Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(469,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3534400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 469.2 | ||
Root | \(-1.81837 + 0.301352i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.469 |
Dual form | 1170.2.e.f.469.5 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.301352 | − | 2.21567i | 0.134769 | − | 0.990877i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.63675i | 1.37456i | 0.726392 | + | 0.687281i | \(0.241196\pi\) | ||||
−0.726392 | + | 0.687281i | \(0.758804\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.21567 | − | 0.301352i | −0.700656 | − | 0.0952960i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 3.63675 | 0.971961 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.67079i | 1.61790i | 0.587875 | + | 0.808952i | \(0.299965\pi\) | ||||
−0.587875 | + | 0.808952i | \(0.700035\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.06808 | −1.85095 | −0.925473 | − | 0.378814i | \(-0.876332\pi\) | ||||
−0.925473 | + | 0.378814i | \(0.876332\pi\) | |||||||
\(20\) | −0.301352 | + | 2.21567i | −0.0673845 | + | 0.495439i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 0.794590i | 0.165683i | 0.996563 | + | 0.0828417i | \(0.0263996\pi\) | ||||
−0.996563 | + | 0.0828417i | \(0.973600\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81837 | − | 1.33539i | −0.963675 | − | 0.267079i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.63675i | − | 0.687281i | ||||||
\(29\) | −8.06808 | −1.49821 | −0.749103 | − | 0.662454i | \(-0.769515\pi\) | ||||
−0.749103 | + | 0.662454i | \(0.769515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.20541 | 0.934919 | 0.467460 | − | 0.884014i | \(-0.345169\pi\) | ||||
0.467460 | + | 0.884014i | \(0.345169\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.67079 | 1.14403 | ||||||||
\(35\) | 8.05783 | + | 1.09594i | 1.36202 | + | 0.185248i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.431337i | 0.0709114i | 0.999371 | + | 0.0354557i | \(0.0112883\pi\) | ||||
−0.999371 | + | 0.0354557i | \(0.988712\pi\) | |||||||
\(38\) | 8.06808i | 1.30882i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.21567 | + | 0.301352i | 0.350328 | + | 0.0476480i | ||||
\(41\) | −6.86267 | −1.07177 | −0.535885 | − | 0.844291i | \(-0.680022\pi\) | ||||
−0.535885 | + | 0.844291i | \(0.680022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.80811i | 0.885729i | 0.896589 | + | 0.442865i | \(0.146038\pi\) | ||||
−0.896589 | + | 0.442865i | \(0.853962\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.794590 | 0.117156 | ||||||||
\(47\) | 7.63675i | 1.11393i | 0.830535 | + | 0.556967i | \(0.188035\pi\) | ||||
−0.830535 | + | 0.556967i | \(0.811965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.22593 | −0.889418 | ||||||||
\(50\) | −1.33539 | + | 4.81837i | −0.188853 | + | 0.681421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | 0.794590i | 0.109145i | 0.998510 | + | 0.0545727i | \(0.0173797\pi\) | ||||
−0.998510 | + | 0.0545727i | \(0.982620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.602705 | + | 4.43134i | −0.0812687 | + | 0.597521i | ||||
\(56\) | −3.63675 | −0.485981 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.06808i | 1.05939i | ||||||||
\(59\) | 8.06808 | 1.05038 | 0.525188 | − | 0.850987i | \(-0.323995\pi\) | ||||
0.525188 | + | 0.850987i | \(0.323995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.86267 | −0.366528 | −0.183264 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183264 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(62\) | − | 5.20541i | − | 0.661088i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.21567 | − | 0.301352i | −0.274820 | − | 0.0373782i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.20541i | − | 0.635942i | −0.948100 | − | 0.317971i | \(-0.896999\pi\) | ||
0.948100 | − | 0.317971i | \(-0.103001\pi\) | |||||||
\(68\) | − | 6.67079i | − | 0.808952i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.09594 | − | 8.05783i | 0.130990 | − | 0.963094i | ||||
\(71\) | 9.46538 | 1.12333 | 0.561667 | − | 0.827363i | \(-0.310160\pi\) | ||||
0.561667 | + | 0.827363i | \(0.310160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0.431337 | 0.0501419 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.06808 | 0.925473 | ||||||||
\(77\) | − | 7.27349i | − | 0.828892i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.93192 | −0.217358 | −0.108679 | − | 0.994077i | \(-0.534662\pi\) | ||||
−0.108679 | + | 0.994077i | \(0.534662\pi\) | |||||||
\(80\) | 0.301352 | − | 2.21567i | 0.0336922 | − | 0.247719i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.86267i | 0.757856i | ||||||||
\(83\) | 2.06808i | 0.227002i | 0.993538 | + | 0.113501i | \(0.0362065\pi\) | ||||
−0.993538 | + | 0.113501i | \(0.963794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7803 | + | 2.01026i | 1.60314 | + | 0.218043i | ||||
\(86\) | 5.80811 | 0.626305 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.00000i | − | 0.213201i | ||||||
\(89\) | −8.06808 | −0.855215 | −0.427608 | − | 0.903964i | \(-0.640643\pi\) | ||||
−0.427608 | + | 0.903964i | \(0.640643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63675 | 0.381235 | ||||||||
\(92\) | − | 0.794590i | − | 0.0828417i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.63675 | 0.787670 | ||||||||
\(95\) | −2.43134 | + | 17.8762i | −0.249450 | + | 1.83406i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.6573i | − | 1.38669i | −0.720608 | − | 0.693343i | \(-0.756137\pi\) | ||
0.720608 | − | 0.693343i | \(-0.243863\pi\) | |||||||
\(98\) | 6.22593i | 0.628914i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.81837 | + | 1.33539i | 0.481837 | + | 0.133539i | ||||
\(101\) | 15.6843 | 1.56065 | 0.780324 | − | 0.625376i | \(-0.215054\pi\) | ||||
0.780324 | + | 0.625376i | \(0.215054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3416i | 1.51165i | 0.654773 | + | 0.755825i | \(0.272764\pi\) | ||||
−0.654773 | + | 0.755825i | \(0.727236\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.794590 | 0.0771774 | ||||||||
\(107\) | − | 1.20541i | − | 0.116531i | −0.998301 | − | 0.0582657i | \(-0.981443\pi\) | ||
0.998301 | − | 0.0582657i | \(-0.0185571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.80811 | −0.939447 | −0.469724 | − | 0.882814i | \(-0.655646\pi\) | ||||
−0.469724 | + | 0.882814i | \(0.655646\pi\) | |||||||
\(110\) | 4.43134 | + | 0.602705i | 0.422511 | + | 0.0574657i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.63675i | 0.343640i | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.76055 | + | 0.239452i | 0.164172 | + | 0.0223290i | ||||
\(116\) | 8.06808 | 0.749103 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.06808i | − | 0.742727i | ||||||
\(119\) | −24.2600 | −2.22391 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 2.86267i | 0.259174i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.20541 | −0.467460 | ||||||||
\(125\) | −4.41082 | + | 10.2735i | −0.394516 | + | 0.918889i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.79459i | 0.425451i | 0.977112 | + | 0.212726i | \(0.0682340\pi\) | ||||
−0.977112 | + | 0.212726i | \(0.931766\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.301352 | + | 2.21567i | −0.0264304 | + | 0.194327i | ||||
\(131\) | 4.02052 | 0.351274 | 0.175637 | − | 0.984455i | \(-0.443801\pi\) | ||||
0.175637 | + | 0.984455i | \(0.443801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 29.3416i | − | 2.54424i | ||||||
\(134\) | −5.20541 | −0.449679 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.67079 | −0.572015 | ||||||||
\(137\) | − | 11.2054i | − | 0.957343i | −0.877994 | − | 0.478671i | \(-0.841119\pi\) | ||
0.877994 | − | 0.478671i | \(-0.158881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.84216 | −0.749982 | −0.374991 | − | 0.927028i | \(-0.622354\pi\) | ||||
−0.374991 | + | 0.927028i | \(0.622354\pi\) | |||||||
\(140\) | −8.05783 | − | 1.09594i | −0.681011 | − | 0.0926241i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 9.46538i | − | 0.794317i | ||||||
\(143\) | 2.00000i | 0.167248i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.43134 | + | 17.8762i | −0.201912 | + | 1.48454i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.431337i | − | 0.0354557i | ||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.05456 | 0.574092 | 0.287046 | − | 0.957917i | \(-0.407327\pi\) | ||||
0.287046 | + | 0.957917i | \(0.407327\pi\) | |||||||
\(152\) | − | 8.06808i | − | 0.654408i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.27349 | −0.586115 | ||||||||
\(155\) | 1.56866 | − | 11.5335i | 0.125998 | − | 0.926390i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.0680837i | − | 0.00543367i | −0.999996 | − | 0.00271683i | \(-0.999135\pi\) | ||
0.999996 | − | 0.00271683i | \(-0.000864796\pi\) | |||||||
\(158\) | 1.93192i | 0.153695i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.21567 | − | 0.301352i | −0.175164 | − | 0.0238240i | ||||
\(161\) | −2.88972 | −0.227742 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.65726i | 0.599763i | 0.953976 | + | 0.299882i | \(0.0969472\pi\) | ||||
−0.953976 | + | 0.299882i | \(0.903053\pi\) | |||||||
\(164\) | 6.86267 | 0.535885 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.06808 | 0.160514 | ||||||||
\(167\) | 4.82164i | 0.373110i | 0.982445 | + | 0.186555i | \(0.0597322\pi\) | ||||
−0.982445 | + | 0.186555i | \(0.940268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 2.01026 | − | 14.7803i | 0.154180 | − | 1.13359i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.80811i | − | 0.442865i | ||||||
\(173\) | − | 12.7946i | − | 0.972755i | −0.873749 | − | 0.486377i | \(-0.838318\pi\) | ||
0.873749 | − | 0.486377i | \(-0.161682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.85649 | − | 17.5232i | 0.367116 | − | 1.32463i | ||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.06808i | 0.604728i | ||||||||
\(179\) | −8.84216 | −0.660894 | −0.330447 | − | 0.943825i | \(-0.607199\pi\) | ||||
−0.330447 | + | 0.943825i | \(0.607199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.61623 | 0.120133 | 0.0600667 | − | 0.998194i | \(-0.480869\pi\) | ||||
0.0600667 | + | 0.998194i | \(0.480869\pi\) | |||||||
\(182\) | − | 3.63675i | − | 0.269574i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.794590 | −0.0585780 | ||||||||
\(185\) | 0.955700 | + | 0.129984i | 0.0702644 | + | 0.00955665i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 13.3416i | − | 0.975633i | ||||||
\(188\) | − | 7.63675i | − | 0.556967i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.8762 | + | 2.43134i | 1.29688 | + | 0.176388i | ||||
\(191\) | −21.3416 | −1.54422 | −0.772111 | − | 0.635487i | \(-0.780799\pi\) | ||||
−0.772111 | + | 0.635487i | \(0.780799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.61623i | 0.404265i | 0.979358 | + | 0.202133i | \(0.0647872\pi\) | ||||
−0.979358 | + | 0.202133i | \(0.935213\pi\) | |||||||
\(194\) | −13.6573 | −0.980534 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.22593 | 0.444709 | ||||||||
\(197\) | − | 14.0205i | − | 0.998920i | −0.866337 | − | 0.499460i | \(-0.833532\pi\) | ||
0.866337 | − | 0.499460i | \(-0.166468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7524 | 1.11666 | 0.558329 | − | 0.829620i | \(-0.311443\pi\) | ||||
0.558329 | + | 0.829620i | \(0.311443\pi\) | |||||||
\(200\) | 1.33539 | − | 4.81837i | 0.0944266 | − | 0.340710i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 15.6843i | − | 1.10354i | ||||||
\(203\) | − | 29.3416i | − | 2.05937i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.06808 | + | 15.2054i | −0.144441 | + | 1.06199i | ||||
\(206\) | 15.3416 | 1.06890 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.00000i | − | 0.0693375i | ||||||
\(209\) | 16.1362 | 1.11616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.70483 | −0.117365 | −0.0586827 | − | 0.998277i | \(-0.518690\pi\) | ||||
−0.0586827 | + | 0.998277i | \(0.518690\pi\) | |||||||
\(212\) | − | 0.794590i | − | 0.0545727i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.20541 | −0.0824001 | ||||||||
\(215\) | 12.8689 | + | 1.75029i | 0.877649 | + | 0.119369i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9308i | 1.28510i | ||||||||
\(218\) | 9.80811i | 0.664289i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.602705 | − | 4.43134i | 0.0406344 | − | 0.298761i | ||||
\(221\) | 6.67079 | 0.448726 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.9513i | − | 1.53693i | −0.639891 | − | 0.768466i | \(-0.721021\pi\) | ||
0.639891 | − | 0.768466i | \(-0.278979\pi\) | |||||||
\(224\) | 3.63675 | 0.242990 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | − | 10.5470i | − | 0.700028i | −0.936744 | − | 0.350014i | \(-0.886177\pi\) | ||
0.936744 | − | 0.350014i | \(-0.113823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.9443 | −1.71445 | −0.857223 | − | 0.514945i | \(-0.827812\pi\) | ||||
−0.857223 | + | 0.514945i | \(0.827812\pi\) | |||||||
\(230\) | 0.239452 | − | 1.76055i | 0.0157890 | − | 0.116087i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.06808i | − | 0.529696i | ||||||
\(233\) | 11.4924i | 0.752894i | 0.926438 | + | 0.376447i | \(0.122854\pi\) | ||||
−0.926438 | + | 0.376447i | \(0.877146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9205 | + | 2.30135i | 1.10377 | + | 0.150124i | ||||
\(236\) | −8.06808 | −0.525188 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.2600i | 1.57254i | ||||||||
\(239\) | 14.6708 | 0.948974 | 0.474487 | − | 0.880262i | \(-0.342634\pi\) | ||||
0.474487 | + | 0.880262i | \(0.342634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6151 | −1.19910 | −0.599551 | − | 0.800337i | \(-0.704654\pi\) | ||||
−0.599551 | + | 0.800337i | \(0.704654\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.86267 | 0.183264 | ||||||||
\(245\) | −1.87620 | + | 13.7946i | −0.119866 | + | 0.881304i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.06808i | 0.513360i | ||||||||
\(248\) | 5.20541i | 0.330544i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.2735 | + | 4.41082i | 0.649753 | + | 0.278965i | ||||
\(251\) | 14.4108 | 0.909603 | 0.454801 | − | 0.890593i | \(-0.349710\pi\) | ||||
0.454801 | + | 0.890593i | \(0.349710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.58918i | − | 0.0999109i | ||||||
\(254\) | 4.79459 | 0.300839 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 0.123802i | − | 0.00772253i | −0.999993 | − | 0.00386126i | \(-0.998771\pi\) | ||
0.999993 | − | 0.00386126i | \(-0.00122908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.56866 | −0.0974720 | ||||||||
\(260\) | 2.21567 | + | 0.301352i | 0.137410 | + | 0.0186891i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 4.02052i | − | 0.248388i | ||||||
\(263\) | 5.27349i | 0.325178i | 0.986694 | + | 0.162589i | \(0.0519844\pi\) | ||||
−0.986694 | + | 0.162589i | \(0.948016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.76055 | + | 0.239452i | 0.108150 | + | 0.0147094i | ||||
\(266\) | −29.3416 | −1.79905 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.20541i | 0.317971i | ||||||||
\(269\) | 1.27349 | 0.0776463 | 0.0388231 | − | 0.999246i | \(-0.487639\pi\) | ||||
0.0388231 | + | 0.999246i | \(0.487639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.28702 | 0.381909 | 0.190955 | − | 0.981599i | \(-0.438842\pi\) | ||||
0.190955 | + | 0.981599i | \(0.438842\pi\) | |||||||
\(272\) | 6.67079i | 0.404476i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.2054 | −0.676944 | ||||||||
\(275\) | 9.63675 | + | 2.67079i | 0.581118 | + | 0.161055i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.9988i | − | 1.38187i | −0.722919 | − | 0.690933i | \(-0.757200\pi\) | ||
0.722919 | − | 0.690933i | \(-0.242800\pi\) | |||||||
\(278\) | 8.84216i | 0.530317i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.09594 | + | 8.05783i | −0.0654951 | + | 0.481547i | ||||
\(281\) | −10.3427 | −0.616996 | −0.308498 | − | 0.951225i | \(-0.599826\pi\) | ||||
−0.308498 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.0270i | − | 0.596046i | −0.954559 | − | 0.298023i | \(-0.903673\pi\) | ||
0.954559 | − | 0.298023i | \(-0.0963272\pi\) | |||||||
\(284\) | −9.46538 | −0.561667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | − | 24.9578i | − | 1.47321i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.4994 | −1.61761 | ||||||||
\(290\) | 17.8762 | + | 2.43134i | 1.04973 | + | 0.142773i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 6.00000i | − | 0.351123i | ||||||
\(293\) | − | 6.11565i | − | 0.357280i | −0.983914 | − | 0.178640i | \(-0.942830\pi\) | ||
0.983914 | − | 0.178640i | \(-0.0571698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.43134 | − | 17.8762i | 0.141558 | − | 1.04079i | ||||
\(296\) | −0.431337 | −0.0250709 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.794590 | 0.0459523 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1226 | −1.21749 | ||||||||
\(302\) | − | 7.05456i | − | 0.405944i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.06808 | −0.462736 | ||||||||
\(305\) | −0.862674 | + | 6.34274i | −0.0493966 | + | 0.363184i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.8627i | − | 0.962404i | −0.876610 | − | 0.481202i | \(-0.840200\pi\) | ||
0.876610 | − | 0.481202i | \(-0.159800\pi\) | |||||||
\(308\) | 7.27349i | 0.414446i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.5335 | − | 1.56866i | −0.655057 | − | 0.0890941i | ||||
\(311\) | −32.9988 | −1.87119 | −0.935596 | − | 0.353072i | \(-0.885137\pi\) | ||||
−0.935596 | + | 0.353072i | \(0.885137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.4654i | − | 1.43939i | −0.694291 | − | 0.719694i | \(-0.744282\pi\) | ||
0.694291 | − | 0.719694i | \(-0.255718\pi\) | |||||||
\(314\) | −0.0680837 | −0.00384218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.93192 | 0.108679 | ||||||||
\(317\) | − | 14.1362i | − | 0.793966i | −0.917826 | − | 0.396983i | \(-0.870057\pi\) | ||
0.917826 | − | 0.396983i | \(-0.129943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.1362 | 0.903452 | ||||||||
\(320\) | −0.301352 | + | 2.21567i | −0.0168461 | + | 0.123860i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.88972i | 0.161038i | ||||||||
\(323\) | − | 53.8205i | − | 2.99465i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.33539 | + | 4.81837i | −0.0740743 | + | 0.267275i | ||||
\(326\) | 7.65726 | 0.424097 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.86267i | − | 0.378928i | ||||||
\(329\) | −27.7729 | −1.53117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5199 | 1.01795 | 0.508974 | − | 0.860782i | \(-0.330025\pi\) | ||||
0.508974 | + | 0.860782i | \(0.330025\pi\) | |||||||
\(332\) | − | 2.06808i | − | 0.113501i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.82164 | 0.263828 | ||||||||
\(335\) | −11.5335 | − | 1.56866i | −0.630140 | − | 0.0857052i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2870i | 1.21405i | 0.794682 | + | 0.607026i | \(0.207637\pi\) | ||||
−0.794682 | + | 0.607026i | \(0.792363\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.7803 | − | 2.01026i | −0.801572 | − | 0.109022i | ||||
\(341\) | −10.4108 | −0.563777 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.81511i | 0.152002i | ||||||||
\(344\) | −5.80811 | −0.313153 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.7946 | −0.687841 | ||||||||
\(347\) | 31.5335i | 1.69280i | 0.532544 | + | 0.846402i | \(0.321236\pi\) | ||||
−0.532544 | + | 0.846402i | \(0.678764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.3551 | −1.73193 | −0.865964 | − | 0.500106i | \(-0.833295\pi\) | ||||
−0.865964 | + | 0.500106i | \(0.833295\pi\) | |||||||
\(350\) | −17.5232 | − | 4.85649i | −0.936655 | − | 0.259590i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000i | 0.106600i | ||||||||
\(353\) | 20.0270i | 1.06593i | 0.846137 | + | 0.532966i | \(0.178923\pi\) | ||||
−0.846137 | + | 0.532966i | \(0.821077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.85242 | − | 20.9721i | 0.151390 | − | 1.11309i | ||||
\(356\) | 8.06808 | 0.427608 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.84216i | 0.467322i | ||||||||
\(359\) | 22.9308 | 1.21024 | 0.605120 | − | 0.796135i | \(-0.293125\pi\) | ||||
0.605120 | + | 0.796135i | \(0.293125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.0940 | 2.42600 | ||||||||
\(362\) | − | 1.61623i | − | 0.0849471i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.63675 | −0.190617 | ||||||||
\(365\) | 13.2940 | + | 1.80811i | 0.695840 | + | 0.0946411i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.1362i | 1.78189i | 0.454108 | + | 0.890947i | \(0.349958\pi\) | ||||
−0.454108 | + | 0.890947i | \(0.650042\pi\) | |||||||
\(368\) | 0.794590i | 0.0414209i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.129984 | − | 0.955700i | 0.00675757 | − | 0.0496845i | ||||
\(371\) | −2.88972 | −0.150027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9988i | 1.39795i | 0.715148 | + | 0.698974i | \(0.246359\pi\) | ||||
−0.715148 | + | 0.698974i | \(0.753641\pi\) | |||||||
\(374\) | −13.3416 | −0.689877 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.63675 | −0.393835 | ||||||||
\(377\) | 8.06808i | 0.415527i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9308 | −0.664208 | −0.332104 | − | 0.943243i | \(-0.607759\pi\) | ||||
−0.332104 | + | 0.943243i | \(0.607759\pi\) | |||||||
\(380\) | 2.43134 | − | 17.8762i | 0.124725 | − | 0.917030i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.3416i | 1.09193i | ||||||||
\(383\) | − | 21.3621i | − | 1.09155i | −0.837931 | − | 0.545776i | \(-0.816235\pi\) | ||
0.837931 | − | 0.545776i | \(-0.183765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.1157 | − | 2.19189i | −0.821330 | − | 0.111709i | ||||
\(386\) | 5.61623 | 0.285859 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.6573i | 0.693343i | ||||||||
\(389\) | −29.4507 | −1.49321 | −0.746605 | − | 0.665268i | \(-0.768317\pi\) | ||||
−0.746605 | + | 0.665268i | \(0.768317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.30054 | −0.268060 | ||||||||
\(392\) | − | 6.22593i | − | 0.314457i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0205 | −0.706343 | ||||||||
\(395\) | −0.582188 | + | 4.28049i | −0.0292930 | + | 0.215375i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6832i | 0.837304i | 0.908147 | + | 0.418652i | \(0.137497\pi\) | ||||
−0.908147 | + | 0.418652i | \(0.862503\pi\) | |||||||
\(398\) | − | 15.7524i | − | 0.789596i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.81837 | − | 1.33539i | −0.240919 | − | 0.0667697i | ||||
\(401\) | 7.34158 | 0.366621 | 0.183310 | − | 0.983055i | \(-0.441319\pi\) | ||||
0.183310 | + | 0.983055i | \(0.441319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.20541i | − | 0.259300i | ||||||
\(404\) | −15.6843 | −0.780324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.3416 | −1.45620 | ||||||||
\(407\) | − | 0.862674i | − | 0.0427612i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.4777 | 1.75426 | 0.877131 | − | 0.480252i | \(-0.159455\pi\) | ||||
0.877131 | + | 0.480252i | \(0.159455\pi\) | |||||||
\(410\) | 15.2054 | + | 2.06808i | 0.750942 | + | 0.102135i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 15.3416i | − | 0.755825i | ||||||
\(413\) | 29.3416i | 1.44380i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.58219 | + | 0.623222i | 0.224931 | + | 0.0305928i | ||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 16.1362i | − | 0.789246i | ||||||
\(419\) | 0.883191 | 0.0431467 | 0.0215734 | − | 0.999767i | \(-0.493132\pi\) | ||||
0.0215734 | + | 0.999767i | \(0.493132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2859 | 1.32983 | 0.664916 | − | 0.746918i | \(-0.268467\pi\) | ||||
0.664916 | + | 0.746918i | \(0.268467\pi\) | |||||||
\(422\) | 1.70483i | 0.0829898i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.794590 | −0.0385887 | ||||||||
\(425\) | 8.90813 | − | 32.1424i | 0.432108 | − | 1.55913i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 10.4108i | − | 0.503815i | ||||||
\(428\) | 1.20541i | 0.0582657i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.75029 | − | 12.8689i | 0.0844065 | − | 0.620591i | ||||
\(431\) | −0.259969 | −0.0125223 | −0.00626113 | − | 0.999980i | \(-0.501993\pi\) | ||||
−0.00626113 | + | 0.999980i | \(0.501993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4654i | 0.839333i | 0.907678 | + | 0.419666i | \(0.137853\pi\) | ||||
−0.907678 | + | 0.419666i | \(0.862147\pi\) | |||||||
\(434\) | 18.9308 | 0.908705 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.80811 | 0.469724 | ||||||||
\(437\) | − | 6.41082i | − | 0.306671i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6843 | −0.844026 | −0.422013 | − | 0.906590i | \(-0.638676\pi\) | ||||
−0.422013 | + | 0.906590i | \(0.638676\pi\) | |||||||
\(440\) | −4.43134 | − | 0.602705i | −0.211256 | − | 0.0287328i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6.67079i | − | 0.317297i | ||||||
\(443\) | 32.4913i | 1.54371i | 0.635801 | + | 0.771853i | \(0.280670\pi\) | ||||
−0.635801 | + | 0.771853i | \(0.719330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.43134 | + | 17.8762i | −0.115256 | + | 0.847413i | ||||
\(446\) | −22.9513 | −1.08677 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.63675i | − | 0.171820i | ||||||
\(449\) | 35.0940 | 1.65619 | 0.828094 | − | 0.560590i | \(-0.189426\pi\) | ||||
0.828094 | + | 0.560590i | \(0.189426\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.7253 | 0.646301 | ||||||||
\(452\) | − | 4.00000i | − | 0.188144i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.5470 | −0.494995 | ||||||||
\(455\) | 1.09594 | − | 8.05783i | 0.0513786 | − | 0.377757i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5470i | 0.961148i | 0.876954 | + | 0.480574i | \(0.159572\pi\) | ||||
−0.876954 | + | 0.480574i | \(0.840428\pi\) | |||||||
\(458\) | 25.9443i | 1.21230i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.76055 | − | 0.239452i | −0.0820860 | − | 0.0111645i | ||||
\(461\) | 7.14969 | 0.332994 | 0.166497 | − | 0.986042i | \(-0.446754\pi\) | ||||
0.166497 | + | 0.986042i | \(0.446754\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.6832i | − | 1.05418i | −0.849811 | − | 0.527088i | \(-0.823284\pi\) | ||
0.849811 | − | 0.527088i | \(-0.176716\pi\) | |||||||
\(464\) | −8.06808 | −0.374551 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.4924 | 0.532376 | ||||||||
\(467\) | 25.2054i | 1.16637i | 0.812340 | + | 0.583184i | \(0.198193\pi\) | ||||
−0.812340 | + | 0.583184i | \(0.801807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.9308 | 0.874141 | ||||||||
\(470\) | 2.30135 | − | 16.9205i | 0.106153 | − | 0.780484i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.06808i | 0.371364i | ||||||||
\(473\) | − | 11.6162i | − | 0.534115i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.8750 | + | 10.7741i | 1.78371 | + | 0.494348i | ||||
\(476\) | 24.2600 | 1.11195 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 14.6708i | − | 0.671026i | ||||||
\(479\) | 4.01237 | 0.183330 | 0.0916648 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916648 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.431337 | 0.0196673 | ||||||||
\(482\) | 18.6151i | 0.847893i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −30.2600 | − | 4.11565i | −1.37403 | − | 0.186882i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | − | 2.86267i | − | 0.129587i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.7946 | + | 1.87620i | 0.623176 | + | 0.0847580i | ||||
\(491\) | 8.88319 | 0.400893 | 0.200446 | − | 0.979705i | \(-0.435761\pi\) | ||||
0.200446 | + | 0.979705i | \(0.435761\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 53.8205i | − | 2.42395i | ||||||
\(494\) | 8.06808 | 0.363000 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.20541 | 0.233730 | ||||||||
\(497\) | 34.4232i | 1.54409i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9988 | 0.492376 | 0.246188 | − | 0.969222i | \(-0.420822\pi\) | ||||
0.246188 | + | 0.969222i | \(0.420822\pi\) | |||||||
\(500\) | 4.41082 | − | 10.2735i | 0.197258 | − | 0.459445i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 14.4108i | − | 0.643186i | ||||||
\(503\) | 5.65726i | 0.252245i | 0.992015 | + | 0.126122i | \(0.0402532\pi\) | ||||
−0.992015 | + | 0.126122i | \(0.959747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.72651 | − | 34.7512i | 0.210327 | − | 1.54641i | ||||
\(506\) | −1.58918 | −0.0706477 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 4.79459i | − | 0.212726i | ||||||
\(509\) | −9.72535 | −0.431068 | −0.215534 | − | 0.976496i | \(-0.569149\pi\) | ||||
−0.215534 | + | 0.976496i | \(0.569149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.8205 | −0.965281 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.123802 | −0.00546065 | ||||||||
\(515\) | 33.9918 | + | 4.62322i | 1.49786 | + | 0.203724i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.2735i | − | 0.671727i | ||||||
\(518\) | 1.56866i | 0.0689231i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.301352 | − | 2.21567i | 0.0132152 | − | 0.0971635i | ||||
\(521\) | 28.7741 | 1.26062 | 0.630308 | − | 0.776346i | \(-0.282929\pi\) | ||||
0.630308 | + | 0.776346i | \(0.282929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.6139i | 1.64474i | 0.568952 | + | 0.822371i | \(0.307349\pi\) | ||||
−0.568952 | + | 0.822371i | \(0.692651\pi\) | |||||||
\(524\) | −4.02052 | −0.175637 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.27349 | 0.229935 | ||||||||
\(527\) | 34.7242i | 1.51261i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3686 | 0.972549 | ||||||||
\(530\) | 0.239452 | − | 1.76055i | 0.0104011 | − | 0.0764733i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 29.3416i | 1.27212i | ||||||||
\(533\) | 6.86267i | 0.297255i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.67079 | − | 0.363253i | −0.115468 | − | 0.0157048i | ||||
\(536\) | 5.20541 | 0.224839 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.27349i | − | 0.0549042i | ||||||
\(539\) | 12.4519 | 0.536339 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.8081 | 0.937604 | 0.468802 | − | 0.883303i | \(-0.344686\pi\) | ||||
0.468802 | + | 0.883303i | \(0.344686\pi\) | |||||||
\(542\) | − | 6.28702i | − | 0.270051i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.67079 | 0.286008 | ||||||||
\(545\) | −2.95570 | + | 21.7315i | −0.126608 | + | 0.930876i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.73887i | − | 0.202620i | −0.994855 | − | 0.101310i | \(-0.967697\pi\) | ||
0.994855 | − | 0.101310i | \(-0.0323033\pi\) | |||||||
\(548\) | 11.2054i | 0.478671i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.67079 | − | 9.63675i | 0.113883 | − | 0.410912i | ||||
\(551\) | 65.0940 | 2.77310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.02589i | − | 0.298771i | ||||||
\(554\) | −22.9988 | −0.977127 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.84216 | 0.374991 | ||||||||
\(557\) | 6.74702i | 0.285881i | 0.989731 | + | 0.142940i | \(0.0456557\pi\) | ||||
−0.989731 | + | 0.142940i | \(0.954344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.80811 | 0.245657 | ||||||||
\(560\) | 8.05783 | + | 1.09594i | 0.340505 | + | 0.0463120i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.3427i | 0.436282i | ||||||||
\(563\) | − | 41.9443i | − | 1.76774i | −0.467732 | − | 0.883870i | \(-0.654929\pi\) | ||
0.467732 | − | 0.883870i | \(-0.345071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.86267 | + | 1.20541i | 0.372855 | + | 0.0507120i | ||||
\(566\) | −10.0270 | −0.421468 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46538i | 0.397158i | ||||||||
\(569\) | −7.95243 | −0.333383 | −0.166692 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166692 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5265 | −0.607914 | −0.303957 | − | 0.952686i | \(-0.598308\pi\) | ||||
−0.303957 | + | 0.952686i | \(0.598308\pi\) | |||||||
\(572\) | − | 2.00000i | − | 0.0836242i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.9578 | −1.04172 | ||||||||
\(575\) | 1.06109 | − | 3.82863i | 0.0442506 | − | 0.159665i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.17836i | 0.215578i | 0.994174 | + | 0.107789i | \(0.0343771\pi\) | ||||
−0.994174 | + | 0.107789i | \(0.965623\pi\) | |||||||
\(578\) | 27.4994i | 1.14383i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.43134 | − | 17.8762i | 0.100956 | − | 0.742269i | ||||
\(581\) | −7.52110 | −0.312028 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.58918i | − | 0.0658171i | ||||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.11565 | −0.252635 | ||||||||
\(587\) | 22.8897i | 0.944760i | 0.881395 | + | 0.472380i | \(0.156605\pi\) | ||||
−0.881395 | + | 0.472380i | \(0.843395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.9977 | −1.73048 | ||||||||
\(590\) | −17.8762 | − | 2.43134i | −0.735951 | − | 0.100097i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.431337i | 0.0177278i | ||||||||
\(593\) | − | 14.3427i | − | 0.588986i | −0.955654 | − | 0.294493i | \(-0.904849\pi\) | ||
0.955654 | − | 0.294493i | \(-0.0951507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.31080 | + | 53.7520i | −0.299714 | + | 2.20362i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 0.794590i | − | 0.0324932i | ||||||
\(599\) | 5.63021 | 0.230044 | 0.115022 | − | 0.993363i | \(-0.463306\pi\) | ||||
0.115022 | + | 0.993363i | \(0.463306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3211 | −0.461796 | −0.230898 | − | 0.972978i | \(-0.574166\pi\) | ||||
−0.230898 | + | 0.972978i | \(0.574166\pi\) | |||||||
\(602\) | 21.1226i | 0.860895i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.05456 | −0.287046 | ||||||||
\(605\) | −2.10947 | + | 15.5097i | −0.0857620 | + | 0.630558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0259i | 1.01577i | 0.861425 | + | 0.507885i | \(0.169572\pi\) | ||||
−0.861425 | + | 0.507885i | \(0.830428\pi\) | |||||||
\(608\) | 8.06808i | 0.327204i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.34274 | + | 0.862674i | 0.256810 | + | 0.0349286i | ||||
\(611\) | 7.63675 | 0.308950 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4507i | 1.02794i | 0.857807 | + | 0.513972i | \(0.171826\pi\) | ||||
−0.857807 | + | 0.513972i | \(0.828174\pi\) | |||||||
\(614\) | −16.8627 | −0.680522 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.27349 | 0.293057 | ||||||||
\(617\) | − | 15.6843i | − | 0.631427i | −0.948855 | − | 0.315713i | \(-0.897756\pi\) | ||
0.948855 | − | 0.315713i | \(-0.102244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.5880 | 1.79214 | 0.896072 | − | 0.443909i | \(-0.146409\pi\) | ||||
0.896072 | + | 0.443909i | \(0.146409\pi\) | |||||||
\(620\) | −1.56866 | + | 11.5335i | −0.0629990 | + | 0.463195i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.9988i | 1.32313i | ||||||||
\(623\) | − | 29.3416i | − | 1.17555i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.4334 | + | 12.8689i | 0.857338 | + | 0.514754i | ||||
\(626\) | −25.4654 | −1.01780 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.0680837i | 0.00271683i | ||||||||
\(629\) | −2.87736 | −0.114728 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.8070 | −1.54488 | −0.772440 | − | 0.635087i | \(-0.780964\pi\) | ||||
−0.772440 | + | 0.635087i | \(0.780964\pi\) | |||||||
\(632\) | − | 1.93192i | − | 0.0768475i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.1362 | −0.561419 | ||||||||
\(635\) | 10.6232 | + | 1.44486i | 0.421570 | + | 0.0573376i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.22593i | 0.246680i | ||||||||
\(638\) | − | 16.1362i | − | 0.638837i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.21567 | + | 0.301352i | 0.0875820 | + | 0.0119120i | ||||
\(641\) | 8.27465 | 0.326829 | 0.163415 | − | 0.986557i | \(-0.447749\pi\) | ||||
0.163415 | + | 0.986557i | \(0.447749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.16322i | − | 0.243054i | −0.992588 | − | 0.121527i | \(-0.961221\pi\) | ||
0.992588 | − | 0.121527i | \(-0.0387790\pi\) | |||||||
\(644\) | 2.88972 | 0.113871 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −53.8205 | −2.11754 | ||||||||
\(647\) | 7.24644i | 0.284887i | 0.989803 | + | 0.142444i | \(0.0454959\pi\) | ||||
−0.989803 | + | 0.142444i | \(0.954504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.1362 | −0.633400 | ||||||||
\(650\) | 4.81837 | + | 1.33539i | 0.188992 | + | 0.0523785i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.65726i | − | 0.299882i | ||||||
\(653\) | 5.27349i | 0.206368i | 0.994662 | + | 0.103184i | \(0.0329030\pi\) | ||||
−0.994662 | + | 0.103184i | \(0.967097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.21159 | − | 8.90813i | 0.0473408 | − | 0.348070i | ||||
\(656\) | −6.86267 | −0.267942 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.7729i | 1.08270i | ||||||||
\(659\) | −18.6832 | −0.727792 | −0.363896 | − | 0.931440i | \(-0.618554\pi\) | ||||
−0.363896 | + | 0.931440i | \(0.618554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3145 | 0.595666 | 0.297833 | − | 0.954618i | \(-0.403736\pi\) | ||||
0.297833 | + | 0.954618i | \(0.403736\pi\) | |||||||
\(662\) | − | 18.5199i | − | 0.719798i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.06808 | −0.0802572 | ||||||||
\(665\) | −65.0112 | − | 8.84216i | −2.52103 | − | 0.342884i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.41082i | − | 0.248228i | ||||||
\(668\) | − | 4.82164i | − | 0.186555i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.56866 | + | 11.5335i | −0.0606027 | + | 0.445577i | ||||
\(671\) | 5.72535 | 0.221025 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.2870i | 0.396535i | 0.980148 | + | 0.198268i | \(0.0635315\pi\) | ||||
−0.980148 | + | 0.198268i | \(0.936468\pi\) | |||||||
\(674\) | 22.2870 | 0.858464 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − | 9.88856i | − | 0.380048i | −0.981779 | − | 0.190024i | \(-0.939143\pi\) | ||
0.981779 | − | 0.190024i | \(-0.0608566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49.6680 | 1.90608 | ||||||||
\(680\) | −2.01026 | + | 14.7803i | −0.0770899 | + | 0.566797i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.4108i | 0.398651i | ||||||||
\(683\) | 2.06808i | 0.0791330i | 0.999217 | + | 0.0395665i | \(0.0125977\pi\) | ||||
−0.999217 | + | 0.0395665i | \(0.987402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.8275 | − | 3.37678i | −0.948609 | − | 0.129020i | ||||
\(686\) | 2.81511 | 0.107481 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.80811i | 0.221432i | ||||||||
\(689\) | 0.794590 | 0.0302715 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8205 | 0.601839 | 0.300920 | − | 0.953649i | \(-0.402706\pi\) | ||||
0.300920 | + | 0.953649i | \(0.402706\pi\) | |||||||
\(692\) | 12.7946i | 0.486377i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.5335 | 1.19699 | ||||||||
\(695\) | −2.66461 | + | 19.5913i | −0.101074 | + | 0.743140i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 45.7794i | − | 1.73402i | ||||||
\(698\) | 32.3551i | 1.22466i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.85649 | + | 17.5232i | −0.183558 | + | 0.662315i | ||||
\(701\) | −14.6561 | −0.553553 | −0.276777 | − | 0.960934i | \(-0.589266\pi\) | ||||
−0.276777 | + | 0.960934i | \(0.589266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.48006i | − | 0.131253i | ||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.0270 | 0.753728 | ||||||||
\(707\) | 57.0399i | 2.14521i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3145 | 0.875595 | 0.437798 | − | 0.899073i | \(-0.355759\pi\) | ||||
0.437798 | + | 0.899073i | \(0.355759\pi\) | |||||||
\(710\) | −20.9721 | − | 2.85242i | −0.787070 | − | 0.107049i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 8.06808i | − | 0.302364i | ||||||
\(713\) | 4.13617i | 0.154901i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.43134 | + | 0.602705i | 0.165723 | + | 0.0225399i | ||||
\(716\) | 8.84216 | 0.330447 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 22.9308i | − | 0.855768i | ||||||
\(719\) | −29.3416 | −1.09426 | −0.547128 | − | 0.837049i | \(-0.684279\pi\) | ||||
−0.547128 | + | 0.837049i | \(0.684279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.7934 | −2.07786 | ||||||||
\(722\) | − | 46.0940i | − | 1.71544i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.61623 | −0.0600667 | ||||||||
\(725\) | 38.8750 | + | 10.7741i | 1.44378 | + | 0.400139i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.4530i | 0.573121i | 0.958062 | + | 0.286560i | \(0.0925119\pi\) | ||||
−0.958062 | + | 0.286560i | \(0.907488\pi\) | |||||||
\(728\) | 3.63675i | 0.134787i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.80811 | − | 13.2940i | 0.0669213 | − | 0.492033i | ||||
\(731\) | −38.7447 | −1.43302 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2108i | 1.11586i | 0.829888 | + | 0.557930i | \(0.188404\pi\) | ||||
−0.829888 | + | 0.557930i | \(0.811596\pi\) | |||||||
\(734\) | 34.1362 | 1.25999 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.794590 | 0.0292890 | ||||||||
\(737\) | 10.4108i | 0.383487i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5880 | 0.904485 | 0.452242 | − | 0.891895i | \(-0.350624\pi\) | ||||
0.452242 | + | 0.891895i | \(0.350624\pi\) | |||||||
\(740\) | −0.955700 | − | 0.129984i | −0.0351322 | − | 0.00477832i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.88972i | 0.106085i | ||||||||
\(743\) | 48.0452i | 1.76261i | 0.472549 | + | 0.881305i | \(0.343334\pi\) | ||||
−0.472549 | + | 0.881305i | \(0.656666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.9988 | 0.988498 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.3416i | 0.487816i | ||||||||
\(749\) | 4.38377 | 0.160179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.90371 | −0.178939 | −0.0894694 | − | 0.995990i | \(-0.528517\pi\) | ||||
−0.0894694 | + | 0.995990i | \(0.528517\pi\) | |||||||
\(752\) | 7.63675i | 0.278484i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.06808 | 0.293822 | ||||||||
\(755\) | 2.12591 | − | 15.6306i | 0.0773697 | − | 0.568854i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.3416i | − | 0.412217i | −0.978529 | − | 0.206108i | \(-0.933920\pi\) | ||
0.978529 | − | 0.206108i | \(-0.0660799\pi\) | |||||||
\(758\) | 12.9308i | 0.469666i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.8762 | − | 2.43134i | −0.648438 | − | 0.0881939i | ||||
\(761\) | −10.3427 | −0.374924 | −0.187462 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187462 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 35.6696i | − | 1.29133i | ||||||
\(764\) | 21.3416 | 0.772111 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.3621 | −0.771844 | ||||||||
\(767\) | − | 8.06808i | − | 0.291322i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6843 | −0.998322 | −0.499161 | − | 0.866509i | \(-0.666358\pi\) | ||||
−0.499161 | + | 0.866509i | \(0.666358\pi\) | |||||||
\(770\) | −2.19189 | + | 16.1157i | −0.0789901 | + | 0.580768i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 5.61623i | − | 0.202133i | ||||||
\(773\) | − | 12.2952i | − | 0.442227i | −0.975248 | − | 0.221113i | \(-0.929031\pi\) | ||
0.975248 | − | 0.221113i | \(-0.0709690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.0816 | − | 6.95127i | −0.900958 | − | 0.249697i | ||||
\(776\) | 13.6573 | 0.490267 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.4507i | 1.05586i | ||||||||
\(779\) | 55.3686 | 1.98379 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.9308 | −0.677396 | ||||||||
\(782\) | 5.30054i | 0.189547i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.22593 | −0.222355 | ||||||||
\(785\) | −0.150851 | − | 0.0205172i | −0.00538410 | − | 0.000732290i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 43.5048i | − | 1.55078i | −0.631484 | − | 0.775389i | \(-0.717554\pi\) | ||
0.631484 | − | 0.775389i | \(-0.282446\pi\) | |||||||
\(788\) | 14.0205i | 0.499460i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.28049 | + | 0.582188i | 0.152293 | + | 0.0207133i | ||||
\(791\) | −14.5470 | −0.517231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.86267i | 0.101657i | ||||||||
\(794\) | 16.6832 | 0.592063 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.7524 | −0.558329 | ||||||||
\(797\) | − | 12.9718i | − | 0.459484i | −0.973252 | − | 0.229742i | \(-0.926212\pi\) | ||
0.973252 | − | 0.229742i | \(-0.0737883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.9431 | −1.80224 | ||||||||
\(800\) | −1.33539 | + | 4.81837i | −0.0472133 | + | 0.170355i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 7.34158i | − | 0.259240i | ||||||
\(803\) | − | 12.0000i | − | 0.423471i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.870825 | + | 6.40267i | −0.0306926 | + | 0.225664i | ||||
\(806\) | −5.20541 | −0.183353 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.6843i | 0.551772i | ||||||||
\(809\) | 8.73304 | 0.307037 | 0.153519 | − | 0.988146i | \(-0.450939\pi\) | ||||
0.153519 | + | 0.988146i | \(0.450939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.3134 | 1.62628 | 0.813141 | − | 0.582067i | \(-0.197756\pi\) | ||||
0.813141 | + | 0.582067i | \(0.197756\pi\) | |||||||
\(812\) | 29.3416i | 1.02969i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.862674 | −0.0302367 | ||||||||
\(815\) | 16.9660 | + | 2.30754i | 0.594292 | + | 0.0808294i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 46.8604i | − | 1.63944i | ||||||
\(818\) | − | 35.4777i | − | 1.24045i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.06808 | − | 15.2054i | 0.0722206 | − | 0.530996i | ||||
\(821\) | −31.9172 | −1.11392 | −0.556960 | − | 0.830540i | \(-0.688032\pi\) | ||||
−0.556960 | + | 0.830540i | \(0.688032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6.42480i | − | 0.223955i | −0.993711 | − | 0.111977i | \(-0.964282\pi\) | ||
0.993711 | − | 0.111977i | \(-0.0357184\pi\) | |||||||
\(824\) | −15.3416 | −0.534449 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.3416 | 1.02092 | ||||||||
\(827\) | − | 38.7242i | − | 1.34657i | −0.739382 | − | 0.673286i | \(-0.764882\pi\) | ||
0.739382 | − | 0.673286i | \(-0.235118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3427 | 0.637070 | 0.318535 | − | 0.947911i | \(-0.396809\pi\) | ||||
0.318535 | + | 0.947911i | \(0.396809\pi\) | |||||||
\(830\) | 0.623222 | − | 4.58219i | 0.0216324 | − | 0.159050i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | − | 41.5318i | − | 1.43899i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6832 | + | 1.45301i | 0.369706 | + | 0.0502836i | ||||
\(836\) | −16.1362 | −0.558081 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 0.883191i | − | 0.0305093i | ||||||
\(839\) | −12.6561 | −0.436937 | −0.218469 | − | 0.975844i | \(-0.570106\pi\) | ||||
−0.218469 | + | 0.975844i | \(0.570106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.0940 | 1.24462 | ||||||||
\(842\) | − | 27.2859i | − | 0.940333i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.70483 | 0.0586827 | ||||||||
\(845\) | −0.301352 | + | 2.21567i | −0.0103668 | + | 0.0762213i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25.4572i | − | 0.874721i | ||||||
\(848\) | 0.794590i | 0.0272863i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −32.1424 | − | 8.90813i | −1.10247 | − | 0.305546i | ||||
\(851\) | −0.342736 | −0.0117488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.7988i | 1.53388i | 0.641718 | + | 0.766941i | \(0.278222\pi\) | ||||
−0.641718 | + | 0.766941i | \(0.721778\pi\) | |||||||
\(854\) | −10.4108 | −0.356251 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.20541 | 0.0412001 | ||||||||
\(857\) | 46.8193i | 1.59932i | 0.600455 | + | 0.799659i | \(0.294986\pi\) | ||||
−0.600455 | + | 0.799659i | \(0.705014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8638 | 0.814223 | 0.407112 | − | 0.913378i | \(-0.366536\pi\) | ||||
0.407112 | + | 0.913378i | \(0.366536\pi\) | |||||||
\(860\) | −12.8689 | − | 1.75029i | −0.438824 | − | 0.0596844i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.259969i | 0.00885458i | ||||||||
\(863\) | 12.2271i | 0.416215i | 0.978106 | + | 0.208107i | \(0.0667304\pi\) | ||||
−0.978106 | + | 0.208107i | \(0.933270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.3486 | − | 3.85568i | −0.963880 | − | 0.131097i | ||||
\(866\) | 17.4654 | 0.593498 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 18.9308i | − | 0.642552i | ||||||
\(869\) | 3.86383 | 0.131072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.20541 | −0.176379 | ||||||||
\(872\) | − | 9.80811i | − | 0.332145i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.41082 | −0.216849 | ||||||||
\(875\) | −37.3621 | − | 16.0410i | −1.26307 | − | 0.542286i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.336204i | − | 0.0113528i | −0.999984 | − | 0.00567640i | \(-0.998193\pi\) | ||
0.999984 | − | 0.00567640i | \(-0.00180686\pi\) | |||||||
\(878\) | 17.6843i | 0.596817i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.602705 | + | 4.43134i | −0.0203172 | + | 0.149380i | ||||
\(881\) | 41.0464 | 1.38289 | 0.691444 | − | 0.722430i | \(-0.256975\pi\) | ||||
0.691444 | + | 0.722430i | \(0.256975\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 40.0534i | − | 1.34790i | −0.738775 | − | 0.673952i | \(-0.764595\pi\) | ||
0.738775 | − | 0.673952i | \(-0.235405\pi\) | |||||||
\(884\) | −6.67079 | −0.224363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.4913 | 1.09157 | ||||||||
\(887\) | − | 28.7242i | − | 0.964464i | −0.876044 | − | 0.482232i | \(-0.839826\pi\) | ||
0.876044 | − | 0.482232i | \(-0.160174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4367 | −0.584808 | ||||||||
\(890\) | 17.8762 | + | 2.43134i | 0.599212 | + | 0.0814986i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.9513i | 0.768466i | ||||||||
\(893\) | − | 61.6139i | − | 2.06183i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.66461 | + | 19.5913i | −0.0890679 | + | 0.654865i | ||||
\(896\) | −3.63675 | −0.121495 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 35.0940i | − | 1.17110i | ||||||
\(899\) | −41.9977 | −1.40070 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.30054 | −0.176587 | ||||||||
\(902\) | − | 13.7253i | − | 0.457004i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | 0.487055 | − | 3.58103i | 0.0161902 | − | 0.119037i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.7636i | 1.61917i | 0.587003 | + | 0.809584i | \(0.300308\pi\) | ||||
−0.587003 | + | 0.809584i | \(0.699692\pi\) | |||||||
\(908\) | 10.5470i | 0.350014i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.05783 | − | 1.09594i | −0.267114 | − | 0.0363301i | ||||
\(911\) | −15.4801 | −0.512877 | −0.256439 | − | 0.966561i | \(-0.582549\pi\) | ||||
−0.256439 | + | 0.966561i | \(0.582549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.13617i | − | 0.136887i | ||||||
\(914\) | 20.5470 | 0.679634 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.9443 | 0.857223 | ||||||||
\(917\) | 14.6216i | 0.482848i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.8615 | −1.51283 | −0.756416 | − | 0.654091i | \(-0.773051\pi\) | ||||
−0.756416 | + | 0.654091i | \(0.773051\pi\) | |||||||
\(920\) | −0.239452 | + | 1.76055i | −0.00789449 | + | 0.0580436i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 7.14969i | − | 0.235463i | ||||||
\(923\) | − | 9.46538i | − | 0.311557i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.576005 | − | 2.07834i | 0.0189389 | − | 0.0683355i | ||||
\(926\) | −22.6832 | −0.745415 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.06808i | 0.264848i | ||||||||
\(929\) | −26.9168 | −0.883111 | −0.441555 | − | 0.897234i | \(-0.645573\pi\) | ||||
−0.441555 | + | 0.897234i | \(0.645573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.2313 | 1.64626 | ||||||||
\(932\) | − | 11.4924i | − | 0.376447i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.2054 | 0.824746 | ||||||||
\(935\) | −29.5605 | − | 4.02052i | −0.966732 | − | 0.131485i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90371i | 0.160197i | 0.996787 | + | 0.0800986i | \(0.0255235\pi\) | ||||
−0.996787 | + | 0.0800986i | \(0.974476\pi\) | |||||||
\(938\) | − | 18.9308i | − | 0.618111i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.9205 | − | 2.30135i | −0.551886 | − | 0.0750618i | ||||
\(941\) | 46.6004 | 1.51913 | 0.759565 | − | 0.650432i | \(-0.225412\pi\) | ||||
0.759565 | + | 0.650432i | \(0.225412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.45301i | − | 0.177575i | ||||||
\(944\) | 8.06808 | 0.262594 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.6162 | −0.377676 | ||||||||
\(947\) | 27.7524i | 0.901832i | 0.892566 | + | 0.450916i | \(0.148903\pi\) | ||||
−0.892566 | + | 0.450916i | \(0.851097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 10.7741 | − | 38.8750i | 0.349557 | − | 1.26127i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 24.2600i | − | 0.786270i | ||||||
\(953\) | 14.9725i | 0.485007i | 0.970151 | + | 0.242503i | \(0.0779685\pi\) | ||||
−0.970151 | + | 0.242503i | \(0.922031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.43134 | + | 47.2859i | −0.208113 | + | 1.53013i | ||||
\(956\) | −14.6708 | −0.474487 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 4.01237i | − | 0.129634i | ||||||
\(959\) | 40.7512 | 1.31593 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.90371 | −0.125926 | ||||||||
\(962\) | − | 0.431337i | − | 0.0139069i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.6151 | 0.599551 | ||||||||
\(965\) | 12.4437 | + | 1.69246i | 0.400577 | + | 0.0544824i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.5946i | 1.69133i | 0.533717 | + | 0.845663i | \(0.320795\pi\) | ||||
−0.533717 | + | 0.845663i | \(0.679205\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.11565 | + | 30.2600i | −0.132146 | + | 0.971589i | ||||
\(971\) | 15.5253 | 0.498231 | 0.249115 | − | 0.968474i | \(-0.419860\pi\) | ||||
0.249115 | + | 0.968474i | \(0.419860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 32.1567i | − | 1.03090i | ||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.86267 | −0.0916320 | ||||||||
\(977\) | − | 47.5729i | − | 1.52199i | −0.648757 | − | 0.760996i | \(-0.724711\pi\) | ||
0.648757 | − | 0.760996i | \(-0.275289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.1362 | 0.515714 | ||||||||
\(980\) | 1.87620 | − | 13.7946i | 0.0599330 | − | 0.440652i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 8.88319i | − | 0.283474i | ||||||
\(983\) | 37.3211i | 1.19036i | 0.803594 | + | 0.595178i | \(0.202919\pi\) | ||||
−0.803594 | + | 0.595178i | \(0.797081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.0648 | − | 4.22512i | −0.989807 | − | 0.134623i | ||||
\(986\) | −53.8205 | −1.71399 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.06808i | − | 0.256680i | ||||||
\(989\) | −4.61507 | −0.146751 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.5060 | 0.714925 | 0.357463 | − | 0.933927i | \(-0.383642\pi\) | ||||
0.357463 | + | 0.933927i | \(0.383642\pi\) | |||||||
\(992\) | − | 5.20541i | − | 0.165272i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 34.4232 | 1.09184 | ||||||||
\(995\) | 4.74702 | − | 34.9021i | 0.150491 | − | 1.10647i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4108i | 0.773098i | 0.922269 | + | 0.386549i | \(0.126333\pi\) | ||||
−0.922269 | + | 0.386549i | \(0.873667\pi\) | |||||||
\(998\) | − | 10.9988i | − | 0.348162i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1170.2.e.f.469.2 | 6 | ||
3.2 | odd | 2 | 130.2.b.a.79.5 | yes | 6 | ||
5.2 | odd | 4 | 5850.2.a.cs.1.1 | 3 | |||
5.3 | odd | 4 | 5850.2.a.cp.1.3 | 3 | |||
5.4 | even | 2 | inner | 1170.2.e.f.469.5 | 6 | ||
12.11 | even | 2 | 1040.2.d.b.209.4 | 6 | |||
15.2 | even | 4 | 650.2.a.n.1.2 | 3 | |||
15.8 | even | 4 | 650.2.a.o.1.2 | 3 | |||
15.14 | odd | 2 | 130.2.b.a.79.2 | ✓ | 6 | ||
39.5 | even | 4 | 1690.2.c.d.1689.3 | 6 | |||
39.8 | even | 4 | 1690.2.c.a.1689.3 | 6 | |||
39.38 | odd | 2 | 1690.2.b.a.339.2 | 6 | |||
60.23 | odd | 4 | 5200.2.a.cf.1.2 | 3 | |||
60.47 | odd | 4 | 5200.2.a.ce.1.2 | 3 | |||
60.59 | even | 2 | 1040.2.d.b.209.3 | 6 | |||
195.38 | even | 4 | 8450.2.a.bs.1.2 | 3 | |||
195.44 | even | 4 | 1690.2.c.a.1689.4 | 6 | |||
195.77 | even | 4 | 8450.2.a.cc.1.2 | 3 | |||
195.164 | even | 4 | 1690.2.c.d.1689.4 | 6 | |||
195.194 | odd | 2 | 1690.2.b.a.339.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.b.a.79.2 | ✓ | 6 | 15.14 | odd | 2 | ||
130.2.b.a.79.5 | yes | 6 | 3.2 | odd | 2 | ||
650.2.a.n.1.2 | 3 | 15.2 | even | 4 | |||
650.2.a.o.1.2 | 3 | 15.8 | even | 4 | |||
1040.2.d.b.209.3 | 6 | 60.59 | even | 2 | |||
1040.2.d.b.209.4 | 6 | 12.11 | even | 2 | |||
1170.2.e.f.469.2 | 6 | 1.1 | even | 1 | trivial | ||
1170.2.e.f.469.5 | 6 | 5.4 | even | 2 | inner | ||
1690.2.b.a.339.2 | 6 | 39.38 | odd | 2 | |||
1690.2.b.a.339.5 | 6 | 195.194 | odd | 2 | |||
1690.2.c.a.1689.3 | 6 | 39.8 | even | 4 | |||
1690.2.c.a.1689.4 | 6 | 195.44 | even | 4 | |||
1690.2.c.d.1689.3 | 6 | 39.5 | even | 4 | |||
1690.2.c.d.1689.4 | 6 | 195.164 | even | 4 | |||
5200.2.a.ce.1.2 | 3 | 60.47 | odd | 4 | |||
5200.2.a.cf.1.2 | 3 | 60.23 | odd | 4 | |||
5850.2.a.cp.1.3 | 3 | 5.3 | odd | 4 | |||
5850.2.a.cs.1.1 | 3 | 5.2 | odd | 4 | |||
8450.2.a.bs.1.2 | 3 | 195.38 | even | 4 | |||
8450.2.a.cc.1.2 | 3 | 195.77 | even | 4 |