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 | 21.8 | ||
Character | \(\chi\) | \(=\) | 32.21 |
Dual form | 32.4.g.a.29.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35043 | − | 2.48522i | 0.477449 | − | 0.878659i | ||||
\(3\) | −1.36212 | + | 0.564209i | −0.262140 | + | 0.108582i | −0.509883 | − | 0.860244i | \(-0.670311\pi\) |
0.247743 | + | 0.968826i | \(0.420311\pi\) | |||||||
\(4\) | −4.35267 | − | 6.71224i | −0.544084 | − | 0.839031i | ||||
\(5\) | 6.58151 | − | 15.8892i | 0.588669 | − | 1.42117i | −0.296107 | − | 0.955155i | \(-0.595689\pi\) |
0.884776 | − | 0.466017i | \(-0.154311\pi\) | |||||||
\(6\) | −0.437264 | + | 4.14710i | −0.0297521 | + | 0.282174i | ||||
\(7\) | 14.5517 | + | 14.5517i | 0.785715 | + | 0.785715i | 0.980789 | − | 0.195073i | \(-0.0624945\pi\) |
−0.195073 | + | 0.980789i | \(0.562494\pi\) | |||||||
\(8\) | −22.5594 | + | 1.75295i | −0.996995 | + | 0.0774700i | ||||
\(9\) | −17.5548 | + | 17.5548i | −0.650179 | + | 0.650179i | ||||
\(10\) | −30.6003 | − | 37.8138i | −0.967666 | − | 1.19578i | ||||
\(11\) | 34.4676 | + | 14.2769i | 0.944761 | + | 0.391333i | 0.801259 | − | 0.598317i | \(-0.204164\pi\) |
0.143502 | + | 0.989650i | \(0.454164\pi\) | |||||||
\(12\) | 9.71598 | + | 6.68707i | 0.233730 | + | 0.160866i | ||||
\(13\) | 15.3924 | + | 37.1606i | 0.328391 | + | 0.792807i | 0.998712 | + | 0.0507354i | \(0.0161565\pi\) |
−0.670321 | + | 0.742071i | \(0.733843\pi\) | |||||||
\(14\) | 55.8151 | − | 16.5131i | 1.06552 | − | 0.315237i | ||||
\(15\) | 25.3563i | 0.436465i | ||||||||
\(16\) | −26.1085 | + | 58.4324i | −0.407945 | + | 0.913007i | ||||
\(17\) | − | 103.310i | − | 1.47390i | −0.675946 | − | 0.736951i | \(-0.736265\pi\) | ||
0.675946 | − | 0.736951i | \(-0.263735\pi\) | |||||||
\(18\) | 19.9211 | + | 67.3343i | 0.260858 | + | 0.881714i | ||||
\(19\) | 12.4092 | + | 29.9584i | 0.149835 | + | 0.361733i | 0.980920 | − | 0.194412i | \(-0.0622799\pi\) |
−0.831085 | + | 0.556145i | \(0.812280\pi\) | |||||||
\(20\) | −135.299 | + | 24.9837i | −1.51269 | + | 0.279326i | ||||
\(21\) | −28.0313 | − | 11.6109i | −0.291282 | − | 0.120653i | ||||
\(22\) | 82.0275 | − | 66.3797i | 0.794924 | − | 0.643281i | ||||
\(23\) | −72.3950 | + | 72.3950i | −0.656322 | + | 0.656322i | −0.954508 | − | 0.298186i | \(-0.903619\pi\) |
0.298186 | + | 0.954508i | \(0.403619\pi\) | |||||||
\(24\) | 29.7396 | − | 15.1160i | 0.252941 | − | 0.128564i | ||||
\(25\) | −120.761 | − | 120.761i | −0.966091 | − | 0.966091i | ||||
\(26\) | 113.139 | + | 11.9292i | 0.853397 | + | 0.0899810i | ||||
\(27\) | 29.2409 | − | 70.5937i | 0.208422 | − | 0.503176i | ||||
\(28\) | 34.3357 | − | 161.013i | 0.231744 | − | 1.08673i | ||||
\(29\) | 23.9061 | − | 9.90225i | 0.153078 | − | 0.0634069i | −0.304829 | − | 0.952407i | \(-0.598599\pi\) |
0.457907 | + | 0.889000i | \(0.348599\pi\) | |||||||
\(30\) | 63.0162 | + | 34.2420i | 0.383504 | + | 0.208390i | ||||
\(31\) | −124.769 | −0.722877 | −0.361439 | − | 0.932396i | \(-0.617714\pi\) | ||||
−0.361439 | + | 0.932396i | \(0.617714\pi\) | |||||||
\(32\) | 109.960 | + | 143.794i | 0.607449 | + | 0.794359i | ||||
\(33\) | −55.0042 | −0.290152 | ||||||||
\(34\) | −256.748 | − | 139.513i | −1.29506 | − | 0.703714i | ||||
\(35\) | 326.986 | − | 135.442i | 1.57916 | − | 0.654110i | ||||
\(36\) | 194.243 | + | 41.4219i | 0.899273 | + | 0.191768i | ||||
\(37\) | 18.0425 | − | 43.5584i | 0.0801667 | − | 0.193540i | −0.878714 | − | 0.477348i | \(-0.841598\pi\) |
0.958881 | + | 0.283809i | \(0.0915980\pi\) | |||||||
\(38\) | 91.2111 | + | 9.61717i | 0.389379 | + | 0.0410555i | ||||
\(39\) | −41.9327 | − | 41.9327i | −0.172169 | − | 0.172169i | ||||
\(40\) | −120.622 | + | 369.988i | −0.476801 | + | 1.46250i | ||||
\(41\) | −45.1360 | + | 45.1360i | −0.171928 | + | 0.171928i | −0.787826 | − | 0.615898i | \(-0.788793\pi\) |
0.615898 | + | 0.787826i | \(0.288793\pi\) | |||||||
\(42\) | −66.7101 | + | 53.9842i | −0.245085 | + | 0.198332i | ||||
\(43\) | −457.470 | − | 189.490i | −1.62241 | − | 0.672023i | −0.628057 | − | 0.778168i | \(-0.716149\pi\) |
−0.994351 | + | 0.106144i | \(0.966149\pi\) | |||||||
\(44\) | −54.1959 | − | 293.498i | −0.185689 | − | 1.00560i | ||||
\(45\) | 163.395 | + | 394.469i | 0.541276 | + | 1.30676i | ||||
\(46\) | 82.1534 | + | 277.682i | 0.263323 | + | 0.890044i | ||||
\(47\) | 582.766i | 1.80862i | 0.426877 | + | 0.904310i | \(0.359614\pi\) | ||||
−0.426877 | + | 0.904310i | \(0.640386\pi\) | |||||||
\(48\) | 2.59478 | − | 94.3227i | 0.00780260 | − | 0.283631i | ||||
\(49\) | 80.5012i | 0.234697i | ||||||||
\(50\) | −463.199 | + | 137.039i | −1.31012 | + | 0.387605i | ||||
\(51\) | 58.2884 | + | 140.721i | 0.160039 | + | 0.386369i | ||||
\(52\) | 182.433 | − | 265.066i | 0.486517 | − | 0.706884i | ||||
\(53\) | 395.810 | + | 163.950i | 1.02582 | + | 0.424910i | 0.831203 | − | 0.555969i | \(-0.187653\pi\) |
0.194620 | + | 0.980879i | \(0.437653\pi\) | |||||||
\(54\) | −135.953 | − | 168.002i | −0.342609 | − | 0.423374i | ||||
\(55\) | 453.698 | − | 453.698i | 1.11230 | − | 1.11230i | ||||
\(56\) | −353.785 | − | 302.768i | −0.844223 | − | 0.722485i | ||||
\(57\) | −33.8056 | − | 33.8056i | −0.0785555 | − | 0.0785555i | ||||
\(58\) | 7.67429 | − | 72.7844i | 0.0173738 | − | 0.164777i | ||||
\(59\) | 142.805 | − | 344.762i | 0.315113 | − | 0.760750i | −0.684387 | − | 0.729119i | \(-0.739930\pi\) |
0.999500 | − | 0.0316306i | \(-0.0100700\pi\) | |||||||
\(60\) | 170.198 | − | 110.368i | 0.366208 | − | 0.237474i | ||||
\(61\) | −34.8958 | + | 14.4543i | −0.0732450 | + | 0.0303391i | −0.419005 | − | 0.907984i | \(-0.637621\pi\) |
0.345760 | + | 0.938323i | \(0.387621\pi\) | |||||||
\(62\) | −168.492 | + | 310.079i | −0.345137 | + | 0.635163i | ||||
\(63\) | −510.904 | −1.02171 | ||||||||
\(64\) | 505.854 | − | 79.0909i | 0.987997 | − | 0.154474i | ||||
\(65\) | 691.757 | 1.32003 | ||||||||
\(66\) | −74.2794 | + | 136.698i | −0.138533 | + | 0.254944i | ||||
\(67\) | 196.686 | − | 81.4699i | 0.358642 | − | 0.148554i | −0.196085 | − | 0.980587i | \(-0.562823\pi\) |
0.554727 | + | 0.832033i | \(0.312823\pi\) | |||||||
\(68\) | −693.442 | + | 449.674i | −1.23665 | + | 0.801927i | ||||
\(69\) | 57.7649 | − | 139.457i | 0.100784 | − | 0.243313i | ||||
\(70\) | 104.968 | − | 995.538i | 0.179230 | − | 1.69985i | ||||
\(71\) | −520.831 | − | 520.831i | −0.870582 | − | 0.870582i | 0.121954 | − | 0.992536i | \(-0.461084\pi\) |
−0.992536 | + | 0.121954i | \(0.961084\pi\) | |||||||
\(72\) | 365.254 | − | 426.800i | 0.597856 | − | 0.698595i | ||||
\(73\) | −582.329 | + | 582.329i | −0.933649 | + | 0.933649i | −0.997932 | − | 0.0642823i | \(-0.979524\pi\) |
0.0642823 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(74\) | −83.8873 | − | 103.662i | −0.131780 | − | 0.162845i | ||||
\(75\) | 232.626 | + | 96.3570i | 0.358152 | + | 0.148351i | ||||
\(76\) | 147.075 | − | 213.693i | 0.221982 | − | 0.322529i | ||||
\(77\) | 293.807 | + | 709.314i | 0.434837 | + | 1.04979i | ||||
\(78\) | −160.839 | + | 47.5849i | −0.233480 | + | 0.0690760i | ||||
\(79\) | − | 157.779i | − | 0.224702i | −0.993669 | − | 0.112351i | \(-0.964162\pi\) | ||
0.993669 | − | 0.112351i | \(-0.0358381\pi\) | |||||||
\(80\) | 756.610 | + | 799.416i | 1.05739 | + | 1.11722i | ||||
\(81\) | − | 557.655i | − | 0.764959i | ||||||
\(82\) | 51.2200 | + | 173.126i | 0.0689792 | + | 0.233153i | ||||
\(83\) | 54.5324 | + | 131.653i | 0.0721170 | + | 0.174106i | 0.955828 | − | 0.293928i | \(-0.0949626\pi\) |
−0.883711 | + | 0.468034i | \(0.844963\pi\) | |||||||
\(84\) | 44.0756 | + | 238.691i | 0.0572505 | + | 0.310040i | ||||
\(85\) | −1641.51 | − | 679.936i | −2.09467 | − | 0.867640i | ||||
\(86\) | −1088.71 | + | 881.022i | −1.36510 | + | 1.10469i | ||||
\(87\) | −26.9761 | + | 26.9761i | −0.0332430 | + | 0.0332430i | ||||
\(88\) | −802.596 | − | 261.660i | −0.972238 | − | 0.316966i | ||||
\(89\) | −272.884 | − | 272.884i | −0.325007 | − | 0.325007i | 0.525677 | − | 0.850684i | \(-0.323812\pi\) |
−0.850684 | + | 0.525677i | \(0.823812\pi\) | |||||||
\(90\) | 1201.00 | + | 126.632i | 1.40663 | + | 0.148313i | ||||
\(91\) | −316.763 | + | 764.733i | −0.364898 | + | 0.880943i | ||||
\(92\) | 801.045 | + | 170.821i | 0.907769 | + | 0.193580i | ||||
\(93\) | 169.951 | − | 70.3959i | 0.189495 | − | 0.0784915i | ||||
\(94\) | 1448.30 | + | 786.985i | 1.58916 | + | 0.863524i | ||||
\(95\) | 557.686 | 0.602288 | ||||||||
\(96\) | −230.909 | − | 133.825i | −0.245490 | − | 0.142275i | ||||
\(97\) | 788.873 | 0.825752 | 0.412876 | − | 0.910787i | \(-0.364524\pi\) | ||||
0.412876 | + | 0.910787i | \(0.364524\pi\) | |||||||
\(98\) | 200.063 | + | 108.711i | 0.206219 | + | 0.112056i | ||||
\(99\) | −855.703 | + | 354.444i | −0.868701 | + | 0.359828i | ||||
\(100\) | −284.945 | + | 1336.22i | −0.284945 | + | 1.33622i | ||||
\(101\) | 585.257 | − | 1412.93i | 0.576586 | − | 1.39200i | −0.319272 | − | 0.947663i | \(-0.603438\pi\) |
0.895858 | − | 0.444339i | \(-0.146562\pi\) | |||||||
\(102\) | 428.437 | + | 45.1738i | 0.415898 | + | 0.0438517i | ||||
\(103\) | 1120.20 | + | 1120.20i | 1.07161 | + | 1.07161i | 0.997230 | + | 0.0743853i | \(0.0236995\pi\) |
0.0743853 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(104\) | −412.384 | − | 811.339i | −0.388823 | − | 0.764984i | ||||
\(105\) | −368.977 | + | 368.977i | −0.342937 | + | 0.342937i | ||||
\(106\) | 941.965 | − | 762.273i | 0.863130 | − | 0.698476i | ||||
\(107\) | −1665.63 | − | 689.926i | −1.50488 | − | 0.623343i | −0.530388 | − | 0.847755i | \(-0.677954\pi\) |
−0.974494 | + | 0.224413i | \(0.927954\pi\) | |||||||
\(108\) | −601.118 | + | 110.999i | −0.535580 | + | 0.0988975i | ||||
\(109\) | −342.786 | − | 827.559i | −0.301220 | − | 0.727209i | −0.999930 | − | 0.0118047i | \(-0.996242\pi\) |
0.698710 | − | 0.715405i | \(-0.253758\pi\) | |||||||
\(110\) | −514.853 | − | 1740.23i | −0.446267 | − | 1.50840i | ||||
\(111\) | 69.5116i | 0.0594392i | ||||||||
\(112\) | −1230.21 | + | 470.367i | −1.03789 | + | 0.396835i | ||||
\(113\) | 924.353i | 0.769521i | 0.923016 | + | 0.384760i | \(0.125716\pi\) | ||||
−0.923016 | + | 0.384760i | \(0.874284\pi\) | |||||||
\(114\) | −129.667 | + | 38.3624i | −0.106530 | + | 0.0315172i | ||||
\(115\) | 673.829 | + | 1626.77i | 0.546390 | + | 1.31910i | ||||
\(116\) | −170.522 | − | 117.363i | −0.136488 | − | 0.0939383i | ||||
\(117\) | −922.559 | − | 382.137i | −0.728980 | − | 0.301953i | ||||
\(118\) | −663.963 | − | 820.481i | −0.517989 | − | 0.640096i | ||||
\(119\) | 1503.33 | − | 1503.33i | 1.15807 | − | 1.15807i | ||||
\(120\) | −44.4483 | − | 572.024i | −0.0338130 | − | 0.435154i | ||||
\(121\) | 43.0249 | + | 43.0249i | 0.0323253 | + | 0.0323253i | ||||
\(122\) | −11.2021 | + | 106.243i | −0.00831307 | + | 0.0788427i | ||||
\(123\) | 36.0145 | − | 86.9467i | 0.0264010 | − | 0.0637376i | ||||
\(124\) | 543.079 | + | 837.481i | 0.393306 | + | 0.606516i | ||||
\(125\) | −727.445 | + | 301.318i | −0.520517 | + | 0.215605i | ||||
\(126\) | −689.940 | + | 1269.71i | −0.487816 | + | 0.897737i | ||||
\(127\) | 569.829 | 0.398143 | 0.199072 | − | 0.979985i | \(-0.436207\pi\) | ||||
0.199072 | + | 0.979985i | \(0.436207\pi\) | |||||||
\(128\) | 486.563 | − | 1363.97i | 0.335988 | − | 0.941866i | ||||
\(129\) | 730.042 | 0.498268 | ||||||||
\(130\) | 934.169 | − | 1719.17i | 0.630247 | − | 1.15986i | ||||
\(131\) | 1171.87 | − | 485.406i | 0.781581 | − | 0.323742i | 0.0440278 | − | 0.999030i | \(-0.485981\pi\) |
0.737553 | + | 0.675289i | \(0.235981\pi\) | |||||||
\(132\) | 239.415 | + | 369.202i | 0.157867 | + | 0.243446i | ||||
\(133\) | −255.370 | + | 616.518i | −0.166492 | + | 0.401947i | ||||
\(134\) | 63.1396 | − | 598.828i | 0.0407047 | − | 0.386051i | ||||
\(135\) | −929.227 | − | 929.227i | −0.592408 | − | 0.592408i | ||||
\(136\) | 181.097 | + | 2330.61i | 0.114183 | + | 1.46947i | ||||
\(137\) | 946.041 | − | 946.041i | 0.589969 | − | 0.589969i | −0.347654 | − | 0.937623i | \(-0.613022\pi\) |
0.937623 | + | 0.347654i | \(0.113022\pi\) | |||||||
\(138\) | −268.574 | − | 331.885i | −0.165670 | − | 0.204724i | ||||
\(139\) | 1313.93 | + | 544.249i | 0.801772 | + | 0.332105i | 0.745666 | − | 0.666320i | \(-0.232131\pi\) |
0.0561063 | + | 0.998425i | \(0.482131\pi\) | |||||||
\(140\) | −2332.38 | − | 1605.27i | −1.40802 | − | 0.969074i | ||||
\(141\) | −328.802 | − | 793.797i | −0.196384 | − | 0.474112i | ||||
\(142\) | −1997.73 | + | 591.036i | −1.18060 | + | 0.349286i | ||||
\(143\) | 1500.59i | 0.877523i | ||||||||
\(144\) | −567.442 | − | 1484.10i | −0.328381 | − | 0.858855i | ||||
\(145\) | − | 445.021i | − | 0.254876i | ||||||
\(146\) | 660.822 | + | 2233.61i | 0.374589 | + | 1.26613i | ||||
\(147\) | −45.4195 | − | 109.652i | −0.0254839 | − | 0.0615236i | ||||
\(148\) | −370.908 | + | 68.4900i | −0.206003 | + | 0.0380395i | ||||
\(149\) | 2438.15 | + | 1009.92i | 1.34054 | + | 0.555272i | 0.933644 | − | 0.358201i | \(-0.116610\pi\) |
0.406900 | + | 0.913473i | \(0.366610\pi\) | |||||||
\(150\) | 553.614 | − | 448.005i | 0.301349 | − | 0.243863i | ||||
\(151\) | −872.975 | + | 872.975i | −0.470475 | + | 0.470475i | −0.902068 | − | 0.431594i | \(-0.857951\pi\) |
0.431594 | + | 0.902068i | \(0.357951\pi\) | |||||||
\(152\) | −332.459 | − | 654.091i | −0.177408 | − | 0.349038i | ||||
\(153\) | 1813.59 | + | 1813.59i | 0.958301 | + | 0.958301i | ||||
\(154\) | 2159.57 | + | 227.702i | 1.13002 | + | 0.119148i | ||||
\(155\) | −821.170 | + | 1982.48i | −0.425535 | + | 1.02733i | ||||
\(156\) | −98.9431 | + | 463.982i | −0.0507807 | + | 0.238130i | ||||
\(157\) | −866.489 | + | 358.912i | −0.440467 | + | 0.182447i | −0.591885 | − | 0.806022i | \(-0.701616\pi\) |
0.151418 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(158\) | −392.115 | − | 213.069i | −0.197437 | − | 0.107284i | ||||
\(159\) | −631.643 | −0.315047 | ||||||||
\(160\) | 3008.48 | − | 800.790i | 1.48651 | − | 0.395675i | ||||
\(161\) | −2106.94 | −1.03136 | ||||||||
\(162\) | −1385.90 | − | 753.074i | −0.672138 | − | 0.365229i | ||||
\(163\) | −745.455 | + | 308.777i | −0.358212 | + | 0.148376i | −0.554529 | − | 0.832164i | \(-0.687102\pi\) |
0.196318 | + | 0.980540i | \(0.437102\pi\) | |||||||
\(164\) | 499.426 | + | 106.501i | 0.237796 | + | 0.0507096i | ||||
\(165\) | −362.011 | + | 873.972i | −0.170803 | + | 0.412355i | ||||
\(166\) | 400.829 | + | 42.2629i | 0.187412 | + | 0.0197605i | ||||
\(167\) | −741.751 | − | 741.751i | −0.343703 | − | 0.343703i | 0.514055 | − | 0.857758i | \(-0.328143\pi\) |
−0.857758 | + | 0.514055i | \(0.828143\pi\) | |||||||
\(168\) | 652.723 | + | 212.799i | 0.299754 | + | 0.0977248i | ||||
\(169\) | 409.532 | − | 409.532i | 0.186405 | − | 0.186405i | ||||
\(170\) | −3906.54 | + | 3161.31i | −1.76246 | + | 1.42625i | ||||
\(171\) | −743.756 | − | 308.074i | −0.332611 | − | 0.137772i | ||||
\(172\) | 719.313 | + | 3895.44i | 0.318878 | + | 1.72689i | ||||
\(173\) | −34.3941 | − | 83.0347i | −0.0151152 | − | 0.0364914i | 0.916142 | − | 0.400854i | \(-0.131287\pi\) |
−0.931257 | + | 0.364363i | \(0.881287\pi\) | |||||||
\(174\) | 30.6123 | + | 103.471i | 0.0133374 | + | 0.0450812i | ||||
\(175\) | − | 3514.56i | − | 1.51815i | ||||||
\(176\) | −1734.13 | + | 1641.28i | −0.742700 | + | 0.702931i | ||||
\(177\) | 550.180i | 0.233639i | ||||||||
\(178\) | −1046.69 | + | 309.666i | −0.440744 | + | 0.130396i | ||||
\(179\) | −1402.83 | − | 3386.73i | −0.585768 | − | 1.41417i | −0.887514 | − | 0.460781i | \(-0.847570\pi\) |
0.301746 | − | 0.953388i | \(-0.402430\pi\) | |||||||
\(180\) | 1936.57 | − | 2813.74i | 0.801909 | − | 1.16513i | ||||
\(181\) | 504.860 | + | 209.120i | 0.207326 | + | 0.0858771i | 0.483930 | − | 0.875107i | \(-0.339209\pi\) |
−0.276604 | + | 0.960984i | \(0.589209\pi\) | |||||||
\(182\) | 1472.77 | + | 1819.94i | 0.599828 | + | 0.741227i | ||||
\(183\) | 39.3770 | − | 39.3770i | 0.0159062 | − | 0.0159062i | ||||
\(184\) | 1506.29 | − | 1760.09i | 0.603504 | − | 0.705195i | ||||
\(185\) | −573.361 | − | 573.361i | −0.227861 | − | 0.227861i | ||||
\(186\) | 54.5571 | − | 517.430i | 0.0215071 | − | 0.203977i | ||||
\(187\) | 1474.95 | − | 3560.85i | 0.576786 | − | 1.39249i | ||||
\(188\) | 3911.67 | − | 2536.59i | 1.51749 | − | 0.984041i | ||||
\(189\) | 1452.76 | − | 601.752i | 0.559114 | − | 0.231593i | ||||
\(190\) | 753.116 | − | 1385.97i | 0.287562 | − | 0.529206i | ||||
\(191\) | −17.6918 | −0.00670226 | −0.00335113 | − | 0.999994i | \(-0.501067\pi\) | ||||
−0.00335113 | + | 0.999994i | \(0.501067\pi\) | |||||||
\(192\) | −644.411 | + | 393.139i | −0.242221 | + | 0.147773i | ||||
\(193\) | −3321.63 | −1.23884 | −0.619420 | − | 0.785059i | \(-0.712632\pi\) | ||||
−0.619420 | + | 0.785059i | \(0.712632\pi\) | |||||||
\(194\) | 1065.32 | − | 1960.53i | 0.394255 | − | 0.725555i | ||||
\(195\) | −942.256 | + | 390.295i | −0.346033 | + | 0.143331i | ||||
\(196\) | 540.344 | − | 350.395i | 0.196918 | − | 0.127695i | ||||
\(197\) | −310.402 | + | 749.376i | −0.112260 | + | 0.271020i | −0.970018 | − | 0.243035i | \(-0.921857\pi\) |
0.857758 | + | 0.514054i | \(0.171857\pi\) | |||||||
\(198\) | −274.695 | + | 2605.26i | −0.0985947 | + | 0.935091i | ||||
\(199\) | 1908.35 | + | 1908.35i | 0.679795 | + | 0.679795i | 0.959954 | − | 0.280158i | \(-0.0903870\pi\) |
−0.280158 | + | 0.959954i | \(0.590387\pi\) | |||||||
\(200\) | 2935.99 | + | 2512.62i | 1.03803 | + | 0.888345i | ||||
\(201\) | −221.944 | + | 221.944i | −0.0778841 | + | 0.0778841i | ||||
\(202\) | −2721.11 | − | 3362.56i | −0.947805 | − | 1.17123i | ||||
\(203\) | 491.968 | + | 203.780i | 0.170095 | + | 0.0704559i | ||||
\(204\) | 690.841 | − | 1003.76i | 0.237101 | − | 0.344495i | ||||
\(205\) | 420.110 | + | 1014.24i | 0.143131 | + | 0.345548i | ||||
\(206\) | 4296.69 | − | 1271.19i | 1.45323 | − | 0.429943i | ||||
\(207\) | − | 2541.77i | − | 0.853454i | ||||||
\(208\) | −2573.25 | − | 70.7893i | −0.857803 | − | 0.0235979i | ||||
\(209\) | 1209.76i | 0.400387i | ||||||||
\(210\) | 418.712 | + | 1415.27i | 0.137590 | + | 0.465060i | ||||
\(211\) | −969.860 | − | 2341.45i | −0.316435 | − | 0.763943i | −0.999438 | − | 0.0335266i | \(-0.989326\pi\) |
0.683002 | − | 0.730416i | \(-0.260674\pi\) | |||||||
\(212\) | −622.360 | − | 3370.39i | −0.201622 | − | 1.09188i | ||||
\(213\) | 1003.29 | + | 415.578i | 0.322744 | + | 0.133685i | ||||
\(214\) | −3963.94 | + | 3207.76i | −1.26621 | + | 1.02466i | ||||
\(215\) | −6021.69 | + | 6021.69i | −1.91012 | + | 1.91012i | ||||
\(216\) | −535.910 | + | 1643.81i | −0.168815 | + | 0.517811i | ||||
\(217\) | −1815.60 | − | 1815.60i | −0.567976 | − | 0.567976i | ||||
\(218\) | −2519.58 | − | 265.661i | −0.782787 | − | 0.0825359i | ||||
\(219\) | 464.647 | − | 1121.76i | 0.143370 | − | 0.346125i | ||||
\(220\) | −5020.13 | − | 1070.53i | −1.53844 | − | 0.328070i | ||||
\(221\) | 3839.06 | − | 1590.19i | 1.16852 | − | 0.484017i | ||||
\(222\) | 172.752 | + | 93.8706i | 0.0522268 | + | 0.0283792i | ||||
\(223\) | −267.474 | −0.0803200 | −0.0401600 | − | 0.999193i | \(-0.512787\pi\) | ||||
−0.0401600 | + | 0.999193i | \(0.512787\pi\) | |||||||
\(224\) | −492.345 | + | 3692.54i | −0.146858 | + | 1.10142i | ||||
\(225\) | 4239.89 | 1.25627 | ||||||||
\(226\) | 2297.23 | + | 1248.28i | 0.676147 | + | 0.367407i | ||||
\(227\) | −721.748 | + | 298.958i | −0.211031 | + | 0.0874120i | −0.485695 | − | 0.874128i | \(-0.661433\pi\) |
0.274664 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(228\) | −79.7667 | + | 374.056i | −0.0231696 | + | 0.108651i | ||||
\(229\) | −1403.35 | + | 3387.98i | −0.404960 | + | 0.977660i | 0.581484 | + | 0.813558i | \(0.302472\pi\) |
−0.986443 | + | 0.164101i | \(0.947528\pi\) | |||||||
\(230\) | 4952.84 | + | 522.220i | 1.41992 | + | 0.149714i | ||||
\(231\) | −800.402 | − | 800.402i | −0.227977 | − | 0.227977i | ||||
\(232\) | −521.950 | + | 265.295i | −0.147706 | + | 0.0750753i | ||||
\(233\) | 95.4522 | − | 95.4522i | 0.0268381 | − | 0.0268381i | −0.693560 | − | 0.720399i | \(-0.743959\pi\) |
0.720399 | + | 0.693560i | \(0.243959\pi\) | |||||||
\(234\) | −2195.55 | + | 1776.72i | −0.613365 | + | 0.496358i | ||||
\(235\) | 9259.67 | + | 3835.48i | 2.57036 | + | 1.06468i | ||||
\(236\) | −2935.71 | + | 542.094i | −0.809740 | + | 0.149523i | ||||
\(237\) | 89.0201 | + | 214.913i | 0.0243986 | + | 0.0589035i | ||||
\(238\) | −1705.97 | − | 5766.26i | −0.464628 | − | 1.57047i | ||||
\(239\) | 2210.32i | 0.598216i | 0.954219 | + | 0.299108i | \(0.0966890\pi\) | ||||
−0.954219 | + | 0.299108i | \(0.903311\pi\) | |||||||
\(240\) | −1481.63 | − | 662.015i | −0.398496 | − | 0.178054i | ||||
\(241\) | − | 3029.15i | − | 0.809645i | −0.914395 | − | 0.404823i | \(-0.867333\pi\) | ||
0.914395 | − | 0.404823i | \(-0.132667\pi\) | |||||||
\(242\) | 165.029 | − | 48.8244i | 0.0438366 | − | 0.0129692i | ||||
\(243\) | 1104.14 | + | 2665.62i | 0.291483 | + | 0.703703i | ||||
\(244\) | 248.911 | + | 171.314i | 0.0653068 | + | 0.0449478i | ||||
\(245\) | 1279.10 | + | 529.820i | 0.333545 | + | 0.138159i | ||||
\(246\) | −167.447 | − | 206.920i | −0.0433985 | − | 0.0536289i | ||||
\(247\) | −922.264 | + | 922.264i | −0.237580 | + | 0.237580i | ||||
\(248\) | 2814.72 | − | 218.714i | 0.720705 | − | 0.0560013i | ||||
\(249\) | −148.560 | − | 148.560i | −0.0378095 | − | 0.0378095i | ||||
\(250\) | −233.522 | + | 2214.77i | −0.0590770 | + | 0.560298i | ||||
\(251\) | −134.300 | + | 324.230i | −0.0337727 | + | 0.0815346i | −0.939866 | − | 0.341543i | \(-0.889050\pi\) |
0.906093 | + | 0.423078i | \(0.139050\pi\) | |||||||
\(252\) | 2223.80 | + | 3429.31i | 0.555897 | + | 0.857247i | ||||
\(253\) | −3528.86 | + | 1461.70i | −0.876908 | + | 0.363227i | ||||
\(254\) | 769.515 | − | 1416.15i | 0.190093 | − | 0.349832i | ||||
\(255\) | 2619.56 | 0.643307 | ||||||||
\(256\) | −2732.70 | − | 3051.16i | −0.667162 | − | 0.744912i | ||||
\(257\) | −7459.69 | −1.81059 | −0.905297 | − | 0.424779i | \(-0.860352\pi\) | ||||
−0.905297 | + | 0.424779i | \(0.860352\pi\) | |||||||
\(258\) | 985.871 | − | 1814.32i | 0.237898 | − | 0.437808i | ||||
\(259\) | 896.396 | − | 371.299i | 0.215055 | − | 0.0890788i | ||||
\(260\) | −3010.99 | − | 4643.24i | −0.718207 | − | 1.10754i | ||||
\(261\) | −245.836 | + | 593.501i | −0.0583022 | + | 0.140754i | ||||
\(262\) | 376.192 | − | 3567.88i | 0.0887070 | − | 0.841314i | ||||
\(263\) | 4192.29 | + | 4192.29i | 0.982919 | + | 0.982919i | 0.999857 | − | 0.0169374i | \(-0.00539160\pi\) |
−0.0169374 | + | 0.999857i | \(0.505392\pi\) | |||||||
\(264\) | 1240.86 | − | 96.4195i | 0.289280 | − | 0.0224781i | ||||
\(265\) | 5210.05 | − | 5210.05i | 1.20774 | − | 1.20774i | ||||
\(266\) | 1187.33 | + | 1467.22i | 0.273683 | + | 0.338199i | ||||
\(267\) | 525.664 | + | 217.737i | 0.120487 | + | 0.0499075i | ||||
\(268\) | −1402.96 | − | 965.591i | −0.319773 | − | 0.220085i | ||||
\(269\) | −1275.44 | − | 3079.18i | −0.289088 | − | 0.697921i | 0.710897 | − | 0.703296i | \(-0.248289\pi\) |
−0.999986 | + | 0.00537488i | \(0.998289\pi\) | |||||||
\(270\) | −3564.19 | + | 1054.48i | −0.803370 | + | 0.237680i | ||||
\(271\) | 1188.89i | 0.266494i | 0.991083 | + | 0.133247i | \(0.0425404\pi\) | ||||
−0.991083 | + | 0.133247i | \(0.957460\pi\) | |||||||
\(272\) | 6036.65 | + | 2697.26i | 1.34568 | + | 0.601271i | ||||
\(273\) | − | 1220.38i | − | 0.270552i | ||||||
\(274\) | −1073.56 | − | 3628.69i | −0.236701 | − | 0.800062i | ||||
\(275\) | −2438.25 | − | 5886.46i | −0.534662 | − | 1.29079i | ||||
\(276\) | −1187.50 | + | 219.278i | −0.258982 | + | 0.0478224i | ||||
\(277\) | 3832.51 | + | 1587.48i | 0.831310 | + | 0.344340i | 0.757421 | − | 0.652926i | \(-0.226459\pi\) |
0.0738890 | + | 0.997266i | \(0.476459\pi\) | |||||||
\(278\) | 3126.96 | − | 2530.45i | 0.674613 | − | 0.545921i | ||||
\(279\) | 2190.30 | − | 2190.30i | 0.470000 | − | 0.470000i | ||||
\(280\) | −7139.18 | + | 3628.68i | −1.52374 | + | 0.774482i | ||||
\(281\) | 230.048 | + | 230.048i | 0.0488382 | + | 0.0488382i | 0.731104 | − | 0.682266i | \(-0.239005\pi\) |
−0.682266 | + | 0.731104i | \(0.739005\pi\) | |||||||
\(282\) | −2416.79 | − | 254.823i | −0.510346 | − | 0.0538102i | ||||
\(283\) | −405.744 | + | 979.554i | −0.0852261 | + | 0.205754i | −0.960747 | − | 0.277426i | \(-0.910519\pi\) |
0.875521 | + | 0.483181i | \(0.160519\pi\) | |||||||
\(284\) | −1228.94 | + | 5762.96i | −0.256775 | + | 1.20411i | ||||
\(285\) | −759.635 | + | 314.651i | −0.157884 | + | 0.0653977i | ||||
\(286\) | 3729.31 | + | 2026.45i | 0.771044 | + | 0.418973i | ||||
\(287\) | −1313.61 | −0.270173 | ||||||||
\(288\) | −4454.62 | − | 593.956i | −0.911426 | − | 0.121525i | ||||
\(289\) | −5759.94 | −1.17239 | ||||||||
\(290\) | −1105.98 | − | 600.970i | −0.223949 | − | 0.121690i | ||||
\(291\) | −1074.54 | + | 445.089i | −0.216463 | + | 0.0896619i | ||||
\(292\) | 6443.42 | + | 1374.05i | 1.29134 | + | 0.275377i | ||||
\(293\) | −614.388 | + | 1483.26i | −0.122501 | + | 0.295744i | −0.973220 | − | 0.229878i | \(-0.926167\pi\) |
0.850718 | + | 0.525622i | \(0.176167\pi\) | |||||||
\(294\) | −333.847 | − | 35.2003i | −0.0662256 | − | 0.00698273i | ||||
\(295\) | −4538.12 | − | 4538.12i | −0.895659 | − | 0.895659i | ||||
\(296\) | −330.673 | + | 1014.28i | −0.0649323 | + | 0.199168i | ||||
\(297\) | 2015.72 | − | 2015.72i | 0.393819 | − | 0.393819i | ||||
\(298\) | 5802.42 | − | 4695.53i | 1.12794 | − | 0.912768i | ||||
\(299\) | −3804.58 | − | 1575.91i | −0.735867 | − | 0.304806i | ||||
\(300\) | −365.775 | − | 1980.86i | −0.0703934 | − | 0.381216i | ||||
\(301\) | −3899.55 | − | 9414.34i | −0.746732 | − | 1.80277i | ||||
\(302\) | 990.646 | + | 3348.43i | 0.188759 | + | 0.638015i | ||||
\(303\) | 2254.80i | 0.427507i | ||||||||
\(304\) | −2074.53 | − | 57.0695i | −0.391389 | − | 0.0107670i | ||||
\(305\) | 649.596i | 0.121953i | ||||||||
\(306\) | 6956.30 | − | 2058.05i | 1.29956 | − | 0.384480i | ||||
\(307\) | 2158.05 | + | 5210.00i | 0.401194 | + | 0.968569i | 0.987377 | + | 0.158390i | \(0.0506302\pi\) |
−0.586182 | + | 0.810179i | \(0.699370\pi\) | |||||||
\(308\) | 3482.24 | − | 5059.52i | 0.644218 | − | 0.936016i | ||||
\(309\) | −2157.87 | − | 893.819i | −0.397272 | − | 0.164555i | ||||
\(310\) | 3817.97 | + | 4717.99i | 0.699504 | + | 0.864400i | ||||
\(311\) | 182.317 | − | 182.317i | 0.0332420 | − | 0.0332420i | −0.690290 | − | 0.723532i | \(-0.742517\pi\) |
0.723532 | + | 0.690290i | \(0.242517\pi\) | |||||||
\(312\) | 1019.48 | + | 872.471i | 0.184990 | + | 0.158314i | ||||
\(313\) | 3731.88 | + | 3731.88i | 0.673924 | + | 0.673924i | 0.958618 | − | 0.284694i | \(-0.0918921\pi\) |
−0.284694 | + | 0.958618i | \(0.591892\pi\) | |||||||
\(314\) | −278.158 | + | 2638.10i | −0.0499916 | + | 0.474130i | ||||
\(315\) | −3362.52 | + | 8117.84i | −0.601450 | + | 1.45203i | ||||
\(316\) | −1059.05 | + | 686.758i | −0.188532 | + | 0.122257i | ||||
\(317\) | 2940.58 | − | 1218.03i | 0.521007 | − | 0.215808i | −0.106652 | − | 0.994296i | \(-0.534013\pi\) |
0.627659 | + | 0.778488i | \(0.284013\pi\) | |||||||
\(318\) | −852.990 | + | 1569.77i | −0.150419 | + | 0.276819i | ||||
\(319\) | 965.361 | 0.169435 | ||||||||
\(320\) | 2072.60 | − | 8558.15i | 0.362068 | − | 1.49505i | ||||
\(321\) | 2658.05 | 0.462174 | ||||||||
\(322\) | −2845.27 | + | 5236.21i | −0.492425 | + | 0.906218i | ||||
\(323\) | 3095.00 | − | 1281.99i | 0.533159 | − | 0.220842i | ||||
\(324\) | −3743.12 | + | 2427.29i | −0.641824 | + | 0.416202i | ||||
\(325\) | 2628.75 | − | 6346.37i | 0.448668 | − | 1.08318i | ||||
\(326\) | −239.304 | + | 2269.60i | −0.0406559 | + | 0.385588i | ||||
\(327\) | 933.833 | + | 933.833i | 0.157924 | + | 0.157924i | ||||
\(328\) | 939.120 | − | 1097.36i | 0.158092 | − | 0.184731i | ||||
\(329\) | −8480.20 | + | 8480.20i | −1.42106 | + | 1.42106i | ||||
\(330\) | 1683.15 | + | 2079.92i | 0.280770 | + | 0.346957i | ||||
\(331\) | −5918.75 | − | 2451.63i | −0.982852 | − | 0.407111i | −0.167371 | − | 0.985894i | \(-0.553528\pi\) |
−0.815481 | + | 0.578783i | \(0.803528\pi\) | |||||||
\(332\) | 646.325 | − | 939.077i | 0.106842 | − | 0.155237i | ||||
\(333\) | 447.928 | + | 1081.39i | 0.0737127 | + | 0.177958i | ||||
\(334\) | −2845.10 | + | 841.734i | −0.466099 | + | 0.137897i | ||||
\(335\) | − | 3661.37i | − | 0.597141i | ||||||
\(336\) | 1410.31 | − | 1334.79i | 0.228984 | − | 0.216723i | ||||
\(337\) | 11283.3i | 1.82385i | 0.410355 | + | 0.911926i | \(0.365405\pi\) | ||||
−0.410355 | + | 0.911926i | \(0.634595\pi\) | |||||||
\(338\) | −464.734 | − | 1570.82i | −0.0747875 | − | 0.252785i | ||||
\(339\) | −521.529 | − | 1259.08i | −0.0835562 | − | 0.201722i | ||||
\(340\) | 2581.06 | + | 13977.8i | 0.411699 | + | 2.22956i | ||||
\(341\) | −4300.49 | − | 1781.32i | −0.682946 | − | 0.282886i | ||||
\(342\) | −1770.02 | + | 1432.37i | −0.279859 | + | 0.226472i | ||||
\(343\) | 3819.79 | − | 3819.79i | 0.601310 | − | 0.601310i | ||||
\(344\) | 10652.4 | + | 3472.87i | 1.66959 | + | 0.544316i | ||||
\(345\) | −1835.67 | − | 1835.67i | −0.286462 | − | 0.286462i | ||||
\(346\) | −252.807 | − | 26.6556i | −0.0392802 | − | 0.00414165i | ||||
\(347\) | 4803.69 | − | 11597.1i | 0.743157 | − | 1.79414i | 0.150630 | − | 0.988590i | \(-0.451870\pi\) |
0.592527 | − | 0.805550i | \(-0.298130\pi\) | |||||||
\(348\) | 298.489 | + | 63.6521i | 0.0459789 | + | 0.00980491i | ||||
\(349\) | −5191.29 | + | 2150.30i | −0.796228 | + | 0.329808i | −0.743445 | − | 0.668798i | \(-0.766809\pi\) |
−0.0527834 | + | 0.998606i | \(0.516809\pi\) | |||||||
\(350\) | −8734.46 | − | 4746.16i | −1.33393 | − | 0.724838i | ||||
\(351\) | 3073.39 | 0.467366 | ||||||||
\(352\) | 1737.11 | + | 6526.14i | 0.263035 | + | 0.988194i | ||||
\(353\) | 9949.61 | 1.50018 | 0.750091 | − | 0.661335i | \(-0.230010\pi\) | ||||
0.750091 | + | 0.661335i | \(0.230010\pi\) | |||||||
\(354\) | 1367.32 | + | 742.980i | 0.205289 | + | 0.111551i | ||||
\(355\) | −11703.4 | + | 4847.72i | −1.74973 | + | 0.724762i | ||||
\(356\) | −643.888 | + | 3019.43i | −0.0958595 | + | 0.449522i | ||||
\(357\) | −1199.53 | + | 2895.91i | −0.177831 | + | 0.429322i | ||||
\(358\) | −10311.2 | − | 1087.20i | −1.52225 | − | 0.160504i | ||||
\(359\) | −3301.10 | − | 3301.10i | −0.485308 | − | 0.485308i | 0.421514 | − | 0.906822i | \(-0.361499\pi\) |
−0.906822 | + | 0.421514i | \(0.861499\pi\) | |||||||
\(360\) | −4377.57 | − | 8612.58i | −0.640884 | − | 1.26090i | ||||
\(361\) | 4106.53 | − | 4106.53i | 0.598706 | − | 0.598706i | ||||
\(362\) | 1201.49 | − | 972.289i | 0.174444 | − | 0.141167i | ||||
\(363\) | −82.8802 | − | 34.3301i | −0.0119837 | − | 0.00496381i | ||||
\(364\) | 6511.84 | − | 1202.44i | 0.937673 | − | 0.173146i | ||||
\(365\) | 5420.12 | + | 13085.3i | 0.777266 | + | 1.87649i | ||||
\(366\) | −44.6847 | − | 151.037i | −0.00638172 | − | 0.0215705i | ||||
\(367\) | − | 10621.1i | − | 1.51067i | −0.655340 | − | 0.755334i | \(-0.727474\pi\) | ||
0.655340 | − | 0.755334i | \(-0.272526\pi\) | |||||||
\(368\) | −2340.09 | − | 6120.34i | −0.331483 | − | 0.866970i | ||||
\(369\) | − | 1584.71i | − | 0.223568i | ||||||
\(370\) | −2199.21 | + | 650.646i | −0.309005 | + | 0.0914202i | ||||
\(371\) | 3373.95 | + | 8145.43i | 0.472147 | + | 1.13986i | ||||
\(372\) | −1212.25 | − | 834.340i | −0.168958 | − | 0.116286i | ||||
\(373\) | −527.627 | − | 218.550i | −0.0732426 | − | 0.0303381i | 0.345761 | − | 0.938322i | \(-0.387621\pi\) |
−0.419004 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(374\) | −6857.68 | − | 8474.26i | −0.948134 | − | 1.17164i | ||||
\(375\) | 820.862 | − | 820.862i | 0.113038 | − | 0.113038i | ||||
\(376\) | −1021.56 | − | 13146.9i | −0.140114 | − | 1.80318i | ||||
\(377\) | 735.947 | + | 735.947i | 0.100539 | + | 0.100539i | ||||
\(378\) | 466.360 | − | 4423.05i | 0.0634576 | − | 0.601845i | ||||
\(379\) | −3589.96 | + | 8666.94i | −0.486554 | + | 1.17465i | 0.469888 | + | 0.882726i | \(0.344294\pi\) |
−0.956443 | + | 0.291920i | \(0.905706\pi\) | |||||||
\(380\) | −2427.42 | − | 3743.32i | −0.327695 | − | 0.505338i | ||||
\(381\) | −776.177 | + | 321.503i | −0.104369 | + | 0.0432312i | ||||
\(382\) | −23.8915 | + | 43.9680i | −0.00319999 | + | 0.00588900i | ||||
\(383\) | −4350.16 | −0.580372 | −0.290186 | − | 0.956970i | \(-0.593717\pi\) | ||||
−0.290186 | + | 0.956970i | \(0.593717\pi\) | |||||||
\(384\) | 106.806 | + | 2132.41i | 0.0141938 | + | 0.283383i | ||||
\(385\) | 13204.1 | 1.74791 | ||||||||
\(386\) | −4485.63 | + | 8255.00i | −0.591484 | + | 1.08852i | ||||
\(387\) | 11357.3 | − | 4704.34i | 1.49179 | − | 0.617920i | ||||
\(388\) | −3433.71 | − | 5295.11i | −0.449279 | − | 0.692831i | ||||
\(389\) | 763.322 | − | 1842.82i | 0.0994909 | − | 0.240192i | −0.866295 | − | 0.499533i | \(-0.833505\pi\) |
0.965786 | + | 0.259340i | \(0.0835051\pi\) | |||||||
\(390\) | −302.481 | + | 2868.78i | −0.0392736 | + | 0.372478i | ||||
\(391\) | 7479.13 | + | 7479.13i | 0.967355 | + | 0.967355i | ||||
\(392\) | −141.114 | − | 1816.06i | −0.0181820 | − | 0.233992i | ||||
\(393\) | −1322.36 | + | 1322.36i | −0.169731 | + | 0.169731i | ||||
\(394\) | 1443.19 | + | 1783.40i | 0.184535 | + | 0.228036i | ||||
\(395\) | −2506.97 | − | 1038.42i | −0.319340 | − | 0.132275i | ||||
\(396\) | 6103.71 | + | 4200.91i | 0.774553 | + | 0.533090i | ||||
\(397\) | 1876.19 | + | 4529.53i | 0.237187 | + | 0.572621i | 0.996990 | − | 0.0775330i | \(-0.0247043\pi\) |
−0.759802 | + | 0.650154i | \(0.774704\pi\) | |||||||
\(398\) | 7319.77 | − | 2165.58i | 0.921876 | − | 0.272741i | ||||
\(399\) | − | 983.855i | − | 0.123444i | ||||||
\(400\) | 10209.3 | − | 3903.49i | 1.27616 | − | 0.487936i | ||||
\(401\) | − | 14992.8i | − | 1.86710i | −0.358450 | − | 0.933549i | \(-0.616695\pi\) | ||
0.358450 | − | 0.933549i | \(-0.383305\pi\) | |||||||
\(402\) | 251.860 | + | 851.300i | 0.0312479 | + | 0.105619i | ||||
\(403\) | −1920.50 | − | 4636.49i | −0.237387 | − | 0.573102i | ||||
\(404\) | −12031.4 | + | 2221.66i | −1.48164 | + | 0.273593i | ||||
\(405\) | −8860.68 | − | 3670.21i | −1.08714 | − | 0.450307i | ||||
\(406\) | 1170.81 | − | 947.460i | 0.143119 | − | 0.115817i | ||||
\(407\) | 1243.76 | − | 1243.76i | 0.151477 | − | 0.151477i | ||||
\(408\) | −1561.63 | − | 3072.40i | −0.189490 | − | 0.372810i | ||||
\(409\) | 8450.62 | + | 8450.62i | 1.02165 | + | 1.02165i | 0.999760 | + | 0.0218936i | \(0.00696949\pi\) |
0.0218936 | + | 0.999760i | \(0.493031\pi\) | |||||||
\(410\) | 3087.93 | + | 325.587i | 0.371957 | + | 0.0392186i | ||||
\(411\) | −754.857 | + | 1822.39i | −0.0905946 | + | 0.218715i | ||||
\(412\) | 2643.19 | − | 12394.9i | 0.316069 | − | 1.48217i | ||||
\(413\) | 7094.91 | − | 2938.81i | 0.845322 | − | 0.350144i | ||||
\(414\) | −6316.86 | − | 3432.48i | −0.749895 | − | 0.407481i | ||||
\(415\) | 2450.76 | 0.289887 | ||||||||
\(416\) | −3650.93 | + | 6299.52i | −0.430292 | + | 0.742450i | ||||
\(417\) | −2096.81 | −0.246238 | ||||||||
\(418\) | 3006.52 | + | 1633.70i | 0.351803 | + | 0.191164i | ||||
\(419\) | −3136.96 | + | 1299.37i | −0.365753 | + | 0.151500i | −0.557988 | − | 0.829849i | \(-0.688426\pi\) |
0.192235 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(420\) | 4082.70 | + | 870.627i | 0.474322 | + | 0.101148i | ||||
\(421\) | 3434.08 | − | 8290.60i | 0.397546 | − | 0.959760i | −0.590701 | − | 0.806891i | \(-0.701149\pi\) |
0.988246 | − | 0.152870i | \(-0.0488514\pi\) | |||||||
\(422\) | −7128.75 | − | 751.645i | −0.822327 | − | 0.0867050i | ||||
\(423\) | −10230.4 | − | 10230.4i | −1.17593 | − | 1.17593i | ||||
\(424\) | −9216.63 | − | 3004.78i | −1.05566 | − | 0.344162i | ||||
\(425\) | −12475.9 | + | 12475.9i | −1.42392 | + | 1.42392i | ||||
\(426\) | 2387.68 | − | 1932.20i | 0.271558 | − | 0.219754i | ||||
\(427\) | −718.125 | − | 297.457i | −0.0813876 | − | 0.0337118i | ||||
\(428\) | 2618.99 | + | 14183.1i | 0.295779 | + | 1.60179i | ||||
\(429\) | −846.648 | − | 2043.99i | −0.0952833 | − | 0.230034i | ||||
\(430\) | 6833.37 | + | 23097.1i | 0.766359 | + | 2.59033i | ||||
\(431\) | 15375.3i | 1.71833i | 0.511699 | + | 0.859165i | \(0.329016\pi\) | ||||
−0.511699 | + | 0.859165i | \(0.670984\pi\) | |||||||
\(432\) | 3361.53 | + | 3551.71i | 0.374379 | + | 0.395559i | ||||
\(433\) | 12522.9i | 1.38987i | 0.719073 | + | 0.694934i | \(0.244567\pi\) | ||||
−0.719073 | + | 0.694934i | \(0.755433\pi\) | |||||||
\(434\) | −6964.00 | + | 2060.33i | −0.770237 | + | 0.227878i | ||||
\(435\) | 251.085 | + | 606.172i | 0.0276749 | + | 0.0668132i | ||||
\(436\) | −4062.74 | + | 5902.96i | −0.446262 | + | 0.648396i | ||||
\(437\) | −3067.20 | − | 1270.48i | −0.335753 | − | 0.139074i | ||||
\(438\) | −2160.34 | − | 2669.61i | −0.235674 | − | 0.291230i | ||||
\(439\) | 6689.38 | − | 6689.38i | 0.727259 | − | 0.727259i | −0.242814 | − | 0.970073i | \(-0.578071\pi\) |
0.970073 | + | 0.242814i | \(0.0780705\pi\) | |||||||
\(440\) | −9439.85 | + | 11030.5i | −1.02279 | + | 1.19513i | ||||
\(441\) | −1413.19 | − | 1413.19i | −0.152595 | − | 0.152595i | ||||
\(442\) | 1232.40 | − | 11688.4i | 0.132623 | − | 1.25782i | ||||
\(443\) | 1232.30 | − | 2975.03i | 0.132163 | − | 0.319070i | −0.843920 | − | 0.536470i | \(-0.819758\pi\) |
0.976083 | + | 0.217400i | \(0.0697576\pi\) | |||||||
\(444\) | 466.579 | − | 302.561i | 0.0498713 | − | 0.0323399i | ||||
\(445\) | −6131.88 | + | 2539.91i | −0.653212 | + | 0.270569i | ||||
\(446\) | −361.205 | + | 664.732i | −0.0383487 | + | 0.0705739i | ||||
\(447\) | −3890.86 | −0.411703 | ||||||||
\(448\) | 8511.92 | + | 6210.11i | 0.897657 | + | 0.654911i | ||||
\(449\) | −2465.75 | −0.259167 | −0.129584 | − | 0.991569i | \(-0.541364\pi\) | ||||
−0.129584 | + | 0.991569i | \(0.541364\pi\) | |||||||
\(450\) | 5725.68 | − | 10537.1i | 0.599803 | − | 1.10383i | ||||
\(451\) | −2200.13 | + | 911.324i | −0.229712 | + | 0.0951498i | ||||
\(452\) | 6204.49 | − | 4023.41i | 0.645652 | − | 0.418684i | ||||
\(453\) | 696.557 | − | 1681.64i | 0.0722453 | − | 0.174415i | ||||
\(454\) | −231.694 | + | 2197.43i | −0.0239514 | + | 0.227159i | ||||
\(455\) | 10066.2 | + | 10066.2i | 1.03717 | + | 1.03717i | ||||
\(456\) | 821.894 | + | 703.375i | 0.0844051 | + | 0.0722337i | ||||
\(457\) | 720.641 | − | 720.641i | 0.0737640 | − | 0.0737640i | −0.669262 | − | 0.743026i | \(-0.733390\pi\) |
0.743026 | + | 0.669262i | \(0.233390\pi\) | |||||||
\(458\) | 6524.77 | + | 8062.86i | 0.665682 | + | 0.822605i | ||||
\(459\) | −7293.03 | − | 3020.87i | −0.741633 | − | 0.307194i | ||||
\(460\) | 7986.30 | − | 11603.7i | 0.809485 | − | 1.17614i | ||||
\(461\) | 94.7149 | + | 228.662i | 0.00956900 | + | 0.0231016i | 0.928592 | − | 0.371103i | \(-0.121020\pi\) |
−0.919023 | + | 0.394204i | \(0.871020\pi\) | |||||||
\(462\) | −3070.07 | + | 908.291i | −0.309161 | + | 0.0914665i | ||||
\(463\) | 6979.44i | 0.700566i | 0.936644 | + | 0.350283i | \(0.113915\pi\) | ||||
−0.936644 | + | 0.350283i | \(0.886085\pi\) | |||||||
\(464\) | −45.5402 | + | 1655.43i | −0.00455636 | + | 0.165628i | ||||
\(465\) | − | 3163.69i | − | 0.315511i | ||||||
\(466\) | −108.319 | − | 366.122i | −0.0107677 | − | 0.0363954i | ||||
\(467\) | 795.725 | + | 1921.05i | 0.0788475 | + | 0.190355i | 0.958388 | − | 0.285470i | \(-0.0921497\pi\) |
−0.879540 | + | 0.475825i | \(0.842150\pi\) | |||||||
\(468\) | 1450.61 | + | 7855.76i | 0.143278 | + | 0.775924i | ||||
\(469\) | 4047.63 | + | 1676.58i | 0.398512 | + | 0.165069i | ||||
\(470\) | 22036.6 | − | 17832.8i | 2.16270 | − | 1.75014i | ||||
\(471\) | 977.762 | − | 977.762i | 0.0956537 | − | 0.0956537i | ||||
\(472\) | −2617.25 | + | 8027.97i | −0.255231 | + | 0.782875i | ||||
\(473\) | −13062.5 | − | 13062.5i | −1.26980 | − | 1.26980i | ||||
\(474\) | 654.323 | + | 68.9909i | 0.0634052 | + | 0.00668536i | ||||
\(475\) | 2119.27 | − | 5116.37i | 0.204713 | − | 0.494221i | ||||
\(476\) | −16634.2 | − | 3547.21i | −1.60174 | − | 0.341568i | ||||
\(477\) | −9826.49 | + | 4070.26i | −0.943237 | + | 0.390702i | ||||
\(478\) | 5493.13 | + | 2984.88i | 0.525628 | + | 0.285618i | ||||
\(479\) | 973.751 | 0.0928848 | 0.0464424 | − | 0.998921i | \(-0.485212\pi\) | ||||
0.0464424 | + | 0.998921i | \(0.485212\pi\) | |||||||
\(480\) | −3646.10 | + | 2788.18i | −0.346710 | + | 0.265130i | ||||
\(481\) | 1896.37 | 0.179766 | ||||||||
\(482\) | −7528.11 | − | 4090.65i | −0.711402 | − | 0.386565i | ||||
\(483\) | 2869.90 | − | 1188.75i | 0.270362 | − | 0.111988i | ||||
\(484\) | 101.520 | − | 476.067i | 0.00953422 | − | 0.0447096i | ||||
\(485\) | 5191.98 | − | 12534.6i | 0.486094 | − | 1.17354i | ||||
\(486\) | 8115.73 | + | 855.711i | 0.757484 | + | 0.0798680i | ||||
\(487\) | −11379.8 | − | 11379.8i | −1.05887 | − | 1.05887i | −0.998155 | − | 0.0607112i | \(-0.980663\pi\) |
−0.0607112 | − | 0.998155i | \(-0.519337\pi\) | |||||||
\(488\) | 761.890 | − | 387.251i | 0.0706745 | − | 0.0359222i | ||||
\(489\) | 841.184 | − | 841.184i | 0.0777907 | − | 0.0777907i | ||||
\(490\) | 3044.05 | − | 2463.36i | 0.280646 | − | 0.227109i | ||||
\(491\) | −1394.56 | − | 577.645i | −0.128178 | − | 0.0530932i | 0.317672 | − | 0.948201i | \(-0.397099\pi\) |
−0.445851 | + | 0.895107i | \(0.647099\pi\) | |||||||
\(492\) | −740.367 | + | 136.713i | −0.0678421 | + | 0.0125274i | ||||
\(493\) | −1023.00 | − | 2469.74i | −0.0934557 | − | 0.225622i | ||||
\(494\) | 1046.58 | + | 3537.49i | 0.0953195 | + | 0.322184i | ||||
\(495\) | 15929.2i | 1.44639i | ||||||||
\(496\) | 3257.53 | − | 7290.56i | 0.294894 | − | 0.659992i | ||||
\(497\) | − | 15157.9i | − | 1.36806i | ||||||
\(498\) | −569.823 | + | 168.584i | −0.0512739 | + | 0.0151696i | ||||
\(499\) | 5429.65 | + | 13108.3i | 0.487103 | + | 1.17597i | 0.956171 | + | 0.292809i | \(0.0945900\pi\) |
−0.469068 | + | 0.883162i | \(0.655410\pi\) | |||||||
\(500\) | 5188.85 | + | 3571.25i | 0.464105 | + | 0.319422i | ||||
\(501\) | 1428.86 | + | 591.852i | 0.127418 | + | 0.0527784i | ||||
\(502\) | 624.420 | + | 771.616i | 0.0555164 | + | 0.0686034i | ||||
\(503\) | 11037.0 | − | 11037.0i | 0.978362 | − | 0.978362i | −0.0214085 | − | 0.999771i | \(-0.506815\pi\) |
0.999771 | + | 0.0214085i | \(0.00681506\pi\) | |||||||
\(504\) | 11525.7 | − | 895.587i | 1.01864 | − | 0.0791520i | ||||
\(505\) | −18598.5 | − | 18598.5i | −1.63886 | − | 1.63886i | ||||
\(506\) | −1132.83 | + | 10743.9i | −0.0995262 | + | 0.943926i | ||||
\(507\) | −326.770 | + | 788.893i | −0.0286240 | + | 0.0691045i | ||||
\(508\) | −2480.28 | − | 3824.83i | −0.216623 | − | 0.334054i | ||||
\(509\) | 13984.8 | − | 5792.71i | 1.21781 | − | 0.504435i | 0.321099 | − | 0.947046i | \(-0.395948\pi\) |
0.896714 | + | 0.442611i | \(0.145948\pi\) | |||||||
\(510\) | 3537.54 | − | 6510.20i | 0.307147 | − | 0.565248i | ||||
\(511\) | −16947.7 | −1.46717 | ||||||||
\(512\) | −11273.1 | + | 2670.98i | −0.973060 | + | 0.230550i | ||||
\(513\) | 2477.73 | 0.213244 | ||||||||
\(514\) | −10073.8 | + | 18539.0i | −0.864467 | + | 1.59090i | ||||
\(515\) | 25171.6 | − | 10426.4i | 2.15377 | − | 0.892123i | ||||
\(516\) | −3177.63 | − | 4900.22i | −0.271100 | − | 0.418062i | ||||
\(517\) | −8320.11 | + | 20086.5i | −0.707772 | + | 1.70871i | ||||
\(518\) | 287.759 | − | 2729.16i | 0.0244081 | − | 0.231491i | ||||
\(519\) | 93.6978 | + | 93.6978i | 0.00792462 | + | 0.00792462i | ||||
\(520\) | −15605.6 | + | 1212.61i | −1.31606 | + | 0.102263i | ||||
\(521\) | 8504.46 | − | 8504.46i | 0.715139 | − | 0.715139i | −0.252467 | − | 0.967606i | \(-0.581242\pi\) |
0.967606 | + | 0.252467i | \(0.0812418\pi\) | |||||||
\(522\) | 1143.00 | + | 1412.44i | 0.0958384 | + | 0.118431i | ||||
\(523\) | −2991.17 | − | 1238.98i | −0.250086 | − | 0.103589i | 0.254119 | − | 0.967173i | \(-0.418214\pi\) |
−0.504205 | + | 0.863584i | \(0.668214\pi\) | |||||||
\(524\) | −8358.95 | − | 5753.09i | −0.696875 | − | 0.479628i | ||||
\(525\) | 1982.94 | + | 4787.25i | 0.164843 | + | 0.397967i | ||||
\(526\) | 16080.2 | − | 4757.38i | 1.33295 | − | 0.394357i | ||||
\(527\) | 12889.9i | 1.06545i | ||||||||
\(528\) | 1436.08 | − | 3214.03i | 0.118366 | − | 0.264910i | ||||
\(529\) | 1684.91i | 0.138482i | ||||||||
\(530\) | −5912.33 | − | 19984.0i | −0.484557 | − | 1.63783i | ||||
\(531\) | 3545.33 | + | 8559.17i | 0.289744 | + | 0.699504i | ||||
\(532\) | 5249.76 | − | 969.395i | 0.427831 | − | 0.0790012i | ||||
\(533\) | −2372.03 | − | 982.527i | −0.192765 | − | 0.0798461i | ||||
\(534\) | 1251.00 | − | 1012.35i | 0.101378 | − | 0.0820390i | ||||
\(535\) | −21924.7 | + | 21924.7i | −1.77175 | + | 1.77175i | ||||
\(536\) | −4294.31 | + | 2182.69i | −0.346055 | + | 0.175892i | ||||
\(537\) | 3821.65 | + | 3821.65i | 0.307107 | + | 0.307107i | ||||
\(538\) | −9374.83 | − | 988.469i | −0.751260 | − | 0.0792118i | ||||
\(539\) | −1149.31 | + | 2774.68i | −0.0918448 | + | 0.221733i | ||||
\(540\) | −2192.58 | + | 10281.8i | −0.174729 | + | 0.819369i | ||||
\(541\) | 4615.58 | − | 1911.84i | 0.366801 | − | 0.151934i | −0.191667 | − | 0.981460i | \(-0.561389\pi\) |
0.558468 | + | 0.829526i | \(0.311389\pi\) | |||||||
\(542\) | 2954.66 | + | 1605.51i | 0.234157 | + | 0.127237i | ||||
\(543\) | −805.668 | −0.0636732 | ||||||||
\(544\) | 14855.4 | − | 11360.0i | 1.17081 | − | 0.895320i | ||||
\(545\) | −15405.3 | −1.21081 | ||||||||
\(546\) | −3032.92 | − | 1648.04i | −0.237723 | − | 0.129175i | ||||
\(547\) | 1759.02 | − | 728.609i | 0.137496 | − | 0.0569526i | −0.312875 | − | 0.949794i | \(-0.601292\pi\) |
0.450370 | + | 0.892842i | \(0.351292\pi\) | |||||||
\(548\) | −10467.9 | − | 2232.25i | −0.815995 | − | 0.174009i | ||||
\(549\) | 358.847 | − | 866.332i | 0.0278965 | − | 0.0673482i | ||||
\(550\) | −17921.9 | − | 1889.66i | −1.38944 | − | 0.146500i | ||||
\(551\) | 593.311 | + | 593.311i | 0.0458728 | + | 0.0458728i | ||||
\(552\) | −1058.68 | + | 3247.32i | −0.0816313 | + | 0.250390i | ||||
\(553\) | 2295.94 | − | 2295.94i | 0.176552 | − | 0.176552i | ||||
\(554\) | 9120.77 | − | 7380.86i | 0.699466 | − | 0.566034i | ||||
\(555\) | 1104.48 | + | 457.492i | 0.0844733 | + | 0.0349900i | ||||
\(556\) | −2065.99 | − | 11188.4i | −0.157585 | − | 0.853405i | ||||
\(557\) | 7305.07 | + | 17636.0i | 0.555702 | + | 1.34158i | 0.913140 | + | 0.407646i | \(0.133650\pi\) |
−0.357438 | + | 0.933937i | \(0.616350\pi\) | |||||||
\(558\) | −2485.54 | − | 8401.24i | −0.188569 | − | 0.637371i | ||||
\(559\) | − | 19916.6i | − | 1.50694i | ||||||
\(560\) | −622.894 | + | 22642.8i | −0.0470037 | + | 1.70863i | ||||
\(561\) | 5682.48i | 0.427655i | ||||||||
\(562\) | 882.386 | − | 261.057i | 0.0662299 | − | 0.0195944i | ||||
\(563\) | 498.470 | + | 1203.41i | 0.0373144 | + | 0.0900849i | 0.941438 | − | 0.337186i | \(-0.109475\pi\) |
−0.904124 | + | 0.427271i | \(0.859475\pi\) | |||||||
\(564\) | −3897.00 | + | 5662.14i | −0.290945 | + | 0.422729i | ||||
\(565\) | 14687.2 | + | 6083.65i | 1.09362 | + | 0.452993i | ||||
\(566\) | 1886.48 | + | 2331.18i | 0.140097 | + | 0.173122i | ||||
\(567\) | 8114.80 | − | 8114.80i | 0.601040 | − | 0.601040i | ||||
\(568\) | 12662.6 | + | 10836.7i | 0.935409 | + | 0.800521i | ||||
\(569\) | 13188.4 | + | 13188.4i | 0.971684 | + | 0.971684i | 0.999610 | − | 0.0279264i | \(-0.00889041\pi\) |
−0.0279264 | + | 0.999610i | \(0.508890\pi\) | |||||||
\(570\) | −243.856 | + | 2312.78i | −0.0179193 | + | 0.169950i | ||||
\(571\) | 5719.51 | − | 13808.1i | 0.419184 | − | 1.01200i | −0.563401 | − | 0.826184i | \(-0.690507\pi\) |
0.982585 | − | 0.185815i | \(-0.0594926\pi\) | |||||||
\(572\) | 10072.3 | − | 6531.59i | 0.736269 | − | 0.477447i | ||||
\(573\) | 24.0983 | − | 9.98186i | 0.00175693 | − | 0.000727746i | ||||
\(574\) | −1773.93 | + | 3264.60i | −0.128994 | + | 0.237390i | ||||
\(575\) | 17485.1 | 1.26813 | ||||||||
\(576\) | −7491.76 | + | 10268.6i | −0.541939 | + | 0.742811i | ||||
\(577\) | 7866.08 | 0.567538 | 0.283769 | − | 0.958893i | \(-0.408415\pi\) | ||||
0.283769 | + | 0.958893i | \(0.408415\pi\) | |||||||
\(578\) | −7778.40 | + | 14314.7i | −0.559756 | + | 1.03013i | ||||
\(579\) | 4524.46 | − | 1874.09i | 0.324750 | − | 0.134516i | ||||
\(580\) | −2987.09 | + | 1937.03i | −0.213848 | + | 0.138674i | ||||
\(581\) | −1122.23 | + | 2709.30i | −0.0801342 | + | 0.193461i | ||||
\(582\) | −344.946 | + | 3271.54i | −0.0245678 | + | 0.233006i | ||||
\(583\) | 11301.9 | + | 11301.9i | 0.802877 | + | 0.802877i | ||||
\(584\) | 12116.2 | − | 14157.8i | 0.858514 | − | 1.00317i | ||||
\(585\) | −12143.7 | + | 12143.7i | −0.858255 | + | 0.858255i | ||||
\(586\) | 2856.55 | + | 3529.93i | 0.201370 | + | 0.248840i | ||||
\(587\) | 13370.3 | + | 5538.16i | 0.940122 | + | 0.389411i | 0.799510 | − | 0.600653i | \(-0.205093\pi\) |
0.140613 | + | 0.990065i | \(0.455093\pi\) | |||||||
\(588\) | −538.317 | + | 782.148i | −0.0377548 | + | 0.0548558i | ||||
\(589\) | −1548.28 | − | 3737.88i | −0.108312 | − | 0.261489i | ||||
\(590\) | −17406.6 | + | 5149.82i | −1.21461 | + | 0.359347i | ||||
\(591\) | − | 1195.87i | − | 0.0832346i | ||||||
\(592\) | 2074.16 | + | 2191.51i | 0.143999 | + | 0.152146i | ||||
\(593\) | 7176.23i | 0.496952i | 0.968638 | + | 0.248476i | \(0.0799297\pi\) | ||||
−0.968638 | + | 0.248476i | \(0.920070\pi\) | |||||||
\(594\) | −2287.43 | − | 7731.62i | −0.158004 | − | 0.534061i | ||||
\(595\) | −13992.5 | − | 33780.9i | −0.964095 | − | 2.32753i | ||||
\(596\) | −3833.68 | − | 20761.3i | −0.263479 | − | 1.42687i | ||||
\(597\) | −3676.11 | − | 1522.69i | −0.252015 | − | 0.104388i | ||||
\(598\) | −9054.30 | + | 7327.07i | −0.619160 | + | 0.501047i | ||||
\(599\) | −11813.4 | + | 11813.4i | −0.805815 | + | 0.805815i | −0.983997 | − | 0.178183i | \(-0.942978\pi\) |
0.178183 | + | 0.983997i | \(0.442978\pi\) | |||||||
\(600\) | −5416.82 | − | 1765.98i | −0.368568 | − | 0.120159i | ||||
\(601\) | −1438.92 | − | 1438.92i | −0.0976618 | − | 0.0976618i | 0.656588 | − | 0.754250i | \(-0.271999\pi\) |
−0.754250 | + | 0.656588i | \(0.771999\pi\) | |||||||
\(602\) | −28662.8 | − | 3022.17i | −1.94055 | − | 0.204609i | ||||
\(603\) | −2022.60 | + | 4882.98i | −0.136595 | + | 0.329768i | ||||
\(604\) | 9659.39 | + | 2059.85i | 0.650720 | + | 0.138765i | ||||
\(605\) | 966.800 | − | 400.462i | 0.0649686 | − | 0.0269109i | ||||
\(606\) | 5603.67 | + | 3044.94i | 0.375633 | + | 0.204113i | ||||
\(607\) | −19331.1 | −1.29263 | −0.646314 | − | 0.763071i | \(-0.723691\pi\) | ||||
−0.646314 | + | 0.763071i | \(0.723691\pi\) | |||||||
\(608\) | −2943.33 | + | 5078.59i | −0.196329 | + | 0.338757i | ||||
\(609\) | −785.094 | −0.0522391 | ||||||||
\(610\) | 1614.39 | + | 877.234i | 0.107155 | + | 0.0582265i | ||||
\(611\) | −21655.9 | + | 8970.17i | −1.43389 | + | 0.593935i | ||||
\(612\) | 4279.29 | − | 20067.2i | 0.282647 | − | 1.32544i | ||||
\(613\) | 2013.56 | − | 4861.15i | 0.132670 | − | 0.320294i | −0.843559 | − | 0.537037i | \(-0.819543\pi\) |
0.976229 | + | 0.216743i | \(0.0695435\pi\) | |||||||
\(614\) | 15862.3 | + | 1672.50i | 1.04259 | + | 0.109929i | ||||
\(615\) | −1144.48 | − | 1144.48i | −0.0750406 | − | 0.0750406i | ||||
\(616\) | −7871.51 | − | 15486.7i | −0.514857 | − | 1.01295i | ||||
\(617\) | −6574.52 | + | 6574.52i | −0.428979 | + | 0.428979i | −0.888281 | − | 0.459301i | \(-0.848100\pi\) |
0.459301 | + | 0.888281i | \(0.348100\pi\) | |||||||
\(618\) | −5135.39 | + | 4155.75i | −0.334265 | + | 0.270500i | ||||
\(619\) | 2395.09 | + | 992.077i | 0.155520 | + | 0.0644183i | 0.459085 | − | 0.888392i | \(-0.348177\pi\) |
−0.303566 | + | 0.952810i | \(0.598177\pi\) | |||||||
\(620\) | 16881.2 | − | 3117.19i | 1.09349 | − | 0.201918i | ||||
\(621\) | 2993.74 | + | 7227.53i | 0.193454 | + | 0.467038i | ||||
\(622\) | −206.892 | − | 699.306i | −0.0133370 | − | 0.0450797i | ||||
\(623\) | − | 7941.81i | − | 0.510726i | ||||||
\(624\) | 3545.02 | − | 1355.43i | 0.227427 | − | 0.0869561i | ||||
\(625\) | − | 7806.17i | − | 0.499595i | ||||||
\(626\) | 14314.2 | − | 4234.91i | 0.913914 | − | 0.270385i | ||||
\(627\) | −682.557 | − | 1647.84i | −0.0434748 | − | 0.104957i | ||||
\(628\) | 6180.65 | + | 4253.86i | 0.392730 | + | 0.270299i | ||||
\(629\) | −4500.02 | − | 1863.97i | −0.285258 | − | 0.118158i | ||||
\(630\) | 15633.8 | + | 19319.2i | 0.988676 | + | 1.22174i | ||||
\(631\) | −2820.94 | + | 2820.94i | −0.177971 | + | 0.177971i | −0.790471 | − | 0.612500i | \(-0.790164\pi\) |
0.612500 | + | 0.790471i | \(0.290164\pi\) | |||||||
\(632\) | 276.577 | + | 3559.39i | 0.0174077 | + | 0.224027i | ||||
\(633\) | 2642.13 | + | 2642.13i | 0.165901 | + | 0.165901i | ||||
\(634\) | 943.976 | − | 8952.85i | 0.0591326 | − | 0.560825i | ||||
\(635\) | 3750.34 | − | 9054.12i | 0.234374 | − | 0.565830i | ||||
\(636\) | 2749.33 | + | 4239.74i | 0.171412 | + | 0.264334i | ||||
\(637\) | −2991.47 | + | 1239.11i | −0.186070 | + | 0.0770726i | ||||
\(638\) | 1303.65 | − | 2399.14i | 0.0808968 | − | 0.148876i | ||||
\(639\) | 18286.2 | 1.13207 | ||||||||
\(640\) | −18470.0 | − | 16708.1i | −1.14077 | − | 1.03194i | ||||
\(641\) | 8220.77 | 0.506553 | 0.253277 | − | 0.967394i | \(-0.418492\pi\) | ||||
0.253277 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(642\) | 3589.51 | − | 6605.85i | 0.220665 | − | 0.406094i | ||||
\(643\) | −21031.3 | + | 8711.45i | −1.28988 | + | 0.534286i | −0.918950 | − | 0.394374i | \(-0.870962\pi\) |
−0.370932 | + | 0.928660i | \(0.620962\pi\) | |||||||
\(644\) | 9170.80 | + | 14142.3i | 0.561149 | + | 0.865347i | ||||
\(645\) | 4804.78 | − | 11599.8i | 0.293315 | − | 0.708124i | ||||
\(646\) | 993.549 | − | 9423.01i | 0.0605119 | − | 0.573906i | ||||
\(647\) | −14749.1 | − | 14749.1i | −0.896208 | − | 0.896208i | 0.0988901 | − | 0.995098i | \(-0.468471\pi\) |
−0.995098 | + | 0.0988901i | \(0.968471\pi\) | |||||||
\(648\) | 977.539 | + | 12580.4i | 0.0592614 | + | 0.762660i | ||||
\(649\) | 9844.31 | − | 9844.31i | 0.595413 | − | 0.595413i | ||||
\(650\) | −12222.2 | − | 15103.4i | −0.737530 | − | 0.911390i | ||||
\(651\) | 3497.44 | + | 1448.69i | 0.210561 | + | 0.0872174i | ||||
\(652\) | 5317.31 | + | 3659.67i | 0.319389 | + | 0.219821i | ||||
\(653\) | −4279.06 | − | 10330.6i | −0.256436 | − | 0.619091i | 0.742262 | − | 0.670110i | \(-0.233753\pi\) |
−0.998698 | + | 0.0510191i | \(0.983753\pi\) | |||||||
\(654\) | 3581.86 | − | 1059.71i | 0.214162 | − | 0.0633606i | ||||
\(655\) | − | 21814.8i | − | 1.30134i | ||||||
\(656\) | −1458.97 | − | 3815.83i | −0.0868343 | − | 0.227109i | ||||
\(657\) | − | 20445.4i | − | 1.21408i | ||||||
\(658\) | 9623.28 | + | 32527.1i | 0.570143 | + | 1.92711i | ||||
\(659\) | −11437.1 | − | 27611.6i | −0.676063 | − | 1.63216i | −0.771121 | − | 0.636689i | \(-0.780304\pi\) |
0.0950580 | − | 0.995472i | \(-0.469696\pi\) | |||||||
\(660\) | 7442.03 | − | 1374.21i | 0.438910 | − | 0.0810469i | ||||
\(661\) | 19843.3 | + | 8219.36i | 1.16765 | + | 0.483655i | 0.880414 | − | 0.474205i | \(-0.157265\pi\) |
0.287233 | + | 0.957861i | \(0.407265\pi\) | |||||||
\(662\) | −14085.7 | + | 11398.7i | −0.826974 | + | 0.669218i | ||||
\(663\) | −4332.06 | + | 4332.06i | −0.253761 | + | 0.253761i | ||||
\(664\) | −1461.00 | − | 2874.42i | −0.0853883 | − | 0.167996i | ||||
\(665\) | 8115.25 | + | 8115.25i | 0.473227 | + | 0.473227i | ||||
\(666\) | 3292.40 | + | 347.146i | 0.191559 | + | 0.0201977i | ||||
\(667\) | −1013.81 | + | 2447.56i | −0.0588530 | + | 0.142084i | ||||
\(668\) | −1750.21 | + | 8207.41i | −0.101374 | + | 0.475381i | ||||
\(669\) | 364.332 | − | 150.911i | 0.0210551 | − | 0.00872132i | ||||
\(670\) | −9099.33 | − | 4944.43i | −0.524683 | − | 0.285104i | ||||
\(671\) | −1409.14 | −0.0810717 | ||||||||
\(672\) | −1412.73 | − | 5307.48i | −0.0810972 | − | 0.304673i | ||||
\(673\) | −13639.3 | −0.781216 | −0.390608 | − | 0.920557i | \(-0.627735\pi\) | ||||
−0.390608 | + | 0.920557i | \(0.627735\pi\) | |||||||
\(674\) | 28041.4 | + | 15237.3i | 1.60254 | + | 0.870797i | ||||
\(675\) | −12056.2 | + | 4993.82i | −0.687469 | + | 0.284759i | ||||
\(676\) | −4531.43 | − | 966.319i | −0.257819 | − | 0.0549795i | ||||
\(677\) | −10163.0 | + | 24535.6i | −0.576951 | + | 1.39288i | 0.318586 | + | 0.947894i | \(0.396792\pi\) |
−0.895537 | + | 0.444988i | \(0.853208\pi\) | |||||||
\(678\) | −3833.39 | − | 404.187i | −0.217139 | − | 0.0228948i | ||||
\(679\) | 11479.4 | + | 11479.4i | 0.648806 | + | 0.648806i | ||||
\(680\) | 38223.4 | + | 12461.5i | 2.15559 | + | 0.702758i | ||||
\(681\) | 814.433 | − | 814.433i | 0.0458284 | − | 0.0458284i | ||||
\(682\) | −10234.5 | + | 8282.13i | −0.574632 | + | 0.465014i | ||||
\(683\) | −12279.3 | − | 5086.25i | −0.687928 | − | 0.284949i | 0.0112089 | − | 0.999937i | \(-0.496432\pi\) |
−0.699136 | + | 0.714988i | \(0.746432\pi\) | |||||||
\(684\) | 1169.46 | + | 6333.22i | 0.0653735 | + | 0.354030i | ||||
\(685\) | −8805.43 | − | 21258.2i | −0.491151 | − | 1.18574i | ||||
\(686\) | −4334.67 | − | 14651.4i | −0.241252 | − | 0.815442i | ||||
\(687\) | − | 5406.62i | − | 0.300255i | ||||||
\(688\) | 23016.2 | − | 21783.8i | 1.27541 | − | 1.20712i | ||||
\(689\) | 17232.1i | 0.952817i | ||||||||
\(690\) | −7041.01 | + | 2083.11i | −0.388473 | + | 0.114931i | ||||
\(691\) | 12427.1 | + | 30001.7i | 0.684153 | + | 1.65169i | 0.756241 | + | 0.654293i | \(0.227034\pi\) |
−0.0720884 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(692\) | −407.643 | + | 592.284i | −0.0223934 | + | 0.0325365i | ||||
\(693\) | −17609.6 | − | 7294.15i | −0.965273 | − | 0.399829i | ||||
\(694\) | −22334.4 | − | 27599.4i | −1.22162 | − | 1.50959i | ||||
\(695\) | 17295.3 | − | 17295.3i | 0.943956 | − | 0.943956i | ||||
\(696\) | 561.278 | − | 655.853i | 0.0305678 | − | 0.0357185i | ||||
\(697\) | 4662.99 | + | 4662.99i | 0.253405 | + | 0.253405i | ||||
\(698\) | −1666.50 | + | 15805.4i | −0.0903693 | + | 0.857080i | ||||
\(699\) | −76.1625 | + | 183.873i | −0.00412122 | + | 0.00994950i | ||||
\(700\) | −23590.6 | + | 15297.7i | −1.27377 | + | 0.825999i | ||||
\(701\) | −24563.9 | + | 10174.7i | −1.32349 | + | 0.548207i | −0.928791 | − | 0.370605i | \(-0.879150\pi\) |
−0.394697 | + | 0.918811i | \(0.629150\pi\) | |||||||
\(702\) | 4150.40 | − | 7638.06i | 0.223144 | − | 0.410655i | ||||
\(703\) | 1528.83 | 0.0820214 | ||||||||
\(704\) | 18564.8 | + | 4495.98i | 0.993872 | + | 0.240694i | ||||
\(705\) | −14776.8 | −0.789399 | ||||||||
\(706\) | 13436.3 | − | 24727.0i | 0.716261 | − | 1.31815i | ||||
\(707\) | 29077.0 | − | 12044.1i | 1.54675 | − | 0.640685i | ||||
\(708\) | 3692.94 | − | 2394.75i | 0.196030 | − | 0.127119i | ||||
\(709\) | −4032.81 | + | 9736.05i | −0.213618 | + | 0.515720i | −0.993974 | − | 0.109616i | \(-0.965038\pi\) |
0.780356 | + | 0.625336i | \(0.215038\pi\) | |||||||
\(710\) | −3757.01 | + | 35632.2i | −0.198589 | + | 1.88345i | ||||
\(711\) | 2769.78 | + | 2769.78i | 0.146097 | + | 0.146097i | ||||
\(712\) | 6634.44 | + | 5677.74i | 0.349208 | + | 0.298852i | ||||
\(713\) | 9032.67 | − | 9032.67i | 0.474440 | − | 0.474440i | ||||
\(714\) | 5577.11 | + | 6891.82i | 0.292322 | + | 0.361232i | ||||
\(715\) | 23843.2 | + | 9876.17i | 1.24711 | + | 0.516570i | ||||
\(716\) | −16626.5 | + | 24157.5i | −0.867824 | + | 1.26090i | ||||
\(717\) | −1247.08 | − | 3010.72i | −0.0649555 | − | 0.156816i | ||||
\(718\) | −12661.9 | + | 3746.07i | −0.658130 | + | 0.194710i | ||||
\(719\) | − | 2159.37i | − | 0.112004i | −0.998431 | − | 0.0560021i | \(-0.982165\pi\) | ||
0.998431 | − | 0.0560021i | \(-0.0178353\pi\) | |||||||
\(720\) | −27315.8 | − | 751.448i | −1.41389 | − | 0.0388956i | ||||
\(721\) | 32601.4i | 1.68397i | ||||||||
\(722\) | −4660.06 | − | 15751.2i | −0.240207 | − | 0.811911i | ||||
\(723\) | 1709.07 | + | 4126.06i | 0.0879129 | + | 0.212241i | ||||
\(724\) | −793.828 | − | 4298.98i | −0.0407491 | − | 0.220677i | ||||
\(725\) | −4082.75 | − | 1691.13i | −0.209144 | − | 0.0866303i | ||||
\(726\) | −197.242 | + | 159.615i | −0.0100831 | + | 0.00815962i | ||||
\(727\) | −15999.3 | + | 15999.3i | −0.816204 | + | 0.816204i | −0.985556 | − | 0.169352i | \(-0.945833\pi\) |
0.169352 | + | 0.985556i | \(0.445833\pi\) | |||||||
\(728\) | 5805.45 | − | 17807.2i | 0.295555 | − | 0.906564i | ||||
\(729\) | 7638.74 | + | 7638.74i | 0.388088 | + | 0.388088i | ||||
\(730\) | 39839.5 | + | 4200.62i | 2.01990 | + | 0.212975i | ||||
\(731\) | −19576.2 | + | 47261.2i | −0.990497 | + | 2.39127i | ||||
\(732\) | −435.703 | − | 92.9128i | −0.0220001 | − | 0.00469147i | ||||
\(733\) | −2232.08 | + | 924.559i | −0.112475 | + | 0.0465885i | −0.438211 | − | 0.898872i | \(-0.644388\pi\) |
0.325737 | + | 0.945461i | \(0.394388\pi\) | |||||||
\(734\) | −26395.7 | − | 14343.0i | −1.32736 | − | 0.721268i | ||||
\(735\) | −2041.22 | −0.102437 | ||||||||
\(736\) | −18370.6 | − | 2449.44i | −0.920037 | − | 0.122673i | ||||
\(737\) | 7942.43 | 0.396965 | ||||||||
\(738\) | −3938.36 | − | 2140.04i | −0.196440 | − | 0.106742i | ||||
\(739\) | −15900.0 | + | 6585.99i | −0.791462 | + | 0.327834i | −0.741531 | − | 0.670919i | \(-0.765900\pi\) |
−0.0499305 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(740\) | −1352.89 | + | 6344.19i | −0.0672069 | + | 0.315158i | ||||
\(741\) | 735.886 | − | 1776.59i | 0.0364824 | − | 0.0880762i | ||||
\(742\) | 24799.5 | + | 2614.82i | 1.22698 | + | 0.129371i | ||||
\(743\) | −6184.20 | − | 6184.20i | −0.305352 | − | 0.305352i | 0.537751 | − | 0.843103i | \(-0.319274\pi\) |
−0.843103 | + | 0.537751i | \(0.819274\pi\) | |||||||
\(744\) | −3710.59 | + | 1886.00i | −0.182845 | + | 0.0929358i | ||||
\(745\) | 32093.4 | − | 32093.4i | 1.57827 | − | 1.57827i | ||||
\(746\) | −1255.67 | + | 1016.13i | −0.0616265 | + | 0.0498704i | ||||
\(747\) | −3268.45 | − | 1353.84i | −0.160089 | − | 0.0663110i | ||||
\(748\) | −30321.2 | + | 5598.97i | −1.48216 | + | 0.273688i | ||||
\(749\) | −14198.1 | − | 34277.2i | −0.692639 | − | 1.67218i | ||||
\(750\) | −931.509 | − | 3148.54i | −0.0453518 | − | 0.153291i | ||||
\(751\) | − | 11095.5i | − | 0.539122i | −0.962983 | − | 0.269561i | \(-0.913121\pi\) | ||
0.962983 | − | 0.269561i | \(-0.0868786\pi\) | |||||||
\(752\) | −34052.4 | − | 15215.1i | −1.65128 | − | 0.737817i | ||||
\(753\) | − | 517.413i | − | 0.0250406i | ||||||
\(754\) | 2822.84 | − | 835.147i | 0.136342 | − | 0.0403372i | ||||
\(755\) | 8125.36 | + | 19616.3i | 0.391672 | + | 0.945579i | ||||
\(756\) | −10362.5 | − | 7132.04i | −0.498519 | − | 0.343108i | ||||
\(757\) | 25020.9 | + | 10364.0i | 1.20132 | + | 0.497604i | 0.891426 | − | 0.453167i | \(-0.149706\pi\) |
0.309896 | + | 0.950771i | \(0.399706\pi\) | |||||||
\(758\) | 16691.3 | + | 20626.0i | 0.799808 | + | 0.988349i | ||||
\(759\) | 3982.03 | − | 3982.03i | 0.190433 | − | 0.190433i | ||||
\(760\) | −12581.1 | + | 977.593i | −0.600478 | + | 0.0466593i | ||||
\(761\) | 2393.12 | + | 2393.12i | 0.113995 | + | 0.113995i | 0.761804 | − | 0.647808i | \(-0.224314\pi\) |
−0.647808 | + | 0.761804i | \(0.724314\pi\) | |||||||
\(762\) | −249.166 | + | 2363.14i | −0.0118456 | + | 0.112346i | ||||
\(763\) | 7054.25 | − | 17030.5i | 0.334706 | − | 0.808053i | ||||
\(764\) | 77.0065 | + | 118.752i | 0.00364660 | + | 0.00562340i | ||||
\(765\) | 40752.6 | − | 16880.3i | 1.92603 | − | 0.797788i | ||||
\(766\) | −5874.59 | + | 10811.1i | −0.277098 | + | 0.509950i | ||||
\(767\) | 15009.7 | 0.706608 | ||||||||
\(768\) | 5443.76 | + | 2614.24i | 0.255774 | + | 0.122830i | ||||
\(769\) | −33544.1 | −1.57299 | −0.786496 | − | 0.617595i | \(-0.788107\pi\) | ||||
−0.786496 | + | 0.617595i | \(0.788107\pi\) | |||||||
\(770\) | 17831.2 | − | 32815.2i | 0.834537 | − | 1.53581i | ||||
\(771\) | 10161.0 | − | 4208.82i | 0.474630 | − | 0.196598i | ||||
\(772\) | 14458.0 | + | 22295.6i | 0.674034 | + | 1.03943i | ||||
\(773\) | 9560.71 | − | 23081.6i | 0.444857 | − | 1.07398i | −0.529366 | − | 0.848394i | \(-0.677570\pi\) |
0.974223 | − | 0.225587i | \(-0.0724300\pi\) | |||||||
\(774\) | 3645.89 | − | 34578.3i | 0.169313 | − | 1.60580i | ||||
\(775\) | 15067.3 | + | 15067.3i | 0.698365 | + | 0.698365i | ||||
\(776\) | −17796.5 | + | 1382.85i | −0.823270 | + | 0.0639710i | ||||
\(777\) | −1011.51 | + | 1011.51i | −0.0467023 | + | 0.0467023i | ||||
\(778\) | −3549.01 | − | 4385.63i | −0.163545 | − | 0.202098i | ||||
\(779\) | −1912.30 | − | 792.101i | −0.0879529 | − | 0.0364313i | ||||
\(780\) | 6721.09 | + | 4625.83i | 0.308530 | + | 0.212348i | ||||
\(781\) | −10515.9 | − | 25387.7i | −0.481804 | − | 1.16318i | ||||
\(782\) | 28687.3 | − | 8487.26i | 1.31184 | − | 0.388112i | ||||
\(783\) | − | 1977.17i | − | 0.0902406i | ||||||
\(784\) | −4703.88 | − | 2101.76i | −0.214280 | − | 0.0957435i | ||||
\(785\) | 16130.0i | 0.733381i | ||||||||
\(786\) | 1500.61 | + | 5072.13i | 0.0680979 | + | 0.230174i | ||||
\(787\) | −6144.82 | − | 14834.9i | −0.278321 | − | 0.671927i | 0.721468 | − | 0.692448i | \(-0.243468\pi\) |
−0.999789 | + | 0.0205203i | \(0.993468\pi\) | |||||||
\(788\) | 6381.08 | − | 1178.30i | 0.288473 | − | 0.0532679i | ||||
\(789\) | −8075.74 | − | 3345.08i | −0.364390 | − | 0.150935i | ||||
\(790\) | −5966.20 | + | 4828.07i | −0.268694 | + | 0.217437i | ||||
\(791\) | −13450.9 | + | 13450.9i | −0.604624 | + | 0.604624i | ||||
\(792\) | 18682.8 | − | 9496.04i | 0.838214 | − | 0.426044i | ||||
\(793\) | −1074.26 | − | 1074.26i | −0.0481060 | − | 0.0481060i | ||||
\(794\) | 13790.6 | + | 1454.06i | 0.616384 | + | 0.0649906i | ||||
\(795\) | −4157.17 | + | 10036.3i | −0.185458 | + | 0.447736i | ||||
\(796\) | 4502.89 | − | 21115.7i | 0.200503 | − | 0.940235i | ||||
\(797\) | −15066.3 | + | 6240.66i | −0.669605 | + | 0.277359i | −0.691474 | − | 0.722401i | \(-0.743038\pi\) |
0.0218691 | + | 0.999761i | \(0.493038\pi\) | |||||||
\(798\) | −2445.10 | − | 1328.63i | −0.108466 | − | 0.0589385i | ||||
\(799\) | 60205.5 | 2.66573 | ||||||||
\(800\) | 4085.88 | − | 30643.7i | 0.180572 | − | 1.35427i | ||||
\(801\) | 9580.85 | 0.422625 | ||||||||
\(802\) | −37260.5 | − | 20246.8i | −1.64054 | − | 0.891445i | ||||
\(803\) | −28385.3 | + | 11757.6i | −1.24744 | + | 0.516708i | ||||
\(804\) | 2455.79 | + | 523.692i | 0.107723 | + | 0.0229716i | ||||
\(805\) | −13866.8 | + | 33477.5i | −0.607132 | + | 1.46575i | ||||
\(806\) | −14116.2 | − | 1488.39i | −0.616902 | − | 0.0650452i | ||||
\(807\) | 3474.60 | + | 3474.60i | 0.151563 | + | 0.151563i | ||||
\(808\) | −10726.2 | + | 32900.9i | −0.467015 | + | 1.43249i | ||||
\(809\) | 2211.65 | − | 2211.65i | 0.0961154 | − | 0.0961154i | −0.657414 | − | 0.753529i | \(-0.728350\pi\) |
0.753529 | + | 0.657414i | \(0.228350\pi\) | |||||||
\(810\) | −21087.0 | + | 17064.4i | −0.914720 | + | 0.740225i | ||||
\(811\) | 19941.1 | + | 8259.86i | 0.863410 | + | 0.357636i | 0.770040 | − | 0.637995i | \(-0.220236\pi\) |
0.0933697 | + | 0.995632i | \(0.470236\pi\) | |||||||
\(812\) | −773.556 | − | 4189.20i | −0.0334317 | − | 0.181049i | ||||
\(813\) | −670.782 | − | 1619.41i | −0.0289365 | − | 0.0698588i | ||||
\(814\) | −1411.41 | − | 4770.65i | −0.0607740 | − | 0.205419i | ||||
\(815\) | 13876.9i | 0.596425i | ||||||||
\(816\) | −9744.47 | − | 268.067i | −0.418045 | − | 0.0115003i | ||||
\(817\) | − | 16056.5i | − | 0.687571i | ||||||
\(818\) | 32413.7 | − | 9589.71i | 1.38547 | − | 0.409898i | ||||
\(819\) | −7864.04 | − | 18985.5i | −0.335521 | − | 0.810020i | ||||
\(820\) | 4979.20 | − | 7234.52i | 0.212050 | − | 0.308098i | ||||
\(821\) | −13446.8 | − | 5569.86i | −0.571617 | − | 0.236772i | 0.0781027 | − | 0.996945i | \(-0.475114\pi\) |
−0.649720 | + | 0.760174i | \(0.725114\pi\) | |||||||
\(822\) | 3509.66 | + | 4337.00i | 0.148921 | + | 0.184027i | ||||
\(823\) | 23548.4 | − | 23548.4i | 0.997383 | − | 0.997383i | −0.00261392 | − | 0.999997i | \(-0.500832\pi\) |
0.999997 | + | 0.00261392i | \(0.000832037\pi\) | |||||||
\(824\) | −27234.6 | − | 23307.4i | −1.15141 | − | 0.985376i | ||||
\(825\) | 6642.39 | + | 6642.39i | 0.280313 | + | 0.280313i | ||||
\(826\) | 2277.59 | − | 21601.1i | 0.0959413 | − | 0.909926i | ||||
\(827\) | −6650.02 | + | 16054.6i | −0.279618 | + | 0.675057i | −0.999825 | − | 0.0187017i | \(-0.994047\pi\) |
0.720207 | + | 0.693759i | \(0.244047\pi\) | |||||||
\(828\) | −17061.0 | + | 11063.5i | −0.716074 | + | 0.464351i | ||||
\(829\) | 1367.19 | − | 566.309i | 0.0572792 | − | 0.0237258i | −0.353860 | − | 0.935298i | \(-0.615131\pi\) |
0.411139 | + | 0.911573i | \(0.365131\pi\) | |||||||
\(830\) | 3309.59 | − | 6090.69i | 0.138406 | − | 0.254712i | ||||
\(831\) | −6116.00 | −0.255309 | ||||||||
\(832\) | 10725.4 | + | 17580.4i | 0.446918 | + | 0.732563i | ||||
\(833\) | 8316.57 | 0.345921 | ||||||||
\(834\) | −2831.59 | + | 5211.03i | −0.117566 | + | 0.216359i | ||||
\(835\) | −16667.7 | + | 6903.97i | −0.690788 | + | 0.286134i | ||||
\(836\) | 8120.20 | − | 5265.69i | 0.335937 | − | 0.217844i | ||||
\(837\) | −3648.36 | + | 8807.91i | −0.150664 | + | 0.363735i | ||||
\(838\) | −1007.02 | + | 9550.75i | −0.0415117 | + | 0.393705i | ||||
\(839\) | −10926.4 | − | 10926.4i | −0.449609 | − | 0.449609i | 0.445616 | − | 0.895224i | \(-0.352985\pi\) |
−0.895224 | + | 0.445616i | \(0.852985\pi\) | |||||||
\(840\) | 7677.10 | − | 8970.69i | 0.315339 | − | 0.368474i | ||||
\(841\) | −16772.2 | + | 16772.2i | −0.687694 | + | 0.687694i | ||||
\(842\) | −15966.5 | − | 19730.3i | −0.653494 | − | 0.807544i | ||||
\(843\) | −443.149 | − | 183.558i | −0.0181054 | − | 0.00749951i | ||||
\(844\) | −11494.9 | + | 16701.5i | −0.468804 | + | 0.681148i | ||||
\(845\) | −3811.78 | − | 9202.46i | −0.155183 | − | 0.374644i | ||||
\(846\) | −39240.1 | + | 11609.3i | −1.59468 | + | 0.471793i | ||||
\(847\) | 1252.17i | 0.0507969i | ||||||||
\(848\) | −19914.0 | + | 18847.6i | −0.806425 | + | 0.763244i | ||||
\(849\) | − | 1563.20i | − | 0.0631905i | ||||||
\(850\) | 14157.5 | + | 47853.1i | 0.571292 | + | 1.93100i | ||||
\(851\) | 1847.23 | + | 4459.60i | 0.0744091 | + | 0.179640i | ||||
\(852\) | −1577.55 | − | 8543.22i | −0.0634342 | − | 0.343528i | ||||
\(853\) | −8874.25 | − | 3675.84i | −0.356212 | − | 0.147548i | 0.197399 | − | 0.980323i | \(-0.436751\pi\) |
−0.553611 | + | 0.832775i | \(0.686751\pi\) | |||||||
\(854\) | −1709.02 | + | 1383.01i | −0.0684797 | + | 0.0554162i | ||||
\(855\) | −9790.08 | + | 9790.08i | −0.391595 | + | 0.391595i | ||||
\(856\) | 38785.0 | + | 12644.6i | 1.54865 | + | 0.504886i | ||||
\(857\) | −16585.9 | − | 16585.9i | −0.661100 | − | 0.661100i | 0.294539 | − | 0.955639i | \(-0.404834\pi\) |
−0.955639 | + | 0.294539i | \(0.904834\pi\) | |||||||
\(858\) | −6223.11 | − | 656.156i | −0.247615 | − | 0.0261081i | ||||
\(859\) | 8809.72 | − | 21268.5i | 0.349923 | − | 0.844788i | −0.646706 | − | 0.762740i | \(-0.723854\pi\) |
0.996628 | − | 0.0820486i | \(-0.0261463\pi\) | |||||||
\(860\) | 66629.5 | + | 14208.6i | 2.64192 | + | 0.563383i | ||||
\(861\) | 1789.29 | − | 741.148i | 0.0708233 | − | 0.0293360i | ||||
\(862\) | 38210.9 | + | 20763.2i | 1.50983 | + | 0.820415i | ||||
\(863\) | −19940.2 | −0.786527 | −0.393263 | − | 0.919426i | \(-0.628654\pi\) | ||||
−0.393263 | + | 0.919426i | \(0.628654\pi\) | |||||||
\(864\) | 13366.3 | − | 3557.81i | 0.526309 | − | 0.140092i | ||||
\(865\) | −1545.72 | −0.0607584 | ||||||||
\(866\) | 31122.3 | + | 16911.3i | 1.22122 | + | 0.663592i | ||||
\(867\) | 7845.74 | − | 3249.81i | 0.307330 | − | 0.127300i | ||||
\(868\) | −4284.03 | + | 20089.4i | −0.167522 | + | 0.785576i | ||||
\(869\) | 2252.60 | − | 5438.25i | 0.0879333 | − | 0.212290i | ||||
\(870\) | 1845.55 | + | 194.592i | 0.0719194 | + | 0.00758308i | ||||
\(871\) | 6054.94 | + | 6054.94i | 0.235550 | + | 0.235550i | ||||
\(872\) | 9183.73 | + | 18068.4i | 0.356652 | + | 0.701688i | ||||
\(873\) | −13848.5 | + | 13848.5i | −0.536887 | + | 0.536887i | ||||
\(874\) | −7299.46 | + | 5906.99i | −0.282504 | + | 0.228612i | ||||
\(875\) | −14970.2 | − | 6200.86i | −0.578383 | − | 0.239574i | ||||
\(876\) | −9551.97 | + | 1763.82i | −0.368414 | + | 0.0680296i | ||||
\(877\) | 11501.0 | + | 27765.8i | 0.442828 | + | 1.06908i | 0.974952 | + | 0.222414i | \(0.0713938\pi\) |
−0.532125 | + | 0.846666i | \(0.678606\pi\) | |||||||
\(878\) | −7591.06 | − | 25658.1i | −0.291783 | − | 0.986242i | ||||
\(879\) | − | 2367.03i | − | 0.0908280i | ||||||
\(880\) | 14665.3 | + | 38356.0i | 0.561782 | + | 1.46930i | ||||
\(881\) | − | 18012.3i | − | 0.688821i | −0.938819 | − | 0.344410i | \(-0.888079\pi\) | ||
0.938819 | − | 0.344410i | \(-0.111921\pi\) | |||||||
\(882\) | −5420.49 | + | 1603.67i | −0.206936 | + | 0.0612228i | ||||
\(883\) | −6581.16 | − | 15888.3i | −0.250819 | − | 0.605532i | 0.747451 | − | 0.664317i | \(-0.231277\pi\) |
−0.998271 | + | 0.0587851i | \(0.981277\pi\) | |||||||
\(884\) | −27383.9 | − | 18847.1i | −1.04188 | − | 0.717078i | ||||
\(885\) | 8741.91 | + | 3621.02i | 0.332041 | + | 0.137536i | ||||
\(886\) | −5729.48 | − | 7080.11i | −0.217252 | − | 0.268466i | ||||
\(887\) | −2226.45 | + | 2226.45i | −0.0842806 | + | 0.0842806i | −0.747990 | − | 0.663710i | \(-0.768981\pi\) |
0.663710 | + | 0.747990i | \(0.268981\pi\) | |||||||
\(888\) | −121.850 | − | 1568.14i | −0.00460476 | − | 0.0592606i | ||||
\(889\) | 8291.96 | + | 8291.96i | 0.312827 | + | 0.312827i | ||||
\(890\) | −1968.44 | + | 18669.1i | −0.0741374 | + | 0.703133i | ||||
\(891\) | 7961.61 | − | 19221.0i | 0.299353 | − | 0.722703i | ||||
\(892\) | 1164.23 | + | 1795.35i | 0.0437009 | + | 0.0673910i | ||||
\(893\) | −17458.7 | + | 7231.64i | −0.654237 | + | 0.270994i | ||||
\(894\) | −5254.34 | + | 9669.66i | −0.196567 | + | 0.361747i | ||||
\(895\) | −63045.1 | −2.35460 | ||||||||
\(896\) | 26928.3 | − | 12767.7i | 1.00403 | − | 0.476048i | ||||
\(897\) | 6071.43 | 0.225997 | ||||||||
\(898\) | −3329.83 | + | 6127.95i | −0.123739 | + | 0.227720i | ||||
\(899\) | −2982.75 | + | 1235.49i | −0.110657 | + | 0.0458354i | ||||
\(900\) | −18454.9 | − | 28459.2i | −0.683514 | − | 1.05404i | ||||
\(901\) | 16937.6 | − | 40891.1i | 0.626276 | − | 1.51196i | ||||
\(902\) | −706.280 | + | 6698.50i | −0.0260716 | + | 0.247268i | ||||
\(903\) | 10623.3 | + | 10623.3i | 0.391497 | + | 0.391497i | ||||
\(904\) | −1620.34 | − | 20852.9i | −0.0596148 | − | 0.767208i | ||||
\(905\) | 6645.49 | − | 6645.49i | 0.244092 | − | 0.244092i | ||||
\(906\) | −3238.59 | − | 4002.03i | −0.118758 | − | 0.146754i | ||||
\(907\) | 43002.0 | + | 17812.0i | 1.57427 | + | 0.652082i | 0.987492 | − | 0.157668i | \(-0.0503977\pi\) |
0.586774 | + | 0.809751i | \(0.300398\pi\) | |||||||
\(908\) | 5148.21 | + | 3543.28i | 0.188160 | + | 0.129502i | ||||
\(909\) | 14529.8 | + | 35077.9i | 0.530167 | + | 1.27994i | ||||
\(910\) | 38610.5 | − | 11423.1i | 1.40651 | − | 0.416121i | ||||
\(911\) | − | 13008.4i | − | 0.473094i | −0.971620 | − | 0.236547i | \(-0.923984\pi\) | ||
0.971620 | − | 0.236547i | \(-0.0760156\pi\) | |||||||
\(912\) | 2857.96 | − | 1092.73i | 0.103768 | − | 0.0396754i | ||||
\(913\) | 5316.32i | 0.192710i | ||||||||
\(914\) | −817.778 | − | 2764.13i | −0.0295948 | − | 0.100032i | ||||
\(915\) | −366.508 | − | 884.828i | −0.0132419 | − | 0.0319689i | ||||
\(916\) | 28849.3 | − | 5327.16i | 1.04062 | − | 0.192155i | ||||
\(917\) | 24116.2 | + | 9989.25i | 0.868469 | + | 0.359732i | ||||
\(918\) | −17356.3 | + | 14045.3i | −0.624011 | + | 0.504973i | ||||
\(919\) | −16677.5 | + | 16677.5i | −0.598628 | + | 0.598628i | −0.939947 | − | 0.341319i | \(-0.889126\pi\) |
0.341319 | + | 0.939947i | \(0.389126\pi\) | |||||||
\(920\) | −18052.8 | − | 35517.7i | −0.646939 | − | 1.27281i | ||||
\(921\) | −5879.06 | − | 5879.06i | −0.210338 | − | 0.210338i | ||||
\(922\) | 696.182 | + | 73.4044i | 0.0248672 | + | 0.00262196i | ||||
\(923\) | 11337.5 | − | 27371.2i | 0.404312 | − | 0.976095i | ||||
\(924\) | −1888.61 | + | 8856.39i | −0.0672409 | + | 0.315318i | ||||
\(925\) | −7439.02 | + | 3081.34i | −0.264425 | + | 0.109529i | ||||
\(926\) | 17345.5 | + | 9425.25i | 0.615559 | + | 0.334485i | ||||
\(927\) | −39329.8 | −1.39348 | ||||||||
\(928\) | 4052.61 | + | 2348.72i | 0.143355 | + | 0.0830823i | ||||
\(929\) | 24373.6 | 0.860786 | 0.430393 | − | 0.902642i | \(-0.358375\pi\) | ||||
0.430393 | + | 0.902642i | \(0.358375\pi\) | |||||||
\(930\) | −7862.47 | − | 4272.34i | −0.277226 | − | 0.150640i | ||||
\(931\) | −2411.69 | + | 998.953i | −0.0848978 | + | 0.0351658i | ||||
\(932\) | −1056.17 | − | 225.226i | −0.0371202 | − | 0.00791581i | ||||
\(933\) | −145.473 | + | 351.203i | −0.00510458 | + | 0.0123235i | ||||
\(934\) | 5848.81 | + | 616.690i | 0.204902 | + | 0.0216046i | ||||
\(935\) | −46871.5 | − | 46871.5i | −1.63942 | − | 1.63942i | ||||
\(936\) | 21482.3 | + | 7003.58i | 0.750181 | + | 0.244572i | ||||
\(937\) | −3495.17 | + | 3495.17i | −0.121859 | + | 0.121859i | −0.765406 | − | 0.643547i | \(-0.777462\pi\) |
0.643547 | + | 0.765406i | \(0.277462\pi\) | |||||||
\(938\) | 9632.72 | − | 7795.15i | 0.335309 | − | 0.271344i | ||||
\(939\) | −7188.83 | − | 2977.71i | −0.249839 | − | 0.103487i | ||||
\(940\) | −14559.6 | − | 78847.8i | −0.505195 | − | 2.73588i | ||||
\(941\) | 15711.1 | + | 37929.9i | 0.544279 | + | 1.31401i | 0.921678 | + | 0.387955i | \(0.126818\pi\) |
−0.377400 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(942\) | −1109.56 | − | 3750.36i | −0.0383772 | − | 0.129717i | ||||
\(943\) | − | 6535.24i | − | 0.225680i | ||||||
\(944\) | 16416.9 | + | 17345.7i | 0.566021 | + | 0.598044i | ||||
\(945\) | − | 27043.6i | − | 0.930928i | ||||||
\(946\) | −50103.4 | + | 14823.3i | −1.72199 | + | 0.509457i | ||||
\(947\) | 3104.11 | + | 7493.99i | 0.106515 | + | 0.257151i | 0.968147 | − | 0.250384i | \(-0.0805568\pi\) |
−0.861631 | + | 0.507535i | \(0.830557\pi\) | |||||||
\(948\) | 1055.08 | − | 1532.97i | 0.0361469 | − | 0.0525197i | ||||
\(949\) | −30603.1 | − | 12676.2i | −1.04681 | − | 0.433601i | ||||
\(950\) | −9853.39 | − | 12176.2i | −0.336512 | − | 0.415839i | ||||
\(951\) | −3318.20 | + | 3318.20i | −0.113144 | + | 0.113144i | ||||
\(952\) | −31279.0 | + | 36549.5i | −1.06487 | + | 1.24430i | ||||
\(953\) | −16440.0 | − | 16440.0i | −0.558808 | − | 0.558808i | 0.370160 | − | 0.928968i | \(-0.379303\pi\) |
−0.928968 | + | 0.370160i | \(0.879303\pi\) | |||||||
\(954\) | −3154.47 | + | 29917.6i | −0.107054 | + | 1.01532i | ||||
\(955\) | −116.439 | + | 281.108i | −0.00394541 | + | 0.00952506i | ||||
\(956\) | 14836.2 | − | 9620.79i | 0.501921 | − | 0.325480i | ||||
\(957\) | −1314.94 | + | 544.665i | −0.0444158 | + | 0.0183976i | ||||
\(958\) | 1314.98 | − | 2419.99i | 0.0443478 | − | 0.0816141i | ||||
\(959\) | 27532.9 | 0.927095 | ||||||||
\(960\) | 2005.46 | + | 12826.6i | 0.0674227 | + | 0.431226i | ||||
\(961\) | −14223.7 | −0.477449 | ||||||||
\(962\) | 2560.92 | − | 4712.92i | 0.0858290 | − | 0.157953i | ||||
\(963\) | 41351.4 | − | 17128.3i | 1.38373 | − | 0.573159i | ||||
\(964\) | −20332.4 | + | 13184.9i | −0.679317 | + | 0.440515i | ||||
\(965\) | −21861.4 | + | 52778.0i | −0.729267 | + | 1.76061i | ||||
\(966\) | 921.288 | − | 8737.67i | 0.0306853 | − | 0.291025i | ||||
\(967\) | 25408.6 | + | 25408.6i | 0.844968 | + | 0.844968i | 0.989500 | − | 0.144532i | \(-0.0461677\pi\) |
−0.144532 | + | 0.989500i | \(0.546168\pi\) | |||||||
\(968\) | −1046.04 | − | 895.197i | −0.0347324 | − | 0.0297239i | ||||
\(969\) | −3492.45 | + | 3492.45i | −0.115783 | + | 0.115783i | ||||
\(970\) | −24139.8 | − | 29830.3i | −0.799052 | − | 0.987415i | ||||
\(971\) | −33005.6 | − | 13671.4i | −1.09083 | − | 0.451838i | −0.236536 | − | 0.971623i | \(-0.576012\pi\) |
−0.854297 | + | 0.519785i | \(0.826012\pi\) | |||||||
\(972\) | 13086.4 | − | 19013.8i | 0.431837 | − | 0.627437i | ||||
\(973\) | 11200.2 | + | 27039.6i | 0.369025 | + | 0.890905i | ||||
\(974\) | −43649.0 | + | 12913.7i | −1.43594 | + | 0.424828i | ||||
\(975\) | 10127.7i | 0.332662i | ||||||||
\(976\) | 66.4749 | − | 2416.42i | 0.00218013 | − | 0.0792498i | ||||
\(977\) | − | 23994.9i | − | 0.785738i | −0.919594 | − | 0.392869i | \(-0.871483\pi\) | ||
0.919594 | − | 0.392869i | \(-0.128517\pi\) | |||||||
\(978\) | −954.570 | − | 3226.49i | −0.0312104 | − | 0.105493i | ||||
\(979\) | −5509.70 | − | 13301.6i | −0.179868 | − | 0.434239i | ||||
\(980\) | −2011.22 | − | 10891.8i | −0.0655571 | − | 0.355025i | ||||
\(981\) | 20545.2 | + | 8510.11i | 0.668663 | + | 0.276969i | ||||
\(982\) | −3318.83 | + | 2685.72i | −0.107849 | + | 0.0872757i | ||||
\(983\) | 11434.9 | − | 11434.9i | 0.371023 | − | 0.371023i | −0.496827 | − | 0.867850i | \(-0.665502\pi\) |
0.867850 | + | 0.496827i | \(0.165502\pi\) | |||||||
\(984\) | −660.053 | + | 2024.60i | −0.0213839 | + | 0.0655913i | ||||
\(985\) | 9864.06 | + | 9864.06i | 0.319081 | + | 0.319081i | ||||
\(986\) | −7519.35 | − | 792.830i | −0.242865 | − | 0.0256074i | ||||
\(987\) | 6766.46 | − | 16335.7i | 0.218215 | − | 0.526819i | ||||
\(988\) | 10204.8 | + | 2176.15i | 0.328600 | + | 0.0700734i | ||||
\(989\) | 46836.7 | − | 19400.4i | 1.50589 | − | 0.623758i | ||||
\(990\) | 39587.6 | + | 21511.3i | 1.27089 | + | 0.690579i | ||||
\(991\) | 49651.4 | 1.59155 | 0.795777 | − | 0.605590i | \(-0.207063\pi\) | ||||
0.795777 | + | 0.605590i | \(0.207063\pi\) | |||||||
\(992\) | −13719.6 | − | 17941.1i | −0.439111 | − | 0.574224i | ||||
\(993\) | 9445.29 | 0.301850 | ||||||||
\(994\) | −37670.8 | − | 20469.7i | −1.20206 | − | 0.653179i | ||||
\(995\) | 42881.9 | − | 17762.3i | 1.36628 | − | 0.565932i | ||||
\(996\) | −350.537 | + | 1643.80i | −0.0111518 | + | 0.0522949i | ||||
\(997\) | 13807.6 | − | 33334.5i | 0.438607 | − | 1.05889i | −0.537823 | − | 0.843058i | \(-0.680753\pi\) |
0.976430 | − | 0.215833i | \(-0.0692468\pi\) | |||||||
\(998\) | 39909.5 | + | 4208.00i | 1.26585 | + | 0.133469i | ||||
\(999\) | −2547.37 | − | 2547.37i | −0.0806760 | − | 0.0806760i |
(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.21.8 | ✓ | 44 | |
4.3 | odd | 2 | 128.4.g.a.49.6 | 44 | |||
8.3 | odd | 2 | 256.4.g.a.97.6 | 44 | |||
8.5 | even | 2 | 256.4.g.b.97.6 | 44 | |||
32.3 | odd | 8 | 128.4.g.a.81.6 | 44 | |||
32.13 | even | 8 | 256.4.g.b.161.6 | 44 | |||
32.19 | odd | 8 | 256.4.g.a.161.6 | 44 | |||
32.29 | even | 8 | inner | 32.4.g.a.29.8 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.8 | ✓ | 44 | 1.1 | even | 1 | trivial | |
32.4.g.a.29.8 | yes | 44 | 32.29 | even | 8 | inner | |
128.4.g.a.49.6 | 44 | 4.3 | odd | 2 | |||
128.4.g.a.81.6 | 44 | 32.3 | odd | 8 | |||
256.4.g.a.97.6 | 44 | 8.3 | odd | 2 | |||
256.4.g.a.161.6 | 44 | 32.19 | odd | 8 | |||
256.4.g.b.97.6 | 44 | 8.5 | even | 2 | |||
256.4.g.b.161.6 | 44 | 32.13 | even | 8 |