Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.231279\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.231279 | 0.163539 | 0.0817696 | − | 0.996651i | \(-0.473943\pi\) | ||||
0.0817696 | + | 0.996651i | \(0.473943\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.94651 | −0.973255 | ||||||||
\(5\) | 3.70694 | 1.65779 | 0.828896 | − | 0.559402i | \(-0.188969\pi\) | ||||
0.828896 | + | 0.559402i | \(0.188969\pi\) | |||||||
\(6\) | −0.231279 | −0.0944194 | ||||||||
\(7\) | −0.911108 | −0.344366 | −0.172183 | − | 0.985065i | \(-0.555082\pi\) | ||||
−0.172183 | + | 0.985065i | \(0.555082\pi\) | |||||||
\(8\) | −0.912746 | −0.322705 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.857338 | 0.271114 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.94651 | 0.561909 | ||||||||
\(13\) | −1.28993 | −0.357761 | −0.178881 | − | 0.983871i | \(-0.557248\pi\) | ||||
−0.178881 | + | 0.983871i | \(0.557248\pi\) | |||||||
\(14\) | −0.210720 | −0.0563174 | ||||||||
\(15\) | −3.70694 | −0.957127 | ||||||||
\(16\) | 3.68192 | 0.920480 | ||||||||
\(17\) | −7.36730 | −1.78683 | −0.893416 | − | 0.449230i | \(-0.851699\pi\) | ||||
−0.893416 | + | 0.449230i | \(0.851699\pi\) | |||||||
\(18\) | 0.231279 | 0.0545131 | ||||||||
\(19\) | 5.91624 | 1.35728 | 0.678640 | − | 0.734472i | \(-0.262570\pi\) | ||||
0.678640 | + | 0.734472i | \(0.262570\pi\) | |||||||
\(20\) | −7.21559 | −1.61346 | ||||||||
\(21\) | 0.911108 | 0.198820 | ||||||||
\(22\) | −0.231279 | −0.0493089 | ||||||||
\(23\) | 6.40611 | 1.33577 | 0.667883 | − | 0.744267i | \(-0.267201\pi\) | ||||
0.667883 | + | 0.744267i | \(0.267201\pi\) | |||||||
\(24\) | 0.912746 | 0.186314 | ||||||||
\(25\) | 8.74139 | 1.74828 | ||||||||
\(26\) | −0.298334 | −0.0585080 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.77348 | 0.335156 | ||||||||
\(29\) | 9.58456 | 1.77981 | 0.889904 | − | 0.456147i | \(-0.150771\pi\) | ||||
0.889904 | + | 0.456147i | \(0.150771\pi\) | |||||||
\(30\) | −0.857338 | −0.156528 | ||||||||
\(31\) | −8.65847 | −1.55511 | −0.777553 | − | 0.628817i | \(-0.783539\pi\) | ||||
−0.777553 | + | 0.628817i | \(0.783539\pi\) | |||||||
\(32\) | 2.67705 | 0.473239 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −1.70390 | −0.292217 | ||||||||
\(35\) | −3.37742 | −0.570888 | ||||||||
\(36\) | −1.94651 | −0.324418 | ||||||||
\(37\) | −8.74406 | −1.43751 | −0.718757 | − | 0.695261i | \(-0.755289\pi\) | ||||
−0.718757 | + | 0.695261i | \(0.755289\pi\) | |||||||
\(38\) | 1.36830 | 0.221968 | ||||||||
\(39\) | 1.28993 | 0.206554 | ||||||||
\(40\) | −3.38349 | −0.534977 | ||||||||
\(41\) | 6.54649 | 1.02239 | 0.511195 | − | 0.859465i | \(-0.329203\pi\) | ||||
0.511195 | + | 0.859465i | \(0.329203\pi\) | |||||||
\(42\) | 0.210720 | 0.0325149 | ||||||||
\(43\) | 9.59278 | 1.46289 | 0.731443 | − | 0.681903i | \(-0.238847\pi\) | ||||
0.731443 | + | 0.681903i | \(0.238847\pi\) | |||||||
\(44\) | 1.94651 | 0.293447 | ||||||||
\(45\) | 3.70694 | 0.552598 | ||||||||
\(46\) | 1.48160 | 0.218450 | ||||||||
\(47\) | 5.82694 | 0.849946 | 0.424973 | − | 0.905206i | \(-0.360284\pi\) | ||||
0.424973 | + | 0.905206i | \(0.360284\pi\) | |||||||
\(48\) | −3.68192 | −0.531439 | ||||||||
\(49\) | −6.16988 | −0.881412 | ||||||||
\(50\) | 2.02170 | 0.285912 | ||||||||
\(51\) | 7.36730 | 1.03163 | ||||||||
\(52\) | 2.51086 | 0.348193 | ||||||||
\(53\) | −5.01034 | −0.688223 | −0.344111 | − | 0.938929i | \(-0.611820\pi\) | ||||
−0.344111 | + | 0.938929i | \(0.611820\pi\) | |||||||
\(54\) | −0.231279 | −0.0314731 | ||||||||
\(55\) | −3.70694 | −0.499843 | ||||||||
\(56\) | 0.831610 | 0.111129 | ||||||||
\(57\) | −5.91624 | −0.783625 | ||||||||
\(58\) | 2.21671 | 0.291069 | ||||||||
\(59\) | 1.55369 | 0.202273 | 0.101137 | − | 0.994873i | \(-0.467752\pi\) | ||||
0.101137 | + | 0.994873i | \(0.467752\pi\) | |||||||
\(60\) | 7.21559 | 0.931529 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −2.00252 | −0.254321 | ||||||||
\(63\) | −0.911108 | −0.114789 | ||||||||
\(64\) | −6.74470 | −0.843087 | ||||||||
\(65\) | −4.78168 | −0.593094 | ||||||||
\(66\) | 0.231279 | 0.0284685 | ||||||||
\(67\) | 12.7209 | 1.55410 | 0.777052 | − | 0.629436i | \(-0.216714\pi\) | ||||
0.777052 | + | 0.629436i | \(0.216714\pi\) | |||||||
\(68\) | 14.3405 | 1.73904 | ||||||||
\(69\) | −6.40611 | −0.771205 | ||||||||
\(70\) | −0.781128 | −0.0933626 | ||||||||
\(71\) | −0.506871 | −0.0601545 | −0.0300773 | − | 0.999548i | \(-0.509575\pi\) | ||||
−0.0300773 | + | 0.999548i | \(0.509575\pi\) | |||||||
\(72\) | −0.912746 | −0.107568 | ||||||||
\(73\) | −3.71011 | −0.434236 | −0.217118 | − | 0.976145i | \(-0.569666\pi\) | ||||
−0.217118 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(74\) | −2.02232 | −0.235090 | ||||||||
\(75\) | −8.74139 | −1.00937 | ||||||||
\(76\) | −11.5160 | −1.32098 | ||||||||
\(77\) | 0.911108 | 0.103830 | ||||||||
\(78\) | 0.298334 | 0.0337796 | ||||||||
\(79\) | −5.28303 | −0.594387 | −0.297194 | − | 0.954817i | \(-0.596051\pi\) | ||||
−0.297194 | + | 0.954817i | \(0.596051\pi\) | |||||||
\(80\) | 13.6486 | 1.52597 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.51407 | 0.167201 | ||||||||
\(83\) | 7.43641 | 0.816252 | 0.408126 | − | 0.912926i | \(-0.366182\pi\) | ||||
0.408126 | + | 0.912926i | \(0.366182\pi\) | |||||||
\(84\) | −1.77348 | −0.193503 | ||||||||
\(85\) | −27.3101 | −2.96220 | ||||||||
\(86\) | 2.21861 | 0.239239 | ||||||||
\(87\) | −9.58456 | −1.02757 | ||||||||
\(88\) | 0.912746 | 0.0972991 | ||||||||
\(89\) | 12.7615 | 1.35272 | 0.676360 | − | 0.736571i | \(-0.263556\pi\) | ||||
0.676360 | + | 0.736571i | \(0.263556\pi\) | |||||||
\(90\) | 0.857338 | 0.0903714 | ||||||||
\(91\) | 1.17526 | 0.123201 | ||||||||
\(92\) | −12.4695 | −1.30004 | ||||||||
\(93\) | 8.65847 | 0.897841 | ||||||||
\(94\) | 1.34765 | 0.139000 | ||||||||
\(95\) | 21.9311 | 2.25009 | ||||||||
\(96\) | −2.67705 | −0.273225 | ||||||||
\(97\) | 19.0085 | 1.93002 | 0.965012 | − | 0.262207i | \(-0.0844504\pi\) | ||||
0.965012 | + | 0.262207i | \(0.0844504\pi\) | |||||||
\(98\) | −1.42697 | −0.144145 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −17.0152 | −1.70152 | ||||||||
\(101\) | −5.60028 | −0.557249 | −0.278624 | − | 0.960400i | \(-0.589878\pi\) | ||||
−0.278624 | + | 0.960400i | \(0.589878\pi\) | |||||||
\(102\) | 1.70390 | 0.168712 | ||||||||
\(103\) | 16.0507 | 1.58153 | 0.790763 | − | 0.612122i | \(-0.209684\pi\) | ||||
0.790763 | + | 0.612122i | \(0.209684\pi\) | |||||||
\(104\) | 1.17738 | 0.115451 | ||||||||
\(105\) | 3.37742 | 0.329602 | ||||||||
\(106\) | −1.15879 | −0.112551 | ||||||||
\(107\) | 16.1333 | 1.55966 | 0.779830 | − | 0.625991i | \(-0.215305\pi\) | ||||
0.779830 | + | 0.625991i | \(0.215305\pi\) | |||||||
\(108\) | 1.94651 | 0.187303 | ||||||||
\(109\) | −15.2826 | −1.46381 | −0.731905 | − | 0.681407i | \(-0.761369\pi\) | ||||
−0.731905 | + | 0.681407i | \(0.761369\pi\) | |||||||
\(110\) | −0.857338 | −0.0817440 | ||||||||
\(111\) | 8.74406 | 0.829949 | ||||||||
\(112\) | −3.35463 | −0.316982 | ||||||||
\(113\) | 13.4720 | 1.26734 | 0.633668 | − | 0.773605i | \(-0.281549\pi\) | ||||
0.633668 | + | 0.773605i | \(0.281549\pi\) | |||||||
\(114\) | −1.36830 | −0.128153 | ||||||||
\(115\) | 23.7470 | 2.21442 | ||||||||
\(116\) | −18.6564 | −1.73221 | ||||||||
\(117\) | −1.28993 | −0.119254 | ||||||||
\(118\) | 0.359337 | 0.0330796 | ||||||||
\(119\) | 6.71240 | 0.615325 | ||||||||
\(120\) | 3.38349 | 0.308869 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.231279 | 0.0209391 | ||||||||
\(123\) | −6.54649 | −0.590277 | ||||||||
\(124\) | 16.8538 | 1.51352 | ||||||||
\(125\) | 13.8691 | 1.24049 | ||||||||
\(126\) | −0.210720 | −0.0187725 | ||||||||
\(127\) | 14.9118 | 1.32321 | 0.661605 | − | 0.749852i | \(-0.269875\pi\) | ||||
0.661605 | + | 0.749852i | \(0.269875\pi\) | |||||||
\(128\) | −6.91400 | −0.611117 | ||||||||
\(129\) | −9.59278 | −0.844597 | ||||||||
\(130\) | −1.10590 | −0.0969942 | ||||||||
\(131\) | 1.52367 | 0.133123 | 0.0665617 | − | 0.997782i | \(-0.478797\pi\) | ||||
0.0665617 | + | 0.997782i | \(0.478797\pi\) | |||||||
\(132\) | −1.94651 | −0.169422 | ||||||||
\(133\) | −5.39033 | −0.467401 | ||||||||
\(134\) | 2.94208 | 0.254157 | ||||||||
\(135\) | −3.70694 | −0.319042 | ||||||||
\(136\) | 6.72448 | 0.576619 | ||||||||
\(137\) | 3.70337 | 0.316400 | 0.158200 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158200 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(138\) | −1.48160 | −0.126122 | ||||||||
\(139\) | 6.10661 | 0.517956 | 0.258978 | − | 0.965883i | \(-0.416614\pi\) | ||||
0.258978 | + | 0.965883i | \(0.416614\pi\) | |||||||
\(140\) | 6.57418 | 0.555620 | ||||||||
\(141\) | −5.82694 | −0.490717 | ||||||||
\(142\) | −0.117229 | −0.00983762 | ||||||||
\(143\) | 1.28993 | 0.107869 | ||||||||
\(144\) | 3.68192 | 0.306827 | ||||||||
\(145\) | 35.5294 | 2.95055 | ||||||||
\(146\) | −0.858073 | −0.0710146 | ||||||||
\(147\) | 6.16988 | 0.508883 | ||||||||
\(148\) | 17.0204 | 1.39907 | ||||||||
\(149\) | −13.5246 | −1.10797 | −0.553987 | − | 0.832525i | \(-0.686894\pi\) | ||||
−0.553987 | + | 0.832525i | \(0.686894\pi\) | |||||||
\(150\) | −2.02170 | −0.165071 | ||||||||
\(151\) | −1.09346 | −0.0889849 | −0.0444924 | − | 0.999010i | \(-0.514167\pi\) | ||||
−0.0444924 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(152\) | −5.40003 | −0.438000 | ||||||||
\(153\) | −7.36730 | −0.595611 | ||||||||
\(154\) | 0.210720 | 0.0169803 | ||||||||
\(155\) | −32.0964 | −2.57804 | ||||||||
\(156\) | −2.51086 | −0.201029 | ||||||||
\(157\) | 14.4608 | 1.15410 | 0.577049 | − | 0.816709i | \(-0.304204\pi\) | ||||
0.577049 | + | 0.816709i | \(0.304204\pi\) | |||||||
\(158\) | −1.22186 | −0.0972057 | ||||||||
\(159\) | 5.01034 | 0.397346 | ||||||||
\(160\) | 9.92364 | 0.784533 | ||||||||
\(161\) | −5.83665 | −0.459993 | ||||||||
\(162\) | 0.231279 | 0.0181710 | ||||||||
\(163\) | 1.40734 | 0.110231 | 0.0551155 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551155 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(164\) | −12.7428 | −0.995046 | ||||||||
\(165\) | 3.70694 | 0.288585 | ||||||||
\(166\) | 1.71989 | 0.133489 | ||||||||
\(167\) | −14.0105 | −1.08416 | −0.542082 | − | 0.840326i | \(-0.682364\pi\) | ||||
−0.542082 | + | 0.840326i | \(0.682364\pi\) | |||||||
\(168\) | −0.831610 | −0.0641601 | ||||||||
\(169\) | −11.3361 | −0.872007 | ||||||||
\(170\) | −6.31627 | −0.484436 | ||||||||
\(171\) | 5.91624 | 0.452426 | ||||||||
\(172\) | −18.6724 | −1.42376 | ||||||||
\(173\) | 2.67772 | 0.203584 | 0.101792 | − | 0.994806i | \(-0.467542\pi\) | ||||
0.101792 | + | 0.994806i | \(0.467542\pi\) | |||||||
\(174\) | −2.21671 | −0.168048 | ||||||||
\(175\) | −7.96434 | −0.602048 | ||||||||
\(176\) | −3.68192 | −0.277535 | ||||||||
\(177\) | −1.55369 | −0.116783 | ||||||||
\(178\) | 2.95148 | 0.221223 | ||||||||
\(179\) | 2.14059 | 0.159995 | 0.0799977 | − | 0.996795i | \(-0.474509\pi\) | ||||
0.0799977 | + | 0.996795i | \(0.474509\pi\) | |||||||
\(180\) | −7.21559 | −0.537818 | ||||||||
\(181\) | 10.4522 | 0.776903 | 0.388451 | − | 0.921469i | \(-0.373010\pi\) | ||||
0.388451 | + | 0.921469i | \(0.373010\pi\) | |||||||
\(182\) | 0.271814 | 0.0201482 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −5.84715 | −0.431058 | ||||||||
\(185\) | −32.4137 | −2.38310 | ||||||||
\(186\) | 2.00252 | 0.146832 | ||||||||
\(187\) | 7.36730 | 0.538750 | ||||||||
\(188\) | −11.3422 | −0.827214 | ||||||||
\(189\) | 0.911108 | 0.0662733 | ||||||||
\(190\) | 5.07222 | 0.367978 | ||||||||
\(191\) | 6.90631 | 0.499723 | 0.249862 | − | 0.968282i | \(-0.419615\pi\) | ||||
0.249862 | + | 0.968282i | \(0.419615\pi\) | |||||||
\(192\) | 6.74470 | 0.486756 | ||||||||
\(193\) | 13.5215 | 0.973300 | 0.486650 | − | 0.873597i | \(-0.338219\pi\) | ||||
0.486650 | + | 0.873597i | \(0.338219\pi\) | |||||||
\(194\) | 4.39628 | 0.315634 | ||||||||
\(195\) | 4.78168 | 0.342423 | ||||||||
\(196\) | 12.0097 | 0.857838 | ||||||||
\(197\) | −12.6509 | −0.901342 | −0.450671 | − | 0.892690i | \(-0.648815\pi\) | ||||
−0.450671 | + | 0.892690i | \(0.648815\pi\) | |||||||
\(198\) | −0.231279 | −0.0164363 | ||||||||
\(199\) | 3.63188 | 0.257457 | 0.128728 | − | 0.991680i | \(-0.458910\pi\) | ||||
0.128728 | + | 0.991680i | \(0.458910\pi\) | |||||||
\(200\) | −7.97867 | −0.564177 | ||||||||
\(201\) | −12.7209 | −0.897263 | ||||||||
\(202\) | −1.29523 | −0.0911320 | ||||||||
\(203\) | −8.73257 | −0.612906 | ||||||||
\(204\) | −14.3405 | −1.00404 | ||||||||
\(205\) | 24.2674 | 1.69491 | ||||||||
\(206\) | 3.71220 | 0.258642 | ||||||||
\(207\) | 6.40611 | 0.445255 | ||||||||
\(208\) | −4.74941 | −0.329312 | ||||||||
\(209\) | −5.91624 | −0.409235 | ||||||||
\(210\) | 0.781128 | 0.0539029 | ||||||||
\(211\) | −18.3470 | −1.26306 | −0.631530 | − | 0.775352i | \(-0.717573\pi\) | ||||
−0.631530 | + | 0.775352i | \(0.717573\pi\) | |||||||
\(212\) | 9.75267 | 0.669816 | ||||||||
\(213\) | 0.506871 | 0.0347302 | ||||||||
\(214\) | 3.73129 | 0.255066 | ||||||||
\(215\) | 35.5598 | 2.42516 | ||||||||
\(216\) | 0.912746 | 0.0621045 | ||||||||
\(217\) | 7.88880 | 0.535526 | ||||||||
\(218\) | −3.53456 | −0.239390 | ||||||||
\(219\) | 3.71011 | 0.250706 | ||||||||
\(220\) | 7.21559 | 0.486475 | ||||||||
\(221\) | 9.50328 | 0.639260 | ||||||||
\(222\) | 2.02232 | 0.135729 | ||||||||
\(223\) | 6.99961 | 0.468729 | 0.234364 | − | 0.972149i | \(-0.424699\pi\) | ||||
0.234364 | + | 0.972149i | \(0.424699\pi\) | |||||||
\(224\) | −2.43908 | −0.162968 | ||||||||
\(225\) | 8.74139 | 0.582759 | ||||||||
\(226\) | 3.11579 | 0.207259 | ||||||||
\(227\) | 6.85426 | 0.454933 | 0.227467 | − | 0.973786i | \(-0.426956\pi\) | ||||
0.227467 | + | 0.973786i | \(0.426956\pi\) | |||||||
\(228\) | 11.5160 | 0.762667 | ||||||||
\(229\) | −2.15050 | −0.142109 | −0.0710544 | − | 0.997472i | \(-0.522636\pi\) | ||||
−0.0710544 | + | 0.997472i | \(0.522636\pi\) | |||||||
\(230\) | 5.49220 | 0.362145 | ||||||||
\(231\) | −0.911108 | −0.0599465 | ||||||||
\(232\) | −8.74827 | −0.574352 | ||||||||
\(233\) | −0.0878610 | −0.00575597 | −0.00287798 | − | 0.999996i | \(-0.500916\pi\) | ||||
−0.00287798 | + | 0.999996i | \(0.500916\pi\) | |||||||
\(234\) | −0.298334 | −0.0195027 | ||||||||
\(235\) | 21.6001 | 1.40903 | ||||||||
\(236\) | −3.02428 | −0.196864 | ||||||||
\(237\) | 5.28303 | 0.343170 | ||||||||
\(238\) | 1.55244 | 0.100630 | ||||||||
\(239\) | −1.34617 | −0.0870763 | −0.0435382 | − | 0.999052i | \(-0.513863\pi\) | ||||
−0.0435382 | + | 0.999052i | \(0.513863\pi\) | |||||||
\(240\) | −13.6486 | −0.881016 | ||||||||
\(241\) | 4.54006 | 0.292451 | 0.146225 | − | 0.989251i | \(-0.453288\pi\) | ||||
0.146225 | + | 0.989251i | \(0.453288\pi\) | |||||||
\(242\) | 0.231279 | 0.0148672 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.94651 | −0.124613 | ||||||||
\(245\) | −22.8714 | −1.46120 | ||||||||
\(246\) | −1.51407 | −0.0965334 | ||||||||
\(247\) | −7.63152 | −0.485582 | ||||||||
\(248\) | 7.90298 | 0.501840 | ||||||||
\(249\) | −7.43641 | −0.471263 | ||||||||
\(250\) | 3.20763 | 0.202869 | ||||||||
\(251\) | −5.83748 | −0.368458 | −0.184229 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184229 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(252\) | 1.77348 | 0.111719 | ||||||||
\(253\) | −6.40611 | −0.402748 | ||||||||
\(254\) | 3.44880 | 0.216397 | ||||||||
\(255\) | 27.3101 | 1.71023 | ||||||||
\(256\) | 11.8903 | 0.743145 | ||||||||
\(257\) | 19.2484 | 1.20068 | 0.600341 | − | 0.799744i | \(-0.295032\pi\) | ||||
0.600341 | + | 0.799744i | \(0.295032\pi\) | |||||||
\(258\) | −2.21861 | −0.138125 | ||||||||
\(259\) | 7.96678 | 0.495032 | ||||||||
\(260\) | 9.30759 | 0.577232 | ||||||||
\(261\) | 9.58456 | 0.593270 | ||||||||
\(262\) | 0.352393 | 0.0217709 | ||||||||
\(263\) | −12.4662 | −0.768698 | −0.384349 | − | 0.923188i | \(-0.625574\pi\) | ||||
−0.384349 | + | 0.923188i | \(0.625574\pi\) | |||||||
\(264\) | −0.912746 | −0.0561757 | ||||||||
\(265\) | −18.5730 | −1.14093 | ||||||||
\(266\) | −1.24667 | −0.0764384 | ||||||||
\(267\) | −12.7615 | −0.780993 | ||||||||
\(268\) | −24.7614 | −1.51254 | ||||||||
\(269\) | −10.9441 | −0.667276 | −0.333638 | − | 0.942701i | \(-0.608276\pi\) | ||||
−0.333638 | + | 0.942701i | \(0.608276\pi\) | |||||||
\(270\) | −0.857338 | −0.0521759 | ||||||||
\(271\) | −17.9716 | −1.09169 | −0.545847 | − | 0.837885i | \(-0.683792\pi\) | ||||
−0.545847 | + | 0.837885i | \(0.683792\pi\) | |||||||
\(272\) | −27.1258 | −1.64474 | ||||||||
\(273\) | −1.17526 | −0.0711301 | ||||||||
\(274\) | 0.856514 | 0.0517439 | ||||||||
\(275\) | −8.74139 | −0.527125 | ||||||||
\(276\) | 12.4695 | 0.750579 | ||||||||
\(277\) | −5.74306 | −0.345067 | −0.172534 | − | 0.985004i | \(-0.555195\pi\) | ||||
−0.172534 | + | 0.985004i | \(0.555195\pi\) | |||||||
\(278\) | 1.41233 | 0.0847061 | ||||||||
\(279\) | −8.65847 | −0.518369 | ||||||||
\(280\) | 3.08273 | 0.184228 | ||||||||
\(281\) | −31.3802 | −1.87199 | −0.935993 | − | 0.352019i | \(-0.885495\pi\) | ||||
−0.935993 | + | 0.352019i | \(0.885495\pi\) | |||||||
\(282\) | −1.34765 | −0.0802514 | ||||||||
\(283\) | −22.4497 | −1.33450 | −0.667248 | − | 0.744835i | \(-0.732528\pi\) | ||||
−0.667248 | + | 0.744835i | \(0.732528\pi\) | |||||||
\(284\) | 0.986629 | 0.0585457 | ||||||||
\(285\) | −21.9311 | −1.29909 | ||||||||
\(286\) | 0.298334 | 0.0176408 | ||||||||
\(287\) | −5.96456 | −0.352077 | ||||||||
\(288\) | 2.67705 | 0.157746 | ||||||||
\(289\) | 37.2771 | 2.19277 | ||||||||
\(290\) | 8.21721 | 0.482531 | ||||||||
\(291\) | −19.0085 | −1.11430 | ||||||||
\(292\) | 7.22177 | 0.422622 | ||||||||
\(293\) | −15.8824 | −0.927861 | −0.463931 | − | 0.885872i | \(-0.653561\pi\) | ||||
−0.463931 | + | 0.885872i | \(0.653561\pi\) | |||||||
\(294\) | 1.42697 | 0.0832224 | ||||||||
\(295\) | 5.75944 | 0.335327 | ||||||||
\(296\) | 7.98111 | 0.463893 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −3.12795 | −0.181197 | ||||||||
\(299\) | −8.26341 | −0.477885 | ||||||||
\(300\) | 17.0152 | 0.982373 | ||||||||
\(301\) | −8.74006 | −0.503769 | ||||||||
\(302\) | −0.252896 | −0.0145525 | ||||||||
\(303\) | 5.60028 | 0.321728 | ||||||||
\(304\) | 21.7831 | 1.24935 | ||||||||
\(305\) | 3.70694 | 0.212259 | ||||||||
\(306\) | −1.70390 | −0.0974057 | ||||||||
\(307\) | 13.2053 | 0.753665 | 0.376832 | − | 0.926281i | \(-0.377013\pi\) | ||||
0.376832 | + | 0.926281i | \(0.377013\pi\) | |||||||
\(308\) | −1.77348 | −0.101053 | ||||||||
\(309\) | −16.0507 | −0.913095 | ||||||||
\(310\) | −7.42323 | −0.421611 | ||||||||
\(311\) | 7.86121 | 0.445768 | 0.222884 | − | 0.974845i | \(-0.428453\pi\) | ||||
0.222884 | + | 0.974845i | \(0.428453\pi\) | |||||||
\(312\) | −1.17738 | −0.0666558 | ||||||||
\(313\) | −17.6385 | −0.996988 | −0.498494 | − | 0.866893i | \(-0.666113\pi\) | ||||
−0.498494 | + | 0.866893i | \(0.666113\pi\) | |||||||
\(314\) | 3.34449 | 0.188740 | ||||||||
\(315\) | −3.37742 | −0.190296 | ||||||||
\(316\) | 10.2835 | 0.578490 | ||||||||
\(317\) | 10.5734 | 0.593859 | 0.296930 | − | 0.954899i | \(-0.404037\pi\) | ||||
0.296930 | + | 0.954899i | \(0.404037\pi\) | |||||||
\(318\) | 1.15879 | 0.0649816 | ||||||||
\(319\) | −9.58456 | −0.536632 | ||||||||
\(320\) | −25.0022 | −1.39766 | ||||||||
\(321\) | −16.1333 | −0.900471 | ||||||||
\(322\) | −1.34990 | −0.0752268 | ||||||||
\(323\) | −43.5867 | −2.42523 | ||||||||
\(324\) | −1.94651 | −0.108139 | ||||||||
\(325\) | −11.2758 | −0.625466 | ||||||||
\(326\) | 0.325488 | 0.0180271 | ||||||||
\(327\) | 15.2826 | 0.845131 | ||||||||
\(328\) | −5.97528 | −0.329930 | ||||||||
\(329\) | −5.30897 | −0.292693 | ||||||||
\(330\) | 0.857338 | 0.0471949 | ||||||||
\(331\) | −25.7221 | −1.41381 | −0.706906 | − | 0.707307i | \(-0.749910\pi\) | ||||
−0.706906 | + | 0.707307i | \(0.749910\pi\) | |||||||
\(332\) | −14.4750 | −0.794421 | ||||||||
\(333\) | −8.74406 | −0.479172 | ||||||||
\(334\) | −3.24034 | −0.177303 | ||||||||
\(335\) | 47.1556 | 2.57638 | ||||||||
\(336\) | 3.35463 | 0.183010 | ||||||||
\(337\) | −22.1471 | −1.20643 | −0.603216 | − | 0.797578i | \(-0.706114\pi\) | ||||
−0.603216 | + | 0.797578i | \(0.706114\pi\) | |||||||
\(338\) | −2.62180 | −0.142607 | ||||||||
\(339\) | −13.4720 | −0.731696 | ||||||||
\(340\) | 53.1594 | 2.88297 | ||||||||
\(341\) | 8.65847 | 0.468882 | ||||||||
\(342\) | 1.36830 | 0.0739895 | ||||||||
\(343\) | 11.9992 | 0.647895 | ||||||||
\(344\) | −8.75578 | −0.472080 | ||||||||
\(345\) | −23.7470 | −1.27850 | ||||||||
\(346\) | 0.619303 | 0.0332939 | ||||||||
\(347\) | 16.8724 | 0.905757 | 0.452879 | − | 0.891572i | \(-0.350397\pi\) | ||||
0.452879 | + | 0.891572i | \(0.350397\pi\) | |||||||
\(348\) | 18.6564 | 1.00009 | ||||||||
\(349\) | −36.7014 | −1.96458 | −0.982291 | − | 0.187362i | \(-0.940006\pi\) | ||||
−0.982291 | + | 0.187362i | \(0.940006\pi\) | |||||||
\(350\) | −1.84199 | −0.0984584 | ||||||||
\(351\) | 1.28993 | 0.0688512 | ||||||||
\(352\) | −2.67705 | −0.142687 | ||||||||
\(353\) | 0.505931 | 0.0269280 | 0.0134640 | − | 0.999909i | \(-0.495714\pi\) | ||||
0.0134640 | + | 0.999909i | \(0.495714\pi\) | |||||||
\(354\) | −0.359337 | −0.0190985 | ||||||||
\(355\) | −1.87894 | −0.0997237 | ||||||||
\(356\) | −24.8405 | −1.31654 | ||||||||
\(357\) | −6.71240 | −0.355258 | ||||||||
\(358\) | 0.495075 | 0.0261655 | ||||||||
\(359\) | 6.62258 | 0.349527 | 0.174763 | − | 0.984610i | \(-0.444084\pi\) | ||||
0.174763 | + | 0.984610i | \(0.444084\pi\) | |||||||
\(360\) | −3.38349 | −0.178326 | ||||||||
\(361\) | 16.0019 | 0.842206 | ||||||||
\(362\) | 2.41737 | 0.127054 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −2.28766 | −0.119906 | ||||||||
\(365\) | −13.7532 | −0.719873 | ||||||||
\(366\) | −0.231279 | −0.0120892 | ||||||||
\(367\) | 19.2989 | 1.00739 | 0.503696 | − | 0.863881i | \(-0.331973\pi\) | ||||
0.503696 | + | 0.863881i | \(0.331973\pi\) | |||||||
\(368\) | 23.5868 | 1.22955 | ||||||||
\(369\) | 6.54649 | 0.340797 | ||||||||
\(370\) | −7.49662 | −0.389731 | ||||||||
\(371\) | 4.56496 | 0.237001 | ||||||||
\(372\) | −16.8538 | −0.873828 | ||||||||
\(373\) | −33.3340 | −1.72597 | −0.862985 | − | 0.505229i | \(-0.831408\pi\) | ||||
−0.862985 | + | 0.505229i | \(0.831408\pi\) | |||||||
\(374\) | 1.70390 | 0.0881068 | ||||||||
\(375\) | −13.8691 | −0.716196 | ||||||||
\(376\) | −5.31852 | −0.274282 | ||||||||
\(377\) | −12.3634 | −0.636747 | ||||||||
\(378\) | 0.210720 | 0.0108383 | ||||||||
\(379\) | 38.6940 | 1.98757 | 0.993787 | − | 0.111294i | \(-0.0354997\pi\) | ||||
0.993787 | + | 0.111294i | \(0.0354997\pi\) | |||||||
\(380\) | −42.6892 | −2.18991 | ||||||||
\(381\) | −14.9118 | −0.763956 | ||||||||
\(382\) | 1.59729 | 0.0817244 | ||||||||
\(383\) | −9.35020 | −0.477773 | −0.238886 | − | 0.971048i | \(-0.576782\pi\) | ||||
−0.238886 | + | 0.971048i | \(0.576782\pi\) | |||||||
\(384\) | 6.91400 | 0.352829 | ||||||||
\(385\) | 3.37742 | 0.172129 | ||||||||
\(386\) | 3.12725 | 0.159173 | ||||||||
\(387\) | 9.59278 | 0.487629 | ||||||||
\(388\) | −37.0003 | −1.87840 | ||||||||
\(389\) | 22.9294 | 1.16257 | 0.581283 | − | 0.813701i | \(-0.302551\pi\) | ||||
0.581283 | + | 0.813701i | \(0.302551\pi\) | |||||||
\(390\) | 1.10590 | 0.0559996 | ||||||||
\(391\) | −47.1957 | −2.38679 | ||||||||
\(392\) | 5.63154 | 0.284436 | ||||||||
\(393\) | −1.52367 | −0.0768589 | ||||||||
\(394\) | −2.92590 | −0.147405 | ||||||||
\(395\) | −19.5839 | −0.985371 | ||||||||
\(396\) | 1.94651 | 0.0978158 | ||||||||
\(397\) | 17.2747 | 0.866993 | 0.433496 | − | 0.901155i | \(-0.357280\pi\) | ||||
0.433496 | + | 0.901155i | \(0.357280\pi\) | |||||||
\(398\) | 0.839978 | 0.0421043 | ||||||||
\(399\) | 5.39033 | 0.269854 | ||||||||
\(400\) | 32.1851 | 1.60925 | ||||||||
\(401\) | −31.6046 | −1.57826 | −0.789129 | − | 0.614228i | \(-0.789468\pi\) | ||||
−0.789129 | + | 0.614228i | \(0.789468\pi\) | |||||||
\(402\) | −2.94208 | −0.146738 | ||||||||
\(403\) | 11.1688 | 0.556357 | ||||||||
\(404\) | 10.9010 | 0.542345 | ||||||||
\(405\) | 3.70694 | 0.184199 | ||||||||
\(406\) | −2.01966 | −0.100234 | ||||||||
\(407\) | 8.74406 | 0.433427 | ||||||||
\(408\) | −6.72448 | −0.332911 | ||||||||
\(409\) | 20.8224 | 1.02960 | 0.514800 | − | 0.857310i | \(-0.327866\pi\) | ||||
0.514800 | + | 0.857310i | \(0.327866\pi\) | |||||||
\(410\) | 5.61255 | 0.277184 | ||||||||
\(411\) | −3.70337 | −0.182674 | ||||||||
\(412\) | −31.2429 | −1.53923 | ||||||||
\(413\) | −1.41558 | −0.0696561 | ||||||||
\(414\) | 1.48160 | 0.0728167 | ||||||||
\(415\) | 27.5663 | 1.35318 | ||||||||
\(416\) | −3.45319 | −0.169307 | ||||||||
\(417\) | −6.10661 | −0.299042 | ||||||||
\(418\) | −1.36830 | −0.0669260 | ||||||||
\(419\) | −12.4302 | −0.607256 | −0.303628 | − | 0.952791i | \(-0.598198\pi\) | ||||
−0.303628 | + | 0.952791i | \(0.598198\pi\) | |||||||
\(420\) | −6.57418 | −0.320787 | ||||||||
\(421\) | −9.53980 | −0.464942 | −0.232471 | − | 0.972603i | \(-0.574681\pi\) | ||||
−0.232471 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(422\) | −4.24328 | −0.206560 | ||||||||
\(423\) | 5.82694 | 0.283315 | ||||||||
\(424\) | 4.57317 | 0.222093 | ||||||||
\(425\) | −64.4004 | −3.12388 | ||||||||
\(426\) | 0.117229 | 0.00567975 | ||||||||
\(427\) | −0.911108 | −0.0440916 | ||||||||
\(428\) | −31.4035 | −1.51795 | ||||||||
\(429\) | −1.28993 | −0.0622783 | ||||||||
\(430\) | 8.22426 | 0.396609 | ||||||||
\(431\) | −12.5341 | −0.603745 | −0.301872 | − | 0.953348i | \(-0.597612\pi\) | ||||
−0.301872 | + | 0.953348i | \(0.597612\pi\) | |||||||
\(432\) | −3.68192 | −0.177146 | ||||||||
\(433\) | −18.0140 | −0.865696 | −0.432848 | − | 0.901467i | \(-0.642491\pi\) | ||||
−0.432848 | + | 0.901467i | \(0.642491\pi\) | |||||||
\(434\) | 1.82452 | 0.0875796 | ||||||||
\(435\) | −35.5294 | −1.70350 | ||||||||
\(436\) | 29.7478 | 1.42466 | ||||||||
\(437\) | 37.9001 | 1.81301 | ||||||||
\(438\) | 0.858073 | 0.0410003 | ||||||||
\(439\) | −4.17247 | −0.199141 | −0.0995707 | − | 0.995030i | \(-0.531747\pi\) | ||||
−0.0995707 | + | 0.995030i | \(0.531747\pi\) | |||||||
\(440\) | 3.38349 | 0.161302 | ||||||||
\(441\) | −6.16988 | −0.293804 | ||||||||
\(442\) | 2.19791 | 0.104544 | ||||||||
\(443\) | −31.4449 | −1.49399 | −0.746995 | − | 0.664830i | \(-0.768504\pi\) | ||||
−0.746995 | + | 0.664830i | \(0.768504\pi\) | |||||||
\(444\) | −17.0204 | −0.807752 | ||||||||
\(445\) | 47.3062 | 2.24253 | ||||||||
\(446\) | 1.61887 | 0.0766556 | ||||||||
\(447\) | 13.5246 | 0.639690 | ||||||||
\(448\) | 6.14514 | 0.290331 | ||||||||
\(449\) | 13.4654 | 0.635471 | 0.317735 | − | 0.948179i | \(-0.397078\pi\) | ||||
0.317735 | + | 0.948179i | \(0.397078\pi\) | |||||||
\(450\) | 2.02170 | 0.0953040 | ||||||||
\(451\) | −6.54649 | −0.308262 | ||||||||
\(452\) | −26.2233 | −1.23344 | ||||||||
\(453\) | 1.09346 | 0.0513755 | ||||||||
\(454\) | 1.58525 | 0.0743994 | ||||||||
\(455\) | 4.35663 | 0.204242 | ||||||||
\(456\) | 5.40003 | 0.252880 | ||||||||
\(457\) | 16.0392 | 0.750280 | 0.375140 | − | 0.926968i | \(-0.377595\pi\) | ||||
0.375140 | + | 0.926968i | \(0.377595\pi\) | |||||||
\(458\) | −0.497365 | −0.0232404 | ||||||||
\(459\) | 7.36730 | 0.343876 | ||||||||
\(460\) | −46.2238 | −2.15520 | ||||||||
\(461\) | −2.07719 | −0.0967444 | −0.0483722 | − | 0.998829i | \(-0.515403\pi\) | ||||
−0.0483722 | + | 0.998829i | \(0.515403\pi\) | |||||||
\(462\) | −0.210720 | −0.00980360 | ||||||||
\(463\) | 22.3955 | 1.04081 | 0.520404 | − | 0.853920i | \(-0.325781\pi\) | ||||
0.520404 | + | 0.853920i | \(0.325781\pi\) | |||||||
\(464\) | 35.2896 | 1.63828 | ||||||||
\(465\) | 32.0964 | 1.48843 | ||||||||
\(466\) | −0.0203204 | −0.000941327 0 | ||||||||
\(467\) | 7.84551 | 0.363047 | 0.181523 | − | 0.983387i | \(-0.441897\pi\) | ||||
0.181523 | + | 0.983387i | \(0.441897\pi\) | |||||||
\(468\) | 2.51086 | 0.116064 | ||||||||
\(469\) | −11.5901 | −0.535181 | ||||||||
\(470\) | 4.99566 | 0.230432 | ||||||||
\(471\) | −14.4608 | −0.666319 | ||||||||
\(472\) | −1.41813 | −0.0652745 | ||||||||
\(473\) | −9.59278 | −0.441077 | ||||||||
\(474\) | 1.22186 | 0.0561217 | ||||||||
\(475\) | 51.7162 | 2.37290 | ||||||||
\(476\) | −13.0658 | −0.598868 | ||||||||
\(477\) | −5.01034 | −0.229408 | ||||||||
\(478\) | −0.311341 | −0.0142404 | ||||||||
\(479\) | −23.9318 | −1.09347 | −0.546736 | − | 0.837305i | \(-0.684130\pi\) | ||||
−0.546736 | + | 0.837305i | \(0.684130\pi\) | |||||||
\(480\) | −9.92364 | −0.452950 | ||||||||
\(481\) | 11.2792 | 0.514287 | ||||||||
\(482\) | 1.05002 | 0.0478272 | ||||||||
\(483\) | 5.83665 | 0.265577 | ||||||||
\(484\) | −1.94651 | −0.0884777 | ||||||||
\(485\) | 70.4634 | 3.19958 | ||||||||
\(486\) | −0.231279 | −0.0104910 | ||||||||
\(487\) | 25.8238 | 1.17019 | 0.585094 | − | 0.810965i | \(-0.301058\pi\) | ||||
0.585094 | + | 0.810965i | \(0.301058\pi\) | |||||||
\(488\) | −0.912746 | −0.0413181 | ||||||||
\(489\) | −1.40734 | −0.0636419 | ||||||||
\(490\) | −5.28968 | −0.238963 | ||||||||
\(491\) | −31.3212 | −1.41351 | −0.706754 | − | 0.707459i | \(-0.749841\pi\) | ||||
−0.706754 | + | 0.707459i | \(0.749841\pi\) | |||||||
\(492\) | 12.7428 | 0.574490 | ||||||||
\(493\) | −70.6123 | −3.18022 | ||||||||
\(494\) | −1.76501 | −0.0794117 | ||||||||
\(495\) | −3.70694 | −0.166614 | ||||||||
\(496\) | −31.8798 | −1.43144 | ||||||||
\(497\) | 0.461814 | 0.0207152 | ||||||||
\(498\) | −1.71989 | −0.0770700 | ||||||||
\(499\) | 24.5909 | 1.10084 | 0.550420 | − | 0.834888i | \(-0.314467\pi\) | ||||
0.550420 | + | 0.834888i | \(0.314467\pi\) | |||||||
\(500\) | −26.9963 | −1.20731 | ||||||||
\(501\) | 14.0105 | 0.625942 | ||||||||
\(502\) | −1.35009 | −0.0602574 | ||||||||
\(503\) | −2.31095 | −0.103040 | −0.0515200 | − | 0.998672i | \(-0.516407\pi\) | ||||
−0.0515200 | + | 0.998672i | \(0.516407\pi\) | |||||||
\(504\) | 0.831610 | 0.0370429 | ||||||||
\(505\) | −20.7599 | −0.923803 | ||||||||
\(506\) | −1.48160 | −0.0658652 | ||||||||
\(507\) | 11.3361 | 0.503453 | ||||||||
\(508\) | −29.0260 | −1.28782 | ||||||||
\(509\) | −29.9915 | −1.32935 | −0.664676 | − | 0.747132i | \(-0.731430\pi\) | ||||
−0.664676 | + | 0.747132i | \(0.731430\pi\) | |||||||
\(510\) | 6.31627 | 0.279689 | ||||||||
\(511\) | 3.38031 | 0.149536 | ||||||||
\(512\) | 16.5780 | 0.732650 | ||||||||
\(513\) | −5.91624 | −0.261208 | ||||||||
\(514\) | 4.45176 | 0.196359 | ||||||||
\(515\) | 59.4991 | 2.62184 | ||||||||
\(516\) | 18.6724 | 0.822009 | ||||||||
\(517\) | −5.82694 | −0.256268 | ||||||||
\(518\) | 1.84255 | 0.0809571 | ||||||||
\(519\) | −2.67772 | −0.117539 | ||||||||
\(520\) | 4.36446 | 0.191394 | ||||||||
\(521\) | −17.7422 | −0.777300 | −0.388650 | − | 0.921385i | \(-0.627058\pi\) | ||||
−0.388650 | + | 0.921385i | \(0.627058\pi\) | |||||||
\(522\) | 2.21671 | 0.0970228 | ||||||||
\(523\) | −16.2858 | −0.712129 | −0.356064 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356064 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(524\) | −2.96583 | −0.129563 | ||||||||
\(525\) | 7.96434 | 0.347592 | ||||||||
\(526\) | −2.88317 | −0.125712 | ||||||||
\(527\) | 63.7895 | 2.77872 | ||||||||
\(528\) | 3.68192 | 0.160235 | ||||||||
\(529\) | 18.0382 | 0.784269 | ||||||||
\(530\) | −4.29555 | −0.186587 | ||||||||
\(531\) | 1.55369 | 0.0674245 | ||||||||
\(532\) | 10.4923 | 0.454901 | ||||||||
\(533\) | −8.44449 | −0.365772 | ||||||||
\(534\) | −2.95148 | −0.127723 | ||||||||
\(535\) | 59.8050 | 2.58559 | ||||||||
\(536\) | −11.6110 | −0.501517 | ||||||||
\(537\) | −2.14059 | −0.0923734 | ||||||||
\(538\) | −2.53115 | −0.109126 | ||||||||
\(539\) | 6.16988 | 0.265756 | ||||||||
\(540\) | 7.21559 | 0.310510 | ||||||||
\(541\) | −4.81097 | −0.206840 | −0.103420 | − | 0.994638i | \(-0.532979\pi\) | ||||
−0.103420 | + | 0.994638i | \(0.532979\pi\) | |||||||
\(542\) | −4.15645 | −0.178535 | ||||||||
\(543\) | −10.4522 | −0.448545 | ||||||||
\(544\) | −19.7226 | −0.845599 | ||||||||
\(545\) | −56.6517 | −2.42669 | ||||||||
\(546\) | −0.271814 | −0.0116326 | ||||||||
\(547\) | 12.5709 | 0.537491 | 0.268745 | − | 0.963211i | \(-0.413391\pi\) | ||||
0.268745 | + | 0.963211i | \(0.413391\pi\) | |||||||
\(548\) | −7.20865 | −0.307938 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.02170 | −0.0862057 | ||||||||
\(551\) | 56.7046 | 2.41570 | ||||||||
\(552\) | 5.84715 | 0.248871 | ||||||||
\(553\) | 4.81341 | 0.204687 | ||||||||
\(554\) | −1.32825 | −0.0564320 | ||||||||
\(555\) | 32.4137 | 1.37588 | ||||||||
\(556\) | −11.8866 | −0.504103 | ||||||||
\(557\) | −31.8497 | −1.34951 | −0.674757 | − | 0.738040i | \(-0.735752\pi\) | ||||
−0.674757 | + | 0.738040i | \(0.735752\pi\) | |||||||
\(558\) | −2.00252 | −0.0847736 | ||||||||
\(559\) | −12.3740 | −0.523364 | ||||||||
\(560\) | −12.4354 | −0.525491 | ||||||||
\(561\) | −7.36730 | −0.311048 | ||||||||
\(562\) | −7.25759 | −0.306143 | ||||||||
\(563\) | 37.6429 | 1.58646 | 0.793229 | − | 0.608923i | \(-0.208398\pi\) | ||||
0.793229 | + | 0.608923i | \(0.208398\pi\) | |||||||
\(564\) | 11.3422 | 0.477592 | ||||||||
\(565\) | 49.9397 | 2.10098 | ||||||||
\(566\) | −5.19216 | −0.218243 | ||||||||
\(567\) | −0.911108 | −0.0382629 | ||||||||
\(568\) | 0.462645 | 0.0194121 | ||||||||
\(569\) | −3.93199 | −0.164838 | −0.0824189 | − | 0.996598i | \(-0.526265\pi\) | ||||
−0.0824189 | + | 0.996598i | \(0.526265\pi\) | |||||||
\(570\) | −5.07222 | −0.212452 | ||||||||
\(571\) | 18.8819 | 0.790185 | 0.395092 | − | 0.918641i | \(-0.370713\pi\) | ||||
0.395092 | + | 0.918641i | \(0.370713\pi\) | |||||||
\(572\) | −2.51086 | −0.104984 | ||||||||
\(573\) | −6.90631 | −0.288515 | ||||||||
\(574\) | −1.37948 | −0.0575783 | ||||||||
\(575\) | 55.9982 | 2.33529 | ||||||||
\(576\) | −6.74470 | −0.281029 | ||||||||
\(577\) | 34.1619 | 1.42218 | 0.711088 | − | 0.703103i | \(-0.248203\pi\) | ||||
0.711088 | + | 0.703103i | \(0.248203\pi\) | |||||||
\(578\) | 8.62143 | 0.358604 | ||||||||
\(579\) | −13.5215 | −0.561935 | ||||||||
\(580\) | −69.1583 | −2.87164 | ||||||||
\(581\) | −6.77537 | −0.281090 | ||||||||
\(582\) | −4.39628 | −0.182232 | ||||||||
\(583\) | 5.01034 | 0.207507 | ||||||||
\(584\) | 3.38639 | 0.140130 | ||||||||
\(585\) | −4.78168 | −0.197698 | ||||||||
\(586\) | −3.67328 | −0.151742 | ||||||||
\(587\) | −4.92186 | −0.203147 | −0.101573 | − | 0.994828i | \(-0.532388\pi\) | ||||
−0.101573 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(588\) | −12.0097 | −0.495273 | ||||||||
\(589\) | −51.2256 | −2.11071 | ||||||||
\(590\) | 1.33204 | 0.0548392 | ||||||||
\(591\) | 12.6509 | 0.520390 | ||||||||
\(592\) | −32.1949 | −1.32320 | ||||||||
\(593\) | 38.0886 | 1.56411 | 0.782056 | − | 0.623208i | \(-0.214171\pi\) | ||||
0.782056 | + | 0.623208i | \(0.214171\pi\) | |||||||
\(594\) | 0.231279 | 0.00948951 | ||||||||
\(595\) | 24.8825 | 1.02008 | ||||||||
\(596\) | 26.3257 | 1.07834 | ||||||||
\(597\) | −3.63188 | −0.148643 | ||||||||
\(598\) | −1.91116 | −0.0781530 | ||||||||
\(599\) | −35.5566 | −1.45280 | −0.726401 | − | 0.687271i | \(-0.758809\pi\) | ||||
−0.726401 | + | 0.687271i | \(0.758809\pi\) | |||||||
\(600\) | 7.97867 | 0.325728 | ||||||||
\(601\) | −3.34841 | −0.136584 | −0.0682922 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682922 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(602\) | −2.02140 | −0.0823859 | ||||||||
\(603\) | 12.7209 | 0.518035 | ||||||||
\(604\) | 2.12844 | 0.0866050 | ||||||||
\(605\) | 3.70694 | 0.150708 | ||||||||
\(606\) | 1.29523 | 0.0526151 | ||||||||
\(607\) | −24.1878 | −0.981753 | −0.490877 | − | 0.871229i | \(-0.663323\pi\) | ||||
−0.490877 | + | 0.871229i | \(0.663323\pi\) | |||||||
\(608\) | 15.8380 | 0.642318 | ||||||||
\(609\) | 8.73257 | 0.353862 | ||||||||
\(610\) | 0.857338 | 0.0347126 | ||||||||
\(611\) | −7.51633 | −0.304078 | ||||||||
\(612\) | 14.3405 | 0.579681 | ||||||||
\(613\) | −19.1329 | −0.772769 | −0.386384 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386384 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(614\) | 3.05411 | 0.123254 | ||||||||
\(615\) | −24.2674 | −0.978557 | ||||||||
\(616\) | −0.831610 | −0.0335065 | ||||||||
\(617\) | 22.2994 | 0.897741 | 0.448870 | − | 0.893597i | \(-0.351827\pi\) | ||||
0.448870 | + | 0.893597i | \(0.351827\pi\) | |||||||
\(618\) | −3.71220 | −0.149327 | ||||||||
\(619\) | 31.9197 | 1.28296 | 0.641480 | − | 0.767140i | \(-0.278321\pi\) | ||||
0.641480 | + | 0.767140i | \(0.278321\pi\) | |||||||
\(620\) | 62.4759 | 2.50909 | ||||||||
\(621\) | −6.40611 | −0.257068 | ||||||||
\(622\) | 1.81814 | 0.0729006 | ||||||||
\(623\) | −11.6271 | −0.465831 | ||||||||
\(624\) | 4.74941 | 0.190129 | ||||||||
\(625\) | 7.70489 | 0.308196 | ||||||||
\(626\) | −4.07943 | −0.163047 | ||||||||
\(627\) | 5.91624 | 0.236272 | ||||||||
\(628\) | −28.1481 | −1.12323 | ||||||||
\(629\) | 64.4201 | 2.56860 | ||||||||
\(630\) | −0.781128 | −0.0311209 | ||||||||
\(631\) | 0.258718 | 0.0102994 | 0.00514971 | − | 0.999987i | \(-0.498361\pi\) | ||||
0.00514971 | + | 0.999987i | \(0.498361\pi\) | |||||||
\(632\) | 4.82207 | 0.191812 | ||||||||
\(633\) | 18.3470 | 0.729228 | ||||||||
\(634\) | 2.44540 | 0.0971193 | ||||||||
\(635\) | 55.2772 | 2.19361 | ||||||||
\(636\) | −9.75267 | −0.386719 | ||||||||
\(637\) | 7.95870 | 0.315335 | ||||||||
\(638\) | −2.21671 | −0.0877605 | ||||||||
\(639\) | −0.506871 | −0.0200515 | ||||||||
\(640\) | −25.6298 | −1.01311 | ||||||||
\(641\) | −26.1212 | −1.03173 | −0.515863 | − | 0.856671i | \(-0.672529\pi\) | ||||
−0.515863 | + | 0.856671i | \(0.672529\pi\) | |||||||
\(642\) | −3.73129 | −0.147262 | ||||||||
\(643\) | 7.45790 | 0.294111 | 0.147056 | − | 0.989128i | \(-0.453020\pi\) | ||||
0.147056 | + | 0.989128i | \(0.453020\pi\) | |||||||
\(644\) | 11.3611 | 0.447690 | ||||||||
\(645\) | −35.5598 | −1.40017 | ||||||||
\(646\) | −10.0807 | −0.396620 | ||||||||
\(647\) | −44.3581 | −1.74390 | −0.871949 | − | 0.489597i | \(-0.837144\pi\) | ||||
−0.871949 | + | 0.489597i | \(0.837144\pi\) | |||||||
\(648\) | −0.912746 | −0.0358561 | ||||||||
\(649\) | −1.55369 | −0.0609877 | ||||||||
\(650\) | −2.60785 | −0.102288 | ||||||||
\(651\) | −7.88880 | −0.309186 | ||||||||
\(652\) | −2.73939 | −0.107283 | ||||||||
\(653\) | −6.14521 | −0.240481 | −0.120240 | − | 0.992745i | \(-0.538367\pi\) | ||||
−0.120240 | + | 0.992745i | \(0.538367\pi\) | |||||||
\(654\) | 3.53456 | 0.138212 | ||||||||
\(655\) | 5.64814 | 0.220691 | ||||||||
\(656\) | 24.1036 | 0.941089 | ||||||||
\(657\) | −3.71011 | −0.144745 | ||||||||
\(658\) | −1.22785 | −0.0478668 | ||||||||
\(659\) | 27.8267 | 1.08398 | 0.541988 | − | 0.840387i | \(-0.317672\pi\) | ||||
0.541988 | + | 0.840387i | \(0.317672\pi\) | |||||||
\(660\) | −7.21559 | −0.280866 | ||||||||
\(661\) | 41.3110 | 1.60681 | 0.803406 | − | 0.595431i | \(-0.203019\pi\) | ||||
0.803406 | + | 0.595431i | \(0.203019\pi\) | |||||||
\(662\) | −5.94898 | −0.231214 | ||||||||
\(663\) | −9.50328 | −0.369077 | ||||||||
\(664\) | −6.78756 | −0.263408 | ||||||||
\(665\) | −19.9816 | −0.774854 | ||||||||
\(666\) | −2.02232 | −0.0783633 | ||||||||
\(667\) | 61.3997 | 2.37741 | ||||||||
\(668\) | 27.2716 | 1.05517 | ||||||||
\(669\) | −6.99961 | −0.270621 | ||||||||
\(670\) | 10.9061 | 0.421340 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 2.43908 | 0.0940894 | ||||||||
\(673\) | −19.1769 | −0.739214 | −0.369607 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369607 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(674\) | −5.12218 | −0.197299 | ||||||||
\(675\) | −8.74139 | −0.336456 | ||||||||
\(676\) | 22.0658 | 0.848685 | ||||||||
\(677\) | −6.49815 | −0.249744 | −0.124872 | − | 0.992173i | \(-0.539852\pi\) | ||||
−0.124872 | + | 0.992173i | \(0.539852\pi\) | |||||||
\(678\) | −3.11579 | −0.119661 | ||||||||
\(679\) | −17.3188 | −0.664635 | ||||||||
\(680\) | 24.9272 | 0.955915 | ||||||||
\(681\) | −6.85426 | −0.262656 | ||||||||
\(682\) | 2.00252 | 0.0766806 | ||||||||
\(683\) | −30.5994 | −1.17085 | −0.585426 | − | 0.810726i | \(-0.699073\pi\) | ||||
−0.585426 | + | 0.810726i | \(0.699073\pi\) | |||||||
\(684\) | −11.5160 | −0.440326 | ||||||||
\(685\) | 13.7282 | 0.524526 | ||||||||
\(686\) | 2.77516 | 0.105956 | ||||||||
\(687\) | 2.15050 | 0.0820465 | ||||||||
\(688\) | 35.3199 | 1.34656 | ||||||||
\(689\) | 6.46297 | 0.246220 | ||||||||
\(690\) | −5.49220 | −0.209084 | ||||||||
\(691\) | 21.3756 | 0.813166 | 0.406583 | − | 0.913614i | \(-0.366720\pi\) | ||||
0.406583 | + | 0.913614i | \(0.366720\pi\) | |||||||
\(692\) | −5.21222 | −0.198139 | ||||||||
\(693\) | 0.911108 | 0.0346101 | ||||||||
\(694\) | 3.90224 | 0.148127 | ||||||||
\(695\) | 22.6368 | 0.858663 | ||||||||
\(696\) | 8.74827 | 0.331603 | ||||||||
\(697\) | −48.2299 | −1.82684 | ||||||||
\(698\) | −8.48828 | −0.321286 | ||||||||
\(699\) | 0.0878610 | 0.00332321 | ||||||||
\(700\) | 15.5027 | 0.585946 | ||||||||
\(701\) | −13.7805 | −0.520483 | −0.260241 | − | 0.965544i | \(-0.583802\pi\) | ||||
−0.260241 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(702\) | 0.298334 | 0.0112599 | ||||||||
\(703\) | −51.7320 | −1.95111 | ||||||||
\(704\) | 6.74470 | 0.254200 | ||||||||
\(705\) | −21.6001 | −0.813507 | ||||||||
\(706\) | 0.117012 | 0.00440379 | ||||||||
\(707\) | 5.10246 | 0.191898 | ||||||||
\(708\) | 3.02428 | 0.113659 | ||||||||
\(709\) | 19.3933 | 0.728332 | 0.364166 | − | 0.931334i | \(-0.381354\pi\) | ||||
0.364166 | + | 0.931334i | \(0.381354\pi\) | |||||||
\(710\) | −0.434560 | −0.0163087 | ||||||||
\(711\) | −5.28303 | −0.198129 | ||||||||
\(712\) | −11.6480 | −0.436529 | ||||||||
\(713\) | −55.4671 | −2.07726 | ||||||||
\(714\) | −1.55244 | −0.0580986 | ||||||||
\(715\) | 4.78168 | 0.178825 | ||||||||
\(716\) | −4.16669 | −0.155716 | ||||||||
\(717\) | 1.34617 | 0.0502735 | ||||||||
\(718\) | 1.53167 | 0.0571613 | ||||||||
\(719\) | 6.37432 | 0.237722 | 0.118861 | − | 0.992911i | \(-0.462076\pi\) | ||||
0.118861 | + | 0.992911i | \(0.462076\pi\) | |||||||
\(720\) | 13.6486 | 0.508655 | ||||||||
\(721\) | −14.6240 | −0.544624 | ||||||||
\(722\) | 3.70091 | 0.137734 | ||||||||
\(723\) | −4.54006 | −0.168847 | ||||||||
\(724\) | −20.3452 | −0.756124 | ||||||||
\(725\) | 83.7824 | 3.11160 | ||||||||
\(726\) | −0.231279 | −0.00858358 | ||||||||
\(727\) | −21.3988 | −0.793637 | −0.396819 | − | 0.917897i | \(-0.629886\pi\) | ||||
−0.396819 | + | 0.917897i | \(0.629886\pi\) | |||||||
\(728\) | −1.07272 | −0.0397575 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.18082 | −0.117728 | ||||||||
\(731\) | −70.6729 | −2.61393 | ||||||||
\(732\) | 1.94651 | 0.0719451 | ||||||||
\(733\) | 23.1610 | 0.855470 | 0.427735 | − | 0.903904i | \(-0.359312\pi\) | ||||
0.427735 | + | 0.903904i | \(0.359312\pi\) | |||||||
\(734\) | 4.46343 | 0.164748 | ||||||||
\(735\) | 22.8714 | 0.843623 | ||||||||
\(736\) | 17.1494 | 0.632137 | ||||||||
\(737\) | −12.7209 | −0.468580 | ||||||||
\(738\) | 1.51407 | 0.0557336 | ||||||||
\(739\) | −31.1840 | −1.14712 | −0.573561 | − | 0.819163i | \(-0.694439\pi\) | ||||
−0.573561 | + | 0.819163i | \(0.694439\pi\) | |||||||
\(740\) | 63.0936 | 2.31937 | ||||||||
\(741\) | 7.63152 | 0.280351 | ||||||||
\(742\) | 1.05578 | 0.0387589 | ||||||||
\(743\) | −11.7663 | −0.431663 | −0.215831 | − | 0.976431i | \(-0.569246\pi\) | ||||
−0.215831 | + | 0.976431i | \(0.569246\pi\) | |||||||
\(744\) | −7.90298 | −0.289737 | ||||||||
\(745\) | −50.1347 | −1.83679 | ||||||||
\(746\) | −7.70947 | −0.282264 | ||||||||
\(747\) | 7.43641 | 0.272084 | ||||||||
\(748\) | −14.3405 | −0.524341 | ||||||||
\(749\) | −14.6991 | −0.537095 | ||||||||
\(750\) | −3.20763 | −0.117126 | ||||||||
\(751\) | −0.685367 | −0.0250094 | −0.0125047 | − | 0.999922i | \(-0.503980\pi\) | ||||
−0.0125047 | + | 0.999922i | \(0.503980\pi\) | |||||||
\(752\) | 21.4543 | 0.782359 | ||||||||
\(753\) | 5.83748 | 0.212730 | ||||||||
\(754\) | −2.85940 | −0.104133 | ||||||||
\(755\) | −4.05341 | −0.147519 | ||||||||
\(756\) | −1.77348 | −0.0645009 | ||||||||
\(757\) | −32.9419 | −1.19730 | −0.598648 | − | 0.801013i | \(-0.704295\pi\) | ||||
−0.598648 | + | 0.801013i | \(0.704295\pi\) | |||||||
\(758\) | 8.94911 | 0.325046 | ||||||||
\(759\) | 6.40611 | 0.232527 | ||||||||
\(760\) | −20.0176 | −0.726114 | ||||||||
\(761\) | 24.4080 | 0.884791 | 0.442396 | − | 0.896820i | \(-0.354129\pi\) | ||||
0.442396 | + | 0.896820i | \(0.354129\pi\) | |||||||
\(762\) | −3.44880 | −0.124937 | ||||||||
\(763\) | 13.9241 | 0.504087 | ||||||||
\(764\) | −13.4432 | −0.486358 | ||||||||
\(765\) | −27.3101 | −0.987399 | ||||||||
\(766\) | −2.16251 | −0.0781346 | ||||||||
\(767\) | −2.00415 | −0.0723656 | ||||||||
\(768\) | −11.8903 | −0.429055 | ||||||||
\(769\) | −0.979264 | −0.0353132 | −0.0176566 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176566 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(770\) | 0.781128 | 0.0281499 | ||||||||
\(771\) | −19.2484 | −0.693214 | ||||||||
\(772\) | −26.3198 | −0.947269 | ||||||||
\(773\) | −47.3585 | −1.70337 | −0.851683 | − | 0.524057i | \(-0.824418\pi\) | ||||
−0.851683 | + | 0.524057i | \(0.824418\pi\) | |||||||
\(774\) | 2.21861 | 0.0797464 | ||||||||
\(775\) | −75.6870 | −2.71876 | ||||||||
\(776\) | −17.3500 | −0.622827 | ||||||||
\(777\) | −7.96678 | −0.285807 | ||||||||
\(778\) | 5.30310 | 0.190125 | ||||||||
\(779\) | 38.7306 | 1.38767 | ||||||||
\(780\) | −9.30759 | −0.333265 | ||||||||
\(781\) | 0.506871 | 0.0181373 | ||||||||
\(782\) | −10.9154 | −0.390334 | ||||||||
\(783\) | −9.58456 | −0.342524 | ||||||||
\(784\) | −22.7170 | −0.811322 | ||||||||
\(785\) | 53.6053 | 1.91326 | ||||||||
\(786\) | −0.352393 | −0.0125694 | ||||||||
\(787\) | −21.9000 | −0.780651 | −0.390326 | − | 0.920677i | \(-0.627638\pi\) | ||||
−0.390326 | + | 0.920677i | \(0.627638\pi\) | |||||||
\(788\) | 24.6252 | 0.877235 | ||||||||
\(789\) | 12.4662 | 0.443808 | ||||||||
\(790\) | −4.52934 | −0.161147 | ||||||||
\(791\) | −12.2744 | −0.436428 | ||||||||
\(792\) | 0.912746 | 0.0324330 | ||||||||
\(793\) | −1.28993 | −0.0458067 | ||||||||
\(794\) | 3.99528 | 0.141787 | ||||||||
\(795\) | 18.5730 | 0.658717 | ||||||||
\(796\) | −7.06948 | −0.250571 | ||||||||
\(797\) | 16.0797 | 0.569571 | 0.284785 | − | 0.958591i | \(-0.408078\pi\) | ||||
0.284785 | + | 0.958591i | \(0.408078\pi\) | |||||||
\(798\) | 1.24667 | 0.0441318 | ||||||||
\(799\) | −42.9288 | −1.51871 | ||||||||
\(800\) | 23.4011 | 0.827353 | ||||||||
\(801\) | 12.7615 | 0.450907 | ||||||||
\(802\) | −7.30949 | −0.258107 | ||||||||
\(803\) | 3.71011 | 0.130927 | ||||||||
\(804\) | 24.7614 | 0.873265 | ||||||||
\(805\) | −21.6361 | −0.762573 | ||||||||
\(806\) | 2.58311 | 0.0909862 | ||||||||
\(807\) | 10.9441 | 0.385252 | ||||||||
\(808\) | 5.11164 | 0.179827 | ||||||||
\(809\) | −11.8133 | −0.415333 | −0.207667 | − | 0.978200i | \(-0.566587\pi\) | ||||
−0.207667 | + | 0.978200i | \(0.566587\pi\) | |||||||
\(810\) | 0.857338 | 0.0301238 | ||||||||
\(811\) | 29.4126 | 1.03281 | 0.516407 | − | 0.856343i | \(-0.327269\pi\) | ||||
0.516407 | + | 0.856343i | \(0.327269\pi\) | |||||||
\(812\) | 16.9980 | 0.596514 | ||||||||
\(813\) | 17.9716 | 0.630290 | ||||||||
\(814\) | 2.02232 | 0.0708823 | ||||||||
\(815\) | 5.21691 | 0.182740 | ||||||||
\(816\) | 27.1258 | 0.949593 | ||||||||
\(817\) | 56.7532 | 1.98554 | ||||||||
\(818\) | 4.81579 | 0.168380 | ||||||||
\(819\) | 1.17526 | 0.0410670 | ||||||||
\(820\) | −47.2368 | −1.64958 | ||||||||
\(821\) | −30.6948 | −1.07125 | −0.535627 | − | 0.844454i | \(-0.679925\pi\) | ||||
−0.535627 | + | 0.844454i | \(0.679925\pi\) | |||||||
\(822\) | −0.856514 | −0.0298743 | ||||||||
\(823\) | 31.6432 | 1.10301 | 0.551505 | − | 0.834171i | \(-0.314054\pi\) | ||||
0.551505 | + | 0.834171i | \(0.314054\pi\) | |||||||
\(824\) | −14.6503 | −0.510366 | ||||||||
\(825\) | 8.74139 | 0.304336 | ||||||||
\(826\) | −0.327394 | −0.0113915 | ||||||||
\(827\) | −13.0222 | −0.452825 | −0.226413 | − | 0.974031i | \(-0.572700\pi\) | ||||
−0.226413 | + | 0.974031i | \(0.572700\pi\) | |||||||
\(828\) | −12.4695 | −0.433347 | ||||||||
\(829\) | 47.5998 | 1.65321 | 0.826604 | − | 0.562783i | \(-0.190269\pi\) | ||||
0.826604 | + | 0.562783i | \(0.190269\pi\) | |||||||
\(830\) | 6.37552 | 0.221298 | ||||||||
\(831\) | 5.74306 | 0.199225 | ||||||||
\(832\) | 8.70017 | 0.301624 | ||||||||
\(833\) | 45.4554 | 1.57494 | ||||||||
\(834\) | −1.41233 | −0.0489051 | ||||||||
\(835\) | −51.9360 | −1.79732 | ||||||||
\(836\) | 11.5160 | 0.398290 | ||||||||
\(837\) | 8.65847 | 0.299280 | ||||||||
\(838\) | −2.87485 | −0.0993102 | ||||||||
\(839\) | −2.77869 | −0.0959309 | −0.0479655 | − | 0.998849i | \(-0.515274\pi\) | ||||
−0.0479655 | + | 0.998849i | \(0.515274\pi\) | |||||||
\(840\) | −3.08273 | −0.106364 | ||||||||
\(841\) | 62.8638 | 2.16772 | ||||||||
\(842\) | −2.20636 | −0.0760362 | ||||||||
\(843\) | 31.3802 | 1.08079 | ||||||||
\(844\) | 35.7126 | 1.22928 | ||||||||
\(845\) | −42.0222 | −1.44561 | ||||||||
\(846\) | 1.34765 | 0.0463332 | ||||||||
\(847\) | −0.911108 | −0.0313060 | ||||||||
\(848\) | −18.4477 | −0.633495 | ||||||||
\(849\) | 22.4497 | 0.770472 | ||||||||
\(850\) | −14.8945 | −0.510877 | ||||||||
\(851\) | −56.0154 | −1.92018 | ||||||||
\(852\) | −0.986629 | −0.0338014 | ||||||||
\(853\) | 19.4760 | 0.666845 | 0.333423 | − | 0.942777i | \(-0.391796\pi\) | ||||
0.333423 | + | 0.942777i | \(0.391796\pi\) | |||||||
\(854\) | −0.210720 | −0.00721071 | ||||||||
\(855\) | 21.9311 | 0.750029 | ||||||||
\(856\) | −14.7256 | −0.503310 | ||||||||
\(857\) | −34.8220 | −1.18950 | −0.594749 | − | 0.803912i | \(-0.702748\pi\) | ||||
−0.594749 | + | 0.803912i | \(0.702748\pi\) | |||||||
\(858\) | −0.298334 | −0.0101849 | ||||||||
\(859\) | −8.18830 | −0.279381 | −0.139691 | − | 0.990195i | \(-0.544611\pi\) | ||||
−0.139691 | + | 0.990195i | \(0.544611\pi\) | |||||||
\(860\) | −69.2176 | −2.36030 | ||||||||
\(861\) | 5.96456 | 0.203272 | ||||||||
\(862\) | −2.89887 | −0.0987359 | ||||||||
\(863\) | 34.4697 | 1.17336 | 0.586681 | − | 0.809818i | \(-0.300434\pi\) | ||||
0.586681 | + | 0.809818i | \(0.300434\pi\) | |||||||
\(864\) | −2.67705 | −0.0910749 | ||||||||
\(865\) | 9.92616 | 0.337500 | ||||||||
\(866\) | −4.16626 | −0.141575 | ||||||||
\(867\) | −37.2771 | −1.26600 | ||||||||
\(868\) | −15.3556 | −0.521204 | ||||||||
\(869\) | 5.28303 | 0.179215 | ||||||||
\(870\) | −8.21721 | −0.278590 | ||||||||
\(871\) | −16.4090 | −0.555999 | ||||||||
\(872\) | 13.9492 | 0.472378 | ||||||||
\(873\) | 19.0085 | 0.643341 | ||||||||
\(874\) | 8.76551 | 0.296498 | ||||||||
\(875\) | −12.6362 | −0.427182 | ||||||||
\(876\) | −7.22177 | −0.244001 | ||||||||
\(877\) | 22.6206 | 0.763845 | 0.381922 | − | 0.924194i | \(-0.375262\pi\) | ||||
0.381922 | + | 0.924194i | \(0.375262\pi\) | |||||||
\(878\) | −0.965007 | −0.0325674 | ||||||||
\(879\) | 15.8824 | 0.535701 | ||||||||
\(880\) | −13.6486 | −0.460096 | ||||||||
\(881\) | 20.0360 | 0.675029 | 0.337514 | − | 0.941320i | \(-0.390414\pi\) | ||||
0.337514 | + | 0.941320i | \(0.390414\pi\) | |||||||
\(882\) | −1.42697 | −0.0480485 | ||||||||
\(883\) | −16.1716 | −0.544217 | −0.272108 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(884\) | −18.4982 | −0.622163 | ||||||||
\(885\) | −5.75944 | −0.193601 | ||||||||
\(886\) | −7.27255 | −0.244326 | ||||||||
\(887\) | −14.1009 | −0.473460 | −0.236730 | − | 0.971575i | \(-0.576076\pi\) | ||||
−0.236730 | + | 0.971575i | \(0.576076\pi\) | |||||||
\(888\) | −7.98111 | −0.267829 | ||||||||
\(889\) | −13.5863 | −0.455669 | ||||||||
\(890\) | 10.9410 | 0.366742 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −13.6248 | −0.456193 | ||||||||
\(893\) | 34.4736 | 1.15361 | ||||||||
\(894\) | 3.12795 | 0.104614 | ||||||||
\(895\) | 7.93504 | 0.265239 | ||||||||
\(896\) | 6.29940 | 0.210448 | ||||||||
\(897\) | 8.26341 | 0.275907 | ||||||||
\(898\) | 3.11427 | 0.103924 | ||||||||
\(899\) | −82.9876 | −2.76779 | ||||||||
\(900\) | −17.0152 | −0.567173 | ||||||||
\(901\) | 36.9127 | 1.22974 | ||||||||
\(902\) | −1.51407 | −0.0504129 | ||||||||
\(903\) | 8.74006 | 0.290851 | ||||||||
\(904\) | −12.2965 | −0.408975 | ||||||||
\(905\) | 38.7455 | 1.28794 | ||||||||
\(906\) | 0.252896 | 0.00840190 | ||||||||
\(907\) | −36.0807 | −1.19804 | −0.599019 | − | 0.800735i | \(-0.704443\pi\) | ||||
−0.599019 | + | 0.800735i | \(0.704443\pi\) | |||||||
\(908\) | −13.3419 | −0.442766 | ||||||||
\(909\) | −5.60028 | −0.185750 | ||||||||
\(910\) | 1.00760 | 0.0334015 | ||||||||
\(911\) | −20.4544 | −0.677684 | −0.338842 | − | 0.940843i | \(-0.610035\pi\) | ||||
−0.338842 | + | 0.940843i | \(0.610035\pi\) | |||||||
\(912\) | −21.7831 | −0.721312 | ||||||||
\(913\) | −7.43641 | −0.246109 | ||||||||
\(914\) | 3.70953 | 0.122700 | ||||||||
\(915\) | −3.70694 | −0.122548 | ||||||||
\(916\) | 4.18596 | 0.138308 | ||||||||
\(917\) | −1.38823 | −0.0458432 | ||||||||
\(918\) | 1.70390 | 0.0562372 | ||||||||
\(919\) | 43.7171 | 1.44209 | 0.721046 | − | 0.692887i | \(-0.243662\pi\) | ||||
0.721046 | + | 0.692887i | \(0.243662\pi\) | |||||||
\(920\) | −21.6750 | −0.714604 | ||||||||
\(921\) | −13.2053 | −0.435129 | ||||||||
\(922\) | −0.480411 | −0.0158215 | ||||||||
\(923\) | 0.653827 | 0.0215210 | ||||||||
\(924\) | 1.77348 | 0.0583432 | ||||||||
\(925\) | −76.4352 | −2.51317 | ||||||||
\(926\) | 5.17962 | 0.170213 | ||||||||
\(927\) | 16.0507 | 0.527175 | ||||||||
\(928\) | 25.6583 | 0.842275 | ||||||||
\(929\) | −34.9056 | −1.14521 | −0.572607 | − | 0.819830i | \(-0.694068\pi\) | ||||
−0.572607 | + | 0.819830i | \(0.694068\pi\) | |||||||
\(930\) | 7.42323 | 0.243417 | ||||||||
\(931\) | −36.5025 | −1.19632 | ||||||||
\(932\) | 0.171022 | 0.00560202 | ||||||||
\(933\) | −7.86121 | −0.257364 | ||||||||
\(934\) | 1.81451 | 0.0593724 | ||||||||
\(935\) | 27.3101 | 0.893136 | ||||||||
\(936\) | 1.17738 | 0.0384838 | ||||||||
\(937\) | 27.5062 | 0.898589 | 0.449294 | − | 0.893384i | \(-0.351675\pi\) | ||||
0.449294 | + | 0.893384i | \(0.351675\pi\) | |||||||
\(938\) | −2.68055 | −0.0875232 | ||||||||
\(939\) | 17.6385 | 0.575612 | ||||||||
\(940\) | −42.0448 | −1.37135 | ||||||||
\(941\) | 35.8790 | 1.16962 | 0.584811 | − | 0.811170i | \(-0.301169\pi\) | ||||
0.584811 | + | 0.811170i | \(0.301169\pi\) | |||||||
\(942\) | −3.34449 | −0.108969 | ||||||||
\(943\) | 41.9375 | 1.36567 | ||||||||
\(944\) | 5.72057 | 0.186189 | ||||||||
\(945\) | 3.37742 | 0.109867 | ||||||||
\(946\) | −2.21861 | −0.0721333 | ||||||||
\(947\) | −11.3161 | −0.367724 | −0.183862 | − | 0.982952i | \(-0.558860\pi\) | ||||
−0.183862 | + | 0.982952i | \(0.558860\pi\) | |||||||
\(948\) | −10.2835 | −0.333992 | ||||||||
\(949\) | 4.78578 | 0.155353 | ||||||||
\(950\) | 11.9609 | 0.388062 | ||||||||
\(951\) | −10.5734 | −0.342865 | ||||||||
\(952\) | −6.12672 | −0.198568 | ||||||||
\(953\) | −2.13994 | −0.0693195 | −0.0346598 | − | 0.999399i | \(-0.511035\pi\) | ||||
−0.0346598 | + | 0.999399i | \(0.511035\pi\) | |||||||
\(954\) | −1.15879 | −0.0375171 | ||||||||
\(955\) | 25.6013 | 0.828438 | ||||||||
\(956\) | 2.62033 | 0.0847475 | ||||||||
\(957\) | 9.58456 | 0.309825 | ||||||||
\(958\) | −5.53493 | −0.178826 | ||||||||
\(959\) | −3.37417 | −0.108958 | ||||||||
\(960\) | 25.0022 | 0.806941 | ||||||||
\(961\) | 43.9690 | 1.41836 | ||||||||
\(962\) | 2.60865 | 0.0841062 | ||||||||
\(963\) | 16.1333 | 0.519887 | ||||||||
\(964\) | −8.83727 | −0.284629 | ||||||||
\(965\) | 50.1234 | 1.61353 | ||||||||
\(966\) | 1.34990 | 0.0434322 | ||||||||
\(967\) | 28.0975 | 0.903555 | 0.451778 | − | 0.892131i | \(-0.350790\pi\) | ||||
0.451778 | + | 0.892131i | \(0.350790\pi\) | |||||||
\(968\) | −0.912746 | −0.0293368 | ||||||||
\(969\) | 43.5867 | 1.40021 | ||||||||
\(970\) | 16.2967 | 0.523257 | ||||||||
\(971\) | −50.8194 | −1.63087 | −0.815436 | − | 0.578847i | \(-0.803503\pi\) | ||||
−0.815436 | + | 0.578847i | \(0.803503\pi\) | |||||||
\(972\) | 1.94651 | 0.0624343 | ||||||||
\(973\) | −5.56378 | −0.178366 | ||||||||
\(974\) | 5.97251 | 0.191372 | ||||||||
\(975\) | 11.2758 | 0.361113 | ||||||||
\(976\) | 3.68192 | 0.117855 | ||||||||
\(977\) | −27.5896 | −0.882670 | −0.441335 | − | 0.897342i | \(-0.645495\pi\) | ||||
−0.441335 | + | 0.897342i | \(0.645495\pi\) | |||||||
\(978\) | −0.325488 | −0.0104080 | ||||||||
\(979\) | −12.7615 | −0.407860 | ||||||||
\(980\) | 44.5193 | 1.42212 | ||||||||
\(981\) | −15.2826 | −0.487937 | ||||||||
\(982\) | −7.24396 | −0.231164 | ||||||||
\(983\) | 28.6548 | 0.913945 | 0.456973 | − | 0.889481i | \(-0.348934\pi\) | ||||
0.456973 | + | 0.889481i | \(0.348934\pi\) | |||||||
\(984\) | 5.97528 | 0.190485 | ||||||||
\(985\) | −46.8962 | −1.49424 | ||||||||
\(986\) | −16.3312 | −0.520091 | ||||||||
\(987\) | 5.30897 | 0.168986 | ||||||||
\(988\) | 14.8548 | 0.472595 | ||||||||
\(989\) | 61.4524 | 1.95407 | ||||||||
\(990\) | −0.857338 | −0.0272480 | ||||||||
\(991\) | 19.1844 | 0.609412 | 0.304706 | − | 0.952447i | \(-0.401442\pi\) | ||||
0.304706 | + | 0.952447i | \(0.401442\pi\) | |||||||
\(992\) | −23.1791 | −0.735937 | ||||||||
\(993\) | 25.7221 | 0.816265 | ||||||||
\(994\) | 0.106808 | 0.00338775 | ||||||||
\(995\) | 13.4631 | 0.426810 | ||||||||
\(996\) | 14.4750 | 0.458659 | ||||||||
\(997\) | −4.14208 | −0.131181 | −0.0655905 | − | 0.997847i | \(-0.520893\pi\) | ||||
−0.0655905 | + | 0.997847i | \(0.520893\pi\) | |||||||
\(998\) | 5.68737 | 0.180031 | ||||||||
\(999\) | 8.74406 | 0.276650 |
(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 | 2013.2.a.h.1.9 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.6 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.9 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.6 | 14 | 3.2 | odd | 2 |