Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(41,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.t (of order \(16\), degree \(8\), 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: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{16})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Character | \(\chi\) | \(=\) | 136.73 |
Dual form | 136.3.t.a.41.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.265432 | + | 0.397247i | 0.0884774 | + | 0.132416i | 0.873068 | − | 0.487598i | \(-0.162127\pi\) |
−0.784591 | + | 0.620014i | \(0.787127\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.373441 | − | 1.87742i | 0.0746883 | − | 0.375483i | −0.925305 | − | 0.379224i | \(-0.876191\pi\) |
0.999993 | + | 0.00374117i | \(0.00119085\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10274 | − | 10.5712i | −0.300391 | − | 1.51017i | −0.776125 | − | 0.630579i | \(-0.782817\pi\) |
0.475733 | − | 0.879589i | \(-0.342183\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.35680 | − | 8.10403i | 0.372978 | − | 0.900448i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.50678 | + | 3.67951i | 0.500617 | + | 0.334501i | 0.780106 | − | 0.625648i | \(-0.215165\pi\) |
−0.279489 | + | 0.960149i | \(0.590165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.0115 | + | 17.0115i | 1.30857 | + | 1.30857i | 0.922444 | + | 0.386130i | \(0.126188\pi\) |
0.386130 | + | 0.922444i | \(0.373812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.844922 | − | 0.349978i | 0.0563281 | − | 0.0233319i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.468896 | − | 16.9935i | −0.0275821 | − | 0.999620i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.7274 | − | 30.7266i | −0.669861 | − | 1.61719i | −0.781841 | − | 0.623478i | \(-0.785719\pi\) |
0.111979 | − | 0.993711i | \(-0.464281\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.64124 | − | 3.64124i | 0.173392 | − | 0.173392i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14.4543 | + | 21.6324i | −0.628447 | + | 0.940537i | 0.371480 | + | 0.928441i | \(0.378850\pi\) |
−0.999927 | + | 0.0120962i | \(0.996150\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.7118 | + | 8.16488i | 0.788470 | + | 0.326595i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.32757 | − | 1.65646i | 0.308429 | − | 0.0613503i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.90826 | + | 0.777401i | 0.134768 | + | 0.0268069i | 0.262013 | − | 0.965064i | \(-0.415614\pi\) |
−0.127246 | + | 0.991871i | \(0.540614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.8342 | + | 20.6027i | −0.994651 | + | 0.664604i | −0.942560 | − | 0.334038i | \(-0.891589\pi\) |
−0.0520911 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.16422i | 0.0958853i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.6318 | −0.589479 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.24177 | − | 13.8313i | −0.249777 | − | 0.373818i | 0.685301 | − | 0.728260i | \(-0.259671\pi\) |
−0.935078 | + | 0.354442i | \(0.884671\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.24237 | + | 11.2732i | −0.0574966 | + | 0.289055i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.9213 | + | 69.9870i | 0.339543 | + | 1.70700i | 0.652968 | + | 0.757386i | \(0.273524\pi\) |
−0.313424 | + | 0.949613i | \(0.601476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.281866 | + | 0.680485i | −0.00655502 | + | 0.0158252i | −0.927123 | − | 0.374757i | \(-0.877726\pi\) |
0.920568 | + | 0.390582i | \(0.127726\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.9611 | − | 9.32849i | −0.310246 | − | 0.207300i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.20162 | − | 9.20162i | −0.195779 | − | 0.195779i | 0.602409 | − | 0.798188i | \(-0.294208\pi\) |
−0.798188 | + | 0.602409i | \(0.794208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −62.0583 | + | 25.7054i | −1.26650 | + | 0.524600i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.62618 | − | 4.69690i | 0.129925 | − | 0.0920960i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1255 | + | 24.4451i | 0.191047 | + | 0.461228i | 0.990158 | − | 0.139956i | \(-0.0446961\pi\) |
−0.799111 | + | 0.601184i | \(0.794696\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.96444 | − | 8.96444i | 0.162990 | − | 0.162990i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.82780 | − | 13.2117i | 0.154874 | − | 0.231785i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 81.0988 | + | 33.5922i | 1.37456 | + | 0.569360i | 0.943020 | − | 0.332736i | \(-0.107972\pi\) |
0.431536 | + | 0.902096i | \(0.357972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −44.2798 | + | 8.80781i | −0.725899 | + | 0.144390i | −0.544190 | − | 0.838962i | \(-0.683163\pi\) |
−0.181709 | + | 0.983352i | \(0.558163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −92.7277 | − | 18.4447i | −1.47187 | − | 0.292773i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 38.2904 | − | 25.5848i | 0.589083 | − | 0.393613i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33.0049i | 0.492611i | 0.969192 | + | 0.246305i | \(0.0792166\pi\) | ||||
−0.969192 | + | 0.246305i | \(0.920783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.4300 | −0.180145 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.6401 | + | 74.2917i | 0.699156 | + | 1.04636i | 0.995816 | + | 0.0913783i | \(0.0291272\pi\) |
−0.296660 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17.0394 | − | 85.6629i | 0.233417 | − | 1.17346i | −0.669221 | − | 0.743063i | \(-0.733372\pi\) |
0.902638 | − | 0.430401i | \(-0.141628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.98866 | + | 9.99766i | 0.0265155 | + | 0.133302i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.3175 | − | 65.9503i | 0.354773 | − | 0.856497i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.2534 | − | 11.5284i | −0.218397 | − | 0.145928i | 0.441559 | − | 0.897232i | \(-0.354425\pi\) |
−0.659957 | + | 0.751304i | \(0.729425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −52.9546 | − | 52.9546i | −0.653760 | − | 0.653760i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 128.971 | − | 53.4216i | 1.55387 | − | 0.643634i | 0.569858 | − | 0.821743i | \(-0.306998\pi\) |
0.984011 | + | 0.178110i | \(0.0569981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32.0790 | − | 5.46577i | −0.377400 | − | 0.0643032i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.728557 | + | 1.75889i | 0.00837422 | + | 0.0202172i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −67.9449 | + | 67.9449i | −0.763426 | + | 0.763426i | −0.976940 | − | 0.213514i | \(-0.931509\pi\) |
0.213514 | + | 0.976940i | \(0.431509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 144.061 | − | 215.602i | 1.58308 | − | 2.36925i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.3688 | − | 6.78016i | −0.176008 | − | 0.0729050i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −62.4395 | + | 12.4200i | −0.657258 | + | 0.130737i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 58.6948 | + | 11.6751i | 0.605101 | + | 0.120362i | 0.488127 | − | 0.872773i | \(-0.337680\pi\) |
0.116975 | + | 0.993135i | \(0.462680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 48.3041 | − | 32.2757i | 0.487920 | − | 0.326018i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 103.479i | 1.02454i | 0.858823 | + | 0.512272i | \(0.171196\pi\) | ||||
−0.858823 | + | 0.512272i | \(0.828804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78.0109 | 0.757388 | 0.378694 | − | 0.925522i | \(-0.376373\pi\) | ||||
0.378694 | + | 0.925522i | \(0.376373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.47633 | − | 8.19591i | −0.0521555 | − | 0.0780563i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8408 | + | 84.6645i | −0.157391 | + | 0.791257i | 0.818755 | + | 0.574142i | \(0.194664\pi\) |
−0.976146 | + | 0.217114i | \(0.930336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2232 | − | 56.4230i | −0.102965 | − | 0.517642i | −0.997501 | − | 0.0706462i | \(-0.977494\pi\) |
0.894536 | − | 0.446996i | \(-0.147506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.04138 | − | 7.34253i | 0.0273998 | − | 0.0661490i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −47.5393 | − | 31.7647i | −0.420701 | − | 0.281104i | 0.327147 | − | 0.944974i | \(-0.393913\pi\) |
−0.747848 | + | 0.663870i | \(0.768913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 35.2151 | + | 35.2151i | 0.306218 | + | 0.306218i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 194.966 | − | 80.7574i | 1.66637 | − | 0.690234i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −178.656 | + | 40.6897i | −1.50131 | + | 0.341931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.5189 | − | 71.2649i | −0.243958 | − | 0.588966i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.1070 | + | 24.1070i | −0.195992 | + | 0.195992i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 49.2768 | − | 73.7480i | 0.394215 | − | 0.589984i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 71.8403 | + | 29.7572i | 0.565672 | + | 0.234309i | 0.647145 | − | 0.762367i | \(-0.275963\pi\) |
−0.0814737 | + | 0.996675i | \(0.525963\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.345137 | + | 0.0686520i | −0.00267548 | + | 0.000532186i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.88727 | − | 1.56888i | −0.0602082 | − | 0.0119762i | 0.164894 | − | 0.986311i | \(-0.447272\pi\) |
−0.225102 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −298.054 | + | 199.153i | −2.24101 | + | 1.49739i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 16.2529i | − | 0.120392i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 23.5715 | 0.172055 | 0.0860273 | − | 0.996293i | \(-0.472583\pi\) | ||||
0.0860273 | + | 0.996293i | \(0.472583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −51.1133 | − | 76.4965i | −0.367722 | − | 0.550334i | 0.600757 | − | 0.799432i | \(-0.294866\pi\) |
−0.968478 | + | 0.249098i | \(0.919866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.21291 | − | 6.09773i | 0.00860222 | − | 0.0432463i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.0845 | + | 156.272i | 0.217374 | + | 1.09281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.91901 | − | 7.04711i | 0.0201311 | − | 0.0486008i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.6837 | − | 17.8295i | −0.181522 | − | 0.121289i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 88.3896 | + | 88.3896i | 0.593219 | + | 0.593219i | 0.938500 | − | 0.345281i | \(-0.112216\pi\) |
−0.345281 | + | 0.938500i | \(0.612216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −119.598 | + | 49.5393i | −0.792042 | + | 0.328075i | −0.741764 | − | 0.670661i | \(-0.766011\pi\) |
−0.0502780 | + | 0.998735i | \(0.516011\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −139.290 | − | 53.2439i | −0.910393 | − | 0.348000i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.1652 | + | 65.5825i | 0.175259 | + | 0.423113i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 57.7710 | − | 57.7710i | 0.367968 | − | 0.367968i | −0.498767 | − | 0.866736i | \(-0.666214\pi\) |
0.866736 | + | 0.498767i | \(0.166214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.02311 | + | 10.5108i | −0.0441705 | + | 0.0661058i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 259.073 | + | 107.312i | 1.60915 | + | 0.666532i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −46.3909 | + | 9.22773i | −0.284607 | + | 0.0566118i | −0.335329 | − | 0.942101i | \(-0.608848\pi\) |
0.0507224 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.94055 | + | 1.18165i | 0.0360033 | + | 0.00716151i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −75.3091 | + | 50.3200i | −0.450953 | + | 0.301317i | −0.760229 | − | 0.649655i | \(-0.774913\pi\) |
0.309276 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 409.780i | 2.42473i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −291.732 | −1.70604 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 94.0015 | + | 140.683i | 0.543362 | + | 0.813198i | 0.996952 | − | 0.0780120i | \(-0.0248573\pi\) |
−0.453591 | + | 0.891210i | \(0.649857\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 44.8637 | − | 225.545i | 0.256364 | − | 1.28883i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.18182 | + | 41.1328i | 0.0462249 | + | 0.232388i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 27.8092 | − | 67.1373i | 0.155359 | − | 0.375069i | −0.826967 | − | 0.562251i | \(-0.809935\pi\) |
0.982325 | + | 0.187182i | \(0.0599355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −236.027 | − | 157.708i | −1.30402 | − | 0.871316i | −0.307247 | − | 0.951630i | \(-0.599408\pi\) |
−0.996770 | + | 0.0803138i | \(0.974408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.2522 | − | 15.2522i | −0.0833452 | − | 0.0833452i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.4183 | + | 12.1855i | −0.159018 | + | 0.0658674i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 59.9458 | − | 95.3050i | 0.320566 | − | 0.509652i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35.0214 | − | 84.5492i | −0.185299 | − | 0.447350i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −37.6324 | + | 37.6324i | −0.197028 | + | 0.197028i | −0.798725 | − | 0.601696i | \(-0.794492\pi\) |
0.601696 | + | 0.798725i | \(0.294492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 67.4583 | − | 100.959i | 0.349525 | − | 0.523101i | −0.614499 | − | 0.788918i | \(-0.710642\pi\) |
0.964024 | + | 0.265817i | \(0.0856416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.3270 | + | 8.41972i | 0.104241 | + | 0.0431780i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.9297 | + | 3.76535i | −0.0960899 | + | 0.0191135i | −0.242901 | − | 0.970051i | \(-0.578099\pi\) |
0.146811 | + | 0.989165i | \(0.453099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −293.722 | − | 58.4248i | −1.47599 | − | 0.293592i | −0.609498 | − | 0.792788i | \(-0.708629\pi\) |
−0.866489 | + | 0.499195i | \(0.833629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1111 | + | 8.76057i | −0.0652294 | + | 0.0435849i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 42.9496i | − | 0.211574i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 136.593 | 0.666309 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 126.789 | + | 189.753i | 0.612508 | + | 0.916683i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42.9721 | − | 216.035i | 0.205608 | − | 1.03366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 59.3560 | + | 298.403i | 0.281308 | + | 1.41423i | 0.820306 | + | 0.571925i | \(0.193803\pi\) |
−0.538998 | + | 0.842307i | \(0.681197\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.3361 | + | 39.4388i | −0.0766952 | + | 0.185159i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.17229 | + | 0.783301i | 0.00545252 | + | 0.00364326i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 282.631 | + | 282.631i | 1.30245 | + | 1.30245i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 38.5522 | − | 15.9688i | 0.176037 | − | 0.0729170i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 281.108 | − | 297.062i | 1.27198 | − | 1.34417i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.53867 | + | 20.6142i | 0.0382900 | + | 0.0924402i | 0.941868 | − | 0.335984i | \(-0.109069\pi\) |
−0.903578 | + | 0.428424i | \(0.859069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 132.337 | − | 132.337i | 0.588164 | − | 0.588164i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 96.2583 | − | 144.061i | 0.424046 | − | 0.634629i | −0.556517 | − | 0.830836i | \(-0.687863\pi\) |
0.980562 | + | 0.196207i | \(0.0628626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 178.614 | + | 73.9844i | 0.779975 | + | 0.323076i | 0.736905 | − | 0.675996i | \(-0.236286\pi\) |
0.0430693 | + | 0.999072i | \(0.486286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.4495 | − | 6.65352i | 0.144803 | − | 0.0288031i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −217.735 | − | 43.3101i | −0.934484 | − | 0.185880i | −0.295713 | − | 0.955277i | \(-0.595557\pi\) |
−0.638772 | + | 0.769396i | \(0.720557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.7115 | + | 13.8390i | −0.0881342 | + | 0.0588894i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.91386i | − | 0.0418306i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −288.072 | −1.20532 | −0.602662 | − | 0.797997i | \(-0.705893\pi\) | ||||
−0.602662 | + | 0.797997i | \(0.705893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.653 | − | 222.476i | −0.616819 | − | 0.923135i | 0.383181 | − | 0.923673i | \(-0.374829\pi\) |
−1.00000 | 0.000538115i | \(0.999829\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.8883 | − | 110.040i | 0.0900755 | − | 0.452840i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.0846 | + | 126.109i | 0.102386 | + | 0.514729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 306.193 | − | 739.215i | 1.23965 | − | 2.99277i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 55.4547 | + | 37.0536i | 0.222710 | + | 0.148810i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −89.2062 | − | 89.2062i | −0.355403 | − | 0.355403i | 0.506712 | − | 0.862115i | \(-0.330861\pi\) |
−0.862115 | + | 0.506712i | \(0.830861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −159.193 | + | 65.9399i | −0.629222 | + | 0.260632i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.34354 | − | 14.1941i | −0.0248766 | − | 0.0556632i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −163.366 | − | 394.401i | −0.635666 | − | 1.53463i | −0.832399 | − | 0.554177i | \(-0.813033\pi\) |
0.196732 | − | 0.980457i | \(-0.436967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −126.780 | + | 126.780i | −0.489498 | + | 0.489498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.4193 | − | 29.0631i | 0.0744035 | − | 0.111353i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 295.151 | + | 122.256i | 1.12225 | + | 0.464851i | 0.865139 | − | 0.501532i | \(-0.167230\pi\) |
0.257109 | + | 0.966382i | \(0.417230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 49.6748 | − | 9.88094i | 0.187452 | − | 0.0372866i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −45.0257 | − | 8.95617i | −0.168636 | − | 0.0335437i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −203.053 | + | 135.676i | −0.754845 | + | 0.504371i | −0.872459 | − | 0.488688i | \(-0.837476\pi\) |
0.117613 | + | 0.993059i | \(0.462476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 97.8004i | − | 0.360887i | −0.983585 | − | 0.180444i | \(-0.942247\pi\) | ||
0.983585 | − | 0.180444i | \(-0.0577533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 123.886 | 0.453794 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 78.5056 | + | 117.492i | 0.285475 | + | 0.427243i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −45.1350 | + | 226.909i | −0.162942 | + | 0.819165i | 0.809698 | + | 0.586847i | \(0.199631\pi\) |
−0.972640 | + | 0.232318i | \(0.925369\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 63.4611 | + | 319.040i | 0.227459 | + | 1.14351i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −51.6369 | + | 124.663i | −0.183761 | + | 0.443639i | −0.988736 | − | 0.149670i | \(-0.952179\pi\) |
0.804975 | + | 0.593309i | \(0.202179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 253.922 | + | 169.665i | 0.897250 | + | 0.599524i | 0.916387 | − | 0.400293i | \(-0.131092\pi\) |
−0.0191367 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.5073 | − | 21.5073i | −0.0754641 | − | 0.0754641i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 710.572 | − | 294.329i | 2.47586 | − | 1.02554i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.560 | + | 15.9364i | −0.998478 | + | 0.0551433i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9416 | + | 26.4153i | 0.0376000 | + | 0.0907743i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 168.378 | − | 168.378i | 0.574670 | − | 0.574670i | −0.358760 | − | 0.933430i | \(-0.616800\pi\) |
0.933430 | + | 0.358760i | \(0.116800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 93.3523 | − | 139.712i | 0.316448 | − | 0.473598i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 51.9531 | + | 21.5197i | 0.174926 | + | 0.0724568i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −613.887 | + | 122.110i | −2.05313 | + | 0.408393i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.78622 | + | 1.54877i | 0.0258678 | + | 0.00514543i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −41.1067 | + | 27.4667i | −0.135666 | + | 0.0906490i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 86.4209i | 0.283347i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 44.6453 | 0.145424 | 0.0727122 | − | 0.997353i | \(-0.476835\pi\) | ||||
0.0727122 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7066 | + | 30.9896i | 0.0670117 | + | 0.100290i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −62.4353 | + | 313.883i | −0.200757 | + | 1.00927i | 0.740623 | + | 0.671921i | \(0.234531\pi\) |
−0.941379 | + | 0.337350i | \(0.890469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −65.3551 | − | 328.563i | −0.208802 | − | 1.04972i | −0.932931 | − | 0.360055i | \(-0.882758\pi\) |
0.724129 | − | 0.689665i | \(-0.242242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −69.2567 | + | 167.200i | −0.219862 | + | 0.530795i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −443.228 | − | 296.155i | −1.39819 | − | 0.934244i | −0.999855 | − | 0.0170055i | \(-0.994587\pi\) |
−0.398339 | − | 0.917238i | \(-0.630413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.6615 | + | 18.6615i | 0.0584999 | + | 0.0584999i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.1028 | + | 15.7827i | −0.118700 | + | 0.0491673i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −516.185 | + | 230.691i | −1.59810 | + | 0.714212i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 196.429 | + | 474.222i | 0.604398 | + | 1.45915i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.4349 | − | 19.4349i | 0.0594339 | − | 0.0594339i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −77.9234 | + | 116.621i | −0.236849 | + | 0.354470i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 258.006 | + | 106.869i | 0.779474 | + | 0.322869i | 0.736703 | − | 0.676216i | \(-0.236382\pi\) |
0.0427705 | + | 0.999085i | \(0.486382\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −143.112 | + | 28.4667i | −0.429765 | + | 0.0854857i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 61.9640 | + | 12.3254i | 0.184967 | + | 0.0367922i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −203.212 | + | 135.782i | −0.603004 | + | 0.402914i | −0.819260 | − | 0.573422i | \(-0.805615\pi\) |
0.216256 | + | 0.976337i | \(0.430615\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 27.3162i | − | 0.0805788i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −245.605 | −0.720250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 108.812 | + | 162.849i | 0.317236 | + | 0.474778i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.64188 | + | 23.3363i | −0.0134547 | + | 0.0676415i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.1831 | − | 181.905i | −0.104274 | − | 0.524221i | −0.997250 | − | 0.0741157i | \(-0.976387\pi\) |
0.892976 | − | 0.450105i | \(-0.148613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 66.9162 | − | 161.550i | 0.191737 | − | 0.462894i | −0.798551 | − | 0.601928i | \(-0.794400\pi\) |
0.990288 | + | 0.139034i | \(0.0443996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 169.843 | + | 113.485i | 0.483883 | + | 0.323320i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −139.607 | − | 139.607i | −0.395487 | − | 0.395487i | 0.481151 | − | 0.876638i | \(-0.340219\pi\) |
−0.876638 | + | 0.481151i | \(0.840219\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 158.014 | − | 65.4516i | 0.445110 | − | 0.184371i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −63.5849 | − | 60.1702i | −0.178109 | − | 0.168544i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −129.099 | − | 311.672i | −0.359607 | − | 0.868168i | −0.995355 | − | 0.0962713i | \(-0.969308\pi\) |
0.635748 | − | 0.771896i | \(-0.280692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −526.871 | + | 526.871i | −1.45948 | + | 1.45948i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.4745 | − | 30.6423i | 0.0564036 | − | 0.0844140i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −154.462 | − | 63.9801i | −0.423183 | − | 0.175288i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 54.7504 | − | 10.8905i | 0.149184 | − | 0.0296745i | −0.119933 | − | 0.992782i | \(-0.538268\pi\) |
0.269117 | + | 0.963107i | \(0.413268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 613.907 | + | 122.114i | 1.66371 | + | 0.330932i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 237.122 | − | 158.440i | 0.639143 | − | 0.427062i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 327.522i | 0.878075i | 0.898469 | + | 0.439038i | \(0.144681\pi\) | ||||
−0.898469 | + | 0.439038i | \(0.855319\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 42.3758 | 0.113002 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.2605 | + | 79.7099i | 0.141274 | + | 0.211432i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −96.7322 | + | 486.306i | −0.255230 | + | 1.28313i | 0.614231 | + | 0.789127i | \(0.289466\pi\) |
−0.869461 | + | 0.494002i | \(0.835534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.24775 | + | 36.4369i | 0.0190230 | + | 0.0956349i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −109.953 | + | 265.451i | −0.287085 | + | 0.693084i | −0.999966 | − | 0.00820042i | \(-0.997390\pi\) |
0.712882 | + | 0.701284i | \(0.247390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −113.615 | − | 75.9148i | −0.295103 | − | 0.197181i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.56850 | + | 4.56850i | 0.0118049 | + | 0.0118049i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −439.801 | + | 182.172i | −1.13059 | + | 0.468307i | −0.867983 | − | 0.496595i | \(-0.834584\pi\) |
−0.262611 | + | 0.964902i | \(0.584584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 374.388 | + | 235.486i | 0.957513 | + | 0.602266i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.47030 | − | 3.54963i | −0.00374123 | − | 0.00903213i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.0866 | + | 28.0866i | −0.0711054 | + | 0.0711054i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 359.417 | − | 537.905i | 0.905331 | − | 1.35492i | −0.0293995 | − | 0.999568i | \(-0.509360\pi\) |
0.934731 | − | 0.355356i | \(-0.115640\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −158.226 | − | 65.5395i | −0.396557 | − | 0.164259i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 330.510 | − | 65.7426i | 0.824215 | − | 0.163947i | 0.235075 | − | 0.971977i | \(-0.424467\pi\) |
0.589140 | + | 0.808031i | \(0.299467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −875.017 | − | 174.052i | −2.17126 | − | 0.431890i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −119.193 | + | 79.6424i | −0.294304 | + | 0.196648i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 110.171i | − | 0.270691i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 290.067 | 0.709211 | 0.354606 | − | 0.935016i | \(-0.384615\pi\) | ||||
0.354606 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.25663 | + | 9.36371i | 0.0152229 | + | 0.0227827i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 184.580 | − | 927.946i | 0.446925 | − | 2.24684i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.1314 | − | 262.082i | −0.125618 | − | 0.631523i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8209 | − | 40.6093i | 0.0403379 | − | 0.0973843i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −414.289 | − | 276.819i | −0.988757 | − | 0.660666i | −0.0476814 | − | 0.998863i | \(-0.515183\pi\) |
−0.941076 | + | 0.338196i | \(0.890183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −53.7087 | − | 53.7087i | −0.127574 | − | 0.127574i | 0.640437 | − | 0.768011i | \(-0.278753\pi\) |
−0.768011 | + | 0.640437i | \(0.778753\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −105.458 | + | 43.6822i | −0.249310 | + | 0.103268i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 129.507 | − | 338.801i | 0.304723 | − | 0.797178i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186.218 | + | 449.570i | 0.436107 | + | 1.05286i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −53.8280 | + | 53.8280i | −0.125473 | + | 0.125473i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 288.768 | − | 432.172i | 0.669995 | − | 1.00272i | −0.328313 | − | 0.944569i | \(-0.606480\pi\) |
0.998308 | − | 0.0581497i | \(-0.0185201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2561 | + | 5.07664i | 0.0283050 | + | 0.0117243i | 0.396791 | − | 0.917909i | \(-0.370124\pi\) |
−0.368486 | + | 0.929633i | \(0.620124\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.57425 | − | 0.710962i | 0.00821666 | − | 0.00163439i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 848.653 | + | 168.808i | 1.94200 | + | 0.386287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 516.086 | − | 344.838i | 1.17560 | − | 0.785508i | 0.194857 | − | 0.980832i | \(-0.437576\pi\) |
0.980739 | + | 0.195324i | \(0.0625758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 589.210i | 1.33608i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 642.505 | 1.45035 | 0.725175 | − | 0.688564i | \(-0.241759\pi\) | ||||
0.725175 | + | 0.688564i | \(0.241759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 102.187 | + | 152.934i | 0.229635 | + | 0.343673i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.6511 | + | 58.5740i | −0.0260651 | + | 0.131038i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 49.3910 | + | 248.306i | 0.110002 | + | 0.553019i | 0.996002 | + | 0.0893328i | \(0.0284735\pi\) |
−0.886000 | + | 0.463686i | \(0.846527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −180.857 | + | 436.626i | −0.401012 | + | 0.968130i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −51.4246 | − | 34.3608i | −0.113520 | − | 0.0758517i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −350.976 | − | 350.976i | −0.771377 | − | 0.771377i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −254.389 | + | 105.372i | −0.556651 | + | 0.230572i | −0.643231 | − | 0.765673i | \(-0.722406\pi\) |
0.0865796 | + | 0.996245i | \(0.472406\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.0538 | − | 140.738i | −0.0698341 | − | 0.306619i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2863 | − | 61.0466i | −0.0548510 | − | 0.132422i | 0.894078 | − | 0.447910i | \(-0.147832\pi\) |
−0.948929 | + | 0.315488i | \(0.897832\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.6885 | + | 35.6885i | −0.0770810 | + | 0.0770810i | −0.744596 | − | 0.667515i | \(-0.767358\pi\) |
0.667515 | + | 0.744596i | \(0.267358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.8420 | + | 28.1990i | −0.0405203 | + | 0.0606430i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −420.363 | − | 174.120i | −0.900134 | − | 0.372848i | −0.115862 | − | 0.993265i | \(-0.536963\pi\) |
−0.784272 | + | 0.620418i | \(0.786963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 348.901 | − | 69.4007i | 0.743925 | − | 0.147976i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.2837 | + | 7.61510i | 0.0812817 | + | 0.0161679i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.05603 | + | 2.71015i | −0.00857511 | + | 0.00572971i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 709.592i | − | 1.49388i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 232.093 | 0.486568 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −322.559 | − | 482.744i | −0.673401 | − | 1.00782i | −0.998077 | − | 0.0619907i | \(-0.980255\pi\) |
0.324675 | − | 0.945825i | \(-0.394745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 78.0744 | − | 392.506i | 0.162317 | − | 0.816021i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.1371 | + | 131.400i | 0.0541141 | + | 0.272050i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.8382 | − | 105.835i | 0.0903879 | − | 0.218216i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 268.281 | + | 179.260i | 0.550886 | + | 0.368090i | 0.799643 | − | 0.600476i | \(-0.205022\pi\) |
−0.248757 | + | 0.968566i | \(0.580022\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.9793 | − | 15.9793i | −0.0326776 | − | 0.0326776i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.63585 | − | 2.74866i | 0.0135150 | − | 0.00559809i | −0.375916 | − | 0.926654i | \(-0.622672\pi\) |
0.389431 | + | 0.921056i | \(0.372672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3782 | − | 66.7796i | 0.0230795 | − | 0.135456i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −42.5563 | − | 102.740i | −0.0859723 | − | 0.207555i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 680.971 | − | 680.971i | 1.37016 | − | 1.37016i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −192.793 | + | 288.536i | −0.386360 | + | 0.578228i | −0.972766 | − | 0.231789i | \(-0.925542\pi\) |
0.586406 | + | 0.810017i | \(0.300542\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.9789 | − | 16.5598i | −0.0797983 | − | 0.0330535i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 320.681 | − | 63.7874i | 0.637537 | − | 0.126814i | 0.134270 | − | 0.990945i | \(-0.457131\pi\) |
0.503267 | + | 0.864131i | \(0.332131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 194.273 | + | 38.6433i | 0.384699 | + | 0.0765214i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −162.784 | + | 108.769i | −0.321073 | + | 0.214534i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 228.751i | 0.449414i | 0.974426 | + | 0.224707i | \(0.0721424\pi\) | ||||
−0.974426 | + | 0.224707i | \(0.927858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −941.388 | −1.84225 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −156.885 | − | 234.796i | −0.305819 | − | 0.457691i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.1325 | − | 146.459i | 0.0565680 | − | 0.284386i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.8138 | − | 84.5288i | −0.0325219 | − | 0.163499i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.9350 | + | 74.6837i | −0.0596050 | + | 0.143899i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 149.591 | + | 99.9538i | 0.287124 | + | 0.191850i | 0.690788 | − | 0.723057i | \(-0.257264\pi\) |
−0.403665 | + | 0.914907i | \(0.632264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.37150 | + | 4.37150i | 0.00835850 | + | 0.00835850i | 0.711274 | − | 0.702915i | \(-0.248119\pi\) |
−0.702915 | + | 0.711274i | \(0.748119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 101.506 | − | 42.0450i | 0.193344 | − | 0.0800856i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 364.571 | + | 514.321i | 0.691786 | + | 0.975941i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −56.5931 | − | 136.628i | −0.106981 | − | 0.258276i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 544.465 | − | 544.465i | 1.02536 | − | 1.02536i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −953.760 | + | 1427.40i | −1.78942 | + | 2.67805i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 152.661 | + | 63.2344i | 0.285348 | + | 0.118195i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.0516 | − | 6.77328i | 0.0634108 | − | 0.0126132i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −436.325 | − | 86.7904i | −0.809508 | − | 0.161021i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 344.826 | − | 230.405i | 0.637386 | − | 0.425888i | −0.194447 | − | 0.980913i | \(-0.562291\pi\) |
0.831834 | + | 0.555025i | \(0.187291\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 135.622i | − | 0.249764i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −110.121 | −0.202056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 232.255 | + | 347.595i | 0.424598 | + | 0.635456i | 0.980668 | − | 0.195679i | \(-0.0626912\pi\) |
−0.556070 | + | 0.831136i | \(0.687691\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −77.2598 | + | 388.411i | −0.140728 | + | 0.707489i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8550 | − | 129.982i | −0.0469237 | − | 0.235901i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −85.5889 | + | 206.630i | −0.154772 | + | 0.373653i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.6492 | − | 8.45194i | −0.0227914 | − | 0.0152287i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 678.412 | + | 678.412i | 1.21798 | + | 1.21798i | 0.968340 | + | 0.249635i | \(0.0803108\pi\) |
0.249635 | + | 0.968340i | \(0.419689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.3710 | + | 6.78109i | −0.0292862 | + | 0.0121307i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 53.7712 | − | 1.48369i | 0.0958489 | − | 0.00264472i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.9909 | + | 98.9608i | 0.0728080 | + | 0.175774i | 0.956094 | − | 0.293061i | \(-0.0946739\pi\) |
−0.883286 | + | 0.468835i | \(0.844674\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −77.3887 | + | 77.3887i | −0.136971 | + | 0.136971i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −448.443 | + | 671.142i | −0.790905 | + | 1.18367i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −438.626 | − | 181.685i | −0.770872 | − | 0.319305i | −0.0376462 | − | 0.999291i | \(-0.511986\pi\) |
−0.733225 | + | 0.679986i | \(0.761986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −481.393 | + | 95.7550i | −0.843069 | + | 0.167697i | −0.597687 | − | 0.801729i | \(-0.703913\pi\) |
−0.245382 | + | 0.969426i | \(0.578913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.9382 | − | 4.96053i | −0.0435223 | − | 0.00865711i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −461.545 | + | 308.394i | −0.802686 | + | 0.536338i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 460.619i | − | 0.798300i | −0.916886 | − | 0.399150i | \(-0.869305\pi\) | ||
0.916886 | − | 0.399150i | \(-0.130695\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 58.0111 | 0.100192 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −835.922 | − | 1251.05i | −1.43876 | − | 2.15326i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.1872 | + | 171.871i | −0.0586401 | + | 0.294804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −78.8070 | − | 396.190i | −0.134713 | − | 0.677247i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 153.696 | − | 371.056i | 0.261834 | − | 0.632122i | −0.737218 | − | 0.675655i | \(-0.763861\pi\) |
0.999052 | + | 0.0435322i | \(0.0138611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1025.49 | + | 685.210i | 1.74107 | + | 1.16334i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.52033 | − | 6.52033i | −0.0110327 | − | 0.0110327i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −285.847 | + | 118.402i | −0.482036 | + | 0.199666i | −0.610450 | − | 0.792055i | \(-0.709011\pi\) |
0.128414 | + | 0.991721i | \(0.459011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.67415 | + | 350.606i | 0.0162591 | + | 0.589254i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −54.7540 | − | 132.188i | −0.0917153 | − | 0.221420i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −710.965 | + | 710.965i | −1.18692 | + | 1.18692i | −0.209006 | + | 0.977914i | \(0.567023\pi\) |
−0.977914 | + | 0.209006i | \(0.932977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −215.893 | + | 323.107i | −0.359224 | + | 0.537616i | −0.966431 | − | 0.256927i | \(-0.917290\pi\) |
0.607207 | + | 0.794544i | \(0.292290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 267.473 | + | 110.791i | 0.443570 | + | 0.183733i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −144.817 | + | 28.8060i | −0.239368 | + | 0.0476132i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −341.087 | − | 67.8463i | −0.561922 | − | 0.111773i | −0.0940468 | − | 0.995568i | \(-0.529980\pi\) |
−0.467875 | + | 0.883795i | \(0.654980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0616 | − | 11.4002i | 0.0280158 | − | 0.0187195i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 313.066i | − | 0.512383i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 192.992 | 0.314832 | 0.157416 | − | 0.987532i | \(-0.449684\pi\) | ||||
0.157416 | + | 0.987532i | \(0.449684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.2563 | + | 54.2614i | 0.0589533 | + | 0.0882299i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −198.328 | + | 997.060i | −0.321439 | + | 1.61598i | 0.395241 | + | 0.918578i | \(0.370661\pi\) |
−0.716679 | + | 0.697403i | \(0.754339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.6399 | + | 219.393i | 0.0705007 | + | 0.354431i | 0.999892 | − | 0.0146637i | \(-0.00466778\pi\) |
−0.929392 | + | 0.369095i | \(0.879668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −84.5360 | + | 204.088i | −0.136129 | + | 0.328644i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 861.129 | + | 575.388i | 1.38223 | + | 0.923576i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 257.114 | + | 257.114i | 0.411383 | + | 0.411383i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 97.2256 | − | 40.2721i | 0.155065 | − | 0.0642299i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −230.709 | + | 163.536i | −0.366787 | + | 0.259993i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −240.805 | − | 581.354i | −0.381624 | − | 0.921322i | −0.991652 | − | 0.128942i | \(-0.958842\pi\) |
0.610028 | − | 0.792380i | \(-0.291158\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −102.785 | + | 102.785i | −0.162377 | + | 0.162377i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 82.6948 | − | 123.762i | 0.130228 | − | 0.194900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1492.99 | − | 618.416i | −2.34378 | − | 0.970826i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 768.694 | − | 152.903i | 1.20296 | − | 0.239284i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −146.678 | − | 29.1761i | −0.228827 | − | 0.0455165i | 0.0793449 | − | 0.996847i | \(-0.474717\pi\) |
−0.308172 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 990.083 | − | 661.552i | 1.53979 | − | 1.02885i | 0.560074 | − | 0.828443i | \(-0.310773\pi\) |
0.979712 | − | 0.200410i | \(-0.0642273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.673603i | 0.00104435i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −669.549 | −1.03485 | −0.517426 | − | 0.855728i | \(-0.673110\pi\) | ||||
−0.517426 | + | 0.855728i | \(0.673110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 322.991 | + | 483.389i | 0.497674 | + | 0.744822i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.2551 | + | 187.294i | −0.0572275 | + | 0.287702i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −149.250 | − | 750.328i | −0.228560 | − | 1.14905i | −0.909177 | − | 0.416409i | \(-0.863288\pi\) |
0.680618 | − | 0.732639i | \(-0.261712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.89087 | + | 14.2218i | −0.00899369 | + | 0.0217127i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −637.017 | − | 425.641i | −0.969584 | − | 0.647856i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 335.360 | + | 335.360i | 0.508892 | + | 0.508892i | 0.914186 | − | 0.405295i | \(-0.132831\pi\) |
−0.405295 | + | 0.914186i | \(0.632831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 308.086 | − | 127.614i | 0.466091 | − | 0.193061i | −0.137263 | − | 0.990535i | \(-0.543831\pi\) |
0.603354 | + | 0.797473i | \(0.293831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 192.622 | + | 32.8198i | 0.290531 | + | 0.0495020i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 262.588 | + | 633.943i | 0.394869 | + | 0.953298i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −73.3081 | + | 73.3081i | −0.109907 | + | 0.109907i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.92249 | + | 8.86363i | −0.00885275 | + | 0.0132491i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −276.248 | − | 114.426i | −0.411696 | − | 0.170530i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −345.950 | + | 68.8138i | −0.514042 | + | 0.102249i | −0.445293 | − | 0.895385i | \(-0.646901\pi\) |
−0.0687485 | + | 0.997634i | \(0.521901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 177.676 | + | 35.3419i | 0.263224 | + | 0.0523584i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 124.723 | − | 83.3373i | 0.184229 | − | 0.123098i | −0.460036 | − | 0.887900i | \(-0.652163\pi\) |
0.644265 | + | 0.764802i | \(0.277163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 645.024i | − | 0.949961i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 82.7778 | 0.121553 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 290.407 | + | 434.625i | 0.425193 | + | 0.636347i | 0.980781 | − | 0.195111i | \(-0.0625068\pi\) |
−0.555588 | + | 0.831458i | \(0.687507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.80256 | − | 44.2535i | 0.0128505 | − | 0.0646036i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.0198 | + | 90.5918i | 0.0262298 | + | 0.131866i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −243.597 | + | 588.096i | −0.353552 | + | 0.853550i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 779.506 | + | 520.849i | 1.12808 | + | 0.753762i | 0.972232 | − | 0.234019i | \(-0.0751877\pi\) |
0.155852 | + | 0.987780i | \(0.450188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −442.764 | − | 442.764i | −0.638909 | − | 0.638909i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −162.704 | + | 67.3940i | −0.234106 | + | 0.0969698i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1182.80 | − | 269.388i | 1.69698 | − | 0.386497i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40.5890 | − | 97.9905i | −0.0580672 | − | 0.140187i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 100.524 | − | 100.524i | 0.143401 | − | 0.143401i | −0.631762 | − | 0.775163i | \(-0.717668\pi\) |
0.775163 | + | 0.631762i | \(0.217668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −307.365 | + | 460.004i | −0.437218 | + | 0.654344i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.9950 | − | 4.55428i | −0.0155958 | − | 0.00645998i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1093.90 | − | 217.589i | 1.54723 | − | 0.307764i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −347.794 | − | 69.1805i | −0.490541 | − | 0.0975747i | −0.0563790 | − | 0.998409i | \(-0.517956\pi\) |
−0.434162 | + | 0.900835i | \(0.642956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −151.342 | + | 101.124i | −0.212858 | + | 0.142227i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 964.813i | − | 1.35317i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 304.996 | 0.426569 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −76.4637 | − | 114.436i | −0.106644 | − | 0.159604i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 186.174 | − | 935.962i | 0.258935 | − | 1.30175i | −0.604221 | − | 0.796817i | \(-0.706515\pi\) |
0.863156 | − | 0.504938i | \(-0.168485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −164.037 | − | 824.668i | −0.227513 | − | 1.14378i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.9204 | − | 118.104i | 0.0676631 | − | 0.163353i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 70.6912 | + | 47.2344i | 0.0975052 | + | 0.0651509i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −829.401 | − | 829.401i | −1.14085 | − | 1.14085i | −0.988294 | − | 0.152560i | \(-0.951248\pi\) |
−0.152560 | − | 0.988294i | \(-0.548752\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −573.173 | + | 237.416i | −0.786246 | + | 0.325674i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6960 | + | 4.47082i | 0.0160000 | + | 0.00611603i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −417.754 | − | 1008.55i | −0.569924 | − | 1.37592i | −0.901619 | − | 0.432532i | \(-0.857620\pi\) |
0.331695 | − | 0.943387i | \(-0.392380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −43.4381 | + | 43.4381i | −0.0590994 | + | 0.0590994i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −121.442 | + | 181.751i | −0.164779 | + | 0.246609i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1105.89 | − | 458.076i | −1.49647 | − | 0.619859i | −0.523758 | − | 0.851867i | \(-0.675470\pi\) |
−0.972714 | + | 0.232008i | \(0.925470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 374.925 | − | 74.5772i | 0.505971 | − | 0.100644i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1289.35 | + | 256.468i | 1.73533 | + | 0.345180i | 0.958623 | − | 0.284677i | \(-0.0918864\pi\) |
0.776711 | + | 0.629857i | \(0.216886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 198.952 | − | 132.936i | 0.267050 | − | 0.178437i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1224.51i | − | 1.63924i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 930.415 | 1.24221 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 359.724 | + | 538.365i | 0.478993 | + | 0.716864i | 0.989742 | − | 0.142866i | \(-0.0456318\pi\) |
−0.510749 | + | 0.859730i | \(0.670632\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7587 | − | 59.1151i | 0.0156158 | − | 0.0785061i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.3429 | + | 243.036i | 0.0640303 | + | 0.321902i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −242.200 | + | 584.722i | −0.319947 | + | 0.772421i | 0.679309 | + | 0.733852i | \(0.262280\pi\) |
−0.999256 | + | 0.0385681i | \(0.987720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −68.4495 | − | 45.7365i | −0.0901837 | − | 0.0602588i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −341.821 | − | 341.821i | −0.449173 | − | 0.449173i | 0.445906 | − | 0.895080i | \(-0.352881\pi\) |
−0.895080 | + | 0.445906i | \(0.852881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −572.858 | + | 237.286i | −0.750797 | + | 0.310990i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −151.978 | + | 241.622i | −0.198664 | + | 0.315846i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 808.157 | + | 1951.06i | 1.05366 | + | 2.54376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 744.788 | − | 744.788i | 0.968515 | − | 0.968515i | −0.0310039 | − | 0.999519i | \(-0.509870\pi\) |
0.999519 | + | 0.0310039i | \(0.00987042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 113.312 | − | 169.584i | 0.146968 | − | 0.219953i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1086.03 | + | 449.849i | 1.40496 | + | 0.581952i | 0.951033 | − | 0.309088i | \(-0.100024\pi\) |
0.453924 | + | 0.891040i | \(0.350024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −776.014 | + | 154.359i | −1.00131 | + | 0.199173i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −84.0145 | − | 16.7115i | −0.108127 | − | 0.0215077i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1973.28 | − | 1318.50i | 2.53309 | − | 1.69256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 591.760i | 0.757695i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.8340 | 0.0432108 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −86.8862 | − | 130.034i | −0.110683 | − | 0.165649i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −102.066 | + | 513.122i | −0.129690 | + | 0.651998i | 0.860176 | + | 0.509997i | \(0.170354\pi\) |
−0.989867 | + | 0.142001i | \(0.954646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.7769 | + | 149.699i | 0.0377401 | + | 0.189732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −235.828 | + | 569.339i | −0.298139 | + | 0.719771i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −903.099 | − | 603.431i | −1.13884 | − | 0.760947i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.1105 | + | 17.1105i | 0.0215226 | + | 0.0215226i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −722.944 | + | 299.453i | −0.907081 | + | 0.375725i | −0.786939 | − | 0.617031i | \(-0.788335\pi\) |
−0.120143 | + | 0.992757i | \(0.538335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −152.053 | + | 160.683i | −0.190305 | + | 0.201105i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 322.550 | + | 778.705i | 0.402685 | + | 0.972167i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 409.030 | − | 409.030i | 0.509378 | − | 0.509378i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 298.217 | − | 446.313i | 0.370456 | − | 0.554427i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −107.794 | − | 44.6497i | −0.133573 | − | 0.0553280i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 916.549 | − | 182.313i | 1.13294 | − | 0.225356i | 0.407209 | − | 0.913335i | \(-0.366502\pi\) |
0.725731 | + | 0.687979i | \(0.241502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1560.86 | + | 310.474i | 1.92461 | + | 0.382829i | 0.999998 | + | 0.00191501i | \(0.000609567\pi\) |
0.924611 | + | 0.380913i | \(0.124390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.8510 | − | 25.9594i | 0.0477872 | − | 0.0319304i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 90.5411i | 0.111093i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.4964 | 0.0299833 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1263.66 | − | 1891.20i | −1.54293 | − | 2.30916i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −114.241 | + | 574.329i | −0.139149 | + | 0.699548i | 0.846721 | + | 0.532037i | \(0.178573\pi\) |
−0.985870 | + | 0.167511i | \(0.946427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −234.940 | − | 1181.12i | −0.285468 | − | 1.43515i | −0.811337 | − | 0.584579i | \(-0.801260\pi\) |
0.525869 | − | 0.850566i | \(-0.323740\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.8354 | + | 62.3723i | −0.0313157 | + | 0.0756027i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1268.38 | − | 847.508i | −1.53372 | − | 1.02480i | −0.981582 | − | 0.191044i | \(-0.938813\pi\) |
−0.552136 | − | 0.833754i | \(-0.686187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −802.324 | − | 802.324i | −0.967821 | − | 0.967821i | 0.0316768 | − | 0.999498i | \(-0.489915\pi\) |
−0.999498 | + | 0.0316768i | \(0.989915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −102.119 | + | 42.2992i | −0.122887 | + | 0.0509015i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 465.924 | + | 1042.54i | 0.559333 | + | 1.25154i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.3480 | + | 160.178i | 0.0794586 | + | 0.191830i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −222.646 | + | 222.646i | −0.266005 | + | 0.266005i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −230.548 | + | 345.040i | −0.274790 | + | 0.411252i | −0.943037 | − | 0.332687i | \(-0.892045\pi\) |
0.668248 | + | 0.743939i | \(0.267045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −762.313 | − | 315.760i | −0.906436 | − | 0.375458i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −63.2280 | + | 12.5768i | −0.0750035 | + | 0.0149191i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 769.328 | + | 153.029i | 0.910447 | + | 0.181099i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −691.283 | + | 461.901i | −0.816155 | + | 0.545337i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 145.904i | 0.171854i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 432.786 | 0.508562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 295.138 | + | 441.705i | 0.345999 | + | 0.517825i | 0.963130 | − | 0.269036i | \(-0.0867050\pi\) |
−0.617131 | + | 0.786861i | \(0.711705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −108.945 | + | 547.703i | −0.127421 | + | 0.640588i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.6435 | + | 138.973i | 0.0322561 | + | 0.162163i | 0.993556 | − | 0.113341i | \(-0.0361553\pi\) |
−0.961300 | + | 0.275504i | \(0.911155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −295.209 | + | 712.697i | −0.343666 | + | 0.829682i | 0.653673 | + | 0.756777i | \(0.273227\pi\) |
−0.997339 | + | 0.0729052i | \(0.976773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 305.530 | + | 204.149i | 0.354855 | + | 0.237106i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −676.655 | − | 676.655i | −0.784073 | − | 0.784073i | 0.196442 | − | 0.980515i | \(-0.437061\pi\) |
−0.980515 | + | 0.196442i | \(0.937061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 299.225 | − | 123.943i | 0.345925 | − | 0.143287i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −82.9239 | − | 110.400i | −0.0956446 | − | 0.127335i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.5920 | − | 126.968i | −0.0605201 | − | 0.146108i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −561.462 | + | 561.462i | −0.644618 | + | 0.644618i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 291.642 | − | 436.474i | 0.334069 | − | 0.499970i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −883.220 | − | 365.842i | −1.00939 | − | 0.418105i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −174.679 | + | 34.7459i | −0.199178 | + | 0.0396190i | −0.293671 | − | 0.955907i | \(-0.594877\pi\) |
0.0944928 | + | 0.995526i | \(0.469877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 111.581 | + | 22.1948i | 0.126941 | + | 0.0252501i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1121.60 | + | 749.432i | −1.27310 | + | 0.850660i | −0.993976 | − | 0.109594i | \(-0.965045\pi\) |
−0.279127 | + | 0.960254i | \(0.590045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 968.110i | 1.09639i | 0.836352 | + | 0.548194i | \(0.184684\pi\) | ||||
−0.836352 | + | 0.548194i | \(0.815316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 80.2787 | 0.0907104 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 121.859 | + | 182.375i | 0.137384 | + | 0.205609i | 0.893781 | − | 0.448503i | \(-0.148043\pi\) |
−0.756398 | + | 0.654112i | \(0.773043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 163.508 | − | 822.009i | 0.183923 | − | 0.924644i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −96.7622 | − | 486.456i | −0.108600 | − | 0.545967i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −165.622 | + | 399.847i | −0.185467 | + | 0.447757i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −115.660 | − | 77.2813i | −0.129229 | − | 0.0863478i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −211.453 | − | 211.453i | −0.235734 | − | 0.235734i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −136.524 | + | 56.5503i | −0.151863 | + | 0.0629035i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 410.660 | − | 183.530i | 0.455783 | − | 0.203696i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.45147 | + | 3.50415i | 0.00160738 | + | 0.00388056i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −384.226 | + | 384.226i | −0.424559 | + | 0.424559i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −639.883 | + | 957.653i | −0.705494 | + | 1.05585i | 0.289623 | + | 0.957141i | \(0.406470\pi\) |
−0.995117 | + | 0.0987056i | \(0.968530\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 838.597 | + | 347.358i | 0.922549 | + | 0.382132i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −683.819 | + | 136.020i | −0.750624 | + | 0.149308i | −0.555554 | − | 0.831481i | \(-0.687494\pi\) |
−0.195071 | + | 0.980789i | \(0.562494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 906.781 | + | 180.370i | 0.993189 | + | 0.197558i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.3305 | + | 22.9389i | −0.0375196 | + | 0.0250698i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 86.6767i | 0.0945221i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 783.867 | 0.852957 | 0.426478 | − | 0.904498i | \(-0.359754\pi\) | ||||
0.426478 | + | 0.904498i | \(0.359754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8503 | + | 17.7352i | 0.0128668 | + | 0.0192565i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −419.359 | + | 2108.26i | −0.454344 | + | 2.28414i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69.2407 | − | 348.097i | −0.0748548 | − | 0.376321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 261.867 | − | 632.203i | 0.282489 | − | 0.681988i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1264.33 | + | 844.800i | 1.36096 | + | 0.909365i | 0.999733 | − | 0.0231127i | \(-0.00735764\pi\) |
0.361228 | + | 0.932478i | \(0.382358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1579.68 | + | 1579.68i | 1.69675 | + | 1.69675i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −141.262 | + | 58.5125i | −0.151406 | + | 0.0627144i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −156.541 | − | 148.134i | −0.167423 | − | 0.158432i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 171.031 | + | 412.905i | 0.182530 | + | 0.440667i | 0.988487 | − | 0.151308i | \(-0.0483485\pi\) |
−0.805956 | + | 0.591975i | \(0.798348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 113.173 | − | 113.173i | 0.120525 | − | 0.120525i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −810.536 | + | 1213.05i | −0.861355 | + | 1.28911i | 0.0945754 | + | 0.995518i | \(0.469851\pi\) |
−0.955931 | + | 0.293592i | \(0.905149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1715.20 | − | 710.461i | −1.81888 | − | 0.753405i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −171.812 | + | 34.1756i | −0.181812 | + | 0.0361647i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −920.267 | − | 183.052i | −0.971771 | − | 0.193297i | −0.316418 | − | 0.948620i | \(-0.602480\pi\) |
−0.655353 | + | 0.755323i | \(0.727480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1747.12 | − | 1167.39i | 1.84101 | − | 1.23012i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 254.680i | − | 0.267802i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −297.586 | −0.312263 | −0.156131 | − | 0.987736i | \(-0.549902\pi\) | ||||
−0.156131 | + | 0.987736i | \(0.549902\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.5982 | + | 84.7053i | 0.0592652 | + | 0.0886966i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.45986 | + | 12.3666i | −0.00257039 | + | 0.0129222i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.5647 | − | 249.178i | −0.0516837 | − | 0.259832i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 158.515 | − | 382.688i | 0.164948 | − | 0.398219i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 629.592 | + | 420.680i | 0.653782 | + | 0.436843i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −164.349 | − | 164.349i | −0.170310 | − | 0.170310i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −244.147 | + | 101.129i | −0.252479 | + | 0.104580i | −0.505333 | − | 0.862924i | \(-0.668630\pi\) |
0.252855 | + | 0.967504i | \(0.418630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −228.653 | − | 143.821i | −0.235968 | − | 0.148422i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −323.427 | − | 780.821i | −0.333086 | − | 0.804142i | −0.998344 | − | 0.0575276i | \(-0.981678\pi\) |
0.665258 | − | 0.746614i | \(-0.268322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −701.180 | + | 701.180i | −0.720637 | + | 0.720637i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −136.245 | + | 203.905i | −0.139738 | + | 0.209133i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1292.13 | − | 535.217i | −1.32255 | − | 0.547817i | −0.394027 | − | 0.919099i | \(-0.628919\pi\) |
−0.928520 | + | 0.371281i | \(0.878919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −624.162 | + | 124.154i | −0.637551 | + | 0.126817i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −494.928 | − | 98.4472i | −0.504514 | − | 0.100354i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1090.94 | + | 728.940i | −1.10980 | + | 0.741546i | −0.968647 | − | 0.248442i | \(-0.920082\pi\) |
−0.141155 | + | 0.989988i | \(0.545082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.9451i | 0.0375077i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −67.0106 | −0.0678932 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.6463 | − | 15.9333i | −0.0107647 | − | 0.0161106i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 293.696 | − | 1476.51i | 0.296363 | − | 1.48992i | −0.489766 | − | 0.871854i | \(-0.662918\pi\) |
0.786129 | − | 0.618063i | \(-0.212082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.0294 | + | 130.859i | 0.0262129 | + | 0.131781i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −219.375 | + | 529.619i | −0.220478 | + | 0.532281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −327.594 | − | 218.891i | −0.328580 | − | 0.219550i | 0.380327 | − | 0.924852i | \(-0.375811\pi\) |
−0.708907 | + | 0.705302i | \(0.750811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −99.8724 | − | 99.8724i | −0.0999724 | − | 0.0999724i |
(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 | 136.3.t.a.73.3 | yes | 32 | |
4.3 | odd | 2 | 272.3.bh.f.209.2 | 32 | |||
17.7 | odd | 16 | inner | 136.3.t.a.41.3 | ✓ | 32 | |
68.7 | even | 16 | 272.3.bh.f.177.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.t.a.41.3 | ✓ | 32 | 17.7 | odd | 16 | inner | |
136.3.t.a.73.3 | yes | 32 | 1.1 | even | 1 | trivial | |
272.3.bh.f.177.2 | 32 | 68.7 | even | 16 | |||
272.3.bh.f.209.2 | 32 | 4.3 | odd | 2 |