Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(489,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.489");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.i (of order \(4\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 489.10 | ||
Character | \(\chi\) | \(=\) | 637.489 |
Dual form | 637.2.i.a.538.9 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.546480 | + | 0.546480i | 0.386420 | + | 0.386420i | 0.873408 | − | 0.486989i | \(-0.161905\pi\) |
−0.486989 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(3\) | 0.487133i | 0.281246i | 0.990063 | + | 0.140623i | \(0.0449106\pi\) | ||||
−0.990063 | + | 0.140623i | \(0.955089\pi\) | |||||||
\(4\) | − | 1.40272i | − | 0.701360i | ||||||
\(5\) | −1.29040 | + | 1.29040i | −0.577084 | + | 0.577084i | −0.934099 | − | 0.357015i | \(-0.883795\pi\) |
0.357015 | + | 0.934099i | \(0.383795\pi\) | |||||||
\(6\) | −0.266208 | + | 0.266208i | −0.108679 | + | 0.108679i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.85952 | − | 1.85952i | 0.657439 | − | 0.657439i | ||||
\(9\) | 2.76270 | 0.920901 | ||||||||
\(10\) | −1.41035 | −0.445993 | ||||||||
\(11\) | −0.725276 | + | 0.725276i | −0.218679 | + | 0.218679i | −0.807942 | − | 0.589263i | \(-0.799418\pi\) |
0.589263 | + | 0.807942i | \(0.299418\pi\) | |||||||
\(12\) | 0.683311 | 0.197255 | ||||||||
\(13\) | 0.266208 | + | 3.59571i | 0.0738329 | + | 0.997271i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.628596 | − | 0.628596i | −0.162303 | − | 0.162303i | ||||
\(16\) | −0.773062 | −0.193266 | ||||||||
\(17\) | 5.20058 | 1.26133 | 0.630663 | − | 0.776057i | \(-0.282783\pi\) | ||||
0.630663 | + | 0.776057i | \(0.282783\pi\) | |||||||
\(18\) | 1.50976 | + | 1.50976i | 0.355854 | + | 0.355854i | ||||
\(19\) | 3.71699 | − | 3.71699i | 0.852736 | − | 0.852736i | −0.137733 | − | 0.990469i | \(-0.543982\pi\) |
0.990469 | + | 0.137733i | \(0.0439816\pi\) | |||||||
\(20\) | 1.81007 | + | 1.81007i | 0.404743 | + | 0.404743i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.792697 | −0.169004 | ||||||||
\(23\) | − | 0.843739i | − | 0.175932i | −0.996123 | − | 0.0879659i | \(-0.971963\pi\) | ||
0.996123 | − | 0.0879659i | \(-0.0280366\pi\) | |||||||
\(24\) | 0.905832 | + | 0.905832i | 0.184902 | + | 0.184902i | ||||
\(25\) | 1.66974i | 0.333948i | ||||||||
\(26\) | −1.81951 | + | 2.11046i | −0.356834 | + | 0.413895i | ||||
\(27\) | 2.80720i | 0.540246i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3454 | 1.92109 | 0.960543 | − | 0.278130i | \(-0.0897147\pi\) | ||||
0.960543 | + | 0.278130i | \(0.0897147\pi\) | |||||||
\(30\) | − | 0.687030i | − | 0.125434i | ||||||
\(31\) | −4.16994 | + | 4.16994i | −0.748943 | + | 0.748943i | −0.974281 | − | 0.225337i | \(-0.927652\pi\) |
0.225337 | + | 0.974281i | \(0.427652\pi\) | |||||||
\(32\) | −4.14150 | − | 4.14150i | −0.732120 | − | 0.732120i | ||||
\(33\) | −0.353306 | − | 0.353306i | −0.0615026 | − | 0.0615026i | ||||
\(34\) | 2.84201 | + | 2.84201i | 0.487401 | + | 0.487401i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 3.87530i | − | 0.645883i | ||||||
\(37\) | 4.41711 | − | 4.41711i | 0.726168 | − | 0.726168i | −0.243686 | − | 0.969854i | \(-0.578357\pi\) |
0.969854 | + | 0.243686i | \(0.0783566\pi\) | |||||||
\(38\) | 4.06252 | 0.659028 | ||||||||
\(39\) | −1.75159 | + | 0.129679i | −0.280479 | + | 0.0207652i | ||||
\(40\) | 4.79904i | 0.758795i | ||||||||
\(41\) | 0.0927742 | − | 0.0927742i | 0.0144889 | − | 0.0144889i | −0.699825 | − | 0.714314i | \(-0.746739\pi\) |
0.714314 | + | 0.699825i | \(0.246739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.36681i | 1.12343i | 0.827331 | + | 0.561714i | \(0.189858\pi\) | ||||
−0.827331 | + | 0.561714i | \(0.810142\pi\) | |||||||
\(44\) | 1.01736 | + | 1.01736i | 0.153373 | + | 0.153373i | ||||
\(45\) | −3.56499 | + | 3.56499i | −0.531437 | + | 0.531437i | ||||
\(46\) | 0.461086 | − | 0.461086i | 0.0679835 | − | 0.0679835i | ||||
\(47\) | 1.59524 | + | 1.59524i | 0.232689 | + | 0.232689i | 0.813814 | − | 0.581125i | \(-0.197387\pi\) |
−0.581125 | + | 0.813814i | \(0.697387\pi\) | |||||||
\(48\) | − | 0.376584i | − | 0.0543552i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.912480 | + | 0.912480i | −0.129044 | + | 0.129044i | ||||
\(51\) | 2.53337i | 0.354743i | ||||||||
\(52\) | 5.04377 | − | 0.373416i | 0.699446 | − | 0.0517834i | ||||
\(53\) | −6.77180 | −0.930178 | −0.465089 | − | 0.885264i | \(-0.653978\pi\) | ||||
−0.465089 | + | 0.885264i | \(0.653978\pi\) | |||||||
\(54\) | −1.53408 | + | 1.53408i | −0.208762 | + | 0.208762i | ||||
\(55\) | − | 1.87179i | − | 0.252392i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.81067 | + | 1.81067i | 0.239829 | + | 0.239829i | ||||
\(58\) | 5.65353 | + | 5.65353i | 0.742345 | + | 0.742345i | ||||
\(59\) | −7.12895 | − | 7.12895i | −0.928110 | − | 0.928110i | 0.0694735 | − | 0.997584i | \(-0.477868\pi\) |
−0.997584 | + | 0.0694735i | \(0.977868\pi\) | |||||||
\(60\) | −0.881744 | + | 0.881744i | −0.113833 | + | 0.113833i | ||||
\(61\) | 1.30682i | 0.167321i | 0.996494 | + | 0.0836604i | \(0.0266611\pi\) | ||||
−0.996494 | + | 0.0836604i | \(0.973339\pi\) | |||||||
\(62\) | −4.55758 | −0.578813 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2.98037i | − | 0.372546i | ||||||
\(65\) | −4.98342 | − | 4.29639i | −0.618117 | − | 0.532901i | ||||
\(66\) | − | 0.386149i | − | 0.0475316i | ||||||
\(67\) | 3.04544 | + | 3.04544i | 0.372059 | + | 0.372059i | 0.868227 | − | 0.496168i | \(-0.165260\pi\) |
−0.496168 | + | 0.868227i | \(0.665260\pi\) | |||||||
\(68\) | − | 7.29496i | − | 0.884643i | ||||||
\(69\) | 0.411013 | 0.0494802 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.02388 | − | 6.02388i | −0.714903 | − | 0.714903i | 0.252654 | − | 0.967557i | \(-0.418697\pi\) |
−0.967557 | + | 0.252654i | \(0.918697\pi\) | |||||||
\(72\) | 5.13729 | − | 5.13729i | 0.605436 | − | 0.605436i | ||||
\(73\) | −8.02243 | − | 8.02243i | −0.938954 | − | 0.938954i | 0.0592870 | − | 0.998241i | \(-0.481117\pi\) |
−0.998241 | + | 0.0592870i | \(0.981117\pi\) | |||||||
\(74\) | 4.82772 | 0.561211 | ||||||||
\(75\) | −0.813386 | −0.0939218 | ||||||||
\(76\) | −5.21390 | − | 5.21390i | −0.598075 | − | 0.598075i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.02807 | − | 0.886341i | −0.116407 | − | 0.100358i | ||||
\(79\) | −10.3248 | −1.16163 | −0.580816 | − | 0.814035i | \(-0.697266\pi\) | ||||
−0.580816 | + | 0.814035i | \(0.697266\pi\) | |||||||
\(80\) | 0.997558 | − | 0.997558i | 0.111530 | − | 0.111530i | ||||
\(81\) | 6.92062 | 0.768958 | ||||||||
\(82\) | 0.101398 | 0.0111976 | ||||||||
\(83\) | 4.16974 | − | 4.16974i | 0.457689 | − | 0.457689i | −0.440207 | − | 0.897896i | \(-0.645095\pi\) |
0.897896 | + | 0.440207i | \(0.145095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.71082 | + | 6.71082i | −0.727891 | + | 0.727891i | ||||
\(86\) | −4.02581 | + | 4.02581i | −0.434115 | + | 0.434115i | ||||
\(87\) | 5.03957i | 0.540299i | ||||||||
\(88\) | 2.69733i | 0.287536i | ||||||||
\(89\) | −5.48933 | − | 5.48933i | −0.581868 | − | 0.581868i | 0.353548 | − | 0.935416i | \(-0.384975\pi\) |
−0.935416 | + | 0.353548i | \(0.884975\pi\) | |||||||
\(90\) | −3.89639 | −0.410715 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.18353 | −0.123391 | ||||||||
\(93\) | −2.03132 | − | 2.03132i | −0.210638 | − | 0.210638i | ||||
\(94\) | 1.74353i | 0.179831i | ||||||||
\(95\) | 9.59280i | 0.984201i | ||||||||
\(96\) | 2.01746 | − | 2.01746i | 0.205906 | − | 0.205906i | ||||
\(97\) | −2.49152 | + | 2.49152i | −0.252976 | + | 0.252976i | −0.822189 | − | 0.569214i | \(-0.807248\pi\) |
0.569214 | + | 0.822189i | \(0.307248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00372 | + | 2.00372i | −0.201381 | + | 0.201381i | ||||
\(100\) | 2.34218 | 0.234218 | ||||||||
\(101\) | 2.43372 | 0.242164 | 0.121082 | − | 0.992642i | \(-0.461364\pi\) | ||||
0.121082 | + | 0.992642i | \(0.461364\pi\) | |||||||
\(102\) | −1.38444 | + | 1.38444i | −0.137080 | + | 0.137080i | ||||
\(103\) | −2.73634 | −0.269620 | −0.134810 | − | 0.990871i | \(-0.543042\pi\) | ||||
−0.134810 | + | 0.990871i | \(0.543042\pi\) | |||||||
\(104\) | 7.18131 | + | 6.19127i | 0.704185 | + | 0.607104i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.70065 | − | 3.70065i | −0.359439 | − | 0.359439i | ||||
\(107\) | 2.25627 | 0.218122 | 0.109061 | − | 0.994035i | \(-0.465216\pi\) | ||||
0.109061 | + | 0.994035i | \(0.465216\pi\) | |||||||
\(108\) | 3.93772 | 0.378907 | ||||||||
\(109\) | 1.15158 | + | 1.15158i | 0.110301 | + | 0.110301i | 0.760103 | − | 0.649802i | \(-0.225148\pi\) |
−0.649802 | + | 0.760103i | \(0.725148\pi\) | |||||||
\(110\) | 1.02290 | − | 1.02290i | 0.0975292 | − | 0.0975292i | ||||
\(111\) | 2.15172 | + | 2.15172i | 0.204232 | + | 0.204232i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.63227 | 0.247623 | 0.123812 | − | 0.992306i | \(-0.460488\pi\) | ||||
0.123812 | + | 0.992306i | \(0.460488\pi\) | |||||||
\(114\) | 1.97899i | 0.185349i | ||||||||
\(115\) | 1.08876 | + | 1.08876i | 0.101527 | + | 0.101527i | ||||
\(116\) | − | 14.5117i | − | 1.34737i | ||||||
\(117\) | 0.735454 | + | 9.93387i | 0.0679928 | + | 0.918387i | ||||
\(118\) | − | 7.79165i | − | 0.717280i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.33777 | −0.213408 | ||||||||
\(121\) | 9.94795i | 0.904359i | ||||||||
\(122\) | −0.714149 | + | 0.714149i | −0.0646560 | + | 0.0646560i | ||||
\(123\) | 0.0451934 | + | 0.0451934i | 0.00407495 | + | 0.00407495i | ||||
\(124\) | 5.84926 | + | 5.84926i | 0.525279 | + | 0.525279i | ||||
\(125\) | −8.60663 | − | 8.60663i | −0.769800 | − | 0.769800i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8104i | 1.04801i | 0.851716 | + | 0.524004i | \(0.175562\pi\) | ||||
−0.851716 | + | 0.524004i | \(0.824438\pi\) | |||||||
\(128\) | −6.65429 | + | 6.65429i | −0.588161 | + | 0.588161i | ||||
\(129\) | −3.58862 | −0.315960 | ||||||||
\(130\) | −0.375448 | − | 5.07122i | −0.0329290 | − | 0.444776i | ||||
\(131\) | − | 15.4467i | − | 1.34959i | −0.738006 | − | 0.674794i | \(-0.764232\pi\) | ||
0.738006 | − | 0.674794i | \(-0.235768\pi\) | |||||||
\(132\) | −0.495589 | + | 0.495589i | −0.0431355 | + | 0.0431355i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.32854i | 0.287542i | ||||||||
\(135\) | −3.62241 | − | 3.62241i | −0.311767 | − | 0.311767i | ||||
\(136\) | 9.67057 | − | 9.67057i | 0.829245 | − | 0.829245i | ||||
\(137\) | −0.724831 | + | 0.724831i | −0.0619265 | + | 0.0619265i | −0.737392 | − | 0.675465i | \(-0.763943\pi\) |
0.675465 | + | 0.737392i | \(0.263943\pi\) | |||||||
\(138\) | 0.224610 | + | 0.224610i | 0.0191201 | + | 0.0191201i | ||||
\(139\) | − | 11.4028i | − | 0.967171i | −0.875297 | − | 0.483585i | \(-0.839334\pi\) | ||
0.875297 | − | 0.483585i | \(-0.160666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.777092 | + | 0.777092i | −0.0654429 | + | 0.0654429i | ||||
\(142\) | − | 6.58385i | − | 0.552505i | ||||||
\(143\) | −2.80096 | − | 2.41481i | −0.234228 | − | 0.201936i | ||||
\(144\) | −2.13574 | −0.177978 | ||||||||
\(145\) | −13.3497 | + | 13.3497i | −1.10863 | + | 1.10863i | ||||
\(146\) | − | 8.76819i | − | 0.725660i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.19597 | − | 6.19597i | −0.509305 | − | 0.509305i | ||||
\(149\) | −5.40106 | − | 5.40106i | −0.442472 | − | 0.442472i | 0.450370 | − | 0.892842i | \(-0.351292\pi\) |
−0.892842 | + | 0.450370i | \(0.851292\pi\) | |||||||
\(150\) | −0.444499 | − | 0.444499i | −0.0362932 | − | 0.0362932i | ||||
\(151\) | 4.84411 | − | 4.84411i | 0.394208 | − | 0.394208i | −0.481976 | − | 0.876184i | \(-0.660081\pi\) |
0.876184 | + | 0.481976i | \(0.160081\pi\) | |||||||
\(152\) | − | 13.8236i | − | 1.12124i | ||||||
\(153\) | 14.3677 | 1.16156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10.7618i | − | 0.864406i | ||||||
\(156\) | 0.181903 | + | 2.45699i | 0.0145639 | + | 0.196717i | ||||
\(157\) | 12.8475i | 1.02534i | 0.858586 | + | 0.512670i | \(0.171343\pi\) | ||||
−0.858586 | + | 0.512670i | \(0.828657\pi\) | |||||||
\(158\) | −5.64230 | − | 5.64230i | −0.448877 | − | 0.448877i | ||||
\(159\) | − | 3.29876i | − | 0.261609i | ||||||
\(160\) | 10.6884 | 0.844990 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.78198 | + | 3.78198i | 0.297140 | + | 0.297140i | ||||
\(163\) | −0.694096 | + | 0.694096i | −0.0543658 | + | 0.0543658i | −0.733767 | − | 0.679401i | \(-0.762240\pi\) |
0.679401 | + | 0.733767i | \(0.262240\pi\) | |||||||
\(164\) | −0.130136 | − | 0.130136i | −0.0101619 | − | 0.0101619i | ||||
\(165\) | 0.911811 | 0.0709844 | ||||||||
\(166\) | 4.55736 | 0.353720 | ||||||||
\(167\) | −9.25126 | − | 9.25126i | −0.715884 | − | 0.715884i | 0.251876 | − | 0.967760i | \(-0.418953\pi\) |
−0.967760 | + | 0.251876i | \(0.918953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8583 | + | 1.91442i | −0.989097 | + | 0.147263i | ||||
\(170\) | −7.33466 | −0.562543 | ||||||||
\(171\) | 10.2689 | − | 10.2689i | 0.785285 | − | 0.785285i | ||||
\(172\) | 10.3336 | 0.787927 | ||||||||
\(173\) | 22.1121 | 1.68115 | 0.840576 | − | 0.541693i | \(-0.182217\pi\) | ||||
0.840576 | + | 0.541693i | \(0.182217\pi\) | |||||||
\(174\) | −2.75402 | + | 2.75402i | −0.208782 | + | 0.208782i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.560683 | − | 0.560683i | 0.0422631 | − | 0.0422631i | ||||
\(177\) | 3.47275 | − | 3.47275i | 0.261028 | − | 0.261028i | ||||
\(178\) | − | 5.99962i | − | 0.449690i | ||||||
\(179\) | 8.07047i | 0.603216i | 0.953432 | + | 0.301608i | \(0.0975233\pi\) | ||||
−0.953432 | + | 0.301608i | \(0.902477\pi\) | |||||||
\(180\) | 5.00068 | + | 5.00068i | 0.372728 | + | 0.372728i | ||||
\(181\) | −20.5622 | −1.52838 | −0.764189 | − | 0.644993i | \(-0.776860\pi\) | ||||
−0.764189 | + | 0.644993i | \(0.776860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.636594 | −0.0470584 | ||||||||
\(184\) | −1.56895 | − | 1.56895i | −0.115664 | − | 0.115664i | ||||
\(185\) | 11.3997i | 0.838120i | ||||||||
\(186\) | − | 2.22015i | − | 0.162789i | ||||||
\(187\) | −3.77186 | + | 3.77186i | −0.275825 | + | 0.275825i | ||||
\(188\) | 2.23767 | − | 2.23767i | 0.163199 | − | 0.163199i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.24227 | + | 5.24227i | −0.380314 | + | 0.380314i | ||||
\(191\) | −13.8382 | −1.00129 | −0.500647 | − | 0.865651i | \(-0.666905\pi\) | ||||
−0.500647 | + | 0.865651i | \(0.666905\pi\) | |||||||
\(192\) | 1.45183 | 0.104777 | ||||||||
\(193\) | 17.2582 | − | 17.2582i | 1.24227 | − | 1.24227i | 0.283212 | − | 0.959057i | \(-0.408600\pi\) |
0.959057 | − | 0.283212i | \(-0.0914000\pi\) | |||||||
\(194\) | −2.72313 | −0.195509 | ||||||||
\(195\) | 2.09291 | − | 2.42759i | 0.149876 | − | 0.173843i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.3424 | − | 14.3424i | −1.02185 | − | 1.02185i | −0.999756 | − | 0.0220979i | \(-0.992965\pi\) |
−0.0220979 | − | 0.999756i | \(-0.507035\pi\) | |||||||
\(198\) | −2.18999 | −0.155635 | ||||||||
\(199\) | −14.8160 | −1.05028 | −0.525140 | − | 0.851016i | \(-0.675987\pi\) | ||||
−0.525140 | + | 0.851016i | \(0.675987\pi\) | |||||||
\(200\) | 3.10491 | + | 3.10491i | 0.219551 | + | 0.219551i | ||||
\(201\) | −1.48353 | + | 1.48353i | −0.104640 | + | 0.104640i | ||||
\(202\) | 1.32998 | + | 1.32998i | 0.0935770 | + | 0.0935770i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.55361 | 0.248803 | ||||||||
\(205\) | 0.239431i | 0.0167226i | ||||||||
\(206\) | −1.49536 | − | 1.49536i | −0.104186 | − | 0.104186i | ||||
\(207\) | − | 2.33100i | − | 0.162016i | ||||||
\(208\) | −0.205796 | − | 2.77971i | −0.0142694 | − | 0.192738i | ||||
\(209\) | 5.39169i | 0.372951i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98585 | 0.480925 | 0.240463 | − | 0.970658i | \(-0.422701\pi\) | ||||
0.240463 | + | 0.970658i | \(0.422701\pi\) | |||||||
\(212\) | 9.49893i | 0.652389i | ||||||||
\(213\) | 2.93443 | − | 2.93443i | 0.201064 | − | 0.201064i | ||||
\(214\) | 1.23301 | + | 1.23301i | 0.0842866 | + | 0.0842866i | ||||
\(215\) | −9.50612 | − | 9.50612i | −0.648312 | − | 0.648312i | ||||
\(216\) | 5.22004 | + | 5.22004i | 0.355179 | + | 0.355179i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.25863i | 0.0852451i | ||||||||
\(219\) | 3.90799 | − | 3.90799i | 0.264077 | − | 0.264077i | ||||
\(220\) | −2.62560 | −0.177018 | ||||||||
\(221\) | 1.38444 | + | 18.6998i | 0.0931274 | + | 1.25788i | ||||
\(222\) | 2.35174i | 0.157839i | ||||||||
\(223\) | −19.4291 | + | 19.4291i | −1.30107 | + | 1.30107i | −0.373403 | + | 0.927669i | \(0.621809\pi\) |
−0.927669 | + | 0.373403i | \(0.878191\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.61300i | 0.307533i | ||||||||
\(226\) | 1.43848 | + | 1.43848i | 0.0956864 | + | 0.0956864i | ||||
\(227\) | −0.0497885 | + | 0.0497885i | −0.00330458 | + | 0.00330458i | −0.708757 | − | 0.705453i | \(-0.750744\pi\) |
0.705453 | + | 0.708757i | \(0.250744\pi\) | |||||||
\(228\) | 2.53986 | − | 2.53986i | 0.168206 | − | 0.168206i | ||||
\(229\) | 3.86548 | + | 3.86548i | 0.255438 | + | 0.255438i | 0.823196 | − | 0.567758i | \(-0.192189\pi\) |
−0.567758 | + | 0.823196i | \(0.692189\pi\) | |||||||
\(230\) | 1.18997i | 0.0784643i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.2374 | − | 19.2374i | 1.26300 | − | 1.26300i | ||||
\(233\) | − | 1.05440i | − | 0.0690762i | −0.999403 | − | 0.0345381i | \(-0.989004\pi\) | ||
0.999403 | − | 0.0345381i | \(-0.0109960\pi\) | |||||||
\(234\) | −5.02675 | + | 5.83057i | −0.328609 | + | 0.381156i | ||||
\(235\) | −4.11698 | −0.268562 | ||||||||
\(236\) | −9.99992 | + | 9.99992i | −0.650939 | + | 0.650939i | ||||
\(237\) | − | 5.02955i | − | 0.326705i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.6963 | + | 18.6963i | 1.20936 | + | 1.20936i | 0.971234 | + | 0.238127i | \(0.0765333\pi\) |
0.238127 | + | 0.971234i | \(0.423467\pi\) | |||||||
\(240\) | 0.485944 | + | 0.485944i | 0.0313675 | + | 0.0313675i | ||||
\(241\) | 6.93020 | + | 6.93020i | 0.446413 | + | 0.446413i | 0.894160 | − | 0.447747i | \(-0.147773\pi\) |
−0.447747 | + | 0.894160i | \(0.647773\pi\) | |||||||
\(242\) | −5.43635 | + | 5.43635i | −0.349462 | + | 0.349462i | ||||
\(243\) | 11.7929i | 0.756513i | ||||||||
\(244\) | 1.83310 | 0.117352 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0493945i | 0.00314928i | ||||||||
\(247\) | 14.3547 | + | 12.3757i | 0.913369 | + | 0.787449i | ||||
\(248\) | 15.5082i | 0.984769i | ||||||||
\(249\) | 2.03122 | + | 2.03122i | 0.128723 | + | 0.128723i | ||||
\(250\) | − | 9.40669i | − | 0.594932i | ||||||
\(251\) | 24.9249 | 1.57325 | 0.786623 | − | 0.617434i | \(-0.211828\pi\) | ||||
0.786623 | + | 0.617434i | \(0.211828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.611943 | + | 0.611943i | 0.0384726 | + | 0.0384726i | ||||
\(254\) | −6.45417 | + | 6.45417i | −0.404971 | + | 0.404971i | ||||
\(255\) | −3.26906 | − | 3.26906i | −0.204717 | − | 0.204717i | ||||
\(256\) | −13.2336 | −0.827100 | ||||||||
\(257\) | −3.96236 | −0.247165 | −0.123583 | − | 0.992334i | \(-0.539438\pi\) | ||||
−0.123583 | + | 0.992334i | \(0.539438\pi\) | |||||||
\(258\) | −1.96111 | − | 1.96111i | −0.122093 | − | 0.122093i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.02662 | + | 6.99033i | −0.373755 | + | 0.433522i | ||||
\(261\) | 28.5812 | 1.76913 | ||||||||
\(262\) | 8.44133 | − | 8.44133i | 0.521507 | − | 0.521507i | ||||
\(263\) | −30.9269 | −1.90703 | −0.953516 | − | 0.301343i | \(-0.902565\pi\) | ||||
−0.953516 | + | 0.301343i | \(0.902565\pi\) | |||||||
\(264\) | −1.31396 | −0.0808684 | ||||||||
\(265\) | 8.73832 | − | 8.73832i | 0.536791 | − | 0.536791i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.67403 | − | 2.67403i | 0.163648 | − | 0.163648i | ||||
\(268\) | 4.27189 | − | 4.27189i | 0.260947 | − | 0.260947i | ||||
\(269\) | − | 11.0114i | − | 0.671378i | −0.941973 | − | 0.335689i | \(-0.891031\pi\) | ||
0.941973 | − | 0.335689i | \(-0.108969\pi\) | |||||||
\(270\) | − | 3.95915i | − | 0.240946i | ||||||
\(271\) | −3.54185 | − | 3.54185i | −0.215152 | − | 0.215152i | 0.591300 | − | 0.806452i | \(-0.298615\pi\) |
−0.806452 | + | 0.591300i | \(0.798615\pi\) | |||||||
\(272\) | −4.02037 | −0.243771 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.792211 | −0.0478592 | ||||||||
\(275\) | −1.21102 | − | 1.21102i | −0.0730275 | − | 0.0730275i | ||||
\(276\) | − | 0.576536i | − | 0.0347034i | ||||||
\(277\) | 12.2075i | 0.733476i | 0.930324 | + | 0.366738i | \(0.119525\pi\) | ||||
−0.930324 | + | 0.366738i | \(0.880475\pi\) | |||||||
\(278\) | 6.23139 | − | 6.23139i | 0.373734 | − | 0.373734i | ||||
\(279\) | −11.5203 | + | 11.5203i | −0.689702 | + | 0.689702i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.8351 | + | 12.8351i | −0.765677 | + | 0.765677i | −0.977342 | − | 0.211665i | \(-0.932111\pi\) |
0.211665 | + | 0.977342i | \(0.432111\pi\) | |||||||
\(282\) | −0.849330 | −0.0505768 | ||||||||
\(283\) | 16.8992 | 1.00455 | 0.502277 | − | 0.864707i | \(-0.332496\pi\) | ||||
0.502277 | + | 0.864707i | \(0.332496\pi\) | |||||||
\(284\) | −8.44981 | + | 8.44981i | −0.501404 | + | 0.501404i | ||||
\(285\) | −4.67297 | −0.276803 | ||||||||
\(286\) | −0.211023 | − | 2.85031i | −0.0124780 | − | 0.168542i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.4417 | − | 11.4417i | −0.674210 | − | 0.674210i | ||||
\(289\) | 10.0460 | 0.590943 | ||||||||
\(290\) | −14.5906 | −0.856791 | ||||||||
\(291\) | −1.21370 | − | 1.21370i | −0.0711484 | − | 0.0711484i | ||||
\(292\) | −11.2532 | + | 11.2532i | −0.658545 | + | 0.658545i | ||||
\(293\) | 11.1183 | + | 11.1183i | 0.649536 | + | 0.649536i | 0.952881 | − | 0.303345i | \(-0.0981033\pi\) |
−0.303345 | + | 0.952881i | \(0.598103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3984 | 1.07120 | ||||||||
\(296\) | − | 16.4274i | − | 0.954822i | ||||||
\(297\) | −2.03600 | − | 2.03600i | −0.118140 | − | 0.118140i | ||||
\(298\) | − | 5.90314i | − | 0.341960i | ||||||
\(299\) | 3.03384 | − | 0.224610i | 0.175452 | − | 0.0129896i | ||||
\(300\) | 1.14095i | 0.0658730i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.29441 | 0.304659 | ||||||||
\(303\) | 1.18555i | 0.0681078i | ||||||||
\(304\) | −2.87347 | + | 2.87347i | −0.164805 | + | 0.164805i | ||||
\(305\) | −1.68632 | − | 1.68632i | −0.0965582 | − | 0.0965582i | ||||
\(306\) | 7.85163 | + | 7.85163i | 0.448848 | + | 0.448848i | ||||
\(307\) | 14.6604 | + | 14.6604i | 0.836715 | + | 0.836715i | 0.988425 | − | 0.151710i | \(-0.0484781\pi\) |
−0.151710 | + | 0.988425i | \(0.548478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.33296i | − | 0.0758296i | ||||||
\(310\) | 5.88109 | − | 5.88109i | 0.334024 | − | 0.334024i | ||||
\(311\) | −10.7063 | −0.607101 | −0.303550 | − | 0.952815i | \(-0.598172\pi\) | ||||
−0.303550 | + | 0.952815i | \(0.598172\pi\) | |||||||
\(312\) | −3.01597 | + | 3.49825i | −0.170746 | + | 0.198049i | ||||
\(313\) | − | 10.7494i | − | 0.607590i | −0.952737 | − | 0.303795i | \(-0.901746\pi\) | ||
0.952737 | − | 0.303795i | \(-0.0982538\pi\) | |||||||
\(314\) | −7.02088 | + | 7.02088i | −0.396211 | + | 0.396211i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4828i | 0.814722i | ||||||||
\(317\) | 8.29001 | + | 8.29001i | 0.465613 | + | 0.465613i | 0.900490 | − | 0.434877i | \(-0.143208\pi\) |
−0.434877 | + | 0.900490i | \(0.643208\pi\) | |||||||
\(318\) | 1.80271 | − | 1.80271i | 0.101091 | − | 0.101091i | ||||
\(319\) | −7.50325 | + | 7.50325i | −0.420101 | + | 0.420101i | ||||
\(320\) | 3.84586 | + | 3.84586i | 0.214990 | + | 0.214990i | ||||
\(321\) | 1.09910i | 0.0613460i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.3305 | − | 19.3305i | 1.07558 | − | 1.07558i | ||||
\(324\) | − | 9.70770i | − | 0.539316i | ||||||
\(325\) | −6.00391 | + | 0.444499i | −0.333037 | + | 0.0246564i | ||||
\(326\) | −0.758619 | −0.0420160 | ||||||||
\(327\) | −0.560972 | + | 0.560972i | −0.0310218 | + | 0.0310218i | ||||
\(328\) | − | 0.345031i | − | 0.0190511i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.498286 | + | 0.498286i | 0.0274297 | + | 0.0274297i | ||||
\(331\) | −19.1719 | − | 19.1719i | −1.05378 | − | 1.05378i | −0.998469 | − | 0.0553146i | \(-0.982384\pi\) |
−0.0553146 | − | 0.998469i | \(-0.517616\pi\) | |||||||
\(332\) | −5.84898 | − | 5.84898i | −0.321005 | − | 0.321005i | ||||
\(333\) | 12.2032 | − | 12.2032i | 0.668729 | − | 0.668729i | ||||
\(334\) | − | 10.1113i | − | 0.553263i | ||||||
\(335\) | −7.85966 | −0.429419 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.5911i | − | 1.12167i | −0.827927 | − | 0.560835i | \(-0.810480\pi\) | ||
0.827927 | − | 0.560835i | \(-0.189520\pi\) | |||||||
\(338\) | −8.07297 | − | 5.98059i | −0.439112 | − | 0.325301i | ||||
\(339\) | 1.28227i | 0.0696431i | ||||||||
\(340\) | 9.41340 | + | 9.41340i | 0.510513 | + | 0.510513i | ||||
\(341\) | − | 6.04871i | − | 0.327556i | ||||||
\(342\) | 11.2235 | 0.606899 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.6987 | + | 13.6987i | 0.738585 | + | 0.738585i | ||||
\(345\) | −0.530371 | + | 0.530371i | −0.0285542 | + | 0.0285542i | ||||
\(346\) | 12.0838 | + | 12.0838i | 0.649630 | + | 0.649630i | ||||
\(347\) | 14.9791 | 0.804122 | 0.402061 | − | 0.915613i | \(-0.368294\pi\) | ||||
0.402061 | + | 0.915613i | \(0.368294\pi\) | |||||||
\(348\) | 7.06910 | 0.378944 | ||||||||
\(349\) | 3.25693 | + | 3.25693i | 0.174340 | + | 0.174340i | 0.788883 | − | 0.614543i | \(-0.210660\pi\) |
−0.614543 | + | 0.788883i | \(0.710660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0939 | + | 0.747300i | −0.538772 | + | 0.0398879i | ||||
\(352\) | 6.00746 | 0.320198 | ||||||||
\(353\) | 3.94222 | − | 3.94222i | 0.209823 | − | 0.209823i | −0.594369 | − | 0.804192i | \(-0.702598\pi\) |
0.804192 | + | 0.594369i | \(0.202598\pi\) | |||||||
\(354\) | 3.79557 | 0.201732 | ||||||||
\(355\) | 15.5464 | 0.825118 | ||||||||
\(356\) | −7.70000 | + | 7.70000i | −0.408099 | + | 0.408099i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.41035 | + | 4.41035i | −0.233094 | + | 0.233094i | ||||
\(359\) | 3.55021 | − | 3.55021i | 0.187373 | − | 0.187373i | −0.607186 | − | 0.794559i | \(-0.707702\pi\) |
0.794559 | + | 0.607186i | \(0.207702\pi\) | |||||||
\(360\) | 13.2583i | 0.698774i | ||||||||
\(361\) | − | 8.63206i | − | 0.454319i | ||||||
\(362\) | −11.2368 | − | 11.2368i | −0.590595 | − | 0.590595i | ||||
\(363\) | −4.84597 | −0.254348 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.7043 | 1.08371 | ||||||||
\(366\) | −0.347886 | − | 0.347886i | −0.0181843 | − | 0.0181843i | ||||
\(367\) | − | 3.07383i | − | 0.160452i | −0.996777 | − | 0.0802262i | \(-0.974436\pi\) | ||
0.996777 | − | 0.0802262i | \(-0.0255643\pi\) | |||||||
\(368\) | 0.652263i | 0.0340015i | ||||||||
\(369\) | 0.256307 | − | 0.256307i | 0.0133428 | − | 0.0133428i | ||||
\(370\) | −6.22969 | + | 6.22969i | −0.323866 | + | 0.323866i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.84937 | + | 2.84937i | −0.147733 | + | 0.147733i | ||||
\(373\) | 23.3509 | 1.20906 | 0.604532 | − | 0.796581i | \(-0.293360\pi\) | ||||
0.604532 | + | 0.796581i | \(0.293360\pi\) | |||||||
\(374\) | −4.12248 | −0.213169 | ||||||||
\(375\) | 4.19257 | − | 4.19257i | 0.216503 | − | 0.216503i | ||||
\(376\) | 5.93273 | 0.305957 | ||||||||
\(377\) | 2.75402 | + | 37.1989i | 0.141839 | + | 1.91584i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97284 | − | 1.97284i | −0.101338 | − | 0.101338i | 0.654620 | − | 0.755958i | \(-0.272829\pi\) |
−0.755958 | + | 0.654620i | \(0.772829\pi\) | |||||||
\(380\) | 13.4560 | 0.690279 | ||||||||
\(381\) | −5.75326 | −0.294748 | ||||||||
\(382\) | −7.56228 | − | 7.56228i | −0.386920 | − | 0.386920i | ||||
\(383\) | −2.18952 | + | 2.18952i | −0.111879 | + | 0.111879i | −0.760830 | − | 0.648951i | \(-0.775208\pi\) |
0.648951 | + | 0.760830i | \(0.275208\pi\) | |||||||
\(384\) | −3.24152 | − | 3.24152i | −0.165418 | − | 0.165418i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.8625 | 0.960074 | ||||||||
\(387\) | 20.3523i | 1.03457i | ||||||||
\(388\) | 3.49490 | + | 3.49490i | 0.177427 | + | 0.177427i | ||||
\(389\) | 11.0113i | 0.558295i | 0.960248 | + | 0.279148i | \(0.0900519\pi\) | ||||
−0.960248 | + | 0.279148i | \(0.909948\pi\) | |||||||
\(390\) | 2.47036 | − | 0.182893i | 0.125092 | − | 0.00926115i | ||||
\(391\) | − | 4.38793i | − | 0.221907i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.52462 | 0.379567 | ||||||||
\(394\) | − | 15.6757i | − | 0.789729i | ||||||
\(395\) | 13.3231 | − | 13.3231i | 0.670359 | − | 0.670359i | ||||
\(396\) | 2.81066 | + | 2.81066i | 0.141241 | + | 0.141241i | ||||
\(397\) | 27.0816 | + | 27.0816i | 1.35918 | + | 1.35918i | 0.874923 | + | 0.484262i | \(0.160912\pi\) |
0.484262 | + | 0.874923i | \(0.339088\pi\) | |||||||
\(398\) | −8.09666 | − | 8.09666i | −0.405849 | − | 0.405849i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 1.29081i | − | 0.0645407i | ||||||
\(401\) | −4.75621 | + | 4.75621i | −0.237514 | + | 0.237514i | −0.815820 | − | 0.578306i | \(-0.803714\pi\) |
0.578306 | + | 0.815820i | \(0.303714\pi\) | |||||||
\(402\) | −1.62144 | −0.0808701 | ||||||||
\(403\) | −16.1040 | − | 13.8838i | −0.802196 | − | 0.691603i | ||||
\(404\) | − | 3.41383i | − | 0.169844i | ||||||
\(405\) | −8.93036 | + | 8.93036i | −0.443753 | + | 0.443753i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.40725i | 0.317595i | ||||||||
\(408\) | 4.71085 | + | 4.71085i | 0.233222 | + | 0.233222i | ||||
\(409\) | −24.0696 | + | 24.0696i | −1.19017 | + | 1.19017i | −0.213146 | + | 0.977020i | \(0.568371\pi\) |
−0.977020 | + | 0.213146i | \(0.931629\pi\) | |||||||
\(410\) | −0.130844 | + | 0.130844i | −0.00646195 | + | 0.00646195i | ||||
\(411\) | −0.353089 | − | 0.353089i | −0.0174166 | − | 0.0174166i | ||||
\(412\) | 3.83832i | 0.189101i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.27384 | − | 1.27384i | 0.0626060 | − | 0.0626060i | ||||
\(415\) | 10.7613i | 0.528250i | ||||||||
\(416\) | 13.7891 | − | 15.9941i | 0.676067 | − | 0.784177i | ||||
\(417\) | 5.55467 | 0.272013 | ||||||||
\(418\) | −2.94645 | + | 2.94645i | −0.144116 | + | 0.144116i | ||||
\(419\) | − | 35.5515i | − | 1.73680i | −0.495862 | − | 0.868401i | \(-0.665148\pi\) | ||
0.495862 | − | 0.868401i | \(-0.334852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.3166 | − | 10.3166i | −0.502802 | − | 0.502802i | 0.409505 | − | 0.912308i | \(-0.365701\pi\) |
−0.912308 | + | 0.409505i | \(0.865701\pi\) | |||||||
\(422\) | 3.81762 | + | 3.81762i | 0.185839 | + | 0.185839i | ||||
\(423\) | 4.40716 | + | 4.40716i | 0.214283 | + | 0.214283i | ||||
\(424\) | −12.5923 | + | 12.5923i | −0.611535 | + | 0.611535i | ||||
\(425\) | 8.68363i | 0.421218i | ||||||||
\(426\) | 3.20721 | 0.155390 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 3.16492i | − | 0.152982i | ||||||
\(429\) | 1.17633 | − | 1.36444i | 0.0567939 | − | 0.0658757i | ||||
\(430\) | − | 10.3898i | − | 0.501041i | ||||||
\(431\) | −25.2499 | − | 25.2499i | −1.21624 | − | 1.21624i | −0.968937 | − | 0.247307i | \(-0.920454\pi\) |
−0.247307 | − | 0.968937i | \(-0.579546\pi\) | |||||||
\(432\) | − | 2.17014i | − | 0.104411i | ||||||
\(433\) | 18.6845 | 0.897919 | 0.448959 | − | 0.893552i | \(-0.351795\pi\) | ||||
0.448959 | + | 0.893552i | \(0.351795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.50305 | − | 6.50305i | −0.311798 | − | 0.311798i | ||||
\(436\) | 1.61534 | − | 1.61534i | 0.0773608 | − | 0.0773608i | ||||
\(437\) | −3.13617 | − | 3.13617i | −0.150023 | − | 0.150023i | ||||
\(438\) | 4.27127 | 0.204089 | ||||||||
\(439\) | −23.8317 | −1.13742 | −0.568712 | − | 0.822537i | \(-0.692558\pi\) | ||||
−0.568712 | + | 0.822537i | \(0.692558\pi\) | |||||||
\(440\) | −3.48063 | − | 3.48063i | −0.165932 | − | 0.165932i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.46248 | + | 10.9756i | −0.450084 | + | 0.522057i | ||||
\(443\) | −23.3815 | −1.11089 | −0.555445 | − | 0.831553i | \(-0.687452\pi\) | ||||
−0.555445 | + | 0.831553i | \(0.687452\pi\) | |||||||
\(444\) | 3.01826 | − | 3.01826i | 0.143240 | − | 0.143240i | ||||
\(445\) | 14.1669 | 0.671573 | ||||||||
\(446\) | −21.2353 | −1.00552 | ||||||||
\(447\) | 2.63104 | − | 2.63104i | 0.124444 | − | 0.124444i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.6188 | + | 17.6188i | −0.831482 | + | 0.831482i | −0.987720 | − | 0.156237i | \(-0.950063\pi\) |
0.156237 | + | 0.987720i | \(0.450063\pi\) | |||||||
\(450\) | −2.52091 | + | 2.52091i | −0.118837 | + | 0.118837i | ||||
\(451\) | 0.134574i | 0.00633683i | ||||||||
\(452\) | − | 3.69234i | − | 0.173673i | ||||||
\(453\) | 2.35972 | + | 2.35972i | 0.110869 | + | 0.110869i | ||||
\(454\) | −0.0544168 | −0.00255391 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.73394 | 0.315346 | ||||||||
\(457\) | 2.86848 | + | 2.86848i | 0.134182 | + | 0.134182i | 0.771008 | − | 0.636826i | \(-0.219753\pi\) |
−0.636826 | + | 0.771008i | \(0.719753\pi\) | |||||||
\(458\) | 4.22481i | 0.197412i | ||||||||
\(459\) | 14.5991i | 0.681427i | ||||||||
\(460\) | 1.52722 | − | 1.52722i | 0.0712072 | − | 0.0712072i | ||||
\(461\) | 7.54874 | − | 7.54874i | 0.351580 | − | 0.351580i | −0.509117 | − | 0.860697i | \(-0.670028\pi\) |
0.860697 | + | 0.509117i | \(0.170028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.5419 | − | 13.5419i | 0.629344 | − | 0.629344i | −0.318559 | − | 0.947903i | \(-0.603199\pi\) |
0.947903 | + | 0.318559i | \(0.103199\pi\) | |||||||
\(464\) | −7.99761 | −0.371280 | ||||||||
\(465\) | 5.24241 | 0.243111 | ||||||||
\(466\) | 0.576209 | − | 0.576209i | 0.0266924 | − | 0.0266924i | ||||
\(467\) | −36.1267 | −1.67175 | −0.835873 | − | 0.548923i | \(-0.815038\pi\) | ||||
−0.835873 | + | 0.548923i | \(0.815038\pi\) | |||||||
\(468\) | 13.9344 | − | 1.03164i | 0.644120 | − | 0.0476874i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.24985 | − | 2.24985i | −0.103778 | − | 0.103778i | ||||
\(471\) | −6.25842 | −0.288373 | ||||||||
\(472\) | −26.5128 | −1.22035 | ||||||||
\(473\) | −5.34297 | − | 5.34297i | −0.245670 | − | 0.245670i | ||||
\(474\) | 2.74855 | − | 2.74855i | 0.126245 | − | 0.126245i | ||||
\(475\) | 6.20642 | + | 6.20642i | 0.284770 | + | 0.284770i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.7085 | −0.856601 | ||||||||
\(478\) | 20.4343i | 0.934641i | ||||||||
\(479\) | 23.3427 | + | 23.3427i | 1.06656 | + | 1.06656i | 0.997621 | + | 0.0689350i | \(0.0219601\pi\) |
0.0689350 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(480\) | 5.20666i | 0.237650i | ||||||||
\(481\) | 17.0585 | + | 14.7068i | 0.777802 | + | 0.670571i | ||||
\(482\) | 7.57443i | 0.345006i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.9542 | 0.634281 | ||||||||
\(485\) | − | 6.43011i | − | 0.291976i | ||||||
\(486\) | −6.44456 | + | 6.44456i | −0.292331 | + | 0.292331i | ||||
\(487\) | −4.37289 | − | 4.37289i | −0.198155 | − | 0.198155i | 0.601054 | − | 0.799209i | \(-0.294748\pi\) |
−0.799209 | + | 0.601054i | \(0.794748\pi\) | |||||||
\(488\) | 2.43005 | + | 2.43005i | 0.110003 | + | 0.110003i | ||||
\(489\) | −0.338117 | − | 0.338117i | −0.0152902 | − | 0.0152902i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.4149i | − | 1.50799i | −0.656879 | − | 0.753996i | \(-0.728124\pi\) | ||
0.656879 | − | 0.753996i | \(-0.271876\pi\) | |||||||
\(492\) | 0.0633936 | − | 0.0633936i | 0.00285801 | − | 0.00285801i | ||||
\(493\) | 53.8019 | 2.42312 | ||||||||
\(494\) | 1.08148 | + | 14.6077i | 0.0486580 | + | 0.657229i | ||||
\(495\) | − | 5.17120i | − | 0.232428i | ||||||
\(496\) | 3.22362 | − | 3.22362i | 0.144745 | − | 0.144745i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.22004i | 0.0994824i | ||||||||
\(499\) | −10.5085 | − | 10.5085i | −0.470427 | − | 0.470427i | 0.431626 | − | 0.902053i | \(-0.357940\pi\) |
−0.902053 | + | 0.431626i | \(0.857940\pi\) | |||||||
\(500\) | −12.0727 | + | 12.0727i | −0.539907 | + | 0.539907i | ||||
\(501\) | 4.50659 | − | 4.50659i | 0.201340 | − | 0.201340i | ||||
\(502\) | 13.6210 | + | 13.6210i | 0.607933 | + | 0.607933i | ||||
\(503\) | − | 24.9299i | − | 1.11157i | −0.831327 | − | 0.555784i | \(-0.812418\pi\) | ||
0.831327 | − | 0.555784i | \(-0.187582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.14047 | + | 3.14047i | −0.139749 | + | 0.139749i | ||||
\(506\) | 0.668829i | 0.0297331i | ||||||||
\(507\) | −0.932575 | − | 6.26369i | −0.0414171 | − | 0.278180i | ||||
\(508\) | 16.5667 | 0.735030 | ||||||||
\(509\) | −1.34716 | + | 1.34716i | −0.0597116 | + | 0.0597116i | −0.736332 | − | 0.676620i | \(-0.763444\pi\) |
0.676620 | + | 0.736332i | \(0.263444\pi\) | |||||||
\(510\) | − | 3.57295i | − | 0.158213i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.07668 | + | 6.07668i | 0.268554 | + | 0.268554i | ||||
\(513\) | 10.4343 | + | 10.4343i | 0.460688 | + | 0.460688i | ||||
\(514\) | −2.16535 | − | 2.16535i | −0.0955094 | − | 0.0955094i | ||||
\(515\) | 3.53098 | − | 3.53098i | 0.155593 | − | 0.155593i | ||||
\(516\) | 5.03382i | 0.221602i | ||||||||
\(517\) | −2.31397 | −0.101768 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7715i | 0.472818i | ||||||||
\(520\) | −17.2560 | + | 1.27754i | −0.756724 | + | 0.0560240i | ||||
\(521\) | − | 10.8700i | − | 0.476222i | −0.971238 | − | 0.238111i | \(-0.923472\pi\) | ||
0.971238 | − | 0.238111i | \(-0.0765283\pi\) | |||||||
\(522\) | 15.6190 | + | 15.6190i | 0.683626 | + | 0.683626i | ||||
\(523\) | − | 23.3792i | − | 1.02230i | −0.859491 | − | 0.511151i | \(-0.829219\pi\) | ||
0.859491 | − | 0.511151i | \(-0.170781\pi\) | |||||||
\(524\) | −21.6675 | −0.946547 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.9009 | − | 16.9009i | −0.736914 | − | 0.736914i | ||||
\(527\) | −21.6861 | + | 21.6861i | −0.944662 | + | 0.944662i | ||||
\(528\) | 0.273127 | + | 0.273127i | 0.0118863 | + | 0.0118863i | ||||
\(529\) | 22.2881 | 0.969048 | ||||||||
\(530\) | 9.55063 | 0.414853 | ||||||||
\(531\) | −19.6952 | − | 19.6952i | −0.854697 | − | 0.854697i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.358286 | + | 0.308892i | 0.0155191 | + | 0.0133796i | ||||
\(534\) | 2.92261 | 0.126474 | ||||||||
\(535\) | −2.91149 | + | 2.91149i | −0.125875 | + | 0.125875i | ||||
\(536\) | 11.3261 | 0.489212 | ||||||||
\(537\) | −3.93139 | −0.169652 | ||||||||
\(538\) | 6.01752 | − | 6.01752i | 0.259434 | − | 0.259434i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.08123 | + | 5.08123i | −0.218661 | + | 0.218661i | ||||
\(541\) | −4.80784 | + | 4.80784i | −0.206705 | + | 0.206705i | −0.802865 | − | 0.596160i | \(-0.796692\pi\) |
0.596160 | + | 0.802865i | \(0.296692\pi\) | |||||||
\(542\) | − | 3.87110i | − | 0.166278i | ||||||
\(543\) | − | 10.0165i | − | 0.429850i | ||||||
\(544\) | −21.5382 | − | 21.5382i | −0.923442 | − | 0.923442i | ||||
\(545\) | −2.97199 | −0.127306 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2303 | −0.608446 | −0.304223 | − | 0.952601i | \(-0.598397\pi\) | ||||
−0.304223 | + | 0.952601i | \(0.598397\pi\) | |||||||
\(548\) | 1.01673 | + | 1.01673i | 0.0434328 | + | 0.0434328i | ||||
\(549\) | 3.61035i | 0.154086i | ||||||||
\(550\) | − | 1.32360i | − | 0.0564385i | ||||||
\(551\) | 38.4537 | − | 38.4537i | 1.63818 | − | 1.63818i | ||||
\(552\) | 0.764286 | − | 0.764286i | 0.0325302 | − | 0.0325302i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.67114 | + | 6.67114i | −0.283429 | + | 0.283429i | ||||
\(555\) | −5.55315 | −0.235718 | ||||||||
\(556\) | −15.9949 | −0.678335 | ||||||||
\(557\) | 5.73436 | − | 5.73436i | 0.242973 | − | 0.242973i | −0.575106 | − | 0.818079i | \(-0.695039\pi\) |
0.818079 | + | 0.575106i | \(0.195039\pi\) | |||||||
\(558\) | −12.5912 | −0.533029 | ||||||||
\(559\) | −26.4889 | + | 1.96111i | −1.12036 | + | 0.0829459i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.83739 | − | 1.83739i | −0.0775749 | − | 0.0775749i | ||||
\(562\) | −14.0282 | −0.591745 | ||||||||
\(563\) | 35.5046 | 1.49634 | 0.748170 | − | 0.663507i | \(-0.230933\pi\) | ||||
0.748170 | + | 0.663507i | \(0.230933\pi\) | |||||||
\(564\) | 1.09004 | + | 1.09004i | 0.0458990 | + | 0.0458990i | ||||
\(565\) | −3.39668 | + | 3.39668i | −0.142899 | + | 0.142899i | ||||
\(566\) | 9.23508 | + | 9.23508i | 0.388179 | + | 0.388179i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.4030 | −0.940009 | ||||||||
\(569\) | − | 31.7463i | − | 1.33087i | −0.746454 | − | 0.665437i | \(-0.768245\pi\) | ||
0.746454 | − | 0.665437i | \(-0.231755\pi\) | |||||||
\(570\) | −2.55368 | − | 2.55368i | −0.106962 | − | 0.106962i | ||||
\(571\) | 8.26604i | 0.345923i | 0.984929 | + | 0.172961i | \(0.0553336\pi\) | ||||
−0.984929 | + | 0.172961i | \(0.944666\pi\) | |||||||
\(572\) | −3.38730 | + | 3.92896i | −0.141630 | + | 0.164278i | ||||
\(573\) | − | 6.74103i | − | 0.281611i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.40883 | 0.0587521 | ||||||||
\(576\) | − | 8.23386i | − | 0.343077i | ||||||
\(577\) | −2.38091 | + | 2.38091i | −0.0991186 | + | 0.0991186i | −0.754927 | − | 0.655809i | \(-0.772328\pi\) |
0.655809 | + | 0.754927i | \(0.272328\pi\) | |||||||
\(578\) | 5.48996 | + | 5.48996i | 0.228352 | + | 0.228352i | ||||
\(579\) | 8.40702 | + | 8.40702i | 0.349384 | + | 0.349384i | ||||
\(580\) | 18.7258 | + | 18.7258i | 0.777547 | + | 0.777547i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1.32653i | − | 0.0549863i | ||||||
\(583\) | 4.91142 | − | 4.91142i | 0.203410 | − | 0.203410i | ||||
\(584\) | −29.8357 | −1.23461 | ||||||||
\(585\) | −13.7677 | − | 11.8696i | −0.569224 | − | 0.490749i | ||||
\(586\) | 12.1518i | 0.501987i | ||||||||
\(587\) | 3.33097 | − | 3.33097i | 0.137484 | − | 0.137484i | −0.635016 | − | 0.772499i | \(-0.719006\pi\) |
0.772499 | + | 0.635016i | \(0.219006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.9993i | 1.27730i | ||||||||
\(590\) | 10.0543 | + | 10.0543i | 0.413931 | + | 0.413931i | ||||
\(591\) | 6.98666 | − | 6.98666i | 0.287393 | − | 0.287393i | ||||
\(592\) | −3.41470 | + | 3.41470i | −0.140343 | + | 0.140343i | ||||
\(593\) | 10.6290 | + | 10.6290i | 0.436480 | + | 0.436480i | 0.890826 | − | 0.454345i | \(-0.150127\pi\) |
−0.454345 | + | 0.890826i | \(0.650127\pi\) | |||||||
\(594\) | − | 2.22526i | − | 0.0913035i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.57618 | + | 7.57618i | −0.310332 | + | 0.310332i | ||||
\(597\) | − | 7.21737i | − | 0.295387i | ||||||
\(598\) | 1.78068 | + | 1.53519i | 0.0728173 | + | 0.0627785i | ||||
\(599\) | 7.27545 | 0.297267 | 0.148633 | − | 0.988892i | \(-0.452513\pi\) | ||||
0.148633 | + | 0.988892i | \(0.452513\pi\) | |||||||
\(600\) | −1.51251 | + | 1.51251i | −0.0617478 | + | 0.0617478i | ||||
\(601\) | 2.83288i | 0.115555i | 0.998329 | + | 0.0577777i | \(0.0184015\pi\) | ||||
−0.998329 | + | 0.0577777i | \(0.981599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.41363 | + | 8.41363i | 0.342630 | + | 0.342630i | ||||
\(604\) | −6.79492 | − | 6.79492i | −0.276481 | − | 0.276481i | ||||
\(605\) | −12.8368 | − | 12.8368i | −0.521891 | − | 0.521891i | ||||
\(606\) | −0.647877 | + | 0.647877i | −0.0263182 | + | 0.0263182i | ||||
\(607\) | − | 27.5502i | − | 1.11823i | −0.829091 | − | 0.559114i | \(-0.811141\pi\) | ||
0.829091 | − | 0.559114i | \(-0.188859\pi\) | |||||||
\(608\) | −30.7878 | −1.24861 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 1.84308i | − | 0.0746239i | ||||||
\(611\) | −5.31134 | + | 6.16067i | −0.214874 | + | 0.249234i | ||||
\(612\) | − | 20.1538i | − | 0.814669i | ||||||
\(613\) | −17.3792 | − | 17.3792i | −0.701941 | − | 0.701941i | 0.262886 | − | 0.964827i | \(-0.415326\pi\) |
−0.964827 | + | 0.262886i | \(0.915326\pi\) | |||||||
\(614\) | 16.0233i | 0.646646i | ||||||||
\(615\) | −0.116635 | −0.00470318 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3106 | − | 10.3106i | −0.415090 | − | 0.415090i | 0.468417 | − | 0.883507i | \(-0.344824\pi\) |
−0.883507 | + | 0.468417i | \(0.844824\pi\) | |||||||
\(618\) | 0.728438 | − | 0.728438i | 0.0293021 | − | 0.0293021i | ||||
\(619\) | −21.4347 | − | 21.4347i | −0.861532 | − | 0.861532i | 0.129984 | − | 0.991516i | \(-0.458508\pi\) |
−0.991516 | + | 0.129984i | \(0.958508\pi\) | |||||||
\(620\) | −15.0958 | −0.606260 | ||||||||
\(621\) | 2.36855 | 0.0950465 | ||||||||
\(622\) | −5.85080 | − | 5.85080i | −0.234596 | − | 0.234596i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.35409 | − | 0.100250i | 0.0542069 | − | 0.00401320i | ||||
\(625\) | 13.8633 | 0.554530 | ||||||||
\(626\) | 5.87431 | − | 5.87431i | 0.234785 | − | 0.234785i | ||||
\(627\) | −2.62647 | −0.104891 | ||||||||
\(628\) | 18.0214 | 0.719132 | ||||||||
\(629\) | 22.9715 | − | 22.9715i | 0.915935 | − | 0.915935i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.56348 | + | 9.56348i | −0.380716 | + | 0.380716i | −0.871360 | − | 0.490644i | \(-0.836762\pi\) |
0.490644 | + | 0.871360i | \(0.336762\pi\) | |||||||
\(632\) | −19.1992 | + | 19.1992i | −0.763701 | + | 0.763701i | ||||
\(633\) | 3.40304i | 0.135259i | ||||||||
\(634\) | 9.06065i | 0.359844i | ||||||||
\(635\) | −15.2402 | − | 15.2402i | −0.604788 | − | 0.604788i | ||||
\(636\) | −4.62724 | −0.183482 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.20074 | −0.324671 | ||||||||
\(639\) | −16.6422 | − | 16.6422i | −0.658354 | − | 0.658354i | ||||
\(640\) | − | 17.1734i | − | 0.678837i | ||||||
\(641\) | − | 27.3055i | − | 1.07850i | −0.842145 | − | 0.539251i | \(-0.818708\pi\) | ||
0.842145 | − | 0.539251i | \(-0.181292\pi\) | |||||||
\(642\) | −0.600638 | + | 0.600638i | −0.0237053 | + | 0.0237053i | ||||
\(643\) | 17.4331 | − | 17.4331i | 0.687495 | − | 0.687495i | −0.274183 | − | 0.961678i | \(-0.588407\pi\) |
0.961678 | + | 0.274183i | \(0.0884073\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.63075 | − | 4.63075i | 0.182335 | − | 0.182335i | ||||
\(646\) | 21.1275 | 0.831249 | ||||||||
\(647\) | −19.2142 | −0.755386 | −0.377693 | − | 0.925931i | \(-0.623283\pi\) | ||||
−0.377693 | + | 0.925931i | \(0.623283\pi\) | |||||||
\(648\) | 12.8690 | − | 12.8690i | 0.505543 | − | 0.505543i | ||||
\(649\) | 10.3409 | 0.405916 | ||||||||
\(650\) | −3.52392 | − | 3.03810i | −0.138220 | − | 0.119164i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.973622 | + | 0.973622i | 0.0381300 | + | 0.0381300i | ||||
\(653\) | −18.1628 | −0.710765 | −0.355383 | − | 0.934721i | \(-0.615649\pi\) | ||||
−0.355383 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(654\) | −0.613119 | −0.0239749 | ||||||||
\(655\) | 19.9325 | + | 19.9325i | 0.778826 | + | 0.778826i | ||||
\(656\) | −0.0717202 | + | 0.0717202i | −0.00280020 | + | 0.00280020i | ||||
\(657\) | −22.1636 | − | 22.1636i | −0.864683 | − | 0.864683i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.6851 | −1.42905 | −0.714525 | − | 0.699610i | \(-0.753357\pi\) | ||||
−0.714525 | + | 0.699610i | \(0.753357\pi\) | |||||||
\(660\) | − | 1.27901i | − | 0.0497856i | ||||||
\(661\) | 1.78106 | + | 1.78106i | 0.0692752 | + | 0.0692752i | 0.740895 | − | 0.671620i | \(-0.234401\pi\) |
−0.671620 | + | 0.740895i | \(0.734401\pi\) | |||||||
\(662\) | − | 20.9541i | − | 0.814405i | ||||||
\(663\) | −9.10928 | + | 0.674405i | −0.353775 | + | 0.0261917i | ||||
\(664\) | − | 15.5074i | − | 0.601805i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.3376 | 0.516820 | ||||||||
\(667\) | − | 8.72879i | − | 0.337980i | ||||||
\(668\) | −12.9769 | + | 12.9769i | −0.502092 | + | 0.502092i | ||||
\(669\) | −9.46458 | − | 9.46458i | −0.365922 | − | 0.365922i | ||||
\(670\) | −4.29514 | − | 4.29514i | −0.165936 | − | 0.165936i | ||||
\(671\) | −0.947803 | − | 0.947803i | −0.0365895 | − | 0.0365895i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.52257i | − | 0.135785i | −0.997693 | − | 0.0678925i | \(-0.978373\pi\) | ||
0.997693 | − | 0.0678925i | \(-0.0216275\pi\) | |||||||
\(674\) | 11.2526 | − | 11.2526i | 0.433436 | − | 0.433436i | ||||
\(675\) | −4.68730 | −0.180414 | ||||||||
\(676\) | 2.68539 | + | 18.0365i | 0.103284 | + | 0.693713i | ||||
\(677\) | 21.2972i | 0.818518i | 0.912418 | + | 0.409259i | \(0.134213\pi\) | ||||
−0.912418 | + | 0.409259i | \(0.865787\pi\) | |||||||
\(678\) | −0.700732 | + | 0.700732i | −0.0269115 | + | 0.0269115i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 24.9578i | 0.957087i | ||||||||
\(681\) | −0.0242536 | − | 0.0242536i | −0.000929400 | − | 0.000929400i | ||||
\(682\) | 3.30550 | − | 3.30550i | 0.126574 | − | 0.126574i | ||||
\(683\) | 1.42970 | − | 1.42970i | 0.0547060 | − | 0.0547060i | −0.679225 | − | 0.733931i | \(-0.737684\pi\) |
0.733931 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(684\) | −14.4044 | − | 14.4044i | −0.550768 | − | 0.550768i | ||||
\(685\) | − | 1.87064i | − | 0.0714736i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.88300 | + | 1.88300i | −0.0718410 | + | 0.0718410i | ||||
\(688\) | − | 5.69500i | − | 0.217120i | ||||||
\(689\) | −1.80271 | − | 24.3494i | −0.0686777 | − | 0.927639i | ||||
\(690\) | −0.579674 | −0.0220678 | ||||||||
\(691\) | 0.899585 | − | 0.899585i | 0.0342218 | − | 0.0342218i | −0.689789 | − | 0.724011i | \(-0.742297\pi\) |
0.724011 | + | 0.689789i | \(0.242297\pi\) | |||||||
\(692\) | − | 31.0171i | − | 1.17909i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.18579 | + | 8.18579i | 0.310728 | + | 0.310728i | ||||
\(695\) | 14.7141 | + | 14.7141i | 0.558139 | + | 0.558139i | ||||
\(696\) | 9.37117 | + | 9.37117i | 0.355213 | + | 0.355213i | ||||
\(697\) | 0.482480 | − | 0.482480i | 0.0182752 | − | 0.0182752i | ||||
\(698\) | 3.55970i | 0.134737i | ||||||||
\(699\) | 0.513634 | 0.0194274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.12113i | − | 0.0801138i | −0.999197 | − | 0.0400569i | \(-0.987246\pi\) | ||
0.999197 | − | 0.0400569i | \(-0.0127539\pi\) | |||||||
\(702\) | −5.92449 | − | 5.10772i | −0.223605 | − | 0.192778i | ||||
\(703\) | − | 32.8367i | − | 1.23846i | ||||||
\(704\) | 2.16159 | + | 2.16159i | 0.0814679 | + | 0.0814679i | ||||
\(705\) | − | 2.00552i | − | 0.0755321i | ||||||
\(706\) | 4.30869 | 0.162160 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.87129 | − | 4.87129i | −0.183074 | − | 0.183074i | ||||
\(709\) | −0.990630 | + | 0.990630i | −0.0372039 | + | 0.0372039i | −0.725464 | − | 0.688260i | \(-0.758375\pi\) |
0.688260 | + | 0.725464i | \(0.258375\pi\) | |||||||
\(710\) | 8.49580 | + | 8.49580i | 0.318842 | + | 0.318842i | ||||
\(711\) | −28.5244 | −1.06975 | ||||||||
\(712\) | −20.4150 | −0.765085 | ||||||||
\(713\) | 3.51834 | + | 3.51834i | 0.131763 | + | 0.131763i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.73041 | − | 0.498286i | 0.251703 | − | 0.0186348i | ||||
\(716\) | 11.3206 | 0.423071 | ||||||||
\(717\) | −9.10757 | + | 9.10757i | −0.340128 | + | 0.340128i | ||||
\(718\) | 3.88024 | 0.144809 | ||||||||
\(719\) | 33.0502 | 1.23256 | 0.616281 | − | 0.787526i | \(-0.288638\pi\) | ||||
0.616281 | + | 0.787526i | \(0.288638\pi\) | |||||||
\(720\) | 2.75596 | − | 2.75596i | 0.102708 | − | 0.102708i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.71725 | − | 4.71725i | 0.175558 | − | 0.175558i | ||||
\(723\) | −3.37593 | + | 3.37593i | −0.125552 | + | 0.125552i | ||||
\(724\) | 28.8430i | 1.07194i | ||||||||
\(725\) | 17.2741i | 0.641544i | ||||||||
\(726\) | −2.64823 | − | 2.64823i | −0.0982849 | − | 0.0982849i | ||||
\(727\) | 33.8896 | 1.25689 | 0.628447 | − | 0.777852i | \(-0.283691\pi\) | ||||
0.628447 | + | 0.777852i | \(0.283691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.0172 | 0.556192 | ||||||||
\(730\) | 11.3145 | + | 11.3145i | 0.418767 | + | 0.418767i | ||||
\(731\) | 38.3117i | 1.41701i | ||||||||
\(732\) | 0.892963i | 0.0330049i | ||||||||
\(733\) | −27.8480 | + | 27.8480i | −1.02859 | + | 1.02859i | −0.0290099 | + | 0.999579i | \(0.509235\pi\) |
−0.999579 | + | 0.0290099i | \(0.990765\pi\) | |||||||
\(734\) | 1.67978 | − | 1.67978i | 0.0620020 | − | 0.0620020i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.49434 | + | 3.49434i | −0.128803 | + | 0.128803i | ||||
\(737\) | −4.41756 | −0.162723 | ||||||||
\(738\) | 0.280134 | 0.0103119 | ||||||||
\(739\) | −26.6484 | + | 26.6484i | −0.980277 | + | 0.980277i | −0.999809 | − | 0.0195327i | \(-0.993782\pi\) |
0.0195327 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(740\) | 15.9905 | 0.587824 | ||||||||
\(741\) | −6.02863 | + | 6.99266i | −0.221467 | + | 0.256882i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.2340 | − | 31.2340i | −1.14587 | − | 1.14587i | −0.987358 | − | 0.158508i | \(-0.949332\pi\) |
−0.158508 | − | 0.987358i | \(-0.550668\pi\) | |||||||
\(744\) | −7.55453 | −0.276963 | ||||||||
\(745\) | 13.9390 | 0.510687 | ||||||||
\(746\) | 12.7608 | + | 12.7608i | 0.467206 | + | 0.467206i | ||||
\(747\) | 11.5198 | − | 11.5198i | 0.421486 | − | 0.421486i | ||||
\(748\) | 5.29086 | + | 5.29086i | 0.193453 | + | 0.193453i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.58231 | 0.167322 | ||||||||
\(751\) | 18.0891i | 0.660080i | 0.943967 | + | 0.330040i | \(0.107062\pi\) | ||||
−0.943967 | + | 0.330040i | \(0.892938\pi\) | |||||||
\(752\) | −1.23322 | − | 1.23322i | −0.0449708 | − | 0.0449708i | ||||
\(753\) | 12.1417i | 0.442470i | ||||||||
\(754\) | −18.8235 | + | 21.8335i | −0.685510 | + | 0.795129i | ||||
\(755\) | 12.5017i | 0.454982i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.04733 | 0.147103 | 0.0735514 | − | 0.997291i | \(-0.476567\pi\) | ||||
0.0735514 | + | 0.997291i | \(0.476567\pi\) | |||||||
\(758\) | − | 2.15623i | − | 0.0783180i | ||||||
\(759\) | −0.298098 | + | 0.298098i | −0.0108203 | + | 0.0108203i | ||||
\(760\) | 17.8380 | + | 17.8380i | 0.647052 | + | 0.647052i | ||||
\(761\) | −27.1193 | − | 27.1193i | −0.983073 | − | 0.983073i | 0.0167862 | − | 0.999859i | \(-0.494657\pi\) |
−0.999859 | + | 0.0167862i | \(0.994657\pi\) | |||||||
\(762\) | −3.14404 | − | 3.14404i | −0.113897 | − | 0.113897i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.4111i | 0.702268i | ||||||||
\(765\) | −18.5400 | + | 18.5400i | −0.670315 | + | 0.670315i | ||||
\(766\) | −2.39305 | −0.0864645 | ||||||||
\(767\) | 23.7359 | − | 27.5314i | 0.857052 | − | 0.994102i | ||||
\(768\) | − | 6.44652i | − | 0.232619i | ||||||
\(769\) | −24.8051 | + | 24.8051i | −0.894496 | + | 0.894496i | −0.994942 | − | 0.100446i | \(-0.967973\pi\) |
0.100446 | + | 0.994942i | \(0.467973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.93020i | − | 0.0695143i | ||||||
\(772\) | −24.2084 | − | 24.2084i | −0.871278 | − | 0.871278i | ||||
\(773\) | 21.3049 | − | 21.3049i | 0.766284 | − | 0.766284i | −0.211166 | − | 0.977450i | \(-0.567726\pi\) |
0.977450 | + | 0.211166i | \(0.0677262\pi\) | |||||||
\(774\) | −11.1221 | + | 11.1221i | −0.399776 | + | 0.399776i | ||||
\(775\) | −6.96273 | − | 6.96273i | −0.250108 | − | 0.250108i | ||||
\(776\) | 9.26605i | 0.332632i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.01745 | + | 6.01745i | −0.215736 | + | 0.215736i | ||||
\(779\) | − | 0.689682i | − | 0.0247104i | ||||||
\(780\) | −3.40522 | − | 2.93577i | −0.121927 | − | 0.105117i | ||||
\(781\) | 8.73794 | 0.312668 | ||||||||
\(782\) | 2.39792 | − | 2.39792i | 0.0857493 | − | 0.0857493i | ||||
\(783\) | 29.0415i | 1.03786i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5784 | − | 16.5784i | −0.591707 | − | 0.591707i | ||||
\(786\) | 4.11205 | + | 4.11205i | 0.146672 | + | 0.146672i | ||||
\(787\) | 6.86137 | + | 6.86137i | 0.244581 | + | 0.244581i | 0.818742 | − | 0.574161i | \(-0.194672\pi\) |
−0.574161 | + | 0.818742i | \(0.694672\pi\) | |||||||
\(788\) | −20.1184 | + | 20.1184i | −0.716687 | + | 0.716687i | ||||
\(789\) | − | 15.0655i | − | 0.536346i | ||||||
\(790\) | 14.5616 | 0.518079 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.45191i | 0.264792i | ||||||||
\(793\) | −4.69894 | + | 0.347886i | −0.166864 | + | 0.0123538i | ||||
\(794\) | 29.5991i | 1.05043i | ||||||||
\(795\) | 4.25672 | + | 4.25672i | 0.150970 | + | 0.150970i | ||||
\(796\) | 20.7827i | 0.736624i | ||||||||
\(797\) | −9.46979 | −0.335437 | −0.167719 | − | 0.985835i | \(-0.553640\pi\) | ||||
−0.167719 | + | 0.985835i | \(0.553640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.29615 | + | 8.29615i | 0.293497 | + | 0.293497i | ||||
\(800\) | 6.91523 | − | 6.91523i | 0.244490 | − | 0.244490i | ||||
\(801\) | −15.1654 | − | 15.1654i | −0.535843 | − | 0.535843i | ||||
\(802\) | −5.19835 | −0.183560 | ||||||||
\(803\) | 11.6369 | 0.410659 | ||||||||
\(804\) | 2.08098 | + | 2.08098i | 0.0733905 | + | 0.0733905i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.21326 | − | 16.3877i | −0.0427354 | − | 0.577233i | ||||
\(807\) | 5.36402 | 0.188823 | ||||||||
\(808\) | 4.52555 | − | 4.52555i | 0.159208 | − | 0.159208i | ||||
\(809\) | 23.7060 | 0.833458 | 0.416729 | − | 0.909031i | \(-0.363176\pi\) | ||||
0.416729 | + | 0.909031i | \(0.363176\pi\) | |||||||
\(810\) | −9.76053 | −0.342950 | ||||||||
\(811\) | −29.4470 | + | 29.4470i | −1.03403 | + | 1.03403i | −0.0346248 | + | 0.999400i | \(0.511024\pi\) |
−0.999400 | + | 0.0346248i | \(0.988976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.72535 | − | 1.72535i | 0.0605108 | − | 0.0605108i | ||||
\(814\) | −3.50143 | + | 3.50143i | −0.122725 | + | 0.122725i | ||||
\(815\) | − | 1.79132i | − | 0.0627473i | ||||||
\(816\) | − | 1.95846i | − | 0.0685597i | ||||||
\(817\) | 27.3824 | + | 27.3824i | 0.957988 | + | 0.957988i | ||||
\(818\) | −26.3071 | −0.919807 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.335855 | 0.0117286 | ||||||||
\(821\) | 15.1774 | + | 15.1774i | 0.529696 | + | 0.529696i | 0.920482 | − | 0.390786i | \(-0.127797\pi\) |
−0.390786 | + | 0.920482i | \(0.627797\pi\) | |||||||
\(822\) | − | 0.385912i | − | 0.0134602i | ||||||
\(823\) | − | 18.9392i | − | 0.660178i | −0.943950 | − | 0.330089i | \(-0.892921\pi\) | ||
0.943950 | − | 0.330089i | \(-0.107079\pi\) | |||||||
\(824\) | −5.08828 | + | 5.08828i | −0.177259 | + | 0.177259i | ||||
\(825\) | 0.589929 | − | 0.589929i | 0.0205387 | − | 0.0205387i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.174463 | − | 0.174463i | 0.00606667 | − | 0.00606667i | −0.704067 | − | 0.710134i | \(-0.748635\pi\) |
0.710134 | + | 0.704067i | \(0.248635\pi\) | |||||||
\(828\) | −3.26974 | −0.113631 | ||||||||
\(829\) | −17.0844 | −0.593365 | −0.296682 | − | 0.954976i | \(-0.595880\pi\) | ||||
−0.296682 | + | 0.954976i | \(0.595880\pi\) | |||||||
\(830\) | −5.88081 | + | 5.88081i | −0.204126 | + | 0.204126i | ||||
\(831\) | −5.94666 | −0.206287 | ||||||||
\(832\) | 10.7165 | − | 0.793398i | 0.371529 | − | 0.0275061i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.03551 | + | 3.03551i | 0.105111 | + | 0.105111i | ||||
\(835\) | 23.8756 | 0.826250 | ||||||||
\(836\) | 7.56303 | 0.261573 | ||||||||
\(837\) | −11.7059 | − | 11.7059i | −0.404614 | − | 0.404614i | ||||
\(838\) | 19.4282 | − | 19.4282i | 0.671134 | − | 0.671134i | ||||
\(839\) | 22.4787 | + | 22.4787i | 0.776052 | + | 0.776052i | 0.979157 | − | 0.203105i | \(-0.0651032\pi\) |
−0.203105 | + | 0.979157i | \(0.565103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78.0266 | 2.69057 | ||||||||
\(842\) | − | 11.2757i | − | 0.388585i | ||||||
\(843\) | −6.25240 | − | 6.25240i | −0.215344 | − | 0.215344i | ||||
\(844\) | − | 9.79918i | − | 0.337302i | ||||||
\(845\) | 14.1219 | − | 19.0627i | 0.485809 | − | 0.655775i | ||||
\(846\) | 4.81685i | 0.165607i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.23502 | 0.179771 | ||||||||
\(849\) | 8.23216i | 0.282527i | ||||||||
\(850\) | −4.74543 | + | 4.74543i | −0.162767 | + | 0.162767i | ||||
\(851\) | −3.72689 | − | 3.72689i | −0.127756 | − | 0.127756i | ||||
\(852\) | −4.11618 | − | 4.11618i | −0.141018 | − | 0.141018i | ||||
\(853\) | 3.63231 | + | 3.63231i | 0.124368 | + | 0.124368i | 0.766551 | − | 0.642183i | \(-0.221971\pi\) |
−0.642183 | + | 0.766551i | \(0.721971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.5021i | 0.906351i | ||||||||
\(856\) | 4.19558 | − | 4.19558i | 0.143402 | − | 0.143402i | ||||
\(857\) | 48.1799 | 1.64579 | 0.822897 | − | 0.568190i | \(-0.192356\pi\) | ||||
0.822897 | + | 0.568190i | \(0.192356\pi\) | |||||||
\(858\) | 1.38848 | − | 0.102796i | 0.0474019 | − | 0.00350940i | ||||
\(859\) | − | 3.08901i | − | 0.105396i | −0.998611 | − | 0.0526978i | \(-0.983218\pi\) | ||
0.998611 | − | 0.0526978i | \(-0.0167820\pi\) | |||||||
\(860\) | −13.3344 | + | 13.3344i | −0.454700 | + | 0.454700i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 27.5971i | − | 0.939961i | ||||||
\(863\) | 18.1969 | + | 18.1969i | 0.619430 | + | 0.619430i | 0.945385 | − | 0.325955i | \(-0.105686\pi\) |
−0.325955 | + | 0.945385i | \(0.605686\pi\) | |||||||
\(864\) | 11.6260 | − | 11.6260i | 0.395525 | − | 0.395525i | ||||
\(865\) | −28.5334 | + | 28.5334i | −0.970166 | + | 0.970166i | ||||
\(866\) | 10.2107 | + | 10.2107i | 0.346973 | + | 0.346973i | ||||
\(867\) | 4.89375i | 0.166201i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.48833 | − | 7.48833i | 0.254024 | − | 0.254024i | ||||
\(870\) | − | 7.10758i | − | 0.240969i | ||||||
\(871\) | −10.1398 | + | 11.7612i | −0.343574 | + | 0.398514i | ||||
\(872\) | 4.28276 | 0.145033 | ||||||||
\(873\) | −6.88333 | + | 6.88333i | −0.232965 | + | 0.232965i | ||||
\(874\) | − | 3.42771i | − | 0.115944i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.48181 | − | 5.48181i | −0.185213 | − | 0.185213i | ||||
\(877\) | 0.845403 | + | 0.845403i | 0.0285472 | + | 0.0285472i | 0.721236 | − | 0.692689i | \(-0.243574\pi\) |
−0.692689 | + | 0.721236i | \(0.743574\pi\) | |||||||
\(878\) | −13.0235 | − | 13.0235i | −0.439523 | − | 0.439523i | ||||
\(879\) | −5.41608 | + | 5.41608i | −0.182680 | + | 0.182680i | ||||
\(880\) | 1.44701i | 0.0487787i | ||||||||
\(881\) | 20.3067 | 0.684151 | 0.342075 | − | 0.939672i | \(-0.388870\pi\) | ||||
0.342075 | + | 0.939672i | \(0.388870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.8309i | − | 0.970238i | −0.874448 | − | 0.485119i | \(-0.838776\pi\) | ||
0.874448 | − | 0.485119i | \(-0.161224\pi\) | |||||||
\(884\) | 26.2306 | − | 1.94198i | 0.882229 | − | 0.0653158i | ||||
\(885\) | 8.96246i | 0.301270i | ||||||||
\(886\) | −12.7775 | − | 12.7775i | −0.429270 | − | 0.429270i | ||||
\(887\) | 1.59150i | 0.0534373i | 0.999643 | + | 0.0267186i | \(0.00850582\pi\) | ||||
−0.999643 | + | 0.0267186i | \(0.991494\pi\) | |||||||
\(888\) | 8.00232 | 0.268540 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.74190 | + | 7.74190i | 0.259509 | + | 0.259509i | ||||
\(891\) | −5.01936 | + | 5.01936i | −0.168155 | + | 0.168155i | ||||
\(892\) | 27.2537 | + | 27.2537i | 0.912520 | + | 0.912520i | ||||
\(893\) | 11.8590 | 0.396845 | ||||||||
\(894\) | 2.87562 | 0.0961750 | ||||||||
\(895\) | −10.4141 | − | 10.4141i | −0.348106 | − | 0.348106i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.109415 | + | 1.47788i | 0.00365326 | + | 0.0493451i | ||||
\(898\) | −19.2566 | −0.642602 | ||||||||
\(899\) | −43.1396 | + | 43.1396i | −1.43879 | + | 1.43879i | ||||
\(900\) | 6.47074 | 0.215691 | ||||||||
\(901\) | −35.2173 | −1.17326 | ||||||||
\(902\) | −0.0735418 | + | 0.0735418i | −0.00244868 | + | 0.00244868i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.89475 | − | 4.89475i | 0.162797 | − | 0.162797i | ||||
\(905\) | 26.5335 | − | 26.5335i | 0.882002 | − | 0.882002i | ||||
\(906\) | 2.57908i | 0.0856843i | ||||||||
\(907\) | 0.116742i | 0.00387636i | 0.999998 | + | 0.00193818i | \(0.000616942\pi\) | ||||
−0.999998 | + | 0.00193818i | \(0.999383\pi\) | |||||||
\(908\) | 0.0698392 | + | 0.0698392i | 0.00231770 | + | 0.00231770i | ||||
\(909\) | 6.72364 | 0.223009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.0003 | 0.629507 | 0.314753 | − | 0.949173i | \(-0.398078\pi\) | ||||
0.314753 | + | 0.949173i | \(0.398078\pi\) | |||||||
\(912\) | −1.39976 | − | 1.39976i | −0.0463507 | − | 0.0463507i | ||||
\(913\) | 6.04843i | 0.200174i | ||||||||
\(914\) | 3.13513i | 0.103701i | ||||||||
\(915\) | 0.821460 | − | 0.821460i | 0.0271566 | − | 0.0271566i | ||||
\(916\) | 5.42218 | − | 5.42218i | 0.179154 | − | 0.179154i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.97810 | + | 7.97810i | −0.263317 | + | 0.263317i | ||||
\(919\) | −11.6437 | −0.384089 | −0.192045 | − | 0.981386i | \(-0.561512\pi\) | ||||
−0.192045 | + | 0.981386i | \(0.561512\pi\) | |||||||
\(920\) | 4.04914 | 0.133496 | ||||||||
\(921\) | −7.14158 | + | 7.14158i | −0.235323 | + | 0.235323i | ||||
\(922\) | 8.25047 | 0.271715 | ||||||||
\(923\) | 20.0565 | − | 23.2637i | 0.660168 | − | 0.765735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.37543 | + | 7.37543i | 0.242503 | + | 0.242503i | ||||
\(926\) | 14.8007 | 0.486382 | ||||||||
\(927\) | −7.55970 | −0.248293 | ||||||||
\(928\) | −42.8453 | − | 42.8453i | −1.40647 | − | 1.40647i | ||||
\(929\) | −36.5980 | + | 36.5980i | −1.20074 | + | 1.20074i | −0.226802 | + | 0.973941i | \(0.572827\pi\) |
−0.973941 | + | 0.226802i | \(0.927173\pi\) | |||||||
\(930\) | 2.86487 | + | 2.86487i | 0.0939429 | + | 0.0939429i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.47903 | −0.0484473 | ||||||||
\(933\) | − | 5.21541i | − | 0.170745i | ||||||
\(934\) | −19.7425 | − | 19.7425i | −0.645995 | − | 0.645995i | ||||
\(935\) | − | 9.73439i | − | 0.318349i | ||||||
\(936\) | 19.8398 | + | 17.1046i | 0.648484 | + | 0.559082i | ||||
\(937\) | − | 47.9005i | − | 1.56484i | −0.622751 | − | 0.782420i | \(-0.713985\pi\) | ||
0.622751 | − | 0.782420i | \(-0.286015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.23637 | 0.170882 | ||||||||
\(940\) | 5.77497i | 0.188359i | ||||||||
\(941\) | 22.2959 | − | 22.2959i | 0.726825 | − | 0.726825i | −0.243161 | − | 0.969986i | \(-0.578184\pi\) |
0.969986 | + | 0.243161i | \(0.0781844\pi\) | |||||||
\(942\) | −3.42010 | − | 3.42010i | −0.111433 | − | 0.111433i | ||||
\(943\) | −0.0782772 | − | 0.0782772i | −0.00254906 | − | 0.00254906i | ||||
\(944\) | 5.51112 | + | 5.51112i | 0.179372 | + | 0.179372i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 5.83965i | − | 0.189863i | ||||||
\(947\) | 19.4568 | − | 19.4568i | 0.632261 | − | 0.632261i | −0.316374 | − | 0.948635i | \(-0.602465\pi\) |
0.948635 | + | 0.316374i | \(0.102465\pi\) | |||||||
\(948\) | −7.05505 | −0.229137 | ||||||||
\(949\) | 26.7107 | − | 30.9820i | 0.867066 | − | 1.00572i | ||||
\(950\) | 6.78336i | 0.220081i | ||||||||
\(951\) | −4.03834 | + | 4.03834i | −0.130952 | + | 0.130952i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.2238i | − | 0.525541i | −0.964858 | − | 0.262771i | \(-0.915364\pi\) | ||
0.964858 | − | 0.262771i | \(-0.0846362\pi\) | |||||||
\(954\) | −10.2238 | − | 10.2238i | −0.331007 | − | 0.331007i | ||||
\(955\) | 17.8568 | − | 17.8568i | 0.577831 | − | 0.577831i | ||||
\(956\) | 26.2256 | − | 26.2256i | 0.848197 | − | 0.848197i | ||||
\(957\) | −3.65508 | − | 3.65508i | −0.118152 | − | 0.118152i | ||||
\(958\) | 25.5127i | 0.824276i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.87344 | + | 1.87344i | −0.0604652 | + | 0.0604652i | ||||
\(961\) | − | 3.77681i | − | 0.121833i | ||||||
\(962\) | 1.28518 | + | 17.3591i | 0.0414359 | + | 0.559680i | ||||
\(963\) | 6.23341 | 0.200869 | ||||||||
\(964\) | 9.72113 | − | 9.72113i | 0.313097 | − | 0.313097i | ||||
\(965\) | 44.5398i | 1.43379i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.2029 | + | 18.2029i | 0.585366 | + | 0.585366i | 0.936373 | − | 0.351007i | \(-0.114161\pi\) |
−0.351007 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(968\) | 18.4984 | + | 18.4984i | 0.594561 | + | 0.594561i | ||||
\(969\) | 9.41653 | + | 9.41653i | 0.302503 | + | 0.302503i | ||||
\(970\) | 3.51392 | − | 3.51392i | 0.112825 | − | 0.112825i | ||||
\(971\) | 41.8891i | 1.34428i | 0.740422 | + | 0.672142i | \(0.234626\pi\) | ||||
−0.740422 | + | 0.672142i | \(0.765374\pi\) | |||||||
\(972\) | 16.5421 | 0.530588 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 4.77939i | − | 0.153142i | ||||||
\(975\) | −0.216530 | − | 2.92470i | −0.00693452 | − | 0.0936654i | ||||
\(976\) | − | 1.01025i | − | 0.0323374i | ||||||
\(977\) | −10.4217 | − | 10.4217i | −0.333420 | − | 0.333420i | 0.520464 | − | 0.853884i | \(-0.325759\pi\) |
−0.853884 | + | 0.520464i | \(0.825759\pi\) | |||||||
\(978\) | − | 0.369548i | − | 0.0118169i | ||||||
\(979\) | 7.96256 | 0.254485 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.18147 | + | 3.18147i | 0.101576 | + | 0.101576i | ||||
\(982\) | 18.2605 | − | 18.2605i | 0.582717 | − | 0.582717i | ||||
\(983\) | 14.2126 | + | 14.2126i | 0.453312 | + | 0.453312i | 0.896452 | − | 0.443140i | \(-0.146136\pi\) |
−0.443140 | + | 0.896452i | \(0.646136\pi\) | |||||||
\(984\) | 0.168076 | 0.00535806 | ||||||||
\(985\) | 37.0148 | 1.17939 | ||||||||
\(986\) | 29.4017 | + | 29.4017i | 0.936340 | + | 0.936340i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.3597 | − | 20.1357i | 0.552285 | − | 0.640600i | ||||
\(989\) | 6.21566 | 0.197647 | ||||||||
\(990\) | 2.82595 | − | 2.82595i | 0.0898147 | − | 0.0898147i | ||||
\(991\) | −27.0650 | −0.859747 | −0.429873 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429873 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(992\) | 34.5396 | 1.09663 | ||||||||
\(993\) | 9.33927 | − | 9.33927i | 0.296373 | − | 0.296373i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.1186 | − | 19.1186i | 0.606100 | − | 0.606100i | ||||
\(996\) | 2.84923 | − | 2.84923i | 0.0902814 | − | 0.0902814i | ||||
\(997\) | 28.3372i | 0.897449i | 0.893670 | + | 0.448725i | \(0.148122\pi\) | ||||
−0.893670 | + | 0.448725i | \(0.851878\pi\) | |||||||
\(998\) | − | 11.4854i | − | 0.363564i | ||||||
\(999\) | 12.3997 | + | 12.3997i | 0.392310 | + | 0.392310i |
(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 | 637.2.i.a.489.10 | 32 | ||
7.2 | even | 3 | 91.2.bb.a.73.5 | yes | 32 | ||
7.3 | odd | 6 | 91.2.bb.a.47.4 | yes | 32 | ||
7.4 | even | 3 | 637.2.bc.b.411.4 | 32 | |||
7.5 | odd | 6 | 637.2.bc.b.619.5 | 32 | |||
7.6 | odd | 2 | inner | 637.2.i.a.489.9 | 32 | ||
13.5 | odd | 4 | inner | 637.2.i.a.538.10 | 32 | ||
21.2 | odd | 6 | 819.2.fn.e.73.4 | 32 | |||
21.17 | even | 6 | 819.2.fn.e.775.5 | 32 | |||
91.5 | even | 12 | 637.2.bc.b.31.4 | 32 | |||
91.18 | odd | 12 | 637.2.bc.b.460.5 | 32 | |||
91.31 | even | 12 | 91.2.bb.a.5.5 | ✓ | 32 | ||
91.44 | odd | 12 | 91.2.bb.a.31.4 | yes | 32 | ||
91.83 | even | 4 | inner | 637.2.i.a.538.9 | 32 | ||
273.44 | even | 12 | 819.2.fn.e.577.5 | 32 | |||
273.122 | odd | 12 | 819.2.fn.e.460.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bb.a.5.5 | ✓ | 32 | 91.31 | even | 12 | ||
91.2.bb.a.31.4 | yes | 32 | 91.44 | odd | 12 | ||
91.2.bb.a.47.4 | yes | 32 | 7.3 | odd | 6 | ||
91.2.bb.a.73.5 | yes | 32 | 7.2 | even | 3 | ||
637.2.i.a.489.9 | 32 | 7.6 | odd | 2 | inner | ||
637.2.i.a.489.10 | 32 | 1.1 | even | 1 | trivial | ||
637.2.i.a.538.9 | 32 | 91.83 | even | 4 | inner | ||
637.2.i.a.538.10 | 32 | 13.5 | odd | 4 | inner | ||
637.2.bc.b.31.4 | 32 | 91.5 | even | 12 | |||
637.2.bc.b.411.4 | 32 | 7.4 | even | 3 | |||
637.2.bc.b.460.5 | 32 | 91.18 | odd | 12 | |||
637.2.bc.b.619.5 | 32 | 7.5 | odd | 6 | |||
819.2.fn.e.73.4 | 32 | 21.2 | odd | 6 | |||
819.2.fn.e.460.4 | 32 | 273.122 | odd | 12 | |||
819.2.fn.e.577.5 | 32 | 273.44 | even | 12 | |||
819.2.fn.e.775.5 | 32 | 21.17 | even | 6 |