Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(191,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1690.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.e (of order \(3\), 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: | \(13.4947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.191 |
Dual form | 1690.2.e.l.991.1 |
$q$-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 \(\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.366025 | + | 0.633975i | −0.211325 | + | 0.366025i | −0.952129 | − | 0.305695i | \(-0.901111\pi\) |
0.740805 | + | 0.671721i | \(0.234444\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.366025 | − | 0.633975i | −0.149429 | − | 0.258819i | ||||
\(7\) | 1.50000 | + | 2.59808i | 0.566947 | + | 0.981981i | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.23205 | + | 2.13397i | 0.410684 | + | 0.711325i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0.732051 | 0.211325 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0.366025 | − | 0.633975i | 0.0945074 | − | 0.163692i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.09808 | + | 7.09808i | 0.993929 | + | 1.72154i | 0.592244 | + | 0.805759i | \(0.298242\pi\) |
0.401685 | + | 0.915778i | \(0.368425\pi\) | |||||||
\(18\) | −2.46410 | −0.580794 | ||||||||
\(19\) | 0.232051 | + | 0.401924i | 0.0532361 | + | 0.0922076i | 0.891415 | − | 0.453187i | \(-0.149713\pi\) |
−0.838179 | + | 0.545395i | \(0.816380\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −2.19615 | −0.479240 | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | 4.73205 | − | 8.19615i | 0.986701 | − | 1.70902i | 0.352581 | − | 0.935781i | \(-0.385304\pi\) |
0.634120 | − | 0.773234i | \(-0.281362\pi\) | |||||||
\(24\) | −0.366025 | + | 0.633975i | −0.0747146 | + | 0.129410i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | 1.26795 | − | 2.19615i | 0.235452 | − | 0.407815i | −0.723952 | − | 0.689851i | \(-0.757676\pi\) |
0.959404 | + | 0.282035i | \(0.0910095\pi\) | |||||||
\(30\) | 0.366025 | + | 0.633975i | 0.0668268 | + | 0.115747i | ||||
\(31\) | 4.73205 | 0.849901 | 0.424951 | − | 0.905216i | \(-0.360291\pi\) | ||||
0.424951 | + | 0.905216i | \(0.360291\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.09808 | − | 1.90192i | −0.191151 | − | 0.331082i | ||||
\(34\) | −8.19615 | −1.40563 | ||||||||
\(35\) | −1.50000 | − | 2.59808i | −0.253546 | − | 0.439155i | ||||
\(36\) | 1.23205 | − | 2.13397i | 0.205342 | − | 0.355662i | ||||
\(37\) | 0.401924 | − | 0.696152i | 0.0660759 | − | 0.114447i | −0.831095 | − | 0.556131i | \(-0.812285\pi\) |
0.897171 | + | 0.441684i | \(0.145619\pi\) | |||||||
\(38\) | −0.464102 | −0.0752872 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.19615 | + | 9.00000i | −0.811503 | + | 1.40556i | 0.100309 | + | 0.994956i | \(0.468017\pi\) |
−0.911812 | + | 0.410608i | \(0.865317\pi\) | |||||||
\(42\) | 1.09808 | − | 1.90192i | 0.169437 | − | 0.293473i | ||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | −1.23205 | − | 2.13397i | −0.183663 | − | 0.318114i | ||||
\(46\) | 4.73205 | + | 8.19615i | 0.697703 | + | 1.20846i | ||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | −0.366025 | − | 0.633975i | −0.0528312 | − | 0.0915064i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.464102 | 0.0637493 | 0.0318746 | − | 0.999492i | \(-0.489852\pi\) | ||||
0.0318746 | + | 0.999492i | \(0.489852\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 1.50000 | − | 2.59808i | 0.202260 | − | 0.350325i | ||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | −0.339746 | −0.0450005 | ||||||||
\(58\) | 1.26795 | + | 2.19615i | 0.166490 | + | 0.288369i | ||||
\(59\) | 5.19615 | + | 9.00000i | 0.676481 | + | 1.17170i | 0.976034 | + | 0.217620i | \(0.0698294\pi\) |
−0.299552 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(60\) | −0.732051 | −0.0945074 | ||||||||
\(61\) | −3.09808 | − | 5.36603i | −0.396668 | − | 0.687049i | 0.596645 | − | 0.802506i | \(-0.296500\pi\) |
−0.993313 | + | 0.115456i | \(0.963167\pi\) | |||||||
\(62\) | −2.36603 | + | 4.09808i | −0.300486 | + | 0.520456i | ||||
\(63\) | −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 | \(0.166667\pi\) | |||||||
\(68\) | 4.09808 | − | 7.09808i | 0.496965 | − | 0.860768i | ||||
\(69\) | 3.46410 | + | 6.00000i | 0.417029 | + | 0.722315i | ||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 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 | ||||
\(75\) | −0.366025 | + | 0.633975i | −0.0422650 | + | 0.0732051i | ||||
\(76\) | 0.232051 | − | 0.401924i | 0.0266181 | − | 0.0461038i | ||||
\(77\) | −9.00000 | −1.02565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.19615 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −2.23205 | + | 3.86603i | −0.248006 | + | 0.429558i | ||||
\(82\) | −5.19615 | − | 9.00000i | −0.573819 | − | 0.993884i | ||||
\(83\) | −8.19615 | −0.899645 | −0.449822 | − | 0.893118i | \(-0.648513\pi\) | ||||
−0.449822 | + | 0.893118i | \(0.648513\pi\) | |||||||
\(84\) | 1.09808 | + | 1.90192i | 0.119810 | + | 0.207517i | ||||
\(85\) | −4.09808 | − | 7.09808i | −0.444499 | − | 0.769894i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0.928203 | + | 1.60770i | 0.0995138 | + | 0.172363i | ||||
\(88\) | −1.50000 | + | 2.59808i | −0.159901 | + | 0.276956i | ||||
\(89\) | −3.40192 | + | 5.89230i | −0.360603 | + | 0.624583i | −0.988060 | − | 0.154068i | \(-0.950762\pi\) |
0.627457 | + | 0.778651i | \(0.284096\pi\) | |||||||
\(90\) | 2.46410 | 0.259739 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.46410 | −0.986701 | ||||||||
\(93\) | −1.73205 | + | 3.00000i | −0.179605 | + | 0.311086i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | −0.232051 | − | 0.401924i | −0.0238079 | − | 0.0412365i | ||||
\(96\) | 0.732051 | 0.0747146 | ||||||||
\(97\) | −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 | ||||
\(99\) | −7.39230 | −0.742955 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 5.36603 | − | 9.29423i | 0.533939 | − | 0.924810i | −0.465274 | − | 0.885167i | \(-0.654044\pi\) |
0.999214 | − | 0.0396438i | \(-0.0126223\pi\) | |||||||
\(102\) | 3.00000 | − | 5.19615i | 0.297044 | − | 0.514496i | ||||
\(103\) | 9.19615 | 0.906124 | 0.453062 | − | 0.891479i | \(-0.350332\pi\) | ||||
0.453062 | + | 0.891479i | \(0.350332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.19615 | 0.214323 | ||||||||
\(106\) | −0.232051 | + | 0.401924i | −0.0225388 | + | 0.0390383i | ||||
\(107\) | −8.83013 | + | 15.2942i | −0.853641 | + | 1.47855i | 0.0242598 | + | 0.999706i | \(0.492277\pi\) |
−0.877900 | + | 0.478843i | \(0.841056\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | −8.53590 | −0.817591 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(110\) | 1.50000 | + | 2.59808i | 0.143019 | + | 0.247717i | ||||
\(111\) | 0.294229 | + | 0.509619i | 0.0279269 | + | 0.0483709i | ||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | −3.46410 | − | 6.00000i | −0.325875 | − | 0.564433i | 0.655814 | − | 0.754923i | \(-0.272326\pi\) |
−0.981689 | + | 0.190490i | \(0.938992\pi\) | |||||||
\(114\) | 0.169873 | − | 0.294229i | 0.0159101 | − | 0.0275570i | ||||
\(115\) | −4.73205 | + | 8.19615i | −0.441266 | + | 0.764295i | ||||
\(116\) | −2.53590 | −0.235452 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.3923 | −0.956689 | ||||||||
\(119\) | −12.2942 | + | 21.2942i | −1.12701 | + | 1.95204i | ||||
\(120\) | 0.366025 | − | 0.633975i | 0.0334134 | − | 0.0578737i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 6.19615 | 0.560973 | ||||||||
\(123\) | −3.80385 | − | 6.58846i | −0.342981 | − | 0.594061i | ||||
\(124\) | −2.36603 | − | 4.09808i | −0.212475 | − | 0.368018i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.69615 | − | 6.40192i | −0.329279 | − | 0.570329i | ||||
\(127\) | 5.40192 | − | 9.35641i | 0.479343 | − | 0.830247i | −0.520376 | − | 0.853937i | \(-0.674208\pi\) |
0.999719 | + | 0.0236904i | \(0.00754158\pi\) | |||||||
\(128\) | −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 | ||||
\(133\) | −0.696152 | + | 1.20577i | −0.0603641 | + | 0.104554i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 4.09808 | + | 7.09808i | 0.351407 | + | 0.608655i | ||||
\(137\) | 1.09808 | + | 1.90192i | 0.0938150 | + | 0.162492i | 0.909113 | − | 0.416549i | \(-0.136760\pi\) |
−0.815298 | + | 0.579041i | \(0.803427\pi\) | |||||||
\(138\) | −6.92820 | −0.589768 | ||||||||
\(139\) | −0.598076 | − | 1.03590i | −0.0507282 | − | 0.0878638i | 0.839546 | − | 0.543288i | \(-0.182821\pi\) |
−0.890274 | + | 0.455424i | \(0.849488\pi\) | |||||||
\(140\) | −1.50000 | + | 2.59808i | −0.126773 | + | 0.219578i | ||||
\(141\) | 1.09808 | − | 1.90192i | 0.0924747 | − | 0.160171i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | −1.26795 | + | 2.19615i | −0.105297 | + | 0.182381i | ||||
\(146\) | 5.83013 | − | 10.0981i | 0.482505 | − | 0.835723i | ||||
\(147\) | −0.732051 | − | 1.26795i | −0.0603785 | − | 0.104579i | ||||
\(148\) | −0.803848 | −0.0660759 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | −0.366025 | − | 0.633975i | −0.0298858 | − | 0.0517638i | ||||
\(151\) | 23.6603 | 1.92544 | 0.962722 | − | 0.270492i | \(-0.0871865\pi\) | ||||
0.962722 | + | 0.270492i | \(0.0871865\pi\) | |||||||
\(152\) | 0.232051 | + | 0.401924i | 0.0188218 | + | 0.0326003i | ||||
\(153\) | −10.0981 | + | 17.4904i | −0.816381 | + | 1.41401i | ||||
\(154\) | 4.50000 | − | 7.79423i | 0.362620 | − | 0.628077i | ||||
\(155\) | −4.73205 | −0.380087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 2.09808 | − | 3.63397i | 0.166914 | − | 0.289103i | ||||
\(159\) | −0.169873 | + | 0.294229i | −0.0134718 | + | 0.0233338i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 28.3923 | 2.23763 | ||||||||
\(162\) | −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 | \(0.971408\pi\) | |||||||
\(164\) | 10.3923 | 0.811503 | ||||||||
\(165\) | 1.09808 | + | 1.90192i | 0.0854851 | + | 0.148065i | ||||
\(166\) | 4.09808 | − | 7.09808i | 0.318072 | − | 0.550918i | ||||
\(167\) | −1.50000 | + | 2.59808i | −0.116073 | + | 0.201045i | −0.918208 | − | 0.396098i | \(-0.870364\pi\) |
0.802135 | + | 0.597143i | \(0.203697\pi\) | |||||||
\(168\) | −2.19615 | −0.169437 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.19615 | 0.628616 | ||||||||
\(171\) | −0.571797 | + | 0.990381i | −0.0437264 | + | 0.0757363i | ||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | −7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | \(-0.973527\pi\) |
0.426329 | − | 0.904568i | \(-0.359807\pi\) | |||||||
\(174\) | −1.85641 | −0.140734 | ||||||||
\(175\) | 1.50000 | + | 2.59808i | 0.113389 | + | 0.196396i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | −7.60770 | −0.571829 | ||||||||
\(178\) | −3.40192 | − | 5.89230i | −0.254985 | − | 0.441647i | ||||
\(179\) | −4.73205 | + | 8.19615i | −0.353690 | + | 0.612609i | −0.986893 | − | 0.161377i | \(-0.948407\pi\) |
0.633203 | + | 0.773986i | \(0.281740\pi\) | |||||||
\(180\) | −1.23205 | + | 2.13397i | −0.0918316 | + | 0.159057i | ||||
\(181\) | −14.5885 | −1.08435 | −0.542176 | − | 0.840265i | \(-0.682399\pi\) | ||||
−0.542176 | + | 0.840265i | \(0.682399\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.53590 | 0.335303 | ||||||||
\(184\) | 4.73205 | − | 8.19615i | 0.348851 | − | 0.604228i | ||||
\(185\) | −0.401924 | + | 0.696152i | −0.0295500 | + | 0.0511821i | ||||
\(186\) | −1.73205 | − | 3.00000i | −0.127000 | − | 0.219971i | ||||
\(187\) | −24.5885 | −1.79809 | ||||||||
\(188\) | 1.50000 | + | 2.59808i | 0.109399 | + | 0.189484i | ||||
\(189\) | −6.00000 | − | 10.3923i | −0.436436 | − | 0.755929i | ||||
\(190\) | 0.464102 | 0.0336695 | ||||||||
\(191\) | 11.3660 | + | 19.6865i | 0.822417 | + | 1.42447i | 0.903878 | + | 0.427791i | \(0.140708\pi\) |
−0.0814609 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(192\) | −0.366025 | + | 0.633975i | −0.0264156 | + | 0.0457532i | ||||
\(193\) | 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 | \(-0.112607\pi\) | |||||||
\(198\) | 3.69615 | − | 6.40192i | 0.262674 | − | 0.454965i | ||||
\(199\) | −3.19615 | − | 5.53590i | −0.226569 | − | 0.392429i | 0.730220 | − | 0.683212i | \(-0.239418\pi\) |
−0.956789 | + | 0.290783i | \(0.906084\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 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 | ||||
\(205\) | 5.19615 | − | 9.00000i | 0.362915 | − | 0.628587i | ||||
\(206\) | −4.59808 | + | 7.96410i | −0.320363 | + | 0.554885i | ||||
\(207\) | 23.3205 | 1.62089 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.39230 | −0.0963077 | ||||||||
\(210\) | −1.09808 | + | 1.90192i | −0.0757745 | + | 0.131245i | ||||
\(211\) | 8.79423 | − | 15.2321i | 0.605420 | − | 1.04862i | −0.386565 | − | 0.922262i | \(-0.626339\pi\) |
0.991985 | − | 0.126356i | \(-0.0403280\pi\) | |||||||
\(212\) | −0.232051 | − | 0.401924i | −0.0159373 | − | 0.0276042i | ||||
\(213\) | −4.39230 | −0.300956 | ||||||||
\(214\) | −8.83013 | − | 15.2942i | −0.603615 | − | 1.04549i | ||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 7.09808 | + | 12.2942i | 0.481849 | + | 0.834587i | ||||
\(218\) | 4.26795 | − | 7.39230i | 0.289062 | − | 0.500670i | ||||
\(219\) | 4.26795 | − | 7.39230i | 0.288401 | − | 0.499526i | ||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.588457 | −0.0394947 | ||||||||
\(223\) | −3.23205 | + | 5.59808i | −0.216434 | + | 0.374875i | −0.953715 | − | 0.300711i | \(-0.902776\pi\) |
0.737281 | + | 0.675586i | \(0.236109\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | 1.23205 | + | 2.13397i | 0.0821367 | + | 0.142265i | ||||
\(226\) | 6.92820 | 0.460857 | ||||||||
\(227\) | −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 | ||||
\(229\) | 1.26795 | 0.0837884 | 0.0418942 | − | 0.999122i | \(-0.486661\pi\) | ||||
0.0418942 | + | 0.999122i | \(0.486661\pi\) | |||||||
\(230\) | −4.73205 | − | 8.19615i | −0.312022 | − | 0.540438i | ||||
\(231\) | 3.29423 | − | 5.70577i | 0.216744 | − | 0.375412i | ||||
\(232\) | 1.26795 | − | 2.19615i | 0.0832449 | − | 0.144184i | ||||
\(233\) | −4.73205 | −0.310007 | −0.155003 | − | 0.987914i | \(-0.549539\pi\) | ||||
−0.155003 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 5.19615 | − | 9.00000i | 0.338241 | − | 0.585850i | ||||
\(237\) | 1.53590 | − | 2.66025i | 0.0997673 | − | 0.172802i | ||||
\(238\) | −12.2942 | − | 21.2942i | −0.796916 | − | 1.38030i | ||||
\(239\) | 2.19615 | 0.142057 | 0.0710286 | − | 0.997474i | \(-0.477372\pi\) | ||||
0.0710286 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(240\) | 0.366025 | + | 0.633975i | 0.0236268 | + | 0.0409229i | ||||
\(241\) | −4.33013 | − | 7.50000i | −0.278928 | − | 0.483117i | 0.692191 | − | 0.721715i | \(-0.256646\pi\) |
−0.971119 | + | 0.238597i | \(0.923312\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | −7.63397 | − | 13.2224i | −0.489720 | − | 0.848219i | ||||
\(244\) | −3.09808 | + | 5.36603i | −0.198334 | + | 0.343525i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 7.60770 | 0.485049 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.73205 | 0.300486 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 8.59808 | + | 14.8923i | 0.542706 | + | 0.939994i | 0.998747 | + | 0.0500355i | \(0.0159335\pi\) |
−0.456042 | + | 0.889958i | \(0.650733\pi\) | |||||||
\(252\) | 7.39230 | 0.465671 | ||||||||
\(253\) | 14.1962 | + | 24.5885i | 0.892504 | + | 1.54586i | ||||
\(254\) | 5.40192 | + | 9.35641i | 0.338947 | + | 0.587073i | ||||
\(255\) | 6.00000 | 0.375735 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.92820 | + | 12.0000i | −0.432169 | + | 0.748539i | −0.997060 | − | 0.0766265i | \(-0.975585\pi\) |
0.564890 | + | 0.825166i | \(0.308918\pi\) | |||||||
\(258\) | 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 | ||||
\(263\) | −1.79423 | + | 3.10770i | −0.110637 | + | 0.191629i | −0.916027 | − | 0.401116i | \(-0.868622\pi\) |
0.805390 | + | 0.592745i | \(0.201956\pi\) | |||||||
\(264\) | −1.09808 | − | 1.90192i | −0.0675819 | − | 0.117055i | ||||
\(265\) | −0.464102 | −0.0285095 | ||||||||
\(266\) | −0.696152 | − | 1.20577i | −0.0426838 | − | 0.0739306i | ||||
\(267\) | −2.49038 | − | 4.31347i | −0.152409 | − | 0.263980i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5622 | + | 23.4904i | 0.826901 | + | 1.43223i | 0.900458 | + | 0.434943i | \(0.143231\pi\) |
−0.0735575 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(270\) | −2.00000 | + | 3.46410i | −0.121716 | + | 0.210819i | ||||
\(271\) | −4.73205 | + | 8.19615i | −0.287452 | + | 0.497881i | −0.973201 | − | 0.229957i | \(-0.926141\pi\) |
0.685749 | + | 0.727838i | \(0.259475\pi\) | |||||||
\(272\) | −8.19615 | −0.496965 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.19615 | −0.132674 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 3.46410 | − | 6.00000i | 0.208514 | − | 0.361158i | ||||
\(277\) | −0.500000 | − | 0.866025i | −0.0300421 | − | 0.0520344i | 0.850613 | − | 0.525792i | \(-0.176231\pi\) |
−0.880656 | + | 0.473757i | \(0.842897\pi\) | |||||||
\(278\) | 1.19615 | 0.0717405 | ||||||||
\(279\) | 5.83013 | + | 10.0981i | 0.349041 | + | 0.604556i | ||||
\(280\) | −1.50000 | − | 2.59808i | −0.0896421 | − | 0.155265i | ||||
\(281\) | 10.3923 | 0.619953 | 0.309976 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309976 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(282\) | 1.09808 | + | 1.90192i | 0.0653895 | + | 0.113258i | ||||
\(283\) | −4.80385 | + | 8.32051i | −0.285559 | + | 0.494603i | −0.972745 | − | 0.231879i | \(-0.925513\pi\) |
0.687186 | + | 0.726482i | \(0.258846\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0.339746 | 0.0201248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.1769 | −1.84032 | ||||||||
\(288\) | 1.23205 | − | 2.13397i | 0.0725993 | − | 0.125746i | ||||
\(289\) | −25.0885 | + | 43.4545i | −1.47579 | + | 2.55615i | ||||
\(290\) | −1.26795 | − | 2.19615i | −0.0744565 | − | 0.128963i | ||||
\(291\) | 6.67949 | 0.391559 | ||||||||
\(292\) | 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 | \(0.727281\pi\) | |||||||
\(294\) | 1.46410 | 0.0853881 | ||||||||
\(295\) | −5.19615 | − | 9.00000i | −0.302532 | − | 0.524000i | ||||
\(296\) | 0.401924 | − | 0.696152i | 0.0233613 | − | 0.0404630i | ||||
\(297\) | 6.00000 | − | 10.3923i | 0.348155 | − | 0.603023i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | −3.00000 | + | 5.19615i | −0.172917 | + | 0.299501i | ||||
\(302\) | −11.8301 | + | 20.4904i | −0.680747 | + | 1.17909i | ||||
\(303\) | 3.92820 | + | 6.80385i | 0.225669 | + | 0.390871i | ||||
\(304\) | −0.464102 | −0.0266181 | ||||||||
\(305\) | 3.09808 | + | 5.36603i | 0.177395 | + | 0.307258i | ||||
\(306\) | −10.0981 | − | 17.4904i | −0.577269 | − | 0.999859i | ||||
\(307\) | 27.4641 | 1.56746 | 0.783730 | − | 0.621102i | \(-0.213315\pi\) | ||||
0.783730 | + | 0.621102i | \(0.213315\pi\) | |||||||
\(308\) | 4.50000 | + | 7.79423i | 0.256411 | + | 0.444117i | ||||
\(309\) | −3.36603 | + | 5.83013i | −0.191486 | + | 0.331664i | ||||
\(310\) | 2.36603 | − | 4.09808i | 0.134381 | − | 0.232755i | ||||
\(311\) | 9.12436 | 0.517395 | 0.258697 | − | 0.965958i | \(-0.416707\pi\) | ||||
0.258697 | + | 0.965958i | \(0.416707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.3923 | 1.49178 | 0.745891 | − | 0.666068i | \(-0.232024\pi\) | ||||
0.745891 | + | 0.666068i | \(0.232024\pi\) | |||||||
\(314\) | 6.50000 | − | 11.2583i | 0.366816 | − | 0.635344i | ||||
\(315\) | 3.69615 | − | 6.40192i | 0.208255 | − | 0.360708i | ||||
\(316\) | 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 | ||||
\(319\) | 3.80385 | + | 6.58846i | 0.212975 | + | 0.368883i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.46410 | − | 11.1962i | −0.360791 | − | 0.624908i | ||||
\(322\) | −14.1962 | + | 24.5885i | −0.791121 | + | 1.37026i | ||||
\(323\) | −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 | ||||
\(328\) | −5.19615 | + | 9.00000i | −0.286910 | + | 0.496942i | ||||
\(329\) | −4.50000 | − | 7.79423i | −0.248093 | − | 0.429710i | ||||
\(330\) | −2.19615 | −0.120894 | ||||||||
\(331\) | −6.46410 | − | 11.1962i | −0.355299 | − | 0.615396i | 0.631870 | − | 0.775074i | \(-0.282288\pi\) |
−0.987169 | + | 0.159678i | \(0.948954\pi\) | |||||||
\(332\) | 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 | ||||||||
\(336\) | 1.09808 | − | 1.90192i | 0.0599050 | − | 0.103758i | ||||
\(337\) | −6.19615 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.07180 | 0.275462 | ||||||||
\(340\) | −4.09808 | + | 7.09808i | −0.222249 | + | 0.384947i | ||||
\(341\) | −7.09808 | + | 12.2942i | −0.384382 | + | 0.665770i | ||||
\(342\) | −0.571797 | − | 0.990381i | −0.0309192 | − | 0.0535537i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 1.00000 | + | 1.73205i | 0.0539164 | + | 0.0933859i | ||||
\(345\) | −3.46410 | − | 6.00000i | −0.186501 | − | 0.323029i | ||||
\(346\) | 15.0000 | 0.806405 | ||||||||
\(347\) | 14.3660 | + | 24.8827i | 0.771209 | + | 1.33577i | 0.936901 | + | 0.349595i | \(0.113681\pi\) |
−0.165692 | + | 0.986178i | \(0.552986\pi\) | |||||||
\(348\) | 0.928203 | − | 1.60770i | 0.0497569 | − | 0.0861815i | ||||
\(349\) | 2.02628 | − | 3.50962i | 0.108464 | − | 0.187866i | −0.806684 | − | 0.590983i | \(-0.798740\pi\) |
0.915148 | + | 0.403117i | \(0.132073\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 4.90192 | − | 8.49038i | 0.260903 | − | 0.451897i | −0.705579 | − | 0.708631i | \(-0.749313\pi\) |
0.966482 | + | 0.256734i | \(0.0826464\pi\) | |||||||
\(354\) | 3.80385 | − | 6.58846i | 0.202172 | − | 0.350173i | ||||
\(355\) | −3.00000 | − | 5.19615i | −0.159223 | − | 0.275783i | ||||
\(356\) | 6.80385 | 0.360603 | ||||||||
\(357\) | −9.00000 | − | 15.5885i | −0.476331 | − | 0.825029i | ||||
\(358\) | −4.73205 | − | 8.19615i | −0.250097 | − | 0.433180i | ||||
\(359\) | −1.60770 | −0.0848509 | −0.0424255 | − | 0.999100i | \(-0.513508\pi\) | ||||
−0.0424255 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(360\) | −1.23205 | − | 2.13397i | −0.0649348 | − | 0.112470i | ||||
\(361\) | 9.39230 | − | 16.2679i | 0.494332 | − | 0.856208i | ||||
\(362\) | 7.29423 | − | 12.6340i | 0.383376 | − | 0.664027i | ||||
\(363\) | −1.46410 | −0.0768454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6603 | 0.610326 | ||||||||
\(366\) | −2.26795 | + | 3.92820i | −0.118548 | + | 0.205330i | ||||
\(367\) | 2.80385 | − | 4.85641i | 0.146360 | − | 0.253502i | −0.783520 | − | 0.621367i | \(-0.786578\pi\) |
0.929879 | + | 0.367865i | \(0.119911\pi\) | |||||||
\(368\) | 4.73205 | + | 8.19615i | 0.246675 | + | 0.427254i | ||||
\(369\) | −25.6077 | −1.33308 | ||||||||
\(370\) | −0.401924 | − | 0.696152i | −0.0208950 | − | 0.0361912i | ||||
\(371\) | 0.696152 | + | 1.20577i | 0.0361424 | + | 0.0626005i | ||||
\(372\) | 3.46410 | 0.179605 | ||||||||
\(373\) | 0.196152 | + | 0.339746i | 0.0101564 | + | 0.0175914i | 0.871059 | − | 0.491179i | \(-0.163434\pi\) |
−0.860903 | + | 0.508770i | \(0.830100\pi\) | |||||||
\(374\) | 12.2942 | − | 21.2942i | 0.635719 | − | 1.10110i | ||||
\(375\) | 0.366025 | − | 0.633975i | 0.0189015 | − | 0.0327383i | ||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 12.0000 | 0.617213 | ||||||||
\(379\) | 14.8923 | − | 25.7942i | 0.764966 | − | 1.32496i | −0.175298 | − | 0.984515i | \(-0.556089\pi\) |
0.940264 | − | 0.340445i | \(-0.110578\pi\) | |||||||
\(380\) | −0.232051 | + | 0.401924i | −0.0119040 | + | 0.0206183i | ||||
\(381\) | 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 | \(-0.972797\pi\) |
0.424254 | − | 0.905543i | \(-0.360536\pi\) | |||||||
\(384\) | −0.366025 | − | 0.633975i | −0.0186787 | − | 0.0323524i | ||||
\(385\) | 9.00000 | 0.458682 | ||||||||
\(386\) | 8.19615 | + | 14.1962i | 0.417173 | + | 0.722565i | ||||
\(387\) | −2.46410 | + | 4.26795i | −0.125257 | + | 0.216952i | ||||
\(388\) | −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 | ||||
\(393\) | −2.24167 | + | 3.88269i | −0.113077 | + | 0.195856i | ||||
\(394\) | 10.7942 | + | 18.6962i | 0.543805 | + | 0.941899i | ||||
\(395\) | 4.19615 | 0.211131 | ||||||||
\(396\) | 3.69615 | + | 6.40192i | 0.185739 | + | 0.321709i | ||||
\(397\) | −5.59808 | − | 9.69615i | −0.280959 | − | 0.486636i | 0.690662 | − | 0.723178i | \(-0.257319\pi\) |
−0.971621 | + | 0.236542i | \(0.923986\pi\) | |||||||
\(398\) | 6.39230 | 0.320417 | ||||||||
\(399\) | −0.509619 | − | 0.882686i | −0.0255129 | − | 0.0441896i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 2.59808 | − | 4.50000i | 0.129742 | − | 0.224719i | −0.793835 | − | 0.608134i | \(-0.791919\pi\) |
0.923576 | + | 0.383414i | \(0.125252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.7321 | −0.533939 | ||||||||
\(405\) | 2.23205 | − | 3.86603i | 0.110911 | − | 0.192104i | ||||
\(406\) | −3.80385 | + | 6.58846i | −0.188782 | + | 0.326980i | ||||
\(407\) | 1.20577 | + | 2.08846i | 0.0597679 | + | 0.103521i | ||||
\(408\) | −6.00000 | −0.297044 | ||||||||
\(409\) | 8.13397 | + | 14.0885i | 0.402199 | + | 0.696629i | 0.993991 | − | 0.109461i | \(-0.0349126\pi\) |
−0.591792 | + | 0.806091i | \(0.701579\pi\) | |||||||
\(410\) | 5.19615 | + | 9.00000i | 0.256620 | + | 0.444478i | ||||
\(411\) | −1.60770 | −0.0793018 | ||||||||
\(412\) | −4.59808 | − | 7.96410i | −0.226531 | − | 0.392363i | ||||
\(413\) | −15.5885 | + | 27.0000i | −0.767058 | + | 1.32858i | ||||
\(414\) | −11.6603 | + | 20.1962i | −0.573070 | + | 0.992587i | ||||
\(415\) | 8.19615 | 0.402333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.875644 | 0.0428805 | ||||||||
\(418\) | 0.696152 | − | 1.20577i | 0.0340499 | − | 0.0589762i | ||||
\(419\) | 8.66025 | − | 15.0000i | 0.423081 | − | 0.732798i | −0.573158 | − | 0.819445i | \(-0.694282\pi\) |
0.996239 | + | 0.0866469i | \(0.0276152\pi\) | |||||||
\(420\) | −1.09808 | − | 1.90192i | −0.0535806 | − | 0.0928044i | ||||
\(421\) | 2.87564 | 0.140150 | 0.0700752 | − | 0.997542i | \(-0.477676\pi\) | ||||
0.0700752 | + | 0.997542i | \(0.477676\pi\) | |||||||
\(422\) | 8.79423 | + | 15.2321i | 0.428096 | + | 0.741485i | ||||
\(423\) | −3.69615 | − | 6.40192i | −0.179713 | − | 0.311272i | ||||
\(424\) | 0.464102 | 0.0225388 | ||||||||
\(425\) | 4.09808 | + | 7.09808i | 0.198786 | + | 0.344307i | ||||
\(426\) | 2.19615 | − | 3.80385i | 0.106404 | − | 0.184297i | ||||
\(427\) | 9.29423 | − | 16.0981i | 0.449779 | − | 0.779041i | ||||
\(428\) | 17.6603 | 0.853641 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | −4.09808 | + | 7.09808i | −0.197397 | + | 0.341902i | −0.947684 | − | 0.319211i | \(-0.896582\pi\) |
0.750286 | + | 0.661113i | \(0.229916\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | 4.19615 | + | 7.26795i | 0.201654 | + | 0.349275i | 0.949062 | − | 0.315091i | \(-0.102035\pi\) |
−0.747407 | + | 0.664366i | \(0.768702\pi\) | |||||||
\(434\) | −14.1962 | −0.681437 | ||||||||
\(435\) | −0.928203 | − | 1.60770i | −0.0445039 | − | 0.0770831i | ||||
\(436\) | 4.26795 | + | 7.39230i | 0.204398 | + | 0.354027i | ||||
\(437\) | 4.39230 | 0.210112 | ||||||||
\(438\) | 4.26795 | + | 7.39230i | 0.203931 | + | 0.353218i | ||||
\(439\) | −1.70577 | + | 2.95448i | −0.0814120 | + | 0.141010i | −0.903857 | − | 0.427835i | \(-0.859276\pi\) |
0.822445 | + | 0.568845i | \(0.192610\pi\) | |||||||
\(440\) | 1.50000 | − | 2.59808i | 0.0715097 | − | 0.123858i | ||||
\(441\) | −4.92820 | −0.234676 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.3923 | −1.06389 | −0.531945 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531945 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(444\) | 0.294229 | − | 0.509619i | 0.0139635 | − | 0.0241854i | ||||
\(445\) | 3.40192 | − | 5.89230i | 0.161267 | − | 0.279322i | ||||
\(446\) | −3.23205 | − | 5.59808i | −0.153042 | − | 0.265077i | ||||
\(447\) | 4.39230 | 0.207749 | ||||||||
\(448\) | 1.50000 | + | 2.59808i | 0.0708683 | + | 0.122748i | ||||
\(449\) | 7.79423 | + | 13.5000i | 0.367832 | + | 0.637104i | 0.989226 | − | 0.146394i | \(-0.0467667\pi\) |
−0.621394 | + | 0.783498i | \(0.713433\pi\) | |||||||
\(450\) | −2.46410 | −0.116159 | ||||||||
\(451\) | −15.5885 | − | 27.0000i | −0.734032 | − | 1.27138i | ||||
\(452\) | −3.46410 | + | 6.00000i | −0.162938 | + | 0.282216i | ||||
\(453\) | −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 | \(0.0255508\pi\) | |||||||
\(458\) | −0.633975 | + | 1.09808i | −0.0296237 | + | 0.0513097i | ||||
\(459\) | −16.3923 | − | 28.3923i | −0.765127 | − | 1.32524i | ||||
\(460\) | 9.46410 | 0.441266 | ||||||||
\(461\) | 15.2942 | + | 26.4904i | 0.712323 | + | 1.23378i | 0.963983 | + | 0.265964i | \(0.0856903\pi\) |
−0.251660 | + | 0.967816i | \(0.580976\pi\) | |||||||
\(462\) | 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 | ||||
\(465\) | 1.73205 | − | 3.00000i | 0.0803219 | − | 0.139122i | ||||
\(466\) | 2.36603 | − | 4.09808i | 0.109604 | − | 0.189840i | ||||
\(467\) | 37.8564 | 1.75179 | 0.875893 | − | 0.482506i | \(-0.160273\pi\) | ||||
0.875893 | + | 0.482506i | \(0.160273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.50000 | + | 2.59808i | −0.0691898 | + | 0.119840i | ||||
\(471\) | 4.75833 | − | 8.24167i | 0.219252 | − | 0.379756i | ||||
\(472\) | 5.19615 | + | 9.00000i | 0.239172 | + | 0.414259i | ||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 1.53590 | + | 2.66025i | 0.0705461 | + | 0.122190i | ||||
\(475\) | 0.232051 | + | 0.401924i | 0.0106472 | + | 0.0184415i | ||||
\(476\) | 24.5885 | 1.12701 | ||||||||
\(477\) | 0.571797 | + | 0.990381i | 0.0261808 | + | 0.0453464i | ||||
\(478\) | −1.09808 | + | 1.90192i | −0.0502248 | + | 0.0869920i | ||||
\(479\) | 20.4904 | − | 35.4904i | 0.936229 | − | 1.62160i | 0.163803 | − | 0.986493i | \(-0.447624\pi\) |
0.772427 | − | 0.635104i | \(-0.219043\pi\) | |||||||
\(480\) | −0.732051 | −0.0334134 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8.66025 | 0.394464 | ||||||||
\(483\) | −10.3923 | + | 18.0000i | −0.472866 | + | 0.819028i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 4.56218 | + | 7.90192i | 0.207158 | + | 0.358808i | ||||
\(486\) | 15.2679 | 0.692568 | ||||||||
\(487\) | 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 | ||||
\(489\) | 7.85641 | 0.355279 | ||||||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | 10.3301 | − | 17.8923i | 0.466192 | − | 0.807468i | −0.533062 | − | 0.846076i | \(-0.678959\pi\) |
0.999254 | + | 0.0386076i | \(0.0122922\pi\) | |||||||
\(492\) | −3.80385 | + | 6.58846i | −0.171491 | + | 0.297031i | ||||
\(493\) | 20.7846 | 0.936092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39230 | 0.332259 | ||||||||
\(496\) | −2.36603 | + | 4.09808i | −0.106238 | + | 0.184009i | ||||
\(497\) | −9.00000 | + | 15.5885i | −0.403705 | + | 0.699238i | ||||
\(498\) | 3.00000 | + | 5.19615i | 0.134433 | + | 0.232845i | ||||
\(499\) | 25.8564 | 1.15749 | 0.578746 | − | 0.815508i | \(-0.303542\pi\) | ||||
0.578746 | + | 0.815508i | \(0.303542\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −1.09808 | − | 1.90192i | −0.0490584 | − | 0.0849717i | ||||
\(502\) | −17.1962 | −0.767502 | ||||||||
\(503\) | 13.3301 | + | 23.0885i | 0.594361 | + | 1.02946i | 0.993637 | + | 0.112633i | \(0.0359283\pi\) |
−0.399276 | + | 0.916831i | \(0.630738\pi\) | |||||||
\(504\) | −3.69615 | + | 6.40192i | −0.164640 | + | 0.285164i | ||||
\(505\) | −5.36603 | + | 9.29423i | −0.238785 | + | 0.413588i | ||||
\(506\) | −28.3923 | −1.26219 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.8038 | −0.479343 | ||||||||
\(509\) | −11.1962 | + | 19.3923i | −0.496261 | + | 0.859549i | −0.999991 | − | 0.00431237i | \(-0.998627\pi\) |
0.503730 | + | 0.863861i | \(0.331961\pi\) | |||||||
\(510\) | −3.00000 | + | 5.19615i | −0.132842 | + | 0.230089i | ||||
\(511\) | −17.4904 | − | 30.2942i | −0.773729 | − | 1.34014i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.928203 | − | 1.60770i | −0.0409812 | − | 0.0709815i | ||||
\(514\) | −6.92820 | − | 12.0000i | −0.305590 | − | 0.529297i | ||||
\(515\) | −9.19615 | −0.405231 | ||||||||
\(516\) | 0.732051 | + | 1.26795i | 0.0322267 | + | 0.0558184i | ||||
\(517\) | 4.50000 | − | 7.79423i | 0.197910 | − | 0.342790i | ||||
\(518\) | −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 | ||||
\(523\) | 1.19615 | − | 2.07180i | 0.0523041 | − | 0.0905933i | −0.838688 | − | 0.544612i | \(-0.816677\pi\) |
0.890992 | + | 0.454019i | \(0.150010\pi\) | |||||||
\(524\) | −3.06218 | − | 5.30385i | −0.133772 | − | 0.231700i | ||||
\(525\) | −2.19615 | −0.0958479 | ||||||||
\(526\) | −1.79423 | − | 3.10770i | −0.0782321 | − | 0.135502i | ||||
\(527\) | 19.3923 | + | 33.5885i | 0.844742 | + | 1.46314i | ||||
\(528\) | 2.19615 | 0.0955753 | ||||||||
\(529\) | −33.2846 | − | 57.6506i | −1.44716 | − | 2.50655i | ||||
\(530\) | 0.232051 | − | 0.401924i | 0.0100796 | − | 0.0174585i | ||||
\(531\) | −12.8038 | + | 22.1769i | −0.555640 | + | 0.962396i | ||||
\(532\) | 1.39230 | 0.0603641 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.98076 | 0.215539 | ||||||||
\(535\) | 8.83013 | − | 15.2942i | 0.381760 | − | 0.661227i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.46410 | − | 6.00000i | −0.149487 | − | 0.258919i | ||||
\(538\) | −27.1244 | −1.16941 | ||||||||
\(539\) | −3.00000 | − | 5.19615i | −0.129219 | − | 0.223814i | ||||
\(540\) | −2.00000 | − | 3.46410i | −0.0860663 | − | 0.149071i | ||||
\(541\) | −22.0526 | −0.948114 | −0.474057 | − | 0.880494i | \(-0.657211\pi\) | ||||
−0.474057 | + | 0.880494i | \(0.657211\pi\) | |||||||
\(542\) | −4.73205 | − | 8.19615i | −0.203259 | − | 0.352055i | ||||
\(543\) | 5.33975 | − | 9.24871i | 0.229150 | − | 0.396900i | ||||
\(544\) | 4.09808 | − | 7.09808i | 0.175704 | − | 0.304328i | ||||
\(545\) | 8.53590 | 0.365638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.78461 | −0.290089 | −0.145044 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145044 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(548\) | 1.09808 | − | 1.90192i | 0.0469075 | − | 0.0812462i | ||||
\(549\) | 7.63397 | − | 13.2224i | 0.325810 | − | 0.564320i | ||||
\(550\) | −1.50000 | − | 2.59808i | −0.0639602 | − | 0.110782i | ||||
\(551\) | 1.17691 | 0.0501382 | ||||||||
\(552\) | 3.46410 | + | 6.00000i | 0.147442 | + | 0.255377i | ||||
\(553\) | −6.29423 | − | 10.9019i | −0.267658 | − | 0.463597i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | −0.294229 | − | 0.509619i | −0.0124893 | − | 0.0216321i | ||||
\(556\) | −0.598076 | + | 1.03590i | −0.0253641 | + | 0.0439319i | ||||
\(557\) | 3.40192 | − | 5.89230i | 0.144144 | − | 0.249665i | −0.784909 | − | 0.619611i | \(-0.787290\pi\) |
0.929053 | + | 0.369946i | \(0.120624\pi\) | |||||||
\(558\) | −11.6603 | −0.493618 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 9.00000 | − | 15.5885i | 0.379980 | − | 0.658145i | ||||
\(562\) | −5.19615 | + | 9.00000i | −0.219186 | + | 0.379642i | ||||
\(563\) | 7.26795 | + | 12.5885i | 0.306308 | + | 0.530540i | 0.977552 | − | 0.210696i | \(-0.0675731\pi\) |
−0.671244 | + | 0.741236i | \(0.734240\pi\) | |||||||
\(564\) | −2.19615 | −0.0924747 | ||||||||
\(565\) | 3.46410 | + | 6.00000i | 0.145736 | + | 0.252422i | ||||
\(566\) | −4.80385 | − | 8.32051i | −0.201921 | − | 0.349737i | ||||
\(567\) | −13.3923 | −0.562424 | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | −13.6244 | + | 23.5981i | −0.571163 | + | 0.989283i | 0.425284 | + | 0.905060i | \(0.360174\pi\) |
−0.996447 | + | 0.0842230i | \(0.973159\pi\) | |||||||
\(570\) | −0.169873 | + | 0.294229i | −0.00711520 | + | 0.0123239i | ||||
\(571\) | 38.3731 | 1.60586 | 0.802931 | − | 0.596071i | \(-0.203272\pi\) | ||||
0.802931 | + | 0.596071i | \(0.203272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6410 | −0.695188 | ||||||||
\(574\) | 15.5885 | − | 27.0000i | 0.650650 | − | 1.12696i | ||||
\(575\) | 4.73205 | − | 8.19615i | 0.197340 | − | 0.341803i | ||||
\(576\) | 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 | ||||
\(579\) | 6.00000 | + | 10.3923i | 0.249351 | + | 0.431889i | ||||
\(580\) | 2.53590 | 0.105297 | ||||||||
\(581\) | −12.2942 | − | 21.2942i | −0.510051 | − | 0.883433i | ||||
\(582\) | −3.33975 | + | 5.78461i | −0.138437 | + | 0.239780i | ||||
\(583\) | −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 | \(-0.0458424\pi\) | |||||||
\(588\) | −0.732051 | + | 1.26795i | −0.0301893 | + | 0.0522893i | ||||
\(589\) | 1.09808 | + | 1.90192i | 0.0452454 | + | 0.0783674i | ||||
\(590\) | 10.3923 | 0.427844 | ||||||||
\(591\) | 7.90192 | + | 13.6865i | 0.325042 | + | 0.562989i | ||||
\(592\) | 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 | ||||
\(595\) | 12.2942 | − | 21.2942i | 0.504014 | − | 0.872978i | ||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | 4.67949 | 0.191519 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8564 | −0.811311 | −0.405655 | − | 0.914026i | \(-0.632957\pi\) | ||||
−0.405655 | + | 0.914026i | \(0.632957\pi\) | |||||||
\(600\) | −0.366025 | + | 0.633975i | −0.0149429 | + | 0.0258819i | ||||
\(601\) | 18.8923 | − | 32.7224i | 0.770633 | − | 1.33478i | −0.166583 | − | 0.986027i | \(-0.553273\pi\) |
0.937216 | − | 0.348748i | \(-0.113393\pi\) | |||||||
\(602\) | −3.00000 | − | 5.19615i | −0.122271 | − | 0.211779i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.8301 | − | 20.4904i | −0.481361 | − | 0.833742i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | −7.85641 | −0.319145 | ||||||||
\(607\) | 18.7942 | + | 32.5526i | 0.762834 | + | 1.32127i | 0.941384 | + | 0.337337i | \(0.109526\pi\) |
−0.178550 | + | 0.983931i | \(0.557141\pi\) | |||||||
\(608\) | 0.232051 | − | 0.401924i | 0.00941090 | − | 0.0163002i | ||||
\(609\) | −2.78461 | + | 4.82309i | −0.112838 | + | 0.195441i | ||||
\(610\) | −6.19615 | −0.250875 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 20.1962 | 0.816381 | ||||||||
\(613\) | 19.4545 | − | 33.6962i | 0.785759 | − | 1.36097i | −0.142785 | − | 0.989754i | \(-0.545606\pi\) |
0.928545 | − | 0.371221i | \(-0.121061\pi\) | |||||||
\(614\) | −13.7321 | + | 23.7846i | −0.554180 | + | 0.959869i | ||||
\(615\) | 3.80385 | + | 6.58846i | 0.153386 | + | 0.265672i | ||||
\(616\) | −9.00000 | −0.362620 | ||||||||
\(617\) | −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 | ||||
\(619\) | 31.3923 | 1.26176 | 0.630882 | − | 0.775879i | \(-0.282693\pi\) | ||||
0.630882 | + | 0.775879i | \(0.282693\pi\) | |||||||
\(620\) | 2.36603 | + | 4.09808i | 0.0950219 | + | 0.164583i | ||||
\(621\) | −18.9282 | + | 32.7846i | −0.759563 | + | 1.31560i | ||||
\(622\) | −4.56218 | + | 7.90192i | −0.182927 | + | 0.316838i | ||||
\(623\) | −20.4115 | −0.817771 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.1962 | + | 22.8564i | −0.527424 | + | 0.913526i | ||||
\(627\) | 0.509619 | − | 0.882686i | 0.0203522 | − | 0.0352511i | ||||
\(628\) | 6.50000 | + | 11.2583i | 0.259378 | + | 0.449256i | ||||
\(629\) | 6.58846 | 0.262699 | ||||||||
\(630\) | 3.69615 | + | 6.40192i | 0.147258 | + | 0.255059i | ||||
\(631\) | −10.3923 | − | 18.0000i | −0.413711 | − | 0.716569i | 0.581581 | − | 0.813488i | \(-0.302434\pi\) |
−0.995292 | + | 0.0969198i | \(0.969101\pi\) | |||||||
\(632\) | −4.19615 | −0.166914 | ||||||||
\(633\) | 6.43782 | + | 11.1506i | 0.255880 | + | 0.443198i | ||||
\(634\) | 11.5981 | − | 20.0885i | 0.460618 | − | 0.797815i | ||||
\(635\) | −5.40192 | + | 9.35641i | −0.214369 | + | 0.371298i | ||||
\(636\) | 0.339746 | 0.0134718 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.60770 | −0.301192 | ||||||||
\(639\) | −7.39230 | + | 12.8038i | −0.292435 | + | 0.506512i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 16.0359 | + | 27.7750i | 0.633380 | + | 1.09705i | 0.986856 | + | 0.161603i | \(0.0516663\pi\) |
−0.353476 | + | 0.935444i | \(0.615000\pi\) | |||||||
\(642\) | 12.9282 | 0.510235 | ||||||||
\(643\) | 5.36603 | + | 9.29423i | 0.211615 | + | 0.366529i | 0.952220 | − | 0.305412i | \(-0.0987943\pi\) |
−0.740605 | + | 0.671941i | \(0.765461\pi\) | |||||||
\(644\) | −14.1962 | − | 24.5885i | −0.559407 | − | 0.968921i | ||||
\(645\) | 1.46410 | 0.0576489 | ||||||||
\(646\) | −1.90192 | − | 3.29423i | −0.0748302 | − | 0.129610i | ||||
\(647\) | −0.401924 | + | 0.696152i | −0.0158013 | + | 0.0273686i | −0.873818 | − | 0.486253i | \(-0.838363\pi\) |
0.858017 | + | 0.513622i | \(0.171697\pi\) | |||||||
\(648\) | −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 | ||||
\(653\) | −0.696152 | + | 1.20577i | −0.0272425 | + | 0.0471855i | −0.879325 | − | 0.476222i | \(-0.842006\pi\) |
0.852083 | + | 0.523407i | \(0.175339\pi\) | |||||||
\(654\) | 3.12436 | + | 5.41154i | 0.122172 | + | 0.211608i | ||||
\(655\) | −6.12436 | −0.239298 | ||||||||
\(656\) | −5.19615 | − | 9.00000i | −0.202876 | − | 0.351391i | ||||
\(657\) | −14.3660 | − | 24.8827i | −0.560472 | − | 0.970766i | ||||
\(658\) | 9.00000 | 0.350857 | ||||||||
\(659\) | 2.66025 | + | 4.60770i | 0.103629 | + | 0.179490i | 0.913177 | − | 0.407563i | \(-0.133621\pi\) |
−0.809548 | + | 0.587053i | \(0.800288\pi\) | |||||||
\(660\) | 1.09808 | − | 1.90192i | 0.0427426 | − | 0.0740323i | ||||
\(661\) | −17.9545 | + | 31.0981i | −0.698348 | + | 1.20957i | 0.270690 | + | 0.962666i | \(0.412748\pi\) |
−0.969039 | + | 0.246909i | \(0.920585\pi\) | |||||||
\(662\) | 12.9282 | 0.502469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.19615 | −0.318072 | ||||||||
\(665\) | 0.696152 | − | 1.20577i | 0.0269956 | − | 0.0467578i | ||||
\(666\) | −0.990381 | + | 1.71539i | −0.0383765 | + | 0.0664700i | ||||
\(667\) | −12.0000 | − | 20.7846i | −0.464642 | − | 0.804783i | ||||
\(668\) | 3.00000 | 0.116073 | ||||||||
\(669\) | −2.36603 | − | 4.09808i | −0.0914758 | − | 0.158441i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5885 | 0.717599 | ||||||||
\(672\) | 1.09808 | + | 1.90192i | 0.0423592 | + | 0.0733683i | ||||
\(673\) | 12.1962 | − | 21.1244i | 0.470127 | − | 0.814284i | −0.529289 | − | 0.848441i | \(-0.677541\pi\) |
0.999416 | + | 0.0341573i | \(0.0108747\pi\) | |||||||
\(674\) | 3.09808 | − | 5.36603i | 0.119333 | − | 0.206692i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.8564 | −0.993742 | −0.496871 | − | 0.867824i | \(-0.665518\pi\) | ||||
−0.496871 | + | 0.867824i | \(0.665518\pi\) | |||||||
\(678\) | −2.53590 | + | 4.39230i | −0.0973906 | + | 0.168685i | ||||
\(679\) | 13.6865 | − | 23.7058i | 0.525241 | − | 0.909744i | ||||
\(680\) | −4.09808 | − | 7.09808i | −0.157154 | − | 0.272199i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | −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 | \(0.629901\pi\) | |||||||
\(684\) | 1.14359 | 0.0437264 | ||||||||
\(685\) | −1.09808 | − | 1.90192i | −0.0419553 | − | 0.0726688i | ||||
\(686\) | −7.50000 | + | 12.9904i | −0.286351 | + | 0.495975i | ||||
\(687\) | −0.464102 | + | 0.803848i | −0.0177066 | + | 0.0306687i | ||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.92820 | 0.263752 | ||||||||
\(691\) | −18.3564 | + | 31.7942i | −0.698311 | + | 1.20951i | 0.270741 | + | 0.962652i | \(0.412731\pi\) |
−0.969052 | + | 0.246857i | \(0.920602\pi\) | |||||||
\(692\) | −7.50000 | + | 12.9904i | −0.285107 | + | 0.493820i | ||||
\(693\) | −11.0885 | − | 19.2058i | −0.421216 | − | 0.729567i | ||||
\(694\) | −28.7321 | −1.09065 | ||||||||
\(695\) | 0.598076 | + | 1.03590i | 0.0226863 | + | 0.0392939i | ||||
\(696\) | 0.928203 | + | 1.60770i | 0.0351835 | + | 0.0609395i | ||||
\(697\) | −85.1769 | −3.22631 | ||||||||
\(698\) | 2.02628 | + | 3.50962i | 0.0766958 | + | 0.132841i | ||||
\(699\) | 1.73205 | − | 3.00000i | 0.0655122 | − | 0.113470i | ||||
\(700\) | 1.50000 | − | 2.59808i | 0.0566947 | − | 0.0981981i | ||||
\(701\) | −35.9090 | −1.35626 | −0.678131 | − | 0.734941i | \(-0.737210\pi\) | ||||
−0.678131 | + | 0.734941i | \(0.737210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.373067 | 0.0140705 | ||||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | −1.09808 | + | 1.90192i | −0.0413559 | + | 0.0716306i | ||||
\(706\) | 4.90192 | + | 8.49038i | 0.184486 | + | 0.319540i | ||||
\(707\) | 32.1962 | 1.21086 | ||||||||
\(708\) | 3.80385 | + | 6.58846i | 0.142957 | + | 0.247609i | ||||
\(709\) | 5.49038 | + | 9.50962i | 0.206196 | + | 0.357141i | 0.950513 | − | 0.310685i | \(-0.100558\pi\) |
−0.744317 | + | 0.667826i | \(0.767225\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | −5.16987 | − | 8.95448i | −0.193885 | − | 0.335819i | ||||
\(712\) | −3.40192 | + | 5.89230i | −0.127492 | + | 0.220823i | ||||
\(713\) | 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 | ||||
\(718\) | 0.803848 | − | 1.39230i | 0.0299993 | − | 0.0519604i | ||||
\(719\) | 12.9282 | + | 22.3923i | 0.482141 | + | 0.835092i | 0.999790 | − | 0.0205009i | \(-0.00652609\pi\) |
−0.517649 | + | 0.855593i | \(0.673193\pi\) | |||||||
\(720\) | 2.46410 | 0.0918316 | ||||||||
\(721\) | 13.7942 | + | 23.8923i | 0.513724 | + | 0.889796i | ||||
\(722\) | 9.39230 | + | 16.2679i | 0.349545 | + | 0.605430i | ||||
\(723\) | 6.33975 | 0.235778 | ||||||||
\(724\) | 7.29423 | + | 12.6340i | 0.271088 | + | 0.469538i | ||||
\(725\) | 1.26795 | − | 2.19615i | 0.0470905 | − | 0.0815631i | ||||
\(726\) | 0.732051 | − | 1.26795i | 0.0271690 | − | 0.0470580i | ||||
\(727\) | −34.3731 | −1.27483 | −0.637413 | − | 0.770522i | \(-0.719996\pi\) | ||||
−0.637413 | + | 0.770522i | \(0.719996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −5.83013 | + | 10.0981i | −0.215783 | + | 0.373747i | ||||
\(731\) | −8.19615 | + | 14.1962i | −0.303146 | + | 0.525064i | ||||
\(732\) | −2.26795 | − | 3.92820i | −0.0838258 | − | 0.145191i | ||||
\(733\) | 14.9090 | 0.550675 | 0.275338 | − | 0.961348i | \(-0.411210\pi\) | ||||
0.275338 | + | 0.961348i | \(0.411210\pi\) | |||||||
\(734\) | 2.80385 | + | 4.85641i | 0.103492 | + | 0.179253i | ||||
\(735\) | 0.732051 | + | 1.26795i | 0.0270021 | + | 0.0467690i | ||||
\(736\) | −9.46410 | −0.348851 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 12.8038 | − | 22.1769i | 0.471316 | − | 0.816344i | ||||
\(739\) | −16.2846 | + | 28.2058i | −0.599039 | + | 1.03757i | 0.393924 | + | 0.919143i | \(0.371117\pi\) |
−0.992963 | + | 0.118423i | \(0.962216\pi\) | |||||||
\(740\) | 0.803848 | 0.0295500 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.39230 | −0.0511131 | ||||||||
\(743\) | −6.80385 | + | 11.7846i | −0.249609 | + | 0.432335i | −0.963417 | − | 0.268006i | \(-0.913635\pi\) |
0.713808 | + | 0.700341i | \(0.246969\pi\) | |||||||
\(744\) | −1.73205 | + | 3.00000i | −0.0635001 | + | 0.109985i | ||||
\(745\) | 3.00000 | + | 5.19615i | 0.109911 | + | 0.190372i | ||||
\(746\) | −0.392305 | −0.0143633 | ||||||||
\(747\) | −10.0981 | − | 17.4904i | −0.369469 | − | 0.639940i | ||||
\(748\) | 12.2942 | + | 21.2942i | 0.449522 | + | 0.778594i | ||||
\(749\) | −52.9808 | −1.93587 | ||||||||
\(750\) | 0.366025 | + | 0.633975i | 0.0133654 | + | 0.0231495i | ||||
\(751\) | −10.1962 | + | 17.6603i | −0.372063 | + | 0.644432i | −0.989883 | − | 0.141888i | \(-0.954683\pi\) |
0.617820 | + | 0.786320i | \(0.288016\pi\) | |||||||
\(752\) | 1.50000 | − | 2.59808i | 0.0546994 | − | 0.0947421i | ||||
\(753\) | −12.5885 | −0.458749 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.6603 | −0.861085 | ||||||||
\(756\) | −6.00000 | + | 10.3923i | −0.218218 | + | 0.377964i | ||||
\(757\) | 18.8923 | − | 32.7224i | 0.686652 | − | 1.18932i | −0.286262 | − | 0.958151i | \(-0.592413\pi\) |
0.972914 | − | 0.231166i | \(-0.0742539\pi\) | |||||||
\(758\) | 14.8923 | + | 25.7942i | 0.540913 | + | 0.936889i | ||||
\(759\) | −20.7846 | −0.754434 | ||||||||
\(760\) | −0.232051 | − | 0.401924i | −0.00841737 | − | 0.0145793i | ||||
\(761\) | 9.40192 | + | 16.2846i | 0.340819 | + | 0.590317i | 0.984585 | − | 0.174906i | \(-0.0559622\pi\) |
−0.643766 | + | 0.765223i | \(0.722629\pi\) | |||||||
\(762\) | −7.90897 | −0.286512 | ||||||||
\(763\) | −12.8038 | − | 22.1769i | −0.463530 | − | 0.802858i | ||||
\(764\) | 11.3660 | − | 19.6865i | 0.411208 | − | 0.712234i | ||||
\(765\) | 10.0981 | − | 17.4904i | 0.365097 | − | 0.632366i | ||||
\(766\) | 22.3923 | 0.809067 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.732051 | 0.0264156 | ||||||||
\(769\) | −19.0526 | + | 33.0000i | −0.687053 | + | 1.19001i | 0.285734 | + | 0.958309i | \(0.407763\pi\) |
−0.972787 | + | 0.231701i | \(0.925571\pi\) | |||||||
\(770\) | −4.50000 | + | 7.79423i | −0.162169 | + | 0.280885i | ||||
\(771\) | −5.07180 | − | 8.78461i | −0.182656 | − | 0.316370i | ||||
\(772\) | −16.3923 | −0.589972 | ||||||||
\(773\) | −1.20577 | − | 2.08846i | −0.0433686 | − | 0.0751166i | 0.843526 | − | 0.537088i | \(-0.180476\pi\) |
−0.886895 | + | 0.461971i | \(0.847142\pi\) | |||||||
\(774\) | −2.46410 | − | 4.26795i | −0.0885703 | − | 0.153408i | ||||
\(775\) | 4.73205 | 0.169980 | ||||||||
\(776\) | −4.56218 | − | 7.90192i | −0.163773 | − | 0.283663i | ||||
\(777\) | −0.882686 | + | 1.52886i | −0.0316662 | + | 0.0548474i | ||||
\(778\) | 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 | ||||
\(783\) | −5.07180 | + | 8.78461i | −0.181251 | + | 0.313936i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 13.0000 | 0.463990 | ||||||||
\(786\) | −2.24167 | − | 3.88269i | −0.0799577 | − | 0.138491i | ||||
\(787\) | −21.4186 | − | 37.0981i | −0.763490 | − | 1.32240i | −0.941041 | − | 0.338292i | \(-0.890151\pi\) |
0.177551 | − | 0.984112i | \(-0.443182\pi\) | |||||||
\(788\) | −21.5885 | −0.769057 | ||||||||
\(789\) | −1.31347 | − | 2.27499i | −0.0467606 | − | 0.0809918i | ||||
\(790\) | −2.09808 | + | 3.63397i | −0.0746462 | + | 0.129291i | ||||
\(791\) | 10.3923 | − | 18.0000i | 0.369508 | − | 0.640006i | ||||
\(792\) | −7.39230 | −0.262674 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.1962 | 0.397337 | ||||||||
\(795\) | 0.169873 | − | 0.294229i | 0.00602477 | − | 0.0104352i | ||||
\(796\) | −3.19615 | + | 5.53590i | −0.113285 | + | 0.196215i | ||||
\(797\) | −6.46410 | − | 11.1962i | −0.228970 | − | 0.396588i | 0.728533 | − | 0.685011i | \(-0.240203\pi\) |
−0.957503 | + | 0.288423i | \(0.906869\pi\) | |||||||
\(798\) | 1.01924 | 0.0360806 | ||||||||
\(799\) | −12.2942 | − | 21.2942i | −0.434939 | − | 0.753336i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −16.7654 | −0.592375 | ||||||||
\(802\) | 2.59808 | + | 4.50000i | 0.0917413 | + | 0.158901i | ||||
\(803\) | 17.4904 | − | 30.2942i | 0.617222 | − | 1.06906i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.3923 | −1.00070 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8564 | −0.698979 | ||||||||
\(808\) | 5.36603 | − | 9.29423i | 0.188776 | − | 0.326970i | ||||
\(809\) | −12.0000 | + | 20.7846i | −0.421898 | + | 0.730748i | −0.996125 | − | 0.0879478i | \(-0.971969\pi\) |
0.574228 | + | 0.818696i | \(0.305302\pi\) | |||||||
\(810\) | 2.23205 | + | 3.86603i | 0.0784263 | + | 0.135838i | ||||
\(811\) | 43.3923 | 1.52371 | 0.761855 | − | 0.647748i | \(-0.224289\pi\) | ||||
0.761855 | + | 0.647748i | \(0.224289\pi\) | |||||||
\(812\) | −3.80385 | − | 6.58846i | −0.133489 | − | 0.231210i | ||||
\(813\) | −3.46410 | − | 6.00000i | −0.121491 | − | 0.210429i | ||||
\(814\) | −2.41154 | −0.0845245 | ||||||||
\(815\) | 5.36603 | + | 9.29423i | 0.187964 | + | 0.325563i | ||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | −0.464102 | + | 0.803848i | −0.0162369 | + | 0.0281231i | ||||
\(818\) | −16.2679 | −0.568796 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.3923 | −0.362915 | ||||||||
\(821\) | 10.0981 | − | 17.4904i | 0.352425 | − | 0.610419i | −0.634249 | − | 0.773129i | \(-0.718690\pi\) |
0.986674 | + | 0.162711i | \(0.0520237\pi\) | |||||||
\(822\) | 0.803848 | − | 1.39230i | 0.0280374 | − | 0.0485622i | ||||
\(823\) | −13.5981 | − | 23.5526i | −0.473999 | − | 0.820991i | 0.525558 | − | 0.850758i | \(-0.323857\pi\) |
−0.999557 | + | 0.0297674i | \(0.990523\pi\) | |||||||
\(824\) | 9.19615 | 0.320363 | ||||||||
\(825\) | −1.09808 | − | 1.90192i | −0.0382301 | − | 0.0662165i | ||||
\(826\) | −15.5885 | − | 27.0000i | −0.542392 | − | 0.939450i | ||||
\(827\) | 42.5885 | 1.48095 | 0.740473 | − | 0.672086i | \(-0.234602\pi\) | ||||
0.740473 | + | 0.672086i | \(0.234602\pi\) | |||||||
\(828\) | −11.6603 | − | 20.1962i | −0.405222 | − | 0.701865i | ||||
\(829\) | −10.0000 | + | 17.3205i | −0.347314 | + | 0.601566i | −0.985771 | − | 0.168091i | \(-0.946240\pi\) |
0.638457 | + | 0.769657i | \(0.279573\pi\) | |||||||
\(830\) | −4.09808 | + | 7.09808i | −0.142246 | + | 0.246378i | ||||
\(831\) | 0.732051 | 0.0253946 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.3923 | −0.567960 | ||||||||
\(834\) | −0.437822 | + | 0.758330i | −0.0151605 | + | 0.0262588i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 0.696152 | + | 1.20577i | 0.0240769 | + | 0.0417025i | ||||
\(837\) | −18.9282 | −0.654254 | ||||||||
\(838\) | 8.66025 | + | 15.0000i | 0.299164 | + | 0.518166i | ||||
\(839\) | 10.9019 | + | 18.8827i | 0.376376 | + | 0.651903i | 0.990532 | − | 0.137282i | \(-0.0438367\pi\) |
−0.614156 | + | 0.789185i | \(0.710503\pi\) | |||||||
\(840\) | 2.19615 | 0.0757745 | ||||||||
\(841\) | 11.2846 | + | 19.5455i | 0.389124 | + | 0.673983i | ||||
\(842\) | −1.43782 | + | 2.49038i | −0.0495506 | + | 0.0858242i | ||||
\(843\) | −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 | ||||
\(848\) | −0.232051 | + | 0.401924i | −0.00796866 | + | 0.0138021i | ||||
\(849\) | −3.51666 | − | 6.09103i | −0.120691 | − | 0.209044i | ||||
\(850\) | −8.19615 | −0.281126 | ||||||||
\(851\) | −3.80385 | − | 6.58846i | −0.130394 | − | 0.225849i | ||||
\(852\) | 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 | ||||
\(855\) | 0.571797 | − | 0.990381i | 0.0195550 | − | 0.0338703i | ||||
\(856\) | −8.83013 | + | 15.2942i | −0.301808 | + | 0.522746i | ||||
\(857\) | 16.7321 | 0.571556 | 0.285778 | − | 0.958296i | \(-0.407748\pi\) | ||||
0.285778 | + | 0.958296i | \(0.407748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3731 | −0.695120 | −0.347560 | − | 0.937658i | \(-0.612990\pi\) | ||||
−0.347560 | + | 0.937658i | \(0.612990\pi\) | |||||||
\(860\) | −1.00000 | + | 1.73205i | −0.0340997 | + | 0.0590624i | ||||
\(861\) | 11.4115 | − | 19.7654i | 0.388904 | − | 0.673602i | ||||
\(862\) | −4.09808 | − | 7.09808i | −0.139581 | − | 0.241761i | ||||
\(863\) | 43.1769 | 1.46976 | 0.734880 | − | 0.678198i | \(-0.237239\pi\) | ||||
0.734880 | + | 0.678198i | \(0.237239\pi\) | |||||||
\(864\) | 2.00000 | + | 3.46410i | 0.0680414 | + | 0.117851i | ||||
\(865\) | 7.50000 | + | 12.9904i | 0.255008 | + | 0.441686i | ||||
\(866\) | −8.39230 | −0.285182 | ||||||||
\(867\) | −18.3660 | − | 31.8109i | −0.623743 | − | 1.08035i | ||||
\(868\) | 7.09808 | − | 12.2942i | 0.240924 | − | 0.417293i | ||||
\(869\) | 6.29423 | − | 10.9019i | 0.213517 | − | 0.369822i | ||||
\(870\) | 1.85641 | 0.0629381 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.53590 | −0.289062 | ||||||||
\(873\) | 11.2417 | − | 19.4711i | 0.380473 | − | 0.658998i | ||||
\(874\) | −2.19615 | + | 3.80385i | −0.0742860 | + | 0.128667i | ||||
\(875\) | −1.50000 | − | 2.59808i | −0.0507093 | − | 0.0878310i | ||||
\(876\) | −8.53590 | −0.288401 | ||||||||
\(877\) | 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 | ||||
\(879\) | −8.19615 | −0.276449 | ||||||||
\(880\) | 1.50000 | + | 2.59808i | 0.0505650 | + | 0.0875811i | ||||
\(881\) | 13.1603 | − | 22.7942i | 0.443380 | − | 0.767957i | −0.554558 | − | 0.832145i | \(-0.687112\pi\) |
0.997938 | + | 0.0641883i | \(0.0204458\pi\) | |||||||
\(882\) | 2.46410 | − | 4.26795i | 0.0829706 | − | 0.143709i | ||||
\(883\) | −4.58846 | −0.154414 | −0.0772069 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772069 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.60770 | 0.255730 | ||||||||
\(886\) | 11.1962 | − | 19.3923i | 0.376142 | − | 0.651497i | ||||
\(887\) | 20.3827 | − | 35.3038i | 0.684384 | − | 1.18539i | −0.289246 | − | 0.957255i | \(-0.593405\pi\) |
0.973630 | − | 0.228133i | \(-0.0732620\pi\) | |||||||
\(888\) | 0.294229 | + | 0.509619i | 0.00987367 | + | 0.0171017i | ||||
\(889\) | 32.4115 | 1.08705 | ||||||||
\(890\) | 3.40192 | + | 5.89230i | 0.114033 | + | 0.197511i | ||||
\(891\) | −6.69615 | − | 11.5981i | −0.224330 | − | 0.388550i | ||||
\(892\) | 6.46410 | 0.216434 | ||||||||
\(893\) | −0.696152 | − | 1.20577i | −0.0232959 | − | 0.0403496i | ||||
\(894\) | −2.19615 | + | 3.80385i | −0.0734503 | + | 0.127220i | ||||
\(895\) | 4.73205 | − | 8.19615i | 0.158175 | − | 0.273967i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.5885 | −0.520194 | ||||||||
\(899\) | 6.00000 | − | 10.3923i | 0.200111 | − | 0.346603i | ||||
\(900\) | 1.23205 | − | 2.13397i | 0.0410684 | − | 0.0711325i | ||||
\(901\) | 1.90192 | + | 3.29423i | 0.0633623 | + | 0.109747i | ||||
\(902\) | 31.1769 | 1.03808 | ||||||||
\(903\) | −2.19615 | − | 3.80385i | −0.0730834 | − | 0.126584i | ||||
\(904\) | −3.46410 | − | 6.00000i | −0.115214 | − | 0.199557i | ||||
\(905\) | 14.5885 | 0.484937 | ||||||||
\(906\) | −8.66025 | − | 15.0000i | −0.287718 | − | 0.498342i | ||||
\(907\) | 2.29423 | − | 3.97372i | 0.0761786 | − | 0.131945i | −0.825420 | − | 0.564520i | \(-0.809061\pi\) |
0.901598 | + | 0.432574i | \(0.142395\pi\) | |||||||
\(908\) | −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 | ||||
\(913\) | 12.2942 | − | 21.2942i | 0.406880 | − | 0.704736i | ||||
\(914\) | 9.16987 | + | 15.8827i | 0.303312 | + | 0.525353i | ||||
\(915\) | −4.53590 | −0.149952 | ||||||||
\(916\) | −0.633975 | − | 1.09808i | −0.0209471 | − | 0.0362815i | ||||
\(917\) | 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 | \(-0.997146\pi\) |
0.492215 | − | 0.870474i | \(-0.336188\pi\) | |||||||
\(920\) | −4.73205 | + | 8.19615i | −0.156011 | + | 0.270219i | ||||
\(921\) | −10.0526 | + | 17.4115i | −0.331243 | + | 0.573730i | ||||
\(922\) | −30.5885 | −1.00738 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −6.58846 | −0.216744 | ||||||||
\(925\) | 0.401924 | − | 0.696152i | 0.0132152 | − | 0.0228894i | ||||
\(926\) | 6.46410 | − | 11.1962i | 0.212424 | − | 0.367928i | ||||
\(927\) | 11.3301 | + | 19.6244i | 0.372130 | + | 0.644548i | ||||
\(928\) | −2.53590 | −0.0832449 | ||||||||
\(929\) | 1.60770 | + | 2.78461i | 0.0527468 | + | 0.0913601i | 0.891193 | − | 0.453624i | \(-0.149869\pi\) |
−0.838446 | + | 0.544984i | \(0.816536\pi\) | |||||||
\(930\) | 1.73205 | + | 3.00000i | 0.0567962 | + | 0.0983739i | ||||
\(931\) | −0.928203 | −0.0304206 | ||||||||
\(932\) | 2.36603 | + | 4.09808i | 0.0775017 | + | 0.134237i | ||||
\(933\) | −3.33975 | + | 5.78461i | −0.109338 | + | 0.189380i | ||||
\(934\) | −18.9282 | + | 32.7846i | −0.619350 | + | 1.07275i | ||||
\(935\) | 24.5885 | 0.804129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.60770 | −0.313870 | −0.156935 | − | 0.987609i | \(-0.550161\pi\) | ||||
−0.156935 | + | 0.987609i | \(0.550161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.66025 | + | 16.7321i | −0.315250 | + | 0.546030i | ||||
\(940\) | −1.50000 | − | 2.59808i | −0.0489246 | − | 0.0847399i | ||||
\(941\) | 3.21539 | 0.104819 | 0.0524094 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524094 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(942\) | 4.75833 | + | 8.24167i | 0.155035 | + | 0.268528i | ||||
\(943\) | 49.1769 | + | 85.1769i | 1.60142 | + | 2.77374i | ||||
\(944\) | −10.3923 | −0.338241 | ||||||||
\(945\) | 6.00000 | + | 10.3923i | 0.195180 | + | 0.338062i | ||||
\(946\) | 3.00000 | − | 5.19615i | 0.0975384 | − | 0.168941i | ||||
\(947\) | −7.68653 | + | 13.3135i | −0.249779 | + | 0.432630i | −0.963464 | − | 0.267837i | \(-0.913691\pi\) |
0.713686 | + | 0.700466i | \(0.247025\pi\) | |||||||
\(948\) | −3.07180 | −0.0997673 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.464102 | −0.0150574 | ||||||||
\(951\) | 8.49038 | − | 14.7058i | 0.275319 | − | 0.476867i | ||||
\(952\) | −12.2942 | + | 21.2942i | −0.398458 | + | 0.690150i | ||||
\(953\) | −3.29423 | − | 5.70577i | −0.106711 | − | 0.184828i | 0.807725 | − | 0.589559i | \(-0.200698\pi\) |
−0.914436 | + | 0.404731i | \(0.867365\pi\) | |||||||
\(954\) | −1.14359 | −0.0370252 | ||||||||
\(955\) | −11.3660 | − | 19.6865i | −0.367796 | − | 0.637041i | ||||
\(956\) | −1.09808 | − | 1.90192i | −0.0355143 | − | 0.0615126i | ||||
\(957\) | −5.56922 | −0.180027 | ||||||||
\(958\) | 20.4904 | + | 35.4904i | 0.662014 | + | 1.14664i | ||||
\(959\) | −3.29423 | + | 5.70577i | −0.106376 | + | 0.184249i | ||||
\(960\) | 0.366025 | − | 0.633975i | 0.0118134 | − | 0.0204614i | ||||
\(961\) | −8.60770 | −0.277668 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.5167 | −1.40230 | ||||||||
\(964\) | −4.33013 | + | 7.50000i | −0.139464 | + | 0.241559i | ||||
\(965\) | −8.19615 | + | 14.1962i | −0.263843 | + | 0.456990i | ||||
\(966\) | −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 | ||||
\(969\) | −1.39230 | − | 2.41154i | −0.0447273 | − | 0.0774699i | ||||
\(970\) | −9.12436 | −0.292965 | ||||||||
\(971\) | −23.3827 | − | 40.5000i | −0.750386 | − | 1.29971i | −0.947636 | − | 0.319354i | \(-0.896534\pi\) |
0.197250 | − | 0.980353i | \(-0.436799\pi\) | |||||||
\(972\) | −7.63397 | + | 13.2224i | −0.244860 | + | 0.424110i | ||||
\(973\) | 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 | \(0.0822127\pi\) | |||||||
\(978\) | −3.92820 | + | 6.80385i | −0.125610 | + | 0.217563i | ||||
\(979\) | −10.2058 | − | 17.6769i | −0.326178 | − | 0.564957i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −10.5167 | − | 18.2154i | −0.335771 | − | 0.581573i | ||||
\(982\) | 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 | ||||
\(985\) | −10.7942 | + | 18.6962i | −0.343933 | + | 0.595709i | ||||
\(986\) | −10.3923 | + | 18.0000i | −0.330958 | + | 0.573237i | ||||
\(987\) | 6.58846 | 0.209713 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.9282 | 0.601882 | ||||||||
\(990\) | −3.69615 | + | 6.40192i | −0.117471 | + | 0.203466i | ||||
\(991\) | 5.58846 | − | 9.67949i | 0.177523 | − | 0.307479i | −0.763508 | − | 0.645798i | \(-0.776525\pi\) |
0.941032 | + | 0.338319i | \(0.109858\pi\) | |||||||
\(992\) | −2.36603 | − | 4.09808i | −0.0751214 | − | 0.130114i | ||||
\(993\) | 9.46410 | 0.300334 | ||||||||
\(994\) | −9.00000 | − | 15.5885i | −0.285463 | − | 0.494436i | ||||
\(995\) | 3.19615 | + | 5.53590i | 0.101325 | + | 0.175500i | ||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | −20.2846 | − | 35.1340i | −0.642420 | − | 1.11270i | −0.984891 | − | 0.173176i | \(-0.944597\pi\) |
0.342471 | − | 0.939528i | \(-0.388736\pi\) | |||||||
\(998\) | −12.9282 | + | 22.3923i | −0.409235 | + | 0.708816i | ||||
\(999\) | −1.60770 | + | 2.78461i | −0.0508652 | + | 0.0881012i |
(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 | 1690.2.e.l.191.1 | 4 | ||
13.2 | odd | 12 | 130.2.l.a.101.1 | ✓ | 4 | ||
13.3 | even | 3 | inner | 1690.2.e.l.991.1 | 4 | ||
13.4 | even | 6 | 1690.2.a.j.1.2 | 2 | |||
13.5 | odd | 4 | 1690.2.l.g.1161.2 | 4 | |||
13.6 | odd | 12 | 1690.2.d.f.1351.2 | 4 | |||
13.7 | odd | 12 | 1690.2.d.f.1351.4 | 4 | |||
13.8 | odd | 4 | 130.2.l.a.121.1 | yes | 4 | ||
13.9 | even | 3 | 1690.2.a.m.1.2 | 2 | |||
13.10 | even | 6 | 1690.2.e.n.991.1 | 4 | |||
13.11 | odd | 12 | 1690.2.l.g.361.2 | 4 | |||
13.12 | even | 2 | 1690.2.e.n.191.1 | 4 | |||
39.2 | even | 12 | 1170.2.bs.c.361.2 | 4 | |||
39.8 | even | 4 | 1170.2.bs.c.901.2 | 4 | |||
52.15 | even | 12 | 1040.2.da.a.881.2 | 4 | |||
52.47 | even | 4 | 1040.2.da.a.641.2 | 4 | |||
65.2 | even | 12 | 650.2.n.a.49.2 | 4 | |||
65.4 | even | 6 | 8450.2.a.bm.1.1 | 2 | |||
65.8 | even | 4 | 650.2.n.a.199.2 | 4 | |||
65.9 | even | 6 | 8450.2.a.bf.1.1 | 2 | |||
65.28 | even | 12 | 650.2.n.b.49.1 | 4 | |||
65.34 | odd | 4 | 650.2.m.a.251.2 | 4 | |||
65.47 | even | 4 | 650.2.n.b.199.1 | 4 | |||
65.54 | odd | 12 | 650.2.m.a.101.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.1 | ✓ | 4 | 13.2 | odd | 12 | ||
130.2.l.a.121.1 | yes | 4 | 13.8 | odd | 4 | ||
650.2.m.a.101.2 | 4 | 65.54 | odd | 12 | |||
650.2.m.a.251.2 | 4 | 65.34 | odd | 4 | |||
650.2.n.a.49.2 | 4 | 65.2 | even | 12 | |||
650.2.n.a.199.2 | 4 | 65.8 | even | 4 | |||
650.2.n.b.49.1 | 4 | 65.28 | even | 12 | |||
650.2.n.b.199.1 | 4 | 65.47 | even | 4 | |||
1040.2.da.a.641.2 | 4 | 52.47 | even | 4 | |||
1040.2.da.a.881.2 | 4 | 52.15 | even | 12 | |||
1170.2.bs.c.361.2 | 4 | 39.2 | even | 12 | |||
1170.2.bs.c.901.2 | 4 | 39.8 | even | 4 | |||
1690.2.a.j.1.2 | 2 | 13.4 | even | 6 | |||
1690.2.a.m.1.2 | 2 | 13.9 | even | 3 | |||
1690.2.d.f.1351.2 | 4 | 13.6 | odd | 12 | |||
1690.2.d.f.1351.4 | 4 | 13.7 | odd | 12 | |||
1690.2.e.l.191.1 | 4 | 1.1 | even | 1 | trivial | ||
1690.2.e.l.991.1 | 4 | 13.3 | even | 3 | inner | ||
1690.2.e.n.191.1 | 4 | 13.12 | even | 2 | |||
1690.2.e.n.991.1 | 4 | 13.10 | even | 6 | |||
1690.2.l.g.361.2 | 4 | 13.11 | odd | 12 | |||
1690.2.l.g.1161.2 | 4 | 13.5 | odd | 4 | |||
8450.2.a.bf.1.1 | 2 | 65.9 | even | 6 | |||
8450.2.a.bm.1.1 | 2 | 65.4 | even | 6 |