Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 743.1 | ||
Character | \(\chi\) | \(=\) | 750.743 |
Dual form | 750.2.l.b.107.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{7}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.891007 | + | 0.453990i | −0.630037 | + | 0.321020i | ||||
\(3\) | −1.73204 | + | 0.00452789i | −0.999997 | + | 0.00261418i | ||||
\(4\) | 0.587785 | − | 0.809017i | 0.293893 | − | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.54121 | − | 0.790366i | 0.629195 | − | 0.322666i | ||||
\(7\) | 0.152718 | − | 0.152718i | 0.0577219 | − | 0.0577219i | −0.677657 | − | 0.735379i | \(-0.737004\pi\) |
0.735379 | + | 0.677657i | \(0.237004\pi\) | |||||||
\(8\) | −0.156434 | + | 0.987688i | −0.0553079 | + | 0.349201i | ||||
\(9\) | 2.99996 | − | 0.0156850i | 0.999986 | − | 0.00522833i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.88609 | − | 1.58759i | −1.47321 | − | 0.478676i | −0.541136 | − | 0.840935i | \(-0.682005\pi\) |
−0.932077 | + | 0.362259i | \(0.882005\pi\) | |||||||
\(12\) | −1.01441 | + | 1.40392i | −0.292834 | + | 0.405275i | ||||
\(13\) | −0.674795 | + | 1.32436i | −0.187155 | + | 0.367312i | −0.965451 | − | 0.260586i | \(-0.916084\pi\) |
0.778296 | + | 0.627897i | \(0.216084\pi\) | |||||||
\(14\) | −0.0667401 | + | 0.205405i | −0.0178371 | + | 0.0548968i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | 4.81543 | + | 0.762690i | 1.16791 | + | 0.184979i | 0.710121 | − | 0.704080i | \(-0.248640\pi\) |
0.457793 | + | 0.889059i | \(0.348640\pi\) | |||||||
\(18\) | −2.66586 | + | 1.37593i | −0.628350 | + | 0.324309i | ||||
\(19\) | 0.283032 | + | 0.389560i | 0.0649319 | + | 0.0893711i | 0.840248 | − | 0.542202i | \(-0.182409\pi\) |
−0.775316 | + | 0.631574i | \(0.782409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.263823 | + | 0.265206i | −0.0575708 | + | 0.0578726i | ||||
\(22\) | 5.07429 | − | 0.803689i | 1.08184 | − | 0.171347i | ||||
\(23\) | −1.21389 | − | 2.38239i | −0.253114 | − | 0.496763i | 0.729130 | − | 0.684376i | \(-0.239925\pi\) |
−0.982243 | + | 0.187612i | \(0.939925\pi\) | |||||||
\(24\) | 0.266479 | − | 1.71143i | 0.0543949 | − | 0.349344i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.48636i | − | 0.291500i | ||||||
\(27\) | −5.19599 | + | 0.0407506i | −0.999969 | + | 0.00784246i | ||||
\(28\) | −0.0337860 | − | 0.213317i | −0.00638496 | − | 0.0403130i | ||||
\(29\) | 7.59423 | + | 5.51753i | 1.41021 | + | 1.02458i | 0.993292 | + | 0.115637i | \(0.0368909\pi\) |
0.416921 | + | 0.908943i | \(0.363109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84019 | + | 1.33698i | −0.330508 | + | 0.240128i | −0.740646 | − | 0.671895i | \(-0.765480\pi\) |
0.410138 | + | 0.912023i | \(0.365480\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 8.47012 | + | 2.72765i | 1.47446 | + | 0.474823i | ||||
\(34\) | −4.63684 | + | 1.50660i | −0.795211 | + | 0.258380i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.75064 | − | 2.43624i | 0.291774 | − | 0.406040i | ||||
\(37\) | −3.83574 | − | 1.95441i | −0.630592 | − | 0.321303i | 0.109320 | − | 0.994007i | \(-0.465133\pi\) |
−0.739912 | + | 0.672704i | \(0.765133\pi\) | |||||||
\(38\) | −0.429039 | − | 0.218606i | −0.0695994 | − | 0.0354627i | ||||
\(39\) | 1.16278 | − | 2.29691i | 0.186194 | − | 0.367800i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.95547 | + | 1.93505i | −0.930087 | + | 0.302204i | −0.734598 | − | 0.678502i | \(-0.762629\pi\) |
−0.195489 | + | 0.980706i | \(0.562629\pi\) | |||||||
\(42\) | 0.114667 | − | 0.356073i | 0.0176935 | − | 0.0549432i | ||||
\(43\) | 2.72225 | + | 2.72225i | 0.415139 | + | 0.415139i | 0.883524 | − | 0.468385i | \(-0.155164\pi\) |
−0.468385 | + | 0.883524i | \(0.655164\pi\) | |||||||
\(44\) | −4.15636 | + | 3.01977i | −0.626595 | + | 0.455248i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.16317 | + | 1.57163i | 0.318942 | + | 0.231725i | ||||
\(47\) | 1.58814 | + | 10.0271i | 0.231654 | + | 1.46260i | 0.779699 | + | 0.626154i | \(0.215372\pi\) |
−0.548046 | + | 0.836448i | \(0.684628\pi\) | |||||||
\(48\) | 0.539538 | + | 1.64587i | 0.0778755 | + | 0.237561i | ||||
\(49\) | 6.95335i | 0.993336i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.34400 | − | 1.29921i | −1.16839 | − | 0.181926i | ||||
\(52\) | 0.674795 | + | 1.32436i | 0.0935773 | + | 0.183656i | ||||
\(53\) | −7.59700 | + | 1.20325i | −1.04353 | + | 0.165279i | −0.654589 | − | 0.755985i | \(-0.727158\pi\) |
−0.388939 | + | 0.921264i | \(0.627158\pi\) | |||||||
\(54\) | 4.61116 | − | 2.39524i | 0.627500 | − | 0.325951i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.126947 | + | 0.174728i | 0.0169640 | + | 0.0233490i | ||||
\(57\) | −0.491987 | − | 0.673453i | −0.0651653 | − | 0.0892011i | ||||
\(58\) | −9.27141 | − | 1.46845i | −1.21740 | − | 0.192817i | ||||
\(59\) | 1.54130 | + | 4.74363i | 0.200660 | + | 0.617569i | 0.999864 | + | 0.0165081i | \(0.00525494\pi\) |
−0.799204 | + | 0.601061i | \(0.794745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.21680 | + | 12.9780i | −0.539906 | + | 1.66166i | 0.192898 | + | 0.981219i | \(0.438211\pi\) |
−0.732803 | + | 0.680440i | \(0.761789\pi\) | |||||||
\(62\) | 1.03265 | − | 2.02668i | 0.131146 | − | 0.257389i | ||||
\(63\) | 0.455752 | − | 0.460543i | 0.0574193 | − | 0.0580229i | ||||
\(64\) | −0.951057 | − | 0.309017i | −0.118882 | − | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.78526 | + | 1.41500i | −1.08139 | + | 0.174175i | ||||
\(67\) | −2.35050 | + | 14.8405i | −0.287159 | + | 1.81305i | 0.248514 | + | 0.968628i | \(0.420058\pi\) |
−0.535673 | + | 0.844425i | \(0.679942\pi\) | |||||||
\(68\) | 3.44747 | − | 3.44747i | 0.418067 | − | 0.418067i | ||||
\(69\) | 2.11330 | + | 4.12092i | 0.254411 | + | 0.496100i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.13100 | − | 9.81498i | 0.846294 | − | 1.16482i | −0.138373 | − | 0.990380i | \(-0.544187\pi\) |
0.984667 | − | 0.174444i | \(-0.0558128\pi\) | |||||||
\(72\) | −0.453805 | + | 2.96548i | −0.0534814 | + | 0.349485i | ||||
\(73\) | −8.36209 | + | 4.26070i | −0.978708 | + | 0.498677i | −0.868745 | − | 0.495259i | \(-0.835073\pi\) |
−0.109963 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(74\) | 4.30495 | 0.500441 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.481522 | 0.0552344 | ||||||||
\(77\) | −0.988647 | + | 0.503741i | −0.112667 | + | 0.0574066i | ||||
\(78\) | 0.00673009 | + | 2.57445i | 0.000762033 | + | 0.291499i | ||||
\(79\) | −1.28502 | + | 1.76867i | −0.144576 | + | 0.198991i | −0.875163 | − | 0.483828i | \(-0.839246\pi\) |
0.730588 | + | 0.682819i | \(0.239246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99951 | − | 0.0941087i | 0.999945 | − | 0.0104565i | ||||
\(82\) | 4.42787 | − | 4.42787i | 0.488976 | − | 0.488976i | ||||
\(83\) | −0.782253 | + | 4.93895i | −0.0858634 | + | 0.542120i | 0.906834 | + | 0.421488i | \(0.138492\pi\) |
−0.992697 | + | 0.120632i | \(0.961508\pi\) | |||||||
\(84\) | 0.0594848 | + | 0.369321i | 0.00649032 | + | 0.0402962i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.66142 | − | 1.18967i | −0.394821 | − | 0.128285i | ||||
\(87\) | −13.1785 | − | 9.52222i | −1.41289 | − | 1.02089i | ||||
\(88\) | 2.33240 | − | 4.57759i | 0.248634 | − | 0.487972i | ||||
\(89\) | 3.38311 | − | 10.4121i | 0.358609 | − | 1.10368i | −0.595279 | − | 0.803519i | \(-0.702958\pi\) |
0.953887 | − | 0.300165i | \(-0.0970417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0992002 | + | 0.305307i | 0.0103990 | + | 0.0320048i | ||||
\(92\) | −2.64090 | − | 0.418278i | −0.275333 | − | 0.0436085i | ||||
\(93\) | 3.18124 | − | 2.32404i | 0.329879 | − | 0.240991i | ||||
\(94\) | −5.96725 | − | 8.21321i | −0.615475 | − | 0.847128i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.22794 | − | 1.22154i | −0.125326 | − | 0.124673i | ||||
\(97\) | 9.96799 | − | 1.57877i | 1.01210 | − | 0.160300i | 0.371706 | − | 0.928350i | \(-0.378773\pi\) |
0.640390 | + | 0.768050i | \(0.278773\pi\) | |||||||
\(98\) | −3.15676 | − | 6.19548i | −0.318881 | − | 0.625838i | ||||
\(99\) | −14.6830 | − | 4.68606i | −1.47570 | − | 0.470967i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.53700i | 0.948967i | 0.880264 | + | 0.474483i | \(0.157365\pi\) | ||||
−0.880264 | + | 0.474483i | \(0.842635\pi\) | |||||||
\(102\) | 8.02438 | − | 2.63049i | 0.794533 | − | 0.260458i | ||||
\(103\) | −1.58215 | − | 9.98929i | −0.155894 | − | 0.984274i | −0.934293 | − | 0.356505i | \(-0.883968\pi\) |
0.778400 | − | 0.627769i | \(-0.216032\pi\) | |||||||
\(104\) | −1.20249 | − | 0.873663i | −0.117914 | − | 0.0856697i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.22271 | − | 4.52106i | 0.604403 | − | 0.439125i | ||||
\(107\) | −7.80873 | − | 7.80873i | −0.754898 | − | 0.754898i | 0.220491 | − | 0.975389i | \(-0.429234\pi\) |
−0.975389 | + | 0.220491i | \(0.929234\pi\) | |||||||
\(108\) | −3.02116 | + | 4.22760i | −0.290711 | + | 0.406801i | ||||
\(109\) | −5.83194 | + | 1.89491i | −0.558598 | + | 0.181500i | −0.574690 | − | 0.818371i | \(-0.694877\pi\) |
0.0160921 | + | 0.999871i | \(0.494877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.65253 | + | 3.36776i | 0.631430 | + | 0.319653i | ||||
\(112\) | −0.192436 | − | 0.0980509i | −0.0181835 | − | 0.00926494i | ||||
\(113\) | 9.78864 | + | 4.98756i | 0.920838 | + | 0.469190i | 0.849099 | − | 0.528233i | \(-0.177145\pi\) |
0.0717385 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(114\) | 0.744105 | + | 0.376694i | 0.0696918 | + | 0.0352806i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.92755 | − | 2.90074i | 0.828902 | − | 0.269327i | ||||
\(117\) | −2.00359 | + | 3.98361i | −0.185232 | + | 0.368285i | ||||
\(118\) | −3.52687 | − | 3.52687i | −0.324675 | − | 0.324675i | ||||
\(119\) | 0.851879 | − | 0.618926i | 0.0780916 | − | 0.0567369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4543 | + | 9.04858i | 1.13221 | + | 0.822598i | ||||
\(122\) | −2.13468 | − | 13.4778i | −0.193265 | − | 1.22023i | ||||
\(123\) | 10.3064 | − | 3.37856i | 0.929294 | − | 0.304634i | ||||
\(124\) | 2.27460i | 0.204265i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.196996 | + | 0.617253i | −0.0175498 | + | 0.0549893i | ||||
\(127\) | 6.82658 | + | 13.3979i | 0.605761 | + | 1.18887i | 0.966611 | + | 0.256249i | \(0.0824868\pi\) |
−0.360850 | + | 0.932624i | \(0.617513\pi\) | |||||||
\(128\) | 0.987688 | − | 0.156434i | 0.0873001 | − | 0.0138270i | ||||
\(129\) | −4.72738 | − | 4.70273i | −0.416223 | − | 0.414052i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.12870 | + | 7.05905i | 0.448097 | + | 0.616752i | 0.971987 | − | 0.235034i | \(-0.0755200\pi\) |
−0.523891 | + | 0.851785i | \(0.675520\pi\) | |||||||
\(132\) | 7.18533 | − | 5.24920i | 0.625403 | − | 0.456884i | ||||
\(133\) | 0.102717 | + | 0.0162687i | 0.00890667 | + | 0.00141068i | ||||
\(134\) | −4.64313 | − | 14.2901i | −0.401105 | − | 1.23447i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50660 | + | 4.63684i | −0.129190 | + | 0.397605i | ||||
\(137\) | 1.28180 | − | 2.51567i | 0.109511 | − | 0.214928i | −0.829747 | − | 0.558140i | \(-0.811515\pi\) |
0.939258 | + | 0.343212i | \(0.111515\pi\) | |||||||
\(138\) | −3.75382 | − | 2.71235i | −0.319546 | − | 0.230890i | ||||
\(139\) | −6.62014 | − | 2.15102i | −0.561513 | − | 0.182447i | 0.0144887 | − | 0.999895i | \(-0.495388\pi\) |
−0.576002 | + | 0.817448i | \(0.695388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.79613 | − | 17.3602i | −0.235476 | − | 1.46199i | ||||
\(142\) | −1.89786 | + | 11.9826i | −0.159265 | + | 1.00556i | ||||
\(143\) | 5.39965 | − | 5.39965i | 0.451542 | − | 0.451542i | ||||
\(144\) | −0.941956 | − | 2.84828i | −0.0784963 | − | 0.237357i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.51636 | − | 7.59261i | 0.456537 | − | 0.628369i | ||||
\(147\) | −0.0314840 | − | 12.0435i | −0.00259676 | − | 0.993333i | ||||
\(148\) | −3.83574 | + | 1.95441i | −0.315296 | + | 0.160651i | ||||
\(149\) | −7.72360 | −0.632742 | −0.316371 | − | 0.948635i | \(-0.602465\pi\) | ||||
−0.316371 | + | 0.948635i | \(0.602465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7868 | −1.20333 | −0.601667 | − | 0.798747i | \(-0.705497\pi\) | ||||
−0.601667 | + | 0.798747i | \(0.705497\pi\) | |||||||
\(152\) | −0.429039 | + | 0.218606i | −0.0347997 | + | 0.0177313i | ||||
\(153\) | 14.4581 | + | 2.21251i | 1.16887 | + | 0.178871i | ||||
\(154\) | 0.652197 | − | 0.897673i | 0.0525556 | − | 0.0723365i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.17477 | − | 2.29080i | −0.0940571 | − | 0.183411i | ||||
\(157\) | 11.5941 | − | 11.5941i | 0.925312 | − | 0.925312i | −0.0720863 | − | 0.997398i | \(-0.522966\pi\) |
0.997398 | + | 0.0720863i | \(0.0229657\pi\) | |||||||
\(158\) | 0.341997 | − | 2.15928i | 0.0272078 | − | 0.171783i | ||||
\(159\) | 13.1529 | − | 2.11847i | 1.04309 | − | 0.168006i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.549217 | − | 0.178451i | −0.0432843 | − | 0.0140639i | ||||
\(162\) | −7.97590 | + | 4.16954i | −0.626646 | + | 0.327590i | ||||
\(163\) | 1.84215 | − | 3.61543i | 0.144289 | − | 0.283182i | −0.807540 | − | 0.589813i | \(-0.799202\pi\) |
0.951829 | + | 0.306630i | \(0.0992016\pi\) | |||||||
\(164\) | −1.93505 | + | 5.95547i | −0.151102 | + | 0.465044i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.54524 | − | 4.75577i | −0.119934 | − | 0.369119i | ||||
\(167\) | 13.6706 | + | 2.16520i | 1.05786 | + | 0.167549i | 0.661042 | − | 0.750349i | \(-0.270114\pi\) |
0.396818 | + | 0.917897i | \(0.370114\pi\) | |||||||
\(168\) | −0.220670 | − | 0.302062i | −0.0170250 | − | 0.0233046i | ||||
\(169\) | 6.34263 | + | 8.72988i | 0.487894 | + | 0.671529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.855194 | + | 1.16422i | 0.0653983 | + | 0.0890304i | ||||
\(172\) | 3.80244 | − | 0.602248i | 0.289934 | − | 0.0459210i | ||||
\(173\) | −0.412278 | − | 0.809140i | −0.0313449 | − | 0.0615178i | 0.874803 | − | 0.484479i | \(-0.160991\pi\) |
−0.906148 | + | 0.422961i | \(0.860991\pi\) | |||||||
\(174\) | 16.0652 | + | 2.50144i | 1.21790 | + | 0.189633i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.13754i | 0.387257i | ||||||||
\(177\) | −2.69108 | − | 8.20921i | −0.202274 | − | 0.617042i | ||||
\(178\) | 1.71264 | + | 10.8132i | 0.128368 | + | 0.810482i | ||||
\(179\) | −9.58645 | − | 6.96496i | −0.716525 | − | 0.520586i | 0.168747 | − | 0.985659i | \(-0.446028\pi\) |
−0.885272 | + | 0.465074i | \(0.846028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.9076 | − | 10.1044i | 1.03374 | − | 0.751057i | 0.0646876 | − | 0.997906i | \(-0.479395\pi\) |
0.969054 | + | 0.246848i | \(0.0793949\pi\) | |||||||
\(182\) | −0.226994 | − | 0.226994i | −0.0168259 | − | 0.0168259i | ||||
\(183\) | 7.24492 | − | 22.4975i | 0.535560 | − | 1.66306i | ||||
\(184\) | 2.54296 | − | 0.826257i | 0.187469 | − | 0.0609125i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.77942 | + | 3.51498i | −0.130473 | + | 0.257731i | ||||
\(187\) | −22.3178 | − | 11.3715i | −1.63204 | − | 0.831566i | ||||
\(188\) | 9.04558 | + | 4.60895i | 0.659716 | + | 0.336142i | ||||
\(189\) | −0.787297 | + | 0.799744i | −0.0572675 | + | 0.0581728i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.70151 | − | 1.52761i | 0.340189 | − | 0.110534i | −0.133940 | − | 0.990989i | \(-0.542763\pi\) |
0.474129 | + | 0.880455i | \(0.342763\pi\) | |||||||
\(192\) | 1.64867 | + | 0.530925i | 0.118983 | + | 0.0383162i | ||||
\(193\) | −2.38356 | − | 2.38356i | −0.171572 | − | 0.171572i | 0.616098 | − | 0.787670i | \(-0.288713\pi\) |
−0.787670 | + | 0.616098i | \(0.788713\pi\) | |||||||
\(194\) | −8.16479 | + | 5.93207i | −0.586198 | + | 0.425898i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.62538 | + | 4.08708i | 0.401813 | + | 0.291934i | ||||
\(197\) | −1.14693 | − | 7.24145i | −0.0817156 | − | 0.515932i | −0.994263 | − | 0.106961i | \(-0.965888\pi\) |
0.912548 | − | 0.408970i | \(-0.134112\pi\) | |||||||
\(198\) | 15.2101 | − | 2.49062i | 1.08093 | − | 0.177001i | ||||
\(199\) | − | 8.34182i | − | 0.591336i | −0.955291 | − | 0.295668i | \(-0.904458\pi\) | ||
0.955291 | − | 0.295668i | \(-0.0955422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00398 | − | 25.7150i | 0.282419 | − | 1.81380i | ||||
\(202\) | −4.32971 | − | 8.49753i | −0.304637 | − | 0.597884i | ||||
\(203\) | 2.00240 | − | 0.317149i | 0.140541 | − | 0.0222595i | ||||
\(204\) | −5.95556 | + | 5.98678i | −0.416973 | + | 0.419158i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.94475 | + | 8.18224i | 0.414190 | + | 0.570084i | ||||
\(207\) | −3.67899 | − | 7.12804i | −0.255707 | − | 0.495433i | ||||
\(208\) | 1.46807 | + | 0.232519i | 0.101792 | + | 0.0161223i | ||||
\(209\) | −0.764459 | − | 2.35276i | −0.0528787 | − | 0.162744i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.32487 | − | 4.07753i | 0.0912078 | − | 0.280709i | −0.895039 | − | 0.445988i | \(-0.852852\pi\) |
0.986247 | + | 0.165279i | \(0.0528525\pi\) | |||||||
\(212\) | −3.49196 | + | 6.85335i | −0.239828 | + | 0.470690i | ||||
\(213\) | −12.3068 | + | 17.0323i | −0.843246 | + | 1.16703i | ||||
\(214\) | 10.5027 | + | 3.41254i | 0.717951 | + | 0.233276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.772583 | − | 5.13840i | 0.0525676 | − | 0.349624i | ||||
\(217\) | −0.0768498 | + | 0.485210i | −0.00521690 | + | 0.0329382i | ||||
\(218\) | 4.33602 | − | 4.33602i | 0.293672 | − | 0.293672i | ||||
\(219\) | 14.4642 | − | 7.41758i | 0.977401 | − | 0.501233i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.25951 | + | 5.86271i | −0.286525 | + | 0.394369i | ||||
\(222\) | −7.45637 | + | 0.0194923i | −0.500439 | + | 0.00130824i | ||||
\(223\) | −0.651256 | + | 0.331831i | −0.0436113 | + | 0.0222211i | −0.475660 | − | 0.879629i | \(-0.657791\pi\) |
0.432049 | + | 0.901850i | \(0.357791\pi\) | |||||||
\(224\) | 0.215976 | 0.0144305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.9860 | −0.730781 | ||||||||
\(227\) | −2.94981 | + | 1.50300i | −0.195786 | + | 0.0997579i | −0.549135 | − | 0.835734i | \(-0.685043\pi\) |
0.353349 | + | 0.935492i | \(0.385043\pi\) | |||||||
\(228\) | −0.834018 | + | 0.00218028i | −0.0552342 | + | 0.000144392i | ||||
\(229\) | −6.20224 | + | 8.53665i | −0.409855 | + | 0.564117i | −0.963183 | − | 0.268846i | \(-0.913358\pi\) |
0.553328 | + | 0.832964i | \(0.313358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.71010 | − | 0.876978i | 0.112516 | − | 0.0577009i | ||||
\(232\) | −6.63760 | + | 6.63760i | −0.435780 | + | 0.435780i | ||||
\(233\) | −1.96935 | + | 12.4340i | −0.129016 | + | 0.814577i | 0.835294 | + | 0.549803i | \(0.185297\pi\) |
−0.964311 | + | 0.264774i | \(0.914703\pi\) | |||||||
\(234\) | −0.0233136 | − | 4.45903i | −0.00152406 | − | 0.291496i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.74363 | + | 1.54130i | 0.308784 | + | 0.100330i | ||||
\(237\) | 2.21770 | − | 3.06924i | 0.144055 | − | 0.199369i | ||||
\(238\) | −0.478043 | + | 0.938212i | −0.0309869 | + | 0.0608152i | ||||
\(239\) | −3.62951 | + | 11.1705i | −0.234773 | + | 0.722558i | 0.762378 | + | 0.647132i | \(0.224032\pi\) |
−0.997151 | + | 0.0754263i | \(0.975968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.375849 | + | 1.15675i | 0.0242106 | + | 0.0745125i | 0.962432 | − | 0.271524i | \(-0.0875275\pi\) |
−0.938221 | + | 0.346036i | \(0.887527\pi\) | |||||||
\(242\) | −15.2048 | − | 2.40821i | −0.977403 | − | 0.154805i | ||||
\(243\) | −15.5871 | + | 0.203749i | −0.999915 | + | 0.0130705i | ||||
\(244\) | 8.02083 | + | 11.0397i | 0.513481 | + | 0.706746i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.64921 | + | 7.68931i | −0.487696 | + | 0.490253i | ||||
\(247\) | −0.706906 | + | 0.111963i | −0.0449793 | + | 0.00712403i | ||||
\(248\) | −1.03265 | − | 2.02668i | −0.0655732 | − | 0.128695i | ||||
\(249\) | 1.33253 | − | 8.55802i | 0.0844459 | − | 0.542343i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6123i | 1.42728i | 0.700515 | + | 0.713638i | \(0.252954\pi\) | ||||
−0.700515 | + | 0.713638i | \(0.747046\pi\) | |||||||
\(252\) | −0.104703 | − | 0.639411i | −0.00659564 | − | 0.0402791i | ||||
\(253\) | 2.14892 | + | 13.5678i | 0.135102 | + | 0.852998i | ||||
\(254\) | −12.1651 | − | 8.83843i | −0.763304 | − | 0.554573i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 2.98436 | + | 2.98436i | 0.186159 | + | 0.186159i | 0.794033 | − | 0.607874i | \(-0.207978\pi\) |
−0.607874 | + | 0.794033i | \(0.707978\pi\) | |||||||
\(258\) | 6.34713 | + | 2.04398i | 0.395155 | + | 0.127252i | ||||
\(259\) | −0.884259 | + | 0.287313i | −0.0549452 | + | 0.0178528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.8689 | + | 16.4332i | 1.41555 | + | 1.01719i | ||||
\(262\) | −7.77445 | − | 3.96128i | −0.480307 | − | 0.244729i | ||||
\(263\) | −2.29146 | − | 1.16756i | −0.141298 | − | 0.0719947i | 0.381912 | − | 0.924199i | \(-0.375266\pi\) |
−0.523210 | + | 0.852204i | \(0.675266\pi\) | |||||||
\(264\) | −4.01909 | + | 7.93914i | −0.247358 | + | 0.488621i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0989071 | + | 0.0321369i | −0.00606438 | + | 0.00197044i | ||||
\(267\) | −5.81255 | + | 18.0496i | −0.355722 | + | 1.10462i | ||||
\(268\) | 10.6246 | + | 10.6246i | 0.649002 | + | 0.649002i | ||||
\(269\) | 19.5493 | − | 14.2034i | 1.19194 | − | 0.865996i | 0.198473 | − | 0.980106i | \(-0.436402\pi\) |
0.993468 | + | 0.114110i | \(0.0364018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.36464 | − | 6.80381i | −0.568861 | − | 0.413302i | 0.265830 | − | 0.964020i | \(-0.414354\pi\) |
−0.834691 | + | 0.550718i | \(0.814354\pi\) | |||||||
\(272\) | −0.762690 | − | 4.81543i | −0.0462448 | − | 0.291978i | ||||
\(273\) | −0.173202 | − | 0.528356i | −0.0104826 | − | 0.0319776i | ||||
\(274\) | 2.82340i | 0.170568i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.57606 | + | 0.712519i | 0.275446 | + | 0.0428886i | ||||
\(277\) | −3.42126 | − | 6.71461i | −0.205564 | − | 0.403442i | 0.765090 | − | 0.643924i | \(-0.222695\pi\) |
−0.970654 | + | 0.240482i | \(0.922695\pi\) | |||||||
\(278\) | 6.87513 | − | 1.08891i | 0.412343 | − | 0.0653087i | ||||
\(279\) | −5.49953 | + | 4.03974i | −0.329248 | + | 0.241853i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8790 | − | 19.1028i | −0.827952 | − | 1.13958i | −0.988301 | − | 0.152517i | \(-0.951262\pi\) |
0.160349 | − | 0.987060i | \(-0.448738\pi\) | |||||||
\(282\) | 10.3727 | + | 14.1986i | 0.617687 | + | 0.845516i | ||||
\(283\) | −9.72347 | − | 1.54005i | −0.578000 | − | 0.0915463i | −0.139412 | − | 0.990234i | \(-0.544521\pi\) |
−0.438588 | + | 0.898688i | \(0.644521\pi\) | |||||||
\(284\) | −3.74899 | − | 11.5382i | −0.222462 | − | 0.684667i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.35974 | + | 7.26252i | −0.139534 | + | 0.429442i | ||||
\(287\) | −0.613989 | + | 1.20502i | −0.0362426 | + | 0.0711302i | ||||
\(288\) | 2.13238 | + | 2.11020i | 0.125652 | + | 0.124345i | ||||
\(289\) | 6.43873 | + | 2.09207i | 0.378749 | + | 0.123063i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2579 | + | 2.77964i | −1.01167 | + | 0.162945i | ||||
\(292\) | −1.46814 | + | 9.26944i | −0.0859161 | + | 0.542453i | ||||
\(293\) | −3.33944 | + | 3.33944i | −0.195092 | + | 0.195092i | −0.797892 | − | 0.602800i | \(-0.794052\pi\) |
0.602800 | + | 0.797892i | \(0.294052\pi\) | |||||||
\(294\) | 5.49570 | + | 10.7166i | 0.320516 | + | 0.625003i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.53039 | − | 3.48278i | 0.147076 | − | 0.202433i | ||||
\(297\) | 25.4528 | + | 8.04999i | 1.47692 | + | 0.467108i | ||||
\(298\) | 6.88178 | − | 3.50644i | 0.398651 | − | 0.203123i | ||||
\(299\) | 3.97428 | 0.229838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.831472 | 0.0479252 | ||||||||
\(302\) | 13.1751 | − | 6.71307i | 0.758145 | − | 0.386294i | ||||
\(303\) | −0.0431824 | − | 16.5185i | −0.00248077 | − | 0.948964i | ||||
\(304\) | 0.283032 | − | 0.389560i | 0.0162330 | − | 0.0223428i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.8867 | + | 4.59246i | −0.793849 | + | 0.262534i | ||||
\(307\) | 11.8133 | − | 11.8133i | 0.674221 | − | 0.674221i | −0.284465 | − | 0.958686i | \(-0.591816\pi\) |
0.958686 | + | 0.284465i | \(0.0918160\pi\) | |||||||
\(308\) | −0.173577 | + | 1.09592i | −0.00989048 | + | 0.0624460i | ||||
\(309\) | 2.78558 | + | 17.2947i | 0.158466 | + | 0.983863i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.7239 | − | 9.33296i | −1.62878 | − | 0.529224i | −0.654791 | − | 0.755810i | \(-0.727244\pi\) |
−0.973991 | + | 0.226586i | \(0.927244\pi\) | |||||||
\(312\) | 2.08673 | + | 1.50778i | 0.118138 | + | 0.0853612i | ||||
\(313\) | 7.57278 | − | 14.8624i | 0.428039 | − | 0.840073i | −0.571768 | − | 0.820415i | \(-0.693742\pi\) |
0.999807 | − | 0.0196580i | \(-0.00625773\pi\) | |||||||
\(314\) | −5.06682 | + | 15.5941i | −0.285937 | + | 0.880024i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.675573 | + | 2.07920i | 0.0380040 | + | 0.116964i | ||||
\(317\) | −10.7129 | − | 1.69675i | −0.601695 | − | 0.0952991i | −0.151847 | − | 0.988404i | \(-0.548522\pi\) |
−0.449848 | + | 0.893105i | \(0.648522\pi\) | |||||||
\(318\) | −10.7575 | + | 7.85886i | −0.603253 | + | 0.440703i | ||||
\(319\) | −28.3466 | − | 39.0157i | −1.58710 | − | 2.18446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5604 | + | 13.4897i | 0.756869 | + | 0.752922i | ||||
\(322\) | 0.570371 | − | 0.0903379i | 0.0317855 | − | 0.00503433i | ||||
\(323\) | 1.06581 | + | 2.09176i | 0.0593031 | + | 0.116389i | ||||
\(324\) | 5.21364 | − | 7.33607i | 0.289647 | − | 0.407559i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.05769i | 0.224735i | ||||||||
\(327\) | 10.0926 | − | 3.30848i | 0.558122 | − | 0.182959i | ||||
\(328\) | −0.979584 | − | 6.18485i | −0.0540885 | − | 0.341501i | ||||
\(329\) | 1.77385 | + | 1.28878i | 0.0977957 | + | 0.0710527i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.79472 | + | 5.66319i | −0.428436 | + | 0.311277i | −0.781023 | − | 0.624502i | \(-0.785302\pi\) |
0.352587 | + | 0.935779i | \(0.385302\pi\) | |||||||
\(332\) | 3.53590 | + | 3.53590i | 0.194058 | + | 0.194058i | ||||
\(333\) | −11.5377 | − | 5.80298i | −0.632263 | − | 0.318001i | ||||
\(334\) | −13.1635 | + | 4.27710i | −0.720277 | + | 0.234032i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.333751 | + | 0.168957i | 0.0182076 | + | 0.00921737i | ||||
\(337\) | 25.0858 | + | 12.7818i | 1.36651 | + | 0.696272i | 0.974646 | − | 0.223752i | \(-0.0718304\pi\) |
0.391864 | + | 0.920023i | \(0.371830\pi\) | |||||||
\(338\) | −9.61460 | − | 4.89888i | −0.522965 | − | 0.266464i | ||||
\(339\) | −16.9769 | − | 8.59436i | −0.922061 | − | 0.466782i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.1139 | − | 3.61113i | 0.601852 | − | 0.195554i | ||||
\(342\) | −1.29053 | − | 0.649081i | −0.0697838 | − | 0.0350983i | ||||
\(343\) | 2.13093 | + | 2.13093i | 0.115059 | + | 0.115059i | ||||
\(344\) | −3.11459 | + | 2.26288i | −0.167927 | + | 0.122006i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.734684 | + | 0.533779i | 0.0394969 | + | 0.0286962i | ||||
\(347\) | 3.02097 | + | 19.0736i | 0.162174 | + | 1.02393i | 0.925730 | + | 0.378185i | \(0.123452\pi\) |
−0.763556 | + | 0.645742i | \(0.776548\pi\) | |||||||
\(348\) | −15.4498 | + | 5.06463i | −0.828195 | + | 0.271493i | ||||
\(349\) | 14.4119i | 0.771451i | 0.922614 | + | 0.385725i | \(0.126049\pi\) | ||||
−0.922614 | + | 0.385725i | \(0.873951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.45226 | − | 6.90887i | 0.184268 | − | 0.368768i | ||||
\(352\) | −2.33240 | − | 4.57759i | −0.124317 | − | 0.243986i | ||||
\(353\) | −34.5802 | + | 5.47696i | −1.84052 | + | 0.291509i | −0.977068 | − | 0.212929i | \(-0.931700\pi\) |
−0.863448 | + | 0.504438i | \(0.831700\pi\) | |||||||
\(354\) | 6.12467 | + | 6.09273i | 0.325523 | + | 0.323825i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.43505 | − | 8.85709i | −0.341057 | − | 0.469425i | ||||
\(357\) | −1.47269 | + | 1.07586i | −0.0779430 | + | 0.0569408i | ||||
\(358\) | 11.7036 | + | 1.85367i | 0.618555 | + | 0.0979695i | ||||
\(359\) | 10.6846 | + | 32.8840i | 0.563914 | + | 1.73555i | 0.671156 | + | 0.741316i | \(0.265798\pi\) |
−0.107242 | + | 0.994233i | \(0.534202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.79967 | − | 17.8496i | 0.305246 | − | 0.939450i | ||||
\(362\) | −7.80442 | + | 15.3170i | −0.410191 | + | 0.805045i | ||||
\(363\) | −21.6124 | − | 15.6161i | −1.13436 | − | 0.819635i | ||||
\(364\) | 0.305307 | + | 0.0992002i | 0.0160024 | + | 0.00519950i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.75839 | + | 23.3346i | 0.196454 | + | 1.21972i | ||||
\(367\) | −0.505240 | + | 3.18996i | −0.0263733 | + | 0.166514i | −0.997360 | − | 0.0726205i | \(-0.976864\pi\) |
0.970986 | + | 0.239135i | \(0.0768638\pi\) | |||||||
\(368\) | −1.89068 | + | 1.89068i | −0.0985584 | + | 0.0985584i | ||||
\(369\) | −17.8358 | + | 5.89848i | −0.928495 | + | 0.307062i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.976440 | + | 1.34395i | −0.0506942 | + | 0.0697746i | ||||
\(372\) | −0.0102991 | − | 3.93971i | −0.000533985 | − | 0.204265i | ||||
\(373\) | −9.65408 | + | 4.91900i | −0.499869 | + | 0.254696i | −0.685698 | − | 0.727886i | \(-0.740503\pi\) |
0.185829 | + | 0.982582i | \(0.440503\pi\) | |||||||
\(374\) | 25.0479 | 1.29519 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1521 | −0.523554 | ||||||||
\(377\) | −12.4317 | + | 6.33429i | −0.640268 | + | 0.326233i | ||||
\(378\) | 0.338411 | − | 1.07000i | 0.0174060 | − | 0.0550350i | ||||
\(379\) | 19.6854 | − | 27.0946i | 1.01117 | − | 1.39176i | 0.0929573 | − | 0.995670i | \(-0.470368\pi\) |
0.918213 | − | 0.396087i | \(-0.129632\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.8846 | − | 23.1749i | −0.608867 | − | 1.18729i | ||||
\(382\) | −3.49555 | + | 3.49555i | −0.178848 | + | 0.178848i | ||||
\(383\) | −2.54182 | + | 16.0484i | −0.129881 | + | 0.820034i | 0.833622 | + | 0.552335i | \(0.186263\pi\) |
−0.963503 | + | 0.267699i | \(0.913737\pi\) | |||||||
\(384\) | −1.71001 | + | 0.275424i | −0.0872637 | + | 0.0140552i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.20588 | + | 1.04165i | 0.163175 | + | 0.0530187i | ||||
\(387\) | 8.20933 | + | 8.12394i | 0.417304 | + | 0.412963i | ||||
\(388\) | 4.58178 | − | 8.99225i | 0.232605 | − | 0.456512i | ||||
\(389\) | 0.804900 | − | 2.47723i | 0.0408101 | − | 0.125600i | −0.928576 | − | 0.371143i | \(-0.878966\pi\) |
0.969386 | + | 0.245542i | \(0.0789660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.02838 | − | 12.3981i | −0.203724 | − | 0.626998i | ||||
\(392\) | −6.86775 | − | 1.08774i | −0.346874 | − | 0.0549394i | ||||
\(393\) | −8.91510 | − | 12.2034i | −0.449707 | − | 0.615578i | ||||
\(394\) | 4.30947 | + | 5.93148i | 0.217108 | + | 0.298824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.4215 | + | 9.12439i | −0.624206 | + | 0.458518i | ||||
\(397\) | −1.86357 | + | 0.295160i | −0.0935298 | + | 0.0148137i | −0.203024 | − | 0.979174i | \(-0.565077\pi\) |
0.109494 | + | 0.993987i | \(0.465077\pi\) | |||||||
\(398\) | 3.78711 | + | 7.43262i | 0.189831 | + | 0.372563i | ||||
\(399\) | −0.177984 | − | 0.0277131i | −0.00891032 | − | 0.00138739i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.16880i | 0.357993i | 0.983850 | + | 0.178996i | \(0.0572850\pi\) | ||||
−0.983850 | + | 0.178996i | \(0.942715\pi\) | |||||||
\(402\) | 8.10681 | + | 24.7300i | 0.404331 | + | 1.23342i | ||||
\(403\) | −0.528887 | − | 3.33926i | −0.0263458 | − | 0.166341i | ||||
\(404\) | 7.71559 | + | 5.60571i | 0.383865 | + | 0.278894i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.64017 | + | 1.19165i | −0.0814002 | + | 0.0591407i | ||||
\(407\) | 15.6390 | + | 15.6390i | 0.775197 | + | 0.775197i | ||||
\(408\) | 2.58850 | − | 8.03803i | 0.128150 | − | 0.397942i | ||||
\(409\) | 15.2838 | − | 4.96600i | 0.755734 | − | 0.245553i | 0.0942874 | − | 0.995545i | \(-0.469943\pi\) |
0.661447 | + | 0.749992i | \(0.269943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.20874 | + | 4.36305i | −0.108949 | + | 0.215214i | ||||
\(412\) | −9.01147 | − | 4.59157i | −0.443963 | − | 0.226211i | ||||
\(413\) | 0.959822 | + | 0.489054i | 0.0472297 | + | 0.0240648i | ||||
\(414\) | 6.51407 | + | 4.68091i | 0.320149 | + | 0.230054i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.41362 | + | 0.459312i | −0.0693083 | + | 0.0225196i | ||||
\(417\) | 11.4761 | + | 3.69568i | 0.561988 | + | 0.180978i | ||||
\(418\) | 1.74927 | + | 1.74927i | 0.0855596 | + | 0.0855596i | ||||
\(419\) | −1.81333 | + | 1.31746i | −0.0885872 | + | 0.0643624i | −0.631197 | − | 0.775622i | \(-0.717436\pi\) |
0.542610 | + | 0.839985i | \(0.317436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.09500 | + | 1.52210i | 0.102104 | + | 0.0741828i | 0.637666 | − | 0.770313i | \(-0.279900\pi\) |
−0.535562 | + | 0.844496i | \(0.679900\pi\) | |||||||
\(422\) | 0.670692 | + | 4.23458i | 0.0326488 | + | 0.206136i | ||||
\(423\) | 4.92162 | + | 30.0560i | 0.239297 | + | 1.46137i | ||||
\(424\) | − | 7.69169i | − | 0.373542i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.23292 | − | 20.7630i | 0.156636 | − | 1.00597i | ||||
\(427\) | 1.33799 | + | 2.62595i | 0.0647498 | + | 0.127079i | ||||
\(428\) | −10.9072 | + | 1.72754i | −0.527222 | + | 0.0835037i | ||||
\(429\) | −9.32799 | + | 9.37689i | −0.450360 | + | 0.452721i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.661426 | + | 0.910375i | 0.0318598 | + | 0.0438512i | 0.824650 | − | 0.565644i | \(-0.191372\pi\) |
−0.792790 | + | 0.609495i | \(0.791372\pi\) | |||||||
\(432\) | 1.64441 | + | 4.92909i | 0.0791165 | + | 0.237151i | ||||
\(433\) | −20.2750 | − | 3.21125i | −0.974355 | − | 0.154323i | −0.351097 | − | 0.936339i | \(-0.614191\pi\) |
−0.623258 | + | 0.782016i | \(0.714191\pi\) | |||||||
\(434\) | −0.151807 | − | 0.467215i | −0.00728698 | − | 0.0224270i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.89491 | + | 5.83194i | −0.0907498 | + | 0.279299i | ||||
\(437\) | 0.584515 | − | 1.14718i | 0.0279611 | − | 0.0548768i | ||||
\(438\) | −9.52020 | + | 13.1757i | −0.454893 | + | 0.629561i | ||||
\(439\) | 22.3736 | + | 7.26963i | 1.06783 | + | 0.346960i | 0.789644 | − | 0.613565i | \(-0.210265\pi\) |
0.278191 | + | 0.960526i | \(0.410265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.109063 | + | 20.8598i | 0.00519350 | + | 0.993323i | ||||
\(442\) | 1.13363 | − | 7.15749i | 0.0539215 | − | 0.340447i | ||||
\(443\) | −13.6168 | + | 13.6168i | −0.646952 | + | 0.646952i | −0.952255 | − | 0.305303i | \(-0.901242\pi\) |
0.305303 | + | 0.952255i | \(0.401242\pi\) | |||||||
\(444\) | 6.63483 | − | 3.40249i | 0.314875 | − | 0.161475i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.429625 | − | 0.591328i | 0.0203433 | − | 0.0280002i | ||||
\(447\) | 13.3776 | − | 0.0349716i | 0.632740 | − | 0.00165410i | ||||
\(448\) | −0.192436 | + | 0.0980509i | −0.00909173 | + | 0.00463247i | ||||
\(449\) | −19.2184 | −0.906973 | −0.453487 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453487 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.1710 | 1.51487 | ||||||||
\(452\) | 9.78864 | − | 4.98756i | 0.460419 | − | 0.234595i | ||||
\(453\) | 25.6114 | − | 0.0669530i | 1.20333 | − | 0.00314573i | ||||
\(454\) | 1.94595 | − | 2.67837i | 0.0913281 | − | 0.125702i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.742126 | − | 0.380579i | 0.0347532 | − | 0.0178222i | ||||
\(457\) | −15.9563 | + | 15.9563i | −0.746405 | + | 0.746405i | −0.973802 | − | 0.227397i | \(-0.926979\pi\) |
0.227397 | + | 0.973802i | \(0.426979\pi\) | |||||||
\(458\) | 1.65068 | − | 10.4220i | 0.0771311 | − | 0.486986i | ||||
\(459\) | −25.0520 | − | 3.76670i | −1.16933 | − | 0.175814i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2184 | − | 4.94475i | −0.708790 | − | 0.230300i | −0.0676337 | − | 0.997710i | \(-0.521545\pi\) |
−0.641156 | + | 0.767410i | \(0.721545\pi\) | |||||||
\(462\) | −1.12557 | + | 1.55776i | −0.0523663 | + | 0.0724737i | ||||
\(463\) | 2.81092 | − | 5.51675i | 0.130635 | − | 0.256385i | −0.816419 | − | 0.577460i | \(-0.804044\pi\) |
0.947054 | + | 0.321075i | \(0.104044\pi\) | |||||||
\(464\) | 2.90074 | − | 8.92755i | 0.134663 | − | 0.414451i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.89021 | − | 11.9728i | −0.180210 | − | 0.554630i | ||||
\(467\) | 22.9270 | + | 3.63127i | 1.06093 | + | 0.168035i | 0.662424 | − | 0.749129i | \(-0.269528\pi\) |
0.398509 | + | 0.917164i | \(0.369528\pi\) | |||||||
\(468\) | 2.04513 | + | 3.96244i | 0.0945362 | + | 0.183164i | ||||
\(469\) | 1.90744 | + | 2.62537i | 0.0880775 | + | 0.121228i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0291 | + | 20.1340i | −0.922890 | + | 0.927728i | ||||
\(472\) | −4.92635 | + | 0.780256i | −0.226753 | + | 0.0359142i | ||||
\(473\) | −8.97936 | − | 17.6230i | −0.412871 | − | 0.810305i | ||||
\(474\) | −0.582577 | + | 3.74153i | −0.0267587 | + | 0.171854i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1.05298i | − | 0.0482633i | ||||||
\(477\) | −22.7718 | + | 3.72885i | −1.04265 | + | 0.170732i | ||||
\(478\) | −1.83738 | − | 11.6007i | −0.0840396 | − | 0.530605i | ||||
\(479\) | 18.1330 | + | 13.1744i | 0.828519 | + | 0.601954i | 0.919140 | − | 0.393931i | \(-0.128885\pi\) |
−0.0906212 | + | 0.995885i | \(0.528885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17668 | − | 3.76108i | 0.236036 | − | 0.171491i | ||||
\(482\) | −0.860035 | − | 0.860035i | −0.0391735 | − | 0.0391735i | ||||
\(483\) | 0.952076 | + | 0.306599i | 0.0433210 | + | 0.0139507i | ||||
\(484\) | 14.6409 | − | 4.75712i | 0.665496 | − | 0.216233i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.7957 | − | 7.25795i | 0.625787 | − | 0.329227i | ||||
\(487\) | −18.8976 | − | 9.62881i | −0.856332 | − | 0.436323i | −0.0300294 | − | 0.999549i | \(-0.509560\pi\) |
−0.826303 | + | 0.563226i | \(0.809560\pi\) | |||||||
\(488\) | −12.1585 | − | 6.19509i | −0.550391 | − | 0.280438i | ||||
\(489\) | −3.17432 | + | 6.27042i | −0.143548 | + | 0.283558i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.6177 | − | 9.62339i | 1.33663 | − | 0.434297i | 0.448456 | − | 0.893805i | \(-0.351974\pi\) |
0.888174 | + | 0.459507i | \(0.151974\pi\) | |||||||
\(492\) | 3.32462 | − | 10.3239i | 0.149886 | − | 0.465437i | ||||
\(493\) | 32.3613 | + | 32.3613i | 1.45748 | + | 1.45748i | ||||
\(494\) | 0.579028 | − | 0.420688i | 0.0260517 | − | 0.0189277i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.84019 | + | 1.33698i | 0.0826270 | + | 0.0600320i | ||||
\(497\) | −0.409892 | − | 2.58795i | −0.0183862 | − | 0.116086i | ||||
\(498\) | 2.69796 | + | 8.23021i | 0.120899 | + | 0.368805i | ||||
\(499\) | 1.25659i | 0.0562528i | 0.999604 | + | 0.0281264i | \(0.00895410\pi\) | ||||
−0.999604 | + | 0.0281264i | \(0.991046\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.6878 | − | 3.68833i | −1.05829 | − | 0.164783i | ||||
\(502\) | −10.2658 | − | 20.1477i | −0.458184 | − | 0.899236i | ||||
\(503\) | 25.9752 | − | 4.11407i | 1.15818 | − | 0.183437i | 0.452363 | − | 0.891834i | \(-0.350581\pi\) |
0.705815 | + | 0.708397i | \(0.250581\pi\) | |||||||
\(504\) | 0.383577 | + | 0.522186i | 0.0170859 | + | 0.0232600i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.07434 | − | 11.1134i | −0.358948 | − | 0.494050i | ||||
\(507\) | −11.0252 | − | 15.0918i | −0.489648 | − | 0.670251i | ||||
\(508\) | 14.8517 | + | 2.35228i | 0.658938 | + | 0.104366i | ||||
\(509\) | 5.31690 | + | 16.3637i | 0.235668 | + | 0.725310i | 0.997032 | + | 0.0769863i | \(0.0245298\pi\) |
−0.761365 | + | 0.648324i | \(0.775470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.626355 | + | 1.92772i | −0.0277083 | + | 0.0852775i | ||||
\(512\) | 0.453990 | − | 0.891007i | 0.0200637 | − | 0.0393773i | ||||
\(513\) | −1.48651 | − | 2.01262i | −0.0656308 | − | 0.0888591i | ||||
\(514\) | −4.01395 | − | 1.30421i | −0.177048 | − | 0.0575263i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.58328 | + | 1.06034i | −0.289813 | + | 0.0466788i | ||||
\(517\) | 8.15912 | − | 51.5147i | 0.358838 | − | 2.26561i | ||||
\(518\) | 0.657443 | − | 0.657443i | 0.0288864 | − | 0.0288864i | ||||
\(519\) | 0.717747 | + | 1.39960i | 0.0315056 | + | 0.0614357i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.91212 | + | 10.8901i | −0.346636 | + | 0.477104i | −0.946365 | − | 0.323099i | \(-0.895275\pi\) |
0.599729 | + | 0.800203i | \(0.295275\pi\) | |||||||
\(522\) | −27.8369 | − | 4.25986i | −1.21839 | − | 0.186449i | ||||
\(523\) | 22.9585 | − | 11.6979i | 1.00390 | − | 0.511514i | 0.126858 | − | 0.991921i | \(-0.459511\pi\) |
0.877046 | + | 0.480407i | \(0.159511\pi\) | |||||||
\(524\) | 8.72546 | 0.381174 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.57177 | 0.112134 | ||||||||
\(527\) | −9.88101 | + | 5.03463i | −0.430424 | + | 0.219312i | ||||
\(528\) | −0.0232622 | − | 8.89846i | −0.00101236 | − | 0.387256i | ||||
\(529\) | 9.31679 | − | 12.8235i | 0.405078 | − | 0.557542i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.69824 | + | 14.2065i | 0.203886 | + | 0.616511i | ||||
\(532\) | 0.0735370 | − | 0.0735370i | 0.00318823 | − | 0.00318823i | ||||
\(533\) | 1.45602 | − | 9.19295i | 0.0630672 | − | 0.398191i | ||||
\(534\) | −3.01533 | − | 18.7212i | −0.130486 | − | 0.810144i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.2901 | − | 4.64313i | −0.617237 | − | 0.200553i | ||||
\(537\) | 16.6357 | + | 12.0202i | 0.717883 | + | 0.518711i | ||||
\(538\) | −10.9703 | + | 21.5305i | −0.472965 | + | 0.928246i | ||||
\(539\) | 11.0391 | − | 33.9747i | 0.475486 | − | 1.46340i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.47364 | − | 19.9238i | −0.278323 | − | 0.856591i | −0.988321 | − | 0.152387i | \(-0.951304\pi\) |
0.709998 | − | 0.704204i | \(-0.248696\pi\) | |||||||
\(542\) | 11.4328 | + | 1.81078i | 0.491082 | + | 0.0777797i | ||||
\(543\) | −24.0428 | + | 17.5643i | −1.03177 | + | 0.753757i | ||||
\(544\) | 2.86572 | + | 3.94433i | 0.122867 | + | 0.169112i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.394192 | + | 0.392137i | 0.0168699 | + | 0.0167819i | ||||
\(547\) | −43.0967 | + | 6.82585i | −1.84268 | + | 0.291852i | −0.977709 | − | 0.209965i | \(-0.932665\pi\) |
−0.864974 | + | 0.501817i | \(0.832665\pi\) | |||||||
\(548\) | −1.28180 | − | 2.51567i | −0.0547557 | − | 0.107464i | ||||
\(549\) | −12.4467 | + | 38.9995i | −0.531211 | + | 1.66446i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.52004i | 0.192560i | ||||||||
\(552\) | −4.40077 | + | 1.44263i | −0.187309 | + | 0.0614023i | ||||
\(553\) | 0.0738630 | + | 0.466353i | 0.00314098 | + | 0.0198313i | ||||
\(554\) | 6.09674 | + | 4.42954i | 0.259025 | + | 0.188193i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.63143 | + | 4.09147i | −0.238826 | + | 0.173517i | ||||
\(557\) | −20.7979 | − | 20.7979i | −0.881236 | − | 0.881236i | 0.112424 | − | 0.993660i | \(-0.464139\pi\) |
−0.993660 | + | 0.112424i | \(0.964139\pi\) | |||||||
\(558\) | 3.06611 | − | 6.09617i | 0.129799 | − | 0.258071i | ||||
\(559\) | −5.44220 | + | 1.76828i | −0.230181 | + | 0.0747902i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.7070 | + | 19.5949i | 1.63421 | + | 0.827297i | ||||
\(562\) | 21.0388 | + | 10.7198i | 0.887467 | + | 0.452187i | ||||
\(563\) | 14.0139 | + | 7.14045i | 0.590616 | + | 0.300934i | 0.723639 | − | 0.690179i | \(-0.242468\pi\) |
−0.133022 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(564\) | −15.6882 | − | 7.94195i | −0.660593 | − | 0.334417i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.36284 | − | 3.04217i | 0.393550 | − | 0.127872i | ||||
\(567\) | 1.36001 | − | 1.38876i | 0.0571152 | − | 0.0583223i | ||||
\(568\) | 8.57861 | + | 8.57861i | 0.359950 | + | 0.359950i | ||||
\(569\) | 3.20445 | − | 2.32817i | 0.134338 | − | 0.0976021i | −0.518587 | − | 0.855025i | \(-0.673542\pi\) |
0.652925 | + | 0.757423i | \(0.273542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7943 | − | 23.0999i | −1.33055 | − | 0.966702i | −0.999735 | − | 0.0230060i | \(-0.992676\pi\) |
−0.330815 | − | 0.943696i | \(-0.607324\pi\) | |||||||
\(572\) | −1.19457 | − | 7.54225i | −0.0499477 | − | 0.315357i | ||||
\(573\) | −8.13631 | + | 2.66718i | −0.339899 | + | 0.111423i | ||||
\(574\) | − | 1.35243i | − | 0.0564492i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85798 | − | 0.912121i | −0.119082 | − | 0.0380050i | ||||
\(577\) | 8.56788 | + | 16.8154i | 0.356685 | + | 0.700034i | 0.997721 | − | 0.0674769i | \(-0.0214949\pi\) |
−0.641036 | + | 0.767511i | \(0.721495\pi\) | |||||||
\(578\) | −6.68673 | + | 1.05907i | −0.278131 | + | 0.0440517i | ||||
\(579\) | 4.13922 | + | 4.11763i | 0.172020 | + | 0.171123i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.634802 | + | 0.873729i | 0.0263360 | + | 0.0362484i | ||||
\(582\) | 14.1149 | − | 10.3116i | 0.585083 | − | 0.427429i | ||||
\(583\) | 39.0299 | + | 6.18173i | 1.61645 | + | 0.256021i | ||||
\(584\) | −2.90012 | − | 8.92565i | −0.120008 | − | 0.369346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.45939 | − | 4.49153i | 0.0602867 | − | 0.185543i | ||||
\(587\) | 2.11434 | − | 4.14963i | 0.0872683 | − | 0.171274i | −0.843247 | − | 0.537526i | \(-0.819359\pi\) |
0.930516 | + | 0.366252i | \(0.119359\pi\) | |||||||
\(588\) | −9.76192 | − | 7.05353i | −0.402575 | − | 0.290883i | ||||
\(589\) | −1.04166 | − | 0.338457i | −0.0429210 | − | 0.0139459i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.01933 | + | 12.5373i | 0.0830640 | + | 0.515716i | ||||
\(592\) | −0.673443 | + | 4.25195i | −0.0276783 | + | 0.174754i | ||||
\(593\) | 32.4687 | − | 32.4687i | 1.33333 | − | 1.33333i | 0.430960 | − | 0.902371i | \(-0.358175\pi\) |
0.902371 | − | 0.430960i | \(-0.141825\pi\) | |||||||
\(594\) | −26.3332 | + | 4.38274i | −1.08047 | + | 0.179826i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.53982 | + | 6.24853i | −0.185958 | + | 0.255950i | ||||
\(597\) | 0.0377708 | + | 14.4484i | 0.00154586 | + | 0.591334i | ||||
\(598\) | −3.54111 | + | 1.80428i | −0.144807 | + | 0.0737826i | ||||
\(599\) | −18.2921 | −0.747393 | −0.373697 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373697 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.981781 | −0.0400477 | −0.0200238 | − | 0.999800i | \(-0.506374\pi\) | ||||
−0.0200238 | + | 0.999800i | \(0.506374\pi\) | |||||||
\(602\) | −0.740847 | + | 0.377480i | −0.0301947 | + | 0.0153850i | ||||
\(603\) | −6.81864 | + | 44.5577i | −0.277676 | + | 1.81453i | ||||
\(604\) | −8.69147 | + | 11.9628i | −0.353651 | + | 0.486759i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.53772 | + | 14.6985i | 0.306199 | + | 0.597086i | ||||
\(607\) | 2.39455 | − | 2.39455i | 0.0971917 | − | 0.0971917i | −0.656839 | − | 0.754031i | \(-0.728107\pi\) |
0.754031 | + | 0.656839i | \(0.228107\pi\) | |||||||
\(608\) | −0.0753267 | + | 0.475594i | −0.00305490 | + | 0.0192879i | ||||
\(609\) | −3.46681 | + | 0.558383i | −0.140482 | + | 0.0226268i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.3512 | − | 4.66298i | −0.580586 | − | 0.188644i | ||||
\(612\) | 10.2882 | − | 10.3963i | 0.415875 | − | 0.420247i | ||||
\(613\) | −6.24017 | + | 12.2470i | −0.252038 | + | 0.494653i | −0.982011 | − | 0.188823i | \(-0.939533\pi\) |
0.729973 | + | 0.683476i | \(0.239533\pi\) | |||||||
\(614\) | −5.16261 | + | 15.8889i | −0.208346 | + | 0.641223i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.342880 | − | 1.05528i | −0.0138150 | − | 0.0425183i | ||||
\(617\) | −10.1292 | − | 1.60431i | −0.407787 | − | 0.0645872i | −0.0508287 | − | 0.998707i | \(-0.516186\pi\) |
−0.356959 | + | 0.934120i | \(0.616186\pi\) | |||||||
\(618\) | −10.3336 | − | 14.1451i | −0.415679 | − | 0.568999i | ||||
\(619\) | 27.3325 | + | 37.6199i | 1.09859 | + | 1.51207i | 0.837247 | + | 0.546825i | \(0.184164\pi\) |
0.261338 | + | 0.965247i | \(0.415836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.40445 | + | 12.3294i | 0.257002 | + | 0.494763i | ||||
\(622\) | 29.8303 | − | 4.72465i | 1.19608 | − | 0.189441i | ||||
\(623\) | −1.07346 | − | 2.10678i | −0.0430072 | − | 0.0844063i | ||||
\(624\) | −2.54381 | − | 0.396086i | −0.101834 | − | 0.0158561i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.6805i | 0.666686i | ||||||||
\(627\) | 1.33473 | + | 4.07163i | 0.0533040 | + | 0.162605i | ||||
\(628\) | −2.56499 | − | 16.1947i | −0.102354 | − | 0.646239i | ||||
\(629\) | −16.9802 | − | 12.3368i | −0.677043 | − | 0.491900i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.6748 | + | 15.0211i | −0.823051 | + | 0.597981i | −0.917585 | − | 0.397540i | \(-0.869864\pi\) |
0.0945340 | + | 0.995522i | \(0.469864\pi\) | |||||||
\(632\) | −1.54588 | − | 1.54588i | −0.0614917 | − | 0.0614917i | ||||
\(633\) | −2.27627 | + | 7.06846i | −0.0904736 | + | 0.280946i | ||||
\(634\) | 10.3155 | − | 3.35172i | 0.409683 | − | 0.133114i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.01719 | − | 11.8861i | 0.238597 | − | 0.471315i | ||||
\(637\) | −9.20875 | − | 4.69209i | −0.364864 | − | 0.185907i | ||||
\(638\) | 42.9697 | + | 21.8942i | 1.70119 | + | 0.866798i | ||||
\(639\) | 21.2388 | − | 29.5564i | 0.840193 | − | 1.16923i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.702023 | + | 0.228101i | −0.0277282 | + | 0.00900945i | −0.322848 | − | 0.946451i | \(-0.604640\pi\) |
0.295120 | + | 0.955460i | \(0.404640\pi\) | |||||||
\(642\) | −18.2066 | − | 5.86312i | −0.718558 | − | 0.231399i | ||||
\(643\) | −17.1573 | − | 17.1573i | −0.676616 | − | 0.676616i | 0.282617 | − | 0.959233i | \(-0.408797\pi\) |
−0.959233 | + | 0.282617i | \(0.908797\pi\) | |||||||
\(644\) | −0.467192 | + | 0.339435i | −0.0184099 | + | 0.0133756i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.89928 | − | 1.37991i | −0.0747262 | − | 0.0542918i | ||||
\(647\) | −0.943217 | − | 5.95524i | −0.0370817 | − | 0.234125i | 0.962186 | − | 0.272394i | \(-0.0878154\pi\) |
−0.999267 | + | 0.0382696i | \(0.987815\pi\) | |||||||
\(648\) | −1.31488 | + | 8.90343i | −0.0516535 | + | 0.349760i | ||||
\(649\) | − | 25.6248i | − | 1.00586i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.130910 | − | 0.840754i | 0.00513078 | − | 0.0329517i | ||||
\(652\) | −1.84215 | − | 3.61543i | −0.0721443 | − | 0.141591i | ||||
\(653\) | −9.97451 | + | 1.57981i | −0.390333 | + | 0.0618226i | −0.348516 | − | 0.937303i | \(-0.613314\pi\) |
−0.0418163 | + | 0.999125i | \(0.513314\pi\) | |||||||
\(654\) | −7.49055 | + | 7.52982i | −0.292904 | + | 0.294439i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.68068 | + | 5.06602i | 0.143706 | + | 0.197795i | ||||
\(657\) | −25.0191 | + | 12.9131i | −0.976087 | + | 0.503787i | ||||
\(658\) | −2.16561 | − | 0.342999i | −0.0844242 | − | 0.0133715i | ||||
\(659\) | −3.59331 | − | 11.0591i | −0.139975 | − | 0.430800i | 0.856355 | − | 0.516387i | \(-0.172723\pi\) |
−0.996331 | + | 0.0855871i | \(0.972723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8291 | − | 39.4838i | 0.498993 | − | 1.53574i | −0.311648 | − | 0.950197i | \(-0.600881\pi\) |
0.810641 | − | 0.585544i | \(-0.199119\pi\) | |||||||
\(662\) | 4.37411 | − | 8.58467i | 0.170005 | − | 0.333653i | ||||
\(663\) | 7.35111 | − | 10.1738i | 0.285494 | − | 0.395116i | ||||
\(664\) | −4.75577 | − | 1.54524i | −0.184560 | − | 0.0599671i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.9147 | − | 0.0675232i | 0.500434 | − | 0.00261647i | ||||
\(667\) | 3.92637 | − | 24.7901i | 0.152030 | − | 0.959877i | ||||
\(668\) | 9.78704 | − | 9.78704i | 0.378672 | − | 0.378672i | ||||
\(669\) | 1.12650 | − | 0.577696i | 0.0435531 | − | 0.0223350i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.2074 | − | 56.7171i | 1.59079 | − | 2.18954i | ||||
\(672\) | −0.374079 | 0.000977913i | −0.0144304 | 3.77238e-5i | ||||||
\(673\) | 23.9046 | − | 12.1800i | 0.921454 | − | 0.469504i | 0.0721411 | − | 0.997394i | \(-0.477017\pi\) |
0.849313 | + | 0.527890i | \(0.177017\pi\) | |||||||
\(674\) | −28.1544 | −1.08447 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.7907 | 0.415028 | ||||||||
\(677\) | 19.6621 | − | 10.0184i | 0.755677 | − | 0.385037i | −0.0333112 | − | 0.999445i | \(-0.510605\pi\) |
0.788988 | + | 0.614408i | \(0.210605\pi\) | |||||||
\(678\) | 19.0283 | − | 0.0497436i | 0.730779 | − | 0.00191039i | ||||
\(679\) | 1.28118 | − | 1.76340i | 0.0491673 | − | 0.0676729i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.10240 | − | 2.61663i | 0.195524 | − | 0.100269i | ||||
\(682\) | −8.26315 | + | 8.26315i | −0.316413 | + | 0.316413i | ||||
\(683\) | 3.06282 | − | 19.3379i | 0.117196 | − | 0.739944i | −0.857180 | − | 0.515017i | \(-0.827786\pi\) |
0.974376 | − | 0.224927i | \(-0.0722144\pi\) | |||||||
\(684\) | 1.44455 | − | 0.00755268i | 0.0552336 | − | 0.000288784i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.86609 | − | 0.931249i | −0.109428 | − | 0.0355552i | ||||
\(687\) | 10.7039 | − | 14.8139i | 0.408379 | − | 0.565187i | ||||
\(688\) | 1.74779 | − | 3.43023i | 0.0666339 | − | 0.130776i | ||||
\(689\) | 3.53289 | − | 10.8731i | 0.134592 | − | 0.414232i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6136 | + | 38.8206i | 0.479843 | + | 1.47681i | 0.839313 | + | 0.543649i | \(0.182958\pi\) |
−0.359469 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(692\) | −0.896939 | − | 0.142061i | −0.0340965 | − | 0.00540036i | ||||
\(693\) | −2.95800 | + | 1.52671i | −0.112365 | + | 0.0579949i | ||||
\(694\) | −11.3510 | − | 15.6232i | −0.430876 | − | 0.593050i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.4666 | − | 11.5267i | 0.434639 | − | 0.436917i | ||||
\(697\) | −30.1540 | + | 4.77592i | −1.14216 | + | 0.180901i | ||||
\(698\) | −6.54286 | − | 12.8411i | −0.247651 | − | 0.486042i | ||||
\(699\) | 3.35470 | − | 21.5451i | 0.126886 | − | 0.814912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.34594i | 0.0508356i | 0.999677 | + | 0.0254178i | \(0.00809161\pi\) | ||||
−0.999677 | + | 0.0254178i | \(0.991908\pi\) | |||||||
\(702\) | 0.0605703 | + | 7.72314i | 0.00228608 | + | 0.291491i | ||||
\(703\) | −0.324278 | − | 2.04741i | −0.0122304 | − | 0.0772195i | ||||
\(704\) | 4.15636 | + | 3.01977i | 0.156649 | + | 0.113812i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.3247 | − | 20.5791i | 1.06601 | − | 0.774503i | ||||
\(707\) | 1.45647 | + | 1.45647i | 0.0547762 | + | 0.0547762i | ||||
\(708\) | −8.22317 | − | 2.64812i | −0.309046 | − | 0.0995225i | ||||
\(709\) | −5.99345 | + | 1.94739i | −0.225089 | + | 0.0731358i | −0.419390 | − | 0.907806i | \(-0.637756\pi\) |
0.194301 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.82725 | + | 5.32610i | −0.143533 | + | 0.199744i | ||||
\(712\) | 9.75471 | + | 4.97027i | 0.365573 | + | 0.186269i | ||||
\(713\) | 5.41900 | + | 2.76112i | 0.202943 | + | 0.103405i | ||||
\(714\) | 0.823744 | − | 1.62719i | 0.0308278 | − | 0.0608960i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.2695 | + | 3.66170i | −0.421163 | + | 0.136844i | ||||
\(717\) | 6.23589 | − | 19.3642i | 0.232884 | − | 0.723170i | ||||
\(718\) | −24.4491 | − | 24.4491i | −0.912432 | − | 0.912432i | ||||
\(719\) | −15.2779 | + | 11.1001i | −0.569770 | + | 0.413962i | −0.835022 | − | 0.550217i | \(-0.814545\pi\) |
0.265251 | + | 0.964179i | \(0.414545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.76717 | − | 1.28392i | −0.0658127 | − | 0.0478157i | ||||
\(722\) | 2.93598 | + | 18.5371i | 0.109266 | + | 0.689878i | ||||
\(723\) | −0.656225 | − | 2.00183i | −0.0244053 | − | 0.0744490i | ||||
\(724\) | − | 17.1907i | − | 0.638888i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.3463 | + | 4.10228i | 0.977805 | + | 0.152250i | ||||
\(727\) | 5.62601 | + | 11.0417i | 0.208657 | + | 0.409513i | 0.971489 | − | 0.237084i | \(-0.0761916\pi\) |
−0.762832 | + | 0.646597i | \(0.776192\pi\) | |||||||
\(728\) | −0.317066 | + | 0.0502184i | −0.0117513 | + | 0.00186122i | ||||
\(729\) | 26.9967 | − | 0.423480i | 0.999877 | − | 0.0156844i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.0326 | + | 15.1850i | 0.408055 | + | 0.561639i | ||||
\(732\) | −13.9424 | − | 19.0850i | −0.515327 | − | 0.705401i | ||||
\(733\) | −9.27418 | − | 1.46889i | −0.342550 | − | 0.0542545i | −0.0172103 | − | 0.999852i | \(-0.505478\pi\) |
−0.325339 | + | 0.945597i | \(0.605478\pi\) | |||||||
\(734\) | −0.998039 | − | 3.07165i | −0.0368383 | − | 0.113377i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.826257 | − | 2.54296i | 0.0304562 | − | 0.0937346i | ||||
\(737\) | 35.0454 | − | 68.7804i | 1.29091 | − | 2.53356i | ||||
\(738\) | 13.2140 | − | 13.3529i | 0.486413 | − | 0.491526i | ||||
\(739\) | −18.0916 | − | 5.87832i | −0.665511 | − | 0.216238i | −0.0432699 | − | 0.999063i | \(-0.513778\pi\) |
−0.622241 | + | 0.782826i | \(0.713778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.22389 | − | 0.197126i | 0.0449606 | − | 0.00724159i | ||||
\(742\) | 0.259872 | − | 1.64077i | 0.00954019 | − | 0.0602344i | ||||
\(743\) | 23.1938 | − | 23.1938i | 0.850899 | − | 0.850899i | −0.139345 | − | 0.990244i | \(-0.544500\pi\) |
0.990244 | + | 0.139345i | \(0.0444997\pi\) | |||||||
\(744\) | 1.79777 | + | 3.50563i | 0.0659094 | + | 0.128523i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.36867 | − | 8.76572i | 0.233174 | − | 0.320936i | ||||
\(747\) | −2.26926 | + | 14.8289i | −0.0830278 | + | 0.542562i | ||||
\(748\) | −22.3178 | + | 11.3715i | −0.816020 | + | 0.415783i | ||||
\(749\) | −2.38506 | −0.0871483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1267 | 1.28179 | 0.640895 | − | 0.767628i | \(-0.278563\pi\) | ||||
0.640895 | + | 0.767628i | \(0.278563\pi\) | |||||||
\(752\) | 9.04558 | − | 4.60895i | 0.329858 | − | 0.168071i | ||||
\(753\) | −0.102386 | − | 39.1655i | −0.00373115 | − | 1.42727i | ||||
\(754\) | 8.20106 | − | 11.2878i | 0.298665 | − | 0.411077i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.184245 | + | 1.10701i | 0.00670092 | + | 0.0402617i | ||||
\(757\) | −20.0652 | + | 20.0652i | −0.729283 | + | 0.729283i | −0.970477 | − | 0.241194i | \(-0.922461\pi\) |
0.241194 | + | 0.970477i | \(0.422461\pi\) | |||||||
\(758\) | −5.23911 | + | 33.0785i | −0.190293 | + | 1.20146i | ||||
\(759\) | −3.78346 | − | 23.4902i | −0.137331 | − | 0.852642i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.4666 | + | 9.89919i | 1.10441 | + | 0.358845i | 0.803799 | − | 0.594901i | \(-0.202809\pi\) |
0.300613 | + | 0.953746i | \(0.402809\pi\) | |||||||
\(762\) | 21.1104 | + | 15.2535i | 0.764751 | + | 0.552575i | ||||
\(763\) | −0.601254 | + | 1.18003i | −0.0217669 | + | 0.0427199i | ||||
\(764\) | 1.52761 | − | 4.70151i | 0.0552671 | − | 0.170095i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.02104 | − | 15.4532i | −0.181418 | − | 0.558346i | ||||
\(767\) | −7.32235 | − | 1.15975i | −0.264395 | − | 0.0418760i | ||||
\(768\) | 1.39859 | − | 1.02173i | 0.0504674 | − | 0.0368686i | ||||
\(769\) | −8.74366 | − | 12.0346i | −0.315305 | − | 0.433980i | 0.621722 | − | 0.783238i | \(-0.286433\pi\) |
−0.937026 | + | 0.349259i | \(0.886433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.18256 | − | 5.15553i | −0.186645 | − | 0.185672i | ||||
\(772\) | −3.32936 | + | 0.527318i | −0.119826 | + | 0.0189786i | ||||
\(773\) | −10.0990 | − | 19.8204i | −0.363235 | − | 0.712889i | 0.634985 | − | 0.772524i | \(-0.281006\pi\) |
−0.998220 | + | 0.0596354i | \(0.981006\pi\) | |||||||
\(774\) | −11.0028 | − | 3.51152i | −0.395486 | − | 0.126219i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0922i | 0.362290i | ||||||||
\(777\) | 1.53028 | − | 0.501643i | 0.0548983 | − | 0.0179964i | ||||
\(778\) | 0.407467 | + | 2.57264i | 0.0146084 | + | 0.0922337i | ||||
\(779\) | −2.43940 | − | 1.77233i | −0.0874006 | − | 0.0635003i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.4249 | + | 36.6358i | −1.80435 | + | 1.31093i | ||||
\(782\) | 9.21792 | + | 9.21792i | 0.329632 | + | 0.329632i | ||||
\(783\) | −39.6844 | − | 28.3596i | −1.41820 | − | 1.01349i | ||||
\(784\) | 6.61303 | − | 2.14870i | 0.236180 | − | 0.0767395i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.4836 | + | 6.82591i | 0.480945 | + | 0.243472i | ||||
\(787\) | 45.7145 | + | 23.2927i | 1.62955 | + | 0.830295i | 0.998512 | + | 0.0545406i | \(0.0173694\pi\) |
0.631035 | + | 0.775755i | \(0.282631\pi\) | |||||||
\(788\) | −6.53260 | − | 3.32853i | −0.232714 | − | 0.118574i | ||||
\(789\) | 3.97420 | + | 2.01189i | 0.141485 | + | 0.0716251i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.25659 | − | 0.733210i | 0.0802351 | − | 0.0260700i | ||||
\(792\) | 6.92529 | − | 13.7692i | 0.246080 | − | 0.489265i | ||||
\(793\) | −14.3420 | − | 14.3420i | −0.509301 | − | 0.509301i | ||||
\(794\) | 1.52645 | − | 1.10903i | 0.0541717 | − | 0.0393580i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.74867 | − | 4.90320i | −0.239200 | − | 0.173789i | ||||
\(797\) | 0.485494 | + | 3.06529i | 0.0171971 | + | 0.108578i | 0.994794 | − | 0.101909i | \(-0.0324950\pi\) |
−0.977597 | + | 0.210487i | \(0.932495\pi\) | |||||||
\(798\) | 0.171166 | − | 0.0561103i | 0.00605921 | − | 0.00198628i | ||||
\(799\) | 49.4961i | 1.75105i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.98587 | − | 31.2890i | 0.352833 | − | 1.10554i | ||||
\(802\) | −3.25457 | − | 6.38745i | −0.114923 | − | 0.225549i | ||||
\(803\) | 47.6222 | − | 7.54261i | 1.68055 | − | 0.266173i | ||||
\(804\) | −18.4504 | − | 18.3542i | −0.650696 | − | 0.647303i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.98724 | + | 2.73520i | 0.0699974 | + | 0.0963431i | ||||
\(807\) | −33.7959 | + | 24.6894i | −1.18967 | + | 0.869109i | ||||
\(808\) | −9.41958 | − | 1.49192i | −0.331380 | − | 0.0524854i | ||||
\(809\) | −4.71934 | − | 14.5246i | −0.165923 | − | 0.510659i | 0.833180 | − | 0.553002i | \(-0.186518\pi\) |
−0.999103 | + | 0.0423432i | \(0.986518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.02202 | − | 3.14544i | 0.0358879 | − | 0.110451i | −0.931508 | − | 0.363721i | \(-0.881506\pi\) |
0.967396 | + | 0.253270i | \(0.0815060\pi\) | |||||||
\(812\) | 0.920402 | − | 1.80639i | 0.0322998 | − | 0.0633919i | ||||
\(813\) | 16.2508 | + | 11.7421i | 0.569940 | + | 0.411814i | ||||
\(814\) | −21.0344 | − | 6.83450i | −0.737256 | − | 0.239549i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.34282 | + | 8.33709i | 0.0470080 | + | 0.291857i | ||||
\(817\) | −0.289996 | + | 1.83096i | −0.0101457 | + | 0.0640572i | ||||
\(818\) | −11.3634 | + | 11.3634i | −0.397313 | + | 0.397313i | ||||
\(819\) | 0.302385 | + | 0.914352i | 0.0105662 | + | 0.0319500i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.3359 | + | 25.2372i | −0.639927 | + | 0.880784i | −0.998612 | − | 0.0526750i | \(-0.983225\pi\) |
0.358685 | + | 0.933459i | \(0.383225\pi\) | |||||||
\(822\) | −0.0127840 | − | 4.89026i | −0.000445895 | − | 0.170567i | ||||
\(823\) | −13.9035 | + | 7.08420i | −0.484647 | + | 0.246940i | −0.679202 | − | 0.733952i | \(-0.737674\pi\) |
0.194555 | + | 0.980892i | \(0.437674\pi\) | |||||||
\(824\) | 10.1138 | 0.352331 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.07723 | −0.0374817 | ||||||||
\(827\) | 3.23908 | − | 1.65039i | 0.112634 | − | 0.0573898i | −0.396766 | − | 0.917920i | \(-0.629868\pi\) |
0.509400 | + | 0.860530i | \(0.329868\pi\) | |||||||
\(828\) | −7.92916 | − | 1.21339i | −0.275557 | − | 0.0421684i | ||||
\(829\) | −14.6691 | + | 20.1903i | −0.509480 | + | 0.701239i | −0.983832 | − | 0.179096i | \(-0.942683\pi\) |
0.474351 | + | 0.880336i | \(0.342683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.95618 | + | 11.6145i | 0.206618 | + | 0.402903i | ||||
\(832\) | 1.05102 | − | 1.05102i | 0.0364375 | − | 0.0364375i | ||||
\(833\) | −5.30325 | + | 33.4834i | −0.183747 | + | 1.16013i | ||||
\(834\) | −11.9031 | + | 1.91718i | −0.412171 | + | 0.0663864i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.35276 | − | 0.764459i | −0.0813720 | − | 0.0264394i | ||||
\(837\) | 9.50714 | − | 7.02191i | 0.328615 | − | 0.242713i | ||||
\(838\) | 1.01758 | − | 1.99711i | 0.0351516 | − | 0.0689889i | ||||
\(839\) | −5.55073 | + | 17.0834i | −0.191632 | + | 0.589784i | 0.808367 | + | 0.588679i | \(0.200352\pi\) |
−0.999999 | + | 0.00110507i | \(0.999648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.2677 | + | 56.2221i | 0.629920 | + | 1.93869i | ||||
\(842\) | −2.55767 | − | 0.405096i | −0.0881433 | − | 0.0139605i | ||||
\(843\) | 24.1255 | + | 33.0241i | 0.830928 | + | 1.13741i | ||||
\(844\) | −2.52005 | − | 3.46855i | −0.0867437 | − | 0.119392i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.0303 | − | 24.5457i | −0.619895 | − | 0.843899i | ||||
\(847\) | 3.28387 | − | 0.520114i | 0.112835 | − | 0.0178713i | ||||
\(848\) | 3.49196 | + | 6.85335i | 0.119914 | + | 0.235345i | ||||
\(849\) | 16.8485 | + | 2.62340i | 0.578238 | + | 0.0900350i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.5107i | 0.394581i | ||||||||
\(852\) | 6.54566 | + | 19.9677i | 0.224251 | + | 0.684083i | ||||
\(853\) | 4.94081 | + | 31.1950i | 0.169170 | + | 1.06810i | 0.915440 | + | 0.402454i | \(0.131843\pi\) |
−0.746270 | + | 0.665643i | \(0.768157\pi\) | |||||||
\(854\) | −2.38431 | − | 1.73230i | −0.0815894 | − | 0.0592782i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.93414 | − | 6.49104i | 0.305363 | − | 0.221859i | ||||
\(857\) | −8.57240 | − | 8.57240i | −0.292828 | − | 0.292828i | 0.545369 | − | 0.838196i | \(-0.316390\pi\) |
−0.838196 | + | 0.545369i | \(0.816390\pi\) | |||||||
\(858\) | 4.05428 | − | 12.5897i | 0.138411 | − | 0.429805i | ||||
\(859\) | 1.99366 | − | 0.647780i | 0.0680228 | − | 0.0221020i | −0.274808 | − | 0.961499i | \(-0.588614\pi\) |
0.342831 | + | 0.939397i | \(0.388614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.05800 | − | 2.08993i | 0.0360566 | − | 0.0712247i | ||||
\(862\) | −1.00264 | − | 0.510869i | −0.0341500 | − | 0.0174003i | ||||
\(863\) | −25.5918 | − | 13.0397i | −0.871155 | − | 0.443876i | −0.0395333 | − | 0.999218i | \(-0.512587\pi\) |
−0.831622 | + | 0.555343i | \(0.812587\pi\) | |||||||
\(864\) | −3.70294 | − | 3.64531i | −0.125976 | − | 0.124016i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.5231 | − | 6.34342i | 0.663420 | − | 0.215558i | ||||
\(867\) | −11.1616 | − | 3.59441i | −0.379069 | − | 0.122072i | ||||
\(868\) | 0.347372 | + | 0.347372i | 0.0117906 | + | 0.0117906i | ||||
\(869\) | 9.08664 | − | 6.60183i | 0.308243 | − | 0.223952i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0680 | − | 13.1272i | −0.612212 | − | 0.444798i | ||||
\(872\) | −0.959266 | − | 6.05656i | −0.0324848 | − | 0.205101i | ||||
\(873\) | 29.8788 | − | 4.89261i | 1.01124 | − | 0.165590i | ||||
\(874\) | 1.28751i | 0.0435505i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.50091 | − | 16.0617i | 0.0844978 | − | 0.542676i | ||||
\(877\) | −7.83550 | − | 15.3780i | −0.264586 | − | 0.519279i | 0.720045 | − | 0.693927i | \(-0.244121\pi\) |
−0.984631 | + | 0.174648i | \(0.944121\pi\) | |||||||
\(878\) | −23.2354 | + | 3.68012i | −0.784156 | + | 0.124198i | ||||
\(879\) | 5.76893 | − | 5.79917i | 0.194581 | − | 0.195601i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5046 | + | 15.8347i | 0.387600 | + | 0.533485i | 0.957578 | − | 0.288175i | \(-0.0930484\pi\) |
−0.569978 | + | 0.821660i | \(0.693048\pi\) | |||||||
\(882\) | −9.56732 | − | 18.5367i | −0.322148 | − | 0.624163i | ||||
\(883\) | −13.3245 | − | 2.11040i | −0.448406 | − | 0.0710206i | −0.0718524 | − | 0.997415i | \(-0.522891\pi\) |
−0.376554 | + | 0.926395i | \(0.622891\pi\) | |||||||
\(884\) | 2.23936 | + | 6.89203i | 0.0753177 | + | 0.231804i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.95075 | − | 18.3145i | 0.199919 | − | 0.615288i | ||||
\(887\) | −23.7996 | + | 46.7094i | −0.799114 | + | 1.56835i | 0.0234837 | + | 0.999724i | \(0.492524\pi\) |
−0.822597 | + | 0.568624i | \(0.807476\pi\) | |||||||
\(888\) | −4.36698 | + | 6.04379i | −0.146546 | + | 0.202816i | ||||
\(889\) | 3.08864 | + | 1.00356i | 0.103590 | + | 0.0336583i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.1219 | − | 13.8277i | −1.47814 | − | 0.463245i | ||||
\(892\) | −0.114341 | + | 0.721923i | −0.00382843 | + | 0.0241718i | ||||
\(893\) | −3.45666 | + | 3.45666i | −0.115673 | + | 0.115673i | ||||
\(894\) | −11.9037 | + | 6.10448i | −0.398119 | + | 0.204164i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.126947 | − | 0.174728i | 0.00424101 | − | 0.00583725i | ||||
\(897\) | −6.88362 | + | 0.0179951i | −0.229838 | + | 0.000600838i | ||||
\(898\) | 17.1237 | − | 8.72498i | 0.571426 | − | 0.291156i | ||||
\(899\) | −21.3516 | −0.712117 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.5005 | −1.24932 | ||||||||
\(902\) | −28.6646 | + | 14.6053i | −0.954427 | + | 0.486305i | ||||
\(903\) | −1.44015 | + | 0.00376481i | −0.0479251 | + | 0.000125285i | ||||
\(904\) | −6.45744 | + | 8.88790i | −0.214771 | + | 0.295607i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22.7896 | + | 11.6870i | −0.757132 | + | 0.388275i | ||||
\(907\) | −7.30011 | + | 7.30011i | −0.242396 | + | 0.242396i | −0.817841 | − | 0.575445i | \(-0.804829\pi\) |
0.575445 | + | 0.817841i | \(0.304829\pi\) | |||||||
\(908\) | −0.517900 | + | 3.26989i | −0.0171871 | + | 0.108515i | ||||
\(909\) | 0.149588 | + | 28.6106i | 0.00496152 | + | 0.948954i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.9954 | − | 8.77133i | −0.894397 | − | 0.290607i | −0.174474 | − | 0.984662i | \(-0.555823\pi\) |
−0.719922 | + | 0.694055i | \(0.755823\pi\) | |||||||
\(912\) | −0.488460 | + | 0.676016i | −0.0161745 | + | 0.0223851i | ||||
\(913\) | 11.6632 | − | 22.8903i | 0.385995 | − | 0.757557i | ||||
\(914\) | 6.97317 | − | 21.4612i | 0.230652 | − | 0.709874i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.26071 | + | 10.0354i | 0.107737 | + | 0.331580i | ||||
\(917\) | 1.86129 | + | 0.294799i | 0.0614651 | + | 0.00973511i | ||||
\(918\) | 24.0316 | − | 8.01723i | 0.793160 | − | 0.264608i | ||||
\(919\) | 4.27526 | + | 5.88440i | 0.141028 | + | 0.194108i | 0.873688 | − | 0.486486i | \(-0.161722\pi\) |
−0.732660 | + | 0.680594i | \(0.761722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.4077 | + | 20.5147i | −0.672457 | + | 0.675982i | ||||
\(922\) | 15.8045 | − | 2.50319i | 0.520494 | − | 0.0824382i | ||||
\(923\) | 8.18661 | + | 16.0671i | 0.269466 | + | 0.528856i | ||||
\(924\) | 0.295681 | − | 1.89897i | 0.00972720 | − | 0.0624717i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.19159i | 0.203468i | ||||||||
\(927\) | −4.90306 | − | 29.9427i | −0.161038 | − | 0.983446i | ||||
\(928\) | 1.46845 | + | 9.27141i | 0.0482041 | + | 0.304349i | ||||
\(929\) | −5.66314 | − | 4.11451i | −0.185802 | − | 0.134993i | 0.490996 | − | 0.871162i | \(-0.336633\pi\) |
−0.676798 | + | 0.736169i | \(0.736633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.70875 | + | 1.96802i | −0.0887756 | + | 0.0644992i | ||||
\(932\) | 8.90175 | + | 8.90175i | 0.291586 | + | 0.291586i | ||||
\(933\) | 49.7933 | + | 16.0350i | 1.63016 | + | 0.524964i | ||||
\(934\) | −22.0766 | + | 7.17313i | −0.722369 | + | 0.234712i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.62114 | − | 2.60209i | −0.118361 | − | 0.0850521i | ||||
\(937\) | 35.4943 | + | 18.0852i | 1.15955 | + | 0.590819i | 0.924506 | − | 0.381167i | \(-0.124478\pi\) |
0.235040 | + | 0.971986i | \(0.424478\pi\) | |||||||
\(938\) | −2.89144 | − | 1.47326i | −0.0944088 | − | 0.0481037i | ||||
\(939\) | −13.0491 | + | 25.7767i | −0.425841 | + | 0.841189i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.912873 | + | 0.296610i | −0.0297588 | + | 0.00966922i | −0.323859 | − | 0.946106i | \(-0.604980\pi\) |
0.294100 | + | 0.955775i | \(0.404980\pi\) | |||||||
\(942\) | 8.70535 | − | 27.0326i | 0.283636 | − | 0.880769i | ||||
\(943\) | 11.8393 | + | 11.8393i | 0.385542 | + | 0.385542i | ||||
\(944\) | 4.03518 | − | 2.93173i | 0.131334 | − | 0.0954196i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0013 | + | 11.6256i | 0.520248 | + | 0.377982i | ||||
\(947\) | −5.95470 | − | 37.5965i | −0.193502 | − | 1.22172i | −0.872880 | − | 0.487935i | \(-0.837750\pi\) |
0.679378 | − | 0.733788i | \(-0.262250\pi\) | |||||||
\(948\) | −1.17954 | − | 3.59821i | −0.0383096 | − | 0.116864i | ||||
\(949\) | − | 13.9495i | − | 0.452820i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.5629 | + | 2.89034i | 0.601942 | + | 0.0937258i | ||||
\(952\) | 0.478043 | + | 0.938212i | 0.0154935 | + | 0.0304076i | ||||
\(953\) | −56.6214 | + | 8.96795i | −1.83415 | + | 0.290500i | −0.975161 | − | 0.221499i | \(-0.928905\pi\) |
−0.858986 | + | 0.511999i | \(0.828905\pi\) | |||||||
\(954\) | 18.5970 | − | 13.6606i | 0.602099 | − | 0.442279i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.90374 | + | 9.50218i | 0.223283 | + | 0.307322i | ||||
\(957\) | 49.2742 | + | 67.4486i | 1.59281 | + | 2.18030i | ||||
\(958\) | −22.1377 | − | 3.50627i | −0.715236 | − | 0.113282i | ||||
\(959\) | −0.188434 | − | 0.579941i | −0.00608486 | − | 0.0187273i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.98073 | + | 24.5622i | −0.257443 | + | 0.792328i | ||||
\(962\) | −2.90496 | + | 5.70131i | −0.0936598 | + | 0.183818i | ||||
\(963\) | −23.5483 | − | 23.3034i | −0.758835 | − | 0.750941i | ||||
\(964\) | 1.15675 | + | 0.375849i | 0.0372563 | + | 0.0121053i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.987499 | + | 0.159052i | −0.0317723 | + | 0.00511741i | ||||
\(967\) | 6.91329 | − | 43.6488i | 0.222316 | − | 1.40365i | −0.583802 | − | 0.811896i | \(-0.698435\pi\) |
0.806118 | − | 0.591755i | \(-0.201565\pi\) | |||||||
\(968\) | −10.8855 | + | 10.8855i | −0.349872 | + | 0.349872i | ||||
\(969\) | −1.85550 | − | 3.61820i | −0.0596071 | − | 0.116233i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.4405 | − | 44.6505i | 1.04107 | − | 1.43290i | 0.144760 | − | 0.989467i | \(-0.453759\pi\) |
0.896306 | − | 0.443437i | \(-0.146241\pi\) | |||||||
\(972\) | −8.99705 | + | 12.7300i | −0.288580 | + | 0.408315i | ||||
\(973\) | −1.33951 | + | 0.682516i | −0.0429428 | + | 0.0218804i | ||||
\(974\) | 21.2093 | 0.679589 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.6458 | 0.436793 | ||||||||
\(977\) | −29.4915 | + | 15.0267i | −0.943516 | + | 0.480746i | −0.856892 | − | 0.515496i | \(-0.827608\pi\) |
−0.0866240 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(978\) | −0.0183728 | − | 7.02810i | −0.000587496 | − | 0.224734i | ||||
\(979\) | −33.0604 | + | 45.5037i | −1.05661 | + | 1.45430i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4658 | + | 5.77613i | −0.557642 | + | 0.184418i | ||||
\(982\) | −22.0207 | + | 22.0207i | −0.702708 | + | 0.702708i | ||||
\(983\) | 3.05030 | − | 19.2588i | 0.0972894 | − | 0.614261i | −0.890077 | − | 0.455809i | \(-0.849350\pi\) |
0.987367 | − | 0.158451i | \(-0.0506501\pi\) | |||||||
\(984\) | 1.72469 | + | 10.7080i | 0.0549811 | + | 0.341359i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.5259 | − | 14.1424i | −1.38615 | − | 0.450386i | ||||
\(987\) | −3.07823 | − | 2.22419i | −0.0979811 | − | 0.0707968i | ||||
\(988\) | −0.324929 | + | 0.637709i | −0.0103374 | + | 0.0202882i | ||||
\(989\) | 3.18096 | − | 9.78998i | 0.101149 | − | 0.311303i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9360 | + | 33.6576i | 0.347394 | + | 1.06917i | 0.960290 | + | 0.279005i | \(0.0900046\pi\) |
−0.612896 | + | 0.790164i | \(0.709995\pi\) | |||||||
\(992\) | −2.24660 | − | 0.355826i | −0.0713295 | − | 0.0112975i | ||||
\(993\) | 13.4752 | − | 9.84420i | 0.427621 | − | 0.312396i | ||||
\(994\) | 1.54012 | + | 2.11980i | 0.0488497 | + | 0.0672359i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.14034 | − | 6.10832i | −0.194564 | − | 0.193550i | ||||
\(997\) | −45.5136 | + | 7.20864i | −1.44143 | + | 0.228300i | −0.827680 | − | 0.561201i | \(-0.810340\pi\) |
−0.613750 | + | 0.789501i | \(0.710340\pi\) | |||||||
\(998\) | −0.570481 | − | 1.11963i | −0.0180583 | − | 0.0354414i | ||||
\(999\) | 20.0101 | + | 9.99878i | 0.633093 | + | 0.316347i |
(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 | 750.2.l.b.743.1 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.743.10 | 80 | ||
5.2 | odd | 4 | 750.2.l.a.257.3 | 80 | |||
5.3 | odd | 4 | 750.2.l.c.257.8 | 80 | |||
5.4 | even | 2 | 150.2.l.a.53.10 | yes | 80 | ||
15.2 | even | 4 | 750.2.l.a.257.7 | 80 | |||
15.8 | even | 4 | 750.2.l.c.257.4 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.53.1 | yes | 80 | ||
25.6 | even | 5 | 750.2.l.a.143.7 | 80 | |||
25.8 | odd | 20 | 150.2.l.a.17.1 | ✓ | 80 | ||
25.17 | odd | 20 | inner | 750.2.l.b.107.10 | 80 | ||
25.19 | even | 10 | 750.2.l.c.143.4 | 80 | |||
75.8 | even | 20 | 150.2.l.a.17.10 | yes | 80 | ||
75.17 | even | 20 | inner | 750.2.l.b.107.1 | 80 | ||
75.44 | odd | 10 | 750.2.l.c.143.8 | 80 | |||
75.56 | odd | 10 | 750.2.l.a.143.3 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.1 | ✓ | 80 | 25.8 | odd | 20 | ||
150.2.l.a.17.10 | yes | 80 | 75.8 | even | 20 | ||
150.2.l.a.53.1 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.53.10 | yes | 80 | 5.4 | even | 2 | ||
750.2.l.a.143.3 | 80 | 75.56 | odd | 10 | |||
750.2.l.a.143.7 | 80 | 25.6 | even | 5 | |||
750.2.l.a.257.3 | 80 | 5.2 | odd | 4 | |||
750.2.l.a.257.7 | 80 | 15.2 | even | 4 | |||
750.2.l.b.107.1 | 80 | 75.17 | even | 20 | inner | ||
750.2.l.b.107.10 | 80 | 25.17 | odd | 20 | inner | ||
750.2.l.b.743.1 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.743.10 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.c.143.4 | 80 | 25.19 | even | 10 | |||
750.2.l.c.143.8 | 80 | 75.44 | odd | 10 | |||
750.2.l.c.257.4 | 80 | 15.8 | even | 4 | |||
750.2.l.c.257.8 | 80 | 5.3 | odd | 4 |