Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(12,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.12");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 12.15 | ||
Character | \(\chi\) | \(=\) | 143.12 |
Dual form | 143.4.b.a.12.22 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.26989i | − | 0.448975i | −0.974477 | − | 0.224487i | \(-0.927929\pi\) | ||
0.974477 | − | 0.224487i | \(-0.0720707\pi\) | |||||||
\(3\) | 3.96847 | 0.763732 | 0.381866 | − | 0.924218i | \(-0.375282\pi\) | ||||
0.381866 | + | 0.924218i | \(0.375282\pi\) | |||||||
\(4\) | 6.38737 | 0.798422 | ||||||||
\(5\) | 4.99906i | 0.447130i | 0.974689 | + | 0.223565i | \(0.0717695\pi\) | ||||
−0.974689 | + | 0.223565i | \(0.928231\pi\) | |||||||
\(6\) | − | 5.03953i | − | 0.342896i | ||||||
\(7\) | − | 32.3730i | − | 1.74798i | −0.485948 | − | 0.873988i | \(-0.661526\pi\) | ||
0.485948 | − | 0.873988i | \(-0.338474\pi\) | |||||||
\(8\) | − | 18.2704i | − | 0.807446i | ||||||
\(9\) | −11.2513 | −0.416714 | ||||||||
\(10\) | 6.34827 | 0.200750 | ||||||||
\(11\) | 11.0000i | 0.301511i | ||||||||
\(12\) | 25.3481 | 0.609780 | ||||||||
\(13\) | 41.9782 | − | 20.8525i | 0.895590 | − | 0.444881i | ||||
\(14\) | −41.1102 | −0.784797 | ||||||||
\(15\) | 19.8386i | 0.341487i | ||||||||
\(16\) | 27.8975 | 0.435899 | ||||||||
\(17\) | 65.4417 | 0.933644 | 0.466822 | − | 0.884351i | \(-0.345399\pi\) | ||||
0.466822 | + | 0.884351i | \(0.345399\pi\) | |||||||
\(18\) | 14.2879i | 0.187094i | ||||||||
\(19\) | 66.3251i | 0.800843i | 0.916331 | + | 0.400421i | \(0.131136\pi\) | ||||
−0.916331 | + | 0.400421i | \(0.868864\pi\) | |||||||
\(20\) | 31.9309i | 0.356998i | ||||||||
\(21\) | − | 128.471i | − | 1.33498i | ||||||
\(22\) | 13.9688 | 0.135371 | ||||||||
\(23\) | −25.5111 | −0.231279 | −0.115640 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115640 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(24\) | − | 72.5055i | − | 0.616672i | ||||||
\(25\) | 100.009 | 0.800075 | ||||||||
\(26\) | −26.4805 | − | 53.3078i | −0.199740 | − | 0.402097i | ||||
\(27\) | −151.799 | −1.08199 | ||||||||
\(28\) | − | 206.778i | − | 1.39562i | ||||||
\(29\) | −195.053 | −1.24898 | −0.624490 | − | 0.781032i | \(-0.714693\pi\) | ||||
−0.624490 | + | 0.781032i | \(0.714693\pi\) | |||||||
\(30\) | 25.1929 | 0.153319 | ||||||||
\(31\) | 23.5247i | 0.136296i | 0.997675 | + | 0.0681478i | \(0.0217089\pi\) | ||||
−0.997675 | + | 0.0681478i | \(0.978291\pi\) | |||||||
\(32\) | − | 181.590i | − | 1.00315i | ||||||
\(33\) | 43.6531i | 0.230274i | ||||||||
\(34\) | − | 83.1040i | − | 0.419183i | ||||||
\(35\) | 161.834 | 0.781572 | ||||||||
\(36\) | −71.8661 | −0.332713 | ||||||||
\(37\) | 95.7674i | 0.425515i | 0.977105 | + | 0.212758i | \(0.0682445\pi\) | ||||
−0.977105 | + | 0.212758i | \(0.931756\pi\) | |||||||
\(38\) | 84.2257 | 0.359558 | ||||||||
\(39\) | 166.589 | − | 82.7526i | 0.683990 | − | 0.339770i | ||||
\(40\) | 91.3350 | 0.361033 | ||||||||
\(41\) | 245.497i | 0.935126i | 0.883960 | + | 0.467563i | \(0.154868\pi\) | ||||
−0.883960 | + | 0.467563i | \(0.845132\pi\) | |||||||
\(42\) | −163.144 | −0.599374 | ||||||||
\(43\) | 397.276 | 1.40893 | 0.704465 | − | 0.709739i | \(-0.251187\pi\) | ||||
0.704465 | + | 0.709739i | \(0.251187\pi\) | |||||||
\(44\) | 70.2611i | 0.240733i | ||||||||
\(45\) | − | 56.2458i | − | 0.186325i | ||||||
\(46\) | 32.3963i | 0.103839i | ||||||||
\(47\) | 139.763i | 0.433755i | 0.976199 | + | 0.216878i | \(0.0695873\pi\) | ||||
−0.976199 | + | 0.216878i | \(0.930413\pi\) | |||||||
\(48\) | 110.710 | 0.332910 | ||||||||
\(49\) | −705.008 | −2.05542 | ||||||||
\(50\) | − | 127.001i | − | 0.359213i | ||||||
\(51\) | 259.703 | 0.713054 | ||||||||
\(52\) | 268.131 | − | 133.193i | 0.715058 | − | 0.355203i | ||||
\(53\) | −224.488 | −0.581808 | −0.290904 | − | 0.956752i | \(-0.593956\pi\) | ||||
−0.290904 | + | 0.956752i | \(0.593956\pi\) | |||||||
\(54\) | 192.768i | 0.485786i | ||||||||
\(55\) | −54.9897 | −0.134815 | ||||||||
\(56\) | −591.467 | −1.41140 | ||||||||
\(57\) | 263.209i | 0.611629i | ||||||||
\(58\) | 247.696i | 0.560761i | ||||||||
\(59\) | 584.190i | 1.28907i | 0.764576 | + | 0.644534i | \(0.222949\pi\) | ||||
−0.764576 | + | 0.644534i | \(0.777051\pi\) | |||||||
\(60\) | 126.717i | 0.272651i | ||||||||
\(61\) | −732.958 | −1.53845 | −0.769226 | − | 0.638977i | \(-0.779358\pi\) | ||||
−0.769226 | + | 0.638977i | \(0.779358\pi\) | |||||||
\(62\) | 29.8738 | 0.0611933 | ||||||||
\(63\) | 364.237i | 0.728405i | ||||||||
\(64\) | −7.41971 | −0.0144916 | ||||||||
\(65\) | 104.243 | + | 209.852i | 0.198920 | + | 0.400445i | ||||
\(66\) | 55.4348 | 0.103387 | ||||||||
\(67\) | − | 211.980i | − | 0.386529i | −0.981147 | − | 0.193264i | \(-0.938092\pi\) | ||
0.981147 | − | 0.193264i | \(-0.0619075\pi\) | |||||||
\(68\) | 418.001 | 0.745442 | ||||||||
\(69\) | −101.240 | −0.176635 | ||||||||
\(70\) | − | 205.512i | − | 0.350906i | ||||||
\(71\) | − | 59.0998i | − | 0.0987867i | −0.998779 | − | 0.0493934i | \(-0.984271\pi\) | ||
0.998779 | − | 0.0493934i | \(-0.0157288\pi\) | |||||||
\(72\) | 205.565i | 0.336474i | ||||||||
\(73\) | − | 19.3785i | − | 0.0310696i | −0.999879 | − | 0.0155348i | \(-0.995055\pi\) | ||
0.999879 | − | 0.0155348i | \(-0.00494509\pi\) | |||||||
\(74\) | 121.614 | 0.191046 | ||||||||
\(75\) | 396.884 | 0.611043 | ||||||||
\(76\) | 423.643i | 0.639410i | ||||||||
\(77\) | 356.102 | 0.527034 | ||||||||
\(78\) | −105.087 | − | 211.550i | −0.152548 | − | 0.307094i | ||||
\(79\) | 282.957 | 0.402976 | 0.201488 | − | 0.979491i | \(-0.435422\pi\) | ||||
0.201488 | + | 0.979491i | \(0.435422\pi\) | |||||||
\(80\) | 139.462i | 0.194903i | ||||||||
\(81\) | −298.625 | −0.409636 | ||||||||
\(82\) | 311.754 | 0.419848 | ||||||||
\(83\) | 1356.44i | 1.79384i | 0.442190 | + | 0.896921i | \(0.354202\pi\) | ||||
−0.442190 | + | 0.896921i | \(0.645798\pi\) | |||||||
\(84\) | − | 820.592i | − | 1.06588i | ||||||
\(85\) | 327.148i | 0.417460i | ||||||||
\(86\) | − | 504.497i | − | 0.632574i | ||||||
\(87\) | −774.062 | −0.953887 | ||||||||
\(88\) | 200.975 | 0.243454 | ||||||||
\(89\) | 856.502i | 1.02010i | 0.860144 | + | 0.510051i | \(0.170373\pi\) | ||||
−0.860144 | + | 0.510051i | \(0.829627\pi\) | |||||||
\(90\) | −71.4261 | −0.0836553 | ||||||||
\(91\) | −675.058 | − | 1358.96i | −0.777641 | − | 1.56547i | ||||
\(92\) | −162.949 | −0.184658 | ||||||||
\(93\) | 93.3570i | 0.104093i | ||||||||
\(94\) | 177.484 | 0.194745 | ||||||||
\(95\) | −331.563 | −0.358081 | ||||||||
\(96\) | − | 720.635i | − | 0.766140i | ||||||
\(97\) | − | 1013.29i | − | 1.06066i | −0.847792 | − | 0.530330i | \(-0.822068\pi\) | ||
0.847792 | − | 0.530330i | \(-0.177932\pi\) | |||||||
\(98\) | 895.284i | 0.922830i | ||||||||
\(99\) | − | 123.764i | − | 0.125644i | ||||||
\(100\) | 638.797 | 0.638797 | ||||||||
\(101\) | 45.1645 | 0.0444954 | 0.0222477 | − | 0.999752i | \(-0.492918\pi\) | ||||
0.0222477 | + | 0.999752i | \(0.492918\pi\) | |||||||
\(102\) | − | 329.795i | − | 0.320143i | ||||||
\(103\) | −683.159 | −0.653530 | −0.326765 | − | 0.945106i | \(-0.605959\pi\) | ||||
−0.326765 | + | 0.945106i | \(0.605959\pi\) | |||||||
\(104\) | −380.984 | − | 766.960i | −0.359217 | − | 0.723140i | ||||
\(105\) | 642.235 | 0.596911 | ||||||||
\(106\) | 285.076i | 0.261217i | ||||||||
\(107\) | 1202.00 | 1.08600 | 0.542999 | − | 0.839733i | \(-0.317289\pi\) | ||||
0.542999 | + | 0.839733i | \(0.317289\pi\) | |||||||
\(108\) | −969.596 | −0.863884 | ||||||||
\(109\) | − | 981.385i | − | 0.862382i | −0.902261 | − | 0.431191i | \(-0.858094\pi\) | ||
0.902261 | − | 0.431191i | \(-0.141906\pi\) | |||||||
\(110\) | 69.8310i | 0.0605284i | ||||||||
\(111\) | 380.050i | 0.324980i | ||||||||
\(112\) | − | 903.125i | − | 0.761940i | ||||||
\(113\) | 252.546 | 0.210244 | 0.105122 | − | 0.994459i | \(-0.466477\pi\) | ||||
0.105122 | + | 0.994459i | \(0.466477\pi\) | |||||||
\(114\) | 334.247 | 0.274606 | ||||||||
\(115\) | − | 127.532i | − | 0.103412i | ||||||
\(116\) | −1245.88 | −0.997213 | ||||||||
\(117\) | −472.308 | + | 234.617i | −0.373204 | + | 0.185388i | ||||
\(118\) | 741.858 | 0.578759 | ||||||||
\(119\) | − | 2118.54i | − | 1.63199i | ||||||
\(120\) | 362.460 | 0.275733 | ||||||||
\(121\) | −121.000 | −0.0909091 | ||||||||
\(122\) | 930.777i | 0.690726i | ||||||||
\(123\) | 974.246i | 0.714185i | ||||||||
\(124\) | 150.261i | 0.108821i | ||||||||
\(125\) | 1124.84i | 0.804867i | ||||||||
\(126\) | 462.541 | 0.327035 | ||||||||
\(127\) | −1513.45 | −1.05745 | −0.528727 | − | 0.848792i | \(-0.677330\pi\) | ||||
−0.528727 | + | 0.848792i | \(0.677330\pi\) | |||||||
\(128\) | − | 1443.30i | − | 0.996647i | ||||||
\(129\) | 1576.58 | 1.07604 | ||||||||
\(130\) | 266.489 | − | 132.378i | 0.179790 | − | 0.0893099i | ||||
\(131\) | 2795.84 | 1.86468 | 0.932341 | − | 0.361579i | \(-0.117762\pi\) | ||||
0.932341 | + | 0.361579i | \(0.117762\pi\) | |||||||
\(132\) | 278.829i | 0.183856i | ||||||||
\(133\) | 2147.14 | 1.39985 | ||||||||
\(134\) | −269.191 | −0.173542 | ||||||||
\(135\) | − | 758.853i | − | 0.483790i | ||||||
\(136\) | − | 1195.65i | − | 0.753867i | ||||||
\(137\) | − | 1651.30i | − | 1.02978i | −0.857255 | − | 0.514892i | \(-0.827832\pi\) | ||
0.857255 | − | 0.514892i | \(-0.172168\pi\) | |||||||
\(138\) | 128.564i | 0.0793049i | ||||||||
\(139\) | −1429.39 | −0.872223 | −0.436112 | − | 0.899893i | \(-0.643645\pi\) | ||||
−0.436112 | + | 0.899893i | \(0.643645\pi\) | |||||||
\(140\) | 1033.70 | 0.624024 | ||||||||
\(141\) | 554.644i | 0.331273i | ||||||||
\(142\) | −75.0504 | −0.0443527 | ||||||||
\(143\) | 229.378 | + | 461.761i | 0.134137 | + | 0.270030i | ||||
\(144\) | −313.883 | −0.181645 | ||||||||
\(145\) | − | 975.083i | − | 0.558457i | ||||||
\(146\) | −24.6086 | −0.0139495 | ||||||||
\(147\) | −2797.80 | −1.56979 | ||||||||
\(148\) | 611.702i | 0.339741i | ||||||||
\(149\) | 514.352i | 0.282801i | 0.989952 | + | 0.141401i | \(0.0451605\pi\) | ||||
−0.989952 | + | 0.141401i | \(0.954839\pi\) | |||||||
\(150\) | − | 504.000i | − | 0.274343i | ||||||
\(151\) | 1547.44i | 0.833963i | 0.908915 | + | 0.416982i | \(0.136912\pi\) | ||||
−0.908915 | + | 0.416982i | \(0.863088\pi\) | |||||||
\(152\) | 1211.79 | 0.646637 | ||||||||
\(153\) | −736.303 | −0.389062 | ||||||||
\(154\) | − | 452.212i | − | 0.236625i | ||||||
\(155\) | −117.602 | −0.0609418 | ||||||||
\(156\) | 1064.07 | − | 528.572i | 0.546113 | − | 0.271280i | ||||
\(157\) | −1704.15 | −0.866278 | −0.433139 | − | 0.901327i | \(-0.642594\pi\) | ||||
−0.433139 | + | 0.901327i | \(0.642594\pi\) | |||||||
\(158\) | − | 359.325i | − | 0.180926i | ||||||
\(159\) | −890.874 | −0.444346 | ||||||||
\(160\) | 907.781 | 0.448540 | ||||||||
\(161\) | 825.869i | 0.404271i | ||||||||
\(162\) | 379.221i | 0.183916i | ||||||||
\(163\) | 3437.52i | 1.65182i | 0.563799 | + | 0.825912i | \(0.309339\pi\) | ||||
−0.563799 | + | 0.825912i | \(0.690661\pi\) | |||||||
\(164\) | 1568.08i | 0.746625i | ||||||||
\(165\) | −218.225 | −0.102962 | ||||||||
\(166\) | 1722.54 | 0.805390 | ||||||||
\(167\) | − | 2060.63i | − | 0.954828i | −0.878679 | − | 0.477414i | \(-0.841574\pi\) | ||
0.878679 | − | 0.477414i | \(-0.158426\pi\) | |||||||
\(168\) | −2347.22 | −1.07793 | ||||||||
\(169\) | 1327.34 | − | 1750.70i | 0.604162 | − | 0.796862i | ||||
\(170\) | 415.442 | 0.187429 | ||||||||
\(171\) | − | 746.241i | − | 0.333722i | ||||||
\(172\) | 2537.55 | 1.12492 | ||||||||
\(173\) | −522.234 | −0.229507 | −0.114754 | − | 0.993394i | \(-0.536608\pi\) | ||||
−0.114754 | + | 0.993394i | \(0.536608\pi\) | |||||||
\(174\) | 982.975i | 0.428271i | ||||||||
\(175\) | − | 3237.60i | − | 1.39851i | ||||||
\(176\) | 306.873i | 0.131428i | ||||||||
\(177\) | 2318.34i | 0.984502i | ||||||||
\(178\) | 1087.67 | 0.458000 | ||||||||
\(179\) | −181.450 | −0.0757667 | −0.0378833 | − | 0.999282i | \(-0.512062\pi\) | ||||
−0.0378833 | + | 0.999282i | \(0.512062\pi\) | |||||||
\(180\) | − | 359.263i | − | 0.148766i | ||||||
\(181\) | 2845.40 | 1.16849 | 0.584246 | − | 0.811576i | \(-0.301390\pi\) | ||||
0.584246 | + | 0.811576i | \(0.301390\pi\) | |||||||
\(182\) | −1725.73 | + | 857.251i | −0.702856 | + | 0.349141i | ||||
\(183\) | −2908.72 | −1.17497 | ||||||||
\(184\) | 466.098i | 0.186746i | ||||||||
\(185\) | −478.747 | −0.190261 | ||||||||
\(186\) | 118.553 | 0.0467352 | ||||||||
\(187\) | 719.859i | 0.281504i | ||||||||
\(188\) | 892.717i | 0.346320i | ||||||||
\(189\) | 4914.18i | 1.89129i | ||||||||
\(190\) | 421.050i | 0.160769i | ||||||||
\(191\) | −4825.05 | −1.82790 | −0.913948 | − | 0.405831i | \(-0.866982\pi\) | ||||
−0.913948 | + | 0.405831i | \(0.866982\pi\) | |||||||
\(192\) | −29.4449 | −0.0110677 | ||||||||
\(193\) | − | 4662.94i | − | 1.73910i | −0.493847 | − | 0.869549i | \(-0.664410\pi\) | ||
0.493847 | − | 0.869549i | \(-0.335590\pi\) | |||||||
\(194\) | −1286.77 | −0.476209 | ||||||||
\(195\) | 413.686 | + | 832.790i | 0.151921 | + | 0.305833i | ||||
\(196\) | −4503.15 | −1.64109 | ||||||||
\(197\) | − | 415.981i | − | 0.150444i | −0.997167 | − | 0.0752218i | \(-0.976034\pi\) | ||
0.997167 | − | 0.0752218i | \(-0.0239665\pi\) | |||||||
\(198\) | −157.167 | −0.0564109 | ||||||||
\(199\) | 4372.09 | 1.55743 | 0.778717 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778717 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(200\) | − | 1827.21i | − | 0.646017i | ||||||
\(201\) | − | 841.234i | − | 0.295205i | ||||||
\(202\) | − | 57.3540i | − | 0.0199773i | ||||||
\(203\) | 6314.44i | 2.18319i | ||||||||
\(204\) | 1658.82 | 0.569318 | ||||||||
\(205\) | −1227.25 | −0.418123 | ||||||||
\(206\) | 867.538i | 0.293419i | ||||||||
\(207\) | 287.032 | 0.0963773 | ||||||||
\(208\) | 1171.09 | − | 581.734i | 0.390387 | − | 0.193923i | ||||
\(209\) | −729.576 | −0.241463 | ||||||||
\(210\) | − | 815.569i | − | 0.267998i | ||||||
\(211\) | −294.344 | −0.0960354 | −0.0480177 | − | 0.998846i | \(-0.515290\pi\) | ||||
−0.0480177 | + | 0.998846i | \(0.515290\pi\) | |||||||
\(212\) | −1433.89 | −0.464528 | ||||||||
\(213\) | − | 234.536i | − | 0.0754466i | ||||||
\(214\) | − | 1526.41i | − | 0.487586i | ||||||
\(215\) | 1986.01i | 0.629975i | ||||||||
\(216\) | 2773.43i | 0.873648i | ||||||||
\(217\) | 761.564 | 0.238241 | ||||||||
\(218\) | −1246.25 | −0.387188 | ||||||||
\(219\) | − | 76.9030i | − | 0.0237289i | ||||||
\(220\) | −351.240 | −0.107639 | ||||||||
\(221\) | 2747.13 | − | 1364.63i | 0.836162 | − | 0.415361i | ||||
\(222\) | 482.622 | 0.145908 | ||||||||
\(223\) | − | 1064.30i | − | 0.319601i | −0.987149 | − | 0.159800i | \(-0.948915\pi\) | ||
0.987149 | − | 0.159800i | \(-0.0510851\pi\) | |||||||
\(224\) | −5878.61 | −1.75349 | ||||||||
\(225\) | −1125.23 | −0.333402 | ||||||||
\(226\) | − | 320.707i | − | 0.0943942i | ||||||
\(227\) | − | 5384.86i | − | 1.57447i | −0.616650 | − | 0.787237i | \(-0.711511\pi\) | ||
0.616650 | − | 0.787237i | \(-0.288489\pi\) | |||||||
\(228\) | 1681.21i | 0.488338i | ||||||||
\(229\) | 732.853i | 0.211477i | 0.994394 | + | 0.105739i | \(0.0337207\pi\) | ||||
−0.994394 | + | 0.105739i | \(0.966279\pi\) | |||||||
\(230\) | −161.951 | −0.0464293 | ||||||||
\(231\) | 1413.18 | 0.402513 | ||||||||
\(232\) | 3563.70i | 1.00848i | ||||||||
\(233\) | 2754.99 | 0.774616 | 0.387308 | − | 0.921950i | \(-0.373405\pi\) | ||||
0.387308 | + | 0.921950i | \(0.373405\pi\) | |||||||
\(234\) | 297.939 | + | 599.781i | 0.0832345 | + | 0.167559i | ||||
\(235\) | −698.683 | −0.193945 | ||||||||
\(236\) | 3731.44i | 1.02922i | ||||||||
\(237\) | 1122.90 | 0.307766 | ||||||||
\(238\) | −2690.32 | −0.732721 | ||||||||
\(239\) | 2395.98i | 0.648464i | 0.945978 | + | 0.324232i | \(0.105106\pi\) | ||||
−0.945978 | + | 0.324232i | \(0.894894\pi\) | |||||||
\(240\) | 553.449i | 0.148854i | ||||||||
\(241\) | − | 3961.59i | − | 1.05887i | −0.848349 | − | 0.529437i | \(-0.822403\pi\) | ||
0.848349 | − | 0.529437i | \(-0.177597\pi\) | |||||||
\(242\) | 153.657i | 0.0408159i | ||||||||
\(243\) | 2913.49 | 0.769137 | ||||||||
\(244\) | −4681.67 | −1.22833 | ||||||||
\(245\) | − | 3524.38i | − | 0.919038i | ||||||
\(246\) | 1237.19 | 0.320651 | ||||||||
\(247\) | 1383.05 | + | 2784.21i | 0.356280 | + | 0.717227i | ||||
\(248\) | 429.806 | 0.110051 | ||||||||
\(249\) | 5383.00i | 1.37001i | ||||||||
\(250\) | 1428.42 | 0.361365 | ||||||||
\(251\) | −146.537 | −0.0368498 | −0.0184249 | − | 0.999830i | \(-0.505865\pi\) | ||||
−0.0184249 | + | 0.999830i | \(0.505865\pi\) | |||||||
\(252\) | 2326.52i | 0.581574i | ||||||||
\(253\) | − | 280.622i | − | 0.0697334i | ||||||
\(254\) | 1921.91i | 0.474770i | ||||||||
\(255\) | 1298.27i | 0.318828i | ||||||||
\(256\) | −1892.19 | −0.461961 | ||||||||
\(257\) | −3590.96 | −0.871586 | −0.435793 | − | 0.900047i | \(-0.643532\pi\) | ||||
−0.435793 | + | 0.900047i | \(0.643532\pi\) | |||||||
\(258\) | − | 2002.08i | − | 0.483117i | ||||||
\(259\) | 3100.27 | 0.743790 | ||||||||
\(260\) | 665.840 | + | 1340.40i | 0.158822 | + | 0.319724i | ||||
\(261\) | 2194.59 | 0.520467 | ||||||||
\(262\) | − | 3550.41i | − | 0.837195i | ||||||
\(263\) | −6675.46 | −1.56512 | −0.782559 | − | 0.622576i | \(-0.786086\pi\) | ||||
−0.782559 | + | 0.622576i | \(0.786086\pi\) | |||||||
\(264\) | 797.561 | 0.185934 | ||||||||
\(265\) | − | 1122.23i | − | 0.260144i | ||||||
\(266\) | − | 2726.63i | − | 0.628499i | ||||||
\(267\) | 3399.00i | 0.779084i | ||||||||
\(268\) | − | 1353.99i | − | 0.308613i | ||||||
\(269\) | 4613.40 | 1.04567 | 0.522833 | − | 0.852435i | \(-0.324875\pi\) | ||||
0.522833 | + | 0.852435i | \(0.324875\pi\) | |||||||
\(270\) | −963.661 | −0.217209 | ||||||||
\(271\) | − | 7795.95i | − | 1.74749i | −0.486383 | − | 0.873746i | \(-0.661684\pi\) | ||
0.486383 | − | 0.873746i | \(-0.338316\pi\) | |||||||
\(272\) | 1825.66 | 0.406975 | ||||||||
\(273\) | −2678.95 | − | 5392.98i | −0.593909 | − | 1.19560i | ||||
\(274\) | −2096.98 | −0.462347 | ||||||||
\(275\) | 1100.10i | 0.241232i | ||||||||
\(276\) | −646.657 | −0.141030 | ||||||||
\(277\) | 5527.75 | 1.19903 | 0.599513 | − | 0.800365i | \(-0.295361\pi\) | ||||
0.599513 | + | 0.800365i | \(0.295361\pi\) | |||||||
\(278\) | 1815.17i | 0.391606i | ||||||||
\(279\) | − | 264.683i | − | 0.0567962i | ||||||
\(280\) | − | 2956.78i | − | 0.631077i | ||||||
\(281\) | 2142.52i | 0.454846i | 0.973796 | + | 0.227423i | \(0.0730300\pi\) | ||||
−0.973796 | + | 0.227423i | \(0.926970\pi\) | |||||||
\(282\) | 704.338 | 0.148733 | ||||||||
\(283\) | 8790.28 | 1.84639 | 0.923194 | − | 0.384335i | \(-0.125569\pi\) | ||||
0.923194 | + | 0.384335i | \(0.125569\pi\) | |||||||
\(284\) | − | 377.493i | − | 0.0788735i | ||||||
\(285\) | −1315.80 | −0.273478 | ||||||||
\(286\) | 586.386 | − | 291.285i | 0.121237 | − | 0.0602240i | ||||
\(287\) | 7947.46 | 1.63458 | ||||||||
\(288\) | 2043.12i | 0.418028i | ||||||||
\(289\) | −630.378 | −0.128308 | ||||||||
\(290\) | −1238.25 | −0.250733 | ||||||||
\(291\) | − | 4021.20i | − | 0.810059i | ||||||
\(292\) | − | 123.778i | − | 0.0248067i | ||||||
\(293\) | − | 9469.04i | − | 1.88801i | −0.329930 | − | 0.944005i | \(-0.607025\pi\) | ||
0.329930 | − | 0.944005i | \(-0.392975\pi\) | |||||||
\(294\) | 3552.91i | 0.704795i | ||||||||
\(295\) | −2920.40 | −0.576381 | ||||||||
\(296\) | 1749.71 | 0.343581 | ||||||||
\(297\) | − | 1669.79i | − | 0.326232i | ||||||
\(298\) | 653.172 | 0.126971 | ||||||||
\(299\) | −1070.91 | + | 531.971i | −0.207131 | + | 0.102892i | ||||
\(300\) | 2535.05 | 0.487870 | ||||||||
\(301\) | − | 12861.0i | − | 2.46277i | ||||||
\(302\) | 1965.08 | 0.374428 | ||||||||
\(303\) | 179.234 | 0.0339825 | ||||||||
\(304\) | 1850.31i | 0.349087i | ||||||||
\(305\) | − | 3664.10i | − | 0.687888i | ||||||
\(306\) | 935.025i | 0.174679i | ||||||||
\(307\) | 10120.2i | 1.88140i | 0.339234 | + | 0.940702i | \(0.389832\pi\) | ||||
−0.339234 | + | 0.940702i | \(0.610168\pi\) | |||||||
\(308\) | 2274.56 | 0.420796 | ||||||||
\(309\) | −2711.09 | −0.499122 | ||||||||
\(310\) | 149.341i | 0.0273613i | ||||||||
\(311\) | −292.541 | −0.0533392 | −0.0266696 | − | 0.999644i | \(-0.508490\pi\) | ||||
−0.0266696 | + | 0.999644i | \(0.508490\pi\) | |||||||
\(312\) | −1511.92 | − | 3043.65i | −0.274346 | − | 0.552285i | ||||
\(313\) | −6584.75 | −1.18911 | −0.594556 | − | 0.804054i | \(-0.702672\pi\) | ||||
−0.594556 | + | 0.804054i | \(0.702672\pi\) | |||||||
\(314\) | 2164.08i | 0.388937i | ||||||||
\(315\) | −1820.84 | −0.325692 | ||||||||
\(316\) | 1807.35 | 0.321745 | ||||||||
\(317\) | − | 7401.38i | − | 1.31137i | −0.755037 | − | 0.655683i | \(-0.772381\pi\) | ||
0.755037 | − | 0.655683i | \(-0.227619\pi\) | |||||||
\(318\) | 1131.31i | 0.199500i | ||||||||
\(319\) | − | 2145.58i | − | 0.376582i | ||||||
\(320\) | − | 37.0916i | − | 0.00647964i | ||||||
\(321\) | 4770.10 | 0.829411 | ||||||||
\(322\) | 1048.76 | 0.181507 | ||||||||
\(323\) | 4340.43i | 0.747702i | ||||||||
\(324\) | −1907.43 | −0.327062 | ||||||||
\(325\) | 4198.22 | − | 2085.45i | 0.716539 | − | 0.355938i | ||||
\(326\) | 4365.28 | 0.741627 | ||||||||
\(327\) | − | 3894.59i | − | 0.658629i | ||||||
\(328\) | 4485.33 | 0.755064 | ||||||||
\(329\) | 4524.53 | 0.758193 | ||||||||
\(330\) | 277.122i | 0.0462275i | ||||||||
\(331\) | − | 5504.40i | − | 0.914046i | −0.889455 | − | 0.457023i | \(-0.848916\pi\) | ||
0.889455 | − | 0.457023i | \(-0.151084\pi\) | |||||||
\(332\) | 8664.11i | 1.43224i | ||||||||
\(333\) | − | 1077.50i | − | 0.177318i | ||||||
\(334\) | −2616.78 | −0.428694 | ||||||||
\(335\) | 1059.70 | 0.172829 | ||||||||
\(336\) | − | 3584.02i | − | 0.581918i | ||||||
\(337\) | −6284.71 | −1.01587 | −0.507937 | − | 0.861394i | \(-0.669592\pi\) | ||||
−0.507937 | + | 0.861394i | \(0.669592\pi\) | |||||||
\(338\) | −2223.21 | − | 1685.58i | −0.357771 | − | 0.271253i | ||||
\(339\) | 1002.22 | 0.160570 | ||||||||
\(340\) | 2089.61i | 0.333309i | ||||||||
\(341\) | −258.772 | −0.0410947 | ||||||||
\(342\) | −947.646 | −0.149833 | ||||||||
\(343\) | 11719.3i | 1.84484i | ||||||||
\(344\) | − | 7258.39i | − | 1.13763i | ||||||
\(345\) | − | 506.105i | − | 0.0789790i | ||||||
\(346\) | 663.181i | 0.103043i | ||||||||
\(347\) | −11558.0 | −1.78809 | −0.894046 | − | 0.447974i | \(-0.852146\pi\) | ||||
−0.894046 | + | 0.447974i | \(0.852146\pi\) | |||||||
\(348\) | −4944.22 | −0.761604 | ||||||||
\(349\) | − | 4235.53i | − | 0.649636i | −0.945777 | − | 0.324818i | \(-0.894697\pi\) | ||
0.945777 | − | 0.324818i | \(-0.105303\pi\) | |||||||
\(350\) | −4111.40 | −0.627896 | ||||||||
\(351\) | −6372.25 | + | 3165.39i | −0.969019 | + | 0.481356i | ||||
\(352\) | 1997.49 | 0.302462 | ||||||||
\(353\) | 5559.11i | 0.838191i | 0.907942 | + | 0.419096i | \(0.137653\pi\) | ||||
−0.907942 | + | 0.419096i | \(0.862347\pi\) | |||||||
\(354\) | 2944.04 | 0.442017 | ||||||||
\(355\) | 295.444 | 0.0441705 | ||||||||
\(356\) | 5470.80i | 0.814471i | ||||||||
\(357\) | − | 8407.37i | − | 1.24640i | ||||||
\(358\) | 230.422i | 0.0340173i | ||||||||
\(359\) | 7592.61i | 1.11622i | 0.829767 | + | 0.558109i | \(0.188473\pi\) | ||||
−0.829767 | + | 0.558109i | \(0.811527\pi\) | |||||||
\(360\) | −1027.63 | −0.150447 | ||||||||
\(361\) | 2459.98 | 0.358651 | ||||||||
\(362\) | − | 3613.36i | − | 0.524624i | ||||||
\(363\) | −480.185 | −0.0694302 | ||||||||
\(364\) | −4311.85 | − | 8680.18i | −0.620885 | − | 1.24990i | ||||
\(365\) | 96.8745 | 0.0138922 | ||||||||
\(366\) | 3693.76i | 0.527530i | ||||||||
\(367\) | 1655.86 | 0.235518 | 0.117759 | − | 0.993042i | \(-0.462429\pi\) | ||||
0.117759 | + | 0.993042i | \(0.462429\pi\) | |||||||
\(368\) | −711.696 | −0.100814 | ||||||||
\(369\) | − | 2762.15i | − | 0.389680i | ||||||
\(370\) | 607.958i | 0.0854222i | ||||||||
\(371\) | 7267.35i | 1.01699i | ||||||||
\(372\) | 596.306i | 0.0831103i | ||||||||
\(373\) | 1380.23 | 0.191597 | 0.0957983 | − | 0.995401i | \(-0.469460\pi\) | ||||
0.0957983 | + | 0.995401i | \(0.469460\pi\) | |||||||
\(374\) | 914.144 | 0.126388 | ||||||||
\(375\) | 4463.88i | 0.614703i | ||||||||
\(376\) | 2553.52 | 0.350234 | ||||||||
\(377\) | −8187.98 | + | 4067.35i | −1.11857 | + | 0.555648i | ||||
\(378\) | 6240.48 | 0.849142 | ||||||||
\(379\) | 11001.2i | 1.49101i | 0.666501 | + | 0.745504i | \(0.267791\pi\) | ||||
−0.666501 | + | 0.745504i | \(0.732209\pi\) | |||||||
\(380\) | −2117.82 | −0.285900 | ||||||||
\(381\) | −6006.06 | −0.807611 | ||||||||
\(382\) | 6127.29i | 0.820679i | ||||||||
\(383\) | 2205.60i | 0.294259i | 0.989117 | + | 0.147129i | \(0.0470034\pi\) | ||||
−0.989117 | + | 0.147129i | \(0.952997\pi\) | |||||||
\(384\) | − | 5727.69i | − | 0.761171i | ||||||
\(385\) | 1780.18i | 0.235653i | ||||||||
\(386\) | −5921.43 | −0.780811 | ||||||||
\(387\) | −4469.86 | −0.587120 | ||||||||
\(388\) | − | 6472.26i | − | 0.846853i | ||||||
\(389\) | −2689.14 | −0.350501 | −0.175250 | − | 0.984524i | \(-0.556074\pi\) | ||||
−0.175250 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(390\) | 1057.55 | − | 525.336i | 0.137311 | − | 0.0682088i | ||||
\(391\) | −1669.49 | −0.215933 | ||||||||
\(392\) | 12880.8i | 1.65964i | ||||||||
\(393\) | 11095.2 | 1.42412 | ||||||||
\(394\) | −528.251 | −0.0675454 | ||||||||
\(395\) | 1414.52i | 0.180183i | ||||||||
\(396\) | − | 790.527i | − | 0.100317i | ||||||
\(397\) | 14239.4i | 1.80013i | 0.435753 | + | 0.900066i | \(0.356482\pi\) | ||||
−0.435753 | + | 0.900066i | \(0.643518\pi\) | |||||||
\(398\) | − | 5552.08i | − | 0.699248i | ||||||
\(399\) | 8520.85 | 1.06911 | ||||||||
\(400\) | 2790.01 | 0.348752 | ||||||||
\(401\) | − | 13243.5i | − | 1.64925i | −0.565680 | − | 0.824625i | \(-0.691386\pi\) | ||
0.565680 | − | 0.824625i | \(-0.308614\pi\) | |||||||
\(402\) | −1068.28 | −0.132539 | ||||||||
\(403\) | 490.550 | + | 987.526i | 0.0606353 | + | 0.122065i | ||||
\(404\) | 288.482 | 0.0355261 | ||||||||
\(405\) | − | 1492.84i | − | 0.183161i | ||||||
\(406\) | 8018.66 | 0.980196 | ||||||||
\(407\) | −1053.44 | −0.128298 | ||||||||
\(408\) | − | 4744.89i | − | 0.575752i | ||||||
\(409\) | 3291.46i | 0.397928i | 0.980007 | + | 0.198964i | \(0.0637576\pi\) | ||||
−0.980007 | + | 0.198964i | \(0.936242\pi\) | |||||||
\(410\) | 1558.48i | 0.187727i | ||||||||
\(411\) | − | 6553.15i | − | 0.786479i | ||||||
\(412\) | −4363.59 | −0.521793 | ||||||||
\(413\) | 18911.9 | 2.25326 | ||||||||
\(414\) | − | 364.500i | − | 0.0432710i | ||||||
\(415\) | −6780.95 | −0.802081 | ||||||||
\(416\) | −3786.62 | − | 7622.83i | −0.446284 | − | 0.898414i | ||||
\(417\) | −5672.47 | −0.666145 | ||||||||
\(418\) | 926.483i | 0.108411i | ||||||||
\(419\) | −10279.4 | −1.19853 | −0.599263 | − | 0.800552i | \(-0.704540\pi\) | ||||
−0.599263 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(420\) | 4102.19 | 0.476587 | ||||||||
\(421\) | 13466.6i | 1.55896i | 0.626427 | + | 0.779480i | \(0.284517\pi\) | ||||
−0.626427 | + | 0.779480i | \(0.715483\pi\) | |||||||
\(422\) | 373.785i | 0.0431175i | ||||||||
\(423\) | − | 1572.51i | − | 0.180752i | ||||||
\(424\) | 4101.49i | 0.469779i | ||||||||
\(425\) | 6544.79 | 0.746985 | ||||||||
\(426\) | −297.835 | −0.0338736 | ||||||||
\(427\) | 23728.0i | 2.68918i | ||||||||
\(428\) | 7677.63 | 0.867084 | ||||||||
\(429\) | 910.279 | + | 1832.48i | 0.102444 | + | 0.206231i | ||||
\(430\) | 2522.02 | 0.282843 | ||||||||
\(431\) | − | 17756.1i | − | 1.98441i | −0.124598 | − | 0.992207i | \(-0.539764\pi\) | ||
0.124598 | − | 0.992207i | \(-0.460236\pi\) | |||||||
\(432\) | −4234.81 | −0.471638 | ||||||||
\(433\) | 1858.88 | 0.206310 | 0.103155 | − | 0.994665i | \(-0.467106\pi\) | ||||
0.103155 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(434\) | − | 967.105i | − | 0.106964i | ||||||
\(435\) | − | 3869.58i | − | 0.426511i | ||||||
\(436\) | − | 6268.47i | − | 0.688545i | ||||||
\(437\) | − | 1692.02i | − | 0.185218i | ||||||
\(438\) | −97.6585 | −0.0106537 | ||||||||
\(439\) | −8311.97 | −0.903664 | −0.451832 | − | 0.892103i | \(-0.649229\pi\) | ||||
−0.451832 | + | 0.892103i | \(0.649229\pi\) | |||||||
\(440\) | 1004.68i | 0.108856i | ||||||||
\(441\) | 7932.23 | 0.856520 | ||||||||
\(442\) | −1732.93 | − | 3488.56i | −0.186486 | − | 0.375416i | ||||
\(443\) | −63.6070 | −0.00682181 | −0.00341090 | − | 0.999994i | \(-0.501086\pi\) | ||||
−0.00341090 | + | 0.999994i | \(0.501086\pi\) | |||||||
\(444\) | 2427.52i | 0.259471i | ||||||||
\(445\) | −4281.71 | −0.456118 | ||||||||
\(446\) | −1351.55 | −0.143493 | ||||||||
\(447\) | 2041.19i | 0.215984i | ||||||||
\(448\) | 240.198i | 0.0253310i | ||||||||
\(449\) | 12006.5i | 1.26196i | 0.775799 | + | 0.630980i | \(0.217347\pi\) | ||||
−0.775799 | + | 0.630980i | \(0.782653\pi\) | |||||||
\(450\) | 1428.92i | 0.149689i | ||||||||
\(451\) | −2700.46 | −0.281951 | ||||||||
\(452\) | 1613.11 | 0.167863 | ||||||||
\(453\) | 6140.95i | 0.636924i | ||||||||
\(454\) | −6838.19 | −0.706899 | ||||||||
\(455\) | 6793.52 | − | 3374.66i | 0.699968 | − | 0.347706i | ||||
\(456\) | 4808.94 | 0.493858 | ||||||||
\(457\) | − | 2723.61i | − | 0.278786i | −0.990237 | − | 0.139393i | \(-0.955485\pi\) | ||
0.990237 | − | 0.139393i | \(-0.0445151\pi\) | |||||||
\(458\) | 930.645 | 0.0949480 | ||||||||
\(459\) | −9933.99 | −1.01019 | ||||||||
\(460\) | − | 814.591i | − | 0.0825663i | ||||||
\(461\) | − | 8513.80i | − | 0.860146i | −0.902794 | − | 0.430073i | \(-0.858488\pi\) | ||
0.902794 | − | 0.430073i | \(-0.141512\pi\) | |||||||
\(462\) | − | 1794.59i | − | 0.180718i | ||||||
\(463\) | − | 7667.09i | − | 0.769590i | −0.923002 | − | 0.384795i | \(-0.874272\pi\) | ||
0.923002 | − | 0.384795i | \(-0.125728\pi\) | |||||||
\(464\) | −5441.50 | −0.544429 | ||||||||
\(465\) | −466.698 | −0.0465432 | ||||||||
\(466\) | − | 3498.54i | − | 0.347783i | ||||||
\(467\) | −9955.18 | −0.986447 | −0.493223 | − | 0.869903i | \(-0.664181\pi\) | ||||
−0.493223 | + | 0.869903i | \(0.664181\pi\) | |||||||
\(468\) | −3016.81 | + | 1498.59i | −0.297975 | + | 0.148018i | ||||
\(469\) | −6862.41 | −0.675643 | ||||||||
\(470\) | 887.252i | 0.0870764i | ||||||||
\(471\) | −6762.85 | −0.661604 | ||||||||
\(472\) | 10673.4 | 1.04085 | ||||||||
\(473\) | 4370.03i | 0.424808i | ||||||||
\(474\) | − | 1425.97i | − | 0.138179i | ||||||
\(475\) | 6633.13i | 0.640734i | ||||||||
\(476\) | − | 13531.9i | − | 1.30301i | ||||||
\(477\) | 2525.78 | 0.242447 | ||||||||
\(478\) | 3042.63 | 0.291144 | ||||||||
\(479\) | 5955.09i | 0.568048i | 0.958817 | + | 0.284024i | \(0.0916696\pi\) | ||||
−0.958817 | + | 0.284024i | \(0.908330\pi\) | |||||||
\(480\) | 3602.50 | 0.342564 | ||||||||
\(481\) | 1996.99 | + | 4020.15i | 0.189304 | + | 0.381087i | ||||
\(482\) | −5030.79 | −0.475407 | ||||||||
\(483\) | 3277.43i | 0.308754i | ||||||||
\(484\) | −772.872 | −0.0725838 | ||||||||
\(485\) | 5065.50 | 0.474252 | ||||||||
\(486\) | − | 3699.82i | − | 0.345323i | ||||||
\(487\) | 12295.1i | 1.14404i | 0.820241 | + | 0.572019i | \(0.193839\pi\) | ||||
−0.820241 | + | 0.572019i | \(0.806161\pi\) | |||||||
\(488\) | 13391.4i | 1.24222i | ||||||||
\(489\) | 13641.7i | 1.26155i | ||||||||
\(490\) | −4475.58 | −0.412625 | ||||||||
\(491\) | 3476.04 | 0.319494 | 0.159747 | − | 0.987158i | \(-0.448932\pi\) | ||||
0.159747 | + | 0.987158i | \(0.448932\pi\) | |||||||
\(492\) | 6222.87i | 0.570221i | ||||||||
\(493\) | −12764.6 | −1.16610 | ||||||||
\(494\) | 3535.65 | − | 1756.32i | 0.322017 | − | 0.159961i | ||||
\(495\) | 618.704 | 0.0561791 | ||||||||
\(496\) | 656.281i | 0.0594111i | ||||||||
\(497\) | −1913.24 | −0.172677 | ||||||||
\(498\) | 6835.83 | 0.615102 | ||||||||
\(499\) | 5515.09i | 0.494768i | 0.968918 | + | 0.247384i | \(0.0795709\pi\) | ||||
−0.968918 | + | 0.247384i | \(0.920429\pi\) | |||||||
\(500\) | 7184.75i | 0.642624i | ||||||||
\(501\) | − | 8177.54i | − | 0.729232i | ||||||
\(502\) | 186.086i | 0.0165446i | ||||||||
\(503\) | 14285.6 | 1.26633 | 0.633164 | − | 0.774018i | \(-0.281756\pi\) | ||||
0.633164 | + | 0.774018i | \(0.281756\pi\) | |||||||
\(504\) | 6654.76 | 0.588148 | ||||||||
\(505\) | 225.780i | 0.0198952i | ||||||||
\(506\) | −356.359 | −0.0313085 | ||||||||
\(507\) | 5267.52 | − | 6947.62i | 0.461418 | − | 0.608589i | ||||
\(508\) | −9666.94 | −0.844293 | ||||||||
\(509\) | − | 13326.9i | − | 1.16052i | −0.814433 | − | 0.580258i | \(-0.802952\pi\) | ||
0.814433 | − | 0.580258i | \(-0.197048\pi\) | |||||||
\(510\) | 1648.67 | 0.143146 | ||||||||
\(511\) | −627.340 | −0.0543090 | ||||||||
\(512\) | − | 9143.51i | − | 0.789238i | ||||||
\(513\) | − | 10068.1i | − | 0.866503i | ||||||
\(514\) | 4560.13i | 0.391320i | ||||||||
\(515\) | − | 3415.16i | − | 0.292213i | ||||||
\(516\) | 10070.2 | 0.859137 | ||||||||
\(517\) | −1537.39 | −0.130782 | ||||||||
\(518\) | − | 3937.01i | − | 0.333943i | ||||||
\(519\) | −2072.47 | −0.175282 | ||||||||
\(520\) | 3834.08 | − | 1904.57i | 0.323338 | − | 0.160617i | ||||
\(521\) | −5713.55 | −0.480451 | −0.240226 | − | 0.970717i | \(-0.577221\pi\) | ||||
−0.240226 | + | 0.970717i | \(0.577221\pi\) | |||||||
\(522\) | − | 2786.90i | − | 0.233677i | ||||||
\(523\) | −15307.5 | −1.27983 | −0.639913 | − | 0.768448i | \(-0.721029\pi\) | ||||
−0.639913 | + | 0.768448i | \(0.721029\pi\) | |||||||
\(524\) | 17858.1 | 1.48880 | ||||||||
\(525\) | − | 12848.3i | − | 1.06809i | ||||||
\(526\) | 8477.11i | 0.702699i | ||||||||
\(527\) | 1539.50i | 0.127252i | ||||||||
\(528\) | 1217.81i | 0.100376i | ||||||||
\(529\) | −11516.2 | −0.946510 | ||||||||
\(530\) | −1425.11 | −0.116798 | ||||||||
\(531\) | − | 6572.88i | − | 0.537172i | ||||||
\(532\) | 13714.6 | 1.11767 | ||||||||
\(533\) | 5119.23 | + | 10305.5i | 0.416020 | + | 0.837489i | ||||
\(534\) | 4316.36 | 0.349789 | ||||||||
\(535\) | 6008.88i | 0.485582i | ||||||||
\(536\) | −3872.96 | −0.312101 | ||||||||
\(537\) | −720.079 | −0.0578654 | ||||||||
\(538\) | − | 5858.52i | − | 0.469477i | ||||||
\(539\) | − | 7755.09i | − | 0.619731i | ||||||
\(540\) | − | 4847.07i | − | 0.386268i | ||||||
\(541\) | − | 14533.6i | − | 1.15498i | −0.816396 | − | 0.577492i | \(-0.804031\pi\) | ||
0.816396 | − | 0.577492i | \(-0.195969\pi\) | |||||||
\(542\) | −9900.01 | −0.784579 | ||||||||
\(543\) | 11291.9 | 0.892415 | ||||||||
\(544\) | − | 11883.6i | − | 0.936589i | ||||||
\(545\) | 4906.01 | 0.385597 | ||||||||
\(546\) | −6848.51 | + | 3401.97i | −0.536793 | + | 0.266650i | ||||
\(547\) | −12963.6 | −1.01332 | −0.506658 | − | 0.862147i | \(-0.669119\pi\) | ||||
−0.506658 | + | 0.862147i | \(0.669119\pi\) | |||||||
\(548\) | − | 10547.5i | − | 0.822202i | ||||||
\(549\) | 8246.70 | 0.641094 | ||||||||
\(550\) | 1397.01 | 0.108307 | ||||||||
\(551\) | − | 12936.9i | − | 1.00024i | ||||||
\(552\) | 1849.69i | 0.142624i | ||||||||
\(553\) | − | 9160.14i | − | 0.704392i | ||||||
\(554\) | − | 7019.64i | − | 0.538332i | ||||||
\(555\) | −1899.89 | −0.145308 | ||||||||
\(556\) | −9130.03 | −0.696402 | ||||||||
\(557\) | 4755.08i | 0.361722i | 0.983509 | + | 0.180861i | \(0.0578885\pi\) | ||||
−0.983509 | + | 0.180861i | \(0.942112\pi\) | |||||||
\(558\) | −336.119 | −0.0255001 | ||||||||
\(559\) | 16676.9 | − | 8284.21i | 1.26182 | − | 0.626806i | ||||
\(560\) | 4514.78 | 0.340686 | ||||||||
\(561\) | 2856.74i | 0.214994i | ||||||||
\(562\) | 2720.76 | 0.204214 | ||||||||
\(563\) | −8702.18 | −0.651426 | −0.325713 | − | 0.945469i | \(-0.605604\pi\) | ||||
−0.325713 | + | 0.945469i | \(0.605604\pi\) | |||||||
\(564\) | 3542.72i | 0.264495i | ||||||||
\(565\) | 1262.50i | 0.0940063i | ||||||||
\(566\) | − | 11162.7i | − | 0.828981i | ||||||
\(567\) | 9667.36i | 0.716034i | ||||||||
\(568\) | −1079.78 | −0.0797649 | ||||||||
\(569\) | −18691.1 | −1.37710 | −0.688552 | − | 0.725187i | \(-0.741753\pi\) | ||||
−0.688552 | + | 0.725187i | \(0.741753\pi\) | |||||||
\(570\) | 1670.92i | 0.122785i | ||||||||
\(571\) | 6006.57 | 0.440223 | 0.220111 | − | 0.975475i | \(-0.429358\pi\) | ||||
0.220111 | + | 0.975475i | \(0.429358\pi\) | |||||||
\(572\) | 1465.12 | + | 2949.44i | 0.107098 | + | 0.215598i | ||||
\(573\) | −19148.0 | −1.39602 | ||||||||
\(574\) | − | 10092.4i | − | 0.733884i | ||||||
\(575\) | −2551.35 | −0.185041 | ||||||||
\(576\) | 83.4811 | 0.00603886 | ||||||||
\(577\) | − | 1612.72i | − | 0.116358i | −0.998306 | − | 0.0581789i | \(-0.981471\pi\) | ||
0.998306 | − | 0.0581789i | \(-0.0185294\pi\) | |||||||
\(578\) | 800.512i | 0.0576071i | ||||||||
\(579\) | − | 18504.7i | − | 1.32820i | ||||||
\(580\) | − | 6228.22i | − | 0.445884i | ||||||
\(581\) | 43912.1 | 3.13559 | ||||||||
\(582\) | −5106.50 | −0.363696 | ||||||||
\(583\) | − | 2469.37i | − | 0.175422i | ||||||
\(584\) | −354.054 | −0.0250871 | ||||||||
\(585\) | −1172.87 | − | 2361.10i | −0.0828925 | − | 0.166871i | ||||
\(586\) | −12024.7 | −0.847669 | ||||||||
\(587\) | − | 7095.81i | − | 0.498936i | −0.968383 | − | 0.249468i | \(-0.919744\pi\) | ||
0.968383 | − | 0.249468i | \(-0.0802558\pi\) | |||||||
\(588\) | −17870.6 | −1.25335 | ||||||||
\(589\) | −1560.28 | −0.109151 | ||||||||
\(590\) | 3708.60i | 0.258780i | ||||||||
\(591\) | − | 1650.81i | − | 0.114899i | ||||||
\(592\) | 2671.67i | 0.185482i | ||||||||
\(593\) | 2171.66i | 0.150387i | 0.997169 | + | 0.0751934i | \(0.0239574\pi\) | ||||
−0.997169 | + | 0.0751934i | \(0.976043\pi\) | |||||||
\(594\) | −2120.45 | −0.146470 | ||||||||
\(595\) | 10590.7 | 0.729710 | ||||||||
\(596\) | 3285.36i | 0.225794i | ||||||||
\(597\) | 17350.5 | 1.18946 | ||||||||
\(598\) | 675.545 | + | 1359.94i | 0.0461958 | + | 0.0929968i | ||||
\(599\) | 24227.4 | 1.65260 | 0.826299 | − | 0.563232i | \(-0.190442\pi\) | ||||
0.826299 | + | 0.563232i | \(0.190442\pi\) | |||||||
\(600\) | − | 7251.23i | − | 0.493384i | ||||||
\(601\) | 20675.9 | 1.40331 | 0.701654 | − | 0.712518i | \(-0.252445\pi\) | ||||
0.701654 | + | 0.712518i | \(0.252445\pi\) | |||||||
\(602\) | −16332.1 | −1.10572 | ||||||||
\(603\) | 2385.04i | 0.161072i | ||||||||
\(604\) | 9884.05i | 0.665854i | ||||||||
\(605\) | − | 604.887i | − | 0.0406482i | ||||||
\(606\) | − | 227.607i | − | 0.0152573i | ||||||
\(607\) | 3796.10 | 0.253837 | 0.126918 | − | 0.991913i | \(-0.459491\pi\) | ||||
0.126918 | + | 0.991913i | \(0.459491\pi\) | |||||||
\(608\) | 12044.0 | 0.803368 | ||||||||
\(609\) | 25058.7i | 1.66737i | ||||||||
\(610\) | −4653.02 | −0.308844 | ||||||||
\(611\) | 2914.41 | + | 5866.99i | 0.192969 | + | 0.388467i | ||||
\(612\) | −4703.04 | −0.310636 | ||||||||
\(613\) | − | 23062.2i | − | 1.51954i | −0.650195 | − | 0.759768i | \(-0.725313\pi\) | ||
0.650195 | − | 0.759768i | \(-0.274687\pi\) | |||||||
\(614\) | 12851.6 | 0.844703 | ||||||||
\(615\) | −4870.32 | −0.319334 | ||||||||
\(616\) | − | 6506.14i | − | 0.425552i | ||||||
\(617\) | 13799.9i | 0.900428i | 0.892921 | + | 0.450214i | \(0.148652\pi\) | ||||
−0.892921 | + | 0.450214i | \(0.851348\pi\) | |||||||
\(618\) | 3442.80i | 0.224093i | ||||||||
\(619\) | 7474.39i | 0.485333i | 0.970110 | + | 0.242666i | \(0.0780220\pi\) | ||||
−0.970110 | + | 0.242666i | \(0.921978\pi\) | |||||||
\(620\) | −751.165 | −0.0486573 | ||||||||
\(621\) | 3872.55 | 0.250242 | ||||||||
\(622\) | 371.496i | 0.0239480i | ||||||||
\(623\) | 27727.5 | 1.78311 | ||||||||
\(624\) | 4647.43 | − | 2308.59i | 0.298151 | − | 0.148105i | ||||
\(625\) | 6878.04 | 0.440195 | ||||||||
\(626\) | 8361.92i | 0.533881i | ||||||||
\(627\) | −2895.30 | −0.184413 | ||||||||
\(628\) | −10885.0 | −0.691655 | ||||||||
\(629\) | 6267.19i | 0.397280i | ||||||||
\(630\) | 2312.27i | 0.146227i | ||||||||
\(631\) | 12919.7i | 0.815092i | 0.913185 | + | 0.407546i | \(0.133615\pi\) | ||||
−0.913185 | + | 0.407546i | \(0.866385\pi\) | |||||||
\(632\) | − | 5169.74i | − | 0.325381i | ||||||
\(633\) | −1168.09 | −0.0733453 | ||||||||
\(634\) | −9398.95 | −0.588770 | ||||||||
\(635\) | − | 7565.81i | − | 0.472819i | ||||||
\(636\) | −5690.35 | −0.354775 | ||||||||
\(637\) | −29595.0 | + | 14701.2i | −1.84081 | + | 0.914416i | ||||
\(638\) | −2724.66 | −0.169076 | ||||||||
\(639\) | 664.948i | 0.0411658i | ||||||||
\(640\) | 7215.15 | 0.445631 | ||||||||
\(641\) | 294.282 | 0.0181333 | 0.00906666 | − | 0.999959i | \(-0.497114\pi\) | ||||
0.00906666 | + | 0.999959i | \(0.497114\pi\) | |||||||
\(642\) | − | 6057.51i | − | 0.372385i | ||||||
\(643\) | 28745.1i | 1.76298i | 0.472205 | + | 0.881489i | \(0.343458\pi\) | ||||
−0.472205 | + | 0.881489i | \(0.656542\pi\) | |||||||
\(644\) | 5275.13i | 0.322778i | ||||||||
\(645\) | 7881.40i | 0.481132i | ||||||||
\(646\) | 5511.88 | 0.335700 | ||||||||
\(647\) | −19531.3 | −1.18680 | −0.593398 | − | 0.804909i | \(-0.702214\pi\) | ||||
−0.593398 | + | 0.804909i | \(0.702214\pi\) | |||||||
\(648\) | 5456.00i | 0.330759i | ||||||||
\(649\) | −6426.09 | −0.388669 | ||||||||
\(650\) | −2648.29 | − | 5331.28i | −0.159807 | − | 0.321708i | ||||
\(651\) | 3022.24 | 0.181952 | ||||||||
\(652\) | 21956.7i | 1.31885i | ||||||||
\(653\) | −19077.8 | −1.14330 | −0.571648 | − | 0.820499i | \(-0.693696\pi\) | ||||
−0.571648 | + | 0.820499i | \(0.693696\pi\) | |||||||
\(654\) | −4945.72 | −0.295708 | ||||||||
\(655\) | 13976.6i | 0.833756i | ||||||||
\(656\) | 6848.75i | 0.407620i | ||||||||
\(657\) | 218.033i | 0.0129471i | ||||||||
\(658\) | − | 5745.67i | − | 0.340410i | ||||||
\(659\) | −7668.16 | −0.453276 | −0.226638 | − | 0.973979i | \(-0.572774\pi\) | ||||
−0.226638 | + | 0.973979i | \(0.572774\pi\) | |||||||
\(660\) | −1393.88 | −0.0822074 | ||||||||
\(661\) | 25112.0i | 1.47767i | 0.673885 | + | 0.738837i | \(0.264625\pi\) | ||||
−0.673885 | + | 0.738837i | \(0.735375\pi\) | |||||||
\(662\) | −6990.00 | −0.410383 | ||||||||
\(663\) | 10901.9 | − | 5415.47i | 0.638604 | − | 0.317224i | ||||
\(664\) | 24782.8 | 1.44843 | ||||||||
\(665\) | 10733.7i | 0.625916i | ||||||||
\(666\) | −1368.32 | −0.0796113 | ||||||||
\(667\) | 4976.01 | 0.288864 | ||||||||
\(668\) | − | 13162.0i | − | 0.762355i | ||||||
\(669\) | − | 4223.65i | − | 0.244089i | ||||||
\(670\) | − | 1345.71i | − | 0.0775957i | ||||||
\(671\) | − | 8062.53i | − | 0.463861i | ||||||
\(672\) | −23329.1 | −1.33919 | ||||||||
\(673\) | −28940.0 | −1.65759 | −0.828793 | − | 0.559555i | \(-0.810972\pi\) | ||||
−0.828793 | + | 0.559555i | \(0.810972\pi\) | |||||||
\(674\) | 7980.90i | 0.456102i | ||||||||
\(675\) | −15181.3 | −0.865672 | ||||||||
\(676\) | 8478.24 | − | 11182.4i | 0.482376 | − | 0.636232i | ||||
\(677\) | 15694.4 | 0.890969 | 0.445484 | − | 0.895290i | \(-0.353032\pi\) | ||||
0.445484 | + | 0.895290i | \(0.353032\pi\) | |||||||
\(678\) | − | 1272.71i | − | 0.0720918i | ||||||
\(679\) | −32803.2 | −1.85401 | ||||||||
\(680\) | 5977.12 | 0.337077 | ||||||||
\(681\) | − | 21369.6i | − | 1.20248i | ||||||
\(682\) | 328.612i | 0.0184505i | ||||||||
\(683\) | 2250.42i | 0.126076i | 0.998011 | + | 0.0630380i | \(0.0200789\pi\) | ||||
−0.998011 | + | 0.0630380i | \(0.979921\pi\) | |||||||
\(684\) | − | 4766.52i | − | 0.266451i | ||||||
\(685\) | 8254.98 | 0.460447 | ||||||||
\(686\) | 14882.2 | 0.828287 | ||||||||
\(687\) | 2908.30i | 0.161512i | ||||||||
\(688\) | 11083.0 | 0.614151 | ||||||||
\(689\) | −9423.62 | + | 4681.15i | −0.521062 | + | 0.258835i | ||||
\(690\) | −642.698 | −0.0354596 | ||||||||
\(691\) | − | 17919.9i | − | 0.986546i | −0.869874 | − | 0.493273i | \(-0.835800\pi\) | ||
0.869874 | − | 0.493273i | \(-0.164200\pi\) | |||||||
\(692\) | −3335.71 | −0.183243 | ||||||||
\(693\) | −4006.60 | −0.219622 | ||||||||
\(694\) | 14677.5i | 0.802808i | ||||||||
\(695\) | − | 7145.60i | − | 0.389997i | ||||||
\(696\) | 14142.4i | 0.770212i | ||||||||
\(697\) | 16065.7i | 0.873075i | ||||||||
\(698\) | −5378.67 | −0.291670 | ||||||||
\(699\) | 10933.1 | 0.591599 | ||||||||
\(700\) | − | 20679.7i | − | 1.11660i | ||||||
\(701\) | −28053.5 | −1.51151 | −0.755753 | − | 0.654857i | \(-0.772729\pi\) | ||||
−0.755753 | + | 0.654857i | \(0.772729\pi\) | |||||||
\(702\) | 4019.71 | + | 8092.07i | 0.216117 | + | 0.435065i | ||||
\(703\) | −6351.78 | −0.340771 | ||||||||
\(704\) | − | 81.6168i | − | 0.00436939i | ||||||
\(705\) | −2772.70 | −0.148122 | ||||||||
\(706\) | 7059.47 | 0.376327 | ||||||||
\(707\) | − | 1462.11i | − | 0.0777768i | ||||||
\(708\) | 14808.1i | 0.786048i | ||||||||
\(709\) | − | 15166.0i | − | 0.803342i | −0.915784 | − | 0.401671i | \(-0.868430\pi\) | ||
0.915784 | − | 0.401671i | \(-0.131570\pi\) | |||||||
\(710\) | − | 375.182i | − | 0.0198314i | ||||||
\(711\) | −3183.62 | −0.167926 | ||||||||
\(712\) | 15648.6 | 0.823677 | ||||||||
\(713\) | − | 600.141i | − | 0.0315224i | ||||||
\(714\) | −10676.4 | −0.559602 | ||||||||
\(715\) | −2308.37 | + | 1146.67i | −0.120739 | + | 0.0599765i | ||||
\(716\) | −1158.99 | −0.0604937 | ||||||||
\(717\) | 9508.36i | 0.495253i | ||||||||
\(718\) | 9641.79 | 0.501154 | ||||||||
\(719\) | 12995.0 | 0.674036 | 0.337018 | − | 0.941498i | \(-0.390582\pi\) | ||||
0.337018 | + | 0.941498i | \(0.390582\pi\) | |||||||
\(720\) | − | 1569.12i | − | 0.0812189i | ||||||
\(721\) | 22115.9i | 1.14235i | ||||||||
\(722\) | − | 3123.92i | − | 0.161025i | ||||||
\(723\) | − | 15721.4i | − | 0.808695i | ||||||
\(724\) | 18174.7 | 0.932950 | ||||||||
\(725\) | −19507.1 | −0.999278 | ||||||||
\(726\) | 609.783i | 0.0311724i | ||||||||
\(727\) | 11214.2 | 0.572091 | 0.286046 | − | 0.958216i | \(-0.407659\pi\) | ||||
0.286046 | + | 0.958216i | \(0.407659\pi\) | |||||||
\(728\) | −24828.7 | + | 12333.6i | −1.26403 | + | 0.627903i | ||||
\(729\) | 19624.9 | 0.997051 | ||||||||
\(730\) | − | 123.020i | − | 0.00623723i | ||||||
\(731\) | 25998.4 | 1.31544 | ||||||||
\(732\) | −18579.1 | −0.938118 | ||||||||
\(733\) | 14541.3i | 0.732736i | 0.930470 | + | 0.366368i | \(0.119399\pi\) | ||||
−0.930470 | + | 0.366368i | \(0.880601\pi\) | |||||||
\(734\) | − | 2102.77i | − | 0.105742i | ||||||
\(735\) | − | 13986.4i | − | 0.701899i | ||||||
\(736\) | 4632.56i | 0.232009i | ||||||||
\(737\) | 2331.78 | 0.116543 | ||||||||
\(738\) | −3507.63 | −0.174956 | ||||||||
\(739\) | − | 3802.12i | − | 0.189260i | −0.995513 | − | 0.0946300i | \(-0.969833\pi\) | ||
0.995513 | − | 0.0946300i | \(-0.0301668\pi\) | |||||||
\(740\) | −3057.94 | −0.151908 | ||||||||
\(741\) | 5488.57 | + | 11049.0i | 0.272102 | + | 0.547769i | ||||
\(742\) | 9228.75 | 0.456601 | ||||||||
\(743\) | − | 1717.74i | − | 0.0848155i | −0.999100 | − | 0.0424077i | \(-0.986497\pi\) | ||
0.999100 | − | 0.0424077i | \(-0.0135029\pi\) | |||||||
\(744\) | 1705.67 | 0.0840497 | ||||||||
\(745\) | −2571.28 | −0.126449 | ||||||||
\(746\) | − | 1752.74i | − | 0.0860221i | ||||||
\(747\) | − | 15261.7i | − | 0.747519i | ||||||
\(748\) | 4598.01i | 0.224759i | ||||||||
\(749\) | − | 38912.3i | − | 1.89830i | ||||||
\(750\) | 5668.64 | 0.275986 | ||||||||
\(751\) | 11166.2 | 0.542559 | 0.271280 | − | 0.962501i | \(-0.412553\pi\) | ||||
0.271280 | + | 0.962501i | \(0.412553\pi\) | |||||||
\(752\) | 3899.04i | 0.189073i | ||||||||
\(753\) | −581.525 | −0.0281434 | ||||||||
\(754\) | 5165.10 | + | 10397.9i | 0.249472 | + | 0.502212i | ||||
\(755\) | −7735.73 | −0.372890 | ||||||||
\(756\) | 31388.7i | 1.51005i | ||||||||
\(757\) | 15801.8 | 0.758689 | 0.379345 | − | 0.925255i | \(-0.376150\pi\) | ||||
0.379345 | + | 0.925255i | \(0.376150\pi\) | |||||||
\(758\) | 13970.3 | 0.669425 | ||||||||
\(759\) | − | 1113.64i | − | 0.0532576i | ||||||
\(760\) | 6057.80i | 0.289131i | ||||||||
\(761\) | − | 17664.7i | − | 0.841450i | −0.907188 | − | 0.420725i | \(-0.861776\pi\) | ||
0.907188 | − | 0.420725i | \(-0.138224\pi\) | |||||||
\(762\) | 7627.05i | 0.362597i | ||||||||
\(763\) | −31770.3 | −1.50742 | ||||||||
\(764\) | −30819.4 | −1.45943 | ||||||||
\(765\) | − | 3680.82i | − | 0.173961i | ||||||
\(766\) | 2800.88 | 0.132115 | ||||||||
\(767\) | 12181.8 | + | 24523.3i | 0.573482 | + | 1.15448i | ||||
\(768\) | −7509.10 | −0.352814 | ||||||||
\(769\) | − | 31530.9i | − | 1.47859i | −0.673382 | − | 0.739295i | \(-0.735159\pi\) | ||
0.673382 | − | 0.739295i | \(-0.264841\pi\) | |||||||
\(770\) | 2260.64 | 0.105802 | ||||||||
\(771\) | −14250.6 | −0.665658 | ||||||||
\(772\) | − | 29784.0i | − | 1.38853i | ||||||
\(773\) | 7958.36i | 0.370300i | 0.982710 | + | 0.185150i | \(0.0592772\pi\) | ||||
−0.982710 | + | 0.185150i | \(0.940723\pi\) | |||||||
\(774\) | 5676.24i | 0.263602i | ||||||||
\(775\) | 2352.69i | 0.109047i | ||||||||
\(776\) | −18513.2 | −0.856425 | ||||||||
\(777\) | 12303.3 | 0.568056 | ||||||||
\(778\) | 3414.92i | 0.157366i | ||||||||
\(779\) | −16282.6 | −0.748889 | ||||||||
\(780\) | 2642.36 | + | 5319.34i | 0.121297 | + | 0.244183i | ||||
\(781\) | 650.098 | 0.0297853 | ||||||||
\(782\) | 2120.07i | 0.0969483i | ||||||||
\(783\) | 29608.8 | 1.35138 | ||||||||
\(784\) | −19668.0 | −0.895954 | ||||||||
\(785\) | − | 8519.14i | − | 0.387339i | ||||||
\(786\) | − | 14089.7i | − | 0.639393i | ||||||
\(787\) | 5185.08i | 0.234852i | 0.993082 | + | 0.117426i | \(0.0374642\pi\) | ||||
−0.993082 | + | 0.117426i | \(0.962536\pi\) | |||||||
\(788\) | − | 2657.02i | − | 0.120117i | ||||||
\(789\) | −26491.3 | −1.19533 | ||||||||
\(790\) | 1796.29 | 0.0808975 | ||||||||
\(791\) | − | 8175.67i | − | 0.367501i | ||||||
\(792\) | −2261.22 | −0.101451 | ||||||||
\(793\) | −30768.3 | + | 15284.0i | −1.37782 | + | 0.684428i | ||||
\(794\) | 18082.4 | 0.808214 | ||||||||
\(795\) | − | 4453.54i | − | 0.198680i | ||||||
\(796\) | 27926.2 | 1.24349 | ||||||||
\(797\) | 13511.3 | 0.600494 | 0.300247 | − | 0.953861i | \(-0.402931\pi\) | ||||
0.300247 | + | 0.953861i | \(0.402931\pi\) | |||||||
\(798\) | − | 10820.6i | − | 0.480005i | ||||||
\(799\) | 9146.32i | 0.404973i | ||||||||
\(800\) | − | 18160.7i | − | 0.802598i | ||||||
\(801\) | − | 9636.73i | − | 0.425090i | ||||||
\(802\) | −16817.8 | −0.740471 | ||||||||
\(803\) | 213.164 | 0.00936785 | ||||||||
\(804\) | − | 5373.28i | − | 0.235698i | ||||||
\(805\) | −4128.57 | −0.180761 | ||||||||
\(806\) | 1254.05 | − | 622.945i | 0.0548041 | − | 0.0272237i | ||||
\(807\) | 18308.1 | 0.798608 | ||||||||
\(808\) | − | 825.173i | − | 0.0359276i | ||||||
\(809\) | 18939.2 | 0.823072 | 0.411536 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411536 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(810\) | −1895.75 | −0.0822345 | ||||||||
\(811\) | − | 27498.0i | − | 1.19061i | −0.803499 | − | 0.595306i | \(-0.797031\pi\) | ||
0.803499 | − | 0.595306i | \(-0.202969\pi\) | |||||||
\(812\) | 40332.7i | 1.74310i | ||||||||
\(813\) | − | 30938.0i | − | 1.33461i | ||||||
\(814\) | 1337.76i | 0.0576024i | ||||||||
\(815\) | −17184.4 | −0.738580 | ||||||||
\(816\) | 7245.08 | 0.310819 | ||||||||
\(817\) | 26349.3i | 1.12833i | ||||||||
\(818\) | 4179.80 | 0.178659 | ||||||||
\(819\) | 7595.26 | + | 15290.0i | 0.324054 | + | 0.652352i | ||||
\(820\) | −7838.93 | −0.333838 | ||||||||
\(821\) | 23049.9i | 0.979840i | 0.871767 | + | 0.489920i | \(0.162974\pi\) | ||||
−0.871767 | + | 0.489920i | \(0.837026\pi\) | |||||||
\(822\) | −8321.79 | −0.353109 | ||||||||
\(823\) | −24031.4 | −1.01784 | −0.508920 | − | 0.860814i | \(-0.669955\pi\) | ||||
−0.508920 | + | 0.860814i | \(0.669955\pi\) | |||||||
\(824\) | 12481.6i | 0.527690i | ||||||||
\(825\) | 4365.72i | 0.184236i | ||||||||
\(826\) | − | 24016.1i | − | 1.01166i | ||||||
\(827\) | 4449.75i | 0.187102i | 0.995615 | + | 0.0935508i | \(0.0298218\pi\) | ||||
−0.995615 | + | 0.0935508i | \(0.970178\pi\) | |||||||
\(828\) | 1833.38 | 0.0769497 | ||||||||
\(829\) | −4554.87 | −0.190829 | −0.0954145 | − | 0.995438i | \(-0.530418\pi\) | ||||
−0.0954145 | + | 0.995438i | \(0.530418\pi\) | |||||||
\(830\) | 8611.07i | 0.360114i | ||||||||
\(831\) | 21936.7 | 0.915734 | ||||||||
\(832\) | −311.466 | + | 154.720i | −0.0129785 | + | 0.00644705i | ||||
\(833\) | −46136.9 | −1.91903 | ||||||||
\(834\) | 7203.43i | 0.299082i | ||||||||
\(835\) | 10301.2 | 0.426932 | ||||||||
\(836\) | −4660.07 | −0.192789 | ||||||||
\(837\) | − | 3571.03i | − | 0.147470i | ||||||
\(838\) | 13053.7i | 0.538108i | ||||||||
\(839\) | − | 31846.2i | − | 1.31043i | −0.755441 | − | 0.655217i | \(-0.772577\pi\) | ||
0.755441 | − | 0.655217i | \(-0.227423\pi\) | |||||||
\(840\) | − | 11733.9i | − | 0.481974i | ||||||
\(841\) | 13656.7 | 0.559953 | ||||||||
\(842\) | 17101.1 | 0.699934 | ||||||||
\(843\) | 8502.51i | 0.347381i | ||||||||
\(844\) | −1880.08 | −0.0766768 | ||||||||
\(845\) | 8751.89 | + | 6635.48i | 0.356301 | + | 0.270139i | ||||
\(846\) | −1996.92 | −0.0811530 | ||||||||
\(847\) | 3917.13i | 0.158907i | ||||||||
\(848\) | −6262.67 | −0.253610 | ||||||||
\(849\) | 34883.9 | 1.41015 | ||||||||
\(850\) | − | 8311.17i | − | 0.335378i | ||||||
\(851\) | − | 2443.13i | − | 0.0984129i | ||||||
\(852\) | − | 1498.07i | − | 0.0602382i | ||||||
\(853\) | − | 43935.5i | − | 1.76357i | −0.471656 | − | 0.881783i | \(-0.656343\pi\) | ||
0.471656 | − | 0.881783i | \(-0.343657\pi\) | |||||||
\(854\) | 30132.0 | 1.20737 | ||||||||
\(855\) | 3730.51 | 0.149217 | ||||||||
\(856\) | − | 21961.0i | − | 0.876885i | ||||||
\(857\) | 33734.8 | 1.34464 | 0.672322 | − | 0.740259i | \(-0.265297\pi\) | ||||
0.672322 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(858\) | 2327.05 | − | 1155.96i | 0.0925924 | − | 0.0459950i | ||||
\(859\) | 30499.0 | 1.21142 | 0.605711 | − | 0.795685i | \(-0.292889\pi\) | ||||
0.605711 | + | 0.795685i | \(0.292889\pi\) | |||||||
\(860\) | 12685.4i | 0.502986i | ||||||||
\(861\) | 31539.2 | 1.24838 | ||||||||
\(862\) | −22548.4 | −0.890952 | ||||||||
\(863\) | − | 5677.31i | − | 0.223937i | −0.993712 | − | 0.111969i | \(-0.964284\pi\) | ||
0.993712 | − | 0.111969i | \(-0.0357156\pi\) | |||||||
\(864\) | 27565.2i | 1.08540i | ||||||||
\(865\) | − | 2610.68i | − | 0.102620i | ||||||
\(866\) | − | 2360.58i | − | 0.0926278i | ||||||
\(867\) | −2501.63 | −0.0979930 | ||||||||
\(868\) | 4864.40 | 0.190217 | ||||||||
\(869\) | 3112.52i | 0.121502i | ||||||||
\(870\) | −4913.96 | −0.191493 | ||||||||
\(871\) | −4420.31 | − | 8898.53i | −0.171959 | − | 0.346171i | ||||
\(872\) | −17930.3 | −0.696327 | ||||||||
\(873\) | 11400.8i | 0.441991i | ||||||||
\(874\) | −2148.69 | −0.0831584 | ||||||||
\(875\) | 36414.3 | 1.40689 | ||||||||
\(876\) | − | 491.208i | − | 0.0189457i | ||||||
\(877\) | − | 6490.42i | − | 0.249904i | −0.992163 | − | 0.124952i | \(-0.960122\pi\) | ||
0.992163 | − | 0.124952i | \(-0.0398777\pi\) | |||||||
\(878\) | 10555.3i | 0.405722i | ||||||||
\(879\) | − | 37577.6i | − | 1.44193i | ||||||
\(880\) | −1534.08 | −0.0587656 | ||||||||
\(881\) | −3334.19 | −0.127505 | −0.0637525 | − | 0.997966i | \(-0.520307\pi\) | ||||
−0.0637525 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(882\) | − | 10073.1i | − | 0.384556i | ||||||
\(883\) | 40609.4 | 1.54769 | 0.773847 | − | 0.633372i | \(-0.218330\pi\) | ||||
0.773847 | + | 0.633372i | \(0.218330\pi\) | |||||||
\(884\) | 17546.9 | − | 8716.38i | 0.667610 | − | 0.331633i | ||||
\(885\) | −11589.5 | −0.440201 | ||||||||
\(886\) | 80.7741i | 0.00306282i | ||||||||
\(887\) | −5984.16 | −0.226526 | −0.113263 | − | 0.993565i | \(-0.536130\pi\) | ||||
−0.113263 | + | 0.993565i | \(0.536130\pi\) | |||||||
\(888\) | 6943.67 | 0.262403 | ||||||||
\(889\) | 48994.7i | 1.84840i | ||||||||
\(890\) | 5437.31i | 0.204785i | ||||||||
\(891\) | − | 3284.87i | − | 0.123510i | ||||||
\(892\) | − | 6798.10i | − | 0.255176i | ||||||
\(893\) | −9269.78 | −0.347370 | ||||||||
\(894\) | 2592.09 | 0.0969714 | ||||||||
\(895\) | − | 907.082i | − | 0.0338775i | ||||||
\(896\) | −46723.9 | −1.74211 | ||||||||
\(897\) | −4249.87 | + | 2111.11i | −0.158193 | + | 0.0785817i | ||||
\(898\) | 15246.9 | 0.566588 | ||||||||
\(899\) | − | 4588.57i | − | 0.170231i | ||||||
\(900\) | −7187.28 | −0.266195 | ||||||||
\(901\) | −14690.9 | −0.543202 | ||||||||
\(902\) | 3429.30i | 0.126589i | ||||||||
\(903\) | − | 51038.4i | − | 1.88090i | ||||||
\(904\) | − | 4614.12i | − | 0.169761i | ||||||
\(905\) | 14224.4i | 0.522468i | ||||||||
\(906\) | 7798.34 | 0.285963 | ||||||||
\(907\) | 18581.3 | 0.680246 | 0.340123 | − | 0.940381i | \(-0.389531\pi\) | ||||
0.340123 | + | 0.940381i | \(0.389531\pi\) | |||||||
\(908\) | − | 34395.1i | − | 1.25709i | ||||||
\(909\) | −508.157 | −0.0185418 | ||||||||
\(910\) | −4285.45 | − | 8627.04i | −0.156111 | − | 0.314268i | ||||
\(911\) | −2418.57 | −0.0879592 | −0.0439796 | − | 0.999032i | \(-0.514004\pi\) | ||||
−0.0439796 | + | 0.999032i | \(0.514004\pi\) | |||||||
\(912\) | 7342.88i | 0.266609i | ||||||||
\(913\) | −14920.9 | −0.540864 | ||||||||
\(914\) | −3458.69 | −0.125168 | ||||||||
\(915\) | − | 14540.9i | − | 0.525362i | ||||||
\(916\) | 4681.01i | 0.168848i | ||||||||
\(917\) | − | 90509.5i | − | 3.25942i | ||||||
\(918\) | 12615.1i | 0.453551i | ||||||||
\(919\) | −25585.2 | −0.918364 | −0.459182 | − | 0.888342i | \(-0.651857\pi\) | ||||
−0.459182 | + | 0.888342i | \(0.651857\pi\) | |||||||
\(920\) | −2330.05 | −0.0834995 | ||||||||
\(921\) | 40161.7i | 1.43689i | ||||||||
\(922\) | −10811.6 | −0.386184 | ||||||||
\(923\) | −1232.38 | − | 2480.91i | −0.0439483 | − | 0.0884724i | ||||
\(924\) | 9026.51 | 0.321375 | ||||||||
\(925\) | 9577.64i | 0.340444i | ||||||||
\(926\) | −9736.38 | −0.345526 | ||||||||
\(927\) | 7686.40 | 0.272335 | ||||||||
\(928\) | 35419.7i | 1.25292i | ||||||||
\(929\) | − | 12091.4i | − | 0.427026i | −0.976940 | − | 0.213513i | \(-0.931509\pi\) | ||
0.976940 | − | 0.213513i | \(-0.0684905\pi\) | |||||||
\(930\) | 592.656i | 0.0208967i | ||||||||
\(931\) | − | 46759.7i | − | 1.64607i | ||||||
\(932\) | 17597.2 | 0.618470 | ||||||||
\(933\) | −1160.94 | −0.0407369 | ||||||||
\(934\) | 12642.0i | 0.442890i | ||||||||
\(935\) | −3598.62 | −0.125869 | ||||||||
\(936\) | 4286.56 | + | 8629.27i | 0.149691 | + | 0.301342i | ||||
\(937\) | 4975.34 | 0.173466 | 0.0867329 | − | 0.996232i | \(-0.472357\pi\) | ||||
0.0867329 | + | 0.996232i | \(0.472357\pi\) | |||||||
\(938\) | 8714.52i | 0.303347i | ||||||||
\(939\) | −26131.4 | −0.908163 | ||||||||
\(940\) | −4462.75 | −0.154850 | ||||||||
\(941\) | 16314.0i | 0.565166i | 0.959243 | + | 0.282583i | \(0.0911913\pi\) | ||||
−0.959243 | + | 0.282583i | \(0.908809\pi\) | |||||||
\(942\) | 8588.09i | 0.297044i | ||||||||
\(943\) | − | 6262.89i | − | 0.216275i | ||||||
\(944\) | 16297.5i | 0.561903i | ||||||||
\(945\) | −24566.3 | −0.845653 | ||||||||
\(946\) | 5549.47 | 0.190728 | ||||||||
\(947\) | − | 29901.2i | − | 1.02604i | −0.858378 | − | 0.513019i | \(-0.828527\pi\) | ||
0.858378 | − | 0.513019i | \(-0.171473\pi\) | |||||||
\(948\) | 7172.41 | 0.245727 | ||||||||
\(949\) | −404.091 | − | 813.476i | −0.0138223 | − | 0.0278257i | ||||
\(950\) | 8423.36 | 0.287673 | ||||||||
\(951\) | − | 29372.1i | − | 1.00153i | ||||||
\(952\) | −38706.6 | −1.31774 | ||||||||
\(953\) | −19450.0 | −0.661120 | −0.330560 | − | 0.943785i | \(-0.607238\pi\) | ||||
−0.330560 | + | 0.943785i | \(0.607238\pi\) | |||||||
\(954\) | − | 3207.47i | − | 0.108853i | ||||||
\(955\) | − | 24120.7i | − | 0.817307i | ||||||
\(956\) | 15304.0i | 0.517748i | ||||||||
\(957\) | − | 8514.68i | − | 0.287608i | ||||||
\(958\) | 7562.33 | 0.255039 | ||||||||
\(959\) | −53457.6 | −1.80004 | ||||||||
\(960\) | − | 147.197i | − | 0.00494871i | ||||||
\(961\) | 29237.6 | 0.981424 | ||||||||
\(962\) | 5105.15 | − | 2535.97i | 0.171098 | − | 0.0849925i | ||||
\(963\) | −13524.0 | −0.452550 | ||||||||
\(964\) | − | 25304.2i | − | 0.845427i | ||||||
\(965\) | 23310.3 | 0.777603 | ||||||||
\(966\) | 4161.99 | 0.138623 | ||||||||
\(967\) | 22015.8i | 0.732141i | 0.930587 | + | 0.366070i | \(0.119297\pi\) | ||||
−0.930587 | + | 0.366070i | \(0.880703\pi\) | |||||||
\(968\) | 2210.72i | 0.0734042i | ||||||||
\(969\) | 17224.8i | 0.571044i | ||||||||
\(970\) | − | 6432.64i | − | 0.212927i | ||||||
\(971\) | 25479.9 | 0.842110 | 0.421055 | − | 0.907035i | \(-0.361660\pi\) | ||||
0.421055 | + | 0.907035i | \(0.361660\pi\) | |||||||
\(972\) | 18609.5 | 0.614096 | ||||||||
\(973\) | 46273.5i | 1.52462i | ||||||||
\(974\) | 15613.5 | 0.513644 | ||||||||
\(975\) | 16660.5 | − | 8276.03i | 0.547243 | − | 0.271841i | ||||
\(976\) | −20447.7 | −0.670610 | ||||||||
\(977\) | 36655.5i | 1.20032i | 0.799880 | + | 0.600160i | \(0.204896\pi\) | ||||
−0.799880 | + | 0.600160i | \(0.795104\pi\) | |||||||
\(978\) | 17323.5 | 0.566404 | ||||||||
\(979\) | −9421.52 | −0.307572 | ||||||||
\(980\) | − | 22511.5i | − | 0.733780i | ||||||
\(981\) | 11041.8i | 0.359366i | ||||||||
\(982\) | − | 4414.20i | − | 0.143445i | ||||||
\(983\) | 23339.6i | 0.757293i | 0.925541 | + | 0.378647i | \(0.123610\pi\) | ||||
−0.925541 | + | 0.378647i | \(0.876390\pi\) | |||||||
\(984\) | 17799.9 | 0.576666 | ||||||||
\(985\) | 2079.51 | 0.0672678 | ||||||||
\(986\) | 16209.7i | 0.523551i | ||||||||
\(987\) | 17955.5 | 0.579056 | ||||||||
\(988\) | 8834.03 | + | 17783.8i | 0.284461 | + | 0.572649i | ||||
\(989\) | −10134.9 | −0.325856 | ||||||||
\(990\) | − | 785.687i | − | 0.0252230i | ||||||
\(991\) | −32249.8 | −1.03375 | −0.516877 | − | 0.856060i | \(-0.672905\pi\) | ||||
−0.516877 | + | 0.856060i | \(0.672905\pi\) | |||||||
\(992\) | 4271.86 | 0.136725 | ||||||||
\(993\) | − | 21844.0i | − | 0.698086i | ||||||
\(994\) | 2429.60i | 0.0775275i | ||||||||
\(995\) | 21856.4i | 0.696375i | ||||||||
\(996\) | 34383.2i | 1.09385i | ||||||||
\(997\) | 38605.4 | 1.22632 | 0.613162 | − | 0.789957i | \(-0.289897\pi\) | ||||
0.613162 | + | 0.789957i | \(0.289897\pi\) | |||||||
\(998\) | 7003.56 | 0.222138 | ||||||||
\(999\) | − | 14537.4i | − | 0.460403i |
(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 | 143.4.b.a.12.15 | ✓ | 36 | |
13.5 | odd | 4 | 1859.4.a.j.1.8 | 18 | |||
13.8 | odd | 4 | 1859.4.a.k.1.11 | 18 | |||
13.12 | even | 2 | inner | 143.4.b.a.12.22 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.b.a.12.15 | ✓ | 36 | 1.1 | even | 1 | trivial | |
143.4.b.a.12.22 | yes | 36 | 13.12 | even | 2 | inner | |
1859.4.a.j.1.8 | 18 | 13.5 | odd | 4 | |||
1859.4.a.k.1.11 | 18 | 13.8 | odd | 4 |