Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,4,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.18307067021\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 8x^{6} + 58x^{5} + 197x^{4} + 26x^{3} + 2x^{2} + 28x + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.1 | ||
Root | \(-0.759936 + 0.759936i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.4.b.a.36.8 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.39603i | − | 1.90779i | −0.300146 | − | 0.953893i | \(-0.597035\pi\) | ||
0.300146 | − | 0.953893i | \(-0.402965\pi\) | |||||||
\(3\) | 2.81527 | 0.541798 | 0.270899 | − | 0.962608i | \(-0.412679\pi\) | ||||
0.270899 | + | 0.962608i | \(0.412679\pi\) | |||||||
\(4\) | −21.1172 | −2.63965 | ||||||||
\(5\) | − | 6.77552i | − | 0.606021i | −0.952987 | − | 0.303010i | \(-0.902008\pi\) | ||
0.952987 | − | 0.303010i | \(-0.0979917\pi\) | |||||||
\(6\) | − | 15.1913i | − | 1.03363i | ||||||
\(7\) | 16.2590 | 0.877904 | 0.438952 | − | 0.898510i | \(-0.355350\pi\) | ||||
0.438952 | + | 0.898510i | \(0.355350\pi\) | |||||||
\(8\) | 70.7808i | 3.12810i | ||||||||
\(9\) | −19.0743 | −0.706455 | ||||||||
\(10\) | −36.5609 | −1.15616 | ||||||||
\(11\) | 56.6781 | 1.55355 | 0.776777 | − | 0.629775i | \(-0.216853\pi\) | ||||
0.776777 | + | 0.629775i | \(0.216853\pi\) | |||||||
\(12\) | −59.4505 | −1.43016 | ||||||||
\(13\) | − | 41.6559i | − | 0.888712i | −0.895850 | − | 0.444356i | \(-0.853433\pi\) | ||
0.895850 | − | 0.444356i | \(-0.146567\pi\) | |||||||
\(14\) | − | 87.7342i | − | 1.67485i | ||||||
\(15\) | − | 19.0749i | − | 0.328341i | ||||||
\(16\) | 212.998 | 3.32810 | ||||||||
\(17\) | 68.5374i | 0.977810i | 0.872337 | + | 0.488905i | \(0.162604\pi\) | ||||
−0.872337 | + | 0.488905i | \(0.837396\pi\) | |||||||
\(18\) | 102.925i | 1.34777i | ||||||||
\(19\) | − | 84.5816i | − | 1.02128i | −0.859794 | − | 0.510641i | \(-0.829408\pi\) | ||
0.859794 | − | 0.510641i | \(-0.170592\pi\) | |||||||
\(20\) | 143.080i | 1.59968i | ||||||||
\(21\) | 45.7734 | 0.475647 | ||||||||
\(22\) | − | 305.837i | − | 2.96385i | ||||||
\(23\) | 70.4909i | 0.639059i | 0.947576 | + | 0.319530i | \(0.103525\pi\) | ||||
−0.947576 | + | 0.319530i | \(0.896475\pi\) | |||||||
\(24\) | 199.267i | 1.69480i | ||||||||
\(25\) | 79.0923 | 0.632739 | ||||||||
\(26\) | −224.776 | −1.69547 | ||||||||
\(27\) | −129.711 | −0.924554 | ||||||||
\(28\) | −343.345 | −2.31736 | ||||||||
\(29\) | 111.643i | 0.714885i | 0.933935 | + | 0.357442i | \(0.116351\pi\) | ||||
−0.933935 | + | 0.357442i | \(0.883649\pi\) | |||||||
\(30\) | −102.929 | −0.626404 | ||||||||
\(31\) | 322.350i | 1.86761i | 0.357786 | + | 0.933804i | \(0.383532\pi\) | ||||
−0.357786 | + | 0.933804i | \(0.616468\pi\) | |||||||
\(32\) | − | 583.099i | − | 3.22120i | ||||||
\(33\) | 159.564 | 0.841713 | ||||||||
\(34\) | 369.830 | 1.86545 | ||||||||
\(35\) | − | 110.163i | − | 0.532028i | ||||||
\(36\) | 402.795 | 1.86479 | ||||||||
\(37\) | −206.337 | + | 89.8770i | −0.916802 | + | 0.399343i | ||||
\(38\) | −456.405 | −1.94839 | ||||||||
\(39\) | − | 117.272i | − | 0.481502i | ||||||
\(40\) | 479.577 | 1.89569 | ||||||||
\(41\) | 131.601 | 0.501282 | 0.250641 | − | 0.968080i | \(-0.419359\pi\) | ||||
0.250641 | + | 0.968080i | \(0.419359\pi\) | |||||||
\(42\) | − | 246.995i | − | 0.907433i | ||||||
\(43\) | − | 112.203i | − | 0.397924i | −0.980007 | − | 0.198962i | \(-0.936243\pi\) | ||
0.980007 | − | 0.198962i | \(-0.0637571\pi\) | |||||||
\(44\) | −1196.88 | −4.10084 | ||||||||
\(45\) | 129.238i | 0.428126i | ||||||||
\(46\) | 380.371 | 1.21919 | ||||||||
\(47\) | −98.6542 | −0.306174 | −0.153087 | − | 0.988213i | \(-0.548922\pi\) | ||||
−0.153087 | + | 0.988213i | \(0.548922\pi\) | |||||||
\(48\) | 599.646 | 1.80316 | ||||||||
\(49\) | −78.6444 | −0.229284 | ||||||||
\(50\) | − | 426.785i | − | 1.20713i | ||||||
\(51\) | 192.951i | 0.529775i | ||||||||
\(52\) | 879.655i | 2.34589i | ||||||||
\(53\) | 215.067 | 0.557390 | 0.278695 | − | 0.960380i | \(-0.410098\pi\) | ||||
0.278695 | + | 0.960380i | \(0.410098\pi\) | |||||||
\(54\) | 699.927i | 1.76385i | ||||||||
\(55\) | − | 384.024i | − | 0.941487i | ||||||
\(56\) | 1150.83i | 2.74617i | ||||||||
\(57\) | − | 238.120i | − | 0.553328i | ||||||
\(58\) | 602.432 | 1.36385 | ||||||||
\(59\) | − | 40.1133i | − | 0.0885136i | −0.999020 | − | 0.0442568i | \(-0.985908\pi\) | ||
0.999020 | − | 0.0442568i | \(-0.0140920\pi\) | |||||||
\(60\) | 402.808i | 0.866705i | ||||||||
\(61\) | − | 720.884i | − | 1.51311i | −0.653930 | − | 0.756555i | \(-0.726881\pi\) | ||
0.653930 | − | 0.756555i | \(-0.273119\pi\) | |||||||
\(62\) | 1739.41 | 3.56300 | ||||||||
\(63\) | −310.129 | −0.620200 | ||||||||
\(64\) | −1442.44 | −2.81726 | ||||||||
\(65\) | −282.240 | −0.538578 | ||||||||
\(66\) | − | 861.013i | − | 1.60581i | ||||||
\(67\) | −476.142 | −0.868209 | −0.434105 | − | 0.900862i | \(-0.642935\pi\) | ||||
−0.434105 | + | 0.900862i | \(0.642935\pi\) | |||||||
\(68\) | − | 1447.32i | − | 2.58107i | ||||||
\(69\) | 198.450i | 0.346241i | ||||||||
\(70\) | −594.445 | −1.01500 | ||||||||
\(71\) | −664.816 | −1.11126 | −0.555628 | − | 0.831431i | \(-0.687522\pi\) | ||||
−0.555628 | + | 0.831431i | \(0.687522\pi\) | |||||||
\(72\) | − | 1350.09i | − | 2.20986i | ||||||
\(73\) | 281.792 | 0.451798 | 0.225899 | − | 0.974151i | \(-0.427468\pi\) | ||||
0.225899 | + | 0.974151i | \(0.427468\pi\) | |||||||
\(74\) | 484.979 | + | 1113.40i | 0.761861 | + | 1.74906i | ||||
\(75\) | 222.666 | 0.342817 | ||||||||
\(76\) | 1786.13i | 2.69582i | ||||||||
\(77\) | 921.531 | 1.36387 | ||||||||
\(78\) | −632.805 | −0.918604 | ||||||||
\(79\) | − | 706.968i | − | 1.00684i | −0.864043 | − | 0.503419i | \(-0.832075\pi\) | ||
0.864043 | − | 0.503419i | \(-0.167925\pi\) | |||||||
\(80\) | − | 1443.17i | − | 2.01690i | ||||||
\(81\) | 149.834 | 0.205533 | ||||||||
\(82\) | − | 710.121i | − | 0.956339i | ||||||
\(83\) | −370.053 | −0.489381 | −0.244690 | − | 0.969601i | \(-0.578686\pi\) | ||||
−0.244690 | + | 0.969601i | \(0.578686\pi\) | |||||||
\(84\) | −966.607 | −1.25554 | ||||||||
\(85\) | 464.377 | 0.592573 | ||||||||
\(86\) | −605.449 | −0.759154 | ||||||||
\(87\) | 314.306i | 0.387323i | ||||||||
\(88\) | 4011.72i | 4.85967i | ||||||||
\(89\) | 818.069i | 0.974327i | 0.873311 | + | 0.487164i | \(0.161968\pi\) | ||||
−0.873311 | + | 0.487164i | \(0.838032\pi\) | |||||||
\(90\) | 697.374 | 0.816774 | ||||||||
\(91\) | − | 677.283i | − | 0.780204i | ||||||
\(92\) | − | 1488.57i | − | 1.68689i | ||||||
\(93\) | 907.502i | 1.01187i | ||||||||
\(94\) | 532.341i | 0.584115i | ||||||||
\(95\) | −573.084 | −0.618918 | ||||||||
\(96\) | − | 1641.58i | − | 1.74524i | ||||||
\(97\) | 63.4075i | 0.0663717i | 0.999449 | + | 0.0331859i | \(0.0105653\pi\) | ||||
−0.999449 | + | 0.0331859i | \(0.989435\pi\) | |||||||
\(98\) | 424.368i | 0.437425i | ||||||||
\(99\) | −1081.09 | −1.09752 | ||||||||
\(100\) | −1670.21 | −1.67021 | ||||||||
\(101\) | −199.047 | −0.196098 | −0.0980492 | − | 0.995182i | \(-0.531260\pi\) | ||||
−0.0980492 | + | 0.995182i | \(0.531260\pi\) | |||||||
\(102\) | 1041.17 | 1.01070 | ||||||||
\(103\) | − | 597.256i | − | 0.571353i | −0.958326 | − | 0.285677i | \(-0.907782\pi\) | ||
0.958326 | − | 0.285677i | \(-0.0922183\pi\) | |||||||
\(104\) | 2948.44 | 2.77998 | ||||||||
\(105\) | − | 310.139i | − | 0.288252i | ||||||
\(106\) | − | 1160.51i | − | 1.06338i | ||||||
\(107\) | 973.289 | 0.879359 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(108\) | 2739.14 | 2.44050 | ||||||||
\(109\) | 1023.51i | 0.899397i | 0.893181 | + | 0.449698i | \(0.148468\pi\) | ||||
−0.893181 | + | 0.449698i | \(0.851532\pi\) | |||||||
\(110\) | −2072.21 | −1.79616 | ||||||||
\(111\) | −580.895 | + | 253.027i | −0.496721 | + | 0.216363i | ||||
\(112\) | 3463.14 | 2.92175 | ||||||||
\(113\) | 1428.78i | 1.18945i | 0.803929 | + | 0.594726i | \(0.202739\pi\) | ||||
−0.803929 | + | 0.594726i | \(0.797261\pi\) | |||||||
\(114\) | −1284.90 | −1.05563 | ||||||||
\(115\) | 477.612 | 0.387283 | ||||||||
\(116\) | − | 2357.60i | − | 1.88705i | ||||||
\(117\) | 794.556i | 0.627835i | ||||||||
\(118\) | −216.452 | −0.168865 | ||||||||
\(119\) | 1114.35i | 0.858424i | ||||||||
\(120\) | 1350.14 | 1.02708 | ||||||||
\(121\) | 1881.41 | 1.41353 | ||||||||
\(122\) | −3889.91 | −2.88669 | ||||||||
\(123\) | 370.491 | 0.271594 | ||||||||
\(124\) | − | 6807.13i | − | 4.92983i | ||||||
\(125\) | − | 1382.83i | − | 0.989474i | ||||||
\(126\) | 1673.47i | 1.18321i | ||||||||
\(127\) | −1310.38 | −0.915570 | −0.457785 | − | 0.889063i | \(-0.651357\pi\) | ||||
−0.457785 | + | 0.889063i | \(0.651357\pi\) | |||||||
\(128\) | 3118.65i | 2.15354i | ||||||||
\(129\) | − | 315.880i | − | 0.215595i | ||||||
\(130\) | 1522.98i | 1.02749i | ||||||||
\(131\) | 961.110i | 0.641012i | 0.947247 | + | 0.320506i | \(0.103853\pi\) | ||||
−0.947247 | + | 0.320506i | \(0.896147\pi\) | |||||||
\(132\) | −3369.54 | −2.22183 | ||||||||
\(133\) | − | 1375.21i | − | 0.896587i | ||||||
\(134\) | 2569.28i | 1.65636i | ||||||||
\(135\) | 878.862i | 0.560299i | ||||||||
\(136\) | −4851.14 | −3.05869 | ||||||||
\(137\) | 1310.93 | 0.817521 | 0.408761 | − | 0.912642i | \(-0.365961\pi\) | ||||
0.408761 | + | 0.912642i | \(0.365961\pi\) | |||||||
\(138\) | 1070.85 | 0.660554 | ||||||||
\(139\) | 1537.86 | 0.938416 | 0.469208 | − | 0.883088i | \(-0.344540\pi\) | ||||
0.469208 | + | 0.883088i | \(0.344540\pi\) | |||||||
\(140\) | 2326.34i | 1.40437i | ||||||||
\(141\) | −277.738 | −0.165885 | ||||||||
\(142\) | 3587.37i | 2.12004i | ||||||||
\(143\) | − | 2360.98i | − | 1.38066i | ||||||
\(144\) | −4062.79 | −2.35115 | ||||||||
\(145\) | 756.442 | 0.433235 | ||||||||
\(146\) | − | 1520.56i | − | 0.861935i | ||||||
\(147\) | −221.405 | −0.124226 | ||||||||
\(148\) | 4357.27 | − | 1897.95i | 2.42003 | − | 1.05412i | ||||
\(149\) | 30.2413 | 0.0166273 | 0.00831363 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831363 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(150\) | − | 1201.51i | − | 0.654021i | ||||||
\(151\) | −1908.44 | −1.02852 | −0.514262 | − | 0.857633i | \(-0.671934\pi\) | ||||
−0.514262 | + | 0.857633i | \(0.671934\pi\) | |||||||
\(152\) | 5986.75 | 3.19467 | ||||||||
\(153\) | − | 1307.30i | − | 0.690779i | ||||||
\(154\) | − | 4972.61i | − | 2.60198i | ||||||
\(155\) | 2184.09 | 1.13181 | ||||||||
\(156\) | 2476.46i | 1.27100i | ||||||||
\(157\) | −1280.88 | −0.651116 | −0.325558 | − | 0.945522i | \(-0.605552\pi\) | ||||
−0.325558 | + | 0.945522i | \(0.605552\pi\) | |||||||
\(158\) | −3814.83 | −1.92083 | ||||||||
\(159\) | 605.469 | 0.301993 | ||||||||
\(160\) | −3950.80 | −1.95211 | ||||||||
\(161\) | 1146.11i | 0.561033i | ||||||||
\(162\) | − | 808.509i | − | 0.392114i | ||||||
\(163\) | − | 3921.25i | − | 1.88427i | −0.335234 | − | 0.942135i | \(-0.608815\pi\) | ||
0.335234 | − | 0.942135i | \(-0.391185\pi\) | |||||||
\(164\) | −2779.04 | −1.32321 | ||||||||
\(165\) | − | 1081.13i | − | 0.510096i | ||||||
\(166\) | 1996.82i | 0.933634i | ||||||||
\(167\) | − | 402.648i | − | 0.186574i | −0.995639 | − | 0.0932870i | \(-0.970263\pi\) | ||
0.995639 | − | 0.0932870i | \(-0.0297374\pi\) | |||||||
\(168\) | 3239.88i | 1.48787i | ||||||||
\(169\) | 461.789 | 0.210191 | ||||||||
\(170\) | − | 2505.79i | − | 1.13050i | ||||||
\(171\) | 1613.33i | 0.721489i | ||||||||
\(172\) | 2369.40i | 1.05038i | ||||||||
\(173\) | 975.927 | 0.428892 | 0.214446 | − | 0.976736i | \(-0.431205\pi\) | ||||
0.214446 | + | 0.976736i | \(0.431205\pi\) | |||||||
\(174\) | 1696.01 | 0.738930 | ||||||||
\(175\) | 1285.96 | 0.555484 | ||||||||
\(176\) | 12072.3 | 5.17038 | ||||||||
\(177\) | − | 112.929i | − | 0.0479565i | ||||||
\(178\) | 4414.33 | 1.85881 | ||||||||
\(179\) | 1963.02i | 0.819682i | 0.912157 | + | 0.409841i | \(0.134416\pi\) | ||||
−0.912157 | + | 0.409841i | \(0.865584\pi\) | |||||||
\(180\) | − | 2729.15i | − | 1.13010i | ||||||
\(181\) | −3578.38 | −1.46950 | −0.734749 | − | 0.678339i | \(-0.762700\pi\) | ||||
−0.734749 | + | 0.678339i | \(0.762700\pi\) | |||||||
\(182\) | −3654.64 | −1.48846 | ||||||||
\(183\) | − | 2029.48i | − | 0.819800i | ||||||
\(184\) | −4989.40 | −1.99904 | ||||||||
\(185\) | 608.963 | + | 1398.04i | 0.242010 | + | 0.555601i | ||||
\(186\) | 4896.91 | 1.93042 | ||||||||
\(187\) | 3884.57i | 1.51908i | ||||||||
\(188\) | 2083.30 | 0.808193 | ||||||||
\(189\) | −2108.98 | −0.811670 | ||||||||
\(190\) | 3092.38i | 1.18076i | ||||||||
\(191\) | 3061.45i | 1.15978i | 0.814694 | + | 0.579892i | \(0.196905\pi\) | ||||
−0.814694 | + | 0.579892i | \(0.803095\pi\) | |||||||
\(192\) | −4060.85 | −1.52639 | ||||||||
\(193\) | − | 1963.06i | − | 0.732144i | −0.930586 | − | 0.366072i | \(-0.880702\pi\) | ||
0.930586 | − | 0.366072i | \(-0.119298\pi\) | |||||||
\(194\) | 342.149 | 0.126623 | ||||||||
\(195\) | −794.581 | −0.291801 | ||||||||
\(196\) | 1660.75 | 0.605229 | ||||||||
\(197\) | −1697.56 | −0.613940 | −0.306970 | − | 0.951719i | \(-0.599315\pi\) | ||||
−0.306970 | + | 0.951719i | \(0.599315\pi\) | |||||||
\(198\) | 5833.62i | 2.09383i | ||||||||
\(199\) | − | 1024.90i | − | 0.365092i | −0.983197 | − | 0.182546i | \(-0.941566\pi\) | ||
0.983197 | − | 0.182546i | \(-0.0584338\pi\) | |||||||
\(200\) | 5598.22i | 1.97927i | ||||||||
\(201\) | −1340.47 | −0.470394 | ||||||||
\(202\) | 1074.07i | 0.374114i | ||||||||
\(203\) | 1815.21i | 0.627601i | ||||||||
\(204\) | − | 4074.58i | − | 1.39842i | ||||||
\(205\) | − | 891.663i | − | 0.303787i | ||||||
\(206\) | −3222.81 | −1.09002 | ||||||||
\(207\) | − | 1344.56i | − | 0.451467i | ||||||
\(208\) | − | 8872.62i | − | 2.95772i | ||||||
\(209\) | − | 4793.93i | − | 1.58662i | ||||||
\(210\) | −1673.52 | −0.549923 | ||||||||
\(211\) | 1652.01 | 0.539000 | 0.269500 | − | 0.963000i | \(-0.413142\pi\) | ||||
0.269500 | + | 0.963000i | \(0.413142\pi\) | |||||||
\(212\) | −4541.60 | −1.47131 | ||||||||
\(213\) | −1871.63 | −0.602076 | ||||||||
\(214\) | − | 5251.90i | − | 1.67763i | ||||||
\(215\) | −760.231 | −0.241150 | ||||||||
\(216\) | − | 9181.07i | − | 2.89210i | ||||||
\(217\) | 5241.10i | 1.63958i | ||||||||
\(218\) | 5522.88 | 1.71586 | ||||||||
\(219\) | 793.320 | 0.244783 | ||||||||
\(220\) | 8109.51i | 2.48519i | ||||||||
\(221\) | 2854.99 | 0.868991 | ||||||||
\(222\) | 1365.35 | + | 3134.53i | 0.412775 | + | 0.947638i | ||||
\(223\) | −1857.71 | −0.557855 | −0.278928 | − | 0.960312i | \(-0.589979\pi\) | ||||
−0.278928 | + | 0.960312i | \(0.589979\pi\) | |||||||
\(224\) | − | 9480.62i | − | 2.82790i | ||||||
\(225\) | −1508.63 | −0.447001 | ||||||||
\(226\) | 7709.73 | 2.26922 | ||||||||
\(227\) | 564.595i | 0.165081i | 0.996588 | + | 0.0825407i | \(0.0263034\pi\) | ||||
−0.996588 | + | 0.0825407i | \(0.973697\pi\) | |||||||
\(228\) | 5028.42i | 1.46059i | ||||||||
\(229\) | −2685.42 | −0.774922 | −0.387461 | − | 0.921886i | \(-0.626648\pi\) | ||||
−0.387461 | + | 0.921886i | \(0.626648\pi\) | |||||||
\(230\) | − | 2577.21i | − | 0.738854i | ||||||
\(231\) | 2594.35 | 0.738943 | ||||||||
\(232\) | −7902.21 | −2.23623 | ||||||||
\(233\) | −3226.02 | −0.907055 | −0.453527 | − | 0.891242i | \(-0.649835\pi\) | ||||
−0.453527 | + | 0.891242i | \(0.649835\pi\) | |||||||
\(234\) | 4287.45 | 1.19778 | ||||||||
\(235\) | 668.434i | 0.185548i | ||||||||
\(236\) | 847.079i | 0.233645i | ||||||||
\(237\) | − | 1990.30i | − | 0.545503i | ||||||
\(238\) | 6013.08 | 1.63769 | ||||||||
\(239\) | − | 2063.21i | − | 0.558400i | −0.960233 | − | 0.279200i | \(-0.909931\pi\) | ||
0.960233 | − | 0.279200i | \(-0.0900693\pi\) | |||||||
\(240\) | − | 4062.92i | − | 1.09275i | ||||||
\(241\) | 5678.71i | 1.51783i | 0.651187 | + | 0.758917i | \(0.274271\pi\) | ||||
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(242\) | − | 10152.2i | − | 2.69672i | ||||||
\(243\) | 3924.03 | 1.03591 | ||||||||
\(244\) | 15223.0i | 3.99408i | ||||||||
\(245\) | 532.856i | 0.138951i | ||||||||
\(246\) | − | 1999.18i | − | 0.518143i | ||||||
\(247\) | −3523.32 | −0.907625 | ||||||||
\(248\) | −22816.2 | −5.84206 | ||||||||
\(249\) | −1041.80 | −0.265146 | ||||||||
\(250\) | −7461.81 | −1.88770 | ||||||||
\(251\) | − | 1378.62i | − | 0.346684i | −0.984862 | − | 0.173342i | \(-0.944543\pi\) | ||
0.984862 | − | 0.173342i | \(-0.0554566\pi\) | |||||||
\(252\) | 6549.06 | 1.63711 | ||||||||
\(253\) | 3995.29i | 0.992813i | ||||||||
\(254\) | 7070.86i | 1.74671i | ||||||||
\(255\) | 1307.34 | 0.321055 | ||||||||
\(256\) | 5288.85 | 1.29122 | ||||||||
\(257\) | − | 7615.70i | − | 1.84846i | −0.381836 | − | 0.924230i | \(-0.624708\pi\) | ||
0.381836 | − | 0.924230i | \(-0.375292\pi\) | |||||||
\(258\) | −1704.50 | −0.411308 | ||||||||
\(259\) | −3354.84 | + | 1461.31i | −0.804864 | + | 0.350585i | ||||
\(260\) | 5960.12 | 1.42166 | ||||||||
\(261\) | − | 2129.52i | − | 0.505034i | ||||||
\(262\) | 5186.18 | 1.22291 | ||||||||
\(263\) | −3536.77 | −0.829226 | −0.414613 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414613 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(264\) | 11294.1i | 2.63296i | ||||||||
\(265\) | − | 1457.19i | − | 0.337790i | ||||||
\(266\) | −7420.70 | −1.71050 | ||||||||
\(267\) | 2303.08i | 0.527889i | ||||||||
\(268\) | 10054.8 | 2.29177 | ||||||||
\(269\) | 6106.13 | 1.38400 | 0.692002 | − | 0.721896i | \(-0.256729\pi\) | ||||
0.692002 | + | 0.721896i | \(0.256729\pi\) | |||||||
\(270\) | 4742.37 | 1.06893 | ||||||||
\(271\) | 3088.62 | 0.692325 | 0.346162 | − | 0.938175i | \(-0.387485\pi\) | ||||
0.346162 | + | 0.938175i | \(0.387485\pi\) | |||||||
\(272\) | 14598.4i | 3.25425i | ||||||||
\(273\) | − | 1906.73i | − | 0.422713i | ||||||
\(274\) | − | 7073.83i | − | 1.55966i | ||||||
\(275\) | 4482.81 | 0.982994 | ||||||||
\(276\) | − | 4190.72i | − | 0.913955i | ||||||
\(277\) | 753.598i | 0.163463i | 0.996654 | + | 0.0817316i | \(0.0260450\pi\) | ||||
−0.996654 | + | 0.0817316i | \(0.973955\pi\) | |||||||
\(278\) | − | 8298.36i | − | 1.79030i | ||||||
\(279\) | − | 6148.60i | − | 1.31938i | ||||||
\(280\) | 7797.45 | 1.66424 | ||||||||
\(281\) | 5418.05i | 1.15023i | 0.818074 | + | 0.575113i | \(0.195042\pi\) | ||||
−0.818074 | + | 0.575113i | \(0.804958\pi\) | |||||||
\(282\) | 1498.68i | 0.316472i | ||||||||
\(283\) | − | 3197.10i | − | 0.671548i | −0.941943 | − | 0.335774i | \(-0.891002\pi\) | ||
0.941943 | − | 0.335774i | \(-0.108998\pi\) | |||||||
\(284\) | 14039.1 | 2.93333 | ||||||||
\(285\) | −1613.38 | −0.335328 | ||||||||
\(286\) | −12739.9 | −2.63401 | ||||||||
\(287\) | 2139.70 | 0.440078 | ||||||||
\(288\) | 11122.2i | 2.27563i | ||||||||
\(289\) | 215.621 | 0.0438878 | ||||||||
\(290\) | − | 4081.79i | − | 0.826520i | ||||||
\(291\) | 178.509i | 0.0359601i | ||||||||
\(292\) | −5950.66 | −1.19259 | ||||||||
\(293\) | 8317.45 | 1.65840 | 0.829199 | − | 0.558953i | \(-0.188797\pi\) | ||||
0.829199 | + | 0.558953i | \(0.188797\pi\) | |||||||
\(294\) | 1194.71i | 0.236996i | ||||||||
\(295\) | −271.788 | −0.0536411 | ||||||||
\(296\) | −6361.57 | − | 14604.7i | −1.24918 | − | 2.86785i | ||||
\(297\) | −7351.80 | −1.43634 | ||||||||
\(298\) | − | 163.183i | − | 0.0317212i | ||||||
\(299\) | 2936.36 | 0.567940 | ||||||||
\(300\) | −4702.08 | −0.904915 | ||||||||
\(301\) | − | 1824.30i | − | 0.349339i | ||||||
\(302\) | 10298.0i | 1.96220i | ||||||||
\(303\) | −560.371 | −0.106246 | ||||||||
\(304\) | − | 18015.7i | − | 3.39892i | ||||||
\(305\) | −4884.36 | −0.916977 | ||||||||
\(306\) | −7054.25 | −1.31786 | ||||||||
\(307\) | 10604.0 | 1.97135 | 0.985676 | − | 0.168650i | \(-0.0539408\pi\) | ||||
0.985676 | + | 0.168650i | \(0.0539408\pi\) | |||||||
\(308\) | −19460.1 | −3.60014 | ||||||||
\(309\) | − | 1681.43i | − | 0.309558i | ||||||
\(310\) | − | 11785.4i | − | 2.15925i | ||||||
\(311\) | − | 3623.18i | − | 0.660617i | −0.943873 | − | 0.330308i | \(-0.892847\pi\) | ||
0.943873 | − | 0.330308i | \(-0.107153\pi\) | |||||||
\(312\) | 8300.63 | 1.50619 | ||||||||
\(313\) | − | 7589.71i | − | 1.37059i | −0.728264 | − | 0.685297i | \(-0.759672\pi\) | ||
0.728264 | − | 0.685297i | \(-0.240328\pi\) | |||||||
\(314\) | 6911.66i | 1.24219i | ||||||||
\(315\) | 2101.29i | 0.375854i | ||||||||
\(316\) | 14929.2i | 2.65770i | ||||||||
\(317\) | 2035.56 | 0.360658 | 0.180329 | − | 0.983606i | \(-0.442284\pi\) | ||||
0.180329 | + | 0.983606i | \(0.442284\pi\) | |||||||
\(318\) | − | 3267.13i | − | 0.576137i | ||||||
\(319\) | 6327.74i | 1.11061i | ||||||||
\(320\) | 9773.27i | 1.70732i | ||||||||
\(321\) | 2740.07 | 0.476435 | ||||||||
\(322\) | 6184.46 | 1.07033 | ||||||||
\(323\) | 5797.00 | 0.998619 | ||||||||
\(324\) | −3164.07 | −0.542536 | ||||||||
\(325\) | − | 3294.66i | − | 0.562322i | ||||||
\(326\) | −21159.2 | −3.59478 | ||||||||
\(327\) | 2881.44i | 0.487291i | ||||||||
\(328\) | 9314.80i | 1.56806i | ||||||||
\(329\) | −1604.02 | −0.268792 | ||||||||
\(330\) | −5833.81 | −0.973153 | ||||||||
\(331\) | 10591.8i | 1.75884i | 0.476043 | + | 0.879422i | \(0.342071\pi\) | ||||
−0.476043 | + | 0.879422i | \(0.657929\pi\) | |||||||
\(332\) | 7814.48 | 1.29179 | ||||||||
\(333\) | 3935.74 | − | 1714.34i | 0.647679 | − | 0.282118i | ||||
\(334\) | −2172.71 | −0.355944 | ||||||||
\(335\) | 3226.11i | 0.526153i | ||||||||
\(336\) | 9749.66 | 1.58300 | ||||||||
\(337\) | −7720.67 | −1.24799 | −0.623993 | − | 0.781430i | \(-0.714491\pi\) | ||||
−0.623993 | + | 0.781430i | \(0.714491\pi\) | |||||||
\(338\) | − | 2491.83i | − | 0.400999i | ||||||
\(339\) | 4022.39i | 0.644443i | ||||||||
\(340\) | −9806.33 | −1.56419 | ||||||||
\(341\) | 18270.2i | 2.90143i | ||||||||
\(342\) | 8705.60 | 1.37645 | ||||||||
\(343\) | −6855.52 | −1.07919 | ||||||||
\(344\) | 7941.79 | 1.24475 | ||||||||
\(345\) | 1344.61 | 0.209829 | ||||||||
\(346\) | − | 5266.14i | − | 0.818235i | ||||||
\(347\) | − | 10529.2i | − | 1.62892i | −0.580218 | − | 0.814461i | \(-0.697033\pi\) | ||
0.580218 | − | 0.814461i | \(-0.302967\pi\) | |||||||
\(348\) | − | 6637.26i | − | 1.02240i | ||||||
\(349\) | −864.634 | −0.132615 | −0.0663077 | − | 0.997799i | \(-0.521122\pi\) | ||||
−0.0663077 | + | 0.997799i | \(0.521122\pi\) | |||||||
\(350\) | − | 6939.10i | − | 1.05974i | ||||||
\(351\) | 5403.24i | 0.821662i | ||||||||
\(352\) | − | 33049.0i | − | 5.00431i | ||||||
\(353\) | − | 7032.15i | − | 1.06029i | −0.847906 | − | 0.530147i | \(-0.822137\pi\) | ||
0.847906 | − | 0.530147i | \(-0.177863\pi\) | |||||||
\(354\) | −609.371 | −0.0914907 | ||||||||
\(355\) | 4504.48i | 0.673445i | ||||||||
\(356\) | − | 17275.3i | − | 2.57188i | ||||||
\(357\) | 3137.19i | 0.465092i | ||||||||
\(358\) | 10592.5 | 1.56378 | ||||||||
\(359\) | −10296.2 | −1.51368 | −0.756839 | − | 0.653602i | \(-0.773257\pi\) | ||||
−0.756839 | + | 0.653602i | \(0.773257\pi\) | |||||||
\(360\) | −9147.58 | −1.33922 | ||||||||
\(361\) | −295.043 | −0.0430155 | ||||||||
\(362\) | 19309.1i | 2.80349i | ||||||||
\(363\) | 5296.67 | 0.765849 | ||||||||
\(364\) | 14302.3i | 2.05947i | ||||||||
\(365\) | − | 1909.29i | − | 0.273799i | ||||||
\(366\) | −10951.1 | −1.56400 | ||||||||
\(367\) | −2445.36 | −0.347812 | −0.173906 | − | 0.984762i | \(-0.555639\pi\) | ||||
−0.173906 | + | 0.984762i | \(0.555639\pi\) | |||||||
\(368\) | 15014.4i | 2.12685i | ||||||||
\(369\) | −2510.19 | −0.354133 | ||||||||
\(370\) | 7543.89 | − | 3285.99i | 1.05997 | − | 0.461704i | ||||
\(371\) | 3496.77 | 0.489335 | ||||||||
\(372\) | − | 19163.9i | − | 2.67097i | ||||||
\(373\) | −1453.10 | −0.201712 | −0.100856 | − | 0.994901i | \(-0.532158\pi\) | ||||
−0.100856 | + | 0.994901i | \(0.532158\pi\) | |||||||
\(374\) | 20961.3 | 2.89808 | ||||||||
\(375\) | − | 3893.04i | − | 0.536095i | ||||||
\(376\) | − | 6982.82i | − | 0.957744i | ||||||
\(377\) | 4650.60 | 0.635327 | ||||||||
\(378\) | 11380.1i | 1.54849i | ||||||||
\(379\) | −356.951 | −0.0483782 | −0.0241891 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241891 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(380\) | 12101.9 | 1.63373 | ||||||||
\(381\) | −3689.07 | −0.496054 | ||||||||
\(382\) | 16519.7 | 2.21262 | ||||||||
\(383\) | − | 8260.99i | − | 1.10213i | −0.834461 | − | 0.551067i | \(-0.814221\pi\) | ||
0.834461 | − | 0.551067i | \(-0.185779\pi\) | |||||||
\(384\) | 8779.83i | 1.16678i | ||||||||
\(385\) | − | 6243.85i | − | 0.826535i | ||||||
\(386\) | −10592.7 | −1.39677 | ||||||||
\(387\) | 2140.18i | 0.281116i | ||||||||
\(388\) | − | 1338.99i | − | 0.175198i | ||||||
\(389\) | 5751.61i | 0.749661i | 0.927093 | + | 0.374831i | \(0.122299\pi\) | ||||
−0.927093 | + | 0.374831i | \(0.877701\pi\) | |||||||
\(390\) | 4287.59i | 0.556693i | ||||||||
\(391\) | −4831.26 | −0.624878 | ||||||||
\(392\) | − | 5566.51i | − | 0.717223i | ||||||
\(393\) | 2705.78i | 0.347299i | ||||||||
\(394\) | 9160.09i | 1.17127i | ||||||||
\(395\) | −4790.08 | −0.610165 | ||||||||
\(396\) | 22829.7 | 2.89706 | ||||||||
\(397\) | −6861.12 | −0.867380 | −0.433690 | − | 0.901062i | \(-0.642789\pi\) | ||||
−0.433690 | + | 0.901062i | \(0.642789\pi\) | |||||||
\(398\) | −5530.40 | −0.696517 | ||||||||
\(399\) | − | 3871.59i | − | 0.485769i | ||||||
\(400\) | 16846.5 | 2.10582 | ||||||||
\(401\) | − | 1404.27i | − | 0.174878i | −0.996170 | − | 0.0874388i | \(-0.972132\pi\) | ||
0.996170 | − | 0.0874388i | \(-0.0278682\pi\) | |||||||
\(402\) | 7233.20i | 0.897411i | ||||||||
\(403\) | 13427.8 | 1.65977 | ||||||||
\(404\) | 4203.32 | 0.517631 | ||||||||
\(405\) | − | 1015.20i | − | 0.124558i | ||||||
\(406\) | 9794.95 | 1.19733 | ||||||||
\(407\) | −11694.8 | + | 5094.06i | −1.42430 | + | 0.620401i | ||||
\(408\) | −13657.2 | −1.65719 | ||||||||
\(409\) | 9142.35i | 1.10528i | 0.833420 | + | 0.552641i | \(0.186380\pi\) | ||||
−0.833420 | + | 0.552641i | \(0.813620\pi\) | |||||||
\(410\) | −4811.44 | −0.579561 | ||||||||
\(411\) | 3690.62 | 0.442932 | ||||||||
\(412\) | 12612.4i | 1.50817i | ||||||||
\(413\) | − | 652.202i | − | 0.0777065i | ||||||
\(414\) | −7255.31 | −0.861302 | ||||||||
\(415\) | 2507.30i | 0.296575i | ||||||||
\(416\) | −24289.5 | −2.86272 | ||||||||
\(417\) | 4329.49 | 0.508432 | ||||||||
\(418\) | −25868.2 | −3.02692 | ||||||||
\(419\) | −10074.7 | −1.17465 | −0.587327 | − | 0.809350i | \(-0.699820\pi\) | ||||
−0.587327 | + | 0.809350i | \(0.699820\pi\) | |||||||
\(420\) | 6549.26i | 0.760884i | ||||||||
\(421\) | − | 12798.1i | − | 1.48158i | −0.671739 | − | 0.740788i | \(-0.734452\pi\) | ||
0.671739 | − | 0.740788i | \(-0.265548\pi\) | |||||||
\(422\) | − | 8914.30i | − | 1.02830i | ||||||
\(423\) | 1881.76 | 0.216298 | ||||||||
\(424\) | 15222.6i | 1.74357i | ||||||||
\(425\) | 5420.78i | 0.618698i | ||||||||
\(426\) | 10099.4i | 1.14863i | ||||||||
\(427\) | − | 11720.9i | − | 1.32837i | ||||||
\(428\) | −20553.1 | −2.32120 | ||||||||
\(429\) | − | 6646.77i | − | 0.748040i | ||||||
\(430\) | 4102.23i | 0.460063i | ||||||||
\(431\) | − | 11612.1i | − | 1.29777i | −0.760888 | − | 0.648883i | \(-0.775236\pi\) | ||
0.760888 | − | 0.648883i | \(-0.224764\pi\) | |||||||
\(432\) | −27628.3 | −3.07701 | ||||||||
\(433\) | 6856.28 | 0.760951 | 0.380476 | − | 0.924791i | \(-0.375760\pi\) | ||||
0.380476 | + | 0.924791i | \(0.375760\pi\) | |||||||
\(434\) | 28281.2 | 3.12797 | ||||||||
\(435\) | 2129.59 | 0.234726 | ||||||||
\(436\) | − | 21613.6i | − | 2.37409i | ||||||
\(437\) | 5962.23 | 0.652659 | ||||||||
\(438\) | − | 4280.78i | − | 0.466995i | ||||||
\(439\) | − | 254.645i | − | 0.0276846i | −0.999904 | − | 0.0138423i | \(-0.995594\pi\) | ||
0.999904 | − | 0.0138423i | \(-0.00440627\pi\) | |||||||
\(440\) | 27181.5 | 2.94506 | ||||||||
\(441\) | 1500.08 | 0.161979 | ||||||||
\(442\) | − | 15405.6i | − | 1.65785i | ||||||
\(443\) | −5451.49 | −0.584669 | −0.292334 | − | 0.956316i | \(-0.594432\pi\) | ||||
−0.292334 | + | 0.956316i | \(0.594432\pi\) | |||||||
\(444\) | 12266.9 | − | 5343.23i | 1.31117 | − | 0.571123i | ||||
\(445\) | 5542.84 | 0.590463 | ||||||||
\(446\) | 10024.3i | 1.06427i | ||||||||
\(447\) | 85.1372 | 0.00900861 | ||||||||
\(448\) | −23452.6 | −2.47329 | ||||||||
\(449\) | 12024.0i | 1.26380i | 0.775050 | + | 0.631900i | \(0.217725\pi\) | ||||
−0.775050 | + | 0.631900i | \(0.782275\pi\) | |||||||
\(450\) | 8140.62i | 0.852783i | ||||||||
\(451\) | 7458.88 | 0.778769 | ||||||||
\(452\) | − | 30171.8i | − | 3.13974i | ||||||
\(453\) | −5372.78 | −0.557252 | ||||||||
\(454\) | 3046.57 | 0.314940 | ||||||||
\(455\) | −4588.95 | −0.472820 | ||||||||
\(456\) | 16854.3 | 1.73087 | ||||||||
\(457\) | 2235.58i | 0.228831i | 0.993433 | + | 0.114416i | \(0.0364995\pi\) | ||||
−0.993433 | + | 0.114416i | \(0.963500\pi\) | |||||||
\(458\) | 14490.6i | 1.47839i | ||||||||
\(459\) | − | 8890.08i | − | 0.904038i | ||||||
\(460\) | −10085.8 | −1.02229 | ||||||||
\(461\) | − | 9012.14i | − | 0.910493i | −0.890366 | − | 0.455246i | \(-0.849551\pi\) | ||
0.890366 | − | 0.455246i | \(-0.150449\pi\) | |||||||
\(462\) | − | 13999.2i | − | 1.40975i | ||||||
\(463\) | 11294.9i | 1.13373i | 0.823811 | + | 0.566865i | \(0.191844\pi\) | ||||
−0.823811 | + | 0.566865i | \(0.808156\pi\) | |||||||
\(464\) | 23779.9i | 2.37921i | ||||||||
\(465\) | 6148.80 | 0.613212 | ||||||||
\(466\) | 17407.7i | 1.73047i | ||||||||
\(467\) | 7336.43i | 0.726959i | 0.931602 | + | 0.363479i | \(0.118411\pi\) | ||||
−0.931602 | + | 0.363479i | \(0.881589\pi\) | |||||||
\(468\) | − | 16778.8i | − | 1.65726i | ||||||
\(469\) | −7741.60 | −0.762205 | ||||||||
\(470\) | 3606.89 | 0.353986 | ||||||||
\(471\) | −3606.01 | −0.352773 | ||||||||
\(472\) | 2839.25 | 0.276879 | ||||||||
\(473\) | − | 6359.44i | − | 0.618197i | ||||||
\(474\) | −10739.7 | −1.04070 | ||||||||
\(475\) | − | 6689.75i | − | 0.646204i | ||||||
\(476\) | − | 23532.0i | − | 2.26594i | ||||||
\(477\) | −4102.24 | −0.393771 | ||||||||
\(478\) | −11133.1 | −1.06531 | ||||||||
\(479\) | − | 14290.6i | − | 1.36316i | −0.731743 | − | 0.681580i | \(-0.761293\pi\) | ||
0.731743 | − | 0.681580i | \(-0.238707\pi\) | |||||||
\(480\) | −11122.6 | −1.05765 | ||||||||
\(481\) | 3743.90 | + | 8595.16i | 0.354901 | + | 0.814773i | ||||
\(482\) | 30642.5 | 2.89570 | ||||||||
\(483\) | 3226.61i | 0.303967i | ||||||||
\(484\) | −39730.1 | −3.73123 | ||||||||
\(485\) | 429.619 | 0.0402226 | ||||||||
\(486\) | − | 21174.2i | − | 1.97630i | ||||||
\(487\) | − | 11788.6i | − | 1.09690i | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||
0.836182 | − | 0.548452i | \(-0.184783\pi\) | |||||||
\(488\) | 51024.8 | 4.73316 | ||||||||
\(489\) | − | 11039.4i | − | 1.02089i | ||||||
\(490\) | 2875.31 | 0.265088 | ||||||||
\(491\) | −5302.95 | −0.487411 | −0.243706 | − | 0.969849i | \(-0.578363\pi\) | ||||
−0.243706 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(492\) | −7823.72 | −0.716912 | ||||||||
\(493\) | −7651.75 | −0.699022 | ||||||||
\(494\) | 19011.9i | 1.73155i | ||||||||
\(495\) | 7324.98i | 0.665118i | ||||||||
\(496\) | 68660.1i | 6.21558i | ||||||||
\(497\) | −10809.3 | −0.975577 | ||||||||
\(498\) | 5621.58i | 0.505841i | ||||||||
\(499\) | 6326.67i | 0.567576i | 0.958887 | + | 0.283788i | \(0.0915912\pi\) | ||||
−0.958887 | + | 0.283788i | \(0.908409\pi\) | |||||||
\(500\) | 29201.5i | 2.61186i | ||||||||
\(501\) | − | 1133.56i | − | 0.101085i | ||||||
\(502\) | −7439.08 | −0.661399 | ||||||||
\(503\) | 7696.81i | 0.682274i | 0.940014 | + | 0.341137i | \(0.110812\pi\) | ||||
−0.940014 | + | 0.341137i | \(0.889188\pi\) | |||||||
\(504\) | − | 21951.2i | − | 1.94005i | ||||||
\(505\) | 1348.65i | 0.118840i | ||||||||
\(506\) | 21558.7 | 1.89408 | ||||||||
\(507\) | 1300.06 | 0.113881 | ||||||||
\(508\) | 27671.5 | 2.41678 | ||||||||
\(509\) | 17475.7 | 1.52180 | 0.760902 | − | 0.648867i | \(-0.224757\pi\) | ||||
0.760902 | + | 0.648867i | \(0.224757\pi\) | |||||||
\(510\) | − | 7054.47i | − | 0.612504i | ||||||
\(511\) | 4581.66 | 0.396636 | ||||||||
\(512\) | − | 3589.61i | − | 0.309843i | ||||||
\(513\) | 10971.2i | 0.944230i | ||||||||
\(514\) | −41094.6 | −3.52647 | ||||||||
\(515\) | −4046.72 | −0.346252 | ||||||||
\(516\) | 6670.50i | 0.569094i | ||||||||
\(517\) | −5591.54 | −0.475659 | ||||||||
\(518\) | 7885.29 | + | 18102.9i | 0.668841 | + | 1.53551i | ||||
\(519\) | 2747.49 | 0.232373 | ||||||||
\(520\) | − | 19977.2i | − | 1.68473i | ||||||
\(521\) | 19380.0 | 1.62966 | 0.814832 | − | 0.579697i | \(-0.196829\pi\) | ||||
0.814832 | + | 0.579697i | \(0.196829\pi\) | |||||||
\(522\) | −11491.0 | −0.963497 | ||||||||
\(523\) | 4938.48i | 0.412896i | 0.978458 | + | 0.206448i | \(0.0661904\pi\) | ||||
−0.978458 | + | 0.206448i | \(0.933810\pi\) | |||||||
\(524\) | − | 20295.9i | − | 1.69205i | ||||||
\(525\) | 3620.33 | 0.300960 | ||||||||
\(526\) | 19084.5i | 1.58199i | ||||||||
\(527\) | −22093.1 | −1.82617 | ||||||||
\(528\) | 33986.8 | 2.80130 | ||||||||
\(529\) | 7198.04 | 0.591603 | ||||||||
\(530\) | −7863.03 | −0.644431 | ||||||||
\(531\) | 765.131i | 0.0625308i | ||||||||
\(532\) | 29040.6i | 2.36668i | ||||||||
\(533\) | − | 5481.94i | − | 0.445495i | ||||||
\(534\) | 12427.5 | 1.00710 | ||||||||
\(535\) | − | 6594.54i | − | 0.532910i | ||||||
\(536\) | − | 33701.7i | − | 2.71584i | ||||||
\(537\) | 5526.42i | 0.444102i | ||||||||
\(538\) | − | 32948.9i | − | 2.64038i | ||||||
\(539\) | −4457.42 | −0.356205 | ||||||||
\(540\) | − | 18559.1i | − | 1.47899i | ||||||
\(541\) | 17881.1i | 1.42101i | 0.703691 | + | 0.710506i | \(0.251534\pi\) | ||||
−0.703691 | + | 0.710506i | \(0.748466\pi\) | |||||||
\(542\) | − | 16666.3i | − | 1.32081i | ||||||
\(543\) | −10074.1 | −0.796171 | ||||||||
\(544\) | 39964.1 | 3.14972 | ||||||||
\(545\) | 6934.80 | 0.545053 | ||||||||
\(546\) | −10288.8 | −0.806446 | ||||||||
\(547\) | − | 817.257i | − | 0.0638819i | −0.999490 | − | 0.0319409i | \(-0.989831\pi\) | ||
0.999490 | − | 0.0319409i | \(-0.0101688\pi\) | |||||||
\(548\) | −27683.2 | −2.15797 | ||||||||
\(549\) | 13750.3i | 1.06894i | ||||||||
\(550\) | − | 24189.4i | − | 1.87534i | ||||||
\(551\) | 9442.98 | 0.730099 | ||||||||
\(552\) | −14046.5 | −1.08308 | ||||||||
\(553\) | − | 11494.6i | − | 0.883907i | ||||||
\(554\) | 4066.44 | 0.311853 | ||||||||
\(555\) | 1714.39 | + | 3935.86i | 0.131121 | + | 0.301024i | ||||
\(556\) | −32475.3 | −2.47709 | ||||||||
\(557\) | 19213.5i | 1.46158i | 0.682601 | + | 0.730791i | \(0.260849\pi\) | ||||
−0.682601 | + | 0.730791i | \(0.739151\pi\) | |||||||
\(558\) | −33178.1 | −2.51710 | ||||||||
\(559\) | −4673.90 | −0.353640 | ||||||||
\(560\) | − | 23464.6i | − | 1.77064i | ||||||
\(561\) | 10936.1i | 0.823035i | ||||||||
\(562\) | 29236.0 | 2.19439 | ||||||||
\(563\) | 1.52747i | 0.000114343i | 1.00000 | 5.71715e-5i | \(1.81983e-5\pi\) | |||||
−1.00000 | 5.71715e-5i | \(0.999982\pi\) | ||||||||
\(564\) | 5865.04 | 0.437877 | ||||||||
\(565\) | 9680.71 | 0.720833 | ||||||||
\(566\) | −17251.7 | −1.28117 | ||||||||
\(567\) | 2436.15 | 0.180439 | ||||||||
\(568\) | − | 47056.2i | − | 3.47612i | ||||||
\(569\) | 1123.19i | 0.0827533i | 0.999144 | + | 0.0413767i | \(0.0131744\pi\) | ||||
−0.999144 | + | 0.0413767i | \(0.986826\pi\) | |||||||
\(570\) | 8705.88i | 0.639735i | ||||||||
\(571\) | −10827.8 | −0.793574 | −0.396787 | − | 0.917911i | \(-0.629875\pi\) | ||||
−0.396787 | + | 0.917911i | \(0.629875\pi\) | |||||||
\(572\) | 49857.2i | 3.64446i | ||||||||
\(573\) | 8618.79i | 0.628368i | ||||||||
\(574\) | − | 11545.9i | − | 0.839574i | ||||||
\(575\) | 5575.29i | 0.404357i | ||||||||
\(576\) | 27513.5 | 1.99027 | ||||||||
\(577\) | − | 19564.6i | − | 1.41159i | −0.708417 | − | 0.705794i | \(-0.750590\pi\) | ||
0.708417 | − | 0.705794i | \(-0.249410\pi\) | |||||||
\(578\) | − | 1163.50i | − | 0.0837285i | ||||||
\(579\) | − | 5526.52i | − | 0.396674i | ||||||
\(580\) | −15973.9 | −1.14359 | ||||||||
\(581\) | −6016.70 | −0.429630 | ||||||||
\(582\) | 963.240 | 0.0686041 | ||||||||
\(583\) | 12189.6 | 0.865935 | ||||||||
\(584\) | 19945.5i | 1.41327i | ||||||||
\(585\) | 5383.53 | 0.380481 | ||||||||
\(586\) | − | 44881.3i | − | 3.16387i | ||||||
\(587\) | 6952.71i | 0.488874i | 0.969665 | + | 0.244437i | \(0.0786032\pi\) | ||||
−0.969665 | + | 0.244437i | \(0.921397\pi\) | |||||||
\(588\) | 4675.45 | 0.327912 | ||||||||
\(589\) | 27264.9 | 1.90735 | ||||||||
\(590\) | 1466.58i | 0.102336i | ||||||||
\(591\) | −4779.08 | −0.332631 | ||||||||
\(592\) | −43949.5 | + | 19143.6i | −3.05121 | + | 1.32905i | ||||
\(593\) | −18925.1 | −1.31055 | −0.655277 | − | 0.755388i | \(-0.727448\pi\) | ||||
−0.655277 | + | 0.755388i | \(0.727448\pi\) | |||||||
\(594\) | 39670.5i | 2.74024i | ||||||||
\(595\) | 7550.31 | 0.520223 | ||||||||
\(596\) | −638.611 | −0.0438901 | ||||||||
\(597\) | − | 2885.37i | − | 0.197806i | ||||||
\(598\) | − | 15844.7i | − | 1.08351i | ||||||
\(599\) | −19111.5 | −1.30363 | −0.651817 | − | 0.758376i | \(-0.725993\pi\) | ||||
−0.651817 | + | 0.758376i | \(0.725993\pi\) | |||||||
\(600\) | 15760.5i | 1.07236i | ||||||||
\(601\) | 18224.7 | 1.23694 | 0.618471 | − | 0.785808i | \(-0.287753\pi\) | ||||
0.618471 | + | 0.785808i | \(0.287753\pi\) | |||||||
\(602\) | −9844.01 | −0.666465 | ||||||||
\(603\) | 9082.07 | 0.613351 | ||||||||
\(604\) | 40301.0 | 2.71494 | ||||||||
\(605\) | − | 12747.5i | − | 0.856630i | ||||||
\(606\) | 3023.78i | 0.202694i | ||||||||
\(607\) | − | 2790.32i | − | 0.186583i | −0.995639 | − | 0.0932914i | \(-0.970261\pi\) | ||
0.995639 | − | 0.0932914i | \(-0.0297388\pi\) | |||||||
\(608\) | −49319.5 | −3.28975 | ||||||||
\(609\) | 5110.30i | 0.340033i | ||||||||
\(610\) | 26356.2i | 1.74940i | ||||||||
\(611\) | 4109.53i | 0.272101i | ||||||||
\(612\) | 27606.6i | 1.82341i | ||||||||
\(613\) | 8454.58 | 0.557059 | 0.278530 | − | 0.960428i | \(-0.410153\pi\) | ||||
0.278530 | + | 0.960428i | \(0.410153\pi\) | |||||||
\(614\) | − | 57219.8i | − | 3.76092i | ||||||
\(615\) | − | 2510.27i | − | 0.164591i | ||||||
\(616\) | 65226.7i | 4.26633i | ||||||||
\(617\) | 4510.28 | 0.294290 | 0.147145 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147145 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(618\) | −9073.08 | −0.590571 | ||||||||
\(619\) | −10525.8 | −0.683470 | −0.341735 | − | 0.939796i | \(-0.611015\pi\) | ||||
−0.341735 | + | 0.939796i | \(0.611015\pi\) | |||||||
\(620\) | −46121.9 | −2.98758 | ||||||||
\(621\) | − | 9143.46i | − | 0.590845i | ||||||
\(622\) | −19550.8 | −1.26032 | ||||||||
\(623\) | 13301.0i | 0.855366i | ||||||||
\(624\) | − | 24978.8i | − | 1.60249i | ||||||
\(625\) | 517.136 | 0.0330967 | ||||||||
\(626\) | −40954.3 | −2.61480 | ||||||||
\(627\) | − | 13496.2i | − | 0.859626i | ||||||
\(628\) | 27048.6 | 1.71872 | ||||||||
\(629\) | −6159.94 | − | 14141.8i | −0.390481 | − | 0.896458i | ||||
\(630\) | 11338.6 | 0.717049 | ||||||||
\(631\) | − | 9440.57i | − | 0.595599i | −0.954628 | − | 0.297800i | \(-0.903747\pi\) | ||
0.954628 | − | 0.297800i | \(-0.0962527\pi\) | |||||||
\(632\) | 50039.8 | 3.14949 | ||||||||
\(633\) | 4650.85 | 0.292029 | ||||||||
\(634\) | − | 10984.0i | − | 0.688059i | ||||||
\(635\) | 8878.51i | 0.554855i | ||||||||
\(636\) | −12785.8 | −0.797155 | ||||||||
\(637\) | 3276.00i | 0.203767i | ||||||||
\(638\) | 34144.7 | 2.11881 | ||||||||
\(639\) | 12680.9 | 0.785052 | ||||||||
\(640\) | 21130.5 | 1.30509 | ||||||||
\(641\) | 7473.20 | 0.460489 | 0.230245 | − | 0.973133i | \(-0.426047\pi\) | ||||
0.230245 | + | 0.973133i | \(0.426047\pi\) | |||||||
\(642\) | − | 14785.5i | − | 0.908936i | ||||||
\(643\) | − | 13277.8i | − | 0.814346i | −0.913351 | − | 0.407173i | \(-0.866515\pi\) | ||
0.913351 | − | 0.407173i | \(-0.133485\pi\) | |||||||
\(644\) | − | 24202.7i | − | 1.48093i | ||||||
\(645\) | −2140.25 | −0.130655 | ||||||||
\(646\) | − | 31280.8i | − | 1.90515i | ||||||
\(647\) | − | 1006.02i | − | 0.0611296i | −0.999533 | − | 0.0305648i | \(-0.990269\pi\) | ||
0.999533 | − | 0.0305648i | \(-0.00973059\pi\) | |||||||
\(648\) | 10605.4i | 0.642929i | ||||||||
\(649\) | − | 2273.54i | − | 0.137511i | ||||||
\(650\) | −17778.1 | −1.07279 | ||||||||
\(651\) | 14755.1i | 0.888322i | ||||||||
\(652\) | 82805.8i | 4.97381i | ||||||||
\(653\) | 17776.7i | 1.06532i | 0.846328 | + | 0.532662i | \(0.178808\pi\) | ||||
−0.846328 | + | 0.532662i | \(0.821192\pi\) | |||||||
\(654\) | 15548.4 | 0.929648 | ||||||||
\(655\) | 6512.02 | 0.388467 | ||||||||
\(656\) | 28030.7 | 1.66832 | ||||||||
\(657\) | −5374.98 | −0.319175 | ||||||||
\(658\) | 8655.35i | 0.512797i | ||||||||
\(659\) | 3178.94 | 0.187912 | 0.0939559 | − | 0.995576i | \(-0.470049\pi\) | ||||
0.0939559 | + | 0.995576i | \(0.470049\pi\) | |||||||
\(660\) | 22830.4i | 1.34647i | ||||||||
\(661\) | − | 30502.9i | − | 1.79490i | −0.441121 | − | 0.897448i | \(-0.645419\pi\) | ||
0.441121 | − | 0.897448i | \(-0.354581\pi\) | |||||||
\(662\) | 57153.7 | 3.35550 | ||||||||
\(663\) | 8037.54 | 0.470818 | ||||||||
\(664\) | − | 26192.7i | − | 1.53083i | ||||||
\(665\) | −9317.79 | −0.543351 | ||||||||
\(666\) | −9250.63 | − | 21237.4i | −0.538220 | − | 1.23563i | ||||
\(667\) | −7869.84 | −0.456854 | ||||||||
\(668\) | 8502.80i | 0.492490i | ||||||||
\(669\) | −5229.96 | −0.302245 | ||||||||
\(670\) | 17408.2 | 1.00379 | ||||||||
\(671\) | − | 40858.4i | − | 2.35070i | ||||||
\(672\) | − | 26690.5i | − | 1.53215i | ||||||
\(673\) | −27578.6 | −1.57961 | −0.789804 | − | 0.613360i | \(-0.789818\pi\) | ||||
−0.789804 | + | 0.613360i | \(0.789818\pi\) | |||||||
\(674\) | 41661.0i | 2.38089i | ||||||||
\(675\) | −10259.2 | −0.585001 | ||||||||
\(676\) | −9751.69 | −0.554830 | ||||||||
\(677\) | 11517.1 | 0.653821 | 0.326910 | − | 0.945055i | \(-0.393992\pi\) | ||||
0.326910 | + | 0.945055i | \(0.393992\pi\) | |||||||
\(678\) | 21704.9 | 1.22946 | ||||||||
\(679\) | 1030.94i | 0.0582680i | ||||||||
\(680\) | 32869.0i | 1.85363i | ||||||||
\(681\) | 1589.48i | 0.0894408i | ||||||||
\(682\) | 98586.7 | 5.53531 | ||||||||
\(683\) | − | 16518.0i | − | 0.925394i | −0.886517 | − | 0.462697i | \(-0.846882\pi\) | ||
0.886517 | − | 0.462697i | \(-0.153118\pi\) | |||||||
\(684\) | − | 34069.1i | − | 1.90448i | ||||||
\(685\) | − | 8882.24i | − | 0.495435i | ||||||
\(686\) | 36992.6i | 2.05887i | ||||||||
\(687\) | −7560.16 | −0.419851 | ||||||||
\(688\) | − | 23899.0i | − | 1.32433i | ||||||
\(689\) | − | 8958.78i | − | 0.495359i | ||||||
\(690\) | − | 7255.54i | − | 0.400310i | ||||||
\(691\) | 11900.6 | 0.655164 | 0.327582 | − | 0.944823i | \(-0.393766\pi\) | ||||
0.327582 | + | 0.944823i | \(0.393766\pi\) | |||||||
\(692\) | −20608.8 | −1.13213 | ||||||||
\(693\) | −17577.5 | −0.963514 | ||||||||
\(694\) | −56815.8 | −3.10764 | ||||||||
\(695\) | − | 10419.8i | − | 0.568700i | ||||||
\(696\) | −22246.8 | −1.21159 | ||||||||
\(697\) | 9019.57i | 0.490159i | ||||||||
\(698\) | 4665.59i | 0.253002i | ||||||||
\(699\) | −9082.11 | −0.491440 | ||||||||
\(700\) | −27155.9 | −1.46628 | ||||||||
\(701\) | 22713.7i | 1.22380i | 0.790935 | + | 0.611901i | \(0.209595\pi\) | ||||
−0.790935 | + | 0.611901i | \(0.790405\pi\) | |||||||
\(702\) | 29156.1 | 1.56756 | ||||||||
\(703\) | 7601.94 | + | 17452.3i | 0.407841 | + | 0.936312i | ||||
\(704\) | −81754.7 | −4.37677 | ||||||||
\(705\) | 1881.82i | 0.100530i | ||||||||
\(706\) | −37945.7 | −2.02281 | ||||||||
\(707\) | −3236.31 | −0.172156 | ||||||||
\(708\) | 2384.75i | 0.126588i | ||||||||
\(709\) | 10384.1i | 0.550046i | 0.961438 | + | 0.275023i | \(0.0886855\pi\) | ||||
−0.961438 | + | 0.275023i | \(0.911315\pi\) | |||||||
\(710\) | 24306.3 | 1.28479 | ||||||||
\(711\) | 13484.9i | 0.711285i | ||||||||
\(712\) | −57903.6 | −3.04779 | ||||||||
\(713\) | −22722.8 | −1.19351 | ||||||||
\(714\) | 16928.4 | 0.887297 | ||||||||
\(715\) | −15996.8 | −0.836711 | ||||||||
\(716\) | − | 41453.5i | − | 2.16367i | ||||||
\(717\) | − | 5808.47i | − | 0.302540i | ||||||
\(718\) | 55558.4i | 2.88777i | ||||||||
\(719\) | −9083.51 | −0.471151 | −0.235576 | − | 0.971856i | \(-0.575698\pi\) | ||||
−0.235576 | + | 0.971856i | \(0.575698\pi\) | |||||||
\(720\) | 27527.5i | 1.42485i | ||||||||
\(721\) | − | 9710.80i | − | 0.501594i | ||||||
\(722\) | 1592.06i | 0.0820644i | ||||||||
\(723\) | 15987.1i | 0.822360i | ||||||||
\(724\) | 75565.4 | 3.87896 | ||||||||
\(725\) | 8830.14i | 0.452335i | ||||||||
\(726\) | − | 28581.0i | − | 1.46108i | ||||||
\(727\) | − | 4180.93i | − | 0.213290i | −0.994297 | − | 0.106645i | \(-0.965989\pi\) | ||
0.994297 | − | 0.106645i | \(-0.0340109\pi\) | |||||||
\(728\) | 47938.7 | 2.44056 | ||||||||
\(729\) | 7001.66 | 0.355721 | ||||||||
\(730\) | −10302.6 | −0.522351 | ||||||||
\(731\) | 7690.08 | 0.389094 | ||||||||
\(732\) | 42856.9i | 2.16398i | ||||||||
\(733\) | 1270.23 | 0.0640070 | 0.0320035 | − | 0.999488i | \(-0.489811\pi\) | ||||
0.0320035 | + | 0.999488i | \(0.489811\pi\) | |||||||
\(734\) | 13195.3i | 0.663550i | ||||||||
\(735\) | 1500.13i | 0.0752833i | ||||||||
\(736\) | 41103.2 | 2.05854 | ||||||||
\(737\) | −26986.8 | −1.34881 | ||||||||
\(738\) | 13545.1i | 0.675610i | ||||||||
\(739\) | 6403.06 | 0.318729 | 0.159364 | − | 0.987220i | \(-0.449056\pi\) | ||||
0.159364 | + | 0.987220i | \(0.449056\pi\) | |||||||
\(740\) | −12859.6 | − | 29522.7i | −0.638822 | − | 1.46659i | ||||
\(741\) | −9919.08 | −0.491749 | ||||||||
\(742\) | − | 18868.7i | − | 0.933546i | ||||||
\(743\) | 32423.7 | 1.60095 | 0.800477 | − | 0.599363i | \(-0.204580\pi\) | ||||
0.800477 | + | 0.599363i | \(0.204580\pi\) | |||||||
\(744\) | −64233.7 | −3.16522 | ||||||||
\(745\) | − | 204.900i | − | 0.0100765i | ||||||
\(746\) | 7840.98i | 0.384824i | ||||||||
\(747\) | 7058.50 | 0.345725 | ||||||||
\(748\) | − | 82031.3i | − | 4.00984i | ||||||
\(749\) | 15824.7 | 0.771993 | ||||||||
\(750\) | −21007.0 | −1.02275 | ||||||||
\(751\) | 13484.1 | 0.655185 | 0.327592 | − | 0.944819i | \(-0.393763\pi\) | ||||
0.327592 | + | 0.944819i | \(0.393763\pi\) | |||||||
\(752\) | −21013.2 | −1.01898 | ||||||||
\(753\) | − | 3881.18i | − | 0.187833i | ||||||
\(754\) | − | 25094.8i | − | 1.21207i | ||||||
\(755\) | 12930.7i | 0.623307i | ||||||||
\(756\) | 44535.7 | 2.14252 | ||||||||
\(757\) | − | 5500.92i | − | 0.264114i | −0.991242 | − | 0.132057i | \(-0.957842\pi\) | ||
0.991242 | − | 0.132057i | \(-0.0421582\pi\) | |||||||
\(758\) | 1926.12i | 0.0922953i | ||||||||
\(759\) | 11247.8i | 0.537904i | ||||||||
\(760\) | − | 40563.4i | − | 1.93604i | ||||||
\(761\) | 41822.3 | 1.99219 | 0.996096 | − | 0.0882810i | \(-0.0281373\pi\) | ||||
0.996096 | + | 0.0882810i | \(0.0281373\pi\) | |||||||
\(762\) | 19906.3i | 0.946365i | ||||||||
\(763\) | 16641.2i | 0.789584i | ||||||||
\(764\) | − | 64649.2i | − | 3.06142i | ||||||
\(765\) | −8857.65 | −0.418626 | ||||||||
\(766\) | −44576.6 | −2.10264 | ||||||||
\(767\) | −1670.95 | −0.0786631 | ||||||||
\(768\) | 14889.5 | 0.699582 | ||||||||
\(769\) | 9397.23i | 0.440667i | 0.975425 | + | 0.220333i | \(0.0707145\pi\) | ||||
−0.975425 | + | 0.220333i | \(0.929285\pi\) | |||||||
\(770\) | −33692.0 | −1.57685 | ||||||||
\(771\) | − | 21440.2i | − | 1.00149i | ||||||
\(772\) | 41454.2i | 1.93260i | ||||||||
\(773\) | −35322.7 | −1.64356 | −0.821779 | − | 0.569807i | \(-0.807018\pi\) | ||||
−0.821779 | + | 0.569807i | \(0.807018\pi\) | |||||||
\(774\) | 11548.5 | 0.536308 | ||||||||
\(775\) | 25495.4i | 1.18171i | ||||||||
\(776\) | −4488.03 | −0.207617 | ||||||||
\(777\) | −9444.77 | + | 4113.98i | −0.436074 | + | 0.189946i | ||||
\(778\) | 31035.9 | 1.43019 | ||||||||
\(779\) | − | 11131.0i | − | 0.511950i | ||||||
\(780\) | 16779.3 | 0.770251 | ||||||||
\(781\) | −37680.6 | −1.72640 | ||||||||
\(782\) | 26069.7i | 1.19213i | ||||||||
\(783\) | − | 14481.4i | − | 0.660950i | ||||||
\(784\) | −16751.1 | −0.763079 | ||||||||
\(785\) | 8678.62i | 0.394590i | ||||||||
\(786\) | 14600.5 | 0.662572 | ||||||||
\(787\) | −7480.97 | −0.338841 | −0.169420 | − | 0.985544i | \(-0.554190\pi\) | ||||
−0.169420 | + | 0.985544i | \(0.554190\pi\) | |||||||
\(788\) | 35847.7 | 1.62059 | ||||||||
\(789\) | −9956.93 | −0.449273 | ||||||||
\(790\) | 25847.4i | 1.16406i | ||||||||
\(791\) | 23230.5i | 1.04422i | ||||||||
\(792\) | − | 76520.8i | − | 3.43314i | ||||||
\(793\) | −30029.0 | −1.34472 | ||||||||
\(794\) | 37022.9i | 1.65478i | ||||||||
\(795\) | − | 4102.37i | − | 0.183014i | ||||||
\(796\) | 21643.0i | 0.963714i | ||||||||
\(797\) | − | 26995.5i | − | 1.19979i | −0.800080 | − | 0.599893i | \(-0.795210\pi\) | ||
0.800080 | − | 0.599893i | \(-0.204790\pi\) | |||||||
\(798\) | −20891.2 | −0.926744 | ||||||||
\(799\) | − | 6761.51i | − | 0.299380i | ||||||
\(800\) | − | 46118.7i | − | 2.03818i | ||||||
\(801\) | − | 15604.1i | − | 0.688318i | ||||||
\(802\) | −7577.49 | −0.333629 | ||||||||
\(803\) | 15971.5 | 0.701893 | ||||||||
\(804\) | 28306.9 | 1.24168 | ||||||||
\(805\) | 7765.51 | 0.339998 | ||||||||
\(806\) | − | 72456.8i | − | 3.16648i | ||||||
\(807\) | 17190.4 | 0.749851 | ||||||||
\(808\) | − | 14088.7i | − | 0.613415i | ||||||
\(809\) | 16765.1i | 0.728592i | 0.931283 | + | 0.364296i | \(0.118690\pi\) | ||||
−0.931283 | + | 0.364296i | \(0.881310\pi\) | |||||||
\(810\) | −5478.07 | −0.237629 | ||||||||
\(811\) | 37839.3 | 1.63837 | 0.819186 | − | 0.573528i | \(-0.194426\pi\) | ||||
0.819186 | + | 0.573528i | \(0.194426\pi\) | |||||||
\(812\) | − | 38332.2i | − | 1.65665i | ||||||
\(813\) | 8695.27 | 0.375100 | ||||||||
\(814\) | 27487.7 | + | 63105.7i | 1.18359 | + | 2.71726i | ||||
\(815\) | −26568.5 | −1.14191 | ||||||||
\(816\) | 41098.2i | 1.76314i | ||||||||
\(817\) | −9490.28 | −0.406393 | ||||||||
\(818\) | 49332.4 | 2.10864 | ||||||||
\(819\) | 12918.7i | 0.551179i | ||||||||
\(820\) | 18829.4i | 0.801892i | ||||||||
\(821\) | −9497.30 | −0.403725 | −0.201862 | − | 0.979414i | \(-0.564699\pi\) | ||||
−0.201862 | + | 0.979414i | \(0.564699\pi\) | |||||||
\(822\) | − | 19914.7i | − | 0.845019i | ||||||
\(823\) | −14347.2 | −0.607669 | −0.303835 | − | 0.952725i | \(-0.598267\pi\) | ||||
−0.303835 | + | 0.952725i | \(0.598267\pi\) | |||||||
\(824\) | 42274.3 | 1.78725 | ||||||||
\(825\) | 12620.3 | 0.532584 | ||||||||
\(826\) | −3519.30 | −0.148247 | ||||||||
\(827\) | 38052.7i | 1.60003i | 0.599982 | + | 0.800014i | \(0.295175\pi\) | ||||
−0.599982 | + | 0.800014i | \(0.704825\pi\) | |||||||
\(828\) | 28393.4i | 1.19171i | ||||||||
\(829\) | 31374.8i | 1.31446i | 0.753688 | + | 0.657232i | \(0.228273\pi\) | ||||
−0.753688 | + | 0.657232i | \(0.771727\pi\) | |||||||
\(830\) | 13529.5 | 0.565802 | ||||||||
\(831\) | 2121.58i | 0.0885641i | ||||||||
\(832\) | 60086.0i | 2.50374i | ||||||||
\(833\) | − | 5390.08i | − | 0.224196i | ||||||
\(834\) | − | 23362.1i | − | 0.969979i | ||||||
\(835\) | −2728.15 | −0.113068 | ||||||||
\(836\) | 101234.i | 4.18811i | ||||||||
\(837\) | − | 41812.5i | − | 1.72670i | ||||||
\(838\) | 54363.2i | 2.24099i | ||||||||
\(839\) | 4964.39 | 0.204279 | 0.102139 | − | 0.994770i | \(-0.467431\pi\) | ||||
0.102139 | + | 0.994770i | \(0.467431\pi\) | |||||||
\(840\) | 21951.9 | 0.901681 | ||||||||
\(841\) | 11924.7 | 0.488939 | ||||||||
\(842\) | −69059.3 | −2.82653 | ||||||||
\(843\) | 15253.2i | 0.623190i | ||||||||
\(844\) | −34885.8 | −1.42277 | ||||||||
\(845\) | − | 3128.86i | − | 0.127380i | ||||||
\(846\) | − | 10154.0i | − | 0.412651i | ||||||
\(847\) | 30589.9 | 1.24095 | ||||||||
\(848\) | 45808.8 | 1.85505 | ||||||||
\(849\) | − | 9000.69i | − | 0.363843i | ||||||
\(850\) | 29250.7 | 1.18034 | ||||||||
\(851\) | −6335.51 | − | 14544.9i | −0.255204 | − | 0.585891i | ||||
\(852\) | 39523.7 | 1.58927 | ||||||||
\(853\) | − | 1052.83i | − | 0.0422606i | −0.999777 | − | 0.0211303i | \(-0.993274\pi\) | ||
0.999777 | − | 0.0211303i | \(-0.00672648\pi\) | |||||||
\(854\) | −63246.2 | −2.53424 | ||||||||
\(855\) | 10931.2 | 0.437238 | ||||||||
\(856\) | 68890.2i | 2.75072i | ||||||||
\(857\) | − | 17715.6i | − | 0.706128i | −0.935599 | − | 0.353064i | \(-0.885140\pi\) | ||
0.935599 | − | 0.353064i | \(-0.114860\pi\) | |||||||
\(858\) | −35866.2 | −1.42710 | ||||||||
\(859\) | − | 24512.7i | − | 0.973648i | −0.873500 | − | 0.486824i | \(-0.838155\pi\) | ||
0.873500 | − | 0.486824i | \(-0.161845\pi\) | |||||||
\(860\) | 16053.9 | 0.636552 | ||||||||
\(861\) | 6023.81 | 0.238433 | ||||||||
\(862\) | −62659.6 | −2.47586 | ||||||||
\(863\) | −86.4617 | −0.00341042 | −0.00170521 | − | 0.999999i | \(-0.500543\pi\) | ||||
−0.00170521 | + | 0.999999i | \(0.500543\pi\) | |||||||
\(864\) | 75634.6i | 2.97817i | ||||||||
\(865\) | − | 6612.41i | − | 0.259918i | ||||||
\(866\) | − | 36996.7i | − | 1.45173i | ||||||
\(867\) | 607.030 | 0.0237783 | ||||||||
\(868\) | − | 110677.i | − | 4.32792i | ||||||
\(869\) | − | 40069.7i | − | 1.56418i | ||||||
\(870\) | − | 11491.3i | − | 0.447807i | ||||||
\(871\) | 19834.1i | 0.771588i | ||||||||
\(872\) | −72444.7 | −2.81340 | ||||||||
\(873\) | − | 1209.45i | − | 0.0468886i | ||||||
\(874\) | − | 32172.4i | − | 1.24513i | ||||||
\(875\) | − | 22483.5i | − | 0.868663i | ||||||
\(876\) | −16752.7 | −0.646142 | ||||||||
\(877\) | −3881.39 | −0.149447 | −0.0747236 | − | 0.997204i | \(-0.523807\pi\) | ||||
−0.0747236 | + | 0.997204i | \(0.523807\pi\) | |||||||
\(878\) | −1374.07 | −0.0528162 | ||||||||
\(879\) | 23415.8 | 0.898517 | ||||||||
\(880\) | − | 81796.4i | − | 3.13336i | ||||||
\(881\) | 48985.9 | 1.87330 | 0.936649 | − | 0.350270i | \(-0.113910\pi\) | ||||
0.936649 | + | 0.350270i | \(0.113910\pi\) | |||||||
\(882\) | − | 8094.51i | − | 0.309021i | ||||||
\(883\) | 11751.2i | 0.447858i | 0.974605 | + | 0.223929i | \(0.0718883\pi\) | ||||
−0.974605 | + | 0.223929i | \(0.928112\pi\) | |||||||
\(884\) | −60289.3 | −2.29383 | ||||||||
\(885\) | −765.156 | −0.0290626 | ||||||||
\(886\) | 29416.4i | 1.11542i | ||||||||
\(887\) | 11678.4 | 0.442076 | 0.221038 | − | 0.975265i | \(-0.429056\pi\) | ||||
0.221038 | + | 0.975265i | \(0.429056\pi\) | |||||||
\(888\) | −17909.5 | − | 41116.2i | −0.676805 | − | 1.55379i | ||||
\(889\) | −21305.5 | −0.803783 | ||||||||
\(890\) | − | 29909.4i | − | 1.12648i | ||||||
\(891\) | 8492.30 | 0.319307 | ||||||||
\(892\) | 39229.7 | 1.47254 | ||||||||
\(893\) | 8344.33i | 0.312690i | ||||||||
\(894\) | − | 459.403i | − | 0.0171865i | ||||||
\(895\) | 13300.5 | 0.496744 | ||||||||
\(896\) | 50706.2i | 1.89060i | ||||||||
\(897\) | 8266.63 | 0.307709 | ||||||||
\(898\) | 64881.8 | 2.41106 | ||||||||
\(899\) | −35988.3 | −1.33512 | ||||||||
\(900\) | 31858.0 | 1.17993 | ||||||||
\(901\) | 14740.1i | 0.545021i | ||||||||
\(902\) | − | 40248.4i | − | 1.48572i | ||||||
\(903\) | − | 5135.90i | − | 0.189271i | ||||||
\(904\) | −101130. | −3.72072 | ||||||||
\(905\) | 24245.4i | 0.890546i | ||||||||
\(906\) | 28991.7i | 1.06312i | ||||||||
\(907\) | − | 43196.8i | − | 1.58139i | −0.612207 | − | 0.790697i | \(-0.709718\pi\) | ||
0.612207 | − | 0.790697i | \(-0.290282\pi\) | |||||||
\(908\) | − | 11922.7i | − | 0.435757i | ||||||
\(909\) | 3796.68 | 0.138535 | ||||||||
\(910\) | 24762.1i | 0.902040i | ||||||||
\(911\) | − | 1508.36i | − | 0.0548563i | −0.999624 | − | 0.0274282i | \(-0.991268\pi\) | ||
0.999624 | − | 0.0274282i | \(-0.00873175\pi\) | |||||||
\(912\) | − | 50719.0i | − | 1.84153i | ||||||
\(913\) | −20973.9 | −0.760280 | ||||||||
\(914\) | 12063.2 | 0.436561 | ||||||||
\(915\) | −13750.8 | −0.496816 | ||||||||
\(916\) | 56708.4 | 2.04552 | ||||||||
\(917\) | 15626.7i | 0.562747i | ||||||||
\(918\) | −47971.2 | −1.72471 | ||||||||
\(919\) | − | 13881.1i | − | 0.498253i | −0.968471 | − | 0.249127i | \(-0.919856\pi\) | ||
0.968471 | − | 0.249127i | \(-0.0801436\pi\) | |||||||
\(920\) | 33805.8i | 1.21146i | ||||||||
\(921\) | 29853.2 | 1.06807 | ||||||||
\(922\) | −48629.8 | −1.73703 | ||||||||
\(923\) | 27693.5i | 0.987587i | ||||||||
\(924\) | −54785.5 | −1.95055 | ||||||||
\(925\) | −16319.7 | + | 7108.58i | −0.580096 | + | 0.252680i | ||||
\(926\) | 60947.5 | 2.16292 | ||||||||
\(927\) | 11392.2i | 0.403635i | ||||||||
\(928\) | 65099.2 | 2.30279 | ||||||||
\(929\) | −10665.2 | −0.376657 | −0.188329 | − | 0.982106i | \(-0.560307\pi\) | ||||
−0.188329 | + | 0.982106i | \(0.560307\pi\) | |||||||
\(930\) | − | 33179.1i | − | 1.16988i | ||||||
\(931\) | 6651.86i | 0.234163i | ||||||||
\(932\) | 68124.5 | 2.39431 | ||||||||
\(933\) | − | 10200.2i | − | 0.357921i | ||||||
\(934\) | 39587.7 | 1.38688 | ||||||||
\(935\) | 26320.0 | 0.920595 | ||||||||
\(936\) | −56239.3 | −1.96393 | ||||||||
\(937\) | 47774.6 | 1.66567 | 0.832833 | − | 0.553525i | \(-0.186718\pi\) | ||||
0.832833 | + | 0.553525i | \(0.186718\pi\) | |||||||
\(938\) | 41774.0i | 1.45412i | ||||||||
\(939\) | − | 21367.0i | − | 0.742585i | ||||||
\(940\) | − | 14115.4i | − | 0.489782i | ||||||
\(941\) | 8817.39 | 0.305461 | 0.152731 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152731 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(942\) | 19458.2i | 0.673016i | ||||||||
\(943\) | 9276.64i | 0.320349i | ||||||||
\(944\) | − | 8544.05i | − | 0.294582i | ||||||
\(945\) | 14289.4i | 0.491889i | ||||||||
\(946\) | −34315.7 | −1.17939 | ||||||||
\(947\) | − | 52689.9i | − | 1.80802i | −0.427516 | − | 0.904008i | \(-0.640611\pi\) | ||
0.427516 | − | 0.904008i | \(-0.359389\pi\) | |||||||
\(948\) | 42029.6i | 1.43994i | ||||||||
\(949\) | − | 11738.3i | − | 0.401519i | ||||||
\(950\) | −36098.1 | −1.23282 | ||||||||
\(951\) | 5730.65 | 0.195404 | ||||||||
\(952\) | −78874.7 | −2.68523 | ||||||||
\(953\) | 35605.1 | 1.21025 | 0.605123 | − | 0.796132i | \(-0.293124\pi\) | ||||
0.605123 | + | 0.796132i | \(0.293124\pi\) | |||||||
\(954\) | 22135.8i | 0.751230i | ||||||||
\(955\) | 20742.9 | 0.702853 | ||||||||
\(956\) | 43569.1i | 1.47398i | ||||||||
\(957\) | 17814.3i | 0.601728i | ||||||||
\(958\) | −77112.6 | −2.60062 | ||||||||
\(959\) | 21314.5 | 0.717706 | ||||||||
\(960\) | 27514.3i | 0.925023i | ||||||||
\(961\) | −74118.7 | −2.48796 | ||||||||
\(962\) | 46379.8 | − | 20202.2i | 1.55441 | − | 0.677075i | ||||
\(963\) | −18564.8 | −0.621227 | ||||||||
\(964\) | − | 119918.i | − | 4.00655i | ||||||
\(965\) | −13300.7 | −0.443695 | ||||||||
\(966\) | 17410.9 | 0.579903 | ||||||||
\(967\) | 40228.2i | 1.33780i | 0.743352 | + | 0.668900i | \(0.233235\pi\) | ||||
−0.743352 | + | 0.668900i | \(0.766765\pi\) | |||||||
\(968\) | 133168.i | 4.42167i | ||||||||
\(969\) | 16320.1 | 0.541050 | ||||||||
\(970\) | − | 2318.24i | − | 0.0767362i | ||||||
\(971\) | −51053.3 | −1.68731 | −0.843656 | − | 0.536884i | \(-0.819601\pi\) | ||||
−0.843656 | + | 0.536884i | \(0.819601\pi\) | |||||||
\(972\) | −82864.4 | −2.73444 | ||||||||
\(973\) | 25004.1 | 0.823839 | ||||||||
\(974\) | −63611.6 | −2.09266 | ||||||||
\(975\) | − | 9275.34i | − | 0.304665i | ||||||
\(976\) | − | 153547.i | − | 5.03578i | ||||||
\(977\) | − | 11131.9i | − | 0.364526i | −0.983250 | − | 0.182263i | \(-0.941658\pi\) | ||
0.983250 | − | 0.182263i | \(-0.0583423\pi\) | |||||||
\(978\) | −59568.8 | −1.94765 | ||||||||
\(979\) | 46366.6i | 1.51367i | ||||||||
\(980\) | − | 11252.4i | − | 0.366781i | ||||||
\(981\) | − | 19522.7i | − | 0.635383i | ||||||
\(982\) | 28614.9i | 0.929877i | ||||||||
\(983\) | −23333.3 | −0.757086 | −0.378543 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378543 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(984\) | 26223.6i | 0.849572i | ||||||||
\(985\) | 11501.9i | 0.372060i | ||||||||
\(986\) | 41289.1i | 1.33358i | ||||||||
\(987\) | −4515.74 | −0.145631 | ||||||||
\(988\) | 74402.6 | 2.39581 | ||||||||
\(989\) | 7909.26 | 0.254297 | ||||||||
\(990\) | 39525.8 | 1.26890 | ||||||||
\(991\) | 41509.7i | 1.33057i | 0.746587 | + | 0.665287i | \(0.231691\pi\) | ||||
−0.746587 | + | 0.665287i | \(0.768309\pi\) | |||||||
\(992\) | 187962. | 6.01594 | ||||||||
\(993\) | 29818.7i | 0.952938i | ||||||||
\(994\) | 58327.1i | 1.86119i | ||||||||
\(995\) | −6944.24 | −0.221253 | ||||||||
\(996\) | 21999.8 | 0.699891 | ||||||||
\(997\) | − | 6314.58i | − | 0.200587i | −0.994958 | − | 0.100293i | \(-0.968022\pi\) | ||
0.994958 | − | 0.100293i | \(-0.0319781\pi\) | |||||||
\(998\) | 34138.9 | 1.08281 | ||||||||
\(999\) | 26764.3 | − | 11658.1i | 0.847633 | − | 0.369214i |
(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 | 37.4.b.a.36.1 | ✓ | 8 | |
3.2 | odd | 2 | 333.4.c.d.73.8 | 8 | |||
4.3 | odd | 2 | 592.4.g.c.369.3 | 8 | |||
37.6 | odd | 4 | 1369.4.a.b.1.1 | 4 | |||
37.31 | odd | 4 | 1369.4.a.a.1.4 | 4 | |||
37.36 | even | 2 | inner | 37.4.b.a.36.8 | yes | 8 | |
111.110 | odd | 2 | 333.4.c.d.73.1 | 8 | |||
148.147 | odd | 2 | 592.4.g.c.369.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.4.b.a.36.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
37.4.b.a.36.8 | yes | 8 | 37.36 | even | 2 | inner | |
333.4.c.d.73.1 | 8 | 111.110 | odd | 2 | |||
333.4.c.d.73.8 | 8 | 3.2 | odd | 2 | |||
592.4.g.c.369.3 | 8 | 4.3 | odd | 2 | |||
592.4.g.c.369.4 | 8 | 148.147 | odd | 2 | |||
1369.4.a.a.1.4 | 4 | 37.31 | odd | 4 | |||
1369.4.a.b.1.1 | 4 | 37.6 | odd | 4 |