Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(323,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.17 | ||
Character | \(\chi\) | \(=\) | 756.323 |
Dual form | 756.2.e.a.323.18 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.575837 | − | 1.29167i | 0.407178 | − | 0.913349i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.33682 | − | 1.48758i | −0.668411 | − | 0.743792i | ||||
\(5\) | − | 0.311265i | − | 0.139202i | −0.997575 | − | 0.0696010i | \(-0.977827\pi\) | ||
0.997575 | − | 0.0696010i | \(-0.0221726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.69126 | + | 0.870128i | −0.951504 | + | 0.307637i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.402052 | − | 0.179238i | −0.127140 | − | 0.0566801i | ||||
\(11\) | −3.59281 | −1.08327 | −0.541636 | − | 0.840613i | \(-0.682195\pi\) | ||||
−0.541636 | + | 0.840613i | \(0.682195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.44348 | −1.78710 | −0.893549 | − | 0.448965i | \(-0.851793\pi\) | ||||
−0.893549 | + | 0.448965i | \(0.851793\pi\) | |||||||
\(14\) | 1.29167 | + | 0.575837i | 0.345213 | + | 0.153899i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.425810 | + | 3.97727i | −0.106452 | + | 0.994318i | ||||
\(17\) | − | 2.96208i | − | 0.718411i | −0.933259 | − | 0.359205i | \(-0.883048\pi\) | ||
0.933259 | − | 0.359205i | \(-0.116952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.684831i | 0.157111i | 0.996910 | + | 0.0785555i | \(0.0250308\pi\) | ||||
−0.996910 | + | 0.0785555i | \(0.974969\pi\) | |||||||
\(20\) | −0.463033 | + | 0.416106i | −0.103537 | + | 0.0930442i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.06887 | + | 4.64072i | −0.441085 | + | 0.989406i | ||||
\(23\) | −7.58964 | −1.58255 | −0.791274 | − | 0.611462i | \(-0.790582\pi\) | ||||
−0.791274 | + | 0.611462i | \(0.790582\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.90311 | 0.980623 | ||||||||
\(26\) | −3.71039 | + | 8.32285i | −0.727668 | + | 1.63224i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.48758 | − | 1.33682i | 0.281127 | − | 0.252636i | ||||
\(29\) | − | 9.26841i | − | 1.72110i | −0.509365 | − | 0.860551i | \(-0.670120\pi\) | ||
0.509365 | − | 0.860551i | \(-0.329880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.91002i | 0.343050i | 0.985180 | + | 0.171525i | \(0.0548695\pi\) | ||||
−0.985180 | + | 0.171525i | \(0.945130\pi\) | |||||||
\(32\) | 4.89212 | + | 2.84027i | 0.864814 | + | 0.502093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.82603 | − | 1.70568i | −0.656159 | − | 0.292521i | ||||
\(35\) | 0.311265 | 0.0526134 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.40625 | −1.38198 | −0.690989 | − | 0.722865i | \(-0.742825\pi\) | ||||
−0.690989 | + | 0.722865i | \(0.742825\pi\) | |||||||
\(38\) | 0.884575 | + | 0.394351i | 0.143497 | + | 0.0639722i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.270841 | + | 0.837695i | 0.0428236 | + | 0.132451i | ||||
\(41\) | − | 7.50419i | − | 1.17196i | −0.810326 | − | 0.585979i | \(-0.800710\pi\) | ||
0.810326 | − | 0.585979i | \(-0.199290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.30454i | 1.41893i | 0.704741 | + | 0.709464i | \(0.251063\pi\) | ||||
−0.704741 | + | 0.709464i | \(0.748937\pi\) | |||||||
\(44\) | 4.80295 | + | 5.34460i | 0.724072 | + | 0.805729i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.37040 | + | 9.80330i | −0.644380 | + | 1.44542i | ||||
\(47\) | 9.82305 | 1.43284 | 0.716419 | − | 0.697670i | \(-0.245780\pi\) | ||||
0.716419 | + | 0.697670i | \(0.245780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.82340 | − | 6.33321i | 0.399288 | − | 0.895650i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.61379 | + | 9.58521i | 1.19452 | + | 1.32923i | ||||
\(53\) | 5.43690i | 0.746816i | 0.927667 | + | 0.373408i | \(0.121811\pi\) | ||||
−0.927667 | + | 0.373408i | \(0.878189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.11832i | 0.150794i | ||||||||
\(56\) | −0.870128 | − | 2.69126i | −0.116276 | − | 0.359635i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.9717 | − | 5.33710i | −1.57197 | − | 0.700795i | ||||
\(59\) | −2.29004 | −0.298138 | −0.149069 | − | 0.988827i | \(-0.547628\pi\) | ||||
−0.149069 | + | 0.988827i | \(0.547628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.486233 | 0.0622557 | 0.0311278 | − | 0.999515i | \(-0.490090\pi\) | ||||
0.0311278 | + | 0.999515i | \(0.490090\pi\) | |||||||
\(62\) | 2.46712 | + | 1.09986i | 0.313325 | + | 0.139683i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.48576 | − | 4.68348i | 0.810719 | − | 0.585435i | ||||
\(65\) | 2.00563i | 0.248768i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.09619i | 0.133920i | 0.997756 | + | 0.0669602i | \(0.0213301\pi\) | ||||
−0.997756 | + | 0.0669602i | \(0.978670\pi\) | |||||||
\(68\) | −4.40635 | + | 3.95978i | −0.534348 | + | 0.480194i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.179238 | − | 0.402052i | 0.0214231 | − | 0.0480544i | ||||
\(71\) | −1.76422 | −0.209375 | −0.104687 | − | 0.994505i | \(-0.533384\pi\) | ||||
−0.104687 | + | 0.994505i | \(0.533384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.32691 | 0.389385 | 0.194692 | − | 0.980864i | \(-0.437629\pi\) | ||||
0.194692 | + | 0.980864i | \(0.437629\pi\) | |||||||
\(74\) | −4.84063 | + | 10.8581i | −0.562712 | + | 1.26223i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.01874 | − | 0.915497i | 0.116858 | − | 0.105015i | ||||
\(77\) | − | 3.59281i | − | 0.409439i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.39005i | 0.156392i | 0.996938 | + | 0.0781962i | \(0.0249161\pi\) | ||||
−0.996938 | + | 0.0781962i | \(0.975084\pi\) | |||||||
\(80\) | 1.23799 | + | 0.132540i | 0.138411 | + | 0.0148184i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.69294 | − | 4.32119i | −1.07041 | − | 0.477196i | ||||
\(83\) | −0.283103 | −0.0310746 | −0.0155373 | − | 0.999879i | \(-0.504946\pi\) | ||||
−0.0155373 | + | 0.999879i | \(0.504946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.921993 | −0.100004 | ||||||||
\(86\) | 12.0184 | + | 5.35790i | 1.29598 | + | 0.577757i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.66918 | − | 3.12620i | 1.03074 | − | 0.333254i | ||||
\(89\) | − | 8.91479i | − | 0.944966i | −0.881340 | − | 0.472483i | \(-0.843358\pi\) | ||
0.881340 | − | 0.472483i | \(-0.156642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.44348i | − | 0.675460i | ||||||
\(92\) | 10.1460 | + | 11.2902i | 1.05779 | + | 1.17709i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.65648 | − | 12.6881i | 0.583421 | − | 1.30868i | ||||
\(95\) | 0.213164 | 0.0218702 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.621922 | 0.0631466 | 0.0315733 | − | 0.999501i | \(-0.489948\pi\) | ||||
0.0315733 | + | 0.999501i | \(0.489948\pi\) | |||||||
\(98\) | −0.575837 | + | 1.29167i | −0.0581684 | + | 0.130478i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.55459 | − | 7.29379i | −0.655459 | − | 0.729379i | ||||
\(101\) | − | 17.7166i | − | 1.76287i | −0.472304 | − | 0.881436i | \(-0.656578\pi\) | ||
0.472304 | − | 0.881436i | \(-0.343422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.5139i | − | 1.52863i | −0.644841 | − | 0.764317i | \(-0.723077\pi\) | ||
0.644841 | − | 0.764317i | \(-0.276923\pi\) | |||||||
\(104\) | 17.3411 | − | 5.60665i | 1.70043 | − | 0.549777i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.02268 | + | 3.13077i | 0.682103 | + | 0.304087i | ||||
\(107\) | −4.26969 | −0.412767 | −0.206383 | − | 0.978471i | \(-0.566169\pi\) | ||||
−0.206383 | + | 0.978471i | \(0.566169\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.03903 | 0.195304 | 0.0976519 | − | 0.995221i | \(-0.468867\pi\) | ||||
0.0976519 | + | 0.995221i | \(0.468867\pi\) | |||||||
\(110\) | 1.44450 | + | 0.643968i | 0.137727 | + | 0.0614000i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.97727 | − | 0.425810i | −0.375817 | − | 0.0402352i | ||||
\(113\) | 8.69512i | 0.817968i | 0.912541 | + | 0.408984i | \(0.134117\pi\) | ||||
−0.912541 | + | 0.408984i | \(0.865883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.36239i | 0.220294i | ||||||||
\(116\) | −13.7875 | + | 12.3902i | −1.28014 | + | 1.15040i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.31869 | + | 2.95798i | −0.121395 | + | 0.272304i | ||||
\(119\) | 2.96208 | 0.271534 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.90828 | 0.173480 | ||||||||
\(122\) | 0.279991 | − | 0.628052i | 0.0253492 | − | 0.0568612i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.84132 | − | 2.55336i | 0.255158 | − | 0.229299i | ||||
\(125\) | − | 3.08250i | − | 0.275707i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.66793i | − | 0.148005i | −0.997258 | − | 0.0740024i | \(-0.976423\pi\) | ||
0.997258 | − | 0.0740024i | \(-0.0235772\pi\) | |||||||
\(128\) | −2.31477 | − | 11.0744i | −0.204599 | − | 0.978846i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.59061 | + | 1.15492i | 0.227212 | + | 0.101293i | ||||
\(131\) | −19.0156 | −1.66140 | −0.830700 | − | 0.556720i | \(-0.812060\pi\) | ||||
−0.830700 | + | 0.556720i | \(0.812060\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.684831 | −0.0593823 | ||||||||
\(134\) | 1.41591 | + | 0.631225i | 0.122316 | + | 0.0545295i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.57739 | + | 7.97173i | 0.221009 | + | 0.683570i | ||||
\(137\) | − | 3.52975i | − | 0.301567i | −0.988567 | − | 0.150784i | \(-0.951820\pi\) | ||
0.988567 | − | 0.150784i | \(-0.0481796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.7977i | − | 1.17030i | −0.810924 | − | 0.585152i | \(-0.801035\pi\) | ||
0.810924 | − | 0.585152i | \(-0.198965\pi\) | |||||||
\(140\) | −0.416106 | − | 0.463033i | −0.0351674 | − | 0.0391334i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.01590 | + | 2.27879i | −0.0852528 | + | 0.191232i | ||||
\(143\) | 23.1502 | 1.93592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.88493 | −0.239581 | ||||||||
\(146\) | 1.91576 | − | 4.29726i | 0.158549 | − | 0.355644i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2377 | + | 12.5050i | 0.923730 | + | 1.02790i | ||||
\(149\) | 10.8370i | 0.887803i | 0.896076 | + | 0.443901i | \(0.146406\pi\) | ||||
−0.896076 | + | 0.443901i | \(0.853594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.421989i | − | 0.0343410i | −0.999853 | − | 0.0171705i | \(-0.994534\pi\) | ||
0.999853 | − | 0.0171705i | \(-0.00546580\pi\) | |||||||
\(152\) | −0.595890 | − | 1.84306i | −0.0483331 | − | 0.149492i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.64072 | − | 2.06887i | −0.373960 | − | 0.166715i | ||||
\(155\) | 0.594524 | 0.0477533 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0436 | 1.20061 | 0.600306 | − | 0.799771i | \(-0.295046\pi\) | ||||
0.600306 | + | 0.799771i | \(0.295046\pi\) | |||||||
\(158\) | 1.79548 | + | 0.800441i | 0.142841 | + | 0.0636797i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.884076 | − | 1.52275i | 0.0698924 | − | 0.120384i | ||||
\(161\) | − | 7.58964i | − | 0.598147i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6329i | − | 0.989489i | −0.869039 | − | 0.494744i | \(-0.835262\pi\) | ||
0.869039 | − | 0.494744i | \(-0.164738\pi\) | |||||||
\(164\) | −11.1631 | + | 10.0318i | −0.871693 | + | 0.783350i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.163021 | + | 0.365675i | −0.0126529 | + | 0.0283819i | ||||
\(167\) | −22.1403 | −1.71327 | −0.856634 | − | 0.515925i | \(-0.827448\pi\) | ||||
−0.856634 | + | 0.515925i | \(0.827448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5184 | 2.19372 | ||||||||
\(170\) | −0.530918 | + | 1.19091i | −0.0407196 | + | 0.0913387i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.8413 | − | 12.4385i | 1.05539 | − | 0.948428i | ||||
\(173\) | 18.6961i | 1.42144i | 0.703478 | + | 0.710718i | \(0.251630\pi\) | ||||
−0.703478 | + | 0.710718i | \(0.748370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.90311i | 0.370641i | ||||||||
\(176\) | 1.52985 | − | 14.2896i | 0.115317 | − | 1.07712i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.5150 | − | 5.13347i | −0.863083 | − | 0.384770i | ||||
\(179\) | 16.3149 | 1.21943 | 0.609716 | − | 0.792620i | \(-0.291284\pi\) | ||||
0.609716 | + | 0.792620i | \(0.291284\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.35019 | −0.546335 | −0.273168 | − | 0.961966i | \(-0.588071\pi\) | ||||
−0.273168 | + | 0.961966i | \(0.588071\pi\) | |||||||
\(182\) | −8.32285 | − | 3.71039i | −0.616930 | − | 0.275033i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.4257 | − | 6.60395i | 1.50580 | − | 0.486850i | ||||
\(185\) | 2.61657i | 0.192374i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6422i | 0.778235i | ||||||||
\(188\) | −13.1317 | − | 14.6126i | −0.957726 | − | 1.06573i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.122748 | − | 0.275337i | 0.00890506 | − | 0.0199751i | ||||
\(191\) | −20.6900 | −1.49708 | −0.748538 | − | 0.663092i | \(-0.769244\pi\) | ||||
−0.748538 | + | 0.663092i | \(0.769244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.76121 | −0.198757 | −0.0993783 | − | 0.995050i | \(-0.531685\pi\) | ||||
−0.0993783 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(194\) | 0.358126 | − | 0.803318i | 0.0257119 | − | 0.0576749i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.33682 | + | 1.48758i | 0.0954873 | + | 0.106256i | ||||
\(197\) | − | 8.02466i | − | 0.571733i | −0.958269 | − | 0.285867i | \(-0.907719\pi\) | ||
0.958269 | − | 0.285867i | \(-0.0922815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2052i | 1.14876i | 0.818590 | + | 0.574378i | \(0.194756\pi\) | ||||
−0.818590 | + | 0.574378i | \(0.805244\pi\) | |||||||
\(200\) | −13.1956 | + | 4.26634i | −0.933066 | + | 0.301676i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.8841 | − | 10.2019i | −1.61012 | − | 0.717803i | ||||
\(203\) | 9.26841 | 0.650515 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.33579 | −0.163139 | ||||||||
\(206\) | −20.0389 | − | 8.93350i | −1.39617 | − | 0.622426i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.74369 | − | 25.6275i | 0.190241 | − | 1.77694i | ||||
\(209\) | − | 2.46047i | − | 0.170194i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0235i | 1.37848i | 0.724535 | + | 0.689238i | \(0.242054\pi\) | ||||
−0.724535 | + | 0.689238i | \(0.757946\pi\) | |||||||
\(212\) | 8.08784 | − | 7.26817i | 0.555475 | − | 0.499180i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.45865 | + | 5.51503i | −0.168070 | + | 0.377000i | ||||
\(215\) | 2.89618 | 0.197518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.91002 | −0.129661 | ||||||||
\(218\) | 1.17415 | − | 2.63376i | 0.0795235 | − | 0.178381i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.66359 | − | 1.49499i | 0.112159 | − | 0.100792i | ||||
\(221\) | 19.0861i | 1.28387i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.9084i | − | 1.60103i | −0.599314 | − | 0.800514i | \(-0.704560\pi\) | ||
0.599314 | − | 0.800514i | \(-0.295440\pi\) | |||||||
\(224\) | −2.84027 | + | 4.89212i | −0.189773 | + | 0.326869i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2312 | + | 5.00698i | 0.747090 | + | 0.333059i | ||||
\(227\) | 11.0598 | 0.734067 | 0.367034 | − | 0.930208i | \(-0.380373\pi\) | ||||
0.367034 | + | 0.930208i | \(0.380373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.0407 | −1.52257 | −0.761287 | − | 0.648416i | \(-0.775432\pi\) | ||||
−0.761287 | + | 0.648416i | \(0.775432\pi\) | |||||||
\(230\) | 3.05143 | + | 1.36035i | 0.201205 | + | 0.0896990i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.06471 | + | 24.9437i | 0.529474 | + | 1.63763i | ||||
\(233\) | − | 5.39550i | − | 0.353471i | −0.984258 | − | 0.176736i | \(-0.943446\pi\) | ||
0.984258 | − | 0.176736i | \(-0.0565538\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.05757i | − | 0.199454i | ||||||
\(236\) | 3.06138 | + | 3.40663i | 0.199279 | + | 0.221753i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.70568 | − | 3.82603i | 0.110563 | − | 0.248005i | ||||
\(239\) | −21.5858 | −1.39627 | −0.698135 | − | 0.715966i | \(-0.745987\pi\) | ||||
−0.698135 | + | 0.715966i | \(0.745987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.30744 | 0.599545 | 0.299772 | − | 0.954011i | \(-0.403089\pi\) | ||||
0.299772 | + | 0.954011i | \(0.403089\pi\) | |||||||
\(242\) | 1.09886 | − | 2.46487i | 0.0706373 | − | 0.158448i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.650007 | − | 0.723311i | −0.0416124 | − | 0.0463053i | ||||
\(245\) | 0.311265i | 0.0198860i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.41269i | − | 0.280773i | ||||||
\(248\) | −1.66197 | − | 5.14037i | −0.105535 | − | 0.326414i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.98157 | − | 1.77502i | −0.251816 | − | 0.112262i | ||||
\(251\) | 7.57302 | 0.478005 | 0.239002 | − | 0.971019i | \(-0.423180\pi\) | ||||
0.239002 | + | 0.971019i | \(0.423180\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2681 | 1.71433 | ||||||||
\(254\) | −2.15441 | − | 0.960456i | −0.135180 | − | 0.0602644i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6374 | − | 3.38712i | −0.977336 | − | 0.211695i | ||||
\(257\) | − | 2.44066i | − | 0.152244i | −0.997099 | − | 0.0761220i | \(-0.975746\pi\) | ||
0.997099 | − | 0.0761220i | \(-0.0242538\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.40625i | − | 0.522339i | ||||||
\(260\) | 2.98354 | − | 2.68117i | 0.185031 | − | 0.166279i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9499 | + | 24.5619i | −0.676487 | + | 1.51744i | ||||
\(263\) | −1.25537 | −0.0774095 | −0.0387048 | − | 0.999251i | \(-0.512323\pi\) | ||||
−0.0387048 | + | 0.999251i | \(0.512323\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.69232 | 0.103958 | ||||||||
\(266\) | −0.394351 | + | 0.884575i | −0.0241792 | + | 0.0542368i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.63067 | − | 1.46541i | 0.0996089 | − | 0.0895139i | ||||
\(269\) | − | 4.24461i | − | 0.258799i | −0.991593 | − | 0.129399i | \(-0.958695\pi\) | ||
0.991593 | − | 0.129399i | \(-0.0413049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.5146i | − | 0.881701i | −0.897581 | − | 0.440851i | \(-0.854677\pi\) | ||
0.897581 | − | 0.440851i | \(-0.145323\pi\) | |||||||
\(272\) | 11.7810 | + | 1.26128i | 0.714328 | + | 0.0764765i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.55927 | − | 2.03256i | −0.275436 | − | 0.122792i | ||||
\(275\) | −17.6160 | −1.06228 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1760 | −1.09209 | −0.546046 | − | 0.837755i | \(-0.683868\pi\) | ||||
−0.546046 | + | 0.837755i | \(0.683868\pi\) | |||||||
\(278\) | −17.8220 | − | 7.94522i | −1.06890 | − | 0.476523i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.837695 | + | 0.270841i | −0.0500619 | + | 0.0161858i | ||||
\(281\) | 23.7048i | 1.41411i | 0.707158 | + | 0.707055i | \(0.249977\pi\) | ||||
−0.707158 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30.4540i | − | 1.81031i | −0.425087 | − | 0.905153i | \(-0.639756\pi\) | ||
0.425087 | − | 0.905153i | \(-0.360244\pi\) | |||||||
\(284\) | 2.35845 | + | 2.62443i | 0.139948 | + | 0.155731i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.3307 | − | 29.9024i | 0.788263 | − | 1.76817i | ||||
\(287\) | 7.50419 | 0.442958 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.22607 | 0.483886 | ||||||||
\(290\) | −1.66125 | + | 3.72638i | −0.0975521 | + | 0.218821i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.44748 | − | 4.94905i | −0.260269 | − | 0.289621i | ||||
\(293\) | 14.8848i | 0.869582i | 0.900531 | + | 0.434791i | \(0.143178\pi\) | ||||
−0.900531 | + | 0.434791i | \(0.856822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.712810i | 0.0415014i | ||||||||
\(296\) | 22.6234 | − | 7.31451i | 1.31496 | − | 0.425147i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.9978 | + | 6.24036i | 0.810874 | + | 0.361494i | ||||
\(299\) | 48.9036 | 2.82817 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.30454 | −0.536305 | ||||||||
\(302\) | −0.545070 | − | 0.242997i | −0.0313653 | − | 0.0139829i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.72376 | − | 0.291607i | −0.156218 | − | 0.0167248i | ||||
\(305\) | − | 0.151347i | − | 0.00866612i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.7491i | 1.07007i | 0.844831 | + | 0.535033i | \(0.179701\pi\) | ||||
−0.844831 | + | 0.535033i | \(0.820299\pi\) | |||||||
\(308\) | −5.34460 | + | 4.80295i | −0.304537 | + | 0.273673i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.342349 | − | 0.767929i | 0.0194441 | − | 0.0436154i | ||||
\(311\) | 19.1097 | 1.08361 | 0.541806 | − | 0.840504i | \(-0.317741\pi\) | ||||
0.541806 | + | 0.840504i | \(0.317741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8663 | −1.00986 | −0.504932 | − | 0.863159i | \(-0.668483\pi\) | ||||
−0.504932 | + | 0.863159i | \(0.668483\pi\) | |||||||
\(314\) | 8.66268 | − | 19.4314i | 0.488863 | − | 1.09658i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.06781 | − | 1.85825i | 0.116323 | − | 0.104535i | ||||
\(317\) | 30.6470i | 1.72131i | 0.509191 | + | 0.860653i | \(0.329945\pi\) | ||||
−0.509191 | + | 0.860653i | \(0.670055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.2996i | 1.86442i | ||||||||
\(320\) | −1.45780 | − | 2.01879i | −0.0814937 | − | 0.112854i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.80330 | − | 4.37040i | −0.546317 | − | 0.243553i | ||||
\(323\) | 2.02852 | 0.112870 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.5931 | −1.75247 | ||||||||
\(326\) | −16.3176 | − | 7.27452i | −0.903748 | − | 0.402899i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.52961 | + | 20.1957i | 0.360537 | + | 1.11512i | ||||
\(329\) | 9.82305i | 0.541562i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0261i | 0.606051i | 0.952982 | + | 0.303026i | \(0.0979968\pi\) | ||||
−0.952982 | + | 0.303026i | \(0.902003\pi\) | |||||||
\(332\) | 0.378458 | + | 0.421139i | 0.0207706 | + | 0.0231130i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.7492 | + | 28.5980i | −0.697606 | + | 1.56481i | ||||
\(335\) | 0.341204 | 0.0186420 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.68990 | 0.146528 | 0.0732640 | − | 0.997313i | \(-0.476658\pi\) | ||||
0.0732640 | + | 0.997313i | \(0.476658\pi\) | |||||||
\(338\) | 16.4220 | − | 36.8364i | 0.893237 | − | 2.00363i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.23254 | + | 1.37154i | 0.0668440 | + | 0.0743823i | ||||
\(341\) | − | 6.86235i | − | 0.371617i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −8.09614 | − | 25.0409i | −0.436514 | − | 1.35012i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.1491 | + | 10.7659i | 1.29827 | + | 0.578778i | ||||
\(347\) | 10.4414 | 0.560525 | 0.280262 | − | 0.959923i | \(-0.409579\pi\) | ||||
0.280262 | + | 0.959923i | \(0.409579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.20342 | −0.117947 | −0.0589733 | − | 0.998260i | \(-0.518783\pi\) | ||||
−0.0589733 | + | 0.998260i | \(0.518783\pi\) | |||||||
\(350\) | 6.33321 | + | 2.82340i | 0.338524 | + | 0.150917i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.5765 | − | 10.2045i | −0.936829 | − | 0.543904i | ||||
\(353\) | 12.1792i | 0.648234i | 0.946017 | + | 0.324117i | \(0.105067\pi\) | ||||
−0.946017 | + | 0.324117i | \(0.894933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.549141i | 0.0291454i | ||||||||
\(356\) | −13.2615 | + | 11.9175i | −0.702858 | + | 0.631626i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.39472 | − | 21.0734i | 0.496526 | − | 1.11377i | ||||
\(359\) | −13.7170 | −0.723953 | −0.361976 | − | 0.932187i | \(-0.617898\pi\) | ||||
−0.361976 | + | 0.932187i | \(0.617898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5310 | 0.975316 | ||||||||
\(362\) | −4.23251 | + | 9.49402i | −0.222456 | + | 0.498995i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.58521 | + | 8.61379i | −0.502402 | + | 0.451485i | ||||
\(365\) | − | 1.03555i | − | 0.0542032i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.1421i | 1.26021i | 0.776512 | + | 0.630103i | \(0.216987\pi\) | ||||
−0.776512 | + | 0.630103i | \(0.783013\pi\) | |||||||
\(368\) | 3.23174 | − | 30.1860i | 0.168466 | − | 1.57356i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.37975 | + | 1.50672i | 0.175705 | + | 0.0783306i | ||||
\(371\) | −5.43690 | −0.282270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.44430 | 0.230117 | 0.115059 | − | 0.993359i | \(-0.463294\pi\) | ||||
0.115059 | + | 0.993359i | \(0.463294\pi\) | |||||||
\(374\) | 13.7462 | + | 6.12817i | 0.710799 | + | 0.316880i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.4364 | + | 8.54731i | −1.36335 | + | 0.440794i | ||||
\(377\) | 59.7208i | 3.07578i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.03014i | 0.463847i | 0.972734 | + | 0.231924i | \(0.0745020\pi\) | ||||
−0.972734 | + | 0.231924i | \(0.925498\pi\) | |||||||
\(380\) | −0.284962 | − | 0.317099i | −0.0146183 | − | 0.0162668i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9141 | + | 26.7246i | −0.609577 | + | 1.36735i | ||||
\(383\) | 20.1601 | 1.03013 | 0.515067 | − | 0.857150i | \(-0.327767\pi\) | ||||
0.515067 | + | 0.857150i | \(0.327767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11832 | −0.0569947 | ||||||||
\(386\) | −1.59001 | + | 3.56658i | −0.0809294 | + | 0.181534i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.831400 | − | 0.925161i | −0.0422079 | − | 0.0469679i | ||||
\(389\) | − | 20.1791i | − | 1.02312i | −0.859247 | − | 0.511562i | \(-0.829067\pi\) | ||
0.859247 | − | 0.511562i | \(-0.170933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.4811i | 1.13692i | ||||||||
\(392\) | 2.69126 | − | 0.870128i | 0.135929 | − | 0.0439481i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.3652 | − | 4.62090i | −0.522192 | − | 0.232798i | ||||
\(395\) | 0.432673 | 0.0217702 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.8932 | −0.998412 | −0.499206 | − | 0.866483i | \(-0.666375\pi\) | ||||
−0.499206 | + | 0.866483i | \(0.666375\pi\) | |||||||
\(398\) | 20.9318 | + | 9.33156i | 1.04922 | + | 0.467749i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.08779 | + | 19.5010i | −0.104390 | + | 0.975051i | ||||
\(401\) | 35.2123i | 1.75842i | 0.476436 | + | 0.879209i | \(0.341928\pi\) | ||||
−0.476436 | + | 0.879209i | \(0.658072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.3072i | − | 0.613065i | ||||||
\(404\) | −26.3550 | + | 23.6840i | −1.31121 | + | 1.17832i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.33710 | − | 11.9717i | 0.264876 | − | 0.594147i | ||||
\(407\) | 30.2020 | 1.49706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4098 | 0.910306 | 0.455153 | − | 0.890413i | \(-0.349585\pi\) | ||||
0.455153 | + | 0.890413i | \(0.349585\pi\) | |||||||
\(410\) | −1.34504 | + | 3.01708i | −0.0664267 | + | 0.149003i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −23.0783 | + | 20.7394i | −1.13698 | + | 1.02176i | ||||
\(413\) | − | 2.29004i | − | 0.112686i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0881200i | 0.00432564i | ||||||||
\(416\) | −31.5223 | − | 18.3012i | −1.54551 | − | 0.897290i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.17811 | − | 1.41683i | −0.155446 | − | 0.0692993i | ||||
\(419\) | −18.5848 | −0.907925 | −0.453962 | − | 0.891021i | \(-0.649990\pi\) | ||||
−0.453962 | + | 0.891021i | \(0.649990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4051 | −1.72554 | −0.862770 | − | 0.505597i | \(-0.831272\pi\) | ||||
−0.862770 | + | 0.505597i | \(0.831272\pi\) | |||||||
\(422\) | 25.8638 | + | 11.5303i | 1.25903 | + | 0.561285i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.73080 | − | 14.6321i | −0.229748 | − | 0.710598i | ||||
\(425\) | − | 14.5234i | − | 0.704490i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.486233i | 0.0235304i | ||||||||
\(428\) | 5.70782 | + | 6.35152i | 0.275898 | + | 0.307012i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.66773 | − | 3.74091i | 0.0804250 | − | 0.180403i | ||||
\(431\) | 23.0972 | 1.11255 | 0.556276 | − | 0.830998i | \(-0.312230\pi\) | ||||
0.556276 | + | 0.830998i | \(0.312230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0020 | 0.865122 | 0.432561 | − | 0.901605i | \(-0.357610\pi\) | ||||
0.432561 | + | 0.901605i | \(0.357610\pi\) | |||||||
\(434\) | −1.09986 | + | 2.46712i | −0.0527951 | + | 0.118426i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.72582 | − | 3.03323i | −0.130543 | − | 0.145265i | ||||
\(437\) | − | 5.19761i | − | 0.248636i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 24.0230i | − | 1.14655i | −0.819361 | − | 0.573277i | \(-0.805672\pi\) | ||
0.819361 | − | 0.573277i | \(-0.194328\pi\) | |||||||
\(440\) | −0.973078 | − | 3.00968i | −0.0463897 | − | 0.143481i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.6530 | + | 10.9905i | 1.17262 | + | 0.522764i | ||||
\(443\) | −34.6101 | −1.64437 | −0.822187 | − | 0.569217i | \(-0.807246\pi\) | ||||
−0.822187 | + | 0.569217i | \(0.807246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.77486 | −0.131541 | ||||||||
\(446\) | −30.8818 | − | 13.7674i | −1.46230 | − | 0.651904i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.68348 | + | 6.48576i | 0.221274 | + | 0.306423i | ||||
\(449\) | − | 19.1474i | − | 0.903620i | −0.892114 | − | 0.451810i | \(-0.850779\pi\) | ||
0.892114 | − | 0.451810i | \(-0.149221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.9611i | 1.26955i | ||||||||
\(452\) | 12.9347 | − | 11.6238i | 0.608398 | − | 0.546739i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.36867 | − | 14.2857i | 0.298896 | − | 0.670459i | ||||
\(455\) | −2.00563 | −0.0940254 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2205 | −0.665208 | −0.332604 | − | 0.943067i | \(-0.607927\pi\) | ||||
−0.332604 | + | 0.943067i | \(0.607927\pi\) | |||||||
\(458\) | −13.2677 | + | 29.7610i | −0.619959 | + | 1.39064i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.51425 | − | 3.15810i | 0.163853 | − | 0.147247i | ||||
\(461\) | − | 28.9424i | − | 1.34798i | −0.738740 | − | 0.673991i | \(-0.764579\pi\) | ||
0.738740 | − | 0.673991i | \(-0.235421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.7876i | 1.43082i | 0.698704 | + | 0.715411i | \(0.253761\pi\) | ||||
−0.698704 | + | 0.715411i | \(0.746239\pi\) | |||||||
\(464\) | 36.8630 | + | 3.94658i | 1.71132 | + | 0.183215i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.96921 | − | 3.10693i | −0.322842 | − | 0.143926i | ||||
\(467\) | 19.6915 | 0.911215 | 0.455608 | − | 0.890181i | \(-0.349422\pi\) | ||||
0.455608 | + | 0.890181i | \(0.349422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.09619 | −0.0506172 | ||||||||
\(470\) | −3.94937 | − | 1.76066i | −0.182171 | − | 0.0812134i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.16309 | − | 1.99263i | 0.283679 | − | 0.0917182i | ||||
\(473\) | − | 33.4294i | − | 1.53709i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.35780i | 0.154067i | ||||||||
\(476\) | −3.95978 | − | 4.40635i | −0.181496 | − | 0.201964i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.4299 | + | 27.8818i | −0.568531 | + | 1.27528i | ||||
\(479\) | −12.4606 | −0.569341 | −0.284671 | − | 0.958625i | \(-0.591884\pi\) | ||||
−0.284671 | + | 0.958625i | \(0.591884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.1655 | 2.46973 | ||||||||
\(482\) | 5.35957 | − | 12.0221i | 0.244122 | − | 0.547593i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.55103 | − | 2.83872i | −0.115956 | − | 0.129033i | ||||
\(485\) | − | 0.193583i | − | 0.00879014i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.92729i | 0.132648i | 0.997798 | + | 0.0663240i | \(0.0211271\pi\) | ||||
−0.997798 | + | 0.0663240i | \(0.978873\pi\) | |||||||
\(488\) | −1.30858 | + | 0.423084i | −0.0592365 | + | 0.0191521i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.402052 | + | 0.179238i | 0.0181629 | + | 0.00809715i | ||||
\(491\) | −16.2661 | −0.734081 | −0.367040 | − | 0.930205i | \(-0.619629\pi\) | ||||
−0.367040 | + | 0.930205i | \(0.619629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.4538 | −1.23646 | ||||||||
\(494\) | −5.69974 | − | 2.54099i | −0.256443 | − | 0.114325i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.59668 | − | 0.813307i | −0.341101 | − | 0.0365185i | ||||
\(497\) | − | 1.76422i | − | 0.0791362i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.8585i | − | 1.15759i | −0.815475 | − | 0.578793i | \(-0.803524\pi\) | ||
0.815475 | − | 0.578793i | \(-0.196476\pi\) | |||||||
\(500\) | −4.58547 | + | 4.12075i | −0.205068 | + | 0.184286i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.36083 | − | 9.78184i | 0.194633 | − | 0.436585i | ||||
\(503\) | −1.22564 | −0.0546487 | −0.0273244 | − | 0.999627i | \(-0.508699\pi\) | ||||
−0.0273244 | + | 0.999627i | \(0.508699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.51457 | −0.245395 | ||||||||
\(506\) | 15.7020 | − | 35.2214i | 0.698039 | − | 1.56578i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.48118 | + | 2.22973i | −0.110085 | + | 0.0989281i | ||||
\(509\) | − | 10.1313i | − | 0.449062i | −0.974467 | − | 0.224531i | \(-0.927915\pi\) | ||
0.974467 | − | 0.224531i | \(-0.0720851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.32691i | 0.147174i | ||||||||
\(512\) | −13.3796 | + | 18.2479i | −0.591301 | + | 0.806451i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.15252 | − | 1.40542i | −0.139052 | − | 0.0619905i | ||||
\(515\) | −4.82895 | −0.212789 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.2923 | −1.55215 | ||||||||
\(518\) | −10.8581 | − | 4.84063i | −0.477077 | − | 0.212685i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.74515 | − | 5.39767i | −0.0765301 | − | 0.236704i | ||||
\(521\) | 18.7198i | 0.820128i | 0.912057 | + | 0.410064i | \(0.134494\pi\) | ||||
−0.912057 | + | 0.410064i | \(0.865506\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2180i | 0.752893i | 0.926438 | + | 0.376446i | \(0.122854\pi\) | ||||
−0.926438 | + | 0.376446i | \(0.877146\pi\) | |||||||
\(524\) | 25.4205 | + | 28.2873i | 1.11050 | + | 1.23574i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.722890 | + | 1.62153i | −0.0315195 | + | 0.0707019i | ||||
\(527\) | 5.65765 | 0.246451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.6026 | 1.50446 | ||||||||
\(530\) | 0.974500 | − | 2.18592i | 0.0423296 | − | 0.0949502i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.915497 | + | 1.01874i | 0.0396918 | + | 0.0441681i | ||||
\(533\) | 48.3531i | 2.09440i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32901i | 0.0574580i | ||||||||
\(536\) | −0.953822 | − | 2.95012i | −0.0411988 | − | 0.127426i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.48264 | − | 2.44421i | −0.236373 | − | 0.105377i | ||||
\(539\) | 3.59281 | 0.154753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0983 | −0.735114 | −0.367557 | − | 0.930001i | \(-0.619806\pi\) | ||||
−0.367557 | + | 0.930001i | \(0.619806\pi\) | |||||||
\(542\) | −18.7481 | − | 8.35807i | −0.805300 | − | 0.359010i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.41310 | − | 14.4909i | 0.360709 | − | 0.621291i | ||||
\(545\) | − | 0.634680i | − | 0.0271867i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15.6670i | − | 0.669875i | −0.942240 | − | 0.334937i | \(-0.891285\pi\) | ||
0.942240 | − | 0.334937i | \(-0.108715\pi\) | |||||||
\(548\) | −5.25080 | + | 4.71865i | −0.224303 | + | 0.201571i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.1439 | + | 22.7540i | −0.432538 | + | 0.970234i | ||||
\(551\) | 6.34729 | 0.270404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.39005 | −0.0591108 | ||||||||
\(554\) | −10.4664 | + | 23.4774i | −0.444677 | + | 0.997461i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.5252 | + | 18.4451i | −0.870462 | + | 0.782244i | ||||
\(557\) | 13.2002i | 0.559310i | 0.960101 | + | 0.279655i | \(0.0902200\pi\) | ||||
−0.960101 | + | 0.279655i | \(0.909780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 59.9536i | − | 2.53577i | ||||||
\(560\) | −0.132540 | + | 1.23799i | −0.00560082 | + | 0.0523145i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.6188 | + | 13.6501i | 1.29158 | + | 0.575795i | ||||
\(563\) | 21.8132 | 0.919316 | 0.459658 | − | 0.888096i | \(-0.347972\pi\) | ||||
0.459658 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.70649 | 0.113863 | ||||||||
\(566\) | −39.3366 | − | 17.5366i | −1.65344 | − | 0.737117i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.74798 | − | 1.53510i | 0.199221 | − | 0.0644113i | ||||
\(569\) | − | 20.1097i | − | 0.843044i | −0.906818 | − | 0.421522i | \(-0.861496\pi\) | ||
0.906818 | − | 0.421522i | \(-0.138504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.0133i | − | 1.46526i | −0.680627 | − | 0.732630i | \(-0.738293\pi\) | ||
0.680627 | − | 0.732630i | \(-0.261707\pi\) | |||||||
\(572\) | −30.9477 | − | 34.4378i | −1.29399 | − | 1.43992i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.32119 | − | 9.69294i | 0.180363 | − | 0.404575i | ||||
\(575\) | −37.2128 | −1.55188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.8963 | 0.745031 | 0.372515 | − | 0.928026i | \(-0.378495\pi\) | ||||
0.372515 | + | 0.928026i | \(0.378495\pi\) | |||||||
\(578\) | 4.73688 | − | 10.6254i | 0.197028 | − | 0.441957i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.85665 | + | 4.29158i | 0.160139 | + | 0.178198i | ||||
\(581\) | − | 0.283103i | − | 0.0117451i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 19.5337i | − | 0.809005i | ||||||
\(584\) | −8.95357 | + | 2.89483i | −0.370501 | + | 0.119789i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.2263 | + | 8.57125i | 0.794232 | + | 0.354075i | ||||
\(587\) | −39.4490 | −1.62823 | −0.814117 | − | 0.580701i | \(-0.802779\pi\) | ||||
−0.814117 | + | 0.580701i | \(0.802779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.30804 | −0.0538970 | ||||||||
\(590\) | 0.920715 | + | 0.410463i | 0.0379053 | + | 0.0168985i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.57946 | − | 33.4339i | 0.147115 | − | 1.37413i | ||||
\(593\) | − | 30.1072i | − | 1.23635i | −0.786039 | − | 0.618177i | \(-0.787872\pi\) | ||
0.786039 | − | 0.618177i | \(-0.212128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.921993i | − | 0.0377980i | ||||||
\(596\) | 16.1210 | − | 14.4872i | 0.660341 | − | 0.593418i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.1605 | − | 63.1674i | 1.15157 | − | 2.58311i | ||||
\(599\) | −0.825158 | −0.0337151 | −0.0168575 | − | 0.999858i | \(-0.505366\pi\) | ||||
−0.0168575 | + | 0.999858i | \(0.505366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3800 | −0.994481 | −0.497240 | − | 0.867613i | \(-0.665653\pi\) | ||||
−0.497240 | + | 0.867613i | \(0.665653\pi\) | |||||||
\(602\) | −5.35790 | + | 12.0184i | −0.218372 | + | 0.489833i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.627744 | + | 0.564124i | −0.0255425 | + | 0.0229539i | ||||
\(605\) | − | 0.593981i | − | 0.0241488i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8238i | 1.08874i | 0.838844 | + | 0.544372i | \(0.183232\pi\) | ||||
−0.838844 | + | 0.544372i | \(0.816768\pi\) | |||||||
\(608\) | −1.94510 | + | 3.35028i | −0.0788843 | + | 0.135872i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.195491 | − | 0.0871514i | −0.00791519 | − | 0.00352866i | ||||
\(611\) | −63.2946 | −2.56062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.30874 | −0.0528594 | −0.0264297 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264297 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(614\) | 24.2176 | + | 10.7964i | 0.977343 | + | 0.435708i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.12620 | + | 9.66918i | 0.125958 | + | 0.389582i | ||||
\(617\) | 3.15629i | 0.127067i | 0.997980 | + | 0.0635337i | \(0.0202370\pi\) | ||||
−0.997980 | + | 0.0635337i | \(0.979763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.9949i | − | 0.763471i | −0.924272 | − | 0.381735i | \(-0.875327\pi\) | ||
0.924272 | − | 0.381735i | \(-0.124673\pi\) | |||||||
\(620\) | −0.794773 | − | 0.884404i | −0.0319189 | − | 0.0355185i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.0041 | − | 24.6834i | 0.441223 | − | 0.989715i | ||||
\(623\) | 8.91479 | 0.357164 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5561 | 0.942244 | ||||||||
\(626\) | −10.2881 | + | 23.0774i | −0.411195 | + | 0.922358i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.1107 | − | 22.3786i | −0.802502 | − | 0.893005i | ||||
\(629\) | 24.9000i | 0.992828i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 37.6706i | − | 1.49964i | −0.661639 | − | 0.749822i | \(-0.730139\pi\) | ||
0.661639 | − | 0.749822i | \(-0.269861\pi\) | |||||||
\(632\) | −1.20952 | − | 3.74098i | −0.0481121 | − | 0.148808i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.5858 | + | 17.6477i | 1.57215 | + | 0.700879i | ||||
\(635\) | −0.519168 | −0.0206026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.44348 | 0.255300 | ||||||||
\(638\) | 43.0122 | + | 19.1752i | 1.70287 | + | 0.759153i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.44707 | + | 0.720508i | −0.136257 | + | 0.0284806i | ||||
\(641\) | − | 33.9077i | − | 1.33927i | −0.742689 | − | 0.669637i | \(-0.766450\pi\) | ||
0.742689 | − | 0.669637i | \(-0.233550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4425i | 1.35828i | 0.734008 | + | 0.679140i | \(0.237647\pi\) | ||||
−0.734008 | + | 0.679140i | \(0.762353\pi\) | |||||||
\(644\) | −11.2902 | + | 10.1460i | −0.444897 | + | 0.399808i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.16810 | − | 2.62018i | 0.0459583 | − | 0.103090i | ||||
\(647\) | 10.9612 | 0.430931 | 0.215465 | − | 0.976512i | \(-0.430873\pi\) | ||||
0.215465 | + | 0.976512i | \(0.430873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.22768 | 0.322965 | ||||||||
\(650\) | −18.1925 | + | 40.8079i | −0.713568 | + | 1.60062i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.7926 | + | 16.8880i | −0.735974 | + | 0.661386i | ||||
\(653\) | − | 19.8426i | − | 0.776501i | −0.921554 | − | 0.388250i | \(-0.873080\pi\) | ||
0.921554 | − | 0.388250i | \(-0.126920\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.91890i | 0.231270i | ||||||||
\(656\) | 29.8462 | + | 3.19536i | 1.16530 | + | 0.124758i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.6881 | + | 5.65648i | 0.494635 | + | 0.220512i | ||||
\(659\) | −0.592911 | −0.0230965 | −0.0115483 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115483 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.1832 | 1.25178 | 0.625890 | − | 0.779911i | \(-0.284736\pi\) | ||||
0.625890 | + | 0.779911i | \(0.284736\pi\) | |||||||
\(662\) | 14.2421 | + | 6.34926i | 0.553536 | + | 0.246771i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.761903 | − | 0.246336i | 0.0295676 | − | 0.00955967i | ||||
\(665\) | 0.213164i | 0.00826614i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 70.3439i | 2.72373i | ||||||||
\(668\) | 29.5976 | + | 32.9355i | 1.14517 | + | 1.27431i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.196478 | − | 0.440724i | 0.00759062 | − | 0.0170266i | ||||
\(671\) | −1.74694 | −0.0674399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2795 | 1.55266 | 0.776331 | − | 0.630326i | \(-0.217079\pi\) | ||||
0.776331 | + | 0.630326i | \(0.217079\pi\) | |||||||
\(674\) | 1.54894 | − | 3.47446i | 0.0596630 | − | 0.133831i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −38.1240 | − | 42.4235i | −1.46631 | − | 1.63167i | ||||
\(677\) | − | 28.8288i | − | 1.10798i | −0.832523 | − | 0.553991i | \(-0.813104\pi\) | ||
0.832523 | − | 0.553991i | \(-0.186896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.621922i | 0.0238672i | ||||||||
\(680\) | 2.48132 | − | 0.802252i | 0.0951544 | − | 0.0307650i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.86390 | − | 3.95160i | −0.339416 | − | 0.151315i | ||||
\(683\) | 9.31381 | 0.356383 | 0.178191 | − | 0.983996i | \(-0.442975\pi\) | ||||
0.178191 | + | 0.983996i | \(0.442975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.09869 | −0.0419787 | ||||||||
\(686\) | −1.29167 | − | 0.575837i | −0.0493162 | − | 0.0219856i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.0067 | − | 3.96196i | −1.41087 | − | 0.151048i | ||||
\(689\) | − | 35.0325i | − | 1.33463i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.0680i | − | 0.801465i | −0.916195 | − | 0.400732i | \(-0.868756\pi\) | ||
0.916195 | − | 0.400732i | \(-0.131244\pi\) | |||||||
\(692\) | 27.8119 | − | 24.9933i | 1.05725 | − | 0.950103i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.01256 | − | 13.4869i | 0.228234 | − | 0.511955i | ||||
\(695\) | −4.29474 | −0.162909 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.2280 | −0.841947 | ||||||||
\(698\) | −1.26881 | + | 2.84610i | −0.0480253 | + | 0.107726i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.29379 | − | 6.55459i | 0.275679 | − | 0.247740i | ||||
\(701\) | − | 12.1558i | − | 0.459118i | −0.973295 | − | 0.229559i | \(-0.926272\pi\) | ||
0.973295 | − | 0.229559i | \(-0.0737284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.75686i | − | 0.217124i | ||||||
\(704\) | −23.3021 | + | 16.8268i | −0.878230 | + | 0.634186i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.7315 | + | 7.01325i | 0.592064 | + | 0.263947i | ||||
\(707\) | 17.7166 | 0.666303 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2513 | −0.722997 | −0.361498 | − | 0.932373i | \(-0.617735\pi\) | ||||
−0.361498 | + | 0.932373i | \(0.617735\pi\) | |||||||
\(710\) | 0.709309 | + | 0.316216i | 0.0266199 | + | 0.0118674i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.75701 | + | 23.9920i | 0.290706 | + | 0.899139i | ||||
\(713\) | − | 14.4964i | − | 0.542894i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.20585i | − | 0.269483i | ||||||
\(716\) | −21.8101 | − | 24.2697i | −0.815082 | − | 0.907003i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.89873 | + | 17.7178i | −0.294778 | + | 0.661221i | ||||
\(719\) | −41.2877 | −1.53977 | −0.769886 | − | 0.638182i | \(-0.779687\pi\) | ||||
−0.769886 | + | 0.638182i | \(0.779687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5139 | 0.577769 | ||||||||
\(722\) | 10.6708 | − | 23.9359i | 0.397128 | − | 0.890804i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.82590 | + | 10.9340i | 0.365177 | + | 0.406360i | ||||
\(725\) | − | 45.4441i | − | 1.68775i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1628i | 0.821973i | 0.911641 | + | 0.410986i | \(0.134816\pi\) | ||||
−0.911641 | + | 0.410986i | \(0.865184\pi\) | |||||||
\(728\) | 5.60665 | + | 17.3411i | 0.207796 | + | 0.642703i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.33759 | − | 0.596308i | −0.0495064 | − | 0.0220704i | ||||
\(731\) | 27.5608 | 1.01937 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.676700 | 0.0249945 | 0.0124972 | − | 0.999922i | \(-0.496022\pi\) | ||||
0.0124972 | + | 0.999922i | \(0.496022\pi\) | |||||||
\(734\) | 31.1836 | + | 13.9019i | 1.15101 | + | 0.513129i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.1294 | − | 21.5566i | −1.36861 | − | 0.794586i | ||||
\(737\) | − | 3.93839i | − | 0.145072i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 10.4848i | − | 0.385691i | −0.981229 | − | 0.192845i | \(-0.938228\pi\) | ||
0.981229 | − | 0.192845i | \(-0.0617716\pi\) | |||||||
\(740\) | 3.89237 | − | 3.49789i | 0.143086 | − | 0.128585i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.13077 | + | 7.02268i | −0.114934 | + | 0.257811i | ||||
\(743\) | 21.0030 | 0.770525 | 0.385263 | − | 0.922807i | \(-0.374111\pi\) | ||||
0.385263 | + | 0.922807i | \(0.374111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.37319 | 0.123584 | ||||||||
\(746\) | 2.55919 | − | 5.74057i | 0.0936987 | − | 0.210177i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.8312 | − | 14.2267i | 0.578844 | − | 0.520181i | ||||
\(749\) | − | 4.26969i | − | 0.156011i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.4787i | − | 0.564825i | −0.959293 | − | 0.282412i | \(-0.908865\pi\) | ||
0.959293 | − | 0.282412i | \(-0.0911347\pi\) | |||||||
\(752\) | −4.18275 | + | 39.0689i | −0.152529 | + | 1.42470i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 77.1396 | + | 34.3895i | 2.80926 | + | 1.25239i | ||||
\(755\) | −0.131350 | −0.00478033 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.902420 | 0.0327990 | 0.0163995 | − | 0.999866i | \(-0.494780\pi\) | ||||
0.0163995 | + | 0.999866i | \(0.494780\pi\) | |||||||
\(758\) | 11.6640 | + | 5.19989i | 0.423654 | + | 0.188869i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.573680 | + | 0.185480i | −0.0208095 | + | 0.00672806i | ||||
\(761\) | 21.3378i | 0.773493i | 0.922186 | + | 0.386747i | \(0.126401\pi\) | ||||
−0.922186 | + | 0.386747i | \(0.873599\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03903i | 0.0738179i | ||||||||
\(764\) | 27.6588 | + | 30.7781i | 1.00066 | + | 1.11351i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.6090 | − | 26.0402i | 0.419449 | − | 0.940872i | ||||
\(767\) | 14.7558 | 0.532802 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.8199 | 0.895029 | 0.447515 | − | 0.894277i | \(-0.352309\pi\) | ||||
0.447515 | + | 0.894277i | \(0.352309\pi\) | |||||||
\(770\) | −0.643968 | + | 1.44450i | −0.0232070 | + | 0.0520560i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.69125 | + | 4.10754i | 0.132851 | + | 0.147833i | ||||
\(773\) | 22.8253i | 0.820969i | 0.911868 | + | 0.410484i | \(0.134640\pi\) | ||||
−0.911868 | + | 0.410484i | \(0.865360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.36507i | 0.336403i | ||||||||
\(776\) | −1.67375 | + | 0.541152i | −0.0600843 | + | 0.0194262i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0648 | − | 11.6199i | −0.934468 | − | 0.416594i | ||||
\(779\) | 5.13910 | 0.184127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.33851 | 0.226810 | ||||||||
\(782\) | 29.0382 | + | 12.9455i | 1.03840 | + | 0.462929i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.425810 | − | 3.97727i | 0.0152075 | − | 0.142045i | ||||
\(785\) | − | 4.68256i | − | 0.167128i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41.9789i | − | 1.49639i | −0.663481 | − | 0.748193i | \(-0.730922\pi\) | ||
0.663481 | − | 0.748193i | \(-0.269078\pi\) | |||||||
\(788\) | −11.9374 | + | 10.7275i | −0.425251 | + | 0.382153i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.249149 | − | 0.558871i | 0.00886434 | − | 0.0198837i | ||||
\(791\) | −8.69512 | −0.309163 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.13303 | −0.111257 | ||||||||
\(794\) | −11.4553 | + | 25.6955i | −0.406532 | + | 0.911898i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.1066 | − | 21.6635i | 0.854436 | − | 0.767842i | ||||
\(797\) | − | 20.0382i | − | 0.709789i | −0.934906 | − | 0.354894i | \(-0.884517\pi\) | ||
0.934906 | − | 0.354894i | \(-0.115483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.0967i | − | 1.02937i | ||||||
\(800\) | 23.9866 | + | 13.9262i | 0.848056 | + | 0.492364i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.4827 | + | 20.2766i | 1.60605 | + | 0.715990i | ||||
\(803\) | −11.9529 | −0.421810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.36239 | −0.0832633 | ||||||||
\(806\) | −15.8968 | − | 7.08694i | −0.559942 | − | 0.249627i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.4157 | + | 47.6801i | 0.542324 | + | 1.67738i | ||||
\(809\) | − | 8.37127i | − | 0.294318i | −0.989113 | − | 0.147159i | \(-0.952987\pi\) | ||
0.989113 | − | 0.147159i | \(-0.0470129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.60694i | − | 0.337345i | −0.985672 | − | 0.168673i | \(-0.946052\pi\) | ||
0.985672 | − | 0.168673i | \(-0.0539480\pi\) | |||||||
\(812\) | −12.3902 | − | 13.7875i | −0.434812 | − | 0.483848i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.3915 | − | 39.0111i | 0.609571 | − | 1.36734i | ||||
\(815\) | −3.93220 | −0.137739 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.37203 | −0.222929 | ||||||||
\(818\) | 10.6010 | − | 23.7794i | 0.370657 | − | 0.831426i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.12254 | + | 3.47469i | 0.109044 | + | 0.121341i | ||||
\(821\) | 12.6594i | 0.441818i | 0.975294 | + | 0.220909i | \(0.0709023\pi\) | ||||
−0.975294 | + | 0.220909i | \(0.929098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1786i | 0.842811i | 0.906872 | + | 0.421406i | \(0.138463\pi\) | ||||
−0.906872 | + | 0.421406i | \(0.861537\pi\) | |||||||
\(824\) | 13.4991 | + | 41.7520i | 0.470264 | + | 1.45450i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.95798 | − | 1.31869i | −0.102921 | − | 0.0458831i | ||||
\(827\) | −35.6652 | −1.24020 | −0.620100 | − | 0.784522i | \(-0.712908\pi\) | ||||
−0.620100 | + | 0.784522i | \(0.712908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.136683 | −0.00474721 | −0.00237360 | − | 0.999997i | \(-0.500756\pi\) | ||||
−0.00237360 | + | 0.999997i | \(0.500756\pi\) | |||||||
\(830\) | 0.113822 | + | 0.0507428i | 0.00395082 | + | 0.00176131i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.7908 | + | 30.1779i | −1.44884 | + | 1.04623i | ||||
\(833\) | 2.96208i | 0.102630i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.89150i | 0.238490i | ||||||||
\(836\) | −3.66015 | + | 3.28921i | −0.126589 | + | 0.113760i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.7018 | + | 24.0054i | −0.369687 | + | 0.829252i | ||||
\(839\) | −40.5086 | −1.39851 | −0.699256 | − | 0.714872i | \(-0.746485\pi\) | ||||
−0.699256 | + | 0.714872i | \(0.746485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −56.9035 | −1.96219 | ||||||||
\(842\) | −20.3876 | + | 45.7317i | −0.702603 | + | 1.57602i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.7866 | − | 26.7679i | 1.02530 | − | 0.921388i | ||||
\(845\) | − | 8.87678i | − | 0.305371i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.90828i | 0.0655692i | ||||||||
\(848\) | −21.6240 | − | 2.31508i | −0.742572 | − | 0.0795003i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.7595 | − | 8.36313i | −0.643445 | − | 0.286853i | ||||
\(851\) | 63.8004 | 2.18705 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.5584 | 1.90228 | 0.951141 | − | 0.308757i | \(-0.0999130\pi\) | ||||
0.951141 | + | 0.308757i | \(0.0999130\pi\) | |||||||
\(854\) | 0.628052 | + | 0.279991i | 0.0214915 | + | 0.00958109i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4908 | − | 3.71518i | 0.392749 | − | 0.126982i | ||||
\(857\) | − | 28.1683i | − | 0.962211i | −0.876663 | − | 0.481105i | \(-0.840235\pi\) | ||
0.876663 | − | 0.481105i | \(-0.159765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37.1189i | − | 1.26648i | −0.773955 | − | 0.633240i | \(-0.781725\pi\) | ||
0.773955 | − | 0.633240i | \(-0.218275\pi\) | |||||||
\(860\) | −3.87168 | − | 4.30831i | −0.132023 | − | 0.146912i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.3002 | − | 29.8339i | 0.453007 | − | 1.01615i | ||||
\(863\) | 7.83813 | 0.266813 | 0.133406 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133406 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.81943 | 0.197867 | ||||||||
\(866\) | 10.3662 | − | 23.2527i | 0.352259 | − | 0.790158i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.55336 | + | 2.84132i | 0.0866668 | + | 0.0964407i | ||||
\(869\) | − | 4.99417i | − | 0.169416i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.06325i | − | 0.239329i | ||||||
\(872\) | −5.48756 | + | 1.77422i | −0.185832 | + | 0.0600826i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.71360 | − | 2.99298i | −0.227091 | − | 0.101239i | ||||
\(875\) | 3.08250 | 0.104207 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.4403 | −0.588918 | −0.294459 | − | 0.955664i | \(-0.595139\pi\) | ||||
−0.294459 | + | 0.955664i | \(0.595139\pi\) | |||||||
\(878\) | −31.0298 | − | 13.8333i | −1.04720 | − | 0.466852i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.44785 | − | 0.476190i | −0.149937 | − | 0.0160524i | ||||
\(881\) | 37.5232i | 1.26419i | 0.774891 | + | 0.632095i | \(0.217805\pi\) | ||||
−0.774891 | + | 0.632095i | \(0.782195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.149324i | − | 0.00502515i | −0.999997 | − | 0.00251258i | \(-0.999200\pi\) | ||
0.999997 | − | 0.00251258i | \(-0.000799779\pi\) | |||||||
\(884\) | 28.3922 | − | 25.5147i | 0.954932 | − | 0.858154i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.9298 | + | 44.7048i | −0.669554 | + | 1.50189i | ||||
\(887\) | 34.2533 | 1.15011 | 0.575057 | − | 0.818113i | \(-0.304980\pi\) | ||||
0.575057 | + | 0.818113i | \(0.304980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.66793 | 0.0559406 | ||||||||
\(890\) | −1.59787 | + | 3.58421i | −0.0535607 | + | 0.120143i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −35.5658 | + | 31.9614i | −1.19083 | + | 1.07015i | ||||
\(893\) | 6.72712i | 0.225115i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.07825i | − | 0.169747i | ||||||
\(896\) | 11.0744 | − | 2.31477i | 0.369969 | − | 0.0773311i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.7321 | − | 11.0258i | −0.825320 | − | 0.367934i | ||||
\(899\) | 17.7029 | 0.590425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.1045 | 0.536520 | ||||||||
\(902\) | 34.8249 | + | 15.5252i | 1.15954 | + | 0.516933i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.56587 | − | 23.4008i | −0.251637 | − | 0.778300i | ||||
\(905\) | 2.28786i | 0.0760510i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.77393i | 0.291334i | 0.989334 | + | 0.145667i | \(0.0465328\pi\) | ||||
−0.989334 | + | 0.145667i | \(0.953467\pi\) | |||||||
\(908\) | −14.7850 | − | 16.4524i | −0.490659 | − | 0.545993i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.15492 | + | 2.59061i | −0.0382851 | + | 0.0858780i | ||||
\(911\) | −22.3335 | −0.739942 | −0.369971 | − | 0.929043i | \(-0.620632\pi\) | ||||
−0.369971 | + | 0.929043i | \(0.620632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.01713 | 0.0336622 | ||||||||
\(914\) | −8.18871 | + | 18.3682i | −0.270859 | + | 0.607567i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.8013 | + | 34.2750i | 1.01771 | + | 1.13248i | ||||
\(917\) | − | 19.0156i | − | 0.627951i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.3537i | − | 0.671406i | −0.941968 | − | 0.335703i | \(-0.891026\pi\) | ||
0.941968 | − | 0.335703i | \(-0.108974\pi\) | |||||||
\(920\) | −2.05558 | − | 6.35780i | −0.0677705 | − | 0.209611i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.3840 | − | 16.6661i | −1.23118 | − | 0.548869i | ||||
\(923\) | 11.3677 | 0.374173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.2168 | −1.35520 | ||||||||
\(926\) | 39.7674 | + | 17.7287i | 1.30684 | + | 0.582600i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.3248 | − | 45.3422i | 0.864153 | − | 1.48843i | ||||
\(929\) | 39.6973i | 1.30242i | 0.758896 | + | 0.651212i | \(0.225739\pi\) | ||||
−0.758896 | + | 0.651212i | \(0.774261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.684831i | − | 0.0224444i | ||||||
\(932\) | −8.02626 | + | 7.21283i | −0.262909 | + | 0.236264i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.3391 | − | 25.4350i | 0.371027 | − | 0.832257i | ||||
\(935\) | 3.31255 | 0.108332 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3076 | 0.826762 | 0.413381 | − | 0.910558i | \(-0.364348\pi\) | ||||
0.413381 | + | 0.910558i | \(0.364348\pi\) | |||||||
\(938\) | −0.631225 | + | 1.41591i | −0.0206102 | + | 0.0462311i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.54839 | + | 4.08743i | −0.148352 | + | 0.133317i | ||||
\(941\) | − | 8.43714i | − | 0.275043i | −0.990499 | − | 0.137521i | \(-0.956086\pi\) | ||
0.990499 | − | 0.137521i | \(-0.0439136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.9541i | 1.85468i | ||||||||
\(944\) | 0.975121 | − | 9.10811i | 0.0317375 | − | 0.296444i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.1798 | − | 19.2499i | −1.40390 | − | 0.625869i | ||||
\(947\) | 23.3318 | 0.758180 | 0.379090 | − | 0.925360i | \(-0.376237\pi\) | ||||
0.379090 | + | 0.925360i | \(0.376237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.4368 | −0.695869 | ||||||||
\(950\) | 4.33717 | + | 1.93355i | 0.140716 | + | 0.0627326i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.97173 | + | 2.57739i | −0.258365 | + | 0.0835337i | ||||
\(953\) | − | 27.5785i | − | 0.893355i | −0.894695 | − | 0.446678i | \(-0.852607\pi\) | ||
0.894695 | − | 0.446678i | \(-0.147393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.44007i | 0.208396i | ||||||||
\(956\) | 28.8564 | + | 32.1107i | 0.933283 | + | 1.03853i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.17530 | + | 16.0950i | −0.231823 | + | 0.520007i | ||||
\(959\) | 3.52975 | 0.113982 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.3518 | 0.882316 | ||||||||
\(962\) | 31.1905 | − | 69.9639i | 1.00562 | − | 2.25573i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.4424 | − | 13.8456i | −0.400743 | − | 0.445936i | ||||
\(965\) | 0.859470i | 0.0276673i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.59047i | − | 0.115462i | −0.998332 | − | 0.0577308i | \(-0.981613\pi\) | ||
0.998332 | − | 0.0577308i | \(-0.0183865\pi\) | |||||||
\(968\) | −5.13567 | + | 1.66045i | −0.165067 | + | 0.0533688i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.250045 | − | 0.111472i | −0.00802846 | − | 0.00357916i | ||||
\(971\) | −4.89788 | −0.157180 | −0.0785902 | − | 0.996907i | \(-0.525042\pi\) | ||||
−0.0785902 | + | 0.996907i | \(0.525042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.7977 | 0.442333 | ||||||||
\(974\) | 3.78109 | + | 1.68564i | 0.121154 | + | 0.0540114i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.207042 | + | 1.93388i | −0.00662727 | + | 0.0619019i | ||||
\(977\) | 6.72581i | 0.215178i | 0.994195 | + | 0.107589i | \(0.0343130\pi\) | ||||
−0.994195 | + | 0.107589i | \(0.965687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.0291i | 1.02366i | ||||||||
\(980\) | 0.463033 | − | 0.416106i | 0.0147910 | − | 0.0132920i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.36665 | + | 21.0105i | −0.298902 | + | 0.670472i | ||||
\(983\) | −34.3802 | −1.09656 | −0.548279 | − | 0.836295i | \(-0.684717\pi\) | ||||
−0.548279 | + | 0.836295i | \(0.684717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.49780 | −0.0795865 | ||||||||
\(986\) | −15.8089 | + | 35.4613i | −0.503459 | + | 1.12932i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.56425 | + | 5.89899i | −0.208836 | + | 0.187672i | ||||
\(989\) | − | 70.6180i | − | 2.24552i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.9495i | − | 1.14197i | −0.820960 | − | 0.570986i | \(-0.806561\pi\) | ||
0.820960 | − | 0.570986i | \(-0.193439\pi\) | |||||||
\(992\) | −5.42498 | + | 9.34408i | −0.172243 | + | 0.296675i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.27879 | − | 1.01590i | −0.0722789 | − | 0.0322225i | ||||
\(995\) | 5.04412 | 0.159909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.3636 | −0.961625 | −0.480812 | − | 0.876824i | \(-0.659658\pi\) | ||||
−0.480812 | + | 0.876824i | \(0.659658\pi\) | |||||||
\(998\) | −33.4007 | − | 14.8903i | −1.05728 | − | 0.471344i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.e.a.323.17 | yes | 24 | |
3.2 | odd | 2 | inner | 756.2.e.a.323.8 | yes | 24 | |
4.3 | odd | 2 | inner | 756.2.e.a.323.7 | ✓ | 24 | |
12.11 | even | 2 | inner | 756.2.e.a.323.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.e.a.323.7 | ✓ | 24 | 4.3 | odd | 2 | inner | |
756.2.e.a.323.8 | yes | 24 | 3.2 | odd | 2 | inner | |
756.2.e.a.323.17 | yes | 24 | 1.1 | even | 1 | trivial | |
756.2.e.a.323.18 | yes | 24 | 12.11 | even | 2 | inner |