Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,3,Mod(736,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.736");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.b (of order \(2\), degree \(1\), 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: | \(31.4714705336\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 736.18 | ||
Character | \(\chi\) | \(=\) | 1155.736 |
Dual form | 1155.3.b.a.736.79 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.89693i | − | 1.44847i | −0.689555 | − | 0.724233i | \(-0.742194\pi\) | ||
0.689555 | − | 0.724233i | \(-0.257806\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −4.39221 | −1.09805 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 5.01763i | 0.836272i | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 1.13621i | 0.142026i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 6.47774i | − | 0.647774i | ||||||
\(11\) | 10.5908 | − | 2.97219i | 0.962804 | − | 0.270199i | ||||
\(12\) | 7.60753 | 0.633961 | ||||||||
\(13\) | − | 0.711740i | − | 0.0547492i | −0.999625 | − | 0.0273746i | \(-0.991285\pi\) | ||
0.999625 | − | 0.0273746i | \(-0.00871470\pi\) | |||||||
\(14\) | 7.66456 | 0.547469 | ||||||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | −14.2773 | −0.892333 | ||||||||
\(17\) | 14.8732i | 0.874892i | 0.899245 | + | 0.437446i | \(0.144117\pi\) | ||||
−0.899245 | + | 0.437446i | \(0.855883\pi\) | |||||||
\(18\) | − | 8.69079i | − | 0.482822i | ||||||
\(19\) | 8.46103i | 0.445317i | 0.974896 | + | 0.222659i | \(0.0714735\pi\) | ||||
−0.974896 | + | 0.222659i | \(0.928526\pi\) | |||||||
\(20\) | −9.82128 | −0.491064 | ||||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | −8.61023 | − | 30.6810i | −0.391374 | − | 1.39459i | ||||
\(23\) | −11.9912 | −0.521355 | −0.260677 | − | 0.965426i | \(-0.583946\pi\) | ||||
−0.260677 | + | 0.965426i | \(0.583946\pi\) | |||||||
\(24\) | − | 1.96797i | − | 0.0819989i | ||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | −2.06186 | −0.0793024 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 11.6207i | − | 0.415025i | ||||||
\(29\) | 46.8706i | 1.61623i | 0.589026 | + | 0.808114i | \(0.299512\pi\) | ||||
−0.589026 | + | 0.808114i | \(0.700488\pi\) | |||||||
\(30\) | 11.2198i | 0.373992i | ||||||||
\(31\) | 51.2760 | 1.65407 | 0.827033 | − | 0.562154i | \(-0.190027\pi\) | ||||
0.827033 | + | 0.562154i | \(0.190027\pi\) | |||||||
\(32\) | 45.9053i | 1.43454i | ||||||||
\(33\) | −18.3439 | + | 5.14798i | −0.555875 | + | 0.155999i | ||||
\(34\) | 43.0865 | 1.26725 | ||||||||
\(35\) | 5.91608i | 0.169031i | ||||||||
\(36\) | −13.1766 | −0.366018 | ||||||||
\(37\) | 49.0328 | 1.32521 | 0.662606 | − | 0.748968i | \(-0.269451\pi\) | ||||
0.662606 | + | 0.748968i | \(0.269451\pi\) | |||||||
\(38\) | 24.5110 | 0.645027 | ||||||||
\(39\) | 1.23277i | 0.0316095i | ||||||||
\(40\) | 2.54064i | 0.0635161i | ||||||||
\(41\) | 15.4167i | 0.376018i | 0.982167 | + | 0.188009i | \(0.0602034\pi\) | ||||
−0.982167 | + | 0.188009i | \(0.939797\pi\) | |||||||
\(42\) | −13.2754 | −0.316081 | ||||||||
\(43\) | 41.8430i | 0.973092i | 0.873655 | + | 0.486546i | \(0.161743\pi\) | ||||
−0.873655 | + | 0.486546i | \(0.838257\pi\) | |||||||
\(44\) | −46.5173 | + | 13.0545i | −1.05721 | + | 0.296693i | ||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | 34.7376i | 0.755164i | ||||||||
\(47\) | 12.2417 | 0.260462 | 0.130231 | − | 0.991484i | \(-0.458428\pi\) | ||||
0.130231 | + | 0.991484i | \(0.458428\pi\) | |||||||
\(48\) | 24.7291 | 0.515189 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | − | 14.4847i | − | 0.289693i | ||||||
\(51\) | − | 25.7611i | − | 0.505119i | ||||||
\(52\) | 3.12611i | 0.0601175i | ||||||||
\(53\) | −12.2476 | −0.231087 | −0.115543 | − | 0.993302i | \(-0.536861\pi\) | ||||
−0.115543 | + | 0.993302i | \(0.536861\pi\) | |||||||
\(54\) | 15.0529i | 0.278757i | ||||||||
\(55\) | 23.6819 | − | 6.64602i | 0.430579 | − | 0.120837i | ||||
\(56\) | −3.00613 | −0.0536809 | ||||||||
\(57\) | − | 14.6549i | − | 0.257104i | ||||||
\(58\) | 135.781 | 2.34105 | ||||||||
\(59\) | 28.8624 | 0.489194 | 0.244597 | − | 0.969625i | \(-0.421344\pi\) | ||||
0.244597 | + | 0.969625i | \(0.421344\pi\) | |||||||
\(60\) | 17.0110 | 0.283516 | ||||||||
\(61\) | − | 112.815i | − | 1.84943i | −0.380659 | − | 0.924715i | \(-0.624303\pi\) | ||
0.380659 | − | 0.924715i | \(-0.375697\pi\) | |||||||
\(62\) | − | 148.543i | − | 2.39586i | ||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | 75.8751 | 1.18555 | ||||||||
\(65\) | − | 1.59150i | − | 0.0244846i | ||||||
\(66\) | 14.9134 | + | 53.1410i | 0.225960 | + | 0.805166i | ||||
\(67\) | −91.9069 | −1.37174 | −0.685872 | − | 0.727722i | \(-0.740579\pi\) | ||||
−0.685872 | + | 0.727722i | \(0.740579\pi\) | |||||||
\(68\) | − | 65.3261i | − | 0.960678i | ||||||
\(69\) | 20.7693 | 0.301004 | ||||||||
\(70\) | 17.1385 | 0.244835 | ||||||||
\(71\) | 116.132 | 1.63566 | 0.817830 | − | 0.575459i | \(-0.195177\pi\) | ||||
0.817830 | + | 0.575459i | \(0.195177\pi\) | |||||||
\(72\) | 3.40863i | 0.0473421i | ||||||||
\(73\) | − | 25.4033i | − | 0.347990i | −0.984747 | − | 0.173995i | \(-0.944332\pi\) | ||
0.984747 | − | 0.173995i | \(-0.0556677\pi\) | |||||||
\(74\) | − | 142.045i | − | 1.91952i | ||||||
\(75\) | −8.66025 | −0.115470 | ||||||||
\(76\) | − | 37.1626i | − | 0.488982i | ||||||
\(77\) | 7.86367 | + | 28.0208i | 0.102126 | + | 0.363906i | ||||
\(78\) | 3.57125 | 0.0457852 | ||||||||
\(79\) | − | 17.1707i | − | 0.217351i | −0.994077 | − | 0.108675i | \(-0.965339\pi\) | ||
0.994077 | − | 0.108675i | \(-0.0346609\pi\) | |||||||
\(80\) | −31.9251 | −0.399063 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 44.6612 | 0.544649 | ||||||||
\(83\) | 145.242i | 1.74991i | 0.484205 | + | 0.874954i | \(0.339109\pi\) | ||||
−0.484205 | + | 0.874954i | \(0.660891\pi\) | |||||||
\(84\) | 20.1276i | 0.239615i | ||||||||
\(85\) | 33.2574i | 0.391264i | ||||||||
\(86\) | 121.216 | 1.40949 | ||||||||
\(87\) | − | 81.1823i | − | 0.933130i | ||||||
\(88\) | 3.37703 | + | 12.0334i | 0.0383753 | + | 0.136743i | ||||
\(89\) | 5.32225 | 0.0598005 | 0.0299003 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0299003 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(90\) | − | 19.4332i | − | 0.215925i | ||||||
\(91\) | 1.88309 | 0.0206933 | ||||||||
\(92\) | 52.6677 | 0.572475 | ||||||||
\(93\) | −88.8127 | −0.954975 | ||||||||
\(94\) | − | 35.4633i | − | 0.377270i | ||||||
\(95\) | 18.9194i | 0.199152i | ||||||||
\(96\) | − | 79.5103i | − | 0.828232i | ||||||
\(97\) | 98.8311 | 1.01888 | 0.509439 | − | 0.860507i | \(-0.329853\pi\) | ||||
0.509439 | + | 0.860507i | \(0.329853\pi\) | |||||||
\(98\) | 20.2785i | 0.206924i | ||||||||
\(99\) | 31.7725 | − | 8.91657i | 0.320935 | − | 0.0900663i | ||||
\(100\) | −21.9611 | −0.219611 | ||||||||
\(101\) | − | 153.234i | − | 1.51717i | −0.651574 | − | 0.758585i | \(-0.725891\pi\) | ||
0.651574 | − | 0.758585i | \(-0.274109\pi\) | |||||||
\(102\) | −74.6281 | −0.731648 | ||||||||
\(103\) | 180.215 | 1.74966 | 0.874832 | − | 0.484427i | \(-0.160972\pi\) | ||||
0.874832 | + | 0.484427i | \(0.160972\pi\) | |||||||
\(104\) | 0.808686 | 0.00777582 | ||||||||
\(105\) | − | 10.2470i | − | 0.0975900i | ||||||
\(106\) | 35.4805i | 0.334722i | ||||||||
\(107\) | − | 113.109i | − | 1.05709i | −0.848904 | − | 0.528547i | \(-0.822737\pi\) | ||
0.848904 | − | 0.528547i | \(-0.177263\pi\) | |||||||
\(108\) | 22.8226 | 0.211320 | ||||||||
\(109\) | 181.876i | 1.66859i | 0.551320 | + | 0.834294i | \(0.314124\pi\) | ||||
−0.551320 | + | 0.834294i | \(0.685876\pi\) | |||||||
\(110\) | −19.2531 | − | 68.6047i | −0.175028 | − | 0.623679i | ||||
\(111\) | −84.9273 | −0.765111 | ||||||||
\(112\) | − | 37.7742i | − | 0.337270i | ||||||
\(113\) | −86.4371 | −0.764930 | −0.382465 | − | 0.923970i | \(-0.624925\pi\) | ||||
−0.382465 | + | 0.923970i | \(0.624925\pi\) | |||||||
\(114\) | −42.4543 | −0.372406 | ||||||||
\(115\) | −26.8130 | −0.233157 | ||||||||
\(116\) | − | 205.866i | − | 1.77470i | ||||||
\(117\) | − | 2.13522i | − | 0.0182497i | ||||||
\(118\) | − | 83.6124i | − | 0.708580i | ||||||
\(119\) | −39.3507 | −0.330678 | ||||||||
\(120\) | − | 4.40052i | − | 0.0366710i | ||||||
\(121\) | 103.332 | − | 62.9560i | 0.853985 | − | 0.520298i | ||||
\(122\) | −326.818 | −2.67884 | ||||||||
\(123\) | − | 26.7026i | − | 0.217094i | ||||||
\(124\) | −225.215 | −1.81625 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 22.9937 | 0.182490 | ||||||||
\(127\) | − | 151.633i | − | 1.19396i | −0.802255 | − | 0.596982i | \(-0.796366\pi\) | ||
0.802255 | − | 0.596982i | \(-0.203634\pi\) | |||||||
\(128\) | − | 36.1839i | − | 0.282687i | ||||||
\(129\) | − | 72.4742i | − | 0.561815i | ||||||
\(130\) | −4.61046 | −0.0354651 | ||||||||
\(131\) | 105.053i | 0.801934i | 0.916093 | + | 0.400967i | \(0.131326\pi\) | ||||
−0.916093 | + | 0.400967i | \(0.868674\pi\) | |||||||
\(132\) | 80.5702 | − | 22.6110i | 0.610381 | − | 0.171296i | ||||
\(133\) | −22.3858 | −0.168314 | ||||||||
\(134\) | 266.248i | 1.98692i | ||||||||
\(135\) | −11.6190 | −0.0860663 | ||||||||
\(136\) | −16.8990 | −0.124258 | ||||||||
\(137\) | −230.503 | −1.68250 | −0.841251 | − | 0.540645i | \(-0.818180\pi\) | ||||
−0.841251 | + | 0.540645i | \(0.818180\pi\) | |||||||
\(138\) | − | 60.1672i | − | 0.435994i | ||||||
\(139\) | 94.7740i | 0.681827i | 0.940095 | + | 0.340914i | \(0.110736\pi\) | ||||
−0.940095 | + | 0.340914i | \(0.889264\pi\) | |||||||
\(140\) | − | 25.9847i | − | 0.185605i | ||||||
\(141\) | −21.2032 | −0.150378 | ||||||||
\(142\) | − | 336.426i | − | 2.36920i | ||||||
\(143\) | −2.11543 | − | 7.53793i | −0.0147932 | − | 0.0527128i | ||||
\(144\) | −42.8320 | −0.297444 | ||||||||
\(145\) | 104.806i | 0.722799i | ||||||||
\(146\) | −73.5915 | −0.504052 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | −215.363 | −1.45515 | ||||||||
\(149\) | − | 242.846i | − | 1.62984i | −0.579574 | − | 0.814919i | \(-0.696781\pi\) | ||
0.579574 | − | 0.814919i | \(-0.303219\pi\) | |||||||
\(150\) | 25.0882i | 0.167254i | ||||||||
\(151\) | 126.564i | 0.838172i | 0.907947 | + | 0.419086i | \(0.137649\pi\) | ||||
−0.907947 | + | 0.419086i | \(0.862351\pi\) | |||||||
\(152\) | −9.61350 | −0.0632467 | ||||||||
\(153\) | 44.6195i | 0.291631i | ||||||||
\(154\) | 81.1742 | − | 22.7805i | 0.527105 | − | 0.147925i | ||||
\(155\) | 114.657 | 0.739721 | ||||||||
\(156\) | − | 5.41458i | − | 0.0347089i | ||||||
\(157\) | 99.0931 | 0.631166 | 0.315583 | − | 0.948898i | \(-0.397800\pi\) | ||||
0.315583 | + | 0.948898i | \(0.397800\pi\) | |||||||
\(158\) | −49.7423 | −0.314825 | ||||||||
\(159\) | 21.2135 | 0.133418 | ||||||||
\(160\) | 102.647i | 0.641546i | ||||||||
\(161\) | − | 31.7256i | − | 0.197054i | ||||||
\(162\) | − | 26.0724i | − | 0.160941i | ||||||
\(163\) | −166.857 | −1.02366 | −0.511831 | − | 0.859086i | \(-0.671033\pi\) | ||||
−0.511831 | + | 0.859086i | \(0.671033\pi\) | |||||||
\(164\) | − | 67.7135i | − | 0.412887i | ||||||
\(165\) | −41.0182 | + | 11.5112i | −0.248595 | + | 0.0697651i | ||||
\(166\) | 420.757 | 2.53468 | ||||||||
\(167\) | − | 204.702i | − | 1.22576i | −0.790177 | − | 0.612879i | \(-0.790011\pi\) | ||
0.790177 | − | 0.612879i | \(-0.209989\pi\) | |||||||
\(168\) | 5.20677 | 0.0309927 | ||||||||
\(169\) | 168.493 | 0.997003 | ||||||||
\(170\) | 96.3445 | 0.566732 | ||||||||
\(171\) | 25.3831i | 0.148439i | ||||||||
\(172\) | − | 183.783i | − | 1.06851i | ||||||
\(173\) | − | 155.004i | − | 0.895979i | −0.894039 | − | 0.447990i | \(-0.852140\pi\) | ||
0.894039 | − | 0.447990i | \(-0.147860\pi\) | |||||||
\(174\) | −235.180 | −1.35161 | ||||||||
\(175\) | 13.2288i | 0.0755929i | ||||||||
\(176\) | −151.209 | + | 42.4349i | −0.859142 | + | 0.241107i | ||||
\(177\) | −49.9912 | −0.282436 | ||||||||
\(178\) | − | 15.4182i | − | 0.0866190i | ||||||
\(179\) | 44.9185 | 0.250941 | 0.125471 | − | 0.992097i | \(-0.459956\pi\) | ||||
0.125471 | + | 0.992097i | \(0.459956\pi\) | |||||||
\(180\) | −29.4639 | −0.163688 | ||||||||
\(181\) | 349.101 | 1.92873 | 0.964367 | − | 0.264567i | \(-0.0852289\pi\) | ||||
0.964367 | + | 0.264567i | \(0.0852289\pi\) | |||||||
\(182\) | − | 5.45517i | − | 0.0299735i | ||||||
\(183\) | 195.402i | 1.06777i | ||||||||
\(184\) | − | 13.6245i | − | 0.0740460i | ||||||
\(185\) | 109.641 | 0.592653 | ||||||||
\(186\) | 257.284i | 1.38325i | ||||||||
\(187\) | 44.2059 | + | 157.519i | 0.236395 | + | 0.842350i | ||||
\(188\) | −53.7681 | −0.286001 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 54.8083 | 0.288465 | ||||||||
\(191\) | 72.8722 | 0.381530 | 0.190765 | − | 0.981636i | \(-0.438903\pi\) | ||||
0.190765 | + | 0.981636i | \(0.438903\pi\) | |||||||
\(192\) | −131.420 | −0.684477 | ||||||||
\(193\) | 65.7576i | 0.340713i | 0.985383 | + | 0.170356i | \(0.0544919\pi\) | ||||
−0.985383 | + | 0.170356i | \(0.945508\pi\) | |||||||
\(194\) | − | 286.307i | − | 1.47581i | ||||||
\(195\) | 2.75656i | 0.0141362i | ||||||||
\(196\) | 30.7455 | 0.156865 | ||||||||
\(197\) | 91.6909i | 0.465436i | 0.972544 | + | 0.232718i | \(0.0747620\pi\) | ||||
−0.972544 | + | 0.232718i | \(0.925238\pi\) | |||||||
\(198\) | −25.8307 | − | 92.0429i | −0.130458 | − | 0.464863i | ||||
\(199\) | −308.023 | −1.54786 | −0.773928 | − | 0.633273i | \(-0.781711\pi\) | ||||
−0.773928 | + | 0.633273i | \(0.781711\pi\) | |||||||
\(200\) | 5.68105i | 0.0284052i | ||||||||
\(201\) | 159.187 | 0.791977 | ||||||||
\(202\) | −443.909 | −2.19757 | ||||||||
\(203\) | −124.008 | −0.610877 | ||||||||
\(204\) | 113.148i | 0.554648i | ||||||||
\(205\) | 34.4729i | 0.168160i | ||||||||
\(206\) | − | 522.071i | − | 2.53433i | ||||||
\(207\) | −35.9735 | −0.173785 | ||||||||
\(208\) | 10.1617i | 0.0488545i | ||||||||
\(209\) | 25.1478 | + | 89.6095i | 0.120324 | + | 0.428753i | ||||
\(210\) | −29.6847 | −0.141356 | ||||||||
\(211\) | − | 24.2083i | − | 0.114731i | −0.998353 | − | 0.0573656i | \(-0.981730\pi\) | ||
0.998353 | − | 0.0573656i | \(-0.0182701\pi\) | |||||||
\(212\) | 53.7941 | 0.253746 | ||||||||
\(213\) | −201.146 | −0.944349 | ||||||||
\(214\) | −327.669 | −1.53117 | ||||||||
\(215\) | 93.5637i | 0.435180i | ||||||||
\(216\) | − | 5.90392i | − | 0.0273330i | ||||||
\(217\) | 135.664i | 0.625178i | ||||||||
\(218\) | 526.882 | 2.41689 | ||||||||
\(219\) | 43.9998i | 0.200912i | ||||||||
\(220\) | −104.016 | + | 29.1907i | −0.472799 | + | 0.132685i | ||||
\(221\) | 10.5858 | 0.0478997 | ||||||||
\(222\) | 246.029i | 1.10824i | ||||||||
\(223\) | −142.571 | −0.639334 | −0.319667 | − | 0.947530i | \(-0.603571\pi\) | ||||
−0.319667 | + | 0.947530i | \(0.603571\pi\) | |||||||
\(224\) | −121.454 | −0.542205 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 250.402i | 1.10797i | ||||||||
\(227\) | − | 104.955i | − | 0.462355i | −0.972912 | − | 0.231178i | \(-0.925742\pi\) | ||
0.972912 | − | 0.231178i | \(-0.0742579\pi\) | |||||||
\(228\) | 64.3676i | 0.282314i | ||||||||
\(229\) | 303.799 | 1.32663 | 0.663316 | − | 0.748339i | \(-0.269148\pi\) | ||||
0.663316 | + | 0.748339i | \(0.269148\pi\) | |||||||
\(230\) | 77.6755i | 0.337720i | ||||||||
\(231\) | −13.6203 | − | 48.5334i | −0.0589623 | − | 0.210101i | ||||
\(232\) | −53.2549 | −0.229547 | ||||||||
\(233\) | 336.730i | 1.44519i | 0.691270 | + | 0.722596i | \(0.257051\pi\) | ||||
−0.691270 | + | 0.722596i | \(0.742949\pi\) | |||||||
\(234\) | −6.18558 | −0.0264341 | ||||||||
\(235\) | 27.3733 | 0.116482 | ||||||||
\(236\) | −126.770 | −0.537160 | ||||||||
\(237\) | 29.7405i | 0.125487i | ||||||||
\(238\) | 113.996i | 0.478976i | ||||||||
\(239\) | 94.1140i | 0.393783i | 0.980425 | + | 0.196891i | \(0.0630846\pi\) | ||||
−0.980425 | + | 0.196891i | \(0.936915\pi\) | |||||||
\(240\) | 55.2958 | 0.230399 | ||||||||
\(241\) | − | 96.7286i | − | 0.401363i | −0.979656 | − | 0.200682i | \(-0.935684\pi\) | ||
0.979656 | − | 0.200682i | \(-0.0643157\pi\) | |||||||
\(242\) | −182.379 | − | 299.346i | −0.753633 | − | 1.23697i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 495.509i | 2.03077i | ||||||||
\(245\) | −15.6525 | −0.0638877 | ||||||||
\(246\) | −77.3555 | −0.314453 | ||||||||
\(247\) | 6.02205 | 0.0243808 | ||||||||
\(248\) | 58.2603i | 0.234921i | ||||||||
\(249\) | − | 251.567i | − | 1.01031i | ||||||
\(250\) | − | 32.3887i | − | 0.129555i | ||||||
\(251\) | 67.9504 | 0.270719 | 0.135359 | − | 0.990797i | \(-0.456781\pi\) | ||||
0.135359 | + | 0.990797i | \(0.456781\pi\) | |||||||
\(252\) | − | 34.8621i | − | 0.138342i | ||||||
\(253\) | −126.997 | + | 35.6400i | −0.501963 | + | 0.140870i | ||||
\(254\) | −439.272 | −1.72942 | ||||||||
\(255\) | − | 57.6035i | − | 0.225896i | ||||||
\(256\) | 198.678 | 0.776086 | ||||||||
\(257\) | −324.191 | −1.26144 | −0.630722 | − | 0.776009i | \(-0.717241\pi\) | ||||
−0.630722 | + | 0.776009i | \(0.717241\pi\) | |||||||
\(258\) | −209.953 | −0.813770 | ||||||||
\(259\) | 129.729i | 0.500883i | ||||||||
\(260\) | 6.99020i | 0.0268854i | ||||||||
\(261\) | 140.612i | 0.538743i | ||||||||
\(262\) | 304.332 | 1.16157 | ||||||||
\(263\) | 273.807i | 1.04109i | 0.853834 | + | 0.520546i | \(0.174272\pi\) | ||||
−0.853834 | + | 0.520546i | \(0.825728\pi\) | |||||||
\(264\) | −5.84919 | − | 20.8425i | −0.0221560 | − | 0.0789489i | ||||
\(265\) | −27.3865 | −0.103345 | ||||||||
\(266\) | 64.8501i | 0.243797i | ||||||||
\(267\) | −9.21840 | −0.0345258 | ||||||||
\(268\) | 403.674 | 1.50625 | ||||||||
\(269\) | 333.929 | 1.24137 | 0.620685 | − | 0.784060i | \(-0.286855\pi\) | ||||
0.620685 | + | 0.784060i | \(0.286855\pi\) | |||||||
\(270\) | 33.6593i | 0.124664i | ||||||||
\(271\) | 187.556i | 0.692090i | 0.938218 | + | 0.346045i | \(0.112475\pi\) | ||||
−0.938218 | + | 0.346045i | \(0.887525\pi\) | |||||||
\(272\) | − | 212.349i | − | 0.780695i | ||||||
\(273\) | −3.26160 | −0.0119473 | ||||||||
\(274\) | 667.750i | 2.43705i | ||||||||
\(275\) | 52.9542 | − | 14.8609i | 0.192561 | − | 0.0540398i | ||||
\(276\) | −91.2231 | −0.330519 | ||||||||
\(277\) | 177.652i | 0.641341i | 0.947191 | + | 0.320671i | \(0.103908\pi\) | ||||
−0.947191 | + | 0.320671i | \(0.896092\pi\) | |||||||
\(278\) | 274.554 | 0.987603 | ||||||||
\(279\) | 153.828 | 0.551355 | ||||||||
\(280\) | −6.72191 | −0.0240068 | ||||||||
\(281\) | 69.4125i | 0.247020i | 0.992343 | + | 0.123510i | \(0.0394150\pi\) | ||||
−0.992343 | + | 0.123510i | \(0.960585\pi\) | |||||||
\(282\) | 61.4243i | 0.217817i | ||||||||
\(283\) | − | 406.335i | − | 1.43581i | −0.696140 | − | 0.717906i | \(-0.745101\pi\) | ||
0.696140 | − | 0.717906i | \(-0.254899\pi\) | |||||||
\(284\) | −510.076 | −1.79604 | ||||||||
\(285\) | − | 32.7694i | − | 0.114980i | ||||||
\(286\) | −21.8369 | + | 6.12824i | −0.0763527 | + | 0.0214274i | ||||
\(287\) | −40.7888 | −0.142121 | ||||||||
\(288\) | 137.716i | 0.478180i | ||||||||
\(289\) | 67.7889 | 0.234564 | ||||||||
\(290\) | 303.616 | 1.04695 | ||||||||
\(291\) | −171.180 | −0.588249 | ||||||||
\(292\) | 111.577i | 0.382112i | ||||||||
\(293\) | − | 489.919i | − | 1.67208i | −0.548669 | − | 0.836039i | \(-0.684865\pi\) | ||
0.548669 | − | 0.836039i | \(-0.315135\pi\) | |||||||
\(294\) | − | 35.1234i | − | 0.119467i | ||||||
\(295\) | 64.5383 | 0.218774 | ||||||||
\(296\) | 55.7116i | 0.188215i | ||||||||
\(297\) | −55.0317 | + | 15.4439i | −0.185292 | + | 0.0519998i | ||||
\(298\) | −703.508 | −2.36077 | ||||||||
\(299\) | 8.53458i | 0.0285438i | ||||||||
\(300\) | 38.0377 | 0.126792 | ||||||||
\(301\) | −110.706 | −0.367794 | ||||||||
\(302\) | 366.647 | 1.21406 | ||||||||
\(303\) | 265.409i | 0.875939i | ||||||||
\(304\) | − | 120.801i | − | 0.397371i | ||||||
\(305\) | − | 252.263i | − | 0.827091i | ||||||
\(306\) | 129.260 | 0.422417 | ||||||||
\(307\) | 370.346i | 1.20634i | 0.797613 | + | 0.603169i | \(0.206096\pi\) | ||||
−0.797613 | + | 0.603169i | \(0.793904\pi\) | |||||||
\(308\) | −34.5389 | − | 123.073i | −0.112139 | − | 0.399588i | ||||
\(309\) | −312.142 | −1.01017 | ||||||||
\(310\) | − | 332.153i | − | 1.07146i | ||||||
\(311\) | −143.777 | −0.462306 | −0.231153 | − | 0.972917i | \(-0.574250\pi\) | ||||
−0.231153 | + | 0.972917i | \(0.574250\pi\) | |||||||
\(312\) | −1.40068 | −0.00448937 | ||||||||
\(313\) | −146.378 | −0.467660 | −0.233830 | − | 0.972277i | \(-0.575126\pi\) | ||||
−0.233830 | + | 0.972277i | \(0.575126\pi\) | |||||||
\(314\) | − | 287.066i | − | 0.914223i | ||||||
\(315\) | 17.7482i | 0.0563436i | ||||||||
\(316\) | 75.4174i | 0.238663i | ||||||||
\(317\) | 28.3508 | 0.0894348 | 0.0447174 | − | 0.999000i | \(-0.485761\pi\) | ||||
0.0447174 | + | 0.999000i | \(0.485761\pi\) | |||||||
\(318\) | − | 61.4540i | − | 0.193252i | ||||||
\(319\) | 139.308 | + | 496.400i | 0.436703 | + | 1.55611i | ||||
\(320\) | 169.662 | 0.530193 | ||||||||
\(321\) | 195.911i | 0.610314i | ||||||||
\(322\) | −91.9069 | −0.285425 | ||||||||
\(323\) | −125.842 | −0.389605 | ||||||||
\(324\) | −39.5299 | −0.122006 | ||||||||
\(325\) | − | 3.55870i | − | 0.0109498i | ||||||
\(326\) | 483.373i | 1.48274i | ||||||||
\(327\) | − | 315.018i | − | 0.963359i | ||||||
\(328\) | −17.5166 | −0.0534044 | ||||||||
\(329\) | 32.3885i | 0.0984452i | ||||||||
\(330\) | 33.3473 | + | 118.827i | 0.101052 | + | 0.360081i | ||||
\(331\) | 602.605 | 1.82056 | 0.910279 | − | 0.413995i | \(-0.135867\pi\) | ||||
0.910279 | + | 0.413995i | \(0.135867\pi\) | |||||||
\(332\) | − | 637.936i | − | 1.92149i | ||||||
\(333\) | 147.098 | 0.441737 | ||||||||
\(334\) | −593.007 | −1.77547 | ||||||||
\(335\) | −205.510 | −0.613463 | ||||||||
\(336\) | 65.4269i | 0.194723i | ||||||||
\(337\) | 92.5156i | 0.274527i | 0.990535 | + | 0.137263i | \(0.0438307\pi\) | ||||
−0.990535 | + | 0.137263i | \(0.956169\pi\) | |||||||
\(338\) | − | 488.114i | − | 1.44412i | ||||||
\(339\) | 149.713 | 0.441633 | ||||||||
\(340\) | − | 146.074i | − | 0.429628i | ||||||
\(341\) | 543.057 | − | 152.402i | 1.59254 | − | 0.446927i | ||||
\(342\) | 73.5331 | 0.215009 | ||||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | −47.5424 | −0.138205 | ||||||||
\(345\) | 46.4416 | 0.134613 | ||||||||
\(346\) | −449.037 | −1.29780 | ||||||||
\(347\) | 142.199i | 0.409796i | 0.978783 | + | 0.204898i | \(0.0656862\pi\) | ||||
−0.978783 | + | 0.204898i | \(0.934314\pi\) | |||||||
\(348\) | 356.570i | 1.02463i | ||||||||
\(349\) | 102.659i | 0.294151i | 0.989125 | + | 0.147076i | \(0.0469861\pi\) | ||||
−0.989125 | + | 0.147076i | \(0.953014\pi\) | |||||||
\(350\) | 38.3228 | 0.109494 | ||||||||
\(351\) | 3.69831i | 0.0105365i | ||||||||
\(352\) | 136.439 | + | 486.176i | 0.387611 | + | 1.38118i | ||||
\(353\) | 399.221 | 1.13094 | 0.565469 | − | 0.824769i | \(-0.308695\pi\) | ||||
0.565469 | + | 0.824769i | \(0.308695\pi\) | |||||||
\(354\) | 144.821i | 0.409099i | ||||||||
\(355\) | 259.679 | 0.731490 | ||||||||
\(356\) | −23.3764 | −0.0656641 | ||||||||
\(357\) | 68.1574 | 0.190917 | ||||||||
\(358\) | − | 130.126i | − | 0.363480i | ||||||
\(359\) | 556.875i | 1.55118i | 0.631235 | + | 0.775592i | \(0.282548\pi\) | ||||
−0.631235 | + | 0.775592i | \(0.717452\pi\) | |||||||
\(360\) | 7.62193i | 0.0211720i | ||||||||
\(361\) | 289.411 | 0.801693 | ||||||||
\(362\) | − | 1011.32i | − | 2.79371i | ||||||
\(363\) | −178.977 | + | 109.043i | −0.493048 | + | 0.300394i | ||||
\(364\) | −8.27091 | −0.0227223 | ||||||||
\(365\) | − | 56.8035i | − | 0.155626i | ||||||
\(366\) | 566.066 | 1.54663 | ||||||||
\(367\) | 73.7263 | 0.200889 | 0.100445 | − | 0.994943i | \(-0.467974\pi\) | ||||
0.100445 | + | 0.994943i | \(0.467974\pi\) | |||||||
\(368\) | 171.202 | 0.465222 | ||||||||
\(369\) | 46.2502i | 0.125339i | ||||||||
\(370\) | − | 317.622i | − | 0.858437i | ||||||
\(371\) | − | 32.4041i | − | 0.0873427i | ||||||
\(372\) | 390.084 | 1.04861 | ||||||||
\(373\) | 182.813i | 0.490114i | 0.969509 | + | 0.245057i | \(0.0788067\pi\) | ||||
−0.969509 | + | 0.245057i | \(0.921193\pi\) | |||||||
\(374\) | 456.323 | − | 128.061i | 1.22012 | − | 0.342410i | ||||
\(375\) | −19.3649 | −0.0516398 | ||||||||
\(376\) | 13.9091i | 0.0369924i | ||||||||
\(377\) | 33.3597 | 0.0884872 | ||||||||
\(378\) | −39.8262 | −0.105360 | ||||||||
\(379\) | −402.562 | −1.06217 | −0.531084 | − | 0.847319i | \(-0.678215\pi\) | ||||
−0.531084 | + | 0.847319i | \(0.678215\pi\) | |||||||
\(380\) | − | 83.0982i | − | 0.218679i | ||||||
\(381\) | 262.637i | 0.689335i | ||||||||
\(382\) | − | 211.106i | − | 0.552633i | ||||||
\(383\) | −17.2465 | −0.0450301 | −0.0225151 | − | 0.999747i | \(-0.507167\pi\) | ||||
−0.0225151 | + | 0.999747i | \(0.507167\pi\) | |||||||
\(384\) | 62.6724i | 0.163209i | ||||||||
\(385\) | 17.5837 | + | 62.6563i | 0.0456720 | + | 0.162744i | ||||
\(386\) | 190.495 | 0.493511 | ||||||||
\(387\) | 125.529i | 0.324364i | ||||||||
\(388\) | −434.087 | −1.11878 | ||||||||
\(389\) | −507.474 | −1.30456 | −0.652281 | − | 0.757978i | \(-0.726188\pi\) | ||||
−0.652281 | + | 0.757978i | \(0.726188\pi\) | |||||||
\(390\) | 7.98555 | 0.0204758 | ||||||||
\(391\) | − | 178.346i | − | 0.456129i | ||||||
\(392\) | − | 7.95347i | − | 0.0202895i | ||||||
\(393\) | − | 181.958i | − | 0.462997i | ||||||
\(394\) | 265.622 | 0.674168 | ||||||||
\(395\) | − | 38.3949i | − | 0.0972022i | ||||||
\(396\) | −139.552 | + | 39.1634i | −0.352403 | + | 0.0988976i | ||||
\(397\) | 42.2426 | 0.106404 | 0.0532022 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532022 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(398\) | 892.323i | 2.24202i | ||||||||
\(399\) | 38.7733 | 0.0971762 | ||||||||
\(400\) | −71.3866 | −0.178467 | ||||||||
\(401\) | −520.772 | −1.29868 | −0.649342 | − | 0.760497i | \(-0.724955\pi\) | ||||
−0.649342 | + | 0.760497i | \(0.724955\pi\) | |||||||
\(402\) | − | 461.155i | − | 1.14715i | ||||||
\(403\) | − | 36.4952i | − | 0.0905588i | ||||||
\(404\) | 673.037i | 1.66593i | ||||||||
\(405\) | 20.1246 | 0.0496904 | ||||||||
\(406\) | 359.243i | 0.884834i | ||||||||
\(407\) | 519.299 | − | 145.735i | 1.27592 | − | 0.358071i | ||||
\(408\) | 29.2700 | 0.0717402 | ||||||||
\(409\) | 52.3323i | 0.127952i | 0.997951 | + | 0.0639760i | \(0.0203781\pi\) | ||||
−0.997951 | + | 0.0639760i | \(0.979622\pi\) | |||||||
\(410\) | 99.8655 | 0.243574 | ||||||||
\(411\) | 399.242 | 0.971393 | ||||||||
\(412\) | −791.544 | −1.92122 | ||||||||
\(413\) | 76.3628i | 0.184898i | ||||||||
\(414\) | 104.213i | 0.251721i | ||||||||
\(415\) | 324.772i | 0.782583i | ||||||||
\(416\) | 32.6726 | 0.0785399 | ||||||||
\(417\) | − | 164.153i | − | 0.393653i | ||||||
\(418\) | 259.592 | − | 72.8514i | 0.621035 | − | 0.174286i | ||||
\(419\) | −576.390 | −1.37563 | −0.687816 | − | 0.725885i | \(-0.741430\pi\) | ||||
−0.687816 | + | 0.725885i | \(0.741430\pi\) | |||||||
\(420\) | 45.0068i | 0.107159i | ||||||||
\(421\) | 358.171 | 0.850761 | 0.425381 | − | 0.905014i | \(-0.360140\pi\) | ||||
0.425381 | + | 0.905014i | \(0.360140\pi\) | |||||||
\(422\) | −70.1297 | −0.166184 | ||||||||
\(423\) | 36.7251 | 0.0868205 | ||||||||
\(424\) | − | 13.9159i | − | 0.0328204i | ||||||
\(425\) | 74.3658i | 0.174978i | ||||||||
\(426\) | 582.707i | 1.36786i | ||||||||
\(427\) | 298.481 | 0.699019 | ||||||||
\(428\) | 496.799i | 1.16075i | ||||||||
\(429\) | 3.66402 | + | 13.0561i | 0.00854085 | + | 0.0304337i | ||||
\(430\) | 271.048 | 0.630344 | ||||||||
\(431\) | 164.732i | 0.382209i | 0.981570 | + | 0.191105i | \(0.0612070\pi\) | ||||
−0.981570 | + | 0.191105i | \(0.938793\pi\) | |||||||
\(432\) | 74.1872 | 0.171730 | ||||||||
\(433\) | 514.038 | 1.18715 | 0.593577 | − | 0.804777i | \(-0.297715\pi\) | ||||
0.593577 | + | 0.804777i | \(0.297715\pi\) | |||||||
\(434\) | 393.008 | 0.905549 | ||||||||
\(435\) | − | 181.529i | − | 0.417308i | ||||||
\(436\) | − | 798.838i | − | 1.83220i | ||||||
\(437\) | − | 101.458i | − | 0.232168i | ||||||
\(438\) | 127.464 | 0.291014 | ||||||||
\(439\) | 715.735i | 1.63038i | 0.579196 | + | 0.815188i | \(0.303367\pi\) | ||||
−0.579196 | + | 0.815188i | \(0.696633\pi\) | |||||||
\(440\) | 7.55127 | + | 26.9076i | 0.0171620 | + | 0.0611535i | ||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 30.6664i | − | 0.0693810i | ||||||
\(443\) | 695.369 | 1.56968 | 0.784841 | − | 0.619697i | \(-0.212745\pi\) | ||||
0.784841 | + | 0.619697i | \(0.212745\pi\) | |||||||
\(444\) | 373.019 | 0.840133 | ||||||||
\(445\) | 11.9009 | 0.0267436 | ||||||||
\(446\) | 413.020i | 0.926053i | ||||||||
\(447\) | 420.622i | 0.940988i | ||||||||
\(448\) | 200.747i | 0.448095i | ||||||||
\(449\) | 468.024 | 1.04237 | 0.521185 | − | 0.853444i | \(-0.325490\pi\) | ||||
0.521185 | + | 0.853444i | \(0.325490\pi\) | |||||||
\(450\) | − | 43.4540i | − | 0.0965644i | ||||||
\(451\) | 45.8214 | + | 163.276i | 0.101600 | + | 0.362032i | ||||
\(452\) | 379.650 | 0.839934 | ||||||||
\(453\) | − | 219.215i | − | 0.483919i | ||||||
\(454\) | −304.046 | −0.669706 | ||||||||
\(455\) | 4.21071 | 0.00925431 | ||||||||
\(456\) | 16.6511 | 0.0365155 | ||||||||
\(457\) | − | 684.861i | − | 1.49860i | −0.662229 | − | 0.749301i | \(-0.730389\pi\) | ||
0.662229 | − | 0.749301i | \(-0.269611\pi\) | |||||||
\(458\) | − | 880.084i | − | 1.92158i | ||||||
\(459\) | − | 77.2833i | − | 0.168373i | ||||||
\(460\) | 117.769 | 0.256019 | ||||||||
\(461\) | 529.665i | 1.14895i | 0.818523 | + | 0.574474i | \(0.194793\pi\) | ||||
−0.818523 | + | 0.574474i | \(0.805207\pi\) | |||||||
\(462\) | −140.598 | + | 39.4570i | −0.304324 | + | 0.0854048i | ||||
\(463\) | −416.136 | −0.898782 | −0.449391 | − | 0.893335i | \(-0.648359\pi\) | ||||
−0.449391 | + | 0.893335i | \(0.648359\pi\) | |||||||
\(464\) | − | 669.187i | − | 1.44221i | ||||||
\(465\) | −198.591 | −0.427078 | ||||||||
\(466\) | 975.483 | 2.09331 | ||||||||
\(467\) | −729.942 | −1.56304 | −0.781522 | − | 0.623877i | \(-0.785556\pi\) | ||||
−0.781522 | + | 0.623877i | \(0.785556\pi\) | |||||||
\(468\) | 9.37833i | 0.0200392i | ||||||||
\(469\) | − | 243.163i | − | 0.518471i | ||||||
\(470\) | − | 79.2984i | − | 0.168720i | ||||||
\(471\) | −171.634 | −0.364404 | ||||||||
\(472\) | 32.7938i | 0.0694783i | ||||||||
\(473\) | 124.365 | + | 443.153i | 0.262929 | + | 0.936898i | ||||
\(474\) | 86.1563 | 0.181764 | ||||||||
\(475\) | 42.3051i | 0.0890635i | ||||||||
\(476\) | 172.837 | 0.363102 | ||||||||
\(477\) | −36.7428 | −0.0770290 | ||||||||
\(478\) | 272.642 | 0.570381 | ||||||||
\(479\) | − | 195.068i | − | 0.407239i | −0.979050 | − | 0.203620i | \(-0.934729\pi\) | ||
0.979050 | − | 0.203620i | \(-0.0652706\pi\) | |||||||
\(480\) | − | 177.790i | − | 0.370397i | ||||||
\(481\) | − | 34.8986i | − | 0.0725543i | ||||||
\(482\) | −280.216 | −0.581361 | ||||||||
\(483\) | 54.9504i | 0.113769i | ||||||||
\(484\) | −453.857 | + | 276.516i | −0.937721 | + | 0.571314i | ||||
\(485\) | 220.993 | 0.455656 | ||||||||
\(486\) | 45.1587i | 0.0929191i | ||||||||
\(487\) | −555.859 | −1.14139 | −0.570697 | − | 0.821161i | \(-0.693327\pi\) | ||||
−0.570697 | + | 0.821161i | \(0.693327\pi\) | |||||||
\(488\) | 128.182 | 0.262668 | ||||||||
\(489\) | 289.005 | 0.591012 | ||||||||
\(490\) | 45.3441i | 0.0925391i | ||||||||
\(491\) | 414.754i | 0.844713i | 0.906430 | + | 0.422357i | \(0.138797\pi\) | ||||
−0.906430 | + | 0.422357i | \(0.861203\pi\) | |||||||
\(492\) | 117.283i | 0.238381i | ||||||||
\(493\) | −697.115 | −1.41403 | ||||||||
\(494\) | − | 17.4455i | − | 0.0353147i | ||||||
\(495\) | 71.0456 | − | 19.9381i | 0.143526 | − | 0.0402789i | ||||
\(496\) | −732.084 | −1.47598 | ||||||||
\(497\) | 307.256i | 0.618222i | ||||||||
\(498\) | −728.773 | −1.46340 | ||||||||
\(499\) | 142.728 | 0.286027 | 0.143014 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143014 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(500\) | −49.1064 | −0.0982128 | ||||||||
\(501\) | 354.554i | 0.707692i | ||||||||
\(502\) | − | 196.848i | − | 0.392127i | ||||||
\(503\) | 133.747i | 0.265898i | 0.991123 | + | 0.132949i | \(0.0424446\pi\) | ||||
−0.991123 | + | 0.132949i | \(0.957555\pi\) | |||||||
\(504\) | −9.01839 | −0.0178936 | ||||||||
\(505\) | − | 342.642i | − | 0.678499i | ||||||
\(506\) | 103.247 | + | 367.900i | 0.204045 | + | 0.727076i | ||||
\(507\) | −291.839 | −0.575620 | ||||||||
\(508\) | 666.006i | 1.31104i | ||||||||
\(509\) | −412.459 | −0.810332 | −0.405166 | − | 0.914243i | \(-0.632786\pi\) | ||||
−0.405166 | + | 0.914243i | \(0.632786\pi\) | |||||||
\(510\) | −166.873 | −0.327203 | ||||||||
\(511\) | 67.2108 | 0.131528 | ||||||||
\(512\) | − | 720.293i | − | 1.40682i | ||||||
\(513\) | − | 43.9648i | − | 0.0857013i | ||||||
\(514\) | 939.160i | 1.82716i | ||||||||
\(515\) | 402.974 | 0.782473 | ||||||||
\(516\) | 318.322i | 0.616903i | ||||||||
\(517\) | 129.650 | − | 36.3846i | 0.250774 | − | 0.0703765i | ||||
\(518\) | 375.815 | 0.725512 | ||||||||
\(519\) | 268.475i | 0.517294i | ||||||||
\(520\) | 1.80828 | 0.00347745 | ||||||||
\(521\) | −630.906 | −1.21095 | −0.605476 | − | 0.795863i | \(-0.707017\pi\) | ||||
−0.605476 | + | 0.795863i | \(0.707017\pi\) | |||||||
\(522\) | 407.343 | 0.780351 | ||||||||
\(523\) | 2.02836i | 0.00387831i | 0.999998 | + | 0.00193915i | \(0.000617252\pi\) | ||||
−0.999998 | + | 0.00193915i | \(0.999383\pi\) | |||||||
\(524\) | − | 461.417i | − | 0.880566i | ||||||
\(525\) | − | 22.9129i | − | 0.0436436i | ||||||
\(526\) | 793.201 | 1.50799 | ||||||||
\(527\) | 762.637i | 1.44713i | ||||||||
\(528\) | 261.902 | − | 73.4994i | 0.496026 | − | 0.139203i | ||||
\(529\) | −385.212 | −0.728189 | ||||||||
\(530\) | 79.3368i | 0.149692i | ||||||||
\(531\) | 86.5873 | 0.163065 | ||||||||
\(532\) | 98.3231 | 0.184818 | ||||||||
\(533\) | 10.9727 | 0.0205867 | ||||||||
\(534\) | 26.7051i | 0.0500095i | ||||||||
\(535\) | − | 252.920i | − | 0.472747i | ||||||
\(536\) | − | 104.425i | − | 0.194824i | ||||||
\(537\) | −77.8011 | −0.144881 | ||||||||
\(538\) | − | 967.368i | − | 1.79808i | ||||||
\(539\) | −74.1359 | + | 20.8053i | −0.137543 | + | 0.0385999i | ||||
\(540\) | 51.0329 | 0.0945053 | ||||||||
\(541\) | − | 540.779i | − | 0.999592i | −0.866143 | − | 0.499796i | \(-0.833408\pi\) | ||
0.866143 | − | 0.499796i | \(-0.166592\pi\) | |||||||
\(542\) | 543.338 | 1.00247 | ||||||||
\(543\) | −604.661 | −1.11356 | ||||||||
\(544\) | −682.757 | −1.25507 | ||||||||
\(545\) | 406.687i | 0.746215i | ||||||||
\(546\) | 9.44863i | 0.0173052i | ||||||||
\(547\) | − | 370.898i | − | 0.678059i | −0.940776 | − | 0.339029i | \(-0.889901\pi\) | ||
0.940776 | − | 0.339029i | \(-0.110099\pi\) | |||||||
\(548\) | 1012.42 | 1.84748 | ||||||||
\(549\) | − | 338.446i | − | 0.616477i | ||||||
\(550\) | −43.0511 | − | 153.405i | −0.0782748 | − | 0.278918i | ||||
\(551\) | −396.574 | −0.719734 | ||||||||
\(552\) | 23.5983i | 0.0427505i | ||||||||
\(553\) | 45.4294 | 0.0821508 | ||||||||
\(554\) | 514.644 | 0.928961 | ||||||||
\(555\) | −189.903 | −0.342168 | ||||||||
\(556\) | − | 416.267i | − | 0.748682i | ||||||
\(557\) | 263.296i | 0.472703i | 0.971668 | + | 0.236351i | \(0.0759517\pi\) | ||||
−0.971668 | + | 0.236351i | \(0.924048\pi\) | |||||||
\(558\) | − | 445.629i | − | 0.798619i | ||||||
\(559\) | 29.7813 | 0.0532760 | ||||||||
\(560\) | − | 84.4658i | − | 0.150832i | ||||||
\(561\) | −76.5668 | − | 272.832i | −0.136483 | − | 0.486331i | ||||
\(562\) | 201.083 | 0.357799 | ||||||||
\(563\) | 731.582i | 1.29944i | 0.760176 | + | 0.649718i | \(0.225113\pi\) | ||||
−0.760176 | + | 0.649718i | \(0.774887\pi\) | |||||||
\(564\) | 93.1291 | 0.165122 | ||||||||
\(565\) | −193.279 | −0.342087 | ||||||||
\(566\) | −1177.12 | −2.07973 | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | 131.950i | 0.232307i | ||||||||
\(569\) | − | 473.306i | − | 0.831821i | −0.909406 | − | 0.415910i | \(-0.863463\pi\) | ||
0.909406 | − | 0.415910i | \(-0.136537\pi\) | |||||||
\(570\) | −94.9308 | −0.166545 | ||||||||
\(571\) | 1012.32i | 1.77289i | 0.462838 | + | 0.886443i | \(0.346831\pi\) | ||||
−0.462838 | + | 0.886443i | \(0.653169\pi\) | |||||||
\(572\) | 9.29139 | + | 33.1082i | 0.0162437 | + | 0.0578814i | ||||
\(573\) | −126.218 | −0.220276 | ||||||||
\(574\) | 118.162i | 0.205858i | ||||||||
\(575\) | −59.9558 | −0.104271 | ||||||||
\(576\) | 227.625 | 0.395183 | ||||||||
\(577\) | 372.070 | 0.644836 | 0.322418 | − | 0.946597i | \(-0.395504\pi\) | ||||
0.322418 | + | 0.946597i | \(0.395504\pi\) | |||||||
\(578\) | − | 196.380i | − | 0.339757i | ||||||
\(579\) | − | 113.895i | − | 0.196711i | ||||||
\(580\) | − | 460.330i | − | 0.793672i | ||||||
\(581\) | −384.275 | −0.661403 | ||||||||
\(582\) | 495.898i | 0.852059i | ||||||||
\(583\) | −129.713 | + | 36.4022i | −0.222492 | + | 0.0624395i | ||||
\(584\) | 28.8635 | 0.0494237 | ||||||||
\(585\) | − | 4.77450i | − | 0.00816153i | ||||||
\(586\) | −1419.26 | −2.42195 | ||||||||
\(587\) | −504.784 | −0.859939 | −0.429969 | − | 0.902843i | \(-0.641476\pi\) | ||||
−0.429969 | + | 0.902843i | \(0.641476\pi\) | |||||||
\(588\) | −53.2527 | −0.0905659 | ||||||||
\(589\) | 433.848i | 0.736584i | ||||||||
\(590\) | − | 186.963i | − | 0.316887i | ||||||
\(591\) | − | 158.813i | − | 0.268720i | ||||||
\(592\) | −700.057 | −1.18253 | ||||||||
\(593\) | − | 573.183i | − | 0.966582i | −0.875460 | − | 0.483291i | \(-0.839441\pi\) | ||
0.875460 | − | 0.483291i | \(-0.160559\pi\) | |||||||
\(594\) | 44.7401 | + | 159.423i | 0.0753200 | + | 0.268389i | ||||
\(595\) | −87.9909 | −0.147884 | ||||||||
\(596\) | 1066.63i | 1.78965i | ||||||||
\(597\) | 533.512 | 0.893655 | ||||||||
\(598\) | 24.7241 | 0.0413446 | ||||||||
\(599\) | −85.7158 | −0.143098 | −0.0715491 | − | 0.997437i | \(-0.522794\pi\) | ||||
−0.0715491 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(600\) | − | 9.83987i | − | 0.0163998i | ||||||
\(601\) | − | 1139.84i | − | 1.89657i | −0.317419 | − | 0.948285i | \(-0.602816\pi\) | ||
0.317419 | − | 0.948285i | \(-0.397184\pi\) | |||||||
\(602\) | 320.708i | 0.532738i | ||||||||
\(603\) | −275.721 | −0.457248 | ||||||||
\(604\) | − | 555.896i | − | 0.920357i | ||||||
\(605\) | 231.058 | − | 140.774i | 0.381914 | − | 0.232684i | ||||
\(606\) | 768.873 | 1.26877 | ||||||||
\(607\) | 409.695i | 0.674950i | 0.941334 | + | 0.337475i | \(0.109573\pi\) | ||||
−0.941334 | + | 0.337475i | \(0.890427\pi\) | |||||||
\(608\) | −388.406 | −0.638825 | ||||||||
\(609\) | 214.788 | 0.352690 | ||||||||
\(610\) | −730.788 | −1.19801 | ||||||||
\(611\) | − | 8.71290i | − | 0.0142601i | ||||||
\(612\) | − | 195.978i | − | 0.320226i | ||||||
\(613\) | 439.482i | 0.716936i | 0.933542 | + | 0.358468i | \(0.116701\pi\) | ||||
−0.933542 | + | 0.358468i | \(0.883299\pi\) | |||||||
\(614\) | 1072.87 | 1.74734 | ||||||||
\(615\) | − | 59.7087i | − | 0.0970874i | ||||||
\(616\) | −31.8375 | + | 8.93478i | −0.0516842 | + | 0.0145045i | ||||
\(617\) | −154.070 | −0.249708 | −0.124854 | − | 0.992175i | \(-0.539846\pi\) | ||||
−0.124854 | + | 0.992175i | \(0.539846\pi\) | |||||||
\(618\) | 904.254i | 1.46319i | ||||||||
\(619\) | 847.420 | 1.36901 | 0.684507 | − | 0.729006i | \(-0.260017\pi\) | ||||
0.684507 | + | 0.729006i | \(0.260017\pi\) | |||||||
\(620\) | −503.596 | −0.812252 | ||||||||
\(621\) | 62.3079 | 0.100335 | ||||||||
\(622\) | 416.512i | 0.669634i | ||||||||
\(623\) | 14.0813i | 0.0226025i | ||||||||
\(624\) | − | 17.6006i | − | 0.0282062i | ||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 424.046i | 0.677390i | ||||||||
\(627\) | −43.5572 | − | 155.208i | −0.0694693 | − | 0.247541i | ||||
\(628\) | −435.238 | −0.693054 | ||||||||
\(629\) | 729.273i | 1.15942i | ||||||||
\(630\) | 51.4154 | 0.0816118 | ||||||||
\(631\) | −1243.23 | −1.97025 | −0.985126 | − | 0.171836i | \(-0.945030\pi\) | ||||
−0.985126 | + | 0.171836i | \(0.945030\pi\) | |||||||
\(632\) | 19.5095 | 0.0308695 | ||||||||
\(633\) | 41.9300i | 0.0662400i | ||||||||
\(634\) | − | 82.1304i | − | 0.129543i | ||||||
\(635\) | − | 339.063i | − | 0.533957i | ||||||
\(636\) | −93.1741 | −0.146500 | ||||||||
\(637\) | 4.98218i | 0.00782132i | ||||||||
\(638\) | 1438.04 | − | 403.567i | 2.25398 | − | 0.632550i | ||||
\(639\) | 348.396 | 0.545220 | ||||||||
\(640\) | − | 80.9097i | − | 0.126421i | ||||||
\(641\) | −547.215 | −0.853689 | −0.426845 | − | 0.904325i | \(-0.640375\pi\) | ||||
−0.426845 | + | 0.904325i | \(0.640375\pi\) | |||||||
\(642\) | 567.540 | 0.884019 | ||||||||
\(643\) | −818.702 | −1.27325 | −0.636627 | − | 0.771172i | \(-0.719671\pi\) | ||||
−0.636627 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(644\) | 139.346i | 0.216375i | ||||||||
\(645\) | − | 162.057i | − | 0.251251i | ||||||
\(646\) | 364.557i | 0.564329i | ||||||||
\(647\) | 853.865 | 1.31973 | 0.659865 | − | 0.751384i | \(-0.270613\pi\) | ||||
0.659865 | + | 0.751384i | \(0.270613\pi\) | |||||||
\(648\) | 10.2259i | 0.0157807i | ||||||||
\(649\) | 305.678 | − | 85.7846i | 0.470998 | − | 0.132180i | ||||
\(650\) | −10.3093 | −0.0158605 | ||||||||
\(651\) | − | 234.976i | − | 0.360947i | ||||||
\(652\) | 732.871 | 1.12404 | ||||||||
\(653\) | −973.029 | −1.49009 | −0.745045 | − | 0.667014i | \(-0.767572\pi\) | ||||
−0.745045 | + | 0.667014i | \(0.767572\pi\) | |||||||
\(654\) | −912.587 | −1.39539 | ||||||||
\(655\) | 234.906i | 0.358636i | ||||||||
\(656\) | − | 220.110i | − | 0.335533i | ||||||
\(657\) | − | 76.2098i | − | 0.115997i | ||||||
\(658\) | 93.8272 | 0.142595 | ||||||||
\(659\) | 608.065i | 0.922709i | 0.887216 | + | 0.461354i | \(0.152636\pi\) | ||||
−0.887216 | + | 0.461354i | \(0.847364\pi\) | |||||||
\(660\) | 180.161 | − | 50.5598i | 0.272971 | − | 0.0766058i | ||||
\(661\) | −845.646 | −1.27934 | −0.639671 | − | 0.768649i | \(-0.720930\pi\) | ||||
−0.639671 | + | 0.768649i | \(0.720930\pi\) | |||||||
\(662\) | − | 1745.70i | − | 2.63702i | ||||||
\(663\) | −18.3352 | −0.0276549 | ||||||||
\(664\) | −165.026 | −0.248533 | ||||||||
\(665\) | −50.0561 | −0.0752724 | ||||||||
\(666\) | − | 426.134i | − | 0.639841i | ||||||
\(667\) | − | 562.033i | − | 0.842628i | ||||||
\(668\) | 899.093i | 1.34595i | ||||||||
\(669\) | 246.941 | 0.369120 | ||||||||
\(670\) | 595.348i | 0.888580i | ||||||||
\(671\) | −335.308 | − | 1194.81i | −0.499714 | − | 1.78064i | ||||
\(672\) | 210.364 | 0.313042 | ||||||||
\(673\) | − | 1059.94i | − | 1.57495i | −0.616343 | − | 0.787477i | \(-0.711387\pi\) | ||
0.616343 | − | 0.787477i | \(-0.288613\pi\) | |||||||
\(674\) | 268.011 | 0.397643 | ||||||||
\(675\) | −25.9808 | −0.0384900 | ||||||||
\(676\) | −740.059 | −1.09476 | ||||||||
\(677\) | − | 105.704i | − | 0.156135i | −0.996948 | − | 0.0780676i | \(-0.975125\pi\) | ||
0.996948 | − | 0.0780676i | \(-0.0248750\pi\) | |||||||
\(678\) | − | 433.710i | − | 0.639690i | ||||||
\(679\) | 261.482i | 0.385099i | ||||||||
\(680\) | −37.7874 | −0.0555697 | ||||||||
\(681\) | 181.787i | 0.266941i | ||||||||
\(682\) | −441.498 | − | 1573.20i | −0.647358 | − | 2.30674i | ||||
\(683\) | −793.770 | −1.16218 | −0.581091 | − | 0.813839i | \(-0.697374\pi\) | ||||
−0.581091 | + | 0.813839i | \(0.697374\pi\) | |||||||
\(684\) | − | 111.488i | − | 0.162994i | ||||||
\(685\) | −515.420 | −0.752437 | ||||||||
\(686\) | −53.6519 | −0.0782098 | ||||||||
\(687\) | −526.195 | −0.765932 | ||||||||
\(688\) | − | 597.406i | − | 0.868322i | ||||||
\(689\) | 8.71711i | 0.0126518i | ||||||||
\(690\) | − | 134.538i | − | 0.194983i | ||||||
\(691\) | −338.653 | −0.490091 | −0.245045 | − | 0.969512i | \(-0.578803\pi\) | ||||
−0.245045 | + | 0.969512i | \(0.578803\pi\) | |||||||
\(692\) | 680.812i | 0.983832i | ||||||||
\(693\) | 23.5910 | + | 84.0623i | 0.0340419 | + | 0.121302i | ||||
\(694\) | 411.941 | 0.593575 | ||||||||
\(695\) | 211.921i | 0.304922i | ||||||||
\(696\) | 92.2401 | 0.132529 | ||||||||
\(697\) | −229.296 | −0.328975 | ||||||||
\(698\) | 297.396 | 0.426068 | ||||||||
\(699\) | − | 583.233i | − | 0.834382i | ||||||
\(700\) | − | 58.1035i | − | 0.0830050i | ||||||
\(701\) | 42.6789i | 0.0608829i | 0.999537 | + | 0.0304415i | \(0.00969132\pi\) | ||||
−0.999537 | + | 0.0304415i | \(0.990309\pi\) | |||||||
\(702\) | 10.7137 | 0.0152617 | ||||||||
\(703\) | 414.868i | 0.590140i | ||||||||
\(704\) | 803.582 | − | 225.515i | 1.14145 | − | 0.320334i | ||||
\(705\) | −47.4119 | −0.0672509 | ||||||||
\(706\) | − | 1156.52i | − | 1.63813i | ||||||
\(707\) | 405.420 | 0.573436 | ||||||||
\(708\) | 219.572 | 0.310130 | ||||||||
\(709\) | 735.890 | 1.03793 | 0.518963 | − | 0.854797i | \(-0.326318\pi\) | ||||
0.518963 | + | 0.854797i | \(0.326318\pi\) | |||||||
\(710\) | − | 752.272i | − | 1.05954i | ||||||
\(711\) | − | 51.5121i | − | 0.0724502i | ||||||
\(712\) | 6.04719i | 0.00849324i | ||||||||
\(713\) | −614.859 | −0.862355 | ||||||||
\(714\) | − | 197.447i | − | 0.276537i | ||||||
\(715\) | −4.73023 | − | 16.8553i | −0.00661571 | − | 0.0235739i | ||||
\(716\) | −197.291 | −0.275547 | ||||||||
\(717\) | − | 163.010i | − | 0.227350i | ||||||
\(718\) | 1613.23 | 2.24684 | ||||||||
\(719\) | −613.250 | −0.852921 | −0.426460 | − | 0.904506i | \(-0.640240\pi\) | ||||
−0.426460 | + | 0.904506i | \(0.640240\pi\) | |||||||
\(720\) | −95.7752 | −0.133021 | ||||||||
\(721\) | 476.805i | 0.661311i | ||||||||
\(722\) | − | 838.404i | − | 1.16122i | ||||||
\(723\) | 167.539i | 0.231727i | ||||||||
\(724\) | −1533.33 | −2.11785 | ||||||||
\(725\) | 234.353i | 0.323246i | ||||||||
\(726\) | 315.890 | + | 518.483i | 0.435110 | + | 0.714164i | ||||
\(727\) | −534.215 | −0.734822 | −0.367411 | − | 0.930059i | \(-0.619756\pi\) | ||||
−0.367411 | + | 0.930059i | \(0.619756\pi\) | |||||||
\(728\) | 2.13958i | 0.00293899i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −164.556 | −0.225419 | ||||||||
\(731\) | −622.338 | −0.851351 | ||||||||
\(732\) | − | 858.246i | − | 1.17247i | ||||||
\(733\) | − | 1244.06i | − | 1.69721i | −0.529024 | − | 0.848607i | \(-0.677442\pi\) | ||
0.529024 | − | 0.848607i | \(-0.322558\pi\) | |||||||
\(734\) | − | 213.580i | − | 0.290981i | ||||||
\(735\) | 27.1109 | 0.0368856 | ||||||||
\(736\) | − | 550.457i | − | 0.747904i | ||||||
\(737\) | −973.372 | + | 273.165i | −1.32072 | + | 0.370644i | ||||
\(738\) | 133.984 | 0.181550 | ||||||||
\(739\) | − | 101.334i | − | 0.137123i | −0.997647 | − | 0.0685616i | \(-0.978159\pi\) | ||
0.997647 | − | 0.0685616i | \(-0.0218410\pi\) | |||||||
\(740\) | −481.565 | −0.650764 | ||||||||
\(741\) | −10.4305 | −0.0140762 | ||||||||
\(742\) | −93.8725 | −0.126513 | ||||||||
\(743\) | 943.645i | 1.27005i | 0.772493 | + | 0.635024i | \(0.219010\pi\) | ||||
−0.772493 | + | 0.635024i | \(0.780990\pi\) | |||||||
\(744\) | − | 100.910i | − | 0.135632i | ||||||
\(745\) | − | 543.020i | − | 0.728886i | ||||||
\(746\) | 529.596 | 0.709914 | ||||||||
\(747\) | 435.727i | 0.583303i | ||||||||
\(748\) | −194.162 | − | 691.859i | −0.259574 | − | 0.924945i | ||||
\(749\) | 299.259 | 0.399544 | ||||||||
\(750\) | 56.0988i | 0.0747984i | ||||||||
\(751\) | 731.692 | 0.974290 | 0.487145 | − | 0.873321i | \(-0.338038\pi\) | ||||
0.487145 | + | 0.873321i | \(0.338038\pi\) | |||||||
\(752\) | −174.779 | −0.232418 | ||||||||
\(753\) | −117.694 | −0.156300 | ||||||||
\(754\) | − | 96.6407i | − | 0.128171i | ||||||
\(755\) | 283.006i | 0.374842i | ||||||||
\(756\) | 60.3829i | 0.0798716i | ||||||||
\(757\) | 174.741 | 0.230834 | 0.115417 | − | 0.993317i | \(-0.463180\pi\) | ||||
0.115417 | + | 0.993317i | \(0.463180\pi\) | |||||||
\(758\) | 1166.19i | 1.53852i | ||||||||
\(759\) | 219.964 | − | 61.7303i | 0.289808 | − | 0.0813310i | ||||
\(760\) | −21.4964 | −0.0282848 | ||||||||
\(761\) | − | 895.484i | − | 1.17672i | −0.808599 | − | 0.588360i | \(-0.799774\pi\) | ||
0.808599 | − | 0.588360i | \(-0.200226\pi\) | |||||||
\(762\) | 760.841 | 0.998479 | ||||||||
\(763\) | −481.199 | −0.630667 | ||||||||
\(764\) | −320.070 | −0.418940 | ||||||||
\(765\) | 99.7722i | 0.130421i | ||||||||
\(766\) | 49.9620i | 0.0652246i | ||||||||
\(767\) | − | 20.5425i | − | 0.0267830i | ||||||
\(768\) | −344.121 | −0.448074 | ||||||||
\(769\) | − | 866.291i | − | 1.12652i | −0.826281 | − | 0.563258i | \(-0.809548\pi\) | ||
0.826281 | − | 0.563258i | \(-0.190452\pi\) | |||||||
\(770\) | 181.511 | − | 50.9388i | 0.235729 | − | 0.0661543i | ||||
\(771\) | 561.516 | 0.728295 | ||||||||
\(772\) | − | 288.821i | − | 0.374121i | ||||||
\(773\) | 26.2361 | 0.0339406 | 0.0169703 | − | 0.999856i | \(-0.494598\pi\) | ||||
0.0169703 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(774\) | 363.649 | 0.469830 | ||||||||
\(775\) | 256.380 | 0.330813 | ||||||||
\(776\) | 112.293i | 0.144707i | ||||||||
\(777\) | − | 224.697i | − | 0.289185i | ||||||
\(778\) | 1470.12i | 1.88961i | ||||||||
\(779\) | −130.441 | −0.167447 | ||||||||
\(780\) | − | 12.1074i | − | 0.0155223i | ||||||
\(781\) | 1229.94 | − | 345.166i | 1.57482 | − | 0.441954i | ||||
\(782\) | −516.658 | −0.660687 | ||||||||
\(783\) | − | 243.547i | − | 0.311043i | ||||||
\(784\) | 99.9413 | 0.127476 | ||||||||
\(785\) | 221.579 | 0.282266 | ||||||||
\(786\) | −527.119 | −0.670635 | ||||||||
\(787\) | 457.871i | 0.581793i | 0.956754 | + | 0.290897i | \(0.0939536\pi\) | ||||
−0.956754 | + | 0.290897i | \(0.906046\pi\) | |||||||
\(788\) | − | 402.726i | − | 0.511074i | ||||||
\(789\) | − | 474.248i | − | 0.601075i | ||||||
\(790\) | −111.227 | −0.140794 | ||||||||
\(791\) | − | 228.691i | − | 0.289116i | ||||||
\(792\) | 10.1311 | + | 36.1003i | 0.0127918 | + | 0.0455812i | ||||
\(793\) | −80.2951 | −0.101255 | ||||||||
\(794\) | − | 122.374i | − | 0.154123i | ||||||
\(795\) | 47.4348 | 0.0596664 | ||||||||
\(796\) | 1352.90 | 1.69963 | ||||||||
\(797\) | 1074.95 | 1.34874 | 0.674372 | − | 0.738392i | \(-0.264415\pi\) | ||||
0.674372 | + | 0.738392i | \(0.264415\pi\) | |||||||
\(798\) | − | 112.324i | − | 0.140756i | ||||||
\(799\) | 182.073i | 0.227876i | ||||||||
\(800\) | 229.526i | 0.286908i | ||||||||
\(801\) | 15.9667 | 0.0199335 | ||||||||
\(802\) | 1508.64i | 1.88110i | ||||||||
\(803\) | −75.5033 | − | 269.042i | −0.0940266 | − | 0.335046i | ||||
\(804\) | −699.185 | −0.869633 | ||||||||
\(805\) | − | 70.9406i | − | 0.0881250i | ||||||
\(806\) | −105.724 | −0.131171 | ||||||||
\(807\) | −578.381 | −0.716705 | ||||||||
\(808\) | 174.106 | 0.215478 | ||||||||
\(809\) | 42.4671i | 0.0524933i | 0.999655 | + | 0.0262466i | \(0.00835552\pi\) | ||||
−0.999655 | + | 0.0262466i | \(0.991644\pi\) | |||||||
\(810\) | − | 58.2996i | − | 0.0719748i | ||||||
\(811\) | 285.790i | 0.352392i | 0.984355 | + | 0.176196i | \(0.0563792\pi\) | ||||
−0.984355 | + | 0.176196i | \(0.943621\pi\) | |||||||
\(812\) | 544.669 | 0.670775 | ||||||||
\(813\) | − | 324.857i | − | 0.399578i | ||||||
\(814\) | −422.184 | − | 1504.37i | −0.518653 | − | 1.84813i | ||||
\(815\) | −373.103 | −0.457796 | ||||||||
\(816\) | 367.799i | 0.450734i | ||||||||
\(817\) | −354.035 | −0.433335 | ||||||||
\(818\) | 151.603 | 0.185334 | ||||||||
\(819\) | 5.64926 | 0.00689775 | ||||||||
\(820\) | − | 151.412i | − | 0.184649i | ||||||
\(821\) | 56.1359i | 0.0683750i | 0.999415 | + | 0.0341875i | \(0.0108843\pi\) | ||||
−0.999415 | + | 0.0341875i | \(0.989116\pi\) | |||||||
\(822\) | − | 1156.58i | − | 1.40703i | ||||||
\(823\) | −729.017 | −0.885804 | −0.442902 | − | 0.896570i | \(-0.646051\pi\) | ||||
−0.442902 | + | 0.896570i | \(0.646051\pi\) | |||||||
\(824\) | 204.762i | 0.248498i | ||||||||
\(825\) | −91.7194 | + | 25.7399i | −0.111175 | + | 0.0311999i | ||||
\(826\) | 221.218 | 0.267818 | ||||||||
\(827\) | − | 126.809i | − | 0.153336i | −0.997057 | − | 0.0766679i | \(-0.975572\pi\) | ||
0.997057 | − | 0.0766679i | \(-0.0244281\pi\) | |||||||
\(828\) | 158.003 | 0.190825 | ||||||||
\(829\) | 251.855 | 0.303806 | 0.151903 | − | 0.988395i | \(-0.451460\pi\) | ||||
0.151903 | + | 0.988395i | \(0.451460\pi\) | |||||||
\(830\) | 940.842 | 1.13354 | ||||||||
\(831\) | − | 307.701i | − | 0.370279i | ||||||
\(832\) | − | 54.0033i | − | 0.0649079i | ||||||
\(833\) | − | 104.112i | − | 0.124985i | ||||||
\(834\) | −475.541 | −0.570193 | ||||||||
\(835\) | − | 457.727i | − | 0.548176i | ||||||
\(836\) | −110.454 | − | 393.584i | −0.132122 | − | 0.470794i | ||||
\(837\) | −266.438 | −0.318325 | ||||||||
\(838\) | 1669.76i | 1.99256i | ||||||||
\(839\) | 199.028 | 0.237220 | 0.118610 | − | 0.992941i | \(-0.462156\pi\) | ||||
0.118610 | + | 0.992941i | \(0.462156\pi\) | |||||||
\(840\) | 11.6427 | 0.0138603 | ||||||||
\(841\) | −1355.86 | −1.61219 | ||||||||
\(842\) | − | 1037.60i | − | 1.23230i | ||||||
\(843\) | − | 120.226i | − | 0.142617i | ||||||
\(844\) | 106.328i | 0.125981i | ||||||||
\(845\) | 376.763 | 0.445873 | ||||||||
\(846\) | − | 106.390i | − | 0.125757i | ||||||
\(847\) | 166.566 | + | 273.391i | 0.196654 | + | 0.322776i | ||||
\(848\) | 174.863 | 0.206206 | ||||||||
\(849\) | 703.793i | 0.828967i | ||||||||
\(850\) | 215.433 | 0.253450 | ||||||||
\(851\) | −587.960 | −0.690905 | ||||||||
\(852\) | 883.478 | 1.03695 | ||||||||
\(853\) | 738.707i | 0.866011i | 0.901391 | + | 0.433005i | \(0.142547\pi\) | ||||
−0.901391 | + | 0.433005i | \(0.857453\pi\) | |||||||
\(854\) | − | 864.679i | − | 1.01251i | ||||||
\(855\) | 56.7583i | 0.0663840i | ||||||||
\(856\) | 128.516 | 0.150135 | ||||||||
\(857\) | − | 574.376i | − | 0.670217i | −0.942180 | − | 0.335109i | \(-0.891227\pi\) | ||
0.942180 | − | 0.335109i | \(-0.108773\pi\) | |||||||
\(858\) | 37.8226 | − | 10.6144i | 0.0440822 | − | 0.0123711i | ||||
\(859\) | 1020.80 | 1.18836 | 0.594178 | − | 0.804334i | \(-0.297478\pi\) | ||||
0.594178 | + | 0.804334i | \(0.297478\pi\) | |||||||
\(860\) | − | 410.952i | − | 0.477851i | ||||||
\(861\) | 70.6483 | 0.0820538 | ||||||||
\(862\) | 477.218 | 0.553617 | ||||||||
\(863\) | 600.040 | 0.695295 | 0.347648 | − | 0.937625i | \(-0.386981\pi\) | ||||
0.347648 | + | 0.937625i | \(0.386981\pi\) | |||||||
\(864\) | − | 238.531i | − | 0.276077i | ||||||
\(865\) | − | 346.600i | − | 0.400694i | ||||||
\(866\) | − | 1489.13i | − | 1.71955i | ||||||
\(867\) | −117.414 | −0.135425 | ||||||||
\(868\) | − | 595.863i | − | 0.686478i | ||||||
\(869\) | −51.0346 | − | 181.852i | −0.0587279 | − | 0.209266i | ||||
\(870\) | −525.878 | −0.604457 | ||||||||
\(871\) | 65.4138i | 0.0751019i | ||||||||
\(872\) | −206.649 | −0.236983 | ||||||||
\(873\) | 296.493 | 0.339626 | ||||||||
\(874\) | −293.915 | −0.336288 | ||||||||
\(875\) | 29.5804i | 0.0338062i | ||||||||
\(876\) | − | 193.256i | − | 0.220612i | ||||||
\(877\) | 901.224i | 1.02762i | 0.857904 | + | 0.513811i | \(0.171767\pi\) | ||||
−0.857904 | + | 0.513811i | \(0.828233\pi\) | |||||||
\(878\) | 2073.44 | 2.36154 | ||||||||
\(879\) | 848.565i | 0.965375i | ||||||||
\(880\) | −338.114 | + | 94.8873i | −0.384220 | + | 0.107827i | ||||
\(881\) | −1631.17 | −1.85150 | −0.925751 | − | 0.378133i | \(-0.876566\pi\) | ||||
−0.925751 | + | 0.378133i | \(0.876566\pi\) | |||||||
\(882\) | 60.8356i | 0.0689746i | ||||||||
\(883\) | 1371.17 | 1.55286 | 0.776430 | − | 0.630204i | \(-0.217029\pi\) | ||||
0.776430 | + | 0.630204i | \(0.217029\pi\) | |||||||
\(884\) | −46.4952 | −0.0525964 | ||||||||
\(885\) | −111.784 | −0.126309 | ||||||||
\(886\) | − | 2014.44i | − | 2.27363i | ||||||
\(887\) | 54.8712i | 0.0618615i | 0.999522 | + | 0.0309308i | \(0.00984714\pi\) | ||||
−0.999522 | + | 0.0309308i | \(0.990153\pi\) | |||||||
\(888\) | − | 96.4953i | − | 0.108666i | ||||||
\(889\) | 401.184 | 0.451276 | ||||||||
\(890\) | − | 34.4761i | − | 0.0387372i | ||||||
\(891\) | 95.3176 | − | 26.7497i | 0.106978 | − | 0.0300221i | ||||
\(892\) | 626.204 | 0.702022 | ||||||||
\(893\) | 103.577i | 0.115988i | ||||||||
\(894\) | 1218.51 | 1.36299 | ||||||||
\(895\) | 100.441 | 0.112224 | ||||||||
\(896\) | 95.7337 | 0.106846 | ||||||||
\(897\) | − | 14.7823i | − | 0.0164797i | ||||||
\(898\) | − | 1355.83i | − | 1.50984i | ||||||
\(899\) | 2403.34i | 2.67335i | ||||||||
\(900\) | −65.8832 | −0.0732035 | ||||||||
\(901\) | − | 182.161i | − | 0.202176i | ||||||
\(902\) | 473.000 | − | 132.742i | 0.524390 | − | 0.147164i | ||||
\(903\) | 191.749 | 0.212346 | ||||||||
\(904\) | − | 98.2107i | − | 0.108640i | ||||||
\(905\) | 780.614 | 0.862556 | ||||||||
\(906\) | −635.051 | −0.700940 | ||||||||
\(907\) | 216.133 | 0.238294 | 0.119147 | − | 0.992877i | \(-0.461984\pi\) | ||||
0.119147 | + | 0.992877i | \(0.461984\pi\) | |||||||
\(908\) | 460.983i | 0.507691i | ||||||||
\(909\) | − | 459.703i | − | 0.505723i | ||||||
\(910\) | − | 12.1981i | − | 0.0134045i | ||||||
\(911\) | −991.648 | −1.08853 | −0.544263 | − | 0.838915i | \(-0.683191\pi\) | ||||
−0.544263 | + | 0.838915i | \(0.683191\pi\) | |||||||
\(912\) | 209.233i | 0.229422i | ||||||||
\(913\) | 431.688 | + | 1538.24i | 0.472824 | + | 1.68482i | ||||
\(914\) | −1984.00 | −2.17067 | ||||||||
\(915\) | 436.932i | 0.477521i | ||||||||
\(916\) | −1334.35 | −1.45671 | ||||||||
\(917\) | −277.945 | −0.303103 | ||||||||
\(918\) | −223.884 | −0.243883 | ||||||||
\(919\) | 567.429i | 0.617442i | 0.951153 | + | 0.308721i | \(0.0999009\pi\) | ||||
−0.951153 | + | 0.308721i | \(0.900099\pi\) | |||||||
\(920\) | − | 30.4652i | − | 0.0331144i | ||||||
\(921\) | − | 641.458i | − | 0.696480i | ||||||
\(922\) | 1534.40 | 1.66421 | ||||||||
\(923\) | − | 82.6557i | − | 0.0895511i | ||||||
\(924\) | 59.8232 | + | 213.169i | 0.0647437 | + | 0.230702i | ||||
\(925\) | 245.164 | 0.265042 | ||||||||
\(926\) | 1205.52i | 1.30186i | ||||||||
\(927\) | 540.646 | 0.583221 | ||||||||
\(928\) | −2151.61 | −2.31854 | ||||||||
\(929\) | 1317.80 | 1.41851 | 0.709257 | − | 0.704950i | \(-0.249031\pi\) | ||||
0.709257 | + | 0.704950i | \(0.249031\pi\) | |||||||
\(930\) | 575.305i | 0.618608i | ||||||||
\(931\) | − | 59.2272i | − | 0.0636168i | ||||||
\(932\) | − | 1478.99i | − | 1.58690i | ||||||
\(933\) | 249.029 | 0.266912 | ||||||||
\(934\) | 2114.59i | 2.26402i | ||||||||
\(935\) | 98.8473 | + | 352.224i | 0.105719 | + | 0.376710i | ||||
\(936\) | 2.42606 | 0.00259194 | ||||||||
\(937\) | − | 1078.36i | − | 1.15086i | −0.817850 | − | 0.575431i | \(-0.804834\pi\) | ||
0.817850 | − | 0.575431i | \(-0.195166\pi\) | |||||||
\(938\) | −704.426 | −0.750987 | ||||||||
\(939\) | 253.534 | 0.270004 | ||||||||
\(940\) | −120.229 | −0.127903 | ||||||||
\(941\) | − | 1421.53i | − | 1.51066i | −0.655344 | − | 0.755331i | \(-0.727476\pi\) | ||
0.655344 | − | 0.755331i | \(-0.272524\pi\) | |||||||
\(942\) | 497.213i | 0.527827i | ||||||||
\(943\) | − | 184.864i | − | 0.196039i | ||||||
\(944\) | −412.078 | −0.436523 | ||||||||
\(945\) | − | 30.7409i | − | 0.0325300i | ||||||
\(946\) | 1283.78 | − | 360.278i | 1.35706 | − | 0.380843i | ||||
\(947\) | 866.866 | 0.915381 | 0.457690 | − | 0.889112i | \(-0.348677\pi\) | ||||
0.457690 | + | 0.889112i | \(0.348677\pi\) | |||||||
\(948\) | − | 130.627i | − | 0.137792i | ||||||
\(949\) | −18.0805 | −0.0190522 | ||||||||
\(950\) | 122.555 | 0.129005 | ||||||||
\(951\) | −49.1051 | −0.0516352 | ||||||||
\(952\) | − | 44.7107i | − | 0.0469650i | ||||||
\(953\) | 525.153i | 0.551053i | 0.961293 | + | 0.275526i | \(0.0888522\pi\) | ||||
−0.961293 | + | 0.275526i | \(0.911148\pi\) | |||||||
\(954\) | 106.441i | 0.111574i | ||||||||
\(955\) | 162.947 | 0.170625 | ||||||||
\(956\) | − | 413.369i | − | 0.432394i | ||||||
\(957\) | −241.289 | − | 859.790i | −0.252131 | − | 0.898422i | ||||
\(958\) | −565.097 | −0.589872 | ||||||||
\(959\) | − | 609.853i | − | 0.635926i | ||||||
\(960\) | −293.863 | −0.306107 | ||||||||
\(961\) | 1668.23 | 1.73593 | ||||||||
\(962\) | −101.099 | −0.105092 | ||||||||
\(963\) | − | 339.327i | − | 0.352365i | ||||||
\(964\) | 424.852i | 0.440718i | ||||||||
\(965\) | 147.038i | 0.152371i | ||||||||
\(966\) | 159.187 | 0.164790 | ||||||||
\(967\) | − | 1703.41i | − | 1.76154i | −0.473543 | − | 0.880771i | \(-0.657025\pi\) | ||
0.473543 | − | 0.880771i | \(-0.342975\pi\) | |||||||
\(968\) | 71.5312 | + | 117.407i | 0.0738959 | + | 0.121288i | ||||
\(969\) | 217.965 | 0.224938 | ||||||||
\(970\) | − | 640.202i | − | 0.660002i | ||||||
\(971\) | 690.121 | 0.710732 | 0.355366 | − | 0.934727i | \(-0.384356\pi\) | ||||
0.355366 | + | 0.934727i | \(0.384356\pi\) | |||||||
\(972\) | 68.4678 | 0.0704401 | ||||||||
\(973\) | −250.748 | −0.257706 | ||||||||
\(974\) | 1610.28i | 1.65327i | ||||||||
\(975\) | 6.16385i | 0.00632189i | ||||||||
\(976\) | 1610.70i | 1.65031i | ||||||||
\(977\) | −617.192 | −0.631721 | −0.315861 | − | 0.948806i | \(-0.602293\pi\) | ||||
−0.315861 | + | 0.948806i | \(0.602293\pi\) | |||||||
\(978\) | − | 837.227i | − | 0.856060i | ||||||
\(979\) | 56.3671 | − | 15.8187i | 0.0575762 | − | 0.0161580i | ||||
\(980\) | 68.7490 | 0.0701520 | ||||||||
\(981\) | 545.628i | 0.556196i | ||||||||
\(982\) | 1201.51 | 1.22354 | ||||||||
\(983\) | 371.796 | 0.378226 | 0.189113 | − | 0.981955i | \(-0.439439\pi\) | ||||
0.189113 | + | 0.981955i | \(0.439439\pi\) | |||||||
\(984\) | 30.3397 | 0.0308330 | ||||||||
\(985\) | 205.027i | 0.208149i | ||||||||
\(986\) | 2019.49i | 2.04817i | ||||||||
\(987\) | − | 56.0985i | − | 0.0568374i | ||||||
\(988\) | −26.4501 | −0.0267714 | ||||||||
\(989\) | − | 501.746i | − | 0.507326i | ||||||
\(990\) | −57.7592 | − | 205.814i | −0.0583426 | − | 0.207893i | ||||
\(991\) | 1315.99 | 1.32794 | 0.663971 | − | 0.747759i | \(-0.268870\pi\) | ||||
0.663971 | + | 0.747759i | \(0.268870\pi\) | |||||||
\(992\) | 2353.84i | 2.37282i | ||||||||
\(993\) | −1043.74 | −1.05110 | ||||||||
\(994\) | 890.100 | 0.895473 | ||||||||
\(995\) | −688.761 | −0.692222 | ||||||||
\(996\) | 1104.94i | 1.10937i | ||||||||
\(997\) | 207.654i | 0.208279i | 0.994563 | + | 0.104139i | \(0.0332088\pi\) | ||||
−0.994563 | + | 0.104139i | \(0.966791\pi\) | |||||||
\(998\) | − | 413.472i | − | 0.414301i | ||||||
\(999\) | −254.782 | −0.255037 |
(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 | 1155.3.b.a.736.18 | ✓ | 96 | |
11.10 | odd | 2 | inner | 1155.3.b.a.736.79 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.3.b.a.736.18 | ✓ | 96 | 1.1 | even | 1 | trivial | |
1155.3.b.a.736.79 | yes | 96 | 11.10 | odd | 2 | inner |