Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.116858\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.116858 | −0.0826312 | −0.0413156 | − | 0.999146i | \(-0.513155\pi\) | ||||
−0.0413156 | + | 0.999146i | \(0.513155\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98634 | −0.993172 | ||||||||
\(5\) | −1.39349 | −0.623188 | −0.311594 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311594 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(6\) | −0.116858 | −0.0477072 | ||||||||
\(7\) | −4.81215 | −1.81882 | −0.909410 | − | 0.415900i | \(-0.863467\pi\) | ||||
−0.909410 | + | 0.415900i | \(0.863467\pi\) | |||||||
\(8\) | 0.465837 | 0.164698 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.162841 | 0.0514948 | ||||||||
\(11\) | 1.77929 | 0.536475 | 0.268237 | − | 0.963353i | \(-0.413559\pi\) | ||||
0.268237 | + | 0.963353i | \(0.413559\pi\) | |||||||
\(12\) | −1.98634 | −0.573408 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.562339 | 0.150291 | ||||||||
\(15\) | −1.39349 | −0.359798 | ||||||||
\(16\) | 3.91825 | 0.979563 | ||||||||
\(17\) | −0.422486 | −0.102468 | −0.0512339 | − | 0.998687i | \(-0.516315\pi\) | ||||
−0.0512339 | + | 0.998687i | \(0.516315\pi\) | |||||||
\(18\) | −0.116858 | −0.0275437 | ||||||||
\(19\) | 1.32976 | 0.305068 | 0.152534 | − | 0.988298i | \(-0.451257\pi\) | ||||
0.152534 | + | 0.988298i | \(0.451257\pi\) | |||||||
\(20\) | 2.76795 | 0.618933 | ||||||||
\(21\) | −4.81215 | −1.05010 | ||||||||
\(22\) | −0.207924 | −0.0443296 | ||||||||
\(23\) | 7.34590 | 1.53173 | 0.765863 | − | 0.643003i | \(-0.222312\pi\) | ||||
0.765863 | + | 0.643003i | \(0.222312\pi\) | |||||||
\(24\) | 0.465837 | 0.0950886 | ||||||||
\(25\) | −3.05819 | −0.611637 | ||||||||
\(26\) | −0.116858 | −0.0229178 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 9.55858 | 1.80640 | ||||||||
\(29\) | −1.65563 | −0.307443 | −0.153721 | − | 0.988114i | \(-0.549126\pi\) | ||||
−0.153721 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(30\) | 0.162841 | 0.0297305 | ||||||||
\(31\) | 8.80975 | 1.58228 | 0.791139 | − | 0.611637i | \(-0.209488\pi\) | ||||
0.791139 | + | 0.611637i | \(0.209488\pi\) | |||||||
\(32\) | −1.38955 | −0.245641 | ||||||||
\(33\) | 1.77929 | 0.309734 | ||||||||
\(34\) | 0.0493709 | 0.00846704 | ||||||||
\(35\) | 6.70568 | 1.13347 | ||||||||
\(36\) | −1.98634 | −0.331057 | ||||||||
\(37\) | 0.494655 | 0.0813208 | 0.0406604 | − | 0.999173i | \(-0.487054\pi\) | ||||
0.0406604 | + | 0.999173i | \(0.487054\pi\) | |||||||
\(38\) | −0.155393 | −0.0252081 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.649139 | −0.102638 | ||||||||
\(41\) | 5.35869 | 0.836887 | 0.418444 | − | 0.908243i | \(-0.362576\pi\) | ||||
0.418444 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(42\) | 0.562339 | 0.0867708 | ||||||||
\(43\) | 1.57793 | 0.240632 | 0.120316 | − | 0.992736i | \(-0.461609\pi\) | ||||
0.120316 | + | 0.992736i | \(0.461609\pi\) | |||||||
\(44\) | −3.53427 | −0.532812 | ||||||||
\(45\) | −1.39349 | −0.207729 | ||||||||
\(46\) | −0.858429 | −0.126568 | ||||||||
\(47\) | −11.4812 | −1.67471 | −0.837356 | − | 0.546658i | \(-0.815900\pi\) | ||||
−0.837356 | + | 0.546658i | \(0.815900\pi\) | |||||||
\(48\) | 3.91825 | 0.565551 | ||||||||
\(49\) | 16.1568 | 2.30811 | ||||||||
\(50\) | 0.357374 | 0.0505403 | ||||||||
\(51\) | −0.422486 | −0.0591598 | ||||||||
\(52\) | −1.98634 | −0.275456 | ||||||||
\(53\) | −8.41172 | −1.15544 | −0.577720 | − | 0.816235i | \(-0.696057\pi\) | ||||
−0.577720 | + | 0.816235i | \(0.696057\pi\) | |||||||
\(54\) | −0.116858 | −0.0159024 | ||||||||
\(55\) | −2.47942 | −0.334324 | ||||||||
\(56\) | −2.24168 | −0.299557 | ||||||||
\(57\) | 1.32976 | 0.176131 | ||||||||
\(58\) | 0.193474 | 0.0254044 | ||||||||
\(59\) | −8.75532 | −1.13985 | −0.569923 | − | 0.821698i | \(-0.693027\pi\) | ||||
−0.569923 | + | 0.821698i | \(0.693027\pi\) | |||||||
\(60\) | 2.76795 | 0.357341 | ||||||||
\(61\) | −3.98372 | −0.510062 | −0.255031 | − | 0.966933i | \(-0.582086\pi\) | ||||
−0.255031 | + | 0.966933i | \(0.582086\pi\) | |||||||
\(62\) | −1.02949 | −0.130746 | ||||||||
\(63\) | −4.81215 | −0.606274 | ||||||||
\(64\) | −7.67412 | −0.959265 | ||||||||
\(65\) | −1.39349 | −0.172841 | ||||||||
\(66\) | −0.207924 | −0.0255937 | ||||||||
\(67\) | −2.56492 | −0.313355 | −0.156678 | − | 0.987650i | \(-0.550078\pi\) | ||||
−0.156678 | + | 0.987650i | \(0.550078\pi\) | |||||||
\(68\) | 0.839202 | 0.101768 | ||||||||
\(69\) | 7.34590 | 0.884343 | ||||||||
\(70\) | −0.783613 | −0.0936597 | ||||||||
\(71\) | −10.8094 | −1.28283 | −0.641417 | − | 0.767192i | \(-0.721653\pi\) | ||||
−0.641417 | + | 0.767192i | \(0.721653\pi\) | |||||||
\(72\) | 0.465837 | 0.0548994 | ||||||||
\(73\) | −10.5596 | −1.23590 | −0.617952 | − | 0.786216i | \(-0.712037\pi\) | ||||
−0.617952 | + | 0.786216i | \(0.712037\pi\) | |||||||
\(74\) | −0.0578045 | −0.00671964 | ||||||||
\(75\) | −3.05819 | −0.353129 | ||||||||
\(76\) | −2.64136 | −0.302985 | ||||||||
\(77\) | −8.56218 | −0.975751 | ||||||||
\(78\) | −0.116858 | −0.0132316 | ||||||||
\(79\) | 12.6272 | 1.42067 | 0.710333 | − | 0.703866i | \(-0.248544\pi\) | ||||
0.710333 | + | 0.703866i | \(0.248544\pi\) | |||||||
\(80\) | −5.46004 | −0.610452 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.626207 | −0.0691530 | ||||||||
\(83\) | 3.36857 | 0.369749 | 0.184875 | − | 0.982762i | \(-0.440812\pi\) | ||||
0.184875 | + | 0.982762i | \(0.440812\pi\) | |||||||
\(84\) | 9.55858 | 1.04293 | ||||||||
\(85\) | 0.588730 | 0.0638567 | ||||||||
\(86\) | −0.184394 | −0.0198837 | ||||||||
\(87\) | −1.65563 | −0.177502 | ||||||||
\(88\) | 0.828857 | 0.0883564 | ||||||||
\(89\) | 10.1717 | 1.07820 | 0.539101 | − | 0.842241i | \(-0.318764\pi\) | ||||
0.539101 | + | 0.842241i | \(0.318764\pi\) | |||||||
\(90\) | 0.162841 | 0.0171649 | ||||||||
\(91\) | −4.81215 | −0.504450 | ||||||||
\(92\) | −14.5915 | −1.52127 | ||||||||
\(93\) | 8.80975 | 0.913529 | ||||||||
\(94\) | 1.34168 | 0.138384 | ||||||||
\(95\) | −1.85301 | −0.190114 | ||||||||
\(96\) | −1.38955 | −0.141821 | ||||||||
\(97\) | −10.2822 | −1.04400 | −0.522000 | − | 0.852945i | \(-0.674814\pi\) | ||||
−0.522000 | + | 0.852945i | \(0.674814\pi\) | |||||||
\(98\) | −1.88805 | −0.190722 | ||||||||
\(99\) | 1.77929 | 0.178825 | ||||||||
\(100\) | 6.07461 | 0.607461 | ||||||||
\(101\) | 8.64965 | 0.860673 | 0.430336 | − | 0.902669i | \(-0.358395\pi\) | ||||
0.430336 | + | 0.902669i | \(0.358395\pi\) | |||||||
\(102\) | 0.0493709 | 0.00488845 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 0.465837 | 0.0456791 | ||||||||
\(105\) | 6.70568 | 0.654407 | ||||||||
\(106\) | 0.982979 | 0.0954753 | ||||||||
\(107\) | −0.872688 | −0.0843659 | −0.0421830 | − | 0.999110i | \(-0.513431\pi\) | ||||
−0.0421830 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(108\) | −1.98634 | −0.191136 | ||||||||
\(109\) | −1.33197 | −0.127580 | −0.0637900 | − | 0.997963i | \(-0.520319\pi\) | ||||
−0.0637900 | + | 0.997963i | \(0.520319\pi\) | |||||||
\(110\) | 0.289740 | 0.0276256 | ||||||||
\(111\) | 0.494655 | 0.0469506 | ||||||||
\(112\) | −18.8552 | −1.78165 | ||||||||
\(113\) | −15.5055 | −1.45864 | −0.729318 | − | 0.684175i | \(-0.760162\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(114\) | −0.155393 | −0.0145539 | ||||||||
\(115\) | −10.2364 | −0.954553 | ||||||||
\(116\) | 3.28865 | 0.305344 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 1.02313 | 0.0941868 | ||||||||
\(119\) | 2.03306 | 0.186371 | ||||||||
\(120\) | −0.649139 | −0.0592580 | ||||||||
\(121\) | −7.83414 | −0.712195 | ||||||||
\(122\) | 0.465530 | 0.0421471 | ||||||||
\(123\) | 5.35869 | 0.483177 | ||||||||
\(124\) | −17.4992 | −1.57147 | ||||||||
\(125\) | 11.2290 | 1.00435 | ||||||||
\(126\) | 0.562339 | 0.0500971 | ||||||||
\(127\) | −2.43320 | −0.215912 | −0.107956 | − | 0.994156i | \(-0.534430\pi\) | ||||
−0.107956 | + | 0.994156i | \(0.534430\pi\) | |||||||
\(128\) | 3.67589 | 0.324906 | ||||||||
\(129\) | 1.57793 | 0.138929 | ||||||||
\(130\) | 0.162841 | 0.0142821 | ||||||||
\(131\) | −2.04123 | −0.178343 | −0.0891714 | − | 0.996016i | \(-0.528422\pi\) | ||||
−0.0891714 | + | 0.996016i | \(0.528422\pi\) | |||||||
\(132\) | −3.53427 | −0.307619 | ||||||||
\(133\) | −6.39900 | −0.554863 | ||||||||
\(134\) | 0.299732 | 0.0258929 | ||||||||
\(135\) | −1.39349 | −0.119933 | ||||||||
\(136\) | −0.196809 | −0.0168763 | ||||||||
\(137\) | −8.78362 | −0.750435 | −0.375218 | − | 0.926937i | \(-0.622432\pi\) | ||||
−0.375218 | + | 0.926937i | \(0.622432\pi\) | |||||||
\(138\) | −0.858429 | −0.0730743 | ||||||||
\(139\) | −9.82806 | −0.833605 | −0.416802 | − | 0.908997i | \(-0.636849\pi\) | ||||
−0.416802 | + | 0.908997i | \(0.636849\pi\) | |||||||
\(140\) | −13.3198 | −1.12573 | ||||||||
\(141\) | −11.4812 | −0.966896 | ||||||||
\(142\) | 1.26316 | 0.106002 | ||||||||
\(143\) | 1.77929 | 0.148791 | ||||||||
\(144\) | 3.91825 | 0.326521 | ||||||||
\(145\) | 2.30710 | 0.191595 | ||||||||
\(146\) | 1.23397 | 0.102124 | ||||||||
\(147\) | 16.1568 | 1.33259 | ||||||||
\(148\) | −0.982556 | −0.0807656 | ||||||||
\(149\) | −3.54934 | −0.290774 | −0.145387 | − | 0.989375i | \(-0.546443\pi\) | ||||
−0.145387 | + | 0.989375i | \(0.546443\pi\) | |||||||
\(150\) | 0.357374 | 0.0291795 | ||||||||
\(151\) | 2.61550 | 0.212846 | 0.106423 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106423 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(152\) | 0.619451 | 0.0502441 | ||||||||
\(153\) | −0.422486 | −0.0341559 | ||||||||
\(154\) | 1.00056 | 0.0806275 | ||||||||
\(155\) | −12.2763 | −0.986056 | ||||||||
\(156\) | −1.98634 | −0.159035 | ||||||||
\(157\) | −6.63499 | −0.529530 | −0.264765 | − | 0.964313i | \(-0.585294\pi\) | ||||
−0.264765 | + | 0.964313i | \(0.585294\pi\) | |||||||
\(158\) | −1.47559 | −0.117391 | ||||||||
\(159\) | −8.41172 | −0.667093 | ||||||||
\(160\) | 1.93633 | 0.153080 | ||||||||
\(161\) | −35.3496 | −2.78594 | ||||||||
\(162\) | −0.116858 | −0.00918125 | ||||||||
\(163\) | 7.81917 | 0.612445 | 0.306222 | − | 0.951960i | \(-0.400935\pi\) | ||||
0.306222 | + | 0.951960i | \(0.400935\pi\) | |||||||
\(164\) | −10.6442 | −0.831173 | ||||||||
\(165\) | −2.47942 | −0.193022 | ||||||||
\(166\) | −0.393645 | −0.0305528 | ||||||||
\(167\) | 0.0202363 | 0.00156593 | 0.000782965 | − | 1.00000i | \(-0.499751\pi\) | ||||
0.000782965 | 1.00000i | \(0.499751\pi\) | ||||||||
\(168\) | −2.24168 | −0.172949 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.0687979 | −0.00527656 | ||||||||
\(171\) | 1.32976 | 0.101689 | ||||||||
\(172\) | −3.13431 | −0.238989 | ||||||||
\(173\) | −7.73211 | −0.587862 | −0.293931 | − | 0.955827i | \(-0.594964\pi\) | ||||
−0.293931 | + | 0.955827i | \(0.594964\pi\) | |||||||
\(174\) | 0.193474 | 0.0146672 | ||||||||
\(175\) | 14.7164 | 1.11246 | ||||||||
\(176\) | 6.97169 | 0.525511 | ||||||||
\(177\) | −8.75532 | −0.658090 | ||||||||
\(178\) | −1.18865 | −0.0890931 | ||||||||
\(179\) | 17.0578 | 1.27496 | 0.637482 | − | 0.770466i | \(-0.279976\pi\) | ||||
0.637482 | + | 0.770466i | \(0.279976\pi\) | |||||||
\(180\) | 2.76795 | 0.206311 | ||||||||
\(181\) | −5.39092 | −0.400704 | −0.200352 | − | 0.979724i | \(-0.564209\pi\) | ||||
−0.200352 | + | 0.979724i | \(0.564209\pi\) | |||||||
\(182\) | 0.562339 | 0.0416833 | ||||||||
\(183\) | −3.98372 | −0.294485 | ||||||||
\(184\) | 3.42199 | 0.252273 | ||||||||
\(185\) | −0.689297 | −0.0506781 | ||||||||
\(186\) | −1.02949 | −0.0754860 | ||||||||
\(187\) | −0.751723 | −0.0549714 | ||||||||
\(188\) | 22.8057 | 1.66328 | ||||||||
\(189\) | −4.81215 | −0.350032 | ||||||||
\(190\) | 0.216539 | 0.0157094 | ||||||||
\(191\) | −2.97334 | −0.215143 | −0.107572 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107572 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(192\) | −7.67412 | −0.553832 | ||||||||
\(193\) | 11.4832 | 0.826582 | 0.413291 | − | 0.910599i | \(-0.364379\pi\) | ||||
0.413291 | + | 0.910599i | \(0.364379\pi\) | |||||||
\(194\) | 1.20156 | 0.0862670 | ||||||||
\(195\) | −1.39349 | −0.0997899 | ||||||||
\(196\) | −32.0929 | −2.29235 | ||||||||
\(197\) | −14.6673 | −1.04500 | −0.522500 | − | 0.852639i | \(-0.675000\pi\) | ||||
−0.522500 | + | 0.852639i | \(0.675000\pi\) | |||||||
\(198\) | −0.207924 | −0.0147765 | ||||||||
\(199\) | 4.55244 | 0.322714 | 0.161357 | − | 0.986896i | \(-0.448413\pi\) | ||||
0.161357 | + | 0.986896i | \(0.448413\pi\) | |||||||
\(200\) | −1.42462 | −0.100736 | ||||||||
\(201\) | −2.56492 | −0.180916 | ||||||||
\(202\) | −1.01078 | −0.0711184 | ||||||||
\(203\) | 7.96713 | 0.559183 | ||||||||
\(204\) | 0.839202 | 0.0587559 | ||||||||
\(205\) | −7.46729 | −0.521538 | ||||||||
\(206\) | 0.116858 | 0.00814190 | ||||||||
\(207\) | 7.34590 | 0.510576 | ||||||||
\(208\) | 3.91825 | 0.271682 | ||||||||
\(209\) | 2.36602 | 0.163661 | ||||||||
\(210\) | −0.783613 | −0.0540745 | ||||||||
\(211\) | −4.76508 | −0.328041 | −0.164021 | − | 0.986457i | \(-0.552446\pi\) | ||||
−0.164021 | + | 0.986457i | \(0.552446\pi\) | |||||||
\(212\) | 16.7086 | 1.14755 | ||||||||
\(213\) | −10.8094 | −0.740645 | ||||||||
\(214\) | 0.101981 | 0.00697126 | ||||||||
\(215\) | −2.19883 | −0.149959 | ||||||||
\(216\) | 0.465837 | 0.0316962 | ||||||||
\(217\) | −42.3938 | −2.87788 | ||||||||
\(218\) | 0.155652 | 0.0105421 | ||||||||
\(219\) | −10.5596 | −0.713549 | ||||||||
\(220\) | 4.92497 | 0.332042 | ||||||||
\(221\) | −0.422486 | −0.0284195 | ||||||||
\(222\) | −0.0578045 | −0.00387959 | ||||||||
\(223\) | −18.2320 | −1.22090 | −0.610451 | − | 0.792054i | \(-0.709012\pi\) | ||||
−0.610451 | + | 0.792054i | \(0.709012\pi\) | |||||||
\(224\) | 6.68674 | 0.446776 | ||||||||
\(225\) | −3.05819 | −0.203879 | ||||||||
\(226\) | 1.81195 | 0.120529 | ||||||||
\(227\) | 1.71695 | 0.113958 | 0.0569789 | − | 0.998375i | \(-0.481853\pi\) | ||||
0.0569789 | + | 0.998375i | \(0.481853\pi\) | |||||||
\(228\) | −2.64136 | −0.174928 | ||||||||
\(229\) | −8.24688 | −0.544969 | −0.272484 | − | 0.962160i | \(-0.587845\pi\) | ||||
−0.272484 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(230\) | 1.19621 | 0.0788759 | ||||||||
\(231\) | −8.56218 | −0.563350 | ||||||||
\(232\) | −0.771253 | −0.0506353 | ||||||||
\(233\) | 3.35942 | 0.220083 | 0.110041 | − | 0.993927i | \(-0.464902\pi\) | ||||
0.110041 | + | 0.993927i | \(0.464902\pi\) | |||||||
\(234\) | −0.116858 | −0.00763926 | ||||||||
\(235\) | 15.9990 | 1.04366 | ||||||||
\(236\) | 17.3911 | 1.13206 | ||||||||
\(237\) | 12.6272 | 0.820222 | ||||||||
\(238\) | −0.237580 | −0.0154000 | ||||||||
\(239\) | −22.3797 | −1.44762 | −0.723810 | − | 0.689999i | \(-0.757611\pi\) | ||||
−0.723810 | + | 0.689999i | \(0.757611\pi\) | |||||||
\(240\) | −5.46004 | −0.352444 | ||||||||
\(241\) | −18.7100 | −1.20522 | −0.602608 | − | 0.798038i | \(-0.705872\pi\) | ||||
−0.602608 | + | 0.798038i | \(0.705872\pi\) | |||||||
\(242\) | 0.915484 | 0.0588495 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.91303 | 0.506580 | ||||||||
\(245\) | −22.5143 | −1.43838 | ||||||||
\(246\) | −0.626207 | −0.0399255 | ||||||||
\(247\) | 1.32976 | 0.0846106 | ||||||||
\(248\) | 4.10391 | 0.260598 | ||||||||
\(249\) | 3.36857 | 0.213475 | ||||||||
\(250\) | −1.31220 | −0.0829909 | ||||||||
\(251\) | 10.3909 | 0.655866 | 0.327933 | − | 0.944701i | \(-0.393648\pi\) | ||||
0.327933 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(252\) | 9.55858 | 0.602134 | ||||||||
\(253\) | 13.0705 | 0.821733 | ||||||||
\(254\) | 0.284339 | 0.0178410 | ||||||||
\(255\) | 0.588730 | 0.0368677 | ||||||||
\(256\) | 14.9187 | 0.932418 | ||||||||
\(257\) | 22.4910 | 1.40295 | 0.701475 | − | 0.712694i | \(-0.252525\pi\) | ||||
0.701475 | + | 0.712694i | \(0.252525\pi\) | |||||||
\(258\) | −0.184394 | −0.0114799 | ||||||||
\(259\) | −2.38035 | −0.147908 | ||||||||
\(260\) | 2.76795 | 0.171661 | ||||||||
\(261\) | −1.65563 | −0.102481 | ||||||||
\(262\) | 0.238534 | 0.0147367 | ||||||||
\(263\) | −10.5012 | −0.647534 | −0.323767 | − | 0.946137i | \(-0.604949\pi\) | ||||
−0.323767 | + | 0.946137i | \(0.604949\pi\) | |||||||
\(264\) | 0.828857 | 0.0510126 | ||||||||
\(265\) | 11.7217 | 0.720055 | ||||||||
\(266\) | 0.747775 | 0.0458490 | ||||||||
\(267\) | 10.1717 | 0.622500 | ||||||||
\(268\) | 5.09482 | 0.311216 | ||||||||
\(269\) | 16.2909 | 0.993276 | 0.496638 | − | 0.867958i | \(-0.334568\pi\) | ||||
0.496638 | + | 0.867958i | \(0.334568\pi\) | |||||||
\(270\) | 0.162841 | 0.00991017 | ||||||||
\(271\) | −23.8669 | −1.44981 | −0.724906 | − | 0.688848i | \(-0.758117\pi\) | ||||
−0.724906 | + | 0.688848i | \(0.758117\pi\) | |||||||
\(272\) | −1.65540 | −0.100374 | ||||||||
\(273\) | −4.81215 | −0.291244 | ||||||||
\(274\) | 1.02644 | 0.0620094 | ||||||||
\(275\) | −5.44138 | −0.328128 | ||||||||
\(276\) | −14.5915 | −0.878305 | ||||||||
\(277\) | 22.8978 | 1.37579 | 0.687897 | − | 0.725809i | \(-0.258534\pi\) | ||||
0.687897 | + | 0.725809i | \(0.258534\pi\) | |||||||
\(278\) | 1.14849 | 0.0688818 | ||||||||
\(279\) | 8.80975 | 0.527426 | ||||||||
\(280\) | 3.12375 | 0.186680 | ||||||||
\(281\) | −6.01797 | −0.359002 | −0.179501 | − | 0.983758i | \(-0.557448\pi\) | ||||
−0.179501 | + | 0.983758i | \(0.557448\pi\) | |||||||
\(282\) | 1.34168 | 0.0798958 | ||||||||
\(283\) | 7.15170 | 0.425125 | 0.212562 | − | 0.977148i | \(-0.431819\pi\) | ||||
0.212562 | + | 0.977148i | \(0.431819\pi\) | |||||||
\(284\) | 21.4711 | 1.27408 | ||||||||
\(285\) | −1.85301 | −0.109763 | ||||||||
\(286\) | −0.207924 | −0.0122948 | ||||||||
\(287\) | −25.7868 | −1.52215 | ||||||||
\(288\) | −1.38955 | −0.0818802 | ||||||||
\(289\) | −16.8215 | −0.989500 | ||||||||
\(290\) | −0.269604 | −0.0158317 | ||||||||
\(291\) | −10.2822 | −0.602754 | ||||||||
\(292\) | 20.9749 | 1.22746 | ||||||||
\(293\) | −16.8469 | −0.984207 | −0.492103 | − | 0.870537i | \(-0.663772\pi\) | ||||
−0.492103 | + | 0.870537i | \(0.663772\pi\) | |||||||
\(294\) | −1.88805 | −0.110113 | ||||||||
\(295\) | 12.2005 | 0.710338 | ||||||||
\(296\) | 0.230429 | 0.0133934 | ||||||||
\(297\) | 1.77929 | 0.103245 | ||||||||
\(298\) | 0.414770 | 0.0240270 | ||||||||
\(299\) | 7.34590 | 0.424825 | ||||||||
\(300\) | 6.07461 | 0.350718 | ||||||||
\(301\) | −7.59322 | −0.437666 | ||||||||
\(302\) | −0.305642 | −0.0175877 | ||||||||
\(303\) | 8.64965 | 0.496910 | ||||||||
\(304\) | 5.21033 | 0.298833 | ||||||||
\(305\) | 5.55127 | 0.317865 | ||||||||
\(306\) | 0.0493709 | 0.00282235 | ||||||||
\(307\) | −17.0692 | −0.974193 | −0.487097 | − | 0.873348i | \(-0.661944\pi\) | ||||
−0.487097 | + | 0.873348i | \(0.661944\pi\) | |||||||
\(308\) | 17.0074 | 0.969089 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 1.43459 | 0.0814790 | ||||||||
\(311\) | −1.92307 | −0.109047 | −0.0545237 | − | 0.998512i | \(-0.517364\pi\) | ||||
−0.0545237 | + | 0.998512i | \(0.517364\pi\) | |||||||
\(312\) | 0.465837 | 0.0263728 | ||||||||
\(313\) | 26.0569 | 1.47282 | 0.736412 | − | 0.676533i | \(-0.236519\pi\) | ||||
0.736412 | + | 0.676533i | \(0.236519\pi\) | |||||||
\(314\) | 0.775353 | 0.0437557 | ||||||||
\(315\) | 6.70568 | 0.377822 | ||||||||
\(316\) | −25.0819 | −1.41097 | ||||||||
\(317\) | −2.38463 | −0.133934 | −0.0669670 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669670 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(318\) | 0.982979 | 0.0551227 | ||||||||
\(319\) | −2.94584 | −0.164935 | ||||||||
\(320\) | 10.6938 | 0.597802 | ||||||||
\(321\) | −0.872688 | −0.0487087 | ||||||||
\(322\) | 4.13089 | 0.230205 | ||||||||
\(323\) | −0.561804 | −0.0312596 | ||||||||
\(324\) | −1.98634 | −0.110352 | ||||||||
\(325\) | −3.05819 | −0.169638 | ||||||||
\(326\) | −0.913734 | −0.0506071 | ||||||||
\(327\) | −1.33197 | −0.0736583 | ||||||||
\(328\) | 2.49628 | 0.137834 | ||||||||
\(329\) | 55.2495 | 3.04600 | ||||||||
\(330\) | 0.289740 | 0.0159497 | ||||||||
\(331\) | 7.90274 | 0.434374 | 0.217187 | − | 0.976130i | \(-0.430312\pi\) | ||||
0.217187 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(332\) | −6.69115 | −0.367224 | ||||||||
\(333\) | 0.494655 | 0.0271069 | ||||||||
\(334\) | −0.00236477 | −0.000129395 0 | ||||||||
\(335\) | 3.57419 | 0.195279 | ||||||||
\(336\) | −18.8552 | −1.02864 | ||||||||
\(337\) | 28.6905 | 1.56287 | 0.781436 | − | 0.623985i | \(-0.214487\pi\) | ||||
0.781436 | + | 0.623985i | \(0.214487\pi\) | |||||||
\(338\) | −0.116858 | −0.00635625 | ||||||||
\(339\) | −15.5055 | −0.842143 | ||||||||
\(340\) | −1.16942 | −0.0634207 | ||||||||
\(341\) | 15.6751 | 0.848852 | ||||||||
\(342\) | −0.155393 | −0.00840270 | ||||||||
\(343\) | −44.0637 | −2.37921 | ||||||||
\(344\) | 0.735057 | 0.0396316 | ||||||||
\(345\) | −10.2364 | −0.551112 | ||||||||
\(346\) | 0.903561 | 0.0485757 | ||||||||
\(347\) | −24.4140 | −1.31061 | −0.655306 | − | 0.755363i | \(-0.727461\pi\) | ||||
−0.655306 | + | 0.755363i | \(0.727461\pi\) | |||||||
\(348\) | 3.28865 | 0.176290 | ||||||||
\(349\) | −8.06869 | −0.431907 | −0.215954 | − | 0.976404i | \(-0.569286\pi\) | ||||
−0.215954 | + | 0.976404i | \(0.569286\pi\) | |||||||
\(350\) | −1.71974 | −0.0919238 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −2.47241 | −0.131780 | ||||||||
\(353\) | 32.1076 | 1.70892 | 0.854459 | − | 0.519519i | \(-0.173889\pi\) | ||||
0.854459 | + | 0.519519i | \(0.173889\pi\) | |||||||
\(354\) | 1.02313 | 0.0543788 | ||||||||
\(355\) | 15.0627 | 0.799447 | ||||||||
\(356\) | −20.2046 | −1.07084 | ||||||||
\(357\) | 2.03306 | 0.107601 | ||||||||
\(358\) | −1.99335 | −0.105352 | ||||||||
\(359\) | 27.9770 | 1.47657 | 0.738284 | − | 0.674490i | \(-0.235636\pi\) | ||||
0.738284 | + | 0.674490i | \(0.235636\pi\) | |||||||
\(360\) | −0.649139 | −0.0342126 | ||||||||
\(361\) | −17.2317 | −0.906934 | ||||||||
\(362\) | 0.629973 | 0.0331107 | ||||||||
\(363\) | −7.83414 | −0.411186 | ||||||||
\(364\) | 9.55858 | 0.501006 | ||||||||
\(365\) | 14.7146 | 0.770200 | ||||||||
\(366\) | 0.465530 | 0.0243336 | ||||||||
\(367\) | −37.8726 | −1.97693 | −0.988467 | − | 0.151439i | \(-0.951609\pi\) | ||||
−0.988467 | + | 0.151439i | \(0.951609\pi\) | |||||||
\(368\) | 28.7831 | 1.50042 | ||||||||
\(369\) | 5.35869 | 0.278962 | ||||||||
\(370\) | 0.0805500 | 0.00418760 | ||||||||
\(371\) | 40.4785 | 2.10154 | ||||||||
\(372\) | −17.4992 | −0.907291 | ||||||||
\(373\) | −14.0427 | −0.727104 | −0.363552 | − | 0.931574i | \(-0.618436\pi\) | ||||
−0.363552 | + | 0.931574i | \(0.618436\pi\) | |||||||
\(374\) | 0.0878449 | 0.00454235 | ||||||||
\(375\) | 11.2290 | 0.579863 | ||||||||
\(376\) | −5.34839 | −0.275822 | ||||||||
\(377\) | −1.65563 | −0.0852693 | ||||||||
\(378\) | 0.562339 | 0.0289236 | ||||||||
\(379\) | −0.111717 | −0.00573850 | −0.00286925 | − | 0.999996i | \(-0.500913\pi\) | ||||
−0.00286925 | + | 0.999996i | \(0.500913\pi\) | |||||||
\(380\) | 3.68071 | 0.188816 | ||||||||
\(381\) | −2.43320 | −0.124657 | ||||||||
\(382\) | 0.347459 | 0.0177776 | ||||||||
\(383\) | −23.1833 | −1.18461 | −0.592305 | − | 0.805714i | \(-0.701782\pi\) | ||||
−0.592305 | + | 0.805714i | \(0.701782\pi\) | |||||||
\(384\) | 3.67589 | 0.187585 | ||||||||
\(385\) | 11.9313 | 0.608076 | ||||||||
\(386\) | −1.34191 | −0.0683014 | ||||||||
\(387\) | 1.57793 | 0.0802106 | ||||||||
\(388\) | 20.4240 | 1.03687 | ||||||||
\(389\) | 16.1072 | 0.816669 | 0.408335 | − | 0.912832i | \(-0.366110\pi\) | ||||
0.408335 | + | 0.912832i | \(0.366110\pi\) | |||||||
\(390\) | 0.162841 | 0.00824576 | ||||||||
\(391\) | −3.10354 | −0.156953 | ||||||||
\(392\) | 7.52641 | 0.380141 | ||||||||
\(393\) | −2.04123 | −0.102966 | ||||||||
\(394\) | 1.71399 | 0.0863496 | ||||||||
\(395\) | −17.5958 | −0.885342 | ||||||||
\(396\) | −3.53427 | −0.177604 | ||||||||
\(397\) | −29.8219 | −1.49672 | −0.748359 | − | 0.663294i | \(-0.769158\pi\) | ||||
−0.748359 | + | 0.663294i | \(0.769158\pi\) | |||||||
\(398\) | −0.531990 | −0.0266662 | ||||||||
\(399\) | −6.39900 | −0.320351 | ||||||||
\(400\) | −11.9827 | −0.599137 | ||||||||
\(401\) | −1.90646 | −0.0952041 | −0.0476021 | − | 0.998866i | \(-0.515158\pi\) | ||||
−0.0476021 | + | 0.998866i | \(0.515158\pi\) | |||||||
\(402\) | 0.299732 | 0.0149493 | ||||||||
\(403\) | 8.80975 | 0.438845 | ||||||||
\(404\) | −17.1812 | −0.854796 | ||||||||
\(405\) | −1.39349 | −0.0692431 | ||||||||
\(406\) | −0.931025 | −0.0462060 | ||||||||
\(407\) | 0.880133 | 0.0436266 | ||||||||
\(408\) | −0.196809 | −0.00974352 | ||||||||
\(409\) | 21.7899 | 1.07744 | 0.538720 | − | 0.842485i | \(-0.318908\pi\) | ||||
0.538720 | + | 0.842485i | \(0.318908\pi\) | |||||||
\(410\) | 0.872614 | 0.0430953 | ||||||||
\(411\) | −8.78362 | −0.433264 | ||||||||
\(412\) | 1.98634 | 0.0978602 | ||||||||
\(413\) | 42.1319 | 2.07317 | ||||||||
\(414\) | −0.858429 | −0.0421895 | ||||||||
\(415\) | −4.69407 | −0.230423 | ||||||||
\(416\) | −1.38955 | −0.0681285 | ||||||||
\(417\) | −9.82806 | −0.481282 | ||||||||
\(418\) | −0.276489 | −0.0135235 | ||||||||
\(419\) | 34.0432 | 1.66312 | 0.831560 | − | 0.555435i | \(-0.187448\pi\) | ||||
0.831560 | + | 0.555435i | \(0.187448\pi\) | |||||||
\(420\) | −13.3198 | −0.649939 | ||||||||
\(421\) | −18.8085 | −0.916669 | −0.458334 | − | 0.888780i | \(-0.651554\pi\) | ||||
−0.458334 | + | 0.888780i | \(0.651554\pi\) | |||||||
\(422\) | 0.556838 | 0.0271065 | ||||||||
\(423\) | −11.4812 | −0.558237 | ||||||||
\(424\) | −3.91849 | −0.190299 | ||||||||
\(425\) | 1.29204 | 0.0626731 | ||||||||
\(426\) | 1.26316 | 0.0612004 | ||||||||
\(427\) | 19.1702 | 0.927712 | ||||||||
\(428\) | 1.73346 | 0.0837899 | ||||||||
\(429\) | 1.77929 | 0.0859047 | ||||||||
\(430\) | 0.256951 | 0.0123913 | ||||||||
\(431\) | −20.7644 | −1.00019 | −0.500093 | − | 0.865972i | \(-0.666701\pi\) | ||||
−0.500093 | + | 0.865972i | \(0.666701\pi\) | |||||||
\(432\) | 3.91825 | 0.188517 | ||||||||
\(433\) | −24.1627 | −1.16119 | −0.580593 | − | 0.814194i | \(-0.697179\pi\) | ||||
−0.580593 | + | 0.814194i | \(0.697179\pi\) | |||||||
\(434\) | 4.95406 | 0.237803 | ||||||||
\(435\) | 2.30710 | 0.110617 | ||||||||
\(436\) | 2.64576 | 0.126709 | ||||||||
\(437\) | 9.76828 | 0.467280 | ||||||||
\(438\) | 1.23397 | 0.0589614 | ||||||||
\(439\) | −13.5640 | −0.647373 | −0.323686 | − | 0.946164i | \(-0.604922\pi\) | ||||
−0.323686 | + | 0.946164i | \(0.604922\pi\) | |||||||
\(440\) | −1.15500 | −0.0550626 | ||||||||
\(441\) | 16.1568 | 0.769369 | ||||||||
\(442\) | 0.0493709 | 0.00234833 | ||||||||
\(443\) | 8.75855 | 0.416131 | 0.208066 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208066 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(444\) | −0.982556 | −0.0466300 | ||||||||
\(445\) | −14.1742 | −0.671922 | ||||||||
\(446\) | 2.13055 | 0.100885 | ||||||||
\(447\) | −3.54934 | −0.167878 | ||||||||
\(448\) | 36.9290 | 1.74473 | ||||||||
\(449\) | −6.13733 | −0.289638 | −0.144819 | − | 0.989458i | \(-0.546260\pi\) | ||||
−0.144819 | + | 0.989458i | \(0.546260\pi\) | |||||||
\(450\) | 0.357374 | 0.0168468 | ||||||||
\(451\) | 9.53465 | 0.448969 | ||||||||
\(452\) | 30.7993 | 1.44868 | ||||||||
\(453\) | 2.61550 | 0.122887 | ||||||||
\(454\) | −0.200639 | −0.00941647 | ||||||||
\(455\) | 6.70568 | 0.314367 | ||||||||
\(456\) | 0.619451 | 0.0290084 | ||||||||
\(457\) | −16.5815 | −0.775648 | −0.387824 | − | 0.921733i | \(-0.626773\pi\) | ||||
−0.387824 | + | 0.921733i | \(0.626773\pi\) | |||||||
\(458\) | 0.963715 | 0.0450314 | ||||||||
\(459\) | −0.422486 | −0.0197199 | ||||||||
\(460\) | 20.3331 | 0.948036 | ||||||||
\(461\) | 19.3497 | 0.901207 | 0.450604 | − | 0.892724i | \(-0.351209\pi\) | ||||
0.450604 | + | 0.892724i | \(0.351209\pi\) | |||||||
\(462\) | 1.00056 | 0.0465503 | ||||||||
\(463\) | 30.2145 | 1.40419 | 0.702093 | − | 0.712085i | \(-0.252249\pi\) | ||||
0.702093 | + | 0.712085i | \(0.252249\pi\) | |||||||
\(464\) | −6.48717 | −0.301159 | ||||||||
\(465\) | −12.2763 | −0.569300 | ||||||||
\(466\) | −0.392576 | −0.0181857 | ||||||||
\(467\) | −22.8581 | −1.05774 | −0.528872 | − | 0.848701i | \(-0.677385\pi\) | ||||
−0.528872 | + | 0.848701i | \(0.677385\pi\) | |||||||
\(468\) | −1.98634 | −0.0918188 | ||||||||
\(469\) | 12.3428 | 0.569937 | ||||||||
\(470\) | −1.86961 | −0.0862389 | ||||||||
\(471\) | −6.63499 | −0.305724 | ||||||||
\(472\) | −4.07855 | −0.187731 | ||||||||
\(473\) | 2.80759 | 0.129093 | ||||||||
\(474\) | −1.47559 | −0.0677759 | ||||||||
\(475\) | −4.06665 | −0.186591 | ||||||||
\(476\) | −4.03836 | −0.185098 | ||||||||
\(477\) | −8.41172 | −0.385146 | ||||||||
\(478\) | 2.61525 | 0.119619 | ||||||||
\(479\) | −14.2821 | −0.652565 | −0.326282 | − | 0.945272i | \(-0.605796\pi\) | ||||
−0.326282 | + | 0.945272i | \(0.605796\pi\) | |||||||
\(480\) | 1.93633 | 0.0883809 | ||||||||
\(481\) | 0.494655 | 0.0225543 | ||||||||
\(482\) | 2.18641 | 0.0995884 | ||||||||
\(483\) | −35.3496 | −1.60846 | ||||||||
\(484\) | 15.5613 | 0.707332 | ||||||||
\(485\) | 14.3282 | 0.650608 | ||||||||
\(486\) | −0.116858 | −0.00530079 | ||||||||
\(487\) | −32.7635 | −1.48465 | −0.742327 | − | 0.670038i | \(-0.766278\pi\) | ||||
−0.742327 | + | 0.670038i | \(0.766278\pi\) | |||||||
\(488\) | −1.85576 | −0.0840064 | ||||||||
\(489\) | 7.81917 | 0.353595 | ||||||||
\(490\) | 2.63098 | 0.118855 | ||||||||
\(491\) | 14.5560 | 0.656902 | 0.328451 | − | 0.944521i | \(-0.393473\pi\) | ||||
0.328451 | + | 0.944521i | \(0.393473\pi\) | |||||||
\(492\) | −10.6442 | −0.479878 | ||||||||
\(493\) | 0.699480 | 0.0315030 | ||||||||
\(494\) | −0.155393 | −0.00699147 | ||||||||
\(495\) | −2.47942 | −0.111441 | ||||||||
\(496\) | 34.5188 | 1.54994 | ||||||||
\(497\) | 52.0162 | 2.33325 | ||||||||
\(498\) | −0.393645 | −0.0176397 | ||||||||
\(499\) | −10.6365 | −0.476154 | −0.238077 | − | 0.971246i | \(-0.576517\pi\) | ||||
−0.238077 | + | 0.971246i | \(0.576517\pi\) | |||||||
\(500\) | −22.3047 | −0.997495 | ||||||||
\(501\) | 0.0202363 | 0.000904090 0 | ||||||||
\(502\) | −1.21426 | −0.0541950 | ||||||||
\(503\) | −23.6781 | −1.05575 | −0.527877 | − | 0.849321i | \(-0.677012\pi\) | ||||
−0.527877 | + | 0.849321i | \(0.677012\pi\) | |||||||
\(504\) | −2.24168 | −0.0998522 | ||||||||
\(505\) | −12.0532 | −0.536361 | ||||||||
\(506\) | −1.52739 | −0.0679008 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 4.83317 | 0.214437 | ||||||||
\(509\) | −30.2953 | −1.34282 | −0.671409 | − | 0.741087i | \(-0.734310\pi\) | ||||
−0.671409 | + | 0.741087i | \(0.734310\pi\) | |||||||
\(510\) | −0.0687979 | −0.00304642 | ||||||||
\(511\) | 50.8142 | 2.24789 | ||||||||
\(512\) | −9.09515 | −0.401953 | ||||||||
\(513\) | 1.32976 | 0.0587103 | ||||||||
\(514\) | −2.62826 | −0.115927 | ||||||||
\(515\) | 1.39349 | 0.0614045 | ||||||||
\(516\) | −3.13431 | −0.137980 | ||||||||
\(517\) | −20.4284 | −0.898441 | ||||||||
\(518\) | 0.278164 | 0.0122218 | ||||||||
\(519\) | −7.73211 | −0.339402 | ||||||||
\(520\) | −0.649139 | −0.0284666 | ||||||||
\(521\) | 27.5866 | 1.20859 | 0.604296 | − | 0.796760i | \(-0.293454\pi\) | ||||
0.604296 | + | 0.796760i | \(0.293454\pi\) | |||||||
\(522\) | 0.193474 | 0.00846812 | ||||||||
\(523\) | −28.3545 | −1.23986 | −0.619928 | − | 0.784659i | \(-0.712838\pi\) | ||||
−0.619928 | + | 0.784659i | \(0.712838\pi\) | |||||||
\(524\) | 4.05458 | 0.177125 | ||||||||
\(525\) | 14.7164 | 0.642278 | ||||||||
\(526\) | 1.22716 | 0.0535065 | ||||||||
\(527\) | −3.72199 | −0.162133 | ||||||||
\(528\) | 6.97169 | 0.303404 | ||||||||
\(529\) | 30.9623 | 1.34619 | ||||||||
\(530\) | −1.36977 | −0.0594991 | ||||||||
\(531\) | −8.75532 | −0.379949 | ||||||||
\(532\) | 12.7106 | 0.551075 | ||||||||
\(533\) | 5.35869 | 0.232111 | ||||||||
\(534\) | −1.18865 | −0.0514379 | ||||||||
\(535\) | 1.21608 | 0.0525758 | ||||||||
\(536\) | −1.19484 | −0.0516090 | ||||||||
\(537\) | 17.0578 | 0.736100 | ||||||||
\(538\) | −1.90373 | −0.0820756 | ||||||||
\(539\) | 28.7475 | 1.23824 | ||||||||
\(540\) | 2.76795 | 0.119114 | ||||||||
\(541\) | −44.0757 | −1.89496 | −0.947482 | − | 0.319810i | \(-0.896381\pi\) | ||||
−0.947482 | + | 0.319810i | \(0.896381\pi\) | |||||||
\(542\) | 2.78904 | 0.119800 | ||||||||
\(543\) | −5.39092 | −0.231347 | ||||||||
\(544\) | 0.587066 | 0.0251703 | ||||||||
\(545\) | 1.85609 | 0.0795063 | ||||||||
\(546\) | 0.562339 | 0.0240659 | ||||||||
\(547\) | −19.0915 | −0.816295 | −0.408147 | − | 0.912916i | \(-0.633825\pi\) | ||||
−0.408147 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(548\) | 17.4473 | 0.745311 | ||||||||
\(549\) | −3.98372 | −0.170021 | ||||||||
\(550\) | 0.635870 | 0.0271136 | ||||||||
\(551\) | −2.20159 | −0.0937908 | ||||||||
\(552\) | 3.42199 | 0.145650 | ||||||||
\(553\) | −60.7637 | −2.58394 | ||||||||
\(554\) | −2.67579 | −0.113683 | ||||||||
\(555\) | −0.689297 | −0.0292590 | ||||||||
\(556\) | 19.5219 | 0.827913 | ||||||||
\(557\) | 0.591202 | 0.0250500 | 0.0125250 | − | 0.999922i | \(-0.496013\pi\) | ||||
0.0125250 | + | 0.999922i | \(0.496013\pi\) | |||||||
\(558\) | −1.02949 | −0.0435818 | ||||||||
\(559\) | 1.57793 | 0.0667393 | ||||||||
\(560\) | 26.2745 | 1.11030 | ||||||||
\(561\) | −0.751723 | −0.0317377 | ||||||||
\(562\) | 0.703250 | 0.0296648 | ||||||||
\(563\) | 24.4996 | 1.03254 | 0.516268 | − | 0.856427i | \(-0.327321\pi\) | ||||
0.516268 | + | 0.856427i | \(0.327321\pi\) | |||||||
\(564\) | 22.8057 | 0.960294 | ||||||||
\(565\) | 21.6068 | 0.909004 | ||||||||
\(566\) | −0.835735 | −0.0351286 | ||||||||
\(567\) | −4.81215 | −0.202091 | ||||||||
\(568\) | −5.03540 | −0.211281 | ||||||||
\(569\) | 9.32414 | 0.390888 | 0.195444 | − | 0.980715i | \(-0.437385\pi\) | ||||
0.195444 | + | 0.980715i | \(0.437385\pi\) | |||||||
\(570\) | 0.216539 | 0.00906982 | ||||||||
\(571\) | −5.05663 | −0.211613 | −0.105807 | − | 0.994387i | \(-0.533742\pi\) | ||||
−0.105807 | + | 0.994387i | \(0.533742\pi\) | |||||||
\(572\) | −3.53427 | −0.147775 | ||||||||
\(573\) | −2.97334 | −0.124213 | ||||||||
\(574\) | 3.01340 | 0.125777 | ||||||||
\(575\) | −22.4651 | −0.936861 | ||||||||
\(576\) | −7.67412 | −0.319755 | ||||||||
\(577\) | 12.8427 | 0.534650 | 0.267325 | − | 0.963606i | \(-0.413860\pi\) | ||||
0.267325 | + | 0.963606i | \(0.413860\pi\) | |||||||
\(578\) | 1.96573 | 0.0817636 | ||||||||
\(579\) | 11.4832 | 0.477227 | ||||||||
\(580\) | −4.58270 | −0.190286 | ||||||||
\(581\) | −16.2101 | −0.672507 | ||||||||
\(582\) | 1.20156 | 0.0498063 | ||||||||
\(583\) | −14.9669 | −0.619864 | ||||||||
\(584\) | −4.91903 | −0.203551 | ||||||||
\(585\) | −1.39349 | −0.0576137 | ||||||||
\(586\) | 1.96870 | 0.0813262 | ||||||||
\(587\) | −11.3776 | −0.469604 | −0.234802 | − | 0.972043i | \(-0.575444\pi\) | ||||
−0.234802 | + | 0.972043i | \(0.575444\pi\) | |||||||
\(588\) | −32.0929 | −1.32349 | ||||||||
\(589\) | 11.7148 | 0.482702 | ||||||||
\(590\) | −1.42572 | −0.0586961 | ||||||||
\(591\) | −14.6673 | −0.603331 | ||||||||
\(592\) | 1.93818 | 0.0796589 | ||||||||
\(593\) | −16.7426 | −0.687538 | −0.343769 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343769 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(594\) | −0.207924 | −0.00853123 | ||||||||
\(595\) | −2.83305 | −0.116144 | ||||||||
\(596\) | 7.05022 | 0.288788 | ||||||||
\(597\) | 4.55244 | 0.186319 | ||||||||
\(598\) | −0.858429 | −0.0351038 | ||||||||
\(599\) | 9.60175 | 0.392317 | 0.196158 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196158 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(600\) | −1.42462 | −0.0581597 | ||||||||
\(601\) | 31.8630 | 1.29972 | 0.649859 | − | 0.760055i | \(-0.274828\pi\) | ||||
0.649859 | + | 0.760055i | \(0.274828\pi\) | |||||||
\(602\) | 0.887330 | 0.0361649 | ||||||||
\(603\) | −2.56492 | −0.104452 | ||||||||
\(604\) | −5.19528 | −0.211393 | ||||||||
\(605\) | 10.9168 | 0.443831 | ||||||||
\(606\) | −1.01078 | −0.0410602 | ||||||||
\(607\) | −21.4685 | −0.871380 | −0.435690 | − | 0.900097i | \(-0.643496\pi\) | ||||
−0.435690 | + | 0.900097i | \(0.643496\pi\) | |||||||
\(608\) | −1.84777 | −0.0749370 | ||||||||
\(609\) | 7.96713 | 0.322845 | ||||||||
\(610\) | −0.648711 | −0.0262655 | ||||||||
\(611\) | −11.4812 | −0.464482 | ||||||||
\(612\) | 0.839202 | 0.0339227 | ||||||||
\(613\) | −11.9214 | −0.481502 | −0.240751 | − | 0.970587i | \(-0.577394\pi\) | ||||
−0.240751 | + | 0.970587i | \(0.577394\pi\) | |||||||
\(614\) | 1.99468 | 0.0804988 | ||||||||
\(615\) | −7.46729 | −0.301110 | ||||||||
\(616\) | −3.98858 | −0.160705 | ||||||||
\(617\) | 0.0130435 | 0.000525112 0 | 0.000262556 | − | 1.00000i | \(-0.499916\pi\) | ||||
0.000262556 | 1.00000i | \(0.499916\pi\) | ||||||||
\(618\) | 0.116858 | 0.00470073 | ||||||||
\(619\) | −38.7865 | −1.55896 | −0.779480 | − | 0.626427i | \(-0.784517\pi\) | ||||
−0.779480 | + | 0.626427i | \(0.784517\pi\) | |||||||
\(620\) | 24.3850 | 0.979323 | ||||||||
\(621\) | 7.34590 | 0.294781 | ||||||||
\(622\) | 0.224727 | 0.00901072 | ||||||||
\(623\) | −48.9479 | −1.96105 | ||||||||
\(624\) | 3.91825 | 0.156856 | ||||||||
\(625\) | −0.356574 | −0.0142630 | ||||||||
\(626\) | −3.04496 | −0.121701 | ||||||||
\(627\) | 2.36602 | 0.0944898 | ||||||||
\(628\) | 13.1794 | 0.525915 | ||||||||
\(629\) | −0.208985 | −0.00833277 | ||||||||
\(630\) | −0.783613 | −0.0312199 | ||||||||
\(631\) | −4.65558 | −0.185336 | −0.0926679 | − | 0.995697i | \(-0.529539\pi\) | ||||
−0.0926679 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(632\) | 5.88220 | 0.233981 | ||||||||
\(633\) | −4.76508 | −0.189395 | ||||||||
\(634\) | 0.278663 | 0.0110671 | ||||||||
\(635\) | 3.39064 | 0.134553 | ||||||||
\(636\) | 16.7086 | 0.662538 | ||||||||
\(637\) | 16.1568 | 0.640154 | ||||||||
\(638\) | 0.344245 | 0.0136288 | ||||||||
\(639\) | −10.8094 | −0.427611 | ||||||||
\(640\) | −5.12232 | −0.202477 | ||||||||
\(641\) | 19.7418 | 0.779753 | 0.389876 | − | 0.920867i | \(-0.372518\pi\) | ||||
0.389876 | + | 0.920867i | \(0.372518\pi\) | |||||||
\(642\) | 0.101981 | 0.00402486 | ||||||||
\(643\) | 41.5140 | 1.63715 | 0.818576 | − | 0.574398i | \(-0.194764\pi\) | ||||
0.818576 | + | 0.574398i | \(0.194764\pi\) | |||||||
\(644\) | 70.2164 | 2.76691 | ||||||||
\(645\) | −2.19883 | −0.0865788 | ||||||||
\(646\) | 0.0656514 | 0.00258302 | ||||||||
\(647\) | −42.1621 | −1.65756 | −0.828782 | − | 0.559572i | \(-0.810966\pi\) | ||||
−0.828782 | + | 0.559572i | \(0.810966\pi\) | |||||||
\(648\) | 0.465837 | 0.0182998 | ||||||||
\(649\) | −15.5782 | −0.611498 | ||||||||
\(650\) | 0.357374 | 0.0140174 | ||||||||
\(651\) | −42.3938 | −1.66154 | ||||||||
\(652\) | −15.5316 | −0.608263 | ||||||||
\(653\) | −5.98773 | −0.234318 | −0.117159 | − | 0.993113i | \(-0.537379\pi\) | ||||
−0.117159 | + | 0.993113i | \(0.537379\pi\) | |||||||
\(654\) | 0.155652 | 0.00608648 | ||||||||
\(655\) | 2.84443 | 0.111141 | ||||||||
\(656\) | 20.9967 | 0.819784 | ||||||||
\(657\) | −10.5596 | −0.411968 | ||||||||
\(658\) | −6.45635 | −0.251695 | ||||||||
\(659\) | −0.560020 | −0.0218153 | −0.0109076 | − | 0.999941i | \(-0.503472\pi\) | ||||
−0.0109076 | + | 0.999941i | \(0.503472\pi\) | |||||||
\(660\) | 4.92497 | 0.191704 | ||||||||
\(661\) | −38.7835 | −1.50850 | −0.754252 | − | 0.656586i | \(-0.772000\pi\) | ||||
−0.754252 | + | 0.656586i | \(0.772000\pi\) | |||||||
\(662\) | −0.923499 | −0.0358928 | ||||||||
\(663\) | −0.422486 | −0.0164080 | ||||||||
\(664\) | 1.56921 | 0.0608970 | ||||||||
\(665\) | 8.91694 | 0.345784 | ||||||||
\(666\) | −0.0578045 | −0.00223988 | ||||||||
\(667\) | −12.1621 | −0.470918 | ||||||||
\(668\) | −0.0401962 | −0.00155524 | ||||||||
\(669\) | −18.2320 | −0.704889 | ||||||||
\(670\) | −0.417674 | −0.0161361 | ||||||||
\(671\) | −7.08817 | −0.273636 | ||||||||
\(672\) | 6.68674 | 0.257946 | ||||||||
\(673\) | −18.4934 | −0.712869 | −0.356434 | − | 0.934320i | \(-0.616008\pi\) | ||||
−0.356434 | + | 0.934320i | \(0.616008\pi\) | |||||||
\(674\) | −3.35272 | −0.129142 | ||||||||
\(675\) | −3.05819 | −0.117710 | ||||||||
\(676\) | −1.98634 | −0.0763979 | ||||||||
\(677\) | 17.8887 | 0.687520 | 0.343760 | − | 0.939058i | \(-0.388299\pi\) | ||||
0.343760 | + | 0.939058i | \(0.388299\pi\) | |||||||
\(678\) | 1.81195 | 0.0695873 | ||||||||
\(679\) | 49.4795 | 1.89885 | ||||||||
\(680\) | 0.274252 | 0.0105171 | ||||||||
\(681\) | 1.71695 | 0.0657936 | ||||||||
\(682\) | −1.83176 | −0.0701417 | ||||||||
\(683\) | 29.2157 | 1.11791 | 0.558954 | − | 0.829199i | \(-0.311203\pi\) | ||||
0.558954 | + | 0.829199i | \(0.311203\pi\) | |||||||
\(684\) | −2.64136 | −0.100995 | ||||||||
\(685\) | 12.2399 | 0.467662 | ||||||||
\(686\) | 5.14920 | 0.196597 | ||||||||
\(687\) | −8.24688 | −0.314638 | ||||||||
\(688\) | 6.18272 | 0.235714 | ||||||||
\(689\) | −8.41172 | −0.320461 | ||||||||
\(690\) | 1.19621 | 0.0455390 | ||||||||
\(691\) | 5.96252 | 0.226825 | 0.113412 | − | 0.993548i | \(-0.463822\pi\) | ||||
0.113412 | + | 0.993548i | \(0.463822\pi\) | |||||||
\(692\) | 15.3586 | 0.583848 | ||||||||
\(693\) | −8.56218 | −0.325250 | ||||||||
\(694\) | 2.85298 | 0.108298 | ||||||||
\(695\) | 13.6953 | 0.519492 | ||||||||
\(696\) | −0.771253 | −0.0292343 | ||||||||
\(697\) | −2.26397 | −0.0857540 | ||||||||
\(698\) | 0.942893 | 0.0356890 | ||||||||
\(699\) | 3.35942 | 0.127065 | ||||||||
\(700\) | −29.2319 | −1.10486 | ||||||||
\(701\) | −13.2418 | −0.500136 | −0.250068 | − | 0.968228i | \(-0.580453\pi\) | ||||
−0.250068 | + | 0.968228i | \(0.580453\pi\) | |||||||
\(702\) | −0.116858 | −0.00441053 | ||||||||
\(703\) | 0.657772 | 0.0248084 | ||||||||
\(704\) | −13.6545 | −0.514622 | ||||||||
\(705\) | 15.9990 | 0.602557 | ||||||||
\(706\) | −3.75204 | −0.141210 | ||||||||
\(707\) | −41.6234 | −1.56541 | ||||||||
\(708\) | 17.3911 | 0.653597 | ||||||||
\(709\) | −12.5713 | −0.472124 | −0.236062 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236062 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(710\) | −1.76020 | −0.0660592 | ||||||||
\(711\) | 12.6272 | 0.473555 | ||||||||
\(712\) | 4.73837 | 0.177578 | ||||||||
\(713\) | 64.7156 | 2.42362 | ||||||||
\(714\) | −0.237580 | −0.00889121 | ||||||||
\(715\) | −2.47942 | −0.0927249 | ||||||||
\(716\) | −33.8828 | −1.26626 | ||||||||
\(717\) | −22.3797 | −0.835784 | ||||||||
\(718\) | −3.26934 | −0.122011 | ||||||||
\(719\) | −31.3084 | −1.16761 | −0.583804 | − | 0.811895i | \(-0.698436\pi\) | ||||
−0.583804 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(720\) | −5.46004 | −0.203484 | ||||||||
\(721\) | 4.81215 | 0.179214 | ||||||||
\(722\) | 2.01367 | 0.0749410 | ||||||||
\(723\) | −18.7100 | −0.695831 | ||||||||
\(724\) | 10.7082 | 0.397968 | ||||||||
\(725\) | 5.06322 | 0.188043 | ||||||||
\(726\) | 0.915484 | 0.0339768 | ||||||||
\(727\) | 13.7216 | 0.508907 | 0.254453 | − | 0.967085i | \(-0.418104\pi\) | ||||
0.254453 | + | 0.967085i | \(0.418104\pi\) | |||||||
\(728\) | −2.24168 | −0.0830820 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.71953 | −0.0636425 | ||||||||
\(731\) | −0.666652 | −0.0246570 | ||||||||
\(732\) | 7.91303 | 0.292474 | ||||||||
\(733\) | 36.9544 | 1.36494 | 0.682471 | − | 0.730913i | \(-0.260905\pi\) | ||||
0.682471 | + | 0.730913i | \(0.260905\pi\) | |||||||
\(734\) | 4.42572 | 0.163356 | ||||||||
\(735\) | −22.5143 | −0.830452 | ||||||||
\(736\) | −10.2075 | −0.376254 | ||||||||
\(737\) | −4.56373 | −0.168107 | ||||||||
\(738\) | −0.626207 | −0.0230510 | ||||||||
\(739\) | −35.5507 | −1.30775 | −0.653877 | − | 0.756601i | \(-0.726859\pi\) | ||||
−0.653877 | + | 0.756601i | \(0.726859\pi\) | |||||||
\(740\) | 1.36918 | 0.0503321 | ||||||||
\(741\) | 1.32976 | 0.0488499 | ||||||||
\(742\) | −4.73024 | −0.173653 | ||||||||
\(743\) | −15.8216 | −0.580438 | −0.290219 | − | 0.956960i | \(-0.593728\pi\) | ||||
−0.290219 | + | 0.956960i | \(0.593728\pi\) | |||||||
\(744\) | 4.10391 | 0.150457 | ||||||||
\(745\) | 4.94598 | 0.181207 | ||||||||
\(746\) | 1.64100 | 0.0600815 | ||||||||
\(747\) | 3.36857 | 0.123250 | ||||||||
\(748\) | 1.49318 | 0.0545961 | ||||||||
\(749\) | 4.19950 | 0.153446 | ||||||||
\(750\) | −1.31220 | −0.0479148 | ||||||||
\(751\) | 2.19342 | 0.0800390 | 0.0400195 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400195 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(752\) | −44.9864 | −1.64049 | ||||||||
\(753\) | 10.3909 | 0.378664 | ||||||||
\(754\) | 0.193474 | 0.00704590 | ||||||||
\(755\) | −3.64467 | −0.132643 | ||||||||
\(756\) | 9.55858 | 0.347642 | ||||||||
\(757\) | 21.0338 | 0.764486 | 0.382243 | − | 0.924062i | \(-0.375152\pi\) | ||||
0.382243 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(758\) | 0.0130550 | 0.000474179 0 | ||||||||
\(759\) | 13.0705 | 0.474428 | ||||||||
\(760\) | −0.863199 | −0.0313115 | ||||||||
\(761\) | 46.7886 | 1.69608 | 0.848042 | − | 0.529929i | \(-0.177781\pi\) | ||||
0.848042 | + | 0.529929i | \(0.177781\pi\) | |||||||
\(762\) | 0.284339 | 0.0103005 | ||||||||
\(763\) | 6.40966 | 0.232045 | ||||||||
\(764\) | 5.90608 | 0.213674 | ||||||||
\(765\) | 0.588730 | 0.0212856 | ||||||||
\(766\) | 2.70915 | 0.0978857 | ||||||||
\(767\) | −8.75532 | −0.316136 | ||||||||
\(768\) | 14.9187 | 0.538332 | ||||||||
\(769\) | −2.92074 | −0.105325 | −0.0526624 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526624 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(770\) | −1.39427 | −0.0502461 | ||||||||
\(771\) | 22.4910 | 0.809993 | ||||||||
\(772\) | −22.8097 | −0.820938 | ||||||||
\(773\) | 20.7785 | 0.747349 | 0.373675 | − | 0.927560i | \(-0.378098\pi\) | ||||
0.373675 | + | 0.927560i | \(0.378098\pi\) | |||||||
\(774\) | −0.184394 | −0.00662790 | ||||||||
\(775\) | −26.9418 | −0.967780 | ||||||||
\(776\) | −4.78983 | −0.171945 | ||||||||
\(777\) | −2.38035 | −0.0853947 | ||||||||
\(778\) | −1.88226 | −0.0674824 | ||||||||
\(779\) | 7.12577 | 0.255307 | ||||||||
\(780\) | 2.76795 | 0.0991085 | ||||||||
\(781\) | −19.2329 | −0.688208 | ||||||||
\(782\) | 0.362674 | 0.0129692 | ||||||||
\(783\) | −1.65563 | −0.0591674 | ||||||||
\(784\) | 63.3062 | 2.26094 | ||||||||
\(785\) | 9.24580 | 0.329997 | ||||||||
\(786\) | 0.238534 | 0.00850823 | ||||||||
\(787\) | 34.6445 | 1.23494 | 0.617471 | − | 0.786594i | \(-0.288157\pi\) | ||||
0.617471 | + | 0.786594i | \(0.288157\pi\) | |||||||
\(788\) | 29.1342 | 1.03786 | ||||||||
\(789\) | −10.5012 | −0.373854 | ||||||||
\(790\) | 2.05622 | 0.0731568 | ||||||||
\(791\) | 74.6148 | 2.65300 | ||||||||
\(792\) | 0.828857 | 0.0294521 | ||||||||
\(793\) | −3.98372 | −0.141466 | ||||||||
\(794\) | 3.48493 | 0.123676 | ||||||||
\(795\) | 11.7217 | 0.415724 | ||||||||
\(796\) | −9.04271 | −0.320510 | ||||||||
\(797\) | −31.0103 | −1.09844 | −0.549220 | − | 0.835678i | \(-0.685075\pi\) | ||||
−0.549220 | + | 0.835678i | \(0.685075\pi\) | |||||||
\(798\) | 0.747775 | 0.0264710 | ||||||||
\(799\) | 4.85066 | 0.171604 | ||||||||
\(800\) | 4.24951 | 0.150243 | ||||||||
\(801\) | 10.1717 | 0.359400 | ||||||||
\(802\) | 0.222786 | 0.00786683 | ||||||||
\(803\) | −18.7885 | −0.663031 | ||||||||
\(804\) | 5.09482 | 0.179680 | ||||||||
\(805\) | 49.2593 | 1.73616 | ||||||||
\(806\) | −1.02949 | −0.0362623 | ||||||||
\(807\) | 16.2909 | 0.573468 | ||||||||
\(808\) | 4.02933 | 0.141751 | ||||||||
\(809\) | −32.9103 | −1.15707 | −0.578533 | − | 0.815659i | \(-0.696375\pi\) | ||||
−0.578533 | + | 0.815659i | \(0.696375\pi\) | |||||||
\(810\) | 0.162841 | 0.00572164 | ||||||||
\(811\) | 14.3377 | 0.503466 | 0.251733 | − | 0.967797i | \(-0.419000\pi\) | ||||
0.251733 | + | 0.967797i | \(0.419000\pi\) | |||||||
\(812\) | −15.8255 | −0.555365 | ||||||||
\(813\) | −23.8669 | −0.837049 | ||||||||
\(814\) | −0.102851 | −0.00360492 | ||||||||
\(815\) | −10.8959 | −0.381668 | ||||||||
\(816\) | −1.65540 | −0.0579508 | ||||||||
\(817\) | 2.09827 | 0.0734090 | ||||||||
\(818\) | −2.54633 | −0.0890302 | ||||||||
\(819\) | −4.81215 | −0.168150 | ||||||||
\(820\) | 14.8326 | 0.517977 | ||||||||
\(821\) | 56.0474 | 1.95607 | 0.978034 | − | 0.208444i | \(-0.0668399\pi\) | ||||
0.978034 | + | 0.208444i | \(0.0668399\pi\) | |||||||
\(822\) | 1.02644 | 0.0358011 | ||||||||
\(823\) | −14.0858 | −0.490999 | −0.245500 | − | 0.969397i | \(-0.578952\pi\) | ||||
−0.245500 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(824\) | −0.465837 | −0.0162282 | ||||||||
\(825\) | −5.44138 | −0.189445 | ||||||||
\(826\) | −4.92346 | −0.171309 | ||||||||
\(827\) | −27.1193 | −0.943029 | −0.471515 | − | 0.881858i | \(-0.656293\pi\) | ||||
−0.471515 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(828\) | −14.5915 | −0.507089 | ||||||||
\(829\) | −8.82440 | −0.306484 | −0.153242 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153242 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(830\) | 0.548541 | 0.0190401 | ||||||||
\(831\) | 22.8978 | 0.794314 | ||||||||
\(832\) | −7.67412 | −0.266052 | ||||||||
\(833\) | −6.82600 | −0.236507 | ||||||||
\(834\) | 1.14849 | 0.0397689 | ||||||||
\(835\) | −0.0281990 | −0.000975868 0 | ||||||||
\(836\) | −4.69973 | −0.162544 | ||||||||
\(837\) | 8.80975 | 0.304510 | ||||||||
\(838\) | −3.97823 | −0.137426 | ||||||||
\(839\) | −1.17546 | −0.0405816 | −0.0202908 | − | 0.999794i | \(-0.506459\pi\) | ||||
−0.0202908 | + | 0.999794i | \(0.506459\pi\) | |||||||
\(840\) | 3.12375 | 0.107780 | ||||||||
\(841\) | −26.2589 | −0.905479 | ||||||||
\(842\) | 2.19792 | 0.0757454 | ||||||||
\(843\) | −6.01797 | −0.207270 | ||||||||
\(844\) | 9.46508 | 0.325802 | ||||||||
\(845\) | −1.39349 | −0.0479375 | ||||||||
\(846\) | 1.34168 | 0.0461278 | ||||||||
\(847\) | 37.6990 | 1.29535 | ||||||||
\(848\) | −32.9593 | −1.13183 | ||||||||
\(849\) | 7.15170 | 0.245446 | ||||||||
\(850\) | −0.150985 | −0.00517876 | ||||||||
\(851\) | 3.63369 | 0.124561 | ||||||||
\(852\) | 21.4711 | 0.735588 | ||||||||
\(853\) | −31.2649 | −1.07049 | −0.535245 | − | 0.844697i | \(-0.679781\pi\) | ||||
−0.535245 | + | 0.844697i | \(0.679781\pi\) | |||||||
\(854\) | −2.24020 | −0.0766580 | ||||||||
\(855\) | −1.85301 | −0.0633715 | ||||||||
\(856\) | −0.406530 | −0.0138949 | ||||||||
\(857\) | −31.7642 | −1.08505 | −0.542523 | − | 0.840041i | \(-0.682531\pi\) | ||||
−0.542523 | + | 0.840041i | \(0.682531\pi\) | |||||||
\(858\) | −0.207924 | −0.00709841 | ||||||||
\(859\) | −20.0582 | −0.684376 | −0.342188 | − | 0.939631i | \(-0.611168\pi\) | ||||
−0.342188 | + | 0.939631i | \(0.611168\pi\) | |||||||
\(860\) | 4.36763 | 0.148935 | ||||||||
\(861\) | −25.7868 | −0.878813 | ||||||||
\(862\) | 2.42649 | 0.0826465 | ||||||||
\(863\) | 8.77730 | 0.298783 | 0.149391 | − | 0.988778i | \(-0.452269\pi\) | ||||
0.149391 | + | 0.988778i | \(0.452269\pi\) | |||||||
\(864\) | −1.38955 | −0.0472736 | ||||||||
\(865\) | 10.7746 | 0.366348 | ||||||||
\(866\) | 2.82361 | 0.0959503 | ||||||||
\(867\) | −16.8215 | −0.571288 | ||||||||
\(868\) | 84.2087 | 2.85823 | ||||||||
\(869\) | 22.4673 | 0.762151 | ||||||||
\(870\) | −0.269604 | −0.00914043 | ||||||||
\(871\) | −2.56492 | −0.0869091 | ||||||||
\(872\) | −0.620483 | −0.0210122 | ||||||||
\(873\) | −10.2822 | −0.348000 | ||||||||
\(874\) | −1.14150 | −0.0386119 | ||||||||
\(875\) | −54.0356 | −1.82674 | ||||||||
\(876\) | 20.9749 | 0.708677 | ||||||||
\(877\) | −9.60909 | −0.324476 | −0.162238 | − | 0.986752i | \(-0.551871\pi\) | ||||
−0.162238 | + | 0.986752i | \(0.551871\pi\) | |||||||
\(878\) | 1.58506 | 0.0534932 | ||||||||
\(879\) | −16.8469 | −0.568232 | ||||||||
\(880\) | −9.71498 | −0.327492 | ||||||||
\(881\) | −15.8766 | −0.534898 | −0.267449 | − | 0.963572i | \(-0.586181\pi\) | ||||
−0.267449 | + | 0.963572i | \(0.586181\pi\) | |||||||
\(882\) | −1.88805 | −0.0635739 | ||||||||
\(883\) | −40.1706 | −1.35185 | −0.675924 | − | 0.736971i | \(-0.736255\pi\) | ||||
−0.675924 | + | 0.736971i | \(0.736255\pi\) | |||||||
\(884\) | 0.839202 | 0.0282254 | ||||||||
\(885\) | 12.2005 | 0.410114 | ||||||||
\(886\) | −1.02351 | −0.0343854 | ||||||||
\(887\) | −15.0215 | −0.504372 | −0.252186 | − | 0.967679i | \(-0.581150\pi\) | ||||
−0.252186 | + | 0.967679i | \(0.581150\pi\) | |||||||
\(888\) | 0.230429 | 0.00773268 | ||||||||
\(889\) | 11.7089 | 0.392704 | ||||||||
\(890\) | 1.65637 | 0.0555217 | ||||||||
\(891\) | 1.77929 | 0.0596083 | ||||||||
\(892\) | 36.2150 | 1.21257 | ||||||||
\(893\) | −15.2673 | −0.510901 | ||||||||
\(894\) | 0.414770 | 0.0138720 | ||||||||
\(895\) | −23.7699 | −0.794541 | ||||||||
\(896\) | −17.6889 | −0.590946 | ||||||||
\(897\) | 7.34590 | 0.245273 | ||||||||
\(898\) | 0.717197 | 0.0239332 | ||||||||
\(899\) | −14.5857 | −0.486460 | ||||||||
\(900\) | 6.07461 | 0.202487 | ||||||||
\(901\) | 3.55383 | 0.118395 | ||||||||
\(902\) | −1.11420 | −0.0370989 | ||||||||
\(903\) | −7.59322 | −0.252687 | ||||||||
\(904\) | −7.22304 | −0.240235 | ||||||||
\(905\) | 7.51220 | 0.249714 | ||||||||
\(906\) | −0.305642 | −0.0101543 | ||||||||
\(907\) | 43.0364 | 1.42900 | 0.714501 | − | 0.699635i | \(-0.246654\pi\) | ||||
0.714501 | + | 0.699635i | \(0.246654\pi\) | |||||||
\(908\) | −3.41045 | −0.113180 | ||||||||
\(909\) | 8.64965 | 0.286891 | ||||||||
\(910\) | −0.783613 | −0.0259765 | ||||||||
\(911\) | 8.04108 | 0.266413 | 0.133206 | − | 0.991088i | \(-0.457473\pi\) | ||||
0.133206 | + | 0.991088i | \(0.457473\pi\) | |||||||
\(912\) | 5.21033 | 0.172531 | ||||||||
\(913\) | 5.99366 | 0.198361 | ||||||||
\(914\) | 1.93768 | 0.0640927 | ||||||||
\(915\) | 5.55127 | 0.183519 | ||||||||
\(916\) | 16.3811 | 0.541248 | ||||||||
\(917\) | 9.82268 | 0.324374 | ||||||||
\(918\) | 0.0493709 | 0.00162948 | ||||||||
\(919\) | 24.4005 | 0.804898 | 0.402449 | − | 0.915442i | \(-0.368159\pi\) | ||||
0.402449 | + | 0.915442i | \(0.368159\pi\) | |||||||
\(920\) | −4.76851 | −0.157213 | ||||||||
\(921\) | −17.0692 | −0.562451 | ||||||||
\(922\) | −2.26117 | −0.0744678 | ||||||||
\(923\) | −10.8094 | −0.355794 | ||||||||
\(924\) | 17.0074 | 0.559504 | ||||||||
\(925\) | −1.51275 | −0.0497388 | ||||||||
\(926\) | −3.53081 | −0.116030 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 2.30059 | 0.0755204 | ||||||||
\(929\) | 35.7768 | 1.17380 | 0.586899 | − | 0.809660i | \(-0.300349\pi\) | ||||
0.586899 | + | 0.809660i | \(0.300349\pi\) | |||||||
\(930\) | 1.43459 | 0.0470419 | ||||||||
\(931\) | 21.4846 | 0.704129 | ||||||||
\(932\) | −6.67296 | −0.218580 | ||||||||
\(933\) | −1.92307 | −0.0629585 | ||||||||
\(934\) | 2.67115 | 0.0874027 | ||||||||
\(935\) | 1.04752 | 0.0342575 | ||||||||
\(936\) | 0.465837 | 0.0152264 | ||||||||
\(937\) | 46.1370 | 1.50723 | 0.753615 | − | 0.657316i | \(-0.228308\pi\) | ||||
0.753615 | + | 0.657316i | \(0.228308\pi\) | |||||||
\(938\) | −1.44236 | −0.0470946 | ||||||||
\(939\) | 26.0569 | 0.850335 | ||||||||
\(940\) | −31.7795 | −1.03653 | ||||||||
\(941\) | 5.35443 | 0.174550 | 0.0872748 | − | 0.996184i | \(-0.472184\pi\) | ||||
0.0872748 | + | 0.996184i | \(0.472184\pi\) | |||||||
\(942\) | 0.775353 | 0.0252624 | ||||||||
\(943\) | 39.3644 | 1.28188 | ||||||||
\(944\) | −34.3055 | −1.11655 | ||||||||
\(945\) | 6.70568 | 0.218136 | ||||||||
\(946\) | −0.328089 | −0.0106671 | ||||||||
\(947\) | 2.50694 | 0.0814647 | 0.0407324 | − | 0.999170i | \(-0.487031\pi\) | ||||
0.0407324 | + | 0.999170i | \(0.487031\pi\) | |||||||
\(948\) | −25.0819 | −0.814621 | ||||||||
\(949\) | −10.5596 | −0.342778 | ||||||||
\(950\) | 0.475221 | 0.0154182 | ||||||||
\(951\) | −2.38463 | −0.0773268 | ||||||||
\(952\) | 0.947076 | 0.0306949 | ||||||||
\(953\) | 11.8481 | 0.383797 | 0.191899 | − | 0.981415i | \(-0.438536\pi\) | ||||
0.191899 | + | 0.981415i | \(0.438536\pi\) | |||||||
\(954\) | 0.982979 | 0.0318251 | ||||||||
\(955\) | 4.14332 | 0.134075 | ||||||||
\(956\) | 44.4537 | 1.43774 | ||||||||
\(957\) | −2.94584 | −0.0952254 | ||||||||
\(958\) | 1.66898 | 0.0539222 | ||||||||
\(959\) | 42.2681 | 1.36491 | ||||||||
\(960\) | 10.6938 | 0.345141 | ||||||||
\(961\) | 46.6117 | 1.50360 | ||||||||
\(962\) | −0.0578045 | −0.00186369 | ||||||||
\(963\) | −0.872688 | −0.0281220 | ||||||||
\(964\) | 37.1644 | 1.19699 | ||||||||
\(965\) | −16.0018 | −0.515115 | ||||||||
\(966\) | 4.13089 | 0.132909 | ||||||||
\(967\) | 59.8113 | 1.92340 | 0.961701 | − | 0.274101i | \(-0.0883802\pi\) | ||||
0.961701 | + | 0.274101i | \(0.0883802\pi\) | |||||||
\(968\) | −3.64943 | −0.117297 | ||||||||
\(969\) | −0.561804 | −0.0180478 | ||||||||
\(970\) | −1.67436 | −0.0537605 | ||||||||
\(971\) | −8.99386 | −0.288627 | −0.144313 | − | 0.989532i | \(-0.546097\pi\) | ||||
−0.144313 | + | 0.989532i | \(0.546097\pi\) | |||||||
\(972\) | −1.98634 | −0.0637120 | ||||||||
\(973\) | 47.2940 | 1.51618 | ||||||||
\(974\) | 3.82868 | 0.122679 | ||||||||
\(975\) | −3.05819 | −0.0979403 | ||||||||
\(976\) | −15.6092 | −0.499638 | ||||||||
\(977\) | −13.4745 | −0.431086 | −0.215543 | − | 0.976494i | \(-0.569152\pi\) | ||||
−0.215543 | + | 0.976494i | \(0.569152\pi\) | |||||||
\(978\) | −0.913734 | −0.0292180 | ||||||||
\(979\) | 18.0984 | 0.578428 | ||||||||
\(980\) | 44.7211 | 1.42856 | ||||||||
\(981\) | −1.33197 | −0.0425267 | ||||||||
\(982\) | −1.70098 | −0.0542806 | ||||||||
\(983\) | 35.9998 | 1.14822 | 0.574108 | − | 0.818779i | \(-0.305349\pi\) | ||||
0.574108 | + | 0.818779i | \(0.305349\pi\) | |||||||
\(984\) | 2.49628 | 0.0795784 | ||||||||
\(985\) | 20.4387 | 0.651231 | ||||||||
\(986\) | −0.0817399 | −0.00260313 | ||||||||
\(987\) | 55.2495 | 1.75861 | ||||||||
\(988\) | −2.64136 | −0.0840328 | ||||||||
\(989\) | 11.5913 | 0.368582 | ||||||||
\(990\) | 0.289740 | 0.00920855 | ||||||||
\(991\) | −24.0162 | −0.762899 | −0.381450 | − | 0.924390i | \(-0.624575\pi\) | ||||
−0.381450 | + | 0.924390i | \(0.624575\pi\) | |||||||
\(992\) | −12.2416 | −0.388672 | ||||||||
\(993\) | 7.90274 | 0.250786 | ||||||||
\(994\) | −6.07852 | −0.192799 | ||||||||
\(995\) | −6.34378 | −0.201111 | ||||||||
\(996\) | −6.69115 | −0.212017 | ||||||||
\(997\) | 19.7276 | 0.624780 | 0.312390 | − | 0.949954i | \(-0.398870\pi\) | ||||
0.312390 | + | 0.949954i | \(0.398870\pi\) | |||||||
\(998\) | 1.24296 | 0.0393452 | ||||||||
\(999\) | 0.494655 | 0.0156502 |
(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 | 4017.2.a.f.1.10 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.f.1.10 | ✓ | 19 | 1.1 | even | 1 | trivial |