Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,3,Mod(151,950)]
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([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("950.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.c (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: | \(25.8856251142\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 68x^{10} + 1670x^{8} + 18282x^{6} + 91461x^{4} + 207270x^{2} + 172225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(-3.53663i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.151 |
Dual form | 950.3.c.b.151.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | − | 3.53663i | − | 1.17888i | −0.807814 | − | 0.589438i | \(-0.799349\pi\) | ||
0.807814 | − | 0.589438i | \(-0.200651\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.00155 | −0.833591 | ||||||||
\(7\) | 0.146462 | 0.0209232 | 0.0104616 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104616 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.50774 | −0.389749 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8960 | 1.44509 | 0.722546 | − | 0.691322i | \(-0.242972\pi\) | ||||
0.722546 | + | 0.691322i | \(0.242972\pi\) | |||||||
\(12\) | 7.07326i | 0.589438i | ||||||||
\(13\) | − | 16.9258i | − | 1.30198i | −0.759086 | − | 0.650991i | \(-0.774354\pi\) | ||
0.759086 | − | 0.650991i | \(-0.225646\pi\) | |||||||
\(14\) | − | 0.207129i | − | 0.0147949i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 27.0986 | 1.59403 | 0.797017 | − | 0.603957i | \(-0.206410\pi\) | ||||
0.797017 | + | 0.603957i | \(0.206410\pi\) | |||||||
\(18\) | 4.96069i | 0.275594i | ||||||||
\(19\) | 11.5499 | + | 15.0864i | 0.607889 | + | 0.794022i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.517983i | − | 0.0246658i | ||||||
\(22\) | − | 22.4804i | − | 1.02183i | ||||||
\(23\) | 20.1654 | 0.876755 | 0.438378 | − | 0.898791i | \(-0.355553\pi\) | ||||
0.438378 | + | 0.898791i | \(0.355553\pi\) | |||||||
\(24\) | 10.0031 | 0.416796 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −23.9366 | −0.920640 | ||||||||
\(27\) | − | 19.4241i | − | 0.719411i | ||||||
\(28\) | −0.292925 | −0.0104616 | ||||||||
\(29\) | − | 5.45043i | − | 0.187946i | −0.995575 | − | 0.0939730i | \(-0.970043\pi\) | ||
0.995575 | − | 0.0939730i | \(-0.0299567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.15415i | 0.295295i | 0.989040 | + | 0.147648i | \(0.0471701\pi\) | ||||
−0.989040 | + | 0.147648i | \(0.952830\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | − | 56.2183i | − | 1.70359i | ||||||
\(34\) | − | 38.3232i | − | 1.12715i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.01547 | 0.194874 | ||||||||
\(37\) | 7.37605i | 0.199353i | 0.995020 | + | 0.0996764i | \(0.0317808\pi\) | ||||
−0.995020 | + | 0.0996764i | \(0.968219\pi\) | |||||||
\(38\) | 21.3354 | − | 16.3340i | 0.561458 | − | 0.429843i | ||||
\(39\) | −59.8601 | −1.53487 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24.0093i | 0.585593i | 0.956175 | + | 0.292797i | \(0.0945859\pi\) | ||||
−0.956175 | + | 0.292797i | \(0.905414\pi\) | |||||||
\(42\) | −0.732538 | −0.0174414 | ||||||||
\(43\) | −40.3144 | −0.937544 | −0.468772 | − | 0.883319i | \(-0.655303\pi\) | ||||
−0.468772 | + | 0.883319i | \(0.655303\pi\) | |||||||
\(44\) | −31.7920 | −0.722546 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 28.5181i | − | 0.619960i | ||||||
\(47\) | 85.7192 | 1.82381 | 0.911906 | − | 0.410398i | \(-0.134610\pi\) | ||||
0.911906 | + | 0.410398i | \(0.134610\pi\) | |||||||
\(48\) | − | 14.1465i | − | 0.294719i | ||||||
\(49\) | −48.9785 | −0.999562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 95.8376i | − | 1.87917i | ||||||
\(52\) | 33.8515i | 0.650991i | ||||||||
\(53\) | − | 59.0413i | − | 1.11399i | −0.830517 | − | 0.556994i | \(-0.811955\pi\) | ||
0.830517 | − | 0.556994i | \(-0.188045\pi\) | |||||||
\(54\) | −27.4698 | −0.508700 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.414258i | 0.00739747i | ||||||||
\(57\) | 53.3550 | − | 40.8477i | 0.936053 | − | 0.716626i | ||||
\(58\) | −7.70807 | −0.132898 | ||||||||
\(59\) | − | 86.4540i | − | 1.46532i | −0.680593 | − | 0.732661i | \(-0.738278\pi\) | ||
0.680593 | − | 0.732661i | \(-0.261722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3251 | −0.251231 | −0.125615 | − | 0.992079i | \(-0.540091\pi\) | ||||
−0.125615 | + | 0.992079i | \(0.540091\pi\) | |||||||
\(62\) | 12.9459 | 0.208805 | ||||||||
\(63\) | −0.513751 | −0.00815478 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −79.5047 | −1.20462 | ||||||||
\(67\) | 100.455i | 1.49933i | 0.661818 | + | 0.749665i | \(0.269785\pi\) | ||||
−0.661818 | + | 0.749665i | \(0.730215\pi\) | |||||||
\(68\) | −54.1971 | −0.797017 | ||||||||
\(69\) | − | 71.3174i | − | 1.03359i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 93.5509i | 1.31762i | 0.752310 | + | 0.658809i | \(0.228940\pi\) | ||||
−0.752310 | + | 0.658809i | \(0.771060\pi\) | |||||||
\(72\) | − | 9.92138i | − | 0.137797i | ||||||
\(73\) | −4.45910 | −0.0610836 | −0.0305418 | − | 0.999533i | \(-0.509723\pi\) | ||||
−0.0305418 | + | 0.999533i | \(0.509723\pi\) | |||||||
\(74\) | 10.4313 | 0.140964 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.0998 | − | 30.1728i | −0.303945 | − | 0.397011i | ||||
\(77\) | 2.32817 | 0.0302360 | ||||||||
\(78\) | 84.6550i | 1.08532i | ||||||||
\(79\) | − | 15.2517i | − | 0.193059i | −0.995330 | − | 0.0965295i | \(-0.969226\pi\) | ||
0.995330 | − | 0.0965295i | \(-0.0307742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.265 | −1.23784 | ||||||||
\(82\) | 33.9543 | 0.414077 | ||||||||
\(83\) | −145.028 | −1.74732 | −0.873661 | − | 0.486535i | \(-0.838261\pi\) | ||||
−0.873661 | + | 0.486535i | \(0.838261\pi\) | |||||||
\(84\) | 1.03597i | 0.0123329i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 57.0132i | 0.662944i | ||||||||
\(87\) | −19.2761 | −0.221565 | ||||||||
\(88\) | 44.9607i | 0.510917i | ||||||||
\(89\) | − | 24.1281i | − | 0.271102i | −0.990770 | − | 0.135551i | \(-0.956720\pi\) | ||
0.990770 | − | 0.135551i | \(-0.0432804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.47899i | − | 0.0272416i | ||||||
\(92\) | −40.3308 | −0.438378 | ||||||||
\(93\) | 32.3748 | 0.348116 | ||||||||
\(94\) | − | 121.225i | − | 1.28963i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20.0062 | −0.208398 | ||||||||
\(97\) | 3.08788i | 0.0318338i | 0.999873 | + | 0.0159169i | \(0.00506673\pi\) | ||||
−0.999873 | + | 0.0159169i | \(0.994933\pi\) | |||||||
\(98\) | 69.2661i | 0.706797i | ||||||||
\(99\) | −55.7591 | −0.563223 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 103.059 | 1.02039 | 0.510193 | − | 0.860060i | \(-0.329574\pi\) | ||||
0.510193 | + | 0.860060i | \(0.329574\pi\) | |||||||
\(102\) | −135.535 | −1.32877 | ||||||||
\(103\) | − | 126.615i | − | 1.22927i | −0.788810 | − | 0.614637i | \(-0.789302\pi\) | ||
0.788810 | − | 0.614637i | \(-0.210698\pi\) | |||||||
\(104\) | 47.8733 | 0.460320 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −83.4970 | −0.787708 | ||||||||
\(107\) | 22.0909i | 0.206457i | 0.994658 | + | 0.103228i | \(0.0329173\pi\) | ||||
−0.994658 | + | 0.103228i | \(0.967083\pi\) | |||||||
\(108\) | 38.8482i | 0.359705i | ||||||||
\(109\) | 91.1256i | 0.836015i | 0.908444 | + | 0.418007i | \(0.137271\pi\) | ||||
−0.908444 | + | 0.418007i | \(0.862729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.0864 | 0.235012 | ||||||||
\(112\) | 0.585849 | 0.00523080 | ||||||||
\(113\) | 170.895i | 1.51234i | 0.654373 | + | 0.756172i | \(0.272933\pi\) | ||||
−0.654373 | + | 0.756172i | \(0.727067\pi\) | |||||||
\(114\) | −57.7674 | − | 75.4554i | −0.506731 | − | 0.661889i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.9009i | 0.0939730i | ||||||||
\(117\) | 59.3711i | 0.507445i | ||||||||
\(118\) | −122.264 | −1.03614 | ||||||||
\(119\) | 3.96892 | 0.0333523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 131.683 | 1.08829 | ||||||||
\(122\) | 21.6729i | 0.177647i | ||||||||
\(123\) | 84.9120 | 0.690342 | ||||||||
\(124\) | − | 18.3083i | − | 0.147648i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.726554i | 0.00576630i | ||||||||
\(127\) | − | 64.0896i | − | 0.504643i | −0.967644 | − | 0.252321i | \(-0.918806\pi\) | ||
0.967644 | − | 0.252321i | \(-0.0811940\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 142.577i | 1.10525i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −141.977 | −1.08380 | −0.541898 | − | 0.840444i | \(-0.682294\pi\) | ||||
−0.541898 | + | 0.840444i | \(0.682294\pi\) | |||||||
\(132\) | 112.437i | 0.851793i | ||||||||
\(133\) | 1.69163 | + | 2.20959i | 0.0127190 | + | 0.0166135i | ||||
\(134\) | 142.065 | 1.06019 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76.6463i | 0.563576i | ||||||||
\(137\) | 96.3583 | 0.703345 | 0.351673 | − | 0.936123i | \(-0.385613\pi\) | ||||
0.351673 | + | 0.936123i | \(0.385613\pi\) | |||||||
\(138\) | −100.858 | −0.730856 | ||||||||
\(139\) | −182.574 | −1.31348 | −0.656739 | − | 0.754118i | \(-0.728065\pi\) | ||||
−0.656739 | + | 0.754118i | \(0.728065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 303.157i | − | 2.15005i | ||||||
\(142\) | 132.301 | 0.931697 | ||||||||
\(143\) | − | 269.052i | − | 1.88148i | ||||||
\(144\) | −14.0309 | −0.0974371 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.30612i | 0.0431926i | ||||||||
\(147\) | 173.219i | 1.17836i | ||||||||
\(148\) | − | 14.7521i | − | 0.0996764i | ||||||
\(149\) | −15.4418 | −0.103636 | −0.0518182 | − | 0.998657i | \(-0.516502\pi\) | ||||
−0.0518182 | + | 0.998657i | \(0.516502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 185.156i | − | 1.22620i | −0.790006 | − | 0.613099i | \(-0.789923\pi\) | ||
0.790006 | − | 0.613099i | \(-0.210077\pi\) | |||||||
\(152\) | −42.6708 | + | 32.6680i | −0.280729 | + | 0.214921i | ||||
\(153\) | −95.0547 | −0.621272 | ||||||||
\(154\) | − | 3.29253i | − | 0.0213800i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 119.720 | 0.767437 | ||||||||
\(157\) | −29.2193 | −0.186110 | −0.0930552 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930552 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(158\) | −21.5691 | −0.136513 | ||||||||
\(159\) | −208.807 | −1.31325 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.95347 | 0.0183445 | ||||||||
\(162\) | 141.797i | 0.875288i | ||||||||
\(163\) | 94.1505 | 0.577611 | 0.288805 | − | 0.957388i | \(-0.406742\pi\) | ||||
0.288805 | + | 0.957388i | \(0.406742\pi\) | |||||||
\(164\) | − | 48.0186i | − | 0.292797i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 205.100i | 1.23554i | ||||||||
\(167\) | − | 56.3258i | − | 0.337280i | −0.985678 | − | 0.168640i | \(-0.946062\pi\) | ||
0.985678 | − | 0.168640i | \(-0.0539376\pi\) | |||||||
\(168\) | 1.46508 | 0.00872069 | ||||||||
\(169\) | −117.481 | −0.695156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −40.5140 | − | 52.9192i | −0.236924 | − | 0.309469i | ||||
\(172\) | 80.6288 | 0.468772 | ||||||||
\(173\) | 45.4392i | 0.262654i | 0.991339 | + | 0.131327i | \(0.0419238\pi\) | ||||
−0.991339 | + | 0.131327i | \(0.958076\pi\) | |||||||
\(174\) | 27.2606i | 0.156670i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 63.5841 | 0.361273 | ||||||||
\(177\) | −305.756 | −1.72743 | ||||||||
\(178\) | −34.1222 | −0.191698 | ||||||||
\(179\) | − | 147.183i | − | 0.822252i | −0.911579 | − | 0.411126i | \(-0.865136\pi\) | ||
0.911579 | − | 0.411126i | \(-0.134864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 243.383i | 1.34466i | 0.740254 | + | 0.672328i | \(0.234705\pi\) | ||||
−0.740254 | + | 0.672328i | \(0.765295\pi\) | |||||||
\(182\) | −3.50582 | −0.0192627 | ||||||||
\(183\) | 54.1991i | 0.296170i | ||||||||
\(184\) | 57.0363i | 0.309980i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 45.7849i | − | 0.246155i | ||||||
\(187\) | 430.759 | 2.30353 | ||||||||
\(188\) | −171.438 | −0.911906 | ||||||||
\(189\) | − | 2.84490i | − | 0.0150524i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −73.8128 | −0.386454 | −0.193227 | − | 0.981154i | \(-0.561895\pi\) | ||||
−0.193227 | + | 0.981154i | \(0.561895\pi\) | |||||||
\(192\) | 28.2930i | 0.147359i | ||||||||
\(193\) | − | 99.7983i | − | 0.517089i | −0.965999 | − | 0.258545i | \(-0.916757\pi\) | ||
0.965999 | − | 0.258545i | \(-0.0832429\pi\) | |||||||
\(194\) | 4.36693 | 0.0225099 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.9571 | 0.499781 | ||||||||
\(197\) | −333.125 | −1.69099 | −0.845494 | − | 0.533985i | \(-0.820694\pi\) | ||||
−0.845494 | + | 0.533985i | \(0.820694\pi\) | |||||||
\(198\) | 78.8552i | 0.398259i | ||||||||
\(199\) | 80.1431 | 0.402729 | 0.201365 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201365 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 355.272 | 1.76752 | ||||||||
\(202\) | − | 145.747i | − | 0.721522i | ||||||
\(203\) | − | 0.798283i | − | 0.00393243i | ||||||
\(204\) | 191.675i | 0.939584i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −179.061 | −0.869229 | ||||||||
\(207\) | −70.7348 | −0.341714 | ||||||||
\(208\) | − | 67.7030i | − | 0.325495i | ||||||
\(209\) | 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 | \(0.944949\pi\) | |||||||
\(212\) | 118.083i | 0.556994i | ||||||||
\(213\) | 330.855 | 1.55331 | ||||||||
\(214\) | 31.2412 | 0.145987 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 54.9396 | 0.254350 | ||||||||
\(217\) | 1.34074i | 0.00617852i | ||||||||
\(218\) | 128.871 | 0.591152 | ||||||||
\(219\) | 15.7702i | 0.0720100i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 458.664i | − | 2.07540i | ||||||
\(222\) | − | 36.8917i | − | 0.166179i | ||||||
\(223\) | − | 323.793i | − | 1.45199i | −0.687702 | − | 0.725993i | \(-0.741380\pi\) | ||
0.687702 | − | 0.725993i | \(-0.258620\pi\) | |||||||
\(224\) | − | 0.828516i | − | 0.00369873i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 241.682 | 1.06939 | ||||||||
\(227\) | − | 433.568i | − | 1.90999i | −0.296618 | − | 0.954996i | \(-0.595859\pi\) | ||
0.296618 | − | 0.954996i | \(-0.404141\pi\) | |||||||
\(228\) | −106.710 | + | 81.6954i | −0.468027 | + | 0.358313i | ||||
\(229\) | 206.994 | 0.903904 | 0.451952 | − | 0.892042i | \(-0.350728\pi\) | ||||
0.451952 | + | 0.892042i | \(0.350728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.23387i | − | 0.0356444i | ||||||
\(232\) | 15.4161 | 0.0664489 | ||||||||
\(233\) | 290.836 | 1.24822 | 0.624112 | − | 0.781335i | \(-0.285461\pi\) | ||||
0.624112 | + | 0.781335i | \(0.285461\pi\) | |||||||
\(234\) | 83.9634 | 0.358818 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 172.908i | 0.732661i | ||||||||
\(237\) | −53.9395 | −0.227593 | ||||||||
\(238\) | − | 5.61290i | − | 0.0235836i | ||||||
\(239\) | −90.0708 | −0.376865 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 85.6209i | − | 0.355273i | −0.984096 | − | 0.177637i | \(-0.943155\pi\) | ||
0.984096 | − | 0.177637i | \(-0.0568452\pi\) | |||||||
\(242\) | − | 186.229i | − | 0.769540i | ||||||
\(243\) | 179.785i | 0.739854i | ||||||||
\(244\) | 30.6501 | 0.125615 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 120.084i | − | 0.488145i | ||||||
\(247\) | 255.349 | − | 195.491i | 1.03380 | − | 0.791461i | ||||
\(248\) | −25.8918 | −0.104403 | ||||||||
\(249\) | 512.909i | 2.05988i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −418.090 | −1.66570 | −0.832849 | − | 0.553500i | \(-0.813292\pi\) | ||||
−0.832849 | + | 0.553500i | \(0.813292\pi\) | |||||||
\(252\) | 1.02750 | 0.00407739 | ||||||||
\(253\) | 320.549 | 1.26699 | ||||||||
\(254\) | −90.6364 | −0.356836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 81.0271i | 0.315281i | 0.987497 | + | 0.157640i | \(0.0503886\pi\) | ||||
−0.987497 | + | 0.157640i | \(0.949611\pi\) | |||||||
\(258\) | 201.634 | 0.781528 | ||||||||
\(259\) | 1.08031i | 0.00417110i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.1187i | 0.0732516i | ||||||||
\(262\) | 200.786i | 0.766360i | ||||||||
\(263\) | 281.473 | 1.07024 | 0.535120 | − | 0.844776i | \(-0.320267\pi\) | ||||
0.535120 | + | 0.844776i | \(0.320267\pi\) | |||||||
\(264\) | 159.009 | 0.602308 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.12483 | − | 2.39232i | 0.0117475 | − | 0.00899368i | ||||
\(267\) | −85.3320 | −0.319596 | ||||||||
\(268\) | − | 200.910i | − | 0.749665i | ||||||
\(269\) | 392.714i | 1.45990i | 0.683499 | + | 0.729951i | \(0.260457\pi\) | ||||
−0.683499 | + | 0.729951i | \(0.739543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 435.861 | 1.60834 | 0.804172 | − | 0.594397i | \(-0.202609\pi\) | ||||
0.804172 | + | 0.594397i | \(0.202609\pi\) | |||||||
\(272\) | 108.394 | 0.398508 | ||||||||
\(273\) | −8.76725 | −0.0321145 | ||||||||
\(274\) | − | 136.271i | − | 0.497340i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 142.635i | 0.516793i | ||||||||
\(277\) | −306.929 | −1.10805 | −0.554024 | − | 0.832501i | \(-0.686908\pi\) | ||||
−0.554024 | + | 0.832501i | \(0.686908\pi\) | |||||||
\(278\) | 258.198i | 0.928770i | ||||||||
\(279\) | − | 32.1103i | − | 0.115091i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 158.309i | 0.563376i | 0.959506 | + | 0.281688i | \(0.0908944\pi\) | ||||
−0.959506 | + | 0.281688i | \(0.909106\pi\) | |||||||
\(282\) | −428.729 | −1.52031 | ||||||||
\(283\) | −109.390 | −0.386539 | −0.193269 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193269 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(284\) | − | 187.102i | − | 0.658809i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −380.497 | −1.33041 | ||||||||
\(287\) | 3.51646i | 0.0122525i | ||||||||
\(288\) | 19.8428i | 0.0688985i | ||||||||
\(289\) | 445.333 | 1.54094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9207 | 0.0375282 | ||||||||
\(292\) | 8.91820 | 0.0305418 | ||||||||
\(293\) | 332.451i | 1.13464i | 0.823496 | + | 0.567322i | \(0.192020\pi\) | ||||
−0.823496 | + | 0.567322i | \(0.807980\pi\) | |||||||
\(294\) | 244.969 | 0.833226 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.8626 | −0.0704818 | ||||||||
\(297\) | − | 308.766i | − | 1.03962i | ||||||
\(298\) | 21.8380i | 0.0732819i | ||||||||
\(299\) | − | 341.314i | − | 1.14152i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.90454 | −0.0196164 | ||||||||
\(302\) | −261.850 | −0.867053 | ||||||||
\(303\) | − | 364.481i | − | 1.20291i | ||||||
\(304\) | 46.1996 | + | 60.3456i | 0.151972 | + | 0.198505i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 134.428i | 0.439306i | ||||||||
\(307\) | − | 469.296i | − | 1.52865i | −0.644830 | − | 0.764326i | \(-0.723072\pi\) | ||
0.644830 | − | 0.764326i | \(-0.276928\pi\) | |||||||
\(308\) | −4.65634 | −0.0151180 | ||||||||
\(309\) | −447.791 | −1.44916 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 50.0531 | 0.160942 | 0.0804712 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804712 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(312\) | − | 169.310i | − | 0.542660i | ||||||
\(313\) | −214.496 | −0.685290 | −0.342645 | − | 0.939465i | \(-0.611323\pi\) | ||||
−0.342645 | + | 0.939465i | \(0.611323\pi\) | |||||||
\(314\) | 41.3224i | 0.131600i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.5033i | 0.0965295i | ||||||||
\(317\) | − | 119.302i | − | 0.376348i | −0.982136 | − | 0.188174i | \(-0.939743\pi\) | ||
0.982136 | − | 0.188174i | \(-0.0602568\pi\) | |||||||
\(318\) | 295.298i | 0.928610i | ||||||||
\(319\) | − | 86.6402i | − | 0.271599i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 78.1272 | 0.243387 | ||||||||
\(322\) | − | 4.17683i | − | 0.0129715i | ||||||
\(323\) | 312.986 | + | 408.820i | 0.968996 | + | 1.26570i | ||||
\(324\) | 200.531 | 0.618922 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 133.149i | − | 0.408432i | ||||||
\(327\) | 322.277 | 0.985557 | ||||||||
\(328\) | −67.9086 | −0.207038 | ||||||||
\(329\) | 12.5546 | 0.0381600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 474.154i | 1.43249i | 0.697849 | + | 0.716245i | \(0.254141\pi\) | ||||
−0.697849 | + | 0.716245i | \(0.745859\pi\) | |||||||
\(332\) | 290.056 | 0.873661 | ||||||||
\(333\) | − | 25.8733i | − | 0.0776975i | ||||||
\(334\) | −79.6567 | −0.238493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 2.07193i | − | 0.00616646i | ||||||
\(337\) | 237.394i | 0.704433i | 0.935919 | + | 0.352216i | \(0.114572\pi\) | ||||
−0.935919 | + | 0.352216i | \(0.885428\pi\) | |||||||
\(338\) | 166.144i | 0.491549i | ||||||||
\(339\) | 604.392 | 1.78287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 145.515i | 0.426729i | ||||||||
\(342\) | −74.8390 | + | 57.2955i | −0.218827 | + | 0.167531i | ||||
\(343\) | −14.3502 | −0.0418372 | ||||||||
\(344\) | − | 114.026i | − | 0.331472i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 64.2607 | 0.185724 | ||||||||
\(347\) | −612.413 | −1.76488 | −0.882440 | − | 0.470426i | \(-0.844100\pi\) | ||||
−0.882440 | + | 0.470426i | \(0.844100\pi\) | |||||||
\(348\) | 38.5523 | 0.110782 | ||||||||
\(349\) | 625.895 | 1.79340 | 0.896698 | − | 0.442644i | \(-0.145959\pi\) | ||||
0.896698 | + | 0.442644i | \(0.145959\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −328.767 | −0.936659 | ||||||||
\(352\) | − | 89.9215i | − | 0.255459i | ||||||
\(353\) | −218.281 | −0.618359 | −0.309179 | − | 0.951004i | \(-0.600054\pi\) | ||||
−0.309179 | + | 0.951004i | \(0.600054\pi\) | |||||||
\(354\) | 432.404i | 1.22148i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.2561i | 0.135551i | ||||||||
\(357\) | − | 14.0366i | − | 0.0393182i | ||||||
\(358\) | −208.148 | −0.581420 | ||||||||
\(359\) | 316.232 | 0.880870 | 0.440435 | − | 0.897784i | \(-0.354824\pi\) | ||||
0.440435 | + | 0.897784i | \(0.354824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −94.1997 | + | 348.493i | −0.260941 | + | 0.965355i | ||||
\(362\) | 344.195 | 0.950815 | ||||||||
\(363\) | − | 465.716i | − | 1.28296i | ||||||
\(364\) | 4.95797i | 0.0136208i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 76.6491 | 0.209424 | ||||||||
\(367\) | 600.077 | 1.63509 | 0.817543 | − | 0.575867i | \(-0.195335\pi\) | ||||
0.817543 | + | 0.575867i | \(0.195335\pi\) | |||||||
\(368\) | 80.6615 | 0.219189 | ||||||||
\(369\) | − | 84.2184i | − | 0.228234i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.64733i | − | 0.0233082i | ||||||
\(372\) | −64.7496 | −0.174058 | ||||||||
\(373\) | 60.9072i | 0.163290i | 0.996661 | + | 0.0816451i | \(0.0260174\pi\) | ||||
−0.996661 | + | 0.0816451i | \(0.973983\pi\) | |||||||
\(374\) | − | 609.186i | − | 1.62884i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 242.450i | 0.644815i | ||||||||
\(377\) | −92.2527 | −0.244702 | ||||||||
\(378\) | −4.02329 | −0.0106436 | ||||||||
\(379\) | 162.907i | 0.429835i | 0.976632 | + | 0.214917i | \(0.0689482\pi\) | ||||
−0.976632 | + | 0.214917i | \(0.931052\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −226.661 | −0.594911 | ||||||||
\(382\) | 104.387i | 0.273264i | ||||||||
\(383\) | 638.343i | 1.66669i | 0.552752 | + | 0.833346i | \(0.313578\pi\) | ||||
−0.552752 | + | 0.833346i | \(0.686422\pi\) | |||||||
\(384\) | 40.0124 | 0.104199 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −141.136 | −0.365637 | ||||||||
\(387\) | 141.412 | 0.365406 | ||||||||
\(388\) | − | 6.17577i | − | 0.0159169i | ||||||
\(389\) | 175.089 | 0.450100 | 0.225050 | − | 0.974347i | \(-0.427746\pi\) | ||||
0.225050 | + | 0.974347i | \(0.427746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 546.453 | 1.39758 | ||||||||
\(392\) | − | 138.532i | − | 0.353399i | ||||||
\(393\) | 502.121i | 1.27766i | ||||||||
\(394\) | 471.109i | 1.19571i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 111.518 | 0.281611 | ||||||||
\(397\) | −725.042 | −1.82630 | −0.913151 | − | 0.407622i | \(-0.866358\pi\) | ||||
−0.913151 | + | 0.407622i | \(0.866358\pi\) | |||||||
\(398\) | − | 113.339i | − | 0.284773i | ||||||
\(399\) | 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 | \(0.750063\pi\) | |||||||
\(402\) | − | 502.431i | − | 1.24983i | ||||||
\(403\) | 154.941 | 0.384469 | ||||||||
\(404\) | −206.118 | −0.510193 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.12894 | −0.00278065 | ||||||||
\(407\) | 117.250i | 0.288083i | ||||||||
\(408\) | 271.070 | 0.664386 | ||||||||
\(409\) | − | 216.398i | − | 0.529091i | −0.964373 | − | 0.264545i | \(-0.914778\pi\) | ||
0.964373 | − | 0.264545i | \(-0.0852219\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 340.783i | − | 0.829157i | ||||||
\(412\) | 253.231i | 0.614637i | ||||||||
\(413\) | − | 12.6623i | − | 0.0306592i | ||||||
\(414\) | 100.034i | 0.241628i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −95.7465 | −0.230160 | ||||||||
\(417\) | 645.695i | 1.54843i | ||||||||
\(418\) | 339.148 | − | 259.646i | 0.811359 | − | 0.621163i | ||||
\(419\) | 484.914 | 1.15731 | 0.578656 | − | 0.815572i | \(-0.303577\pi\) | ||||
0.578656 | + | 0.815572i | \(0.303577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 413.265i | − | 0.981626i | −0.871265 | − | 0.490813i | \(-0.836700\pi\) | ||
0.871265 | − | 0.490813i | \(-0.163300\pi\) | |||||||
\(422\) | 102.701 | 0.243368 | ||||||||
\(423\) | −300.680 | −0.710828 | ||||||||
\(424\) | 166.994 | 0.393854 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 467.899i | − | 1.09836i | ||||||
\(427\) | −2.24455 | −0.00525655 | ||||||||
\(428\) | − | 44.1818i | − | 0.103228i | ||||||
\(429\) | −951.538 | −2.21804 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 450.677i | 1.04565i | 0.852439 | + | 0.522827i | \(0.175123\pi\) | ||||
−0.852439 | + | 0.522827i | \(0.824877\pi\) | |||||||
\(432\) | − | 77.6964i | − | 0.179853i | ||||||
\(433\) | 2.50133i | 0.00577673i | 0.999996 | + | 0.00288837i | \(0.000919397\pi\) | ||||
−0.999996 | + | 0.00288837i | \(0.999081\pi\) | |||||||
\(434\) | 1.89609 | 0.00436887 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 182.251i | − | 0.418007i | ||||||
\(437\) | 232.908 | + | 304.223i | 0.532970 | + | 0.696163i | ||||
\(438\) | 22.3024 | 0.0509187 | ||||||||
\(439\) | 491.152i | 1.11880i | 0.828898 | + | 0.559399i | \(0.188968\pi\) | ||||
−0.828898 | + | 0.559399i | \(0.811032\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 171.804 | 0.389578 | ||||||||
\(442\) | −648.649 | −1.46753 | ||||||||
\(443\) | −238.895 | −0.539267 | −0.269634 | − | 0.962963i | \(-0.586903\pi\) | ||||
−0.269634 | + | 0.962963i | \(0.586903\pi\) | |||||||
\(444\) | −52.1727 | −0.117506 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −457.912 | −1.02671 | ||||||||
\(447\) | 54.6119i | 0.122174i | ||||||||
\(448\) | −1.17170 | −0.00261540 | ||||||||
\(449\) | − | 452.733i | − | 1.00832i | −0.863612 | − | 0.504158i | \(-0.831803\pi\) | ||
0.863612 | − | 0.504158i | \(-0.168197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 381.653i | 0.846236i | ||||||||
\(452\) | − | 341.790i | − | 0.756172i | ||||||
\(453\) | −654.828 | −1.44554 | ||||||||
\(454\) | −613.158 | −1.35057 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 115.535 | + | 150.911i | 0.253366 | + | 0.330945i | ||||
\(457\) | 697.754 | 1.52681 | 0.763407 | − | 0.645918i | \(-0.223525\pi\) | ||||
0.763407 | + | 0.645918i | \(0.223525\pi\) | |||||||
\(458\) | − | 292.734i | − | 0.639156i | ||||||
\(459\) | − | 526.365i | − | 1.14677i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 420.342 | 0.911804 | 0.455902 | − | 0.890030i | \(-0.349317\pi\) | ||||
0.455902 | + | 0.890030i | \(0.349317\pi\) | |||||||
\(462\) | −11.6444 | −0.0252044 | ||||||||
\(463\) | −480.580 | −1.03797 | −0.518985 | − | 0.854783i | \(-0.673690\pi\) | ||||
−0.518985 | + | 0.854783i | \(0.673690\pi\) | |||||||
\(464\) | − | 21.8017i | − | 0.0469865i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 411.304i | − | 0.882627i | ||||||
\(467\) | −559.285 | −1.19761 | −0.598806 | − | 0.800894i | \(-0.704358\pi\) | ||||
−0.598806 | + | 0.800894i | \(0.704358\pi\) | |||||||
\(468\) | − | 118.742i | − | 0.253723i | ||||||
\(469\) | 14.7129i | 0.0313708i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 103.338i | 0.219401i | ||||||||
\(472\) | 244.529 | 0.518070 | ||||||||
\(473\) | −640.838 | −1.35484 | ||||||||
\(474\) | 76.2819i | 0.160932i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.93784 | −0.0166761 | ||||||||
\(477\) | 207.101i | 0.434175i | ||||||||
\(478\) | 127.379i | 0.266484i | ||||||||
\(479\) | 246.678 | 0.514986 | 0.257493 | − | 0.966280i | \(-0.417104\pi\) | ||||
0.257493 | + | 0.966280i | \(0.417104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 124.845 | 0.259554 | ||||||||
\(482\) | −121.086 | −0.251216 | ||||||||
\(483\) | − | 10.4453i | − | 0.0216259i | ||||||
\(484\) | −263.367 | −0.544147 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 254.254 | 0.523156 | ||||||||
\(487\) | − | 418.804i | − | 0.859968i | −0.902837 | − | 0.429984i | \(-0.858519\pi\) | ||
0.902837 | − | 0.429984i | \(-0.141481\pi\) | |||||||
\(488\) | − | 43.3459i | − | 0.0888235i | ||||||
\(489\) | − | 332.975i | − | 0.680931i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −514.657 | −1.04818 | −0.524091 | − | 0.851662i | \(-0.675595\pi\) | ||||
−0.524091 | + | 0.851662i | \(0.675595\pi\) | |||||||
\(492\) | −169.824 | −0.345171 | ||||||||
\(493\) | − | 147.699i | − | 0.299592i | ||||||
\(494\) | −276.466 | − | 361.118i | −0.559647 | − | 0.731008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.6166i | 0.0738238i | ||||||||
\(497\) | 13.7017i | 0.0275688i | ||||||||
\(498\) | 725.363 | 1.45655 | ||||||||
\(499\) | −152.709 | −0.306031 | −0.153015 | − | 0.988224i | \(-0.548898\pi\) | ||||
−0.153015 | + | 0.988224i | \(0.548898\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −199.203 | −0.397612 | ||||||||
\(502\) | 591.269i | 1.17783i | ||||||||
\(503\) | −173.503 | −0.344937 | −0.172469 | − | 0.985015i | \(-0.555174\pi\) | ||||
−0.172469 | + | 0.985015i | \(0.555174\pi\) | |||||||
\(504\) | − | 1.45311i | − | 0.00288315i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 453.325i | − | 0.895899i | ||||||
\(507\) | 415.488i | 0.819502i | ||||||||
\(508\) | 128.179i | 0.252321i | ||||||||
\(509\) | 856.653i | 1.68301i | 0.540247 | + | 0.841506i | \(0.318331\pi\) | ||||
−0.540247 | + | 0.841506i | \(0.681669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.653090 | −0.00127806 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 293.040 | − | 224.346i | 0.571228 | − | 0.437322i | ||||
\(514\) | 114.590 | 0.222937 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 285.154i | − | 0.552624i | ||||||
\(517\) | 1362.59 | 2.63558 | ||||||||
\(518\) | 1.52779 | 0.00294941 | ||||||||
\(519\) | 160.701 | 0.309637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 99.1018i | − | 0.190215i | −0.995467 | − | 0.0951073i | \(-0.969681\pi\) | ||
0.995467 | − | 0.0951073i | \(-0.0303194\pi\) | |||||||
\(522\) | 27.0379 | 0.0517967 | ||||||||
\(523\) | 56.3564i | 0.107756i | 0.998548 | + | 0.0538780i | \(0.0171582\pi\) | ||||
−0.998548 | + | 0.0538780i | \(0.982842\pi\) | |||||||
\(524\) | 283.955 | 0.541898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 398.063i | − | 0.756773i | ||||||
\(527\) | 248.064i | 0.470710i | ||||||||
\(528\) | − | 224.873i | − | 0.425896i | ||||||
\(529\) | −122.358 | −0.231300 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 303.258i | 0.571107i | ||||||||
\(532\) | −3.38325 | − | 4.41918i | −0.00635949 | − | 0.00830673i | ||||
\(533\) | 406.376 | 0.762431 | ||||||||
\(534\) | 120.678i | 0.225988i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −284.130 | −0.530093 | ||||||||
\(537\) | −520.532 | −0.969333 | ||||||||
\(538\) | 555.381 | 1.03231 | ||||||||
\(539\) | −778.564 | −1.44446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 909.463 | 1.68108 | 0.840538 | − | 0.541752i | \(-0.182239\pi\) | ||||
0.840538 | + | 0.541752i | \(0.182239\pi\) | |||||||
\(542\) | − | 616.401i | − | 1.13727i | ||||||
\(543\) | 860.754 | 1.58518 | ||||||||
\(544\) | − | 153.293i | − | 0.281788i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.3988i | 0.0227084i | ||||||||
\(547\) | − | 174.393i | − | 0.318817i | −0.987213 | − | 0.159408i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159408i | \(-0.0509587\pi\) | |||||||
\(548\) | −192.717 | −0.351673 | ||||||||
\(549\) | 53.7563 | 0.0979168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 82.2275 | − | 62.9519i | 0.149233 | − | 0.114250i | ||||
\(552\) | 201.716 | 0.365428 | ||||||||
\(553\) | − | 2.23379i | − | 0.00403941i | ||||||
\(554\) | 434.064i | 0.783508i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 365.147 | 0.656739 | ||||||||
\(557\) | −134.156 | −0.240854 | −0.120427 | − | 0.992722i | \(-0.538426\pi\) | ||||
−0.120427 | + | 0.992722i | \(0.538426\pi\) | |||||||
\(558\) | −45.4109 | −0.0813815 | ||||||||
\(559\) | 682.352i | 1.22066i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1523.44i | − | 2.71557i | ||||||
\(562\) | 223.882 | 0.398367 | ||||||||
\(563\) | 178.310i | 0.316715i | 0.987382 | + | 0.158357i | \(0.0506198\pi\) | ||||
−0.987382 | + | 0.158357i | \(0.949380\pi\) | |||||||
\(564\) | 606.314i | 1.07502i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 154.702i | 0.273324i | ||||||||
\(567\) | −14.6851 | −0.0258997 | ||||||||
\(568\) | −264.602 | −0.465849 | ||||||||
\(569\) | 189.835i | 0.333629i | 0.985988 | + | 0.166815i | \(0.0533482\pi\) | ||||
−0.985988 | + | 0.166815i | \(0.946652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −604.730 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(572\) | 538.104i | 0.940742i | ||||||||
\(573\) | 261.048i | 0.455582i | ||||||||
\(574\) | 4.97303 | 0.00866381 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 28.0619 | 0.0487186 | ||||||||
\(577\) | −1138.28 | −1.97276 | −0.986379 | − | 0.164488i | \(-0.947403\pi\) | ||||
−0.986379 | + | 0.164488i | \(0.947403\pi\) | |||||||
\(578\) | − | 629.795i | − | 1.08961i | ||||||
\(579\) | −352.949 | −0.609584 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.2411 | −0.0365596 | ||||||||
\(582\) | − | 15.4442i | − | 0.0265364i | ||||||
\(583\) | − | 938.522i | − | 1.60982i | ||||||
\(584\) | − | 12.6122i | − | 0.0215963i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 470.156 | 0.802314 | ||||||||
\(587\) | −103.008 | −0.175482 | −0.0877410 | − | 0.996143i | \(-0.527965\pi\) | ||||
−0.0877410 | + | 0.996143i | \(0.527965\pi\) | |||||||
\(588\) | − | 346.438i | − | 0.589180i | ||||||
\(589\) | −138.103 | + | 105.730i | −0.234471 | + | 0.179507i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1178.14i | 1.99346i | ||||||||
\(592\) | 29.5042i | 0.0498382i | ||||||||
\(593\) | 354.332 | 0.597525 | 0.298763 | − | 0.954327i | \(-0.403426\pi\) | ||||
0.298763 | + | 0.954327i | \(0.403426\pi\) | |||||||
\(594\) | −436.661 | −0.735119 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.8836 | 0.0518182 | ||||||||
\(597\) | − | 283.436i | − | 0.474768i | ||||||
\(598\) | −482.691 | −0.807176 | ||||||||
\(599\) | − | 1112.64i | − | 1.85750i | −0.370704 | − | 0.928751i | \(-0.620884\pi\) | ||
0.370704 | − | 0.928751i | \(-0.379116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8624i | 0.0746463i | 0.999303 | + | 0.0373231i | \(0.0118831\pi\) | ||||
−0.999303 | + | 0.0373231i | \(0.988117\pi\) | |||||||
\(602\) | 8.35028i | 0.0138709i | ||||||||
\(603\) | − | 352.370i | − | 0.584361i | ||||||
\(604\) | 370.312i | 0.613099i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −515.455 | −0.850585 | ||||||||
\(607\) | 740.250i | 1.21952i | 0.792585 | + | 0.609762i | \(0.208735\pi\) | ||||
−0.792585 | + | 0.609762i | \(0.791265\pi\) | |||||||
\(608\) | 85.3416 | − | 65.3361i | 0.140365 | − | 0.107461i | ||||
\(609\) | −2.82323 | −0.00463585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1450.86i | − | 2.37457i | ||||||
\(612\) | 190.109 | 0.310636 | ||||||||
\(613\) | −758.605 | −1.23753 | −0.618764 | − | 0.785577i | \(-0.712366\pi\) | ||||
−0.618764 | + | 0.785577i | \(0.712366\pi\) | |||||||
\(614\) | −663.685 | −1.08092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.58505i | 0.0106900i | ||||||||
\(617\) | −617.701 | −1.00114 | −0.500568 | − | 0.865697i | \(-0.666875\pi\) | ||||
−0.500568 | + | 0.865697i | \(0.666875\pi\) | |||||||
\(618\) | 633.272i | 1.02471i | ||||||||
\(619\) | −434.677 | −0.702224 | −0.351112 | − | 0.936333i | \(-0.614196\pi\) | ||||
−0.351112 | + | 0.936333i | \(0.614196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 391.694i | − | 0.630747i | ||||||
\(622\) | − | 70.7858i | − | 0.113803i | ||||||
\(623\) | − | 3.53385i | − | 0.00567232i | ||||||
\(624\) | −239.440 | −0.383719 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 303.343i | 0.484573i | ||||||||
\(627\) | 848.133 | − | 649.316i | 1.35268 | − | 1.03559i | ||||
\(628\) | 58.4387 | 0.0930552 | ||||||||
\(629\) | 199.881i | 0.317775i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −406.725 | −0.644571 | −0.322286 | − | 0.946642i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946642i | \(0.604451\pi\) | |||||||
\(632\) | 43.1382 | 0.0682567 | ||||||||
\(633\) | 256.832 | 0.405738 | ||||||||
\(634\) | −168.719 | −0.266118 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 417.614 | 0.656626 | ||||||||
\(637\) | 828.999i | 1.30141i | ||||||||
\(638\) | −122.528 | −0.192050 | ||||||||
\(639\) | − | 328.152i | − | 0.513540i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 994.339i | − | 1.55123i | −0.631206 | − | 0.775616i | \(-0.717440\pi\) | ||
0.631206 | − | 0.775616i | \(-0.282560\pi\) | |||||||
\(642\) | − | 110.489i | − | 0.172101i | ||||||
\(643\) | 847.680 | 1.31832 | 0.659160 | − | 0.752003i | \(-0.270912\pi\) | ||||
0.659160 | + | 0.752003i | \(0.270912\pi\) | |||||||
\(644\) | −5.90694 | −0.00917226 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 578.159 | − | 442.629i | 0.894983 | − | 0.685184i | ||||
\(647\) | 731.308 | 1.13031 | 0.565153 | − | 0.824986i | \(-0.308817\pi\) | ||||
0.565153 | + | 0.824986i | \(0.308817\pi\) | |||||||
\(648\) | − | 283.593i | − | 0.437644i | ||||||
\(649\) | − | 1374.28i | − | 2.11753i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.74169 | 0.00728370 | ||||||||
\(652\) | −188.301 | −0.288805 | ||||||||
\(653\) | −1111.60 | −1.70230 | −0.851150 | − | 0.524922i | \(-0.824094\pi\) | ||||
−0.851150 | + | 0.524922i | \(0.824094\pi\) | |||||||
\(654\) | − | 455.769i | − | 0.696894i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 96.0373i | 0.146398i | ||||||||
\(657\) | 15.6414 | 0.0238072 | ||||||||
\(658\) | − | 17.7549i | − | 0.0269832i | ||||||
\(659\) | − | 363.690i | − | 0.551881i | −0.961175 | − | 0.275941i | \(-0.911011\pi\) | ||
0.961175 | − | 0.275941i | \(-0.0889893\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1069.74i | 1.61836i | 0.587560 | + | 0.809180i | \(0.300089\pi\) | ||||
−0.587560 | + | 0.809180i | \(0.699911\pi\) | |||||||
\(662\) | 670.555 | 1.01292 | ||||||||
\(663\) | −1622.12 | −2.44664 | ||||||||
\(664\) | − | 410.200i | − | 0.617772i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −36.5903 | −0.0549404 | ||||||||
\(667\) | − | 109.910i | − | 0.164783i | ||||||
\(668\) | 112.652i | 0.168640i | ||||||||
\(669\) | −1145.14 | −1.71171 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −243.608 | −0.363052 | ||||||||
\(672\) | −2.93015 | −0.00436035 | ||||||||
\(673\) | 270.027i | 0.401228i | 0.979670 | + | 0.200614i | \(0.0642938\pi\) | ||||
−0.979670 | + | 0.200614i | \(0.935706\pi\) | |||||||
\(674\) | 335.726 | 0.498109 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 234.963 | 0.347578 | ||||||||
\(677\) | 826.165i | 1.22033i | 0.792274 | + | 0.610166i | \(0.208897\pi\) | ||||
−0.792274 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(678\) | − | 854.739i | − | 1.26068i | ||||||
\(679\) | 0.452259i | 0.000666066i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1533.37 | −2.25164 | ||||||||
\(682\) | 205.789 | 0.301743 | ||||||||
\(683\) | 865.671i | 1.26745i | 0.773557 | + | 0.633727i | \(0.218476\pi\) | ||||
−0.773557 | + | 0.633727i | \(0.781524\pi\) | |||||||
\(684\) | 81.0280 | + | 105.838i | 0.118462 | + | 0.154734i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.2942i | 0.0295834i | ||||||||
\(687\) | − | 732.060i | − | 1.06559i | ||||||
\(688\) | −161.258 | −0.234386 | ||||||||
\(689\) | −999.319 | −1.45039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2977 | 0.0409518 | 0.0204759 | − | 0.999790i | \(-0.493482\pi\) | ||||
0.0204759 | + | 0.999790i | \(0.493482\pi\) | |||||||
\(692\) | − | 90.8783i | − | 0.131327i | ||||||
\(693\) | −8.16660 | −0.0117844 | ||||||||
\(694\) | 866.083i | 1.24796i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 54.5212i | − | 0.0783350i | ||||||
\(697\) | 650.618i | 0.933455i | ||||||||
\(698\) | − | 885.149i | − | 1.26812i | ||||||
\(699\) | − | 1028.58i | − | 1.47150i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 134.912 | 0.192456 | 0.0962282 | − | 0.995359i | \(-0.469322\pi\) | ||||
0.0962282 | + | 0.995359i | \(0.469322\pi\) | |||||||
\(702\) | 464.947i | 0.662318i | ||||||||
\(703\) | −111.278 | + | 85.1927i | −0.158290 | + | 0.121184i | ||||
\(704\) | −127.168 | −0.180637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 308.695i | 0.437246i | ||||||||
\(707\) | 15.0943 | 0.0213497 | ||||||||
\(708\) | 611.512 | 0.863717 | ||||||||
\(709\) | −328.768 | −0.463707 | −0.231853 | − | 0.972751i | \(-0.574479\pi\) | ||||
−0.231853 | + | 0.972751i | \(0.574479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.4988i | 0.0752445i | ||||||||
\(712\) | 68.2445 | 0.0958490 | ||||||||
\(713\) | 184.597i | 0.258902i | ||||||||
\(714\) | −19.8507 | −0.0278022 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 294.366i | 0.411126i | ||||||||
\(717\) | 318.547i | 0.444277i | ||||||||
\(718\) | − | 447.220i | − | 0.622869i | ||||||
\(719\) | 132.152 | 0.183799 | 0.0918997 | − | 0.995768i | \(-0.470706\pi\) | ||||
0.0918997 | + | 0.995768i | \(0.470706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.5444i | − | 0.0257204i | ||||||
\(722\) | 492.844 | + | 133.218i | 0.682609 | + | 0.184513i | ||||
\(723\) | −302.809 | −0.418823 | ||||||||
\(724\) | − | 486.765i | − | 0.672328i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −658.621 | −0.907192 | ||||||||
\(727\) | 370.952 | 0.510250 | 0.255125 | − | 0.966908i | \(-0.417883\pi\) | ||||
0.255125 | + | 0.966908i | \(0.417883\pi\) | |||||||
\(728\) | 7.01163 | 0.00963136 | ||||||||
\(729\) | −266.557 | −0.365648 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1092.46 | −1.49448 | ||||||||
\(732\) | − | 108.398i | − | 0.148085i | ||||||
\(733\) | −778.543 | −1.06213 | −0.531066 | − | 0.847331i | \(-0.678208\pi\) | ||||
−0.531066 | + | 0.847331i | \(0.678208\pi\) | |||||||
\(734\) | − | 848.637i | − | 1.15618i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 114.073i | − | 0.154990i | ||||||
\(737\) | 1596.84i | 2.16667i | ||||||||
\(738\) | −119.103 | −0.161386 | ||||||||
\(739\) | 686.378 | 0.928793 | 0.464396 | − | 0.885627i | \(-0.346271\pi\) | ||||
0.464396 | + | 0.885627i | \(0.346271\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −691.378 | − | 903.074i | −0.933034 | − | 1.21872i | ||||
\(742\) | −12.2292 | −0.0164814 | ||||||||
\(743\) | 944.989i | 1.27186i | 0.771748 | + | 0.635928i | \(0.219383\pi\) | ||||
−0.771748 | + | 0.635928i | \(0.780617\pi\) | |||||||
\(744\) | 91.5698i | 0.123078i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 86.1358 | 0.115464 | ||||||||
\(747\) | 508.719 | 0.681016 | ||||||||
\(748\) | −861.519 | −1.15176 | ||||||||
\(749\) | 3.23548i | 0.00431974i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 372.272i | 0.495701i | 0.968798 | + | 0.247851i | \(0.0797243\pi\) | ||||
−0.968798 | + | 0.247851i | \(0.920276\pi\) | |||||||
\(752\) | 342.877 | 0.455953 | ||||||||
\(753\) | 1478.63i | 1.96365i | ||||||||
\(754\) | 130.465i | 0.173031i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.68980i | 0.00752618i | ||||||||
\(757\) | 65.8572 | 0.0869977 | 0.0434988 | − | 0.999053i | \(-0.486150\pi\) | ||||
0.0434988 | + | 0.999053i | \(0.486150\pi\) | |||||||
\(758\) | 230.386 | 0.303939 | ||||||||
\(759\) | − | 1133.66i | − | 1.49363i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1305.80 | −1.71590 | −0.857951 | − | 0.513732i | \(-0.828263\pi\) | ||||
−0.857951 | + | 0.513732i | \(0.828263\pi\) | |||||||
\(762\) | 320.547i | 0.420666i | ||||||||
\(763\) | 13.3465i | 0.0174921i | ||||||||
\(764\) | 147.626 | 0.193227 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 902.753 | 1.17853 | ||||||||
\(767\) | −1463.30 | −1.90782 | ||||||||
\(768\) | − | 56.5860i | − | 0.0736797i | ||||||
\(769\) | 320.091 | 0.416244 | 0.208122 | − | 0.978103i | \(-0.433265\pi\) | ||||
0.208122 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 286.563 | 0.371677 | ||||||||
\(772\) | 199.597i | 0.258545i | ||||||||
\(773\) | − | 892.160i | − | 1.15415i | −0.816690 | − | 0.577076i | \(-0.804194\pi\) | ||
0.816690 | − | 0.577076i | \(-0.195806\pi\) | |||||||
\(774\) | − | 199.987i | − | 0.258381i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.73385 | −0.0112550 | ||||||||
\(777\) | 3.82067 | 0.00491721 | ||||||||
\(778\) | − | 247.613i | − | 0.318269i | ||||||
\(779\) | −362.214 | + | 277.305i | −0.464974 | + | 0.355976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1487.09i | 1.90408i | ||||||||
\(782\) | − | 772.801i | − | 0.988237i | ||||||
\(783\) | −105.870 | −0.135210 | ||||||||
\(784\) | −195.914 | −0.249891 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 710.107 | 0.903444 | ||||||||
\(787\) | − | 1088.23i | − | 1.38276i | −0.722493 | − | 0.691378i | \(-0.757004\pi\) | ||
0.722493 | − | 0.691378i | \(-0.242996\pi\) | |||||||
\(788\) | 666.249 | 0.845494 | ||||||||
\(789\) | − | 995.465i | − | 1.26168i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.0297i | 0.0316431i | ||||||||
\(792\) | − | 157.710i | − | 0.199129i | ||||||
\(793\) | 259.388i | 0.327098i | ||||||||
\(794\) | 1025.36i | 1.29139i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −160.286 | −0.201365 | ||||||||
\(797\) | − | 1371.00i | − | 1.72020i | −0.510123 | − | 0.860102i | \(-0.670400\pi\) | ||
0.510123 | − | 0.860102i | \(-0.329600\pi\) | |||||||
\(798\) | −8.46074 | − | 11.0514i | −0.0106024 | − | 0.0138488i | ||||
\(799\) | 2322.87 | 2.90722 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.6349i | 0.105662i | ||||||||
\(802\) | 801.840 | 0.999801 | ||||||||
\(803\) | −70.8820 | −0.0882714 | ||||||||
\(804\) | −710.544 | −0.883762 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 219.120i | − | 0.271860i | ||||||
\(807\) | 1388.88 | 1.72104 | ||||||||
\(808\) | 291.495i | 0.360761i | ||||||||
\(809\) | −580.084 | −0.717038 | −0.358519 | − | 0.933522i | \(-0.616718\pi\) | ||||
−0.358519 | + | 0.933522i | \(0.616718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1339.70i | 1.65191i | 0.563738 | + | 0.825954i | \(0.309363\pi\) | ||||
−0.563738 | + | 0.825954i | \(0.690637\pi\) | |||||||
\(812\) | 1.59657i | 0.00196621i | ||||||||
\(813\) | − | 1541.48i | − | 1.89604i | ||||||
\(814\) | 165.816 | 0.203706 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 383.350i | − | 0.469792i | ||||||
\(817\) | −465.627 | − | 608.199i | −0.569923 | − | 0.744430i | ||||
\(818\) | −306.033 | −0.374124 | ||||||||
\(819\) | 8.69563i | 0.0106174i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1526.64 | 1.85949 | 0.929747 | − | 0.368199i | \(-0.120025\pi\) | ||||
0.929747 | + | 0.368199i | \(0.120025\pi\) | |||||||
\(822\) | −481.941 | −0.586302 | ||||||||
\(823\) | 238.601 | 0.289916 | 0.144958 | − | 0.989438i | \(-0.453695\pi\) | ||||
0.144958 | + | 0.989438i | \(0.453695\pi\) | |||||||
\(824\) | 358.122 | 0.434614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.9071 | −0.0216793 | ||||||||
\(827\) | − | 1190.01i | − | 1.43895i | −0.694521 | − | 0.719473i | \(-0.744383\pi\) | ||
0.694521 | − | 0.719473i | \(-0.255617\pi\) | |||||||
\(828\) | 141.470 | 0.170857 | ||||||||
\(829\) | 1208.18i | 1.45739i | 0.684838 | + | 0.728696i | \(0.259873\pi\) | ||||
−0.684838 | + | 0.728696i | \(0.740127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1085.49i | 1.30625i | ||||||||
\(832\) | 135.406i | 0.162748i | ||||||||
\(833\) | −1327.25 | −1.59334 | ||||||||
\(834\) | 913.150 | 1.09490 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −367.195 | − | 479.628i | −0.439228 | − | 0.573718i | ||||
\(837\) | 177.811 | 0.212439 | ||||||||
\(838\) | − | 685.771i | − | 0.818343i | ||||||
\(839\) | − | 360.467i | − | 0.429639i | −0.976654 | − | 0.214819i | \(-0.931084\pi\) | ||
0.976654 | − | 0.214819i | \(-0.0689163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 811.293 | 0.964676 | ||||||||
\(842\) | −584.444 | −0.694114 | ||||||||
\(843\) | 559.879 | 0.664151 | ||||||||
\(844\) | − | 145.241i | − | 0.172087i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 425.226i | 0.502632i | ||||||||
\(847\) | 19.2867 | 0.0227706 | ||||||||
\(848\) | − | 236.165i | − | 0.278497i | ||||||
\(849\) | 386.873i | 0.455681i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 148.741i | 0.174784i | ||||||||
\(852\) | −661.710 | −0.776655 | ||||||||
\(853\) | 625.741 | 0.733577 | 0.366788 | − | 0.930304i | \(-0.380457\pi\) | ||||
0.366788 | + | 0.930304i | \(0.380457\pi\) | |||||||
\(854\) | 3.17427i | 0.00371694i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −62.4825 | −0.0729935 | ||||||||
\(857\) | 1576.70i | 1.83979i | 0.392167 | + | 0.919894i | \(0.371726\pi\) | ||||
−0.392167 | + | 0.919894i | \(0.628274\pi\) | |||||||
\(858\) | 1345.68i | 1.56839i | ||||||||
\(859\) | 954.288 | 1.11093 | 0.555464 | − | 0.831540i | \(-0.312540\pi\) | ||||
0.555464 | + | 0.831540i | \(0.312540\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.4364 | 0.0144441 | ||||||||
\(862\) | 637.353 | 0.739389 | ||||||||
\(863\) | 363.759i | 0.421505i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) | ||||
−0.977539 | + | 0.210752i | \(0.932409\pi\) | |||||||
\(864\) | −109.879 | −0.127175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.53741 | 0.00408477 | ||||||||
\(867\) | − | 1574.98i | − | 1.81658i | ||||||
\(868\) | − | 2.68148i | − | 0.00308926i | ||||||
\(869\) | − | 242.441i | − | 0.278988i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1700.28 | 1.95210 | ||||||||
\(872\) | −257.742 | −0.295576 | ||||||||
\(873\) | − | 10.8315i | − | 0.0124072i | ||||||
\(874\) | 430.237 | − | 329.382i | 0.492261 | − | 0.376867i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 31.5404i | − | 0.0360050i | ||||||
\(877\) | 1186.98i | 1.35346i | 0.736231 | + | 0.676730i | \(0.236604\pi\) | ||||
−0.736231 | + | 0.676730i | \(0.763396\pi\) | |||||||
\(878\) | 694.594 | 0.791110 | ||||||||
\(879\) | 1175.75 | 1.33760 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 316.952 | 0.359764 | 0.179882 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179882 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(882\) | − | 242.967i | − | 0.275473i | ||||||
\(883\) | 846.927 | 0.959148 | 0.479574 | − | 0.877502i | \(-0.340791\pi\) | ||||
0.479574 | + | 0.877502i | \(0.340791\pi\) | |||||||
\(884\) | 917.328i | 1.03770i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 337.849i | 0.381319i | ||||||||
\(887\) | 443.640i | 0.500157i | 0.968226 | + | 0.250079i | \(0.0804565\pi\) | ||||
−0.968226 | + | 0.250079i | \(0.919544\pi\) | |||||||
\(888\) | 73.7834i | 0.0830894i | ||||||||
\(889\) | − | 9.38671i | − | 0.0105587i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1593.82 | −1.78880 | ||||||||
\(892\) | 647.586i | 0.725993i | ||||||||
\(893\) | 990.048 | + | 1293.20i | 1.10868 | + | 1.44815i | ||||
\(894\) | 77.2329 | 0.0863903 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.65703i | 0.00184937i | ||||||||
\(897\) | −1207.10 | −1.34571 | ||||||||
\(898\) | −640.262 | −0.712986 | ||||||||
\(899\) | 49.8941 | 0.0554995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1599.94i | − | 1.77573i | ||||||
\(902\) | 539.738 | 0.598379 | ||||||||
\(903\) | 20.8822i | 0.0231253i | ||||||||
\(904\) | −483.364 | −0.534694 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 926.066i | 1.02215i | ||||||||
\(907\) | 5.46337i | 0.00602356i | 0.999995 | + | 0.00301178i | \(0.000958681\pi\) | ||||
−0.999995 | + | 0.00301178i | \(0.999041\pi\) | |||||||
\(908\) | 867.137i | 0.954996i | ||||||||
\(909\) | −361.504 | −0.397694 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1403.59i | 1.54071i | 0.637614 | + | 0.770356i | \(0.279922\pi\) | ||||
−0.637614 | + | 0.770356i | \(0.720078\pi\) | |||||||
\(912\) | 213.420 | − | 163.391i | 0.234013 | − | 0.179157i | ||||
\(913\) | −2305.36 | −2.52504 | ||||||||
\(914\) | − | 986.773i | − | 1.07962i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −413.988 | −0.451952 | ||||||||
\(917\) | −20.7943 | −0.0226765 | ||||||||
\(918\) | −744.393 | −0.810885 | ||||||||
\(919\) | −357.449 | −0.388954 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1659.73 | −1.80209 | ||||||||
\(922\) | − | 594.453i | − | 0.644743i | ||||||
\(923\) | 1583.42 | 1.71552 | ||||||||
\(924\) | 16.4677i | 0.0178222i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 679.643i | 0.733956i | ||||||||
\(927\) | 444.133i | 0.479108i | ||||||||
\(928\) | −30.8323 | −0.0332245 | ||||||||
\(929\) | −261.924 | −0.281942 | −0.140971 | − | 0.990014i | \(-0.545022\pi\) | ||||
−0.140971 | + | 0.990014i | \(0.545022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −565.697 | − | 738.911i | −0.607623 | − | 0.793674i | ||||
\(932\) | −581.672 | −0.624112 | ||||||||
\(933\) | − | 177.019i | − | 0.189731i | ||||||
\(934\) | 790.948i | 0.846839i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −167.927 | −0.179409 | ||||||||
\(937\) | 1286.88 | 1.37340 | 0.686700 | − | 0.726941i | \(-0.259059\pi\) | ||||
0.686700 | + | 0.726941i | \(0.259059\pi\) | |||||||
\(938\) | 20.8072 | 0.0221825 | ||||||||
\(939\) | 758.592i | 0.807872i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1118.46i | − | 1.18858i | −0.804249 | − | 0.594292i | \(-0.797432\pi\) | ||
0.804249 | − | 0.594292i | \(-0.202568\pi\) | |||||||
\(942\) | 146.142 | 0.155140 | ||||||||
\(943\) | 484.157i | 0.513422i | ||||||||
\(944\) | − | 345.816i | − | 0.366331i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 906.282i | 0.958015i | ||||||||
\(947\) | −1040.70 | −1.09895 | −0.549473 | − | 0.835512i | \(-0.685171\pi\) | ||||
−0.549473 | + | 0.835512i | \(0.685171\pi\) | |||||||
\(948\) | 107.879 | 0.113796 | ||||||||
\(949\) | 75.4737i | 0.0795297i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −421.928 | −0.443667 | ||||||||
\(952\) | 11.2258i | 0.0117918i | ||||||||
\(953\) | − | 158.536i | − | 0.166354i | −0.996535 | − | 0.0831771i | \(-0.973493\pi\) | ||
0.996535 | − | 0.0831771i | \(-0.0265067\pi\) | |||||||
\(954\) | 292.886 | 0.307008 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 180.142 | 0.188433 | ||||||||
\(957\) | −306.414 | −0.320182 | ||||||||
\(958\) | − | 348.856i | − | 0.364150i | ||||||
\(959\) | 14.1129 | 0.0147162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 877.202 | 0.912801 | ||||||||
\(962\) | − | 176.558i | − | 0.183532i | ||||||
\(963\) | − | 77.4890i | − | 0.0804663i | ||||||
\(964\) | 171.242i | 0.177637i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.7719 | −0.0152918 | ||||||||
\(967\) | 462.170 | 0.477942 | 0.238971 | − | 0.971027i | \(-0.423190\pi\) | ||||
0.238971 | + | 0.971027i | \(0.423190\pi\) | |||||||
\(968\) | 372.457i | 0.384770i | ||||||||
\(969\) | 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 | \(-0.281336\pi\) | |||||||
\(972\) | − | 359.569i | − | 0.369927i | ||||||
\(973\) | −26.7401 | −0.0274822 | ||||||||
\(974\) | −592.279 | −0.608089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.3003 | −0.0628077 | ||||||||
\(977\) | − | 1097.99i | − | 1.12384i | −0.827191 | − | 0.561921i | \(-0.810063\pi\) | ||
0.827191 | − | 0.561921i | \(-0.189937\pi\) | |||||||
\(978\) | −470.898 | −0.481491 | ||||||||
\(979\) | − | 383.540i | − | 0.391767i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 319.645i | − | 0.325835i | ||||||
\(982\) | 727.835i | 0.741176i | ||||||||
\(983\) | − | 938.538i | − | 0.954769i | −0.878694 | − | 0.477385i | \(-0.841585\pi\) | ||
0.878694 | − | 0.477385i | \(-0.158415\pi\) | |||||||
\(984\) | 240.167i | 0.244073i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −208.878 | −0.211844 | ||||||||
\(987\) | − | 44.4011i | − | 0.0449859i | ||||||
\(988\) | −510.698 | + | 390.982i | −0.516901 | + | 0.395730i | ||||
\(989\) | −812.955 | −0.821997 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 540.016i | − | 0.544920i | −0.962167 | − | 0.272460i | \(-0.912163\pi\) | ||
0.962167 | − | 0.272460i | \(-0.0878372\pi\) | |||||||
\(992\) | 51.7837 | 0.0522013 | ||||||||
\(993\) | 1676.91 | 1.68873 | ||||||||
\(994\) | 19.3771 | 0.0194941 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1025.82i | − | 1.02994i | ||||||
\(997\) | 406.644 | 0.407868 | 0.203934 | − | 0.978985i | \(-0.434627\pi\) | ||||
0.203934 | + | 0.978985i | \(0.434627\pi\) | |||||||
\(998\) | 215.964i | 0.216396i | ||||||||
\(999\) | 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.c.b.151.2 | ✓ | 12 | |
5.2 | odd | 4 | 950.3.d.b.949.17 | 24 | |||
5.3 | odd | 4 | 950.3.d.b.949.8 | 24 | |||
5.4 | even | 2 | 950.3.c.c.151.11 | yes | 12 | ||
19.18 | odd | 2 | inner | 950.3.c.b.151.11 | yes | 12 | |
95.18 | even | 4 | 950.3.d.b.949.20 | 24 | |||
95.37 | even | 4 | 950.3.d.b.949.5 | 24 | |||
95.94 | odd | 2 | 950.3.c.c.151.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.3.c.b.151.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
950.3.c.b.151.11 | yes | 12 | 19.18 | odd | 2 | inner | |
950.3.c.c.151.2 | yes | 12 | 95.94 | odd | 2 | ||
950.3.c.c.151.11 | yes | 12 | 5.4 | even | 2 | ||
950.3.d.b.949.5 | 24 | 95.37 | even | 4 | |||
950.3.d.b.949.8 | 24 | 5.3 | odd | 4 | |||
950.3.d.b.949.17 | 24 | 5.2 | odd | 4 | |||
950.3.d.b.949.20 | 24 | 95.18 | even | 4 |