Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [650,2,Mod(49,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.n (of order \(6\), degree \(2\), not 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: | \(5.19027613138\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.199 |
Dual form | 650.2.n.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.633975 | − | 0.366025i | −0.366025 | − | 0.211325i | 0.305695 | − | 0.952129i | \(-0.401111\pi\) |
−0.671721 | + | 0.740805i | \(0.734444\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.633975 | − | 0.366025i | 0.258819 | − | 0.149429i | ||||
\(7\) | −1.50000 | − | 2.59808i | −0.566947 | − | 0.981981i | −0.996866 | − | 0.0791130i | \(-0.974791\pi\) |
0.429919 | − | 0.902867i | \(-0.358542\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.23205 | − | 2.13397i | −0.410684 | − | 0.711325i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0.732051i | 0.211325i | ||||||||
\(13\) | 0.866025 | + | 3.50000i | 0.240192 | + | 0.970725i | ||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −7.09808 | + | 4.09808i | −1.72154 | + | 0.993929i | −0.805759 | + | 0.592244i | \(0.798242\pi\) |
−0.915778 | + | 0.401685i | \(0.868425\pi\) | |||||||
\(18\) | 2.46410 | 0.580794 | ||||||||
\(19\) | 0.401924 | − | 0.232051i | 0.0922076 | − | 0.0532361i | −0.453187 | − | 0.891415i | \(-0.649713\pi\) |
0.545395 | + | 0.838179i | \(0.316380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.19615i | 0.479240i | ||||||||
\(22\) | −2.59808 | + | 1.50000i | −0.553912 | + | 0.319801i | ||||
\(23\) | −8.19615 | − | 4.73205i | −1.70902 | − | 0.986701i | −0.935781 | − | 0.352581i | \(-0.885304\pi\) |
−0.773234 | − | 0.634120i | \(-0.781362\pi\) | |||||||
\(24\) | −0.633975 | − | 0.366025i | −0.129410 | − | 0.0747146i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.46410 | − | 1.00000i | −0.679366 | − | 0.196116i | ||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | −1.50000 | + | 2.59808i | −0.283473 | + | 0.490990i | ||||
\(29\) | −1.26795 | + | 2.19615i | −0.235452 | + | 0.407815i | −0.959404 | − | 0.282035i | \(-0.908990\pi\) |
0.723952 | + | 0.689851i | \(0.242324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.73205i | 0.849901i | 0.905216 | + | 0.424951i | \(0.139709\pi\) | ||||
−0.905216 | + | 0.424951i | \(0.860291\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.09808 | − | 1.90192i | −0.191151 | − | 0.331082i | ||||
\(34\) | − | 8.19615i | − | 1.40563i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.23205 | + | 2.13397i | −0.205342 | + | 0.355662i | ||||
\(37\) | −0.401924 | + | 0.696152i | −0.0660759 | + | 0.114447i | −0.897171 | − | 0.441684i | \(-0.854381\pi\) |
0.831095 | + | 0.556131i | \(0.187715\pi\) | |||||||
\(38\) | 0.464102i | 0.0752872i | ||||||||
\(39\) | 0.732051 | − | 2.53590i | 0.117222 | − | 0.406069i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | − | 5.19615i | −1.40556 | − | 0.811503i | −0.410608 | − | 0.911812i | \(-0.634683\pi\) |
−0.994956 | + | 0.100309i | \(0.968017\pi\) | |||||||
\(42\) | −1.90192 | − | 1.09808i | −0.293473 | − | 0.169437i | ||||
\(43\) | 1.73205 | − | 1.00000i | 0.264135 | − | 0.152499i | −0.362084 | − | 0.932145i | \(-0.617935\pi\) |
0.626219 | + | 0.779647i | \(0.284601\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.19615 | − | 4.73205i | 1.20846 | − | 0.697703i | ||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 0.633975 | − | 0.366025i | 0.0915064 | − | 0.0528312i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 2.59808 | − | 2.50000i | 0.360288 | − | 0.346688i | ||||
\(53\) | 0.464102i | 0.0637493i | 0.999492 | + | 0.0318746i | \(0.0101477\pi\) | ||||
−0.999492 | + | 0.0318746i | \(0.989852\pi\) | |||||||
\(54\) | −3.46410 | − | 2.00000i | −0.471405 | − | 0.272166i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | −0.339746 | −0.0450005 | ||||||||
\(58\) | −1.26795 | − | 2.19615i | −0.166490 | − | 0.288369i | ||||
\(59\) | −9.00000 | + | 5.19615i | −1.17170 | + | 0.676481i | −0.954080 | − | 0.299552i | \(-0.903163\pi\) |
−0.217620 | + | 0.976034i | \(0.569829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.09808 | − | 5.36603i | −0.396668 | − | 0.687049i | 0.596645 | − | 0.802506i | \(-0.296500\pi\) |
−0.993313 | + | 0.115456i | \(0.963167\pi\) | |||||||
\(62\) | −4.09808 | − | 2.36603i | −0.520456 | − | 0.300486i | ||||
\(63\) | −3.69615 | + | 6.40192i | −0.465671 | + | 0.806567i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.19615 | 0.270328 | ||||||||
\(67\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(68\) | 7.09808 | + | 4.09808i | 0.860768 | + | 0.496965i | ||||
\(69\) | 3.46410 | + | 6.00000i | 0.417029 | + | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.19615 | + | 3.00000i | −0.616670 | + | 0.356034i | −0.775571 | − | 0.631260i | \(-0.782538\pi\) |
0.158901 | + | 0.987294i | \(0.449205\pi\) | |||||||
\(72\) | −1.23205 | − | 2.13397i | −0.145199 | − | 0.251491i | ||||
\(73\) | −11.6603 | −1.36473 | −0.682365 | − | 0.731012i | \(-0.739048\pi\) | ||||
−0.682365 | + | 0.731012i | \(0.739048\pi\) | |||||||
\(74\) | −0.401924 | − | 0.696152i | −0.0467227 | − | 0.0809261i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.401924 | − | 0.232051i | −0.0461038 | − | 0.0266181i | ||||
\(77\) | − | 9.00000i | − | 1.02565i | ||||||
\(78\) | 1.83013 | + | 1.90192i | 0.207221 | + | 0.215350i | ||||
\(79\) | 4.19615 | 0.472104 | 0.236052 | − | 0.971740i | \(-0.424146\pi\) | ||||
0.236052 | + | 0.971740i | \(0.424146\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.23205 | + | 3.86603i | −0.248006 | + | 0.429558i | ||||
\(82\) | 9.00000 | − | 5.19615i | 0.993884 | − | 0.573819i | ||||
\(83\) | 8.19615 | 0.899645 | 0.449822 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449822 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(84\) | 1.90192 | − | 1.09808i | 0.207517 | − | 0.119810i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000i | 0.215666i | ||||||||
\(87\) | 1.60770 | − | 0.928203i | 0.172363 | − | 0.0995138i | ||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | −5.89230 | − | 3.40192i | −0.624583 | − | 0.360603i | 0.154068 | − | 0.988060i | \(-0.450762\pi\) |
−0.778651 | + | 0.627457i | \(0.784096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.79423 | − | 7.50000i | 0.817057 | − | 0.786214i | ||||
\(92\) | 9.46410i | 0.986701i | ||||||||
\(93\) | 1.73205 | − | 3.00000i | 0.179605 | − | 0.311086i | ||||
\(94\) | −1.50000 | + | 2.59808i | −0.154713 | + | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.732051i | 0.0747146i | ||||||||
\(97\) | −4.56218 | − | 7.90192i | −0.463219 | − | 0.802319i | 0.535900 | − | 0.844281i | \(-0.319972\pi\) |
−0.999119 | + | 0.0419625i | \(0.986639\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | − | 7.39230i | − | 0.742955i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.36603 | + | 9.29423i | −0.533939 | + | 0.924810i | 0.465274 | + | 0.885167i | \(0.345956\pi\) |
−0.999214 | + | 0.0396438i | \(0.987378\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | − | 9.19615i | − | 0.906124i | −0.891479 | − | 0.453062i | \(-0.850332\pi\) | ||
0.891479 | − | 0.453062i | \(-0.149668\pi\) | |||||||
\(104\) | 0.866025 | + | 3.50000i | 0.0849208 | + | 0.343203i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.401924 | − | 0.232051i | −0.0390383 | − | 0.0225388i | ||||
\(107\) | 15.2942 | + | 8.83013i | 1.47855 | + | 0.853641i | 0.999706 | − | 0.0242598i | \(-0.00772291\pi\) |
0.478843 | + | 0.877900i | \(0.341056\pi\) | |||||||
\(108\) | 3.46410 | − | 2.00000i | 0.333333 | − | 0.192450i | ||||
\(109\) | 8.53590i | 0.817591i | 0.912626 | + | 0.408795i | \(0.134051\pi\) | ||||
−0.912626 | + | 0.408795i | \(0.865949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.509619 | − | 0.294229i | 0.0483709 | − | 0.0279269i | ||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 6.00000 | − | 3.46410i | 0.564433 | − | 0.325875i | −0.190490 | − | 0.981689i | \(-0.561008\pi\) |
0.754923 | + | 0.655814i | \(0.227674\pi\) | |||||||
\(114\) | 0.169873 | − | 0.294229i | 0.0159101 | − | 0.0275570i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.53590 | 0.235452 | ||||||||
\(117\) | 6.40192 | − | 6.16025i | 0.591858 | − | 0.569516i | ||||
\(118\) | − | 10.3923i | − | 0.956689i | ||||||
\(119\) | 21.2942 | + | 12.2942i | 1.95204 | + | 1.12701i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 6.19615 | 0.560973 | ||||||||
\(123\) | 3.80385 | + | 6.58846i | 0.342981 | + | 0.594061i | ||||
\(124\) | 4.09808 | − | 2.36603i | 0.368018 | − | 0.212475i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.69615 | − | 6.40192i | −0.329279 | − | 0.570329i | ||||
\(127\) | 9.35641 | + | 5.40192i | 0.830247 | + | 0.479343i | 0.853937 | − | 0.520376i | \(-0.174208\pi\) |
−0.0236904 | + | 0.999719i | \(0.507542\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.46410 | −0.128907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.12436 | 0.535087 | 0.267544 | − | 0.963546i | \(-0.413788\pi\) | ||||
0.267544 | + | 0.963546i | \(0.413788\pi\) | |||||||
\(132\) | −1.09808 | + | 1.90192i | −0.0955753 | + | 0.165541i | ||||
\(133\) | −1.20577 | − | 0.696152i | −0.104554 | − | 0.0603641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.09808 | + | 4.09808i | −0.608655 | + | 0.351407i | ||||
\(137\) | −1.09808 | − | 1.90192i | −0.0938150 | − | 0.162492i | 0.815298 | − | 0.579041i | \(-0.196573\pi\) |
−0.909113 | + | 0.416549i | \(0.863240\pi\) | |||||||
\(138\) | −6.92820 | −0.589768 | ||||||||
\(139\) | 0.598076 | + | 1.03590i | 0.0507282 | + | 0.0878638i | 0.890274 | − | 0.455424i | \(-0.150512\pi\) |
−0.839546 | + | 0.543288i | \(0.817179\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.90192 | − | 1.09808i | −0.160171 | − | 0.0924747i | ||||
\(142\) | − | 6.00000i | − | 0.503509i | ||||||
\(143\) | −3.00000 | + | 10.3923i | −0.250873 | + | 0.869048i | ||||
\(144\) | 2.46410 | 0.205342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.83013 | − | 10.0981i | 0.482505 | − | 0.835723i | ||||
\(147\) | 1.26795 | − | 0.732051i | 0.104579 | − | 0.0603785i | ||||
\(148\) | 0.803848 | 0.0660759 | ||||||||
\(149\) | −5.19615 | + | 3.00000i | −0.425685 | + | 0.245770i | −0.697507 | − | 0.716578i | \(-0.745707\pi\) |
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.6603i | − | 1.92544i | −0.270492 | − | 0.962722i | \(-0.587187\pi\) | ||
0.270492 | − | 0.962722i | \(-0.412813\pi\) | |||||||
\(152\) | 0.401924 | − | 0.232051i | 0.0326003 | − | 0.0188218i | ||||
\(153\) | 17.4904 | + | 10.0981i | 1.41401 | + | 0.816381i | ||||
\(154\) | 7.79423 | + | 4.50000i | 0.628077 | + | 0.362620i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.56218 | + | 0.633975i | −0.205138 | + | 0.0507586i | ||||
\(157\) | 13.0000i | 1.03751i | 0.854922 | + | 0.518756i | \(0.173605\pi\) | ||||
−0.854922 | + | 0.518756i | \(0.826395\pi\) | |||||||
\(158\) | −2.09808 | + | 3.63397i | −0.166914 | + | 0.289103i | ||||
\(159\) | 0.169873 | − | 0.294229i | 0.0134718 | − | 0.0233338i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.3923i | 2.23763i | ||||||||
\(162\) | −2.23205 | − | 3.86603i | −0.175366 | − | 0.303744i | ||||
\(163\) | −5.36603 | − | 9.29423i | −0.420300 | − | 0.727980i | 0.575669 | − | 0.817683i | \(-0.304742\pi\) |
−0.995969 | + | 0.0897026i | \(0.971408\pi\) | |||||||
\(164\) | 10.3923i | 0.811503i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.09808 | + | 7.09808i | −0.318072 | + | 0.550918i | ||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | 2.19615i | 0.169437i | ||||||||
\(169\) | −11.5000 | + | 6.06218i | −0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.990381 | − | 0.571797i | −0.0757363 | − | 0.0437264i | ||||
\(172\) | −1.73205 | − | 1.00000i | −0.132068 | − | 0.0762493i | ||||
\(173\) | −12.9904 | + | 7.50000i | −0.987640 | + | 0.570214i | −0.904568 | − | 0.426329i | \(-0.859807\pi\) |
−0.0830722 | + | 0.996544i | \(0.526473\pi\) | |||||||
\(174\) | 1.85641i | 0.140734i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.59808 | + | 1.50000i | −0.195837 | + | 0.113067i | ||||
\(177\) | 7.60770 | 0.571829 | ||||||||
\(178\) | 5.89230 | − | 3.40192i | 0.441647 | − | 0.254985i | ||||
\(179\) | −4.73205 | + | 8.19615i | −0.353690 | + | 0.612609i | −0.986893 | − | 0.161377i | \(-0.948407\pi\) |
0.633203 | + | 0.773986i | \(0.281740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5885 | 1.08435 | 0.542176 | − | 0.840265i | \(-0.317601\pi\) | ||||
0.542176 | + | 0.840265i | \(0.317601\pi\) | |||||||
\(182\) | 2.59808 | + | 10.5000i | 0.192582 | + | 0.778312i | ||||
\(183\) | 4.53590i | 0.335303i | ||||||||
\(184\) | −8.19615 | − | 4.73205i | −0.604228 | − | 0.348851i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.73205 | + | 3.00000i | 0.127000 | + | 0.219971i | ||||
\(187\) | −24.5885 | −1.79809 | ||||||||
\(188\) | −1.50000 | − | 2.59808i | −0.109399 | − | 0.189484i | ||||
\(189\) | 10.3923 | − | 6.00000i | 0.755929 | − | 0.436436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3660 | + | 19.6865i | 0.822417 | + | 1.42447i | 0.903878 | + | 0.427791i | \(0.140708\pi\) |
−0.0814609 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(192\) | −0.633975 | − | 0.366025i | −0.0457532 | − | 0.0264156i | ||||
\(193\) | 8.19615 | − | 14.1962i | 0.589972 | − | 1.02186i | −0.404263 | − | 0.914643i | \(-0.632472\pi\) |
0.994235 | − | 0.107219i | \(-0.0341945\pi\) | |||||||
\(194\) | 9.12436 | 0.655091 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 10.7942 | − | 18.6962i | 0.769057 | − | 1.33205i | −0.169018 | − | 0.985613i | \(-0.554060\pi\) |
0.938075 | − | 0.346433i | \(-0.112607\pi\) | |||||||
\(198\) | 6.40192 | + | 3.69615i | 0.454965 | + | 0.262674i | ||||
\(199\) | −3.19615 | − | 5.53590i | −0.226569 | − | 0.392429i | 0.730220 | − | 0.683212i | \(-0.239418\pi\) |
−0.956789 | + | 0.290783i | \(0.906084\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.36603 | − | 9.29423i | −0.377552 | − | 0.653940i | ||||
\(203\) | 7.60770 | 0.533956 | ||||||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.96410 | + | 4.59808i | 0.554885 | + | 0.320363i | ||||
\(207\) | 23.3205i | 1.62089i | ||||||||
\(208\) | −3.46410 | − | 1.00000i | −0.240192 | − | 0.0693375i | ||||
\(209\) | 1.39230 | 0.0963077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.79423 | − | 15.2321i | 0.605420 | − | 1.04862i | −0.386565 | − | 0.922262i | \(-0.626339\pi\) |
0.991985 | − | 0.126356i | \(-0.0403280\pi\) | |||||||
\(212\) | 0.401924 | − | 0.232051i | 0.0276042 | − | 0.0159373i | ||||
\(213\) | 4.39230 | 0.300956 | ||||||||
\(214\) | −15.2942 | + | 8.83013i | −1.04549 | + | 0.603615i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | 12.2942 | − | 7.09808i | 0.834587 | − | 0.481849i | ||||
\(218\) | −7.39230 | − | 4.26795i | −0.500670 | − | 0.289062i | ||||
\(219\) | 7.39230 | + | 4.26795i | 0.499526 | + | 0.288401i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.4904 | − | 21.2942i | −1.37833 | − | 1.43240i | ||||
\(222\) | 0.588457i | 0.0394947i | ||||||||
\(223\) | 3.23205 | − | 5.59808i | 0.216434 | − | 0.374875i | −0.737281 | − | 0.675586i | \(-0.763891\pi\) |
0.953715 | + | 0.300711i | \(0.0972240\pi\) | |||||||
\(224\) | −1.50000 | + | 2.59808i | −0.100223 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.92820i | 0.460857i | ||||||||
\(227\) | −8.19615 | − | 14.1962i | −0.543998 | − | 0.942232i | −0.998669 | − | 0.0515725i | \(-0.983577\pi\) |
0.454672 | − | 0.890659i | \(-0.349757\pi\) | |||||||
\(228\) | 0.169873 | + | 0.294229i | 0.0112501 | + | 0.0194858i | ||||
\(229\) | 1.26795i | 0.0837884i | 0.999122 | + | 0.0418942i | \(0.0133392\pi\) | ||||
−0.999122 | + | 0.0418942i | \(0.986661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.29423 | + | 5.70577i | −0.216744 | + | 0.375412i | ||||
\(232\) | −1.26795 | + | 2.19615i | −0.0832449 | + | 0.144184i | ||||
\(233\) | 4.73205i | 0.310007i | 0.987914 | + | 0.155003i | \(0.0495389\pi\) | ||||
−0.987914 | + | 0.155003i | \(0.950461\pi\) | |||||||
\(234\) | 2.13397 | + | 8.62436i | 0.139502 | + | 0.563792i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.00000 | + | 5.19615i | 0.585850 | + | 0.338241i | ||||
\(237\) | −2.66025 | − | 1.53590i | −0.172802 | − | 0.0997673i | ||||
\(238\) | −21.2942 | + | 12.2942i | −1.38030 | + | 0.796916i | ||||
\(239\) | − | 2.19615i | − | 0.142057i | −0.997474 | − | 0.0710286i | \(-0.977372\pi\) | ||
0.997474 | − | 0.0710286i | \(-0.0226282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | + | 4.33013i | −0.483117 | + | 0.278928i | −0.721715 | − | 0.692191i | \(-0.756646\pi\) |
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 13.2224 | − | 7.63397i | 0.848219 | − | 0.489720i | ||||
\(244\) | −3.09808 | + | 5.36603i | −0.198334 | + | 0.343525i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.60770 | −0.485049 | ||||||||
\(247\) | 1.16025 | + | 1.20577i | 0.0738252 | + | 0.0767214i | ||||
\(248\) | 4.73205i | 0.300486i | ||||||||
\(249\) | −5.19615 | − | 3.00000i | −0.329293 | − | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.59808 | − | 14.8923i | −0.542706 | − | 0.939994i | −0.998747 | − | 0.0500355i | \(-0.984067\pi\) |
0.456042 | − | 0.889958i | \(-0.349267\pi\) | |||||||
\(252\) | 7.39230 | 0.465671 | ||||||||
\(253\) | −14.1962 | − | 24.5885i | −0.892504 | − | 1.54586i | ||||
\(254\) | −9.35641 | + | 5.40192i | −0.587073 | + | 0.338947i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.0000 | − | 6.92820i | −0.748539 | − | 0.432169i | 0.0766265 | − | 0.997060i | \(-0.475585\pi\) |
−0.825166 | + | 0.564890i | \(0.808918\pi\) | |||||||
\(258\) | 0.732051 | − | 1.26795i | 0.0455755 | − | 0.0789391i | ||||
\(259\) | 2.41154 | 0.149846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.24871 | 0.386786 | ||||||||
\(262\) | −3.06218 | + | 5.30385i | −0.189182 | + | 0.327673i | ||||
\(263\) | −3.10770 | − | 1.79423i | −0.191629 | − | 0.110637i | 0.401116 | − | 0.916027i | \(-0.368622\pi\) |
−0.592745 | + | 0.805390i | \(0.701956\pi\) | |||||||
\(264\) | −1.09808 | − | 1.90192i | −0.0675819 | − | 0.117055i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.20577 | − | 0.696152i | 0.0739306 | − | 0.0426838i | ||||
\(267\) | 2.49038 | + | 4.31347i | 0.152409 | + | 0.263980i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5622 | − | 23.4904i | −0.826901 | − | 1.43223i | −0.900458 | − | 0.434943i | \(-0.856769\pi\) |
0.0735575 | − | 0.997291i | \(-0.476565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.19615 | + | 4.73205i | 0.497881 | + | 0.287452i | 0.727838 | − | 0.685749i | \(-0.240525\pi\) |
−0.229957 | + | 0.973201i | \(0.573859\pi\) | |||||||
\(272\) | − | 8.19615i | − | 0.496965i | ||||||
\(273\) | −7.68653 | + | 1.90192i | −0.465210 | + | 0.115110i | ||||
\(274\) | 2.19615 | 0.132674 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.46410 | − | 6.00000i | 0.208514 | − | 0.361158i | ||||
\(277\) | 0.866025 | − | 0.500000i | 0.0520344 | − | 0.0300421i | −0.473757 | − | 0.880656i | \(-0.657103\pi\) |
0.525792 | + | 0.850613i | \(0.323769\pi\) | |||||||
\(278\) | −1.19615 | −0.0717405 | ||||||||
\(279\) | 10.0981 | − | 5.83013i | 0.604556 | − | 0.349041i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.3923i | − | 0.619953i | −0.950744 | − | 0.309976i | \(-0.899679\pi\) | ||
0.950744 | − | 0.309976i | \(-0.100321\pi\) | |||||||
\(282\) | 1.90192 | − | 1.09808i | 0.113258 | − | 0.0653895i | ||||
\(283\) | 8.32051 | + | 4.80385i | 0.494603 | + | 0.285559i | 0.726482 | − | 0.687186i | \(-0.241154\pi\) |
−0.231879 | + | 0.972745i | \(0.574487\pi\) | |||||||
\(284\) | 5.19615 | + | 3.00000i | 0.308335 | + | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.50000 | − | 7.79423i | −0.443484 | − | 0.460882i | ||||
\(287\) | 31.1769i | 1.84032i | ||||||||
\(288\) | −1.23205 | + | 2.13397i | −0.0725993 | + | 0.125746i | ||||
\(289\) | 25.0885 | − | 43.4545i | 1.47579 | − | 2.55615i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.67949i | 0.391559i | ||||||||
\(292\) | 5.83013 | + | 10.0981i | 0.341182 | + | 0.590945i | ||||
\(293\) | 5.59808 | + | 9.69615i | 0.327043 | + | 0.566455i | 0.981924 | − | 0.189277i | \(-0.0606144\pi\) |
−0.654881 | + | 0.755732i | \(0.727281\pi\) | |||||||
\(294\) | 1.46410i | 0.0853881i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.401924 | + | 0.696152i | −0.0233613 | + | 0.0404630i | ||||
\(297\) | −6.00000 | + | 10.3923i | −0.348155 | + | 0.603023i | ||||
\(298\) | − | 6.00000i | − | 0.347571i | ||||||
\(299\) | 9.46410 | − | 32.7846i | 0.547323 | − | 1.89598i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.19615 | − | 3.00000i | −0.299501 | − | 0.172917i | ||||
\(302\) | 20.4904 | + | 11.8301i | 1.17909 | + | 0.680747i | ||||
\(303\) | 6.80385 | − | 3.92820i | 0.390871 | − | 0.225669i | ||||
\(304\) | 0.464102i | 0.0266181i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −17.4904 | + | 10.0981i | −0.999859 | + | 0.577269i | ||||
\(307\) | −27.4641 | −1.56746 | −0.783730 | − | 0.621102i | \(-0.786685\pi\) | ||||
−0.783730 | + | 0.621102i | \(0.786685\pi\) | |||||||
\(308\) | −7.79423 | + | 4.50000i | −0.444117 | + | 0.256411i | ||||
\(309\) | −3.36603 | + | 5.83013i | −0.191486 | + | 0.331664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.12436 | −0.517395 | −0.258697 | − | 0.965958i | \(-0.583293\pi\) | ||||
−0.258697 | + | 0.965958i | \(0.583293\pi\) | |||||||
\(312\) | 0.732051 | − | 2.53590i | 0.0414442 | − | 0.143567i | ||||
\(313\) | 26.3923i | 1.49178i | 0.666068 | + | 0.745891i | \(0.267976\pi\) | ||||
−0.666068 | + | 0.745891i | \(0.732024\pi\) | |||||||
\(314\) | −11.2583 | − | 6.50000i | −0.635344 | − | 0.366816i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.09808 | − | 3.63397i | −0.118026 | − | 0.204427i | ||||
\(317\) | −23.1962 | −1.30283 | −0.651413 | − | 0.758723i | \(-0.725823\pi\) | ||||
−0.651413 | + | 0.758723i | \(0.725823\pi\) | |||||||
\(318\) | 0.169873 | + | 0.294229i | 0.00952600 | + | 0.0164995i | ||||
\(319\) | −6.58846 | + | 3.80385i | −0.368883 | + | 0.212975i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.46410 | − | 11.1962i | −0.360791 | − | 0.624908i | ||||
\(322\) | −24.5885 | − | 14.1962i | −1.37026 | − | 0.791121i | ||||
\(323\) | −1.90192 | + | 3.29423i | −0.105826 | + | 0.183296i | ||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.7321 | 0.594393 | ||||||||
\(327\) | 3.12436 | − | 5.41154i | 0.172777 | − | 0.299259i | ||||
\(328\) | −9.00000 | − | 5.19615i | −0.496942 | − | 0.286910i | ||||
\(329\) | −4.50000 | − | 7.79423i | −0.248093 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1962 | − | 6.46410i | 0.615396 | − | 0.355299i | −0.159678 | − | 0.987169i | \(-0.551046\pi\) |
0.775074 | + | 0.631870i | \(0.217712\pi\) | |||||||
\(332\) | −4.09808 | − | 7.09808i | −0.224911 | − | 0.389558i | ||||
\(333\) | 1.98076 | 0.108545 | ||||||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.90192 | − | 1.09808i | −0.103758 | − | 0.0599050i | ||||
\(337\) | − | 6.19615i | − | 0.337526i | −0.985657 | − | 0.168763i | \(-0.946023\pi\) | ||
0.985657 | − | 0.168763i | \(-0.0539772\pi\) | |||||||
\(338\) | 0.500000 | − | 12.9904i | 0.0271964 | − | 0.706584i | ||||
\(339\) | −5.07180 | −0.275462 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.09808 | + | 12.2942i | −0.384382 | + | 0.665770i | ||||
\(342\) | 0.990381 | − | 0.571797i | 0.0535537 | − | 0.0309192i | ||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 1.73205 | − | 1.00000i | 0.0933859 | − | 0.0539164i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.0000i | − | 0.806405i | ||||||
\(347\) | 24.8827 | − | 14.3660i | 1.33577 | − | 0.771209i | 0.349595 | − | 0.936901i | \(-0.386319\pi\) |
0.986178 | + | 0.165692i | \(0.0529858\pi\) | |||||||
\(348\) | −1.60770 | − | 0.928203i | −0.0861815 | − | 0.0497569i | ||||
\(349\) | 3.50962 | + | 2.02628i | 0.187866 | + | 0.108464i | 0.590983 | − | 0.806684i | \(-0.298740\pi\) |
−0.403117 | + | 0.915148i | \(0.632073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.0000 | + | 3.46410i | −0.747265 | + | 0.184900i | ||||
\(352\) | − | 3.00000i | − | 0.159901i | ||||||
\(353\) | −4.90192 | + | 8.49038i | −0.260903 | + | 0.451897i | −0.966482 | − | 0.256734i | \(-0.917354\pi\) |
0.705579 | + | 0.708631i | \(0.250687\pi\) | |||||||
\(354\) | −3.80385 | + | 6.58846i | −0.202172 | + | 0.350173i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.80385i | 0.360603i | ||||||||
\(357\) | −9.00000 | − | 15.5885i | −0.476331 | − | 0.825029i | ||||
\(358\) | −4.73205 | − | 8.19615i | −0.250097 | − | 0.433180i | ||||
\(359\) | − | 1.60770i | − | 0.0848509i | −0.999100 | − | 0.0424255i | \(-0.986492\pi\) | ||
0.999100 | − | 0.0424255i | \(-0.0135085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.39230 | + | 16.2679i | −0.494332 | + | 0.856208i | ||||
\(362\) | −7.29423 | + | 12.6340i | −0.383376 | + | 0.664027i | ||||
\(363\) | 1.46410i | 0.0768454i | ||||||||
\(364\) | −10.3923 | − | 3.00000i | −0.544705 | − | 0.157243i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.92820 | − | 2.26795i | −0.205330 | − | 0.118548i | ||||
\(367\) | −4.85641 | − | 2.80385i | −0.253502 | − | 0.146360i | 0.367865 | − | 0.929879i | \(-0.380089\pi\) |
−0.621367 | + | 0.783520i | \(0.713422\pi\) | |||||||
\(368\) | 8.19615 | − | 4.73205i | 0.427254 | − | 0.246675i | ||||
\(369\) | 25.6077i | 1.33308i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.20577 | − | 0.696152i | 0.0626005 | − | 0.0361424i | ||||
\(372\) | −3.46410 | −0.179605 | ||||||||
\(373\) | −0.339746 | + | 0.196152i | −0.0175914 | + | 0.0101564i | −0.508770 | − | 0.860903i | \(-0.669900\pi\) |
0.491179 | + | 0.871059i | \(0.336566\pi\) | |||||||
\(374\) | 12.2942 | − | 21.2942i | 0.635719 | − | 1.10110i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −8.78461 | − | 2.53590i | −0.452430 | − | 0.130605i | ||||
\(378\) | 12.0000i | 0.617213i | ||||||||
\(379\) | −25.7942 | − | 14.8923i | −1.32496 | − | 0.764966i | −0.340445 | − | 0.940264i | \(-0.610578\pi\) |
−0.984515 | + | 0.175298i | \(0.943911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.95448 | − | 6.84936i | −0.202594 | − | 0.350904i | ||||
\(382\) | −22.7321 | −1.16307 | ||||||||
\(383\) | 11.1962 | + | 19.3923i | 0.572097 | + | 0.990900i | 0.996350 | + | 0.0853571i | \(0.0272031\pi\) |
−0.424254 | + | 0.905543i | \(0.639464\pi\) | |||||||
\(384\) | 0.633975 | − | 0.366025i | 0.0323524 | − | 0.0186787i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.19615 | + | 14.1962i | 0.417173 | + | 0.722565i | ||||
\(387\) | −4.26795 | − | 2.46410i | −0.216952 | − | 0.125257i | ||||
\(388\) | −4.56218 | + | 7.90192i | −0.231609 | + | 0.401159i | ||||
\(389\) | −22.7321 | −1.15256 | −0.576280 | − | 0.817252i | \(-0.695496\pi\) | ||||
−0.576280 | + | 0.817252i | \(0.695496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 77.5692 | 3.92284 | ||||||||
\(392\) | −1.00000 | + | 1.73205i | −0.0505076 | + | 0.0874818i | ||||
\(393\) | −3.88269 | − | 2.24167i | −0.195856 | − | 0.113077i | ||||
\(394\) | 10.7942 | + | 18.6962i | 0.543805 | + | 0.941899i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.40192 | + | 3.69615i | −0.321709 | + | 0.185739i | ||||
\(397\) | 5.59808 | + | 9.69615i | 0.280959 | + | 0.486636i | 0.971621 | − | 0.236542i | \(-0.0760140\pi\) |
−0.690662 | + | 0.723178i | \(0.742681\pi\) | |||||||
\(398\) | 6.39230 | 0.320417 | ||||||||
\(399\) | 0.509619 | + | 0.882686i | 0.0255129 | + | 0.0441896i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.50000 | − | 2.59808i | −0.224719 | − | 0.129742i | 0.383414 | − | 0.923576i | \(-0.374748\pi\) |
−0.608134 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.5622 | + | 4.09808i | −0.825021 | + | 0.204140i | ||||
\(404\) | 10.7321 | 0.533939 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.80385 | + | 6.58846i | −0.188782 | + | 0.326980i | ||||
\(407\) | −2.08846 | + | 1.20577i | −0.103521 | + | 0.0597679i | ||||
\(408\) | 6.00000 | 0.297044 | ||||||||
\(409\) | 14.0885 | − | 8.13397i | 0.696629 | − | 0.402199i | −0.109461 | − | 0.993991i | \(-0.534913\pi\) |
0.806091 | + | 0.591792i | \(0.201579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.60770i | 0.0793018i | ||||||||
\(412\) | −7.96410 | + | 4.59808i | −0.392363 | + | 0.226531i | ||||
\(413\) | 27.0000 | + | 15.5885i | 1.32858 | + | 0.767058i | ||||
\(414\) | −20.1962 | − | 11.6603i | −0.992587 | − | 0.573070i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.59808 | − | 2.50000i | 0.127381 | − | 0.122573i | ||||
\(417\) | − | 0.875644i | − | 0.0428805i | ||||||
\(418\) | −0.696152 | + | 1.20577i | −0.0340499 | + | 0.0589762i | ||||
\(419\) | −8.66025 | + | 15.0000i | −0.423081 | + | 0.732798i | −0.996239 | − | 0.0866469i | \(-0.972385\pi\) |
0.573158 | + | 0.819445i | \(0.305718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.87564i | 0.140150i | 0.997542 | + | 0.0700752i | \(0.0223239\pi\) | ||||
−0.997542 | + | 0.0700752i | \(0.977676\pi\) | |||||||
\(422\) | 8.79423 | + | 15.2321i | 0.428096 | + | 0.741485i | ||||
\(423\) | −3.69615 | − | 6.40192i | −0.179713 | − | 0.311272i | ||||
\(424\) | 0.464102i | 0.0225388i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.19615 | + | 3.80385i | −0.106404 | + | 0.184297i | ||||
\(427\) | −9.29423 | + | 16.0981i | −0.449779 | + | 0.779041i | ||||
\(428\) | − | 17.6603i | − | 0.853641i | ||||||
\(429\) | 5.70577 | − | 5.49038i | 0.275477 | − | 0.265078i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.09808 | − | 4.09808i | −0.341902 | − | 0.197397i | 0.319211 | − | 0.947684i | \(-0.396582\pi\) |
−0.661113 | + | 0.750286i | \(0.729916\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | 7.26795 | − | 4.19615i | 0.349275 | − | 0.201654i | −0.315091 | − | 0.949062i | \(-0.602035\pi\) |
0.664366 | + | 0.747407i | \(0.268702\pi\) | |||||||
\(434\) | 14.1962i | 0.681437i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.39230 | − | 4.26795i | 0.354027 | − | 0.204398i | ||||
\(437\) | −4.39230 | −0.210112 | ||||||||
\(438\) | −7.39230 | + | 4.26795i | −0.353218 | + | 0.203931i | ||||
\(439\) | −1.70577 | + | 2.95448i | −0.0814120 | + | 0.141010i | −0.903857 | − | 0.427835i | \(-0.859276\pi\) |
0.822445 | + | 0.568845i | \(0.192610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.92820 | 0.234676 | ||||||||
\(442\) | 28.6865 | − | 7.09808i | 1.36448 | − | 0.337621i | ||||
\(443\) | − | 22.3923i | − | 1.06389i | −0.846779 | − | 0.531945i | \(-0.821461\pi\) | ||
0.846779 | − | 0.531945i | \(-0.178539\pi\) | |||||||
\(444\) | −0.509619 | − | 0.294229i | −0.0241854 | − | 0.0139635i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.23205 | + | 5.59808i | 0.153042 | + | 0.265077i | ||||
\(447\) | 4.39230 | 0.207749 | ||||||||
\(448\) | −1.50000 | − | 2.59808i | −0.0708683 | − | 0.122748i | ||||
\(449\) | −13.5000 | + | 7.79423i | −0.637104 | + | 0.367832i | −0.783498 | − | 0.621394i | \(-0.786567\pi\) |
0.146394 | + | 0.989226i | \(0.453233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.5885 | − | 27.0000i | −0.734032 | − | 1.27138i | ||||
\(452\) | −6.00000 | − | 3.46410i | −0.282216 | − | 0.162938i | ||||
\(453\) | −8.66025 | + | 15.0000i | −0.406894 | + | 0.704761i | ||||
\(454\) | 16.3923 | 0.769329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.339746 | −0.0159101 | ||||||||
\(457\) | 9.16987 | − | 15.8827i | 0.428949 | − | 0.742961i | −0.567832 | − | 0.823145i | \(-0.692217\pi\) |
0.996780 | + | 0.0801841i | \(0.0255508\pi\) | |||||||
\(458\) | −1.09808 | − | 0.633975i | −0.0513097 | − | 0.0296237i | ||||
\(459\) | −16.3923 | − | 28.3923i | −0.765127 | − | 1.32524i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4904 | + | 15.2942i | −1.23378 | + | 0.712323i | −0.967816 | − | 0.251660i | \(-0.919024\pi\) |
−0.265964 | + | 0.963983i | \(0.585690\pi\) | |||||||
\(462\) | −3.29423 | − | 5.70577i | −0.153261 | − | 0.265457i | ||||
\(463\) | −12.9282 | −0.600825 | −0.300412 | − | 0.953809i | \(-0.597124\pi\) | ||||
−0.300412 | + | 0.953809i | \(0.597124\pi\) | |||||||
\(464\) | −1.26795 | − | 2.19615i | −0.0588631 | − | 0.101954i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.09808 | − | 2.36603i | −0.189840 | − | 0.109604i | ||||
\(467\) | 37.8564i | 1.75179i | 0.482506 | + | 0.875893i | \(0.339727\pi\) | ||||
−0.482506 | + | 0.875893i | \(0.660273\pi\) | |||||||
\(468\) | −8.53590 | − | 2.46410i | −0.394572 | − | 0.113903i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.75833 | − | 8.24167i | 0.219252 | − | 0.379756i | ||||
\(472\) | −9.00000 | + | 5.19615i | −0.414259 | + | 0.239172i | ||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 2.66025 | − | 1.53590i | 0.122190 | − | 0.0705461i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 24.5885i | − | 1.12701i | ||||||
\(477\) | 0.990381 | − | 0.571797i | 0.0453464 | − | 0.0261808i | ||||
\(478\) | 1.90192 | + | 1.09808i | 0.0869920 | + | 0.0502248i | ||||
\(479\) | 35.4904 | + | 20.4904i | 1.62160 | + | 0.936229i | 0.986493 | + | 0.163803i | \(0.0523760\pi\) |
0.635104 | + | 0.772427i | \(0.280957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.78461 | − | 0.803848i | −0.126967 | − | 0.0366523i | ||||
\(482\) | − | 8.66025i | − | 0.394464i | ||||||
\(483\) | 10.3923 | − | 18.0000i | 0.472866 | − | 0.819028i | ||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.2679i | 0.692568i | ||||||||
\(487\) | 7.62436 | + | 13.2058i | 0.345493 | + | 0.598411i | 0.985443 | − | 0.170005i | \(-0.0543785\pi\) |
−0.639951 | + | 0.768416i | \(0.721045\pi\) | |||||||
\(488\) | −3.09808 | − | 5.36603i | −0.140243 | − | 0.242909i | ||||
\(489\) | 7.85641i | 0.355279i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3301 | + | 17.8923i | −0.466192 | + | 0.807468i | −0.999254 | − | 0.0386076i | \(-0.987708\pi\) |
0.533062 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(492\) | 3.80385 | − | 6.58846i | 0.171491 | − | 0.297031i | ||||
\(493\) | − | 20.7846i | − | 0.936092i | ||||||
\(494\) | −1.62436 | + | 0.401924i | −0.0730832 | + | 0.0180834i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.09808 | − | 2.36603i | −0.184009 | − | 0.106238i | ||||
\(497\) | 15.5885 | + | 9.00000i | 0.699238 | + | 0.403705i | ||||
\(498\) | 5.19615 | − | 3.00000i | 0.232845 | − | 0.134433i | ||||
\(499\) | − | 25.8564i | − | 1.15749i | −0.815508 | − | 0.578746i | \(-0.803542\pi\) | ||
0.815508 | − | 0.578746i | \(-0.196458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.90192 | + | 1.09808i | −0.0849717 | + | 0.0490584i | ||||
\(502\) | 17.1962 | 0.767502 | ||||||||
\(503\) | −23.0885 | + | 13.3301i | −1.02946 | + | 0.594361i | −0.916831 | − | 0.399276i | \(-0.869262\pi\) |
−0.112633 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(504\) | −3.69615 | + | 6.40192i | −0.164640 | + | 0.285164i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.3923 | 1.26219 | ||||||||
\(507\) | 9.50962 | + | 0.366025i | 0.422337 | + | 0.0162558i | ||||
\(508\) | − | 10.8038i | − | 0.479343i | ||||||
\(509\) | 19.3923 | + | 11.1962i | 0.859549 | + | 0.496261i | 0.863861 | − | 0.503730i | \(-0.168039\pi\) |
−0.00431237 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.4904 | + | 30.2942i | 0.773729 | + | 1.34014i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.928203 | + | 1.60770i | 0.0409812 | + | 0.0709815i | ||||
\(514\) | 12.0000 | − | 6.92820i | 0.529297 | − | 0.305590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.732051 | + | 1.26795i | 0.0322267 | + | 0.0558184i | ||||
\(517\) | 7.79423 | + | 4.50000i | 0.342790 | + | 0.197910i | ||||
\(518\) | −1.20577 | + | 2.08846i | −0.0529786 | + | 0.0917615i | ||||
\(519\) | 10.9808 | 0.482002 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.46410 | 0.283197 | 0.141599 | − | 0.989924i | \(-0.454776\pi\) | ||||
0.141599 | + | 0.989924i | \(0.454776\pi\) | |||||||
\(522\) | −3.12436 | + | 5.41154i | −0.136749 | + | 0.236857i | ||||
\(523\) | 2.07180 | + | 1.19615i | 0.0905933 | + | 0.0523041i | 0.544612 | − | 0.838688i | \(-0.316677\pi\) |
−0.454019 | + | 0.890992i | \(0.650010\pi\) | |||||||
\(524\) | −3.06218 | − | 5.30385i | −0.133772 | − | 0.231700i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.10770 | − | 1.79423i | 0.135502 | − | 0.0782321i | ||||
\(527\) | −19.3923 | − | 33.5885i | −0.844742 | − | 1.46314i | ||||
\(528\) | 2.19615 | 0.0955753 | ||||||||
\(529\) | 33.2846 | + | 57.6506i | 1.44716 | + | 2.50655i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.1769 | + | 12.8038i | 0.962396 | + | 0.555640i | ||||
\(532\) | 1.39230i | 0.0603641i | ||||||||
\(533\) | 10.3923 | − | 36.0000i | 0.450141 | − | 1.55933i | ||||
\(534\) | −4.98076 | −0.215539 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | − | 3.46410i | 0.258919 | − | 0.149487i | ||||
\(538\) | 27.1244 | 1.16941 | ||||||||
\(539\) | −5.19615 | + | 3.00000i | −0.223814 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0526i | 0.948114i | 0.880494 | + | 0.474057i | \(0.157211\pi\) | ||||
−0.880494 | + | 0.474057i | \(0.842789\pi\) | |||||||
\(542\) | −8.19615 | + | 4.73205i | −0.352055 | + | 0.203259i | ||||
\(543\) | −9.24871 | − | 5.33975i | −0.396900 | − | 0.229150i | ||||
\(544\) | 7.09808 | + | 4.09808i | 0.304328 | + | 0.175704i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.19615 | − | 7.60770i | 0.0939866 | − | 0.325579i | ||||
\(547\) | 6.78461i | 0.290089i | 0.989425 | + | 0.145044i | \(0.0463325\pi\) | ||||
−0.989425 | + | 0.145044i | \(0.953667\pi\) | |||||||
\(548\) | −1.09808 | + | 1.90192i | −0.0469075 | + | 0.0812462i | ||||
\(549\) | −7.63397 | + | 13.2224i | −0.325810 | + | 0.564320i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17691i | 0.0501382i | ||||||||
\(552\) | 3.46410 | + | 6.00000i | 0.147442 | + | 0.255377i | ||||
\(553\) | −6.29423 | − | 10.9019i | −0.267658 | − | 0.463597i | ||||
\(554\) | 1.00000i | 0.0424859i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.598076 | − | 1.03590i | 0.0253641 | − | 0.0439319i | ||||
\(557\) | −3.40192 | + | 5.89230i | −0.144144 | + | 0.249665i | −0.929053 | − | 0.369946i | \(-0.879376\pi\) |
0.784909 | + | 0.619611i | \(0.212710\pi\) | |||||||
\(558\) | 11.6603i | 0.493618i | ||||||||
\(559\) | 5.00000 | + | 5.19615i | 0.211477 | + | 0.219774i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5885 | + | 9.00000i | 0.658145 | + | 0.379980i | ||||
\(562\) | 9.00000 | + | 5.19615i | 0.379642 | + | 0.219186i | ||||
\(563\) | 12.5885 | − | 7.26795i | 0.530540 | − | 0.306308i | −0.210696 | − | 0.977552i | \(-0.567573\pi\) |
0.741236 | + | 0.671244i | \(0.234240\pi\) | |||||||
\(564\) | 2.19615i | 0.0924747i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.32051 | + | 4.80385i | −0.349737 | + | 0.201921i | ||||
\(567\) | 13.3923 | 0.562424 | ||||||||
\(568\) | −5.19615 | + | 3.00000i | −0.218026 | + | 0.125877i | ||||
\(569\) | −13.6244 | + | 23.5981i | −0.571163 | + | 0.989283i | 0.425284 | + | 0.905060i | \(0.360174\pi\) |
−0.996447 | + | 0.0842230i | \(0.973159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3731 | −1.60586 | −0.802931 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802931 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(572\) | 10.5000 | − | 2.59808i | 0.439027 | − | 0.108631i | ||||
\(573\) | − | 16.6410i | − | 0.695188i | ||||||
\(574\) | −27.0000 | − | 15.5885i | −1.12696 | − | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.23205 | − | 2.13397i | −0.0513355 | − | 0.0889156i | ||||
\(577\) | −26.4449 | −1.10091 | −0.550457 | − | 0.834863i | \(-0.685547\pi\) | ||||
−0.550457 | + | 0.834863i | \(0.685547\pi\) | |||||||
\(578\) | 25.0885 | + | 43.4545i | 1.04354 | + | 1.80747i | ||||
\(579\) | −10.3923 | + | 6.00000i | −0.431889 | + | 0.249351i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.2942 | − | 21.2942i | −0.510051 | − | 0.883433i | ||||
\(582\) | −5.78461 | − | 3.33975i | −0.239780 | − | 0.138437i | ||||
\(583\) | −0.696152 | + | 1.20577i | −0.0288317 | + | 0.0499379i | ||||
\(584\) | −11.6603 | −0.482505 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.1962 | −0.462509 | ||||||||
\(587\) | 15.0000 | − | 25.9808i | 0.619116 | − | 1.07234i | −0.370531 | − | 0.928820i | \(-0.620824\pi\) |
0.989647 | − | 0.143521i | \(-0.0458424\pi\) | |||||||
\(588\) | −1.26795 | − | 0.732051i | −0.0522893 | − | 0.0301893i | ||||
\(589\) | 1.09808 | + | 1.90192i | 0.0452454 | + | 0.0783674i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.6865 | + | 7.90192i | −0.562989 | + | 0.325042i | ||||
\(592\) | −0.401924 | − | 0.696152i | −0.0165190 | − | 0.0286117i | ||||
\(593\) | 20.7846 | 0.853522 | 0.426761 | − | 0.904365i | \(-0.359655\pi\) | ||||
0.426761 | + | 0.904365i | \(0.359655\pi\) | |||||||
\(594\) | −6.00000 | − | 10.3923i | −0.246183 | − | 0.426401i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.19615 | + | 3.00000i | 0.212843 | + | 0.122885i | ||||
\(597\) | 4.67949i | 0.191519i | ||||||||
\(598\) | 23.6603 | + | 24.5885i | 0.967540 | + | 1.00550i | ||||
\(599\) | 19.8564 | 0.811311 | 0.405655 | − | 0.914026i | \(-0.367043\pi\) | ||||
0.405655 | + | 0.914026i | \(0.367043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8923 | − | 32.7224i | 0.770633 | − | 1.33478i | −0.166583 | − | 0.986027i | \(-0.553273\pi\) |
0.937216 | − | 0.348748i | \(-0.113393\pi\) | |||||||
\(602\) | 5.19615 | − | 3.00000i | 0.211779 | − | 0.122271i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.4904 | + | 11.8301i | −0.833742 | + | 0.481361i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.85641i | 0.319145i | ||||||||
\(607\) | 32.5526 | − | 18.7942i | 1.32127 | − | 0.762834i | 0.337337 | − | 0.941384i | \(-0.390474\pi\) |
0.983931 | + | 0.178550i | \(0.0571406\pi\) | |||||||
\(608\) | −0.401924 | − | 0.232051i | −0.0163002 | − | 0.00941090i | ||||
\(609\) | −4.82309 | − | 2.78461i | −0.195441 | − | 0.112838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.59808 | + | 10.5000i | 0.105107 | + | 0.424785i | ||||
\(612\) | − | 20.1962i | − | 0.816381i | ||||||
\(613\) | −19.4545 | + | 33.6962i | −0.785759 | + | 1.36097i | 0.142785 | + | 0.989754i | \(0.454394\pi\) |
−0.928545 | + | 0.371221i | \(0.878939\pi\) | |||||||
\(614\) | 13.7321 | − | 23.7846i | 0.554180 | − | 0.959869i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 9.00000i | − | 0.362620i | ||||||
\(617\) | −9.00000 | − | 15.5885i | −0.362326 | − | 0.627568i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.988343 | + | 0.152242i | \(0.951351\pi\) | |||||||
\(618\) | −3.36603 | − | 5.83013i | −0.135401 | − | 0.234522i | ||||
\(619\) | 31.3923i | 1.26176i | 0.775879 | + | 0.630882i | \(0.217307\pi\) | ||||
−0.775879 | + | 0.630882i | \(0.782693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9282 | − | 32.7846i | 0.759563 | − | 1.31560i | ||||
\(622\) | 4.56218 | − | 7.90192i | 0.182927 | − | 0.316838i | ||||
\(623\) | 20.4115i | 0.817771i | ||||||||
\(624\) | 1.83013 | + | 1.90192i | 0.0732637 | + | 0.0761379i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.8564 | − | 13.1962i | −0.913526 | − | 0.527424i | ||||
\(627\) | −0.882686 | − | 0.509619i | −0.0352511 | − | 0.0203522i | ||||
\(628\) | 11.2583 | − | 6.50000i | 0.449256 | − | 0.259378i | ||||
\(629\) | − | 6.58846i | − | 0.262699i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | + | 10.3923i | −0.716569 | + | 0.413711i | −0.813488 | − | 0.581581i | \(-0.802434\pi\) |
0.0969198 | + | 0.995292i | \(0.469101\pi\) | |||||||
\(632\) | 4.19615 | 0.166914 | ||||||||
\(633\) | −11.1506 | + | 6.43782i | −0.443198 | + | 0.255880i | ||||
\(634\) | 11.5981 | − | 20.0885i | 0.460618 | − | 0.797815i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.339746 | −0.0134718 | ||||||||
\(637\) | −6.92820 | − | 2.00000i | −0.274505 | − | 0.0792429i | ||||
\(638\) | − | 7.60770i | − | 0.301192i | ||||||
\(639\) | 12.8038 | + | 7.39230i | 0.506512 | + | 0.292435i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0359 | − | 27.7750i | −0.633380 | − | 1.09705i | −0.986856 | − | 0.161603i | \(-0.948334\pi\) |
0.353476 | − | 0.935444i | \(-0.385000\pi\) | |||||||
\(642\) | 12.9282 | 0.510235 | ||||||||
\(643\) | −5.36603 | − | 9.29423i | −0.211615 | − | 0.366529i | 0.740605 | − | 0.671941i | \(-0.234539\pi\) |
−0.952220 | + | 0.305412i | \(0.901206\pi\) | |||||||
\(644\) | 24.5885 | − | 14.1962i | 0.968921 | − | 0.559407i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.90192 | − | 3.29423i | −0.0748302 | − | 0.129610i | ||||
\(647\) | −0.696152 | − | 0.401924i | −0.0273686 | − | 0.0158013i | 0.486253 | − | 0.873818i | \(-0.338363\pi\) |
−0.513622 | + | 0.858017i | \(0.671697\pi\) | |||||||
\(648\) | −2.23205 | + | 3.86603i | −0.0876832 | + | 0.151872i | ||||
\(649\) | −31.1769 | −1.22380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3923 | −0.407307 | ||||||||
\(652\) | −5.36603 | + | 9.29423i | −0.210150 | + | 0.363990i | ||||
\(653\) | −1.20577 | − | 0.696152i | −0.0471855 | − | 0.0272425i | 0.476222 | − | 0.879325i | \(-0.342006\pi\) |
−0.523407 | + | 0.852083i | \(0.675339\pi\) | |||||||
\(654\) | 3.12436 | + | 5.41154i | 0.122172 | + | 0.211608i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.00000 | − | 5.19615i | 0.351391 | − | 0.202876i | ||||
\(657\) | 14.3660 | + | 24.8827i | 0.560472 | + | 0.970766i | ||||
\(658\) | 9.00000 | 0.350857 | ||||||||
\(659\) | −2.66025 | − | 4.60770i | −0.103629 | − | 0.179490i | 0.809548 | − | 0.587053i | \(-0.199712\pi\) |
−0.913177 | + | 0.407563i | \(0.866379\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0981 | + | 17.9545i | 1.20957 | + | 0.698348i | 0.962666 | − | 0.270690i | \(-0.0872520\pi\) |
0.246909 | + | 0.969039i | \(0.420585\pi\) | |||||||
\(662\) | 12.9282i | 0.502469i | ||||||||
\(663\) | 5.19615 | + | 21.0000i | 0.201802 | + | 0.815572i | ||||
\(664\) | 8.19615 | 0.318072 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.990381 | + | 1.71539i | −0.0383765 | + | 0.0664700i | ||||
\(667\) | 20.7846 | − | 12.0000i | 0.804783 | − | 0.464642i | ||||
\(668\) | −3.00000 | −0.116073 | ||||||||
\(669\) | −4.09808 | + | 2.36603i | −0.158441 | + | 0.0914758i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.5885i | − | 0.717599i | ||||||
\(672\) | 1.90192 | − | 1.09808i | 0.0733683 | − | 0.0423592i | ||||
\(673\) | −21.1244 | − | 12.1962i | −0.814284 | − | 0.470127i | 0.0341573 | − | 0.999416i | \(-0.489125\pi\) |
−0.848441 | + | 0.529289i | \(0.822459\pi\) | |||||||
\(674\) | 5.36603 | + | 3.09808i | 0.206692 | + | 0.119333i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | 25.8564i | 0.993742i | 0.867824 | + | 0.496871i | \(0.165518\pi\) | ||||
−0.867824 | + | 0.496871i | \(0.834482\pi\) | |||||||
\(678\) | 2.53590 | − | 4.39230i | 0.0973906 | − | 0.168685i | ||||
\(679\) | −13.6865 | + | 23.7058i | −0.525241 | + | 0.909744i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000i | 0.459841i | ||||||||
\(682\) | −7.09808 | − | 12.2942i | −0.271799 | − | 0.470770i | ||||
\(683\) | 15.5885 | + | 27.0000i | 0.596476 | + | 1.03313i | 0.993337 | + | 0.115248i | \(0.0367661\pi\) |
−0.396861 | + | 0.917879i | \(0.629901\pi\) | |||||||
\(684\) | 1.14359i | 0.0437264i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.50000 | − | 12.9904i | 0.286351 | − | 0.495975i | ||||
\(687\) | 0.464102 | − | 0.803848i | 0.0177066 | − | 0.0306687i | ||||
\(688\) | 2.00000i | 0.0762493i | ||||||||
\(689\) | −1.62436 | + | 0.401924i | −0.0618830 | + | 0.0153121i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.7942 | − | 18.3564i | −1.20951 | − | 0.698311i | −0.246857 | − | 0.969052i | \(-0.579398\pi\) |
−0.962652 | + | 0.270741i | \(0.912731\pi\) | |||||||
\(692\) | 12.9904 | + | 7.50000i | 0.493820 | + | 0.285107i | ||||
\(693\) | −19.2058 | + | 11.0885i | −0.729567 | + | 0.421216i | ||||
\(694\) | 28.7321i | 1.09065i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.60770 | − | 0.928203i | 0.0609395 | − | 0.0351835i | ||||
\(697\) | 85.1769 | 3.22631 | ||||||||
\(698\) | −3.50962 | + | 2.02628i | −0.132841 | + | 0.0766958i | ||||
\(699\) | 1.73205 | − | 3.00000i | 0.0655122 | − | 0.113470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.9090 | 1.35626 | 0.678131 | − | 0.734941i | \(-0.262790\pi\) | ||||
0.678131 | + | 0.734941i | \(0.262790\pi\) | |||||||
\(702\) | 4.00000 | − | 13.8564i | 0.150970 | − | 0.522976i | ||||
\(703\) | 0.373067i | 0.0140705i | ||||||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.90192 | − | 8.49038i | −0.184486 | − | 0.319540i | ||||
\(707\) | 32.1962 | 1.21086 | ||||||||
\(708\) | −3.80385 | − | 6.58846i | −0.142957 | − | 0.247609i | ||||
\(709\) | −9.50962 | + | 5.49038i | −0.357141 | + | 0.206196i | −0.667826 | − | 0.744317i | \(-0.732775\pi\) |
0.310685 | + | 0.950513i | \(0.399442\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.16987 | − | 8.95448i | −0.193885 | − | 0.335819i | ||||
\(712\) | −5.89230 | − | 3.40192i | −0.220823 | − | 0.127492i | ||||
\(713\) | 22.3923 | − | 38.7846i | 0.838598 | − | 1.45250i | ||||
\(714\) | 18.0000 | 0.673633 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.46410 | 0.353690 | ||||||||
\(717\) | −0.803848 | + | 1.39230i | −0.0300202 | + | 0.0519966i | ||||
\(718\) | 1.39230 | + | 0.803848i | 0.0519604 | + | 0.0299993i | ||||
\(719\) | 12.9282 | + | 22.3923i | 0.482141 | + | 0.835092i | 0.999790 | − | 0.0205009i | \(-0.00652609\pi\) |
−0.517649 | + | 0.855593i | \(0.673193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.8923 | + | 13.7942i | −0.889796 | + | 0.513724i | ||||
\(722\) | −9.39230 | − | 16.2679i | −0.349545 | − | 0.605430i | ||||
\(723\) | 6.33975 | 0.235778 | ||||||||
\(724\) | −7.29423 | − | 12.6340i | −0.271088 | − | 0.469538i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.26795 | − | 0.732051i | −0.0470580 | − | 0.0271690i | ||||
\(727\) | − | 34.3731i | − | 1.27483i | −0.770522 | − | 0.637413i | \(-0.780004\pi\) | ||
0.770522 | − | 0.637413i | \(-0.219996\pi\) | |||||||
\(728\) | 7.79423 | − | 7.50000i | 0.288873 | − | 0.277968i | ||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.19615 | + | 14.1962i | −0.303146 | + | 0.525064i | ||||
\(732\) | 3.92820 | − | 2.26795i | 0.145191 | − | 0.0838258i | ||||
\(733\) | −14.9090 | −0.550675 | −0.275338 | − | 0.961348i | \(-0.588790\pi\) | ||||
−0.275338 | + | 0.961348i | \(0.588790\pi\) | |||||||
\(734\) | 4.85641 | − | 2.80385i | 0.179253 | − | 0.103492i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.46410i | 0.348851i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −22.1769 | − | 12.8038i | −0.816344 | − | 0.471316i | ||||
\(739\) | −28.2058 | − | 16.2846i | −1.03757 | − | 0.599039i | −0.118423 | − | 0.992963i | \(-0.537784\pi\) |
−0.919143 | + | 0.393924i | \(0.871117\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.294229 | − | 1.18911i | −0.0108088 | − | 0.0436831i | ||||
\(742\) | 1.39230i | 0.0511131i | ||||||||
\(743\) | 6.80385 | − | 11.7846i | 0.249609 | − | 0.432335i | −0.713808 | − | 0.700341i | \(-0.753031\pi\) |
0.963417 | + | 0.268006i | \(0.0863646\pi\) | |||||||
\(744\) | 1.73205 | − | 3.00000i | 0.0635001 | − | 0.109985i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 0.392305i | − | 0.0143633i | ||||||
\(747\) | −10.0981 | − | 17.4904i | −0.369469 | − | 0.639940i | ||||
\(748\) | 12.2942 | + | 21.2942i | 0.449522 | + | 0.778594i | ||||
\(749\) | − | 52.9808i | − | 1.93587i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1962 | − | 17.6603i | 0.372063 | − | 0.644432i | −0.617820 | − | 0.786320i | \(-0.711984\pi\) |
0.989883 | + | 0.141888i | \(0.0453172\pi\) | |||||||
\(752\) | −1.50000 | + | 2.59808i | −0.0546994 | + | 0.0947421i | ||||
\(753\) | 12.5885i | 0.458749i | ||||||||
\(754\) | 6.58846 | − | 6.33975i | 0.239937 | − | 0.230880i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.3923 | − | 6.00000i | −0.377964 | − | 0.218218i | ||||
\(757\) | −32.7224 | − | 18.8923i | −1.18932 | − | 0.686652i | −0.231166 | − | 0.972914i | \(-0.574254\pi\) |
−0.958151 | + | 0.286262i | \(0.907587\pi\) | |||||||
\(758\) | 25.7942 | − | 14.8923i | 0.936889 | − | 0.540913i | ||||
\(759\) | 20.7846i | 0.754434i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.2846 | − | 9.40192i | 0.590317 | − | 0.340819i | −0.174906 | − | 0.984585i | \(-0.555962\pi\) |
0.765223 | + | 0.643766i | \(0.222629\pi\) | |||||||
\(762\) | 7.90897 | 0.286512 | ||||||||
\(763\) | 22.1769 | − | 12.8038i | 0.802858 | − | 0.463530i | ||||
\(764\) | 11.3660 | − | 19.6865i | 0.411208 | − | 0.712234i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.3923 | −0.809067 | ||||||||
\(767\) | −25.9808 | − | 27.0000i | −0.938111 | − | 0.974913i | ||||
\(768\) | 0.732051i | 0.0264156i | ||||||||
\(769\) | 33.0000 | + | 19.0526i | 1.19001 | + | 0.687053i | 0.958309 | − | 0.285734i | \(-0.0922374\pi\) |
0.231701 | + | 0.972787i | \(0.425571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.07180 | + | 8.78461i | 0.182656 | + | 0.316370i | ||||
\(772\) | −16.3923 | −0.589972 | ||||||||
\(773\) | 1.20577 | + | 2.08846i | 0.0433686 | + | 0.0751166i | 0.886895 | − | 0.461971i | \(-0.152858\pi\) |
−0.843526 | + | 0.537088i | \(0.819524\pi\) | |||||||
\(774\) | 4.26795 | − | 2.46410i | 0.153408 | − | 0.0885703i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.56218 | − | 7.90192i | −0.163773 | − | 0.283663i | ||||
\(777\) | −1.52886 | − | 0.882686i | −0.0548474 | − | 0.0316662i | ||||
\(778\) | 11.3660 | − | 19.6865i | 0.407492 | − | 0.705796i | ||||
\(779\) | −4.82309 | −0.172805 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | −38.7846 | + | 67.1769i | −1.38693 | + | 2.40224i | ||||
\(783\) | −8.78461 | − | 5.07180i | −0.313936 | − | 0.181251i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.88269 | − | 2.24167i | 0.138491 | − | 0.0799577i | ||||
\(787\) | 21.4186 | + | 37.0981i | 0.763490 | + | 1.32240i | 0.941041 | + | 0.338292i | \(0.109849\pi\) |
−0.177551 | + | 0.984112i | \(0.556818\pi\) | |||||||
\(788\) | −21.5885 | −0.769057 | ||||||||
\(789\) | 1.31347 | + | 2.27499i | 0.0467606 | + | 0.0809918i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | − | 10.3923i | −0.640006 | − | 0.369508i | ||||
\(792\) | − | 7.39230i | − | 0.262674i | ||||||
\(793\) | 16.0981 | − | 15.4904i | 0.571659 | − | 0.550080i | ||||
\(794\) | −11.1962 | −0.397337 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.19615 | + | 5.53590i | −0.113285 | + | 0.196215i | ||||
\(797\) | 11.1962 | − | 6.46410i | 0.396588 | − | 0.228970i | −0.288423 | − | 0.957503i | \(-0.593131\pi\) |
0.685011 | + | 0.728533i | \(0.259797\pi\) | |||||||
\(798\) | −1.01924 | −0.0360806 | ||||||||
\(799\) | −21.2942 | + | 12.2942i | −0.753336 | + | 0.434939i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.7654i | 0.592375i | ||||||||
\(802\) | 4.50000 | − | 2.59808i | 0.158901 | − | 0.0917413i | ||||
\(803\) | −30.2942 | − | 17.4904i | −1.06906 | − | 0.617222i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.73205 | − | 16.3923i | 0.166679 | − | 0.577394i | ||||
\(807\) | 19.8564i | 0.698979i | ||||||||
\(808\) | −5.36603 | + | 9.29423i | −0.188776 | + | 0.326970i | ||||
\(809\) | 12.0000 | − | 20.7846i | 0.421898 | − | 0.730748i | −0.574228 | − | 0.818696i | \(-0.694698\pi\) |
0.996125 | + | 0.0879478i | \(0.0280309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.3923i | 1.52371i | 0.647748 | + | 0.761855i | \(0.275711\pi\) | ||||
−0.647748 | + | 0.761855i | \(0.724289\pi\) | |||||||
\(812\) | −3.80385 | − | 6.58846i | −0.133489 | − | 0.231210i | ||||
\(813\) | −3.46410 | − | 6.00000i | −0.121491 | − | 0.210429i | ||||
\(814\) | − | 2.41154i | − | 0.0845245i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 0.464102 | − | 0.803848i | 0.0162369 | − | 0.0281231i | ||||
\(818\) | 16.2679i | 0.568796i | ||||||||
\(819\) | −25.6077 | − | 7.39230i | −0.894805 | − | 0.258308i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4904 | + | 10.0981i | 0.610419 | + | 0.352425i | 0.773129 | − | 0.634249i | \(-0.218690\pi\) |
−0.162711 | + | 0.986674i | \(0.552024\pi\) | |||||||
\(822\) | −1.39230 | − | 0.803848i | −0.0485622 | − | 0.0280374i | ||||
\(823\) | −23.5526 | + | 13.5981i | −0.820991 | + | 0.473999i | −0.850758 | − | 0.525558i | \(-0.823857\pi\) |
0.0297674 | + | 0.999557i | \(0.490523\pi\) | |||||||
\(824\) | − | 9.19615i | − | 0.320363i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.0000 | + | 15.5885i | −0.939450 | + | 0.542392i | ||||
\(827\) | −42.5885 | −1.48095 | −0.740473 | − | 0.672086i | \(-0.765398\pi\) | ||||
−0.740473 | + | 0.672086i | \(0.765398\pi\) | |||||||
\(828\) | 20.1962 | − | 11.6603i | 0.701865 | − | 0.405222i | ||||
\(829\) | −10.0000 | + | 17.3205i | −0.347314 | + | 0.601566i | −0.985771 | − | 0.168091i | \(-0.946240\pi\) |
0.638457 | + | 0.769657i | \(0.279573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.732051 | −0.0253946 | ||||||||
\(832\) | 0.866025 | + | 3.50000i | 0.0300240 | + | 0.121341i | ||||
\(833\) | − | 16.3923i | − | 0.567960i | ||||||
\(834\) | 0.758330 | + | 0.437822i | 0.0262588 | + | 0.0151605i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.696152 | − | 1.20577i | −0.0240769 | − | 0.0417025i | ||||
\(837\) | −18.9282 | −0.654254 | ||||||||
\(838\) | −8.66025 | − | 15.0000i | −0.299164 | − | 0.518166i | ||||
\(839\) | −18.8827 | + | 10.9019i | −0.651903 | + | 0.376376i | −0.789185 | − | 0.614156i | \(-0.789497\pi\) |
0.137282 | + | 0.990532i | \(0.456163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.2846 | + | 19.5455i | 0.389124 | + | 0.673983i | ||||
\(842\) | −2.49038 | − | 1.43782i | −0.0858242 | − | 0.0495506i | ||||
\(843\) | −3.80385 | + | 6.58846i | −0.131011 | + | 0.226919i | ||||
\(844\) | −17.5885 | −0.605420 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.39230 | 0.254153 | ||||||||
\(847\) | −3.00000 | + | 5.19615i | −0.103081 | + | 0.178542i | ||||
\(848\) | −0.401924 | − | 0.232051i | −0.0138021 | − | 0.00796866i | ||||
\(849\) | −3.51666 | − | 6.09103i | −0.120691 | − | 0.209044i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.58846 | − | 3.80385i | 0.225849 | − | 0.130394i | ||||
\(852\) | −2.19615 | − | 3.80385i | −0.0752389 | − | 0.130318i | ||||
\(853\) | −13.8564 | −0.474434 | −0.237217 | − | 0.971457i | \(-0.576235\pi\) | ||||
−0.237217 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(854\) | −9.29423 | − | 16.0981i | −0.318042 | − | 0.550865i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.2942 | + | 8.83013i | 0.522746 | + | 0.301808i | ||||
\(857\) | 16.7321i | 0.571556i | 0.958296 | + | 0.285778i | \(0.0922520\pi\) | ||||
−0.958296 | + | 0.285778i | \(0.907748\pi\) | |||||||
\(858\) | 1.90192 | + | 7.68653i | 0.0649306 | + | 0.262414i | ||||
\(859\) | 20.3731 | 0.695120 | 0.347560 | − | 0.937658i | \(-0.387010\pi\) | ||||
0.347560 | + | 0.937658i | \(0.387010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4115 | − | 19.7654i | 0.388904 | − | 0.673602i | ||||
\(862\) | 7.09808 | − | 4.09808i | 0.241761 | − | 0.139581i | ||||
\(863\) | −43.1769 | −1.46976 | −0.734880 | − | 0.678198i | \(-0.762761\pi\) | ||||
−0.734880 | + | 0.678198i | \(0.762761\pi\) | |||||||
\(864\) | 3.46410 | − | 2.00000i | 0.117851 | − | 0.0680414i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.39230i | 0.285182i | ||||||||
\(867\) | −31.8109 | + | 18.3660i | −1.08035 | + | 0.623743i | ||||
\(868\) | −12.2942 | − | 7.09808i | −0.417293 | − | 0.240924i | ||||
\(869\) | 10.9019 | + | 6.29423i | 0.369822 | + | 0.213517i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.53590i | 0.289062i | ||||||||
\(873\) | −11.2417 | + | 19.4711i | −0.380473 | + | 0.658998i | ||||
\(874\) | 2.19615 | − | 3.80385i | 0.0742860 | − | 0.128667i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 8.53590i | − | 0.288401i | ||||||
\(877\) | 13.7321 | + | 23.7846i | 0.463698 | + | 0.803149i | 0.999142 | − | 0.0414220i | \(-0.0131888\pi\) |
−0.535443 | + | 0.844571i | \(0.679855\pi\) | |||||||
\(878\) | −1.70577 | − | 2.95448i | −0.0575670 | − | 0.0997090i | ||||
\(879\) | − | 8.19615i | − | 0.276449i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1603 | + | 22.7942i | −0.443380 | + | 0.767957i | −0.997938 | − | 0.0641883i | \(-0.979554\pi\) |
0.554558 | + | 0.832145i | \(0.312888\pi\) | |||||||
\(882\) | −2.46410 | + | 4.26795i | −0.0829706 | + | 0.143709i | ||||
\(883\) | 4.58846i | 0.154414i | 0.997015 | + | 0.0772069i | \(0.0246002\pi\) | ||||
−0.997015 | + | 0.0772069i | \(0.975400\pi\) | |||||||
\(884\) | −8.19615 | + | 28.3923i | −0.275666 | + | 0.954937i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.3923 | + | 11.1962i | 0.651497 | + | 0.376142i | ||||
\(887\) | −35.3038 | − | 20.3827i | −1.18539 | − | 0.684384i | −0.228133 | − | 0.973630i | \(-0.573262\pi\) |
−0.957255 | + | 0.289246i | \(0.906595\pi\) | |||||||
\(888\) | 0.509619 | − | 0.294229i | 0.0171017 | − | 0.00987367i | ||||
\(889\) | − | 32.4115i | − | 1.08705i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.5981 | + | 6.69615i | −0.388550 | + | 0.224330i | ||||
\(892\) | −6.46410 | −0.216434 | ||||||||
\(893\) | 1.20577 | − | 0.696152i | 0.0403496 | − | 0.0232959i | ||||
\(894\) | −2.19615 | + | 3.80385i | −0.0734503 | + | 0.127220i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | −18.0000 | + | 17.3205i | −0.601003 | + | 0.578315i | ||||
\(898\) | − | 15.5885i | − | 0.520194i | ||||||
\(899\) | −10.3923 | − | 6.00000i | −0.346603 | − | 0.200111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.90192 | − | 3.29423i | −0.0633623 | − | 0.109747i | ||||
\(902\) | 31.1769 | 1.03808 | ||||||||
\(903\) | 2.19615 | + | 3.80385i | 0.0730834 | + | 0.126584i | ||||
\(904\) | 6.00000 | − | 3.46410i | 0.199557 | − | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.66025 | − | 15.0000i | −0.287718 | − | 0.498342i | ||||
\(907\) | 3.97372 | + | 2.29423i | 0.131945 | + | 0.0761786i | 0.564520 | − | 0.825420i | \(-0.309061\pi\) |
−0.432574 | + | 0.901598i | \(0.642395\pi\) | |||||||
\(908\) | −8.19615 | + | 14.1962i | −0.271999 | + | 0.471116i | ||||
\(909\) | 26.4449 | 0.877121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.4641 | −0.711137 | −0.355569 | − | 0.934650i | \(-0.615713\pi\) | ||||
−0.355569 | + | 0.934650i | \(0.615713\pi\) | |||||||
\(912\) | 0.169873 | − | 0.294229i | 0.00562506 | − | 0.00974288i | ||||
\(913\) | 21.2942 | + | 12.2942i | 0.704736 | + | 0.406880i | ||||
\(914\) | 9.16987 | + | 15.8827i | 0.303312 | + | 0.525353i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.09808 | − | 0.633975i | 0.0362815 | − | 0.0209471i | ||||
\(917\) | −9.18653 | − | 15.9115i | −0.303366 | − | 0.525445i | ||||
\(918\) | 32.7846 | 1.08205 | ||||||||
\(919\) | 15.3923 | + | 26.6603i | 0.507745 | + | 0.879441i | 0.999960 | + | 0.00896670i | \(0.00285423\pi\) |
−0.492215 | + | 0.870474i | \(0.663812\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.4115 | + | 10.0526i | 0.573730 | + | 0.331243i | ||||
\(922\) | − | 30.5885i | − | 1.00738i | ||||||
\(923\) | −15.0000 | − | 15.5885i | −0.493731 | − | 0.513100i | ||||
\(924\) | 6.58846 | 0.216744 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.46410 | − | 11.1962i | 0.212424 | − | 0.367928i | ||||
\(927\) | −19.6244 | + | 11.3301i | −0.644548 | + | 0.372130i | ||||
\(928\) | 2.53590 | 0.0832449 | ||||||||
\(929\) | 2.78461 | − | 1.60770i | 0.0913601 | − | 0.0527468i | −0.453624 | − | 0.891193i | \(-0.649869\pi\) |
0.544984 | + | 0.838446i | \(0.316536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.928203i | 0.0304206i | ||||||||
\(932\) | 4.09808 | − | 2.36603i | 0.134237 | − | 0.0775017i | ||||
\(933\) | 5.78461 | + | 3.33975i | 0.189380 | + | 0.109338i | ||||
\(934\) | −32.7846 | − | 18.9282i | −1.07275 | − | 0.619350i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.40192 | − | 6.16025i | 0.209253 | − | 0.201354i | ||||
\(937\) | 9.60770i | 0.313870i | 0.987609 | + | 0.156935i | \(0.0501613\pi\) | ||||
−0.987609 | + | 0.156935i | \(0.949839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.66025 | − | 16.7321i | 0.315250 | − | 0.546030i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.21539i | 0.104819i | 0.998626 | + | 0.0524094i | \(0.0166901\pi\) | ||||
−0.998626 | + | 0.0524094i | \(0.983310\pi\) | |||||||
\(942\) | 4.75833 | + | 8.24167i | 0.155035 | + | 0.268528i | ||||
\(943\) | 49.1769 | + | 85.1769i | 1.60142 | + | 2.77374i | ||||
\(944\) | − | 10.3923i | − | 0.338241i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.00000 | + | 5.19615i | −0.0975384 | + | 0.168941i | ||||
\(947\) | 7.68653 | − | 13.3135i | 0.249779 | − | 0.432630i | −0.713686 | − | 0.700466i | \(-0.752975\pi\) |
0.963464 | + | 0.267837i | \(0.0863088\pi\) | |||||||
\(948\) | 3.07180i | 0.0997673i | ||||||||
\(949\) | −10.0981 | − | 40.8109i | −0.327797 | − | 1.32478i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.7058 | + | 8.49038i | 0.476867 | + | 0.275319i | ||||
\(952\) | 21.2942 | + | 12.2942i | 0.690150 | + | 0.398458i | ||||
\(953\) | −5.70577 | + | 3.29423i | −0.184828 | + | 0.106711i | −0.589559 | − | 0.807725i | \(-0.700698\pi\) |
0.404731 | + | 0.914436i | \(0.367365\pi\) | |||||||
\(954\) | 1.14359i | 0.0370252i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.90192 | + | 1.09808i | −0.0615126 | + | 0.0355143i | ||||
\(957\) | 5.56922 | 0.180027 | ||||||||
\(958\) | −35.4904 | + | 20.4904i | −1.14664 | + | 0.662014i | ||||
\(959\) | −3.29423 | + | 5.70577i | −0.106376 | + | 0.184249i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.60770 | 0.277668 | ||||||||
\(962\) | 2.08846 | − | 2.00962i | 0.0673346 | − | 0.0647927i | ||||
\(963\) | − | 43.5167i | − | 1.40230i | ||||||
\(964\) | 7.50000 | + | 4.33013i | 0.241559 | + | 0.139464i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.3923 | + | 18.0000i | 0.334367 | + | 0.579141i | ||||
\(967\) | −44.5692 | −1.43325 | −0.716625 | − | 0.697459i | \(-0.754314\pi\) | ||||
−0.716625 | + | 0.697459i | \(0.754314\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 2.41154 | − | 1.39230i | 0.0774699 | − | 0.0447273i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.3827 | − | 40.5000i | −0.750386 | − | 1.29971i | −0.947636 | − | 0.319354i | \(-0.896534\pi\) |
0.197250 | − | 0.980353i | \(-0.436799\pi\) | |||||||
\(972\) | −13.2224 | − | 7.63397i | −0.424110 | − | 0.244860i | ||||
\(973\) | 1.79423 | − | 3.10770i | 0.0575203 | − | 0.0996281i | ||||
\(974\) | −15.2487 | −0.488600 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.19615 | 0.198334 | ||||||||
\(977\) | 8.19615 | − | 14.1962i | 0.262218 | − | 0.454175i | −0.704613 | − | 0.709592i | \(-0.748879\pi\) |
0.966831 | + | 0.255417i | \(0.0822127\pi\) | |||||||
\(978\) | −6.80385 | − | 3.92820i | −0.217563 | − | 0.125610i | ||||
\(979\) | −10.2058 | − | 17.6769i | −0.326178 | − | 0.564957i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2154 | − | 10.5167i | 0.581573 | − | 0.335771i | ||||
\(982\) | −10.3301 | − | 17.8923i | −0.329648 | − | 0.570966i | ||||
\(983\) | −44.5692 | −1.42154 | −0.710769 | − | 0.703426i | \(-0.751653\pi\) | ||||
−0.710769 | + | 0.703426i | \(0.751653\pi\) | |||||||
\(984\) | 3.80385 | + | 6.58846i | 0.121262 | + | 0.210032i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | + | 10.3923i | 0.573237 | + | 0.330958i | ||||
\(987\) | 6.58846i | 0.209713i | ||||||||
\(988\) | 0.464102 | − | 1.60770i | 0.0147650 | − | 0.0511476i | ||||
\(989\) | −18.9282 | −0.601882 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.58846 | − | 9.67949i | 0.177523 | − | 0.307479i | −0.763508 | − | 0.645798i | \(-0.776525\pi\) |
0.941032 | + | 0.338319i | \(0.109858\pi\) | |||||||
\(992\) | 4.09808 | − | 2.36603i | 0.130114 | − | 0.0751214i | ||||
\(993\) | −9.46410 | −0.300334 | ||||||||
\(994\) | −15.5885 | + | 9.00000i | −0.494436 | + | 0.285463i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.00000i | 0.190117i | ||||||||
\(997\) | −35.1340 | + | 20.2846i | −1.11270 | + | 0.642420i | −0.939528 | − | 0.342471i | \(-0.888736\pi\) |
−0.173176 | + | 0.984891i | \(0.555403\pi\) | |||||||
\(998\) | 22.3923 | + | 12.9282i | 0.708816 | + | 0.409235i | ||||
\(999\) | −2.78461 | − | 1.60770i | −0.0881012 | − | 0.0508652i |
(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 | 650.2.n.a.199.2 | 4 | ||
5.2 | odd | 4 | 130.2.l.a.121.1 | yes | 4 | ||
5.3 | odd | 4 | 650.2.m.a.251.2 | 4 | |||
5.4 | even | 2 | 650.2.n.b.199.1 | 4 | |||
13.10 | even | 6 | 650.2.n.b.49.1 | 4 | |||
15.2 | even | 4 | 1170.2.bs.c.901.2 | 4 | |||
20.7 | even | 4 | 1040.2.da.a.641.2 | 4 | |||
65.2 | even | 12 | 1690.2.e.l.991.1 | 4 | |||
65.7 | even | 12 | 1690.2.a.j.1.2 | 2 | |||
65.12 | odd | 4 | 1690.2.l.g.1161.2 | 4 | |||
65.17 | odd | 12 | 1690.2.d.f.1351.2 | 4 | |||
65.22 | odd | 12 | 1690.2.d.f.1351.4 | 4 | |||
65.23 | odd | 12 | 650.2.m.a.101.2 | 4 | |||
65.32 | even | 12 | 1690.2.a.m.1.2 | 2 | |||
65.33 | even | 12 | 8450.2.a.bm.1.1 | 2 | |||
65.37 | even | 12 | 1690.2.e.n.991.1 | 4 | |||
65.42 | odd | 12 | 1690.2.l.g.361.2 | 4 | |||
65.47 | even | 4 | 1690.2.e.n.191.1 | 4 | |||
65.49 | even | 6 | inner | 650.2.n.a.49.2 | 4 | ||
65.57 | even | 4 | 1690.2.e.l.191.1 | 4 | |||
65.58 | even | 12 | 8450.2.a.bf.1.1 | 2 | |||
65.62 | odd | 12 | 130.2.l.a.101.1 | ✓ | 4 | ||
195.62 | even | 12 | 1170.2.bs.c.361.2 | 4 | |||
260.127 | even | 12 | 1040.2.da.a.881.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.1 | ✓ | 4 | 65.62 | odd | 12 | ||
130.2.l.a.121.1 | yes | 4 | 5.2 | odd | 4 | ||
650.2.m.a.101.2 | 4 | 65.23 | odd | 12 | |||
650.2.m.a.251.2 | 4 | 5.3 | odd | 4 | |||
650.2.n.a.49.2 | 4 | 65.49 | even | 6 | inner | ||
650.2.n.a.199.2 | 4 | 1.1 | even | 1 | trivial | ||
650.2.n.b.49.1 | 4 | 13.10 | even | 6 | |||
650.2.n.b.199.1 | 4 | 5.4 | even | 2 | |||
1040.2.da.a.641.2 | 4 | 20.7 | even | 4 | |||
1040.2.da.a.881.2 | 4 | 260.127 | even | 12 | |||
1170.2.bs.c.361.2 | 4 | 195.62 | even | 12 | |||
1170.2.bs.c.901.2 | 4 | 15.2 | even | 4 | |||
1690.2.a.j.1.2 | 2 | 65.7 | even | 12 | |||
1690.2.a.m.1.2 | 2 | 65.32 | even | 12 | |||
1690.2.d.f.1351.2 | 4 | 65.17 | odd | 12 | |||
1690.2.d.f.1351.4 | 4 | 65.22 | odd | 12 | |||
1690.2.e.l.191.1 | 4 | 65.57 | even | 4 | |||
1690.2.e.l.991.1 | 4 | 65.2 | even | 12 | |||
1690.2.e.n.191.1 | 4 | 65.47 | even | 4 | |||
1690.2.e.n.991.1 | 4 | 65.37 | even | 12 | |||
1690.2.l.g.361.2 | 4 | 65.42 | odd | 12 | |||
1690.2.l.g.1161.2 | 4 | 65.12 | odd | 4 | |||
8450.2.a.bf.1.1 | 2 | 65.58 | even | 12 | |||
8450.2.a.bm.1.1 | 2 | 65.33 | even | 12 |