Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(361,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.471 |
Dual form | 490.4.e.m.361.1 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.0962250 | − | 0.166667i | 0.813894 | − | 0.581013i | \(-0.197344\pi\) |
−0.910119 | + | 0.414346i | \(0.864010\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | −2.00000 | −0.136083 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 13.0000 | − | 22.5167i | 0.481481 | − | 0.833950i | ||||
\(10\) | 5.00000 | + | 8.66025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.0274101 | + | 0.0474757i | 0.879405 | − | 0.476074i | \(-0.157941\pi\) |
−0.851995 | + | 0.523550i | \(0.824607\pi\) | |||||||
\(12\) | −2.00000 | + | 3.46410i | −0.0481125 | + | 0.0833333i | ||||
\(13\) | 8.00000 | 0.170677 | 0.0853385 | − | 0.996352i | \(-0.472803\pi\) | ||||
0.0853385 | + | 0.996352i | \(0.472803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000 | 0.0860663 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −26.0000 | − | 45.0333i | −0.370937 | − | 0.642481i | 0.618773 | − | 0.785570i | \(-0.287630\pi\) |
−0.989710 | + | 0.143088i | \(0.954297\pi\) | |||||||
\(18\) | −26.0000 | − | 45.0333i | −0.340459 | − | 0.589692i | ||||
\(19\) | 13.0000 | − | 22.5167i | 0.156969 | − | 0.271878i | −0.776805 | − | 0.629741i | \(-0.783161\pi\) |
0.933774 | + | 0.357863i | \(0.116495\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.0387638 | ||||||||
\(23\) | −33.5000 | + | 58.0237i | −0.303706 | + | 0.526034i | −0.976972 | − | 0.213366i | \(-0.931557\pi\) |
0.673267 | + | 0.739400i | \(0.264891\pi\) | |||||||
\(24\) | 4.00000 | + | 6.92820i | 0.0340207 | + | 0.0589256i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 8.00000 | − | 13.8564i | 0.0603434 | − | 0.104518i | ||||
\(27\) | −53.0000 | −0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 69.0000 | 0.441827 | 0.220913 | − | 0.975293i | \(-0.429096\pi\) | ||||
0.220913 | + | 0.975293i | \(0.429096\pi\) | |||||||
\(30\) | 5.00000 | − | 8.66025i | 0.0304290 | − | 0.0527046i | ||||
\(31\) | −166.000 | − | 287.520i | −0.961757 | − | 1.66581i | −0.718085 | − | 0.695955i | \(-0.754981\pi\) |
−0.243672 | − | 0.969858i | \(-0.578352\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.00000 | − | 1.73205i | 0.00527508 | − | 0.00913671i | ||||
\(34\) | −104.000 | −0.524584 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | −98.0000 | + | 169.741i | −0.435435 | + | 0.754196i | −0.997331 | − | 0.0730121i | \(-0.976739\pi\) |
0.561896 | + | 0.827208i | \(0.310072\pi\) | |||||||
\(38\) | −26.0000 | − | 45.0333i | −0.110994 | − | 0.192247i | ||||
\(39\) | −4.00000 | − | 6.92820i | −0.0164234 | − | 0.0284462i | ||||
\(40\) | 20.0000 | − | 34.6410i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −353.000 | −1.34462 | −0.672309 | − | 0.740271i | \(-0.734697\pi\) | ||||
−0.672309 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.000 | −1.30865 | −0.654325 | − | 0.756213i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756213i | \(0.727047\pi\) | |||||||
\(44\) | 4.00000 | − | 6.92820i | 0.0137051 | − | 0.0237379i | ||||
\(45\) | 65.0000 | + | 112.583i | 0.215325 | + | 0.372954i | ||||
\(46\) | 67.0000 | + | 116.047i | 0.214752 | + | 0.371962i | ||||
\(47\) | 44.0000 | − | 76.2102i | 0.136554 | − | 0.236519i | −0.789636 | − | 0.613576i | \(-0.789730\pi\) |
0.926190 | + | 0.377057i | \(0.123064\pi\) | |||||||
\(48\) | 16.0000 | 0.0481125 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | −26.0000 | + | 45.0333i | −0.0713868 | + | 0.123646i | ||||
\(52\) | −16.0000 | − | 27.7128i | −0.0426692 | − | 0.0739053i | ||||
\(53\) | −291.000 | − | 504.027i | −0.754187 | − | 1.30629i | −0.945777 | − | 0.324816i | \(-0.894698\pi\) |
0.191590 | − | 0.981475i | \(-0.438636\pi\) | |||||||
\(54\) | −53.0000 | + | 91.7987i | −0.133563 | + | 0.231337i | ||||
\(55\) | −10.0000 | −0.0245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26.0000 | −0.0604173 | ||||||||
\(58\) | 69.0000 | − | 119.512i | 0.156209 | − | 0.270563i | ||||
\(59\) | −175.000 | − | 303.109i | −0.386154 | − | 0.668838i | 0.605775 | − | 0.795636i | \(-0.292863\pi\) |
−0.991928 | + | 0.126798i | \(0.959530\pi\) | |||||||
\(60\) | −10.0000 | − | 17.3205i | −0.0215166 | − | 0.0372678i | ||||
\(61\) | −233.500 | + | 404.434i | −0.490108 | + | 0.848893i | −0.999935 | − | 0.0113844i | \(-0.996376\pi\) |
0.509827 | + | 0.860277i | \(0.329709\pi\) | |||||||
\(62\) | −664.000 | −1.36013 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −20.0000 | + | 34.6410i | −0.0381645 | + | 0.0661029i | ||||
\(66\) | −2.00000 | − | 3.46410i | −0.00373005 | − | 0.00646063i | ||||
\(67\) | −145.500 | − | 252.013i | −0.265308 | − | 0.459527i | 0.702336 | − | 0.711846i | \(-0.252140\pi\) |
−0.967644 | + | 0.252318i | \(0.918807\pi\) | |||||||
\(68\) | −104.000 | + | 180.133i | −0.185468 | + | 0.321241i | ||||
\(69\) | 67.0000 | 0.116896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 770.000 | 1.28707 | 0.643537 | − | 0.765415i | \(-0.277466\pi\) | ||||
0.643537 | + | 0.765415i | \(0.277466\pi\) | |||||||
\(72\) | −104.000 | + | 180.133i | −0.170229 | + | 0.294846i | ||||
\(73\) | 314.000 | + | 543.864i | 0.503437 | + | 0.871979i | 0.999992 | + | 0.00397357i | \(0.00126483\pi\) |
−0.496555 | + | 0.868005i | \(0.665402\pi\) | |||||||
\(74\) | 196.000 | + | 339.482i | 0.307899 | + | 0.533297i | ||||
\(75\) | −12.5000 | + | 21.6506i | −0.0192450 | + | 0.0333333i | ||||
\(76\) | −104.000 | −0.156969 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −16.0000 | −0.0232262 | ||||||||
\(79\) | −585.000 | + | 1013.25i | −0.833135 | + | 1.44303i | 0.0624054 | + | 0.998051i | \(0.480123\pi\) |
−0.895540 | + | 0.444981i | \(0.853211\pi\) | |||||||
\(80\) | −40.0000 | − | 69.2820i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −324.500 | − | 562.050i | −0.445130 | − | 0.770988i | ||||
\(82\) | −353.000 | + | 611.414i | −0.475394 | + | 0.823407i | ||||
\(83\) | −525.000 | −0.694292 | −0.347146 | − | 0.937811i | \(-0.612849\pi\) | ||||
−0.347146 | + | 0.937811i | \(0.612849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 260.000 | 0.331776 | ||||||||
\(86\) | −369.000 | + | 639.127i | −0.462678 | + | 0.801382i | ||||
\(87\) | −34.5000 | − | 59.7558i | −0.0425148 | − | 0.0736378i | ||||
\(88\) | −8.00000 | − | 13.8564i | −0.00969094 | − | 0.0167852i | ||||
\(89\) | 44.5000 | − | 77.0763i | 0.0529999 | − | 0.0917985i | −0.838308 | − | 0.545197i | \(-0.816455\pi\) |
0.891308 | + | 0.453398i | \(0.149788\pi\) | |||||||
\(90\) | 260.000 | 0.304516 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 268.000 | 0.303706 | ||||||||
\(93\) | −166.000 | + | 287.520i | −0.185090 | + | 0.320586i | ||||
\(94\) | −88.0000 | − | 152.420i | −0.0965586 | − | 0.167244i | ||||
\(95\) | 65.0000 | + | 112.583i | 0.0701985 | + | 0.121587i | ||||
\(96\) | 16.0000 | − | 27.7128i | 0.0170103 | − | 0.0294628i | ||||
\(97\) | 290.000 | 0.303557 | 0.151779 | − | 0.988415i | \(-0.451500\pi\) | ||||
0.151779 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 52.0000 | 0.0527899 | ||||||||
\(100\) | −50.0000 | + | 86.6025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −616.500 | − | 1067.81i | −0.607367 | − | 1.05199i | −0.991673 | − | 0.128784i | \(-0.958893\pi\) |
0.384306 | − | 0.923206i | \(-0.374441\pi\) | |||||||
\(102\) | 52.0000 | + | 90.0666i | 0.0504781 | + | 0.0874307i | ||||
\(103\) | 776.500 | − | 1344.94i | 0.742823 | − | 1.28661i | −0.208381 | − | 0.978048i | \(-0.566819\pi\) |
0.951205 | − | 0.308560i | \(-0.0998472\pi\) | |||||||
\(104\) | −64.0000 | −0.0603434 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1164.00 | −1.06658 | ||||||||
\(107\) | −915.500 | + | 1585.69i | −0.827147 | + | 1.43266i | 0.0731204 | + | 0.997323i | \(0.476704\pi\) |
−0.900267 | + | 0.435337i | \(0.856629\pi\) | |||||||
\(108\) | 106.000 | + | 183.597i | 0.0944431 | + | 0.163580i | ||||
\(109\) | −405.500 | − | 702.347i | −0.356329 | − | 0.617180i | 0.631016 | − | 0.775770i | \(-0.282638\pi\) |
−0.987344 | + | 0.158590i | \(0.949305\pi\) | |||||||
\(110\) | −10.0000 | + | 17.3205i | −0.00866784 | + | 0.0150131i | ||||
\(111\) | 196.000 | 0.167599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2170.00 | 1.80652 | 0.903259 | − | 0.429097i | \(-0.141168\pi\) | ||||
0.903259 | + | 0.429097i | \(0.141168\pi\) | |||||||
\(114\) | −26.0000 | + | 45.0333i | −0.0213607 | + | 0.0369979i | ||||
\(115\) | −167.500 | − | 290.119i | −0.135821 | − | 0.235249i | ||||
\(116\) | −138.000 | − | 239.023i | −0.110457 | − | 0.191317i | ||||
\(117\) | 104.000 | − | 180.133i | 0.0821778 | − | 0.142336i | ||||
\(118\) | −700.000 | −0.546104 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −40.0000 | −0.0304290 | ||||||||
\(121\) | 663.500 | − | 1149.22i | 0.498497 | − | 0.863423i | ||||
\(122\) | 467.000 | + | 808.868i | 0.346559 | + | 0.600258i | ||||
\(123\) | 176.500 | + | 305.707i | 0.129386 | + | 0.224103i | ||||
\(124\) | −664.000 | + | 1150.08i | −0.480879 | + | 0.832906i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 48.0000 | 0.0335379 | 0.0167689 | − | 0.999859i | \(-0.494662\pi\) | ||||
0.0167689 | + | 0.999859i | \(0.494662\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 184.500 | + | 319.563i | 0.125925 | + | 0.218108i | ||||
\(130\) | 40.0000 | + | 69.2820i | 0.0269864 | + | 0.0467418i | ||||
\(131\) | −396.000 | + | 685.892i | −0.264112 | + | 0.457456i | −0.967331 | − | 0.253518i | \(-0.918412\pi\) |
0.703219 | + | 0.710974i | \(0.251746\pi\) | |||||||
\(132\) | −8.00000 | −0.00527508 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −582.000 | −0.375203 | ||||||||
\(135\) | 132.500 | − | 229.497i | 0.0844725 | − | 0.146311i | ||||
\(136\) | 208.000 | + | 360.267i | 0.131146 | + | 0.227151i | ||||
\(137\) | −542.000 | − | 938.772i | −0.338001 | − | 0.585436i | 0.646055 | − | 0.763291i | \(-0.276418\pi\) |
−0.984057 | + | 0.177855i | \(0.943084\pi\) | |||||||
\(138\) | 67.0000 | − | 116.047i | 0.0413291 | − | 0.0715841i | ||||
\(139\) | 46.0000 | 0.0280696 | 0.0140348 | − | 0.999902i | \(-0.495532\pi\) | ||||
0.0140348 | + | 0.999902i | \(0.495532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −88.0000 | −0.0525598 | ||||||||
\(142\) | 770.000 | − | 1333.68i | 0.455049 | − | 0.788168i | ||||
\(143\) | 8.00000 | + | 13.8564i | 0.00467828 | + | 0.00810301i | ||||
\(144\) | 208.000 | + | 360.267i | 0.120370 | + | 0.208488i | ||||
\(145\) | −172.500 | + | 298.779i | −0.0987955 | + | 0.171119i | ||||
\(146\) | 1256.00 | 0.711968 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 784.000 | 0.435435 | ||||||||
\(149\) | 184.500 | − | 319.563i | 0.101442 | − | 0.175702i | −0.810837 | − | 0.585272i | \(-0.800988\pi\) |
0.912279 | + | 0.409570i | \(0.134321\pi\) | |||||||
\(150\) | 25.0000 | + | 43.3013i | 0.0136083 | + | 0.0235702i | ||||
\(151\) | −1240.00 | − | 2147.74i | −0.668277 | − | 1.15749i | −0.978386 | − | 0.206788i | \(-0.933699\pi\) |
0.310109 | − | 0.950701i | \(-0.399634\pi\) | |||||||
\(152\) | −104.000 | + | 180.133i | −0.0554968 | + | 0.0961233i | ||||
\(153\) | −1352.00 | −0.714397 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1660.00 | 0.860222 | ||||||||
\(156\) | −16.0000 | + | 27.7128i | −0.00821170 | + | 0.0142231i | ||||
\(157\) | 613.000 | + | 1061.75i | 0.311610 | + | 0.539724i | 0.978711 | − | 0.205243i | \(-0.0657985\pi\) |
−0.667101 | + | 0.744967i | \(0.732465\pi\) | |||||||
\(158\) | 1170.00 | + | 2026.50i | 0.589115 | + | 1.02038i | ||||
\(159\) | −291.000 | + | 504.027i | −0.145143 | + | 0.251396i | ||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1298.00 | −0.629509 | ||||||||
\(163\) | 330.000 | − | 571.577i | 0.158574 | − | 0.274659i | −0.775781 | − | 0.631003i | \(-0.782644\pi\) |
0.934355 | + | 0.356344i | \(0.115977\pi\) | |||||||
\(164\) | 706.000 | + | 1222.83i | 0.336154 | + | 0.582237i | ||||
\(165\) | 5.00000 | + | 8.66025i | 0.00235909 | + | 0.00408606i | ||||
\(166\) | −525.000 | + | 909.327i | −0.245469 | + | 0.425165i | ||||
\(167\) | 949.000 | 0.439735 | 0.219868 | − | 0.975530i | \(-0.429437\pi\) | ||||
0.219868 | + | 0.975530i | \(0.429437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2133.00 | −0.970869 | ||||||||
\(170\) | 260.000 | − | 450.333i | 0.117301 | − | 0.203170i | ||||
\(171\) | −338.000 | − | 585.433i | −0.151155 | − | 0.261808i | ||||
\(172\) | 738.000 | + | 1278.25i | 0.327163 | + | 0.566662i | ||||
\(173\) | 1696.00 | − | 2937.56i | 0.745344 | − | 1.29097i | −0.204690 | − | 0.978827i | \(-0.565619\pi\) |
0.950034 | − | 0.312147i | \(-0.101048\pi\) | |||||||
\(174\) | −138.000 | −0.0601250 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −32.0000 | −0.0137051 | ||||||||
\(177\) | −175.000 | + | 303.109i | −0.0743153 | + | 0.128718i | ||||
\(178\) | −89.0000 | − | 154.153i | −0.0374766 | − | 0.0649113i | ||||
\(179\) | −134.000 | − | 232.095i | −0.0559532 | − | 0.0969139i | 0.836692 | − | 0.547674i | \(-0.184486\pi\) |
−0.892645 | + | 0.450760i | \(0.851153\pi\) | |||||||
\(180\) | 260.000 | − | 450.333i | 0.107663 | − | 0.186477i | ||||
\(181\) | 4093.00 | 1.68083 | 0.840415 | − | 0.541943i | \(-0.182311\pi\) | ||||
0.840415 | + | 0.541943i | \(0.182311\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 467.000 | 0.188643 | ||||||||
\(184\) | 268.000 | − | 464.190i | 0.107376 | − | 0.185981i | ||||
\(185\) | −490.000 | − | 848.705i | −0.194733 | − | 0.337287i | ||||
\(186\) | 332.000 | + | 575.041i | 0.130879 | + | 0.226688i | ||||
\(187\) | 52.0000 | − | 90.0666i | 0.0203348 | − | 0.0352210i | ||||
\(188\) | −352.000 | −0.136554 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 260.000 | 0.0992757 | ||||||||
\(191\) | 989.000 | − | 1713.00i | 0.374668 | − | 0.648943i | −0.615610 | − | 0.788051i | \(-0.711090\pi\) |
0.990277 | + | 0.139108i | \(0.0444235\pi\) | |||||||
\(192\) | −32.0000 | − | 55.4256i | −0.0120281 | − | 0.0208333i | ||||
\(193\) | 1999.00 | + | 3462.37i | 0.745550 | + | 1.29133i | 0.949937 | + | 0.312441i | \(0.101146\pi\) |
−0.204387 | + | 0.978890i | \(0.565520\pi\) | |||||||
\(194\) | 290.000 | − | 502.295i | 0.107324 | − | 0.185890i | ||||
\(195\) | 40.0000 | 0.0146895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3030.00 | −1.09583 | −0.547915 | − | 0.836534i | \(-0.684578\pi\) | ||||
−0.547915 | + | 0.836534i | \(0.684578\pi\) | |||||||
\(198\) | 52.0000 | − | 90.0666i | 0.0186640 | − | 0.0323271i | ||||
\(199\) | 178.000 | + | 308.305i | 0.0634075 | + | 0.109825i | 0.895986 | − | 0.444081i | \(-0.146470\pi\) |
−0.832579 | + | 0.553906i | \(0.813137\pi\) | |||||||
\(200\) | 100.000 | + | 173.205i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −145.500 | + | 252.013i | −0.0510586 | + | 0.0884361i | ||||
\(202\) | −2466.00 | −0.858946 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 208.000 | 0.0713868 | ||||||||
\(205\) | 882.500 | − | 1528.53i | 0.300666 | − | 0.520768i | ||||
\(206\) | −1553.00 | − | 2689.87i | −0.525256 | − | 0.909769i | ||||
\(207\) | 871.000 | + | 1508.62i | 0.292457 | + | 0.506551i | ||||
\(208\) | −64.0000 | + | 110.851i | −0.0213346 | + | 0.0369527i | ||||
\(209\) | 52.0000 | 0.0172101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2602.00 | −0.848953 | −0.424476 | − | 0.905439i | \(-0.639542\pi\) | ||||
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(212\) | −1164.00 | + | 2016.11i | −0.377094 | + | 0.653145i | ||||
\(213\) | −385.000 | − | 666.840i | −0.123849 | − | 0.214512i | ||||
\(214\) | 1831.00 | + | 3171.39i | 0.584881 | + | 1.01304i | ||||
\(215\) | 922.500 | − | 1597.82i | 0.292623 | − | 0.506838i | ||||
\(216\) | 424.000 | 0.133563 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1622.00 | −0.503925 | ||||||||
\(219\) | 314.000 | − | 543.864i | 0.0968865 | − | 0.167812i | ||||
\(220\) | 20.0000 | + | 34.6410i | 0.00612909 | + | 0.0106159i | ||||
\(221\) | −208.000 | − | 360.267i | −0.0633104 | − | 0.109657i | ||||
\(222\) | 196.000 | − | 339.482i | 0.0592552 | − | 0.102633i | ||||
\(223\) | 3156.00 | 0.947719 | 0.473860 | − | 0.880600i | \(-0.342860\pi\) | ||||
0.473860 | + | 0.880600i | \(0.342860\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −650.000 | −0.192593 | ||||||||
\(226\) | 2170.00 | − | 3758.55i | 0.638700 | − | 1.10626i | ||||
\(227\) | 2118.00 | + | 3668.48i | 0.619280 | + | 1.07262i | 0.989617 | + | 0.143727i | \(0.0459088\pi\) |
−0.370337 | + | 0.928897i | \(0.620758\pi\) | |||||||
\(228\) | 52.0000 | + | 90.0666i | 0.0151043 | + | 0.0261614i | ||||
\(229\) | 3167.00 | − | 5485.40i | 0.913892 | − | 1.58291i | 0.105376 | − | 0.994432i | \(-0.466395\pi\) |
0.808516 | − | 0.588475i | \(-0.200271\pi\) | |||||||
\(230\) | −670.000 | −0.192080 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −552.000 | −0.156209 | ||||||||
\(233\) | 2344.00 | − | 4059.93i | 0.659058 | − | 1.14152i | −0.321802 | − | 0.946807i | \(-0.604288\pi\) |
0.980860 | − | 0.194715i | \(-0.0623782\pi\) | |||||||
\(234\) | −208.000 | − | 360.267i | −0.0581085 | − | 0.100647i | ||||
\(235\) | 220.000 | + | 381.051i | 0.0610690 | + | 0.105775i | ||||
\(236\) | −700.000 | + | 1212.44i | −0.193077 | + | 0.334419i | ||||
\(237\) | 1170.00 | 0.320674 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1856.00 | 0.502321 | 0.251160 | − | 0.967945i | \(-0.419188\pi\) | ||||
0.251160 | + | 0.967945i | \(0.419188\pi\) | |||||||
\(240\) | −40.0000 | + | 69.2820i | −0.0107583 | + | 0.0186339i | ||||
\(241\) | −2403.00 | − | 4162.12i | −0.642286 | − | 1.11247i | −0.984921 | − | 0.173003i | \(-0.944653\pi\) |
0.342636 | − | 0.939468i | \(-0.388680\pi\) | |||||||
\(242\) | −1327.00 | − | 2298.43i | −0.352491 | − | 0.610532i | ||||
\(243\) | −1040.00 | + | 1801.33i | −0.274552 | + | 0.475537i | ||||
\(244\) | 1868.00 | 0.490108 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 706.000 | 0.182979 | ||||||||
\(247\) | 104.000 | − | 180.133i | 0.0267909 | − | 0.0464033i | ||||
\(248\) | 1328.00 | + | 2300.16i | 0.340033 | + | 0.588954i | ||||
\(249\) | 262.500 | + | 454.663i | 0.0668083 | + | 0.115715i | ||||
\(250\) | 125.000 | − | 216.506i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 3200.00 | 0.804710 | 0.402355 | − | 0.915484i | \(-0.368192\pi\) | ||||
0.402355 | + | 0.915484i | \(0.368192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −134.000 | −0.0332984 | ||||||||
\(254\) | 48.0000 | − | 83.1384i | 0.0118574 | − | 0.0205377i | ||||
\(255\) | −130.000 | − | 225.167i | −0.0319252 | − | 0.0552960i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −560.000 | + | 969.948i | −0.135922 | + | 0.235423i | −0.925949 | − | 0.377648i | \(-0.876733\pi\) |
0.790028 | + | 0.613071i | \(0.210066\pi\) | |||||||
\(258\) | 738.000 | 0.178085 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 160.000 | 0.0381645 | ||||||||
\(261\) | 897.000 | − | 1553.65i | 0.212731 | − | 0.368462i | ||||
\(262\) | 792.000 | + | 1371.78i | 0.186755 | + | 0.323470i | ||||
\(263\) | −3202.50 | − | 5546.89i | −0.750854 | − | 1.30052i | −0.947409 | − | 0.320025i | \(-0.896309\pi\) |
0.196555 | − | 0.980493i | \(-0.437025\pi\) | |||||||
\(264\) | −8.00000 | + | 13.8564i | −0.00186502 | + | 0.00323031i | ||||
\(265\) | 2910.00 | 0.674566 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −89.0000 | −0.0203997 | ||||||||
\(268\) | −582.000 | + | 1008.05i | −0.132654 | + | 0.229764i | ||||
\(269\) | 2467.50 | + | 4273.84i | 0.559279 | + | 0.968700i | 0.997557 | + | 0.0698604i | \(0.0222554\pi\) |
−0.438277 | + | 0.898840i | \(0.644411\pi\) | |||||||
\(270\) | −265.000 | − | 458.993i | −0.0597311 | − | 0.103457i | ||||
\(271\) | −723.000 | + | 1252.27i | −0.162063 | + | 0.280702i | −0.935608 | − | 0.353039i | \(-0.885148\pi\) |
0.773545 | + | 0.633741i | \(0.218482\pi\) | |||||||
\(272\) | 832.000 | 0.185468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2168.00 | −0.478006 | ||||||||
\(275\) | 25.0000 | − | 43.3013i | 0.00548202 | − | 0.00949514i | ||||
\(276\) | −134.000 | − | 232.095i | −0.0292241 | − | 0.0506176i | ||||
\(277\) | 4010.00 | + | 6945.52i | 0.869811 | + | 1.50656i | 0.862190 | + | 0.506585i | \(0.169092\pi\) |
0.00762078 | + | 0.999971i | \(0.497574\pi\) | |||||||
\(278\) | 46.0000 | − | 79.6743i | 0.00992409 | − | 0.0171890i | ||||
\(279\) | −8632.00 | −1.85227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4978.00 | 1.05681 | 0.528403 | − | 0.848994i | \(-0.322791\pi\) | ||||
0.528403 | + | 0.848994i | \(0.322791\pi\) | |||||||
\(282\) | −88.0000 | + | 152.420i | −0.0185827 | + | 0.0321862i | ||||
\(283\) | 2926.00 | + | 5067.98i | 0.614603 | + | 1.06452i | 0.990454 | + | 0.137844i | \(0.0440171\pi\) |
−0.375851 | + | 0.926680i | \(0.622650\pi\) | |||||||
\(284\) | −1540.00 | − | 2667.36i | −0.321768 | − | 0.557319i | ||||
\(285\) | 65.0000 | − | 112.583i | 0.0135097 | − | 0.0233995i | ||||
\(286\) | 32.0000 | 0.00661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 832.000 | 0.170229 | ||||||||
\(289\) | 1104.50 | − | 1913.05i | 0.224812 | − | 0.389385i | ||||
\(290\) | 345.000 | + | 597.558i | 0.0698590 | + | 0.120999i | ||||
\(291\) | −145.000 | − | 251.147i | −0.0292098 | − | 0.0505929i | ||||
\(292\) | 1256.00 | − | 2175.46i | 0.251719 | − | 0.435989i | ||||
\(293\) | 3012.00 | 0.600556 | 0.300278 | − | 0.953852i | \(-0.402921\pi\) | ||||
0.300278 | + | 0.953852i | \(0.402921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1750.00 | 0.345386 | ||||||||
\(296\) | 784.000 | − | 1357.93i | 0.153950 | − | 0.266648i | ||||
\(297\) | −53.0000 | − | 91.7987i | −0.0103548 | − | 0.0179350i | ||||
\(298\) | −369.000 | − | 639.127i | −0.0717302 | − | 0.124240i | ||||
\(299\) | −268.000 | + | 464.190i | −0.0518356 | + | 0.0897819i | ||||
\(300\) | 100.000 | 0.0192450 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4960.00 | −0.945086 | ||||||||
\(303\) | −616.500 | + | 1067.81i | −0.116888 | + | 0.202456i | ||||
\(304\) | 208.000 | + | 360.267i | 0.0392422 | + | 0.0679694i | ||||
\(305\) | −1167.50 | − | 2022.17i | −0.219183 | − | 0.379636i | ||||
\(306\) | −1352.00 | + | 2341.73i | −0.252577 | + | 0.437477i | ||||
\(307\) | −9443.00 | −1.75551 | −0.877753 | − | 0.479113i | \(-0.840958\pi\) | ||||
−0.877753 | + | 0.479113i | \(0.840958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1553.00 | −0.285913 | ||||||||
\(310\) | 1660.00 | − | 2875.20i | 0.304134 | − | 0.526776i | ||||
\(311\) | −4997.00 | − | 8655.06i | −0.911106 | − | 1.57808i | −0.812505 | − | 0.582954i | \(-0.801897\pi\) |
−0.0986008 | − | 0.995127i | \(-0.531437\pi\) | |||||||
\(312\) | 32.0000 | + | 55.4256i | 0.00580655 | + | 0.0100572i | ||||
\(313\) | 728.000 | − | 1260.93i | 0.131466 | − | 0.227707i | −0.792776 | − | 0.609514i | \(-0.791365\pi\) |
0.924242 | + | 0.381807i | \(0.124698\pi\) | |||||||
\(314\) | 2452.00 | 0.440683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4680.00 | 0.833135 | ||||||||
\(317\) | −3436.00 | + | 5951.33i | −0.608785 | + | 1.05445i | 0.382655 | + | 0.923891i | \(0.375010\pi\) |
−0.991441 | + | 0.130556i | \(0.958324\pi\) | |||||||
\(318\) | 582.000 | + | 1008.05i | 0.102632 | + | 0.177764i | ||||
\(319\) | 69.0000 | + | 119.512i | 0.0121105 | + | 0.0209760i | ||||
\(320\) | −160.000 | + | 277.128i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 1831.00 | 0.318369 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1352.00 | −0.232902 | ||||||||
\(324\) | −1298.00 | + | 2248.20i | −0.222565 | + | 0.385494i | ||||
\(325\) | −100.000 | − | 173.205i | −0.0170677 | − | 0.0295621i | ||||
\(326\) | −660.000 | − | 1143.15i | −0.112129 | − | 0.194213i | ||||
\(327\) | −405.500 | + | 702.347i | −0.0685755 | + | 0.118776i | ||||
\(328\) | 2824.00 | 0.475394 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 20.0000 | 0.00333625 | ||||||||
\(331\) | 196.000 | − | 339.482i | 0.0325472 | − | 0.0563735i | −0.849293 | − | 0.527922i | \(-0.822971\pi\) |
0.881840 | + | 0.471548i | \(0.156305\pi\) | |||||||
\(332\) | 1050.00 | + | 1818.65i | 0.173573 | + | 0.300637i | ||||
\(333\) | 2548.00 | + | 4413.27i | 0.419308 | + | 0.726263i | ||||
\(334\) | 949.000 | − | 1643.72i | 0.155470 | − | 0.269282i | ||||
\(335\) | 1455.00 | 0.237299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3926.00 | 0.634608 | 0.317304 | − | 0.948324i | \(-0.397222\pi\) | ||||
0.317304 | + | 0.948324i | \(0.397222\pi\) | |||||||
\(338\) | −2133.00 | + | 3694.46i | −0.343254 | + | 0.594534i | ||||
\(339\) | −1085.00 | − | 1879.28i | −0.173832 | − | 0.301086i | ||||
\(340\) | −520.000 | − | 900.666i | −0.0829440 | − | 0.143663i | ||||
\(341\) | 332.000 | − | 575.041i | 0.0527238 | − | 0.0913203i | ||||
\(342\) | −1352.00 | −0.213765 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2952.00 | 0.462678 | ||||||||
\(345\) | −167.500 | + | 290.119i | −0.0261388 | + | 0.0452738i | ||||
\(346\) | −3392.00 | − | 5875.12i | −0.527038 | − | 0.912856i | ||||
\(347\) | 892.500 | + | 1545.86i | 0.138075 | + | 0.239152i | 0.926768 | − | 0.375635i | \(-0.122575\pi\) |
−0.788693 | + | 0.614787i | \(0.789242\pi\) | |||||||
\(348\) | −138.000 | + | 239.023i | −0.0212574 | + | 0.0368189i | ||||
\(349\) | 1591.00 | 0.244024 | 0.122012 | − | 0.992529i | \(-0.461065\pi\) | ||||
0.122012 | + | 0.992529i | \(0.461065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −424.000 | −0.0644771 | ||||||||
\(352\) | −32.0000 | + | 55.4256i | −0.00484547 | + | 0.00839260i | ||||
\(353\) | 843.000 | + | 1460.12i | 0.127106 | + | 0.220154i | 0.922554 | − | 0.385868i | \(-0.126098\pi\) |
−0.795448 | + | 0.606021i | \(0.792765\pi\) | |||||||
\(354\) | 350.000 | + | 606.218i | 0.0525488 | + | 0.0910173i | ||||
\(355\) | −1925.00 | + | 3334.20i | −0.287798 | + | 0.498481i | ||||
\(356\) | −356.000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −536.000 | −0.0791298 | ||||||||
\(359\) | −3686.00 | + | 6384.34i | −0.541893 | + | 0.938586i | 0.456902 | + | 0.889517i | \(0.348959\pi\) |
−0.998795 | + | 0.0490695i | \(0.984374\pi\) | |||||||
\(360\) | −520.000 | − | 900.666i | −0.0761289 | − | 0.131859i | ||||
\(361\) | 3091.50 | + | 5354.64i | 0.450722 | + | 0.780673i | ||||
\(362\) | 4093.00 | − | 7089.28i | 0.594263 | − | 1.02929i | ||||
\(363\) | −1327.00 | −0.191872 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3140.00 | −0.450288 | ||||||||
\(366\) | 467.000 | − | 808.868i | 0.0666953 | − | 0.115520i | ||||
\(367\) | 3318.50 | + | 5747.81i | 0.472001 | + | 0.817529i | 0.999487 | − | 0.0320344i | \(-0.0101986\pi\) |
−0.527486 | + | 0.849564i | \(0.676865\pi\) | |||||||
\(368\) | −536.000 | − | 928.379i | −0.0759264 | − | 0.131508i | ||||
\(369\) | −4589.00 | + | 7948.38i | −0.647409 | + | 1.12134i | ||||
\(370\) | −1960.00 | −0.275393 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1328.00 | 0.185090 | ||||||||
\(373\) | −1738.00 | + | 3010.30i | −0.241261 | + | 0.417876i | −0.961074 | − | 0.276292i | \(-0.910894\pi\) |
0.719813 | + | 0.694168i | \(0.244228\pi\) | |||||||
\(374\) | −104.000 | − | 180.133i | −0.0143789 | − | 0.0249050i | ||||
\(375\) | −62.5000 | − | 108.253i | −0.00860663 | − | 0.0149071i | ||||
\(376\) | −352.000 | + | 609.682i | −0.0482793 | + | 0.0836222i | ||||
\(377\) | 552.000 | 0.0754097 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2378.00 | −0.322295 | −0.161147 | − | 0.986930i | \(-0.551519\pi\) | ||||
−0.161147 | + | 0.986930i | \(0.551519\pi\) | |||||||
\(380\) | 260.000 | − | 450.333i | 0.0350993 | − | 0.0607937i | ||||
\(381\) | −24.0000 | − | 41.5692i | −0.00322718 | − | 0.00558965i | ||||
\(382\) | −1978.00 | − | 3426.00i | −0.264930 | − | 0.458872i | ||||
\(383\) | −1228.50 | + | 2127.82i | −0.163899 | + | 0.283882i | −0.936264 | − | 0.351298i | \(-0.885741\pi\) |
0.772365 | + | 0.635179i | \(0.219074\pi\) | |||||||
\(384\) | −128.000 | −0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7996.00 | 1.05437 | ||||||||
\(387\) | −4797.00 | + | 8308.65i | −0.630091 | + | 1.09135i | ||||
\(388\) | −580.000 | − | 1004.59i | −0.0758893 | − | 0.131444i | ||||
\(389\) | −4281.00 | − | 7414.91i | −0.557983 | − | 0.966455i | −0.997665 | − | 0.0683010i | \(-0.978242\pi\) |
0.439682 | − | 0.898154i | \(-0.355091\pi\) | |||||||
\(390\) | 40.0000 | − | 69.2820i | 0.00519354 | − | 0.00899547i | ||||
\(391\) | 3484.00 | 0.450623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 792.000 | 0.101657 | ||||||||
\(394\) | −3030.00 | + | 5248.11i | −0.387435 | + | 0.671056i | ||||
\(395\) | −2925.00 | − | 5066.25i | −0.372589 | − | 0.645343i | ||||
\(396\) | −104.000 | − | 180.133i | −0.0131975 | − | 0.0228587i | ||||
\(397\) | −4921.00 | + | 8523.42i | −0.622111 | + | 1.07753i | 0.366981 | + | 0.930228i | \(0.380391\pi\) |
−0.989092 | + | 0.147299i | \(0.952942\pi\) | |||||||
\(398\) | 712.000 | 0.0896717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 4048.50 | − | 7012.21i | 0.504171 | − | 0.873249i | −0.495818 | − | 0.868427i | \(-0.665132\pi\) |
0.999988 | − | 0.00482260i | \(-0.00153509\pi\) | |||||||
\(402\) | 291.000 | + | 504.027i | 0.0361039 | + | 0.0625338i | ||||
\(403\) | −1328.00 | − | 2300.16i | −0.164150 | − | 0.284316i | ||||
\(404\) | −2466.00 | + | 4271.24i | −0.303683 | + | 0.525995i | ||||
\(405\) | 3245.00 | 0.398137 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −392.000 | −0.0477413 | ||||||||
\(408\) | 208.000 | − | 360.267i | 0.0252391 | − | 0.0437153i | ||||
\(409\) | 7629.50 | + | 13214.7i | 0.922383 | + | 1.59761i | 0.795717 | + | 0.605668i | \(0.207094\pi\) |
0.126665 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(410\) | −1765.00 | − | 3057.07i | −0.212603 | − | 0.368239i | ||||
\(411\) | −542.000 | + | 938.772i | −0.0650484 | + | 0.112667i | ||||
\(412\) | −6212.00 | −0.742823 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3484.00 | 0.413597 | ||||||||
\(415\) | 1312.50 | − | 2273.32i | 0.155248 | − | 0.268898i | ||||
\(416\) | 128.000 | + | 221.703i | 0.0150859 | + | 0.0261295i | ||||
\(417\) | −23.0000 | − | 39.8372i | −0.00270099 | − | 0.00467826i | ||||
\(418\) | 52.0000 | − | 90.0666i | 0.00608470 | − | 0.0105390i | ||||
\(419\) | −16224.0 | −1.89163 | −0.945817 | − | 0.324701i | \(-0.894736\pi\) | ||||
−0.945817 | + | 0.324701i | \(0.894736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2977.00 | 0.344632 | 0.172316 | − | 0.985042i | \(-0.444875\pi\) | ||||
0.172316 | + | 0.985042i | \(0.444875\pi\) | |||||||
\(422\) | −2602.00 | + | 4506.80i | −0.300150 | + | 0.519875i | ||||
\(423\) | −1144.00 | − | 1981.47i | −0.131497 | − | 0.227759i | ||||
\(424\) | 2328.00 | + | 4032.21i | 0.266645 | + | 0.461843i | ||||
\(425\) | −650.000 | + | 1125.83i | −0.0741874 | + | 0.128496i | ||||
\(426\) | −1540.00 | −0.175148 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7324.00 | 0.827147 | ||||||||
\(429\) | 8.00000 | − | 13.8564i | 0.000900335 | − | 0.00155943i | ||||
\(430\) | −1845.00 | − | 3195.63i | −0.206916 | − | 0.358389i | ||||
\(431\) | −7101.00 | − | 12299.3i | −0.793604 | − | 1.37456i | −0.923722 | − | 0.383063i | \(-0.874869\pi\) |
0.130119 | − | 0.991498i | \(-0.458464\pi\) | |||||||
\(432\) | 424.000 | − | 734.390i | 0.0472215 | − | 0.0817901i | ||||
\(433\) | −14310.0 | −1.58821 | −0.794105 | − | 0.607781i | \(-0.792060\pi\) | ||||
−0.794105 | + | 0.607781i | \(0.792060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 345.000 | 0.0380264 | ||||||||
\(436\) | −1622.00 | + | 2809.39i | −0.178164 | + | 0.308590i | ||||
\(437\) | 871.000 | + | 1508.62i | 0.0953446 | + | 0.165142i | ||||
\(438\) | −628.000 | − | 1087.73i | −0.0685091 | − | 0.118661i | ||||
\(439\) | −1178.00 | + | 2040.36i | −0.128070 | + | 0.221824i | −0.922929 | − | 0.384970i | \(-0.874212\pi\) |
0.794859 | + | 0.606795i | \(0.207545\pi\) | |||||||
\(440\) | 80.0000 | 0.00866784 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −832.000 | −0.0895344 | ||||||||
\(443\) | −4145.50 | + | 7180.22i | −0.444602 | + | 0.770073i | −0.998024 | − | 0.0628276i | \(-0.979988\pi\) |
0.553422 | + | 0.832901i | \(0.313322\pi\) | |||||||
\(444\) | −392.000 | − | 678.964i | −0.0418998 | − | 0.0725725i | ||||
\(445\) | 222.500 | + | 385.381i | 0.0237023 | + | 0.0410535i | ||||
\(446\) | 3156.00 | − | 5466.35i | 0.335069 | − | 0.580357i | ||||
\(447\) | −369.000 | −0.0390450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3521.00 | −0.370081 | −0.185040 | − | 0.982731i | \(-0.559242\pi\) | ||||
−0.185040 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(450\) | −650.000 | + | 1125.83i | −0.0680918 | + | 0.117938i | ||||
\(451\) | −353.000 | − | 611.414i | −0.0368561 | − | 0.0638367i | ||||
\(452\) | −4340.00 | − | 7517.10i | −0.451629 | − | 0.782245i | ||||
\(453\) | −1240.00 | + | 2147.74i | −0.128610 | + | 0.222759i | ||||
\(454\) | 8472.00 | 0.875794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 208.000 | 0.0213607 | ||||||||
\(457\) | 2716.00 | − | 4704.25i | 0.278007 | − | 0.481522i | −0.692882 | − | 0.721051i | \(-0.743660\pi\) |
0.970889 | + | 0.239529i | \(0.0769929\pi\) | |||||||
\(458\) | −6334.00 | − | 10970.8i | −0.646219 | − | 1.11928i | ||||
\(459\) | 1378.00 | + | 2386.77i | 0.140130 | + | 0.242712i | ||||
\(460\) | −670.000 | + | 1160.47i | −0.0679107 | + | 0.117625i | ||||
\(461\) | 5350.00 | 0.540508 | 0.270254 | − | 0.962789i | \(-0.412892\pi\) | ||||
0.270254 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10123.0 | −1.01610 | −0.508052 | − | 0.861327i | \(-0.669634\pi\) | ||||
−0.508052 | + | 0.861327i | \(0.669634\pi\) | |||||||
\(464\) | −552.000 | + | 956.092i | −0.0552284 | + | 0.0956583i | ||||
\(465\) | −830.000 | − | 1437.60i | −0.0827749 | − | 0.143370i | ||||
\(466\) | −4688.00 | − | 8119.85i | −0.466024 | − | 0.807178i | ||||
\(467\) | 3231.50 | − | 5597.12i | 0.320206 | − | 0.554612i | −0.660325 | − | 0.750980i | \(-0.729581\pi\) |
0.980530 | + | 0.196368i | \(0.0629147\pi\) | |||||||
\(468\) | −832.000 | −0.0821778 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 880.000 | 0.0863646 | ||||||||
\(471\) | 613.000 | − | 1061.75i | 0.0599693 | − | 0.103870i | ||||
\(472\) | 1400.00 | + | 2424.87i | 0.136526 | + | 0.236470i | ||||
\(473\) | −369.000 | − | 639.127i | −0.0358703 | − | 0.0621291i | ||||
\(474\) | 1170.00 | − | 2026.50i | 0.113375 | − | 0.196372i | ||||
\(475\) | −650.000 | −0.0627875 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15132.0 | −1.45251 | ||||||||
\(478\) | 1856.00 | − | 3214.69i | 0.177597 | − | 0.307607i | ||||
\(479\) | −8820.00 | − | 15276.7i | −0.841328 | − | 1.45722i | −0.888772 | − | 0.458349i | \(-0.848441\pi\) |
0.0474444 | − | 0.998874i | \(-0.484892\pi\) | |||||||
\(480\) | 80.0000 | + | 138.564i | 0.00760726 | + | 0.0131762i | ||||
\(481\) | −784.000 | + | 1357.93i | −0.0743188 | + | 0.128724i | ||||
\(482\) | −9612.00 | −0.908329 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5308.00 | −0.498497 | ||||||||
\(485\) | −725.000 | + | 1255.74i | −0.0678774 | + | 0.117567i | ||||
\(486\) | 2080.00 | + | 3602.67i | 0.194137 | + | 0.336256i | ||||
\(487\) | 5016.00 | + | 8687.97i | 0.466728 | + | 0.808397i | 0.999278 | − | 0.0380019i | \(-0.0120993\pi\) |
−0.532549 | + | 0.846399i | \(0.678766\pi\) | |||||||
\(488\) | 1868.00 | − | 3235.47i | 0.173279 | − | 0.300129i | ||||
\(489\) | −660.000 | −0.0610352 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5916.00 | 0.543758 | 0.271879 | − | 0.962331i | \(-0.412355\pi\) | ||||
0.271879 | + | 0.962331i | \(0.412355\pi\) | |||||||
\(492\) | 706.000 | − | 1222.83i | 0.0646930 | − | 0.112051i | ||||
\(493\) | −1794.00 | − | 3107.30i | −0.163890 | − | 0.283866i | ||||
\(494\) | −208.000 | − | 360.267i | −0.0189441 | − | 0.0328121i | ||||
\(495\) | −130.000 | + | 225.167i | −0.0118042 | + | 0.0204454i | ||||
\(496\) | 5312.00 | 0.480879 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1050.00 | 0.0944812 | ||||||||
\(499\) | −6947.00 | + | 12032.6i | −0.623227 | + | 1.07946i | 0.365653 | + | 0.930751i | \(0.380846\pi\) |
−0.988881 | + | 0.148710i | \(0.952488\pi\) | |||||||
\(500\) | −250.000 | − | 433.013i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −474.500 | − | 821.858i | −0.0423136 | − | 0.0732892i | ||||
\(502\) | 3200.00 | − | 5542.56i | 0.284508 | − | 0.492782i | ||||
\(503\) | −18427.0 | −1.63344 | −0.816719 | − | 0.577036i | \(-0.804209\pi\) | ||||
−0.816719 | + | 0.577036i | \(0.804209\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6165.00 | 0.543245 | ||||||||
\(506\) | −134.000 | + | 232.095i | −0.0117728 | + | 0.0203911i | ||||
\(507\) | 1066.50 | + | 1847.23i | 0.0934219 | + | 0.161812i | ||||
\(508\) | −96.0000 | − | 166.277i | −0.00838447 | − | 0.0145223i | ||||
\(509\) | 9278.50 | − | 16070.8i | 0.807981 | − | 1.39946i | −0.106279 | − | 0.994336i | \(-0.533894\pi\) |
0.914260 | − | 0.405128i | \(-0.132773\pi\) | |||||||
\(510\) | −520.000 | −0.0451490 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −689.000 | + | 1193.38i | −0.0592984 | + | 0.102708i | ||||
\(514\) | 1120.00 | + | 1939.90i | 0.0961111 | + | 0.166469i | ||||
\(515\) | 3882.50 | + | 6724.69i | 0.332201 | + | 0.575389i | ||||
\(516\) | 738.000 | − | 1278.25i | 0.0629625 | − | 0.109054i | ||||
\(517\) | 176.000 | 0.0149719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3392.00 | −0.286883 | ||||||||
\(520\) | 160.000 | − | 277.128i | 0.0134932 | − | 0.0233709i | ||||
\(521\) | −4965.00 | − | 8599.63i | −0.417506 | − | 0.723142i | 0.578182 | − | 0.815908i | \(-0.303762\pi\) |
−0.995688 | + | 0.0927663i | \(0.970429\pi\) | |||||||
\(522\) | −1794.00 | − | 3107.30i | −0.150424 | − | 0.260542i | ||||
\(523\) | −3962.00 | + | 6862.39i | −0.331255 | + | 0.573750i | −0.982758 | − | 0.184896i | \(-0.940805\pi\) |
0.651504 | + | 0.758646i | \(0.274139\pi\) | |||||||
\(524\) | 3168.00 | 0.264112 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12810.0 | −1.06187 | ||||||||
\(527\) | −8632.00 | + | 14951.1i | −0.713503 | + | 1.23582i | ||||
\(528\) | 16.0000 | + | 27.7128i | 0.00131877 | + | 0.00228418i | ||||
\(529\) | 3839.00 | + | 6649.34i | 0.315526 | + | 0.546506i | ||||
\(530\) | 2910.00 | − | 5040.27i | 0.238495 | − | 0.413085i | ||||
\(531\) | −9100.00 | −0.743703 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2824.00 | −0.229495 | ||||||||
\(534\) | −89.0000 | + | 154.153i | −0.00721237 | + | 0.0124922i | ||||
\(535\) | −4577.50 | − | 7928.46i | −0.369911 | − | 0.640705i | ||||
\(536\) | 1164.00 | + | 2016.11i | 0.0938006 | + | 0.162467i | ||||
\(537\) | −134.000 | + | 232.095i | −0.0107682 | + | 0.0186511i | ||||
\(538\) | 9870.00 | 0.790940 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1060.00 | −0.0844725 | ||||||||
\(541\) | 11748.5 | − | 20349.0i | 0.933655 | − | 1.61714i | 0.156641 | − | 0.987656i | \(-0.449934\pi\) |
0.777015 | − | 0.629483i | \(-0.216733\pi\) | |||||||
\(542\) | 1446.00 | + | 2504.55i | 0.114596 | + | 0.198486i | ||||
\(543\) | −2046.50 | − | 3544.64i | −0.161738 | − | 0.280138i | ||||
\(544\) | 832.000 | − | 1441.07i | 0.0655730 | − | 0.113576i | ||||
\(545\) | 4055.00 | 0.318710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11131.0 | 0.870068 | 0.435034 | − | 0.900414i | \(-0.356736\pi\) | ||||
0.435034 | + | 0.900414i | \(0.356736\pi\) | |||||||
\(548\) | −2168.00 | + | 3755.09i | −0.169001 | + | 0.292718i | ||||
\(549\) | 6071.00 | + | 10515.3i | 0.471956 | + | 0.817452i | ||||
\(550\) | −50.0000 | − | 86.6025i | −0.00387638 | − | 0.00671408i | ||||
\(551\) | 897.000 | − | 1553.65i | 0.0693530 | − | 0.120123i | ||||
\(552\) | −536.000 | −0.0413291 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16040.0 | 1.23010 | ||||||||
\(555\) | −490.000 | + | 848.705i | −0.0374763 | + | 0.0649108i | ||||
\(556\) | −92.0000 | − | 159.349i | −0.00701739 | − | 0.0121545i | ||||
\(557\) | 5989.00 | + | 10373.3i | 0.455587 | + | 0.789100i | 0.998722 | − | 0.0505455i | \(-0.0160960\pi\) |
−0.543135 | + | 0.839646i | \(0.682763\pi\) | |||||||
\(558\) | −8632.00 | + | 14951.1i | −0.654878 | + | 1.13428i | ||||
\(559\) | −2952.00 | −0.223357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −104.000 | −0.00782689 | ||||||||
\(562\) | 4978.00 | − | 8622.15i | 0.373637 | − | 0.647159i | ||||
\(563\) | −5029.50 | − | 8711.35i | −0.376498 | − | 0.652113i | 0.614052 | − | 0.789265i | \(-0.289538\pi\) |
−0.990550 | + | 0.137152i | \(0.956205\pi\) | |||||||
\(564\) | 176.000 | + | 304.841i | 0.0131400 | + | 0.0227591i | ||||
\(565\) | −5425.00 | + | 9396.38i | −0.403949 | + | 0.699661i | ||||
\(566\) | 11704.0 | 0.869180 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6160.00 | −0.455049 | ||||||||
\(569\) | 7833.00 | − | 13567.2i | 0.577111 | − | 0.999586i | −0.418697 | − | 0.908126i | \(-0.637513\pi\) |
0.995809 | − | 0.0914605i | \(-0.0291535\pi\) | |||||||
\(570\) | −130.000 | − | 225.167i | −0.00955281 | − | 0.0165459i | ||||
\(571\) | −1265.00 | − | 2191.04i | −0.0927121 | − | 0.160582i | 0.815939 | − | 0.578138i | \(-0.196220\pi\) |
−0.908651 | + | 0.417555i | \(0.862887\pi\) | |||||||
\(572\) | 32.0000 | − | 55.4256i | 0.00233914 | − | 0.00405151i | ||||
\(573\) | −1978.00 | −0.144210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1675.00 | 0.121482 | ||||||||
\(576\) | 832.000 | − | 1441.07i | 0.0601852 | − | 0.104244i | ||||
\(577\) | 6409.00 | + | 11100.7i | 0.462409 | + | 0.800916i | 0.999080 | − | 0.0428751i | \(-0.0136518\pi\) |
−0.536671 | + | 0.843791i | \(0.680318\pi\) | |||||||
\(578\) | −2209.00 | − | 3826.10i | −0.158966 | − | 0.275337i | ||||
\(579\) | 1999.00 | − | 3462.37i | 0.143481 | − | 0.248517i | ||||
\(580\) | 1380.00 | 0.0987955 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −580.000 | −0.0413089 | ||||||||
\(583\) | 582.000 | − | 1008.05i | 0.0413447 | − | 0.0716112i | ||||
\(584\) | −2512.00 | − | 4350.91i | −0.177992 | − | 0.308291i | ||||
\(585\) | 520.000 | + | 900.666i | 0.0367510 | + | 0.0636547i | ||||
\(586\) | 3012.00 | − | 5216.94i | 0.212329 | − | 0.367764i | ||||
\(587\) | 15228.0 | 1.07074 | 0.535372 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535372 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8632.00 | −0.603863 | ||||||||
\(590\) | 1750.00 | − | 3031.09i | 0.122112 | − | 0.211505i | ||||
\(591\) | 1515.00 | + | 2624.06i | 0.105446 | + | 0.182638i | ||||
\(592\) | −1568.00 | − | 2715.86i | −0.108859 | − | 0.188549i | ||||
\(593\) | −1299.00 | + | 2249.93i | −0.0899554 | + | 0.155807i | −0.907492 | − | 0.420069i | \(-0.862006\pi\) |
0.817537 | + | 0.575877i | \(0.195339\pi\) | |||||||
\(594\) | −212.000 | −0.0146439 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1476.00 | −0.101442 | ||||||||
\(597\) | 178.000 | − | 308.305i | 0.0122028 | − | 0.0211358i | ||||
\(598\) | 536.000 | + | 928.379i | 0.0366533 | + | 0.0634854i | ||||
\(599\) | 1274.00 | + | 2206.63i | 0.0869019 | + | 0.150518i | 0.906200 | − | 0.422849i | \(-0.138970\pi\) |
−0.819298 | + | 0.573368i | \(0.805637\pi\) | |||||||
\(600\) | 100.000 | − | 173.205i | 0.00680414 | − | 0.0117851i | ||||
\(601\) | −1706.00 | −0.115789 | −0.0578945 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578945 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7566.00 | −0.510964 | ||||||||
\(604\) | −4960.00 | + | 8590.97i | −0.334138 | + | 0.578745i | ||||
\(605\) | 3317.50 | + | 5746.08i | 0.222935 | + | 0.386134i | ||||
\(606\) | 1233.00 | + | 2135.62i | 0.0826521 | + | 0.143158i | ||||
\(607\) | −6283.50 | + | 10883.3i | −0.420164 | + | 0.727745i | −0.995955 | − | 0.0898517i | \(-0.971361\pi\) |
0.575791 | + | 0.817597i | \(0.304694\pi\) | |||||||
\(608\) | 832.000 | 0.0554968 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4670.00 | −0.309972 | ||||||||
\(611\) | 352.000 | − | 609.682i | 0.0233067 | − | 0.0403684i | ||||
\(612\) | 2704.00 | + | 4683.47i | 0.178599 | + | 0.309343i | ||||
\(613\) | 4814.00 | + | 8338.09i | 0.317187 | + | 0.549384i | 0.979900 | − | 0.199490i | \(-0.0639284\pi\) |
−0.662713 | + | 0.748874i | \(0.730595\pi\) | |||||||
\(614\) | −9443.00 | + | 16355.8i | −0.620665 | + | 1.07502i | ||||
\(615\) | −1765.00 | −0.115726 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4316.00 | −0.281614 | −0.140807 | − | 0.990037i | \(-0.544970\pi\) | ||||
−0.140807 | + | 0.990037i | \(0.544970\pi\) | |||||||
\(618\) | −1553.00 | + | 2689.87i | −0.101085 | + | 0.175085i | ||||
\(619\) | 8201.00 | + | 14204.5i | 0.532514 | + | 0.922341i | 0.999279 | + | 0.0379598i | \(0.0120859\pi\) |
−0.466766 | + | 0.884381i | \(0.654581\pi\) | |||||||
\(620\) | −3320.00 | − | 5750.41i | −0.215055 | − | 0.372487i | ||||
\(621\) | 1775.50 | − | 3075.26i | 0.114732 | − | 0.198721i | ||||
\(622\) | −19988.0 | −1.28850 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 128.000 | 0.00821170 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −1456.00 | − | 2521.87i | −0.0929608 | − | 0.161013i | ||||
\(627\) | −26.0000 | − | 45.0333i | −0.00165604 | − | 0.00286835i | ||||
\(628\) | 2452.00 | − | 4246.99i | 0.155805 | − | 0.269862i | ||||
\(629\) | 10192.0 | 0.646076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8490.00 | 0.535628 | 0.267814 | − | 0.963471i | \(-0.413699\pi\) | ||||
0.267814 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(632\) | 4680.00 | − | 8106.00i | 0.294558 | − | 0.510189i | ||||
\(633\) | 1301.00 | + | 2253.40i | 0.0816905 | + | 0.141492i | ||||
\(634\) | 6872.00 | + | 11902.7i | 0.430476 | + | 0.745607i | ||||
\(635\) | −120.000 | + | 207.846i | −0.00749930 | + | 0.0129892i | ||||
\(636\) | 2328.00 | 0.145143 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 276.000 | 0.0171269 | ||||||||
\(639\) | 10010.0 | − | 17337.8i | 0.619702 | − | 1.07336i | ||||
\(640\) | 320.000 | + | 554.256i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 61.5000 | + | 106.521i | 0.00378955 | + | 0.00656370i | 0.867914 | − | 0.496715i | \(-0.165460\pi\) |
−0.864124 | + | 0.503278i | \(0.832127\pi\) | |||||||
\(642\) | 1831.00 | − | 3171.39i | 0.112560 | − | 0.194960i | ||||
\(643\) | 23924.0 | 1.46729 | 0.733647 | − | 0.679530i | \(-0.237816\pi\) | ||||
0.733647 | + | 0.679530i | \(0.237816\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1845.00 | −0.112631 | ||||||||
\(646\) | −1352.00 | + | 2341.73i | −0.0823432 | + | 0.142623i | ||||
\(647\) | 90.5000 | + | 156.751i | 0.00549911 | + | 0.00952473i | 0.868762 | − | 0.495230i | \(-0.164916\pi\) |
−0.863263 | + | 0.504755i | \(0.831583\pi\) | |||||||
\(648\) | 2596.00 | + | 4496.40i | 0.157377 | + | 0.272586i | ||||
\(649\) | 350.000 | − | 606.218i | 0.0211690 | − | 0.0366658i | ||||
\(650\) | −400.000 | −0.0241374 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2640.00 | −0.158574 | ||||||||
\(653\) | 8906.00 | − | 15425.6i | 0.533719 | − | 0.924429i | −0.465505 | − | 0.885045i | \(-0.654127\pi\) |
0.999224 | − | 0.0393836i | \(-0.0125394\pi\) | |||||||
\(654\) | 811.000 | + | 1404.69i | 0.0484902 | + | 0.0839875i | ||||
\(655\) | −1980.00 | − | 3429.46i | −0.118115 | − | 0.204580i | ||||
\(656\) | 2824.00 | − | 4891.31i | 0.168077 | − | 0.291118i | ||||
\(657\) | 16328.0 | 0.969583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15334.0 | 0.906416 | 0.453208 | − | 0.891405i | \(-0.350280\pi\) | ||||
0.453208 | + | 0.891405i | \(0.350280\pi\) | |||||||
\(660\) | 20.0000 | − | 34.6410i | 0.00117954 | − | 0.00204303i | ||||
\(661\) | 668.500 | + | 1157.88i | 0.0393368 | + | 0.0681334i | 0.885024 | − | 0.465546i | \(-0.154142\pi\) |
−0.845687 | + | 0.533680i | \(0.820809\pi\) | |||||||
\(662\) | −392.000 | − | 678.964i | −0.0230144 | − | 0.0398621i | ||||
\(663\) | −208.000 | + | 360.267i | −0.0121841 | + | 0.0211035i | ||||
\(664\) | 4200.00 | 0.245469 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10192.0 | 0.592991 | ||||||||
\(667\) | −2311.50 | + | 4003.64i | −0.134185 | + | 0.232416i | ||||
\(668\) | −1898.00 | − | 3287.43i | −0.109934 | − | 0.190411i | ||||
\(669\) | −1578.00 | − | 2733.18i | −0.0911943 | − | 0.157953i | ||||
\(670\) | 1455.00 | − | 2520.13i | 0.0838978 | − | 0.145315i | ||||
\(671\) | −934.000 | −0.0537357 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15112.0 | −0.865564 | −0.432782 | − | 0.901499i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(674\) | 3926.00 | − | 6800.03i | 0.224368 | − | 0.388616i | ||||
\(675\) | 662.500 | + | 1147.48i | 0.0377772 | + | 0.0654321i | ||||
\(676\) | 4266.00 | + | 7388.93i | 0.242717 | + | 0.420399i | ||||
\(677\) | 12696.0 | − | 21990.1i | 0.720749 | − | 1.24837i | −0.239951 | − | 0.970785i | \(-0.577131\pi\) |
0.960700 | − | 0.277589i | \(-0.0895352\pi\) | |||||||
\(678\) | −4340.00 | −0.245836 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2080.00 | −0.117301 | ||||||||
\(681\) | 2118.00 | − | 3668.48i | 0.119181 | − | 0.206427i | ||||
\(682\) | −664.000 | − | 1150.08i | −0.0372813 | − | 0.0645732i | ||||
\(683\) | −14615.5 | − | 25314.8i | −0.818809 | − | 1.41822i | −0.906560 | − | 0.422076i | \(-0.861301\pi\) |
0.0877512 | − | 0.996142i | \(-0.472032\pi\) | |||||||
\(684\) | −1352.00 | + | 2341.73i | −0.0755775 | + | 0.130904i | ||||
\(685\) | 5420.00 | 0.302318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6334.00 | −0.351757 | ||||||||
\(688\) | 2952.00 | − | 5113.01i | 0.163581 | − | 0.283331i | ||||
\(689\) | −2328.00 | − | 4032.21i | −0.128722 | − | 0.222954i | ||||
\(690\) | 335.000 | + | 580.237i | 0.0184829 | + | 0.0320134i | ||||
\(691\) | −3769.00 | + | 6528.10i | −0.207496 | + | 0.359393i | −0.950925 | − | 0.309421i | \(-0.899865\pi\) |
0.743429 | + | 0.668814i | \(0.233198\pi\) | |||||||
\(692\) | −13568.0 | −0.745344 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3570.00 | 0.195267 | ||||||||
\(695\) | −115.000 | + | 199.186i | −0.00627654 | + | 0.0108713i | ||||
\(696\) | 276.000 | + | 478.046i | 0.0150313 | + | 0.0260349i | ||||
\(697\) | 9178.00 | + | 15896.8i | 0.498768 | + | 0.863892i | ||||
\(698\) | 1591.00 | − | 2755.69i | 0.0862754 | − | 0.149433i | ||||
\(699\) | −4688.00 | −0.253672 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22125.0 | 1.19208 | 0.596041 | − | 0.802954i | \(-0.296739\pi\) | ||||
0.596041 | + | 0.802954i | \(0.296739\pi\) | |||||||
\(702\) | −424.000 | + | 734.390i | −0.0227961 | + | 0.0394840i | ||||
\(703\) | 2548.00 | + | 4413.27i | 0.136699 | + | 0.236770i | ||||
\(704\) | 64.0000 | + | 110.851i | 0.00342627 | + | 0.00593447i | ||||
\(705\) | 220.000 | − | 381.051i | 0.0117527 | − | 0.0203563i | ||||
\(706\) | 3372.00 | 0.179755 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1400.00 | 0.0743153 | ||||||||
\(709\) | 2219.50 | − | 3844.29i | 0.117567 | − | 0.203632i | −0.801236 | − | 0.598349i | \(-0.795824\pi\) |
0.918803 | + | 0.394716i | \(0.129157\pi\) | |||||||
\(710\) | 3850.00 | + | 6668.40i | 0.203504 | + | 0.352479i | ||||
\(711\) | 15210.0 | + | 26344.5i | 0.802278 | + | 1.38959i | ||||
\(712\) | −356.000 | + | 616.610i | −0.0187383 | + | 0.0324557i | ||||
\(713\) | 22244.0 | 1.16837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −80.0000 | −0.00418438 | ||||||||
\(716\) | −536.000 | + | 928.379i | −0.0279766 | + | 0.0484569i | ||||
\(717\) | −928.000 | − | 1607.34i | −0.0483358 | − | 0.0837201i | ||||
\(718\) | 7372.00 | + | 12768.7i | 0.383176 | + | 0.663681i | ||||
\(719\) | 6825.00 | − | 11821.2i | 0.354005 | − | 0.613155i | −0.632942 | − | 0.774199i | \(-0.718153\pi\) |
0.986947 | + | 0.161045i | \(0.0514863\pi\) | |||||||
\(720\) | −2080.00 | −0.107663 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12366.0 | 0.637417 | ||||||||
\(723\) | −2403.00 | + | 4162.12i | −0.123608 | + | 0.214095i | ||||
\(724\) | −8186.00 | − | 14178.6i | −0.420208 | − | 0.727821i | ||||
\(725\) | −862.500 | − | 1493.89i | −0.0441827 | − | 0.0765267i | ||||
\(726\) | −1327.00 | + | 2298.43i | −0.0678369 | + | 0.117497i | ||||
\(727\) | 11397.0 | 0.581419 | 0.290709 | − | 0.956811i | \(-0.406109\pi\) | ||||
0.290709 | + | 0.956811i | \(0.406109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | −3140.00 | + | 5438.64i | −0.159201 | + | 0.275744i | ||||
\(731\) | 9594.00 | + | 16617.3i | 0.485427 | + | 0.840784i | ||||
\(732\) | −934.000 | − | 1617.74i | −0.0471607 | − | 0.0816847i | ||||
\(733\) | 8343.00 | − | 14450.5i | 0.420403 | − | 0.728160i | −0.575575 | − | 0.817749i | \(-0.695222\pi\) |
0.995979 | + | 0.0895886i | \(0.0285552\pi\) | |||||||
\(734\) | 13274.0 | 0.667510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2144.00 | −0.107376 | ||||||||
\(737\) | 291.000 | − | 504.027i | 0.0145443 | − | 0.0251914i | ||||
\(738\) | 9178.00 | + | 15896.8i | 0.457787 | + | 0.792910i | ||||
\(739\) | −11235.0 | − | 19459.6i | −0.559251 | − | 0.968650i | −0.997559 | − | 0.0698258i | \(-0.977756\pi\) |
0.438309 | − | 0.898825i | \(-0.355578\pi\) | |||||||
\(740\) | −1960.00 | + | 3394.82i | −0.0973663 | + | 0.168643i | ||||
\(741\) | −208.000 | −0.0103118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5625.00 | 0.277741 | 0.138870 | − | 0.990311i | \(-0.455653\pi\) | ||||
0.138870 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(744\) | 1328.00 | − | 2300.16i | 0.0654393 | − | 0.113344i | ||||
\(745\) | 922.500 | + | 1597.82i | 0.0453662 | + | 0.0785765i | ||||
\(746\) | 3476.00 | + | 6020.61i | 0.170597 | + | 0.295483i | ||||
\(747\) | −6825.00 | + | 11821.2i | −0.334289 | + | 0.579005i | ||||
\(748\) | −416.000 | −0.0203348 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −250.000 | −0.0121716 | ||||||||
\(751\) | −8810.00 | + | 15259.4i | −0.428071 | + | 0.741441i | −0.996702 | − | 0.0811520i | \(-0.974140\pi\) |
0.568631 | + | 0.822593i | \(0.307473\pi\) | |||||||
\(752\) | 704.000 | + | 1219.36i | 0.0341386 | + | 0.0591298i | ||||
\(753\) | −1600.00 | − | 2771.28i | −0.0774333 | − | 0.134118i | ||||
\(754\) | 552.000 | − | 956.092i | 0.0266613 | − | 0.0461788i | ||||
\(755\) | 12400.0 | 0.597725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39056.0 | 1.87518 | 0.937592 | − | 0.347737i | \(-0.113050\pi\) | ||||
0.937592 | + | 0.347737i | \(0.113050\pi\) | |||||||
\(758\) | −2378.00 | + | 4118.82i | −0.113948 | + | 0.197364i | ||||
\(759\) | 67.0000 | + | 116.047i | 0.00320414 | + | 0.00554974i | ||||
\(760\) | −520.000 | − | 900.666i | −0.0248189 | − | 0.0429876i | ||||
\(761\) | 14869.0 | − | 25753.9i | 0.708280 | − | 1.22678i | −0.257215 | − | 0.966354i | \(-0.582805\pi\) |
0.965495 | − | 0.260422i | \(-0.0838618\pi\) | |||||||
\(762\) | −96.0000 | −0.00456393 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7912.00 | −0.374668 | ||||||||
\(765\) | 3380.00 | − | 5854.33i | 0.159744 | − | 0.276685i | ||||
\(766\) | 2457.00 | + | 4255.65i | 0.115894 | + | 0.200735i | ||||
\(767\) | −1400.00 | − | 2424.87i | −0.0659075 | − | 0.114155i | ||||
\(768\) | −128.000 | + | 221.703i | −0.00601407 | + | 0.0104167i | ||||
\(769\) | 1118.00 | 0.0524267 | 0.0262133 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262133 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1120.00 | 0.0523162 | ||||||||
\(772\) | 7996.00 | − | 13849.5i | 0.372775 | − | 0.645665i | ||||
\(773\) | 6716.00 | + | 11632.5i | 0.312494 | + | 0.541255i | 0.978902 | − | 0.204332i | \(-0.0655023\pi\) |
−0.666408 | + | 0.745587i | \(0.732169\pi\) | |||||||
\(774\) | 9594.00 | + | 16617.3i | 0.445542 | + | 0.771701i | ||||
\(775\) | −4150.00 | + | 7188.01i | −0.192351 | + | 0.333163i | ||||
\(776\) | −2320.00 | −0.107324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17124.0 | −0.789107 | ||||||||
\(779\) | −4589.00 | + | 7948.38i | −0.211063 | + | 0.365572i | ||||
\(780\) | −80.0000 | − | 138.564i | −0.00367238 | − | 0.00636076i | ||||
\(781\) | 770.000 | + | 1333.68i | 0.0352788 | + | 0.0611047i | ||||
\(782\) | 3484.00 | − | 6034.47i | 0.159319 | − | 0.275949i | ||||
\(783\) | −3657.00 | −0.166910 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6130.00 | −0.278712 | ||||||||
\(786\) | 792.000 | − | 1371.78i | 0.0359411 | − | 0.0622518i | ||||
\(787\) | −4674.50 | − | 8096.47i | −0.211725 | − | 0.366719i | 0.740529 | − | 0.672024i | \(-0.234575\pi\) |
−0.952255 | + | 0.305305i | \(0.901242\pi\) | |||||||
\(788\) | 6060.00 | + | 10496.2i | 0.273958 | + | 0.474508i | ||||
\(789\) | −3202.50 | + | 5546.89i | −0.144502 | + | 0.250285i | ||||
\(790\) | −11700.0 | −0.526921 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −416.000 | −0.0186640 | ||||||||
\(793\) | −1868.00 | + | 3235.47i | −0.0836502 | + | 0.144886i | ||||
\(794\) | 9842.00 | + | 17046.8i | 0.439899 | + | 0.761927i | ||||
\(795\) | −1455.00 | − | 2520.13i | −0.0649101 | − | 0.112428i | ||||
\(796\) | 712.000 | − | 1233.22i | 0.0317037 | − | 0.0549125i | ||||
\(797\) | 28008.0 | 1.24479 | 0.622393 | − | 0.782705i | \(-0.286161\pi\) | ||||
0.622393 | + | 0.782705i | \(0.286161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4576.00 | −0.202612 | ||||||||
\(800\) | 400.000 | − | 692.820i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −1157.00 | − | 2003.98i | −0.0510369 | − | 0.0883986i | ||||
\(802\) | −8097.00 | − | 14024.4i | −0.356503 | − | 0.617480i | ||||
\(803\) | −628.000 | + | 1087.73i | −0.0275986 | + | 0.0478021i | ||||
\(804\) | 1164.00 | 0.0510586 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5312.00 | −0.232143 | ||||||||
\(807\) | 2467.50 | − | 4273.84i | 0.107633 | − | 0.186426i | ||||
\(808\) | 4932.00 | + | 8542.47i | 0.214737 | + | 0.371935i | ||||
\(809\) | −9834.50 | − | 17033.9i | −0.427395 | − | 0.740270i | 0.569246 | − | 0.822167i | \(-0.307235\pi\) |
−0.996641 | + | 0.0818975i | \(0.973902\pi\) | |||||||
\(810\) | 3245.00 | − | 5620.50i | 0.140763 | − | 0.243808i | ||||
\(811\) | −31860.0 | −1.37948 | −0.689739 | − | 0.724059i | \(-0.742275\pi\) | ||||
−0.689739 | + | 0.724059i | \(0.742275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1446.00 | 0.0623781 | ||||||||
\(814\) | −392.000 | + | 678.964i | −0.0168791 | + | 0.0292355i | ||||
\(815\) | 1650.00 | + | 2857.88i | 0.0709165 | + | 0.122831i | ||||
\(816\) | −416.000 | − | 720.533i | −0.0178467 | − | 0.0309114i | ||||
\(817\) | −4797.00 | + | 8308.65i | −0.205417 | + | 0.355793i | ||||
\(818\) | 30518.0 | 1.30445 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7060.00 | −0.300666 | ||||||||
\(821\) | −1115.00 | + | 1931.24i | −0.0473980 | + | 0.0820958i | −0.888751 | − | 0.458390i | \(-0.848426\pi\) |
0.841353 | + | 0.540486i | \(0.181760\pi\) | |||||||
\(822\) | 1084.00 | + | 1877.54i | 0.0459962 | + | 0.0796677i | ||||
\(823\) | −7401.50 | − | 12819.8i | −0.313487 | − | 0.542976i | 0.665627 | − | 0.746284i | \(-0.268164\pi\) |
−0.979115 | + | 0.203308i | \(0.934831\pi\) | |||||||
\(824\) | −6212.00 | + | 10759.5i | −0.262628 | + | 0.454885i | ||||
\(825\) | −50.0000 | −0.00211003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13257.0 | 0.557426 | 0.278713 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278713 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(828\) | 3484.00 | − | 6034.47i | 0.146229 | − | 0.253276i | ||||
\(829\) | −10787.0 | − | 18683.6i | −0.451928 | − | 0.782762i | 0.546578 | − | 0.837408i | \(-0.315930\pi\) |
−0.998506 | + | 0.0546465i | \(0.982597\pi\) | |||||||
\(830\) | −2625.00 | − | 4546.63i | −0.109777 | − | 0.190140i | ||||
\(831\) | 4010.00 | − | 6945.52i | 0.167395 | − | 0.289937i | ||||
\(832\) | 512.000 | 0.0213346 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −92.0000 | −0.00381978 | ||||||||
\(835\) | −2372.50 | + | 4109.29i | −0.0983278 | + | 0.170309i | ||||
\(836\) | −104.000 | − | 180.133i | −0.00430253 | − | 0.00745220i | ||||
\(837\) | 8798.00 | + | 15238.6i | 0.363325 | + | 0.629298i | ||||
\(838\) | −16224.0 | + | 28100.8i | −0.668793 | + | 1.15838i | ||||
\(839\) | −12990.0 | −0.534523 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19628.0 | −0.804789 | ||||||||
\(842\) | 2977.00 | − | 5156.32i | 0.121846 | − | 0.211043i | ||||
\(843\) | −2489.00 | − | 4311.07i | −0.101691 | − | 0.176134i | ||||
\(844\) | 5204.00 | + | 9013.59i | 0.212238 | + | 0.367607i | ||||
\(845\) | 5332.50 | − | 9236.16i | 0.217093 | − | 0.376016i | ||||
\(846\) | −4576.00 | −0.185965 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9312.00 | 0.377094 | ||||||||
\(849\) | 2926.00 | − | 5067.98i | 0.118280 | − | 0.204868i | ||||
\(850\) | 1300.00 | + | 2251.67i | 0.0524584 | + | 0.0908606i | ||||
\(851\) | −6566.00 | − | 11372.6i | −0.264488 | − | 0.458107i | ||||
\(852\) | −1540.00 | + | 2667.36i | −0.0619243 | + | 0.107256i | ||||
\(853\) | −24838.0 | −0.996995 | −0.498498 | − | 0.866891i | \(-0.666115\pi\) | ||||
−0.498498 | + | 0.866891i | \(0.666115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3380.00 | 0.135197 | ||||||||
\(856\) | 7324.00 | − | 12685.5i | 0.292441 | − | 0.506522i | ||||
\(857\) | −8513.00 | − | 14744.9i | −0.339322 | − | 0.587722i | 0.644984 | − | 0.764196i | \(-0.276864\pi\) |
−0.984305 | + | 0.176474i | \(0.943531\pi\) | |||||||
\(858\) | −16.0000 | − | 27.7128i | −0.000636633 | − | 0.00110268i | ||||
\(859\) | 3364.00 | − | 5826.62i | 0.133618 | − | 0.231434i | −0.791450 | − | 0.611233i | \(-0.790674\pi\) |
0.925069 | + | 0.379800i | \(0.124007\pi\) | |||||||
\(860\) | −7380.00 | −0.292623 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28404.0 | −1.12232 | ||||||||
\(863\) | 15049.5 | − | 26066.5i | 0.593616 | − | 1.02817i | −0.400124 | − | 0.916461i | \(-0.631033\pi\) |
0.993741 | − | 0.111713i | \(-0.0356337\pi\) | |||||||
\(864\) | −848.000 | − | 1468.78i | −0.0333907 | − | 0.0578344i | ||||
\(865\) | 8480.00 | + | 14687.8i | 0.333328 | + | 0.577341i | ||||
\(866\) | −14310.0 | + | 24785.6i | −0.561517 | + | 0.972576i | ||||
\(867\) | −2209.00 | −0.0865301 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2340.00 | −0.0913453 | ||||||||
\(870\) | 345.000 | − | 597.558i | 0.0134444 | − | 0.0232863i | ||||
\(871\) | −1164.00 | − | 2016.11i | −0.0452820 | − | 0.0784308i | ||||
\(872\) | 3244.00 | + | 5618.77i | 0.125981 | + | 0.218206i | ||||
\(873\) | 3770.00 | − | 6529.83i | 0.146157 | − | 0.253152i | ||||
\(874\) | 3484.00 | 0.134838 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2512.00 | −0.0968865 | ||||||||
\(877\) | 2813.00 | − | 4872.26i | 0.108310 | − | 0.187599i | −0.806775 | − | 0.590858i | \(-0.798789\pi\) |
0.915086 | + | 0.403259i | \(0.132123\pi\) | |||||||
\(878\) | 2356.00 | + | 4080.71i | 0.0905594 | + | 0.156853i | ||||
\(879\) | −1506.00 | − | 2608.47i | −0.0577885 | − | 0.100093i | ||||
\(880\) | 80.0000 | − | 138.564i | 0.00306454 | − | 0.00530795i | ||||
\(881\) | 15927.0 | 0.609074 | 0.304537 | − | 0.952500i | \(-0.401498\pi\) | ||||
0.304537 | + | 0.952500i | \(0.401498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39124.0 | 1.49108 | 0.745542 | − | 0.666458i | \(-0.232191\pi\) | ||||
0.745542 | + | 0.666458i | \(0.232191\pi\) | |||||||
\(884\) | −832.000 | + | 1441.07i | −0.0316552 | + | 0.0548284i | ||||
\(885\) | −875.000 | − | 1515.54i | −0.0332348 | − | 0.0575644i | ||||
\(886\) | 8291.00 | + | 14360.4i | 0.314381 | + | 0.544524i | ||||
\(887\) | −12665.5 | + | 21937.3i | −0.479443 | + | 0.830419i | −0.999722 | − | 0.0235768i | \(-0.992495\pi\) |
0.520279 | + | 0.853996i | \(0.325828\pi\) | |||||||
\(888\) | −1568.00 | −0.0592552 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 890.000 | 0.0335201 | ||||||||
\(891\) | 649.000 | − | 1124.10i | 0.0244022 | − | 0.0422658i | ||||
\(892\) | −6312.00 | − | 10932.7i | −0.236930 | − | 0.410374i | ||||
\(893\) | −1144.00 | − | 1981.47i | −0.0428695 | − | 0.0742522i | ||||
\(894\) | −369.000 | + | 639.127i | −0.0138045 | + | 0.0239101i | ||||
\(895\) | 1340.00 | 0.0500461 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 536.000 | 0.0199515 | ||||||||
\(898\) | −3521.00 | + | 6098.55i | −0.130843 | + | 0.226627i | ||||
\(899\) | −11454.0 | − | 19838.9i | −0.424930 | − | 0.736001i | ||||
\(900\) | 1300.00 | + | 2251.67i | 0.0481481 | + | 0.0833950i | ||||
\(901\) | −15132.0 | + | 26209.4i | −0.559512 | + | 0.969103i | ||||
\(902\) | −1412.00 | −0.0521225 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17360.0 | −0.638700 | ||||||||
\(905\) | −10232.5 | + | 17723.2i | −0.375845 | + | 0.650983i | ||||
\(906\) | 2480.00 | + | 4295.49i | 0.0909409 | + | 0.157514i | ||||
\(907\) | −13192.5 | − | 22850.1i | −0.482966 | − | 0.836521i | 0.516843 | − | 0.856080i | \(-0.327107\pi\) |
−0.999809 | + | 0.0195592i | \(0.993774\pi\) | |||||||
\(908\) | 8472.00 | − | 14673.9i | 0.309640 | − | 0.536312i | ||||
\(909\) | −32058.0 | −1.16974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40770.0 | −1.48273 | −0.741367 | − | 0.671100i | \(-0.765822\pi\) | ||||
−0.741367 | + | 0.671100i | \(0.765822\pi\) | |||||||
\(912\) | 208.000 | − | 360.267i | 0.00755216 | − | 0.0130807i | ||||
\(913\) | −525.000 | − | 909.327i | −0.0190306 | − | 0.0329620i | ||||
\(914\) | −5432.00 | − | 9408.50i | −0.196581 | − | 0.340487i | ||||
\(915\) | −1167.50 | + | 2022.17i | −0.0421818 | + | 0.0730610i | ||||
\(916\) | −25336.0 | −0.913892 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5512.00 | 0.198173 | ||||||||
\(919\) | 7309.00 | − | 12659.6i | 0.262352 | − | 0.454407i | −0.704514 | − | 0.709690i | \(-0.748835\pi\) |
0.966867 | + | 0.255282i | \(0.0821685\pi\) | |||||||
\(920\) | 1340.00 | + | 2320.95i | 0.0480201 | + | 0.0831733i | ||||
\(921\) | 4721.50 | + | 8177.88i | 0.168924 | + | 0.292584i | ||||
\(922\) | 5350.00 | − | 9266.47i | 0.191099 | − | 0.330992i | ||||
\(923\) | 6160.00 | 0.219674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4900.00 | 0.174174 | ||||||||
\(926\) | −10123.0 | + | 17533.6i | −0.359247 | + | 0.622233i | ||||
\(927\) | −20189.0 | − | 34968.4i | −0.715311 | − | 1.23896i | ||||
\(928\) | 1104.00 | + | 1912.18i | 0.0390523 | + | 0.0676406i | ||||
\(929\) | 20661.5 | − | 35786.8i | 0.729690 | − | 1.26386i | −0.227324 | − | 0.973819i | \(-0.572998\pi\) |
0.957014 | − | 0.290041i | \(-0.0936689\pi\) | |||||||
\(930\) | −3320.00 | −0.117061 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18752.0 | −0.659058 | ||||||||
\(933\) | −4997.00 | + | 8655.06i | −0.175342 | + | 0.303702i | ||||
\(934\) | −6463.00 | − | 11194.2i | −0.226420 | − | 0.392170i | ||||
\(935\) | 260.000 | + | 450.333i | 0.00909402 | + | 0.0157513i | ||||
\(936\) | −832.000 | + | 1441.07i | −0.0290542 | + | 0.0503234i | ||||
\(937\) | 22620.0 | 0.788648 | 0.394324 | − | 0.918971i | \(-0.370979\pi\) | ||||
0.394324 | + | 0.918971i | \(0.370979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1456.00 | −0.0506015 | ||||||||
\(940\) | 880.000 | − | 1524.20i | 0.0305345 | − | 0.0528873i | ||||
\(941\) | 25989.0 | + | 45014.3i | 0.900337 | + | 1.55943i | 0.827057 | + | 0.562118i | \(0.190013\pi\) |
0.0732801 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(942\) | −1226.00 | − | 2123.49i | −0.0424047 | − | 0.0734471i | ||||
\(943\) | 11825.5 | − | 20482.4i | 0.408368 | − | 0.707315i | ||||
\(944\) | 5600.00 | 0.193077 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1476.00 | −0.0507282 | ||||||||
\(947\) | −4993.50 | + | 8649.00i | −0.171348 | + | 0.296784i | −0.938892 | − | 0.344213i | \(-0.888146\pi\) |
0.767543 | + | 0.640997i | \(0.221479\pi\) | |||||||
\(948\) | −2340.00 | − | 4053.00i | −0.0801684 | − | 0.138856i | ||||
\(949\) | 2512.00 | + | 4350.91i | 0.0859252 | + | 0.148827i | ||||
\(950\) | −650.000 | + | 1125.83i | −0.0221987 | + | 0.0384493i | ||||
\(951\) | 6872.00 | 0.234322 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6588.00 | 0.223931 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(954\) | −15132.0 | + | 26209.4i | −0.513539 | + | 0.889476i | ||||
\(955\) | 4945.00 | + | 8564.99i | 0.167556 | + | 0.290216i | ||||
\(956\) | −3712.00 | − | 6429.37i | −0.125580 | − | 0.217511i | ||||
\(957\) | 69.0000 | − | 119.512i | 0.00233067 | − | 0.00403684i | ||||
\(958\) | −35280.0 | −1.18982 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 320.000 | 0.0107583 | ||||||||
\(961\) | −40216.5 | + | 69657.0i | −1.34995 | + | 2.33819i | ||||
\(962\) | 1568.00 | + | 2715.86i | 0.0525513 | + | 0.0910215i | ||||
\(963\) | 23803.0 | + | 41228.0i | 0.796512 | + | 1.37960i | ||||
\(964\) | −9612.00 | + | 16648.5i | −0.321143 | + | 0.556236i | ||||
\(965\) | −19990.0 | −0.666840 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4091.00 | −0.136047 | −0.0680236 | − | 0.997684i | \(-0.521669\pi\) | ||||
−0.0680236 | + | 0.997684i | \(0.521669\pi\) | |||||||
\(968\) | −5308.00 | + | 9193.73i | −0.176245 | + | 0.305266i | ||||
\(969\) | 676.000 | + | 1170.87i | 0.0224110 | + | 0.0388170i | ||||
\(970\) | 1450.00 | + | 2511.47i | 0.0479966 | + | 0.0831325i | ||||
\(971\) | 11820.0 | − | 20472.8i | 0.390651 | − | 0.676627i | −0.601885 | − | 0.798583i | \(-0.705583\pi\) |
0.992536 | + | 0.121956i | \(0.0389167\pi\) | |||||||
\(972\) | 8320.00 | 0.274552 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20064.0 | 0.660053 | ||||||||
\(975\) | −100.000 | + | 173.205i | −0.00328468 | + | 0.00568923i | ||||
\(976\) | −3736.00 | − | 6470.94i | −0.122527 | − | 0.212223i | ||||
\(977\) | −18333.0 | − | 31753.7i | −0.600332 | − | 1.03981i | −0.992771 | − | 0.120028i | \(-0.961702\pi\) |
0.392438 | − | 0.919778i | \(-0.371632\pi\) | |||||||
\(978\) | −660.000 | + | 1143.15i | −0.0215792 | + | 0.0373763i | ||||
\(979\) | 178.000 | 0.00581093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21086.0 | −0.686263 | ||||||||
\(982\) | 5916.00 | − | 10246.8i | 0.192248 | − | 0.332983i | ||||
\(983\) | −20535.5 | − | 35568.5i | −0.666308 | − | 1.15408i | −0.978929 | − | 0.204201i | \(-0.934540\pi\) |
0.312621 | − | 0.949878i | \(-0.398793\pi\) | |||||||
\(984\) | −1412.00 | − | 2445.66i | −0.0457448 | − | 0.0792324i | ||||
\(985\) | 7575.00 | − | 13120.3i | 0.245035 | − | 0.424413i | ||||
\(986\) | −7176.00 | −0.231775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −832.000 | −0.0267909 | ||||||||
\(989\) | 12361.5 | − | 21410.7i | 0.397445 | − | 0.688394i | ||||
\(990\) | 260.000 | + | 450.333i | 0.00834681 | + | 0.0144571i | ||||
\(991\) | −15992.0 | − | 27699.0i | −0.512616 | − | 0.887877i | −0.999893 | − | 0.0146297i | \(-0.995343\pi\) |
0.487277 | − | 0.873248i | \(-0.337990\pi\) | |||||||
\(992\) | 5312.00 | − | 9200.65i | 0.170016 | − | 0.294477i | ||||
\(993\) | −392.000 | −0.0125274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1780.00 | −0.0567134 | ||||||||
\(996\) | 1050.00 | − | 1818.65i | 0.0334041 | − | 0.0578577i | ||||
\(997\) | −21947.0 | − | 38013.3i | −0.697160 | − | 1.20752i | −0.969447 | − | 0.245300i | \(-0.921113\pi\) |
0.272287 | − | 0.962216i | \(-0.412220\pi\) | |||||||
\(998\) | 13894.0 | + | 24065.1i | 0.440688 | + | 0.763294i | ||||
\(999\) | 5194.00 | − | 8996.27i | 0.164495 | − | 0.284914i |
(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 | 490.4.e.m.471.1 | 2 | ||
7.2 | even | 3 | 490.4.a.e.1.1 | 1 | |||
7.3 | odd | 6 | 70.4.e.c.11.1 | ✓ | 2 | ||
7.4 | even | 3 | inner | 490.4.e.m.361.1 | 2 | ||
7.5 | odd | 6 | 490.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 70.4.e.c.51.1 | yes | 2 | ||
21.17 | even | 6 | 630.4.k.b.361.1 | 2 | |||
21.20 | even | 2 | 630.4.k.b.541.1 | 2 | |||
28.3 | even | 6 | 560.4.q.d.81.1 | 2 | |||
28.27 | even | 2 | 560.4.q.d.401.1 | 2 | |||
35.3 | even | 12 | 350.4.j.e.249.2 | 4 | |||
35.9 | even | 6 | 2450.4.a.be.1.1 | 1 | |||
35.13 | even | 4 | 350.4.j.e.149.1 | 4 | |||
35.17 | even | 12 | 350.4.j.e.249.1 | 4 | |||
35.19 | odd | 6 | 2450.4.a.bg.1.1 | 1 | |||
35.24 | odd | 6 | 350.4.e.a.151.1 | 2 | |||
35.27 | even | 4 | 350.4.j.e.149.2 | 4 | |||
35.34 | odd | 2 | 350.4.e.a.51.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.e.c.11.1 | ✓ | 2 | 7.3 | odd | 6 | ||
70.4.e.c.51.1 | yes | 2 | 7.6 | odd | 2 | ||
350.4.e.a.51.1 | 2 | 35.34 | odd | 2 | |||
350.4.e.a.151.1 | 2 | 35.24 | odd | 6 | |||
350.4.j.e.149.1 | 4 | 35.13 | even | 4 | |||
350.4.j.e.149.2 | 4 | 35.27 | even | 4 | |||
350.4.j.e.249.1 | 4 | 35.17 | even | 12 | |||
350.4.j.e.249.2 | 4 | 35.3 | even | 12 | |||
490.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
490.4.a.e.1.1 | 1 | 7.2 | even | 3 | |||
490.4.e.m.361.1 | 2 | 7.4 | even | 3 | inner | ||
490.4.e.m.471.1 | 2 | 1.1 | even | 1 | trivial | ||
560.4.q.d.81.1 | 2 | 28.3 | even | 6 | |||
560.4.q.d.401.1 | 2 | 28.27 | even | 2 | |||
630.4.k.b.361.1 | 2 | 21.17 | even | 6 | |||
630.4.k.b.541.1 | 2 | 21.20 | even | 2 | |||
2450.4.a.be.1.1 | 1 | 35.9 | even | 6 | |||
2450.4.a.bg.1.1 | 1 | 35.19 | odd | 6 |