Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.24 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.b.769.23 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.219070 | −0.154906 | −0.0774530 | − | 0.996996i | \(-0.524679\pi\) | ||||
−0.0774530 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.95201 | −0.976004 | ||||||||
\(5\) | 1.49883 | + | 1.65937i | 0.670298 | + | 0.742092i | ||||
\(6\) | −0.219070 | −0.0894350 | ||||||||
\(7\) | 2.26343 | + | 1.37000i | 0.855495 | + | 0.517811i | ||||
\(8\) | 0.865767 | 0.306095 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.328349 | − | 0.363518i | −0.103833 | − | 0.114955i | ||||
\(11\) | −3.31662 | + | 0.00596877i | −0.999998 | + | 0.00179965i | ||||
\(12\) | −1.95201 | −0.563496 | ||||||||
\(13\) | 4.76056i | 1.32034i | 0.751116 | + | 0.660171i | \(0.229516\pi\) | ||||
−0.751116 | + | 0.660171i | \(0.770484\pi\) | |||||||
\(14\) | −0.495849 | − | 0.300126i | −0.132521 | − | 0.0802120i | ||||
\(15\) | 1.49883 | + | 1.65937i | 0.386997 | + | 0.428447i | ||||
\(16\) | 3.71435 | 0.928588 | ||||||||
\(17\) | 1.75010i | 0.424461i | 0.977220 | + | 0.212230i | \(0.0680727\pi\) | ||||
−0.977220 | + | 0.212230i | \(0.931927\pi\) | |||||||
\(18\) | −0.219070 | −0.0516353 | ||||||||
\(19\) | −3.98889 | −0.915115 | −0.457557 | − | 0.889180i | \(-0.651276\pi\) | ||||
−0.457557 | + | 0.889180i | \(0.651276\pi\) | |||||||
\(20\) | −2.92573 | − | 3.23910i | −0.654213 | − | 0.724285i | ||||
\(21\) | 2.26343 | + | 1.37000i | 0.493920 | + | 0.298958i | ||||
\(22\) | 0.726572 | − | 0.00130758i | 0.154906 | − | 0.000278777i | ||||
\(23\) | − | 5.32653i | − | 1.11066i | −0.831631 | − | 0.555329i | \(-0.812592\pi\) | ||
0.831631 | − | 0.555329i | \(-0.187408\pi\) | |||||||
\(24\) | 0.865767 | 0.176724 | ||||||||
\(25\) | −0.507009 | + | 4.97423i | −0.101402 | + | 0.994846i | ||||
\(26\) | − | 1.04290i | − | 0.204529i | ||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.41823 | − | 2.67425i | −0.834967 | − | 0.505385i | ||||
\(29\) | 7.93087i | 1.47273i | 0.676587 | + | 0.736363i | \(0.263458\pi\) | ||||
−0.676587 | + | 0.736363i | \(0.736542\pi\) | |||||||
\(30\) | −0.328349 | − | 0.363518i | −0.0599481 | − | 0.0663690i | ||||
\(31\) | − | 0.416788i | − | 0.0748573i | −0.999299 | − | 0.0374287i | \(-0.988083\pi\) | ||
0.999299 | − | 0.0374287i | \(-0.0119167\pi\) | |||||||
\(32\) | −2.54524 | −0.449939 | ||||||||
\(33\) | −3.31662 | + | 0.00596877i | −0.577349 | + | 0.00103903i | ||||
\(34\) | − | 0.383394i | − | 0.0657515i | ||||||
\(35\) | 1.11916 | + | 5.80926i | 0.189173 | + | 0.981944i | ||||
\(36\) | −1.95201 | −0.325335 | ||||||||
\(37\) | − | 8.40684i | − | 1.38208i | −0.722819 | − | 0.691038i | \(-0.757154\pi\) | ||
0.722819 | − | 0.691038i | \(-0.242846\pi\) | |||||||
\(38\) | 0.873847 | 0.141757 | ||||||||
\(39\) | 4.76056i | 0.762299i | ||||||||
\(40\) | 1.29764 | + | 1.43663i | 0.205175 | + | 0.227151i | ||||
\(41\) | 5.12766 | 0.800807 | 0.400403 | − | 0.916339i | \(-0.368870\pi\) | ||||
0.400403 | + | 0.916339i | \(0.368870\pi\) | |||||||
\(42\) | −0.495849 | − | 0.300126i | −0.0765112 | − | 0.0463104i | ||||
\(43\) | −10.5926 | −1.61535 | −0.807676 | − | 0.589627i | \(-0.799275\pi\) | ||||
−0.807676 | + | 0.589627i | \(0.799275\pi\) | |||||||
\(44\) | 6.47407 | − | 0.0116511i | 0.976003 | − | 0.00175647i | ||||
\(45\) | 1.49883 | + | 1.65937i | 0.223433 | + | 0.247364i | ||||
\(46\) | 1.16688i | 0.172048i | ||||||||
\(47\) | 1.02252 | 0.149150 | 0.0745751 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745751 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(48\) | 3.71435 | 0.536121 | ||||||||
\(49\) | 3.24621 | + | 6.20178i | 0.463744 | + | 0.885969i | ||||
\(50\) | 0.111070 | − | 1.08970i | 0.0157077 | − | 0.154108i | ||||
\(51\) | 1.75010i | 0.245063i | ||||||||
\(52\) | − | 9.29265i | − | 1.28866i | ||||||
\(53\) | 4.16120i | 0.571585i | 0.958292 | + | 0.285793i | \(0.0922568\pi\) | ||||
−0.958292 | + | 0.285793i | \(0.907743\pi\) | |||||||
\(54\) | −0.219070 | −0.0298117 | ||||||||
\(55\) | −4.98096 | − | 5.49455i | −0.671632 | − | 0.740885i | ||||
\(56\) | 1.95960 | + | 1.18610i | 0.261863 | + | 0.158499i | ||||
\(57\) | −3.98889 | −0.528342 | ||||||||
\(58\) | − | 1.73742i | − | 0.228134i | ||||||
\(59\) | − | 1.47657i | − | 0.192233i | −0.995370 | − | 0.0961166i | \(-0.969358\pi\) | ||
0.995370 | − | 0.0961166i | \(-0.0306422\pi\) | |||||||
\(60\) | −2.92573 | − | 3.23910i | −0.377710 | − | 0.418166i | ||||
\(61\) | 7.08776 | 0.907495 | 0.453747 | − | 0.891130i | \(-0.350087\pi\) | ||||
0.453747 | + | 0.891130i | \(0.350087\pi\) | |||||||
\(62\) | 0.0913058i | 0.0115958i | ||||||||
\(63\) | 2.26343 | + | 1.37000i | 0.285165 | + | 0.172604i | ||||
\(64\) | −6.87112 | −0.858890 | ||||||||
\(65\) | −7.89952 | + | 7.13527i | −0.979815 | + | 0.885022i | ||||
\(66\) | 0.726572 | − | 0.00130758i | 0.0894349 | − | 0.000160952i | ||||
\(67\) | 12.2899i | 1.50145i | 0.660616 | + | 0.750724i | \(0.270295\pi\) | ||||
−0.660616 | + | 0.750724i | \(0.729705\pi\) | |||||||
\(68\) | − | 3.41620i | − | 0.414275i | ||||||
\(69\) | − | 5.32653i | − | 0.641239i | ||||||
\(70\) | −0.245176 | − | 1.27263i | −0.0293041 | − | 0.152109i | ||||
\(71\) | −5.14350 | −0.610422 | −0.305211 | − | 0.952285i | \(-0.598727\pi\) | ||||
−0.305211 | + | 0.952285i | \(0.598727\pi\) | |||||||
\(72\) | 0.865767 | 0.102032 | ||||||||
\(73\) | 14.7437i | 1.72562i | 0.505526 | + | 0.862812i | \(0.331299\pi\) | ||||
−0.505526 | + | 0.862812i | \(0.668701\pi\) | |||||||
\(74\) | 1.84169i | 0.214092i | ||||||||
\(75\) | −0.507009 | + | 4.97423i | −0.0585443 | + | 0.574374i | ||||
\(76\) | 7.78635 | 0.893156 | ||||||||
\(77\) | −7.51511 | − | 4.53025i | −0.856426 | − | 0.516270i | ||||
\(78\) | − | 1.04290i | − | 0.118085i | ||||||
\(79\) | 4.99740i | 0.562252i | 0.959671 | + | 0.281126i | \(0.0907079\pi\) | ||||
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(80\) | 5.56719 | + | 6.16348i | 0.622431 | + | 0.689098i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.12332 | −0.124050 | ||||||||
\(83\) | − | 4.77780i | − | 0.524432i | −0.965009 | − | 0.262216i | \(-0.915547\pi\) | ||
0.965009 | − | 0.262216i | \(-0.0844533\pi\) | |||||||
\(84\) | −4.41823 | − | 2.67425i | −0.482068 | − | 0.291784i | ||||
\(85\) | −2.90405 | + | 2.62310i | −0.314989 | + | 0.284515i | ||||
\(86\) | 2.32051 | 0.250228 | ||||||||
\(87\) | 7.93087i | 0.850279i | ||||||||
\(88\) | −2.87142 | + | 0.00516756i | −0.306094 | + | 0.000550864i | ||||
\(89\) | − | 8.37576i | − | 0.887828i | −0.896069 | − | 0.443914i | \(-0.853590\pi\) | ||
0.896069 | − | 0.443914i | \(-0.146410\pi\) | |||||||
\(90\) | −0.328349 | − | 0.363518i | −0.0346110 | − | 0.0383182i | ||||
\(91\) | −6.52196 | + | 10.7752i | −0.683687 | + | 1.12955i | ||||
\(92\) | 10.3974i | 1.08401i | ||||||||
\(93\) | − | 0.416788i | − | 0.0432189i | ||||||
\(94\) | −0.224004 | −0.0231043 | ||||||||
\(95\) | −5.97868 | − | 6.61904i | −0.613399 | − | 0.679099i | ||||
\(96\) | −2.54524 | −0.259772 | ||||||||
\(97\) | 8.91729 | 0.905414 | 0.452707 | − | 0.891659i | \(-0.350458\pi\) | ||||
0.452707 | + | 0.891659i | \(0.350458\pi\) | |||||||
\(98\) | −0.711148 | − | 1.35863i | −0.0718368 | − | 0.137242i | ||||
\(99\) | −3.31662 | + | 0.00596877i | −0.333333 | + | 0.000599884i | ||||
\(100\) | 0.989685 | − | 9.70973i | 0.0989685 | − | 0.970973i | ||||
\(101\) | 15.5775 | 1.55002 | 0.775008 | − | 0.631951i | \(-0.217746\pi\) | ||||
0.775008 | + | 0.631951i | \(0.217746\pi\) | |||||||
\(102\) | − | 0.383394i | − | 0.0379617i | ||||||
\(103\) | −1.22728 | −0.120928 | −0.0604638 | − | 0.998170i | \(-0.519258\pi\) | ||||
−0.0604638 | + | 0.998170i | \(0.519258\pi\) | |||||||
\(104\) | 4.12153i | 0.404150i | ||||||||
\(105\) | 1.11916 | + | 5.80926i | 0.109219 | + | 0.566925i | ||||
\(106\) | − | 0.911595i | − | 0.0885420i | ||||||
\(107\) | −2.52487 | −0.244088 | −0.122044 | − | 0.992525i | \(-0.538945\pi\) | ||||
−0.122044 | + | 0.992525i | \(0.538945\pi\) | |||||||
\(108\) | −1.95201 | −0.187832 | ||||||||
\(109\) | 19.4843i | 1.86625i | 0.359547 | + | 0.933127i | \(0.382931\pi\) | ||||
−0.359547 | + | 0.933127i | \(0.617069\pi\) | |||||||
\(110\) | 1.09118 | + | 1.20369i | 0.104040 | + | 0.114767i | ||||
\(111\) | − | 8.40684i | − | 0.797942i | ||||||
\(112\) | 8.40717 | + | 5.08866i | 0.794403 | + | 0.480833i | ||||
\(113\) | 3.00342i | 0.282538i | 0.989971 | + | 0.141269i | \(0.0451182\pi\) | ||||
−0.989971 | + | 0.141269i | \(0.954882\pi\) | |||||||
\(114\) | 0.873847 | 0.0818433 | ||||||||
\(115\) | 8.83868 | − | 7.98357i | 0.824211 | − | 0.744472i | ||||
\(116\) | − | 15.4811i | − | 1.43739i | ||||||
\(117\) | 4.76056i | 0.440114i | ||||||||
\(118\) | 0.323473i | 0.0297781i | ||||||||
\(119\) | −2.39763 | + | 3.96122i | −0.219790 | + | 0.363124i | ||||
\(120\) | 1.29764 | + | 1.43663i | 0.118458 | + | 0.131145i | ||||
\(121\) | 10.9999 | − | 0.0395923i | 0.999994 | − | 0.00359930i | ||||
\(122\) | −1.55272 | −0.140576 | ||||||||
\(123\) | 5.12766 | 0.462346 | ||||||||
\(124\) | 0.813573i | 0.0730610i | ||||||||
\(125\) | −9.01400 | + | 6.61421i | −0.806237 | + | 0.591593i | ||||
\(126\) | −0.495849 | − | 0.300126i | −0.0441738 | − | 0.0267373i | ||||
\(127\) | 16.2867 | 1.44521 | 0.722606 | − | 0.691260i | \(-0.242944\pi\) | ||||
0.722606 | + | 0.691260i | \(0.242944\pi\) | |||||||
\(128\) | 6.59573 | 0.582986 | ||||||||
\(129\) | −10.5926 | −0.932623 | ||||||||
\(130\) | 1.73055 | − | 1.56313i | 0.151779 | − | 0.137095i | ||||
\(131\) | 20.6593 | 1.80501 | 0.902506 | − | 0.430678i | \(-0.141726\pi\) | ||||
0.902506 | + | 0.430678i | \(0.141726\pi\) | |||||||
\(132\) | 6.47407 | − | 0.0116511i | 0.563495 | − | 0.00101410i | ||||
\(133\) | −9.02857 | − | 5.46478i | −0.782876 | − | 0.473856i | ||||
\(134\) | − | 2.69234i | − | 0.232583i | ||||||
\(135\) | 1.49883 | + | 1.65937i | 0.128999 | + | 0.142816i | ||||
\(136\) | 1.51518i | 0.129925i | ||||||||
\(137\) | − | 16.2074i | − | 1.38469i | −0.721566 | − | 0.692345i | \(-0.756577\pi\) | ||
0.721566 | − | 0.692345i | \(-0.243423\pi\) | |||||||
\(138\) | 1.16688i | 0.0993318i | ||||||||
\(139\) | −17.7663 | −1.50692 | −0.753459 | − | 0.657495i | \(-0.771616\pi\) | ||||
−0.753459 | + | 0.657495i | \(0.771616\pi\) | |||||||
\(140\) | −2.18462 | − | 11.3397i | −0.184634 | − | 0.958381i | ||||
\(141\) | 1.02252 | 0.0861119 | ||||||||
\(142\) | 1.12679 | 0.0945580 | ||||||||
\(143\) | −0.0284147 | − | 15.7890i | −0.00237615 | − | 1.32034i | ||||
\(144\) | 3.71435 | 0.309529 | ||||||||
\(145\) | −13.1602 | + | 11.8870i | −1.09290 | + | 0.987165i | ||||
\(146\) | − | 3.22991i | − | 0.267309i | ||||||
\(147\) | 3.24621 | + | 6.20178i | 0.267743 | + | 0.511515i | ||||
\(148\) | 16.4102i | 1.34891i | ||||||||
\(149\) | − | 19.3124i | − | 1.58214i | −0.611728 | − | 0.791068i | \(-0.709525\pi\) | ||
0.611728 | − | 0.791068i | \(-0.290475\pi\) | |||||||
\(150\) | 0.111070 | − | 1.08970i | 0.00906887 | − | 0.0889740i | ||||
\(151\) | − | 15.0336i | − | 1.22341i | −0.791084 | − | 0.611707i | \(-0.790483\pi\) | ||
0.791084 | − | 0.611707i | \(-0.209517\pi\) | |||||||
\(152\) | −3.45345 | −0.280112 | ||||||||
\(153\) | 1.75010i | 0.141487i | ||||||||
\(154\) | 1.64634 | + | 0.992443i | 0.132665 | + | 0.0799734i | ||||
\(155\) | 0.691605 | − | 0.624695i | 0.0555510 | − | 0.0501767i | ||||
\(156\) | − | 9.29265i | − | 0.744007i | ||||||
\(157\) | −9.76184 | −0.779080 | −0.389540 | − | 0.921010i | \(-0.627366\pi\) | ||||
−0.389540 | + | 0.921010i | \(0.627366\pi\) | |||||||
\(158\) | − | 1.09478i | − | 0.0870962i | ||||||
\(159\) | 4.16120i | 0.330005i | ||||||||
\(160\) | −3.81488 | − | 4.22349i | −0.301593 | − | 0.333896i | ||||
\(161\) | 7.29734 | − | 12.0562i | 0.575111 | − | 0.950163i | ||||
\(162\) | −0.219070 | −0.0172118 | ||||||||
\(163\) | − | 2.65834i | − | 0.208217i | −0.994566 | − | 0.104108i | \(-0.966801\pi\) | ||
0.994566 | − | 0.104108i | \(-0.0331989\pi\) | |||||||
\(164\) | −10.0092 | −0.781591 | ||||||||
\(165\) | −4.98096 | − | 5.49455i | −0.387767 | − | 0.427750i | ||||
\(166\) | 1.04667i | 0.0812377i | ||||||||
\(167\) | − | 12.3713i | − | 0.957321i | −0.878000 | − | 0.478661i | \(-0.841122\pi\) | ||
0.878000 | − | 0.478661i | \(-0.158878\pi\) | |||||||
\(168\) | 1.95960 | + | 1.18610i | 0.151187 | + | 0.0915096i | ||||
\(169\) | −9.66291 | −0.743301 | ||||||||
\(170\) | 0.636192 | − | 0.574643i | 0.0487937 | − | 0.0440731i | ||||
\(171\) | −3.98889 | −0.305038 | ||||||||
\(172\) | 20.6768 | 1.57659 | ||||||||
\(173\) | − | 5.30683i | − | 0.403471i | −0.979440 | − | 0.201735i | \(-0.935342\pi\) | ||
0.979440 | − | 0.201735i | \(-0.0646581\pi\) | |||||||
\(174\) | − | 1.73742i | − | 0.131713i | ||||||
\(175\) | −7.96226 | + | 10.5642i | −0.601890 | + | 0.798579i | ||||
\(176\) | −12.3191 | + | 0.0221701i | −0.928587 | + | 0.00167113i | ||||
\(177\) | − | 1.47657i | − | 0.110986i | ||||||
\(178\) | 1.83488i | 0.137530i | ||||||||
\(179\) | 6.03351 | 0.450966 | 0.225483 | − | 0.974247i | \(-0.427604\pi\) | ||||
0.225483 | + | 0.974247i | \(0.427604\pi\) | |||||||
\(180\) | −2.92573 | − | 3.23910i | −0.218071 | − | 0.241428i | ||||
\(181\) | − | 15.0417i | − | 1.11804i | −0.829153 | − | 0.559021i | \(-0.811177\pi\) | ||
0.829153 | − | 0.559021i | \(-0.188823\pi\) | |||||||
\(182\) | 1.42877 | − | 2.36052i | 0.105907 | − | 0.174973i | ||||
\(183\) | 7.08776 | 0.523942 | ||||||||
\(184\) | − | 4.61154i | − | 0.339967i | ||||||
\(185\) | 13.9500 | − | 12.6004i | 1.02563 | − | 0.926402i | ||||
\(186\) | 0.0913058i | 0.00669487i | ||||||||
\(187\) | −0.0104459 | − | 5.80440i | −0.000763881 | − | 0.424460i | ||||
\(188\) | −1.99597 | −0.145571 | ||||||||
\(189\) | 2.26343 | + | 1.37000i | 0.164640 | + | 0.0996527i | ||||
\(190\) | 1.30975 | + | 1.45003i | 0.0950192 | + | 0.105197i | ||||
\(191\) | 18.7953 | 1.35998 | 0.679991 | − | 0.733220i | \(-0.261984\pi\) | ||||
0.679991 | + | 0.733220i | \(0.261984\pi\) | |||||||
\(192\) | −6.87112 | −0.495880 | ||||||||
\(193\) | −1.81009 | −0.130293 | −0.0651467 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651467 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(194\) | −1.95351 | −0.140254 | ||||||||
\(195\) | −7.89952 | + | 7.13527i | −0.565696 | + | 0.510968i | ||||
\(196\) | −6.33663 | − | 12.1059i | −0.452616 | − | 0.864710i | ||||
\(197\) | −14.2265 | −1.01360 | −0.506799 | − | 0.862064i | \(-0.669171\pi\) | ||||
−0.506799 | + | 0.862064i | \(0.669171\pi\) | |||||||
\(198\) | 0.726572 | − | 0.00130758i | 0.0516352 | − | 9.29256e-5i | ||||
\(199\) | 7.65140i | 0.542394i | 0.962524 | + | 0.271197i | \(0.0874194\pi\) | ||||
−0.962524 | + | 0.271197i | \(0.912581\pi\) | |||||||
\(200\) | −0.438951 | + | 4.30652i | −0.0310386 | + | 0.304517i | ||||
\(201\) | 12.2899i | 0.866861i | ||||||||
\(202\) | −3.41256 | −0.240107 | ||||||||
\(203\) | −10.8653 | + | 17.9510i | −0.762593 | + | 1.25991i | ||||
\(204\) | − | 3.41620i | − | 0.239182i | ||||||
\(205\) | 7.68550 | + | 8.50869i | 0.536779 | + | 0.594272i | ||||
\(206\) | 0.268861 | 0.0187324 | ||||||||
\(207\) | − | 5.32653i | − | 0.370220i | ||||||
\(208\) | 17.6824i | 1.22605i | ||||||||
\(209\) | 13.2296 | − | 0.0238088i | 0.915113 | − | 0.00164689i | ||||
\(210\) | −0.245176 | − | 1.27263i | −0.0169187 | − | 0.0878202i | ||||
\(211\) | 2.11088i | 0.145319i | 0.997357 | + | 0.0726596i | \(0.0231487\pi\) | ||||
−0.997357 | + | 0.0726596i | \(0.976851\pi\) | |||||||
\(212\) | − | 8.12270i | − | 0.557869i | ||||||
\(213\) | −5.14350 | −0.352427 | ||||||||
\(214\) | 0.553123 | 0.0378107 | ||||||||
\(215\) | −15.8765 | − | 17.5770i | −1.08277 | − | 1.19874i | ||||
\(216\) | 0.865767 | 0.0589080 | ||||||||
\(217\) | 0.570999 | − | 0.943369i | 0.0387619 | − | 0.0640401i | ||||
\(218\) | − | 4.26842i | − | 0.289094i | ||||||
\(219\) | 14.7437i | 0.996289i | ||||||||
\(220\) | 9.72287 | + | 10.7254i | 0.655516 | + | 0.723107i | ||||
\(221\) | −8.33143 | −0.560433 | ||||||||
\(222\) | 1.84169i | 0.123606i | ||||||||
\(223\) | 16.3707 | 1.09626 | 0.548131 | − | 0.836392i | \(-0.315339\pi\) | ||||
0.548131 | + | 0.836392i | \(0.315339\pi\) | |||||||
\(224\) | −5.76096 | − | 3.48697i | −0.384920 | − | 0.232983i | ||||
\(225\) | −0.507009 | + | 4.97423i | −0.0338006 | + | 0.331615i | ||||
\(226\) | − | 0.657959i | − | 0.0437668i | ||||||
\(227\) | − | 9.80413i | − | 0.650723i | −0.945590 | − | 0.325362i | \(-0.894514\pi\) | ||
0.945590 | − | 0.325362i | \(-0.105486\pi\) | |||||||
\(228\) | 7.78635 | 0.515664 | ||||||||
\(229\) | 8.04004i | 0.531301i | 0.964069 | + | 0.265650i | \(0.0855867\pi\) | ||||
−0.964069 | + | 0.265650i | \(0.914413\pi\) | |||||||
\(230\) | −1.93629 | + | 1.74896i | −0.127675 | + | 0.115323i | ||||
\(231\) | −7.51511 | − | 4.53025i | −0.494458 | − | 0.298069i | ||||
\(232\) | 6.86629i | 0.450794i | ||||||||
\(233\) | −5.02365 | −0.329110 | −0.164555 | − | 0.986368i | \(-0.552619\pi\) | ||||
−0.164555 | + | 0.986368i | \(0.552619\pi\) | |||||||
\(234\) | − | 1.04290i | − | 0.0681763i | ||||||
\(235\) | 1.53259 | + | 1.69674i | 0.0999751 | + | 0.110683i | ||||
\(236\) | 2.88228i | 0.187620i | ||||||||
\(237\) | 4.99740i | 0.324616i | ||||||||
\(238\) | 0.525249 | − | 0.867784i | 0.0340468 | − | 0.0562501i | ||||
\(239\) | 1.83401i | 0.118632i | 0.998239 | + | 0.0593162i | \(0.0188920\pi\) | ||||
−0.998239 | + | 0.0593162i | \(0.981108\pi\) | |||||||
\(240\) | 5.56719 | + | 6.16348i | 0.359360 | + | 0.397851i | ||||
\(241\) | 16.4629 | 1.06047 | 0.530233 | − | 0.847852i | \(-0.322104\pi\) | ||||
0.530233 | + | 0.847852i | \(0.322104\pi\) | |||||||
\(242\) | −2.40976 | + | 0.00867348i | −0.154905 | + | 0.000557552i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −13.8354 | −0.885718 | ||||||||
\(245\) | −5.42552 | + | 14.6821i | −0.346624 | + | 0.938004i | ||||
\(246\) | −1.12332 | −0.0716202 | ||||||||
\(247\) | − | 18.9894i | − | 1.20826i | ||||||
\(248\) | − | 0.360841i | − | 0.0229134i | ||||||
\(249\) | − | 4.77780i | − | 0.302781i | ||||||
\(250\) | 1.97470 | − | 1.44898i | 0.124891 | − | 0.0916414i | ||||
\(251\) | 29.2562i | 1.84663i | 0.384040 | + | 0.923316i | \(0.374532\pi\) | ||||
−0.384040 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(252\) | −4.41823 | − | 2.67425i | −0.278322 | − | 0.168462i | ||||
\(253\) | 0.0317928 | + | 17.6661i | 0.00199880 | + | 1.11066i | ||||
\(254\) | −3.56793 | −0.223872 | ||||||||
\(255\) | −2.90405 | + | 2.62310i | −0.181859 | + | 0.164265i | ||||
\(256\) | 12.2973 | 0.768582 | ||||||||
\(257\) | 13.1186 | 0.818316 | 0.409158 | − | 0.912463i | \(-0.365822\pi\) | ||||
0.409158 | + | 0.912463i | \(0.365822\pi\) | |||||||
\(258\) | 2.32051 | 0.144469 | ||||||||
\(259\) | 11.5174 | − | 19.0283i | 0.715653 | − | 1.18236i | ||||
\(260\) | 15.4199 | − | 13.9281i | 0.956303 | − | 0.863785i | ||||
\(261\) | 7.93087i | 0.490909i | ||||||||
\(262\) | −4.52584 | −0.279607 | ||||||||
\(263\) | −7.58284 | −0.467578 | −0.233789 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233789 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(264\) | −2.87142 | + | 0.00516756i | −0.176724 | + | 0.000318041i | ||||
\(265\) | −6.90497 | + | 6.23694i | −0.424169 | + | 0.383132i | ||||
\(266\) | 1.97789 | + | 1.19717i | 0.121272 | + | 0.0734032i | ||||
\(267\) | − | 8.37576i | − | 0.512588i | ||||||
\(268\) | − | 23.9899i | − | 1.46542i | ||||||
\(269\) | − | 24.5700i | − | 1.49806i | −0.662535 | − | 0.749031i | \(-0.730520\pi\) | ||
0.662535 | − | 0.749031i | \(-0.269480\pi\) | |||||||
\(270\) | −0.328349 | − | 0.363518i | −0.0199827 | − | 0.0221230i | ||||
\(271\) | −15.0926 | −0.916810 | −0.458405 | − | 0.888743i | \(-0.651579\pi\) | ||||
−0.458405 | + | 0.888743i | \(0.651579\pi\) | |||||||
\(272\) | 6.50048i | 0.394149i | ||||||||
\(273\) | −6.52196 | + | 10.7752i | −0.394727 | + | 0.652143i | ||||
\(274\) | 3.55056i | 0.214497i | ||||||||
\(275\) | 1.65186 | − | 16.5006i | 0.0996112 | − | 0.995026i | ||||
\(276\) | 10.3974i | 0.625852i | ||||||||
\(277\) | −5.23707 | −0.314665 | −0.157332 | − | 0.987546i | \(-0.550289\pi\) | ||||
−0.157332 | + | 0.987546i | \(0.550289\pi\) | |||||||
\(278\) | 3.89207 | 0.233431 | ||||||||
\(279\) | − | 0.416788i | − | 0.0249524i | ||||||
\(280\) | 0.968936 | + | 5.02946i | 0.0579050 | + | 0.300568i | ||||
\(281\) | − | 19.5161i | − | 1.16423i | −0.813105 | − | 0.582117i | \(-0.802224\pi\) | ||
0.813105 | − | 0.582117i | \(-0.197776\pi\) | |||||||
\(282\) | −0.224004 | −0.0133393 | ||||||||
\(283\) | − | 14.0410i | − | 0.834650i | −0.908757 | − | 0.417325i | \(-0.862968\pi\) | ||
0.908757 | − | 0.417325i | \(-0.137032\pi\) | |||||||
\(284\) | 10.0402 | 0.595774 | ||||||||
\(285\) | −5.97868 | − | 6.61904i | −0.354146 | − | 0.392078i | ||||
\(286\) | 0.00622480 | + | 3.45889i | 0.000368080 | + | 0.204528i | ||||
\(287\) | 11.6061 | + | 7.02489i | 0.685086 | + | 0.414666i | ||||
\(288\) | −2.54524 | −0.149980 | ||||||||
\(289\) | 13.9372 | 0.819833 | ||||||||
\(290\) | 2.88302 | − | 2.60410i | 0.169296 | − | 0.152918i | ||||
\(291\) | 8.91729 | 0.522741 | ||||||||
\(292\) | − | 28.7799i | − | 1.68422i | ||||||
\(293\) | − | 15.9012i | − | 0.928957i | −0.885584 | − | 0.464478i | \(-0.846242\pi\) | ||
0.885584 | − | 0.464478i | \(-0.153758\pi\) | |||||||
\(294\) | −0.711148 | − | 1.35863i | −0.0414750 | − | 0.0792367i | ||||
\(295\) | 2.45018 | − | 2.21313i | 0.142655 | − | 0.128854i | ||||
\(296\) | − | 7.27836i | − | 0.423046i | ||||||
\(297\) | −3.31662 | + | 0.00596877i | −0.192450 | + | 0.000346343i | ||||
\(298\) | 4.23078i | 0.245082i | ||||||||
\(299\) | 25.3573 | 1.46645 | ||||||||
\(300\) | 0.989685 | − | 9.70973i | 0.0571395 | − | 0.560592i | ||||
\(301\) | −23.9755 | − | 14.5118i | −1.38193 | − | 0.836446i | ||||
\(302\) | 3.29341i | 0.189514i | ||||||||
\(303\) | 15.5775 | 0.894903 | ||||||||
\(304\) | −14.8162 | −0.849765 | ||||||||
\(305\) | 10.6234 | + | 11.7612i | 0.608292 | + | 0.673445i | ||||
\(306\) | − | 0.383394i | − | 0.0219172i | ||||||
\(307\) | 15.3444i | 0.875754i | 0.899035 | + | 0.437877i | \(0.144269\pi\) | ||||
−0.899035 | + | 0.437877i | \(0.855731\pi\) | |||||||
\(308\) | 14.6695 | + | 8.84309i | 0.835875 | + | 0.503882i | ||||
\(309\) | −1.22728 | −0.0698176 | ||||||||
\(310\) | −0.151510 | + | 0.136852i | −0.00860519 | + | 0.00777267i | ||||
\(311\) | − | 29.9189i | − | 1.69655i | −0.529558 | − | 0.848274i | \(-0.677642\pi\) | ||
0.529558 | − | 0.848274i | \(-0.322358\pi\) | |||||||
\(312\) | 4.12153i | 0.233336i | ||||||||
\(313\) | −12.8166 | −0.724440 | −0.362220 | − | 0.932093i | \(-0.617981\pi\) | ||||
−0.362220 | + | 0.932093i | \(0.617981\pi\) | |||||||
\(314\) | 2.13853 | 0.120684 | ||||||||
\(315\) | 1.11916 | + | 5.80926i | 0.0630578 | + | 0.327315i | ||||
\(316\) | − | 9.75497i | − | 0.548760i | ||||||
\(317\) | − | 0.0935753i | − | 0.00525571i | −0.999997 | − | 0.00262786i | \(-0.999164\pi\) | ||
0.999997 | − | 0.00262786i | \(-0.000836474\pi\) | |||||||
\(318\) | − | 0.911595i | − | 0.0511197i | ||||||
\(319\) | −0.0473375 | − | 26.3037i | −0.00265039 | − | 1.47272i | ||||
\(320\) | −10.2987 | − | 11.4017i | −0.575712 | − | 0.637376i | ||||
\(321\) | −2.52487 | −0.140924 | ||||||||
\(322\) | −1.59863 | + | 2.64116i | −0.0890881 | + | 0.147186i | ||||
\(323\) | − | 6.98095i | − | 0.388430i | ||||||
\(324\) | −1.95201 | −0.108445 | ||||||||
\(325\) | −23.6801 | − | 2.41364i | −1.31354 | − | 0.133885i | ||||
\(326\) | 0.582362i | 0.0322540i | ||||||||
\(327\) | 19.4843i | 1.07748i | ||||||||
\(328\) | 4.43936 | 0.245123 | ||||||||
\(329\) | 2.31441 | + | 1.40085i | 0.127597 | + | 0.0772316i | ||||
\(330\) | 1.09118 | + | 1.20369i | 0.0600674 | + | 0.0662610i | ||||
\(331\) | 2.60137 | 0.142984 | 0.0714922 | − | 0.997441i | \(-0.477224\pi\) | ||||
0.0714922 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(332\) | 9.32631i | 0.511848i | ||||||||
\(333\) | − | 8.40684i | − | 0.460692i | ||||||
\(334\) | 2.71019i | 0.148295i | ||||||||
\(335\) | −20.3934 | + | 18.4205i | −1.11421 | + | 1.00642i | ||||
\(336\) | 8.40717 | + | 5.08866i | 0.458649 | + | 0.277609i | ||||
\(337\) | 9.63959 | 0.525102 | 0.262551 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262551 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(338\) | 2.11686 | 0.115142 | ||||||||
\(339\) | 3.00342i | 0.163123i | ||||||||
\(340\) | 5.66874 | − | 5.12031i | 0.307431 | − | 0.277688i | ||||
\(341\) | 0.00248771 | + | 1.38233i | 0.000134717 | + | 0.0748572i | ||||
\(342\) | 0.873847 | 0.0472522 | ||||||||
\(343\) | −1.14887 | + | 18.4846i | −0.0620332 | + | 0.998074i | ||||
\(344\) | −9.17069 | −0.494451 | ||||||||
\(345\) | 8.83868 | − | 7.98357i | 0.475859 | − | 0.429821i | ||||
\(346\) | 1.16257i | 0.0625000i | ||||||||
\(347\) | 4.68884 | 0.251710 | 0.125855 | − | 0.992049i | \(-0.459833\pi\) | ||||
0.125855 | + | 0.992049i | \(0.459833\pi\) | |||||||
\(348\) | − | 15.4811i | − | 0.829875i | ||||||
\(349\) | 22.7013 | 1.21517 | 0.607586 | − | 0.794254i | \(-0.292138\pi\) | ||||
0.607586 | + | 0.794254i | \(0.292138\pi\) | |||||||
\(350\) | 1.74429 | − | 2.31430i | 0.0932364 | − | 0.123705i | ||||
\(351\) | 4.76056i | 0.254100i | ||||||||
\(352\) | 8.44159 | − | 0.0151919i | 0.449938 | − | 0.000809733i | ||||
\(353\) | 12.5022 | 0.665427 | 0.332713 | − | 0.943028i | \(-0.392036\pi\) | ||||
0.332713 | + | 0.943028i | \(0.392036\pi\) | |||||||
\(354\) | 0.323473i | 0.0171924i | ||||||||
\(355\) | −7.70924 | − | 8.53497i | −0.409164 | − | 0.452989i | ||||
\(356\) | 16.3495i | 0.866524i | ||||||||
\(357\) | −2.39763 | + | 3.96122i | −0.126896 | + | 0.209650i | ||||
\(358\) | −1.32176 | −0.0698573 | ||||||||
\(359\) | − | 17.7385i | − | 0.936201i | −0.883675 | − | 0.468100i | \(-0.844939\pi\) | ||
0.883675 | − | 0.468100i | \(-0.155061\pi\) | |||||||
\(360\) | 1.29764 | + | 1.43663i | 0.0683916 | + | 0.0757169i | ||||
\(361\) | −3.08874 | −0.162565 | ||||||||
\(362\) | 3.29519i | 0.173192i | ||||||||
\(363\) | 10.9999 | − | 0.0395923i | 0.577347 | − | 0.00207805i | ||||
\(364\) | 12.7309 | − | 21.0332i | 0.667281 | − | 1.10244i | ||||
\(365\) | −24.4653 | + | 22.0984i | −1.28057 | + | 1.15668i | ||||
\(366\) | −1.55272 | −0.0811618 | ||||||||
\(367\) | −7.93121 | −0.414006 | −0.207003 | − | 0.978340i | \(-0.566371\pi\) | ||||
−0.207003 | + | 0.978340i | \(0.566371\pi\) | |||||||
\(368\) | − | 19.7846i | − | 1.03134i | ||||||
\(369\) | 5.12766 | 0.266936 | ||||||||
\(370\) | −3.05604 | + | 2.76038i | −0.158876 | + | 0.143505i | ||||
\(371\) | −5.70084 | + | 9.41858i | −0.295973 | + | 0.488988i | ||||
\(372\) | 0.813573i | 0.0421818i | ||||||||
\(373\) | −24.8316 | −1.28573 | −0.642865 | − | 0.765979i | \(-0.722255\pi\) | ||||
−0.642865 | + | 0.765979i | \(0.722255\pi\) | |||||||
\(374\) | 0.00228839 | + | 1.27157i | 0.000118330 | + | 0.0657514i | ||||
\(375\) | −9.01400 | + | 6.61421i | −0.465481 | + | 0.341557i | ||||
\(376\) | 0.885266 | 0.0456541 | ||||||||
\(377\) | −37.7554 | −1.94450 | ||||||||
\(378\) | −0.495849 | − | 0.300126i | −0.0255037 | − | 0.0154368i | ||||
\(379\) | −14.0392 | −0.721146 | −0.360573 | − | 0.932731i | \(-0.617419\pi\) | ||||
−0.360573 | + | 0.932731i | \(0.617419\pi\) | |||||||
\(380\) | 11.6704 | + | 12.9204i | 0.598680 | + | 0.662804i | ||||
\(381\) | 16.2867 | 0.834393 | ||||||||
\(382\) | −4.11749 | −0.210669 | ||||||||
\(383\) | −3.60704 | −0.184311 | −0.0921556 | − | 0.995745i | \(-0.529376\pi\) | ||||
−0.0921556 | + | 0.995745i | \(0.529376\pi\) | |||||||
\(384\) | 6.59573 | 0.336587 | ||||||||
\(385\) | −3.74652 | − | 19.2604i | −0.190940 | − | 0.981602i | ||||
\(386\) | 0.396537 | 0.0201832 | ||||||||
\(387\) | −10.5926 | −0.538450 | ||||||||
\(388\) | −17.4066 | −0.883688 | ||||||||
\(389\) | 16.4302 | 0.833042 | 0.416521 | − | 0.909126i | \(-0.363249\pi\) | ||||
0.416521 | + | 0.909126i | \(0.363249\pi\) | |||||||
\(390\) | 1.73055 | − | 1.56313i | 0.0876298 | − | 0.0791519i | ||||
\(391\) | 9.32194 | 0.471431 | ||||||||
\(392\) | 2.81046 | + | 5.36930i | 0.141950 | + | 0.271191i | ||||
\(393\) | 20.6593 | 1.04212 | ||||||||
\(394\) | 3.11661 | 0.157013 | ||||||||
\(395\) | −8.29253 | + | 7.49027i | −0.417243 | + | 0.376876i | ||||
\(396\) | 6.47407 | − | 0.0116511i | 0.325334 | − | 0.000585489i | ||||
\(397\) | 22.2690 | 1.11765 | 0.558825 | − | 0.829285i | \(-0.311252\pi\) | ||||
0.558825 | + | 0.829285i | \(0.311252\pi\) | |||||||
\(398\) | − | 1.67619i | − | 0.0840200i | ||||||
\(399\) | −9.02857 | − | 5.46478i | −0.451994 | − | 0.273581i | ||||
\(400\) | −1.88321 | + | 18.4760i | −0.0941604 | + | 0.923802i | ||||
\(401\) | 15.4955 | 0.773808 | 0.386904 | − | 0.922120i | \(-0.373544\pi\) | ||||
0.386904 | + | 0.922120i | \(0.373544\pi\) | |||||||
\(402\) | − | 2.69234i | − | 0.134282i | ||||||
\(403\) | 1.98414 | 0.0988372 | ||||||||
\(404\) | −30.4074 | −1.51282 | ||||||||
\(405\) | 1.49883 | + | 1.65937i | 0.0744775 | + | 0.0824547i | ||||
\(406\) | 2.38026 | − | 3.93252i | 0.118130 | − | 0.195168i | ||||
\(407\) | 0.0501784 | + | 27.8823i | 0.00248725 | + | 1.38207i | ||||
\(408\) | 1.51518i | 0.0750124i | ||||||||
\(409\) | 27.9722 | 1.38314 | 0.691568 | − | 0.722311i | \(-0.256920\pi\) | ||||
0.691568 | + | 0.722311i | \(0.256920\pi\) | |||||||
\(410\) | −1.68366 | − | 1.86400i | −0.0831503 | − | 0.0920564i | ||||
\(411\) | − | 16.2074i | − | 0.799452i | ||||||
\(412\) | 2.39566 | 0.118026 | ||||||||
\(413\) | 2.02290 | − | 3.34211i | 0.0995404 | − | 0.164455i | ||||
\(414\) | 1.16688i | 0.0573492i | ||||||||
\(415\) | 7.92814 | − | 7.16112i | 0.389177 | − | 0.351526i | ||||
\(416\) | − | 12.1168i | − | 0.594073i | ||||||
\(417\) | −17.7663 | −0.870019 | ||||||||
\(418\) | −2.89822 | + | 0.00521579i | −0.141757 | + | 0.000255113i | ||||
\(419\) | 39.1953i | 1.91482i | 0.288740 | + | 0.957408i | \(0.406764\pi\) | ||||
−0.288740 | + | 0.957408i | \(0.593236\pi\) | |||||||
\(420\) | −2.18462 | − | 11.3397i | −0.106598 | − | 0.553322i | ||||
\(421\) | 2.18571 | 0.106525 | 0.0532625 | − | 0.998581i | \(-0.483038\pi\) | ||||
0.0532625 | + | 0.998581i | \(0.483038\pi\) | |||||||
\(422\) | − | 0.462431i | − | 0.0225108i | ||||||
\(423\) | 1.02252 | 0.0497167 | ||||||||
\(424\) | 3.60263i | 0.174959i | ||||||||
\(425\) | −8.70538 | − | 0.887314i | −0.422273 | − | 0.0430410i | ||||
\(426\) | 1.12679 | 0.0545931 | ||||||||
\(427\) | 16.0426 | + | 9.71022i | 0.776357 | + | 0.469910i | ||||
\(428\) | 4.92856 | 0.238231 | ||||||||
\(429\) | −0.0284147 | − | 15.7890i | −0.00137187 | − | 0.762298i | ||||
\(430\) | 3.47806 | + | 3.85059i | 0.167727 | + | 0.185692i | ||||
\(431\) | 12.4815i | 0.601214i | 0.953748 | + | 0.300607i | \(0.0971892\pi\) | ||||
−0.953748 | + | 0.300607i | \(0.902811\pi\) | |||||||
\(432\) | 3.71435 | 0.178707 | ||||||||
\(433\) | 39.1498 | 1.88142 | 0.940711 | − | 0.339210i | \(-0.110160\pi\) | ||||
0.940711 | + | 0.339210i | \(0.110160\pi\) | |||||||
\(434\) | −0.125089 | + | 0.206664i | −0.00600445 | + | 0.00992019i | ||||
\(435\) | −13.1602 | + | 11.8870i | −0.630985 | + | 0.569940i | ||||
\(436\) | − | 38.0334i | − | 1.82147i | ||||||
\(437\) | 21.2470i | 1.01638i | ||||||||
\(438\) | − | 3.22991i | − | 0.154331i | ||||||
\(439\) | −9.40386 | −0.448822 | −0.224411 | − | 0.974495i | \(-0.572046\pi\) | ||||
−0.224411 | + | 0.974495i | \(0.572046\pi\) | |||||||
\(440\) | −4.31235 | − | 4.75700i | −0.205583 | − | 0.226781i | ||||
\(441\) | 3.24621 | + | 6.20178i | 0.154581 | + | 0.295323i | ||||
\(442\) | 1.82517 | 0.0868144 | ||||||||
\(443\) | − | 25.4918i | − | 1.21115i | −0.795787 | − | 0.605576i | \(-0.792943\pi\) | ||
0.795787 | − | 0.605576i | \(-0.207057\pi\) | |||||||
\(444\) | 16.4102i | 0.778794i | ||||||||
\(445\) | 13.8985 | − | 12.5538i | 0.658850 | − | 0.595109i | ||||
\(446\) | −3.58633 | −0.169818 | ||||||||
\(447\) | − | 19.3124i | − | 0.913447i | ||||||
\(448\) | −15.5523 | − | 9.41342i | −0.734776 | − | 0.444742i | ||||
\(449\) | −16.8178 | −0.793680 | −0.396840 | − | 0.917888i | \(-0.629893\pi\) | ||||
−0.396840 | + | 0.917888i | \(0.629893\pi\) | |||||||
\(450\) | 0.111070 | − | 1.08970i | 0.00523591 | − | 0.0513692i | ||||
\(451\) | −17.0065 | + | 0.0306058i | −0.800805 | + | 0.00144117i | ||||
\(452\) | − | 5.86270i | − | 0.275758i | ||||||
\(453\) | − | 15.0336i | − | 0.706339i | ||||||
\(454\) | 2.14779i | 0.100801i | ||||||||
\(455\) | −27.6553 | + | 5.32785i | −1.29650 | + | 0.249773i | ||||
\(456\) | −3.45345 | −0.161723 | ||||||||
\(457\) | −7.02926 | −0.328815 | −0.164408 | − | 0.986392i | \(-0.552571\pi\) | ||||
−0.164408 | + | 0.986392i | \(0.552571\pi\) | |||||||
\(458\) | − | 1.76133i | − | 0.0823017i | ||||||
\(459\) | 1.75010i | 0.0816875i | ||||||||
\(460\) | −17.2532 | + | 15.5840i | −0.804433 | + | 0.726608i | ||||
\(461\) | 16.0285 | 0.746520 | 0.373260 | − | 0.927727i | \(-0.378240\pi\) | ||||
0.373260 | + | 0.927727i | \(0.378240\pi\) | |||||||
\(462\) | 1.64634 | + | 0.992443i | 0.0765945 | + | 0.0461726i | ||||
\(463\) | − | 24.3558i | − | 1.13191i | −0.824437 | − | 0.565954i | \(-0.808508\pi\) | ||
0.824437 | − | 0.565954i | \(-0.191492\pi\) | |||||||
\(464\) | 29.4580i | 1.36756i | ||||||||
\(465\) | 0.691605 | − | 0.624695i | 0.0320724 | − | 0.0289695i | ||||
\(466\) | 1.10053 | 0.0509811 | ||||||||
\(467\) | 33.4675 | 1.54869 | 0.774346 | − | 0.632762i | \(-0.218079\pi\) | ||||
0.774346 | + | 0.632762i | \(0.218079\pi\) | |||||||
\(468\) | − | 9.29265i | − | 0.429553i | ||||||
\(469\) | −16.8371 | + | 27.8172i | −0.777465 | + | 1.28448i | ||||
\(470\) | −0.335744 | − | 0.371705i | −0.0154867 | − | 0.0171455i | ||||
\(471\) | −9.76184 | −0.449802 | ||||||||
\(472\) | − | 1.27837i | − | 0.0588416i | ||||||
\(473\) | 35.1315 | − | 0.0632245i | 1.61535 | − | 0.00290707i | ||||
\(474\) | − | 1.09478i | − | 0.0502850i | ||||||
\(475\) | 2.02240 | − | 19.8417i | 0.0927942 | − | 0.910398i | ||||
\(476\) | 4.68019 | − | 7.73233i | 0.214516 | − | 0.354411i | ||||
\(477\) | 4.16120i | 0.190528i | ||||||||
\(478\) | − | 0.401778i | − | 0.0183769i | ||||||
\(479\) | 6.33570 | 0.289485 | 0.144743 | − | 0.989469i | \(-0.453765\pi\) | ||||
0.144743 | + | 0.989469i | \(0.453765\pi\) | |||||||
\(480\) | −3.81488 | − | 4.22349i | −0.174125 | − | 0.192775i | ||||
\(481\) | 40.0212 | 1.82481 | ||||||||
\(482\) | −3.60652 | −0.164273 | ||||||||
\(483\) | 7.29734 | − | 12.0562i | 0.332040 | − | 0.548577i | ||||
\(484\) | −21.4720 | + | 0.0772844i | −0.975998 | + | 0.00351293i | ||||
\(485\) | 13.3655 | + | 14.7971i | 0.606897 | + | 0.671901i | ||||
\(486\) | −0.219070 | −0.00993722 | ||||||||
\(487\) | − | 1.38135i | − | 0.0625949i | −0.999510 | − | 0.0312974i | \(-0.990036\pi\) | ||
0.999510 | − | 0.0312974i | \(-0.00996391\pi\) | |||||||
\(488\) | 6.13635 | 0.277779 | ||||||||
\(489\) | − | 2.65834i | − | 0.120214i | ||||||
\(490\) | 1.18857 | − | 3.21641i | 0.0536941 | − | 0.145302i | ||||
\(491\) | − | 26.5710i | − | 1.19913i | −0.800326 | − | 0.599565i | \(-0.795340\pi\) | ||
0.800326 | − | 0.599565i | \(-0.204660\pi\) | |||||||
\(492\) | −10.0092 | −0.451252 | ||||||||
\(493\) | −13.8798 | −0.625114 | ||||||||
\(494\) | 4.16000i | 0.187167i | ||||||||
\(495\) | −4.98096 | − | 5.49455i | −0.223877 | − | 0.246962i | ||||
\(496\) | − | 1.54810i | − | 0.0695116i | ||||||
\(497\) | −11.6419 | − | 7.04659i | −0.522213 | − | 0.316083i | ||||
\(498\) | 1.04667i | 0.0469026i | ||||||||
\(499\) | 21.9537 | 0.982781 | 0.491391 | − | 0.870939i | \(-0.336489\pi\) | ||||
0.491391 | + | 0.870939i | \(0.336489\pi\) | |||||||
\(500\) | 17.5954 | − | 12.9110i | 0.786890 | − | 0.577398i | ||||
\(501\) | − | 12.3713i | − | 0.552710i | ||||||
\(502\) | − | 6.40915i | − | 0.286054i | ||||||
\(503\) | 34.3973i | 1.53370i | 0.641827 | + | 0.766849i | \(0.278177\pi\) | ||||
−0.641827 | + | 0.766849i | \(0.721823\pi\) | |||||||
\(504\) | 1.95960 | + | 1.18610i | 0.0872876 | + | 0.0528331i | ||||
\(505\) | 23.3480 | + | 25.8488i | 1.03897 | + | 1.15026i | ||||
\(506\) | −0.00696486 | − | 3.87011i | −0.000309626 | − | 0.172047i | ||||
\(507\) | −9.66291 | −0.429145 | ||||||||
\(508\) | −31.7918 | −1.41053 | ||||||||
\(509\) | 23.1473i | 1.02598i | 0.858393 | + | 0.512992i | \(0.171463\pi\) | ||||
−0.858393 | + | 0.512992i | \(0.828537\pi\) | |||||||
\(510\) | 0.636192 | − | 0.574643i | 0.0281710 | − | 0.0254456i | ||||
\(511\) | −20.1989 | + | 33.3714i | −0.893546 | + | 1.47626i | ||||
\(512\) | −15.8854 | −0.702044 | ||||||||
\(513\) | −3.98889 | −0.176114 | ||||||||
\(514\) | −2.87390 | −0.126762 | ||||||||
\(515\) | −1.83949 | − | 2.03651i | −0.0810575 | − | 0.0897394i | ||||
\(516\) | 20.6768 | 0.910244 | ||||||||
\(517\) | −3.39132 | + | 0.00610320i | −0.149150 | + | 0.000268418i | ||||
\(518\) | −2.52311 | + | 4.16853i | −0.110859 | + | 0.183154i | ||||
\(519\) | − | 5.30683i | − | 0.232944i | ||||||
\(520\) | −6.83914 | + | 6.17749i | −0.299916 | + | 0.270901i | ||||
\(521\) | 31.3896i | 1.37520i | 0.726089 | + | 0.687601i | \(0.241336\pi\) | ||||
−0.726089 | + | 0.687601i | \(0.758664\pi\) | |||||||
\(522\) | − | 1.73742i | − | 0.0760447i | ||||||
\(523\) | 29.0877i | 1.27192i | 0.771723 | + | 0.635959i | \(0.219395\pi\) | ||||
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(524\) | −40.3271 | −1.76170 | ||||||||
\(525\) | −7.96226 | + | 10.5642i | −0.347502 | + | 0.461060i | ||||
\(526\) | 1.66117 | 0.0724307 | ||||||||
\(527\) | 0.729419 | 0.0317740 | ||||||||
\(528\) | −12.3191 | + | 0.0221701i | −0.536120 | + | 0.000964830i | ||||
\(529\) | −5.37194 | −0.233563 | ||||||||
\(530\) | 1.51267 | − | 1.36633i | 0.0657063 | − | 0.0593495i | ||||
\(531\) | − | 1.47657i | − | 0.0640778i | ||||||
\(532\) | 17.6238 | + | 10.6673i | 0.764090 | + | 0.462486i | ||||
\(533\) | 24.4105i | 1.05734i | ||||||||
\(534\) | 1.83488i | 0.0794029i | ||||||||
\(535\) | −3.78435 | − | 4.18969i | −0.163612 | − | 0.181136i | ||||
\(536\) | 10.6402i | 0.459585i | ||||||||
\(537\) | 6.03351 | 0.260365 | ||||||||
\(538\) | 5.38256i | 0.232059i | ||||||||
\(539\) | −10.8035 | − | 20.5496i | −0.465338 | − | 0.885133i | ||||
\(540\) | −2.92573 | − | 3.23910i | −0.125903 | − | 0.139389i | ||||
\(541\) | 32.1045i | 1.38028i | 0.723677 | + | 0.690139i | \(0.242451\pi\) | ||||
−0.723677 | + | 0.690139i | \(0.757549\pi\) | |||||||
\(542\) | 3.30634 | 0.142019 | ||||||||
\(543\) | − | 15.0417i | − | 0.645502i | ||||||
\(544\) | − | 4.45441i | − | 0.190981i | ||||||
\(545\) | −32.3316 | + | 29.2036i | −1.38493 | + | 1.25095i | ||||
\(546\) | 1.42877 | − | 2.36052i | 0.0611455 | − | 0.101021i | ||||
\(547\) | −34.3259 | −1.46767 | −0.733834 | − | 0.679329i | \(-0.762271\pi\) | ||||
−0.733834 | + | 0.679329i | \(0.762271\pi\) | |||||||
\(548\) | 31.6370i | 1.35146i | ||||||||
\(549\) | 7.08776 | 0.302498 | ||||||||
\(550\) | −0.361874 | + | 3.61480i | −0.0154304 | + | 0.154136i | ||||
\(551\) | − | 31.6354i | − | 1.34771i | ||||||
\(552\) | − | 4.61154i | − | 0.196280i | ||||||
\(553\) | −6.84643 | + | 11.3113i | −0.291140 | + | 0.481004i | ||||
\(554\) | 1.14728 | 0.0487435 | ||||||||
\(555\) | 13.9500 | − | 12.6004i | 0.592146 | − | 0.534858i | ||||
\(556\) | 34.6800 | 1.47076 | ||||||||
\(557\) | −8.73363 | −0.370056 | −0.185028 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185028 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(558\) | 0.0913058i | 0.00386528i | ||||||||
\(559\) | − | 50.4265i | − | 2.13281i | ||||||
\(560\) | 4.15697 | + | 21.5776i | 0.175664 | + | 0.911821i | ||||
\(561\) | −0.0104459 | − | 5.80440i | −0.000441027 | − | 0.245062i | ||||
\(562\) | 4.27540i | 0.180347i | ||||||||
\(563\) | − | 3.77704i | − | 0.159183i | −0.996828 | − | 0.0795917i | \(-0.974638\pi\) | ||
0.996828 | − | 0.0795917i | \(-0.0253617\pi\) | |||||||
\(564\) | −1.99597 | −0.0840456 | ||||||||
\(565\) | −4.98378 | + | 4.50162i | −0.209669 | + | 0.189384i | ||||
\(566\) | 3.07596i | 0.129292i | ||||||||
\(567\) | 2.26343 | + | 1.37000i | 0.0950550 | + | 0.0575345i | ||||
\(568\) | −4.45308 | −0.186847 | ||||||||
\(569\) | 33.3725i | 1.39905i | 0.714608 | + | 0.699525i | \(0.246605\pi\) | ||||
−0.714608 | + | 0.699525i | \(0.753395\pi\) | |||||||
\(570\) | 1.30975 | + | 1.45003i | 0.0548594 | + | 0.0607353i | ||||
\(571\) | 20.4207i | 0.854579i | 0.904115 | + | 0.427289i | \(0.140531\pi\) | ||||
−0.904115 | + | 0.427289i | \(0.859469\pi\) | |||||||
\(572\) | 0.0554656 | + | 30.8202i | 0.00231914 | + | 1.28866i | ||||
\(573\) | 18.7953 | 0.785186 | ||||||||
\(574\) | −2.54255 | − | 1.53894i | −0.106124 | − | 0.0642343i | ||||
\(575\) | 26.4954 | + | 2.70060i | 1.10493 | + | 0.112623i | ||||
\(576\) | −6.87112 | −0.286297 | ||||||||
\(577\) | −28.1851 | −1.17336 | −0.586680 | − | 0.809819i | \(-0.699565\pi\) | ||||
−0.586680 | + | 0.809819i | \(0.699565\pi\) | |||||||
\(578\) | −3.05322 | −0.126997 | ||||||||
\(579\) | −1.81009 | −0.0752249 | ||||||||
\(580\) | 25.6889 | − | 23.2036i | 1.06667 | − | 0.963477i | ||||
\(581\) | 6.54558 | − | 10.8142i | 0.271557 | − | 0.448649i | ||||
\(582\) | −1.95351 | −0.0809757 | ||||||||
\(583\) | −0.0248372 | − | 13.8011i | −0.00102865 | − | 0.571584i | ||||
\(584\) | 12.7646i | 0.528204i | ||||||||
\(585\) | −7.89952 | + | 7.13527i | −0.326605 | + | 0.295007i | ||||
\(586\) | 3.48347i | 0.143901i | ||||||||
\(587\) | −46.9856 | −1.93930 | −0.969651 | − | 0.244492i | \(-0.921379\pi\) | ||||
−0.969651 | + | 0.244492i | \(0.921379\pi\) | |||||||
\(588\) | −6.33663 | − | 12.1059i | −0.261318 | − | 0.499240i | ||||
\(589\) | 1.66252i | 0.0685030i | ||||||||
\(590\) | −0.536761 | + | 0.484831i | −0.0220981 | + | 0.0199602i | ||||
\(591\) | −14.2265 | −0.585201 | ||||||||
\(592\) | − | 31.2260i | − | 1.28338i | ||||||
\(593\) | 9.05085i | 0.371674i | 0.982581 | + | 0.185837i | \(0.0594996\pi\) | ||||
−0.982581 | + | 0.185837i | \(0.940500\pi\) | |||||||
\(594\) | 0.726572 | − | 0.00130758i | 0.0298116 | − | 5.36506e-5i | ||||
\(595\) | −10.1668 | + | 1.95865i | −0.416797 | + | 0.0802966i | ||||
\(596\) | 37.6980i | 1.54417i | ||||||||
\(597\) | 7.65140i | 0.313151i | ||||||||
\(598\) | −5.55502 | −0.227162 | ||||||||
\(599\) | 30.1385 | 1.23143 | 0.615713 | − | 0.787971i | \(-0.288868\pi\) | ||||
0.615713 | + | 0.787971i | \(0.288868\pi\) | |||||||
\(600\) | −0.438951 | + | 4.30652i | −0.0179201 | + | 0.175813i | ||||
\(601\) | 4.88298 | 0.199181 | 0.0995905 | − | 0.995029i | \(-0.468247\pi\) | ||||
0.0995905 | + | 0.995029i | \(0.468247\pi\) | |||||||
\(602\) | 5.25232 | + | 3.17910i | 0.214068 | + | 0.129570i | ||||
\(603\) | 12.2899i | 0.500482i | ||||||||
\(604\) | 29.3457i | 1.19406i | ||||||||
\(605\) | 16.5527 | + | 18.1936i | 0.672964 | + | 0.739675i | ||||
\(606\) | −3.41256 | −0.138626 | ||||||||
\(607\) | 0.685604i | 0.0278278i | 0.999903 | + | 0.0139139i | \(0.00442908\pi\) | ||||
−0.999903 | + | 0.0139139i | \(0.995571\pi\) | |||||||
\(608\) | 10.1527 | 0.411746 | ||||||||
\(609\) | −10.8653 | + | 17.9510i | −0.440283 | + | 0.727409i | ||||
\(610\) | −2.32726 | − | 2.57653i | −0.0942280 | − | 0.104321i | ||||
\(611\) | 4.86778i | 0.196929i | ||||||||
\(612\) | − | 3.41620i | − | 0.138092i | ||||||
\(613\) | −32.2070 | −1.30083 | −0.650414 | − | 0.759580i | \(-0.725404\pi\) | ||||
−0.650414 | + | 0.759580i | \(0.725404\pi\) | |||||||
\(614\) | − | 3.36151i | − | 0.135659i | ||||||
\(615\) | 7.68550 | + | 8.50869i | 0.309909 | + | 0.343103i | ||||
\(616\) | −6.50633 | − | 3.92214i | −0.262148 | − | 0.158028i | ||||
\(617\) | − | 28.7997i | − | 1.15943i | −0.814819 | − | 0.579716i | \(-0.803163\pi\) | ||
0.814819 | − | 0.579716i | \(-0.196837\pi\) | |||||||
\(618\) | 0.268861 | 0.0108152 | ||||||||
\(619\) | − | 18.4418i | − | 0.741239i | −0.928785 | − | 0.370619i | \(-0.879145\pi\) | ||
0.928785 | − | 0.370619i | \(-0.120855\pi\) | |||||||
\(620\) | −1.35002 | + | 1.21941i | −0.0542180 | + | 0.0489727i | ||||
\(621\) | − | 5.32653i | − | 0.213746i | ||||||
\(622\) | 6.55435i | 0.262805i | ||||||||
\(623\) | 11.4748 | − | 18.9579i | 0.459727 | − | 0.759533i | ||||
\(624\) | 17.6824i | 0.707862i | ||||||||
\(625\) | −24.4859 | − | 5.04395i | −0.979435 | − | 0.201758i | ||||
\(626\) | 2.80774 | 0.112220 | ||||||||
\(627\) | 13.2296 | − | 0.0238088i | 0.528341 | − | 0.000950831i | ||||
\(628\) | 19.0552 | 0.760385 | ||||||||
\(629\) | 14.7128 | 0.586637 | ||||||||
\(630\) | −0.245176 | − | 1.27263i | −0.00976803 | − | 0.0507030i | ||||
\(631\) | 21.1920 | 0.843641 | 0.421821 | − | 0.906679i | \(-0.361391\pi\) | ||||
0.421821 | + | 0.906679i | \(0.361391\pi\) | |||||||
\(632\) | 4.32659i | 0.172102i | ||||||||
\(633\) | 2.11088i | 0.0839000i | ||||||||
\(634\) | 0.0204996i | 0.000814141i | ||||||||
\(635\) | 24.4110 | + | 27.0257i | 0.968722 | + | 1.07248i | ||||
\(636\) | − | 8.12270i | − | 0.322086i | ||||||
\(637\) | −29.5240 | + | 15.4538i | −1.16978 | + | 0.612301i | ||||
\(638\) | 0.0103702 | + | 5.76235i | 0.000410562 | + | 0.228134i | ||||
\(639\) | −5.14350 | −0.203474 | ||||||||
\(640\) | 9.88589 | + | 10.9448i | 0.390774 | + | 0.432629i | ||||
\(641\) | −25.4119 | −1.00371 | −0.501855 | − | 0.864952i | \(-0.667349\pi\) | ||||
−0.501855 | + | 0.864952i | \(0.667349\pi\) | |||||||
\(642\) | 0.553123 | 0.0218300 | ||||||||
\(643\) | 12.1435 | 0.478893 | 0.239447 | − | 0.970910i | \(-0.423034\pi\) | ||||
0.239447 | + | 0.970910i | \(0.423034\pi\) | |||||||
\(644\) | −14.2445 | + | 23.5338i | −0.561311 | + | 0.927363i | ||||
\(645\) | −15.8765 | − | 17.5770i | −0.625135 | − | 0.692093i | ||||
\(646\) | 1.52932i | 0.0601702i | ||||||||
\(647\) | −13.9580 | −0.548745 | −0.274373 | − | 0.961623i | \(-0.588470\pi\) | ||||
−0.274373 | + | 0.961623i | \(0.588470\pi\) | |||||||
\(648\) | 0.865767 | 0.0340105 | ||||||||
\(649\) | 0.00881331 | + | 4.89723i | 0.000345953 | + | 0.192233i | ||||
\(650\) | 5.18760 | + | 0.528757i | 0.203475 | + | 0.0207396i | ||||
\(651\) | 0.570999 | − | 0.943369i | 0.0223792 | − | 0.0369736i | ||||
\(652\) | 5.18909i | 0.203221i | ||||||||
\(653\) | − | 25.7898i | − | 1.00923i | −0.863344 | − | 0.504616i | \(-0.831634\pi\) | ||
0.863344 | − | 0.504616i | \(-0.168366\pi\) | |||||||
\(654\) | − | 4.26842i | − | 0.166908i | ||||||
\(655\) | 30.9648 | + | 34.2814i | 1.20990 | + | 1.33948i | ||||
\(656\) | 19.0460 | 0.743620 | ||||||||
\(657\) | 14.7437i | 0.575208i | ||||||||
\(658\) | −0.507017 | − | 0.306885i | −0.0197656 | − | 0.0119636i | ||||
\(659\) | − | 5.42636i | − | 0.211381i | −0.994399 | − | 0.105690i | \(-0.966295\pi\) | ||
0.994399 | − | 0.105690i | \(-0.0337053\pi\) | |||||||
\(660\) | 9.72287 | + | 10.7254i | 0.378462 | + | 0.417486i | ||||
\(661\) | 36.7560i | 1.42964i | 0.699307 | + | 0.714821i | \(0.253492\pi\) | ||||
−0.699307 | + | 0.714821i | \(0.746508\pi\) | |||||||
\(662\) | −0.569883 | −0.0221491 | ||||||||
\(663\) | −8.33143 | −0.323566 | ||||||||
\(664\) | − | 4.13647i | − | 0.160526i | ||||||
\(665\) | −4.46423 | − | 23.1725i | −0.173115 | − | 0.898591i | ||||
\(666\) | 1.84169i | 0.0713639i | ||||||||
\(667\) | 42.2440 | 1.63570 | ||||||||
\(668\) | 24.1489i | 0.934350i | ||||||||
\(669\) | 16.3707 | 0.632928 | ||||||||
\(670\) | 4.46759 | − | 4.03537i | 0.172598 | − | 0.155900i | ||||
\(671\) | −23.5074 | + | 0.0423052i | −0.907493 | + | 0.00163317i | ||||
\(672\) | −5.76096 | − | 3.48697i | −0.222234 | − | 0.134513i | ||||
\(673\) | −33.7245 | −1.29998 | −0.649991 | − | 0.759942i | \(-0.725228\pi\) | ||||
−0.649991 | + | 0.759942i | \(0.725228\pi\) | |||||||
\(674\) | −2.11175 | −0.0813414 | ||||||||
\(675\) | −0.507009 | + | 4.97423i | −0.0195148 | + | 0.191458i | ||||
\(676\) | 18.8621 | 0.725465 | ||||||||
\(677\) | 22.1771i | 0.852334i | 0.904644 | + | 0.426167i | \(0.140136\pi\) | ||||
−0.904644 | + | 0.426167i | \(0.859864\pi\) | |||||||
\(678\) | − | 0.657959i | − | 0.0252688i | ||||||
\(679\) | 20.1837 | + | 12.2167i | 0.774577 | + | 0.468833i | ||||
\(680\) | −2.51424 | + | 2.27099i | −0.0964165 | + | 0.0870886i | ||||
\(681\) | − | 9.80413i | − | 0.375695i | ||||||
\(682\) | −0.000544983 | − | 0.302827i | −2.08685e−5 | − | 0.0115958i | ||||
\(683\) | − | 5.37195i | − | 0.205552i | −0.994705 | − | 0.102776i | \(-0.967228\pi\) | ||
0.994705 | − | 0.102776i | \(-0.0327725\pi\) | |||||||
\(684\) | 7.78635 | 0.297719 | ||||||||
\(685\) | 26.8940 | − | 24.2921i | 1.02757 | − | 0.928155i | ||||
\(686\) | 0.251683 | − | 4.04942i | 0.00960932 | − | 0.154608i | ||||
\(687\) | 8.04004i | 0.306747i | ||||||||
\(688\) | −39.3445 | −1.50000 | ||||||||
\(689\) | −19.8096 | −0.754687 | ||||||||
\(690\) | −1.93629 | + | 1.74896i | −0.0737133 | + | 0.0665819i | ||||
\(691\) | 14.5410i | 0.553167i | 0.960990 | + | 0.276584i | \(0.0892023\pi\) | ||||
−0.960990 | + | 0.276584i | \(0.910798\pi\) | |||||||
\(692\) | 10.3590i | 0.393789i | ||||||||
\(693\) | −7.51511 | − | 4.53025i | −0.285475 | − | 0.172090i | ||||
\(694\) | −1.02719 | −0.0389914 | ||||||||
\(695\) | −26.6287 | − | 29.4808i | −1.01008 | − | 1.11827i | ||||
\(696\) | 6.86629i | 0.260266i | ||||||||
\(697\) | 8.97391i | 0.339911i | ||||||||
\(698\) | −4.97317 | −0.188237 | ||||||||
\(699\) | −5.02365 | −0.190012 | ||||||||
\(700\) | 15.5424 | − | 20.6214i | 0.587447 | − | 0.779416i | ||||
\(701\) | 22.9952i | 0.868517i | 0.900788 | + | 0.434258i | \(0.142990\pi\) | ||||
−0.900788 | + | 0.434258i | \(0.857010\pi\) | |||||||
\(702\) | − | 1.04290i | − | 0.0393616i | ||||||
\(703\) | 33.5340i | 1.26476i | ||||||||
\(704\) | 22.7889 | − | 0.0410121i | 0.858889 | − | 0.00154570i | ||||
\(705\) | 1.53259 | + | 1.69674i | 0.0577206 | + | 0.0639030i | ||||
\(706\) | −2.73887 | −0.103079 | ||||||||
\(707\) | 35.2585 | + | 21.3411i | 1.32603 | + | 0.802615i | ||||
\(708\) | 2.88228i | 0.108323i | ||||||||
\(709\) | 11.8461 | 0.444890 | 0.222445 | − | 0.974945i | \(-0.428596\pi\) | ||||
0.222445 | + | 0.974945i | \(0.428596\pi\) | |||||||
\(710\) | 1.68887 | + | 1.86976i | 0.0633820 | + | 0.0701707i | ||||
\(711\) | 4.99740i | 0.187417i | ||||||||
\(712\) | − | 7.25145i | − | 0.271760i | ||||||
\(713\) | −2.22003 | −0.0831409 | ||||||||
\(714\) | 0.525249 | − | 0.867784i | 0.0196569 | − | 0.0324760i | ||||
\(715\) | 26.1571 | − | 23.7121i | 0.978221 | − | 0.886784i | ||||
\(716\) | −11.7775 | −0.440145 | ||||||||
\(717\) | 1.83401i | 0.0684925i | ||||||||
\(718\) | 3.88597i | 0.145023i | ||||||||
\(719\) | − | 27.9271i | − | 1.04151i | −0.853708 | − | 0.520753i | \(-0.825651\pi\) | ||
0.853708 | − | 0.520753i | \(-0.174349\pi\) | |||||||
\(720\) | 5.56719 | + | 6.16348i | 0.207477 | + | 0.229699i | ||||
\(721\) | −2.77786 | − | 1.68137i | −0.103453 | − | 0.0626176i | ||||
\(722\) | 0.676651 | 0.0251823 | ||||||||
\(723\) | 16.4629 | 0.612260 | ||||||||
\(724\) | 29.3616i | 1.09121i | ||||||||
\(725\) | −39.4500 | − | 4.02102i | −1.46513 | − | 0.149337i | ||||
\(726\) | −2.40976 | + | 0.00867348i | −0.0894344 | + | 0.000321903i | ||||
\(727\) | −38.8892 | −1.44232 | −0.721161 | − | 0.692767i | \(-0.756391\pi\) | ||||
−0.721161 | + | 0.692767i | \(0.756391\pi\) | |||||||
\(728\) | −5.64649 | + | 9.32879i | −0.209273 | + | 0.345748i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.35961 | − | 4.84109i | 0.198368 | − | 0.179177i | ||||
\(731\) | − | 18.5380i | − | 0.685653i | ||||||
\(732\) | −13.8354 | −0.511370 | ||||||||
\(733\) | 12.2498i | 0.452458i | 0.974074 | + | 0.226229i | \(0.0726398\pi\) | ||||
−0.974074 | + | 0.226229i | \(0.927360\pi\) | |||||||
\(734\) | 1.73749 | 0.0641320 | ||||||||
\(735\) | −5.42552 | + | 14.6821i | −0.200123 | + | 0.541557i | ||||
\(736\) | 13.5573i | 0.499728i | ||||||||
\(737\) | −0.0733554 | − | 40.7608i | −0.00270208 | − | 1.50144i | ||||
\(738\) | −1.12332 | −0.0413499 | ||||||||
\(739\) | − | 12.3392i | − | 0.453903i | −0.973906 | − | 0.226952i | \(-0.927124\pi\) | ||
0.973906 | − | 0.226952i | \(-0.0728759\pi\) | |||||||
\(740\) | −27.2306 | + | 24.5961i | −1.00102 | + | 0.904172i | ||||
\(741\) | − | 18.9894i | − | 0.697591i | ||||||
\(742\) | 1.24888 | − | 2.06333i | 0.0458480 | − | 0.0757472i | ||||
\(743\) | 37.7653 | 1.38547 | 0.692737 | − | 0.721191i | \(-0.256405\pi\) | ||||
0.692737 | + | 0.721191i | \(0.256405\pi\) | |||||||
\(744\) | − | 0.360841i | − | 0.0132291i | ||||||
\(745\) | 32.0464 | − | 28.9461i | 1.17409 | − | 1.06050i | ||||
\(746\) | 5.43986 | 0.199167 | ||||||||
\(747\) | − | 4.77780i | − | 0.174811i | ||||||
\(748\) | 0.0203905 | + | 11.3302i | 0.000745551 | + | 0.414275i | ||||
\(749\) | −5.71486 | − | 3.45906i | −0.208816 | − | 0.126391i | ||||
\(750\) | 1.97470 | − | 1.44898i | 0.0721058 | − | 0.0529092i | ||||
\(751\) | 10.2252 | 0.373124 | 0.186562 | − | 0.982443i | \(-0.440266\pi\) | ||||
0.186562 | + | 0.982443i | \(0.440266\pi\) | |||||||
\(752\) | 3.79801 | 0.138499 | ||||||||
\(753\) | 29.2562i | 1.06615i | ||||||||
\(754\) | 8.27107 | 0.301215 | ||||||||
\(755\) | 24.9462 | − | 22.5328i | 0.907887 | − | 0.820052i | ||||
\(756\) | −4.41823 | − | 2.67425i | −0.160689 | − | 0.0972615i | ||||
\(757\) | 0.670498i | 0.0243696i | 0.999926 | + | 0.0121848i | \(0.00387865\pi\) | ||||
−0.999926 | + | 0.0121848i | \(0.996121\pi\) | |||||||
\(758\) | 3.07557 | 0.111710 | ||||||||
\(759\) | 0.0317928 | + | 17.6661i | 0.00115401 | + | 0.641238i | ||||
\(760\) | −5.17614 | − | 5.73055i | −0.187758 | − | 0.207869i | ||||
\(761\) | −46.2002 | −1.67476 | −0.837378 | − | 0.546624i | \(-0.815913\pi\) | ||||
−0.837378 | + | 0.546624i | \(0.815913\pi\) | |||||||
\(762\) | −3.56793 | −0.129253 | ||||||||
\(763\) | −26.6934 | + | 44.1012i | −0.966366 | + | 1.59657i | ||||
\(764\) | −36.6886 | −1.32735 | ||||||||
\(765\) | −2.90405 | + | 2.62310i | −0.104996 | + | 0.0948384i | ||||
\(766\) | 0.790195 | 0.0285509 | ||||||||
\(767\) | 7.02931 | 0.253814 | ||||||||
\(768\) | 12.2973 | 0.443741 | ||||||||
\(769\) | −0.657059 | −0.0236942 | −0.0118471 | − | 0.999930i | \(-0.503771\pi\) | ||||
−0.0118471 | + | 0.999930i | \(0.503771\pi\) | |||||||
\(770\) | 0.820750 | + | 4.21938i | 0.0295778 | + | 0.152056i | ||||
\(771\) | 13.1186 | 0.472455 | ||||||||
\(772\) | 3.53332 | 0.127167 | ||||||||
\(773\) | −2.59489 | −0.0933316 | −0.0466658 | − | 0.998911i | \(-0.514860\pi\) | ||||
−0.0466658 | + | 0.998911i | \(0.514860\pi\) | |||||||
\(774\) | 2.32051 | 0.0834092 | ||||||||
\(775\) | 2.07320 | + | 0.211315i | 0.0744715 | + | 0.00759066i | ||||
\(776\) | 7.72030 | 0.277143 | ||||||||
\(777\) | 11.5174 | − | 19.0283i | 0.413183 | − | 0.682635i | ||||
\(778\) | −3.59936 | −0.129043 | ||||||||
\(779\) | −20.4537 | −0.732830 | ||||||||
\(780\) | 15.4199 | − | 13.9281i | 0.552122 | − | 0.498706i | ||||
\(781\) | 17.0590 | − | 0.0307004i | 0.610421 | − | 0.00109855i | ||||
\(782\) | −2.04216 | −0.0730275 | ||||||||
\(783\) | 7.93087i | 0.283426i | ||||||||
\(784\) | 12.0576 | + | 23.0356i | 0.430627 | + | 0.822700i | ||||
\(785\) | −14.6314 | − | 16.1985i | −0.522216 | − | 0.578149i | ||||
\(786\) | −4.52584 | −0.161431 | ||||||||
\(787\) | − | 29.5992i | − | 1.05510i | −0.849525 | − | 0.527549i | \(-0.823111\pi\) | ||
0.849525 | − | 0.527549i | \(-0.176889\pi\) | |||||||
\(788\) | 27.7703 | 0.989277 | ||||||||
\(789\) | −7.58284 | −0.269956 | ||||||||
\(790\) | 1.81665 | − | 1.64089i | 0.0646334 | − | 0.0583804i | ||||
\(791\) | −4.11468 | + | 6.79802i | −0.146301 | + | 0.241710i | ||||
\(792\) | −2.87142 | + | 0.00516756i | −0.102031 | + | 0.000183621i | ||||
\(793\) | 33.7417i | 1.19820i | ||||||||
\(794\) | −4.87848 | −0.173131 | ||||||||
\(795\) | −6.90497 | + | 6.23694i | −0.244894 | + | 0.221201i | ||||
\(796\) | − | 14.9356i | − | 0.529378i | ||||||
\(797\) | −18.3391 | −0.649603 | −0.324801 | − | 0.945782i | \(-0.605297\pi\) | ||||
−0.324801 | + | 0.945782i | \(0.605297\pi\) | |||||||
\(798\) | 1.97789 | + | 1.19717i | 0.0700165 | + | 0.0423793i | ||||
\(799\) | 1.78951i | 0.0633084i | ||||||||
\(800\) | 1.29046 | − | 12.6606i | 0.0456246 | − | 0.447620i | ||||
\(801\) | − | 8.37576i | − | 0.295943i | ||||||
\(802\) | −3.39460 | −0.119868 | ||||||||
\(803\) | −0.0880019 | − | 48.8993i | −0.00310552 | − | 1.72562i | ||||
\(804\) | − | 23.9899i | − | 0.846060i | ||||||
\(805\) | 30.9432 | − | 5.96127i | 1.09060 | − | 0.210107i | ||||
\(806\) | −0.434666 | −0.0153105 | ||||||||
\(807\) | − | 24.5700i | − | 0.864906i | ||||||
\(808\) | 13.4865 | 0.474452 | ||||||||
\(809\) | − | 19.7647i | − | 0.694890i | −0.937700 | − | 0.347445i | \(-0.887049\pi\) | ||
0.937700 | − | 0.347445i | \(-0.112951\pi\) | |||||||
\(810\) | −0.328349 | − | 0.363518i | −0.0115370 | − | 0.0127727i | ||||
\(811\) | −20.7871 | −0.729935 | −0.364967 | − | 0.931020i | \(-0.618920\pi\) | ||||
−0.364967 | + | 0.931020i | \(0.618920\pi\) | |||||||
\(812\) | 21.2091 | − | 35.0404i | 0.744294 | − | 1.22968i | ||||
\(813\) | −15.0926 | −0.529320 | ||||||||
\(814\) | −0.0109926 | − | 6.10817i | −0.000385290 | − | 0.214091i | ||||
\(815\) | 4.41116 | − | 3.98440i | 0.154516 | − | 0.139567i | ||||
\(816\) | 6.50048i | 0.227562i | ||||||||
\(817\) | 42.2526 | 1.47823 | ||||||||
\(818\) | −6.12787 | −0.214256 | ||||||||
\(819\) | −6.52196 | + | 10.7752i | −0.227896 | + | 0.376515i | ||||
\(820\) | −15.0022 | − | 16.6090i | −0.523898 | − | 0.580012i | ||||
\(821\) | 4.20073i | 0.146607i | 0.997310 | + | 0.0733033i | \(0.0233541\pi\) | ||||
−0.997310 | + | 0.0733033i | \(0.976646\pi\) | |||||||
\(822\) | 3.55056i | 0.123840i | ||||||||
\(823\) | 0.993153i | 0.0346191i | 0.999850 | + | 0.0173096i | \(0.00551008\pi\) | ||||
−0.999850 | + | 0.0173096i | \(0.994490\pi\) | |||||||
\(824\) | −1.06254 | −0.0370153 | ||||||||
\(825\) | 1.65186 | − | 16.5006i | 0.0575105 | − | 0.574479i | ||||
\(826\) | −0.443157 | + | 0.732157i | −0.0154194 | + | 0.0254750i | ||||
\(827\) | 45.7635 | 1.59135 | 0.795676 | − | 0.605722i | \(-0.207116\pi\) | ||||
0.795676 | + | 0.605722i | \(0.207116\pi\) | |||||||
\(828\) | 10.3974i | 0.361336i | ||||||||
\(829\) | 12.6023i | 0.437697i | 0.975759 | + | 0.218848i | \(0.0702300\pi\) | ||||
−0.975759 | + | 0.218848i | \(0.929770\pi\) | |||||||
\(830\) | −1.73682 | + | 1.56879i | −0.0602858 | + | 0.0544534i | ||||
\(831\) | −5.23707 | −0.181672 | ||||||||
\(832\) | − | 32.7104i | − | 1.13403i | ||||||
\(833\) | −10.8537 | + | 5.68118i | −0.376059 | + | 0.196841i | ||||
\(834\) | 3.89207 | 0.134771 | ||||||||
\(835\) | 20.5286 | − | 18.5425i | 0.710421 | − | 0.641690i | ||||
\(836\) | −25.8244 | + | 0.0464749i | −0.893154 | + | 0.00160737i | ||||
\(837\) | − | 0.416788i | − | 0.0144063i | ||||||
\(838\) | − | 8.58652i | − | 0.296616i | ||||||
\(839\) | 42.7111i | 1.47455i | 0.675592 | + | 0.737276i | \(0.263888\pi\) | ||||
−0.675592 | + | 0.737276i | \(0.736112\pi\) | |||||||
\(840\) | 0.968936 | + | 5.02946i | 0.0334315 | + | 0.173533i | ||||
\(841\) | −33.8987 | −1.16892 | ||||||||
\(842\) | −0.478824 | −0.0165014 | ||||||||
\(843\) | − | 19.5161i | − | 0.672171i | ||||||
\(844\) | − | 4.12046i | − | 0.141832i | ||||||
\(845\) | −14.4831 | − | 16.0343i | −0.498233 | − | 0.551598i | ||||
\(846\) | −0.224004 | −0.00770142 | ||||||||
\(847\) | 24.9518 | + | 14.9803i | 0.857353 | + | 0.514728i | ||||
\(848\) | 15.4562i | 0.530767i | ||||||||
\(849\) | − | 14.0410i | − | 0.481885i | ||||||
\(850\) | 1.90709 | + | 0.194384i | 0.0654126 | + | 0.00666732i | ||||
\(851\) | −44.7793 | −1.53501 | ||||||||
\(852\) | 10.0402 | 0.343970 | ||||||||
\(853\) | − | 33.1450i | − | 1.13486i | −0.823421 | − | 0.567431i | \(-0.807937\pi\) | ||
0.823421 | − | 0.567431i | \(-0.192063\pi\) | |||||||
\(854\) | −3.51446 | − | 2.12722i | −0.120262 | − | 0.0727919i | ||||
\(855\) | −5.97868 | − | 6.61904i | −0.204466 | − | 0.226366i | ||||
\(856\) | −2.18595 | −0.0747141 | ||||||||
\(857\) | − | 13.9133i | − | 0.475268i | −0.971355 | − | 0.237634i | \(-0.923628\pi\) | ||
0.971355 | − | 0.237634i | \(-0.0763718\pi\) | |||||||
\(858\) | 0.00622480 | + | 3.45889i | 0.000212511 | + | 0.118085i | ||||
\(859\) | − | 54.9993i | − | 1.87655i | −0.345886 | − | 0.938277i | \(-0.612422\pi\) | ||
0.345886 | − | 0.938277i | \(-0.387578\pi\) | |||||||
\(860\) | 30.9910 | + | 34.3104i | 1.05678 | + | 1.16997i | ||||
\(861\) | 11.6061 | + | 7.02489i | 0.395535 | + | 0.239408i | ||||
\(862\) | − | 2.73433i | − | 0.0931316i | ||||||
\(863\) | − | 0.856611i | − | 0.0291594i | −0.999894 | − | 0.0145797i | \(-0.995359\pi\) | ||
0.999894 | − | 0.0145797i | \(-0.00464102\pi\) | |||||||
\(864\) | −2.54524 | −0.0865908 | ||||||||
\(865\) | 8.80598 | − | 7.95404i | 0.299412 | − | 0.270445i | ||||
\(866\) | −8.57656 | −0.291443 | ||||||||
\(867\) | 13.9372 | 0.473331 | ||||||||
\(868\) | −1.11459 | + | 1.84146i | −0.0378318 | + | 0.0625034i | ||||
\(869\) | −0.0298283 | − | 16.5745i | −0.00101186 | − | 0.562251i | ||||
\(870\) | 2.88302 | − | 2.60410i | 0.0977434 | − | 0.0882871i | ||||
\(871\) | −58.5067 | −1.98242 | ||||||||
\(872\) | 16.8688i | 0.571251i | ||||||||
\(873\) | 8.91729 | 0.301805 | ||||||||
\(874\) | − | 4.65458i | − | 0.157443i | ||||||
\(875\) | −29.4640 | + | 2.62164i | −0.996065 | + | 0.0886275i | ||||
\(876\) | − | 28.7799i | − | 0.972382i | ||||||
\(877\) | −44.0077 | −1.48603 | −0.743017 | − | 0.669272i | \(-0.766606\pi\) | ||||
−0.743017 | + | 0.669272i | \(0.766606\pi\) | |||||||
\(878\) | 2.06010 | 0.0695252 | ||||||||
\(879\) | − | 15.9012i | − | 0.536333i | ||||||
\(880\) | −18.5010 | − | 20.4087i | −0.623670 | − | 0.687977i | ||||
\(881\) | 3.83174i | 0.129094i | 0.997915 | + | 0.0645472i | \(0.0205603\pi\) | ||||
−0.997915 | + | 0.0645472i | \(0.979440\pi\) | |||||||
\(882\) | −0.711148 | − | 1.35863i | −0.0239456 | − | 0.0457473i | ||||
\(883\) | − | 45.6823i | − | 1.53733i | −0.639651 | − | 0.768665i | \(-0.720921\pi\) | ||
0.639651 | − | 0.768665i | \(-0.279079\pi\) | |||||||
\(884\) | 16.2630 | 0.546985 | ||||||||
\(885\) | 2.45018 | − | 2.21313i | 0.0823618 | − | 0.0743936i | ||||
\(886\) | 5.58450i | 0.187615i | ||||||||
\(887\) | − | 40.4637i | − | 1.35864i | −0.733844 | − | 0.679319i | \(-0.762275\pi\) | ||
0.733844 | − | 0.679319i | \(-0.237725\pi\) | |||||||
\(888\) | − | 7.27836i | − | 0.244246i | ||||||
\(889\) | 36.8638 | + | 22.3128i | 1.23637 | + | 0.748346i | ||||
\(890\) | −3.04474 | + | 2.75017i | −0.102060 | + | 0.0921860i | ||||
\(891\) | −3.31662 | + | 0.00596877i | −0.111111 | + | 0.000199961i | ||||
\(892\) | −31.9557 | −1.06996 | ||||||||
\(893\) | −4.07873 | −0.136490 | ||||||||
\(894\) | 4.23078i | 0.141498i | ||||||||
\(895\) | 9.04322 | + | 10.0118i | 0.302281 | + | 0.334658i | ||||
\(896\) | 14.9290 | + | 9.03614i | 0.498742 | + | 0.301876i | ||||
\(897\) | 25.3573 | 0.846654 | ||||||||
\(898\) | 3.68427 | 0.122946 | ||||||||
\(899\) | 3.30549 | 0.110244 | ||||||||
\(900\) | 0.989685 | − | 9.70973i | 0.0329895 | − | 0.323658i | ||||
\(901\) | −7.28250 | −0.242615 | ||||||||
\(902\) | 3.72562 | − | 0.00670482i | 0.124050 | − | 0.000223246i | ||||
\(903\) | −23.9755 | − | 14.5118i | −0.797855 | − | 0.482922i | ||||
\(904\) | 2.60026i | 0.0864834i | ||||||||
\(905\) | 24.9598 | − | 22.5450i | 0.829691 | − | 0.749422i | ||||
\(906\) | 3.29341i | 0.109416i | ||||||||
\(907\) | 15.3807i | 0.510708i | 0.966848 | + | 0.255354i | \(0.0821921\pi\) | ||||
−0.966848 | + | 0.255354i | \(0.917808\pi\) | |||||||
\(908\) | 19.1377i | 0.635108i | ||||||||
\(909\) | 15.5775 | 0.516672 | ||||||||
\(910\) | 6.05845 | − | 1.16717i | 0.200836 | − | 0.0386914i | ||||
\(911\) | 35.4906 | 1.17586 | 0.587928 | − | 0.808913i | \(-0.299944\pi\) | ||||
0.587928 | + | 0.808913i | \(0.299944\pi\) | |||||||
\(912\) | −14.8162 | −0.490612 | ||||||||
\(913\) | 0.0285176 | + | 15.8462i | 0.000943795 | + | 0.524431i | ||||
\(914\) | 1.53990 | 0.0509354 | ||||||||
\(915\) | 10.6234 | + | 11.7612i | 0.351197 | + | 0.388813i | ||||
\(916\) | − | 15.6942i | − | 0.518552i | ||||||
\(917\) | 46.7608 | + | 28.3032i | 1.54418 | + | 0.934654i | ||||
\(918\) | − | 0.383394i | − | 0.0126539i | ||||||
\(919\) | − | 24.5333i | − | 0.809277i | −0.914477 | − | 0.404639i | \(-0.867397\pi\) | ||
0.914477 | − | 0.404639i | \(-0.132603\pi\) | |||||||
\(920\) | 7.65224 | − | 6.91191i | 0.252287 | − | 0.227879i | ||||
\(921\) | 15.3444i | 0.505617i | ||||||||
\(922\) | −3.51136 | −0.115640 | ||||||||
\(923\) | − | 24.4859i | − | 0.805965i | ||||||
\(924\) | 14.6695 | + | 8.84309i | 0.482593 | + | 0.290916i | ||||
\(925\) | 41.8175 | + | 4.26234i | 1.37495 | + | 0.140145i | ||||
\(926\) | 5.33562i | 0.175339i | ||||||||
\(927\) | −1.22728 | −0.0403092 | ||||||||
\(928\) | − | 20.1860i | − | 0.662636i | ||||||
\(929\) | 8.88182i | 0.291403i | 0.989329 | + | 0.145701i | \(0.0465439\pi\) | ||||
−0.989329 | + | 0.145701i | \(0.953456\pi\) | |||||||
\(930\) | −0.151510 | + | 0.136852i | −0.00496821 | + | 0.00448755i | ||||
\(931\) | −12.9488 | − | 24.7382i | −0.424379 | − | 0.810763i | ||||
\(932\) | 9.80620 | 0.321213 | ||||||||
\(933\) | − | 29.9189i | − | 0.979502i | ||||||
\(934\) | −7.33173 | −0.239902 | ||||||||
\(935\) | 9.61599 | − | 8.71716i | 0.314476 | − | 0.285081i | ||||
\(936\) | 4.12153i | 0.134717i | ||||||||
\(937\) | 14.8334i | 0.484587i | 0.970203 | + | 0.242294i | \(0.0778997\pi\) | ||||
−0.970203 | + | 0.242294i | \(0.922100\pi\) | |||||||
\(938\) | 3.68851 | − | 6.09393i | 0.120434 | − | 0.198974i | ||||
\(939\) | −12.8166 | −0.418255 | ||||||||
\(940\) | −2.99163 | − | 3.31205i | −0.0975761 | − | 0.108027i | ||||
\(941\) | −9.65898 | −0.314874 | −0.157437 | − | 0.987529i | \(-0.550323\pi\) | ||||
−0.157437 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(942\) | 2.13853 | 0.0696770 | ||||||||
\(943\) | − | 27.3127i | − | 0.889423i | ||||||
\(944\) | − | 5.48451i | − | 0.178506i | ||||||
\(945\) | 1.11916 | + | 5.80926i | 0.0364064 | + | 0.188975i | ||||
\(946\) | −7.69626 | + | 0.0138506i | −0.250227 | + | 0.000450322i | ||||
\(947\) | 21.8372i | 0.709613i | 0.934940 | + | 0.354806i | \(0.115453\pi\) | ||||
−0.934940 | + | 0.354806i | \(0.884547\pi\) | |||||||
\(948\) | − | 9.75497i | − | 0.316827i | ||||||
\(949\) | −70.1884 | −2.27841 | ||||||||
\(950\) | −0.443048 | + | 4.34672i | −0.0143744 | + | 0.141026i | ||||
\(951\) | − | 0.0935753i | − | 0.00303439i | ||||||
\(952\) | −2.07579 | + | 3.42949i | −0.0672767 | + | 0.111150i | ||||
\(953\) | −8.84782 | −0.286609 | −0.143304 | − | 0.989679i | \(-0.545773\pi\) | ||||
−0.143304 | + | 0.989679i | \(0.545773\pi\) | |||||||
\(954\) | − | 0.911595i | − | 0.0295140i | ||||||
\(955\) | 28.1710 | + | 31.1884i | 0.911593 | + | 1.00923i | ||||
\(956\) | − | 3.58001i | − | 0.115786i | ||||||
\(957\) | −0.0473375 | − | 26.3037i | −0.00153020 | − | 0.850277i | ||||
\(958\) | −1.38796 | −0.0448430 | ||||||||
\(959\) | 22.2041 | − | 36.6843i | 0.717008 | − | 1.18460i | ||||
\(960\) | −10.2987 | − | 11.4017i | −0.332388 | − | 0.367989i | ||||
\(961\) | 30.8263 | 0.994396 | ||||||||
\(962\) | −8.76746 | −0.282674 | ||||||||
\(963\) | −2.52487 | −0.0813627 | ||||||||
\(964\) | −32.1356 | −1.03502 | ||||||||
\(965\) | −2.71303 | − | 3.00361i | −0.0873354 | − | 0.0966897i | ||||
\(966\) | −1.59863 | + | 2.64116i | −0.0514351 | + | 0.0849779i | ||||
\(967\) | 13.5577 | 0.435987 | 0.217994 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217994 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(968\) | 9.52338 | − | 0.0342777i | 0.306093 | − | 0.00110173i | ||||
\(969\) | − | 6.98095i | − | 0.224260i | ||||||
\(970\) | −2.92799 | − | 3.24160i | −0.0940120 | − | 0.104081i | ||||
\(971\) | 33.7112i | 1.08184i | 0.841073 | + | 0.540921i | \(0.181924\pi\) | ||||
−0.841073 | + | 0.540921i | \(0.818076\pi\) | |||||||
\(972\) | −1.95201 | −0.0626107 | ||||||||
\(973\) | −40.2127 | − | 24.3398i | −1.28916 | − | 0.780298i | ||||
\(974\) | 0.302612i | 0.00969632i | ||||||||
\(975\) | −23.6801 | − | 2.41364i | −0.758370 | − | 0.0772985i | ||||
\(976\) | 26.3264 | 0.842689 | ||||||||
\(977\) | 47.1128i | 1.50727i | 0.657293 | + | 0.753635i | \(0.271701\pi\) | ||||
−0.657293 | + | 0.753635i | \(0.728299\pi\) | |||||||
\(978\) | 0.582362i | 0.0186219i | ||||||||
\(979\) | 0.0499929 | + | 27.7792i | 0.00159778 | + | 0.887827i | ||||
\(980\) | 10.5907 | − | 28.6596i | 0.338306 | − | 0.915496i | ||||
\(981\) | 19.4843i | 0.622085i | ||||||||
\(982\) | 5.82091i | 0.185753i | ||||||||
\(983\) | 18.7123 | 0.596831 | 0.298416 | − | 0.954436i | \(-0.403542\pi\) | ||||
0.298416 | + | 0.954436i | \(0.403542\pi\) | |||||||
\(984\) | 4.43936 | 0.141522 | ||||||||
\(985\) | −21.3232 | − | 23.6071i | −0.679413 | − | 0.752184i | ||||
\(986\) | 3.04065 | 0.0968339 | ||||||||
\(987\) | 2.31441 | + | 1.40085i | 0.0736683 | + | 0.0445897i | ||||
\(988\) | 37.0674i | 1.17927i | ||||||||
\(989\) | 56.4216i | 1.79410i | ||||||||
\(990\) | 1.09118 | + | 1.20369i | 0.0346800 | + | 0.0382558i | ||||
\(991\) | 0.578234 | 0.0183682 | 0.00918411 | − | 0.999958i | \(-0.497077\pi\) | ||||
0.00918411 | + | 0.999958i | \(0.497077\pi\) | |||||||
\(992\) | 1.06082i | 0.0336812i | ||||||||
\(993\) | 2.60137 | 0.0825521 | ||||||||
\(994\) | 2.55040 | + | 1.54370i | 0.0808939 | + | 0.0489631i | ||||
\(995\) | −12.6965 | + | 11.4682i | −0.402506 | + | 0.363565i | ||||
\(996\) | 9.32631i | 0.295516i | ||||||||
\(997\) | − | 1.90956i | − | 0.0604763i | −0.999543 | − | 0.0302381i | \(-0.990373\pi\) | ||
0.999543 | − | 0.0302381i | \(-0.00962657\pi\) | |||||||
\(998\) | −4.80940 | −0.152239 | ||||||||
\(999\) | − | 8.40684i | − | 0.265981i |
(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 | 1155.2.k.b.769.24 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.a.769.25 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.a.769.23 | ✓ | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.b.769.25 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.b.769.26 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.a.769.24 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.a.769.26 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.b.769.23 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.23 | ✓ | 48 | 7.6 | odd | 2 | ||
1155.2.k.a.769.24 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.a.769.25 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.a.769.26 | yes | 48 | 77.76 | even | 2 | ||
1155.2.k.b.769.23 | yes | 48 | 385.384 | even | 2 | inner | |
1155.2.k.b.769.24 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.b.769.25 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.b.769.26 | yes | 48 | 35.34 | odd | 2 | inner |