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 | 107.10 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.b.743.10 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
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 | ||||
\(3\) | 1.64867 | + | 0.530925i | 0.951861 | + | 0.306530i | ||||
\(4\) | 0.587785 | + | 0.809017i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22794 | + | 1.22154i | 0.501305 | + | 0.498691i | ||||
\(7\) | 0.152718 | + | 0.152718i | 0.0577219 | + | 0.0577219i | 0.735379 | − | 0.677657i | \(-0.237004\pi\) |
−0.677657 | + | 0.735379i | \(0.737004\pi\) | |||||||
\(8\) | 0.156434 | + | 0.987688i | 0.0553079 | + | 0.349201i | ||||
\(9\) | 2.43624 | + | 1.75064i | 0.812079 | + | 0.583547i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.88609 | − | 1.58759i | 1.47321 | − | 0.478676i | 0.541136 | − | 0.840935i | \(-0.317995\pi\) |
0.932077 | + | 0.362259i | \(0.117995\pi\) | |||||||
\(12\) | 0.539538 | + | 1.64587i | 0.155751 | + | 0.475123i | ||||
\(13\) | −0.674795 | − | 1.32436i | −0.187155 | − | 0.367312i | 0.778296 | − | 0.627897i | \(-0.216084\pi\) |
−0.965451 | + | 0.260586i | \(0.916084\pi\) | |||||||
\(14\) | 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 | \(-0.751360\pi\) |
−0.457793 | + | 0.889059i | \(0.651360\pi\) | |||||||
\(18\) | 1.37593 | + | 2.66586i | 0.324309 | + | 0.628350i | ||||
\(19\) | 0.283032 | − | 0.389560i | 0.0649319 | − | 0.0893711i | −0.775316 | − | 0.631574i | \(-0.782409\pi\) |
0.840248 | + | 0.542202i | \(0.182409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.170700 | + | 0.332863i | 0.0372498 | + | 0.0726367i | ||||
\(22\) | 5.07429 | + | 0.803689i | 1.08184 | + | 0.171347i | ||||
\(23\) | 1.21389 | − | 2.38239i | 0.253114 | − | 0.496763i | −0.729130 | − | 0.684376i | \(-0.760075\pi\) |
0.982243 | + | 0.187612i | \(0.0600748\pi\) | |||||||
\(24\) | −0.266479 | + | 1.71143i | −0.0543949 | + | 0.349344i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.48636i | − | 0.291500i | ||||||
\(27\) | 3.08710 | + | 4.17969i | 0.594112 | + | 0.804382i | ||||
\(28\) | −0.0337860 | + | 0.213317i | −0.00638496 | + | 0.0403130i | ||||
\(29\) | −7.59423 | + | 5.51753i | −1.41021 | + | 1.02458i | −0.416921 | + | 0.908943i | \(0.636891\pi\) |
−0.993292 | + | 0.115637i | \(0.963109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84019 | − | 1.33698i | −0.330508 | − | 0.240128i | 0.410138 | − | 0.912023i | \(-0.365480\pi\) |
−0.740646 | + | 0.671895i | \(0.765480\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 8.89846 | − | 0.0232622i | 1.54902 | − | 0.00404943i | ||||
\(34\) | −4.63684 | − | 1.50660i | −0.795211 | − | 0.258380i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0156850 | + | 2.99996i | 0.00261417 | + | 0.499993i | ||||
\(37\) | −3.83574 | + | 1.95441i | −0.630592 | + | 0.321303i | −0.739912 | − | 0.672704i | \(-0.765133\pi\) |
0.109320 | + | 0.994007i | \(0.465133\pi\) | |||||||
\(38\) | 0.429039 | − | 0.218606i | 0.0695994 | − | 0.0354627i | ||||
\(39\) | −0.409380 | − | 2.54170i | −0.0655533 | − | 0.406998i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.95547 | + | 1.93505i | 0.930087 | + | 0.302204i | 0.734598 | − | 0.678502i | \(-0.237371\pi\) |
0.195489 | + | 0.980706i | \(0.437371\pi\) | |||||||
\(42\) | 0.000977913 | 0.374079i | 0.000150895 | 0.0577217i | ||||||
\(43\) | 2.72225 | − | 2.72225i | 0.415139 | − | 0.415139i | −0.468385 | − | 0.883524i | \(-0.655164\pi\) |
0.883524 | + | 0.468385i | \(0.155164\pi\) | |||||||
\(44\) | 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 | 0.548046 | + | 0.836448i | \(0.315372\pi\) |
−0.779699 | + | 0.626154i | \(0.784628\pi\) | |||||||
\(48\) | −1.01441 | + | 1.40392i | −0.146417 | + | 0.202638i | ||||
\(49\) | − | 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 | \(-0.272842\pi\) |
0.388939 | + | 0.921264i | \(0.372842\pi\) | |||||||
\(54\) | 0.853081 | + | 5.12565i | 0.116090 | + | 0.697512i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.126947 | + | 0.174728i | −0.0169640 | + | 0.0233490i | ||||
\(57\) | 0.673453 | − | 0.491987i | 0.0892011 | − | 0.0651653i | ||||
\(58\) | −9.27141 | + | 1.46845i | −1.21740 | + | 0.192817i | ||||
\(59\) | −1.54130 | + | 4.74363i | −0.200660 | + | 0.617569i | 0.799204 | + | 0.601061i | \(0.205255\pi\) |
−0.999864 | + | 0.0165081i | \(0.994745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.21680 | − | 12.9780i | −0.539906 | − | 1.66166i | −0.732803 | − | 0.680440i | \(-0.761789\pi\) |
0.192898 | − | 0.981219i | \(-0.438211\pi\) | |||||||
\(62\) | −1.03265 | − | 2.02668i | −0.131146 | − | 0.257389i | ||||
\(63\) | 0.104703 | + | 0.639411i | 0.0131913 | + | 0.0805582i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.93914 | + | 4.01909i | 0.977241 | + | 0.494716i | ||||
\(67\) | −2.35050 | − | 14.8405i | −0.287159 | − | 1.81305i | −0.535673 | − | 0.844425i | \(-0.679942\pi\) |
0.248514 | − | 0.968628i | \(-0.420058\pi\) | |||||||
\(68\) | −3.44747 | − | 3.44747i | −0.418067 | − | 0.418067i | ||||
\(69\) | 3.26618 | − | 3.28330i | 0.393202 | − | 0.395263i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.13100 | − | 9.81498i | −0.846294 | − | 1.16482i | −0.984667 | − | 0.174444i | \(-0.944187\pi\) |
0.138373 | − | 0.990380i | \(-0.455813\pi\) | |||||||
\(72\) | −1.34798 | + | 2.68010i | −0.158861 | + | 0.315853i | ||||
\(73\) | −8.36209 | − | 4.26070i | −0.978708 | − | 0.498677i | −0.109963 | − | 0.993936i | \(-0.535073\pi\) |
−0.868745 | + | 0.495259i | \(0.835073\pi\) | |||||||
\(74\) | −4.30495 | −0.500441 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.481522 | 0.0552344 | ||||||||
\(77\) | 0.988647 | + | 0.503741i | 0.112667 | + | 0.0574066i | ||||
\(78\) | 0.789148 | − | 2.45053i | 0.0893534 | − | 0.277468i | ||||
\(79\) | −1.28502 | − | 1.76867i | −0.144576 | − | 0.198991i | 0.730588 | − | 0.682819i | \(-0.239246\pi\) |
−0.875163 | + | 0.483828i | \(0.839246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.87050 | + | 8.52996i | 0.318945 | + | 0.947773i | ||||
\(82\) | 4.42787 | + | 4.42787i | 0.488976 | + | 0.488976i | ||||
\(83\) | 0.782253 | + | 4.93895i | 0.0858634 | + | 0.542120i | 0.992697 | + | 0.120632i | \(0.0384921\pi\) |
−0.906834 | + | 0.421488i | \(0.861508\pi\) | |||||||
\(84\) | −0.168957 | + | 0.333751i | −0.0184347 | + | 0.0364152i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.66142 | − | 1.18967i | 0.394821 | − | 0.128285i | ||||
\(87\) | −15.4498 | + | 5.06463i | −1.65639 | + | 0.542985i | ||||
\(88\) | 2.33240 | + | 4.57759i | 0.248634 | + | 0.487972i | ||||
\(89\) | −3.38311 | − | 10.4121i | −0.358609 | − | 1.10368i | −0.953887 | − | 0.300165i | \(-0.902958\pi\) |
0.595279 | − | 0.803519i | \(-0.297042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0992002 | − | 0.305307i | 0.0103990 | − | 0.0320048i | ||||
\(92\) | 2.64090 | − | 0.418278i | 0.275333 | − | 0.0436085i | ||||
\(93\) | −2.32404 | − | 3.18124i | −0.240991 | − | 0.329879i | ||||
\(94\) | −5.96725 | + | 8.21321i | −0.615475 | + | 0.847128i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.54121 | + | 0.790366i | −0.157299 | + | 0.0806664i | ||||
\(97\) | 9.96799 | + | 1.57877i | 1.01210 | + | 0.160300i | 0.640390 | − | 0.768050i | \(-0.278773\pi\) |
0.371706 | + | 0.928350i | \(0.378773\pi\) | |||||||
\(98\) | 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 | \(0.842635\pi\) | |||||||
\(102\) | −6.84473 | − | 4.94570i | −0.677729 | − | 0.489697i | ||||
\(103\) | −1.58215 | + | 9.98929i | −0.155894 | + | 0.984274i | 0.778400 | + | 0.627769i | \(0.216032\pi\) |
−0.934293 | + | 0.356505i | \(0.883968\pi\) | |||||||
\(104\) | 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 | \(-0.570766\pi\) |
0.975389 | + | 0.220491i | \(0.0707659\pi\) | |||||||
\(108\) | −1.56689 | + | 4.95428i | −0.150774 | + | 0.476725i | ||||
\(109\) | −5.83194 | − | 1.89491i | −0.558598 | − | 0.181500i | 0.0160921 | − | 0.999871i | \(-0.494877\pi\) |
−0.574690 | + | 0.818371i | \(0.694877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.36152 | + | 1.18569i | −0.698725 | + | 0.112540i | ||||
\(112\) | −0.192436 | + | 0.0980509i | −0.0181835 | + | 0.00926494i | ||||
\(113\) | −9.78864 | + | 4.98756i | −0.920838 | + | 0.469190i | −0.849099 | − | 0.528233i | \(-0.822855\pi\) |
−0.0717385 | + | 0.997423i | \(0.522855\pi\) | |||||||
\(114\) | 0.823409 | − | 0.132623i | 0.0771193 | − | 0.0124212i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.92755 | − | 2.90074i | −0.828902 | − | 0.269327i | ||||
\(117\) | 0.674520 | − | 4.40778i | 0.0623594 | − | 0.407500i | ||||
\(118\) | −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 | ||||
\(123\) | 8.79124 | + | 6.35216i | 0.792680 | + | 0.572755i | ||||
\(124\) | − | 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 | −0.360850 | − | 0.932624i | \(-0.617513\pi\) |
0.966611 | − | 0.256249i | \(-0.0824868\pi\) | |||||||
\(128\) | −0.987688 | − | 0.156434i | −0.0873001 | − | 0.0138270i | ||||
\(129\) | 5.93341 | − | 3.04279i | 0.522407 | − | 0.267902i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12870 | + | 7.05905i | −0.448097 | + | 0.616752i | −0.971987 | − | 0.235034i | \(-0.924480\pi\) |
0.523891 | + | 0.851785i | \(0.324480\pi\) | |||||||
\(132\) | 5.24920 | + | 7.18533i | 0.456884 | + | 0.625403i | ||||
\(133\) | 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 | \(-0.188485\pi\) |
−0.939258 | + | 0.343212i | \(0.888485\pi\) | |||||||
\(138\) | 4.40077 | − | 1.44263i | 0.374619 | − | 0.122805i | ||||
\(139\) | −6.62014 | + | 2.15102i | −0.561513 | + | 0.182447i | −0.576002 | − | 0.817448i | \(-0.695388\pi\) |
0.0144887 | + | 0.999895i | \(0.495388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.94195 | + | 15.6882i | −0.668833 | + | 1.32119i | ||||
\(142\) | −1.89786 | − | 11.9826i | −0.159265 | − | 1.00556i | ||||
\(143\) | −5.39965 | − | 5.39965i | −0.451542 | − | 0.451542i | ||||
\(144\) | −2.41780 | + | 1.77602i | −0.201483 | + | 0.148002i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.51636 | − | 7.59261i | −0.456537 | − | 0.628369i | ||||
\(147\) | 3.69171 | − | 11.4638i | 0.304487 | − | 0.945518i | ||||
\(148\) | −3.83574 | − | 1.95441i | −0.315296 | − | 0.160651i | ||||
\(149\) | 7.72360 | 0.632742 | 0.316371 | − | 0.948635i | \(-0.397535\pi\) | ||||
0.316371 | + | 0.948635i | \(0.397535\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | −13.0667 | − | 6.57201i | −1.05638 | − | 0.531315i | ||||
\(154\) | 0.652197 | + | 0.897673i | 0.0525556 | + | 0.0723365i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.81565 | − | 1.82517i | 0.145369 | − | 0.146131i | ||||
\(157\) | 11.5941 | + | 11.5941i | 0.925312 | + | 0.925312i | 0.997398 | − | 0.0720863i | \(-0.0229657\pi\) |
−0.0720863 | + | 0.997398i | \(0.522966\pi\) | |||||||
\(158\) | −0.341997 | − | 2.15928i | −0.0272078 | − | 0.171783i | ||||
\(159\) | 11.8861 | + | 6.01719i | 0.942630 | + | 0.477194i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.549217 | − | 0.178451i | 0.0432843 | − | 0.0140639i | ||||
\(162\) | −1.31488 | + | 8.90343i | −0.103307 | + | 0.699520i | ||||
\(163\) | 1.84215 | + | 3.61543i | 0.144289 | + | 0.283182i | 0.951829 | − | 0.306630i | \(-0.0992016\pi\) |
−0.807540 | + | 0.589813i | \(0.799202\pi\) | |||||||
\(164\) | 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 | \(-0.729886\pi\) |
−0.396818 | + | 0.917897i | \(0.629886\pi\) | |||||||
\(168\) | −0.302062 | + | 0.220670i | −0.0233046 | + | 0.0170250i | ||||
\(169\) | 6.34263 | − | 8.72988i | 0.487894 | − | 0.671529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.37151 | − | 0.453573i | 0.104882 | − | 0.0346856i | ||||
\(172\) | 3.80244 | + | 0.602248i | 0.289934 | + | 0.0459210i | ||||
\(173\) | 0.412278 | − | 0.809140i | 0.0313449 | − | 0.0615178i | −0.874803 | − | 0.484479i | \(-0.839009\pi\) |
0.906148 | + | 0.422961i | \(0.139009\pi\) | |||||||
\(174\) | −16.0652 | − | 2.50144i | −1.21790 | − | 0.189633i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.13754i | 0.387257i | ||||||||
\(177\) | −5.05961 | + | 7.00238i | −0.380304 | + | 0.526331i | ||||
\(178\) | 1.71264 | − | 10.8132i | 0.128368 | − | 0.810482i | ||||
\(179\) | 9.58645 | − | 6.96496i | 0.716525 | − | 0.520586i | −0.168747 | − | 0.985659i | \(-0.553972\pi\) |
0.885272 | + | 0.465074i | \(0.153972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.9076 | + | 10.1044i | 1.03374 | + | 0.751057i | 0.969054 | − | 0.246848i | \(-0.0793949\pi\) |
0.0646876 | + | 0.997906i | \(0.479395\pi\) | |||||||
\(182\) | 0.226994 | − | 0.226994i | 0.0168259 | − | 0.0168259i | ||||
\(183\) | −0.0617869 | − | 23.6352i | −0.00456742 | − | 1.74717i | ||||
\(184\) | 2.54296 | + | 0.826257i | 0.187469 | + | 0.0609125i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.626479 | − | 3.88960i | −0.0459357 | − | 0.285199i | ||||
\(187\) | −22.3178 | + | 11.3715i | −1.63204 | + | 0.831566i | ||||
\(188\) | −9.04558 | + | 4.60895i | −0.659716 | + | 0.336142i | ||||
\(189\) | −0.166859 | + | 1.10977i | −0.0121372 | + | 0.0807238i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.70151 | − | 1.52761i | −0.340189 | − | 0.110534i | 0.133940 | − | 0.990989i | \(-0.457237\pi\) |
−0.474129 | + | 0.880455i | \(0.657237\pi\) | |||||||
\(192\) | −1.73204 | + | 0.00452789i | −0.125000 | + | 0.000326772i | ||||
\(193\) | −2.38356 | + | 2.38356i | −0.171572 | + | 0.171572i | −0.787670 | − | 0.616098i | \(-0.788713\pi\) |
0.616098 | + | 0.787670i | \(0.288713\pi\) | |||||||
\(194\) | 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 | −0.912548 | − | 0.408970i | \(-0.865888\pi\) |
0.994263 | − | 0.106961i | \(-0.0341121\pi\) | |||||||
\(198\) | 10.9552 | + | 10.8412i | 0.778553 | + | 0.770454i | ||||
\(199\) | 8.34182i | 0.591336i | 0.955291 | + | 0.295668i | \(0.0955422\pi\) | ||||
−0.955291 | + | 0.295668i | \(0.904458\pi\) | |||||||
\(200\) | 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 | ||||
\(204\) | −3.85340 | − | 7.51409i | −0.269792 | − | 0.526092i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.94475 | + | 8.18224i | −0.414190 | + | 0.570084i | ||||
\(207\) | 7.12804 | − | 3.67899i | 0.495433 | − | 0.255707i | ||||
\(208\) | 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 | 0.986247 | − | 0.165279i | \(-0.0528525\pi\) |
−0.895039 | + | 0.445988i | \(0.852852\pi\) | |||||||
\(212\) | 3.49196 | + | 6.85335i | 0.239828 | + | 0.470690i | ||||
\(213\) | −6.54566 | − | 19.9677i | −0.448501 | − | 1.36817i | ||||
\(214\) | 10.5027 | − | 3.41254i | 0.717951 | − | 0.233276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.64531 | + | 3.70294i | −0.248032 | + | 0.251953i | ||||
\(217\) | −0.0768498 | − | 0.485210i | −0.00521690 | − | 0.0329382i | ||||
\(218\) | −4.33602 | − | 4.33602i | −0.293672 | − | 0.293672i | ||||
\(219\) | −11.5242 | − | 11.4641i | −0.778735 | − | 0.774674i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.25951 | + | 5.86271i | 0.286525 | + | 0.394369i | ||||
\(222\) | −7.09746 | − | 2.28561i | −0.476350 | − | 0.153400i | ||||
\(223\) | −0.651256 | − | 0.331831i | −0.0436113 | − | 0.0222211i | 0.432049 | − | 0.901850i | \(-0.357791\pi\) |
−0.475660 | + | 0.879629i | \(0.657791\pi\) | |||||||
\(224\) | −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 | \(-0.314957\pi\) |
−0.353349 | + | 0.935492i | \(0.614957\pi\) | |||||||
\(228\) | 0.793872 | + | 0.255652i | 0.0525755 | + | 0.0169310i | ||||
\(229\) | −6.20224 | − | 8.53665i | −0.409855 | − | 0.564117i | 0.553328 | − | 0.832964i | \(-0.313358\pi\) |
−0.963183 | + | 0.268846i | \(0.913358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36251 | + | 1.35540i | 0.0896463 | + | 0.0891788i | ||||
\(232\) | −6.63760 | − | 6.63760i | −0.435780 | − | 0.435780i | ||||
\(233\) | 1.96935 | + | 12.4340i | 0.129016 | + | 0.814577i | 0.964311 | + | 0.264774i | \(0.0852973\pi\) |
−0.835294 | + | 0.549803i | \(0.814703\pi\) | |||||||
\(234\) | 2.60209 | − | 3.62114i | 0.170104 | − | 0.236721i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.74363 | + | 1.54130i | −0.308784 | + | 0.100330i | ||||
\(237\) | −1.17954 | − | 3.59821i | −0.0766192 | − | 0.233729i | ||||
\(238\) | −0.478043 | − | 0.938212i | −0.0309869 | − | 0.0608152i | ||||
\(239\) | 3.62951 | + | 11.1705i | 0.234773 | + | 0.722558i | 0.997151 | + | 0.0754263i | \(0.0240318\pi\) |
−0.762378 | + | 0.647132i | \(0.775968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.375849 | − | 1.15675i | 0.0242106 | − | 0.0745125i | −0.938221 | − | 0.346036i | \(-0.887527\pi\) |
0.962432 | + | 0.271524i | \(0.0875275\pi\) | |||||||
\(242\) | 15.2048 | − | 2.40821i | 0.977403 | − | 0.154805i | ||||
\(243\) | 0.203749 | + | 15.5871i | 0.0130705 | + | 0.999915i | ||||
\(244\) | 8.02083 | − | 11.0397i | 0.513481 | − | 0.706746i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94923 | + | 9.65096i | 0.315552 | + | 0.615323i | ||||
\(247\) | −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 | \(0.747046\pi\) | |||||||
\(252\) | −0.455752 | + | 0.460543i | −0.0287097 | + | 0.0290115i | ||||
\(253\) | 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 | \(-0.792022\pi\) |
0.607874 | + | 0.794033i | \(0.292022\pi\) | |||||||
\(258\) | 6.66810 | − | 0.0174316i | 0.415138 | − | 0.00108525i | ||||
\(259\) | −0.884259 | − | 0.287313i | −0.0549452 | − | 0.0178528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.1606 | + | 0.147235i | −1.74309 | + | 0.00911361i | ||||
\(262\) | −7.77445 | + | 3.96128i | −0.480307 | + | 0.244729i | ||||
\(263\) | 2.29146 | − | 1.16756i | 0.141298 | − | 0.0719947i | −0.381912 | − | 0.924199i | \(-0.624734\pi\) |
0.523210 | + | 0.852204i | \(0.324734\pi\) | |||||||
\(264\) | 1.41500 | + | 8.78526i | 0.0870873 | + | 0.540696i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0989071 | + | 0.0321369i | 0.00606438 | + | 0.00197044i | ||||
\(267\) | −0.0495712 | − | 18.9624i | −0.00303371 | − | 1.16048i | ||||
\(268\) | 10.6246 | − | 10.6246i | 0.649002 | − | 0.649002i | ||||
\(269\) | −19.5493 | − | 14.2034i | −1.19194 | − | 0.865996i | −0.198473 | − | 0.980106i | \(-0.563598\pi\) |
−0.993468 | + | 0.114110i | \(0.963598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.36464 | + | 6.80381i | −0.568861 | + | 0.413302i | −0.834691 | − | 0.550718i | \(-0.814354\pi\) |
0.265830 | + | 0.964020i | \(0.414354\pi\) | |||||||
\(272\) | 0.762690 | − | 4.81543i | 0.0462448 | − | 0.291978i | ||||
\(273\) | 0.325644 | − | 0.450683i | 0.0197088 | − | 0.0272766i | ||||
\(274\) | − | 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 | −0.970654 | − | 0.240482i | \(-0.922695\pi\) |
0.765090 | + | 0.643924i | \(0.222695\pi\) | |||||||
\(278\) | −6.87513 | − | 1.08891i | −0.412343 | − | 0.0653087i | ||||
\(279\) | −2.14257 | − | 6.47871i | −0.128273 | − | 0.387870i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8790 | − | 19.1028i | 0.827952 | − | 1.13958i | −0.160349 | − | 0.987060i | \(-0.551262\pi\) |
0.988301 | − | 0.152517i | \(-0.0487380\pi\) | |||||||
\(282\) | −14.1986 | + | 10.3727i | −0.845516 | + | 0.617687i | ||||
\(283\) | −9.72347 | + | 1.54005i | −0.578000 | + | 0.0915463i | −0.438588 | − | 0.898688i | \(-0.644521\pi\) |
−0.139412 | + | 0.990234i | \(0.544521\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | −2.96057 | + | 0.484789i | −0.174453 | + | 0.0285665i | ||||
\(289\) | 6.43873 | − | 2.09207i | 0.378749 | − | 0.123063i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5957 | + | 7.89513i | 0.914238 | + | 0.462821i | ||||
\(292\) | −1.46814 | − | 9.26944i | −0.0859161 | − | 0.542453i | ||||
\(293\) | 3.33944 | + | 3.33944i | 0.195092 | + | 0.195092i | 0.797892 | − | 0.602800i | \(-0.205948\pi\) |
−0.602800 | + | 0.797892i | \(0.705948\pi\) | |||||||
\(294\) | 8.49379 | − | 8.53832i | 0.495368 | − | 0.497965i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.53039 | − | 3.48278i | −0.147076 | − | 0.202433i | ||||
\(297\) | 21.7195 | + | 15.5213i | 1.26029 | + | 0.900640i | ||||
\(298\) | 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 | ||||
\(303\) | −5.06343 | + | 15.7234i | −0.290887 | + | 0.903285i | ||||
\(304\) | 0.283032 | + | 0.389560i | 0.0162330 | + | 0.0223428i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.65891 | − | 11.7879i | −0.494997 | − | 0.673868i | ||||
\(307\) | 11.8133 | + | 11.8133i | 0.674221 | + | 0.674221i | 0.958686 | − | 0.284465i | \(-0.0918160\pi\) |
−0.284465 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(308\) | 0.173577 | + | 1.09592i | 0.00989048 | + | 0.0624460i | ||||
\(309\) | −7.91201 | + | 15.6291i | −0.450098 | + | 0.889106i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.7239 | − | 9.33296i | 1.62878 | − | 0.529224i | 0.654791 | − | 0.755810i | \(-0.272756\pi\) |
0.973991 | + | 0.226586i | \(0.0727564\pi\) | |||||||
\(312\) | 2.44637 | − | 0.801950i | 0.138498 | − | 0.0454015i | ||||
\(313\) | 7.57278 | + | 14.8624i | 0.428039 | + | 0.840073i | 0.999807 | + | 0.0196580i | \(0.00625773\pi\) |
−0.571768 | + | 0.820415i | \(0.693742\pi\) | |||||||
\(314\) | 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 | \(-0.451478\pi\) |
0.449848 | + | 0.893105i | \(0.351478\pi\) | |||||||
\(318\) | 7.85886 | + | 10.7575i | 0.440703 | + | 0.603253i | ||||
\(319\) | −28.3466 | + | 39.0157i | −1.58710 | + | 2.18446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.0199 | − | 8.72818i | 0.949957 | − | 0.487160i | ||||
\(322\) | 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 | ||||||||
\(327\) | −8.60889 | − | 6.22041i | −0.476073 | − | 0.343989i | ||||
\(328\) | −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 | 0.352587 | − | 0.935779i | \(-0.385302\pi\) |
−0.781023 | + | 0.624502i | \(0.785302\pi\) | |||||||
\(332\) | −3.53590 | + | 3.53590i | −0.194058 | + | 0.194058i | ||||
\(333\) | −12.7662 | − | 1.95361i | −0.699586 | − | 0.107057i | ||||
\(334\) | −13.1635 | − | 4.27710i | −0.720277 | − | 0.234032i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.369321 | + | 0.0594848i | −0.0201481 | + | 0.00324516i | ||||
\(337\) | 25.0858 | − | 12.7818i | 1.36651 | − | 0.696272i | 0.391864 | − | 0.920023i | \(-0.371830\pi\) |
0.974646 | + | 0.223752i | \(0.0718304\pi\) | |||||||
\(338\) | 9.61460 | − | 4.89888i | 0.522965 | − | 0.266464i | ||||
\(339\) | −18.7863 | + | 3.02582i | −1.02033 | + | 0.164340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1139 | − | 3.61113i | −0.601852 | − | 0.195554i | ||||
\(342\) | 1.42794 | + | 0.218517i | 0.0772143 | + | 0.0118161i | ||||
\(343\) | 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 | 0.763556 | + | 0.645742i | \(0.223452\pi\) |
−0.925730 | + | 0.378185i | \(0.876548\pi\) | |||||||
\(348\) | −13.1785 | − | 9.52222i | −0.706443 | − | 0.510445i | ||||
\(349\) | − | 14.4119i | − | 0.771451i | −0.922614 | − | 0.385725i | \(-0.873951\pi\) | ||
0.922614 | − | 0.385725i | \(-0.126049\pi\) | |||||||
\(350\) | 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 | \(-0.0683002\pi\) |
0.863448 | + | 0.504438i | \(0.168300\pi\) | |||||||
\(354\) | −7.68716 | + | 3.94215i | −0.408568 | + | 0.209523i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.43505 | − | 8.85709i | 0.341057 | − | 0.469425i | ||||
\(357\) | −1.07586 | − | 1.47269i | −0.0569408 | − | 0.0779430i | ||||
\(358\) | 11.7036 | − | 1.85367i | 0.618555 | − | 0.0979695i | ||||
\(359\) | −10.6846 | + | 32.8840i | −0.563914 | + | 1.73555i | 0.107242 | + | 0.994233i | \(0.465798\pi\) |
−0.671156 | + | 0.741316i | \(0.734202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.79967 | + | 17.8496i | 0.305246 | + | 0.939450i | ||||
\(362\) | 7.80442 | + | 15.3170i | 0.410191 | + | 0.805045i | ||||
\(363\) | 25.3372 | − | 8.30583i | 1.32986 | − | 0.435943i | ||||
\(364\) | 0.305307 | − | 0.0992002i | 0.0160024 | − | 0.00519950i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6751 | − | 21.0872i | 0.557997 | − | 1.10224i | ||||
\(367\) | −0.505240 | − | 3.18996i | −0.0263733 | − | 0.166514i | 0.970986 | − | 0.239135i | \(-0.0768638\pi\) |
−0.997360 | + | 0.0726205i | \(0.976864\pi\) | |||||||
\(368\) | 1.89068 | + | 1.89068i | 0.0985584 | + | 0.0985584i | ||||
\(369\) | 11.1214 | + | 15.1401i | 0.578954 | + | 0.788163i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.976440 | + | 1.34395i | 0.0506942 | + | 0.0697746i | ||||
\(372\) | 1.20764 | − | 3.75007i | 0.0626134 | − | 0.194432i | ||||
\(373\) | −9.65408 | − | 4.91900i | −0.499869 | − | 0.254696i | 0.185829 | − | 0.982582i | \(-0.440503\pi\) |
−0.685698 | + | 0.727886i | \(0.740503\pi\) | |||||||
\(374\) | −25.0479 | −1.29519 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1521 | −0.523554 | ||||||||
\(377\) | 12.4317 | + | 6.33429i | 0.640268 | + | 0.326233i | ||||
\(378\) | −0.652497 | + | 0.913058i | −0.0335608 | + | 0.0469627i | ||||
\(379\) | 19.6854 | + | 27.0946i | 1.01117 | + | 1.39176i | 0.918213 | + | 0.396087i | \(0.129632\pi\) |
0.0929573 | + | 0.995670i | \(0.470368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3681 | − | 18.4644i | 0.941025 | − | 0.945958i | ||||
\(382\) | −3.49555 | − | 3.49555i | −0.178848 | − | 0.178848i | ||||
\(383\) | 2.54182 | + | 16.0484i | 0.129881 | + | 0.820034i | 0.963503 | + | 0.267699i | \(0.0862632\pi\) |
−0.833622 | + | 0.552335i | \(0.813737\pi\) | |||||||
\(384\) | −1.54532 | − | 0.782298i | −0.0788592 | − | 0.0399215i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.20588 | + | 1.04165i | −0.163175 | + | 0.0530187i | ||||
\(387\) | 11.3977 | − | 1.86636i | 0.579379 | − | 0.0948724i | ||||
\(388\) | 4.58178 | + | 8.99225i | 0.232605 | + | 0.456512i | ||||
\(389\) | −0.804900 | − | 2.47723i | −0.0408101 | − | 0.125600i | 0.928576 | − | 0.371143i | \(-0.121034\pi\) |
−0.969386 | + | 0.245542i | \(0.921034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.02838 | + | 12.3981i | −0.203724 | + | 0.626998i | ||||
\(392\) | 6.86775 | − | 1.08774i | 0.346874 | − | 0.0549394i | ||||
\(393\) | −12.2034 | + | 8.91510i | −0.615578 | + | 0.449707i | ||||
\(394\) | 4.30947 | − | 5.93148i | 0.217108 | − | 0.298824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.83934 | + | 14.6332i | 0.243186 | + | 0.735345i | ||||
\(397\) | −1.86357 | − | 0.295160i | −0.0935298 | − | 0.0148137i | 0.109494 | − | 0.993987i | \(-0.465077\pi\) |
−0.203024 | + | 0.979174i | \(0.565077\pi\) | |||||||
\(398\) | −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 | \(0.942715\pi\) | |||||||
\(402\) | 15.2419 | − | 21.0945i | 0.760199 | − | 1.05210i | ||||
\(403\) | −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 | ||||
\(408\) | −0.0220755 | − | 8.44451i | −0.00109290 | − | 0.418066i | ||||
\(409\) | 15.2838 | + | 4.96600i | 0.755734 | + | 0.245553i | 0.661447 | − | 0.749992i | \(-0.269943\pi\) |
0.0942874 | + | 0.995545i | \(0.469943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.777631 | − | 4.82805i | −0.0383577 | − | 0.238150i | ||||
\(412\) | −9.01147 | + | 4.59157i | −0.443963 | + | 0.226211i | ||||
\(413\) | −0.959822 | + | 0.489054i | −0.0472297 | + | 0.0240648i | ||||
\(414\) | 8.02136 | − | 0.0419389i | 0.394228 | − | 0.00206119i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.41362 | + | 0.459312i | 0.0693083 | + | 0.0225196i | ||||
\(417\) | −12.0565 | + | 0.0315179i | −0.590408 | + | 0.00154344i | ||||
\(418\) | 1.74927 | − | 1.74927i | 0.0855596 | − | 0.0855596i | ||||
\(419\) | 1.81333 | + | 1.31746i | 0.0885872 | + | 0.0643624i | 0.631197 | − | 0.775622i | \(-0.282564\pi\) |
−0.542610 | + | 0.839985i | \(0.682564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.09500 | − | 1.52210i | 0.102104 | − | 0.0741828i | −0.535562 | − | 0.844496i | \(-0.679900\pi\) |
0.637666 | + | 0.770313i | \(0.279900\pi\) | |||||||
\(422\) | −0.670692 | + | 4.23458i | −0.0326488 | + | 0.206136i | ||||
\(423\) | −21.4229 | + | 21.6481i | −1.04162 | + | 1.05257i | ||||
\(424\) | 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 | ||||
\(429\) | −6.03545 | − | 11.7691i | −0.291394 | − | 0.568216i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.661426 | + | 0.910375i | −0.0318598 | + | 0.0438512i | −0.824650 | − | 0.565644i | \(-0.808628\pi\) |
0.792790 | + | 0.609495i | \(0.208628\pi\) | |||||||
\(432\) | −4.92909 | + | 1.64441i | −0.237151 | + | 0.0791165i | ||||
\(433\) | −20.2750 | + | 3.21125i | −0.974355 | + | 0.154323i | −0.623258 | − | 0.782016i | \(-0.714191\pi\) |
−0.351097 | + | 0.936339i | \(0.614191\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | −5.06355 | − | 15.4465i | −0.241946 | − | 0.738062i | ||||
\(439\) | 22.3736 | − | 7.26963i | 1.06783 | − | 0.346960i | 0.278191 | − | 0.960526i | \(-0.410265\pi\) |
0.789644 | + | 0.613565i | \(0.210265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1728 | − | 16.9400i | 0.579659 | − | 0.806668i | ||||
\(442\) | 1.13363 | + | 7.15749i | 0.0539215 | + | 0.340447i | ||||
\(443\) | 13.6168 | + | 13.6168i | 0.646952 | + | 0.646952i | 0.952255 | − | 0.305303i | \(-0.0987577\pi\) |
−0.305303 | + | 0.952255i | \(0.598758\pi\) | |||||||
\(444\) | −5.28624 | − | 5.25867i | −0.250874 | − | 0.249565i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.429625 | − | 0.591328i | −0.0203433 | − | 0.0280002i | ||||
\(447\) | 12.7337 | + | 4.10066i | 0.602283 | + | 0.193954i | ||||
\(448\) | −0.192436 | − | 0.0980509i | −0.00909173 | − | 0.00463247i | ||||
\(449\) | 19.2184 | 0.906973 | 0.453487 | − | 0.891263i | \(-0.350180\pi\) | ||||
0.453487 | + | 0.891263i | \(0.350180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.1710 | 1.51487 | ||||||||
\(452\) | −9.78864 | − | 4.98756i | −0.460419 | − | 0.234595i | ||||
\(453\) | −24.3786 | − | 7.85069i | −1.14541 | − | 0.368858i | ||||
\(454\) | 1.94595 | + | 2.67837i | 0.0913281 | + | 0.125702i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.591281 | + | 0.588198i | 0.0276893 | + | 0.0275449i | ||||
\(457\) | −15.9563 | − | 15.9563i | −0.746405 | − | 0.746405i | 0.227397 | − | 0.973802i | \(-0.426979\pi\) |
−0.973802 | + | 0.227397i | \(0.926979\pi\) | |||||||
\(458\) | −1.65068 | − | 10.4220i | −0.0771311 | − | 0.486986i | ||||
\(459\) | −18.0535 | − | 17.7725i | −0.842666 | − | 0.829551i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2184 | − | 4.94475i | 0.708790 | − | 0.230300i | 0.0676337 | − | 0.997710i | \(-0.478455\pi\) |
0.641156 | + | 0.767410i | \(0.278455\pi\) | |||||||
\(462\) | 0.598662 | + | 1.82624i | 0.0278523 | + | 0.0849642i | ||||
\(463\) | 2.81092 | + | 5.51675i | 0.130635 | + | 0.256385i | 0.947054 | − | 0.321075i | \(-0.104044\pi\) |
−0.816419 | + | 0.577460i | \(0.804044\pi\) | |||||||
\(464\) | −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 | \(-0.730472\pi\) |
−0.398509 | + | 0.917164i | \(0.630472\pi\) | |||||||
\(468\) | 3.96244 | − | 2.04513i | 0.183164 | − | 0.0945362i | ||||
\(469\) | 1.90744 | − | 2.62537i | 0.0880775 | − | 0.121228i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9593 | + | 25.2705i | 0.597133 | + | 1.16440i | ||||
\(472\) | −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 | ||||||
\(477\) | 16.4016 | + | 16.2310i | 0.750979 | + | 0.743167i | ||||
\(478\) | −1.83738 | + | 11.6007i | −0.0840396 | + | 0.530605i | ||||
\(479\) | −18.1330 | + | 13.1744i | −0.828519 | + | 0.601954i | −0.919140 | − | 0.393931i | \(-0.871115\pi\) |
0.0906212 | + | 0.995885i | \(0.471115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17668 | + | 3.76108i | 0.236036 | + | 0.171491i | ||||
\(482\) | 0.860035 | − | 0.860035i | 0.0391735 | − | 0.0391735i | ||||
\(483\) | 1.00022 | − | 0.00261477i | 0.0455117 | − | 0.000118976i | ||||
\(484\) | 14.6409 | + | 4.75712i | 0.665496 | + | 0.216233i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.89486 | + | 13.9807i | −0.312757 | + | 0.634179i | ||||
\(487\) | −18.8976 | + | 9.62881i | −0.856332 | + | 0.436323i | −0.826303 | − | 0.563226i | \(-0.809560\pi\) |
−0.0300294 | + | 0.999549i | \(0.509560\pi\) | |||||||
\(488\) | 12.1585 | − | 6.19509i | 0.550391 | − | 0.280438i | ||||
\(489\) | 1.11758 | + | 6.93870i | 0.0505389 | + | 0.313779i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.6177 | − | 9.62339i | −1.33663 | − | 0.434297i | −0.448456 | − | 0.893805i | \(-0.648026\pi\) |
−0.888174 | + | 0.459507i | \(0.848026\pi\) | |||||||
\(492\) | 0.0283534 | + | 10.8460i | 0.00127827 | + | 0.488974i | ||||
\(493\) | 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 | ||||
\(498\) | −5.07256 | + | 7.02030i | −0.227307 | + | 0.314587i | ||||
\(499\) | − | 1.25659i | − | 0.0562528i | −0.999604 | − | 0.0281264i | \(-0.991046\pi\) | ||
0.999604 | − | 0.0281264i | \(-0.00895410\pi\) | |||||||
\(500\) | 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 | \(-0.649419\pi\) |
−0.705815 | + | 0.708397i | \(0.749419\pi\) | |||||||
\(504\) | −0.615160 | + | 0.203439i | −0.0274014 | + | 0.00906191i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.07434 | − | 11.1134i | 0.358948 | − | 0.494050i | ||||
\(507\) | 15.0918 | − | 11.0252i | 0.670251 | − | 0.489648i | ||||
\(508\) | 14.8517 | − | 2.35228i | 0.658938 | − | 0.104366i | ||||
\(509\) | −5.31690 | + | 16.3637i | −0.235668 | + | 0.725310i | 0.761365 | + | 0.648324i | \(0.224530\pi\) |
−0.997032 | + | 0.0769863i | \(0.975470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.626355 | − | 1.92772i | −0.0277083 | − | 0.0852775i | ||||
\(512\) | −0.453990 | − | 0.891007i | −0.0200637 | − | 0.0393773i | ||||
\(513\) | 2.50199 | − | 0.0196223i | 0.110465 | − | 0.000866347i | ||||
\(514\) | −4.01395 | + | 1.30421i | −0.177048 | + | 0.0575263i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.94923 | + | 3.01172i | 0.261900 | + | 0.132584i | ||||
\(517\) | 8.15912 | + | 51.5147i | 0.358838 | + | 2.26561i | ||||
\(518\) | −0.657443 | − | 0.657443i | −0.0288864 | − | 0.0288864i | ||||
\(519\) | 1.10930 | − | 1.11512i | 0.0486930 | − | 0.0489483i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.91212 | + | 10.8901i | 0.346636 | + | 0.477104i | 0.946365 | − | 0.323099i | \(-0.104725\pi\) |
−0.599729 | + | 0.800203i | \(0.704725\pi\) | |||||||
\(522\) | −25.1581 | − | 12.6534i | −1.10114 | − | 0.553826i | ||||
\(523\) | 22.9585 | + | 11.6979i | 1.00390 | + | 0.511514i | 0.877046 | − | 0.480407i | \(-0.159511\pi\) |
0.126858 | + | 0.991921i | \(0.459511\pi\) | |||||||
\(524\) | −8.72546 | −0.381174 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.57177 | 0.112134 | ||||||||
\(527\) | 9.88101 | + | 5.03463i | 0.430424 | + | 0.219312i | ||||
\(528\) | −2.72765 | + | 8.47012i | −0.118706 | + | 0.368615i | ||||
\(529\) | 9.31679 | + | 12.8235i | 0.405078 | + | 0.557542i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0594 | + | 8.85835i | −0.523333 | + | 0.384420i | ||||
\(532\) | 0.0735370 | + | 0.0735370i | 0.00318823 | + | 0.00318823i | ||||
\(533\) | −1.45602 | − | 9.19295i | −0.0630672 | − | 0.398191i | ||||
\(534\) | 8.56457 | − | 16.9181i | 0.370625 | − | 0.732118i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.2901 | − | 4.64313i | 0.617237 | − | 0.200553i | ||||
\(537\) | 19.5028 | − | 6.39325i | 0.841607 | − | 0.275889i | ||||
\(538\) | −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 | 0.709998 | + | 0.704204i | \(0.248696\pi\) |
−0.988321 | + | 0.152387i | \(0.951304\pi\) | |||||||
\(542\) | −11.4328 | + | 1.81078i | −0.491082 | + | 0.0777797i | ||||
\(543\) | 17.5643 | + | 24.0428i | 0.753757 | + | 1.03177i | ||||
\(544\) | 2.86572 | − | 3.94433i | 0.122867 | − | 0.169112i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.494756 | − | 0.253722i | 0.0211736 | − | 0.0108583i | ||||
\(547\) | −43.0967 | − | 6.82585i | −1.84268 | − | 0.291852i | −0.864974 | − | 0.501817i | \(-0.832665\pi\) |
−0.977709 | + | 0.209965i | \(0.932665\pi\) | |||||||
\(548\) | 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 | ||||||||
\(552\) | 3.75382 | + | 2.71235i | 0.159773 | + | 0.115445i | ||||
\(553\) | 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 | \(-0.535861\pi\) |
0.993660 | + | 0.112424i | \(0.0358615\pi\) | |||||||
\(558\) | 1.03223 | − | 6.74528i | 0.0436976 | − | 0.285551i | ||||
\(559\) | −5.44220 | − | 1.76828i | −0.230181 | − | 0.0747902i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.8322 | + | 6.89878i | −1.80838 | + | 0.291267i | ||||
\(562\) | 21.0388 | − | 10.7198i | 0.887467 | − | 0.452187i | ||||
\(563\) | −14.0139 | + | 7.14045i | −0.590616 | + | 0.300934i | −0.723639 | − | 0.690179i | \(-0.757532\pi\) |
0.133022 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(564\) | −17.3602 | + | 2.79613i | −0.730996 | + | 0.117738i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.36284 | − | 3.04217i | −0.393550 | − | 0.127872i | ||||
\(567\) | −0.864300 | + | 1.74105i | −0.0362972 | + | 0.0731174i | ||||
\(568\) | 8.57861 | − | 8.57861i | 0.359950 | − | 0.359950i | ||||
\(569\) | −3.20445 | − | 2.32817i | −0.134338 | − | 0.0976021i | 0.518587 | − | 0.855025i | \(-0.326458\pi\) |
−0.652925 | + | 0.757423i | \(0.726458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7943 | + | 23.0999i | −1.33055 | + | 0.966702i | −0.330815 | + | 0.943696i | \(0.607324\pi\) |
−0.999735 | + | 0.0230060i | \(0.992676\pi\) | |||||||
\(572\) | 1.19457 | − | 7.54225i | 0.0499477 | − | 0.315357i | ||||
\(573\) | −6.94020 | − | 5.01468i | −0.289931 | − | 0.209491i | ||||
\(574\) | 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 | −0.641036 | − | 0.767511i | \(-0.721495\pi\) |
0.997721 | + | 0.0674769i | \(0.0214949\pi\) | |||||||
\(578\) | 6.68673 | + | 1.05907i | 0.278131 | + | 0.0440517i | ||||
\(579\) | −5.19519 | + | 2.66421i | −0.215905 | + | 0.110721i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.634802 | + | 0.873729i | −0.0263360 | + | 0.0362484i | ||||
\(582\) | 10.3116 | + | 14.1149i | 0.427429 | + | 0.585083i | ||||
\(583\) | 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 | \(-0.180641\pi\) |
−0.930516 | + | 0.366252i | \(0.880641\pi\) | |||||||
\(588\) | 11.4443 | − | 3.75160i | 0.471957 | − | 0.154713i | ||||
\(589\) | −1.04166 | + | 0.338457i | −0.0429210 | + | 0.0139459i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.73558 | − | 11.3298i | 0.235930 | − | 0.466047i | ||||
\(592\) | −0.673443 | − | 4.25195i | −0.0276783 | − | 0.174754i | ||||
\(593\) | −32.4687 | − | 32.4687i | −1.33333 | − | 1.33333i | −0.902371 | − | 0.430960i | \(-0.858175\pi\) |
−0.430960 | − | 0.902371i | \(-0.641825\pi\) | |||||||
\(594\) | 12.3057 | + | 23.6901i | 0.504907 | + | 0.972015i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.53982 | + | 6.24853i | 0.185958 | + | 0.255950i | ||||
\(597\) | −4.42888 | + | 13.7529i | −0.181262 | + | 0.562870i | ||||
\(598\) | −3.54111 | − | 1.80428i | −0.144807 | − | 0.0737826i | ||||
\(599\) | 18.2921 | 0.747393 | 0.373697 | − | 0.927551i | \(-0.378090\pi\) | ||||
0.373697 | + | 0.927551i | \(0.378090\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 20.2540 | − | 40.2698i | 0.824807 | − | 1.63991i | ||||
\(604\) | −8.69147 | − | 11.9628i | −0.353651 | − | 0.486759i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.6498 | + | 11.7109i | −0.473241 | + | 0.475722i | ||||
\(607\) | 2.39455 | + | 2.39455i | 0.0971917 | + | 0.0971917i | 0.754031 | − | 0.656839i | \(-0.228107\pi\) |
−0.656839 | + | 0.754031i | \(0.728107\pi\) | |||||||
\(608\) | 0.0753267 | + | 0.475594i | 0.00305490 | + | 0.0192879i | ||||
\(609\) | −3.13292 | − | 1.58600i | −0.126952 | − | 0.0642679i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3512 | − | 4.66298i | 0.580586 | − | 0.188644i | ||||
\(612\) | −2.36357 | − | 14.4341i | −0.0955415 | − | 0.583465i | ||||
\(613\) | −6.24017 | − | 12.2470i | −0.252038 | − | 0.494653i | 0.729973 | − | 0.683476i | \(-0.239533\pi\) |
−0.982011 | + | 0.188823i | \(0.939533\pi\) | |||||||
\(614\) | 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 | \(-0.483814\pi\) |
0.356959 | + | 0.934120i | \(0.383814\pi\) | |||||||
\(618\) | −14.1451 | + | 10.3336i | −0.568999 | + | 0.415679i | ||||
\(619\) | 27.3325 | − | 37.6199i | 1.09859 | − | 1.51207i | 0.261338 | − | 0.965247i | \(-0.415836\pi\) |
0.837247 | − | 0.546825i | \(-0.184164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.7051 | − | 2.28099i | 0.549966 | − | 0.0915329i | ||||
\(622\) | 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 | ||||||||
\(627\) | 2.50948 | − | 3.47306i | 0.100219 | − | 0.138701i | ||||
\(628\) | −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 | 0.0945340 | − | 0.995522i | \(-0.469864\pi\) |
−0.917585 | + | 0.397540i | \(0.869864\pi\) | |||||||
\(632\) | 1.54588 | − | 1.54588i | 0.0614917 | − | 0.0614917i | ||||
\(633\) | 0.0194127 | + | 7.42591i | 0.000771586 | + | 0.295153i | ||||
\(634\) | 10.3155 | + | 3.35172i | 0.409683 | + | 0.133114i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.11847 | + | 13.1529i | 0.0840030 | + | 0.521546i | ||||
\(637\) | −9.20875 | + | 4.69209i | −0.364864 | + | 0.185907i | ||||
\(638\) | −42.9697 | + | 21.8942i | −1.70119 | + | 0.866798i | ||||
\(639\) | −0.190290 | − | 36.3955i | −0.00752777 | − | 1.43978i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.702023 | + | 0.228101i | 0.0277282 | + | 0.00900945i | 0.322848 | − | 0.946451i | \(-0.395360\pi\) |
−0.295120 | + | 0.955460i | \(0.595360\pi\) | |||||||
\(642\) | 19.1273 | − | 0.0500024i | 0.754896 | − | 0.00197344i | ||||
\(643\) | −17.1573 | + | 17.1573i | −0.676616 | + | 0.676616i | −0.959233 | − | 0.282617i | \(-0.908797\pi\) |
0.282617 | + | 0.959233i | \(0.408797\pi\) | |||||||
\(644\) | 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 | \(-0.912185\pi\) |
0.999267 | + | 0.0382696i | \(0.0121846\pi\) | |||||||
\(648\) | −7.97590 | + | 4.16954i | −0.313323 | + | 0.163795i | ||||
\(649\) | 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 | \(-0.386686\pi\) |
0.0418163 | + | 0.999125i | \(0.486686\pi\) | |||||||
\(654\) | −4.84657 | − | 9.45078i | −0.189516 | − | 0.369555i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.68068 | + | 5.06602i | −0.143706 | + | 0.197795i | ||||
\(657\) | −12.9131 | − | 25.0191i | −0.503787 | − | 0.976087i | ||||
\(658\) | −2.16561 | + | 0.342999i | −0.0844242 | + | 0.0133715i | ||||
\(659\) | 3.59331 | − | 11.0591i | 0.139975 | − | 0.430800i | −0.856355 | − | 0.516387i | \(-0.827277\pi\) |
0.996331 | + | 0.0855871i | \(0.0272766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8291 | + | 39.4838i | 0.498993 | + | 1.53574i | 0.810641 | + | 0.585544i | \(0.199119\pi\) |
−0.311648 | + | 0.950197i | \(0.600881\pi\) | |||||||
\(662\) | −4.37411 | − | 8.58467i | −0.170005 | − | 0.333653i | ||||
\(663\) | 3.90987 | + | 11.9272i | 0.151847 | + | 0.463213i | ||||
\(664\) | −4.75577 | + | 1.54524i | −0.184560 | + | 0.0599671i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4879 | − | 7.53643i | −0.406397 | − | 0.292031i | ||||
\(667\) | 3.92637 | + | 24.7901i | 0.152030 | + | 0.959877i | ||||
\(668\) | −9.78704 | − | 9.78704i | −0.378672 | − | 0.378672i | ||||
\(669\) | −0.897530 | − | 0.892849i | −0.0347005 | − | 0.0345195i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.2074 | − | 56.7171i | −1.59079 | − | 2.18954i | ||||
\(672\) | −0.356073 | − | 0.114667i | −0.0137358 | − | 0.00442337i | ||||
\(673\) | 23.9046 | + | 12.1800i | 0.921454 | + | 0.469504i | 0.849313 | − | 0.527890i | \(-0.177017\pi\) |
0.0721411 | + | 0.997394i | \(0.477017\pi\) | |||||||
\(674\) | 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 | \(-0.489395\pi\) |
−0.788988 | + | 0.614408i | \(0.789395\pi\) | |||||||
\(678\) | −18.1124 | − | 5.83277i | −0.695602 | − | 0.224006i | ||||
\(679\) | 1.28118 | + | 1.76340i | 0.0491673 | + | 0.0676729i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.06529 | + | 4.04409i | 0.155782 | + | 0.154970i | ||||
\(682\) | −8.26315 | − | 8.26315i | −0.316413 | − | 0.316413i | ||||
\(683\) | −3.06282 | − | 19.3379i | −0.117196 | − | 0.739944i | −0.974376 | − | 0.224927i | \(-0.927786\pi\) |
0.857180 | − | 0.515017i | \(-0.172214\pi\) | |||||||
\(684\) | 1.17310 | + | 0.842973i | 0.0448547 | + | 0.0322319i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.86609 | − | 0.931249i | 0.109428 | − | 0.0355552i | ||||
\(687\) | −5.69313 | − | 17.3670i | −0.217207 | − | 0.662594i | ||||
\(688\) | 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 | −0.359469 | − | 0.933157i | \(-0.617042\pi\) |
0.839313 | − | 0.543649i | \(-0.182958\pi\) | |||||||
\(692\) | 0.896939 | − | 0.142061i | 0.0340965 | − | 0.00540036i | ||||
\(693\) | 1.52671 | + | 2.95800i | 0.0579949 | + | 0.112365i | ||||
\(694\) | −11.3510 | + | 15.6232i | −0.430876 | + | 0.593050i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.41915 | − | 14.4673i | −0.281222 | − | 0.548381i | ||||
\(697\) | −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 | \(0.991908\pi\) | |||||||
\(702\) | 6.21255 | − | 4.58855i | 0.234478 | − | 0.173184i | ||||
\(703\) | −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 | ||||
\(708\) | −8.63901 | + | 0.0225840i | −0.324674 | + | 0.000848758i | ||||
\(709\) | −5.99345 | − | 1.94739i | −0.225089 | − | 0.0731358i | 0.194301 | − | 0.980942i | \(-0.437756\pi\) |
−0.419390 | + | 0.907806i | \(0.637756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0342906 | − | 6.55851i | −0.00128600 | − | 0.245963i | ||||
\(712\) | 9.75471 | − | 4.97027i | 0.365573 | − | 0.186269i | ||||
\(713\) | −5.41900 | + | 2.76112i | −0.202943 | + | 0.103405i | ||||
\(714\) | −0.290016 | − | 1.80061i | −0.0108536 | − | 0.0673861i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.2695 | + | 3.66170i | 0.421163 | + | 0.136844i | ||||
\(717\) | 0.0531816 | + | 20.3435i | 0.00198610 | + | 0.759740i | ||||
\(718\) | −24.4491 | + | 24.4491i | −0.912432 | + | 0.912432i | ||||
\(719\) | 15.2779 | + | 11.1001i | 0.569770 | + | 0.413962i | 0.835022 | − | 0.550217i | \(-0.185455\pi\) |
−0.265251 | + | 0.964179i | \(0.585455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.76717 | + | 1.28392i | −0.0658127 | + | 0.0478157i | ||||
\(722\) | −2.93598 | + | 18.5371i | −0.109266 | + | 0.689878i | ||||
\(723\) | 1.23380 | − | 1.70755i | 0.0458854 | − | 0.0635043i | ||||
\(724\) | 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 | −0.762832 | − | 0.646597i | \(-0.776192\pi\) |
0.971489 | + | 0.237084i | \(0.0761916\pi\) | |||||||
\(728\) | 0.317066 | + | 0.0502184i | 0.0117513 | + | 0.00186122i | ||||
\(729\) | −7.93968 | + | 25.8062i | −0.294062 | + | 0.955786i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0326 | + | 15.1850i | −0.408055 | + | 0.561639i | ||||
\(732\) | 19.0850 | − | 13.9424i | 0.705401 | − | 0.515327i | ||||
\(733\) | −9.27418 | + | 1.46889i | −0.342550 | + | 0.0542545i | −0.325339 | − | 0.945597i | \(-0.605478\pi\) |
−0.0172103 | + | 0.999852i | \(0.505478\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 3.03572 | + | 18.5389i | 0.111746 | + | 0.682428i | ||||
\(739\) | −18.0916 | + | 5.87832i | −0.665511 | + | 0.216238i | −0.622241 | − | 0.782826i | \(-0.713778\pi\) |
−0.0432699 | + | 0.999063i | \(0.513778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.10601 | − | 0.559904i | −0.0406304 | − | 0.0205686i | ||||
\(742\) | 0.259872 | + | 1.64077i | 0.00954019 | + | 0.0602344i | ||||
\(743\) | −23.1938 | − | 23.1938i | −0.850899 | − | 0.850899i | 0.139345 | − | 0.990244i | \(-0.455500\pi\) |
−0.990244 | + | 0.139345i | \(0.955500\pi\) | |||||||
\(744\) | 2.77851 | − | 2.79308i | 0.101865 | − | 0.102399i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.36867 | − | 8.76572i | −0.233174 | − | 0.320936i | ||||
\(747\) | −6.74058 | + | 13.4019i | −0.246625 | + | 0.490350i | ||||
\(748\) | −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 | ||||
\(753\) | −12.0054 | + | 37.2803i | −0.437502 | + | 1.35857i | ||||
\(754\) | 8.20106 | + | 11.2878i | 0.298665 | + | 0.411077i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.995899 | + | 0.517314i | −0.0362205 | + | 0.0188145i | ||||
\(757\) | −20.0652 | − | 20.0652i | −0.729283 | − | 0.729283i | 0.241194 | − | 0.970477i | \(-0.422461\pi\) |
−0.970477 | + | 0.241194i | \(0.922461\pi\) | |||||||
\(758\) | 5.23911 | + | 33.0785i | 0.190293 | + | 1.20146i | ||||
\(759\) | 10.7463 | − | 21.2279i | 0.390067 | − | 0.770523i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.4666 | + | 9.89919i | −1.10441 | + | 0.358845i | −0.803799 | − | 0.594901i | \(-0.797191\pi\) |
−0.300613 | + | 0.953746i | \(0.597191\pi\) | |||||||
\(762\) | 24.7487 | − | 8.11294i | 0.896552 | − | 0.293901i | ||||
\(763\) | −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 | ||||
\(768\) | −1.02173 | − | 1.39859i | −0.0368686 | − | 0.0504674i | ||||
\(769\) | −8.74366 | + | 12.0346i | −0.315305 | + | 0.433980i | −0.937026 | − | 0.349259i | \(-0.886433\pi\) |
0.621722 | + | 0.783238i | \(0.286433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.50470 | + | 3.33576i | −0.234261 | + | 0.120134i | ||||
\(772\) | −3.32936 | − | 0.527318i | −0.119826 | − | 0.0189786i | ||||
\(773\) | 10.0990 | − | 19.8204i | 0.363235 | − | 0.712889i | −0.634985 | − | 0.772524i | \(-0.718994\pi\) |
0.998220 | + | 0.0596354i | \(0.0189938\pi\) | |||||||
\(774\) | 11.0028 | + | 3.51152i | 0.395486 | + | 0.126219i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0922i | 0.362290i | ||||||||
\(777\) | −1.30531 | − | 0.943161i | −0.0468278 | − | 0.0338357i | ||||
\(778\) | 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 | ||||
\(783\) | −46.5057 | − | 14.7084i | −1.66198 | − | 0.525635i | ||||
\(784\) | 6.61303 | + | 2.14870i | 0.236180 | + | 0.0767395i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.9207 | + | 2.40320i | −0.532202 | + | 0.0857193i | ||||
\(787\) | 45.7145 | − | 23.2927i | 1.62955 | − | 0.830295i | 0.631035 | − | 0.775755i | \(-0.282631\pi\) |
0.998512 | − | 0.0545406i | \(-0.0173694\pi\) | |||||||
\(788\) | 6.53260 | − | 3.32853i | 0.232714 | − | 0.118574i | ||||
\(789\) | 4.39775 | − | 0.708326i | 0.156564 | − | 0.0252171i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.25659 | − | 0.733210i | −0.0802351 | − | 0.0260700i | ||||
\(792\) | −2.33144 | + | 15.2353i | −0.0828442 | + | 0.541362i | ||||
\(793\) | −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 | \(-0.967505\pi\) |
0.977597 | + | 0.210487i | \(0.0675050\pi\) | |||||||
\(798\) | 0.146003 | + | 0.105495i | 0.00516845 | + | 0.00373450i | ||||
\(799\) | − | 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 | ||||
\(804\) | 23.1574 | − | 11.8756i | 0.816698 | − | 0.418821i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.98724 | + | 2.73520i | −0.0699974 | + | 0.0963431i | ||||
\(807\) | −24.6894 | − | 33.7959i | −0.869109 | − | 1.18967i | ||||
\(808\) | −9.41958 | + | 1.49192i | −0.331380 | + | 0.0524854i | ||||
\(809\) | 4.71934 | − | 14.5246i | 0.165923 | − | 0.510659i | −0.833180 | − | 0.553002i | \(-0.813482\pi\) |
0.999103 | + | 0.0423432i | \(0.0134823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.02202 | + | 3.14544i | 0.0358879 | + | 0.110451i | 0.967396 | − | 0.253270i | \(-0.0815060\pi\) |
−0.931508 | + | 0.363721i | \(0.881506\pi\) | |||||||
\(812\) | −0.920402 | − | 1.80639i | −0.0322998 | − | 0.0633919i | ||||
\(813\) | −19.0515 | + | 6.24533i | −0.668166 | + | 0.219033i | ||||
\(814\) | −21.0344 | + | 6.83450i | −0.737256 | + | 0.239549i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.81406 | − | 7.53414i | 0.133519 | − | 0.263748i | ||||
\(817\) | −0.289996 | − | 1.83096i | −0.0101457 | − | 0.0640572i | ||||
\(818\) | 11.3634 | + | 11.3634i | 0.397313 | + | 0.397313i | ||||
\(819\) | 0.776158 | − | 0.570136i | 0.0271212 | − | 0.0199222i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3359 | + | 25.2372i | 0.639927 | + | 0.880784i | 0.998612 | − | 0.0526750i | \(-0.0167748\pi\) |
−0.358685 | + | 0.933459i | \(0.616775\pi\) | |||||||
\(822\) | 1.49901 | − | 4.65486i | 0.0522841 | − | 0.162357i | ||||
\(823\) | −13.9035 | − | 7.08420i | −0.484647 | − | 0.246940i | 0.194555 | − | 0.980892i | \(-0.437674\pi\) |
−0.679202 | + | 0.733952i | \(0.737674\pi\) | |||||||
\(824\) | −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 | \(-0.370132\pi\) |
−0.509400 | + | 0.860530i | \(0.670132\pi\) | |||||||
\(828\) | 7.16612 | + | 3.60425i | 0.249040 | + | 0.125256i | ||||
\(829\) | −14.6691 | − | 20.1903i | −0.509480 | − | 0.701239i | 0.474351 | − | 0.880336i | \(-0.342683\pi\) |
−0.983832 | + | 0.179096i | \(0.942683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.20549 | + | 9.25375i | −0.319335 | + | 0.321009i | ||||
\(832\) | 1.05102 | + | 1.05102i | 0.0364375 | + | 0.0364375i | ||||
\(833\) | 5.30325 | + | 33.4834i | 0.183747 | + | 1.16013i | ||||
\(834\) | −10.7567 | − | 5.44544i | −0.372474 | − | 0.188560i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.35276 | − | 0.764459i | 0.0813720 | − | 0.0264394i | ||||
\(837\) | −0.0926914 | − | 11.8188i | −0.00320388 | − | 0.408518i | ||||
\(838\) | 1.01758 | + | 1.99711i | 0.0351516 | + | 0.0689889i | ||||
\(839\) | 5.55073 | + | 17.0834i | 0.191632 | + | 0.589784i | 0.999999 | + | 0.00110507i | \(0.000351754\pi\) |
−0.808367 | + | 0.588679i | \(0.799648\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.2677 | − | 56.2221i | 0.629920 | − | 1.93869i | ||||
\(842\) | 2.55767 | − | 0.405096i | 0.0881433 | − | 0.0139605i | ||||
\(843\) | 33.0241 | − | 24.1255i | 1.13741 | − | 0.830928i | ||||
\(844\) | −2.52005 | + | 3.46855i | −0.0867437 | + | 0.119392i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.9160 | + | 9.56282i | −0.994153 | + | 0.328776i | ||||
\(847\) | 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 | ||||||||
\(852\) | 12.3068 | − | 17.0323i | 0.421623 | − | 0.583516i | ||||
\(853\) | 4.94081 | − | 31.1950i | 0.169170 | − | 1.06810i | −0.746270 | − | 0.665643i | \(-0.768157\pi\) |
0.915440 | − | 0.402454i | \(-0.131843\pi\) | |||||||
\(854\) | 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 | \(-0.683610\pi\) |
0.838196 | + | 0.545369i | \(0.183610\pi\) | |||||||
\(858\) | −0.0345761 | − | 13.2264i | −0.00118041 | − | 0.451540i | ||||
\(859\) | 1.99366 | + | 0.647780i | 0.0680228 | + | 0.0221020i | 0.342831 | − | 0.939397i | \(-0.388614\pi\) |
−0.274808 | + | 0.961499i | \(0.588614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.372491 | + | 2.31267i | 0.0126944 | + | 0.0788155i | ||||
\(862\) | −1.00264 | + | 0.510869i | −0.0341500 | + | 0.0174003i | ||||
\(863\) | 25.5918 | − | 13.0397i | 0.871155 | − | 0.443876i | 0.0395333 | − | 0.999218i | \(-0.487413\pi\) |
0.831622 | + | 0.555343i | \(0.187413\pi\) | |||||||
\(864\) | −5.13840 | − | 0.772583i | −0.174812 | − | 0.0262838i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.5231 | − | 6.34342i | −0.663420 | − | 0.215558i | ||||
\(867\) | 11.7261 | − | 0.0306542i | 0.398239 | − | 0.00104107i | ||||
\(868\) | 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 | ||||
\(873\) | 21.5205 | + | 21.2966i | 0.728359 | + | 0.720782i | ||||
\(874\) | − | 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 | −0.984631 | − | 0.174648i | \(-0.944121\pi\) |
0.720045 | + | 0.693927i | \(0.244121\pi\) | |||||||
\(878\) | 23.2354 | + | 3.68012i | 0.784156 | + | 0.124198i | ||||
\(879\) | 3.73264 | + | 7.27862i | 0.125899 | + | 0.245502i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.5046 | + | 15.8347i | −0.387600 | + | 0.533485i | −0.957578 | − | 0.288175i | \(-0.906952\pi\) |
0.569978 | + | 0.821660i | \(0.306952\pi\) | |||||||
\(882\) | 18.5367 | − | 9.56732i | 0.624163 | − | 0.322148i | ||||
\(883\) | −13.3245 | + | 2.11040i | −0.448406 | + | 0.0710206i | −0.376554 | − | 0.926395i | \(-0.622891\pi\) |
−0.0718524 | + | 0.997415i | \(0.522891\pi\) | |||||||
\(884\) | −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 | 0.822597 | + | 0.568624i | \(0.192524\pi\) |
−0.0234837 | + | 0.999724i | \(0.507476\pi\) | |||||||
\(888\) | −2.32268 | − | 7.08541i | −0.0779442 | − | 0.237771i | ||||
\(889\) | 3.08864 | − | 1.00356i | 0.103590 | − | 0.0336583i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5676 | + | 37.1210i | 0.923550 | + | 1.24360i | ||||
\(892\) | −0.114341 | − | 0.721923i | −0.00382843 | − | 0.0241718i | ||||
\(893\) | 3.45666 | + | 3.45666i | 0.115673 | + | 0.115673i | ||||
\(894\) | 9.48414 | + | 9.43468i | 0.317197 | + | 0.315543i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.126947 | − | 0.174728i | −0.00424101 | − | 0.00583725i | ||||
\(897\) | −6.55228 | − | 2.11004i | −0.218774 | − | 0.0704523i | ||||
\(898\) | 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 | ||||
\(903\) | 1.37082 | + | 0.441449i | 0.0456182 | + | 0.0146905i | ||||
\(904\) | −6.45744 | − | 8.88790i | −0.214771 | − | 0.295607i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.1574 | − | 18.0627i | −0.603238 | − | 0.600092i | ||||
\(907\) | −7.30011 | − | 7.30011i | −0.242396 | − | 0.242396i | 0.575445 | − | 0.817841i | \(-0.304829\pi\) |
−0.817841 | + | 0.575445i | \(0.804829\pi\) | |||||||
\(908\) | 0.517900 | + | 3.26989i | 0.0171871 | + | 0.108515i | ||||
\(909\) | −16.6959 | + | 23.2344i | −0.553767 | + | 0.770636i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9954 | − | 8.77133i | 0.894397 | − | 0.290607i | 0.174474 | − | 0.984662i | \(-0.444177\pi\) |
0.719922 | + | 0.694055i | \(0.244177\pi\) | |||||||
\(912\) | 0.259799 | + | 0.792525i | 0.00860281 | + | 0.0262431i | ||||
\(913\) | 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 | ||||
\(918\) | −8.01723 | − | 24.0316i | −0.264608 | − | 0.793160i | ||||
\(919\) | 4.27526 | − | 5.88440i | 0.141028 | − | 0.194108i | −0.732660 | − | 0.680594i | \(-0.761722\pi\) |
0.873688 | + | 0.486486i | \(0.161722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2043 | + | 25.7483i | 0.435096 | + | 0.848434i | ||||
\(922\) | 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 | ||||||||
\(927\) | −21.3422 | + | 21.5665i | −0.700969 | + | 0.708337i | ||||
\(928\) | 1.46845 | − | 9.27141i | 0.0482041 | − | 0.304349i | ||||
\(929\) | 5.66314 | − | 4.11451i | 0.185802 | − | 0.134993i | −0.490996 | − | 0.871162i | \(-0.663367\pi\) |
0.676798 | + | 0.736169i | \(0.263367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.70875 | − | 1.96802i | −0.0887756 | − | 0.0644992i | ||||
\(932\) | −8.90175 | + | 8.90175i | −0.291586 | + | 0.291586i | ||||
\(933\) | 52.3114 | − | 0.136752i | 1.71260 | − | 0.00447705i | ||||
\(934\) | −22.0766 | − | 7.17313i | −0.722369 | − | 0.234712i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.45903 | − | 0.0233136i | 0.145748 | − | 0.000762030i | ||||
\(937\) | 35.4943 | − | 18.0852i | 1.15955 | − | 0.590819i | 0.235040 | − | 0.971986i | \(-0.424478\pi\) |
0.924506 | + | 0.381167i | \(0.124478\pi\) | |||||||
\(938\) | 2.89144 | − | 1.47326i | 0.0944088 | − | 0.0481037i | ||||
\(939\) | 4.59420 | + | 28.5238i | 0.149926 | + | 0.930840i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.912873 | + | 0.296610i | 0.0297588 | + | 0.00966922i | 0.323859 | − | 0.946106i | \(-0.395020\pi\) |
−0.294100 | + | 0.955775i | \(0.595020\pi\) | |||||||
\(942\) | 0.0742418 | + | 28.3996i | 0.00241893 | + | 0.925309i | ||||
\(943\) | 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 | −0.679378 | − | 0.733788i | \(-0.737750\pi\) |
0.872880 | − | 0.487935i | \(-0.162250\pi\) | |||||||
\(948\) | 2.21770 | − | 3.06924i | 0.0720275 | − | 0.0996843i | ||||
\(949\) | 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 | \(-0.0710949\pi\) |
0.858986 | + | 0.511999i | \(0.171095\pi\) | |||||||
\(954\) | 7.24523 | + | 21.9081i | 0.234573 | + | 0.709302i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.90374 | + | 9.50218i | −0.223283 | + | 0.307322i | ||||
\(957\) | −67.4486 | + | 49.2742i | −2.18030 | + | 1.59281i | ||||
\(958\) | −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 | ||||
\(963\) | 32.6942 | − | 5.35363i | 1.05356 | − | 0.172518i | ||||
\(964\) | 1.15675 | − | 0.375849i | 0.0372563 | − | 0.0121053i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.892392 | + | 0.451762i | 0.0287122 | + | 0.0145352i | ||||
\(967\) | 6.91329 | + | 43.6488i | 0.222316 | + | 1.40365i | 0.806118 | + | 0.591755i | \(0.201565\pi\) |
−0.583802 | + | 0.811896i | \(0.698435\pi\) | |||||||
\(968\) | 10.8855 | + | 10.8855i | 0.349872 | + | 0.349872i | ||||
\(969\) | −2.86773 | + | 2.88277i | −0.0921249 | + | 0.0926078i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4405 | − | 44.6505i | −1.04107 | − | 1.43290i | −0.896306 | − | 0.443437i | \(-0.853759\pi\) |
−0.144760 | − | 0.989467i | \(-0.546241\pi\) | |||||||
\(972\) | −12.4905 | + | 9.32672i | −0.400633 | + | 0.299155i | ||||
\(973\) | −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 | \(-0.172392\pi\) |
0.0866240 | + | 0.996241i | \(0.472392\pi\) | |||||||
\(978\) | −2.15433 | + | 6.68980i | −0.0688878 | + | 0.213916i | ||||
\(979\) | −33.0604 | − | 45.5037i | −1.05661 | − | 1.45430i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8907 | − | 14.8261i | −0.347712 | − | 0.473360i | ||||
\(982\) | −22.0207 | − | 22.0207i | −0.702708 | − | 0.702708i | ||||
\(983\) | −3.05030 | − | 19.2588i | −0.0972894 | − | 0.614261i | −0.987367 | − | 0.158451i | \(-0.949350\pi\) |
0.890077 | − | 0.455809i | \(-0.150650\pi\) | |||||||
\(984\) | −4.89871 | + | 9.67671i | −0.156165 | + | 0.308482i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 43.5259 | − | 14.1424i | 1.38615 | − | 0.450386i | ||||
\(987\) | −3.60875 | + | 1.18299i | −0.114868 | + | 0.0376550i | ||||
\(988\) | −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 | −0.612896 | − | 0.790164i | \(-0.709995\pi\) |
0.960290 | − | 0.279005i | \(-0.0900046\pi\) | |||||||
\(992\) | 2.24660 | − | 0.355826i | 0.0713295 | − | 0.0112975i | ||||
\(993\) | −9.84420 | − | 13.4752i | −0.312396 | − | 0.427621i | ||||
\(994\) | 1.54012 | − | 2.11980i | 0.0488497 | − | 0.0672359i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.70683 | + | 3.95224i | −0.244200 | + | 0.125231i | ||||
\(997\) | −45.5136 | − | 7.20864i | −1.44143 | − | 0.228300i | −0.613750 | − | 0.789501i | \(-0.710340\pi\) |
−0.827680 | + | 0.561201i | \(0.810340\pi\) | |||||||
\(998\) | 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.107.10 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.107.1 | 80 | ||
5.2 | odd | 4 | 750.2.l.c.143.4 | 80 | |||
5.3 | odd | 4 | 750.2.l.a.143.7 | 80 | |||
5.4 | even | 2 | 150.2.l.a.17.1 | ✓ | 80 | ||
15.2 | even | 4 | 750.2.l.c.143.8 | 80 | |||
15.8 | even | 4 | 750.2.l.a.143.3 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.17.10 | yes | 80 | ||
25.3 | odd | 20 | inner | 750.2.l.b.743.1 | 80 | ||
25.4 | even | 10 | 750.2.l.c.257.8 | 80 | |||
25.21 | even | 5 | 750.2.l.a.257.3 | 80 | |||
25.22 | odd | 20 | 150.2.l.a.53.10 | yes | 80 | ||
75.29 | odd | 10 | 750.2.l.c.257.4 | 80 | |||
75.47 | even | 20 | 150.2.l.a.53.1 | yes | 80 | ||
75.53 | even | 20 | inner | 750.2.l.b.743.10 | 80 | ||
75.71 | odd | 10 | 750.2.l.a.257.7 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.1 | ✓ | 80 | 5.4 | even | 2 | ||
150.2.l.a.17.10 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.53.1 | yes | 80 | 75.47 | even | 20 | ||
150.2.l.a.53.10 | yes | 80 | 25.22 | odd | 20 | ||
750.2.l.a.143.3 | 80 | 15.8 | even | 4 | |||
750.2.l.a.143.7 | 80 | 5.3 | odd | 4 | |||
750.2.l.a.257.3 | 80 | 25.21 | even | 5 | |||
750.2.l.a.257.7 | 80 | 75.71 | odd | 10 | |||
750.2.l.b.107.1 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.107.10 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.743.1 | 80 | 25.3 | odd | 20 | inner | ||
750.2.l.b.743.10 | 80 | 75.53 | even | 20 | inner | ||
750.2.l.c.143.4 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.143.8 | 80 | 15.2 | even | 4 | |||
750.2.l.c.257.4 | 80 | 75.29 | odd | 10 | |||
750.2.l.c.257.8 | 80 | 25.4 | even | 10 |