Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(305,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1064.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.q (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 305.8 | ||
Root | \(1.29764 - 2.24758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.305 |
Dual form | 1064.2.q.n.457.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(799\) | \(913\) | \(1009\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.29764 | − | 2.24758i | 0.749192 | − | 1.29764i | −0.199019 | − | 0.979996i | \(-0.563775\pi\) |
0.948210 | − | 0.317643i | \(-0.102891\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.833107 | − | 1.44298i | −0.372577 | − | 0.645322i | 0.617384 | − | 0.786662i | \(-0.288192\pi\) |
−0.989961 | + | 0.141340i | \(0.954859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29509 | + | 1.31627i | 0.867461 | + | 0.497505i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.86773 | − | 3.23500i | −0.622577 | − | 1.07833i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0726443 | + | 0.125824i | −0.0219031 | + | 0.0379372i | −0.876769 | − | 0.480911i | \(-0.840306\pi\) |
0.854866 | + | 0.518849i | \(0.173639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.47949 | −0.410337 | −0.205169 | − | 0.978727i | \(-0.565774\pi\) | ||||
−0.205169 | + | 0.978727i | \(0.565774\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.32429 | −1.11653 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.95447 | − | 5.11729i | 0.716564 | − | 1.24113i | −0.245789 | − | 0.969323i | \(-0.579047\pi\) |
0.962353 | − | 0.271802i | \(-0.0876196\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.93662 | − | 3.45033i | 1.29548 | − | 0.752924i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.11003 | − | 5.38673i | −0.648486 | − | 1.12321i | −0.983485 | − | 0.180992i | \(-0.942069\pi\) |
0.334999 | − | 0.942219i | \(-0.391264\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.11187 | − | 1.92581i | 0.222373 | − | 0.385162i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.90873 | −0.367335 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.13688 | −0.582504 | −0.291252 | − | 0.956646i | \(-0.594072\pi\) | ||||
−0.291252 | + | 0.956646i | \(0.594072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.441263 | − | 0.764290i | 0.0792532 | − | 0.137271i | −0.823675 | − | 0.567063i | \(-0.808080\pi\) |
0.902928 | + | 0.429792i | \(0.141413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.188532 | + | 0.326547i | 0.0328192 | + | 0.0568446i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0126906 | − | 4.40837i | −0.00214511 | − | 0.745150i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.981199 | + | 1.69949i | 0.161308 | + | 0.279394i | 0.935338 | − | 0.353755i | \(-0.115095\pi\) |
−0.774030 | + | 0.633149i | \(0.781762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.91984 | + | 3.32527i | −0.307421 | + | 0.532469i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.05954 | −0.314076 | −0.157038 | − | 0.987593i | \(-0.550195\pi\) | ||||
−0.157038 | + | 0.987593i | \(0.550195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.11204 | + | 5.39021i | −0.463915 | + | 0.803525i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0872023 | + | 0.151039i | 0.0127198 | + | 0.0220313i | 0.872315 | − | 0.488944i | \(-0.162618\pi\) |
−0.859595 | + | 0.510975i | \(0.829284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.53484 | + | 6.04193i | 0.504978 | + | 0.863132i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.66767 | − | 13.2808i | −1.07369 | − | 1.85968i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.21921 | + | 7.30789i | −0.579553 | + | 1.00382i | 0.415977 | + | 0.909375i | \(0.363440\pi\) |
−0.995530 | + | 0.0944409i | \(0.969894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.242082 | 0.0326423 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.59528 | −0.343753 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.790938 | − | 1.36994i | 0.102971 | − | 0.178352i | −0.809936 | − | 0.586518i | \(-0.800498\pi\) |
0.912908 | + | 0.408166i | \(0.133832\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.27622 | + | 7.40663i | 0.547514 | + | 0.948322i | 0.998444 | + | 0.0557626i | \(0.0177590\pi\) |
−0.450930 | + | 0.892559i | \(0.648908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0284509 | − | 9.88306i | −0.00358448 | − | 1.24515i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.23257 | + | 2.13488i | 0.152882 | + | 0.264799i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.669653 | + | 1.15987i | −0.0818112 | + | 0.141701i | −0.904028 | − | 0.427473i | \(-0.859404\pi\) |
0.822217 | + | 0.569174i | \(0.192737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.1428 | −1.94336 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.37135 | 0.874819 | 0.437409 | − | 0.899263i | \(-0.355896\pi\) | ||||
0.437409 | + | 0.899263i | \(0.355896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.36212 | + | 4.09132i | −0.276466 | + | 0.478853i | −0.970504 | − | 0.241086i | \(-0.922497\pi\) |
0.694038 | + | 0.719938i | \(0.255830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.88560 | − | 4.99801i | −0.333201 | − | 0.577120i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.332343 | + | 0.193156i | −0.0378740 | + | 0.0220122i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.74929 | − | 9.95806i | −0.646846 | − | 1.12037i | −0.983872 | − | 0.178874i | \(-0.942754\pi\) |
0.337026 | − | 0.941495i | \(-0.390579\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.12636 | − | 5.41501i | 0.347373 | − | 0.601667i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.37769 | 0.480514 | 0.240257 | − | 0.970709i | \(-0.422768\pi\) | ||||
0.240257 | + | 0.970709i | \(0.422768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.84555 | −1.06790 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.07054 | + | 7.05038i | −0.436408 | + | 0.755880i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.696489 | + | 1.20635i | 0.0738277 | + | 0.127873i | 0.900576 | − | 0.434699i | \(-0.143145\pi\) |
−0.826748 | + | 0.562572i | \(0.809812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.39556 | − | 1.94742i | −0.355952 | − | 0.204145i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.14520 | − | 1.98354i | −0.118752 | − | 0.205684i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.833107 | + | 1.44298i | −0.0854749 | + | 0.148047i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6777 | 1.08416 | 0.542080 | − | 0.840327i | \(-0.317637\pi\) | ||||
0.542080 | + | 0.840327i | \(0.317637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.542720 | 0.0545454 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.601227 | − | 1.04136i | 0.0598244 | − | 0.103619i | −0.834562 | − | 0.550914i | \(-0.814279\pi\) |
0.894386 | + | 0.447295i | \(0.147613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.77362 | + | 16.9284i | 0.963024 | + | 1.66801i | 0.714834 | + | 0.699295i | \(0.246502\pi\) |
0.248190 | + | 0.968711i | \(0.420164\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.92461 | − | 5.69194i | −0.968543 | − | 0.555477i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.01055 | − | 6.94647i | −0.387714 | − | 0.671541i | 0.604427 | − | 0.796660i | \(-0.293402\pi\) |
−0.992142 | + | 0.125119i | \(0.960069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1921 | + | 17.6532i | −0.976226 | + | 1.69087i | −0.300398 | + | 0.953814i | \(0.597119\pi\) |
−0.675828 | + | 0.737059i | \(0.736214\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.09297 | 0.483403 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.93908 | 0.840918 | 0.420459 | − | 0.907312i | \(-0.361869\pi\) | ||||
0.420459 | + | 0.907312i | \(0.361869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.18197 | + | 8.97544i | −0.483221 | + | 0.836964i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.76329 | + | 4.78616i | 0.255466 | + | 0.442481i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.5165 | − | 7.85573i | 1.23906 | − | 0.720134i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.48945 | + | 9.50800i | 0.499041 | + | 0.864364i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.59528 | + | 4.49515i | −0.234008 | + | 0.405314i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0363 | −1.07656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.76063 | 0.156231 | 0.0781154 | − | 0.996944i | \(-0.475110\pi\) | ||||
0.0781154 | + | 0.996944i | \(0.475110\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.67253 | + | 4.62896i | −0.235303 | + | 0.407557i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.02136 | − | 3.50109i | −0.176607 | − | 0.305892i | 0.764109 | − | 0.645087i | \(-0.223179\pi\) |
−0.940716 | + | 0.339195i | \(0.889845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.00761644 | − | 2.64574i | −0.000660429 | − | 0.229415i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.59017 | + | 2.75426i | 0.136860 | + | 0.237049i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.2042 | − | 17.6742i | 0.871805 | − | 1.51001i | 0.0116777 | − | 0.999932i | \(-0.496283\pi\) |
0.860127 | − | 0.510079i | \(-0.170384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2435 | 0.953662 | 0.476831 | − | 0.878995i | \(-0.341785\pi\) | ||||
0.476831 | + | 0.878995i | \(0.341785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.452628 | 0.0381182 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.107477 | − | 0.186155i | 0.00898765 | − | 0.0155671i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.61336 | + | 4.52647i | 0.217028 | + | 0.375903i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.1666 | − | 0.104595i | 1.49836 | − | 0.00862689i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.79348 | + | 4.83846i | 0.228851 | + | 0.396382i | 0.957468 | − | 0.288540i | \(-0.0931697\pi\) |
−0.728617 | + | 0.684922i | \(0.759836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.67873 | − | 16.7641i | 0.787644 | − | 1.36424i | −0.139763 | − | 0.990185i | \(-0.544634\pi\) |
0.927407 | − | 0.374054i | \(-0.122033\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.0726 | −1.78446 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.47048 | −0.118112 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.46176 | − | 9.46004i | 0.435896 | − | 0.754994i | −0.561472 | − | 0.827495i | \(-0.689765\pi\) |
0.997368 | + | 0.0725017i | \(0.0230983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.9500 | + | 18.9660i | 0.868393 | + | 1.50410i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0473747 | − | 16.4567i | −0.00373365 | − | 1.29697i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.14940 | − | 14.1152i | −0.638310 | − | 1.10559i | −0.985803 | − | 0.167903i | \(-0.946300\pi\) |
0.347493 | − | 0.937683i | \(-0.387033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.314135 | − | 0.544097i | 0.0244553 | − | 0.0423579i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.7379 | 1.29522 | 0.647610 | − | 0.761972i | \(-0.275769\pi\) | ||||
0.647610 | + | 0.761972i | \(0.275769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8111 | −0.831623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.86773 | + | 3.23500i | −0.142829 | + | 0.247387i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.12010 | + | 15.7965i | 0.693389 | + | 1.20098i | 0.970721 | + | 0.240210i | \(0.0772164\pi\) |
−0.277332 | + | 0.960774i | \(0.589450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.08672 | − | 2.95638i | 0.384520 | − | 0.223481i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.05270 | − | 3.55538i | −0.154291 | − | 0.267239i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.01913 | − | 1.76519i | 0.0761737 | − | 0.131937i | −0.825422 | − | 0.564516i | \(-0.809063\pi\) |
0.901596 | + | 0.432579i | \(0.142396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.70643 | −0.647144 | −0.323572 | − | 0.946204i | \(-0.604884\pi\) | ||||
−0.323572 | + | 0.946204i | \(0.604884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.1960 | 1.64077 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.63489 | − | 2.83171i | 0.120199 | − | 0.208191i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.429251 | + | 0.743484i | 0.0313899 | + | 0.0543689i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.38069 | − | 2.51241i | −0.318649 | − | 0.182751i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.32901 | − | 12.6942i | −0.530309 | − | 0.918522i | −0.999375 | − | 0.0353584i | \(-0.988743\pi\) |
0.469066 | − | 0.883163i | \(-0.344591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.39024 | + | 14.5323i | −0.603943 | + | 1.04606i | 0.388275 | + | 0.921544i | \(0.373071\pi\) |
−0.992218 | + | 0.124516i | \(0.960262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.39774 | 0.458152 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0559 | 1.71391 | 0.856955 | − | 0.515391i | \(-0.172353\pi\) | ||||
0.856955 | + | 0.515391i | \(0.172353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.13214 | + | 5.42502i | −0.222031 | + | 0.384569i | −0.955425 | − | 0.295235i | \(-0.904602\pi\) |
0.733393 | + | 0.679804i | \(0.237935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.73794 | + | 3.01019i | 0.122585 | + | 0.212323i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.19942 | − | 4.12900i | −0.505300 | − | 0.289799i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.66621 | + | 2.88597i | 0.116373 | + | 0.201565i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.6174 | + | 20.1219i | −0.807465 | + | 1.39857i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.145289 | 0.0100498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.39876 | −0.302823 | −0.151412 | − | 0.988471i | \(-0.548382\pi\) | ||||
−0.151412 | + | 0.988471i | \(0.548382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.56535 | − | 16.5677i | 0.655407 | − | 1.13520i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.71581 | + | 2.97187i | 0.117017 | + | 0.202680i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.01875 | − | 1.17329i | 0.137042 | − | 0.0796480i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.13037 | + | 10.6181i | 0.414252 | + | 0.717505i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.37111 | + | 7.57099i | −0.294033 | + | 0.509280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.7309 | 1.32128 | 0.660639 | − | 0.750703i | \(-0.270285\pi\) | ||||
0.660639 | + | 0.750703i | \(0.270285\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.30667 | −0.553778 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.07360 | − | 7.05568i | 0.270374 | − | 0.468302i | −0.698583 | − | 0.715529i | \(-0.746186\pi\) |
0.968958 | + | 0.247227i | \(0.0795192\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.48851 | + | 14.7025i | 0.560937 | + | 0.971571i | 0.997415 | + | 0.0718559i | \(0.0228922\pi\) |
−0.436478 | + | 0.899715i | \(0.643774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.00287189 | + | 0.997614i | 0.000188956 | + | 0.0656382i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.59596 | + | 2.76428i | 0.104555 | + | 0.181094i | 0.913556 | − | 0.406713i | \(-0.133325\pi\) |
−0.809002 | + | 0.587807i | \(0.799992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.145298 | − | 0.251663i | 0.00947817 | − | 0.0164167i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.8420 | −1.93845 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9212 | −1.28859 | −0.644297 | − | 0.764775i | \(-0.722850\pi\) | ||||
−0.644297 | + | 0.764775i | \(0.722850\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.14573 | − | 7.18061i | 0.267050 | − | 0.462544i | −0.701049 | − | 0.713113i | \(-0.747285\pi\) |
0.968099 | + | 0.250570i | \(0.0806179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9768 | − | 19.0125i | −0.704165 | − | 1.21965i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.77349 | − | 10.1343i | 0.368855 | − | 0.647456i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.739746 | + | 1.28128i | 0.0470689 | + | 0.0815257i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.68066 | − | 9.83919i | 0.359997 | − | 0.623534i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2504 | −0.647002 | −0.323501 | − | 0.946228i | \(-0.604860\pi\) | ||||
−0.323501 | + | 0.946228i | \(0.604860\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.903703 | 0.0568153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.7760 | + | 22.1286i | −0.800062 | + | 1.38575i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.57142 | + | 7.91793i | 0.285157 | + | 0.493907i | 0.972647 | − | 0.232287i | \(-0.0746208\pi\) |
−0.687490 | + | 0.726194i | \(0.741287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0149465 | + | 5.19200i | 0.000928730 | + | 0.322615i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.85885 | + | 10.1478i | 0.362654 | + | 0.628135i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.33961 | + | 2.32026i | −0.0826036 | + | 0.143074i | −0.904368 | − | 0.426754i | \(-0.859657\pi\) |
0.821764 | + | 0.569828i | \(0.192990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0602 | 0.863712 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.61516 | 0.221244 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.6031 | + | 21.8293i | −0.768426 | + | 1.33095i | 0.169990 | + | 0.985446i | \(0.445627\pi\) |
−0.938416 | + | 0.345508i | \(0.887707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.33513 | + | 10.9728i | 0.384831 | + | 0.666548i | 0.991746 | − | 0.128220i | \(-0.0409262\pi\) |
−0.606914 | + | 0.794767i | \(0.707593\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.78318 | + | 5.10474i | −0.531582 | + | 0.308953i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.161542 | + | 0.279798i | 0.00974132 | + | 0.0168725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0243 | + | 19.0946i | −0.662386 | + | 1.14729i | 0.317601 | + | 0.948224i | \(0.397123\pi\) |
−0.979987 | + | 0.199061i | \(0.936211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.29664 | −0.197365 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9385 | 0.652539 | 0.326270 | − | 0.945277i | \(-0.394208\pi\) | ||||
0.326270 | + | 0.945277i | \(0.394208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3108 | + | 17.8589i | −0.612916 | + | 1.06160i | 0.377830 | + | 0.925875i | \(0.376670\pi\) |
−0.990746 | + | 0.135727i | \(0.956663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.16214 | + | 3.74494i | 0.128074 | + | 0.221831i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.59017 | − | 2.63255i | −0.270949 | − | 0.155394i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.95778 | − | 15.5153i | −0.526928 | − | 0.912666i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.8558 | − | 23.9990i | 0.812244 | − | 1.40685i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.8496 | 1.39331 | 0.696654 | − | 0.717407i | \(-0.254671\pi\) | ||||
0.696654 | + | 0.717407i | \(0.254671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.63574 | −0.153459 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.138658 | − | 0.240163i | 0.00804576 | − | 0.0139357i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.60126 | + | 7.96962i | 0.266098 | + | 0.460895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.72681 | − | 2.71091i | −0.272449 | − | 0.156254i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.56035 | − | 2.70261i | −0.0896398 | − | 0.155261i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.12510 | − | 12.3410i | 0.407982 | − | 0.706645i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6943 | −0.838647 | −0.419323 | − | 0.907837i | \(-0.637733\pi\) | ||||
−0.419323 | + | 0.907837i | \(0.637733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.7305 | 2.88596 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.95754 | + | 5.12260i | −0.167706 | + | 0.290476i | −0.937613 | − | 0.347680i | \(-0.886969\pi\) |
0.769907 | + | 0.638157i | \(0.220303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.455326 | − | 0.788648i | −0.0257365 | − | 0.0445770i | 0.852870 | − | 0.522123i | \(-0.174860\pi\) |
−0.878607 | + | 0.477546i | \(0.841526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.2374 | + | 8.27470i | −0.802186 | + | 0.466227i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7054 | + | 22.0064i | 0.713607 | + | 1.23600i | 0.963494 | + | 0.267729i | \(0.0862733\pi\) |
−0.249887 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.227877 | − | 0.394694i | 0.0127586 | − | 0.0220986i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.8170 | −1.16189 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.90894 | −0.328782 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.64500 | + | 2.84922i | −0.0912480 | + | 0.158046i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.4513 | + | 45.8150i | 1.46276 | + | 2.53358i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.00132834 | + | 0.461429i | 7.32339e−5 | + | 0.0254394i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.89762 | − | 8.48293i | −0.269198 | − | 0.466264i | 0.699457 | − | 0.714675i | \(-0.253425\pi\) |
−0.968655 | + | 0.248410i | \(0.920092\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.66523 | − | 6.34837i | 0.200853 | − | 0.347888i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.23157 | 0.121924 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8358 | 1.29842 | 0.649210 | − | 0.760609i | \(-0.275100\pi\) | ||||
0.649210 | + | 0.760609i | \(0.275100\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5997 | − | 20.0913i | 0.630009 | − | 1.09121i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0641105 | + | 0.111043i | 0.00347178 | + | 0.00601330i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.159943 | + | 18.5196i | 0.00863614 | + | 0.999963i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.4486 | + | 23.2937i | 0.724051 | + | 1.25409i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3196 | + | 23.0703i | −0.715035 | + | 1.23848i | 0.247911 | + | 0.968783i | \(0.420256\pi\) |
−0.962946 | + | 0.269694i | \(0.913077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.31857 | −0.338225 | −0.169113 | − | 0.985597i | \(-0.554090\pi\) | ||||
−0.169113 | + | 0.985597i | \(0.554090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82395 | 0.150731 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.56235 | + | 2.70608i | −0.0831557 | + | 0.144030i | −0.904604 | − | 0.426253i | \(-0.859833\pi\) |
0.821448 | + | 0.570283i | \(0.193167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.14112 | − | 10.6367i | −0.325937 | − | 0.564539i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.116801 | − | 40.5733i | −0.00618175 | − | 2.14737i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.56219 | + | 13.0981i | 0.399117 | + | 0.691291i | 0.993617 | − | 0.112804i | \(-0.0359833\pi\) |
−0.594500 | + | 0.804096i | \(0.702650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.4933 | 1.49551 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.87161 | 0.412019 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.22586 | + | 3.85531i | −0.116189 | + | 0.201246i | −0.918254 | − | 0.395991i | \(-0.870401\pi\) |
0.802065 | + | 0.597236i | \(0.203735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.73546 | + | 6.47001i | 0.194460 | + | 0.336815i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.3026 | + | 11.2186i | −1.00214 | + | 0.582441i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.83058 | − | 10.0989i | −0.301896 | − | 0.522899i | 0.674669 | − | 0.738120i | \(-0.264286\pi\) |
−0.976565 | + | 0.215221i | \(0.930953\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.6187 | + | 27.0525i | −0.806548 | + | 1.39698i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.64099 | 0.239023 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0926 | 1.85395 | 0.926976 | − | 0.375122i | \(-0.122399\pi\) | ||||
0.926976 | + | 0.375122i | \(0.122399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.28466 | − | 3.95715i | 0.117047 | − | 0.202731i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.29960 | − | 12.6433i | −0.372992 | − | 0.646041i | 0.617032 | − | 0.786938i | \(-0.288335\pi\) |
−0.990024 | + | 0.140897i | \(0.955002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.555599 | + | 0.318646i | 0.0283159 | + | 0.0162397i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.84666 | + | 6.66261i | 0.195537 | + | 0.338679i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.26994 | + | 3.93165i | −0.115090 | + | 0.199342i | −0.917816 | − | 0.397006i | \(-0.870049\pi\) |
0.802726 | + | 0.596349i | \(0.203382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.7539 | −1.85873 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4920 | −0.529249 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.57955 | + | 16.5923i | −0.481999 | + | 0.834847i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9422 | − | 18.9525i | −0.549175 | − | 0.951198i | −0.998331 | − | 0.0577452i | \(-0.981609\pi\) |
0.449157 | − | 0.893453i | \(-0.351724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.95638 | − | 3.41610i | −0.298192 | − | 0.171019i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.03673 | − | 6.99182i | −0.201585 | − | 0.349155i | 0.747455 | − | 0.664313i | \(-0.231276\pi\) |
−0.949039 | + | 0.315158i | \(0.897942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.652845 | + | 1.13076i | −0.0325205 | + | 0.0563272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.4184 | −0.517692 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.285114 | −0.0141326 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.7633 | + | 32.4989i | −0.927784 | + | 1.60697i | −0.140762 | + | 0.990043i | \(0.544955\pi\) |
−0.787022 | + | 0.616925i | \(0.788378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.4828 | − | 45.8695i | −1.30630 | − | 2.26258i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.61849 | − | 2.10305i | 0.178054 | − | 0.103484i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.64708 | − | 6.31694i | −0.179028 | − | 0.310086i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.5900 | − | 25.2706i | 0.714476 | − | 1.23751i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.9638 | −1.21956 | −0.609782 | − | 0.792569i | \(-0.708743\pi\) | ||||
−0.609782 | + | 0.792569i | \(0.708743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.4710 | 0.851485 | 0.425743 | − | 0.904844i | \(-0.360013\pi\) | ||||
0.425743 | + | 0.904844i | \(0.360013\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.325741 | − | 0.564200i | 0.0158381 | − | 0.0274323i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.56995 | − | 11.3795i | −0.318689 | − | 0.551986i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0651392 | + | 22.6275i | 0.00315230 | + | 1.09502i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.278932 | − | 0.483124i | −0.0134669 | − | 0.0233254i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7879 | + | 22.1494i | −0.615973 | + | 1.06690i | 0.374240 | + | 0.927332i | \(0.377904\pi\) |
−0.990213 | + | 0.139565i | \(0.955430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.5603 | −1.03612 | −0.518060 | − | 0.855344i | \(-0.673346\pi\) | ||||
−0.518060 | + | 0.855344i | \(0.673346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.5648 | 0.650381 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.11003 | + | 5.38673i | −0.148773 | + | 0.257682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.9215 | − | 22.3807i | −0.616710 | − | 1.06817i | −0.990082 | − | 0.140491i | \(-0.955132\pi\) |
0.373372 | − | 0.927682i | \(-0.378202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9435 | − | 22.7199i | 0.616358 | − | 1.08190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5285 | − | 25.1641i | −0.690270 | − | 1.19558i | −0.971749 | − | 0.236016i | \(-0.924158\pi\) |
0.281479 | − | 0.959567i | \(-0.409175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.16050 | − | 2.01004i | 0.0550129 | − | 0.0952852i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.4997 | 0.685814 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6266 | 1.39817 | 0.699083 | − | 0.715040i | \(-0.253592\pi\) | ||||
0.699083 | + | 0.715040i | \(0.253592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.145289 | − | 0.251647i | 0.00684137 | − | 0.0118496i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.1190 | − | 43.5074i | −1.18019 | − | 2.04415i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0187757 | + | 6.52214i | 0.000880216 | + | 0.305763i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.01616 | + | 3.49209i | 0.0943119 | + | 0.163353i | 0.909321 | − | 0.416095i | \(-0.136602\pi\) |
−0.815009 | + | 0.579448i | \(0.803268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.63927 | + | 9.76751i | −0.263219 | + | 0.455908i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.6181 | 0.820555 | 0.410277 | − | 0.911961i | \(-0.365432\pi\) | ||||
0.410277 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.2595 | −1.22038 | −0.610192 | − | 0.792253i | \(-0.708908\pi\) | ||||
−0.610192 | + | 0.792253i | \(0.708908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.90815 | + | 3.30501i | −0.0884882 | + | 0.153266i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.4759 | − | 30.2691i | −0.808688 | − | 1.40069i | −0.913773 | − | 0.406226i | \(-0.866845\pi\) |
0.105085 | − | 0.994463i | \(-0.466489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.06362 | + | 1.78056i | −0.141465 | + | 0.0822188i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1748 | − | 24.5514i | −0.653139 | − | 1.13127i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.149614 | − | 0.259138i | 0.00687924 | − | 0.0119152i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.22373 | −0.102032 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.5214 | 1.44327 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.5239 | − | 23.4242i | 0.617925 | − | 1.07028i | −0.371939 | − | 0.928257i | \(-0.621307\pi\) |
0.989864 | − | 0.142020i | \(-0.0453597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.45168 | − | 2.51438i | −0.0661907 | − | 0.114646i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.0491 | − | 21.2483i | −1.68579 | − | 0.966832i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.89569 | − | 15.4078i | −0.403933 | − | 0.699632i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.60833 | + | 16.6421i | −0.435395 | + | 0.754126i | −0.997328 | − | 0.0730565i | \(-0.976725\pi\) |
0.561933 | + | 0.827183i | \(0.310058\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −42.2999 | −1.91287 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.6972 | 1.43048 | 0.715238 | − | 0.698881i | \(-0.246318\pi\) | ||||
0.715238 | + | 0.698881i | \(0.246318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.26782 | + | 16.0523i | −0.417402 | + | 0.722961i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.452144 | − | 0.783136i | −0.0203223 | − | 0.0351993i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.9179 | + | 9.70272i | 0.758871 | + | 0.435227i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7795 | − | 18.6706i | −0.482556 | − | 0.835812i | 0.517243 | − | 0.855838i | \(-0.326958\pi\) |
−0.999799 | + | 0.0200267i | \(0.993625\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.7198 | − | 37.6198i | 0.970368 | − | 1.68073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.27173 | −0.324230 | −0.162115 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162115 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00355 | −0.0891566 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.0289 | + | 24.2988i | −0.623046 | + | 1.07915i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3403 | − | 35.2304i | −0.901567 | − | 1.56156i | −0.825461 | − | 0.564459i | \(-0.809085\pi\) |
−0.0761058 | − | 0.997100i | \(-0.524249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8066 | + | 6.28073i | −0.478055 | + | 0.277843i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.954363 | + | 1.65301i | 0.0421362 | + | 0.0729820i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.2849 | − | 28.2063i | 0.717600 | − | 1.24292i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0253390 | −0.00111441 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 47.3384 | 2.07792 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01935 | − | 1.76556i | 0.0446583 | − | 0.0773505i | −0.842832 | − | 0.538176i | \(-0.819113\pi\) |
0.887491 | + | 0.460826i | \(0.152447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7965 | + | 32.5565i | 0.821914 | + | 1.42360i | 0.904255 | + | 0.426993i | \(0.140427\pi\) |
−0.0823405 | + | 0.996604i | \(0.526239\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0439560 | − | 15.2691i | −0.00191840 | − | 0.666398i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.60740 | − | 4.51614i | −0.113580 | − | 0.196726i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.84455 | + | 13.5872i | −0.341068 | + | 0.590746i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.90904 | −0.256430 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.95898 | 0.128168 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.68243 | + | 11.5743i | −0.288907 | + | 0.500401i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.64493 | − | 4.58116i | −0.114137 | − | 0.197692i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.01700 | + | 0.00585546i | −0.0438054 | + | 0.000252212i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.1595 | − | 27.9891i | −0.694751 | − | 1.20334i | −0.970264 | − | 0.242047i | \(-0.922181\pi\) |
0.275513 | − | 0.961297i | \(-0.411152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.2978 | + | 19.5684i | −0.484835 | + | 0.839759i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.9644 | 1.45488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.52462 | 0.236216 | 0.118108 | − | 0.993001i | \(-0.462317\pi\) | ||||
0.118108 | + | 0.993001i | \(0.462317\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.9737 | − | 27.6672i | 0.681739 | − | 1.18081i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56844 | + | 2.71662i | 0.0668178 | + | 0.115732i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0875783 | − | 30.4223i | −0.00372421 | − | 1.29369i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.24298 | − | 7.34907i | −0.180105 | − | 0.311950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.8530 | − | 27.4582i | 0.671712 | − | 1.16344i | −0.305706 | − | 0.952126i | \(-0.598893\pi\) |
0.977418 | − | 0.211314i | \(-0.0677741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.04707 | 0.128877 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.22805 | 0.0940683 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3777 | + | 30.0991i | −0.732383 | + | 1.26852i | 0.223479 | + | 0.974709i | \(0.428259\pi\) |
−0.955862 | + | 0.293816i | \(0.905075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.44721 | − | 12.8989i | −0.313306 | − | 0.542663i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.3029 | − | 8.31277i | 0.600665 | − | 0.349103i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.9493 | + | 31.0891i | 0.752473 | + | 1.30332i | 0.946621 | + | 0.322349i | \(0.104472\pi\) |
−0.194148 | + | 0.980972i | \(0.562194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5441 | − | 37.3154i | 0.901592 | − | 1.56160i | 0.0761632 | − | 0.997095i | \(-0.475733\pi\) |
0.825428 | − | 0.564507i | \(-0.190934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.0416 | −1.58921 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8317 | −0.576824 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3082 | + | 40.3711i | −0.970335 | + | 1.68067i | −0.275792 | + | 0.961217i | \(0.588940\pi\) |
−0.694543 | + | 0.719452i | \(0.744393\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.7750 | + | 37.7154i | 0.904938 | + | 1.56740i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0472 | + | 5.76224i | 0.416827 | + | 0.239058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.613003 | − | 1.06175i | −0.0253880 | − | 0.0439733i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.60423 | − | 7.97477i | 0.190362 | − | 0.329716i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.4370 | 1.91666 | 0.958331 | − | 0.285661i | \(-0.0922132\pi\) | ||||
0.958331 | + | 0.285661i | \(0.0922132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.882526 | −0.0363639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.2158 | − | 54.0674i | 1.28405 | − | 2.22404i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.1502 | − | 34.9011i | −0.827468 | − | 1.43322i | −0.900018 | − | 0.435852i | \(-0.856447\pi\) |
0.0725505 | − | 0.997365i | \(-0.476886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.5964 | − | 12.9594i | −0.926362 | − | 0.531285i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.12876 | + | 14.0794i | 0.332688 | + | 0.576233i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.89620 | − | 17.1407i | 0.404348 | − | 0.700351i | −0.589898 | − | 0.807478i | \(-0.700832\pi\) |
0.994245 | + | 0.107127i | \(0.0341653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2064 | 1.59926 | 0.799631 | − | 0.600492i | \(-0.205029\pi\) | ||||
0.799631 | + | 0.600492i | \(0.205029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.00293 | 0.203735 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.14659 | − | 15.8424i | 0.371862 | − | 0.644083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.61466 | + | 14.9210i | 0.349658 | + | 0.605626i | 0.986189 | − | 0.165626i | \(-0.0529644\pi\) |
−0.636531 | + | 0.771252i | \(0.719631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.6225 | + | 10.8233i | −0.754621 | + | 0.438582i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.129015 | − | 0.223461i | −0.00521939 | − | 0.00904025i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0565 | + | 20.8825i | −0.486959 | + | 0.843437i | −0.999888 | − | 0.0149940i | \(-0.995227\pi\) |
0.512929 | + | 0.858431i | \(0.328560\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.64857 | 0.348744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.6161 | −1.79618 | −0.898089 | − | 0.439814i | \(-0.855044\pi\) | ||||
−0.898089 | + | 0.439814i | \(0.855044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.2775 | − | 17.8011i | 0.413086 | − | 0.715486i | −0.582139 | − | 0.813089i | \(-0.697784\pi\) |
0.995225 | + | 0.0976031i | \(0.0311176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.93619 | + | 10.2818i | 0.238211 | + | 0.412594i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0106095 | + | 3.68546i | 0.000425062 | + | 0.147655i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.46817 | + | 7.73911i | 0.178727 | + | 0.309564i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.188532 | − | 0.326547i | 0.00752925 | − | 0.0130410i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.5957 | 0.462350 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.35794 | 0.133678 | 0.0668388 | − | 0.997764i | \(-0.478709\pi\) | ||||
0.0668388 | + | 0.997764i | \(0.478709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.70800 | + | 9.88655i | −0.226873 | + | 0.392955i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.46679 | − | 2.54056i | −0.0582079 | − | 0.100819i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.22977 | − | 8.93898i | −0.207211 | − | 0.354175i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.7677 | − | 23.8464i | −0.544642 | − | 0.943347i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.32930 | − | 4.03447i | 0.0920020 | − | 0.159352i | −0.816351 | − | 0.577555i | \(-0.804007\pi\) |
0.908353 | + | 0.418203i | \(0.137340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.50546 | 0.374859 | 0.187429 | − | 0.982278i | \(-0.439984\pi\) | ||||
0.187429 | + | 0.982278i | \(0.439984\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.90602 | 0.350674 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.51540 | + | 11.2850i | −0.256147 | + | 0.443660i | −0.965206 | − | 0.261489i | \(-0.915786\pi\) |
0.709059 | + | 0.705149i | \(0.249120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.114914 | + | 0.199037i | 0.00451078 | + | 0.00781290i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0174447 | − | 6.05980i | −0.000683712 | − | 0.237502i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.51227 | − | 6.08344i | −0.137446 | − | 0.238063i | 0.789083 | − | 0.614286i | \(-0.210556\pi\) |
−0.926529 | + | 0.376223i | \(0.877223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.36801 | + | 5.83357i | −0.131599 | + | 0.227936i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.6472 | 0.688485 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.92031 | −0.308532 | −0.154266 | − | 0.988029i | \(-0.549301\pi\) | ||||
−0.154266 | + | 0.988029i | \(0.549301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.37679 | + | 9.31287i | −0.209133 | + | 0.362228i | −0.951442 | − | 0.307829i | \(-0.900397\pi\) |
0.742309 | + | 0.670058i | \(0.233731\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3442 | + | 19.6488i | 0.440574 | + | 0.763097i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.81141 | + | 2.21517i | −0.147800 | + | 0.0859008i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.75579 | + | 16.8975i | 0.377746 | + | 0.654275i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.6036 | − | 44.3467i | 0.989891 | − | 1.71454i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.24257 | −0.0479690 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6941 | −1.26027 | −0.630133 | − | 0.776487i | \(-0.717000\pi\) | ||||
−0.630133 | + | 0.776487i | \(0.717000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.12225 | + | 3.67584i | −0.0816854 | + | 0.141483i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.2997 | − | 31.6960i | −0.703314 | − | 1.21818i | −0.967297 | − | 0.253648i | \(-0.918370\pi\) |
0.263983 | − | 0.964527i | \(-0.414964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.5063 | + | 14.0548i | 0.940466 | + | 0.539375i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5721 | − | 18.3114i | −0.405124 | − | 0.701696i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.48720 | + | 2.57591i | −0.0569062 | + | 0.0985644i | −0.893075 | − | 0.449908i | \(-0.851457\pi\) |
0.836169 | + | 0.548472i | \(0.184790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.0048 | −1.29926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44.0601 | 1.68100 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.24229 | − | 10.8120i | 0.237812 | − | 0.411903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.911558 | + | 1.57886i | 0.0346773 | + | 0.0600628i | 0.882843 | − | 0.469668i | \(-0.155626\pi\) |
−0.848166 | + | 0.529731i | \(0.822293\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.24559 | + | 0.714368i | 0.0473160 | + | 0.0271366i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.36705 | − | 16.2242i | −0.355312 | − | 0.615419i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.90894 | + | 10.2346i | −0.223817 | + | 0.387662i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.28390 | 0.313326 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.7699 | −1.87978 | −0.939891 | − | 0.341474i | \(-0.889074\pi\) | ||||
−0.939891 | + | 0.341474i | \(0.889074\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.981199 | − | 1.69949i | 0.0370066 | − | 0.0640974i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.377088 | − | 0.653135i | −0.0142019 | − | 0.0245985i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.75058 | − | 1.59862i | 0.103446 | − | 0.0601224i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.47624 | + | 12.9492i | 0.280776 | + | 0.486318i | 0.971576 | − | 0.236727i | \(-0.0760748\pi\) |
−0.690800 | + | 0.723046i | \(0.742742\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.4763 | + | 37.1980i | −0.805422 | + | 1.39503i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.48936 | −0.205578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.358158 | −0.0133943 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.8505 | + | 44.7744i | −0.965404 | + | 1.67213i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.13480 | − | 12.3578i | −0.266083 | − | 0.460870i | 0.701764 | − | 0.712410i | \(-0.252396\pi\) |
−0.967847 | + | 0.251540i | \(0.919063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.148880 | + | 51.7169i | 0.00554460 | + | 1.92604i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7593 | − | 18.6357i | −0.400143 | − | 0.693068i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.48779 | + | 6.04104i | −0.129533 | + | 0.224358i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.40032 | −0.0890231 | −0.0445115 | − | 0.999009i | \(-0.514173\pi\) | ||||
−0.0445115 | + | 0.999009i | \(0.514173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.2178 | −1.41547 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.08483 | + | 10.5392i | −0.225056 | + | 0.389808i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.20364 | + | 10.7450i | 0.229137 | + | 0.396876i | 0.957552 | − | 0.288259i | \(-0.0930764\pi\) |
−0.728416 | + | 0.685135i | \(0.759743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.2857 | − | 26.1270i | −0.563821 | − | 0.963709i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0972930 | − | 0.168516i | −0.00358383 | − | 0.00620738i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.0240469 | − | 0.0416505i | 0.000884580 | − | 0.00153214i | −0.865583 | − | 0.500766i | \(-0.833052\pi\) |
0.866467 | + | 0.499234i | \(0.166385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.83969 | 0.141055 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5507 | −1.04742 | −0.523712 | − | 0.851895i | \(-0.675453\pi\) | ||||
−0.523712 | + | 0.851895i | \(0.675453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.65454 | − | 8.06190i | 0.170529 | − | 0.295365i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.17635 | − | 14.1619i | −0.299157 | − | 0.518155i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0610922 | − | 21.2217i | −0.00223226 | − | 0.775425i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.42782 | + | 9.40126i | 0.198064 | + | 0.343057i | 0.947901 | − | 0.318566i | \(-0.103201\pi\) |
−0.749837 | + | 0.661623i | \(0.769868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.3014 | + | 23.0386i | −0.484728 | + | 0.839574i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.2537 | −1.17383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.1699 | −0.733089 | −0.366545 | − | 0.930400i | \(-0.619459\pi\) | ||||
−0.366545 | + | 0.930400i | \(0.619459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.17268 | − | 2.03114i | 0.0425656 | − | 0.0737258i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9613 | + | 25.9137i | 0.542347 | + | 0.939373i | 0.998769 | + | 0.0496090i | \(0.0157975\pi\) |
−0.456422 | + | 0.889764i | \(0.650869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.6282 | + | 27.1001i | −1.68806 | + | 0.981090i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.3888 | + | 31.8504i | 0.664850 | + | 1.15155i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.17019 | + | 2.02682i | −0.0422530 | + | 0.0731843i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.7701 | −0.568685 | −0.284343 | − | 0.958723i | \(-0.591775\pi\) | ||||
−0.284343 | + | 0.958723i | \(0.591775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.7282 | 0.854550 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.6138 | + | 30.5081i | −0.633526 | + | 1.09730i | 0.353300 | + | 0.935510i | \(0.385060\pi\) |
−0.986825 | + | 0.161789i | \(0.948274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.981251 | − | 1.69958i | −0.0352476 | − | 0.0610506i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6888 | + | 6.70374i | 0.419333 | + | 0.240495i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | + | 1.73205i | 0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.535487 | + | 0.927490i | −0.0191612 | + | 0.0331882i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.98745 | 0.213974 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2009 | −0.649618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.9558 | + | 39.7606i | −0.818286 | + | 1.41731i | 0.0886576 | + | 0.996062i | \(0.471742\pi\) |
−0.906944 | + | 0.421251i | \(0.861591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.47665 | + | 6.02173i | 0.123772 | + | 0.214379i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.5160 | + | 11.7663i | 0.729464 | + | 0.418361i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.32663 | − | 10.9580i | −0.224665 | − | 0.389132i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.2451 | − | 31.6014i | 0.647086 | − | 1.12079i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.14407 | −0.0759468 | −0.0379734 | − | 0.999279i | \(-0.512090\pi\) | ||||
−0.0379734 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.03055 | 0.0364581 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.60171 | − | 4.50629i | 0.0919268 | − | 0.159222i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.343190 | − | 0.594422i | −0.0121109 | − | 0.0209767i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.7072 | + | 13.7785i | −0.835569 | + | 0.485629i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.7086 | + | 56.6530i | 1.15140 | + | 1.99428i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.6682 | − | 20.2098i | 0.410230 | − | 0.710540i | −0.584684 | − | 0.811261i | \(-0.698782\pi\) |
0.994915 | + | 0.100721i | \(0.0321149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.5527 | 1.45911 | 0.729556 | − | 0.683921i | \(-0.239727\pi\) | ||||
0.729556 | + | 0.683921i | \(0.239727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.8828 | 1.15325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5786 | + | 23.5189i | −0.475639 | + | 0.823831i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.02977 | + | 1.78361i | 0.0360270 | + | 0.0624006i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0420929 | + | 14.6219i | 0.00147084 | + | 0.510931i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5848 | − | 26.9936i | −0.543912 | − | 0.942083i | −0.998675 | − | 0.0514705i | \(-0.983609\pi\) |
0.454762 | − | 0.890613i | \(-0.349724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.62864 | − | 14.9452i | 0.300775 | − | 0.520958i | −0.675536 | − | 0.737327i | \(-0.736088\pi\) |
0.976312 | + | 0.216368i | \(0.0694212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.838490 | 0.0291925 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.1385 | −1.22188 | −0.610942 | − | 0.791675i | \(-0.709209\pi\) | ||||
−0.610942 | + | 0.791675i | \(0.709209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6235 | − | 25.3287i | 0.507897 | − | 0.879703i | −0.492061 | − | 0.870561i | \(-0.663756\pi\) |
0.999958 | − | 0.00914267i | \(-0.00291024\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.6111 | + | 49.5559i | 0.992508 | + | 1.71907i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.3619 | − | 0.238144i | 1.43310 | − | 0.00825118i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9445 | − | 24.1526i | −0.482569 | − | 0.835834i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.842251 | + | 1.45882i | −0.0291124 | + | 0.0504242i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6637 | −0.575294 | −0.287647 | − | 0.957737i | \(-0.592873\pi\) | ||||
−0.287647 | + | 0.957737i | \(0.592873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.1600 | −0.660689 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.1943 | − | 24.5852i | 0.488877 | − | 0.846760i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00680 | + | 15.6002i | 0.309843 | + | 0.536665i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0836201 | + | 29.0473i | 0.00287322 | + | 0.998077i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.7595 | + | 46.3488i | 0.918383 | + | 1.59069i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.10311 | − | 10.5709i | 0.209212 | − | 0.362366i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0759 | 0.687386 | 0.343693 | − | 0.939082i | \(-0.388322\pi\) | ||||
0.343693 | + | 0.939082i | \(0.388322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.22408 | 0.212859 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7412 | + | 18.6042i | −0.366911 | + | 0.635509i | −0.989081 | − | 0.147373i | \(-0.952918\pi\) |
0.622170 | + | 0.782882i | \(0.286251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.97298 | − | 12.0776i | −0.237915 | − | 0.412081i | 0.722201 | − | 0.691683i | \(-0.243131\pi\) |
−0.960116 | + | 0.279603i | \(0.909797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.8732 | + | 6.90067i | −0.404639 | + | 0.235174i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.01491 | + | 8.68608i | 0.170709 | + | 0.295678i | 0.938668 | − | 0.344822i | \(-0.112061\pi\) |
−0.767959 | + | 0.640499i | \(0.778727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.1960 | − | 26.3203i | 0.516681 | − | 0.894917i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −46.4958 | −1.57908 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.67061 | 0.0566717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.990746 | − | 1.71602i | 0.0335702 | − | 0.0581452i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.9431 | − | 34.5425i | −0.674973 | − | 1.16909i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.6243 | − | 15.8430i | −0.933872 | − | 0.535593i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.13290 | − | 12.3546i | −0.240861 | − | 0.417184i | 0.720099 | − | 0.693872i | \(-0.244096\pi\) |
−0.960960 | + | 0.276688i | \(0.910763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.9482 | − | 53.6038i | 1.04386 | − | 1.80801i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.3253 | 1.12276 | 0.561379 | − | 0.827559i | \(-0.310271\pi\) | ||||
0.561379 | + | 0.827559i | \(0.310271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.1473 | 1.35107 | 0.675533 | − | 0.737330i | \(-0.263914\pi\) | ||||
0.675533 | + | 0.737330i | \(0.263914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.42024 | + | 5.92403i | −0.114970 | + | 0.199134i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.76916 | + | 15.1886i | 0.294440 | + | 0.509985i | 0.974854 | − | 0.222843i | \(-0.0715336\pi\) |
−0.680415 | + | 0.732827i | \(0.738200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.04080 | + | 2.31747i | 0.135524 | + | 0.0777256i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.454224 | + | 0.786739i | 0.0152171 | + | 0.0263567i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0872023 | − | 0.151039i | 0.00291811 | − | 0.00505432i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.39619 | −0.113522 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.8831 | 0.797433 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38419 | + | 2.39749i | −0.0461653 | + | 0.0799607i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.9311 | + | 43.1819i | 0.830574 | + | 1.43860i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.2267 | + | 7.10608i | −0.406878 | + | 0.236476i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.25339 | + | 12.5632i | 0.241111 | + | 0.417616i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.3986 | + | 26.6711i | −0.511301 | + | 0.885600i | 0.488613 | + | 0.872501i | \(0.337503\pi\) |
−0.999914 | + | 0.0130993i | \(0.995830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.49172 | −0.148981 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5837 | −0.880758 | −0.440379 | − | 0.897812i | \(-0.645156\pi\) | ||||
−0.440379 | + | 0.897812i | \(0.645156\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.318014 | + | 0.550817i | −0.0105247 | + | 0.0182294i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.4916 | − | 32.0284i | −0.611313 | − | 1.05883i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.0307911 | − | 10.6960i | −0.00101681 | − | 0.353212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.07346 | + | 10.5195i | 0.200345 | + | 0.347008i | 0.948640 | − | 0.316359i | \(-0.102460\pi\) |
−0.748295 | + | 0.663367i | \(0.769127\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0679 | + | 33.0265i | −0.628307 | + | 1.08826i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9059 | −0.358971 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.36385 | 0.143482 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.5090 | − | 63.2354i | 1.19911 | − | 2.07692i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4092 | + | 23.2254i | 0.439940 | + | 0.761999i | 0.997684 | − | 0.0680139i | \(-0.0216662\pi\) |
−0.557744 | + | 0.830013i | \(0.688333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.46504 | − | 6.08223i | 0.113562 | − | 0.199337i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.67562 | + | 13.2946i | 0.251289 | + | 0.435245i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.715223 | − | 1.23880i | 0.0233903 | − | 0.0405132i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.6816 | 1.39435 | 0.697174 | − | 0.716902i | \(-0.254441\pi\) | ||||
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.36339 | −0.0771264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2276 | + | 22.9109i | −0.431208 | + | 0.746874i | −0.996978 | − | 0.0776893i | \(-0.975246\pi\) |
0.565770 | + | 0.824563i | \(0.308579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.22006 | + | 10.7735i | 0.202553 | + | 0.350832i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0242229 | + | 8.41437i | 0.000787972 | + | 0.273719i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.62554 | + | 6.27962i | 0.117814 | + | 0.204060i | 0.918901 | − | 0.394488i | \(-0.129078\pi\) |
−0.801087 | + | 0.598548i | \(0.795745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.49474 | − | 6.05307i | 0.113444 | − | 0.196491i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65.9482 | 2.13852 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.1832 | −0.621404 | −0.310702 | − | 0.950507i | \(-0.600564\pi\) | ||||
−0.310702 | + | 0.950507i | \(0.600564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.2117 | + | 21.1513i | −0.395161 | + | 0.684439i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.591403 | − | 1.02434i | −0.0191173 | − | 0.0331122i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.6837 | − | 27.1323i | 1.50749 | − | 0.876149i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1106 | + | 26.1723i | 0.487438 | + | 0.844267i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.9813 | + | 25.9483i | −0.482764 | + | 0.836172i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.9599 | 0.900060 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.6363 | −0.824407 | −0.412203 | − | 0.911092i | \(-0.635241\pi\) | ||||
−0.412203 | + | 0.911092i | \(0.635241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.66767 | + | 13.2808i | −0.246321 | + | 0.426640i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.1446 | − | 31.4274i | −0.582289 | − | 1.00855i | −0.995207 | − | 0.0977858i | \(-0.968824\pi\) |
0.412919 | − | 0.910768i | \(-0.364509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.8048 | + | 14.7995i | 0.827265 | + | 0.474452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.26922 | + | 7.39451i | 0.136725 | + | 0.236814i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.14552 | + | 1.98409i | −0.0366483 | + | 0.0634768i | −0.883768 | − | 0.467926i | \(-0.845001\pi\) |
0.847119 | + | 0.531403i | \(0.178335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.202384 | −0.00646822 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 76.1444 | 2.43110 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.33524 | − | 9.24091i | 0.170168 | − | 0.294739i | −0.768311 | − | 0.640077i | \(-0.778902\pi\) |
0.938478 | + | 0.345338i | \(0.112236\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0411 | − | 34.7122i | −0.638563 | − | 1.10602i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.03882 | + | 0.595783i | 0.0330660 | + | 0.0189640i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.40521 | + | 11.0942i | 0.203674 | + | 0.352774i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.36208 | + | 16.2156i | −0.297396 | + | 0.515105i | −0.975539 | − | 0.219824i | \(-0.929452\pi\) |
0.678143 | + | 0.734930i | \(0.262785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.4214 | −0.806723 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.4376 | 0.330895 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.22465 | − | 12.5135i | 0.228807 | − | 0.396305i | −0.728648 | − | 0.684889i | \(-0.759851\pi\) |
0.957455 | + | 0.288583i | \(0.0931842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.87284 | − | 3.24386i | −0.0592541 | − | 0.102631i |
(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 | 1064.2.q.n.305.8 | ✓ | 16 | |
7.2 | even | 3 | inner | 1064.2.q.n.457.8 | yes | 16 | |
7.3 | odd | 6 | 7448.2.a.br.1.8 | 8 | |||
7.4 | even | 3 | 7448.2.a.bq.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1064.2.q.n.457.8 | yes | 16 | 7.2 | even | 3 | inner | |
7448.2.a.bq.1.1 | 8 | 7.4 | even | 3 | |||
7448.2.a.br.1.8 | 8 | 7.3 | odd | 6 |