Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} - 439644 x^{11} + 460536 x^{10} - 1833716 x^{9} + 16970128 x^{8} + \cdots + 88804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 93.6 | ||
Root | \(0.608645 + 0.608645i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.93 |
Dual form | 230.3.f.a.47.6 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.608645 | + | 0.608645i | 0.202882 | + | 0.202882i | 0.801233 | − | 0.598352i | \(-0.204177\pi\) |
−0.598352 | + | 0.801233i | \(0.704177\pi\) | |||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 4.88434 | − | 1.06922i | 0.976868 | − | 0.213844i | ||||
\(6\) | −1.21729 | −0.202882 | ||||||||
\(7\) | 3.48181 | − | 3.48181i | 0.497402 | − | 0.497402i | −0.413226 | − | 0.910628i | \(-0.635598\pi\) |
0.910628 | + | 0.413226i | \(0.135598\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 8.25910i | − | 0.917678i | ||||||
\(10\) | −3.81512 | + | 5.95356i | −0.381512 | + | 0.595356i | ||||
\(11\) | −3.82644 | −0.347858 | −0.173929 | − | 0.984758i | \(-0.555646\pi\) | ||||
−0.173929 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(12\) | 1.21729 | − | 1.21729i | 0.101441 | − | 0.101441i | ||||
\(13\) | −13.1059 | − | 13.1059i | −1.00815 | − | 1.00815i | −0.999967 | − | 0.00818068i | \(-0.997396\pi\) |
−0.00818068 | − | 0.999967i | \(-0.502604\pi\) | |||||||
\(14\) | 6.96363i | 0.497402i | ||||||||
\(15\) | 3.62360 | + | 2.32205i | 0.241574 | + | 0.154804i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 15.9881 | − | 15.9881i | 0.940479 | − | 0.940479i | −0.0578462 | − | 0.998326i | \(-0.518423\pi\) |
0.998326 | + | 0.0578462i | \(0.0184233\pi\) | |||||||
\(18\) | 8.25910 | + | 8.25910i | 0.458839 | + | 0.458839i | ||||
\(19\) | 6.16230i | 0.324332i | 0.986764 | + | 0.162166i | \(0.0518479\pi\) | ||||
−0.986764 | + | 0.162166i | \(0.948152\pi\) | |||||||
\(20\) | −2.13844 | − | 9.76868i | −0.106922 | − | 0.488434i | ||||
\(21\) | 4.23838 | 0.201827 | ||||||||
\(22\) | 3.82644 | − | 3.82644i | 0.173929 | − | 0.173929i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | 2.43458i | 0.101441i | ||||||||
\(25\) | 22.7135 | − | 10.4449i | 0.908541 | − | 0.417795i | ||||
\(26\) | 26.2118 | 1.00815 | ||||||||
\(27\) | 10.5047 | − | 10.5047i | 0.389062 | − | 0.389062i | ||||
\(28\) | −6.96363 | − | 6.96363i | −0.248701 | − | 0.248701i | ||||
\(29\) | 32.8492i | 1.13273i | 0.824154 | + | 0.566366i | \(0.191651\pi\) | ||||
−0.824154 | + | 0.566366i | \(0.808349\pi\) | |||||||
\(30\) | −5.94566 | + | 1.30155i | −0.198189 | + | 0.0433850i | ||||
\(31\) | 27.0235 | 0.871725 | 0.435863 | − | 0.900013i | \(-0.356443\pi\) | ||||
0.435863 | + | 0.900013i | \(0.356443\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.32894 | − | 2.32894i | −0.0705741 | − | 0.0705741i | ||||
\(34\) | 31.9763i | 0.940479i | ||||||||
\(35\) | 13.2835 | − | 20.7292i | 0.379530 | − | 0.592262i | ||||
\(36\) | −16.5182 | −0.458839 | ||||||||
\(37\) | −20.0504 | + | 20.0504i | −0.541903 | + | 0.541903i | −0.924086 | − | 0.382184i | \(-0.875172\pi\) |
0.382184 | + | 0.924086i | \(0.375172\pi\) | |||||||
\(38\) | −6.16230 | − | 6.16230i | −0.162166 | − | 0.162166i | ||||
\(39\) | − | 15.9537i | − | 0.409069i | ||||||
\(40\) | 11.9071 | + | 7.63024i | 0.297678 | + | 0.190756i | ||||
\(41\) | 17.5188 | 0.427287 | 0.213643 | − | 0.976912i | \(-0.431467\pi\) | ||||
0.213643 | + | 0.976912i | \(0.431467\pi\) | |||||||
\(42\) | −4.23838 | + | 4.23838i | −0.100914 | + | 0.100914i | ||||
\(43\) | 26.6029 | + | 26.6029i | 0.618672 | + | 0.618672i | 0.945191 | − | 0.326519i | \(-0.105876\pi\) |
−0.326519 | + | 0.945191i | \(0.605876\pi\) | |||||||
\(44\) | 7.65288i | 0.173929i | ||||||||
\(45\) | −8.83080 | − | 40.3403i | −0.196240 | − | 0.896450i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 33.3658 | − | 33.3658i | 0.709911 | − | 0.709911i | −0.256605 | − | 0.966516i | \(-0.582604\pi\) |
0.966516 | + | 0.256605i | \(0.0826040\pi\) | |||||||
\(48\) | −2.43458 | − | 2.43458i | −0.0507204 | − | 0.0507204i | ||||
\(49\) | 24.7540i | 0.505183i | ||||||||
\(50\) | −12.2687 | + | 33.1584i | −0.245373 | + | 0.663168i | ||||
\(51\) | 19.4622 | 0.381612 | ||||||||
\(52\) | −26.2118 | + | 26.2118i | −0.504074 | + | 0.504074i | ||||
\(53\) | −42.6629 | − | 42.6629i | −0.804960 | − | 0.804960i | 0.178906 | − | 0.983866i | \(-0.442744\pi\) |
−0.983866 | + | 0.178906i | \(0.942744\pi\) | |||||||
\(54\) | 21.0093i | 0.389062i | ||||||||
\(55\) | −18.6896 | + | 4.09131i | −0.339812 | + | 0.0743874i | ||||
\(56\) | 13.9273 | 0.248701 | ||||||||
\(57\) | −3.75065 | + | 3.75065i | −0.0658009 | + | 0.0658009i | ||||
\(58\) | −32.8492 | − | 32.8492i | −0.566366 | − | 0.566366i | ||||
\(59\) | 28.9195i | 0.490161i | 0.969503 | + | 0.245080i | \(0.0788143\pi\) | ||||
−0.969503 | + | 0.245080i | \(0.921186\pi\) | |||||||
\(60\) | 4.64411 | − | 7.24721i | 0.0774018 | − | 0.120787i | ||||
\(61\) | −3.95181 | −0.0647838 | −0.0323919 | − | 0.999475i | \(-0.510312\pi\) | ||||
−0.0323919 | + | 0.999475i | \(0.510312\pi\) | |||||||
\(62\) | −27.0235 | + | 27.0235i | −0.435863 | + | 0.435863i | ||||
\(63\) | −28.7567 | − | 28.7567i | −0.456455 | − | 0.456455i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −78.0268 | − | 50.0006i | −1.20041 | − | 0.769240i | ||||
\(66\) | 4.65789 | 0.0705741 | ||||||||
\(67\) | −69.4085 | + | 69.4085i | −1.03595 | + | 1.03595i | −0.0366182 | + | 0.999329i | \(0.511659\pi\) |
−0.999329 | + | 0.0366182i | \(0.988341\pi\) | |||||||
\(68\) | −31.9763 | − | 31.9763i | −0.470240 | − | 0.470240i | ||||
\(69\) | 4.12803i | 0.0598265i | ||||||||
\(70\) | 7.44565 | + | 34.0127i | 0.106366 | + | 0.485896i | ||||
\(71\) | 65.0625 | 0.916373 | 0.458186 | − | 0.888856i | \(-0.348499\pi\) | ||||
0.458186 | + | 0.888856i | \(0.348499\pi\) | |||||||
\(72\) | 16.5182 | − | 16.5182i | 0.229420 | − | 0.229420i | ||||
\(73\) | −52.2889 | − | 52.2889i | −0.716286 | − | 0.716286i | 0.251557 | − | 0.967843i | \(-0.419057\pi\) |
−0.967843 | + | 0.251557i | \(0.919057\pi\) | |||||||
\(74\) | − | 40.1008i | − | 0.541903i | ||||||
\(75\) | 20.1817 | + | 7.46726i | 0.269089 | + | 0.0995635i | ||||
\(76\) | 12.3246 | 0.162166 | ||||||||
\(77\) | −13.3230 | + | 13.3230i | −0.173025 | + | 0.173025i | ||||
\(78\) | 15.9537 | + | 15.9537i | 0.204535 | + | 0.204535i | ||||
\(79\) | 62.2321i | 0.787749i | 0.919164 | + | 0.393874i | \(0.128865\pi\) | ||||
−0.919164 | + | 0.393874i | \(0.871135\pi\) | |||||||
\(80\) | −19.5374 | + | 4.27688i | −0.244217 | + | 0.0534610i | ||||
\(81\) | −61.5447 | −0.759811 | ||||||||
\(82\) | −17.5188 | + | 17.5188i | −0.213643 | + | 0.213643i | ||||
\(83\) | −95.2795 | − | 95.2795i | −1.14795 | − | 1.14795i | −0.986956 | − | 0.160989i | \(-0.948532\pi\) |
−0.160989 | − | 0.986956i | \(-0.551468\pi\) | |||||||
\(84\) | − | 8.47675i | − | 0.100914i | ||||||
\(85\) | 60.9967 | − | 95.1864i | 0.717608 | − | 1.11984i | ||||
\(86\) | −53.2058 | −0.618672 | ||||||||
\(87\) | −19.9935 | + | 19.9935i | −0.229810 | + | 0.229810i | ||||
\(88\) | −7.65288 | − | 7.65288i | −0.0869646 | − | 0.0869646i | ||||
\(89\) | 131.536i | 1.47793i | 0.673744 | + | 0.738964i | \(0.264685\pi\) | ||||
−0.673744 | + | 0.738964i | \(0.735315\pi\) | |||||||
\(90\) | 49.1711 | + | 31.5095i | 0.546345 | + | 0.350105i | ||||
\(91\) | −91.2647 | −1.00291 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 16.4477 | + | 16.4477i | 0.176857 | + | 0.176857i | ||||
\(94\) | 66.7316i | 0.709911i | ||||||||
\(95\) | 6.58885 | + | 30.0988i | 0.0693564 | + | 0.316829i | ||||
\(96\) | 4.86916 | 0.0507204 | ||||||||
\(97\) | 20.1747 | − | 20.1747i | 0.207986 | − | 0.207986i | −0.595425 | − | 0.803411i | \(-0.703016\pi\) |
0.803411 | + | 0.595425i | \(0.203016\pi\) | |||||||
\(98\) | −24.7540 | − | 24.7540i | −0.252591 | − | 0.252591i | ||||
\(99\) | 31.6030i | 0.319222i | ||||||||
\(100\) | −20.8897 | − | 45.4271i | −0.208897 | − | 0.454271i | ||||
\(101\) | −21.2449 | −0.210345 | −0.105173 | − | 0.994454i | \(-0.533540\pi\) | ||||
−0.105173 | + | 0.994454i | \(0.533540\pi\) | |||||||
\(102\) | −19.4622 | + | 19.4622i | −0.190806 | + | 0.190806i | ||||
\(103\) | 111.237 | + | 111.237i | 1.07997 | + | 1.07997i | 0.996511 | + | 0.0834631i | \(0.0265981\pi\) |
0.0834631 | + | 0.996511i | \(0.473402\pi\) | |||||||
\(104\) | − | 52.4237i | − | 0.504074i | ||||||
\(105\) | 20.7017 | − | 4.53176i | 0.197159 | − | 0.0431596i | ||||
\(106\) | 85.3257 | 0.804960 | ||||||||
\(107\) | 44.1284 | − | 44.1284i | 0.412415 | − | 0.412415i | −0.470164 | − | 0.882579i | \(-0.655805\pi\) |
0.882579 | + | 0.470164i | \(0.155805\pi\) | |||||||
\(108\) | −21.0093 | − | 21.0093i | −0.194531 | − | 0.194531i | ||||
\(109\) | 56.9538i | 0.522512i | 0.965270 | + | 0.261256i | \(0.0841367\pi\) | ||||
−0.965270 | + | 0.261256i | \(0.915863\pi\) | |||||||
\(110\) | 14.5983 | − | 22.7809i | 0.132712 | − | 0.207100i | ||||
\(111\) | −24.4071 | −0.219884 | ||||||||
\(112\) | −13.9273 | + | 13.9273i | −0.124350 | + | 0.124350i | ||||
\(113\) | −15.3107 | − | 15.3107i | −0.135493 | − | 0.135493i | 0.636107 | − | 0.771601i | \(-0.280544\pi\) |
−0.771601 | + | 0.636107i | \(0.780544\pi\) | |||||||
\(114\) | − | 7.50130i | − | 0.0658009i | ||||||
\(115\) | 20.1895 | + | 12.9377i | 0.175561 | + | 0.112502i | ||||
\(116\) | 65.6984 | 0.566366 | ||||||||
\(117\) | −108.243 | + | 108.243i | −0.925155 | + | 0.925155i | ||||
\(118\) | −28.9195 | − | 28.9195i | −0.245080 | − | 0.245080i | ||||
\(119\) | − | 111.335i | − | 0.935592i | ||||||
\(120\) | 2.60310 | + | 11.8913i | 0.0216925 | + | 0.0990943i | ||||
\(121\) | −106.358 | −0.878995 | ||||||||
\(122\) | 3.95181 | − | 3.95181i | 0.0323919 | − | 0.0323919i | ||||
\(123\) | 10.6627 | + | 10.6627i | 0.0866886 | + | 0.0866886i | ||||
\(124\) | − | 54.0470i | − | 0.435863i | ||||||
\(125\) | 99.7728 | − | 75.3020i | 0.798182 | − | 0.602416i | ||||
\(126\) | 57.5133 | 0.456455 | ||||||||
\(127\) | −121.636 | + | 121.636i | −0.957760 | + | 0.957760i | −0.999143 | − | 0.0413833i | \(-0.986824\pi\) |
0.0413833 | + | 0.999143i | \(0.486824\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 32.3834i | 0.251034i | ||||||||
\(130\) | 128.027 | − | 28.0262i | 0.984827 | − | 0.215586i | ||||
\(131\) | 70.2174 | 0.536011 | 0.268005 | − | 0.963417i | \(-0.413635\pi\) | ||||
0.268005 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(132\) | −4.65789 | + | 4.65789i | −0.0352870 | + | 0.0352870i | ||||
\(133\) | 21.4560 | + | 21.4560i | 0.161323 | + | 0.161323i | ||||
\(134\) | − | 138.817i | − | 1.03595i | ||||||
\(135\) | 40.0765 | − | 62.5401i | 0.296863 | − | 0.463260i | ||||
\(136\) | 63.9526 | 0.470240 | ||||||||
\(137\) | 90.3324 | − | 90.3324i | 0.659360 | − | 0.659360i | −0.295868 | − | 0.955229i | \(-0.595609\pi\) |
0.955229 | + | 0.295868i | \(0.0956090\pi\) | |||||||
\(138\) | −4.12803 | − | 4.12803i | −0.0299133 | − | 0.0299133i | ||||
\(139\) | 35.1379i | 0.252791i | 0.991980 | + | 0.126395i | \(0.0403408\pi\) | ||||
−0.991980 | + | 0.126395i | \(0.959659\pi\) | |||||||
\(140\) | −41.4584 | − | 26.5671i | −0.296131 | − | 0.189765i | ||||
\(141\) | 40.6159 | 0.288056 | ||||||||
\(142\) | −65.0625 | + | 65.0625i | −0.458186 | + | 0.458186i | ||||
\(143\) | 50.1490 | + | 50.1490i | 0.350692 | + | 0.350692i | ||||
\(144\) | 33.0364i | 0.229420i | ||||||||
\(145\) | 35.1230 | + | 160.447i | 0.242228 | + | 1.10653i | ||||
\(146\) | 104.578 | 0.716286 | ||||||||
\(147\) | −15.0664 | + | 15.0664i | −0.102492 | + | 0.102492i | ||||
\(148\) | 40.1008 | + | 40.1008i | 0.270951 | + | 0.270951i | ||||
\(149\) | − | 82.9264i | − | 0.556553i | −0.960501 | − | 0.278277i | \(-0.910237\pi\) | ||
0.960501 | − | 0.278277i | \(-0.0897632\pi\) | |||||||
\(150\) | −27.6490 | + | 12.7144i | −0.184326 | + | 0.0847629i | ||||
\(151\) | 256.123 | 1.69618 | 0.848088 | − | 0.529856i | \(-0.177754\pi\) | ||||
0.848088 | + | 0.529856i | \(0.177754\pi\) | |||||||
\(152\) | −12.3246 | + | 12.3246i | −0.0810829 | + | 0.0810829i | ||||
\(153\) | −132.048 | − | 132.048i | −0.863057 | − | 0.863057i | ||||
\(154\) | − | 26.6459i | − | 0.173025i | ||||||
\(155\) | 131.992 | − | 28.8941i | 0.851561 | − | 0.186413i | ||||
\(156\) | −31.9074 | −0.204535 | ||||||||
\(157\) | 114.268 | − | 114.268i | 0.727821 | − | 0.727821i | −0.242364 | − | 0.970185i | \(-0.577923\pi\) |
0.970185 | + | 0.242364i | \(0.0779228\pi\) | |||||||
\(158\) | −62.2321 | − | 62.2321i | −0.393874 | − | 0.393874i | ||||
\(159\) | − | 51.9331i | − | 0.326623i | ||||||
\(160\) | 15.2605 | − | 23.8142i | 0.0953780 | − | 0.148839i | ||||
\(161\) | 23.6148 | 0.146676 | ||||||||
\(162\) | 61.5447 | − | 61.5447i | 0.379906 | − | 0.379906i | ||||
\(163\) | 200.462 | + | 200.462i | 1.22983 | + | 1.22983i | 0.964028 | + | 0.265802i | \(0.0856368\pi\) |
0.265802 | + | 0.964028i | \(0.414363\pi\) | |||||||
\(164\) | − | 35.0375i | − | 0.213643i | ||||||
\(165\) | −13.8655 | − | 8.88520i | −0.0840334 | − | 0.0538497i | ||||
\(166\) | 190.559 | 1.14795 | ||||||||
\(167\) | 1.21328 | − | 1.21328i | 0.00726515 | − | 0.00726515i | −0.703465 | − | 0.710730i | \(-0.748365\pi\) |
0.710730 | + | 0.703465i | \(0.248365\pi\) | |||||||
\(168\) | 8.47675 | + | 8.47675i | 0.0504569 | + | 0.0504569i | ||||
\(169\) | 174.530i | 1.03272i | ||||||||
\(170\) | 34.1897 | + | 156.183i | 0.201116 | + | 0.918724i | ||||
\(171\) | 50.8951 | 0.297632 | ||||||||
\(172\) | 53.2058 | − | 53.2058i | 0.309336 | − | 0.309336i | ||||
\(173\) | −186.625 | − | 186.625i | −1.07876 | − | 1.07876i | −0.996621 | − | 0.0821339i | \(-0.973826\pi\) |
−0.0821339 | − | 0.996621i | \(-0.526174\pi\) | |||||||
\(174\) | − | 39.9870i | − | 0.229810i | ||||||
\(175\) | 42.7172 | − | 115.451i | 0.244098 | − | 0.659722i | ||||
\(176\) | 15.3058 | 0.0869646 | ||||||||
\(177\) | −17.6017 | + | 17.6017i | −0.0994446 | + | 0.0994446i | ||||
\(178\) | −131.536 | − | 131.536i | −0.738964 | − | 0.738964i | ||||
\(179\) | − | 156.890i | − | 0.876479i | −0.898858 | − | 0.438240i | \(-0.855602\pi\) | ||
0.898858 | − | 0.438240i | \(-0.144398\pi\) | |||||||
\(180\) | −80.6805 | + | 17.6616i | −0.448225 | + | 0.0981200i | ||||
\(181\) | −110.482 | −0.610396 | −0.305198 | − | 0.952289i | \(-0.598723\pi\) | ||||
−0.305198 | + | 0.952289i | \(0.598723\pi\) | |||||||
\(182\) | 91.2647 | − | 91.2647i | 0.501454 | − | 0.501454i | ||||
\(183\) | −2.40525 | − | 2.40525i | −0.0131434 | − | 0.0131434i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −76.4947 | + | 119.371i | −0.413485 | + | 0.645250i | ||||
\(186\) | −32.8954 | −0.176857 | ||||||||
\(187\) | −61.1777 | + | 61.1777i | −0.327154 | + | 0.327154i | ||||
\(188\) | −66.7316 | − | 66.7316i | −0.354955 | − | 0.354955i | ||||
\(189\) | − | 73.1506i | − | 0.387040i | ||||||
\(190\) | −36.6876 | − | 23.5099i | −0.193093 | − | 0.123736i | ||||
\(191\) | −101.977 | −0.533913 | −0.266956 | − | 0.963709i | \(-0.586018\pi\) | ||||
−0.266956 | + | 0.963709i | \(0.586018\pi\) | |||||||
\(192\) | −4.86916 | + | 4.86916i | −0.0253602 | + | 0.0253602i | ||||
\(193\) | 213.999 | + | 213.999i | 1.10880 | + | 1.10880i | 0.993308 | + | 0.115497i | \(0.0368461\pi\) |
0.115497 | + | 0.993308i | \(0.463154\pi\) | |||||||
\(194\) | 40.3493i | 0.207986i | ||||||||
\(195\) | −17.0580 | − | 77.9233i | −0.0874770 | − | 0.399606i | ||||
\(196\) | 49.5079 | 0.252591 | ||||||||
\(197\) | −187.001 | + | 187.001i | −0.949243 | + | 0.949243i | −0.998773 | − | 0.0495299i | \(-0.984228\pi\) |
0.0495299 | + | 0.998773i | \(0.484228\pi\) | |||||||
\(198\) | −31.6030 | − | 31.6030i | −0.159611 | − | 0.159611i | ||||
\(199\) | 365.937i | 1.83888i | 0.393229 | + | 0.919441i | \(0.371358\pi\) | ||||
−0.393229 | + | 0.919441i | \(0.628642\pi\) | |||||||
\(200\) | 66.3168 | + | 24.5373i | 0.331584 | + | 0.122687i | ||||
\(201\) | −84.4902 | −0.420349 | ||||||||
\(202\) | 21.2449 | − | 21.2449i | 0.105173 | − | 0.105173i | ||||
\(203\) | 114.375 | + | 114.375i | 0.563423 | + | 0.563423i | ||||
\(204\) | − | 38.9244i | − | 0.190806i | ||||||
\(205\) | 85.5675 | − | 18.7314i | 0.417403 | − | 0.0913727i | ||||
\(206\) | −222.475 | −1.07997 | ||||||||
\(207\) | 28.0080 | − | 28.0080i | 0.135304 | − | 0.135304i | ||||
\(208\) | 52.4237 | + | 52.4237i | 0.252037 | + | 0.252037i | ||||
\(209\) | − | 23.5797i | − | 0.112821i | ||||||
\(210\) | −16.1699 | + | 25.2334i | −0.0769996 | + | 0.120159i | ||||
\(211\) | −269.478 | −1.27715 | −0.638575 | − | 0.769560i | \(-0.720476\pi\) | ||||
−0.638575 | + | 0.769560i | \(0.720476\pi\) | |||||||
\(212\) | −85.3257 | + | 85.3257i | −0.402480 | + | 0.402480i | ||||
\(213\) | 39.5999 | + | 39.5999i | 0.185915 | + | 0.185915i | ||||
\(214\) | 88.2569i | 0.412415i | ||||||||
\(215\) | 158.382 | + | 101.493i | 0.736660 | + | 0.472062i | ||||
\(216\) | 42.0187 | 0.194531 | ||||||||
\(217\) | 94.0907 | − | 94.0907i | 0.433598 | − | 0.433598i | ||||
\(218\) | −56.9538 | − | 56.9538i | −0.261256 | − | 0.261256i | ||||
\(219\) | − | 63.6507i | − | 0.290642i | ||||||
\(220\) | 8.18262 | + | 37.3793i | 0.0371937 | + | 0.169906i | ||||
\(221\) | −419.079 | −1.89628 | ||||||||
\(222\) | 24.4071 | − | 24.4071i | 0.109942 | − | 0.109942i | ||||
\(223\) | −182.711 | − | 182.711i | −0.819333 | − | 0.819333i | 0.166678 | − | 0.986011i | \(-0.446696\pi\) |
−0.986011 | + | 0.166678i | \(0.946696\pi\) | |||||||
\(224\) | − | 27.8545i | − | 0.124350i | ||||||
\(225\) | −86.2652 | − | 187.593i | −0.383401 | − | 0.833749i | ||||
\(226\) | 30.6214 | 0.135493 | ||||||||
\(227\) | 71.0092 | − | 71.0092i | 0.312816 | − | 0.312816i | −0.533184 | − | 0.846000i | \(-0.679005\pi\) |
0.846000 | + | 0.533184i | \(0.179005\pi\) | |||||||
\(228\) | 7.50130 | + | 7.50130i | 0.0329005 | + | 0.0329005i | ||||
\(229\) | − | 97.6089i | − | 0.426240i | −0.977026 | − | 0.213120i | \(-0.931638\pi\) | ||
0.977026 | − | 0.213120i | \(-0.0683625\pi\) | |||||||
\(230\) | −33.1272 | + | 7.25180i | −0.144031 | + | 0.0315296i | ||||
\(231\) | −16.2179 | −0.0702074 | ||||||||
\(232\) | −65.6984 | + | 65.6984i | −0.283183 | + | 0.283183i | ||||
\(233\) | −93.7032 | − | 93.7032i | −0.402160 | − | 0.402160i | 0.476834 | − | 0.878993i | \(-0.341784\pi\) |
−0.878993 | + | 0.476834i | \(0.841784\pi\) | |||||||
\(234\) | − | 216.486i | − | 0.925155i | ||||||
\(235\) | 127.295 | − | 198.645i | 0.541679 | − | 0.845299i | ||||
\(236\) | 57.8390 | 0.245080 | ||||||||
\(237\) | −37.8773 | + | 37.8773i | −0.159820 | + | 0.159820i | ||||
\(238\) | 111.335 | + | 111.335i | 0.467796 | + | 0.467796i | ||||
\(239\) | 229.877i | 0.961826i | 0.876768 | + | 0.480913i | \(0.159695\pi\) | ||||
−0.876768 | + | 0.480913i | \(0.840305\pi\) | |||||||
\(240\) | −14.4944 | − | 9.28821i | −0.0603934 | − | 0.0387009i | ||||
\(241\) | −410.897 | −1.70497 | −0.852484 | − | 0.522753i | \(-0.824905\pi\) | ||||
−0.852484 | + | 0.522753i | \(0.824905\pi\) | |||||||
\(242\) | 106.358 | − | 106.358i | 0.439497 | − | 0.439497i | ||||
\(243\) | −132.001 | − | 132.001i | −0.543213 | − | 0.543213i | ||||
\(244\) | 7.90362i | 0.0323919i | ||||||||
\(245\) | 26.4674 | + | 120.907i | 0.108030 | + | 0.493497i | ||||
\(246\) | −21.3254 | −0.0866886 | ||||||||
\(247\) | 80.7626 | − | 80.7626i | 0.326974 | − | 0.326974i | ||||
\(248\) | 54.0470 | + | 54.0470i | 0.217931 | + | 0.217931i | ||||
\(249\) | − | 115.983i | − | 0.465794i | ||||||
\(250\) | −24.4707 | + | 175.075i | −0.0978828 | + | 0.700299i | ||||
\(251\) | 220.598 | 0.878875 | 0.439437 | − | 0.898273i | \(-0.355178\pi\) | ||||
0.439437 | + | 0.898273i | \(0.355178\pi\) | |||||||
\(252\) | −57.5133 | + | 57.5133i | −0.228227 | + | 0.228227i | ||||
\(253\) | −12.9761 | − | 12.9761i | −0.0512889 | − | 0.0512889i | ||||
\(254\) | − | 243.271i | − | 0.957760i | ||||||
\(255\) | 95.0600 | − | 20.8094i | 0.372784 | − | 0.0816054i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 222.012 | − | 222.012i | 0.863860 | − | 0.863860i | −0.127924 | − | 0.991784i | \(-0.540831\pi\) |
0.991784 | + | 0.127924i | \(0.0408313\pi\) | |||||||
\(258\) | −32.3834 | − | 32.3834i | −0.125517 | − | 0.125517i | ||||
\(259\) | 139.623i | 0.539087i | ||||||||
\(260\) | −100.001 | + | 156.054i | −0.384620 | + | 0.600206i | ||||
\(261\) | 271.305 | 1.03948 | ||||||||
\(262\) | −70.2174 | + | 70.2174i | −0.268005 | + | 0.268005i | ||||
\(263\) | 273.600 | + | 273.600i | 1.04030 | + | 1.04030i | 0.999153 | + | 0.0411516i | \(0.0131027\pi\) |
0.0411516 | + | 0.999153i | \(0.486897\pi\) | |||||||
\(264\) | − | 9.31578i | − | 0.0352870i | ||||||
\(265\) | −253.996 | − | 162.764i | −0.958475 | − | 0.614203i | ||||
\(266\) | −42.9120 | −0.161323 | ||||||||
\(267\) | −80.0585 | + | 80.0585i | −0.299845 | + | 0.299845i | ||||
\(268\) | 138.817 | + | 138.817i | 0.517974 | + | 0.517974i | ||||
\(269\) | 306.939i | 1.14104i | 0.821285 | + | 0.570518i | \(0.193258\pi\) | ||||
−0.821285 | + | 0.570518i | \(0.806742\pi\) | |||||||
\(270\) | 22.4636 | + | 102.617i | 0.0831985 | + | 0.380062i | ||||
\(271\) | −423.942 | −1.56436 | −0.782181 | − | 0.623051i | \(-0.785893\pi\) | ||||
−0.782181 | + | 0.623051i | \(0.785893\pi\) | |||||||
\(272\) | −63.9526 | + | 63.9526i | −0.235120 | + | 0.235120i | ||||
\(273\) | −55.5478 | − | 55.5478i | −0.203472 | − | 0.203472i | ||||
\(274\) | 180.665i | 0.659360i | ||||||||
\(275\) | −86.9120 | + | 39.9667i | −0.316044 | + | 0.145333i | ||||
\(276\) | 8.25606 | 0.0299133 | ||||||||
\(277\) | −123.494 | + | 123.494i | −0.445828 | + | 0.445828i | −0.893965 | − | 0.448137i | \(-0.852088\pi\) |
0.448137 | + | 0.893965i | \(0.352088\pi\) | |||||||
\(278\) | −35.1379 | − | 35.1379i | −0.126395 | − | 0.126395i | ||||
\(279\) | − | 223.190i | − | 0.799963i | ||||||
\(280\) | 68.0254 | − | 14.8913i | 0.242948 | − | 0.0531832i | ||||
\(281\) | 99.1668 | 0.352907 | 0.176453 | − | 0.984309i | \(-0.443537\pi\) | ||||
0.176453 | + | 0.984309i | \(0.443537\pi\) | |||||||
\(282\) | −40.6159 | + | 40.6159i | −0.144028 | + | 0.144028i | ||||
\(283\) | 200.417 | + | 200.417i | 0.708186 | + | 0.708186i | 0.966154 | − | 0.257968i | \(-0.0830528\pi\) |
−0.257968 | + | 0.966154i | \(0.583053\pi\) | |||||||
\(284\) | − | 130.125i | − | 0.458186i | ||||||
\(285\) | −14.3092 | + | 22.3297i | −0.0502077 | + | 0.0783499i | ||||
\(286\) | −100.298 | −0.350692 | ||||||||
\(287\) | 60.9970 | − | 60.9970i | 0.212533 | − | 0.212533i | ||||
\(288\) | −33.0364 | − | 33.0364i | −0.114710 | − | 0.114710i | ||||
\(289\) | − | 222.242i | − | 0.769003i | ||||||
\(290\) | −195.570 | − | 125.324i | −0.674379 | − | 0.432151i | ||||
\(291\) | 24.5584 | 0.0843932 | ||||||||
\(292\) | −104.578 | + | 104.578i | −0.358143 | + | 0.358143i | ||||
\(293\) | 147.035 | + | 147.035i | 0.501826 | + | 0.501826i | 0.912005 | − | 0.410179i | \(-0.134534\pi\) |
−0.410179 | + | 0.912005i | \(0.634534\pi\) | |||||||
\(294\) | − | 30.1327i | − | 0.102492i | ||||||
\(295\) | 30.9213 | + | 141.253i | 0.104818 | + | 0.478822i | ||||
\(296\) | −80.2016 | −0.270951 | ||||||||
\(297\) | −40.1955 | + | 40.1955i | −0.135338 | + | 0.135338i | ||||
\(298\) | 82.9264 | + | 82.9264i | 0.278277 | + | 0.278277i | ||||
\(299\) | − | 88.8886i | − | 0.297286i | ||||||
\(300\) | 14.9345 | − | 40.3634i | 0.0497818 | − | 0.134545i | ||||
\(301\) | 185.253 | 0.615457 | ||||||||
\(302\) | −256.123 | + | 256.123i | −0.848088 | + | 0.848088i | ||||
\(303\) | −12.9306 | − | 12.9306i | −0.0426752 | − | 0.0426752i | ||||
\(304\) | − | 24.6492i | − | 0.0810829i | ||||||
\(305\) | −19.3020 | + | 4.22536i | −0.0632852 | + | 0.0138536i | ||||
\(306\) | 264.096 | 0.863057 | ||||||||
\(307\) | 170.158 | − | 170.158i | 0.554262 | − | 0.554262i | −0.373406 | − | 0.927668i | \(-0.621810\pi\) |
0.927668 | + | 0.373406i | \(0.121810\pi\) | |||||||
\(308\) | 26.6459 | + | 26.6459i | 0.0865127 | + | 0.0865127i | ||||
\(309\) | 135.408i | 0.438214i | ||||||||
\(310\) | −103.098 | + | 160.886i | −0.332574 | + | 0.518987i | ||||
\(311\) | 86.2595 | 0.277362 | 0.138681 | − | 0.990337i | \(-0.455714\pi\) | ||||
0.138681 | + | 0.990337i | \(0.455714\pi\) | |||||||
\(312\) | 31.9074 | − | 31.9074i | 0.102267 | − | 0.102267i | ||||
\(313\) | −352.517 | − | 352.517i | −1.12625 | − | 1.12625i | −0.990781 | − | 0.135472i | \(-0.956745\pi\) |
−0.135472 | − | 0.990781i | \(-0.543255\pi\) | |||||||
\(314\) | 228.536i | 0.727821i | ||||||||
\(315\) | −171.204 | − | 109.710i | −0.543506 | − | 0.348286i | ||||
\(316\) | 124.464 | 0.393874 | ||||||||
\(317\) | −79.7816 | + | 79.7816i | −0.251677 | + | 0.251677i | −0.821658 | − | 0.569981i | \(-0.806951\pi\) |
0.569981 | + | 0.821658i | \(0.306951\pi\) | |||||||
\(318\) | 51.9331 | + | 51.9331i | 0.163312 | + | 0.163312i | ||||
\(319\) | − | 125.696i | − | 0.394030i | ||||||
\(320\) | 8.55376 | + | 39.0747i | 0.0267305 | + | 0.122108i | ||||
\(321\) | 53.7171 | 0.167343 | ||||||||
\(322\) | −23.6148 | + | 23.6148i | −0.0733379 | + | 0.0733379i | ||||
\(323\) | 98.5237 | + | 98.5237i | 0.305027 | + | 0.305027i | ||||
\(324\) | 123.089i | 0.379906i | ||||||||
\(325\) | −434.571 | − | 160.792i | −1.33714 | − | 0.494745i | ||||
\(326\) | −400.924 | −1.22983 | ||||||||
\(327\) | −34.6646 | + | 34.6646i | −0.106008 | + | 0.106008i | ||||
\(328\) | 35.0375 | + | 35.0375i | 0.106822 | + | 0.106822i | ||||
\(329\) | − | 232.347i | − | 0.706222i | ||||||
\(330\) | 22.7507 | − | 4.98031i | 0.0689415 | − | 0.0150918i | ||||
\(331\) | −123.045 | −0.371738 | −0.185869 | − | 0.982575i | \(-0.559510\pi\) | ||||
−0.185869 | + | 0.982575i | \(0.559510\pi\) | |||||||
\(332\) | −190.559 | + | 190.559i | −0.573973 | + | 0.573973i | ||||
\(333\) | 165.598 | + | 165.598i | 0.497292 | + | 0.497292i | ||||
\(334\) | 2.42656i | 0.00726515i | ||||||||
\(335\) | −264.802 | + | 413.228i | −0.790453 | + | 1.23351i | ||||
\(336\) | −16.9535 | −0.0504569 | ||||||||
\(337\) | 329.255 | − | 329.255i | 0.977018 | − | 0.977018i | −0.0227234 | − | 0.999742i | \(-0.507234\pi\) |
0.999742 | + | 0.0227234i | \(0.00723371\pi\) | |||||||
\(338\) | −174.530 | − | 174.530i | −0.516361 | − | 0.516361i | ||||
\(339\) | − | 18.6376i | − | 0.0549781i | ||||||
\(340\) | −190.373 | − | 121.993i | −0.559920 | − | 0.358804i | ||||
\(341\) | −103.404 | −0.303237 | ||||||||
\(342\) | −50.8951 | + | 50.8951i | −0.148816 | + | 0.148816i | ||||
\(343\) | 256.797 | + | 256.797i | 0.748681 | + | 0.748681i | ||||
\(344\) | 106.412i | 0.309336i | ||||||||
\(345\) | 4.41377 | + | 20.1627i | 0.0127935 | + | 0.0584426i | ||||
\(346\) | 373.249 | 1.07876 | ||||||||
\(347\) | 78.9165 | − | 78.9165i | 0.227425 | − | 0.227425i | −0.584191 | − | 0.811616i | \(-0.698588\pi\) |
0.811616 | + | 0.584191i | \(0.198588\pi\) | |||||||
\(348\) | 39.9870 | + | 39.9870i | 0.114905 | + | 0.114905i | ||||
\(349\) | − | 209.184i | − | 0.599381i | −0.954037 | − | 0.299690i | \(-0.903117\pi\) | ||
0.954037 | − | 0.299690i | \(-0.0968834\pi\) | |||||||
\(350\) | 72.7342 | + | 158.169i | 0.207812 | + | 0.451910i | ||||
\(351\) | −275.346 | −0.784463 | ||||||||
\(352\) | −15.3058 | + | 15.3058i | −0.0434823 | + | 0.0434823i | ||||
\(353\) | 181.293 | + | 181.293i | 0.513578 | + | 0.513578i | 0.915621 | − | 0.402043i | \(-0.131700\pi\) |
−0.402043 | + | 0.915621i | \(0.631700\pi\) | |||||||
\(354\) | − | 35.2034i | − | 0.0994446i | ||||||
\(355\) | 317.787 | − | 69.5661i | 0.895175 | − | 0.195961i | ||||
\(356\) | 263.071 | 0.738964 | ||||||||
\(357\) | 67.7638 | − | 67.7638i | 0.189815 | − | 0.189815i | ||||
\(358\) | 156.890 | + | 156.890i | 0.438240 | + | 0.438240i | ||||
\(359\) | − | 701.621i | − | 1.95438i | −0.212378 | − | 0.977188i | \(-0.568121\pi\) | ||
0.212378 | − | 0.977188i | \(-0.431879\pi\) | |||||||
\(360\) | 63.0189 | − | 98.3421i | 0.175053 | − | 0.273173i | ||||
\(361\) | 323.026 | 0.894809 | ||||||||
\(362\) | 110.482 | − | 110.482i | 0.305198 | − | 0.305198i | ||||
\(363\) | −64.7345 | − | 64.7345i | −0.178332 | − | 0.178332i | ||||
\(364\) | 182.529i | 0.501454i | ||||||||
\(365\) | −311.305 | − | 199.488i | −0.852890 | − | 0.546543i | ||||
\(366\) | 4.81050 | 0.0131434 | ||||||||
\(367\) | 159.383 | − | 159.383i | 0.434287 | − | 0.434287i | −0.455797 | − | 0.890084i | \(-0.650646\pi\) |
0.890084 | + | 0.455797i | \(0.150646\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 144.689i | − | 0.392112i | ||||||
\(370\) | −42.8766 | − | 195.866i | −0.115883 | − | 0.529367i | ||||
\(371\) | −297.088 | −0.800777 | ||||||||
\(372\) | 32.8954 | − | 32.8954i | 0.0884285 | − | 0.0884285i | ||||
\(373\) | 267.254 | + | 267.254i | 0.716499 | + | 0.716499i | 0.967886 | − | 0.251388i | \(-0.0808870\pi\) |
−0.251388 | + | 0.967886i | \(0.580887\pi\) | |||||||
\(374\) | − | 122.355i | − | 0.327154i | ||||||
\(375\) | 106.558 | + | 14.8940i | 0.284156 | + | 0.0397173i | ||||
\(376\) | 133.463 | 0.354955 | ||||||||
\(377\) | 430.519 | − | 430.519i | 1.14196 | − | 1.14196i | ||||
\(378\) | 73.1506 | + | 73.1506i | 0.193520 | + | 0.193520i | ||||
\(379\) | 204.998i | 0.540893i | 0.962735 | + | 0.270446i | \(0.0871713\pi\) | ||||
−0.962735 | + | 0.270446i | \(0.912829\pi\) | |||||||
\(380\) | 60.1975 | − | 13.1777i | 0.158415 | − | 0.0346782i | ||||
\(381\) | −148.066 | −0.388624 | ||||||||
\(382\) | 101.977 | − | 101.977i | 0.266956 | − | 0.266956i | ||||
\(383\) | 463.802 | + | 463.802i | 1.21097 | + | 1.21097i | 0.970707 | + | 0.240265i | \(0.0772344\pi\) |
0.240265 | + | 0.970707i | \(0.422766\pi\) | |||||||
\(384\) | − | 9.73832i | − | 0.0253602i | ||||||
\(385\) | −50.8287 | + | 79.3190i | −0.132022 | + | 0.206023i | ||||
\(386\) | −427.999 | −1.10880 | ||||||||
\(387\) | 219.716 | − | 219.716i | 0.567742 | − | 0.567742i | ||||
\(388\) | −40.3493 | − | 40.3493i | −0.103993 | − | 0.103993i | ||||
\(389\) | 507.724i | 1.30520i | 0.757701 | + | 0.652602i | \(0.226322\pi\) | ||||
−0.757701 | + | 0.652602i | \(0.773678\pi\) | |||||||
\(390\) | 94.9813 | + | 60.8652i | 0.243542 | + | 0.156065i | ||||
\(391\) | 108.437 | 0.277332 | ||||||||
\(392\) | −49.5079 | + | 49.5079i | −0.126296 | + | 0.126296i | ||||
\(393\) | 42.7375 | + | 42.7375i | 0.108747 | + | 0.108747i | ||||
\(394\) | − | 374.002i | − | 0.949243i | ||||||
\(395\) | 66.5399 | + | 303.963i | 0.168455 | + | 0.769526i | ||||
\(396\) | 63.2059 | 0.159611 | ||||||||
\(397\) | −41.7475 | + | 41.7475i | −0.105157 | + | 0.105157i | −0.757728 | − | 0.652571i | \(-0.773691\pi\) |
0.652571 | + | 0.757728i | \(0.273691\pi\) | |||||||
\(398\) | −365.937 | − | 365.937i | −0.919441 | − | 0.919441i | ||||
\(399\) | 26.1181i | 0.0654590i | ||||||||
\(400\) | −90.8541 | + | 41.7795i | −0.227135 | + | 0.104449i | ||||
\(401\) | 662.900 | 1.65312 | 0.826558 | − | 0.562851i | \(-0.190296\pi\) | ||||
0.826558 | + | 0.562851i | \(0.190296\pi\) | |||||||
\(402\) | 84.4902 | − | 84.4902i | 0.210175 | − | 0.210175i | ||||
\(403\) | −354.168 | − | 354.168i | −0.878828 | − | 0.878828i | ||||
\(404\) | 42.4898i | 0.105173i | ||||||||
\(405\) | −300.605 | + | 65.8048i | −0.742235 | + | 0.162481i | ||||
\(406\) | −228.750 | −0.563423 | ||||||||
\(407\) | 76.7217 | − | 76.7217i | 0.188505 | − | 0.188505i | ||||
\(408\) | 38.9244 | + | 38.9244i | 0.0954030 | + | 0.0954030i | ||||
\(409\) | 4.51129i | 0.0110300i | 0.999985 | + | 0.00551502i | \(0.00175550\pi\) | ||||
−0.999985 | + | 0.00551502i | \(0.998245\pi\) | |||||||
\(410\) | −66.8361 | + | 104.299i | −0.163015 | + | 0.254388i | ||||
\(411\) | 109.961 | 0.267544 | ||||||||
\(412\) | 222.475 | − | 222.475i | 0.539987 | − | 0.539987i | ||||
\(413\) | 100.692 | + | 100.692i | 0.243807 | + | 0.243807i | ||||
\(414\) | 56.0160i | 0.135304i | ||||||||
\(415\) | −567.252 | − | 363.503i | −1.36687 | − | 0.875910i | ||||
\(416\) | −104.847 | −0.252037 | ||||||||
\(417\) | −21.3865 | + | 21.3865i | −0.0512866 | + | 0.0512866i | ||||
\(418\) | 23.5797 | + | 23.5797i | 0.0564107 | + | 0.0564107i | ||||
\(419\) | 239.199i | 0.570880i | 0.958397 | + | 0.285440i | \(0.0921397\pi\) | ||||
−0.958397 | + | 0.285440i | \(0.907860\pi\) | |||||||
\(420\) | −9.06351 | − | 41.4033i | −0.0215798 | − | 0.0985794i | ||||
\(421\) | 222.759 | 0.529119 | 0.264559 | − | 0.964369i | \(-0.414773\pi\) | ||||
0.264559 | + | 0.964369i | \(0.414773\pi\) | |||||||
\(422\) | 269.478 | − | 269.478i | 0.638575 | − | 0.638575i | ||||
\(423\) | −275.572 | − | 275.572i | −0.651470 | − | 0.651470i | ||||
\(424\) | − | 170.651i | − | 0.402480i | ||||||
\(425\) | 196.153 | − | 530.141i | 0.461537 | − | 1.24739i | ||||
\(426\) | −79.1999 | −0.185915 | ||||||||
\(427\) | −13.7595 | + | 13.7595i | −0.0322236 | + | 0.0322236i | ||||
\(428\) | −88.2569 | − | 88.2569i | −0.206208 | − | 0.206208i | ||||
\(429\) | 61.0459i | 0.142298i | ||||||||
\(430\) | −259.875 | + | 56.8887i | −0.604361 | + | 0.132299i | ||||
\(431\) | −708.039 | −1.64278 | −0.821391 | − | 0.570366i | \(-0.806801\pi\) | ||||
−0.821391 | + | 0.570366i | \(0.806801\pi\) | |||||||
\(432\) | −42.0187 | + | 42.0187i | −0.0972654 | + | 0.0972654i | ||||
\(433\) | −179.204 | − | 179.204i | −0.413866 | − | 0.413866i | 0.469217 | − | 0.883083i | \(-0.344536\pi\) |
−0.883083 | + | 0.469217i | \(0.844536\pi\) | |||||||
\(434\) | 188.181i | 0.433598i | ||||||||
\(435\) | −76.2776 | + | 119.033i | −0.175351 | + | 0.273638i | ||||
\(436\) | 113.908 | 0.261256 | ||||||||
\(437\) | −20.8974 | + | 20.8974i | −0.0478201 | + | 0.0478201i | ||||
\(438\) | 63.6507 | + | 63.6507i | 0.145321 | + | 0.145321i | ||||
\(439\) | − | 574.258i | − | 1.30810i | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||
0.756449 | − | 0.654052i | \(-0.226932\pi\) | |||||||
\(440\) | −45.5619 | − | 29.1967i | −0.103550 | − | 0.0663560i | ||||
\(441\) | 204.445 | 0.463595 | ||||||||
\(442\) | 419.079 | − | 419.079i | 0.948142 | − | 0.948142i | ||||
\(443\) | −83.8605 | − | 83.8605i | −0.189301 | − | 0.189301i | 0.606093 | − | 0.795394i | \(-0.292736\pi\) |
−0.795394 | + | 0.606093i | \(0.792736\pi\) | |||||||
\(444\) | 48.8143i | 0.109942i | ||||||||
\(445\) | 140.641 | + | 642.465i | 0.316046 | + | 1.44374i | ||||
\(446\) | 365.422 | 0.819333 | ||||||||
\(447\) | 50.4727 | − | 50.4727i | 0.112914 | − | 0.112914i | ||||
\(448\) | 27.8545 | + | 27.8545i | 0.0621752 | + | 0.0621752i | ||||
\(449\) | 139.847i | 0.311464i | 0.987799 | + | 0.155732i | \(0.0497736\pi\) | ||||
−0.987799 | + | 0.155732i | \(0.950226\pi\) | |||||||
\(450\) | 273.859 | + | 101.328i | 0.608575 | + | 0.225174i | ||||
\(451\) | −67.0345 | −0.148635 | ||||||||
\(452\) | −30.6214 | + | 30.6214i | −0.0677465 | + | 0.0677465i | ||||
\(453\) | 155.888 | + | 155.888i | 0.344123 | + | 0.344123i | ||||
\(454\) | 142.018i | 0.312816i | ||||||||
\(455\) | −445.768 | + | 97.5820i | −0.979709 | + | 0.214466i | ||||
\(456\) | −15.0026 | −0.0329005 | ||||||||
\(457\) | 55.0666 | − | 55.0666i | 0.120496 | − | 0.120496i | −0.644288 | − | 0.764783i | \(-0.722846\pi\) |
0.764783 | + | 0.644288i | \(0.222846\pi\) | |||||||
\(458\) | 97.6089 | + | 97.6089i | 0.213120 | + | 0.213120i | ||||
\(459\) | − | 335.900i | − | 0.731809i | ||||||
\(460\) | 25.8754 | − | 40.3790i | 0.0562509 | − | 0.0877804i | ||||
\(461\) | 833.889 | 1.80887 | 0.904434 | − | 0.426613i | \(-0.140293\pi\) | ||||
0.904434 | + | 0.426613i | \(0.140293\pi\) | |||||||
\(462\) | 16.2179 | − | 16.2179i | 0.0351037 | − | 0.0351037i | ||||
\(463\) | −25.0740 | − | 25.0740i | −0.0541555 | − | 0.0541555i | 0.679510 | − | 0.733666i | \(-0.262192\pi\) |
−0.733666 | + | 0.679510i | \(0.762192\pi\) | |||||||
\(464\) | − | 131.397i | − | 0.283183i | ||||||
\(465\) | 97.9224 | + | 62.7500i | 0.210586 | + | 0.134946i | ||||
\(466\) | 187.406 | 0.402160 | ||||||||
\(467\) | 5.39172 | − | 5.39172i | 0.0115454 | − | 0.0115454i | −0.701310 | − | 0.712856i | \(-0.747401\pi\) |
0.712856 | + | 0.701310i | \(0.247401\pi\) | |||||||
\(468\) | 216.486 | + | 216.486i | 0.462577 | + | 0.462577i | ||||
\(469\) | 483.335i | 1.03056i | ||||||||
\(470\) | 71.3508 | + | 325.940i | 0.151810 | + | 0.693489i | ||||
\(471\) | 139.097 | 0.295323 | ||||||||
\(472\) | −57.8390 | + | 57.8390i | −0.122540 | + | 0.122540i | ||||
\(473\) | −101.794 | − | 101.794i | −0.215210 | − | 0.215210i | ||||
\(474\) | − | 75.7546i | − | 0.159820i | ||||||
\(475\) | 64.3644 | + | 139.968i | 0.135504 | + | 0.294669i | ||||
\(476\) | −222.671 | −0.467796 | ||||||||
\(477\) | −352.357 | + | 352.357i | −0.738694 | + | 0.738694i | ||||
\(478\) | −229.877 | − | 229.877i | −0.480913 | − | 0.480913i | ||||
\(479\) | 272.405i | 0.568695i | 0.958721 | + | 0.284348i | \(0.0917770\pi\) | ||||
−0.958721 | + | 0.284348i | \(0.908223\pi\) | |||||||
\(480\) | 23.7826 | − | 5.20620i | 0.0495471 | − | 0.0108463i | ||||
\(481\) | 525.558 | 1.09264 | ||||||||
\(482\) | 410.897 | − | 410.897i | 0.852484 | − | 0.852484i | ||||
\(483\) | 14.3730 | + | 14.3730i | 0.0297578 | + | 0.0297578i | ||||
\(484\) | 212.717i | 0.439497i | ||||||||
\(485\) | 76.9688 | − | 120.111i | 0.158698 | − | 0.247652i | ||||
\(486\) | 264.002 | 0.543213 | ||||||||
\(487\) | −343.544 | + | 343.544i | −0.705428 | + | 0.705428i | −0.965570 | − | 0.260142i | \(-0.916231\pi\) |
0.260142 | + | 0.965570i | \(0.416231\pi\) | |||||||
\(488\) | −7.90362 | − | 7.90362i | −0.0161959 | − | 0.0161959i | ||||
\(489\) | 244.021i | 0.499020i | ||||||||
\(490\) | −147.374 | − | 94.4393i | −0.300763 | − | 0.192733i | ||||
\(491\) | −490.578 | −0.999140 | −0.499570 | − | 0.866273i | \(-0.666509\pi\) | ||||
−0.499570 | + | 0.866273i | \(0.666509\pi\) | |||||||
\(492\) | 21.3254 | − | 21.3254i | 0.0433443 | − | 0.0433443i | ||||
\(493\) | 525.198 | + | 525.198i | 1.06531 | + | 1.06531i | ||||
\(494\) | 161.525i | 0.326974i | ||||||||
\(495\) | 33.7905 | + | 154.360i | 0.0682637 | + | 0.311838i | ||||
\(496\) | −108.094 | −0.217931 | ||||||||
\(497\) | 226.535 | − | 226.535i | 0.455806 | − | 0.455806i | ||||
\(498\) | 115.983 | + | 115.983i | 0.232897 | + | 0.232897i | ||||
\(499\) | − | 668.332i | − | 1.33934i | −0.742657 | − | 0.669672i | \(-0.766435\pi\) | ||
0.742657 | − | 0.669672i | \(-0.233565\pi\) | |||||||
\(500\) | −150.604 | − | 199.546i | −0.301208 | − | 0.399091i | ||||
\(501\) | 1.47691 | 0.00294793 | ||||||||
\(502\) | −220.598 | + | 220.598i | −0.439437 | + | 0.439437i | ||||
\(503\) | 139.902 | + | 139.902i | 0.278135 | + | 0.278135i | 0.832364 | − | 0.554229i | \(-0.186987\pi\) |
−0.554229 | + | 0.832364i | \(0.686987\pi\) | |||||||
\(504\) | − | 115.027i | − | 0.228227i | ||||||
\(505\) | −103.767 | + | 22.7155i | −0.205480 | + | 0.0449811i | ||||
\(506\) | 25.9522 | 0.0512889 | ||||||||
\(507\) | −106.227 | + | 106.227i | −0.209520 | + | 0.209520i | ||||
\(508\) | 243.271 | + | 243.271i | 0.478880 | + | 0.478880i | ||||
\(509\) | 428.803i | 0.842442i | 0.906958 | + | 0.421221i | \(0.138398\pi\) | ||||
−0.906958 | + | 0.421221i | \(0.861602\pi\) | |||||||
\(510\) | −74.2506 | + | 115.869i | −0.145589 | + | 0.227195i | ||||
\(511\) | −364.120 | −0.712564 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 64.7329 | + | 64.7329i | 0.126185 | + | 0.126185i | ||||
\(514\) | 444.024i | 0.863860i | ||||||||
\(515\) | 662.258 | + | 424.384i | 1.28594 | + | 0.824046i | ||||
\(516\) | 64.7669 | 0.125517 | ||||||||
\(517\) | −127.672 | + | 127.672i | −0.246948 | + | 0.246948i | ||||
\(518\) | −139.623 | − | 139.623i | −0.269543 | − | 0.269543i | ||||
\(519\) | − | 227.176i | − | 0.437719i | ||||||
\(520\) | −56.0524 | − | 256.055i | −0.107793 | − | 0.492413i | ||||
\(521\) | 432.637 | 0.830398 | 0.415199 | − | 0.909731i | \(-0.363712\pi\) | ||||
0.415199 | + | 0.909731i | \(0.363712\pi\) | |||||||
\(522\) | −271.305 | + | 271.305i | −0.519742 | + | 0.519742i | ||||
\(523\) | −240.769 | − | 240.769i | −0.460361 | − | 0.460361i | 0.438413 | − | 0.898774i | \(-0.355541\pi\) |
−0.898774 | + | 0.438413i | \(0.855541\pi\) | |||||||
\(524\) | − | 140.435i | − | 0.268005i | ||||||
\(525\) | 96.2685 | − | 44.2693i | 0.183369 | − | 0.0843224i | ||||
\(526\) | −547.200 | −1.04030 | ||||||||
\(527\) | 432.056 | − | 432.056i | 0.819840 | − | 0.819840i | ||||
\(528\) | 9.31578 | + | 9.31578i | 0.0176435 | + | 0.0176435i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 416.760 | − | 91.2320i | 0.786339 | − | 0.172136i | ||||
\(531\) | 238.849 | 0.449810 | ||||||||
\(532\) | 42.9120 | − | 42.9120i | 0.0806616 | − | 0.0806616i | ||||
\(533\) | −229.599 | − | 229.599i | −0.430768 | − | 0.430768i | ||||
\(534\) | − | 160.117i | − | 0.299845i | ||||||
\(535\) | 168.355 | − | 262.721i | 0.314683 | − | 0.491068i | ||||
\(536\) | −277.634 | −0.517974 | ||||||||
\(537\) | 95.4902 | − | 95.4902i | 0.177822 | − | 0.177822i | ||||
\(538\) | −306.939 | − | 306.939i | −0.570518 | − | 0.570518i | ||||
\(539\) | − | 94.7195i | − | 0.175732i | ||||||
\(540\) | −125.080 | − | 80.1531i | −0.231630 | − | 0.148432i | ||||
\(541\) | −914.332 | −1.69008 | −0.845039 | − | 0.534705i | \(-0.820423\pi\) | ||||
−0.845039 | + | 0.534705i | \(0.820423\pi\) | |||||||
\(542\) | 423.942 | − | 423.942i | 0.782181 | − | 0.782181i | ||||
\(543\) | −67.2441 | − | 67.2441i | −0.123838 | − | 0.123838i | ||||
\(544\) | − | 127.905i | − | 0.235120i | ||||||
\(545\) | 60.8961 | + | 278.182i | 0.111736 | + | 0.510425i | ||||
\(546\) | 111.096 | 0.203472 | ||||||||
\(547\) | −636.733 | + | 636.733i | −1.16405 | + | 1.16405i | −0.180465 | + | 0.983581i | \(0.557760\pi\) |
−0.983581 | + | 0.180465i | \(0.942240\pi\) | |||||||
\(548\) | −180.665 | − | 180.665i | −0.329680 | − | 0.329680i | ||||
\(549\) | 32.6384i | 0.0594507i | ||||||||
\(550\) | 46.9453 | − | 126.879i | 0.0853552 | − | 0.230689i | ||||
\(551\) | −202.427 | −0.367381 | ||||||||
\(552\) | −8.25606 | + | 8.25606i | −0.0149566 | + | 0.0149566i | ||||
\(553\) | 216.681 | + | 216.681i | 0.391828 | + | 0.391828i | ||||
\(554\) | − | 246.989i | − | 0.445828i | ||||||
\(555\) | −119.213 | + | 26.0966i | −0.214798 | + | 0.0470209i | ||||
\(556\) | 70.2758 | 0.126395 | ||||||||
\(557\) | −414.033 | + | 414.033i | −0.743326 | + | 0.743326i | −0.973217 | − | 0.229890i | \(-0.926163\pi\) |
0.229890 | + | 0.973217i | \(0.426163\pi\) | |||||||
\(558\) | 223.190 | + | 223.190i | 0.399982 | + | 0.399982i | ||||
\(559\) | − | 697.311i | − | 1.24743i | ||||||
\(560\) | −53.1341 | + | 82.9167i | −0.0948824 | + | 0.148066i | ||||
\(561\) | −74.4710 | −0.132747 | ||||||||
\(562\) | −99.1668 | + | 99.1668i | −0.176453 | + | 0.176453i | ||||
\(563\) | −324.082 | − | 324.082i | −0.575634 | − | 0.575634i | 0.358063 | − | 0.933697i | \(-0.383437\pi\) |
−0.933697 | + | 0.358063i | \(0.883437\pi\) | |||||||
\(564\) | − | 81.2317i | − | 0.144028i | ||||||
\(565\) | −91.1533 | − | 58.4122i | −0.161333 | − | 0.103384i | ||||
\(566\) | −400.833 | −0.708186 | ||||||||
\(567\) | −214.287 | + | 214.287i | −0.377932 | + | 0.377932i | ||||
\(568\) | 130.125 | + | 130.125i | 0.229093 | + | 0.229093i | ||||
\(569\) | − | 521.104i | − | 0.915824i | −0.888998 | − | 0.457912i | \(-0.848598\pi\) | ||
0.888998 | − | 0.457912i | \(-0.151402\pi\) | |||||||
\(570\) | −8.02054 | − | 36.6389i | −0.0140711 | − | 0.0642788i | ||||
\(571\) | −308.824 | −0.540847 | −0.270423 | − | 0.962741i | \(-0.587164\pi\) | ||||
−0.270423 | + | 0.962741i | \(0.587164\pi\) | |||||||
\(572\) | 100.298 | − | 100.298i | 0.175346 | − | 0.175346i | ||||
\(573\) | −62.0680 | − | 62.0680i | −0.108321 | − | 0.108321i | ||||
\(574\) | 121.994i | 0.212533i | ||||||||
\(575\) | 112.446 | + | 41.6051i | 0.195558 | + | 0.0723567i | ||||
\(576\) | 66.0728 | 0.114710 | ||||||||
\(577\) | −243.906 | + | 243.906i | −0.422714 | + | 0.422714i | −0.886137 | − | 0.463423i | \(-0.846621\pi\) |
0.463423 | + | 0.886137i | \(0.346621\pi\) | |||||||
\(578\) | 222.242 | + | 222.242i | 0.384501 | + | 0.384501i | ||||
\(579\) | 260.499i | 0.449912i | ||||||||
\(580\) | 320.893 | − | 70.2461i | 0.553265 | − | 0.121114i | ||||
\(581\) | −663.491 | −1.14198 | ||||||||
\(582\) | −24.5584 | + | 24.5584i | −0.0421966 | + | 0.0421966i | ||||
\(583\) | 163.247 | + | 163.247i | 0.280012 | + | 0.280012i | ||||
\(584\) | − | 209.155i | − | 0.358143i | ||||||
\(585\) | −412.960 | + | 644.432i | −0.705915 | + | 1.10159i | ||||
\(586\) | −294.070 | −0.501826 | ||||||||
\(587\) | −153.926 | + | 153.926i | −0.262226 | + | 0.262226i | −0.825958 | − | 0.563732i | \(-0.809365\pi\) |
0.563732 | + | 0.825958i | \(0.309365\pi\) | |||||||
\(588\) | 30.1327 | + | 30.1327i | 0.0512461 | + | 0.0512461i | ||||
\(589\) | 166.527i | 0.282728i | ||||||||
\(590\) | −172.174 | − | 110.331i | −0.291820 | − | 0.187002i | ||||
\(591\) | −227.634 | −0.385168 | ||||||||
\(592\) | 80.2016 | − | 80.2016i | 0.135476 | − | 0.135476i | ||||
\(593\) | −506.955 | − | 506.955i | −0.854899 | − | 0.854899i | 0.135832 | − | 0.990732i | \(-0.456629\pi\) |
−0.990732 | + | 0.135832i | \(0.956629\pi\) | |||||||
\(594\) | − | 80.3910i | − | 0.135338i | ||||||
\(595\) | −119.042 | − | 543.800i | −0.200071 | − | 0.913950i | ||||
\(596\) | −165.853 | −0.278277 | ||||||||
\(597\) | −222.726 | + | 222.726i | −0.373075 | + | 0.373075i | ||||
\(598\) | 88.8886 | + | 88.8886i | 0.148643 | + | 0.148643i | ||||
\(599\) | 884.769i | 1.47708i | 0.674211 | + | 0.738539i | \(0.264484\pi\) | ||||
−0.674211 | + | 0.738539i | \(0.735516\pi\) | |||||||
\(600\) | 25.4289 | + | 55.2979i | 0.0423814 | + | 0.0921632i | ||||
\(601\) | −142.836 | −0.237664 | −0.118832 | − | 0.992914i | \(-0.537915\pi\) | ||||
−0.118832 | + | 0.992914i | \(0.537915\pi\) | |||||||
\(602\) | −185.253 | + | 185.253i | −0.307729 | + | 0.307729i | ||||
\(603\) | 573.252 | + | 573.252i | 0.950666 | + | 0.950666i | ||||
\(604\) | − | 512.245i | − | 0.848088i | ||||||
\(605\) | −519.490 | + | 113.720i | −0.858662 | + | 0.187968i | ||||
\(606\) | 25.8612 | 0.0426752 | ||||||||
\(607\) | −560.960 | + | 560.960i | −0.924152 | + | 0.924152i | −0.997320 | − | 0.0731676i | \(-0.976689\pi\) |
0.0731676 | + | 0.997320i | \(0.476689\pi\) | |||||||
\(608\) | 24.6492 | + | 24.6492i | 0.0405414 | + | 0.0405414i | ||||
\(609\) | 139.227i | 0.228616i | ||||||||
\(610\) | 15.0766 | − | 23.5273i | 0.0247158 | − | 0.0385694i | ||||
\(611\) | −874.579 | −1.43139 | ||||||||
\(612\) | −264.096 | + | 264.096i | −0.431529 | + | 0.431529i | ||||
\(613\) | −240.604 | − | 240.604i | −0.392502 | − | 0.392502i | 0.483076 | − | 0.875578i | \(-0.339519\pi\) |
−0.875578 | + | 0.483076i | \(0.839519\pi\) | |||||||
\(614\) | 340.317i | 0.554262i | ||||||||
\(615\) | 63.4810 | + | 40.6795i | 0.103221 | + | 0.0661455i | ||||
\(616\) | −53.2918 | −0.0865127 | ||||||||
\(617\) | 634.877 | − | 634.877i | 1.02897 | − | 1.02897i | 0.0294068 | − | 0.999568i | \(-0.490638\pi\) |
0.999568 | − | 0.0294068i | \(-0.00936183\pi\) | |||||||
\(618\) | −135.408 | − | 135.408i | −0.219107 | − | 0.219107i | ||||
\(619\) | 339.323i | 0.548179i | 0.961704 | + | 0.274089i | \(0.0883764\pi\) | ||||
−0.961704 | + | 0.274089i | \(0.911624\pi\) | |||||||
\(620\) | −57.7881 | − | 263.984i | −0.0932066 | − | 0.425780i | ||||
\(621\) | 71.2461 | 0.114728 | ||||||||
\(622\) | −86.2595 | + | 86.2595i | −0.138681 | + | 0.138681i | ||||
\(623\) | 457.983 | + | 457.983i | 0.735125 | + | 0.735125i | ||||
\(624\) | 63.8148i | 0.102267i | ||||||||
\(625\) | 406.810 | − | 474.480i | 0.650895 | − | 0.759168i | ||||
\(626\) | 705.035 | 1.12625 | ||||||||
\(627\) | 14.3517 | − | 14.3517i | 0.0228894 | − | 0.0228894i | ||||
\(628\) | −228.536 | − | 228.536i | −0.363911 | − | 0.363911i | ||||
\(629\) | 641.137i | 1.01930i | ||||||||
\(630\) | 280.915 | − | 61.4944i | 0.445896 | − | 0.0976101i | ||||
\(631\) | 913.051 | 1.44699 | 0.723495 | − | 0.690329i | \(-0.242534\pi\) | ||||
0.723495 | + | 0.690329i | \(0.242534\pi\) | |||||||
\(632\) | −124.464 | + | 124.464i | −0.196937 | + | 0.196937i | ||||
\(633\) | −164.017 | − | 164.017i | −0.259110 | − | 0.259110i | ||||
\(634\) | − | 159.563i | − | 0.251677i | ||||||
\(635\) | −464.054 | + | 724.164i | −0.730794 | + | 1.14042i | ||||
\(636\) | −103.866 | −0.163312 | ||||||||
\(637\) | 324.423 | − | 324.423i | 0.509298 | − | 0.509298i | ||||
\(638\) | 125.696 | + | 125.696i | 0.197015 | + | 0.197015i | ||||
\(639\) | − | 537.358i | − | 0.840935i | ||||||
\(640\) | −47.6285 | − | 30.5210i | −0.0744195 | − | 0.0476890i | ||||
\(641\) | 799.743 | 1.24765 | 0.623824 | − | 0.781565i | \(-0.285578\pi\) | ||||
0.623824 | + | 0.781565i | \(0.285578\pi\) | |||||||
\(642\) | −53.7171 | + | 53.7171i | −0.0836715 | + | 0.0836715i | ||||
\(643\) | −362.899 | − | 362.899i | −0.564385 | − | 0.564385i | 0.366165 | − | 0.930550i | \(-0.380670\pi\) |
−0.930550 | + | 0.366165i | \(0.880670\pi\) | |||||||
\(644\) | − | 47.2296i | − | 0.0733379i | ||||||
\(645\) | 34.6250 | + | 158.172i | 0.0536822 | + | 0.245227i | ||||
\(646\) | −197.047 | −0.305027 | ||||||||
\(647\) | −735.285 | + | 735.285i | −1.13645 | + | 1.13645i | −0.147372 | + | 0.989081i | \(0.547081\pi\) |
−0.989081 | + | 0.147372i | \(0.952919\pi\) | |||||||
\(648\) | −123.089 | − | 123.089i | −0.189953 | − | 0.189953i | ||||
\(649\) | − | 110.659i | − | 0.170506i | ||||||
\(650\) | 595.363 | − | 273.779i | 0.915944 | − | 0.421199i | ||||
\(651\) | 114.536 | 0.175938 | ||||||||
\(652\) | 400.924 | − | 400.924i | 0.614915 | − | 0.614915i | ||||
\(653\) | −633.952 | − | 633.952i | −0.970831 | − | 0.970831i | 0.0287558 | − | 0.999586i | \(-0.490845\pi\) |
−0.999586 | + | 0.0287558i | \(0.990845\pi\) | |||||||
\(654\) | − | 69.3293i | − | 0.106008i | ||||||
\(655\) | 342.966 | − | 75.0779i | 0.523612 | − | 0.114623i | ||||
\(656\) | −70.0750 | −0.106822 | ||||||||
\(657\) | −431.859 | + | 431.859i | −0.657320 | + | 0.657320i | ||||
\(658\) | 232.347 | + | 232.347i | 0.353111 | + | 0.353111i | ||||
\(659\) | − | 378.146i | − | 0.573817i | −0.957958 | − | 0.286909i | \(-0.907372\pi\) | ||
0.957958 | − | 0.286909i | \(-0.0926276\pi\) | |||||||
\(660\) | −17.7704 | + | 27.7310i | −0.0269248 | + | 0.0420167i | ||||
\(661\) | −417.405 | −0.631476 | −0.315738 | − | 0.948846i | \(-0.602252\pi\) | ||||
−0.315738 | + | 0.948846i | \(0.602252\pi\) | |||||||
\(662\) | 123.045 | − | 123.045i | 0.185869 | − | 0.185869i | ||||
\(663\) | −255.070 | − | 255.070i | −0.384721 | − | 0.384721i | ||||
\(664\) | − | 381.118i | − | 0.573973i | ||||||
\(665\) | 127.739 | + | 81.8571i | 0.192089 | + | 0.123093i | ||||
\(666\) | −331.197 | −0.497292 | ||||||||
\(667\) | −111.397 | + | 111.397i | −0.167012 | + | 0.167012i | ||||
\(668\) | −2.42656 | − | 2.42656i | −0.00363257 | − | 0.00363257i | ||||
\(669\) | − | 222.413i | − | 0.332455i | ||||||
\(670\) | −148.426 | − | 678.029i | −0.221531 | − | 1.01198i | ||||
\(671\) | 15.1214 | 0.0225356 | ||||||||
\(672\) | 16.9535 | − | 16.9535i | 0.0252284 | − | 0.0252284i | ||||
\(673\) | −591.106 | − | 591.106i | −0.878316 | − | 0.878316i | 0.115045 | − | 0.993360i | \(-0.463299\pi\) |
−0.993360 | + | 0.115045i | \(0.963299\pi\) | |||||||
\(674\) | 658.510i | 0.977018i | ||||||||
\(675\) | 128.878 | − | 348.318i | 0.190931 | − | 0.516027i | ||||
\(676\) | 349.060 | 0.516361 | ||||||||
\(677\) | 415.702 | − | 415.702i | 0.614035 | − | 0.614035i | −0.329960 | − | 0.943995i | \(-0.607035\pi\) |
0.943995 | + | 0.329960i | \(0.107035\pi\) | |||||||
\(678\) | 18.6376 | + | 18.6376i | 0.0274891 | + | 0.0274891i | ||||
\(679\) | − | 140.489i | − | 0.206906i | ||||||
\(680\) | 312.366 | − | 68.3794i | 0.459362 | − | 0.100558i | ||||
\(681\) | 86.4388 | 0.126929 | ||||||||
\(682\) | 103.404 | − | 103.404i | 0.151618 | − | 0.151618i | ||||
\(683\) | −286.643 | − | 286.643i | −0.419682 | − | 0.419682i | 0.465412 | − | 0.885094i | \(-0.345906\pi\) |
−0.885094 | + | 0.465412i | \(0.845906\pi\) | |||||||
\(684\) | − | 101.790i | − | 0.148816i | ||||||
\(685\) | 344.629 | − | 537.799i | 0.503108 | − | 0.785108i | ||||
\(686\) | −513.595 | −0.748681 | ||||||||
\(687\) | 59.4091 | − | 59.4091i | 0.0864762 | − | 0.0864762i | ||||
\(688\) | −106.412 | − | 106.412i | −0.154668 | − | 0.154668i | ||||
\(689\) | 1118.27i | 1.62304i | ||||||||
\(690\) | −24.5765 | − | 15.7489i | −0.0356181 | − | 0.0228245i | ||||
\(691\) | 830.206 | 1.20146 | 0.600728 | − | 0.799453i | \(-0.294877\pi\) | ||||
0.600728 | + | 0.799453i | \(0.294877\pi\) | |||||||
\(692\) | −373.249 | + | 373.249i | −0.539378 | + | 0.539378i | ||||
\(693\) | 110.036 | + | 110.036i | 0.158782 | + | 0.158782i | ||||
\(694\) | 157.833i | 0.227425i | ||||||||
\(695\) | 37.5701 | + | 171.625i | 0.0540577 | + | 0.246943i | ||||
\(696\) | −79.9740 | −0.114905 | ||||||||
\(697\) | 280.092 | − | 280.092i | 0.401854 | − | 0.401854i | ||||
\(698\) | 209.184 | + | 209.184i | 0.299690 | + | 0.299690i | ||||
\(699\) | − | 114.064i | − | 0.163182i | ||||||
\(700\) | −230.903 | − | 85.4344i | −0.329861 | − | 0.122049i | ||||
\(701\) | 228.321 | 0.325708 | 0.162854 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162854 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(702\) | 275.346 | − | 275.346i | 0.392231 | − | 0.392231i | ||||
\(703\) | −123.557 | − | 123.557i | −0.175756 | − | 0.175756i | ||||
\(704\) | − | 30.6115i | − | 0.0434823i | ||||||
\(705\) | 198.382 | − | 43.4273i | 0.281392 | − | 0.0615990i | ||||
\(706\) | −362.586 | −0.513578 | ||||||||
\(707\) | −73.9707 | + | 73.9707i | −0.104626 | + | 0.104626i | ||||
\(708\) | 35.2034 | + | 35.2034i | 0.0497223 | + | 0.0497223i | ||||
\(709\) | 701.099i | 0.988856i | 0.869219 | + | 0.494428i | \(0.164622\pi\) | ||||
−0.869219 | + | 0.494428i | \(0.835378\pi\) | |||||||
\(710\) | −248.221 | + | 387.353i | −0.349607 | + | 0.545568i | ||||
\(711\) | 513.982 | 0.722900 | ||||||||
\(712\) | −263.071 | + | 263.071i | −0.369482 | + | 0.369482i | ||||
\(713\) | 91.6411 | + | 91.6411i | 0.128529 | + | 0.128529i | ||||
\(714\) | 135.528i | 0.189815i | ||||||||
\(715\) | 298.565 | + | 191.324i | 0.417574 | + | 0.267587i | ||||
\(716\) | −313.780 | −0.438240 | ||||||||
\(717\) | −139.913 | + | 139.913i | −0.195137 | + | 0.195137i | ||||
\(718\) | 701.621 | + | 701.621i | 0.977188 | + | 0.977188i | ||||
\(719\) | − | 955.252i | − | 1.32858i | −0.747473 | − | 0.664292i | \(-0.768733\pi\) | ||
0.747473 | − | 0.664292i | \(-0.231267\pi\) | |||||||
\(720\) | 35.3232 | + | 161.361i | 0.0490600 | + | 0.224113i | ||||
\(721\) | 774.615 | 1.07436 | ||||||||
\(722\) | −323.026 | + | 323.026i | −0.447405 | + | 0.447405i | ||||
\(723\) | −250.091 | − | 250.091i | −0.345907 | − | 0.345907i | ||||
\(724\) | 220.963i | 0.305198i | ||||||||
\(725\) | 343.106 | + | 746.122i | 0.473249 | + | 1.02913i | ||||
\(726\) | 129.469 | 0.178332 | ||||||||
\(727\) | −131.313 | + | 131.313i | −0.180623 | + | 0.180623i | −0.791627 | − | 0.611004i | \(-0.790766\pi\) |
0.611004 | + | 0.791627i | \(0.290766\pi\) | |||||||
\(728\) | −182.529 | − | 182.529i | −0.250727 | − | 0.250727i | ||||
\(729\) | 393.219i | 0.539395i | ||||||||
\(730\) | 510.793 | − | 111.817i | 0.699716 | − | 0.153173i | ||||
\(731\) | 850.662 | 1.16370 | ||||||||
\(732\) | −4.81050 | + | 4.81050i | −0.00657172 | + | 0.00657172i | ||||
\(733\) | 590.972 | + | 590.972i | 0.806237 | + | 0.806237i | 0.984062 | − | 0.177825i | \(-0.0569060\pi\) |
−0.177825 | + | 0.984062i | \(0.556906\pi\) | |||||||
\(734\) | 318.766i | 0.434287i | ||||||||
\(735\) | −57.4800 | + | 89.6985i | −0.0782041 | + | 0.122039i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 265.588 | − | 265.588i | 0.360363 | − | 0.360363i | ||||
\(738\) | 144.689 | + | 144.689i | 0.196056 | + | 0.196056i | ||||
\(739\) | − | 764.194i | − | 1.03409i | −0.855958 | − | 0.517046i | \(-0.827032\pi\) | ||
0.855958 | − | 0.517046i | \(-0.172968\pi\) | |||||||
\(740\) | 238.742 | + | 152.989i | 0.322625 | + | 0.206742i | ||||
\(741\) | 98.3114 | 0.132674 | ||||||||
\(742\) | 297.088 | − | 297.088i | 0.400388 | − | 0.400388i | ||||
\(743\) | −864.163 | − | 864.163i | −1.16307 | − | 1.16307i | −0.983799 | − | 0.179273i | \(-0.942625\pi\) |
−0.179273 | − | 0.983799i | \(-0.557375\pi\) | |||||||
\(744\) | 65.7908i | 0.0884285i | ||||||||
\(745\) | −88.6666 | − | 405.041i | −0.119016 | − | 0.543679i | ||||
\(746\) | −534.508 | −0.716499 | ||||||||
\(747\) | −786.923 | + | 786.923i | −1.05344 | + | 1.05344i | ||||
\(748\) | 122.355 | + | 122.355i | 0.163577 | + | 0.163577i | ||||
\(749\) | − | 307.294i | − | 0.410272i | ||||||
\(750\) | −121.452 | + | 91.6644i | −0.161936 | + | 0.122219i | ||||
\(751\) | −285.420 | −0.380053 | −0.190027 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190027 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(752\) | −133.463 | + | 133.463i | −0.177478 | + | 0.177478i | ||||
\(753\) | 134.266 | + | 134.266i | 0.178308 | + | 0.178308i | ||||
\(754\) | 861.038i | 1.14196i | ||||||||
\(755\) | 1250.99 | − | 273.851i | 1.65694 | − | 0.362717i | ||||
\(756\) | −146.301 | −0.193520 | ||||||||
\(757\) | 410.339 | − | 410.339i | 0.542060 | − | 0.542060i | −0.382072 | − | 0.924132i | \(-0.624790\pi\) |
0.924132 | + | 0.382072i | \(0.124790\pi\) | |||||||
\(758\) | −204.998 | − | 204.998i | −0.270446 | − | 0.270446i | ||||
\(759\) | − | 15.7957i | − | 0.0208112i | ||||||
\(760\) | −47.0198 | + | 73.3752i | −0.0618682 | + | 0.0965463i | ||||
\(761\) | 1360.01 | 1.78713 | 0.893565 | − | 0.448934i | \(-0.148196\pi\) | ||||
0.893565 | + | 0.448934i | \(0.148196\pi\) | |||||||
\(762\) | 148.066 | − | 148.066i | 0.194312 | − | 0.194312i | ||||
\(763\) | 198.302 | + | 198.302i | 0.259898 | + | 0.259898i | ||||
\(764\) | 203.955i | 0.266956i | ||||||||
\(765\) | −786.154 | − | 503.778i | −1.02765 | − | 0.658533i | ||||
\(766\) | −927.605 | −1.21097 | ||||||||
\(767\) | 379.016 | − | 379.016i | 0.494154 | − | 0.494154i | ||||
\(768\) | 9.73832 | + | 9.73832i | 0.0126801 | + | 0.0126801i | ||||
\(769\) | − | 1442.78i | − | 1.87618i | −0.346393 | − | 0.938090i | \(-0.612594\pi\) | ||
0.346393 | − | 0.938090i | \(-0.387406\pi\) | |||||||
\(770\) | −28.4903 | − | 130.148i | −0.0370004 | − | 0.169023i | ||||
\(771\) | 270.253 | 0.350523 | ||||||||
\(772\) | 427.999 | − | 427.999i | 0.554402 | − | 0.554402i | ||||
\(773\) | 176.154 | + | 176.154i | 0.227883 | + | 0.227883i | 0.811808 | − | 0.583925i | \(-0.198484\pi\) |
−0.583925 | + | 0.811808i | \(0.698484\pi\) | |||||||
\(774\) | 439.432i | 0.567742i | ||||||||
\(775\) | 613.799 | − | 282.257i | 0.791999 | − | 0.364202i | ||||
\(776\) | 80.6987 | 0.103993 | ||||||||
\(777\) | −84.9811 | + | 84.9811i | −0.109371 | + | 0.109371i | ||||
\(778\) | −507.724 | − | 507.724i | −0.652602 | − | 0.652602i | ||||
\(779\) | 107.956i | 0.138583i | ||||||||
\(780\) | −155.847 | + | 34.1160i | −0.199803 | + | 0.0437385i | ||||
\(781\) | −248.958 | −0.318768 | ||||||||
\(782\) | −108.437 | + | 108.437i | −0.138666 | + | 0.138666i | ||||
\(783\) | 345.070 | + | 345.070i | 0.440702 | + | 0.440702i | ||||
\(784\) | − | 99.0158i | − | 0.126296i | ||||||
\(785\) | 435.946 | − | 680.301i | 0.555345 | − | 0.866626i | ||||
\(786\) | −85.4750 | −0.108747 | ||||||||
\(787\) | −310.617 | + | 310.617i | −0.394685 | + | 0.394685i | −0.876354 | − | 0.481668i | \(-0.840031\pi\) |
0.481668 | + | 0.876354i | \(0.340031\pi\) | |||||||
\(788\) | 374.002 | + | 374.002i | 0.474621 | + | 0.474621i | ||||
\(789\) | 333.051i | 0.422117i | ||||||||
\(790\) | −370.503 | − | 237.423i | −0.468991 | − | 0.300535i | ||||
\(791\) | −106.618 | −0.134789 | ||||||||
\(792\) | −63.2059 | + | 63.2059i | −0.0798055 | + | 0.0798055i | ||||
\(793\) | 51.7921 | + | 51.7921i | 0.0653116 | + | 0.0653116i | ||||
\(794\) | − | 83.4949i | − | 0.105157i | ||||||
\(795\) | −55.5279 | − | 253.659i | −0.0698464 | − | 0.319068i | ||||
\(796\) | 731.875 | 0.919441 | ||||||||
\(797\) | 446.213 | − | 446.213i | 0.559866 | − | 0.559866i | −0.369403 | − | 0.929269i | \(-0.620438\pi\) |
0.929269 | + | 0.369403i | \(0.120438\pi\) | |||||||
\(798\) | −26.1181 | − | 26.1181i | −0.0327295 | − | 0.0327295i | ||||
\(799\) | − | 1066.92i | − | 1.33531i | ||||||
\(800\) | 49.0747 | − | 132.634i | 0.0613433 | − | 0.165792i | ||||
\(801\) | 1086.37 | 1.35626 | ||||||||
\(802\) | −662.900 | + | 662.900i | −0.826558 | + | 0.826558i | ||||
\(803\) | 200.080 | + | 200.080i | 0.249166 | + | 0.249166i | ||||
\(804\) | 168.980i | 0.210175i | ||||||||
\(805\) | 115.343 | − | 25.2494i | 0.143283 | − | 0.0313657i | ||||
\(806\) | 708.335 | 0.878828 | ||||||||
\(807\) | −186.817 | + | 186.817i | −0.231495 | + | 0.231495i | ||||
\(808\) | −42.4898 | − | 42.4898i | −0.0525864 | − | 0.0525864i | ||||
\(809\) | − | 399.170i | − | 0.493411i | −0.969090 | − | 0.246706i | \(-0.920652\pi\) | ||
0.969090 | − | 0.246706i | \(-0.0793481\pi\) | |||||||
\(810\) | 234.800 | − | 366.410i | 0.289877 | − | 0.452358i | ||||
\(811\) | −1016.76 | −1.25371 | −0.626855 | − | 0.779136i | \(-0.715658\pi\) | ||||
−0.626855 | + | 0.779136i | \(0.715658\pi\) | |||||||
\(812\) | 228.750 | − | 228.750i | 0.281711 | − | 0.281711i | ||||
\(813\) | −258.030 | − | 258.030i | −0.317380 | − | 0.317380i | ||||
\(814\) | 153.443i | 0.188505i | ||||||||
\(815\) | 1193.46 | + | 764.787i | 1.46437 | + | 0.938389i | ||||
\(816\) | −77.8488 | −0.0954030 | ||||||||
\(817\) | −163.935 | + | 163.935i | −0.200655 | + | 0.200655i | ||||
\(818\) | −4.51129 | − | 4.51129i | −0.00551502 | − | 0.00551502i | ||||
\(819\) | 753.764i | 0.920347i | ||||||||
\(820\) | −37.4628 | − | 171.135i | −0.0456864 | − | 0.208701i | ||||
\(821\) | 231.396 | 0.281847 | 0.140923 | − | 0.990021i | \(-0.454993\pi\) | ||||
0.140923 | + | 0.990021i | \(0.454993\pi\) | |||||||
\(822\) | −109.961 | + | 109.961i | −0.133772 | + | 0.133772i | ||||
\(823\) | −298.923 | − | 298.923i | −0.363211 | − | 0.363211i | 0.501783 | − | 0.864994i | \(-0.332678\pi\) |
−0.864994 | + | 0.501783i | \(0.832678\pi\) | |||||||
\(824\) | 444.949i | 0.539987i | ||||||||
\(825\) | −77.2241 | − | 28.5730i | −0.0936049 | − | 0.0346340i | ||||
\(826\) | −201.384 | −0.243807 | ||||||||
\(827\) | 19.4139 | − | 19.4139i | 0.0234750 | − | 0.0234750i | −0.695272 | − | 0.718747i | \(-0.744716\pi\) |
0.718747 | + | 0.695272i | \(0.244716\pi\) | |||||||
\(828\) | −56.0160 | − | 56.0160i | −0.0676521 | − | 0.0676521i | ||||
\(829\) | 626.889i | 0.756199i | 0.925765 | + | 0.378099i | \(0.123422\pi\) | ||||
−0.925765 | + | 0.378099i | \(0.876578\pi\) | |||||||
\(830\) | 930.755 | − | 203.749i | 1.12139 | − | 0.245481i | ||||
\(831\) | −150.329 | −0.180901 | ||||||||
\(832\) | 104.847 | − | 104.847i | 0.126018 | − | 0.126018i | ||||
\(833\) | 395.770 | + | 395.770i | 0.475114 | + | 0.475114i | ||||
\(834\) | − | 42.7730i | − | 0.0512866i | ||||||
\(835\) | 4.62880 | − | 7.22333i | 0.00554348 | − | 0.00865069i | ||||
\(836\) | −47.1594 | −0.0564107 | ||||||||
\(837\) | 283.873 | − | 283.873i | 0.339155 | − | 0.339155i | ||||
\(838\) | −239.199 | − | 239.199i | −0.285440 | − | 0.285440i | ||||
\(839\) | 144.679i | 0.172442i | 0.996276 | + | 0.0862211i | \(0.0274792\pi\) | ||||
−0.996276 | + | 0.0862211i | \(0.972521\pi\) | |||||||
\(840\) | 50.4668 | + | 32.3398i | 0.0600796 | + | 0.0384998i | ||||
\(841\) | −238.071 | −0.283081 | ||||||||
\(842\) | −222.759 | + | 222.759i | −0.264559 | + | 0.264559i | ||||
\(843\) | 60.3574 | + | 60.3574i | 0.0715983 | + | 0.0715983i | ||||
\(844\) | 538.957i | 0.638575i | ||||||||
\(845\) | 186.611 | + | 852.463i | 0.220841 | + | 1.00883i | ||||
\(846\) | 551.143 | 0.651470 | ||||||||
\(847\) | −370.320 | + | 370.320i | −0.437214 | + | 0.437214i | ||||
\(848\) | 170.651 | + | 170.651i | 0.201240 | + | 0.201240i | ||||
\(849\) | 243.965i | 0.287356i | ||||||||
\(850\) | 333.988 | + | 726.295i | 0.392927 | + | 0.854464i | ||||
\(851\) | −135.988 | −0.159798 | ||||||||
\(852\) | 79.1999 | − | 79.1999i | 0.0929576 | − | 0.0929576i | ||||
\(853\) | −47.8789 | − | 47.8789i | −0.0561300 | − | 0.0561300i | 0.678485 | − | 0.734615i | \(-0.262637\pi\) |
−0.734615 | + | 0.678485i | \(0.762637\pi\) | |||||||
\(854\) | − | 27.5189i | − | 0.0322236i | ||||||
\(855\) | 248.589 | − | 54.4180i | 0.290747 | − | 0.0636468i | ||||
\(856\) | 176.514 | 0.206208 | ||||||||
\(857\) | −3.82783 | + | 3.82783i | −0.00446655 | + | 0.00446655i | −0.709337 | − | 0.704870i | \(-0.751005\pi\) |
0.704870 | + | 0.709337i | \(0.251005\pi\) | |||||||
\(858\) | −61.0459 | − | 61.0459i | −0.0711490 | − | 0.0711490i | ||||
\(859\) | − | 843.353i | − | 0.981785i | −0.871220 | − | 0.490892i | \(-0.836671\pi\) | ||
0.871220 | − | 0.490892i | \(-0.163329\pi\) | |||||||
\(860\) | 202.986 | − | 316.764i | 0.236031 | − | 0.368330i | ||||
\(861\) | 74.2511 | 0.0862382 | ||||||||
\(862\) | 708.039 | − | 708.039i | 0.821391 | − | 0.821391i | ||||
\(863\) | −1167.76 | − | 1167.76i | −1.35314 | − | 1.35314i | −0.882121 | − | 0.471022i | \(-0.843885\pi\) |
−0.471022 | − | 0.882121i | \(-0.656115\pi\) | |||||||
\(864\) | − | 84.0373i | − | 0.0972654i | ||||||
\(865\) | −1111.08 | − | 711.995i | −1.28449 | − | 0.823116i | ||||
\(866\) | 358.408 | 0.413866 | ||||||||
\(867\) | 135.266 | − | 135.266i | 0.156016 | − | 0.156016i | ||||
\(868\) | −188.181 | − | 188.181i | −0.216799 | − | 0.216799i | ||||
\(869\) | − | 238.128i | − | 0.274025i | ||||||
\(870\) | −42.7549 | − | 195.310i | −0.0491436 | − | 0.224494i | ||||
\(871\) | 1819.32 | 2.08878 | ||||||||
\(872\) | −113.908 | + | 113.908i | −0.130628 | + | 0.130628i | ||||
\(873\) | −166.625 | − | 166.625i | −0.190864 | − | 0.190864i | ||||
\(874\) | − | 41.7947i | − | 0.0478201i | ||||||
\(875\) | 85.2025 | − | 609.578i | 0.0973742 | − | 0.696660i | ||||
\(876\) | −127.301 | −0.145321 | ||||||||
\(877\) | 542.109 | − | 542.109i | 0.618140 | − | 0.618140i | −0.326914 | − | 0.945054i | \(-0.606009\pi\) |
0.945054 | + | 0.326914i | \(0.106009\pi\) | |||||||
\(878\) | 574.258 | + | 574.258i | 0.654052 | + | 0.654052i | ||||
\(879\) | 178.984i | 0.203622i | ||||||||
\(880\) | 74.7586 | − | 16.3652i | 0.0849529 | − | 0.0185969i | ||||
\(881\) | −585.615 | −0.664716 | −0.332358 | − | 0.943153i | \(-0.607844\pi\) | ||||
−0.332358 | + | 0.943153i | \(0.607844\pi\) | |||||||
\(882\) | −204.445 | + | 204.445i | −0.231798 | + | 0.231798i | ||||
\(883\) | −224.300 | − | 224.300i | −0.254020 | − | 0.254020i | 0.568597 | − | 0.822616i | \(-0.307487\pi\) |
−0.822616 | + | 0.568597i | \(0.807487\pi\) | |||||||
\(884\) | 838.157i | 0.948142i | ||||||||
\(885\) | −67.1526 | + | 104.793i | −0.0758786 | + | 0.118410i | ||||
\(886\) | 167.721 | 0.189301 | ||||||||
\(887\) | −644.816 | + | 644.816i | −0.726963 | + | 0.726963i | −0.970014 | − | 0.243051i | \(-0.921852\pi\) |
0.243051 | + | 0.970014i | \(0.421852\pi\) | |||||||
\(888\) | −48.8143 | − | 48.8143i | −0.0549710 | − | 0.0549710i | ||||
\(889\) | 847.024i | 0.952783i | ||||||||
\(890\) | −783.105 | − | 501.824i | −0.879894 | − | 0.563847i | ||||
\(891\) | 235.497 | 0.264307 | ||||||||
\(892\) | −365.422 | + | 365.422i | −0.409666 | + | 0.409666i | ||||
\(893\) | 205.610 | + | 205.610i | 0.230247 | + | 0.230247i | ||||
\(894\) | 100.945i | 0.112914i | ||||||||
\(895\) | −167.750 | − | 766.303i | −0.187430 | − | 0.856204i | ||||
\(896\) | −55.7090 | −0.0621752 | ||||||||
\(897\) | 54.1016 | − | 54.1016i | 0.0603139 | − | 0.0603139i | ||||
\(898\) | −139.847 | − | 139.847i | −0.155732 | − | 0.155732i | ||||
\(899\) | 887.701i | 0.987431i | ||||||||
\(900\) | −375.187 | + | 172.530i | −0.416874 | + | 0.191701i | ||||
\(901\) | −1364.20 | −1.51410 | ||||||||
\(902\) | 67.0345 | − | 67.0345i | 0.0743176 | − | 0.0743176i | ||||
\(903\) | 112.753 | + | 112.753i | 0.124865 | + | 0.124865i | ||||
\(904\) | − | 61.2429i | − | 0.0677465i | ||||||
\(905\) | −539.630 | + | 118.129i | −0.596276 | + | 0.130530i | ||||
\(906\) | −311.775 | −0.344123 | ||||||||
\(907\) | 155.510 | − | 155.510i | 0.171455 | − | 0.171455i | −0.616163 | − | 0.787618i | \(-0.711314\pi\) |
0.787618 | + | 0.616163i | \(0.211314\pi\) | |||||||
\(908\) | −142.018 | − | 142.018i | −0.156408 | − | 0.156408i | ||||
\(909\) | 175.464i | 0.193029i | ||||||||
\(910\) | 348.186 | − | 543.350i | 0.382622 | − | 0.597088i | ||||
\(911\) | 852.459 | 0.935740 | 0.467870 | − | 0.883797i | \(-0.345021\pi\) | ||||
0.467870 | + | 0.883797i | \(0.345021\pi\) | |||||||
\(912\) | 15.0026 | − | 15.0026i | 0.0164502 | − | 0.0164502i | ||||
\(913\) | 364.581 | + | 364.581i | 0.399322 | + | 0.399322i | ||||
\(914\) | 110.133i | 0.120496i | ||||||||
\(915\) | −14.3198 | − | 9.17631i | −0.0156501 | − | 0.0100288i | ||||
\(916\) | −195.218 | −0.213120 | ||||||||
\(917\) | 244.484 | − | 244.484i | 0.266613 | − | 0.266613i | ||||
\(918\) | 335.900 | + | 335.900i | 0.365904 | + | 0.365904i | ||||
\(919\) | − | 648.546i | − | 0.705708i | −0.935678 | − | 0.352854i | \(-0.885211\pi\) | ||
0.935678 | − | 0.352854i | \(-0.114789\pi\) | |||||||
\(920\) | 14.5036 | + | 66.2544i | 0.0157648 | + | 0.0720157i | ||||
\(921\) | 207.132 | 0.224899 | ||||||||
\(922\) | −833.889 | + | 833.889i | −0.904434 | + | 0.904434i | ||||
\(923\) | −852.703 | − | 852.703i | −0.923839 | − | 0.923839i | ||||
\(924\) | 32.4358i | 0.0351037i | ||||||||
\(925\) | −245.992 | + | 664.839i | −0.265937 | + | 0.718745i | ||||
\(926\) | 50.1480 | 0.0541555 | ||||||||
\(927\) | 918.720 | − | 918.720i | 0.991068 | − | 0.991068i | ||||
\(928\) | 131.397 | + | 131.397i | 0.141591 | + | 0.141591i | ||||
\(929\) | − | 1006.77i | − | 1.08371i | −0.840472 | − | 0.541855i | \(-0.817722\pi\) | ||
0.840472 | − | 0.541855i | \(-0.182278\pi\) | |||||||
\(930\) | −160.672 | + | 35.1724i | −0.172766 | + | 0.0378198i | ||||
\(931\) | −152.541 | −0.163847 | ||||||||
\(932\) | −187.406 | + | 187.406i | −0.201080 | + | 0.201080i | ||||
\(933\) | 52.5014 | + | 52.5014i | 0.0562716 | + | 0.0562716i | ||||
\(934\) | 10.7834i | 0.0115454i | ||||||||
\(935\) | −233.400 | + | 364.225i | −0.249626 | + | 0.389546i | ||||
\(936\) | −432.972 | −0.462577 | ||||||||
\(937\) | −926.870 | + | 926.870i | −0.989189 | + | 0.989189i | −0.999942 | − | 0.0107534i | \(-0.996577\pi\) |
0.0107534 | + | 0.999942i | \(0.496577\pi\) | |||||||
\(938\) | −483.335 | − | 483.335i | −0.515282 | − | 0.515282i | ||||
\(939\) | − | 429.116i | − | 0.456992i | ||||||
\(940\) | −397.291 | − | 254.589i | −0.422650 | − | 0.270839i | ||||
\(941\) | −482.722 | −0.512989 | −0.256494 | − | 0.966546i | \(-0.582567\pi\) | ||||
−0.256494 | + | 0.966546i | \(0.582567\pi\) | |||||||
\(942\) | −139.097 | + | 139.097i | −0.147662 | + | 0.147662i | ||||
\(943\) | 59.4090 | + | 59.4090i | 0.0630000 | + | 0.0630000i | ||||
\(944\) | − | 115.678i | − | 0.122540i | ||||||
\(945\) | −78.2141 | − | 357.292i | −0.0827662 | − | 0.378087i | ||||
\(946\) | 203.589 | 0.215210 | ||||||||
\(947\) | 97.7843 | − | 97.7843i | 0.103257 | − | 0.103257i | −0.653591 | − | 0.756848i | \(-0.726738\pi\) |
0.756848 | + | 0.653591i | \(0.226738\pi\) | |||||||
\(948\) | 75.7546 | + | 75.7546i | 0.0799099 | + | 0.0799099i | ||||
\(949\) | 1370.59i | 1.44424i | ||||||||
\(950\) | −204.332 | − | 75.6032i | −0.215086 | − | 0.0795823i | ||||
\(951\) | −97.1174 | −0.102121 | ||||||||
\(952\) | 222.671 | − | 222.671i | 0.233898 | − | 0.233898i | ||||
\(953\) | −1062.06 | − | 1062.06i | −1.11444 | − | 1.11444i | −0.992543 | − | 0.121895i | \(-0.961103\pi\) |
−0.121895 | − | 0.992543i | \(-0.538897\pi\) | |||||||
\(954\) | − | 704.714i | − | 0.738694i | ||||||
\(955\) | −498.092 | + | 109.036i | −0.521562 | + | 0.114174i | ||||
\(956\) | 459.753 | 0.480913 | ||||||||
\(957\) | 76.5040 | − | 76.5040i | 0.0799415 | − | 0.0799415i | ||||
\(958\) | −272.405 | − | 272.405i | −0.284348 | − | 0.284348i | ||||
\(959\) | − | 629.041i | − | 0.655934i | ||||||
\(960\) | −18.5764 | + | 28.9888i | −0.0193504 | + | 0.0301967i | ||||
\(961\) | −230.731 | −0.240095 | ||||||||
\(962\) | −525.558 | + | 525.558i | −0.546318 | + | 0.546318i | ||||
\(963\) | −364.461 | − | 364.461i | −0.378465 | − | 0.378465i | ||||
\(964\) | 821.795i | 0.852484i | ||||||||
\(965\) | 1274.06 | + | 816.433i | 1.32027 | + | 0.846045i | ||||
\(966\) | −28.7461 | −0.0297578 | ||||||||
\(967\) | −1144.22 | + | 1144.22i | −1.18327 | + | 1.18327i | −0.204378 | + | 0.978892i | \(0.565517\pi\) |
−0.978892 | + | 0.204378i | \(0.934483\pi\) | |||||||
\(968\) | −212.717 | − | 212.717i | −0.219749 | − | 0.219749i | ||||
\(969\) | 119.932i | 0.123769i | ||||||||
\(970\) | 43.1423 | + | 197.080i | 0.0444766 | + | 0.203175i | ||||
\(971\) | −950.040 | −0.978414 | −0.489207 | − | 0.872168i | \(-0.662714\pi\) | ||||
−0.489207 | + | 0.872168i | \(0.662714\pi\) | |||||||
\(972\) | −264.002 | + | 264.002i | −0.271607 | + | 0.271607i | ||||
\(973\) | 122.344 | + | 122.344i | 0.125739 | + | 0.125739i | ||||
\(974\) | − | 687.087i | − | 0.705428i | ||||||
\(975\) | −166.634 | − | 362.365i | −0.170907 | − | 0.371656i | ||||
\(976\) | 15.8072 | 0.0161959 | ||||||||
\(977\) | −188.141 | + | 188.141i | −0.192570 | + | 0.192570i | −0.796806 | − | 0.604236i | \(-0.793479\pi\) |
0.604236 | + | 0.796806i | \(0.293479\pi\) | |||||||
\(978\) | −244.021 | − | 244.021i | −0.249510 | − | 0.249510i | ||||
\(979\) | − | 503.314i | − | 0.514110i | ||||||
\(980\) | 241.813 | − | 52.9348i | 0.246748 | − | 0.0540151i | ||||
\(981\) | 470.387 | 0.479498 | ||||||||
\(982\) | 490.578 | − | 490.578i | 0.499570 | − | 0.499570i | ||||
\(983\) | −351.121 | − | 351.121i | −0.357194 | − | 0.357194i | 0.505584 | − | 0.862778i | \(-0.331277\pi\) |
−0.862778 | + | 0.505584i | \(0.831277\pi\) | |||||||
\(984\) | 42.6508i | 0.0433443i | ||||||||
\(985\) | −713.430 | + | 1113.32i | −0.724295 | + | 1.13027i | ||||
\(986\) | −1050.40 | −1.06531 | ||||||||
\(987\) | 141.417 | − | 141.417i | 0.143280 | − | 0.143280i | ||||
\(988\) | −161.525 | − | 161.525i | −0.163487 | − | 0.163487i | ||||
\(989\) | 180.430i | 0.182436i | ||||||||
\(990\) | −188.150 | − | 120.569i | −0.190051 | − | 0.121787i | ||||
\(991\) | −1558.95 | −1.57311 | −0.786555 | − | 0.617520i | \(-0.788137\pi\) | ||||
−0.786555 | + | 0.617520i | \(0.788137\pi\) | |||||||
\(992\) | 108.094 | − | 108.094i | 0.108966 | − | 0.108966i | ||||
\(993\) | −74.8908 | − | 74.8908i | −0.0754187 | − | 0.0754187i | ||||
\(994\) | 453.071i | 0.455806i | ||||||||
\(995\) | 391.268 | + | 1787.36i | 0.393234 | + | 1.79634i | ||||
\(996\) | −231.965 | −0.232897 | ||||||||
\(997\) | −947.149 | + | 947.149i | −0.949999 | + | 0.949999i | −0.998808 | − | 0.0488095i | \(-0.984457\pi\) |
0.0488095 | + | 0.998808i | \(0.484457\pi\) | |||||||
\(998\) | 668.332 | + | 668.332i | 0.669672 | + | 0.669672i | ||||
\(999\) | 421.245i | 0.421667i |
(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 | 230.3.f.a.93.6 | yes | 20 | |
5.2 | odd | 4 | inner | 230.3.f.a.47.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.a.47.6 | ✓ | 20 | 5.2 | odd | 4 | inner | |
230.3.f.a.93.6 | yes | 20 | 1.1 | even | 1 | trivial |