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 | 257.4 | ||
Character | \(\chi\) | \(=\) | 750.257 |
Dual form | 750.2.l.c.143.4 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{17}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.453990 | − | 0.891007i | −0.321020 | − | 0.630037i | ||||
\(3\) | 0.530925 | + | 1.64867i | 0.306530 | + | 0.951861i | ||||
\(4\) | −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 | 0.677657 | − | 0.735379i | \(-0.262996\pi\) |
−0.735379 | + | 0.677657i | \(0.762996\pi\) | |||||||
\(8\) | 0.987688 | + | 0.156434i | 0.349201 | + | 0.0553079i | ||||
\(9\) | −2.43624 | + | 1.75064i | −0.812079 | + | 0.583547i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.88609 | + | 1.58759i | 1.47321 | + | 0.478676i | 0.932077 | − | 0.362259i | \(-0.117995\pi\) |
0.541136 | + | 0.840935i | \(0.317995\pi\) | |||||||
\(12\) | −1.64587 | − | 0.539538i | −0.475123 | − | 0.155751i | ||||
\(13\) | −1.32436 | − | 0.674795i | −0.367312 | − | 0.187155i | 0.260586 | − | 0.965451i | \(-0.416084\pi\) |
−0.627897 | + | 0.778296i | \(0.716084\pi\) | |||||||
\(14\) | −0.0667401 | + | 0.205405i | −0.0178371 | + | 0.0548968i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | −0.762690 | + | 4.81543i | −0.184979 | + | 1.16791i | 0.704080 | + | 0.710121i | \(0.251360\pi\) |
−0.889059 | + | 0.457793i | \(0.848640\pi\) | |||||||
\(18\) | 2.66586 | + | 1.37593i | 0.628350 | + | 0.324309i | ||||
\(19\) | −0.283032 | − | 0.389560i | −0.0649319 | − | 0.0893711i | 0.775316 | − | 0.631574i | \(-0.217591\pi\) |
−0.840248 | + | 0.542202i | \(0.817591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.170700 | − | 0.332863i | 0.0372498 | − | 0.0726367i | ||||
\(22\) | −0.803689 | − | 5.07429i | −0.171347 | − | 1.08184i | ||||
\(23\) | −2.38239 | + | 1.21389i | −0.496763 | + | 0.253114i | −0.684376 | − | 0.729130i | \(-0.739925\pi\) |
0.187612 | + | 0.982243i | \(0.439925\pi\) | |||||||
\(24\) | 0.266479 | + | 1.71143i | 0.0543949 | + | 0.349344i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.48636i | 0.291500i | ||||||||
\(27\) | −4.17969 | − | 3.08710i | −0.804382 | − | 0.594112i | ||||
\(28\) | 0.213317 | − | 0.0337860i | 0.0403130 | − | 0.00638496i | ||||
\(29\) | 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 | ||||
\(33\) | −0.0232622 | + | 8.89846i | −0.00404943 | + | 1.54902i | ||||
\(34\) | 4.63684 | − | 1.50660i | 0.795211 | − | 0.258380i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0156850 | − | 2.99996i | 0.00261417 | − | 0.499993i | ||||
\(37\) | −1.95441 | + | 3.83574i | −0.321303 | + | 0.630592i | −0.994007 | − | 0.109320i | \(-0.965133\pi\) |
0.672704 | + | 0.739912i | \(0.265133\pi\) | |||||||
\(38\) | −0.218606 | + | 0.429039i | −0.0354627 | + | 0.0695994i | ||||
\(39\) | 0.409380 | − | 2.54170i | 0.0655533 | − | 0.406998i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.95547 | − | 1.93505i | 0.930087 | − | 0.302204i | 0.195489 | − | 0.980706i | \(-0.437371\pi\) |
0.734598 | + | 0.678502i | \(0.237371\pi\) | |||||||
\(42\) | −0.374079 | 0.000977913i | −0.0577217 | 0.000150895i | ||||||
\(43\) | −2.72225 | + | 2.72225i | −0.415139 | + | 0.415139i | −0.883524 | − | 0.468385i | \(-0.844836\pi\) |
0.468385 | + | 0.883524i | \(0.344836\pi\) | |||||||
\(44\) | −4.15636 | + | 3.01977i | −0.626595 | + | 0.455248i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.16317 | + | 1.57163i | 0.318942 | + | 0.231725i | ||||
\(47\) | −10.0271 | + | 1.58814i | −1.46260 | + | 0.231654i | −0.836448 | − | 0.548046i | \(-0.815372\pi\) |
−0.626154 | + | 0.779699i | \(0.715372\pi\) | |||||||
\(48\) | 1.40392 | − | 1.01441i | 0.202638 | − | 0.146417i | ||||
\(49\) | − | 6.95335i | − | 0.993336i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.34400 | + | 1.29921i | −1.16839 | + | 0.181926i | ||||
\(52\) | 1.32436 | − | 0.674795i | 0.183656 | − | 0.0935773i | ||||
\(53\) | 1.20325 | + | 7.59700i | 0.165279 | + | 1.04353i | 0.921264 | + | 0.388939i | \(0.127158\pi\) |
−0.755985 | + | 0.654589i | \(0.772842\pi\) | |||||||
\(54\) | −0.853081 | + | 5.12565i | −0.116090 | + | 0.697512i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.126947 | − | 0.174728i | −0.0169640 | − | 0.0233490i | ||||
\(57\) | 0.491987 | − | 0.673453i | 0.0651653 | − | 0.0892011i | ||||
\(58\) | 1.46845 | − | 9.27141i | 0.192817 | − | 1.21740i | ||||
\(59\) | 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 | \(0.761789\pi\) | |||||||
\(62\) | 2.02668 | + | 1.03265i | 0.257389 | + | 0.131146i | ||||
\(63\) | 0.639411 | + | 0.104703i | 0.0805582 | + | 0.0131913i | ||||
\(64\) | 0.951057 | + | 0.309017i | 0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.93914 | − | 4.01909i | 0.977241 | − | 0.494716i | ||||
\(67\) | 14.8405 | + | 2.35050i | 1.81305 | + | 0.287159i | 0.968628 | − | 0.248514i | \(-0.0799422\pi\) |
0.844425 | + | 0.535673i | \(0.179942\pi\) | |||||||
\(68\) | −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 | 0.138373 | + | 0.990380i | \(0.455813\pi\) |
−0.984667 | + | 0.174444i | \(0.944187\pi\) | |||||||
\(72\) | −2.68010 | + | 1.34798i | −0.315853 | + | 0.158861i | ||||
\(73\) | −4.26070 | − | 8.36209i | −0.498677 | − | 0.978708i | −0.993936 | − | 0.109963i | \(-0.964927\pi\) |
0.495259 | − | 0.868745i | \(-0.335073\pi\) | |||||||
\(74\) | 4.30495 | 0.500441 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.481522 | 0.0552344 | ||||||||
\(77\) | −0.503741 | − | 0.988647i | −0.0574066 | − | 0.112667i | ||||
\(78\) | −2.45053 | + | 0.789148i | −0.277468 | + | 0.0893534i | ||||
\(79\) | 1.28502 | − | 1.76867i | 0.144576 | − | 0.198991i | −0.730588 | − | 0.682819i | \(-0.760754\pi\) |
0.875163 | + | 0.483828i | \(0.160754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.87050 | − | 8.52996i | 0.318945 | − | 0.947773i | ||||
\(82\) | −4.42787 | − | 4.42787i | −0.488976 | − | 0.488976i | ||||
\(83\) | 4.93895 | + | 0.782253i | 0.542120 | + | 0.0858634i | 0.421488 | − | 0.906834i | \(-0.361508\pi\) |
0.120632 | + | 0.992697i | \(0.461508\pi\) | |||||||
\(84\) | 0.168957 | + | 0.333751i | 0.0184347 | + | 0.0364152i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.66142 | + | 1.18967i | 0.394821 | + | 0.128285i | ||||
\(87\) | −5.06463 | + | 15.4498i | −0.542985 | + | 1.65639i | ||||
\(88\) | 4.57759 | + | 2.33240i | 0.487972 | + | 0.248634i | ||||
\(89\) | 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 | ||||
\(92\) | 0.418278 | − | 2.64090i | 0.0436085 | − | 0.275333i | ||||
\(93\) | −3.18124 | − | 2.32404i | −0.329879 | − | 0.240991i | ||||
\(94\) | 5.96725 | + | 8.21321i | 0.615475 | + | 0.847128i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.54121 | − | 0.790366i | −0.157299 | − | 0.0806664i | ||||
\(97\) | −1.57877 | − | 9.96799i | −0.160300 | − | 1.01210i | −0.928350 | − | 0.371706i | \(-0.878773\pi\) |
0.768050 | − | 0.640390i | \(-0.221227\pi\) | |||||||
\(98\) | −6.19548 | + | 3.15676i | −0.625838 | + | 0.318881i | ||||
\(99\) | −14.6830 | + | 4.68606i | −1.47570 | + | 0.470967i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.53700i | − | 0.948967i | −0.880264 | − | 0.474483i | \(-0.842635\pi\) | ||
0.880264 | − | 0.474483i | \(-0.157365\pi\) | |||||||
\(102\) | 4.94570 | + | 6.84473i | 0.489697 | + | 0.677729i | ||||
\(103\) | 9.98929 | − | 1.58215i | 0.984274 | − | 0.155894i | 0.356505 | − | 0.934293i | \(-0.383968\pi\) |
0.627769 | + | 0.778400i | \(0.283968\pi\) | |||||||
\(104\) | −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 | \(0.0707659\pi\) | |||||||
\(108\) | 4.95428 | − | 1.56689i | 0.476725 | − | 0.150774i | ||||
\(109\) | 5.83194 | − | 1.89491i | 0.558598 | − | 0.181500i | −0.0160921 | − | 0.999871i | \(-0.505123\pi\) |
0.574690 | + | 0.818371i | \(0.305123\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.36152 | − | 1.18569i | −0.698725 | − | 0.112540i | ||||
\(112\) | −0.0980509 | + | 0.192436i | −0.00926494 | + | 0.0181835i | ||||
\(113\) | 4.98756 | − | 9.78864i | 0.469190 | − | 0.920838i | −0.528233 | − | 0.849099i | \(-0.677145\pi\) |
0.997423 | − | 0.0717385i | \(-0.0228547\pi\) | |||||||
\(114\) | −0.823409 | − | 0.132623i | −0.0771193 | − | 0.0124212i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.92755 | + | 2.90074i | −0.828902 | + | 0.269327i | ||||
\(117\) | 4.40778 | − | 0.674520i | 0.407500 | − | 0.0623594i | ||||
\(118\) | 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 | ||||
\(122\) | 13.4778 | − | 2.13468i | 1.22023 | − | 0.193265i | ||||
\(123\) | 6.35216 | + | 8.79124i | 0.572755 | + | 0.792680i | ||||
\(124\) | − | 2.27460i | − | 0.204265i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.196996 | − | 0.617253i | −0.0175498 | − | 0.0549893i | ||||
\(127\) | 13.3979 | − | 6.82658i | 1.18887 | − | 0.605761i | 0.256249 | − | 0.966611i | \(-0.417513\pi\) |
0.932624 | + | 0.360850i | \(0.117513\pi\) | |||||||
\(128\) | −0.156434 | − | 0.987688i | −0.0138270 | − | 0.0873001i | ||||
\(129\) | −5.93341 | − | 3.04279i | −0.522407 | − | 0.267902i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.12870 | − | 7.05905i | −0.448097 | − | 0.616752i | 0.523891 | − | 0.851785i | \(-0.324480\pi\) |
−0.971987 | + | 0.235034i | \(0.924480\pi\) | |||||||
\(132\) | −7.18533 | − | 5.24920i | −0.625403 | − | 0.456884i | ||||
\(133\) | −0.0162687 | + | 0.102717i | −0.00141068 | + | 0.00890667i | ||||
\(134\) | −4.64313 | − | 14.2901i | −0.401105 | − | 1.23447i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50660 | + | 4.63684i | −0.129190 | + | 0.397605i | ||||
\(137\) | 2.51567 | + | 1.28180i | 0.214928 | + | 0.109511i | 0.558140 | − | 0.829747i | \(-0.311515\pi\) |
−0.343212 | + | 0.939258i | \(0.611515\pi\) | |||||||
\(138\) | −1.44263 | + | 4.40077i | −0.122805 | + | 0.374619i | ||||
\(139\) | 6.62014 | + | 2.15102i | 0.561513 | + | 0.182447i | 0.576002 | − | 0.817448i | \(-0.304612\pi\) |
−0.0144887 | + | 0.999895i | \(0.504612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.94195 | − | 15.6882i | −0.668833 | − | 1.32119i | ||||
\(142\) | 11.9826 | + | 1.89786i | 1.00556 | + | 0.159265i | ||||
\(143\) | −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 | ||||
\(147\) | 11.4638 | − | 3.69171i | 0.945518 | − | 0.304487i | ||||
\(148\) | −1.95441 | − | 3.83574i | −0.160651 | − | 0.315296i | ||||
\(149\) | −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 | \(0.705497\pi\) | |||||||
\(152\) | −0.218606 | − | 0.429039i | −0.0177313 | − | 0.0347997i | ||||
\(153\) | −6.57201 | − | 13.0667i | −0.531315 | − | 1.05638i | ||||
\(154\) | −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 | 0.0720863 | − | 0.997398i | \(-0.477034\pi\) |
−0.997398 | + | 0.0720863i | \(0.977034\pi\) | |||||||
\(158\) | −2.15928 | − | 0.341997i | −0.171783 | − | 0.0272078i | ||||
\(159\) | −11.8861 | + | 6.01719i | −0.942630 | + | 0.477194i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.549217 | + | 0.178451i | 0.0432843 | + | 0.0140639i | ||||
\(162\) | −8.90343 | + | 1.31488i | −0.699520 | + | 0.103307i | ||||
\(163\) | 3.61543 | + | 1.84215i | 0.283182 | + | 0.144289i | 0.589813 | − | 0.807540i | \(-0.299202\pi\) |
−0.306630 | + | 0.951829i | \(0.599202\pi\) | |||||||
\(164\) | −1.93505 | + | 5.95547i | −0.151102 | + | 0.465044i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.54524 | − | 4.75577i | −0.119934 | − | 0.369119i | ||||
\(167\) | −2.16520 | + | 13.6706i | −0.167549 | + | 1.05786i | 0.750349 | + | 0.661042i | \(0.229886\pi\) |
−0.917897 | + | 0.396818i | \(0.870114\pi\) | |||||||
\(168\) | 0.220670 | − | 0.302062i | 0.0170250 | − | 0.0233046i | ||||
\(169\) | −6.34263 | − | 8.72988i | −0.487894 | − | 0.671529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.37151 | + | 0.453573i | 0.104882 | + | 0.0346856i | ||||
\(172\) | −0.602248 | − | 3.80244i | −0.0459210 | − | 0.289934i | ||||
\(173\) | −0.809140 | + | 0.412278i | −0.0615178 | + | 0.0313449i | −0.484479 | − | 0.874803i | \(-0.660991\pi\) |
0.422961 | + | 0.906148i | \(0.360991\pi\) | |||||||
\(174\) | 16.0652 | − | 2.50144i | 1.21790 | − | 0.189633i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.13754i | − | 0.387257i | ||||||
\(177\) | −7.00238 | + | 5.05961i | −0.526331 | + | 0.380304i | ||||
\(178\) | −10.8132 | + | 1.71264i | −0.810482 | + | 0.128368i | ||||
\(179\) | −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 | ||||
\(183\) | −23.6352 | − | 0.0617869i | −1.74717 | − | 0.00456742i | ||||
\(184\) | −2.54296 | + | 0.826257i | −0.187469 | + | 0.0609125i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.626479 | + | 3.88960i | −0.0459357 | + | 0.285199i | ||||
\(187\) | −11.3715 | + | 22.3178i | −0.831566 | + | 1.63204i | ||||
\(188\) | 4.60895 | − | 9.04558i | 0.336142 | − | 0.659716i | ||||
\(189\) | 0.166859 | + | 1.10977i | 0.0121372 | + | 0.0807238i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.70151 | + | 1.52761i | −0.340189 | + | 0.110534i | −0.474129 | − | 0.880455i | \(-0.657237\pi\) |
0.133940 | + | 0.990989i | \(0.457237\pi\) | |||||||
\(192\) | −0.00452789 | + | 1.73204i | −0.000326772 | + | 0.125000i | ||||
\(193\) | 2.38356 | − | 2.38356i | 0.171572 | − | 0.171572i | −0.616098 | − | 0.787670i | \(-0.711287\pi\) |
0.787670 | + | 0.616098i | \(0.211287\pi\) | |||||||
\(194\) | −8.16479 | + | 5.93207i | −0.586198 | + | 0.425898i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.62538 | + | 4.08708i | 0.401813 | + | 0.291934i | ||||
\(197\) | 7.24145 | − | 1.14693i | 0.515932 | − | 0.0817156i | 0.106961 | − | 0.994263i | \(-0.465888\pi\) |
0.408970 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(198\) | 10.8412 | + | 10.9552i | 0.770454 | + | 0.778553i | ||||
\(199\) | 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 | ||||
\(202\) | −8.49753 | + | 4.32971i | −0.597884 | + | 0.304637i | ||||
\(203\) | −0.317149 | − | 2.00240i | −0.0222595 | − | 0.140541i | ||||
\(204\) | 3.85340 | − | 7.51409i | 0.269792 | − | 0.526092i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.94475 | − | 8.18224i | −0.414190 | − | 0.570084i | ||||
\(207\) | 3.67899 | − | 7.12804i | 0.255707 | − | 0.495433i | ||||
\(208\) | −0.232519 | + | 1.46807i | −0.0161223 | + | 0.101792i | ||||
\(209\) | −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 | \(0.0528525\pi\) | |||||||
\(212\) | −6.85335 | − | 3.49196i | −0.470690 | − | 0.239828i | ||||
\(213\) | −19.9677 | − | 6.54566i | −1.36817 | − | 0.448501i | ||||
\(214\) | −10.5027 | − | 3.41254i | −0.717951 | − | 0.233276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.64531 | − | 3.70294i | −0.248032 | − | 0.251953i | ||||
\(217\) | 0.485210 | + | 0.0768498i | 0.0329382 | + | 0.00521690i | ||||
\(218\) | −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 | ||||
\(222\) | 2.28561 | + | 7.09746i | 0.153400 | + | 0.476350i | ||||
\(223\) | −0.331831 | − | 0.651256i | −0.0222211 | − | 0.0436113i | 0.879629 | − | 0.475660i | \(-0.157791\pi\) |
−0.901850 | + | 0.432049i | \(0.857791\pi\) | |||||||
\(224\) | 0.215976 | 0.0144305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.9860 | −0.730781 | ||||||||
\(227\) | −1.50300 | − | 2.94981i | −0.0997579 | − | 0.195786i | 0.835734 | − | 0.549135i | \(-0.185043\pi\) |
−0.935492 | + | 0.353349i | \(0.885043\pi\) | |||||||
\(228\) | 0.255652 | + | 0.793872i | 0.0169310 | + | 0.0525755i | ||||
\(229\) | 6.20224 | − | 8.53665i | 0.409855 | − | 0.564117i | −0.553328 | − | 0.832964i | \(-0.686642\pi\) |
0.963183 | + | 0.268846i | \(0.0866423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.36251 | − | 1.35540i | 0.0896463 | − | 0.0891788i | ||||
\(232\) | 6.63760 | + | 6.63760i | 0.435780 | + | 0.435780i | ||||
\(233\) | 12.4340 | + | 1.96935i | 0.814577 | + | 0.129016i | 0.549803 | − | 0.835294i | \(-0.314703\pi\) |
0.264774 | + | 0.964311i | \(0.414703\pi\) | |||||||
\(234\) | −2.60209 | − | 3.62114i | −0.170104 | − | 0.236721i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.74363 | − | 1.54130i | −0.308784 | − | 0.100330i | ||||
\(237\) | 3.59821 | + | 1.17954i | 0.233729 | + | 0.0766192i | ||||
\(238\) | −0.938212 | − | 0.478043i | −0.0608152 | − | 0.0309869i | ||||
\(239\) | −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 | \(0.887527\pi\) | |||||||
\(242\) | 2.40821 | − | 15.2048i | 0.154805 | − | 0.977403i | ||||
\(243\) | 15.5871 | + | 0.203749i | 0.999915 | + | 0.0130705i | ||||
\(244\) | −8.02083 | − | 11.0397i | −0.513481 | − | 0.706746i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94923 | − | 9.65096i | 0.315552 | − | 0.615323i | ||||
\(247\) | 0.111963 | + | 0.706906i | 0.00712403 | + | 0.0449793i | ||||
\(248\) | −2.02668 | + | 1.03265i | −0.128695 | + | 0.0655732i | ||||
\(249\) | 1.33253 | + | 8.55802i | 0.0844459 | + | 0.542343i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.6123i | − | 1.42728i | −0.700515 | − | 0.713638i | \(-0.747046\pi\) | ||
0.700515 | − | 0.713638i | \(-0.252954\pi\) | |||||||
\(252\) | −0.460543 | + | 0.455752i | −0.0290115 | + | 0.0287097i | ||||
\(253\) | −13.5678 | + | 2.14892i | −0.852998 | + | 0.135102i | ||||
\(254\) | −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 | \(0.292022\pi\) | |||||||
\(258\) | −0.0174316 | + | 6.66810i | −0.00108525 | + | 0.415138i | ||||
\(259\) | 0.884259 | − | 0.287313i | 0.0549452 | − | 0.0178528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.1606 | − | 0.147235i | −1.74309 | − | 0.00911361i | ||||
\(262\) | −3.96128 | + | 7.77445i | −0.244729 | + | 0.480307i | ||||
\(263\) | −1.16756 | + | 2.29146i | −0.0719947 | + | 0.141298i | −0.924199 | − | 0.381912i | \(-0.875266\pi\) |
0.852204 | + | 0.523210i | \(0.175266\pi\) | |||||||
\(264\) | −1.41500 | + | 8.78526i | −0.0870873 | + | 0.540696i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0989071 | − | 0.0321369i | 0.00606438 | − | 0.00197044i | ||||
\(267\) | 18.9624 | + | 0.0495712i | 1.16048 | + | 0.00303371i | ||||
\(268\) | −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 | \(0.814354\pi\) | |||||||
\(272\) | 4.81543 | − | 0.762690i | 0.291978 | − | 0.0462448i | ||||
\(273\) | −0.450683 | + | 0.325644i | −0.0272766 | + | 0.0197088i | ||||
\(274\) | − | 2.82340i | − | 0.170568i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.57606 | − | 0.712519i | 0.275446 | − | 0.0428886i | ||||
\(277\) | −6.71461 | + | 3.42126i | −0.403442 | + | 0.205564i | −0.643924 | − | 0.765090i | \(-0.722695\pi\) |
0.240482 | + | 0.970654i | \(0.422695\pi\) | |||||||
\(278\) | −1.08891 | − | 6.87513i | −0.0653087 | − | 0.412343i | ||||
\(279\) | 2.14257 | − | 6.47871i | 0.128273 | − | 0.387870i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8790 | + | 19.1028i | 0.827952 | + | 1.13958i | 0.988301 | + | 0.152517i | \(0.0487380\pi\) |
−0.160349 | + | 0.987060i | \(0.551262\pi\) | |||||||
\(282\) | −10.3727 | + | 14.1986i | −0.617687 | + | 0.845516i | ||||
\(283\) | 1.54005 | − | 9.72347i | 0.0915463 | − | 0.578000i | −0.898688 | − | 0.438588i | \(-0.855479\pi\) |
0.990234 | − | 0.139412i | \(-0.0445213\pi\) | |||||||
\(284\) | −3.74899 | − | 11.5382i | −0.222462 | − | 0.684667i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.35974 | + | 7.26252i | −0.139534 | + | 0.429442i | ||||
\(287\) | −1.20502 | − | 0.613989i | −0.0711302 | − | 0.0362426i | ||||
\(288\) | 0.484789 | − | 2.96057i | 0.0285665 | − | 0.174453i | ||||
\(289\) | −6.43873 | − | 2.09207i | −0.378749 | − | 0.123063i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5957 | − | 7.89513i | 0.914238 | − | 0.462821i | ||||
\(292\) | 9.26944 | + | 1.46814i | 0.542453 | + | 0.0859161i | ||||
\(293\) | 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 | ||||
\(297\) | −15.5213 | − | 21.7195i | −0.900640 | − | 1.26029i | ||||
\(298\) | 3.50644 | + | 6.88178i | 0.203123 | + | 0.398651i | ||||
\(299\) | 3.97428 | 0.229838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.831472 | 0.0479252 | ||||||||
\(302\) | 6.71307 | + | 13.1751i | 0.386294 | + | 0.758145i | ||||
\(303\) | 15.7234 | − | 5.06343i | 0.903285 | − | 0.290887i | ||||
\(304\) | −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 | 0.284465 | − | 0.958686i | \(-0.408184\pi\) |
−0.958686 | + | 0.284465i | \(0.908184\pi\) | |||||||
\(308\) | 1.09592 | + | 0.173577i | 0.0624460 | + | 0.00989048i | ||||
\(309\) | 7.91201 | + | 15.6291i | 0.450098 | + | 0.889106i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.7239 | + | 9.33296i | 1.62878 | + | 0.529224i | 0.973991 | − | 0.226586i | \(-0.0727564\pi\) |
0.654791 | + | 0.755810i | \(0.272756\pi\) | |||||||
\(312\) | 0.801950 | − | 2.44637i | 0.0454015 | − | 0.138498i | ||||
\(313\) | 14.8624 | + | 7.57278i | 0.840073 | + | 0.428039i | 0.820415 | − | 0.571768i | \(-0.193742\pi\) |
0.0196580 | + | 0.999807i | \(0.493742\pi\) | |||||||
\(314\) | −5.06682 | + | 15.5941i | −0.285937 | + | 0.880024i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.675573 | + | 2.07920i | 0.0380040 | + | 0.116964i | ||||
\(317\) | 1.69675 | − | 10.7129i | 0.0952991 | − | 0.601695i | −0.893105 | − | 0.449848i | \(-0.851478\pi\) |
0.988404 | − | 0.151847i | \(-0.0485219\pi\) | |||||||
\(318\) | 10.7575 | + | 7.85886i | 0.603253 | + | 0.440703i | ||||
\(319\) | 28.3466 | + | 39.0157i | 1.58710 | + | 2.18446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.0199 | + | 8.72818i | 0.949957 | + | 0.487160i | ||||
\(322\) | −0.0903379 | − | 0.570371i | −0.00503433 | − | 0.0317855i | ||||
\(323\) | 2.09176 | − | 1.06581i | 0.116389 | − | 0.0593031i | ||||
\(324\) | 5.21364 | + | 7.33607i | 0.289647 | + | 0.407559i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 4.05769i | − | 0.224735i | ||||||
\(327\) | 6.22041 | + | 8.60889i | 0.343989 | + | 0.476073i | ||||
\(328\) | 6.18485 | − | 0.979584i | 0.341501 | − | 0.0540885i | ||||
\(329\) | 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 | ||||
\(333\) | −1.95361 | − | 12.7662i | −0.107057 | − | 0.699586i | ||||
\(334\) | 13.1635 | − | 4.27710i | 0.720277 | − | 0.234032i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.369321 | − | 0.0594848i | −0.0201481 | − | 0.00324516i | ||||
\(337\) | 12.7818 | − | 25.0858i | 0.696272 | − | 1.36651i | −0.223752 | − | 0.974646i | \(-0.571830\pi\) |
0.920023 | − | 0.391864i | \(-0.128170\pi\) | |||||||
\(338\) | −4.89888 | + | 9.61460i | −0.266464 | + | 0.522965i | ||||
\(339\) | 18.7863 | + | 3.02582i | 1.02033 | + | 0.164340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1139 | + | 3.61113i | −0.601852 | + | 0.195554i | ||||
\(342\) | −0.218517 | − | 1.42794i | −0.0118161 | − | 0.0772143i | ||||
\(343\) | −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 | ||||
\(347\) | −19.0736 | + | 3.02097i | −1.02393 | + | 0.162174i | −0.645742 | − | 0.763556i | \(-0.723452\pi\) |
−0.378185 | + | 0.925730i | \(0.623452\pi\) | |||||||
\(348\) | −9.52222 | − | 13.1785i | −0.510445 | − | 0.706443i | ||||
\(349\) | − | 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 | ||||
\(352\) | −4.57759 | + | 2.33240i | −0.243986 | + | 0.124317i | ||||
\(353\) | 5.47696 | + | 34.5802i | 0.291509 | + | 1.84052i | 0.504438 | + | 0.863448i | \(0.331700\pi\) |
−0.212929 | + | 0.977068i | \(0.568300\pi\) | |||||||
\(354\) | 7.68716 | + | 3.94215i | 0.408568 | + | 0.209523i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.43505 | + | 8.85709i | 0.341057 | + | 0.469425i | ||||
\(357\) | 1.47269 | + | 1.07586i | 0.0779430 | + | 0.0569408i | ||||
\(358\) | −1.85367 | + | 11.7036i | −0.0979695 | + | 0.618555i | ||||
\(359\) | 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 | ||||
\(362\) | −15.3170 | − | 7.80442i | −0.805045 | − | 0.410191i | ||||
\(363\) | −8.30583 | + | 25.3372i | −0.435943 | + | 1.32986i | ||||
\(364\) | −0.305307 | − | 0.0992002i | −0.0160024 | − | 0.00519950i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6751 | + | 21.0872i | 0.557997 | + | 1.10224i | ||||
\(367\) | 3.18996 | + | 0.505240i | 0.166514 | + | 0.0263733i | 0.239135 | − | 0.970986i | \(-0.423136\pi\) |
−0.0726205 | + | 0.997360i | \(0.523136\pi\) | |||||||
\(368\) | 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 | ||||
\(372\) | 3.75007 | − | 1.20764i | 0.194432 | − | 0.0626134i | ||||
\(373\) | −4.91900 | − | 9.65408i | −0.254696 | − | 0.499869i | 0.727886 | − | 0.685698i | \(-0.240503\pi\) |
−0.982582 | + | 0.185829i | \(0.940503\pi\) | |||||||
\(374\) | 25.0479 | 1.29519 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1521 | −0.523554 | ||||||||
\(377\) | −6.33429 | − | 12.4317i | −0.326233 | − | 0.640268i | ||||
\(378\) | 0.913058 | − | 0.652497i | 0.0469627 | − | 0.0335608i | ||||
\(379\) | −19.6854 | + | 27.0946i | −1.01117 | + | 1.39176i | −0.0929573 | + | 0.995670i | \(0.529632\pi\) |
−0.918213 | + | 0.396087i | \(0.870368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3681 | + | 18.4644i | 0.941025 | + | 0.945958i | ||||
\(382\) | 3.49555 | + | 3.49555i | 0.178848 | + | 0.178848i | ||||
\(383\) | 16.0484 | + | 2.54182i | 0.820034 | + | 0.129881i | 0.552335 | − | 0.833622i | \(-0.313737\pi\) |
0.267699 | + | 0.963503i | \(0.413737\pi\) | |||||||
\(384\) | 1.54532 | − | 0.782298i | 0.0788592 | − | 0.0399215i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.20588 | − | 1.04165i | −0.163175 | − | 0.0530187i | ||||
\(387\) | 1.86636 | − | 11.3977i | 0.0948724 | − | 0.579379i | ||||
\(388\) | 8.99225 | + | 4.58178i | 0.456512 | + | 0.232605i | ||||
\(389\) | 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 | ||||
\(392\) | 1.08774 | − | 6.86775i | 0.0549394 | − | 0.346874i | ||||
\(393\) | 8.91510 | − | 12.2034i | 0.449707 | − | 0.615578i | ||||
\(394\) | −4.30947 | − | 5.93148i | −0.217108 | − | 0.298824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.83934 | − | 14.6332i | 0.243186 | − | 0.735345i | ||||
\(397\) | 0.295160 | + | 1.86357i | 0.0148137 | + | 0.0935298i | 0.993987 | − | 0.109494i | \(-0.0349231\pi\) |
−0.979174 | + | 0.203024i | \(0.934923\pi\) | |||||||
\(398\) | 7.43262 | − | 3.78711i | 0.372563 | − | 0.189831i | ||||
\(399\) | −0.177984 | + | 0.0277131i | −0.00891032 | + | 0.00138739i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.16880i | − | 0.357993i | −0.983850 | − | 0.178996i | \(-0.942715\pi\) | ||
0.983850 | − | 0.178996i | \(-0.0572850\pi\) | |||||||
\(402\) | 21.0945 | − | 15.2419i | 1.05210 | − | 0.760199i | ||||
\(403\) | 3.33926 | − | 0.528887i | 0.166341 | − | 0.0263458i | ||||
\(404\) | 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 | ||||
\(408\) | −8.44451 | − | 0.0220755i | −0.418066 | − | 0.00109290i | ||||
\(409\) | −15.2838 | + | 4.96600i | −0.755734 | + | 0.245553i | −0.661447 | − | 0.749992i | \(-0.730057\pi\) |
−0.0942874 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.777631 | + | 4.82805i | −0.0383577 | + | 0.238150i | ||||
\(412\) | −4.59157 | + | 9.01147i | −0.226211 | + | 0.443963i | ||||
\(413\) | 0.489054 | − | 0.959822i | 0.0240648 | − | 0.0472297i | ||||
\(414\) | −8.02136 | − | 0.0419389i | −0.394228 | − | 0.00206119i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.41362 | − | 0.459312i | 0.0693083 | − | 0.0225196i | ||||
\(417\) | −0.0315179 | + | 12.0565i | −0.00154344 | + | 0.590408i | ||||
\(418\) | −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 | \(0.679900\pi\) | |||||||
\(422\) | −4.23458 | + | 0.670692i | −0.206136 | + | 0.0326488i | ||||
\(423\) | 21.6481 | − | 21.4229i | 1.05257 | − | 1.04162i | ||||
\(424\) | 7.69169i | 0.373542i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.23292 | + | 20.7630i | 0.156636 | + | 1.00597i | ||||
\(427\) | 2.62595 | − | 1.33799i | 0.127079 | − | 0.0647498i | ||||
\(428\) | 1.72754 | + | 10.9072i | 0.0835037 | + | 0.527222i | ||||
\(429\) | 6.03545 | − | 11.7691i | 0.291394 | − | 0.568216i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.661426 | − | 0.910375i | −0.0318598 | − | 0.0438512i | 0.792790 | − | 0.609495i | \(-0.208628\pi\) |
−0.824650 | + | 0.565644i | \(0.808628\pi\) | |||||||
\(432\) | −1.64441 | + | 4.92909i | −0.0791165 | + | 0.237151i | ||||
\(433\) | 3.21125 | − | 20.2750i | 0.154323 | − | 0.974355i | −0.782016 | − | 0.623258i | \(-0.785809\pi\) |
0.936339 | − | 0.351097i | \(-0.114191\pi\) | |||||||
\(434\) | −0.151807 | − | 0.467215i | −0.00728698 | − | 0.0224270i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.89491 | + | 5.83194i | −0.0907498 | + | 0.279299i | ||||
\(437\) | 1.14718 | + | 0.584515i | 0.0548768 | + | 0.0279611i | ||||
\(438\) | −15.4465 | − | 5.06355i | −0.738062 | − | 0.241946i | ||||
\(439\) | −22.3736 | − | 7.26963i | −1.06783 | − | 0.346960i | −0.278191 | − | 0.960526i | \(-0.589735\pi\) |
−0.789644 | + | 0.613565i | \(0.789735\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1728 | + | 16.9400i | 0.579659 | + | 0.806668i | ||||
\(442\) | −7.15749 | − | 1.13363i | −0.340447 | − | 0.0539215i | ||||
\(443\) | 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 | ||||
\(447\) | −4.10066 | − | 12.7337i | −0.193954 | − | 0.602283i | ||||
\(448\) | −0.0980509 | − | 0.192436i | −0.00463247 | − | 0.00909173i | ||||
\(449\) | −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 | ||||||||
\(452\) | 4.98756 | + | 9.78864i | 0.234595 | + | 0.460419i | ||||
\(453\) | −7.85069 | − | 24.3786i | −0.368858 | − | 1.14541i | ||||
\(454\) | −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 | 0.973802 | − | 0.227397i | \(-0.0730215\pi\) |
−0.227397 | + | 0.973802i | \(0.573021\pi\) | |||||||
\(458\) | −10.4220 | − | 1.65068i | −0.486986 | − | 0.0771311i | ||||
\(459\) | 18.0535 | − | 17.7725i | 0.842666 | − | 0.829551i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2184 | + | 4.94475i | 0.708790 | + | 0.230300i | 0.641156 | − | 0.767410i | \(-0.278455\pi\) |
0.0676337 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(462\) | −1.82624 | − | 0.598662i | −0.0849642 | − | 0.0278523i | ||||
\(463\) | 5.51675 | + | 2.81092i | 0.256385 | + | 0.130635i | 0.577460 | − | 0.816419i | \(-0.304044\pi\) |
−0.321075 | + | 0.947054i | \(0.604044\pi\) | |||||||
\(464\) | 2.90074 | − | 8.92755i | 0.134663 | − | 0.414451i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.89021 | − | 11.9728i | −0.180210 | − | 0.554630i | ||||
\(467\) | −3.63127 | + | 22.9270i | −0.168035 | + | 1.06093i | 0.749129 | + | 0.662424i | \(0.230472\pi\) |
−0.917164 | + | 0.398509i | \(0.869528\pi\) | |||||||
\(468\) | −2.04513 | + | 3.96244i | −0.0945362 | + | 0.183164i | ||||
\(469\) | −1.90744 | − | 2.62537i | −0.0880775 | − | 0.121228i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9593 | − | 25.2705i | 0.597133 | − | 1.16440i | ||||
\(472\) | 0.780256 | + | 4.92635i | 0.0359142 | + | 0.226753i | ||||
\(473\) | −17.6230 | + | 8.97936i | −0.810305 | + | 0.412871i | ||||
\(474\) | −0.582577 | − | 3.74153i | −0.0267587 | − | 0.171854i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.05298i | 0.0482633i | ||||||||
\(477\) | −16.2310 | − | 16.4016i | −0.743167 | − | 0.750979i | ||||
\(478\) | 11.6007 | − | 1.83738i | 0.530605 | − | 0.0840396i | ||||
\(479\) | 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 | ||||
\(483\) | −0.00261477 | + | 1.00022i | −0.000118976 | + | 0.0455117i | ||||
\(484\) | −14.6409 | + | 4.75712i | −0.665496 | + | 0.216233i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.89486 | − | 13.9807i | −0.312757 | − | 0.634179i | ||||
\(487\) | −9.62881 | + | 18.8976i | −0.436323 | + | 0.856332i | 0.563226 | + | 0.826303i | \(0.309560\pi\) |
−0.999549 | + | 0.0300294i | \(0.990440\pi\) | |||||||
\(488\) | −6.19509 | + | 12.1585i | −0.280438 | + | 0.550391i | ||||
\(489\) | −1.11758 | + | 6.93870i | −0.0505389 | + | 0.313779i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.6177 | + | 9.62339i | −1.33663 | + | 0.434297i | −0.888174 | − | 0.459507i | \(-0.848026\pi\) |
−0.448456 | + | 0.893805i | \(0.648026\pi\) | |||||||
\(492\) | −10.8460 | − | 0.0283534i | −0.488974 | − | 0.00127827i | ||||
\(493\) | −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 | ||||
\(497\) | 2.58795 | − | 0.409892i | 0.116086 | − | 0.0183862i | ||||
\(498\) | 7.02030 | − | 5.07256i | 0.314587 | − | 0.227307i | ||||
\(499\) | − | 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 | ||||
\(502\) | −20.1477 | + | 10.2658i | −0.899236 | + | 0.458184i | ||||
\(503\) | −4.11407 | − | 25.9752i | −0.183437 | − | 1.15818i | −0.891834 | − | 0.452363i | \(-0.850581\pi\) |
0.708397 | − | 0.705815i | \(-0.249419\pi\) | |||||||
\(504\) | 0.615160 | + | 0.203439i | 0.0274014 | + | 0.00906191i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.07434 | + | 11.1134i | 0.358948 | + | 0.494050i | ||||
\(507\) | 11.0252 | − | 15.0918i | 0.489648 | − | 0.670251i | ||||
\(508\) | −2.35228 | + | 14.8517i | −0.104366 | + | 0.658938i | ||||
\(509\) | 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 | ||||
\(512\) | 0.891007 | + | 0.453990i | 0.0393773 | + | 0.0200637i | ||||
\(513\) | −0.0196223 | + | 2.50199i | −0.000866347 | + | 0.110465i | ||||
\(514\) | 4.01395 | + | 1.30421i | 0.177048 | + | 0.0575263i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.94923 | − | 3.01172i | 0.261900 | − | 0.132584i | ||||
\(517\) | −51.5147 | − | 8.15912i | −2.26561 | − | 0.358838i | ||||
\(518\) | −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 | −0.599729 | − | 0.800203i | \(-0.704725\pi\) |
0.946365 | + | 0.323099i | \(0.104725\pi\) | |||||||
\(522\) | 12.6534 | + | 25.1581i | 0.553826 | + | 1.10114i | ||||
\(523\) | 11.6979 | + | 22.9585i | 0.511514 | + | 1.00390i | 0.991921 | + | 0.126858i | \(0.0404891\pi\) |
−0.480407 | + | 0.877046i | \(0.659511\pi\) | |||||||
\(524\) | 8.72546 | 0.381174 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.57177 | 0.112134 | ||||||||
\(527\) | −5.03463 | − | 9.88101i | −0.219312 | − | 0.430424i | ||||
\(528\) | 8.47012 | − | 2.72765i | 0.368615 | − | 0.118706i | ||||
\(529\) | −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 | ||||
\(533\) | −9.19295 | − | 1.45602i | −0.398191 | − | 0.0630672i | ||||
\(534\) | −8.56457 | − | 16.9181i | −0.370625 | − | 0.732118i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.2901 | + | 4.64313i | 0.617237 | + | 0.200553i | ||||
\(537\) | 6.39325 | − | 19.5028i | 0.275889 | − | 0.841607i | ||||
\(538\) | −21.5305 | − | 10.9703i | −0.928246 | − | 0.472965i | ||||
\(539\) | 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 | \(-0.248696\pi\) | |||||||
\(542\) | −1.81078 | + | 11.4328i | −0.0777797 | + | 0.491082i | ||||
\(543\) | 24.0428 | + | 17.5643i | 1.03177 | + | 0.753757i | ||||
\(544\) | −2.86572 | − | 3.94433i | −0.122867 | − | 0.169112i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.494756 | + | 0.253722i | 0.0211736 | + | 0.0108583i | ||||
\(547\) | 6.82585 | + | 43.0967i | 0.291852 | + | 1.84268i | 0.501817 | + | 0.864974i | \(0.332665\pi\) |
−0.209965 | + | 0.977709i | \(0.567335\pi\) | |||||||
\(548\) | −2.51567 | + | 1.28180i | −0.107464 | + | 0.0547557i | ||||
\(549\) | −12.4467 | − | 38.9995i | −0.531211 | − | 1.66446i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.52004i | − | 0.192560i | ||||||
\(552\) | −2.71235 | − | 3.75382i | −0.115445 | − | 0.159773i | ||||
\(553\) | −0.466353 | + | 0.0738630i | −0.0198313 | + | 0.00314098i | ||||
\(554\) | 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 | \(0.0358615\pi\) | |||||||
\(558\) | −6.74528 | + | 1.03223i | −0.285551 | + | 0.0436976i | ||||
\(559\) | 5.44220 | − | 1.76828i | 0.230181 | − | 0.0747902i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.8322 | − | 6.89878i | −1.80838 | − | 0.291267i | ||||
\(562\) | 10.7198 | − | 21.0388i | 0.452187 | − | 0.887467i | ||||
\(563\) | 7.14045 | − | 14.0139i | 0.300934 | − | 0.590616i | −0.690179 | − | 0.723639i | \(-0.742468\pi\) |
0.991113 | + | 0.133022i | \(0.0424682\pi\) | |||||||
\(564\) | 17.3602 | + | 2.79613i | 0.730996 | + | 0.117738i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.36284 | + | 3.04217i | −0.393550 | + | 0.127872i | ||||
\(567\) | −1.74105 | + | 0.864300i | −0.0731174 | + | 0.0362972i | ||||
\(568\) | −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 | \(-0.607324\pi\) | |||||||
\(572\) | 7.54225 | − | 1.19457i | 0.315357 | − | 0.0499477i | ||||
\(573\) | −5.01468 | − | 6.94020i | −0.209491 | − | 0.289931i | ||||
\(574\) | 1.35243i | 0.0564492i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.85798 | + | 0.912121i | −0.119082 | + | 0.0380050i | ||||
\(577\) | 16.8154 | − | 8.56788i | 0.700034 | − | 0.356685i | −0.0674769 | − | 0.997721i | \(-0.521495\pi\) |
0.767511 | + | 0.641036i | \(0.221495\pi\) | |||||||
\(578\) | 1.05907 | + | 6.68673i | 0.0440517 | + | 0.278131i | ||||
\(579\) | 5.19519 | + | 2.66421i | 0.215905 | + | 0.110721i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.634802 | − | 0.873729i | −0.0263360 | − | 0.0362484i | ||||
\(582\) | −14.1149 | − | 10.3116i | −0.585083 | − | 0.427429i | ||||
\(583\) | −6.18173 | + | 39.0299i | −0.256021 | + | 1.61645i | ||||
\(584\) | −2.90012 | − | 8.92565i | −0.120008 | − | 0.369346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.45939 | − | 4.49153i | 0.0602867 | − | 0.185543i | ||||
\(587\) | 4.14963 | + | 2.11434i | 0.171274 | + | 0.0872683i | 0.537526 | − | 0.843247i | \(-0.319359\pi\) |
−0.366252 | + | 0.930516i | \(0.619359\pi\) | |||||||
\(588\) | −3.75160 | + | 11.4443i | −0.154713 | + | 0.471957i | ||||
\(589\) | 1.04166 | + | 0.338457i | 0.0429210 | + | 0.0139459i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.73558 | + | 11.3298i | 0.235930 | + | 0.466047i | ||||
\(592\) | 4.25195 | + | 0.673443i | 0.174754 | + | 0.0276783i | ||||
\(593\) | −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 | ||||
\(597\) | −13.7529 | + | 4.42888i | −0.562870 | + | 0.181262i | ||||
\(598\) | −1.80428 | − | 3.54111i | −0.0737826 | − | 0.144807i | ||||
\(599\) | −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 | \(0.506374\pi\) | |||||||
\(602\) | −0.377480 | − | 0.740847i | −0.0153850 | − | 0.0301947i | ||||
\(603\) | −40.2698 | + | 20.2540i | −1.63991 | + | 0.824807i | ||||
\(604\) | 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 | 0.656839 | − | 0.754031i | \(-0.271893\pi\) |
−0.754031 | + | 0.656839i | \(0.771893\pi\) | |||||||
\(608\) | 0.475594 | + | 0.0753267i | 0.0192879 | + | 0.00305490i | ||||
\(609\) | 3.13292 | − | 1.58600i | 0.126952 | − | 0.0642679i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3512 | + | 4.66298i | 0.580586 | + | 0.188644i | ||||
\(612\) | 14.4341 | + | 2.36357i | 0.583465 | + | 0.0955415i | ||||
\(613\) | −12.2470 | − | 6.24017i | −0.494653 | − | 0.252038i | 0.188823 | − | 0.982011i | \(-0.439533\pi\) |
−0.683476 | + | 0.729973i | \(0.739533\pi\) | |||||||
\(614\) | −5.16261 | + | 15.8889i | −0.208346 | + | 0.641223i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.342880 | − | 1.05528i | −0.0138150 | − | 0.0425183i | ||||
\(617\) | 1.60431 | − | 10.1292i | 0.0645872 | − | 0.407787i | −0.934120 | − | 0.356959i | \(-0.883814\pi\) |
0.998707 | − | 0.0508287i | \(-0.0161863\pi\) | |||||||
\(618\) | 10.3336 | − | 14.1451i | 0.415679 | − | 0.568999i | ||||
\(619\) | −27.3325 | − | 37.6199i | −1.09859 | − | 1.51207i | −0.837247 | − | 0.546825i | \(-0.815836\pi\) |
−0.261338 | − | 0.965247i | \(-0.584164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.7051 | + | 2.28099i | 0.549966 | + | 0.0915329i | ||||
\(622\) | −4.72465 | − | 29.8303i | −0.189441 | − | 1.19608i | ||||
\(623\) | −2.10678 | + | 1.07346i | −0.0844063 | + | 0.0430072i | ||||
\(624\) | −2.54381 | + | 0.396086i | −0.101834 | + | 0.0158561i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 16.6805i | − | 0.666686i | ||||||
\(627\) | 3.47306 | − | 2.50948i | 0.138701 | − | 0.100219i | ||||
\(628\) | 16.1947 | − | 2.56499i | 0.646239 | − | 0.102354i | ||||
\(629\) | −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 | ||||
\(633\) | 7.42591 | + | 0.0194127i | 0.295153 | + | 0.000771586i | ||||
\(634\) | −10.3155 | + | 3.35172i | −0.409683 | + | 0.133114i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.11847 | − | 13.1529i | 0.0840030 | − | 0.521546i | ||||
\(637\) | −4.69209 | + | 9.20875i | −0.185907 | + | 0.364864i | ||||
\(638\) | 21.8942 | − | 42.9697i | 0.866798 | − | 1.70119i | ||||
\(639\) | 0.190290 | − | 36.3955i | 0.00752777 | − | 1.43978i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.702023 | − | 0.228101i | 0.0277282 | − | 0.00900945i | −0.295120 | − | 0.955460i | \(-0.595360\pi\) |
0.322848 | + | 0.946451i | \(0.395360\pi\) | |||||||
\(642\) | 0.0500024 | − | 19.1273i | 0.00197344 | − | 0.754896i | ||||
\(643\) | 17.1573 | − | 17.1573i | 0.676616 | − | 0.676616i | −0.282617 | − | 0.959233i | \(-0.591203\pi\) |
0.959233 | + | 0.282617i | \(0.0912025\pi\) | |||||||
\(644\) | −0.467192 | + | 0.339435i | −0.0184099 | + | 0.0133756i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.89928 | − | 1.37991i | −0.0747262 | − | 0.0542918i | ||||
\(647\) | 5.95524 | − | 0.943217i | 0.234125 | − | 0.0370817i | −0.0382696 | − | 0.999267i | \(-0.512185\pi\) |
0.272394 | + | 0.962186i | \(0.412185\pi\) | |||||||
\(648\) | 4.16954 | − | 7.97590i | 0.163795 | − | 0.313323i | ||||
\(649\) | 25.6248i | 1.00586i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.130910 | + | 0.840754i | 0.00513078 | + | 0.0329517i | ||||
\(652\) | −3.61543 | + | 1.84215i | −0.141591 | + | 0.0721443i | ||||
\(653\) | 1.57981 | + | 9.97451i | 0.0618226 | + | 0.390333i | 0.999125 | + | 0.0418163i | \(0.0133144\pi\) |
−0.937303 | + | 0.348516i | \(0.886686\pi\) | |||||||
\(654\) | 4.84657 | − | 9.45078i | 0.189516 | − | 0.369555i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.68068 | − | 5.06602i | −0.143706 | − | 0.197795i | ||||
\(657\) | 25.0191 | + | 12.9131i | 0.976087 | + | 0.503787i | ||||
\(658\) | 0.342999 | − | 2.16561i | 0.0133715 | − | 0.0844242i | ||||
\(659\) | −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 | \(-0.199119\pi\) | |||||||
\(662\) | 8.58467 | + | 4.37411i | 0.333653 | + | 0.170005i | ||||
\(663\) | 11.9272 | + | 3.90987i | 0.463213 | + | 0.151847i | ||||
\(664\) | 4.75577 | + | 1.54524i | 0.184560 | + | 0.0599671i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4879 | + | 7.53643i | −0.406397 | + | 0.292031i | ||||
\(667\) | −24.7901 | − | 3.92637i | −0.959877 | − | 0.152030i | ||||
\(668\) | −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 | ||||
\(672\) | 0.114667 | + | 0.356073i | 0.00442337 | + | 0.0137358i | ||||
\(673\) | 12.1800 | + | 23.9046i | 0.469504 | + | 0.921454i | 0.997394 | + | 0.0721411i | \(0.0229832\pi\) |
−0.527890 | + | 0.849313i | \(0.677017\pi\) | |||||||
\(674\) | −28.1544 | −1.08447 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.7907 | 0.415028 | ||||||||
\(677\) | 10.0184 | + | 19.6621i | 0.385037 | + | 0.755677i | 0.999445 | − | 0.0333112i | \(-0.0106052\pi\) |
−0.614408 | + | 0.788988i | \(0.710605\pi\) | |||||||
\(678\) | −5.83277 | − | 18.1124i | −0.224006 | − | 0.695602i | ||||
\(679\) | −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 | ||||
\(683\) | −19.3379 | − | 3.06282i | −0.739944 | − | 0.117196i | −0.224927 | − | 0.974376i | \(-0.572214\pi\) |
−0.515017 | + | 0.857180i | \(0.672214\pi\) | |||||||
\(684\) | −1.17310 | + | 0.842973i | −0.0448547 | + | 0.0322319i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.86609 | + | 0.931249i | 0.109428 | + | 0.0355552i | ||||
\(687\) | 17.3670 | + | 5.69313i | 0.662594 | + | 0.217207i | ||||
\(688\) | 3.43023 | + | 1.74779i | 0.130776 | + | 0.0666339i | ||||
\(689\) | 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 | \(0.617042\pi\) | |||||||
\(692\) | 0.142061 | − | 0.896939i | 0.00540036 | − | 0.0340965i | ||||
\(693\) | 2.95800 | + | 1.52671i | 0.112365 | + | 0.0579949i | ||||
\(694\) | 11.3510 | + | 15.6232i | 0.430876 | + | 0.593050i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.41915 | + | 14.4673i | −0.281222 | + | 0.548381i | ||||
\(697\) | 4.77592 | + | 30.1540i | 0.180901 | + | 1.14216i | ||||
\(698\) | −12.8411 | + | 6.54286i | −0.486042 | + | 0.247651i | ||||
\(699\) | 3.35470 | + | 21.5451i | 0.126886 | + | 0.814912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.34594i | − | 0.0508356i | −0.999677 | − | 0.0254178i | \(-0.991908\pi\) | ||
0.999677 | − | 0.0254178i | \(-0.00809161\pi\) | |||||||
\(702\) | 4.58855 | − | 6.21255i | 0.173184 | − | 0.234478i | ||||
\(703\) | 2.04741 | − | 0.324278i | 0.0772195 | − | 0.0122304i | ||||
\(704\) | 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 | ||||
\(708\) | 0.0225840 | − | 8.63901i | 0.000848758 | − | 0.324674i | ||||
\(709\) | 5.99345 | − | 1.94739i | 0.225089 | − | 0.0731358i | −0.194301 | − | 0.980942i | \(-0.562244\pi\) |
0.419390 | + | 0.907806i | \(0.362244\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0342906 | + | 6.55851i | −0.00128600 | + | 0.245963i | ||||
\(712\) | 4.97027 | − | 9.75471i | 0.186269 | − | 0.365573i | ||||
\(713\) | 2.76112 | − | 5.41900i | 0.103405 | − | 0.202943i | ||||
\(714\) | 0.290016 | − | 1.80061i | 0.0108536 | − | 0.0673861i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.2695 | − | 3.66170i | 0.421163 | − | 0.136844i | ||||
\(717\) | −20.3435 | − | 0.0531816i | −0.759740 | − | 0.00198610i | ||||
\(718\) | 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 | ||||
\(722\) | −18.5371 | + | 2.93598i | −0.689878 | + | 0.109266i | ||||
\(723\) | −1.70755 | + | 1.23380i | −0.0635043 | + | 0.0458854i | ||||
\(724\) | 17.1907i | 0.638888i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.3463 | − | 4.10228i | 0.977805 | − | 0.152250i | ||||
\(727\) | 11.0417 | − | 5.62601i | 0.409513 | − | 0.208657i | −0.237084 | − | 0.971489i | \(-0.576192\pi\) |
0.646597 | + | 0.762832i | \(0.276192\pi\) | |||||||
\(728\) | 0.0502184 | + | 0.317066i | 0.00186122 | + | 0.0117513i | ||||
\(729\) | 7.93968 | + | 25.8062i | 0.294062 | + | 0.955786i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0326 | − | 15.1850i | −0.408055 | − | 0.561639i | ||||
\(732\) | 13.9424 | − | 19.0850i | 0.515327 | − | 0.705401i | ||||
\(733\) | 1.46889 | − | 9.27418i | 0.0542545 | − | 0.342550i | −0.945597 | − | 0.325339i | \(-0.894522\pi\) |
0.999852 | − | 0.0172103i | \(-0.00547849\pi\) | |||||||
\(734\) | −0.998039 | − | 3.07165i | −0.0368383 | − | 0.113377i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.826257 | − | 2.54296i | 0.0304562 | − | 0.0937346i | ||||
\(737\) | 68.7804 | + | 35.0454i | 2.53356 | + | 1.29091i | ||||
\(738\) | 18.5389 | + | 3.03572i | 0.682428 | + | 0.111746i | ||||
\(739\) | 18.0916 | + | 5.87832i | 0.665511 | + | 0.216238i | 0.622241 | − | 0.782826i | \(-0.286222\pi\) |
0.0432699 | + | 0.999063i | \(0.486222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.10601 | + | 0.559904i | −0.0406304 | + | 0.0205686i | ||||
\(742\) | −1.64077 | − | 0.259872i | −0.0602344 | − | 0.00954019i | ||||
\(743\) | −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 | ||||
\(747\) | −13.4019 | + | 6.74058i | −0.490350 | + | 0.246625i | ||||
\(748\) | −11.3715 | − | 22.3178i | −0.415783 | − | 0.816020i | ||||
\(749\) | −2.38506 | −0.0871483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1267 | 1.28179 | 0.640895 | − | 0.767628i | \(-0.278563\pi\) | ||||
0.640895 | + | 0.767628i | \(0.278563\pi\) | |||||||
\(752\) | 4.60895 | + | 9.04558i | 0.168071 | + | 0.329858i | ||||
\(753\) | 37.2803 | − | 12.0054i | 1.35857 | − | 0.437502i | ||||
\(754\) | −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 | 0.970477 | − | 0.241194i | \(-0.0775389\pi\) |
−0.241194 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(758\) | 33.0785 | + | 5.23911i | 1.20146 | + | 0.190293i | ||||
\(759\) | −10.7463 | − | 21.2279i | −0.390067 | − | 0.770523i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.4666 | − | 9.89919i | −1.10441 | − | 0.358845i | −0.300613 | − | 0.953746i | \(-0.597191\pi\) |
−0.803799 | + | 0.594901i | \(0.797191\pi\) | |||||||
\(762\) | 8.11294 | − | 24.7487i | 0.293901 | − | 0.896552i | ||||
\(763\) | −1.18003 | − | 0.601254i | −0.0427199 | − | 0.0217669i | ||||
\(764\) | 1.52761 | − | 4.70151i | 0.0552671 | − | 0.170095i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.02104 | − | 15.4532i | −0.181418 | − | 0.558346i | ||||
\(767\) | 1.15975 | − | 7.32235i | 0.0418760 | − | 0.264395i | ||||
\(768\) | −1.39859 | − | 1.02173i | −0.0504674 | − | 0.0368686i | ||||
\(769\) | 8.74366 | + | 12.0346i | 0.315305 | + | 0.433980i | 0.937026 | − | 0.349259i | \(-0.113567\pi\) |
−0.621722 | + | 0.783238i | \(0.713567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.50470 | − | 3.33576i | −0.234261 | − | 0.120134i | ||||
\(772\) | 0.527318 | + | 3.32936i | 0.0189786 | + | 0.119826i | ||||
\(773\) | −19.8204 | + | 10.0990i | −0.712889 | + | 0.363235i | −0.772524 | − | 0.634985i | \(-0.781006\pi\) |
0.0596354 | + | 0.998220i | \(0.481006\pi\) | |||||||
\(774\) | −11.0028 | + | 3.51152i | −0.395486 | + | 0.126219i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.0922i | − | 0.362290i | ||||||
\(777\) | 0.943161 | + | 1.30531i | 0.0338357 | + | 0.0468278i | ||||
\(778\) | −2.57264 | + | 0.407467i | −0.0922337 | + | 0.0146084i | ||||
\(779\) | −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 | ||||
\(783\) | −14.7084 | − | 46.5057i | −0.525635 | − | 1.66198i | ||||
\(784\) | −6.61303 | + | 2.14870i | −0.236180 | + | 0.0767395i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.9207 | − | 2.40320i | −0.532202 | − | 0.0857193i | ||||
\(787\) | 23.2927 | − | 45.7145i | 0.830295 | − | 1.62955i | 0.0545406 | − | 0.998512i | \(-0.482631\pi\) |
0.775755 | − | 0.631035i | \(-0.217369\pi\) | |||||||
\(788\) | −3.32853 | + | 6.53260i | −0.118574 | + | 0.232714i | ||||
\(789\) | −4.39775 | − | 0.708326i | −0.156564 | − | 0.0252171i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.25659 | + | 0.733210i | −0.0802351 | + | 0.0260700i | ||||
\(792\) | −15.2353 | + | 2.33144i | −0.541362 | + | 0.0828442i | ||||
\(793\) | 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 | ||||
\(797\) | −3.06529 | + | 0.485494i | −0.108578 | + | 0.0171971i | −0.210487 | − | 0.977597i | \(-0.567505\pi\) |
0.101909 | + | 0.994794i | \(0.467505\pi\) | |||||||
\(798\) | 0.105495 | + | 0.146003i | 0.00373450 | + | 0.00516845i | ||||
\(799\) | − | 49.4961i | − | 1.75105i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.98587 | + | 31.2890i | 0.352833 | + | 1.10554i | ||||
\(802\) | −6.38745 | + | 3.25457i | −0.225549 | + | 0.114923i | ||||
\(803\) | −7.54261 | − | 47.6222i | −0.266173 | − | 1.68055i | ||||
\(804\) | −23.1574 | − | 11.8756i | −0.816698 | − | 0.418821i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.98724 | − | 2.73520i | −0.0699974 | − | 0.0963431i | ||||
\(807\) | 33.7959 | + | 24.6894i | 1.18967 | + | 0.869109i | ||||
\(808\) | 1.49192 | − | 9.41958i | 0.0524854 | − | 0.331380i | ||||
\(809\) | −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 | \(0.0815060\pi\) | |||||||
\(812\) | 1.80639 | + | 0.920402i | 0.0633919 | + | 0.0322998i | ||||
\(813\) | 6.24533 | − | 19.0515i | 0.219033 | − | 0.668166i | ||||
\(814\) | 21.0344 | + | 6.83450i | 0.737256 | + | 0.239549i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.81406 | + | 7.53414i | 0.133519 | + | 0.263748i | ||||
\(817\) | 1.83096 | + | 0.289996i | 0.0640572 | + | 0.0101457i | ||||
\(818\) | 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 | −0.358685 | − | 0.933459i | \(-0.616775\pi\) |
0.998612 | + | 0.0526750i | \(0.0167748\pi\) | |||||||
\(822\) | 4.65486 | − | 1.49901i | 0.162357 | − | 0.0522841i | ||||
\(823\) | −7.08420 | − | 13.9035i | −0.246940 | − | 0.484647i | 0.733952 | − | 0.679202i | \(-0.237674\pi\) |
−0.980892 | + | 0.194555i | \(0.937674\pi\) | |||||||
\(824\) | 10.1138 | 0.352331 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.07723 | −0.0374817 | ||||||||
\(827\) | 1.65039 | + | 3.23908i | 0.0573898 | + | 0.112634i | 0.917920 | − | 0.396766i | \(-0.129868\pi\) |
−0.860530 | + | 0.509400i | \(0.829868\pi\) | |||||||
\(828\) | 3.60425 | + | 7.16612i | 0.125256 | + | 0.249040i | ||||
\(829\) | 14.6691 | − | 20.1903i | 0.509480 | − | 0.701239i | −0.474351 | − | 0.880336i | \(-0.657317\pi\) |
0.983832 | + | 0.179096i | \(0.0573174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.20549 | − | 9.25375i | −0.319335 | − | 0.321009i | ||||
\(832\) | −1.05102 | − | 1.05102i | −0.0364375 | − | 0.0364375i | ||||
\(833\) | 33.4834 | + | 5.30325i | 1.16013 | + | 0.183747i | ||||
\(834\) | 10.7567 | − | 5.44544i | 0.372474 | − | 0.188560i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.35276 | + | 0.764459i | 0.0813720 | + | 0.0264394i | ||||
\(837\) | 11.8188 | + | 0.0926914i | 0.408518 | + | 0.00320388i | ||||
\(838\) | 1.99711 | + | 1.01758i | 0.0689889 | + | 0.0351516i | ||||
\(839\) | −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 | ||||
\(842\) | 0.405096 | − | 2.55767i | 0.0139605 | − | 0.0881433i | ||||
\(843\) | −24.1255 | + | 33.0241i | −0.830928 | + | 1.13741i | ||||
\(844\) | 2.52005 | + | 3.46855i | 0.0867437 | + | 0.119392i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.9160 | − | 9.56282i | −0.994153 | − | 0.328776i | ||||
\(847\) | −0.520114 | − | 3.28387i | −0.0178713 | − | 0.112835i | ||||
\(848\) | 6.85335 | − | 3.49196i | 0.235345 | − | 0.119914i | ||||
\(849\) | 16.8485 | − | 2.62340i | 0.578238 | − | 0.0900350i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 11.5107i | − | 0.394581i | ||||||
\(852\) | 17.0323 | − | 12.3068i | 0.583516 | − | 0.421623i | ||||
\(853\) | −31.1950 | + | 4.94081i | −1.06810 | + | 0.169170i | −0.665643 | − | 0.746270i | \(-0.731843\pi\) |
−0.402454 | + | 0.915440i | \(0.631843\pi\) | |||||||
\(854\) | −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 | \(0.183610\pi\) | |||||||
\(858\) | −13.2264 | − | 0.0345761i | −0.451540 | − | 0.00118041i | ||||
\(859\) | −1.99366 | + | 0.647780i | −0.0680228 | + | 0.0221020i | −0.342831 | − | 0.939397i | \(-0.611386\pi\) |
0.274808 | + | 0.961499i | \(0.411386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.372491 | − | 2.31267i | 0.0126944 | − | 0.0788155i | ||||
\(862\) | −0.510869 | + | 1.00264i | −0.0174003 | + | 0.0341500i | ||||
\(863\) | −13.0397 | + | 25.5918i | −0.443876 | + | 0.871155i | 0.555343 | + | 0.831622i | \(0.312587\pi\) |
−0.999218 | + | 0.0395333i | \(0.987413\pi\) | |||||||
\(864\) | 5.13840 | − | 0.772583i | 0.174812 | − | 0.0262838i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.5231 | + | 6.34342i | −0.663420 | + | 0.215558i | ||||
\(867\) | 0.0306542 | − | 11.7261i | 0.00104107 | − | 0.398239i | ||||
\(868\) | −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 | ||||
\(872\) | 6.05656 | − | 0.959266i | 0.205101 | − | 0.0324848i | ||||
\(873\) | 21.2966 | + | 21.5205i | 0.720782 | + | 0.728359i | ||||
\(874\) | − | 1.28751i | − | 0.0435505i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.50091 | + | 16.0617i | 0.0844978 | + | 0.542676i | ||||
\(877\) | −15.3780 | + | 7.83550i | −0.519279 | + | 0.264586i | −0.693927 | − | 0.720045i | \(-0.744121\pi\) |
0.174648 | + | 0.984631i | \(0.444121\pi\) | |||||||
\(878\) | 3.68012 | + | 23.2354i | 0.124198 | + | 0.784156i | ||||
\(879\) | −3.73264 | + | 7.27862i | −0.125899 | + | 0.245502i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.5046 | − | 15.8347i | −0.387600 | − | 0.533485i | 0.569978 | − | 0.821660i | \(-0.306952\pi\) |
−0.957578 | + | 0.288175i | \(0.906952\pi\) | |||||||
\(882\) | 9.56732 | − | 18.5367i | 0.322148 | − | 0.624163i | ||||
\(883\) | 2.11040 | − | 13.3245i | 0.0710206 | − | 0.448406i | −0.926395 | − | 0.376554i | \(-0.877109\pi\) |
0.997415 | − | 0.0718524i | \(-0.0228910\pi\) | |||||||
\(884\) | 2.23936 | + | 6.89203i | 0.0753177 | + | 0.231804i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.95075 | − | 18.3145i | 0.199919 | − | 0.615288i | ||||
\(887\) | −46.7094 | − | 23.7996i | −1.56835 | − | 0.799114i | −0.568624 | − | 0.822597i | \(-0.692524\pi\) |
−0.999724 | + | 0.0234837i | \(0.992524\pi\) | |||||||
\(888\) | −7.08541 | − | 2.32268i | −0.237771 | − | 0.0779442i | ||||
\(889\) | −3.08864 | − | 1.00356i | −0.103590 | − | 0.0336583i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5676 | − | 37.1210i | 0.923550 | − | 1.24360i | ||||
\(892\) | 0.721923 | + | 0.114341i | 0.0241718 | + | 0.00382843i | ||||
\(893\) | 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 | ||||
\(897\) | 2.11004 | + | 6.55228i | 0.0704523 | + | 0.218774i | ||||
\(898\) | 8.72498 | + | 17.1237i | 0.291156 | + | 0.571426i | ||||
\(899\) | −21.3516 | −0.712117 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.5005 | −1.24932 | ||||||||
\(902\) | −14.6053 | − | 28.6646i | −0.486305 | − | 0.954427i | ||||
\(903\) | 0.441449 | + | 1.37082i | 0.0146905 | + | 0.0456182i | ||||
\(904\) | 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 | 0.817841 | − | 0.575445i | \(-0.195171\pi\) |
−0.575445 | + | 0.817841i | \(0.695171\pi\) | |||||||
\(908\) | 3.26989 | + | 0.517900i | 0.108515 | + | 0.0171871i | ||||
\(909\) | 16.6959 | + | 23.2344i | 0.553767 | + | 0.770636i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9954 | + | 8.77133i | 0.894397 | + | 0.290607i | 0.719922 | − | 0.694055i | \(-0.244177\pi\) |
0.174474 | + | 0.984662i | \(0.444177\pi\) | |||||||
\(912\) | −0.792525 | − | 0.259799i | −0.0262431 | − | 0.00860281i | ||||
\(913\) | 22.8903 | + | 11.6632i | 0.757557 | + | 0.385995i | ||||
\(914\) | 6.97317 | − | 21.4612i | 0.230652 | − | 0.709874i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.26071 | + | 10.0354i | 0.107737 | + | 0.331580i | ||||
\(917\) | −0.294799 | + | 1.86129i | −0.00973511 | + | 0.0614651i | ||||
\(918\) | −24.0316 | − | 8.01723i | −0.793160 | − | 0.264608i | ||||
\(919\) | −4.27526 | − | 5.88440i | −0.141028 | − | 0.194108i | 0.732660 | − | 0.680594i | \(-0.238278\pi\) |
−0.873688 | + | 0.486486i | \(0.838278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2043 | − | 25.7483i | 0.435096 | − | 0.848434i | ||||
\(922\) | −2.50319 | − | 15.8045i | −0.0824382 | − | 0.520494i | ||||
\(923\) | 16.0671 | − | 8.18661i | 0.528856 | − | 0.269466i | ||||
\(924\) | 0.295681 | + | 1.89897i | 0.00972720 | + | 0.0624717i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 6.19159i | − | 0.203468i | ||||||
\(927\) | −21.5665 | + | 21.3422i | −0.708337 | + | 0.700969i | ||||
\(928\) | −9.27141 | + | 1.46845i | −0.304349 | + | 0.0482041i | ||||
\(929\) | −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 | ||||
\(933\) | −0.136752 | + | 52.3114i | −0.00447705 | + | 1.71260i | ||||
\(934\) | 22.0766 | − | 7.17313i | 0.722369 | − | 0.234712i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.45903 | + | 0.0233136i | 0.145748 | + | 0.000762030i | ||||
\(937\) | 18.0852 | − | 35.4943i | 0.590819 | − | 1.15955i | −0.381167 | − | 0.924506i | \(-0.624478\pi\) |
0.971986 | − | 0.235040i | \(-0.0755223\pi\) | |||||||
\(938\) | −1.47326 | + | 2.89144i | −0.0481037 | + | 0.0944088i | ||||
\(939\) | −4.59420 | + | 28.5238i | −0.149926 | + | 0.930840i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.912873 | − | 0.296610i | 0.0297588 | − | 0.00966922i | −0.294100 | − | 0.955775i | \(-0.595020\pi\) |
0.323859 | + | 0.946106i | \(0.395020\pi\) | |||||||
\(942\) | −28.3996 | − | 0.0742418i | −0.925309 | − | 0.00241893i | ||||
\(943\) | −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 | ||||
\(947\) | 37.5965 | − | 5.95470i | 1.22172 | − | 0.193502i | 0.487935 | − | 0.872880i | \(-0.337750\pi\) |
0.733788 | + | 0.679378i | \(0.237750\pi\) | |||||||
\(948\) | −3.06924 | + | 2.21770i | −0.0996843 | + | 0.0720275i | ||||
\(949\) | 13.9495i | 0.452820i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.5629 | − | 2.89034i | 0.601942 | − | 0.0937258i | ||||
\(952\) | 0.938212 | − | 0.478043i | 0.0304076 | − | 0.0154935i | ||||
\(953\) | 8.96795 | + | 56.6214i | 0.290500 | + | 1.83415i | 0.511999 | + | 0.858986i | \(0.328905\pi\) |
−0.221499 | + | 0.975161i | \(0.571095\pi\) | |||||||
\(954\) | −7.24523 | + | 21.9081i | −0.234573 | + | 0.709302i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.90374 | − | 9.50218i | −0.223283 | − | 0.307322i | ||||
\(957\) | −49.2742 | + | 67.4486i | −1.59281 | + | 2.18030i | ||||
\(958\) | 3.50627 | − | 22.1377i | 0.113282 | − | 0.715236i | ||||
\(959\) | −0.188434 | − | 0.579941i | −0.00608486 | − | 0.0187273i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.98073 | + | 24.5622i | −0.257443 | + | 0.792328i | ||||
\(962\) | −5.70131 | − | 2.90496i | −0.183818 | − | 0.0936598i | ||||
\(963\) | −5.35363 | + | 32.6942i | −0.172518 | + | 1.05356i | ||||
\(964\) | −1.15675 | − | 0.375849i | −0.0372563 | − | 0.0121053i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.892392 | − | 0.451762i | 0.0287122 | − | 0.0145352i | ||||
\(967\) | −43.6488 | − | 6.91329i | −1.40365 | − | 0.222316i | −0.591755 | − | 0.806118i | \(-0.701565\pi\) |
−0.811896 | + | 0.583802i | \(0.801565\pi\) | |||||||
\(968\) | 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 | −0.144760 | + | 0.989467i | \(0.546241\pi\) |
−0.896306 | + | 0.443437i | \(0.853759\pi\) | |||||||
\(972\) | −9.32672 | + | 12.4905i | −0.299155 | + | 0.400633i | ||||
\(973\) | −0.682516 | − | 1.33951i | −0.0218804 | − | 0.0429428i | ||||
\(974\) | 21.2093 | 0.679589 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.6458 | 0.436793 | ||||||||
\(977\) | −15.0267 | − | 29.4915i | −0.480746 | − | 0.943516i | −0.996241 | − | 0.0866240i | \(-0.972392\pi\) |
0.515496 | − | 0.856892i | \(-0.327608\pi\) | |||||||
\(978\) | 6.68980 | − | 2.15433i | 0.213916 | − | 0.0688878i | ||||
\(979\) | 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 | ||||
\(983\) | −19.2588 | − | 3.05030i | −0.614261 | − | 0.0972894i | −0.158451 | − | 0.987367i | \(-0.550650\pi\) |
−0.455809 | + | 0.890077i | \(0.650650\pi\) | |||||||
\(984\) | 4.89871 | + | 9.67671i | 0.156165 | + | 0.308482i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 43.5259 | + | 14.1424i | 1.38615 | + | 0.450386i | ||||
\(987\) | −1.18299 | + | 3.60875i | −0.0376550 | + | 0.114868i | ||||
\(988\) | −0.637709 | − | 0.324929i | −0.0202882 | − | 0.0103374i | ||||
\(989\) | 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 | \(0.709995\pi\) | |||||||
\(992\) | 0.355826 | − | 2.24660i | 0.0112975 | − | 0.0713295i | ||||
\(993\) | −13.4752 | − | 9.84420i | −0.427621 | − | 0.312396i | ||||
\(994\) | −1.54012 | − | 2.11980i | −0.0488497 | − | 0.0672359i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.70683 | − | 3.95224i | −0.244200 | − | 0.125231i | ||||
\(997\) | 7.20864 | + | 45.5136i | 0.228300 | + | 1.44143i | 0.789501 | + | 0.613750i | \(0.210340\pi\) |
−0.561201 | + | 0.827680i | \(0.689660\pi\) | |||||||
\(998\) | −1.11963 | + | 0.570481i | −0.0354414 | + | 0.0180583i | ||||
\(999\) | 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.c.257.4 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.c.257.8 | 80 | ||
5.2 | odd | 4 | 750.2.l.b.743.10 | 80 | |||
5.3 | odd | 4 | 150.2.l.a.53.1 | yes | 80 | ||
5.4 | even | 2 | 750.2.l.a.257.7 | 80 | |||
15.2 | even | 4 | 750.2.l.b.743.1 | 80 | |||
15.8 | even | 4 | 150.2.l.a.53.10 | yes | 80 | ||
15.14 | odd | 2 | 750.2.l.a.257.3 | 80 | |||
25.6 | even | 5 | 150.2.l.a.17.10 | yes | 80 | ||
25.8 | odd | 20 | inner | 750.2.l.c.143.8 | 80 | ||
25.17 | odd | 20 | 750.2.l.a.143.3 | 80 | |||
25.19 | even | 10 | 750.2.l.b.107.1 | 80 | |||
75.8 | even | 20 | inner | 750.2.l.c.143.4 | 80 | ||
75.17 | even | 20 | 750.2.l.a.143.7 | 80 | |||
75.44 | odd | 10 | 750.2.l.b.107.10 | 80 | |||
75.56 | odd | 10 | 150.2.l.a.17.1 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.1 | ✓ | 80 | 75.56 | odd | 10 | ||
150.2.l.a.17.10 | yes | 80 | 25.6 | even | 5 | ||
150.2.l.a.53.1 | yes | 80 | 5.3 | odd | 4 | ||
150.2.l.a.53.10 | yes | 80 | 15.8 | even | 4 | ||
750.2.l.a.143.3 | 80 | 25.17 | odd | 20 | |||
750.2.l.a.143.7 | 80 | 75.17 | even | 20 | |||
750.2.l.a.257.3 | 80 | 15.14 | odd | 2 | |||
750.2.l.a.257.7 | 80 | 5.4 | even | 2 | |||
750.2.l.b.107.1 | 80 | 25.19 | even | 10 | |||
750.2.l.b.107.10 | 80 | 75.44 | odd | 10 | |||
750.2.l.b.743.1 | 80 | 15.2 | even | 4 | |||
750.2.l.b.743.10 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.143.4 | 80 | 75.8 | even | 20 | inner | ||
750.2.l.c.143.8 | 80 | 25.8 | odd | 20 | inner | ||
750.2.l.c.257.4 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.257.8 | 80 | 3.2 | odd | 2 | inner |