Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.b.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 0.866025 | + | 1.50000i | 0.261116 | + | 0.452267i | 0.966539 | − | 0.256520i | \(-0.0825760\pi\) |
−0.705422 | + | 0.708787i | \(0.749243\pi\) | |||||||
\(12\) | −0.866025 | + | 1.50000i | −0.250000 | + | 0.433013i | ||||
\(13\) | 6.00000 | − | 3.46410i | 1.66410 | − | 0.960769i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | −0.866025 | − | 0.500000i | −0.231455 | − | 0.133631i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −2.59808 | + | 1.50000i | −0.612372 | + | 0.353553i | ||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | −0.866025 | − | 1.50000i | −0.188982 | − | 0.327327i | ||||
\(22\) | 1.50000 | − | 0.866025i | 0.319801 | − | 0.184637i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −3.46410 | − | 6.00000i | −0.679366 | − | 1.17670i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −0.500000 | + | 0.866025i | −0.0944911 | + | 0.163663i | ||||
\(29\) | −5.19615 | −0.964901 | −0.482451 | − | 0.875923i | \(-0.660253\pi\) | ||||
−0.482451 | + | 0.875923i | \(0.660253\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | −5.50000 | − | 0.866025i | −0.987829 | − | 0.155543i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | −3.00000 | − | 1.73205i | −0.493197 | − | 0.284747i | 0.232703 | − | 0.972548i | \(-0.425243\pi\) |
−0.725900 | + | 0.687800i | \(0.758576\pi\) | |||||||
\(38\) | −1.73205 | − | 1.00000i | −0.280976 | − | 0.162221i | ||||
\(39\) | − | 12.0000i | − | 1.92154i | ||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | −1.50000 | + | 0.866025i | −0.231455 | + | 0.133631i | ||||
\(43\) | 3.00000 | + | 1.73205i | 0.457496 | + | 0.264135i | 0.710991 | − | 0.703201i | \(-0.248247\pi\) |
−0.253495 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(44\) | −0.866025 | − | 1.50000i | −0.130558 | − | 0.226134i | ||||
\(45\) | −2.59808 | − | 1.50000i | −0.387298 | − | 0.223607i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0.866025 | − | 1.50000i | 0.125000 | − | 0.216506i | ||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | + | 3.46410i | −0.832050 | + | 0.480384i | ||||
\(53\) | 0.866025 | + | 1.50000i | 0.118958 | + | 0.206041i | 0.919355 | − | 0.393429i | \(-0.128711\pi\) |
−0.800397 | + | 0.599470i | \(0.795378\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 1.50000 | + | 0.866025i | 0.202260 | + | 0.116775i | ||||
\(56\) | 0.866025 | + | 0.500000i | 0.115728 | + | 0.0668153i | ||||
\(57\) | −1.73205 | − | 3.00000i | −0.229416 | − | 0.397360i | ||||
\(58\) | 5.19615i | 0.682288i | ||||||||
\(59\) | −2.59808 | − | 1.50000i | −0.338241 | − | 0.195283i | 0.321253 | − | 0.946993i | \(-0.395896\pi\) |
−0.659494 | + | 0.751710i | \(0.729229\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | − | 3.46410i | − | 0.443533i | −0.975100 | − | 0.221766i | \(-0.928818\pi\) | ||
0.975100 | − | 0.221766i | \(-0.0711822\pi\) | |||||||
\(62\) | −0.866025 | + | 5.50000i | −0.109985 | + | 0.698501i | ||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.46410 | − | 6.00000i | 0.429669 | − | 0.744208i | ||||
\(66\) | − | 3.00000i | − | 0.369274i | ||||||
\(67\) | −2.00000 | − | 3.46410i | −0.244339 | − | 0.423207i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
−0.961946 | + | 0.273241i | \(0.911904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(72\) | 2.59808 | − | 1.50000i | 0.306186 | − | 0.176777i | ||||
\(73\) | 6.00000 | − | 3.46410i | 0.702247 | − | 0.405442i | −0.105937 | − | 0.994373i | \(-0.533784\pi\) |
0.808184 | + | 0.588930i | \(0.200451\pi\) | |||||||
\(74\) | −1.73205 | + | 3.00000i | −0.201347 | + | 0.348743i | ||||
\(75\) | −0.866025 | − | 1.50000i | −0.100000 | − | 0.173205i | ||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 1.73205 | 0.197386 | ||||||||
\(78\) | −12.0000 | −1.35873 | ||||||||
\(79\) | 9.00000 | + | 5.19615i | 1.01258 | + | 0.584613i | 0.911946 | − | 0.410311i | \(-0.134580\pi\) |
0.100633 | + | 0.994924i | \(0.467913\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.06218 | + | 10.5000i | 0.665410 | + | 1.15252i | 0.979174 | + | 0.203024i | \(0.0650768\pi\) |
−0.313763 | + | 0.949501i | \(0.601590\pi\) | |||||||
\(84\) | 0.866025 | + | 1.50000i | 0.0944911 | + | 0.163663i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.73205 | − | 3.00000i | 0.186772 | − | 0.323498i | ||||
\(87\) | −4.50000 | + | 7.79423i | −0.482451 | + | 0.835629i | ||||
\(88\) | −1.50000 | + | 0.866025i | −0.159901 | + | 0.0923186i | ||||
\(89\) | −13.8564 | −1.46878 | −0.734388 | − | 0.678730i | \(-0.762531\pi\) | ||||
−0.734388 | + | 0.678730i | \(0.762531\pi\) | |||||||
\(90\) | −1.50000 | + | 2.59808i | −0.158114 | + | 0.273861i | ||||
\(91\) | − | 6.92820i | − | 0.726273i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.06218 | + | 7.50000i | −0.628619 | + | 0.777714i | ||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | − | 2.00000i | − | 0.205196i | ||||||
\(96\) | −1.50000 | − | 0.866025i | −0.153093 | − | 0.0883883i | ||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 5.19615 | − | 3.00000i | 0.524891 | − | 0.303046i | ||||
\(99\) | 2.59808 | − | 4.50000i | 0.261116 | − | 0.452267i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | − | 15.0000i | − | 1.49256i | −0.665635 | − | 0.746278i | \(-0.731839\pi\) | ||
0.665635 | − | 0.746278i | \(-0.268161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50000 | + | 4.33013i | 0.246332 | + | 0.426660i | 0.962505 | − | 0.271263i | \(-0.0874412\pi\) |
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(104\) | 3.46410 | + | 6.00000i | 0.339683 | + | 0.588348i | ||||
\(105\) | −1.50000 | − | 0.866025i | −0.146385 | − | 0.0845154i | ||||
\(106\) | 1.50000 | − | 0.866025i | 0.145693 | − | 0.0841158i | ||||
\(107\) | 2.59808 | + | 1.50000i | 0.251166 | + | 0.145010i | 0.620298 | − | 0.784366i | \(-0.287012\pi\) |
−0.369132 | + | 0.929377i | \(0.620345\pi\) | |||||||
\(108\) | 5.19615 | 0.500000 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0.866025 | − | 1.50000i | 0.0825723 | − | 0.143019i | ||||
\(111\) | −5.19615 | + | 3.00000i | −0.493197 | + | 0.284747i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | −15.5885 | + | 9.00000i | −1.46644 | + | 0.846649i | −0.999295 | − | 0.0375328i | \(-0.988050\pi\) |
−0.467143 | + | 0.884182i | \(0.654717\pi\) | |||||||
\(114\) | −3.00000 | + | 1.73205i | −0.280976 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.19615 | 0.482451 | ||||||||
\(117\) | −18.0000 | − | 10.3923i | −1.66410 | − | 0.960769i | ||||
\(118\) | −1.50000 | + | 2.59808i | −0.138086 | + | 0.239172i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.73205 | 0.158114 | ||||||||
\(121\) | 4.00000 | − | 6.92820i | 0.363636 | − | 0.629837i | ||||
\(122\) | −3.46410 | −0.313625 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.50000 | + | 0.866025i | 0.493915 | + | 0.0777714i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.00000i | 0.267261i | ||||||||
\(127\) | −7.50000 | − | 4.33013i | −0.665517 | − | 0.384237i | 0.128859 | − | 0.991663i | \(-0.458869\pi\) |
−0.794376 | + | 0.607426i | \(0.792202\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 5.19615 | − | 3.00000i | 0.457496 | − | 0.264135i | ||||
\(130\) | −6.00000 | − | 3.46410i | −0.526235 | − | 0.303822i | ||||
\(131\) | 10.3923 | + | 6.00000i | 0.907980 | + | 0.524222i | 0.879781 | − | 0.475380i | \(-0.157689\pi\) |
0.0281993 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | −1.00000 | − | 1.73205i | −0.0867110 | − | 0.150188i | ||||
\(134\) | −3.46410 | + | 2.00000i | −0.299253 | + | 0.172774i | ||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410 | + | 6.00000i | 0.295958 | + | 0.512615i | 0.975207 | − | 0.221293i | \(-0.0710278\pi\) |
−0.679249 | + | 0.733908i | \(0.737694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 1.00000i | 0.0845154i | ||||||||
\(141\) | 9.00000 | + | 5.19615i | 0.757937 | + | 0.437595i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3923 | + | 6.00000i | 0.869048 | + | 0.501745i | ||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | −4.50000 | + | 2.59808i | −0.373705 | + | 0.215758i | ||||
\(146\) | −3.46410 | − | 6.00000i | −0.286691 | − | 0.496564i | ||||
\(147\) | 10.3923 | 0.857143 | ||||||||
\(148\) | 3.00000 | + | 1.73205i | 0.246598 | + | 0.142374i | ||||
\(149\) | 12.9904 | + | 7.50000i | 1.06421 | + | 0.614424i | 0.926595 | − | 0.376061i | \(-0.122722\pi\) |
0.137619 | + | 0.990485i | \(0.456055\pi\) | |||||||
\(150\) | −1.50000 | + | 0.866025i | −0.122474 | + | 0.0707107i | ||||
\(151\) | 12.1244i | 0.986666i | 0.869841 | + | 0.493333i | \(0.164222\pi\) | ||||
−0.869841 | + | 0.493333i | \(0.835778\pi\) | |||||||
\(152\) | 1.73205 | + | 1.00000i | 0.140488 | + | 0.0811107i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 1.73205i | − | 0.139573i | ||||||
\(155\) | −5.19615 | + | 2.00000i | −0.417365 | + | 0.160644i | ||||
\(156\) | 12.0000i | 0.960769i | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 5.19615 | − | 9.00000i | 0.413384 | − | 0.716002i | ||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.79423 | + | 4.50000i | 0.612372 | + | 0.353553i | ||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.59808 | − | 1.50000i | 0.202260 | − | 0.116775i | ||||
\(166\) | 10.5000 | − | 6.06218i | 0.814958 | − | 0.470516i | ||||
\(167\) | −10.3923 | + | 18.0000i | −0.804181 | + | 1.39288i | 0.112662 | + | 0.993633i | \(0.464062\pi\) |
−0.916843 | + | 0.399248i | \(0.869271\pi\) | |||||||
\(168\) | 1.50000 | − | 0.866025i | 0.115728 | − | 0.0668153i | ||||
\(169\) | 17.5000 | − | 30.3109i | 1.34615 | − | 2.33161i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | −3.00000 | − | 1.73205i | −0.228748 | − | 0.132068i | ||||
\(173\) | 7.79423 | − | 4.50000i | 0.592584 | − | 0.342129i | −0.173534 | − | 0.984828i | \(-0.555519\pi\) |
0.766119 | + | 0.642699i | \(0.222185\pi\) | |||||||
\(174\) | 7.79423 | + | 4.50000i | 0.590879 | + | 0.341144i | ||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 0.866025 | + | 1.50000i | 0.0652791 | + | 0.113067i | ||||
\(177\) | −4.50000 | + | 2.59808i | −0.338241 | + | 0.195283i | ||||
\(178\) | 13.8564i | 1.03858i | ||||||||
\(179\) | 7.79423 | − | 13.5000i | 0.582568 | − | 1.00904i | −0.412606 | − | 0.910910i | \(-0.635381\pi\) |
0.995174 | − | 0.0981277i | \(-0.0312854\pi\) | |||||||
\(180\) | 2.59808 | + | 1.50000i | 0.193649 | + | 0.111803i | ||||
\(181\) | 12.0000 | − | 6.92820i | 0.891953 | − | 0.514969i | 0.0173722 | − | 0.999849i | \(-0.494470\pi\) |
0.874581 | + | 0.484880i | \(0.161137\pi\) | |||||||
\(182\) | −6.92820 | −0.513553 | ||||||||
\(183\) | −5.19615 | − | 3.00000i | −0.384111 | − | 0.221766i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.46410 | −0.254686 | ||||||||
\(186\) | 7.50000 | + | 6.06218i | 0.549927 | + | 0.444500i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 6.00000i | − | 0.437595i | ||||||
\(189\) | −2.59808 | + | 4.50000i | −0.188982 | + | 0.327327i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 5.19615 | − | 3.00000i | 0.375980 | − | 0.217072i | −0.300088 | − | 0.953912i | \(-0.597016\pi\) |
0.676068 | + | 0.736839i | \(0.263683\pi\) | |||||||
\(192\) | −0.866025 | + | 1.50000i | −0.0625000 | + | 0.108253i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 1.00000i | 0.0717958i | ||||||||
\(195\) | −6.00000 | − | 10.3923i | −0.429669 | − | 0.744208i | ||||
\(196\) | −3.00000 | − | 5.19615i | −0.214286 | − | 0.371154i | ||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | −4.50000 | − | 2.59808i | −0.319801 | − | 0.184637i | ||||
\(199\) | −10.5000 | + | 6.06218i | −0.744325 | + | 0.429736i | −0.823640 | − | 0.567113i | \(-0.808060\pi\) |
0.0793146 | + | 0.996850i | \(0.474727\pi\) | |||||||
\(200\) | 0.866025 | + | 0.500000i | 0.0612372 | + | 0.0353553i | ||||
\(201\) | −6.92820 | −0.488678 | ||||||||
\(202\) | −15.0000 | −1.05540 | ||||||||
\(203\) | −2.59808 | + | 4.50000i | −0.182349 | + | 0.315838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.33013 | − | 2.50000i | 0.301694 | − | 0.174183i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.00000 | − | 3.46410i | 0.416025 | − | 0.240192i | ||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | −0.866025 | + | 1.50000i | −0.0597614 | + | 0.103510i | ||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | −0.866025 | − | 1.50000i | −0.0594789 | − | 0.103020i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | 3.46410 | 0.236250 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | −3.50000 | + | 4.33013i | −0.237595 | + | 0.293948i | ||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | −1.50000 | − | 0.866025i | −0.101130 | − | 0.0583874i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.00000 | + | 5.19615i | 0.201347 | + | 0.348743i | ||||
\(223\) | 13.5000 | + | 7.79423i | 0.904027 | + | 0.521940i | 0.878504 | − | 0.477734i | \(-0.158542\pi\) |
0.0255224 | + | 0.999674i | \(0.491875\pi\) | |||||||
\(224\) | −0.866025 | − | 0.500000i | −0.0578638 | − | 0.0334077i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 9.00000 | + | 15.5885i | 0.598671 | + | 1.03693i | ||||
\(227\) | −2.59808 | + | 1.50000i | −0.172440 | + | 0.0995585i | −0.583736 | − | 0.811943i | \(-0.698410\pi\) |
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(228\) | 1.73205 | + | 3.00000i | 0.114708 | + | 0.198680i | ||||
\(229\) | 3.00000 | + | 1.73205i | 0.198246 | + | 0.114457i | 0.595837 | − | 0.803105i | \(-0.296820\pi\) |
−0.397591 | + | 0.917563i | \(0.630154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | − | 5.19615i | − | 0.341144i | ||||||
\(233\) | 12.0000i | 0.786146i | 0.919507 | + | 0.393073i | \(0.128588\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(234\) | −10.3923 | + | 18.0000i | −0.679366 | + | 1.17670i | ||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | 2.59808 | + | 1.50000i | 0.169120 | + | 0.0976417i | ||||
\(237\) | 15.5885 | − | 9.00000i | 1.01258 | − | 0.584613i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.19615 | + | 9.00000i | 0.336111 | + | 0.582162i | 0.983698 | − | 0.179830i | \(-0.0575549\pi\) |
−0.647586 | + | 0.761992i | \(0.724222\pi\) | |||||||
\(240\) | − | 1.73205i | − | 0.111803i | ||||||
\(241\) | −13.5000 | − | 7.79423i | −0.869611 | − | 0.502070i | −0.00239235 | − | 0.999997i | \(-0.500762\pi\) |
−0.867219 | + | 0.497927i | \(0.834095\pi\) | |||||||
\(242\) | −6.92820 | − | 4.00000i | −0.445362 | − | 0.257130i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 3.46410i | 0.221766i | ||||||||
\(245\) | 5.19615 | + | 3.00000i | 0.331970 | + | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.8564i | − | 0.881662i | ||||||
\(248\) | 0.866025 | − | 5.50000i | 0.0549927 | − | 0.349250i | ||||
\(249\) | 21.0000 | 1.33082 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 8.66025 | − | 15.0000i | 0.546630 | − | 0.946792i | −0.451872 | − | 0.892083i | \(-0.649244\pi\) |
0.998502 | − | 0.0547088i | \(-0.0174231\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.33013 | + | 7.50000i | −0.271696 | + | 0.470592i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.3923 | + | 6.00000i | −0.648254 | + | 0.374270i | −0.787787 | − | 0.615948i | \(-0.788773\pi\) |
0.139533 | + | 0.990217i | \(0.455440\pi\) | |||||||
\(258\) | −3.00000 | − | 5.19615i | −0.186772 | − | 0.323498i | ||||
\(259\) | −3.00000 | + | 1.73205i | −0.186411 | + | 0.107624i | ||||
\(260\) | −3.46410 | + | 6.00000i | −0.214834 | + | 0.372104i | ||||
\(261\) | 7.79423 | + | 13.5000i | 0.482451 | + | 0.835629i | ||||
\(262\) | 6.00000 | − | 10.3923i | 0.370681 | − | 0.642039i | ||||
\(263\) | 24.2487 | 1.49524 | 0.747620 | − | 0.664127i | \(-0.231197\pi\) | ||||
0.747620 | + | 0.664127i | \(0.231197\pi\) | |||||||
\(264\) | 3.00000i | 0.184637i | ||||||||
\(265\) | 1.50000 | + | 0.866025i | 0.0921443 | + | 0.0531995i | ||||
\(266\) | −1.73205 | + | 1.00000i | −0.106199 | + | 0.0613139i | ||||
\(267\) | −12.0000 | + | 20.7846i | −0.734388 | + | 1.27200i | ||||
\(268\) | 2.00000 | + | 3.46410i | 0.122169 | + | 0.211604i | ||||
\(269\) | 6.92820 | + | 12.0000i | 0.422420 | + | 0.731653i | 0.996176 | − | 0.0873736i | \(-0.0278474\pi\) |
−0.573756 | + | 0.819027i | \(0.694514\pi\) | |||||||
\(270\) | 2.59808 | + | 4.50000i | 0.158114 | + | 0.273861i | ||||
\(271\) | 12.1244i | 0.736502i | 0.929726 | + | 0.368251i | \(0.120043\pi\) | ||||
−0.929726 | + | 0.368251i | \(0.879957\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3923 | − | 6.00000i | −0.628971 | − | 0.363137i | ||||
\(274\) | 6.00000 | − | 3.46410i | 0.362473 | − | 0.209274i | ||||
\(275\) | 1.73205 | 0.104447 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.3923i | − | 0.624413i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||
0.950014 | − | 0.312207i | \(-0.101068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | + | 15.5885i | 0.359211 | + | 0.933257i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 5.19615 | − | 9.00000i | 0.309426 | − | 0.535942i | ||||
\(283\) | −28.0000 | −1.66443 | −0.832214 | − | 0.554455i | \(-0.812927\pi\) | ||||
−0.832214 | + | 0.554455i | \(0.812927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 6.00000 | − | 10.3923i | 0.354787 | − | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.59808 | + | 1.50000i | −0.153093 | + | 0.0883883i | ||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 2.59808 | + | 4.50000i | 0.152564 | + | 0.264249i | ||||
\(291\) | −0.866025 | + | 1.50000i | −0.0507673 | + | 0.0879316i | ||||
\(292\) | −6.00000 | + | 3.46410i | −0.351123 | + | 0.202721i | ||||
\(293\) | −12.9904 | − | 7.50000i | −0.758906 | − | 0.438155i | 0.0699967 | − | 0.997547i | \(-0.477701\pi\) |
−0.828903 | + | 0.559393i | \(0.811034\pi\) | |||||||
\(294\) | − | 10.3923i | − | 0.606092i | ||||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | 1.73205 | − | 3.00000i | 0.100673 | − | 0.174371i | ||||
\(297\) | −4.50000 | − | 7.79423i | −0.261116 | − | 0.452267i | ||||
\(298\) | 7.50000 | − | 12.9904i | 0.434463 | − | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.866025 | + | 1.50000i | 0.0500000 | + | 0.0866025i | ||||
\(301\) | 3.00000 | − | 1.73205i | 0.172917 | − | 0.0998337i | ||||
\(302\) | 12.1244 | 0.697678 | ||||||||
\(303\) | −22.5000 | − | 12.9904i | −1.29259 | − | 0.746278i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | −1.73205 | − | 3.00000i | −0.0991769 | − | 0.171780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0000 | + | 19.0526i | −0.627803 | + | 1.08739i | 0.360188 | + | 0.932880i | \(0.382712\pi\) |
−0.987992 | + | 0.154507i | \(0.950621\pi\) | |||||||
\(308\) | −1.73205 | −0.0986928 | ||||||||
\(309\) | 8.66025 | 0.492665 | ||||||||
\(310\) | 2.00000 | + | 5.19615i | 0.113592 | + | 0.295122i | ||||
\(311\) | 24.0000i | 1.36092i | 0.732787 | + | 0.680458i | \(0.238219\pi\) | ||||
−0.732787 | + | 0.680458i | \(0.761781\pi\) | |||||||
\(312\) | 12.0000 | 0.679366 | ||||||||
\(313\) | 13.5000 | + | 7.79423i | 0.763065 | + | 0.440556i | 0.830395 | − | 0.557175i | \(-0.188115\pi\) |
−0.0673300 | + | 0.997731i | \(0.521448\pi\) | |||||||
\(314\) | 14.0000i | 0.790066i | ||||||||
\(315\) | −2.59808 | + | 1.50000i | −0.146385 | + | 0.0845154i | ||||
\(316\) | −9.00000 | − | 5.19615i | −0.506290 | − | 0.292306i | ||||
\(317\) | 12.9904 | + | 7.50000i | 0.729612 | + | 0.421242i | 0.818280 | − | 0.574819i | \(-0.194928\pi\) |
−0.0886679 | + | 0.996061i | \(0.528261\pi\) | |||||||
\(318\) | − | 3.00000i | − | 0.168232i | ||||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | 4.50000 | − | 2.59808i | 0.251166 | − | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | − | 6.92820i | − | 0.384308i | ||||||
\(326\) | − | 20.0000i | − | 1.10770i | ||||||
\(327\) | 12.1244 | − | 21.0000i | 0.670478 | − | 1.16130i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.19615 | + | 3.00000i | 0.286473 | + | 0.165395i | ||||
\(330\) | −1.50000 | − | 2.59808i | −0.0825723 | − | 0.143019i | ||||
\(331\) | −15.0000 | + | 8.66025i | −0.824475 | + | 0.476011i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
0.0274825 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(332\) | −6.06218 | − | 10.5000i | −0.332705 | − | 0.576262i | ||||
\(333\) | 10.3923i | 0.569495i | ||||||||
\(334\) | 18.0000 | + | 10.3923i | 0.984916 | + | 0.568642i | ||||
\(335\) | −3.46410 | − | 2.00000i | −0.189264 | − | 0.109272i | ||||
\(336\) | −0.866025 | − | 1.50000i | −0.0472456 | − | 0.0818317i | ||||
\(337\) | 12.1244i | 0.660456i | 0.943901 | + | 0.330228i | \(0.107126\pi\) | ||||
−0.943901 | + | 0.330228i | \(0.892874\pi\) | |||||||
\(338\) | −30.3109 | − | 17.5000i | −1.64870 | − | 0.951875i | ||||
\(339\) | 31.1769i | 1.69330i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.46410 | − | 9.00000i | −0.187592 | − | 0.487377i | ||||
\(342\) | 6.00000i | 0.324443i | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −1.73205 | + | 3.00000i | −0.0933859 | + | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.50000 | − | 7.79423i | −0.241921 | − | 0.419020i | ||||
\(347\) | −0.866025 | + | 1.50000i | −0.0464907 | + | 0.0805242i | −0.888334 | − | 0.459197i | \(-0.848137\pi\) |
0.841844 | + | 0.539721i | \(0.181470\pi\) | |||||||
\(348\) | 4.50000 | − | 7.79423i | 0.241225 | − | 0.417815i | ||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | −0.866025 | + | 0.500000i | −0.0462910 | + | 0.0267261i | ||||
\(351\) | −31.1769 | + | 18.0000i | −1.66410 | + | 0.960769i | ||||
\(352\) | 1.50000 | − | 0.866025i | 0.0799503 | − | 0.0461593i | ||||
\(353\) | 6.92820 | − | 12.0000i | 0.368751 | − | 0.638696i | −0.620620 | − | 0.784112i | \(-0.713119\pi\) |
0.989371 | + | 0.145416i | \(0.0464522\pi\) | |||||||
\(354\) | 2.59808 | + | 4.50000i | 0.138086 | + | 0.239172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.8564 | 0.734388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5000 | − | 7.79423i | −0.713497 | − | 0.411938i | ||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 1.50000 | − | 2.59808i | 0.0790569 | − | 0.136931i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −6.92820 | − | 12.0000i | −0.364138 | − | 0.630706i | ||||
\(363\) | −6.92820 | − | 12.0000i | −0.363636 | − | 0.629837i | ||||
\(364\) | 6.92820i | 0.363137i | ||||||||
\(365\) | 3.46410 | − | 6.00000i | 0.181319 | − | 0.314054i | ||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −9.00000 | + | 5.19615i | −0.469796 | + | 0.271237i | −0.716154 | − | 0.697942i | \(-0.754099\pi\) |
0.246358 | + | 0.969179i | \(0.420766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.46410i | 0.180090i | ||||||||
\(371\) | 1.73205 | 0.0899236 | ||||||||
\(372\) | 6.06218 | − | 7.50000i | 0.314309 | − | 0.388857i | ||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | − | 0.866025i | −0.0774597 | − | 0.0447214i | ||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | −31.1769 | + | 18.0000i | −1.60569 | + | 0.927047i | ||||
\(378\) | 4.50000 | + | 2.59808i | 0.231455 | + | 0.133631i | ||||
\(379\) | −16.0000 | + | 27.7128i | −0.821865 | + | 1.42351i | 0.0824272 | + | 0.996597i | \(0.473733\pi\) |
−0.904292 | + | 0.426914i | \(0.859601\pi\) | |||||||
\(380\) | 2.00000i | 0.102598i | ||||||||
\(381\) | −12.9904 | + | 7.50000i | −0.665517 | + | 0.384237i | ||||
\(382\) | −3.00000 | − | 5.19615i | −0.153493 | − | 0.265858i | ||||
\(383\) | −17.3205 | − | 30.0000i | −0.885037 | − | 1.53293i | −0.845672 | − | 0.533703i | \(-0.820800\pi\) |
−0.0393649 | − | 0.999225i | \(-0.512533\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 1.50000 | − | 0.866025i | 0.0764471 | − | 0.0441367i | ||||
\(386\) | −19.9186 | − | 11.5000i | −1.01383 | − | 0.585335i | ||||
\(387\) | − | 10.3923i | − | 0.528271i | ||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | 6.92820 | − | 12.0000i | 0.351274 | − | 0.608424i | −0.635199 | − | 0.772348i | \(-0.719082\pi\) |
0.986473 | + | 0.163924i | \(0.0524153\pi\) | |||||||
\(390\) | −10.3923 | + | 6.00000i | −0.526235 | + | 0.303822i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.19615 | + | 3.00000i | −0.262445 | + | 0.151523i | ||||
\(393\) | 18.0000 | − | 10.3923i | 0.907980 | − | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.3923 | 0.522894 | ||||||||
\(396\) | −2.59808 | + | 4.50000i | −0.130558 | + | 0.226134i | ||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | 6.06218 | + | 10.5000i | 0.303870 | + | 0.526317i | ||||
\(399\) | −3.46410 | −0.173422 | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 17.3205 | 0.864945 | 0.432472 | − | 0.901647i | \(-0.357641\pi\) | ||||
0.432472 | + | 0.901647i | \(0.357641\pi\) | |||||||
\(402\) | 6.92820i | 0.345547i | ||||||||
\(403\) | −36.0000 | + | 13.8564i | −1.79329 | + | 0.690237i | ||||
\(404\) | 15.0000i | 0.746278i | ||||||||
\(405\) | 9.00000i | 0.447214i | ||||||||
\(406\) | 4.50000 | + | 2.59808i | 0.223331 | + | 0.128940i | ||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.5000 | − | 16.4545i | −1.40923 | − | 0.813622i | −0.413920 | − | 0.910313i | \(-0.635841\pi\) |
−0.995314 | + | 0.0966915i | \(0.969174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | −2.50000 | − | 4.33013i | −0.123166 | − | 0.213330i | ||||
\(413\) | −2.59808 | + | 1.50000i | −0.127843 | + | 0.0738102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5000 | + | 6.06218i | 0.515425 | + | 0.297581i | ||||
\(416\) | −3.46410 | − | 6.00000i | −0.169842 | − | 0.294174i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 3.46410i | − | 0.169435i | ||||||
\(419\) | 3.00000i | 0.146560i | 0.997311 | + | 0.0732798i | \(0.0233466\pi\) | ||||
−0.997311 | + | 0.0732798i | \(0.976653\pi\) | |||||||
\(420\) | 1.50000 | + | 0.866025i | 0.0731925 | + | 0.0422577i | ||||
\(421\) | −8.00000 | − | 13.8564i | −0.389896 | − | 0.675320i | 0.602539 | − | 0.798089i | \(-0.294156\pi\) |
−0.992435 | + | 0.122769i | \(0.960822\pi\) | |||||||
\(422\) | 6.92820 | + | 4.00000i | 0.337260 | + | 0.194717i | ||||
\(423\) | 15.5885 | − | 9.00000i | 0.757937 | − | 0.437595i | ||||
\(424\) | −1.50000 | + | 0.866025i | −0.0728464 | + | 0.0420579i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.00000 | − | 1.73205i | −0.145180 | − | 0.0838198i | ||||
\(428\) | −2.59808 | − | 1.50000i | −0.125583 | − | 0.0725052i | ||||
\(429\) | 18.0000 | − | 10.3923i | 0.869048 | − | 0.501745i | ||||
\(430\) | − | 3.46410i | − | 0.167054i | ||||||
\(431\) | −25.9808 | − | 15.0000i | −1.25145 | − | 0.722525i | −0.280052 | − | 0.959985i | \(-0.590352\pi\) |
−0.971397 | + | 0.237460i | \(0.923685\pi\) | |||||||
\(432\) | −5.19615 | −0.250000 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 4.33013 | + | 3.50000i | 0.207853 | + | 0.168005i | ||||
\(435\) | 9.00000i | 0.431517i | ||||||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | −9.50000 | − | 16.4545i | −0.453410 | − | 0.785330i | 0.545185 | − | 0.838316i | \(-0.316459\pi\) |
−0.998595 | + | 0.0529862i | \(0.983126\pi\) | |||||||
\(440\) | −0.866025 | + | 1.50000i | −0.0412861 | + | 0.0715097i | ||||
\(441\) | 9.00000 | − | 15.5885i | 0.428571 | − | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1769 | + | 18.0000i | −1.48126 | + | 0.855206i | −0.999774 | − | 0.0212481i | \(-0.993236\pi\) |
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(444\) | 5.19615 | − | 3.00000i | 0.246598 | − | 0.142374i | ||||
\(445\) | −12.0000 | + | 6.92820i | −0.568855 | + | 0.328428i | ||||
\(446\) | 7.79423 | − | 13.5000i | 0.369067 | − | 0.639244i | ||||
\(447\) | 22.5000 | − | 12.9904i | 1.06421 | − | 0.614424i | ||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −10.3923 | −0.490443 | −0.245222 | − | 0.969467i | \(-0.578861\pi\) | ||||
−0.245222 | + | 0.969467i | \(0.578861\pi\) | |||||||
\(450\) | 3.00000i | 0.141421i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | 18.1865 | + | 10.5000i | 0.854478 | + | 0.493333i | ||||
\(454\) | 1.50000 | + | 2.59808i | 0.0703985 | + | 0.121934i | ||||
\(455\) | −3.46410 | − | 6.00000i | −0.162400 | − | 0.281284i | ||||
\(456\) | 3.00000 | − | 1.73205i | 0.140488 | − | 0.0811107i | ||||
\(457\) | 6.92820i | 0.324088i | 0.986784 | + | 0.162044i | \(0.0518086\pi\) | ||||
−0.986784 | + | 0.162044i | \(0.948191\pi\) | |||||||
\(458\) | 1.73205 | − | 3.00000i | 0.0809334 | − | 0.140181i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5885 | 0.726027 | 0.363013 | − | 0.931784i | \(-0.381748\pi\) | ||||
0.363013 | + | 0.931784i | \(0.381748\pi\) | |||||||
\(462\) | −2.59808 | − | 1.50000i | −0.120873 | − | 0.0697863i | ||||
\(463\) | − | 12.1244i | − | 0.563467i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909093\pi\) | |||||||
\(464\) | −5.19615 | −0.241225 | ||||||||
\(465\) | −1.50000 | + | 9.52628i | −0.0695608 | + | 0.441771i | ||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | − | 39.0000i | − | 1.80470i | −0.430999 | − | 0.902352i | \(-0.641839\pi\) | ||
0.430999 | − | 0.902352i | \(-0.358161\pi\) | |||||||
\(468\) | 18.0000 | + | 10.3923i | 0.832050 | + | 0.480384i | ||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 5.19615 | − | 3.00000i | 0.239681 | − | 0.138380i | ||||
\(471\) | −12.1244 | + | 21.0000i | −0.558661 | + | 0.967629i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | 6.00000i | 0.275880i | ||||||||
\(474\) | −9.00000 | − | 15.5885i | −0.413384 | − | 0.716002i | ||||
\(475\) | −1.00000 | − | 1.73205i | −0.0458831 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.59808 | − | 4.50000i | 0.118958 | − | 0.206041i | ||||
\(478\) | 9.00000 | − | 5.19615i | 0.411650 | − | 0.237666i | ||||
\(479\) | −15.5885 | − | 9.00000i | −0.712255 | − | 0.411220i | 0.0996406 | − | 0.995023i | \(-0.468231\pi\) |
−0.811895 | + | 0.583803i | \(0.801564\pi\) | |||||||
\(480\) | −1.73205 | −0.0790569 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | −7.79423 | + | 13.5000i | −0.355017 | + | 0.614908i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00000 | + | 6.92820i | −0.181818 | + | 0.314918i | ||||
\(485\) | −0.866025 | + | 0.500000i | −0.0393242 | + | 0.0227038i | ||||
\(486\) | 13.5000 | − | 7.79423i | 0.612372 | − | 0.353553i | ||||
\(487\) | 31.5000 | − | 18.1865i | 1.42740 | − | 0.824110i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 3.46410 | 0.156813 | ||||||||
\(489\) | 17.3205 | − | 30.0000i | 0.783260 | − | 1.35665i | ||||
\(490\) | 3.00000 | − | 5.19615i | 0.135526 | − | 0.234738i | ||||
\(491\) | 14.7224 | + | 25.5000i | 0.664414 | + | 1.15080i | 0.979444 | + | 0.201717i | \(0.0646522\pi\) |
−0.315030 | + | 0.949082i | \(0.602015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −13.8564 | −0.623429 | ||||||||
\(495\) | − | 5.19615i | − | 0.233550i | ||||||
\(496\) | −5.50000 | − | 0.866025i | −0.246957 | − | 0.0388857i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 21.0000i | − | 0.941033i | ||||||
\(499\) | −30.0000 | − | 17.3205i | −1.34298 | − | 0.775372i | −0.355740 | − | 0.934585i | \(-0.615771\pi\) |
−0.987244 | + | 0.159212i | \(0.949105\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 18.0000 | + | 31.1769i | 0.804181 | + | 1.39288i | ||||
\(502\) | −15.0000 | − | 8.66025i | −0.669483 | − | 0.386526i | ||||
\(503\) | 5.19615 | + | 3.00000i | 0.231685 | + | 0.133763i | 0.611349 | − | 0.791361i | \(-0.290627\pi\) |
−0.379664 | + | 0.925124i | \(0.623960\pi\) | |||||||
\(504\) | − | 3.00000i | − | 0.133631i | ||||||
\(505\) | −7.50000 | − | 12.9904i | −0.333746 | − | 0.578064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.3109 | − | 52.5000i | −1.34615 | − | 2.33161i | ||||
\(508\) | 7.50000 | + | 4.33013i | 0.332759 | + | 0.192118i | ||||
\(509\) | −16.4545 | − | 28.5000i | −0.729332 | − | 1.26324i | −0.957166 | − | 0.289540i | \(-0.906498\pi\) |
0.227834 | − | 0.973700i | \(-0.426836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.92820i | − | 0.306486i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.19615 | + | 9.00000i | −0.229416 | + | 0.397360i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | 4.33013 | + | 2.50000i | 0.190808 | + | 0.110163i | ||||
\(516\) | −5.19615 | + | 3.00000i | −0.228748 | + | 0.132068i | ||||
\(517\) | −9.00000 | + | 5.19615i | −0.395820 | + | 0.228527i | ||||
\(518\) | 1.73205 | + | 3.00000i | 0.0761019 | + | 0.131812i | ||||
\(519\) | − | 15.5885i | − | 0.684257i | ||||||
\(520\) | 6.00000 | + | 3.46410i | 0.263117 | + | 0.151911i | ||||
\(521\) | −25.9808 | − | 15.0000i | −1.13824 | − | 0.657162i | −0.192244 | − | 0.981347i | \(-0.561577\pi\) |
−0.945994 | + | 0.324185i | \(0.894910\pi\) | |||||||
\(522\) | 13.5000 | − | 7.79423i | 0.590879 | − | 0.341144i | ||||
\(523\) | 45.0333i | 1.96917i | 0.174908 | + | 0.984585i | \(0.444037\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | −10.3923 | − | 6.00000i | −0.453990 | − | 0.262111i | ||||
\(525\) | −1.73205 | −0.0755929 | ||||||||
\(526\) | − | 24.2487i | − | 1.05729i | ||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0.866025 | − | 1.50000i | 0.0376177 | − | 0.0651558i | ||||
\(531\) | 9.00000i | 0.390567i | ||||||||
\(532\) | 1.00000 | + | 1.73205i | 0.0433555 | + | 0.0750939i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.7846 | + | 12.0000i | 0.899438 | + | 0.519291i | ||||
\(535\) | 3.00000 | 0.129701 | ||||||||
\(536\) | 3.46410 | − | 2.00000i | 0.149626 | − | 0.0863868i | ||||
\(537\) | −13.5000 | − | 23.3827i | −0.582568 | − | 1.00904i | ||||
\(538\) | 12.0000 | − | 6.92820i | 0.517357 | − | 0.298696i | ||||
\(539\) | −5.19615 | + | 9.00000i | −0.223814 | + | 0.387657i | ||||
\(540\) | 4.50000 | − | 2.59808i | 0.193649 | − | 0.111803i | ||||
\(541\) | 10.0000 | − | 17.3205i | 0.429934 | − | 0.744667i | −0.566933 | − | 0.823764i | \(-0.691870\pi\) |
0.996867 | + | 0.0790969i | \(0.0252036\pi\) | |||||||
\(542\) | 12.1244 | 0.520786 | ||||||||
\(543\) | − | 24.0000i | − | 1.02994i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1244 | − | 7.00000i | 0.519350 | − | 0.299847i | ||||
\(546\) | −6.00000 | + | 10.3923i | −0.256776 | + | 0.444750i | ||||
\(547\) | 4.00000 | + | 6.92820i | 0.171028 | + | 0.296229i | 0.938779 | − | 0.344519i | \(-0.111958\pi\) |
−0.767752 | + | 0.640747i | \(0.778625\pi\) | |||||||
\(548\) | −3.46410 | − | 6.00000i | −0.147979 | − | 0.256307i | ||||
\(549\) | −9.00000 | + | 5.19615i | −0.384111 | + | 0.221766i | ||||
\(550\) | − | 1.73205i | − | 0.0738549i | ||||||
\(551\) | −5.19615 | + | 9.00000i | −0.221364 | + | 0.383413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00000 | − | 5.19615i | 0.382719 | − | 0.220963i | ||||
\(554\) | −10.3923 | −0.441527 | ||||||||
\(555\) | −3.00000 | + | 5.19615i | −0.127343 | + | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0526 | −0.807283 | −0.403641 | − | 0.914917i | \(-0.632256\pi\) | ||||
−0.403641 | + | 0.914917i | \(0.632256\pi\) | |||||||
\(558\) | 15.5885 | − | 6.00000i | 0.659912 | − | 0.254000i | ||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | − | 1.00000i | − | 0.0422577i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | −33.7750 | + | 19.5000i | −1.42345 | + | 0.821827i | −0.996592 | − | 0.0824933i | \(-0.973712\pi\) |
−0.426855 | + | 0.904320i | \(0.640378\pi\) | |||||||
\(564\) | −9.00000 | − | 5.19615i | −0.378968 | − | 0.218797i | ||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 28.0000i | 1.17693i | ||||||||
\(567\) | 4.50000 | + | 7.79423i | 0.188982 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.66025 | − | 15.0000i | −0.363057 | − | 0.628833i | 0.625406 | − | 0.780300i | \(-0.284934\pi\) |
−0.988462 | + | 0.151467i | \(0.951600\pi\) | |||||||
\(570\) | −1.73205 | + | 3.00000i | −0.0725476 | + | 0.125656i | ||||
\(571\) | −27.0000 | + | 15.5885i | −1.12991 | + | 0.652357i | −0.943913 | − | 0.330193i | \(-0.892886\pi\) |
−0.186001 | + | 0.982549i | \(0.559553\pi\) | |||||||
\(572\) | −10.3923 | − | 6.00000i | −0.434524 | − | 0.250873i | ||||
\(573\) | − | 10.3923i | − | 0.434145i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −17.0000 | + | 29.4449i | −0.707719 | + | 1.22581i | 0.257982 | + | 0.966150i | \(0.416942\pi\) |
−0.965701 | + | 0.259656i | \(0.916391\pi\) | |||||||
\(578\) | 14.7224 | − | 8.50000i | 0.612372 | − | 0.353553i | ||||
\(579\) | −19.9186 | − | 34.5000i | −0.827788 | − | 1.43377i | ||||
\(580\) | 4.50000 | − | 2.59808i | 0.186852 | − | 0.107879i | ||||
\(581\) | 12.1244 | 0.503003 | ||||||||
\(582\) | 1.50000 | + | 0.866025i | 0.0621770 | + | 0.0358979i | ||||
\(583\) | −1.50000 | + | 2.59808i | −0.0621237 | + | 0.107601i | ||||
\(584\) | 3.46410 | + | 6.00000i | 0.143346 | + | 0.248282i | ||||
\(585\) | −20.7846 | −0.859338 | ||||||||
\(586\) | −7.50000 | + | 12.9904i | −0.309822 | + | 0.536628i | ||||
\(587\) | 8.66025 | 0.357447 | 0.178723 | − | 0.983899i | \(-0.442803\pi\) | ||||
0.178723 | + | 0.983899i | \(0.442803\pi\) | |||||||
\(588\) | −10.3923 | −0.428571 | ||||||||
\(589\) | −7.00000 | + | 8.66025i | −0.288430 | + | 0.356840i | ||||
\(590\) | 3.00000i | 0.123508i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | − | 1.73205i | −0.123299 | − | 0.0711868i | ||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | −7.79423 | + | 4.50000i | −0.319801 | + | 0.184637i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9904 | − | 7.50000i | −0.532107 | − | 0.307212i | ||||
\(597\) | 21.0000i | 0.859473i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5885 | + | 9.00000i | −0.636927 | + | 0.367730i | −0.783430 | − | 0.621480i | \(-0.786532\pi\) |
0.146503 | + | 0.989210i | \(0.453198\pi\) | |||||||
\(600\) | 1.50000 | − | 0.866025i | 0.0612372 | − | 0.0353553i | ||||
\(601\) | 6.00000 | + | 3.46410i | 0.244745 | + | 0.141304i | 0.617356 | − | 0.786684i | \(-0.288204\pi\) |
−0.372611 | + | 0.927988i | \(0.621537\pi\) | |||||||
\(602\) | −1.73205 | − | 3.00000i | −0.0705931 | − | 0.122271i | ||||
\(603\) | −6.00000 | + | 10.3923i | −0.244339 | + | 0.423207i | ||||
\(604\) | − | 12.1244i | − | 0.493333i | ||||||
\(605\) | − | 8.00000i | − | 0.325246i | ||||||
\(606\) | −12.9904 | + | 22.5000i | −0.527698 | + | 0.914000i | ||||
\(607\) | −2.00000 | − | 3.46410i | −0.0811775 | − | 0.140604i | 0.822578 | − | 0.568652i | \(-0.192535\pi\) |
−0.903756 | + | 0.428048i | \(0.859201\pi\) | |||||||
\(608\) | −1.73205 | − | 1.00000i | −0.0702439 | − | 0.0405554i | ||||
\(609\) | 4.50000 | + | 7.79423i | 0.182349 | + | 0.315838i | ||||
\(610\) | −3.00000 | + | 1.73205i | −0.121466 | + | 0.0701287i | ||||
\(611\) | 20.7846 | + | 36.0000i | 0.840855 | + | 1.45640i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0000 | − | 8.66025i | −0.605844 | − | 0.349784i | 0.165493 | − | 0.986211i | \(-0.447078\pi\) |
−0.771337 | + | 0.636427i | \(0.780412\pi\) | |||||||
\(614\) | 19.0526 | + | 11.0000i | 0.768899 | + | 0.443924i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.73205i | 0.0697863i | ||||||||
\(617\) | −5.19615 | − | 3.00000i | −0.209189 | − | 0.120775i | 0.391745 | − | 0.920074i | \(-0.371871\pi\) |
−0.600935 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(618\) | − | 8.66025i | − | 0.348367i | ||||||
\(619\) | − | 10.3923i | − | 0.417702i | −0.977947 | − | 0.208851i | \(-0.933028\pi\) | ||
0.977947 | − | 0.208851i | \(-0.0669724\pi\) | |||||||
\(620\) | 5.19615 | − | 2.00000i | 0.208683 | − | 0.0803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | −6.92820 | + | 12.0000i | −0.277573 | + | 0.480770i | ||||
\(624\) | − | 12.0000i | − | 0.480384i | ||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7.79423 | − | 13.5000i | 0.311520 | − | 0.539569i | ||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.50000 | + | 2.59808i | 0.0597614 | + | 0.103510i | ||||
\(631\) | 28.5000 | − | 16.4545i | 1.13457 | − | 0.655043i | 0.189488 | − | 0.981883i | \(-0.439317\pi\) |
0.945080 | + | 0.326841i | \(0.105984\pi\) | |||||||
\(632\) | −5.19615 | + | 9.00000i | −0.206692 | + | 0.358001i | ||||
\(633\) | 6.92820 | + | 12.0000i | 0.275371 | + | 0.476957i | ||||
\(634\) | 7.50000 | − | 12.9904i | 0.297863 | − | 0.515914i | ||||
\(635\) | −8.66025 | −0.343672 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 36.0000 | + | 20.7846i | 1.42637 | + | 0.823516i | ||||
\(638\) | −7.79423 | + | 4.50000i | −0.308576 | + | 0.178157i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −8.66025 | − | 15.0000i | −0.342059 | − | 0.592464i | 0.642756 | − | 0.766071i | \(-0.277791\pi\) |
−0.984815 | + | 0.173607i | \(0.944458\pi\) | |||||||
\(642\) | −2.59808 | − | 4.50000i | −0.102538 | − | 0.177601i | ||||
\(643\) | 17.3205i | 0.683054i | 0.939872 | + | 0.341527i | \(0.110944\pi\) | ||||
−0.939872 | + | 0.341527i | \(0.889056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00000 | − | 5.19615i | 0.118125 | − | 0.204598i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | −7.79423 | − | 4.50000i | −0.306186 | − | 0.176777i | ||||
\(649\) | − | 5.19615i | − | 0.203967i | ||||||
\(650\) | −6.92820 | −0.271746 | ||||||||
\(651\) | 3.46410 | + | 9.00000i | 0.135769 | + | 0.352738i | ||||
\(652\) | −20.0000 | −0.783260 | ||||||||
\(653\) | 27.0000i | 1.05659i | 0.849060 | + | 0.528296i | \(0.177169\pi\) | ||||
−0.849060 | + | 0.528296i | \(0.822831\pi\) | |||||||
\(654\) | −21.0000 | − | 12.1244i | −0.821165 | − | 0.474100i | ||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.0000 | − | 10.3923i | −0.702247 | − | 0.405442i | ||||
\(658\) | 3.00000 | − | 5.19615i | 0.116952 | − | 0.202567i | ||||
\(659\) | − | 39.0000i | − | 1.51922i | −0.650376 | − | 0.759612i | \(-0.725389\pi\) | ||
0.650376 | − | 0.759612i | \(-0.274611\pi\) | |||||||
\(660\) | −2.59808 | + | 1.50000i | −0.101130 | + | 0.0583874i | ||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | 8.66025 | + | 15.0000i | 0.336590 | + | 0.582992i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5000 | + | 6.06218i | −0.407479 | + | 0.235258i | ||||
\(665\) | −1.73205 | − | 1.00000i | −0.0671660 | − | 0.0387783i | ||||
\(666\) | 10.3923 | 0.402694 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | − | 18.0000i | 0.402090 | − | 0.696441i | ||||
\(669\) | 23.3827 | − | 13.5000i | 0.904027 | − | 0.521940i | ||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | 5.19615 | − | 3.00000i | 0.200595 | − | 0.115814i | ||||
\(672\) | −1.50000 | + | 0.866025i | −0.0578638 | + | 0.0334077i | ||||
\(673\) | 22.5000 | − | 12.9904i | 0.867311 | − | 0.500742i | 0.000857451 | − | 1.00000i | \(-0.499727\pi\) |
0.866454 | + | 0.499257i | \(0.166394\pi\) | |||||||
\(674\) | 12.1244 | 0.467013 | ||||||||
\(675\) | −2.59808 | + | 4.50000i | −0.100000 | + | 0.173205i | ||||
\(676\) | −17.5000 | + | 30.3109i | −0.673077 | + | 1.16580i | ||||
\(677\) | 14.7224 | + | 25.5000i | 0.565829 | + | 0.980045i | 0.996972 | + | 0.0777610i | \(0.0247771\pi\) |
−0.431143 | + | 0.902284i | \(0.641890\pi\) | |||||||
\(678\) | 31.1769 | 1.19734 | ||||||||
\(679\) | −0.500000 | + | 0.866025i | −0.0191882 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.19615i | 0.199117i | ||||||||
\(682\) | −9.00000 | + | 3.46410i | −0.344628 | + | 0.132647i | ||||
\(683\) | 51.0000i | 1.95146i | 0.218975 | + | 0.975730i | \(0.429729\pi\) | ||||
−0.218975 | + | 0.975730i | \(0.570271\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | 6.00000 | + | 3.46410i | 0.229248 | + | 0.132357i | ||||
\(686\) | − | 13.0000i | − | 0.496342i | ||||||
\(687\) | 5.19615 | − | 3.00000i | 0.198246 | − | 0.114457i | ||||
\(688\) | 3.00000 | + | 1.73205i | 0.114374 | + | 0.0660338i | ||||
\(689\) | 10.3923 | + | 6.00000i | 0.395915 | + | 0.228582i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0000 | + | 45.0333i | 0.989087 | + | 1.71315i | 0.622139 | + | 0.782907i | \(0.286264\pi\) |
0.366947 | + | 0.930242i | \(0.380403\pi\) | |||||||
\(692\) | −7.79423 | + | 4.50000i | −0.296292 | + | 0.171064i | ||||
\(693\) | −2.59808 | − | 4.50000i | −0.0986928 | − | 0.170941i | ||||
\(694\) | 1.50000 | + | 0.866025i | 0.0569392 | + | 0.0328739i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.79423 | − | 4.50000i | −0.295439 | − | 0.170572i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 22.0000i | − | 0.832712i | ||||||
\(699\) | 18.0000 | + | 10.3923i | 0.680823 | + | 0.393073i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 23.3827 | + | 13.5000i | 0.883152 | + | 0.509888i | 0.871696 | − | 0.490046i | \(-0.163020\pi\) |
0.0114555 | + | 0.999934i | \(0.496354\pi\) | |||||||
\(702\) | 18.0000 | + | 31.1769i | 0.679366 | + | 1.17670i | ||||
\(703\) | −6.00000 | + | 3.46410i | −0.226294 | + | 0.130651i | ||||
\(704\) | −0.866025 | − | 1.50000i | −0.0326396 | − | 0.0565334i | ||||
\(705\) | 10.3923 | 0.391397 | ||||||||
\(706\) | −12.0000 | − | 6.92820i | −0.451626 | − | 0.260746i | ||||
\(707\) | −12.9904 | − | 7.50000i | −0.488554 | − | 0.282067i | ||||
\(708\) | 4.50000 | − | 2.59808i | 0.169120 | − | 0.0976417i | ||||
\(709\) | 6.92820i | 0.260194i | 0.991501 | + | 0.130097i | \(0.0415289\pi\) | ||||
−0.991501 | + | 0.130097i | \(0.958471\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 31.1769i | − | 1.16923i | ||||||
\(712\) | − | 13.8564i | − | 0.519291i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | −7.79423 | + | 13.5000i | −0.291284 | + | 0.504519i | ||||
\(717\) | 18.0000 | 0.672222 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92820 | − | 12.0000i | 0.258378 | − | 0.447524i | −0.707429 | − | 0.706784i | \(-0.750145\pi\) |
0.965808 | + | 0.259260i | \(0.0834785\pi\) | |||||||
\(720\) | −2.59808 | − | 1.50000i | −0.0968246 | − | 0.0559017i | ||||
\(721\) | 5.00000 | 0.186210 | ||||||||
\(722\) | 12.9904 | − | 7.50000i | 0.483452 | − | 0.279121i | ||||
\(723\) | −23.3827 | + | 13.5000i | −0.869611 | + | 0.502070i | ||||
\(724\) | −12.0000 | + | 6.92820i | −0.445976 | + | 0.257485i | ||||
\(725\) | −2.59808 | + | 4.50000i | −0.0964901 | + | 0.167126i | ||||
\(726\) | −12.0000 | + | 6.92820i | −0.445362 | + | 0.257130i | ||||
\(727\) | 0.500000 | − | 0.866025i | 0.0185440 | − | 0.0321191i | −0.856605 | − | 0.515974i | \(-0.827430\pi\) |
0.875148 | + | 0.483854i | \(0.160764\pi\) | |||||||
\(728\) | 6.92820 | 0.256776 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −6.00000 | − | 3.46410i | −0.222070 | − | 0.128212i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 5.19615 | + | 3.00000i | 0.192055 | + | 0.110883i | ||||
\(733\) | −17.0000 | − | 29.4449i | −0.627909 | − | 1.08757i | −0.987971 | − | 0.154642i | \(-0.950578\pi\) |
0.360061 | − | 0.932929i | \(-0.382756\pi\) | |||||||
\(734\) | 5.19615 | + | 9.00000i | 0.191793 | + | 0.332196i | ||||
\(735\) | 9.00000 | − | 5.19615i | 0.331970 | − | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.46410 | − | 6.00000i | 0.127602 | − | 0.221013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.0000 | + | 22.5167i | −1.43464 | + | 0.828289i | −0.997470 | − | 0.0710909i | \(-0.977352\pi\) |
−0.437168 | + | 0.899380i | \(0.644019\pi\) | |||||||
\(740\) | 3.46410 | 0.127343 | ||||||||
\(741\) | −20.7846 | − | 12.0000i | −0.763542 | − | 0.440831i | ||||
\(742\) | − | 1.73205i | − | 0.0635856i | ||||||
\(743\) | 17.3205 | 0.635428 | 0.317714 | − | 0.948187i | \(-0.397085\pi\) | ||||
0.317714 | + | 0.948187i | \(0.397085\pi\) | |||||||
\(744\) | −7.50000 | − | 6.06218i | −0.274963 | − | 0.222250i | ||||
\(745\) | 15.0000 | 0.549557 | ||||||||
\(746\) | 10.0000i | 0.366126i | ||||||||
\(747\) | 18.1865 | − | 31.5000i | 0.665410 | − | 1.15252i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.59808 | − | 1.50000i | 0.0949316 | − | 0.0548088i | ||||
\(750\) | −0.866025 | + | 1.50000i | −0.0316228 | + | 0.0547723i | ||||
\(751\) | −3.50000 | + | 6.06218i | −0.127717 | + | 0.221212i | −0.922792 | − | 0.385299i | \(-0.874098\pi\) |
0.795075 | + | 0.606511i | \(0.207432\pi\) | |||||||
\(752\) | 6.00000i | 0.218797i | ||||||||
\(753\) | −15.0000 | − | 25.9808i | −0.546630 | − | 0.946792i | ||||
\(754\) | 18.0000 | + | 31.1769i | 0.655521 | + | 1.13540i | ||||
\(755\) | 6.06218 | + | 10.5000i | 0.220625 | + | 0.382134i | ||||
\(756\) | 2.59808 | − | 4.50000i | 0.0944911 | − | 0.163663i | ||||
\(757\) | 33.0000 | − | 19.0526i | 1.19941 | − | 0.692477i | 0.238983 | − | 0.971024i | \(-0.423186\pi\) |
0.960423 | + | 0.278547i | \(0.0898527\pi\) | |||||||
\(758\) | 27.7128 | + | 16.0000i | 1.00657 | + | 0.581146i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | 0.0725476 | ||||||||
\(761\) | 20.7846 | − | 36.0000i | 0.753442 | − | 1.30500i | −0.192704 | − | 0.981257i | \(-0.561726\pi\) |
0.946145 | − | 0.323742i | \(-0.104941\pi\) | |||||||
\(762\) | 7.50000 | + | 12.9904i | 0.271696 | + | 0.470592i | ||||
\(763\) | 7.00000 | − | 12.1244i | 0.253417 | − | 0.438931i | ||||
\(764\) | −5.19615 | + | 3.00000i | −0.187990 | + | 0.108536i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.0000 | + | 17.3205i | −1.08394 | + | 0.625815i | ||||
\(767\) | −20.7846 | −0.750489 | ||||||||
\(768\) | 0.866025 | − | 1.50000i | 0.0312500 | − | 0.0541266i | ||||
\(769\) | 11.5000 | − | 19.9186i | 0.414701 | − | 0.718283i | −0.580696 | − | 0.814120i | \(-0.697220\pi\) |
0.995397 | + | 0.0958377i | \(0.0305530\pi\) | |||||||
\(770\) | −0.866025 | − | 1.50000i | −0.0312094 | − | 0.0540562i | ||||
\(771\) | 20.7846i | 0.748539i | ||||||||
\(772\) | −11.5000 | + | 19.9186i | −0.413894 | + | 0.716886i | ||||
\(773\) | 27.7128 | 0.996761 | 0.498380 | − | 0.866959i | \(-0.333928\pi\) | ||||
0.498380 | + | 0.866959i | \(0.333928\pi\) | |||||||
\(774\) | −10.3923 | −0.373544 | ||||||||
\(775\) | −3.50000 | + | 4.33013i | −0.125724 | + | 0.155543i | ||||
\(776\) | − | 1.00000i | − | 0.0358979i | ||||||
\(777\) | 6.00000i | 0.215249i | ||||||||
\(778\) | −12.0000 | − | 6.92820i | −0.430221 | − | 0.248388i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.00000 | + | 10.3923i | 0.214834 | + | 0.372104i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.0000 | 0.964901 | ||||||||
\(784\) | 3.00000 | + | 5.19615i | 0.107143 | + | 0.185577i | ||||
\(785\) | −12.1244 | + | 7.00000i | −0.432737 | + | 0.249841i | ||||
\(786\) | −10.3923 | − | 18.0000i | −0.370681 | − | 0.642039i | ||||
\(787\) | 9.00000 | + | 5.19615i | 0.320815 | + | 0.185223i | 0.651756 | − | 0.758429i | \(-0.274033\pi\) |
−0.330941 | + | 0.943652i | \(0.607366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0000 | − | 36.3731i | 0.747620 | − | 1.29492i | ||||
\(790\) | − | 10.3923i | − | 0.369742i | ||||||
\(791\) | 18.0000i | 0.640006i | ||||||||
\(792\) | 4.50000 | + | 2.59808i | 0.159901 | + | 0.0923186i | ||||
\(793\) | −12.0000 | − | 20.7846i | −0.426132 | − | 0.738083i | ||||
\(794\) | 1.73205 | + | 1.00000i | 0.0614682 | + | 0.0354887i | ||||
\(795\) | 2.59808 | − | 1.50000i | 0.0921443 | − | 0.0531995i | ||||
\(796\) | 10.5000 | − | 6.06218i | 0.372163 | − | 0.214868i | ||||
\(797\) | 19.9186 | + | 34.5000i | 0.705552 | + | 1.22205i | 0.966492 | + | 0.256697i | \(0.0826344\pi\) |
−0.260939 | + | 0.965355i | \(0.584032\pi\) | |||||||
\(798\) | 3.46410i | 0.122628i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 20.7846 | + | 36.0000i | 0.734388 | + | 1.27200i | ||||
\(802\) | − | 17.3205i | − | 0.611608i | ||||||
\(803\) | 10.3923 | + | 6.00000i | 0.366736 | + | 0.211735i | ||||
\(804\) | 6.92820 | 0.244339 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.8564 | + | 36.0000i | 0.488071 | + | 1.26805i | ||||
\(807\) | 24.0000 | 0.844840 | ||||||||
\(808\) | 15.0000 | 0.527698 | ||||||||
\(809\) | 19.0526 | − | 33.0000i | 0.669852 | − | 1.16022i | −0.308093 | − | 0.951356i | \(-0.599691\pi\) |
0.977945 | − | 0.208862i | \(-0.0669759\pi\) | |||||||
\(810\) | 9.00000 | 0.316228 | ||||||||
\(811\) | −20.0000 | − | 34.6410i | −0.702295 | − | 1.21641i | −0.967659 | − | 0.252262i | \(-0.918825\pi\) |
0.265364 | − | 0.964148i | \(-0.414508\pi\) | |||||||
\(812\) | 2.59808 | − | 4.50000i | 0.0911746 | − | 0.157919i | ||||
\(813\) | 18.1865 | + | 10.5000i | 0.637830 | + | 0.368251i | ||||
\(814\) | −6.00000 | −0.210300 | ||||||||
\(815\) | 17.3205 | − | 10.0000i | 0.606711 | − | 0.350285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | − | 3.46410i | 0.209913 | − | 0.121194i | ||||
\(818\) | −16.4545 | + | 28.5000i | −0.575317 | + | 0.996479i | ||||
\(819\) | −18.0000 | + | 10.3923i | −0.628971 | + | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8372 | 1.39033 | 0.695163 | − | 0.718852i | \(-0.255332\pi\) | ||||
0.695163 | + | 0.718852i | \(0.255332\pi\) | |||||||
\(822\) | − | 12.0000i | − | 0.418548i | ||||||
\(823\) | −34.5000 | − | 19.9186i | −1.20259 | − | 0.694318i | −0.241463 | − | 0.970410i | \(-0.577627\pi\) |
−0.961131 | + | 0.276092i | \(0.910961\pi\) | |||||||
\(824\) | −4.33013 | + | 2.50000i | −0.150847 | + | 0.0870916i | ||||
\(825\) | 1.50000 | − | 2.59808i | 0.0522233 | − | 0.0904534i | ||||
\(826\) | 1.50000 | + | 2.59808i | 0.0521917 | + | 0.0903986i | ||||
\(827\) | 8.66025 | + | 15.0000i | 0.301147 | + | 0.521601i | 0.976396 | − | 0.215988i | \(-0.0692973\pi\) |
−0.675249 | + | 0.737589i | \(0.735964\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6410i | 1.20313i | 0.798823 | + | 0.601566i | \(0.205456\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 6.06218 | − | 10.5000i | 0.210421 | − | 0.364460i | ||||
\(831\) | −15.5885 | − | 9.00000i | −0.540758 | − | 0.312207i | ||||
\(832\) | −6.00000 | + | 3.46410i | −0.208013 | + | 0.120096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.7846i | 0.719281i | ||||||||
\(836\) | −3.46410 | −0.119808 | ||||||||
\(837\) | 28.5788 | + | 4.50000i | 0.987829 | + | 0.155543i | ||||
\(838\) | 3.00000 | 0.103633 | ||||||||
\(839\) | 30.0000i | 1.03572i | 0.855467 | + | 0.517858i | \(0.173270\pi\) | ||||
−0.855467 | + | 0.517858i | \(0.826730\pi\) | |||||||
\(840\) | 0.866025 | − | 1.50000i | 0.0298807 | − | 0.0517549i | ||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | −13.8564 | + | 8.00000i | −0.477523 | + | 0.275698i | ||||
\(843\) | −9.00000 | − | 5.19615i | −0.309976 | − | 0.178965i | ||||
\(844\) | 4.00000 | − | 6.92820i | 0.137686 | − | 0.238479i | ||||
\(845\) | − | 35.0000i | − | 1.20404i | ||||||
\(846\) | −9.00000 | − | 15.5885i | −0.309426 | − | 0.535942i | ||||
\(847\) | −4.00000 | − | 6.92820i | −0.137442 | − | 0.238056i | ||||
\(848\) | 0.866025 | + | 1.50000i | 0.0297394 | + | 0.0515102i | ||||
\(849\) | −24.2487 | + | 42.0000i | −0.832214 | + | 1.44144i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.0000 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(854\) | −1.73205 | + | 3.00000i | −0.0592696 | + | 0.102658i | ||||
\(855\) | −5.19615 | + | 3.00000i | −0.177705 | + | 0.102598i | ||||
\(856\) | −1.50000 | + | 2.59808i | −0.0512689 | + | 0.0888004i | ||||
\(857\) | −46.7654 | + | 27.0000i | −1.59747 | + | 0.922302i | −0.605503 | + | 0.795843i | \(0.707028\pi\) |
−0.991972 | + | 0.126459i | \(0.959639\pi\) | |||||||
\(858\) | −10.3923 | − | 18.0000i | −0.354787 | − | 0.614510i | ||||
\(859\) | 6.00000 | − | 3.46410i | 0.204717 | − | 0.118194i | −0.394137 | − | 0.919052i | \(-0.628956\pi\) |
0.598854 | + | 0.800858i | \(0.295623\pi\) | |||||||
\(860\) | −3.46410 | −0.118125 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.0000 | + | 25.9808i | −0.510902 | + | 0.884908i | ||||
\(863\) | 3.46410 | + | 6.00000i | 0.117919 | + | 0.204242i | 0.918943 | − | 0.394390i | \(-0.129044\pi\) |
−0.801024 | + | 0.598633i | \(0.795711\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 4.50000 | − | 7.79423i | 0.153005 | − | 0.265012i | ||||
\(866\) | 34.6410 | 1.17715 | ||||||||
\(867\) | 29.4449 | 1.00000 | ||||||||
\(868\) | 3.50000 | − | 4.33013i | 0.118798 | − | 0.146974i | ||||
\(869\) | 18.0000i | 0.610608i | ||||||||
\(870\) | 9.00000 | 0.305129 | ||||||||
\(871\) | −24.0000 | − | 13.8564i | −0.813209 | − | 0.469506i | ||||
\(872\) | 14.0000i | 0.474100i | ||||||||
\(873\) | 1.50000 | + | 2.59808i | 0.0507673 | + | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.866025 | − | 0.500000i | −0.0292770 | − | 0.0169031i | ||||
\(876\) | 12.0000i | 0.405442i | ||||||||
\(877\) | 1.00000 | + | 1.73205i | 0.0337676 | + | 0.0584872i | 0.882415 | − | 0.470471i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(878\) | −16.4545 | + | 9.50000i | −0.555312 | + | 0.320609i | ||||
\(879\) | −22.5000 | + | 12.9904i | −0.758906 | + | 0.438155i | ||||
\(880\) | 1.50000 | + | 0.866025i | 0.0505650 | + | 0.0291937i | ||||
\(881\) | −29.4449 | − | 51.0000i | −0.992023 | − | 1.71823i | −0.605182 | − | 0.796087i | \(-0.706900\pi\) |
−0.386840 | − | 0.922147i | \(-0.626434\pi\) | |||||||
\(882\) | −15.5885 | − | 9.00000i | −0.524891 | − | 0.303046i | ||||
\(883\) | − | 10.3923i | − | 0.349729i | −0.984593 | − | 0.174864i | \(-0.944051\pi\) | ||
0.984593 | − | 0.174864i | \(-0.0559487\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.59808 | + | 4.50000i | −0.0873334 | + | 0.151266i | ||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | 25.9808 | + | 15.0000i | 0.872349 | + | 0.503651i | 0.868128 | − | 0.496340i | \(-0.165323\pi\) |
0.00422062 | + | 0.999991i | \(0.498657\pi\) | |||||||
\(888\) | −3.00000 | − | 5.19615i | −0.100673 | − | 0.174371i | ||||
\(889\) | −7.50000 | + | 4.33013i | −0.251542 | + | 0.145228i | ||||
\(890\) | 6.92820 | + | 12.0000i | 0.232234 | + | 0.402241i | ||||
\(891\) | −15.5885 | −0.522233 | ||||||||
\(892\) | −13.5000 | − | 7.79423i | −0.452013 | − | 0.260970i | ||||
\(893\) | 10.3923 | + | 6.00000i | 0.347765 | + | 0.200782i | ||||
\(894\) | −12.9904 | − | 22.5000i | −0.434463 | − | 0.752513i | ||||
\(895\) | − | 15.5885i | − | 0.521065i | ||||||
\(896\) | 0.866025 | + | 0.500000i | 0.0289319 | + | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.3923i | 0.346796i | ||||||||
\(899\) | 28.5788 | + | 4.50000i | 0.953158 | + | 0.150083i | ||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.00000i | − | 0.199667i | ||||||
\(904\) | −9.00000 | − | 15.5885i | −0.299336 | − | 0.518464i | ||||
\(905\) | 6.92820 | − | 12.0000i | 0.230301 | − | 0.398893i | ||||
\(906\) | 10.5000 | − | 18.1865i | 0.348839 | − | 0.604207i | ||||
\(907\) | 10.0000 | 0.332045 | 0.166022 | − | 0.986122i | \(-0.446908\pi\) | ||||
0.166022 | + | 0.986122i | \(0.446908\pi\) | |||||||
\(908\) | 2.59808 | − | 1.50000i | 0.0862202 | − | 0.0497792i | ||||
\(909\) | −38.9711 | + | 22.5000i | −1.29259 | + | 0.746278i | ||||
\(910\) | −6.00000 | + | 3.46410i | −0.198898 | + | 0.114834i | ||||
\(911\) | −15.5885 | + | 27.0000i | −0.516469 | + | 0.894550i | 0.483349 | + | 0.875428i | \(0.339420\pi\) |
−0.999817 | + | 0.0191219i | \(0.993913\pi\) | |||||||
\(912\) | −1.73205 | − | 3.00000i | −0.0573539 | − | 0.0993399i | ||||
\(913\) | −10.5000 | + | 18.1865i | −0.347499 | + | 0.601886i | ||||
\(914\) | 6.92820 | 0.229165 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −3.00000 | − | 1.73205i | −0.0991228 | − | 0.0572286i | ||||
\(917\) | 10.3923 | − | 6.00000i | 0.343184 | − | 0.198137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5000 | − | 37.2391i | −0.709220 | − | 1.22840i | −0.965147 | − | 0.261708i | \(-0.915714\pi\) |
0.255927 | − | 0.966696i | \(-0.417619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.0526 | + | 33.0000i | 0.627803 | + | 1.08739i | ||||
\(922\) | − | 15.5885i | − | 0.513378i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.50000 | + | 2.59808i | −0.0493464 | + | 0.0854704i | ||||
\(925\) | −3.00000 | + | 1.73205i | −0.0986394 | + | 0.0569495i | ||||
\(926\) | −12.1244 | −0.398431 | ||||||||
\(927\) | 7.50000 | − | 12.9904i | 0.246332 | − | 0.426660i | ||||
\(928\) | 5.19615i | 0.170572i | ||||||||
\(929\) | −20.7846 | −0.681921 | −0.340960 | − | 0.940078i | \(-0.610752\pi\) | ||||
−0.340960 | + | 0.940078i | \(0.610752\pi\) | |||||||
\(930\) | 9.52628 | + | 1.50000i | 0.312379 | + | 0.0491869i | ||||
\(931\) | 12.0000 | 0.393284 | ||||||||
\(932\) | − | 12.0000i | − | 0.393073i | ||||||
\(933\) | 36.0000 | + | 20.7846i | 1.17859 | + | 0.680458i | ||||
\(934\) | −39.0000 | −1.27612 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3923 | − | 18.0000i | 0.339683 | − | 0.588348i | ||||
\(937\) | 1.00000 | − | 1.73205i | 0.0326686 | − | 0.0565836i | −0.849229 | − | 0.528025i | \(-0.822933\pi\) |
0.881897 | + | 0.471441i | \(0.156266\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | 23.3827 | − | 13.5000i | 0.763065 | − | 0.440556i | ||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | −9.52628 | − | 16.5000i | −0.310548 | − | 0.537885i | 0.667933 | − | 0.744221i | \(-0.267179\pi\) |
−0.978481 | + | 0.206337i | \(0.933846\pi\) | |||||||
\(942\) | 21.0000 | + | 12.1244i | 0.684217 | + | 0.395033i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −2.59808 | − | 1.50000i | −0.0845602 | − | 0.0488208i | ||||
\(945\) | 5.19615i | 0.169031i | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −8.66025 | + | 15.0000i | −0.281420 | + | 0.487435i | −0.971735 | − | 0.236075i | \(-0.924139\pi\) |
0.690314 | + | 0.723510i | \(0.257472\pi\) | |||||||
\(948\) | −15.5885 | + | 9.00000i | −0.506290 | + | 0.292306i | ||||
\(949\) | 24.0000 | − | 41.5692i | 0.779073 | − | 1.34939i | ||||
\(950\) | −1.73205 | + | 1.00000i | −0.0561951 | + | 0.0324443i | ||||
\(951\) | 22.5000 | − | 12.9904i | 0.729612 | − | 0.421242i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1769 | 1.00992 | 0.504960 | − | 0.863143i | \(-0.331507\pi\) | ||||
0.504960 | + | 0.863143i | \(0.331507\pi\) | |||||||
\(954\) | −4.50000 | − | 2.59808i | −0.145693 | − | 0.0841158i | ||||
\(955\) | 3.00000 | − | 5.19615i | 0.0970777 | − | 0.168144i | ||||
\(956\) | −5.19615 | − | 9.00000i | −0.168056 | − | 0.291081i | ||||
\(957\) | −15.5885 | −0.503903 | ||||||||
\(958\) | −9.00000 | + | 15.5885i | −0.290777 | + | 0.503640i | ||||
\(959\) | 6.92820 | 0.223723 | ||||||||
\(960\) | 1.73205i | 0.0559017i | ||||||||
\(961\) | 29.5000 | + | 9.52628i | 0.951613 | + | 0.307299i | ||||
\(962\) | 24.0000i | 0.773791i | ||||||||
\(963\) | − | 9.00000i | − | 0.290021i | ||||||
\(964\) | 13.5000 | + | 7.79423i | 0.434806 | + | 0.251035i | ||||
\(965\) | − | 23.0000i | − | 0.740396i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.00000 | + | 5.19615i | 0.289420 | + | 0.167097i | 0.637680 | − | 0.770301i | \(-0.279894\pi\) |
−0.348260 | + | 0.937398i | \(0.613227\pi\) | |||||||
\(968\) | 6.92820 | + | 4.00000i | 0.222681 | + | 0.128565i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.500000 | + | 0.866025i | 0.0160540 | + | 0.0278064i | ||||
\(971\) | 7.79423 | − | 4.50000i | 0.250129 | − | 0.144412i | −0.369694 | − | 0.929153i | \(-0.620538\pi\) |
0.619823 | + | 0.784741i | \(0.287204\pi\) | |||||||
\(972\) | −7.79423 | − | 13.5000i | −0.250000 | − | 0.433013i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.1865 | − | 31.5000i | −0.582734 | − | 1.00933i | ||||
\(975\) | −10.3923 | − | 6.00000i | −0.332820 | − | 0.192154i | ||||
\(976\) | − | 3.46410i | − | 0.110883i | ||||||
\(977\) | − | 24.0000i | − | 0.767828i | −0.923369 | − | 0.383914i | \(-0.874576\pi\) | ||
0.923369 | − | 0.383914i | \(-0.125424\pi\) | |||||||
\(978\) | −30.0000 | − | 17.3205i | −0.959294 | − | 0.553849i | ||||
\(979\) | −12.0000 | − | 20.7846i | −0.383522 | − | 0.664279i | ||||
\(980\) | −5.19615 | − | 3.00000i | −0.165985 | − | 0.0958315i | ||||
\(981\) | −21.0000 | − | 36.3731i | −0.670478 | − | 1.16130i | ||||
\(982\) | 25.5000 | − | 14.7224i | 0.813738 | − | 0.469812i | ||||
\(983\) | −10.3923 | − | 18.0000i | −0.331463 | − | 0.574111i | 0.651336 | − | 0.758790i | \(-0.274209\pi\) |
−0.982799 | + | 0.184679i | \(0.940876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.00000 | − | 5.19615i | 0.286473 | − | 0.165395i | ||||
\(988\) | 13.8564i | 0.440831i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −5.19615 | −0.165145 | ||||||||
\(991\) | − | 17.3205i | − | 0.550204i | −0.961415 | − | 0.275102i | \(-0.911288\pi\) | ||
0.961415 | − | 0.275102i | \(-0.0887116\pi\) | |||||||
\(992\) | −0.866025 | + | 5.50000i | −0.0274963 | + | 0.174625i | ||||
\(993\) | 30.0000i | 0.952021i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.06218 | + | 10.5000i | −0.192184 | + | 0.332872i | ||||
\(996\) | −21.0000 | −0.665410 | ||||||||
\(997\) | 14.0000 | + | 24.2487i | 0.443384 | + | 0.767964i | 0.997938 | − | 0.0641836i | \(-0.0204443\pi\) |
−0.554554 | + | 0.832148i | \(0.687111\pi\) | |||||||
\(998\) | −17.3205 | + | 30.0000i | −0.548271 | + | 0.949633i | ||||
\(999\) | 15.5885 | + | 9.00000i | 0.493197 | + | 0.284747i |
(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 | 930.2.o.b.491.1 | yes | 4 | |
3.2 | odd | 2 | inner | 930.2.o.b.491.2 | yes | 4 | |
31.6 | odd | 6 | inner | 930.2.o.b.161.1 | ✓ | 4 | |
93.68 | even | 6 | inner | 930.2.o.b.161.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.b.161.1 | ✓ | 4 | 31.6 | odd | 6 | inner | |
930.2.o.b.161.2 | yes | 4 | 93.68 | even | 6 | inner | |
930.2.o.b.491.1 | yes | 4 | 1.1 | even | 1 | trivial | |
930.2.o.b.491.2 | yes | 4 | 3.2 | odd | 2 | inner |