Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(1.74461\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74461 | 1.23363 | 0.616814 | − | 0.787109i | \(-0.288423\pi\) | ||||
0.616814 | + | 0.787109i | \(0.288423\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.04367 | 0.521837 | ||||||||
\(5\) | 0.892571 | 0.399170 | 0.199585 | − | 0.979881i | \(-0.436041\pi\) | ||||
0.199585 | + | 0.979881i | \(0.436041\pi\) | |||||||
\(6\) | 1.74461 | 0.712235 | ||||||||
\(7\) | 3.89655 | 1.47276 | 0.736379 | − | 0.676570i | \(-0.236534\pi\) | ||||
0.736379 | + | 0.676570i | \(0.236534\pi\) | |||||||
\(8\) | −1.66842 | −0.589875 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.55719 | 0.492427 | ||||||||
\(11\) | 4.47217 | 1.34841 | 0.674205 | − | 0.738544i | \(-0.264486\pi\) | ||||
0.674205 | + | 0.738544i | \(0.264486\pi\) | |||||||
\(12\) | 1.04367 | 0.301283 | ||||||||
\(13\) | 2.21315 | 0.613817 | 0.306909 | − | 0.951739i | \(-0.400705\pi\) | ||||
0.306909 | + | 0.951739i | \(0.400705\pi\) | |||||||
\(14\) | 6.79797 | 1.81683 | ||||||||
\(15\) | 0.892571 | 0.230461 | ||||||||
\(16\) | −4.99809 | −1.24952 | ||||||||
\(17\) | −5.25735 | −1.27510 | −0.637548 | − | 0.770411i | \(-0.720051\pi\) | ||||
−0.637548 | + | 0.770411i | \(0.720051\pi\) | |||||||
\(18\) | 1.74461 | 0.411209 | ||||||||
\(19\) | 0.817209 | 0.187481 | 0.0937403 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937403 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(20\) | 0.931553 | 0.208302 | ||||||||
\(21\) | 3.89655 | 0.850297 | ||||||||
\(22\) | 7.80221 | 1.66344 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.66842 | −0.340565 | ||||||||
\(25\) | −4.20332 | −0.840663 | ||||||||
\(26\) | 3.86109 | 0.757222 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.06673 | 0.768539 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.55719 | 0.284303 | ||||||||
\(31\) | −4.19787 | −0.753961 | −0.376980 | − | 0.926221i | \(-0.623038\pi\) | ||||
−0.376980 | + | 0.926221i | \(0.623038\pi\) | |||||||
\(32\) | −5.38290 | −0.951571 | ||||||||
\(33\) | 4.47217 | 0.778505 | ||||||||
\(34\) | −9.17204 | −1.57299 | ||||||||
\(35\) | 3.47795 | 0.587880 | ||||||||
\(36\) | 1.04367 | 0.173946 | ||||||||
\(37\) | 8.35747 | 1.37396 | 0.686980 | − | 0.726676i | \(-0.258936\pi\) | ||||
0.686980 | + | 0.726676i | \(0.258936\pi\) | |||||||
\(38\) | 1.42571 | 0.231281 | ||||||||
\(39\) | 2.21315 | 0.354388 | ||||||||
\(40\) | −1.48918 | −0.235460 | ||||||||
\(41\) | −1.95546 | −0.305392 | −0.152696 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152696 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(42\) | 6.79797 | 1.04895 | ||||||||
\(43\) | −1.55005 | −0.236381 | −0.118190 | − | 0.992991i | \(-0.537709\pi\) | ||||
−0.118190 | + | 0.992991i | \(0.537709\pi\) | |||||||
\(44\) | 4.66749 | 0.703650 | ||||||||
\(45\) | 0.892571 | 0.133057 | ||||||||
\(46\) | 1.74461 | 0.257229 | ||||||||
\(47\) | −1.09928 | −0.160347 | −0.0801735 | − | 0.996781i | \(-0.525547\pi\) | ||||
−0.0801735 | + | 0.996781i | \(0.525547\pi\) | |||||||
\(48\) | −4.99809 | −0.721413 | ||||||||
\(49\) | 8.18310 | 1.16901 | ||||||||
\(50\) | −7.33316 | −1.03707 | ||||||||
\(51\) | −5.25735 | −0.736177 | ||||||||
\(52\) | 2.30981 | 0.320312 | ||||||||
\(53\) | −0.517604 | −0.0710983 | −0.0355492 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355492 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(54\) | 1.74461 | 0.237412 | ||||||||
\(55\) | 3.99173 | 0.538245 | ||||||||
\(56\) | −6.50108 | −0.868743 | ||||||||
\(57\) | 0.817209 | 0.108242 | ||||||||
\(58\) | 1.74461 | 0.229079 | ||||||||
\(59\) | −6.99779 | −0.911035 | −0.455518 | − | 0.890227i | \(-0.650546\pi\) | ||||
−0.455518 | + | 0.890227i | \(0.650546\pi\) | |||||||
\(60\) | 0.931553 | 0.120263 | ||||||||
\(61\) | −0.394355 | −0.0504919 | −0.0252460 | − | 0.999681i | \(-0.508037\pi\) | ||||
−0.0252460 | + | 0.999681i | \(0.508037\pi\) | |||||||
\(62\) | −7.32367 | −0.930106 | ||||||||
\(63\) | 3.89655 | 0.490919 | ||||||||
\(64\) | 0.605114 | 0.0756392 | ||||||||
\(65\) | 1.97539 | 0.245017 | ||||||||
\(66\) | 7.80221 | 0.960385 | ||||||||
\(67\) | 7.01521 | 0.857044 | 0.428522 | − | 0.903531i | \(-0.359034\pi\) | ||||
0.428522 | + | 0.903531i | \(0.359034\pi\) | |||||||
\(68\) | −5.48696 | −0.665392 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 6.06767 | 0.725225 | ||||||||
\(71\) | −4.42865 | −0.525585 | −0.262792 | − | 0.964852i | \(-0.584643\pi\) | ||||
−0.262792 | + | 0.964852i | \(0.584643\pi\) | |||||||
\(72\) | −1.66842 | −0.196625 | ||||||||
\(73\) | −0.726062 | −0.0849791 | −0.0424896 | − | 0.999097i | \(-0.513529\pi\) | ||||
−0.0424896 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(74\) | 14.5806 | 1.69495 | ||||||||
\(75\) | −4.20332 | −0.485357 | ||||||||
\(76\) | 0.852899 | 0.0978342 | ||||||||
\(77\) | 17.4260 | 1.98588 | ||||||||
\(78\) | 3.86109 | 0.437182 | ||||||||
\(79\) | −7.50686 | −0.844587 | −0.422294 | − | 0.906459i | \(-0.638775\pi\) | ||||
−0.422294 | + | 0.906459i | \(0.638775\pi\) | |||||||
\(80\) | −4.46115 | −0.498772 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.41153 | −0.376740 | ||||||||
\(83\) | 8.09267 | 0.888286 | 0.444143 | − | 0.895956i | \(-0.353508\pi\) | ||||
0.444143 | + | 0.895956i | \(0.353508\pi\) | |||||||
\(84\) | 4.06673 | 0.443716 | ||||||||
\(85\) | −4.69256 | −0.508980 | ||||||||
\(86\) | −2.70424 | −0.291606 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −7.46146 | −0.795394 | ||||||||
\(89\) | −10.4230 | −1.10484 | −0.552418 | − | 0.833567i | \(-0.686295\pi\) | ||||
−0.552418 | + | 0.833567i | \(0.686295\pi\) | |||||||
\(90\) | 1.55719 | 0.164142 | ||||||||
\(91\) | 8.62365 | 0.904004 | ||||||||
\(92\) | 1.04367 | 0.108810 | ||||||||
\(93\) | −4.19787 | −0.435299 | ||||||||
\(94\) | −1.91783 | −0.197809 | ||||||||
\(95\) | 0.729417 | 0.0748366 | ||||||||
\(96\) | −5.38290 | −0.549390 | ||||||||
\(97\) | 12.3546 | 1.25442 | 0.627209 | − | 0.778851i | \(-0.284197\pi\) | ||||
0.627209 | + | 0.778851i | \(0.284197\pi\) | |||||||
\(98\) | 14.2763 | 1.44213 | ||||||||
\(99\) | 4.47217 | 0.449470 | ||||||||
\(100\) | −4.38689 | −0.438689 | ||||||||
\(101\) | −2.45708 | −0.244489 | −0.122244 | − | 0.992500i | \(-0.539009\pi\) | ||||
−0.122244 | + | 0.992500i | \(0.539009\pi\) | |||||||
\(102\) | −9.17204 | −0.908168 | ||||||||
\(103\) | −9.41863 | −0.928046 | −0.464023 | − | 0.885823i | \(-0.653594\pi\) | ||||
−0.464023 | + | 0.885823i | \(0.653594\pi\) | |||||||
\(104\) | −3.69246 | −0.362076 | ||||||||
\(105\) | 3.47795 | 0.339413 | ||||||||
\(106\) | −0.903018 | −0.0877088 | ||||||||
\(107\) | 7.89713 | 0.763445 | 0.381722 | − | 0.924277i | \(-0.375331\pi\) | ||||
0.381722 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(108\) | 1.04367 | 0.100428 | ||||||||
\(109\) | 15.7824 | 1.51168 | 0.755840 | − | 0.654756i | \(-0.227229\pi\) | ||||
0.755840 | + | 0.654756i | \(0.227229\pi\) | |||||||
\(110\) | 6.96402 | 0.663993 | ||||||||
\(111\) | 8.35747 | 0.793256 | ||||||||
\(112\) | −19.4753 | −1.84024 | ||||||||
\(113\) | 3.23551 | 0.304372 | 0.152186 | − | 0.988352i | \(-0.451369\pi\) | ||||
0.152186 | + | 0.988352i | \(0.451369\pi\) | |||||||
\(114\) | 1.42571 | 0.133530 | ||||||||
\(115\) | 0.892571 | 0.0832327 | ||||||||
\(116\) | 1.04367 | 0.0969027 | ||||||||
\(117\) | 2.21315 | 0.204606 | ||||||||
\(118\) | −12.2084 | −1.12388 | ||||||||
\(119\) | −20.4855 | −1.87791 | ||||||||
\(120\) | −1.48918 | −0.135943 | ||||||||
\(121\) | 9.00031 | 0.818210 | ||||||||
\(122\) | −0.687996 | −0.0622882 | ||||||||
\(123\) | −1.95546 | −0.176318 | ||||||||
\(124\) | −4.38121 | −0.393444 | ||||||||
\(125\) | −8.21461 | −0.734737 | ||||||||
\(126\) | 6.79797 | 0.605611 | ||||||||
\(127\) | −2.01959 | −0.179209 | −0.0896046 | − | 0.995977i | \(-0.528560\pi\) | ||||
−0.0896046 | + | 0.995977i | \(0.528560\pi\) | |||||||
\(128\) | 11.8215 | 1.04488 | ||||||||
\(129\) | −1.55005 | −0.136474 | ||||||||
\(130\) | 3.44630 | 0.302260 | ||||||||
\(131\) | −9.92888 | −0.867491 | −0.433745 | − | 0.901036i | \(-0.642808\pi\) | ||||
−0.433745 | + | 0.901036i | \(0.642808\pi\) | |||||||
\(132\) | 4.66749 | 0.406253 | ||||||||
\(133\) | 3.18429 | 0.276113 | ||||||||
\(134\) | 12.2388 | 1.05727 | ||||||||
\(135\) | 0.892571 | 0.0768203 | ||||||||
\(136\) | 8.77147 | 0.752147 | ||||||||
\(137\) | 6.37499 | 0.544652 | 0.272326 | − | 0.962205i | \(-0.412207\pi\) | ||||
0.272326 | + | 0.962205i | \(0.412207\pi\) | |||||||
\(138\) | 1.74461 | 0.148511 | ||||||||
\(139\) | 10.8258 | 0.918236 | 0.459118 | − | 0.888375i | \(-0.348165\pi\) | ||||
0.459118 | + | 0.888375i | \(0.348165\pi\) | |||||||
\(140\) | 3.62984 | 0.306778 | ||||||||
\(141\) | −1.09928 | −0.0925764 | ||||||||
\(142\) | −7.72629 | −0.648376 | ||||||||
\(143\) | 9.89758 | 0.827678 | ||||||||
\(144\) | −4.99809 | −0.416508 | ||||||||
\(145\) | 0.892571 | 0.0741240 | ||||||||
\(146\) | −1.26670 | −0.104833 | ||||||||
\(147\) | 8.18310 | 0.674930 | ||||||||
\(148\) | 8.72247 | 0.716983 | ||||||||
\(149\) | −13.0542 | −1.06944 | −0.534721 | − | 0.845029i | \(-0.679583\pi\) | ||||
−0.534721 | + | 0.845029i | \(0.679583\pi\) | |||||||
\(150\) | −7.33316 | −0.598750 | ||||||||
\(151\) | −11.5418 | −0.939262 | −0.469631 | − | 0.882863i | \(-0.655613\pi\) | ||||
−0.469631 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(152\) | −1.36345 | −0.110590 | ||||||||
\(153\) | −5.25735 | −0.425032 | ||||||||
\(154\) | 30.4017 | 2.44984 | ||||||||
\(155\) | −3.74690 | −0.300958 | ||||||||
\(156\) | 2.30981 | 0.184933 | ||||||||
\(157\) | −9.86331 | −0.787178 | −0.393589 | − | 0.919287i | \(-0.628767\pi\) | ||||
−0.393589 | + | 0.919287i | \(0.628767\pi\) | |||||||
\(158\) | −13.0966 | −1.04191 | ||||||||
\(159\) | −0.517604 | −0.0410486 | ||||||||
\(160\) | −4.80462 | −0.379838 | ||||||||
\(161\) | 3.89655 | 0.307091 | ||||||||
\(162\) | 1.74461 | 0.137070 | ||||||||
\(163\) | −17.8041 | −1.39452 | −0.697260 | − | 0.716818i | \(-0.745598\pi\) | ||||
−0.697260 | + | 0.716818i | \(0.745598\pi\) | |||||||
\(164\) | −2.04086 | −0.159365 | ||||||||
\(165\) | 3.99173 | 0.310756 | ||||||||
\(166\) | 14.1186 | 1.09581 | ||||||||
\(167\) | −18.7004 | −1.44708 | −0.723539 | − | 0.690283i | \(-0.757486\pi\) | ||||
−0.723539 | + | 0.690283i | \(0.757486\pi\) | |||||||
\(168\) | −6.50108 | −0.501569 | ||||||||
\(169\) | −8.10197 | −0.623228 | ||||||||
\(170\) | −8.18670 | −0.627891 | ||||||||
\(171\) | 0.817209 | 0.0624935 | ||||||||
\(172\) | −1.61775 | −0.123352 | ||||||||
\(173\) | 4.95268 | 0.376545 | 0.188273 | − | 0.982117i | \(-0.439711\pi\) | ||||
0.188273 | + | 0.982117i | \(0.439711\pi\) | |||||||
\(174\) | 1.74461 | 0.132259 | ||||||||
\(175\) | −16.3784 | −1.23809 | ||||||||
\(176\) | −22.3523 | −1.68487 | ||||||||
\(177\) | −6.99779 | −0.525986 | ||||||||
\(178\) | −18.1841 | −1.36296 | ||||||||
\(179\) | −7.53642 | −0.563298 | −0.281649 | − | 0.959517i | \(-0.590881\pi\) | ||||
−0.281649 | + | 0.959517i | \(0.590881\pi\) | |||||||
\(180\) | 0.931553 | 0.0694338 | ||||||||
\(181\) | 11.5859 | 0.861175 | 0.430588 | − | 0.902549i | \(-0.358306\pi\) | ||||
0.430588 | + | 0.902549i | \(0.358306\pi\) | |||||||
\(182\) | 15.0449 | 1.11520 | ||||||||
\(183\) | −0.394355 | −0.0291515 | ||||||||
\(184\) | −1.66842 | −0.122997 | ||||||||
\(185\) | 7.45964 | 0.548443 | ||||||||
\(186\) | −7.32367 | −0.536997 | ||||||||
\(187\) | −23.5118 | −1.71935 | ||||||||
\(188\) | −1.14729 | −0.0836750 | ||||||||
\(189\) | 3.89655 | 0.283432 | ||||||||
\(190\) | 1.27255 | 0.0923205 | ||||||||
\(191\) | −15.3233 | −1.10875 | −0.554376 | − | 0.832266i | \(-0.687043\pi\) | ||||
−0.554376 | + | 0.832266i | \(0.687043\pi\) | |||||||
\(192\) | 0.605114 | 0.0436703 | ||||||||
\(193\) | 7.59424 | 0.546646 | 0.273323 | − | 0.961922i | \(-0.411877\pi\) | ||||
0.273323 | + | 0.961922i | \(0.411877\pi\) | |||||||
\(194\) | 21.5540 | 1.54748 | ||||||||
\(195\) | 1.97539 | 0.141461 | ||||||||
\(196\) | 8.54048 | 0.610034 | ||||||||
\(197\) | −2.72033 | −0.193816 | −0.0969078 | − | 0.995293i | \(-0.530895\pi\) | ||||
−0.0969078 | + | 0.995293i | \(0.530895\pi\) | |||||||
\(198\) | 7.80221 | 0.554479 | ||||||||
\(199\) | −11.5802 | −0.820896 | −0.410448 | − | 0.911884i | \(-0.634628\pi\) | ||||
−0.410448 | + | 0.911884i | \(0.634628\pi\) | |||||||
\(200\) | 7.01290 | 0.495887 | ||||||||
\(201\) | 7.01521 | 0.494815 | ||||||||
\(202\) | −4.28666 | −0.301608 | ||||||||
\(203\) | 3.89655 | 0.273484 | ||||||||
\(204\) | −5.48696 | −0.384164 | ||||||||
\(205\) | −1.74539 | −0.121903 | ||||||||
\(206\) | −16.4319 | −1.14486 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −11.0615 | −0.766979 | ||||||||
\(209\) | 3.65470 | 0.252801 | ||||||||
\(210\) | 6.06767 | 0.418709 | ||||||||
\(211\) | −2.39087 | −0.164594 | −0.0822970 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822970 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(212\) | −0.540209 | −0.0371017 | ||||||||
\(213\) | −4.42865 | −0.303446 | ||||||||
\(214\) | 13.7774 | 0.941806 | ||||||||
\(215\) | −1.38353 | −0.0943560 | ||||||||
\(216\) | −1.66842 | −0.113522 | ||||||||
\(217\) | −16.3572 | −1.11040 | ||||||||
\(218\) | 27.5342 | 1.86485 | ||||||||
\(219\) | −0.726062 | −0.0490627 | ||||||||
\(220\) | 4.16606 | 0.280876 | ||||||||
\(221\) | −11.6353 | −0.782676 | ||||||||
\(222\) | 14.5806 | 0.978582 | ||||||||
\(223\) | 4.99410 | 0.334430 | 0.167215 | − | 0.985920i | \(-0.446523\pi\) | ||||
0.167215 | + | 0.985920i | \(0.446523\pi\) | |||||||
\(224\) | −20.9747 | −1.40143 | ||||||||
\(225\) | −4.20332 | −0.280221 | ||||||||
\(226\) | 5.64472 | 0.375481 | ||||||||
\(227\) | 9.07560 | 0.602369 | 0.301184 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301184 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(228\) | 0.852899 | 0.0564846 | ||||||||
\(229\) | −10.2011 | −0.674106 | −0.337053 | − | 0.941486i | \(-0.609430\pi\) | ||||
−0.337053 | + | 0.941486i | \(0.609430\pi\) | |||||||
\(230\) | 1.55719 | 0.102678 | ||||||||
\(231\) | 17.4260 | 1.14655 | ||||||||
\(232\) | −1.66842 | −0.109537 | ||||||||
\(233\) | 17.5259 | 1.14816 | 0.574080 | − | 0.818799i | \(-0.305360\pi\) | ||||
0.574080 | + | 0.818799i | \(0.305360\pi\) | |||||||
\(234\) | 3.86109 | 0.252407 | ||||||||
\(235\) | −0.981189 | −0.0640057 | ||||||||
\(236\) | −7.30341 | −0.475412 | ||||||||
\(237\) | −7.50686 | −0.487623 | ||||||||
\(238\) | −35.7393 | −2.31664 | ||||||||
\(239\) | 18.0140 | 1.16523 | 0.582614 | − | 0.812749i | \(-0.302030\pi\) | ||||
0.582614 | + | 0.812749i | \(0.302030\pi\) | |||||||
\(240\) | −4.46115 | −0.287966 | ||||||||
\(241\) | −10.3862 | −0.669037 | −0.334519 | − | 0.942389i | \(-0.608574\pi\) | ||||
−0.334519 | + | 0.942389i | \(0.608574\pi\) | |||||||
\(242\) | 15.7021 | 1.00937 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.411577 | −0.0263485 | ||||||||
\(245\) | 7.30399 | 0.466635 | ||||||||
\(246\) | −3.41153 | −0.217511 | ||||||||
\(247\) | 1.80861 | 0.115079 | ||||||||
\(248\) | 7.00381 | 0.444743 | ||||||||
\(249\) | 8.09267 | 0.512852 | ||||||||
\(250\) | −14.3313 | −0.906392 | ||||||||
\(251\) | 29.6513 | 1.87158 | 0.935788 | − | 0.352564i | \(-0.114690\pi\) | ||||
0.935788 | + | 0.352564i | \(0.114690\pi\) | |||||||
\(252\) | 4.06673 | 0.256180 | ||||||||
\(253\) | 4.47217 | 0.281163 | ||||||||
\(254\) | −3.52339 | −0.221077 | ||||||||
\(255\) | −4.69256 | −0.293859 | ||||||||
\(256\) | 19.4137 | 1.21336 | ||||||||
\(257\) | −21.8985 | −1.36599 | −0.682996 | − | 0.730422i | \(-0.739323\pi\) | ||||
−0.682996 | + | 0.730422i | \(0.739323\pi\) | |||||||
\(258\) | −2.70424 | −0.168359 | ||||||||
\(259\) | 32.5653 | 2.02351 | ||||||||
\(260\) | 2.06167 | 0.127859 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −17.3221 | −1.07016 | ||||||||
\(263\) | −7.83697 | −0.483248 | −0.241624 | − | 0.970370i | \(-0.577680\pi\) | ||||
−0.241624 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(264\) | −7.46146 | −0.459221 | ||||||||
\(265\) | −0.461998 | −0.0283803 | ||||||||
\(266\) | 5.55536 | 0.340621 | ||||||||
\(267\) | −10.4230 | −0.637878 | ||||||||
\(268\) | 7.32159 | 0.447237 | ||||||||
\(269\) | 6.81186 | 0.415326 | 0.207663 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207663 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(270\) | 1.55719 | 0.0947676 | ||||||||
\(271\) | −20.9427 | −1.27218 | −0.636090 | − | 0.771615i | \(-0.719449\pi\) | ||||
−0.636090 | + | 0.771615i | \(0.719449\pi\) | |||||||
\(272\) | 26.2767 | 1.59326 | ||||||||
\(273\) | 8.62365 | 0.521927 | ||||||||
\(274\) | 11.1219 | 0.671898 | ||||||||
\(275\) | −18.7980 | −1.13356 | ||||||||
\(276\) | 1.04367 | 0.0628218 | ||||||||
\(277\) | 30.7080 | 1.84506 | 0.922531 | − | 0.385922i | \(-0.126117\pi\) | ||||
0.922531 | + | 0.385922i | \(0.126117\pi\) | |||||||
\(278\) | 18.8869 | 1.13276 | ||||||||
\(279\) | −4.19787 | −0.251320 | ||||||||
\(280\) | −5.80267 | −0.346776 | ||||||||
\(281\) | −29.8255 | −1.77924 | −0.889620 | − | 0.456701i | \(-0.849031\pi\) | ||||
−0.889620 | + | 0.456701i | \(0.849031\pi\) | |||||||
\(282\) | −1.91783 | −0.114205 | ||||||||
\(283\) | −17.8218 | −1.05940 | −0.529699 | − | 0.848185i | \(-0.677695\pi\) | ||||
−0.529699 | + | 0.848185i | \(0.677695\pi\) | |||||||
\(284\) | −4.62207 | −0.274269 | ||||||||
\(285\) | 0.729417 | 0.0432069 | ||||||||
\(286\) | 17.2675 | 1.02105 | ||||||||
\(287\) | −7.61956 | −0.449768 | ||||||||
\(288\) | −5.38290 | −0.317190 | ||||||||
\(289\) | 10.6397 | 0.625868 | ||||||||
\(290\) | 1.55719 | 0.0914414 | ||||||||
\(291\) | 12.3546 | 0.724239 | ||||||||
\(292\) | −0.757772 | −0.0443452 | ||||||||
\(293\) | −27.0066 | −1.57774 | −0.788871 | − | 0.614559i | \(-0.789334\pi\) | ||||
−0.788871 | + | 0.614559i | \(0.789334\pi\) | |||||||
\(294\) | 14.2763 | 0.832613 | ||||||||
\(295\) | −6.24603 | −0.363658 | ||||||||
\(296\) | −13.9438 | −0.810465 | ||||||||
\(297\) | 4.47217 | 0.259502 | ||||||||
\(298\) | −22.7745 | −1.31929 | ||||||||
\(299\) | 2.21315 | 0.127990 | ||||||||
\(300\) | −4.38689 | −0.253277 | ||||||||
\(301\) | −6.03985 | −0.348131 | ||||||||
\(302\) | −20.1360 | −1.15870 | ||||||||
\(303\) | −2.45708 | −0.141156 | ||||||||
\(304\) | −4.08448 | −0.234261 | ||||||||
\(305\) | −0.351989 | −0.0201549 | ||||||||
\(306\) | −9.17204 | −0.524331 | ||||||||
\(307\) | 12.7269 | 0.726365 | 0.363183 | − | 0.931718i | \(-0.381690\pi\) | ||||
0.363183 | + | 0.931718i | \(0.381690\pi\) | |||||||
\(308\) | 18.1871 | 1.03631 | ||||||||
\(309\) | −9.41863 | −0.535807 | ||||||||
\(310\) | −6.53689 | −0.371270 | ||||||||
\(311\) | −17.6022 | −0.998131 | −0.499066 | − | 0.866564i | \(-0.666323\pi\) | ||||
−0.499066 | + | 0.866564i | \(0.666323\pi\) | |||||||
\(312\) | −3.69246 | −0.209045 | ||||||||
\(313\) | −10.2142 | −0.577341 | −0.288671 | − | 0.957428i | \(-0.593213\pi\) | ||||
−0.288671 | + | 0.957428i | \(0.593213\pi\) | |||||||
\(314\) | −17.2077 | −0.971084 | ||||||||
\(315\) | 3.47795 | 0.195960 | ||||||||
\(316\) | −7.83471 | −0.440737 | ||||||||
\(317\) | −16.0811 | −0.903207 | −0.451603 | − | 0.892219i | \(-0.649148\pi\) | ||||
−0.451603 | + | 0.892219i | \(0.649148\pi\) | |||||||
\(318\) | −0.903018 | −0.0506387 | ||||||||
\(319\) | 4.47217 | 0.250393 | ||||||||
\(320\) | 0.540107 | 0.0301929 | ||||||||
\(321\) | 7.89713 | 0.440775 | ||||||||
\(322\) | 6.79797 | 0.378836 | ||||||||
\(323\) | −4.29635 | −0.239056 | ||||||||
\(324\) | 1.04367 | 0.0579819 | ||||||||
\(325\) | −9.30257 | −0.516014 | ||||||||
\(326\) | −31.0612 | −1.72032 | ||||||||
\(327\) | 15.7824 | 0.872769 | ||||||||
\(328\) | 3.26253 | 0.180143 | ||||||||
\(329\) | −4.28342 | −0.236152 | ||||||||
\(330\) | 6.96402 | 0.383357 | ||||||||
\(331\) | 31.5407 | 1.73364 | 0.866818 | − | 0.498625i | \(-0.166161\pi\) | ||||
0.866818 | + | 0.498625i | \(0.166161\pi\) | |||||||
\(332\) | 8.44611 | 0.463540 | ||||||||
\(333\) | 8.35747 | 0.457987 | ||||||||
\(334\) | −32.6249 | −1.78516 | ||||||||
\(335\) | 6.26157 | 0.342106 | ||||||||
\(336\) | −19.4753 | −1.06247 | ||||||||
\(337\) | −10.3837 | −0.565635 | −0.282817 | − | 0.959174i | \(-0.591269\pi\) | ||||
−0.282817 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(338\) | −14.1348 | −0.768831 | ||||||||
\(339\) | 3.23551 | 0.175729 | ||||||||
\(340\) | −4.89750 | −0.265604 | ||||||||
\(341\) | −18.7736 | −1.01665 | ||||||||
\(342\) | 1.42571 | 0.0770937 | ||||||||
\(343\) | 4.60999 | 0.248916 | ||||||||
\(344\) | 2.58614 | 0.139435 | ||||||||
\(345\) | 0.892571 | 0.0480544 | ||||||||
\(346\) | 8.64050 | 0.464516 | ||||||||
\(347\) | −16.0250 | −0.860266 | −0.430133 | − | 0.902765i | \(-0.641533\pi\) | ||||
−0.430133 | + | 0.902765i | \(0.641533\pi\) | |||||||
\(348\) | 1.04367 | 0.0559468 | ||||||||
\(349\) | 36.3793 | 1.94734 | 0.973670 | − | 0.227962i | \(-0.0732061\pi\) | ||||
0.973670 | + | 0.227962i | \(0.0732061\pi\) | |||||||
\(350\) | −28.5740 | −1.52735 | ||||||||
\(351\) | 2.21315 | 0.118129 | ||||||||
\(352\) | −24.0732 | −1.28311 | ||||||||
\(353\) | 26.5184 | 1.41143 | 0.705716 | − | 0.708495i | \(-0.250626\pi\) | ||||
0.705716 | + | 0.708495i | \(0.250626\pi\) | |||||||
\(354\) | −12.2084 | −0.648871 | ||||||||
\(355\) | −3.95289 | −0.209797 | ||||||||
\(356\) | −10.8782 | −0.576544 | ||||||||
\(357\) | −20.4855 | −1.08421 | ||||||||
\(358\) | −13.1481 | −0.694900 | ||||||||
\(359\) | 9.97949 | 0.526697 | 0.263349 | − | 0.964701i | \(-0.415173\pi\) | ||||
0.263349 | + | 0.964701i | \(0.415173\pi\) | |||||||
\(360\) | −1.48918 | −0.0784868 | ||||||||
\(361\) | −18.3322 | −0.964851 | ||||||||
\(362\) | 20.2130 | 1.06237 | ||||||||
\(363\) | 9.00031 | 0.472394 | ||||||||
\(364\) | 9.00027 | 0.471743 | ||||||||
\(365\) | −0.648062 | −0.0339211 | ||||||||
\(366\) | −0.687996 | −0.0359621 | ||||||||
\(367\) | −0.780644 | −0.0407493 | −0.0203746 | − | 0.999792i | \(-0.506486\pi\) | ||||
−0.0203746 | + | 0.999792i | \(0.506486\pi\) | |||||||
\(368\) | −4.99809 | −0.260544 | ||||||||
\(369\) | −1.95546 | −0.101797 | ||||||||
\(370\) | 13.0142 | 0.676575 | ||||||||
\(371\) | −2.01687 | −0.104711 | ||||||||
\(372\) | −4.38121 | −0.227155 | ||||||||
\(373\) | −19.3681 | −1.00284 | −0.501420 | − | 0.865204i | \(-0.667189\pi\) | ||||
−0.501420 | + | 0.865204i | \(0.667189\pi\) | |||||||
\(374\) | −41.0189 | −2.12104 | ||||||||
\(375\) | −8.21461 | −0.424201 | ||||||||
\(376\) | 1.83407 | 0.0945848 | ||||||||
\(377\) | 2.21315 | 0.113983 | ||||||||
\(378\) | 6.79797 | 0.349650 | ||||||||
\(379\) | 24.2021 | 1.24318 | 0.621590 | − | 0.783343i | \(-0.286487\pi\) | ||||
0.621590 | + | 0.783343i | \(0.286487\pi\) | |||||||
\(380\) | 0.761273 | 0.0390525 | ||||||||
\(381\) | −2.01959 | −0.103466 | ||||||||
\(382\) | −26.7332 | −1.36779 | ||||||||
\(383\) | −25.5806 | −1.30711 | −0.653553 | − | 0.756881i | \(-0.726722\pi\) | ||||
−0.653553 | + | 0.756881i | \(0.726722\pi\) | |||||||
\(384\) | 11.8215 | 0.603263 | ||||||||
\(385\) | 15.5540 | 0.792704 | ||||||||
\(386\) | 13.2490 | 0.674357 | ||||||||
\(387\) | −1.55005 | −0.0787935 | ||||||||
\(388\) | 12.8942 | 0.654601 | ||||||||
\(389\) | 7.52819 | 0.381694 | 0.190847 | − | 0.981620i | \(-0.438877\pi\) | ||||
0.190847 | + | 0.981620i | \(0.438877\pi\) | |||||||
\(390\) | 3.44630 | 0.174510 | ||||||||
\(391\) | −5.25735 | −0.265876 | ||||||||
\(392\) | −13.6528 | −0.689572 | ||||||||
\(393\) | −9.92888 | −0.500846 | ||||||||
\(394\) | −4.74593 | −0.239096 | ||||||||
\(395\) | −6.70040 | −0.337134 | ||||||||
\(396\) | 4.66749 | 0.234550 | ||||||||
\(397\) | 32.5670 | 1.63449 | 0.817245 | − | 0.576290i | \(-0.195500\pi\) | ||||
0.817245 | + | 0.576290i | \(0.195500\pi\) | |||||||
\(398\) | −20.2029 | −1.01268 | ||||||||
\(399\) | 3.18429 | 0.159414 | ||||||||
\(400\) | 21.0086 | 1.05043 | ||||||||
\(401\) | −13.5106 | −0.674689 | −0.337345 | − | 0.941381i | \(-0.609529\pi\) | ||||
−0.337345 | + | 0.941381i | \(0.609529\pi\) | |||||||
\(402\) | 12.2388 | 0.610417 | ||||||||
\(403\) | −9.29053 | −0.462794 | ||||||||
\(404\) | −2.56439 | −0.127583 | ||||||||
\(405\) | 0.892571 | 0.0443522 | ||||||||
\(406\) | 6.79797 | 0.337378 | ||||||||
\(407\) | 37.3760 | 1.85266 | ||||||||
\(408\) | 8.77147 | 0.434252 | ||||||||
\(409\) | 21.3259 | 1.05450 | 0.527248 | − | 0.849711i | \(-0.323224\pi\) | ||||
0.527248 | + | 0.849711i | \(0.323224\pi\) | |||||||
\(410\) | −3.04503 | −0.150383 | ||||||||
\(411\) | 6.37499 | 0.314455 | ||||||||
\(412\) | −9.82998 | −0.484288 | ||||||||
\(413\) | −27.2672 | −1.34173 | ||||||||
\(414\) | 1.74461 | 0.0857430 | ||||||||
\(415\) | 7.22328 | 0.354577 | ||||||||
\(416\) | −11.9132 | −0.584091 | ||||||||
\(417\) | 10.8258 | 0.530144 | ||||||||
\(418\) | 6.37603 | 0.311862 | ||||||||
\(419\) | −3.88439 | −0.189765 | −0.0948825 | − | 0.995488i | \(-0.530248\pi\) | ||||
−0.0948825 | + | 0.995488i | \(0.530248\pi\) | |||||||
\(420\) | 3.62984 | 0.177118 | ||||||||
\(421\) | −0.915374 | −0.0446126 | −0.0223063 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223063 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(422\) | −4.17113 | −0.203048 | ||||||||
\(423\) | −1.09928 | −0.0534490 | ||||||||
\(424\) | 0.863580 | 0.0419391 | ||||||||
\(425\) | 22.0983 | 1.07193 | ||||||||
\(426\) | −7.72629 | −0.374340 | ||||||||
\(427\) | −1.53662 | −0.0743623 | ||||||||
\(428\) | 8.24203 | 0.398393 | ||||||||
\(429\) | 9.89758 | 0.477860 | ||||||||
\(430\) | −2.41373 | −0.116400 | ||||||||
\(431\) | −3.51349 | −0.169239 | −0.0846195 | − | 0.996413i | \(-0.526967\pi\) | ||||
−0.0846195 | + | 0.996413i | \(0.526967\pi\) | |||||||
\(432\) | −4.99809 | −0.240471 | ||||||||
\(433\) | −15.7078 | −0.754868 | −0.377434 | − | 0.926036i | \(-0.623194\pi\) | ||||
−0.377434 | + | 0.926036i | \(0.623194\pi\) | |||||||
\(434\) | −28.5370 | −1.36982 | ||||||||
\(435\) | 0.892571 | 0.0427955 | ||||||||
\(436\) | 16.4717 | 0.788850 | ||||||||
\(437\) | 0.817209 | 0.0390924 | ||||||||
\(438\) | −1.26670 | −0.0605251 | ||||||||
\(439\) | 22.0238 | 1.05114 | 0.525569 | − | 0.850751i | \(-0.323852\pi\) | ||||
0.525569 | + | 0.850751i | \(0.323852\pi\) | |||||||
\(440\) | −6.65988 | −0.317497 | ||||||||
\(441\) | 8.18310 | 0.389671 | ||||||||
\(442\) | −20.2991 | −0.965530 | ||||||||
\(443\) | 17.2084 | 0.817595 | 0.408798 | − | 0.912625i | \(-0.365948\pi\) | ||||
0.408798 | + | 0.912625i | \(0.365948\pi\) | |||||||
\(444\) | 8.72247 | 0.413950 | ||||||||
\(445\) | −9.30327 | −0.441017 | ||||||||
\(446\) | 8.71277 | 0.412562 | ||||||||
\(447\) | −13.0542 | −0.617443 | ||||||||
\(448\) | 2.35786 | 0.111398 | ||||||||
\(449\) | −20.5864 | −0.971531 | −0.485766 | − | 0.874089i | \(-0.661459\pi\) | ||||
−0.485766 | + | 0.874089i | \(0.661459\pi\) | |||||||
\(450\) | −7.33316 | −0.345689 | ||||||||
\(451\) | −8.74516 | −0.411794 | ||||||||
\(452\) | 3.37682 | 0.158832 | ||||||||
\(453\) | −11.5418 | −0.542283 | ||||||||
\(454\) | 15.8334 | 0.743099 | ||||||||
\(455\) | 7.69722 | 0.360851 | ||||||||
\(456\) | −1.36345 | −0.0638492 | ||||||||
\(457\) | 6.35046 | 0.297062 | 0.148531 | − | 0.988908i | \(-0.452545\pi\) | ||||
0.148531 | + | 0.988908i | \(0.452545\pi\) | |||||||
\(458\) | −17.7969 | −0.831596 | ||||||||
\(459\) | −5.25735 | −0.245392 | ||||||||
\(460\) | 0.931553 | 0.0434339 | ||||||||
\(461\) | 22.8900 | 1.06609 | 0.533047 | − | 0.846086i | \(-0.321047\pi\) | ||||
0.533047 | + | 0.846086i | \(0.321047\pi\) | |||||||
\(462\) | 30.4017 | 1.41441 | ||||||||
\(463\) | 5.69016 | 0.264444 | 0.132222 | − | 0.991220i | \(-0.457789\pi\) | ||||
0.132222 | + | 0.991220i | \(0.457789\pi\) | |||||||
\(464\) | −4.99809 | −0.232031 | ||||||||
\(465\) | −3.74690 | −0.173758 | ||||||||
\(466\) | 30.5759 | 1.41640 | ||||||||
\(467\) | 31.9619 | 1.47902 | 0.739510 | − | 0.673146i | \(-0.235057\pi\) | ||||
0.739510 | + | 0.673146i | \(0.235057\pi\) | |||||||
\(468\) | 2.30981 | 0.106771 | ||||||||
\(469\) | 27.3351 | 1.26222 | ||||||||
\(470\) | −1.71180 | −0.0789592 | ||||||||
\(471\) | −9.86331 | −0.454477 | ||||||||
\(472\) | 11.6753 | 0.537397 | ||||||||
\(473\) | −6.93209 | −0.318738 | ||||||||
\(474\) | −13.0966 | −0.601545 | ||||||||
\(475\) | −3.43499 | −0.157608 | ||||||||
\(476\) | −21.3802 | −0.979960 | ||||||||
\(477\) | −0.517604 | −0.0236994 | ||||||||
\(478\) | 31.4274 | 1.43746 | ||||||||
\(479\) | 32.8406 | 1.50053 | 0.750263 | − | 0.661140i | \(-0.229927\pi\) | ||||
0.750263 | + | 0.661140i | \(0.229927\pi\) | |||||||
\(480\) | −4.80462 | −0.219300 | ||||||||
\(481\) | 18.4963 | 0.843360 | ||||||||
\(482\) | −18.1200 | −0.825342 | ||||||||
\(483\) | 3.89655 | 0.177299 | ||||||||
\(484\) | 9.39338 | 0.426972 | ||||||||
\(485\) | 11.0273 | 0.500726 | ||||||||
\(486\) | 1.74461 | 0.0791372 | ||||||||
\(487\) | 38.6272 | 1.75036 | 0.875182 | − | 0.483793i | \(-0.160741\pi\) | ||||
0.875182 | + | 0.483793i | \(0.160741\pi\) | |||||||
\(488\) | 0.657949 | 0.0297839 | ||||||||
\(489\) | −17.8041 | −0.805127 | ||||||||
\(490\) | 12.7426 | 0.575654 | ||||||||
\(491\) | −23.2977 | −1.05141 | −0.525704 | − | 0.850667i | \(-0.676198\pi\) | ||||
−0.525704 | + | 0.850667i | \(0.676198\pi\) | |||||||
\(492\) | −2.04086 | −0.0920093 | ||||||||
\(493\) | −5.25735 | −0.236779 | ||||||||
\(494\) | 3.15532 | 0.141964 | ||||||||
\(495\) | 3.99173 | 0.179415 | ||||||||
\(496\) | 20.9814 | 0.942091 | ||||||||
\(497\) | −17.2565 | −0.774058 | ||||||||
\(498\) | 14.1186 | 0.632669 | ||||||||
\(499\) | 14.8514 | 0.664841 | 0.332421 | − | 0.943131i | \(-0.392135\pi\) | ||||
0.332421 | + | 0.943131i | \(0.392135\pi\) | |||||||
\(500\) | −8.57337 | −0.383413 | ||||||||
\(501\) | −18.7004 | −0.835471 | ||||||||
\(502\) | 51.7301 | 2.30883 | ||||||||
\(503\) | −44.0329 | −1.96333 | −0.981666 | − | 0.190610i | \(-0.938953\pi\) | ||||
−0.981666 | + | 0.190610i | \(0.938953\pi\) | |||||||
\(504\) | −6.50108 | −0.289581 | ||||||||
\(505\) | −2.19312 | −0.0975925 | ||||||||
\(506\) | 7.80221 | 0.346850 | ||||||||
\(507\) | −8.10197 | −0.359821 | ||||||||
\(508\) | −2.10779 | −0.0935179 | ||||||||
\(509\) | 26.1277 | 1.15809 | 0.579044 | − | 0.815296i | \(-0.303426\pi\) | ||||
0.579044 | + | 0.815296i | \(0.303426\pi\) | |||||||
\(510\) | −8.18670 | −0.362513 | ||||||||
\(511\) | −2.82914 | −0.125154 | ||||||||
\(512\) | 10.2264 | 0.451947 | ||||||||
\(513\) | 0.817209 | 0.0360806 | ||||||||
\(514\) | −38.2044 | −1.68513 | ||||||||
\(515\) | −8.40680 | −0.370448 | ||||||||
\(516\) | −1.61775 | −0.0712174 | ||||||||
\(517\) | −4.91619 | −0.216214 | ||||||||
\(518\) | 56.8138 | 2.49626 | ||||||||
\(519\) | 4.95268 | 0.217398 | ||||||||
\(520\) | −3.29578 | −0.144530 | ||||||||
\(521\) | −19.9360 | −0.873412 | −0.436706 | − | 0.899604i | \(-0.643855\pi\) | ||||
−0.436706 | + | 0.899604i | \(0.643855\pi\) | |||||||
\(522\) | 1.74461 | 0.0763596 | ||||||||
\(523\) | 31.3922 | 1.37268 | 0.686342 | − | 0.727279i | \(-0.259215\pi\) | ||||
0.686342 | + | 0.727279i | \(0.259215\pi\) | |||||||
\(524\) | −10.3625 | −0.452689 | ||||||||
\(525\) | −16.3784 | −0.714813 | ||||||||
\(526\) | −13.6725 | −0.596148 | ||||||||
\(527\) | 22.0697 | 0.961371 | ||||||||
\(528\) | −22.3523 | −0.972760 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.806007 | −0.0350107 | ||||||||
\(531\) | −6.99779 | −0.303678 | ||||||||
\(532\) | 3.32336 | 0.144086 | ||||||||
\(533\) | −4.32773 | −0.187455 | ||||||||
\(534\) | −18.1841 | −0.786904 | ||||||||
\(535\) | 7.04875 | 0.304744 | ||||||||
\(536\) | −11.7043 | −0.505549 | ||||||||
\(537\) | −7.53642 | −0.325221 | ||||||||
\(538\) | 11.8841 | 0.512358 | ||||||||
\(539\) | 36.5962 | 1.57631 | ||||||||
\(540\) | 0.931553 | 0.0400876 | ||||||||
\(541\) | −7.55331 | −0.324742 | −0.162371 | − | 0.986730i | \(-0.551914\pi\) | ||||
−0.162371 | + | 0.986730i | \(0.551914\pi\) | |||||||
\(542\) | −36.5370 | −1.56940 | ||||||||
\(543\) | 11.5859 | 0.497200 | ||||||||
\(544\) | 28.2998 | 1.21334 | ||||||||
\(545\) | 14.0869 | 0.603417 | ||||||||
\(546\) | 15.0449 | 0.643863 | ||||||||
\(547\) | −0.579523 | −0.0247786 | −0.0123893 | − | 0.999923i | \(-0.503944\pi\) | ||||
−0.0123893 | + | 0.999923i | \(0.503944\pi\) | |||||||
\(548\) | 6.65341 | 0.284220 | ||||||||
\(549\) | −0.394355 | −0.0168306 | ||||||||
\(550\) | −32.7951 | −1.39839 | ||||||||
\(551\) | 0.817209 | 0.0348143 | ||||||||
\(552\) | −1.66842 | −0.0710126 | ||||||||
\(553\) | −29.2508 | −1.24387 | ||||||||
\(554\) | 53.5735 | 2.27612 | ||||||||
\(555\) | 7.45964 | 0.316644 | ||||||||
\(556\) | 11.2986 | 0.479169 | ||||||||
\(557\) | −10.3346 | −0.437891 | −0.218945 | − | 0.975737i | \(-0.570262\pi\) | ||||
−0.218945 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(558\) | −7.32367 | −0.310035 | ||||||||
\(559\) | −3.43050 | −0.145095 | ||||||||
\(560\) | −17.3831 | −0.734570 | ||||||||
\(561\) | −23.5118 | −0.992668 | ||||||||
\(562\) | −52.0340 | −2.19492 | ||||||||
\(563\) | −15.2717 | −0.643627 | −0.321814 | − | 0.946803i | \(-0.604292\pi\) | ||||
−0.321814 | + | 0.946803i | \(0.604292\pi\) | |||||||
\(564\) | −1.14729 | −0.0483098 | ||||||||
\(565\) | 2.88793 | 0.121496 | ||||||||
\(566\) | −31.0922 | −1.30690 | ||||||||
\(567\) | 3.89655 | 0.163640 | ||||||||
\(568\) | 7.38885 | 0.310029 | ||||||||
\(569\) | 10.9113 | 0.457424 | 0.228712 | − | 0.973494i | \(-0.426549\pi\) | ||||
0.228712 | + | 0.973494i | \(0.426549\pi\) | |||||||
\(570\) | 1.27255 | 0.0533012 | ||||||||
\(571\) | 31.1468 | 1.30345 | 0.651726 | − | 0.758455i | \(-0.274045\pi\) | ||||
0.651726 | + | 0.758455i | \(0.274045\pi\) | |||||||
\(572\) | 10.3298 | 0.431913 | ||||||||
\(573\) | −15.3233 | −0.640138 | ||||||||
\(574\) | −13.2932 | −0.554846 | ||||||||
\(575\) | −4.20332 | −0.175290 | ||||||||
\(576\) | 0.605114 | 0.0252131 | ||||||||
\(577\) | 20.3250 | 0.846141 | 0.423071 | − | 0.906097i | \(-0.360952\pi\) | ||||
0.423071 | + | 0.906097i | \(0.360952\pi\) | |||||||
\(578\) | 18.5622 | 0.772087 | ||||||||
\(579\) | 7.59424 | 0.315606 | ||||||||
\(580\) | 0.931553 | 0.0386806 | ||||||||
\(581\) | 31.5335 | 1.30823 | ||||||||
\(582\) | 21.5540 | 0.893441 | ||||||||
\(583\) | −2.31481 | −0.0958697 | ||||||||
\(584\) | 1.21138 | 0.0501271 | ||||||||
\(585\) | 1.97539 | 0.0816725 | ||||||||
\(586\) | −47.1161 | −1.94635 | ||||||||
\(587\) | −25.9647 | −1.07168 | −0.535839 | − | 0.844320i | \(-0.680004\pi\) | ||||
−0.535839 | + | 0.844320i | \(0.680004\pi\) | |||||||
\(588\) | 8.54048 | 0.352204 | ||||||||
\(589\) | −3.43054 | −0.141353 | ||||||||
\(590\) | −10.8969 | −0.448618 | ||||||||
\(591\) | −2.72033 | −0.111899 | ||||||||
\(592\) | −41.7714 | −1.71679 | ||||||||
\(593\) | −26.0859 | −1.07122 | −0.535609 | − | 0.844466i | \(-0.679918\pi\) | ||||
−0.535609 | + | 0.844466i | \(0.679918\pi\) | |||||||
\(594\) | 7.80221 | 0.320128 | ||||||||
\(595\) | −18.2848 | −0.749603 | ||||||||
\(596\) | −13.6243 | −0.558074 | ||||||||
\(597\) | −11.5802 | −0.473945 | ||||||||
\(598\) | 3.86109 | 0.157892 | ||||||||
\(599\) | 28.1346 | 1.14955 | 0.574774 | − | 0.818312i | \(-0.305090\pi\) | ||||
0.574774 | + | 0.818312i | \(0.305090\pi\) | |||||||
\(600\) | 7.01290 | 0.286300 | ||||||||
\(601\) | −16.9863 | −0.692884 | −0.346442 | − | 0.938071i | \(-0.612610\pi\) | ||||
−0.346442 | + | 0.938071i | \(0.612610\pi\) | |||||||
\(602\) | −10.5372 | −0.429464 | ||||||||
\(603\) | 7.01521 | 0.285681 | ||||||||
\(604\) | −12.0459 | −0.490141 | ||||||||
\(605\) | 8.03341 | 0.326605 | ||||||||
\(606\) | −4.28666 | −0.174133 | ||||||||
\(607\) | 7.50970 | 0.304809 | 0.152405 | − | 0.988318i | \(-0.451298\pi\) | ||||
0.152405 | + | 0.988318i | \(0.451298\pi\) | |||||||
\(608\) | −4.39895 | −0.178401 | ||||||||
\(609\) | 3.89655 | 0.157896 | ||||||||
\(610\) | −0.614085 | −0.0248636 | ||||||||
\(611\) | −2.43288 | −0.0984238 | ||||||||
\(612\) | −5.48696 | −0.221797 | ||||||||
\(613\) | 44.6186 | 1.80213 | 0.901065 | − | 0.433684i | \(-0.142787\pi\) | ||||
0.901065 | + | 0.433684i | \(0.142787\pi\) | |||||||
\(614\) | 22.2036 | 0.896064 | ||||||||
\(615\) | −1.74539 | −0.0703809 | ||||||||
\(616\) | −29.0739 | −1.17142 | ||||||||
\(617\) | 9.13991 | 0.367959 | 0.183980 | − | 0.982930i | \(-0.441102\pi\) | ||||
0.183980 | + | 0.982930i | \(0.441102\pi\) | |||||||
\(618\) | −16.4319 | −0.660987 | ||||||||
\(619\) | −12.9320 | −0.519779 | −0.259890 | − | 0.965638i | \(-0.583686\pi\) | ||||
−0.259890 | + | 0.965638i | \(0.583686\pi\) | |||||||
\(620\) | −3.91054 | −0.157051 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −30.7091 | −1.23132 | ||||||||
\(623\) | −40.6138 | −1.62716 | ||||||||
\(624\) | −11.0615 | −0.442816 | ||||||||
\(625\) | 13.6845 | 0.547378 | ||||||||
\(626\) | −17.8198 | −0.712224 | ||||||||
\(627\) | 3.65470 | 0.145955 | ||||||||
\(628\) | −10.2941 | −0.410778 | ||||||||
\(629\) | −43.9382 | −1.75193 | ||||||||
\(630\) | 6.06767 | 0.241742 | ||||||||
\(631\) | −10.7411 | −0.427598 | −0.213799 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213799 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(632\) | 12.5246 | 0.498201 | ||||||||
\(633\) | −2.39087 | −0.0950284 | ||||||||
\(634\) | −28.0554 | −1.11422 | ||||||||
\(635\) | −1.80262 | −0.0715349 | ||||||||
\(636\) | −0.540209 | −0.0214207 | ||||||||
\(637\) | 18.1104 | 0.717561 | ||||||||
\(638\) | 7.80221 | 0.308892 | ||||||||
\(639\) | −4.42865 | −0.175195 | ||||||||
\(640\) | 10.5515 | 0.417085 | ||||||||
\(641\) | −7.68854 | −0.303679 | −0.151839 | − | 0.988405i | \(-0.548520\pi\) | ||||
−0.151839 | + | 0.988405i | \(0.548520\pi\) | |||||||
\(642\) | 13.7774 | 0.543752 | ||||||||
\(643\) | 17.2471 | 0.680161 | 0.340080 | − | 0.940396i | \(-0.389546\pi\) | ||||
0.340080 | + | 0.940396i | \(0.389546\pi\) | |||||||
\(644\) | 4.06673 | 0.160251 | ||||||||
\(645\) | −1.38353 | −0.0544765 | ||||||||
\(646\) | −7.49547 | −0.294905 | ||||||||
\(647\) | −4.19619 | −0.164969 | −0.0824846 | − | 0.996592i | \(-0.526286\pi\) | ||||
−0.0824846 | + | 0.996592i | \(0.526286\pi\) | |||||||
\(648\) | −1.66842 | −0.0655417 | ||||||||
\(649\) | −31.2953 | −1.22845 | ||||||||
\(650\) | −16.2294 | −0.636569 | ||||||||
\(651\) | −16.3572 | −0.641090 | ||||||||
\(652\) | −18.5816 | −0.727712 | ||||||||
\(653\) | −6.76412 | −0.264701 | −0.132350 | − | 0.991203i | \(-0.542252\pi\) | ||||
−0.132350 | + | 0.991203i | \(0.542252\pi\) | |||||||
\(654\) | 27.5342 | 1.07667 | ||||||||
\(655\) | −8.86223 | −0.346276 | ||||||||
\(656\) | 9.77358 | 0.381594 | ||||||||
\(657\) | −0.726062 | −0.0283264 | ||||||||
\(658\) | −7.47290 | −0.291324 | ||||||||
\(659\) | −35.0908 | −1.36694 | −0.683471 | − | 0.729977i | \(-0.739531\pi\) | ||||
−0.683471 | + | 0.729977i | \(0.739531\pi\) | |||||||
\(660\) | 4.16606 | 0.162164 | ||||||||
\(661\) | 18.0132 | 0.700632 | 0.350316 | − | 0.936632i | \(-0.386074\pi\) | ||||
0.350316 | + | 0.936632i | \(0.386074\pi\) | |||||||
\(662\) | 55.0264 | 2.13866 | ||||||||
\(663\) | −11.6353 | −0.451878 | ||||||||
\(664\) | −13.5020 | −0.523978 | ||||||||
\(665\) | 2.84221 | 0.110216 | ||||||||
\(666\) | 14.5806 | 0.564985 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −19.5171 | −0.755139 | ||||||||
\(669\) | 4.99410 | 0.193083 | ||||||||
\(670\) | 10.9240 | 0.422032 | ||||||||
\(671\) | −1.76362 | −0.0680838 | ||||||||
\(672\) | −20.9747 | −0.809118 | ||||||||
\(673\) | 37.7043 | 1.45339 | 0.726697 | − | 0.686958i | \(-0.241054\pi\) | ||||
0.726697 | + | 0.686958i | \(0.241054\pi\) | |||||||
\(674\) | −18.1155 | −0.697782 | ||||||||
\(675\) | −4.20332 | −0.161786 | ||||||||
\(676\) | −8.45581 | −0.325223 | ||||||||
\(677\) | 10.7829 | 0.414421 | 0.207211 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207211 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(678\) | 5.64472 | 0.216784 | ||||||||
\(679\) | 48.1402 | 1.84745 | ||||||||
\(680\) | 7.82916 | 0.300234 | ||||||||
\(681\) | 9.07560 | 0.347778 | ||||||||
\(682\) | −32.7527 | −1.25416 | ||||||||
\(683\) | 17.3465 | 0.663744 | 0.331872 | − | 0.943324i | \(-0.392320\pi\) | ||||
0.331872 | + | 0.943324i | \(0.392320\pi\) | |||||||
\(684\) | 0.852899 | 0.0326114 | ||||||||
\(685\) | 5.69013 | 0.217409 | ||||||||
\(686\) | 8.04266 | 0.307070 | ||||||||
\(687\) | −10.2011 | −0.389196 | ||||||||
\(688\) | 7.74730 | 0.295363 | ||||||||
\(689\) | −1.14553 | −0.0436414 | ||||||||
\(690\) | 1.55719 | 0.0592812 | ||||||||
\(691\) | 7.94187 | 0.302123 | 0.151061 | − | 0.988524i | \(-0.451731\pi\) | ||||
0.151061 | + | 0.988524i | \(0.451731\pi\) | |||||||
\(692\) | 5.16898 | 0.196495 | ||||||||
\(693\) | 17.4260 | 0.661960 | ||||||||
\(694\) | −27.9574 | −1.06125 | ||||||||
\(695\) | 9.66283 | 0.366532 | ||||||||
\(696\) | −1.66842 | −0.0632413 | ||||||||
\(697\) | 10.2806 | 0.389404 | ||||||||
\(698\) | 63.4678 | 2.40229 | ||||||||
\(699\) | 17.5259 | 0.662891 | ||||||||
\(700\) | −17.0937 | −0.646083 | ||||||||
\(701\) | 31.3499 | 1.18407 | 0.592035 | − | 0.805913i | \(-0.298325\pi\) | ||||
0.592035 | + | 0.805913i | \(0.298325\pi\) | |||||||
\(702\) | 3.86109 | 0.145727 | ||||||||
\(703\) | 6.82980 | 0.257591 | ||||||||
\(704\) | 2.70617 | 0.101993 | ||||||||
\(705\) | −0.981189 | −0.0369537 | ||||||||
\(706\) | 46.2643 | 1.74118 | ||||||||
\(707\) | −9.57414 | −0.360073 | ||||||||
\(708\) | −7.30341 | −0.274479 | ||||||||
\(709\) | 3.77036 | 0.141599 | 0.0707995 | − | 0.997491i | \(-0.477445\pi\) | ||||
0.0707995 | + | 0.997491i | \(0.477445\pi\) | |||||||
\(710\) | −6.89626 | −0.258812 | ||||||||
\(711\) | −7.50686 | −0.281529 | ||||||||
\(712\) | 17.3899 | 0.651716 | ||||||||
\(713\) | −4.19787 | −0.157212 | ||||||||
\(714\) | −35.7393 | −1.33751 | ||||||||
\(715\) | 8.83430 | 0.330384 | ||||||||
\(716\) | −7.86556 | −0.293950 | ||||||||
\(717\) | 18.0140 | 0.672745 | ||||||||
\(718\) | 17.4103 | 0.649748 | ||||||||
\(719\) | 2.39941 | 0.0894828 | 0.0447414 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447414 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(720\) | −4.46115 | −0.166257 | ||||||||
\(721\) | −36.7002 | −1.36679 | ||||||||
\(722\) | −31.9825 | −1.19027 | ||||||||
\(723\) | −10.3862 | −0.386269 | ||||||||
\(724\) | 12.0919 | 0.449393 | ||||||||
\(725\) | −4.20332 | −0.156107 | ||||||||
\(726\) | 15.7021 | 0.582758 | ||||||||
\(727\) | 5.76498 | 0.213811 | 0.106906 | − | 0.994269i | \(-0.465906\pi\) | ||||
0.106906 | + | 0.994269i | \(0.465906\pi\) | |||||||
\(728\) | −14.3879 | −0.533250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.13062 | −0.0418460 | ||||||||
\(731\) | 8.14917 | 0.301408 | ||||||||
\(732\) | −0.411577 | −0.0152123 | ||||||||
\(733\) | −9.54781 | −0.352656 | −0.176328 | − | 0.984331i | \(-0.556422\pi\) | ||||
−0.176328 | + | 0.984331i | \(0.556422\pi\) | |||||||
\(734\) | −1.36192 | −0.0502694 | ||||||||
\(735\) | 7.30399 | 0.269412 | ||||||||
\(736\) | −5.38290 | −0.198416 | ||||||||
\(737\) | 31.3732 | 1.15565 | ||||||||
\(738\) | −3.41153 | −0.125580 | ||||||||
\(739\) | 7.33328 | 0.269759 | 0.134879 | − | 0.990862i | \(-0.456935\pi\) | ||||
0.134879 | + | 0.990862i | \(0.456935\pi\) | |||||||
\(740\) | 7.78542 | 0.286198 | ||||||||
\(741\) | 1.80861 | 0.0664408 | ||||||||
\(742\) | −3.51865 | −0.129174 | ||||||||
\(743\) | 33.1647 | 1.21670 | 0.608348 | − | 0.793671i | \(-0.291833\pi\) | ||||
0.608348 | + | 0.793671i | \(0.291833\pi\) | |||||||
\(744\) | 7.00381 | 0.256772 | ||||||||
\(745\) | −11.6518 | −0.426889 | ||||||||
\(746\) | −33.7898 | −1.23713 | ||||||||
\(747\) | 8.09267 | 0.296095 | ||||||||
\(748\) | −24.5386 | −0.897221 | ||||||||
\(749\) | 30.7716 | 1.12437 | ||||||||
\(750\) | −14.3313 | −0.523306 | ||||||||
\(751\) | −18.2886 | −0.667362 | −0.333681 | − | 0.942686i | \(-0.608291\pi\) | ||||
−0.333681 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(752\) | 5.49432 | 0.200357 | ||||||||
\(753\) | 29.6513 | 1.08055 | ||||||||
\(754\) | 3.86109 | 0.140613 | ||||||||
\(755\) | −10.3019 | −0.374925 | ||||||||
\(756\) | 4.06673 | 0.147905 | ||||||||
\(757\) | −16.9297 | −0.615320 | −0.307660 | − | 0.951496i | \(-0.599546\pi\) | ||||
−0.307660 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(758\) | 42.2234 | 1.53362 | ||||||||
\(759\) | 4.47217 | 0.162330 | ||||||||
\(760\) | −1.21697 | −0.0441442 | ||||||||
\(761\) | −14.6565 | −0.531297 | −0.265649 | − | 0.964070i | \(-0.585586\pi\) | ||||
−0.265649 | + | 0.964070i | \(0.585586\pi\) | |||||||
\(762\) | −3.52339 | −0.127639 | ||||||||
\(763\) | 61.4969 | 2.22634 | ||||||||
\(764\) | −15.9925 | −0.578588 | ||||||||
\(765\) | −4.69256 | −0.169660 | ||||||||
\(766\) | −44.6282 | −1.61248 | ||||||||
\(767\) | −15.4872 | −0.559209 | ||||||||
\(768\) | 19.4137 | 0.700531 | ||||||||
\(769\) | −15.9253 | −0.574282 | −0.287141 | − | 0.957888i | \(-0.592705\pi\) | ||||
−0.287141 | + | 0.957888i | \(0.592705\pi\) | |||||||
\(770\) | 27.1357 | 0.977901 | ||||||||
\(771\) | −21.8985 | −0.788656 | ||||||||
\(772\) | 7.92591 | 0.285260 | ||||||||
\(773\) | 29.0904 | 1.04631 | 0.523154 | − | 0.852238i | \(-0.324755\pi\) | ||||
0.523154 | + | 0.852238i | \(0.324755\pi\) | |||||||
\(774\) | −2.70424 | −0.0972019 | ||||||||
\(775\) | 17.6450 | 0.633827 | ||||||||
\(776\) | −20.6126 | −0.739950 | ||||||||
\(777\) | 32.5653 | 1.16827 | ||||||||
\(778\) | 13.1338 | 0.470869 | ||||||||
\(779\) | −1.59802 | −0.0572551 | ||||||||
\(780\) | 2.06167 | 0.0738195 | ||||||||
\(781\) | −19.8057 | −0.708704 | ||||||||
\(782\) | −9.17204 | −0.327992 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −40.8999 | −1.46071 | ||||||||
\(785\) | −8.80370 | −0.314218 | ||||||||
\(786\) | −17.3221 | −0.617857 | ||||||||
\(787\) | 4.37350 | 0.155898 | 0.0779492 | − | 0.996957i | \(-0.475163\pi\) | ||||
0.0779492 | + | 0.996957i | \(0.475163\pi\) | |||||||
\(788\) | −2.83914 | −0.101140 | ||||||||
\(789\) | −7.83697 | −0.279003 | ||||||||
\(790\) | −11.6896 | −0.415898 | ||||||||
\(791\) | 12.6073 | 0.448266 | ||||||||
\(792\) | −7.46146 | −0.265131 | ||||||||
\(793\) | −0.872766 | −0.0309928 | ||||||||
\(794\) | 56.8168 | 2.01635 | ||||||||
\(795\) | −0.461998 | −0.0163854 | ||||||||
\(796\) | −12.0859 | −0.428374 | ||||||||
\(797\) | −3.40045 | −0.120450 | −0.0602251 | − | 0.998185i | \(-0.519182\pi\) | ||||
−0.0602251 | + | 0.998185i | \(0.519182\pi\) | |||||||
\(798\) | 5.55536 | 0.196658 | ||||||||
\(799\) | 5.77932 | 0.204458 | ||||||||
\(800\) | 22.6260 | 0.799951 | ||||||||
\(801\) | −10.4230 | −0.368279 | ||||||||
\(802\) | −23.5708 | −0.832315 | ||||||||
\(803\) | −3.24707 | −0.114587 | ||||||||
\(804\) | 7.32159 | 0.258213 | ||||||||
\(805\) | 3.47795 | 0.122582 | ||||||||
\(806\) | −16.2084 | −0.570916 | ||||||||
\(807\) | 6.81186 | 0.239789 | ||||||||
\(808\) | 4.09944 | 0.144218 | ||||||||
\(809\) | −30.2188 | −1.06244 | −0.531218 | − | 0.847235i | \(-0.678266\pi\) | ||||
−0.531218 | + | 0.847235i | \(0.678266\pi\) | |||||||
\(810\) | 1.55719 | 0.0547141 | ||||||||
\(811\) | 35.8361 | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283388\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283388\pi\) | |||||||
\(812\) | 4.06673 | 0.142714 | ||||||||
\(813\) | −20.9427 | −0.734494 | ||||||||
\(814\) | 65.2067 | 2.28549 | ||||||||
\(815\) | −15.8914 | −0.556651 | ||||||||
\(816\) | 26.2767 | 0.919870 | ||||||||
\(817\) | −1.26672 | −0.0443168 | ||||||||
\(818\) | 37.2054 | 1.30086 | ||||||||
\(819\) | 8.62365 | 0.301335 | ||||||||
\(820\) | −1.82162 | −0.0636136 | ||||||||
\(821\) | −35.2255 | −1.22938 | −0.614689 | − | 0.788770i | \(-0.710718\pi\) | ||||
−0.614689 | + | 0.788770i | \(0.710718\pi\) | |||||||
\(822\) | 11.1219 | 0.387921 | ||||||||
\(823\) | −31.0109 | −1.08097 | −0.540485 | − | 0.841353i | \(-0.681759\pi\) | ||||
−0.540485 | + | 0.841353i | \(0.681759\pi\) | |||||||
\(824\) | 15.7142 | 0.547431 | ||||||||
\(825\) | −18.7980 | −0.654461 | ||||||||
\(826\) | −47.5708 | −1.65520 | ||||||||
\(827\) | −6.42598 | −0.223453 | −0.111727 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111727 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(828\) | 1.04367 | 0.0362702 | ||||||||
\(829\) | −9.29528 | −0.322838 | −0.161419 | − | 0.986886i | \(-0.551607\pi\) | ||||
−0.161419 | + | 0.986886i | \(0.551607\pi\) | |||||||
\(830\) | 12.6018 | 0.437416 | ||||||||
\(831\) | 30.7080 | 1.06525 | ||||||||
\(832\) | 1.33921 | 0.0464287 | ||||||||
\(833\) | −43.0214 | −1.49060 | ||||||||
\(834\) | 18.8869 | 0.654000 | ||||||||
\(835\) | −16.6914 | −0.577630 | ||||||||
\(836\) | 3.81431 | 0.131921 | ||||||||
\(837\) | −4.19787 | −0.145100 | ||||||||
\(838\) | −6.77676 | −0.234099 | ||||||||
\(839\) | 19.1022 | 0.659481 | 0.329740 | − | 0.944072i | \(-0.393039\pi\) | ||||
0.329740 | + | 0.944072i | \(0.393039\pi\) | |||||||
\(840\) | −5.80267 | −0.200211 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.59697 | −0.0550353 | ||||||||
\(843\) | −29.8255 | −1.02725 | ||||||||
\(844\) | −2.49528 | −0.0858912 | ||||||||
\(845\) | −7.23158 | −0.248774 | ||||||||
\(846\) | −1.91783 | −0.0659362 | ||||||||
\(847\) | 35.0701 | 1.20502 | ||||||||
\(848\) | 2.58703 | 0.0888390 | ||||||||
\(849\) | −17.8218 | −0.611644 | ||||||||
\(850\) | 38.5530 | 1.32236 | ||||||||
\(851\) | 8.35747 | 0.286490 | ||||||||
\(852\) | −4.62207 | −0.158349 | ||||||||
\(853\) | −25.2028 | −0.862929 | −0.431465 | − | 0.902130i | \(-0.642003\pi\) | ||||
−0.431465 | + | 0.902130i | \(0.642003\pi\) | |||||||
\(854\) | −2.68081 | −0.0917354 | ||||||||
\(855\) | 0.729417 | 0.0249455 | ||||||||
\(856\) | −13.1757 | −0.450337 | ||||||||
\(857\) | 13.0587 | 0.446075 | 0.223038 | − | 0.974810i | \(-0.428403\pi\) | ||||
0.223038 | + | 0.974810i | \(0.428403\pi\) | |||||||
\(858\) | 17.2675 | 0.589501 | ||||||||
\(859\) | 10.3899 | 0.354498 | 0.177249 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177249 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(860\) | −1.44395 | −0.0492384 | ||||||||
\(861\) | −7.61956 | −0.259674 | ||||||||
\(862\) | −6.12968 | −0.208778 | ||||||||
\(863\) | −4.29004 | −0.146035 | −0.0730173 | − | 0.997331i | \(-0.523263\pi\) | ||||
−0.0730173 | + | 0.997331i | \(0.523263\pi\) | |||||||
\(864\) | −5.38290 | −0.183130 | ||||||||
\(865\) | 4.42061 | 0.150305 | ||||||||
\(866\) | −27.4040 | −0.931226 | ||||||||
\(867\) | 10.6397 | 0.361345 | ||||||||
\(868\) | −17.0716 | −0.579448 | ||||||||
\(869\) | −33.5719 | −1.13885 | ||||||||
\(870\) | 1.55719 | 0.0527937 | ||||||||
\(871\) | 15.5257 | 0.526069 | ||||||||
\(872\) | −26.3317 | −0.891703 | ||||||||
\(873\) | 12.3546 | 0.418139 | ||||||||
\(874\) | 1.42571 | 0.0482255 | ||||||||
\(875\) | −32.0086 | −1.08209 | ||||||||
\(876\) | −0.757772 | −0.0256027 | ||||||||
\(877\) | −45.0380 | −1.52082 | −0.760412 | − | 0.649441i | \(-0.775003\pi\) | ||||
−0.760412 | + | 0.649441i | \(0.775003\pi\) | |||||||
\(878\) | 38.4230 | 1.29671 | ||||||||
\(879\) | −27.0066 | −0.910910 | ||||||||
\(880\) | −19.9510 | −0.672549 | ||||||||
\(881\) | −57.5805 | −1.93994 | −0.969969 | − | 0.243229i | \(-0.921793\pi\) | ||||
−0.969969 | + | 0.243229i | \(0.921793\pi\) | |||||||
\(882\) | 14.2763 | 0.480709 | ||||||||
\(883\) | 30.9156 | 1.04039 | 0.520197 | − | 0.854046i | \(-0.325859\pi\) | ||||
0.520197 | + | 0.854046i | \(0.325859\pi\) | |||||||
\(884\) | −12.1435 | −0.408429 | ||||||||
\(885\) | −6.24603 | −0.209958 | ||||||||
\(886\) | 30.0220 | 1.00861 | ||||||||
\(887\) | −45.0355 | −1.51214 | −0.756072 | − | 0.654488i | \(-0.772884\pi\) | ||||
−0.756072 | + | 0.654488i | \(0.772884\pi\) | |||||||
\(888\) | −13.9438 | −0.467922 | ||||||||
\(889\) | −7.86941 | −0.263932 | ||||||||
\(890\) | −16.2306 | −0.544051 | ||||||||
\(891\) | 4.47217 | 0.149823 | ||||||||
\(892\) | 5.21221 | 0.174518 | ||||||||
\(893\) | −0.898345 | −0.0300620 | ||||||||
\(894\) | −22.7745 | −0.761694 | ||||||||
\(895\) | −6.72679 | −0.224852 | ||||||||
\(896\) | 46.0630 | 1.53886 | ||||||||
\(897\) | 2.21315 | 0.0738949 | ||||||||
\(898\) | −35.9153 | −1.19851 | ||||||||
\(899\) | −4.19787 | −0.140007 | ||||||||
\(900\) | −4.38689 | −0.146230 | ||||||||
\(901\) | 2.72122 | 0.0906571 | ||||||||
\(902\) | −15.2569 | −0.508000 | ||||||||
\(903\) | −6.03985 | −0.200994 | ||||||||
\(904\) | −5.39820 | −0.179541 | ||||||||
\(905\) | 10.3413 | 0.343755 | ||||||||
\(906\) | −20.1360 | −0.668975 | ||||||||
\(907\) | 39.2826 | 1.30436 | 0.652179 | − | 0.758065i | \(-0.273855\pi\) | ||||
0.652179 | + | 0.758065i | \(0.273855\pi\) | |||||||
\(908\) | 9.47197 | 0.314338 | ||||||||
\(909\) | −2.45708 | −0.0814963 | ||||||||
\(910\) | 13.4287 | 0.445156 | ||||||||
\(911\) | 15.1711 | 0.502640 | 0.251320 | − | 0.967904i | \(-0.419135\pi\) | ||||
0.251320 | + | 0.967904i | \(0.419135\pi\) | |||||||
\(912\) | −4.08448 | −0.135251 | ||||||||
\(913\) | 36.1918 | 1.19777 | ||||||||
\(914\) | 11.0791 | 0.366464 | ||||||||
\(915\) | −0.351989 | −0.0116364 | ||||||||
\(916\) | −10.6466 | −0.351774 | ||||||||
\(917\) | −38.6884 | −1.27760 | ||||||||
\(918\) | −9.17204 | −0.302723 | ||||||||
\(919\) | 34.8813 | 1.15063 | 0.575315 | − | 0.817932i | \(-0.304880\pi\) | ||||
0.575315 | + | 0.817932i | \(0.304880\pi\) | |||||||
\(920\) | −1.48918 | −0.0490969 | ||||||||
\(921\) | 12.7269 | 0.419367 | ||||||||
\(922\) | 39.9342 | 1.31516 | ||||||||
\(923\) | −9.80128 | −0.322613 | ||||||||
\(924\) | 18.1871 | 0.598311 | ||||||||
\(925\) | −35.1291 | −1.15504 | ||||||||
\(926\) | 9.92713 | 0.326226 | ||||||||
\(927\) | −9.41863 | −0.309349 | ||||||||
\(928\) | −5.38290 | −0.176702 | ||||||||
\(929\) | 5.52578 | 0.181295 | 0.0906475 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906475 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(930\) | −6.53689 | −0.214353 | ||||||||
\(931\) | 6.68730 | 0.219167 | ||||||||
\(932\) | 18.2913 | 0.599152 | ||||||||
\(933\) | −17.6022 | −0.576271 | ||||||||
\(934\) | 55.7611 | 1.82456 | ||||||||
\(935\) | −20.9859 | −0.686313 | ||||||||
\(936\) | −3.69246 | −0.120692 | ||||||||
\(937\) | 19.9977 | 0.653297 | 0.326649 | − | 0.945146i | \(-0.394081\pi\) | ||||
0.326649 | + | 0.945146i | \(0.394081\pi\) | |||||||
\(938\) | 47.6892 | 1.55711 | ||||||||
\(939\) | −10.2142 | −0.333328 | ||||||||
\(940\) | −1.02404 | −0.0334005 | ||||||||
\(941\) | 12.5532 | 0.409221 | 0.204611 | − | 0.978843i | \(-0.434407\pi\) | ||||
0.204611 | + | 0.978843i | \(0.434407\pi\) | |||||||
\(942\) | −17.2077 | −0.560656 | ||||||||
\(943\) | −1.95546 | −0.0636786 | ||||||||
\(944\) | 34.9756 | 1.13836 | ||||||||
\(945\) | 3.47795 | 0.113138 | ||||||||
\(946\) | −12.0938 | −0.393204 | ||||||||
\(947\) | −27.7156 | −0.900635 | −0.450317 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(948\) | −7.83471 | −0.254459 | ||||||||
\(949\) | −1.60688 | −0.0521617 | ||||||||
\(950\) | −5.99272 | −0.194430 | ||||||||
\(951\) | −16.0811 | −0.521467 | ||||||||
\(952\) | 34.1785 | 1.10773 | ||||||||
\(953\) | −30.6448 | −0.992683 | −0.496342 | − | 0.868127i | \(-0.665324\pi\) | ||||
−0.496342 | + | 0.868127i | \(0.665324\pi\) | |||||||
\(954\) | −0.903018 | −0.0292363 | ||||||||
\(955\) | −13.6771 | −0.442580 | ||||||||
\(956\) | 18.8007 | 0.608059 | ||||||||
\(957\) | 4.47217 | 0.144565 | ||||||||
\(958\) | 57.2942 | 1.85109 | ||||||||
\(959\) | 24.8405 | 0.802141 | ||||||||
\(960\) | 0.540107 | 0.0174319 | ||||||||
\(961\) | −13.3778 | −0.431544 | ||||||||
\(962\) | 32.2689 | 1.04039 | ||||||||
\(963\) | 7.89713 | 0.254482 | ||||||||
\(964\) | −10.8399 | −0.349128 | ||||||||
\(965\) | 6.77840 | 0.218204 | ||||||||
\(966\) | 6.79797 | 0.218721 | ||||||||
\(967\) | 53.6612 | 1.72563 | 0.862813 | − | 0.505522i | \(-0.168700\pi\) | ||||
0.862813 | + | 0.505522i | \(0.168700\pi\) | |||||||
\(968\) | −15.0163 | −0.482642 | ||||||||
\(969\) | −4.29635 | −0.138019 | ||||||||
\(970\) | 19.2384 | 0.617709 | ||||||||
\(971\) | 22.8654 | 0.733786 | 0.366893 | − | 0.930263i | \(-0.380422\pi\) | ||||
0.366893 | + | 0.930263i | \(0.380422\pi\) | |||||||
\(972\) | 1.04367 | 0.0334758 | ||||||||
\(973\) | 42.1834 | 1.35234 | ||||||||
\(974\) | 67.3895 | 2.15930 | ||||||||
\(975\) | −9.30257 | −0.297921 | ||||||||
\(976\) | 1.97102 | 0.0630908 | ||||||||
\(977\) | 40.5499 | 1.29731 | 0.648653 | − | 0.761084i | \(-0.275333\pi\) | ||||
0.648653 | + | 0.761084i | \(0.275333\pi\) | |||||||
\(978\) | −31.0612 | −0.993227 | ||||||||
\(979\) | −46.6135 | −1.48977 | ||||||||
\(980\) | 7.62299 | 0.243507 | ||||||||
\(981\) | 15.7824 | 0.503893 | ||||||||
\(982\) | −40.6454 | −1.29705 | ||||||||
\(983\) | 27.8600 | 0.888595 | 0.444297 | − | 0.895879i | \(-0.353453\pi\) | ||||
0.444297 | + | 0.895879i | \(0.353453\pi\) | |||||||
\(984\) | 3.26253 | 0.104006 | ||||||||
\(985\) | −2.42809 | −0.0773654 | ||||||||
\(986\) | −9.17204 | −0.292097 | ||||||||
\(987\) | −4.28342 | −0.136343 | ||||||||
\(988\) | 1.88759 | 0.0600524 | ||||||||
\(989\) | −1.55005 | −0.0492888 | ||||||||
\(990\) | 6.96402 | 0.221331 | ||||||||
\(991\) | 11.8396 | 0.376096 | 0.188048 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188048 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(992\) | 22.5967 | 0.717447 | ||||||||
\(993\) | 31.5407 | 1.00092 | ||||||||
\(994\) | −30.1059 | −0.954900 | ||||||||
\(995\) | −10.3361 | −0.327677 | ||||||||
\(996\) | 8.44611 | 0.267625 | ||||||||
\(997\) | 2.47262 | 0.0783087 | 0.0391544 | − | 0.999233i | \(-0.487534\pi\) | ||||
0.0391544 | + | 0.999233i | \(0.487534\pi\) | |||||||
\(998\) | 25.9100 | 0.820167 | ||||||||
\(999\) | 8.35747 | 0.264419 |
(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 | 2001.2.a.o.1.15 | ✓ | 20 | |
3.2 | odd | 2 | 6003.2.a.s.1.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.15 | ✓ | 20 | 1.1 | even | 1 | trivial | |
6003.2.a.s.1.6 | 20 | 3.2 | odd | 2 |