Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(36,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.m (of order \(6\), 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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 56.4 | ||
Root | \(0.665665 + 1.24775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.56 |
Dual form | 65.2.m.a.36.4 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29515 | + | 0.747754i | 0.915808 | + | 0.528742i | 0.882295 | − | 0.470696i | \(-0.155997\pi\) |
0.0335125 | + | 0.999438i | \(0.489331\pi\) | |||||||
\(3\) | −0.0473938 | + | 0.0820885i | −0.0273628 | + | 0.0473938i | −0.879383 | − | 0.476116i | \(-0.842044\pi\) |
0.852020 | + | 0.523510i | \(0.175378\pi\) | |||||||
\(4\) | 0.118272 | + | 0.204852i | 0.0591358 | + | 0.102426i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.122764 | + | 0.0708778i | −0.0501182 | + | 0.0289357i | ||||
\(7\) | −4.18016 | + | 2.41342i | −1.57995 | + | 0.912187i | −0.585089 | + | 0.810969i | \(0.698941\pi\) |
−0.994864 | + | 0.101218i | \(0.967726\pi\) | |||||||
\(8\) | − | 2.63726i | − | 0.932413i | ||||||
\(9\) | 1.49551 | + | 2.59030i | 0.498503 | + | 0.863432i | ||||
\(10\) | 0.747754 | − | 1.29515i | 0.236461 | − | 0.409562i | ||||
\(11\) | −0.926118 | − | 0.534695i | −0.279235 | − | 0.161217i | 0.353842 | − | 0.935305i | \(-0.384875\pi\) |
−0.633077 | + | 0.774089i | \(0.718208\pi\) | |||||||
\(12\) | −0.0224214 | −0.00647249 | ||||||||
\(13\) | 0.331331 | − | 3.59030i | 0.0918946 | − | 0.995769i | ||||
\(14\) | −7.21857 | −1.92924 | ||||||||
\(15\) | 0.0820885 | + | 0.0473938i | 0.0211951 | + | 0.0122370i | ||||
\(16\) | 2.20857 | − | 3.82535i | 0.552142 | − | 0.956337i | ||||
\(17\) | 1.77944 | + | 3.08209i | 0.431579 | + | 0.747516i | 0.997009 | − | 0.0772795i | \(-0.0246234\pi\) |
−0.565431 | + | 0.824796i | \(0.691290\pi\) | |||||||
\(18\) | 4.47309i | 1.05432i | ||||||||
\(19\) | 4.96410 | − | 2.86603i | 1.13884 | − | 0.657511i | 0.192699 | − | 0.981258i | \(-0.438276\pi\) |
0.946144 | + | 0.323747i | \(0.104943\pi\) | |||||||
\(20\) | 0.204852 | − | 0.118272i | 0.0458064 | − | 0.0264463i | ||||
\(21\) | − | 0.457524i | − | 0.0998400i | ||||||
\(22\) | −0.799640 | − | 1.38502i | −0.170484 | − | 0.295287i | ||||
\(23\) | −3.54290 | + | 6.13649i | −0.738746 | + | 1.27955i | 0.214314 | + | 0.976765i | \(0.431248\pi\) |
−0.953060 | + | 0.302781i | \(0.902085\pi\) | |||||||
\(24\) | 0.216489 | + | 0.124990i | 0.0441906 | + | 0.0255135i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.11378 | − | 4.40221i | 0.610662 | − | 0.863344i | ||||
\(27\) | −0.567874 | −0.109287 | ||||||||
\(28\) | −0.988789 | − | 0.570878i | −0.186864 | − | 0.107886i | ||||
\(29\) | −0.736543 | + | 1.27573i | −0.136773 | + | 0.236897i | −0.926273 | − | 0.376853i | \(-0.877006\pi\) |
0.789501 | + | 0.613750i | \(0.210340\pi\) | |||||||
\(30\) | 0.0708778 | + | 0.122764i | 0.0129405 | + | 0.0224135i | ||||
\(31\) | − | 1.46410i | − | 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | 1.15297 | − | 0.665665i | 0.203818 | − | 0.117674i | ||||
\(33\) | 0.0877845 | − | 0.0506824i | 0.0152813 | − | 0.00882268i | ||||
\(34\) | 5.32235i | 0.912775i | ||||||||
\(35\) | 2.41342 | + | 4.18016i | 0.407942 | + | 0.706577i | ||||
\(36\) | −0.353752 | + | 0.612717i | −0.0589587 | + | 0.102119i | ||||
\(37\) | −0.0219955 | − | 0.0126991i | −0.00361604 | − | 0.00208772i | 0.498191 | − | 0.867067i | \(-0.333998\pi\) |
−0.501807 | + | 0.864980i | \(0.667331\pi\) | |||||||
\(38\) | 8.57233 | 1.39061 | ||||||||
\(39\) | 0.279019 | + | 0.197356i | 0.0446788 | + | 0.0316023i | ||||
\(40\) | −2.63726 | −0.416988 | ||||||||
\(41\) | −0.232051 | − | 0.133975i | −0.0362402 | − | 0.0209233i | 0.481770 | − | 0.876297i | \(-0.339994\pi\) |
−0.518011 | + | 0.855374i | \(0.673327\pi\) | |||||||
\(42\) | 0.342116 | − | 0.592562i | 0.0527896 | − | 0.0914342i | ||||
\(43\) | 1.77944 | + | 3.08209i | 0.271363 | + | 0.470014i | 0.969211 | − | 0.246232i | \(-0.0791924\pi\) |
−0.697848 | + | 0.716246i | \(0.745859\pi\) | |||||||
\(44\) | − | 0.252957i | − | 0.0381347i | ||||||
\(45\) | 2.59030 | − | 1.49551i | 0.386138 | − | 0.222937i | ||||
\(46\) | −9.17716 | + | 5.29844i | −1.35310 | + | 0.781212i | ||||
\(47\) | − | 6.51793i | − | 0.950738i | −0.879787 | − | 0.475369i | \(-0.842315\pi\) | ||
0.879787 | − | 0.475369i | \(-0.157685\pi\) | |||||||
\(48\) | 0.209345 | + | 0.362596i | 0.0302163 | + | 0.0523362i | ||||
\(49\) | 8.14918 | − | 14.1148i | 1.16417 | − | 2.01640i | ||||
\(50\) | −1.29515 | − | 0.747754i | −0.183162 | − | 0.105748i | ||||
\(51\) | −0.337339 | −0.0472368 | ||||||||
\(52\) | 0.774668 | − | 0.356756i | 0.107427 | − | 0.0494732i | ||||
\(53\) | 0.991015 | 0.136126 | 0.0680632 | − | 0.997681i | \(-0.478318\pi\) | ||||
0.0680632 | + | 0.997681i | \(0.478318\pi\) | |||||||
\(54\) | −0.735481 | − | 0.424630i | −0.100086 | − | 0.0577848i | ||||
\(55\) | −0.534695 | + | 0.926118i | −0.0720982 | + | 0.124878i | ||||
\(56\) | 6.36482 | + | 11.0242i | 0.850535 | + | 1.47317i | ||||
\(57\) | 0.543327i | 0.0719655i | ||||||||
\(58\) | −1.90786 | + | 1.10151i | −0.250515 | + | 0.144635i | ||||
\(59\) | −7.55440 | + | 4.36153i | −0.983499 | + | 0.567823i | −0.903325 | − | 0.428958i | \(-0.858881\pi\) |
−0.0801741 | + | 0.996781i | \(0.525548\pi\) | |||||||
\(60\) | 0.0224214i | 0.00289458i | ||||||||
\(61\) | −3.16867 | − | 5.48830i | −0.405707 | − | 0.702704i | 0.588697 | − | 0.808354i | \(-0.299641\pi\) |
−0.994403 | + | 0.105650i | \(0.966308\pi\) | |||||||
\(62\) | 1.09479 | − | 1.89623i | 0.139038 | − | 0.240821i | ||||
\(63\) | −12.5029 | − | 7.21857i | −1.57522 | − | 0.909455i | ||||
\(64\) | −6.84325 | −0.855406 | ||||||||
\(65\) | −3.59030 | − | 0.331331i | −0.445321 | − | 0.0410965i | ||||
\(66\) | 0.151592 | 0.0186597 | ||||||||
\(67\) | −4.48009 | − | 2.58658i | −0.547330 | − | 0.316001i | 0.200714 | − | 0.979650i | \(-0.435674\pi\) |
−0.748044 | + | 0.663649i | \(0.769007\pi\) | |||||||
\(68\) | −0.420915 | + | 0.729047i | −0.0510435 | + | 0.0884099i | ||||
\(69\) | −0.335823 | − | 0.581663i | −0.0404283 | − | 0.0700240i | ||||
\(70\) | 7.21857i | 0.862785i | ||||||||
\(71\) | −6.72458 | + | 3.88244i | −0.798061 | + | 0.460761i | −0.842793 | − | 0.538238i | \(-0.819090\pi\) |
0.0447317 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(72\) | 6.83129 | − | 3.94405i | 0.805075 | − | 0.464810i | ||||
\(73\) | − | 10.1088i | − | 1.18314i | −0.806252 | − | 0.591572i | \(-0.798507\pi\) | ||
0.806252 | − | 0.591572i | \(-0.201493\pi\) | |||||||
\(74\) | −0.0189916 | − | 0.0328945i | −0.00220773 | − | 0.00382391i | ||||
\(75\) | 0.0473938 | − | 0.0820885i | 0.00547256 | − | 0.00947876i | ||||
\(76\) | 1.17422 | + | 0.677939i | 0.134693 | + | 0.0777649i | ||||
\(77\) | 5.16177 | 0.588238 | ||||||||
\(78\) | 0.213797 | + | 0.464243i | 0.0242077 | + | 0.0525651i | ||||
\(79\) | 8.78347 | 0.988218 | 0.494109 | − | 0.869400i | \(-0.335494\pi\) | ||||
0.494109 | + | 0.869400i | \(0.335494\pi\) | |||||||
\(80\) | −3.82535 | − | 2.20857i | −0.427687 | − | 0.246925i | ||||
\(81\) | −4.45961 | + | 7.72427i | −0.495512 | + | 0.858252i | ||||
\(82\) | −0.200360 | − | 0.347034i | −0.0221261 | − | 0.0383235i | ||||
\(83\) | − | 0.725474i | − | 0.0796311i | −0.999207 | − | 0.0398155i | \(-0.987323\pi\) | ||
0.999207 | − | 0.0398155i | \(-0.0126770\pi\) | |||||||
\(84\) | 0.0937250 | − | 0.0541121i | 0.0102262 | − | 0.00590412i | ||||
\(85\) | 3.08209 | − | 1.77944i | 0.334299 | − | 0.193008i | ||||
\(86\) | 5.32235i | 0.573923i | ||||||||
\(87\) | −0.0698151 | − | 0.120923i | −0.00748497 | − | 0.0129643i | ||||
\(88\) | −1.41013 | + | 2.44242i | −0.150320 | + | 0.260363i | ||||
\(89\) | 11.6970 | + | 6.75327i | 1.23988 | + | 0.715845i | 0.969070 | − | 0.246788i | \(-0.0793750\pi\) |
0.270810 | + | 0.962633i | \(0.412708\pi\) | |||||||
\(90\) | 4.47309 | 0.471505 | ||||||||
\(91\) | 7.27987 | + | 15.8077i | 0.763138 | + | 1.65709i | ||||
\(92\) | −1.67610 | −0.174745 | ||||||||
\(93\) | 0.120186 | + | 0.0693893i | 0.0124627 | + | 0.00719534i | ||||
\(94\) | 4.87381 | − | 8.44168i | 0.502695 | − | 0.870693i | ||||
\(95\) | −2.86603 | − | 4.96410i | −0.294048 | − | 0.509306i | ||||
\(96\) | 0.126194i | 0.0128796i | ||||||||
\(97\) | −2.97800 | + | 1.71935i | −0.302371 | + | 0.174574i | −0.643507 | − | 0.765440i | \(-0.722521\pi\) |
0.341137 | + | 0.940014i | \(0.389188\pi\) | |||||||
\(98\) | 21.1088 | − | 12.1872i | 2.13231 | − | 1.23109i | ||||
\(99\) | − | 3.19856i | − | 0.321467i | ||||||
\(100\) | −0.118272 | − | 0.204852i | −0.0118272 | − | 0.0204852i | ||||
\(101\) | 1.42763 | − | 2.47273i | 0.142055 | − | 0.246046i | −0.786215 | − | 0.617953i | \(-0.787962\pi\) |
0.928270 | + | 0.371906i | \(0.121296\pi\) | |||||||
\(102\) | −0.436903 | − | 0.252246i | −0.0432599 | − | 0.0249761i | ||||
\(103\) | 5.54488 | 0.546354 | 0.273177 | − | 0.961964i | \(-0.411926\pi\) | ||||
0.273177 | + | 0.961964i | \(0.411926\pi\) | |||||||
\(104\) | −9.46855 | − | 0.873806i | −0.928468 | − | 0.0856838i | ||||
\(105\) | −0.457524 | −0.0446498 | ||||||||
\(106\) | 1.28351 | + | 0.741035i | 0.124666 | + | 0.0719757i | ||||
\(107\) | 2.22056 | − | 3.84611i | 0.214669 | − | 0.371818i | −0.738501 | − | 0.674252i | \(-0.764466\pi\) |
0.953170 | + | 0.302434i | \(0.0977993\pi\) | |||||||
\(108\) | −0.0671633 | − | 0.116330i | −0.00646280 | − | 0.0111939i | ||||
\(109\) | 13.7804i | 1.31993i | 0.751298 | + | 0.659963i | \(0.229428\pi\) | ||||
−0.751298 | + | 0.659963i | \(0.770572\pi\) | |||||||
\(110\) | −1.38502 | + | 0.799640i | −0.132056 | + | 0.0762427i | ||||
\(111\) | 0.00208490 | − | 0.00120372i | 0.000197890 | − | 0.000114252i | ||||
\(112\) | 21.3208i | 2.01463i | ||||||||
\(113\) | 4.02200 | + | 6.96630i | 0.378358 | + | 0.655334i | 0.990823 | − | 0.135163i | \(-0.0431557\pi\) |
−0.612466 | + | 0.790497i | \(0.709822\pi\) | |||||||
\(114\) | −0.406275 | + | 0.703689i | −0.0380511 | + | 0.0659065i | ||||
\(115\) | 6.13649 | + | 3.54290i | 0.572230 | + | 0.330377i | ||||
\(116\) | −0.348448 | −0.0323526 | ||||||||
\(117\) | 9.79543 | − | 4.51107i | 0.905588 | − | 0.417049i | ||||
\(118\) | −13.0454 | −1.20093 | ||||||||
\(119\) | −14.8767 | − | 8.58909i | −1.36375 | − | 0.787361i | ||||
\(120\) | 0.124990 | − | 0.216489i | 0.0114100 | − | 0.0197626i | ||||
\(121\) | −4.92820 | − | 8.53590i | −0.448018 | − | 0.775991i | ||||
\(122\) | − | 9.47754i | − | 0.858056i | ||||||
\(123\) | 0.0219955 | − | 0.0126991i | 0.00198327 | − | 0.00114504i | ||||
\(124\) | 0.299925 | − | 0.173162i | 0.0269340 | − | 0.0155504i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −10.7954 | − | 18.6982i | −0.961734 | − | 1.66577i | ||||
\(127\) | 0.353326 | − | 0.611979i | 0.0313526 | − | 0.0543044i | −0.849923 | − | 0.526906i | \(-0.823352\pi\) |
0.881276 | + | 0.472602i | \(0.156685\pi\) | |||||||
\(128\) | −11.1690 | − | 6.44840i | −0.987205 | − | 0.569963i | ||||
\(129\) | −0.337339 | −0.0297010 | ||||||||
\(130\) | −4.40221 | − | 3.11378i | −0.386099 | − | 0.273097i | ||||
\(131\) | 6.26554 | 0.547423 | 0.273711 | − | 0.961812i | \(-0.411749\pi\) | ||||
0.273711 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(132\) | 0.0207648 | + | 0.0119886i | 0.00180735 | + | 0.00104347i | ||||
\(133\) | −13.8338 | + | 23.9609i | −1.19955 | + | 2.07767i | ||||
\(134\) | −3.86825 | − | 6.70001i | −0.334166 | − | 0.578793i | ||||
\(135\) | 0.567874i | 0.0488748i | ||||||||
\(136\) | 8.12828 | − | 4.69286i | 0.696994 | − | 0.402410i | ||||
\(137\) | −14.1212 | + | 8.15290i | −1.20646 | + | 0.696549i | −0.961984 | − | 0.273107i | \(-0.911949\pi\) |
−0.244475 | + | 0.969656i | \(0.578616\pi\) | |||||||
\(138\) | − | 1.00445i | − | 0.0855046i | ||||||
\(139\) | 3.41264 | + | 5.91087i | 0.289456 | + | 0.501353i | 0.973680 | − | 0.227919i | \(-0.0731921\pi\) |
−0.684224 | + | 0.729272i | \(0.739859\pi\) | |||||||
\(140\) | −0.570878 | + | 0.988789i | −0.0482480 | + | 0.0835680i | ||||
\(141\) | 0.535047 | + | 0.308909i | 0.0450591 | + | 0.0260149i | ||||
\(142\) | −11.6124 | −0.974494 | ||||||||
\(143\) | −2.22656 | + | 3.14788i | −0.186195 | + | 0.263239i | ||||
\(144\) | 13.2117 | 1.10098 | ||||||||
\(145\) | 1.27573 | + | 0.736543i | 0.105944 | + | 0.0611666i | ||||
\(146\) | 7.55889 | − | 13.0924i | 0.625578 | − | 1.08353i | ||||
\(147\) | 0.772442 | + | 1.33791i | 0.0637099 | + | 0.110349i | ||||
\(148\) | − | 0.00600778i | − | 0.000493837i | ||||||
\(149\) | −7.30887 | + | 4.21978i | −0.598766 | + | 0.345698i | −0.768556 | − | 0.639783i | \(-0.779024\pi\) |
0.169790 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(150\) | 0.122764 | − | 0.0708778i | 0.0100236 | − | 0.00578715i | ||||
\(151\) | 1.37017i | 0.111503i | 0.998445 | + | 0.0557513i | \(0.0177554\pi\) | ||||
−0.998445 | + | 0.0557513i | \(0.982245\pi\) | |||||||
\(152\) | −7.55846 | − | 13.0916i | −0.613072 | − | 1.06187i | ||||
\(153\) | −5.32235 | + | 9.21857i | −0.430286 | + | 0.745278i | ||||
\(154\) | 6.68525 | + | 3.85973i | 0.538713 | + | 0.311026i | ||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | −0.00742888 | + | 0.0804993i | −0.000594787 | + | 0.00644510i | ||||
\(157\) | 11.9700 | 0.955311 | 0.477656 | − | 0.878547i | \(-0.341487\pi\) | ||||
0.477656 | + | 0.878547i | \(0.341487\pi\) | |||||||
\(158\) | 11.3759 | + | 6.56787i | 0.905017 | + | 0.522512i | ||||
\(159\) | −0.0469680 | + | 0.0813509i | −0.00372480 | + | 0.00645155i | ||||
\(160\) | −0.665665 | − | 1.15297i | −0.0526255 | − | 0.0911500i | ||||
\(161\) | − | 34.2020i | − | 2.69550i | ||||||
\(162\) | −11.5517 | + | 6.66938i | −0.907588 | + | 0.523996i | ||||
\(163\) | 19.5474 | − | 11.2857i | 1.53107 | − | 0.883962i | 0.531754 | − | 0.846899i | \(-0.321533\pi\) |
0.999313 | − | 0.0370630i | \(-0.0118002\pi\) | |||||||
\(164\) | − | 0.0633815i | − | 0.00494927i | ||||||
\(165\) | −0.0506824 | − | 0.0877845i | −0.00394562 | − | 0.00683402i | ||||
\(166\) | 0.542476 | − | 0.939595i | 0.0421043 | − | 0.0729267i | ||||
\(167\) | 7.09881 | + | 4.09850i | 0.549323 | + | 0.317152i | 0.748849 | − | 0.662741i | \(-0.230607\pi\) |
−0.199526 | + | 0.979893i | \(0.563940\pi\) | |||||||
\(168\) | −1.20661 | −0.0930922 | ||||||||
\(169\) | −12.7804 | − | 2.37915i | −0.983111 | − | 0.183012i | ||||
\(170\) | 5.32235 | 0.408205 | ||||||||
\(171\) | 14.8477 | + | 8.57233i | 1.13543 | + | 0.655542i | ||||
\(172\) | −0.420915 | + | 0.729047i | −0.0320945 | + | 0.0555893i | ||||
\(173\) | −4.58386 | − | 7.93948i | −0.348505 | − | 0.603628i | 0.637479 | − | 0.770467i | \(-0.279977\pi\) |
−0.985984 | + | 0.166840i | \(0.946644\pi\) | |||||||
\(174\) | − | 0.208818i | − | 0.0158305i | ||||||
\(175\) | 4.18016 | − | 2.41342i | 0.315991 | − | 0.182437i | ||||
\(176\) | −4.09079 | + | 2.36182i | −0.308355 | + | 0.178029i | ||||
\(177\) | − | 0.826838i | − | 0.0621490i | ||||||
\(178\) | 10.0996 | + | 17.4930i | 0.756994 | + | 1.31115i | ||||
\(179\) | −5.01850 | + | 8.69229i | −0.375100 | + | 0.649693i | −0.990342 | − | 0.138646i | \(-0.955725\pi\) |
0.615242 | + | 0.788338i | \(0.289058\pi\) | |||||||
\(180\) | 0.612717 | + | 0.353752i | 0.0456692 | + | 0.0263671i | ||||
\(181\) | −17.0238 | −1.26537 | −0.632686 | − | 0.774408i | \(-0.718048\pi\) | ||||
−0.632686 | + | 0.774408i | \(0.718048\pi\) | |||||||
\(182\) | −2.39174 | + | 25.9168i | −0.177287 | + | 1.92108i | ||||
\(183\) | 0.600701 | 0.0444051 | ||||||||
\(184\) | 16.1835 | + | 9.34356i | 1.19307 | + | 0.688817i | ||||
\(185\) | −0.0126991 | + | 0.0219955i | −0.000933659 | + | 0.00161714i | ||||
\(186\) | 0.103772 | + | 0.179739i | 0.00760895 | + | 0.0131791i | ||||
\(187\) | − | 3.80584i | − | 0.278310i | ||||||
\(188\) | 1.33521 | − | 0.770886i | 0.0973804 | − | 0.0562226i | ||||
\(189\) | 2.37381 | − | 1.37052i | 0.172669 | − | 0.0996905i | ||||
\(190\) | − | 8.57233i | − | 0.621902i | ||||||
\(191\) | 1.93870 | + | 3.35793i | 0.140280 | + | 0.242971i | 0.927602 | − | 0.373570i | \(-0.121867\pi\) |
−0.787322 | + | 0.616542i | \(0.788533\pi\) | |||||||
\(192\) | 0.324328 | − | 0.561752i | 0.0234063 | − | 0.0405410i | ||||
\(193\) | 1.08595 | + | 0.626972i | 0.0781681 | + | 0.0451304i | 0.538575 | − | 0.842578i | \(-0.318963\pi\) |
−0.460406 | + | 0.887708i | \(0.652296\pi\) | |||||||
\(194\) | −5.14261 | −0.369218 | ||||||||
\(195\) | 0.197356 | − | 0.279019i | 0.0141330 | − | 0.0199810i | ||||
\(196\) | 3.85527 | 0.275376 | ||||||||
\(197\) | 13.2346 | + | 7.64098i | 0.942923 | + | 0.544397i | 0.890876 | − | 0.454247i | \(-0.150092\pi\) |
0.0520479 | + | 0.998645i | \(0.483425\pi\) | |||||||
\(198\) | 2.39174 | − | 4.14261i | 0.169973 | − | 0.294402i | ||||
\(199\) | −6.61480 | − | 11.4572i | −0.468911 | − | 0.812177i | 0.530458 | − | 0.847711i | \(-0.322020\pi\) |
−0.999368 | + | 0.0355340i | \(0.988687\pi\) | |||||||
\(200\) | 2.63726i | 0.186483i | ||||||||
\(201\) | 0.424657 | − | 0.245176i | 0.0299530 | − | 0.0172934i | ||||
\(202\) | 3.69799 | − | 2.13504i | 0.260190 | − | 0.150221i | ||||
\(203\) | − | 7.11035i | − | 0.499049i | ||||||
\(204\) | −0.0398976 | − | 0.0691046i | −0.00279339 | − | 0.00483829i | ||||
\(205\) | −0.133975 | + | 0.232051i | −0.00935719 | + | 0.0162071i | ||||
\(206\) | 7.18144 | + | 4.14621i | 0.500355 | + | 0.288880i | ||||
\(207\) | −21.1937 | −1.47307 | ||||||||
\(208\) | −13.0024 | − | 9.19686i | −0.901552 | − | 0.637688i | ||||
\(209\) | −6.12979 | −0.424007 | ||||||||
\(210\) | −0.592562 | − | 0.342116i | −0.0408906 | − | 0.0236082i | ||||
\(211\) | 2.40521 | − | 4.16595i | 0.165582 | − | 0.286796i | −0.771280 | − | 0.636496i | \(-0.780383\pi\) |
0.936862 | + | 0.349700i | \(0.113717\pi\) | |||||||
\(212\) | 0.117209 | + | 0.203012i | 0.00804994 | + | 0.0139429i | ||||
\(213\) | − | 0.736014i | − | 0.0504309i | ||||||
\(214\) | 5.75189 | − | 3.32086i | 0.393191 | − | 0.227009i | ||||
\(215\) | 3.08209 | − | 1.77944i | 0.210197 | − | 0.121357i | ||||
\(216\) | 1.49763i | 0.101901i | ||||||||
\(217\) | 3.53349 | + | 6.12019i | 0.239869 | + | 0.415465i | ||||
\(218\) | −10.3044 | + | 17.8477i | −0.697900 | + | 1.20880i | ||||
\(219\) | 0.829815 | + | 0.479094i | 0.0560737 | + | 0.0323742i | ||||
\(220\) | −0.252957 | −0.0170543 | ||||||||
\(221\) | 11.6552 | − | 5.36754i | 0.784013 | − | 0.361060i | ||||
\(222\) | 0.00360034 | 0.000241639 | ||||||||
\(223\) | −12.7420 | − | 7.35661i | −0.853269 | − | 0.492635i | 0.00848317 | − | 0.999964i | \(-0.497300\pi\) |
−0.861753 | + | 0.507329i | \(0.830633\pi\) | |||||||
\(224\) | −3.21306 | + | 5.56518i | −0.214682 | + | 0.371839i | ||||
\(225\) | −1.49551 | − | 2.59030i | −0.0997005 | − | 0.172686i | ||||
\(226\) | 12.0299i | 0.800214i | ||||||||
\(227\) | 12.9062 | − | 7.45140i | 0.856615 | − | 0.494567i | −0.00626222 | − | 0.999980i | \(-0.501993\pi\) |
0.862877 | + | 0.505413i | \(0.168660\pi\) | |||||||
\(228\) | −0.111302 | + | 0.0642602i | −0.00737115 | + | 0.00425573i | ||||
\(229\) | 19.3074i | 1.27587i | 0.770092 | + | 0.637933i | \(0.220210\pi\) | ||||
−0.770092 | + | 0.637933i | \(0.779790\pi\) | |||||||
\(230\) | 5.29844 | + | 9.17716i | 0.349369 | + | 0.605124i | ||||
\(231\) | −0.244636 | + | 0.423722i | −0.0160959 | + | 0.0278788i | ||||
\(232\) | 3.36444 | + | 1.94246i | 0.220886 | + | 0.127529i | ||||
\(233\) | 21.1937 | 1.38845 | 0.694224 | − | 0.719759i | \(-0.255748\pi\) | ||||
0.694224 | + | 0.719759i | \(0.255748\pi\) | |||||||
\(234\) | 16.0597 | + | 1.48207i | 1.04986 | + | 0.0968860i | ||||
\(235\) | −6.51793 | −0.425183 | ||||||||
\(236\) | −1.78694 | − | 1.03169i | −0.116320 | − | 0.0671573i | ||||
\(237\) | −0.416282 | + | 0.721022i | −0.0270404 | + | 0.0468354i | ||||
\(238\) | −12.8451 | − | 22.2483i | −0.832621 | − | 1.44214i | ||||
\(239\) | − | 14.8971i | − | 0.963612i | −0.876278 | − | 0.481806i | \(-0.839981\pi\) | ||
0.876278 | − | 0.481806i | \(-0.160019\pi\) | |||||||
\(240\) | 0.362596 | − | 0.209345i | 0.0234055 | − | 0.0135131i | ||||
\(241\) | −8.13343 | + | 4.69584i | −0.523921 | + | 0.302486i | −0.738537 | − | 0.674213i | \(-0.764483\pi\) |
0.214617 | + | 0.976698i | \(0.431150\pi\) | |||||||
\(242\) | − | 14.7403i | − | 0.947544i | ||||||
\(243\) | −1.27453 | − | 2.20754i | −0.0817609 | − | 0.141614i | ||||
\(244\) | 0.749527 | − | 1.29822i | 0.0479835 | − | 0.0831099i | ||||
\(245\) | −14.1148 | − | 8.14918i | −0.901762 | − | 0.520632i | ||||
\(246\) | 0.0379833 | 0.00242173 | ||||||||
\(247\) | −8.64512 | − | 18.7722i | −0.550076 | − | 1.19445i | ||||
\(248\) | −3.86122 | −0.245188 | ||||||||
\(249\) | 0.0595530 | + | 0.0343829i | 0.00377402 | + | 0.00217893i | ||||
\(250\) | −0.747754 | + | 1.29515i | −0.0472921 | + | 0.0819123i | ||||
\(251\) | 5.65817 | + | 9.80024i | 0.357140 | + | 0.618585i | 0.987482 | − | 0.157733i | \(-0.0504184\pi\) |
−0.630341 | + | 0.776318i | \(0.717085\pi\) | |||||||
\(252\) | − | 3.41501i | − | 0.215125i | ||||||
\(253\) | 6.56229 | − | 3.78874i | 0.412568 | − | 0.238196i | ||||
\(254\) | 0.915219 | − | 0.528402i | 0.0574260 | − | 0.0331549i | ||||
\(255\) | 0.337339i | 0.0211250i | ||||||||
\(256\) | −2.80038 | − | 4.85040i | −0.175024 | − | 0.303150i | ||||
\(257\) | −13.2660 | + | 22.9773i | −0.827508 | + | 1.43329i | 0.0724788 | + | 0.997370i | \(0.476909\pi\) |
−0.899987 | + | 0.435917i | \(0.856424\pi\) | |||||||
\(258\) | −0.436903 | − | 0.252246i | −0.0272004 | − | 0.0157042i | ||||
\(259\) | 0.122593 | 0.00761758 | ||||||||
\(260\) | −0.356756 | − | 0.774668i | −0.0221251 | − | 0.0480428i | ||||
\(261\) | −4.40602 | −0.272726 | ||||||||
\(262\) | 8.11480 | + | 4.68508i | 0.501334 | + | 0.289445i | ||||
\(263\) | 7.07038 | − | 12.2463i | 0.435979 | − | 0.755137i | −0.561396 | − | 0.827547i | \(-0.689736\pi\) |
0.997375 | + | 0.0724100i | \(0.0230690\pi\) | |||||||
\(264\) | −0.133663 | − | 0.231511i | −0.00822638 | − | 0.0142485i | ||||
\(265\) | − | 0.991015i | − | 0.0608776i | ||||||
\(266\) | −35.8337 | + | 20.6886i | −2.19711 | + | 1.26850i | ||||
\(267\) | −1.10873 | + | 0.640126i | −0.0678532 | + | 0.0391751i | ||||
\(268\) | − | 1.22368i | − | 0.0747479i | ||||||
\(269\) | −12.3872 | − | 21.4553i | −0.755264 | − | 1.30815i | −0.945243 | − | 0.326367i | \(-0.894176\pi\) |
0.189980 | − | 0.981788i | \(-0.439158\pi\) | |||||||
\(270\) | −0.424630 | + | 0.735481i | −0.0258422 | + | 0.0447599i | ||||
\(271\) | 16.2095 | + | 9.35856i | 0.984657 | + | 0.568492i | 0.903673 | − | 0.428224i | \(-0.140860\pi\) |
0.0809839 | + | 0.996715i | \(0.474194\pi\) | |||||||
\(272\) | 15.7201 | 0.953170 | ||||||||
\(273\) | −1.64265 | − | 0.151592i | −0.0994176 | − | 0.00917476i | ||||
\(274\) | −24.3854 | −1.47318 | ||||||||
\(275\) | 0.926118 | + | 0.534695i | 0.0558470 | + | 0.0322433i | ||||
\(276\) | 0.0794367 | − | 0.137588i | 0.00478152 | − | 0.00828184i | ||||
\(277\) | −11.3323 | − | 19.6282i | −0.680893 | − | 1.17934i | −0.974709 | − | 0.223480i | \(-0.928258\pi\) |
0.293815 | − | 0.955862i | \(-0.405075\pi\) | |||||||
\(278\) | 10.2073i | 0.612191i | ||||||||
\(279\) | 3.79246 | − | 2.18958i | 0.227048 | − | 0.131086i | ||||
\(280\) | 11.0242 | − | 6.36482i | 0.658822 | − | 0.380371i | ||||
\(281\) | 27.8384i | 1.66070i | 0.557241 | + | 0.830351i | \(0.311860\pi\) | ||||
−0.557241 | + | 0.830351i | \(0.688140\pi\) | |||||||
\(282\) | 0.461976 | + | 0.800167i | 0.0275103 | + | 0.0476492i | ||||
\(283\) | 3.96004 | − | 6.85898i | 0.235400 | − | 0.407724i | −0.723989 | − | 0.689811i | \(-0.757693\pi\) |
0.959389 | + | 0.282087i | \(0.0910268\pi\) | |||||||
\(284\) | −1.59065 | − | 0.918364i | −0.0943879 | − | 0.0544949i | ||||
\(285\) | 0.543327 | 0.0321839 | ||||||||
\(286\) | −5.23757 | + | 2.41204i | −0.309704 | + | 0.142627i | ||||
\(287\) | 1.29335 | 0.0763439 | ||||||||
\(288\) | 3.44854 | + | 1.99102i | 0.203207 | + | 0.117322i | ||||
\(289\) | 2.16715 | − | 3.75362i | 0.127480 | − | 0.220801i | ||||
\(290\) | 1.10151 | + | 1.90786i | 0.0646827 | + | 0.112034i | ||||
\(291\) | − | 0.325946i | − | 0.0191073i | ||||||
\(292\) | 2.07081 | − | 1.19558i | 0.121185 | − | 0.0699662i | ||||
\(293\) | 0.236400 | − | 0.136485i | 0.0138106 | − | 0.00797356i | −0.493079 | − | 0.869985i | \(-0.664129\pi\) |
0.506889 | + | 0.862011i | \(0.330795\pi\) | |||||||
\(294\) | 2.31038i | 0.134744i | ||||||||
\(295\) | 4.36153 | + | 7.55440i | 0.253938 | + | 0.439834i | ||||
\(296\) | −0.0334909 | + | 0.0580080i | −0.00194662 | + | 0.00337165i | ||||
\(297\) | 0.525918 | + | 0.303639i | 0.0305169 | + | 0.0176189i | ||||
\(298\) | −12.6214 | −0.731139 | ||||||||
\(299\) | 20.8579 | + | 14.7533i | 1.20624 | + | 0.853204i | ||||
\(300\) | 0.0224214 | 0.00129450 | ||||||||
\(301\) | −14.8767 | − | 8.58909i | −0.857481 | − | 0.495067i | ||||
\(302\) | −1.02455 | + | 1.77457i | −0.0589560 | + | 0.102115i | ||||
\(303\) | 0.135322 | + | 0.234385i | 0.00777404 | + | 0.0134650i | ||||
\(304\) | − | 25.3192i | − | 1.45216i | ||||||
\(305\) | −5.48830 | + | 3.16867i | −0.314259 | + | 0.181437i | ||||
\(306\) | −13.7864 | + | 7.95961i | −0.788119 | + | 0.455021i | ||||
\(307\) | − | 6.85224i | − | 0.391078i | −0.980696 | − | 0.195539i | \(-0.937354\pi\) | ||
0.980696 | − | 0.195539i | \(-0.0626456\pi\) | |||||||
\(308\) | 0.610491 | + | 1.05740i | 0.0347859 | + | 0.0602510i | ||||
\(309\) | −0.262793 | + | 0.455171i | −0.0149498 | + | 0.0258938i | ||||
\(310\) | −1.89623 | − | 1.09479i | −0.107698 | − | 0.0621798i | ||||
\(311\) | −10.6447 | −0.603605 | −0.301803 | − | 0.953370i | \(-0.597588\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597588\pi\) | |||||||
\(312\) | 0.520480 | − | 0.735846i | 0.0294664 | − | 0.0416591i | ||||
\(313\) | 17.8236 | 1.00745 | 0.503724 | − | 0.863865i | \(-0.331963\pi\) | ||||
0.503724 | + | 0.863865i | \(0.331963\pi\) | |||||||
\(314\) | 15.5029 | + | 8.95062i | 0.874881 | + | 0.505113i | ||||
\(315\) | −7.21857 | + | 12.5029i | −0.406721 | + | 0.704461i | ||||
\(316\) | 1.03883 | + | 1.79931i | 0.0584390 | + | 0.101219i | ||||
\(317\) | 8.17161i | 0.458963i | 0.973313 | + | 0.229482i | \(0.0737031\pi\) | ||||
−0.973313 | + | 0.229482i | \(0.926297\pi\) | |||||||
\(318\) | −0.121661 | + | 0.0702410i | −0.00682241 | + | 0.00393892i | ||||
\(319\) | 1.36425 | − | 0.787651i | 0.0763835 | − | 0.0441000i | ||||
\(320\) | 6.84325i | 0.382549i | ||||||||
\(321\) | 0.210481 | + | 0.364564i | 0.0117479 | + | 0.0203480i | ||||
\(322\) | 25.5747 | − | 44.2967i | 1.42522 | − | 2.46856i | ||||
\(323\) | 17.6667 | + | 10.1999i | 0.983001 | + | 0.567536i | ||||
\(324\) | −2.10978 | −0.117210 | ||||||||
\(325\) | −0.331331 | + | 3.59030i | −0.0183789 | + | 0.199154i | ||||
\(326\) | 33.7556 | 1.86955 | ||||||||
\(327\) | −1.13122 | − | 0.653107i | −0.0625563 | − | 0.0361169i | ||||
\(328\) | −0.353326 | + | 0.611979i | −0.0195092 | + | 0.0337909i | ||||
\(329\) | 15.7305 | + | 27.2460i | 0.867250 | + | 1.50212i | ||||
\(330\) | − | 0.151592i | − | 0.00834486i | ||||||
\(331\) | 21.5983 | − | 12.4698i | 1.18715 | − | 0.685400i | 0.229490 | − | 0.973311i | \(-0.426294\pi\) |
0.957657 | + | 0.287911i | \(0.0929608\pi\) | |||||||
\(332\) | 0.148615 | − | 0.0858029i | 0.00815631 | − | 0.00470905i | ||||
\(333\) | − | 0.0759666i | − | 0.00416294i | ||||||
\(334\) | 6.12934 | + | 10.6163i | 0.335383 | + | 0.580900i | ||||
\(335\) | −2.58658 | + | 4.48009i | −0.141320 | + | 0.244773i | ||||
\(336\) | −1.75019 | − | 1.01047i | −0.0954807 | − | 0.0551258i | ||||
\(337\) | 19.6057 | 1.06799 | 0.533996 | − | 0.845487i | \(-0.320690\pi\) | ||||
0.533996 | + | 0.845487i | \(0.320690\pi\) | |||||||
\(338\) | −14.7735 | − | 12.6380i | −0.803575 | − | 0.687415i | ||||
\(339\) | −0.762471 | −0.0414117 | ||||||||
\(340\) | 0.729047 | + | 0.420915i | 0.0395381 | + | 0.0228273i | ||||
\(341\) | −0.782847 | + | 1.35593i | −0.0423936 | + | 0.0734278i | ||||
\(342\) | 12.8200 | + | 22.2049i | 0.693225 | + | 1.20070i | ||||
\(343\) | 44.8817i | 2.42339i | ||||||||
\(344\) | 8.12828 | − | 4.69286i | 0.438247 | − | 0.253022i | ||||
\(345\) | −0.581663 | + | 0.335823i | −0.0313157 | + | 0.0180801i | ||||
\(346\) | − | 13.7104i | − | 0.737076i | ||||||
\(347\) | −8.54049 | − | 14.7926i | −0.458478 | − | 0.794107i | 0.540403 | − | 0.841406i | \(-0.318272\pi\) |
−0.998881 | + | 0.0472996i | \(0.984938\pi\) | |||||||
\(348\) | 0.0165143 | − | 0.0286036i | 0.000885259 | − | 0.00153331i | ||||
\(349\) | −24.5708 | − | 14.1860i | −1.31525 | − | 0.759357i | −0.332286 | − | 0.943179i | \(-0.607820\pi\) |
−0.982960 | + | 0.183822i | \(0.941153\pi\) | |||||||
\(350\) | 7.21857 | 0.385849 | ||||||||
\(351\) | −0.188154 | + | 2.03883i | −0.0100429 | + | 0.108825i | ||||
\(352\) | −1.42371 | −0.0758840 | ||||||||
\(353\) | −18.4047 | − | 10.6260i | −0.979586 | − | 0.565564i | −0.0774407 | − | 0.996997i | \(-0.524675\pi\) |
−0.902145 | + | 0.431433i | \(0.858008\pi\) | |||||||
\(354\) | 0.618272 | − | 1.07088i | 0.0328608 | − | 0.0569165i | ||||
\(355\) | 3.88244 | + | 6.72458i | 0.206058 | + | 0.356904i | ||||
\(356\) | 3.19488i | 0.169328i | ||||||||
\(357\) | 1.41013 | − | 0.814139i | 0.0746320 | − | 0.0430888i | ||||
\(358\) | −12.9994 | + | 7.50520i | −0.687039 | + | 0.396662i | ||||
\(359\) | − | 32.6519i | − | 1.72330i | −0.507502 | − | 0.861650i | \(-0.669431\pi\) | ||
0.507502 | − | 0.861650i | \(-0.330569\pi\) | |||||||
\(360\) | −3.94405 | − | 6.83129i | −0.207870 | − | 0.360041i | ||||
\(361\) | 6.92820 | − | 12.0000i | 0.364642 | − | 0.631579i | ||||
\(362\) | −22.0484 | − | 12.7296i | −1.15884 | − | 0.669055i | ||||
\(363\) | 0.934265 | 0.0490362 | ||||||||
\(364\) | −2.37724 | + | 3.36090i | −0.124601 | + | 0.176159i | ||||
\(365\) | −10.1088 | −0.529118 | ||||||||
\(366\) | 0.777997 | + | 0.449176i | 0.0406665 | + | 0.0234788i | ||||
\(367\) | 2.95918 | − | 5.12546i | 0.154468 | − | 0.267547i | −0.778397 | − | 0.627772i | \(-0.783967\pi\) |
0.932865 | + | 0.360226i | \(0.117300\pi\) | |||||||
\(368\) | 15.6495 | + | 27.1057i | 0.815785 | + | 1.41298i | ||||
\(369\) | − | 0.801440i | − | 0.0417213i | ||||||
\(370\) | −0.0328945 | + | 0.0189916i | −0.00171010 | + | 0.000987329i | ||||
\(371\) | −4.14261 | + | 2.39174i | −0.215073 | + | 0.124173i | ||||
\(372\) | 0.0328271i | 0.00170201i | ||||||||
\(373\) | 6.65926 | + | 11.5342i | 0.344803 | + | 0.597217i | 0.985318 | − | 0.170729i | \(-0.0546123\pi\) |
−0.640515 | + | 0.767946i | \(0.721279\pi\) | |||||||
\(374\) | 2.84583 | − | 4.92912i | 0.147154 | − | 0.254879i | ||||
\(375\) | −0.0820885 | − | 0.0473938i | −0.00423903 | − | 0.00244740i | ||||
\(376\) | −17.1895 | −0.886480 | ||||||||
\(377\) | 4.33621 | + | 3.06710i | 0.223326 | + | 0.157963i | ||||
\(378\) | 4.09924 | 0.210842 | ||||||||
\(379\) | −22.0131 | − | 12.7093i | −1.13074 | − | 0.652832i | −0.186617 | − | 0.982433i | \(-0.559752\pi\) |
−0.944120 | + | 0.329601i | \(0.893086\pi\) | |||||||
\(380\) | 0.677939 | − | 1.17422i | 0.0347775 | − | 0.0602364i | ||||
\(381\) | 0.0334909 | + | 0.0580080i | 0.00171579 | + | 0.00297184i | ||||
\(382\) | 5.79869i | 0.296687i | ||||||||
\(383\) | −9.37632 | + | 5.41342i | −0.479107 | + | 0.276613i | −0.720044 | − | 0.693928i | \(-0.755879\pi\) |
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(384\) | 1.05868 | − | 0.611228i | 0.0540254 | − | 0.0311916i | ||||
\(385\) | − | 5.16177i | − | 0.263068i | ||||||
\(386\) | 0.937641 | + | 1.62404i | 0.0477247 | + | 0.0826615i | ||||
\(387\) | −5.32235 | + | 9.21857i | −0.270550 | + | 0.468606i | ||||
\(388\) | −0.704427 | − | 0.406701i | −0.0357618 | − | 0.0206471i | ||||
\(389\) | 23.0370 | 1.16802 | 0.584011 | − | 0.811746i | \(-0.301482\pi\) | ||||
0.584011 | + | 0.811746i | \(0.301482\pi\) | |||||||
\(390\) | 0.464243 | − | 0.213797i | 0.0235078 | − | 0.0108260i | ||||
\(391\) | −25.2176 | −1.27531 | ||||||||
\(392\) | −37.2244 | − | 21.4915i | −1.88012 | − | 1.08549i | ||||
\(393\) | −0.296948 | + | 0.514329i | −0.0149790 | + | 0.0259444i | ||||
\(394\) | 11.4271 | + | 19.7924i | 0.575691 | + | 0.997126i | ||||
\(395\) | − | 8.78347i | − | 0.441944i | ||||||
\(396\) | 0.655233 | − | 0.378299i | 0.0329267 | − | 0.0190102i | ||||
\(397\) | −18.2614 | + | 10.5432i | −0.916512 | + | 0.529149i | −0.882521 | − | 0.470273i | \(-0.844155\pi\) |
−0.0339917 | + | 0.999422i | \(0.510822\pi\) | |||||||
\(398\) | − | 19.7850i | − | 0.991731i | ||||||
\(399\) | −1.31128 | − | 2.27120i | −0.0656459 | − | 0.113702i | ||||
\(400\) | −2.20857 | + | 3.82535i | −0.110428 | + | 0.191267i | ||||
\(401\) | −17.1273 | − | 9.88845i | −0.855296 | − | 0.493805i | 0.00713812 | − | 0.999975i | \(-0.497728\pi\) |
−0.862434 | + | 0.506169i | \(0.831061\pi\) | |||||||
\(402\) | 0.733324 | 0.0365749 | ||||||||
\(403\) | −5.25656 | − | 0.485102i | −0.261848 | − | 0.0241646i | ||||
\(404\) | 0.675394 | 0.0336021 | ||||||||
\(405\) | 7.72427 | + | 4.45961i | 0.383822 | + | 0.221600i | ||||
\(406\) | 5.31679 | − | 9.20895i | 0.263868 | − | 0.457033i | ||||
\(407\) | 0.0135803 | + | 0.0235218i | 0.000673151 | + | 0.00116593i | ||||
\(408\) | 0.889650i | 0.0440443i | ||||||||
\(409\) | −27.6096 | + | 15.9404i | −1.36521 | + | 0.788204i | −0.990312 | − | 0.138862i | \(-0.955655\pi\) |
−0.374897 | + | 0.927066i | \(0.622322\pi\) | |||||||
\(410\) | −0.347034 | + | 0.200360i | −0.0171388 | + | 0.00989508i | ||||
\(411\) | − | 1.54559i | − | 0.0762382i | ||||||
\(412\) | 0.655802 | + | 1.13588i | 0.0323090 | + | 0.0559609i | ||||
\(413\) | 21.0524 | − | 36.4639i | 1.03592 | − | 1.79427i | ||||
\(414\) | −27.4490 | − | 15.8477i | −1.34905 | − | 0.778872i | ||||
\(415\) | −0.725474 | −0.0356121 | ||||||||
\(416\) | −2.00792 | − | 4.36004i | −0.0984465 | − | 0.213769i | ||||
\(417\) | −0.646952 | −0.0316814 | ||||||||
\(418\) | −7.93899 | − | 4.58358i | −0.388309 | − | 0.224190i | ||||
\(419\) | −15.3648 | + | 26.6127i | −0.750621 | + | 1.30011i | 0.196902 | + | 0.980423i | \(0.436912\pi\) |
−0.947522 | + | 0.319690i | \(0.896421\pi\) | |||||||
\(420\) | −0.0541121 | − | 0.0937250i | −0.00264040 | − | 0.00457331i | ||||
\(421\) | 17.9820i | 0.876391i | 0.898880 | + | 0.438195i | \(0.144382\pi\) | ||||
−0.898880 | + | 0.438195i | \(0.855618\pi\) | |||||||
\(422\) | 6.23021 | − | 3.59701i | 0.303282 | − | 0.175100i | ||||
\(423\) | 16.8834 | − | 9.74761i | 0.820897 | − | 0.473945i | ||||
\(424\) | − | 2.61357i | − | 0.126926i | ||||||
\(425\) | −1.77944 | − | 3.08209i | −0.0863157 | − | 0.149503i | ||||
\(426\) | 0.550357 | − | 0.953247i | 0.0266649 | − | 0.0461850i | ||||
\(427\) | 26.4911 | + | 15.2947i | 1.28200 | + | 0.740160i | ||||
\(428\) | 1.05051 | 0.0507785 | ||||||||
\(429\) | −0.152879 | − | 0.331965i | −0.00738107 | − | 0.0160274i | ||||
\(430\) | 5.32235 | 0.256666 | ||||||||
\(431\) | −4.24308 | − | 2.44974i | −0.204382 | − | 0.118000i | 0.394316 | − | 0.918975i | \(-0.370982\pi\) |
−0.598698 | + | 0.800975i | \(0.704315\pi\) | |||||||
\(432\) | −1.25419 | + | 2.17232i | −0.0603421 | + | 0.104516i | ||||
\(433\) | −9.61972 | − | 16.6618i | −0.462294 | − | 0.800717i | 0.536781 | − | 0.843722i | \(-0.319640\pi\) |
−0.999075 | + | 0.0430048i | \(0.986307\pi\) | |||||||
\(434\) | 10.5687i | 0.507315i | ||||||||
\(435\) | −0.120923 | + | 0.0698151i | −0.00579783 | + | 0.00334738i | ||||
\(436\) | −2.82296 | + | 1.62983i | −0.135195 | + | 0.0780549i | ||||
\(437\) | 40.6162i | 1.94294i | ||||||||
\(438\) | 0.716489 | + | 1.24100i | 0.0342352 | + | 0.0592970i | ||||
\(439\) | −4.27987 | + | 7.41295i | −0.204267 | + | 0.353801i | −0.949899 | − | 0.312557i | \(-0.898814\pi\) |
0.745632 | + | 0.666358i | \(0.232148\pi\) | |||||||
\(440\) | 2.44242 | + | 1.41013i | 0.116438 | + | 0.0672253i | ||||
\(441\) | 48.7487 | 2.32137 | ||||||||
\(442\) | 19.1088 | + | 1.76346i | 0.908913 | + | 0.0838791i | ||||
\(443\) | −37.9652 | −1.80378 | −0.901891 | − | 0.431965i | \(-0.857821\pi\) | ||||
−0.901891 | + | 0.431965i | \(0.857821\pi\) | |||||||
\(444\) | 0.000493170 | 0 | 0.000284732i | 2.34048e−5 | 0 | 1.35128e-5i | ||||
\(445\) | 6.75327 | − | 11.6970i | 0.320136 | − | 0.554491i | ||||
\(446\) | −11.0019 | − | 19.0558i | −0.520954 | − | 0.902318i | ||||
\(447\) | − | 0.799965i | − | 0.0378370i | ||||||
\(448\) | 28.6059 | − | 16.5156i | 1.35150 | − | 0.780290i | ||||
\(449\) | 23.1283 | − | 13.3531i | 1.09149 | − | 0.630173i | 0.157518 | − | 0.987516i | \(-0.449651\pi\) |
0.933973 | + | 0.357344i | \(0.116317\pi\) | |||||||
\(450\) | − | 4.47309i | − | 0.210863i | ||||||
\(451\) | 0.143271 | + | 0.248153i | 0.00674637 | + | 0.0116851i | ||||
\(452\) | −0.951375 | + | 1.64783i | −0.0447489 | + | 0.0775074i | ||||
\(453\) | −0.112475 | − | 0.0649373i | −0.00528453 | − | 0.00305102i | ||||
\(454\) | 22.2873 | 1.04599 | ||||||||
\(455\) | 15.8077 | − | 7.27987i | 0.741075 | − | 0.341286i | ||||
\(456\) | 1.43290 | 0.0671016 | ||||||||
\(457\) | 3.69903 | + | 2.13563i | 0.173033 | + | 0.0999007i | 0.584015 | − | 0.811743i | \(-0.301481\pi\) |
−0.410982 | + | 0.911643i | \(0.634814\pi\) | |||||||
\(458\) | −14.4371 | + | 25.0059i | −0.674604 | + | 1.16845i | ||||
\(459\) | −1.01050 | − | 1.75024i | −0.0471661 | − | 0.0816941i | ||||
\(460\) | 1.67610i | 0.0781485i | ||||||||
\(461\) | 17.8767 | − | 10.3211i | 0.832603 | − | 0.480704i | −0.0221401 | − | 0.999755i | \(-0.507048\pi\) |
0.854743 | + | 0.519051i | \(0.173715\pi\) | |||||||
\(462\) | −0.633679 | + | 0.365855i | −0.0294814 | + | 0.0170211i | ||||
\(463\) | 32.1040i | 1.49200i | 0.665947 | + | 0.745999i | \(0.268028\pi\) | ||||
−0.665947 | + | 0.745999i | \(0.731972\pi\) | |||||||
\(464\) | 3.25341 | + | 5.63507i | 0.151036 | + | 0.261602i | ||||
\(465\) | 0.0693893 | − | 0.120186i | 0.00321785 | − | 0.00557349i | ||||
\(466\) | 27.4490 | + | 15.8477i | 1.27155 | + | 0.734131i | ||||
\(467\) | −23.3774 | −1.08178 | −0.540888 | − | 0.841095i | \(-0.681912\pi\) | ||||
−0.540888 | + | 0.841095i | \(0.681912\pi\) | |||||||
\(468\) | 2.08262 | + | 1.47309i | 0.0962694 | + | 0.0680934i | ||||
\(469\) | 24.9700 | 1.15301 | ||||||||
\(470\) | −8.44168 | − | 4.87381i | −0.389386 | − | 0.224812i | ||||
\(471\) | −0.567304 | + | 0.982600i | −0.0261400 | + | 0.0452758i | ||||
\(472\) | 11.5025 | + | 19.9229i | 0.529446 | + | 0.917027i | ||||
\(473\) | − | 3.80584i | − | 0.174993i | ||||||
\(474\) | −1.07829 | + | 0.622553i | −0.0495277 | + | 0.0285948i | ||||
\(475\) | −4.96410 | + | 2.86603i | −0.227769 | + | 0.131502i | ||||
\(476\) | − | 4.06338i | − | 0.186245i | ||||||
\(477\) | 1.48207 | + | 2.56702i | 0.0678594 | + | 0.117536i | ||||
\(478\) | 11.1393 | − | 19.2939i | 0.509502 | − | 0.882483i | ||||
\(479\) | −4.48198 | − | 2.58767i | −0.204787 | − | 0.118234i | 0.394100 | − | 0.919068i | \(-0.371057\pi\) |
−0.598886 | + | 0.800834i | \(0.704390\pi\) | |||||||
\(480\) | 0.126194 | 0.00575992 | ||||||||
\(481\) | −0.0528814 | + | 0.0747629i | −0.00241119 | + | 0.00340889i | ||||
\(482\) | −14.0453 | −0.639747 | ||||||||
\(483\) | 2.80759 | + | 1.62096i | 0.127750 | + | 0.0737564i | ||||
\(484\) | 1.16573 | − | 2.01911i | 0.0529879 | − | 0.0917777i | ||||
\(485\) | 1.71935 | + | 2.97800i | 0.0780717 | + | 0.135224i | ||||
\(486\) | − | 3.81213i | − | 0.172922i | ||||||
\(487\) | −26.6501 | + | 15.3865i | −1.20763 | + | 0.697227i | −0.962242 | − | 0.272197i | \(-0.912250\pi\) |
−0.245391 | + | 0.969424i | \(0.578917\pi\) | |||||||
\(488\) | −14.4741 | + | 8.35661i | −0.655211 | + | 0.378286i | ||||
\(489\) | 2.13948i | 0.0967508i | ||||||||
\(490\) | −12.1872 | − | 21.1088i | −0.550560 | − | 0.953598i | ||||
\(491\) | 17.8992 | − | 31.0023i | 0.807778 | − | 1.39911i | −0.106622 | − | 0.994300i | \(-0.534003\pi\) |
0.914400 | − | 0.404813i | \(-0.132663\pi\) | |||||||
\(492\) | 0.00520289 | + | 0.00300389i | 0.000234565 | + | 0.000135426i | ||||
\(493\) | −5.24255 | −0.236113 | ||||||||
\(494\) | 2.84028 | − | 30.7772i | 0.127790 | − | 1.38473i | ||||
\(495\) | −3.19856 | −0.143765 | ||||||||
\(496\) | −5.60070 | − | 3.23357i | −0.251479 | − | 0.145191i | ||||
\(497\) | 18.7399 | − | 32.4585i | 0.840600 | − | 1.45596i | ||||
\(498\) | 0.0514200 | + | 0.0890620i | 0.00230418 | + | 0.00399096i | ||||
\(499\) | 28.8971i | 1.29361i | 0.762655 | + | 0.646805i | \(0.223895\pi\) | ||||
−0.762655 | + | 0.646805i | \(0.776105\pi\) | |||||||
\(500\) | −0.204852 | + | 0.118272i | −0.00916128 | + | 0.00528927i | ||||
\(501\) | −0.672879 | + | 0.388487i | −0.0300620 | + | 0.0173563i | ||||
\(502\) | 16.9237i | 0.755340i | ||||||||
\(503\) | 3.93161 | + | 6.80974i | 0.175302 | + | 0.303631i | 0.940266 | − | 0.340442i | \(-0.110577\pi\) |
−0.764964 | + | 0.644073i | \(0.777243\pi\) | |||||||
\(504\) | −19.0373 | + | 32.9735i | −0.847988 | + | 1.46876i | ||||
\(505\) | −2.47273 | − | 1.42763i | −0.110035 | − | 0.0635289i | ||||
\(506\) | 11.3322 | 0.503777 | ||||||||
\(507\) | 0.801014 | − | 0.936370i | 0.0355743 | − | 0.0415856i | ||||
\(508\) | 0.167154 | 0.00741625 | ||||||||
\(509\) | 24.2585 | + | 14.0057i | 1.07524 | + | 0.620790i | 0.929608 | − | 0.368549i | \(-0.120145\pi\) |
0.145631 | + | 0.989339i | \(0.453479\pi\) | |||||||
\(510\) | −0.252246 | + | 0.436903i | −0.0111696 | + | 0.0193464i | ||||
\(511\) | 24.3968 | + | 42.2564i | 1.07925 | + | 1.86931i | ||||
\(512\) | 17.4176i | 0.769757i | ||||||||
\(513\) | −2.81898 | + | 1.62754i | −0.124461 | + | 0.0718577i | ||||
\(514\) | −34.3628 | + | 19.8394i | −1.51568 | + | 0.875076i | ||||
\(515\) | − | 5.54488i | − | 0.244337i | ||||||
\(516\) | −0.0398976 | − | 0.0691046i | −0.00175639 | − | 0.00304216i | ||||
\(517\) | −3.48510 | + | 6.03637i | −0.153275 | + | 0.265479i | ||||
\(518\) | 0.158776 | + | 0.0916696i | 0.00697623 | + | 0.00402773i | ||||
\(519\) | 0.868986 | 0.0381443 | ||||||||
\(520\) | −0.873806 | + | 9.46855i | −0.0383189 | + | 0.415224i | ||||
\(521\) | −37.5609 | −1.64557 | −0.822786 | − | 0.568351i | \(-0.807581\pi\) | ||||
−0.822786 | + | 0.568351i | \(0.807581\pi\) | |||||||
\(522\) | −5.70645 | − | 3.29462i | −0.249765 | − | 0.144202i | ||||
\(523\) | 22.6553 | − | 39.2401i | 0.990647 | − | 1.71585i | 0.377154 | − | 0.926151i | \(-0.376903\pi\) |
0.613493 | − | 0.789700i | \(-0.289764\pi\) | |||||||
\(524\) | 0.741035 | + | 1.28351i | 0.0323723 | + | 0.0560704i | ||||
\(525\) | 0.457524i | 0.0199680i | ||||||||
\(526\) | 18.3144 | − | 10.5738i | 0.798545 | − | 0.461040i | ||||
\(527\) | 4.51249 | − | 2.60529i | 0.196567 | − | 0.113488i | ||||
\(528\) | − | 0.447742i | − | 0.0194855i | ||||||
\(529\) | −13.6043 | − | 23.5633i | −0.591491 | − | 1.02449i | ||||
\(530\) | 0.741035 | − | 1.28351i | 0.0321885 | − | 0.0557522i | ||||
\(531\) | −22.5953 | − | 13.0454i | −0.980553 | − | 0.566123i | ||||
\(532\) | −6.54460 | −0.283744 | ||||||||
\(533\) | −0.557894 | + | 0.788741i | −0.0241651 | + | 0.0341642i | ||||
\(534\) | −1.91463 | −0.0828540 | ||||||||
\(535\) | −3.84611 | − | 2.22056i | −0.166282 | − | 0.0960030i | ||||
\(536\) | −6.82149 | + | 11.8152i | −0.294644 | + | 0.510338i | ||||
\(537\) | −0.475691 | − | 0.823922i | −0.0205276 | − | 0.0355548i | ||||
\(538\) | − | 37.0504i | − | 1.59736i | ||||||
\(539\) | −15.0942 | + | 8.71465i | −0.650154 | + | 0.375367i | ||||
\(540\) | −0.116330 | + | 0.0671633i | −0.00500606 | + | 0.00289025i | ||||
\(541\) | − | 19.7445i | − | 0.848882i | −0.905456 | − | 0.424441i | \(-0.860471\pi\) | ||
0.905456 | − | 0.424441i | \(-0.139529\pi\) | |||||||
\(542\) | 13.9958 | + | 24.2414i | 0.601171 | + | 1.04126i | ||||
\(543\) | 0.806824 | − | 1.39746i | 0.0346242 | − | 0.0599708i | ||||
\(544\) | 4.10328 | + | 2.36903i | 0.175927 | + | 0.101571i | ||||
\(545\) | 13.7804 | 0.590289 | ||||||||
\(546\) | −2.01412 | − | 1.42463i | −0.0861963 | − | 0.0609685i | ||||
\(547\) | −11.8312 | −0.505867 | −0.252934 | − | 0.967484i | \(-0.581395\pi\) | ||||
−0.252934 | + | 0.967484i | \(0.581395\pi\) | |||||||
\(548\) | −3.34028 | − | 1.92851i | −0.142690 | − | 0.0823820i | ||||
\(549\) | 9.47754 | − | 16.4156i | 0.404491 | − | 0.700600i | ||||
\(550\) | 0.799640 | + | 1.38502i | 0.0340968 | + | 0.0590573i | ||||
\(551\) | 8.44381i | 0.359718i | ||||||||
\(552\) | −1.53400 | + | 0.885654i | −0.0652913 | + | 0.0376959i | ||||
\(553\) | −36.7164 | + | 21.1982i | −1.56134 | + | 0.901439i | ||||
\(554\) | − | 33.8952i | − | 1.44007i | ||||||
\(555\) | −0.00120372 | − | 0.00208490i | −5.10951e−5 | − | 8.84992e-5i | ||||
\(556\) | −0.807237 | + | 1.39818i | −0.0342345 | + | 0.0592958i | ||||
\(557\) | −3.50412 | − | 2.02310i | −0.148474 | − | 0.0857217i | 0.423922 | − | 0.905699i | \(-0.360653\pi\) |
−0.572397 | + | 0.819977i | \(0.693986\pi\) | |||||||
\(558\) | 6.54905 | 0.277244 | ||||||||
\(559\) | 11.6552 | − | 5.36754i | 0.492962 | − | 0.227023i | ||||
\(560\) | 21.3208 | 0.900968 | ||||||||
\(561\) | 0.312415 | + | 0.180373i | 0.0131902 | + | 0.00761536i | ||||
\(562\) | −20.8163 | + | 36.0549i | −0.878083 | + | 1.52088i | ||||
\(563\) | 1.94963 | + | 3.37686i | 0.0821671 | + | 0.142318i | 0.904181 | − | 0.427151i | \(-0.140483\pi\) |
−0.822013 | + | 0.569468i | \(0.807149\pi\) | |||||||
\(564\) | 0.146141i | 0.00615364i | ||||||||
\(565\) | 6.96630 | − | 4.02200i | 0.293074 | − | 0.169207i | ||||
\(566\) | 10.2577 | − | 5.92226i | 0.431162 | − | 0.248931i | ||||
\(567\) | − | 43.0516i | − | 1.80800i | ||||||
\(568\) | 10.2390 | + | 17.7345i | 0.429619 | + | 0.744123i | ||||
\(569\) | −8.66778 | + | 15.0130i | −0.363372 | + | 0.629379i | −0.988514 | − | 0.151133i | \(-0.951708\pi\) |
0.625141 | + | 0.780512i | \(0.285041\pi\) | |||||||
\(570\) | 0.703689 | + | 0.406275i | 0.0294743 | + | 0.0170170i | ||||
\(571\) | −29.5118 | −1.23503 | −0.617515 | − | 0.786559i | \(-0.711860\pi\) | ||||
−0.617515 | + | 0.786559i | \(0.711860\pi\) | |||||||
\(572\) | −0.908189 | − | 0.0838123i | −0.0379733 | − | 0.00350437i | ||||
\(573\) | −0.367530 | −0.0153538 | ||||||||
\(574\) | 1.67508 | + | 0.967106i | 0.0699163 | + | 0.0403662i | ||||
\(575\) | 3.54290 | − | 6.13649i | 0.147749 | − | 0.255909i | ||||
\(576\) | −10.2341 | − | 17.7260i | −0.426422 | − | 0.738585i | ||||
\(577\) | − | 28.3684i | − | 1.18099i | −0.807041 | − | 0.590496i | \(-0.798932\pi\) | ||
0.807041 | − | 0.590496i | \(-0.201068\pi\) | |||||||
\(578\) | 5.61357 | − | 3.24100i | 0.233494 | − | 0.134808i | ||||
\(579\) | −0.102934 | + | 0.0594291i | −0.00427780 | + | 0.00246979i | ||||
\(580\) | 0.348448i | 0.0144685i | ||||||||
\(581\) | 1.75087 | + | 3.03260i | 0.0726384 | + | 0.125813i | ||||
\(582\) | 0.243728 | − | 0.422149i | 0.0101028 | − | 0.0174986i | ||||
\(583\) | −0.917797 | − | 0.529891i | −0.0380113 | − | 0.0219458i | ||||
\(584\) | −26.6595 | −1.10318 | ||||||||
\(585\) | −4.51107 | − | 9.79543i | −0.186510 | − | 0.404991i | ||||
\(586\) | 0.408230 | 0.0168638 | ||||||||
\(587\) | 29.7806 | + | 17.1939i | 1.22918 | + | 0.709667i | 0.966858 | − | 0.255314i | \(-0.0821790\pi\) |
0.262320 | + | 0.964981i | \(0.415512\pi\) | |||||||
\(588\) | −0.182716 | + | 0.316473i | −0.00753507 | + | 0.0130511i | ||||
\(589\) | −4.19615 | − | 7.26795i | −0.172899 | − | 0.299471i | ||||
\(590\) | 13.0454i | 0.537071i | ||||||||
\(591\) | −1.25447 | + | 0.724270i | −0.0516021 | + | 0.0297925i | ||||
\(592\) | −0.0971572 | + | 0.0560937i | −0.00399314 | + | 0.00230544i | ||||
\(593\) | 5.47612i | 0.224877i | 0.993659 | + | 0.112439i | \(0.0358662\pi\) | ||||
−0.993659 | + | 0.112439i | \(0.964134\pi\) | |||||||
\(594\) | 0.454095 | + | 0.786515i | 0.0186317 | + | 0.0322711i | ||||
\(595\) | −8.58909 | + | 14.8767i | −0.352118 | + | 0.609887i | ||||
\(596\) | −1.72886 | − | 0.998159i | −0.0708170 | − | 0.0408862i | ||||
\(597\) | 1.25400 | 0.0513229 | ||||||||
\(598\) | 15.9823 | + | 34.7043i | 0.653564 | + | 1.41916i | ||||
\(599\) | 38.6039 | 1.57731 | 0.788657 | − | 0.614833i | \(-0.210777\pi\) | ||||
0.788657 | + | 0.614833i | \(0.210777\pi\) | |||||||
\(600\) | −0.216489 | − | 0.124990i | −0.00883812 | − | 0.00510269i | ||||
\(601\) | −3.28948 | + | 5.69754i | −0.134181 | + | 0.232408i | −0.925284 | − | 0.379275i | \(-0.876174\pi\) |
0.791104 | + | 0.611682i | \(0.209507\pi\) | |||||||
\(602\) | −12.8451 | − | 22.2483i | −0.523525 | − | 0.906772i | ||||
\(603\) | − | 15.4730i | − | 0.630109i | ||||||
\(604\) | −0.280682 | + | 0.162052i | −0.0114208 | + | 0.00659379i | ||||
\(605\) | −8.53590 | + | 4.92820i | −0.347034 | + | 0.200360i | ||||
\(606\) | 0.404750i | 0.0164418i | ||||||||
\(607\) | 8.38318 | + | 14.5201i | 0.340263 | + | 0.589352i | 0.984481 | − | 0.175489i | \(-0.0561507\pi\) |
−0.644219 | + | 0.764841i | \(0.722817\pi\) | |||||||
\(608\) | 3.81563 | − | 6.60886i | 0.154744 | − | 0.268025i | ||||
\(609\) | 0.583678 | + | 0.336986i | 0.0236518 | + | 0.0136554i | ||||
\(610\) | −9.47754 | −0.383734 | ||||||||
\(611\) | −23.4013 | − | 2.15959i | −0.946715 | − | 0.0873677i | ||||
\(612\) | −2.51793 | −0.101781 | ||||||||
\(613\) | 24.9232 | + | 14.3894i | 1.00664 | + | 0.581184i | 0.910206 | − | 0.414155i | \(-0.135923\pi\) |
0.0964341 | + | 0.995339i | \(0.469256\pi\) | |||||||
\(614\) | 5.12379 | − | 8.87466i | 0.206779 | − | 0.358152i | ||||
\(615\) | −0.0126991 | − | 0.0219955i | −0.000512078 | − | 0.000886946i | ||||
\(616\) | − | 13.6129i | − | 0.548481i | ||||||
\(617\) | 32.3279 | − | 18.6645i | 1.30147 | − | 0.751406i | 0.320817 | − | 0.947141i | \(-0.396043\pi\) |
0.980657 | + | 0.195735i | \(0.0627093\pi\) | |||||||
\(618\) | −0.680712 | + | 0.393009i | −0.0273822 | + | 0.0158091i | ||||
\(619\) | 12.7535i | 0.512606i | 0.966597 | + | 0.256303i | \(0.0825045\pi\) | ||||
−0.966597 | + | 0.256303i | \(0.917496\pi\) | |||||||
\(620\) | −0.173162 | − | 0.299925i | −0.00695434 | − | 0.0120453i | ||||
\(621\) | 2.01192 | − | 3.48475i | 0.0807356 | − | 0.139838i | ||||
\(622\) | −13.7864 | − | 7.95961i | −0.552786 | − | 0.319151i | ||||
\(623\) | −65.1939 | −2.61194 | ||||||||
\(624\) | 1.37119 | − | 0.631470i | 0.0548914 | − | 0.0252790i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.0842 | + | 13.3276i | 0.922629 | + | 0.532680i | ||||
\(627\) | 0.290514 | − | 0.503185i | 0.0116020 | − | 0.0200953i | ||||
\(628\) | 1.41571 | + | 2.45209i | 0.0564931 | + | 0.0978489i | ||||
\(629\) | − | 0.0903896i | − | 0.00360407i | ||||||
\(630\) | −18.6982 | + | 10.7954i | −0.744956 | + | 0.430100i | ||||
\(631\) | 24.8759 | − | 14.3621i | 0.990294 | − | 0.571746i | 0.0849315 | − | 0.996387i | \(-0.472933\pi\) |
0.905362 | + | 0.424641i | \(0.139600\pi\) | |||||||
\(632\) | − | 23.1643i | − | 0.921427i | ||||||
\(633\) | 0.227984 | + | 0.394880i | 0.00906156 | + | 0.0156951i | ||||
\(634\) | −6.11035 | + | 10.5834i | −0.242673 | + | 0.420322i | ||||
\(635\) | −0.611979 | − | 0.353326i | −0.0242856 | − | 0.0140213i | ||||
\(636\) | −0.0222199 | −0.000881077 | ||||||||
\(637\) | −47.9762 | − | 33.9346i | −1.90089 | − | 1.34454i | ||||
\(638\) | 2.35588 | 0.0932701 | ||||||||
\(639\) | −20.1133 | − | 11.6124i | −0.795671 | − | 0.459381i | ||||
\(640\) | −6.44840 | + | 11.1690i | −0.254895 | + | 0.441492i | ||||
\(641\) | −11.1985 | − | 19.3964i | −0.442315 | − | 0.766112i | 0.555546 | − | 0.831486i | \(-0.312509\pi\) |
−0.997861 | + | 0.0653739i | \(0.979176\pi\) | |||||||
\(642\) | 0.629552i | 0.0248464i | ||||||||
\(643\) | 12.2665 | − | 7.08209i | 0.483745 | − | 0.279290i | −0.238231 | − | 0.971209i | \(-0.576567\pi\) |
0.721976 | + | 0.691918i | \(0.243234\pi\) | |||||||
\(644\) | 7.00637 | − | 4.04513i | 0.276090 | − | 0.159400i | ||||
\(645\) | 0.337339i | 0.0132827i | ||||||||
\(646\) | 15.2540 | + | 26.4207i | 0.600160 | + | 1.03951i | ||||
\(647\) | −11.8048 | + | 20.4466i | −0.464096 | + | 0.803838i | −0.999160 | − | 0.0409732i | \(-0.986954\pi\) |
0.535064 | + | 0.844812i | \(0.320287\pi\) | |||||||
\(648\) | 20.3709 | + | 11.7612i | 0.800246 | + | 0.462022i | ||||
\(649\) | 9.32835 | 0.366170 | ||||||||
\(650\) | −3.11378 | + | 4.40221i | −0.122132 | + | 0.172669i | ||||
\(651\) | −0.669862 | −0.0262540 | ||||||||
\(652\) | 4.62379 | + | 2.66955i | 0.181082 | + | 0.104548i | ||||
\(653\) | −16.6383 | + | 28.8183i | −0.651105 | + | 1.12775i | 0.331750 | + | 0.943367i | \(0.392361\pi\) |
−0.982855 | + | 0.184380i | \(0.940972\pi\) | |||||||
\(654\) | −0.976727 | − | 1.69174i | −0.0381930 | − | 0.0661523i | ||||
\(655\) | − | 6.26554i | − | 0.244815i | ||||||
\(656\) | −1.02500 | + | 0.591784i | −0.0400195 | + | 0.0231053i | ||||
\(657\) | 26.1848 | − | 15.1178i | 1.02156 | − | 0.589801i | ||||
\(658\) | 47.0502i | 1.83421i | ||||||||
\(659\) | −11.5454 | − | 19.9972i | −0.449745 | − | 0.778982i | 0.548624 | − | 0.836069i | \(-0.315152\pi\) |
−0.998369 | + | 0.0570875i | \(0.981819\pi\) | |||||||
\(660\) | 0.0119886 | − | 0.0207648i | 0.000466655 | − | 0.000808270i | ||||
\(661\) | 11.6364 | + | 6.71826i | 0.452602 | + | 0.261310i | 0.708929 | − | 0.705280i | \(-0.249179\pi\) |
−0.256326 | + | 0.966590i | \(0.582512\pi\) | |||||||
\(662\) | 37.2972 | 1.44960 | ||||||||
\(663\) | −0.111771 | + | 1.21114i | −0.00434081 | + | 0.0470370i | ||||
\(664\) | −1.91326 | −0.0742491 | ||||||||
\(665\) | 23.9609 | + | 13.8338i | 0.929164 | + | 0.536453i | ||||
\(666\) | 0.0568043 | − | 0.0983879i | 0.00220112 | − | 0.00381245i | ||||
\(667\) | −5.21900 | − | 9.03957i | −0.202080 | − | 0.350014i | ||||
\(668\) | 1.93895i | 0.0750200i | ||||||||
\(669\) | 1.20779 | − | 0.697316i | 0.0466957 | − | 0.0269598i | ||||
\(670\) | −6.70001 | + | 3.86825i | −0.258844 | + | 0.149444i | ||||
\(671\) | 6.77708i | 0.261626i | ||||||||
\(672\) | −0.304558 | − | 0.527510i | −0.0117486 | − | 0.0203491i | ||||
\(673\) | −0.972620 | + | 1.68463i | −0.0374918 | + | 0.0649376i | −0.884162 | − | 0.467180i | \(-0.845270\pi\) |
0.846671 | + | 0.532117i | \(0.178603\pi\) | |||||||
\(674\) | 25.3923 | + | 14.6603i | 0.978075 | + | 0.564692i | ||||
\(675\) | 0.567874 | 0.0218575 | ||||||||
\(676\) | −1.02419 | − | 2.89949i | −0.0393919 | − | 0.111519i | ||||
\(677\) | 24.8683 | 0.955768 | 0.477884 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477884 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(678\) | −0.987512 | − | 0.570140i | −0.0379252 | − | 0.0218961i | ||||
\(679\) | 8.29903 | − | 14.3743i | 0.318488 | − | 0.551637i | ||||
\(680\) | −4.69286 | − | 8.12828i | −0.179963 | − | 0.311705i | ||||
\(681\) | 1.41260i | 0.0541310i | ||||||||
\(682\) | −2.02781 | + | 1.17075i | −0.0776487 | + | 0.0448305i | ||||
\(683\) | −12.6631 | + | 7.31107i | −0.484542 | + | 0.279750i | −0.722307 | − | 0.691572i | \(-0.756918\pi\) |
0.237766 | + | 0.971323i | \(0.423585\pi\) | |||||||
\(684\) | 4.05545i | 0.155064i | ||||||||
\(685\) | 8.15290 | + | 14.1212i | 0.311506 | + | 0.539545i | ||||
\(686\) | −33.5605 | + | 58.1285i | −1.28135 | + | 2.21935i | ||||
\(687\) | −1.58491 | − | 0.915049i | −0.0604681 | − | 0.0349113i | ||||
\(688\) | 15.7201 | 0.599323 | ||||||||
\(689\) | 0.328354 | − | 3.55804i | 0.0125093 | − | 0.135550i | ||||
\(690\) | −1.00445 | −0.0382388 | ||||||||
\(691\) | −3.05231 | − | 1.76225i | −0.116115 | − | 0.0670393i | 0.440817 | − | 0.897597i | \(-0.354689\pi\) |
−0.556933 | + | 0.830558i | \(0.688022\pi\) | |||||||
\(692\) | 1.08428 | − | 1.87803i | 0.0412182 | − | 0.0713920i | ||||
\(693\) | 7.71947 | + | 13.3705i | 0.293238 | + | 0.507904i | ||||
\(694\) | − | 25.5447i | − | 0.969665i | ||||||
\(695\) | 5.91087 | − | 3.41264i | 0.224212 | − | 0.129449i | ||||
\(696\) | −0.318907 | + | 0.184121i | −0.0120881 | + | 0.00697909i | ||||
\(697\) | − | 0.953601i | − | 0.0361202i | ||||||
\(698\) | −21.2152 | − | 36.7458i | −0.803008 | − | 1.39085i | ||||
\(699\) | −1.00445 | + | 1.73976i | −0.0379919 | + | 0.0658038i | ||||
\(700\) | 0.988789 | + | 0.570878i | 0.0373727 | + | 0.0215772i | ||||
\(701\) | 1.53457 | 0.0579599 | 0.0289800 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289800 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(702\) | −1.76823 | + | 2.49990i | −0.0667377 | + | 0.0943526i | ||||
\(703\) | −0.145584 | −0.00549081 | ||||||||
\(704\) | 6.33766 | + | 3.65905i | 0.238860 | + | 0.137906i | ||||
\(705\) | 0.308909 | − | 0.535047i | 0.0116342 | − | 0.0201510i | ||||
\(706\) | −15.8912 | − | 27.5244i | −0.598075 | − | 1.03590i | ||||
\(707\) | 13.7819i | 0.518322i | ||||||||
\(708\) | 0.169380 | − | 0.0977915i | 0.00636568 | − | 0.00367523i | ||||
\(709\) | 12.1289 | − | 7.00262i | 0.455510 | − | 0.262989i | −0.254644 | − | 0.967035i | \(-0.581958\pi\) |
0.710155 | + | 0.704046i | \(0.248625\pi\) | |||||||
\(710\) | 11.6124i | 0.435807i | ||||||||
\(711\) | 13.1357 | + | 22.7518i | 0.492629 | + | 0.853259i | ||||
\(712\) | 17.8101 | − | 30.8481i | 0.667463 | − | 1.15608i | ||||
\(713\) | 8.98444 | + | 5.18717i | 0.336470 | + | 0.194261i | ||||
\(714\) | 2.43510 | 0.0911314 | ||||||||
\(715\) | 3.14788 | + | 2.22656i | 0.117724 | + | 0.0832687i | ||||
\(716\) | −2.37418 | −0.0887274 | ||||||||
\(717\) | 1.22288 | + | 0.706029i | 0.0456692 | + | 0.0263671i | ||||
\(718\) | 24.4156 | − | 42.2890i | 0.911181 | − | 1.57821i | ||||
\(719\) | 11.2381 | + | 19.4649i | 0.419109 | + | 0.725918i | 0.995850 | − | 0.0910091i | \(-0.0290092\pi\) |
−0.576741 | + | 0.816927i | \(0.695676\pi\) | |||||||
\(720\) | − | 13.2117i | − | 0.492372i | ||||||
\(721\) | −23.1785 | + | 13.3821i | −0.863213 | + | 0.498376i | ||||
\(722\) | 17.9461 | − | 10.3612i | 0.667884 | − | 0.385603i | ||||
\(723\) | − | 0.890215i | − | 0.0331074i | ||||||
\(724\) | −2.01344 | − | 3.48737i | −0.0748288 | − | 0.129607i | ||||
\(725\) | 0.736543 | − | 1.27573i | 0.0273545 | − | 0.0473794i | ||||
\(726\) | 1.21001 | + | 0.698600i | 0.0449077 | + | 0.0259275i | ||||
\(727\) | 10.3421 | 0.383566 | 0.191783 | − | 0.981437i | \(-0.438573\pi\) | ||||
0.191783 | + | 0.981437i | \(0.438573\pi\) | |||||||
\(728\) | 41.6890 | − | 19.1989i | 1.54510 | − | 0.711560i | ||||
\(729\) | −26.5160 | −0.982075 | ||||||||
\(730\) | −13.0924 | − | 7.55889i | −0.484571 | − | 0.279767i | ||||
\(731\) | −6.33285 | + | 10.9688i | −0.234229 | + | 0.405696i | ||||
\(732\) | 0.0710459 | + | 0.123055i | 0.00262593 | + | 0.00454824i | ||||
\(733\) | − | 27.3533i | − | 1.01032i | −0.863026 | − | 0.505159i | \(-0.831434\pi\) | ||
0.863026 | − | 0.505159i | \(-0.168566\pi\) | |||||||
\(734\) | 7.66516 | − | 4.42548i | 0.282926 | − | 0.163348i | ||||
\(735\) | 1.33791 | − | 0.772442i | 0.0493495 | − | 0.0284919i | ||||
\(736\) | 9.43355i | 0.347725i | ||||||||
\(737\) | 2.76606 | + | 4.79096i | 0.101889 | + | 0.176477i | ||||
\(738\) | 0.599280 | − | 1.03798i | 0.0220598 | − | 0.0382087i | ||||
\(739\) | 11.6495 | + | 6.72583i | 0.428533 | + | 0.247413i | 0.698721 | − | 0.715394i | \(-0.253753\pi\) |
−0.270189 | + | 0.962807i | \(0.587086\pi\) | |||||||
\(740\) | −0.00600778 | −0.000220851 | ||||||||
\(741\) | 1.95071 | + | 0.180021i | 0.0716610 | + | 0.00661324i | ||||
\(742\) | −7.15372 | −0.262621 | ||||||||
\(743\) | 14.1964 | + | 8.19632i | 0.520817 | + | 0.300694i | 0.737269 | − | 0.675599i | \(-0.236115\pi\) |
−0.216452 | + | 0.976293i | \(0.569448\pi\) | |||||||
\(744\) | 0.182998 | − | 0.316962i | 0.00670903 | − | 0.0116204i | ||||
\(745\) | 4.21978 | + | 7.30887i | 0.154601 | + | 0.267776i | ||||
\(746\) | 19.9179i | 0.729248i | ||||||||
\(747\) | 1.87919 | − | 1.08495i | 0.0687560 | − | 0.0396963i | ||||
\(748\) | 0.779635 | − | 0.450122i | 0.0285063 | − | 0.0164581i | ||||
\(749\) | 21.4365i | 0.783274i | ||||||||
\(750\) | −0.0708778 | − | 0.122764i | −0.00258809 | − | 0.00448270i | ||||
\(751\) | −13.8328 | + | 23.9590i | −0.504764 | + | 0.874277i | 0.495221 | + | 0.868767i | \(0.335087\pi\) |
−0.999985 | + | 0.00551009i | \(0.998246\pi\) | |||||||
\(752\) | −24.9334 | − | 14.3953i | −0.909226 | − | 0.524942i | ||||
\(753\) | −1.07265 | −0.0390895 | ||||||||
\(754\) | 3.32260 | + | 7.21476i | 0.121002 | + | 0.262746i | ||||
\(755\) | 1.37017 | 0.0498654 | ||||||||
\(756\) | 0.561508 | + | 0.324187i | 0.0204218 | + | 0.0117906i | ||||
\(757\) | −11.4989 | + | 19.9167i | −0.417935 | + | 0.723885i | −0.995732 | − | 0.0922961i | \(-0.970579\pi\) |
0.577797 | + | 0.816181i | \(0.303913\pi\) | |||||||
\(758\) | −19.0068 | − | 32.9208i | −0.690359 | − | 1.19574i | ||||
\(759\) | 0.718251i | 0.0260709i | ||||||||
\(760\) | −13.0916 | + | 7.55846i | −0.474884 | + | 0.274174i | ||||
\(761\) | 6.63759 | − | 3.83221i | 0.240612 | − | 0.138918i | −0.374846 | − | 0.927087i | \(-0.622304\pi\) |
0.615458 | + | 0.788170i | \(0.288971\pi\) | |||||||
\(762\) | 0.100172i | 0.00362885i | ||||||||
\(763\) | −33.2580 | − | 57.6045i | −1.20402 | − | 2.08542i | ||||
\(764\) | −0.458587 | + | 0.794296i | −0.0165911 | + | 0.0287366i | ||||
\(765\) | 9.21857 | + | 5.32235i | 0.333298 | + | 0.192430i | ||||
\(766\) | −16.1916 | −0.585027 | ||||||||
\(767\) | 13.1562 | + | 28.5676i | 0.475042 | + | 1.03152i | ||||
\(768\) | 0.530882 | 0.0191566 | ||||||||
\(769\) | 6.26219 | + | 3.61548i | 0.225820 | + | 0.130377i | 0.608642 | − | 0.793445i | \(-0.291714\pi\) |
−0.382822 | + | 0.923822i | \(0.625048\pi\) | |||||||
\(770\) | 3.85973 | − | 6.68525i | 0.139095 | − | 0.240920i | ||||
\(771\) | −1.25745 | − | 2.17797i | −0.0452859 | − | 0.0784375i | ||||
\(772\) | 0.296612i | 0.0106753i | ||||||||
\(773\) | −29.0981 | + | 16.7998i | −1.04658 | + | 0.604246i | −0.921691 | − | 0.387924i | \(-0.873192\pi\) |
−0.124893 | + | 0.992170i | \(0.539859\pi\) | |||||||
\(774\) | −13.7864 | + | 7.95961i | −0.495544 | + | 0.286102i | ||||
\(775\) | 1.46410i | 0.0525921i | ||||||||
\(776\) | 4.53438 | + | 7.85378i | 0.162775 | + | 0.281934i | ||||
\(777\) | −0.00581016 | + | 0.0100635i | −0.000208438 | + | 0.000361026i | ||||
\(778\) | 29.8363 | + | 17.2260i | 1.06968 | + | 0.617582i | ||||
\(779\) | −1.53590 | −0.0550293 | ||||||||
\(780\) | 0.0804993 | + | 0.00742888i | 0.00288234 | + | 0.000265997i | ||||
\(781\) | 8.30368 | 0.297129 | ||||||||
\(782\) | −32.6605 | − | 18.8565i | −1.16794 | − | 0.674309i | ||||
\(783\) | 0.418264 | − | 0.724454i | 0.0149475 | − | 0.0258899i | ||||
\(784\) | −35.9960 | − | 62.3470i | −1.28557 | − | 2.22668i | ||||
\(785\) | − | 11.9700i | − | 0.427228i | ||||||
\(786\) | −0.769182 | + | 0.444088i | −0.0274358 | + | 0.0158401i | ||||
\(787\) | 2.57355 | − | 1.48584i | 0.0917371 | − | 0.0529645i | −0.453430 | − | 0.891292i | \(-0.649800\pi\) |
0.545167 | + | 0.838328i | \(0.316466\pi\) | |||||||
\(788\) | 3.61484i | 0.128773i | ||||||||
\(789\) | 0.670185 | + | 1.16079i | 0.0238592 | + | 0.0413254i | ||||
\(790\) | 6.56787 | − | 11.3759i | 0.233674 | − | 0.404736i | ||||
\(791\) | −33.6252 | − | 19.4135i | −1.19557 | − | 0.690265i | ||||
\(792\) | −8.43544 | −0.299740 | ||||||||
\(793\) | −20.7545 | + | 9.55802i | −0.737013 | + | 0.339415i | ||||
\(794\) | −31.5349 | −1.11913 | ||||||||
\(795\) | 0.0813509 | + | 0.0469680i | 0.00288522 | + | 0.00166578i | ||||
\(796\) | 1.56469 | − | 2.71012i | 0.0554588 | − | 0.0960575i | ||||
\(797\) | −11.2875 | − | 19.5506i | −0.399825 | − | 0.692517i | 0.593879 | − | 0.804554i | \(-0.297596\pi\) |
−0.993704 | + | 0.112037i | \(0.964262\pi\) | |||||||
\(798\) | − | 3.92205i | − | 0.138839i | ||||||
\(799\) | 20.0888 | − | 11.5983i | 0.710692 | − | 0.410318i | ||||
\(800\) | −1.15297 | + | 0.665665i | −0.0407635 | + | 0.0235348i | ||||
\(801\) | 40.3983i | 1.42740i | ||||||||
\(802\) | −14.7882 | − | 25.6140i | −0.522191 | − | 0.904462i | ||||
\(803\) | −5.40512 | + | 9.36194i | −0.190742 | + | 0.330376i | ||||
\(804\) | 0.100450 | + | 0.0579946i | 0.00354259 | + | 0.00204531i | ||||
\(805\) | −34.2020 | −1.20546 | ||||||||
\(806\) | −6.44528 | − | 4.55889i | −0.227025 | − | 0.160580i | ||||
\(807\) | 2.34831 | 0.0826646 | ||||||||
\(808\) | −6.52125 | − | 3.76505i | −0.229417 | − | 0.132454i | ||||
\(809\) | −6.82921 | + | 11.8285i | −0.240102 | + | 0.415869i | −0.960743 | − | 0.277439i | \(-0.910514\pi\) |
0.720641 | + | 0.693308i | \(0.243848\pi\) | |||||||
\(810\) | 6.66938 | + | 11.5517i | 0.234338 | + | 0.405886i | ||||
\(811\) | 14.1147i | 0.495636i | 0.968807 | + | 0.247818i | \(0.0797135\pi\) | ||||
−0.968807 | + | 0.247818i | \(0.920287\pi\) | |||||||
\(812\) | 1.45657 | − | 0.840952i | 0.0511157 | − | 0.0295116i | ||||
\(813\) | −1.53646 | + | 0.887075i | −0.0538860 | + | 0.0311111i | ||||
\(814\) | 0.0406189i | 0.00142369i | ||||||||
\(815\) | −11.2857 | − | 19.5474i | −0.395320 | − | 0.684714i | ||||
\(816\) | −0.745035 | + | 1.29044i | −0.0260814 | + | 0.0451744i | ||||
\(817\) | 17.6667 | + | 10.1999i | 0.618079 | + | 0.356848i | ||||
\(818\) | −47.6781 | −1.66703 | ||||||||
\(819\) | −30.0594 | + | 42.4975i | −1.05036 | + | 1.48498i | ||||
\(820\) | −0.0633815 | −0.00221338 | ||||||||
\(821\) | −1.37318 | − | 0.792808i | −0.0479244 | − | 0.0276692i | 0.475846 | − | 0.879528i | \(-0.342142\pi\) |
−0.523771 | + | 0.851859i | \(0.675475\pi\) | |||||||
\(822\) | 1.15572 | − | 2.00176i | 0.0403103 | − | 0.0698195i | ||||
\(823\) | 9.28238 | + | 16.0776i | 0.323563 | + | 0.560428i | 0.981221 | − | 0.192889i | \(-0.0617857\pi\) |
−0.657657 | + | 0.753317i | \(0.728452\pi\) | |||||||
\(824\) | − | 14.6233i | − | 0.509427i | ||||||
\(825\) | −0.0877845 | + | 0.0506824i | −0.00305626 | + | 0.00176454i | ||||
\(826\) | 54.5320 | − | 31.4840i | 1.89741 | − | 1.09547i | ||||
\(827\) | − | 9.01023i | − | 0.313316i | −0.987653 | − | 0.156658i | \(-0.949928\pi\) | ||
0.987653 | − | 0.156658i | \(-0.0500721\pi\) | |||||||
\(828\) | −2.50662 | − | 4.34159i | −0.0871110 | − | 0.150881i | ||||
\(829\) | 23.5588 | − | 40.8051i | 0.818233 | − | 1.41722i | −0.0887506 | − | 0.996054i | \(-0.528287\pi\) |
0.906983 | − | 0.421167i | \(-0.138379\pi\) | |||||||
\(830\) | −0.939595 | − | 0.542476i | −0.0326138 | − | 0.0188296i | ||||
\(831\) | 2.14833 | 0.0745247 | ||||||||
\(832\) | −2.26738 | + | 24.5693i | −0.0786072 | + | 0.851787i | ||||
\(833\) | 58.0041 | 2.00972 | ||||||||
\(834\) | −0.837898 | − | 0.483761i | −0.0290141 | − | 0.0167513i | ||||
\(835\) | 4.09850 | − | 7.09881i | 0.141835 | − | 0.245665i | ||||
\(836\) | −0.724980 | − | 1.25570i | −0.0250740 | − | 0.0434294i | ||||
\(837\) | 0.831425i | 0.0287383i | ||||||||
\(838\) | −39.7994 | + | 22.9782i | −1.37485 | + | 0.793769i | ||||
\(839\) | 46.3121 | − | 26.7383i | 1.59887 | − | 0.923108i | 0.607164 | − | 0.794576i | \(-0.292307\pi\) |
0.991705 | − | 0.128531i | \(-0.0410263\pi\) | |||||||
\(840\) | 1.20661i | 0.0416321i | ||||||||
\(841\) | 13.4150 | + | 23.2355i | 0.462586 | + | 0.801223i | ||||
\(842\) | −13.4461 | + | 23.2894i | −0.463384 | + | 0.802605i | ||||
\(843\) | −2.28521 | − | 1.31937i | −0.0787070 | − | 0.0454415i | ||||
\(844\) | 1.13787 | 0.0391672 | ||||||||
\(845\) | −2.37915 | + | 12.7804i | −0.0818453 | + | 0.439660i | ||||
\(846\) | 29.1553 | 1.00238 | ||||||||
\(847\) | 41.2014 | + | 23.7876i | 1.41570 | + | 0.817353i | ||||
\(848\) | 2.18872 | − | 3.79098i | 0.0751611 | − | 0.130183i | ||||
\(849\) | 0.375362 | + | 0.650146i | 0.0128824 | + | 0.0223130i | ||||
\(850\) | − | 5.32235i | − | 0.182555i | ||||||
\(851\) | 0.155856 | − | 0.0899835i | 0.00534268 | − | 0.00308460i | ||||
\(852\) | 0.150774 | − | 0.0870495i | 0.00516544 | − | 0.00298227i | ||||
\(853\) | − | 27.7756i | − | 0.951019i | −0.879711 | − | 0.475510i | \(-0.842264\pi\) | ||
0.879711 | − | 0.475510i | \(-0.157736\pi\) | |||||||
\(854\) | 22.8733 | + | 39.6177i | 0.782707 | + | 1.35569i | ||||
\(855\) | 8.57233 | − | 14.8477i | 0.293167 | − | 0.507781i | ||||
\(856\) | −10.1432 | − | 5.85619i | −0.346688 | − | 0.200160i | ||||
\(857\) | −53.6917 | −1.83407 | −0.917037 | − | 0.398801i | \(-0.869426\pi\) | ||||
−0.917037 | + | 0.398801i | \(0.869426\pi\) | |||||||
\(858\) | 0.0502271 | − | 0.544260i | 0.00171472 | − | 0.0185807i | ||||
\(859\) | 2.08958 | 0.0712955 | 0.0356477 | − | 0.999364i | \(-0.488651\pi\) | ||||
0.0356477 | + | 0.999364i | \(0.488651\pi\) | |||||||
\(860\) | 0.729047 | + | 0.420915i | 0.0248603 | + | 0.0143531i | ||||
\(861\) | −0.0612966 | + | 0.106169i | −0.00208898 | + | 0.00361823i | ||||
\(862\) | −3.66361 | − | 6.34556i | −0.124783 | − | 0.216131i | ||||
\(863\) | 1.75413i | 0.0597113i | 0.999554 | + | 0.0298557i | \(0.00950476\pi\) | ||||
−0.999554 | + | 0.0298557i | \(0.990495\pi\) | |||||||
\(864\) | −0.654739 | + | 0.378014i | −0.0222747 | + | 0.0128603i | ||||
\(865\) | −7.93948 | + | 4.58386i | −0.269950 | + | 0.155856i | ||||
\(866\) | − | 28.7727i | − | 0.977737i | ||||||
\(867\) | 0.205419 | + | 0.355797i | 0.00697640 | + | 0.0120835i | ||||
\(868\) | −0.835823 | + | 1.44769i | −0.0283697 | + | 0.0491377i | ||||
\(869\) | −8.13453 | − | 4.69647i | −0.275945 | − | 0.159317i | ||||
\(870\) | −0.208818 | −0.00707960 | ||||||||
\(871\) | −10.7710 | + | 15.2278i | −0.364961 | + | 0.515975i | ||||
\(872\) | 36.3426 | 1.23072 | ||||||||
\(873\) | −8.90726 | − | 5.14261i | −0.301465 | − | 0.174051i | ||||
\(874\) | −30.3709 | + | 52.6040i | −1.02731 | + | 1.77936i | ||||
\(875\) | −2.41342 | − | 4.18016i | −0.0815885 | − | 0.141315i | ||||
\(876\) | 0.226653i | 0.00765789i | ||||||||
\(877\) | −18.6777 | + | 10.7836i | −0.630702 | + | 0.364136i | −0.781024 | − | 0.624501i | \(-0.785302\pi\) |
0.150322 | + | 0.988637i | \(0.451969\pi\) | |||||||
\(878\) | −11.0861 | + | 6.40058i | −0.374139 | + | 0.216009i | ||||
\(879\) | 0.0258742i | 0.000872716i | ||||||||
\(880\) | 2.36182 | + | 4.09079i | 0.0796169 | + | 0.137900i | ||||
\(881\) | 12.5132 | − | 21.6734i | 0.421579 | − | 0.730196i | −0.574515 | − | 0.818494i | \(-0.694809\pi\) |
0.996094 | + | 0.0882978i | \(0.0281427\pi\) | |||||||
\(882\) | 63.1367 | + | 36.4520i | 2.12592 | + | 1.22740i | ||||
\(883\) | 48.7832 | 1.64169 | 0.820843 | − | 0.571154i | \(-0.193504\pi\) | ||||
0.820843 | + | 0.571154i | \(0.193504\pi\) | |||||||
\(884\) | 2.47803 | + | 1.75277i | 0.0833452 | + | 0.0589519i | ||||
\(885\) | −0.826838 | −0.0277939 | ||||||||
\(886\) | −49.1705 | − | 28.3886i | −1.65192 | − | 0.953734i | ||||
\(887\) | 16.8967 | − | 29.2659i | 0.567334 | − | 0.982651i | −0.429494 | − | 0.903070i | \(-0.641308\pi\) |
0.996828 | − | 0.0795819i | \(-0.0253585\pi\) | |||||||
\(888\) | −0.00317453 | − | 0.00549844i | −0.000106530 | − | 0.000184516i | ||||
\(889\) | 3.41090i | 0.114398i | ||||||||
\(890\) | 17.4930 | − | 10.0996i | 0.586365 | − | 0.338538i | ||||
\(891\) | 8.26025 | − | 4.76906i | 0.276729 | − | 0.159769i | ||||
\(892\) | − | 3.48031i | − | 0.116530i | ||||||
\(893\) | −18.6806 | − | 32.3557i | −0.625121 | − | 1.08274i | ||||
\(894\) | 0.598177 | − | 1.03607i | 0.0200060 | − | 0.0346515i | ||||
\(895\) | 8.69229 | + | 5.01850i | 0.290551 | + | 0.167750i | ||||
\(896\) | 62.2508 | 2.07965 | ||||||||
\(897\) | −2.19961 | + | 1.01298i | −0.0734428 | + | 0.0338225i | ||||
\(898\) | 39.9394 | 1.33279 | ||||||||
\(899\) | 1.86780 | + | 1.07837i | 0.0622946 | + | 0.0359658i | ||||
\(900\) | 0.353752 | − | 0.612717i | 0.0117917 | − | 0.0204239i | ||||
\(901\) | 1.76346 | + | 3.05440i | 0.0587493 | + | 0.101757i | ||||
\(902\) | 0.428526i | 0.0142683i | ||||||||
\(903\) | 1.41013 | − | 0.814139i | 0.0469262 | − | 0.0270929i | ||||
\(904\) | 18.3720 | − | 10.6071i | 0.611043 | − | 0.352786i | ||||
\(905\) | 17.0238i | 0.565892i | ||||||||
\(906\) | −0.0971143 | − | 0.168207i | −0.00322641 | − | 0.00558830i | ||||
\(907\) | −17.3135 | + | 29.9879i | −0.574885 | + | 0.995731i | 0.421169 | + | 0.906982i | \(0.361620\pi\) |
−0.996054 | + | 0.0887485i | \(0.971713\pi\) | |||||||
\(908\) | 3.05288 | + | 1.76258i | 0.101313 | + | 0.0584932i | ||||
\(909\) | 8.54015 | 0.283259 | ||||||||
\(910\) | 25.9168 | + | 2.39174i | 0.859134 | + | 0.0792853i | ||||
\(911\) | 31.1865 | 1.03326 | 0.516628 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516628 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(912\) | 2.07842 | + | 1.19997i | 0.0688233 | + | 0.0397351i | ||||
\(913\) | −0.387907 | + | 0.671874i | −0.0128378 | + | 0.0222358i | ||||
\(914\) | 3.19386 | + | 5.53192i | 0.105643 | + | 0.182980i | ||||
\(915\) | − | 0.600701i | − | 0.0198586i | ||||||
\(916\) | −3.95516 | + | 2.28351i | −0.130682 | + | 0.0754493i | ||||
\(917\) | −26.1910 | + | 15.1214i | −0.864903 | + | 0.499352i | ||||
\(918\) | − | 3.02242i | − | 0.0997548i | ||||||
\(919\) | 25.9610 | + | 44.9658i | 0.856374 | + | 1.48328i | 0.875364 | + | 0.483464i | \(0.160621\pi\) |
−0.0189904 | + | 0.999820i | \(0.506045\pi\) | |||||||
\(920\) | 9.34356 | − | 16.1835i | 0.308048 | − | 0.533555i | ||||
\(921\) | 0.562490 | + | 0.324753i | 0.0185347 | + | 0.0107010i | ||||
\(922\) | 30.8707 | 1.01667 | ||||||||
\(923\) | 11.7110 | + | 25.4296i | 0.385474 | + | 0.837026i | ||||
\(924\) | −0.115734 | −0.00380736 | ||||||||
\(925\) | 0.0219955 | + | 0.0126991i | 0.000723209 | + | 0.000417545i | ||||
\(926\) | −24.0059 | + | 41.5794i | −0.788882 | + | 1.36638i | ||||
\(927\) | 8.29242 | + | 14.3629i | 0.272359 | + | 0.471739i | ||||
\(928\) | 1.96117i | 0.0643784i | ||||||||
\(929\) | −17.7462 | + | 10.2457i | −0.582232 | + | 0.336152i | −0.762020 | − | 0.647553i | \(-0.775792\pi\) |
0.179788 | + | 0.983705i | \(0.442459\pi\) | |||||||
\(930\) | 0.179739 | − | 0.103772i | 0.00589387 | − | 0.00340283i | ||||
\(931\) | − | 93.4231i | − | 3.06182i | ||||||
\(932\) | 2.50662 | + | 4.34159i | 0.0821070 | + | 0.142213i | ||||
\(933\) | 0.504492 | − | 0.873806i | 0.0165163 | − | 0.0286071i | ||||
\(934\) | −30.2771 | − | 17.4805i | −0.990698 | − | 0.571980i | ||||
\(935\) | −3.80584 | −0.124464 | ||||||||
\(936\) | −11.8969 | − | 25.8331i | −0.388862 | − | 0.844382i | ||||
\(937\) | −39.6806 | −1.29631 | −0.648154 | − | 0.761510i | \(-0.724459\pi\) | ||||
−0.648154 | + | 0.761510i | \(0.724459\pi\) | |||||||
\(938\) | 32.3399 | + | 18.6714i | 1.05593 | + | 0.609644i | ||||
\(939\) | −0.844727 | + | 1.46311i | −0.0275666 | + | 0.0477468i | ||||
\(940\) | −0.770886 | − | 1.33521i | −0.0251435 | − | 0.0435499i | ||||
\(941\) | 19.6189i | 0.639557i | 0.947492 | + | 0.319779i | \(0.103609\pi\) | ||||
−0.947492 | + | 0.319779i | \(0.896391\pi\) | |||||||
\(942\) | −1.46949 | + | 0.848408i | −0.0478784 | + | 0.0276426i | ||||
\(943\) | 1.64427 | − | 0.949318i | 0.0535447 | − | 0.0309140i | ||||
\(944\) | 38.5309i | 1.25408i | ||||||||
\(945\) | −1.37052 | − | 2.37381i | −0.0445829 | − | 0.0772199i | ||||
\(946\) | 2.84583 | − | 4.92912i | 0.0925259 | − | 0.160260i | ||||
\(947\) | −49.5474 | − | 28.6062i | −1.61007 | − | 0.929576i | −0.989352 | − | 0.145544i | \(-0.953507\pi\) |
−0.620721 | − | 0.784032i | \(-0.713160\pi\) | |||||||
\(948\) | −0.196937 | −0.00639623 | ||||||||
\(949\) | −36.2936 | − | 3.34935i | −1.17814 | − | 0.108725i | ||||
\(950\) | −8.57233 | −0.278123 | ||||||||
\(951\) | −0.670795 | − | 0.387283i | −0.0217520 | − | 0.0125585i | ||||
\(952\) | −22.6517 | + | 39.2339i | −0.734146 | + | 1.27158i | ||||
\(953\) | 13.7385 | + | 23.7958i | 0.445033 | + | 0.770820i | 0.998055 | − | 0.0623470i | \(-0.0198586\pi\) |
−0.553021 | + | 0.833167i | \(0.686525\pi\) | |||||||
\(954\) | 4.43290i | 0.143520i | ||||||||
\(955\) | 3.35793 | − | 1.93870i | 0.108660 | − | 0.0627350i | ||||
\(956\) | 3.05170 | − | 1.76190i | 0.0986991 | − | 0.0569840i | ||||
\(957\) | 0.149319i | 0.00482680i | ||||||||
\(958\) | −3.86988 | − | 6.70283i | −0.125030 | − | 0.216559i | ||||
\(959\) | 39.3527 | − | 68.1609i | 1.27077 | − | 2.20103i | ||||
\(960\) | −0.561752 | − | 0.324328i | −0.0181305 | − | 0.0104676i | ||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | −0.124393 | + | 0.0572867i | −0.00401061 | + | 0.00184700i | ||||
\(963\) | 13.2834 | 0.428053 | ||||||||
\(964\) | −1.92391 | − | 1.11077i | −0.0619649 | − | 0.0357755i | ||||
\(965\) | 0.626972 | − | 1.08595i | 0.0201829 | − | 0.0349579i | ||||
\(966\) | 2.42416 | + | 4.19877i | 0.0779962 | + | 0.135093i | ||||
\(967\) | 10.3643i | 0.333293i | 0.986017 | + | 0.166647i | \(0.0532939\pi\) | ||||
−0.986017 | + | 0.166647i | \(0.946706\pi\) | |||||||
\(968\) | −22.5114 | + | 12.9970i | −0.723544 | + | 0.417738i | ||||
\(969\) | −1.67458 | + | 0.966821i | −0.0537953 | + | 0.0310588i | ||||
\(970\) | 5.14261i | 0.165119i | ||||||||
\(971\) | −20.8758 | − | 36.1579i | −0.669935 | − | 1.16036i | −0.977922 | − | 0.208971i | \(-0.932989\pi\) |
0.307987 | − | 0.951391i | \(-0.400345\pi\) | |||||||
\(972\) | 0.301481 | − | 0.522180i | 0.00966999 | − | 0.0167489i | ||||
\(973\) | −28.5308 | − | 16.4723i | −0.914656 | − | 0.528077i | ||||
\(974\) | −46.0212 | −1.47461 | ||||||||
\(975\) | −0.279019 | − | 0.197356i | −0.00893575 | − | 0.00632045i | ||||
\(976\) | −27.9929 | −0.896030 | ||||||||
\(977\) | −11.9458 | − | 6.89691i | −0.382180 | − | 0.220652i | 0.296586 | − | 0.955006i | \(-0.404152\pi\) |
−0.678766 | + | 0.734354i | \(0.737485\pi\) | |||||||
\(978\) | −1.59981 | + | 2.77095i | −0.0511562 | + | 0.0886051i | ||||
\(979\) | −7.22187 | − | 12.5087i | −0.230812 | − | 0.399778i | ||||
\(980\) | − | 3.85527i | − | 0.123152i | ||||||
\(981\) | −35.6954 | + | 20.6088i | −1.13967 | + | 0.657987i | ||||
\(982\) | 46.3641 | − | 26.7683i | 1.47954 | − | 0.854212i | ||||
\(983\) | 37.9997i | 1.21200i | 0.795463 | + | 0.606002i | \(0.207227\pi\) | ||||
−0.795463 | + | 0.606002i | \(0.792773\pi\) | |||||||
\(984\) | −0.0334909 | − | 0.0580080i | −0.00106765 | − | 0.00184923i | ||||
\(985\) | 7.64098 | − | 13.2346i | 0.243462 | − | 0.421688i | ||||
\(986\) | −6.78988 | − | 3.92014i | −0.216234 | − | 0.124843i | ||||
\(987\) | −2.98211 | −0.0949217 | ||||||||
\(988\) | 2.82306 | − | 3.99119i | 0.0898134 | − | 0.126977i | ||||
\(989\) | −25.2176 | −0.801873 | ||||||||
\(990\) | −4.14261 | − | 2.39174i | −0.131661 | − | 0.0760143i | ||||
\(991\) | 26.2765 | − | 45.5122i | 0.834700 | − | 1.44574i | −0.0595748 | − | 0.998224i | \(-0.518974\pi\) |
0.894275 | − | 0.447519i | \(-0.147692\pi\) | |||||||
\(992\) | −0.974602 | − | 1.68806i | −0.0309436 | − | 0.0535960i | ||||
\(993\) | 2.36396i | 0.0750179i | ||||||||
\(994\) | 48.5419 | − | 28.0257i | 1.53966 | − | 0.888920i | ||||
\(995\) | −11.4572 | + | 6.61480i | −0.363217 | + | 0.209703i | ||||
\(996\) | 0.0162661i | 0.000515411i | ||||||||
\(997\) | −9.29497 | − | 16.0994i | −0.294375 | − | 0.509872i | 0.680465 | − | 0.732781i | \(-0.261778\pi\) |
−0.974839 | + | 0.222909i | \(0.928445\pi\) | |||||||
\(998\) | −21.6079 | + | 37.4260i | −0.683986 | + | 1.18470i | ||||
\(999\) | 0.0124907 | + | 0.00721150i | 0.000395188 | + | 0.000228162i |
(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 | 65.2.m.a.56.4 | yes | 8 | |
3.2 | odd | 2 | 585.2.bu.c.316.1 | 8 | |||
4.3 | odd | 2 | 1040.2.da.b.641.3 | 8 | |||
5.2 | odd | 4 | 325.2.m.c.199.1 | 8 | |||
5.3 | odd | 4 | 325.2.m.b.199.4 | 8 | |||
5.4 | even | 2 | 325.2.n.d.251.1 | 8 | |||
13.2 | odd | 12 | 845.2.e.m.146.4 | 8 | |||
13.3 | even | 3 | 845.2.m.g.361.1 | 8 | |||
13.4 | even | 6 | 845.2.c.g.506.7 | 8 | |||
13.5 | odd | 4 | 845.2.e.m.191.4 | 8 | |||
13.6 | odd | 12 | 845.2.a.m.1.1 | 4 | |||
13.7 | odd | 12 | 845.2.a.l.1.4 | 4 | |||
13.8 | odd | 4 | 845.2.e.n.191.1 | 8 | |||
13.9 | even | 3 | 845.2.c.g.506.2 | 8 | |||
13.10 | even | 6 | inner | 65.2.m.a.36.4 | ✓ | 8 | |
13.11 | odd | 12 | 845.2.e.n.146.1 | 8 | |||
13.12 | even | 2 | 845.2.m.g.316.1 | 8 | |||
39.20 | even | 12 | 7605.2.a.cj.1.1 | 4 | |||
39.23 | odd | 6 | 585.2.bu.c.361.1 | 8 | |||
39.32 | even | 12 | 7605.2.a.cf.1.4 | 4 | |||
52.23 | odd | 6 | 1040.2.da.b.881.3 | 8 | |||
65.19 | odd | 12 | 4225.2.a.bi.1.4 | 4 | |||
65.23 | odd | 12 | 325.2.m.c.49.1 | 8 | |||
65.49 | even | 6 | 325.2.n.d.101.1 | 8 | |||
65.59 | odd | 12 | 4225.2.a.bl.1.1 | 4 | |||
65.62 | odd | 12 | 325.2.m.b.49.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.4 | ✓ | 8 | 13.10 | even | 6 | inner | |
65.2.m.a.56.4 | yes | 8 | 1.1 | even | 1 | trivial | |
325.2.m.b.49.4 | 8 | 65.62 | odd | 12 | |||
325.2.m.b.199.4 | 8 | 5.3 | odd | 4 | |||
325.2.m.c.49.1 | 8 | 65.23 | odd | 12 | |||
325.2.m.c.199.1 | 8 | 5.2 | odd | 4 | |||
325.2.n.d.101.1 | 8 | 65.49 | even | 6 | |||
325.2.n.d.251.1 | 8 | 5.4 | even | 2 | |||
585.2.bu.c.316.1 | 8 | 3.2 | odd | 2 | |||
585.2.bu.c.361.1 | 8 | 39.23 | odd | 6 | |||
845.2.a.l.1.4 | 4 | 13.7 | odd | 12 | |||
845.2.a.m.1.1 | 4 | 13.6 | odd | 12 | |||
845.2.c.g.506.2 | 8 | 13.9 | even | 3 | |||
845.2.c.g.506.7 | 8 | 13.4 | even | 6 | |||
845.2.e.m.146.4 | 8 | 13.2 | odd | 12 | |||
845.2.e.m.191.4 | 8 | 13.5 | odd | 4 | |||
845.2.e.n.146.1 | 8 | 13.11 | odd | 12 | |||
845.2.e.n.191.1 | 8 | 13.8 | odd | 4 | |||
845.2.m.g.316.1 | 8 | 13.12 | even | 2 | |||
845.2.m.g.361.1 | 8 | 13.3 | even | 3 | |||
1040.2.da.b.641.3 | 8 | 4.3 | odd | 2 | |||
1040.2.da.b.881.3 | 8 | 52.23 | odd | 6 | |||
4225.2.a.bi.1.4 | 4 | 65.19 | odd | 12 | |||
4225.2.a.bl.1.1 | 4 | 65.59 | odd | 12 | |||
7605.2.a.cf.1.4 | 4 | 39.32 | even | 12 | |||
7605.2.a.cj.1.1 | 4 | 39.20 | even | 12 |