Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(371,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.371");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.h (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 371.3 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.371 |
Dual form | 930.2.h.a.371.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −1.22474 | − | 1.22474i | −0.500000 | − | 0.500000i | ||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 1.22474 | − | 1.22474i | 0.353553 | − | 0.353553i | ||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | − | 4.00000i | − | 1.06904i | ||||||
\(15\) | 1.22474 | + | 1.22474i | 0.316228 | + | 0.316228i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.34847 | 1.78227 | 0.891133 | − | 0.453743i | \(-0.149911\pi\) | ||||
0.891133 | + | 0.453743i | \(0.149911\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 4.89898 | − | 4.89898i | 1.06904 | − | 1.06904i | ||||
\(22\) | − | 4.89898i | − | 1.04447i | ||||||
\(23\) | 7.34847 | 1.53226 | 0.766131 | − | 0.642685i | \(-0.222179\pi\) | ||||
0.766131 | + | 0.642685i | \(0.222179\pi\) | |||||||
\(24\) | 1.22474 | + | 1.22474i | 0.250000 | + | 0.250000i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −1.22474 | + | 1.22474i | −0.223607 | + | 0.223607i | ||||
\(31\) | 5.00000 | + | 2.44949i | 0.898027 | + | 0.439941i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.00000 | − | 6.00000i | 1.04447 | − | 1.04447i | ||||
\(34\) | 7.34847i | 1.26025i | ||||||||
\(35\) | 4.00000i | 0.676123i | ||||||||
\(36\) | 3.00000i | 0.500000i | ||||||||
\(37\) | − | 2.44949i | − | 0.402694i | −0.979520 | − | 0.201347i | \(-0.935468\pi\) | ||
0.979520 | − | 0.201347i | \(-0.0645318\pi\) | |||||||
\(38\) | − | 2.00000i | − | 0.324443i | ||||||
\(39\) | −3.00000 | − | 3.00000i | −0.480384 | − | 0.480384i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − | 12.0000i | − | 1.87409i | −0.349215 | − | 0.937043i | \(-0.613552\pi\) | ||
0.349215 | − | 0.937043i | \(-0.386448\pi\) | |||||||
\(42\) | 4.89898 | + | 4.89898i | 0.755929 | + | 0.755929i | ||||
\(43\) | − | 2.44949i | − | 0.373544i | −0.982403 | − | 0.186772i | \(-0.940197\pi\) | ||
0.982403 | − | 0.186772i | \(-0.0598025\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 7.34847i | 1.08347i | ||||||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | −1.22474 | + | 1.22474i | −0.176777 | + | 0.176777i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | −9.00000 | + | 9.00000i | −1.26025 | + | 1.26025i | ||||
\(52\) | − | 2.44949i | − | 0.339683i | ||||||
\(53\) | 2.44949 | 0.336463 | 0.168232 | − | 0.985747i | \(-0.446194\pi\) | ||||
0.168232 | + | 0.985747i | \(0.446194\pi\) | |||||||
\(54\) | −3.67423 | + | 3.67423i | −0.500000 | + | 0.500000i | ||||
\(55\) | 4.89898i | 0.660578i | ||||||||
\(56\) | 4.00000i | 0.534522i | ||||||||
\(57\) | 2.44949 | − | 2.44949i | 0.324443 | − | 0.324443i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | −1.22474 | − | 1.22474i | −0.158114 | − | 0.158114i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −2.44949 | + | 5.00000i | −0.311086 | + | 0.635001i | ||||
\(63\) | 12.0000i | 1.51186i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.44949 | 0.303822 | ||||||||
\(66\) | 6.00000 | + | 6.00000i | 0.738549 | + | 0.738549i | ||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | −7.34847 | −0.891133 | ||||||||
\(69\) | −9.00000 | + | 9.00000i | −1.08347 | + | 1.08347i | ||||
\(70\) | −4.00000 | −0.478091 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | − | 2.44949i | − | 0.286691i | −0.989673 | − | 0.143346i | \(-0.954214\pi\) | ||
0.989673 | − | 0.143346i | \(-0.0457860\pi\) | |||||||
\(74\) | 2.44949 | 0.284747 | ||||||||
\(75\) | 1.22474 | − | 1.22474i | 0.141421 | − | 0.141421i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 19.5959 | 2.23316 | ||||||||
\(78\) | 3.00000 | − | 3.00000i | 0.339683 | − | 0.339683i | ||||
\(79\) | 4.89898i | 0.551178i | 0.961276 | + | 0.275589i | \(0.0888729\pi\) | ||||
−0.961276 | + | 0.275589i | \(0.911127\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 12.0000 | 1.32518 | ||||||||
\(83\) | −12.2474 | −1.34433 | −0.672166 | − | 0.740400i | \(-0.734636\pi\) | ||||
−0.672166 | + | 0.740400i | \(0.734636\pi\) | |||||||
\(84\) | −4.89898 | + | 4.89898i | −0.534522 | + | 0.534522i | ||||
\(85\) | − | 7.34847i | − | 0.797053i | ||||||
\(86\) | 2.44949 | 0.264135 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.89898i | 0.522233i | ||||||||
\(89\) | 4.89898 | 0.519291 | 0.259645 | − | 0.965704i | \(-0.416394\pi\) | ||||
0.259645 | + | 0.965704i | \(0.416394\pi\) | |||||||
\(90\) | − | 3.00000i | − | 0.316228i | ||||||
\(91\) | − | 9.79796i | − | 1.02711i | ||||||
\(92\) | −7.34847 | −0.766131 | ||||||||
\(93\) | −9.12372 | + | 3.12372i | −0.946086 | + | 0.323915i | ||||
\(94\) | 12.0000 | 1.23771 | ||||||||
\(95\) | 2.00000i | 0.205196i | ||||||||
\(96\) | −1.22474 | − | 1.22474i | −0.125000 | − | 0.125000i | ||||
\(97\) | 14.0000 | 1.42148 | 0.710742 | − | 0.703452i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 14.6969i | 1.47710i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | − | 6.00000i | − | 0.597022i | −0.954406 | − | 0.298511i | \(-0.903510\pi\) | ||
0.954406 | − | 0.298511i | \(-0.0964900\pi\) | |||||||
\(102\) | −9.00000 | − | 9.00000i | −0.891133 | − | 0.891133i | ||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | −4.89898 | − | 4.89898i | −0.478091 | − | 0.478091i | ||||
\(106\) | 2.44949i | 0.237915i | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | −3.67423 | − | 3.67423i | −0.353553 | − | 0.353553i | ||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | −4.89898 | −0.467099 | ||||||||
\(111\) | 3.00000 | + | 3.00000i | 0.284747 | + | 0.284747i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 2.44949 | + | 2.44949i | 0.229416 | + | 0.229416i | ||||
\(115\) | − | 7.34847i | − | 0.685248i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.34847 | 0.679366 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | −29.3939 | −2.69453 | ||||||||
\(120\) | 1.22474 | − | 1.22474i | 0.111803 | − | 0.111803i | ||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.6969 | + | 14.6969i | 1.32518 | + | 1.32518i | ||||
\(124\) | −5.00000 | − | 2.44949i | −0.449013 | − | 0.219971i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | − | 7.34847i | − | 0.652071i | −0.945357 | − | 0.326036i | \(-0.894287\pi\) | ||
0.945357 | − | 0.326036i | \(-0.105713\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 3.00000 | + | 3.00000i | 0.264135 | + | 0.264135i | ||||
\(130\) | 2.44949i | 0.214834i | ||||||||
\(131\) | − | 12.0000i | − | 1.04844i | −0.851581 | − | 0.524222i | \(-0.824356\pi\) | ||
0.851581 | − | 0.524222i | \(-0.175644\pi\) | |||||||
\(132\) | −6.00000 | + | 6.00000i | −0.522233 | + | 0.522233i | ||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | 4.00000i | 0.345547i | ||||||||
\(135\) | 3.67423 | − | 3.67423i | 0.316228 | − | 0.316228i | ||||
\(136\) | − | 7.34847i | − | 0.630126i | ||||||
\(137\) | −12.2474 | −1.04637 | −0.523185 | − | 0.852219i | \(-0.675256\pi\) | ||||
−0.523185 | + | 0.852219i | \(0.675256\pi\) | |||||||
\(138\) | −9.00000 | − | 9.00000i | −0.766131 | − | 0.766131i | ||||
\(139\) | − | 4.89898i | − | 0.415526i | −0.978179 | − | 0.207763i | \(-0.933382\pi\) | ||
0.978179 | − | 0.207763i | \(-0.0666183\pi\) | |||||||
\(140\) | − | 4.00000i | − | 0.338062i | ||||||
\(141\) | 14.6969 | + | 14.6969i | 1.23771 | + | 1.23771i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.44949 | 0.202721 | ||||||||
\(147\) | −11.0227 | + | 11.0227i | −0.909137 | + | 0.909137i | ||||
\(148\) | 2.44949i | 0.201347i | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 1.22474 | + | 1.22474i | 0.100000 | + | 0.100000i | ||||
\(151\) | − | 14.6969i | − | 1.19602i | −0.801489 | − | 0.598010i | \(-0.795958\pi\) | ||
0.801489 | − | 0.598010i | \(-0.204042\pi\) | |||||||
\(152\) | 2.00000i | 0.162221i | ||||||||
\(153\) | − | 22.0454i | − | 1.78227i | ||||||
\(154\) | 19.5959i | 1.57908i | ||||||||
\(155\) | 2.44949 | − | 5.00000i | 0.196748 | − | 0.401610i | ||||
\(156\) | 3.00000 | + | 3.00000i | 0.240192 | + | 0.240192i | ||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −4.89898 | −0.389742 | ||||||||
\(159\) | −3.00000 | + | 3.00000i | −0.237915 | + | 0.237915i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −29.3939 | −2.31656 | ||||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 12.0000i | 0.937043i | ||||||||
\(165\) | −6.00000 | − | 6.00000i | −0.467099 | − | 0.467099i | ||||
\(166\) | − | 12.2474i | − | 0.950586i | ||||||
\(167\) | 7.34847 | 0.568642 | 0.284321 | − | 0.958729i | \(-0.408232\pi\) | ||||
0.284321 | + | 0.958729i | \(0.408232\pi\) | |||||||
\(168\) | −4.89898 | − | 4.89898i | −0.377964 | − | 0.377964i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 7.34847 | 0.563602 | ||||||||
\(171\) | 6.00000i | 0.458831i | ||||||||
\(172\) | 2.44949i | 0.186772i | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −4.89898 | −0.369274 | ||||||||
\(177\) | −7.34847 | − | 7.34847i | −0.552345 | − | 0.552345i | ||||
\(178\) | 4.89898i | 0.367194i | ||||||||
\(179\) | −14.6969 | −1.09850 | −0.549250 | − | 0.835658i | \(-0.685087\pi\) | ||||
−0.549250 | + | 0.835658i | \(0.685087\pi\) | |||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | − | 24.4949i | − | 1.82069i | −0.413849 | − | 0.910346i | \(-0.635816\pi\) | ||
0.413849 | − | 0.910346i | \(-0.364184\pi\) | |||||||
\(182\) | 9.79796 | 0.726273 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 7.34847i | − | 0.541736i | ||||||
\(185\) | −2.44949 | −0.180090 | ||||||||
\(186\) | −3.12372 | − | 9.12372i | −0.229043 | − | 0.668984i | ||||
\(187\) | −36.0000 | −2.63258 | ||||||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | −14.6969 | − | 14.6969i | −1.06904 | − | 1.06904i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | − | 18.0000i | − | 1.30243i | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||
0.758891 | − | 0.651217i | \(-0.225741\pi\) | |||||||
\(192\) | 1.22474 | − | 1.22474i | 0.0883883 | − | 0.0883883i | ||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 14.0000i | 1.00514i | ||||||||
\(195\) | −3.00000 | + | 3.00000i | −0.214834 | + | 0.214834i | ||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | 22.0454 | 1.57067 | 0.785335 | − | 0.619071i | \(-0.212491\pi\) | ||||
0.785335 | + | 0.619071i | \(0.212491\pi\) | |||||||
\(198\) | −14.6969 | −1.04447 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −4.89898 | + | 4.89898i | −0.345547 | + | 0.345547i | ||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.00000 | − | 9.00000i | 0.630126 | − | 0.630126i | ||||
\(205\) | −12.0000 | −0.838116 | ||||||||
\(206\) | 4.00000i | 0.278693i | ||||||||
\(207\) | − | 22.0454i | − | 1.53226i | ||||||
\(208\) | 2.44949i | 0.169842i | ||||||||
\(209\) | 9.79796 | 0.677739 | ||||||||
\(210\) | 4.89898 | − | 4.89898i | 0.338062 | − | 0.338062i | ||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −2.44949 | −0.168232 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | −2.44949 | −0.167054 | ||||||||
\(216\) | 3.67423 | − | 3.67423i | 0.250000 | − | 0.250000i | ||||
\(217\) | −20.0000 | − | 9.79796i | −1.35769 | − | 0.665129i | ||||
\(218\) | − | 16.0000i | − | 1.08366i | ||||||
\(219\) | 3.00000 | + | 3.00000i | 0.202721 | + | 0.202721i | ||||
\(220\) | − | 4.89898i | − | 0.330289i | ||||||
\(221\) | 18.0000i | 1.21081i | ||||||||
\(222\) | −3.00000 | + | 3.00000i | −0.201347 | + | 0.201347i | ||||
\(223\) | 26.9444i | 1.80433i | 0.431392 | + | 0.902165i | \(0.358023\pi\) | ||||
−0.431392 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(224\) | − | 4.00000i | − | 0.267261i | ||||||
\(225\) | 3.00000i | 0.200000i | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | −2.44949 | + | 2.44949i | −0.162221 | + | 0.162221i | ||||
\(229\) | − | 9.79796i | − | 0.647467i | −0.946148 | − | 0.323734i | \(-0.895062\pi\) | ||
0.946148 | − | 0.323734i | \(-0.104938\pi\) | |||||||
\(230\) | 7.34847 | 0.484544 | ||||||||
\(231\) | −24.0000 | + | 24.0000i | −1.57908 | + | 1.57908i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 7.34847i | 0.480384i | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | − | 6.00000i | − | 0.390567i | ||||||
\(237\) | −6.00000 | − | 6.00000i | −0.389742 | − | 0.389742i | ||||
\(238\) | − | 29.3939i | − | 1.90532i | ||||||
\(239\) | −14.6969 | −0.950666 | −0.475333 | − | 0.879806i | \(-0.657672\pi\) | ||||
−0.475333 | + | 0.879806i | \(0.657672\pi\) | |||||||
\(240\) | 1.22474 | + | 1.22474i | 0.0790569 | + | 0.0790569i | ||||
\(241\) | 4.89898i | 0.315571i | 0.987473 | + | 0.157786i | \(0.0504355\pi\) | ||||
−0.987473 | + | 0.157786i | \(0.949565\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.707107 | − | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.00000i | − | 0.574989i | ||||||
\(246\) | −14.6969 | + | 14.6969i | −0.937043 | + | 0.937043i | ||||
\(247\) | − | 4.89898i | − | 0.311715i | ||||||
\(248\) | 2.44949 | − | 5.00000i | 0.155543 | − | 0.317500i | ||||
\(249\) | 15.0000 | − | 15.0000i | 0.950586 | − | 0.950586i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 9.79796 | 0.618442 | 0.309221 | − | 0.950990i | \(-0.399932\pi\) | ||||
0.309221 | + | 0.950990i | \(0.399932\pi\) | |||||||
\(252\) | − | 12.0000i | − | 0.755929i | ||||||
\(253\) | −36.0000 | −2.26330 | ||||||||
\(254\) | 7.34847 | 0.461084 | ||||||||
\(255\) | 9.00000 | + | 9.00000i | 0.563602 | + | 0.563602i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.0000i | − | 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | −3.00000 | + | 3.00000i | −0.186772 | + | 0.186772i | ||||
\(259\) | 9.79796i | 0.608816i | ||||||||
\(260\) | −2.44949 | −0.151911 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | 0.741362 | ||||||||
\(263\) | 31.8434 | 1.96355 | 0.981773 | − | 0.190057i | \(-0.0608673\pi\) | ||||
0.981773 | + | 0.190057i | \(0.0608673\pi\) | |||||||
\(264\) | −6.00000 | − | 6.00000i | −0.369274 | − | 0.369274i | ||||
\(265\) | − | 2.44949i | − | 0.150471i | ||||||
\(266\) | 8.00000i | 0.490511i | ||||||||
\(267\) | −6.00000 | + | 6.00000i | −0.367194 | + | 0.367194i | ||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 4.89898 | 0.298696 | 0.149348 | − | 0.988785i | \(-0.452283\pi\) | ||||
0.149348 | + | 0.988785i | \(0.452283\pi\) | |||||||
\(270\) | 3.67423 | + | 3.67423i | 0.223607 | + | 0.223607i | ||||
\(271\) | 9.79796i | 0.595184i | 0.954693 | + | 0.297592i | \(0.0961834\pi\) | ||||
−0.954693 | + | 0.297592i | \(0.903817\pi\) | |||||||
\(272\) | 7.34847 | 0.445566 | ||||||||
\(273\) | 12.0000 | + | 12.0000i | 0.726273 | + | 0.726273i | ||||
\(274\) | − | 12.2474i | − | 0.739895i | ||||||
\(275\) | 4.89898 | 0.295420 | ||||||||
\(276\) | 9.00000 | − | 9.00000i | 0.541736 | − | 0.541736i | ||||
\(277\) | − | 17.1464i | − | 1.03023i | −0.857121 | − | 0.515115i | \(-0.827749\pi\) | ||
0.857121 | − | 0.515115i | \(-0.172251\pi\) | |||||||
\(278\) | 4.89898 | 0.293821 | ||||||||
\(279\) | 7.34847 | − | 15.0000i | 0.439941 | − | 0.898027i | ||||
\(280\) | 4.00000 | 0.239046 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | −14.6969 | + | 14.6969i | −0.875190 | + | 0.875190i | ||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.44949 | − | 2.44949i | −0.145095 | − | 0.145095i | ||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 48.0000i | 2.83335i | ||||||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | 37.0000 | 2.17647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.1464 | + | 17.1464i | −1.00514 | + | 1.00514i | ||||
\(292\) | 2.44949i | 0.143346i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | −11.0227 | − | 11.0227i | −0.642857 | − | 0.642857i | ||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | −2.44949 | −0.142374 | ||||||||
\(297\) | −18.0000 | − | 18.0000i | −1.04447 | − | 1.04447i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0000i | 1.04097i | ||||||||
\(300\) | −1.22474 | + | 1.22474i | −0.0707107 | + | 0.0707107i | ||||
\(301\) | 9.79796i | 0.564745i | ||||||||
\(302\) | 14.6969 | 0.845714 | ||||||||
\(303\) | 7.34847 | + | 7.34847i | 0.422159 | + | 0.422159i | ||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 22.0454 | 1.26025 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | −19.5959 | −1.11658 | ||||||||
\(309\) | −4.89898 | + | 4.89898i | −0.278693 | + | 0.278693i | ||||
\(310\) | 5.00000 | + | 2.44949i | 0.283981 | + | 0.139122i | ||||
\(311\) | − | 6.00000i | − | 0.340229i | −0.985424 | − | 0.170114i | \(-0.945586\pi\) | ||
0.985424 | − | 0.170114i | \(-0.0544137\pi\) | |||||||
\(312\) | −3.00000 | + | 3.00000i | −0.169842 | + | 0.169842i | ||||
\(313\) | 17.1464i | 0.969173i | 0.874743 | + | 0.484587i | \(0.161030\pi\) | ||||
−0.874743 | + | 0.484587i | \(0.838970\pi\) | |||||||
\(314\) | 10.0000i | 0.564333i | ||||||||
\(315\) | 12.0000 | 0.676123 | ||||||||
\(316\) | − | 4.89898i | − | 0.275589i | ||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | −3.00000 | − | 3.00000i | −0.168232 | − | 0.168232i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 14.6969 | + | 14.6969i | 0.820303 | + | 0.820303i | ||||
\(322\) | − | 29.3939i | − | 1.63806i | ||||||
\(323\) | −14.6969 | −0.817760 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | − | 2.44949i | − | 0.135873i | ||||||
\(326\) | 20.0000i | 1.10770i | ||||||||
\(327\) | 19.5959 | − | 19.5959i | 1.08366 | − | 1.08366i | ||||
\(328\) | −12.0000 | −0.662589 | ||||||||
\(329\) | 48.0000i | 2.64633i | ||||||||
\(330\) | 6.00000 | − | 6.00000i | 0.330289 | − | 0.330289i | ||||
\(331\) | 24.4949i | 1.34636i | 0.739478 | + | 0.673181i | \(0.235072\pi\) | ||||
−0.739478 | + | 0.673181i | \(0.764928\pi\) | |||||||
\(332\) | 12.2474 | 0.672166 | ||||||||
\(333\) | −7.34847 | −0.402694 | ||||||||
\(334\) | 7.34847i | 0.402090i | ||||||||
\(335\) | − | 4.00000i | − | 0.218543i | ||||||
\(336\) | 4.89898 | − | 4.89898i | 0.267261 | − | 0.267261i | ||||
\(337\) | 26.9444i | 1.46775i | 0.679282 | + | 0.733877i | \(0.262291\pi\) | ||||
−0.679282 | + | 0.733877i | \(0.737709\pi\) | |||||||
\(338\) | 7.00000i | 0.380750i | ||||||||
\(339\) | −22.0454 | − | 22.0454i | −1.19734 | − | 1.19734i | ||||
\(340\) | 7.34847i | 0.398527i | ||||||||
\(341\) | −24.4949 | − | 12.0000i | −1.32647 | − | 0.649836i | ||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −2.44949 | −0.132068 | ||||||||
\(345\) | 9.00000 | + | 9.00000i | 0.484544 | + | 0.484544i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | −17.1464 | −0.920468 | −0.460234 | − | 0.887798i | \(-0.652235\pi\) | ||||
−0.460234 | + | 0.887798i | \(0.652235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 4.00000i | 0.213809i | ||||||||
\(351\) | −9.00000 | + | 9.00000i | −0.480384 | + | 0.480384i | ||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | −2.44949 | −0.130373 | −0.0651866 | − | 0.997873i | \(-0.520764\pi\) | ||||
−0.0651866 | + | 0.997873i | \(0.520764\pi\) | |||||||
\(354\) | 7.34847 | − | 7.34847i | 0.390567 | − | 0.390567i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.89898 | −0.259645 | ||||||||
\(357\) | 36.0000 | − | 36.0000i | 1.90532 | − | 1.90532i | ||||
\(358\) | − | 14.6969i | − | 0.776757i | ||||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 3.00000i | 0.158114i | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 24.4949 | 1.28742 | ||||||||
\(363\) | −15.9217 | + | 15.9217i | −0.835672 | + | 0.835672i | ||||
\(364\) | 9.79796i | 0.513553i | ||||||||
\(365\) | −2.44949 | −0.128212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 26.9444i | − | 1.40649i | −0.710950 | − | 0.703243i | \(-0.751735\pi\) | ||
0.710950 | − | 0.703243i | \(-0.248265\pi\) | |||||||
\(368\) | 7.34847 | 0.383065 | ||||||||
\(369\) | −36.0000 | −1.87409 | ||||||||
\(370\) | − | 2.44949i | − | 0.127343i | ||||||
\(371\) | −9.79796 | −0.508685 | ||||||||
\(372\) | 9.12372 | − | 3.12372i | 0.473043 | − | 0.161958i | ||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | − | 36.0000i | − | 1.86152i | ||||||
\(375\) | −1.22474 | − | 1.22474i | −0.0632456 | − | 0.0632456i | ||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 14.6969 | − | 14.6969i | 0.755929 | − | 0.755929i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | − | 2.00000i | − | 0.102598i | ||||||
\(381\) | 9.00000 | + | 9.00000i | 0.461084 | + | 0.461084i | ||||
\(382\) | 18.0000 | 0.920960 | ||||||||
\(383\) | −26.9444 | −1.37679 | −0.688397 | − | 0.725334i | \(-0.741685\pi\) | ||||
−0.688397 | + | 0.725334i | \(0.741685\pi\) | |||||||
\(384\) | 1.22474 | + | 1.22474i | 0.0625000 | + | 0.0625000i | ||||
\(385\) | − | 19.5959i | − | 0.998700i | ||||||
\(386\) | − | 2.00000i | − | 0.101797i | ||||||
\(387\) | −7.34847 | −0.373544 | ||||||||
\(388\) | −14.0000 | −0.710742 | ||||||||
\(389\) | 4.89898 | 0.248388 | 0.124194 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124194 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(390\) | −3.00000 | − | 3.00000i | −0.151911 | − | 0.151911i | ||||
\(391\) | 54.0000 | 2.73090 | ||||||||
\(392\) | − | 9.00000i | − | 0.454569i | ||||||
\(393\) | 14.6969 | + | 14.6969i | 0.741362 | + | 0.741362i | ||||
\(394\) | 22.0454i | 1.11063i | ||||||||
\(395\) | 4.89898 | 0.246494 | ||||||||
\(396\) | − | 14.6969i | − | 0.738549i | ||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −9.79796 | −0.491127 | ||||||||
\(399\) | −9.79796 | + | 9.79796i | −0.490511 | + | 0.490511i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 19.5959 | 0.978573 | 0.489287 | − | 0.872123i | \(-0.337257\pi\) | ||||
0.489287 | + | 0.872123i | \(0.337257\pi\) | |||||||
\(402\) | −4.89898 | − | 4.89898i | −0.244339 | − | 0.244339i | ||||
\(403\) | −6.00000 | + | 12.2474i | −0.298881 | + | 0.610089i | ||||
\(404\) | 6.00000i | 0.298511i | ||||||||
\(405\) | 9.00000i | 0.447214i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 9.00000 | + | 9.00000i | 0.445566 | + | 0.445566i | ||||
\(409\) | − | 19.5959i | − | 0.968956i | −0.874804 | − | 0.484478i | \(-0.839010\pi\) | ||
0.874804 | − | 0.484478i | \(-0.160990\pi\) | |||||||
\(410\) | − | 12.0000i | − | 0.592638i | ||||||
\(411\) | 15.0000 | − | 15.0000i | 0.739895 | − | 0.739895i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | − | 24.0000i | − | 1.18096i | ||||||
\(414\) | 22.0454 | 1.08347 | ||||||||
\(415\) | 12.2474i | 0.601204i | ||||||||
\(416\) | −2.44949 | −0.120096 | ||||||||
\(417\) | 6.00000 | + | 6.00000i | 0.293821 | + | 0.293821i | ||||
\(418\) | 9.79796i | 0.479234i | ||||||||
\(419\) | 30.0000i | 1.46560i | 0.680446 | + | 0.732798i | \(0.261786\pi\) | ||||
−0.680446 | + | 0.732798i | \(0.738214\pi\) | |||||||
\(420\) | 4.89898 | + | 4.89898i | 0.239046 | + | 0.239046i | ||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 14.0000i | 0.681509i | ||||||||
\(423\) | −36.0000 | −1.75038 | ||||||||
\(424\) | − | 2.44949i | − | 0.118958i | ||||||
\(425\) | −7.34847 | −0.356453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 14.6969 | + | 14.6969i | 0.709575 | + | 0.709575i | ||||
\(430\) | − | 2.44949i | − | 0.118125i | ||||||
\(431\) | − | 24.0000i | − | 1.15604i | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||
0.816023 | − | 0.578020i | \(-0.196174\pi\) | |||||||
\(432\) | 3.67423 | + | 3.67423i | 0.176777 | + | 0.176777i | ||||
\(433\) | 17.1464i | 0.824005i | 0.911183 | + | 0.412002i | \(0.135170\pi\) | ||||
−0.911183 | + | 0.412002i | \(0.864830\pi\) | |||||||
\(434\) | 9.79796 | − | 20.0000i | 0.470317 | − | 0.960031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | 0.766261 | ||||||||
\(437\) | −14.6969 | −0.703050 | ||||||||
\(438\) | −3.00000 | + | 3.00000i | −0.143346 | + | 0.143346i | ||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 4.89898 | 0.233550 | ||||||||
\(441\) | − | 27.0000i | − | 1.28571i | ||||||
\(442\) | −18.0000 | −0.856173 | ||||||||
\(443\) | − | 24.0000i | − | 1.14027i | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||
0.821549 | − | 0.570137i | \(-0.193110\pi\) | |||||||
\(444\) | −3.00000 | − | 3.00000i | −0.142374 | − | 0.142374i | ||||
\(445\) | − | 4.89898i | − | 0.232234i | ||||||
\(446\) | −26.9444 | −1.27585 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.00000 | 0.188982 | ||||||||
\(449\) | 29.3939 | 1.38718 | 0.693591 | − | 0.720369i | \(-0.256027\pi\) | ||||
0.693591 | + | 0.720369i | \(0.256027\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | 58.7878i | 2.76821i | ||||||||
\(452\) | − | 18.0000i | − | 0.846649i | ||||||
\(453\) | 18.0000 | + | 18.0000i | 0.845714 | + | 0.845714i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.79796 | −0.459335 | ||||||||
\(456\) | −2.44949 | − | 2.44949i | −0.114708 | − | 0.114708i | ||||
\(457\) | − | 7.34847i | − | 0.343747i | −0.985119 | − | 0.171873i | \(-0.945018\pi\) | ||
0.985119 | − | 0.171873i | \(-0.0549820\pi\) | |||||||
\(458\) | 9.79796 | 0.457829 | ||||||||
\(459\) | 27.0000 | + | 27.0000i | 1.26025 | + | 1.26025i | ||||
\(460\) | 7.34847i | 0.342624i | ||||||||
\(461\) | 14.6969 | 0.684505 | 0.342252 | − | 0.939608i | \(-0.388810\pi\) | ||||
0.342252 | + | 0.939608i | \(0.388810\pi\) | |||||||
\(462\) | −24.0000 | − | 24.0000i | −1.11658 | − | 1.11658i | ||||
\(463\) | 2.44949i | 0.113837i | 0.998379 | + | 0.0569187i | \(0.0181276\pi\) | ||||
−0.998379 | + | 0.0569187i | \(0.981872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.12372 | + | 9.12372i | 0.144859 | + | 0.423103i | ||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 36.0000i | 1.66588i | 0.553362 | + | 0.832941i | \(0.313345\pi\) | ||||
−0.553362 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(468\) | −7.34847 | −0.339683 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | − | 12.0000i | − | 0.553519i | ||||||
\(471\) | −12.2474 | + | 12.2474i | −0.564333 | + | 0.564333i | ||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | 12.0000i | 0.551761i | ||||||||
\(474\) | 6.00000 | − | 6.00000i | 0.275589 | − | 0.275589i | ||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 29.3939 | 1.34727 | ||||||||
\(477\) | − | 7.34847i | − | 0.336463i | ||||||
\(478\) | − | 14.6969i | − | 0.672222i | ||||||
\(479\) | − | 30.0000i | − | 1.37073i | −0.728197 | − | 0.685367i | \(-0.759642\pi\) | ||
0.728197 | − | 0.685367i | \(-0.240358\pi\) | |||||||
\(480\) | −1.22474 | + | 1.22474i | −0.0559017 | + | 0.0559017i | ||||
\(481\) | 6.00000 | 0.273576 | ||||||||
\(482\) | −4.89898 | −0.223142 | ||||||||
\(483\) | 36.0000 | − | 36.0000i | 1.63806 | − | 1.63806i | ||||
\(484\) | −13.0000 | −0.590909 | ||||||||
\(485\) | − | 14.0000i | − | 0.635707i | ||||||
\(486\) | 11.0227 | + | 11.0227i | 0.500000 | + | 0.500000i | ||||
\(487\) | 31.8434i | 1.44296i | 0.692435 | + | 0.721480i | \(0.256538\pi\) | ||||
−0.692435 | + | 0.721480i | \(0.743462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.4949 | + | 24.4949i | −1.10770 | + | 1.10770i | ||||
\(490\) | 9.00000 | 0.406579 | ||||||||
\(491\) | 19.5959 | 0.884351 | 0.442176 | − | 0.896928i | \(-0.354207\pi\) | ||||
0.442176 | + | 0.896928i | \(0.354207\pi\) | |||||||
\(492\) | −14.6969 | − | 14.6969i | −0.662589 | − | 0.662589i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.89898 | 0.220416 | ||||||||
\(495\) | 14.6969 | 0.660578 | ||||||||
\(496\) | 5.00000 | + | 2.44949i | 0.224507 | + | 0.109985i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.0000 | + | 15.0000i | 0.672166 | + | 0.672166i | ||||
\(499\) | − | 9.79796i | − | 0.438617i | −0.975656 | − | 0.219308i | \(-0.929620\pi\) | ||
0.975656 | − | 0.219308i | \(-0.0703801\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | −9.00000 | + | 9.00000i | −0.402090 | + | 0.402090i | ||||
\(502\) | 9.79796i | 0.437304i | ||||||||
\(503\) | − | 24.0000i | − | 1.07011i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) | ||
0.844818 | − | 0.535054i | \(-0.179709\pi\) | |||||||
\(504\) | 12.0000 | 0.534522 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | − | 36.0000i | − | 1.60040i | ||||||
\(507\) | −8.57321 | + | 8.57321i | −0.380750 | + | 0.380750i | ||||
\(508\) | 7.34847i | 0.326036i | ||||||||
\(509\) | −39.1918 | −1.73715 | −0.868574 | − | 0.495560i | \(-0.834963\pi\) | ||||
−0.868574 | + | 0.495560i | \(0.834963\pi\) | |||||||
\(510\) | −9.00000 | + | 9.00000i | −0.398527 | + | 0.398527i | ||||
\(511\) | 9.79796i | 0.433436i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −7.34847 | − | 7.34847i | −0.324443 | − | 0.324443i | ||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | − | 4.00000i | − | 0.176261i | ||||||
\(516\) | −3.00000 | − | 3.00000i | −0.132068 | − | 0.132068i | ||||
\(517\) | 58.7878i | 2.58548i | ||||||||
\(518\) | −9.79796 | −0.430498 | ||||||||
\(519\) | −7.34847 | − | 7.34847i | −0.322562 | − | 0.322562i | ||||
\(520\) | − | 2.44949i | − | 0.107417i | ||||||
\(521\) | − | 18.0000i | − | 0.788594i | −0.918983 | − | 0.394297i | \(-0.870988\pi\) | ||
0.918983 | − | 0.394297i | \(-0.129012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0454i | 0.963978i | 0.876177 | + | 0.481989i | \(0.160086\pi\) | ||||
−0.876177 | + | 0.481989i | \(0.839914\pi\) | |||||||
\(524\) | 12.0000i | 0.524222i | ||||||||
\(525\) | −4.89898 | + | 4.89898i | −0.213809 | + | 0.213809i | ||||
\(526\) | 31.8434i | 1.38844i | ||||||||
\(527\) | 36.7423 | + | 18.0000i | 1.60052 | + | 0.784092i | ||||
\(528\) | 6.00000 | − | 6.00000i | 0.261116 | − | 0.261116i | ||||
\(529\) | 31.0000 | 1.34783 | ||||||||
\(530\) | 2.44949 | 0.106399 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 29.3939 | 1.27319 | ||||||||
\(534\) | −6.00000 | − | 6.00000i | −0.259645 | − | 0.259645i | ||||
\(535\) | −12.0000 | −0.518805 | ||||||||
\(536\) | − | 4.00000i | − | 0.172774i | ||||||
\(537\) | 18.0000 | − | 18.0000i | 0.776757 | − | 0.776757i | ||||
\(538\) | 4.89898i | 0.211210i | ||||||||
\(539\) | −44.0908 | −1.89913 | ||||||||
\(540\) | −3.67423 | + | 3.67423i | −0.158114 | + | 0.158114i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | −9.79796 | −0.420858 | ||||||||
\(543\) | 30.0000 | + | 30.0000i | 1.28742 | + | 1.28742i | ||||
\(544\) | 7.34847i | 0.315063i | ||||||||
\(545\) | 16.0000i | 0.685365i | ||||||||
\(546\) | −12.0000 | + | 12.0000i | −0.513553 | + | 0.513553i | ||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 12.2474 | 0.523185 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.89898i | 0.208893i | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 9.00000 | + | 9.00000i | 0.383065 | + | 0.383065i | ||||
\(553\) | − | 19.5959i | − | 0.833303i | ||||||
\(554\) | 17.1464 | 0.728482 | ||||||||
\(555\) | 3.00000 | − | 3.00000i | 0.127343 | − | 0.127343i | ||||
\(556\) | 4.89898i | 0.207763i | ||||||||
\(557\) | 26.9444 | 1.14167 | 0.570835 | − | 0.821065i | \(-0.306620\pi\) | ||||
0.570835 | + | 0.821065i | \(0.306620\pi\) | |||||||
\(558\) | 15.0000 | + | 7.34847i | 0.635001 | + | 0.311086i | ||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 4.00000i | 0.169031i | ||||||||
\(561\) | 44.0908 | − | 44.0908i | 1.86152 | − | 1.86152i | ||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | − | 12.0000i | − | 0.505740i | −0.967500 | − | 0.252870i | \(-0.918626\pi\) | ||
0.967500 | − | 0.252870i | \(-0.0813744\pi\) | |||||||
\(564\) | −14.6969 | − | 14.6969i | −0.618853 | − | 0.618853i | ||||
\(565\) | 18.0000 | 0.757266 | ||||||||
\(566\) | − | 4.00000i | − | 0.168133i | ||||||
\(567\) | 36.0000 | 1.51186 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5959 | 0.821504 | 0.410752 | − | 0.911747i | \(-0.365266\pi\) | ||||
0.410752 | + | 0.911747i | \(0.365266\pi\) | |||||||
\(570\) | 2.44949 | − | 2.44949i | 0.102598 | − | 0.102598i | ||||
\(571\) | − | 44.0908i | − | 1.84514i | −0.385826 | − | 0.922572i | \(-0.626083\pi\) | ||
0.385826 | − | 0.922572i | \(-0.373917\pi\) | |||||||
\(572\) | 12.0000i | 0.501745i | ||||||||
\(573\) | 22.0454 | + | 22.0454i | 0.920960 | + | 0.920960i | ||||
\(574\) | −48.0000 | −2.00348 | ||||||||
\(575\) | −7.34847 | −0.306452 | ||||||||
\(576\) | 3.00000i | 0.125000i | ||||||||
\(577\) | −26.0000 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(578\) | 37.0000i | 1.53900i | ||||||||
\(579\) | 2.44949 | − | 2.44949i | 0.101797 | − | 0.101797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.9898 | 2.03244 | ||||||||
\(582\) | −17.1464 | − | 17.1464i | −0.710742 | − | 0.710742i | ||||
\(583\) | −12.0000 | −0.496989 | ||||||||
\(584\) | −2.44949 | −0.101361 | ||||||||
\(585\) | − | 7.34847i | − | 0.303822i | ||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −12.2474 | −0.505506 | −0.252753 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252753 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(588\) | 11.0227 | − | 11.0227i | 0.454569 | − | 0.454569i | ||||
\(589\) | −10.0000 | − | 4.89898i | −0.412043 | − | 0.201859i | ||||
\(590\) | 6.00000i | 0.247016i | ||||||||
\(591\) | −27.0000 | + | 27.0000i | −1.11063 | + | 1.11063i | ||||
\(592\) | − | 2.44949i | − | 0.100673i | ||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 18.0000 | − | 18.0000i | 0.738549 | − | 0.738549i | ||||
\(595\) | 29.3939i | 1.20503i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.0000 | − | 12.0000i | −0.491127 | − | 0.491127i | ||||
\(598\) | −18.0000 | −0.736075 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −1.22474 | − | 1.22474i | −0.0500000 | − | 0.0500000i | ||||
\(601\) | 4.89898i | 0.199834i | 0.994996 | + | 0.0999168i | \(0.0318577\pi\) | ||||
−0.994996 | + | 0.0999168i | \(0.968142\pi\) | |||||||
\(602\) | −9.79796 | −0.399335 | ||||||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 14.6969i | 0.598010i | ||||||||
\(605\) | − | 13.0000i | − | 0.528525i | ||||||
\(606\) | −7.34847 | + | 7.34847i | −0.298511 | + | 0.298511i | ||||
\(607\) | 4.00000 | 0.162355 | 0.0811775 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811775 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(608\) | − | 2.00000i | − | 0.0811107i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3939 | 1.18915 | ||||||||
\(612\) | 22.0454i | 0.891133i | ||||||||
\(613\) | − | 41.6413i | − | 1.68188i | −0.541130 | − | 0.840939i | \(-0.682003\pi\) | ||
0.541130 | − | 0.840939i | \(-0.317997\pi\) | |||||||
\(614\) | 16.0000i | 0.645707i | ||||||||
\(615\) | 14.6969 | − | 14.6969i | 0.592638 | − | 0.592638i | ||||
\(616\) | − | 19.5959i | − | 0.789542i | ||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | −4.89898 | − | 4.89898i | −0.197066 | − | 0.197066i | ||||
\(619\) | − | 29.3939i | − | 1.18144i | −0.806877 | − | 0.590720i | \(-0.798844\pi\) | ||
0.806877 | − | 0.590720i | \(-0.201156\pi\) | |||||||
\(620\) | −2.44949 | + | 5.00000i | −0.0983739 | + | 0.200805i | ||||
\(621\) | 27.0000 | + | 27.0000i | 1.08347 | + | 1.08347i | ||||
\(622\) | 6.00000 | 0.240578 | ||||||||
\(623\) | −19.5959 | −0.785094 | ||||||||
\(624\) | −3.00000 | − | 3.00000i | −0.120096 | − | 0.120096i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.1464 | −0.685309 | ||||||||
\(627\) | −12.0000 | + | 12.0000i | −0.479234 | + | 0.479234i | ||||
\(628\) | −10.0000 | −0.399043 | ||||||||
\(629\) | − | 18.0000i | − | 0.717707i | ||||||
\(630\) | 12.0000i | 0.478091i | ||||||||
\(631\) | − | 9.79796i | − | 0.390051i | −0.980798 | − | 0.195025i | \(-0.937521\pi\) | ||
0.980798 | − | 0.195025i | \(-0.0624789\pi\) | |||||||
\(632\) | 4.89898 | 0.194871 | ||||||||
\(633\) | −17.1464 | + | 17.1464i | −0.681509 | + | 0.681509i | ||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | −7.34847 | −0.291615 | ||||||||
\(636\) | 3.00000 | − | 3.00000i | 0.118958 | − | 0.118958i | ||||
\(637\) | 22.0454i | 0.873471i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.89898 | 0.193498 | 0.0967490 | − | 0.995309i | \(-0.469156\pi\) | ||||
0.0967490 | + | 0.995309i | \(0.469156\pi\) | |||||||
\(642\) | −14.6969 | + | 14.6969i | −0.580042 | + | 0.580042i | ||||
\(643\) | 22.0454i | 0.869386i | 0.900579 | + | 0.434693i | \(0.143143\pi\) | ||||
−0.900579 | + | 0.434693i | \(0.856857\pi\) | |||||||
\(644\) | 29.3939 | 1.15828 | ||||||||
\(645\) | 3.00000 | − | 3.00000i | 0.118125 | − | 0.118125i | ||||
\(646\) | − | 14.6969i | − | 0.578243i | ||||||
\(647\) | −36.7423 | −1.44449 | −0.722245 | − | 0.691637i | \(-0.756890\pi\) | ||||
−0.722245 | + | 0.691637i | \(0.756890\pi\) | |||||||
\(648\) | 9.00000i | 0.353553i | ||||||||
\(649\) | − | 29.3939i | − | 1.15381i | ||||||
\(650\) | 2.44949 | 0.0960769 | ||||||||
\(651\) | 36.4949 | − | 12.4949i | 1.43035 | − | 0.489714i | ||||
\(652\) | −20.0000 | −0.783260 | ||||||||
\(653\) | − | 42.0000i | − | 1.64359i | −0.569785 | − | 0.821794i | \(-0.692974\pi\) | ||
0.569785 | − | 0.821794i | \(-0.307026\pi\) | |||||||
\(654\) | 19.5959 | + | 19.5959i | 0.766261 | + | 0.766261i | ||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | − | 12.0000i | − | 0.468521i | ||||||
\(657\) | −7.34847 | −0.286691 | ||||||||
\(658\) | −48.0000 | −1.87123 | ||||||||
\(659\) | − | 36.0000i | − | 1.40236i | −0.712984 | − | 0.701180i | \(-0.752657\pi\) | ||
0.712984 | − | 0.701180i | \(-0.247343\pi\) | |||||||
\(660\) | 6.00000 | + | 6.00000i | 0.233550 | + | 0.233550i | ||||
\(661\) | −4.00000 | −0.155582 | −0.0777910 | − | 0.996970i | \(-0.524787\pi\) | ||||
−0.0777910 | + | 0.996970i | \(0.524787\pi\) | |||||||
\(662\) | −24.4949 | −0.952021 | ||||||||
\(663\) | −22.0454 | − | 22.0454i | −0.856173 | − | 0.856173i | ||||
\(664\) | 12.2474i | 0.475293i | ||||||||
\(665\) | − | 8.00000i | − | 0.310227i | ||||||
\(666\) | − | 7.34847i | − | 0.284747i | ||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −7.34847 | −0.284321 | ||||||||
\(669\) | −33.0000 | − | 33.0000i | −1.27585 | − | 1.27585i | ||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.89898 | + | 4.89898i | 0.188982 | + | 0.188982i | ||||
\(673\) | 26.9444i | 1.03863i | 0.854583 | + | 0.519315i | \(0.173813\pi\) | ||||
−0.854583 | + | 0.519315i | \(0.826187\pi\) | |||||||
\(674\) | −26.9444 | −1.03786 | ||||||||
\(675\) | −3.67423 | − | 3.67423i | −0.141421 | − | 0.141421i | ||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | −31.8434 | −1.22384 | −0.611920 | − | 0.790920i | \(-0.709603\pi\) | ||||
−0.611920 | + | 0.790920i | \(0.709603\pi\) | |||||||
\(678\) | 22.0454 | − | 22.0454i | 0.846649 | − | 0.846649i | ||||
\(679\) | −56.0000 | −2.14908 | ||||||||
\(680\) | −7.34847 | −0.281801 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | − | 24.4949i | 0.459504 | − | 0.937958i | ||||
\(683\) | 48.0000i | 1.83667i | 0.395805 | + | 0.918334i | \(0.370466\pi\) | ||||
−0.395805 | + | 0.918334i | \(0.629534\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | 12.2474i | 0.467951i | ||||||||
\(686\) | − | 8.00000i | − | 0.305441i | ||||||
\(687\) | 12.0000 | + | 12.0000i | 0.457829 | + | 0.457829i | ||||
\(688\) | − | 2.44949i | − | 0.0933859i | ||||||
\(689\) | 6.00000i | 0.228582i | ||||||||
\(690\) | −9.00000 | + | 9.00000i | −0.342624 | + | 0.342624i | ||||
\(691\) | −4.00000 | −0.152167 | −0.0760836 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760836 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(692\) | − | 6.00000i | − | 0.228086i | ||||||
\(693\) | − | 58.7878i | − | 2.23316i | ||||||
\(694\) | − | 17.1464i | − | 0.650870i | ||||||
\(695\) | −4.89898 | −0.185829 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 88.1816i | − | 3.34012i | ||||||
\(698\) | − | 2.00000i | − | 0.0757011i | ||||||
\(699\) | 7.34847 | + | 7.34847i | 0.277945 | + | 0.277945i | ||||
\(700\) | −4.00000 | −0.151186 | ||||||||
\(701\) | 36.0000i | 1.35970i | 0.733351 | + | 0.679851i | \(0.237955\pi\) | ||||
−0.733351 | + | 0.679851i | \(0.762045\pi\) | |||||||
\(702\) | −9.00000 | − | 9.00000i | −0.339683 | − | 0.339683i | ||||
\(703\) | 4.89898i | 0.184769i | ||||||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 14.6969 | − | 14.6969i | 0.553519 | − | 0.553519i | ||||
\(706\) | − | 2.44949i | − | 0.0921878i | ||||||
\(707\) | 24.0000i | 0.902613i | ||||||||
\(708\) | 7.34847 | + | 7.34847i | 0.276172 | + | 0.276172i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6969 | 0.551178 | ||||||||
\(712\) | − | 4.89898i | − | 0.183597i | ||||||
\(713\) | 36.7423 | + | 18.0000i | 1.37601 | + | 0.674105i | ||||
\(714\) | 36.0000 | + | 36.0000i | 1.34727 | + | 1.34727i | ||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 14.6969 | 0.549250 | ||||||||
\(717\) | 18.0000 | − | 18.0000i | 0.672222 | − | 0.672222i | ||||
\(718\) | 24.0000 | 0.895672 | ||||||||
\(719\) | 4.89898 | 0.182701 | 0.0913506 | − | 0.995819i | \(-0.470882\pi\) | ||||
0.0913506 | + | 0.995819i | \(0.470882\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | − | 15.0000i | − | 0.558242i | ||||||
\(723\) | −6.00000 | − | 6.00000i | −0.223142 | − | 0.223142i | ||||
\(724\) | 24.4949i | 0.910346i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.9217 | − | 15.9217i | −0.590909 | − | 0.590909i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | −9.79796 | −0.363137 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | − | 2.44949i | − | 0.0906597i | ||||||
\(731\) | − | 18.0000i | − | 0.665754i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | 26.9444 | 0.994535 | ||||||||
\(735\) | 11.0227 | + | 11.0227i | 0.406579 | + | 0.406579i | ||||
\(736\) | 7.34847i | 0.270868i | ||||||||
\(737\) | −19.5959 | −0.721825 | ||||||||
\(738\) | − | 36.0000i | − | 1.32518i | ||||||
\(739\) | 14.6969i | 0.540636i | 0.962771 | + | 0.270318i | \(0.0871288\pi\) | ||||
−0.962771 | + | 0.270318i | \(0.912871\pi\) | |||||||
\(740\) | 2.44949 | 0.0900450 | ||||||||
\(741\) | 6.00000 | + | 6.00000i | 0.220416 | + | 0.220416i | ||||
\(742\) | − | 9.79796i | − | 0.359694i | ||||||
\(743\) | −2.44949 | −0.0898631 | −0.0449315 | − | 0.998990i | \(-0.514307\pi\) | ||||
−0.0449315 | + | 0.998990i | \(0.514307\pi\) | |||||||
\(744\) | 3.12372 | + | 9.12372i | 0.114521 | + | 0.334492i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.00000i | 0.0732252i | ||||||||
\(747\) | 36.7423i | 1.34433i | ||||||||
\(748\) | 36.0000 | 1.31629 | ||||||||
\(749\) | 48.0000i | 1.75388i | ||||||||
\(750\) | 1.22474 | − | 1.22474i | 0.0447214 | − | 0.0447214i | ||||
\(751\) | 10.0000 | 0.364905 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(752\) | − | 12.0000i | − | 0.437595i | ||||||
\(753\) | −12.0000 | + | 12.0000i | −0.437304 | + | 0.437304i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.6969 | −0.534876 | ||||||||
\(756\) | 14.6969 | + | 14.6969i | 0.534522 | + | 0.534522i | ||||
\(757\) | 51.4393i | 1.86959i | 0.355184 | + | 0.934796i | \(0.384418\pi\) | ||||
−0.355184 | + | 0.934796i | \(0.615582\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | 44.0908 | − | 44.0908i | 1.60040 | − | 1.60040i | ||||
\(760\) | 2.00000 | 0.0725476 | ||||||||
\(761\) | −29.3939 | −1.06553 | −0.532764 | − | 0.846264i | \(-0.678847\pi\) | ||||
−0.532764 | + | 0.846264i | \(0.678847\pi\) | |||||||
\(762\) | −9.00000 | + | 9.00000i | −0.326036 | + | 0.326036i | ||||
\(763\) | 64.0000 | 2.31696 | ||||||||
\(764\) | 18.0000i | 0.651217i | ||||||||
\(765\) | −22.0454 | −0.797053 | ||||||||
\(766\) | − | 26.9444i | − | 0.973540i | ||||||
\(767\) | −14.6969 | −0.530676 | ||||||||
\(768\) | −1.22474 | + | 1.22474i | −0.0441942 | + | 0.0441942i | ||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 19.5959 | 0.706188 | ||||||||
\(771\) | 22.0454 | + | 22.0454i | 0.793946 | + | 0.793946i | ||||
\(772\) | 2.00000 | 0.0719816 | ||||||||
\(773\) | −46.5403 | −1.67394 | −0.836969 | − | 0.547250i | \(-0.815675\pi\) | ||||
−0.836969 | + | 0.547250i | \(0.815675\pi\) | |||||||
\(774\) | − | 7.34847i | − | 0.264135i | ||||||
\(775\) | −5.00000 | − | 2.44949i | −0.179605 | − | 0.0879883i | ||||
\(776\) | − | 14.0000i | − | 0.502571i | ||||||
\(777\) | −12.0000 | − | 12.0000i | −0.430498 | − | 0.430498i | ||||
\(778\) | 4.89898i | 0.175637i | ||||||||
\(779\) | 24.0000i | 0.859889i | ||||||||
\(780\) | 3.00000 | − | 3.00000i | 0.107417 | − | 0.107417i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 54.0000i | 1.93104i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | − | 10.0000i | − | 0.356915i | ||||||
\(786\) | −14.6969 | + | 14.6969i | −0.524222 | + | 0.524222i | ||||
\(787\) | − | 7.34847i | − | 0.261945i | −0.991386 | − | 0.130972i | \(-0.958190\pi\) | ||
0.991386 | − | 0.130972i | \(-0.0418099\pi\) | |||||||
\(788\) | −22.0454 | −0.785335 | ||||||||
\(789\) | −39.0000 | + | 39.0000i | −1.38844 | + | 1.38844i | ||||
\(790\) | 4.89898i | 0.174298i | ||||||||
\(791\) | − | 72.0000i | − | 2.56003i | ||||||
\(792\) | 14.6969 | 0.522233 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 34.0000i | − | 1.20661i | ||||||
\(795\) | 3.00000 | + | 3.00000i | 0.106399 | + | 0.106399i | ||||
\(796\) | − | 9.79796i | − | 0.347279i | ||||||
\(797\) | 12.2474 | 0.433827 | 0.216913 | − | 0.976191i | \(-0.430401\pi\) | ||||
0.216913 | + | 0.976191i | \(0.430401\pi\) | |||||||
\(798\) | −9.79796 | − | 9.79796i | −0.346844 | − | 0.346844i | ||||
\(799\) | − | 88.1816i | − | 3.11964i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | − | 14.6969i | − | 0.519291i | ||||||
\(802\) | 19.5959i | 0.691956i | ||||||||
\(803\) | 12.0000i | 0.423471i | ||||||||
\(804\) | 4.89898 | − | 4.89898i | 0.172774 | − | 0.172774i | ||||
\(805\) | 29.3939i | 1.03600i | ||||||||
\(806\) | −12.2474 | − | 6.00000i | −0.431398 | − | 0.211341i | ||||
\(807\) | −6.00000 | + | 6.00000i | −0.211210 | + | 0.211210i | ||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | 24.4949 | 0.861195 | 0.430597 | − | 0.902544i | \(-0.358303\pi\) | ||||
0.430597 | + | 0.902544i | \(0.358303\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | − | 12.0000i | −0.420858 | − | 0.420858i | ||||
\(814\) | −12.0000 | −0.420600 | ||||||||
\(815\) | − | 20.0000i | − | 0.700569i | ||||||
\(816\) | −9.00000 | + | 9.00000i | −0.315063 | + | 0.315063i | ||||
\(817\) | 4.89898i | 0.171394i | ||||||||
\(818\) | 19.5959 | 0.685155 | ||||||||
\(819\) | −29.3939 | −1.02711 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | −48.9898 | −1.70976 | −0.854878 | − | 0.518829i | \(-0.826368\pi\) | ||||
−0.854878 | + | 0.518829i | \(0.826368\pi\) | |||||||
\(822\) | 15.0000 | + | 15.0000i | 0.523185 | + | 0.523185i | ||||
\(823\) | − | 41.6413i | − | 1.45153i | −0.687945 | − | 0.725763i | \(-0.741487\pi\) | ||
0.687945 | − | 0.725763i | \(-0.258513\pi\) | |||||||
\(824\) | − | 4.00000i | − | 0.139347i | ||||||
\(825\) | −6.00000 | + | 6.00000i | −0.208893 | + | 0.208893i | ||||
\(826\) | 24.0000 | 0.835067 | ||||||||
\(827\) | 46.5403 | 1.61836 | 0.809182 | − | 0.587557i | \(-0.199910\pi\) | ||||
0.809182 | + | 0.587557i | \(0.199910\pi\) | |||||||
\(828\) | 22.0454i | 0.766131i | ||||||||
\(829\) | 34.2929i | 1.19104i | 0.803340 | + | 0.595520i | \(0.203054\pi\) | ||||
−0.803340 | + | 0.595520i | \(0.796946\pi\) | |||||||
\(830\) | −12.2474 | −0.425115 | ||||||||
\(831\) | 21.0000 | + | 21.0000i | 0.728482 | + | 0.728482i | ||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | 66.1362 | 2.29148 | ||||||||
\(834\) | −6.00000 | + | 6.00000i | −0.207763 | + | 0.207763i | ||||
\(835\) | − | 7.34847i | − | 0.254304i | ||||||
\(836\) | −9.79796 | −0.338869 | ||||||||
\(837\) | 9.37117 | + | 27.3712i | 0.323915 | + | 0.946086i | ||||
\(838\) | −30.0000 | −1.03633 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | −4.89898 | + | 4.89898i | −0.169031 | + | 0.169031i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | − | 26.0000i | − | 0.896019i | ||||||
\(843\) | −7.34847 | − | 7.34847i | −0.253095 | − | 0.253095i | ||||
\(844\) | −14.0000 | −0.481900 | ||||||||
\(845\) | − | 7.00000i | − | 0.240807i | ||||||
\(846\) | − | 36.0000i | − | 1.23771i | ||||||
\(847\) | −52.0000 | −1.78674 | ||||||||
\(848\) | 2.44949 | 0.0841158 | ||||||||
\(849\) | 4.89898 | − | 4.89898i | 0.168133 | − | 0.168133i | ||||
\(850\) | − | 7.34847i | − | 0.252050i | ||||||
\(851\) | − | 18.0000i | − | 0.617032i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | −14.6969 | + | 14.6969i | −0.501745 | + | 0.501745i | ||||
\(859\) | 19.5959i | 0.668604i | 0.942466 | + | 0.334302i | \(0.108501\pi\) | ||||
−0.942466 | + | 0.334302i | \(0.891499\pi\) | |||||||
\(860\) | 2.44949 | 0.0835269 | ||||||||
\(861\) | −58.7878 | − | 58.7878i | −2.00348 | − | 2.00348i | ||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | 2.44949 | 0.0833816 | 0.0416908 | − | 0.999131i | \(-0.486726\pi\) | ||||
0.0416908 | + | 0.999131i | \(0.486726\pi\) | |||||||
\(864\) | −3.67423 | + | 3.67423i | −0.125000 | + | 0.125000i | ||||
\(865\) | 6.00000 | 0.204006 | ||||||||
\(866\) | −17.1464 | −0.582659 | ||||||||
\(867\) | −45.3156 | + | 45.3156i | −1.53900 | + | 1.53900i | ||||
\(868\) | 20.0000 | + | 9.79796i | 0.678844 | + | 0.332564i | ||||
\(869\) | − | 24.0000i | − | 0.814144i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.79796i | 0.331991i | ||||||||
\(872\) | 16.0000i | 0.541828i | ||||||||
\(873\) | − | 42.0000i | − | 1.42148i | ||||||
\(874\) | − | 14.6969i | − | 0.497131i | ||||||
\(875\) | − | 4.00000i | − | 0.135225i | ||||||
\(876\) | −3.00000 | − | 3.00000i | −0.101361 | − | 0.101361i | ||||
\(877\) | 22.0000 | 0.742887 | 0.371444 | − | 0.928456i | \(-0.378863\pi\) | ||||
0.371444 | + | 0.928456i | \(0.378863\pi\) | |||||||
\(878\) | − | 8.00000i | − | 0.269987i | ||||||
\(879\) | −7.34847 | − | 7.34847i | −0.247858 | − | 0.247858i | ||||
\(880\) | 4.89898i | 0.165145i | ||||||||
\(881\) | −53.8888 | −1.81556 | −0.907779 | − | 0.419448i | \(-0.862224\pi\) | ||||
−0.907779 | + | 0.419448i | \(0.862224\pi\) | |||||||
\(882\) | 27.0000 | 0.909137 | ||||||||
\(883\) | − | 36.7423i | − | 1.23648i | −0.785990 | − | 0.618239i | \(-0.787846\pi\) | ||
0.785990 | − | 0.618239i | \(-0.212154\pi\) | |||||||
\(884\) | − | 18.0000i | − | 0.605406i | ||||||
\(885\) | −7.34847 | + | 7.34847i | −0.247016 | + | 0.247016i | ||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | − | 48.0000i | − | 1.61168i | −0.592132 | − | 0.805841i | \(-0.701714\pi\) | ||
0.592132 | − | 0.805841i | \(-0.298286\pi\) | |||||||
\(888\) | 3.00000 | − | 3.00000i | 0.100673 | − | 0.100673i | ||||
\(889\) | 29.3939i | 0.985839i | ||||||||
\(890\) | 4.89898 | 0.164214 | ||||||||
\(891\) | 44.0908 | 1.47710 | ||||||||
\(892\) | − | 26.9444i | − | 0.902165i | ||||||
\(893\) | 24.0000i | 0.803129i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969i | 0.491264i | ||||||||
\(896\) | 4.00000i | 0.133631i | ||||||||
\(897\) | −22.0454 | − | 22.0454i | −0.736075 | − | 0.736075i | ||||
\(898\) | 29.3939i | 0.980886i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | − | 3.00000i | − | 0.100000i | ||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | −58.7878 | −1.95742 | ||||||||
\(903\) | −12.0000 | − | 12.0000i | −0.399335 | − | 0.399335i | ||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | −24.4949 | −0.814238 | ||||||||
\(906\) | −18.0000 | + | 18.0000i | −0.598010 | + | 0.598010i | ||||
\(907\) | 16.0000 | 0.531271 | 0.265636 | − | 0.964073i | \(-0.414418\pi\) | ||||
0.265636 | + | 0.964073i | \(0.414418\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | − | 9.79796i | − | 0.324799i | ||||||
\(911\) | −29.3939 | −0.973863 | −0.486931 | − | 0.873440i | \(-0.661884\pi\) | ||||
−0.486931 | + | 0.873440i | \(0.661884\pi\) | |||||||
\(912\) | 2.44949 | − | 2.44949i | 0.0811107 | − | 0.0811107i | ||||
\(913\) | 60.0000 | 1.98571 | ||||||||
\(914\) | 7.34847 | 0.243066 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.79796i | 0.323734i | ||||||||
\(917\) | 48.0000i | 1.58510i | ||||||||
\(918\) | −27.0000 | + | 27.0000i | −0.891133 | + | 0.891133i | ||||
\(919\) | −2.00000 | −0.0659739 | −0.0329870 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329870 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(920\) | −7.34847 | −0.242272 | ||||||||
\(921\) | −19.5959 | + | 19.5959i | −0.645707 | + | 0.645707i | ||||
\(922\) | 14.6969i | 0.484018i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 24.0000 | − | 24.0000i | 0.789542 | − | 0.789542i | ||||
\(925\) | 2.44949i | 0.0805387i | ||||||||
\(926\) | −2.44949 | −0.0804952 | ||||||||
\(927\) | − | 12.0000i | − | 0.394132i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | −9.12372 | + | 3.12372i | −0.299179 | + | 0.102431i | ||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 7.34847 | + | 7.34847i | 0.240578 | + | 0.240578i | ||||
\(934\) | −36.0000 | −1.17796 | ||||||||
\(935\) | 36.0000i | 1.17733i | ||||||||
\(936\) | − | 7.34847i | − | 0.240192i | ||||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | − | 16.0000i | − | 0.522419i | ||||||
\(939\) | −21.0000 | − | 21.0000i | −0.685309 | − | 0.685309i | ||||
\(940\) | 12.0000 | 0.391397 | ||||||||
\(941\) | −4.89898 | −0.159702 | −0.0798511 | − | 0.996807i | \(-0.525444\pi\) | ||||
−0.0798511 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(942\) | −12.2474 | − | 12.2474i | −0.399043 | − | 0.399043i | ||||
\(943\) | − | 88.1816i | − | 2.87159i | ||||||
\(944\) | 6.00000i | 0.195283i | ||||||||
\(945\) | −14.6969 | + | 14.6969i | −0.478091 | + | 0.478091i | ||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 12.2474 | 0.397989 | 0.198994 | − | 0.980001i | \(-0.436232\pi\) | ||||
0.198994 | + | 0.980001i | \(0.436232\pi\) | |||||||
\(948\) | 6.00000 | + | 6.00000i | 0.194871 | + | 0.194871i | ||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 2.00000i | 0.0648886i | ||||||||
\(951\) | 7.34847 | + | 7.34847i | 0.238290 | + | 0.238290i | ||||
\(952\) | 29.3939i | 0.952661i | ||||||||
\(953\) | 22.0454 | 0.714121 | 0.357060 | − | 0.934081i | \(-0.383779\pi\) | ||||
0.357060 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(954\) | 7.34847 | 0.237915 | ||||||||
\(955\) | −18.0000 | −0.582466 | ||||||||
\(956\) | 14.6969 | 0.475333 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.0000 | 0.969256 | ||||||||
\(959\) | 48.9898 | 1.58196 | ||||||||
\(960\) | −1.22474 | − | 1.22474i | −0.0395285 | − | 0.0395285i | ||||
\(961\) | 19.0000 | + | 24.4949i | 0.612903 | + | 0.790158i | ||||
\(962\) | 6.00000i | 0.193448i | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | − | 4.89898i | − | 0.157786i | ||||||
\(965\) | 2.00000i | 0.0643823i | ||||||||
\(966\) | 36.0000 | + | 36.0000i | 1.15828 | + | 1.15828i | ||||
\(967\) | − | 46.5403i | − | 1.49664i | −0.663341 | − | 0.748318i | \(-0.730862\pi\) | ||
0.663341 | − | 0.748318i | \(-0.269138\pi\) | |||||||
\(968\) | − | 13.0000i | − | 0.417836i | ||||||
\(969\) | 18.0000 | − | 18.0000i | 0.578243 | − | 0.578243i | ||||
\(970\) | 14.0000 | 0.449513 | ||||||||
\(971\) | 54.0000i | 1.73294i | 0.499227 | + | 0.866471i | \(0.333617\pi\) | ||||
−0.499227 | + | 0.866471i | \(0.666383\pi\) | |||||||
\(972\) | −11.0227 | + | 11.0227i | −0.353553 | + | 0.353553i | ||||
\(973\) | 19.5959i | 0.628216i | ||||||||
\(974\) | −31.8434 | −1.02033 | ||||||||
\(975\) | 3.00000 | + | 3.00000i | 0.0960769 | + | 0.0960769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30.0000i | − | 0.959785i | −0.877327 | − | 0.479893i | \(-0.840676\pi\) | ||
0.877327 | − | 0.479893i | \(-0.159324\pi\) | |||||||
\(978\) | −24.4949 | − | 24.4949i | −0.783260 | − | 0.783260i | ||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 9.00000i | 0.287494i | ||||||||
\(981\) | 48.0000i | 1.53252i | ||||||||
\(982\) | 19.5959i | 0.625331i | ||||||||
\(983\) | 22.0454 | 0.703139 | 0.351570 | − | 0.936162i | \(-0.385648\pi\) | ||||
0.351570 | + | 0.936162i | \(0.385648\pi\) | |||||||
\(984\) | 14.6969 | − | 14.6969i | 0.468521 | − | 0.468521i | ||||
\(985\) | − | 22.0454i | − | 0.702425i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −58.7878 | − | 58.7878i | −1.87123 | − | 1.87123i | ||||
\(988\) | 4.89898i | 0.155857i | ||||||||
\(989\) | − | 18.0000i | − | 0.572367i | ||||||
\(990\) | 14.6969i | 0.467099i | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −2.44949 | + | 5.00000i | −0.0777714 | + | 0.158750i | ||||
\(993\) | −30.0000 | − | 30.0000i | −0.952021 | − | 0.952021i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.79796 | 0.310616 | ||||||||
\(996\) | −15.0000 | + | 15.0000i | −0.475293 | + | 0.475293i | ||||
\(997\) | −10.0000 | −0.316703 | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 9.79796 | 0.310149 | ||||||||
\(999\) | 9.00000 | − | 9.00000i | 0.284747 | − | 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.h.a.371.3 | yes | 4 | |
3.2 | odd | 2 | inner | 930.2.h.a.371.2 | yes | 4 | |
31.30 | odd | 2 | inner | 930.2.h.a.371.4 | yes | 4 | |
93.92 | even | 2 | inner | 930.2.h.a.371.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.h.a.371.1 | ✓ | 4 | 93.92 | even | 2 | inner | |
930.2.h.a.371.2 | yes | 4 | 3.2 | odd | 2 | inner | |
930.2.h.a.371.3 | yes | 4 | 1.1 | even | 1 | trivial | |
930.2.h.a.371.4 | yes | 4 | 31.30 | odd | 2 | inner |