Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,4,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not 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: | \(20.6506685020\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.149 |
Dual form | 350.4.j.d.249.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.166667 | + | 0.0962250i | −0.581013 | − | 0.813894i | \(-0.697344\pi\) |
0.414346 | + | 0.910119i | \(0.364010\pi\) | |||||||
\(4\) | 2.00000 | + | 3.46410i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.136083 | ||||||||
\(7\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −13.0000 | + | 22.5167i | −0.481481 | + | 0.833950i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.5000 | − | 30.3109i | −0.479677 | − | 0.830825i | 0.520051 | − | 0.854135i | \(-0.325913\pi\) |
−0.999728 | + | 0.0233099i | \(0.992580\pi\) | |||||||
\(12\) | −3.46410 | − | 2.00000i | −0.0833333 | − | 0.0481125i | ||||
\(13\) | 66.0000i | 1.40809i | 0.710158 | + | 0.704043i | \(0.248624\pi\) | ||||
−0.710158 | + | 0.704043i | \(0.751376\pi\) | |||||||
\(14\) | −17.0000 | − | 32.9090i | −0.324532 | − | 0.628235i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −51.0955 | + | 29.5000i | −0.728969 | + | 0.420871i | −0.818045 | − | 0.575154i | \(-0.804942\pi\) |
0.0890757 | + | 0.996025i | \(0.471609\pi\) | |||||||
\(18\) | 45.0333 | − | 26.0000i | 0.589692 | − | 0.340459i | ||||
\(19\) | 68.5000 | − | 118.645i | 0.827104 | − | 1.43259i | −0.0731965 | − | 0.997318i | \(-0.523320\pi\) |
0.900301 | − | 0.435269i | \(-0.143347\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.5000 | − | 0.866025i | −0.192240 | − | 0.00899915i | ||||
\(22\) | 70.0000i | 0.678366i | ||||||||
\(23\) | 6.06218 | + | 3.50000i | 0.0549588 | + | 0.0317305i | 0.527228 | − | 0.849724i | \(-0.323232\pi\) |
−0.472269 | + | 0.881455i | \(0.656565\pi\) | |||||||
\(24\) | 4.00000 | + | 6.92820i | 0.0340207 | + | 0.0589256i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 66.0000 | − | 114.315i | 0.497833 | − | 0.862273i | ||||
\(27\) | − | 53.0000i | − | 0.377772i | ||||||
\(28\) | −3.46410 | + | 74.0000i | −0.0233805 | + | 0.499453i | ||||
\(29\) | −106.000 | −0.678748 | −0.339374 | − | 0.940651i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940651i | \(0.610215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.5000 | − | 64.9519i | −0.217264 | − | 0.376313i | 0.736706 | − | 0.676213i | \(-0.236380\pi\) |
−0.953971 | + | 0.299900i | \(0.903047\pi\) | |||||||
\(32\) | 27.7128 | − | 16.0000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 30.3109 | + | 17.5000i | 0.159892 | + | 0.0923139i | ||||
\(34\) | 118.000 | 0.595201 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | 9.52628 | + | 5.50000i | 0.0423273 | + | 0.0244377i | 0.521014 | − | 0.853548i | \(-0.325554\pi\) |
−0.478687 | + | 0.877986i | \(0.658887\pi\) | |||||||
\(38\) | −237.291 | + | 137.000i | −1.01299 | + | 0.584851i | ||||
\(39\) | −33.0000 | − | 57.1577i | −0.135493 | − | 0.234681i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −498.000 | −1.89694 | −0.948470 | − | 0.316867i | \(-0.897369\pi\) | ||||
−0.948470 | + | 0.316867i | \(0.897369\pi\) | |||||||
\(42\) | 31.1769 | + | 20.0000i | 0.114541 | + | 0.0734778i | ||||
\(43\) | 260.000i | 0.922084i | 0.887378 | + | 0.461042i | \(0.152524\pi\) | ||||
−0.887378 | + | 0.461042i | \(0.847476\pi\) | |||||||
\(44\) | 70.0000 | − | 121.244i | 0.239839 | − | 0.415413i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.00000 | − | 12.1244i | −0.0224368 | − | 0.0388617i | ||||
\(47\) | −148.090 | − | 85.5000i | −0.459600 | − | 0.265350i | 0.252276 | − | 0.967655i | \(-0.418821\pi\) |
−0.711876 | + | 0.702305i | \(0.752154\pi\) | |||||||
\(48\) | − | 16.0000i | − | 0.0481125i | ||||||
\(49\) | 143.000 | + | 311.769i | 0.416910 | + | 0.908948i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 29.5000 | − | 51.0955i | 0.0809966 | − | 0.140290i | ||||
\(52\) | −228.631 | + | 132.000i | −0.609719 | + | 0.352021i | ||||
\(53\) | −361.133 | + | 208.500i | −0.935951 | + | 0.540371i | −0.888689 | − | 0.458511i | \(-0.848383\pi\) |
−0.0472619 | + | 0.998883i | \(0.515050\pi\) | |||||||
\(54\) | −53.0000 | + | 91.7987i | −0.133563 | + | 0.231337i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 80.0000 | − | 124.708i | 0.190901 | − | 0.297585i | ||||
\(57\) | 137.000i | 0.318353i | ||||||||
\(58\) | 183.597 | + | 106.000i | 0.415647 | + | 0.239974i | ||||
\(59\) | −8.50000 | − | 14.7224i | −0.0187560 | − | 0.0324864i | 0.856495 | − | 0.516155i | \(-0.172637\pi\) |
−0.875251 | + | 0.483669i | \(0.839304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −25.5000 | + | 44.1673i | −0.0535236 | + | 0.0927056i | −0.891546 | − | 0.452930i | \(-0.850379\pi\) |
0.838022 | + | 0.545636i | \(0.183712\pi\) | |||||||
\(62\) | 150.000i | 0.307258i | ||||||||
\(63\) | −427.817 | + | 221.000i | −0.855553 | + | 0.441958i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −35.0000 | − | 60.6218i | −0.0652758 | − | 0.113061i | ||||
\(67\) | −380.185 | + | 219.500i | −0.693239 | + | 0.400242i | −0.804824 | − | 0.593513i | \(-0.797740\pi\) |
0.111585 | + | 0.993755i | \(0.464407\pi\) | |||||||
\(68\) | −204.382 | − | 118.000i | −0.364485 | − | 0.210435i | ||||
\(69\) | −7.00000 | −0.0122131 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −784.000 | −1.31047 | −0.655237 | − | 0.755423i | \(-0.727431\pi\) | ||||
−0.655237 | + | 0.755423i | \(0.727431\pi\) | |||||||
\(72\) | 180.133 | + | 104.000i | 0.294846 | + | 0.170229i | ||||
\(73\) | 255.477 | − | 147.500i | 0.409608 | − | 0.236487i | −0.281013 | − | 0.959704i | \(-0.590671\pi\) |
0.690621 | + | 0.723217i | \(0.257337\pi\) | |||||||
\(74\) | −11.0000 | − | 19.0526i | −0.0172801 | − | 0.0299299i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 548.000 | 0.827104 | ||||||||
\(77\) | 30.3109 | − | 647.500i | 0.0448603 | − | 0.958305i | ||||
\(78\) | 132.000i | 0.191616i | ||||||||
\(79\) | −247.500 | + | 428.683i | −0.352480 | + | 0.610513i | −0.986683 | − | 0.162653i | \(-0.947995\pi\) |
0.634203 | + | 0.773166i | \(0.281328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −324.500 | − | 562.050i | −0.445130 | − | 0.770988i | ||||
\(82\) | 862.561 | + | 498.000i | 1.16163 | + | 0.670670i | ||||
\(83\) | 932.000i | 1.23253i | 0.787537 | + | 0.616267i | \(0.211356\pi\) | ||||
−0.787537 | + | 0.616267i | \(0.788644\pi\) | |||||||
\(84\) | −34.0000 | − | 65.8179i | −0.0441631 | − | 0.0854920i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 260.000 | − | 450.333i | 0.326006 | − | 0.564659i | ||||
\(87\) | 91.7987 | − | 53.0000i | 0.113125 | − | 0.0653126i | ||||
\(88\) | −242.487 | + | 140.000i | −0.293741 | + | 0.169591i | ||||
\(89\) | −436.500 | + | 756.040i | −0.519875 | + | 0.900451i | 0.479858 | + | 0.877346i | \(0.340688\pi\) |
−0.999733 | + | 0.0231042i | \(0.992645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −660.000 | + | 1028.84i | −0.760294 | + | 1.18518i | ||||
\(92\) | 28.0000i | 0.0317305i | ||||||||
\(93\) | 64.9519 | + | 37.5000i | 0.0724215 | + | 0.0418126i | ||||
\(94\) | 171.000 | + | 296.181i | 0.187631 | + | 0.324986i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.0000 | + | 27.7128i | −0.0170103 | + | 0.0294628i | ||||
\(97\) | 290.000i | 0.303557i | 0.988415 | + | 0.151779i | \(0.0485001\pi\) | ||||
−0.988415 | + | 0.151779i | \(0.951500\pi\) | |||||||
\(98\) | 64.0859 | − | 683.000i | 0.0660577 | − | 0.704014i | ||||
\(99\) | 910.000 | 0.923823 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 542.500 | + | 939.638i | 0.534463 | + | 0.925717i | 0.999189 | + | 0.0402627i | \(0.0128195\pi\) |
−0.464726 | + | 0.885454i | \(0.653847\pi\) | |||||||
\(102\) | −102.191 | + | 59.0000i | −0.0992002 | + | 0.0572732i | ||||
\(103\) | −1344.94 | − | 776.500i | −1.28661 | − | 0.742823i | −0.308560 | − | 0.951205i | \(-0.599847\pi\) |
−0.978048 | + | 0.208381i | \(0.933181\pi\) | |||||||
\(104\) | 528.000 | 0.497833 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 834.000 | 0.764200 | ||||||||
\(107\) | 111.717 | + | 64.5000i | 0.100936 | + | 0.0582752i | 0.549618 | − | 0.835416i | \(-0.314773\pi\) |
−0.448682 | + | 0.893691i | \(0.648107\pi\) | |||||||
\(108\) | 183.597 | − | 106.000i | 0.163580 | − | 0.0944431i | ||||
\(109\) | −482.500 | − | 835.715i | −0.423992 | − | 0.734376i | 0.572334 | − | 0.820021i | \(-0.306038\pi\) |
−0.996326 | + | 0.0856452i | \(0.972705\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0000 | −0.00940607 | ||||||||
\(112\) | −263.272 | + | 136.000i | −0.222115 | + | 0.114739i | ||||
\(113\) | − | 50.0000i | − | 0.0416248i | −0.999783 | − | 0.0208124i | \(-0.993375\pi\) | ||
0.999783 | − | 0.0208124i | \(-0.00662527\pi\) | |||||||
\(114\) | 137.000 | − | 237.291i | 0.112555 | − | 0.194950i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −212.000 | − | 367.195i | −0.169687 | − | 0.293907i | ||||
\(117\) | −1486.10 | − | 858.000i | −1.17427 | − | 0.677967i | ||||
\(118\) | 34.0000i | 0.0265250i | ||||||||
\(119\) | −1091.50 | − | 51.0955i | −0.840821 | − | 0.0393606i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 53.0000 | − | 91.7987i | 0.0398197 | − | 0.0689697i | ||||
\(122\) | 88.3346 | − | 51.0000i | 0.0655528 | − | 0.0378469i | ||||
\(123\) | 431.281 | − | 249.000i | 0.316157 | − | 0.182533i | ||||
\(124\) | 150.000 | − | 259.808i | 0.108632 | − | 0.188157i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 962.000 | + | 45.0333i | 0.680173 | + | 0.0318404i | ||||
\(127\) | − | 936.000i | − | 0.653989i | −0.945026 | − | 0.326994i | \(-0.893964\pi\) | ||
0.945026 | − | 0.326994i | \(-0.106036\pi\) | |||||||
\(128\) | 110.851 | + | 64.0000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −130.000 | − | 225.167i | −0.0887276 | − | 0.153681i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 377.500 | − | 653.849i | 0.251773 | − | 0.436084i | −0.712241 | − | 0.701935i | \(-0.752320\pi\) |
0.964014 | + | 0.265851i | \(0.0856529\pi\) | |||||||
\(132\) | 140.000i | 0.0923139i | ||||||||
\(133\) | 2254.26 | − | 1164.50i | 1.46970 | − | 0.759210i | ||||
\(134\) | 878.000 | 0.566027 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 236.000 | + | 408.764i | 0.148800 | + | 0.257730i | ||||
\(137\) | 2041.22 | − | 1178.50i | 1.27294 | − | 0.734935i | 0.297403 | − | 0.954752i | \(-0.403879\pi\) |
0.975541 | + | 0.219817i | \(0.0705461\pi\) | |||||||
\(138\) | 12.1244 | + | 7.00000i | 0.00747894 | + | 0.00431797i | ||||
\(139\) | −28.0000 | −0.0170858 | −0.00854291 | − | 0.999964i | \(-0.502719\pi\) | ||||
−0.00854291 | + | 0.999964i | \(0.502719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 171.000 | 0.102133 | ||||||||
\(142\) | 1357.93 | + | 784.000i | 0.802498 | + | 0.463323i | ||||
\(143\) | 2000.52 | − | 1155.00i | 1.16987 | − | 0.675426i | ||||
\(144\) | −208.000 | − | 360.267i | −0.120370 | − | 0.208488i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −590.000 | −0.334443 | ||||||||
\(147\) | −279.726 | − | 198.500i | −0.156948 | − | 0.111374i | ||||
\(148\) | 44.0000i | 0.0244377i | ||||||||
\(149\) | 1147.50 | − | 1987.53i | 0.630919 | − | 1.09278i | −0.356446 | − | 0.934316i | \(-0.616012\pi\) |
0.987364 | − | 0.158467i | \(-0.0506551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 554.500 | + | 960.422i | 0.298838 | + | 0.517603i | 0.975870 | − | 0.218350i | \(-0.0700676\pi\) |
−0.677032 | + | 0.735953i | \(0.736734\pi\) | |||||||
\(152\) | −949.164 | − | 548.000i | −0.506496 | − | 0.292425i | ||||
\(153\) | − | 1534.00i | − | 0.810566i | ||||||
\(154\) | −700.000 | + | 1091.19i | −0.366283 | + | 0.570979i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 132.000 | − | 228.631i | 0.0677465 | − | 0.117340i | ||||
\(157\) | −1350.13 | + | 779.500i | −0.686321 | + | 0.396248i | −0.802232 | − | 0.597012i | \(-0.796354\pi\) |
0.115911 | + | 0.993260i | \(0.463021\pi\) | |||||||
\(158\) | 857.365 | − | 495.000i | 0.431698 | − | 0.249241i | ||||
\(159\) | 208.500 | − | 361.133i | 0.103995 | − | 0.180124i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 59.5000 | + | 115.181i | 0.0291258 | + | 0.0563824i | ||||
\(162\) | 1298.00i | 0.629509i | ||||||||
\(163\) | 1949.42 | + | 1125.50i | 0.936752 | + | 0.540834i | 0.888941 | − | 0.458022i | \(-0.151442\pi\) |
0.0478115 | + | 0.998856i | \(0.484775\pi\) | |||||||
\(164\) | −996.000 | − | 1725.12i | −0.474235 | − | 0.821399i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 932.000 | − | 1614.27i | 0.435766 | − | 0.754770i | ||||
\(167\) | − | 2788.00i | − | 1.29187i | −0.763393 | − | 0.645934i | \(-0.776468\pi\) | ||
0.763393 | − | 0.645934i | \(-0.223532\pi\) | |||||||
\(168\) | −6.92820 | + | 148.000i | −0.00318168 | + | 0.0679670i | ||||
\(169\) | −2159.00 | −0.982704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1781.00 | + | 3084.78i | 0.796471 | + | 1.37953i | ||||
\(172\) | −900.666 | + | 520.000i | −0.399274 | + | 0.230521i | ||||
\(173\) | −1367.45 | − | 789.500i | −0.600957 | − | 0.346963i | 0.168461 | − | 0.985708i | \(-0.446120\pi\) |
−0.769418 | + | 0.638746i | \(0.779454\pi\) | |||||||
\(174\) | −212.000 | −0.0923660 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 560.000 | 0.239839 | ||||||||
\(177\) | 14.7224 | + | 8.50000i | 0.00625201 | + | 0.00360960i | ||||
\(178\) | 1512.08 | − | 873.000i | 0.636715 | − | 0.367607i | ||||
\(179\) | 1225.50 | + | 2122.63i | 0.511722 | + | 0.886328i | 0.999908 | + | 0.0135883i | \(0.00432541\pi\) |
−0.488186 | + | 0.872740i | \(0.662341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1170.00 | −0.480472 | −0.240236 | − | 0.970715i | \(-0.577225\pi\) | ||||
−0.240236 | + | 0.970715i | \(0.577225\pi\) | |||||||
\(182\) | 2171.99 | − | 1122.00i | 0.884608 | − | 0.456968i | ||||
\(183\) | − | 51.0000i | − | 0.0206012i | ||||||
\(184\) | 28.0000 | − | 48.4974i | 0.0112184 | − | 0.0194309i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −75.0000 | − | 129.904i | −0.0295660 | − | 0.0512097i | ||||
\(187\) | 1788.34 | + | 1032.50i | 0.699340 | + | 0.403764i | ||||
\(188\) | − | 684.000i | − | 0.265350i | ||||||
\(189\) | 530.000 | − | 826.188i | 0.203978 | − | 0.317970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 637.500 | − | 1104.18i | 0.241507 | − | 0.418303i | −0.719637 | − | 0.694351i | \(-0.755692\pi\) |
0.961144 | + | 0.276048i | \(0.0890249\pi\) | |||||||
\(192\) | 55.4256 | − | 32.0000i | 0.0208333 | − | 0.0120281i | ||||
\(193\) | 30.3109 | − | 17.5000i | 0.0113048 | − | 0.00652683i | −0.494337 | − | 0.869270i | \(-0.664589\pi\) |
0.505642 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(194\) | 290.000 | − | 502.295i | 0.107324 | − | 0.185890i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −794.000 | + | 1118.90i | −0.289359 | + | 0.407764i | ||||
\(197\) | 2734.00i | 0.988779i | 0.869241 | + | 0.494389i | \(0.164608\pi\) | ||||
−0.869241 | + | 0.494389i | \(0.835392\pi\) | |||||||
\(198\) | −1576.17 | − | 910.000i | −0.565724 | − | 0.326621i | ||||
\(199\) | 1121.50 | + | 1942.49i | 0.399503 | + | 0.691959i | 0.993665 | − | 0.112387i | \(-0.0358495\pi\) |
−0.594162 | + | 0.804345i | \(0.702516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 219.500 | − | 380.185i | 0.0770265 | − | 0.133414i | ||||
\(202\) | − | 2170.00i | − | 0.755845i | ||||||
\(203\) | −1652.38 | − | 1060.00i | −0.571301 | − | 0.366490i | ||||
\(204\) | 236.000 | 0.0809966 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1553.00 | + | 2689.87i | 0.525256 | + | 0.909769i | ||||
\(207\) | −157.617 | + | 91.0000i | −0.0529232 | + | 0.0305553i | ||||
\(208\) | −914.523 | − | 528.000i | −0.304859 | − | 0.176011i | ||||
\(209\) | −4795.00 | −1.58697 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1172.00 | 0.382388 | 0.191194 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191194 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(212\) | −1444.53 | − | 834.000i | −0.467975 | − | 0.270186i | ||||
\(213\) | 678.964 | − | 392.000i | 0.218412 | − | 0.126100i | ||||
\(214\) | −129.000 | − | 223.435i | −0.0412068 | − | 0.0713723i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −424.000 | −0.133563 | ||||||||
\(217\) | 64.9519 | − | 1387.50i | 0.0203190 | − | 0.434054i | ||||
\(218\) | 1930.00i | 0.599615i | ||||||||
\(219\) | −147.500 | + | 255.477i | −0.0455120 | + | 0.0788291i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1947.00 | − | 3372.30i | −0.592622 | − | 1.02645i | ||||
\(222\) | 19.0526 | + | 11.0000i | 0.00576002 | + | 0.00332555i | ||||
\(223\) | 2024.00i | 0.607790i | 0.952706 | + | 0.303895i | \(0.0982871\pi\) | ||||
−0.952706 | + | 0.303895i | \(0.901713\pi\) | |||||||
\(224\) | 592.000 | + | 27.7128i | 0.176583 | + | 0.00826625i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.0000 | + | 86.6025i | −0.0147166 | + | 0.0254899i | ||||
\(227\) | −2226.55 | + | 1285.50i | −0.651019 | + | 0.375866i | −0.788847 | − | 0.614590i | \(-0.789321\pi\) |
0.137827 | + | 0.990456i | \(0.455988\pi\) | |||||||
\(228\) | −474.582 | + | 274.000i | −0.137851 | + | 0.0795881i | ||||
\(229\) | 447.500 | − | 775.093i | 0.129134 | − | 0.223666i | −0.794207 | − | 0.607647i | \(-0.792114\pi\) |
0.923341 | + | 0.383980i | \(0.125447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 297.500 | + | 575.907i | 0.0847362 | + | 0.164034i | ||||
\(232\) | 848.000i | 0.239974i | ||||||||
\(233\) | −1547.59 | − | 893.500i | −0.435132 | − | 0.251224i | 0.266398 | − | 0.963863i | \(-0.414166\pi\) |
−0.701531 | + | 0.712639i | \(0.747500\pi\) | |||||||
\(234\) | 1716.00 | + | 2972.20i | 0.479395 | + | 0.830336i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 34.0000 | − | 58.8897i | 0.00937801 | − | 0.0162432i | ||||
\(237\) | − | 495.000i | − | 0.135670i | ||||||
\(238\) | 1839.44 | + | 1180.00i | 0.500979 | + | 0.321378i | ||||
\(239\) | 5100.00 | 1.38030 | 0.690150 | − | 0.723667i | \(-0.257545\pi\) | ||||
0.690150 | + | 0.723667i | \(0.257545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2088.50 | + | 3617.39i | 0.558225 | + | 0.966873i | 0.997645 | + | 0.0685917i | \(0.0218506\pi\) |
−0.439420 | + | 0.898282i | \(0.644816\pi\) | |||||||
\(242\) | −183.597 | + | 106.000i | −0.0487690 | + | 0.0281568i | ||||
\(243\) | 1801.33 | + | 1040.00i | 0.475537 | + | 0.274552i | ||||
\(244\) | −204.000 | −0.0535236 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −996.000 | −0.258141 | ||||||||
\(247\) | 7830.60 | + | 4521.00i | 2.01720 | + | 1.16463i | ||||
\(248\) | −519.615 | + | 300.000i | −0.133047 | + | 0.0768146i | ||||
\(249\) | −466.000 | − | 807.136i | −0.118601 | − | 0.205422i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4680.00 | −1.17689 | −0.588444 | − | 0.808538i | \(-0.700259\pi\) | ||||
−0.588444 | + | 0.808538i | \(0.700259\pi\) | |||||||
\(252\) | −1621.20 | − | 1040.00i | −0.405262 | − | 0.259976i | ||||
\(253\) | − | 245.000i | − | 0.0608815i | ||||||
\(254\) | −936.000 | + | 1621.20i | −0.231220 | + | 0.400485i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1514.68 | − | 874.500i | −0.367638 | − | 0.212256i | 0.304788 | − | 0.952420i | \(-0.401414\pi\) |
−0.672426 | + | 0.740164i | \(0.734748\pi\) | |||||||
\(258\) | 520.000i | 0.125480i | ||||||||
\(259\) | 93.5000 | + | 180.999i | 0.0224317 | + | 0.0434237i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1378.00 | − | 2386.77i | 0.326805 | − | 0.566043i | ||||
\(262\) | −1307.70 | + | 755.000i | −0.308358 | + | 0.178031i | ||||
\(263\) | −3873.73 | + | 2236.50i | −0.908230 | + | 0.524367i | −0.879861 | − | 0.475231i | \(-0.842365\pi\) |
−0.0283689 | + | 0.999598i | \(0.509031\pi\) | |||||||
\(264\) | 140.000 | − | 242.487i | 0.0326379 | − | 0.0565305i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5069.00 | − | 237.291i | −1.16842 | − | 0.0546964i | ||||
\(267\) | − | 873.000i | − | 0.200100i | ||||||
\(268\) | −1520.74 | − | 878.000i | −0.346619 | − | 0.200121i | ||||
\(269\) | 987.500 | + | 1710.40i | 0.223825 | + | 0.387676i | 0.955966 | − | 0.293476i | \(-0.0948122\pi\) |
−0.732141 | + | 0.681153i | \(0.761479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4219.50 | − | 7308.39i | 0.945817 | − | 1.63820i | 0.191710 | − | 0.981452i | \(-0.438597\pi\) |
0.754107 | − | 0.656751i | \(-0.228070\pi\) | |||||||
\(272\) | − | 944.000i | − | 0.210435i | ||||||
\(273\) | 57.1577 | − | 1221.00i | 0.0126716 | − | 0.270690i | ||||
\(274\) | −4714.00 | −1.03935 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.0000 | − | 24.2487i | −0.00305326 | − | 0.00528841i | ||||
\(277\) | −456.395 | + | 263.500i | −0.0989969 | + | 0.0571559i | −0.548681 | − | 0.836032i | \(-0.684870\pi\) |
0.449684 | + | 0.893188i | \(0.351537\pi\) | |||||||
\(278\) | 48.4974 | + | 28.0000i | 0.0104629 | + | 0.00604075i | ||||
\(279\) | 1950.00 | 0.418435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −202.000 | −0.0428837 | −0.0214418 | − | 0.999770i | \(-0.506826\pi\) | ||||
−0.0214418 | + | 0.999770i | \(0.506826\pi\) | |||||||
\(282\) | −296.181 | − | 171.000i | −0.0625436 | − | 0.0361096i | ||||
\(283\) | −6884.04 | + | 3974.50i | −1.44598 | + | 0.834839i | −0.998239 | − | 0.0593220i | \(-0.981106\pi\) |
−0.447745 | + | 0.894161i | \(0.647773\pi\) | |||||||
\(284\) | −1568.00 | − | 2715.86i | −0.327619 | − | 0.567452i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4620.00 | −0.955197 | ||||||||
\(287\) | −7763.05 | − | 4980.00i | −1.59665 | − | 1.02425i | ||||
\(288\) | 832.000i | 0.170229i | ||||||||
\(289\) | −716.000 | + | 1240.15i | −0.145736 | + | 0.252422i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −145.000 | − | 251.147i | −0.0292098 | − | 0.0505929i | ||||
\(292\) | 1021.91 | + | 590.000i | 0.204804 | + | 0.118244i | ||||
\(293\) | 318.000i | 0.0634053i | 0.999497 | + | 0.0317027i | \(0.0100930\pi\) | ||||
−0.999497 | + | 0.0317027i | \(0.989907\pi\) | |||||||
\(294\) | 286.000 | + | 623.538i | 0.0567342 | + | 0.123692i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 44.0000 | − | 76.2102i | 0.00864003 | − | 0.0149650i | ||||
\(297\) | −1606.48 | + | 927.500i | −0.313863 | + | 0.181209i | ||||
\(298\) | −3975.06 | + | 2295.00i | −0.772714 | + | 0.446127i | ||||
\(299\) | −231.000 | + | 400.104i | −0.0446792 | + | 0.0773866i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2600.00 | + | 4053.00i | −0.497879 | + | 0.776116i | ||||
\(302\) | − | 2218.00i | − | 0.422621i | ||||||
\(303\) | −939.638 | − | 542.500i | −0.178154 | − | 0.102857i | ||||
\(304\) | 1096.00 | + | 1898.33i | 0.206776 | + | 0.358147i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1534.00 | + | 2656.97i | −0.286578 | + | 0.496368i | ||||
\(307\) | 8132.00i | 1.51178i | 0.654696 | + | 0.755892i | \(0.272797\pi\) | ||||
−0.654696 | + | 0.755892i | \(0.727203\pi\) | |||||||
\(308\) | 2303.63 | − | 1190.00i | 0.426173 | − | 0.220151i | ||||
\(309\) | 1553.00 | 0.285913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 464.500 | + | 804.538i | 0.0846925 | + | 0.146692i | 0.905260 | − | 0.424858i | \(-0.139676\pi\) |
−0.820568 | + | 0.571549i | \(0.806343\pi\) | |||||||
\(312\) | −457.261 | + | 264.000i | −0.0829722 | + | 0.0479040i | ||||
\(313\) | 180.999 | + | 104.500i | 0.0326859 | + | 0.0188712i | 0.516254 | − | 0.856436i | \(-0.327326\pi\) |
−0.483568 | + | 0.875307i | \(0.660659\pi\) | |||||||
\(314\) | 3118.00 | 0.560379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1980.00 | −0.352480 | ||||||||
\(317\) | 6175.63 | + | 3565.50i | 1.09419 | + | 0.631730i | 0.934689 | − | 0.355468i | \(-0.115678\pi\) |
0.159500 | + | 0.987198i | \(0.449012\pi\) | |||||||
\(318\) | −722.265 | + | 417.000i | −0.127367 | + | 0.0735352i | ||||
\(319\) | 1855.00 | + | 3212.95i | 0.325580 | + | 0.563921i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −129.000 | −0.0224301 | ||||||||
\(322\) | 12.1244 | − | 259.000i | 0.00209834 | − | 0.0448246i | ||||
\(323\) | 8083.00i | 1.39242i | ||||||||
\(324\) | 1298.00 | − | 2248.20i | 0.222565 | − | 0.385494i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2251.00 | − | 3898.85i | −0.382427 | − | 0.662384i | ||||
\(327\) | 835.715 | + | 482.500i | 0.141331 | + | 0.0815973i | ||||
\(328\) | 3984.00i | 0.670670i | ||||||||
\(329\) | −1453.50 | − | 2813.72i | −0.243569 | − | 0.471505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3285.50 | − | 5690.65i | 0.545581 | − | 0.944975i | −0.452989 | − | 0.891516i | \(-0.649642\pi\) |
0.998570 | − | 0.0534583i | \(-0.0170244\pi\) | |||||||
\(332\) | −3228.54 | + | 1864.00i | −0.533703 | + | 0.308133i | ||||
\(333\) | −247.683 | + | 143.000i | −0.0407596 | + | 0.0235326i | ||||
\(334\) | −2788.00 | + | 4828.96i | −0.456744 | + | 0.791104i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 160.000 | − | 249.415i | 0.0259783 | − | 0.0404962i | ||||
\(337\) | 11466.0i | 1.85339i | 0.375813 | + | 0.926696i | \(0.377364\pi\) | ||||
−0.375813 | + | 0.926696i | \(0.622636\pi\) | |||||||
\(338\) | 3739.50 | + | 2159.00i | 0.601781 | + | 0.347438i | ||||
\(339\) | 25.0000 | + | 43.3013i | 0.00400535 | + | 0.00693747i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1312.50 | + | 2273.32i | −0.208434 | + | 0.361018i | ||||
\(342\) | − | 7124.00i | − | 1.12638i | ||||||
\(343\) | −888.542 | + | 6290.00i | −0.139874 | + | 0.990169i | ||||
\(344\) | 2080.00 | 0.326006 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1579.00 | + | 2734.91i | 0.245340 | + | 0.424941i | ||||
\(347\) | 8467.13 | − | 4888.50i | 1.30991 | − | 0.756278i | 0.327831 | − | 0.944737i | \(-0.393682\pi\) |
0.982081 | + | 0.188459i | \(0.0603491\pi\) | |||||||
\(348\) | 367.195 | + | 212.000i | 0.0565624 | + | 0.0326563i | ||||
\(349\) | −11914.0 | −1.82734 | −0.913670 | − | 0.406456i | \(-0.866764\pi\) | ||||
−0.913670 | + | 0.406456i | \(0.866764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3498.00 | 0.531936 | ||||||||
\(352\) | −969.948 | − | 560.000i | −0.146871 | − | 0.0847957i | ||||
\(353\) | 7900.75 | − | 4561.50i | 1.19126 | − | 0.687774i | 0.232667 | − | 0.972556i | \(-0.425255\pi\) |
0.958592 | + | 0.284783i | \(0.0919214\pi\) | |||||||
\(354\) | −17.0000 | − | 29.4449i | −0.00255237 | − | 0.00442084i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3492.00 | −0.519875 | ||||||||
\(357\) | 970.814 | − | 501.500i | 0.143924 | − | 0.0743479i | ||||
\(358\) | − | 4902.00i | − | 0.723684i | ||||||
\(359\) | 4074.50 | − | 7057.24i | 0.599008 | − | 1.03751i | −0.393960 | − | 0.919128i | \(-0.628895\pi\) |
0.992968 | − | 0.118385i | \(-0.0377716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5955.00 | − | 10314.4i | −0.868202 | − | 1.50377i | ||||
\(362\) | 2026.50 | + | 1170.00i | 0.294228 | + | 0.169872i | ||||
\(363\) | 106.000i | 0.0153266i | ||||||||
\(364\) | −4884.00 | − | 228.631i | −0.703272 | − | 0.0329217i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −51.0000 | + | 88.3346i | −0.00728364 | + | 0.0126156i | ||||
\(367\) | −8375.33 | + | 4835.50i | −1.19125 | + | 0.687769i | −0.958590 | − | 0.284790i | \(-0.908076\pi\) |
−0.232660 | + | 0.972558i | \(0.574743\pi\) | |||||||
\(368\) | −96.9948 | + | 56.0000i | −0.0137397 | + | 0.00793261i | ||||
\(369\) | 6474.00 | − | 11213.3i | 0.913341 | − | 1.58195i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7714.50 | − | 361.133i | −1.07956 | − | 0.0505366i | ||||
\(372\) | 300.000i | 0.0418126i | ||||||||
\(373\) | 3558.50 | + | 2054.50i | 0.493973 | + | 0.285196i | 0.726221 | − | 0.687461i | \(-0.241275\pi\) |
−0.232248 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(374\) | −2065.00 | − | 3576.68i | −0.285504 | − | 0.494508i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −684.000 | + | 1184.72i | −0.0938154 | + | 0.162493i | ||||
\(377\) | − | 6996.00i | − | 0.955736i | ||||||
\(378\) | −1744.18 | + | 901.000i | −0.237330 | + | 0.122599i | ||||
\(379\) | 3488.00 | 0.472735 | 0.236367 | − | 0.971664i | \(-0.424043\pi\) | ||||
0.236367 | + | 0.971664i | \(0.424043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 468.000 | + | 810.600i | 0.0629301 | + | 0.108998i | ||||
\(382\) | −2208.36 | + | 1275.00i | −0.295785 | + | 0.170771i | ||||
\(383\) | −7549.14 | − | 4358.50i | −1.00716 | − | 0.581485i | −0.0968028 | − | 0.995304i | \(-0.530862\pi\) |
−0.910360 | + | 0.413818i | \(0.864195\pi\) | |||||||
\(384\) | −128.000 | −0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −70.0000 | −0.00923033 | ||||||||
\(387\) | −5854.33 | − | 3380.00i | −0.768973 | − | 0.443967i | ||||
\(388\) | −1004.59 | + | 580.000i | −0.131444 | + | 0.0758893i | ||||
\(389\) | 81.5000 | + | 141.162i | 0.0106227 | + | 0.0183990i | 0.871288 | − | 0.490772i | \(-0.163285\pi\) |
−0.860665 | + | 0.509171i | \(0.829952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −413.000 | −0.0534177 | ||||||||
\(392\) | 2494.15 | − | 1144.00i | 0.321362 | − | 0.147400i | ||||
\(393\) | 755.000i | 0.0969077i | ||||||||
\(394\) | 2734.00 | − | 4735.43i | 0.349586 | − | 0.605501i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1820.00 | + | 3152.33i | 0.230956 | + | 0.400027i | ||||
\(397\) | 865.159 | + | 499.500i | 0.109373 | + | 0.0631466i | 0.553689 | − | 0.832724i | \(-0.313220\pi\) |
−0.444316 | + | 0.895870i | \(0.646553\pi\) | |||||||
\(398\) | − | 4486.00i | − | 0.564982i | ||||||
\(399\) | −1370.00 | + | 2135.62i | −0.171894 | + | 0.267957i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7378.50 | − | 12779.9i | 0.918865 | − | 1.59152i | 0.117722 | − | 0.993047i | \(-0.462441\pi\) |
0.801143 | − | 0.598474i | \(-0.204226\pi\) | |||||||
\(402\) | −760.370 | + | 439.000i | −0.0943379 | + | 0.0544660i | ||||
\(403\) | 4286.83 | − | 2475.00i | 0.529881 | − | 0.305927i | ||||
\(404\) | −2170.00 | + | 3758.55i | −0.267232 | + | 0.462859i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1802.00 | + | 3488.35i | 0.220275 | + | 0.426414i | ||||
\(407\) | − | 385.000i | − | 0.0468888i | ||||||
\(408\) | −408.764 | − | 236.000i | −0.0496001 | − | 0.0286366i | ||||
\(409\) | −66.5000 | − | 115.181i | −0.00803964 | − | 0.0139251i | 0.861978 | − | 0.506946i | \(-0.169226\pi\) |
−0.870017 | + | 0.493021i | \(0.835892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1178.50 | + | 2041.22i | −0.141438 | + | 0.244978i | ||||
\(412\) | − | 6212.00i | − | 0.742823i | ||||||
\(413\) | 14.7224 | − | 314.500i | 0.00175410 | − | 0.0374710i | ||||
\(414\) | 364.000 | 0.0432117 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1056.00 | + | 1829.05i | 0.124458 | + | 0.215568i | ||||
\(417\) | 24.2487 | − | 14.0000i | 0.00284764 | − | 0.00164408i | ||||
\(418\) | 8305.18 | + | 4795.00i | 0.971818 | + | 0.561079i | ||||
\(419\) | 6420.00 | 0.748538 | 0.374269 | − | 0.927320i | \(-0.377894\pi\) | ||||
0.374269 | + | 0.927320i | \(0.377894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10266.0 | 1.18844 | 0.594221 | − | 0.804302i | \(-0.297460\pi\) | ||||
0.594221 | + | 0.804302i | \(0.297460\pi\) | |||||||
\(422\) | −2029.96 | − | 1172.00i | −0.234164 | − | 0.135194i | ||||
\(423\) | 3850.35 | − | 2223.00i | 0.442578 | − | 0.255522i | ||||
\(424\) | 1668.00 | + | 2889.06i | 0.191050 | + | 0.330908i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1568.00 | −0.178333 | ||||||||
\(427\) | −839.179 | + | 433.500i | −0.0951070 | + | 0.0491301i | ||||
\(428\) | 516.000i | 0.0582752i | ||||||||
\(429\) | −1155.00 | + | 2000.52i | −0.129986 | + | 0.225142i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7606.50 | + | 13174.8i | 0.850098 | + | 1.47241i | 0.881119 | + | 0.472894i | \(0.156791\pi\) |
−0.0310213 | + | 0.999519i | \(0.509876\pi\) | |||||||
\(432\) | 734.390 | + | 424.000i | 0.0817901 | + | 0.0472215i | ||||
\(433\) | − | 1378.00i | − | 0.152939i | −0.997072 | − | 0.0764693i | \(-0.975635\pi\) | ||
0.997072 | − | 0.0764693i | \(-0.0243647\pi\) | |||||||
\(434\) | −1500.00 | + | 2338.27i | −0.165904 | + | 0.258619i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1930.00 | − | 3342.86i | 0.211996 | − | 0.367188i | ||||
\(437\) | 830.518 | − | 479.500i | 0.0909132 | − | 0.0524888i | ||||
\(438\) | 510.955 | − | 295.000i | 0.0557406 | − | 0.0321818i | ||||
\(439\) | −1381.50 | + | 2392.83i | −0.150195 | + | 0.260145i | −0.931299 | − | 0.364256i | \(-0.881323\pi\) |
0.781104 | + | 0.624401i | \(0.214657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8879.00 | − | 833.116i | −0.958752 | − | 0.0899597i | ||||
\(442\) | 7788.00i | 0.838094i | ||||||||
\(443\) | −5065.38 | − | 2924.50i | −0.543259 | − | 0.313651i | 0.203140 | − | 0.979150i | \(-0.434885\pi\) |
−0.746399 | + | 0.665499i | \(0.768219\pi\) | |||||||
\(444\) | −22.0000 | − | 38.1051i | −0.00235152 | − | 0.00407295i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2024.00 | − | 3505.67i | 0.214886 | − | 0.372194i | ||||
\(447\) | 2295.00i | 0.242841i | ||||||||
\(448\) | −997.661 | − | 640.000i | −0.105212 | − | 0.0674937i | ||||
\(449\) | −4582.00 | −0.481599 | −0.240799 | − | 0.970575i | \(-0.577410\pi\) | ||||
−0.240799 | + | 0.970575i | \(0.577410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8715.00 | + | 15094.8i | 0.909919 | + | 1.57603i | ||||
\(452\) | 173.205 | − | 100.000i | 0.0180241 | − | 0.0104062i | ||||
\(453\) | −960.422 | − | 554.500i | −0.0996127 | − | 0.0575114i | ||||
\(454\) | 5142.00 | 0.531555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1096.00 | 0.112555 | ||||||||
\(457\) | 10003.5 | + | 5775.50i | 1.02394 | + | 0.591174i | 0.915244 | − | 0.402901i | \(-0.131998\pi\) |
0.108700 | + | 0.994075i | \(0.465331\pi\) | |||||||
\(458\) | −1550.19 | + | 895.000i | −0.158156 | + | 0.0913114i | ||||
\(459\) | 1563.50 | + | 2708.06i | 0.158993 | + | 0.275384i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9494.00 | −0.959175 | −0.479587 | − | 0.877494i | \(-0.659214\pi\) | ||||
−0.479587 | + | 0.877494i | \(0.659214\pi\) | |||||||
\(462\) | 60.6218 | − | 1295.00i | 0.00610472 | − | 0.130409i | ||||
\(463\) | − | 10160.0i | − | 1.01982i | −0.860229 | − | 0.509908i | \(-0.829679\pi\) | ||
0.860229 | − | 0.509908i | \(-0.170321\pi\) | |||||||
\(464\) | 848.000 | − | 1468.78i | 0.0848436 | − | 0.146953i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1787.00 | + | 3095.17i | 0.177642 | + | 0.307685i | ||||
\(467\) | −1131.90 | − | 653.500i | −0.112158 | − | 0.0647545i | 0.442872 | − | 0.896585i | \(-0.353960\pi\) |
−0.555030 | + | 0.831831i | \(0.687293\pi\) | |||||||
\(468\) | − | 6864.00i | − | 0.677967i | ||||||
\(469\) | −8121.50 | − | 380.185i | −0.799608 | − | 0.0374314i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 779.500 | − | 1350.13i | 0.0762579 | − | 0.132083i | ||||
\(472\) | −117.779 | + | 68.0000i | −0.0114857 | + | 0.00663126i | ||||
\(473\) | 7880.83 | − | 4550.00i | 0.766091 | − | 0.442303i | ||||
\(474\) | −495.000 | + | 857.365i | −0.0479665 | + | 0.0830803i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2006.00 | − | 3883.26i | −0.193161 | − | 0.373926i | ||||
\(477\) | − | 10842.0i | − | 1.04072i | ||||||
\(478\) | −8833.46 | − | 5100.00i | −0.845257 | − | 0.488010i | ||||
\(479\) | 9143.50 | + | 15837.0i | 0.872186 | + | 1.51067i | 0.859730 | + | 0.510748i | \(0.170632\pi\) |
0.0124559 | + | 0.999922i | \(0.496035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −363.000 | + | 628.734i | −0.0344103 | + | 0.0596005i | ||||
\(482\) | − | 8354.00i | − | 0.789449i | ||||||
\(483\) | −109.119 | − | 70.0000i | −0.0102797 | − | 0.00659443i | ||||
\(484\) | 424.000 | 0.0398197 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2080.00 | − | 3602.67i | −0.194137 | − | 0.336256i | ||||
\(487\) | 12949.7 | − | 7476.50i | 1.20494 | − | 0.695673i | 0.243291 | − | 0.969953i | \(-0.421773\pi\) |
0.961650 | + | 0.274281i | \(0.0884398\pi\) | |||||||
\(488\) | 353.338 | + | 204.000i | 0.0327764 | + | 0.0189235i | ||||
\(489\) | −2251.00 | −0.208167 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14352.0 | 1.31914 | 0.659569 | − | 0.751644i | \(-0.270739\pi\) | ||||
0.659569 | + | 0.751644i | \(0.270739\pi\) | |||||||
\(492\) | 1725.12 | + | 996.000i | 0.158078 | + | 0.0912666i | ||||
\(493\) | 5416.12 | − | 3127.00i | 0.494787 | − | 0.285665i | ||||
\(494\) | −9042.00 | − | 15661.2i | −0.823520 | − | 1.42638i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1200.00 | 0.108632 | ||||||||
\(497\) | −12221.4 | − | 7840.00i | −1.10302 | − | 0.707590i | ||||
\(498\) | 1864.00i | 0.167727i | ||||||||
\(499\) | −2765.50 | + | 4789.99i | −0.248098 | + | 0.429718i | −0.962998 | − | 0.269509i | \(-0.913139\pi\) |
0.714900 | + | 0.699226i | \(0.246472\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1394.00 | + | 2414.48i | 0.124310 | + | 0.215311i | ||||
\(502\) | 8106.00 | + | 4680.00i | 0.720694 | + | 0.416093i | ||||
\(503\) | 8400.00i | 0.744607i | 0.928111 | + | 0.372304i | \(0.121432\pi\) | ||||
−0.928111 | + | 0.372304i | \(0.878568\pi\) | |||||||
\(504\) | 1768.00 | + | 3422.53i | 0.156256 | + | 0.302484i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −245.000 | + | 424.352i | −0.0215249 | + | 0.0372821i | ||||
\(507\) | 1869.75 | − | 1079.50i | 0.163784 | − | 0.0945607i | ||||
\(508\) | 3242.40 | − | 1872.00i | 0.283185 | − | 0.163497i | ||||
\(509\) | −1192.50 | + | 2065.47i | −0.103844 | + | 0.179863i | −0.913265 | − | 0.407365i | \(-0.866448\pi\) |
0.809421 | + | 0.587228i | \(0.199781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5457.50 | + | 255.477i | 0.472457 | + | 0.0221167i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | −6288.21 | − | 3630.50i | −0.541192 | − | 0.312457i | ||||
\(514\) | 1749.00 | + | 3029.36i | 0.150088 | + | 0.259960i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 520.000 | − | 900.666i | 0.0443638 | − | 0.0768404i | ||||
\(517\) | 5985.00i | 0.509130i | ||||||||
\(518\) | 19.0526 | − | 407.000i | 0.00161606 | − | 0.0345223i | ||||
\(519\) | 1579.00 | 0.133546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4576.50 | + | 7926.73i | 0.384837 | + | 0.666557i | 0.991747 | − | 0.128214i | \(-0.0409243\pi\) |
−0.606910 | + | 0.794771i | \(0.707591\pi\) | |||||||
\(522\) | −4773.53 | + | 2756.00i | −0.400253 | + | 0.231086i | ||||
\(523\) | 11957.2 | + | 6903.50i | 0.999718 | + | 0.577187i | 0.908165 | − | 0.418613i | \(-0.137484\pi\) |
0.0915530 | + | 0.995800i | \(0.470817\pi\) | |||||||
\(524\) | 3020.00 | 0.251773 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8946.00 | 0.741567 | ||||||||
\(527\) | 3832.16 | + | 2212.50i | 0.316758 | + | 0.182880i | ||||
\(528\) | −484.974 | + | 280.000i | −0.0399731 | + | 0.0230785i | ||||
\(529\) | −6059.00 | − | 10494.5i | −0.497986 | − | 0.862538i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 442.000 | 0.0361227 | ||||||||
\(532\) | 8542.47 | + | 5480.00i | 0.696172 | + | 0.446594i | ||||
\(533\) | − | 32868.0i | − | 2.67105i | ||||||
\(534\) | −873.000 | + | 1512.08i | −0.0707461 | + | 0.122536i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1756.00 | + | 3041.48i | 0.141507 | + | 0.245097i | ||||
\(537\) | −2122.63 | − | 1225.50i | −0.170574 | − | 0.0984809i | ||||
\(538\) | − | 3950.00i | − | 0.316536i | ||||||
\(539\) | 6947.50 | − | 9790.42i | 0.555195 | − | 0.782381i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4087.50 | + | 7079.76i | −0.324834 | + | 0.562629i | −0.981479 | − | 0.191571i | \(-0.938642\pi\) |
0.656645 | + | 0.754200i | \(0.271975\pi\) | |||||||
\(542\) | −14616.8 | + | 8439.00i | −1.15838 | + | 0.668794i | ||||
\(543\) | 1013.25 | − | 585.000i | 0.0800787 | − | 0.0462334i | ||||
\(544\) | −944.000 | + | 1635.06i | −0.0744001 | + | 0.128865i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1320.00 | + | 2057.68i | −0.103463 | + | 0.161283i | ||||
\(547\) | − | 4656.00i | − | 0.363942i | −0.983304 | − | 0.181971i | \(-0.941752\pi\) | ||
0.983304 | − | 0.181971i | \(-0.0582477\pi\) | |||||||
\(548\) | 8164.89 | + | 4714.00i | 0.636472 | + | 0.367467i | ||||
\(549\) | −663.000 | − | 1148.35i | −0.0515413 | − | 0.0892721i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7261.00 | + | 12576.4i | −0.561396 | + | 0.972366i | ||||
\(552\) | 56.0000i | 0.00431797i | ||||||||
\(553\) | −8144.97 | + | 4207.50i | −0.626328 | + | 0.323546i | ||||
\(554\) | 1054.00 | 0.0808306 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −56.0000 | − | 96.9948i | −0.00427146 | − | 0.00739838i | ||||
\(557\) | −6064.78 | + | 3501.50i | −0.461352 | + | 0.266361i | −0.712612 | − | 0.701558i | \(-0.752488\pi\) |
0.251261 | + | 0.967919i | \(0.419155\pi\) | |||||||
\(558\) | −3377.50 | − | 1950.00i | −0.256238 | − | 0.147939i | ||||
\(559\) | −17160.0 | −1.29837 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2065.00 | −0.155409 | ||||||||
\(562\) | 349.874 | + | 202.000i | 0.0262608 | + | 0.0151617i | ||||
\(563\) | −17106.6 | + | 9876.50i | −1.28056 | + | 0.739334i | −0.976951 | − | 0.213462i | \(-0.931526\pi\) |
−0.303612 | + | 0.952796i | \(0.598193\pi\) | |||||||
\(564\) | 342.000 | + | 592.361i | 0.0255333 | + | 0.0442250i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15898.0 | 1.18064 | ||||||||
\(567\) | 562.050 | − | 12006.5i | 0.0416295 | − | 0.889287i | ||||
\(568\) | 6272.00i | 0.463323i | ||||||||
\(569\) | −3448.50 | + | 5972.98i | −0.254075 | + | 0.440071i | −0.964644 | − | 0.263557i | \(-0.915104\pi\) |
0.710569 | + | 0.703628i | \(0.248438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12457.5 | − | 21577.0i | −0.913013 | − | 1.58138i | −0.809785 | − | 0.586726i | \(-0.800416\pi\) |
−0.103227 | − | 0.994658i | \(-0.532917\pi\) | |||||||
\(572\) | 8002.07 | + | 4620.00i | 0.584936 | + | 0.337713i | ||||
\(573\) | 1275.00i | 0.0929562i | ||||||||
\(574\) | 8466.00 | + | 16388.7i | 0.615617 | + | 1.19172i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 832.000 | − | 1441.07i | 0.0601852 | − | 0.104244i | ||||
\(577\) | −109.985 | + | 63.5000i | −0.00793543 | + | 0.00458152i | −0.503962 | − | 0.863726i | \(-0.668125\pi\) |
0.496027 | + | 0.868307i | \(0.334792\pi\) | |||||||
\(578\) | 2480.30 | − | 1432.00i | 0.178489 | − | 0.103051i | ||||
\(579\) | −17.5000 | + | 30.3109i | −0.00125609 | + | 0.00217561i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9320.00 | + | 14528.4i | −0.665506 | + | 1.03742i | ||||
\(582\) | 580.000i | 0.0413089i | ||||||||
\(583\) | 12639.6 | + | 7297.50i | 0.897908 | + | 0.518407i | ||||
\(584\) | −1180.00 | − | 2043.82i | −0.0836109 | − | 0.144818i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 318.000 | − | 550.792i | 0.0224172 | − | 0.0388277i | ||||
\(587\) | − | 9044.00i | − | 0.635921i | −0.948104 | − | 0.317961i | \(-0.897002\pi\) | ||
0.948104 | − | 0.317961i | \(-0.102998\pi\) | |||||||
\(588\) | 128.172 | − | 1366.00i | 0.00898931 | − | 0.0958042i | ||||
\(589\) | −10275.0 | −0.718801 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1367.00 | − | 2367.71i | −0.0951453 | − | 0.164796i | ||||
\(592\) | −152.420 | + | 88.0000i | −0.0105818 | + | 0.00610942i | ||||
\(593\) | 9267.34 | + | 5350.50i | 0.641760 | + | 0.370521i | 0.785292 | − | 0.619125i | \(-0.212513\pi\) |
−0.143532 | + | 0.989646i | \(0.545846\pi\) | |||||||
\(594\) | 3710.00 | 0.256268 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9180.00 | 0.630919 | ||||||||
\(597\) | −1942.49 | − | 1121.50i | −0.133168 | − | 0.0768843i | ||||
\(598\) | 800.207 | − | 462.000i | 0.0547206 | − | 0.0315930i | ||||
\(599\) | 10399.5 | + | 18012.5i | 0.709369 | + | 1.22866i | 0.965091 | + | 0.261913i | \(0.0843533\pi\) |
−0.255722 | + | 0.966750i | \(0.582313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1402.00 | −0.0951560 | −0.0475780 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475780 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(602\) | 8556.33 | − | 4420.00i | 0.579286 | − | 0.299245i | ||||
\(603\) | − | 11414.0i | − | 0.770836i | ||||||
\(604\) | −2218.00 | + | 3841.69i | −0.149419 | + | 0.258801i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1085.00 | + | 1879.28i | 0.0727312 | + | 0.125974i | ||||
\(607\) | 5650.82 | + | 3262.50i | 0.377858 | + | 0.218156i | 0.676886 | − | 0.736088i | \(-0.263329\pi\) |
−0.299028 | + | 0.954244i | \(0.596662\pi\) | |||||||
\(608\) | − | 4384.00i | − | 0.292425i | ||||||
\(609\) | 1961.00 | + | 91.7987i | 0.130482 | + | 0.00610816i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5643.00 | − | 9773.96i | 0.373636 | − | 0.647156i | ||||
\(612\) | 5313.93 | − | 3068.00i | 0.350985 | − | 0.202641i | ||||
\(613\) | 13034.5 | − | 7525.50i | 0.858826 | − | 0.495844i | −0.00479285 | − | 0.999989i | \(-0.501526\pi\) |
0.863619 | + | 0.504145i | \(0.168192\pi\) | |||||||
\(614\) | 8132.00 | − | 14085.0i | 0.534496 | − | 0.925775i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5180.00 | − | 242.487i | −0.338812 | − | 0.0158605i | ||||
\(617\) | − | 11150.0i | − | 0.727524i | −0.931492 | − | 0.363762i | \(-0.881492\pi\) | ||
0.931492 | − | 0.363762i | \(-0.118508\pi\) | |||||||
\(618\) | −2689.87 | − | 1553.00i | −0.175085 | − | 0.101085i | ||||
\(619\) | 1707.50 | + | 2957.48i | 0.110873 | + | 0.192037i | 0.916122 | − | 0.400899i | \(-0.131302\pi\) |
−0.805250 | + | 0.592936i | \(0.797969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 185.500 | − | 321.295i | 0.0119869 | − | 0.0207619i | ||||
\(622\) | − | 1858.00i | − | 0.119773i | ||||||
\(623\) | −14364.8 | + | 7420.50i | −0.923775 | + | 0.477201i | ||||
\(624\) | 1056.00 | 0.0677465 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −209.000 | − | 361.999i | −0.0133440 | − | 0.0231124i | ||||
\(627\) | 4152.59 | − | 2397.50i | 0.264495 | − | 0.152706i | ||||
\(628\) | −5400.53 | − | 3118.00i | −0.343160 | − | 0.198124i | ||||
\(629\) | −649.000 | −0.0411404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21184.0 | −1.33648 | −0.668242 | − | 0.743944i | \(-0.732953\pi\) | ||||
−0.668242 | + | 0.743944i | \(0.732953\pi\) | |||||||
\(632\) | 3429.46 | + | 1980.00i | 0.215849 | + | 0.124621i | ||||
\(633\) | −1014.98 | + | 586.000i | −0.0637313 | + | 0.0367953i | ||||
\(634\) | −7131.00 | − | 12351.3i | −0.446701 | − | 0.773708i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1668.00 | 0.103995 | ||||||||
\(637\) | −20576.8 | + | 9438.00i | −1.27988 | + | 0.587044i | ||||
\(638\) | − | 7420.00i | − | 0.460440i | ||||||
\(639\) | 10192.0 | − | 17653.1i | 0.630969 | − | 1.09287i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5352.50 | + | 9270.80i | 0.329814 | + | 0.571255i | 0.982475 | − | 0.186395i | \(-0.0596805\pi\) |
−0.652660 | + | 0.757651i | \(0.726347\pi\) | |||||||
\(642\) | 223.435 | + | 129.000i | 0.0137356 | + | 0.00793026i | ||||
\(643\) | 6860.00i | 0.420734i | 0.977622 | + | 0.210367i | \(0.0674659\pi\) | ||||
−0.977622 | + | 0.210367i | \(0.932534\pi\) | |||||||
\(644\) | −280.000 | + | 436.477i | −0.0171328 | + | 0.0267074i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8083.00 | − | 14000.2i | 0.492293 | − | 0.852677i | ||||
\(647\) | −12525.3 | + | 7231.50i | −0.761084 | + | 0.439412i | −0.829685 | − | 0.558232i | \(-0.811480\pi\) |
0.0686008 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(648\) | −4496.40 | + | 2596.00i | −0.272586 | + | 0.157377i | ||||
\(649\) | −297.500 | + | 515.285i | −0.0179937 | + | 0.0311660i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 637.500 | + | 1234.09i | 0.0383803 | + | 0.0742975i | ||||
\(652\) | 9004.00i | 0.540834i | ||||||||
\(653\) | −5177.97 | − | 2989.50i | −0.310305 | − | 0.179155i | 0.336758 | − | 0.941591i | \(-0.390670\pi\) |
−0.647063 | + | 0.762436i | \(0.724003\pi\) | |||||||
\(654\) | −965.000 | − | 1671.43i | −0.0576980 | − | 0.0999359i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3984.00 | − | 6900.49i | 0.237117 | − | 0.410700i | ||||
\(657\) | 7670.00i | 0.455457i | ||||||||
\(658\) | −296.181 | + | 6327.00i | −0.0175476 | + | 0.374851i | ||||
\(659\) | 6940.00 | 0.410234 | 0.205117 | − | 0.978737i | \(-0.434243\pi\) | ||||
0.205117 | + | 0.978737i | \(0.434243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6699.50 | − | 11603.9i | −0.394221 | − | 0.682812i | 0.598780 | − | 0.800914i | \(-0.295652\pi\) |
−0.993001 | + | 0.118102i | \(0.962319\pi\) | |||||||
\(662\) | −11381.3 | + | 6571.00i | −0.668198 | + | 0.385784i | ||||
\(663\) | 3372.30 | + | 1947.00i | 0.197541 | + | 0.114050i | ||||
\(664\) | 7456.00 | 0.435766 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 572.000 | 0.0332801 | ||||||||
\(667\) | −642.591 | − | 371.000i | −0.0373032 | − | 0.0215370i | ||||
\(668\) | 9657.92 | − | 5576.00i | 0.559395 | − | 0.322967i | ||||
\(669\) | −1012.00 | − | 1752.84i | −0.0584846 | − | 0.101298i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1785.00 | 0.102696 | ||||||||
\(672\) | −526.543 | + | 272.000i | −0.0302260 | + | 0.0156140i | ||||
\(673\) | 29510.0i | 1.69023i | 0.534582 | + | 0.845117i | \(0.320469\pi\) | ||||
−0.534582 | + | 0.845117i | \(0.679531\pi\) | |||||||
\(674\) | 11466.0 | − | 19859.7i | 0.655273 | − | 1.13497i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4318.00 | − | 7479.00i | −0.245676 | − | 0.425523i | ||||
\(677\) | −22517.5 | − | 13000.5i | −1.27831 | − | 0.738035i | −0.301776 | − | 0.953379i | \(-0.597579\pi\) |
−0.976538 | + | 0.215344i | \(0.930913\pi\) | |||||||
\(678\) | − | 100.000i | − | 0.00566442i | ||||||
\(679\) | −2900.00 | + | 4520.65i | −0.163905 | + | 0.255503i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1285.50 | − | 2226.55i | 0.0723355 | − | 0.125289i | ||||
\(682\) | 4546.63 | − | 2625.00i | 0.255278 | − | 0.147385i | ||||
\(683\) | −7625.35 | + | 4402.50i | −0.427198 | + | 0.246643i | −0.698152 | − | 0.715949i | \(-0.745994\pi\) |
0.270954 | + | 0.962592i | \(0.412661\pi\) | |||||||
\(684\) | −7124.00 | + | 12339.1i | −0.398235 | + | 0.689764i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7829.00 | − | 10006.1i | 0.435733 | − | 0.556899i | ||||
\(687\) | 895.000i | 0.0497036i | ||||||||
\(688\) | −3602.67 | − | 2080.00i | −0.199637 | − | 0.115261i | ||||
\(689\) | −13761.0 | − | 23834.8i | −0.760889 | − | 1.31790i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14342.5 | + | 24841.9i | −0.789601 | + | 1.36763i | 0.136610 | + | 0.990625i | \(0.456379\pi\) |
−0.926211 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(692\) | − | 6316.00i | − | 0.346963i | ||||||
\(693\) | 14185.5 | + | 9100.00i | 0.777579 | + | 0.498817i | ||||
\(694\) | −19554.0 | −1.06954 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −424.000 | − | 734.390i | −0.0230915 | − | 0.0399956i | ||||
\(697\) | 25445.6 | − | 14691.0i | 1.38281 | − | 0.798366i | ||||
\(698\) | 20635.7 | + | 11914.0i | 1.11901 | + | 0.646062i | ||||
\(699\) | 1787.00 | 0.0966961 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3146.00 | −0.169505 | −0.0847523 | − | 0.996402i | \(-0.527010\pi\) | ||||
−0.0847523 | + | 0.996402i | \(0.527010\pi\) | |||||||
\(702\) | −6058.71 | − | 3498.00i | −0.325743 | − | 0.188068i | ||||
\(703\) | 1305.10 | − | 753.500i | 0.0700182 | − | 0.0404250i | ||||
\(704\) | 1120.00 | + | 1939.90i | 0.0599596 | + | 0.103853i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18246.0 | −0.972659 | ||||||||
\(707\) | −939.638 | + | 20072.5i | −0.0499840 | + | 1.06776i | ||||
\(708\) | 68.0000i | 0.00360960i | ||||||||
\(709\) | 629.500 | − | 1090.33i | 0.0333447 | − | 0.0577547i | −0.848871 | − | 0.528599i | \(-0.822717\pi\) |
0.882216 | + | 0.470845i | \(0.156051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6435.00 | − | 11145.7i | −0.339425 | − | 0.587902i | ||||
\(712\) | 6048.32 | + | 3492.00i | 0.318357 | + | 0.183804i | ||||
\(713\) | − | 525.000i | − | 0.0275756i | ||||||
\(714\) | −2183.00 | − | 102.191i | −0.114421 | − | 0.00535631i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4902.00 | + | 8490.51i | −0.255861 | + | 0.443164i | ||||
\(717\) | −4416.73 | + | 2550.00i | −0.230050 | + | 0.132819i | ||||
\(718\) | −14114.5 | + | 8149.00i | −0.733632 | + | 0.423563i | ||||
\(719\) | 8212.50 | − | 14224.5i | 0.425973 | − | 0.737807i | −0.570538 | − | 0.821271i | \(-0.693265\pi\) |
0.996511 | + | 0.0834645i | \(0.0265985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13200.5 | − | 25553.8i | −0.681848 | − | 1.31994i | ||||
\(722\) | 23820.0i | 1.22782i | ||||||||
\(723\) | −3617.39 | − | 2088.50i | −0.186075 | − | 0.107430i | ||||
\(724\) | −2340.00 | − | 4053.00i | −0.120118 | − | 0.208050i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 106.000 | − | 183.597i | 0.00541877 | − | 0.00938559i | ||||
\(727\) | 6032.00i | 0.307723i | 0.988092 | + | 0.153861i | \(0.0491709\pi\) | ||||
−0.988092 | + | 0.153861i | \(0.950829\pi\) | |||||||
\(728\) | 8230.71 | + | 5280.00i | 0.419025 | + | 0.268805i | ||||
\(729\) | 15443.0 | 0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7670.00 | − | 13284.8i | −0.388078 | − | 0.672171i | ||||
\(732\) | 176.669 | − | 102.000i | 0.00892060 | − | 0.00515031i | ||||
\(733\) | −13200.8 | − | 7621.50i | −0.665189 | − | 0.384047i | 0.129062 | − | 0.991636i | \(-0.458803\pi\) |
−0.794251 | + | 0.607589i | \(0.792137\pi\) | |||||||
\(734\) | 19342.0 | 0.972652 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 224.000 | 0.0112184 | ||||||||
\(737\) | 13306.5 | + | 7682.50i | 0.665062 | + | 0.383974i | ||||
\(738\) | −22426.6 | + | 12948.0i | −1.11861 | + | 0.645830i | ||||
\(739\) | −5026.50 | − | 8706.15i | −0.250207 | − | 0.433371i | 0.713376 | − | 0.700782i | \(-0.247165\pi\) |
−0.963583 | + | 0.267411i | \(0.913832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9042.00 | −0.448267 | ||||||||
\(742\) | 13000.8 | + | 8340.00i | 0.643226 | + | 0.412629i | ||||
\(743\) | 24384.0i | 1.20399i | 0.798501 | + | 0.601993i | \(0.205627\pi\) | ||||
−0.798501 | + | 0.601993i | \(0.794373\pi\) | |||||||
\(744\) | 300.000 | − | 519.615i | 0.0147830 | − | 0.0256049i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4109.00 | − | 7117.00i | −0.201664 | − | 0.349292i | ||||
\(747\) | −20985.5 | − | 12116.0i | −1.02787 | − | 0.593442i | ||||
\(748\) | 8260.00i | 0.403764i | ||||||||
\(749\) | 1096.50 | + | 2122.63i | 0.0534916 | + | 0.103550i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5794.50 | + | 10036.4i | −0.281550 | + | 0.487660i | −0.971767 | − | 0.235943i | \(-0.924182\pi\) |
0.690216 | + | 0.723603i | \(0.257515\pi\) | |||||||
\(752\) | 2369.45 | − | 1368.00i | 0.114900 | − | 0.0663375i | ||||
\(753\) | 4053.00 | − | 2340.00i | 0.196148 | − | 0.113246i | ||||
\(754\) | −6996.00 | + | 12117.4i | −0.337904 | + | 0.585266i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3922.00 | + | 183.597i | 0.188680 | + | 0.00883250i | ||||
\(757\) | − | 14562.0i | − | 0.699161i | −0.936906 | − | 0.349581i | \(-0.886324\pi\) | ||
0.936906 | − | 0.349581i | \(-0.113676\pi\) | |||||||
\(758\) | −6041.39 | − | 3488.00i | −0.289490 | − | 0.167137i | ||||
\(759\) | 122.500 | + | 212.176i | 0.00585832 | + | 0.0101469i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11382.5 | − | 19715.1i | 0.542201 | − | 0.939120i | −0.456576 | − | 0.889684i | \(-0.650924\pi\) |
0.998777 | − | 0.0494360i | \(-0.0157424\pi\) | |||||||
\(762\) | − | 1872.00i | − | 0.0889966i | ||||||
\(763\) | 835.715 | − | 17852.5i | 0.0396526 | − | 0.847056i | ||||
\(764\) | 5100.00 | 0.241507 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8717.00 | + | 15098.3i | 0.411172 | + | 0.712171i | ||||
\(767\) | 971.681 | − | 561.000i | 0.0457436 | − | 0.0264101i | ||||
\(768\) | 221.703 | + | 128.000i | 0.0104167 | + | 0.00601407i | ||||
\(769\) | −3766.00 | −0.176600 | −0.0883000 | − | 0.996094i | \(-0.528143\pi\) | ||||
−0.0883000 | + | 0.996094i | \(0.528143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1749.00 | 0.0816974 | ||||||||
\(772\) | 121.244 | + | 70.0000i | 0.00565240 | + | 0.00326341i | ||||
\(773\) | −23262.3 | + | 13430.5i | −1.08239 | + | 0.624918i | −0.931540 | − | 0.363639i | \(-0.881534\pi\) |
−0.150849 | + | 0.988557i | \(0.548201\pi\) | |||||||
\(774\) | 6760.00 | + | 11708.7i | 0.313932 | + | 0.543746i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2320.00 | 0.107324 | ||||||||
\(777\) | −171.473 | − | 110.000i | −0.00791707 | − | 0.00507880i | ||||
\(778\) | − | 326.000i | − | 0.0150227i | ||||||
\(779\) | −34113.0 | + | 59085.4i | −1.56897 | + | 2.71753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13720.0 | + | 23763.7i | 0.628605 | + | 1.08878i | ||||
\(782\) | 715.337 | + | 413.000i | 0.0327115 | + | 0.0188860i | ||||
\(783\) | 5618.00i | 0.256412i | ||||||||
\(784\) | −5464.00 | − | 512.687i | −0.248907 | − | 0.0233549i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 755.000 | − | 1307.70i | 0.0342620 | − | 0.0593436i | ||||
\(787\) | 1816.06 | − | 1048.50i | 0.0822559 | − | 0.0474905i | −0.458308 | − | 0.888793i | \(-0.651544\pi\) |
0.540564 | + | 0.841303i | \(0.318211\pi\) | |||||||
\(788\) | −9470.85 | + | 5468.00i | −0.428154 | + | 0.247195i | ||||
\(789\) | 2236.50 | − | 3873.73i | 0.100914 | − | 0.174789i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 500.000 | − | 779.423i | 0.0224753 | − | 0.0350355i | ||||
\(792\) | − | 7280.00i | − | 0.326621i | ||||||
\(793\) | −2915.04 | − | 1683.00i | −0.130537 | − | 0.0753658i | ||||
\(794\) | −999.000 | − | 1730.32i | −0.0446514 | − | 0.0773384i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4486.00 | + | 7769.98i | −0.199751 | + | 0.345979i | ||||
\(797\) | 35334.0i | 1.57038i | 0.619254 | + | 0.785191i | \(0.287435\pi\) | ||||
−0.619254 | + | 0.785191i | \(0.712565\pi\) | |||||||
\(798\) | 4508.53 | − | 2329.00i | 0.200000 | − | 0.103315i | ||||
\(799\) | 10089.0 | 0.446712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11349.0 | − | 19657.0i | −0.500621 | − | 0.867101i | ||||
\(802\) | −25559.9 | + | 14757.0i | −1.12537 | + | 0.649735i | ||||
\(803\) | −8941.71 | − | 5162.50i | −0.392959 | − | 0.226875i | ||||
\(804\) | 1756.00 | 0.0770265 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9900.00 | −0.432646 | ||||||||
\(807\) | −1710.40 | − | 987.500i | −0.0746083 | − | 0.0430752i | ||||
\(808\) | 7517.10 | − | 4340.00i | 0.327290 | − | 0.188961i | ||||
\(809\) | 21267.5 | + | 36836.4i | 0.924259 | + | 1.60086i | 0.792749 | + | 0.609549i | \(0.208649\pi\) |
0.131510 | + | 0.991315i | \(0.458017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30676.0 | 1.32821 | 0.664106 | − | 0.747638i | \(-0.268812\pi\) | ||||
0.664106 | + | 0.747638i | \(0.268812\pi\) | |||||||
\(812\) | 367.195 | − | 7844.00i | 0.0158695 | − | 0.339003i | ||||
\(813\) | 8439.00i | 0.364045i | ||||||||
\(814\) | −385.000 | + | 666.840i | −0.0165777 | + | 0.0287134i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 472.000 | + | 817.528i | 0.0202491 | + | 0.0350726i | ||||
\(817\) | 30847.8 | + | 17810.0i | 1.32097 | + | 0.762660i | ||||
\(818\) | 266.000i | 0.0113698i | ||||||||
\(819\) | −14586.0 | − | 28235.9i | −0.622315 | − | 1.20469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18671.5 | + | 32340.0i | −0.793715 | + | 1.37475i | 0.129937 | + | 0.991522i | \(0.458522\pi\) |
−0.923652 | + | 0.383232i | \(0.874811\pi\) | |||||||
\(822\) | 4082.44 | − | 2357.00i | 0.173226 | − | 0.100012i | ||||
\(823\) | 2437.86 | − | 1407.50i | 0.103255 | − | 0.0596141i | −0.447483 | − | 0.894292i | \(-0.647680\pi\) |
0.550738 | + | 0.834678i | \(0.314346\pi\) | |||||||
\(824\) | −6212.00 | + | 10759.5i | −0.262628 | + | 0.454885i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −340.000 | + | 530.008i | −0.0143222 | + | 0.0223261i | ||||
\(827\) | 9276.00i | 0.390034i | 0.980800 | + | 0.195017i | \(0.0624762\pi\) | ||||
−0.980800 | + | 0.195017i | \(0.937524\pi\) | |||||||
\(828\) | −630.466 | − | 364.000i | −0.0264616 | − | 0.0152776i | ||||
\(829\) | 9285.50 | + | 16083.0i | 0.389021 | + | 0.673805i | 0.992318 | − | 0.123712i | \(-0.0394799\pi\) |
−0.603297 | + | 0.797517i | \(0.706147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 263.500 | − | 456.395i | 0.0109997 | − | 0.0190520i | ||||
\(832\) | − | 4224.00i | − | 0.176011i | ||||||
\(833\) | −16503.8 | − | 11711.5i | −0.686464 | − | 0.487130i | ||||
\(834\) | −56.0000 | −0.00232509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9590.00 | − | 16610.4i | −0.396743 | − | 0.687179i | ||||
\(837\) | −3442.45 | + | 1987.50i | −0.142161 | + | 0.0820765i | ||||
\(838\) | −11119.8 | − | 6420.00i | −0.458384 | − | 0.264648i | ||||
\(839\) | −29048.0 | −1.19529 | −0.597645 | − | 0.801761i | \(-0.703897\pi\) | ||||
−0.597645 | + | 0.801761i | \(0.703897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13153.0 | −0.539301 | ||||||||
\(842\) | −17781.2 | − | 10266.0i | −0.727769 | − | 0.420178i | ||||
\(843\) | 174.937 | − | 101.000i | 0.00714728 | − | 0.00412648i | ||||
\(844\) | 2344.00 | + | 4059.93i | 0.0955969 | + | 0.165579i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8892.00 | −0.361363 | ||||||||
\(847\) | 1744.18 | − | 901.000i | 0.0707563 | − | 0.0365510i | ||||
\(848\) | − | 6672.00i | − | 0.270186i | ||||||
\(849\) | 3974.50 | − | 6884.04i | 0.160665 | − | 0.278280i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.5000 | + | 66.6840i | 0.00155084 | + | 0.00268613i | ||||
\(852\) | 2715.86 | + | 1568.00i | 0.109206 | + | 0.0630502i | ||||
\(853\) | 32090.0i | 1.28809i | 0.764988 | + | 0.644045i | \(0.222745\pi\) | ||||
−0.764988 | + | 0.644045i | \(0.777255\pi\) | |||||||
\(854\) | 1887.00 | + | 88.3346i | 0.0756110 | + | 0.00353952i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 516.000 | − | 893.738i | 0.0206034 | − | 0.0356861i | ||||
\(857\) | 21249.7 | − | 12268.5i | 0.846995 | − | 0.489013i | −0.0126408 | − | 0.999920i | \(-0.504024\pi\) |
0.859636 | + | 0.510907i | \(0.170690\pi\) | |||||||
\(858\) | 4001.04 | − | 2310.00i | 0.159199 | − | 0.0919139i | ||||
\(859\) | 10412.5 | − | 18035.0i | 0.413585 | − | 0.716351i | −0.581693 | − | 0.813408i | \(-0.697610\pi\) |
0.995279 | + | 0.0970571i | \(0.0309430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9213.00 | + | 431.281i | 0.364667 | + | 0.0170709i | ||||
\(862\) | − | 30426.0i | − | 1.20222i | ||||||
\(863\) | 19786.1 | + | 11423.5i | 0.780447 | + | 0.450591i | 0.836589 | − | 0.547831i | \(-0.184546\pi\) |
−0.0561414 | + | 0.998423i | \(0.517880\pi\) | |||||||
\(864\) | −848.000 | − | 1468.78i | −0.0333907 | − | 0.0578344i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1378.00 | + | 2386.77i | −0.0540720 | + | 0.0936554i | ||||
\(867\) | − | 1432.00i | − | 0.0560937i | ||||||
\(868\) | 4936.34 | − | 2550.00i | 0.193030 | − | 0.0997150i | ||||
\(869\) | 17325.0 | 0.676307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14487.0 | − | 25092.2i | −0.563574 | − | 0.976139i | ||||
\(872\) | −6685.72 | + | 3860.00i | −0.259641 | + | 0.149904i | ||||
\(873\) | −6529.83 | − | 3770.00i | −0.253152 | − | 0.146157i | ||||
\(874\) | −1918.00 | −0.0742303 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1180.00 | −0.0455120 | ||||||||
\(877\) | −37011.3 | − | 21368.5i | −1.42507 | − | 0.822763i | −0.428341 | − | 0.903617i | \(-0.640902\pi\) |
−0.996726 | + | 0.0808543i | \(0.974235\pi\) | |||||||
\(878\) | 4785.66 | − | 2763.00i | 0.183950 | − | 0.106204i | ||||
\(879\) | −159.000 | − | 275.396i | −0.00610118 | − | 0.0105676i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6162.00 | 0.235645 | 0.117822 | − | 0.993035i | \(-0.462409\pi\) | ||||
0.117822 | + | 0.993035i | \(0.462409\pi\) | |||||||
\(882\) | 14545.8 | + | 10322.0i | 0.555308 | + | 0.394059i | ||||
\(883\) | 7748.00i | 0.295290i | 0.989040 | + | 0.147645i | \(0.0471693\pi\) | ||||
−0.989040 | + | 0.147645i | \(0.952831\pi\) | |||||||
\(884\) | 7788.00 | − | 13489.2i | 0.296311 | − | 0.513225i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5849.00 | + | 10130.8i | 0.221784 | + | 0.384142i | ||||
\(887\) | −22450.0 | − | 12961.5i | −0.849827 | − | 0.490648i | 0.0107656 | − | 0.999942i | \(-0.496573\pi\) |
−0.860592 | + | 0.509294i | \(0.829906\pi\) | |||||||
\(888\) | 88.0000i | 0.00332555i | ||||||||
\(889\) | 9360.00 | − | 14590.8i | 0.353121 | − | 0.550461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11357.5 | + | 19671.8i | −0.427038 | + | 0.739651i | ||||
\(892\) | −7011.34 | + | 4048.00i | −0.263181 | + | 0.151947i | ||||
\(893\) | −20288.4 | + | 11713.5i | −0.760274 | + | 0.438944i | ||||
\(894\) | 2295.00 | − | 3975.06i | 0.0858571 | − | 0.148709i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1088.00 | + | 2106.17i | 0.0405664 | + | 0.0785294i | ||||
\(897\) | − | 462.000i | − | 0.0171970i | ||||||
\(898\) | 7936.26 | + | 4582.00i | 0.294918 | + | 0.170271i | ||||
\(899\) | 3975.00 | + | 6884.90i | 0.147468 | + | 0.255422i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12301.5 | − | 21306.8i | 0.454853 | − | 0.787828i | ||||
\(902\) | − | 34860.0i | − | 1.28682i | ||||||
\(903\) | 225.167 | − | 4810.00i | 0.00829798 | − | 0.177261i | ||||
\(904\) | −400.000 | −0.0147166 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1109.00 | + | 1920.84i | 0.0406667 | + | 0.0704368i | ||||
\(907\) | −27656.5 | + | 15967.5i | −1.01248 | + | 0.584556i | −0.911917 | − | 0.410375i | \(-0.865398\pi\) |
−0.100563 | + | 0.994931i | \(0.532065\pi\) | |||||||
\(908\) | −8906.21 | − | 5142.00i | −0.325510 | − | 0.187933i | ||||
\(909\) | −28210.0 | −1.02934 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3408.00 | 0.123943 | 0.0619715 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619715 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(912\) | −1898.33 | − | 1096.00i | −0.0689253 | − | 0.0397941i | ||||
\(913\) | 28249.7 | − | 16310.0i | 1.02402 | − | 0.591218i | ||||
\(914\) | −11551.0 | − | 20006.9i | −0.418023 | − | 0.724037i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3580.00 | 0.129134 | ||||||||
\(917\) | 12423.1 | − | 6417.50i | 0.447381 | − | 0.231106i | ||||
\(918\) | − | 6254.00i | − | 0.224850i | ||||||
\(919\) | 6954.50 | − | 12045.5i | 0.249628 | − | 0.432368i | −0.713795 | − | 0.700355i | \(-0.753025\pi\) |
0.963423 | + | 0.267987i | \(0.0863585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4066.00 | − | 7042.52i | −0.145472 | − | 0.251964i | ||||
\(922\) | 16444.1 | + | 9494.00i | 0.587372 | + | 0.339120i | ||||
\(923\) | − | 51744.0i | − | 1.84526i | ||||||
\(924\) | −1400.00 | + | 2182.38i | −0.0498448 | + | 0.0777004i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10160.0 | + | 17597.6i | −0.360560 | + | 0.624508i | ||||
\(927\) | 34968.4 | − | 20189.0i | 1.23896 | − | 0.715311i | ||||
\(928\) | −2937.56 | + | 1696.00i | −0.103912 | + | 0.0599935i | ||||
\(929\) | −12268.5 | + | 21249.7i | −0.433279 | + | 0.750462i | −0.997153 | − | 0.0753990i | \(-0.975977\pi\) |
0.563874 | + | 0.825861i | \(0.309310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46785.5 | + | 4389.88i | 1.64697 | + | 0.154536i | ||||
\(932\) | − | 7148.00i | − | 0.251224i | ||||||
\(933\) | −804.538 | − | 464.500i | −0.0282308 | − | 0.0162991i | ||||
\(934\) | 1307.00 | + | 2263.79i | 0.0457884 | + | 0.0793078i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6864.00 | + | 11888.8i | −0.239697 | + | 0.415168i | ||||
\(937\) | 32758.0i | 1.14211i | 0.820912 | + | 0.571055i | \(0.193466\pi\) | ||||
−0.820912 | + | 0.571055i | \(0.806534\pi\) | |||||||
\(938\) | 13686.7 | + | 8780.00i | 0.476424 | + | 0.305626i | ||||
\(939\) | −209.000 | −0.00726353 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19280.5 | + | 33394.8i | 0.667934 | + | 1.15690i | 0.978481 | + | 0.206338i | \(0.0661547\pi\) |
−0.310546 | + | 0.950558i | \(0.600512\pi\) | |||||||
\(942\) | −2700.27 | + | 1559.00i | −0.0933965 | + | 0.0539225i | ||||
\(943\) | −3018.96 | − | 1743.00i | −0.104253 | − | 0.0601908i | ||||
\(944\) | 272.000 | 0.00937801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18200.0 | −0.625511 | ||||||||
\(947\) | 34347.4 | + | 19830.5i | 1.17861 | + | 0.680470i | 0.955692 | − | 0.294368i | \(-0.0951092\pi\) |
0.222916 | + | 0.974838i | \(0.428443\pi\) | |||||||
\(948\) | 1714.73 | − | 990.000i | 0.0587467 | − | 0.0339174i | ||||
\(949\) | 9735.00 | + | 16861.5i | 0.332994 | + | 0.576763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7131.00 | −0.243153 | ||||||||
\(952\) | −408.764 | + | 8732.00i | −0.0139161 | + | 0.297275i | ||||
\(953\) | − | 46618.0i | − | 1.58458i | −0.610144 | − | 0.792290i | \(-0.708889\pi\) | ||
0.610144 | − | 0.792290i | \(-0.291111\pi\) | |||||||
\(954\) | −10842.0 | + | 18778.9i | −0.367948 | + | 0.637305i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10200.0 | + | 17666.9i | 0.345075 | + | 0.597687i | ||||
\(957\) | −3212.95 | − | 1855.00i | −0.108527 | − | 0.0626579i | ||||
\(958\) | − | 36574.0i | − | 1.23346i | ||||||
\(959\) | 43604.5 | + | 2041.22i | 1.46826 | + | 0.0687325i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12083.0 | − | 20928.4i | 0.405592 | − | 0.702506i | ||||
\(962\) | 1257.47 | − | 726.000i | 0.0421439 | − | 0.0243318i | ||||
\(963\) | −2904.65 | + | 1677.00i | −0.0971973 | + | 0.0561169i | ||||
\(964\) | −8354.00 | + | 14469.6i | −0.279112 | + | 0.483437i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 119.000 | + | 230.363i | 0.00396352 | + | 0.00767267i | ||||
\(967\) | − | 14816.0i | − | 0.492710i | −0.969180 | − | 0.246355i | \(-0.920767\pi\) | ||
0.969180 | − | 0.246355i | \(-0.0792329\pi\) | |||||||
\(968\) | −734.390 | − | 424.000i | −0.0243845 | − | 0.0140784i | ||||
\(969\) | −4041.50 | − | 7000.08i | −0.133985 | − | 0.232069i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8437.50 | − | 14614.2i | 0.278859 | − | 0.482998i | −0.692242 | − | 0.721665i | \(-0.743377\pi\) |
0.971102 | + | 0.238667i | \(0.0767104\pi\) | |||||||
\(972\) | 8320.00i | 0.274552i | ||||||||
\(973\) | −436.477 | − | 280.000i | −0.0143811 | − | 0.00922548i | ||||
\(974\) | −29906.0 | −0.983830 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −408.000 | − | 706.677i | −0.0133809 | − | 0.0231764i | ||||
\(977\) | 13715.2 | − | 7918.50i | 0.449119 | − | 0.259299i | −0.258339 | − | 0.966054i | \(-0.583175\pi\) |
0.707458 | + | 0.706755i | \(0.249842\pi\) | |||||||
\(978\) | 3898.85 | + | 2251.00i | 0.127476 | + | 0.0735982i | ||||
\(979\) | 30555.0 | 0.997489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25090.0 | 0.816577 | ||||||||
\(982\) | −24858.4 | − | 14352.0i | −0.807804 | − | 0.466386i | ||||
\(983\) | 8586.64 | − | 4957.50i | 0.278608 | − | 0.160854i | −0.354185 | − | 0.935175i | \(-0.615242\pi\) |
0.632793 | + | 0.774321i | \(0.281908\pi\) | |||||||
\(984\) | −1992.00 | − | 3450.25i | −0.0645352 | − | 0.111778i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12508.0 | −0.403992 | ||||||||
\(987\) | 2665.63 | + | 1710.00i | 0.0859654 | + | 0.0551468i | ||||
\(988\) | 36168.0i | 1.16463i | ||||||||
\(989\) | −910.000 | + | 1576.17i | −0.0292582 | + | 0.0506766i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21840.5 | + | 37828.9i | 0.700087 | + | 1.21259i | 0.968435 | + | 0.249265i | \(0.0801889\pi\) |
−0.268348 | + | 0.963322i | \(0.586478\pi\) | |||||||
\(992\) | −2078.46 | − | 1200.00i | −0.0665234 | − | 0.0384073i | ||||
\(993\) | 6571.00i | 0.209994i | ||||||||
\(994\) | 13328.0 | + | 25800.6i | 0.425290 | + | 0.823286i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1864.00 | − | 3228.54i | 0.0593003 | − | 0.102711i | ||||
\(997\) | 40801.1 | − | 23556.5i | 1.29607 | − | 0.748287i | 0.316348 | − | 0.948643i | \(-0.397543\pi\) |
0.979723 | + | 0.200357i | \(0.0642101\pi\) | |||||||
\(998\) | 9579.97 | − | 5531.00i | 0.303856 | − | 0.175432i | ||||
\(999\) | 291.500 | − | 504.893i | 0.00923188 | − | 0.0159901i |
(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 | 350.4.j.d.149.1 | 4 | ||
5.2 | odd | 4 | 14.4.c.b.9.1 | ✓ | 2 | ||
5.3 | odd | 4 | 350.4.e.b.51.1 | 2 | |||
5.4 | even | 2 | inner | 350.4.j.d.149.2 | 4 | ||
7.4 | even | 3 | inner | 350.4.j.d.249.2 | 4 | ||
15.2 | even | 4 | 126.4.g.c.37.1 | 2 | |||
20.7 | even | 4 | 112.4.i.b.65.1 | 2 | |||
35.2 | odd | 12 | 98.4.a.b.1.1 | 1 | |||
35.4 | even | 6 | inner | 350.4.j.d.249.1 | 4 | ||
35.12 | even | 12 | 98.4.a.c.1.1 | 1 | |||
35.17 | even | 12 | 98.4.c.e.67.1 | 2 | |||
35.18 | odd | 12 | 350.4.e.b.151.1 | 2 | |||
35.23 | odd | 12 | 2450.4.a.bh.1.1 | 1 | |||
35.27 | even | 4 | 98.4.c.e.79.1 | 2 | |||
35.32 | odd | 12 | 14.4.c.b.11.1 | yes | 2 | ||
35.33 | even | 12 | 2450.4.a.bf.1.1 | 1 | |||
40.27 | even | 4 | 448.4.i.d.65.1 | 2 | |||
40.37 | odd | 4 | 448.4.i.c.65.1 | 2 | |||
105.2 | even | 12 | 882.4.a.k.1.1 | 1 | |||
105.17 | odd | 12 | 882.4.g.d.361.1 | 2 | |||
105.32 | even | 12 | 126.4.g.c.109.1 | 2 | |||
105.47 | odd | 12 | 882.4.a.p.1.1 | 1 | |||
105.62 | odd | 4 | 882.4.g.d.667.1 | 2 | |||
140.47 | odd | 12 | 784.4.a.j.1.1 | 1 | |||
140.67 | even | 12 | 112.4.i.b.81.1 | 2 | |||
140.107 | even | 12 | 784.4.a.l.1.1 | 1 | |||
280.67 | even | 12 | 448.4.i.d.193.1 | 2 | |||
280.277 | odd | 12 | 448.4.i.c.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.c.b.9.1 | ✓ | 2 | 5.2 | odd | 4 | ||
14.4.c.b.11.1 | yes | 2 | 35.32 | odd | 12 | ||
98.4.a.b.1.1 | 1 | 35.2 | odd | 12 | |||
98.4.a.c.1.1 | 1 | 35.12 | even | 12 | |||
98.4.c.e.67.1 | 2 | 35.17 | even | 12 | |||
98.4.c.e.79.1 | 2 | 35.27 | even | 4 | |||
112.4.i.b.65.1 | 2 | 20.7 | even | 4 | |||
112.4.i.b.81.1 | 2 | 140.67 | even | 12 | |||
126.4.g.c.37.1 | 2 | 15.2 | even | 4 | |||
126.4.g.c.109.1 | 2 | 105.32 | even | 12 | |||
350.4.e.b.51.1 | 2 | 5.3 | odd | 4 | |||
350.4.e.b.151.1 | 2 | 35.18 | odd | 12 | |||
350.4.j.d.149.1 | 4 | 1.1 | even | 1 | trivial | ||
350.4.j.d.149.2 | 4 | 5.4 | even | 2 | inner | ||
350.4.j.d.249.1 | 4 | 35.4 | even | 6 | inner | ||
350.4.j.d.249.2 | 4 | 7.4 | even | 3 | inner | ||
448.4.i.c.65.1 | 2 | 40.37 | odd | 4 | |||
448.4.i.c.193.1 | 2 | 280.277 | odd | 12 | |||
448.4.i.d.65.1 | 2 | 40.27 | even | 4 | |||
448.4.i.d.193.1 | 2 | 280.67 | even | 12 | |||
784.4.a.j.1.1 | 1 | 140.47 | odd | 12 | |||
784.4.a.l.1.1 | 1 | 140.107 | even | 12 | |||
882.4.a.k.1.1 | 1 | 105.2 | even | 12 | |||
882.4.a.p.1.1 | 1 | 105.47 | odd | 12 | |||
882.4.g.d.361.1 | 2 | 105.17 | odd | 12 | |||
882.4.g.d.667.1 | 2 | 105.62 | odd | 4 | |||
2450.4.a.bf.1.1 | 1 | 35.33 | even | 12 | |||
2450.4.a.bh.1.1 | 1 | 35.23 | odd | 12 |