.37606 | 0.127217 | ||||||||
\(118\) | −2.93882 | −0.270540 | ||||||||
\(119\) | 24.0921 | 2.20852 | ||||||||
\(120\) | 3.74004 | 0.341418 | ||||||||
\(121\) | −9.53244 | −0.866586 | ||||||||
\(122\) | −0.722314 | −0.0653952 | ||||||||
\(123\) | −5.23930 | −0.472412 | ||||||||
\(124\) | −4.49280 | −0.403466 | ||||||||
\(125\) | −4.91731 | −0.439817 | ||||||||
\(126\) | 4.69847 | 0.418573 | ||||||||
\(127\) | 22.2684 | 1.97600 | 0.987998 | − | 0.154464i | \(-0.0493650\pi\) | ||||
0.987998 | + | 0.154464i | \(0.0493650\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.76217 | −0.155150 | ||||||||
\(130\) | −3.01759 | −0.264660 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −1.57338 | −0.136945 | ||||||||
\(133\) | 9.05283 | 0.784980 | ||||||||
\(134\) | −12.0647 | −1.04223 | ||||||||
\(135\) | −16.1314 | −1.38837 | ||||||||
\(136\) | −6.73345 | −0.577389 | ||||||||
\(137\) | −13.2723 | −1.13393 | −0.566964 | − | 0.823743i | \(-0.691882\pi\) | ||||
−0.566964 | + | 0.823743i | \(0.691882\pi\) | |||||||
\(138\) | 1.29878 | 0.110560 | ||||||||
\(139\) | −4.60002 | −0.390169 | −0.195084 | − | 0.980786i | \(-0.562498\pi\) | ||||
−0.195084 | + | 0.980786i | \(0.562498\pi\) | |||||||
\(140\) | −10.3033 | −0.870790 | ||||||||
\(141\) | 11.4157 | 0.961373 | ||||||||
\(142\) | −1.34627 | −0.112976 | ||||||||
\(143\) | 1.26945 | 0.106157 | ||||||||
\(144\) | −1.31316 | −0.109430 | ||||||||
\(145\) | −6.81641 | −0.566072 | ||||||||
\(146\) | −14.3307 | −1.18602 | ||||||||
\(147\) | 7.53541 | 0.621510 | ||||||||
\(148\) | 3.59289 | 0.295334 | ||||||||
\(149\) | 11.8855 | 0.973695 | 0.486847 | − | 0.873487i | \(-0.338147\pi\) | ||||
0.486847 | + | 0.873487i | \(0.338147\pi\) | |||||||
\(150\) | 4.27611 | 0.349143 | ||||||||
\(151\) | −16.0358 | −1.30497 | −0.652487 | − | 0.757800i | \(-0.726274\pi\) | ||||
−0.652487 | + | 0.757800i | \(0.726274\pi\) | |||||||
\(152\) | −2.53015 | −0.205223 | ||||||||
\(153\) | 8.84213 | 0.714844 | ||||||||
\(154\) | 4.33446 | 0.349281 | ||||||||
\(155\) | −12.9377 | −1.03918 | ||||||||
\(156\) | −1.36099 | −0.108967 | ||||||||
\(157\) | 9.20977 | 0.735020 | 0.367510 | − | 0.930020i | \(-0.380210\pi\) | ||||
0.367510 | + | 0.930020i | \(0.380210\pi\) | |||||||
\(158\) | 8.17446 | 0.650325 | ||||||||
\(159\) | 3.92024 | 0.310895 | ||||||||
\(160\) | 2.87965 | 0.227656 | ||||||||
\(161\) | −3.57798 | −0.281984 | ||||||||
\(162\) | −3.33611 | −0.262109 | ||||||||
\(163\) | −7.37833 | −0.577916 | −0.288958 | − | 0.957342i | \(-0.593309\pi\) | ||||
−0.288958 | + | 0.957342i | \(0.593309\pi\) | |||||||
\(164\) | −4.03401 | −0.315003 | ||||||||
\(165\) | −4.53079 | −0.352722 | ||||||||
\(166\) | −2.57120 | −0.199564 | ||||||||
\(167\) | −9.50905 | −0.735832 | −0.367916 | − | 0.929859i | \(-0.619929\pi\) | ||||
−0.367916 | + | 0.929859i | \(0.619929\pi\) | |||||||
\(168\) | −4.64701 | −0.358525 | ||||||||
\(169\) | −11.9019 | −0.915531 | ||||||||
\(170\) | −19.3900 | −1.48714 | ||||||||
\(171\) | 3.32251 | 0.254078 | ||||||||
\(172\) | −1.35679 | −0.103454 | ||||||||
\(173\) | 7.14326 | 0.543092 | 0.271546 | − | 0.962425i | \(-0.412465\pi\) | ||||
0.271546 | + | 0.962425i | \(0.412465\pi\) | |||||||
\(174\) | −3.07434 | −0.233065 | ||||||||
\(175\) | −11.7801 | −0.890493 | ||||||||
\(176\) | −1.21143 | −0.0913148 | ||||||||
\(177\) | −3.81689 | −0.286895 | ||||||||
\(178\) | −8.39887 | −0.629522 | ||||||||
\(179\) | 1.15119 | 0.0860443 | 0.0430222 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430222 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(180\) | −3.78146 | −0.281853 | ||||||||
\(181\) | 10.6770 | 0.793614 | 0.396807 | − | 0.917902i | \(-0.370118\pi\) | ||||
0.396807 | + | 0.917902i | \(0.370118\pi\) | |||||||
\(182\) | 3.74936 | 0.277921 | ||||||||
\(183\) | −0.938128 | −0.0693485 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 10.3463 | 0.760674 | ||||||||
\(186\) | −5.83517 | −0.427856 | ||||||||
\(187\) | 8.15709 | 0.596505 | ||||||||
\(188\) | 8.78952 | 0.641042 | ||||||||
\(189\) | 20.0433 | 1.45794 | ||||||||
\(190\) | −7.28596 | −0.528579 | ||||||||
\(191\) | 6.95720 | 0.503406 | 0.251703 | − | 0.967805i | \(-0.419009\pi\) | ||||
0.251703 | + | 0.967805i | \(0.419009\pi\) | |||||||
\(192\) | 1.29878 | 0.0937316 | ||||||||
\(193\) | −18.3198 | −1.31869 | −0.659345 | − | 0.751841i | \(-0.729166\pi\) | ||||
−0.659345 | + | 0.751841i | \(0.729166\pi\) | |||||||
\(194\) | −1.82015 | −0.130679 | ||||||||
\(195\) | −3.91919 | −0.280659 | ||||||||
\(196\) | 5.80191 | 0.414422 | ||||||||
\(197\) | −6.99960 | −0.498701 | −0.249350 | − | 0.968413i | \(-0.580217\pi\) | ||||
−0.249350 | + | 0.968413i | \(0.580217\pi\) | |||||||
\(198\) | 1.59080 | 0.113053 | ||||||||
\(199\) | −9.68250 | −0.686374 | −0.343187 | − | 0.939267i | \(-0.611506\pi\) | ||||
−0.343187 | + | 0.939267i | \(0.611506\pi\) | |||||||
\(200\) | 3.29240 | 0.232808 | ||||||||
\(201\) | −15.6694 | −1.10524 | ||||||||
\(202\) | 5.20144 | 0.365972 | ||||||||
\(203\) | 8.46940 | 0.594436 | ||||||||
\(204\) | −8.74529 | −0.612293 | ||||||||
\(205\) | −11.6165 | −0.811334 | ||||||||
\(206\) | 17.7702 | 1.23811 | ||||||||
\(207\) | −1.31316 | −0.0912712 | ||||||||
\(208\) | −1.04790 | −0.0726588 | ||||||||
\(209\) | 3.06510 | 0.212017 | ||||||||
\(210\) | −13.3818 | −0.923430 | ||||||||
\(211\) | −0.926514 | −0.0637839 | −0.0318919 | − | 0.999491i | \(-0.510153\pi\) | ||||
−0.0318919 | + | 0.999491i | \(0.510153\pi\) | |||||||
\(212\) | 3.01840 | 0.207304 | ||||||||
\(213\) | −1.74851 | −0.119806 | ||||||||
\(214\) | 6.79008 | 0.464160 | ||||||||
\(215\) | −3.90707 | −0.266460 | ||||||||
\(216\) | −5.60186 | −0.381158 | ||||||||
\(217\) | 16.0751 | 1.09125 | ||||||||
\(218\) | 8.16821 | 0.553221 | ||||||||
\(219\) | −18.6125 | −1.25771 | ||||||||
\(220\) | −3.48849 | −0.235194 | ||||||||
\(221\) | 7.05598 | 0.474637 | ||||||||
\(222\) | 4.66639 | 0.313187 | ||||||||
\(223\) | −25.2594 | −1.69150 | −0.845749 | − | 0.533582i | \(-0.820846\pi\) | ||||
−0.845749 | + | 0.533582i | \(0.820846\pi\) | |||||||
\(224\) | −3.57798 | −0.239064 | ||||||||
\(225\) | −4.32346 | −0.288230 | ||||||||
\(226\) | −3.26557 | −0.217223 | ||||||||
\(227\) | 12.0184 | 0.797692 | 0.398846 | − | 0.917018i | \(-0.369411\pi\) | ||||
0.398846 | + | 0.917018i | \(0.369411\pi\) | |||||||
\(228\) | −3.28612 | −0.217629 | ||||||||
\(229\) | 21.5872 | 1.42653 | 0.713263 | − | 0.700897i | \(-0.247217\pi\) | ||||
0.713263 | + | 0.700897i | \(0.247217\pi\) | |||||||
\(230\) | 2.87965 | 0.189879 | ||||||||
\(231\) | 5.62952 | 0.370395 | ||||||||
\(232\) | −2.36709 | −0.155407 | ||||||||
\(233\) | 0.772477 | 0.0506066 | 0.0253033 | − | 0.999680i | \(-0.491945\pi\) | ||||
0.0253033 | + | 0.999680i | \(0.491945\pi\) | |||||||
\(234\) | 1.37606 | 0.0899561 | ||||||||
\(235\) | 25.3108 | 1.65109 | ||||||||
\(236\) | −2.93882 | −0.191301 | ||||||||
\(237\) | 10.6168 | 0.689638 | ||||||||
\(238\) | 24.0921 | 1.56166 | ||||||||
\(239\) | 11.3578 | 0.734677 | 0.367339 | − | 0.930087i | \(-0.380269\pi\) | ||||
0.367339 | + | 0.930087i | \(0.380269\pi\) | |||||||
\(240\) | 3.74004 | 0.241419 | ||||||||
\(241\) | −8.33944 | −0.537191 | −0.268595 | − | 0.963253i | \(-0.586559\pi\) | ||||
−0.268595 | + | 0.963253i | \(0.586559\pi\) | |||||||
\(242\) | −9.53244 | −0.612769 | ||||||||
\(243\) | 12.4727 | 0.800125 | ||||||||
\(244\) | −0.722314 | −0.0462414 | ||||||||
\(245\) | 16.7075 | 1.06740 | ||||||||
\(246\) | −5.23930 | −0.334045 | ||||||||
\(247\) | 2.65135 | 0.168701 | ||||||||
\(248\) | −4.49280 | −0.285293 | ||||||||
\(249\) | −3.33943 | −0.211628 | ||||||||
\(250\) | −4.91731 | −0.310998 | ||||||||
\(251\) | 1.91642 | 0.120963 | 0.0604815 | − | 0.998169i | \(-0.480736\pi\) | ||||
0.0604815 | + | 0.998169i | \(0.480736\pi\) | |||||||
\(252\) | 4.69847 | 0.295976 | ||||||||
\(253\) | −1.21143 | −0.0761618 | ||||||||
\(254\) | 22.2684 | 1.39724 | ||||||||
\(255\) | −25.1834 | −1.57704 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.91386 | 0.556031 | 0.278016 | − | 0.960577i | \(-0.410323\pi\) | ||||
0.278016 | + | 0.960577i | \(0.410323\pi\) | |||||||
\(258\) | −1.76217 | −0.109708 | ||||||||
\(259\) | −12.8553 | −0.798789 | ||||||||
\(260\) | −3.01759 | −0.187143 | ||||||||
\(261\) | 3.10838 | 0.192404 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | −20.1270 | −1.24108 | −0.620542 | − | 0.784174i | \(-0.713087\pi\) | ||||
−0.620542 | + | 0.784174i | \(0.713087\pi\) | |||||||
\(264\) | −1.57338 | −0.0968349 | ||||||||
\(265\) | 8.69193 | 0.533941 | ||||||||
\(266\) | 9.05283 | 0.555064 | ||||||||
\(267\) | −10.9083 | −0.667578 | ||||||||
\(268\) | −12.0647 | −0.736970 | ||||||||
\(269\) | −4.97063 | −0.303065 | −0.151532 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151532 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(270\) | −16.1314 | −0.981727 | ||||||||
\(271\) | 0.105264 | 0.00639432 | 0.00319716 | − | 0.999995i | \(-0.498982\pi\) | ||||
0.00319716 | + | 0.999995i | \(0.498982\pi\) | |||||||
\(272\) | −6.73345 | −0.408275 | ||||||||
\(273\) | 4.86960 | 0.294722 | ||||||||
\(274\) | −13.2723 | −0.801808 | ||||||||
\(275\) | −3.98850 | −0.240516 | ||||||||
\(276\) | 1.29878 | 0.0781775 | ||||||||
\(277\) | 2.27158 | 0.136486 | 0.0682431 | − | 0.997669i | \(-0.478261\pi\) | ||||
0.0682431 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(278\) | −4.60002 | −0.275891 | ||||||||
\(279\) | 5.89979 | 0.353211 | ||||||||
\(280\) | −10.3033 | −0.615741 | ||||||||
\(281\) | 26.1385 | 1.55929 | 0.779646 | − | 0.626221i | \(-0.215399\pi\) | ||||
0.779646 | + | 0.626221i | \(0.215399\pi\) | |||||||
\(282\) | 11.4157 | 0.679794 | ||||||||
\(283\) | −5.64096 | −0.335320 | −0.167660 | − | 0.985845i | \(-0.553621\pi\) | ||||
−0.167660 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(284\) | −1.34627 | −0.0798864 | ||||||||
\(285\) | −9.46288 | −0.560533 | ||||||||
\(286\) | 1.26945 | 0.0750644 | ||||||||
\(287\) | 14.4336 | 0.851987 | ||||||||
\(288\) | −1.31316 | −0.0773789 | ||||||||
\(289\) | 28.3394 | 1.66702 | ||||||||
\(290\) | −6.81641 | −0.400273 | ||||||||
\(291\) | −2.36398 | −0.138579 | ||||||||
\(292\) | −14.3307 | −0.838641 | ||||||||
\(293\) | −25.3398 | −1.48037 | −0.740183 | − | 0.672406i | \(-0.765261\pi\) | ||||
−0.740183 | + | 0.672406i | \(0.765261\pi\) | |||||||
\(294\) | 7.53541 | 0.439474 | ||||||||
\(295\) | −8.46277 | −0.492722 | ||||||||
\(296\) | 3.59289 | 0.208833 | ||||||||
\(297\) | 6.78625 | 0.393778 | ||||||||
\(298\) | 11.8855 | 0.688506 | ||||||||
\(299\) | −1.04790 | −0.0606016 | ||||||||
\(300\) | 4.27611 | 0.246881 | ||||||||
\(301\) | 4.85455 | 0.279811 | ||||||||
\(302\) | −16.0358 | −0.922756 | ||||||||
\(303\) | 6.75554 | 0.388095 | ||||||||
\(304\) | −2.53015 | −0.145114 | ||||||||
\(305\) | −2.08001 | −0.119101 | ||||||||
\(306\) | 8.84213 | 0.505471 | ||||||||
\(307\) | 30.2571 | 1.72687 | 0.863433 | − | 0.504464i | \(-0.168310\pi\) | ||||
0.863433 | + | 0.504464i | \(0.168310\pi\) | |||||||
\(308\) | 4.33446 | 0.246979 | ||||||||
\(309\) | 23.0796 | 1.31295 | ||||||||
\(310\) | −12.9377 | −0.734812 | ||||||||
\(311\) | 10.5052 | 0.595694 | 0.297847 | − | 0.954614i | \(-0.403731\pi\) | ||||
0.297847 | + | 0.954614i | \(0.403731\pi\) | |||||||
\(312\) | −1.36099 | −0.0770511 | ||||||||
\(313\) | 19.7062 | 1.11386 | 0.556930 | − | 0.830559i | \(-0.311979\pi\) | ||||
0.556930 | + | 0.830559i | \(0.311979\pi\) | |||||||
\(314\) | 9.20977 | 0.519737 | ||||||||
\(315\) | 13.5300 | 0.762327 | ||||||||
\(316\) | 8.17446 | 0.459849 | ||||||||
\(317\) | −23.6058 | −1.32583 | −0.662916 | − | 0.748694i | \(-0.730681\pi\) | ||||
−0.662916 | + | 0.748694i | \(0.730681\pi\) | |||||||
\(318\) | 3.92024 | 0.219836 | ||||||||
\(319\) | 2.86756 | 0.160553 | ||||||||
\(320\) | 2.87965 | 0.160977 | ||||||||
\(321\) | 8.81884 | 0.492219 | ||||||||
\(322\) | −3.57798 | −0.199393 | ||||||||
\(323\) | 17.0367 | 0.947945 | ||||||||
\(324\) | −3.33611 | −0.185339 | ||||||||
\(325\) | −3.45010 | −0.191377 | ||||||||
\(326\) | −7.37833 | −0.408648 | ||||||||
\(327\) | 10.6087 | 0.586664 | ||||||||
\(328\) | −4.03401 | −0.222741 | ||||||||
\(329\) | −31.4487 | −1.73382 | ||||||||
\(330\) | −4.53079 | −0.249412 | ||||||||
\(331\) | 24.5531 | 1.34956 | 0.674779 | − | 0.738020i | \(-0.264239\pi\) | ||||
0.674779 | + | 0.738020i | \(0.264239\pi\) | |||||||
\(332\) | −2.57120 | −0.141113 | ||||||||
\(333\) | −4.71806 | −0.258548 | ||||||||
\(334\) | −9.50905 | −0.520312 | ||||||||
\(335\) | −34.7422 | −1.89817 | ||||||||
\(336\) | −4.64701 | −0.253515 | ||||||||
\(337\) | 0.827698 | 0.0450876 | 0.0225438 | − | 0.999746i | \(-0.492823\pi\) | ||||
0.0225438 | + | 0.999746i | \(0.492823\pi\) | |||||||
\(338\) | −11.9019 | −0.647378 | ||||||||
\(339\) | −4.24127 | −0.230354 | ||||||||
\(340\) | −19.3900 | −1.05157 | ||||||||
\(341\) | 5.44271 | 0.294739 | ||||||||
\(342\) | 3.32251 | 0.179661 | ||||||||
\(343\) | 4.28675 | 0.231463 | ||||||||
\(344\) | −1.35679 | −0.0731530 | ||||||||
\(345\) | 3.74004 | 0.201357 | ||||||||
\(346\) | 7.14326 | 0.384024 | ||||||||
\(347\) | −1.61910 | −0.0869177 | −0.0434589 | − | 0.999055i | \(-0.513838\pi\) | ||||
−0.0434589 | + | 0.999055i | \(0.513838\pi\) | |||||||
\(348\) | −3.07434 | −0.164802 | ||||||||
\(349\) | −10.1191 | −0.541661 | −0.270831 | − | 0.962627i | \(-0.587298\pi\) | ||||
−0.270831 | + | 0.962627i | \(0.587298\pi\) | |||||||
\(350\) | −11.7801 | −0.629673 | ||||||||
\(351\) | 5.87019 | 0.313328 | ||||||||
\(352\) | −1.21143 | −0.0645693 | ||||||||
\(353\) | −20.1340 | −1.07162 | −0.535812 | − | 0.844337i | \(-0.679994\pi\) | ||||
−0.535812 | + | 0.844337i | \(0.679994\pi\) | |||||||
\(354\) | −3.81689 | −0.202865 | ||||||||
\(355\) | −3.87679 | −0.205759 | ||||||||
\(356\) | −8.39887 | −0.445139 | ||||||||
\(357\) | 31.2904 | 1.65606 | ||||||||
\(358\) | 1.15119 | 0.0608425 | ||||||||
\(359\) | −18.7206 | −0.988035 | −0.494017 | − | 0.869452i | \(-0.664472\pi\) | ||||
−0.494017 | + | 0.869452i | \(0.664472\pi\) | |||||||
\(360\) | −3.78146 | −0.199300 | ||||||||
\(361\) | −12.5983 | −0.663070 | ||||||||
\(362\) | 10.6770 | 0.561170 | ||||||||
\(363\) | −12.3806 | −0.649811 | ||||||||
\(364\) | 3.74936 | 0.196520 | ||||||||
\(365\) | −41.2674 | −2.16004 | ||||||||
\(366\) | −0.938128 | −0.0490368 | ||||||||
\(367\) | 27.6525 | 1.44345 | 0.721723 | − | 0.692182i | \(-0.243350\pi\) | ||||
0.721723 | + | 0.692182i | \(0.243350\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 5.29731 | 0.275767 | ||||||||
\(370\) | 10.3463 | 0.537878 | ||||||||
\(371\) | −10.7997 | −0.560695 | ||||||||
\(372\) | −5.83517 | −0.302540 | ||||||||
\(373\) | −16.0419 | −0.830621 | −0.415310 | − | 0.909680i | \(-0.636327\pi\) | ||||
−0.415310 | + | 0.909680i | \(0.636327\pi\) | |||||||
\(374\) | 8.15709 | 0.421793 | ||||||||
\(375\) | −6.38651 | −0.329798 | ||||||||
\(376\) | 8.78952 | 0.453285 | ||||||||
\(377\) | 2.48048 | 0.127751 | ||||||||
\(378\) | 20.0433 | 1.03092 | ||||||||
\(379\) | 6.99216 | 0.359163 | 0.179582 | − | 0.983743i | \(-0.442526\pi\) | ||||
0.179582 | + | 0.983743i | \(0.442526\pi\) | |||||||
\(380\) | −7.28596 | −0.373762 | ||||||||
\(381\) | 28.9217 | 1.48171 | ||||||||
\(382\) | 6.95720 | 0.355962 | ||||||||
\(383\) | 18.2335 | 0.931688 | 0.465844 | − | 0.884867i | \(-0.345751\pi\) | ||||
0.465844 | + | 0.884867i | \(0.345751\pi\) | |||||||
\(384\) | 1.29878 | 0.0662782 | ||||||||
\(385\) | 12.4817 | 0.636128 | ||||||||
\(386\) | −18.3198 | −0.932455 | ||||||||
\(387\) | 1.78168 | 0.0905680 | ||||||||
\(388\) | −1.82015 | −0.0924041 | ||||||||
\(389\) | −18.8141 | −0.953913 | −0.476956 | − | 0.878927i | \(-0.658260\pi\) | ||||
−0.476956 | + | 0.878927i | \(0.658260\pi\) | |||||||
\(390\) | −3.91919 | −0.198456 | ||||||||
\(391\) | −6.73345 | −0.340525 | ||||||||
\(392\) | 5.80191 | 0.293040 | ||||||||
\(393\) | −1.29878 | −0.0655149 | ||||||||
\(394\) | −6.99960 | −0.352635 | ||||||||
\(395\) | 23.5396 | 1.18441 | ||||||||
\(396\) | 1.59080 | 0.0799409 | ||||||||
\(397\) | 16.8205 | 0.844196 | 0.422098 | − | 0.906550i | \(-0.361294\pi\) | ||||
0.422098 | + | 0.906550i | \(0.361294\pi\) | |||||||
\(398\) | −9.68250 | −0.485340 | ||||||||
\(399\) | 11.7577 | 0.588619 | ||||||||
\(400\) | 3.29240 | 0.164620 | ||||||||
\(401\) | 24.0199 | 1.19950 | 0.599749 | − | 0.800188i | \(-0.295267\pi\) | ||||
0.599749 | + | 0.800188i | \(0.295267\pi\) | |||||||
\(402\) | −15.6694 | −0.781521 | ||||||||
\(403\) | 4.70801 | 0.234523 | ||||||||
\(404\) | 5.20144 | 0.258781 | ||||||||
\(405\) | −9.60683 | −0.477367 | ||||||||
\(406\) | 8.46940 | 0.420329 | ||||||||
\(407\) | −4.35253 | −0.215747 | ||||||||
\(408\) | −8.74529 | −0.432956 | ||||||||
\(409\) | −1.45554 | −0.0719718 | −0.0359859 | − | 0.999352i | \(-0.511457\pi\) | ||||
−0.0359859 | + | 0.999352i | \(0.511457\pi\) | |||||||
\(410\) | −11.6165 | −0.573700 | ||||||||
\(411\) | −17.2378 | −0.850279 | ||||||||
\(412\) | 17.7702 | 0.875473 | ||||||||
\(413\) | 10.5150 | 0.517410 | ||||||||
\(414\) | −1.31316 | −0.0645385 | ||||||||
\(415\) | −7.40416 | −0.363456 | ||||||||
\(416\) | −1.04790 | −0.0513775 | ||||||||
\(417\) | −5.97442 | −0.292569 | ||||||||
\(418\) | 3.06510 | 0.149919 | ||||||||
\(419\) | 33.6359 | 1.64322 | 0.821612 | − | 0.570047i | \(-0.193075\pi\) | ||||
0.821612 | + | 0.570047i | \(0.193075\pi\) | |||||||
\(420\) | −13.3818 | −0.652964 | ||||||||
\(421\) | −29.1473 | −1.42055 | −0.710276 | − | 0.703923i | \(-0.751430\pi\) | ||||
−0.710276 | + | 0.703923i | \(0.751430\pi\) | |||||||
\(422\) | −0.926514 | −0.0451020 | ||||||||
\(423\) | −11.5421 | −0.561195 | ||||||||
\(424\) | 3.01840 | 0.146586 | ||||||||
\(425\) | −22.1692 | −1.07536 | ||||||||
\(426\) | −1.74851 | −0.0847156 | ||||||||
\(427\) | 2.58442 | 0.125069 | ||||||||
\(428\) | 6.79008 | 0.328211 | ||||||||
\(429\) | 1.64875 | 0.0796022 | ||||||||
\(430\) | −3.90707 | −0.188416 | ||||||||
\(431\) | −28.2169 | −1.35916 | −0.679581 | − | 0.733601i | \(-0.737838\pi\) | ||||
−0.679581 | + | 0.733601i | \(0.737838\pi\) | |||||||
\(432\) | −5.60186 | −0.269520 | ||||||||
\(433\) | −1.85854 | −0.0893158 | −0.0446579 | − | 0.999002i | \(-0.514220\pi\) | ||||
−0.0446579 | + | 0.999002i | \(0.514220\pi\) | |||||||
\(434\) | 16.0751 | 0.771631 | ||||||||
\(435\) | −8.85303 | −0.424470 | ||||||||
\(436\) | 8.16821 | 0.391186 | ||||||||
\(437\) | −2.53015 | −0.121034 | ||||||||
\(438\) | −18.6125 | −0.889338 | ||||||||
\(439\) | 28.4457 | 1.35764 | 0.678819 | − | 0.734306i | \(-0.262492\pi\) | ||||
0.678819 | + | 0.734306i | \(0.262492\pi\) | |||||||
\(440\) | −3.48849 | −0.166307 | ||||||||
\(441\) | −7.61885 | −0.362803 | ||||||||
\(442\) | 7.05598 | 0.335619 | ||||||||
\(443\) | −12.7941 | −0.607867 | −0.303934 | − | 0.952693i | \(-0.598300\pi\) | ||||
−0.303934 | + | 0.952693i | \(0.598300\pi\) | |||||||
\(444\) | 4.66639 | 0.221457 | ||||||||
\(445\) | −24.1858 | −1.14652 | ||||||||
\(446\) | −25.2594 | −1.19607 | ||||||||
\(447\) | 15.4366 | 0.730127 | ||||||||
\(448\) | −3.57798 | −0.169043 | ||||||||
\(449\) | −3.35017 | −0.158104 | −0.0790521 | − | 0.996870i | \(-0.525189\pi\) | ||||
−0.0790521 | + | 0.996870i | \(0.525189\pi\) | |||||||
\(450\) | −4.32346 | −0.203810 | ||||||||
\(451\) | 4.88691 | 0.230115 | ||||||||
\(452\) | −3.26557 | −0.153600 | ||||||||
\(453\) | −20.8270 | −0.978538 | ||||||||
\(454\) | 12.0184 | 0.564053 | ||||||||
\(455\) | 10.7969 | 0.506164 | ||||||||
\(456\) | −3.28612 | −0.153887 | ||||||||
\(457\) | −9.79457 | −0.458170 | −0.229085 | − | 0.973406i | \(-0.573573\pi\) | ||||
−0.229085 | + | 0.973406i | \(0.573573\pi\) | |||||||
\(458\) | 21.5872 | 1.00871 | ||||||||
\(459\) | 37.7199 | 1.76061 | ||||||||
\(460\) | 2.87965 | 0.134264 | ||||||||
\(461\) | −3.92003 | −0.182574 | −0.0912869 | − | 0.995825i | \(-0.529098\pi\) | ||||
−0.0912869 | + | 0.995825i | \(0.529098\pi\) | |||||||
\(462\) | 5.62952 | 0.261909 | ||||||||
\(463\) | 30.5027 | 1.41758 | 0.708791 | − | 0.705419i | \(-0.249241\pi\) | ||||
0.708791 | + | 0.705419i | \(0.249241\pi\) | |||||||
\(464\) | −2.36709 | −0.109890 | ||||||||
\(465\) | −16.8033 | −0.779233 | ||||||||
\(466\) | 0.772477 | 0.0357843 | ||||||||
\(467\) | 38.6037 | 1.78637 | 0.893183 | − | 0.449692i | \(-0.148466\pi\) | ||||
0.893183 | + | 0.449692i | \(0.148466\pi\) | |||||||
\(468\) | 1.37606 | 0.0636086 | ||||||||
\(469\) | 43.1673 | 1.99328 | ||||||||
\(470\) | 25.3108 | 1.16750 | ||||||||
\(471\) | 11.9615 | 0.551156 | ||||||||
\(472\) | −2.93882 | −0.135270 | ||||||||
\(473\) | 1.64365 | 0.0755750 | ||||||||
\(474\) | 10.6168 | 0.487648 | ||||||||
\(475\) | −8.33027 | −0.382219 | ||||||||
\(476\) | 24.0921 | 1.10426 | ||||||||
\(477\) | −3.96365 | −0.181483 | ||||||||
\(478\) | 11.3578 | 0.519495 | ||||||||
\(479\) | 14.5801 | 0.666180 | 0.333090 | − | 0.942895i | \(-0.391909\pi\) | ||||
0.333090 | + | 0.942895i | \(0.391909\pi\) | |||||||
\(480\) | 3.74004 | 0.170709 | ||||||||
\(481\) | −3.76499 | −0.171669 | ||||||||
\(482\) | −8.33944 | −0.379851 | ||||||||
\(483\) | −4.64701 | −0.211446 | ||||||||
\(484\) | −9.53244 | −0.433293 | ||||||||
\(485\) | −5.24139 | −0.237999 | ||||||||
\(486\) | 12.4727 | 0.565773 | ||||||||
\(487\) | −27.0085 | −1.22387 | −0.611935 | − | 0.790908i | \(-0.709609\pi\) | ||||
−0.611935 | + | 0.790908i | \(0.709609\pi\) | |||||||
\(488\) | −0.722314 | −0.0326976 | ||||||||
\(489\) | −9.58285 | −0.433351 | ||||||||
\(490\) | 16.7075 | 0.754767 | ||||||||
\(491\) | 3.42553 | 0.154592 | 0.0772960 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772960 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(492\) | −5.23930 | −0.236206 | ||||||||
\(493\) | 15.9387 | 0.717843 | ||||||||
\(494\) | 2.65135 | 0.119290 | ||||||||
\(495\) | 4.58096 | 0.205899 | ||||||||
\(496\) | −4.49280 | −0.201733 | ||||||||
\(497\) | 4.81692 | 0.216068 | ||||||||
\(498\) | −3.33943 | −0.149643 | ||||||||
\(499\) | 24.9775 | 1.11815 | 0.559073 | − | 0.829119i | \(-0.311157\pi\) | ||||
0.559073 | + | 0.829119i | \(0.311157\pi\) | |||||||
\(500\) | −4.91731 | −0.219909 | ||||||||
\(501\) | −12.3502 | −0.551766 | ||||||||
\(502\) | 1.91642 | 0.0855338 | ||||||||
\(503\) | −1.55078 | −0.0691460 | −0.0345730 | − | 0.999402i | \(-0.511007\pi\) | ||||
−0.0345730 | + | 0.999402i | \(0.511007\pi\) | |||||||
\(504\) | 4.69847 | 0.209286 | ||||||||
\(505\) | 14.9783 | 0.666527 | ||||||||
\(506\) | −1.21143 | −0.0538545 | ||||||||
\(507\) | −15.4580 | −0.686513 | ||||||||
\(508\) | 22.2684 | 0.987998 | ||||||||
\(509\) | −17.3850 | −0.770575 | −0.385287 | − | 0.922797i | \(-0.625898\pi\) | ||||
−0.385287 | + | 0.922797i | \(0.625898\pi\) | |||||||
\(510\) | −25.1834 | −1.11514 | ||||||||
\(511\) | 51.2749 | 2.26827 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 14.1736 | 0.625778 | ||||||||
\(514\) | 8.91386 | 0.393174 | ||||||||
\(515\) | 51.1719 | 2.25490 | ||||||||
\(516\) | −1.76217 | −0.0775752 | ||||||||
\(517\) | −10.6479 | −0.468293 | ||||||||
\(518\) | −12.8553 | −0.564829 | ||||||||
\(519\) | 9.27754 | 0.407239 | ||||||||
\(520\) | −3.01759 | −0.132330 | ||||||||
\(521\) | 10.6051 | 0.464619 | 0.232309 | − | 0.972642i | \(-0.425372\pi\) | ||||
0.232309 | + | 0.972642i | \(0.425372\pi\) | |||||||
\(522\) | 3.10838 | 0.136050 | ||||||||
\(523\) | −23.4166 | −1.02394 | −0.511969 | − | 0.859004i | \(-0.671084\pi\) | ||||
−0.511969 | + | 0.859004i | \(0.671084\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −15.2998 | −0.667738 | ||||||||
\(526\) | −20.1270 | −0.877578 | ||||||||
\(527\) | 30.2521 | 1.31780 | ||||||||
\(528\) | −1.57338 | −0.0684726 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 8.69193 | 0.377553 | ||||||||
\(531\) | 3.85915 | 0.167473 | ||||||||
\(532\) | 9.05283 | 0.392490 | ||||||||
\(533\) | 4.22724 | 0.183102 | ||||||||
\(534\) | −10.9083 | −0.472049 | ||||||||
\(535\) | 19.5531 | 0.845353 | ||||||||
\(536\) | −12.0647 | −0.521117 | ||||||||
\(537\) | 1.49515 | 0.0645205 | ||||||||
\(538\) | −4.97063 | −0.214299 | ||||||||
\(539\) | −7.02859 | −0.302743 | ||||||||
\(540\) | −16.1314 | −0.694185 | ||||||||
\(541\) | −20.1763 | −0.867445 | −0.433723 | − | 0.901046i | \(-0.642800\pi\) | ||||
−0.433723 | + | 0.901046i | \(0.642800\pi\) | |||||||
\(542\) | 0.105264 | 0.00452147 | ||||||||
\(543\) | 13.8671 | 0.595093 | ||||||||
\(544\) | −6.73345 | −0.288694 | ||||||||
\(545\) | 23.5216 | 1.00756 | ||||||||
\(546\) | 4.86960 | 0.208400 | ||||||||
\(547\) | −41.1622 | −1.75997 | −0.879984 | − | 0.475004i | \(-0.842447\pi\) | ||||
−0.879984 | + | 0.475004i | \(0.842447\pi\) | |||||||
\(548\) | −13.2723 | −0.566964 | ||||||||
\(549\) | 0.948517 | 0.0404817 | ||||||||
\(550\) | −3.98850 | −0.170070 | ||||||||
\(551\) | 5.98911 | 0.255145 | ||||||||
\(552\) | 1.29878 | 0.0552799 | ||||||||
\(553\) | −29.2480 | −1.24375 | ||||||||
\(554\) | 2.27158 | 0.0965104 | ||||||||
\(555\) | 13.4376 | 0.570393 | ||||||||
\(556\) | −4.60002 | −0.195084 | ||||||||
\(557\) | 1.30671 | 0.0553670 | 0.0276835 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276835 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(558\) | 5.89979 | 0.249758 | ||||||||
\(559\) | 1.42178 | 0.0601347 | ||||||||
\(560\) | −10.3033 | −0.435395 | ||||||||
\(561\) | 10.5943 | 0.447291 | ||||||||
\(562\) | 26.1385 | 1.10259 | ||||||||
\(563\) | −37.6195 | −1.58547 | −0.792737 | − | 0.609563i | \(-0.791345\pi\) | ||||
−0.792737 | + | 0.609563i | \(0.791345\pi\) | |||||||
\(564\) | 11.4157 | 0.480687 | ||||||||
\(565\) | −9.40371 | −0.395617 | ||||||||
\(566\) | −5.64096 | −0.237107 | ||||||||
\(567\) | 11.9365 | 0.501286 | ||||||||
\(568\) | −1.34627 | −0.0564882 | ||||||||
\(569\) | −4.25748 | −0.178483 | −0.0892414 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892414 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(570\) | −9.46288 | −0.396356 | ||||||||
\(571\) | −14.2901 | −0.598021 | −0.299011 | − | 0.954250i | \(-0.596657\pi\) | ||||
−0.299011 | + | 0.954250i | \(0.596657\pi\) | |||||||
\(572\) | 1.26945 | 0.0530786 | ||||||||
\(573\) | 9.03590 | 0.377480 | ||||||||
\(574\) | 14.4336 | 0.602446 | ||||||||
\(575\) | 3.29240 | 0.137302 | ||||||||
\(576\) | −1.31316 | −0.0547152 | ||||||||
\(577\) | −16.7062 | −0.695490 | −0.347745 | − | 0.937589i | \(-0.613053\pi\) | ||||
−0.347745 | + | 0.937589i | \(0.613053\pi\) | |||||||
\(578\) | 28.3394 | 1.17876 | ||||||||
\(579\) | −23.7935 | −0.988823 | ||||||||
\(580\) | −6.81641 | −0.283036 | ||||||||
\(581\) | 9.19968 | 0.381667 | ||||||||
\(582\) | −2.36398 | −0.0979900 | ||||||||
\(583\) | −3.65657 | −0.151440 | ||||||||
\(584\) | −14.3307 | −0.593008 | ||||||||
\(585\) | 3.96259 | 0.163833 | ||||||||
\(586\) | −25.3398 | −1.04678 | ||||||||
\(587\) | −23.1764 | −0.956591 | −0.478295 | − | 0.878199i | \(-0.658745\pi\) | ||||
−0.478295 | + | 0.878199i | \(0.658745\pi\) | |||||||
\(588\) | 7.53541 | 0.310755 | ||||||||
\(589\) | 11.3675 | 0.468389 | ||||||||
\(590\) | −8.46277 | −0.348407 | ||||||||
\(591\) | −9.09096 | −0.373952 | ||||||||
\(592\) | 3.59289 | 0.147667 | ||||||||
\(593\) | −36.2015 | −1.48662 | −0.743308 | − | 0.668949i | \(-0.766744\pi\) | ||||
−0.743308 | + | 0.668949i | \(0.766744\pi\) | |||||||
\(594\) | 6.78625 | 0.278443 | ||||||||
\(595\) | 69.3769 | 2.84418 | ||||||||
\(596\) | 11.8855 | 0.486847 | ||||||||
\(597\) | −12.5755 | −0.514679 | ||||||||
\(598\) | −1.04790 | −0.0428518 | ||||||||
\(599\) | −46.1700 | −1.88645 | −0.943227 | − | 0.332148i | \(-0.892227\pi\) | ||||
−0.943227 | + | 0.332148i | \(0.892227\pi\) | |||||||
\(600\) | 4.27611 | 0.174571 | ||||||||
\(601\) | 14.5421 | 0.593186 | 0.296593 | − | 0.955004i | \(-0.404150\pi\) | ||||
0.296593 | + | 0.955004i | \(0.404150\pi\) | |||||||
\(602\) | 4.85455 | 0.197857 | ||||||||
\(603\) | 15.8430 | 0.645175 | ||||||||
\(604\) | −16.0358 | −0.652487 | ||||||||
\(605\) | −27.4501 | −1.11601 | ||||||||
\(606\) | 6.75554 | 0.274425 | ||||||||
\(607\) | 26.1879 | 1.06293 | 0.531466 | − | 0.847080i | \(-0.321641\pi\) | ||||
0.531466 | + | 0.847080i | \(0.321641\pi\) | |||||||
\(608\) | −2.53015 | −0.102611 | ||||||||
\(609\) | 10.9999 | 0.445739 | ||||||||
\(610\) | −2.08001 | −0.0842172 | ||||||||
\(611\) | −9.21054 | −0.372619 | ||||||||
\(612\) | 8.84213 | 0.357422 | ||||||||
\(613\) | 15.2030 | 0.614045 | 0.307022 | − | 0.951702i | \(-0.400667\pi\) | ||||
0.307022 | + | 0.951702i | \(0.400667\pi\) | |||||||
\(614\) | 30.2571 | 1.22108 | ||||||||
\(615\) | −15.0874 | −0.608381 | ||||||||
\(616\) | 4.33446 | 0.174640 | ||||||||
\(617\) | −35.3715 | −1.42400 | −0.712001 | − | 0.702178i | \(-0.752211\pi\) | ||||
−0.712001 | + | 0.702178i | \(0.752211\pi\) | |||||||
\(618\) | 23.0796 | 0.928397 | ||||||||
\(619\) | −40.6458 | −1.63369 | −0.816846 | − | 0.576855i | \(-0.804280\pi\) | ||||
−0.816846 | + | 0.576855i | \(0.804280\pi\) | |||||||
\(620\) | −12.9377 | −0.519591 | ||||||||
\(621\) | −5.60186 | −0.224795 | ||||||||
\(622\) | 10.5052 | 0.421219 | ||||||||
\(623\) | 30.0510 | 1.20397 | ||||||||
\(624\) | −1.36099 | −0.0544834 | ||||||||
\(625\) | −30.6221 | −1.22488 | ||||||||
\(626\) | 19.7062 | 0.787618 | ||||||||
\(627\) | 3.98090 | 0.158982 | ||||||||
\(628\) | 9.20977 | 0.367510 | ||||||||
\(629\) | −24.1926 | −0.964621 | ||||||||
\(630\) | 13.5300 | 0.539046 | ||||||||
\(631\) | −7.47816 | −0.297701 | −0.148850 | − | 0.988860i | \(-0.547557\pi\) | ||||
−0.148850 | + | 0.988860i | \(0.547557\pi\) | |||||||
\(632\) | 8.17446 | 0.325163 | ||||||||
\(633\) | −1.20334 | −0.0478285 | ||||||||
\(634\) | −23.6058 | −0.937505 | ||||||||
\(635\) | 64.1251 | 2.54473 | ||||||||
\(636\) | 3.92024 | 0.155448 | ||||||||
\(637\) | −6.07982 | −0.240891 | ||||||||
\(638\) | 2.86756 | 0.113528 | ||||||||
\(639\) | 1.76787 | 0.0699360 | ||||||||
\(640\) | 2.87965 | 0.113828 | ||||||||
\(641\) | −26.4093 | −1.04310 | −0.521552 | − | 0.853220i | \(-0.674647\pi\) | ||||
−0.521552 | + | 0.853220i | \(0.674647\pi\) | |||||||
\(642\) | 8.81884 | 0.348052 | ||||||||
\(643\) | −25.1848 | −0.993193 | −0.496597 | − | 0.867982i | \(-0.665417\pi\) | ||||
−0.496597 | + | 0.867982i | \(0.665417\pi\) | |||||||
\(644\) | −3.57798 | −0.140992 | ||||||||
\(645\) | −5.07444 | −0.199806 | ||||||||
\(646\) | 17.0367 | 0.670299 | ||||||||
\(647\) | 17.5582 | 0.690286 | 0.345143 | − | 0.938550i | \(-0.387830\pi\) | ||||
0.345143 | + | 0.938550i | \(0.387830\pi\) | |||||||
\(648\) | −3.33611 | −0.131055 | ||||||||
\(649\) | 3.56017 | 0.139749 | ||||||||
\(650\) | −3.45010 | −0.135324 | ||||||||
\(651\) | 20.8781 | 0.818277 | ||||||||
\(652\) | −7.37833 | −0.288958 | ||||||||
\(653\) | −2.55328 | −0.0999174 | −0.0499587 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499587 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(654\) | 10.6087 | 0.414834 | ||||||||
\(655\) | −2.87965 | −0.112517 | ||||||||
\(656\) | −4.03401 | −0.157502 | ||||||||
\(657\) | 18.8186 | 0.734182 | ||||||||
\(658\) | −31.4487 | −1.22600 | ||||||||
\(659\) | −35.2149 | −1.37178 | −0.685889 | − | 0.727706i | \(-0.740586\pi\) | ||||
−0.685889 | + | 0.727706i | \(0.740586\pi\) | |||||||
\(660\) | −4.53079 | −0.176361 | ||||||||
\(661\) | 13.5417 | 0.526712 | 0.263356 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263356 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(662\) | 24.5531 | 0.954282 | ||||||||
\(663\) | 9.16419 | 0.355908 | ||||||||
\(664\) | −2.57120 | −0.0997818 | ||||||||
\(665\) | 26.0690 | 1.01091 | ||||||||
\(666\) | −4.71806 | −0.182821 | ||||||||
\(667\) | −2.36709 | −0.0916542 | ||||||||
\(668\) | −9.50905 | −0.367916 | ||||||||
\(669\) | −32.8065 | −1.26837 | ||||||||
\(670\) | −34.7422 | −1.34221 | ||||||||
\(671\) | 0.875031 | 0.0337802 | ||||||||
\(672\) | −4.64701 | −0.179262 | ||||||||
\(673\) | 10.5669 | 0.407322 | 0.203661 | − | 0.979041i | \(-0.434716\pi\) | ||||
0.203661 | + | 0.979041i | \(0.434716\pi\) | |||||||
\(674\) | 0.827698 | 0.0318817 | ||||||||
\(675\) | −18.4435 | −0.709892 | ||||||||
\(676\) | −11.9019 | −0.457766 | ||||||||
\(677\) | −24.6734 | −0.948274 | −0.474137 | − | 0.880451i | \(-0.657240\pi\) | ||||
−0.474137 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(678\) | −4.24127 | −0.162885 | ||||||||
\(679\) | 6.51245 | 0.249925 | ||||||||
\(680\) | −19.3900 | −0.743572 | ||||||||
\(681\) | 15.6093 | 0.598151 | ||||||||
\(682\) | 5.44271 | 0.208412 | ||||||||
\(683\) | −44.9833 | −1.72124 | −0.860618 | − | 0.509251i | \(-0.829923\pi\) | ||||
−0.860618 | + | 0.509251i | \(0.829923\pi\) | |||||||
\(684\) | 3.32251 | 0.127039 | ||||||||
\(685\) | −38.2196 | −1.46029 | ||||||||
\(686\) | 4.28675 | 0.163669 | ||||||||
\(687\) | 28.0371 | 1.06968 | ||||||||
\(688\) | −1.35679 | −0.0517270 | ||||||||
\(689\) | −3.16298 | −0.120500 | ||||||||
\(690\) | 3.74004 | 0.142381 | ||||||||
\(691\) | −17.4954 | −0.665558 | −0.332779 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332779 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(692\) | 7.14326 | 0.271546 | ||||||||
\(693\) | −5.69185 | −0.216216 | ||||||||
\(694\) | −1.61910 | −0.0614601 | ||||||||
\(695\) | −13.2465 | −0.502467 | ||||||||
\(696\) | −3.07434 | −0.116533 | ||||||||
\(697\) | 27.1628 | 1.02886 | ||||||||
\(698\) | −10.1191 | −0.383012 | ||||||||
\(699\) | 1.00328 | 0.0379475 | ||||||||
\(700\) | −11.7801 | −0.445246 | ||||||||
\(701\) | −12.4027 | −0.468445 | −0.234222 | − | 0.972183i | \(-0.575254\pi\) | ||||
−0.234222 | + | 0.972183i | \(0.575254\pi\) | |||||||
\(702\) | 5.87019 | 0.221556 | ||||||||
\(703\) | −9.09057 | −0.342858 | ||||||||
\(704\) | −1.21143 | −0.0456574 | ||||||||
\(705\) | 32.8732 | 1.23808 | ||||||||
\(706\) | −20.1340 | −0.757753 | ||||||||
\(707\) | −18.6106 | −0.699924 | ||||||||
\(708\) | −3.81689 | −0.143447 | ||||||||
\(709\) | 14.7913 | 0.555500 | 0.277750 | − | 0.960653i | \(-0.410411\pi\) | ||||
0.277750 | + | 0.960653i | \(0.410411\pi\) | |||||||
\(710\) | −3.87679 | −0.145493 | ||||||||
\(711\) | −10.7344 | −0.402572 | ||||||||
\(712\) | −8.39887 | −0.314761 | ||||||||
\(713\) | −4.49280 | −0.168257 | ||||||||
\(714\) | 31.2904 | 1.17101 | ||||||||
\(715\) | 3.65559 | 0.136711 | ||||||||
\(716\) | 1.15119 | 0.0430222 | ||||||||
\(717\) | 14.7514 | 0.550900 | ||||||||
\(718\) | −18.7206 | −0.698646 | ||||||||
\(719\) | 36.8121 | 1.37286 | 0.686431 | − | 0.727195i | \(-0.259177\pi\) | ||||
0.686431 | + | 0.727195i | \(0.259177\pi\) | |||||||
\(720\) | −3.78146 | −0.140927 | ||||||||
\(721\) | −63.5812 | −2.36789 | ||||||||
\(722\) | −12.5983 | −0.468861 | ||||||||
\(723\) | −10.8311 | −0.402814 | ||||||||
\(724\) | 10.6770 | 0.396807 | ||||||||
\(725\) | −7.79341 | −0.289440 | ||||||||
\(726\) | −12.3806 | −0.459486 | ||||||||
\(727\) | 5.97159 | 0.221474 | 0.110737 | − | 0.993850i | \(-0.464679\pi\) | ||||
0.110737 | + | 0.993850i | \(0.464679\pi\) | |||||||
\(728\) | 3.74936 | 0.138961 | ||||||||
\(729\) | 26.2077 | 0.970654 | ||||||||
\(730\) | −41.2674 | −1.52738 | ||||||||
\(731\) | 9.13585 | 0.337902 | ||||||||
\(732\) | −0.938128 | −0.0346742 | ||||||||
\(733\) | 5.02248 | 0.185509 | 0.0927547 | − | 0.995689i | \(-0.470433\pi\) | ||||
0.0927547 | + | 0.995689i | \(0.470433\pi\) | |||||||
\(734\) | 27.6525 | 1.02067 | ||||||||
\(735\) | 21.6994 | 0.800393 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 14.6155 | 0.538370 | ||||||||
\(738\) | 5.29731 | 0.194997 | ||||||||
\(739\) | −15.0999 | −0.555459 | −0.277729 | − | 0.960659i | \(-0.589582\pi\) | ||||
−0.277729 | + | 0.960659i | \(0.589582\pi\) | |||||||
\(740\) | 10.3463 | 0.380337 | ||||||||
\(741\) | 3.44352 | 0.126501 | ||||||||
\(742\) | −10.7997 | −0.396471 | ||||||||
\(743\) | −22.4975 | −0.825353 | −0.412676 | − | 0.910878i | \(-0.635406\pi\) | ||||
−0.412676 | + | 0.910878i | \(0.635406\pi\) | |||||||
\(744\) | −5.83517 | −0.213928 | ||||||||
\(745\) | 34.2260 | 1.25394 | ||||||||
\(746\) | −16.0419 | −0.587337 | ||||||||
\(747\) | 3.37640 | 0.123536 | ||||||||
\(748\) | 8.15709 | 0.298253 | ||||||||
\(749\) | −24.2947 | −0.887710 | ||||||||
\(750\) | −6.38651 | −0.233202 | ||||||||
\(751\) | −6.19706 | −0.226134 | −0.113067 | − | 0.993587i | \(-0.536067\pi\) | ||||
−0.113067 | + | 0.993587i | \(0.536067\pi\) | |||||||
\(752\) | 8.78952 | 0.320521 | ||||||||
\(753\) | 2.48901 | 0.0907045 | ||||||||
\(754\) | 2.48048 | 0.0903337 | ||||||||
\(755\) | −46.1775 | −1.68057 | ||||||||
\(756\) | 20.0433 | 0.728969 | ||||||||
\(757\) | 40.3843 | 1.46779 | 0.733897 | − | 0.679261i | \(-0.237699\pi\) | ||||
0.733897 | + | 0.679261i | \(0.237699\pi\) | |||||||
\(758\) | 6.99216 | 0.253967 | ||||||||
\(759\) | −1.57338 | −0.0571101 | ||||||||
\(760\) | −7.28596 | −0.264290 | ||||||||
\(761\) | −23.0516 | −0.835620 | −0.417810 | − | 0.908534i | \(-0.637202\pi\) | ||||
−0.417810 | + | 0.908534i | \(0.637202\pi\) | |||||||
\(762\) | 28.9217 | 1.04772 | ||||||||
\(763\) | −29.2257 | −1.05804 | ||||||||
\(764\) | 6.95720 | 0.251703 | ||||||||
\(765\) | 25.4622 | 0.920589 | ||||||||
\(766\) | 18.2335 | 0.658803 | ||||||||
\(767\) | 3.07959 | 0.111197 | ||||||||
\(768\) | 1.29878 | 0.0468658 | ||||||||
\(769\) | 37.1987 | 1.34142 | 0.670709 | − | 0.741721i | \(-0.265990\pi\) | ||||
0.670709 | + | 0.741721i | \(0.265990\pi\) | |||||||
\(770\) | 12.4817 | 0.449810 | ||||||||
\(771\) | 11.5772 | 0.416942 | ||||||||
\(772\) | −18.3198 | −0.659345 | ||||||||
\(773\) | −38.0295 | −1.36783 | −0.683913 | − | 0.729564i | \(-0.739723\pi\) | ||||
−0.683913 | + | 0.729564i | \(0.739723\pi\) | |||||||
\(774\) | 1.78168 | 0.0640413 | ||||||||
\(775\) | −14.7921 | −0.531347 | ||||||||
\(776\) | −1.82015 | −0.0653395 | ||||||||
\(777\) | −16.6962 | −0.598974 | ||||||||
\(778\) | −18.8141 | −0.674518 | ||||||||
\(779\) | 10.2067 | 0.365691 | ||||||||
\(780\) | −3.91919 | −0.140329 | ||||||||
\(781\) | 1.63091 | 0.0583585 | ||||||||
\(782\) | −6.73345 | −0.240788 | ||||||||
\(783\) | 13.2601 | 0.473878 | ||||||||
\(784\) | 5.80191 | 0.207211 | ||||||||
\(785\) | 26.5209 | 0.946573 | ||||||||
\(786\) | −1.29878 | −0.0463260 | ||||||||
\(787\) | 24.2669 | 0.865022 | 0.432511 | − | 0.901629i | \(-0.357628\pi\) | ||||
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(788\) | −6.99960 | −0.249350 | ||||||||
\(789\) | −26.1406 | −0.930629 | ||||||||
\(790\) | 23.5396 | 0.837501 | ||||||||
\(791\) | 11.6841 | 0.415440 | ||||||||
\(792\) | 1.59080 | 0.0565267 | ||||||||
\(793\) | 0.756913 | 0.0268788 | ||||||||
\(794\) | 16.8205 | 0.596936 | ||||||||
\(795\) | 11.2889 | 0.400377 | ||||||||
\(796\) | −9.68250 | −0.343187 | ||||||||
\(797\) | 25.9410 | 0.918879 | 0.459439 | − | 0.888209i | \(-0.348050\pi\) | ||||
0.459439 | + | 0.888209i | \(0.348050\pi\) | |||||||
\(798\) | 11.7577 | 0.416216 | ||||||||
\(799\) | −59.1838 | −2.09377 | ||||||||
\(800\) | 3.29240 | 0.116404 | ||||||||
\(801\) | 11.0291 | 0.389694 | ||||||||
\(802\) | 24.0199 | 0.848173 | ||||||||
\(803\) | 17.3606 | 0.612642 | ||||||||
\(804\) | −15.6694 | −0.552619 | ||||||||
\(805\) | −10.3033 | −0.363144 | ||||||||
\(806\) | 4.70801 | 0.165832 | ||||||||
\(807\) | −6.45577 | −0.227254 | ||||||||
\(808\) | 5.20144 | 0.182986 | ||||||||
\(809\) | −46.6891 | −1.64150 | −0.820750 | − | 0.571287i | \(-0.806444\pi\) | ||||
−0.820750 | + | 0.571287i | \(0.806444\pi\) | |||||||
\(810\) | −9.60683 | −0.337550 | ||||||||
\(811\) | −23.9964 | −0.842629 | −0.421314 | − | 0.906915i | \(-0.638431\pi\) | ||||
−0.421314 | + | 0.906915i | \(0.638431\pi\) | |||||||
\(812\) | 8.46940 | 0.297218 | ||||||||
\(813\) | 0.136715 | 0.00479480 | ||||||||
\(814\) | −4.35253 | −0.152556 | ||||||||
\(815\) | −21.2470 | −0.744251 | ||||||||
\(816\) | −8.74529 | −0.306146 | ||||||||
\(817\) | 3.43288 | 0.120101 | ||||||||
\(818\) | −1.45554 | −0.0508917 | ||||||||
\(819\) | −4.92352 | −0.172042 | ||||||||
\(820\) | −11.6165 | −0.405667 | ||||||||
\(821\) | −21.3105 | −0.743743 | −0.371872 | − | 0.928284i | \(-0.621284\pi\) | ||||
−0.371872 | + | 0.928284i | \(0.621284\pi\) | |||||||
\(822\) | −17.2378 | −0.601238 | ||||||||
\(823\) | 33.3082 | 1.16105 | 0.580525 | − | 0.814243i | \(-0.302847\pi\) | ||||
0.580525 | + | 0.814243i | \(0.302847\pi\) | |||||||
\(824\) | 17.7702 | 0.619053 | ||||||||
\(825\) | −5.18019 | −0.180351 | ||||||||
\(826\) | 10.5150 | 0.365864 | ||||||||
\(827\) | 48.1541 | 1.67448 | 0.837242 | − | 0.546833i | \(-0.184167\pi\) | ||||
0.837242 | + | 0.546833i | \(0.184167\pi\) | |||||||
\(828\) | −1.31316 | −0.0456356 | ||||||||
\(829\) | 53.8596 | 1.87062 | 0.935311 | − | 0.353827i | \(-0.115120\pi\) | ||||
0.935311 | + | 0.353827i | \(0.115120\pi\) | |||||||
\(830\) | −7.40416 | −0.257002 | ||||||||
\(831\) | 2.95029 | 0.102345 | ||||||||
\(832\) | −1.04790 | −0.0363294 | ||||||||
\(833\) | −39.0668 | −1.35359 | ||||||||
\(834\) | −5.97442 | −0.206877 | ||||||||
\(835\) | −27.3828 | −0.947619 | ||||||||
\(836\) | 3.06510 | 0.106009 | ||||||||
\(837\) | 25.1681 | 0.869935 | ||||||||
\(838\) | 33.6359 | 1.16193 | ||||||||
\(839\) | 7.76511 | 0.268081 | 0.134041 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134041 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(840\) | −13.3818 | −0.461715 | ||||||||
\(841\) | −23.3969 | −0.806789 | ||||||||
\(842\) | −29.1473 | −1.00448 | ||||||||
\(843\) | 33.9482 | 1.16924 | ||||||||
\(844\) | −0.926514 | −0.0318919 | ||||||||
\(845\) | −34.2733 | −1.17904 | ||||||||
\(846\) | −11.5421 | −0.396825 | ||||||||
\(847\) | 34.1068 | 1.17193 | ||||||||
\(848\) | 3.01840 | 0.103652 | ||||||||
\(849\) | −7.32638 | −0.251441 | ||||||||
\(850\) | −22.1692 | −0.760397 | ||||||||
\(851\) | 3.59289 | 0.123163 | ||||||||
\(852\) | −1.74851 | −0.0599030 | ||||||||
\(853\) | −27.8503 | −0.953575 | −0.476788 | − | 0.879019i | \(-0.658199\pi\) | ||||
−0.476788 | + | 0.879019i | \(0.658199\pi\) | |||||||
\(854\) | 2.58442 | 0.0884371 | ||||||||
\(855\) | 9.56766 | 0.327207 | ||||||||
\(856\) | 6.79008 | 0.232080 | ||||||||
\(857\) | −39.2785 | −1.34173 | −0.670865 | − | 0.741580i | \(-0.734077\pi\) | ||||
−0.670865 | + | 0.741580i | \(0.734077\pi\) | |||||||
\(858\) | 1.64875 | 0.0562873 | ||||||||
\(859\) | −31.8716 | −1.08745 | −0.543723 | − | 0.839265i | \(-0.682986\pi\) | ||||
−0.543723 | + | 0.839265i | \(0.682986\pi\) | |||||||
\(860\) | −3.90707 | −0.133230 | ||||||||
\(861\) | 18.7461 | 0.638865 | ||||||||
\(862\) | −28.2169 | −0.961072 | ||||||||
\(863\) | −35.5983 | −1.21178 | −0.605890 | − | 0.795549i | \(-0.707183\pi\) | ||||
−0.605890 | + | 0.795549i | \(0.707183\pi\) | |||||||
\(864\) | −5.60186 | −0.190579 | ||||||||
\(865\) | 20.5701 | 0.699405 | ||||||||
\(866\) | −1.85854 | −0.0631558 | ||||||||
\(867\) | 36.8067 | 1.25002 | ||||||||
\(868\) | 16.0751 | 0.545626 | ||||||||
\(869\) | −9.90277 | −0.335928 | ||||||||
\(870\) | −8.85303 | −0.300146 | ||||||||
\(871\) | 12.6426 | 0.428379 | ||||||||
\(872\) | 8.16821 | 0.276611 | ||||||||
\(873\) | 2.39015 | 0.0808945 | ||||||||
\(874\) | −2.53015 | −0.0855837 | ||||||||
\(875\) | 17.5940 | 0.594786 | ||||||||
\(876\) | −18.6125 | −0.628857 | ||||||||
\(877\) | 11.3252 | 0.382426 | 0.191213 | − | 0.981549i | \(-0.438758\pi\) | ||||
0.191213 | + | 0.981549i | \(0.438758\pi\) | |||||||
\(878\) | 28.4457 | 0.959995 | ||||||||
\(879\) | −32.9109 | −1.11006 | ||||||||
\(880\) | −3.48849 | −0.117597 | ||||||||
\(881\) | −35.6260 | −1.20027 | −0.600134 | − | 0.799899i | \(-0.704886\pi\) | ||||
−0.600134 | + | 0.799899i | \(0.704886\pi\) | |||||||
\(882\) | −7.61885 | −0.256540 | ||||||||
\(883\) | 20.4132 | 0.686960 | 0.343480 | − | 0.939160i | \(-0.388394\pi\) | ||||
0.343480 | + | 0.939160i | \(0.388394\pi\) | |||||||
\(884\) | 7.05598 | 0.237318 | ||||||||
\(885\) | −10.9913 | −0.369469 | ||||||||
\(886\) | −12.7941 | −0.429827 | ||||||||
\(887\) | 28.9673 | 0.972627 | 0.486314 | − | 0.873784i | \(-0.338341\pi\) | ||||
0.486314 | + | 0.873784i | \(0.338341\pi\) | |||||||
\(888\) | 4.66639 | 0.156594 | ||||||||
\(889\) | −79.6756 | −2.67223 | ||||||||
\(890\) | −24.1858 | −0.810711 | ||||||||
\(891\) | 4.04145 | 0.135394 | ||||||||
\(892\) | −25.2594 | −0.845749 | ||||||||
\(893\) | −22.2388 | −0.744194 | ||||||||
\(894\) | 15.4366 | 0.516278 | ||||||||
\(895\) | 3.31504 | 0.110810 | ||||||||
\(896\) | −3.57798 | −0.119532 | ||||||||
\(897\) | −1.36099 | −0.0454423 | ||||||||
\(898\) | −3.35017 | −0.111797 | ||||||||
\(899\) | 10.6349 | 0.354693 | ||||||||
\(900\) | −4.32346 | −0.144115 | ||||||||
\(901\) | −20.3242 | −0.677098 | ||||||||
\(902\) | 4.88691 | 0.162716 | ||||||||
\(903\) | 6.30500 | 0.209817 | ||||||||
\(904\) | −3.26557 | −0.108611 | ||||||||
\(905\) | 30.7460 | 1.02203 | ||||||||
\(906\) | −20.8270 | −0.691931 | ||||||||
\(907\) | 58.2775 | 1.93507 | 0.967537 | − | 0.252730i | \(-0.0813285\pi\) | ||||
0.967537 | + | 0.252730i | \(0.0813285\pi\) | |||||||
\(908\) | 12.0184 | 0.398846 | ||||||||
\(909\) | −6.83034 | −0.226548 | ||||||||
\(910\) | 10.7969 | 0.357912 | ||||||||
\(911\) | 23.8413 | 0.789899 | 0.394949 | − | 0.918703i | \(-0.370762\pi\) | ||||
0.394949 | + | 0.918703i | \(0.370762\pi\) | |||||||
\(912\) | −3.28612 | −0.108814 | ||||||||
\(913\) | 3.11482 | 0.103086 | ||||||||
\(914\) | −9.79457 | −0.323975 | ||||||||
\(915\) | −2.70148 | −0.0893083 | ||||||||
\(916\) | 21.5872 | 0.713263 | ||||||||
\(917\) | 3.57798 | 0.118155 | ||||||||
\(918\) | 37.7199 | 1.24494 | ||||||||
\(919\) | −8.95728 | −0.295474 | −0.147737 | − | 0.989027i | \(-0.547199\pi\) | ||||
−0.147737 | + | 0.989027i | \(0.547199\pi\) | |||||||
\(920\) | 2.87965 | 0.0949393 | ||||||||
\(921\) | 39.2974 | 1.29489 | ||||||||
\(922\) | −3.92003 | −0.129099 | ||||||||
\(923\) | 1.41076 | 0.0464356 | ||||||||
\(924\) | 5.62952 | 0.185198 | ||||||||
\(925\) | 11.8292 | 0.388943 | ||||||||
\(926\) | 30.5027 | 1.00238 | ||||||||
\(927\) | −23.3351 | −0.766427 | ||||||||
\(928\) | −2.36709 | −0.0777037 | ||||||||
\(929\) | 6.77862 | 0.222399 | 0.111200 | − | 0.993798i | \(-0.464531\pi\) | ||||
0.111200 | + | 0.993798i | \(0.464531\pi\) | |||||||
\(930\) | −16.8033 | −0.551001 | ||||||||
\(931\) | −14.6797 | −0.481108 | ||||||||
\(932\) | 0.772477 | 0.0253033 | ||||||||
\(933\) | 13.6439 | 0.446683 | ||||||||
\(934\) | 38.6037 | 1.26315 | ||||||||
\(935\) | 23.4896 | 0.768191 | ||||||||
\(936\) | 1.37606 | 0.0449781 | ||||||||
\(937\) | 9.72972 | 0.317856 | 0.158928 | − | 0.987290i | \(-0.449196\pi\) | ||||
0.158928 | + | 0.987290i | \(0.449196\pi\) | |||||||
\(938\) | 43.1673 | 1.40946 | ||||||||
\(939\) | 25.5941 | 0.835231 | ||||||||
\(940\) | 25.3108 | 0.825546 | ||||||||
\(941\) | −57.7289 | −1.88191 | −0.940955 | − | 0.338532i | \(-0.890070\pi\) | ||||
−0.940955 | + | 0.338532i | \(0.890070\pi\) | |||||||
\(942\) | 11.9615 | 0.389726 | ||||||||
\(943\) | −4.03401 | −0.131365 | ||||||||
\(944\) | −2.93882 | −0.0956504 | ||||||||
\(945\) | 57.7178 | 1.87756 | ||||||||
\(946\) | 1.64365 | 0.0534396 | ||||||||
\(947\) | −19.1054 | −0.620843 | −0.310421 | − | 0.950599i | \(-0.600470\pi\) | ||||
−0.310421 | + | 0.950599i | \(0.600470\pi\) | |||||||
\(948\) | 10.6168 | 0.344819 | ||||||||
\(949\) | 15.0171 | 0.487477 | ||||||||
\(950\) | −8.33027 | −0.270270 | ||||||||
\(951\) | −30.6588 | −0.994178 | ||||||||
\(952\) | 24.0921 | 0.780830 | ||||||||
\(953\) | 2.67308 | 0.0865896 | 0.0432948 | − | 0.999062i | \(-0.486215\pi\) | ||||
0.0432948 | + | 0.999062i | \(0.486215\pi\) | |||||||
\(954\) | −3.96365 | −0.128328 | ||||||||
\(955\) | 20.0343 | 0.648296 | ||||||||
\(956\) | 11.3578 | 0.367339 | ||||||||
\(957\) | 3.72434 | 0.120391 | ||||||||
\(958\) | 14.5801 | 0.471061 | ||||||||
\(959\) | 47.4879 | 1.53346 | ||||||||
\(960\) | 3.74004 | 0.120709 | ||||||||
\(961\) | −10.8147 | −0.348862 | ||||||||
\(962\) | −3.76499 | −0.121388 | ||||||||
\(963\) | −8.91649 | −0.287330 | ||||||||
\(964\) | −8.33944 | −0.268595 | ||||||||
\(965\) | −52.7547 | −1.69823 | ||||||||
\(966\) | −4.64701 | −0.149515 | ||||||||
\(967\) | 23.3728 | 0.751617 | 0.375809 | − | 0.926697i | \(-0.377365\pi\) | ||||
0.375809 | + | 0.926697i | \(0.377365\pi\) | |||||||
\(968\) | −9.53244 | −0.306384 | ||||||||
\(969\) | 22.1269 | 0.710819 | ||||||||
\(970\) | −5.24139 | −0.168291 | ||||||||
\(971\) | 7.56455 | 0.242758 | 0.121379 | − | 0.992606i | \(-0.461268\pi\) | ||||
0.121379 | + | 0.992606i | \(0.461268\pi\) | |||||||
\(972\) | 12.4727 | 0.400062 | ||||||||
\(973\) | 16.4588 | 0.527643 | ||||||||
\(974\) | −27.0085 | −0.865407 | ||||||||
\(975\) | −4.48093 | −0.143505 | ||||||||
\(976\) | −0.722314 | −0.0231207 | ||||||||
\(977\) | −7.26805 | −0.232526 | −0.116263 | − | 0.993218i | \(-0.537091\pi\) | ||||
−0.116263 | + | 0.993218i | \(0.537091\pi\) | |||||||
\(978\) | −9.58285 | −0.306426 | ||||||||
\(979\) | 10.1746 | 0.325182 | ||||||||
\(980\) | 16.7075 | 0.533701 | ||||||||
\(981\) | −10.7262 | −0.342461 | ||||||||
\(982\) | 3.42553 | 0.109313 | ||||||||
\(983\) | 8.27376 | 0.263892 | 0.131946 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131946 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(984\) | −5.23930 | −0.167023 | ||||||||
\(985\) | −20.1564 | −0.642237 | ||||||||
\(986\) | 15.9387 | 0.507592 | ||||||||
\(987\) | −40.8450 | −1.30011 | ||||||||
\(988\) | 2.65135 | 0.0843506 | ||||||||
\(989\) | −1.35679 | −0.0431433 | ||||||||
\(990\) | 4.58096 | 0.145592 | ||||||||
\(991\) | 51.1780 | 1.62572 | 0.812861 | − | 0.582457i | \(-0.197909\pi\) | ||||
0.812861 | + | 0.582457i | \(0.197909\pi\) | |||||||
\(992\) | −4.49280 | −0.142647 | ||||||||
\(993\) | 31.8891 | 1.01197 | ||||||||
\(994\) | 4.81692 | 0.152783 | ||||||||
\(995\) | −27.8822 | −0.883926 | ||||||||
\(996\) | −3.33943 | −0.105814 | ||||||||
\(997\) | −21.9378 | −0.694776 | −0.347388 | − | 0.937721i | \(-0.612931\pi\) | ||||
−0.347388 | + | 0.937721i | \(0.612931\pi\) | |||||||
\(998\) | 24.9775 | 0.790648 | ||||||||
\(999\) | −20.1269 | −0.636787 |
(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 | 6026.2.a.f.1.15 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.f.1.15 | ✓ | 20 | 1.1 | even | 1 | trivial |