Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.95630\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.209057 | 0.147826 | 0.0739128 | − | 0.997265i | \(-0.476451\pi\) | ||||
0.0739128 | + | 0.997265i | \(0.476451\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.95630 | −0.978148 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.209057 | −0.0853471 | ||||||||
\(7\) | −0.488830 | −0.184760 | −0.0923801 | − | 0.995724i | \(-0.529447\pi\) | ||||
−0.0923801 | + | 0.995724i | \(0.529447\pi\) | |||||||
\(8\) | −0.827091 | −0.292421 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.209057 | 0.0661096 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.95630 | 0.564734 | ||||||||
\(13\) | −3.26755 | −0.906254 | −0.453127 | − | 0.891446i | \(-0.649692\pi\) | ||||
−0.453127 | + | 0.891446i | \(0.649692\pi\) | |||||||
\(14\) | −0.102193 | −0.0273123 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 3.73968 | 0.934920 | ||||||||
\(17\) | 3.33070 | 0.807814 | 0.403907 | − | 0.914800i | \(-0.367652\pi\) | ||||
0.403907 | + | 0.914800i | \(0.367652\pi\) | |||||||
\(18\) | 0.209057 | 0.0492752 | ||||||||
\(19\) | 3.86889 | 0.887583 | 0.443792 | − | 0.896130i | \(-0.353633\pi\) | ||||
0.443792 | + | 0.896130i | \(0.353633\pi\) | |||||||
\(20\) | −1.95630 | −0.437441 | ||||||||
\(21\) | 0.488830 | 0.106671 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.267545 | −0.0557871 | −0.0278935 | − | 0.999611i | \(-0.508880\pi\) | ||||
−0.0278935 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(24\) | 0.827091 | 0.168829 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.683103 | −0.133968 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.956295 | 0.180723 | ||||||||
\(29\) | −6.31592 | −1.17284 | −0.586419 | − | 0.810008i | \(-0.699463\pi\) | ||||
−0.586419 | + | 0.810008i | \(0.699463\pi\) | |||||||
\(30\) | −0.209057 | −0.0381684 | ||||||||
\(31\) | −5.83274 | −1.04759 | −0.523795 | − | 0.851844i | \(-0.675484\pi\) | ||||
−0.523795 | + | 0.851844i | \(0.675484\pi\) | |||||||
\(32\) | 2.43599 | 0.430626 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.696307 | 0.119416 | ||||||||
\(35\) | −0.488830 | −0.0826273 | ||||||||
\(36\) | −1.95630 | −0.326049 | ||||||||
\(37\) | 7.50361 | 1.23359 | 0.616793 | − | 0.787125i | \(-0.288431\pi\) | ||||
0.616793 | + | 0.787125i | \(0.288431\pi\) | |||||||
\(38\) | 0.808817 | 0.131207 | ||||||||
\(39\) | 3.26755 | 0.523226 | ||||||||
\(40\) | −0.827091 | −0.130775 | ||||||||
\(41\) | −4.18769 | −0.654008 | −0.327004 | − | 0.945023i | \(-0.606039\pi\) | ||||
−0.327004 | + | 0.945023i | \(0.606039\pi\) | |||||||
\(42\) | 0.102193 | 0.0157688 | ||||||||
\(43\) | 2.26657 | 0.345649 | 0.172824 | − | 0.984953i | \(-0.444711\pi\) | ||||
0.172824 | + | 0.984953i | \(0.444711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −0.0559322 | −0.00824675 | ||||||||
\(47\) | −5.58347 | −0.814432 | −0.407216 | − | 0.913332i | \(-0.633500\pi\) | ||||
−0.407216 | + | 0.913332i | \(0.633500\pi\) | |||||||
\(48\) | −3.73968 | −0.539777 | ||||||||
\(49\) | −6.76105 | −0.965864 | ||||||||
\(50\) | 0.209057 | 0.0295651 | ||||||||
\(51\) | −3.33070 | −0.466392 | ||||||||
\(52\) | 6.39228 | 0.886450 | ||||||||
\(53\) | −1.14301 | −0.157005 | −0.0785024 | − | 0.996914i | \(-0.525014\pi\) | ||||
−0.0785024 | + | 0.996914i | \(0.525014\pi\) | |||||||
\(54\) | −0.209057 | −0.0284490 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.404307 | 0.0540277 | ||||||||
\(57\) | −3.86889 | −0.512446 | ||||||||
\(58\) | −1.32039 | −0.173375 | ||||||||
\(59\) | −4.51742 | −0.588118 | −0.294059 | − | 0.955787i | \(-0.595006\pi\) | ||||
−0.294059 | + | 0.955787i | \(0.595006\pi\) | |||||||
\(60\) | 1.95630 | 0.252557 | ||||||||
\(61\) | −12.5743 | −1.60998 | −0.804989 | − | 0.593290i | \(-0.797829\pi\) | ||||
−0.804989 | + | 0.593290i | \(0.797829\pi\) | |||||||
\(62\) | −1.21937 | −0.154861 | ||||||||
\(63\) | −0.488830 | −0.0615868 | ||||||||
\(64\) | −6.97010 | −0.871263 | ||||||||
\(65\) | −3.26755 | −0.405289 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.97575 | 1.09656 | 0.548281 | − | 0.836294i | \(-0.315282\pi\) | ||||
0.548281 | + | 0.836294i | \(0.315282\pi\) | |||||||
\(68\) | −6.51584 | −0.790162 | ||||||||
\(69\) | 0.267545 | 0.0322087 | ||||||||
\(70\) | −0.102193 | −0.0122144 | ||||||||
\(71\) | 5.31592 | 0.630884 | 0.315442 | − | 0.948945i | \(-0.397847\pi\) | ||||
0.315442 | + | 0.948945i | \(0.397847\pi\) | |||||||
\(72\) | −0.827091 | −0.0974736 | ||||||||
\(73\) | −9.65885 | −1.13048 | −0.565242 | − | 0.824925i | \(-0.691217\pi\) | ||||
−0.565242 | + | 0.824925i | \(0.691217\pi\) | |||||||
\(74\) | 1.56868 | 0.182356 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −7.56868 | −0.868187 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.683103 | 0.0773462 | ||||||||
\(79\) | 1.50828 | 0.169695 | 0.0848476 | − | 0.996394i | \(-0.472960\pi\) | ||||
0.0848476 | + | 0.996394i | \(0.472960\pi\) | |||||||
\(80\) | 3.73968 | 0.418109 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.875466 | −0.0966791 | ||||||||
\(83\) | −17.6428 | −1.93655 | −0.968275 | − | 0.249888i | \(-0.919606\pi\) | ||||
−0.968275 | + | 0.249888i | \(0.919606\pi\) | |||||||
\(84\) | −0.956295 | −0.104340 | ||||||||
\(85\) | 3.33070 | 0.361266 | ||||||||
\(86\) | 0.473842 | 0.0510957 | ||||||||
\(87\) | 6.31592 | 0.677138 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.9226 | 1.68779 | 0.843895 | − | 0.536509i | \(-0.180257\pi\) | ||||
0.843895 | + | 0.536509i | \(0.180257\pi\) | |||||||
\(90\) | 0.209057 | 0.0220365 | ||||||||
\(91\) | 1.59727 | 0.167440 | ||||||||
\(92\) | 0.523398 | 0.0545680 | ||||||||
\(93\) | 5.83274 | 0.604827 | ||||||||
\(94\) | −1.16726 | −0.120394 | ||||||||
\(95\) | 3.86889 | 0.396939 | ||||||||
\(96\) | −2.43599 | −0.248622 | ||||||||
\(97\) | −16.3364 | −1.65871 | −0.829353 | − | 0.558726i | \(-0.811290\pi\) | ||||
−0.829353 | + | 0.558726i | \(0.811290\pi\) | |||||||
\(98\) | −1.41344 | −0.142779 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.95630 | −0.195630 | ||||||||
\(101\) | −17.8522 | −1.77636 | −0.888180 | − | 0.459496i | \(-0.848030\pi\) | ||||
−0.888180 | + | 0.459496i | \(0.848030\pi\) | |||||||
\(102\) | −0.696307 | −0.0689446 | ||||||||
\(103\) | 15.3370 | 1.51120 | 0.755598 | − | 0.655036i | \(-0.227347\pi\) | ||||
0.755598 | + | 0.655036i | \(0.227347\pi\) | |||||||
\(104\) | 2.70256 | 0.265008 | ||||||||
\(105\) | 0.488830 | 0.0477049 | ||||||||
\(106\) | −0.238954 | −0.0232093 | ||||||||
\(107\) | 5.83932 | 0.564508 | 0.282254 | − | 0.959340i | \(-0.408918\pi\) | ||||
0.282254 | + | 0.959340i | \(0.408918\pi\) | |||||||
\(108\) | 1.95630 | 0.188245 | ||||||||
\(109\) | −7.05284 | −0.675540 | −0.337770 | − | 0.941229i | \(-0.609673\pi\) | ||||
−0.337770 | + | 0.941229i | \(0.609673\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.50361 | −0.712211 | ||||||||
\(112\) | −1.82807 | −0.172736 | ||||||||
\(113\) | −13.6019 | −1.27956 | −0.639782 | − | 0.768557i | \(-0.720975\pi\) | ||||
−0.639782 | + | 0.768557i | \(0.720975\pi\) | |||||||
\(114\) | −0.808817 | −0.0757527 | ||||||||
\(115\) | −0.267545 | −0.0249487 | ||||||||
\(116\) | 12.3558 | 1.14721 | ||||||||
\(117\) | −3.26755 | −0.302085 | ||||||||
\(118\) | −0.944398 | −0.0869389 | ||||||||
\(119\) | −1.62815 | −0.149252 | ||||||||
\(120\) | 0.827091 | 0.0755027 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.62875 | −0.237996 | ||||||||
\(123\) | 4.18769 | 0.377592 | ||||||||
\(124\) | 11.4106 | 1.02470 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.102193 | −0.00910410 | ||||||||
\(127\) | −22.0900 | −1.96017 | −0.980087 | − | 0.198568i | \(-0.936371\pi\) | ||||
−0.980087 | + | 0.198568i | \(0.936371\pi\) | |||||||
\(128\) | −6.32912 | −0.559421 | ||||||||
\(129\) | −2.26657 | −0.199560 | ||||||||
\(130\) | −0.683103 | −0.0599121 | ||||||||
\(131\) | −3.87993 | −0.338991 | −0.169496 | − | 0.985531i | \(-0.554214\pi\) | ||||
−0.169496 | + | 0.985531i | \(0.554214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.89123 | −0.163990 | ||||||||
\(134\) | 1.87644 | 0.162100 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −2.75480 | −0.236222 | ||||||||
\(137\) | −5.36625 | −0.458470 | −0.229235 | − | 0.973371i | \(-0.573622\pi\) | ||||
−0.229235 | + | 0.973371i | \(0.573622\pi\) | |||||||
\(138\) | 0.0559322 | 0.00476127 | ||||||||
\(139\) | −12.6237 | −1.07073 | −0.535363 | − | 0.844622i | \(-0.679825\pi\) | ||||
−0.535363 | + | 0.844622i | \(0.679825\pi\) | |||||||
\(140\) | 0.956295 | 0.0808217 | ||||||||
\(141\) | 5.58347 | 0.470213 | ||||||||
\(142\) | 1.11133 | 0.0932607 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.73968 | 0.311640 | ||||||||
\(145\) | −6.31592 | −0.524509 | ||||||||
\(146\) | −2.01925 | −0.167114 | ||||||||
\(147\) | 6.76105 | 0.557642 | ||||||||
\(148\) | −14.6793 | −1.20663 | ||||||||
\(149\) | 4.69947 | 0.384995 | 0.192498 | − | 0.981297i | \(-0.438341\pi\) | ||||
0.192498 | + | 0.981297i | \(0.438341\pi\) | |||||||
\(150\) | −0.209057 | −0.0170694 | ||||||||
\(151\) | −14.5712 | −1.18579 | −0.592895 | − | 0.805280i | \(-0.702015\pi\) | ||||
−0.592895 | + | 0.805280i | \(0.702015\pi\) | |||||||
\(152\) | −3.19992 | −0.259548 | ||||||||
\(153\) | 3.33070 | 0.269271 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.83274 | −0.468497 | ||||||||
\(156\) | −6.39228 | −0.511792 | ||||||||
\(157\) | 0.334194 | 0.0266716 | 0.0133358 | − | 0.999911i | \(-0.495755\pi\) | ||||
0.0133358 | + | 0.999911i | \(0.495755\pi\) | |||||||
\(158\) | 0.315317 | 0.0250853 | ||||||||
\(159\) | 1.14301 | 0.0906467 | ||||||||
\(160\) | 2.43599 | 0.192582 | ||||||||
\(161\) | 0.130784 | 0.0103072 | ||||||||
\(162\) | 0.209057 | 0.0164251 | ||||||||
\(163\) | 1.98935 | 0.155818 | 0.0779091 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779091 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(164\) | 8.19236 | 0.639716 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.68835 | −0.286272 | ||||||||
\(167\) | 19.2322 | 1.48824 | 0.744118 | − | 0.668048i | \(-0.232870\pi\) | ||||
0.744118 | + | 0.668048i | \(0.232870\pi\) | |||||||
\(168\) | −0.404307 | −0.0311929 | ||||||||
\(169\) | −2.32315 | −0.178704 | ||||||||
\(170\) | 0.696307 | 0.0534043 | ||||||||
\(171\) | 3.86889 | 0.295861 | ||||||||
\(172\) | −4.43408 | −0.338095 | ||||||||
\(173\) | −13.9713 | −1.06222 | −0.531108 | − | 0.847304i | \(-0.678224\pi\) | ||||
−0.531108 | + | 0.847304i | \(0.678224\pi\) | |||||||
\(174\) | 1.32039 | 0.100098 | ||||||||
\(175\) | −0.488830 | −0.0369521 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.51742 | 0.339550 | ||||||||
\(178\) | 3.32873 | 0.249498 | ||||||||
\(179\) | −7.85995 | −0.587480 | −0.293740 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293740 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(180\) | −1.95630 | −0.145814 | ||||||||
\(181\) | 7.39268 | 0.549494 | 0.274747 | − | 0.961517i | \(-0.411406\pi\) | ||||
0.274747 | + | 0.961517i | \(0.411406\pi\) | |||||||
\(182\) | 0.333921 | 0.0247519 | ||||||||
\(183\) | 12.5743 | 0.929521 | ||||||||
\(184\) | 0.221284 | 0.0163133 | ||||||||
\(185\) | 7.50361 | 0.551677 | ||||||||
\(186\) | 1.21937 | 0.0894089 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.9229 | 0.796635 | ||||||||
\(189\) | 0.488830 | 0.0355571 | ||||||||
\(190\) | 0.808817 | 0.0586778 | ||||||||
\(191\) | −0.429738 | −0.0310947 | −0.0155474 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155474 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(192\) | 6.97010 | 0.503024 | ||||||||
\(193\) | −1.95004 | −0.140367 | −0.0701837 | − | 0.997534i | \(-0.522359\pi\) | ||||
−0.0701837 | + | 0.997534i | \(0.522359\pi\) | |||||||
\(194\) | −3.41523 | −0.245199 | ||||||||
\(195\) | 3.26755 | 0.233994 | ||||||||
\(196\) | 13.2266 | 0.944757 | ||||||||
\(197\) | 22.2892 | 1.58804 | 0.794018 | − | 0.607894i | \(-0.207985\pi\) | ||||
0.794018 | + | 0.607894i | \(0.207985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.45077 | 0.457283 | 0.228642 | − | 0.973511i | \(-0.426572\pi\) | ||||
0.228642 | + | 0.973511i | \(0.426572\pi\) | |||||||
\(200\) | −0.827091 | −0.0584842 | ||||||||
\(201\) | −8.97575 | −0.633101 | ||||||||
\(202\) | −3.73212 | −0.262591 | ||||||||
\(203\) | 3.08741 | 0.216694 | ||||||||
\(204\) | 6.51584 | 0.456200 | ||||||||
\(205\) | −4.18769 | −0.292481 | ||||||||
\(206\) | 3.20630 | 0.223393 | ||||||||
\(207\) | −0.267545 | −0.0185957 | ||||||||
\(208\) | −12.2196 | −0.847275 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.102193 | 0.00705200 | ||||||||
\(211\) | −22.2379 | −1.53092 | −0.765460 | − | 0.643484i | \(-0.777488\pi\) | ||||
−0.765460 | + | 0.643484i | \(0.777488\pi\) | |||||||
\(212\) | 2.23607 | 0.153574 | ||||||||
\(213\) | −5.31592 | −0.364241 | ||||||||
\(214\) | 1.22075 | 0.0834487 | ||||||||
\(215\) | 2.26657 | 0.154579 | ||||||||
\(216\) | 0.827091 | 0.0562764 | ||||||||
\(217\) | 2.85122 | 0.193553 | ||||||||
\(218\) | −1.47445 | −0.0998620 | ||||||||
\(219\) | 9.65885 | 0.652685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8832 | −0.732085 | ||||||||
\(222\) | −1.56868 | −0.105283 | ||||||||
\(223\) | 13.7759 | 0.922501 | 0.461250 | − | 0.887270i | \(-0.347401\pi\) | ||||
0.461250 | + | 0.887270i | \(0.347401\pi\) | |||||||
\(224\) | −1.19078 | −0.0795626 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.84358 | −0.189152 | ||||||||
\(227\) | 25.8554 | 1.71608 | 0.858040 | − | 0.513583i | \(-0.171682\pi\) | ||||
0.858040 | + | 0.513583i | \(0.171682\pi\) | |||||||
\(228\) | 7.56868 | 0.501248 | ||||||||
\(229\) | 14.3391 | 0.947555 | 0.473778 | − | 0.880645i | \(-0.342890\pi\) | ||||
0.473778 | + | 0.880645i | \(0.342890\pi\) | |||||||
\(230\) | −0.0559322 | −0.00368806 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.22384 | 0.342962 | ||||||||
\(233\) | −3.66332 | −0.239992 | −0.119996 | − | 0.992774i | \(-0.538288\pi\) | ||||
−0.119996 | + | 0.992774i | \(0.538288\pi\) | |||||||
\(234\) | −0.683103 | −0.0446558 | ||||||||
\(235\) | −5.58347 | −0.364225 | ||||||||
\(236\) | 8.83741 | 0.575266 | ||||||||
\(237\) | −1.50828 | −0.0979736 | ||||||||
\(238\) | −0.340375 | −0.0220633 | ||||||||
\(239\) | −1.07794 | −0.0697263 | −0.0348632 | − | 0.999392i | \(-0.511100\pi\) | ||||
−0.0348632 | + | 0.999392i | \(0.511100\pi\) | |||||||
\(240\) | −3.73968 | −0.241395 | ||||||||
\(241\) | −27.1803 | −1.75084 | −0.875420 | − | 0.483363i | \(-0.839415\pi\) | ||||
−0.875420 | + | 0.483363i | \(0.839415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 24.5991 | 1.57480 | ||||||||
\(245\) | −6.76105 | −0.431947 | ||||||||
\(246\) | 0.875466 | 0.0558177 | ||||||||
\(247\) | −12.6418 | −0.804376 | ||||||||
\(248\) | 4.82420 | 0.306337 | ||||||||
\(249\) | 17.6428 | 1.11807 | ||||||||
\(250\) | 0.209057 | 0.0132219 | ||||||||
\(251\) | −2.60016 | −0.164121 | −0.0820603 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820603 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(252\) | 0.956295 | 0.0602409 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.61808 | −0.289764 | ||||||||
\(255\) | −3.33070 | −0.208577 | ||||||||
\(256\) | 12.6171 | 0.788566 | ||||||||
\(257\) | 5.67343 | 0.353899 | 0.176949 | − | 0.984220i | \(-0.443377\pi\) | ||||
0.176949 | + | 0.984220i | \(0.443377\pi\) | |||||||
\(258\) | −0.473842 | −0.0295001 | ||||||||
\(259\) | −3.66799 | −0.227918 | ||||||||
\(260\) | 6.39228 | 0.396433 | ||||||||
\(261\) | −6.31592 | −0.390946 | ||||||||
\(262\) | −0.811127 | −0.0501116 | ||||||||
\(263\) | 23.4448 | 1.44567 | 0.722834 | − | 0.691022i | \(-0.242839\pi\) | ||||
0.722834 | + | 0.691022i | \(0.242839\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.14301 | −0.0702146 | ||||||||
\(266\) | −0.395374 | −0.0242419 | ||||||||
\(267\) | −15.9226 | −0.974446 | ||||||||
\(268\) | −17.5592 | −1.07260 | ||||||||
\(269\) | −5.46398 | −0.333144 | −0.166572 | − | 0.986029i | \(-0.553270\pi\) | ||||
−0.166572 | + | 0.986029i | \(0.553270\pi\) | |||||||
\(270\) | −0.209057 | −0.0127228 | ||||||||
\(271\) | −2.52319 | −0.153273 | −0.0766365 | − | 0.997059i | \(-0.524418\pi\) | ||||
−0.0766365 | + | 0.997059i | \(0.524418\pi\) | |||||||
\(272\) | 12.4558 | 0.755242 | ||||||||
\(273\) | −1.59727 | −0.0966714 | ||||||||
\(274\) | −1.12185 | −0.0677735 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.523398 | −0.0315048 | ||||||||
\(277\) | 22.4067 | 1.34629 | 0.673145 | − | 0.739510i | \(-0.264943\pi\) | ||||
0.673145 | + | 0.739510i | \(0.264943\pi\) | |||||||
\(278\) | −2.63907 | −0.158281 | ||||||||
\(279\) | −5.83274 | −0.349197 | ||||||||
\(280\) | 0.404307 | 0.0241619 | ||||||||
\(281\) | 11.2790 | 0.672851 | 0.336426 | − | 0.941710i | \(-0.390782\pi\) | ||||
0.336426 | + | 0.941710i | \(0.390782\pi\) | |||||||
\(282\) | 1.16726 | 0.0695095 | ||||||||
\(283\) | 11.6925 | 0.695046 | 0.347523 | − | 0.937671i | \(-0.387023\pi\) | ||||
0.347523 | + | 0.937671i | \(0.387023\pi\) | |||||||
\(284\) | −10.3995 | −0.617097 | ||||||||
\(285\) | −3.86889 | −0.229173 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.04707 | 0.120835 | ||||||||
\(288\) | 2.43599 | 0.143542 | ||||||||
\(289\) | −5.90641 | −0.347436 | ||||||||
\(290\) | −1.32039 | −0.0775358 | ||||||||
\(291\) | 16.3364 | 0.957654 | ||||||||
\(292\) | 18.8956 | 1.10578 | ||||||||
\(293\) | 13.4918 | 0.788199 | 0.394100 | − | 0.919068i | \(-0.371057\pi\) | ||||
0.394100 | + | 0.919068i | \(0.371057\pi\) | |||||||
\(294\) | 1.41344 | 0.0824337 | ||||||||
\(295\) | −4.51742 | −0.263014 | ||||||||
\(296\) | −6.20617 | −0.360726 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.982456 | 0.0569121 | ||||||||
\(299\) | 0.874217 | 0.0505573 | ||||||||
\(300\) | 1.95630 | 0.112947 | ||||||||
\(301\) | −1.10797 | −0.0638621 | ||||||||
\(302\) | −3.04622 | −0.175290 | ||||||||
\(303\) | 17.8522 | 1.02558 | ||||||||
\(304\) | 14.4684 | 0.829820 | ||||||||
\(305\) | −12.5743 | −0.720004 | ||||||||
\(306\) | 0.696307 | 0.0398052 | ||||||||
\(307\) | 0.364626 | 0.0208103 | 0.0104052 | − | 0.999946i | \(-0.496688\pi\) | ||||
0.0104052 | + | 0.999946i | \(0.496688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3370 | −0.872489 | ||||||||
\(310\) | −1.21937 | −0.0692558 | ||||||||
\(311\) | 23.2542 | 1.31863 | 0.659313 | − | 0.751869i | \(-0.270847\pi\) | ||||
0.659313 | + | 0.751869i | \(0.270847\pi\) | |||||||
\(312\) | −2.70256 | −0.153002 | ||||||||
\(313\) | −12.2326 | −0.691430 | −0.345715 | − | 0.938340i | \(-0.612364\pi\) | ||||
−0.345715 | + | 0.938340i | \(0.612364\pi\) | |||||||
\(314\) | 0.0698656 | 0.00394274 | ||||||||
\(315\) | −0.488830 | −0.0275424 | ||||||||
\(316\) | −2.95065 | −0.165987 | ||||||||
\(317\) | 32.0176 | 1.79829 | 0.899144 | − | 0.437653i | \(-0.144190\pi\) | ||||
0.899144 | + | 0.437653i | \(0.144190\pi\) | |||||||
\(318\) | 0.238954 | 0.0133999 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −6.97010 | −0.389641 | ||||||||
\(321\) | −5.83932 | −0.325919 | ||||||||
\(322\) | 0.0273413 | 0.00152367 | ||||||||
\(323\) | 12.8861 | 0.717003 | ||||||||
\(324\) | −1.95630 | −0.108683 | ||||||||
\(325\) | −3.26755 | −0.181251 | ||||||||
\(326\) | 0.415888 | 0.0230339 | ||||||||
\(327\) | 7.05284 | 0.390023 | ||||||||
\(328\) | 3.46360 | 0.191245 | ||||||||
\(329\) | 2.72936 | 0.150475 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.5705 | −1.13066 | −0.565328 | − | 0.824867i | \(-0.691250\pi\) | ||||
−0.565328 | + | 0.824867i | \(0.691250\pi\) | |||||||
\(332\) | 34.5145 | 1.89423 | ||||||||
\(333\) | 7.50361 | 0.411195 | ||||||||
\(334\) | 4.02063 | 0.219999 | ||||||||
\(335\) | 8.97575 | 0.490398 | ||||||||
\(336\) | 1.82807 | 0.0997292 | ||||||||
\(337\) | −22.3442 | −1.21717 | −0.608583 | − | 0.793491i | \(-0.708262\pi\) | ||||
−0.608583 | + | 0.793491i | \(0.708262\pi\) | |||||||
\(338\) | −0.485670 | −0.0264170 | ||||||||
\(339\) | 13.6019 | 0.738756 | ||||||||
\(340\) | −6.51584 | −0.353371 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.808817 | 0.0437358 | ||||||||
\(343\) | 6.72681 | 0.363213 | ||||||||
\(344\) | −1.87466 | −0.101075 | ||||||||
\(345\) | 0.267545 | 0.0144042 | ||||||||
\(346\) | −2.92079 | −0.157023 | ||||||||
\(347\) | 24.0053 | 1.28867 | 0.644336 | − | 0.764742i | \(-0.277134\pi\) | ||||
0.644336 | + | 0.764742i | \(0.277134\pi\) | |||||||
\(348\) | −12.3558 | −0.662341 | ||||||||
\(349\) | −13.6284 | −0.729509 | −0.364754 | − | 0.931104i | \(-0.618847\pi\) | ||||
−0.364754 | + | 0.931104i | \(0.618847\pi\) | |||||||
\(350\) | −0.102193 | −0.00546246 | ||||||||
\(351\) | 3.26755 | 0.174409 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.4058 | −1.67156 | −0.835780 | − | 0.549065i | \(-0.814984\pi\) | ||||
−0.835780 | + | 0.549065i | \(0.814984\pi\) | |||||||
\(354\) | 0.944398 | 0.0501942 | ||||||||
\(355\) | 5.31592 | 0.282140 | ||||||||
\(356\) | −31.1493 | −1.65091 | ||||||||
\(357\) | 1.62815 | 0.0861707 | ||||||||
\(358\) | −1.64318 | −0.0868446 | ||||||||
\(359\) | −2.87356 | −0.151660 | −0.0758302 | − | 0.997121i | \(-0.524161\pi\) | ||||
−0.0758302 | + | 0.997121i | \(0.524161\pi\) | |||||||
\(360\) | −0.827091 | −0.0435915 | ||||||||
\(361\) | −4.03172 | −0.212196 | ||||||||
\(362\) | 1.54549 | 0.0812292 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.12474 | −0.163781 | ||||||||
\(365\) | −9.65885 | −0.505567 | ||||||||
\(366\) | 2.62875 | 0.137407 | ||||||||
\(367\) | 24.0611 | 1.25598 | 0.627990 | − | 0.778221i | \(-0.283878\pi\) | ||||
0.627990 | + | 0.778221i | \(0.283878\pi\) | |||||||
\(368\) | −1.00053 | −0.0521565 | ||||||||
\(369\) | −4.18769 | −0.218003 | ||||||||
\(370\) | 1.56868 | 0.0815519 | ||||||||
\(371\) | 0.558738 | 0.0290082 | ||||||||
\(372\) | −11.4106 | −0.591610 | ||||||||
\(373\) | −17.5348 | −0.907915 | −0.453958 | − | 0.891023i | \(-0.649988\pi\) | ||||
−0.453958 | + | 0.891023i | \(0.649988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 4.61803 | 0.238157 | ||||||||
\(377\) | 20.6376 | 1.06289 | ||||||||
\(378\) | 0.102193 | 0.00525625 | ||||||||
\(379\) | −32.6393 | −1.67657 | −0.838285 | − | 0.545232i | \(-0.816442\pi\) | ||||
−0.838285 | + | 0.545232i | \(0.816442\pi\) | |||||||
\(380\) | −7.56868 | −0.388265 | ||||||||
\(381\) | 22.0900 | 1.13171 | ||||||||
\(382\) | −0.0898397 | −0.00459660 | ||||||||
\(383\) | 10.5167 | 0.537378 | 0.268689 | − | 0.963227i | \(-0.413410\pi\) | ||||
0.268689 | + | 0.963227i | \(0.413410\pi\) | |||||||
\(384\) | 6.32912 | 0.322982 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.407670 | −0.0207499 | ||||||||
\(387\) | 2.26657 | 0.115216 | ||||||||
\(388\) | 31.9587 | 1.62246 | ||||||||
\(389\) | 23.3467 | 1.18373 | 0.591863 | − | 0.806038i | \(-0.298393\pi\) | ||||
0.591863 | + | 0.806038i | \(0.298393\pi\) | |||||||
\(390\) | 0.683103 | 0.0345903 | ||||||||
\(391\) | −0.891114 | −0.0450656 | ||||||||
\(392\) | 5.59200 | 0.282439 | ||||||||
\(393\) | 3.87993 | 0.195717 | ||||||||
\(394\) | 4.65970 | 0.234752 | ||||||||
\(395\) | 1.50828 | 0.0758900 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.04740 | 0.353699 | 0.176849 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176849 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(398\) | 1.34858 | 0.0675981 | ||||||||
\(399\) | 1.89123 | 0.0946797 | ||||||||
\(400\) | 3.73968 | 0.186984 | ||||||||
\(401\) | 22.4645 | 1.12182 | 0.560911 | − | 0.827876i | \(-0.310451\pi\) | ||||
0.560911 | + | 0.827876i | \(0.310451\pi\) | |||||||
\(402\) | −1.87644 | −0.0935884 | ||||||||
\(403\) | 19.0587 | 0.949383 | ||||||||
\(404\) | 34.9242 | 1.73754 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0.645444 | 0.0320329 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.75480 | 0.136383 | ||||||||
\(409\) | −1.01918 | −0.0503953 | −0.0251976 | − | 0.999682i | \(-0.508022\pi\) | ||||
−0.0251976 | + | 0.999682i | \(0.508022\pi\) | |||||||
\(410\) | −0.875466 | −0.0432362 | ||||||||
\(411\) | 5.36625 | 0.264698 | ||||||||
\(412\) | −30.0036 | −1.47817 | ||||||||
\(413\) | 2.20825 | 0.108661 | ||||||||
\(414\) | −0.0559322 | −0.00274892 | ||||||||
\(415\) | −17.6428 | −0.866051 | ||||||||
\(416\) | −7.95970 | −0.390256 | ||||||||
\(417\) | 12.6237 | 0.618184 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.54074 | 0.368389 | 0.184195 | − | 0.982890i | \(-0.441032\pi\) | ||||
0.184195 | + | 0.982890i | \(0.441032\pi\) | |||||||
\(420\) | −0.956295 | −0.0466624 | ||||||||
\(421\) | 11.7585 | 0.573076 | 0.286538 | − | 0.958069i | \(-0.407496\pi\) | ||||
0.286538 | + | 0.958069i | \(0.407496\pi\) | |||||||
\(422\) | −4.64899 | −0.226309 | ||||||||
\(423\) | −5.58347 | −0.271477 | ||||||||
\(424\) | 0.945374 | 0.0459114 | ||||||||
\(425\) | 3.33070 | 0.161563 | ||||||||
\(426\) | −1.11133 | −0.0538441 | ||||||||
\(427\) | 6.14671 | 0.297460 | ||||||||
\(428\) | −11.4234 | −0.552172 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.473842 | 0.0228507 | ||||||||
\(431\) | 27.0506 | 1.30298 | 0.651491 | − | 0.758657i | \(-0.274144\pi\) | ||||
0.651491 | + | 0.758657i | \(0.274144\pi\) | |||||||
\(432\) | −3.73968 | −0.179926 | ||||||||
\(433\) | −25.6704 | −1.23364 | −0.616821 | − | 0.787104i | \(-0.711580\pi\) | ||||
−0.616821 | + | 0.787104i | \(0.711580\pi\) | |||||||
\(434\) | 0.596066 | 0.0286121 | ||||||||
\(435\) | 6.31592 | 0.302825 | ||||||||
\(436\) | 13.7974 | 0.660778 | ||||||||
\(437\) | −1.03510 | −0.0495157 | ||||||||
\(438\) | 2.01925 | 0.0964835 | ||||||||
\(439\) | −0.512954 | −0.0244820 | −0.0122410 | − | 0.999925i | \(-0.503897\pi\) | ||||
−0.0122410 | + | 0.999925i | \(0.503897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.76105 | −0.321955 | ||||||||
\(442\) | −2.27521 | −0.108221 | ||||||||
\(443\) | −33.2667 | −1.58055 | −0.790274 | − | 0.612754i | \(-0.790062\pi\) | ||||
−0.790274 | + | 0.612754i | \(0.790062\pi\) | |||||||
\(444\) | 14.6793 | 0.696648 | ||||||||
\(445\) | 15.9226 | 0.754803 | ||||||||
\(446\) | 2.87994 | 0.136369 | ||||||||
\(447\) | −4.69947 | −0.222277 | ||||||||
\(448\) | 3.40719 | 0.160975 | ||||||||
\(449\) | 5.95841 | 0.281195 | 0.140597 | − | 0.990067i | \(-0.455098\pi\) | ||||
0.140597 | + | 0.990067i | \(0.455098\pi\) | |||||||
\(450\) | 0.209057 | 0.00985504 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 26.6094 | 1.25160 | ||||||||
\(453\) | 14.5712 | 0.684617 | ||||||||
\(454\) | 5.40524 | 0.253680 | ||||||||
\(455\) | 1.59727 | 0.0748813 | ||||||||
\(456\) | 3.19992 | 0.149850 | ||||||||
\(457\) | −20.4665 | −0.957384 | −0.478692 | − | 0.877983i | \(-0.658889\pi\) | ||||
−0.478692 | + | 0.877983i | \(0.658889\pi\) | |||||||
\(458\) | 2.99769 | 0.140073 | ||||||||
\(459\) | −3.33070 | −0.155464 | ||||||||
\(460\) | 0.523398 | 0.0244035 | ||||||||
\(461\) | −31.1778 | −1.45210 | −0.726048 | − | 0.687644i | \(-0.758645\pi\) | ||||
−0.726048 | + | 0.687644i | \(0.758645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9989 | 0.511164 | 0.255582 | − | 0.966787i | \(-0.417733\pi\) | ||||
0.255582 | + | 0.966787i | \(0.417733\pi\) | |||||||
\(464\) | −23.6195 | −1.09651 | ||||||||
\(465\) | 5.83274 | 0.270487 | ||||||||
\(466\) | −0.765842 | −0.0354770 | ||||||||
\(467\) | −35.4060 | −1.63839 | −0.819196 | − | 0.573513i | \(-0.805580\pi\) | ||||
−0.819196 | + | 0.573513i | \(0.805580\pi\) | |||||||
\(468\) | 6.39228 | 0.295483 | ||||||||
\(469\) | −4.38761 | −0.202601 | ||||||||
\(470\) | −1.16726 | −0.0538418 | ||||||||
\(471\) | −0.334194 | −0.0153989 | ||||||||
\(472\) | 3.73632 | 0.171978 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.315317 | −0.0144830 | ||||||||
\(475\) | 3.86889 | 0.177517 | ||||||||
\(476\) | 3.18514 | 0.145990 | ||||||||
\(477\) | −1.14301 | −0.0523349 | ||||||||
\(478\) | −0.225351 | −0.0103073 | ||||||||
\(479\) | −19.3816 | −0.885570 | −0.442785 | − | 0.896628i | \(-0.646009\pi\) | ||||
−0.442785 | + | 0.896628i | \(0.646009\pi\) | |||||||
\(480\) | −2.43599 | −0.111187 | ||||||||
\(481\) | −24.5184 | −1.11794 | ||||||||
\(482\) | −5.68224 | −0.258819 | ||||||||
\(483\) | −0.130784 | −0.00595088 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3364 | −0.741795 | ||||||||
\(486\) | −0.209057 | −0.00948301 | ||||||||
\(487\) | −16.3500 | −0.740891 | −0.370445 | − | 0.928854i | \(-0.620795\pi\) | ||||
−0.370445 | + | 0.928854i | \(0.620795\pi\) | |||||||
\(488\) | 10.4001 | 0.470791 | ||||||||
\(489\) | −1.98935 | −0.0899616 | ||||||||
\(490\) | −1.41344 | −0.0638529 | ||||||||
\(491\) | 13.7855 | 0.622131 | 0.311065 | − | 0.950388i | \(-0.399314\pi\) | ||||
0.311065 | + | 0.950388i | \(0.399314\pi\) | |||||||
\(492\) | −8.19236 | −0.369340 | ||||||||
\(493\) | −21.0365 | −0.947435 | ||||||||
\(494\) | −2.64285 | −0.118907 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.8126 | −0.979414 | ||||||||
\(497\) | −2.59858 | −0.116562 | ||||||||
\(498\) | 3.68835 | 0.165279 | ||||||||
\(499\) | 19.7828 | 0.885599 | 0.442799 | − | 0.896621i | \(-0.353985\pi\) | ||||
0.442799 | + | 0.896621i | \(0.353985\pi\) | |||||||
\(500\) | −1.95630 | −0.0874882 | ||||||||
\(501\) | −19.2322 | −0.859233 | ||||||||
\(502\) | −0.543581 | −0.0242612 | ||||||||
\(503\) | 12.0127 | 0.535622 | 0.267811 | − | 0.963471i | \(-0.413700\pi\) | ||||
0.267811 | + | 0.963471i | \(0.413700\pi\) | |||||||
\(504\) | 0.404307 | 0.0180092 | ||||||||
\(505\) | −17.8522 | −0.794412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.32315 | 0.103175 | ||||||||
\(508\) | 43.2146 | 1.91734 | ||||||||
\(509\) | −7.98102 | −0.353753 | −0.176876 | − | 0.984233i | \(-0.556599\pi\) | ||||
−0.176876 | + | 0.984233i | \(0.556599\pi\) | |||||||
\(510\) | −0.696307 | −0.0308330 | ||||||||
\(511\) | 4.72153 | 0.208868 | ||||||||
\(512\) | 15.2959 | 0.675991 | ||||||||
\(513\) | −3.86889 | −0.170815 | ||||||||
\(514\) | 1.18607 | 0.0523153 | ||||||||
\(515\) | 15.3370 | 0.675827 | ||||||||
\(516\) | 4.43408 | 0.195199 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.766819 | −0.0336921 | ||||||||
\(519\) | 13.9713 | 0.613271 | ||||||||
\(520\) | 2.70256 | 0.118515 | ||||||||
\(521\) | −44.4424 | −1.94705 | −0.973527 | − | 0.228571i | \(-0.926595\pi\) | ||||
−0.973527 | + | 0.228571i | \(0.926595\pi\) | |||||||
\(522\) | −1.32039 | −0.0577918 | ||||||||
\(523\) | 12.0607 | 0.527376 | 0.263688 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263688 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(524\) | 7.59029 | 0.331584 | ||||||||
\(525\) | 0.488830 | 0.0213343 | ||||||||
\(526\) | 4.90130 | 0.213707 | ||||||||
\(527\) | −19.4271 | −0.846259 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9284 | −0.996888 | ||||||||
\(530\) | −0.238954 | −0.0103795 | ||||||||
\(531\) | −4.51742 | −0.196039 | ||||||||
\(532\) | 3.69980 | 0.160407 | ||||||||
\(533\) | 13.6835 | 0.592697 | ||||||||
\(534\) | −3.32873 | −0.144048 | ||||||||
\(535\) | 5.83932 | 0.252456 | ||||||||
\(536\) | −7.42376 | −0.320658 | ||||||||
\(537\) | 7.85995 | 0.339182 | ||||||||
\(538\) | −1.14228 | −0.0492473 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.95630 | 0.0841855 | ||||||||
\(541\) | −37.7990 | −1.62510 | −0.812552 | − | 0.582888i | \(-0.801923\pi\) | ||||
−0.812552 | + | 0.582888i | \(0.801923\pi\) | |||||||
\(542\) | −0.527491 | −0.0226577 | ||||||||
\(543\) | −7.39268 | −0.317250 | ||||||||
\(544\) | 8.11356 | 0.347866 | ||||||||
\(545\) | −7.05284 | −0.302111 | ||||||||
\(546\) | −0.333921 | −0.0142905 | ||||||||
\(547\) | 14.9409 | 0.638825 | 0.319412 | − | 0.947616i | \(-0.396515\pi\) | ||||
0.319412 | + | 0.947616i | \(0.396515\pi\) | |||||||
\(548\) | 10.4980 | 0.448451 | ||||||||
\(549\) | −12.5743 | −0.536659 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4356 | −1.04099 | ||||||||
\(552\) | −0.221284 | −0.00941849 | ||||||||
\(553\) | −0.737294 | −0.0313529 | ||||||||
\(554\) | 4.68428 | 0.199016 | ||||||||
\(555\) | −7.50361 | −0.318511 | ||||||||
\(556\) | 24.6956 | 1.04733 | ||||||||
\(557\) | −7.30060 | −0.309336 | −0.154668 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154668 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(558\) | −1.21937 | −0.0516202 | ||||||||
\(559\) | −7.40612 | −0.313245 | ||||||||
\(560\) | −1.82807 | −0.0772499 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.35796 | 0.0994646 | ||||||||
\(563\) | −23.3440 | −0.983832 | −0.491916 | − | 0.870643i | \(-0.663703\pi\) | ||||
−0.491916 | + | 0.870643i | \(0.663703\pi\) | |||||||
\(564\) | −10.9229 | −0.459937 | ||||||||
\(565\) | −13.6019 | −0.572238 | ||||||||
\(566\) | 2.44440 | 0.102746 | ||||||||
\(567\) | −0.488830 | −0.0205289 | ||||||||
\(568\) | −4.39675 | −0.184484 | ||||||||
\(569\) | −44.4220 | −1.86227 | −0.931134 | − | 0.364678i | \(-0.881179\pi\) | ||||
−0.931134 | + | 0.364678i | \(0.881179\pi\) | |||||||
\(570\) | −0.808817 | −0.0338776 | ||||||||
\(571\) | 0.347203 | 0.0145300 | 0.00726499 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726499 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.429738 | 0.0179526 | ||||||||
\(574\) | 0.427954 | 0.0178624 | ||||||||
\(575\) | −0.267545 | −0.0111574 | ||||||||
\(576\) | −6.97010 | −0.290421 | ||||||||
\(577\) | 9.94354 | 0.413955 | 0.206978 | − | 0.978346i | \(-0.433637\pi\) | ||||
0.206978 | + | 0.978346i | \(0.433637\pi\) | |||||||
\(578\) | −1.23478 | −0.0513599 | ||||||||
\(579\) | 1.95004 | 0.0810411 | ||||||||
\(580\) | 12.3558 | 0.513047 | ||||||||
\(581\) | 8.62433 | 0.357797 | ||||||||
\(582\) | 3.41523 | 0.141566 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.98875 | 0.330577 | ||||||||
\(585\) | −3.26755 | −0.135096 | ||||||||
\(586\) | 2.82055 | 0.116516 | ||||||||
\(587\) | −8.07388 | −0.333245 | −0.166622 | − | 0.986021i | \(-0.553286\pi\) | ||||
−0.166622 | + | 0.986021i | \(0.553286\pi\) | |||||||
\(588\) | −13.2266 | −0.545456 | ||||||||
\(589\) | −22.5662 | −0.929824 | ||||||||
\(590\) | −0.944398 | −0.0388803 | ||||||||
\(591\) | −22.2892 | −0.916853 | ||||||||
\(592\) | 28.0611 | 1.15331 | ||||||||
\(593\) | 25.5393 | 1.04877 | 0.524387 | − | 0.851480i | \(-0.324295\pi\) | ||||
0.524387 | + | 0.851480i | \(0.324295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.62815 | −0.0667475 | ||||||||
\(596\) | −9.19354 | −0.376582 | ||||||||
\(597\) | −6.45077 | −0.264013 | ||||||||
\(598\) | 0.182761 | 0.00747365 | ||||||||
\(599\) | 3.77156 | 0.154102 | 0.0770508 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770508 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(600\) | 0.827091 | 0.0337658 | ||||||||
\(601\) | −2.48063 | −0.101187 | −0.0505934 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505934 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(602\) | −0.231628 | −0.00944045 | ||||||||
\(603\) | 8.97575 | 0.365521 | ||||||||
\(604\) | 28.5056 | 1.15988 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.73212 | 0.151607 | ||||||||
\(607\) | 7.44537 | 0.302198 | 0.151099 | − | 0.988519i | \(-0.451719\pi\) | ||||
0.151099 | + | 0.988519i | \(0.451719\pi\) | |||||||
\(608\) | 9.42456 | 0.382216 | ||||||||
\(609\) | −3.08741 | −0.125108 | ||||||||
\(610\) | −2.62875 | −0.106435 | ||||||||
\(611\) | 18.2442 | 0.738082 | ||||||||
\(612\) | −6.51584 | −0.263387 | ||||||||
\(613\) | 28.9464 | 1.16914 | 0.584568 | − | 0.811345i | \(-0.301264\pi\) | ||||
0.584568 | + | 0.811345i | \(0.301264\pi\) | |||||||
\(614\) | 0.0762276 | 0.00307630 | ||||||||
\(615\) | 4.18769 | 0.168864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7581 | −0.755172 | −0.377586 | − | 0.925975i | \(-0.623246\pi\) | ||||
−0.377586 | + | 0.925975i | \(0.623246\pi\) | |||||||
\(618\) | −3.20630 | −0.128976 | ||||||||
\(619\) | −29.4451 | −1.18350 | −0.591749 | − | 0.806123i | \(-0.701562\pi\) | ||||
−0.591749 | + | 0.806123i | \(0.701562\pi\) | |||||||
\(620\) | 11.4106 | 0.458259 | ||||||||
\(621\) | 0.267545 | 0.0107362 | ||||||||
\(622\) | 4.86145 | 0.194927 | ||||||||
\(623\) | −7.78343 | −0.311836 | ||||||||
\(624\) | 12.2196 | 0.489175 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.55732 | −0.102211 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.653783 | −0.0260888 | ||||||||
\(629\) | 24.9923 | 0.996509 | ||||||||
\(630\) | −0.102193 | −0.00407148 | ||||||||
\(631\) | 40.6457 | 1.61808 | 0.809040 | − | 0.587754i | \(-0.199988\pi\) | ||||
0.809040 | + | 0.587754i | \(0.199988\pi\) | |||||||
\(632\) | −1.24749 | −0.0496224 | ||||||||
\(633\) | 22.2379 | 0.883877 | ||||||||
\(634\) | 6.69350 | 0.265833 | ||||||||
\(635\) | −22.0900 | −0.876617 | ||||||||
\(636\) | −2.23607 | −0.0886659 | ||||||||
\(637\) | 22.0920 | 0.875318 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.31592 | 0.210295 | ||||||||
\(640\) | −6.32912 | −0.250181 | ||||||||
\(641\) | 22.8967 | 0.904365 | 0.452183 | − | 0.891925i | \(-0.350645\pi\) | ||||
0.452183 | + | 0.891925i | \(0.350645\pi\) | |||||||
\(642\) | −1.22075 | −0.0481792 | ||||||||
\(643\) | 30.4536 | 1.20097 | 0.600486 | − | 0.799635i | \(-0.294974\pi\) | ||||
0.600486 | + | 0.799635i | \(0.294974\pi\) | |||||||
\(644\) | −0.255852 | −0.0100820 | ||||||||
\(645\) | −2.26657 | −0.0892461 | ||||||||
\(646\) | 2.69393 | 0.105991 | ||||||||
\(647\) | −14.4006 | −0.566145 | −0.283072 | − | 0.959099i | \(-0.591354\pi\) | ||||
−0.283072 | + | 0.959099i | \(0.591354\pi\) | |||||||
\(648\) | −0.827091 | −0.0324912 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.683103 | −0.0267935 | ||||||||
\(651\) | −2.85122 | −0.111748 | ||||||||
\(652\) | −3.89176 | −0.152413 | ||||||||
\(653\) | 30.3188 | 1.18646 | 0.593232 | − | 0.805031i | \(-0.297852\pi\) | ||||
0.593232 | + | 0.805031i | \(0.297852\pi\) | |||||||
\(654\) | 1.47445 | 0.0576554 | ||||||||
\(655\) | −3.87993 | −0.151602 | ||||||||
\(656\) | −15.6606 | −0.611445 | ||||||||
\(657\) | −9.65885 | −0.376828 | ||||||||
\(658\) | 0.570592 | 0.0222440 | ||||||||
\(659\) | 25.8802 | 1.00815 | 0.504076 | − | 0.863659i | \(-0.331833\pi\) | ||||
0.504076 | + | 0.863659i | \(0.331833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.41852 | −0.366338 | −0.183169 | − | 0.983081i | \(-0.558636\pi\) | ||||
−0.183169 | + | 0.983081i | \(0.558636\pi\) | |||||||
\(662\) | −4.30040 | −0.167140 | ||||||||
\(663\) | 10.8832 | 0.422670 | ||||||||
\(664\) | 14.5922 | 0.566287 | ||||||||
\(665\) | −1.89123 | −0.0733386 | ||||||||
\(666\) | 1.56868 | 0.0607852 | ||||||||
\(667\) | 1.68980 | 0.0654291 | ||||||||
\(668\) | −37.6240 | −1.45571 | ||||||||
\(669\) | −13.7759 | −0.532606 | ||||||||
\(670\) | 1.87644 | 0.0724933 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.19078 | 0.0459355 | ||||||||
\(673\) | −13.3259 | −0.513676 | −0.256838 | − | 0.966454i | \(-0.582681\pi\) | ||||
−0.256838 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(674\) | −4.67121 | −0.179928 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 4.54476 | 0.174799 | ||||||||
\(677\) | −5.08029 | −0.195252 | −0.0976258 | − | 0.995223i | \(-0.531125\pi\) | ||||
−0.0976258 | + | 0.995223i | \(0.531125\pi\) | |||||||
\(678\) | 2.84358 | 0.109207 | ||||||||
\(679\) | 7.98569 | 0.306463 | ||||||||
\(680\) | −2.75480 | −0.105642 | ||||||||
\(681\) | −25.8554 | −0.990779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.0765 | 0.729942 | 0.364971 | − | 0.931019i | \(-0.381079\pi\) | ||||
0.364971 | + | 0.931019i | \(0.381079\pi\) | |||||||
\(684\) | −7.56868 | −0.289396 | ||||||||
\(685\) | −5.36625 | −0.205034 | ||||||||
\(686\) | 1.40629 | 0.0536922 | ||||||||
\(687\) | −14.3391 | −0.547071 | ||||||||
\(688\) | 8.47625 | 0.323154 | ||||||||
\(689\) | 3.73484 | 0.142286 | ||||||||
\(690\) | 0.0559322 | 0.00212930 | ||||||||
\(691\) | 8.69891 | 0.330922 | 0.165461 | − | 0.986216i | \(-0.447089\pi\) | ||||
0.165461 | + | 0.986216i | \(0.447089\pi\) | |||||||
\(692\) | 27.3320 | 1.03900 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.01848 | 0.190499 | ||||||||
\(695\) | −12.6237 | −0.478844 | ||||||||
\(696\) | −5.22384 | −0.198009 | ||||||||
\(697\) | −13.9480 | −0.528317 | ||||||||
\(698\) | −2.84910 | −0.107840 | ||||||||
\(699\) | 3.66332 | 0.138559 | ||||||||
\(700\) | 0.956295 | 0.0361446 | ||||||||
\(701\) | 40.2941 | 1.52189 | 0.760944 | − | 0.648818i | \(-0.224736\pi\) | ||||
0.760944 | + | 0.648818i | \(0.224736\pi\) | |||||||
\(702\) | 0.683103 | 0.0257821 | ||||||||
\(703\) | 29.0306 | 1.09491 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.58347 | 0.210285 | ||||||||
\(706\) | −6.56559 | −0.247099 | ||||||||
\(707\) | 8.72668 | 0.328201 | ||||||||
\(708\) | −8.83741 | −0.332130 | ||||||||
\(709\) | 23.6968 | 0.889950 | 0.444975 | − | 0.895543i | \(-0.353212\pi\) | ||||
0.444975 | + | 0.895543i | \(0.353212\pi\) | |||||||
\(710\) | 1.11133 | 0.0417075 | ||||||||
\(711\) | 1.50828 | 0.0565651 | ||||||||
\(712\) | −13.1694 | −0.493545 | ||||||||
\(713\) | 1.56052 | 0.0584420 | ||||||||
\(714\) | 0.340375 | 0.0127382 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.3764 | 0.574643 | ||||||||
\(717\) | 1.07794 | 0.0402565 | ||||||||
\(718\) | −0.600737 | −0.0224193 | ||||||||
\(719\) | −17.3576 | −0.647330 | −0.323665 | − | 0.946172i | \(-0.604915\pi\) | ||||
−0.323665 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(720\) | 3.73968 | 0.139370 | ||||||||
\(721\) | −7.49716 | −0.279209 | ||||||||
\(722\) | −0.842860 | −0.0313680 | ||||||||
\(723\) | 27.1803 | 1.01085 | ||||||||
\(724\) | −14.4623 | −0.537486 | ||||||||
\(725\) | −6.31592 | −0.234567 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.5895 | 1.06033 | 0.530163 | − | 0.847896i | \(-0.322131\pi\) | ||||
0.530163 | + | 0.847896i | \(0.322131\pi\) | |||||||
\(728\) | −1.32109 | −0.0489629 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.01925 | −0.0747358 | ||||||||
\(731\) | 7.54927 | 0.279220 | ||||||||
\(732\) | −24.5991 | −0.909209 | ||||||||
\(733\) | 32.4058 | 1.19694 | 0.598468 | − | 0.801146i | \(-0.295776\pi\) | ||||
0.598468 | + | 0.801146i | \(0.295776\pi\) | |||||||
\(734\) | 5.03014 | 0.185666 | ||||||||
\(735\) | 6.76105 | 0.249385 | ||||||||
\(736\) | −0.651737 | −0.0240234 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.875466 | −0.0322264 | ||||||||
\(739\) | −4.16917 | −0.153365 | −0.0766827 | − | 0.997056i | \(-0.524433\pi\) | ||||
−0.0766827 | + | 0.997056i | \(0.524433\pi\) | |||||||
\(740\) | −14.6793 | −0.539621 | ||||||||
\(741\) | 12.6418 | 0.464407 | ||||||||
\(742\) | 0.116808 | 0.00428816 | ||||||||
\(743\) | −48.8869 | −1.79349 | −0.896743 | − | 0.442551i | \(-0.854074\pi\) | ||||
−0.896743 | + | 0.442551i | \(0.854074\pi\) | |||||||
\(744\) | −4.82420 | −0.176864 | ||||||||
\(745\) | 4.69947 | 0.172175 | ||||||||
\(746\) | −3.66576 | −0.134213 | ||||||||
\(747\) | −17.6428 | −0.645516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.85443 | −0.104299 | ||||||||
\(750\) | −0.209057 | −0.00763368 | ||||||||
\(751\) | −40.5342 | −1.47912 | −0.739558 | − | 0.673093i | \(-0.764965\pi\) | ||||
−0.739558 | + | 0.673093i | \(0.764965\pi\) | |||||||
\(752\) | −20.8804 | −0.761429 | ||||||||
\(753\) | 2.60016 | 0.0947551 | ||||||||
\(754\) | 4.31442 | 0.157122 | ||||||||
\(755\) | −14.5712 | −0.530302 | ||||||||
\(756\) | −0.956295 | −0.0347801 | ||||||||
\(757\) | −21.8143 | −0.792854 | −0.396427 | − | 0.918066i | \(-0.629750\pi\) | ||||
−0.396427 | + | 0.918066i | \(0.629750\pi\) | |||||||
\(758\) | −6.82348 | −0.247840 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.19992 | −0.116073 | ||||||||
\(761\) | −28.6123 | −1.03720 | −0.518598 | − | 0.855018i | \(-0.673546\pi\) | ||||
−0.518598 | + | 0.855018i | \(0.673546\pi\) | |||||||
\(762\) | 4.61808 | 0.167295 | ||||||||
\(763\) | 3.44764 | 0.124813 | ||||||||
\(764\) | 0.840694 | 0.0304152 | ||||||||
\(765\) | 3.33070 | 0.120422 | ||||||||
\(766\) | 2.19859 | 0.0794382 | ||||||||
\(767\) | 14.7609 | 0.532984 | ||||||||
\(768\) | −12.6171 | −0.455279 | ||||||||
\(769\) | 11.2690 | 0.406372 | 0.203186 | − | 0.979140i | \(-0.434870\pi\) | ||||
0.203186 | + | 0.979140i | \(0.434870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.67343 | −0.204324 | ||||||||
\(772\) | 3.81486 | 0.137300 | ||||||||
\(773\) | −15.7132 | −0.565166 | −0.282583 | − | 0.959243i | \(-0.591191\pi\) | ||||
−0.282583 | + | 0.959243i | \(0.591191\pi\) | |||||||
\(774\) | 0.473842 | 0.0170319 | ||||||||
\(775\) | −5.83274 | −0.209518 | ||||||||
\(776\) | 13.5116 | 0.485040 | ||||||||
\(777\) | 3.66799 | 0.131588 | ||||||||
\(778\) | 4.88080 | 0.174985 | ||||||||
\(779\) | −16.2017 | −0.580486 | ||||||||
\(780\) | −6.39228 | −0.228880 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.186294 | −0.00666185 | ||||||||
\(783\) | 6.31592 | 0.225713 | ||||||||
\(784\) | −25.2842 | −0.903006 | ||||||||
\(785\) | 0.334194 | 0.0119279 | ||||||||
\(786\) | 0.811127 | 0.0289319 | ||||||||
\(787\) | −18.4148 | −0.656416 | −0.328208 | − | 0.944606i | \(-0.606445\pi\) | ||||
−0.328208 | + | 0.944606i | \(0.606445\pi\) | |||||||
\(788\) | −43.6042 | −1.55333 | ||||||||
\(789\) | −23.4448 | −0.834657 | ||||||||
\(790\) | 0.315317 | 0.0112185 | ||||||||
\(791\) | 6.64903 | 0.236412 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.0872 | 1.45905 | ||||||||
\(794\) | 1.47331 | 0.0522857 | ||||||||
\(795\) | 1.14301 | 0.0405384 | ||||||||
\(796\) | −12.6196 | −0.447290 | ||||||||
\(797\) | 25.2719 | 0.895176 | 0.447588 | − | 0.894240i | \(-0.352283\pi\) | ||||
0.447588 | + | 0.894240i | \(0.352283\pi\) | |||||||
\(798\) | 0.395374 | 0.0139961 | ||||||||
\(799\) | −18.5969 | −0.657910 | ||||||||
\(800\) | 2.43599 | 0.0861252 | ||||||||
\(801\) | 15.9226 | 0.562597 | ||||||||
\(802\) | 4.69635 | 0.165834 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 17.5592 | 0.619266 | ||||||||
\(805\) | 0.130784 | 0.00460953 | ||||||||
\(806\) | 3.98436 | 0.140343 | ||||||||
\(807\) | 5.46398 | 0.192341 | ||||||||
\(808\) | 14.7654 | 0.519444 | ||||||||
\(809\) | 11.2635 | 0.396002 | 0.198001 | − | 0.980202i | \(-0.436555\pi\) | ||||
0.198001 | + | 0.980202i | \(0.436555\pi\) | |||||||
\(810\) | 0.209057 | 0.00734551 | ||||||||
\(811\) | 24.3405 | 0.854710 | 0.427355 | − | 0.904084i | \(-0.359445\pi\) | ||||
0.427355 | + | 0.904084i | \(0.359445\pi\) | |||||||
\(812\) | −6.03988 | −0.211958 | ||||||||
\(813\) | 2.52319 | 0.0884923 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.98935 | 0.0696840 | ||||||||
\(816\) | −12.4558 | −0.436039 | ||||||||
\(817\) | 8.76910 | 0.306792 | ||||||||
\(818\) | −0.213067 | −0.00744971 | ||||||||
\(819\) | 1.59727 | 0.0558132 | ||||||||
\(820\) | 8.19236 | 0.286090 | ||||||||
\(821\) | −3.53529 | −0.123383 | −0.0616913 | − | 0.998095i | \(-0.519649\pi\) | ||||
−0.0616913 | + | 0.998095i | \(0.519649\pi\) | |||||||
\(822\) | 1.12185 | 0.0391291 | ||||||||
\(823\) | −46.9230 | −1.63563 | −0.817817 | − | 0.575478i | \(-0.804816\pi\) | ||||
−0.817817 | + | 0.575478i | \(0.804816\pi\) | |||||||
\(824\) | −12.6851 | −0.441905 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.461650 | 0.0160629 | ||||||||
\(827\) | 43.7647 | 1.52185 | 0.760923 | − | 0.648842i | \(-0.224746\pi\) | ||||
0.760923 | + | 0.648842i | \(0.224746\pi\) | |||||||
\(828\) | 0.523398 | 0.0181893 | ||||||||
\(829\) | −20.2447 | −0.703126 | −0.351563 | − | 0.936164i | \(-0.614350\pi\) | ||||
−0.351563 | + | 0.936164i | \(0.614350\pi\) | |||||||
\(830\) | −3.68835 | −0.128025 | ||||||||
\(831\) | −22.4067 | −0.777281 | ||||||||
\(832\) | 22.7751 | 0.789585 | ||||||||
\(833\) | −22.5190 | −0.780239 | ||||||||
\(834\) | 2.63907 | 0.0913834 | ||||||||
\(835\) | 19.2322 | 0.665559 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.83274 | 0.201609 | ||||||||
\(838\) | 1.57644 | 0.0544573 | ||||||||
\(839\) | 39.0495 | 1.34814 | 0.674070 | − | 0.738668i | \(-0.264545\pi\) | ||||
0.674070 | + | 0.738668i | \(0.264545\pi\) | |||||||
\(840\) | −0.404307 | −0.0139499 | ||||||||
\(841\) | 10.8909 | 0.375547 | ||||||||
\(842\) | 2.45820 | 0.0847153 | ||||||||
\(843\) | −11.2790 | −0.388471 | ||||||||
\(844\) | 43.5039 | 1.49747 | ||||||||
\(845\) | −2.32315 | −0.0799187 | ||||||||
\(846\) | −1.16726 | −0.0401313 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.27450 | −0.146787 | ||||||||
\(849\) | −11.6925 | −0.401285 | ||||||||
\(850\) | 0.696307 | 0.0238831 | ||||||||
\(851\) | −2.00756 | −0.0688182 | ||||||||
\(852\) | 10.3995 | 0.356281 | ||||||||
\(853\) | 41.1973 | 1.41057 | 0.705285 | − | 0.708924i | \(-0.250819\pi\) | ||||
0.705285 | + | 0.708924i | \(0.250819\pi\) | |||||||
\(854\) | 1.28501 | 0.0439722 | ||||||||
\(855\) | 3.86889 | 0.132313 | ||||||||
\(856\) | −4.82965 | −0.165074 | ||||||||
\(857\) | −39.6853 | −1.35563 | −0.677813 | − | 0.735235i | \(-0.737072\pi\) | ||||
−0.677813 | + | 0.735235i | \(0.737072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6446 | 0.772625 | 0.386313 | − | 0.922368i | \(-0.373749\pi\) | ||||
0.386313 | + | 0.922368i | \(0.373749\pi\) | |||||||
\(860\) | −4.43408 | −0.151201 | ||||||||
\(861\) | −2.04707 | −0.0697639 | ||||||||
\(862\) | 5.65512 | 0.192614 | ||||||||
\(863\) | −34.0135 | −1.15783 | −0.578916 | − | 0.815387i | \(-0.696524\pi\) | ||||
−0.578916 | + | 0.815387i | \(0.696524\pi\) | |||||||
\(864\) | −2.43599 | −0.0828740 | ||||||||
\(865\) | −13.9713 | −0.475038 | ||||||||
\(866\) | −5.36658 | −0.182364 | ||||||||
\(867\) | 5.90641 | 0.200592 | ||||||||
\(868\) | −5.57782 | −0.189324 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.32039 | 0.0447653 | ||||||||
\(871\) | −29.3287 | −0.993764 | ||||||||
\(872\) | 5.83334 | 0.197542 | ||||||||
\(873\) | −16.3364 | −0.552902 | ||||||||
\(874\) | −0.216395 | −0.00731968 | ||||||||
\(875\) | −0.488830 | −0.0165255 | ||||||||
\(876\) | −18.8956 | −0.638422 | ||||||||
\(877\) | −27.4935 | −0.928389 | −0.464195 | − | 0.885733i | \(-0.653656\pi\) | ||||
−0.464195 | + | 0.885733i | \(0.653656\pi\) | |||||||
\(878\) | −0.107237 | −0.00361906 | ||||||||
\(879\) | −13.4918 | −0.455067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.2585 | 1.39003 | 0.695017 | − | 0.718993i | \(-0.255397\pi\) | ||||
0.695017 | + | 0.718993i | \(0.255397\pi\) | |||||||
\(882\) | −1.41344 | −0.0475931 | ||||||||
\(883\) | −15.1814 | −0.510895 | −0.255447 | − | 0.966823i | \(-0.582223\pi\) | ||||
−0.255447 | + | 0.966823i | \(0.582223\pi\) | |||||||
\(884\) | 21.2908 | 0.716087 | ||||||||
\(885\) | 4.51742 | 0.151851 | ||||||||
\(886\) | −6.95463 | −0.233645 | ||||||||
\(887\) | −34.1080 | −1.14523 | −0.572617 | − | 0.819823i | \(-0.694072\pi\) | ||||
−0.572617 | + | 0.819823i | \(0.694072\pi\) | |||||||
\(888\) | 6.20617 | 0.208265 | ||||||||
\(889\) | 10.7983 | 0.362162 | ||||||||
\(890\) | 3.32873 | 0.111579 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.9497 | −0.902342 | ||||||||
\(893\) | −21.6018 | −0.722876 | ||||||||
\(894\) | −0.982456 | −0.0328582 | ||||||||
\(895\) | −7.85995 | −0.262729 | ||||||||
\(896\) | 3.09386 | 0.103359 | ||||||||
\(897\) | −0.874217 | −0.0291892 | ||||||||
\(898\) | 1.24565 | 0.0415678 | ||||||||
\(899\) | 36.8391 | 1.22865 | ||||||||
\(900\) | −1.95630 | −0.0652098 | ||||||||
\(901\) | −3.80703 | −0.126831 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.10797 | 0.0368708 | ||||||||
\(904\) | 11.2500 | 0.374171 | ||||||||
\(905\) | 7.39268 | 0.245741 | ||||||||
\(906\) | 3.04622 | 0.101204 | ||||||||
\(907\) | −17.9230 | −0.595123 | −0.297561 | − | 0.954703i | \(-0.596173\pi\) | ||||
−0.297561 | + | 0.954703i | \(0.596173\pi\) | |||||||
\(908\) | −50.5807 | −1.67858 | ||||||||
\(909\) | −17.8522 | −0.592120 | ||||||||
\(910\) | 0.333921 | 0.0110694 | ||||||||
\(911\) | −21.9045 | −0.725727 | −0.362864 | − | 0.931842i | \(-0.618201\pi\) | ||||
−0.362864 | + | 0.931842i | \(0.618201\pi\) | |||||||
\(912\) | −14.4684 | −0.479097 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.27867 | −0.141526 | ||||||||
\(915\) | 12.5743 | 0.415695 | ||||||||
\(916\) | −28.0515 | −0.926849 | ||||||||
\(917\) | 1.89663 | 0.0626321 | ||||||||
\(918\) | −0.696307 | −0.0229815 | ||||||||
\(919\) | −4.04370 | −0.133390 | −0.0666948 | − | 0.997773i | \(-0.521245\pi\) | ||||
−0.0666948 | + | 0.997773i | \(0.521245\pi\) | |||||||
\(920\) | 0.221284 | 0.00729553 | ||||||||
\(921\) | −0.364626 | −0.0120148 | ||||||||
\(922\) | −6.51794 | −0.214657 | ||||||||
\(923\) | −17.3700 | −0.571741 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.50361 | 0.246717 | ||||||||
\(926\) | 2.29940 | 0.0755631 | ||||||||
\(927\) | 15.3370 | 0.503732 | ||||||||
\(928\) | −15.3855 | −0.505054 | ||||||||
\(929\) | −10.3334 | −0.339027 | −0.169514 | − | 0.985528i | \(-0.554220\pi\) | ||||
−0.169514 | + | 0.985528i | \(0.554220\pi\) | |||||||
\(930\) | 1.21937 | 0.0399849 | ||||||||
\(931\) | −26.1577 | −0.857284 | ||||||||
\(932\) | 7.16653 | 0.234748 | ||||||||
\(933\) | −23.2542 | −0.761309 | ||||||||
\(934\) | −7.40186 | −0.242196 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.70256 | 0.0883358 | ||||||||
\(937\) | −32.5450 | −1.06320 | −0.531600 | − | 0.846996i | \(-0.678409\pi\) | ||||
−0.531600 | + | 0.846996i | \(0.678409\pi\) | |||||||
\(938\) | −0.917261 | −0.0299496 | ||||||||
\(939\) | 12.2326 | 0.399197 | ||||||||
\(940\) | 10.9229 | 0.356266 | ||||||||
\(941\) | 12.3962 | 0.404104 | 0.202052 | − | 0.979375i | \(-0.435239\pi\) | ||||
0.202052 | + | 0.979375i | \(0.435239\pi\) | |||||||
\(942\) | −0.0698656 | −0.00227634 | ||||||||
\(943\) | 1.12040 | 0.0364852 | ||||||||
\(944\) | −16.8937 | −0.549844 | ||||||||
\(945\) | 0.488830 | 0.0159016 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.7602 | 1.45451 | 0.727256 | − | 0.686366i | \(-0.240795\pi\) | ||||
0.727256 | + | 0.686366i | \(0.240795\pi\) | |||||||
\(948\) | 2.95065 | 0.0958326 | ||||||||
\(949\) | 31.5607 | 1.02450 | ||||||||
\(950\) | 0.808817 | 0.0262415 | ||||||||
\(951\) | −32.0176 | −1.03824 | ||||||||
\(952\) | 1.34663 | 0.0436444 | ||||||||
\(953\) | 21.3562 | 0.691794 | 0.345897 | − | 0.938273i | \(-0.387575\pi\) | ||||
0.345897 | + | 0.938273i | \(0.387575\pi\) | |||||||
\(954\) | −0.238954 | −0.00773644 | ||||||||
\(955\) | −0.429738 | −0.0139060 | ||||||||
\(956\) | 2.10877 | 0.0682026 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.05187 | −0.130910 | ||||||||
\(959\) | 2.62318 | 0.0847070 | ||||||||
\(960\) | 6.97010 | 0.224959 | ||||||||
\(961\) | 3.02083 | 0.0974461 | ||||||||
\(962\) | −5.12574 | −0.165261 | ||||||||
\(963\) | 5.83932 | 0.188169 | ||||||||
\(964\) | 53.1728 | 1.71258 | ||||||||
\(965\) | −1.95004 | −0.0627742 | ||||||||
\(966\) | −0.0273413 | −0.000879693 0 | ||||||||
\(967\) | 31.3251 | 1.00735 | 0.503674 | − | 0.863894i | \(-0.331981\pi\) | ||||
0.503674 | + | 0.863894i | \(0.331981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.8861 | −0.413962 | ||||||||
\(970\) | −3.41523 | −0.109656 | ||||||||
\(971\) | 15.7125 | 0.504239 | 0.252119 | − | 0.967696i | \(-0.418872\pi\) | ||||
0.252119 | + | 0.967696i | \(0.418872\pi\) | |||||||
\(972\) | 1.95630 | 0.0627482 | ||||||||
\(973\) | 6.17083 | 0.197828 | ||||||||
\(974\) | −3.41809 | −0.109523 | ||||||||
\(975\) | 3.26755 | 0.104645 | ||||||||
\(976\) | −47.0240 | −1.50520 | ||||||||
\(977\) | −22.5622 | −0.721828 | −0.360914 | − | 0.932599i | \(-0.617535\pi\) | ||||
−0.360914 | + | 0.932599i | \(0.617535\pi\) | |||||||
\(978\) | −0.415888 | −0.0132986 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 13.2266 | 0.422508 | ||||||||
\(981\) | −7.05284 | −0.225180 | ||||||||
\(982\) | 2.88195 | 0.0919669 | ||||||||
\(983\) | 45.9795 | 1.46652 | 0.733259 | − | 0.679950i | \(-0.237998\pi\) | ||||
0.733259 | + | 0.679950i | \(0.237998\pi\) | |||||||
\(984\) | −3.46360 | −0.110416 | ||||||||
\(985\) | 22.2892 | 0.710192 | ||||||||
\(986\) | −4.39782 | −0.140055 | ||||||||
\(987\) | −2.72936 | −0.0868766 | ||||||||
\(988\) | 24.7310 | 0.786798 | ||||||||
\(989\) | −0.606410 | −0.0192827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.48050 | 0.174094 | 0.0870469 | − | 0.996204i | \(-0.472257\pi\) | ||||
0.0870469 | + | 0.996204i | \(0.472257\pi\) | |||||||
\(992\) | −14.2085 | −0.451120 | ||||||||
\(993\) | 20.5705 | 0.652784 | ||||||||
\(994\) | −0.543251 | −0.0172309 | ||||||||
\(995\) | 6.45077 | 0.204503 | ||||||||
\(996\) | −34.5145 | −1.09363 | ||||||||
\(997\) | −18.2558 | −0.578167 | −0.289083 | − | 0.957304i | \(-0.593350\pi\) | ||||
−0.289083 | + | 0.957304i | \(0.593350\pi\) | |||||||
\(998\) | 4.13573 | 0.130914 | ||||||||
\(999\) | −7.50361 | −0.237404 |
(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 | 1815.2.a.q.1.3 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bq.1.2 | 4 | |||
5.4 | even | 2 | 9075.2.a.df.1.2 | 4 | |||
11.7 | odd | 10 | 165.2.m.c.16.1 | ✓ | 8 | ||
11.8 | odd | 10 | 165.2.m.c.31.1 | yes | 8 | ||
11.10 | odd | 2 | 1815.2.a.u.1.2 | 4 | |||
33.8 | even | 10 | 495.2.n.c.361.2 | 8 | |||
33.29 | even | 10 | 495.2.n.c.181.2 | 8 | |||
33.32 | even | 2 | 5445.2.a.bj.1.3 | 4 | |||
55.7 | even | 20 | 825.2.bx.e.49.3 | 16 | |||
55.8 | even | 20 | 825.2.bx.e.724.3 | 16 | |||
55.18 | even | 20 | 825.2.bx.e.49.2 | 16 | |||
55.19 | odd | 10 | 825.2.n.j.526.2 | 8 | |||
55.29 | odd | 10 | 825.2.n.j.676.2 | 8 | |||
55.52 | even | 20 | 825.2.bx.e.724.2 | 16 | |||
55.54 | odd | 2 | 9075.2.a.co.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.c.16.1 | ✓ | 8 | 11.7 | odd | 10 | ||
165.2.m.c.31.1 | yes | 8 | 11.8 | odd | 10 | ||
495.2.n.c.181.2 | 8 | 33.29 | even | 10 | |||
495.2.n.c.361.2 | 8 | 33.8 | even | 10 | |||
825.2.n.j.526.2 | 8 | 55.19 | odd | 10 | |||
825.2.n.j.676.2 | 8 | 55.29 | odd | 10 | |||
825.2.bx.e.49.2 | 16 | 55.18 | even | 20 | |||
825.2.bx.e.49.3 | 16 | 55.7 | even | 20 | |||
825.2.bx.e.724.2 | 16 | 55.52 | even | 20 | |||
825.2.bx.e.724.3 | 16 | 55.8 | even | 20 | |||
1815.2.a.q.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.u.1.2 | 4 | 11.10 | odd | 2 | |||
5445.2.a.bj.1.3 | 4 | 33.32 | even | 2 | |||
5445.2.a.bq.1.2 | 4 | 3.2 | odd | 2 | |||
9075.2.a.co.1.3 | 4 | 55.54 | odd | 2 | |||
9075.2.a.df.1.2 | 4 | 5.4 | even | 2 |