Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(703,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.q (of order \(6\), degree \(2\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} - 24 x^{13} + 104 x^{12} - 196 x^{11} + 312 x^{10} - 236 x^{9} + 31 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 831.4 | ||
Root | \(0.219056 + 1.66389i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.831 |
Dual form | 896.2.q.c.703.4 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.753671 | + | 0.435132i | −0.435132 | + | 0.251224i | −0.701531 | − | 0.712639i | \(-0.747500\pi\) |
0.266399 | + | 0.963863i | \(0.414166\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.866025 | − | 1.50000i | 0.387298 | − | 0.670820i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.615370 | − | 2.57319i | 0.232588 | − | 0.972575i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.12132 | + | 1.94218i | −0.373773 | + | 0.647395i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81952 | − | 3.15150i | −0.548607 | − | 0.950214i | −0.998370 | − | 0.0570668i | \(-0.981825\pi\) |
0.449764 | − | 0.893148i | \(-0.351508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.01461 | −0.281403 | −0.140701 | − | 0.990052i | \(-0.544936\pi\) | ||||
−0.140701 | + | 0.990052i | \(0.544936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50734i | 0.389194i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.621320 | + | 0.358719i | −0.150692 | + | 0.0870023i | −0.573450 | − | 0.819240i | \(-0.694395\pi\) |
0.422758 | + | 0.906243i | \(0.361062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.45857 | − | 3.15150i | −1.25228 | − | 0.723005i | −0.280719 | − | 0.959790i | \(-0.590573\pi\) |
−0.971562 | + | 0.236785i | \(0.923906\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.655892 | + | 2.20711i | 0.143127 | + | 0.481630i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.15150 | − | 1.81952i | −0.657134 | − | 0.379397i | 0.134050 | − | 0.990975i | \(-0.457202\pi\) |
−0.791184 | + | 0.611578i | \(0.790535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.56248i | − | 0.878050i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.58579i | 0.851559i | 0.904827 | + | 0.425780i | \(0.140000\pi\) | ||||
−0.904827 | + | 0.425780i | \(0.860000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.76687 | + | 6.52442i | 0.676551 | + | 1.17182i | 0.976013 | + | 0.217712i | \(0.0698593\pi\) |
−0.299463 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.74264 | + | 1.58346i | 0.477432 | + | 0.275646i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.32686 | − | 3.15150i | −0.562343 | − | 0.532701i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.27231 | − | 3.62132i | −1.03116 | − | 0.595341i | −0.113844 | − | 0.993499i | \(-0.536317\pi\) |
−0.917317 | + | 0.398157i | \(0.869650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.764683 | − | 0.441490i | 0.122447 | − | 0.0706950i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.34847i | − | 1.14764i | −0.818982 | − | 0.573819i | \(-0.805461\pi\) | ||
0.818982 | − | 0.573819i | \(-0.194539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2928 | −1.56963 | −0.784816 | − | 0.619728i | \(-0.787243\pi\) | ||||
−0.784816 | + | 0.619728i | \(0.787243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.94218 | + | 3.36396i | 0.289524 | + | 0.501470i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.30540 | + | 2.26101i | −0.190412 | + | 0.329802i | −0.945387 | − | 0.325951i | \(-0.894316\pi\) |
0.754975 | + | 0.655753i | \(0.227649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.24264 | − | 3.16693i | −0.891806 | − | 0.452418i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.312181 | − | 0.540713i | 0.0437140 | − | 0.0757149i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.82282 | − | 2.20711i | 0.525105 | − | 0.303169i | −0.213916 | − | 0.976852i | \(-0.568622\pi\) |
0.739021 | + | 0.673683i | \(0.235289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.30301 | −0.849898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.48528 | 0.726543 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.753671 | + | 0.435132i | −0.0981196 | + | 0.0566494i | −0.548257 | − | 0.836310i | \(-0.684708\pi\) |
0.450137 | + | 0.892959i | \(0.351375\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.27231 | − | 10.8640i | 0.803087 | − | 1.39099i | −0.114488 | − | 0.993425i | \(-0.536523\pi\) |
0.917575 | − | 0.397563i | \(-0.130144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.30759 | + | 4.08053i | 0.542705 | + | 0.514099i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.878680 | + | 1.52192i | −0.108987 | + | 0.188771i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.88537 | − | 4.99761i | −0.352504 | − | 0.610556i | 0.634183 | − | 0.773183i | \(-0.281337\pi\) |
−0.986688 | + | 0.162627i | \(0.948003\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.16693 | 0.381253 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.5562i | − | 1.72750i | −0.503920 | − | 0.863750i | \(-0.668110\pi\) | ||
0.503920 | − | 0.863750i | \(-0.331890\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.25736 | + | 1.88064i | −0.381245 | + | 0.220112i | −0.678360 | − | 0.734730i | \(-0.737309\pi\) |
0.297115 | + | 0.954842i | \(0.403976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50734 | − | 0.870264i | −0.174053 | − | 0.100489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.22911 | + | 2.74264i | −1.05175 | + | 0.312553i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.76230 | + | 3.32686i | 0.648309 | + | 0.374301i | 0.787808 | − | 0.615921i | \(-0.211216\pi\) |
−0.139499 | + | 0.990222i | \(0.544549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.37868 | − | 2.38794i | −0.153187 | − | 0.265327i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.48106i | − | 0.382096i | −0.981581 | − | 0.191048i | \(-0.938811\pi\) | ||
0.981581 | − | 0.191048i | \(-0.0611885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.24264i | 0.134783i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.99542 | − | 3.45617i | −0.213932 | − | 0.370541i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.98528 | − | 4.03295i | −0.740438 | − | 0.427492i | 0.0817903 | − | 0.996650i | \(-0.473936\pi\) |
−0.822229 | + | 0.569157i | \(0.807270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.624361 | + | 2.61079i | −0.0654508 | + | 0.273685i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.67796 | − | 3.27817i | −0.588778 | − | 0.339931i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.45451 | + | 5.45857i | −0.970013 | + | 0.560037i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01461i | 0.103018i | 0.998673 | + | 0.0515091i | \(0.0164031\pi\) | ||||
−0.998673 | + | 0.0515091i | \(0.983597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.16107 | 0.820218 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.76500 | + | 9.98528i | 0.573639 | + | 0.993573i | 0.996188 | + | 0.0872323i | \(0.0278023\pi\) |
−0.422549 | + | 0.906340i | \(0.638864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.99304 | − | 12.1123i | 0.689044 | − | 1.19346i | −0.283103 | − | 0.959089i | \(-0.591364\pi\) |
0.972147 | − | 0.234370i | \(-0.0753028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.87868 | + | 0.927572i | 0.378520 | + | 0.0905218i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.32686 | − | 5.76230i | 0.321620 | − | 0.557062i | −0.659202 | − | 0.751966i | \(-0.729106\pi\) |
0.980822 | + | 0.194903i | \(0.0624393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.59808 | + | 1.50000i | −0.248851 | + | 0.143674i | −0.619238 | − | 0.785203i | \(-0.712558\pi\) |
0.370387 | + | 0.928877i | \(0.379225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.30301 | 0.598255 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264 | 0.399114 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.45857 | + | 3.15150i | −0.509014 | + | 0.293879i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.13770 | − | 1.97056i | 0.105181 | − | 0.182179i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.540713 | + | 1.81952i | 0.0495671 | + | 0.166795i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.12132 | + | 1.94218i | −0.101938 | + | 0.176562i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.19755 | + | 5.53833i | 0.288314 | + | 0.499374i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.02937i | 0.535020i | 0.963555 | + | 0.267510i | \(0.0862008\pi\) | ||||
−0.963555 | + | 0.267510i | \(0.913799\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.75736 | − | 4.47871i | 0.682997 | − | 0.394329i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6708 | + | 6.73814i | 1.01968 | + | 0.588714i | 0.914012 | − | 0.405687i | \(-0.132968\pi\) |
0.105671 | + | 0.994401i | \(0.466301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4685 | + | 12.1066i | −0.994442 | + | 1.04978i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.84372 | − | 3.95122i | −0.589014 | − | 0.340067i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.62132 | + | 11.4685i | 0.565698 | + | 0.979817i | 0.996984 | + | 0.0776021i | \(0.0247264\pi\) |
−0.431287 | + | 0.902215i | \(0.641940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8276i | 1.51212i | 0.654504 | + | 0.756059i | \(0.272878\pi\) | ||||
−0.654504 | + | 0.756059i | \(0.727122\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.27208i | − | 0.191343i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.84611 | + | 3.19755i | 0.154379 | + | 0.267393i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.87868 | + | 3.97141i | 0.571243 | + | 0.329807i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.08293 | − | 0.329551i | 0.501711 | − | 0.0271809i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0417 | − | 11.5711i | −1.64188 | − | 0.947939i | −0.980165 | − | 0.198181i | \(-0.936496\pi\) |
−0.661713 | − | 0.749757i | \(-0.730170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9114 | + | 8.03176i | −1.13209 | + | 0.653615i | −0.944461 | − | 0.328624i | \(-0.893415\pi\) |
−0.187634 | + | 0.982239i | \(0.560082\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.60896i | − | 0.130077i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.0488 | 1.04811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.28692 | + | 12.6213i | 0.581560 | + | 1.00729i | 0.995295 | + | 0.0968937i | \(0.0308907\pi\) |
−0.413735 | + | 0.910397i | \(0.635776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.92077 | + | 3.32686i | −0.152327 | + | 0.263837i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.62132 | + | 6.98975i | −0.521833 | + | 0.550869i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.03176 | + | 13.9114i | −0.629096 | + | 1.08963i | 0.358638 | + | 0.933477i | \(0.383241\pi\) |
−0.987733 | + | 0.156149i | \(0.950092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.75039 | − | 2.74264i | 0.369818 | − | 0.213514i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1354 | 1.09383 | 0.546914 | − | 0.837189i | \(-0.315802\pi\) | ||||
0.546914 | + | 0.837189i | \(0.315802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9706 | −0.920813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.2416 | − | 7.06769i | 0.936139 | − | 0.540480i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.43924 | − | 16.3492i | 0.717652 | − | 1.24301i | −0.244276 | − | 0.969706i | \(-0.578550\pi\) |
0.961928 | − | 0.273304i | \(-0.0881165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.07227 | − | 1.50734i | 0.383428 | − | 0.113944i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.378680 | − | 0.655892i | 0.0284633 | − | 0.0492999i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6050 | + | 18.3683i | 0.792651 | + | 1.37291i | 0.924320 | + | 0.381618i | \(0.124633\pi\) |
−0.131669 | + | 0.991294i | \(0.542033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7554 | 1.39408 | 0.697038 | − | 0.717034i | \(-0.254501\pi\) | ||||
0.697038 | + | 0.717034i | \(0.254501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9171i | 0.807018i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8640 | + | 6.27231i | −0.798734 | + | 0.461149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.26101 | + | 1.30540i | 0.165342 | + | 0.0954600i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.7401 | − | 2.80761i | −0.853970 | − | 0.204224i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.91619 | − | 2.26101i | −0.283365 | − | 0.163601i | 0.351581 | − | 0.936158i | \(-0.385644\pi\) |
−0.634946 | + | 0.772557i | \(0.718978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.62132 | − | 14.9326i | −0.620576 | − | 1.07487i | −0.989379 | − | 0.145362i | \(-0.953565\pi\) |
0.368802 | − | 0.929508i | \(-0.379768\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.52937i | − | 0.109520i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.07107i | 0.0763104i | 0.999272 | + | 0.0381552i | \(0.0121481\pi\) | ||||
−0.999272 | + | 0.0381552i | \(0.987852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.53613 | − | 4.39271i | −0.179782 | − | 0.311391i | 0.762024 | − | 0.647549i | \(-0.224206\pi\) |
−0.941806 | + | 0.336158i | \(0.890873\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.34924 | + | 2.51104i | 0.306772 | + | 0.177115i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8001 | + | 2.82195i | 0.828205 | + | 0.198062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0227 | − | 6.36396i | −0.769859 | − | 0.444478i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.06769 | − | 4.08053i | 0.491239 | − | 0.283617i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.9369i | 1.58658i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.24872 | −0.0859656 | −0.0429828 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429828 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.33386 | + | 10.9706i | 0.433989 | + | 0.751691i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.91380 | + | 15.4392i | −0.607916 | + | 1.05294i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.1066 | − | 5.67796i | 1.29704 | − | 0.385445i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.63665 | − | 2.83476i | 0.110595 | − | 0.191555i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.630399 | − | 0.363961i | 0.0424052 | − | 0.0244827i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1445 | −0.679329 | −0.339664 | − | 0.940547i | \(-0.610313\pi\) | ||||
−0.339664 | + | 0.940547i | \(0.610313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.48528 | −0.299019 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.8684 | − | 8.58425i | 0.986847 | − | 0.569757i | 0.0825170 | − | 0.996590i | \(-0.473704\pi\) |
0.904330 | + | 0.426833i | \(0.140371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.94655 | − | 17.2279i | 0.657286 | − | 1.13845i | −0.324029 | − | 0.946047i | \(-0.605038\pi\) |
0.981315 | − | 0.192406i | \(-0.0616291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.76230 | − | 6.08293i | 0.379131 | − | 0.400227i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1066 | − | 20.9692i | 0.793130 | − | 1.37374i | −0.130890 | − | 0.991397i | \(-0.541783\pi\) |
0.924020 | − | 0.382344i | \(-0.124883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.26101 | + | 3.91619i | 0.147492 | + | 0.255464i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.79050 | −0.376133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.4392i | − | 0.998676i | −0.866407 | − | 0.499338i | \(-0.833577\pi\) | ||
0.866407 | − | 0.499338i | \(-0.166423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.2279 | − | 8.21449i | 0.916501 | − | 0.529142i | 0.0339839 | − | 0.999422i | \(-0.489181\pi\) |
0.882517 | + | 0.470280i | \(0.155847\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9318 | + | 8.04354i | 0.893726 | + | 0.515993i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.1567 | + | 6.62132i | −0.648886 | + | 0.423021i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.53833 | + | 3.19755i | 0.352395 | + | 0.203455i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.51472 | + | 2.62357i | 0.0959914 | + | 0.166262i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.17327i | 0.452773i | 0.974038 | + | 0.226386i | \(0.0726912\pi\) | ||||
−0.974038 | + | 0.226386i | \(0.927309\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.2426i | 0.832558i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.540713 | − | 0.936542i | −0.0338607 | − | 0.0586485i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8640 | − | 6.27231i | −0.677675 | − | 0.391256i | 0.121303 | − | 0.992615i | \(-0.461293\pi\) |
−0.798979 | + | 0.601359i | \(0.794626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.1781 | + | 13.9114i | −0.818850 | + | 0.864413i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.90644 | − | 5.14214i | −0.551295 | − | 0.318290i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0605 | − | 12.7367i | 1.36031 | − | 0.785376i | 0.370646 | − | 0.928774i | \(-0.379136\pi\) |
0.989665 | + | 0.143399i | \(0.0458031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.64564i | − | 0.469668i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.01947 | 0.429585 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1713 | + | 19.3492i | 0.681126 | + | 1.17974i | 0.974638 | + | 0.223789i | \(0.0718426\pi\) |
−0.293512 | + | 0.955955i | \(0.594824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.99304 | − | 12.1123i | 0.424797 | − | 0.735769i | −0.571605 | − | 0.820529i | \(-0.693679\pi\) |
0.996401 | + | 0.0847597i | \(0.0270123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.665476 | − | 2.23936i | −0.0402765 | − | 0.135532i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.63904 | − | 6.30301i | 0.219443 | − | 0.380086i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96768 | − | 1.13604i | 0.118226 | − | 0.0682580i | −0.439721 | − | 0.898135i | \(-0.644923\pi\) |
0.557947 | + | 0.829877i | \(0.311589\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.8955 | −1.01151 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.75736 | −0.462765 | −0.231383 | − | 0.972863i | \(-0.574325\pi\) | ||||
−0.231383 | + | 0.972863i | \(0.574325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.8977 | + | 12.0653i | −1.24224 | + | 0.717208i | −0.969550 | − | 0.244894i | \(-0.921247\pi\) |
−0.272691 | + | 0.962102i | \(0.587914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.75039 | − | 8.22792i | 0.281389 | − | 0.487380i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.9090 | − | 4.52202i | −1.11616 | − | 0.266927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.24264 | + | 14.2767i | −0.484861 | + | 0.839804i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.441490 | − | 0.764683i | −0.0258806 | − | 0.0448265i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.49333 | −0.320923 | −0.160462 | − | 0.987042i | \(-0.551298\pi\) | ||||
−0.160462 | + | 0.987042i | \(0.551298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50734i | 0.0877608i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.3787 | + | 8.30153i | −0.834336 | + | 0.481704i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.19755 | + | 1.84611i | 0.184919 | + | 0.106763i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.33386 | + | 26.4853i | −0.365077 | + | 1.52659i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.68983 | − | 5.01708i | −0.499218 | − | 0.288223i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8640 | − | 18.8169i | −0.622069 | − | 1.07745i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.6060i | − | 0.719463i | −0.933056 | − | 0.359732i | \(-0.882868\pi\) | ||
0.933056 | − | 0.359732i | \(-0.117132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1716i | 0.692417i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6761 | + | 25.4197i | 0.832205 | + | 1.44142i | 0.896286 | + | 0.443477i | \(0.146255\pi\) |
−0.0640807 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.25736 | − | 5.34474i | −0.523257 | − | 0.302103i | 0.215009 | − | 0.976612i | \(-0.431022\pi\) |
−0.738266 | + | 0.674510i | \(0.764355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.85128 | − | 2.92753i | 0.555057 | − | 0.164948i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.7597 | − | 15.4497i | −1.50298 | − | 0.867744i | −0.999994 | − | 0.00344803i | \(-0.998902\pi\) |
−0.502983 | − | 0.864296i | \(-0.667764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4521 | − | 8.34394i | 0.809164 | − | 0.467171i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.79050i | 0.323194i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.52202 | 0.251612 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.01461 | − | 1.75736i | −0.0562805 | − | 0.0974808i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.30540 | − | 2.26101i | 0.0721886 | − | 0.125034i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.01472 | + | 4.75039i | 0.276470 | + | 0.261898i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.40740 | + | 12.8300i | −0.407147 | + | 0.705200i | −0.994569 | − | 0.104081i | \(-0.966810\pi\) |
0.587421 | + | 0.809281i | \(0.300143\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0665 | − | 8.12132i | 0.770842 | − | 0.445046i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.99523 | −0.546098 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.24264 | −0.340058 | −0.170029 | − | 0.985439i | \(-0.554386\pi\) | ||||
−0.170029 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.19755 | + | 1.84611i | −0.173667 | + | 0.100267i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.7078 | − | 23.7426i | 0.742320 | − | 1.28574i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9906 | + | 14.1147i | −0.647434 | + | 0.762121i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.74264 | − | 4.75039i | 0.147659 | − | 0.255753i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5538 | − | 21.7438i | −0.673922 | − | 1.16727i | −0.976783 | − | 0.214233i | \(-0.931275\pi\) |
0.302860 | − | 0.953035i | \(-0.402058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0162 | 1.07144 | 0.535721 | − | 0.844395i | \(-0.320040\pi\) | ||||
0.535721 | + | 0.844395i | \(0.320040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.62915i | 0.247086i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.3492 | − | 18.0995i | 1.66855 | − | 0.963339i | 0.700132 | − | 0.714013i | \(-0.253124\pi\) |
0.968420 | − | 0.249325i | \(-0.0802089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8343 | − | 12.6060i | −1.15884 | − | 0.669058i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.19925 | − | 1.13604i | −0.0634711 | − | 0.0601256i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1282 | + | 16.8172i | 1.53733 | + | 0.887577i | 0.998994 | + | 0.0448462i | \(0.0142798\pi\) |
0.538335 | + | 0.842731i | \(0.319054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3640 | + | 17.9509i | 0.545472 | + | 0.944785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.95169i | − | 0.102437i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.51472i | 0.340996i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6853 | − | 18.5074i | −0.557766 | − | 0.966078i | −0.997683 | − | 0.0680400i | \(-0.978325\pi\) |
0.439917 | − | 0.898038i | \(-0.355008\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.2721 | + | 8.23999i | 0.742975 | + | 0.428957i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.32686 | − | 11.1950i | −0.172722 | − | 0.581218i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4685 | − | 6.62132i | −0.593815 | − | 0.342839i | 0.172790 | − | 0.984959i | \(-0.444722\pi\) |
−0.766604 | + | 0.642120i | \(0.778055\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.13777 | + | 5.27569i | −0.471872 | + | 0.272436i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.65279i | − | 0.239631i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.2294 | −1.45005 | −0.725023 | − | 0.688725i | \(-0.758171\pi\) | ||||
−0.725023 | + | 0.688725i | \(0.758171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.62357 | − | 4.54416i | −0.134410 | − | 0.232804i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.38682 | + | 4.13410i | −0.121961 | + | 0.211242i | −0.920541 | − | 0.390646i | \(-0.872252\pi\) |
0.798580 | + | 0.601889i | \(0.205585\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.87868 | + | 16.2189i | −0.197676 | + | 0.826589i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.5415 | − | 19.9905i | 0.586687 | − | 1.01617i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.04757 | − | 2.91421i | 0.255922 | − | 0.147756i | −0.366551 | − | 0.930398i | \(-0.619461\pi\) |
0.622473 | + | 0.782641i | \(0.286128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61079 | 0.132033 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.7279 | −0.591595 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.98059 | − | 5.76230i | 0.502178 | − | 0.289933i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.94655 | − | 17.2279i | 0.499203 | − | 0.864645i | −0.500797 | − | 0.865565i | \(-0.666960\pi\) |
1.00000 | 0.000920276i | \(0.000292933\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.37548 | − | 14.1147i | 0.168985 | − | 0.706618i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.62132 | − | 11.4685i | 0.330653 | − | 0.572708i | −0.651987 | − | 0.758230i | \(-0.726064\pi\) |
0.982640 | + | 0.185522i | \(0.0593977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.82192 | − | 6.61975i | −0.190383 | − | 0.329753i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.77589 | −0.237316 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.3563i | 1.30643i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.3492 | + | 11.1713i | −0.956758 | + | 0.552385i | −0.895174 | − | 0.445717i | \(-0.852949\pi\) |
−0.0615846 | + | 0.998102i | \(0.519615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.98059 | − | 5.76230i | −0.492306 | − | 0.284233i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.655892 | + | 2.20711i | 0.0322744 | + | 0.108605i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.22158 | − | 3.01468i | −0.256317 | − | 0.147985i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.75736 | − | 13.4361i | −0.379880 | − | 0.657971i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.74053i | 0.0850304i | 0.999096 | + | 0.0425152i | \(0.0135371\pi\) | ||||
−0.999096 | + | 0.0425152i | \(0.986463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.75736i | 0.378071i | 0.981970 | + | 0.189035i | \(0.0605361\pi\) | ||||
−0.981970 | + | 0.189035i | \(0.939464\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.92753 | − | 5.07064i | −0.142342 | − | 0.246543i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.24264 | − | 0.717439i | −0.0602769 | − | 0.0348009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0953 | − | 22.8252i | −1.16605 | − | 1.10459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.78272 | − | 1.60660i | −0.134351 | − | 0.0775675i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.91619 | + | 2.26101i | −0.188636 | + | 0.108909i | −0.591344 | − | 0.806419i | \(-0.701402\pi\) |
0.402708 | + | 0.915329i | \(0.368069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6105i | 0.990479i | 0.868757 | + | 0.495239i | \(0.164920\pi\) | ||||
−0.868757 | + | 0.495239i | \(0.835080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.91235 | −0.331422 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4685 | + | 19.8640i | 0.548611 | + | 0.950222i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.2915 | + | 26.4856i | −0.729822 | + | 1.26409i | 0.227136 | + | 0.973863i | \(0.427064\pi\) |
−0.956958 | + | 0.290226i | \(0.906270\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.1508 | − | 8.57321i | 0.626227 | − | 0.408248i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.95122 | − | 6.84372i | 0.187728 | − | 0.325155i | −0.756764 | − | 0.653688i | \(-0.773221\pi\) |
0.944492 | + | 0.328533i | \(0.106554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0989 | + | 6.98528i | −0.573541 | + | 0.331134i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.1398 | 0.952578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.2426 | 1.04970 | 0.524848 | − | 0.851196i | \(-0.324122\pi\) | ||||
0.524848 | + | 0.851196i | \(0.324122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.1587 | + | 13.3707i | −1.09050 | + | 0.629602i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.98975 | − | 12.1066i | 0.328407 | − | 0.568818i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.37548 | + | 3.19755i | 0.158245 | + | 0.149904i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.25736 | − | 2.17781i | 0.0588168 | − | 0.101874i | −0.835118 | − | 0.550071i | \(-0.814601\pi\) |
0.893935 | + | 0.448198i | \(0.147934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.63665 | + | 2.83476i | 0.0763923 | + | 0.132315i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.31925 | −0.247742 | −0.123871 | − | 0.992298i | \(-0.539531\pi\) | ||||
−0.123871 | + | 0.992298i | \(0.539531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.27809i | − | 0.338241i | −0.985595 | − | 0.169121i | \(-0.945907\pi\) | ||
0.985595 | − | 0.169121i | \(-0.0540928\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.83452 | + | 5.67796i | −0.456065 | + | 0.263309i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7149 | − | 11.9597i | −0.958569 | − | 0.553430i | −0.0628367 | − | 0.998024i | \(-0.520015\pi\) |
−0.895732 | + | 0.444594i | \(0.853348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6354 | + | 4.34924i | −0.675800 | + | 0.200829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9839 | − | 6.34155i | −0.506110 | − | 0.292203i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.7279 | + | 32.4377i | 0.861111 | + | 1.49149i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12.6060i | − | 0.578404i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.89949i | 0.453267i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.9791 | − | 36.3369i | −0.958560 | − | 1.66027i | −0.726003 | − | 0.687691i | \(-0.758624\pi\) |
−0.232557 | − | 0.972583i | \(-0.574709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.36396 | + | 3.67423i | 0.290172 | + | 0.167531i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.94883 | − | 8.14912i | 0.0886749 | − | 0.370798i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.52192 | + | 0.878680i | 0.0691067 | + | 0.0398988i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1467 | − | 7.59027i | 0.595735 | − | 0.343948i | −0.171627 | − | 0.985162i | \(-0.554902\pi\) |
0.767362 | + | 0.641214i | \(0.221569\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 13.9795i | − | 0.632175i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.1758 | −0.504355 | −0.252177 | − | 0.967681i | \(-0.581147\pi\) | ||||
−0.252177 | + | 0.967681i | \(0.581147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.64501 | − | 2.84924i | −0.0740876 | − | 0.128323i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.06769 | − | 12.2416i | 0.317669 | − | 0.550219i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.4558 | − | 8.95743i | −1.68012 | − | 0.401796i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1781 | + | 22.8252i | −0.589935 | + | 1.02180i | 0.404306 | + | 0.914624i | \(0.367513\pi\) |
−0.994240 | + | 0.107173i | \(0.965820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6534 | + | 6.15076i | −0.475960 | + | 0.274796i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4336 | 1.35697 | 0.678484 | − | 0.734615i | \(-0.262637\pi\) | ||||
0.678484 | + | 0.734615i | \(0.262637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.9706 | 0.888678 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.02186 | − | 5.20877i | 0.400675 | − | 0.231330i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.51167 | + | 14.7426i | −0.377273 | + | 0.653456i | −0.990664 | − | 0.136323i | \(-0.956471\pi\) |
0.613391 | + | 0.789779i | \(0.289805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.83476 | + | 9.53910i | 0.125403 | + | 0.421985i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.3787 | + | 24.9046i | −0.634834 | + | 1.09957i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.1123 | − | 20.9791i | −0.533731 | − | 0.924450i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.50079 | 0.417844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.4293i | 0.721164i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2574 | + | 7.07679i | −0.537005 | + | 0.310040i | −0.743864 | − | 0.668331i | \(-0.767009\pi\) |
0.206859 | + | 0.978371i | \(0.433676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8537 | − | 6.84372i | −0.518325 | − | 0.299255i | 0.217924 | − | 0.975966i | \(-0.430071\pi\) |
−0.736249 | + | 0.676711i | \(0.763405\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.16693 | + | 3.34315i | −0.138216 | + | 0.145907i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.68087 | − | 2.70250i | −0.203902 | − | 0.117723i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.87868 | − | 8.45012i | −0.212117 | − | 0.367397i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.95169i | − | 0.0846961i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.45584i | 0.322948i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.76230 | − | 9.98059i | −0.249126 | − | 0.431499i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9853 | − | 9.22911i | −0.689816 | − | 0.398265i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.37803 | + | 25.4360i | 0.0593560 | + | 1.09561i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.1865 | − | 10.5000i | −0.781900 | − | 0.451430i | 0.0552031 | − | 0.998475i | \(-0.482419\pi\) |
−0.837103 | + | 0.547045i | \(0.815753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.1354 | + | 8.16107i | −0.606607 | + | 0.350225i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.19615i | 0.222579i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.4392 | −0.660131 | −0.330065 | − | 0.943958i | \(-0.607071\pi\) | ||||
−0.330065 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0665 | + | 24.3640i | 0.600345 | + | 1.03983i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4521 | − | 25.0318i | 0.615681 | − | 1.06639i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1066 | − | 12.7802i | 0.514825 | − | 0.543471i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.45857 | − | 9.45451i | 0.231703 | − | 0.401322i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.4778 | − | 19.3284i | 1.41850 | − | 0.818972i | 0.422333 | − | 0.906441i | \(-0.361211\pi\) |
0.996167 | + | 0.0874688i | \(0.0278778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4432 | 0.441699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.27208 | −0.0959272 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.76835 | − | 2.17566i | 0.158817 | − | 0.0916931i | −0.418485 | − | 0.908224i | \(-0.637439\pi\) |
0.577302 | + | 0.816531i | \(0.304105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.67423 | − | 6.36396i | 0.154576 | − | 0.267734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.99304 | + | 2.07814i | −0.293680 | + | 0.0872737i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.74264 | + | 4.75039i | −0.114977 | + | 0.199147i | −0.917771 | − | 0.397111i | \(-0.870013\pi\) |
0.802793 | + | 0.596257i | \(0.203346\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.83420 | − | 8.37309i | −0.202305 | − | 0.350403i | 0.746966 | − | 0.664863i | \(-0.231510\pi\) |
−0.949271 | + | 0.314460i | \(0.898177\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.93535 | 0.164402 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.27809i | − | 0.303517i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5000 | − | 14.7224i | 1.06158 | − | 0.612903i | 0.135710 | − | 0.990749i | \(-0.456668\pi\) |
0.925869 | + | 0.377846i | \(0.123335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9953 | + | 7.50282i | 0.540065 | + | 0.311807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.95743 | − | 2.14214i | −0.371617 | − | 0.0888708i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9114 | − | 8.03176i | −0.576152 | − | 0.332641i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.97056 | − | 3.41311i | −0.0814727 | − | 0.141115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 44.7802i | − | 1.84828i | −0.382060 | − | 0.924138i | \(-0.624785\pi\) | ||
0.382060 | − | 0.924138i | \(-0.375215\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 47.4853i | − | 1.95660i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.466056 | − | 0.807232i | −0.0191710 | − | 0.0332051i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.8640 | + | 6.27231i | 0.446129 | + | 0.257573i | 0.706194 | − | 0.708018i | \(-0.250411\pi\) |
−0.260065 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.19755 | + | 0.764683i | 0.131087 | + | 0.0313490i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.82282 | + | 2.20711i | 0.156458 | + | 0.0903309i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9839 | + | 6.34155i | −0.448789 | + | 0.259109i | −0.707319 | − | 0.706895i | \(-0.750095\pi\) |
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.2357i | − | 1.72283i | −0.507903 | − | 0.861414i | \(-0.669579\pi\) | ||
0.507903 | − | 0.861414i | \(-0.330421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.9417 | 0.527027 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94218 | + | 3.36396i | 0.0789610 | + | 0.136764i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.14693 | + | 8.91474i | −0.208907 | + | 0.361838i | −0.951371 | − | 0.308049i | \(-0.900324\pi\) |
0.742463 | + | 0.669887i | \(0.233657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1213 | + | 3.00778i | −0.410137 | + | 0.121881i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.32447 | − | 2.29405i | 0.0535823 | − | 0.0928073i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3389 | + | 11.7426i | −0.821478 | + | 0.474281i | −0.850926 | − | 0.525286i | \(-0.823959\pi\) |
0.0294476 | + | 0.999566i | \(0.490625\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0767 | 0.446654 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.21320 | 0.129359 | 0.0646793 | − | 0.997906i | \(-0.479398\pi\) | ||||
0.0646793 | + | 0.997906i | \(0.479398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0512 | + | 8.68983i | −0.604960 | + | 0.349274i | −0.770990 | − | 0.636847i | \(-0.780238\pi\) |
0.166030 | + | 0.986121i | \(0.446905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.30153 | + | 14.3787i | −0.333129 | + | 0.576997i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6761 | + | 15.4927i | −0.587985 | + | 0.620703i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.98059 | − | 17.2869i | −0.398586 | − | 0.690372i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.19615 | 0.207184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.2928i | − | 0.409749i | −0.978788 | − | 0.204874i | \(-0.934321\pi\) | ||
0.978788 | − | 0.204874i | \(-0.0656786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.941125 | − | 0.543359i | 0.0374064 | − | 0.0215966i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.04405 | + | 5.22158i | 0.358902 | + | 0.207212i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.33386 | + | 3.21320i | 0.250957 | + | 0.127312i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.2708 | + | 16.3221i | 1.11837 | + | 0.645694i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.01472 | − | 8.68575i | −0.198069 | − | 0.343066i | 0.749833 | − | 0.661627i | \(-0.230134\pi\) |
−0.947902 | + | 0.318561i | \(0.896800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0492i | 0.908971i | 0.890754 | + | 0.454486i | \(0.150177\pi\) | ||||
−0.890754 | + | 0.454486i | \(0.849823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 15.5147i | − | 0.610891i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.15150 | − | 5.45857i | −0.123898 | − | 0.214598i | 0.797403 | − | 0.603447i | \(-0.206206\pi\) |
−0.921302 | + | 0.388848i | \(0.872873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.74264 | + | 1.58346i | 0.107658 | + | 0.0621564i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9294 | + | 12.5932i | −0.467551 | + | 0.493567i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.41717 | + | 2.55025i | 0.172857 | + | 0.0997991i | 0.583932 | − | 0.811802i | \(-0.301513\pi\) |
−0.411075 | + | 0.911601i | \(0.634847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.2144 | − | 11.6708i | 0.789843 | − | 0.456016i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.43519i | − | 0.329088i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.5415 | 0.449593 | 0.224796 | − | 0.974406i | \(-0.427828\pi\) | ||||
0.224796 | + | 0.974406i | \(0.427828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.8169 | − | 32.5919i | −0.731894 | − | 1.26768i | −0.956073 | − | 0.293129i | \(-0.905303\pi\) |
0.224179 | − | 0.974548i | \(-0.428030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.316742 | + | 0.548614i | −0.0123012 | + | 0.0213064i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.22792 | + | 27.6873i | 0.319065 | + | 1.07367i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.34394 | − | 14.4521i | 0.323079 | − | 0.559589i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.64564 | − | 4.41421i | 0.295598 | − | 0.170663i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.6504 | −1.76232 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.24264 | 0.240636 | 0.120318 | − | 0.992735i | \(-0.461609\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.90245 | − | 4.56248i | 0.304165 | − | 0.175610i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.34474 | + | 9.25736i | −0.205415 | + | 0.355789i | −0.950265 | − | 0.311443i | \(-0.899188\pi\) |
0.744850 | + | 0.667232i | \(0.232521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.61079 | + | 0.624361i | 0.100193 | + | 0.0239608i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.47056 | + | 12.9394i | −0.286273 | + | 0.495839i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.4051 | + | 38.8067i | 0.857306 | + | 1.48490i | 0.874489 | + | 0.485045i | \(0.161197\pi\) |
−0.0171833 | + | 0.999852i | \(0.505470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.9369 | 0.876375 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.3122i | 0.660503i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.87868 | + | 2.23936i | −0.147766 | + | 0.0853127i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.26101 | + | 1.30540i | 0.0860130 | + | 0.0496596i | 0.542390 | − | 0.840127i | \(-0.317520\pi\) |
−0.456377 | + | 0.889787i | \(0.650853\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.02207 | − | 21.0000i | 0.190773 | − | 0.797724i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.7414 | + | 15.4392i | 1.01436 | + | 0.585641i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.63604 | + | 4.56575i | 0.0998471 | + | 0.172940i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0719i | 0.797012i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1421i | 0.534141i | 0.963677 | + | 0.267071i | \(0.0860557\pi\) | ||||
−0.963677 | + | 0.267071i | \(0.913944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.8252 | + | 39.5344i | 0.860869 | + | 1.49107i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.40812 | − | 1.96768i | −0.128357 | − | 0.0741070i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.2417 | − | 8.68983i | 1.09975 | − | 0.326815i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.1654 | + | 15.1066i | 0.982662 | + | 0.567340i | 0.903073 | − | 0.429487i | \(-0.141306\pi\) |
0.0795894 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9228 | + | 7.46096i | −0.484641 | + | 0.279808i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.4156i | − | 1.02672i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.39511 | 0.239163 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.71807 | + | 11.6360i | 0.250891 | + | 0.434556i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.15150 | + | 5.45857i | −0.117531 | + | 0.203570i | −0.918789 | − | 0.394750i | \(-0.870831\pi\) |
0.801257 | + | 0.598320i | \(0.204165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.8640 | − | 25.4480i | −1.00047 | − | 0.947732i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.14878 | + | 12.3820i | −0.265866 | + | 0.460493i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.94282 | + | 4.58579i | −0.294989 | + | 0.170312i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.2795 | −1.49389 | −0.746943 | − | 0.664889i | \(-0.768479\pi\) | ||||
−0.746943 | + | 0.664889i | \(0.768479\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.72792 | −0.212145 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.39511 | − | 3.69222i | 0.236532 | − | 0.136562i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.0615465 | − | 0.106602i | 0.00227327 | − | 0.00393742i | −0.864887 | − | 0.501967i | \(-0.832610\pi\) |
0.867160 | + | 0.498030i | \(0.165943\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.77364 | − | 9.40979i | 0.176078 | − | 0.347085i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5000 | + | 18.1865i | −0.386772 | + | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.3757 | + | 28.3635i | 0.602390 | + | 1.04337i | 0.992458 | + | 0.122584i | \(0.0391180\pi\) |
−0.390068 | + | 0.920786i | \(0.627549\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.56543 | −0.204451 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.3464i | − | 1.00324i | −0.865088 | − | 0.501621i | \(-0.832737\pi\) | ||
0.865088 | − | 0.501621i | \(-0.167263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.7132 | + | 20.0417i | −1.27179 | + | 0.734270i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.76085 | + | 3.90338i | 0.247367 | + | 0.142817i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.7802 | − | 12.1066i | −0.466980 | − | 0.442366i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.3820 | + | 7.14878i | 0.451827 | + | 0.260863i | 0.708602 | − | 0.705609i | \(-0.249326\pi\) |
−0.256774 | + | 0.966471i | \(0.582660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.12132 | − | 5.40629i | −0.113747 | − | 0.197016i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.8228i | 1.01258i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.78680i | 0.319362i | 0.987169 | + | 0.159681i | \(0.0510465\pi\) | ||||
−0.987169 | + | 0.159681i | \(0.948954\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.76230 | − | 9.98059i | −0.209158 | − | 0.362272i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.1066 | − | 12.1859i | −0.765114 | − | 0.441739i | 0.0660150 | − | 0.997819i | \(-0.478971\pi\) |
−0.831129 | + | 0.556080i | \(0.812305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.26101 | + | 7.60840i | 0.0818541 | + | 0.275443i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.41344 | − | 1.39340i | −0.0872580 | − | 0.0503784i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.764683 | − | 0.441490i | 0.0276111 | − | 0.0159413i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.31925i | 0.191817i | 0.995390 | + | 0.0959084i | \(0.0305756\pi\) | ||||
−0.995390 | + | 0.0959084i | \(0.969424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9171 | 0.393171 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.59808 | − | 4.50000i | −0.0934463 | − | 0.161854i | 0.815513 | − | 0.578739i | \(-0.196455\pi\) |
−0.908959 | + | 0.416885i | \(0.863122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.53375 | + | 13.0488i | −0.270620 | + | 0.468728i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.87868 | − | 16.2189i | 0.139147 | − | 0.581848i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.1587 | + | 40.1121i | −0.829748 | + | 1.43717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.8739 | + | 26.4853i | −1.64150 | + | 0.947718i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.9226 | 0.747711 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.2426 | 0.900948 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1393 | − | 19.1330i | 1.18129 | − | 0.682018i | 0.224977 | − | 0.974364i | \(-0.427769\pi\) |
0.956312 | + | 0.292346i | \(0.0944360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0843 | + | 19.1985i | −0.394610 | + | 0.683484i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.61079 | − | 10.9171i | 0.0928291 | − | 0.388169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.36396 | + | 11.0227i | −0.225991 | + | 0.391428i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.32686 | + | 5.76230i | 0.117992 | + | 0.204368i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.3059 | −0.577584 | −0.288792 | − | 0.957392i | \(-0.593254\pi\) | ||||
−0.288792 | + | 0.957392i | \(0.593254\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.87308i | − | 0.0662649i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6655 | − | 9.04447i | 0.553512 | − | 0.319571i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8537 | + | 6.84372i | 0.418307 | + | 0.241510i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.75039 | + | 15.9853i | 0.167429 | + | 0.563407i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8389 | − | 9.72197i | −0.592759 | − | 0.342230i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.2279 | + | 35.0358i | 0.711176 | + | 1.23179i | 0.964416 | + | 0.264389i | \(0.0851704\pi\) |
−0.253240 | + | 0.967403i | \(0.581496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9905i | 0.701960i | 0.936383 | + | 0.350980i | \(0.114151\pi\) | ||||
−0.936383 | + | 0.350980i | \(0.885849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.1716i | 0.426876i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.9114 | + | 24.0953i | 0.487296 | + | 0.844021i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.1838 | + | 32.4377i | 1.96562 | + | 1.13485i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.37053 | − | 4.14016i | −0.152719 | − | 0.144669i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3314 | + | 9.42893i | 0.569969 | + | 0.329072i | 0.757137 | − | 0.653256i | \(-0.226597\pi\) |
−0.187168 | + | 0.982328i | \(0.559931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8929 | − | 17.2587i | 1.04200 | − | 0.601600i | 0.121602 | − | 0.992579i | \(-0.461197\pi\) |
0.920399 | + | 0.390979i | \(0.127864\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.33386i | 0.220517i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.9077 | 1.28341 | 0.641703 | − | 0.766953i | \(-0.278228\pi\) | ||||
0.641703 | + | 0.766953i | \(0.278228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0989 | − | 20.9558i | −0.420211 | − | 0.727827i | 0.575749 | − | 0.817627i | \(-0.304711\pi\) |
−0.995960 | + | 0.0898000i | \(0.971377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.988654 | + | 1.71240i | −0.0342960 | + | 0.0594024i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.01472 | − | 0.271680i | 0.173750 | − | 0.00941314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2416 | − | 21.2031i | 0.423638 | − | 0.733763i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.7675 | − | 17.1863i | 1.02892 | − | 0.594045i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.5965 | −1.12536 | −0.562678 | − | 0.826676i | \(-0.690229\pi\) | ||||
−0.562678 | + | 0.826676i | \(0.690229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.97056 | 0.274847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.84649 | − | 3.37548i | 0.201364 | − | 0.116258i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3668 | + | 17.9558i | −0.356629 | + | 0.617700i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.30759 | + | 4.08053i | 0.148010 | + | 0.140209i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5000 | − | 18.1865i | 0.360359 | − | 0.624160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1781 | + | 22.8252i | 0.451741 | + | 0.782438i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.01461 | −0.0347396 | −0.0173698 | − | 0.999849i | \(-0.505529\pi\) | ||||
−0.0173698 | + | 0.999849i | \(0.505529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 24.4832i | − | 0.837308i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.2574 | − | 7.07679i | 0.418703 | − | 0.241739i | −0.275819 | − | 0.961210i | \(-0.588949\pi\) |
0.694522 | + | 0.719471i | \(0.255616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.3369 | + | 20.9791i | 1.23980 | + | 0.715798i | 0.969053 | − | 0.246853i | \(-0.0793965\pi\) |
0.270745 | + | 0.962651i | \(0.412730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.2189 | − | 4.81981i | 0.552737 | − | 0.164259i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.4989 | − | 24.5368i | −1.44668 | − | 0.835241i | −0.448398 | − | 0.893834i | \(-0.648005\pi\) |
−0.998282 | + | 0.0585927i | \(0.981339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3492 | − | 28.3177i | −0.555891 | − | 0.962831i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 14.3465i | − | 0.487234i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 24.2132i | − | 0.821377i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.92753 | + | 5.07064i | 0.0991957 | + | 0.171812i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.97056 | − | 1.13770i | −0.0666934 | − | 0.0385055i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.46096 | − | 31.1983i | 0.252226 | − | 1.05470i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.9920 | + | 18.4706i | 1.08029 | + | 0.623707i | 0.930975 | − | 0.365083i | \(-0.118959\pi\) |
0.149316 | + | 0.988789i | \(0.452293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.14016 | − | 2.39032i | 0.139644 | − | 0.0806235i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.7436i | 1.64221i | 0.570774 | + | 0.821107i | \(0.306643\pi\) | ||||
−0.570774 | + | 0.821107i | \(0.693357\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.24872 | 0.0420229 | 0.0210114 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210114 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.655892 | − | 1.13604i | −0.0220476 | − | 0.0381875i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.9066 | − | 41.4075i | 0.802706 | − | 1.39033i | −0.115122 | − | 0.993351i | \(-0.536726\pi\) |
0.917829 | − | 0.396977i | \(-0.129941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.5147 | + | 3.71029i | 0.520347 | + | 0.124439i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.01708 | + | 8.68983i | −0.168078 | + | 0.291120i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.2512 | − | 8.22792i | 0.476898 | − | 0.275337i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.7366 | 1.22797 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.21320 | −0.107286 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.9196 | + | 17.2741i | −0.997874 | + | 0.576123i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.58346 | + | 2.74264i | −0.0527528 | + | 0.0913706i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.75095 | − | 22.7172i | −0.224658 | − | 0.755983i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.2426 | − | 28.1331i | 0.539924 | − | 0.935175i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.26101 | − | 3.91619i | −0.0750757 | − | 0.130035i | 0.826044 | − | 0.563606i | \(-0.190587\pi\) |
−0.901119 | + | 0.433571i | \(0.857253\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.8577 | −0.857645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.9224i | 1.32269i | 0.750083 | + | 0.661343i | \(0.230013\pi\) | ||||
−0.750083 | + | 0.661343i | \(0.769987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.9706 | + | 6.33386i | −0.363073 | + | 0.209620i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.3757 | + | 9.45451i | 0.541364 | + | 0.312557i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.5204 | − | 25.8848i | 0.809735 | − | 0.854791i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.9606 | − | 21.3392i | −1.21922 | − | 0.703916i | −0.254467 | − | 0.967081i | \(-0.581900\pi\) |
−0.964751 | + | 0.263166i | \(0.915233\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.48528 | + | 9.50079i | 0.180746 | + | 0.313062i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7689i | 0.486123i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 14.4853i | − | 0.476273i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.6829 | + | 27.1635i | 0.515093 | + | 0.892167i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.9558 | − | 22.4912i | −1.27810 | − | 0.737911i | −0.301601 | − | 0.953434i | \(-0.597521\pi\) |
−0.976499 | + | 0.215523i | \(0.930854\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0953 | + | 36.9606i | 0.789691 | + | 1.21133i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.1219 | − | 12.7721i | −0.724238 | − | 0.418139i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.91619 | − | 2.26101i | 0.128073 | − | 0.0739430i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4949i | 0.800213i | 0.916469 | + | 0.400107i | \(0.131027\pi\) | ||||
−0.916469 | + | 0.400107i | \(0.868973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.30267 | 0.303581 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.7949 | − | 23.8934i | −0.449700 | − | 0.778903i | 0.548667 | − | 0.836041i | \(-0.315136\pi\) |
−0.998366 | + | 0.0571387i | \(0.981802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3707 | + | 23.1587i | −0.435410 | + | 0.754152i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.3787 | + | 15.1788i | −0.467738 | + | 0.493765i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.7196 | − | 42.8157i | 0.803280 | − | 1.39132i | −0.114166 | − | 0.993462i | \(-0.536419\pi\) |
0.917446 | − | 0.397861i | \(-0.130247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.30496 | − | 1.90812i | 0.107283 | − | 0.0619401i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8907 | 0.871991 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.1838 | −0.848175 | −0.424088 | − | 0.905621i | \(-0.639405\pi\) | ||||
−0.424088 | + | 0.905621i | \(0.639405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.78304 | + | 3.91619i | −0.219494 | + | 0.126725i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.26143 | + | 12.5772i | −0.234729 | + | 0.406562i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.5851 | − | 9.98059i | 1.08452 | − | 0.322290i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.8787 | + | 22.3065i | −0.415441 | + | 0.719565i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.46096 | + | 12.9228i | 0.240426 | + | 0.416430i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.8651 | −0.961393 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.8489i | − | 0.799088i | −0.916714 | − | 0.399544i | \(-0.869168\pi\) | ||
0.916714 | − | 0.399544i | \(-0.130832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.40812 | + | 1.96768i | −0.109484 | + | 0.0632109i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.29038 | + | 4.78645i | 0.266051 | + | 0.153605i | 0.627092 | − | 0.778945i | \(-0.284245\pi\) |
−0.361041 | + | 0.932550i | \(0.617578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.8739 | + | 10.9706i | 1.47065 | + | 0.351700i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.52937 | + | 0.882980i | 0.0489789 | + | 0.0282780i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.34924 | + | 7.53311i | 0.139145 | + | 0.241006i | 0.927173 | − | 0.374633i | \(-0.122231\pi\) |
−0.788028 | + | 0.615639i | \(0.788898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.3522i | 0.938100i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.72792i | − | 0.214806i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.60840 | − | 13.1781i | −0.242670 | − | 0.420318i | 0.718804 | − | 0.695213i | \(-0.244690\pi\) |
−0.961474 | + | 0.274896i | \(0.911357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.60660 | + | 0.927572i | 0.0511906 | + | 0.0295549i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.84649 | − | 1.39817i | −0.186096 | − | 0.0445042i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.4377 | + | 18.7279i | 1.03146 | + | 0.595513i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7527 | + | 14.8684i | −0.818063 | + | 0.472309i | −0.849748 | − | 0.527189i | \(-0.823246\pi\) |
0.0316850 | + | 0.999498i | \(0.489913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 12.8928i | − | 0.409140i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.78543 | −0.278517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.1508 | − | 43.5624i | −0.796534 | − | 1.37964i | −0.921861 | − | 0.387521i | \(-0.873331\pi\) |
0.125327 | − | 0.992115i | \(-0.460002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.5222 | + | 28.6173i | −0.522739 | + | 0.905411i |
(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 | 896.2.q.c.831.4 | yes | 16 | |
4.3 | odd | 2 | inner | 896.2.q.c.831.6 | yes | 16 | |
7.3 | odd | 6 | inner | 896.2.q.c.703.3 | ✓ | 16 | |
8.3 | odd | 2 | inner | 896.2.q.c.831.3 | yes | 16 | |
8.5 | even | 2 | inner | 896.2.q.c.831.5 | yes | 16 | |
28.3 | even | 6 | inner | 896.2.q.c.703.5 | yes | 16 | |
56.3 | even | 6 | inner | 896.2.q.c.703.4 | yes | 16 | |
56.45 | odd | 6 | inner | 896.2.q.c.703.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.q.c.703.3 | ✓ | 16 | 7.3 | odd | 6 | inner | |
896.2.q.c.703.4 | yes | 16 | 56.3 | even | 6 | inner | |
896.2.q.c.703.5 | yes | 16 | 28.3 | even | 6 | inner | |
896.2.q.c.703.6 | yes | 16 | 56.45 | odd | 6 | inner | |
896.2.q.c.831.3 | yes | 16 | 8.3 | odd | 2 | inner | |
896.2.q.c.831.4 | yes | 16 | 1.1 | even | 1 | trivial | |
896.2.q.c.831.5 | yes | 16 | 8.5 | even | 2 | inner | |
896.2.q.c.831.6 | yes | 16 | 4.3 | odd | 2 | inner |