Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{13} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.3 | ||
Root | \(1.09722 + 1.90044i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.46 |
Dual form | 135.4.e.c.91.3 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09722 | + | 1.90044i | −0.387927 | + | 0.671909i | −0.992170 | − | 0.124891i | \(-0.960142\pi\) |
0.604244 | + | 0.796799i | \(0.293475\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.59221 | + | 2.75778i | 0.199026 | + | 0.344723i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.38302 | + | 2.39547i | −0.0746763 | + | 0.129343i | −0.900945 | − | 0.433932i | \(-0.857126\pi\) |
0.826269 | + | 0.563275i | \(0.190459\pi\) | |||||||
\(8\) | −24.5436 | −1.08468 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.9722 | 0.346972 | ||||||||
\(11\) | −26.3295 | + | 45.6040i | −0.721694 | + | 1.25001i | 0.238626 | + | 0.971112i | \(0.423303\pi\) |
−0.960320 | + | 0.278900i | \(0.910030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.2267 | − | 17.7132i | −0.218183 | − | 0.377905i | 0.736069 | − | 0.676906i | \(-0.236680\pi\) |
−0.954253 | + | 0.299002i | \(0.903346\pi\) | |||||||
\(14\) | −3.03497 | − | 5.25672i | −0.0579378 | − | 0.100351i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1921 | − | 24.5814i | 0.221751 | − | 0.384085i | ||||
\(17\) | −3.66084 | −0.0522285 | −0.0261142 | − | 0.999659i | \(-0.508313\pi\) | ||||
−0.0261142 | + | 0.999659i | \(0.508313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −95.6705 | −1.15517 | −0.577587 | − | 0.816329i | \(-0.696006\pi\) | ||||
−0.577587 | + | 0.816329i | \(0.696006\pi\) | |||||||
\(20\) | 7.96104 | − | 13.7889i | 0.0890071 | − | 0.154165i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −57.7786 | − | 100.075i | −0.559929 | − | 0.969825i | ||||
\(23\) | −44.9206 | − | 77.8047i | −0.407243 | − | 0.705365i | 0.587337 | − | 0.809343i | \(-0.300176\pi\) |
−0.994580 | + | 0.103977i | \(0.966843\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 44.8840 | 0.338556 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.80825 | −0.0594501 | ||||||||
\(29\) | −113.890 | + | 197.264i | −0.729272 | + | 1.26314i | 0.227919 | + | 0.973680i | \(0.426808\pi\) |
−0.957191 | + | 0.289456i | \(0.906526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −139.569 | − | 241.741i | −0.808625 | − | 1.40058i | −0.913816 | − | 0.406128i | \(-0.866879\pi\) |
0.105191 | − | 0.994452i | \(-0.466455\pi\) | |||||||
\(32\) | −67.0306 | − | 116.100i | −0.370295 | − | 0.641370i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.01675 | − | 6.95722i | 0.0202608 | − | 0.0350928i | ||||
\(35\) | 13.8302 | 0.0667925 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 273.725 | 1.21622 | 0.608110 | − | 0.793852i | \(-0.291928\pi\) | ||||
0.608110 | + | 0.793852i | \(0.291928\pi\) | |||||||
\(38\) | 104.972 | − | 181.816i | 0.448123 | − | 0.776172i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 61.3589 | + | 106.277i | 0.242542 | + | 0.420096i | ||||
\(41\) | 32.4323 | + | 56.1744i | 0.123539 | + | 0.213975i | 0.921161 | − | 0.389182i | \(-0.127242\pi\) |
−0.797622 | + | 0.603157i | \(0.793909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −209.381 | + | 362.658i | −0.742565 | + | 1.28616i | 0.208759 | + | 0.977967i | \(0.433057\pi\) |
−0.951324 | + | 0.308193i | \(0.900276\pi\) | |||||||
\(44\) | −167.688 | −0.574544 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 197.151 | 0.631921 | ||||||||
\(47\) | 69.3544 | − | 120.125i | 0.215242 | − | 0.372810i | −0.738105 | − | 0.674685i | \(-0.764279\pi\) |
0.953347 | + | 0.301875i | \(0.0976126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 167.674 | + | 290.421i | 0.488847 | + | 0.846708i | ||||
\(50\) | −27.4306 | − | 47.5111i | −0.0775853 | − | 0.134382i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 32.5661 | − | 56.4062i | 0.0868483 | − | 0.150426i | ||||
\(53\) | 197.063 | 0.510730 | 0.255365 | − | 0.966845i | \(-0.417804\pi\) | ||||
0.255365 | + | 0.966845i | \(0.417804\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 263.295 | 0.645503 | ||||||||
\(56\) | 33.9444 | − | 58.7934i | 0.0810001 | − | 0.140296i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −249.926 | − | 432.884i | −0.565808 | − | 0.980008i | ||||
\(59\) | 370.552 | + | 641.814i | 0.817656 | + | 1.41622i | 0.907405 | + | 0.420257i | \(0.138060\pi\) |
−0.0897490 | + | 0.995964i | \(0.528606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −244.234 | + | 423.026i | −0.512639 | + | 0.887916i | 0.487254 | + | 0.873260i | \(0.337999\pi\) |
−0.999893 | + | 0.0146560i | \(0.995335\pi\) | |||||||
\(62\) | 612.554 | 1.25475 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 521.263 | 1.01809 | ||||||||
\(65\) | −51.1336 | + | 88.5660i | −0.0975746 | + | 0.169004i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 205.734 | + | 356.341i | 0.375140 | + | 0.649762i | 0.990348 | − | 0.138603i | \(-0.0442613\pi\) |
−0.615208 | + | 0.788365i | \(0.710928\pi\) | |||||||
\(68\) | −5.82882 | − | 10.0958i | −0.0103948 | − | 0.0180044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −15.1748 | + | 26.2836i | −0.0259106 | + | 0.0448785i | ||||
\(71\) | 310.343 | 0.518746 | 0.259373 | − | 0.965777i | \(-0.416484\pi\) | ||||
0.259373 | + | 0.965777i | \(0.416484\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51.0260 | −0.0818101 | −0.0409051 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409051 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(74\) | −300.338 | + | 520.200i | −0.471804 | + | 0.817189i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −152.327 | − | 263.839i | −0.229910 | − | 0.398215i | ||||
\(77\) | −72.8286 | − | 126.143i | −0.107787 | − | 0.186692i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −603.999 | + | 1046.16i | −0.860193 | + | 1.48990i | 0.0115496 | + | 0.999933i | \(0.496324\pi\) |
−0.871742 | + | 0.489964i | \(0.837010\pi\) | |||||||
\(80\) | −141.921 | −0.198340 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −142.342 | −0.191695 | ||||||||
\(83\) | 452.611 | − | 783.945i | 0.598560 | − | 1.03674i | −0.394474 | − | 0.918907i | \(-0.629073\pi\) |
0.993034 | − | 0.117829i | \(-0.0375935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.15210 | + | 15.8519i | 0.0116786 | + | 0.0202280i | ||||
\(86\) | −459.475 | − | 795.833i | −0.576121 | − | 0.997871i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 646.220 | − | 1119.29i | 0.782810 | − | 1.35587i | ||||
\(89\) | −663.633 | −0.790393 | −0.395197 | − | 0.918597i | \(-0.629324\pi\) | ||||
−0.395197 | + | 0.918597i | \(0.629324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56.5752 | 0.0651725 | ||||||||
\(92\) | 143.046 | − | 247.763i | 0.162104 | − | 0.280772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 152.194 | + | 263.608i | 0.166996 | + | 0.289246i | ||||
\(95\) | 239.176 | + | 414.265i | 0.258305 | + | 0.447397i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 362.668 | − | 628.159i | 0.379622 | − | 0.657525i | −0.611385 | − | 0.791333i | \(-0.709387\pi\) |
0.991007 | + | 0.133809i | \(0.0427207\pi\) | |||||||
\(98\) | −735.905 | −0.758547 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −79.6104 | −0.0796104 | ||||||||
\(101\) | 488.891 | − | 846.784i | 0.481648 | − | 0.834239i | −0.518130 | − | 0.855302i | \(-0.673372\pi\) |
0.999778 | + | 0.0210629i | \(0.00670503\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −793.852 | − | 1374.99i | −0.759423 | − | 1.31536i | −0.943145 | − | 0.332381i | \(-0.892148\pi\) |
0.183722 | − | 0.982978i | \(-0.441185\pi\) | |||||||
\(104\) | 251.000 | + | 434.745i | 0.236660 | + | 0.409907i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −216.222 | + | 374.507i | −0.198126 | + | 0.343164i | ||||
\(107\) | −897.731 | −0.811093 | −0.405546 | − | 0.914074i | \(-0.632919\pi\) | ||||
−0.405546 | + | 0.914074i | \(0.632919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 855.492 | 0.751754 | 0.375877 | − | 0.926669i | \(-0.377341\pi\) | ||||
0.375877 | + | 0.926669i | \(0.377341\pi\) | |||||||
\(110\) | −288.893 | + | 500.377i | −0.250408 | + | 0.433719i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 39.2560 | + | 67.9934i | 0.0331191 | + | 0.0573640i | ||||
\(113\) | 455.121 | + | 788.292i | 0.378886 | + | 0.656250i | 0.990900 | − | 0.134597i | \(-0.0429738\pi\) |
−0.612014 | + | 0.790847i | \(0.709641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −224.603 | + | 389.024i | −0.182125 | + | 0.315449i | ||||
\(116\) | −725.348 | −0.580576 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1626.31 | −1.26876 | ||||||||
\(119\) | 5.06303 | − | 8.76943i | 0.00390023 | − | 0.00675539i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −720.984 | − | 1248.78i | −0.541686 | − | 0.938227i | ||||
\(122\) | −535.958 | − | 928.306i | −0.397732 | − | 0.688893i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 444.447 | − | 769.804i | 0.321875 | − | 0.557504i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2038.25 | −1.42414 | −0.712068 | − | 0.702111i | \(-0.752241\pi\) | ||||
−0.712068 | + | 0.702111i | \(0.752241\pi\) | |||||||
\(128\) | −35.6968 | + | 61.8287i | −0.0246499 | + | 0.0426948i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −112.210 | − | 194.353i | −0.0757035 | − | 0.131122i | ||||
\(131\) | 117.823 | + | 204.075i | 0.0785817 | + | 0.136108i | 0.902638 | − | 0.430400i | \(-0.141628\pi\) |
−0.824057 | + | 0.566508i | \(0.808294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 132.315 | − | 229.176i | 0.0862642 | − | 0.149414i | ||||
\(134\) | −902.942 | −0.582107 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 89.8501 | 0.0566513 | ||||||||
\(137\) | −1486.45 | + | 2574.60i | −0.926975 | + | 1.60557i | −0.138621 | + | 0.990345i | \(0.544267\pi\) |
−0.788354 | + | 0.615222i | \(0.789066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1047.32 | + | 1814.00i | 0.639080 | + | 1.10692i | 0.985635 | + | 0.168890i | \(0.0540182\pi\) |
−0.346555 | + | 0.938030i | \(0.612648\pi\) | |||||||
\(140\) | 22.0206 | + | 38.1408i | 0.0132934 | + | 0.0230249i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −340.515 | + | 589.790i | −0.201235 | + | 0.348550i | ||||
\(143\) | 1077.06 | 0.629847 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1138.90 | 0.652281 | ||||||||
\(146\) | 55.9868 | − | 96.9720i | 0.0317363 | − | 0.0549689i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 435.828 | + | 754.876i | 0.242060 | + | 0.419259i | ||||
\(149\) | 136.969 | + | 237.237i | 0.0753081 | + | 0.130437i | 0.901220 | − | 0.433361i | \(-0.142673\pi\) |
−0.825912 | + | 0.563799i | \(0.809339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 468.422 | − | 811.331i | 0.252448 | − | 0.437253i | −0.711751 | − | 0.702432i | \(-0.752098\pi\) |
0.964199 | + | 0.265179i | \(0.0854310\pi\) | |||||||
\(152\) | 2348.10 | 1.25300 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 319.637 | 0.167254 | ||||||||
\(155\) | −697.846 | + | 1208.71i | −0.361628 | + | 0.626358i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −199.218 | − | 345.055i | −0.101269 | − | 0.175404i | 0.810938 | − | 0.585131i | \(-0.198957\pi\) |
−0.912208 | + | 0.409728i | \(0.865624\pi\) | |||||||
\(158\) | −1325.44 | − | 2295.73i | −0.667383 | − | 1.15594i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −335.153 | + | 580.502i | −0.165601 | + | 0.286829i | ||||
\(161\) | 248.505 | 0.121646 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 478.154 | 0.229766 | 0.114883 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114883 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(164\) | −103.278 | + | 178.883i | −0.0491747 | + | 0.0851732i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 993.229 | + | 1720.32i | 0.464395 | + | 0.804355i | ||||
\(167\) | −170.181 | − | 294.763i | −0.0788564 | − | 0.136583i | 0.823900 | − | 0.566735i | \(-0.191794\pi\) |
−0.902757 | + | 0.430151i | \(0.858460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 889.328 | − | 1540.36i | 0.404792 | − | 0.701120i | ||||
\(170\) | −40.1675 | −0.0181218 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1333.51 | −0.591159 | ||||||||
\(173\) | 1888.03 | − | 3270.17i | 0.829738 | − | 1.43715i | −0.0685065 | − | 0.997651i | \(-0.521823\pi\) |
0.898244 | − | 0.439497i | \(-0.144843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34.5756 | − | 59.8867i | −0.0149353 | − | 0.0258686i | ||||
\(176\) | 747.341 | + | 1294.43i | 0.320073 | + | 0.554384i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 728.153 | − | 1261.20i | 0.306615 | − | 0.531072i | ||||
\(179\) | −186.652 | −0.0779385 | −0.0389693 | − | 0.999240i | \(-0.512407\pi\) | ||||
−0.0389693 | + | 0.999240i | \(0.512407\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1438.75 | 0.590837 | 0.295418 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295418 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(182\) | −62.0756 | + | 107.518i | −0.0252821 | + | 0.0437900i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1102.51 | + | 1909.61i | 0.441729 | + | 0.765098i | ||||
\(185\) | −684.313 | − | 1185.27i | −0.271955 | − | 0.471040i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 96.3880 | − | 166.949i | 0.0376930 | − | 0.0652862i | ||||
\(188\) | 441.706 | 0.171355 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1049.72 | −0.400813 | ||||||||
\(191\) | −195.218 | + | 338.127i | −0.0739552 | + | 0.128094i | −0.900631 | − | 0.434584i | \(-0.856896\pi\) |
0.826676 | + | 0.562678i | \(0.190229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1957.52 | + | 3390.53i | 0.730081 | + | 1.26454i | 0.956848 | + | 0.290588i | \(0.0938510\pi\) |
−0.226767 | + | 0.973949i | \(0.572816\pi\) | |||||||
\(194\) | 795.854 | + | 1378.46i | 0.294531 | + | 0.510143i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −533.945 | + | 924.820i | −0.194586 | + | 0.337034i | ||||
\(197\) | 892.680 | 0.322847 | 0.161423 | − | 0.986885i | \(-0.448392\pi\) | ||||
0.161423 | + | 0.986885i | \(0.448392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2770.50 | −0.986913 | −0.493457 | − | 0.869770i | \(-0.664267\pi\) | ||||
−0.493457 | + | 0.869770i | \(0.664267\pi\) | |||||||
\(200\) | 306.795 | − | 531.384i | 0.108468 | − | 0.187873i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1072.84 | + | 1858.22i | 0.373688 | + | 0.647247i | ||||
\(203\) | −315.026 | − | 545.641i | −0.108919 | − | 0.188653i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 162.162 | − | 280.872i | 0.0552481 | − | 0.0956925i | ||||
\(206\) | 3484.13 | 1.17840 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −580.554 | −0.193530 | ||||||||
\(209\) | 2518.96 | − | 4362.96i | 0.833683 | − | 1.44398i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2291.25 | − | 3968.57i | −0.747566 | − | 1.29482i | −0.948986 | − | 0.315318i | \(-0.897889\pi\) |
0.201420 | − | 0.979505i | \(-0.435444\pi\) | |||||||
\(212\) | 313.765 | + | 543.458i | 0.101649 | + | 0.176060i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 985.010 | − | 1706.09i | 0.314644 | − | 0.544980i | ||||
\(215\) | 2093.81 | 0.664170 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 772.111 | 0.241541 | ||||||||
\(218\) | −938.664 | + | 1625.81i | −0.291626 | + | 0.505110i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 419.220 | + | 726.111i | 0.128472 | + | 0.222520i | ||||
\(221\) | 37.4384 | + | 64.8452i | 0.0113954 | + | 0.0197374i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2047.67 | + | 3546.66i | −0.614897 | + | 1.06503i | 0.375506 | + | 0.926820i | \(0.377469\pi\) |
−0.990403 | + | 0.138212i | \(0.955864\pi\) | |||||||
\(224\) | 370.820 | 0.110609 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1997.47 | −0.587920 | ||||||||
\(227\) | −1934.68 | + | 3350.96i | −0.565678 | + | 0.979784i | 0.431308 | + | 0.902205i | \(0.358052\pi\) |
−0.996986 | + | 0.0775789i | \(0.975281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −618.006 | − | 1070.42i | −0.178336 | − | 0.308887i | 0.762975 | − | 0.646429i | \(-0.223738\pi\) |
−0.941311 | + | 0.337541i | \(0.890405\pi\) | |||||||
\(230\) | −492.878 | − | 853.690i | −0.141302 | − | 0.244742i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2795.27 | − | 4841.56i | 0.791029 | − | 1.37010i | ||||
\(233\) | −2207.05 | −0.620552 | −0.310276 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310276 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −693.544 | −0.192518 | ||||||||
\(236\) | −1179.99 | + | 2043.80i | −0.325470 | + | 0.563730i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.1105 | + | 19.2440i | 0.00302600 | + | 0.00524119i | ||||
\(239\) | 438.324 | + | 759.199i | 0.118631 | + | 0.205475i | 0.919225 | − | 0.393732i | \(-0.128816\pi\) |
−0.800594 | + | 0.599207i | \(0.795483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 238.931 | − | 413.840i | 0.0638626 | − | 0.110613i | −0.832326 | − | 0.554286i | \(-0.812991\pi\) |
0.896189 | + | 0.443673i | \(0.146325\pi\) | |||||||
\(242\) | 3164.32 | 0.840537 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1555.49 | −0.408114 | ||||||||
\(245\) | 838.372 | − | 1452.10i | 0.218619 | − | 0.378659i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 978.396 | + | 1694.63i | 0.252040 | + | 0.436546i | ||||
\(248\) | 3425.53 | + | 5933.19i | 0.877102 | + | 1.51919i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −137.153 | + | 237.556i | −0.0346972 | + | 0.0600973i | ||||
\(251\) | −6892.28 | −1.73322 | −0.866608 | − | 0.498990i | \(-0.833704\pi\) | ||||
−0.866608 | + | 0.498990i | \(0.833704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4730.94 | 1.17562 | ||||||||
\(254\) | 2236.41 | − | 3873.57i | 0.552460 | − | 0.956889i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2006.72 | + | 3475.74i | 0.489921 | + | 0.848568i | ||||
\(257\) | −3628.35 | − | 6284.49i | −0.880664 | − | 1.52535i | −0.850605 | − | 0.525806i | \(-0.823764\pi\) |
−0.0300589 | − | 0.999548i | \(-0.509569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −378.569 | + | 655.701i | −0.0908229 | + | 0.157310i | ||||
\(260\) | −325.661 | −0.0776795 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −517.110 | −0.121936 | ||||||||
\(263\) | −3158.78 | + | 5471.16i | −0.740603 | + | 1.28276i | 0.211618 | + | 0.977352i | \(0.432127\pi\) |
−0.952221 | + | 0.305409i | \(0.901207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −492.658 | − | 853.308i | −0.114203 | − | 0.197805i | ||||
\(266\) | 290.357 | + | 502.913i | 0.0669283 | + | 0.115923i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −655.142 | + | 1134.74i | −0.149325 | + | 0.258639i | ||||
\(269\) | −5746.22 | −1.30243 | −0.651214 | − | 0.758894i | \(-0.725740\pi\) | ||||
−0.651214 | + | 0.758894i | \(0.725740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4925.20 | 1.10400 | 0.552001 | − | 0.833844i | \(-0.313865\pi\) | ||||
0.552001 | + | 0.833844i | \(0.313865\pi\) | |||||||
\(272\) | −51.9550 | + | 89.9886i | −0.0115817 | + | 0.0200602i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3261.92 | − | 5649.81i | −0.719196 | − | 1.24568i | ||||
\(275\) | −658.237 | − | 1140.10i | −0.144339 | − | 0.250002i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1162.94 | + | 2014.27i | −0.252254 | + | 0.436917i | −0.964146 | − | 0.265372i | \(-0.914505\pi\) |
0.711892 | + | 0.702289i | \(0.247839\pi\) | |||||||
\(278\) | −4596.55 | −0.991665 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −339.444 | −0.0724487 | ||||||||
\(281\) | 1641.71 | − | 2843.52i | 0.348527 | − | 0.603667i | −0.637461 | − | 0.770483i | \(-0.720015\pi\) |
0.985988 | + | 0.166816i | \(0.0533485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1007.11 | − | 1744.36i | −0.211541 | − | 0.366400i | 0.740656 | − | 0.671885i | \(-0.234515\pi\) |
−0.952197 | + | 0.305484i | \(0.901182\pi\) | |||||||
\(284\) | 494.131 | + | 855.860i | 0.103244 | + | 0.178824i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1181.77 | + | 2046.89i | −0.244334 | + | 0.423199i | ||||
\(287\) | −179.419 | −0.0369016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4899.60 | −0.997272 | ||||||||
\(290\) | −1249.63 | + | 2164.42i | −0.253037 | + | 0.438273i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −81.2440 | − | 140.719i | −0.0162823 | − | 0.0282018i | ||||
\(293\) | 240.348 | + | 416.295i | 0.0479225 | + | 0.0830042i | 0.888992 | − | 0.457923i | \(-0.151407\pi\) |
−0.841069 | + | 0.540928i | \(0.818073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1852.76 | − | 3209.07i | 0.365667 | − | 0.633354i | ||||
\(296\) | −6718.20 | −1.31921 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −601.140 | −0.116856 | ||||||||
\(299\) | −918.781 | + | 1591.37i | −0.177707 | + | 0.307798i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −579.158 | − | 1003.13i | −0.110904 | − | 0.192091i | ||||
\(302\) | 1027.93 | + | 1780.42i | 0.195863 | + | 0.339244i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1357.76 | + | 2351.72i | −0.256162 | + | 0.443685i | ||||
\(305\) | 2442.34 | 0.458518 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3222.21 | 0.599026 | 0.299513 | − | 0.954092i | \(-0.403176\pi\) | ||||
0.299513 | + | 0.954092i | \(0.403176\pi\) | |||||||
\(308\) | 231.917 | − | 401.691i | 0.0429048 | − | 0.0743133i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1531.38 | − | 2652.44i | −0.280570 | − | 0.485962i | ||||
\(311\) | 1207.00 | + | 2090.59i | 0.220074 | + | 0.381179i | 0.954830 | − | 0.297152i | \(-0.0960369\pi\) |
−0.734757 | + | 0.678331i | \(0.762704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1253.47 | − | 2171.07i | 0.226359 | − | 0.392065i | −0.730368 | − | 0.683054i | \(-0.760651\pi\) |
0.956726 | + | 0.290990i | \(0.0939846\pi\) | |||||||
\(314\) | 874.344 | 0.157140 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3846.77 | −0.684803 | ||||||||
\(317\) | 1853.56 | − | 3210.46i | 0.328411 | − | 0.568825i | −0.653786 | − | 0.756680i | \(-0.726820\pi\) |
0.982197 | + | 0.187855i | \(0.0601535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5997.34 | − | 10387.7i | −1.05262 | − | 1.82320i | ||||
\(320\) | −1303.16 | − | 2257.13i | −0.227652 | − | 0.394305i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −272.665 | + | 472.270i | −0.0471895 | + | 0.0817347i | ||||
\(323\) | 350.234 | 0.0603330 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 511.336 | 0.0872733 | ||||||||
\(326\) | −524.641 | + | 908.704i | −0.0891324 | + | 0.154382i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −796.005 | − | 1378.72i | −0.134000 | − | 0.232095i | ||||
\(329\) | 191.838 | + | 332.272i | 0.0321470 | + | 0.0556802i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1276.72 | + | 2211.35i | −0.212009 | + | 0.367211i | −0.952343 | − | 0.305029i | \(-0.901334\pi\) |
0.740334 | + | 0.672239i | \(0.234667\pi\) | |||||||
\(332\) | 2882.60 | 0.476516 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 746.906 | 0.122362 | ||||||||
\(335\) | 1028.67 | − | 1781.71i | 0.167768 | − | 0.290582i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1776.44 | − | 3076.89i | −0.287148 | − | 0.497356i | 0.685979 | − | 0.727621i | \(-0.259374\pi\) |
−0.973128 | + | 0.230265i | \(0.926041\pi\) | |||||||
\(338\) | 1951.58 | + | 3380.24i | 0.314059 | + | 0.543966i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.1441 | + | 50.4790i | −0.00464871 | + | 0.00805179i | ||||
\(341\) | 14699.2 | 2.33432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1876.35 | −0.295374 | ||||||||
\(344\) | 5138.95 | − | 8900.93i | 0.805447 | − | 1.39508i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4143.19 | + | 7176.21i | 0.643754 | + | 1.11502i | ||||
\(347\) | −3884.01 | − | 6727.30i | −0.600878 | − | 1.04075i | −0.992688 | − | 0.120705i | \(-0.961485\pi\) |
0.391811 | − | 0.920046i | \(-0.371849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −348.003 | + | 602.760i | −0.0533759 | + | 0.0924498i | −0.891479 | − | 0.453062i | \(-0.850331\pi\) |
0.838103 | + | 0.545512i | \(0.183665\pi\) | |||||||
\(350\) | 151.748 | 0.0231751 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7059.52 | 1.06896 | ||||||||
\(353\) | −2725.94 | + | 4721.46i | −0.411011 | + | 0.711892i | −0.995001 | − | 0.0998692i | \(-0.968158\pi\) |
0.583990 | + | 0.811761i | \(0.301491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −775.858 | − | 1343.83i | −0.115995 | − | 0.200909i | ||||
\(356\) | −1056.64 | − | 1830.16i | −0.157309 | − | 0.272467i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 204.798 | − | 354.721i | 0.0302344 | − | 0.0523675i | ||||
\(359\) | −4036.41 | −0.593408 | −0.296704 | − | 0.954969i | \(-0.595887\pi\) | ||||
−0.296704 | + | 0.954969i | \(0.595887\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2293.85 | 0.334429 | ||||||||
\(362\) | −1578.63 | + | 2734.26i | −0.229201 | + | 0.396988i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 90.0795 | + | 156.022i | 0.0129710 | + | 0.0224665i | ||||
\(365\) | 127.565 | + | 220.949i | 0.0182933 | + | 0.0316849i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5619.96 | + | 9734.06i | −0.799345 | + | 1.38451i | 0.120698 | + | 0.992689i | \(0.461487\pi\) |
−0.920043 | + | 0.391817i | \(0.871847\pi\) | |||||||
\(368\) | −2550.07 | −0.361227 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3003.38 | 0.421995 | ||||||||
\(371\) | −272.543 | + | 472.059i | −0.0381394 | + | 0.0660595i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3160.36 | + | 5473.90i | 0.438706 | + | 0.759860i | 0.997590 | − | 0.0693853i | \(-0.0221038\pi\) |
−0.558884 | + | 0.829246i | \(0.688770\pi\) | |||||||
\(374\) | 211.518 | + | 366.360i | 0.0292442 | + | 0.0506525i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1702.20 | + | 2948.30i | −0.233469 | + | 0.404381i | ||||
\(377\) | 4658.90 | 0.636460 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9325.49 | 1.26390 | 0.631950 | − | 0.775009i | \(-0.282255\pi\) | ||||
0.631950 | + | 0.775009i | \(0.282255\pi\) | |||||||
\(380\) | −761.637 | + | 1319.19i | −0.102819 | + | 0.178087i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −428.394 | − | 742.000i | −0.0573784 | − | 0.0993823i | ||||
\(383\) | 5574.01 | + | 9654.47i | 0.743652 | + | 1.28804i | 0.950822 | + | 0.309738i | \(0.100241\pi\) |
−0.207170 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −364.143 | + | 630.715i | −0.0482038 | + | 0.0834914i | ||||
\(386\) | −8591.35 | −1.13287 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2309.77 | 0.302219 | ||||||||
\(389\) | 3285.41 | − | 5690.49i | 0.428218 | − | 0.741695i | −0.568497 | − | 0.822685i | \(-0.692475\pi\) |
0.996715 | + | 0.0809902i | \(0.0258082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 164.447 | + | 284.831i | 0.0212697 | + | 0.0368402i | ||||
\(392\) | −4115.33 | − | 7127.96i | −0.530244 | − | 0.918409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −979.469 | + | 1696.49i | −0.125241 | + | 0.216924i | ||||
\(395\) | 6039.99 | 0.769380 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3969.33 | 0.501800 | 0.250900 | − | 0.968013i | \(-0.419273\pi\) | ||||
0.250900 | + | 0.968013i | \(0.419273\pi\) | |||||||
\(398\) | 3039.86 | − | 5265.19i | 0.382850 | − | 0.663115i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 354.802 | + | 614.535i | 0.0443503 | + | 0.0768169i | ||||
\(401\) | 2187.35 | + | 3788.60i | 0.272396 | + | 0.471804i | 0.969475 | − | 0.245190i | \(-0.0788505\pi\) |
−0.697079 | + | 0.716995i | \(0.745517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2854.67 | + | 4944.44i | −0.352857 | + | 0.611166i | ||||
\(404\) | 3113.66 | 0.383442 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1382.61 | 0.169010 | ||||||||
\(407\) | −7207.05 | + | 12483.0i | −0.877740 | + | 1.52029i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4436.16 | + | 7683.66i | 0.536318 | + | 0.928930i | 0.999098 | + | 0.0424573i | \(0.0135186\pi\) |
−0.462780 | + | 0.886473i | \(0.653148\pi\) | |||||||
\(410\) | 355.855 | + | 616.358i | 0.0428644 | + | 0.0742433i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2527.95 | − | 4378.55i | 0.302290 | − | 0.523581i | ||||
\(413\) | −2049.93 | −0.244238 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4526.11 | −0.535368 | ||||||||
\(416\) | −1371.01 | + | 2374.65i | −0.161584 | + | 0.279872i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5527.71 | + | 9574.27i | 0.646816 | + | 1.12032i | ||||
\(419\) | −507.087 | − | 878.300i | −0.0591236 | − | 0.102405i | 0.834949 | − | 0.550328i | \(-0.185497\pi\) |
−0.894072 | + | 0.447923i | \(0.852164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7446.57 | − | 12897.8i | 0.862051 | − | 1.49312i | −0.00789511 | − | 0.999969i | \(-0.502513\pi\) |
0.869946 | − | 0.493147i | \(-0.164154\pi\) | |||||||
\(422\) | 10056.1 | 1.16000 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4836.63 | −0.553980 | ||||||||
\(425\) | 45.7605 | − | 79.2595i | 0.00522285 | − | 0.00904624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −675.563 | − | 1170.11i | −0.0765639 | − | 0.132613i | ||||
\(428\) | −1429.37 | − | 2475.75i | −0.161429 | − | 0.279602i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2297.37 | + | 3979.17i | −0.257649 | + | 0.446261i | ||||
\(431\) | 4363.90 | 0.487707 | 0.243853 | − | 0.969812i | \(-0.421588\pi\) | ||||
0.243853 | + | 0.969812i | \(0.421588\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9301.59 | 1.03235 | 0.516173 | − | 0.856484i | \(-0.327356\pi\) | ||||
0.516173 | + | 0.856484i | \(0.327356\pi\) | |||||||
\(434\) | −847.177 | + | 1467.35i | −0.0937000 | + | 0.162293i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1362.12 | + | 2359.26i | 0.149619 | + | 0.259147i | ||||
\(437\) | 4297.57 | + | 7443.62i | 0.470437 | + | 0.814820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −760.076 | + | 1316.49i | −0.0826343 | + | 0.143127i | −0.904381 | − | 0.426727i | \(-0.859667\pi\) |
0.821746 | + | 0.569853i | \(0.193000\pi\) | |||||||
\(440\) | −6462.20 | −0.700166 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −164.313 | −0.0176823 | ||||||||
\(443\) | 2231.24 | − | 3864.62i | 0.239299 | − | 0.414478i | −0.721214 | − | 0.692712i | \(-0.756416\pi\) |
0.960513 | + | 0.278234i | \(0.0897490\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1659.08 | + | 2873.62i | 0.176737 | + | 0.306118i | ||||
\(446\) | −4493.49 | − | 7782.96i | −0.477070 | − | 0.826309i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −720.919 | + | 1248.67i | −0.0760273 | + | 0.131683i | ||||
\(449\) | 5371.66 | 0.564598 | 0.282299 | − | 0.959326i | \(-0.408903\pi\) | ||||
0.282299 | + | 0.959326i | \(0.408903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3415.71 | −0.356628 | ||||||||
\(452\) | −1449.29 | + | 2510.25i | −0.150816 | + | 0.261222i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4245.54 | − | 7353.49i | −0.438883 | − | 0.760168i | ||||
\(455\) | −141.438 | − | 244.978i | −0.0145730 | − | 0.0252412i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7762.71 | + | 13445.4i | −0.794583 | + | 1.37626i | 0.128520 | + | 0.991707i | \(0.458977\pi\) |
−0.923104 | + | 0.384551i | \(0.874356\pi\) | |||||||
\(458\) | 2712.36 | 0.276725 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1430.46 | −0.144990 | ||||||||
\(461\) | −28.2090 | + | 48.8594i | −0.00284994 | + | 0.00493624i | −0.867447 | − | 0.497530i | \(-0.834240\pi\) |
0.864597 | + | 0.502466i | \(0.167574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6686.89 | − | 11582.0i | −0.671201 | − | 1.16255i | −0.977564 | − | 0.210640i | \(-0.932445\pi\) |
0.306363 | − | 0.951915i | \(-0.400888\pi\) | |||||||
\(464\) | 3232.68 | + | 5599.17i | 0.323434 | + | 0.560204i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2421.62 | − | 4194.37i | 0.240729 | − | 0.416954i | ||||
\(467\) | −2677.46 | −0.265306 | −0.132653 | − | 0.991163i | \(-0.542350\pi\) | ||||
−0.132653 | + | 0.991163i | \(0.542350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1138.14 | −0.112056 | ||||||||
\(470\) | 760.972 | − | 1318.04i | 0.0746830 | − | 0.129355i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9094.66 | − | 15752.4i | −0.886898 | − | 1.53615i | ||||
\(473\) | −11025.8 | − | 19097.2i | −1.07181 | − | 1.85643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1195.88 | − | 2071.33i | 0.115517 | − | 0.200082i | ||||
\(476\) | 32.2456 | 0.00310499 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1923.75 | −0.184080 | ||||||||
\(479\) | −1734.96 | + | 3005.05i | −0.165496 | + | 0.286647i | −0.936831 | − | 0.349782i | \(-0.886256\pi\) |
0.771335 | + | 0.636429i | \(0.219589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2799.31 | − | 4848.55i | −0.265359 | − | 0.459616i | ||||
\(482\) | 524.320 | + | 908.149i | 0.0495480 | + | 0.0858196i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2295.91 | − | 3976.64i | 0.215619 | − | 0.373463i | ||||
\(485\) | −3626.68 | −0.339544 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14040.6 | −1.30645 | −0.653224 | − | 0.757165i | \(-0.726584\pi\) | ||||
−0.653224 | + | 0.757165i | \(0.726584\pi\) | |||||||
\(488\) | 5994.38 | − | 10382.6i | 0.556051 | − | 0.963108i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1839.76 | + | 3186.56i | 0.169616 | + | 0.293784i | ||||
\(491\) | 4907.72 | + | 8500.42i | 0.451084 | + | 0.781301i | 0.998454 | − | 0.0555902i | \(-0.0177040\pi\) |
−0.547369 | + | 0.836891i | \(0.684371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 416.934 | − | 722.151i | 0.0380888 | − | 0.0659717i | ||||
\(494\) | −4294.07 | −0.391092 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7923.12 | −0.717255 | ||||||||
\(497\) | −429.212 | + | 743.418i | −0.0387380 | + | 0.0670962i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6026.00 | + | 10437.3i | 0.540603 | + | 0.936351i | 0.998869 | + | 0.0475367i | \(0.0151371\pi\) |
−0.458267 | + | 0.888815i | \(0.651530\pi\) | |||||||
\(500\) | 199.026 | + | 344.723i | 0.0178014 | + | 0.0308330i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7562.36 | − | 13098.4i | 0.672360 | − | 1.16456i | ||||
\(503\) | 4695.09 | 0.416191 | 0.208095 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208095 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4888.91 | −0.430799 | ||||||||
\(506\) | −5190.89 | + | 8990.89i | −0.456054 | + | 0.789909i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3245.31 | − | 5621.05i | −0.283440 | − | 0.490932i | ||||
\(509\) | −409.907 | − | 709.979i | −0.0356951 | − | 0.0618257i | 0.847626 | − | 0.530594i | \(-0.178031\pi\) |
−0.883321 | + | 0.468769i | \(0.844698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 70.5702 | − | 122.231i | 0.00610928 | − | 0.0105816i | ||||
\(512\) | −9378.41 | −0.809514 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15924.4 | 1.36653 | ||||||||
\(515\) | −3969.26 | + | 6874.96i | −0.339624 | + | 0.588247i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3652.13 | + | 6325.68i | 0.310678 | + | 0.538110i | ||||
\(518\) | −830.748 | − | 1438.90i | −0.0704652 | − | 0.122049i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1255.00 | − | 2173.73i | 0.105837 | − | 0.183316i | ||||
\(521\) | −3282.80 | −0.276050 | −0.138025 | − | 0.990429i | \(-0.544075\pi\) | ||||
−0.138025 | + | 0.990429i | \(0.544075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10768.1 | −0.900300 | −0.450150 | − | 0.892953i | \(-0.648629\pi\) | ||||
−0.450150 | + | 0.892953i | \(0.648629\pi\) | |||||||
\(524\) | −375.196 | + | 649.859i | −0.0312796 | + | 0.0541779i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6931.76 | − | 12006.2i | −0.574599 | − | 0.995235i | ||||
\(527\) | 510.941 | + | 884.975i | 0.0422333 | + | 0.0731502i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2047.78 | − | 3546.87i | 0.168306 | − | 0.291515i | ||||
\(530\) | 2162.22 | 0.177209 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 842.690 | 0.0686752 | ||||||||
\(533\) | 663.353 | − | 1148.96i | 0.0539081 | − | 0.0933716i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2244.33 | + | 3887.29i | 0.181366 | + | 0.314135i | ||||
\(536\) | −5049.44 | − | 8745.89i | −0.406908 | − | 0.704785i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6304.88 | − | 10920.4i | 0.505247 | − | 0.875113i | ||||
\(539\) | −17659.1 | −1.41119 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16037.9 | −1.27453 | −0.637266 | − | 0.770644i | \(-0.719935\pi\) | ||||
−0.637266 | + | 0.770644i | \(0.719935\pi\) | |||||||
\(542\) | −5404.04 | + | 9360.06i | −0.428272 | + | 0.741788i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 245.388 | + | 425.025i | 0.0193399 | + | 0.0334978i | ||||
\(545\) | −2138.73 | − | 3704.39i | −0.168097 | − | 0.291153i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1024.56 | + | 1774.59i | −0.0800862 | + | 0.138713i | −0.903287 | − | 0.429037i | \(-0.858853\pi\) |
0.823201 | + | 0.567751i | \(0.192186\pi\) | |||||||
\(548\) | −9466.92 | −0.737968 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2888.93 | 0.223972 | ||||||||
\(551\) | 10895.9 | − | 18872.3i | 0.842437 | − | 1.45914i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1670.69 | − | 2893.72i | −0.128472 | − | 0.222520i | ||||
\(554\) | −2552.01 | − | 4420.21i | −0.195712 | − | 0.338983i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3335.09 | + | 5776.54i | −0.254387 | + | 0.440611i | ||||
\(557\) | −3644.07 | −0.277207 | −0.138603 | − | 0.990348i | \(-0.544261\pi\) | ||||
−0.138603 | + | 0.990348i | \(0.544261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8565.12 | 0.648061 | ||||||||
\(560\) | 196.280 | − | 339.967i | 0.0148113 | − | 0.0256540i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3602.64 | + | 6239.96i | 0.270406 | + | 0.468357i | ||||
\(563\) | 175.368 | + | 303.746i | 0.0131277 | + | 0.0227378i | 0.872515 | − | 0.488588i | \(-0.162488\pi\) |
−0.859387 | + | 0.511326i | \(0.829155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2275.60 | − | 3941.46i | 0.169443 | − | 0.293484i | ||||
\(566\) | 4420.07 | 0.328250 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7616.93 | −0.562675 | ||||||||
\(569\) | −9724.34 | + | 16843.1i | −0.716460 | + | 1.24095i | 0.245934 | + | 0.969287i | \(0.420905\pi\) |
−0.962394 | + | 0.271658i | \(0.912428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7572.97 | + | 13116.8i | 0.555024 | + | 0.961330i | 0.997902 | + | 0.0647480i | \(0.0206244\pi\) |
−0.442877 | + | 0.896582i | \(0.646042\pi\) | |||||||
\(572\) | 1714.90 | + | 2970.29i | 0.125356 | + | 0.217123i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 196.862 | − | 340.975i | 0.0143151 | − | 0.0247945i | ||||
\(575\) | 2246.03 | 0.162897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6365.11 | −0.459243 | −0.229621 | − | 0.973280i | \(-0.573749\pi\) | ||||
−0.229621 | + | 0.973280i | \(0.573749\pi\) | |||||||
\(578\) | 5375.95 | − | 9311.41i | 0.386868 | − | 0.670076i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1813.37 | + | 3140.85i | 0.129821 | + | 0.224856i | ||||
\(581\) | 1251.94 | + | 2168.43i | 0.0893965 | + | 0.154839i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5188.57 | + | 8986.87i | −0.368591 | + | 0.638419i | ||||
\(584\) | 1252.36 | 0.0887381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1054.86 | −0.0743617 | ||||||||
\(587\) | 5142.18 | − | 8906.52i | 0.361568 | − | 0.626254i | −0.626651 | − | 0.779300i | \(-0.715575\pi\) |
0.988219 | + | 0.153046i | \(0.0489081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13352.7 | + | 23127.5i | 0.934103 | + | 1.61791i | ||||
\(590\) | 4065.77 | + | 7042.13i | 0.283704 | + | 0.491389i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3884.73 | − | 6728.56i | 0.269699 | − | 0.467132i | ||||
\(593\) | −666.566 | −0.0461595 | −0.0230798 | − | 0.999734i | \(-0.507347\pi\) | ||||
−0.0230798 | + | 0.999734i | \(0.507347\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −50.6303 | −0.00348847 | ||||||||
\(596\) | −436.165 | + | 755.460i | −0.0299765 | + | 0.0519209i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2016.21 | − | 3492.18i | −0.137875 | − | 0.238806i | ||||
\(599\) | 12606.6 | + | 21835.3i | 0.859922 | + | 1.48943i | 0.872003 | + | 0.489501i | \(0.162821\pi\) |
−0.0120807 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10309.3 | − | 17856.3i | 0.699712 | − | 1.21194i | −0.268855 | − | 0.963181i | \(-0.586645\pi\) |
0.968566 | − | 0.248755i | \(-0.0800215\pi\) | |||||||
\(602\) | 2541.86 | 0.172090 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2983.30 | 0.200975 | ||||||||
\(605\) | −3604.92 | + | 6243.90i | −0.242249 | + | 0.419588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2541.76 | + | 4402.45i | 0.169962 | + | 0.294382i | 0.938406 | − | 0.345534i | \(-0.112302\pi\) |
−0.768444 | + | 0.639916i | \(0.778969\pi\) | |||||||
\(608\) | 6412.85 | + | 11107.4i | 0.427755 | + | 0.740894i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2679.79 | + | 4641.53i | −0.177871 | + | 0.308082i | ||||
\(611\) | −2837.07 | −0.187849 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2625.18 | 0.172969 | 0.0864845 | − | 0.996253i | \(-0.472437\pi\) | ||||
0.0864845 | + | 0.996253i | \(0.472437\pi\) | |||||||
\(614\) | −3535.47 | + | 6123.62i | −0.232378 | + | 0.402491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1787.48 | + | 3096.00i | 0.116915 | + | 0.202502i | ||||
\(617\) | −815.659 | − | 1412.76i | −0.0532208 | − | 0.0921811i | 0.838188 | − | 0.545382i | \(-0.183615\pi\) |
−0.891408 | + | 0.453201i | \(0.850282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1592.33 | + | 2758.00i | −0.103395 | + | 0.179085i | −0.913081 | − | 0.407778i | \(-0.866304\pi\) |
0.809687 | + | 0.586863i | \(0.199637\pi\) | |||||||
\(620\) | −4444.47 | −0.287894 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5297.40 | −0.341489 | ||||||||
\(623\) | 917.821 | − | 1589.71i | 0.0590236 | − | 0.102232i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 2750.67 | + | 4764.29i | 0.175621 | + | 0.304184i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 634.392 | − | 1098.80i | 0.0403105 | − | 0.0698199i | ||||
\(629\) | −1002.06 | −0.0635214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10436.7 | 0.658447 | 0.329223 | − | 0.944252i | \(-0.393213\pi\) | ||||
0.329223 | + | 0.944252i | \(0.393213\pi\) | |||||||
\(632\) | 14824.3 | − | 25676.4i | 0.933037 | − | 1.61607i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4067.54 | + | 7045.18i | 0.254799 | + | 0.441325i | ||||
\(635\) | 5095.62 | + | 8825.87i | 0.318446 | + | 0.551565i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3429.52 | − | 5940.11i | 0.213316 | − | 0.369475i | ||||
\(638\) | 26321.7 | 1.63336 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 356.968 | 0.0220475 | ||||||||
\(641\) | 4541.73 | − | 7866.50i | 0.279856 | − | 0.484724i | −0.691493 | − | 0.722383i | \(-0.743047\pi\) |
0.971349 | + | 0.237659i | \(0.0763801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8593.81 | − | 14884.9i | −0.527071 | − | 0.912914i | −0.999502 | − | 0.0315465i | \(-0.989957\pi\) |
0.472431 | − | 0.881368i | \(-0.343377\pi\) | |||||||
\(644\) | 395.672 | + | 685.323i | 0.0242106 | + | 0.0419340i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −384.285 | + | 665.601i | −0.0234048 | + | 0.0405383i | ||||
\(647\) | −2359.17 | −0.143352 | −0.0716758 | − | 0.997428i | \(-0.522835\pi\) | ||||
−0.0716758 | + | 0.997428i | \(0.522835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39025.7 | −2.36039 | ||||||||
\(650\) | −561.049 | + | 971.766i | −0.0338556 | + | 0.0586397i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 761.320 | + | 1318.64i | 0.0457294 | + | 0.0792057i | ||||
\(653\) | 2718.06 | + | 4707.81i | 0.162888 | + | 0.282130i | 0.935903 | − | 0.352257i | \(-0.114586\pi\) |
−0.773015 | + | 0.634387i | \(0.781252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 589.113 | − | 1020.37i | 0.0351428 | − | 0.0608691i | ||||
\(656\) | 1841.13 | 0.109579 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −841.954 | −0.0498826 | ||||||||
\(659\) | 1544.45 | − | 2675.07i | 0.0912950 | − | 0.158128i | −0.816761 | − | 0.576976i | \(-0.804233\pi\) |
0.908056 | + | 0.418848i | \(0.137566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9526.94 | + | 16501.2i | 0.560598 | + | 0.970984i | 0.997444 | + | 0.0714479i | \(0.0227620\pi\) |
−0.436846 | + | 0.899536i | \(0.643905\pi\) | |||||||
\(662\) | −2801.70 | − | 4852.68i | −0.164488 | − | 0.284902i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11108.7 | + | 19240.8i | −0.649248 | + | 1.12453i | ||||
\(665\) | −1323.15 | −0.0771570 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20464.1 | 1.18796 | ||||||||
\(668\) | 541.928 | − | 938.646i | 0.0313889 | − | 0.0543672i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2257.36 | + | 3909.86i | 0.130163 | + | 0.225449i | ||||
\(671\) | −12861.1 | − | 22276.1i | −0.739937 | − | 1.28161i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14618.7 | − | 25320.4i | 0.837312 | − | 1.45027i | −0.0548215 | − | 0.998496i | \(-0.517459\pi\) |
0.892134 | − | 0.451771i | \(-0.149208\pi\) | |||||||
\(674\) | 7796.61 | 0.445570 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5663.98 | 0.322257 | ||||||||
\(677\) | 7235.62 | − | 12532.5i | 0.410764 | − | 0.711465i | −0.584209 | − | 0.811603i | \(-0.698595\pi\) |
0.994974 | + | 0.100138i | \(0.0319285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1003.16 | + | 1737.52i | 0.0566975 | + | 0.0982030i | ||||
\(680\) | −224.625 | − | 389.062i | −0.0126676 | − | 0.0219410i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16128.2 | + | 27934.9i | −0.905545 | + | 1.56845i | ||||
\(683\) | −5782.94 | −0.323980 | −0.161990 | − | 0.986792i | \(-0.551791\pi\) | ||||
−0.161990 | + | 0.986792i | \(0.551791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14864.5 | 0.829112 | ||||||||
\(686\) | 2058.77 | − | 3565.89i | 0.114583 | − | 0.198464i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5943.10 | + | 10293.8i | 0.329329 | + | 0.570415i | ||||
\(689\) | −2015.31 | − | 3490.62i | −0.111433 | − | 0.193007i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5527.56 | + | 9574.01i | −0.304310 | + | 0.527080i | −0.977107 | − | 0.212746i | \(-0.931759\pi\) |
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(692\) | 12024.6 | 0.660557 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17046.5 | 0.932386 | ||||||||
\(695\) | 5236.58 | − | 9070.02i | 0.285805 | − | 0.495029i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −118.730 | − | 205.646i | −0.00645223 | − | 0.0111756i | ||||
\(698\) | −763.674 | − | 1322.72i | −0.0414119 | − | 0.0717275i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 110.103 | − | 190.704i | 0.00594501 | − | 0.0102971i | ||||
\(701\) | 13554.2 | 0.730294 | 0.365147 | − | 0.930950i | \(-0.381019\pi\) | ||||
0.365147 | + | 0.930950i | \(0.381019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26187.4 | −1.40495 | ||||||||
\(704\) | −13724.6 | + | 23771.7i | −0.734751 | + | 1.27263i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5981.91 | − | 10361.0i | −0.318884 | − | 0.552324i | ||||
\(707\) | 1352.30 | + | 2342.25i | 0.0719354 | + | 0.124596i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4694.58 | − | 8131.26i | 0.248672 | − | 0.430713i | −0.714485 | − | 0.699650i | \(-0.753339\pi\) |
0.963158 | + | 0.268937i | \(0.0866724\pi\) | |||||||
\(710\) | 3405.15 | 0.179990 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16287.9 | 0.857326 | ||||||||
\(713\) | −12539.1 | + | 21718.3i | −0.658614 | + | 1.14075i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2692.64 | − | 4663.80i | −0.140838 | − | 0.243939i | ||||
\(716\) | −297.188 | − | 514.745i | −0.0155118 | − | 0.0268672i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4428.84 | − | 7670.97i | 0.230199 | − | 0.398716i | ||||
\(719\) | 26301.8 | 1.36424 | 0.682122 | − | 0.731238i | \(-0.261057\pi\) | ||||
0.682122 | + | 0.731238i | \(0.261057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4391.67 | 0.226844 | ||||||||
\(722\) | −2516.86 | + | 4359.33i | −0.129734 | + | 0.224705i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2290.79 | + | 3967.76i | 0.117592 | + | 0.203675i | ||||
\(725\) | −2847.26 | − | 4931.59i | −0.145854 | − | 0.252627i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12769.3 | − | 22117.1i | 0.651427 | − | 1.12830i | −0.331350 | − | 0.943508i | \(-0.607504\pi\) |
0.982777 | − | 0.184797i | \(-0.0591626\pi\) | |||||||
\(728\) | −1388.56 | −0.0706915 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −559.868 | −0.0283858 | ||||||||
\(731\) | 766.510 | − | 1327.63i | 0.0387830 | − | 0.0671742i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3491.06 | − | 6046.70i | −0.175914 | − | 0.304693i | 0.764563 | − | 0.644549i | \(-0.222955\pi\) |
−0.940477 | + | 0.339856i | \(0.889622\pi\) | |||||||
\(734\) | −12332.7 | − | 21360.8i | −0.620174 | − | 1.07417i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6022.10 | + | 10430.6i | −0.301600 | + | 0.522387i | ||||
\(737\) | −21667.5 | −1.08295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8863.91 | 0.441224 | 0.220612 | − | 0.975362i | \(-0.429195\pi\) | ||||
0.220612 | + | 0.975362i | \(0.429195\pi\) | |||||||
\(740\) | 2179.14 | − | 3774.38i | 0.108252 | − | 0.187499i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −598.081 | − | 1035.91i | −0.0295906 | − | 0.0512524i | ||||
\(743\) | −19472.4 | − | 33727.3i | −0.961473 | − | 1.66532i | −0.718806 | − | 0.695211i | \(-0.755311\pi\) |
−0.242668 | − | 0.970110i | \(-0.578022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 684.843 | − | 1186.18i | 0.0336788 | − | 0.0583334i | ||||
\(746\) | −13870.5 | −0.680742 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 613.879 | 0.0300075 | ||||||||
\(749\) | 1241.58 | − | 2150.49i | 0.0605694 | − | 0.104909i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8795.16 | − | 15233.7i | −0.427350 | − | 0.740192i | 0.569287 | − | 0.822139i | \(-0.307220\pi\) |
−0.996637 | + | 0.0819470i | \(0.973886\pi\) | |||||||
\(752\) | −1968.57 | − | 3409.66i | −0.0954604 | − | 0.165342i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5111.84 | + | 8853.97i | −0.246900 | + | 0.427643i | ||||
\(755\) | −4684.22 | −0.225796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4075.85 | −0.195693 | −0.0978463 | − | 0.995202i | \(-0.531195\pi\) | ||||
−0.0978463 | + | 0.995202i | \(0.531195\pi\) | |||||||
\(758\) | −10232.1 | + | 17722.6i | −0.490300 | + | 0.849225i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5870.24 | − | 10167.6i | −0.280179 | − | 0.485284i | ||||
\(761\) | 20268.5 | + | 35106.1i | 0.965483 | + | 1.67227i | 0.708312 | + | 0.705899i | \(0.249457\pi\) |
0.257171 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1183.17 | + | 2049.30i | −0.0561382 | + | 0.0972343i | ||||
\(764\) | −1243.31 | −0.0588761 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24463.7 | −1.15393 | ||||||||
\(767\) | 7579.06 | − | 13127.3i | 0.356798 | − | 0.617992i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12016.3 | − | 20812.9i | −0.563485 | − | 0.975985i | −0.997189 | − | 0.0749293i | \(-0.976127\pi\) |
0.433704 | − | 0.901056i | \(-0.357206\pi\) | |||||||
\(770\) | −799.092 | − | 1384.07i | −0.0373991 | − | 0.0647771i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6233.57 | + | 10796.9i | −0.290610 | + | 0.503351i | ||||
\(773\) | 20881.5 | 0.971611 | 0.485805 | − | 0.874067i | \(-0.338526\pi\) | ||||
0.485805 | + | 0.874067i | \(0.338526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6978.46 | 0.323450 | ||||||||
\(776\) | −8901.16 | + | 15417.3i | −0.411770 | + | 0.713206i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7209.64 | + | 12487.5i | 0.332234 | + | 0.575446i | ||||
\(779\) | −3102.82 | − | 5374.24i | −0.142709 | − | 0.247179i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8171.18 | + | 14152.9i | −0.374376 | + | 0.648439i | ||||
\(782\) | −721.740 | −0.0330043 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9518.60 | 0.433610 | ||||||||
\(785\) | −996.089 | + | 1725.28i | −0.0452891 | + | 0.0784430i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2568.20 | + | 4448.25i | 0.116323 | + | 0.201478i | 0.918308 | − | 0.395867i | \(-0.129556\pi\) |
−0.801985 | + | 0.597345i | \(0.796223\pi\) | |||||||
\(788\) | 1421.33 | + | 2461.82i | 0.0642549 | + | 0.111293i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6627.21 | + | 11478.7i | −0.298463 | + | 0.516953i | ||||
\(791\) | −2517.77 | −0.113175 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9990.86 | 0.447397 | ||||||||
\(794\) | −4355.23 | + | 7543.48i | −0.194662 | + | 0.337164i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4411.22 | − | 7640.45i | −0.196421 | − | 0.340212i | ||||
\(797\) | 10998.0 | + | 19049.1i | 0.488794 | + | 0.846615i | 0.999917 | − | 0.0128922i | \(-0.00410382\pi\) |
−0.511123 | + | 0.859507i | \(0.670770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −253.895 | + | 439.760i | −0.0112418 | + | 0.0194713i | ||||
\(800\) | 3351.53 | 0.148118 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9600.03 | −0.422679 | ||||||||
\(803\) | 1343.49 | − | 2326.99i | 0.0590419 | − | 0.102264i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −621.262 | − | 1076.06i | −0.0272008 | − | 0.0471131i | ||||
\(806\) | −6264.42 | − | 10850.3i | −0.273765 | − | 0.474175i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11999.1 | + | 20783.1i | −0.522435 | + | 0.904885i | ||||
\(809\) | −31094.2 | −1.35132 | −0.675658 | − | 0.737215i | \(-0.736140\pi\) | ||||
−0.675658 | + | 0.737215i | \(0.736140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19130.6 | 0.828320 | 0.414160 | − | 0.910204i | \(-0.364075\pi\) | ||||
0.414160 | + | 0.910204i | \(0.364075\pi\) | |||||||
\(812\) | 1003.17 | − | 1737.55i | 0.0433553 | − | 0.0750936i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15815.5 | − | 27393.2i | −0.680997 | − | 1.17952i | ||||
\(815\) | −1195.38 | − | 2070.47i | −0.0513773 | − | 0.0889881i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20031.6 | − | 34695.7i | 0.857792 | − | 1.48574i | ||||
\(818\) | −19469.8 | −0.832208 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1032.78 | 0.0439832 | ||||||||
\(821\) | −1778.81 | + | 3080.99i | −0.0756162 | + | 0.130971i | −0.901354 | − | 0.433083i | \(-0.857426\pi\) |
0.825738 | + | 0.564054i | \(0.190759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3074.69 | − | 5325.52i | −0.130227 | − | 0.225560i | 0.793537 | − | 0.608522i | \(-0.208237\pi\) |
−0.923764 | + | 0.382962i | \(0.874904\pi\) | |||||||
\(824\) | 19484.0 | + | 33747.2i | 0.823733 | + | 1.42675i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2249.23 | − | 3895.77i | 0.0947464 | − | 0.164106i | ||||
\(827\) | −21152.8 | −0.889425 | −0.444713 | − | 0.895673i | \(-0.646694\pi\) | ||||
−0.444713 | + | 0.895673i | \(0.646694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17402.4 | −0.729083 | −0.364541 | − | 0.931187i | \(-0.618774\pi\) | ||||
−0.364541 | + | 0.931187i | \(0.618774\pi\) | |||||||
\(830\) | 4966.14 | − | 8601.61i | 0.207684 | − | 0.359719i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5330.81 | − | 9233.24i | −0.222131 | − | 0.384742i | ||||
\(833\) | −613.829 | − | 1063.18i | −0.0255317 | − | 0.0442222i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −850.906 | + | 1473.81i | −0.0352657 | + | 0.0610819i | ||||
\(836\) | 16042.8 | 0.663698 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2225.55 | 0.0917425 | ||||||||
\(839\) | −9037.12 | + | 15652.8i | −0.371867 | + | 0.644092i | −0.989853 | − | 0.142097i | \(-0.954615\pi\) |
0.617986 | + | 0.786189i | \(0.287949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13747.5 | − | 23811.3i | −0.563675 | − | 0.976314i | ||||
\(842\) | 16341.1 | + | 28303.6i | 0.668825 | + | 1.15844i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7296.31 | − | 12637.6i | 0.297570 | − | 0.515407i | ||||
\(845\) | −8893.28 | −0.362057 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3988.55 | 0.161804 | ||||||||
\(848\) | 2796.74 | − | 4844.09i | 0.113255 | − | 0.196164i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 100.419 | + | 173.931i | 0.00405216 | + | 0.00701855i | ||||
\(851\) | −12295.9 | − | 21297.1i | −0.495297 | − | 0.857880i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20396.1 | + | 35327.2i | −0.818699 | + | 1.41803i | 0.0879416 | + | 0.996126i | \(0.471971\pi\) |
−0.906641 | + | 0.421903i | \(0.861362\pi\) | |||||||
\(854\) | 2964.97 | 0.118805 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22033.5 | 0.879778 | ||||||||
\(857\) | −5528.93 | + | 9576.39i | −0.220379 | + | 0.381707i | −0.954923 | − | 0.296854i | \(-0.904063\pi\) |
0.734544 | + | 0.678561i | \(0.237396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 876.815 | + | 1518.69i | 0.0348272 | + | 0.0603224i | 0.882914 | − | 0.469535i | \(-0.155579\pi\) |
−0.848086 | + | 0.529858i | \(0.822245\pi\) | |||||||
\(860\) | 3333.78 | + | 5774.27i | 0.132187 | + | 0.228955i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4788.17 | + | 8293.35i | −0.189194 | + | 0.327694i | ||||
\(863\) | 19186.5 | 0.756796 | 0.378398 | − | 0.925643i | \(-0.376475\pi\) | ||||
0.378398 | + | 0.925643i | \(0.376475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18880.3 | −0.742140 | ||||||||
\(866\) | −10205.9 | + | 17677.2i | −0.400475 | + | 0.693642i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1229.36 | + | 2129.32i | 0.0480728 | + | 0.0832646i | ||||
\(869\) | −31806.0 | − | 55089.6i | −1.24159 | − | 2.15050i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4207.97 | − | 7288.41i | 0.163699 | − | 0.283534i | ||||
\(872\) | −20996.8 | −0.815415 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18861.6 | −0.729980 | ||||||||
\(875\) | −172.878 | + | 299.434i | −0.00667925 | + | 0.0115688i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4257.30 | + | 7373.86i | 0.163921 | + | 0.283920i | 0.936272 | − | 0.351277i | \(-0.114252\pi\) |
−0.772350 | + | 0.635197i | \(0.780919\pi\) | |||||||
\(878\) | −1667.94 | − | 2888.96i | −0.0641121 | − | 0.111045i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3736.70 | − | 6472.16i | 0.143141 | − | 0.247928i | ||||
\(881\) | −41177.0 | −1.57467 | −0.787337 | − | 0.616522i | \(-0.788541\pi\) | ||||
−0.787337 | + | 0.616522i | \(0.788541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32540.4 | 1.24017 | 0.620086 | − | 0.784533i | \(-0.287098\pi\) | ||||
0.620086 | + | 0.784533i | \(0.287098\pi\) | |||||||
\(884\) | −119.219 | + | 206.494i | −0.00453595 | + | 0.00785650i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4896.34 | + | 8480.70i | 0.185661 | + | 0.321574i | ||||
\(887\) | 1083.05 | + | 1875.90i | 0.0409980 | + | 0.0710106i | 0.885796 | − | 0.464074i | \(-0.153613\pi\) |
−0.844798 | + | 0.535085i | \(0.820280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2818.95 | − | 4882.56i | 0.106349 | − | 0.184202i | ||||
\(890\) | −7281.53 | −0.274244 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13041.2 | −0.489522 | ||||||||
\(893\) | −6635.17 | + | 11492.4i | −0.248642 | + | 0.430661i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 466.629 | + | 808.225i | 0.0174276 | + | 0.0301855i | ||||
\(896\) | −98.7391 | − | 171.021i | −0.00368152 | − | 0.00637658i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5893.91 | + | 10208.5i | −0.219023 | + | 0.379358i | ||||
\(899\) | 63582.3 | 2.35883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −721.416 | −0.0266747 | ||||||||
\(902\) | 3747.79 | − | 6491.36i | 0.138346 | − | 0.239622i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11170.3 | − | 19347.5i | −0.410971 | − | 0.711823i | ||||
\(905\) | −3596.88 | − | 6229.97i | −0.132115 | − | 0.228830i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 353.031 | − | 611.468i | 0.0129241 | − | 0.0223853i | −0.859491 | − | 0.511151i | \(-0.829219\pi\) |
0.872415 | + | 0.488766i | \(0.162553\pi\) | |||||||
\(908\) | −12321.6 | −0.450339 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 620.756 | 0.0226130 | ||||||||
\(911\) | −247.743 | + | 429.103i | −0.00900997 | + | 0.0156057i | −0.870495 | − | 0.492177i | \(-0.836201\pi\) |
0.861485 | + | 0.507783i | \(0.169535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23834.0 | + | 41281.7i | 0.863955 | + | 1.49641i | ||||
\(914\) | −17034.8 | − | 29505.2i | −0.616480 | − | 1.06777i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1967.99 | − | 3408.66i | 0.0709871 | − | 0.122953i | ||||
\(917\) | −651.806 | −0.0234728 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20473.6 | 0.734889 | 0.367445 | − | 0.930045i | \(-0.380233\pi\) | ||||
0.367445 | + | 0.930045i | \(0.380233\pi\) | |||||||
\(920\) | 5512.56 | − | 9548.03i | 0.197547 | − | 0.342162i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −61.9030 | − | 107.219i | −0.00221114 | − | 0.00382980i | ||||
\(923\) | −3173.80 | − | 5497.17i | −0.113182 | − | 0.196037i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3421.57 | + | 5926.33i | −0.121622 | + | 0.210656i | ||||
\(926\) | 29348.0 | 1.04151 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30536.5 | 1.08018 | ||||||||
\(929\) | 24857.7 | − | 43054.7i | 0.877883 | − | 1.52054i | 0.0242231 | − | 0.999707i | \(-0.492289\pi\) |
0.853660 | − | 0.520831i | \(-0.174378\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16041.5 | − | 27784.7i | −0.564704 | − | 0.978095i | ||||
\(932\) | −3514.08 | − | 6086.57i | −0.123506 | − | 0.213919i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2937.77 | − | 5088.36i | 0.102919 | − | 0.178261i | ||||
\(935\) | −963.880 | −0.0337136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31524.9 | −1.09912 | −0.549560 | − | 0.835454i | \(-0.685204\pi\) | ||||
−0.549560 | + | 0.835454i | \(0.685204\pi\) | |||||||
\(938\) | 1248.79 | − | 2162.97i | 0.0434696 | − | 0.0752916i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1104.27 | − | 1912.64i | −0.0383161 | − | 0.0663655i | ||||
\(941\) | 18764.2 | + | 32500.6i | 0.650050 | + | 1.12592i | 0.983110 | + | 0.183014i | \(0.0585854\pi\) |
−0.333060 | + | 0.942905i | \(0.608081\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2913.76 | − | 5046.78i | 0.100620 | − | 0.174280i | ||||
\(944\) | 21035.6 | 0.725265 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48390.9 | 1.66313 | ||||||||
\(947\) | 12931.7 | − | 22398.3i | 0.443741 | − | 0.768582i | −0.554222 | − | 0.832369i | \(-0.686984\pi\) |
0.997964 | + | 0.0637862i | \(0.0203176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 521.829 | + | 903.834i | 0.0178496 | + | 0.0309164i | ||||
\(950\) | 2624.29 | + | 4545.41i | 0.0896246 | + | 0.155234i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −124.265 | + | 215.233i | −0.00423051 | + | 0.00732746i | ||||
\(953\) | −1060.03 | −0.0360312 | −0.0180156 | − | 0.999838i | \(-0.505735\pi\) | ||||
−0.0180156 | + | 0.999838i | \(0.505735\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1952.18 | 0.0661476 | ||||||||
\(956\) | −1395.81 | + | 2417.61i | −0.0472213 | + | 0.0817897i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3807.28 | − | 6594.40i | −0.128400 | − | 0.222396i | ||||
\(959\) | −4111.58 | − | 7121.46i | −0.138446 | − | 0.239796i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24063.7 | + | 41679.5i | −0.807750 | + | 1.39906i | ||||
\(962\) | 12285.9 | 0.411759 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1521.71 | 0.0508412 | ||||||||
\(965\) | 9787.62 | − | 16952.6i | 0.326502 | − | 0.565518i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2592.51 | + | 4490.35i | 0.0862145 | + | 0.149328i | 0.905908 | − | 0.423474i | \(-0.139190\pi\) |
−0.819694 | + | 0.572802i | \(0.805856\pi\) | |||||||
\(968\) | 17695.5 | + | 30649.5i | 0.587557 | + | 1.01768i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3979.27 | − | 6892.30i | 0.131718 | − | 0.228143i | ||||
\(971\) | −28314.9 | −0.935805 | −0.467903 | − | 0.883780i | \(-0.654990\pi\) | ||||
−0.467903 | + | 0.883780i | \(0.654990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5793.85 | −0.190897 | ||||||||
\(974\) | 15405.6 | − | 26683.4i | 0.506806 | − | 0.877813i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6932.38 | + | 12007.2i | 0.227357 | + | 0.393793i | ||||
\(977\) | 22448.3 | + | 38881.6i | 0.735093 | + | 1.27322i | 0.954683 | + | 0.297626i | \(0.0961948\pi\) |
−0.219590 | + | 0.975592i | \(0.570472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17473.1 | − | 30264.3i | 0.570422 | − | 0.988001i | ||||
\(980\) | 5339.45 | 0.174043 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21539.4 | −0.699950 | ||||||||
\(983\) | −7286.40 | + | 12620.4i | −0.236419 | + | 0.409490i | −0.959684 | − | 0.281081i | \(-0.909307\pi\) |
0.723265 | + | 0.690571i | \(0.242640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2231.70 | − | 3865.42i | −0.0721908 | − | 0.125038i | ||||
\(986\) | 914.938 | + | 1584.72i | 0.0295513 | + | 0.0511843i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3115.62 | + | 5396.41i | −0.100325 | + | 0.173768i | ||||
\(989\) | 37622.0 | 1.20962 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10602.1 | 0.339844 | 0.169922 | − | 0.985457i | \(-0.445648\pi\) | ||||
0.169922 | + | 0.985457i | \(0.445648\pi\) | |||||||
\(992\) | −18710.8 | + | 32408.1i | −0.598860 | + | 1.03726i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −941.882 | − | 1631.39i | −0.0300550 | − | 0.0520568i | ||||
\(995\) | 6926.26 | + | 11996.6i | 0.220681 | + | 0.382230i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13948.5 | + | 24159.5i | −0.443082 | + | 0.767441i | −0.997916 | − | 0.0645202i | \(-0.979448\pi\) |
0.554834 | + | 0.831961i | \(0.312782\pi\) | |||||||
\(998\) | −26447.4 | −0.838857 | ||||||||
\(999\) | 0 | 0 |
(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 | 135.4.e.c.46.3 | 14 | ||
3.2 | odd | 2 | 45.4.e.c.16.5 | ✓ | 14 | ||
9.2 | odd | 6 | 405.4.a.m.1.3 | 7 | |||
9.4 | even | 3 | inner | 135.4.e.c.91.3 | 14 | ||
9.5 | odd | 6 | 45.4.e.c.31.5 | yes | 14 | ||
9.7 | even | 3 | 405.4.a.n.1.5 | 7 | |||
15.2 | even | 4 | 225.4.k.d.124.10 | 28 | |||
15.8 | even | 4 | 225.4.k.d.124.5 | 28 | |||
15.14 | odd | 2 | 225.4.e.d.151.3 | 14 | |||
45.14 | odd | 6 | 225.4.e.d.76.3 | 14 | |||
45.23 | even | 12 | 225.4.k.d.49.10 | 28 | |||
45.29 | odd | 6 | 2025.4.a.bb.1.5 | 7 | |||
45.32 | even | 12 | 225.4.k.d.49.5 | 28 | |||
45.34 | even | 6 | 2025.4.a.ba.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.5 | ✓ | 14 | 3.2 | odd | 2 | ||
45.4.e.c.31.5 | yes | 14 | 9.5 | odd | 6 | ||
135.4.e.c.46.3 | 14 | 1.1 | even | 1 | trivial | ||
135.4.e.c.91.3 | 14 | 9.4 | even | 3 | inner | ||
225.4.e.d.76.3 | 14 | 45.14 | odd | 6 | |||
225.4.e.d.151.3 | 14 | 15.14 | odd | 2 | |||
225.4.k.d.49.5 | 28 | 45.32 | even | 12 | |||
225.4.k.d.49.10 | 28 | 45.23 | even | 12 | |||
225.4.k.d.124.5 | 28 | 15.8 | even | 4 | |||
225.4.k.d.124.10 | 28 | 15.2 | even | 4 | |||
405.4.a.m.1.3 | 7 | 9.2 | odd | 6 | |||
405.4.a.n.1.5 | 7 | 9.7 | even | 3 | |||
2025.4.a.ba.1.3 | 7 | 45.34 | even | 6 | |||
2025.4.a.bb.1.5 | 7 | 45.29 | odd | 6 |