Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6988960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 22x^{4} - 11x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.716111\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.716111 | −0.506367 | −0.253184 | − | 0.967418i | \(-0.581478\pi\) | ||||
−0.253184 | + | 0.967418i | \(0.581478\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.48718 | −0.743592 | ||||||||
\(5\) | 1.54336 | 0.690212 | 0.345106 | − | 0.938564i | \(-0.387843\pi\) | ||||
0.345106 | + | 0.938564i | \(0.387843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.49721 | 0.882898 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.10522 | −0.349501 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.301097 | −0.0835092 | −0.0417546 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417546 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(14\) | 0.716111 | 0.191389 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.18609 | 0.296522 | ||||||||
\(17\) | 0.0579114 | 0.0140456 | 0.00702279 | − | 0.999975i | \(-0.497765\pi\) | ||||
0.00702279 | + | 0.999975i | \(0.497765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70741 | 0.621123 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(20\) | −2.29526 | −0.513237 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50757 | −0.314350 | −0.157175 | − | 0.987571i | \(-0.550239\pi\) | ||||
−0.157175 | + | 0.987571i | \(0.550239\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.61803 | −0.523607 | ||||||||
\(26\) | 0.215619 | 0.0422863 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.48718 | 0.281052 | ||||||||
\(29\) | −2.04096 | −0.378997 | −0.189498 | − | 0.981881i | \(-0.560686\pi\) | ||||
−0.189498 | + | 0.981881i | \(0.560686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.94348 | 0.887875 | 0.443938 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443938 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(32\) | −5.84379 | −1.03305 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0414710 | −0.00711222 | ||||||||
\(35\) | −1.54336 | −0.260876 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.43195 | −0.728607 | −0.364304 | − | 0.931280i | \(-0.618693\pi\) | ||||
−0.364304 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(38\) | −1.93881 | −0.314516 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.85410 | 0.609387 | ||||||||
\(41\) | 2.69916 | 0.421538 | 0.210769 | − | 0.977536i | \(-0.432403\pi\) | ||||
0.210769 | + | 0.977536i | \(0.432403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.09671 | 0.167247 | 0.0836233 | − | 0.996497i | \(-0.473351\pi\) | ||||
0.0836233 | + | 0.996497i | \(0.473351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.07959 | 0.159177 | ||||||||
\(47\) | −7.68803 | −1.12141 | −0.560707 | − | 0.828014i | \(-0.689471\pi\) | ||||
−0.560707 | + | 0.828014i | \(0.689471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.87480 | 0.265137 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.447786 | 0.0620968 | ||||||||
\(53\) | −7.18521 | −0.986964 | −0.493482 | − | 0.869756i | \(-0.664276\pi\) | ||||
−0.493482 | + | 0.869756i | \(0.664276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.49721 | −0.333704 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.46155 | 0.191911 | ||||||||
\(59\) | −0.0782427 | −0.0101863 | −0.00509317 | − | 0.999987i | \(-0.501621\pi\) | ||||
−0.00509317 | + | 0.999987i | \(0.501621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.27547 | 0.931528 | 0.465764 | − | 0.884909i | \(-0.345780\pi\) | ||||
0.465764 | + | 0.884909i | \(0.345780\pi\) | |||||||
\(62\) | −3.54008 | −0.449591 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.81263 | 0.226579 | ||||||||
\(65\) | −0.464701 | −0.0576391 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.09996 | −0.745229 | −0.372614 | − | 0.927986i | \(-0.621539\pi\) | ||||
−0.372614 | + | 0.927986i | \(0.621539\pi\) | |||||||
\(68\) | −0.0861249 | −0.0104442 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.10522 | 0.132099 | ||||||||
\(71\) | 3.72280 | 0.441815 | 0.220908 | − | 0.975295i | \(-0.429098\pi\) | ||||
0.220908 | + | 0.975295i | \(0.429098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.61278 | 0.188761 | 0.0943805 | − | 0.995536i | \(-0.469913\pi\) | ||||
0.0943805 | + | 0.995536i | \(0.469913\pi\) | |||||||
\(74\) | 3.17377 | 0.368943 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.02642 | −0.461862 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.86866 | −0.997802 | −0.498901 | − | 0.866659i | \(-0.666263\pi\) | ||||
−0.498901 | + | 0.866659i | \(0.666263\pi\) | |||||||
\(80\) | 1.83056 | 0.204663 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.93290 | −0.213453 | ||||||||
\(83\) | −5.03866 | −0.553065 | −0.276533 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276533 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0893782 | 0.00969443 | ||||||||
\(86\) | −0.785366 | −0.0846882 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.6900 | 1.87514 | 0.937569 | − | 0.347800i | \(-0.113071\pi\) | ||||
0.937569 | + | 0.347800i | \(0.113071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.301097 | 0.0315635 | ||||||||
\(92\) | 2.24204 | 0.233748 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.50548 | 0.567847 | ||||||||
\(95\) | 4.17852 | 0.428707 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.95804 | 0.808017 | 0.404008 | − | 0.914755i | \(-0.367617\pi\) | ||||
0.404008 | + | 0.914755i | \(0.367617\pi\) | |||||||
\(98\) | −0.716111 | −0.0723382 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.89350 | 0.389350 | ||||||||
\(101\) | 7.07407 | 0.703896 | 0.351948 | − | 0.936020i | \(-0.385519\pi\) | ||||
0.351948 | + | 0.936020i | \(0.385519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0828 | −1.19056 | −0.595279 | − | 0.803519i | \(-0.702958\pi\) | ||||
−0.595279 | + | 0.803519i | \(0.702958\pi\) | |||||||
\(104\) | −0.751902 | −0.0737301 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.14541 | 0.499766 | ||||||||
\(107\) | −2.30371 | −0.222708 | −0.111354 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111354 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1783 | −1.26225 | −0.631125 | − | 0.775682i | \(-0.717406\pi\) | ||||
−0.631125 | + | 0.775682i | \(0.717406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.18609 | −0.112075 | ||||||||
\(113\) | −14.0149 | −1.31841 | −0.659204 | − | 0.751964i | \(-0.729107\pi\) | ||||
−0.659204 | + | 0.751964i | \(0.729107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.32673 | −0.216968 | ||||||||
\(116\) | 3.03528 | 0.281819 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0560305 | 0.00515803 | ||||||||
\(119\) | −0.0579114 | −0.00530873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.21004 | −0.471695 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.35187 | −0.660217 | ||||||||
\(125\) | −11.7574 | −1.05161 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.58389 | 0.850433 | 0.425217 | − | 0.905092i | \(-0.360198\pi\) | ||||
0.425217 | + | 0.905092i | \(0.360198\pi\) | |||||||
\(128\) | 10.3895 | 0.918315 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.332778 | 0.0291865 | ||||||||
\(131\) | 16.0393 | 1.40136 | 0.700679 | − | 0.713477i | \(-0.252881\pi\) | ||||
0.700679 | + | 0.713477i | \(0.252881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.70741 | −0.234762 | ||||||||
\(134\) | 4.36825 | 0.377359 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.144617 | 0.0124008 | ||||||||
\(137\) | −14.8017 | −1.26459 | −0.632295 | − | 0.774727i | \(-0.717887\pi\) | ||||
−0.632295 | + | 0.774727i | \(0.717887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.71799 | 0.654632 | 0.327316 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327316 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(140\) | 2.29526 | 0.193985 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.66594 | −0.223721 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.14994 | −0.261588 | ||||||||
\(146\) | −1.15493 | −0.0955824 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.59112 | 0.541787 | ||||||||
\(149\) | 5.72976 | 0.469400 | 0.234700 | − | 0.972068i | \(-0.424589\pi\) | ||||
0.234700 | + | 0.972068i | \(0.424589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.98942 | −0.243275 | −0.121638 | − | 0.992575i | \(-0.538815\pi\) | ||||
−0.121638 | + | 0.992575i | \(0.538815\pi\) | |||||||
\(152\) | 6.76098 | 0.548388 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.62958 | 0.612823 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8036 | −0.942032 | −0.471016 | − | 0.882125i | \(-0.656113\pi\) | ||||
−0.471016 | + | 0.882125i | \(0.656113\pi\) | |||||||
\(158\) | 6.35095 | 0.505254 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.01909 | −0.713022 | ||||||||
\(161\) | 1.50757 | 0.118813 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.09385 | −0.477307 | −0.238653 | − | 0.971105i | \(-0.576706\pi\) | ||||
−0.238653 | + | 0.971105i | \(0.576706\pi\) | |||||||
\(164\) | −4.01415 | −0.313452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.60824 | 0.280054 | ||||||||
\(167\) | 22.8761 | 1.77021 | 0.885105 | − | 0.465392i | \(-0.154087\pi\) | ||||
0.885105 | + | 0.465392i | \(0.154087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9093 | −0.993026 | ||||||||
\(170\) | −0.0640048 | −0.00490894 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.63101 | −0.124363 | ||||||||
\(173\) | −25.0524 | −1.90470 | −0.952349 | − | 0.305011i | \(-0.901340\pi\) | ||||
−0.952349 | + | 0.305011i | \(0.901340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.61803 | 0.197905 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.6680 | −0.949508 | ||||||||
\(179\) | 1.98705 | 0.148519 | 0.0742595 | − | 0.997239i | \(-0.476341\pi\) | ||||
0.0742595 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.71750 | 0.573638 | 0.286819 | − | 0.957985i | \(-0.407402\pi\) | ||||
0.286819 | + | 0.957985i | \(0.407402\pi\) | |||||||
\(182\) | −0.215619 | −0.0159827 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.76472 | −0.277539 | ||||||||
\(185\) | −6.84010 | −0.502894 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.4335 | 0.833875 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.99228 | −0.217083 | ||||||||
\(191\) | 16.2668 | 1.17702 | 0.588511 | − | 0.808489i | \(-0.299714\pi\) | ||||
0.588511 | + | 0.808489i | \(0.299714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.77244 | 0.343528 | 0.171764 | − | 0.985138i | \(-0.445053\pi\) | ||||
0.171764 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(194\) | −5.69884 | −0.409153 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.48718 | −0.106227 | ||||||||
\(197\) | 22.4382 | 1.59866 | 0.799329 | − | 0.600893i | \(-0.205188\pi\) | ||||
0.799329 | + | 0.600893i | \(0.205188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5985 | −0.822193 | −0.411096 | − | 0.911592i | \(-0.634854\pi\) | ||||
−0.411096 | + | 0.911592i | \(0.634854\pi\) | |||||||
\(200\) | −6.53779 | −0.462291 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.06582 | −0.356430 | ||||||||
\(203\) | 2.04096 | 0.143247 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.16578 | 0.290951 | ||||||||
\(206\) | 8.65266 | 0.602859 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.357127 | −0.0247623 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.5301 | −1.13798 | −0.568991 | − | 0.822344i | \(-0.692666\pi\) | ||||
−0.568991 | + | 0.822344i | \(0.692666\pi\) | |||||||
\(212\) | 10.6857 | 0.733899 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.64972 | 0.112772 | ||||||||
\(215\) | 1.69262 | 0.115436 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.94348 | −0.335585 | ||||||||
\(218\) | 9.43710 | 0.639161 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0174369 | −0.00117293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.3932 | −1.90135 | −0.950676 | − | 0.310186i | \(-0.899609\pi\) | ||||
−0.950676 | + | 0.310186i | \(0.899609\pi\) | |||||||
\(224\) | 5.84379 | 0.390455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0362 | 0.667599 | ||||||||
\(227\) | 21.9479 | 1.45673 | 0.728366 | − | 0.685188i | \(-0.240280\pi\) | ||||
0.728366 | + | 0.685188i | \(0.240280\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1717 | 0.738249 | 0.369124 | − | 0.929380i | \(-0.379658\pi\) | ||||
0.369124 | + | 0.929380i | \(0.379658\pi\) | |||||||
\(230\) | 1.66620 | 0.109866 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.09671 | −0.334615 | ||||||||
\(233\) | −15.1572 | −0.992981 | −0.496490 | − | 0.868042i | \(-0.665378\pi\) | ||||
−0.496490 | + | 0.868042i | \(0.665378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8654 | −0.774014 | ||||||||
\(236\) | 0.116361 | 0.00757448 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0414710 | 0.00268817 | ||||||||
\(239\) | −13.8246 | −0.894238 | −0.447119 | − | 0.894475i | \(-0.647550\pi\) | ||||
−0.447119 | + | 0.894475i | \(0.647550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6432 | −0.943250 | −0.471625 | − | 0.881799i | \(-0.656332\pi\) | ||||
−0.471625 | + | 0.881799i | \(0.656332\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.8200 | −0.692677 | ||||||||
\(245\) | 1.54336 | 0.0986018 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.815193 | −0.0518695 | ||||||||
\(248\) | 12.3449 | 0.783903 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.41959 | 0.532502 | ||||||||
\(251\) | −19.1636 | −1.20959 | −0.604797 | − | 0.796380i | \(-0.706746\pi\) | ||||
−0.604797 | + | 0.796380i | \(0.706746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.86313 | −0.430631 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.0653 | −0.691583 | ||||||||
\(257\) | −14.3335 | −0.894101 | −0.447050 | − | 0.894509i | \(-0.647525\pi\) | ||||
−0.447050 | + | 0.894509i | \(0.647525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.43195 | 0.275388 | ||||||||
\(260\) | 0.691097 | 0.0428600 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.4859 | −0.709602 | ||||||||
\(263\) | −27.3223 | −1.68476 | −0.842382 | − | 0.538881i | \(-0.818847\pi\) | ||||
−0.842382 | + | 0.538881i | \(0.818847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0894 | −0.681215 | ||||||||
\(266\) | 1.93881 | 0.118876 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.07177 | 0.554146 | ||||||||
\(269\) | 23.4293 | 1.42851 | 0.714256 | − | 0.699885i | \(-0.246765\pi\) | ||||
0.714256 | + | 0.699885i | \(0.246765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.1574 | 1.58895 | 0.794475 | − | 0.607297i | \(-0.207746\pi\) | ||||
0.794475 | + | 0.607297i | \(0.207746\pi\) | |||||||
\(272\) | 0.0686880 | 0.00416482 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.5996 | 0.640347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.06257 | −0.304180 | −0.152090 | − | 0.988367i | \(-0.548600\pi\) | ||||
−0.152090 | + | 0.988367i | \(0.548600\pi\) | |||||||
\(278\) | −5.52694 | −0.331484 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.85410 | −0.230327 | ||||||||
\(281\) | 9.97449 | 0.595028 | 0.297514 | − | 0.954717i | \(-0.403842\pi\) | ||||
0.297514 | + | 0.954717i | \(0.403842\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6792 | −1.46703 | −0.733514 | − | 0.679675i | \(-0.762121\pi\) | ||||
−0.733514 | + | 0.679675i | \(0.762121\pi\) | |||||||
\(284\) | −5.53650 | −0.328531 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.69916 | −0.159326 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9966 | −0.999803 | ||||||||
\(290\) | 2.25571 | 0.132460 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.39849 | −0.140361 | ||||||||
\(293\) | 6.70505 | 0.391713 | 0.195857 | − | 0.980633i | \(-0.437251\pi\) | ||||
0.195857 | + | 0.980633i | \(0.437251\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.120757 | −0.00703074 | ||||||||
\(296\) | −11.0675 | −0.643286 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.10315 | −0.237689 | ||||||||
\(299\) | 0.453925 | 0.0262511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.09671 | −0.0632133 | ||||||||
\(302\) | 2.14076 | 0.123187 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.21123 | 0.184177 | ||||||||
\(305\) | 11.2287 | 0.642952 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.4156 | −0.765670 | −0.382835 | − | 0.923817i | \(-0.625052\pi\) | ||||
−0.382835 | + | 0.923817i | \(0.625052\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.46363 | −0.310313 | ||||||||
\(311\) | 30.5081 | 1.72995 | 0.864977 | − | 0.501811i | \(-0.167333\pi\) | ||||
0.864977 | + | 0.501811i | \(0.167333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9621 | −1.07180 | −0.535901 | − | 0.844281i | \(-0.680028\pi\) | ||||
−0.535901 | + | 0.844281i | \(0.680028\pi\) | |||||||
\(314\) | 8.45271 | 0.477014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.1893 | 0.741958 | ||||||||
\(317\) | 0.834594 | 0.0468755 | 0.0234377 | − | 0.999725i | \(-0.492539\pi\) | ||||
0.0234377 | + | 0.999725i | \(0.492539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.79755 | 0.156388 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.07959 | −0.0601631 | ||||||||
\(323\) | 0.156790 | 0.00872403 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.788281 | 0.0437260 | ||||||||
\(326\) | 4.36387 | 0.241692 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.74037 | 0.372175 | ||||||||
\(329\) | 7.68803 | 0.423855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7431 | −0.810356 | −0.405178 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405178 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(332\) | 7.49342 | 0.411255 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.3819 | −0.896376 | ||||||||
\(335\) | −9.41445 | −0.514366 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3874 | 1.76426 | 0.882128 | − | 0.471010i | \(-0.156111\pi\) | ||||
0.882128 | + | 0.471010i | \(0.156111\pi\) | |||||||
\(338\) | 9.24452 | 0.502836 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.132922 | −0.00720870 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.73872 | 0.147662 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.9403 | 0.964476 | ||||||||
\(347\) | −12.9058 | −0.692822 | −0.346411 | − | 0.938083i | \(-0.612600\pi\) | ||||
−0.346411 | + | 0.938083i | \(0.612600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4321 | 0.772535 | 0.386267 | − | 0.922387i | \(-0.373764\pi\) | ||||
0.386267 | + | 0.922387i | \(0.373764\pi\) | |||||||
\(350\) | −1.87480 | −0.100212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2973 | −0.707745 | −0.353872 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353872 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.74563 | 0.304947 | ||||||||
\(356\) | −26.3083 | −1.39434 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.42295 | −0.0752051 | ||||||||
\(359\) | 9.74033 | 0.514075 | 0.257038 | − | 0.966401i | \(-0.417254\pi\) | ||||
0.257038 | + | 0.966401i | \(0.417254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.6699 | −0.614206 | ||||||||
\(362\) | −5.52659 | −0.290471 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.447786 | −0.0234704 | ||||||||
\(365\) | 2.48910 | 0.130285 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.5818 | −0.865564 | −0.432782 | − | 0.901499i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(368\) | −1.78811 | −0.0932118 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.89827 | 0.254649 | ||||||||
\(371\) | 7.18521 | 0.373037 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.52329 | 0.285985 | 0.142993 | − | 0.989724i | \(-0.454327\pi\) | ||||
0.142993 | + | 0.989724i | \(0.454327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.1986 | −0.990094 | ||||||||
\(377\) | 0.614526 | 0.0316497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.2684 | −1.29795 | −0.648975 | − | 0.760810i | \(-0.724802\pi\) | ||||
−0.648975 | + | 0.760810i | \(0.724802\pi\) | |||||||
\(380\) | −6.21423 | −0.318783 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.6488 | −0.596005 | ||||||||
\(383\) | 9.49680 | 0.485264 | 0.242632 | − | 0.970118i | \(-0.421989\pi\) | ||||
0.242632 | + | 0.970118i | \(0.421989\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.41760 | −0.173951 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.8351 | −0.600835 | ||||||||
\(389\) | 5.51635 | 0.279690 | 0.139845 | − | 0.990173i | \(-0.455340\pi\) | ||||
0.139845 | + | 0.990173i | \(0.455340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0873055 | −0.00441523 | ||||||||
\(392\) | 2.49721 | 0.126128 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.0683 | −0.809508 | ||||||||
\(395\) | −13.6876 | −0.688696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0365 | −1.20635 | −0.603177 | − | 0.797607i | \(-0.706099\pi\) | ||||
−0.603177 | + | 0.797607i | \(0.706099\pi\) | |||||||
\(398\) | 8.30578 | 0.416331 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.10522 | −0.155261 | ||||||||
\(401\) | 26.7585 | 1.33625 | 0.668127 | − | 0.744047i | \(-0.267096\pi\) | ||||
0.668127 | + | 0.744047i | \(0.267096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.48847 | −0.0741458 | ||||||||
\(404\) | −10.5204 | −0.523412 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.46155 | −0.0725357 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.68832 | −0.132929 | −0.0664645 | − | 0.997789i | \(-0.521172\pi\) | ||||
−0.0664645 | + | 0.997789i | \(0.521172\pi\) | |||||||
\(410\) | −2.98316 | −0.147328 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.9694 | 0.885289 | ||||||||
\(413\) | 0.0782427 | 0.00385007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.77648 | −0.381733 | ||||||||
\(416\) | 1.75955 | 0.0862689 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.2419 | −1.23315 | −0.616573 | − | 0.787297i | \(-0.711480\pi\) | ||||
−0.616573 | + | 0.787297i | \(0.711480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.42461 | −0.459328 | −0.229664 | − | 0.973270i | \(-0.573763\pi\) | ||||
−0.229664 | + | 0.973270i | \(0.573763\pi\) | |||||||
\(422\) | 11.8374 | 0.576236 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.9430 | −0.871389 | ||||||||
\(425\) | −0.151614 | −0.00735436 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.27547 | −0.352084 | ||||||||
\(428\) | 3.42605 | 0.165604 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.21210 | −0.0584529 | ||||||||
\(431\) | −27.6107 | −1.32996 | −0.664981 | − | 0.746860i | \(-0.731560\pi\) | ||||
−0.664981 | + | 0.746860i | \(0.731560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.2973 | −1.74434 | −0.872169 | − | 0.489205i | \(-0.837287\pi\) | ||||
−0.872169 | + | 0.489205i | \(0.837287\pi\) | |||||||
\(434\) | 3.54008 | 0.169929 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.5985 | 0.938599 | ||||||||
\(437\) | −4.08162 | −0.195250 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.8022 | 1.70875 | 0.854374 | − | 0.519659i | \(-0.173941\pi\) | ||||
0.854374 | + | 0.519659i | \(0.173941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0124868 | 0.000593936 0 | ||||||||
\(443\) | 5.99164 | 0.284672 | 0.142336 | − | 0.989818i | \(-0.454539\pi\) | ||||
0.142336 | + | 0.989818i | \(0.454539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.3021 | 1.29424 | ||||||||
\(446\) | 20.3327 | 0.962782 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.81263 | −0.0856388 | ||||||||
\(449\) | −3.76704 | −0.177778 | −0.0888889 | − | 0.996042i | \(-0.528332\pi\) | ||||
−0.0888889 | + | 0.996042i | \(0.528332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 20.8427 | 0.980359 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.7171 | −0.737641 | ||||||||
\(455\) | 0.464701 | 0.0217855 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0048 | 0.748672 | 0.374336 | − | 0.927293i | \(-0.377871\pi\) | ||||
0.374336 | + | 0.927293i | \(0.377871\pi\) | |||||||
\(458\) | −8.00020 | −0.373825 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46027 | 0.161336 | ||||||||
\(461\) | −15.9848 | −0.744486 | −0.372243 | − | 0.928135i | \(-0.621411\pi\) | ||||
−0.372243 | + | 0.928135i | \(0.621411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.13966 | −0.424756 | −0.212378 | − | 0.977188i | \(-0.568121\pi\) | ||||
−0.212378 | + | 0.977188i | \(0.568121\pi\) | |||||||
\(464\) | −2.42076 | −0.112381 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.8542 | 0.502813 | ||||||||
\(467\) | 1.90358 | 0.0880874 | 0.0440437 | − | 0.999030i | \(-0.485976\pi\) | ||||
0.0440437 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.09996 | 0.281670 | ||||||||
\(470\) | 8.49695 | 0.391935 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.195389 | −0.00899349 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.08810 | −0.325224 | ||||||||
\(476\) | 0.0861249 | 0.00394753 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.89994 | 0.452813 | ||||||||
\(479\) | −32.6386 | −1.49130 | −0.745648 | − | 0.666340i | \(-0.767860\pi\) | ||||
−0.745648 | + | 0.666340i | \(0.767860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.33444 | 0.0608454 | ||||||||
\(482\) | 10.4861 | 0.477631 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2821 | 0.557703 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.2014 | −1.41387 | −0.706936 | − | 0.707277i | \(-0.749923\pi\) | ||||
−0.706936 | + | 0.707277i | \(0.749923\pi\) | |||||||
\(488\) | 18.1684 | 0.822444 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.10522 | −0.0499287 | ||||||||
\(491\) | −24.4486 | −1.10335 | −0.551676 | − | 0.834059i | \(-0.686011\pi\) | ||||
−0.551676 | + | 0.834059i | \(0.686011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.118195 | −0.00532323 | ||||||||
\(494\) | 0.583769 | 0.0262650 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.86340 | 0.263275 | ||||||||
\(497\) | −3.72280 | −0.166991 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9389 | 0.668757 | 0.334379 | − | 0.942439i | \(-0.391474\pi\) | ||||
0.334379 | + | 0.942439i | \(0.391474\pi\) | |||||||
\(500\) | 17.4854 | 0.781971 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.7233 | 0.612499 | ||||||||
\(503\) | 24.2545 | 1.08145 | 0.540727 | − | 0.841198i | \(-0.318149\pi\) | ||||
0.540727 | + | 0.841198i | \(0.318149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9178 | 0.485838 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.2530 | −0.632376 | ||||||||
\(509\) | −10.5548 | −0.467833 | −0.233916 | − | 0.972257i | \(-0.575154\pi\) | ||||
−0.233916 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.61278 | −0.0713450 | ||||||||
\(512\) | −12.8551 | −0.568120 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.2644 | 0.452743 | ||||||||
\(515\) | −18.6482 | −0.821738 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.17377 | −0.139447 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.16046 | −0.0508894 | ||||||||
\(521\) | −21.9932 | −0.963540 | −0.481770 | − | 0.876298i | \(-0.660006\pi\) | ||||
−0.481770 | + | 0.876298i | \(0.660006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.42545 | 0.237238 | 0.118619 | − | 0.992940i | \(-0.462153\pi\) | ||||
0.118619 | + | 0.992940i | \(0.462153\pi\) | |||||||
\(524\) | −23.8534 | −1.04204 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.5658 | 0.853109 | ||||||||
\(527\) | 0.286284 | 0.0124707 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7272 | −0.901184 | ||||||||
\(530\) | 7.94123 | 0.344945 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.02642 | 0.174568 | ||||||||
\(533\) | −0.812708 | −0.0352023 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.55546 | −0.153716 | ||||||||
\(536\) | −15.2329 | −0.657961 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7780 | −0.723351 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.637614 | 0.0274132 | 0.0137066 | − | 0.999906i | \(-0.495637\pi\) | ||||
0.0137066 | + | 0.999906i | \(0.495637\pi\) | |||||||
\(542\) | −18.7316 | −0.804592 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.338422 | −0.0145097 | ||||||||
\(545\) | −20.3388 | −0.871220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.50358 | −0.107045 | −0.0535226 | − | 0.998567i | \(-0.517045\pi\) | ||||
−0.0535226 | + | 0.998567i | \(0.517045\pi\) | |||||||
\(548\) | 22.0128 | 0.940340 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.52572 | −0.235404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.86866 | 0.377134 | ||||||||
\(554\) | 3.62536 | 0.154027 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4781 | −0.486779 | ||||||||
\(557\) | 4.55740 | 0.193103 | 0.0965516 | − | 0.995328i | \(-0.469219\pi\) | ||||
0.0965516 | + | 0.995328i | \(0.469219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.330216 | −0.0139666 | ||||||||
\(560\) | −1.83056 | −0.0773554 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.14285 | −0.301303 | ||||||||
\(563\) | 8.98017 | 0.378469 | 0.189235 | − | 0.981932i | \(-0.439399\pi\) | ||||
0.189235 | + | 0.981932i | \(0.439399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.6300 | −0.909982 | ||||||||
\(566\) | 17.6731 | 0.742854 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.29663 | 0.390078 | ||||||||
\(569\) | −35.8298 | −1.50206 | −0.751032 | − | 0.660266i | \(-0.770444\pi\) | ||||
−0.751032 | + | 0.660266i | \(0.770444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.5090 | −0.774576 | −0.387288 | − | 0.921959i | \(-0.626588\pi\) | ||||
−0.387288 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.93290 | 0.0806776 | ||||||||
\(575\) | 3.94687 | 0.164596 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.02086 | −0.292282 | −0.146141 | − | 0.989264i | \(-0.546685\pi\) | ||||
−0.146141 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(578\) | 12.1715 | 0.506267 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.68454 | 0.194515 | ||||||||
\(581\) | 5.03866 | 0.209039 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.02744 | 0.166657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.80156 | −0.198351 | ||||||||
\(587\) | 14.7290 | 0.607931 | 0.303965 | − | 0.952683i | \(-0.401689\pi\) | ||||
0.303965 | + | 0.952683i | \(0.401689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3840 | 0.551480 | ||||||||
\(590\) | 0.0864753 | 0.00356013 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.25668 | −0.216048 | ||||||||
\(593\) | −5.91081 | −0.242728 | −0.121364 | − | 0.992608i | \(-0.538727\pi\) | ||||
−0.121364 | + | 0.992608i | \(0.538727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0893782 | −0.00366415 | ||||||||
\(596\) | −8.52121 | −0.349042 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.325061 | −0.0132927 | ||||||||
\(599\) | −44.8922 | −1.83424 | −0.917122 | − | 0.398606i | \(-0.869494\pi\) | ||||
−0.917122 | + | 0.398606i | \(0.869494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.9081 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(602\) | 0.785366 | 0.0320091 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.44582 | 0.180898 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1454 | −0.655320 | −0.327660 | − | 0.944796i | \(-0.606260\pi\) | ||||
−0.327660 | + | 0.944796i | \(0.606260\pi\) | |||||||
\(608\) | −15.8216 | −0.641649 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.04098 | −0.325570 | ||||||||
\(611\) | 2.31484 | 0.0936484 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.6127 | −1.27682 | −0.638412 | − | 0.769695i | \(-0.720408\pi\) | ||||
−0.638412 | + | 0.769695i | \(0.720408\pi\) | |||||||
\(614\) | 9.60707 | 0.387710 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3149 | −0.455523 | −0.227761 | − | 0.973717i | \(-0.573141\pi\) | ||||
−0.227761 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.92065 | −0.398745 | −0.199372 | − | 0.979924i | \(-0.563890\pi\) | ||||
−0.199372 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(620\) | −11.3466 | −0.455690 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.8472 | −0.875992 | ||||||||
\(623\) | −17.6900 | −0.708735 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.05573 | −0.202229 | ||||||||
\(626\) | 13.5790 | 0.542725 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.5542 | 0.700488 | ||||||||
\(629\) | −0.256660 | −0.0102337 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.26080 | −0.368667 | −0.184333 | − | 0.982864i | \(-0.559013\pi\) | ||||
−0.184333 | + | 0.982864i | \(0.559013\pi\) | |||||||
\(632\) | −22.1469 | −0.880958 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.597662 | −0.0237362 | ||||||||
\(635\) | 14.7914 | 0.586980 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.301097 | −0.0119299 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.0348 | 0.633832 | ||||||||
\(641\) | −11.4592 | −0.452611 | −0.226305 | − | 0.974056i | \(-0.572665\pi\) | ||||
−0.226305 | + | 0.974056i | \(0.572665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8446 | 1.29526 | 0.647632 | − | 0.761953i | \(-0.275760\pi\) | ||||
0.647632 | + | 0.761953i | \(0.275760\pi\) | |||||||
\(644\) | −2.24204 | −0.0883486 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.112279 | −0.00441756 | ||||||||
\(647\) | 47.9724 | 1.88599 | 0.942995 | − | 0.332806i | \(-0.107996\pi\) | ||||
0.942995 | + | 0.332806i | \(0.107996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.564497 | −0.0221414 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.06267 | 0.354922 | ||||||||
\(653\) | −18.1875 | −0.711732 | −0.355866 | − | 0.934537i | \(-0.615814\pi\) | ||||
−0.355866 | + | 0.934537i | \(0.615814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.7544 | 0.967235 | ||||||||
\(656\) | 3.20144 | 0.124995 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.50548 | −0.214626 | ||||||||
\(659\) | 9.72544 | 0.378849 | 0.189425 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189425 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8857 | −1.00684 | −0.503419 | − | 0.864042i | \(-0.667925\pi\) | ||||
−0.503419 | + | 0.864042i | \(0.667925\pi\) | |||||||
\(662\) | 10.5577 | 0.410338 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.5826 | −0.488300 | ||||||||
\(665\) | −4.17852 | −0.162036 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.07689 | 0.119138 | ||||||||
\(668\) | −34.0211 | −1.31631 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.74179 | 0.260458 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.66072 | 0.218205 | 0.109102 | − | 0.994031i | \(-0.465202\pi\) | ||||
0.109102 | + | 0.994031i | \(0.465202\pi\) | |||||||
\(674\) | −23.1930 | −0.893361 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.1986 | 0.738407 | ||||||||
\(677\) | −12.0626 | −0.463604 | −0.231802 | − | 0.972763i | \(-0.574462\pi\) | ||||
−0.231802 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.95804 | −0.305402 | ||||||||
\(680\) | 0.223196 | 0.00855919 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.9182 | 0.609094 | 0.304547 | − | 0.952497i | \(-0.401495\pi\) | ||||
0.304547 | + | 0.952497i | \(0.401495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.8443 | −0.872836 | ||||||||
\(686\) | 0.716111 | 0.0273413 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.30079 | 0.0495923 | ||||||||
\(689\) | 2.16344 | 0.0824206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7539 | 1.05581 | 0.527903 | − | 0.849305i | \(-0.322978\pi\) | ||||
0.527903 | + | 0.849305i | \(0.322978\pi\) | |||||||
\(692\) | 37.2575 | 1.41632 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.24201 | 0.350822 | ||||||||
\(695\) | 11.9117 | 0.451835 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.156312 | 0.00592074 | ||||||||
\(698\) | −10.3350 | −0.391186 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.89350 | −0.147160 | ||||||||
\(701\) | 25.5593 | 0.965362 | 0.482681 | − | 0.875796i | \(-0.339663\pi\) | ||||
0.482681 | + | 0.875796i | \(0.339663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9991 | −0.452555 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.52235 | 0.358379 | ||||||||
\(707\) | −7.07407 | −0.266048 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.8010 | −1.64498 | −0.822491 | − | 0.568778i | \(-0.807416\pi\) | ||||
−0.822491 | + | 0.568778i | \(0.807416\pi\) | |||||||
\(710\) | −4.11451 | −0.154415 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 44.1757 | 1.65555 | ||||||||
\(713\) | −7.45265 | −0.279104 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.95511 | −0.110438 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.97516 | −0.260311 | ||||||||
\(719\) | 24.7256 | 0.922109 | 0.461054 | − | 0.887372i | \(-0.347471\pi\) | ||||
0.461054 | + | 0.887372i | \(0.347471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0828 | 0.449988 | ||||||||
\(722\) | 8.35696 | 0.311014 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.4774 | −0.426553 | ||||||||
\(725\) | 5.34330 | 0.198445 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.0630 | −0.558654 | −0.279327 | − | 0.960196i | \(-0.590111\pi\) | ||||
−0.279327 | + | 0.960196i | \(0.590111\pi\) | |||||||
\(728\) | 0.751902 | 0.0278674 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.78247 | −0.0659722 | ||||||||
\(731\) | 0.0635120 | 0.00234908 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.4833 | 0.941249 | 0.470624 | − | 0.882334i | \(-0.344029\pi\) | ||||
0.470624 | + | 0.882334i | \(0.344029\pi\) | |||||||
\(734\) | 11.8744 | 0.438293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.80993 | 0.324738 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00152 | −0.0368415 | −0.0184207 | − | 0.999830i | \(-0.505864\pi\) | ||||
−0.0184207 | + | 0.999830i | \(0.505864\pi\) | |||||||
\(740\) | 10.1725 | 0.373948 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.14541 | −0.188894 | ||||||||
\(743\) | −20.8622 | −0.765361 | −0.382680 | − | 0.923881i | \(-0.624999\pi\) | ||||
−0.382680 | + | 0.923881i | \(0.624999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.84310 | 0.323986 | ||||||||
\(746\) | −3.95529 | −0.144814 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.30371 | 0.0841759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7300 | 1.44977 | 0.724884 | − | 0.688871i | \(-0.241893\pi\) | ||||
0.724884 | + | 0.688871i | \(0.241893\pi\) | |||||||
\(752\) | −9.11868 | −0.332524 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.440069 | −0.0160264 | ||||||||
\(755\) | −4.61375 | −0.167912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.5382 | −1.25531 | −0.627656 | − | 0.778491i | \(-0.715986\pi\) | ||||
−0.627656 | + | 0.778491i | \(0.715986\pi\) | |||||||
\(758\) | 18.0950 | 0.657239 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.4346 | 0.378504 | ||||||||
\(761\) | −41.2704 | −1.49605 | −0.748025 | − | 0.663670i | \(-0.768998\pi\) | ||||
−0.748025 | + | 0.663670i | \(0.768998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1783 | 0.477085 | ||||||||
\(764\) | −24.1917 | −0.875225 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.80077 | −0.245722 | ||||||||
\(767\) | 0.0235586 | 0.000850653 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.6907 | −1.53946 | −0.769732 | − | 0.638367i | \(-0.779610\pi\) | ||||
−0.769732 | + | 0.638367i | \(0.779610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.09750 | −0.255445 | ||||||||
\(773\) | 19.6821 | 0.707916 | 0.353958 | − | 0.935261i | \(-0.384836\pi\) | ||||
0.353958 | + | 0.935261i | \(0.384836\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9422 | −0.464898 | ||||||||
\(776\) | 19.8729 | 0.713396 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.95032 | −0.141626 | ||||||||
\(779\) | 7.30774 | 0.261827 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.0625205 | 0.00223573 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.18609 | 0.0423603 | ||||||||
\(785\) | −18.2173 | −0.650203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.64715 | 0.165653 | 0.0828266 | − | 0.996564i | \(-0.473605\pi\) | ||||
0.0828266 | + | 0.996564i | \(0.473605\pi\) | |||||||
\(788\) | −33.3698 | −1.18875 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.80181 | 0.348733 | ||||||||
\(791\) | 14.0149 | 0.498312 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.19062 | −0.0777912 | ||||||||
\(794\) | 17.2128 | 0.610858 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.2490 | 0.611376 | ||||||||
\(797\) | −32.7314 | −1.15941 | −0.579703 | − | 0.814828i | \(-0.696832\pi\) | ||||
−0.579703 | + | 0.814828i | \(0.696832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.445224 | −0.0157509 | ||||||||
\(800\) | 15.2993 | 0.540910 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.1620 | −0.676635 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.32673 | 0.0820064 | ||||||||
\(806\) | 1.06591 | 0.0375450 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.6655 | 0.621468 | ||||||||
\(809\) | −2.51503 | −0.0884237 | −0.0442118 | − | 0.999022i | \(-0.514078\pi\) | ||||
−0.0442118 | + | 0.999022i | \(0.514078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.1236 | −0.425716 | −0.212858 | − | 0.977083i | \(-0.568277\pi\) | ||||
−0.212858 | + | 0.977083i | \(0.568277\pi\) | |||||||
\(812\) | −3.03528 | −0.106518 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.40501 | −0.329443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.96925 | 0.103881 | ||||||||
\(818\) | 1.92514 | 0.0673108 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.19529 | −0.216349 | ||||||||
\(821\) | −38.6448 | −1.34871 | −0.674356 | − | 0.738406i | \(-0.735579\pi\) | ||||
−0.674356 | + | 0.738406i | \(0.735579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0250 | 0.976889 | 0.488445 | − | 0.872595i | \(-0.337564\pi\) | ||||
0.488445 | + | 0.872595i | \(0.337564\pi\) | |||||||
\(824\) | −30.1734 | −1.05114 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0560305 | −0.00194955 | ||||||||
\(827\) | −30.2810 | −1.05297 | −0.526487 | − | 0.850183i | \(-0.676491\pi\) | ||||
−0.526487 | + | 0.850183i | \(0.676491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34783 | −0.0815434 | −0.0407717 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407717 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(830\) | 5.56883 | 0.193297 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.545777 | −0.0189214 | ||||||||
\(833\) | 0.0579114 | 0.00200651 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.3062 | 1.22182 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.0760 | 0.624425 | ||||||||
\(839\) | 29.4521 | 1.01680 | 0.508399 | − | 0.861121i | \(-0.330237\pi\) | ||||
0.508399 | + | 0.861121i | \(0.330237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8345 | −0.856361 | ||||||||
\(842\) | 6.74907 | 0.232588 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.5834 | 0.846194 | ||||||||
\(845\) | −19.9238 | −0.685399 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.52229 | −0.292657 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.108572 | 0.00372401 | ||||||||
\(851\) | 6.68147 | 0.229038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.3933 | −1.07489 | −0.537443 | − | 0.843300i | \(-0.680610\pi\) | ||||
−0.537443 | + | 0.843300i | \(0.680610\pi\) | |||||||
\(854\) | 5.21004 | 0.178284 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.75286 | −0.196629 | ||||||||
\(857\) | 12.6273 | 0.431339 | 0.215670 | − | 0.976466i | \(-0.430807\pi\) | ||||
0.215670 | + | 0.976466i | \(0.430807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4647 | 0.391172 | 0.195586 | − | 0.980687i | \(-0.437339\pi\) | ||||
0.195586 | + | 0.980687i | \(0.437339\pi\) | |||||||
\(860\) | −2.51724 | −0.0858371 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.7724 | 0.673449 | ||||||||
\(863\) | 3.68221 | 0.125344 | 0.0626720 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626720 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.6649 | −1.31465 | ||||||||
\(866\) | 25.9929 | 0.883275 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.35187 | 0.249539 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.83668 | 0.0622335 | ||||||||
\(872\) | −32.9089 | −1.11444 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.92289 | 0.0988682 | ||||||||
\(875\) | 11.7574 | 0.397472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.1256 | −1.52378 | −0.761892 | − | 0.647704i | \(-0.775729\pi\) | ||||
−0.761892 | + | 0.647704i | \(0.775729\pi\) | |||||||
\(878\) | −25.6384 | −0.865254 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.4792 | −0.555198 | −0.277599 | − | 0.960697i | \(-0.589539\pi\) | ||||
−0.277599 | + | 0.960697i | \(0.589539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9017 | 1.64567 | 0.822837 | − | 0.568278i | \(-0.192390\pi\) | ||||
0.822837 | + | 0.568278i | \(0.192390\pi\) | |||||||
\(884\) | 0.0259319 | 0.000872185 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.29068 | −0.144148 | ||||||||
\(887\) | 32.7168 | 1.09852 | 0.549262 | − | 0.835650i | \(-0.314909\pi\) | ||||
0.549262 | + | 0.835650i | \(0.314909\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.58389 | −0.321434 | ||||||||
\(890\) | −19.5513 | −0.655362 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.2260 | 1.41383 | ||||||||
\(893\) | −20.8147 | −0.696536 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.06674 | 0.102510 | ||||||||
\(896\) | −10.3895 | −0.347090 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.69762 | 0.0900208 | ||||||||
\(899\) | −10.0894 | −0.336502 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.416105 | −0.0138625 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.9981 | −1.16402 | ||||||||
\(905\) | 11.9109 | 0.395932 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.14064 | −0.104283 | −0.0521416 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521416 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(908\) | −32.6405 | −1.08321 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.332778 | −0.0110315 | ||||||||
\(911\) | −44.8693 | −1.48659 | −0.743293 | − | 0.668966i | \(-0.766737\pi\) | ||||
−0.743293 | + | 0.668966i | \(0.766737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −11.4612 | −0.379103 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.6144 | −0.548956 | ||||||||
\(917\) | −16.0393 | −0.529663 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4504 | 1.16940 | 0.584701 | − | 0.811249i | \(-0.301212\pi\) | ||||
0.584701 | + | 0.811249i | \(0.301212\pi\) | |||||||
\(920\) | −5.81033 | −0.191561 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.4469 | 0.376983 | ||||||||
\(923\) | −1.12092 | −0.0368957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6030 | 0.381504 | ||||||||
\(926\) | 6.54501 | 0.215082 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.9270 | 0.391521 | ||||||||
\(929\) | 9.97464 | 0.327257 | 0.163629 | − | 0.986522i | \(-0.447680\pi\) | ||||
0.163629 | + | 0.986522i | \(0.447680\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.70741 | 0.0887319 | ||||||||
\(932\) | 22.5415 | 0.738373 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.36318 | −0.0446045 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.9782 | 0.717997 | 0.358999 | − | 0.933338i | \(-0.383118\pi\) | ||||
0.358999 | + | 0.933338i | \(0.383118\pi\) | |||||||
\(938\) | −4.36825 | −0.142628 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.6461 | 0.575551 | ||||||||
\(941\) | 52.0209 | 1.69583 | 0.847916 | − | 0.530130i | \(-0.177857\pi\) | ||||
0.847916 | + | 0.530130i | \(0.177857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.06917 | −0.132511 | ||||||||
\(944\) | −0.0928028 | −0.00302047 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.79616 | −0.123359 | −0.0616793 | − | 0.998096i | \(-0.519646\pi\) | ||||
−0.0616793 | + | 0.998096i | \(0.519646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.485601 | −0.0157633 | ||||||||
\(950\) | 5.07587 | 0.164683 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.144617 | −0.00468706 | ||||||||
\(953\) | −15.7640 | −0.510646 | −0.255323 | − | 0.966856i | \(-0.582182\pi\) | ||||
−0.255323 | + | 0.966856i | \(0.582182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.1055 | 0.812396 | ||||||||
\(956\) | 20.5597 | 0.664948 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.3729 | 0.755143 | ||||||||
\(959\) | 14.8017 | 0.477970 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.56200 | −0.211678 | ||||||||
\(962\) | −0.955611 | −0.0308101 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.7771 | 0.701393 | ||||||||
\(965\) | 7.36560 | 0.237107 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5059 | 0.498635 | 0.249317 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249317 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.79537 | −0.282402 | ||||||||
\(971\) | 61.0347 | 1.95870 | 0.979348 | − | 0.202182i | \(-0.0648034\pi\) | ||||
0.979348 | + | 0.202182i | \(0.0648034\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.71799 | −0.247428 | ||||||||
\(974\) | 22.3437 | 0.715938 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.62934 | 0.276219 | ||||||||
\(977\) | 51.7989 | 1.65719 | 0.828597 | − | 0.559845i | \(-0.189139\pi\) | ||||
0.828597 | + | 0.559845i | \(0.189139\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.29526 | −0.0733195 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.5079 | 0.558701 | ||||||||
\(983\) | 12.8521 | 0.409918 | 0.204959 | − | 0.978771i | \(-0.434294\pi\) | ||||
0.204959 | + | 0.978771i | \(0.434294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.6303 | 1.10341 | ||||||||
\(986\) | 0.0846406 | 0.00269551 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.21234 | 0.0385698 | ||||||||
\(989\) | −1.65337 | −0.0525740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3450 | 0.455685 | 0.227842 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227842 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(992\) | −28.8887 | −0.917217 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.66594 | 0.0845585 | ||||||||
\(995\) | −17.9006 | −0.567488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.1668 | −0.987063 | −0.493531 | − | 0.869728i | \(-0.664294\pi\) | ||||
−0.493531 | + | 0.869728i | \(0.664294\pi\) | |||||||
\(998\) | −10.6979 | −0.338637 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.cu.1.3 | 8 | ||
3.2 | odd | 2 | inner | 7623.2.a.cu.1.6 | 8 | ||
11.3 | even | 5 | 693.2.m.h.64.2 | ✓ | 16 | ||
11.4 | even | 5 | 693.2.m.h.379.2 | yes | 16 | ||
11.10 | odd | 2 | 7623.2.a.cv.1.6 | 8 | |||
33.14 | odd | 10 | 693.2.m.h.64.3 | yes | 16 | ||
33.26 | odd | 10 | 693.2.m.h.379.3 | yes | 16 | ||
33.32 | even | 2 | 7623.2.a.cv.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.h.64.2 | ✓ | 16 | 11.3 | even | 5 | ||
693.2.m.h.64.3 | yes | 16 | 33.14 | odd | 10 | ||
693.2.m.h.379.2 | yes | 16 | 11.4 | even | 5 | ||
693.2.m.h.379.3 | yes | 16 | 33.26 | odd | 10 | ||
7623.2.a.cu.1.3 | 8 | 1.1 | even | 1 | trivial | ||
7623.2.a.cu.1.6 | 8 | 3.2 | odd | 2 | inner | ||
7623.2.a.cv.1.3 | 8 | 33.32 | even | 2 | |||
7623.2.a.cv.1.6 | 8 | 11.10 | odd | 2 |