Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 157.2 | ||
Character | \(\chi\) | \(=\) | 525.157 |
Dual form | 525.2.bc.e.418.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.602389 | + | 2.24814i | −0.425953 | + | 1.58968i | 0.335880 | + | 0.941905i | \(0.390966\pi\) |
−0.761833 | + | 0.647774i | \(0.775700\pi\) | |||||||
\(3\) | −0.965926 | + | 0.258819i | −0.557678 | + | 0.149429i | ||||
\(4\) | −2.95923 | − | 1.70851i | −1.47962 | − | 0.854257i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.32745i | − | 0.950178i | ||||||
\(7\) | −0.519864 | + | 2.59417i | −0.196490 | + | 0.980506i | ||||
\(8\) | 2.33208 | − | 2.33208i | 0.824516 | − | 0.824516i | ||||
\(9\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.76389 | + | 3.05515i | −0.531834 | + | 0.921163i | 0.467476 | + | 0.884006i | \(0.345163\pi\) |
−0.999309 | + | 0.0371569i | \(0.988170\pi\) | |||||||
\(12\) | 3.30060 | + | 0.884392i | 0.952800 | + | 0.255302i | ||||
\(13\) | −4.49057 | − | 4.49057i | −1.24546 | − | 1.24546i | −0.957704 | − | 0.287756i | \(-0.907091\pi\) |
−0.287756 | − | 0.957704i | \(-0.592909\pi\) | |||||||
\(14\) | −5.51892 | − | 2.73143i | −1.47499 | − | 0.730005i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.421011 | + | 0.729213i | 0.105253 | + | 0.182303i | ||||
\(17\) | −0.481759 | − | 1.79795i | −0.116844 | − | 0.436066i | 0.882575 | − | 0.470172i | \(-0.155808\pi\) |
−0.999418 | + | 0.0341060i | \(0.989142\pi\) | |||||||
\(18\) | 0.602389 | + | 2.24814i | 0.141984 | + | 0.529893i | ||||
\(19\) | −0.0699116 | − | 0.121090i | −0.0160388 | − | 0.0277800i | 0.857895 | − | 0.513826i | \(-0.171772\pi\) |
−0.873933 | + | 0.486046i | \(0.838439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.169272 | − | 2.64033i | −0.0369382 | − | 0.576167i | ||||
\(22\) | −5.80587 | − | 5.80587i | −1.23782 | − | 1.23782i | ||||
\(23\) | 3.72112 | + | 0.997072i | 0.775908 | + | 0.207904i | 0.624980 | − | 0.780641i | \(-0.285107\pi\) |
0.150928 | + | 0.988545i | \(0.451774\pi\) | |||||||
\(24\) | −1.64903 | + | 2.85621i | −0.336607 | + | 0.583021i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.8005 | − | 7.39038i | 2.51039 | − | 1.44937i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 5.97058 | − | 6.78857i | 1.12833 | − | 1.28292i | ||||
\(29\) | − | 2.01969i | − | 0.375047i | −0.982260 | − | 0.187524i | \(-0.939954\pi\) | ||
0.982260 | − | 0.187524i | \(-0.0600462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.56612 | − | 2.63625i | −0.820100 | − | 0.473485i | 0.0303510 | − | 0.999539i | \(-0.490337\pi\) |
−0.850451 | + | 0.526054i | \(0.823671\pi\) | |||||||
\(32\) | 4.47838 | − | 1.19998i | 0.791673 | − | 0.212128i | ||||
\(33\) | 0.913058 | − | 3.40758i | 0.158943 | − | 0.593183i | ||||
\(34\) | 4.33225 | 0.742975 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.41703 | −0.569505 | ||||||||
\(37\) | 1.50406 | − | 5.61323i | 0.247266 | − | 0.922810i | −0.724965 | − | 0.688786i | \(-0.758144\pi\) |
0.972231 | − | 0.234024i | \(-0.0751893\pi\) | |||||||
\(38\) | 0.314343 | − | 0.0842279i | 0.0509931 | − | 0.0136636i | ||||
\(39\) | 5.49980 | + | 3.17531i | 0.880673 | + | 0.508457i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.903323i | 0.141075i | 0.997509 | + | 0.0705377i | \(0.0224715\pi\) | ||||
−0.997509 | + | 0.0705377i | \(0.977529\pi\) | |||||||
\(42\) | 6.03781 | + | 1.20996i | 0.931655 | + | 0.186700i | ||||
\(43\) | −2.38469 | + | 2.38469i | −0.363663 | + | 0.363663i | −0.865159 | − | 0.501497i | \(-0.832783\pi\) |
0.501497 | + | 0.865159i | \(0.332783\pi\) | |||||||
\(44\) | 10.4395 | − | 6.02727i | 1.57382 | − | 0.908645i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.48312 | + | 7.76500i | −0.661001 | + | 1.14489i | ||||
\(47\) | 2.38655 | + | 0.639474i | 0.348114 | + | 0.0932768i | 0.428639 | − | 0.903476i | \(-0.358993\pi\) |
−0.0805254 | + | 0.996753i | \(0.525660\pi\) | |||||||
\(48\) | −0.595400 | − | 0.595400i | −0.0859386 | − | 0.0859386i | ||||
\(49\) | −6.45948 | − | 2.69723i | −0.922783 | − | 0.385319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.930686 | + | 1.61200i | 0.130322 | + | 0.225725i | ||||
\(52\) | 5.61644 | + | 20.9608i | 0.778860 | + | 2.90675i | ||||
\(53\) | 0.726718 | + | 2.71215i | 0.0998224 | + | 0.372542i | 0.997706 | − | 0.0676898i | \(-0.0215628\pi\) |
−0.897884 | + | 0.440232i | \(0.854896\pi\) | |||||||
\(54\) | −1.16373 | − | 2.01563i | −0.158363 | − | 0.274293i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.83746 | + | 7.26219i | 0.646433 | + | 0.970451i | ||||
\(57\) | 0.0988699 | + | 0.0988699i | 0.0130956 | + | 0.0130956i | ||||
\(58\) | 4.54056 | + | 1.21664i | 0.596205 | + | 0.159753i | ||||
\(59\) | 3.15338 | − | 5.46181i | 0.410535 | − | 0.711067i | −0.584414 | − | 0.811456i | \(-0.698675\pi\) |
0.994948 | + | 0.100389i | \(0.0320087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.69243 | + | 5.01858i | −1.11295 | + | 0.642563i | −0.939592 | − | 0.342296i | \(-0.888795\pi\) |
−0.173359 | + | 0.984859i | \(0.555462\pi\) | |||||||
\(62\) | 8.67726 | − | 8.67726i | 1.10201 | − | 1.10201i | ||||
\(63\) | 0.846872 | + | 2.50655i | 0.106696 | + | 0.315796i | ||||
\(64\) | 12.4749i | 1.55937i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.11071 | + | 4.10537i | 0.875268 | + | 0.505336i | ||||
\(67\) | −10.3615 | + | 2.77634i | −1.26585 | + | 0.339184i | −0.828441 | − | 0.560077i | \(-0.810772\pi\) |
−0.437412 | + | 0.899261i | \(0.644105\pi\) | |||||||
\(68\) | −1.64618 | + | 6.14364i | −0.199629 | + | 0.745025i | ||||
\(69\) | −3.85239 | −0.463773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.09892 | −0.605130 | −0.302565 | − | 0.953129i | \(-0.597843\pi\) | ||||
−0.302565 | + | 0.953129i | \(0.597843\pi\) | |||||||
\(72\) | 0.853601 | − | 3.18568i | 0.100598 | − | 0.375436i | ||||
\(73\) | −9.04441 | + | 2.42344i | −1.05857 | + | 0.283643i | −0.745788 | − | 0.666183i | \(-0.767927\pi\) |
−0.312780 | + | 0.949826i | \(0.601260\pi\) | |||||||
\(74\) | 11.7133 | + | 6.76269i | 1.36165 | + | 0.786147i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.477780i | 0.0548051i | ||||||||
\(77\) | −7.00861 | − | 6.16411i | −0.798705 | − | 0.702465i | ||||
\(78\) | −10.4516 | + | 10.4516i | −1.18341 | + | 1.18341i | ||||
\(79\) | 7.30150 | − | 4.21552i | 0.821483 | − | 0.474284i | −0.0294445 | − | 0.999566i | \(-0.509374\pi\) |
0.850928 | + | 0.525283i | \(0.176040\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.03080 | − | 0.544151i | −0.224264 | − | 0.0600915i | ||||
\(83\) | −7.37852 | − | 7.37852i | −0.809898 | − | 0.809898i | 0.174720 | − | 0.984618i | \(-0.444098\pi\) |
−0.984618 | + | 0.174720i | \(0.944098\pi\) | |||||||
\(84\) | −4.01013 | + | 8.10256i | −0.437541 | + | 0.884061i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.92463 | − | 6.79765i | −0.423203 | − | 0.733010i | ||||
\(87\) | 0.522735 | + | 1.95087i | 0.0560431 | + | 0.209156i | ||||
\(88\) | 3.01132 | + | 11.2384i | 0.321008 | + | 1.19802i | ||||
\(89\) | 1.75399 | + | 3.03799i | 0.185922 | + | 0.322027i | 0.943887 | − | 0.330269i | \(-0.107139\pi\) |
−0.757965 | + | 0.652296i | \(0.773806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9838 | − | 9.31484i | 1.46590 | − | 0.976460i | ||||
\(92\) | −9.30816 | − | 9.30816i | −0.970443 | − | 0.970443i | ||||
\(93\) | 5.09285 | + | 1.36462i | 0.528104 | + | 0.141505i | ||||
\(94\) | −2.87526 | + | 4.98010i | −0.296560 | + | 0.513658i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.01520 | + | 2.31818i | −0.409800 | + | 0.236598i | ||||
\(97\) | 8.70237 | − | 8.70237i | 0.883592 | − | 0.883592i | −0.110306 | − | 0.993898i | \(-0.535183\pi\) |
0.993898 | + | 0.110306i | \(0.0351831\pi\) | |||||||
\(98\) | 9.95489 | − | 12.8971i | 1.00560 | − | 1.30280i | ||||
\(99\) | 3.52778i | 0.354556i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.24483 | − | 0.718705i | −0.123866 | − | 0.0715138i | 0.436787 | − | 0.899565i | \(-0.356116\pi\) |
−0.560653 | + | 0.828051i | \(0.689450\pi\) | |||||||
\(102\) | −4.18463 | + | 1.12127i | −0.414341 | + | 0.111022i | ||||
\(103\) | 1.60502 | − | 5.99000i | 0.158147 | − | 0.590212i | −0.840668 | − | 0.541550i | \(-0.817838\pi\) |
0.998815 | − | 0.0486620i | \(-0.0154957\pi\) | |||||||
\(104\) | −20.9448 | −2.05380 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.53507 | −0.634742 | ||||||||
\(107\) | −4.64750 | + | 17.3447i | −0.449291 | + | 1.67678i | 0.255061 | + | 0.966925i | \(0.417905\pi\) |
−0.704352 | + | 0.709851i | \(0.748762\pi\) | |||||||
\(108\) | 3.30060 | − | 0.884392i | 0.317600 | − | 0.0851006i | ||||
\(109\) | −11.0263 | − | 6.36604i | −1.05613 | − | 0.609756i | −0.131770 | − | 0.991280i | \(-0.542066\pi\) |
−0.924359 | + | 0.381524i | \(0.875399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.81124i | 0.551579i | ||||||||
\(112\) | −2.11057 | + | 0.713086i | −0.199431 | + | 0.0673803i | ||||
\(113\) | −11.1631 | + | 11.1631i | −1.05013 | + | 1.05013i | −0.0514580 | + | 0.998675i | \(0.516387\pi\) |
−0.998675 | + | 0.0514580i | \(0.983613\pi\) | |||||||
\(114\) | −0.281832 | + | 0.162716i | −0.0263960 | + | 0.0152397i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.45067 | + | 5.97674i | −0.320387 | + | 0.554926i | ||||
\(117\) | −6.13423 | − | 1.64366i | −0.567110 | − | 0.151957i | ||||
\(118\) | 10.3794 | + | 10.3794i | 0.955499 | + | 0.955499i | ||||
\(119\) | 4.91464 | − | 0.315078i | 0.450524 | − | 0.0288832i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.722631 | − | 1.25163i | −0.0656938 | − | 0.113785i | ||||
\(122\) | −6.04627 | − | 22.5650i | −0.547403 | − | 2.04294i | ||||
\(123\) | −0.233797 | − | 0.872543i | −0.0210808 | − | 0.0786745i | ||||
\(124\) | 9.00815 | + | 15.6026i | 0.808955 | + | 1.40115i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.14524 | + | 0.393972i | −0.547462 | + | 0.0350978i | ||||
\(127\) | 4.84282 | + | 4.84282i | 0.429731 | + | 0.429731i | 0.888537 | − | 0.458806i | \(-0.151723\pi\) |
−0.458806 | + | 0.888537i | \(0.651723\pi\) | |||||||
\(128\) | −19.0887 | − | 5.11481i | −1.68722 | − | 0.452089i | ||||
\(129\) | 1.68623 | − | 2.92064i | 0.148465 | − | 0.257148i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.49109 | − | 1.43823i | 0.217648 | − | 0.125659i | −0.387213 | − | 0.921990i | \(-0.626562\pi\) |
0.604861 | + | 0.796331i | \(0.293229\pi\) | |||||||
\(132\) | −8.52384 | + | 8.52384i | −0.741905 | + | 0.741905i | ||||
\(133\) | 0.350474 | − | 0.118412i | 0.0303900 | − | 0.0102677i | ||||
\(134\) | − | 24.9665i | − | 2.15678i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.31646 | − | 3.06946i | −0.455883 | − | 0.263204i | ||||
\(137\) | −19.8248 | + | 5.31203i | −1.69375 | + | 0.453838i | −0.971352 | − | 0.237645i | \(-0.923625\pi\) |
−0.722393 | + | 0.691482i | \(0.756958\pi\) | |||||||
\(138\) | 2.32064 | − | 8.66073i | 0.197546 | − | 0.737250i | ||||
\(139\) | −10.4910 | −0.889832 | −0.444916 | − | 0.895572i | \(-0.646766\pi\) | ||||
−0.444916 | + | 0.895572i | \(0.646766\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.47074 | −0.208074 | ||||||||
\(142\) | 3.07153 | − | 11.4631i | 0.257757 | − | 0.961963i | ||||
\(143\) | 21.6402 | − | 5.79849i | 1.80965 | − | 0.484894i | ||||
\(144\) | 0.729213 | + | 0.421011i | 0.0607678 | + | 0.0350843i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 21.7930i | − | 1.80360i | ||||||
\(147\) | 6.93748 | + | 0.933491i | 0.572194 | + | 0.0769930i | ||||
\(148\) | −14.0411 | + | 14.0411i | −1.15418 | + | 1.15418i | ||||
\(149\) | −11.4119 | + | 6.58864i | −0.934896 | + | 0.539763i | −0.888357 | − | 0.459154i | \(-0.848153\pi\) |
−0.0465396 | + | 0.998916i | \(0.514819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.10520 | − | 3.64631i | 0.171319 | − | 0.296732i | −0.767563 | − | 0.640974i | \(-0.778531\pi\) |
0.938881 | + | 0.344242i | \(0.111864\pi\) | |||||||
\(152\) | −0.445432 | − | 0.119353i | −0.0361293 | − | 0.00968083i | ||||
\(153\) | −1.31619 | − | 1.31619i | −0.106408 | − | 0.106408i | ||||
\(154\) | 18.0797 | − | 12.0432i | 1.45690 | − | 0.970468i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.8501 | − | 18.7930i | −0.868706 | − | 1.50464i | ||||
\(157\) | 0.250229 | + | 0.933866i | 0.0199704 | + | 0.0745306i | 0.975192 | − | 0.221361i | \(-0.0710499\pi\) |
−0.955222 | + | 0.295892i | \(0.904383\pi\) | |||||||
\(158\) | 5.07877 | + | 18.9542i | 0.404045 | + | 1.50792i | ||||
\(159\) | −1.40391 | − | 2.43165i | −0.111337 | − | 0.192842i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.52106 | + | 9.13490i | −0.356309 | + | 0.719931i | ||||
\(162\) | 1.64576 | + | 1.64576i | 0.129303 | + | 0.129303i | ||||
\(163\) | −9.91429 | − | 2.65652i | −0.776547 | − | 0.208075i | −0.151285 | − | 0.988490i | \(-0.548341\pi\) |
−0.625262 | + | 0.780415i | \(0.715008\pi\) | |||||||
\(164\) | 1.54334 | − | 2.67314i | 0.120515 | − | 0.208737i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.0327 | − | 12.1432i | 1.63246 | − | 0.942499i | ||||
\(167\) | −5.80633 | + | 5.80633i | −0.449307 | + | 0.449307i | −0.895124 | − | 0.445817i | \(-0.852913\pi\) |
0.445817 | + | 0.895124i | \(0.352913\pi\) | |||||||
\(168\) | −6.55223 | − | 5.76271i | −0.505515 | − | 0.444603i | ||||
\(169\) | 27.3304i | 2.10234i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.121090 | − | 0.0699116i | −0.00926001 | − | 0.00534627i | ||||
\(172\) | 11.1312 | − | 2.98258i | 0.848742 | − | 0.227420i | ||||
\(173\) | −1.16854 | + | 4.36106i | −0.0888426 | + | 0.331565i | −0.996014 | − | 0.0891961i | \(-0.971570\pi\) |
0.907172 | + | 0.420761i | \(0.138237\pi\) | |||||||
\(174\) | −4.70074 | −0.356362 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.97048 | −0.223908 | ||||||||
\(177\) | −1.63231 | + | 6.09186i | −0.122692 | + | 0.457892i | ||||
\(178\) | −7.88643 | + | 2.11316i | −0.591113 | + | 0.158388i | ||||
\(179\) | −12.7668 | − | 7.37089i | −0.954232 | − | 0.550926i | −0.0598390 | − | 0.998208i | \(-0.519059\pi\) |
−0.894393 | + | 0.447282i | \(0.852392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.11772i | 0.454727i | 0.973810 | + | 0.227363i | \(0.0730105\pi\) | ||||
−0.973810 | + | 0.227363i | \(0.926989\pi\) | |||||||
\(182\) | 12.5174 | + | 37.0488i | 0.927853 | + | 2.74624i | ||||
\(183\) | 7.09734 | − | 7.09734i | 0.524650 | − | 0.524650i | ||||
\(184\) | 11.0032 | − | 6.35271i | 0.811168 | − | 0.468328i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.13575 | + | 10.6274i | −0.449895 | + | 0.779241i | ||||
\(187\) | 6.34277 | + | 1.69954i | 0.463829 | + | 0.124283i | ||||
\(188\) | −5.96980 | − | 5.96980i | −0.435393 | − | 0.435393i | ||||
\(189\) | −1.46676 | − | 2.20196i | −0.106691 | − | 0.160169i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2238 | + | 19.4402i | 0.812124 | + | 1.40664i | 0.911375 | + | 0.411578i | \(0.135022\pi\) |
−0.0992508 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(192\) | −3.22875 | − | 12.0499i | −0.233015 | − | 0.869624i | ||||
\(193\) | −4.64744 | − | 17.3445i | −0.334530 | − | 1.24848i | −0.904378 | − | 0.426733i | \(-0.859664\pi\) |
0.569848 | − | 0.821750i | \(-0.307002\pi\) | |||||||
\(194\) | 14.3220 | + | 24.8064i | 1.02826 | + | 1.78100i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.5069 | + | 19.0179i | 1.03620 | + | 1.35842i | ||||
\(197\) | 12.1280 | + | 12.1280i | 0.864085 | + | 0.864085i | 0.991810 | − | 0.127724i | \(-0.0407673\pi\) |
−0.127724 | + | 0.991810i | \(0.540767\pi\) | |||||||
\(198\) | −7.93097 | − | 2.12510i | −0.563630 | − | 0.151024i | ||||
\(199\) | −3.39732 | + | 5.88433i | −0.240830 | + | 0.417129i | −0.960951 | − | 0.276719i | \(-0.910753\pi\) |
0.720121 | + | 0.693848i | \(0.244086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.28983 | − | 5.36348i | 0.655254 | − | 0.378311i | ||||
\(202\) | 2.36563 | − | 2.36563i | 0.166445 | − | 0.166445i | ||||
\(203\) | 5.23943 | + | 1.04996i | 0.367736 | + | 0.0736931i | ||||
\(204\) | − | 6.36036i | − | 0.445314i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.4995 | + | 7.21662i | 0.870885 | + | 0.502805i | ||||
\(207\) | 3.72112 | − | 0.997072i | 0.258636 | − | 0.0693013i | ||||
\(208\) | 1.38400 | − | 5.16516i | 0.0959632 | − | 0.358140i | ||||
\(209\) | 0.493266 | 0.0341199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.53741 | 0.174683 | 0.0873414 | − | 0.996178i | \(-0.472163\pi\) | ||||
0.0873414 | + | 0.996178i | \(0.472163\pi\) | |||||||
\(212\) | 2.48322 | − | 9.26749i | 0.170548 | − | 0.636494i | ||||
\(213\) | 4.92518 | − | 1.31970i | 0.337468 | − | 0.0904242i | ||||
\(214\) | −36.1938 | − | 20.8965i | −2.47416 | − | 1.42846i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.29806i | 0.224405i | ||||||||
\(217\) | 9.21266 | − | 10.4748i | 0.625396 | − | 0.711078i | ||||
\(218\) | 20.9539 | − | 20.9539i | 1.41918 | − | 1.41918i | ||||
\(219\) | 8.10900 | − | 4.68173i | 0.547955 | − | 0.316362i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.91044 | + | 10.2372i | −0.397579 | + | 0.688627i | ||||
\(222\) | −13.0645 | − | 3.50063i | −0.876833 | − | 0.234947i | ||||
\(223\) | 7.81577 | + | 7.81577i | 0.523383 | + | 0.523383i | 0.918591 | − | 0.395209i | \(-0.129328\pi\) |
−0.395209 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(224\) | 0.784806 | + | 12.2415i | 0.0524370 | + | 0.817921i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.3717 | − | 31.8207i | −1.22207 | − | 2.11668i | ||||
\(227\) | −6.35498 | − | 23.7171i | −0.421795 | − | 1.57416i | −0.770824 | − | 0.637049i | \(-0.780155\pi\) |
0.349029 | − | 0.937112i | \(-0.386512\pi\) | |||||||
\(228\) | −0.123658 | − | 0.461500i | −0.00818948 | − | 0.0305636i | ||||
\(229\) | 3.69144 | + | 6.39377i | 0.243937 | + | 0.422512i | 0.961832 | − | 0.273640i | \(-0.0882275\pi\) |
−0.717895 | + | 0.696151i | \(0.754894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.36519 | + | 4.14011i | 0.550389 | + | 0.272399i | ||||
\(232\) | −4.71009 | − | 4.71009i | −0.309232 | − | 0.309232i | ||||
\(233\) | 7.04458 | + | 1.88759i | 0.461505 | + | 0.123660i | 0.482078 | − | 0.876128i | \(-0.339882\pi\) |
−0.0205724 | + | 0.999788i | \(0.506549\pi\) | |||||||
\(234\) | 7.39038 | − | 12.8005i | 0.483124 | − | 0.836796i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.6632 | + | 10.7752i | −1.21487 | + | 0.701404i | ||||
\(237\) | −5.96165 | + | 5.96165i | −0.387251 | + | 0.387251i | ||||
\(238\) | −2.25218 | + | 11.2386i | −0.145987 | + | 0.728492i | ||||
\(239\) | 9.88581i | 0.639460i | 0.947509 | + | 0.319730i | \(0.103592\pi\) | ||||
−0.947509 | + | 0.319730i | \(0.896408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.91713 | − | 1.68420i | −0.187909 | − | 0.108489i | 0.403095 | − | 0.915158i | \(-0.367935\pi\) |
−0.591003 | + | 0.806669i | \(0.701268\pi\) | |||||||
\(242\) | 3.24916 | − | 0.870610i | 0.208864 | − | 0.0559649i | ||||
\(243\) | −0.258819 | + | 0.965926i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | 34.2972 | 2.19565 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.10244 | 0.134047 | ||||||||
\(247\) | −0.229822 | + | 0.857708i | −0.0146232 | + | 0.0545746i | ||||
\(248\) | −16.7965 | + | 4.50062i | −1.06658 | + | 0.285789i | ||||
\(249\) | 9.03681 | + | 5.21740i | 0.572684 | + | 0.330639i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.93770i | 0.311665i | 0.987784 | + | 0.155832i | \(0.0498060\pi\) | ||||
−0.987784 | + | 0.155832i | \(0.950194\pi\) | |||||||
\(252\) | 1.77639 | − | 8.86437i | 0.111902 | − | 0.558403i | ||||
\(253\) | −9.60986 | + | 9.60986i | −0.604167 | + | 0.604167i | ||||
\(254\) | −13.8046 | + | 7.97010i | −0.866179 | + | 0.500089i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.5227 | − | 18.2259i | 0.657670 | − | 1.13912i | ||||
\(257\) | 19.8010 | + | 5.30566i | 1.23515 | + | 0.330958i | 0.816584 | − | 0.577227i | \(-0.195865\pi\) |
0.418569 | + | 0.908185i | \(0.362532\pi\) | |||||||
\(258\) | 5.55026 | + | 5.55026i | 0.345544 | + | 0.345544i | ||||
\(259\) | 13.7798 | + | 6.81991i | 0.856235 | + | 0.423769i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00985 | − | 1.74910i | −0.0625079 | − | 0.108267i | ||||
\(262\) | 1.73275 | + | 6.46671i | 0.107050 | + | 0.399515i | ||||
\(263\) | 0.900371 | + | 3.36023i | 0.0555192 | + | 0.207201i | 0.988114 | − | 0.153726i | \(-0.0491272\pi\) |
−0.932594 | + | 0.360926i | \(0.882461\pi\) | |||||||
\(264\) | −5.81743 | − | 10.0761i | −0.358038 | − | 0.620140i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0550865 | + | 0.859247i | 0.00337757 | + | 0.0526838i | ||||
\(267\) | −2.48051 | − | 2.48051i | −0.151805 | − | 0.151805i | ||||
\(268\) | 35.4054 | + | 9.48684i | 2.16273 | + | 0.579501i | ||||
\(269\) | 9.35542 | − | 16.2041i | 0.570410 | − | 0.987979i | −0.426114 | − | 0.904670i | \(-0.640118\pi\) |
0.996524 | − | 0.0833095i | \(-0.0265490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.07958 | − | 3.51005i | 0.369308 | − | 0.213220i | −0.303848 | − | 0.952721i | \(-0.598272\pi\) |
0.673156 | + | 0.739500i | \(0.264938\pi\) | |||||||
\(272\) | 1.10826 | − | 1.10826i | 0.0671982 | − | 0.0671982i | ||||
\(273\) | −11.0965 | + | 12.6167i | −0.671588 | + | 0.763599i | ||||
\(274\) | − | 47.7689i | − | 2.88582i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.4001 | + | 6.58186i | 0.686206 | + | 0.396181i | ||||
\(277\) | −7.53340 | + | 2.01857i | −0.452638 | + | 0.121284i | −0.477934 | − | 0.878396i | \(-0.658614\pi\) |
0.0252953 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(278\) | 6.31964 | − | 23.5852i | 0.379027 | − | 1.41455i | ||||
\(279\) | −5.27250 | −0.315657 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.11841 | −0.186029 | −0.0930143 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930143 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(282\) | 1.48834 | − | 5.55457i | 0.0886296 | − | 0.330770i | ||||
\(283\) | 30.3411 | − | 8.12988i | 1.80359 | − | 0.483271i | 0.809063 | − | 0.587721i | \(-0.199975\pi\) |
0.994530 | + | 0.104450i | \(0.0333082\pi\) | |||||||
\(284\) | 15.0889 | + | 8.71157i | 0.895361 | + | 0.516937i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 52.1434i | 3.08330i | ||||||||
\(287\) | −2.34338 | − | 0.469605i | −0.138325 | − | 0.0277199i | ||||
\(288\) | 3.27840 | − | 3.27840i | 0.193182 | − | 0.193182i | ||||
\(289\) | 11.7219 | − | 6.76765i | 0.689524 | − | 0.398097i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.15350 | + | 10.6582i | −0.360725 | + | 0.624794i | ||||
\(292\) | 30.9050 | + | 8.28097i | 1.80858 | + | 0.484607i | ||||
\(293\) | 1.77405 | + | 1.77405i | 0.103641 | + | 0.103641i | 0.757026 | − | 0.653385i | \(-0.226652\pi\) |
−0.653385 | + | 0.757026i | \(0.726652\pi\) | |||||||
\(294\) | −6.27768 | + | 15.0341i | −0.366122 | + | 0.876808i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.58292 | − | 16.5981i | −0.556996 | − | 0.964746i | ||||
\(297\) | −0.913058 | − | 3.40758i | −0.0529810 | − | 0.197728i | ||||
\(298\) | −7.93785 | − | 29.6245i | −0.459827 | − | 1.71610i | ||||
\(299\) | −12.2325 | − | 21.1874i | −0.707426 | − | 1.22530i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.94660 | − | 7.42603i | −0.285117 | − | 0.428029i | ||||
\(302\) | 6.92929 | + | 6.92929i | 0.398736 | + | 0.398736i | ||||
\(303\) | 1.38843 | + | 0.372029i | 0.0797633 | + | 0.0213725i | ||||
\(304\) | 0.0588671 | − | 0.101961i | 0.00337626 | − | 0.00584786i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.75184 | − | 2.16613i | 0.214478 | − | 0.123829i | ||||
\(307\) | −10.6518 | + | 10.6518i | −0.607929 | + | 0.607929i | −0.942404 | − | 0.334476i | \(-0.891441\pi\) |
0.334476 | + | 0.942404i | \(0.391441\pi\) | |||||||
\(308\) | 10.2087 | + | 30.2153i | 0.581692 | + | 1.72168i | ||||
\(309\) | 6.20130i | 0.352780i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1465 | − | 9.32219i | −0.915584 | − | 0.528613i | −0.0333607 | − | 0.999443i | \(-0.510621\pi\) |
−0.882224 | + | 0.470831i | \(0.843954\pi\) | |||||||
\(312\) | 20.2311 | − | 5.42090i | 1.14536 | − | 0.306898i | ||||
\(313\) | 5.31635 | − | 19.8409i | 0.300498 | − | 1.12147i | −0.636254 | − | 0.771479i | \(-0.719517\pi\) |
0.936752 | − | 0.349994i | \(-0.113816\pi\) | |||||||
\(314\) | −2.25020 | −0.126986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.8091 | −1.62064 | ||||||||
\(317\) | 7.55924 | − | 28.2115i | 0.424569 | − | 1.58451i | −0.340292 | − | 0.940320i | \(-0.610526\pi\) |
0.764862 | − | 0.644195i | \(-0.222807\pi\) | |||||||
\(318\) | 6.31239 | − | 1.69140i | 0.353981 | − | 0.0948490i | ||||
\(319\) | 6.17047 | + | 3.56252i | 0.345480 | + | 0.199463i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 17.9566i | − | 1.00224i | ||||||
\(322\) | −17.8131 | − | 15.6667i | −0.992688 | − | 0.873074i | ||||
\(323\) | −0.184034 | + | 0.184034i | −0.0102399 | + | 0.0102399i | ||||
\(324\) | −2.95923 | + | 1.70851i | −0.164402 | + | 0.0949174i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.9445 | − | 20.6885i | 0.661545 | − | 1.14583i | ||||
\(327\) | 12.2983 | + | 3.29531i | 0.680095 | + | 0.182231i | ||||
\(328\) | 2.10662 | + | 2.10662i | 0.116319 | + | 0.116319i | ||||
\(329\) | −2.89959 | + | 5.85868i | −0.159859 | + | 0.323000i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.8275 | + | 20.4858i | 0.650098 | + | 1.12600i | 0.983099 | + | 0.183076i | \(0.0586054\pi\) |
−0.333001 | + | 0.942926i | \(0.608061\pi\) | |||||||
\(332\) | 9.22846 | + | 34.4411i | 0.506477 | + | 1.89020i | ||||
\(333\) | −1.50406 | − | 5.61323i | −0.0824220 | − | 0.307603i | ||||
\(334\) | −9.55580 | − | 16.5511i | −0.522870 | − | 0.905638i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.85410 | − | 1.23504i | 0.101149 | − | 0.0673772i | ||||
\(337\) | 8.38731 | + | 8.38731i | 0.456886 | + | 0.456886i | 0.897632 | − | 0.440746i | \(-0.145286\pi\) |
−0.440746 | + | 0.897632i | \(0.645286\pi\) | |||||||
\(338\) | −61.4428 | − | 16.4635i | −3.34205 | − | 0.895499i | ||||
\(339\) | 7.89348 | − | 13.6719i | 0.428715 | − | 0.742556i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.1083 | − | 9.30013i | 0.872313 | − | 0.503630i | ||||
\(342\) | 0.230115 | − | 0.230115i | 0.0124432 | − | 0.0124432i | ||||
\(343\) | 10.3551 | − | 15.3548i | 0.559125 | − | 0.829083i | ||||
\(344\) | 11.1226i | 0.599691i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.10037 | − | 5.25410i | −0.489239 | − | 0.282462i | ||||
\(347\) | 10.5150 | − | 2.81748i | 0.564473 | − | 0.151250i | 0.0347126 | − | 0.999397i | \(-0.488948\pi\) |
0.529761 | + | 0.848147i | \(0.322282\pi\) | |||||||
\(348\) | 1.78620 | − | 6.66619i | 0.0957503 | − | 0.357345i | ||||
\(349\) | −5.13321 | −0.274775 | −0.137387 | − | 0.990517i | \(-0.543870\pi\) | ||||
−0.137387 | + | 0.990517i | \(0.543870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.35062 | 0.338971 | ||||||||
\(352\) | −4.23326 | + | 15.7988i | −0.225634 | + | 0.842076i | ||||
\(353\) | −20.8591 | + | 5.58918i | −1.11022 | + | 0.297482i | −0.766919 | − | 0.641744i | \(-0.778211\pi\) |
−0.343299 | + | 0.939226i | \(0.611544\pi\) | |||||||
\(354\) | −12.7121 | − | 7.33933i | −0.675640 | − | 0.390081i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.9868i | − | 0.635301i | ||||||
\(357\) | −4.66563 | + | 1.57634i | −0.246931 | + | 0.0834290i | ||||
\(358\) | 24.2614 | − | 24.2614i | 1.28225 | − | 1.28225i | ||||
\(359\) | −3.58984 | + | 2.07260i | −0.189465 | + | 0.109388i | −0.591732 | − | 0.806135i | \(-0.701556\pi\) |
0.402267 | + | 0.915522i | \(0.368222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49022 | − | 16.4376i | 0.499486 | − | 0.865134i | ||||
\(362\) | −13.7535 | − | 3.68525i | −0.722869 | − | 0.193692i | ||||
\(363\) | 1.02196 | + | 1.02196i | 0.0536387 | + | 0.0536387i | ||||
\(364\) | −57.2959 | + | 3.67325i | −3.00312 | + | 0.192530i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.6805 | + | 20.2312i | 0.610549 | + | 1.05750i | ||||
\(367\) | −0.879473 | − | 3.28224i | −0.0459081 | − | 0.171331i | 0.939166 | − | 0.343465i | \(-0.111601\pi\) |
−0.985074 | + | 0.172133i | \(0.944934\pi\) | |||||||
\(368\) | 0.839557 | + | 3.13327i | 0.0437650 | + | 0.163333i | ||||
\(369\) | 0.451661 | + | 0.782300i | 0.0235126 | + | 0.0407249i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.41358 | + | 0.475286i | −0.384894 | + | 0.0246756i | ||||
\(372\) | −12.7394 | − | 12.7394i | −0.660509 | − | 0.660509i | ||||
\(373\) | −34.6439 | − | 9.28280i | −1.79379 | − | 0.480645i | −0.800812 | − | 0.598916i | \(-0.795598\pi\) |
−0.992981 | + | 0.118271i | \(0.962265\pi\) | |||||||
\(374\) | −7.64163 | + | 13.2357i | −0.395139 | + | 0.684401i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.05693 | − | 4.07432i | 0.363934 | − | 0.210117i | ||||
\(377\) | −9.06957 | + | 9.06957i | −0.467107 | + | 0.467107i | ||||
\(378\) | 5.83388 | − | 1.97105i | 0.300062 | − | 0.101380i | ||||
\(379\) | − | 8.02575i | − | 0.412255i | −0.978525 | − | 0.206128i | \(-0.933914\pi\) | ||
0.978525 | − | 0.206128i | \(-0.0660862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.93122 | − | 3.42439i | −0.303866 | − | 0.175437i | ||||
\(382\) | −50.4654 | + | 13.5222i | −2.58203 | + | 0.691853i | ||||
\(383\) | −8.49599 | + | 31.7075i | −0.434125 | + | 1.62018i | 0.309028 | + | 0.951053i | \(0.399996\pi\) |
−0.743152 | + | 0.669122i | \(0.766670\pi\) | |||||||
\(384\) | 19.7621 | 1.00848 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7925 | 2.12718 | ||||||||
\(387\) | −0.872859 | + | 3.25755i | −0.0443699 | + | 0.165591i | ||||
\(388\) | −40.6205 | + | 10.8842i | −2.06219 | + | 0.552562i | ||||
\(389\) | 13.4380 | + | 7.75844i | 0.681334 | + | 0.393369i | 0.800358 | − | 0.599523i | \(-0.204643\pi\) |
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.17073i | − | 0.362640i | ||||||
\(392\) | −21.3542 | + | 8.77387i | −1.07855 | + | 0.443148i | ||||
\(393\) | −2.03397 | + | 2.03397i | −0.102600 | + | 0.102600i | ||||
\(394\) | −34.5713 | + | 19.9598i | −1.74168 | + | 1.00556i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.02727 | − | 10.4395i | 0.302882 | − | 0.524606i | ||||
\(397\) | −20.3268 | − | 5.44656i | −1.02017 | − | 0.273355i | −0.290299 | − | 0.956936i | \(-0.593755\pi\) |
−0.729875 | + | 0.683581i | \(0.760422\pi\) | |||||||
\(398\) | −11.1823 | − | 11.1823i | −0.560519 | − | 0.560519i | ||||
\(399\) | −0.307885 | + | 0.205087i | −0.0154135 | + | 0.0102672i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.34890 | − | 16.1928i | −0.466862 | − | 0.808628i | 0.532422 | − | 0.846479i | \(-0.321282\pi\) |
−0.999283 | + | 0.0378510i | \(0.987949\pi\) | |||||||
\(402\) | 6.46180 | + | 24.1158i | 0.322285 | + | 1.20279i | ||||
\(403\) | 8.66622 | + | 32.3428i | 0.431695 | + | 1.61111i | ||||
\(404\) | 2.45584 | + | 4.25363i | 0.122182 | + | 0.211626i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.51665 | + | 11.1465i | −0.273787 | + | 0.553193i | ||||
\(407\) | 14.4963 | + | 14.4963i | 0.718553 | + | 0.718553i | ||||
\(408\) | 5.92974 | + | 1.58887i | 0.293566 | + | 0.0786608i | ||||
\(409\) | −11.9001 | + | 20.6115i | −0.588421 | + | 1.01918i | 0.406018 | + | 0.913865i | \(0.366917\pi\) |
−0.994439 | + | 0.105310i | \(0.966416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7744 | − | 10.2621i | 0.876747 | − | 0.506190i | ||||
\(412\) | −14.9836 | + | 14.9836i | −0.738190 | + | 0.738190i | ||||
\(413\) | 12.5296 | + | 11.0198i | 0.616539 | + | 0.542249i | ||||
\(414\) | 8.96625i | 0.440667i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −25.4991 | − | 14.7219i | −1.25019 | − | 0.721800i | ||||
\(417\) | 10.1335 | − | 2.71526i | 0.496239 | − | 0.132967i | ||||
\(418\) | −0.297138 | + | 1.10893i | −0.0145335 | + | 0.0542397i | ||||
\(419\) | −9.72005 | −0.474856 | −0.237428 | − | 0.971405i | \(-0.576304\pi\) | ||||
−0.237428 | + | 0.971405i | \(0.576304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0095 | 0.634043 | 0.317022 | − | 0.948418i | \(-0.397317\pi\) | ||||
0.317022 | + | 0.948418i | \(0.397317\pi\) | |||||||
\(422\) | −1.52851 | + | 5.70448i | −0.0744067 | + | 0.277690i | ||||
\(423\) | 2.38655 | − | 0.639474i | 0.116038 | − | 0.0310923i | ||||
\(424\) | 8.01972 | + | 4.63019i | 0.389472 | + | 0.224862i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.8675i | 0.574981i | ||||||||
\(427\) | −8.50018 | − | 25.1586i | −0.411353 | − | 1.21751i | ||||
\(428\) | 43.3867 | − | 43.3867i | 2.09718 | − | 2.09718i | ||||
\(429\) | −19.4021 | + | 11.2018i | −0.936743 | + | 0.540829i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.60239 | + | 11.4357i | −0.318026 | + | 0.550837i | −0.980076 | − | 0.198622i | \(-0.936353\pi\) |
0.662050 | + | 0.749460i | \(0.269687\pi\) | |||||||
\(432\) | −0.813332 | − | 0.217932i | −0.0391314 | − | 0.0104852i | ||||
\(433\) | 13.9321 | + | 13.9321i | 0.669535 | + | 0.669535i | 0.957608 | − | 0.288074i | \(-0.0930148\pi\) |
−0.288074 | + | 0.957608i | \(0.593015\pi\) | |||||||
\(434\) | 17.9993 | + | 27.0213i | 0.863995 | + | 1.29706i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.7529 | + | 37.6772i | 1.04178 | + | 1.80441i | ||||
\(437\) | −0.139414 | − | 0.520299i | −0.00666906 | − | 0.0248893i | ||||
\(438\) | 5.64044 | + | 21.0504i | 0.269511 | + | 1.00583i | ||||
\(439\) | −6.30838 | − | 10.9264i | −0.301083 | − | 0.521490i | 0.675299 | − | 0.737544i | \(-0.264015\pi\) |
−0.976381 | + | 0.216054i | \(0.930681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.94269 | + | 0.893868i | −0.330604 | + | 0.0425652i | ||||
\(442\) | −19.4543 | − | 19.4543i | −0.925346 | − | 0.925346i | ||||
\(443\) | 18.4828 | + | 4.95246i | 0.878146 | + | 0.235299i | 0.669607 | − | 0.742716i | \(-0.266463\pi\) |
0.208539 | + | 0.978014i | \(0.433129\pi\) | |||||||
\(444\) | 9.92859 | − | 17.1968i | 0.471190 | − | 0.816125i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22.2791 | + | 12.8629i | −1.05495 | + | 0.609074i | ||||
\(447\) | 9.31775 | − | 9.31775i | 0.440714 | − | 0.440714i | ||||
\(448\) | −32.3622 | − | 6.48527i | −1.52897 | − | 0.306400i | ||||
\(449\) | − | 22.2412i | − | 1.04963i | −0.851217 | − | 0.524814i | \(-0.824135\pi\) | ||
0.851217 | − | 0.524814i | \(-0.175865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.75979 | − | 1.59336i | −0.129953 | − | 0.0750286i | ||||
\(452\) | 52.1064 | − | 13.9619i | 2.45088 | − | 0.656711i | ||||
\(453\) | −1.08973 | + | 4.06693i | −0.0512000 | + | 0.191081i | ||||
\(454\) | 57.1477 | 2.68207 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.461145 | 0.0215951 | ||||||||
\(457\) | 2.74748 | − | 10.2537i | 0.128522 | − | 0.479650i | −0.871419 | − | 0.490540i | \(-0.836800\pi\) |
0.999941 | + | 0.0108896i | \(0.00346635\pi\) | |||||||
\(458\) | −16.5978 | + | 4.44737i | −0.775564 | + | 0.207812i | ||||
\(459\) | 1.61200 | + | 0.930686i | 0.0752415 | + | 0.0434407i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.43806i | − | 0.299851i | −0.988697 | − | 0.149925i | \(-0.952097\pi\) | ||
0.988697 | − | 0.149925i | \(-0.0479033\pi\) | |||||||
\(462\) | −14.3467 | + | 16.3122i | −0.667467 | + | 0.758912i | ||||
\(463\) | 10.4584 | − | 10.4584i | 0.486041 | − | 0.486041i | −0.421014 | − | 0.907054i | \(-0.638326\pi\) |
0.907054 | + | 0.421014i | \(0.138326\pi\) | |||||||
\(464\) | 1.47279 | − | 0.850314i | 0.0683724 | − | 0.0394748i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.48714 | + | 14.7002i | −0.393159 | + | 0.680972i | ||||
\(467\) | −10.0867 | − | 2.70272i | −0.466756 | − | 0.125067i | 0.0177729 | − | 0.999842i | \(-0.494342\pi\) |
−0.484529 | + | 0.874775i | \(0.661009\pi\) | |||||||
\(468\) | 15.3444 | + | 15.3444i | 0.709295 | + | 0.709295i | ||||
\(469\) | −1.81578 | − | 28.3227i | −0.0838447 | − | 1.30782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.483404 | − | 0.837281i | −0.0222741 | − | 0.0385799i | ||||
\(472\) | −5.38345 | − | 20.0913i | −0.247794 | − | 0.924778i | ||||
\(473\) | −3.07926 | − | 11.4919i | −0.141584 | − | 0.528400i | ||||
\(474\) | −9.81143 | − | 16.9939i | −0.450654 | − | 0.780555i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.0819 | − | 7.46434i | −0.691277 | − | 0.342127i | ||||
\(477\) | 1.98543 | + | 1.98543i | 0.0909066 | + | 0.0909066i | ||||
\(478\) | −22.2247 | − | 5.95510i | −1.01654 | − | 0.272380i | ||||
\(479\) | −15.3074 | + | 26.5132i | −0.699412 | + | 1.21142i | 0.269258 | + | 0.963068i | \(0.413222\pi\) |
−0.968670 | + | 0.248350i | \(0.920112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.9607 | + | 18.4525i | −1.45728 | + | 0.841362i | ||||
\(482\) | 5.54358 | − | 5.54358i | 0.252503 | − | 0.252503i | ||||
\(483\) | 2.00272 | − | 9.99377i | 0.0911268 | − | 0.454732i | ||||
\(484\) | 4.93850i | 0.224477i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.01563 | − | 1.16373i | −0.0914309 | − | 0.0527877i | ||||
\(487\) | 17.3396 | − | 4.64613i | 0.785733 | − | 0.210536i | 0.156422 | − | 0.987690i | \(-0.450004\pi\) |
0.629311 | + | 0.777154i | \(0.283337\pi\) | |||||||
\(488\) | −8.56773 | + | 31.9752i | −0.387843 | + | 1.44745i | ||||
\(489\) | 10.2640 | 0.464155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.26968 | 0.237817 | 0.118909 | − | 0.992905i | \(-0.462060\pi\) | ||||
0.118909 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(492\) | −0.798891 | + | 2.98150i | −0.0360168 | + | 0.134417i | ||||
\(493\) | −3.63130 | + | 0.973004i | −0.163546 | + | 0.0438219i | ||||
\(494\) | −1.78981 | − | 1.03335i | −0.0805273 | − | 0.0464925i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.43957i | − | 0.199343i | ||||||
\(497\) | 2.65074 | − | 13.2275i | 0.118902 | − | 0.593334i | ||||
\(498\) | −17.1731 | + | 17.1731i | −0.769547 | + | 0.769547i | ||||
\(499\) | 31.1135 | − | 17.9634i | 1.39283 | − | 0.804150i | 0.399202 | − | 0.916863i | \(-0.369287\pi\) |
0.993628 | + | 0.112713i | \(0.0359540\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.10569 | − | 7.11127i | 0.183429 | − | 0.317708i | ||||
\(502\) | −11.1007 | − | 2.97441i | −0.495447 | − | 0.132755i | ||||
\(503\) | −2.39146 | − | 2.39146i | −0.106630 | − | 0.106630i | 0.651779 | − | 0.758409i | \(-0.274023\pi\) |
−0.758409 | + | 0.651779i | \(0.774023\pi\) | |||||||
\(504\) | 7.82046 | + | 3.87051i | 0.348351 | + | 0.172406i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.8155 | − | 27.3932i | −0.703085 | − | 1.21778i | ||||
\(507\) | −7.07364 | − | 26.3992i | −0.314151 | − | 1.17243i | ||||
\(508\) | −6.05701 | − | 22.6051i | −0.268736 | − | 1.00294i | ||||
\(509\) | 16.3136 | + | 28.2560i | 0.723087 | + | 1.25242i | 0.959756 | + | 0.280834i | \(0.0906110\pi\) |
−0.236669 | + | 0.971590i | \(0.576056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.58497 | − | 24.7226i | −0.0701151 | − | 1.09367i | ||||
\(512\) | 6.68782 | + | 6.68782i | 0.295563 | + | 0.295563i | ||||
\(513\) | 0.135059 | + | 0.0361889i | 0.00596299 | + | 0.00159778i | ||||
\(514\) | −23.8558 | + | 41.3194i | −1.05223 | + | 1.82252i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.97992 | + | 5.76191i | −0.439341 | + | 0.253654i | ||||
\(517\) | −6.16330 | + | 6.16330i | −0.271062 | + | 0.271062i | ||||
\(518\) | −23.6329 | + | 26.8707i | −1.03837 | + | 1.18063i | ||||
\(519\) | − | 4.51490i | − | 0.198182i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.77709 | + | 3.33540i | 0.253099 | + | 0.146127i | 0.621182 | − | 0.783666i | \(-0.286653\pi\) |
−0.368084 | + | 0.929793i | \(0.619986\pi\) | |||||||
\(522\) | 4.54056 | − | 1.21664i | 0.198735 | − | 0.0532509i | ||||
\(523\) | −5.72338 | + | 21.3599i | −0.250266 | + | 0.934005i | 0.720397 | + | 0.693562i | \(0.243960\pi\) |
−0.970663 | + | 0.240444i | \(0.922707\pi\) | |||||||
\(524\) | −9.82896 | −0.429380 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.09666 | −0.353031 | ||||||||
\(527\) | −2.54007 | + | 9.47969i | −0.110647 | + | 0.412942i | ||||
\(528\) | 2.86926 | − | 0.768816i | 0.124868 | − | 0.0334584i | ||||
\(529\) | −7.06598 | − | 4.07955i | −0.307217 | − | 0.177372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.30675i | − | 0.273690i | ||||||
\(532\) | −1.23944 | − | 0.248380i | −0.0537367 | − | 0.0107686i | ||||
\(533\) | 4.05643 | − | 4.05643i | 0.175704 | − | 0.175704i | ||||
\(534\) | 7.07078 | − | 4.08232i | 0.305983 | − | 0.176659i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17.6891 | + | 30.6384i | −0.764053 | + | 1.32338i | ||||
\(537\) | 14.2395 | + | 3.81545i | 0.614478 | + | 0.164649i | ||||
\(538\) | 30.7935 | + | 30.7935i | 1.32760 | + | 1.32760i | ||||
\(539\) | 19.6343 | − | 14.9771i | 0.845709 | − | 0.645108i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.12948 | − | 12.3486i | −0.306520 | − | 0.530909i | 0.671078 | − | 0.741386i | \(-0.265831\pi\) |
−0.977599 | + | 0.210478i | \(0.932498\pi\) | |||||||
\(542\) | 4.22882 | + | 15.7822i | 0.181644 | + | 0.677903i | ||||
\(543\) | −1.58338 | − | 5.90927i | −0.0679495 | − | 0.253591i | ||||
\(544\) | −4.31499 | − | 7.47379i | −0.185004 | − | 0.320436i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −21.6798 | − | 32.5466i | −0.927811 | − | 1.39287i | ||||
\(547\) | 11.2527 | + | 11.2527i | 0.481132 | + | 0.481132i | 0.905493 | − | 0.424361i | \(-0.139501\pi\) |
−0.424361 | + | 0.905493i | \(0.639501\pi\) | |||||||
\(548\) | 67.7418 | + | 18.1514i | 2.89379 | + | 0.775388i | ||||
\(549\) | −5.01858 | + | 8.69243i | −0.214188 | + | 0.370984i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.244565 | + | 0.141200i | −0.0104188 | + | 0.00601532i | ||||
\(552\) | −8.98409 | + | 8.98409i | −0.382388 | + | 0.382388i | ||||
\(553\) | 7.14002 | + | 21.1329i | 0.303625 | + | 0.898661i | ||||
\(554\) | − | 18.1521i | − | 0.771211i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.0452 | + | 17.9240i | 1.31661 | + | 0.760145i | ||||
\(557\) | 13.5980 | − | 3.64356i | 0.576164 | − | 0.154383i | 0.0410418 | − | 0.999157i | \(-0.486932\pi\) |
0.535122 | + | 0.844775i | \(0.320266\pi\) | |||||||
\(558\) | 3.17610 | − | 11.8534i | 0.134455 | − | 0.501793i | ||||
\(559\) | 21.4173 | 0.905854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.56652 | −0.277239 | ||||||||
\(562\) | 1.87849 | − | 7.01063i | 0.0792395 | − | 0.295726i | ||||
\(563\) | −33.9375 | + | 9.09354i | −1.43030 | + | 0.383247i | −0.889125 | − | 0.457665i | \(-0.848686\pi\) |
−0.541172 | + | 0.840912i | \(0.682019\pi\) | |||||||
\(564\) | 7.31149 | + | 4.22129i | 0.307869 | + | 0.177748i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 73.1086i | 3.07299i | ||||||||
\(567\) | 1.98669 | + | 1.74730i | 0.0834331 | + | 0.0733798i | ||||
\(568\) | −11.8911 | + | 11.8911i | −0.498939 | + | 0.498939i | ||||
\(569\) | 22.1757 | − | 12.8031i | 0.929652 | − | 0.536735i | 0.0429507 | − | 0.999077i | \(-0.486324\pi\) |
0.886702 | + | 0.462342i | \(0.152991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1850 | + | 26.3013i | −0.635474 | + | 1.10067i | 0.350941 | + | 0.936398i | \(0.385862\pi\) |
−0.986415 | + | 0.164275i | \(0.947471\pi\) | |||||||
\(572\) | −73.9453 | − | 19.8136i | −3.09181 | − | 0.828448i | ||||
\(573\) | −15.8728 | − | 15.8728i | −0.663096 | − | 0.663096i | ||||
\(574\) | 2.46736 | − | 4.98537i | 0.102986 | − | 0.208085i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.23747 | + | 10.8036i | 0.259895 | + | 0.450151i | ||||
\(577\) | −5.93273 | − | 22.1412i | −0.246983 | − | 0.921752i | −0.972376 | − | 0.233418i | \(-0.925009\pi\) |
0.725394 | − | 0.688334i | \(-0.241658\pi\) | |||||||
\(578\) | 8.15351 | + | 30.4293i | 0.339141 | + | 1.26569i | ||||
\(579\) | 8.97817 | + | 15.5506i | 0.373120 | + | 0.646263i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.9770 | − | 15.3053i | 0.953247 | − | 0.634973i | ||||
\(582\) | −20.2543 | − | 20.2543i | −0.839569 | − | 0.839569i | ||||
\(583\) | −9.56788 | − | 2.56370i | −0.396261 | − | 0.106178i | ||||
\(584\) | −15.4406 | + | 26.7440i | −0.638938 | + | 1.10667i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.05699 | + | 2.91966i | −0.208902 | + | 0.120610i | ||||
\(587\) | −3.26809 | + | 3.26809i | −0.134888 | + | 0.134888i | −0.771327 | − | 0.636439i | \(-0.780407\pi\) |
0.636439 | + | 0.771327i | \(0.280407\pi\) | |||||||
\(588\) | −18.9347 | − | 14.6152i | −0.780855 | − | 0.602720i | ||||
\(589\) | 0.737218i | 0.0303765i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.8537 | − | 8.57580i | −0.611001 | − | 0.352761i | ||||
\(592\) | 4.72647 | − | 1.26645i | 0.194257 | − | 0.0520509i | ||||
\(593\) | 3.38581 | − | 12.6360i | 0.139038 | − | 0.518899i | −0.860910 | − | 0.508757i | \(-0.830105\pi\) |
0.999949 | − | 0.0101415i | \(-0.00322821\pi\) | |||||||
\(594\) | 8.21074 | 0.336891 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.0272 | 1.84438 | ||||||||
\(597\) | 1.75858 | − | 6.56312i | 0.0719740 | − | 0.268610i | ||||
\(598\) | 55.0011 | − | 14.7375i | 2.24916 | − | 0.602661i | ||||
\(599\) | 1.72270 | + | 0.994603i | 0.0703877 | + | 0.0406384i | 0.534781 | − | 0.844991i | \(-0.320394\pi\) |
−0.464393 | + | 0.885629i | \(0.653728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.1436i | − | 1.14800i | −0.818855 | − | 0.574001i | \(-0.805391\pi\) | ||
0.818855 | − | 0.574001i | \(-0.194609\pi\) | |||||||
\(602\) | 19.6746 | − | 6.64731i | 0.801876 | − | 0.270924i | ||||
\(603\) | −7.58511 | + | 7.58511i | −0.308890 | + | 0.308890i | ||||
\(604\) | −12.4595 | + | 7.19352i | −0.506972 | + | 0.292700i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.67275 | + | 2.89729i | −0.0679509 | + | 0.117694i | ||||
\(607\) | 42.8022 | + | 11.4688i | 1.73729 | + | 0.465505i | 0.981841 | − | 0.189706i | \(-0.0607535\pi\) |
0.755446 | + | 0.655211i | \(0.227420\pi\) | |||||||
\(608\) | −0.458396 | − | 0.458396i | −0.0185904 | − | 0.0185904i | ||||
\(609\) | −5.33266 | + | 0.341877i | −0.216090 | + | 0.0138536i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.84536 | − | 13.5886i | −0.317389 | − | 0.549734i | ||||
\(612\) | 1.64618 | + | 6.14364i | 0.0665430 | + | 0.248342i | ||||
\(613\) | −4.91551 | − | 18.3450i | −0.198536 | − | 0.740946i | −0.991323 | − | 0.131447i | \(-0.958038\pi\) |
0.792787 | − | 0.609498i | \(-0.208629\pi\) | |||||||
\(614\) | −17.5302 | − | 30.3632i | −0.707462 | − | 1.22536i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.7199 | + | 1.96946i | −1.23774 | + | 0.0793516i | ||||
\(617\) | −8.02128 | − | 8.02128i | −0.322924 | − | 0.322924i | 0.526963 | − | 0.849888i | \(-0.323330\pi\) |
−0.849888 | + | 0.526963i | \(0.823330\pi\) | |||||||
\(618\) | −13.9414 | − | 3.73560i | −0.560807 | − | 0.150268i | ||||
\(619\) | 15.2997 | − | 26.4998i | 0.614945 | − | 1.06512i | −0.375449 | − | 0.926843i | \(-0.622512\pi\) |
0.990394 | − | 0.138273i | \(-0.0441552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.33627 | + | 1.92619i | −0.133880 | + | 0.0772955i | ||||
\(622\) | 30.6841 | − | 30.6841i | 1.23032 | − | 1.23032i | ||||
\(623\) | −8.79292 | + | 2.97080i | −0.352281 | + | 0.119023i | ||||
\(624\) | 5.34737i | 0.214066i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 41.4027 | + | 23.9038i | 1.65478 | + | 0.955390i | ||||
\(627\) | −0.476458 | + | 0.127667i | −0.0190279 | + | 0.00509851i | ||||
\(628\) | 0.855038 | − | 3.19105i | 0.0341197 | − | 0.127337i | ||||
\(629\) | −10.8169 | −0.431298 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.68706 | 0.266207 | 0.133104 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133104 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(632\) | 7.19675 | − | 26.8587i | 0.286272 | − | 1.06838i | ||||
\(633\) | −2.45095 | + | 0.656731i | −0.0974167 | + | 0.0261027i | ||||
\(634\) | 58.8699 | + | 33.9885i | 2.33802 | + | 1.34986i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.59441i | 0.380443i | ||||||||
\(637\) | 16.8946 | + | 41.1189i | 0.669390 | + | 1.62919i | ||||
\(638\) | −11.7261 | + | 11.7261i | −0.464240 | + | 0.464240i | ||||
\(639\) | −4.41579 | + | 2.54946i | −0.174686 | + | 0.100855i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4639 | + | 42.3726i | −0.966264 | + | 1.67362i | −0.260085 | + | 0.965586i | \(0.583751\pi\) |
−0.706179 | + | 0.708033i | \(0.749583\pi\) | |||||||
\(642\) | 40.3690 | + | 10.8168i | 1.59324 | + | 0.426906i | ||||
\(643\) | −3.55117 | − | 3.55117i | −0.140044 | − | 0.140044i | 0.633609 | − | 0.773653i | \(-0.281573\pi\) |
−0.773653 | + | 0.633609i | \(0.781573\pi\) | |||||||
\(644\) | 28.9860 | − | 19.3080i | 1.14221 | − | 0.760842i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.302875 | − | 0.524594i | −0.0119164 | − | 0.0206399i | ||||
\(647\) | 7.51337 | + | 28.0403i | 0.295381 | + | 1.10238i | 0.940914 | + | 0.338645i | \(0.109969\pi\) |
−0.645533 | + | 0.763732i | \(0.723365\pi\) | |||||||
\(648\) | −0.853601 | − | 3.18568i | −0.0335326 | − | 0.125145i | ||||
\(649\) | 11.1244 | + | 19.2681i | 0.436672 | + | 0.756338i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.18766 | + | 12.5023i | −0.242514 | + | 0.490005i | ||||
\(652\) | 24.8000 | + | 24.8000i | 0.971242 | + | 0.971242i | ||||
\(653\) | 9.80085 | + | 2.62613i | 0.383537 | + | 0.102768i | 0.445436 | − | 0.895314i | \(-0.353049\pi\) |
−0.0618985 | + | 0.998082i | \(0.519716\pi\) | |||||||
\(654\) | −14.8167 | + | 25.6632i | −0.579377 | + | 1.00351i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.658715 | + | 0.380309i | −0.0257185 | + | 0.0148486i | ||||
\(657\) | −6.62097 | + | 6.62097i | −0.258309 | + | 0.258309i | ||||
\(658\) | −11.4245 | − | 10.0479i | −0.445373 | − | 0.391708i | ||||
\(659\) | 19.2380i | 0.749405i | 0.927145 | + | 0.374703i | \(0.122255\pi\) | ||||
−0.927145 | + | 0.374703i | \(0.877745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0842 | + | 9.28623i | 0.625604 | + | 0.361193i | 0.779048 | − | 0.626965i | \(-0.215703\pi\) |
−0.153444 | + | 0.988157i | \(0.549036\pi\) | |||||||
\(662\) | −53.1798 | + | 14.2495i | −2.06689 | + | 0.553822i | ||||
\(663\) | 3.05947 | − | 11.4181i | 0.118820 | − | 0.443442i | ||||
\(664\) | −34.4146 | −1.33555 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.5254 | 0.524098 | ||||||||
\(667\) | 2.01378 | − | 7.51552i | 0.0779738 | − | 0.291002i | ||||
\(668\) | 27.1025 | − | 7.26209i | 1.04863 | − | 0.280979i | ||||
\(669\) | −9.57233 | − | 5.52659i | −0.370088 | − | 0.213670i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 35.4089i | − | 1.36695i | ||||||
\(672\) | −3.92640 | − | 11.6213i | −0.151464 | − | 0.448300i | ||||
\(673\) | −11.7627 | + | 11.7627i | −0.453420 | + | 0.453420i | −0.896488 | − | 0.443068i | \(-0.853890\pi\) |
0.443068 | + | 0.896488i | \(0.353890\pi\) | |||||||
\(674\) | −23.9083 | + | 13.8035i | −0.920913 | + | 0.531690i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 46.6944 | − | 80.8771i | 1.79594 | − | 3.11066i | ||||
\(677\) | −48.0456 | − | 12.8738i | −1.84654 | − | 0.494780i | −0.847209 | − | 0.531259i | \(-0.821719\pi\) |
−0.999334 | + | 0.0364792i | \(0.988386\pi\) | |||||||
\(678\) | 25.9815 | + | 25.9815i | 0.997813 | + | 0.997813i | ||||
\(679\) | 18.0514 | + | 27.0995i | 0.692750 | + | 1.03998i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2769 | + | 21.2642i | 0.470451 | + | 0.814846i | ||||
\(682\) | 11.2046 | + | 41.8161i | 0.429046 | + | 1.60122i | ||||
\(683\) | −11.7226 | − | 43.7494i | −0.448553 | − | 1.67402i | −0.706380 | − | 0.707833i | \(-0.749673\pi\) |
0.257827 | − | 0.966191i | \(-0.416994\pi\) | |||||||
\(684\) | 0.238890 | + | 0.413769i | 0.00913418 | + | 0.0158209i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28.2821 | + | 32.5294i | 1.07981 | + | 1.24198i | ||||
\(687\) | −5.22049 | − | 5.22049i | −0.199174 | − | 0.199174i | ||||
\(688\) | −2.74293 | − | 0.734967i | −0.104573 | − | 0.0280204i | ||||
\(689\) | 8.91571 | − | 15.4425i | 0.339662 | − | 0.588311i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.7216 | + | 10.2316i | −0.674161 | + | 0.389227i | −0.797652 | − | 0.603119i | \(-0.793925\pi\) |
0.123490 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(692\) | 10.9089 | − | 10.9089i | 0.414695 | − | 0.414695i | ||||
\(693\) | −9.15169 | − | 1.83397i | −0.347644 | − | 0.0696666i | ||||
\(694\) | 25.3364i | 0.961756i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.76866 | + | 3.33054i | 0.218660 | + | 0.126244i | ||||
\(697\) | 1.62413 | − | 0.435184i | 0.0615182 | − | 0.0164838i | ||||
\(698\) | 3.09219 | − | 11.5402i | 0.117041 | − | 0.436803i | ||||
\(699\) | −7.29308 | −0.275850 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5198 | −0.926099 | −0.463049 | − | 0.886332i | \(-0.653245\pi\) | ||||
−0.463049 | + | 0.886332i | \(0.653245\pi\) | |||||||
\(702\) | −3.82554 | + | 14.2771i | −0.144386 | + | 0.538855i | ||||
\(703\) | −0.784860 | + | 0.210303i | −0.0296015 | + | 0.00793171i | ||||
\(704\) | −38.1128 | − | 22.0045i | −1.43643 | − | 0.829324i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 50.2611i | − | 1.89160i | ||||||
\(707\) | 2.51159 | − | 2.85569i | 0.0944581 | − | 0.107399i | ||||
\(708\) | 15.2384 | − | 15.2384i | 0.572694 | − | 0.572694i | ||||
\(709\) | −8.72879 | + | 5.03957i | −0.327817 | + | 0.189265i | −0.654871 | − | 0.755740i | \(-0.727277\pi\) |
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.21552 | − | 7.30150i | 0.158095 | − | 0.273828i | ||||
\(712\) | 11.1753 | + | 2.99441i | 0.418812 | + | 0.112220i | ||||
\(713\) | −14.3626 | − | 14.3626i | −0.537883 | − | 0.537883i | ||||
\(714\) | −0.733329 | − | 11.4386i | −0.0274442 | − | 0.428078i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.1865 | + | 43.6244i | 0.941265 | + | 1.63032i | ||||
\(717\) | −2.55864 | − | 9.54896i | −0.0955540 | − | 0.356612i | ||||
\(718\) | −2.49702 | − | 9.31900i | −0.0931879 | − | 0.347782i | ||||
\(719\) | 1.67817 | + | 2.90667i | 0.0625851 | + | 0.108401i | 0.895620 | − | 0.444820i | \(-0.146732\pi\) |
−0.833035 | + | 0.553220i | \(0.813399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7047 | + | 7.27767i | 0.547632 | + | 0.271035i | ||||
\(722\) | 31.2372 | + | 31.2372i | 1.16253 | + | 1.16253i | ||||
\(723\) | 3.25363 | + | 0.871808i | 0.121004 | + | 0.0324229i | ||||
\(724\) | 10.4522 | − | 18.1038i | 0.388454 | − | 0.672821i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.91312 | + | 1.68189i | −0.108116 | + | 0.0624208i | ||||
\(727\) | −23.0330 | + | 23.0330i | −0.854247 | + | 0.854247i | −0.990653 | − | 0.136406i | \(-0.956445\pi\) |
0.136406 | + | 0.990653i | \(0.456445\pi\) | |||||||
\(728\) | 10.8884 | − | 54.3344i | 0.403552 | − | 2.01377i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.43640 | + | 3.13871i | 0.201073 | + | 0.116089i | ||||
\(732\) | −33.1286 | + | 8.87677i | −1.22447 | + | 0.328095i | ||||
\(733\) | −12.4202 | + | 46.3528i | −0.458751 | + | 1.71208i | 0.218071 | + | 0.975933i | \(0.430024\pi\) |
−0.676821 | + | 0.736147i | \(0.736643\pi\) | |||||||
\(734\) | 7.90873 | 0.291917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.8611 | 0.658367 | ||||||||
\(737\) | 9.79434 | − | 36.5530i | 0.360779 | − | 1.34645i | ||||
\(738\) | −2.03080 | + | 0.544151i | −0.0747548 | + | 0.0200305i | ||||
\(739\) | −16.4664 | − | 9.50689i | −0.605727 | − | 0.349717i | 0.165564 | − | 0.986199i | \(-0.447055\pi\) |
−0.771291 | + | 0.636482i | \(0.780389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.887964i | − | 0.0326202i | ||||||
\(742\) | 3.39735 | − | 16.9531i | 0.124720 | − | 0.622368i | ||||
\(743\) | 2.50371 | − | 2.50371i | 0.0918524 | − | 0.0918524i | −0.659688 | − | 0.751540i | \(-0.729311\pi\) |
0.751540 | + | 0.659688i | \(0.229311\pi\) | |||||||
\(744\) | 15.0594 | − | 8.69452i | 0.552103 | − | 0.318757i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 41.7382 | − | 72.2926i | 1.52814 | − | 2.64682i | ||||
\(747\) | −10.0792 | − | 2.70073i | −0.368780 | − | 0.0988144i | ||||
\(748\) | −15.8660 | − | 15.8660i | −0.580120 | − | 0.580120i | ||||
\(749\) | −42.5791 | − | 21.0733i | −1.55581 | − | 0.770002i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4684 | − | 21.5959i | −0.454978 | − | 0.788046i | 0.543708 | − | 0.839274i | \(-0.317020\pi\) |
−0.998687 | + | 0.0512283i | \(0.983686\pi\) | |||||||
\(752\) | 0.538452 | + | 2.00953i | 0.0196353 | + | 0.0732800i | ||||
\(753\) | −1.27797 | − | 4.76945i | −0.0465718 | − | 0.173808i | ||||
\(754\) | −14.9263 | − | 25.8531i | −0.543584 | − | 0.941515i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.578407 | + | 9.02208i | 0.0210365 | + | 0.328130i | ||||
\(757\) | 0.224148 | + | 0.224148i | 0.00814681 | + | 0.00814681i | 0.711168 | − | 0.703022i | \(-0.248166\pi\) |
−0.703022 | + | 0.711168i | \(0.748166\pi\) | |||||||
\(758\) | 18.0431 | + | 4.83462i | 0.655353 | + | 0.175601i | ||||
\(759\) | 6.79520 | − | 11.7696i | 0.246650 | − | 0.427211i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1337 | + | 7.00541i | −0.439847 | + | 0.253946i | −0.703533 | − | 0.710663i | \(-0.748395\pi\) |
0.263685 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(762\) | 11.2714 | − | 11.2714i | 0.408321 | − | 0.408321i | ||||
\(763\) | 22.2468 | − | 25.2947i | 0.805389 | − | 0.915730i | ||||
\(764\) | − | 76.7039i | − | 2.77505i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −66.1651 | − | 38.2004i | −2.39064 | − | 1.38024i | ||||
\(767\) | −38.6871 | + | 10.3662i | −1.39691 | + | 0.374301i | ||||
\(768\) | −5.44696 | + | 20.3283i | −0.196550 | + | 0.733535i | ||||
\(769\) | −49.1264 | −1.77154 | −0.885772 | − | 0.464120i | \(-0.846371\pi\) | ||||
−0.885772 | + | 0.464120i | \(0.846371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4995 | −0.738272 | ||||||||
\(772\) | −15.8804 | + | 59.2666i | −0.571549 | + | 2.13305i | ||||
\(773\) | 22.4052 | − | 6.00345i | 0.805858 | − | 0.215929i | 0.167704 | − | 0.985837i | \(-0.446365\pi\) |
0.638154 | + | 0.769908i | \(0.279698\pi\) | |||||||
\(774\) | −6.79765 | − | 3.92463i | −0.244337 | − | 0.141068i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 40.5893i | − | 1.45707i | ||||||
\(777\) | −15.0754 | − | 3.02106i | −0.540826 | − | 0.108380i | ||||
\(778\) | −25.5370 | + | 25.5370i | −0.915546 | + | 0.915546i | ||||
\(779\) | 0.109384 | − | 0.0631527i | 0.00391908 | − | 0.00226268i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.99394 | − | 15.5780i | 0.321829 | − | 0.557423i | ||||
\(782\) | 16.1208 | + | 4.31957i | 0.576480 | + | 0.154467i | ||||
\(783\) | 1.42814 | + | 1.42814i | 0.0510375 | + | 0.0510375i | ||||
\(784\) | −0.752658 | − | 5.84591i | −0.0268806 | − | 0.208782i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.34742 | − | 5.79789i | −0.119398 | − | 0.206804i | ||||
\(787\) | −3.76964 | − | 14.0685i | −0.134373 | − | 0.501488i | −1.00000 | 0.000797382i | \(-0.999746\pi\) | |
0.865626 | − | 0.500690i | \(-0.166920\pi\) | |||||||
\(788\) | −15.1687 | − | 56.6105i | −0.540364 | − | 2.01667i | ||||
\(789\) | −1.73938 | − | 3.01270i | −0.0619237 | − | 0.107255i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.1557 | − | 34.7622i | −0.823321 | − | 1.23600i | ||||
\(792\) | 8.22708 | + | 8.22708i | 0.292337 | + | 0.292337i | ||||
\(793\) | 61.5702 | + | 16.4977i | 2.18642 | + | 0.585850i | ||||
\(794\) | 24.4893 | − | 42.4167i | 0.869093 | − | 1.50531i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.1069 | − | 11.6087i | 0.712671 | − | 0.411461i | ||||
\(797\) | 38.0535 | − | 38.0535i | 1.34792 | − | 1.34792i | 0.460013 | − | 0.887912i | \(-0.347845\pi\) |
0.887912 | − | 0.460013i | \(-0.152155\pi\) | |||||||
\(798\) | −0.275599 | − | 0.815711i | −0.00975609 | − | 0.0288759i | ||||
\(799\) | − | 4.59896i | − | 0.162700i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.03799 | + | 1.75399i | 0.107342 | + | 0.0619740i | ||||
\(802\) | 42.0354 | − | 11.2633i | 1.48432 | − | 0.397722i | ||||
\(803\) | 8.54938 | − | 31.9067i | 0.301701 | − | 1.12596i | ||||
\(804\) | −36.6543 | −1.29270 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −77.9317 | −2.74503 | ||||||||
\(807\) | −4.84272 | + | 18.0733i | −0.170472 | + | 0.636210i | ||||
\(808\) | −4.57913 | + | 1.22698i | −0.161093 | + | 0.0431648i | ||||
\(809\) | 15.3437 | + | 8.85869i | 0.539456 | + | 0.311455i | 0.744858 | − | 0.667222i | \(-0.232517\pi\) |
−0.205402 | + | 0.978678i | \(0.565850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9256i | 0.980600i | 0.871554 | + | 0.490300i | \(0.163113\pi\) | ||||
−0.871554 | + | 0.490300i | \(0.836887\pi\) | |||||||
\(812\) | −13.7108 | − | 12.0587i | −0.481156 | − | 0.423179i | ||||
\(813\) | −4.96396 | + | 4.96396i | −0.174094 | + | 0.174094i | ||||
\(814\) | −41.3221 | + | 23.8573i | −1.44834 | + | 0.836199i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.783659 | + | 1.35734i | −0.0274336 | + | 0.0475163i | ||||
\(817\) | 0.455481 | + | 0.122046i | 0.0159353 | + | 0.00426984i | ||||
\(818\) | −39.1693 | − | 39.1693i | −1.36952 | − | 1.36952i | ||||
\(819\) | 7.45291 | − | 15.0588i | 0.260426 | − | 0.526197i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.80771 | + | 16.9874i | 0.342291 | + | 0.592866i | 0.984858 | − | 0.173364i | \(-0.0554637\pi\) |
−0.642566 | + | 0.766230i | \(0.722130\pi\) | |||||||
\(822\) | 12.3635 | + | 46.1412i | 0.431227 | + | 1.60936i | ||||
\(823\) | 13.0933 | + | 48.8650i | 0.456405 | + | 1.70333i | 0.683924 | + | 0.729553i | \(0.260272\pi\) |
−0.227519 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(824\) | −10.2261 | − | 17.7122i | −0.356245 | − | 0.617034i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.3218 | + | 21.5301i | −1.12462 | + | 0.749127i | ||||
\(827\) | −18.2487 | − | 18.2487i | −0.634570 | − | 0.634570i | 0.314641 | − | 0.949211i | \(-0.398116\pi\) |
−0.949211 | + | 0.314641i | \(0.898116\pi\) | |||||||
\(828\) | −12.7152 | − | 3.40702i | −0.441883 | − | 0.118402i | ||||
\(829\) | 20.5574 | − | 35.6064i | 0.713988 | − | 1.23666i | −0.249361 | − | 0.968411i | \(-0.580221\pi\) |
0.963349 | − | 0.268252i | \(-0.0864460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.75426 | − | 3.89958i | 0.234303 | − | 0.135275i | ||||
\(832\) | 56.0196 | − | 56.0196i | 1.94213 | − | 1.94213i | ||||
\(833\) | −1.73757 | + | 12.9132i | −0.0602034 | + | 0.447417i | ||||
\(834\) | 24.4172i | 0.845499i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.45969 | − | 0.842752i | −0.0504844 | − | 0.0291472i | ||||
\(837\) | 5.09285 | − | 1.36462i | 0.176035 | − | 0.0471683i | ||||
\(838\) | 5.85525 | − | 21.8521i | 0.202266 | − | 0.754868i | ||||
\(839\) | −46.0286 | −1.58908 | −0.794541 | − | 0.607210i | \(-0.792289\pi\) | ||||
−0.794541 | + | 0.607210i | \(0.792289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9208 | 0.859339 | ||||||||
\(842\) | −7.83676 | + | 29.2472i | −0.270073 | + | 1.00793i | ||||
\(843\) | 3.01215 | − | 0.807103i | 0.103744 | − | 0.0277981i | ||||
\(844\) | −7.50880 | − | 4.33521i | −0.258464 | − | 0.149224i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.75052i | 0.197707i | ||||||||
\(847\) | 3.62263 | − | 1.22395i | 0.124475 | − | 0.0420555i | ||||
\(848\) | −1.67178 | + | 1.67178i | −0.0574091 | + | 0.0574091i | ||||
\(849\) | −27.2031 | + | 15.7057i | −0.933609 | + | 0.539019i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1936 | − | 19.3879i | 0.383711 | − | 0.664608i | ||||
\(852\) | −16.8295 | − | 4.50944i | −0.576568 | − | 0.154491i | ||||
\(853\) | −22.9994 | − | 22.9994i | −0.787484 | − | 0.787484i | 0.193597 | − | 0.981081i | \(-0.437984\pi\) |
−0.981081 | + | 0.193597i | \(0.937984\pi\) | |||||||
\(854\) | 61.6807 | − | 3.95436i | 2.11067 | − | 0.135315i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6109 | + | 51.2876i | 1.01208 | + | 1.75298i | ||||
\(857\) | −2.22400 | − | 8.30009i | −0.0759705 | − | 0.283526i | 0.917481 | − | 0.397779i | \(-0.130219\pi\) |
−0.993452 | + | 0.114254i | \(0.963552\pi\) | |||||||
\(858\) | −13.4957 | − | 50.3666i | −0.460735 | − | 1.71949i | ||||
\(859\) | 1.33433 | + | 2.31112i | 0.0455266 | + | 0.0788544i | 0.887891 | − | 0.460054i | \(-0.152170\pi\) |
−0.842364 | + | 0.538909i | \(0.818837\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.38507 | − | 0.152907i | 0.0812830 | − | 0.00521107i | ||||
\(862\) | −21.7319 | − | 21.7319i | −0.740190 | − | 0.740190i | ||||
\(863\) | 0.515877 | + | 0.138229i | 0.0175607 | + | 0.00470537i | 0.267589 | − | 0.963533i | \(-0.413773\pi\) |
−0.250028 | + | 0.968239i | \(0.580440\pi\) | |||||||
\(864\) | −2.31818 | + | 4.01520i | −0.0788660 | + | 0.136600i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.7140 | + | 22.9289i | −1.34954 | + | 0.779155i | ||||
\(867\) | −9.57090 | + | 9.57090i | −0.325045 | + | 0.325045i | ||||
\(868\) | −45.1588 | + | 15.2575i | −1.53279 | + | 0.517873i | ||||
\(869\) | 29.7429i | 1.00896i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.9962 | + | 34.0615i | 1.99901 | + | 1.15413i | ||||
\(872\) | −40.5604 | + | 10.8681i | −1.37355 | + | 0.368041i | ||||
\(873\) | 3.18529 | − | 11.8877i | 0.107806 | − | 0.402336i | ||||
\(874\) | 1.25369 | 0.0424067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.9952 | −1.08102 | ||||||||
\(877\) | −10.7066 | + | 39.9574i | −0.361535 | + | 1.34927i | 0.510523 | + | 0.859864i | \(0.329452\pi\) |
−0.872058 | + | 0.489402i | \(0.837215\pi\) | |||||||
\(878\) | 28.3643 | − | 7.60019i | 0.957249 | − | 0.256494i | ||||
\(879\) | −2.17276 | − | 1.25444i | −0.0732854 | − | 0.0423113i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.0542i | − | 0.776715i | −0.921509 | − | 0.388358i | \(-0.873043\pi\) | ||
0.921509 | − | 0.388358i | \(-0.126957\pi\) | |||||||
\(882\) | 2.17265 | − | 16.1466i | 0.0731571 | − | 0.543686i | ||||
\(883\) | 7.73430 | − | 7.73430i | 0.260280 | − | 0.260280i | −0.564888 | − | 0.825168i | \(-0.691081\pi\) |
0.825168 | + | 0.564888i | \(0.191081\pi\) | |||||||
\(884\) | 34.9807 | − | 20.1961i | 1.17653 | − | 0.679269i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.2677 | + | 38.5688i | −0.748098 | + | 1.29574i | ||||
\(887\) | 49.6024 | + | 13.2909i | 1.66549 | + | 0.446265i | 0.963888 | − | 0.266308i | \(-0.0858039\pi\) |
0.701597 | + | 0.712574i | \(0.252471\pi\) | |||||||
\(888\) | 13.5523 | + | 13.5523i | 0.454785 | + | 0.454785i | ||||
\(889\) | −15.0807 | + | 10.0455i | −0.505791 | + | 0.336916i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.76389 | + | 3.05515i | 0.0590926 | + | 0.102351i | ||||
\(892\) | −9.77533 | − | 36.4820i | −0.327302 | − | 1.22151i | ||||
\(893\) | −0.0894132 | − | 0.333695i | −0.00299210 | − | 0.0111667i | ||||
\(894\) | 15.3347 | + | 26.5606i | 0.512871 | + | 0.888318i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.1922 | − | 46.8605i | 0.774798 | − | 1.56550i | ||||
\(897\) | 17.2994 | + | 17.2994i | 0.577611 | + | 0.577611i | ||||
\(898\) | 50.0015 | + | 13.3979i | 1.66857 | + | 0.447092i | ||||
\(899\) | −5.32442 | + | 9.22216i | −0.177579 | + | 0.307576i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.52620 | − | 2.61320i | 0.150790 | − | 0.0870584i | ||||
\(902\) | 5.24458 | − | 5.24458i | 0.174625 | − | 0.174625i | ||||
\(903\) | 6.70005 | + | 5.89272i | 0.222964 | + | 0.196097i | ||||
\(904\) | 52.0664i | 1.73170i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.48661 | − | 4.89974i | −0.281949 | − | 0.162783i | ||||
\(907\) | −13.5581 | + | 3.63289i | −0.450191 | + | 0.120628i | −0.476789 | − | 0.879018i | \(-0.658199\pi\) |
0.0265979 | + | 0.999646i | \(0.491533\pi\) | |||||||
\(908\) | −21.7152 | + | 81.0421i | −0.720643 | + | 2.68948i | ||||
\(909\) | −1.43741 | −0.0476759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2471 | 1.39971 | 0.699854 | − | 0.714286i | \(-0.253248\pi\) | ||||
0.699854 | + | 0.714286i | \(0.253248\pi\) | |||||||
\(912\) | −0.0304719 | + | 0.113723i | −0.00100902 | + | 0.00376573i | ||||
\(913\) | 35.5574 | − | 9.52758i | 1.17678 | − | 0.315317i | ||||
\(914\) | 21.3969 | + | 12.3535i | 0.707745 | + | 0.408617i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 25.2275i | − | 0.833541i | ||||||
\(917\) | 2.43600 | + | 7.21001i | 0.0804437 | + | 0.238096i | ||||
\(918\) | −3.06337 | + | 3.06337i | −0.101106 | + | 0.101106i | ||||
\(919\) | 3.66062 | − | 2.11346i | 0.120753 | − | 0.0697166i | −0.438407 | − | 0.898777i | \(-0.644457\pi\) |
0.559160 | + | 0.829060i | \(0.311124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.53194 | − | 13.0457i | 0.248186 | − | 0.429870i | ||||
\(922\) | 14.4737 | + | 3.87822i | 0.476666 | + | 0.127722i | ||||
\(923\) | 22.8970 | + | 22.8970i | 0.753665 | + | 0.753665i | ||||
\(924\) | −17.6811 | − | 26.5436i | −0.581666 | − | 0.873220i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.2119 | + | 29.8119i | 0.565618 | + | 0.979679i | ||||
\(927\) | −1.60502 | − | 5.99000i | −0.0527156 | − | 0.196737i | ||||
\(928\) | −2.42359 | − | 9.04495i | −0.0795581 | − | 0.296915i | ||||
\(929\) | 3.81103 | + | 6.60089i | 0.125036 | + | 0.216568i | 0.921747 | − | 0.387792i | \(-0.126762\pi\) |
−0.796711 | + | 0.604360i | \(0.793429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.124983 | + | 0.970749i | 0.00409617 | + | 0.0318150i | ||||
\(932\) | −17.6216 | − | 17.6216i | −0.577214 | − | 0.577214i | ||||
\(933\) | 18.0091 | + | 4.82552i | 0.589591 | + | 0.157980i | ||||
\(934\) | 12.1522 | − | 21.0483i | 0.397633 | − | 0.688720i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.1387 | + | 10.4724i | −0.592882 | + | 0.342300i | ||||
\(937\) | −31.1453 | + | 31.1453i | −1.01747 | + | 1.01747i | −0.0176276 | + | 0.999845i | \(0.505611\pi\) |
−0.999845 | + | 0.0176276i | \(0.994389\pi\) | |||||||
\(938\) | 64.7674 | + | 12.9792i | 2.11473 | + | 0.423785i | ||||
\(939\) | 20.5408i | 0.670324i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5296 | + | 20.5130i | 1.15823 | + | 0.668706i | 0.950880 | − | 0.309561i | \(-0.100182\pi\) |
0.207352 | + | 0.978266i | \(0.433515\pi\) | |||||||
\(942\) | 2.17353 | − | 0.582395i | 0.0708173 | − | 0.0189754i | ||||
\(943\) | −0.900678 | + | 3.36137i | −0.0293301 | + | 0.109461i | ||||
\(944\) | 5.31043 | 0.172840 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.6905 | 0.900295 | ||||||||
\(947\) | −13.8565 | + | 51.7131i | −0.450276 | + | 1.68045i | 0.251343 | + | 0.967898i | \(0.419128\pi\) |
−0.701618 | + | 0.712553i | \(0.747539\pi\) | |||||||
\(948\) | 27.8275 | − | 7.45635i | 0.903795 | − | 0.242171i | ||||
\(949\) | 51.4972 | + | 29.7319i | 1.67167 | + | 0.965139i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.2067i | 0.947091i | ||||||||
\(952\) | 10.7266 | − | 12.1961i | 0.347650 | − | 0.395279i | ||||
\(953\) | −35.5644 | + | 35.5644i | −1.15204 | + | 1.15204i | −0.165900 | + | 0.986143i | \(0.553053\pi\) |
−0.986143 | + | 0.165900i | \(0.946947\pi\) | |||||||
\(954\) | −5.65954 | + | 3.26753i | −0.183234 | + | 0.105790i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.8900 | − | 29.2544i | 0.546263 | − | 0.946155i | ||||
\(957\) | −6.88226 | − | 1.84410i | −0.222472 | − | 0.0596112i | ||||
\(958\) | −50.3845 | − | 50.3845i | −1.62785 | − | 1.62785i | ||||
\(959\) | −3.47416 | − | 54.1905i | −0.112186 | − | 1.74990i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.60035 | − | 2.77188i | −0.0516241 | − | 0.0894156i | ||||
\(962\) | −22.2312 | − | 82.9679i | −0.716762 | − | 2.67499i | ||||
\(963\) | 4.64750 | + | 17.3447i | 0.149764 | + | 0.558925i | ||||
\(964\) | 5.75497 | + | 9.96790i | 0.185355 | + | 0.321044i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.2610 | + | 10.5225i | 0.684063 | + | 0.338557i | ||||
\(967\) | 5.89078 | + | 5.89078i | 0.189435 | + | 0.189435i | 0.795452 | − | 0.606017i | \(-0.207234\pi\) |
−0.606017 | + | 0.795452i | \(0.707234\pi\) | |||||||
\(968\) | −4.60415 | − | 1.23368i | −0.147983 | − | 0.0396519i | ||||
\(969\) | 0.130131 | − | 0.225394i | 0.00418043 | − | 0.00724071i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.71844 | + | 1.56949i | −0.0872389 | + | 0.0503674i | −0.542985 | − | 0.839742i | \(-0.682706\pi\) |
0.455746 | + | 0.890110i | \(0.349373\pi\) | |||||||
\(972\) | 2.41620 | − | 2.41620i | 0.0774998 | − | 0.0774998i | ||||
\(973\) | 5.45387 | − | 27.2154i | 0.174843 | − | 0.872485i | ||||
\(974\) | 41.7807i | 1.33874i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.31922 | − | 4.22576i | −0.234283 | − | 0.135263i | ||||
\(977\) | 28.5027 | − | 7.63727i | 0.911882 | − | 0.244338i | 0.227770 | − | 0.973715i | \(-0.426857\pi\) |
0.684112 | + | 0.729377i | \(0.260190\pi\) | |||||||
\(978\) | −6.18293 | + | 23.0750i | −0.197708 | + | 0.737858i | ||||
\(979\) | −12.3754 | −0.395518 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.7321 | −0.406504 | ||||||||
\(982\) | −3.17439 | + | 11.8470i | −0.101299 | + | 0.378053i | ||||
\(983\) | −52.8361 | + | 14.1574i | −1.68521 | + | 0.451551i | −0.969147 | − | 0.246484i | \(-0.920725\pi\) |
−0.716064 | + | 0.698035i | \(0.754058\pi\) | |||||||
\(984\) | −2.58008 | − | 1.48961i | −0.0822498 | − | 0.0474869i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 8.74982i | − | 0.278651i | ||||||
\(987\) | 1.28445 | − | 6.40952i | 0.0408844 | − | 0.204017i | ||||
\(988\) | 2.14550 | − | 2.14550i | 0.0682575 | − | 0.0682575i | ||||
\(989\) | −11.2515 | + | 6.49603i | −0.357775 | + | 0.206562i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3059 | + | 42.0991i | −0.772104 | + | 1.33732i | 0.164304 | + | 0.986410i | \(0.447462\pi\) |
−0.936408 | + | 0.350913i | \(0.885871\pi\) | |||||||
\(992\) | −23.6123 | − | 6.32689i | −0.749690 | − | 0.200879i | ||||
\(993\) | −16.7266 | − | 16.7266i | −0.530803 | − | 0.530803i | ||||
\(994\) | 28.1405 | + | 13.9273i | 0.892563 | + | 0.441748i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.8280 | − | 30.8790i | −0.564902 | − | 0.978439i | ||||
\(997\) | 2.81774 | + | 10.5159i | 0.0892387 | + | 0.333043i | 0.996083 | − | 0.0884222i | \(-0.0281825\pi\) |
−0.906844 | + | 0.421466i | \(0.861516\pi\) | |||||||
\(998\) | 21.6418 | + | 80.7685i | 0.685061 | + | 2.55668i | ||||
\(999\) | 2.90562 | + | 5.03269i | 0.0919298 | + | 0.159227i |
(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 | 525.2.bc.e.157.2 | 32 | ||
5.2 | odd | 4 | 105.2.u.a.73.2 | yes | 32 | ||
5.3 | odd | 4 | inner | 525.2.bc.e.493.7 | 32 | ||
5.4 | even | 2 | 105.2.u.a.52.7 | ✓ | 32 | ||
7.5 | odd | 6 | inner | 525.2.bc.e.82.7 | 32 | ||
15.2 | even | 4 | 315.2.bz.d.73.7 | 32 | |||
15.14 | odd | 2 | 315.2.bz.d.262.2 | 32 | |||
35.2 | odd | 12 | 735.2.v.b.313.7 | 32 | |||
35.4 | even | 6 | 735.2.m.c.97.13 | 32 | |||
35.9 | even | 6 | 735.2.v.b.607.2 | 32 | |||
35.12 | even | 12 | 105.2.u.a.103.7 | yes | 32 | ||
35.17 | even | 12 | 735.2.m.c.538.13 | 32 | |||
35.19 | odd | 6 | 105.2.u.a.82.2 | yes | 32 | ||
35.24 | odd | 6 | 735.2.m.c.97.14 | 32 | |||
35.27 | even | 4 | 735.2.v.b.178.2 | 32 | |||
35.32 | odd | 12 | 735.2.m.c.538.14 | 32 | |||
35.33 | even | 12 | inner | 525.2.bc.e.418.2 | 32 | ||
35.34 | odd | 2 | 735.2.v.b.472.7 | 32 | |||
105.47 | odd | 12 | 315.2.bz.d.208.2 | 32 | |||
105.89 | even | 6 | 315.2.bz.d.82.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.u.a.52.7 | ✓ | 32 | 5.4 | even | 2 | ||
105.2.u.a.73.2 | yes | 32 | 5.2 | odd | 4 | ||
105.2.u.a.82.2 | yes | 32 | 35.19 | odd | 6 | ||
105.2.u.a.103.7 | yes | 32 | 35.12 | even | 12 | ||
315.2.bz.d.73.7 | 32 | 15.2 | even | 4 | |||
315.2.bz.d.82.7 | 32 | 105.89 | even | 6 | |||
315.2.bz.d.208.2 | 32 | 105.47 | odd | 12 | |||
315.2.bz.d.262.2 | 32 | 15.14 | odd | 2 | |||
525.2.bc.e.82.7 | 32 | 7.5 | odd | 6 | inner | ||
525.2.bc.e.157.2 | 32 | 1.1 | even | 1 | trivial | ||
525.2.bc.e.418.2 | 32 | 35.33 | even | 12 | inner | ||
525.2.bc.e.493.7 | 32 | 5.3 | odd | 4 | inner | ||
735.2.m.c.97.13 | 32 | 35.4 | even | 6 | |||
735.2.m.c.97.14 | 32 | 35.24 | odd | 6 | |||
735.2.m.c.538.13 | 32 | 35.17 | even | 12 | |||
735.2.m.c.538.14 | 32 | 35.32 | odd | 12 | |||
735.2.v.b.178.2 | 32 | 35.27 | even | 4 | |||
735.2.v.b.313.7 | 32 | 35.2 | odd | 12 | |||
735.2.v.b.472.7 | 32 | 35.34 | odd | 2 | |||
735.2.v.b.607.2 | 32 | 35.9 | even | 6 |