Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} - 11338 x^{11} - 56744 x^{10} + 50183 x^{9} + 120237 x^{8} - 102992 x^{7} + \cdots + 4222 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.64365\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 | ||||||||
\(3\) | −1.64365 | −0.948964 | −0.474482 | − | 0.880265i | \(-0.657365\pi\) | ||||
−0.474482 | + | 0.880265i | \(0.657365\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.210142 | −0.0939783 | −0.0469891 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469891 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(6\) | 1.64365 | 0.671019 | ||||||||
\(7\) | −4.29873 | −1.62477 | −0.812384 | − | 0.583123i | \(-0.801830\pi\) | ||||
−0.812384 | + | 0.583123i | \(0.801830\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.298402 | −0.0994674 | ||||||||
\(10\) | 0.210142 | 0.0664527 | ||||||||
\(11\) | −5.53220 | −1.66802 | −0.834010 | − | 0.551749i | \(-0.813961\pi\) | ||||
−0.834010 | + | 0.551749i | \(0.813961\pi\) | |||||||
\(12\) | −1.64365 | −0.474482 | ||||||||
\(13\) | 1.08532 | 0.301014 | 0.150507 | − | 0.988609i | \(-0.451909\pi\) | ||||
0.150507 | + | 0.988609i | \(0.451909\pi\) | |||||||
\(14\) | 4.29873 | 1.14888 | ||||||||
\(15\) | 0.345400 | 0.0891820 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.80403 | −0.922612 | −0.461306 | − | 0.887241i | \(-0.652619\pi\) | ||||
−0.461306 | + | 0.887241i | \(0.652619\pi\) | |||||||
\(18\) | 0.298402 | 0.0703341 | ||||||||
\(19\) | −7.09967 | −1.62878 | −0.814388 | − | 0.580321i | \(-0.802927\pi\) | ||||
−0.814388 | + | 0.580321i | \(0.802927\pi\) | |||||||
\(20\) | −0.210142 | −0.0469891 | ||||||||
\(21\) | 7.06562 | 1.54185 | ||||||||
\(22\) | 5.53220 | 1.17947 | ||||||||
\(23\) | 2.95120 | 0.615369 | 0.307684 | − | 0.951489i | \(-0.400446\pi\) | ||||
0.307684 | + | 0.951489i | \(0.400446\pi\) | |||||||
\(24\) | 1.64365 | 0.335509 | ||||||||
\(25\) | −4.95584 | −0.991168 | ||||||||
\(26\) | −1.08532 | −0.212849 | ||||||||
\(27\) | 5.42143 | 1.04335 | ||||||||
\(28\) | −4.29873 | −0.812384 | ||||||||
\(29\) | −3.08121 | −0.572166 | −0.286083 | − | 0.958205i | \(-0.592353\pi\) | ||||
−0.286083 | + | 0.958205i | \(0.592353\pi\) | |||||||
\(30\) | −0.345400 | −0.0630612 | ||||||||
\(31\) | 6.63740 | 1.19211 | 0.596056 | − | 0.802943i | \(-0.296734\pi\) | ||||
0.596056 | + | 0.802943i | \(0.296734\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.09302 | 1.58289 | ||||||||
\(34\) | 3.80403 | 0.652386 | ||||||||
\(35\) | 0.903343 | 0.152693 | ||||||||
\(36\) | −0.298402 | −0.0497337 | ||||||||
\(37\) | 4.14968 | 0.682203 | 0.341101 | − | 0.940026i | \(-0.389200\pi\) | ||||
0.341101 | + | 0.940026i | \(0.389200\pi\) | |||||||
\(38\) | 7.09967 | 1.15172 | ||||||||
\(39\) | −1.78389 | −0.285652 | ||||||||
\(40\) | 0.210142 | 0.0332263 | ||||||||
\(41\) | 2.73766 | 0.427550 | 0.213775 | − | 0.976883i | \(-0.431424\pi\) | ||||
0.213775 | + | 0.976883i | \(0.431424\pi\) | |||||||
\(42\) | −7.06562 | −1.09025 | ||||||||
\(43\) | −11.9305 | −1.81938 | −0.909691 | − | 0.415286i | \(-0.863681\pi\) | ||||
−0.909691 | + | 0.415286i | \(0.863681\pi\) | |||||||
\(44\) | −5.53220 | −0.834010 | ||||||||
\(45\) | 0.0627068 | 0.00934778 | ||||||||
\(46\) | −2.95120 | −0.435131 | ||||||||
\(47\) | −6.80185 | −0.992151 | −0.496076 | − | 0.868279i | \(-0.665226\pi\) | ||||
−0.496076 | + | 0.868279i | \(0.665226\pi\) | |||||||
\(48\) | −1.64365 | −0.237241 | ||||||||
\(49\) | 11.4791 | 1.63987 | ||||||||
\(50\) | 4.95584 | 0.700862 | ||||||||
\(51\) | 6.25251 | 0.875526 | ||||||||
\(52\) | 1.08532 | 0.150507 | ||||||||
\(53\) | 3.05280 | 0.419334 | 0.209667 | − | 0.977773i | \(-0.432762\pi\) | ||||
0.209667 | + | 0.977773i | \(0.432762\pi\) | |||||||
\(54\) | −5.42143 | −0.737763 | ||||||||
\(55\) | 1.16255 | 0.156758 | ||||||||
\(56\) | 4.29873 | 0.574442 | ||||||||
\(57\) | 11.6694 | 1.54565 | ||||||||
\(58\) | 3.08121 | 0.404582 | ||||||||
\(59\) | −9.49532 | −1.23619 | −0.618093 | − | 0.786105i | \(-0.712094\pi\) | ||||
−0.618093 | + | 0.786105i | \(0.712094\pi\) | |||||||
\(60\) | 0.345400 | 0.0445910 | ||||||||
\(61\) | −2.70135 | −0.345872 | −0.172936 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172936 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(62\) | −6.63740 | −0.842951 | ||||||||
\(63\) | 1.28275 | 0.161611 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.228072 | −0.0282888 | ||||||||
\(66\) | −9.09302 | −1.11927 | ||||||||
\(67\) | 15.7797 | 1.92780 | 0.963898 | − | 0.266273i | \(-0.0857923\pi\) | ||||
0.963898 | + | 0.266273i | \(0.0857923\pi\) | |||||||
\(68\) | −3.80403 | −0.461306 | ||||||||
\(69\) | −4.85076 | −0.583963 | ||||||||
\(70\) | −0.903343 | −0.107970 | ||||||||
\(71\) | −5.51340 | −0.654320 | −0.327160 | − | 0.944969i | \(-0.606092\pi\) | ||||
−0.327160 | + | 0.944969i | \(0.606092\pi\) | |||||||
\(72\) | 0.298402 | 0.0351671 | ||||||||
\(73\) | 3.31672 | 0.388193 | 0.194096 | − | 0.980982i | \(-0.437823\pi\) | ||||
0.194096 | + | 0.980982i | \(0.437823\pi\) | |||||||
\(74\) | −4.14968 | −0.482390 | ||||||||
\(75\) | 8.14569 | 0.940583 | ||||||||
\(76\) | −7.09967 | −0.814388 | ||||||||
\(77\) | 23.7814 | 2.71015 | ||||||||
\(78\) | 1.78389 | 0.201986 | ||||||||
\(79\) | −7.06174 | −0.794508 | −0.397254 | − | 0.917709i | \(-0.630037\pi\) | ||||
−0.397254 | + | 0.917709i | \(0.630037\pi\) | |||||||
\(80\) | −0.210142 | −0.0234946 | ||||||||
\(81\) | −8.01575 | −0.890639 | ||||||||
\(82\) | −2.73766 | −0.302324 | ||||||||
\(83\) | 4.61960 | 0.507067 | 0.253534 | − | 0.967327i | \(-0.418407\pi\) | ||||
0.253534 | + | 0.967327i | \(0.418407\pi\) | |||||||
\(84\) | 7.06562 | 0.770923 | ||||||||
\(85\) | 0.799386 | 0.0867055 | ||||||||
\(86\) | 11.9305 | 1.28650 | ||||||||
\(87\) | 5.06444 | 0.542965 | ||||||||
\(88\) | 5.53220 | 0.589734 | ||||||||
\(89\) | −11.7469 | −1.24517 | −0.622583 | − | 0.782554i | \(-0.713917\pi\) | ||||
−0.622583 | + | 0.782554i | \(0.713917\pi\) | |||||||
\(90\) | −0.0627068 | −0.00660988 | ||||||||
\(91\) | −4.66551 | −0.489078 | ||||||||
\(92\) | 2.95120 | 0.307684 | ||||||||
\(93\) | −10.9096 | −1.13127 | ||||||||
\(94\) | 6.80185 | 0.701557 | ||||||||
\(95\) | 1.49194 | 0.153070 | ||||||||
\(96\) | 1.64365 | 0.167755 | ||||||||
\(97\) | −0.942349 | −0.0956810 | −0.0478405 | − | 0.998855i | \(-0.515234\pi\) | ||||
−0.0478405 | + | 0.998855i | \(0.515234\pi\) | |||||||
\(98\) | −11.4791 | −1.15956 | ||||||||
\(99\) | 1.65082 | 0.165914 | ||||||||
\(100\) | −4.95584 | −0.495584 | ||||||||
\(101\) | 15.8815 | 1.58027 | 0.790134 | − | 0.612935i | \(-0.210011\pi\) | ||||
0.790134 | + | 0.612935i | \(0.210011\pi\) | |||||||
\(102\) | −6.25251 | −0.619090 | ||||||||
\(103\) | −0.796754 | −0.0785065 | −0.0392532 | − | 0.999229i | \(-0.512498\pi\) | ||||
−0.0392532 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(104\) | −1.08532 | −0.106425 | ||||||||
\(105\) | −1.48478 | −0.144900 | ||||||||
\(106\) | −3.05280 | −0.296514 | ||||||||
\(107\) | −14.3543 | −1.38768 | −0.693842 | − | 0.720127i | \(-0.744083\pi\) | ||||
−0.693842 | + | 0.720127i | \(0.744083\pi\) | |||||||
\(108\) | 5.42143 | 0.521677 | ||||||||
\(109\) | 6.51756 | 0.624269 | 0.312134 | − | 0.950038i | \(-0.398956\pi\) | ||||
0.312134 | + | 0.950038i | \(0.398956\pi\) | |||||||
\(110\) | −1.16255 | −0.110844 | ||||||||
\(111\) | −6.82064 | −0.647386 | ||||||||
\(112\) | −4.29873 | −0.406192 | ||||||||
\(113\) | 1.99662 | 0.187826 | 0.0939129 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939129 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(114\) | −11.6694 | −1.09294 | ||||||||
\(115\) | −0.620171 | −0.0578313 | ||||||||
\(116\) | −3.08121 | −0.286083 | ||||||||
\(117\) | −0.323863 | −0.0299411 | ||||||||
\(118\) | 9.49532 | 0.874115 | ||||||||
\(119\) | 16.3525 | 1.49903 | ||||||||
\(120\) | −0.345400 | −0.0315306 | ||||||||
\(121\) | 19.6052 | 1.78229 | ||||||||
\(122\) | 2.70135 | 0.244568 | ||||||||
\(123\) | −4.49976 | −0.405730 | ||||||||
\(124\) | 6.63740 | 0.596056 | ||||||||
\(125\) | 2.09214 | 0.187127 | ||||||||
\(126\) | −1.28275 | −0.114277 | ||||||||
\(127\) | 10.8564 | 0.963348 | 0.481674 | − | 0.876350i | \(-0.340029\pi\) | ||||
0.481674 | + | 0.876350i | \(0.340029\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 19.6096 | 1.72653 | ||||||||
\(130\) | 0.228072 | 0.0200032 | ||||||||
\(131\) | −16.4182 | −1.43446 | −0.717232 | − | 0.696834i | \(-0.754591\pi\) | ||||
−0.717232 | + | 0.696834i | \(0.754591\pi\) | |||||||
\(132\) | 9.09302 | 0.791446 | ||||||||
\(133\) | 30.5196 | 2.64638 | ||||||||
\(134\) | −15.7797 | −1.36316 | ||||||||
\(135\) | −1.13927 | −0.0980527 | ||||||||
\(136\) | 3.80403 | 0.326193 | ||||||||
\(137\) | 22.5222 | 1.92420 | 0.962100 | − | 0.272697i | \(-0.0879155\pi\) | ||||
0.962100 | + | 0.272697i | \(0.0879155\pi\) | |||||||
\(138\) | 4.85076 | 0.412924 | ||||||||
\(139\) | −12.3368 | −1.04639 | −0.523197 | − | 0.852212i | \(-0.675261\pi\) | ||||
−0.523197 | + | 0.852212i | \(0.675261\pi\) | |||||||
\(140\) | 0.903343 | 0.0763464 | ||||||||
\(141\) | 11.1799 | 0.941516 | ||||||||
\(142\) | 5.51340 | 0.462674 | ||||||||
\(143\) | −6.00422 | −0.502098 | ||||||||
\(144\) | −0.298402 | −0.0248669 | ||||||||
\(145\) | 0.647491 | 0.0537712 | ||||||||
\(146\) | −3.31672 | −0.274494 | ||||||||
\(147\) | −18.8676 | −1.55618 | ||||||||
\(148\) | 4.14968 | 0.341101 | ||||||||
\(149\) | 3.36969 | 0.276056 | 0.138028 | − | 0.990428i | \(-0.455924\pi\) | ||||
0.138028 | + | 0.990428i | \(0.455924\pi\) | |||||||
\(150\) | −8.14569 | −0.665092 | ||||||||
\(151\) | 19.6668 | 1.60046 | 0.800230 | − | 0.599694i | \(-0.204711\pi\) | ||||
0.800230 | + | 0.599694i | \(0.204711\pi\) | |||||||
\(152\) | 7.09967 | 0.575859 | ||||||||
\(153\) | 1.13513 | 0.0917699 | ||||||||
\(154\) | −23.7814 | −1.91636 | ||||||||
\(155\) | −1.39480 | −0.112033 | ||||||||
\(156\) | −1.78389 | −0.142826 | ||||||||
\(157\) | 22.7381 | 1.81470 | 0.907349 | − | 0.420378i | \(-0.138102\pi\) | ||||
0.907349 | + | 0.420378i | \(0.138102\pi\) | |||||||
\(158\) | 7.06174 | 0.561802 | ||||||||
\(159\) | −5.01774 | −0.397933 | ||||||||
\(160\) | 0.210142 | 0.0166132 | ||||||||
\(161\) | −12.6864 | −0.999831 | ||||||||
\(162\) | 8.01575 | 0.629777 | ||||||||
\(163\) | −0.524356 | −0.0410708 | −0.0205354 | − | 0.999789i | \(-0.506537\pi\) | ||||
−0.0205354 | + | 0.999789i | \(0.506537\pi\) | |||||||
\(164\) | 2.73766 | 0.213775 | ||||||||
\(165\) | −1.91082 | −0.148757 | ||||||||
\(166\) | −4.61960 | −0.358551 | ||||||||
\(167\) | 7.09344 | 0.548907 | 0.274453 | − | 0.961600i | \(-0.411503\pi\) | ||||
0.274453 | + | 0.961600i | \(0.411503\pi\) | |||||||
\(168\) | −7.06562 | −0.545125 | ||||||||
\(169\) | −11.8221 | −0.909391 | ||||||||
\(170\) | −0.799386 | −0.0613101 | ||||||||
\(171\) | 2.11856 | 0.162010 | ||||||||
\(172\) | −11.9305 | −0.909691 | ||||||||
\(173\) | −20.1340 | −1.53076 | −0.765381 | − | 0.643577i | \(-0.777450\pi\) | ||||
−0.765381 | + | 0.643577i | \(0.777450\pi\) | |||||||
\(174\) | −5.06444 | −0.383934 | ||||||||
\(175\) | 21.3038 | 1.61042 | ||||||||
\(176\) | −5.53220 | −0.417005 | ||||||||
\(177\) | 15.6070 | 1.17310 | ||||||||
\(178\) | 11.7469 | 0.880465 | ||||||||
\(179\) | −13.3020 | −0.994242 | −0.497121 | − | 0.867681i | \(-0.665609\pi\) | ||||
−0.497121 | + | 0.867681i | \(0.665609\pi\) | |||||||
\(180\) | 0.0627068 | 0.00467389 | ||||||||
\(181\) | −18.2102 | −1.35355 | −0.676776 | − | 0.736189i | \(-0.736623\pi\) | ||||
−0.676776 | + | 0.736189i | \(0.736623\pi\) | |||||||
\(182\) | 4.66551 | 0.345830 | ||||||||
\(183\) | 4.44008 | 0.328220 | ||||||||
\(184\) | −2.95120 | −0.217566 | ||||||||
\(185\) | −0.872021 | −0.0641123 | ||||||||
\(186\) | 10.9096 | 0.799930 | ||||||||
\(187\) | 21.0446 | 1.53894 | ||||||||
\(188\) | −6.80185 | −0.496076 | ||||||||
\(189\) | −23.3053 | −1.69521 | ||||||||
\(190\) | −1.49194 | −0.108237 | ||||||||
\(191\) | 15.2620 | 1.10432 | 0.552158 | − | 0.833739i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833739i | \(0.313805\pi\) | |||||||
\(192\) | −1.64365 | −0.118620 | ||||||||
\(193\) | −9.87710 | −0.710969 | −0.355485 | − | 0.934682i | \(-0.615684\pi\) | ||||
−0.355485 | + | 0.934682i | \(0.615684\pi\) | |||||||
\(194\) | 0.942349 | 0.0676567 | ||||||||
\(195\) | 0.374871 | 0.0268450 | ||||||||
\(196\) | 11.4791 | 0.819935 | ||||||||
\(197\) | 17.9712 | 1.28039 | 0.640197 | − | 0.768210i | \(-0.278853\pi\) | ||||
0.640197 | + | 0.768210i | \(0.278853\pi\) | |||||||
\(198\) | −1.65082 | −0.117319 | ||||||||
\(199\) | 22.5180 | 1.59626 | 0.798129 | − | 0.602486i | \(-0.205823\pi\) | ||||
0.798129 | + | 0.602486i | \(0.205823\pi\) | |||||||
\(200\) | 4.95584 | 0.350431 | ||||||||
\(201\) | −25.9363 | −1.82941 | ||||||||
\(202\) | −15.8815 | −1.11742 | ||||||||
\(203\) | 13.2453 | 0.929637 | ||||||||
\(204\) | 6.25251 | 0.437763 | ||||||||
\(205\) | −0.575296 | −0.0401804 | ||||||||
\(206\) | 0.796754 | 0.0555125 | ||||||||
\(207\) | −0.880646 | −0.0612091 | ||||||||
\(208\) | 1.08532 | 0.0752535 | ||||||||
\(209\) | 39.2768 | 2.71683 | ||||||||
\(210\) | 1.48478 | 0.102460 | ||||||||
\(211\) | 7.71129 | 0.530867 | 0.265433 | − | 0.964129i | \(-0.414485\pi\) | ||||
0.265433 | + | 0.964129i | \(0.414485\pi\) | |||||||
\(212\) | 3.05280 | 0.209667 | ||||||||
\(213\) | 9.06212 | 0.620926 | ||||||||
\(214\) | 14.3543 | 0.981241 | ||||||||
\(215\) | 2.50709 | 0.170982 | ||||||||
\(216\) | −5.42143 | −0.368882 | ||||||||
\(217\) | −28.5324 | −1.93691 | ||||||||
\(218\) | −6.51756 | −0.441425 | ||||||||
\(219\) | −5.45154 | −0.368381 | ||||||||
\(220\) | 1.16255 | 0.0783789 | ||||||||
\(221\) | −4.12860 | −0.277719 | ||||||||
\(222\) | 6.82064 | 0.457771 | ||||||||
\(223\) | 7.65080 | 0.512335 | 0.256168 | − | 0.966632i | \(-0.417540\pi\) | ||||
0.256168 | + | 0.966632i | \(0.417540\pi\) | |||||||
\(224\) | 4.29873 | 0.287221 | ||||||||
\(225\) | 1.47883 | 0.0985890 | ||||||||
\(226\) | −1.99662 | −0.132813 | ||||||||
\(227\) | −13.2776 | −0.881266 | −0.440633 | − | 0.897687i | \(-0.645246\pi\) | ||||
−0.440633 | + | 0.897687i | \(0.645246\pi\) | |||||||
\(228\) | 11.6694 | 0.772825 | ||||||||
\(229\) | −6.61574 | −0.437180 | −0.218590 | − | 0.975817i | \(-0.570146\pi\) | ||||
−0.218590 | + | 0.975817i | \(0.570146\pi\) | |||||||
\(230\) | 0.620171 | 0.0408929 | ||||||||
\(231\) | −39.0884 | −2.57183 | ||||||||
\(232\) | 3.08121 | 0.202291 | ||||||||
\(233\) | −17.6112 | −1.15375 | −0.576873 | − | 0.816834i | \(-0.695727\pi\) | ||||
−0.576873 | + | 0.816834i | \(0.695727\pi\) | |||||||
\(234\) | 0.323863 | 0.0211716 | ||||||||
\(235\) | 1.42935 | 0.0932407 | ||||||||
\(236\) | −9.49532 | −0.618093 | ||||||||
\(237\) | 11.6071 | 0.753960 | ||||||||
\(238\) | −16.3525 | −1.05997 | ||||||||
\(239\) | 4.20632 | 0.272084 | 0.136042 | − | 0.990703i | \(-0.456562\pi\) | ||||
0.136042 | + | 0.990703i | \(0.456562\pi\) | |||||||
\(240\) | 0.345400 | 0.0222955 | ||||||||
\(241\) | −24.0169 | −1.54706 | −0.773531 | − | 0.633759i | \(-0.781511\pi\) | ||||
−0.773531 | + | 0.633759i | \(0.781511\pi\) | |||||||
\(242\) | −19.6052 | −1.26027 | ||||||||
\(243\) | −3.08918 | −0.198171 | ||||||||
\(244\) | −2.70135 | −0.172936 | ||||||||
\(245\) | −2.41224 | −0.154112 | ||||||||
\(246\) | 4.49976 | 0.286894 | ||||||||
\(247\) | −7.70543 | −0.490284 | ||||||||
\(248\) | −6.63740 | −0.421475 | ||||||||
\(249\) | −7.59303 | −0.481189 | ||||||||
\(250\) | −2.09214 | −0.132318 | ||||||||
\(251\) | −15.5276 | −0.980092 | −0.490046 | − | 0.871697i | \(-0.663020\pi\) | ||||
−0.490046 | + | 0.871697i | \(0.663020\pi\) | |||||||
\(252\) | 1.28275 | 0.0808057 | ||||||||
\(253\) | −16.3266 | −1.02645 | ||||||||
\(254\) | −10.8564 | −0.681190 | ||||||||
\(255\) | −1.31391 | −0.0822804 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.67507 | −0.354001 | −0.177001 | − | 0.984211i | \(-0.556639\pi\) | ||||
−0.177001 | + | 0.984211i | \(0.556639\pi\) | |||||||
\(258\) | −19.6096 | −1.22084 | ||||||||
\(259\) | −17.8384 | −1.10842 | ||||||||
\(260\) | −0.228072 | −0.0141444 | ||||||||
\(261\) | 0.919440 | 0.0569119 | ||||||||
\(262\) | 16.4182 | 1.01432 | ||||||||
\(263\) | −23.2605 | −1.43430 | −0.717151 | − | 0.696917i | \(-0.754554\pi\) | ||||
−0.717151 | + | 0.696917i | \(0.754554\pi\) | |||||||
\(264\) | −9.09302 | −0.559637 | ||||||||
\(265\) | −0.641520 | −0.0394083 | ||||||||
\(266\) | −30.5196 | −1.87127 | ||||||||
\(267\) | 19.3078 | 1.18162 | ||||||||
\(268\) | 15.7797 | 0.963898 | ||||||||
\(269\) | −3.18536 | −0.194215 | −0.0971074 | − | 0.995274i | \(-0.530959\pi\) | ||||
−0.0971074 | + | 0.995274i | \(0.530959\pi\) | |||||||
\(270\) | 1.13927 | 0.0693337 | ||||||||
\(271\) | −25.4698 | −1.54718 | −0.773589 | − | 0.633687i | \(-0.781541\pi\) | ||||
−0.773589 | + | 0.633687i | \(0.781541\pi\) | |||||||
\(272\) | −3.80403 | −0.230653 | ||||||||
\(273\) | 7.66848 | 0.464117 | ||||||||
\(274\) | −22.5222 | −1.36061 | ||||||||
\(275\) | 27.4167 | 1.65329 | ||||||||
\(276\) | −4.85076 | −0.291981 | ||||||||
\(277\) | 16.5221 | 0.992719 | 0.496359 | − | 0.868117i | \(-0.334670\pi\) | ||||
0.496359 | + | 0.868117i | \(0.334670\pi\) | |||||||
\(278\) | 12.3368 | 0.739912 | ||||||||
\(279\) | −1.98062 | −0.118576 | ||||||||
\(280\) | −0.903343 | −0.0539851 | ||||||||
\(281\) | −26.9021 | −1.60485 | −0.802424 | − | 0.596755i | \(-0.796457\pi\) | ||||
−0.802424 | + | 0.596755i | \(0.796457\pi\) | |||||||
\(282\) | −11.1799 | −0.665752 | ||||||||
\(283\) | −6.89172 | −0.409670 | −0.204835 | − | 0.978796i | \(-0.565666\pi\) | ||||
−0.204835 | + | 0.978796i | \(0.565666\pi\) | |||||||
\(284\) | −5.51340 | −0.327160 | ||||||||
\(285\) | −2.45223 | −0.145257 | ||||||||
\(286\) | 6.00422 | 0.355037 | ||||||||
\(287\) | −11.7684 | −0.694669 | ||||||||
\(288\) | 0.298402 | 0.0175835 | ||||||||
\(289\) | −2.52937 | −0.148786 | ||||||||
\(290\) | −0.647491 | −0.0380220 | ||||||||
\(291\) | 1.54889 | 0.0907978 | ||||||||
\(292\) | 3.31672 | 0.194096 | ||||||||
\(293\) | 16.9443 | 0.989895 | 0.494948 | − | 0.868923i | \(-0.335187\pi\) | ||||
0.494948 | + | 0.868923i | \(0.335187\pi\) | |||||||
\(294\) | 18.8676 | 1.10038 | ||||||||
\(295\) | 1.99536 | 0.116175 | ||||||||
\(296\) | −4.14968 | −0.241195 | ||||||||
\(297\) | −29.9924 | −1.74034 | ||||||||
\(298\) | −3.36969 | −0.195201 | ||||||||
\(299\) | 3.20301 | 0.185235 | ||||||||
\(300\) | 8.14569 | 0.470291 | ||||||||
\(301\) | 51.2859 | 2.95607 | ||||||||
\(302\) | −19.6668 | −1.13170 | ||||||||
\(303\) | −26.1037 | −1.49962 | ||||||||
\(304\) | −7.09967 | −0.407194 | ||||||||
\(305\) | 0.567666 | 0.0325045 | ||||||||
\(306\) | −1.13513 | −0.0648911 | ||||||||
\(307\) | 26.7963 | 1.52934 | 0.764672 | − | 0.644420i | \(-0.222901\pi\) | ||||
0.764672 | + | 0.644420i | \(0.222901\pi\) | |||||||
\(308\) | 23.7814 | 1.35507 | ||||||||
\(309\) | 1.30959 | 0.0744998 | ||||||||
\(310\) | 1.39480 | 0.0792191 | ||||||||
\(311\) | 10.1369 | 0.574810 | 0.287405 | − | 0.957809i | \(-0.407207\pi\) | ||||
0.287405 | + | 0.957809i | \(0.407207\pi\) | |||||||
\(312\) | 1.78389 | 0.100993 | ||||||||
\(313\) | 7.82461 | 0.442273 | 0.221136 | − | 0.975243i | \(-0.429023\pi\) | ||||
0.221136 | + | 0.975243i | \(0.429023\pi\) | |||||||
\(314\) | −22.7381 | −1.28319 | ||||||||
\(315\) | −0.269560 | −0.0151880 | ||||||||
\(316\) | −7.06174 | −0.397254 | ||||||||
\(317\) | −29.0296 | −1.63046 | −0.815231 | − | 0.579136i | \(-0.803390\pi\) | ||||
−0.815231 | + | 0.579136i | \(0.803390\pi\) | |||||||
\(318\) | 5.01774 | 0.281381 | ||||||||
\(319\) | 17.0459 | 0.954385 | ||||||||
\(320\) | −0.210142 | −0.0117473 | ||||||||
\(321\) | 23.5935 | 1.31686 | ||||||||
\(322\) | 12.6864 | 0.706987 | ||||||||
\(323\) | 27.0073 | 1.50273 | ||||||||
\(324\) | −8.01575 | −0.445319 | ||||||||
\(325\) | −5.37868 | −0.298356 | ||||||||
\(326\) | 0.524356 | 0.0290414 | ||||||||
\(327\) | −10.7126 | −0.592409 | ||||||||
\(328\) | −2.73766 | −0.151162 | ||||||||
\(329\) | 29.2393 | 1.61202 | ||||||||
\(330\) | 1.91082 | 0.105187 | ||||||||
\(331\) | −14.7746 | −0.812087 | −0.406044 | − | 0.913854i | \(-0.633092\pi\) | ||||
−0.406044 | + | 0.913854i | \(0.633092\pi\) | |||||||
\(332\) | 4.61960 | 0.253534 | ||||||||
\(333\) | −1.23827 | −0.0678570 | ||||||||
\(334\) | −7.09344 | −0.388136 | ||||||||
\(335\) | −3.31597 | −0.181171 | ||||||||
\(336\) | 7.06562 | 0.385461 | ||||||||
\(337\) | −8.26719 | −0.450342 | −0.225171 | − | 0.974319i | \(-0.572294\pi\) | ||||
−0.225171 | + | 0.974319i | \(0.572294\pi\) | |||||||
\(338\) | 11.8221 | 0.643036 | ||||||||
\(339\) | −3.28175 | −0.178240 | ||||||||
\(340\) | 0.799386 | 0.0433528 | ||||||||
\(341\) | −36.7194 | −1.98847 | ||||||||
\(342\) | −2.11856 | −0.114558 | ||||||||
\(343\) | −19.2544 | −1.03964 | ||||||||
\(344\) | 11.9305 | 0.643248 | ||||||||
\(345\) | 1.01935 | 0.0548798 | ||||||||
\(346\) | 20.1340 | 1.08241 | ||||||||
\(347\) | −10.9550 | −0.588095 | −0.294048 | − | 0.955791i | \(-0.595002\pi\) | ||||
−0.294048 | + | 0.955791i | \(0.595002\pi\) | |||||||
\(348\) | 5.06444 | 0.271482 | ||||||||
\(349\) | −7.67321 | −0.410737 | −0.205369 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205369 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(350\) | −21.3038 | −1.13874 | ||||||||
\(351\) | 5.88400 | 0.314065 | ||||||||
\(352\) | 5.53220 | 0.294867 | ||||||||
\(353\) | −18.3730 | −0.977895 | −0.488947 | − | 0.872313i | \(-0.662619\pi\) | ||||
−0.488947 | + | 0.872313i | \(0.662619\pi\) | |||||||
\(354\) | −15.6070 | −0.829504 | ||||||||
\(355\) | 1.15860 | 0.0614919 | ||||||||
\(356\) | −11.7469 | −0.622583 | ||||||||
\(357\) | −26.8778 | −1.42253 | ||||||||
\(358\) | 13.3020 | 0.703035 | ||||||||
\(359\) | −19.6442 | −1.03678 | −0.518391 | − | 0.855144i | \(-0.673469\pi\) | ||||
−0.518391 | + | 0.855144i | \(0.673469\pi\) | |||||||
\(360\) | −0.0627068 | −0.00330494 | ||||||||
\(361\) | 31.4053 | 1.65291 | ||||||||
\(362\) | 18.2102 | 0.957105 | ||||||||
\(363\) | −32.2242 | −1.69133 | ||||||||
\(364\) | −4.66551 | −0.244539 | ||||||||
\(365\) | −0.696982 | −0.0364817 | ||||||||
\(366\) | −4.44008 | −0.232087 | ||||||||
\(367\) | 21.5291 | 1.12381 | 0.561904 | − | 0.827203i | \(-0.310069\pi\) | ||||
0.561904 | + | 0.827203i | \(0.310069\pi\) | |||||||
\(368\) | 2.95120 | 0.153842 | ||||||||
\(369\) | −0.816923 | −0.0425273 | ||||||||
\(370\) | 0.872021 | 0.0453342 | ||||||||
\(371\) | −13.1231 | −0.681320 | ||||||||
\(372\) | −10.9096 | −0.565636 | ||||||||
\(373\) | −14.6387 | −0.757963 | −0.378981 | − | 0.925404i | \(-0.623726\pi\) | ||||
−0.378981 | + | 0.925404i | \(0.623726\pi\) | |||||||
\(374\) | −21.0446 | −1.08819 | ||||||||
\(375\) | −3.43875 | −0.177576 | ||||||||
\(376\) | 6.80185 | 0.350778 | ||||||||
\(377\) | −3.34410 | −0.172230 | ||||||||
\(378\) | 23.3053 | 1.19869 | ||||||||
\(379\) | −2.19800 | −0.112904 | −0.0564519 | − | 0.998405i | \(-0.517979\pi\) | ||||
−0.0564519 | + | 0.998405i | \(0.517979\pi\) | |||||||
\(380\) | 1.49194 | 0.0765348 | ||||||||
\(381\) | −17.8441 | −0.914183 | ||||||||
\(382\) | −15.2620 | −0.780869 | ||||||||
\(383\) | −19.2884 | −0.985590 | −0.492795 | − | 0.870145i | \(-0.664025\pi\) | ||||
−0.492795 | + | 0.870145i | \(0.664025\pi\) | |||||||
\(384\) | 1.64365 | 0.0838774 | ||||||||
\(385\) | −4.99747 | −0.254695 | ||||||||
\(386\) | 9.87710 | 0.502731 | ||||||||
\(387\) | 3.56008 | 0.180969 | ||||||||
\(388\) | −0.942349 | −0.0478405 | ||||||||
\(389\) | −22.3365 | −1.13251 | −0.566253 | − | 0.824232i | \(-0.691607\pi\) | ||||
−0.566253 | + | 0.824232i | \(0.691607\pi\) | |||||||
\(390\) | −0.374871 | −0.0189823 | ||||||||
\(391\) | −11.2265 | −0.567747 | ||||||||
\(392\) | −11.4791 | −0.579781 | ||||||||
\(393\) | 26.9858 | 1.36126 | ||||||||
\(394\) | −17.9712 | −0.905376 | ||||||||
\(395\) | 1.48397 | 0.0746665 | ||||||||
\(396\) | 1.65082 | 0.0829569 | ||||||||
\(397\) | 33.8282 | 1.69779 | 0.848895 | − | 0.528562i | \(-0.177268\pi\) | ||||
0.848895 | + | 0.528562i | \(0.177268\pi\) | |||||||
\(398\) | −22.5180 | −1.12873 | ||||||||
\(399\) | −50.1636 | −2.51132 | ||||||||
\(400\) | −4.95584 | −0.247792 | ||||||||
\(401\) | 26.8410 | 1.34038 | 0.670188 | − | 0.742192i | \(-0.266214\pi\) | ||||
0.670188 | + | 0.742192i | \(0.266214\pi\) | |||||||
\(402\) | 25.9363 | 1.29359 | ||||||||
\(403\) | 7.20372 | 0.358843 | ||||||||
\(404\) | 15.8815 | 0.790134 | ||||||||
\(405\) | 1.68444 | 0.0837007 | ||||||||
\(406\) | −13.2453 | −0.657352 | ||||||||
\(407\) | −22.9568 | −1.13793 | ||||||||
\(408\) | −6.25251 | −0.309545 | ||||||||
\(409\) | −15.4994 | −0.766397 | −0.383199 | − | 0.923666i | \(-0.625178\pi\) | ||||
−0.383199 | + | 0.923666i | \(0.625178\pi\) | |||||||
\(410\) | 0.575296 | 0.0284119 | ||||||||
\(411\) | −37.0187 | −1.82600 | ||||||||
\(412\) | −0.796754 | −0.0392532 | ||||||||
\(413\) | 40.8178 | 2.00851 | ||||||||
\(414\) | 0.880646 | 0.0432814 | ||||||||
\(415\) | −0.970772 | −0.0476533 | ||||||||
\(416\) | −1.08532 | −0.0532123 | ||||||||
\(417\) | 20.2774 | 0.992990 | ||||||||
\(418\) | −39.2768 | −1.92109 | ||||||||
\(419\) | 10.4030 | 0.508218 | 0.254109 | − | 0.967176i | \(-0.418218\pi\) | ||||
0.254109 | + | 0.967176i | \(0.418218\pi\) | |||||||
\(420\) | −1.48478 | −0.0724500 | ||||||||
\(421\) | −9.76094 | −0.475719 | −0.237860 | − | 0.971300i | \(-0.576446\pi\) | ||||
−0.237860 | + | 0.971300i | \(0.576446\pi\) | |||||||
\(422\) | −7.71129 | −0.375380 | ||||||||
\(423\) | 2.02969 | 0.0986868 | ||||||||
\(424\) | −3.05280 | −0.148257 | ||||||||
\(425\) | 18.8522 | 0.914464 | ||||||||
\(426\) | −9.06212 | −0.439061 | ||||||||
\(427\) | 11.6124 | 0.561962 | ||||||||
\(428\) | −14.3543 | −0.693842 | ||||||||
\(429\) | 9.86885 | 0.476473 | ||||||||
\(430\) | −2.50709 | −0.120903 | ||||||||
\(431\) | −9.18053 | −0.442210 | −0.221105 | − | 0.975250i | \(-0.570966\pi\) | ||||
−0.221105 | + | 0.975250i | \(0.570966\pi\) | |||||||
\(432\) | 5.42143 | 0.260839 | ||||||||
\(433\) | 26.8684 | 1.29121 | 0.645607 | − | 0.763670i | \(-0.276604\pi\) | ||||
0.645607 | + | 0.763670i | \(0.276604\pi\) | |||||||
\(434\) | 28.5324 | 1.36960 | ||||||||
\(435\) | −1.06425 | −0.0510269 | ||||||||
\(436\) | 6.51756 | 0.312134 | ||||||||
\(437\) | −20.9526 | −1.00230 | ||||||||
\(438\) | 5.45154 | 0.260485 | ||||||||
\(439\) | 21.0844 | 1.00630 | 0.503152 | − | 0.864198i | \(-0.332174\pi\) | ||||
0.503152 | + | 0.864198i | \(0.332174\pi\) | |||||||
\(440\) | −1.16255 | −0.0554222 | ||||||||
\(441\) | −3.42539 | −0.163114 | ||||||||
\(442\) | 4.12860 | 0.196377 | ||||||||
\(443\) | −37.0110 | −1.75845 | −0.879223 | − | 0.476410i | \(-0.841938\pi\) | ||||
−0.879223 | + | 0.476410i | \(0.841938\pi\) | |||||||
\(444\) | −6.82064 | −0.323693 | ||||||||
\(445\) | 2.46851 | 0.117019 | ||||||||
\(446\) | −7.65080 | −0.362276 | ||||||||
\(447\) | −5.53860 | −0.261967 | ||||||||
\(448\) | −4.29873 | −0.203096 | ||||||||
\(449\) | −0.401494 | −0.0189477 | −0.00947384 | − | 0.999955i | \(-0.503016\pi\) | ||||
−0.00947384 | + | 0.999955i | \(0.503016\pi\) | |||||||
\(450\) | −1.47883 | −0.0697129 | ||||||||
\(451\) | −15.1453 | −0.713162 | ||||||||
\(452\) | 1.99662 | 0.0939129 | ||||||||
\(453\) | −32.3254 | −1.51878 | ||||||||
\(454\) | 13.2776 | 0.623149 | ||||||||
\(455\) | 0.980418 | 0.0459627 | ||||||||
\(456\) | −11.6694 | −0.546470 | ||||||||
\(457\) | −15.4830 | −0.724265 | −0.362133 | − | 0.932127i | \(-0.617951\pi\) | ||||
−0.362133 | + | 0.932127i | \(0.617951\pi\) | |||||||
\(458\) | 6.61574 | 0.309133 | ||||||||
\(459\) | −20.6233 | −0.962612 | ||||||||
\(460\) | −0.620171 | −0.0289156 | ||||||||
\(461\) | 13.4457 | 0.626229 | 0.313115 | − | 0.949715i | \(-0.398628\pi\) | ||||
0.313115 | + | 0.949715i | \(0.398628\pi\) | |||||||
\(462\) | 39.0884 | 1.81856 | ||||||||
\(463\) | 37.6315 | 1.74888 | 0.874442 | − | 0.485130i | \(-0.161228\pi\) | ||||
0.874442 | + | 0.485130i | \(0.161228\pi\) | |||||||
\(464\) | −3.08121 | −0.143041 | ||||||||
\(465\) | 2.29256 | 0.106315 | ||||||||
\(466\) | 17.6112 | 0.815821 | ||||||||
\(467\) | 30.1127 | 1.39345 | 0.696725 | − | 0.717338i | \(-0.254640\pi\) | ||||
0.696725 | + | 0.717338i | \(0.254640\pi\) | |||||||
\(468\) | −0.323863 | −0.0149706 | ||||||||
\(469\) | −67.8326 | −3.13222 | ||||||||
\(470\) | −1.42935 | −0.0659311 | ||||||||
\(471\) | −37.3736 | −1.72208 | ||||||||
\(472\) | 9.49532 | 0.437058 | ||||||||
\(473\) | 66.0018 | 3.03477 | ||||||||
\(474\) | −11.6071 | −0.533130 | ||||||||
\(475\) | 35.1848 | 1.61439 | ||||||||
\(476\) | 16.3525 | 0.749515 | ||||||||
\(477\) | −0.910961 | −0.0417100 | ||||||||
\(478\) | −4.20632 | −0.192393 | ||||||||
\(479\) | 3.74467 | 0.171098 | 0.0855491 | − | 0.996334i | \(-0.472736\pi\) | ||||
0.0855491 | + | 0.996334i | \(0.472736\pi\) | |||||||
\(480\) | −0.345400 | −0.0157653 | ||||||||
\(481\) | 4.50374 | 0.205353 | ||||||||
\(482\) | 24.0169 | 1.09394 | ||||||||
\(483\) | 20.8521 | 0.948803 | ||||||||
\(484\) | 19.6052 | 0.891146 | ||||||||
\(485\) | 0.198027 | 0.00899194 | ||||||||
\(486\) | 3.08918 | 0.140128 | ||||||||
\(487\) | 14.1799 | 0.642552 | 0.321276 | − | 0.946986i | \(-0.395888\pi\) | ||||
0.321276 | + | 0.946986i | \(0.395888\pi\) | |||||||
\(488\) | 2.70135 | 0.122284 | ||||||||
\(489\) | 0.861860 | 0.0389747 | ||||||||
\(490\) | 2.41224 | 0.108974 | ||||||||
\(491\) | −34.2896 | −1.54747 | −0.773734 | − | 0.633511i | \(-0.781613\pi\) | ||||
−0.773734 | + | 0.633511i | \(0.781613\pi\) | |||||||
\(492\) | −4.49976 | −0.202865 | ||||||||
\(493\) | 11.7210 | 0.527887 | ||||||||
\(494\) | 7.70543 | 0.346683 | ||||||||
\(495\) | −0.346907 | −0.0155923 | ||||||||
\(496\) | 6.63740 | 0.298028 | ||||||||
\(497\) | 23.7006 | 1.06312 | ||||||||
\(498\) | 7.59303 | 0.340252 | ||||||||
\(499\) | 11.8419 | 0.530115 | 0.265057 | − | 0.964233i | \(-0.414609\pi\) | ||||
0.265057 | + | 0.964233i | \(0.414609\pi\) | |||||||
\(500\) | 2.09214 | 0.0935633 | ||||||||
\(501\) | −11.6592 | −0.520893 | ||||||||
\(502\) | 15.5276 | 0.693029 | ||||||||
\(503\) | −2.80121 | −0.124900 | −0.0624499 | − | 0.998048i | \(-0.519891\pi\) | ||||
−0.0624499 | + | 0.998048i | \(0.519891\pi\) | |||||||
\(504\) | −1.28275 | −0.0571383 | ||||||||
\(505\) | −3.33737 | −0.148511 | ||||||||
\(506\) | 16.3266 | 0.725808 | ||||||||
\(507\) | 19.4314 | 0.862979 | ||||||||
\(508\) | 10.8564 | 0.481674 | ||||||||
\(509\) | 6.49918 | 0.288071 | 0.144036 | − | 0.989573i | \(-0.453992\pi\) | ||||
0.144036 | + | 0.989573i | \(0.453992\pi\) | |||||||
\(510\) | 1.31391 | 0.0581811 | ||||||||
\(511\) | −14.2577 | −0.630723 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −38.4904 | −1.69939 | ||||||||
\(514\) | 5.67507 | 0.250317 | ||||||||
\(515\) | 0.167431 | 0.00737790 | ||||||||
\(516\) | 19.6096 | 0.863264 | ||||||||
\(517\) | 37.6292 | 1.65493 | ||||||||
\(518\) | 17.8384 | 0.783772 | ||||||||
\(519\) | 33.0934 | 1.45264 | ||||||||
\(520\) | 0.228072 | 0.0100016 | ||||||||
\(521\) | 25.8051 | 1.13054 | 0.565271 | − | 0.824905i | \(-0.308772\pi\) | ||||
0.565271 | + | 0.824905i | \(0.308772\pi\) | |||||||
\(522\) | −0.919440 | −0.0402428 | ||||||||
\(523\) | 22.5447 | 0.985812 | 0.492906 | − | 0.870083i | \(-0.335935\pi\) | ||||
0.492906 | + | 0.870083i | \(0.335935\pi\) | |||||||
\(524\) | −16.4182 | −0.717232 | ||||||||
\(525\) | −35.0161 | −1.52823 | ||||||||
\(526\) | 23.2605 | 1.01421 | ||||||||
\(527\) | −25.2489 | −1.09986 | ||||||||
\(528\) | 9.09302 | 0.395723 | ||||||||
\(529\) | −14.2904 | −0.621322 | ||||||||
\(530\) | 0.641520 | 0.0278658 | ||||||||
\(531\) | 2.83343 | 0.122960 | ||||||||
\(532\) | 30.5196 | 1.32319 | ||||||||
\(533\) | 2.97124 | 0.128699 | ||||||||
\(534\) | −19.3078 | −0.835530 | ||||||||
\(535\) | 3.01644 | 0.130412 | ||||||||
\(536\) | −15.7797 | −0.681579 | ||||||||
\(537\) | 21.8640 | 0.943499 | ||||||||
\(538\) | 3.18536 | 0.137331 | ||||||||
\(539\) | −63.5046 | −2.73534 | ||||||||
\(540\) | −1.13927 | −0.0490264 | ||||||||
\(541\) | 15.9763 | 0.686876 | 0.343438 | − | 0.939175i | \(-0.388408\pi\) | ||||
0.343438 | + | 0.939175i | \(0.388408\pi\) | |||||||
\(542\) | 25.4698 | 1.09402 | ||||||||
\(543\) | 29.9312 | 1.28447 | ||||||||
\(544\) | 3.80403 | 0.163096 | ||||||||
\(545\) | −1.36961 | −0.0586677 | ||||||||
\(546\) | −7.66848 | −0.328181 | ||||||||
\(547\) | 7.75254 | 0.331475 | 0.165737 | − | 0.986170i | \(-0.447000\pi\) | ||||
0.165737 | + | 0.986170i | \(0.447000\pi\) | |||||||
\(548\) | 22.5222 | 0.962100 | ||||||||
\(549\) | 0.806088 | 0.0344030 | ||||||||
\(550\) | −27.4167 | −1.16905 | ||||||||
\(551\) | 21.8756 | 0.931930 | ||||||||
\(552\) | 4.85076 | 0.206462 | ||||||||
\(553\) | 30.3565 | 1.29089 | ||||||||
\(554\) | −16.5221 | −0.701958 | ||||||||
\(555\) | 1.43330 | 0.0608402 | ||||||||
\(556\) | −12.3368 | −0.523197 | ||||||||
\(557\) | −3.24760 | −0.137605 | −0.0688026 | − | 0.997630i | \(-0.521918\pi\) | ||||
−0.0688026 | + | 0.997630i | \(0.521918\pi\) | |||||||
\(558\) | 1.98062 | 0.0838462 | ||||||||
\(559\) | −12.9484 | −0.547660 | ||||||||
\(560\) | 0.903343 | 0.0381732 | ||||||||
\(561\) | −34.5901 | −1.46040 | ||||||||
\(562\) | 26.9021 | 1.13480 | ||||||||
\(563\) | 14.7866 | 0.623183 | 0.311591 | − | 0.950216i | \(-0.399138\pi\) | ||||
0.311591 | + | 0.950216i | \(0.399138\pi\) | |||||||
\(564\) | 11.1799 | 0.470758 | ||||||||
\(565\) | −0.419573 | −0.0176516 | ||||||||
\(566\) | 6.89172 | 0.289681 | ||||||||
\(567\) | 34.4575 | 1.44708 | ||||||||
\(568\) | 5.51340 | 0.231337 | ||||||||
\(569\) | −17.0785 | −0.715970 | −0.357985 | − | 0.933727i | \(-0.616536\pi\) | ||||
−0.357985 | + | 0.933727i | \(0.616536\pi\) | |||||||
\(570\) | 2.45223 | 0.102713 | ||||||||
\(571\) | 14.4469 | 0.604585 | 0.302293 | − | 0.953215i | \(-0.402248\pi\) | ||||
0.302293 | + | 0.953215i | \(0.402248\pi\) | |||||||
\(572\) | −6.00422 | −0.251049 | ||||||||
\(573\) | −25.0854 | −1.04796 | ||||||||
\(574\) | 11.7684 | 0.491205 | ||||||||
\(575\) | −14.6257 | −0.609934 | ||||||||
\(576\) | −0.298402 | −0.0124334 | ||||||||
\(577\) | 31.9489 | 1.33005 | 0.665024 | − | 0.746822i | \(-0.268421\pi\) | ||||
0.665024 | + | 0.746822i | \(0.268421\pi\) | |||||||
\(578\) | 2.52937 | 0.105208 | ||||||||
\(579\) | 16.2345 | 0.674684 | ||||||||
\(580\) | 0.647491 | 0.0268856 | ||||||||
\(581\) | −19.8584 | −0.823866 | ||||||||
\(582\) | −1.54889 | −0.0642038 | ||||||||
\(583\) | −16.8887 | −0.699457 | ||||||||
\(584\) | −3.31672 | −0.137247 | ||||||||
\(585\) | 0.0680571 | 0.00281381 | ||||||||
\(586\) | −16.9443 | −0.699962 | ||||||||
\(587\) | −12.9026 | −0.532548 | −0.266274 | − | 0.963897i | \(-0.585793\pi\) | ||||
−0.266274 | + | 0.963897i | \(0.585793\pi\) | |||||||
\(588\) | −18.8676 | −0.778088 | ||||||||
\(589\) | −47.1233 | −1.94168 | ||||||||
\(590\) | −1.99536 | −0.0821478 | ||||||||
\(591\) | −29.5384 | −1.21505 | ||||||||
\(592\) | 4.14968 | 0.170551 | ||||||||
\(593\) | 21.6512 | 0.889108 | 0.444554 | − | 0.895752i | \(-0.353362\pi\) | ||||
0.444554 | + | 0.895752i | \(0.353362\pi\) | |||||||
\(594\) | 29.9924 | 1.23060 | ||||||||
\(595\) | −3.43634 | −0.140876 | ||||||||
\(596\) | 3.36969 | 0.138028 | ||||||||
\(597\) | −37.0118 | −1.51479 | ||||||||
\(598\) | −3.20301 | −0.130981 | ||||||||
\(599\) | −37.8688 | −1.54728 | −0.773640 | − | 0.633626i | \(-0.781566\pi\) | ||||
−0.773640 | + | 0.633626i | \(0.781566\pi\) | |||||||
\(600\) | −8.14569 | −0.332546 | ||||||||
\(601\) | 7.71790 | 0.314820 | 0.157410 | − | 0.987533i | \(-0.449686\pi\) | ||||
0.157410 | + | 0.987533i | \(0.449686\pi\) | |||||||
\(602\) | −51.2859 | −2.09026 | ||||||||
\(603\) | −4.70869 | −0.191753 | ||||||||
\(604\) | 19.6668 | 0.800230 | ||||||||
\(605\) | −4.11988 | −0.167497 | ||||||||
\(606\) | 26.1037 | 1.06039 | ||||||||
\(607\) | 11.5734 | 0.469750 | 0.234875 | − | 0.972026i | \(-0.424532\pi\) | ||||
0.234875 | + | 0.972026i | \(0.424532\pi\) | |||||||
\(608\) | 7.09967 | 0.287930 | ||||||||
\(609\) | −21.7707 | −0.882192 | ||||||||
\(610\) | −0.567666 | −0.0229841 | ||||||||
\(611\) | −7.38219 | −0.298652 | ||||||||
\(612\) | 1.13513 | 0.0458850 | ||||||||
\(613\) | −11.2636 | −0.454934 | −0.227467 | − | 0.973786i | \(-0.573044\pi\) | ||||
−0.227467 | + | 0.973786i | \(0.573044\pi\) | |||||||
\(614\) | −26.7963 | −1.08141 | ||||||||
\(615\) | 0.945588 | 0.0381298 | ||||||||
\(616\) | −23.7814 | −0.958181 | ||||||||
\(617\) | −33.5643 | −1.35125 | −0.675625 | − | 0.737246i | \(-0.736126\pi\) | ||||
−0.675625 | + | 0.737246i | \(0.736126\pi\) | |||||||
\(618\) | −1.30959 | −0.0526793 | ||||||||
\(619\) | −33.2642 | −1.33700 | −0.668501 | − | 0.743711i | \(-0.733064\pi\) | ||||
−0.668501 | + | 0.743711i | \(0.733064\pi\) | |||||||
\(620\) | −1.39480 | −0.0560163 | ||||||||
\(621\) | 15.9997 | 0.642048 | ||||||||
\(622\) | −10.1369 | −0.406452 | ||||||||
\(623\) | 50.4966 | 2.02311 | ||||||||
\(624\) | −1.78389 | −0.0714129 | ||||||||
\(625\) | 24.3396 | 0.973582 | ||||||||
\(626\) | −7.82461 | −0.312734 | ||||||||
\(627\) | −64.5574 | −2.57818 | ||||||||
\(628\) | 22.7381 | 0.907349 | ||||||||
\(629\) | −15.7855 | −0.629409 | ||||||||
\(630\) | 0.269560 | 0.0107395 | ||||||||
\(631\) | −5.81031 | −0.231305 | −0.115652 | − | 0.993290i | \(-0.536896\pi\) | ||||
−0.115652 | + | 0.993290i | \(0.536896\pi\) | |||||||
\(632\) | 7.06174 | 0.280901 | ||||||||
\(633\) | −12.6747 | −0.503774 | ||||||||
\(634\) | 29.0296 | 1.15291 | ||||||||
\(635\) | −2.28138 | −0.0905338 | ||||||||
\(636\) | −5.01774 | −0.198966 | ||||||||
\(637\) | 12.4585 | 0.493624 | ||||||||
\(638\) | −17.0459 | −0.674852 | ||||||||
\(639\) | 1.64521 | 0.0650835 | ||||||||
\(640\) | 0.210142 | 0.00830659 | ||||||||
\(641\) | 11.1411 | 0.440049 | 0.220024 | − | 0.975494i | \(-0.429386\pi\) | ||||
0.220024 | + | 0.975494i | \(0.429386\pi\) | |||||||
\(642\) | −23.5935 | −0.931162 | ||||||||
\(643\) | 16.1937 | 0.638617 | 0.319309 | − | 0.947651i | \(-0.396549\pi\) | ||||
0.319309 | + | 0.947651i | \(0.396549\pi\) | |||||||
\(644\) | −12.6864 | −0.499915 | ||||||||
\(645\) | −4.12079 | −0.162256 | ||||||||
\(646\) | −27.0073 | −1.06259 | ||||||||
\(647\) | −6.74976 | −0.265360 | −0.132680 | − | 0.991159i | \(-0.542358\pi\) | ||||
−0.132680 | + | 0.991159i | \(0.542358\pi\) | |||||||
\(648\) | 8.01575 | 0.314888 | ||||||||
\(649\) | 52.5300 | 2.06198 | ||||||||
\(650\) | 5.37868 | 0.210969 | ||||||||
\(651\) | 46.8974 | 1.83805 | ||||||||
\(652\) | −0.524356 | −0.0205354 | ||||||||
\(653\) | −4.57421 | −0.179003 | −0.0895014 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0895014 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(654\) | 10.7126 | 0.418896 | ||||||||
\(655\) | 3.45015 | 0.134809 | ||||||||
\(656\) | 2.73766 | 0.106888 | ||||||||
\(657\) | −0.989718 | −0.0386126 | ||||||||
\(658\) | −29.2393 | −1.13987 | ||||||||
\(659\) | 1.97216 | 0.0768244 | 0.0384122 | − | 0.999262i | \(-0.487770\pi\) | ||||
0.0384122 | + | 0.999262i | \(0.487770\pi\) | |||||||
\(660\) | −1.91082 | −0.0743787 | ||||||||
\(661\) | 17.3944 | 0.676564 | 0.338282 | − | 0.941045i | \(-0.390154\pi\) | ||||
0.338282 | + | 0.941045i | \(0.390154\pi\) | |||||||
\(662\) | 14.7746 | 0.574232 | ||||||||
\(663\) | 6.78598 | 0.263546 | ||||||||
\(664\) | −4.61960 | −0.179275 | ||||||||
\(665\) | −6.41344 | −0.248702 | ||||||||
\(666\) | 1.23827 | 0.0479821 | ||||||||
\(667\) | −9.09327 | −0.352093 | ||||||||
\(668\) | 7.09344 | 0.274453 | ||||||||
\(669\) | −12.5753 | −0.486188 | ||||||||
\(670\) | 3.31597 | 0.128107 | ||||||||
\(671\) | 14.9444 | 0.576922 | ||||||||
\(672\) | −7.06562 | −0.272562 | ||||||||
\(673\) | 24.4371 | 0.941980 | 0.470990 | − | 0.882138i | \(-0.343897\pi\) | ||||
0.470990 | + | 0.882138i | \(0.343897\pi\) | |||||||
\(674\) | 8.26719 | 0.318440 | ||||||||
\(675\) | −26.8677 | −1.03414 | ||||||||
\(676\) | −11.8221 | −0.454695 | ||||||||
\(677\) | −45.1930 | −1.73691 | −0.868454 | − | 0.495771i | \(-0.834886\pi\) | ||||
−0.868454 | + | 0.495771i | \(0.834886\pi\) | |||||||
\(678\) | 3.28175 | 0.126035 | ||||||||
\(679\) | 4.05090 | 0.155459 | ||||||||
\(680\) | −0.799386 | −0.0306550 | ||||||||
\(681\) | 21.8238 | 0.836290 | ||||||||
\(682\) | 36.7194 | 1.40606 | ||||||||
\(683\) | 17.9571 | 0.687108 | 0.343554 | − | 0.939133i | \(-0.388369\pi\) | ||||
0.343554 | + | 0.939133i | \(0.388369\pi\) | |||||||
\(684\) | 2.11856 | 0.0810051 | ||||||||
\(685\) | −4.73285 | −0.180833 | ||||||||
\(686\) | 19.2544 | 0.735136 | ||||||||
\(687\) | 10.8740 | 0.414868 | ||||||||
\(688\) | −11.9305 | −0.454845 | ||||||||
\(689\) | 3.31327 | 0.126225 | ||||||||
\(690\) | −1.01935 | −0.0388059 | ||||||||
\(691\) | 26.8021 | 1.01960 | 0.509801 | − | 0.860292i | \(-0.329719\pi\) | ||||
0.509801 | + | 0.860292i | \(0.329719\pi\) | |||||||
\(692\) | −20.1340 | −0.765381 | ||||||||
\(693\) | −7.09644 | −0.269571 | ||||||||
\(694\) | 10.9550 | 0.415846 | ||||||||
\(695\) | 2.59248 | 0.0983383 | ||||||||
\(696\) | −5.06444 | −0.191967 | ||||||||
\(697\) | −10.4141 | −0.394463 | ||||||||
\(698\) | 7.67321 | 0.290435 | ||||||||
\(699\) | 28.9466 | 1.09486 | ||||||||
\(700\) | 21.3038 | 0.805209 | ||||||||
\(701\) | 29.2426 | 1.10448 | 0.552238 | − | 0.833687i | \(-0.313774\pi\) | ||||
0.552238 | + | 0.833687i | \(0.313774\pi\) | |||||||
\(702\) | −5.88400 | −0.222077 | ||||||||
\(703\) | −29.4613 | −1.11116 | ||||||||
\(704\) | −5.53220 | −0.208503 | ||||||||
\(705\) | −2.34936 | −0.0884821 | ||||||||
\(706\) | 18.3730 | 0.691476 | ||||||||
\(707\) | −68.2702 | −2.56757 | ||||||||
\(708\) | 15.6070 | 0.586548 | ||||||||
\(709\) | −12.8858 | −0.483935 | −0.241967 | − | 0.970284i | \(-0.577793\pi\) | ||||
−0.241967 | + | 0.970284i | \(0.577793\pi\) | |||||||
\(710\) | −1.15860 | −0.0434813 | ||||||||
\(711\) | 2.10724 | 0.0790277 | ||||||||
\(712\) | 11.7469 | 0.440233 | ||||||||
\(713\) | 19.5883 | 0.733588 | ||||||||
\(714\) | 26.8778 | 1.00588 | ||||||||
\(715\) | 1.26174 | 0.0471863 | ||||||||
\(716\) | −13.3020 | −0.497121 | ||||||||
\(717\) | −6.91373 | −0.258198 | ||||||||
\(718\) | 19.6442 | 0.733115 | ||||||||
\(719\) | 8.42286 | 0.314120 | 0.157060 | − | 0.987589i | \(-0.449798\pi\) | ||||
0.157060 | + | 0.987589i | \(0.449798\pi\) | |||||||
\(720\) | 0.0627068 | 0.00233695 | ||||||||
\(721\) | 3.42503 | 0.127555 | ||||||||
\(722\) | −31.4053 | −1.16878 | ||||||||
\(723\) | 39.4754 | 1.46811 | ||||||||
\(724\) | −18.2102 | −0.676776 | ||||||||
\(725\) | 15.2700 | 0.567113 | ||||||||
\(726\) | 32.2242 | 1.19595 | ||||||||
\(727\) | −23.7113 | −0.879405 | −0.439702 | − | 0.898144i | \(-0.644916\pi\) | ||||
−0.439702 | + | 0.898144i | \(0.644916\pi\) | |||||||
\(728\) | 4.66551 | 0.172915 | ||||||||
\(729\) | 29.1248 | 1.07870 | ||||||||
\(730\) | 0.696982 | 0.0257965 | ||||||||
\(731\) | 45.3839 | 1.67858 | ||||||||
\(732\) | 4.44008 | 0.164110 | ||||||||
\(733\) | −1.53367 | −0.0566473 | −0.0283236 | − | 0.999599i | \(-0.509017\pi\) | ||||
−0.0283236 | + | 0.999599i | \(0.509017\pi\) | |||||||
\(734\) | −21.5291 | −0.794652 | ||||||||
\(735\) | 3.96488 | 0.146247 | ||||||||
\(736\) | −2.95120 | −0.108783 | ||||||||
\(737\) | −87.2963 | −3.21560 | ||||||||
\(738\) | 0.816923 | 0.0300714 | ||||||||
\(739\) | −28.6951 | −1.05557 | −0.527783 | − | 0.849380i | \(-0.676976\pi\) | ||||
−0.527783 | + | 0.849380i | \(0.676976\pi\) | |||||||
\(740\) | −0.872021 | −0.0320561 | ||||||||
\(741\) | 12.6651 | 0.465262 | ||||||||
\(742\) | 13.1231 | 0.481766 | ||||||||
\(743\) | 38.6729 | 1.41877 | 0.709385 | − | 0.704821i | \(-0.248973\pi\) | ||||
0.709385 | + | 0.704821i | \(0.248973\pi\) | |||||||
\(744\) | 10.9096 | 0.399965 | ||||||||
\(745\) | −0.708113 | −0.0259433 | ||||||||
\(746\) | 14.6387 | 0.535960 | ||||||||
\(747\) | −1.37850 | −0.0504367 | ||||||||
\(748\) | 21.0446 | 0.769468 | ||||||||
\(749\) | 61.7053 | 2.25466 | ||||||||
\(750\) | 3.43875 | 0.125565 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | −6.80185 | −0.248038 | ||||||||
\(753\) | 25.5219 | 0.930072 | ||||||||
\(754\) | 3.34410 | 0.121785 | ||||||||
\(755\) | −4.13281 | −0.150408 | ||||||||
\(756\) | −23.3053 | −0.847605 | ||||||||
\(757\) | −26.2491 | −0.954040 | −0.477020 | − | 0.878892i | \(-0.658283\pi\) | ||||
−0.477020 | + | 0.878892i | \(0.658283\pi\) | |||||||
\(758\) | 2.19800 | 0.0798350 | ||||||||
\(759\) | 26.8354 | 0.974062 | ||||||||
\(760\) | −1.49194 | −0.0541183 | ||||||||
\(761\) | 40.8421 | 1.48053 | 0.740263 | − | 0.672317i | \(-0.234701\pi\) | ||||
0.740263 | + | 0.672317i | \(0.234701\pi\) | |||||||
\(762\) | 17.8441 | 0.646425 | ||||||||
\(763\) | −28.0172 | −1.01429 | ||||||||
\(764\) | 15.2620 | 0.552158 | ||||||||
\(765\) | −0.238539 | −0.00862438 | ||||||||
\(766\) | 19.2884 | 0.696917 | ||||||||
\(767\) | −10.3055 | −0.372109 | ||||||||
\(768\) | −1.64365 | −0.0593102 | ||||||||
\(769\) | 1.81384 | 0.0654088 | 0.0327044 | − | 0.999465i | \(-0.489588\pi\) | ||||
0.0327044 | + | 0.999465i | \(0.489588\pi\) | |||||||
\(770\) | 4.99747 | 0.180096 | ||||||||
\(771\) | 9.32785 | 0.335934 | ||||||||
\(772\) | −9.87710 | −0.355485 | ||||||||
\(773\) | −34.5877 | −1.24403 | −0.622016 | − | 0.783004i | \(-0.713686\pi\) | ||||
−0.622016 | + | 0.783004i | \(0.713686\pi\) | |||||||
\(774\) | −3.56008 | −0.127965 | ||||||||
\(775\) | −32.8939 | −1.18158 | ||||||||
\(776\) | 0.942349 | 0.0338283 | ||||||||
\(777\) | 29.3201 | 1.05185 | ||||||||
\(778\) | 22.3365 | 0.800802 | ||||||||
\(779\) | −19.4365 | −0.696383 | ||||||||
\(780\) | 0.374871 | 0.0134225 | ||||||||
\(781\) | 30.5012 | 1.09142 | ||||||||
\(782\) | 11.2265 | 0.401458 | ||||||||
\(783\) | −16.7046 | −0.596972 | ||||||||
\(784\) | 11.4791 | 0.409967 | ||||||||
\(785\) | −4.77823 | −0.170542 | ||||||||
\(786\) | −26.9858 | −0.962553 | ||||||||
\(787\) | −9.25606 | −0.329943 | −0.164972 | − | 0.986298i | \(-0.552753\pi\) | ||||
−0.164972 | + | 0.986298i | \(0.552753\pi\) | |||||||
\(788\) | 17.9712 | 0.640197 | ||||||||
\(789\) | 38.2322 | 1.36110 | ||||||||
\(790\) | −1.48397 | −0.0527972 | ||||||||
\(791\) | −8.58292 | −0.305173 | ||||||||
\(792\) | −1.65082 | −0.0586594 | ||||||||
\(793\) | −2.93183 | −0.104112 | ||||||||
\(794\) | −33.8282 | −1.20052 | ||||||||
\(795\) | 1.05444 | 0.0373970 | ||||||||
\(796\) | 22.5180 | 0.798129 | ||||||||
\(797\) | −49.7407 | −1.76191 | −0.880953 | − | 0.473204i | \(-0.843097\pi\) | ||||
−0.880953 | + | 0.473204i | \(0.843097\pi\) | |||||||
\(798\) | 50.1636 | 1.77577 | ||||||||
\(799\) | 25.8744 | 0.915371 | ||||||||
\(800\) | 4.95584 | 0.175215 | ||||||||
\(801\) | 3.50529 | 0.123853 | ||||||||
\(802\) | −26.8410 | −0.947789 | ||||||||
\(803\) | −18.3488 | −0.647514 | ||||||||
\(804\) | −25.9363 | −0.914704 | ||||||||
\(805\) | 2.66595 | 0.0939624 | ||||||||
\(806\) | −7.20372 | −0.253740 | ||||||||
\(807\) | 5.23563 | 0.184303 | ||||||||
\(808\) | −15.8815 | −0.558709 | ||||||||
\(809\) | 13.3531 | 0.469469 | 0.234734 | − | 0.972060i | \(-0.424578\pi\) | ||||
0.234734 | + | 0.972060i | \(0.424578\pi\) | |||||||
\(810\) | −1.68444 | −0.0591853 | ||||||||
\(811\) | 3.83503 | 0.134666 | 0.0673330 | − | 0.997731i | \(-0.478551\pi\) | ||||
0.0673330 | + | 0.997731i | \(0.478551\pi\) | |||||||
\(812\) | 13.2453 | 0.464818 | ||||||||
\(813\) | 41.8635 | 1.46822 | ||||||||
\(814\) | 22.9568 | 0.804637 | ||||||||
\(815\) | 0.110189 | 0.00385976 | ||||||||
\(816\) | 6.25251 | 0.218881 | ||||||||
\(817\) | 84.7025 | 2.96336 | ||||||||
\(818\) | 15.4994 | 0.541925 | ||||||||
\(819\) | 1.39220 | 0.0486473 | ||||||||
\(820\) | −0.575296 | −0.0200902 | ||||||||
\(821\) | −15.3533 | −0.535832 | −0.267916 | − | 0.963442i | \(-0.586335\pi\) | ||||
−0.267916 | + | 0.963442i | \(0.586335\pi\) | |||||||
\(822\) | 37.0187 | 1.29117 | ||||||||
\(823\) | −29.9003 | −1.04226 | −0.521129 | − | 0.853478i | \(-0.674489\pi\) | ||||
−0.521129 | + | 0.853478i | \(0.674489\pi\) | |||||||
\(824\) | 0.796754 | 0.0277562 | ||||||||
\(825\) | −45.0636 | −1.56891 | ||||||||
\(826\) | −40.8178 | −1.42023 | ||||||||
\(827\) | 53.7563 | 1.86929 | 0.934644 | − | 0.355585i | \(-0.115718\pi\) | ||||
0.934644 | + | 0.355585i | \(0.115718\pi\) | |||||||
\(828\) | −0.880646 | −0.0306046 | ||||||||
\(829\) | 6.40991 | 0.222625 | 0.111313 | − | 0.993785i | \(-0.464494\pi\) | ||||
0.111313 | + | 0.993785i | \(0.464494\pi\) | |||||||
\(830\) | 0.970772 | 0.0336960 | ||||||||
\(831\) | −27.1567 | −0.942054 | ||||||||
\(832\) | 1.08532 | 0.0376268 | ||||||||
\(833\) | −43.6668 | −1.51296 | ||||||||
\(834\) | −20.2774 | −0.702150 | ||||||||
\(835\) | −1.49063 | −0.0515853 | ||||||||
\(836\) | 39.2768 | 1.35842 | ||||||||
\(837\) | 35.9842 | 1.24380 | ||||||||
\(838\) | −10.4030 | −0.359365 | ||||||||
\(839\) | 12.4566 | 0.430048 | 0.215024 | − | 0.976609i | \(-0.431017\pi\) | ||||
0.215024 | + | 0.976609i | \(0.431017\pi\) | |||||||
\(840\) | 1.48478 | 0.0512299 | ||||||||
\(841\) | −19.5062 | −0.672626 | ||||||||
\(842\) | 9.76094 | 0.336384 | ||||||||
\(843\) | 44.2178 | 1.52294 | ||||||||
\(844\) | 7.71129 | 0.265433 | ||||||||
\(845\) | 2.48431 | 0.0854630 | ||||||||
\(846\) | −2.02969 | −0.0697821 | ||||||||
\(847\) | −84.2776 | −2.89581 | ||||||||
\(848\) | 3.05280 | 0.104833 | ||||||||
\(849\) | 11.3276 | 0.388763 | ||||||||
\(850\) | −18.8522 | −0.646624 | ||||||||
\(851\) | 12.2465 | 0.419806 | ||||||||
\(852\) | 9.06212 | 0.310463 | ||||||||
\(853\) | 25.3375 | 0.867539 | 0.433769 | − | 0.901024i | \(-0.357183\pi\) | ||||
0.433769 | + | 0.901024i | \(0.357183\pi\) | |||||||
\(854\) | −11.6124 | −0.397367 | ||||||||
\(855\) | −0.445198 | −0.0152254 | ||||||||
\(856\) | 14.3543 | 0.490620 | ||||||||
\(857\) | 18.0280 | 0.615826 | 0.307913 | − | 0.951415i | \(-0.400369\pi\) | ||||
0.307913 | + | 0.951415i | \(0.400369\pi\) | |||||||
\(858\) | −9.86885 | −0.336917 | ||||||||
\(859\) | −12.7900 | −0.436389 | −0.218195 | − | 0.975905i | \(-0.570017\pi\) | ||||
−0.218195 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(860\) | 2.50709 | 0.0854912 | ||||||||
\(861\) | 19.3433 | 0.659216 | ||||||||
\(862\) | 9.18053 | 0.312690 | ||||||||
\(863\) | 34.9638 | 1.19018 | 0.595090 | − | 0.803659i | \(-0.297116\pi\) | ||||
0.595090 | + | 0.803659i | \(0.297116\pi\) | |||||||
\(864\) | −5.42143 | −0.184441 | ||||||||
\(865\) | 4.23101 | 0.143858 | ||||||||
\(866\) | −26.8684 | −0.913026 | ||||||||
\(867\) | 4.15740 | 0.141193 | ||||||||
\(868\) | −28.5324 | −0.968453 | ||||||||
\(869\) | 39.0670 | 1.32526 | ||||||||
\(870\) | 1.06425 | 0.0360815 | ||||||||
\(871\) | 17.1260 | 0.580294 | ||||||||
\(872\) | −6.51756 | −0.220712 | ||||||||
\(873\) | 0.281199 | 0.00951715 | ||||||||
\(874\) | 20.9526 | 0.708731 | ||||||||
\(875\) | −8.99354 | −0.304037 | ||||||||
\(876\) | −5.45154 | −0.184191 | ||||||||
\(877\) | −23.9968 | −0.810313 | −0.405157 | − | 0.914247i | \(-0.632783\pi\) | ||||
−0.405157 | + | 0.914247i | \(0.632783\pi\) | |||||||
\(878\) | −21.0844 | −0.711564 | ||||||||
\(879\) | −27.8505 | −0.939375 | ||||||||
\(880\) | 1.16255 | 0.0391894 | ||||||||
\(881\) | −12.6147 | −0.425001 | −0.212500 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212500 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(882\) | 3.42539 | 0.115339 | ||||||||
\(883\) | −14.7897 | −0.497712 | −0.248856 | − | 0.968541i | \(-0.580055\pi\) | ||||
−0.248856 | + | 0.968541i | \(0.580055\pi\) | |||||||
\(884\) | −4.12860 | −0.138860 | ||||||||
\(885\) | −3.27969 | −0.110246 | ||||||||
\(886\) | 37.0110 | 1.24341 | ||||||||
\(887\) | 22.7477 | 0.763793 | 0.381896 | − | 0.924205i | \(-0.375271\pi\) | ||||
0.381896 | + | 0.924205i | \(0.375271\pi\) | |||||||
\(888\) | 6.82064 | 0.228886 | ||||||||
\(889\) | −46.6687 | −1.56522 | ||||||||
\(890\) | −2.46851 | −0.0827446 | ||||||||
\(891\) | 44.3447 | 1.48560 | ||||||||
\(892\) | 7.65080 | 0.256168 | ||||||||
\(893\) | 48.2909 | 1.61599 | ||||||||
\(894\) | 5.53860 | 0.185239 | ||||||||
\(895\) | 2.79532 | 0.0934371 | ||||||||
\(896\) | 4.29873 | 0.143611 | ||||||||
\(897\) | −5.26463 | −0.175781 | ||||||||
\(898\) | 0.401494 | 0.0133980 | ||||||||
\(899\) | −20.4512 | −0.682086 | ||||||||
\(900\) | 1.47883 | 0.0492945 | ||||||||
\(901\) | −11.6129 | −0.386882 | ||||||||
\(902\) | 15.1453 | 0.504282 | ||||||||
\(903\) | −84.2963 | −2.80521 | ||||||||
\(904\) | −1.99662 | −0.0664065 | ||||||||
\(905\) | 3.82672 | 0.127204 | ||||||||
\(906\) | 32.3254 | 1.07394 | ||||||||
\(907\) | −33.7575 | −1.12090 | −0.560450 | − | 0.828188i | \(-0.689372\pi\) | ||||
−0.560450 | + | 0.828188i | \(0.689372\pi\) | |||||||
\(908\) | −13.2776 | −0.440633 | ||||||||
\(909\) | −4.73907 | −0.157185 | ||||||||
\(910\) | −0.980418 | −0.0325005 | ||||||||
\(911\) | 39.3121 | 1.30247 | 0.651235 | − | 0.758877i | \(-0.274251\pi\) | ||||
0.651235 | + | 0.758877i | \(0.274251\pi\) | |||||||
\(912\) | 11.6694 | 0.386412 | ||||||||
\(913\) | −25.5566 | −0.845799 | ||||||||
\(914\) | 15.4830 | 0.512133 | ||||||||
\(915\) | −0.933047 | −0.0308456 | ||||||||
\(916\) | −6.61574 | −0.218590 | ||||||||
\(917\) | 70.5774 | 2.33067 | ||||||||
\(918\) | 20.6233 | 0.680670 | ||||||||
\(919\) | 35.7082 | 1.17791 | 0.588953 | − | 0.808167i | \(-0.299540\pi\) | ||||
0.588953 | + | 0.808167i | \(0.299540\pi\) | |||||||
\(920\) | 0.620171 | 0.0204464 | ||||||||
\(921\) | −44.0438 | −1.45129 | ||||||||
\(922\) | −13.4457 | −0.442811 | ||||||||
\(923\) | −5.98381 | −0.196960 | ||||||||
\(924\) | −39.0884 | −1.28592 | ||||||||
\(925\) | −20.5651 | −0.676178 | ||||||||
\(926\) | −37.6315 | −1.23665 | ||||||||
\(927\) | 0.237753 | 0.00780884 | ||||||||
\(928\) | 3.08121 | 0.101146 | ||||||||
\(929\) | 48.8337 | 1.60218 | 0.801091 | − | 0.598542i | \(-0.204253\pi\) | ||||
0.801091 | + | 0.598542i | \(0.204253\pi\) | |||||||
\(930\) | −2.29256 | −0.0751760 | ||||||||
\(931\) | −81.4977 | −2.67098 | ||||||||
\(932\) | −17.6112 | −0.576873 | ||||||||
\(933\) | −16.6615 | −0.545474 | ||||||||
\(934\) | −30.1127 | −0.985318 | ||||||||
\(935\) | −4.42236 | −0.144627 | ||||||||
\(936\) | 0.323863 | 0.0105858 | ||||||||
\(937\) | −36.5109 | −1.19276 | −0.596379 | − | 0.802703i | \(-0.703395\pi\) | ||||
−0.596379 | + | 0.802703i | \(0.703395\pi\) | |||||||
\(938\) | 67.8326 | 2.21481 | ||||||||
\(939\) | −12.8609 | −0.419701 | ||||||||
\(940\) | 1.42935 | 0.0466203 | ||||||||
\(941\) | 3.25315 | 0.106050 | 0.0530249 | − | 0.998593i | \(-0.483114\pi\) | ||||
0.0530249 | + | 0.998593i | \(0.483114\pi\) | |||||||
\(942\) | 37.3736 | 1.21770 | ||||||||
\(943\) | 8.07938 | 0.263101 | ||||||||
\(944\) | −9.49532 | −0.309046 | ||||||||
\(945\) | 4.89741 | 0.159313 | ||||||||
\(946\) | −66.0018 | −2.14590 | ||||||||
\(947\) | 16.3429 | 0.531074 | 0.265537 | − | 0.964101i | \(-0.414451\pi\) | ||||
0.265537 | + | 0.964101i | \(0.414451\pi\) | |||||||
\(948\) | 11.6071 | 0.376980 | ||||||||
\(949\) | 3.59971 | 0.116852 | ||||||||
\(950\) | −35.1848 | −1.14155 | ||||||||
\(951\) | 47.7145 | 1.54725 | ||||||||
\(952\) | −16.3525 | −0.529987 | ||||||||
\(953\) | 35.3966 | 1.14661 | 0.573304 | − | 0.819343i | \(-0.305662\pi\) | ||||
0.573304 | + | 0.819343i | \(0.305662\pi\) | |||||||
\(954\) | 0.910961 | 0.0294935 | ||||||||
\(955\) | −3.20717 | −0.103782 | ||||||||
\(956\) | 4.20632 | 0.136042 | ||||||||
\(957\) | −28.0175 | −0.905677 | ||||||||
\(958\) | −3.74467 | −0.120985 | ||||||||
\(959\) | −96.8168 | −3.12638 | ||||||||
\(960\) | 0.345400 | 0.0111478 | ||||||||
\(961\) | 13.0551 | 0.421132 | ||||||||
\(962\) | −4.50374 | −0.145206 | ||||||||
\(963\) | 4.28336 | 0.138029 | ||||||||
\(964\) | −24.0169 | −0.773531 | ||||||||
\(965\) | 2.07559 | 0.0668157 | ||||||||
\(966\) | −20.8521 | −0.670905 | ||||||||
\(967\) | 33.2805 | 1.07023 | 0.535115 | − | 0.844779i | \(-0.320268\pi\) | ||||
0.535115 | + | 0.844779i | \(0.320268\pi\) | |||||||
\(968\) | −19.6052 | −0.630136 | ||||||||
\(969\) | −44.3907 | −1.42604 | ||||||||
\(970\) | −0.198027 | −0.00635826 | ||||||||
\(971\) | 48.2451 | 1.54826 | 0.774129 | − | 0.633028i | \(-0.218188\pi\) | ||||
0.774129 | + | 0.633028i | \(0.218188\pi\) | |||||||
\(972\) | −3.08918 | −0.0990854 | ||||||||
\(973\) | 53.0326 | 1.70015 | ||||||||
\(974\) | −14.1799 | −0.454353 | ||||||||
\(975\) | 8.84069 | 0.283129 | ||||||||
\(976\) | −2.70135 | −0.0864680 | ||||||||
\(977\) | 19.4436 | 0.622056 | 0.311028 | − | 0.950401i | \(-0.399327\pi\) | ||||
0.311028 | + | 0.950401i | \(0.399327\pi\) | |||||||
\(978\) | −0.861860 | −0.0275593 | ||||||||
\(979\) | 64.9860 | 2.07696 | ||||||||
\(980\) | −2.41224 | −0.0770561 | ||||||||
\(981\) | −1.94485 | −0.0620944 | ||||||||
\(982\) | 34.2896 | 1.09422 | ||||||||
\(983\) | −44.1183 | −1.40716 | −0.703578 | − | 0.710618i | \(-0.748415\pi\) | ||||
−0.703578 | + | 0.710618i | \(0.748415\pi\) | |||||||
\(984\) | 4.49976 | 0.143447 | ||||||||
\(985\) | −3.77650 | −0.120329 | ||||||||
\(986\) | −11.7210 | −0.373273 | ||||||||
\(987\) | −48.0593 | −1.52974 | ||||||||
\(988\) | −7.70543 | −0.245142 | ||||||||
\(989\) | −35.2093 | −1.11959 | ||||||||
\(990\) | 0.346907 | 0.0110254 | ||||||||
\(991\) | 15.0817 | 0.479086 | 0.239543 | − | 0.970886i | \(-0.423002\pi\) | ||||
0.239543 | + | 0.970886i | \(0.423002\pi\) | |||||||
\(992\) | −6.63740 | −0.210738 | ||||||||
\(993\) | 24.2844 | 0.770642 | ||||||||
\(994\) | −23.7006 | −0.751738 | ||||||||
\(995\) | −4.73197 | −0.150014 | ||||||||
\(996\) | −7.59303 | −0.240594 | ||||||||
\(997\) | −28.0852 | −0.889466 | −0.444733 | − | 0.895663i | \(-0.646701\pi\) | ||||
−0.444733 | + | 0.895663i | \(0.646701\pi\) | |||||||
\(998\) | −11.8419 | −0.374848 | ||||||||
\(999\) | 22.4972 | 0.711780 |
(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 | 1502.2.a.h.1.5 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.h.1.5 | ✓ | 19 | 1.1 | even | 1 | trivial |