Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.19 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.19 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.45244 | + | 2.27502i | −0.890489 | + | 0.455005i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −3.57605 | − | 3.57605i | −0.510865 | − | 0.510865i | 0.403927 | − | 0.914791i | \(-0.367645\pi\) |
−0.914791 | + | 0.403927i | \(0.867645\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −6.72747 | − | 2.17742i | −0.672747 | − | 0.217742i | ||||
\(11\) | 15.2817 | 1.38925 | 0.694625 | − | 0.719372i | \(-0.255570\pi\) | ||||
0.694625 | + | 0.719372i | \(0.255570\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | 9.30559 | − | 9.30559i | 0.715815 | − | 0.715815i | −0.251931 | − | 0.967745i | \(-0.581065\pi\) |
0.967745 | + | 0.251931i | \(0.0810654\pi\) | |||||||
\(14\) | − | 7.15211i | − | 0.510865i | ||||||
\(15\) | −2.66678 | + | 8.23943i | −0.177786 | + | 0.549296i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 7.64975 | + | 7.64975i | 0.449986 | + | 0.449986i | 0.895350 | − | 0.445364i | \(-0.146926\pi\) |
−0.445364 | + | 0.895350i | \(0.646926\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 16.6289i | − | 0.875203i | −0.899169 | − | 0.437602i | \(-0.855828\pi\) | ||
0.899169 | − | 0.437602i | \(-0.144172\pi\) | |||||||
\(20\) | −4.55005 | − | 8.90489i | −0.227502 | − | 0.445244i | ||||
\(21\) | −8.75951 | −0.417119 | ||||||||
\(22\) | 15.2817 | + | 15.2817i | 0.694625 | + | 0.694625i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 14.6485 | − | 20.2588i | 0.585941 | − | 0.810354i | ||||
\(26\) | 18.6112 | 0.715815 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 7.15211 | − | 7.15211i | 0.255432 | − | 0.255432i | ||||
\(29\) | 28.4867i | 0.982301i | 0.871075 | + | 0.491150i | \(0.163423\pi\) | ||||
−0.871075 | + | 0.491150i | \(0.836577\pi\) | |||||||
\(30\) | −10.9062 | + | 5.57265i | −0.363541 | + | 0.185755i | ||||
\(31\) | 46.8375 | 1.51089 | 0.755443 | − | 0.655214i | \(-0.227422\pi\) | ||||
0.755443 | + | 0.655214i | \(0.227422\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 18.7162 | − | 18.7162i | 0.567159 | − | 0.567159i | ||||
\(34\) | 15.2995i | 0.449986i | ||||||||
\(35\) | 24.0578 | + | 7.78657i | 0.687366 | + | 0.222473i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 38.8008 | + | 38.8008i | 1.04867 | + | 1.04867i | 0.998753 | + | 0.0499156i | \(0.0158952\pi\) |
0.0499156 | + | 0.998753i | \(0.484105\pi\) | |||||||
\(38\) | 16.6289 | − | 16.6289i | 0.437602 | − | 0.437602i | ||||
\(39\) | − | 22.7940i | − | 0.584460i | ||||||
\(40\) | 4.35484 | − | 13.4549i | 0.108871 | − | 0.336373i | ||||
\(41\) | 49.1688 | 1.19924 | 0.599620 | − | 0.800285i | \(-0.295319\pi\) | ||||
0.599620 | + | 0.800285i | \(0.295319\pi\) | |||||||
\(42\) | −8.75951 | − | 8.75951i | −0.208560 | − | 0.208560i | ||||
\(43\) | −39.9675 | + | 39.9675i | −0.929477 | + | 0.929477i | −0.997672 | − | 0.0681954i | \(-0.978276\pi\) |
0.0681954 | + | 0.997672i | \(0.478276\pi\) | |||||||
\(44\) | 30.5635i | 0.694625i | ||||||||
\(45\) | 6.82507 | + | 13.3573i | 0.151668 | + | 0.296830i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 42.2681 | + | 42.2681i | 0.899322 | + | 0.899322i | 0.995376 | − | 0.0960544i | \(-0.0306223\pi\) |
−0.0960544 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 23.4237i | − | 0.478034i | ||||||
\(50\) | 34.9074 | − | 5.61032i | 0.698147 | − | 0.112206i | ||||
\(51\) | 18.7380 | 0.367412 | ||||||||
\(52\) | 18.6112 | + | 18.6112i | 0.357907 | + | 0.357907i | ||||
\(53\) | 40.9030 | − | 40.9030i | 0.771756 | − | 0.771756i | −0.206658 | − | 0.978413i | \(-0.566259\pi\) |
0.978413 | + | 0.206658i | \(0.0662587\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | −68.0411 | + | 34.7664i | −1.23711 | + | 0.632115i | ||||
\(56\) | 14.3042 | 0.255432 | ||||||||
\(57\) | −20.3661 | − | 20.3661i | −0.357300 | − | 0.357300i | ||||
\(58\) | −28.4867 | + | 28.4867i | −0.491150 | + | 0.491150i | ||||
\(59\) | − | 115.558i | − | 1.95860i | −0.202409 | − | 0.979301i | \(-0.564877\pi\) | ||
0.202409 | − | 0.979301i | \(-0.435123\pi\) | |||||||
\(60\) | −16.4789 | − | 5.33357i | −0.274648 | − | 0.0888928i | ||||
\(61\) | −39.5522 | −0.648397 | −0.324199 | − | 0.945989i | \(-0.605095\pi\) | ||||
−0.324199 | + | 0.945989i | \(0.605095\pi\) | |||||||
\(62\) | 46.8375 | + | 46.8375i | 0.755443 | + | 0.755443i | ||||
\(63\) | −10.7282 | + | 10.7282i | −0.170288 | + | 0.170288i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −20.2622 | + | 62.6031i | −0.311726 | + | 0.963124i | ||||
\(66\) | 37.4325 | 0.567159 | ||||||||
\(67\) | 30.0611 | + | 30.0611i | 0.448673 | + | 0.448673i | 0.894913 | − | 0.446240i | \(-0.147237\pi\) |
−0.446240 | + | 0.894913i | \(0.647237\pi\) | |||||||
\(68\) | −15.2995 | + | 15.2995i | −0.224993 | + | 0.224993i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 16.2712 | + | 31.8444i | 0.232446 | + | 0.454920i | ||||
\(71\) | −109.516 | −1.54247 | −0.771237 | − | 0.636548i | \(-0.780362\pi\) | ||||
−0.771237 | + | 0.636548i | \(0.780362\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 37.5852 | − | 37.5852i | 0.514865 | − | 0.514865i | −0.401148 | − | 0.916013i | \(-0.631389\pi\) |
0.916013 | + | 0.401148i | \(0.131389\pi\) | |||||||
\(74\) | 77.6015i | 1.04867i | ||||||||
\(75\) | −6.87121 | − | 42.7526i | −0.0916162 | − | 0.570035i | ||||
\(76\) | 33.2577 | 0.437602 | ||||||||
\(77\) | −54.6484 | − | 54.6484i | −0.709719 | − | 0.709719i | ||||
\(78\) | 22.7940 | − | 22.7940i | 0.292230 | − | 0.292230i | ||||
\(79\) | − | 116.711i | − | 1.47736i | −0.674057 | − | 0.738679i | \(-0.735450\pi\) | ||
0.674057 | − | 0.738679i | \(-0.264550\pi\) | |||||||
\(80\) | 17.8098 | − | 9.10010i | 0.222622 | − | 0.113751i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 49.1688 | + | 49.1688i | 0.599620 | + | 0.599620i | ||||
\(83\) | 97.5863 | − | 97.5863i | 1.17574 | − | 1.17574i | 0.194920 | − | 0.980819i | \(-0.437555\pi\) |
0.980819 | − | 0.194920i | \(-0.0624447\pi\) | |||||||
\(84\) | − | 17.5190i | − | 0.208560i | ||||||
\(85\) | −51.4635 | − | 16.6567i | −0.605453 | − | 0.195961i | ||||
\(86\) | −79.9350 | −0.929477 | ||||||||
\(87\) | 34.8890 | + | 34.8890i | 0.401023 | + | 0.401023i | ||||
\(88\) | −30.5635 | + | 30.5635i | −0.347312 | + | 0.347312i | ||||
\(89\) | 26.3345i | 0.295893i | 0.988995 | + | 0.147946i | \(0.0472663\pi\) | ||||
−0.988995 | + | 0.147946i | \(0.952734\pi\) | |||||||
\(90\) | −6.53226 | + | 20.1824i | −0.0725807 | + | 0.224249i | ||||
\(91\) | −66.5546 | −0.731369 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 57.3640 | − | 57.3640i | 0.616817 | − | 0.616817i | ||||
\(94\) | 84.5362i | 0.899322i | ||||||||
\(95\) | 37.8311 | + | 74.0391i | 0.398222 | + | 0.779359i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −70.0462 | − | 70.0462i | −0.722126 | − | 0.722126i | 0.246912 | − | 0.969038i | \(-0.420584\pi\) |
−0.969038 | + | 0.246912i | \(0.920584\pi\) | |||||||
\(98\) | 23.4237 | − | 23.4237i | 0.239017 | − | 0.239017i | ||||
\(99\) | − | 45.8452i | − | 0.463083i | ||||||
\(100\) | 40.5177 | + | 29.2970i | 0.405177 | + | 0.292970i | ||||
\(101\) | 157.618 | 1.56057 | 0.780285 | − | 0.625424i | \(-0.215074\pi\) | ||||
0.780285 | + | 0.625424i | \(0.215074\pi\) | |||||||
\(102\) | 18.7380 | + | 18.7380i | 0.183706 | + | 0.183706i | ||||
\(103\) | −133.113 | + | 133.113i | −1.29236 | + | 1.29236i | −0.359032 | + | 0.933325i | \(0.616893\pi\) |
−0.933325 | + | 0.359032i | \(0.883107\pi\) | |||||||
\(104\) | 37.2224i | 0.357907i | ||||||||
\(105\) | 39.0012 | − | 19.9281i | 0.371440 | − | 0.189791i | ||||
\(106\) | 81.8061 | 0.771756 | ||||||||
\(107\) | −14.8025 | − | 14.8025i | −0.138341 | − | 0.138341i | 0.634545 | − | 0.772886i | \(-0.281188\pi\) |
−0.772886 | + | 0.634545i | \(0.781188\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 0.102683i | − | 0.000942049i | −1.00000 | 0.000471024i | \(-0.999850\pi\) | |||
1.00000 | 0.000471024i | \(-0.000149932\pi\) | ||||||||
\(110\) | −102.807 | − | 33.2748i | −0.934613 | − | 0.302498i | ||||
\(111\) | 95.0421 | 0.856235 | ||||||||
\(112\) | 14.3042 | + | 14.3042i | 0.127716 | + | 0.127716i | ||||
\(113\) | −54.9742 | + | 54.9742i | −0.486497 | + | 0.486497i | −0.907199 | − | 0.420702i | \(-0.861784\pi\) |
0.420702 | + | 0.907199i | \(0.361784\pi\) | |||||||
\(114\) | − | 40.7322i | − | 0.357300i | ||||||
\(115\) | 7.38399 | − | 22.8140i | 0.0642086 | − | 0.198382i | ||||
\(116\) | −56.9734 | −0.491150 | ||||||||
\(117\) | −27.9168 | − | 27.9168i | −0.238605 | − | 0.238605i | ||||
\(118\) | 115.558 | − | 115.558i | 0.979301 | − | 0.979301i | ||||
\(119\) | − | 54.7119i | − | 0.459764i | ||||||
\(120\) | −11.1453 | − | 21.8124i | −0.0928775 | − | 0.181770i | ||||
\(121\) | 112.532 | 0.930014 | ||||||||
\(122\) | −39.5522 | − | 39.5522i | −0.324199 | − | 0.324199i | ||||
\(123\) | 60.2193 | − | 60.2193i | 0.489587 | − | 0.489587i | ||||
\(124\) | 93.6750i | 0.755443i | ||||||||
\(125\) | −19.1324 | + | 123.527i | −0.153059 | + | 0.988217i | ||||
\(126\) | −21.4563 | −0.170288 | ||||||||
\(127\) | −159.860 | − | 159.860i | −1.25874 | − | 1.25874i | −0.951696 | − | 0.307042i | \(-0.900661\pi\) |
−0.307042 | − | 0.951696i | \(-0.599339\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 97.9000i | 0.758914i | ||||||||
\(130\) | −82.8653 | + | 42.3409i | −0.637425 | + | 0.325699i | ||||
\(131\) | −249.753 | −1.90651 | −0.953257 | − | 0.302161i | \(-0.902292\pi\) | ||||
−0.953257 | + | 0.302161i | \(0.902292\pi\) | |||||||
\(132\) | 37.4325 | + | 37.4325i | 0.283579 | + | 0.283579i | ||||
\(133\) | −59.4657 | + | 59.4657i | −0.447111 | + | 0.447111i | ||||
\(134\) | 60.1222i | 0.448673i | ||||||||
\(135\) | 24.7183 | + | 8.00035i | 0.183099 | + | 0.0592619i | ||||
\(136\) | −30.5990 | −0.224993 | ||||||||
\(137\) | 24.1535 | + | 24.1535i | 0.176303 | + | 0.176303i | 0.789742 | − | 0.613439i | \(-0.210214\pi\) |
−0.613439 | + | 0.789742i | \(0.710214\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | 107.895i | 0.776221i | 0.921613 | + | 0.388111i | \(0.126872\pi\) | ||||
−0.921613 | + | 0.388111i | \(0.873128\pi\) | |||||||
\(140\) | −15.5731 | + | 48.1156i | −0.111237 | + | 0.343683i | ||||
\(141\) | 103.535 | 0.734293 | ||||||||
\(142\) | −109.516 | − | 109.516i | −0.771237 | − | 0.771237i | ||||
\(143\) | 142.206 | − | 142.206i | 0.994445 | − | 0.994445i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −64.8080 | − | 126.836i | −0.446952 | − | 0.874728i | ||||
\(146\) | 75.1703 | 0.514865 | ||||||||
\(147\) | −28.6880 | − | 28.6880i | −0.195157 | − | 0.195157i | ||||
\(148\) | −77.6015 | + | 77.6015i | −0.524335 | + | 0.524335i | ||||
\(149\) | 149.146i | 1.00098i | 0.865741 | + | 0.500492i | \(0.166847\pi\) | ||||
−0.865741 | + | 0.500492i | \(0.833153\pi\) | |||||||
\(150\) | 35.8814 | − | 49.6238i | 0.239209 | − | 0.330826i | ||||
\(151\) | −87.3637 | −0.578568 | −0.289284 | − | 0.957243i | \(-0.593417\pi\) | ||||
−0.289284 | + | 0.957243i | \(0.593417\pi\) | |||||||
\(152\) | 33.2577 | + | 33.2577i | 0.218801 | + | 0.218801i | ||||
\(153\) | 22.9493 | − | 22.9493i | 0.149995 | − | 0.149995i | ||||
\(154\) | − | 109.297i | − | 0.709719i | ||||||
\(155\) | −208.541 | + | 106.556i | −1.34543 | + | 0.687461i | ||||
\(156\) | 45.5879 | 0.292230 | ||||||||
\(157\) | 81.1651 | + | 81.1651i | 0.516975 | + | 0.516975i | 0.916655 | − | 0.399680i | \(-0.130879\pi\) |
−0.399680 | + | 0.916655i | \(0.630879\pi\) | |||||||
\(158\) | 116.711 | − | 116.711i | 0.738679 | − | 0.738679i | ||||
\(159\) | − | 100.192i | − | 0.630136i | ||||||
\(160\) | 26.9099 | + | 8.70968i | 0.168187 | + | 0.0544355i | ||||
\(161\) | 24.2540 | 0.150646 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −56.4577 | + | 56.4577i | −0.346366 | + | 0.346366i | −0.858754 | − | 0.512388i | \(-0.828761\pi\) |
0.512388 | + | 0.858754i | \(0.328761\pi\) | |||||||
\(164\) | 98.3376i | 0.599620i | ||||||||
\(165\) | −40.7531 | + | 125.913i | −0.246989 | + | 0.763109i | ||||
\(166\) | 195.173 | 1.17574 | ||||||||
\(167\) | 161.337 | + | 161.337i | 0.966088 | + | 0.966088i | 0.999444 | − | 0.0333553i | \(-0.0106193\pi\) |
−0.0333553 | + | 0.999444i | \(0.510619\pi\) | |||||||
\(168\) | 17.5190 | − | 17.5190i | 0.104280 | − | 0.104280i | ||||
\(169\) | − | 4.18809i | − | 0.0247816i | ||||||
\(170\) | −34.8068 | − | 68.1202i | −0.204746 | − | 0.400707i | ||||
\(171\) | −49.8866 | −0.291734 | ||||||||
\(172\) | −79.9350 | − | 79.9350i | −0.464738 | − | 0.464738i | ||||
\(173\) | −113.686 | + | 113.686i | −0.657146 | + | 0.657146i | −0.954704 | − | 0.297558i | \(-0.903828\pi\) |
0.297558 | + | 0.954704i | \(0.403828\pi\) | |||||||
\(174\) | 69.7779i | 0.401023i | ||||||||
\(175\) | −124.831 | + | 20.0628i | −0.713318 | + | 0.114645i | ||||
\(176\) | −61.1270 | −0.347312 | ||||||||
\(177\) | −141.528 | − | 141.528i | −0.799596 | − | 0.799596i | ||||
\(178\) | −26.3345 | + | 26.3345i | −0.147946 | + | 0.147946i | ||||
\(179\) | − | 202.276i | − | 1.13003i | −0.825080 | − | 0.565016i | \(-0.808870\pi\) | ||
0.825080 | − | 0.565016i | \(-0.191130\pi\) | |||||||
\(180\) | −26.7147 | + | 13.6501i | −0.148415 | + | 0.0758342i | ||||
\(181\) | −119.692 | −0.661281 | −0.330640 | − | 0.943757i | \(-0.607265\pi\) | ||||
−0.330640 | + | 0.943757i | \(0.607265\pi\) | |||||||
\(182\) | −66.5546 | − | 66.5546i | −0.365685 | − | 0.365685i | ||||
\(183\) | −48.4414 | + | 48.4414i | −0.264707 | + | 0.264707i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | −261.031 | − | 84.4855i | −1.41098 | − | 0.456679i | ||||
\(186\) | 114.728 | 0.616817 | ||||||||
\(187\) | 116.902 | + | 116.902i | 0.625142 | + | 0.625142i | ||||
\(188\) | −84.5362 | + | 84.5362i | −0.449661 | + | 0.449661i | ||||
\(189\) | 26.2785i | 0.139040i | ||||||||
\(190\) | −36.2080 | + | 111.870i | −0.190568 | + | 0.588790i | ||||
\(191\) | 354.419 | 1.85560 | 0.927798 | − | 0.373084i | \(-0.121700\pi\) | ||||
0.927798 | + | 0.373084i | \(0.121700\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 89.8493 | − | 89.8493i | 0.465541 | − | 0.465541i | −0.434926 | − | 0.900466i | \(-0.643225\pi\) |
0.900466 | + | 0.434926i | \(0.143225\pi\) | |||||||
\(194\) | − | 140.092i | − | 0.722126i | ||||||
\(195\) | 51.8568 | + | 101.489i | 0.265932 | + | 0.520455i | ||||
\(196\) | 46.8473 | 0.239017 | ||||||||
\(197\) | 244.917 | + | 244.917i | 1.24323 | + | 1.24323i | 0.958652 | + | 0.284582i | \(0.0918548\pi\) |
0.284582 | + | 0.958652i | \(0.408145\pi\) | |||||||
\(198\) | 45.8452 | − | 45.8452i | 0.231542 | − | 0.231542i | ||||
\(199\) | 201.091i | 1.01051i | 0.862971 | + | 0.505253i | \(0.168601\pi\) | ||||
−0.862971 | + | 0.505253i | \(0.831399\pi\) | |||||||
\(200\) | 11.2206 | + | 69.8147i | 0.0561032 | + | 0.349074i | ||||
\(201\) | 73.6343 | 0.366340 | ||||||||
\(202\) | 157.618 | + | 157.618i | 0.780285 | + | 0.780285i | ||||
\(203\) | 101.870 | − | 101.870i | 0.501823 | − | 0.501823i | ||||
\(204\) | 37.4760i | 0.183706i | ||||||||
\(205\) | −218.921 | + | 111.860i | −1.06791 | + | 0.545660i | ||||
\(206\) | −266.226 | −1.29236 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | −37.2224 | + | 37.2224i | −0.178954 | + | 0.178954i | ||||
\(209\) | − | 254.118i | − | 1.21588i | ||||||
\(210\) | 58.9293 | + | 19.0731i | 0.280616 | + | 0.0908244i | ||||
\(211\) | −56.8261 | −0.269318 | −0.134659 | − | 0.990892i | \(-0.542994\pi\) | ||||
−0.134659 | + | 0.990892i | \(0.542994\pi\) | |||||||
\(212\) | 81.8061 | + | 81.8061i | 0.385878 | + | 0.385878i | ||||
\(213\) | −134.129 | + | 134.129i | −0.629712 | + | 0.629712i | ||||
\(214\) | − | 29.6049i | − | 0.138341i | ||||||
\(215\) | 87.0260 | − | 268.880i | 0.404772 | − | 1.25061i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −167.493 | − | 167.493i | −0.771859 | − | 0.771859i | ||||
\(218\) | 0.102683 | − | 0.102683i | 0.000471024 | − | 0.000471024i | ||||
\(219\) | − | 92.0645i | − | 0.420386i | ||||||
\(220\) | −69.5327 | − | 136.082i | −0.316058 | − | 0.618556i | ||||
\(221\) | 142.371 | 0.644213 | ||||||||
\(222\) | 95.0421 | + | 95.0421i | 0.428117 | + | 0.428117i | ||||
\(223\) | 50.8364 | − | 50.8364i | 0.227966 | − | 0.227966i | −0.583876 | − | 0.811843i | \(-0.698465\pi\) |
0.811843 | + | 0.583876i | \(0.198465\pi\) | |||||||
\(224\) | 28.6084i | 0.127716i | ||||||||
\(225\) | −60.7765 | − | 43.9456i | −0.270118 | − | 0.195314i | ||||
\(226\) | −109.948 | −0.486497 | ||||||||
\(227\) | −75.8315 | − | 75.8315i | −0.334060 | − | 0.334060i | 0.520066 | − | 0.854126i | \(-0.325907\pi\) |
−0.854126 | + | 0.520066i | \(0.825907\pi\) | |||||||
\(228\) | 40.7322 | − | 40.7322i | 0.178650 | − | 0.178650i | ||||
\(229\) | − | 70.0263i | − | 0.305792i | −0.988242 | − | 0.152896i | \(-0.951140\pi\) | ||
0.988242 | − | 0.152896i | \(-0.0488599\pi\) | |||||||
\(230\) | 30.1979 | − | 15.4300i | 0.131295 | − | 0.0670868i | ||||
\(231\) | −133.861 | −0.579483 | ||||||||
\(232\) | −56.9734 | − | 56.9734i | −0.245575 | − | 0.245575i | ||||
\(233\) | 4.02362 | − | 4.02362i | 0.0172687 | − | 0.0172687i | −0.698420 | − | 0.715688i | \(-0.746113\pi\) |
0.715688 | + | 0.698420i | \(0.246113\pi\) | |||||||
\(234\) | − | 55.8336i | − | 0.238605i | ||||||
\(235\) | −284.357 | − | 92.0354i | −1.21003 | − | 0.391640i | ||||
\(236\) | 231.115 | 0.979301 | ||||||||
\(237\) | −142.942 | − | 142.942i | −0.603129 | − | 0.603129i | ||||
\(238\) | 54.7119 | − | 54.7119i | 0.229882 | − | 0.229882i | ||||
\(239\) | − | 268.560i | − | 1.12368i | −0.827245 | − | 0.561842i | \(-0.810093\pi\) | ||
0.827245 | − | 0.561842i | \(-0.189907\pi\) | |||||||
\(240\) | 10.6671 | − | 32.9577i | 0.0444464 | − | 0.137324i | ||||
\(241\) | −265.941 | −1.10349 | −0.551745 | − | 0.834013i | \(-0.686038\pi\) | ||||
−0.551745 | + | 0.834013i | \(0.686038\pi\) | |||||||
\(242\) | 112.532 | + | 112.532i | 0.465007 | + | 0.465007i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 79.1045i | − | 0.324199i | ||||||
\(245\) | 53.2894 | + | 104.293i | 0.217508 | + | 0.425684i | ||||
\(246\) | 120.439 | 0.489587 | ||||||||
\(247\) | −154.741 | − | 154.741i | −0.626483 | − | 0.626483i | ||||
\(248\) | −93.6750 | + | 93.6750i | −0.377722 | + | 0.377722i | ||||
\(249\) | − | 239.037i | − | 0.959987i | ||||||
\(250\) | −142.659 | + | 104.395i | −0.570638 | + | 0.417579i | ||||
\(251\) | 167.641 | 0.667893 | 0.333947 | − | 0.942592i | \(-0.391619\pi\) | ||||
0.333947 | + | 0.942592i | \(0.391619\pi\) | |||||||
\(252\) | −21.4563 | − | 21.4563i | −0.0851442 | − | 0.0851442i | ||||
\(253\) | −51.8229 | + | 51.8229i | −0.204834 | + | 0.204834i | ||||
\(254\) | − | 319.719i | − | 1.25874i | ||||||
\(255\) | −83.4299 | + | 42.6294i | −0.327176 | + | 0.167174i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 64.2388 | + | 64.2388i | 0.249956 | + | 0.249956i | 0.820953 | − | 0.570996i | \(-0.193443\pi\) |
−0.570996 | + | 0.820953i | \(0.693443\pi\) | |||||||
\(258\) | −97.9000 | + | 97.9000i | −0.379457 | + | 0.379457i | ||||
\(259\) | − | 277.507i | − | 1.07146i | ||||||
\(260\) | −125.206 | − | 40.5244i | −0.481562 | − | 0.155863i | ||||
\(261\) | 85.4602 | 0.327434 | ||||||||
\(262\) | −249.753 | − | 249.753i | −0.953257 | − | 0.953257i | ||||
\(263\) | −26.1375 | + | 26.1375i | −0.0993820 | + | 0.0993820i | −0.755050 | − | 0.655668i | \(-0.772387\pi\) |
0.655668 | + | 0.755050i | \(0.272387\pi\) | |||||||
\(264\) | 74.8650i | 0.283579i | ||||||||
\(265\) | −89.0631 | + | 275.174i | −0.336087 | + | 1.03839i | ||||
\(266\) | −118.931 | −0.447111 | ||||||||
\(267\) | 32.2530 | + | 32.2530i | 0.120798 | + | 0.120798i | ||||
\(268\) | −60.1222 | + | 60.1222i | −0.224336 | + | 0.224336i | ||||
\(269\) | − | 114.873i | − | 0.427036i | −0.976939 | − | 0.213518i | \(-0.931508\pi\) | ||
0.976939 | − | 0.213518i | \(-0.0684922\pi\) | |||||||
\(270\) | 16.7180 | + | 32.7187i | 0.0619183 | + | 0.121180i | ||||
\(271\) | 263.414 | 0.972007 | 0.486004 | − | 0.873957i | \(-0.338454\pi\) | ||||
0.486004 | + | 0.873957i | \(0.338454\pi\) | |||||||
\(272\) | −30.5990 | − | 30.5990i | −0.112496 | − | 0.112496i | ||||
\(273\) | −81.5124 | + | 81.5124i | −0.298580 | + | 0.298580i | ||||
\(274\) | 48.3070i | 0.176303i | ||||||||
\(275\) | 223.855 | − | 309.590i | 0.814018 | − | 1.12578i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −247.635 | − | 247.635i | −0.893990 | − | 0.893990i | 0.100906 | − | 0.994896i | \(-0.467826\pi\) |
−0.994896 | + | 0.100906i | \(0.967826\pi\) | |||||||
\(278\) | −107.895 | + | 107.895i | −0.388111 | + | 0.388111i | ||||
\(279\) | − | 140.512i | − | 0.503629i | ||||||
\(280\) | −63.6887 | + | 32.5425i | −0.227460 | + | 0.116223i | ||||
\(281\) | −503.134 | −1.79051 | −0.895257 | − | 0.445550i | \(-0.853008\pi\) | ||||
−0.895257 | + | 0.445550i | \(0.853008\pi\) | |||||||
\(282\) | 103.535 | + | 103.535i | 0.367147 | + | 0.367147i | ||||
\(283\) | −334.802 | + | 334.802i | −1.18304 | + | 1.18304i | −0.204093 | + | 0.978951i | \(0.565425\pi\) |
−0.978951 | + | 0.204093i | \(0.934575\pi\) | |||||||
\(284\) | − | 219.031i | − | 0.771237i | ||||||
\(285\) | 137.012 | + | 44.3456i | 0.480745 | + | 0.155598i | ||||
\(286\) | 284.411 | 0.994445 | ||||||||
\(287\) | −175.830 | − | 175.830i | −0.612649 | − | 0.612649i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 171.963i | − | 0.595026i | ||||||
\(290\) | 62.0275 | − | 191.644i | 0.213888 | − | 0.660840i | ||||
\(291\) | −171.578 | −0.589614 | ||||||||
\(292\) | 75.1703 | + | 75.1703i | 0.257433 | + | 0.257433i | ||||
\(293\) | −103.910 | + | 103.910i | −0.354642 | + | 0.354642i | −0.861833 | − | 0.507192i | \(-0.830684\pi\) |
0.507192 | + | 0.861833i | \(0.330684\pi\) | |||||||
\(294\) | − | 57.3760i | − | 0.195157i | ||||||
\(295\) | 262.896 | + | 514.513i | 0.891174 | + | 1.74411i | ||||
\(296\) | −155.203 | −0.524335 | ||||||||
\(297\) | −56.1487 | − | 56.1487i | −0.189053 | − | 0.189053i | ||||
\(298\) | −149.146 | + | 149.146i | −0.500492 | + | 0.500492i | ||||
\(299\) | 63.1136i | 0.211082i | ||||||||
\(300\) | 85.5052 | − | 13.7424i | 0.285017 | − | 0.0458081i | ||||
\(301\) | 285.852 | 0.949674 | ||||||||
\(302\) | −87.3637 | − | 87.3637i | −0.289284 | − | 0.289284i | ||||
\(303\) | 193.041 | − | 193.041i | 0.637100 | − | 0.637100i | ||||
\(304\) | 66.5154i | 0.218801i | ||||||||
\(305\) | 176.104 | − | 89.9823i | 0.577391 | − | 0.295024i | ||||
\(306\) | 45.8985 | 0.149995 | ||||||||
\(307\) | 15.9914 | + | 15.9914i | 0.0520893 | + | 0.0520893i | 0.732672 | − | 0.680582i | \(-0.238273\pi\) |
−0.680582 | + | 0.732672i | \(0.738273\pi\) | |||||||
\(308\) | 109.297 | − | 109.297i | 0.354859 | − | 0.354859i | ||||
\(309\) | 326.058i | 1.05521i | ||||||||
\(310\) | −315.098 | − | 101.985i | −1.01644 | − | 0.328983i | ||||
\(311\) | 430.485 | 1.38420 | 0.692098 | − | 0.721804i | \(-0.256687\pi\) | ||||
0.692098 | + | 0.721804i | \(0.256687\pi\) | |||||||
\(312\) | 45.5879 | + | 45.5879i | 0.146115 | + | 0.146115i | ||||
\(313\) | −215.563 | + | 215.563i | −0.688699 | + | 0.688699i | −0.961944 | − | 0.273246i | \(-0.911903\pi\) |
0.273246 | + | 0.961944i | \(0.411903\pi\) | |||||||
\(314\) | 162.330i | 0.516975i | ||||||||
\(315\) | 23.3597 | − | 72.1734i | 0.0741578 | − | 0.229122i | ||||
\(316\) | 233.423 | 0.738679 | ||||||||
\(317\) | −74.4937 | − | 74.4937i | −0.234996 | − | 0.234996i | 0.579778 | − | 0.814774i | \(-0.303139\pi\) |
−0.814774 | + | 0.579778i | \(0.803139\pi\) | |||||||
\(318\) | 100.192 | − | 100.192i | 0.315068 | − | 0.315068i | ||||
\(319\) | 435.327i | 1.36466i | ||||||||
\(320\) | 18.2002 | + | 35.6196i | 0.0568756 | + | 0.111311i | ||||
\(321\) | −36.2585 | −0.112955 | ||||||||
\(322\) | 24.2540 | + | 24.2540i | 0.0753229 | + | 0.0753229i | ||||
\(323\) | 127.207 | − | 127.207i | 0.393829 | − | 0.393829i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −52.2074 | − | 324.834i | −0.160638 | − | 0.999488i | ||||
\(326\) | −112.915 | −0.346366 | ||||||||
\(327\) | −0.125761 | − | 0.125761i | −0.000384590 | − | 0.000384590i | ||||
\(328\) | −98.3376 | + | 98.3376i | −0.299810 | + | 0.299810i | ||||
\(329\) | − | 302.306i | − | 0.918864i | ||||||
\(330\) | −166.666 | + | 85.1598i | −0.505049 | + | 0.258060i | ||||
\(331\) | 316.884 | 0.957354 | 0.478677 | − | 0.877991i | \(-0.341116\pi\) | ||||
0.478677 | + | 0.877991i | \(0.341116\pi\) | |||||||
\(332\) | 195.173 | + | 195.173i | 0.587870 | + | 0.587870i | ||||
\(333\) | 116.402 | − | 116.402i | 0.349556 | − | 0.349556i | ||||
\(334\) | 322.673i | 0.966088i | ||||||||
\(335\) | −202.235 | − | 65.4556i | −0.603687 | − | 0.195390i | ||||
\(336\) | 35.0380 | 0.104280 | ||||||||
\(337\) | 81.9442 | + | 81.9442i | 0.243158 | + | 0.243158i | 0.818155 | − | 0.574997i | \(-0.194997\pi\) |
−0.574997 | + | 0.818155i | \(0.694997\pi\) | |||||||
\(338\) | 4.18809 | − | 4.18809i | 0.0123908 | − | 0.0123908i | ||||
\(339\) | 134.659i | 0.397223i | ||||||||
\(340\) | 33.3134 | − | 102.927i | 0.0979807 | − | 0.302726i | ||||
\(341\) | 715.758 | 2.09900 | ||||||||
\(342\) | −49.8866 | − | 49.8866i | −0.145867 | − | 0.145867i | ||||
\(343\) | −258.991 | + | 258.991i | −0.755076 | + | 0.755076i | ||||
\(344\) | − | 159.870i | − | 0.464738i | ||||||
\(345\) | −18.8978 | − | 36.9848i | −0.0547762 | − | 0.107202i | ||||
\(346\) | −227.372 | −0.657146 | ||||||||
\(347\) | 253.677 | + | 253.677i | 0.731058 | + | 0.731058i | 0.970829 | − | 0.239771i | \(-0.0770724\pi\) |
−0.239771 | + | 0.970829i | \(0.577072\pi\) | |||||||
\(348\) | −69.7779 | + | 69.7779i | −0.200511 | + | 0.200511i | ||||
\(349\) | − | 162.699i | − | 0.466186i | −0.972454 | − | 0.233093i | \(-0.925115\pi\) | ||
0.972454 | − | 0.233093i | \(-0.0748847\pi\) | |||||||
\(350\) | −144.893 | − | 104.768i | −0.413981 | − | 0.299337i | ||||
\(351\) | −68.3819 | −0.194820 | ||||||||
\(352\) | −61.1270 | − | 61.1270i | −0.173656 | − | 0.173656i | ||||
\(353\) | 19.9049 | − | 19.9049i | 0.0563877 | − | 0.0563877i | −0.678351 | − | 0.734738i | \(-0.737305\pi\) |
0.734738 | + | 0.678351i | \(0.237305\pi\) | |||||||
\(354\) | − | 283.057i | − | 0.799596i | ||||||
\(355\) | 487.612 | − | 249.151i | 1.37356 | − | 0.701833i | ||||
\(356\) | −52.6689 | −0.147946 | ||||||||
\(357\) | −67.0081 | − | 67.0081i | −0.187698 | − | 0.187698i | ||||
\(358\) | 202.276 | − | 202.276i | 0.565016 | − | 0.565016i | ||||
\(359\) | − | 414.391i | − | 1.15429i | −0.816641 | − | 0.577146i | \(-0.804166\pi\) | ||
0.816641 | − | 0.577146i | \(-0.195834\pi\) | |||||||
\(360\) | −40.3648 | − | 13.0645i | −0.112124 | − | 0.0362903i | ||||
\(361\) | 84.4810 | 0.234019 | ||||||||
\(362\) | −119.692 | − | 119.692i | −0.330640 | − | 0.330640i | ||||
\(363\) | 137.823 | − | 137.823i | 0.379677 | − | 0.379677i | ||||
\(364\) | − | 133.109i | − | 0.365685i | ||||||
\(365\) | −81.8387 | + | 252.853i | −0.224215 | + | 0.692748i | ||||
\(366\) | −96.8828 | −0.264707 | ||||||||
\(367\) | 105.693 | + | 105.693i | 0.287991 | + | 0.287991i | 0.836286 | − | 0.548294i | \(-0.184723\pi\) |
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 147.506i | − | 0.399746i | ||||||
\(370\) | −176.545 | − | 345.516i | −0.477150 | − | 0.933828i | ||||
\(371\) | −292.543 | −0.788526 | ||||||||
\(372\) | 114.728 | + | 114.728i | 0.308408 | + | 0.308408i | ||||
\(373\) | −322.018 | + | 322.018i | −0.863319 | + | 0.863319i | −0.991722 | − | 0.128403i | \(-0.959015\pi\) |
0.128403 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(374\) | 233.803i | 0.625142i | ||||||||
\(375\) | 127.857 | + | 174.721i | 0.340952 | + | 0.465924i | ||||
\(376\) | −169.072 | −0.449661 | ||||||||
\(377\) | 265.086 | + | 265.086i | 0.703145 | + | 0.703145i | ||||
\(378\) | −26.2785 | + | 26.2785i | −0.0695199 | + | 0.0695199i | ||||
\(379\) | 46.2839i | 0.122121i | 0.998134 | + | 0.0610605i | \(0.0194483\pi\) | ||||
−0.998134 | + | 0.0610605i | \(0.980552\pi\) | |||||||
\(380\) | −148.078 | + | 75.6621i | −0.389679 | + | 0.199111i | ||||
\(381\) | −391.575 | −1.02776 | ||||||||
\(382\) | 354.419 | + | 354.419i | 0.927798 | + | 0.927798i | ||||
\(383\) | −456.507 | + | 456.507i | −1.19192 | + | 1.19192i | −0.215397 | + | 0.976527i | \(0.569105\pi\) |
−0.976527 | + | 0.215397i | \(0.930895\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 367.645 | + | 118.992i | 0.954922 | + | 0.309071i | ||||
\(386\) | 179.699 | 0.465541 | ||||||||
\(387\) | 119.902 | + | 119.902i | 0.309826 | + | 0.309826i | ||||
\(388\) | 140.092 | − | 140.092i | 0.361063 | − | 0.361063i | ||||
\(389\) | − | 423.277i | − | 1.08812i | −0.839048 | − | 0.544058i | \(-0.816887\pi\) | ||
0.839048 | − | 0.544058i | \(-0.183113\pi\) | |||||||
\(390\) | −49.6320 | + | 153.346i | −0.127262 | + | 0.393194i | ||||
\(391\) | −51.8832 | −0.132693 | ||||||||
\(392\) | 46.8473 | + | 46.8473i | 0.119509 | + | 0.119509i | ||||
\(393\) | −305.884 | + | 305.884i | −0.778331 | + | 0.778331i | ||||
\(394\) | 489.834i | 1.24323i | ||||||||
\(395\) | 265.521 | + | 519.651i | 0.672206 | + | 1.31557i | ||||
\(396\) | 91.6905 | 0.231542 | ||||||||
\(397\) | 114.959 | + | 114.959i | 0.289569 | + | 0.289569i | 0.836910 | − | 0.547341i | \(-0.184360\pi\) |
−0.547341 | + | 0.836910i | \(0.684360\pi\) | |||||||
\(398\) | −201.091 | + | 201.091i | −0.505253 | + | 0.505253i | ||||
\(399\) | 145.661i | 0.365064i | ||||||||
\(400\) | −58.5941 | + | 81.0354i | −0.146485 | + | 0.202588i | ||||
\(401\) | −545.562 | −1.36050 | −0.680252 | − | 0.732978i | \(-0.738130\pi\) | ||||
−0.680252 | + | 0.732978i | \(0.738130\pi\) | |||||||
\(402\) | 73.6343 | + | 73.6343i | 0.183170 | + | 0.183170i | ||||
\(403\) | 435.850 | − | 435.850i | 1.08151 | − | 1.08151i | ||||
\(404\) | 315.235i | 0.780285i | ||||||||
\(405\) | 40.0720 | − | 20.4752i | 0.0989432 | − | 0.0505561i | ||||
\(406\) | 203.740 | 0.501823 | ||||||||
\(407\) | 592.943 | + | 592.943i | 1.45686 | + | 1.45686i | ||||
\(408\) | −37.4760 | + | 37.4760i | −0.0918529 | + | 0.0918529i | ||||
\(409\) | 400.154i | 0.978371i | 0.872180 | + | 0.489185i | \(0.162706\pi\) | ||||
−0.872180 | + | 0.489185i | \(0.837294\pi\) | |||||||
\(410\) | −330.782 | − | 107.061i | −0.806785 | − | 0.261125i | ||||
\(411\) | 59.1637 | 0.143951 | ||||||||
\(412\) | −266.226 | − | 266.226i | −0.646179 | − | 0.646179i | ||||
\(413\) | −413.240 | + | 413.240i | −1.00058 | + | 1.00058i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | −212.486 | + | 656.509i | −0.512015 | + | 1.58195i | ||||
\(416\) | −74.4447 | −0.178954 | ||||||||
\(417\) | 132.144 | + | 132.144i | 0.316891 | + | 0.316891i | ||||
\(418\) | 254.118 | − | 254.118i | 0.607938 | − | 0.607938i | ||||
\(419\) | − | 100.320i | − | 0.239428i | −0.992808 | − | 0.119714i | \(-0.961802\pi\) | ||
0.992808 | − | 0.119714i | \(-0.0381978\pi\) | |||||||
\(420\) | 39.8562 | + | 78.0025i | 0.0948957 | + | 0.185720i | ||||
\(421\) | 115.474 | 0.274286 | 0.137143 | − | 0.990551i | \(-0.456208\pi\) | ||||
0.137143 | + | 0.990551i | \(0.456208\pi\) | |||||||
\(422\) | −56.8261 | − | 56.8261i | −0.134659 | − | 0.134659i | ||||
\(423\) | 126.804 | − | 126.804i | 0.299774 | − | 0.299774i | ||||
\(424\) | 163.612i | 0.385878i | ||||||||
\(425\) | 267.033 | − | 42.9176i | 0.628312 | − | 0.100983i | ||||
\(426\) | −268.257 | −0.629712 | ||||||||
\(427\) | 141.441 | + | 141.441i | 0.331243 | + | 0.331243i | ||||
\(428\) | 29.6049 | − | 29.6049i | 0.0691704 | − | 0.0691704i | ||||
\(429\) | − | 348.331i | − | 0.811961i | ||||||
\(430\) | 355.906 | − | 181.854i | 0.827689 | − | 0.422916i | ||||
\(431\) | 341.266 | 0.791801 | 0.395901 | − | 0.918293i | \(-0.370432\pi\) | ||||
0.395901 | + | 0.918293i | \(0.370432\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −364.495 | + | 364.495i | −0.841791 | + | 0.841791i | −0.989092 | − | 0.147301i | \(-0.952941\pi\) |
0.147301 | + | 0.989092i | \(0.452941\pi\) | |||||||
\(434\) | − | 334.987i | − | 0.771859i | ||||||
\(435\) | −234.714 | − | 75.9679i | −0.539573 | − | 0.174639i | ||||
\(436\) | 0.205367 | 0.000471024 | ||||||||
\(437\) | 56.3912 | + | 56.3912i | 0.129042 | + | 0.129042i | ||||
\(438\) | 92.0645 | − | 92.0645i | 0.210193 | − | 0.210193i | ||||
\(439\) | − | 745.512i | − | 1.69821i | −0.528228 | − | 0.849103i | \(-0.677143\pi\) | ||
0.528228 | − | 0.849103i | \(-0.322857\pi\) | |||||||
\(440\) | 66.5495 | − | 205.615i | 0.151249 | − | 0.467307i | ||||
\(441\) | −70.2710 | −0.159345 | ||||||||
\(442\) | 142.371 | + | 142.371i | 0.322106 | + | 0.322106i | ||||
\(443\) | 426.726 | − | 426.726i | 0.963264 | − | 0.963264i | −0.0360845 | − | 0.999349i | \(-0.511489\pi\) |
0.999349 | + | 0.0360845i | \(0.0114886\pi\) | |||||||
\(444\) | 190.084i | 0.428117i | ||||||||
\(445\) | −59.9116 | − | 117.253i | −0.134633 | − | 0.263489i | ||||
\(446\) | 101.673 | 0.227966 | ||||||||
\(447\) | 182.666 | + | 182.666i | 0.408650 | + | 0.408650i | ||||
\(448\) | −28.6084 | + | 28.6084i | −0.0638581 | + | 0.0638581i | ||||
\(449\) | − | 183.403i | − | 0.408470i | −0.978922 | − | 0.204235i | \(-0.934529\pi\) | ||
0.978922 | − | 0.204235i | \(-0.0654707\pi\) | |||||||
\(450\) | −16.8310 | − | 104.722i | −0.0374021 | − | 0.232716i | ||||
\(451\) | 751.385 | 1.66604 | ||||||||
\(452\) | −109.948 | − | 109.948i | −0.243248 | − | 0.243248i | ||||
\(453\) | −106.998 | + | 106.998i | −0.236199 | + | 0.236199i | ||||
\(454\) | − | 151.663i | − | 0.334060i | ||||||
\(455\) | 296.331 | − | 151.413i | 0.651276 | − | 0.332777i | ||||
\(456\) | 81.4644 | 0.178650 | ||||||||
\(457\) | −68.1150 | − | 68.1150i | −0.149048 | − | 0.149048i | 0.628645 | − | 0.777693i | \(-0.283610\pi\) |
−0.777693 | + | 0.628645i | \(0.783610\pi\) | |||||||
\(458\) | 70.0263 | − | 70.0263i | 0.152896 | − | 0.152896i | ||||
\(459\) | − | 56.2140i | − | 0.122471i | ||||||
\(460\) | 45.6279 | + | 14.7680i | 0.0991911 | + | 0.0321043i | ||||
\(461\) | −386.997 | −0.839472 | −0.419736 | − | 0.907646i | \(-0.637877\pi\) | ||||
−0.419736 | + | 0.907646i | \(0.637877\pi\) | |||||||
\(462\) | −133.861 | − | 133.861i | −0.289742 | − | 0.289742i | ||||
\(463\) | −111.577 | + | 111.577i | −0.240986 | + | 0.240986i | −0.817258 | − | 0.576272i | \(-0.804507\pi\) |
0.576272 | + | 0.817258i | \(0.304507\pi\) | |||||||
\(464\) | − | 113.947i | − | 0.245575i | ||||||
\(465\) | −124.905 | + | 385.914i | −0.268614 | + | 0.829923i | ||||
\(466\) | 8.04723 | 0.0172687 | ||||||||
\(467\) | −8.27939 | − | 8.27939i | −0.0177289 | − | 0.0177289i | 0.698187 | − | 0.715916i | \(-0.253991\pi\) |
−0.715916 | + | 0.698187i | \(0.753991\pi\) | |||||||
\(468\) | 55.8336 | − | 55.8336i | 0.119302 | − | 0.119302i | ||||
\(469\) | − | 215.000i | − | 0.458422i | ||||||
\(470\) | −192.322 | − | 376.393i | −0.409196 | − | 0.800836i | ||||
\(471\) | 198.813 | 0.422108 | ||||||||
\(472\) | 231.115 | + | 231.115i | 0.489651 | + | 0.489651i | ||||
\(473\) | −610.773 | + | 610.773i | −1.29128 | + | 1.29128i | ||||
\(474\) | − | 285.883i | − | 0.603129i | ||||||
\(475\) | −336.881 | − | 243.588i | −0.709224 | − | 0.512817i | ||||
\(476\) | 109.424 | 0.229882 | ||||||||
\(477\) | −122.709 | − | 122.709i | −0.257252 | − | 0.257252i | ||||
\(478\) | 268.560 | − | 268.560i | 0.561842 | − | 0.561842i | ||||
\(479\) | 391.487i | 0.817301i | 0.912691 | + | 0.408651i | \(0.134001\pi\) | ||||
−0.912691 | + | 0.408651i | \(0.865999\pi\) | |||||||
\(480\) | 43.6249 | − | 22.2906i | 0.0908851 | − | 0.0464388i | ||||
\(481\) | 722.128 | 1.50131 | ||||||||
\(482\) | −265.941 | − | 265.941i | −0.551745 | − | 0.551745i | ||||
\(483\) | 29.7049 | − | 29.7049i | 0.0615009 | − | 0.0615009i | ||||
\(484\) | 225.063i | 0.465007i | ||||||||
\(485\) | 471.234 | + | 152.520i | 0.971616 | + | 0.314474i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −282.428 | − | 282.428i | −0.579933 | − | 0.579933i | 0.354951 | − | 0.934885i | \(-0.384497\pi\) |
−0.934885 | + | 0.354951i | \(0.884497\pi\) | |||||||
\(488\) | 79.1045 | − | 79.1045i | 0.162099 | − | 0.162099i | ||||
\(489\) | 138.292i | 0.282807i | ||||||||
\(490\) | −51.0032 | + | 157.582i | −0.104088 | + | 0.321596i | ||||
\(491\) | 15.3095 | 0.0311802 | 0.0155901 | − | 0.999878i | \(-0.495037\pi\) | ||||
0.0155901 | + | 0.999878i | \(0.495037\pi\) | |||||||
\(492\) | 120.439 | + | 120.439i | 0.244794 | + | 0.244794i | ||||
\(493\) | −217.916 | + | 217.916i | −0.442021 | + | 0.442021i | ||||
\(494\) | − | 309.483i | − | 0.626483i | ||||||
\(495\) | 104.299 | + | 204.123i | 0.210705 | + | 0.412370i | ||||
\(496\) | −187.350 | −0.377722 | ||||||||
\(497\) | 391.634 | + | 391.634i | 0.787996 | + | 0.787996i | ||||
\(498\) | 239.037 | − | 239.037i | 0.479993 | − | 0.479993i | ||||
\(499\) | − | 823.731i | − | 1.65076i | −0.564575 | − | 0.825382i | \(-0.690960\pi\) | ||
0.564575 | − | 0.825382i | \(-0.309040\pi\) | |||||||
\(500\) | −247.054 | − | 38.2647i | −0.494109 | − | 0.0765294i | ||||
\(501\) | 395.193 | 0.788808 | ||||||||
\(502\) | 167.641 | + | 167.641i | 0.333947 | + | 0.333947i | ||||
\(503\) | −230.664 | + | 230.664i | −0.458577 | + | 0.458577i | −0.898188 | − | 0.439611i | \(-0.855116\pi\) |
0.439611 | + | 0.898188i | \(0.355116\pi\) | |||||||
\(504\) | − | 42.9127i | − | 0.0851442i | ||||||
\(505\) | −701.784 | + | 358.584i | −1.38967 | + | 0.710067i | ||||
\(506\) | −103.646 | −0.204834 | ||||||||
\(507\) | −5.12934 | − | 5.12934i | −0.0101170 | − | 0.0101170i | ||||
\(508\) | 319.719 | − | 319.719i | 0.629369 | − | 0.629369i | ||||
\(509\) | 879.412i | 1.72772i | 0.503728 | + | 0.863862i | \(0.331961\pi\) | ||||
−0.503728 | + | 0.863862i | \(0.668039\pi\) | |||||||
\(510\) | −126.059 | − | 40.8005i | −0.247175 | − | 0.0800009i | ||||
\(511\) | −268.813 | −0.526053 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −61.0983 | + | 61.0983i | −0.119100 | + | 0.119100i | ||||
\(514\) | 128.478i | 0.249956i | ||||||||
\(515\) | 289.842 | − | 895.512i | 0.562801 | − | 1.73886i | ||||
\(516\) | −195.800 | −0.379457 | ||||||||
\(517\) | 645.931 | + | 645.931i | 1.24938 | + | 1.24938i | ||||
\(518\) | 277.507 | − | 277.507i | 0.535728 | − | 0.535728i | ||||
\(519\) | 278.473i | 0.536557i | ||||||||
\(520\) | −84.6818 | − | 165.731i | −0.162850 | − | 0.318713i | ||||
\(521\) | −207.118 | −0.397540 | −0.198770 | − | 0.980046i | \(-0.563695\pi\) | ||||
−0.198770 | + | 0.980046i | \(0.563695\pi\) | |||||||
\(522\) | 85.4602 | + | 85.4602i | 0.163717 | + | 0.163717i | ||||
\(523\) | 222.354 | − | 222.354i | 0.425151 | − | 0.425151i | −0.461822 | − | 0.886973i | \(-0.652804\pi\) |
0.886973 | + | 0.461822i | \(0.152804\pi\) | |||||||
\(524\) | − | 499.507i | − | 0.953257i | ||||||
\(525\) | −128.314 | + | 177.458i | −0.244407 | + | 0.338014i | ||||
\(526\) | −52.2749 | −0.0993820 | ||||||||
\(527\) | 358.295 | + | 358.295i | 0.679877 | + | 0.679877i | ||||
\(528\) | −74.8650 | + | 74.8650i | −0.141790 | + | 0.141790i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −364.237 | + | 186.111i | −0.687240 | + | 0.351153i | ||||
\(531\) | −346.673 | −0.652867 | ||||||||
\(532\) | −118.931 | − | 118.931i | −0.223555 | − | 0.223555i | ||||
\(533\) | 457.545 | − | 457.545i | 0.858433 | − | 0.858433i | ||||
\(534\) | 64.5060i | 0.120798i | ||||||||
\(535\) | 99.5832 | + | 32.2312i | 0.186137 | + | 0.0602452i | ||||
\(536\) | −120.244 | −0.224336 | ||||||||
\(537\) | −247.736 | − | 247.736i | −0.461333 | − | 0.461333i | ||||
\(538\) | 114.873 | − | 114.873i | 0.213518 | − | 0.213518i | ||||
\(539\) | − | 357.955i | − | 0.664109i | ||||||
\(540\) | −16.0007 | + | 49.4366i | −0.0296309 | + | 0.0915493i | ||||
\(541\) | 209.995 | 0.388160 | 0.194080 | − | 0.980986i | \(-0.437828\pi\) | ||||
0.194080 | + | 0.980986i | \(0.437828\pi\) | |||||||
\(542\) | 263.414 | + | 263.414i | 0.486004 | + | 0.486004i | ||||
\(543\) | −146.592 | + | 146.592i | −0.269967 | + | 0.269967i | ||||
\(544\) | − | 61.1980i | − | 0.112496i | ||||||
\(545\) | 0.233607 | + | 0.457192i | 0.000428637 | + | 0.000838884i | ||||
\(546\) | −163.025 | −0.298580 | ||||||||
\(547\) | −56.6666 | − | 56.6666i | −0.103595 | − | 0.103595i | 0.653409 | − | 0.757005i | \(-0.273338\pi\) |
−0.757005 | + | 0.653409i | \(0.773338\pi\) | |||||||
\(548\) | −48.3070 | + | 48.3070i | −0.0881514 | + | 0.0881514i | ||||
\(549\) | 118.657i | 0.216132i | ||||||||
\(550\) | 533.446 | − | 85.7355i | 0.969901 | − | 0.155883i | ||||
\(551\) | 473.702 | 0.859713 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −417.366 | + | 417.366i | −0.754731 | + | 0.754731i | ||||
\(554\) | − | 495.271i | − | 0.893990i | ||||||
\(555\) | −423.169 | + | 216.223i | −0.762468 | + | 0.389591i | ||||
\(556\) | −215.789 | −0.388111 | ||||||||
\(557\) | −51.0912 | − | 51.0912i | −0.0917256 | − | 0.0917256i | 0.659755 | − | 0.751481i | \(-0.270660\pi\) |
−0.751481 | + | 0.659755i | \(0.770660\pi\) | |||||||
\(558\) | 140.512 | − | 140.512i | 0.251814 | − | 0.251814i | ||||
\(559\) | 743.842i | 1.33067i | ||||||||
\(560\) | −96.2312 | − | 31.1463i | −0.171841 | − | 0.0556184i | ||||
\(561\) | 286.349 | 0.510426 | ||||||||
\(562\) | −503.134 | − | 503.134i | −0.895257 | − | 0.895257i | ||||
\(563\) | −189.263 | + | 189.263i | −0.336169 | + | 0.336169i | −0.854923 | − | 0.518755i | \(-0.826396\pi\) |
0.518755 | + | 0.854923i | \(0.326396\pi\) | |||||||
\(564\) | 207.071i | 0.367147i | ||||||||
\(565\) | 119.702 | − | 369.837i | 0.211862 | − | 0.654579i | ||||
\(566\) | −669.603 | −1.18304 | ||||||||
\(567\) | 32.1845 | + | 32.1845i | 0.0567628 | + | 0.0567628i | ||||
\(568\) | 219.031 | − | 219.031i | 0.385618 | − | 0.385618i | ||||
\(569\) | 743.025i | 1.30584i | 0.757426 | + | 0.652921i | \(0.226457\pi\) | ||||
−0.757426 | + | 0.652921i | \(0.773543\pi\) | |||||||
\(570\) | 92.6668 | + | 181.358i | 0.162573 | + | 0.318172i | ||||
\(571\) | 630.678 | 1.10452 | 0.552258 | − | 0.833673i | \(-0.313766\pi\) | ||||
0.552258 | + | 0.833673i | \(0.313766\pi\) | |||||||
\(572\) | 284.411 | + | 284.411i | 0.497223 | + | 0.497223i | ||||
\(573\) | 434.072 | − | 434.072i | 0.757544 | − | 0.757544i | ||||
\(574\) | − | 351.661i | − | 0.612649i | ||||||
\(575\) | 19.0255 | + | 118.377i | 0.0330879 | + | 0.205872i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 87.5513 | + | 87.5513i | 0.151735 | + | 0.151735i | 0.778893 | − | 0.627157i | \(-0.215782\pi\) |
−0.627157 | + | 0.778893i | \(0.715782\pi\) | |||||||
\(578\) | 171.963 | − | 171.963i | 0.297513 | − | 0.297513i | ||||
\(579\) | − | 220.085i | − | 0.380112i | ||||||
\(580\) | 253.671 | − | 129.616i | 0.437364 | − | 0.223476i | ||||
\(581\) | −697.948 | −1.20129 | ||||||||
\(582\) | −171.578 | − | 171.578i | −0.294807 | − | 0.294807i | ||||
\(583\) | 625.070 | − | 625.070i | 1.07216 | − | 1.07216i | ||||
\(584\) | 150.341i | 0.257433i | ||||||||
\(585\) | 187.809 | + | 60.7865i | 0.321041 | + | 0.103909i | ||||
\(586\) | −207.820 | −0.354642 | ||||||||
\(587\) | −358.680 | − | 358.680i | −0.611039 | − | 0.611039i | 0.332178 | − | 0.943217i | \(-0.392217\pi\) |
−0.943217 | + | 0.332178i | \(0.892217\pi\) | |||||||
\(588\) | 57.3760 | − | 57.3760i | 0.0975783 | − | 0.0975783i | ||||
\(589\) | − | 778.854i | − | 1.32233i | ||||||
\(590\) | −251.617 | + | 777.410i | −0.426470 | + | 1.31764i | ||||
\(591\) | 599.922 | 1.01510 | ||||||||
\(592\) | −155.203 | − | 155.203i | −0.262167 | − | 0.262167i | ||||
\(593\) | 388.968 | − | 388.968i | 0.655933 | − | 0.655933i | −0.298482 | − | 0.954415i | \(-0.596480\pi\) |
0.954415 | + | 0.298482i | \(0.0964804\pi\) | |||||||
\(594\) | − | 112.297i | − | 0.189053i | ||||||
\(595\) | 124.471 | + | 243.602i | 0.209195 | + | 0.409414i | ||||
\(596\) | −298.293 | −0.500492 | ||||||||
\(597\) | 246.285 | + | 246.285i | 0.412538 | + | 0.412538i | ||||
\(598\) | −63.1136 | + | 63.1136i | −0.105541 | + | 0.105541i | ||||
\(599\) | 430.104i | 0.718036i | 0.933331 | + | 0.359018i | \(0.116888\pi\) | ||||
−0.933331 | + | 0.359018i | \(0.883112\pi\) | |||||||
\(600\) | 99.2477 | + | 71.7628i | 0.165413 | + | 0.119605i | ||||
\(601\) | 613.240 | 1.02037 | 0.510183 | − | 0.860066i | \(-0.329578\pi\) | ||||
0.510183 | + | 0.860066i | \(0.329578\pi\) | |||||||
\(602\) | 285.852 | + | 285.852i | 0.474837 | + | 0.474837i | ||||
\(603\) | 90.1833 | − | 90.1833i | 0.149558 | − | 0.149558i | ||||
\(604\) | − | 174.727i | − | 0.289284i | ||||||
\(605\) | −501.041 | + | 256.013i | −0.828168 | + | 0.423161i | ||||
\(606\) | 386.083 | 0.637100 | ||||||||
\(607\) | −332.149 | − | 332.149i | −0.547198 | − | 0.547198i | 0.378432 | − | 0.925629i | \(-0.376464\pi\) |
−0.925629 | + | 0.378432i | \(0.876464\pi\) | |||||||
\(608\) | −66.5154 | + | 66.5154i | −0.109400 | + | 0.109400i | ||||
\(609\) | − | 249.530i | − | 0.409737i | ||||||
\(610\) | 266.086 | + | 86.1218i | 0.436207 | + | 0.141183i | ||||
\(611\) | 786.660 | 1.28750 | ||||||||
\(612\) | 45.8985 | + | 45.8985i | 0.0749976 | + | 0.0749976i | ||||
\(613\) | −766.001 | + | 766.001i | −1.24959 | + | 1.24959i | −0.293693 | + | 0.955900i | \(0.594884\pi\) |
−0.955900 | + | 0.293693i | \(0.905116\pi\) | |||||||
\(614\) | 31.9828i | 0.0520893i | ||||||||
\(615\) | −131.123 | + | 405.123i | −0.213207 | + | 0.658737i | ||||
\(616\) | 218.593 | 0.354859 | ||||||||
\(617\) | 255.443 | + | 255.443i | 0.414008 | + | 0.414008i | 0.883132 | − | 0.469124i | \(-0.155430\pi\) |
−0.469124 | + | 0.883132i | \(0.655430\pi\) | |||||||
\(618\) | −326.058 | + | 326.058i | −0.527603 | + | 0.527603i | ||||
\(619\) | − | 750.831i | − | 1.21297i | −0.795093 | − | 0.606487i | \(-0.792578\pi\) | ||
0.795093 | − | 0.606487i | \(-0.207422\pi\) | |||||||
\(620\) | −213.113 | − | 417.083i | −0.343730 | − | 0.672714i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 430.485 | + | 430.485i | 0.692098 | + | 0.692098i | ||||
\(623\) | 94.1735 | − | 94.1735i | 0.151161 | − | 0.151161i | ||||
\(624\) | 91.1758i | 0.146115i | ||||||||
\(625\) | −195.842 | − | 593.524i | −0.313346 | − | 0.949639i | ||||
\(626\) | −431.125 | −0.688699 | ||||||||
\(627\) | −311.230 | − | 311.230i | −0.496379 | − | 0.496379i | ||||
\(628\) | −162.330 | + | 162.330i | −0.258488 | + | 0.258488i | ||||
\(629\) | 593.632i | 0.943772i | ||||||||
\(630\) | 95.5331 | − | 48.8137i | 0.151640 | − | 0.0774820i | ||||
\(631\) | 695.761 | 1.10263 | 0.551316 | − | 0.834297i | \(-0.314126\pi\) | ||||
0.551316 | + | 0.834297i | \(0.314126\pi\) | |||||||
\(632\) | 233.423 | + | 233.423i | 0.369340 | + | 0.369340i | ||||
\(633\) | −69.5975 | + | 69.5975i | −0.109949 | + | 0.109949i | ||||
\(634\) | − | 148.987i | − | 0.234996i | ||||||
\(635\) | 1075.45 | + | 348.082i | 1.69362 | + | 0.548160i | ||||
\(636\) | 200.383 | 0.315068 | ||||||||
\(637\) | −217.971 | − | 217.971i | −0.342184 | − | 0.342184i | ||||
\(638\) | −435.327 | + | 435.327i | −0.682330 | + | 0.682330i | ||||
\(639\) | 328.547i | 0.514158i | ||||||||
\(640\) | −17.4194 | + | 53.8198i | −0.0272177 | + | 0.0840934i | ||||
\(641\) | −108.436 | −0.169168 | −0.0845838 | − | 0.996416i | \(-0.526956\pi\) | ||||
−0.0845838 | + | 0.996416i | \(0.526956\pi\) | |||||||
\(642\) | −36.2585 | − | 36.2585i | −0.0564774 | − | 0.0564774i | ||||
\(643\) | 748.186 | − | 748.186i | 1.16359 | − | 1.16359i | 0.179901 | − | 0.983685i | \(-0.442422\pi\) |
0.983685 | − | 0.179901i | \(-0.0575778\pi\) | |||||||
\(644\) | 48.5080i | 0.0753229i | ||||||||
\(645\) | −222.725 | − | 435.894i | −0.345310 | − | 0.675805i | ||||
\(646\) | 254.413 | 0.393829 | ||||||||
\(647\) | 175.618 | + | 175.618i | 0.271435 | + | 0.271435i | 0.829678 | − | 0.558243i | \(-0.188524\pi\) |
−0.558243 | + | 0.829678i | \(0.688524\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 1765.92i | − | 2.72099i | ||||||
\(650\) | 272.626 | − | 377.041i | 0.419425 | − | 0.580063i | ||||
\(651\) | −410.273 | −0.630220 | ||||||||
\(652\) | −112.915 | − | 112.915i | −0.173183 | − | 0.173183i | ||||
\(653\) | −752.118 | + | 752.118i | −1.15179 | + | 1.15179i | −0.165595 | + | 0.986194i | \(0.552954\pi\) |
−0.986194 | + | 0.165595i | \(0.947046\pi\) | |||||||
\(654\) | − | 0.251522i | − | 0.000384590i | ||||||
\(655\) | 1112.01 | − | 568.195i | 1.69773 | − | 0.867473i | ||||
\(656\) | −196.675 | −0.299810 | ||||||||
\(657\) | −112.755 | − | 112.755i | −0.171622 | − | 0.171622i | ||||
\(658\) | 302.306 | − | 302.306i | 0.459432 | − | 0.459432i | ||||
\(659\) | − | 651.736i | − | 0.988977i | −0.869184 | − | 0.494488i | \(-0.835355\pi\) | ||
0.869184 | − | 0.494488i | \(-0.164645\pi\) | |||||||
\(660\) | −251.826 | − | 81.5062i | −0.381554 | − | 0.123494i | ||||
\(661\) | −104.721 | −0.158428 | −0.0792141 | − | 0.996858i | \(-0.525241\pi\) | ||||
−0.0792141 | + | 0.996858i | \(0.525241\pi\) | |||||||
\(662\) | 316.884 | + | 316.884i | 0.478677 | + | 0.478677i | ||||
\(663\) | 174.368 | − | 174.368i | 0.262999 | − | 0.262999i | ||||
\(664\) | 390.345i | 0.587870i | ||||||||
\(665\) | 129.482 | − | 400.054i | 0.194709 | − | 0.601585i | ||||
\(666\) | 232.805 | 0.349556 | ||||||||
\(667\) | −96.6032 | − | 96.6032i | −0.144832 | − | 0.144832i | ||||
\(668\) | −322.673 | + | 322.673i | −0.483044 | + | 0.483044i | ||||
\(669\) | − | 124.523i | − | 0.186134i | ||||||
\(670\) | −136.779 | − | 267.691i | −0.204148 | − | 0.399538i | ||||
\(671\) | −604.427 | −0.900786 | ||||||||
\(672\) | 35.0380 | + | 35.0380i | 0.0521399 | + | 0.0521399i | ||||
\(673\) | 175.443 | − | 175.443i | 0.260688 | − | 0.260688i | −0.564646 | − | 0.825333i | \(-0.690987\pi\) |
0.825333 | + | 0.564646i | \(0.190987\pi\) | |||||||
\(674\) | 163.888i | 0.243158i | ||||||||
\(675\) | −128.258 | + | 20.6136i | −0.190012 | + | 0.0305387i | ||||
\(676\) | 8.37618 | 0.0123908 | ||||||||
\(677\) | 366.104 | + | 366.104i | 0.540775 | + | 0.540775i | 0.923756 | − | 0.382981i | \(-0.125103\pi\) |
−0.382981 | + | 0.923756i | \(0.625103\pi\) | |||||||
\(678\) | −134.659 | + | 134.659i | −0.198612 | + | 0.198612i | ||||
\(679\) | 500.978i | 0.737818i | ||||||||
\(680\) | 136.240 | − | 69.6135i | 0.200354 | − | 0.102373i | ||||
\(681\) | −185.749 | −0.272758 | ||||||||
\(682\) | 715.758 | + | 715.758i | 1.04950 | + | 1.04950i | ||||
\(683\) | −397.528 | + | 397.528i | −0.582032 | + | 0.582032i | −0.935461 | − | 0.353429i | \(-0.885016\pi\) |
0.353429 | + | 0.935461i | \(0.385016\pi\) | |||||||
\(684\) | − | 99.7732i | − | 0.145867i | ||||||
\(685\) | −162.492 | − | 52.5923i | −0.237214 | − | 0.0767770i | ||||
\(686\) | −517.982 | −0.755076 | ||||||||
\(687\) | −85.7644 | − | 85.7644i | −0.124839 | − | 0.124839i | ||||
\(688\) | 159.870 | − | 159.870i | 0.232369 | − | 0.232369i | ||||
\(689\) | − | 761.254i | − | 1.10487i | ||||||
\(690\) | 18.0870 | − | 55.8826i | 0.0262131 | − | 0.0809892i | ||||
\(691\) | −827.604 | −1.19769 | −0.598846 | − | 0.800865i | \(-0.704374\pi\) | ||||
−0.598846 | + | 0.800865i | \(0.704374\pi\) | |||||||
\(692\) | −227.372 | − | 227.372i | −0.328573 | − | 0.328573i | ||||
\(693\) | −163.945 | + | 163.945i | −0.236573 | + | 0.236573i | ||||
\(694\) | 507.354i | 0.731058i | ||||||||
\(695\) | −245.463 | − | 480.395i | −0.353184 | − | 0.691216i | ||||
\(696\) | −139.556 | −0.200511 | ||||||||
\(697\) | 376.129 | + | 376.129i | 0.539640 | + | 0.539640i | ||||
\(698\) | 162.699 | − | 162.699i | 0.233093 | − | 0.233093i | ||||
\(699\) | − | 9.85581i | − | 0.0140999i | ||||||
\(700\) | −40.1256 | − | 249.661i | −0.0573223 | − | 0.356659i | ||||
\(701\) | −1107.02 | −1.57920 | −0.789600 | − | 0.613621i | \(-0.789712\pi\) | ||||
−0.789600 | + | 0.613621i | \(0.789712\pi\) | |||||||
\(702\) | −68.3819 | − | 68.3819i | −0.0974101 | − | 0.0974101i | ||||
\(703\) | 645.212 | − | 645.212i | 0.917798 | − | 0.917798i | ||||
\(704\) | − | 122.254i | − | 0.173656i | ||||||
\(705\) | −460.985 | + | 235.545i | −0.653880 | + | 0.334107i | ||||
\(706\) | 39.8097 | 0.0563877 | ||||||||
\(707\) | −563.649 | − | 563.649i | −0.797241 | − | 0.797241i | ||||
\(708\) | 283.057 | − | 283.057i | 0.399798 | − | 0.399798i | ||||
\(709\) | 369.641i | 0.521356i | 0.965426 | + | 0.260678i | \(0.0839460\pi\) | ||||
−0.965426 | + | 0.260678i | \(0.916054\pi\) | |||||||
\(710\) | 736.763 | + | 238.461i | 1.03769 | + | 0.335861i | ||||
\(711\) | −350.134 | −0.492453 | ||||||||
\(712\) | −52.6689 | − | 52.6689i | −0.0739732 | − | 0.0739732i | ||||
\(713\) | −158.834 | + | 158.834i | −0.222768 | + | 0.222768i | ||||
\(714\) | − | 134.016i | − | 0.187698i | ||||||
\(715\) | −309.641 | + | 956.684i | −0.433065 | + | 1.33802i | ||||
\(716\) | 404.551 | 0.565016 | ||||||||
\(717\) | −328.918 | − | 328.918i | −0.458742 | − | 0.458742i | ||||
\(718\) | 414.391 | − | 414.391i | 0.577146 | − | 0.577146i | ||||
\(719\) | 700.854i | 0.974762i | 0.873189 | + | 0.487381i | \(0.162048\pi\) | ||||
−0.873189 | + | 0.487381i | \(0.837952\pi\) | |||||||
\(720\) | −27.3003 | − | 53.4293i | −0.0379171 | − | 0.0742074i | ||||
\(721\) | 952.037 | 1.32044 | ||||||||
\(722\) | 84.4810 | + | 84.4810i | 0.117010 | + | 0.117010i | ||||
\(723\) | −325.710 | + | 325.710i | −0.450498 | + | 0.450498i | ||||
\(724\) | − | 239.384i | − | 0.330640i | ||||||
\(725\) | 577.108 | + | 417.288i | 0.796011 | + | 0.575570i | ||||
\(726\) | 275.645 | 0.379677 | ||||||||
\(727\) | −160.008 | − | 160.008i | −0.220093 | − | 0.220093i | 0.588445 | − | 0.808538i | \(-0.299740\pi\) |
−0.808538 | + | 0.588445i | \(0.799740\pi\) | |||||||
\(728\) | 133.109 | − | 133.109i | 0.182842 | − | 0.182842i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −334.692 | + | 171.014i | −0.458482 | + | 0.234266i | ||||
\(731\) | −611.483 | −0.836502 | ||||||||
\(732\) | −96.8828 | − | 96.8828i | −0.132354 | − | 0.132354i | ||||
\(733\) | −104.240 | + | 104.240i | −0.142210 | + | 0.142210i | −0.774628 | − | 0.632417i | \(-0.782063\pi\) |
0.632417 | + | 0.774628i | \(0.282063\pi\) | |||||||
\(734\) | 211.386i | 0.287991i | ||||||||
\(735\) | 192.998 | + | 62.4659i | 0.262582 | + | 0.0849876i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 459.386 | + | 459.386i | 0.623319 | + | 0.623319i | ||||
\(738\) | 147.506 | − | 147.506i | 0.199873 | − | 0.199873i | ||||
\(739\) | 761.948i | 1.03105i | 0.856874 | + | 0.515526i | \(0.172403\pi\) | ||||
−0.856874 | + | 0.515526i | \(0.827597\pi\) | |||||||
\(740\) | 168.971 | − | 522.062i | 0.228339 | − | 0.705489i | ||||
\(741\) | −379.037 | −0.511521 | ||||||||
\(742\) | −292.543 | − | 292.543i | −0.394263 | − | 0.394263i | ||||
\(743\) | −222.730 | + | 222.730i | −0.299772 | + | 0.299772i | −0.840924 | − | 0.541153i | \(-0.817988\pi\) |
0.541153 | + | 0.840924i | \(0.317988\pi\) | |||||||
\(744\) | 229.456i | 0.308408i | ||||||||
\(745\) | −339.312 | − | 664.066i | −0.455452 | − | 0.891364i | ||||
\(746\) | −644.036 | −0.863319 | ||||||||
\(747\) | −292.759 | − | 292.759i | −0.391913 | − | 0.391913i | ||||
\(748\) | −233.803 | + | 233.803i | −0.312571 | + | 0.312571i | ||||
\(749\) | 105.869i | 0.141347i | ||||||||
\(750\) | −46.8645 | + | 302.578i | −0.0624860 | + | 0.403438i | ||||
\(751\) | −276.810 | −0.368589 | −0.184294 | − | 0.982871i | \(-0.559000\pi\) | ||||
−0.184294 | + | 0.982871i | \(0.559000\pi\) | |||||||
\(752\) | −169.072 | − | 169.072i | −0.224830 | − | 0.224830i | ||||
\(753\) | 205.318 | − | 205.318i | 0.272666 | − | 0.272666i | ||||
\(754\) | 530.172i | 0.703145i | ||||||||
\(755\) | 388.982 | − | 198.755i | 0.515208 | − | 0.263251i | ||||
\(756\) | −52.5571 | −0.0695199 | ||||||||
\(757\) | −762.159 | − | 762.159i | −1.00681 | − | 1.00681i | −0.999977 | − | 0.00683824i | \(-0.997823\pi\) |
−0.00683824 | − | 0.999977i | \(-0.502177\pi\) | |||||||
\(758\) | −46.2839 | + | 46.2839i | −0.0610605 | + | 0.0610605i | ||||
\(759\) | 126.940i | 0.167246i | ||||||||
\(760\) | −223.740 | − | 72.4160i | −0.294395 | − | 0.0952842i | ||||
\(761\) | 458.239 | 0.602153 | 0.301077 | − | 0.953600i | \(-0.402654\pi\) | ||||
0.301077 | + | 0.953600i | \(0.402654\pi\) | |||||||
\(762\) | −391.575 | − | 391.575i | −0.513878 | − | 0.513878i | ||||
\(763\) | −0.367201 | + | 0.367201i | −0.000481260 | + | 0.000481260i | ||||
\(764\) | 708.837i | 0.927798i | ||||||||
\(765\) | −49.9702 | + | 154.390i | −0.0653205 | + | 0.201818i | ||||
\(766\) | −913.014 | −1.19192 | ||||||||
\(767\) | −1075.33 | − | 1075.33i | −1.40200 | − | 1.40200i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 493.914i | 0.642281i | 0.947032 | + | 0.321141i | \(0.104066\pi\) | ||||
−0.947032 | + | 0.321141i | \(0.895934\pi\) | |||||||
\(770\) | 248.653 | + | 486.638i | 0.322926 | + | 0.631997i | ||||
\(771\) | 157.352 | 0.204088 | ||||||||
\(772\) | 179.699 | + | 179.699i | 0.232770 | + | 0.232770i | ||||
\(773\) | −429.285 | + | 429.285i | −0.555349 | + | 0.555349i | −0.927980 | − | 0.372631i | \(-0.878456\pi\) |
0.372631 | + | 0.927980i | \(0.378456\pi\) | |||||||
\(774\) | 239.805i | 0.309826i | ||||||||
\(775\) | 686.100 | − | 948.873i | 0.885290 | − | 1.22435i | ||||
\(776\) | 280.185 | 0.361063 | ||||||||
\(777\) | −339.876 | − | 339.876i | −0.437420 | − | 0.437420i | ||||
\(778\) | 423.277 | − | 423.277i | 0.544058 | − | 0.544058i | ||||
\(779\) | − | 817.621i | − | 1.04958i | ||||||
\(780\) | −202.978 | + | 103.714i | −0.260228 | + | 0.132966i | ||||
\(781\) | −1673.59 | −2.14288 | ||||||||
\(782\) | −51.8832 | − | 51.8832i | −0.0663467 | − | 0.0663467i | ||||
\(783\) | 104.667 | − | 104.667i | 0.133674 | − | 0.133674i | ||||
\(784\) | 93.6947i | 0.119509i | ||||||||
\(785\) | −546.036 | − | 176.730i | −0.695587 | − | 0.225134i | ||||
\(786\) | −611.768 | −0.778331 | ||||||||
\(787\) | 599.373 | + | 599.373i | 0.761592 | + | 0.761592i | 0.976610 | − | 0.215018i | \(-0.0689809\pi\) |
−0.215018 | + | 0.976610i | \(0.568981\pi\) | |||||||
\(788\) | −489.834 | + | 489.834i | −0.621617 | + | 0.621617i | ||||
\(789\) | 64.0234i | 0.0811450i | ||||||||
\(790\) | −254.130 | + | 785.172i | −0.321683 | + | 0.993889i | ||||
\(791\) | 393.181 | 0.497068 | ||||||||
\(792\) | 91.6905 | + | 91.6905i | 0.115771 | + | 0.115771i | ||||
\(793\) | −368.057 | + | 368.057i | −0.464132 | + | 0.464132i | ||||
\(794\) | 229.918i | 0.289569i | ||||||||
\(795\) | 227.938 | + | 446.097i | 0.286715 | + | 0.561129i | ||||
\(796\) | −402.182 | −0.505253 | ||||||||
\(797\) | −453.375 | − | 453.375i | −0.568853 | − | 0.568853i | 0.362954 | − | 0.931807i | \(-0.381768\pi\) |
−0.931807 | + | 0.362954i | \(0.881768\pi\) | |||||||
\(798\) | −145.661 | + | 145.661i | −0.182532 | + | 0.182532i | ||||
\(799\) | 646.681i | 0.809363i | ||||||||
\(800\) | −139.629 | + | 22.4413i | −0.174537 | + | 0.0280516i | ||||
\(801\) | 79.0034 | 0.0986310 | ||||||||
\(802\) | −545.562 | − | 545.562i | −0.680252 | − | 0.680252i | ||||
\(803\) | 574.367 | − | 574.367i | 0.715276 | − | 0.715276i | ||||
\(804\) | 147.269i | 0.183170i | ||||||||
\(805\) | −107.990 | + | 55.1784i | −0.134148 | + | 0.0685446i | ||||
\(806\) | 871.701 | 1.08151 | ||||||||
\(807\) | −140.690 | − | 140.690i | −0.174337 | − | 0.174337i | ||||
\(808\) | −315.235 | + | 315.235i | −0.390143 | + | 0.390143i | ||||
\(809\) | 495.664i | 0.612687i | 0.951921 | + | 0.306344i | \(0.0991057\pi\) | ||||
−0.951921 | + | 0.306344i | \(0.900894\pi\) | |||||||
\(810\) | 60.5472 | + | 19.5968i | 0.0747497 | + | 0.0241936i | ||||
\(811\) | −360.435 | −0.444432 | −0.222216 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222216 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(812\) | 203.740 | + | 203.740i | 0.250911 | + | 0.250911i | ||||
\(813\) | 322.615 | − | 322.615i | 0.396820 | − | 0.396820i | ||||
\(814\) | 1185.89i | 1.45686i | ||||||||
\(815\) | 122.932 | − | 379.817i | 0.150837 | − | 0.466033i | ||||
\(816\) | −74.9520 | −0.0918529 | ||||||||
\(817\) | 664.614 | + | 664.614i | 0.813481 | + | 0.813481i | ||||
\(818\) | −400.154 | + | 400.154i | −0.489185 | + | 0.489185i | ||||
\(819\) | 199.664i | 0.243790i | ||||||||
\(820\) | −223.721 | − | 437.843i | −0.272830 | − | 0.533955i | ||||
\(821\) | −1487.19 | −1.81144 | −0.905720 | − | 0.423876i | \(-0.860669\pi\) | ||||
−0.905720 | + | 0.423876i | \(0.860669\pi\) | |||||||
\(822\) | 59.1637 | + | 59.1637i | 0.0719753 | + | 0.0719753i | ||||
\(823\) | −474.095 | + | 474.095i | −0.576057 | + | 0.576057i | −0.933814 | − | 0.357758i | \(-0.883541\pi\) |
0.357758 | + | 0.933814i | \(0.383541\pi\) | |||||||
\(824\) | − | 532.451i | − | 0.646179i | ||||||
\(825\) | −105.004 | − | 653.335i | −0.127278 | − | 0.791921i | ||||
\(826\) | −826.480 | −1.00058 | ||||||||
\(827\) | −120.262 | − | 120.262i | −0.145420 | − | 0.145420i | 0.630649 | − | 0.776069i | \(-0.282789\pi\) |
−0.776069 | + | 0.630649i | \(0.782789\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 124.989i | − | 0.150771i | −0.997154 | − | 0.0753853i | \(-0.975981\pi\) | ||
0.997154 | − | 0.0753853i | \(-0.0240187\pi\) | |||||||
\(830\) | −868.996 | + | 444.023i | −1.04698 | + | 0.534967i | ||||
\(831\) | −606.580 | −0.729940 | ||||||||
\(832\) | −74.4447 | − | 74.4447i | −0.0894768 | − | 0.0894768i | ||||
\(833\) | 179.185 | − | 179.185i | 0.215108 | − | 0.215108i | ||||
\(834\) | 264.287i | 0.316891i | ||||||||
\(835\) | −1085.39 | − | 351.298i | −1.29987 | − | 0.420716i | ||||
\(836\) | 508.236 | 0.607938 | ||||||||
\(837\) | −172.092 | − | 172.092i | −0.205606 | − | 0.205606i | ||||
\(838\) | 100.320 | − | 100.320i | 0.119714 | − | 0.119714i | ||||
\(839\) | 489.898i | 0.583907i | 0.956432 | + | 0.291954i | \(0.0943053\pi\) | ||||
−0.956432 | + | 0.291954i | \(0.905695\pi\) | |||||||
\(840\) | −38.1463 | + | 117.859i | −0.0454122 | + | 0.140308i | ||||
\(841\) | 29.5068 | 0.0350854 | ||||||||
\(842\) | 115.474 | + | 115.474i | 0.137143 | + | 0.137143i | ||||
\(843\) | −616.211 | + | 616.211i | −0.730974 | + | 0.730974i | ||||
\(844\) | − | 113.652i | − | 0.134659i | ||||||
\(845\) | 9.52801 | + | 18.6472i | 0.0112758 | + | 0.0220677i | ||||
\(846\) | 253.609 | 0.299774 | ||||||||
\(847\) | −402.420 | − | 402.420i | −0.475112 | − | 0.475112i | ||||
\(848\) | −163.612 | + | 163.612i | −0.192939 | + | 0.192939i | ||||
\(849\) | 820.093i | 0.965952i | ||||||||
\(850\) | 309.950 | + | 224.115i | 0.364647 | + | 0.263665i | ||||
\(851\) | −263.160 | −0.309236 | ||||||||
\(852\) | −268.257 | − | 268.257i | −0.314856 | − | 0.314856i | ||||
\(853\) | −223.302 | + | 223.302i | −0.261785 | + | 0.261785i | −0.825779 | − | 0.563994i | \(-0.809264\pi\) |
0.563994 | + | 0.825779i | \(0.309264\pi\) | |||||||
\(854\) | 282.882i | 0.331243i | ||||||||
\(855\) | 222.117 | − | 113.493i | 0.259786 | − | 0.132741i | ||||
\(856\) | 59.2099 | 0.0691704 | ||||||||
\(857\) | −573.623 | − | 573.623i | −0.669338 | − | 0.669338i | 0.288225 | − | 0.957563i | \(-0.406935\pi\) |
−0.957563 | + | 0.288225i | \(0.906935\pi\) | |||||||
\(858\) | 348.331 | − | 348.331i | 0.405981 | − | 0.405981i | ||||
\(859\) | − | 1232.45i | − | 1.43475i | −0.696686 | − | 0.717376i | \(-0.745343\pi\) | ||
0.696686 | − | 0.717376i | \(-0.254657\pi\) | |||||||
\(860\) | 537.760 | + | 174.052i | 0.625303 | + | 0.202386i | ||||
\(861\) | −430.695 | −0.500226 | ||||||||
\(862\) | 341.266 | + | 341.266i | 0.395901 | + | 0.395901i | ||||
\(863\) | −426.752 | + | 426.752i | −0.494498 | + | 0.494498i | −0.909720 | − | 0.415222i | \(-0.863704\pi\) |
0.415222 | + | 0.909720i | \(0.363704\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 247.543 | − | 764.821i | 0.286176 | − | 0.884186i | ||||
\(866\) | −728.991 | −0.841791 | ||||||||
\(867\) | −210.610 | − | 210.610i | −0.242918 | − | 0.242918i | ||||
\(868\) | 334.987 | − | 334.987i | 0.385929 | − | 0.385929i | ||||
\(869\) | − | 1783.55i | − | 2.05242i | ||||||
\(870\) | −158.747 | − | 310.682i | −0.182467 | − | 0.357106i | ||||
\(871\) | 559.472 | 0.642333 | ||||||||
\(872\) | 0.205367 | + | 0.205367i | 0.000235512 | + | 0.000235512i | ||||
\(873\) | −210.139 | + | 210.139i | −0.240709 | + | 0.240709i | ||||
\(874\) | 112.782i | 0.129042i | ||||||||
\(875\) | 510.158 | − | 373.321i | 0.583038 | − | 0.426653i | ||||
\(876\) | 184.129 | 0.210193 | ||||||||
\(877\) | −606.515 | − | 606.515i | −0.691579 | − | 0.691579i | 0.271000 | − | 0.962579i | \(-0.412646\pi\) |
−0.962579 | + | 0.271000i | \(0.912646\pi\) | |||||||
\(878\) | 745.512 | − | 745.512i | 0.849103 | − | 0.849103i | ||||
\(879\) | 254.526i | 0.289564i | ||||||||
\(880\) | 272.164 | − | 139.065i | 0.309278 | − | 0.158029i | ||||
\(881\) | −1194.70 | −1.35607 | −0.678035 | − | 0.735030i | \(-0.737168\pi\) | ||||
−0.678035 | + | 0.735030i | \(0.737168\pi\) | |||||||
\(882\) | −70.2710 | − | 70.2710i | −0.0796723 | − | 0.0796723i | ||||
\(883\) | −993.400 | + | 993.400i | −1.12503 | + | 1.12503i | −0.134054 | + | 0.990974i | \(0.542799\pi\) |
−0.990974 | + | 0.134054i | \(0.957201\pi\) | |||||||
\(884\) | 284.742i | 0.322106i | ||||||||
\(885\) | 952.129 | + | 308.167i | 1.07585 | + | 0.348211i | ||||
\(886\) | 853.452 | 0.963264 | ||||||||
\(887\) | 1102.52 | + | 1102.52i | 1.24298 | + | 1.24298i | 0.958760 | + | 0.284217i | \(0.0917337\pi\) |
0.284217 | + | 0.958760i | \(0.408266\pi\) | |||||||
\(888\) | −190.084 | + | 190.084i | −0.214059 | + | 0.214059i | ||||
\(889\) | 1143.33i | 1.28609i | ||||||||
\(890\) | 57.3412 | − | 177.164i | 0.0644283 | − | 0.199061i | ||||
\(891\) | −137.536 | −0.154361 | ||||||||
\(892\) | 101.673 | + | 101.673i | 0.113983 | + | 0.113983i | ||||
\(893\) | 702.871 | − | 702.871i | 0.787089 | − | 0.787089i | ||||
\(894\) | 365.333i | 0.408650i | ||||||||
\(895\) | 460.182 | + | 900.621i | 0.514170 | + | 1.00628i | ||||
\(896\) | −57.2169 | −0.0638581 | ||||||||
\(897\) | 77.2981 | + | 77.2981i | 0.0861740 | + | 0.0861740i | ||||
\(898\) | 183.403 | − | 183.403i | 0.204235 | − | 0.204235i | ||||
\(899\) | 1334.25i | 1.48414i | ||||||||
\(900\) | 87.8911 | − | 121.553i | 0.0976568 | − | 0.135059i | ||||
\(901\) | 625.796 | 0.694558 | ||||||||
\(902\) | 751.385 | + | 751.385i | 0.833021 | + | 0.833021i | ||||
\(903\) | 350.096 | − | 350.096i | 0.387703 | − | 0.387703i | ||||
\(904\) | − | 219.897i | − | 0.243248i | ||||||
\(905\) | 532.921 | − | 272.302i | 0.588863 | − | 0.300886i | ||||
\(906\) | −213.996 | −0.236199 | ||||||||
\(907\) | −884.694 | − | 884.694i | −0.975407 | − | 0.975407i | 0.0242975 | − | 0.999705i | \(-0.492265\pi\) |
−0.999705 | + | 0.0242975i | \(0.992265\pi\) | |||||||
\(908\) | 151.663 | − | 151.663i | 0.167030 | − | 0.167030i | ||||
\(909\) | − | 472.853i | − | 0.520190i | ||||||
\(910\) | 447.744 | + | 144.917i | 0.492026 | + | 0.159250i | ||||
\(911\) | −225.502 | −0.247532 | −0.123766 | − | 0.992311i | \(-0.539497\pi\) | ||||
−0.123766 | + | 0.992311i | \(0.539497\pi\) | |||||||
\(912\) | 81.4644 | + | 81.4644i | 0.0893250 | + | 0.0893250i | ||||
\(913\) | 1491.29 | − | 1491.29i | 1.63340 | − | 1.63340i | ||||
\(914\) | − | 136.230i | − | 0.149048i | ||||||
\(915\) | 105.477 | − | 325.888i | 0.115276 | − | 0.356162i | ||||
\(916\) | 140.053 | 0.152896 | ||||||||
\(917\) | 893.132 | + | 893.132i | 0.973971 | + | 0.973971i | ||||
\(918\) | 56.2140 | − | 56.2140i | 0.0612353 | − | 0.0612353i | ||||
\(919\) | 262.008i | 0.285101i | 0.989787 | + | 0.142551i | \(0.0455304\pi\) | ||||
−0.989787 | + | 0.142551i | \(0.954470\pi\) | |||||||
\(920\) | 30.8599 | + | 60.3959i | 0.0335434 | + | 0.0656477i | ||||
\(921\) | 39.1708 | 0.0425307 | ||||||||
\(922\) | −386.997 | − | 386.997i | −0.419736 | − | 0.419736i | ||||
\(923\) | −1019.11 | + | 1019.11i | −1.10413 | + | 1.10413i | ||||
\(924\) | − | 267.721i | − | 0.289742i | ||||||
\(925\) | 1354.43 | − | 217.685i | 1.46425 | − | 0.235335i | ||||
\(926\) | −223.153 | −0.240986 | ||||||||
\(927\) | 399.338 | + | 399.338i | 0.430786 | + | 0.430786i | ||||
\(928\) | 113.947 | − | 113.947i | 0.122788 | − | 0.122788i | ||||
\(929\) | − | 837.652i | − | 0.901671i | −0.892607 | − | 0.450836i | \(-0.851126\pi\) | ||
0.892607 | − | 0.450836i | \(-0.148874\pi\) | |||||||
\(930\) | −510.820 | + | 261.009i | −0.549268 | + | 0.280655i | ||||
\(931\) | −389.509 | −0.418377 | ||||||||
\(932\) | 8.04723 | + | 8.04723i | 0.00863437 | + | 0.00863437i | ||||
\(933\) | 527.234 | − | 527.234i | 0.565096 | − | 0.565096i | ||||
\(934\) | − | 16.5588i | − | 0.0177289i | ||||||
\(935\) | −786.452 | − | 254.544i | −0.841125 | − | 0.272239i | ||||
\(936\) | 111.667 | 0.119302 | ||||||||
\(937\) | 198.243 | + | 198.243i | 0.211572 | + | 0.211572i | 0.804935 | − | 0.593363i | \(-0.202200\pi\) |
−0.593363 | + | 0.804935i | \(0.702200\pi\) | |||||||
\(938\) | 215.000 | − | 215.000i | 0.229211 | − | 0.229211i | ||||
\(939\) | 528.019i | 0.562320i | ||||||||
\(940\) | 184.071 | − | 568.715i | 0.195820 | − | 0.605016i | ||||
\(941\) | 601.841 | 0.639576 | 0.319788 | − | 0.947489i | \(-0.396388\pi\) | ||||
0.319788 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(942\) | 198.813 | + | 198.813i | 0.211054 | + | 0.211054i | ||||
\(943\) | −166.740 | + | 166.740i | −0.176818 | + | 0.176818i | ||||
\(944\) | 462.230i | 0.489651i | ||||||||
\(945\) | −59.7843 | − | 117.004i | −0.0632638 | − | 0.123813i | ||||
\(946\) | −1221.55 | −1.29128 | ||||||||
\(947\) | −861.408 | − | 861.408i | −0.909618 | − | 0.909618i | 0.0866233 | − | 0.996241i | \(-0.472392\pi\) |
−0.996241 | + | 0.0866233i | \(0.972392\pi\) | |||||||
\(948\) | 285.883 | − | 285.883i | 0.301565 | − | 0.301565i | ||||
\(949\) | − | 699.504i | − | 0.737096i | ||||||
\(950\) | −93.2932 | − | 580.470i | −0.0982034 | − | 0.611021i | ||||
\(951\) | −182.472 | −0.191873 | ||||||||
\(952\) | 109.424 | + | 109.424i | 0.114941 | + | 0.114941i | ||||
\(953\) | −500.153 | + | 500.153i | −0.524819 | + | 0.524819i | −0.919023 | − | 0.394204i | \(-0.871020\pi\) |
0.394204 | + | 0.919023i | \(0.371020\pi\) | |||||||
\(954\) | − | 245.418i | − | 0.257252i | ||||||
\(955\) | −1578.03 | + | 806.311i | −1.65239 | + | 0.844305i | ||||
\(956\) | 537.121 | 0.561842 | ||||||||
\(957\) | 533.164 | + | 533.164i | 0.557120 | + | 0.557120i | ||||
\(958\) | −391.487 | + | 391.487i | −0.408651 | + | 0.408651i | ||||
\(959\) | − | 172.748i | − | 0.180134i | ||||||
\(960\) | 65.9155 | + | 21.3343i | 0.0686619 | + | 0.0222232i | ||||
\(961\) | 1232.75 | 1.28278 | ||||||||
\(962\) | 722.128 | + | 722.128i | 0.750653 | + | 0.750653i | ||||
\(963\) | −44.4074 | + | 44.4074i | −0.0461136 | + | 0.0461136i | ||||
\(964\) | − | 531.882i | − | 0.551745i | ||||||
\(965\) | −195.640 | + | 604.459i | −0.202735 | + | 0.626382i | ||||
\(966\) | 59.4099 | 0.0615009 | ||||||||
\(967\) | −820.417 | − | 820.417i | −0.848415 | − | 0.848415i | 0.141521 | − | 0.989935i | \(-0.454801\pi\) |
−0.989935 | + | 0.141521i | \(0.954801\pi\) | |||||||
\(968\) | −225.063 | + | 225.063i | −0.232504 | + | 0.232504i | ||||
\(969\) | − | 311.591i | − | 0.321560i | ||||||
\(970\) | 318.714 | + | 623.754i | 0.328571 | + | 0.643045i | ||||
\(971\) | 247.015 | 0.254392 | 0.127196 | − | 0.991878i | \(-0.459402\pi\) | ||||
0.127196 | + | 0.991878i | \(0.459402\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 385.837 | − | 385.837i | 0.396544 | − | 0.396544i | ||||
\(974\) | − | 564.855i | − | 0.579933i | ||||||
\(975\) | −461.779 | − | 333.898i | −0.473620 | − | 0.342459i | ||||
\(976\) | 158.209 | 0.162099 | ||||||||
\(977\) | 327.784 | + | 327.784i | 0.335501 | + | 0.335501i | 0.854671 | − | 0.519170i | \(-0.173759\pi\) |
−0.519170 | + | 0.854671i | \(0.673759\pi\) | |||||||
\(978\) | −138.292 | + | 138.292i | −0.141403 | + | 0.141403i | ||||
\(979\) | 402.437i | 0.411069i | ||||||||
\(980\) | −208.585 | + | 106.579i | −0.212842 | + | 0.108754i | ||||
\(981\) | −0.308050 | −0.000314016 | ||||||||
\(982\) | 15.3095 | + | 15.3095i | 0.0155901 | + | 0.0155901i | ||||
\(983\) | −565.846 | + | 565.846i | −0.575632 | + | 0.575632i | −0.933697 | − | 0.358065i | \(-0.883437\pi\) |
0.358065 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(984\) | 240.877i | 0.244794i | ||||||||
\(985\) | −1647.67 | − | 533.287i | −1.67276 | − | 0.541408i | ||||
\(986\) | −435.833 | −0.442021 | ||||||||
\(987\) | −370.248 | − | 370.248i | −0.375125 | − | 0.375125i | ||||
\(988\) | 309.483 | − | 309.483i | 0.313242 | − | 0.313242i | ||||
\(989\) | − | 271.073i | − | 0.274088i | ||||||
\(990\) | −99.8243 | + | 308.422i | −0.100833 | + | 0.311538i | ||||
\(991\) | 1093.78 | 1.10371 | 0.551856 | − | 0.833939i | \(-0.313920\pi\) | ||||
0.551856 | + | 0.833939i | \(0.313920\pi\) | |||||||
\(992\) | −187.350 | − | 187.350i | −0.188861 | − | 0.188861i | ||||
\(993\) | 388.102 | − | 388.102i | 0.390838 | − | 0.390838i | ||||
\(994\) | 783.268i | 0.787996i | ||||||||
\(995\) | −457.487 | − | 895.346i | −0.459786 | − | 0.899845i | ||||
\(996\) | 478.073 | 0.479993 | ||||||||
\(997\) | 652.866 | + | 652.866i | 0.654831 | + | 0.654831i | 0.954152 | − | 0.299321i | \(-0.0967603\pi\) |
−0.299321 | + | 0.954152i | \(0.596760\pi\) | |||||||
\(998\) | 823.731 | − | 823.731i | 0.825382 | − | 0.825382i | ||||
\(999\) | − | 285.126i | − | 0.285412i |
(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 | 690.3.k.a.277.19 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.19 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.19 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.19 | yes | 40 | 5.3 | odd | 4 | inner |