Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.14 | ||
Root | \(-0.807586 + 1.94969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.c.1077.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.765367i | 0.441885i | 0.975287 | + | 0.220942i | \(0.0709133\pi\) | ||||
−0.975287 | + | 0.220942i | \(0.929087\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.05161i | 0.917509i | 0.888563 | + | 0.458755i | \(0.151704\pi\) | ||||
−0.888563 | + | 0.458755i | \(0.848296\pi\) | |||||||
\(6\) | −0.765367 | −0.312460 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.41421 | 0.804738 | ||||||||
\(10\) | −2.05161 | −0.648777 | ||||||||
\(11\) | 2.49222 | + | 2.18834i | 0.751434 | + | 0.659808i | ||||
\(12\) | − | 0.765367i | − | 0.220942i | ||||||
\(13\) | 6.59694 | 1.82966 | 0.914830 | − | 0.403838i | \(-0.132324\pi\) | ||||
0.914830 | + | 0.403838i | \(0.132324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.57024 | −0.405433 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.61108 | −0.875815 | −0.437908 | − | 0.899020i | \(-0.644280\pi\) | ||||
−0.437908 | + | 0.899020i | \(0.644280\pi\) | |||||||
\(18\) | 2.41421i | 0.569036i | ||||||||
\(19\) | −0.878539 | −0.201551 | −0.100775 | − | 0.994909i | \(-0.532132\pi\) | ||||
−0.100775 | + | 0.994909i | \(0.532132\pi\) | |||||||
\(20\) | − | 2.05161i | − | 0.458755i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.18834 | + | 2.49222i | −0.466555 | + | 0.531344i | ||||
\(23\) | 6.61931 | 1.38022 | 0.690111 | − | 0.723703i | \(-0.257562\pi\) | ||||
0.690111 | + | 0.723703i | \(0.257562\pi\) | |||||||
\(24\) | 0.765367 | 0.156230 | ||||||||
\(25\) | 0.790886 | 0.158177 | ||||||||
\(26\) | 6.59694i | 1.29377i | ||||||||
\(27\) | 4.14386i | 0.797486i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.18955i | − | 1.14937i | −0.818375 | − | 0.574685i | \(-0.805124\pi\) | ||
0.818375 | − | 0.574685i | \(-0.194876\pi\) | |||||||
\(30\) | − | 1.57024i | − | 0.286685i | ||||||
\(31\) | 6.48376i | 1.16452i | 0.813003 | + | 0.582259i | \(0.197831\pi\) | ||||
−0.813003 | + | 0.582259i | \(0.802169\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.67488 | + | 1.90747i | −0.291559 | + | 0.332047i | ||||
\(34\) | − | 3.61108i | − | 0.619295i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.41421 | −0.402369 | ||||||||
\(37\) | −11.0491 | −1.81646 | −0.908229 | − | 0.418475i | \(-0.862565\pi\) | ||||
−0.908229 | + | 0.418475i | \(0.862565\pi\) | |||||||
\(38\) | − | 0.878539i | − | 0.142518i | ||||||
\(39\) | 5.04908i | 0.808499i | ||||||||
\(40\) | 2.05161 | 0.324388 | ||||||||
\(41\) | −2.36864 | −0.369919 | −0.184960 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184960 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.81288i | − | 1.19145i | −0.803188 | − | 0.595726i | \(-0.796864\pi\) | ||
0.803188 | − | 0.595726i | \(-0.203136\pi\) | |||||||
\(44\) | −2.49222 | − | 2.18834i | −0.375717 | − | 0.329904i | ||||
\(45\) | 4.95303i | 0.738354i | ||||||||
\(46\) | 6.61931i | 0.975964i | ||||||||
\(47\) | 5.74713i | 0.838305i | 0.907916 | + | 0.419153i | \(0.137673\pi\) | ||||
−0.907916 | + | 0.419153i | \(0.862327\pi\) | |||||||
\(48\) | 0.765367i | 0.110471i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.790886i | 0.111848i | ||||||||
\(51\) | − | 2.76380i | − | 0.387009i | ||||||
\(52\) | −6.59694 | −0.914830 | ||||||||
\(53\) | 0.429764 | 0.0590326 | 0.0295163 | − | 0.999564i | \(-0.490603\pi\) | ||||
0.0295163 | + | 0.999564i | \(0.490603\pi\) | |||||||
\(54\) | −4.14386 | −0.563908 | ||||||||
\(55\) | −4.48962 | + | 5.11308i | −0.605380 | + | 0.689448i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.672404i | − | 0.0890621i | ||||||
\(58\) | 6.18955 | 0.812728 | ||||||||
\(59\) | 3.21844i | 0.419006i | 0.977808 | + | 0.209503i | \(0.0671845\pi\) | ||||
−0.977808 | + | 0.209503i | \(0.932815\pi\) | |||||||
\(60\) | 1.57024 | 0.202717 | ||||||||
\(61\) | −11.3342 | −1.45120 | −0.725599 | − | 0.688118i | \(-0.758437\pi\) | ||||
−0.725599 | + | 0.688118i | \(0.758437\pi\) | |||||||
\(62\) | −6.48376 | −0.823439 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 13.5344i | 1.67873i | ||||||||
\(66\) | −1.90747 | − | 1.67488i | −0.234793 | − | 0.206163i | ||||
\(67\) | 2.96246 | 0.361922 | 0.180961 | − | 0.983490i | \(-0.442079\pi\) | ||||
0.180961 | + | 0.983490i | \(0.442079\pi\) | |||||||
\(68\) | 3.61108 | 0.437908 | ||||||||
\(69\) | 5.06620i | 0.609899i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.13403 | −0.253263 | −0.126631 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126631 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(72\) | − | 2.41421i | − | 0.284518i | ||||||
\(73\) | −10.8252 | −1.26700 | −0.633499 | − | 0.773744i | \(-0.718382\pi\) | ||||
−0.633499 | + | 0.773744i | \(0.718382\pi\) | |||||||
\(74\) | − | 11.0491i | − | 1.28443i | ||||||
\(75\) | 0.605318i | 0.0698961i | ||||||||
\(76\) | 0.878539 | 0.100775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.04908 | −0.571695 | ||||||||
\(79\) | − | 8.48528i | − | 0.954669i | −0.878722 | − | 0.477334i | \(-0.841603\pi\) | ||
0.878722 | − | 0.477334i | \(-0.158397\pi\) | |||||||
\(80\) | 2.05161i | 0.229377i | ||||||||
\(81\) | 4.07107 | 0.452341 | ||||||||
\(82\) | − | 2.36864i | − | 0.261572i | ||||||
\(83\) | 12.3153 | 1.35178 | 0.675892 | − | 0.737001i | \(-0.263759\pi\) | ||||
0.675892 | + | 0.737001i | \(0.263759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.40854i | − | 0.803569i | ||||||
\(86\) | 7.81288 | 0.842484 | ||||||||
\(87\) | 4.73728 | 0.507889 | ||||||||
\(88\) | 2.18834 | − | 2.49222i | 0.233277 | − | 0.265672i | ||||
\(89\) | − | 6.72825i | − | 0.713193i | −0.934258 | − | 0.356597i | \(-0.883937\pi\) | ||
0.934258 | − | 0.356597i | \(-0.116063\pi\) | |||||||
\(90\) | −4.95303 | −0.522095 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.61931 | −0.690111 | ||||||||
\(93\) | −4.96246 | −0.514583 | ||||||||
\(94\) | −5.74713 | −0.592771 | ||||||||
\(95\) | − | 1.80242i | − | 0.184924i | ||||||
\(96\) | −0.765367 | −0.0781149 | ||||||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.01676 | + | 5.28311i | 0.604707 | + | 0.530973i | ||||
\(100\) | −0.790886 | −0.0790886 | ||||||||
\(101\) | 1.85966 | 0.185043 | 0.0925216 | − | 0.995711i | \(-0.470507\pi\) | ||||
0.0925216 | + | 0.995711i | \(0.470507\pi\) | |||||||
\(102\) | 2.76380 | 0.273657 | ||||||||
\(103\) | − | 6.71011i | − | 0.661167i | −0.943777 | − | 0.330583i | \(-0.892755\pi\) | ||
0.943777 | − | 0.330583i | \(-0.107245\pi\) | |||||||
\(104\) | − | 6.59694i | − | 0.646883i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.429764i | 0.0417423i | ||||||||
\(107\) | 14.7533i | 1.42626i | 0.701032 | + | 0.713130i | \(0.252723\pi\) | ||||
−0.701032 | + | 0.713130i | \(0.747277\pi\) | |||||||
\(108\) | − | 4.14386i | − | 0.398743i | ||||||
\(109\) | 6.00000i | 0.574696i | 0.957826 | + | 0.287348i | \(0.0927736\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | −5.11308 | − | 4.48962i | −0.487513 | − | 0.428068i | ||||
\(111\) | − | 8.45660i | − | 0.802665i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.597322 | −0.0561913 | −0.0280956 | − | 0.999605i | \(-0.508944\pi\) | ||||
−0.0280956 | + | 0.999605i | \(0.508944\pi\) | |||||||
\(114\) | 0.672404 | 0.0629764 | ||||||||
\(115\) | 13.5803i | 1.26637i | ||||||||
\(116\) | 6.18955i | 0.574685i | ||||||||
\(117\) | 15.9264 | 1.47240 | ||||||||
\(118\) | −3.21844 | −0.296282 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.57024i | 0.143342i | ||||||||
\(121\) | 1.42237 | + | 10.9077i | 0.129306 | + | 0.991605i | ||||
\(122\) | − | 11.3342i | − | 1.02615i | ||||||
\(123\) | − | 1.81288i | − | 0.163462i | ||||||
\(124\) | − | 6.48376i | − | 0.582259i | ||||||
\(125\) | 11.8807i | 1.06264i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.33002i | 0.650434i | 0.945639 | + | 0.325217i | \(0.105437\pi\) | ||||
−0.945639 | + | 0.325217i | \(0.894563\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 5.97972 | 0.526485 | ||||||||
\(130\) | −13.5344 | −1.18704 | ||||||||
\(131\) | −8.82050 | −0.770651 | −0.385325 | − | 0.922781i | \(-0.625911\pi\) | ||||
−0.385325 | + | 0.922781i | \(0.625911\pi\) | |||||||
\(132\) | 1.67488 | − | 1.90747i | 0.145780 | − | 0.166024i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.96246i | 0.255917i | ||||||||
\(135\) | −8.50159 | −0.731701 | ||||||||
\(136\) | 3.61108i | 0.309647i | ||||||||
\(137\) | 3.23620 | 0.276487 | 0.138244 | − | 0.990398i | \(-0.455854\pi\) | ||||
0.138244 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(138\) | −5.06620 | −0.431264 | ||||||||
\(139\) | −2.47122 | −0.209606 | −0.104803 | − | 0.994493i | \(-0.533421\pi\) | ||||
−0.104803 | + | 0.994493i | \(0.533421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.39866 | −0.370434 | ||||||||
\(142\) | − | 2.13403i | − | 0.179084i | ||||||
\(143\) | 16.4410 | + | 14.4363i | 1.37487 | + | 1.20723i | ||||
\(144\) | 2.41421 | 0.201184 | ||||||||
\(145\) | 12.6986 | 1.05456 | ||||||||
\(146\) | − | 10.8252i | − | 0.895903i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.0491 | 0.908229 | ||||||||
\(149\) | − | 3.90860i | − | 0.320205i | −0.987100 | − | 0.160103i | \(-0.948817\pi\) | ||
0.987100 | − | 0.160103i | \(-0.0511825\pi\) | |||||||
\(150\) | −0.605318 | −0.0494240 | ||||||||
\(151\) | − | 24.1895i | − | 1.96852i | −0.176733 | − | 0.984259i | \(-0.556553\pi\) | ||
0.176733 | − | 0.984259i | \(-0.443447\pi\) | |||||||
\(152\) | 0.878539i | 0.0712589i | ||||||||
\(153\) | −8.71792 | −0.704802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3022 | −1.06846 | ||||||||
\(156\) | − | 5.04908i | − | 0.404250i | ||||||
\(157\) | − | 20.3029i | − | 1.62034i | −0.586192 | − | 0.810172i | \(-0.699374\pi\) | ||
0.586192 | − | 0.810172i | \(-0.300626\pi\) | |||||||
\(158\) | 8.48528 | 0.675053 | ||||||||
\(159\) | 0.328927i | 0.0260856i | ||||||||
\(160\) | −2.05161 | −0.162194 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.07107i | 0.319853i | ||||||||
\(163\) | −13.2606 | −1.03865 | −0.519326 | − | 0.854576i | \(-0.673817\pi\) | ||||
−0.519326 | + | 0.854576i | \(0.673817\pi\) | |||||||
\(164\) | 2.36864 | 0.184960 | ||||||||
\(165\) | −3.91338 | − | 3.43620i | −0.304656 | − | 0.267508i | ||||
\(166\) | 12.3153i | 0.955855i | ||||||||
\(167\) | 20.4160 | 1.57984 | 0.789920 | − | 0.613210i | \(-0.210122\pi\) | ||||
0.789920 | + | 0.613210i | \(0.210122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.5196 | 2.34766 | ||||||||
\(170\) | 7.40854 | 0.568209 | ||||||||
\(171\) | −2.12098 | −0.162195 | ||||||||
\(172\) | 7.81288i | 0.595726i | ||||||||
\(173\) | −15.5762 | −1.18423 | −0.592117 | − | 0.805852i | \(-0.701708\pi\) | ||||
−0.592117 | + | 0.805852i | \(0.701708\pi\) | |||||||
\(174\) | 4.73728i | 0.359132i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.49222 | + | 2.18834i | 0.187859 | + | 0.164952i | ||||
\(177\) | −2.46329 | −0.185152 | ||||||||
\(178\) | 6.72825 | 0.504304 | ||||||||
\(179\) | −4.50159 | −0.336465 | −0.168232 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168232 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(180\) | − | 4.95303i | − | 0.369177i | ||||||
\(181\) | 8.18338i | 0.608266i | 0.952630 | + | 0.304133i | \(0.0983667\pi\) | ||||
−0.952630 | + | 0.304133i | \(0.901633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.67483i | − | 0.641262i | ||||||
\(184\) | − | 6.61931i | − | 0.487982i | ||||||
\(185\) | − | 22.6684i | − | 1.66662i | ||||||
\(186\) | − | 4.96246i | − | 0.363865i | ||||||
\(187\) | −8.99962 | − | 7.90226i | −0.658118 | − | 0.577870i | ||||
\(188\) | − | 5.74713i | − | 0.419153i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.80242 | 0.130761 | ||||||||
\(191\) | 10.3662 | 0.750073 | 0.375037 | − | 0.927010i | \(-0.377630\pi\) | ||||
0.375037 | + | 0.927010i | \(0.377630\pi\) | |||||||
\(192\) | − | 0.765367i | − | 0.0552356i | ||||||
\(193\) | − | 1.62333i | − | 0.116850i | −0.998292 | − | 0.0584248i | \(-0.981392\pi\) | ||
0.998292 | − | 0.0584248i | \(-0.0186078\pi\) | |||||||
\(194\) | 9.23880 | 0.663307 | ||||||||
\(195\) | −10.3587 | −0.741805 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.38713i | 0.312570i | 0.987712 | + | 0.156285i | \(0.0499518\pi\) | ||||
−0.987712 | + | 0.156285i | \(0.950048\pi\) | |||||||
\(198\) | −5.28311 | + | 6.01676i | −0.375454 | + | 0.427593i | ||||
\(199\) | − | 20.0640i | − | 1.42230i | −0.703040 | − | 0.711151i | \(-0.748174\pi\) | ||
0.703040 | − | 0.711151i | \(-0.251826\pi\) | |||||||
\(200\) | − | 0.790886i | − | 0.0559241i | ||||||
\(201\) | 2.26737i | 0.159928i | ||||||||
\(202\) | 1.85966i | 0.130845i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.76380i | 0.193505i | ||||||||
\(205\) | − | 4.85953i | − | 0.339404i | ||||||
\(206\) | 6.71011 | 0.467515 | ||||||||
\(207\) | 15.9804 | 1.11072 | ||||||||
\(208\) | 6.59694 | 0.457415 | ||||||||
\(209\) | −2.18952 | − | 1.92254i | −0.151452 | − | 0.132985i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.56380i | 0.589556i | 0.955566 | + | 0.294778i | \(0.0952457\pi\) | ||||
−0.955566 | + | 0.294778i | \(0.904754\pi\) | |||||||
\(212\) | −0.429764 | −0.0295163 | ||||||||
\(213\) | − | 1.63332i | − | 0.111913i | ||||||
\(214\) | −14.7533 | −1.00852 | ||||||||
\(215\) | 16.0290 | 1.09317 | ||||||||
\(216\) | 4.14386 | 0.281954 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | − | 8.28528i | − | 0.559867i | ||||||
\(220\) | 4.48962 | − | 5.11308i | 0.302690 | − | 0.344724i | ||||
\(221\) | −23.8221 | −1.60245 | ||||||||
\(222\) | 8.45660 | 0.567570 | ||||||||
\(223\) | 8.24084i | 0.551848i | 0.961180 | + | 0.275924i | \(0.0889837\pi\) | ||||
−0.961180 | + | 0.275924i | \(0.911016\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.90937 | 0.127291 | ||||||||
\(226\) | − | 0.597322i | − | 0.0397332i | ||||||
\(227\) | 27.4795 | 1.82388 | 0.911938 | − | 0.410329i | \(-0.134586\pi\) | ||||
0.911938 | + | 0.410329i | \(0.134586\pi\) | |||||||
\(228\) | 0.672404i | 0.0445311i | ||||||||
\(229\) | 0.104343i | 0.00689519i | 0.999994 | + | 0.00344759i | \(0.00109741\pi\) | ||||
−0.999994 | + | 0.00344759i | \(0.998903\pi\) | |||||||
\(230\) | −13.5803 | −0.895456 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.18955 | −0.406364 | ||||||||
\(233\) | − | 15.1577i | − | 0.993013i | −0.868033 | − | 0.496507i | \(-0.834616\pi\) | ||
0.868033 | − | 0.496507i | \(-0.165384\pi\) | |||||||
\(234\) | 15.9264i | 1.04114i | ||||||||
\(235\) | −11.7909 | −0.769153 | ||||||||
\(236\) | − | 3.21844i | − | 0.209503i | ||||||
\(237\) | 6.49435 | 0.421854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.9135i | 1.67620i | 0.545515 | + | 0.838101i | \(0.316334\pi\) | ||||
−0.545515 | + | 0.838101i | \(0.683666\pi\) | |||||||
\(240\) | −1.57024 | −0.101358 | ||||||||
\(241\) | −7.31108 | −0.470948 | −0.235474 | − | 0.971881i | \(-0.575664\pi\) | ||||
−0.235474 | + | 0.971881i | \(0.575664\pi\) | |||||||
\(242\) | −10.9077 | + | 1.42237i | −0.701170 | + | 0.0914334i | ||||
\(243\) | 15.5474i | 0.997369i | ||||||||
\(244\) | 11.3342 | 0.725599 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.81288 | 0.115585 | ||||||||
\(247\) | −5.79566 | −0.368769 | ||||||||
\(248\) | 6.48376 | 0.411719 | ||||||||
\(249\) | 9.42575i | 0.597333i | ||||||||
\(250\) | −11.8807 | −0.751399 | ||||||||
\(251\) | − | 10.0161i | − | 0.632208i | −0.948724 | − | 0.316104i | \(-0.897625\pi\) | ||
0.948724 | − | 0.316104i | \(-0.102375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.4968 | + | 14.4853i | 1.03715 | + | 0.910682i | ||||
\(254\) | −7.33002 | −0.459926 | ||||||||
\(255\) | 5.67025 | 0.355085 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 17.5115i | − | 1.09234i | −0.837674 | − | 0.546170i | \(-0.816085\pi\) | ||
0.837674 | − | 0.546170i | \(-0.183915\pi\) | |||||||
\(258\) | 5.97972i | 0.372281i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 13.5344i | − | 0.839365i | ||||||
\(261\) | − | 14.9429i | − | 0.924942i | ||||||
\(262\) | − | 8.82050i | − | 0.544932i | ||||||
\(263\) | − | 8.48528i | − | 0.523225i | −0.965173 | − | 0.261612i | \(-0.915746\pi\) | ||
0.965173 | − | 0.261612i | \(-0.0842542\pi\) | |||||||
\(264\) | 1.90747 | + | 1.67488i | 0.117396 | + | 0.103082i | ||||
\(265\) | 0.881709i | 0.0541629i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.14958 | 0.315149 | ||||||||
\(268\) | −2.96246 | −0.180961 | ||||||||
\(269\) | − | 6.75523i | − | 0.411873i | −0.978565 | − | 0.205937i | \(-0.933976\pi\) | ||
0.978565 | − | 0.205937i | \(-0.0660241\pi\) | |||||||
\(270\) | − | 8.50159i | − | 0.517391i | ||||||
\(271\) | 19.5432 | 1.18716 | 0.593581 | − | 0.804774i | \(-0.297714\pi\) | ||||
0.593581 | + | 0.804774i | \(0.297714\pi\) | |||||||
\(272\) | −3.61108 | −0.218954 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.23620i | 0.195506i | ||||||||
\(275\) | 1.97107 | + | 1.73072i | 0.118860 | + | 0.104367i | ||||
\(276\) | − | 5.06620i | − | 0.304950i | ||||||
\(277\) | 26.6748i | 1.60274i | 0.598172 | + | 0.801368i | \(0.295894\pi\) | ||||
−0.598172 | + | 0.801368i | \(0.704106\pi\) | |||||||
\(278\) | − | 2.47122i | − | 0.148214i | ||||||
\(279\) | 15.6532i | 0.937132i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.9533i | − | 1.24997i | −0.780636 | − | 0.624986i | \(-0.785105\pi\) | ||
0.780636 | − | 0.624986i | \(-0.214895\pi\) | |||||||
\(282\) | − | 4.39866i | − | 0.261937i | ||||||
\(283\) | −10.0629 | −0.598180 | −0.299090 | − | 0.954225i | \(-0.596683\pi\) | ||||
−0.299090 | + | 0.954225i | \(0.596683\pi\) | |||||||
\(284\) | 2.13403 | 0.126631 | ||||||||
\(285\) | 1.37951 | 0.0817153 | ||||||||
\(286\) | −14.4363 | + | 16.4410i | −0.853637 | + | 0.972180i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.41421i | 0.142259i | ||||||||
\(289\) | −3.96011 | −0.232947 | ||||||||
\(290\) | 12.6986i | 0.745685i | ||||||||
\(291\) | 7.07107 | 0.414513 | ||||||||
\(292\) | 10.8252 | 0.633499 | ||||||||
\(293\) | 29.6429 | 1.73176 | 0.865879 | − | 0.500253i | \(-0.166760\pi\) | ||||
0.865879 | + | 0.500253i | \(0.166760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.60300 | −0.384442 | ||||||||
\(296\) | 11.0491i | 0.642215i | ||||||||
\(297\) | −9.06816 | + | 10.3274i | −0.526188 | + | 0.599258i | ||||
\(298\) | 3.90860 | 0.226419 | ||||||||
\(299\) | 43.6672 | 2.52534 | ||||||||
\(300\) | − | 0.605318i | − | 0.0349480i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.1895 | 1.39195 | ||||||||
\(303\) | 1.42332i | 0.0817677i | ||||||||
\(304\) | −0.878539 | −0.0503876 | ||||||||
\(305\) | − | 23.2534i | − | 1.33149i | ||||||
\(306\) | − | 8.71792i | − | 0.498370i | ||||||
\(307\) | −16.1877 | −0.923883 | −0.461941 | − | 0.886910i | \(-0.652847\pi\) | ||||
−0.461941 | + | 0.886910i | \(0.652847\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.13569 | 0.292159 | ||||||||
\(310\) | − | 13.3022i | − | 0.755513i | ||||||
\(311\) | − | 1.42639i | − | 0.0808832i | −0.999182 | − | 0.0404416i | \(-0.987124\pi\) | ||
0.999182 | − | 0.0404416i | \(-0.0128765\pi\) | |||||||
\(312\) | 5.04908 | 0.285848 | ||||||||
\(313\) | − | 11.5468i | − | 0.652664i | −0.945255 | − | 0.326332i | \(-0.894187\pi\) | ||
0.945255 | − | 0.326332i | \(-0.105813\pi\) | |||||||
\(314\) | 20.3029 | 1.14576 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | 31.7239 | 1.78179 | 0.890896 | − | 0.454207i | \(-0.150077\pi\) | ||||
0.890896 | + | 0.454207i | \(0.150077\pi\) | |||||||
\(318\) | −0.328927 | −0.0184453 | ||||||||
\(319\) | 13.5448 | − | 15.4257i | 0.758364 | − | 0.863676i | ||||
\(320\) | − | 2.05161i | − | 0.114689i | ||||||
\(321\) | −11.2917 | −0.630242 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.17247 | 0.176521 | ||||||||
\(324\) | −4.07107 | −0.226170 | ||||||||
\(325\) | 5.21742 | 0.289411 | ||||||||
\(326\) | − | 13.2606i | − | 0.734438i | ||||||
\(327\) | −4.59220 | −0.253949 | ||||||||
\(328\) | 2.36864i | 0.130786i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.43620 | − | 3.91338i | 0.189157 | − | 0.215425i | ||||
\(331\) | 31.9239 | 1.75470 | 0.877348 | − | 0.479854i | \(-0.159310\pi\) | ||||
0.877348 | + | 0.479854i | \(0.159310\pi\) | |||||||
\(332\) | −12.3153 | −0.675892 | ||||||||
\(333\) | −26.6748 | −1.46177 | ||||||||
\(334\) | 20.4160i | 1.11712i | ||||||||
\(335\) | 6.07782i | 0.332067i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.40854i | 0.0767278i | 0.999264 | + | 0.0383639i | \(0.0122146\pi\) | ||||
−0.999264 | + | 0.0383639i | \(0.987785\pi\) | |||||||
\(338\) | 30.5196i | 1.66005i | ||||||||
\(339\) | − | 0.457170i | − | 0.0248301i | ||||||
\(340\) | 7.40854i | 0.401784i | ||||||||
\(341\) | −14.1887 | + | 16.1590i | −0.768359 | + | 0.875059i | ||||
\(342\) | − | 2.12098i | − | 0.114689i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.81288 | −0.421242 | ||||||||
\(345\) | −10.3939 | −0.559588 | ||||||||
\(346\) | − | 15.5762i | − | 0.837380i | ||||||
\(347\) | − | 11.0386i | − | 0.592584i | −0.955097 | − | 0.296292i | \(-0.904250\pi\) | ||
0.955097 | − | 0.296292i | \(-0.0957502\pi\) | |||||||
\(348\) | −4.73728 | −0.253945 | ||||||||
\(349\) | −15.5762 | −0.833773 | −0.416887 | − | 0.908958i | \(-0.636879\pi\) | ||||
−0.416887 | + | 0.908958i | \(0.636879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.3368i | 1.45913i | ||||||||
\(352\) | −2.18834 | + | 2.49222i | −0.116639 | + | 0.132836i | ||||
\(353\) | − | 6.28791i | − | 0.334672i | −0.985900 | − | 0.167336i | \(-0.946484\pi\) | ||
0.985900 | − | 0.167336i | \(-0.0535165\pi\) | |||||||
\(354\) | − | 2.46329i | − | 0.130922i | ||||||
\(355\) | − | 4.37821i | − | 0.232371i | ||||||
\(356\) | 6.72825i | 0.356597i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 4.50159i | − | 0.237917i | ||||||
\(359\) | − | 10.2877i | − | 0.542964i | −0.962443 | − | 0.271482i | \(-0.912486\pi\) | ||
0.962443 | − | 0.271482i | \(-0.0875138\pi\) | |||||||
\(360\) | 4.95303 | 0.261048 | ||||||||
\(361\) | −18.2282 | −0.959377 | ||||||||
\(362\) | −8.18338 | −0.430109 | ||||||||
\(363\) | −8.34836 | + | 1.08864i | −0.438175 | + | 0.0571385i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 22.2092i | − | 1.16248i | ||||||
\(366\) | 8.67483 | 0.453441 | ||||||||
\(367\) | 4.52152i | 0.236021i | 0.993012 | + | 0.118011i | \(0.0376517\pi\) | ||||
−0.993012 | + | 0.118011i | \(0.962348\pi\) | |||||||
\(368\) | 6.61931 | 0.345056 | ||||||||
\(369\) | −5.71840 | −0.297688 | ||||||||
\(370\) | 22.6684 | 1.17848 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.96246 | 0.257291 | ||||||||
\(373\) | 19.7239i | 1.02127i | 0.859799 | + | 0.510633i | \(0.170589\pi\) | ||||
−0.859799 | + | 0.510633i | \(0.829411\pi\) | |||||||
\(374\) | 7.90226 | − | 8.99962i | 0.408616 | − | 0.465359i | ||||
\(375\) | −9.09306 | −0.469564 | ||||||||
\(376\) | 5.74713 | 0.296386 | ||||||||
\(377\) | − | 40.8321i | − | 2.10296i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.6268 | −1.83003 | −0.915014 | − | 0.403423i | \(-0.867820\pi\) | ||||
−0.915014 | + | 0.403423i | \(0.867820\pi\) | |||||||
\(380\) | 1.80242i | 0.0924622i | ||||||||
\(381\) | −5.61016 | −0.287417 | ||||||||
\(382\) | 10.3662i | 0.530382i | ||||||||
\(383\) | 21.6373i | 1.10561i | 0.833310 | + | 0.552806i | \(0.186443\pi\) | ||||
−0.833310 | + | 0.552806i | \(0.813557\pi\) | |||||||
\(384\) | 0.765367 | 0.0390575 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.62333 | 0.0826252 | ||||||||
\(387\) | − | 18.8620i | − | 0.958807i | ||||||
\(388\) | 9.23880i | 0.469029i | ||||||||
\(389\) | −8.64698 | −0.438419 | −0.219210 | − | 0.975678i | \(-0.570348\pi\) | ||||
−0.219210 | + | 0.975678i | \(0.570348\pi\) | |||||||
\(390\) | − | 10.3587i | − | 0.524536i | ||||||
\(391\) | −23.9029 | −1.20882 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.75092i | − | 0.340539i | ||||||
\(394\) | −4.38713 | −0.221020 | ||||||||
\(395\) | 17.4085 | 0.875917 | ||||||||
\(396\) | −6.01676 | − | 5.28311i | −0.302354 | − | 0.265486i | ||||
\(397\) | − | 36.1718i | − | 1.81541i | −0.419608 | − | 0.907705i | \(-0.637832\pi\) | ||
0.419608 | − | 0.907705i | \(-0.362168\pi\) | |||||||
\(398\) | 20.0640 | 1.00572 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.790886 | 0.0395443 | ||||||||
\(401\) | −8.99356 | −0.449117 | −0.224558 | − | 0.974461i | \(-0.572094\pi\) | ||||
−0.224558 | + | 0.974461i | \(0.572094\pi\) | |||||||
\(402\) | −2.26737 | −0.113086 | ||||||||
\(403\) | 42.7730i | 2.13067i | ||||||||
\(404\) | −1.85966 | −0.0925216 | ||||||||
\(405\) | 8.35225i | 0.415027i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.5368 | − | 24.1791i | −1.36495 | − | 1.19851i | ||||
\(408\) | −2.76380 | −0.136829 | ||||||||
\(409\) | −9.58279 | −0.473839 | −0.236919 | − | 0.971529i | \(-0.576138\pi\) | ||||
−0.236919 | + | 0.971529i | \(0.576138\pi\) | |||||||
\(410\) | 4.85953 | 0.239995 | ||||||||
\(411\) | 2.47688i | 0.122175i | ||||||||
\(412\) | 6.71011i | 0.330583i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 15.9804i | 0.785396i | ||||||||
\(415\) | 25.2663i | 1.24027i | ||||||||
\(416\) | 6.59694i | 0.323441i | ||||||||
\(417\) | − | 1.89139i | − | 0.0926218i | ||||||
\(418\) | 1.92254 | − | 2.18952i | 0.0940344 | − | 0.107093i | ||||
\(419\) | − | 37.9064i | − | 1.85185i | −0.377709 | − | 0.925924i | \(-0.623288\pi\) | ||
0.377709 | − | 0.925924i | \(-0.376712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.88394 | 0.140555 | 0.0702774 | − | 0.997527i | \(-0.477612\pi\) | ||||
0.0702774 | + | 0.997527i | \(0.477612\pi\) | |||||||
\(422\) | −8.56380 | −0.416879 | ||||||||
\(423\) | 13.8748i | 0.674616i | ||||||||
\(424\) | − | 0.429764i | − | 0.0208712i | ||||||
\(425\) | −2.85595 | −0.138534 | ||||||||
\(426\) | 1.63332 | 0.0791345 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 14.7533i | − | 0.713130i | ||||||
\(429\) | −11.0491 | + | 12.5834i | −0.533454 | + | 0.607534i | ||||
\(430\) | 16.0290i | 0.772987i | ||||||||
\(431\) | 32.4068i | 1.56098i | 0.625169 | + | 0.780490i | \(0.285030\pi\) | ||||
−0.625169 | + | 0.780490i | \(0.714970\pi\) | |||||||
\(432\) | 4.14386i | 0.199372i | ||||||||
\(433\) | − | 10.2319i | − | 0.491714i | −0.969306 | − | 0.245857i | \(-0.920931\pi\) | ||
0.969306 | − | 0.245857i | \(-0.0790694\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.71905i | 0.465993i | ||||||||
\(436\) | − | 6.00000i | − | 0.287348i | ||||||
\(437\) | −5.81532 | −0.278185 | ||||||||
\(438\) | 8.28528 | 0.395886 | ||||||||
\(439\) | −28.8726 | −1.37802 | −0.689008 | − | 0.724754i | \(-0.741953\pi\) | ||||
−0.689008 | + | 0.724754i | \(0.741953\pi\) | |||||||
\(440\) | 5.11308 | + | 4.48962i | 0.243757 | + | 0.214034i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 23.8221i | − | 1.13310i | ||||||
\(443\) | −8.56036 | −0.406715 | −0.203358 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203358 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(444\) | 8.45660i | 0.401332i | ||||||||
\(445\) | 13.8038 | 0.654361 | ||||||||
\(446\) | −8.24084 | −0.390215 | ||||||||
\(447\) | 2.99152 | 0.141494 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.8089 | −0.510102 | −0.255051 | − | 0.966928i | \(-0.582092\pi\) | ||||
−0.255051 | + | 0.966928i | \(0.582092\pi\) | |||||||
\(450\) | 1.90937i | 0.0900084i | ||||||||
\(451\) | −5.90318 | − | 5.18338i | −0.277970 | − | 0.244076i | ||||
\(452\) | 0.597322 | 0.0280956 | ||||||||
\(453\) | 18.5139 | 0.869858 | ||||||||
\(454\) | 27.4795i | 1.28967i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.672404 | −0.0314882 | ||||||||
\(457\) | − | 24.3896i | − | 1.14090i | −0.821334 | − | 0.570448i | \(-0.806770\pi\) | ||
0.821334 | − | 0.570448i | \(-0.193230\pi\) | |||||||
\(458\) | −0.104343 | −0.00487563 | ||||||||
\(459\) | − | 14.9638i | − | 0.698451i | ||||||
\(460\) | − | 13.5803i | − | 0.633183i | ||||||
\(461\) | −1.13186 | −0.0527158 | −0.0263579 | − | 0.999653i | \(-0.508391\pi\) | ||||
−0.0263579 | + | 0.999653i | \(0.508391\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.38388 | 0.296684 | 0.148342 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148342 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(464\) | − | 6.18955i | − | 0.287343i | ||||||
\(465\) | − | 10.1810i | − | 0.472135i | ||||||
\(466\) | 15.1577 | 0.702166 | ||||||||
\(467\) | 35.6840i | 1.65126i | 0.564213 | + | 0.825629i | \(0.309180\pi\) | ||||
−0.564213 | + | 0.825629i | \(0.690820\pi\) | |||||||
\(468\) | −15.9264 | −0.736199 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 11.7909i | − | 0.543873i | ||||||
\(471\) | 15.5391 | 0.716006 | ||||||||
\(472\) | 3.21844 | 0.148141 | ||||||||
\(473\) | 17.0972 | − | 19.4714i | 0.786130 | − | 0.895298i | ||||
\(474\) | 6.49435i | 0.298296i | ||||||||
\(475\) | −0.694824 | −0.0318807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.03754 | 0.0475058 | ||||||||
\(478\) | −25.9135 | −1.18525 | ||||||||
\(479\) | −11.5819 | −0.529189 | −0.264595 | − | 0.964360i | \(-0.585238\pi\) | ||||
−0.264595 | + | 0.964360i | \(0.585238\pi\) | |||||||
\(480\) | − | 1.57024i | − | 0.0716712i | ||||||
\(481\) | −72.8901 | −3.32350 | ||||||||
\(482\) | − | 7.31108i | − | 0.333011i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.42237 | − | 10.9077i | −0.0646532 | − | 0.495802i | ||||
\(485\) | 18.9544 | 0.860676 | ||||||||
\(486\) | −15.5474 | −0.705246 | ||||||||
\(487\) | 40.0638 | 1.81546 | 0.907732 | − | 0.419550i | \(-0.137812\pi\) | ||||
0.907732 | + | 0.419550i | \(0.137812\pi\) | |||||||
\(488\) | 11.3342i | 0.513076i | ||||||||
\(489\) | − | 10.1492i | − | 0.458964i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7876i | 0.893003i | 0.894783 | + | 0.446502i | \(0.147330\pi\) | ||||
−0.894783 | + | 0.446502i | \(0.852670\pi\) | |||||||
\(492\) | 1.81288i | 0.0817308i | ||||||||
\(493\) | 22.3510i | 1.00664i | ||||||||
\(494\) | − | 5.79566i | − | 0.260759i | ||||||
\(495\) | −10.8389 | + | 12.3441i | −0.487172 | + | 0.554825i | ||||
\(496\) | 6.48376i | 0.291130i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.42575 | −0.422378 | ||||||||
\(499\) | −26.6553 | −1.19325 | −0.596627 | − | 0.802519i | \(-0.703493\pi\) | ||||
−0.596627 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(500\) | − | 11.8807i | − | 0.531319i | ||||||
\(501\) | 15.6258i | 0.698107i | ||||||||
\(502\) | 10.0161 | 0.447039 | ||||||||
\(503\) | 10.9142 | 0.486638 | 0.243319 | − | 0.969946i | \(-0.421764\pi\) | ||||
0.243319 | + | 0.969946i | \(0.421764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.81530i | 0.169779i | ||||||||
\(506\) | −14.4853 | + | 16.4968i | −0.643949 | + | 0.733373i | ||||
\(507\) | 23.3587i | 1.03739i | ||||||||
\(508\) | − | 7.33002i | − | 0.325217i | ||||||
\(509\) | − | 22.4340i | − | 0.994369i | −0.867645 | − | 0.497184i | \(-0.834367\pi\) | ||
0.867645 | − | 0.497184i | \(-0.165633\pi\) | |||||||
\(510\) | 5.67025i | 0.251083i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 3.64054i | − | 0.160734i | ||||||
\(514\) | 17.5115 | 0.772401 | ||||||||
\(515\) | 13.7665 | 0.606626 | ||||||||
\(516\) | −5.97972 | −0.263242 | ||||||||
\(517\) | −12.5767 | + | 14.3231i | −0.553121 | + | 0.629931i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 11.9215i | − | 0.523295i | ||||||
\(520\) | 13.5344 | 0.593521 | ||||||||
\(521\) | − | 39.2106i | − | 1.71785i | −0.512102 | − | 0.858925i | \(-0.671133\pi\) | ||
0.512102 | − | 0.858925i | \(-0.328867\pi\) | |||||||
\(522\) | 14.9429 | 0.654033 | ||||||||
\(523\) | 18.0899 | 0.791015 | 0.395508 | − | 0.918463i | \(-0.370569\pi\) | ||||
0.395508 | + | 0.918463i | \(0.370569\pi\) | |||||||
\(524\) | 8.82050 | 0.385325 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.48528 | 0.369976 | ||||||||
\(527\) | − | 23.4134i | − | 1.01990i | ||||||
\(528\) | −1.67488 | + | 1.90747i | −0.0728898 | + | 0.0830118i | ||||
\(529\) | 20.8153 | 0.905013 | ||||||||
\(530\) | −0.881709 | −0.0382990 | ||||||||
\(531\) | 7.77001i | 0.337190i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.6258 | −0.676827 | ||||||||
\(534\) | 5.14958i | 0.222844i | ||||||||
\(535\) | −30.2681 | −1.30861 | ||||||||
\(536\) | − | 2.96246i | − | 0.127959i | ||||||
\(537\) | − | 3.44537i | − | 0.148679i | ||||||
\(538\) | 6.75523 | 0.291238 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.50159 | 0.365850 | ||||||||
\(541\) | − | 9.62575i | − | 0.413843i | −0.978357 | − | 0.206922i | \(-0.933655\pi\) | ||
0.978357 | − | 0.206922i | \(-0.0663446\pi\) | |||||||
\(542\) | 19.5432i | 0.839450i | ||||||||
\(543\) | −6.26328 | −0.268783 | ||||||||
\(544\) | − | 3.61108i | − | 0.154824i | ||||||
\(545\) | −12.3097 | −0.527289 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2834i | 0.439685i | 0.975535 | + | 0.219843i | \(0.0705544\pi\) | ||||
−0.975535 | + | 0.219843i | \(0.929446\pi\) | |||||||
\(548\) | −3.23620 | −0.138244 | ||||||||
\(549\) | −27.3632 | −1.16783 | ||||||||
\(550\) | −1.73072 | + | 1.97107i | −0.0737983 | + | 0.0840465i | ||||
\(551\) | 5.43776i | 0.231656i | ||||||||
\(552\) | 5.06620 | 0.215632 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.6748 | −1.13330 | ||||||||
\(555\) | 17.3497 | 0.736452 | ||||||||
\(556\) | 2.47122 | 0.104803 | ||||||||
\(557\) | 37.2306i | 1.57751i | 0.614707 | + | 0.788755i | \(0.289274\pi\) | ||||
−0.614707 | + | 0.788755i | \(0.710726\pi\) | |||||||
\(558\) | −15.6532 | −0.662652 | ||||||||
\(559\) | − | 51.5411i | − | 2.17995i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.04812 | − | 6.88801i | 0.255352 | − | 0.290812i | ||||
\(562\) | 20.9533 | 0.883864 | ||||||||
\(563\) | −16.1877 | −0.682232 | −0.341116 | − | 0.940021i | \(-0.610805\pi\) | ||||
−0.341116 | + | 0.940021i | \(0.610805\pi\) | |||||||
\(564\) | 4.39866 | 0.185217 | ||||||||
\(565\) | − | 1.22547i | − | 0.0515560i | ||||||
\(566\) | − | 10.0629i | − | 0.422977i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.13403i | 0.0895420i | ||||||||
\(569\) | 30.4901i | 1.27821i | 0.769118 | + | 0.639106i | \(0.220696\pi\) | ||||
−0.769118 | + | 0.639106i | \(0.779304\pi\) | |||||||
\(570\) | 1.37951i | 0.0577815i | ||||||||
\(571\) | − | 40.4877i | − | 1.69436i | −0.531308 | − | 0.847179i | \(-0.678299\pi\) | ||
0.531308 | − | 0.847179i | \(-0.321701\pi\) | |||||||
\(572\) | −16.4410 | − | 14.4363i | −0.687435 | − | 0.603613i | ||||
\(573\) | 7.93396i | 0.331446i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.23512 | 0.218320 | ||||||||
\(576\) | −2.41421 | −0.100592 | ||||||||
\(577\) | 25.5604i | 1.06409i | 0.846715 | + | 0.532047i | \(0.178577\pi\) | ||||
−0.846715 | + | 0.532047i | \(0.821423\pi\) | |||||||
\(578\) | − | 3.96011i | − | 0.164719i | ||||||
\(579\) | 1.24244 | 0.0516341 | ||||||||
\(580\) | −12.6986 | −0.527279 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.07107i | 0.293105i | ||||||||
\(583\) | 1.07107 | + | 0.940467i | 0.0443591 | + | 0.0389502i | ||||
\(584\) | 10.8252i | 0.447951i | ||||||||
\(585\) | 32.6748i | 1.35094i | ||||||||
\(586\) | 29.6429i | 1.22454i | ||||||||
\(587\) | 7.18094i | 0.296389i | 0.988958 | + | 0.148195i | \(0.0473462\pi\) | ||||
−0.988958 | + | 0.148195i | \(0.952654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.69624i | − | 0.234709i | ||||||
\(590\) | − | 6.60300i | − | 0.271841i | ||||||
\(591\) | −3.35776 | −0.138120 | ||||||||
\(592\) | −11.0491 | −0.454114 | ||||||||
\(593\) | −19.7771 | −0.812150 | −0.406075 | − | 0.913840i | \(-0.633103\pi\) | ||||
−0.406075 | + | 0.913840i | \(0.633103\pi\) | |||||||
\(594\) | −10.3274 | − | 9.06816i | −0.423740 | − | 0.372071i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.90860i | 0.160103i | ||||||||
\(597\) | 15.3563 | 0.628493 | ||||||||
\(598\) | 43.6672i | 1.78568i | ||||||||
\(599\) | −13.7598 | −0.562210 | −0.281105 | − | 0.959677i | \(-0.590701\pi\) | ||||
−0.281105 | + | 0.959677i | \(0.590701\pi\) | |||||||
\(600\) | 0.605318 | 0.0247120 | ||||||||
\(601\) | −11.0384 | −0.450266 | −0.225133 | − | 0.974328i | \(-0.572282\pi\) | ||||
−0.225133 | + | 0.974328i | \(0.572282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.15201 | 0.291252 | ||||||||
\(604\) | 24.1895i | 0.984259i | ||||||||
\(605\) | −22.3783 | + | 2.91815i | −0.909806 | + | 0.118640i | ||||
\(606\) | −1.42332 | −0.0578185 | ||||||||
\(607\) | 11.8144 | 0.479530 | 0.239765 | − | 0.970831i | \(-0.422930\pi\) | ||||
0.239765 | + | 0.970831i | \(0.422930\pi\) | |||||||
\(608\) | − | 0.878539i | − | 0.0356294i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.2534 | 0.941503 | ||||||||
\(611\) | 37.9135i | 1.53381i | ||||||||
\(612\) | 8.71792 | 0.352401 | ||||||||
\(613\) | 21.1472i | 0.854129i | 0.904221 | + | 0.427064i | \(0.140452\pi\) | ||||
−0.904221 | + | 0.427064i | \(0.859548\pi\) | |||||||
\(614\) | − | 16.1877i | − | 0.653284i | ||||||
\(615\) | 3.71932 | 0.149978 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.8743 | −1.76631 | −0.883157 | − | 0.469078i | \(-0.844586\pi\) | ||||
−0.883157 | + | 0.469078i | \(0.844586\pi\) | |||||||
\(618\) | 5.13569i | 0.206588i | ||||||||
\(619\) | − | 4.76850i | − | 0.191662i | −0.995398 | − | 0.0958310i | \(-0.969449\pi\) | ||
0.995398 | − | 0.0958310i | \(-0.0305509\pi\) | |||||||
\(620\) | 13.3022 | 0.534228 | ||||||||
\(621\) | 27.4295i | 1.10071i | ||||||||
\(622\) | 1.42639 | 0.0571931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.04908i | 0.202125i | ||||||||
\(625\) | −20.4201 | −0.816803 | ||||||||
\(626\) | 11.5468 | 0.461503 | ||||||||
\(627\) | 1.47145 | − | 1.67578i | 0.0587639 | − | 0.0669243i | ||||
\(628\) | 20.3029i | 0.810172i | ||||||||
\(629\) | 39.8991 | 1.59088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.66195 | −0.265208 | −0.132604 | − | 0.991169i | \(-0.542334\pi\) | ||||
−0.132604 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(632\) | −8.48528 | −0.337526 | ||||||||
\(633\) | −6.55445 | −0.260516 | ||||||||
\(634\) | 31.7239i | 1.25992i | ||||||||
\(635\) | −15.0384 | −0.596779 | ||||||||
\(636\) | − | 0.328927i | − | 0.0130428i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 15.4257 | + | 13.5448i | 0.610711 | + | 0.536244i | ||||
\(639\) | −5.15201 | −0.203810 | ||||||||
\(640\) | 2.05161 | 0.0810971 | ||||||||
\(641\) | −11.5215 | −0.455071 | −0.227535 | − | 0.973770i | \(-0.573067\pi\) | ||||
−0.227535 | + | 0.973770i | \(0.573067\pi\) | |||||||
\(642\) | − | 11.2917i | − | 0.445649i | ||||||
\(643\) | 21.7793i | 0.858892i | 0.903093 | + | 0.429446i | \(0.141291\pi\) | ||||
−0.903093 | + | 0.429446i | \(0.858709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.2681i | 0.483055i | ||||||||
\(646\) | 3.17247i | 0.124819i | ||||||||
\(647\) | 17.5615i | 0.690413i | 0.938527 | + | 0.345207i | \(0.112191\pi\) | ||||
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(648\) | − | 4.07107i | − | 0.159927i | ||||||
\(649\) | −7.04304 | + | 8.02109i | −0.276463 | + | 0.314855i | ||||
\(650\) | 5.21742i | 0.204644i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.2606 | 0.519326 | ||||||||
\(653\) | 26.4426 | 1.03478 | 0.517390 | − | 0.855750i | \(-0.326904\pi\) | ||||
0.517390 | + | 0.855750i | \(0.326904\pi\) | |||||||
\(654\) | − | 4.59220i | − | 0.179569i | ||||||
\(655\) | − | 18.0962i | − | 0.707079i | ||||||
\(656\) | −2.36864 | −0.0924798 | ||||||||
\(657\) | −26.1344 | −1.01960 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.9324i | − | 1.51659i | −0.651910 | − | 0.758296i | \(-0.726032\pi\) | ||
0.651910 | − | 0.758296i | \(-0.273968\pi\) | |||||||
\(660\) | 3.91338 | + | 3.43620i | 0.152328 | + | 0.133754i | ||||
\(661\) | − | 11.8914i | − | 0.462521i | −0.972892 | − | 0.231261i | \(-0.925715\pi\) | ||
0.972892 | − | 0.231261i | \(-0.0742850\pi\) | |||||||
\(662\) | 31.9239i | 1.24076i | ||||||||
\(663\) | − | 18.2326i | − | 0.708096i | ||||||
\(664\) | − | 12.3153i | − | 0.477928i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 26.6748i | − | 1.03363i | ||||||
\(667\) | − | 40.9706i | − | 1.58639i | ||||||
\(668\) | −20.4160 | −0.789920 | ||||||||
\(669\) | −6.30727 | −0.243853 | ||||||||
\(670\) | −6.07782 | −0.234807 | ||||||||
\(671\) | −28.2474 | − | 24.8031i | −1.09048 | − | 0.957512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17.4386i | − | 0.672210i | −0.941825 | − | 0.336105i | \(-0.890890\pi\) | ||
0.941825 | − | 0.336105i | \(-0.109110\pi\) | |||||||
\(674\) | −1.40854 | −0.0542548 | ||||||||
\(675\) | 3.27732i | 0.126144i | ||||||||
\(676\) | −30.5196 | −1.17383 | ||||||||
\(677\) | 41.4300 | 1.59228 | 0.796141 | − | 0.605111i | \(-0.206871\pi\) | ||||
0.796141 | + | 0.605111i | \(0.206871\pi\) | |||||||
\(678\) | 0.457170 | 0.0175575 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.40854 | −0.284104 | ||||||||
\(681\) | 21.0319i | 0.805943i | ||||||||
\(682\) | −16.1590 | − | 14.1887i | −0.618760 | − | 0.543312i | ||||
\(683\) | 21.4153 | 0.819433 | 0.409717 | − | 0.912213i | \(-0.365628\pi\) | ||||
0.409717 | + | 0.912213i | \(0.365628\pi\) | |||||||
\(684\) | 2.12098 | 0.0810977 | ||||||||
\(685\) | 6.63943i | 0.253679i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0798608 | −0.00304688 | ||||||||
\(688\) | − | 7.81288i | − | 0.297863i | ||||||
\(689\) | 2.83512 | 0.108010 | ||||||||
\(690\) | − | 10.3939i | − | 0.395688i | ||||||
\(691\) | 13.4791i | 0.512769i | 0.966575 | + | 0.256384i | \(0.0825313\pi\) | ||||
−0.966575 | + | 0.256384i | \(0.917469\pi\) | |||||||
\(692\) | 15.5762 | 0.592117 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0386 | 0.419020 | ||||||||
\(695\) | − | 5.06999i | − | 0.192316i | ||||||
\(696\) | − | 4.73728i | − | 0.179566i | ||||||
\(697\) | 8.55334 | 0.323981 | ||||||||
\(698\) | − | 15.5762i | − | 0.589567i | ||||||
\(699\) | 11.6012 | 0.438797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4644i | 0.999545i | 0.866157 | + | 0.499773i | \(0.166583\pi\) | ||||
−0.866157 | + | 0.499773i | \(0.833417\pi\) | |||||||
\(702\) | −27.3368 | −1.03176 | ||||||||
\(703\) | 9.70704 | 0.366108 | ||||||||
\(704\) | −2.49222 | − | 2.18834i | −0.0939293 | − | 0.0824760i | ||||
\(705\) | − | 9.02435i | − | 0.339877i | ||||||
\(706\) | 6.28791 | 0.236649 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.46329 | 0.0925761 | ||||||||
\(709\) | 18.7778 | 0.705214 | 0.352607 | − | 0.935772i | \(-0.385295\pi\) | ||||
0.352607 | + | 0.935772i | \(0.385295\pi\) | |||||||
\(710\) | 4.37821 | 0.164311 | ||||||||
\(711\) | − | 20.4853i | − | 0.768258i | ||||||
\(712\) | −6.72825 | −0.252152 | ||||||||
\(713\) | 42.9181i | 1.60729i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.6177 | + | 33.7307i | −1.10764 | + | 1.26146i | ||||
\(716\) | 4.50159 | 0.168232 | ||||||||
\(717\) | −19.8333 | −0.740688 | ||||||||
\(718\) | 10.2877 | 0.383934 | ||||||||
\(719\) | − | 3.46741i | − | 0.129313i | −0.997908 | − | 0.0646564i | \(-0.979405\pi\) | ||
0.997908 | − | 0.0646564i | \(-0.0205951\pi\) | |||||||
\(720\) | 4.95303i | 0.184589i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.2282i | − | 0.678382i | ||||||
\(723\) | − | 5.59566i | − | 0.208105i | ||||||
\(724\) | − | 8.18338i | − | 0.304133i | ||||||
\(725\) | − | 4.89523i | − | 0.181804i | ||||||
\(726\) | −1.08864 | − | 8.34836i | −0.0404030 | − | 0.309837i | ||||
\(727\) | 21.6647i | 0.803500i | 0.915749 | + | 0.401750i | \(0.131598\pi\) | ||||
−0.915749 | + | 0.401750i | \(0.868402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.313708 | 0.0116188 | ||||||||
\(730\) | 22.2092 | 0.821999 | ||||||||
\(731\) | 28.2129i | 1.04349i | ||||||||
\(732\) | 8.67483i | 0.320631i | ||||||||
\(733\) | 14.9085 | 0.550656 | 0.275328 | − | 0.961350i | \(-0.411213\pi\) | ||||
0.275328 | + | 0.961350i | \(0.411213\pi\) | |||||||
\(734\) | −4.52152 | −0.166892 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.61931i | 0.243991i | ||||||||
\(737\) | 7.38311 | + | 6.48286i | 0.271960 | + | 0.238799i | ||||
\(738\) | − | 5.71840i | − | 0.210497i | ||||||
\(739\) | − | 4.75577i | − | 0.174944i | −0.996167 | − | 0.0874719i | \(-0.972121\pi\) | ||
0.996167 | − | 0.0874719i | \(-0.0278788\pi\) | |||||||
\(740\) | 22.6684i | 0.833308i | ||||||||
\(741\) | − | 4.43581i | − | 0.162954i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.8792i | − | 0.545864i | −0.962033 | − | 0.272932i | \(-0.912007\pi\) | ||
0.962033 | − | 0.272932i | \(-0.0879934\pi\) | |||||||
\(744\) | 4.96246i | 0.181933i | ||||||||
\(745\) | 8.01894 | 0.293791 | ||||||||
\(746\) | −19.7239 | −0.722144 | ||||||||
\(747\) | 29.7318 | 1.08783 | ||||||||
\(748\) | 8.99962 | + | 7.90226i | 0.329059 | + | 0.288935i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 9.09306i | − | 0.332032i | ||||||
\(751\) | 16.4820 | 0.601438 | 0.300719 | − | 0.953713i | \(-0.402773\pi\) | ||||
0.300719 | + | 0.953713i | \(0.402773\pi\) | |||||||
\(752\) | 5.74713i | 0.209576i | ||||||||
\(753\) | 7.66596 | 0.279363 | ||||||||
\(754\) | 40.8321 | 1.48702 | ||||||||
\(755\) | 49.6276 | 1.80613 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.82008 | −0.138843 | −0.0694216 | − | 0.997587i | \(-0.522115\pi\) | ||||
−0.0694216 | + | 0.997587i | \(0.522115\pi\) | |||||||
\(758\) | − | 35.6268i | − | 1.29402i | ||||||
\(759\) | −11.0866 | + | 12.6261i | −0.402416 | + | 0.458299i | ||||
\(760\) | −1.80242 | −0.0653807 | ||||||||
\(761\) | −1.85400 | −0.0672075 | −0.0336038 | − | 0.999435i | \(-0.510698\pi\) | ||||
−0.0336038 | + | 0.999435i | \(0.510698\pi\) | |||||||
\(762\) | − | 5.61016i | − | 0.203235i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3662 | −0.375037 | ||||||||
\(765\) | − | 17.8858i | − | 0.646662i | ||||||
\(766\) | −21.6373 | −0.781786 | ||||||||
\(767\) | 21.2319i | 0.766638i | ||||||||
\(768\) | 0.765367i | 0.0276178i | ||||||||
\(769\) | 8.92308 | 0.321775 | 0.160887 | − | 0.986973i | \(-0.448564\pi\) | ||||
0.160887 | + | 0.986973i | \(0.448564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.4028 | 0.482688 | ||||||||
\(772\) | 1.62333i | 0.0584248i | ||||||||
\(773\) | − | 20.3267i | − | 0.731099i | −0.930792 | − | 0.365550i | \(-0.880881\pi\) | ||
0.930792 | − | 0.365550i | \(-0.119119\pi\) | |||||||
\(774\) | 18.8620 | 0.677979 | ||||||||
\(775\) | 5.12792i | 0.184200i | ||||||||
\(776\) | −9.23880 | −0.331653 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 8.64698i | − | 0.310009i | ||||||
\(779\) | 2.08094 | 0.0745574 | ||||||||
\(780\) | 10.3587 | 0.370903 | ||||||||
\(781\) | −5.31849 | − | 4.66998i | −0.190310 | − | 0.167105i | ||||
\(782\) | − | 23.9029i | − | 0.854765i | ||||||
\(783\) | 25.6486 | 0.916607 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.6536 | 1.48668 | ||||||||
\(786\) | 6.75092 | 0.240797 | ||||||||
\(787\) | 38.4016 | 1.36887 | 0.684435 | − | 0.729074i | \(-0.260049\pi\) | ||||
0.684435 | + | 0.729074i | \(0.260049\pi\) | |||||||
\(788\) | − | 4.38713i | − | 0.156285i | ||||||
\(789\) | 6.49435 | 0.231205 | ||||||||
\(790\) | 17.4085i | 0.619367i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.28311 | − | 6.01676i | 0.187727 | − | 0.213796i | ||||
\(793\) | −74.7711 | −2.65520 | ||||||||
\(794\) | 36.1718 | 1.28369 | ||||||||
\(795\) | −0.674831 | −0.0239338 | ||||||||
\(796\) | 20.0640i | 0.711151i | ||||||||
\(797\) | − | 42.5849i | − | 1.50843i | −0.656625 | − | 0.754217i | \(-0.728017\pi\) | ||
0.656625 | − | 0.754217i | \(-0.271983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20.7533i | − | 0.734201i | ||||||
\(800\) | 0.790886i | 0.0279620i | ||||||||
\(801\) | − | 16.2434i | − | 0.573934i | ||||||
\(802\) | − | 8.99356i | − | 0.317574i | ||||||
\(803\) | −26.9789 | − | 23.6893i | −0.952065 | − | 0.835976i | ||||
\(804\) | − | 2.26737i | − | 0.0799639i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.7730 | −1.50661 | ||||||||
\(807\) | 5.17023 | 0.182001 | ||||||||
\(808\) | − | 1.85966i | − | 0.0654226i | ||||||
\(809\) | 7.41899i | 0.260838i | 0.991459 | + | 0.130419i | \(0.0416322\pi\) | ||||
−0.991459 | + | 0.130419i | \(0.958368\pi\) | |||||||
\(810\) | −8.35225 | −0.293468 | ||||||||
\(811\) | −43.2953 | −1.52030 | −0.760151 | − | 0.649746i | \(-0.774875\pi\) | ||||
−0.760151 | + | 0.649746i | \(0.774875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.9577i | 0.524589i | ||||||||
\(814\) | 24.1791 | − | 27.5368i | 0.847477 | − | 0.965164i | ||||
\(815\) | − | 27.2056i | − | 0.952972i | ||||||
\(816\) | − | 2.76380i | − | 0.0967524i | ||||||
\(817\) | 6.86391i | 0.240138i | ||||||||
\(818\) | − | 9.58279i | − | 0.335055i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.85953i | 0.169702i | ||||||||
\(821\) | − | 24.0962i | − | 0.840965i | −0.907301 | − | 0.420482i | \(-0.861861\pi\) | ||
0.907301 | − | 0.420482i | \(-0.138139\pi\) | |||||||
\(822\) | −2.47688 | −0.0863911 | ||||||||
\(823\) | 2.50007 | 0.0871469 | 0.0435735 | − | 0.999050i | \(-0.486126\pi\) | ||||
0.0435735 | + | 0.999050i | \(0.486126\pi\) | |||||||
\(824\) | −6.71011 | −0.233758 | ||||||||
\(825\) | −1.32464 | + | 1.50859i | −0.0461180 | + | 0.0525223i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.9902i | − | 1.14718i | −0.819142 | − | 0.573591i | \(-0.805550\pi\) | ||
0.819142 | − | 0.573591i | \(-0.194450\pi\) | |||||||
\(828\) | −15.9804 | −0.555359 | ||||||||
\(829\) | − | 28.4543i | − | 0.988260i | −0.869388 | − | 0.494130i | \(-0.835487\pi\) | ||
0.869388 | − | 0.494130i | \(-0.164513\pi\) | |||||||
\(830\) | −25.2663 | −0.877006 | ||||||||
\(831\) | −20.4160 | −0.708224 | ||||||||
\(832\) | −6.59694 | −0.228708 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.89139 | 0.0654935 | ||||||||
\(835\) | 41.8858i | 1.44952i | ||||||||
\(836\) | 2.18952 | + | 1.92254i | 0.0757260 | + | 0.0664924i | ||||
\(837\) | −26.8678 | −0.928687 | ||||||||
\(838\) | 37.9064 | 1.30945 | ||||||||
\(839\) | 26.5407i | 0.916288i | 0.888878 | + | 0.458144i | \(0.151486\pi\) | ||||
−0.888878 | + | 0.458144i | \(0.848514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.31052 | −0.321052 | ||||||||
\(842\) | 2.88394i | 0.0993873i | ||||||||
\(843\) | 16.0370 | 0.552344 | ||||||||
\(844\) | − | 8.56380i | − | 0.294778i | ||||||
\(845\) | 62.6143i | 2.15400i | ||||||||
\(846\) | −13.8748 | −0.477025 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.429764 | 0.0147581 | ||||||||
\(849\) | − | 7.70184i | − | 0.264327i | ||||||
\(850\) | − | 2.85595i | − | 0.0979583i | ||||||
\(851\) | −73.1373 | −2.50711 | ||||||||
\(852\) | 1.63332i | 0.0559565i | ||||||||
\(853\) | −0.431373 | −0.0147699 | −0.00738496 | − | 0.999973i | \(-0.502351\pi\) | ||||
−0.00738496 | + | 0.999973i | \(0.502351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.35143i | − | 0.148816i | ||||||
\(856\) | 14.7533 | 0.504259 | ||||||||
\(857\) | 17.5134 | 0.598248 | 0.299124 | − | 0.954214i | \(-0.403306\pi\) | ||||
0.299124 | + | 0.954214i | \(0.403306\pi\) | |||||||
\(858\) | −12.5834 | − | 11.0491i | −0.429591 | − | 0.377209i | ||||
\(859\) | 45.4813i | 1.55180i | 0.630855 | + | 0.775901i | \(0.282704\pi\) | ||||
−0.630855 | + | 0.775901i | \(0.717296\pi\) | |||||||
\(860\) | −16.0290 | −0.546584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.4068 | −1.10378 | ||||||||
\(863\) | 23.7319 | 0.807845 | 0.403922 | − | 0.914793i | \(-0.367647\pi\) | ||||
0.403922 | + | 0.914793i | \(0.367647\pi\) | |||||||
\(864\) | −4.14386 | −0.140977 | ||||||||
\(865\) | − | 31.9563i | − | 1.08655i | ||||||
\(866\) | 10.2319 | 0.347695 | ||||||||
\(867\) | − | 3.03093i | − | 0.102936i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.5686 | − | 21.1472i | 0.629898 | − | 0.717371i | ||||
\(870\) | −9.71905 | −0.329507 | ||||||||
\(871\) | 19.5432 | 0.662194 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | − | 22.3044i | − | 0.754890i | ||||||
\(874\) | − | 5.81532i | − | 0.196706i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.28528i | 0.279934i | ||||||||
\(877\) | 33.3577i | 1.12641i | 0.826317 | + | 0.563205i | \(0.190432\pi\) | ||||
−0.826317 | + | 0.563205i | \(0.809568\pi\) | |||||||
\(878\) | − | 28.8726i | − | 0.974404i | ||||||
\(879\) | 22.6877i | 0.765238i | ||||||||
\(880\) | −4.48962 | + | 5.11308i | −0.151345 | + | 0.172362i | ||||
\(881\) | 18.7347i | 0.631187i | 0.948895 | + | 0.315593i | \(0.102204\pi\) | ||||
−0.948895 | + | 0.315593i | \(0.897796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0705 | 0.877342 | 0.438671 | − | 0.898648i | \(-0.355449\pi\) | ||||
0.438671 | + | 0.898648i | \(0.355449\pi\) | |||||||
\(884\) | 23.8221 | 0.801223 | ||||||||
\(885\) | − | 5.05372i | − | 0.169879i | ||||||
\(886\) | − | 8.56036i | − | 0.287591i | ||||||
\(887\) | 52.1238 | 1.75015 | 0.875073 | − | 0.483992i | \(-0.160813\pi\) | ||||
0.875073 | + | 0.483992i | \(0.160813\pi\) | |||||||
\(888\) | −8.45660 | −0.283785 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.8038i | 0.462703i | ||||||||
\(891\) | 10.1460 | + | 8.90886i | 0.339904 | + | 0.298458i | ||||
\(892\) | − | 8.24084i | − | 0.275924i | ||||||
\(893\) | − | 5.04908i | − | 0.168961i | ||||||
\(894\) | 2.99152i | 0.100051i | ||||||||
\(895\) | − | 9.23553i | − | 0.308710i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.4214i | 1.11591i | ||||||||
\(898\) | − | 10.8089i | − | 0.360696i | ||||||
\(899\) | 40.1316 | 1.33846 | ||||||||
\(900\) | −1.90937 | −0.0636456 | ||||||||
\(901\) | −1.55191 | −0.0517016 | ||||||||
\(902\) | 5.18338 | − | 5.90318i | 0.172588 | − | 0.196554i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.597322i | 0.0198666i | ||||||||
\(905\) | −16.7891 | −0.558089 | ||||||||
\(906\) | 18.5139i | 0.615082i | ||||||||
\(907\) | 30.5734 | 1.01517 | 0.507587 | − | 0.861601i | \(-0.330538\pi\) | ||||
0.507587 | + | 0.861601i | \(0.330538\pi\) | |||||||
\(908\) | −27.4795 | −0.911938 | ||||||||
\(909\) | 4.48962 | 0.148911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.343220 | 0.0113714 | 0.00568569 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568569 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(912\) | − | 0.672404i | − | 0.0222655i | ||||||
\(913\) | 30.6926 | + | 26.9501i | 1.01578 | + | 0.891918i | ||||
\(914\) | 24.3896 | 0.806735 | ||||||||
\(915\) | 17.7974 | 0.588364 | ||||||||
\(916\) | − | 0.104343i | − | 0.00344759i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14.9638 | 0.493879 | ||||||||
\(919\) | − | 51.0687i | − | 1.68460i | −0.539008 | − | 0.842301i | \(-0.681201\pi\) | ||
0.539008 | − | 0.842301i | \(-0.318799\pi\) | |||||||
\(920\) | 13.5803 | 0.447728 | ||||||||
\(921\) | − | 12.3896i | − | 0.408250i | ||||||
\(922\) | − | 1.13186i | − | 0.0372757i | ||||||
\(923\) | −14.0781 | −0.463385 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.73856 | −0.287322 | ||||||||
\(926\) | 6.38388i | 0.209787i | ||||||||
\(927\) | − | 16.1996i | − | 0.532066i | ||||||
\(928\) | 6.18955 | 0.203182 | ||||||||
\(929\) | − | 58.6389i | − | 1.92388i | −0.273263 | − | 0.961939i | \(-0.588103\pi\) | ||
0.273263 | − | 0.961939i | \(-0.411897\pi\) | |||||||
\(930\) | 10.1810 | 0.333850 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.1577i | 0.496507i | ||||||||
\(933\) | 1.09171 | 0.0357410 | ||||||||
\(934\) | −35.6840 | −1.16762 | ||||||||
\(935\) | 16.2124 | − | 18.4637i | 0.530201 | − | 0.603829i | ||||
\(936\) | − | 15.9264i | − | 0.520571i | ||||||
\(937\) | 40.2806 | 1.31591 | 0.657955 | − | 0.753057i | \(-0.271422\pi\) | ||||
0.657955 | + | 0.753057i | \(0.271422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.83754 | 0.288402 | ||||||||
\(940\) | 11.7909 | 0.384576 | ||||||||
\(941\) | 2.74386 | 0.0894472 | 0.0447236 | − | 0.998999i | \(-0.485759\pi\) | ||||
0.0447236 | + | 0.998999i | \(0.485759\pi\) | |||||||
\(942\) | 15.5391i | 0.506292i | ||||||||
\(943\) | −15.6788 | −0.510571 | ||||||||
\(944\) | 3.21844i | 0.104751i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.4714 | + | 17.0972i | 0.633071 | + | 0.555878i | ||||
\(947\) | −40.8459 | −1.32731 | −0.663657 | − | 0.748037i | \(-0.730996\pi\) | ||||
−0.663657 | + | 0.748037i | \(0.730996\pi\) | |||||||
\(948\) | −6.49435 | −0.210927 | ||||||||
\(949\) | −71.4134 | −2.31818 | ||||||||
\(950\) | − | 0.694824i | − | 0.0225431i | ||||||
\(951\) | 24.2804i | 0.787347i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.21096i | − | 0.104013i | −0.998647 | − | 0.0520065i | \(-0.983438\pi\) | ||
0.998647 | − | 0.0520065i | \(-0.0165617\pi\) | |||||||
\(954\) | 1.03754i | 0.0335916i | ||||||||
\(955\) | 21.2675i | 0.688199i | ||||||||
\(956\) | − | 25.9135i | − | 0.838101i | ||||||
\(957\) | 11.8064 | + | 10.3668i | 0.381645 | + | 0.335109i | ||||
\(958\) | − | 11.5819i | − | 0.374193i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.57024 | 0.0506792 | ||||||||
\(961\) | −11.0392 | −0.356103 | ||||||||
\(962\) | − | 72.8901i | − | 2.35007i | ||||||
\(963\) | 35.6177i | 1.14777i | ||||||||
\(964\) | 7.31108 | 0.235474 | ||||||||
\(965\) | 3.33044 | 0.107211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.1521i | 1.00178i | 0.865510 | + | 0.500892i | \(0.166995\pi\) | ||||
−0.865510 | + | 0.500892i | \(0.833005\pi\) | |||||||
\(968\) | 10.9077 | − | 1.42237i | 0.350585 | − | 0.0457167i | ||||
\(969\) | 2.42811i | 0.0780020i | ||||||||
\(970\) | 18.9544i | 0.608590i | ||||||||
\(971\) | − | 22.3787i | − | 0.718167i | −0.933305 | − | 0.359084i | \(-0.883089\pi\) | ||
0.933305 | − | 0.359084i | \(-0.116911\pi\) | |||||||
\(972\) | − | 15.5474i | − | 0.498684i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 40.0638i | 1.28373i | ||||||||
\(975\) | 3.99324i | 0.127886i | ||||||||
\(976\) | −11.3342 | −0.362799 | ||||||||
\(977\) | 17.6641 | 0.565123 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(978\) | 10.1492 | 0.324537 | ||||||||
\(979\) | 14.7237 | − | 16.7683i | 0.470571 | − | 0.535918i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4853i | 0.462479i | ||||||||
\(982\) | −19.7876 | −0.631449 | ||||||||
\(983\) | − | 42.2471i | − | 1.34747i | −0.738971 | − | 0.673737i | \(-0.764688\pi\) | ||
0.738971 | − | 0.673737i | \(-0.235312\pi\) | |||||||
\(984\) | −1.81288 | −0.0577924 | ||||||||
\(985\) | −9.00069 | −0.286786 | ||||||||
\(986\) | −22.3510 | −0.711799 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.79566 | 0.184385 | ||||||||
\(989\) | − | 51.7159i | − | 1.64447i | ||||||
\(990\) | −12.3441 | − | 10.8389i | −0.392320 | − | 0.344483i | ||||
\(991\) | −3.45577 | −0.109776 | −0.0548881 | − | 0.998493i | \(-0.517480\pi\) | ||||
−0.0548881 | + | 0.998493i | \(0.517480\pi\) | |||||||
\(992\) | −6.48376 | −0.205860 | ||||||||
\(993\) | 24.4335i | 0.775374i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.1636 | 1.30497 | ||||||||
\(996\) | − | 9.42575i | − | 0.298666i | ||||||
\(997\) | −18.5677 | −0.588045 | −0.294022 | − | 0.955799i | \(-0.594994\pi\) | ||||
−0.294022 | + | 0.955799i | \(0.594994\pi\) | |||||||
\(998\) | − | 26.6553i | − | 0.843758i | ||||||
\(999\) | − | 45.7858i | − | 1.44860i |
(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 | 1078.2.c.c.1077.14 | yes | 16 | |
7.2 | even | 3 | 1078.2.i.d.1011.13 | 32 | |||
7.3 | odd | 6 | 1078.2.i.d.901.7 | 32 | |||
7.4 | even | 3 | 1078.2.i.d.901.8 | 32 | |||
7.5 | odd | 6 | 1078.2.i.d.1011.14 | 32 | |||
7.6 | odd | 2 | inner | 1078.2.c.c.1077.11 | yes | 16 | |
11.10 | odd | 2 | inner | 1078.2.c.c.1077.6 | yes | 16 | |
77.10 | even | 6 | 1078.2.i.d.901.13 | 32 | |||
77.32 | odd | 6 | 1078.2.i.d.901.14 | 32 | |||
77.54 | even | 6 | 1078.2.i.d.1011.8 | 32 | |||
77.65 | odd | 6 | 1078.2.i.d.1011.7 | 32 | |||
77.76 | even | 2 | inner | 1078.2.c.c.1077.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.c.1077.3 | ✓ | 16 | 77.76 | even | 2 | inner | |
1078.2.c.c.1077.6 | yes | 16 | 11.10 | odd | 2 | inner | |
1078.2.c.c.1077.11 | yes | 16 | 7.6 | odd | 2 | inner | |
1078.2.c.c.1077.14 | yes | 16 | 1.1 | even | 1 | trivial | |
1078.2.i.d.901.7 | 32 | 7.3 | odd | 6 | |||
1078.2.i.d.901.8 | 32 | 7.4 | even | 3 | |||
1078.2.i.d.901.13 | 32 | 77.10 | even | 6 | |||
1078.2.i.d.901.14 | 32 | 77.32 | odd | 6 | |||
1078.2.i.d.1011.7 | 32 | 77.65 | odd | 6 | |||
1078.2.i.d.1011.8 | 32 | 77.54 | even | 6 | |||
1078.2.i.d.1011.13 | 32 | 7.2 | even | 3 | |||
1078.2.i.d.1011.14 | 32 | 7.5 | odd | 6 |