Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,3,Mod(949,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8856251142\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.8 | ||
Character | \(\chi\) | \(=\) | 950.949 |
Dual form | 950.3.d.b.949.5 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 3.53663 | 1.17888 | 0.589438 | − | 0.807814i | \(-0.299349\pi\) | ||||
0.589438 | + | 0.807814i | \(0.299349\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.00155 | −0.833591 | ||||||||
\(7\) | − | 0.146462i | − | 0.0209232i | −0.999945 | − | 0.0104616i | \(-0.996670\pi\) | ||
0.999945 | − | 0.0104616i | \(-0.00333009\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.50774 | 0.389749 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8960 | 1.44509 | 0.722546 | − | 0.691322i | \(-0.242972\pi\) | ||||
0.722546 | + | 0.691322i | \(0.242972\pi\) | |||||||
\(12\) | 7.07326 | 0.589438 | ||||||||
\(13\) | 16.9258 | 1.30198 | 0.650991 | − | 0.759086i | \(-0.274354\pi\) | ||||
0.650991 | + | 0.759086i | \(0.274354\pi\) | |||||||
\(14\) | 0.207129i | 0.0147949i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 27.0986i | − | 1.59403i | −0.603957 | − | 0.797017i | \(-0.706410\pi\) | ||
0.603957 | − | 0.797017i | \(-0.293590\pi\) | |||||||
\(18\) | −4.96069 | −0.275594 | ||||||||
\(19\) | −11.5499 | − | 15.0864i | −0.607889 | − | 0.794022i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.517983i | − | 0.0246658i | ||||||
\(22\) | −22.4804 | −1.02183 | ||||||||
\(23\) | 20.1654i | 0.876755i | 0.898791 | + | 0.438378i | \(0.144447\pi\) | ||||
−0.898791 | + | 0.438378i | \(0.855553\pi\) | |||||||
\(24\) | −10.0031 | −0.416796 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −23.9366 | −0.920640 | ||||||||
\(27\) | −19.4241 | −0.719411 | ||||||||
\(28\) | − | 0.292925i | − | 0.0104616i | ||||||
\(29\) | 5.45043i | 0.187946i | 0.995575 | + | 0.0939730i | \(0.0299567\pi\) | ||||
−0.995575 | + | 0.0939730i | \(0.970043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.15415i | 0.295295i | 0.989040 | + | 0.147648i | \(0.0471701\pi\) | ||||
−0.989040 | + | 0.147648i | \(0.952830\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 56.2183 | 1.70359 | ||||||||
\(34\) | 38.3232i | 1.12715i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.01547 | 0.194874 | ||||||||
\(37\) | 7.37605 | 0.199353 | 0.0996764 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996764 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(38\) | 16.3340 | + | 21.3354i | 0.429843 | + | 0.561458i | ||||
\(39\) | 59.8601 | 1.53487 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24.0093i | 0.585593i | 0.956175 | + | 0.292797i | \(0.0945859\pi\) | ||||
−0.956175 | + | 0.292797i | \(0.905414\pi\) | |||||||
\(42\) | 0.732538i | 0.0174414i | ||||||||
\(43\) | − | 40.3144i | − | 0.937544i | −0.883319 | − | 0.468772i | \(-0.844697\pi\) | ||
0.883319 | − | 0.468772i | \(-0.155303\pi\) | |||||||
\(44\) | 31.7920 | 0.722546 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 28.5181i | − | 0.619960i | ||||||
\(47\) | − | 85.7192i | − | 1.82381i | −0.410398 | − | 0.911906i | \(-0.634610\pi\) | ||
0.410398 | − | 0.911906i | \(-0.365390\pi\) | |||||||
\(48\) | 14.1465 | 0.294719 | ||||||||
\(49\) | 48.9785 | 0.999562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 95.8376i | − | 1.87917i | ||||||
\(52\) | 33.8515 | 0.650991 | ||||||||
\(53\) | 59.0413 | 1.11399 | 0.556994 | − | 0.830517i | \(-0.311955\pi\) | ||||
0.556994 | + | 0.830517i | \(0.311955\pi\) | |||||||
\(54\) | 27.4698 | 0.508700 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.414258i | 0.00739747i | ||||||||
\(57\) | −40.8477 | − | 53.3550i | −0.716626 | − | 0.936053i | ||||
\(58\) | − | 7.70807i | − | 0.132898i | ||||||
\(59\) | 86.4540i | 1.46532i | 0.680593 | + | 0.732661i | \(0.261722\pi\) | ||||
−0.680593 | + | 0.732661i | \(0.738278\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3251 | −0.251231 | −0.125615 | − | 0.992079i | \(-0.540091\pi\) | ||||
−0.125615 | + | 0.992079i | \(0.540091\pi\) | |||||||
\(62\) | − | 12.9459i | − | 0.208805i | ||||||
\(63\) | − | 0.513751i | − | 0.00815478i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −79.5047 | −1.20462 | ||||||||
\(67\) | 100.455 | 1.49933 | 0.749665 | − | 0.661818i | \(-0.230215\pi\) | ||||
0.749665 | + | 0.661818i | \(0.230215\pi\) | |||||||
\(68\) | − | 54.1971i | − | 0.797017i | ||||||
\(69\) | 71.3174i | 1.03359i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 93.5509i | 1.31762i | 0.752310 | + | 0.658809i | \(0.228940\pi\) | ||||
−0.752310 | + | 0.658809i | \(0.771060\pi\) | |||||||
\(72\) | −9.92138 | −0.137797 | ||||||||
\(73\) | − | 4.45910i | − | 0.0610836i | −0.999533 | − | 0.0305418i | \(-0.990277\pi\) | ||
0.999533 | − | 0.0305418i | \(-0.00972327\pi\) | |||||||
\(74\) | −10.4313 | −0.140964 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.0998 | − | 30.1728i | −0.303945 | − | 0.397011i | ||||
\(77\) | − | 2.32817i | − | 0.0302360i | ||||||
\(78\) | −84.6550 | −1.08532 | ||||||||
\(79\) | 15.2517i | 0.193059i | 0.995330 | + | 0.0965295i | \(0.0307742\pi\) | ||||
−0.995330 | + | 0.0965295i | \(0.969226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.265 | −1.23784 | ||||||||
\(82\) | − | 33.9543i | − | 0.414077i | ||||||
\(83\) | − | 145.028i | − | 1.74732i | −0.486535 | − | 0.873661i | \(-0.661739\pi\) | ||
0.486535 | − | 0.873661i | \(-0.338261\pi\) | |||||||
\(84\) | − | 1.03597i | − | 0.0123329i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57.0132i | 0.662944i | ||||||||
\(87\) | 19.2761i | 0.221565i | ||||||||
\(88\) | −44.9607 | −0.510917 | ||||||||
\(89\) | 24.1281i | 0.271102i | 0.990770 | + | 0.135551i | \(0.0432804\pi\) | ||||
−0.990770 | + | 0.135551i | \(0.956720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.47899i | − | 0.0272416i | ||||||
\(92\) | 40.3308i | 0.438378i | ||||||||
\(93\) | 32.3748i | 0.348116i | ||||||||
\(94\) | 121.225i | 1.28963i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20.0062 | −0.208398 | ||||||||
\(97\) | 3.08788 | 0.0318338 | 0.0159169 | − | 0.999873i | \(-0.494933\pi\) | ||||
0.0159169 | + | 0.999873i | \(0.494933\pi\) | |||||||
\(98\) | −69.2661 | −0.706797 | ||||||||
\(99\) | 55.7591 | 0.563223 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 103.059 | 1.02039 | 0.510193 | − | 0.860060i | \(-0.329574\pi\) | ||||
0.510193 | + | 0.860060i | \(0.329574\pi\) | |||||||
\(102\) | 135.535i | 1.32877i | ||||||||
\(103\) | 126.615 | 1.22927 | 0.614637 | − | 0.788810i | \(-0.289302\pi\) | ||||
0.614637 | + | 0.788810i | \(0.289302\pi\) | |||||||
\(104\) | −47.8733 | −0.460320 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −83.4970 | −0.787708 | ||||||||
\(107\) | 22.0909 | 0.206457 | 0.103228 | − | 0.994658i | \(-0.467083\pi\) | ||||
0.103228 | + | 0.994658i | \(0.467083\pi\) | |||||||
\(108\) | −38.8482 | −0.359705 | ||||||||
\(109\) | − | 91.1256i | − | 0.836015i | −0.908444 | − | 0.418007i | \(-0.862729\pi\) | ||
0.908444 | − | 0.418007i | \(-0.137271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.0864 | 0.235012 | ||||||||
\(112\) | − | 0.585849i | − | 0.00523080i | ||||||
\(113\) | −170.895 | −1.51234 | −0.756172 | − | 0.654373i | \(-0.772933\pi\) | ||||
−0.756172 | + | 0.654373i | \(0.772933\pi\) | |||||||
\(114\) | 57.7674 | + | 75.4554i | 0.506731 | + | 0.661889i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.9009i | 0.0939730i | ||||||||
\(117\) | 59.3711 | 0.507445 | ||||||||
\(118\) | − | 122.264i | − | 1.03614i | ||||||
\(119\) | −3.96892 | −0.0333523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 131.683 | 1.08829 | ||||||||
\(122\) | 21.6729 | 0.177647 | ||||||||
\(123\) | 84.9120i | 0.690342i | ||||||||
\(124\) | 18.3083i | 0.147648i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.726554i | 0.00576630i | ||||||||
\(127\) | −64.0896 | −0.504643 | −0.252321 | − | 0.967644i | \(-0.581194\pi\) | ||||
−0.252321 | + | 0.967644i | \(0.581194\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − | 142.577i | − | 1.10525i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −141.977 | −1.08380 | −0.541898 | − | 0.840444i | \(-0.682294\pi\) | ||||
−0.541898 | + | 0.840444i | \(0.682294\pi\) | |||||||
\(132\) | 112.437 | 0.851793 | ||||||||
\(133\) | −2.20959 | + | 1.69163i | −0.0166135 | + | 0.0127190i | ||||
\(134\) | −142.065 | −1.06019 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76.6463i | 0.563576i | ||||||||
\(137\) | − | 96.3583i | − | 0.703345i | −0.936123 | − | 0.351673i | \(-0.885613\pi\) | ||
0.936123 | − | 0.351673i | \(-0.114387\pi\) | |||||||
\(138\) | − | 100.858i | − | 0.730856i | ||||||
\(139\) | 182.574 | 1.31348 | 0.656739 | − | 0.754118i | \(-0.271935\pi\) | ||||
0.656739 | + | 0.754118i | \(0.271935\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 303.157i | − | 2.15005i | ||||||
\(142\) | − | 132.301i | − | 0.931697i | ||||||
\(143\) | 269.052 | 1.88148 | ||||||||
\(144\) | 14.0309 | 0.0974371 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.30612i | 0.0431926i | ||||||||
\(147\) | 173.219 | 1.17836 | ||||||||
\(148\) | 14.7521 | 0.0996764 | ||||||||
\(149\) | 15.4418 | 0.103636 | 0.0518182 | − | 0.998657i | \(-0.483498\pi\) | ||||
0.0518182 | + | 0.998657i | \(0.483498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 185.156i | − | 1.22620i | −0.790006 | − | 0.613099i | \(-0.789923\pi\) | ||
0.790006 | − | 0.613099i | \(-0.210077\pi\) | |||||||
\(152\) | 32.6680 | + | 42.6708i | 0.214921 | + | 0.280729i | ||||
\(153\) | − | 95.0547i | − | 0.621272i | ||||||
\(154\) | 3.29253i | 0.0213800i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 119.720 | 0.767437 | ||||||||
\(157\) | 29.2193i | 0.186110i | 0.995661 | + | 0.0930552i | \(0.0296633\pi\) | ||||
−0.995661 | + | 0.0930552i | \(0.970337\pi\) | |||||||
\(158\) | − | 21.5691i | − | 0.136513i | ||||||
\(159\) | 208.807 | 1.31325 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.95347 | 0.0183445 | ||||||||
\(162\) | 141.797 | 0.875288 | ||||||||
\(163\) | 94.1505i | 0.577611i | 0.957388 | + | 0.288805i | \(0.0932580\pi\) | ||||
−0.957388 | + | 0.288805i | \(0.906742\pi\) | |||||||
\(164\) | 48.0186i | 0.292797i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 205.100i | 1.23554i | ||||||||
\(167\) | −56.3258 | −0.337280 | −0.168640 | − | 0.985678i | \(-0.553938\pi\) | ||||
−0.168640 | + | 0.985678i | \(0.553938\pi\) | |||||||
\(168\) | 1.46508i | 0.00872069i | ||||||||
\(169\) | 117.481 | 0.695156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −40.5140 | − | 52.9192i | −0.236924 | − | 0.309469i | ||||
\(172\) | − | 80.6288i | − | 0.468772i | ||||||
\(173\) | −45.4392 | −0.262654 | −0.131327 | − | 0.991339i | \(-0.541924\pi\) | ||||
−0.131327 | + | 0.991339i | \(0.541924\pi\) | |||||||
\(174\) | − | 27.2606i | − | 0.156670i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 63.5841 | 0.361273 | ||||||||
\(177\) | 305.756i | 1.72743i | ||||||||
\(178\) | − | 34.1222i | − | 0.191698i | ||||||
\(179\) | 147.183i | 0.822252i | 0.911579 | + | 0.411126i | \(0.134864\pi\) | ||||
−0.911579 | + | 0.411126i | \(0.865136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 243.383i | 1.34466i | 0.740254 | + | 0.672328i | \(0.234705\pi\) | ||||
−0.740254 | + | 0.672328i | \(0.765295\pi\) | |||||||
\(182\) | 3.50582i | 0.0192627i | ||||||||
\(183\) | −54.1991 | −0.296170 | ||||||||
\(184\) | − | 57.0363i | − | 0.309980i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 45.7849i | − | 0.246155i | ||||||
\(187\) | − | 430.759i | − | 2.30353i | ||||||
\(188\) | − | 171.438i | − | 0.911906i | ||||||
\(189\) | 2.84490i | 0.0150524i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −73.8128 | −0.386454 | −0.193227 | − | 0.981154i | \(-0.561895\pi\) | ||||
−0.193227 | + | 0.981154i | \(0.561895\pi\) | |||||||
\(192\) | 28.2930 | 0.147359 | ||||||||
\(193\) | 99.7983 | 0.517089 | 0.258545 | − | 0.965999i | \(-0.416757\pi\) | ||||
0.258545 | + | 0.965999i | \(0.416757\pi\) | |||||||
\(194\) | −4.36693 | −0.0225099 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.9571 | 0.499781 | ||||||||
\(197\) | 333.125i | 1.69099i | 0.533985 | + | 0.845494i | \(0.320694\pi\) | ||||
−0.533985 | + | 0.845494i | \(0.679306\pi\) | |||||||
\(198\) | −78.8552 | −0.398259 | ||||||||
\(199\) | −80.1431 | −0.402729 | −0.201365 | − | 0.979516i | \(-0.564538\pi\) | ||||
−0.201365 | + | 0.979516i | \(0.564538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 355.272 | 1.76752 | ||||||||
\(202\) | −145.747 | −0.721522 | ||||||||
\(203\) | 0.798283 | 0.00393243 | ||||||||
\(204\) | − | 191.675i | − | 0.939584i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −179.061 | −0.869229 | ||||||||
\(207\) | 70.7348i | 0.341714i | ||||||||
\(208\) | 67.7030 | 0.325495 | ||||||||
\(209\) | −183.597 | − | 239.814i | −0.878457 | − | 1.14744i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 72.6207i | 0.344174i | 0.985082 | + | 0.172087i | \(0.0550510\pi\) | ||||
−0.985082 | + | 0.172087i | \(0.944949\pi\) | |||||||
\(212\) | 118.083 | 0.556994 | ||||||||
\(213\) | 330.855i | 1.55331i | ||||||||
\(214\) | −31.2412 | −0.145987 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 54.9396 | 0.254350 | ||||||||
\(217\) | 1.34074 | 0.00617852 | ||||||||
\(218\) | 128.871i | 0.591152i | ||||||||
\(219\) | − | 15.7702i | − | 0.0720100i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 458.664i | − | 2.07540i | ||||||
\(222\) | −36.8917 | −0.166179 | ||||||||
\(223\) | 323.793 | 1.45199 | 0.725993 | − | 0.687702i | \(-0.241380\pi\) | ||||
0.725993 | + | 0.687702i | \(0.241380\pi\) | |||||||
\(224\) | 0.828516i | 0.00369873i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 241.682 | 1.06939 | ||||||||
\(227\) | −433.568 | −1.90999 | −0.954996 | − | 0.296618i | \(-0.904141\pi\) | ||||
−0.954996 | + | 0.296618i | \(0.904141\pi\) | |||||||
\(228\) | −81.6954 | − | 106.710i | −0.358313 | − | 0.468027i | ||||
\(229\) | −206.994 | −0.903904 | −0.451952 | − | 0.892042i | \(-0.649272\pi\) | ||||
−0.451952 | + | 0.892042i | \(0.649272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.23387i | − | 0.0356444i | ||||||
\(232\) | − | 15.4161i | − | 0.0664489i | ||||||
\(233\) | 290.836i | 1.24822i | 0.781335 | + | 0.624112i | \(0.214539\pi\) | ||||
−0.781335 | + | 0.624112i | \(0.785461\pi\) | |||||||
\(234\) | −83.9634 | −0.358818 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 172.908i | 0.732661i | ||||||||
\(237\) | 53.9395i | 0.227593i | ||||||||
\(238\) | 5.61290 | 0.0235836 | ||||||||
\(239\) | 90.0708 | 0.376865 | 0.188433 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188433 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 85.6209i | − | 0.355273i | −0.984096 | − | 0.177637i | \(-0.943155\pi\) | ||
0.984096 | − | 0.177637i | \(-0.0568452\pi\) | |||||||
\(242\) | −186.229 | −0.769540 | ||||||||
\(243\) | −179.785 | −0.739854 | ||||||||
\(244\) | −30.6501 | −0.125615 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 120.084i | − | 0.488145i | ||||||
\(247\) | −195.491 | − | 255.349i | −0.791461 | − | 1.03380i | ||||
\(248\) | − | 25.8918i | − | 0.104403i | ||||||
\(249\) | − | 512.909i | − | 2.05988i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −418.090 | −1.66570 | −0.832849 | − | 0.553500i | \(-0.813292\pi\) | ||||
−0.832849 | + | 0.553500i | \(0.813292\pi\) | |||||||
\(252\) | − | 1.02750i | − | 0.00407739i | ||||||
\(253\) | 320.549i | 1.26699i | ||||||||
\(254\) | 90.6364 | 0.356836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 81.0271 | 0.315281 | 0.157640 | − | 0.987497i | \(-0.449611\pi\) | ||||
0.157640 | + | 0.987497i | \(0.449611\pi\) | |||||||
\(258\) | 201.634i | 0.781528i | ||||||||
\(259\) | − | 1.08031i | − | 0.00417110i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.1187i | 0.0732516i | ||||||||
\(262\) | 200.786 | 0.766360 | ||||||||
\(263\) | 281.473i | 1.07024i | 0.844776 | + | 0.535120i | \(0.179733\pi\) | ||||
−0.844776 | + | 0.535120i | \(0.820267\pi\) | |||||||
\(264\) | −159.009 | −0.602308 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.12483 | − | 2.39232i | 0.0117475 | − | 0.00899368i | ||||
\(267\) | 85.3320i | 0.319596i | ||||||||
\(268\) | 200.910 | 0.749665 | ||||||||
\(269\) | − | 392.714i | − | 1.45990i | −0.683499 | − | 0.729951i | \(-0.739543\pi\) | ||
0.683499 | − | 0.729951i | \(-0.260457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 435.861 | 1.60834 | 0.804172 | − | 0.594397i | \(-0.202609\pi\) | ||||
0.804172 | + | 0.594397i | \(0.202609\pi\) | |||||||
\(272\) | − | 108.394i | − | 0.398508i | ||||||
\(273\) | − | 8.76725i | − | 0.0321145i | ||||||
\(274\) | 136.271i | 0.497340i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 142.635i | 0.516793i | ||||||||
\(277\) | 306.929i | 1.10805i | 0.832501 | + | 0.554024i | \(0.186908\pi\) | ||||
−0.832501 | + | 0.554024i | \(0.813092\pi\) | |||||||
\(278\) | −258.198 | −0.928770 | ||||||||
\(279\) | 32.1103i | 0.115091i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 158.309i | 0.563376i | 0.959506 | + | 0.281688i | \(0.0908944\pi\) | ||||
−0.959506 | + | 0.281688i | \(0.909106\pi\) | |||||||
\(282\) | 428.729i | 1.52031i | ||||||||
\(283\) | − | 109.390i | − | 0.386539i | −0.981146 | − | 0.193269i | \(-0.938091\pi\) | ||
0.981146 | − | 0.193269i | \(-0.0619091\pi\) | |||||||
\(284\) | 187.102i | 0.658809i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −380.497 | −1.33041 | ||||||||
\(287\) | 3.51646 | 0.0122525 | ||||||||
\(288\) | −19.8428 | −0.0688985 | ||||||||
\(289\) | −445.333 | −1.54094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9207 | 0.0375282 | ||||||||
\(292\) | − | 8.91820i | − | 0.0305418i | ||||||
\(293\) | −332.451 | −1.13464 | −0.567322 | − | 0.823496i | \(-0.692020\pi\) | ||||
−0.567322 | + | 0.823496i | \(0.692020\pi\) | |||||||
\(294\) | −244.969 | −0.833226 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.8626 | −0.0704818 | ||||||||
\(297\) | −308.766 | −1.03962 | ||||||||
\(298\) | −21.8380 | −0.0732819 | ||||||||
\(299\) | 341.314i | 1.14152i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.90454 | −0.0196164 | ||||||||
\(302\) | 261.850i | 0.867053i | ||||||||
\(303\) | 364.481 | 1.20291 | ||||||||
\(304\) | −46.1996 | − | 60.3456i | −0.151972 | − | 0.198505i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 134.428i | 0.439306i | ||||||||
\(307\) | −469.296 | −1.52865 | −0.764326 | − | 0.644830i | \(-0.776928\pi\) | ||||
−0.764326 | + | 0.644830i | \(0.776928\pi\) | |||||||
\(308\) | − | 4.65634i | − | 0.0151180i | ||||||
\(309\) | 447.791 | 1.44916 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 50.0531 | 0.160942 | 0.0804712 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804712 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(312\) | −169.310 | −0.542660 | ||||||||
\(313\) | − | 214.496i | − | 0.685290i | −0.939465 | − | 0.342645i | \(-0.888677\pi\) | ||
0.939465 | − | 0.342645i | \(-0.111323\pi\) | |||||||
\(314\) | − | 41.3224i | − | 0.131600i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.5033i | 0.0965295i | ||||||||
\(317\) | −119.302 | −0.376348 | −0.188174 | − | 0.982136i | \(-0.560257\pi\) | ||||
−0.188174 | + | 0.982136i | \(0.560257\pi\) | |||||||
\(318\) | −295.298 | −0.928610 | ||||||||
\(319\) | 86.6402i | 0.271599i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 78.1272 | 0.243387 | ||||||||
\(322\) | −4.17683 | −0.0129715 | ||||||||
\(323\) | −408.820 | + | 312.986i | −1.26570 | + | 0.968996i | ||||
\(324\) | −200.531 | −0.618922 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 133.149i | − | 0.408432i | ||||||
\(327\) | − | 322.277i | − | 0.985557i | ||||||
\(328\) | − | 67.9086i | − | 0.207038i | ||||||
\(329\) | −12.5546 | −0.0381600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 474.154i | 1.43249i | 0.697849 | + | 0.716245i | \(0.254141\pi\) | ||||
−0.697849 | + | 0.716245i | \(0.745859\pi\) | |||||||
\(332\) | − | 290.056i | − | 0.873661i | ||||||
\(333\) | 25.8733 | 0.0776975 | ||||||||
\(334\) | 79.6567 | 0.238493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 2.07193i | − | 0.00616646i | ||||||
\(337\) | 237.394 | 0.704433 | 0.352216 | − | 0.935919i | \(-0.385428\pi\) | ||||
0.352216 | + | 0.935919i | \(0.385428\pi\) | |||||||
\(338\) | −166.144 | −0.491549 | ||||||||
\(339\) | −604.392 | −1.78287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 145.515i | 0.426729i | ||||||||
\(342\) | 57.2955 | + | 74.8390i | 0.167531 | + | 0.218827i | ||||
\(343\) | − | 14.3502i | − | 0.0418372i | ||||||
\(344\) | 114.026i | 0.331472i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 64.2607 | 0.185724 | ||||||||
\(347\) | 612.413i | 1.76488i | 0.470426 | + | 0.882440i | \(0.344100\pi\) | ||||
−0.470426 | + | 0.882440i | \(0.655900\pi\) | |||||||
\(348\) | 38.5523i | 0.110782i | ||||||||
\(349\) | −625.895 | −1.79340 | −0.896698 | − | 0.442644i | \(-0.854041\pi\) | ||||
−0.896698 | + | 0.442644i | \(0.854041\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −328.767 | −0.936659 | ||||||||
\(352\) | −89.9215 | −0.255459 | ||||||||
\(353\) | − | 218.281i | − | 0.618359i | −0.951004 | − | 0.309179i | \(-0.899946\pi\) | ||
0.951004 | − | 0.309179i | \(-0.100054\pi\) | |||||||
\(354\) | − | 432.404i | − | 1.22148i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.2561i | 0.135551i | ||||||||
\(357\) | −14.0366 | −0.0393182 | ||||||||
\(358\) | − | 208.148i | − | 0.581420i | ||||||
\(359\) | −316.232 | −0.880870 | −0.440435 | − | 0.897784i | \(-0.645176\pi\) | ||||
−0.440435 | + | 0.897784i | \(0.645176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −94.1997 | + | 348.493i | −0.260941 | + | 0.965355i | ||||
\(362\) | − | 344.195i | − | 0.950815i | ||||||
\(363\) | 465.716 | 1.28296 | ||||||||
\(364\) | − | 4.95797i | − | 0.0136208i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 76.6491 | 0.209424 | ||||||||
\(367\) | − | 600.077i | − | 1.63509i | −0.575867 | − | 0.817543i | \(-0.695335\pi\) | ||
0.575867 | − | 0.817543i | \(-0.304665\pi\) | |||||||
\(368\) | 80.6615i | 0.219189i | ||||||||
\(369\) | 84.2184i | 0.228234i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.64733i | − | 0.0233082i | ||||||
\(372\) | 64.7496i | 0.174058i | ||||||||
\(373\) | −60.9072 | −0.163290 | −0.0816451 | − | 0.996661i | \(-0.526017\pi\) | ||||
−0.0816451 | + | 0.996661i | \(0.526017\pi\) | |||||||
\(374\) | 609.186i | 1.62884i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 242.450i | 0.644815i | ||||||||
\(377\) | 92.2527i | 0.244702i | ||||||||
\(378\) | − | 4.02329i | − | 0.0106436i | ||||||
\(379\) | − | 162.907i | − | 0.429835i | −0.976632 | − | 0.214917i | \(-0.931052\pi\) | ||
0.976632 | − | 0.214917i | \(-0.0689482\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −226.661 | −0.594911 | ||||||||
\(382\) | 104.387 | 0.273264 | ||||||||
\(383\) | −638.343 | −1.66669 | −0.833346 | − | 0.552752i | \(-0.813578\pi\) | ||||
−0.833346 | + | 0.552752i | \(0.813578\pi\) | |||||||
\(384\) | −40.0124 | −0.104199 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −141.136 | −0.365637 | ||||||||
\(387\) | − | 141.412i | − | 0.365406i | ||||||
\(388\) | 6.17577 | 0.0159169 | ||||||||
\(389\) | −175.089 | −0.450100 | −0.225050 | − | 0.974347i | \(-0.572254\pi\) | ||||
−0.225050 | + | 0.974347i | \(0.572254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 546.453 | 1.39758 | ||||||||
\(392\) | −138.532 | −0.353399 | ||||||||
\(393\) | −502.121 | −1.27766 | ||||||||
\(394\) | − | 471.109i | − | 1.19571i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 111.518 | 0.281611 | ||||||||
\(397\) | 725.042i | 1.82630i | 0.407622 | + | 0.913151i | \(0.366358\pi\) | ||||
−0.407622 | + | 0.913151i | \(0.633642\pi\) | |||||||
\(398\) | 113.339 | 0.284773 | ||||||||
\(399\) | −7.81450 | + | 5.98265i | −0.0195852 | + | 0.0149941i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 566.987i | 1.41393i | 0.707248 | + | 0.706966i | \(0.249937\pi\) | ||||
−0.707248 | + | 0.706966i | \(0.750063\pi\) | |||||||
\(402\) | −502.431 | −1.24983 | ||||||||
\(403\) | 154.941i | 0.384469i | ||||||||
\(404\) | 206.118 | 0.510193 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.12894 | −0.00278065 | ||||||||
\(407\) | 117.250 | 0.288083 | ||||||||
\(408\) | 271.070i | 0.664386i | ||||||||
\(409\) | 216.398i | 0.529091i | 0.964373 | + | 0.264545i | \(0.0852219\pi\) | ||||
−0.964373 | + | 0.264545i | \(0.914778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 340.783i | − | 0.829157i | ||||||
\(412\) | 253.231 | 0.614637 | ||||||||
\(413\) | 12.6623 | 0.0306592 | ||||||||
\(414\) | − | 100.034i | − | 0.241628i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −95.7465 | −0.230160 | ||||||||
\(417\) | 645.695 | 1.54843 | ||||||||
\(418\) | 259.646 | + | 339.148i | 0.621163 | + | 0.811359i | ||||
\(419\) | −484.914 | −1.15731 | −0.578656 | − | 0.815572i | \(-0.696423\pi\) | ||||
−0.578656 | + | 0.815572i | \(0.696423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 413.265i | − | 0.981626i | −0.871265 | − | 0.490813i | \(-0.836700\pi\) | ||
0.871265 | − | 0.490813i | \(-0.163300\pi\) | |||||||
\(422\) | − | 102.701i | − | 0.243368i | ||||||
\(423\) | − | 300.680i | − | 0.710828i | ||||||
\(424\) | −166.994 | −0.393854 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 467.899i | − | 1.09836i | ||||||
\(427\) | 2.24455i | 0.00525655i | ||||||||
\(428\) | 44.1818 | 0.103228 | ||||||||
\(429\) | 951.538 | 2.21804 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 450.677i | 1.04565i | 0.852439 | + | 0.522827i | \(0.175123\pi\) | ||||
−0.852439 | + | 0.522827i | \(0.824877\pi\) | |||||||
\(432\) | −77.6964 | −0.179853 | ||||||||
\(433\) | −2.50133 | −0.00577673 | −0.00288837 | − | 0.999996i | \(-0.500919\pi\) | ||||
−0.00288837 | + | 0.999996i | \(0.500919\pi\) | |||||||
\(434\) | −1.89609 | −0.00436887 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 182.251i | − | 0.418007i | ||||||
\(437\) | 304.223 | − | 232.908i | 0.696163 | − | 0.532970i | ||||
\(438\) | 22.3024i | 0.0509187i | ||||||||
\(439\) | − | 491.152i | − | 1.11880i | −0.828898 | − | 0.559399i | \(-0.811032\pi\) | ||
0.828898 | − | 0.559399i | \(-0.188968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 171.804 | 0.389578 | ||||||||
\(442\) | 648.649i | 1.46753i | ||||||||
\(443\) | − | 238.895i | − | 0.539267i | −0.962963 | − | 0.269634i | \(-0.913097\pi\) | ||
0.962963 | − | 0.269634i | \(-0.0869026\pi\) | |||||||
\(444\) | 52.1727 | 0.117506 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −457.912 | −1.02671 | ||||||||
\(447\) | 54.6119 | 0.122174 | ||||||||
\(448\) | − | 1.17170i | − | 0.00261540i | ||||||
\(449\) | 452.733i | 1.00832i | 0.863612 | + | 0.504158i | \(0.168197\pi\) | ||||
−0.863612 | + | 0.504158i | \(0.831803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 381.653i | 0.846236i | ||||||||
\(452\) | −341.790 | −0.756172 | ||||||||
\(453\) | − | 654.828i | − | 1.44554i | ||||||
\(454\) | 613.158 | 1.35057 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 115.535 | + | 150.911i | 0.253366 | + | 0.330945i | ||||
\(457\) | − | 697.754i | − | 1.52681i | −0.645918 | − | 0.763407i | \(-0.723525\pi\) | ||
0.645918 | − | 0.763407i | \(-0.276475\pi\) | |||||||
\(458\) | 292.734 | 0.639156 | ||||||||
\(459\) | 526.365i | 1.14677i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 420.342 | 0.911804 | 0.455902 | − | 0.890030i | \(-0.349317\pi\) | ||||
0.455902 | + | 0.890030i | \(0.349317\pi\) | |||||||
\(462\) | 11.6444i | 0.0252044i | ||||||||
\(463\) | − | 480.580i | − | 1.03797i | −0.854783 | − | 0.518985i | \(-0.826310\pi\) | ||
0.854783 | − | 0.518985i | \(-0.173690\pi\) | |||||||
\(464\) | 21.8017i | 0.0469865i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 411.304i | − | 0.882627i | ||||||
\(467\) | 559.285i | 1.19761i | 0.800894 | + | 0.598806i | \(0.204358\pi\) | ||||
−0.800894 | + | 0.598806i | \(0.795642\pi\) | |||||||
\(468\) | 118.742 | 0.253723 | ||||||||
\(469\) | − | 14.7129i | − | 0.0313708i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 103.338i | 0.219401i | ||||||||
\(472\) | − | 244.529i | − | 0.518070i | ||||||
\(473\) | − | 640.838i | − | 1.35484i | ||||||
\(474\) | − | 76.2819i | − | 0.160932i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.93784 | −0.0166761 | ||||||||
\(477\) | 207.101 | 0.434175 | ||||||||
\(478\) | −127.379 | −0.266484 | ||||||||
\(479\) | −246.678 | −0.514986 | −0.257493 | − | 0.966280i | \(-0.582896\pi\) | ||||
−0.257493 | + | 0.966280i | \(0.582896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 124.845 | 0.259554 | ||||||||
\(482\) | 121.086i | 0.251216i | ||||||||
\(483\) | 10.4453 | 0.0216259 | ||||||||
\(484\) | 263.367 | 0.544147 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 254.254 | 0.523156 | ||||||||
\(487\) | −418.804 | −0.859968 | −0.429984 | − | 0.902837i | \(-0.641481\pi\) | ||||
−0.429984 | + | 0.902837i | \(0.641481\pi\) | |||||||
\(488\) | 43.3459 | 0.0888235 | ||||||||
\(489\) | 332.975i | 0.680931i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −514.657 | −1.04818 | −0.524091 | − | 0.851662i | \(-0.675595\pi\) | ||||
−0.524091 | + | 0.851662i | \(0.675595\pi\) | |||||||
\(492\) | 169.824i | 0.345171i | ||||||||
\(493\) | 147.699 | 0.299592 | ||||||||
\(494\) | 276.466 | + | 361.118i | 0.559647 | + | 0.731008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.6166i | 0.0738238i | ||||||||
\(497\) | 13.7017 | 0.0275688 | ||||||||
\(498\) | 725.363i | 1.45655i | ||||||||
\(499\) | 152.709 | 0.306031 | 0.153015 | − | 0.988224i | \(-0.451102\pi\) | ||||
0.153015 | + | 0.988224i | \(0.451102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −199.203 | −0.397612 | ||||||||
\(502\) | 591.269 | 1.17783 | ||||||||
\(503\) | − | 173.503i | − | 0.344937i | −0.985015 | − | 0.172469i | \(-0.944826\pi\) | ||
0.985015 | − | 0.172469i | \(-0.0551743\pi\) | |||||||
\(504\) | 1.45311i | 0.00288315i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 453.325i | − | 0.895899i | ||||||
\(507\) | 415.488 | 0.819502 | ||||||||
\(508\) | −128.179 | −0.252321 | ||||||||
\(509\) | − | 856.653i | − | 1.68301i | −0.540247 | − | 0.841506i | \(-0.681669\pi\) | ||
0.540247 | − | 0.841506i | \(-0.318331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.653090 | −0.00127806 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 224.346 | + | 293.040i | 0.437322 | + | 0.571228i | ||||
\(514\) | −114.590 | −0.222937 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 285.154i | − | 0.552624i | ||||||
\(517\) | − | 1362.59i | − | 2.63558i | ||||||
\(518\) | 1.52779i | 0.00294941i | ||||||||
\(519\) | −160.701 | −0.309637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 99.1018i | − | 0.190215i | −0.995467 | − | 0.0951073i | \(-0.969681\pi\) | ||
0.995467 | − | 0.0951073i | \(-0.0303194\pi\) | |||||||
\(522\) | − | 27.0379i | − | 0.0517967i | ||||||
\(523\) | −56.3564 | −0.107756 | −0.0538780 | − | 0.998548i | \(-0.517158\pi\) | ||||
−0.0538780 | + | 0.998548i | \(0.517158\pi\) | |||||||
\(524\) | −283.955 | −0.541898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 398.063i | − | 0.756773i | ||||||
\(527\) | 248.064 | 0.470710 | ||||||||
\(528\) | 224.873 | 0.425896 | ||||||||
\(529\) | 122.358 | 0.231300 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 303.258i | 0.571107i | ||||||||
\(532\) | −4.41918 | + | 3.38325i | −0.00830673 | + | 0.00635949i | ||||
\(533\) | 406.376i | 0.762431i | ||||||||
\(534\) | − | 120.678i | − | 0.225988i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −284.130 | −0.530093 | ||||||||
\(537\) | 520.532i | 0.969333i | ||||||||
\(538\) | 555.381i | 1.03231i | ||||||||
\(539\) | 778.564 | 1.44446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 909.463 | 1.68108 | 0.840538 | − | 0.541752i | \(-0.182239\pi\) | ||||
0.840538 | + | 0.541752i | \(0.182239\pi\) | |||||||
\(542\) | −616.401 | −1.13727 | ||||||||
\(543\) | 860.754i | 1.58518i | ||||||||
\(544\) | 153.293i | 0.281788i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.3988i | 0.0227084i | ||||||||
\(547\) | −174.393 | −0.318817 | −0.159408 | − | 0.987213i | \(-0.550959\pi\) | ||||
−0.159408 | + | 0.987213i | \(0.550959\pi\) | |||||||
\(548\) | − | 192.717i | − | 0.351673i | ||||||
\(549\) | −53.7563 | −0.0979168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 82.2275 | − | 62.9519i | 0.149233 | − | 0.114250i | ||||
\(552\) | − | 201.716i | − | 0.365428i | ||||||
\(553\) | 2.23379 | 0.00403941 | ||||||||
\(554\) | − | 434.064i | − | 0.783508i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 365.147 | 0.656739 | ||||||||
\(557\) | 134.156i | 0.240854i | 0.992722 | + | 0.120427i | \(0.0384264\pi\) | ||||
−0.992722 | + | 0.120427i | \(0.961574\pi\) | |||||||
\(558\) | − | 45.4109i | − | 0.0813815i | ||||||
\(559\) | − | 682.352i | − | 1.22066i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1523.44i | − | 2.71557i | ||||||
\(562\) | − | 223.882i | − | 0.398367i | ||||||
\(563\) | −178.310 | −0.316715 | −0.158357 | − | 0.987382i | \(-0.550620\pi\) | ||||
−0.158357 | + | 0.987382i | \(0.550620\pi\) | |||||||
\(564\) | − | 606.314i | − | 1.07502i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 154.702i | 0.273324i | ||||||||
\(567\) | 14.6851i | 0.0258997i | ||||||||
\(568\) | − | 264.602i | − | 0.465849i | ||||||
\(569\) | − | 189.835i | − | 0.333629i | −0.985988 | − | 0.166815i | \(-0.946652\pi\) | ||
0.985988 | − | 0.166815i | \(-0.0533482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −604.730 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(572\) | 538.104 | 0.940742 | ||||||||
\(573\) | −261.048 | −0.455582 | ||||||||
\(574\) | −4.97303 | −0.00866381 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 28.0619 | 0.0487186 | ||||||||
\(577\) | 1138.28i | 1.97276i | 0.164488 | + | 0.986379i | \(0.447403\pi\) | ||||
−0.164488 | + | 0.986379i | \(0.552597\pi\) | |||||||
\(578\) | 629.795 | 1.08961 | ||||||||
\(579\) | 352.949 | 0.609584 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.2411 | −0.0365596 | ||||||||
\(582\) | −15.4442 | −0.0265364 | ||||||||
\(583\) | 938.522 | 1.60982 | ||||||||
\(584\) | 12.6122i | 0.0215963i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 470.156 | 0.802314 | ||||||||
\(587\) | 103.008i | 0.175482i | 0.996143 | + | 0.0877410i | \(0.0279648\pi\) | ||||
−0.996143 | + | 0.0877410i | \(0.972035\pi\) | |||||||
\(588\) | 346.438 | 0.589180 | ||||||||
\(589\) | 138.103 | − | 105.730i | 0.234471 | − | 0.179507i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1178.14i | 1.99346i | ||||||||
\(592\) | 29.5042 | 0.0498382 | ||||||||
\(593\) | 354.332i | 0.597525i | 0.954327 | + | 0.298763i | \(0.0965739\pi\) | ||||
−0.954327 | + | 0.298763i | \(0.903426\pi\) | |||||||
\(594\) | 436.661 | 0.735119 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.8836 | 0.0518182 | ||||||||
\(597\) | −283.436 | −0.474768 | ||||||||
\(598\) | − | 482.691i | − | 0.807176i | ||||||
\(599\) | 1112.64i | 1.85750i | 0.370704 | + | 0.928751i | \(0.379116\pi\) | ||||
−0.370704 | + | 0.928751i | \(0.620884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8624i | 0.0746463i | 0.999303 | + | 0.0373231i | \(0.0118831\pi\) | ||||
−0.999303 | + | 0.0373231i | \(0.988117\pi\) | |||||||
\(602\) | 8.35028 | 0.0138709 | ||||||||
\(603\) | 352.370 | 0.584361 | ||||||||
\(604\) | − | 370.312i | − | 0.613099i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −515.455 | −0.850585 | ||||||||
\(607\) | 740.250 | 1.21952 | 0.609762 | − | 0.792585i | \(-0.291265\pi\) | ||||
0.609762 | + | 0.792585i | \(0.291265\pi\) | |||||||
\(608\) | 65.3361 | + | 85.3416i | 0.107461 | + | 0.140365i | ||||
\(609\) | 2.82323 | 0.00463585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1450.86i | − | 2.37457i | ||||||
\(612\) | − | 190.109i | − | 0.310636i | ||||||
\(613\) | − | 758.605i | − | 1.23753i | −0.785577 | − | 0.618764i | \(-0.787634\pi\) | ||
0.785577 | − | 0.618764i | \(-0.212366\pi\) | |||||||
\(614\) | 663.685 | 1.08092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.58505i | 0.0106900i | ||||||||
\(617\) | 617.701i | 1.00114i | 0.865697 | + | 0.500568i | \(0.166875\pi\) | ||||
−0.865697 | + | 0.500568i | \(0.833125\pi\) | |||||||
\(618\) | −633.272 | −1.02471 | ||||||||
\(619\) | 434.677 | 0.702224 | 0.351112 | − | 0.936333i | \(-0.385804\pi\) | ||||
0.351112 | + | 0.936333i | \(0.385804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 391.694i | − | 0.630747i | ||||||
\(622\) | −70.7858 | −0.113803 | ||||||||
\(623\) | 3.53385 | 0.00567232 | ||||||||
\(624\) | 239.440 | 0.383719 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 303.343i | 0.484573i | ||||||||
\(627\) | −649.316 | − | 848.133i | −1.03559 | − | 1.35268i | ||||
\(628\) | 58.4387i | 0.0930552i | ||||||||
\(629\) | − | 199.881i | − | 0.317775i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −406.725 | −0.644571 | −0.322286 | − | 0.946642i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946642i | \(0.604451\pi\) | |||||||
\(632\) | − | 43.1382i | − | 0.0682567i | ||||||
\(633\) | 256.832i | 0.405738i | ||||||||
\(634\) | 168.719 | 0.266118 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 417.614 | 0.656626 | ||||||||
\(637\) | 828.999 | 1.30141 | ||||||||
\(638\) | − | 122.528i | − | 0.192050i | ||||||
\(639\) | 328.152i | 0.513540i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 994.339i | − | 1.55123i | −0.631206 | − | 0.775616i | \(-0.717440\pi\) | ||
0.631206 | − | 0.775616i | \(-0.282560\pi\) | |||||||
\(642\) | −110.489 | −0.172101 | ||||||||
\(643\) | 847.680i | 1.31832i | 0.752003 | + | 0.659160i | \(0.229088\pi\) | ||||
−0.752003 | + | 0.659160i | \(0.770912\pi\) | |||||||
\(644\) | 5.90694 | 0.00917226 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 578.159 | − | 442.629i | 0.894983 | − | 0.685184i | ||||
\(647\) | − | 731.308i | − | 1.13031i | −0.824986 | − | 0.565153i | \(-0.808817\pi\) | ||
0.824986 | − | 0.565153i | \(-0.191183\pi\) | |||||||
\(648\) | 283.593 | 0.437644 | ||||||||
\(649\) | 1374.28i | 2.11753i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.74169 | 0.00728370 | ||||||||
\(652\) | 188.301i | 0.288805i | ||||||||
\(653\) | − | 1111.60i | − | 1.70230i | −0.524922 | − | 0.851150i | \(-0.675906\pi\) | ||
0.524922 | − | 0.851150i | \(-0.324094\pi\) | |||||||
\(654\) | 455.769i | 0.696894i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 96.0373i | 0.146398i | ||||||||
\(657\) | − | 15.6414i | − | 0.0238072i | ||||||
\(658\) | 17.7549 | 0.0269832 | ||||||||
\(659\) | 363.690i | 0.551881i | 0.961175 | + | 0.275941i | \(0.0889893\pi\) | ||||
−0.961175 | + | 0.275941i | \(0.911011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1069.74i | 1.61836i | 0.587560 | + | 0.809180i | \(0.300089\pi\) | ||||
−0.587560 | + | 0.809180i | \(0.699911\pi\) | |||||||
\(662\) | − | 670.555i | − | 1.01292i | ||||||
\(663\) | − | 1622.12i | − | 2.44664i | ||||||
\(664\) | 410.200i | 0.617772i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −36.5903 | −0.0549404 | ||||||||
\(667\) | −109.910 | −0.164783 | ||||||||
\(668\) | −112.652 | −0.168640 | ||||||||
\(669\) | 1145.14 | 1.71171 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −243.608 | −0.363052 | ||||||||
\(672\) | 2.93015i | 0.00436035i | ||||||||
\(673\) | −270.027 | −0.401228 | −0.200614 | − | 0.979670i | \(-0.564294\pi\) | ||||
−0.200614 | + | 0.979670i | \(0.564294\pi\) | |||||||
\(674\) | −335.726 | −0.498109 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 234.963 | 0.347578 | ||||||||
\(677\) | 826.165 | 1.22033 | 0.610166 | − | 0.792274i | \(-0.291103\pi\) | ||||
0.610166 | + | 0.792274i | \(0.291103\pi\) | |||||||
\(678\) | 854.739 | 1.26068 | ||||||||
\(679\) | − | 0.452259i | − | 0.000666066i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1533.37 | −2.25164 | ||||||||
\(682\) | − | 205.789i | − | 0.301743i | ||||||
\(683\) | −865.671 | −1.26745 | −0.633727 | − | 0.773557i | \(-0.718476\pi\) | ||||
−0.633727 | + | 0.773557i | \(0.718476\pi\) | |||||||
\(684\) | −81.0280 | − | 105.838i | −0.118462 | − | 0.154734i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.2942i | 0.0295834i | ||||||||
\(687\) | −732.060 | −1.06559 | ||||||||
\(688\) | − | 161.258i | − | 0.234386i | ||||||
\(689\) | 999.319 | 1.45039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2977 | 0.0409518 | 0.0204759 | − | 0.999790i | \(-0.493482\pi\) | ||||
0.0204759 | + | 0.999790i | \(0.493482\pi\) | |||||||
\(692\) | −90.8783 | −0.131327 | ||||||||
\(693\) | − | 8.16660i | − | 0.0117844i | ||||||
\(694\) | − | 866.083i | − | 1.24796i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 54.5212i | − | 0.0783350i | ||||||
\(697\) | 650.618 | 0.933455 | ||||||||
\(698\) | 885.149 | 1.26812 | ||||||||
\(699\) | 1028.58i | 1.47150i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 134.912 | 0.192456 | 0.0962282 | − | 0.995359i | \(-0.469322\pi\) | ||||
0.0962282 | + | 0.995359i | \(0.469322\pi\) | |||||||
\(702\) | 464.947 | 0.662318 | ||||||||
\(703\) | −85.1927 | − | 111.278i | −0.121184 | − | 0.158290i | ||||
\(704\) | 127.168 | 0.180637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 308.695i | 0.437246i | ||||||||
\(707\) | − | 15.0943i | − | 0.0213497i | ||||||
\(708\) | 611.512i | 0.863717i | ||||||||
\(709\) | 328.768 | 0.463707 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.4988i | 0.0752445i | ||||||||
\(712\) | − | 68.2445i | − | 0.0958490i | ||||||
\(713\) | −184.597 | −0.258902 | ||||||||
\(714\) | 19.8507 | 0.0278022 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 294.366i | 0.411126i | ||||||||
\(717\) | 318.547 | 0.444277 | ||||||||
\(718\) | 447.220 | 0.622869 | ||||||||
\(719\) | −132.152 | −0.183799 | −0.0918997 | − | 0.995768i | \(-0.529294\pi\) | ||||
−0.0918997 | + | 0.995768i | \(0.529294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.5444i | − | 0.0257204i | ||||||
\(722\) | 133.218 | − | 492.844i | 0.184513 | − | 0.682609i | ||||
\(723\) | − | 302.809i | − | 0.418823i | ||||||
\(724\) | 486.765i | 0.672328i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −658.621 | −0.907192 | ||||||||
\(727\) | − | 370.952i | − | 0.510250i | −0.966908 | − | 0.255125i | \(-0.917883\pi\) | ||
0.966908 | − | 0.255125i | \(-0.0821166\pi\) | |||||||
\(728\) | 7.01163i | 0.00963136i | ||||||||
\(729\) | 266.557 | 0.365648 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1092.46 | −1.49448 | ||||||||
\(732\) | −108.398 | −0.148085 | ||||||||
\(733\) | − | 778.543i | − | 1.06213i | −0.847331 | − | 0.531066i | \(-0.821792\pi\) | ||
0.847331 | − | 0.531066i | \(-0.178208\pi\) | |||||||
\(734\) | 848.637i | 1.15618i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 114.073i | − | 0.154990i | ||||||
\(737\) | 1596.84 | 2.16667 | ||||||||
\(738\) | − | 119.103i | − | 0.161386i | ||||||
\(739\) | −686.378 | −0.928793 | −0.464396 | − | 0.885627i | \(-0.653729\pi\) | ||||
−0.464396 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −691.378 | − | 903.074i | −0.933034 | − | 1.21872i | ||||
\(742\) | 12.2292i | 0.0164814i | ||||||||
\(743\) | −944.989 | −1.27186 | −0.635928 | − | 0.771748i | \(-0.719383\pi\) | ||||
−0.635928 | + | 0.771748i | \(0.719383\pi\) | |||||||
\(744\) | − | 91.5698i | − | 0.123078i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 86.1358 | 0.115464 | ||||||||
\(747\) | − | 508.719i | − | 0.681016i | ||||||
\(748\) | − | 861.519i | − | 1.15176i | ||||||
\(749\) | − | 3.23548i | − | 0.00431974i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 372.272i | 0.495701i | 0.968798 | + | 0.247851i | \(0.0797243\pi\) | ||||
−0.968798 | + | 0.247851i | \(0.920276\pi\) | |||||||
\(752\) | − | 342.877i | − | 0.455953i | ||||||
\(753\) | −1478.63 | −1.96365 | ||||||||
\(754\) | − | 130.465i | − | 0.173031i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.68980i | 0.00752618i | ||||||||
\(757\) | − | 65.8572i | − | 0.0869977i | −0.999053 | − | 0.0434988i | \(-0.986150\pi\) | ||
0.999053 | − | 0.0434988i | \(-0.0138505\pi\) | |||||||
\(758\) | 230.386i | 0.303939i | ||||||||
\(759\) | 1133.66i | 1.49363i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1305.80 | −1.71590 | −0.857951 | − | 0.513732i | \(-0.828263\pi\) | ||||
−0.857951 | + | 0.513732i | \(0.828263\pi\) | |||||||
\(762\) | 320.547 | 0.420666 | ||||||||
\(763\) | −13.3465 | −0.0174921 | ||||||||
\(764\) | −147.626 | −0.193227 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 902.753 | 1.17853 | ||||||||
\(767\) | 1463.30i | 1.90782i | ||||||||
\(768\) | 56.5860 | 0.0736797 | ||||||||
\(769\) | −320.091 | −0.416244 | −0.208122 | − | 0.978103i | \(-0.566735\pi\) | ||||
−0.208122 | + | 0.978103i | \(0.566735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 286.563 | 0.371677 | ||||||||
\(772\) | 199.597 | 0.258545 | ||||||||
\(773\) | 892.160 | 1.15415 | 0.577076 | − | 0.816690i | \(-0.304194\pi\) | ||||
0.577076 | + | 0.816690i | \(0.304194\pi\) | |||||||
\(774\) | 199.987i | 0.258381i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.73385 | −0.0112550 | ||||||||
\(777\) | − | 3.82067i | − | 0.00491721i | ||||||
\(778\) | 247.613 | 0.318269 | ||||||||
\(779\) | 362.214 | − | 277.305i | 0.464974 | − | 0.355976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1487.09i | 1.90408i | ||||||||
\(782\) | −772.801 | −0.988237 | ||||||||
\(783\) | − | 105.870i | − | 0.135210i | ||||||
\(784\) | 195.914 | 0.249891 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 710.107 | 0.903444 | ||||||||
\(787\) | −1088.23 | −1.38276 | −0.691378 | − | 0.722493i | \(-0.742996\pi\) | ||||
−0.691378 | + | 0.722493i | \(0.742996\pi\) | |||||||
\(788\) | 666.249i | 0.845494i | ||||||||
\(789\) | 995.465i | 1.26168i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.0297i | 0.0316431i | ||||||||
\(792\) | −157.710 | −0.199129 | ||||||||
\(793\) | −259.388 | −0.327098 | ||||||||
\(794\) | − | 1025.36i | − | 1.29139i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −160.286 | −0.201365 | ||||||||
\(797\) | −1371.00 | −1.72020 | −0.860102 | − | 0.510123i | \(-0.829600\pi\) | ||||
−0.860102 | + | 0.510123i | \(0.829600\pi\) | |||||||
\(798\) | 11.0514 | − | 8.46074i | 0.0138488 | − | 0.0106024i | ||||
\(799\) | −2322.87 | −2.90722 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.6349i | 0.105662i | ||||||||
\(802\) | − | 801.840i | − | 0.999801i | ||||||
\(803\) | − | 70.8820i | − | 0.0882714i | ||||||
\(804\) | 710.544 | 0.883762 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 219.120i | − | 0.271860i | ||||||
\(807\) | − | 1388.88i | − | 1.72104i | ||||||
\(808\) | −291.495 | −0.360761 | ||||||||
\(809\) | 580.084 | 0.717038 | 0.358519 | − | 0.933522i | \(-0.383282\pi\) | ||||
0.358519 | + | 0.933522i | \(0.383282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1339.70i | 1.65191i | 0.563738 | + | 0.825954i | \(0.309363\pi\) | ||||
−0.563738 | + | 0.825954i | \(0.690637\pi\) | |||||||
\(812\) | 1.59657 | 0.00196621 | ||||||||
\(813\) | 1541.48 | 1.89604 | ||||||||
\(814\) | −165.816 | −0.203706 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 383.350i | − | 0.469792i | ||||||
\(817\) | −608.199 | + | 465.627i | −0.744430 | + | 0.569923i | ||||
\(818\) | − | 306.033i | − | 0.374124i | ||||||
\(819\) | − | 8.69563i | − | 0.0106174i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1526.64 | 1.85949 | 0.929747 | − | 0.368199i | \(-0.120025\pi\) | ||||
0.929747 | + | 0.368199i | \(0.120025\pi\) | |||||||
\(822\) | 481.941i | 0.586302i | ||||||||
\(823\) | 238.601i | 0.289916i | 0.989438 | + | 0.144958i | \(0.0463048\pi\) | ||||
−0.989438 | + | 0.144958i | \(0.953695\pi\) | |||||||
\(824\) | −358.122 | −0.434614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.9071 | −0.0216793 | ||||||||
\(827\) | −1190.01 | −1.43895 | −0.719473 | − | 0.694521i | \(-0.755617\pi\) | ||||
−0.719473 | + | 0.694521i | \(0.755617\pi\) | |||||||
\(828\) | 141.470i | 0.170857i | ||||||||
\(829\) | − | 1208.18i | − | 1.45739i | −0.684838 | − | 0.728696i | \(-0.740127\pi\) | ||
0.684838 | − | 0.728696i | \(-0.259873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1085.49i | 1.30625i | ||||||||
\(832\) | 135.406 | 0.162748 | ||||||||
\(833\) | − | 1327.25i | − | 1.59334i | ||||||
\(834\) | −913.150 | −1.09490 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −367.195 | − | 479.628i | −0.439228 | − | 0.573718i | ||||
\(837\) | − | 177.811i | − | 0.212439i | ||||||
\(838\) | 685.771 | 0.818343 | ||||||||
\(839\) | 360.467i | 0.429639i | 0.976654 | + | 0.214819i | \(0.0689163\pi\) | ||||
−0.976654 | + | 0.214819i | \(0.931084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 811.293 | 0.964676 | ||||||||
\(842\) | 584.444i | 0.694114i | ||||||||
\(843\) | 559.879i | 0.664151i | ||||||||
\(844\) | 145.241i | 0.172087i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 425.226i | 0.502632i | ||||||||
\(847\) | − | 19.2867i | − | 0.0227706i | ||||||
\(848\) | 236.165 | 0.278497 | ||||||||
\(849\) | − | 386.873i | − | 0.455681i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 148.741i | 0.174784i | ||||||||
\(852\) | 661.710i | 0.776655i | ||||||||
\(853\) | 625.741i | 0.733577i | 0.930304 | + | 0.366788i | \(0.119543\pi\) | ||||
−0.930304 | + | 0.366788i | \(0.880457\pi\) | |||||||
\(854\) | − | 3.17427i | − | 0.00371694i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −62.4825 | −0.0729935 | ||||||||
\(857\) | 1576.70 | 1.83979 | 0.919894 | − | 0.392167i | \(-0.128274\pi\) | ||||
0.919894 | + | 0.392167i | \(0.128274\pi\) | |||||||
\(858\) | −1345.68 | −1.56839 | ||||||||
\(859\) | −954.288 | −1.11093 | −0.555464 | − | 0.831540i | \(-0.687460\pi\) | ||||
−0.555464 | + | 0.831540i | \(0.687460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.4364 | 0.0144441 | ||||||||
\(862\) | − | 637.353i | − | 0.739389i | ||||||
\(863\) | −363.759 | −0.421505 | −0.210752 | − | 0.977539i | \(-0.567591\pi\) | ||||
−0.210752 | + | 0.977539i | \(0.567591\pi\) | |||||||
\(864\) | 109.879 | 0.127175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.53741 | 0.00408477 | ||||||||
\(867\) | −1574.98 | −1.81658 | ||||||||
\(868\) | 2.68148 | 0.00308926 | ||||||||
\(869\) | 242.441i | 0.278988i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1700.28 | 1.95210 | ||||||||
\(872\) | 257.742i | 0.295576i | ||||||||
\(873\) | 10.8315 | 0.0124072 | ||||||||
\(874\) | −430.237 | + | 329.382i | −0.492261 | + | 0.376867i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 31.5404i | − | 0.0360050i | ||||||
\(877\) | 1186.98 | 1.35346 | 0.676730 | − | 0.736231i | \(-0.263396\pi\) | ||||
0.676730 | + | 0.736231i | \(0.263396\pi\) | |||||||
\(878\) | 694.594i | 0.791110i | ||||||||
\(879\) | −1175.75 | −1.33760 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 316.952 | 0.359764 | 0.179882 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179882 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(882\) | −242.967 | −0.275473 | ||||||||
\(883\) | 846.927i | 0.959148i | 0.877502 | + | 0.479574i | \(0.159209\pi\) | ||||
−0.877502 | + | 0.479574i | \(0.840791\pi\) | |||||||
\(884\) | − | 917.328i | − | 1.03770i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 337.849i | 0.381319i | ||||||||
\(887\) | 443.640 | 0.500157 | 0.250079 | − | 0.968226i | \(-0.419544\pi\) | ||||
0.250079 | + | 0.968226i | \(0.419544\pi\) | |||||||
\(888\) | −73.7834 | −0.0830894 | ||||||||
\(889\) | 9.38671i | 0.0105587i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1593.82 | −1.78880 | ||||||||
\(892\) | 647.586 | 0.725993 | ||||||||
\(893\) | −1293.20 | + | 990.048i | −1.44815 | + | 1.10868i | ||||
\(894\) | −77.2329 | −0.0863903 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.65703i | 0.00184937i | ||||||||
\(897\) | 1207.10i | 1.34571i | ||||||||
\(898\) | − | 640.262i | − | 0.712986i | ||||||
\(899\) | −49.8941 | −0.0554995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1599.94i | − | 1.77573i | ||||||
\(902\) | − | 539.738i | − | 0.598379i | ||||||
\(903\) | −20.8822 | −0.0231253 | ||||||||
\(904\) | 483.364 | 0.534694 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 926.066i | 1.02215i | ||||||||
\(907\) | 5.46337 | 0.00602356 | 0.00301178 | − | 0.999995i | \(-0.499041\pi\) | ||||
0.00301178 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(908\) | −867.137 | −0.954996 | ||||||||
\(909\) | 361.504 | 0.397694 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1403.59i | 1.54071i | 0.637614 | + | 0.770356i | \(0.279922\pi\) | ||||
−0.637614 | + | 0.770356i | \(0.720078\pi\) | |||||||
\(912\) | −163.391 | − | 213.420i | −0.179157 | − | 0.234013i | ||||
\(913\) | − | 2305.36i | − | 2.52504i | ||||||
\(914\) | 986.773i | 1.07962i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −413.988 | −0.451952 | ||||||||
\(917\) | 20.7943i | 0.0226765i | ||||||||
\(918\) | − | 744.393i | − | 0.810885i | ||||||
\(919\) | 357.449 | 0.388954 | 0.194477 | − | 0.980907i | \(-0.437699\pi\) | ||||
0.194477 | + | 0.980907i | \(0.437699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1659.73 | −1.80209 | ||||||||
\(922\) | −594.453 | −0.644743 | ||||||||
\(923\) | 1583.42i | 1.71552i | ||||||||
\(924\) | − | 16.4677i | − | 0.0178222i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 679.643i | 0.733956i | ||||||||
\(927\) | 444.133 | 0.479108 | ||||||||
\(928\) | − | 30.8323i | − | 0.0332245i | ||||||
\(929\) | 261.924 | 0.281942 | 0.140971 | − | 0.990014i | \(-0.454978\pi\) | ||||
0.140971 | + | 0.990014i | \(0.454978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −565.697 | − | 738.911i | −0.607623 | − | 0.793674i | ||||
\(932\) | 581.672i | 0.624112i | ||||||||
\(933\) | 177.019 | 0.189731 | ||||||||
\(934\) | − | 790.948i | − | 0.846839i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −167.927 | −0.179409 | ||||||||
\(937\) | − | 1286.88i | − | 1.37340i | −0.726941 | − | 0.686700i | \(-0.759059\pi\) | ||
0.726941 | − | 0.686700i | \(-0.240941\pi\) | |||||||
\(938\) | 20.8072i | 0.0221825i | ||||||||
\(939\) | − | 758.592i | − | 0.807872i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1118.46i | − | 1.18858i | −0.804249 | − | 0.594292i | \(-0.797432\pi\) | ||
0.804249 | − | 0.594292i | \(-0.202568\pi\) | |||||||
\(942\) | − | 146.142i | − | 0.155140i | ||||||
\(943\) | −484.157 | −0.513422 | ||||||||
\(944\) | 345.816i | 0.366331i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 906.282i | 0.958015i | ||||||||
\(947\) | 1040.70i | 1.09895i | 0.835512 | + | 0.549473i | \(0.185171\pi\) | ||||
−0.835512 | + | 0.549473i | \(0.814829\pi\) | |||||||
\(948\) | 107.879i | 0.113796i | ||||||||
\(949\) | − | 75.4737i | − | 0.0795297i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −421.928 | −0.443667 | ||||||||
\(952\) | 11.2258 | 0.0117918 | ||||||||
\(953\) | 158.536 | 0.166354 | 0.0831771 | − | 0.996535i | \(-0.473493\pi\) | ||||
0.0831771 | + | 0.996535i | \(0.473493\pi\) | |||||||
\(954\) | −292.886 | −0.307008 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 180.142 | 0.188433 | ||||||||
\(957\) | 306.414i | 0.320182i | ||||||||
\(958\) | 348.856 | 0.364150 | ||||||||
\(959\) | −14.1129 | −0.0147162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 877.202 | 0.912801 | ||||||||
\(962\) | −176.558 | −0.183532 | ||||||||
\(963\) | 77.4890 | 0.0804663 | ||||||||
\(964\) | − | 171.242i | − | 0.177637i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.7719 | −0.0152918 | ||||||||
\(967\) | − | 462.170i | − | 0.477942i | −0.971027 | − | 0.238971i | \(-0.923190\pi\) | ||
0.971027 | − | 0.238971i | \(-0.0768101\pi\) | |||||||
\(968\) | −372.457 | −0.384770 | ||||||||
\(969\) | −1445.85 | + | 1106.91i | −1.49210 | + | 1.14233i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1501.52i | − | 1.54636i | −0.634184 | − | 0.773182i | \(-0.718664\pi\) | ||
0.634184 | − | 0.773182i | \(-0.281336\pi\) | |||||||
\(972\) | −359.569 | −0.369927 | ||||||||
\(973\) | − | 26.7401i | − | 0.0274822i | ||||||
\(974\) | 592.279 | 0.608089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.3003 | −0.0628077 | ||||||||
\(977\) | −1097.99 | −1.12384 | −0.561921 | − | 0.827191i | \(-0.689937\pi\) | ||||
−0.561921 | + | 0.827191i | \(0.689937\pi\) | |||||||
\(978\) | − | 470.898i | − | 0.481491i | ||||||
\(979\) | 383.540i | 0.391767i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 319.645i | − | 0.325835i | ||||||
\(982\) | 727.835 | 0.741176 | ||||||||
\(983\) | 938.538 | 0.954769 | 0.477385 | − | 0.878694i | \(-0.341585\pi\) | ||||
0.477385 | + | 0.878694i | \(0.341585\pi\) | |||||||
\(984\) | − | 240.167i | − | 0.244073i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −208.878 | −0.211844 | ||||||||
\(987\) | −44.4011 | −0.0449859 | ||||||||
\(988\) | −390.982 | − | 510.698i | −0.395730 | − | 0.516901i | ||||
\(989\) | 812.955 | 0.821997 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 540.016i | − | 0.544920i | −0.962167 | − | 0.272460i | \(-0.912163\pi\) | ||
0.962167 | − | 0.272460i | \(-0.0878372\pi\) | |||||||
\(992\) | − | 51.7837i | − | 0.0522013i | ||||||
\(993\) | 1676.91i | 1.68873i | ||||||||
\(994\) | −19.3771 | −0.0194941 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1025.82i | − | 1.02994i | ||||||
\(997\) | − | 406.644i | − | 0.407868i | −0.978985 | − | 0.203934i | \(-0.934627\pi\) | ||
0.978985 | − | 0.203934i | \(-0.0653728\pi\) | |||||||
\(998\) | −215.964 | −0.216396 | ||||||||
\(999\) | −143.273 | −0.143417 |
(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 | 950.3.d.b.949.8 | 24 | ||
5.2 | odd | 4 | 950.3.c.b.151.2 | ✓ | 12 | ||
5.3 | odd | 4 | 950.3.c.c.151.11 | yes | 12 | ||
5.4 | even | 2 | inner | 950.3.d.b.949.17 | 24 | ||
19.18 | odd | 2 | inner | 950.3.d.b.949.20 | 24 | ||
95.18 | even | 4 | 950.3.c.c.151.2 | yes | 12 | ||
95.37 | even | 4 | 950.3.c.b.151.11 | yes | 12 | ||
95.94 | odd | 2 | inner | 950.3.d.b.949.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.3.c.b.151.2 | ✓ | 12 | 5.2 | odd | 4 | ||
950.3.c.b.151.11 | yes | 12 | 95.37 | even | 4 | ||
950.3.c.c.151.2 | yes | 12 | 95.18 | even | 4 | ||
950.3.c.c.151.11 | yes | 12 | 5.3 | odd | 4 | ||
950.3.d.b.949.5 | 24 | 95.94 | odd | 2 | inner | ||
950.3.d.b.949.8 | 24 | 1.1 | even | 1 | trivial | ||
950.3.d.b.949.17 | 24 | 5.4 | even | 2 | inner | ||
950.3.d.b.949.20 | 24 | 19.18 | odd | 2 | inner |