Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.38197 | −0.564185 | ||||||||
\(7\) | 4.23607 | 1.60108 | 0.800542 | − | 0.599277i | \(-0.204545\pi\) | ||||
0.800542 | + | 0.599277i | \(0.204545\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | −0.618034 | −0.195440 | ||||||||
\(11\) | −0.236068 | −0.0711772 | −0.0355886 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355886 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(12\) | −3.61803 | −1.04444 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −3.47214 | −0.842117 | −0.421058 | − | 0.907034i | \(-0.638341\pi\) | ||||
−0.421058 | + | 0.907034i | \(0.638341\pi\) | |||||||
\(18\) | −1.23607 | −0.291344 | ||||||||
\(19\) | 4.23607 | 0.971821 | 0.485910 | − | 0.874009i | \(-0.338488\pi\) | ||||
0.485910 | + | 0.874009i | \(0.338488\pi\) | |||||||
\(20\) | −1.61803 | −0.361803 | ||||||||
\(21\) | 9.47214 | 2.06699 | ||||||||
\(22\) | 0.145898 | 0.0311056 | ||||||||
\(23\) | 3.76393 | 0.784834 | 0.392417 | − | 0.919787i | \(-0.371639\pi\) | ||||
0.392417 | + | 0.919787i | \(0.371639\pi\) | |||||||
\(24\) | 5.00000 | 1.02062 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −6.85410 | −1.29530 | ||||||||
\(29\) | −7.47214 | −1.38754 | −0.693770 | − | 0.720196i | \(-0.744052\pi\) | ||||
−0.693770 | + | 0.720196i | \(0.744052\pi\) | |||||||
\(30\) | −1.38197 | −0.252311 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −0.527864 | −0.0918893 | ||||||||
\(34\) | 2.14590 | 0.368018 | ||||||||
\(35\) | 4.23607 | 0.716026 | ||||||||
\(36\) | −3.23607 | −0.539345 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −2.61803 | −0.424701 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23607 | 0.353553 | ||||||||
\(41\) | 11.9443 | 1.86538 | 0.932691 | − | 0.360677i | \(-0.117454\pi\) | ||||
0.932691 | + | 0.360677i | \(0.117454\pi\) | |||||||
\(42\) | −5.85410 | −0.903308 | ||||||||
\(43\) | −6.23607 | −0.950991 | −0.475496 | − | 0.879718i | \(-0.657731\pi\) | ||||
−0.475496 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(44\) | 0.381966 | 0.0575835 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | −2.32624 | −0.342985 | ||||||||
\(47\) | −4.94427 | −0.721196 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(48\) | 4.14590 | 0.598409 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | −0.618034 | −0.0874032 | ||||||||
\(51\) | −7.76393 | −1.08717 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 1.38197 | 0.188062 | ||||||||
\(55\) | −0.236068 | −0.0318314 | ||||||||
\(56\) | 9.47214 | 1.26577 | ||||||||
\(57\) | 9.47214 | 1.25462 | ||||||||
\(58\) | 4.61803 | 0.606378 | ||||||||
\(59\) | −0.708204 | −0.0922003 | −0.0461001 | − | 0.998937i | \(-0.514679\pi\) | ||||
−0.0461001 | + | 0.998937i | \(0.514679\pi\) | |||||||
\(60\) | −3.61803 | −0.467086 | ||||||||
\(61\) | 14.4164 | 1.84583 | 0.922916 | − | 0.385002i | \(-0.125799\pi\) | ||||
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.47214 | 1.06739 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.326238 | 0.0401571 | ||||||||
\(67\) | −2.70820 | −0.330860 | −0.165430 | − | 0.986222i | \(-0.552901\pi\) | ||||
−0.165430 | + | 0.986222i | \(0.552901\pi\) | |||||||
\(68\) | 5.61803 | 0.681287 | ||||||||
\(69\) | 8.41641 | 1.01322 | ||||||||
\(70\) | −2.61803 | −0.312915 | ||||||||
\(71\) | −6.23607 | −0.740085 | −0.370043 | − | 0.929015i | \(-0.620657\pi\) | ||||
−0.370043 | + | 0.929015i | \(0.620657\pi\) | |||||||
\(72\) | 4.47214 | 0.527046 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −1.85410 | −0.215535 | ||||||||
\(75\) | 2.23607 | 0.258199 | ||||||||
\(76\) | −6.85410 | −0.786219 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.85410 | 0.207295 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −7.38197 | −0.815202 | ||||||||
\(83\) | 8.94427 | 0.981761 | 0.490881 | − | 0.871227i | \(-0.336675\pi\) | ||||
0.490881 | + | 0.871227i | \(0.336675\pi\) | |||||||
\(84\) | −15.3262 | −1.67223 | ||||||||
\(85\) | −3.47214 | −0.376606 | ||||||||
\(86\) | 3.85410 | 0.415599 | ||||||||
\(87\) | −16.7082 | −1.79131 | ||||||||
\(88\) | −0.527864 | −0.0562705 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | −1.23607 | −0.130293 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.09017 | −0.634944 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.05573 | 0.315174 | ||||||||
\(95\) | 4.23607 | 0.434611 | ||||||||
\(96\) | −12.5623 | −1.28213 | ||||||||
\(97\) | −3.47214 | −0.352542 | −0.176271 | − | 0.984342i | \(-0.556404\pi\) | ||||
−0.176271 | + | 0.984342i | \(0.556404\pi\) | |||||||
\(98\) | −6.76393 | −0.683260 | ||||||||
\(99\) | −0.472136 | −0.0474514 | ||||||||
\(100\) | −1.61803 | −0.161803 | ||||||||
\(101\) | 0.527864 | 0.0525244 | 0.0262622 | − | 0.999655i | \(-0.491640\pi\) | ||||
0.0262622 | + | 0.999655i | \(0.491640\pi\) | |||||||
\(102\) | 4.79837 | 0.475110 | ||||||||
\(103\) | 12.9443 | 1.27544 | 0.637719 | − | 0.770270i | \(-0.279878\pi\) | ||||
0.637719 | + | 0.770270i | \(0.279878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.47214 | 0.924386 | ||||||||
\(106\) | −3.70820 | −0.360173 | ||||||||
\(107\) | −5.76393 | −0.557220 | −0.278610 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278610 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(108\) | 3.61803 | 0.348145 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0.145898 | 0.0139108 | ||||||||
\(111\) | 6.70820 | 0.636715 | ||||||||
\(112\) | 7.85410 | 0.742143 | ||||||||
\(113\) | 1.47214 | 0.138487 | 0.0692435 | − | 0.997600i | \(-0.477941\pi\) | ||||
0.0692435 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(114\) | −5.85410 | −0.548287 | ||||||||
\(115\) | 3.76393 | 0.350988 | ||||||||
\(116\) | 12.0902 | 1.12254 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.437694 | 0.0402930 | ||||||||
\(119\) | −14.7082 | −1.34830 | ||||||||
\(120\) | 5.00000 | 0.456435 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | −8.90983 | −0.806658 | ||||||||
\(123\) | 26.7082 | 2.40820 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.23607 | −0.466466 | ||||||||
\(127\) | −4.23607 | −0.375890 | −0.187945 | − | 0.982180i | \(-0.560183\pi\) | ||||
−0.187945 | + | 0.982180i | \(0.560183\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −13.9443 | −1.22772 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0.854102 | 0.0743400 | ||||||||
\(133\) | 17.9443 | 1.55597 | ||||||||
\(134\) | 1.67376 | 0.144591 | ||||||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | −7.76393 | −0.665752 | ||||||||
\(137\) | 1.47214 | 0.125773 | 0.0628865 | − | 0.998021i | \(-0.479969\pi\) | ||||
0.0628865 | + | 0.998021i | \(0.479969\pi\) | |||||||
\(138\) | −5.20163 | −0.442792 | ||||||||
\(139\) | −16.7082 | −1.41717 | −0.708586 | − | 0.705625i | \(-0.750666\pi\) | ||||
−0.708586 | + | 0.705625i | \(0.750666\pi\) | |||||||
\(140\) | −6.85410 | −0.579277 | ||||||||
\(141\) | −11.0557 | −0.931060 | ||||||||
\(142\) | 3.85410 | 0.323429 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.70820 | 0.309017 | ||||||||
\(145\) | −7.47214 | −0.620527 | ||||||||
\(146\) | 3.70820 | 0.306893 | ||||||||
\(147\) | 24.4721 | 2.01843 | ||||||||
\(148\) | −4.85410 | −0.399005 | ||||||||
\(149\) | 4.52786 | 0.370937 | 0.185469 | − | 0.982650i | \(-0.440620\pi\) | ||||
0.185469 | + | 0.982650i | \(0.440620\pi\) | |||||||
\(150\) | −1.38197 | −0.112837 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 9.47214 | 0.768292 | ||||||||
\(153\) | −6.94427 | −0.561411 | ||||||||
\(154\) | 0.618034 | 0.0498026 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4164 | 1.06399 | ||||||||
\(160\) | −5.61803 | −0.444145 | ||||||||
\(161\) | 15.9443 | 1.25658 | ||||||||
\(162\) | 6.79837 | 0.534131 | ||||||||
\(163\) | 14.7082 | 1.15204 | 0.576018 | − | 0.817437i | \(-0.304606\pi\) | ||||
0.576018 | + | 0.817437i | \(0.304606\pi\) | |||||||
\(164\) | −19.3262 | −1.50913 | ||||||||
\(165\) | −0.527864 | −0.0410942 | ||||||||
\(166\) | −5.52786 | −0.429045 | ||||||||
\(167\) | −17.1803 | −1.32945 | −0.664727 | − | 0.747086i | \(-0.731452\pi\) | ||||
−0.664727 | + | 0.747086i | \(0.731452\pi\) | |||||||
\(168\) | 21.1803 | 1.63410 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.14590 | 0.164583 | ||||||||
\(171\) | 8.47214 | 0.647880 | ||||||||
\(172\) | 10.0902 | 0.769368 | ||||||||
\(173\) | −18.8885 | −1.43607 | −0.718035 | − | 0.696007i | \(-0.754958\pi\) | ||||
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(174\) | 10.3262 | 0.782830 | ||||||||
\(175\) | 4.23607 | 0.320217 | ||||||||
\(176\) | −0.437694 | −0.0329924 | ||||||||
\(177\) | −1.58359 | −0.119030 | ||||||||
\(178\) | 5.56231 | 0.416912 | ||||||||
\(179\) | −8.23607 | −0.615593 | −0.307796 | − | 0.951452i | \(-0.599592\pi\) | ||||
−0.307796 | + | 0.951452i | \(0.599592\pi\) | |||||||
\(180\) | −3.23607 | −0.241202 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.2361 | 2.38296 | ||||||||
\(184\) | 8.41641 | 0.620466 | ||||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.819660 | 0.0599395 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | −9.47214 | −0.688997 | ||||||||
\(190\) | −2.61803 | −0.189932 | ||||||||
\(191\) | −27.1803 | −1.96670 | −0.983350 | − | 0.181721i | \(-0.941833\pi\) | ||||
−0.983350 | + | 0.181721i | \(0.941833\pi\) | |||||||
\(192\) | −0.527864 | −0.0380953 | ||||||||
\(193\) | −3.47214 | −0.249930 | −0.124965 | − | 0.992161i | \(-0.539882\pi\) | ||||
−0.124965 | + | 0.992161i | \(0.539882\pi\) | |||||||
\(194\) | 2.14590 | 0.154067 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.7082 | −1.26487 | ||||||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 0.291796 | 0.0207370 | ||||||||
\(199\) | −1.29180 | −0.0915730 | −0.0457865 | − | 0.998951i | \(-0.514579\pi\) | ||||
−0.0457865 | + | 0.998951i | \(0.514579\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | −6.05573 | −0.427138 | ||||||||
\(202\) | −0.326238 | −0.0229540 | ||||||||
\(203\) | −31.6525 | −2.22157 | ||||||||
\(204\) | 12.5623 | 0.879537 | ||||||||
\(205\) | 11.9443 | 0.834224 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 7.52786 | 0.523223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −5.85410 | −0.403971 | ||||||||
\(211\) | −13.1803 | −0.907372 | −0.453686 | − | 0.891162i | \(-0.649891\pi\) | ||||
−0.453686 | + | 0.891162i | \(0.649891\pi\) | |||||||
\(212\) | −9.70820 | −0.666762 | ||||||||
\(213\) | −13.9443 | −0.955446 | ||||||||
\(214\) | 3.56231 | 0.243514 | ||||||||
\(215\) | −6.23607 | −0.425296 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.23607 | 0.0837171 | ||||||||
\(219\) | −13.4164 | −0.906597 | ||||||||
\(220\) | 0.381966 | 0.0257521 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.14590 | −0.278254 | ||||||||
\(223\) | 0.708204 | 0.0474248 | 0.0237124 | − | 0.999719i | \(-0.492451\pi\) | ||||
0.0237124 | + | 0.999719i | \(0.492451\pi\) | |||||||
\(224\) | −23.7984 | −1.59010 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | −0.909830 | −0.0605210 | ||||||||
\(227\) | −6.23607 | −0.413902 | −0.206951 | − | 0.978351i | \(-0.566354\pi\) | ||||
−0.206951 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(228\) | −15.3262 | −1.01500 | ||||||||
\(229\) | 15.8885 | 1.04994 | 0.524972 | − | 0.851119i | \(-0.324076\pi\) | ||||
0.524972 | + | 0.851119i | \(0.324076\pi\) | |||||||
\(230\) | −2.32624 | −0.153388 | ||||||||
\(231\) | −2.23607 | −0.147122 | ||||||||
\(232\) | −16.7082 | −1.09695 | ||||||||
\(233\) | −15.8885 | −1.04089 | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520447 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.94427 | −0.322529 | ||||||||
\(236\) | 1.14590 | 0.0745916 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.09017 | 0.589228 | ||||||||
\(239\) | −25.8885 | −1.67459 | −0.837295 | − | 0.546751i | \(-0.815864\pi\) | ||||
−0.837295 | + | 0.546751i | \(0.815864\pi\) | |||||||
\(240\) | 4.14590 | 0.267617 | ||||||||
\(241\) | 15.0000 | 0.966235 | 0.483117 | − | 0.875556i | \(-0.339504\pi\) | ||||
0.483117 | + | 0.875556i | \(0.339504\pi\) | |||||||
\(242\) | 6.76393 | 0.434802 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | −23.3262 | −1.49331 | ||||||||
\(245\) | 10.9443 | 0.699204 | ||||||||
\(246\) | −16.5066 | −1.05242 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.0000 | 1.26745 | ||||||||
\(250\) | −0.618034 | −0.0390879 | ||||||||
\(251\) | 20.2361 | 1.27729 | 0.638645 | − | 0.769502i | \(-0.279495\pi\) | ||||
0.638645 | + | 0.769502i | \(0.279495\pi\) | |||||||
\(252\) | −13.7082 | −0.863536 | ||||||||
\(253\) | −0.888544 | −0.0558623 | ||||||||
\(254\) | 2.61803 | 0.164270 | ||||||||
\(255\) | −7.76393 | −0.486196 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 17.4721 | 1.08988 | 0.544941 | − | 0.838474i | \(-0.316552\pi\) | ||||
0.544941 | + | 0.838474i | \(0.316552\pi\) | |||||||
\(258\) | 8.61803 | 0.536535 | ||||||||
\(259\) | 12.7082 | 0.789649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.9443 | −0.925027 | ||||||||
\(262\) | 7.41641 | 0.458187 | ||||||||
\(263\) | 3.76393 | 0.232094 | 0.116047 | − | 0.993244i | \(-0.462978\pi\) | ||||
0.116047 | + | 0.993244i | \(0.462978\pi\) | |||||||
\(264\) | −1.18034 | −0.0726449 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −11.0902 | −0.679982 | ||||||||
\(267\) | −20.1246 | −1.23161 | ||||||||
\(268\) | 4.38197 | 0.267671 | ||||||||
\(269\) | −6.52786 | −0.398011 | −0.199005 | − | 0.979998i | \(-0.563771\pi\) | ||||
−0.199005 | + | 0.979998i | \(0.563771\pi\) | |||||||
\(270\) | 1.38197 | 0.0841038 | ||||||||
\(271\) | 1.29180 | 0.0784710 | 0.0392355 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392355 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(272\) | −6.43769 | −0.390343 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.909830 | −0.0549648 | ||||||||
\(275\) | −0.236068 | −0.0142354 | ||||||||
\(276\) | −13.6180 | −0.819709 | ||||||||
\(277\) | 16.8885 | 1.01473 | 0.507367 | − | 0.861730i | \(-0.330619\pi\) | ||||
0.507367 | + | 0.861730i | \(0.330619\pi\) | |||||||
\(278\) | 10.3262 | 0.619327 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.47214 | 0.566068 | ||||||||
\(281\) | −15.8885 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(282\) | 6.83282 | 0.406888 | ||||||||
\(283\) | −10.7082 | −0.636537 | −0.318268 | − | 0.948001i | \(-0.603101\pi\) | ||||
−0.318268 | + | 0.948001i | \(0.603101\pi\) | |||||||
\(284\) | 10.0902 | 0.598741 | ||||||||
\(285\) | 9.47214 | 0.561081 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 50.5967 | 2.98663 | ||||||||
\(288\) | −11.2361 | −0.662092 | ||||||||
\(289\) | −4.94427 | −0.290840 | ||||||||
\(290\) | 4.61803 | 0.271180 | ||||||||
\(291\) | −7.76393 | −0.455130 | ||||||||
\(292\) | 9.70820 | 0.568130 | ||||||||
\(293\) | −29.9443 | −1.74936 | −0.874682 | − | 0.484698i | \(-0.838929\pi\) | ||||
−0.874682 | + | 0.484698i | \(0.838929\pi\) | |||||||
\(294\) | −15.1246 | −0.882085 | ||||||||
\(295\) | −0.708204 | −0.0412332 | ||||||||
\(296\) | 6.70820 | 0.389906 | ||||||||
\(297\) | 0.527864 | 0.0306298 | ||||||||
\(298\) | −2.79837 | −0.162105 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.61803 | −0.208887 | ||||||||
\(301\) | −26.4164 | −1.52262 | ||||||||
\(302\) | −4.94427 | −0.284511 | ||||||||
\(303\) | 1.18034 | 0.0678088 | ||||||||
\(304\) | 7.85410 | 0.450464 | ||||||||
\(305\) | 14.4164 | 0.825481 | ||||||||
\(306\) | 4.29180 | 0.245346 | ||||||||
\(307\) | 24.9443 | 1.42364 | 0.711822 | − | 0.702360i | \(-0.247870\pi\) | ||||
0.711822 | + | 0.702360i | \(0.247870\pi\) | |||||||
\(308\) | 1.61803 | 0.0921960 | ||||||||
\(309\) | 28.9443 | 1.64658 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.88854 | 0.219793 | 0.109897 | − | 0.993943i | \(-0.464948\pi\) | ||||
0.109897 | + | 0.993943i | \(0.464948\pi\) | |||||||
\(314\) | 11.1246 | 0.627798 | ||||||||
\(315\) | 8.47214 | 0.477351 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.8885 | −0.667727 | −0.333864 | − | 0.942621i | \(-0.608352\pi\) | ||||
−0.333864 | + | 0.942621i | \(0.608352\pi\) | |||||||
\(318\) | −8.29180 | −0.464981 | ||||||||
\(319\) | 1.76393 | 0.0987612 | ||||||||
\(320\) | −0.236068 | −0.0131966 | ||||||||
\(321\) | −12.8885 | −0.719368 | ||||||||
\(322\) | −9.85410 | −0.549148 | ||||||||
\(323\) | −14.7082 | −0.818386 | ||||||||
\(324\) | 17.7984 | 0.988799 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.09017 | −0.503458 | ||||||||
\(327\) | −4.47214 | −0.247310 | ||||||||
\(328\) | 26.7082 | 1.47471 | ||||||||
\(329\) | −20.9443 | −1.15470 | ||||||||
\(330\) | 0.326238 | 0.0179588 | ||||||||
\(331\) | −5.65248 | −0.310688 | −0.155344 | − | 0.987860i | \(-0.549649\pi\) | ||||
−0.155344 | + | 0.987860i | \(0.549649\pi\) | |||||||
\(332\) | −14.4721 | −0.794262 | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | 10.6180 | 0.580993 | ||||||||
\(335\) | −2.70820 | −0.147965 | ||||||||
\(336\) | 17.5623 | 0.958102 | ||||||||
\(337\) | −7.88854 | −0.429716 | −0.214858 | − | 0.976645i | \(-0.568929\pi\) | ||||
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.29180 | 0.178786 | ||||||||
\(340\) | 5.61803 | 0.304681 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.23607 | −0.283134 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | −13.9443 | −0.751825 | ||||||||
\(345\) | 8.41641 | 0.453124 | ||||||||
\(346\) | 11.6738 | 0.627585 | ||||||||
\(347\) | 30.7082 | 1.64850 | 0.824251 | − | 0.566224i | \(-0.191596\pi\) | ||||
0.824251 | + | 0.566224i | \(0.191596\pi\) | |||||||
\(348\) | 27.0344 | 1.44920 | ||||||||
\(349\) | 2.41641 | 0.129347 | 0.0646737 | − | 0.997906i | \(-0.479399\pi\) | ||||
0.0646737 | + | 0.997906i | \(0.479399\pi\) | |||||||
\(350\) | −2.61803 | −0.139940 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.32624 | 0.0706887 | ||||||||
\(353\) | −19.4721 | −1.03640 | −0.518199 | − | 0.855260i | \(-0.673397\pi\) | ||||
−0.518199 | + | 0.855260i | \(0.673397\pi\) | |||||||
\(354\) | 0.978714 | 0.0520180 | ||||||||
\(355\) | −6.23607 | −0.330976 | ||||||||
\(356\) | 14.5623 | 0.771801 | ||||||||
\(357\) | −32.8885 | −1.74065 | ||||||||
\(358\) | 5.09017 | 0.269024 | ||||||||
\(359\) | 17.8885 | 0.944121 | 0.472061 | − | 0.881566i | \(-0.343510\pi\) | ||||
0.472061 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(360\) | 4.47214 | 0.235702 | ||||||||
\(361\) | −1.05573 | −0.0555646 | ||||||||
\(362\) | −3.70820 | −0.194899 | ||||||||
\(363\) | −24.4721 | −1.28445 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −19.9230 | −1.04139 | ||||||||
\(367\) | 5.65248 | 0.295057 | 0.147528 | − | 0.989058i | \(-0.452868\pi\) | ||||
0.147528 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(368\) | 6.97871 | 0.363791 | ||||||||
\(369\) | 23.8885 | 1.24359 | ||||||||
\(370\) | −1.85410 | −0.0963902 | ||||||||
\(371\) | 25.4164 | 1.31955 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9443 | 1.44690 | 0.723450 | − | 0.690377i | \(-0.242555\pi\) | ||||
0.723450 | + | 0.690377i | \(0.242555\pi\) | |||||||
\(374\) | −0.506578 | −0.0261945 | ||||||||
\(375\) | 2.23607 | 0.115470 | ||||||||
\(376\) | −11.0557 | −0.570156 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.85410 | 0.301103 | ||||||||
\(379\) | 10.8197 | 0.555769 | 0.277884 | − | 0.960615i | \(-0.410367\pi\) | ||||
0.277884 | + | 0.960615i | \(0.410367\pi\) | |||||||
\(380\) | −6.85410 | −0.351608 | ||||||||
\(381\) | −9.47214 | −0.485272 | ||||||||
\(382\) | 16.7984 | 0.859480 | ||||||||
\(383\) | 4.23607 | 0.216453 | 0.108226 | − | 0.994126i | \(-0.465483\pi\) | ||||
0.108226 | + | 0.994126i | \(0.465483\pi\) | |||||||
\(384\) | 25.4508 | 1.29878 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 2.14590 | 0.109223 | ||||||||
\(387\) | −12.4721 | −0.633994 | ||||||||
\(388\) | 5.61803 | 0.285212 | ||||||||
\(389\) | −0.111456 | −0.00565105 | −0.00282553 | − | 0.999996i | \(-0.500899\pi\) | ||||
−0.00282553 | + | 0.999996i | \(0.500899\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.0689 | −0.660922 | ||||||||
\(392\) | 24.4721 | 1.23603 | ||||||||
\(393\) | −26.8328 | −1.35354 | ||||||||
\(394\) | −1.85410 | −0.0934083 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.763932 | 0.0383890 | ||||||||
\(397\) | 27.9443 | 1.40248 | 0.701241 | − | 0.712924i | \(-0.252630\pi\) | ||||
0.701241 | + | 0.712924i | \(0.252630\pi\) | |||||||
\(398\) | 0.798374 | 0.0400189 | ||||||||
\(399\) | 40.1246 | 2.00874 | ||||||||
\(400\) | 1.85410 | 0.0927051 | ||||||||
\(401\) | 8.88854 | 0.443873 | 0.221936 | − | 0.975061i | \(-0.428762\pi\) | ||||
0.221936 | + | 0.975061i | \(0.428762\pi\) | |||||||
\(402\) | 3.74265 | 0.186666 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.854102 | −0.0424932 | ||||||||
\(405\) | −11.0000 | −0.546594 | ||||||||
\(406\) | 19.5623 | 0.970861 | ||||||||
\(407\) | −0.708204 | −0.0351044 | ||||||||
\(408\) | −17.3607 | −0.859482 | ||||||||
\(409\) | 24.8885 | 1.23066 | 0.615330 | − | 0.788270i | \(-0.289023\pi\) | ||||
0.615330 | + | 0.788270i | \(0.289023\pi\) | |||||||
\(410\) | −7.38197 | −0.364569 | ||||||||
\(411\) | 3.29180 | 0.162372 | ||||||||
\(412\) | −20.9443 | −1.03185 | ||||||||
\(413\) | −3.00000 | −0.147620 | ||||||||
\(414\) | −4.65248 | −0.228657 | ||||||||
\(415\) | 8.94427 | 0.439057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.3607 | −1.82956 | ||||||||
\(418\) | 0.618034 | 0.0302290 | ||||||||
\(419\) | 17.6525 | 0.862380 | 0.431190 | − | 0.902261i | \(-0.358094\pi\) | ||||
0.431190 | + | 0.902261i | \(0.358094\pi\) | |||||||
\(420\) | −15.3262 | −0.747844 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 8.14590 | 0.396536 | ||||||||
\(423\) | −9.88854 | −0.480797 | ||||||||
\(424\) | 13.4164 | 0.651558 | ||||||||
\(425\) | −3.47214 | −0.168423 | ||||||||
\(426\) | 8.61803 | 0.417545 | ||||||||
\(427\) | 61.0689 | 2.95533 | ||||||||
\(428\) | 9.32624 | 0.450801 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.85410 | 0.185861 | ||||||||
\(431\) | 27.1803 | 1.30923 | 0.654615 | − | 0.755962i | \(-0.272831\pi\) | ||||
0.654615 | + | 0.755962i | \(0.272831\pi\) | |||||||
\(432\) | −4.14590 | −0.199470 | ||||||||
\(433\) | −14.5279 | −0.698165 | −0.349082 | − | 0.937092i | \(-0.613507\pi\) | ||||
−0.349082 | + | 0.937092i | \(0.613507\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.7082 | −0.801097 | ||||||||
\(436\) | 3.23607 | 0.154980 | ||||||||
\(437\) | 15.9443 | 0.762718 | ||||||||
\(438\) | 8.29180 | 0.396197 | ||||||||
\(439\) | −22.7082 | −1.08380 | −0.541902 | − | 0.840442i | \(-0.682296\pi\) | ||||
−0.541902 | + | 0.840442i | \(0.682296\pi\) | |||||||
\(440\) | −0.527864 | −0.0251649 | ||||||||
\(441\) | 21.8885 | 1.04231 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.944272 | 0.0448637 | 0.0224319 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224319 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(444\) | −10.8541 | −0.515113 | ||||||||
\(445\) | −9.00000 | −0.426641 | ||||||||
\(446\) | −0.437694 | −0.0207254 | ||||||||
\(447\) | 10.1246 | 0.478878 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 3.94427 | 0.186142 | 0.0930709 | − | 0.995659i | \(-0.470332\pi\) | ||||
0.0930709 | + | 0.995659i | \(0.470332\pi\) | |||||||
\(450\) | −1.23607 | −0.0582688 | ||||||||
\(451\) | −2.81966 | −0.132773 | ||||||||
\(452\) | −2.38197 | −0.112038 | ||||||||
\(453\) | 17.8885 | 0.840477 | ||||||||
\(454\) | 3.85410 | 0.180882 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.1803 | 0.991860 | ||||||||
\(457\) | −1.58359 | −0.0740773 | −0.0370387 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370387 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(458\) | −9.81966 | −0.458843 | ||||||||
\(459\) | 7.76393 | 0.362389 | ||||||||
\(460\) | −6.09017 | −0.283956 | ||||||||
\(461\) | −1.58359 | −0.0737552 | −0.0368776 | − | 0.999320i | \(-0.511741\pi\) | ||||
−0.0368776 | + | 0.999320i | \(0.511741\pi\) | |||||||
\(462\) | 1.38197 | 0.0642949 | ||||||||
\(463\) | 11.0557 | 0.513803 | 0.256902 | − | 0.966438i | \(-0.417298\pi\) | ||||
0.256902 | + | 0.966438i | \(0.417298\pi\) | |||||||
\(464\) | −13.8541 | −0.643161 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.81966 | 0.454887 | ||||||||
\(467\) | 8.94427 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4721 | −0.529734 | ||||||||
\(470\) | 3.05573 | 0.140950 | ||||||||
\(471\) | −40.2492 | −1.85459 | ||||||||
\(472\) | −1.58359 | −0.0728907 | ||||||||
\(473\) | 1.47214 | 0.0676889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.23607 | 0.194364 | ||||||||
\(476\) | 23.7984 | 1.09080 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | 32.1246 | 1.46781 | 0.733905 | − | 0.679252i | \(-0.237695\pi\) | ||||
0.733905 | + | 0.679252i | \(0.237695\pi\) | |||||||
\(480\) | −12.5623 | −0.573388 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.27051 | −0.422260 | ||||||||
\(483\) | 35.6525 | 1.62224 | ||||||||
\(484\) | 17.7082 | 0.804918 | ||||||||
\(485\) | −3.47214 | −0.157662 | ||||||||
\(486\) | 11.0557 | 0.501498 | ||||||||
\(487\) | 14.1246 | 0.640047 | 0.320024 | − | 0.947410i | \(-0.396309\pi\) | ||||
0.320024 | + | 0.947410i | \(0.396309\pi\) | |||||||
\(488\) | 32.2361 | 1.45926 | ||||||||
\(489\) | 32.8885 | 1.48727 | ||||||||
\(490\) | −6.76393 | −0.305563 | ||||||||
\(491\) | −0.236068 | −0.0106536 | −0.00532680 | − | 0.999986i | \(-0.501696\pi\) | ||||
−0.00532680 | + | 0.999986i | \(0.501696\pi\) | |||||||
\(492\) | −43.2148 | −1.94827 | ||||||||
\(493\) | 25.9443 | 1.16847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.472136 | −0.0212209 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.4164 | −1.18494 | ||||||||
\(498\) | −12.3607 | −0.553895 | ||||||||
\(499\) | −21.8885 | −0.979866 | −0.489933 | − | 0.871760i | \(-0.662979\pi\) | ||||
−0.489933 | + | 0.871760i | \(0.662979\pi\) | |||||||
\(500\) | −1.61803 | −0.0723607 | ||||||||
\(501\) | −38.4164 | −1.71632 | ||||||||
\(502\) | −12.5066 | −0.558196 | ||||||||
\(503\) | 9.18034 | 0.409331 | 0.204666 | − | 0.978832i | \(-0.434389\pi\) | ||||
0.204666 | + | 0.978832i | \(0.434389\pi\) | |||||||
\(504\) | 18.9443 | 0.843845 | ||||||||
\(505\) | 0.527864 | 0.0234896 | ||||||||
\(506\) | 0.549150 | 0.0244127 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.85410 | 0.304102 | ||||||||
\(509\) | −33.3607 | −1.47869 | −0.739343 | − | 0.673329i | \(-0.764864\pi\) | ||||
−0.739343 | + | 0.673329i | \(0.764864\pi\) | |||||||
\(510\) | 4.79837 | 0.212476 | ||||||||
\(511\) | −25.4164 | −1.12436 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −9.47214 | −0.418205 | ||||||||
\(514\) | −10.7984 | −0.476296 | ||||||||
\(515\) | 12.9443 | 0.570393 | ||||||||
\(516\) | 22.5623 | 0.993250 | ||||||||
\(517\) | 1.16718 | 0.0513327 | ||||||||
\(518\) | −7.85410 | −0.345089 | ||||||||
\(519\) | −42.2361 | −1.85396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.7771 | 1.30456 | 0.652279 | − | 0.757979i | \(-0.273813\pi\) | ||||
0.652279 | + | 0.757979i | \(0.273813\pi\) | |||||||
\(522\) | 9.23607 | 0.404252 | ||||||||
\(523\) | 5.29180 | 0.231394 | 0.115697 | − | 0.993285i | \(-0.463090\pi\) | ||||
0.115697 | + | 0.993285i | \(0.463090\pi\) | |||||||
\(524\) | 19.4164 | 0.848210 | ||||||||
\(525\) | 9.47214 | 0.413398 | ||||||||
\(526\) | −2.32624 | −0.101429 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.978714 | −0.0425930 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | −3.70820 | −0.161074 | ||||||||
\(531\) | −1.41641 | −0.0614669 | ||||||||
\(532\) | −29.0344 | −1.25880 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.4377 | 0.538232 | ||||||||
\(535\) | −5.76393 | −0.249197 | ||||||||
\(536\) | −6.05573 | −0.261568 | ||||||||
\(537\) | −18.4164 | −0.794727 | ||||||||
\(538\) | 4.03444 | 0.173937 | ||||||||
\(539\) | −2.58359 | −0.111283 | ||||||||
\(540\) | 3.61803 | 0.155695 | ||||||||
\(541\) | −27.8885 | −1.19902 | −0.599511 | − | 0.800366i | \(-0.704638\pi\) | ||||
−0.599511 | + | 0.800366i | \(0.704638\pi\) | |||||||
\(542\) | −0.798374 | −0.0342931 | ||||||||
\(543\) | 13.4164 | 0.575753 | ||||||||
\(544\) | 19.5066 | 0.836338 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.8328 | 0.805233 | 0.402617 | − | 0.915369i | \(-0.368101\pi\) | ||||
0.402617 | + | 0.915369i | \(0.368101\pi\) | |||||||
\(548\) | −2.38197 | −0.101753 | ||||||||
\(549\) | 28.8328 | 1.23055 | ||||||||
\(550\) | 0.145898 | 0.00622111 | ||||||||
\(551\) | −31.6525 | −1.34844 | ||||||||
\(552\) | 18.8197 | 0.801018 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.4377 | −0.443455 | ||||||||
\(555\) | 6.70820 | 0.284747 | ||||||||
\(556\) | 27.0344 | 1.14652 | ||||||||
\(557\) | −9.94427 | −0.421352 | −0.210676 | − | 0.977556i | \(-0.567567\pi\) | ||||
−0.210676 | + | 0.977556i | \(0.567567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.85410 | 0.331896 | ||||||||
\(561\) | 1.83282 | 0.0773815 | ||||||||
\(562\) | 9.81966 | 0.414217 | ||||||||
\(563\) | 30.7082 | 1.29420 | 0.647098 | − | 0.762407i | \(-0.275982\pi\) | ||||
0.647098 | + | 0.762407i | \(0.275982\pi\) | |||||||
\(564\) | 17.8885 | 0.753244 | ||||||||
\(565\) | 1.47214 | 0.0619332 | ||||||||
\(566\) | 6.61803 | 0.278177 | ||||||||
\(567\) | −46.5967 | −1.95688 | ||||||||
\(568\) | −13.9443 | −0.585089 | ||||||||
\(569\) | 16.8885 | 0.708005 | 0.354002 | − | 0.935245i | \(-0.384821\pi\) | ||||
0.354002 | + | 0.935245i | \(0.384821\pi\) | |||||||
\(570\) | −5.85410 | −0.245201 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −60.7771 | −2.53900 | ||||||||
\(574\) | −31.2705 | −1.30521 | ||||||||
\(575\) | 3.76393 | 0.156967 | ||||||||
\(576\) | −0.472136 | −0.0196723 | ||||||||
\(577\) | 27.8885 | 1.16102 | 0.580508 | − | 0.814255i | \(-0.302854\pi\) | ||||
0.580508 | + | 0.814255i | \(0.302854\pi\) | |||||||
\(578\) | 3.05573 | 0.127102 | ||||||||
\(579\) | −7.76393 | −0.322658 | ||||||||
\(580\) | 12.0902 | 0.502017 | ||||||||
\(581\) | 37.8885 | 1.57188 | ||||||||
\(582\) | 4.79837 | 0.198899 | ||||||||
\(583\) | −1.41641 | −0.0586616 | ||||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5066 | 0.764500 | ||||||||
\(587\) | 10.2361 | 0.422488 | 0.211244 | − | 0.977433i | \(-0.432249\pi\) | ||||
0.211244 | + | 0.977433i | \(0.432249\pi\) | |||||||
\(588\) | −39.5967 | −1.63294 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.437694 | 0.0180196 | ||||||||
\(591\) | 6.70820 | 0.275939 | ||||||||
\(592\) | 5.56231 | 0.228609 | ||||||||
\(593\) | −7.88854 | −0.323944 | −0.161972 | − | 0.986795i | \(-0.551785\pi\) | ||||
−0.161972 | + | 0.986795i | \(0.551785\pi\) | |||||||
\(594\) | −0.326238 | −0.0133857 | ||||||||
\(595\) | −14.7082 | −0.602978 | ||||||||
\(596\) | −7.32624 | −0.300094 | ||||||||
\(597\) | −2.88854 | −0.118220 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 5.00000 | 0.204124 | ||||||||
\(601\) | 43.9443 | 1.79252 | 0.896262 | − | 0.443525i | \(-0.146272\pi\) | ||||
0.896262 | + | 0.443525i | \(0.146272\pi\) | |||||||
\(602\) | 16.3262 | 0.665408 | ||||||||
\(603\) | −5.41641 | −0.220573 | ||||||||
\(604\) | −12.9443 | −0.526695 | ||||||||
\(605\) | −10.9443 | −0.444948 | ||||||||
\(606\) | −0.729490 | −0.0296335 | ||||||||
\(607\) | −0.708204 | −0.0287451 | −0.0143726 | − | 0.999897i | \(-0.504575\pi\) | ||||
−0.0143726 | + | 0.999897i | \(0.504575\pi\) | |||||||
\(608\) | −23.7984 | −0.965152 | ||||||||
\(609\) | −70.7771 | −2.86803 | ||||||||
\(610\) | −8.90983 | −0.360748 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 11.2361 | 0.454191 | ||||||||
\(613\) | 39.9443 | 1.61333 | 0.806667 | − | 0.591006i | \(-0.201269\pi\) | ||||
0.806667 | + | 0.591006i | \(0.201269\pi\) | |||||||
\(614\) | −15.4164 | −0.622156 | ||||||||
\(615\) | 26.7082 | 1.07698 | ||||||||
\(616\) | −2.23607 | −0.0900937 | ||||||||
\(617\) | −40.4164 | −1.62710 | −0.813552 | − | 0.581493i | \(-0.802469\pi\) | ||||
−0.813552 | + | 0.581493i | \(0.802469\pi\) | |||||||
\(618\) | −17.8885 | −0.719583 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.41641 | −0.337739 | ||||||||
\(622\) | 14.8328 | 0.594742 | ||||||||
\(623\) | −38.1246 | −1.52743 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.40325 | −0.0960533 | ||||||||
\(627\) | −2.23607 | −0.0893000 | ||||||||
\(628\) | 29.1246 | 1.16220 | ||||||||
\(629\) | −10.4164 | −0.415329 | ||||||||
\(630\) | −5.23607 | −0.208610 | ||||||||
\(631\) | −16.1246 | −0.641911 | −0.320955 | − | 0.947094i | \(-0.604004\pi\) | ||||
−0.320955 | + | 0.947094i | \(0.604004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.4721 | −1.17141 | ||||||||
\(634\) | 7.34752 | 0.291807 | ||||||||
\(635\) | −4.23607 | −0.168103 | ||||||||
\(636\) | −21.7082 | −0.860786 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.09017 | −0.0431602 | ||||||||
\(639\) | −12.4721 | −0.493390 | ||||||||
\(640\) | 11.3820 | 0.449912 | ||||||||
\(641\) | 8.88854 | 0.351076 | 0.175538 | − | 0.984473i | \(-0.443833\pi\) | ||||
0.175538 | + | 0.984473i | \(0.443833\pi\) | |||||||
\(642\) | 7.96556 | 0.314376 | ||||||||
\(643\) | −17.2918 | −0.681922 | −0.340961 | − | 0.940077i | \(-0.610752\pi\) | ||||
−0.340961 | + | 0.940077i | \(0.610752\pi\) | |||||||
\(644\) | −25.7984 | −1.01660 | ||||||||
\(645\) | −13.9443 | −0.549055 | ||||||||
\(646\) | 9.09017 | 0.357648 | ||||||||
\(647\) | 2.59675 | 0.102089 | 0.0510443 | − | 0.998696i | \(-0.483745\pi\) | ||||
0.0510443 | + | 0.998696i | \(0.483745\pi\) | |||||||
\(648\) | −24.5967 | −0.966252 | ||||||||
\(649\) | 0.167184 | 0.00656256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.7984 | −0.932016 | ||||||||
\(653\) | −21.0000 | −0.821794 | −0.410897 | − | 0.911682i | \(-0.634784\pi\) | ||||
−0.410897 | + | 0.911682i | \(0.634784\pi\) | |||||||
\(654\) | 2.76393 | 0.108078 | ||||||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | 22.1459 | 0.864652 | ||||||||
\(657\) | −12.0000 | −0.468165 | ||||||||
\(658\) | 12.9443 | 0.504620 | ||||||||
\(659\) | −43.7639 | −1.70480 | −0.852400 | − | 0.522890i | \(-0.824854\pi\) | ||||
−0.852400 | + | 0.522890i | \(0.824854\pi\) | |||||||
\(660\) | 0.854102 | 0.0332459 | ||||||||
\(661\) | −41.3607 | −1.60874 | −0.804372 | − | 0.594126i | \(-0.797498\pi\) | ||||
−0.804372 | + | 0.594126i | \(0.797498\pi\) | |||||||
\(662\) | 3.49342 | 0.135776 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.0000 | 0.776151 | ||||||||
\(665\) | 17.9443 | 0.695849 | ||||||||
\(666\) | −3.70820 | −0.143690 | ||||||||
\(667\) | −28.1246 | −1.08899 | ||||||||
\(668\) | 27.7984 | 1.07555 | ||||||||
\(669\) | 1.58359 | 0.0612252 | ||||||||
\(670\) | 1.67376 | 0.0646631 | ||||||||
\(671\) | −3.40325 | −0.131381 | ||||||||
\(672\) | −53.2148 | −2.05280 | ||||||||
\(673\) | −9.58359 | −0.369420 | −0.184710 | − | 0.982793i | \(-0.559135\pi\) | ||||
−0.184710 | + | 0.982793i | \(0.559135\pi\) | |||||||
\(674\) | 4.87539 | 0.187793 | ||||||||
\(675\) | −2.23607 | −0.0860663 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1115 | 0.465481 | 0.232741 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232741 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(678\) | −2.03444 | −0.0781323 | ||||||||
\(679\) | −14.7082 | −0.564449 | ||||||||
\(680\) | −7.76393 | −0.297733 | ||||||||
\(681\) | −13.9443 | −0.534346 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7639 | 0.985829 | 0.492915 | − | 0.870078i | \(-0.335931\pi\) | ||||
0.492915 | + | 0.870078i | \(0.335931\pi\) | |||||||
\(684\) | −13.7082 | −0.524146 | ||||||||
\(685\) | 1.47214 | 0.0562474 | ||||||||
\(686\) | −10.3262 | −0.394258 | ||||||||
\(687\) | 35.5279 | 1.35547 | ||||||||
\(688\) | −11.5623 | −0.440809 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.20163 | −0.198023 | ||||||||
\(691\) | 38.5967 | 1.46829 | 0.734145 | − | 0.678993i | \(-0.237583\pi\) | ||||
0.734145 | + | 0.678993i | \(0.237583\pi\) | |||||||
\(692\) | 30.5623 | 1.16180 | ||||||||
\(693\) | −2.00000 | −0.0759737 | ||||||||
\(694\) | −18.9787 | −0.720422 | ||||||||
\(695\) | −16.7082 | −0.633778 | ||||||||
\(696\) | −37.3607 | −1.41615 | ||||||||
\(697\) | −41.4721 | −1.57087 | ||||||||
\(698\) | −1.49342 | −0.0565269 | ||||||||
\(699\) | −35.5279 | −1.34379 | ||||||||
\(700\) | −6.85410 | −0.259061 | ||||||||
\(701\) | 7.88854 | 0.297946 | 0.148973 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148973 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7082 | 0.479299 | ||||||||
\(704\) | 0.0557281 | 0.00210033 | ||||||||
\(705\) | −11.0557 | −0.416383 | ||||||||
\(706\) | 12.0344 | 0.452922 | ||||||||
\(707\) | 2.23607 | 0.0840960 | ||||||||
\(708\) | 2.56231 | 0.0962974 | ||||||||
\(709\) | 24.3050 | 0.912792 | 0.456396 | − | 0.889777i | \(-0.349140\pi\) | ||||
0.456396 | + | 0.889777i | \(0.349140\pi\) | |||||||
\(710\) | 3.85410 | 0.144642 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.1246 | −0.754202 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 20.3262 | 0.760690 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.3262 | 0.498025 | ||||||||
\(717\) | −57.8885 | −2.16189 | ||||||||
\(718\) | −11.0557 | −0.412596 | ||||||||
\(719\) | −32.1246 | −1.19805 | −0.599023 | − | 0.800732i | \(-0.704444\pi\) | ||||
−0.599023 | + | 0.800732i | \(0.704444\pi\) | |||||||
\(720\) | 3.70820 | 0.138197 | ||||||||
\(721\) | 54.8328 | 2.04208 | ||||||||
\(722\) | 0.652476 | 0.0242826 | ||||||||
\(723\) | 33.5410 | 1.24740 | ||||||||
\(724\) | −9.70820 | −0.360803 | ||||||||
\(725\) | −7.47214 | −0.277508 | ||||||||
\(726\) | 15.1246 | 0.561327 | ||||||||
\(727\) | 28.9443 | 1.07348 | 0.536742 | − | 0.843747i | \(-0.319655\pi\) | ||||
0.536742 | + | 0.843747i | \(0.319655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 3.70820 | 0.137247 | ||||||||
\(731\) | 21.6525 | 0.800846 | ||||||||
\(732\) | −52.1591 | −1.92785 | ||||||||
\(733\) | −43.8885 | −1.62106 | −0.810530 | − | 0.585697i | \(-0.800821\pi\) | ||||
−0.810530 | + | 0.585697i | \(0.800821\pi\) | |||||||
\(734\) | −3.49342 | −0.128945 | ||||||||
\(735\) | 24.4721 | 0.902668 | ||||||||
\(736\) | −21.1459 | −0.779448 | ||||||||
\(737\) | 0.639320 | 0.0235497 | ||||||||
\(738\) | −14.7639 | −0.543468 | ||||||||
\(739\) | 27.5410 | 1.01311 | 0.506556 | − | 0.862207i | \(-0.330918\pi\) | ||||
0.506556 | + | 0.862207i | \(0.330918\pi\) | |||||||
\(740\) | −4.85410 | −0.178440 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.7082 | −0.576666 | ||||||||
\(743\) | −38.1246 | −1.39866 | −0.699328 | − | 0.714801i | \(-0.746517\pi\) | ||||
−0.699328 | + | 0.714801i | \(0.746517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.52786 | 0.165888 | ||||||||
\(746\) | −17.2705 | −0.632318 | ||||||||
\(747\) | 17.8885 | 0.654508 | ||||||||
\(748\) | −1.32624 | −0.0484921 | ||||||||
\(749\) | −24.4164 | −0.892156 | ||||||||
\(750\) | −1.38197 | −0.0504623 | ||||||||
\(751\) | −30.7082 | −1.12056 | −0.560279 | − | 0.828304i | \(-0.689306\pi\) | ||||
−0.560279 | + | 0.828304i | \(0.689306\pi\) | |||||||
\(752\) | −9.16718 | −0.334293 | ||||||||
\(753\) | 45.2492 | 1.64897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 15.3262 | 0.557410 | ||||||||
\(757\) | −6.88854 | −0.250368 | −0.125184 | − | 0.992134i | \(-0.539952\pi\) | ||||
−0.125184 | + | 0.992134i | \(0.539952\pi\) | |||||||
\(758\) | −6.68692 | −0.242880 | ||||||||
\(759\) | −1.98684 | −0.0721179 | ||||||||
\(760\) | 9.47214 | 0.343590 | ||||||||
\(761\) | −37.9443 | −1.37548 | −0.687739 | − | 0.725958i | \(-0.741397\pi\) | ||||
−0.687739 | + | 0.725958i | \(0.741397\pi\) | |||||||
\(762\) | 5.85410 | 0.212072 | ||||||||
\(763\) | −8.47214 | −0.306712 | ||||||||
\(764\) | 43.9787 | 1.59109 | ||||||||
\(765\) | −6.94427 | −0.251071 | ||||||||
\(766\) | −2.61803 | −0.0945934 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −14.6738 | −0.529494 | ||||||||
\(769\) | 29.8328 | 1.07580 | 0.537899 | − | 0.843009i | \(-0.319218\pi\) | ||||
0.537899 | + | 0.843009i | \(0.319218\pi\) | |||||||
\(770\) | 0.618034 | 0.0222724 | ||||||||
\(771\) | 39.0689 | 1.40703 | ||||||||
\(772\) | 5.61803 | 0.202197 | ||||||||
\(773\) | −20.0557 | −0.721354 | −0.360677 | − | 0.932691i | \(-0.617454\pi\) | ||||
−0.360677 | + | 0.932691i | \(0.617454\pi\) | |||||||
\(774\) | 7.70820 | 0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.76393 | −0.278709 | ||||||||
\(777\) | 28.4164 | 1.01943 | ||||||||
\(778\) | 0.0688837 | 0.00246960 | ||||||||
\(779\) | 50.5967 | 1.81282 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.47214 | 0.0526772 | ||||||||
\(782\) | 8.07701 | 0.288833 | ||||||||
\(783\) | 16.7082 | 0.597102 | ||||||||
\(784\) | 20.2918 | 0.724707 | ||||||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | 16.5836 | 0.591517 | ||||||||
\(787\) | 29.5410 | 1.05302 | 0.526512 | − | 0.850168i | \(-0.323500\pi\) | ||||
0.526512 | + | 0.850168i | \(0.323500\pi\) | |||||||
\(788\) | −4.85410 | −0.172920 | ||||||||
\(789\) | 8.41641 | 0.299632 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.23607 | 0.221729 | ||||||||
\(792\) | −1.05573 | −0.0375137 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17.2705 | −0.612907 | ||||||||
\(795\) | 13.4164 | 0.475831 | ||||||||
\(796\) | 2.09017 | 0.0740841 | ||||||||
\(797\) | 53.8328 | 1.90686 | 0.953428 | − | 0.301620i | \(-0.0975275\pi\) | ||||
0.953428 | + | 0.301620i | \(0.0975275\pi\) | |||||||
\(798\) | −24.7984 | −0.877853 | ||||||||
\(799\) | 17.1672 | 0.607331 | ||||||||
\(800\) | −5.61803 | −0.198627 | ||||||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | −5.49342 | −0.193979 | ||||||||
\(803\) | 1.41641 | 0.0499839 | ||||||||
\(804\) | 9.79837 | 0.345562 | ||||||||
\(805\) | 15.9443 | 0.561962 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.5967 | −0.513830 | ||||||||
\(808\) | 1.18034 | 0.0415242 | ||||||||
\(809\) | −2.88854 | −0.101556 | −0.0507779 | − | 0.998710i | \(-0.516170\pi\) | ||||
−0.0507779 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(810\) | 6.79837 | 0.238871 | ||||||||
\(811\) | 31.7771 | 1.11584 | 0.557922 | − | 0.829893i | \(-0.311599\pi\) | ||||
0.557922 | + | 0.829893i | \(0.311599\pi\) | |||||||
\(812\) | 51.2148 | 1.79729 | ||||||||
\(813\) | 2.88854 | 0.101306 | ||||||||
\(814\) | 0.437694 | 0.0153412 | ||||||||
\(815\) | 14.7082 | 0.515206 | ||||||||
\(816\) | −14.3951 | −0.503930 | ||||||||
\(817\) | −26.4164 | −0.924193 | ||||||||
\(818\) | −15.3820 | −0.537818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.3262 | −0.674902 | ||||||||
\(821\) | −25.3607 | −0.885094 | −0.442547 | − | 0.896745i | \(-0.645925\pi\) | ||||
−0.442547 | + | 0.896745i | \(0.645925\pi\) | |||||||
\(822\) | −2.03444 | −0.0709593 | ||||||||
\(823\) | −26.5967 | −0.927104 | −0.463552 | − | 0.886070i | \(-0.653425\pi\) | ||||
−0.463552 | + | 0.886070i | \(0.653425\pi\) | |||||||
\(824\) | 28.9443 | 1.00832 | ||||||||
\(825\) | −0.527864 | −0.0183779 | ||||||||
\(826\) | 1.85410 | 0.0645125 | ||||||||
\(827\) | −8.94427 | −0.311023 | −0.155511 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155511 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(828\) | −12.1803 | −0.423296 | ||||||||
\(829\) | −43.2492 | −1.50211 | −0.751054 | − | 0.660241i | \(-0.770454\pi\) | ||||
−0.751054 | + | 0.660241i | \(0.770454\pi\) | |||||||
\(830\) | −5.52786 | −0.191875 | ||||||||
\(831\) | 37.7639 | 1.31002 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.0000 | −1.31662 | ||||||||
\(834\) | 23.0902 | 0.799547 | ||||||||
\(835\) | −17.1803 | −0.594550 | ||||||||
\(836\) | 1.61803 | 0.0559609 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.9098 | −0.376874 | ||||||||
\(839\) | 30.7082 | 1.06016 | 0.530082 | − | 0.847946i | \(-0.322161\pi\) | ||||
0.530082 | + | 0.847946i | \(0.322161\pi\) | |||||||
\(840\) | 21.1803 | 0.730791 | ||||||||
\(841\) | 26.8328 | 0.925270 | ||||||||
\(842\) | −3.70820 | −0.127793 | ||||||||
\(843\) | −35.5279 | −1.22364 | ||||||||
\(844\) | 21.3262 | 0.734079 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.11146 | 0.210116 | ||||||||
\(847\) | −46.3607 | −1.59297 | ||||||||
\(848\) | 11.1246 | 0.382021 | ||||||||
\(849\) | −23.9443 | −0.821765 | ||||||||
\(850\) | 2.14590 | 0.0736037 | ||||||||
\(851\) | 11.2918 | 0.387078 | ||||||||
\(852\) | 22.5623 | 0.772972 | ||||||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | −37.7426 | −1.29153 | ||||||||
\(855\) | 8.47214 | 0.289741 | ||||||||
\(856\) | −12.8885 | −0.440521 | ||||||||
\(857\) | 35.8885 | 1.22593 | 0.612965 | − | 0.790110i | \(-0.289977\pi\) | ||||
0.612965 | + | 0.790110i | \(0.289977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.8885 | 0.746827 | 0.373414 | − | 0.927665i | \(-0.378187\pi\) | ||||
0.373414 | + | 0.927665i | \(0.378187\pi\) | |||||||
\(860\) | 10.0902 | 0.344072 | ||||||||
\(861\) | 113.138 | 3.85572 | ||||||||
\(862\) | −16.7984 | −0.572155 | ||||||||
\(863\) | 14.8328 | 0.504915 | 0.252457 | − | 0.967608i | \(-0.418761\pi\) | ||||
0.252457 | + | 0.967608i | \(0.418761\pi\) | |||||||
\(864\) | 12.5623 | 0.427378 | ||||||||
\(865\) | −18.8885 | −0.642230 | ||||||||
\(866\) | 8.97871 | 0.305109 | ||||||||
\(867\) | −11.0557 | −0.375472 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.3262 | 0.350092 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.47214 | −0.151446 | ||||||||
\(873\) | −6.94427 | −0.235028 | ||||||||
\(874\) | −9.85410 | −0.333320 | ||||||||
\(875\) | 4.23607 | 0.143205 | ||||||||
\(876\) | 21.7082 | 0.733452 | ||||||||
\(877\) | −33.7214 | −1.13869 | −0.569345 | − | 0.822099i | \(-0.692803\pi\) | ||||
−0.569345 | + | 0.822099i | \(0.692803\pi\) | |||||||
\(878\) | 14.0344 | 0.473639 | ||||||||
\(879\) | −66.9574 | −2.25842 | ||||||||
\(880\) | −0.437694 | −0.0147547 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | −13.5279 | −0.455507 | ||||||||
\(883\) | −42.8328 | −1.44144 | −0.720720 | − | 0.693227i | \(-0.756188\pi\) | ||||
−0.720720 | + | 0.693227i | \(0.756188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.58359 | −0.0532319 | ||||||||
\(886\) | −0.583592 | −0.0196062 | ||||||||
\(887\) | 44.4853 | 1.49367 | 0.746835 | − | 0.665009i | \(-0.231572\pi\) | ||||
0.746835 | + | 0.665009i | \(0.231572\pi\) | |||||||
\(888\) | 15.0000 | 0.503367 | ||||||||
\(889\) | −17.9443 | −0.601832 | ||||||||
\(890\) | 5.56231 | 0.186449 | ||||||||
\(891\) | 2.59675 | 0.0869943 | ||||||||
\(892\) | −1.14590 | −0.0383675 | ||||||||
\(893\) | −20.9443 | −0.700873 | ||||||||
\(894\) | −6.25735 | −0.209277 | ||||||||
\(895\) | −8.23607 | −0.275301 | ||||||||
\(896\) | 48.2148 | 1.61074 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.43769 | −0.0813469 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.23607 | −0.107869 | ||||||||
\(901\) | −20.8328 | −0.694042 | ||||||||
\(902\) | 1.74265 | 0.0580238 | ||||||||
\(903\) | −59.0689 | −1.96569 | ||||||||
\(904\) | 3.29180 | 0.109484 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | −11.0557 | −0.367302 | ||||||||
\(907\) | 20.1246 | 0.668227 | 0.334113 | − | 0.942533i | \(-0.391563\pi\) | ||||
0.334113 | + | 0.942533i | \(0.391563\pi\) | |||||||
\(908\) | 10.0902 | 0.334854 | ||||||||
\(909\) | 1.05573 | 0.0350163 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 17.5623 | 0.581546 | ||||||||
\(913\) | −2.11146 | −0.0698790 | ||||||||
\(914\) | 0.978714 | 0.0323730 | ||||||||
\(915\) | 32.2361 | 1.06569 | ||||||||
\(916\) | −25.7082 | −0.849423 | ||||||||
\(917\) | −50.8328 | −1.67865 | ||||||||
\(918\) | −4.79837 | −0.158370 | ||||||||
\(919\) | 46.7082 | 1.54076 | 0.770381 | − | 0.637584i | \(-0.220066\pi\) | ||||
0.770381 | + | 0.637584i | \(0.220066\pi\) | |||||||
\(920\) | 8.41641 | 0.277481 | ||||||||
\(921\) | 55.7771 | 1.83792 | ||||||||
\(922\) | 0.978714 | 0.0322322 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.61803 | 0.119025 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | −6.83282 | −0.224540 | ||||||||
\(927\) | 25.8885 | 0.850291 | ||||||||
\(928\) | 41.9787 | 1.37802 | ||||||||
\(929\) | 19.9443 | 0.654350 | 0.327175 | − | 0.944964i | \(-0.393903\pi\) | ||||
0.327175 | + | 0.944964i | \(0.393903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.3607 | 1.51941 | ||||||||
\(932\) | 25.7082 | 0.842100 | ||||||||
\(933\) | −53.6656 | −1.75693 | ||||||||
\(934\) | −5.52786 | −0.180877 | ||||||||
\(935\) | 0.819660 | 0.0268058 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 7.09017 | 0.231502 | ||||||||
\(939\) | 8.69505 | 0.283752 | ||||||||
\(940\) | 8.00000 | 0.260931 | ||||||||
\(941\) | −11.8885 | −0.387555 | −0.193778 | − | 0.981045i | \(-0.562074\pi\) | ||||
−0.193778 | + | 0.981045i | \(0.562074\pi\) | |||||||
\(942\) | 24.8754 | 0.810484 | ||||||||
\(943\) | 44.9574 | 1.46402 | ||||||||
\(944\) | −1.31308 | −0.0427372 | ||||||||
\(945\) | −9.47214 | −0.308129 | ||||||||
\(946\) | −0.909830 | −0.0295811 | ||||||||
\(947\) | 39.1803 | 1.27319 | 0.636595 | − | 0.771198i | \(-0.280342\pi\) | ||||
0.636595 | + | 0.771198i | \(0.280342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.61803 | −0.0849402 | ||||||||
\(951\) | −26.5836 | −0.862032 | ||||||||
\(952\) | −32.8885 | −1.06592 | ||||||||
\(953\) | 42.1935 | 1.36678 | 0.683391 | − | 0.730053i | \(-0.260505\pi\) | ||||
0.683391 | + | 0.730053i | \(0.260505\pi\) | |||||||
\(954\) | −7.41641 | −0.240115 | ||||||||
\(955\) | −27.1803 | −0.879535 | ||||||||
\(956\) | 41.8885 | 1.35477 | ||||||||
\(957\) | 3.94427 | 0.127500 | ||||||||
\(958\) | −19.8541 | −0.641457 | ||||||||
\(959\) | 6.23607 | 0.201373 | ||||||||
\(960\) | −0.527864 | −0.0170367 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.5279 | −0.371480 | ||||||||
\(964\) | −24.2705 | −0.781700 | ||||||||
\(965\) | −3.47214 | −0.111772 | ||||||||
\(966\) | −22.0344 | −0.708947 | ||||||||
\(967\) | −54.8328 | −1.76330 | −0.881652 | − | 0.471900i | \(-0.843568\pi\) | ||||
−0.881652 | + | 0.471900i | \(0.843568\pi\) | |||||||
\(968\) | −24.4721 | −0.786564 | ||||||||
\(969\) | −32.8885 | −1.05653 | ||||||||
\(970\) | 2.14590 | 0.0689006 | ||||||||
\(971\) | −11.7639 | −0.377523 | −0.188761 | − | 0.982023i | \(-0.560447\pi\) | ||||
−0.188761 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(972\) | 28.9443 | 0.928388 | ||||||||
\(973\) | −70.7771 | −2.26901 | ||||||||
\(974\) | −8.72949 | −0.279711 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.7295 | 0.855590 | ||||||||
\(977\) | 7.58359 | 0.242621 | 0.121310 | − | 0.992615i | \(-0.461290\pi\) | ||||
0.121310 | + | 0.992615i | \(0.461290\pi\) | |||||||
\(978\) | −20.3262 | −0.649961 | ||||||||
\(979\) | 2.12461 | 0.0679029 | ||||||||
\(980\) | −17.7082 | −0.565668 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 0.145898 | 0.00465579 | ||||||||
\(983\) | 38.8328 | 1.23857 | 0.619287 | − | 0.785165i | \(-0.287422\pi\) | ||||
0.619287 | + | 0.785165i | \(0.287422\pi\) | |||||||
\(984\) | 59.7214 | 1.90385 | ||||||||
\(985\) | 3.00000 | 0.0955879 | ||||||||
\(986\) | −16.0344 | −0.510641 | ||||||||
\(987\) | −46.8328 | −1.49070 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.4721 | −0.746371 | ||||||||
\(990\) | 0.291796 | 0.00927389 | ||||||||
\(991\) | −46.7082 | −1.48373 | −0.741867 | − | 0.670547i | \(-0.766060\pi\) | ||||
−0.741867 | + | 0.670547i | \(0.766060\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.6393 | −0.401097 | ||||||||
\(994\) | 16.3262 | 0.517837 | ||||||||
\(995\) | −1.29180 | −0.0409527 | ||||||||
\(996\) | −32.3607 | −1.02539 | ||||||||
\(997\) | −18.8885 | −0.598206 | −0.299103 | − | 0.954221i | \(-0.596687\pi\) | ||||
−0.299103 | + | 0.954221i | \(0.596687\pi\) | |||||||
\(998\) | 13.5279 | 0.428217 | ||||||||
\(999\) | −6.70820 | −0.212238 |
(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 | 845.2.a.e.1.1 | 2 | ||
3.2 | odd | 2 | 7605.2.a.ba.1.2 | 2 | |||
5.4 | even | 2 | 4225.2.a.u.1.2 | 2 | |||
13.2 | odd | 12 | 845.2.m.e.316.2 | 8 | |||
13.3 | even | 3 | 65.2.e.a.61.2 | yes | 4 | ||
13.4 | even | 6 | 845.2.e.g.146.1 | 4 | |||
13.5 | odd | 4 | 845.2.c.c.506.3 | 4 | |||
13.6 | odd | 12 | 845.2.m.e.361.3 | 8 | |||
13.7 | odd | 12 | 845.2.m.e.361.2 | 8 | |||
13.8 | odd | 4 | 845.2.c.c.506.2 | 4 | |||
13.9 | even | 3 | 65.2.e.a.16.2 | ✓ | 4 | ||
13.10 | even | 6 | 845.2.e.g.191.1 | 4 | |||
13.11 | odd | 12 | 845.2.m.e.316.3 | 8 | |||
13.12 | even | 2 | 845.2.a.b.1.2 | 2 | |||
39.29 | odd | 6 | 585.2.j.e.451.1 | 4 | |||
39.35 | odd | 6 | 585.2.j.e.406.1 | 4 | |||
39.38 | odd | 2 | 7605.2.a.bf.1.1 | 2 | |||
52.3 | odd | 6 | 1040.2.q.n.321.2 | 4 | |||
52.35 | odd | 6 | 1040.2.q.n.81.2 | 4 | |||
65.3 | odd | 12 | 325.2.o.a.74.2 | 8 | |||
65.9 | even | 6 | 325.2.e.b.276.1 | 4 | |||
65.22 | odd | 12 | 325.2.o.a.224.2 | 8 | |||
65.29 | even | 6 | 325.2.e.b.126.1 | 4 | |||
65.42 | odd | 12 | 325.2.o.a.74.3 | 8 | |||
65.48 | odd | 12 | 325.2.o.a.224.3 | 8 | |||
65.64 | even | 2 | 4225.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.a.16.2 | ✓ | 4 | 13.9 | even | 3 | ||
65.2.e.a.61.2 | yes | 4 | 13.3 | even | 3 | ||
325.2.e.b.126.1 | 4 | 65.29 | even | 6 | |||
325.2.e.b.276.1 | 4 | 65.9 | even | 6 | |||
325.2.o.a.74.2 | 8 | 65.3 | odd | 12 | |||
325.2.o.a.74.3 | 8 | 65.42 | odd | 12 | |||
325.2.o.a.224.2 | 8 | 65.22 | odd | 12 | |||
325.2.o.a.224.3 | 8 | 65.48 | odd | 12 | |||
585.2.j.e.406.1 | 4 | 39.35 | odd | 6 | |||
585.2.j.e.451.1 | 4 | 39.29 | odd | 6 | |||
845.2.a.b.1.2 | 2 | 13.12 | even | 2 | |||
845.2.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
845.2.c.c.506.2 | 4 | 13.8 | odd | 4 | |||
845.2.c.c.506.3 | 4 | 13.5 | odd | 4 | |||
845.2.e.g.146.1 | 4 | 13.4 | even | 6 | |||
845.2.e.g.191.1 | 4 | 13.10 | even | 6 | |||
845.2.m.e.316.2 | 8 | 13.2 | odd | 12 | |||
845.2.m.e.316.3 | 8 | 13.11 | odd | 12 | |||
845.2.m.e.361.2 | 8 | 13.7 | odd | 12 | |||
845.2.m.e.361.3 | 8 | 13.6 | odd | 12 | |||
1040.2.q.n.81.2 | 4 | 52.35 | odd | 6 | |||
1040.2.q.n.321.2 | 4 | 52.3 | odd | 6 | |||
4225.2.a.u.1.2 | 2 | 5.4 | even | 2 | |||
4225.2.a.y.1.1 | 2 | 65.64 | even | 2 | |||
7605.2.a.ba.1.2 | 2 | 3.2 | odd | 2 | |||
7605.2.a.bf.1.1 | 2 | 39.38 | odd | 2 |