Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(971,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.971");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.e (of order \(2\), degree \(1\), 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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 971.25 | ||
Character | \(\chi\) | \(=\) | 1620.971 |
Dual form | 1620.2.e.a.971.26 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.192668 | − | 1.40103i | 0.136237 | − | 0.990676i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.92576 | − | 0.539867i | −0.962879 | − | 0.269933i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.01091i | − | 1.89395i | −0.321311 | − | 0.946974i | \(-0.604123\pi\) | ||
0.321311 | − | 0.946974i | \(-0.395877\pi\) | |||||||
\(8\) | −1.12740 | + | 2.59403i | −0.398596 | + | 0.917127i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.40103 | + | 0.192668i | 0.443044 | + | 0.0609270i | ||||
\(11\) | −4.38659 | −1.32261 | −0.661303 | − | 0.750119i | \(-0.729996\pi\) | ||||
−0.661303 | + | 0.750119i | \(0.729996\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.13042 | −1.14557 | −0.572786 | − | 0.819705i | \(-0.694137\pi\) | ||||
−0.572786 | + | 0.819705i | \(0.694137\pi\) | |||||||
\(14\) | −7.02043 | − | 0.965443i | −1.87629 | − | 0.258025i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.41709 | + | 2.07930i | 0.854272 | + | 0.519826i | ||||
\(17\) | 1.34325i | 0.325786i | 0.986644 | + | 0.162893i | \(0.0520826\pi\) | ||||
−0.986644 | + | 0.162893i | \(0.947917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.39602i | − | 0.320269i | −0.987095 | − | 0.160135i | \(-0.948807\pi\) | ||
0.987095 | − | 0.160135i | \(-0.0511928\pi\) | |||||||
\(20\) | 0.539867 | − | 1.92576i | 0.120718 | − | 0.430613i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.845155 | + | 6.14573i | −0.180188 | + | 1.31027i | ||||
\(23\) | 7.65734 | 1.59667 | 0.798333 | − | 0.602216i | \(-0.205716\pi\) | ||||
0.798333 | + | 0.602216i | \(0.205716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.795799 | + | 5.78683i | −0.156069 | + | 1.13489i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.70522 | + | 9.64981i | −0.511239 | + | 1.82364i | ||||
\(29\) | 0.167976i | 0.0311923i | 0.999878 | + | 0.0155962i | \(0.00496462\pi\) | ||||
−0.999878 | + | 0.0155962i | \(0.995035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.53478i | 0.634865i | 0.948281 | + | 0.317432i | \(0.102821\pi\) | ||||
−0.948281 | + | 0.317432i | \(0.897179\pi\) | |||||||
\(32\) | 3.57153 | − | 4.38682i | 0.631363 | − | 0.775488i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.88193 | + | 0.258802i | 0.322749 | + | 0.0443841i | ||||
\(35\) | 5.01091 | 0.846999 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.98701 | −0.819860 | −0.409930 | − | 0.912117i | \(-0.634447\pi\) | ||||
−0.409930 | + | 0.912117i | \(0.634447\pi\) | |||||||
\(38\) | −1.95586 | − | 0.268969i | −0.317283 | − | 0.0436325i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.59403 | − | 1.12740i | −0.410151 | − | 0.178258i | ||||
\(41\) | 6.52844i | 1.01957i | 0.860302 | + | 0.509786i | \(0.170275\pi\) | ||||
−0.860302 | + | 0.509786i | \(0.829725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6725i | 1.78005i | 0.455915 | + | 0.890024i | \(0.349312\pi\) | ||||
−0.455915 | + | 0.890024i | \(0.650688\pi\) | |||||||
\(44\) | 8.44751 | + | 2.36817i | 1.27351 | + | 0.357015i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.47532 | − | 10.7281i | 0.217525 | − | 1.58178i | ||||
\(47\) | −0.0180070 | −0.00262659 | −0.00131330 | − | 0.999999i | \(-0.500418\pi\) | ||||
−0.00131330 | + | 0.999999i | \(0.500418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.1093 | −2.58704 | ||||||||
\(50\) | −0.192668 | + | 1.40103i | −0.0272474 | + | 0.198135i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.95419 | + | 2.22987i | 1.10305 | + | 0.309228i | ||||
\(53\) | 5.66076i | 0.777566i | 0.921329 | + | 0.388783i | \(0.127104\pi\) | ||||
−0.921329 | + | 0.388783i | \(0.872896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.38659i | − | 0.591487i | ||||||
\(56\) | 12.9984 | + | 5.64930i | 1.73699 | + | 0.754920i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.235339 | + | 0.0323636i | 0.0309015 | + | 0.00424955i | ||||
\(59\) | −8.57807 | −1.11677 | −0.558385 | − | 0.829582i | \(-0.688579\pi\) | ||||
−0.558385 | + | 0.829582i | \(0.688579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.81677 | −0.488687 | −0.244343 | − | 0.969689i | \(-0.578572\pi\) | ||||
−0.244343 | + | 0.969689i | \(0.578572\pi\) | |||||||
\(62\) | 4.95232 | + | 0.681038i | 0.628945 | + | 0.0864919i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.45794 | − | 5.84901i | −0.682242 | − | 0.731126i | ||||
\(65\) | − | 4.13042i | − | 0.512315i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.96182i | − | 0.484014i | −0.970275 | − | 0.242007i | \(-0.922194\pi\) | ||
0.970275 | − | 0.242007i | \(-0.0778057\pi\) | |||||||
\(68\) | 0.725176 | − | 2.58678i | 0.0879406 | − | 0.313693i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.965443 | − | 7.02043i | 0.115392 | − | 0.839102i | ||||
\(71\) | −2.16175 | −0.256553 | −0.128276 | − | 0.991738i | \(-0.540944\pi\) | ||||
−0.128276 | + | 0.991738i | \(0.540944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2156 | −1.78085 | −0.890423 | − | 0.455133i | \(-0.849592\pi\) | ||||
−0.890423 | + | 0.455133i | \(0.849592\pi\) | |||||||
\(74\) | −0.960838 | + | 6.98694i | −0.111695 | + | 0.812216i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.753665 | + | 2.68840i | −0.0864513 | + | 0.308381i | ||||
\(77\) | 21.9808i | 2.50495i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.99947i | − | 0.900011i | −0.893026 | − | 0.450006i | \(-0.851422\pi\) | ||
0.893026 | − | 0.450006i | \(-0.148578\pi\) | |||||||
\(80\) | −2.07930 | + | 3.41709i | −0.232473 | + | 0.382042i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.14653 | + | 1.25782i | 1.01006 | + | 0.138903i | ||||
\(83\) | 11.7253 | 1.28702 | 0.643512 | − | 0.765436i | \(-0.277477\pi\) | ||||
0.643512 | + | 0.765436i | \(0.277477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34325 | −0.145696 | ||||||||
\(86\) | 16.3536 | + | 2.24893i | 1.76345 | + | 0.242508i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.94544 | − | 11.3789i | 0.527186 | − | 1.21300i | ||||
\(89\) | − | 13.4268i | − | 1.42324i | −0.702563 | − | 0.711622i | \(-0.747961\pi\) | ||
0.702563 | − | 0.711622i | \(-0.252039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.6972i | 2.16965i | ||||||||
\(92\) | −14.7462 | − | 4.13394i | −1.53740 | − | 0.430993i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.00346937 | + | 0.0252283i | −0.000357839 | + | 0.00260210i | ||||
\(95\) | 1.39602 | 0.143229 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.4411 | 1.46628 | 0.733138 | − | 0.680080i | \(-0.238055\pi\) | ||||
0.733138 | + | 0.680080i | \(0.238055\pi\) | |||||||
\(98\) | −3.48908 | + | 25.3716i | −0.352450 | + | 2.56292i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.92576 | + | 0.539867i | 0.192576 | + | 0.0539867i | ||||
\(101\) | 11.5704i | 1.15130i | 0.817696 | + | 0.575650i | \(0.195251\pi\) | ||||
−0.817696 | + | 0.575650i | \(0.804749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.59136i | 0.649466i | 0.945806 | + | 0.324733i | \(0.105274\pi\) | ||||
−0.945806 | + | 0.324733i | \(0.894726\pi\) | |||||||
\(104\) | 4.65663 | − | 10.7144i | 0.456620 | − | 1.05063i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.93089 | + | 1.09065i | 0.770316 | + | 0.105933i | ||||
\(107\) | −14.2524 | −1.37783 | −0.688916 | − | 0.724841i | \(-0.741913\pi\) | ||||
−0.688916 | + | 0.724841i | \(0.741913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.72081 | 0.260607 | 0.130303 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130303 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(110\) | −6.14573 | − | 0.845155i | −0.585972 | − | 0.0805824i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.4192 | − | 17.1227i | 0.984523 | − | 1.61795i | ||||
\(113\) | 11.1171i | 1.04581i | 0.852391 | + | 0.522904i | \(0.175152\pi\) | ||||
−0.852391 | + | 0.522904i | \(0.824848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.65734i | 0.714051i | ||||||||
\(116\) | 0.0906846 | − | 0.323481i | 0.00841985 | − | 0.0300344i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.65272 | + | 12.0181i | −0.152145 | + | 1.10636i | ||||
\(119\) | 6.73092 | 0.617022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.24215 | 0.749286 | ||||||||
\(122\) | −0.735369 | + | 5.34740i | −0.0665772 | + | 0.484131i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.90831 | − | 6.80712i | 0.171371 | − | 0.611298i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.21713i | 0.551681i | 0.961203 | + | 0.275840i | \(0.0889562\pi\) | ||||
−0.961203 | + | 0.275840i | \(0.911044\pi\) | |||||||
\(128\) | −9.24619 | + | 6.51981i | −0.817256 | + | 0.576275i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.78683 | − | 0.795799i | −0.507539 | − | 0.0697962i | ||||
\(131\) | −5.86793 | −0.512683 | −0.256342 | − | 0.966586i | \(-0.582517\pi\) | ||||
−0.256342 | + | 0.966586i | \(0.582517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.99534 | −0.606573 | ||||||||
\(134\) | −5.55063 | − | 0.763317i | −0.479501 | − | 0.0659405i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.48443 | − | 1.51438i | −0.298787 | − | 0.129857i | ||||
\(137\) | 6.87606i | 0.587461i | 0.955888 | + | 0.293731i | \(0.0948969\pi\) | ||||
−0.955888 | + | 0.293731i | \(0.905103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.66986i | 0.820187i | 0.912043 | + | 0.410094i | \(0.134504\pi\) | ||||
−0.912043 | + | 0.410094i | \(0.865496\pi\) | |||||||
\(140\) | −9.64981 | − | 2.70522i | −0.815558 | − | 0.228633i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.416500 | + | 3.02867i | −0.0349519 | + | 0.254161i | ||||
\(143\) | 18.1184 | 1.51514 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.167976 | −0.0139496 | ||||||||
\(146\) | −2.93155 | + | 21.3174i | −0.242617 | + | 1.76424i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.60378 | + | 2.69232i | 0.789426 | + | 0.221307i | ||||
\(149\) | 5.02129i | 0.411360i | 0.978619 | + | 0.205680i | \(0.0659407\pi\) | ||||
−0.978619 | + | 0.205680i | \(0.934059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.5963i | − | 1.10645i | −0.833031 | − | 0.553227i | \(-0.813396\pi\) | ||
0.833031 | − | 0.553227i | \(-0.186604\pi\) | |||||||
\(152\) | 3.62131 | + | 1.57387i | 0.293727 | + | 0.127658i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 30.7957 | + | 4.23500i | 2.48159 | + | 0.341266i | ||||
\(155\) | −3.53478 | −0.283920 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4647 | −0.914981 | −0.457491 | − | 0.889214i | \(-0.651252\pi\) | ||||
−0.457491 | + | 0.889214i | \(0.651252\pi\) | |||||||
\(158\) | −11.2075 | − | 1.54124i | −0.891620 | − | 0.122615i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.38682 | + | 3.57153i | 0.346809 | + | 0.282354i | ||||
\(161\) | − | 38.3703i | − | 3.02400i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.2335i | − | 1.66313i | −0.555424 | − | 0.831567i | \(-0.687444\pi\) | ||
0.555424 | − | 0.831567i | \(-0.312556\pi\) | |||||||
\(164\) | 3.52449 | − | 12.5722i | 0.275216 | − | 0.981724i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.25910 | − | 16.4275i | 0.175340 | − | 1.27502i | ||||
\(167\) | 10.1062 | 0.782037 | 0.391019 | − | 0.920383i | \(-0.372123\pi\) | ||||
0.391019 | + | 0.920383i | \(0.372123\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.06035 | 0.312335 | ||||||||
\(170\) | −0.258802 | + | 1.88193i | −0.0198492 | + | 0.144338i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.30162 | − | 22.4785i | 0.480494 | − | 1.71397i | ||||
\(173\) | − | 6.64217i | − | 0.504995i | −0.967598 | − | 0.252497i | \(-0.918748\pi\) | ||
0.967598 | − | 0.252497i | \(-0.0812519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.01091i | 0.378789i | ||||||||
\(176\) | −14.9894 | − | 9.12105i | −1.12987 | − | 0.687525i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.8114 | − | 2.58692i | −1.40997 | − | 0.193898i | ||||
\(179\) | −6.88682 | −0.514745 | −0.257372 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257372 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.17574 | −0.459039 | −0.229520 | − | 0.973304i | \(-0.573715\pi\) | ||||
−0.229520 | + | 0.973304i | \(0.573715\pi\) | |||||||
\(182\) | 28.9973 | + | 3.98768i | 2.14942 | + | 0.295587i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.63288 | + | 19.8633i | −0.636425 | + | 1.46434i | ||||
\(185\) | − | 4.98701i | − | 0.366653i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.89229i | − | 0.430887i | ||||||
\(188\) | 0.0346771 | + | 0.00972138i | 0.00252909 | + | 0.000709004i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.268969 | − | 1.95586i | 0.0195130 | − | 0.141893i | ||||
\(191\) | 1.01197 | 0.0732234 | 0.0366117 | − | 0.999330i | \(-0.488344\pi\) | ||||
0.0366117 | + | 0.999330i | \(0.488344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.26563 | −0.307046 | −0.153523 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153523 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(194\) | 2.78234 | − | 20.2324i | 0.199761 | − | 1.45260i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 34.8741 | + | 9.77658i | 2.49100 | + | 0.698327i | ||||
\(197\) | − | 14.4901i | − | 1.03238i | −0.856474 | − | 0.516190i | \(-0.827350\pi\) | ||
0.856474 | − | 0.516190i | \(-0.172650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.54569i | − | 0.251348i | −0.992072 | − | 0.125674i | \(-0.959891\pi\) | ||
0.992072 | − | 0.125674i | \(-0.0401093\pi\) | |||||||
\(200\) | 1.12740 | − | 2.59403i | 0.0797192 | − | 0.183425i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.2105 | + | 2.22925i | 1.14057 | + | 0.156850i | ||||
\(203\) | 0.841713 | 0.0590767 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.52844 | −0.455966 | ||||||||
\(206\) | 9.23467 | + | 1.26994i | 0.643410 | + | 0.0884812i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1140 | − | 8.58840i | −0.978630 | − | 0.595498i | ||||
\(209\) | 6.12377i | 0.423590i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.7065i | − | 1.70087i | −0.526082 | − | 0.850434i | \(-0.676340\pi\) | ||
0.526082 | − | 0.850434i | \(-0.323660\pi\) | |||||||
\(212\) | 3.05606 | − | 10.9013i | 0.209891 | − | 0.748702i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.74598 | + | 19.9680i | −0.187712 | + | 1.36499i | ||||
\(215\) | −11.6725 | −0.796061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.7125 | 1.20240 | ||||||||
\(218\) | 0.524214 | − | 3.81193i | 0.0355042 | − | 0.258177i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.36817 | + | 8.44751i | −0.159662 | + | 0.569531i | ||||
\(221\) | − | 5.54819i | − | 0.373212i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.482284i | 0.0322962i | 0.999870 | + | 0.0161481i | \(0.00514032\pi\) | ||||
−0.999870 | + | 0.0161481i | \(0.994860\pi\) | |||||||
\(224\) | −21.9820 | − | 17.8966i | −1.46873 | − | 1.19577i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.5754 | + | 2.14191i | 1.03606 | + | 0.142478i | ||||
\(227\) | −5.09597 | −0.338232 | −0.169116 | − | 0.985596i | \(-0.554091\pi\) | ||||
−0.169116 | + | 0.985596i | \(0.554091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.77234 | −0.645774 | −0.322887 | − | 0.946437i | \(-0.604653\pi\) | ||||
−0.322887 | + | 0.946437i | \(0.604653\pi\) | |||||||
\(230\) | 10.7281 | + | 1.47532i | 0.707393 | + | 0.0972800i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.435734 | − | 0.189376i | −0.0286073 | − | 0.0124331i | ||||
\(233\) | 12.3013i | 0.805882i | 0.915226 | + | 0.402941i | \(0.132012\pi\) | ||||
−0.915226 | + | 0.402941i | \(0.867988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.0180070i | − | 0.00117465i | ||||||
\(236\) | 16.5193 | + | 4.63101i | 1.07531 | + | 0.301453i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.29683 | − | 9.43020i | 0.0840612 | − | 0.611269i | ||||
\(239\) | 18.7092 | 1.21020 | 0.605099 | − | 0.796150i | \(-0.293133\pi\) | ||||
0.605099 | + | 0.796150i | \(0.293133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9029 | −1.34648 | −0.673239 | − | 0.739425i | \(-0.735097\pi\) | ||||
−0.673239 | + | 0.739425i | \(0.735097\pi\) | |||||||
\(242\) | 1.58800 | − | 11.5475i | 0.102080 | − | 0.742300i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.35017 | + | 2.06054i | 0.470546 | + | 0.131913i | ||||
\(245\) | − | 18.1093i | − | 1.15696i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.76615i | 0.366891i | ||||||||
\(248\) | −9.16930 | − | 3.98511i | −0.582251 | − | 0.253055i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.40103 | − | 0.192668i | −0.0886088 | − | 0.0121854i | ||||
\(251\) | −20.5810 | −1.29906 | −0.649531 | − | 0.760335i | \(-0.725035\pi\) | ||||
−0.649531 | + | 0.760335i | \(0.725035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.5896 | −2.11176 | ||||||||
\(254\) | 8.71037 | + | 1.19784i | 0.546537 | + | 0.0751593i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.35299 | + | 14.2103i | 0.459562 | + | 0.888146i | ||||
\(257\) | − | 0.971388i | − | 0.0605935i | −0.999541 | − | 0.0302967i | \(-0.990355\pi\) | ||
0.999541 | − | 0.0302967i | \(-0.00964523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.9895i | 1.55277i | ||||||||
\(260\) | −2.22987 | + | 7.95419i | −0.138291 | + | 0.493298i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.13056 | + | 8.22113i | −0.0698463 | + | 0.507903i | ||||
\(263\) | −18.7818 | −1.15813 | −0.579067 | − | 0.815280i | \(-0.696583\pi\) | ||||
−0.579067 | + | 0.815280i | \(0.696583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.66076 | −0.347738 | ||||||||
\(266\) | −1.34778 | + | 9.80067i | −0.0826376 | + | 0.600918i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.13886 | + | 7.62952i | −0.130651 | + | 0.466047i | ||||
\(269\) | − | 2.57026i | − | 0.156712i | −0.996925 | − | 0.0783559i | \(-0.975033\pi\) | ||
0.996925 | − | 0.0783559i | \(-0.0249670\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.5299i | − | 1.67232i | −0.548482 | − | 0.836162i | \(-0.684794\pi\) | ||
0.548482 | − | 0.836162i | \(-0.315206\pi\) | |||||||
\(272\) | −2.79303 | + | 4.59001i | −0.169352 | + | 0.278310i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.63355 | + | 1.32480i | 0.581984 | + | 0.0800339i | ||||
\(275\) | 4.38659 | 0.264521 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.45076 | −0.147252 | −0.0736260 | − | 0.997286i | \(-0.523457\pi\) | ||||
−0.0736260 | + | 0.997286i | \(0.523457\pi\) | |||||||
\(278\) | 13.5477 | + | 1.86307i | 0.812540 | + | 0.111740i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.64930 | + | 12.9984i | −0.337611 | + | 0.776805i | ||||
\(281\) | − | 10.9842i | − | 0.655263i | −0.944806 | − | 0.327631i | \(-0.893750\pi\) | ||
0.944806 | − | 0.327631i | \(-0.106250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.3114i | − | 1.26683i | −0.773811 | − | 0.633416i | \(-0.781652\pi\) | ||
0.773811 | − | 0.633416i | \(-0.218348\pi\) | |||||||
\(284\) | 4.16301 | + | 1.16706i | 0.247029 | + | 0.0692521i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.49084 | − | 25.3844i | 0.206418 | − | 1.50101i | ||||
\(287\) | 32.7135 | 1.93101 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1957 | 0.893863 | ||||||||
\(290\) | −0.0323636 | + | 0.235339i | −0.00190045 | + | 0.0138196i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29.3015 | + | 8.21437i | 1.71474 | + | 0.480710i | ||||
\(293\) | 22.0638i | 1.28898i | 0.764611 | + | 0.644492i | \(0.222931\pi\) | ||||
−0.764611 | + | 0.644492i | \(0.777069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.57807i | − | 0.499434i | ||||||
\(296\) | 5.62236 | − | 12.9364i | 0.326793 | − | 0.751915i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.03497 | + | 0.967443i | 0.407525 | + | 0.0560425i | ||||
\(299\) | −31.6280 | −1.82910 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 58.4901 | 3.37132 | ||||||||
\(302\) | −19.0488 | − | 2.61958i | −1.09614 | − | 0.150740i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.90275 | − | 4.77033i | 0.166484 | − | 0.273597i | ||||
\(305\) | − | 3.81677i | − | 0.218547i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.78159i | − | 0.558265i | −0.960253 | − | 0.279132i | \(-0.909953\pi\) | ||
0.960253 | − | 0.279132i | \(-0.0900468\pi\) | |||||||
\(308\) | 11.8667 | − | 42.3297i | 0.676168 | − | 2.41196i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.681038 | + | 4.95232i | −0.0386804 | + | 0.281273i | ||||
\(311\) | −1.58383 | −0.0898106 | −0.0449053 | − | 0.998991i | \(-0.514299\pi\) | ||||
−0.0449053 | + | 0.998991i | \(0.514299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2310 | −1.59571 | −0.797855 | − | 0.602849i | \(-0.794032\pi\) | ||||
−0.797855 | + | 0.602849i | \(0.794032\pi\) | |||||||
\(314\) | −2.20888 | + | 16.0623i | −0.124654 | + | 0.906450i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.31865 | + | 15.4051i | −0.242943 | + | 0.866602i | ||||
\(317\) | 27.2511i | 1.53057i | 0.643690 | + | 0.765287i | \(0.277403\pi\) | ||||
−0.643690 | + | 0.765287i | \(0.722597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.736841i | − | 0.0412552i | ||||||
\(320\) | 5.84901 | − | 5.45794i | 0.326970 | − | 0.305108i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −53.7578 | − | 7.39272i | −2.99581 | − | 0.411980i | ||||
\(323\) | 1.87521 | 0.104339 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.13042 | 0.229114 | ||||||||
\(326\) | −29.7487 | − | 4.09101i | −1.64763 | − | 0.226580i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.9349 | − | 7.36016i | −0.935076 | − | 0.406397i | ||||
\(329\) | 0.0902316i | 0.00497463i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.737840i | − | 0.0405554i | −0.999794 | − | 0.0202777i | \(-0.993545\pi\) | ||
0.999794 | − | 0.0202777i | \(-0.00645503\pi\) | |||||||
\(332\) | −22.5802 | − | 6.33012i | −1.23925 | − | 0.347410i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.94713 | − | 14.1590i | 0.106542 | − | 0.774746i | ||||
\(335\) | 3.96182 | 0.216458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.5564 | −1.22872 | −0.614362 | − | 0.789024i | \(-0.710586\pi\) | ||||
−0.614362 | + | 0.789024i | \(0.710586\pi\) | |||||||
\(338\) | 0.782300 | − | 5.68866i | 0.0425515 | − | 0.309423i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.58678 | + | 0.725176i | 0.140288 | + | 0.0393282i | ||||
\(341\) | − | 15.5056i | − | 0.839676i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55.6675i | 3.00576i | ||||||||
\(344\) | −30.2789 | − | 13.1596i | −1.63253 | − | 0.709520i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.30587 | − | 1.27973i | −0.500287 | − | 0.0687989i | ||||
\(347\) | −19.7568 | −1.06060 | −0.530301 | − | 0.847809i | \(-0.677921\pi\) | ||||
−0.530301 | + | 0.847809i | \(0.677921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.52380 | 0.0815670 | 0.0407835 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407835 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(350\) | 7.02043 | + | 0.965443i | 0.375258 | + | 0.0516051i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.6668 | + | 19.2432i | −0.835044 | + | 1.02566i | ||||
\(353\) | − | 26.2442i | − | 1.39684i | −0.715688 | − | 0.698420i | \(-0.753887\pi\) | ||
0.715688 | − | 0.698420i | \(-0.246113\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.16175i | − | 0.114734i | ||||||
\(356\) | −7.24871 | + | 25.8569i | −0.384181 | + | 1.37041i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.32687 | + | 9.64862i | −0.0701272 | + | 0.509945i | ||||
\(359\) | −23.6017 | −1.24565 | −0.622826 | − | 0.782360i | \(-0.714016\pi\) | ||||
−0.622826 | + | 0.782360i | \(0.714016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0511 | 0.897428 | ||||||||
\(362\) | −1.18987 | + | 8.65238i | −0.0625381 | + | 0.454759i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.1737 | − | 39.8577i | 0.585661 | − | 2.08911i | ||||
\(365\) | − | 15.2156i | − | 0.796419i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7055i | 1.08082i | 0.841402 | + | 0.540410i | \(0.181731\pi\) | ||||
−0.841402 | + | 0.540410i | \(0.818269\pi\) | |||||||
\(368\) | 26.1658 | + | 15.9219i | 1.36399 | + | 0.829989i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.98694 | − | 0.960838i | −0.363234 | − | 0.0499516i | ||||
\(371\) | 28.3656 | 1.47267 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.72557 | 0.451793 | 0.225896 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225896 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(374\) | −8.25526 | − | 1.13526i | −0.426869 | − | 0.0587027i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0203011 | − | 0.0467106i | 0.00104695 | − | 0.00240892i | ||||
\(377\) | − | 0.693811i | − | 0.0357331i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6877i | 0.959924i | 0.877289 | + | 0.479962i | \(0.159350\pi\) | ||||
−0.877289 | + | 0.479962i | \(0.840650\pi\) | |||||||
\(380\) | −2.68840 | − | 0.753665i | −0.137912 | − | 0.0386622i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.194974 | − | 1.41779i | 0.00997572 | − | 0.0725407i | ||||
\(383\) | −24.5215 | −1.25299 | −0.626494 | − | 0.779426i | \(-0.715511\pi\) | ||||
−0.626494 | + | 0.779426i | \(0.715511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.9808 | −1.12025 | ||||||||
\(386\) | −0.821850 | + | 5.97626i | −0.0418310 | + | 0.304184i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.8101 | − | 7.79629i | −1.41185 | − | 0.395796i | ||||
\(389\) | − | 10.0847i | − | 0.511314i | −0.966768 | − | 0.255657i | \(-0.917708\pi\) | ||
0.966768 | − | 0.255657i | \(-0.0822918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2857i | 0.520172i | ||||||||
\(392\) | 20.4164 | − | 46.9759i | 1.03118 | − | 2.37264i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.3011 | − | 2.79179i | −1.02275 | − | 0.140648i | ||||
\(395\) | 7.99947 | 0.402497 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7934 | −1.24435 | −0.622174 | − | 0.782879i | \(-0.713750\pi\) | ||||
−0.622174 | + | 0.782879i | \(0.713750\pi\) | |||||||
\(398\) | −4.96762 | − | 0.683142i | −0.249004 | − | 0.0342428i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.41709 | − | 2.07930i | −0.170854 | − | 0.103965i | ||||
\(401\) | − | 10.8737i | − | 0.543008i | −0.962437 | − | 0.271504i | \(-0.912479\pi\) | ||
0.962437 | − | 0.271504i | \(-0.0875210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 14.6001i | − | 0.727283i | ||||||
\(404\) | 6.24649 | − | 22.2819i | 0.310774 | − | 1.10856i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.162171 | − | 1.17926i | 0.00804842 | − | 0.0585258i | ||||
\(407\) | 21.8760 | 1.08435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6773 | 0.775192 | 0.387596 | − | 0.921829i | \(-0.373306\pi\) | ||||
0.387596 | + | 0.921829i | \(0.373306\pi\) | |||||||
\(410\) | −1.25782 | + | 9.14653i | −0.0621194 | + | 0.451715i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.55845 | − | 12.6934i | 0.175312 | − | 0.625357i | ||||
\(413\) | 42.9840i | 2.11510i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7253i | 0.575574i | ||||||||
\(416\) | −14.7519 | + | 18.1194i | −0.723271 | + | 0.888377i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.57957 | + | 1.17985i | 0.419641 | + | 0.0577086i | ||||
\(419\) | 3.90987 | 0.191010 | 0.0955048 | − | 0.995429i | \(-0.469553\pi\) | ||||
0.0955048 | + | 0.995429i | \(0.469553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0305 | −1.07370 | −0.536849 | − | 0.843678i | \(-0.680386\pi\) | ||||
−0.536849 | + | 0.843678i | \(0.680386\pi\) | |||||||
\(422\) | −34.6145 | − | 4.76016i | −1.68501 | − | 0.231721i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.6842 | − | 6.38194i | −0.713126 | − | 0.309935i | ||||
\(425\) | − | 1.34325i | − | 0.0651573i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.1255i | 0.925547i | ||||||||
\(428\) | 27.4467 | + | 7.69440i | 1.32669 | + | 0.371923i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.24893 | + | 16.3536i | −0.108453 | + | 0.788639i | ||||
\(431\) | 10.0937 | 0.486198 | 0.243099 | − | 0.970001i | \(-0.421836\pi\) | ||||
0.243099 | + | 0.970001i | \(0.421836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3622 | 1.21883 | 0.609414 | − | 0.792852i | \(-0.291405\pi\) | ||||
0.609414 | + | 0.792852i | \(0.291405\pi\) | |||||||
\(434\) | 3.41262 | − | 24.8156i | 0.163811 | − | 1.19119i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.23963 | − | 1.46888i | −0.250933 | − | 0.0703464i | ||||
\(437\) | − | 10.6898i | − | 0.511363i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.8378i | − | 0.803625i | −0.915722 | − | 0.401813i | \(-0.868380\pi\) | ||
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(440\) | 11.3789 | + | 4.94544i | 0.542469 | + | 0.235765i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.77317 | − | 1.06896i | −0.369732 | − | 0.0508452i | ||||
\(443\) | −2.50744 | −0.119132 | −0.0595659 | − | 0.998224i | \(-0.518972\pi\) | ||||
−0.0595659 | + | 0.998224i | \(0.518972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4268 | 0.636494 | ||||||||
\(446\) | 0.675694 | + | 0.0929208i | 0.0319950 | + | 0.00439993i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.3089 | + | 27.3493i | −1.38471 | + | 1.29213i | ||||
\(449\) | 24.1651i | 1.14042i | 0.821498 | + | 0.570211i | \(0.193139\pi\) | ||||
−0.821498 | + | 0.570211i | \(0.806861\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 28.6376i | − | 1.34849i | ||||||
\(452\) | 6.00175 | − | 21.4088i | 0.282299 | − | 1.00699i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.981831 | + | 7.13960i | −0.0460796 | + | 0.335078i | ||||
\(455\) | −20.6972 | −0.970298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.8994 | 1.39863 | 0.699317 | − | 0.714812i | \(-0.253488\pi\) | ||||
0.699317 | + | 0.714812i | \(0.253488\pi\) | |||||||
\(458\) | −1.88282 | + | 13.6913i | −0.0879783 | + | 0.639753i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.13394 | − | 14.7462i | 0.192746 | − | 0.687544i | ||||
\(461\) | − | 8.67332i | − | 0.403957i | −0.979390 | − | 0.201978i | \(-0.935263\pi\) | ||
0.979390 | − | 0.201978i | \(-0.0647371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9686i | 0.602702i | 0.953513 | + | 0.301351i | \(0.0974376\pi\) | ||||
−0.953513 | + | 0.301351i | \(0.902562\pi\) | |||||||
\(464\) | −0.349273 | + | 0.573988i | −0.0162146 | + | 0.0266467i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.2344 | + | 2.37006i | 0.798369 | + | 0.109791i | ||||
\(467\) | −2.72723 | −0.126201 | −0.0631007 | − | 0.998007i | \(-0.520099\pi\) | ||||
−0.0631007 | + | 0.998007i | \(0.520099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.8524 | −0.916697 | ||||||||
\(470\) | −0.0252283 | − | 0.00346937i | −0.00116370 | − | 0.000160030i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.67091 | − | 22.2517i | 0.445140 | − | 1.02422i | ||||
\(473\) | − | 51.2027i | − | 2.35430i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.39602i | 0.0640538i | ||||||||
\(476\) | −12.9621 | − | 3.63380i | −0.594118 | − | 0.166555i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.60467 | − | 26.2121i | 0.164874 | − | 1.19892i | ||||
\(479\) | 37.5562 | 1.71599 | 0.857993 | − | 0.513661i | \(-0.171711\pi\) | ||||
0.857993 | + | 0.513661i | \(0.171711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5984 | 0.939208 | ||||||||
\(482\) | −4.02733 | + | 29.2856i | −0.183440 | + | 1.33392i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.8724 | − | 4.44966i | −0.721472 | − | 0.202257i | ||||
\(485\) | 14.4411i | 0.655738i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.48987i | 0.112827i | 0.998407 | + | 0.0564133i | \(0.0179665\pi\) | ||||
−0.998407 | + | 0.0564133i | \(0.982034\pi\) | |||||||
\(488\) | 4.30302 | − | 9.90079i | 0.194789 | − | 0.448188i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −25.3716 | − | 3.48908i | −1.14617 | − | 0.157620i | ||||
\(491\) | 22.7785 | 1.02798 | 0.513990 | − | 0.857796i | \(-0.328167\pi\) | ||||
0.513990 | + | 0.857796i | \(0.328167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.225634 | −0.0101620 | ||||||||
\(494\) | 8.07854 | + | 1.11095i | 0.363471 | + | 0.0499841i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.34988 | + | 12.0786i | −0.330019 | + | 0.542347i | ||||
\(497\) | 10.8323i | 0.485897i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3606i | 0.777167i | 0.921414 | + | 0.388583i | \(0.127035\pi\) | ||||
−0.921414 | + | 0.388583i | \(0.872965\pi\) | |||||||
\(500\) | −0.539867 | + | 1.92576i | −0.0241436 | + | 0.0861225i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.96530 | + | 28.8346i | −0.176980 | + | 1.28695i | ||||
\(503\) | −17.0746 | −0.761320 | −0.380660 | − | 0.924715i | \(-0.624303\pi\) | ||||
−0.380660 | + | 0.924715i | \(0.624303\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.5704 | −0.514877 | ||||||||
\(506\) | −6.47164 | + | 47.0600i | −0.287699 | + | 2.09207i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.35642 | − | 11.9727i | 0.148917 | − | 0.531202i | ||||
\(509\) | 16.4468i | 0.728990i | 0.931205 | + | 0.364495i | \(0.118758\pi\) | ||||
−0.931205 | + | 0.364495i | \(0.881242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 76.2439i | 3.37283i | ||||||||
\(512\) | 21.3258 | − | 7.56386i | 0.942474 | − | 0.334279i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.36094 | − | 0.187155i | −0.0600285 | − | 0.00825507i | ||||
\(515\) | −6.59136 | −0.290450 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0789893 | 0.00347395 | ||||||||
\(518\) | 35.0110 | + | 4.81468i | 1.53829 | + | 0.211545i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.7144 | + | 4.65663i | 0.469858 | + | 0.204207i | ||||
\(521\) | − | 25.9938i | − | 1.13881i | −0.822058 | − | 0.569404i | \(-0.807174\pi\) | ||
0.822058 | − | 0.569404i | \(-0.192826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.16669i | 0.357105i | 0.983930 | + | 0.178552i | \(0.0571414\pi\) | ||||
−0.983930 | + | 0.178552i | \(0.942859\pi\) | |||||||
\(524\) | 11.3002 | + | 3.16790i | 0.493652 | + | 0.138390i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.61865 | + | 26.3138i | −0.157780 | + | 1.14734i | ||||
\(527\) | −4.74809 | −0.206830 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6349 | 1.54934 | ||||||||
\(530\) | −1.09065 | + | 7.93089i | −0.0473747 | + | 0.344496i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.4713 | + | 3.77655i | 0.584057 | + | 0.163734i | ||||
\(533\) | − | 26.9652i | − | 1.16799i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.2524i | − | 0.616185i | ||||||
\(536\) | 10.2771 | + | 4.46656i | 0.443902 | + | 0.192926i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.60101 | − | 0.495208i | −0.155251 | − | 0.0213499i | ||||
\(539\) | 79.4379 | 3.42163 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8341 | 0.895726 | 0.447863 | − | 0.894102i | \(-0.352185\pi\) | ||||
0.447863 | + | 0.894102i | \(0.352185\pi\) | |||||||
\(542\) | −38.5702 | − | 5.30414i | −1.65673 | − | 0.227832i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.89260 | + | 4.79746i | 0.252643 | + | 0.205689i | ||||
\(545\) | 2.72081i | 0.116547i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.79142i | − | 0.0765955i | −0.999266 | − | 0.0382978i | \(-0.987806\pi\) | ||
0.999266 | − | 0.0382978i | \(-0.0121935\pi\) | |||||||
\(548\) | 3.71215 | − | 13.2416i | 0.158575 | − | 0.565654i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.845155 | − | 6.14573i | 0.0360375 | − | 0.262055i | ||||
\(551\) | 0.234498 | 0.00998995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.0847 | −1.70457 | ||||||||
\(554\) | −0.472184 | + | 3.43359i | −0.0200612 | + | 0.145879i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.22044 | − | 18.6218i | 0.221396 | − | 0.789741i | ||||
\(557\) | 45.1743i | 1.91409i | 0.289931 | + | 0.957047i | \(0.406368\pi\) | ||||
−0.289931 | + | 0.957047i | \(0.593632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.2125i | − | 2.03917i | ||||||
\(560\) | 17.1227 | + | 10.4192i | 0.723568 | + | 0.440292i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.3892 | − | 2.11630i | −0.649153 | − | 0.0892709i | ||||
\(563\) | 17.1060 | 0.720934 | 0.360467 | − | 0.932772i | \(-0.382617\pi\) | ||||
0.360467 | + | 0.932772i | \(0.382617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1171 | −0.467700 | ||||||||
\(566\) | −29.8579 | − | 4.10603i | −1.25502 | − | 0.172589i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.43716 | − | 5.60764i | 0.102261 | − | 0.235291i | ||||
\(569\) | − | 16.4106i | − | 0.687969i | −0.938975 | − | 0.343985i | \(-0.888223\pi\) | ||
0.938975 | − | 0.343985i | \(-0.111777\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.9013i | − | 0.498056i | −0.968496 | − | 0.249028i | \(-0.919889\pi\) | ||
0.968496 | − | 0.249028i | \(-0.0801111\pi\) | |||||||
\(572\) | −34.8917 | − | 9.78154i | −1.45890 | − | 0.408987i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.30284 | − | 45.8325i | 0.263075 | − | 1.91301i | ||||
\(575\) | −7.65734 | −0.319333 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.29742 | 0.345426 | 0.172713 | − | 0.984972i | \(-0.444747\pi\) | ||||
0.172713 | + | 0.984972i | \(0.444747\pi\) | |||||||
\(578\) | 2.92772 | − | 21.2896i | 0.121777 | − | 0.885529i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.323481 | + | 0.0906846i | 0.0134318 | + | 0.00376547i | ||||
\(581\) | − | 58.7547i | − | 2.43755i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.8314i | − | 1.02841i | ||||||
\(584\) | 17.1540 | − | 39.4696i | 0.709839 | − | 1.63326i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.9121 | + | 4.25100i | 1.27697 | + | 0.175607i | ||||
\(587\) | −13.0818 | −0.539942 | −0.269971 | − | 0.962868i | \(-0.587014\pi\) | ||||
−0.269971 | + | 0.962868i | \(0.587014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.93462 | 0.203328 | ||||||||
\(590\) | −12.0181 | − | 1.65272i | −0.494778 | − | 0.0680414i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.0411 | − | 10.3695i | −0.700383 | − | 0.426185i | ||||
\(593\) | 11.5590i | 0.474669i | 0.971428 | + | 0.237335i | \(0.0762738\pi\) | ||||
−0.971428 | + | 0.237335i | \(0.923726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.73092i | 0.275941i | ||||||||
\(596\) | 2.71083 | − | 9.66980i | 0.111040 | − | 0.396090i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.09371 | + | 44.3117i | −0.249190 | + | 1.81204i | ||||
\(599\) | −36.3548 | −1.48542 | −0.742709 | − | 0.669614i | \(-0.766460\pi\) | ||||
−0.742709 | + | 0.669614i | \(0.766460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8417 | −0.809361 | −0.404680 | − | 0.914458i | \(-0.632617\pi\) | ||||
−0.404680 | + | 0.914458i | \(0.632617\pi\) | |||||||
\(602\) | 11.2692 | − | 81.9463i | 0.459297 | − | 3.33988i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.34020 | + | 26.1832i | −0.298669 | + | 1.06538i | ||||
\(605\) | 8.24215i | 0.335091i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.5620i | − | 0.996939i | −0.866907 | − | 0.498470i | \(-0.833896\pi\) | ||
0.866907 | − | 0.498470i | \(-0.166104\pi\) | |||||||
\(608\) | −6.12409 | − | 4.98593i | −0.248365 | − | 0.202206i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.34740 | − | 0.735369i | −0.216510 | − | 0.0297742i | ||||
\(611\) | 0.0743765 | 0.00300895 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.74574 | 0.312848 | 0.156424 | − | 0.987690i | \(-0.450003\pi\) | ||||
0.156424 | + | 0.987690i | \(0.450003\pi\) | |||||||
\(614\) | −13.7043 | − | 1.88460i | −0.553060 | − | 0.0760562i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −57.0188 | − | 24.7812i | −2.29735 | − | 0.998462i | ||||
\(617\) | 4.49553i | 0.180983i | 0.995897 | + | 0.0904915i | \(0.0288438\pi\) | ||||
−0.995897 | + | 0.0904915i | \(0.971156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 34.4576i | − | 1.38497i | −0.721434 | − | 0.692483i | \(-0.756517\pi\) | ||
0.721434 | − | 0.692483i | \(-0.243483\pi\) | |||||||
\(620\) | 6.80712 | + | 1.90831i | 0.273381 | + | 0.0766395i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.305153 | + | 2.21899i | −0.0122355 | + | 0.0889732i | ||||
\(623\) | −67.2808 | −2.69555 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.43921 | + | 39.5524i | −0.217395 | + | 1.58083i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.0782 | + | 6.18940i | 0.881016 | + | 0.246984i | ||||
\(629\) | − | 6.69881i | − | 0.267099i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.07657i | − | 0.281714i | −0.990030 | − | 0.140857i | \(-0.955014\pi\) | ||
0.990030 | − | 0.140857i | \(-0.0449858\pi\) | |||||||
\(632\) | 20.7508 | + | 9.01861i | 0.825424 | + | 0.358741i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38.1795 | + | 5.25041i | 1.51630 | + | 0.208520i | ||||
\(635\) | −6.21713 | −0.246719 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 74.7988 | 2.96364 | ||||||||
\(638\) | −1.03233 | − | 0.141966i | −0.0408705 | − | 0.00562048i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.51981 | − | 9.24619i | −0.257718 | − | 0.365488i | ||||
\(641\) | − | 5.47961i | − | 0.216431i | −0.994127 | − | 0.108216i | \(-0.965486\pi\) | ||
0.994127 | − | 0.108216i | \(-0.0345137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7194i | 0.974836i | 0.873169 | + | 0.487418i | \(0.162061\pi\) | ||||
−0.873169 | + | 0.487418i | \(0.837939\pi\) | |||||||
\(644\) | −20.7148 | + | 73.8919i | −0.816278 | + | 2.91175i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.361292 | − | 2.62722i | 0.0142149 | − | 0.103366i | ||||
\(647\) | −48.5385 | −1.90825 | −0.954123 | − | 0.299416i | \(-0.903208\pi\) | ||||
−0.954123 | + | 0.299416i | \(0.903208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.6284 | 1.47705 | ||||||||
\(650\) | 0.795799 | − | 5.78683i | 0.0312138 | − | 0.226978i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.4632 | + | 40.8906i | −0.448935 | + | 1.60140i | ||||
\(653\) | 7.83902i | 0.306765i | 0.988167 | + | 0.153382i | \(0.0490166\pi\) | ||||
−0.988167 | + | 0.153382i | \(0.950983\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.86793i | − | 0.229279i | ||||||
\(656\) | −13.5746 | + | 22.3083i | −0.530000 | + | 0.870991i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.126417 | + | 0.0173847i | 0.00492824 | + | 0.000677728i | ||||
\(659\) | −22.1705 | −0.863641 | −0.431821 | − | 0.901959i | \(-0.642129\pi\) | ||||
−0.431821 | + | 0.901959i | \(0.642129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2880 | 1.13917 | 0.569585 | − | 0.821932i | \(-0.307104\pi\) | ||||
0.569585 | + | 0.821932i | \(0.307104\pi\) | |||||||
\(662\) | −1.03373 | − | 0.142158i | −0.0401772 | − | 0.00552513i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.2191 | + | 30.4158i | −0.513002 | + | 1.18036i | ||||
\(665\) | − | 6.99534i | − | 0.271268i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28625i | 0.0498037i | ||||||||
\(668\) | −19.4620 | − | 5.45597i | −0.753008 | − | 0.211098i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.763317 | − | 5.55063i | 0.0294895 | − | 0.214439i | ||||
\(671\) | 16.7426 | 0.646340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.8428 | 1.57437 | 0.787186 | − | 0.616715i | \(-0.211537\pi\) | ||||
0.787186 | + | 0.616715i | \(0.211537\pi\) | |||||||
\(674\) | −4.34589 | + | 31.6021i | −0.167397 | + | 1.21727i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.81925 | − | 2.19205i | −0.300741 | − | 0.0843095i | ||||
\(677\) | 41.9168i | 1.61099i | 0.592600 | + | 0.805497i | \(0.298101\pi\) | ||||
−0.592600 | + | 0.805497i | \(0.701899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 72.3633i | − | 2.77705i | ||||||
\(680\) | 1.51438 | − | 3.48443i | 0.0580739 | − | 0.133622i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.7238 | − | 2.98743i | −0.831847 | − | 0.114395i | ||||
\(683\) | −46.0471 | −1.76194 | −0.880972 | − | 0.473168i | \(-0.843110\pi\) | ||||
−0.880972 | + | 0.473168i | \(0.843110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.87606 | −0.262721 | ||||||||
\(686\) | 77.9918 | + | 10.7254i | 2.97774 | + | 0.409496i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.2708 | + | 39.8861i | −0.925315 | + | 1.52064i | ||||
\(689\) | − | 23.3813i | − | 0.890757i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 41.3646i | − | 1.57358i | −0.617219 | − | 0.786792i | \(-0.711741\pi\) | ||
0.617219 | − | 0.786792i | \(-0.288259\pi\) | |||||||
\(692\) | −3.58589 | + | 12.7912i | −0.136315 | + | 0.486249i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.80651 | + | 27.6799i | −0.144493 | + | 1.05071i | ||||
\(695\) | −9.66986 | −0.366799 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.76934 | −0.332162 | ||||||||
\(698\) | 0.293587 | − | 2.13488i | 0.0111124 | − | 0.0808065i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.70522 | − | 9.64981i | 0.102248 | − | 0.364728i | ||||
\(701\) | − | 9.16505i | − | 0.346159i | −0.984908 | − | 0.173080i | \(-0.944628\pi\) | ||
0.984908 | − | 0.173080i | \(-0.0553718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.96198i | 0.262576i | ||||||||
\(704\) | 23.9417 | + | 25.6572i | 0.902338 | + | 0.966992i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.7689 | − | 5.05643i | −1.38382 | − | 0.190301i | ||||
\(707\) | 57.9784 | 2.18050 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0730 | 0.716302 | 0.358151 | − | 0.933664i | \(-0.383407\pi\) | ||||
0.358151 | + | 0.933664i | \(0.383407\pi\) | |||||||
\(710\) | −3.02867 | − | 0.416500i | −0.113664 | − | 0.0156310i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.8296 | + | 15.1374i | 1.30529 | + | 0.567299i | ||||
\(713\) | 27.0670i | 1.01367i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.1184i | 0.677591i | ||||||||
\(716\) | 13.2623 | + | 3.71796i | 0.495637 | + | 0.138947i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.54730 | + | 33.0667i | −0.169704 | + | 1.23404i | ||||
\(719\) | −36.7611 | −1.37096 | −0.685478 | − | 0.728093i | \(-0.740407\pi\) | ||||
−0.685478 | + | 0.728093i | \(0.740407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.0287 | 1.23005 | ||||||||
\(722\) | 3.28521 | − | 23.8891i | 0.122263 | − | 0.889060i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.8930 | + | 3.33408i | 0.441999 | + | 0.123910i | ||||
\(725\) | − | 0.167976i | − | 0.00623847i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.46515i | − | 0.165603i | −0.996566 | − | 0.0828017i | \(-0.973613\pi\) | ||
0.996566 | − | 0.0828017i | \(-0.0263868\pi\) | |||||||
\(728\) | −53.6890 | − | 23.3340i | −1.98985 | − | 0.864815i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.3174 | − | 2.93155i | −0.788993 | − | 0.108502i | ||||
\(731\) | −15.6792 | −0.579915 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.99033 | 0.369001 | 0.184501 | − | 0.982832i | \(-0.440933\pi\) | ||||
0.184501 | + | 0.982832i | \(0.440933\pi\) | |||||||
\(734\) | 29.0090 | + | 3.98929i | 1.07074 | + | 0.147247i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.3484 | − | 33.5914i | 1.00808 | − | 1.23819i | ||||
\(737\) | 17.3789i | 0.640160i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7581i | 0.432527i | 0.976335 | + | 0.216264i | \(0.0693870\pi\) | ||||
−0.976335 | + | 0.216264i | \(0.930613\pi\) | |||||||
\(740\) | −2.69232 | + | 9.60378i | −0.0989717 | + | 0.353042i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.46514 | − | 39.7410i | 0.200632 | − | 1.45894i | ||||
\(743\) | −21.4878 | −0.788309 | −0.394155 | − | 0.919044i | \(-0.628963\pi\) | ||||
−0.394155 | + | 0.919044i | \(0.628963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.02129 | −0.183966 | ||||||||
\(746\) | 1.68114 | − | 12.2248i | 0.0615509 | − | 0.447581i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.18105 | + | 11.3471i | −0.116311 | + | 0.414892i | ||||
\(749\) | 71.4176i | 2.60954i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3689i | 0.487838i | 0.969796 | + | 0.243919i | \(0.0784331\pi\) | ||||
−0.969796 | + | 0.243919i | \(0.921567\pi\) | |||||||
\(752\) | −0.0615315 | − | 0.0374420i | −0.00224382 | − | 0.00136537i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.972048 | − | 0.133675i | −0.0353999 | − | 0.00486816i | ||||
\(755\) | 13.5963 | 0.494821 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.899166 | 0.0326808 | 0.0163404 | − | 0.999866i | \(-0.494798\pi\) | ||||
0.0163404 | + | 0.999866i | \(0.494798\pi\) | |||||||
\(758\) | 26.1820 | + | 3.60053i | 0.950974 | + | 0.130777i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.57387 | + | 3.62131i | −0.0570904 | + | 0.131359i | ||||
\(761\) | − | 16.7534i | − | 0.607310i | −0.952782 | − | 0.303655i | \(-0.901793\pi\) | ||
0.952782 | − | 0.303655i | \(-0.0982071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 13.6338i | − | 0.493575i | ||||||
\(764\) | −1.94880 | − | 0.546327i | −0.0705053 | − | 0.0197654i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.72450 | + | 34.3553i | −0.170703 | + | 1.24131i | ||||
\(767\) | 35.4310 | 1.27934 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.2917 | −1.59720 | −0.798600 | − | 0.601862i | \(-0.794426\pi\) | ||||
−0.798600 | + | 0.601862i | \(0.794426\pi\) | |||||||
\(770\) | −4.23500 | + | 30.7957i | −0.152619 | + | 1.10980i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.21456 | + | 2.30287i | 0.295649 | + | 0.0828820i | ||||
\(773\) | 7.37167i | 0.265141i | 0.991174 | + | 0.132570i | \(0.0423230\pi\) | ||||
−0.991174 | + | 0.132570i | \(0.957677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.53478i | − | 0.126973i | ||||||
\(776\) | −16.2809 | + | 37.4607i | −0.584452 | + | 1.34476i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.1289 | − | 1.94300i | −0.506547 | − | 0.0696598i | ||||
\(779\) | 9.11384 | 0.326537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.48271 | 0.339318 | ||||||||
\(782\) | 14.4106 | + | 1.98173i | 0.515322 | + | 0.0708666i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −61.8809 | − | 37.6547i | −2.21003 | − | 1.34481i | ||||
\(785\) | − | 11.4647i | − | 0.409192i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.21381i | − | 0.114560i | −0.998358 | − | 0.0572799i | \(-0.981757\pi\) | ||
0.998358 | − | 0.0572799i | \(-0.0182427\pi\) | |||||||
\(788\) | −7.82274 | + | 27.9045i | −0.278674 | + | 0.994057i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.54124 | − | 11.2075i | 0.0548350 | − | 0.398744i | ||||
\(791\) | 55.7068 | 1.98071 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7648 | 0.559826 | ||||||||
\(794\) | −4.77690 | + | 34.7363i | −0.169526 | + | 1.23275i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.91420 | + | 6.82815i | −0.0678471 | + | 0.242017i | ||||
\(797\) | 25.6042i | 0.906948i | 0.891270 | + | 0.453474i | \(0.149815\pi\) | ||||
−0.891270 | + | 0.453474i | \(0.850185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.0241879i | − | 0.000855708i | ||||||
\(800\) | −3.57153 | + | 4.38682i | −0.126273 | + | 0.155098i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.2344 | − | 2.09502i | −0.537945 | − | 0.0739777i | ||||
\(803\) | 66.7444 | 2.35536 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.3703 | 1.35237 | ||||||||
\(806\) | −20.4551 | − | 2.81297i | −0.720502 | − | 0.0990827i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −30.0140 | − | 13.0445i | −1.05589 | − | 0.458904i | ||||
\(809\) | 39.2342i | 1.37940i | 0.724095 | + | 0.689700i | \(0.242258\pi\) | ||||
−0.724095 | + | 0.689700i | \(0.757742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2911i | 0.642286i | 0.947031 | + | 0.321143i | \(0.104067\pi\) | ||||
−0.947031 | + | 0.321143i | \(0.895933\pi\) | |||||||
\(812\) | −1.62094 | − | 0.454413i | −0.0568837 | − | 0.0159468i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.21480 | − | 30.6488i | 0.147729 | − | 1.07424i | ||||
\(815\) | 21.2335 | 0.743777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2951 | 0.570094 | ||||||||
\(818\) | 3.02051 | − | 21.9643i | 0.105610 | − | 0.767964i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.5722 | + | 3.52449i | 0.439040 | + | 0.123080i | ||||
\(821\) | 21.0781i | 0.735632i | 0.929899 | + | 0.367816i | \(0.119894\pi\) | ||||
−0.929899 | + | 0.367816i | \(0.880106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.47366i | 0.225657i | 0.993614 | + | 0.112829i | \(0.0359911\pi\) | ||||
−0.993614 | + | 0.112829i | \(0.964009\pi\) | |||||||
\(824\) | −17.0981 | − | 7.43109i | −0.595642 | − | 0.258874i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 60.2217 | + | 8.28163i | 2.09538 | + | 0.288155i | ||||
\(827\) | 41.3708 | 1.43860 | 0.719301 | − | 0.694698i | \(-0.244462\pi\) | ||||
0.719301 | + | 0.694698i | \(0.244462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.2056 | −1.50059 | −0.750297 | − | 0.661101i | \(-0.770089\pi\) | ||||
−0.750297 | + | 0.661101i | \(0.770089\pi\) | |||||||
\(830\) | 16.4275 | + | 2.25910i | 0.570208 | + | 0.0784144i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.5436 | + | 24.1589i | 0.781558 | + | 0.837557i | ||||
\(833\) | − | 24.3253i | − | 0.842821i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1062i | 0.349738i | ||||||||
\(836\) | 3.30602 | − | 11.7929i | 0.114341 | − | 0.407866i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.753306 | − | 5.47783i | 0.0260225 | − | 0.189229i | ||||
\(839\) | 30.1689 | 1.04155 | 0.520774 | − | 0.853695i | \(-0.325644\pi\) | ||||
0.520774 | + | 0.853695i | \(0.325644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9718 | 0.999027 | ||||||||
\(842\) | −4.24456 | + | 30.8653i | −0.146277 | + | 1.06369i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3382 | + | 47.5788i | −0.459121 | + | 1.63773i | ||||
\(845\) | 4.06035i | 0.139680i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 41.3007i | − | 1.41911i | ||||||
\(848\) | −11.7705 | + | 19.3433i | −0.404199 | + | 0.664253i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.88193 | − | 0.258802i | −0.0645498 | − | 0.00887682i | ||||
\(851\) | −38.1873 | −1.30904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.7562 | 0.881875 | 0.440937 | − | 0.897538i | \(-0.354646\pi\) | ||||
0.440937 | + | 0.897538i | \(0.354646\pi\) | |||||||
\(854\) | 26.7953 | + | 3.68487i | 0.916918 | + | 0.126094i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.0682 | − | 36.9711i | 0.549199 | − | 1.26365i | ||||
\(857\) | 5.04937i | 0.172483i | 0.996274 | + | 0.0862416i | \(0.0274857\pi\) | ||||
−0.996274 | + | 0.0862416i | \(0.972514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0894i | 0.412486i | 0.978501 | + | 0.206243i | \(0.0661237\pi\) | ||||
−0.978501 | + | 0.206243i | \(0.933876\pi\) | |||||||
\(860\) | 22.4785 | + | 6.30162i | 0.766511 | + | 0.214883i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.94474 | − | 14.1416i | 0.0662382 | − | 0.481665i | ||||
\(863\) | 42.8144 | 1.45742 | 0.728709 | − | 0.684824i | \(-0.240121\pi\) | ||||
0.728709 | + | 0.684824i | \(0.240121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.64217 | 0.225841 | ||||||||
\(866\) | 4.88648 | − | 35.5331i | 0.166049 | − | 1.20746i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −34.1099 | − | 9.56236i | −1.15777 | − | 0.324568i | ||||
\(869\) | 35.0904i | 1.19036i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.3640i | 0.554473i | ||||||||
\(872\) | −3.06744 | + | 7.05786i | −0.103877 | + | 0.239009i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.9767 | − | 2.05958i | −0.506595 | − | 0.0696665i | ||||
\(875\) | −5.01091 | −0.169400 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.2401 | −0.548391 | −0.274195 | − | 0.961674i | \(-0.588411\pi\) | ||||
−0.274195 | + | 0.961674i | \(0.588411\pi\) | |||||||
\(878\) | −23.5902 | − | 3.24411i | −0.796132 | − | 0.109483i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.12105 | − | 14.9894i | 0.307471 | − | 0.505291i | ||||
\(881\) | − | 10.2669i | − | 0.345899i | −0.984931 | − | 0.172949i | \(-0.944670\pi\) | ||
0.984931 | − | 0.172949i | \(-0.0553297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 55.9619i | − | 1.88327i | −0.336638 | − | 0.941634i | \(-0.609290\pi\) | ||
0.336638 | − | 0.941634i | \(-0.390710\pi\) | |||||||
\(884\) | −2.99528 | + | 10.6845i | −0.100742 | + | 0.359358i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.483103 | + | 3.51299i | −0.0162302 | + | 0.118021i | ||||
\(887\) | −8.19837 | −0.275274 | −0.137637 | − | 0.990483i | \(-0.543951\pi\) | ||||
−0.137637 | + | 0.990483i | \(0.543951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.1535 | 1.04485 | ||||||||
\(890\) | 2.58692 | − | 18.8114i | 0.0867139 | − | 0.630559i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.260369 | − | 0.928763i | 0.00871781 | − | 0.0310973i | ||||
\(893\) | 0.0251382i | 0.000841216i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.88682i | − | 0.230201i | ||||||
\(896\) | 32.6702 | + | 46.3319i | 1.09143 | + | 1.54784i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.8560 | + | 4.65584i | 1.12979 | + | 0.155368i | ||||
\(899\) | −0.593757 | −0.0198029 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.60383 | −0.253320 | ||||||||
\(902\) | −40.1220 | − | 5.51754i | −1.33592 | − | 0.183714i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.8380 | − | 12.5334i | −0.959139 | − | 0.416855i | ||||
\(905\) | − | 6.17574i | − | 0.205289i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 56.1230i | − | 1.86353i | −0.363058 | − | 0.931766i | \(-0.618267\pi\) | ||
0.363058 | − | 0.931766i | \(-0.381733\pi\) | |||||||
\(908\) | 9.81361 | + | 2.75115i | 0.325676 | + | 0.0913000i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.98768 | + | 28.9973i | −0.132190 | + | 0.961251i | ||||
\(911\) | −35.7150 | −1.18329 | −0.591646 | − | 0.806198i | \(-0.701522\pi\) | ||||
−0.591646 | + | 0.806198i | \(0.701522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.4342 | −1.70222 | ||||||||
\(914\) | 5.76065 | − | 41.8898i | 0.190545 | − | 1.38559i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.8192 | + | 5.27576i | 0.621803 | + | 0.174316i | ||||
\(917\) | 29.4037i | 0.970995i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.1866i | 0.929789i | 0.885366 | + | 0.464895i | \(0.153908\pi\) | ||||
−0.885366 | + | 0.464895i | \(0.846092\pi\) | |||||||
\(920\) | −19.8633 | − | 8.63288i | −0.654875 | − | 0.284618i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.1516 | − | 1.67107i | −0.400191 | − | 0.0550338i | ||||
\(923\) | 8.92893 | 0.293899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.98701 | 0.163972 | ||||||||
\(926\) | 18.1694 | + | 2.49864i | 0.597083 | + | 0.0821103i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.736880 | + | 0.599930i | 0.0241893 | + | 0.0196937i | ||||
\(929\) | 28.0950i | 0.921767i | 0.887461 | + | 0.460883i | \(0.152467\pi\) | ||||
−0.887461 | + | 0.460883i | \(0.847533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.2809i | 0.828548i | ||||||||
\(932\) | 6.64104 | − | 23.6893i | 0.217534 | − | 0.775967i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.525451 | + | 3.82093i | −0.0171933 | + | 0.125025i | ||||
\(935\) | 5.89229 | 0.192698 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3568 | 0.665026 | 0.332513 | − | 0.943099i | \(-0.392103\pi\) | ||||
0.332513 | + | 0.943099i | \(0.392103\pi\) | |||||||
\(938\) | −3.82492 | + | 27.8137i | −0.124888 | + | 0.908150i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.00972138 | + | 0.0346771i | −0.000317076 | + | 0.00113104i | ||||
\(941\) | − | 25.1556i | − | 0.820050i | −0.912074 | − | 0.410025i | \(-0.865520\pi\) | ||
0.912074 | − | 0.410025i | \(-0.134480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.9905i | 1.62791i | ||||||||
\(944\) | −29.3120 | − | 17.8364i | −0.954025 | − | 0.580526i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −71.7364 | − | 9.86511i | −2.33235 | − | 0.320743i | ||||
\(947\) | 52.6385 | 1.71052 | 0.855261 | − | 0.518197i | \(-0.173397\pi\) | ||||
0.855261 | + | 0.518197i | \(0.173397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.8466 | 2.04009 | ||||||||
\(950\) | 1.95586 | + | 0.268969i | 0.0634566 | + | 0.00872649i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.58844 | + | 17.4602i | −0.245943 | + | 0.565887i | ||||
\(953\) | − | 12.7002i | − | 0.411399i | −0.978615 | − | 0.205700i | \(-0.934053\pi\) | ||
0.978615 | − | 0.205700i | \(-0.0659470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.01197i | 0.0327465i | ||||||||
\(956\) | −36.0294 | − | 10.1005i | −1.16527 | − | 0.326673i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.23588 | − | 52.6173i | 0.233781 | − | 1.69999i | ||||
\(959\) | 34.4553 | 1.11262 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5054 | 0.596947 | ||||||||
\(962\) | 3.96866 | − | 28.8590i | 0.127955 | − | 0.930452i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.2540 | + | 11.2848i | 1.29649 | + | 0.363459i | ||||
\(965\) | − | 4.26563i | − | 0.137315i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.7362i | 1.05272i | 0.850260 | + | 0.526362i | \(0.176444\pi\) | ||||
−0.850260 | + | 0.526362i | \(0.823556\pi\) | |||||||
\(968\) | −9.29220 | + | 21.3803i | −0.298663 | + | 0.687190i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.2324 | + | 2.78234i | 0.649624 | + | 0.0893357i | ||||
\(971\) | −53.1517 | −1.70572 | −0.852860 | − | 0.522140i | \(-0.825134\pi\) | ||||
−0.852860 | + | 0.522140i | \(0.825134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.4549 | 1.55339 | ||||||||
\(974\) | 3.48837 | + | 0.479718i | 0.111775 | + | 0.0153712i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.0422 | − | 7.93622i | −0.417472 | − | 0.254032i | ||||
\(977\) | − | 1.96623i | − | 0.0629054i | −0.999505 | − | 0.0314527i | \(-0.989987\pi\) | ||
0.999505 | − | 0.0314527i | \(-0.0100134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.8980i | 1.88239i | ||||||||
\(980\) | −9.77658 | + | 34.8741i | −0.312301 | + | 1.11401i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.38869 | − | 31.9133i | 0.140049 | − | 1.01840i | ||||
\(983\) | 4.44401 | 0.141742 | 0.0708709 | − | 0.997485i | \(-0.477422\pi\) | ||||
0.0708709 | + | 0.997485i | \(0.477422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4901 | 0.461694 | ||||||||
\(986\) | −0.0434724 | + | 0.316119i | −0.00138444 | + | 0.0100673i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.11295 | − | 11.1042i | 0.0990362 | − | 0.353272i | ||||
\(989\) | 89.3807i | 2.84214i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.8186i | 1.70960i | 0.518955 | + | 0.854802i | \(0.326321\pi\) | ||||
−0.518955 | + | 0.854802i | \(0.673679\pi\) | |||||||
\(992\) | 15.5064 | + | 12.6245i | 0.492330 | + | 0.400830i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.1764 | + | 2.08705i | 0.481367 | + | 0.0661971i | ||||
\(995\) | 3.54569 | 0.112406 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.46125 | −0.204630 | −0.102315 | − | 0.994752i | \(-0.532625\pi\) | ||||
−0.102315 | + | 0.994752i | \(0.532625\pi\) | |||||||
\(998\) | 24.3227 | + | 3.34483i | 0.769920 | + | 0.105879i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.2.e.a.971.25 | yes | 48 | |
3.2 | odd | 2 | inner | 1620.2.e.a.971.24 | yes | 48 | |
4.3 | odd | 2 | inner | 1620.2.e.a.971.23 | ✓ | 48 | |
12.11 | even | 2 | inner | 1620.2.e.a.971.26 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.e.a.971.23 | ✓ | 48 | 4.3 | odd | 2 | inner | |
1620.2.e.a.971.24 | yes | 48 | 3.2 | odd | 2 | inner | |
1620.2.e.a.971.25 | yes | 48 | 1.1 | even | 1 | trivial | |
1620.2.e.a.971.26 | yes | 48 | 12.11 | even | 2 | inner |