Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,4,Mod(5,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\), degree \(4\), 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: | \(1.88806112018\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Character | \(\chi\) | \(=\) | 32.5 |
Dual form | 32.4.g.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51802 | + | 1.28824i | −0.890255 | + | 0.455462i | ||||
\(3\) | −0.998206 | − | 2.40988i | −0.192105 | − | 0.463782i | 0.798252 | − | 0.602324i | \(-0.205758\pi\) |
−0.990357 | + | 0.138542i | \(0.955758\pi\) | |||||||
\(4\) | 4.68088 | − | 6.48763i | 0.585110 | − | 0.810954i | ||||
\(5\) | 17.4005 | + | 7.20752i | 1.55635 | + | 0.644661i | 0.984450 | − | 0.175664i | \(-0.0562073\pi\) |
0.571898 | + | 0.820325i | \(0.306207\pi\) | |||||||
\(6\) | 5.61801 | + | 4.78221i | 0.382257 | + | 0.325388i | ||||
\(7\) | 4.37099 | + | 4.37099i | 0.236012 | + | 0.236012i | 0.815196 | − | 0.579185i | \(-0.196629\pi\) |
−0.579185 | + | 0.815196i | \(0.696629\pi\) | |||||||
\(8\) | −3.42892 | + | 22.3661i | −0.151538 | + | 0.988451i | ||||
\(9\) | 14.2808 | − | 14.2808i | 0.528917 | − | 0.528917i | ||||
\(10\) | −53.0999 | + | 4.26731i | −1.67917 | + | 0.134944i | ||||
\(11\) | 11.7977 | − | 28.4821i | 0.323375 | − | 0.780697i | −0.675678 | − | 0.737197i | \(-0.736149\pi\) |
0.999053 | − | 0.0435002i | \(-0.0138509\pi\) | |||||||
\(12\) | −20.3069 | − | 4.80437i | −0.488508 | − | 0.115575i | ||||
\(13\) | −12.9230 | + | 5.35288i | −0.275707 | + | 0.114202i | −0.516253 | − | 0.856436i | \(-0.672674\pi\) |
0.240546 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(14\) | −16.6372 | − | 5.37537i | −0.317605 | − | 0.102616i | ||||
\(15\) | − | 49.1278i | − | 0.845649i | ||||||
\(16\) | −20.1788 | − | 60.7356i | −0.315294 | − | 0.948994i | ||||
\(17\) | 72.9239i | 1.04039i | 0.854047 | + | 0.520195i | \(0.174141\pi\) | ||||
−0.854047 | + | 0.520195i | \(0.825859\pi\) | |||||||
\(18\) | −17.5622 | + | 54.3563i | −0.229970 | + | 0.711773i | ||||
\(19\) | −143.136 | + | 59.2889i | −1.72830 | + | 0.715884i | −0.728783 | + | 0.684745i | \(0.759914\pi\) |
−0.999515 | + | 0.0311397i | \(0.990086\pi\) | |||||||
\(20\) | 128.209 | − | 79.1506i | 1.43342 | − | 0.884930i | ||||
\(21\) | 6.17043 | − | 14.8967i | 0.0641190 | − | 0.154797i | ||||
\(22\) | 6.98496 | + | 86.9167i | 0.0676909 | + | 0.842305i | ||||
\(23\) | 83.6411 | − | 83.6411i | 0.758278 | − | 0.758278i | −0.217731 | − | 0.976009i | \(-0.569866\pi\) |
0.976009 | + | 0.217731i | \(0.0698656\pi\) | |||||||
\(24\) | 57.3225 | − | 14.0627i | 0.487537 | − | 0.119605i | ||||
\(25\) | 162.441 | + | 162.441i | 1.29953 | + | 1.29953i | ||||
\(26\) | 25.6446 | − | 30.1266i | 0.193435 | − | 0.227243i | ||||
\(27\) | −113.737 | − | 47.1114i | −0.810692 | − | 0.335800i | ||||
\(28\) | 48.8175 | − | 7.89733i | 0.329487 | − | 0.0533020i | ||||
\(29\) | −39.6554 | − | 95.7367i | −0.253925 | − | 0.613030i | 0.744589 | − | 0.667523i | \(-0.232646\pi\) |
−0.998514 | + | 0.0544937i | \(0.982646\pi\) | |||||||
\(30\) | 63.2883 | + | 123.705i | 0.385161 | + | 0.752844i | ||||
\(31\) | −29.0324 | −0.168206 | −0.0841029 | − | 0.996457i | \(-0.526802\pi\) | ||||
−0.0841029 | + | 0.996457i | \(0.526802\pi\) | |||||||
\(32\) | 129.053 | + | 126.939i | 0.712922 | + | 0.701243i | ||||
\(33\) | −80.4149 | −0.424195 | ||||||||
\(34\) | −93.9435 | − | 183.624i | −0.473858 | − | 0.926214i | ||||
\(35\) | 44.5534 | + | 107.562i | 0.215169 | + | 0.519463i | ||||
\(36\) | −25.8019 | − | 159.495i | −0.119453 | − | 0.738402i | ||||
\(37\) | −267.681 | − | 110.877i | −1.18936 | − | 0.492650i | −0.301815 | − | 0.953366i | \(-0.597593\pi\) |
−0.887547 | + | 0.460716i | \(0.847593\pi\) | |||||||
\(38\) | 284.041 | − | 333.684i | 1.21257 | − | 1.42449i | ||||
\(39\) | 25.7996 | + | 25.7996i | 0.105929 | + | 0.105929i | ||||
\(40\) | −220.869 | + | 364.467i | −0.873062 | + | 1.44068i | ||||
\(41\) | −124.918 | + | 124.918i | −0.475827 | + | 0.475827i | −0.903794 | − | 0.427968i | \(-0.859230\pi\) |
0.427968 | + | 0.903794i | \(0.359230\pi\) | |||||||
\(42\) | 3.65329 | + | 45.4593i | 0.0134218 | + | 0.167012i | ||||
\(43\) | −27.0156 | + | 65.2215i | −0.0958103 | + | 0.231306i | −0.964517 | − | 0.264020i | \(-0.914952\pi\) |
0.868707 | + | 0.495326i | \(0.164952\pi\) | |||||||
\(44\) | −129.558 | − | 209.860i | −0.443900 | − | 0.719036i | ||||
\(45\) | 351.421 | − | 145.564i | 1.16415 | − | 0.482207i | ||||
\(46\) | −102.860 | + | 318.360i | −0.329694 | + | 1.02043i | ||||
\(47\) | 282.627i | 0.877136i | 0.898698 | + | 0.438568i | \(0.144514\pi\) | ||||
−0.898698 | + | 0.438568i | \(0.855486\pi\) | |||||||
\(48\) | −126.223 | + | 109.255i | −0.379557 | + | 0.328534i | ||||
\(49\) | − | 304.789i | − | 0.888597i | ||||||
\(50\) | −618.292 | − | 199.767i | −1.74879 | − | 0.565026i | ||||
\(51\) | 175.738 | − | 72.7931i | 0.482515 | − | 0.199864i | ||||
\(52\) | −25.7634 | + | 108.896i | −0.0687065 | + | 0.290406i | ||||
\(53\) | −51.4343 | + | 124.173i | −0.133303 | + | 0.321821i | −0.976410 | − | 0.215924i | \(-0.930724\pi\) |
0.843107 | + | 0.537745i | \(0.180724\pi\) | |||||||
\(54\) | 347.083 | − | 27.8929i | 0.874667 | − | 0.0702916i | ||||
\(55\) | 410.570 | − | 410.570i | 1.00657 | − | 1.00657i | ||||
\(56\) | −112.750 | + | 82.7743i | −0.269051 | + | 0.197521i | ||||
\(57\) | 285.759 | + | 285.759i | 0.664029 | + | 0.664029i | ||||
\(58\) | 223.185 | + | 189.981i | 0.505270 | + | 0.430100i | ||||
\(59\) | −222.476 | − | 92.1524i | −0.490913 | − | 0.203343i | 0.123474 | − | 0.992348i | \(-0.460596\pi\) |
−0.614387 | + | 0.789005i | \(0.710596\pi\) | |||||||
\(60\) | −318.723 | − | 229.961i | −0.685783 | − | 0.494797i | ||||
\(61\) | −226.809 | − | 547.566i | −0.476065 | − | 1.14932i | −0.961440 | − | 0.275016i | \(-0.911317\pi\) |
0.485374 | − | 0.874306i | \(-0.338683\pi\) | |||||||
\(62\) | 73.1043 | − | 37.4007i | 0.149746 | − | 0.0766112i | ||||
\(63\) | 124.842 | 0.249661 | ||||||||
\(64\) | −488.485 | − | 153.383i | −0.954072 | − | 0.299577i | ||||
\(65\) | −263.447 | −0.502717 | ||||||||
\(66\) | 202.487 | − | 103.594i | 0.377642 | − | 0.193205i | ||||
\(67\) | 356.015 | + | 859.496i | 0.649166 | + | 1.56723i | 0.813975 | + | 0.580900i | \(0.197299\pi\) |
−0.164808 | + | 0.986326i | \(0.552701\pi\) | |||||||
\(68\) | 473.104 | + | 341.348i | 0.843709 | + | 0.608743i | ||||
\(69\) | −285.056 | − | 118.074i | −0.497344 | − | 0.206007i | ||||
\(70\) | −250.752 | − | 213.447i | −0.428151 | − | 0.364454i | ||||
\(71\) | 690.837 | + | 690.837i | 1.15475 | + | 1.15475i | 0.985588 | + | 0.169163i | \(0.0541063\pi\) |
0.169163 | + | 0.985588i | \(0.445894\pi\) | |||||||
\(72\) | 270.437 | + | 368.373i | 0.442658 | + | 0.602960i | ||||
\(73\) | 223.345 | − | 223.345i | 0.358089 | − | 0.358089i | −0.505019 | − | 0.863108i | \(-0.668515\pi\) |
0.863108 | + | 0.505019i | \(0.168515\pi\) | |||||||
\(74\) | 816.862 | − | 65.6462i | 1.28322 | − | 0.103125i | ||||
\(75\) | 229.314 | − | 553.612i | 0.353052 | − | 0.852342i | ||||
\(76\) | −285.357 | + | 1206.14i | −0.430694 | + | 1.82044i | ||||
\(77\) | 176.062 | − | 72.9275i | 0.260574 | − | 0.107933i | ||||
\(78\) | −98.2001 | − | 31.7279i | −0.142551 | − | 0.0460574i | ||||
\(79\) | − | 698.000i | − | 0.994065i | −0.867732 | − | 0.497033i | \(-0.834423\pi\) | ||
0.867732 | − | 0.497033i | \(-0.165577\pi\) | |||||||
\(80\) | 86.6322 | − | 1202.27i | 0.121072 | − | 1.68022i | ||||
\(81\) | − | 224.174i | − | 0.307509i | ||||||
\(82\) | 153.622 | − | 475.470i | 0.206886 | − | 0.640328i | ||||
\(83\) | −915.116 | + | 379.053i | −1.21020 | + | 0.501283i | −0.894283 | − | 0.447502i | \(-0.852314\pi\) |
−0.315922 | + | 0.948785i | \(0.602314\pi\) | |||||||
\(84\) | −67.7616 | − | 109.761i | −0.0880166 | − | 0.142571i | ||||
\(85\) | −525.601 | + | 1268.91i | −0.670699 | + | 1.61921i | ||||
\(86\) | −15.9950 | − | 199.032i | −0.0200556 | − | 0.249560i | ||||
\(87\) | −191.130 | + | 191.130i | −0.235532 | + | 0.235532i | ||||
\(88\) | 596.580 | + | 361.530i | 0.722677 | + | 0.437946i | ||||
\(89\) | −163.738 | − | 163.738i | −0.195014 | − | 0.195014i | 0.602845 | − | 0.797859i | \(-0.294034\pi\) |
−0.797859 | + | 0.602845i | \(0.794034\pi\) | |||||||
\(90\) | −697.366 | + | 819.247i | −0.816765 | + | 0.959514i | ||||
\(91\) | −79.8837 | − | 33.0889i | −0.0920229 | − | 0.0381171i | ||||
\(92\) | −151.119 | − | 934.147i | −0.171253 | − | 1.05860i | ||||
\(93\) | 28.9803 | + | 69.9647i | 0.0323131 | + | 0.0780108i | ||||
\(94\) | −364.091 | − | 711.661i | −0.399502 | − | 0.780875i | ||||
\(95\) | −2917.97 | −3.15134 | ||||||||
\(96\) | 177.086 | − | 437.713i | 0.188268 | − | 0.465353i | ||||
\(97\) | −839.460 | −0.878704 | −0.439352 | − | 0.898315i | \(-0.644792\pi\) | ||||
−0.439352 | + | 0.898315i | \(0.644792\pi\) | |||||||
\(98\) | 392.641 | + | 767.465i | 0.404722 | + | 0.791078i | ||||
\(99\) | −238.266 | − | 575.225i | −0.241885 | − | 0.583963i | ||||
\(100\) | 1814.22 | − | 293.491i | 1.81422 | − | 0.293491i | ||||
\(101\) | 1561.02 | + | 646.594i | 1.53789 | + | 0.637015i | 0.981076 | − | 0.193622i | \(-0.0620235\pi\) |
0.556814 | + | 0.830637i | \(0.312024\pi\) | |||||||
\(102\) | −348.737 | + | 409.687i | −0.338531 | + | 0.397697i | ||||
\(103\) | −80.1481 | − | 80.1481i | −0.0766721 | − | 0.0766721i | 0.667731 | − | 0.744403i | \(-0.267266\pi\) |
−0.744403 | + | 0.667731i | \(0.767266\pi\) | |||||||
\(104\) | −75.4110 | − | 307.391i | −0.0711025 | − | 0.289829i | ||||
\(105\) | 214.737 | − | 214.737i | 0.199583 | − | 0.199583i | ||||
\(106\) | −30.4524 | − | 378.931i | −0.0279037 | − | 0.347218i | ||||
\(107\) | 552.814 | − | 1334.61i | 0.499463 | − | 1.20581i | −0.450310 | − | 0.892872i | \(-0.648687\pi\) |
0.949773 | − | 0.312939i | \(-0.101313\pi\) | |||||||
\(108\) | −838.030 | + | 517.361i | −0.746662 | + | 0.460955i | ||||
\(109\) | 490.666 | − | 203.241i | 0.431168 | − | 0.178596i | −0.156535 | − | 0.987672i | \(-0.550032\pi\) |
0.587703 | + | 0.809077i | \(0.300032\pi\) | |||||||
\(110\) | −504.912 | + | 1562.74i | −0.437650 | + | 1.35456i | ||||
\(111\) | 755.757i | 0.646246i | ||||||||
\(112\) | 177.274 | − | 353.676i | 0.149561 | − | 0.298386i | ||||
\(113\) | − | 109.197i | − | 0.0909060i | −0.998966 | − | 0.0454530i | \(-0.985527\pi\) | ||
0.998966 | − | 0.0454530i | \(-0.0144731\pi\) | |||||||
\(114\) | −1087.67 | − | 351.421i | −0.893595 | − | 0.288716i | ||||
\(115\) | 2058.24 | − | 852.552i | 1.66898 | − | 0.691312i | ||||
\(116\) | −806.727 | − | 190.862i | −0.645713 | − | 0.152768i | ||||
\(117\) | −108.107 | + | 260.993i | −0.0854230 | + | 0.206229i | ||||
\(118\) | 678.913 | − | 54.5601i | 0.529653 | − | 0.0425649i | ||||
\(119\) | −318.750 | + | 318.750i | −0.245544 | + | 0.245544i | ||||
\(120\) | 1098.80 | + | 168.455i | 0.835883 | + | 0.128148i | ||||
\(121\) | 269.116 | + | 269.116i | 0.202191 | + | 0.202191i | ||||
\(122\) | 1276.51 | + | 1086.60i | 0.947292 | + | 0.806362i | ||||
\(123\) | 425.731 | + | 176.344i | 0.312088 | + | 0.129271i | ||||
\(124\) | −135.897 | + | 188.352i | −0.0984188 | + | 0.136407i | ||||
\(125\) | 754.814 | + | 1822.28i | 0.540101 | + | 1.30392i | ||||
\(126\) | −314.356 | + | 160.827i | −0.222262 | + | 0.113711i | ||||
\(127\) | 1519.49 | 1.06167 | 0.530837 | − | 0.847474i | \(-0.321878\pi\) | ||||
0.530837 | + | 0.847474i | \(0.321878\pi\) | |||||||
\(128\) | 1427.61 | − | 243.063i | 0.985814 | − | 0.167843i | ||||
\(129\) | 184.143 | 0.125681 | ||||||||
\(130\) | 663.366 | − | 339.383i | 0.447547 | − | 0.228968i | ||||
\(131\) | 386.047 | + | 932.000i | 0.257474 | + | 0.621597i | 0.998770 | − | 0.0495811i | \(-0.0157886\pi\) |
−0.741296 | + | 0.671178i | \(0.765789\pi\) | |||||||
\(132\) | −376.412 | + | 521.703i | −0.248201 | + | 0.344003i | ||||
\(133\) | −884.798 | − | 366.495i | −0.576855 | − | 0.238941i | ||||
\(134\) | −2003.69 | − | 1705.60i | −1.29174 | − | 1.09956i | ||||
\(135\) | −1639.52 | − | 1639.52i | −1.04524 | − | 1.04524i | ||||
\(136\) | −1631.02 | − | 250.050i | −1.02838 | − | 0.157659i | ||||
\(137\) | 121.798 | − | 121.798i | 0.0759557 | − | 0.0759557i | −0.668108 | − | 0.744064i | \(-0.732896\pi\) |
0.744064 | + | 0.668108i | \(0.232896\pi\) | |||||||
\(138\) | 869.887 | − | 69.9075i | 0.536592 | − | 0.0431226i | ||||
\(139\) | −2.36667 | + | 5.71364i | −0.00144416 | + | 0.00348651i | −0.924600 | − | 0.380939i | \(-0.875601\pi\) |
0.923156 | + | 0.384426i | \(0.125601\pi\) | |||||||
\(140\) | 906.369 | + | 214.436i | 0.547158 | + | 0.129451i | ||||
\(141\) | 681.098 | − | 282.120i | 0.406800 | − | 0.168502i | ||||
\(142\) | −2629.51 | − | 849.580i | −1.55397 | − | 0.502079i | ||||
\(143\) | 431.225i | 0.252174i | ||||||||
\(144\) | −1155.52 | − | 579.182i | −0.668704 | − | 0.335175i | ||||
\(145\) | − | 1951.68i | − | 1.11778i | ||||||
\(146\) | −274.665 | + | 850.108i | −0.155695 | + | 0.481886i | ||||
\(147\) | −734.505 | + | 304.242i | −0.412115 | + | 0.170704i | ||||
\(148\) | −1972.31 | + | 1217.61i | −1.09542 | + | 0.676265i | ||||
\(149\) | 311.513 | − | 752.060i | 0.171276 | − | 0.413497i | −0.814811 | − | 0.579727i | \(-0.803159\pi\) |
0.986087 | + | 0.166229i | \(0.0531592\pi\) | |||||||
\(150\) | 135.768 | + | 1689.42i | 0.0739029 | + | 0.919604i | ||||
\(151\) | 571.254 | − | 571.254i | 0.307868 | − | 0.307868i | −0.536214 | − | 0.844082i | \(-0.680146\pi\) |
0.844082 | + | 0.536214i | \(0.180146\pi\) | |||||||
\(152\) | −835.259 | − | 3404.69i | −0.445713 | − | 1.81682i | ||||
\(153\) | 1041.41 | + | 1041.41i | 0.550281 | + | 0.550281i | ||||
\(154\) | −349.381 | + | 410.444i | −0.182818 | + | 0.214769i | ||||
\(155\) | −505.179 | − | 209.252i | −0.261787 | − | 0.108436i | ||||
\(156\) | 288.143 | − | 46.6136i | 0.147884 | − | 0.0239236i | ||||
\(157\) | −219.641 | − | 530.260i | −0.111651 | − | 0.269550i | 0.858171 | − | 0.513365i | \(-0.171601\pi\) |
−0.969822 | + | 0.243814i | \(0.921601\pi\) | |||||||
\(158\) | 899.192 | + | 1757.58i | 0.452758 | + | 0.884972i | ||||
\(159\) | 350.585 | 0.174863 | ||||||||
\(160\) | 1330.67 | + | 3138.95i | 0.657492 | + | 1.55097i | ||||
\(161\) | 731.190 | 0.357924 | ||||||||
\(162\) | 288.790 | + | 564.475i | 0.140058 | + | 0.273761i | ||||
\(163\) | −570.638 | − | 1377.64i | −0.274207 | − | 0.661995i | 0.725447 | − | 0.688278i | \(-0.241633\pi\) |
−0.999655 | + | 0.0262826i | \(0.991633\pi\) | |||||||
\(164\) | 225.696 | + | 1395.15i | 0.107463 | + | 0.664284i | ||||
\(165\) | −1399.26 | − | 579.593i | −0.660196 | − | 0.273462i | ||||
\(166\) | 1815.97 | − | 2133.35i | 0.849076 | − | 0.997472i | ||||
\(167\) | 642.374 | + | 642.374i | 0.297655 | + | 0.297655i | 0.840095 | − | 0.542440i | \(-0.182499\pi\) |
−0.542440 | + | 0.840095i | \(0.682499\pi\) | |||||||
\(168\) | 312.024 | + | 189.088i | 0.143293 | + | 0.0868361i | ||||
\(169\) | −1415.16 | + | 1415.16i | −0.644134 | + | 0.644134i | ||||
\(170\) | −311.189 | − | 3872.25i | −0.140395 | − | 1.74699i | ||||
\(171\) | −1197.40 | + | 2890.78i | −0.535483 | + | 1.29277i | ||||
\(172\) | 296.676 | + | 480.561i | 0.131519 | + | 0.213037i | ||||
\(173\) | −1861.21 | + | 770.937i | −0.817948 | + | 0.338805i | −0.752120 | − | 0.659026i | \(-0.770969\pi\) |
−0.0658275 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(174\) | 235.048 | − | 727.491i | 0.102408 | − | 0.316959i | ||||
\(175\) | 1420.06i | 0.613406i | ||||||||
\(176\) | −1967.94 | − | 141.804i | −0.842835 | − | 0.0607324i | ||||
\(177\) | 628.127i | 0.266740i | ||||||||
\(178\) | 623.231 | + | 201.363i | 0.262434 | + | 0.0847909i | ||||
\(179\) | −317.221 | + | 131.397i | −0.132459 | + | 0.0548664i | −0.447928 | − | 0.894069i | \(-0.647838\pi\) |
0.315469 | + | 0.948936i | \(0.397838\pi\) | |||||||
\(180\) | 700.597 | − | 2961.26i | 0.290108 | − | 1.22622i | ||||
\(181\) | 532.578 | − | 1285.76i | 0.218708 | − | 0.528008i | −0.776002 | − | 0.630731i | \(-0.782755\pi\) |
0.994710 | + | 0.102722i | \(0.0327553\pi\) | |||||||
\(182\) | 243.775 | − | 19.5907i | 0.0992848 | − | 0.00797891i | ||||
\(183\) | −1093.17 | + | 1093.17i | −0.441581 | + | 0.441581i | ||||
\(184\) | 1583.93 | + | 2157.53i | 0.634612 | + | 0.864429i | ||||
\(185\) | −3858.63 | − | 3858.63i | −1.53347 | − | 1.53347i | ||||
\(186\) | −163.105 | − | 138.839i | −0.0642979 | − | 0.0547322i | ||||
\(187\) | 2077.02 | + | 860.331i | 0.812230 | + | 0.336437i | ||||
\(188\) | 1833.58 | + | 1322.94i | 0.711317 | + | 0.513221i | ||||
\(189\) | −291.220 | − | 703.067i | −0.112080 | − | 0.270585i | ||||
\(190\) | 7347.50 | − | 3759.04i | 2.80549 | − | 1.43531i | ||||
\(191\) | 3161.63 | 1.19773 | 0.598867 | − | 0.800848i | \(-0.295618\pi\) | ||||
0.598867 | + | 0.800848i | \(0.295618\pi\) | |||||||
\(192\) | 117.973 | + | 1330.30i | 0.0443436 | + | 0.500032i | ||||
\(193\) | −1428.55 | −0.532796 | −0.266398 | − | 0.963863i | \(-0.585834\pi\) | ||||
−0.266398 | + | 0.963863i | \(0.585834\pi\) | |||||||
\(194\) | 2113.78 | − | 1081.43i | 0.782271 | − | 0.400216i | ||||
\(195\) | 262.975 | + | 634.877i | 0.0965744 | + | 0.233151i | ||||
\(196\) | −1977.36 | − | 1426.68i | −0.720612 | − | 0.519927i | ||||
\(197\) | 1377.48 | + | 570.573i | 0.498181 | + | 0.206353i | 0.617603 | − | 0.786490i | \(-0.288104\pi\) |
−0.119421 | + | 0.992844i | \(0.538104\pi\) | |||||||
\(198\) | 1340.99 | + | 1141.49i | 0.481312 | + | 0.409707i | ||||
\(199\) | 1207.72 | + | 1207.72i | 0.430217 | + | 0.430217i | 0.888702 | − | 0.458485i | \(-0.151608\pi\) |
−0.458485 | + | 0.888702i | \(0.651608\pi\) | |||||||
\(200\) | −4190.16 | + | 3076.17i | −1.48145 | + | 1.08759i | ||||
\(201\) | 1715.91 | − | 1715.91i | 0.602143 | − | 0.602143i | ||||
\(202\) | −4763.64 | + | 382.825i | −1.65925 | + | 0.133344i | ||||
\(203\) | 245.131 | − | 591.798i | 0.0847528 | − | 0.204611i | ||||
\(204\) | 350.353 | − | 1480.86i | 0.120243 | − | 0.508240i | ||||
\(205\) | −3073.98 | + | 1273.28i | −1.04730 | + | 0.433805i | ||||
\(206\) | 305.065 | + | 98.5648i | 0.103179 | + | 0.0333366i | ||||
\(207\) | − | 2388.92i | − | 0.802132i | ||||||
\(208\) | 585.880 | + | 676.871i | 0.195305 | + | 0.225637i | ||||
\(209\) | 4776.28i | 1.58078i | ||||||||
\(210\) | −264.080 | + | 817.346i | −0.0867774 | + | 0.268582i | ||||
\(211\) | −627.654 | + | 259.983i | −0.204784 | + | 0.0848245i | −0.482718 | − | 0.875776i | \(-0.660350\pi\) |
0.277934 | + | 0.960600i | \(0.410350\pi\) | |||||||
\(212\) | 564.834 | + | 914.928i | 0.182986 | + | 0.296403i | ||||
\(213\) | 975.239 | − | 2354.43i | 0.313720 | − | 0.757386i | ||||
\(214\) | 327.301 | + | 4072.74i | 0.104551 | + | 1.30097i | ||||
\(215\) | −940.170 | + | 940.170i | −0.298228 | + | 0.298228i | ||||
\(216\) | 1443.69 | − | 2382.31i | 0.454773 | − | 0.750443i | ||||
\(217\) | −126.901 | − | 126.901i | −0.0396985 | − | 0.0396985i | ||||
\(218\) | −973.686 | + | 1143.86i | −0.302506 | + | 0.355376i | ||||
\(219\) | −761.178 | − | 315.290i | −0.234866 | − | 0.0972846i | ||||
\(220\) | −741.801 | − | 4585.46i | −0.227328 | − | 1.40523i | ||||
\(221\) | −390.353 | − | 942.394i | −0.118814 | − | 0.286843i | ||||
\(222\) | −973.596 | − | 1903.01i | −0.294340 | − | 0.575324i | ||||
\(223\) | 1684.85 | 0.505946 | 0.252973 | − | 0.967473i | \(-0.418592\pi\) | ||||
0.252973 | + | 0.967473i | \(0.418592\pi\) | |||||||
\(224\) | 9.24107 | + | 1118.94i | 0.00275645 | + | 0.333759i | ||||
\(225\) | 4639.56 | 1.37468 | ||||||||
\(226\) | 140.672 | + | 274.960i | 0.0414042 | + | 0.0809295i | ||||
\(227\) | −1751.96 | − | 4229.60i | −0.512254 | − | 1.23669i | −0.942569 | − | 0.334011i | \(-0.891598\pi\) |
0.430315 | − | 0.902679i | \(-0.358402\pi\) | |||||||
\(228\) | 3191.50 | − | 516.297i | 0.927027 | − | 0.149967i | ||||
\(229\) | 1072.62 | + | 444.292i | 0.309521 | + | 0.128208i | 0.532037 | − | 0.846721i | \(-0.321427\pi\) |
−0.222515 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(230\) | −4084.41 | + | 4798.26i | −1.17095 | + | 1.37560i | ||||
\(231\) | −351.493 | − | 351.493i | −0.100115 | − | 0.100115i | ||||
\(232\) | 2277.23 | − | 558.664i | 0.644429 | − | 0.158095i | ||||
\(233\) | −224.008 | + | 224.008i | −0.0629840 | + | 0.0629840i | −0.737897 | − | 0.674913i | \(-0.764181\pi\) |
0.674913 | + | 0.737897i | \(0.264181\pi\) | |||||||
\(234\) | −64.0062 | − | 796.455i | −0.0178813 | − | 0.222504i | ||||
\(235\) | −2037.04 | + | 4917.85i | −0.565455 | + | 1.36513i | ||||
\(236\) | −1639.23 | + | 1011.99i | −0.452139 | + | 0.279130i | ||||
\(237\) | −1682.10 | + | 696.748i | −0.461030 | + | 0.190965i | ||||
\(238\) | 391.993 | − | 1213.25i | 0.106761 | − | 0.330433i | ||||
\(239\) | − | 5695.35i | − | 1.54143i | −0.637181 | − | 0.770714i | \(-0.719899\pi\) | ||
0.637181 | − | 0.770714i | \(-0.280101\pi\) | |||||||
\(240\) | −2983.81 | + | 991.339i | −0.802516 | + | 0.266628i | ||||
\(241\) | 5864.62i | 1.56752i | 0.621061 | + | 0.783762i | \(0.286702\pi\) | ||||
−0.621061 | + | 0.783762i | \(0.713298\pi\) | |||||||
\(242\) | −1024.32 | − | 330.954i | −0.272091 | − | 0.0879112i | ||||
\(243\) | −3611.13 | + | 1495.78i | −0.953309 | + | 0.394874i | ||||
\(244\) | −4614.08 | − | 1091.63i | −1.21060 | − | 0.286413i | ||||
\(245\) | 2196.77 | − | 5303.48i | 0.572844 | − | 1.38297i | ||||
\(246\) | −1299.17 | + | 104.407i | −0.336717 | + | 0.0270598i | ||||
\(247\) | 1532.38 | − | 1532.38i | 0.394749 | − | 0.394749i | ||||
\(248\) | 99.5499 | − | 649.342i | 0.0254896 | − | 0.166263i | ||||
\(249\) | 1826.95 | + | 1826.95i | 0.464972 | + | 0.464972i | ||||
\(250\) | −4248.18 | − | 3616.17i | −1.07471 | − | 0.914826i | ||||
\(251\) | 1284.55 | + | 532.079i | 0.323029 | + | 0.133803i | 0.538305 | − | 0.842750i | \(-0.319065\pi\) |
−0.215276 | + | 0.976553i | \(0.569065\pi\) | |||||||
\(252\) | 584.371 | − | 809.931i | 0.146079 | − | 0.202464i | ||||
\(253\) | −1395.50 | − | 3369.04i | −0.346777 | − | 0.837193i | ||||
\(254\) | −3826.10 | + | 1957.46i | −0.945161 | + | 0.483552i | ||||
\(255\) | 3582.59 | 0.879805 | ||||||||
\(256\) | −3281.63 | + | 2451.14i | −0.801180 | + | 0.598424i | ||||
\(257\) | 6068.35 | 1.47289 | 0.736446 | − | 0.676497i | \(-0.236503\pi\) | ||||
0.736446 | + | 0.676497i | \(0.236503\pi\) | |||||||
\(258\) | −463.677 | + | 237.221i | −0.111889 | + | 0.0572431i | ||||
\(259\) | −685.388 | − | 1654.67i | −0.164432 | − | 0.396974i | ||||
\(260\) | −1233.16 | + | 1709.15i | −0.294145 | + | 0.407681i | ||||
\(261\) | −1933.50 | − | 800.883i | −0.458547 | − | 0.189937i | ||||
\(262\) | −2172.71 | − | 1849.48i | −0.512331 | − | 0.436111i | ||||
\(263\) | −1919.51 | − | 1919.51i | −0.450046 | − | 0.450046i | 0.445324 | − | 0.895370i | \(-0.353089\pi\) |
−0.895370 | + | 0.445324i | \(0.853089\pi\) | |||||||
\(264\) | 275.737 | − | 1798.57i | 0.0642819 | − | 0.419296i | ||||
\(265\) | −1789.97 | + | 1789.97i | −0.414931 | + | 0.414931i | ||||
\(266\) | 2700.08 | − | 216.989i | 0.622377 | − | 0.0500166i | ||||
\(267\) | −231.146 | + | 558.035i | −0.0529808 | + | 0.127907i | ||||
\(268\) | 7242.56 | + | 1713.50i | 1.65078 | + | 0.390555i | ||||
\(269\) | 3969.40 | − | 1644.18i | 0.899697 | − | 0.372667i | 0.115593 | − | 0.993297i | \(-0.463123\pi\) |
0.784103 | + | 0.620630i | \(0.213123\pi\) | |||||||
\(270\) | 6240.46 | + | 2016.26i | 1.40660 | + | 0.454465i | ||||
\(271\) | 4538.69i | 1.01736i | 0.860954 | + | 0.508682i | \(0.169867\pi\) | ||||
−0.860954 | + | 0.508682i | \(0.830133\pi\) | |||||||
\(272\) | 4429.08 | − | 1471.52i | 0.987325 | − | 0.328029i | ||||
\(273\) | 225.540i | 0.0500011i | ||||||||
\(274\) | −149.786 | + | 463.597i | −0.0330251 | + | 0.102215i | ||||
\(275\) | 6543.07 | − | 2710.23i | 1.43477 | − | 0.594301i | ||||
\(276\) | −2100.34 | + | 1296.65i | −0.458063 | + | 0.282787i | ||||
\(277\) | −1889.91 | + | 4562.63i | −0.409940 | + | 0.989683i | 0.575213 | + | 0.818004i | \(0.304919\pi\) |
−0.985153 | + | 0.171679i | \(0.945081\pi\) | |||||||
\(278\) | −1.40122 | − | 17.4359i | −0.000302300 | − | 0.00376164i | ||||
\(279\) | −414.605 | + | 414.605i | −0.0889669 | + | 0.0889669i | ||||
\(280\) | −2558.50 | + | 627.667i | −0.546071 | + | 0.133965i | ||||
\(281\) | −30.7223 | − | 30.7223i | −0.00652220 | − | 0.00652220i | 0.703838 | − | 0.710360i | \(-0.251468\pi\) |
−0.710360 | + | 0.703838i | \(0.751468\pi\) | |||||||
\(282\) | −1351.58 | + | 1587.80i | −0.285410 | + | 0.335292i | ||||
\(283\) | −5549.45 | − | 2298.66i | −1.16565 | − | 0.482830i | −0.285901 | − | 0.958259i | \(-0.592293\pi\) |
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(284\) | 7715.62 | − | 1248.18i | 1.61211 | − | 0.260794i | ||||
\(285\) | 2912.73 | + | 7031.95i | 0.605387 | + | 1.46153i | ||||
\(286\) | −555.521 | − | 1085.83i | −0.114855 | − | 0.224499i | ||||
\(287\) | −1092.03 | −0.224601 | ||||||||
\(288\) | 3655.75 | − | 30.1921i | 0.747976 | − | 0.00617738i | ||||
\(289\) | −404.895 | −0.0824130 | ||||||||
\(290\) | 2514.24 | + | 4914.38i | 0.509107 | + | 0.995112i | ||||
\(291\) | 837.954 | + | 2023.00i | 0.168803 | + | 0.407527i | ||||
\(292\) | −403.530 | − | 2494.43i | −0.0808725 | − | 0.499915i | ||||
\(293\) | 2663.79 | + | 1103.38i | 0.531128 | + | 0.220000i | 0.632097 | − | 0.774889i | \(-0.282194\pi\) |
−0.100969 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(294\) | 1457.56 | − | 1712.31i | 0.289139 | − | 0.339673i | ||||
\(295\) | −3207.00 | − | 3207.00i | −0.632944 | − | 0.632944i | ||||
\(296\) | 3397.74 | − | 5606.78i | 0.667195 | − | 1.10097i | ||||
\(297\) | −2683.66 | + | 2683.66i | −0.524316 | + | 0.524316i | ||||
\(298\) | 184.436 | + | 2295.01i | 0.0358526 | + | 0.446128i | ||||
\(299\) | −633.173 | + | 1528.61i | −0.122466 | + | 0.295659i | ||||
\(300\) | −2518.25 | − | 4079.09i | −0.484637 | − | 0.785022i | ||||
\(301\) | −403.168 | + | 166.998i | −0.0772033 | + | 0.0319787i | ||||
\(302\) | −702.518 | + | 2174.34i | −0.133859 | + | 0.414303i | ||||
\(303\) | − | 4407.30i | − | 0.835620i | ||||||
\(304\) | 6489.26 | + | 7497.08i | 1.22429 | + | 1.41443i | ||||
\(305\) | − | 11162.7i | − | 2.09565i | ||||||
\(306\) | −3963.88 | − | 1280.71i | −0.740522 | − | 0.239259i | ||||
\(307\) | 401.539 | − | 166.323i | 0.0746484 | − | 0.0309204i | −0.345047 | − | 0.938585i | \(-0.612137\pi\) |
0.419695 | + | 0.907665i | \(0.362137\pi\) | |||||||
\(308\) | 351.000 | − | 1483.59i | 0.0649353 | − | 0.274466i | ||||
\(309\) | −113.143 | + | 273.152i | −0.0208301 | + | 0.0502883i | ||||
\(310\) | 1541.62 | − | 123.890i | 0.282445 | − | 0.0226984i | ||||
\(311\) | −5345.11 | + | 5345.11i | −0.974577 | + | 0.974577i | −0.999685 | − | 0.0251081i | \(-0.992007\pi\) |
0.0251081 | + | 0.999685i | \(0.492007\pi\) | |||||||
\(312\) | −665.501 | + | 488.572i | −0.120758 | + | 0.0886536i | ||||
\(313\) | −1787.53 | − | 1787.53i | −0.322803 | − | 0.322803i | 0.527039 | − | 0.849841i | \(-0.323302\pi\) |
−0.849841 | + | 0.527039i | \(0.823302\pi\) | |||||||
\(314\) | 1236.16 | + | 1052.26i | 0.222168 | + | 0.189116i | ||||
\(315\) | 2172.32 | + | 899.804i | 0.388560 | + | 0.160947i | ||||
\(316\) | −4528.37 | − | 3267.25i | −0.806141 | − | 0.581637i | ||||
\(317\) | 2370.77 | + | 5723.55i | 0.420050 | + | 1.01409i | 0.982332 | + | 0.187145i | \(0.0599234\pi\) |
−0.562282 | + | 0.826945i | \(0.690077\pi\) | |||||||
\(318\) | −882.782 | + | 451.638i | −0.155673 | + | 0.0796434i | ||||
\(319\) | −3194.62 | −0.560703 | ||||||||
\(320\) | −7394.37 | − | 6189.71i | −1.29174 | − | 1.08130i | ||||
\(321\) | −3768.08 | −0.655183 | ||||||||
\(322\) | −1841.15 | + | 941.948i | −0.318644 | + | 0.163021i | ||||
\(323\) | −4323.58 | − | 10438.0i | −0.744800 | − | 1.79811i | ||||
\(324\) | −1454.36 | − | 1049.33i | −0.249375 | − | 0.179926i | ||||
\(325\) | −2968.74 | − | 1229.69i | −0.506696 | − | 0.209880i | ||||
\(326\) | 3211.61 | + | 2733.81i | 0.545628 | + | 0.464454i | ||||
\(327\) | −979.572 | − | 979.572i | −0.165659 | − | 0.165659i | ||||
\(328\) | −2365.59 | − | 3222.26i | −0.398225 | − | 0.542437i | ||||
\(329\) | −1235.36 | + | 1235.36i | −0.207014 | + | 0.207014i | ||||
\(330\) | 4270.02 | − | 343.156i | 0.712294 | − | 0.0572427i | ||||
\(331\) | 1696.86 | − | 4096.57i | 0.281775 | − | 0.680265i | −0.718102 | − | 0.695938i | \(-0.754989\pi\) |
0.999877 | + | 0.0156724i | \(0.00498888\pi\) | |||||||
\(332\) | −1824.38 | + | 7711.24i | −0.301584 | + | 1.27473i | ||||
\(333\) | −5406.09 | + | 2239.28i | −0.889646 | + | 0.368503i | ||||
\(334\) | −2445.04 | − | 789.980i | −0.400559 | − | 0.129419i | ||||
\(335\) | 17521.6i | 2.85764i | ||||||||
\(336\) | −1029.27 | − | 74.1667i | −0.167118 | − | 0.0120420i | ||||
\(337\) | 927.470i | 0.149918i | 0.997187 | + | 0.0749592i | \(0.0238826\pi\) | ||||
−0.997187 | + | 0.0749592i | \(0.976117\pi\) | |||||||
\(338\) | 1740.34 | − | 5386.48i | 0.280066 | − | 0.866823i | ||||
\(339\) | −263.152 | + | 109.001i | −0.0421606 | + | 0.0174635i | ||||
\(340\) | 5771.97 | + | 9349.53i | 0.920673 | + | 1.49132i | ||||
\(341\) | −342.515 | + | 826.904i | −0.0543936 | + | 0.131318i | ||||
\(342\) | −708.938 | − | 8821.60i | −0.112091 | − | 1.39479i | ||||
\(343\) | 2831.48 | − | 2831.48i | 0.445731 | − | 0.445731i | ||||
\(344\) | −1366.12 | − | 827.873i | −0.214116 | − | 0.129756i | ||||
\(345\) | −4109.10 | − | 4109.10i | −0.641237 | − | 0.641237i | ||||
\(346\) | 3693.41 | − | 4338.92i | 0.573870 | − | 0.674167i | ||||
\(347\) | 3765.13 | + | 1559.57i | 0.582487 | + | 0.241274i | 0.654415 | − | 0.756136i | \(-0.272915\pi\) |
−0.0719277 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(348\) | 345.326 | + | 2134.64i | 0.0531937 | + | 0.328818i | ||||
\(349\) | −1631.14 | − | 3937.93i | −0.250181 | − | 0.603990i | 0.748037 | − | 0.663657i | \(-0.230996\pi\) |
−0.998218 | + | 0.0596662i | \(0.980996\pi\) | |||||||
\(350\) | −1829.37 | − | 3575.73i | −0.279383 | − | 0.546088i | ||||
\(351\) | 1722.00 | 0.261862 | ||||||||
\(352\) | 5137.99 | − | 2178.11i | 0.778000 | − | 0.329812i | ||||
\(353\) | −11289.2 | −1.70216 | −0.851080 | − | 0.525037i | \(-0.824052\pi\) | ||||
−0.851080 | + | 0.525037i | \(0.824052\pi\) | |||||||
\(354\) | −809.178 | − | 1581.64i | −0.121490 | − | 0.237466i | ||||
\(355\) | 7041.69 | + | 17000.1i | 1.05277 | + | 2.54162i | ||||
\(356\) | −1828.71 | + | 295.836i | −0.272252 | + | 0.0440429i | ||||
\(357\) | 1086.33 | + | 449.972i | 0.161049 | + | 0.0667088i | ||||
\(358\) | 629.498 | − | 739.518i | 0.0929330 | − | 0.109175i | ||||
\(359\) | 2970.97 | + | 2970.97i | 0.436774 | + | 0.436774i | 0.890925 | − | 0.454151i | \(-0.150057\pi\) |
−0.454151 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(360\) | 2050.69 | + | 8359.05i | 0.300225 | + | 1.22378i | ||||
\(361\) | 12122.7 | − | 12122.7i | 1.76742 | − | 1.76742i | ||||
\(362\) | 315.320 | + | 3923.65i | 0.0457813 | + | 0.569676i | ||||
\(363\) | 379.904 | − | 917.170i | 0.0549306 | − | 0.132614i | ||||
\(364\) | −588.594 | + | 363.371i | −0.0847547 | + | 0.0523237i | ||||
\(365\) | 5496.07 | − | 2276.55i | 0.788157 | − | 0.326465i | ||||
\(366\) | 1344.36 | − | 4160.89i | 0.191997 | − | 0.594243i | ||||
\(367\) | − | 12266.5i | − | 1.74470i | −0.488882 | − | 0.872350i | \(-0.662595\pi\) | ||
0.488882 | − | 0.872350i | \(-0.337405\pi\) | |||||||
\(368\) | −6767.78 | − | 3392.22i | −0.958681 | − | 0.480521i | ||||
\(369\) | 3567.84i | 0.503346i | ||||||||
\(370\) | 14687.0 | + | 4745.28i | 2.06362 | + | 0.666744i | ||||
\(371\) | −767.581 | + | 317.942i | −0.107415 | + | 0.0444926i | ||||
\(372\) | 589.559 | + | 139.482i | 0.0821699 | + | 0.0194404i | ||||
\(373\) | −905.804 | + | 2186.80i | −0.125739 | + | 0.303561i | −0.974196 | − | 0.225703i | \(-0.927532\pi\) |
0.848457 | + | 0.529265i | \(0.177532\pi\) | |||||||
\(374\) | −6338.31 | + | 509.371i | −0.876326 | + | 0.0704250i | ||||
\(375\) | 3638.03 | − | 3638.03i | 0.500979 | − | 0.500979i | ||||
\(376\) | −6321.26 | − | 969.106i | −0.867006 | − | 0.132920i | ||||
\(377\) | 1024.93 | + | 1024.93i | 0.140018 | + | 0.140018i | ||||
\(378\) | 1639.02 | + | 1395.18i | 0.223021 | + | 0.189842i | ||||
\(379\) | 6881.62 | + | 2850.46i | 0.932679 | + | 0.386328i | 0.796694 | − | 0.604383i | \(-0.206580\pi\) |
0.135985 | + | 0.990711i | \(0.456580\pi\) | |||||||
\(380\) | −13658.6 | + | 18930.7i | −1.84388 | + | 2.55559i | ||||
\(381\) | −1516.76 | − | 3661.78i | −0.203953 | − | 0.492385i | ||||
\(382\) | −7961.05 | + | 4072.93i | −1.06629 | + | 0.545522i | ||||
\(383\) | −2433.37 | −0.324645 | −0.162323 | − | 0.986738i | \(-0.551899\pi\) | ||||
−0.162323 | + | 0.986738i | \(0.551899\pi\) | |||||||
\(384\) | −2010.80 | − | 3197.75i | −0.267222 | − | 0.424959i | ||||
\(385\) | 3589.20 | 0.475124 | ||||||||
\(386\) | 3597.13 | − | 1840.32i | 0.474325 | − | 0.242668i | ||||
\(387\) | 545.609 | + | 1317.22i | 0.0716663 | + | 0.173018i | ||||
\(388\) | −3929.41 | + | 5446.11i | −0.514138 | + | 0.712589i | ||||
\(389\) | 4253.32 | + | 1761.78i | 0.554375 | + | 0.229630i | 0.642241 | − | 0.766503i | \(-0.278005\pi\) |
−0.0878663 | + | 0.996132i | \(0.528005\pi\) | |||||||
\(390\) | −1480.05 | − | 1259.86i | −0.192167 | − | 0.163578i | ||||
\(391\) | 6099.44 | + | 6099.44i | 0.788905 | + | 0.788905i | ||||
\(392\) | 6816.94 | + | 1045.10i | 0.878335 | + | 0.134657i | ||||
\(393\) | 1860.66 | − | 1860.66i | 0.238824 | − | 0.238824i | ||||
\(394\) | −4203.57 | + | 337.815i | −0.537495 | + | 0.0431952i | ||||
\(395\) | 5030.85 | − | 12145.6i | 0.640835 | − | 1.54711i | ||||
\(396\) | −4847.15 | − | 1146.77i | −0.615097 | − | 0.145524i | ||||
\(397\) | −306.541 | + | 126.974i | −0.0387528 | + | 0.0160519i | −0.401976 | − | 0.915650i | \(-0.631676\pi\) |
0.363223 | + | 0.931702i | \(0.381676\pi\) | |||||||
\(398\) | −4596.91 | − | 1485.24i | −0.578950 | − | 0.187056i | ||||
\(399\) | 2498.10i | 0.313437i | ||||||||
\(400\) | 6588.08 | − | 13143.8i | 0.823510 | − | 1.64297i | ||||
\(401\) | − | 10975.6i | − | 1.36682i | −0.730036 | − | 0.683409i | \(-0.760497\pi\) | ||
0.730036 | − | 0.683409i | \(-0.239503\pi\) | |||||||
\(402\) | −2110.19 | + | 6531.20i | −0.261808 | + | 0.810315i | ||||
\(403\) | 375.186 | − | 155.407i | 0.0463755 | − | 0.0192094i | ||||
\(404\) | 11501.8 | − | 7100.68i | 1.41642 | − | 0.874435i | ||||
\(405\) | 1615.74 | − | 3900.74i | 0.198239 | − | 0.478591i | ||||
\(406\) | 145.133 | + | 1805.95i | 0.0177410 | + | 0.220758i | ||||
\(407\) | −6316.01 | + | 6316.01i | −0.769221 | + | 0.769221i | ||||
\(408\) | 1025.51 | + | 4180.18i | 0.124436 | + | 0.507229i | ||||
\(409\) | 8384.88 | + | 8384.88i | 1.01371 | + | 1.01371i | 0.999905 | + | 0.0138007i | \(0.00439304\pi\) |
0.0138007 | + | 0.999905i | \(0.495607\pi\) | |||||||
\(410\) | 6100.06 | − | 7166.19i | 0.734782 | − | 0.863202i | ||||
\(411\) | −415.100 | − | 171.940i | −0.0498184 | − | 0.0206355i | ||||
\(412\) | −895.135 | + | 144.808i | −0.107039 | + | 0.0173160i | ||||
\(413\) | −569.642 | − | 1375.24i | −0.0678698 | − | 0.163852i | ||||
\(414\) | 3077.50 | + | 6015.35i | 0.365340 | + | 0.714102i | ||||
\(415\) | −18655.5 | −2.20666 | ||||||||
\(416\) | −2347.23 | − | 949.622i | −0.276641 | − | 0.111921i | ||||
\(417\) | 16.1316 | 0.00189441 | ||||||||
\(418\) | −6153.00 | − | 12026.8i | −0.719983 | − | 1.40729i | ||||
\(419\) | 533.639 | + | 1288.32i | 0.0622195 | + | 0.150211i | 0.951931 | − | 0.306311i | \(-0.0990948\pi\) |
−0.889712 | + | 0.456522i | \(0.849095\pi\) | |||||||
\(420\) | −387.978 | − | 2398.29i | −0.0450748 | − | 0.278630i | ||||
\(421\) | 1963.49 | + | 813.303i | 0.227303 | + | 0.0941520i | 0.493428 | − | 0.869786i | \(-0.335744\pi\) |
−0.266125 | + | 0.963938i | \(0.585744\pi\) | |||||||
\(422\) | 1245.53 | − | 1463.21i | 0.143676 | − | 0.168787i | ||||
\(423\) | 4036.13 | + | 4036.13i | 0.463932 | + | 0.463932i | ||||
\(424\) | −2600.91 | − | 1576.17i | −0.297904 | − | 0.180532i | ||||
\(425\) | −11845.8 | + | 11845.8i | −1.35201 | + | 1.35201i | ||||
\(426\) | 577.403 | + | 7184.86i | 0.0656697 | + | 0.817154i | ||||
\(427\) | 1402.03 | − | 3384.79i | 0.158897 | − | 0.383610i | ||||
\(428\) | −6070.82 | − | 9833.61i | −0.685617 | − | 1.11057i | ||||
\(429\) | 1039.20 | − | 430.451i | 0.116954 | − | 0.0484438i | ||||
\(430\) | 1156.21 | − | 3578.54i | 0.129668 | − | 0.401331i | ||||
\(431\) | − | 4521.29i | − | 0.505297i | −0.967558 | − | 0.252649i | \(-0.918698\pi\) | ||
0.967558 | − | 0.252649i | \(-0.0813016\pi\) | |||||||
\(432\) | −566.264 | + | 7858.54i | −0.0630658 | + | 0.875217i | ||||
\(433\) | − | 2122.80i | − | 0.235601i | −0.993037 | − | 0.117801i | \(-0.962416\pi\) | ||
0.993037 | − | 0.117801i | \(-0.0375844\pi\) | |||||||
\(434\) | 483.017 | + | 156.060i | 0.0534229 | + | 0.0172607i | ||||
\(435\) | −4703.33 | + | 1948.18i | −0.518408 | + | 0.214732i | ||||
\(436\) | 978.197 | − | 4134.61i | 0.107448 | − | 0.454155i | ||||
\(437\) | −7013.07 | + | 16931.1i | −0.767691 | + | 1.85337i | ||||
\(438\) | 2322.83 | − | 186.672i | 0.253400 | − | 0.0203642i | ||||
\(439\) | 8028.12 | − | 8028.12i | 0.872805 | − | 0.872805i | −0.119972 | − | 0.992777i | \(-0.538281\pi\) |
0.992777 | + | 0.119972i | \(0.0382806\pi\) | |||||||
\(440\) | 7775.04 | + | 10590.7i | 0.842411 | + | 1.14748i | ||||
\(441\) | −4352.62 | − | 4352.62i | −0.469994 | − | 0.469994i | ||||
\(442\) | 2196.95 | + | 1870.10i | 0.236421 | + | 0.201248i | ||||
\(443\) | 3136.09 | + | 1299.01i | 0.336343 | + | 0.139318i | 0.544462 | − | 0.838786i | \(-0.316734\pi\) |
−0.208119 | + | 0.978104i | \(0.566734\pi\) | |||||||
\(444\) | 4903.07 | + | 3537.60i | 0.524076 | + | 0.378124i | ||||
\(445\) | −1668.98 | − | 4029.28i | −0.177792 | − | 0.429227i | ||||
\(446\) | −4242.50 | + | 2170.49i | −0.450422 | + | 0.230439i | ||||
\(447\) | −2123.33 | −0.224676 | ||||||||
\(448\) | −1464.73 | − | 2805.60i | −0.154468 | − | 0.295876i | ||||
\(449\) | −16955.9 | −1.78218 | −0.891088 | − | 0.453832i | \(-0.850057\pi\) | ||||
−0.891088 | + | 0.453832i | \(0.850057\pi\) | |||||||
\(450\) | −11682.5 | + | 5976.86i | −1.22382 | + | 0.626115i | ||||
\(451\) | 2084.18 | + | 5031.66i | 0.217606 | + | 0.525347i | ||||
\(452\) | −708.429 | − | 511.137i | −0.0737206 | − | 0.0531900i | ||||
\(453\) | −1946.88 | − | 806.426i | −0.201926 | − | 0.0836406i | ||||
\(454\) | 9860.21 | + | 8393.29i | 1.01930 | + | 0.867658i | ||||
\(455\) | −1151.53 | − | 1151.53i | −0.118647 | − | 0.118647i | ||||
\(456\) | −7371.15 | + | 5411.46i | −0.756986 | + | 0.555734i | ||||
\(457\) | 6223.46 | − | 6223.46i | 0.637027 | − | 0.637027i | −0.312794 | − | 0.949821i | \(-0.601265\pi\) |
0.949821 | + | 0.312794i | \(0.101265\pi\) | |||||||
\(458\) | −3273.22 | + | 263.049i | −0.333947 | + | 0.0268373i | ||||
\(459\) | 3435.55 | − | 8294.14i | 0.349363 | − | 0.843437i | ||||
\(460\) | 4103.33 | − | 17343.8i | 0.415911 | − | 1.75796i | ||||
\(461\) | 10872.5 | − | 4503.54i | 1.09844 | − | 0.454991i | 0.241501 | − | 0.970401i | \(-0.422360\pi\) |
0.856944 | + | 0.515410i | \(0.172360\pi\) | |||||||
\(462\) | 1337.88 | + | 432.260i | 0.134726 | + | 0.0435294i | ||||
\(463\) | 13182.5i | 1.32320i | 0.749858 | + | 0.661599i | \(0.230122\pi\) | ||||
−0.749858 | + | 0.661599i | \(0.769878\pi\) | |||||||
\(464\) | −5014.43 | + | 4340.35i | −0.501700 | + | 0.434258i | ||||
\(465\) | 1426.30i | 0.142243i | ||||||||
\(466\) | 275.482 | − | 852.634i | 0.0273851 | − | 0.0847586i | ||||
\(467\) | 7043.25 | − | 2917.41i | 0.697907 | − | 0.289083i | −0.00538305 | − | 0.999986i | \(-0.501713\pi\) |
0.703290 | + | 0.710903i | \(0.251713\pi\) | |||||||
\(468\) | 1187.19 | + | 1923.04i | 0.117261 | + | 0.189941i | ||||
\(469\) | −2200.71 | + | 5312.99i | −0.216673 | + | 0.523094i | ||||
\(470\) | −1206.06 | − | 15007.5i | −0.118364 | − | 1.47286i | ||||
\(471\) | −1058.62 | + | 1058.62i | −0.103564 | + | 0.103564i | ||||
\(472\) | 2823.94 | − | 4659.93i | 0.275387 | − | 0.454429i | ||||
\(473\) | 1538.92 | + | 1538.92i | 0.149598 | + | 0.149598i | ||||
\(474\) | 3337.98 | − | 3921.37i | 0.323457 | − | 0.379989i | ||||
\(475\) | −32882.1 | − | 13620.2i | −3.17628 | − | 1.31566i | ||||
\(476\) | 575.904 | + | 3559.96i | 0.0554549 | + | 0.342795i | ||||
\(477\) | 1038.77 | + | 2507.81i | 0.0997107 | + | 0.240723i | ||||
\(478\) | 7336.98 | + | 14341.0i | 0.702062 | + | 1.37227i | ||||
\(479\) | 4612.37 | 0.439968 | 0.219984 | − | 0.975503i | \(-0.429399\pi\) | ||||
0.219984 | + | 0.975503i | \(0.429399\pi\) | |||||||
\(480\) | 6236.21 | − | 6340.07i | 0.593005 | − | 0.602882i | ||||
\(481\) | 4052.74 | 0.384177 | ||||||||
\(482\) | −7555.04 | − | 14767.3i | −0.713947 | − | 1.39550i | ||||
\(483\) | −729.878 | − | 1762.08i | −0.0687590 | − | 0.165999i | ||||
\(484\) | 3005.62 | − | 486.227i | 0.282271 | − | 0.0456637i | ||||
\(485\) | −14607.0 | − | 6050.43i | −1.36757 | − | 0.566466i | ||||
\(486\) | 7165.98 | − | 8418.41i | 0.668839 | − | 0.785734i | ||||
\(487\) | −10988.9 | − | 10988.9i | −1.02249 | − | 1.02249i | −0.999741 | − | 0.0227515i | \(-0.992757\pi\) |
−0.0227515 | − | 0.999741i | \(-0.507243\pi\) | |||||||
\(488\) | 13024.6 | − | 3195.28i | 1.20819 | − | 0.296401i | ||||
\(489\) | −2750.34 | + | 2750.34i | −0.254345 | + | 0.254345i | ||||
\(490\) | 1300.63 | + | 16184.2i | 0.119911 | + | 1.49210i | ||||
\(491\) | −7836.91 | + | 18920.0i | −0.720316 | + | 1.73900i | −0.0478645 | + | 0.998854i | \(0.515242\pi\) |
−0.672451 | + | 0.740142i | \(0.734758\pi\) | |||||||
\(492\) | 3136.85 | − | 1936.55i | 0.287439 | − | 0.177452i | ||||
\(493\) | 6981.49 | − | 2891.83i | 0.637790 | − | 0.264181i | ||||
\(494\) | −1884.49 | + | 5832.64i | −0.171634 | + | 0.531220i | ||||
\(495\) | − | 11726.5i | − | 1.06478i | ||||||
\(496\) | 585.839 | + | 1763.30i | 0.0530342 | + | 0.159626i | ||||
\(497\) | 6039.29i | 0.545069i | ||||||||
\(498\) | −6953.84 | − | 2246.75i | −0.625721 | − | 0.202167i | ||||
\(499\) | −6404.45 | + | 2652.81i | −0.574554 | + | 0.237988i | −0.650990 | − | 0.759086i | \(-0.725646\pi\) |
0.0764356 | + | 0.997075i | \(0.475646\pi\) | |||||||
\(500\) | 15355.5 | + | 3632.92i | 1.37344 | + | 0.324938i | ||||
\(501\) | 906.824 | − | 2189.27i | 0.0808661 | − | 0.195228i | ||||
\(502\) | −3919.98 | + | 315.025i | −0.348520 | + | 0.0280085i | ||||
\(503\) | 2553.60 | − | 2553.60i | 0.226361 | − | 0.226361i | −0.584810 | − | 0.811171i | \(-0.698831\pi\) |
0.811171 | + | 0.584810i | \(0.198831\pi\) | |||||||
\(504\) | −428.075 | + | 2792.24i | −0.0378332 | + | 0.246778i | ||||
\(505\) | 22502.1 | + | 22502.1i | 1.98283 | + | 1.98283i | ||||
\(506\) | 7854.04 | + | 6685.58i | 0.690029 | + | 0.587372i | ||||
\(507\) | 4823.00 | + | 1997.75i | 0.422479 | + | 0.174997i | ||||
\(508\) | 7112.52 | − | 9857.87i | 0.621195 | − | 0.860969i | ||||
\(509\) | 3141.82 | + | 7585.02i | 0.273593 | + | 0.660511i | 0.999632 | − | 0.0271425i | \(-0.00864080\pi\) |
−0.726039 | + | 0.687654i | \(0.758641\pi\) | |||||||
\(510\) | −9021.04 | + | 4615.23i | −0.783251 | + | 0.400718i | ||||
\(511\) | 1952.48 | 0.169026 | ||||||||
\(512\) | 5105.56 | − | 10399.6i | 0.440696 | − | 0.897657i | ||||
\(513\) | 19073.0 | 1.64151 | ||||||||
\(514\) | −15280.2 | + | 7817.48i | −1.31125 | + | 0.670845i | ||||
\(515\) | −816.948 | − | 1972.29i | −0.0699010 | − | 0.168756i | ||||
\(516\) | 861.951 | − | 1194.65i | 0.0735374 | − | 0.101922i | ||||
\(517\) | 8049.80 | + | 3334.34i | 0.684777 | + | 0.283644i | ||||
\(518\) | 3857.44 | + | 3283.56i | 0.327193 | + | 0.278516i | ||||
\(519\) | 3715.74 | + | 3715.74i | 0.314263 | + | 0.314263i | ||||
\(520\) | 903.341 | − | 5892.29i | 0.0761810 | − | 0.496912i | ||||
\(521\) | −7065.05 | + | 7065.05i | −0.594099 | + | 0.594099i | −0.938736 | − | 0.344637i | \(-0.888002\pi\) |
0.344637 | + | 0.938736i | \(0.388002\pi\) | |||||||
\(522\) | 5900.33 | − | 474.174i | 0.494733 | − | 0.0397587i | ||||
\(523\) | −111.041 | + | 268.077i | −0.00928391 | + | 0.0224134i | −0.928454 | − | 0.371449i | \(-0.878861\pi\) |
0.919170 | + | 0.393862i | \(0.128861\pi\) | |||||||
\(524\) | 7853.51 | + | 1858.04i | 0.654737 | + | 0.154903i | ||||
\(525\) | 3422.17 | − | 1417.51i | 0.284487 | − | 0.117838i | ||||
\(526\) | 7306.16 | + | 2360.58i | 0.605634 | + | 0.195677i | ||||
\(527\) | − | 2117.16i | − | 0.175000i | ||||||
\(528\) | 1622.68 | + | 4884.05i | 0.133746 | + | 0.402559i | ||||
\(529\) | − | 1824.68i | − | 0.149970i | ||||||
\(530\) | 2201.27 | − | 6813.08i | 0.180410 | − | 0.558380i | ||||
\(531\) | −4493.13 | + | 1861.11i | −0.367204 | + | 0.152101i | ||||
\(532\) | −6519.32 | + | 4024.73i | −0.531294 | + | 0.327996i | ||||
\(533\) | 945.642 | − | 2282.98i | 0.0768486 | − | 0.185529i | ||||
\(534\) | −136.853 | − | 1702.92i | −0.0110903 | − | 0.138001i | ||||
\(535\) | 19238.5 | − | 19238.5i | 1.55468 | − | 1.55468i | ||||
\(536\) | −20444.3 | + | 5015.52i | −1.64750 | + | 0.404174i | ||||
\(537\) | 633.304 | + | 633.304i | 0.0508921 | + | 0.0508921i | ||||
\(538\) | −7876.94 | + | 9253.61i | −0.631225 | + | 0.741546i | ||||
\(539\) | −8681.02 | − | 3595.79i | −0.693725 | − | 0.287350i | ||||
\(540\) | −18311.0 | + | 2962.22i | −1.45922 | + | 0.236063i | ||||
\(541\) | −8420.37 | − | 20328.6i | −0.669168 | − | 1.61552i | −0.783005 | − | 0.622016i | \(-0.786314\pi\) |
0.113837 | − | 0.993499i | \(-0.463686\pi\) | |||||||
\(542\) | −5846.92 | − | 11428.5i | −0.463370 | − | 0.905714i | ||||
\(543\) | −3630.14 | −0.286896 | ||||||||
\(544\) | −9256.85 | + | 9411.03i | −0.729567 | + | 0.741718i | ||||
\(545\) | 10002.7 | 0.786181 | ||||||||
\(546\) | −290.549 | − | 567.914i | −0.0227736 | − | 0.0445137i | ||||
\(547\) | 646.357 | + | 1560.44i | 0.0505233 | + | 0.121974i | 0.947126 | − | 0.320862i | \(-0.103972\pi\) |
−0.896603 | + | 0.442836i | \(0.853972\pi\) | |||||||
\(548\) | −220.060 | − | 1360.31i | −0.0171542 | − | 0.106039i | ||||
\(549\) | −11058.7 | − | 4580.65i | −0.859696 | − | 0.356098i | ||||
\(550\) | −12984.2 | + | 15253.5i | −1.00663 | + | 1.18256i | ||||
\(551\) | 11352.2 | + | 11352.2i | 0.877717 | + | 0.877717i | ||||
\(552\) | 3618.30 | − | 5970.73i | 0.278994 | − | 0.460383i | ||||
\(553\) | 3050.95 | − | 3050.95i | 0.234611 | − | 0.234611i | ||||
\(554\) | −1118.94 | − | 13923.5i | −0.0858111 | − | 1.06778i | ||||
\(555\) | −5447.14 | + | 13150.5i | −0.416609 | + | 1.00578i | ||||
\(556\) | 25.9899 | + | 42.0989i | 0.00198241 | + | 0.00321114i | ||||
\(557\) | −6482.01 | + | 2684.93i | −0.493091 | + | 0.204245i | −0.615351 | − | 0.788253i | \(-0.710986\pi\) |
0.122260 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(558\) | 509.874 | − | 1578.10i | 0.0386823 | − | 0.119724i | ||||
\(559\) | − | 987.467i | − | 0.0747145i | ||||||
\(560\) | 5633.78 | − | 4876.44i | 0.425126 | − | 0.367977i | ||||
\(561\) | − | 5864.17i | − | 0.441329i | ||||||
\(562\) | 116.937 | + | 37.7818i | 0.00877704 | + | 0.00283581i | ||||
\(563\) | −945.289 | + | 391.551i | −0.0707623 | + | 0.0293107i | −0.417784 | − | 0.908546i | \(-0.637193\pi\) |
0.347022 | + | 0.937857i | \(0.387193\pi\) | |||||||
\(564\) | 1357.84 | − | 5739.28i | 0.101375 | − | 0.428488i | ||||
\(565\) | 787.039 | − | 1900.08i | 0.0586035 | − | 0.141481i | ||||
\(566\) | 16934.9 | − | 1360.95i | 1.25764 | − | 0.101069i | ||||
\(567\) | 979.862 | − | 979.862i | 0.0725756 | − | 0.0725756i | ||||
\(568\) | −17820.2 | + | 13082.5i | −1.31640 | + | 0.966426i | ||||
\(569\) | −3760.45 | − | 3760.45i | −0.277058 | − | 0.277058i | 0.554875 | − | 0.831934i | \(-0.312766\pi\) |
−0.831934 | + | 0.554875i | \(0.812766\pi\) | |||||||
\(570\) | −16393.2 | − | 13954.3i | −1.20462 | − | 1.02541i | ||||
\(571\) | 2056.20 | + | 851.705i | 0.150699 | + | 0.0624216i | 0.456758 | − | 0.889591i | \(-0.349010\pi\) |
−0.306059 | + | 0.952013i | \(0.599010\pi\) | |||||||
\(572\) | 2797.63 | + | 2018.51i | 0.204501 | + | 0.147549i | ||||
\(573\) | −3155.95 | − | 7619.15i | −0.230091 | − | 0.555488i | ||||
\(574\) | 2749.76 | − | 1406.80i | 0.199952 | − | 0.102297i | ||||
\(575\) | 27173.5 | 1.97080 | ||||||||
\(576\) | −9166.37 | + | 4785.51i | −0.663076 | + | 0.346174i | ||||
\(577\) | −23621.3 | −1.70427 | −0.852137 | − | 0.523318i | \(-0.824694\pi\) | ||||
−0.852137 | + | 0.523318i | \(0.824694\pi\) | |||||||
\(578\) | 1019.53 | − | 521.602i | 0.0733686 | − | 0.0375359i | ||||
\(579\) | 1425.99 | + | 3442.65i | 0.102353 | + | 0.247101i | ||||
\(580\) | −12661.8 | − | 9135.59i | −0.906471 | − | 0.654026i | ||||
\(581\) | −5656.80 | − | 2343.13i | −0.403931 | − | 0.167314i | ||||
\(582\) | −4716.10 | − | 4014.48i | −0.335891 | − | 0.285920i | ||||
\(583\) | 2929.91 | + | 2929.91i | 0.208138 | + | 0.208138i | ||||
\(584\) | 4229.51 | + | 5761.18i | 0.299689 | + | 0.408218i | ||||
\(585\) | −3762.23 | + | 3762.23i | −0.265896 | + | 0.265896i | ||||
\(586\) | −8128.91 | + | 653.271i | −0.573041 | + | 0.0460518i | ||||
\(587\) | 7316.12 | − | 17662.7i | 0.514427 | − | 1.24194i | −0.426857 | − | 0.904319i | \(-0.640379\pi\) |
0.941283 | − | 0.337617i | \(-0.109621\pi\) | |||||||
\(588\) | −1464.32 | + | 6189.32i | −0.102700 | + | 0.434087i | ||||
\(589\) | 4155.59 | − | 1721.30i | 0.290710 | − | 0.120416i | ||||
\(590\) | 12206.7 | + | 3943.91i | 0.851764 | + | 0.275200i | ||||
\(591\) | − | 3889.13i | − | 0.270689i | ||||||
\(592\) | −1332.71 | + | 18495.1i | −0.0925235 | + | 1.28403i | ||||
\(593\) | 16542.0i | 1.14553i | 0.819720 | + | 0.572764i | \(0.194129\pi\) | ||||
−0.819720 | + | 0.572764i | \(0.805871\pi\) | |||||||
\(594\) | 3300.32 | − | 10214.7i | 0.227969 | − | 0.705580i | ||||
\(595\) | −7843.81 | + | 3249.01i | −0.540445 | + | 0.223860i | ||||
\(596\) | −3420.93 | − | 5541.28i | −0.235112 | − | 0.380839i | ||||
\(597\) | 1704.91 | − | 4116.02i | 0.116880 | − | 0.282174i | ||||
\(598\) | −374.878 | − | 4664.76i | −0.0256353 | − | 0.318990i | ||||
\(599\) | −8579.81 | + | 8579.81i | −0.585244 | + | 0.585244i | −0.936340 | − | 0.351095i | \(-0.885809\pi\) |
0.351095 | + | 0.936340i | \(0.385809\pi\) | |||||||
\(600\) | 11595.9 | + | 7027.15i | 0.788998 | + | 0.478137i | ||||
\(601\) | −13633.8 | − | 13633.8i | −0.925346 | − | 0.925346i | 0.0720542 | − | 0.997401i | \(-0.477045\pi\) |
−0.997401 | + | 0.0720542i | \(0.977045\pi\) | |||||||
\(602\) | 800.052 | − | 939.880i | 0.0541656 | − | 0.0636323i | ||||
\(603\) | 17358.4 | + | 7190.09i | 1.17229 | + | 0.485578i | ||||
\(604\) | −1032.12 | − | 6380.06i | −0.0695303 | − | 0.429803i | ||||
\(605\) | 2743.09 | + | 6622.41i | 0.184335 | + | 0.445023i | ||||
\(606\) | 5677.66 | + | 11097.7i | 0.380593 | + | 0.743915i | ||||
\(607\) | −23984.1 | −1.60376 | −0.801881 | − | 0.597484i | \(-0.796167\pi\) | ||||
−0.801881 | + | 0.597484i | \(0.796167\pi\) | |||||||
\(608\) | −25998.1 | − | 10518.1i | −1.73415 | − | 0.701587i | ||||
\(609\) | −1670.86 | −0.111176 | ||||||||
\(610\) | 14380.2 | + | 28107.8i | 0.954487 | + | 1.86566i | ||||
\(611\) | −1512.87 | − | 3652.38i | −0.100170 | − | 0.241833i | ||||
\(612\) | 11631.0 | − | 1881.57i | 0.768227 | − | 0.124278i | ||||
\(613\) | 18072.9 | + | 7486.04i | 1.19080 | + | 0.493244i | 0.888014 | − | 0.459816i | \(-0.152085\pi\) |
0.302782 | + | 0.953060i | \(0.402085\pi\) | |||||||
\(614\) | −796.821 | + | 936.084i | −0.0523731 | + | 0.0615265i | ||||
\(615\) | 6136.93 | + | 6136.93i | 0.402382 | + | 0.402382i | ||||
\(616\) | 1027.40 | + | 4187.89i | 0.0671998 | + | 0.273921i | ||||
\(617\) | 18674.2 | − | 18674.2i | 1.21847 | − | 1.21847i | 0.250301 | − | 0.968168i | \(-0.419470\pi\) |
0.968168 | − | 0.250301i | \(-0.0805297\pi\) | |||||||
\(618\) | −66.9880 | − | 833.558i | −0.00436028 | − | 0.0542567i | ||||
\(619\) | 3214.09 | − | 7759.51i | 0.208700 | − | 0.503846i | −0.784519 | − | 0.620105i | \(-0.787090\pi\) |
0.993219 | + | 0.116258i | \(0.0370901\pi\) | |||||||
\(620\) | −3722.23 | + | 2297.93i | −0.241110 | + | 0.148850i | ||||
\(621\) | −13453.5 | + | 5572.64i | −0.869359 | + | 0.360100i | ||||
\(622\) | 6573.32 | − | 20344.9i | 0.423740 | − | 1.31150i | ||||
\(623\) | − | 1431.40i | − | 0.0920511i | ||||||
\(624\) | 1046.35 | − | 2087.56i | 0.0671274 | − | 0.133925i | ||||
\(625\) | 8433.25i | 0.539728i | ||||||||
\(626\) | 6803.82 | + | 2198.28i | 0.434401 | + | 0.140353i | ||||
\(627\) | 11510.3 | − | 4767.71i | 0.733136 | − | 0.303675i | ||||
\(628\) | −4468.25 | − | 1057.13i | −0.283921 | − | 0.0671723i | ||||
\(629\) | 8085.58 | − | 19520.3i | 0.512549 | − | 1.23740i | ||||
\(630\) | −6629.11 | + | 532.741i | −0.419222 | + | 0.0336903i | ||||
\(631\) | −20023.0 | + | 20023.0i | −1.26324 | + | 1.26324i | −0.313722 | + | 0.949515i | \(0.601576\pi\) |
−0.949515 | + | 0.313722i | \(0.898424\pi\) | |||||||
\(632\) | 15611.5 | + | 2393.39i | 0.982585 | + | 0.150639i | ||||
\(633\) | 1253.06 | + | 1253.06i | 0.0786801 | + | 0.0786801i | ||||
\(634\) | −13343.0 | − | 11357.9i | −0.835831 | − | 0.711483i | ||||
\(635\) | 26439.8 | + | 10951.7i | 1.65233 | + | 0.684419i | ||||
\(636\) | 1641.05 | − | 2274.47i | 0.102314 | − | 0.141806i | ||||
\(637\) | 1631.50 | + | 3938.78i | 0.101479 | + | 0.244992i | ||||
\(638\) | 8044.13 | − | 4115.44i | 0.499169 | − | 0.255379i | ||||
\(639\) | 19731.4 | 1.22154 | ||||||||
\(640\) | 26593.0 | + | 6060.11i | 1.64247 | + | 0.374292i | ||||
\(641\) | 8637.88 | 0.532255 | 0.266128 | − | 0.963938i | \(-0.414256\pi\) | ||||
0.266128 | + | 0.963938i | \(0.414256\pi\) | |||||||
\(642\) | 9488.11 | − | 4854.19i | 0.583280 | − | 0.298411i | ||||
\(643\) | 5274.73 | + | 12734.3i | 0.323507 | + | 0.781015i | 0.999045 | + | 0.0436901i | \(0.0139114\pi\) |
−0.675538 | + | 0.737325i | \(0.736089\pi\) | |||||||
\(644\) | 3422.61 | − | 4743.69i | 0.209425 | − | 0.290260i | ||||
\(645\) | 3204.18 | + | 1327.22i | 0.195604 | + | 0.0810219i | ||||
\(646\) | 24333.6 | + | 20713.4i | 1.48203 | + | 1.26155i | ||||
\(647\) | −14785.3 | − | 14785.3i | −0.898406 | − | 0.898406i | 0.0968891 | − | 0.995295i | \(-0.469111\pi\) |
−0.995295 | + | 0.0968891i | \(0.969111\pi\) | |||||||
\(648\) | 5013.89 | + | 768.675i | 0.303957 | + | 0.0465994i | ||||
\(649\) | −5249.38 | + | 5249.38i | −0.317498 | + | 0.317498i | ||||
\(650\) | 9059.51 | − | 728.057i | 0.546682 | − | 0.0439335i | ||||
\(651\) | −179.143 | + | 432.488i | −0.0107852 | + | 0.0260377i | ||||
\(652\) | −11608.7 | − | 2746.48i | −0.697289 | − | 0.164970i | ||||
\(653\) | −25046.7 | + | 10374.7i | −1.50100 | + | 0.621733i | −0.973677 | − | 0.227933i | \(-0.926803\pi\) |
−0.527321 | + | 0.849666i | \(0.676803\pi\) | |||||||
\(654\) | 3728.51 | + | 1204.66i | 0.222930 | + | 0.0720275i | ||||
\(655\) | 18999.7i | 1.13340i | ||||||||
\(656\) | 10107.7 | + | 5066.27i | 0.601582 | + | 0.301531i | ||||
\(657\) | − | 6379.06i | − | 0.378799i | ||||||
\(658\) | 1519.23 | − | 4702.11i | 0.0900085 | − | 0.278583i | ||||
\(659\) | −23962.3 | + | 9925.50i | −1.41645 | + | 0.586711i | −0.953965 | − | 0.299918i | \(-0.903041\pi\) |
−0.462481 | + | 0.886629i | \(0.653041\pi\) | |||||||
\(660\) | −10309.9 | + | 6364.89i | −0.608052 | + | 0.375383i | ||||
\(661\) | −398.063 | + | 961.010i | −0.0234234 | + | 0.0565491i | −0.935158 | − | 0.354230i | \(-0.884743\pi\) |
0.911735 | + | 0.410779i | \(0.134743\pi\) | |||||||
\(662\) | 1004.65 | + | 12501.2i | 0.0589829 | + | 0.733948i | ||||
\(663\) | −1881.41 | + | 1881.41i | −0.110208 | + | 0.110208i | ||||
\(664\) | −5340.08 | − | 21767.3i | −0.312102 | − | 1.27219i | ||||
\(665\) | −12754.4 | − | 12754.4i | −0.743752 | − | 0.743752i | ||||
\(666\) | 10727.9 | − | 12602.9i | 0.624173 | − | 0.733261i | ||||
\(667\) | −11324.4 | − | 4690.70i | −0.657392 | − | 0.272301i | ||||
\(668\) | 7174.36 | − | 1160.61i | 0.415545 | − | 0.0672238i | ||||
\(669\) | −1681.83 | − | 4060.30i | −0.0971948 | − | 0.234649i | ||||
\(670\) | −22572.1 | − | 44119.9i | −1.30155 | − | 2.54403i | ||||
\(671\) | −18271.6 | −1.05122 | ||||||||
\(672\) | 2687.28 | − | 1139.20i | 0.154262 | − | 0.0653952i | ||||
\(673\) | −15307.7 | −0.876775 | −0.438387 | − | 0.898786i | \(-0.644450\pi\) | ||||
−0.438387 | + | 0.898786i | \(0.644450\pi\) | |||||||
\(674\) | −1194.80 | − | 2335.39i | −0.0682821 | − | 0.133466i | ||||
\(675\) | −10822.7 | − | 26128.3i | −0.617135 | − | 1.48990i | ||||
\(676\) | 2556.86 | + | 15805.3i | 0.145474 | + | 0.899253i | ||||
\(677\) | −1043.10 | − | 432.068i | −0.0592168 | − | 0.0245284i | 0.352878 | − | 0.935669i | \(-0.385203\pi\) |
−0.412095 | + | 0.911141i | \(0.635203\pi\) | |||||||
\(678\) | 522.202 | − | 613.469i | 0.0295797 | − | 0.0347495i | ||||
\(679\) | −3669.28 | − | 3669.28i | −0.207384 | − | 0.207384i | ||||
\(680\) | −26578.4 | − | 16106.6i | −1.49887 | − | 0.908326i | ||||
\(681\) | −8444.03 | + | 8444.03i | −0.475148 | + | 0.475148i | ||||
\(682\) | −202.790 | − | 2523.40i | −0.0113860 | − | 0.141680i | ||||
\(683\) | −8946.40 | + | 21598.5i | −0.501207 | + | 1.21002i | 0.447619 | + | 0.894224i | \(0.352272\pi\) |
−0.948827 | + | 0.315797i | \(0.897728\pi\) | |||||||
\(684\) | 13149.5 | + | 21299.7i | 0.735061 | + | 1.19066i | ||||
\(685\) | 2997.22 | − | 1241.49i | 0.167179 | − | 0.0692479i | ||||
\(686\) | −3482.11 | + | 10777.4i | −0.193801 | + | 0.599827i | ||||
\(687\) | − | 3028.37i | − | 0.168180i | ||||||
\(688\) | 4506.41 | + | 324.719i | 0.249717 | + | 0.0179939i | ||||
\(689\) | − | 1880.01i | − | 0.103952i | ||||||
\(690\) | 15640.3 | + | 5053.30i | 0.862923 | + | 0.278806i | ||||
\(691\) | 19676.4 | − | 8150.22i | 1.08325 | − | 0.448696i | 0.231600 | − | 0.972811i | \(-0.425604\pi\) |
0.851647 | + | 0.524115i | \(0.175604\pi\) | |||||||
\(692\) | −3710.52 | + | 15683.5i | −0.203834 | + | 0.861556i | ||||
\(693\) | 1472.85 | − | 3555.77i | 0.0807342 | − | 0.194910i | ||||
\(694\) | −11489.8 | + | 923.364i | −0.628453 | + | 0.0505049i | ||||
\(695\) | −82.3624 | + | 82.3624i | −0.00449523 | + | 0.00449523i | ||||
\(696\) | −3619.46 | − | 4930.20i | −0.197120 | − | 0.268504i | ||||
\(697\) | −9109.50 | − | 9109.50i | −0.495046 | − | 0.495046i | ||||
\(698\) | 9180.26 | + | 7814.49i | 0.497819 | + | 0.423758i | ||||
\(699\) | 763.440 | + | 316.227i | 0.0413104 | + | 0.0171113i | ||||
\(700\) | 9212.80 | + | 6647.10i | 0.497444 | + | 0.358910i | ||||
\(701\) | 2739.27 | + | 6613.19i | 0.147591 | + | 0.356315i | 0.980334 | − | 0.197343i | \(-0.0632313\pi\) |
−0.832744 | + | 0.553658i | \(0.813231\pi\) | |||||||
\(702\) | −4336.04 | + | 2218.35i | −0.233124 | + | 0.119268i | ||||
\(703\) | 44888.5 | 2.40825 | ||||||||
\(704\) | −10131.7 | + | 12103.5i | −0.542402 | + | 0.647966i | ||||
\(705\) | 13884.8 | 0.741749 | ||||||||
\(706\) | 28426.4 | − | 14543.2i | 1.51536 | − | 0.775268i | ||||
\(707\) | 3996.93 | + | 9649.45i | 0.212617 | + | 0.513303i | ||||
\(708\) | 4075.06 | + | 2940.19i | 0.216314 | + | 0.156072i | ||||
\(709\) | −2388.26 | − | 989.248i | −0.126506 | − | 0.0524005i | 0.318532 | − | 0.947912i | \(-0.396810\pi\) |
−0.445039 | + | 0.895511i | \(0.646810\pi\) | |||||||
\(710\) | −39631.4 | − | 33735.4i | −2.09484 | − | 1.78319i | ||||
\(711\) | −9967.97 | − | 9967.97i | −0.525778 | − | 0.525778i | ||||
\(712\) | 4223.64 | − | 3100.74i | 0.222314 | − | 0.163210i | ||||
\(713\) | −2428.31 | + | 2428.31i | −0.127547 | + | 0.127547i | ||||
\(714\) | −3315.07 | + | 266.412i | −0.173758 | + | 0.0139639i | ||||
\(715\) | −3108.06 | + | 7503.53i | −0.162566 | + | 0.392470i | ||||
\(716\) | −632.415 | + | 2673.07i | −0.0330090 | + | 0.139521i | ||||
\(717\) | −13725.1 | + | 5685.13i | −0.714887 | + | 0.296116i | ||||
\(718\) | −11308.3 | − | 3653.65i | −0.587774 | − | 0.189907i | ||||
\(719\) | − | 11843.1i | − | 0.614288i | −0.951663 | − | 0.307144i | \(-0.900627\pi\) | ||
0.951663 | − | 0.307144i | \(-0.0993734\pi\) | |||||||
\(720\) | −15932.2 | − | 18406.5i | −0.824662 | − | 0.952736i | ||||
\(721\) | − | 700.654i | − | 0.0361910i | ||||||
\(722\) | −14908.3 | + | 46142.2i | −0.768462 | + | 2.37844i | ||||
\(723\) | 14133.0 | − | 5854.10i | 0.726990 | − | 0.301129i | ||||
\(724\) | −5848.59 | − | 9473.64i | −0.300222 | − | 0.486305i | ||||
\(725\) | 9109.88 | − | 21993.2i | 0.466665 | − | 1.12663i | ||||
\(726\) | 224.927 | + | 2798.86i | 0.0114984 | + | 0.143079i | ||||
\(727\) | −4691.36 | + | 4691.36i | −0.239330 | + | 0.239330i | −0.816573 | − | 0.577243i | \(-0.804129\pi\) |
0.577243 | + | 0.816573i | \(0.304129\pi\) | |||||||
\(728\) | 1013.98 | − | 1673.23i | 0.0516219 | − | 0.0851840i | ||||
\(729\) | 2929.40 | + | 2929.40i | 0.148829 | + | 0.148829i | ||||
\(730\) | −10906.5 | + | 12812.6i | −0.552969 | + | 0.649613i | ||||
\(731\) | −4756.20 | − | 1970.08i | −0.240649 | − | 0.0996801i | ||||
\(732\) | 1975.09 | + | 12209.1i | 0.0997288 | + | 0.616475i | ||||
\(733\) | 13224.6 | + | 31927.0i | 0.666386 | + | 1.60880i | 0.787610 | + | 0.616174i | \(0.211318\pi\) |
−0.121224 | + | 0.992625i | \(0.538682\pi\) | |||||||
\(734\) | 15802.2 | + | 30887.3i | 0.794644 | + | 1.55323i | ||||
\(735\) | −14973.6 | −0.751441 | ||||||||
\(736\) | 21411.4 | − | 176.832i | 1.07233 | − | 0.00885615i | ||||
\(737\) | 28680.4 | 1.43345 | ||||||||
\(738\) | −4596.24 | − | 8983.91i | −0.229255 | − | 0.448106i | ||||
\(739\) | −13199.0 | − | 31865.1i | −0.657012 | − | 1.58617i | −0.802396 | − | 0.596793i | \(-0.796442\pi\) |
0.145383 | − | 0.989375i | \(-0.453558\pi\) | |||||||
\(740\) | −43095.1 | + | 6971.61i | −2.14082 | + | 0.346326i | ||||
\(741\) | −5222.48 | − | 2163.22i | −0.258911 | − | 0.107244i | ||||
\(742\) | 1523.20 | − | 1789.41i | 0.0753617 | − | 0.0885329i | ||||
\(743\) | −14307.6 | − | 14307.6i | −0.706452 | − | 0.706452i | 0.259335 | − | 0.965787i | \(-0.416497\pi\) |
−0.965787 | + | 0.259335i | \(0.916497\pi\) | |||||||
\(744\) | −1664.21 | + | 408.274i | −0.0820066 | + | 0.0201183i | ||||
\(745\) | 10841.0 | − | 10841.0i | 0.533131 | − | 0.533131i | ||||
\(746\) | −536.293 | − | 6673.31i | −0.0263205 | − | 0.327517i | ||||
\(747\) | −7655.38 | + | 18481.7i | −0.374961 | + | 0.905235i | ||||
\(748\) | 15303.8 | − | 9447.86i | 0.748078 | − | 0.461829i | ||||
\(749\) | 8249.93 | − | 3417.23i | 0.402464 | − | 0.166706i | ||||
\(750\) | −4473.98 | + | 13847.3i | −0.217822 | + | 0.674175i | ||||
\(751\) | 15781.7i | 0.766820i | 0.923578 | + | 0.383410i | \(0.125250\pi\) | ||||
−0.923578 | + | 0.383410i | \(0.874750\pi\) | |||||||
\(752\) | 17165.5 | − | 5703.07i | 0.832397 | − | 0.276555i | ||||
\(753\) | − | 3626.75i | − | 0.175519i | ||||||
\(754\) | −3901.16 | − | 1260.45i | −0.188424 | − | 0.0608789i | ||||
\(755\) | 14057.4 | − | 5822.78i | 0.677619 | − | 0.280679i | ||||
\(756\) | −5924.41 | − | 1401.64i | −0.285011 | − | 0.0674302i | ||||
\(757\) | −15069.9 | + | 36382.0i | −0.723548 | + | 1.74680i | −0.0605650 | + | 0.998164i | \(0.519290\pi\) |
−0.662983 | + | 0.748635i | \(0.730710\pi\) | |||||||
\(758\) | −21000.2 | + | 1687.65i | −1.00628 | + | 0.0808686i | ||||
\(759\) | −6726.00 | + | 6726.00i | −0.321658 | + | 0.321658i | ||||
\(760\) | 10005.5 | − | 65263.5i | 0.477548 | − | 3.11494i | ||||
\(761\) | −12120.7 | − | 12120.7i | −0.577363 | − | 0.577363i | 0.356813 | − | 0.934176i | \(-0.383863\pi\) |
−0.934176 | + | 0.356813i | \(0.883863\pi\) | |||||||
\(762\) | 8536.49 | + | 7266.50i | 0.405833 | + | 0.345456i | ||||
\(763\) | 3033.06 | + | 1256.34i | 0.143911 | + | 0.0596100i | ||||
\(764\) | 14799.2 | − | 20511.5i | 0.700806 | − | 0.971308i | ||||
\(765\) | 10615.1 | + | 25627.0i | 0.501684 | + | 1.21117i | ||||
\(766\) | 6127.27 | − | 3134.76i | 0.289017 | − | 0.147864i | ||||
\(767\) | 3368.33 | 0.158570 | ||||||||
\(768\) | 9182.71 | + | 5461.60i | 0.431449 | + | 0.256613i | ||||
\(769\) | 5213.88 | 0.244496 | 0.122248 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122248 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(770\) | −9037.69 | + | 4623.75i | −0.422982 | + | 0.216401i | ||||
\(771\) | −6057.46 | − | 14624.0i | −0.282950 | − | 0.683101i | ||||
\(772\) | −6686.89 | + | 9267.94i | −0.311744 | + | 0.432073i | ||||
\(773\) | 25960.5 | + | 10753.2i | 1.20793 | + | 0.500343i | 0.893555 | − | 0.448954i | \(-0.148203\pi\) |
0.314380 | + | 0.949297i | \(0.398203\pi\) | |||||||
\(774\) | −3070.74 | − | 2613.90i | −0.142604 | − | 0.121389i | ||||
\(775\) | −4716.05 | − | 4716.05i | −0.218588 | − | 0.218588i | ||||
\(776\) | 2878.44 | − | 18775.5i | 0.133157 | − | 0.868556i | ||||
\(777\) | −3303.41 | + | 3303.41i | −0.152521 | + | 0.152521i | ||||
\(778\) | −12979.5 | + | 1043.09i | −0.598123 | + | 0.0480675i | ||||
\(779\) | 10474.0 | − | 25286.5i | 0.481733 | − | 1.16301i | ||||
\(780\) | 5349.80 | + | 1265.70i | 0.245582 | + | 0.0581016i | ||||
\(781\) | 27826.7 | − | 11526.2i | 1.27493 | − | 0.528093i | ||||
\(782\) | −23216.1 | − | 7500.98i | −1.06164 | − | 0.343011i | ||||
\(783\) | 12757.0i | 0.582246i | ||||||||
\(784\) | −18511.5 | + | 6150.27i | −0.843273 | + | 0.280169i | ||||
\(785\) | − | 10809.9i | − | 0.491491i | ||||||
\(786\) | −2288.20 | + | 7082.14i | −0.103839 | + | 0.321389i | ||||
\(787\) | 31369.3 | − | 12993.6i | 1.42083 | − | 0.588528i | 0.465762 | − | 0.884910i | \(-0.345780\pi\) |
0.955069 | + | 0.296382i | \(0.0957801\pi\) | |||||||
\(788\) | 10149.5 | − | 6265.84i | 0.458834 | − | 0.283263i | ||||
\(789\) | −2709.73 | + | 6541.86i | −0.122267 | + | 0.295179i | ||||
\(790\) | 2978.58 | + | 37063.7i | 0.134143 | + | 1.66920i | ||||
\(791\) | 477.299 | − | 477.299i | 0.0214549 | − | 0.0214549i | ||||
\(792\) | 13682.5 | − | 3356.68i | 0.613874 | − | 0.150599i | ||||
\(793\) | 5862.11 | + | 5862.11i | 0.262509 | + | 0.262509i | ||||
\(794\) | 608.306 | − | 714.621i | 0.0271889 | − | 0.0319408i | ||||
\(795\) | 6100.36 | + | 2526.85i | 0.272148 | + | 0.112727i | ||||
\(796\) | 13488.5 | − | 2182.06i | 0.600610 | − | 0.0971622i | ||||
\(797\) | 8986.32 | + | 21694.9i | 0.399387 | + | 0.964207i | 0.987812 | + | 0.155654i | \(0.0497485\pi\) |
−0.588424 | + | 0.808552i | \(0.700251\pi\) | |||||||
\(798\) | −3218.15 | − | 6290.27i | −0.142758 | − | 0.279039i | ||||
\(799\) | −20610.3 | −0.912564 | ||||||||
\(800\) | 343.429 | + | 41583.4i | 0.0151776 | + | 1.83774i | ||||
\(801\) | −4676.62 | −0.206292 | ||||||||
\(802\) | 14139.2 | + | 27636.7i | 0.622533 | + | 1.21682i | ||||
\(803\) | −3726.37 | − | 8996.26i | −0.163762 | − | 0.395356i | ||||
\(804\) | −3100.23 | − | 19164.1i | −0.135991 | − | 0.840631i | ||||
\(805\) | 12723.1 | + | 5270.07i | 0.557055 | + | 0.230740i | ||||
\(806\) | −744.524 | + | 874.647i | −0.0325369 | + | 0.0382235i | ||||
\(807\) | −7924.55 | − | 7924.55i | −0.345672 | − | 0.345672i | ||||
\(808\) | −19814.4 | + | 32696.7i | −0.862708 | + | 1.42360i | ||||
\(809\) | −13193.6 | + | 13193.6i | −0.573376 | + | 0.573376i | −0.933070 | − | 0.359694i | \(-0.882881\pi\) |
0.359694 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(810\) | 956.620 | + | 11903.6i | 0.0414965 | + | 0.516358i | ||||
\(811\) | 140.367 | − | 338.877i | 0.00607764 | − | 0.0146727i | −0.920812 | − | 0.390008i | \(-0.872472\pi\) |
0.926889 | + | 0.375335i | \(0.122472\pi\) | |||||||
\(812\) | −2691.94 | − | 4360.45i | −0.116341 | − | 0.188451i | ||||
\(813\) | 10937.7 | − | 4530.55i | 0.471835 | − | 0.195441i | ||||
\(814\) | 7767.32 | − | 24040.4i | 0.334453 | − | 1.03515i | ||||
\(815\) | − | 28084.5i | − | 1.20707i | ||||||
\(816\) | −7967.32 | − | 9204.68i | −0.341804 | − | 0.394888i | ||||
\(817\) | − | 10937.3i | − | 0.468356i | ||||||
\(818\) | −31915.0 | − | 10311.6i | −1.36416 | − | 0.440753i | ||||
\(819\) | −1613.33 | + | 668.265i | −0.0688333 | + | 0.0285117i | ||||
\(820\) | −6128.32 | + | 25903.0i | −0.260988 | + | 1.10313i | ||||
\(821\) | 6304.96 | − | 15221.5i | 0.268020 | − | 0.647058i | −0.731370 | − | 0.681981i | \(-0.761119\pi\) |
0.999390 | + | 0.0349231i | \(0.0111186\pi\) | |||||||
\(822\) | 1266.73 | − | 101.799i | 0.0537497 | − | 0.00431954i | ||||
\(823\) | −769.291 | + | 769.291i | −0.0325830 | + | 0.0325830i | −0.723211 | − | 0.690628i | \(-0.757334\pi\) |
0.690628 | + | 0.723211i | \(0.257334\pi\) | |||||||
\(824\) | 2067.42 | − | 1517.78i | 0.0874055 | − | 0.0641679i | ||||
\(825\) | −13062.7 | − | 13062.7i | −0.551253 | − | 0.551253i | ||||
\(826\) | 3206.01 | + | 2729.04i | 0.135050 | + | 0.114958i | ||||
\(827\) | 22898.4 | + | 9484.82i | 0.962823 | + | 0.398815i | 0.808036 | − | 0.589133i | \(-0.200531\pi\) |
0.154788 | + | 0.987948i | \(0.450531\pi\) | |||||||
\(828\) | −15498.4 | − | 11182.2i | −0.650492 | − | 0.469335i | ||||
\(829\) | −10844.8 | − | 26181.7i | −0.454350 | − | 1.09690i | −0.970651 | − | 0.240492i | \(-0.922691\pi\) |
0.516301 | − | 0.856407i | \(-0.327309\pi\) | |||||||
\(830\) | 46975.0 | − | 24032.8i | 1.96449 | − | 1.00505i | ||||
\(831\) | 12881.9 | 0.537749 | ||||||||
\(832\) | 7133.72 | − | 632.630i | 0.297257 | − | 0.0263612i | ||||
\(833\) | 22226.4 | 0.924488 | ||||||||
\(834\) | −40.6198 | + | 20.7814i | −0.00168651 | + | 0.000862831i | ||||
\(835\) | 6547.70 | + | 15807.5i | 0.271368 | + | 0.655141i | ||||
\(836\) | 30986.8 | + | 22357.2i | 1.28194 | + | 0.924927i | ||||
\(837\) | 3302.06 | + | 1367.76i | 0.136363 | + | 0.0564834i | ||||
\(838\) | −3003.38 | − | 2556.56i | −0.123807 | − | 0.105388i | ||||
\(839\) | 23945.5 | + | 23945.5i | 0.985327 | + | 0.985327i | 0.999894 | − | 0.0145666i | \(-0.00463684\pi\) |
−0.0145666 | + | 0.999894i | \(0.504637\pi\) | |||||||
\(840\) | 4066.52 | + | 5539.15i | 0.167033 | + | 0.227522i | ||||
\(841\) | 9652.67 | − | 9652.67i | 0.395779 | − | 0.395779i | ||||
\(842\) | −5991.84 | + | 481.527i | −0.245240 | + | 0.0197085i | ||||
\(843\) | −43.3699 | + | 104.704i | −0.00177193 | + | 0.00427783i | ||||
\(844\) | −1251.30 | + | 5288.94i | −0.0510325 | + | 0.215702i | ||||
\(845\) | −34824.4 | + | 14424.7i | −1.41775 | + | 0.587249i | ||||
\(846\) | −15362.6 | − | 4963.56i | −0.624322 | − | 0.201715i | ||||
\(847\) | 2352.61i | 0.0954386i | ||||||||
\(848\) | 8579.63 | + | 618.225i | 0.347436 | + | 0.0250353i | ||||
\(849\) | 15668.0i | 0.633364i | ||||||||
\(850\) | 14567.8 | − | 45088.3i | 0.587848 | − | 1.81943i | ||||
\(851\) | −31663.0 | + | 13115.2i | −1.27543 | + | 0.528302i | ||||
\(852\) | −10709.7 | − | 17347.8i | −0.430645 | − | 0.697566i | ||||
\(853\) | 8663.21 | − | 20914.8i | 0.347740 | − | 0.839520i | −0.649146 | − | 0.760664i | \(-0.724873\pi\) |
0.996886 | − | 0.0788554i | \(-0.0251266\pi\) | |||||||
\(854\) | 830.089 | + | 10329.1i | 0.0332612 | + | 0.413882i | ||||
\(855\) | −41670.8 | + | 41670.8i | −1.66680 | + | 1.66680i | ||||
\(856\) | 27954.5 | + | 16940.6i | 1.11620 | + | 0.676422i | ||||
\(857\) | −9119.55 | − | 9119.55i | −0.363498 | − | 0.363498i | 0.501601 | − | 0.865099i | \(-0.332745\pi\) |
−0.865099 | + | 0.501601i | \(0.832745\pi\) | |||||||
\(858\) | −2062.21 | + | 2422.63i | −0.0820543 | + | 0.0963952i | ||||
\(859\) | −30582.3 | − | 12667.6i | −1.21473 | − | 0.503159i | −0.319002 | − | 0.947754i | \(-0.603348\pi\) |
−0.895732 | + | 0.444595i | \(0.853348\pi\) | |||||||
\(860\) | 1698.66 | + | 10500.3i | 0.0673533 | + | 0.416346i | ||||
\(861\) | 1090.07 | + | 2631.66i | 0.0431470 | + | 0.104166i | ||||
\(862\) | 5824.51 | + | 11384.7i | 0.230143 | + | 0.449844i | ||||
\(863\) | 1210.85 | 0.0477612 | 0.0238806 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238806 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(864\) | −8697.81 | − | 20517.5i | −0.342483 | − | 0.807891i | ||||
\(865\) | −37942.5 | −1.49143 | ||||||||
\(866\) | 2734.68 | + | 5345.26i | 0.107307 | + | 0.209745i | ||||
\(867\) | 404.169 | + | 975.749i | 0.0158319 | + | 0.0382217i | ||||
\(868\) | −1417.29 | + | 229.279i | −0.0554216 | + | 0.00896570i | ||||
\(869\) | −19880.5 | − | 8234.77i | −0.776064 | − | 0.321456i | ||||
\(870\) | 9333.36 | − | 10964.6i | 0.363713 | − | 0.427281i | ||||
\(871\) | −9201.55 | − | 9201.55i | −0.357959 | − | 0.357959i | ||||
\(872\) | 2863.24 | + | 11671.2i | 0.111195 | + | 0.453253i | ||||
\(873\) | −11988.1 | + | 11988.1i | −0.464762 | + | 0.464762i | ||||
\(874\) | −4152.18 | − | 51667.3i | −0.160698 | − | 1.99963i | ||||
\(875\) | −4665.90 | + | 11264.5i | −0.180270 | + | 0.435210i | ||||
\(876\) | −5608.47 | + | 3462.41i | −0.216316 | + | 0.133543i | ||||
\(877\) | −36421.4 | + | 15086.2i | −1.40235 | + | 0.580873i | −0.950361 | − | 0.311150i | \(-0.899286\pi\) |
−0.451990 | + | 0.892023i | \(0.649286\pi\) | |||||||
\(878\) | −9872.85 | + | 30557.1i | −0.379490 | + | 1.17455i | ||||
\(879\) | − | 7520.83i | − | 0.288591i | ||||||
\(880\) | −33221.1 | − | 16651.4i | −1.27259 | − | 0.637863i | ||||
\(881\) | 39286.1i | 1.50236i | 0.660095 | + | 0.751182i | \(0.270516\pi\) | ||||
−0.660095 | + | 0.751182i | \(0.729484\pi\) | |||||||
\(882\) | 16567.2 | + | 5352.77i | 0.632479 | + | 0.204351i | ||||
\(883\) | −234.092 | + | 96.9642i | −0.00892167 | + | 0.00369548i | −0.387140 | − | 0.922021i | \(-0.626537\pi\) |
0.378218 | + | 0.925717i | \(0.376537\pi\) | |||||||
\(884\) | −7941.10 | − | 1878.77i | −0.302136 | − | 0.0714816i | ||||
\(885\) | −4527.24 | + | 10929.7i | −0.171957 | + | 0.415140i | ||||
\(886\) | −9570.17 | + | 769.096i | −0.362885 | + | 0.0291629i | ||||
\(887\) | 13552.8 | − | 13552.8i | 0.513032 | − | 0.513032i | −0.402422 | − | 0.915454i | \(-0.631832\pi\) |
0.915454 | + | 0.402422i | \(0.131832\pi\) | |||||||
\(888\) | −16903.3 | − | 2591.43i | −0.638782 | − | 0.0979310i | ||||
\(889\) | 6641.66 | + | 6641.66i | 0.250567 | + | 0.250567i | ||||
\(890\) | 9393.21 | + | 7995.77i | 0.353777 | + | 0.301145i | ||||
\(891\) | −6384.93 | − | 2644.73i | −0.240071 | − | 0.0994407i | ||||
\(892\) | 7886.59 | − | 10930.7i | 0.296034 | − | 0.410299i | ||||
\(893\) | −16756.6 | − | 40454.1i | −0.627928 | − | 1.51595i | ||||
\(894\) | 5346.59 | − | 2735.36i | 0.200019 | − | 0.102331i | ||||
\(895\) | −6466.85 | −0.241523 | ||||||||
\(896\) | 7302.51 | + | 5177.65i | 0.272276 | + | 0.193050i | ||||
\(897\) | 4315.82 | 0.160648 | ||||||||
\(898\) | 42695.2 | − | 21843.2i | 1.58659 | − | 0.811712i | ||||
\(899\) | 1151.29 | + | 2779.47i | 0.0427117 | + | 0.103115i | ||||
\(900\) | 21717.2 | − | 30099.7i | 0.804340 | − | 1.11481i | ||||
\(901\) | −9055.21 | − | 3750.79i | −0.334820 | − | 0.138687i | ||||
\(902\) | −11730.0 | − | 9984.90i | −0.433000 | − | 0.368582i | ||||
\(903\) | 804.889 | + | 804.889i | 0.0296623 | + | 0.0296623i | ||||
\(904\) | 2442.31 | + | 374.428i | 0.0898561 | + | 0.0137757i | ||||
\(905\) | 18534.2 | − | 18534.2i | 0.680772 | − | 0.680772i | ||||
\(906\) | 5941.17 | − | 477.455i | 0.217861 | − | 0.0175082i | ||||
\(907\) | −2600.00 | + | 6276.95i | −0.0951835 | + | 0.229793i | −0.964299 | − | 0.264816i | \(-0.914689\pi\) |
0.869115 | + | 0.494609i | \(0.164689\pi\) | |||||||
\(908\) | −35640.8 | − | 8432.18i | −1.30262 | − | 0.308185i | ||||
\(909\) | 31526.4 | − | 13058.6i | 1.15034 | − | 0.476488i | ||||
\(910\) | 4383.01 | + | 1416.13i | 0.159665 | + | 0.0515870i | ||||
\(911\) | − | 22984.1i | − | 0.835891i | −0.908472 | − | 0.417946i | \(-0.862750\pi\) | ||
0.908472 | − | 0.417946i | \(-0.137250\pi\) | |||||||
\(912\) | 11589.5 | − | 23122.0i | 0.420795 | − | 0.839524i | ||||
\(913\) | 30536.3i | 1.10691i | ||||||||
\(914\) | −7653.51 | + | 23688.1i | −0.276975 | + | 0.857258i | ||||
\(915\) | −26900.7 | + | 11142.6i | −0.971924 | + | 0.402584i | ||||
\(916\) | 7903.18 | − | 4879.06i | 0.285075 | − | 0.175992i | ||||
\(917\) | −2386.36 | + | 5761.17i | −0.0859372 | + | 0.207471i | ||||
\(918\) | 2034.06 | + | 25310.6i | 0.0731307 | + | 0.909995i | ||||
\(919\) | 38048.0 | − | 38048.0i | 1.36571 | − | 1.36571i | 0.499258 | − | 0.866453i | \(-0.333606\pi\) |
0.866453 | − | 0.499258i | \(-0.166394\pi\) | |||||||
\(920\) | 12010.7 | + | 48958.2i | 0.430415 | + | 1.75446i | ||||
\(921\) | −801.638 | − | 801.638i | −0.0286806 | − | 0.0286806i | ||||
\(922\) | −21575.6 | + | 25346.4i | −0.770666 | + | 0.905358i | ||||
\(923\) | −12625.6 | − | 5229.71i | −0.450247 | − | 0.186499i | ||||
\(924\) | −3925.66 | + | 635.063i | −0.139767 | + | 0.0226104i | ||||
\(925\) | −25471.3 | − | 61493.2i | −0.905396 | − | 2.18582i | ||||
\(926\) | −16982.2 | − | 33193.7i | −0.602666 | − | 1.17798i | ||||
\(927\) | −2289.15 | −0.0811064 | ||||||||
\(928\) | 7035.03 | − | 17388.9i | 0.248854 | − | 0.615106i | ||||
\(929\) | 28435.1 | 1.00423 | 0.502113 | − | 0.864802i | \(-0.332556\pi\) | ||||
0.502113 | + | 0.864802i | \(0.332556\pi\) | |||||||
\(930\) | −1837.41 | − | 3591.45i | −0.0647862 | − | 0.126633i | ||||
\(931\) | 18070.6 | + | 43626.3i | 0.636133 | + | 1.53576i | ||||
\(932\) | 404.729 | + | 2501.84i | 0.0142246 | + | 0.0879297i | ||||
\(933\) | 18216.6 | + | 7545.57i | 0.639212 | + | 0.264770i | ||||
\(934\) | −13976.7 | + | 16419.5i | −0.489650 | + | 0.575227i | ||||
\(935\) | 29940.4 | + | 29940.4i | 1.04723 | + | 1.04723i | ||||
\(936\) | −5466.71 | − | 3312.86i | −0.190903 | − | 0.115688i | ||||
\(937\) | 10599.3 | − | 10599.3i | 0.369546 | − | 0.369546i | −0.497766 | − | 0.867311i | \(-0.665846\pi\) |
0.867311 | + | 0.497766i | \(0.165846\pi\) | |||||||
\(938\) | −1302.96 | − | 16213.3i | −0.0453552 | − | 0.564373i | ||||
\(939\) | −2523.42 | + | 6092.07i | −0.0876982 | + | 0.211722i | ||||
\(940\) | 22370.1 | + | 36235.4i | 0.776204 | + | 1.25731i | ||||
\(941\) | −17446.0 | + | 7226.38i | −0.604383 | + | 0.250344i | −0.663825 | − | 0.747888i | \(-0.731068\pi\) |
0.0594418 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(942\) | 1301.87 | − | 4029.38i | 0.0450289 | − | 0.139368i | ||||
\(943\) | 20896.5i | 0.721617i | ||||||||
\(944\) | −1107.64 | + | 15371.7i | −0.0381893 | + | 0.529986i | ||||
\(945\) | − | 14332.7i | − | 0.493378i | ||||||
\(946\) | −5857.54 | − | 1892.54i | −0.201316 | − | 0.0650441i | ||||
\(947\) | −8125.64 | + | 3365.75i | −0.278826 | + | 0.115493i | −0.517714 | − | 0.855554i | \(-0.673217\pi\) |
0.238889 | + | 0.971047i | \(0.423217\pi\) | |||||||
\(948\) | −3353.45 | + | 14174.2i | −0.114889 | + | 0.485609i | ||||
\(949\) | −1690.74 | + | 4081.81i | −0.0578333 | + | 0.139622i | ||||
\(950\) | 100344. | − | 8064.02i | 3.42693 | − | 0.275401i | ||||
\(951\) | 11426.6 | − | 11426.6i | 0.389623 | − | 0.389623i | ||||
\(952\) | −6036.22 | − | 8222.16i | −0.205499 | − | 0.279918i | ||||
\(953\) | 20053.9 | + | 20053.9i | 0.681648 | + | 0.681648i | 0.960371 | − | 0.278723i | \(-0.0899113\pi\) |
−0.278723 | + | 0.960371i | \(0.589911\pi\) | |||||||
\(954\) | −5846.31 | − | 4976.55i | −0.198408 | − | 0.168891i | ||||
\(955\) | 55013.9 | + | 22787.5i | 1.86409 | + | 0.772132i | ||||
\(956\) | −36949.3 | − | 26659.2i | −1.25003 | − | 0.901905i | ||||
\(957\) | 3188.89 | + | 7698.66i | 0.107714 | + | 0.260044i | ||||
\(958\) | −11614.1 | + | 5941.84i | −0.391684 | + | 0.200389i | ||||
\(959\) | 1064.76 | 0.0358529 | ||||||||
\(960\) | −7535.38 | + | 23998.2i | −0.253337 | + | 0.806810i | ||||
\(961\) | −28948.1 | −0.971707 | ||||||||
\(962\) | −10204.9 | + | 5220.90i | −0.342016 | + | 0.174978i | ||||
\(963\) | −11164.7 | − | 26953.9i | −0.373599 | − | 0.901949i | ||||
\(964\) | 38047.5 | + | 27451.6i | 1.27119 | + | 0.917174i | ||||
\(965\) | −24857.6 | − | 10296.3i | −0.829216 | − | 0.343473i | ||||
\(966\) | 4107.83 | + | 3496.70i | 0.136819 | + | 0.116464i | ||||
\(967\) | 17483.6 | + | 17483.6i | 0.581421 | + | 0.581421i | 0.935294 | − | 0.353872i | \(-0.115135\pi\) |
−0.353872 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(968\) | −6941.84 | + | 5096.29i | −0.230495 | + | 0.169216i | ||||
\(969\) | −20838.6 | + | 20838.6i | −0.690849 | + | 0.690849i | ||||
\(970\) | 44575.2 | − | 3582.24i | 1.47549 | − | 0.118576i | ||||
\(971\) | 2567.45 | − | 6198.36i | 0.0848540 | − | 0.204856i | −0.875757 | − | 0.482752i | \(-0.839637\pi\) |
0.960611 | + | 0.277896i | \(0.0896372\pi\) | |||||||
\(972\) | −7199.18 | + | 30429.2i | −0.237566 | + | 1.00413i | ||||
\(973\) | −35.3190 | + | 14.6296i | −0.00116369 | + | 0.000482018i | ||||
\(974\) | 41826.6 | + | 13513.9i | 1.37599 | + | 0.444574i | ||||
\(975\) | 8381.81i | 0.275316i | ||||||||
\(976\) | −28680.0 | + | 24824.6i | −0.940600 | + | 0.814157i | ||||
\(977\) | − | 31111.6i | − | 1.01878i | −0.860536 | − | 0.509390i | \(-0.829871\pi\) | ||
0.860536 | − | 0.509390i | \(-0.170129\pi\) | |||||||
\(978\) | 3382.32 | − | 10468.5i | 0.110588 | − | 0.342276i | ||||
\(979\) | −6595.34 | + | 2731.88i | −0.215309 | + | 0.0891841i | ||||
\(980\) | −24124.2 | − | 39076.8i | −0.786347 | − | 1.27374i | ||||
\(981\) | 4104.66 | − | 9909.52i | 0.133590 | − | 0.322514i | ||||
\(982\) | −4639.95 | − | 57736.8i | −0.150781 | − | 1.87623i | ||||
\(983\) | 17048.2 | − | 17048.2i | 0.553156 | − | 0.553156i | −0.374194 | − | 0.927350i | \(-0.622081\pi\) |
0.927350 | + | 0.374194i | \(0.122081\pi\) | |||||||
\(984\) | −5403.92 | + | 8917.28i | −0.175072 | + | 0.288895i | ||||
\(985\) | 19856.5 | + | 19856.5i | 0.642316 | + | 0.642316i | ||||
\(986\) | −13854.2 | + | 16275.5i | −0.447472 | + | 0.525678i | ||||
\(987\) | 4210.22 | + | 1743.93i | 0.135778 | + | 0.0562410i | ||||
\(988\) | −2768.64 | − | 17114.4i | −0.0891519 | − | 0.551094i | ||||
\(989\) | 3195.58 | + | 7714.81i | 0.102744 | + | 0.248045i | ||||
\(990\) | 15106.6 | + | 29527.6i | 0.484968 | + | 0.947929i | ||||
\(991\) | 32857.3 | 1.05323 | 0.526613 | − | 0.850105i | \(-0.323462\pi\) | ||||
0.526613 | + | 0.850105i | \(0.323462\pi\) | |||||||
\(992\) | −3746.71 | − | 3685.33i | −0.119918 | − | 0.117953i | ||||
\(993\) | −11566.1 | −0.369625 | ||||||||
\(994\) | −7780.06 | − | 15207.1i | −0.248258 | − | 0.485251i | ||||
\(995\) | 12310.3 | + | 29719.7i | 0.392223 | + | 0.946911i | ||||
\(996\) | 20404.3 | − | 3300.85i | 0.649131 | − | 0.105012i | ||||
\(997\) | −30160.2 | − | 12492.8i | −0.958057 | − | 0.396840i | −0.151804 | − | 0.988411i | \(-0.548508\pi\) |
−0.806253 | + | 0.591570i | \(0.798508\pi\) | |||||||
\(998\) | 12709.1 | − | 14930.3i | 0.403106 | − | 0.473558i | ||||
\(999\) | 25221.6 | + | 25221.6i | 0.798775 | + | 0.798775i |
(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 | 32.4.g.a.5.2 | ✓ | 44 | |
4.3 | odd | 2 | 128.4.g.a.113.7 | 44 | |||
8.3 | odd | 2 | 256.4.g.a.225.5 | 44 | |||
8.5 | even | 2 | 256.4.g.b.225.7 | 44 | |||
32.3 | odd | 8 | 256.4.g.a.33.5 | 44 | |||
32.13 | even | 8 | inner | 32.4.g.a.13.2 | yes | 44 | |
32.19 | odd | 8 | 128.4.g.a.17.7 | 44 | |||
32.29 | even | 8 | 256.4.g.b.33.7 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.2 | ✓ | 44 | 1.1 | even | 1 | trivial | |
32.4.g.a.13.2 | yes | 44 | 32.13 | even | 8 | inner | |
128.4.g.a.17.7 | 44 | 32.19 | odd | 8 | |||
128.4.g.a.113.7 | 44 | 4.3 | odd | 2 | |||
256.4.g.a.33.5 | 44 | 32.3 | odd | 8 | |||
256.4.g.a.225.5 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.33.7 | 44 | 32.29 | even | 8 | |||
256.4.g.b.225.7 | 44 | 8.5 | even | 2 |