Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,4,Mod(137,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.137");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.e (of order \(4\), degree \(2\), 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: | \(13.5704393013\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 137.16 | ||
Character | \(\chi\) | \(=\) | 230.137 |
Dual form | 230.4.e.a.183.16 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | − | 1.41421i | −0.500000 | − | 0.500000i | ||||
\(3\) | 5.03526 | − | 5.03526i | 0.969036 | − | 0.969036i | −0.0304990 | − | 0.999535i | \(-0.509710\pi\) |
0.999535 | + | 0.0304990i | \(0.00970965\pi\) | |||||||
\(4\) | 4.00000i | 0.500000i | ||||||||
\(5\) | 6.80528 | + | 8.87064i | 0.608682 | + | 0.793414i | ||||
\(6\) | −14.2419 | −0.969036 | ||||||||
\(7\) | −11.1481 | + | 11.1481i | −0.601941 | + | 0.601941i | −0.940827 | − | 0.338887i | \(-0.889950\pi\) |
0.338887 | + | 0.940827i | \(0.389950\pi\) | |||||||
\(8\) | 5.65685 | − | 5.65685i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 23.7076i | − | 0.878061i | ||||||
\(10\) | 2.92086 | − | 22.1691i | 0.0923658 | − | 0.701048i | ||||
\(11\) | 8.94113i | 0.245078i | 0.992464 | + | 0.122539i | \(0.0391036\pi\) | ||||
−0.992464 | + | 0.122539i | \(0.960896\pi\) | |||||||
\(12\) | 20.1410 | + | 20.1410i | 0.484518 | + | 0.484518i | ||||
\(13\) | 43.6579 | − | 43.6579i | 0.931426 | − | 0.931426i | −0.0663693 | − | 0.997795i | \(-0.521142\pi\) |
0.997795 | + | 0.0663693i | \(0.0211415\pi\) | |||||||
\(14\) | 31.5316 | 0.601941 | ||||||||
\(15\) | 78.9323 | + | 10.3996i | 1.35868 | + | 0.179011i | ||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | 33.1397 | − | 33.1397i | 0.472797 | − | 0.472797i | −0.430022 | − | 0.902819i | \(-0.641494\pi\) |
0.902819 | + | 0.430022i | \(0.141494\pi\) | |||||||
\(18\) | −33.5277 | + | 33.5277i | −0.439030 | + | 0.439030i | ||||
\(19\) | 107.253 | 1.29503 | 0.647514 | − | 0.762053i | \(-0.275809\pi\) | ||||
0.647514 | + | 0.762053i | \(0.275809\pi\) | |||||||
\(20\) | −35.4826 | + | 27.2211i | −0.396707 | + | 0.304341i | ||||
\(21\) | 112.267i | 1.16660i | ||||||||
\(22\) | 12.6447 | − | 12.6447i | 0.122539 | − | 0.122539i | ||||
\(23\) | 105.143 | − | 33.3466i | 0.953208 | − | 0.302315i | ||||
\(24\) | − | 56.9674i | − | 0.484518i | ||||||
\(25\) | −32.3764 | + | 120.734i | −0.259011 | + | 0.965874i | ||||
\(26\) | −123.483 | −0.931426 | ||||||||
\(27\) | 16.5779 | + | 16.5779i | 0.118164 | + | 0.118164i | ||||
\(28\) | −44.5924 | − | 44.5924i | −0.300970 | − | 0.300970i | ||||
\(29\) | − | 25.7005i | − | 0.164568i | −0.996609 | − | 0.0822838i | \(-0.973779\pi\) | ||
0.996609 | − | 0.0822838i | \(-0.0262214\pi\) | |||||||
\(30\) | −96.9198 | − | 126.334i | −0.589835 | − | 0.768846i | ||||
\(31\) | 81.0455 | 0.469555 | 0.234777 | − | 0.972049i | \(-0.424564\pi\) | ||||
0.234777 | + | 0.972049i | \(0.424564\pi\) | |||||||
\(32\) | 22.6274 | + | 22.6274i | 0.125000 | + | 0.125000i | ||||
\(33\) | 45.0209 | + | 45.0209i | 0.237489 | + | 0.237489i | ||||
\(34\) | −93.7331 | −0.472797 | ||||||||
\(35\) | −174.757 | − | 23.0248i | −0.843979 | − | 0.111197i | ||||
\(36\) | 94.8305 | 0.439030 | ||||||||
\(37\) | 109.732 | − | 109.732i | 0.487561 | − | 0.487561i | −0.419975 | − | 0.907536i | \(-0.637961\pi\) |
0.907536 | + | 0.419975i | \(0.137961\pi\) | |||||||
\(38\) | −151.679 | − | 151.679i | −0.647514 | − | 0.647514i | ||||
\(39\) | − | 439.658i | − | 1.80517i | ||||||
\(40\) | 88.6764 | + | 11.6834i | 0.350524 | + | 0.0461829i | ||||
\(41\) | −276.972 | −1.05502 | −0.527510 | − | 0.849549i | \(-0.676874\pi\) | ||||
−0.527510 | + | 0.849549i | \(0.676874\pi\) | |||||||
\(42\) | 158.770 | − | 158.770i | 0.583302 | − | 0.583302i | ||||
\(43\) | −91.0717 | − | 91.0717i | −0.322984 | − | 0.322984i | 0.526927 | − | 0.849911i | \(-0.323344\pi\) |
−0.849911 | + | 0.526927i | \(0.823344\pi\) | |||||||
\(44\) | −35.7645 | −0.122539 | ||||||||
\(45\) | 210.302 | − | 161.337i | 0.696666 | − | 0.534460i | ||||
\(46\) | −195.854 | − | 101.535i | −0.627762 | − | 0.325446i | ||||
\(47\) | 147.078 | + | 147.078i | 0.456458 | + | 0.456458i | 0.897491 | − | 0.441033i | \(-0.145388\pi\) |
−0.441033 | + | 0.897491i | \(0.645388\pi\) | |||||||
\(48\) | −80.5641 | + | 80.5641i | −0.242259 | + | 0.242259i | ||||
\(49\) | 94.4399i | 0.275335i | ||||||||
\(50\) | 216.531 | − | 124.957i | 0.612443 | − | 0.353431i | ||||
\(51\) | − | 333.733i | − | 0.916314i | ||||||
\(52\) | 174.632 | + | 174.632i | 0.465713 | + | 0.465713i | ||||
\(53\) | 299.388 | + | 299.388i | 0.775928 | + | 0.775928i | 0.979136 | − | 0.203208i | \(-0.0651368\pi\) |
−0.203208 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(54\) | − | 46.8894i | − | 0.118164i | ||||||
\(55\) | −79.3135 | + | 60.8469i | −0.194448 | + | 0.149174i | ||||
\(56\) | 126.126i | 0.300970i | ||||||||
\(57\) | 540.047 | − | 540.047i | 1.25493 | − | 1.25493i | ||||
\(58\) | −36.3460 | + | 36.3460i | −0.0822838 | + | 0.0822838i | ||||
\(59\) | − | 613.321i | − | 1.35335i | −0.736283 | − | 0.676674i | \(-0.763421\pi\) | ||
0.736283 | − | 0.676674i | \(-0.236579\pi\) | |||||||
\(60\) | −41.5985 | + | 315.729i | −0.0895057 | + | 0.679341i | ||||
\(61\) | − | 40.4771i | − | 0.0849600i | −0.999097 | − | 0.0424800i | \(-0.986474\pi\) | ||
0.999097 | − | 0.0424800i | \(-0.0135259\pi\) | |||||||
\(62\) | −114.616 | − | 114.616i | −0.234777 | − | 0.234777i | ||||
\(63\) | 264.295 | + | 264.295i | 0.528540 | + | 0.528540i | ||||
\(64\) | − | 64.0000i | − | 0.125000i | ||||||
\(65\) | 684.378 | + | 90.1694i | 1.30595 | + | 0.172064i | ||||
\(66\) | − | 127.338i | − | 0.237489i | ||||||
\(67\) | −317.182 | + | 317.182i | −0.578358 | + | 0.578358i | −0.934451 | − | 0.356093i | \(-0.884109\pi\) |
0.356093 | + | 0.934451i | \(0.384109\pi\) | |||||||
\(68\) | 132.559 | + | 132.559i | 0.236399 | + | 0.236399i | ||||
\(69\) | 361.512 | − | 697.330i | 0.630739 | − | 1.21665i | ||||
\(70\) | 214.581 | + | 279.705i | 0.366391 | + | 0.477588i | ||||
\(71\) | −748.659 | −1.25140 | −0.625701 | − | 0.780063i | \(-0.715187\pi\) | ||||
−0.625701 | + | 0.780063i | \(0.715187\pi\) | |||||||
\(72\) | −134.111 | − | 134.111i | −0.219515 | − | 0.219515i | ||||
\(73\) | −142.851 | + | 142.851i | −0.229033 | + | 0.229033i | −0.812289 | − | 0.583256i | \(-0.801779\pi\) |
0.583256 | + | 0.812289i | \(0.301779\pi\) | |||||||
\(74\) | −310.368 | −0.487561 | ||||||||
\(75\) | 444.905 | + | 770.952i | 0.684975 | + | 1.18696i | ||||
\(76\) | 429.012i | 0.647514i | ||||||||
\(77\) | −99.6766 | − | 99.6766i | −0.147522 | − | 0.147522i | ||||
\(78\) | −621.770 | + | 621.770i | −0.902585 | + | 0.902585i | ||||
\(79\) | −1335.64 | −1.90217 | −0.951083 | − | 0.308935i | \(-0.900028\pi\) | ||||
−0.951083 | + | 0.308935i | \(0.900028\pi\) | |||||||
\(80\) | −108.884 | − | 141.930i | −0.152171 | − | 0.198353i | ||||
\(81\) | 807.054 | 1.10707 | ||||||||
\(82\) | 391.698 | + | 391.698i | 0.527510 | + | 0.527510i | ||||
\(83\) | −30.2308 | − | 30.2308i | −0.0399790 | − | 0.0399790i | 0.686835 | − | 0.726814i | \(-0.259000\pi\) |
−0.726814 | + | 0.686835i | \(0.759000\pi\) | |||||||
\(84\) | −449.068 | −0.583302 | ||||||||
\(85\) | 519.495 | + | 68.4454i | 0.662907 | + | 0.0873405i | ||||
\(86\) | 257.590i | 0.322984i | ||||||||
\(87\) | −129.408 | − | 129.408i | −0.159472 | − | 0.159472i | ||||
\(88\) | 50.5787 | + | 50.5787i | 0.0612694 | + | 0.0612694i | ||||
\(89\) | −358.594 | −0.427088 | −0.213544 | − | 0.976933i | \(-0.568501\pi\) | ||||
−0.213544 | + | 0.976933i | \(0.568501\pi\) | |||||||
\(90\) | −525.577 | − | 69.2467i | −0.615563 | − | 0.0811027i | ||||
\(91\) | 973.406i | 1.12133i | ||||||||
\(92\) | 133.386 | + | 420.571i | 0.151158 | + | 0.476604i | ||||
\(93\) | 408.085 | − | 408.085i | 0.455015 | − | 0.455015i | ||||
\(94\) | − | 415.999i | − | 0.456458i | ||||||
\(95\) | 729.887 | + | 951.403i | 0.788261 | + | 1.02749i | ||||
\(96\) | 227.870 | 0.242259 | ||||||||
\(97\) | −679.077 | + | 679.077i | −0.710822 | + | 0.710822i | −0.966707 | − | 0.255885i | \(-0.917633\pi\) |
0.255885 | + | 0.966707i | \(0.417633\pi\) | |||||||
\(98\) | 133.558 | − | 133.558i | 0.137668 | − | 0.137668i | ||||
\(99\) | 211.973 | 0.215193 | ||||||||
\(100\) | −482.937 | − | 129.506i | −0.482937 | − | 0.129506i | ||||
\(101\) | 1031.02 | 1.01575 | 0.507873 | − | 0.861432i | \(-0.330432\pi\) | ||||
0.507873 | + | 0.861432i | \(0.330432\pi\) | |||||||
\(102\) | −471.970 | + | 471.970i | −0.458157 | + | 0.458157i | ||||
\(103\) | −1017.16 | − | 1017.16i | −0.973045 | − | 0.973045i | 0.0266009 | − | 0.999646i | \(-0.491532\pi\) |
−0.999646 | + | 0.0266009i | \(0.991532\pi\) | |||||||
\(104\) | − | 493.933i | − | 0.465713i | ||||||
\(105\) | −995.880 | + | 764.008i | −0.925600 | + | 0.710091i | ||||
\(106\) | − | 846.798i | − | 0.775928i | ||||||
\(107\) | −903.362 | + | 903.362i | −0.816180 | + | 0.816180i | −0.985552 | − | 0.169372i | \(-0.945826\pi\) |
0.169372 | + | 0.985552i | \(0.445826\pi\) | |||||||
\(108\) | −66.3116 | + | 66.3116i | −0.0590818 | + | 0.0590818i | ||||
\(109\) | −1211.42 | −1.06453 | −0.532263 | − | 0.846579i | \(-0.678658\pi\) | ||||
−0.532263 | + | 0.846579i | \(0.678658\pi\) | |||||||
\(110\) | 198.217 | + | 26.1158i | 0.171811 | + | 0.0226368i | ||||
\(111\) | − | 1105.05i | − | 0.944928i | ||||||
\(112\) | 178.370 | − | 178.370i | 0.150485 | − | 0.150485i | ||||
\(113\) | 1194.23 | + | 1194.23i | 0.994193 | + | 0.994193i | 0.999983 | − | 0.00579025i | \(-0.00184310\pi\) |
−0.00579025 | + | 0.999983i | \(0.501843\pi\) | |||||||
\(114\) | −1527.48 | −1.25493 | ||||||||
\(115\) | 1011.33 | + | 705.751i | 0.820062 | + | 0.572275i | ||||
\(116\) | 102.802 | 0.0822838 | ||||||||
\(117\) | −1035.03 | − | 1035.03i | −0.817848 | − | 0.817848i | ||||
\(118\) | −867.366 | + | 867.366i | −0.676674 | + | 0.676674i | ||||
\(119\) | 738.888i | 0.569191i | ||||||||
\(120\) | 505.337 | − | 387.679i | 0.384423 | − | 0.294918i | ||||
\(121\) | 1251.06 | 0.939937 | ||||||||
\(122\) | −57.2433 | + | 57.2433i | −0.0424800 | + | 0.0424800i | ||||
\(123\) | −1394.63 | + | 1394.63i | −1.02235 | + | 1.02235i | ||||
\(124\) | 324.182i | 0.234777i | ||||||||
\(125\) | −1291.32 | + | 534.431i | −0.923994 | + | 0.382407i | ||||
\(126\) | − | 747.539i | − | 0.528540i | ||||||
\(127\) | −1085.96 | − | 1085.96i | −0.758764 | − | 0.758764i | 0.217333 | − | 0.976097i | \(-0.430264\pi\) |
−0.976097 | + | 0.217333i | \(0.930264\pi\) | |||||||
\(128\) | −90.5097 | + | 90.5097i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −917.139 | −0.625966 | ||||||||
\(130\) | −840.338 | − | 1095.38i | −0.566943 | − | 0.739006i | ||||
\(131\) | 1337.41 | 0.891984 | 0.445992 | − | 0.895037i | \(-0.352851\pi\) | ||||
0.445992 | + | 0.895037i | \(0.352851\pi\) | |||||||
\(132\) | −180.084 | + | 180.084i | −0.118744 | + | 0.118744i | ||||
\(133\) | −1195.67 | + | 1195.67i | −0.779530 | + | 0.779530i | ||||
\(134\) | 897.127 | 0.578358 | ||||||||
\(135\) | −34.2394 | + | 259.874i | −0.0218286 | + | 0.165677i | ||||
\(136\) | − | 374.932i | − | 0.236399i | ||||||
\(137\) | −1475.55 | + | 1475.55i | −0.920182 | + | 0.920182i | −0.997042 | − | 0.0768601i | \(-0.975511\pi\) |
0.0768601 | + | 0.997042i | \(0.475511\pi\) | |||||||
\(138\) | −1497.43 | + | 474.918i | −0.923693 | + | 0.292954i | ||||
\(139\) | − | 1223.04i | − | 0.746306i | −0.927770 | − | 0.373153i | \(-0.878277\pi\) | ||
0.927770 | − | 0.373153i | \(-0.121723\pi\) | |||||||
\(140\) | 92.0994 | − | 699.026i | 0.0555987 | − | 0.421989i | ||||
\(141\) | 1481.15 | 0.884648 | ||||||||
\(142\) | 1058.76 | + | 1058.76i | 0.625701 | + | 0.625701i | ||||
\(143\) | 390.351 | + | 390.351i | 0.228272 | + | 0.228272i | ||||
\(144\) | 379.322i | 0.219515i | ||||||||
\(145\) | 227.980 | − | 174.899i | 0.130570 | − | 0.100169i | ||||
\(146\) | 404.043 | 0.229033 | ||||||||
\(147\) | 475.529 | + | 475.529i | 0.266809 | + | 0.266809i | ||||
\(148\) | 438.926 | + | 438.926i | 0.243781 | + | 0.243781i | ||||
\(149\) | 3171.57 | 1.74379 | 0.871895 | − | 0.489692i | \(-0.162891\pi\) | ||||
0.871895 | + | 0.489692i | \(0.162891\pi\) | |||||||
\(150\) | 461.101 | − | 1719.48i | 0.250991 | − | 0.935967i | ||||
\(151\) | −240.377 | −0.129547 | −0.0647735 | − | 0.997900i | \(-0.520632\pi\) | ||||
−0.0647735 | + | 0.997900i | \(0.520632\pi\) | |||||||
\(152\) | 606.715 | − | 606.715i | 0.323757 | − | 0.323757i | ||||
\(153\) | −785.663 | − | 785.663i | −0.415144 | − | 0.415144i | ||||
\(154\) | 281.928i | 0.147522i | ||||||||
\(155\) | 551.537 | + | 718.925i | 0.285810 | + | 0.372551i | ||||
\(156\) | 1758.63 | 0.902585 | ||||||||
\(157\) | 1477.32 | − | 1477.32i | 0.750975 | − | 0.750975i | −0.223687 | − | 0.974661i | \(-0.571809\pi\) |
0.974661 | + | 0.223687i | \(0.0718092\pi\) | |||||||
\(158\) | 1888.88 | + | 1888.88i | 0.951083 | + | 0.951083i | ||||
\(159\) | 3015.00 | 1.50380 | ||||||||
\(160\) | −46.7338 | + | 354.705i | −0.0230914 | + | 0.175262i | ||||
\(161\) | −800.391 | + | 1543.89i | −0.391799 | + | 0.755750i | ||||
\(162\) | −1141.35 | − | 1141.35i | −0.553535 | − | 0.553535i | ||||
\(163\) | 502.637 | − | 502.637i | 0.241531 | − | 0.241531i | −0.575952 | − | 0.817483i | \(-0.695369\pi\) |
0.817483 | + | 0.575952i | \(0.195369\pi\) | |||||||
\(164\) | − | 1107.89i | − | 0.527510i | ||||||
\(165\) | −92.9844 | + | 705.744i | −0.0438717 | + | 0.332982i | ||||
\(166\) | 85.5055i | 0.0399790i | ||||||||
\(167\) | −605.669 | − | 605.669i | −0.280647 | − | 0.280647i | 0.552720 | − | 0.833367i | \(-0.313590\pi\) |
−0.833367 | + | 0.552720i | \(0.813590\pi\) | |||||||
\(168\) | 635.078 | + | 635.078i | 0.291651 | + | 0.291651i | ||||
\(169\) | − | 1615.03i | − | 0.735108i | ||||||
\(170\) | −637.880 | − | 831.473i | −0.287783 | − | 0.375124i | ||||
\(171\) | − | 2542.72i | − | 1.13711i | ||||||
\(172\) | 364.287 | − | 364.287i | 0.161492 | − | 0.161492i | ||||
\(173\) | 1550.68 | − | 1550.68i | 0.681479 | − | 0.681479i | −0.278855 | − | 0.960333i | \(-0.589955\pi\) |
0.960333 | + | 0.278855i | \(0.0899548\pi\) | |||||||
\(174\) | 366.022i | 0.159472i | ||||||||
\(175\) | −985.022 | − | 1706.89i | −0.425489 | − | 0.737308i | ||||
\(176\) | − | 143.058i | − | 0.0612694i | ||||||
\(177\) | −3088.23 | − | 3088.23i | −1.31144 | − | 1.31144i | ||||
\(178\) | 507.128 | + | 507.128i | 0.213544 | + | 0.213544i | ||||
\(179\) | − | 394.455i | − | 0.164709i | −0.996603 | − | 0.0823546i | \(-0.973756\pi\) | ||
0.996603 | − | 0.0823546i | \(-0.0262440\pi\) | |||||||
\(180\) | 645.348 | + | 841.207i | 0.267230 | + | 0.348333i | ||||
\(181\) | − | 583.628i | − | 0.239673i | −0.992794 | − | 0.119836i | \(-0.961763\pi\) | ||
0.992794 | − | 0.119836i | \(-0.0382370\pi\) | |||||||
\(182\) | 1376.60 | − | 1376.60i | 0.560663 | − | 0.560663i | ||||
\(183\) | −203.813 | − | 203.813i | −0.0823293 | − | 0.0823293i | ||||
\(184\) | 406.141 | − | 783.414i | 0.162723 | − | 0.313881i | ||||
\(185\) | 1720.14 | + | 226.635i | 0.683608 | + | 0.0900679i | ||||
\(186\) | −1154.24 | −0.455015 | ||||||||
\(187\) | 296.306 | + | 296.306i | 0.115872 | + | 0.115872i | ||||
\(188\) | −588.312 | + | 588.312i | −0.228229 | + | 0.228229i | ||||
\(189\) | −369.624 | −0.142255 | ||||||||
\(190\) | 313.271 | − | 2377.70i | 0.119616 | − | 0.907877i | ||||
\(191\) | − | 3016.41i | − | 1.14272i | −0.820700 | − | 0.571360i | \(-0.806416\pi\) | ||
0.820700 | − | 0.571360i | \(-0.193584\pi\) | |||||||
\(192\) | −322.256 | − | 322.256i | −0.121129 | − | 0.121129i | ||||
\(193\) | −467.908 | + | 467.908i | −0.174512 | + | 0.174512i | −0.788958 | − | 0.614447i | \(-0.789379\pi\) |
0.614447 | + | 0.788958i | \(0.289379\pi\) | |||||||
\(194\) | 1920.72 | 0.710822 | ||||||||
\(195\) | 3900.05 | − | 2991.99i | 1.43225 | − | 1.09878i | ||||
\(196\) | −377.760 | −0.137668 | ||||||||
\(197\) | 2139.35 | + | 2139.35i | 0.773718 | + | 0.773718i | 0.978754 | − | 0.205037i | \(-0.0657313\pi\) |
−0.205037 | + | 0.978754i | \(0.565731\pi\) | |||||||
\(198\) | −299.775 | − | 299.775i | −0.107596 | − | 0.107596i | ||||
\(199\) | −3530.92 | −1.25779 | −0.628896 | − | 0.777490i | \(-0.716493\pi\) | ||||
−0.628896 | + | 0.777490i | \(0.716493\pi\) | |||||||
\(200\) | 499.828 | + | 866.125i | 0.176716 | + | 0.306221i | ||||
\(201\) | 3194.19i | 1.12090i | ||||||||
\(202\) | −1458.08 | − | 1458.08i | −0.507873 | − | 0.507873i | ||||
\(203\) | 286.511 | + | 286.511i | 0.0990599 | + | 0.0990599i | ||||
\(204\) | 1334.93 | 0.458157 | ||||||||
\(205\) | −1884.87 | − | 2456.92i | −0.642172 | − | 0.837067i | ||||
\(206\) | 2876.96i | 0.973045i | ||||||||
\(207\) | −790.569 | − | 2492.69i | −0.265451 | − | 0.836974i | ||||
\(208\) | −698.527 | + | 698.527i | −0.232856 | + | 0.232856i | ||||
\(209\) | 958.964i | 0.317382i | ||||||||
\(210\) | 2488.86 | + | 327.917i | 0.817846 | + | 0.107754i | ||||
\(211\) | −1037.26 | −0.338428 | −0.169214 | − | 0.985579i | \(-0.554123\pi\) | ||||
−0.169214 | + | 0.985579i | \(0.554123\pi\) | |||||||
\(212\) | −1197.55 | + | 1197.55i | −0.387964 | + | 0.387964i | ||||
\(213\) | −3769.69 | + | 3769.69i | −1.21265 | + | 1.21265i | ||||
\(214\) | 2555.09 | 0.816180 | ||||||||
\(215\) | 188.096 | − | 1427.63i | 0.0596653 | − | 0.452854i | ||||
\(216\) | 187.558 | 0.0590818 | ||||||||
\(217\) | −903.503 | + | 903.503i | −0.282644 | + | 0.282644i | ||||
\(218\) | 1713.21 | + | 1713.21i | 0.532263 | + | 0.532263i | ||||
\(219\) | 1438.58i | 0.443882i | ||||||||
\(220\) | −243.387 | − | 317.254i | −0.0745872 | − | 0.0972240i | ||||
\(221\) | − | 2893.62i | − | 0.880751i | ||||||
\(222\) | −1562.78 | + | 1562.78i | −0.472464 | + | 0.472464i | ||||
\(223\) | −3511.04 | + | 3511.04i | −1.05433 | + | 1.05433i | −0.0558979 | + | 0.998436i | \(0.517802\pi\) |
−0.998436 | + | 0.0558979i | \(0.982198\pi\) | |||||||
\(224\) | −504.505 | −0.150485 | ||||||||
\(225\) | 2862.32 | + | 767.569i | 0.848096 | + | 0.227428i | ||||
\(226\) | − | 3377.80i | − | 0.994193i | ||||||
\(227\) | 3286.82 | − | 3286.82i | 0.961030 | − | 0.961030i | −0.0382385 | − | 0.999269i | \(-0.512175\pi\) |
0.999269 | + | 0.0382385i | \(0.0121747\pi\) | |||||||
\(228\) | 2160.19 | + | 2160.19i | 0.627464 | + | 0.627464i | ||||
\(229\) | −6525.58 | −1.88307 | −0.941534 | − | 0.336917i | \(-0.890616\pi\) | ||||
−0.941534 | + | 0.336917i | \(0.890616\pi\) | |||||||
\(230\) | −432.156 | − | 2428.32i | −0.123894 | − | 0.696168i | ||||
\(231\) | −1003.79 | −0.285908 | ||||||||
\(232\) | −145.384 | − | 145.384i | −0.0411419 | − | 0.0411419i | ||||
\(233\) | −2072.58 | + | 2072.58i | −0.582744 | + | 0.582744i | −0.935656 | − | 0.352913i | \(-0.885191\pi\) |
0.352913 | + | 0.935656i | \(0.385191\pi\) | |||||||
\(234\) | 2927.50i | 0.817848i | ||||||||
\(235\) | −303.769 | + | 2305.58i | −0.0843222 | + | 0.639998i | ||||
\(236\) | 2453.28 | 0.676674 | ||||||||
\(237\) | −6725.29 | + | 6725.29i | −1.84327 | + | 1.84327i | ||||
\(238\) | 1044.95 | − | 1044.95i | 0.284596 | − | 0.284596i | ||||
\(239\) | − | 62.4305i | − | 0.0168966i | −0.999964 | − | 0.00844831i | \(-0.997311\pi\) | ||
0.999964 | − | 0.00844831i | \(-0.00268921\pi\) | |||||||
\(240\) | −1262.92 | − | 166.394i | −0.339670 | − | 0.0447529i | ||||
\(241\) | − | 2948.93i | − | 0.788204i | −0.919067 | − | 0.394102i | \(-0.871056\pi\) | ||
0.919067 | − | 0.394102i | \(-0.128944\pi\) | |||||||
\(242\) | −1769.26 | − | 1769.26i | −0.469969 | − | 0.469969i | ||||
\(243\) | 3616.12 | − | 3616.12i | 0.954627 | − | 0.954627i | ||||
\(244\) | 161.908 | 0.0424800 | ||||||||
\(245\) | −837.742 | + | 642.690i | −0.218455 | + | 0.167592i | ||||
\(246\) | 3944.60 | 1.02235 | ||||||||
\(247\) | 4682.45 | − | 4682.45i | 1.20622 | − | 1.20622i | ||||
\(248\) | 458.463 | − | 458.463i | 0.117389 | − | 0.117389i | ||||
\(249\) | −304.439 | −0.0774822 | ||||||||
\(250\) | 2582.00 | + | 1070.40i | 0.653201 | + | 0.270793i | ||||
\(251\) | − | 713.823i | − | 0.179506i | −0.995964 | − | 0.0897532i | \(-0.971392\pi\) | ||
0.995964 | − | 0.0897532i | \(-0.0286078\pi\) | |||||||
\(252\) | −1057.18 | + | 1057.18i | −0.264270 | + | 0.264270i | ||||
\(253\) | 298.156 | + | 940.095i | 0.0740906 | + | 0.233610i | ||||
\(254\) | 3071.55i | 0.758764i | ||||||||
\(255\) | 2960.43 | − | 2271.15i | 0.727017 | − | 0.557744i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 386.393 | + | 386.393i | 0.0937841 | + | 0.0937841i | 0.752442 | − | 0.658658i | \(-0.228876\pi\) |
−0.658658 | + | 0.752442i | \(0.728876\pi\) | |||||||
\(258\) | 1297.03 | + | 1297.03i | 0.312983 | + | 0.312983i | ||||
\(259\) | 2446.60i | 0.586966i | ||||||||
\(260\) | −360.678 | + | 2737.51i | −0.0860319 | + | 0.652974i | ||||
\(261\) | −609.297 | −0.144500 | ||||||||
\(262\) | −1891.38 | − | 1891.38i | −0.445992 | − | 0.445992i | ||||
\(263\) | −5228.19 | − | 5228.19i | −1.22580 | − | 1.22580i | −0.965540 | − | 0.260256i | \(-0.916193\pi\) |
−0.260256 | − | 0.965540i | \(-0.583807\pi\) | |||||||
\(264\) | 509.353 | 0.118744 | ||||||||
\(265\) | −618.345 | + | 4693.19i | −0.143338 | + | 1.08793i | ||||
\(266\) | 3381.86 | 0.779530 | ||||||||
\(267\) | −1805.61 | + | 1805.61i | −0.413864 | + | 0.413864i | ||||
\(268\) | −1268.73 | − | 1268.73i | −0.289179 | − | 0.289179i | ||||
\(269\) | − | 7766.80i | − | 1.76041i | −0.474593 | − | 0.880205i | \(-0.657405\pi\) | ||
0.474593 | − | 0.880205i | \(-0.342595\pi\) | |||||||
\(270\) | 415.939 | − | 319.095i | 0.0937527 | − | 0.0719241i | ||||
\(271\) | −7465.38 | −1.67339 | −0.836696 | − | 0.547667i | \(-0.815516\pi\) | ||||
−0.836696 | + | 0.547667i | \(0.815516\pi\) | |||||||
\(272\) | −530.235 | + | 530.235i | −0.118199 | + | 0.118199i | ||||
\(273\) | 4901.35 | + | 4901.35i | 1.08661 | + | 1.08661i | ||||
\(274\) | 4173.49 | 0.920182 | ||||||||
\(275\) | −1079.50 | − | 289.482i | −0.236714 | − | 0.0634779i | ||||
\(276\) | 2789.32 | + | 1446.05i | 0.608323 | + | 0.315369i | ||||
\(277\) | −1302.75 | − | 1302.75i | −0.282579 | − | 0.282579i | 0.551558 | − | 0.834137i | \(-0.314034\pi\) |
−0.834137 | + | 0.551558i | \(0.814034\pi\) | |||||||
\(278\) | −1729.63 | + | 1729.63i | −0.373153 | + | 0.373153i | ||||
\(279\) | − | 1921.40i | − | 0.412298i | ||||||
\(280\) | −1118.82 | + | 858.324i | −0.238794 | + | 0.183195i | ||||
\(281\) | 7864.44i | 1.66958i | 0.550565 | + | 0.834792i | \(0.314412\pi\) | ||||
−0.550565 | + | 0.834792i | \(0.685588\pi\) | |||||||
\(282\) | −2094.66 | − | 2094.66i | −0.442324 | − | 0.442324i | ||||
\(283\) | 927.127 | + | 927.127i | 0.194742 | + | 0.194742i | 0.797742 | − | 0.603000i | \(-0.206028\pi\) |
−0.603000 | + | 0.797742i | \(0.706028\pi\) | |||||||
\(284\) | − | 2994.64i | − | 0.625701i | ||||||
\(285\) | 8465.73 | + | 1115.39i | 1.75953 | + | 0.231825i | ||||
\(286\) | − | 1104.08i | − | 0.228272i | ||||||
\(287\) | 3087.71 | − | 3087.71i | 0.635059 | − | 0.635059i | ||||
\(288\) | 536.443 | − | 536.443i | 0.109758 | − | 0.109758i | ||||
\(289\) | 2716.53i | 0.552926i | ||||||||
\(290\) | −569.756 | − | 75.0675i | −0.115370 | − | 0.0152004i | ||||
\(291\) | 6838.65i | 1.37762i | ||||||||
\(292\) | −571.403 | − | 571.403i | −0.114516 | − | 0.114516i | ||||
\(293\) | 4777.76 | + | 4777.76i | 0.952626 | + | 0.952626i | 0.998928 | − | 0.0463011i | \(-0.0147434\pi\) |
−0.0463011 | + | 0.998928i | \(0.514743\pi\) | |||||||
\(294\) | − | 1345.00i | − | 0.266809i | ||||||
\(295\) | 5440.55 | − | 4173.82i | 1.07377 | − | 0.823759i | ||||
\(296\) | − | 1241.47i | − | 0.243781i | ||||||
\(297\) | −148.225 | + | 148.225i | −0.0289593 | + | 0.0289593i | ||||
\(298\) | −4485.27 | − | 4485.27i | −0.871895 | − | 0.871895i | ||||
\(299\) | 3134.47 | − | 6046.16i | 0.606259 | − | 1.16943i | ||||
\(300\) | −3083.81 | + | 1779.62i | −0.593479 | + | 0.342488i | ||||
\(301\) | 2030.55 | 0.388834 | ||||||||
\(302\) | 339.944 | + | 339.944i | 0.0647735 | + | 0.0647735i | ||||
\(303\) | 5191.46 | − | 5191.46i | 0.984295 | − | 0.984295i | ||||
\(304\) | −1716.05 | −0.323757 | ||||||||
\(305\) | 359.058 | − | 275.458i | 0.0674085 | − | 0.0517137i | ||||
\(306\) | 2222.19i | 0.415144i | ||||||||
\(307\) | 2300.15 | + | 2300.15i | 0.427610 | + | 0.427610i | 0.887813 | − | 0.460204i | \(-0.152224\pi\) |
−0.460204 | + | 0.887813i | \(0.652224\pi\) | |||||||
\(308\) | 398.706 | − | 398.706i | 0.0737610 | − | 0.0737610i | ||||
\(309\) | −10243.3 | −1.88583 | ||||||||
\(310\) | 236.723 | − | 1796.70i | 0.0433708 | − | 0.329181i | ||||
\(311\) | −10041.4 | −1.83086 | −0.915430 | − | 0.402477i | \(-0.868150\pi\) | ||||
−0.915430 | + | 0.402477i | \(0.868150\pi\) | |||||||
\(312\) | −2487.08 | − | 2487.08i | −0.451292 | − | 0.451292i | ||||
\(313\) | −634.081 | − | 634.081i | −0.114506 | − | 0.114506i | 0.647532 | − | 0.762038i | \(-0.275801\pi\) |
−0.762038 | + | 0.647532i | \(0.775801\pi\) | |||||||
\(314\) | −4178.49 | −0.750975 | ||||||||
\(315\) | −545.865 | + | 4143.07i | −0.0976381 | + | 0.741064i | ||||
\(316\) | − | 5342.56i | − | 0.951083i | ||||||
\(317\) | 7828.57 | + | 7828.57i | 1.38705 | + | 1.38705i | 0.831441 | + | 0.555614i | \(0.187517\pi\) |
0.555614 | + | 0.831441i | \(0.312483\pi\) | |||||||
\(318\) | −4263.85 | − | 4263.85i | −0.751902 | − | 0.751902i | ||||
\(319\) | 229.791 | 0.0403318 | ||||||||
\(320\) | 567.721 | − | 435.538i | 0.0991767 | − | 0.0760853i | ||||
\(321\) | 9097.32i | 1.58182i | ||||||||
\(322\) | 3315.32 | − | 1051.47i | 0.573775 | − | 0.181976i | ||||
\(323\) | 3554.33 | − | 3554.33i | 0.612286 | − | 0.612286i | ||||
\(324\) | 3228.22i | 0.553535i | ||||||||
\(325\) | 3857.52 | + | 6684.50i | 0.658390 | + | 1.14089i | ||||
\(326\) | −1421.67 | −0.241531 | ||||||||
\(327\) | −6099.83 | + | 6099.83i | −1.03156 | + | 1.03156i | ||||
\(328\) | −1566.79 | + | 1566.79i | −0.263755 | + | 0.263755i | ||||
\(329\) | −3279.28 | −0.549521 | ||||||||
\(330\) | 1129.57 | − | 866.573i | 0.188427 | − | 0.144555i | ||||
\(331\) | −9594.36 | −1.59321 | −0.796607 | − | 0.604498i | \(-0.793374\pi\) | ||||
−0.796607 | + | 0.604498i | \(0.793374\pi\) | |||||||
\(332\) | 120.923 | − | 120.923i | 0.0199895 | − | 0.0199895i | ||||
\(333\) | −2601.48 | − | 2601.48i | −0.428108 | − | 0.428108i | ||||
\(334\) | 1713.09i | 0.280647i | ||||||||
\(335\) | −4972.12 | − | 655.096i | −0.810914 | − | 0.106841i | ||||
\(336\) | − | 1796.27i | − | 0.291651i | ||||||
\(337\) | −2114.12 | + | 2114.12i | −0.341731 | + | 0.341731i | −0.857018 | − | 0.515287i | \(-0.827686\pi\) |
0.515287 | + | 0.857018i | \(0.327686\pi\) | |||||||
\(338\) | −2284.00 | + | 2284.00i | −0.367554 | + | 0.367554i | ||||
\(339\) | 12026.5 | 1.92682 | ||||||||
\(340\) | −273.782 | + | 2077.98i | −0.0436703 | + | 0.331453i | ||||
\(341\) | 724.638i | 0.115077i | ||||||||
\(342\) | −3595.94 | + | 3595.94i | −0.568557 | + | 0.568557i | ||||
\(343\) | −4876.62 | − | 4876.62i | −0.767676 | − | 0.767676i | ||||
\(344\) | −1030.36 | −0.161492 | ||||||||
\(345\) | 8645.95 | − | 1538.68i | 1.34922 | − | 0.240115i | ||||
\(346\) | −4385.98 | −0.681479 | ||||||||
\(347\) | 4685.81 | + | 4685.81i | 0.724921 | + | 0.724921i | 0.969603 | − | 0.244682i | \(-0.0786836\pi\) |
−0.244682 | + | 0.969603i | \(0.578684\pi\) | |||||||
\(348\) | 517.634 | − | 517.634i | 0.0797359 | − | 0.0797359i | ||||
\(349\) | − | 7557.11i | − | 1.15909i | −0.814940 | − | 0.579545i | \(-0.803230\pi\) | ||
0.814940 | − | 0.579545i | \(-0.196770\pi\) | |||||||
\(350\) | −1020.88 | + | 3806.94i | −0.155909 | + | 0.581399i | ||||
\(351\) | 1447.51 | 0.220121 | ||||||||
\(352\) | −202.315 | + | 202.315i | −0.0306347 | + | 0.0306347i | ||||
\(353\) | −2822.75 | + | 2822.75i | −0.425609 | + | 0.425609i | −0.887130 | − | 0.461520i | \(-0.847304\pi\) |
0.461520 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(354\) | 8734.83i | 1.31144i | ||||||||
\(355\) | −5094.83 | − | 6641.09i | −0.761706 | − | 0.992879i | ||||
\(356\) | − | 1434.37i | − | 0.213544i | ||||||
\(357\) | 3720.49 | + | 3720.49i | 0.551567 | + | 0.551567i | ||||
\(358\) | −557.844 | + | 557.844i | −0.0823546 | + | 0.0823546i | ||||
\(359\) | −2400.09 | −0.352846 | −0.176423 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176423 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(360\) | 276.987 | − | 2102.31i | 0.0405514 | − | 0.307781i | ||||
\(361\) | 4644.22 | 0.677098 | ||||||||
\(362\) | −825.375 | + | 825.375i | −0.119836 | + | 0.119836i | ||||
\(363\) | 6299.39 | − | 6299.39i | 0.910833 | − | 0.910833i | ||||
\(364\) | −3893.62 | −0.560663 | ||||||||
\(365\) | −2239.31 | − | 295.038i | −0.321126 | − | 0.0423096i | ||||
\(366\) | 576.469i | 0.0823293i | ||||||||
\(367\) | 6417.00 | − | 6417.00i | 0.912710 | − | 0.912710i | −0.0837748 | − | 0.996485i | \(-0.526698\pi\) |
0.996485 | + | 0.0837748i | \(0.0266976\pi\) | |||||||
\(368\) | −1682.28 | + | 533.546i | −0.238302 | + | 0.0755788i | ||||
\(369\) | 6566.36i | 0.926371i | ||||||||
\(370\) | −2112.14 | − | 2753.16i | −0.296770 | − | 0.386838i | ||||
\(371\) | −6675.22 | −0.934125 | ||||||||
\(372\) | 1632.34 | + | 1632.34i | 0.227508 | + | 0.227508i | ||||
\(373\) | −7525.86 | − | 7525.86i | −1.04470 | − | 1.04470i | −0.998953 | − | 0.0457508i | \(-0.985432\pi\) |
−0.0457508 | − | 0.998953i | \(-0.514568\pi\) | |||||||
\(374\) | − | 838.080i | − | 0.115872i | ||||||
\(375\) | −3811.14 | + | 9193.13i | −0.524817 | + | 1.26595i | ||||
\(376\) | 1664.00 | 0.228229 | ||||||||
\(377\) | −1122.03 | − | 1122.03i | −0.153282 | − | 0.153282i | ||||
\(378\) | 522.727 | + | 522.727i | 0.0711275 | + | 0.0711275i | ||||
\(379\) | 6482.76 | 0.878620 | 0.439310 | − | 0.898335i | \(-0.355223\pi\) | ||||
0.439310 | + | 0.898335i | \(0.355223\pi\) | |||||||
\(380\) | −3805.61 | + | 2919.55i | −0.513747 | + | 0.394130i | ||||
\(381\) | −10936.1 | −1.47054 | ||||||||
\(382\) | −4265.84 | + | 4265.84i | −0.571360 | + | 0.571360i | ||||
\(383\) | −3396.23 | − | 3396.23i | −0.453105 | − | 0.453105i | 0.443279 | − | 0.896384i | \(-0.353815\pi\) |
−0.896384 | + | 0.443279i | \(0.853815\pi\) | |||||||
\(384\) | 911.479i | 0.121129i | ||||||||
\(385\) | 205.868 | − | 1562.52i | 0.0272520 | − | 0.206840i | ||||
\(386\) | 1323.44 | 0.174512 | ||||||||
\(387\) | −2159.09 | + | 2159.09i | −0.283599 | + | 0.283599i | ||||
\(388\) | −2716.31 | − | 2716.31i | −0.355411 | − | 0.355411i | ||||
\(389\) | −5629.42 | −0.733734 | −0.366867 | − | 0.930273i | \(-0.619570\pi\) | ||||
−0.366867 | + | 0.930273i | \(0.619570\pi\) | |||||||
\(390\) | −9746.82 | − | 1284.18i | −1.26551 | − | 0.166736i | ||||
\(391\) | 2379.30 | − | 4589.49i | 0.307740 | − | 0.593608i | ||||
\(392\) | 534.233 | + | 534.233i | 0.0688338 | + | 0.0688338i | ||||
\(393\) | 6734.19 | − | 6734.19i | 0.864364 | − | 0.864364i | ||||
\(394\) | − | 6051.00i | − | 0.773718i | ||||||
\(395\) | −9089.39 | − | 11848.0i | −1.15782 | − | 1.50921i | ||||
\(396\) | 847.892i | 0.107596i | ||||||||
\(397\) | 382.000 | + | 382.000i | 0.0482923 | + | 0.0482923i | 0.730841 | − | 0.682548i | \(-0.239128\pi\) |
−0.682548 | + | 0.730841i | \(0.739128\pi\) | |||||||
\(398\) | 4993.48 | + | 4993.48i | 0.628896 | + | 0.628896i | ||||
\(399\) | 12041.0i | 1.51079i | ||||||||
\(400\) | 518.023 | − | 1931.75i | 0.0647529 | − | 0.241469i | ||||
\(401\) | − | 11716.5i | − | 1.45909i | −0.683931 | − | 0.729547i | \(-0.739731\pi\) | ||
0.683931 | − | 0.729547i | \(-0.260269\pi\) | |||||||
\(402\) | 4517.26 | − | 4517.26i | 0.560449 | − | 0.560449i | ||||
\(403\) | 3538.28 | − | 3538.28i | 0.437356 | − | 0.437356i | ||||
\(404\) | 4124.08i | 0.507873i | ||||||||
\(405\) | 5492.23 | + | 7159.09i | 0.673854 | + | 0.878365i | ||||
\(406\) | − | 810.376i | − | 0.0990599i | ||||||
\(407\) | 981.124 | + | 981.124i | 0.119490 | + | 0.119490i | ||||
\(408\) | −1887.88 | − | 1887.88i | −0.229079 | − | 0.229079i | ||||
\(409\) | − | 13931.8i | − | 1.68431i | −0.539236 | − | 0.842155i | \(-0.681287\pi\) | ||
0.539236 | − | 0.842155i | \(-0.318713\pi\) | |||||||
\(410\) | −808.998 | + | 6140.22i | −0.0974477 | + | 0.739619i | ||||
\(411\) | 14859.6i | 1.78338i | ||||||||
\(412\) | 4068.64 | − | 4068.64i | 0.486523 | − | 0.486523i | ||||
\(413\) | 6837.36 | + | 6837.36i | 0.814635 | + | 0.814635i | ||||
\(414\) | −2407.16 | + | 4643.22i | −0.285762 | + | 0.551213i | ||||
\(415\) | 62.4375 | − | 473.895i | 0.00738539 | − | 0.0560544i | ||||
\(416\) | 1975.73 | 0.232856 | ||||||||
\(417\) | −6158.30 | − | 6158.30i | −0.723198 | − | 0.723198i | ||||
\(418\) | 1356.18 | − | 1356.18i | 0.158691 | − | 0.158691i | ||||
\(419\) | −799.822 | −0.0932551 | −0.0466275 | − | 0.998912i | \(-0.514847\pi\) | ||||
−0.0466275 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(420\) | −3056.03 | − | 3983.52i | −0.355046 | − | 0.462800i | ||||
\(421\) | 16334.9i | 1.89101i | 0.325612 | + | 0.945503i | \(0.394430\pi\) | ||||
−0.325612 | + | 0.945503i | \(0.605570\pi\) | |||||||
\(422\) | 1466.91 | + | 1466.91i | 0.169214 | + | 0.169214i | ||||
\(423\) | 3486.87 | − | 3486.87i | 0.400798 | − | 0.400798i | ||||
\(424\) | 3387.19 | 0.387964 | ||||||||
\(425\) | 2928.15 | + | 5074.04i | 0.334203 | + | 0.579122i | ||||
\(426\) | 10662.3 | 1.21265 | ||||||||
\(427\) | 451.243 | + | 451.243i | 0.0511409 | + | 0.0511409i | ||||
\(428\) | −3613.45 | − | 3613.45i | −0.408090 | − | 0.408090i | ||||
\(429\) | 3931.04 | 0.442407 | ||||||||
\(430\) | −2284.98 | + | 1752.97i | −0.256260 | + | 0.196595i | ||||
\(431\) | 6798.48i | 0.759795i | 0.925029 | + | 0.379897i | \(0.124041\pi\) | ||||
−0.925029 | + | 0.379897i | \(0.875959\pi\) | |||||||
\(432\) | −265.246 | − | 265.246i | −0.0295409 | − | 0.0295409i | ||||
\(433\) | 2823.98 | + | 2823.98i | 0.313422 | + | 0.313422i | 0.846234 | − | 0.532812i | \(-0.178865\pi\) |
−0.532812 | + | 0.846234i | \(0.678865\pi\) | |||||||
\(434\) | 2555.49 | 0.282644 | ||||||||
\(435\) | 267.275 | − | 2028.60i | 0.0294595 | − | 0.223595i | ||||
\(436\) | − | 4845.69i | − | 0.532263i | ||||||
\(437\) | 11276.9 | − | 3576.52i | 1.23443 | − | 0.391507i | ||||
\(438\) | 2034.46 | − | 2034.46i | 0.221941 | − | 0.221941i | ||||
\(439\) | 5973.05i | 0.649380i | 0.945820 | + | 0.324690i | \(0.105260\pi\) | ||||
−0.945820 | + | 0.324690i | \(0.894740\pi\) | |||||||
\(440\) | −104.463 | + | 792.867i | −0.0113184 | + | 0.0859056i | ||||
\(441\) | 2238.95 | 0.241761 | ||||||||
\(442\) | −4092.20 | + | 4092.20i | −0.440375 | + | 0.440375i | ||||
\(443\) | 3648.17 | − | 3648.17i | 0.391264 | − | 0.391264i | −0.483874 | − | 0.875138i | \(-0.660771\pi\) |
0.875138 | + | 0.483874i | \(0.160771\pi\) | |||||||
\(444\) | 4420.21 | 0.472464 | ||||||||
\(445\) | −2440.33 | − | 3180.95i | −0.259961 | − | 0.338858i | ||||
\(446\) | 9930.72 | 1.05433 | ||||||||
\(447\) | 15969.7 | − | 15969.7i | 1.68980 | − | 1.68980i | ||||
\(448\) | 713.478 | + | 713.478i | 0.0752426 | + | 0.0752426i | ||||
\(449\) | 6112.59i | 0.642475i | 0.946999 | + | 0.321237i | \(0.104099\pi\) | ||||
−0.946999 | + | 0.321237i | \(0.895901\pi\) | |||||||
\(450\) | −2962.43 | − | 5133.44i | −0.310334 | − | 0.537762i | ||||
\(451\) | − | 2476.44i | − | 0.258561i | ||||||
\(452\) | −4776.92 | + | 4776.92i | −0.497096 | + | 0.497096i | ||||
\(453\) | −1210.36 | + | 1210.36i | −0.125536 | + | 0.125536i | ||||
\(454\) | −9296.53 | −0.961030 | ||||||||
\(455\) | −8634.73 | + | 6624.30i | −0.889676 | + | 0.682531i | ||||
\(456\) | − | 6109.93i | − | 0.627464i | ||||||
\(457\) | −626.853 | + | 626.853i | −0.0641640 | + | 0.0641640i | −0.738461 | − | 0.674297i | \(-0.764447\pi\) |
0.674297 | + | 0.738461i | \(0.264447\pi\) | |||||||
\(458\) | 9228.57 | + | 9228.57i | 0.941534 | + | 0.941534i | ||||
\(459\) | 1098.77 | 0.111735 | ||||||||
\(460\) | −2823.00 | + | 4045.33i | −0.286137 | + | 0.410031i | ||||
\(461\) | 715.928 | 0.0723299 | 0.0361650 | − | 0.999346i | \(-0.488486\pi\) | ||||
0.0361650 | + | 0.999346i | \(0.488486\pi\) | |||||||
\(462\) | 1419.58 | + | 1419.58i | 0.142954 | + | 0.142954i | ||||
\(463\) | 1427.39 | − | 1427.39i | 0.143275 | − | 0.143275i | −0.631831 | − | 0.775106i | \(-0.717696\pi\) |
0.775106 | + | 0.631831i | \(0.217696\pi\) | |||||||
\(464\) | 411.208i | 0.0411419i | ||||||||
\(465\) | 6397.10 | + | 842.843i | 0.637975 | + | 0.0840557i | ||||
\(466\) | 5862.14 | 0.582744 | ||||||||
\(467\) | −6463.77 | + | 6463.77i | −0.640488 | + | 0.640488i | −0.950675 | − | 0.310188i | \(-0.899608\pi\) |
0.310188 | + | 0.950675i | \(0.399608\pi\) | |||||||
\(468\) | 4140.11 | − | 4140.11i | 0.408924 | − | 0.408924i | ||||
\(469\) | − | 7071.96i | − | 0.696274i | ||||||
\(470\) | 3690.18 | − | 2830.99i | 0.362160 | − | 0.277838i | ||||
\(471\) | − | 14877.4i | − | 1.45544i | ||||||
\(472\) | −3469.47 | − | 3469.47i | −0.338337 | − | 0.338337i | ||||
\(473\) | 814.284 | − | 814.284i | 0.0791561 | − | 0.0791561i | ||||
\(474\) | 19022.0 | 1.84327 | ||||||||
\(475\) | −3472.47 | + | 12949.1i | −0.335427 | + | 1.25083i | ||||
\(476\) | −2955.55 | −0.284596 | ||||||||
\(477\) | 7097.79 | − | 7097.79i | 0.681311 | − | 0.681311i | ||||
\(478\) | −88.2901 | + | 88.2901i | −0.00844831 | + | 0.00844831i | ||||
\(479\) | 13521.6 | 1.28980 | 0.644902 | − | 0.764265i | \(-0.276898\pi\) | ||||
0.644902 | + | 0.764265i | \(0.276898\pi\) | |||||||
\(480\) | 1550.72 | + | 2021.35i | 0.147459 | + | 0.192212i | ||||
\(481\) | − | 9581.31i | − | 0.908254i | ||||||
\(482\) | −4170.42 | + | 4170.42i | −0.394102 | + | 0.394102i | ||||
\(483\) | 3743.73 | + | 11804.1i | 0.352682 | + | 1.11202i | ||||
\(484\) | 5004.22i | 0.469969i | ||||||||
\(485\) | −10645.1 | − | 1402.54i | −0.996642 | − | 0.131311i | ||||
\(486\) | −10227.9 | −0.954627 | ||||||||
\(487\) | 12591.7 | + | 12591.7i | 1.17163 | + | 1.17163i | 0.981820 | + | 0.189813i | \(0.0607882\pi\) |
0.189813 | + | 0.981820i | \(0.439212\pi\) | |||||||
\(488\) | −228.973 | − | 228.973i | −0.0212400 | − | 0.0212400i | ||||
\(489\) | − | 5061.82i | − | 0.468105i | ||||||
\(490\) | 2093.65 | + | 275.846i | 0.193023 | + | 0.0254315i | ||||
\(491\) | 12457.1 | 1.14497 | 0.572486 | − | 0.819915i | \(-0.305979\pi\) | ||||
0.572486 | + | 0.819915i | \(0.305979\pi\) | |||||||
\(492\) | −5578.51 | − | 5578.51i | −0.511176 | − | 0.511176i | ||||
\(493\) | −851.705 | − | 851.705i | −0.0778070 | − | 0.0778070i | ||||
\(494\) | −13244.0 | −1.20622 | ||||||||
\(495\) | 1442.54 | + | 1880.34i | 0.130984 | + | 0.170737i | ||||
\(496\) | −1296.73 | −0.117389 | ||||||||
\(497\) | 8346.13 | − | 8346.13i | 0.753269 | − | 0.753269i | ||||
\(498\) | 430.542 | + | 430.542i | 0.0387411 | + | 0.0387411i | ||||
\(499\) | 17849.9i | 1.60135i | 0.599100 | + | 0.800675i | \(0.295525\pi\) | ||||
−0.599100 | + | 0.800675i | \(0.704475\pi\) | |||||||
\(500\) | −2137.72 | − | 5165.28i | −0.191204 | − | 0.461997i | ||||
\(501\) | −6099.40 | −0.543914 | ||||||||
\(502\) | −1009.50 | + | 1009.50i | −0.0897532 | + | 0.0897532i | ||||
\(503\) | −4849.45 | − | 4849.45i | −0.429874 | − | 0.429874i | 0.458712 | − | 0.888585i | \(-0.348311\pi\) |
−0.888585 | + | 0.458712i | \(0.848311\pi\) | |||||||
\(504\) | 2990.16 | 0.264270 | ||||||||
\(505\) | 7016.38 | + | 9145.81i | 0.618267 | + | 0.805908i | ||||
\(506\) | 907.839 | − | 1751.15i | 0.0797596 | − | 0.153850i | ||||
\(507\) | −8132.11 | − | 8132.11i | −0.712346 | − | 0.712346i | ||||
\(508\) | 4343.82 | − | 4343.82i | 0.379382 | − | 0.379382i | ||||
\(509\) | − | 11927.2i | − | 1.03863i | −0.854582 | − | 0.519316i | \(-0.826187\pi\) | ||
0.854582 | − | 0.519316i | \(-0.173813\pi\) | |||||||
\(510\) | −7398.57 | − | 974.789i | −0.642381 | − | 0.0846361i | ||||
\(511\) | − | 3185.03i | − | 0.275728i | ||||||
\(512\) | −362.039 | − | 362.039i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 1778.03 | + | 1778.03i | 0.153025 | + | 0.153025i | ||||
\(514\) | − | 1092.88i | − | 0.0937841i | ||||||
\(515\) | 2100.80 | − | 15944.9i | 0.179752 | − | 1.36430i | ||||
\(516\) | − | 3668.56i | − | 0.312983i | ||||||
\(517\) | −1315.04 | + | 1315.04i | −0.111868 | + | 0.111868i | ||||
\(518\) | 3460.01 | − | 3460.01i | 0.293483 | − | 0.293483i | ||||
\(519\) | − | 15616.1i | − | 1.32075i | ||||||
\(520\) | 4381.50 | − | 3361.35i | 0.369503 | − | 0.283471i | ||||
\(521\) | − | 7777.43i | − | 0.654003i | −0.945024 | − | 0.327001i | \(-0.893962\pi\) | ||
0.945024 | − | 0.327001i | \(-0.106038\pi\) | |||||||
\(522\) | 861.677 | + | 861.677i | 0.0722501 | + | 0.0722501i | ||||
\(523\) | 589.813 | + | 589.813i | 0.0493130 | + | 0.0493130i | 0.731333 | − | 0.682020i | \(-0.238898\pi\) |
−0.682020 | + | 0.731333i | \(0.738898\pi\) | |||||||
\(524\) | 5349.63i | 0.445992i | ||||||||
\(525\) | −13554.5 | − | 3634.81i | −1.12679 | − | 0.302164i | ||||
\(526\) | 14787.6i | 1.22580i | ||||||||
\(527\) | 2685.82 | − | 2685.82i | 0.222004 | − | 0.222004i | ||||
\(528\) | −720.334 | − | 720.334i | −0.0593722 | − | 0.0593722i | ||||
\(529\) | 9943.01 | − | 7012.31i | 0.817211 | − | 0.576338i | ||||
\(530\) | 7511.64 | − | 5762.70i | 0.615632 | − | 0.472293i | ||||
\(531\) | −14540.4 | −1.18832 | ||||||||
\(532\) | −4782.67 | − | 4782.67i | −0.389765 | − | 0.389765i | ||||
\(533\) | −12092.0 | + | 12092.0i | −0.982672 | + | 0.982672i | ||||
\(534\) | 5107.04 | 0.413864 | ||||||||
\(535\) | −14161.0 | − | 1865.77i | −1.14436 | − | 0.150774i | ||||
\(536\) | 3588.51i | 0.289179i | ||||||||
\(537\) | −1986.18 | − | 1986.18i | −0.159609 | − | 0.159609i | ||||
\(538\) | −10983.9 | + | 10983.9i | −0.880205 | + | 0.880205i | ||||
\(539\) | −844.400 | −0.0674784 | ||||||||
\(540\) | −1039.50 | − | 136.957i | −0.0828384 | − | 0.0109143i | ||||
\(541\) | 7654.78 | 0.608326 | 0.304163 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304163 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(542\) | 10557.6 | + | 10557.6i | 0.836696 | + | 0.836696i | ||||
\(543\) | −2938.72 | − | 2938.72i | −0.232251 | − | 0.232251i | ||||
\(544\) | 1499.73 | 0.118199 | ||||||||
\(545\) | −8244.07 | − | 10746.1i | −0.647958 | − | 0.844609i | ||||
\(546\) | − | 13863.1i | − | 1.08661i | ||||||
\(547\) | 5952.34 | + | 5952.34i | 0.465272 | + | 0.465272i | 0.900379 | − | 0.435107i | \(-0.143289\pi\) |
−0.435107 | + | 0.900379i | \(0.643289\pi\) | |||||||
\(548\) | −5902.21 | − | 5902.21i | −0.460091 | − | 0.460091i | ||||
\(549\) | −959.616 | −0.0746001 | ||||||||
\(550\) | 1117.26 | + | 1936.03i | 0.0866181 | + | 0.150096i | ||||
\(551\) | − | 2756.45i | − | 0.213120i | ||||||
\(552\) | −1899.67 | − | 5989.71i | −0.146477 | − | 0.461846i | ||||
\(553\) | 14889.8 | − | 14889.8i | 1.14499 | − | 1.14499i | ||||
\(554\) | 3684.72i | 0.282579i | ||||||||
\(555\) | 9802.53 | − | 7520.19i | 0.749719 | − | 0.575161i | ||||
\(556\) | 4892.15 | 0.373153 | ||||||||
\(557\) | 7363.50 | − | 7363.50i | 0.560147 | − | 0.560147i | −0.369202 | − | 0.929349i | \(-0.620369\pi\) |
0.929349 | + | 0.369202i | \(0.120369\pi\) | |||||||
\(558\) | −2717.27 | + | 2717.27i | −0.206149 | + | 0.206149i | ||||
\(559\) | −7952.01 | −0.601671 | ||||||||
\(560\) | 2796.11 | + | 368.398i | 0.210995 | + | 0.0277994i | ||||
\(561\) | 2983.95 | 0.224568 | ||||||||
\(562\) | 11122.0 | − | 11122.0i | 0.834792 | − | 0.834792i | ||||
\(563\) | −10541.5 | − | 10541.5i | −0.789112 | − | 0.789112i | 0.192237 | − | 0.981349i | \(-0.438426\pi\) |
−0.981349 | + | 0.192237i | \(0.938426\pi\) | |||||||
\(564\) | 5924.60i | 0.442324i | ||||||||
\(565\) | −2466.52 | + | 18720.7i | −0.183659 | + | 1.39395i | ||||
\(566\) | − | 2622.31i | − | 0.194742i | ||||||
\(567\) | −8997.12 | + | 8997.12i | −0.666391 | + | 0.666391i | ||||
\(568\) | −4235.06 | + | 4235.06i | −0.312850 | + | 0.312850i | ||||
\(569\) | −2659.83 | −0.195968 | −0.0979841 | − | 0.995188i | \(-0.531239\pi\) | ||||
−0.0979841 | + | 0.995188i | \(0.531239\pi\) | |||||||
\(570\) | −10394.9 | − | 13549.7i | −0.763853 | − | 0.995678i | ||||
\(571\) | 2661.99i | 0.195098i | 0.995231 | + | 0.0975490i | \(0.0311003\pi\) | ||||
−0.995231 | + | 0.0975490i | \(0.968900\pi\) | |||||||
\(572\) | −1561.41 | + | 1561.41i | −0.114136 | + | 0.114136i | ||||
\(573\) | −15188.4 | − | 15188.4i | −1.10734 | − | 1.10734i | ||||
\(574\) | −8733.37 | −0.635059 | ||||||||
\(575\) | 621.930 | + | 13774.0i | 0.0451066 | + | 0.998982i | ||||
\(576\) | −1517.29 | −0.109758 | ||||||||
\(577\) | 3146.05 | + | 3146.05i | 0.226988 | + | 0.226988i | 0.811433 | − | 0.584445i | \(-0.198688\pi\) |
−0.584445 | + | 0.811433i | \(0.698688\pi\) | |||||||
\(578\) | 3841.75 | − | 3841.75i | 0.276463 | − | 0.276463i | ||||
\(579\) | 4712.07i | 0.338216i | ||||||||
\(580\) | 699.595 | + | 911.918i | 0.0500847 | + | 0.0652851i | ||||
\(581\) | 674.031 | 0.0481300 | ||||||||
\(582\) | 9671.31 | − | 9671.31i | 0.688812 | − | 0.688812i | ||||
\(583\) | −2676.87 | + | 2676.87i | −0.190162 | + | 0.190162i | ||||
\(584\) | 1616.17i | 0.114516i | ||||||||
\(585\) | 2137.70 | − | 16225.0i | 0.151082 | − | 1.14670i | ||||
\(586\) | − | 13513.5i | − | 0.952626i | ||||||
\(587\) | 3610.31 | + | 3610.31i | 0.253856 | + | 0.253856i | 0.822550 | − | 0.568693i | \(-0.192551\pi\) |
−0.568693 | + | 0.822550i | \(0.692551\pi\) | |||||||
\(588\) | −1902.12 | + | 1902.12i | −0.133405 | + | 0.133405i | ||||
\(589\) | 8692.38 | 0.608087 | ||||||||
\(590\) | −13596.8 | − | 1791.43i | −0.948762 | − | 0.125003i | ||||
\(591\) | 21544.4 | 1.49952 | ||||||||
\(592\) | −1755.71 | + | 1755.71i | −0.121890 | + | 0.121890i | ||||
\(593\) | 927.983 | − | 927.983i | 0.0642626 | − | 0.0642626i | −0.674245 | − | 0.738508i | \(-0.735531\pi\) |
0.738508 | + | 0.674245i | \(0.235531\pi\) | |||||||
\(594\) | 419.244 | 0.0289593 | ||||||||
\(595\) | −6554.41 | + | 5028.34i | −0.451604 | + | 0.346457i | ||||
\(596\) | 12686.3i | 0.871895i | ||||||||
\(597\) | −17779.1 | + | 17779.1i | −1.21884 | + | 1.21884i | ||||
\(598\) | −12983.4 | + | 4117.75i | −0.887843 | + | 0.281584i | ||||
\(599\) | 28083.7i | 1.91564i | 0.287370 | + | 0.957820i | \(0.407219\pi\) | ||||
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(600\) | 6877.92 | + | 1844.40i | 0.467983 | + | 0.125496i | ||||
\(601\) | −8979.33 | −0.609442 | −0.304721 | − | 0.952442i | \(-0.598563\pi\) | ||||
−0.304721 | + | 0.952442i | \(0.598563\pi\) | |||||||
\(602\) | −2871.63 | − | 2871.63i | −0.194417 | − | 0.194417i | ||||
\(603\) | 7519.64 | + | 7519.64i | 0.507833 | + | 0.507833i | ||||
\(604\) | − | 961.508i | − | 0.0647735i | ||||||
\(605\) | 8513.78 | + | 11097.7i | 0.572123 | + | 0.745759i | ||||
\(606\) | −14683.7 | −0.984295 | ||||||||
\(607\) | −10379.3 | − | 10379.3i | −0.694043 | − | 0.694043i | 0.269076 | − | 0.963119i | \(-0.413282\pi\) |
−0.963119 | + | 0.269076i | \(0.913282\pi\) | |||||||
\(608\) | 2426.86 | + | 2426.86i | 0.161879 | + | 0.161879i | ||||
\(609\) | 2885.32 | 0.191985 | ||||||||
\(610\) | −897.341 | − | 118.228i | −0.0595611 | − | 0.00784740i | ||||
\(611\) | 12842.2 | 0.850314 | ||||||||
\(612\) | 3142.65 | − | 3142.65i | 0.207572 | − | 0.207572i | ||||
\(613\) | 8311.56 | + | 8311.56i | 0.547636 | + | 0.547636i | 0.925756 | − | 0.378120i | \(-0.123429\pi\) |
−0.378120 | + | 0.925756i | \(0.623429\pi\) | |||||||
\(614\) | − | 6505.79i | − | 0.427610i | ||||||
\(615\) | −21862.0 | − | 2880.41i | −1.43344 | − | 0.188861i | ||||
\(616\) | −1127.71 | −0.0737610 | ||||||||
\(617\) | −10641.0 | + | 10641.0i | −0.694315 | + | 0.694315i | −0.963178 | − | 0.268863i | \(-0.913352\pi\) |
0.268863 | + | 0.963178i | \(0.413352\pi\) | |||||||
\(618\) | 14486.2 | + | 14486.2i | 0.942916 | + | 0.942916i | ||||
\(619\) | −26773.6 | −1.73848 | −0.869241 | − | 0.494388i | \(-0.835392\pi\) | ||||
−0.869241 | + | 0.494388i | \(0.835392\pi\) | |||||||
\(620\) | −2875.70 | + | 2206.15i | −0.186276 | + | 0.142905i | ||||
\(621\) | 2295.86 | + | 1190.23i | 0.148357 | + | 0.0769119i | ||||
\(622\) | 14200.7 | + | 14200.7i | 0.915430 | + | 0.915430i | ||||
\(623\) | 3997.63 | − | 3997.63i | 0.257082 | − | 0.257082i | ||||
\(624\) | 7034.53i | 0.451292i | ||||||||
\(625\) | −13528.5 | − | 7817.89i | −0.865826 | − | 0.500345i | ||||
\(626\) | 1793.45i | 0.114506i | ||||||||
\(627\) | 4828.63 | + | 4828.63i | 0.307555 | + | 0.307555i | ||||
\(628\) | 5909.28 | + | 5909.28i | 0.375487 | + | 0.375487i | ||||
\(629\) | − | 7272.93i | − | 0.461035i | ||||||
\(630\) | 6631.15 | − | 5087.21i | 0.419351 | − | 0.321713i | ||||
\(631\) | 6798.32i | 0.428902i | 0.976735 | + | 0.214451i | \(0.0687962\pi\) | ||||
−0.976735 | + | 0.214451i | \(0.931204\pi\) | |||||||
\(632\) | −7555.52 | + | 7555.52i | −0.475542 | + | 0.475542i | ||||
\(633\) | −5222.90 | + | 5222.90i | −0.327949 | + | 0.327949i | ||||
\(634\) | − | 22142.5i | − | 1.38705i | ||||||
\(635\) | 2242.89 | − | 17023.4i | 0.140168 | − | 1.06386i | ||||
\(636\) | 12060.0i | 0.751902i | ||||||||
\(637\) | 4123.05 | + | 4123.05i | 0.256454 | + | 0.256454i | ||||
\(638\) | −324.974 | − | 324.974i | −0.0201659 | − | 0.0201659i | ||||
\(639\) | 17748.9i | 1.09881i | ||||||||
\(640\) | −1418.82 | − | 186.935i | −0.0876310 | − | 0.0115457i | ||||
\(641\) | 20456.5i | 1.26051i | 0.776389 | + | 0.630253i | \(0.217049\pi\) | ||||
−0.776389 | + | 0.630253i | \(0.782951\pi\) | |||||||
\(642\) | 12865.6 | − | 12865.6i | 0.790908 | − | 0.790908i | ||||
\(643\) | 13047.3 | + | 13047.3i | 0.800213 | + | 0.800213i | 0.983129 | − | 0.182915i | \(-0.0585534\pi\) |
−0.182915 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(644\) | −6175.57 | − | 3201.56i | −0.377875 | − | 0.195899i | ||||
\(645\) | −6241.38 | − | 8135.61i | −0.381014 | − | 0.496650i | ||||
\(646\) | −10053.2 | −0.612286 | ||||||||
\(647\) | 4439.60 | + | 4439.60i | 0.269766 | + | 0.269766i | 0.829006 | − | 0.559240i | \(-0.188907\pi\) |
−0.559240 | + | 0.829006i | \(0.688907\pi\) | |||||||
\(648\) | 4565.39 | − | 4565.39i | 0.276768 | − | 0.276768i | ||||
\(649\) | 5483.78 | 0.331675 | ||||||||
\(650\) | 3997.95 | − | 14908.7i | 0.241250 | − | 0.899640i | ||||
\(651\) | 9098.74i | 0.547785i | ||||||||
\(652\) | 2010.55 | + | 2010.55i | 0.120766 | + | 0.120766i | ||||
\(653\) | −14019.8 | + | 14019.8i | −0.840180 | + | 0.840180i | −0.988882 | − | 0.148702i | \(-0.952490\pi\) |
0.148702 | + | 0.988882i | \(0.452490\pi\) | |||||||
\(654\) | 17252.9 | 1.03156 | ||||||||
\(655\) | 9101.43 | + | 11863.7i | 0.542935 | + | 0.707712i | ||||
\(656\) | 4431.56 | 0.263755 | ||||||||
\(657\) | 3386.65 | + | 3386.65i | 0.201105 | + | 0.201105i | ||||
\(658\) | 4637.60 | + | 4637.60i | 0.274761 | + | 0.274761i | ||||
\(659\) | −13786.1 | −0.814917 | −0.407459 | − | 0.913224i | \(-0.633585\pi\) | ||||
−0.407459 | + | 0.913224i | \(0.633585\pi\) | |||||||
\(660\) | −2822.97 | − | 371.938i | −0.166491 | − | 0.0219358i | ||||
\(661\) | 3702.98i | 0.217896i | 0.994047 | + | 0.108948i | \(0.0347482\pi\) | ||||
−0.994047 | + | 0.108948i | \(0.965252\pi\) | |||||||
\(662\) | 13568.5 | + | 13568.5i | 0.796607 | + | 0.796607i | ||||
\(663\) | −14570.1 | − | 14570.1i | −0.853479 | − | 0.853479i | ||||
\(664\) | −342.022 | −0.0199895 | ||||||||
\(665\) | −18743.2 | − | 2469.49i | −1.09298 | − | 0.144004i | ||||
\(666\) | 7358.09i | 0.428108i | ||||||||
\(667\) | −857.023 | − | 2702.22i | −0.0497512 | − | 0.156867i | ||||
\(668\) | 2422.68 | − | 2422.68i | 0.140324 | − | 0.140324i | ||||
\(669\) | 35358.0i | 2.04338i | ||||||||
\(670\) | 6105.20 | + | 7958.09i | 0.352036 | + | 0.458877i | ||||
\(671\) | 361.911 | 0.0208218 | ||||||||
\(672\) | −2540.31 | + | 2540.31i | −0.145825 | + | 0.145825i | ||||
\(673\) | 8639.72 | − | 8639.72i | 0.494854 | − | 0.494854i | −0.414978 | − | 0.909832i | \(-0.636211\pi\) |
0.909832 | + | 0.414978i | \(0.136211\pi\) | |||||||
\(674\) | 5979.64 | 0.341731 | ||||||||
\(675\) | −2538.25 | + | 1464.79i | −0.144737 | + | 0.0835255i | ||||
\(676\) | 6460.13 | 0.367554 | ||||||||
\(677\) | 23219.7 | − | 23219.7i | 1.31818 | − | 1.31818i | 0.402961 | − | 0.915217i | \(-0.367981\pi\) |
0.915217 | − | 0.402961i | \(-0.132019\pi\) | |||||||
\(678\) | −17008.1 | − | 17008.1i | −0.963409 | − | 0.963409i | ||||
\(679\) | − | 15140.8i | − | 0.855746i | ||||||
\(680\) | 3325.89 | − | 2551.52i | 0.187562 | − | 0.143892i | ||||
\(681\) | − | 33100.0i | − | 1.86255i | ||||||
\(682\) | 1024.79 | − | 1024.79i | 0.0575387 | − | 0.0575387i | ||||
\(683\) | 10006.5 | − | 10006.5i | 0.560598 | − | 0.560598i | −0.368879 | − | 0.929477i | \(-0.620258\pi\) |
0.929477 | + | 0.368879i | \(0.120258\pi\) | |||||||
\(684\) | 10170.9 | 0.568557 | ||||||||
\(685\) | −23130.6 | − | 3047.55i | −1.29018 | − | 0.169987i | ||||
\(686\) | 13793.2i | 0.767676i | ||||||||
\(687\) | −32858.0 | + | 32858.0i | −1.82476 | + | 1.82476i | ||||
\(688\) | 1457.15 | + | 1457.15i | 0.0807459 | + | 0.0807459i | ||||
\(689\) | 26141.4 | 1.44544 | ||||||||
\(690\) | −14403.2 | − | 10051.2i | −0.794669 | − | 0.554555i | ||||
\(691\) | −19391.5 | −1.06756 | −0.533782 | − | 0.845622i | \(-0.679230\pi\) | ||||
−0.533782 | + | 0.845622i | \(0.679230\pi\) | |||||||
\(692\) | 6202.71 | + | 6202.71i | 0.340739 | + | 0.340739i | ||||
\(693\) | −2363.10 | + | 2363.10i | −0.129533 | + | 0.129533i | ||||
\(694\) | − | 13253.5i | − | 0.724921i | ||||||
\(695\) | 10849.1 | − | 8323.10i | 0.592130 | − | 0.454264i | ||||
\(696\) | −1464.09 | −0.0797359 | ||||||||
\(697\) | −9178.77 | + | 9178.77i | −0.498810 | + | 0.498810i | ||||
\(698\) | −10687.4 | + | 10687.4i | −0.579545 | + | 0.579545i | ||||
\(699\) | 20872.0i | 1.12940i | ||||||||
\(700\) | 6827.57 | − | 3940.09i | 0.368654 | − | 0.212745i | ||||
\(701\) | − | 21513.0i | − | 1.15911i | −0.814933 | − | 0.579555i | \(-0.803226\pi\) | ||
0.814933 | − | 0.579555i | \(-0.196774\pi\) | |||||||
\(702\) | −2047.09 | − | 2047.09i | −0.110061 | − | 0.110061i | ||||
\(703\) | 11769.0 | − | 11769.0i | 0.631405 | − | 0.631405i | ||||
\(704\) | 572.232 | 0.0306347 | ||||||||
\(705\) | 10079.6 | + | 13138.8i | 0.538470 | + | 0.701892i | ||||
\(706\) | 7983.95 | 0.425609 | ||||||||
\(707\) | −11493.9 | + | 11493.9i | −0.611419 | + | 0.611419i | ||||
\(708\) | 12352.9 | − | 12352.9i | 0.655721 | − | 0.655721i | ||||
\(709\) | −23973.3 | −1.26987 | −0.634933 | − | 0.772567i | \(-0.718972\pi\) | ||||
−0.634933 | + | 0.772567i | \(0.718972\pi\) | |||||||
\(710\) | −2186.73 | + | 16597.1i | −0.115587 | + | 0.877293i | ||||
\(711\) | 31664.8i | 1.67022i | ||||||||
\(712\) | −2028.51 | + | 2028.51i | −0.106772 | + | 0.106772i | ||||
\(713\) | 8521.35 | − | 2702.59i | 0.447583 | − | 0.141954i | ||||
\(714\) | − | 10523.1i | − | 0.551567i | ||||||
\(715\) | −806.217 | + | 6119.12i | −0.0421690 | + | 0.320059i | ||||
\(716\) | 1577.82 | 0.0823546 | ||||||||
\(717\) | −314.354 | − | 314.354i | −0.0163734 | − | 0.0163734i | ||||
\(718\) | 3394.24 | + | 3394.24i | 0.176423 | + | 0.176423i | ||||
\(719\) | 20926.9i | 1.08545i | 0.839909 | + | 0.542727i | \(0.182608\pi\) | ||||
−0.839909 | + | 0.542727i | \(0.817392\pi\) | |||||||
\(720\) | −3364.83 | + | 2581.39i | −0.174166 | + | 0.133615i | ||||
\(721\) | 22678.8 | 1.17143 | ||||||||
\(722\) | −6567.92 | − | 6567.92i | −0.338549 | − | 0.338549i | ||||
\(723\) | −14848.6 | − | 14848.6i | −0.763798 | − | 0.763798i | ||||
\(724\) | 2334.51 | 0.119836 | ||||||||
\(725\) | 3102.93 | + | 832.089i | 0.158952 | + | 0.0426249i | ||||
\(726\) | −17817.4 | −0.910833 | ||||||||
\(727\) | 5380.89 | − | 5380.89i | 0.274507 | − | 0.274507i | −0.556405 | − | 0.830911i | \(-0.687820\pi\) |
0.830911 | + | 0.556405i | \(0.187820\pi\) | |||||||
\(728\) | 5506.42 | + | 5506.42i | 0.280332 | + | 0.280332i | ||||
\(729\) | − | 14625.7i | − | 0.743065i | ||||||
\(730\) | 2749.62 | + | 3584.12i | 0.139408 | + | 0.181718i | ||||
\(731\) | −6036.17 | −0.305412 | ||||||||
\(732\) | 815.251 | − | 815.251i | 0.0411647 | − | 0.0411647i | ||||
\(733\) | −12601.9 | − | 12601.9i | −0.635008 | − | 0.635008i | 0.314311 | − | 0.949320i | \(-0.398226\pi\) |
−0.949320 | + | 0.314311i | \(0.898226\pi\) | |||||||
\(734\) | −18150.0 | −0.912710 | ||||||||
\(735\) | −982.140 | + | 7454.36i | −0.0492881 | + | 0.374093i | ||||
\(736\) | 3133.66 | + | 1624.56i | 0.156940 | + | 0.0813616i | ||||
\(737\) | −2835.97 | − | 2835.97i | −0.141743 | − | 0.141743i | ||||
\(738\) | 9286.23 | − | 9286.23i | 0.463185 | − | 0.463185i | ||||
\(739\) | 12100.4i | 0.602326i | 0.953573 | + | 0.301163i | \(0.0973749\pi\) | ||||
−0.953573 | + | 0.301163i | \(0.902625\pi\) | |||||||
\(740\) | −906.541 | + | 6880.57i | −0.0450340 | + | 0.341804i | ||||
\(741\) | − | 47154.7i | − | 2.33775i | ||||||
\(742\) | 9440.19 | + | 9440.19i | 0.467062 | + | 0.467062i | ||||
\(743\) | −6441.47 | − | 6441.47i | −0.318054 | − | 0.318054i | 0.529965 | − | 0.848020i | \(-0.322205\pi\) |
−0.848020 | + | 0.529965i | \(0.822205\pi\) | |||||||
\(744\) | − | 4616.95i | − | 0.227508i | ||||||
\(745\) | 21583.4 | + | 28133.8i | 1.06141 | + | 1.38355i | ||||
\(746\) | 21286.4i | 1.04470i | ||||||||
\(747\) | −716.700 | + | 716.700i | −0.0351040 | + | 0.0351040i | ||||
\(748\) | −1185.22 | + | 1185.22i | −0.0579360 | + | 0.0579360i | ||||
\(749\) | − | 20141.5i | − | 0.982584i | ||||||
\(750\) | 18390.8 | − | 7611.28i | 0.895383 | − | 0.370566i | ||||
\(751\) | 27627.2i | 1.34238i | 0.741283 | + | 0.671192i | \(0.234218\pi\) | ||||
−0.741283 | + | 0.671192i | \(0.765782\pi\) | |||||||
\(752\) | −2353.25 | − | 2353.25i | −0.114114 | − | 0.114114i | ||||
\(753\) | −3594.28 | − | 3594.28i | −0.173948 | − | 0.173948i | ||||
\(754\) | 3173.58i | 0.153282i | ||||||||
\(755\) | −1635.83 | − | 2132.30i | −0.0788530 | − | 0.102784i | ||||
\(756\) | − | 1478.50i | − | 0.0711275i | ||||||
\(757\) | −21890.4 | + | 21890.4i | −1.05102 | + | 1.05102i | −0.0523915 | + | 0.998627i | \(0.516684\pi\) |
−0.998627 | + | 0.0523915i | \(0.983316\pi\) | |||||||
\(758\) | −9168.01 | − | 9168.01i | −0.439310 | − | 0.439310i | ||||
\(759\) | 6234.92 | + | 3232.33i | 0.298173 | + | 0.154580i | ||||
\(760\) | 9510.81 | + | 1253.09i | 0.453939 | + | 0.0598081i | ||||
\(761\) | −10670.3 | −0.508276 | −0.254138 | − | 0.967168i | \(-0.581792\pi\) | ||||
−0.254138 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(762\) | 15466.0 | + | 15466.0i | 0.735269 | + | 0.735269i | ||||
\(763\) | 13505.1 | − | 13505.1i | 0.640781 | − | 0.640781i | ||||
\(764\) | 12065.6 | 0.571360 | ||||||||
\(765\) | 1622.68 | − | 12316.0i | 0.0766903 | − | 0.582072i | ||||
\(766\) | 9605.99i | 0.453105i | ||||||||
\(767\) | −26776.3 | − | 26776.3i | −1.26054 | − | 1.26054i | ||||
\(768\) | 1289.03 | − | 1289.03i | 0.0605647 | − | 0.0605647i | ||||
\(769\) | 10059.6 | 0.471725 | 0.235863 | − | 0.971786i | \(-0.424208\pi\) | ||||
0.235863 | + | 0.971786i | \(0.424208\pi\) | |||||||
\(770\) | −2500.88 | + | 1918.60i | −0.117046 | + | 0.0897941i | ||||
\(771\) | 3891.17 | 0.181760 | ||||||||
\(772\) | −1871.63 | − | 1871.63i | −0.0872558 | − | 0.0872558i | ||||
\(773\) | −20372.3 | − | 20372.3i | −0.947917 | − | 0.947917i | 0.0507921 | − | 0.998709i | \(-0.483825\pi\) |
−0.998709 | + | 0.0507921i | \(0.983825\pi\) | |||||||
\(774\) | 6106.84 | 0.283599 | ||||||||
\(775\) | −2623.96 | + | 9784.97i | −0.121620 | + | 0.453531i | ||||
\(776\) | 7682.87i | 0.355411i | ||||||||
\(777\) | 12319.2 | + | 12319.2i | 0.568791 | + | 0.568791i | ||||
\(778\) | 7961.20 | + | 7961.20i | 0.366867 | + | 0.366867i | ||||
\(779\) | −29706.1 | −1.36628 | ||||||||
\(780\) | 11968.0 | + | 15600.2i | 0.549388 | + | 0.716124i | ||||
\(781\) | − | 6693.86i | − | 0.306690i | ||||||
\(782\) | −9855.36 | + | 3125.68i | −0.450674 | + | 0.142934i | ||||
\(783\) | 426.060 | − | 426.060i | 0.0194459 | − | 0.0194459i | ||||
\(784\) | − | 1511.04i | − | 0.0688338i | ||||||
\(785\) | 23158.3 | + | 3051.20i | 1.05294 | + | 0.138729i | ||||
\(786\) | −19047.2 | −0.864364 | ||||||||
\(787\) | 22918.0 | − | 22918.0i | 1.03804 | − | 1.03804i | 0.0387932 | − | 0.999247i | \(-0.487649\pi\) |
0.999247 | − | 0.0387932i | \(-0.0123514\pi\) | |||||||
\(788\) | −8557.40 | + | 8557.40i | −0.386859 | + | 0.386859i | ||||
\(789\) | −52650.6 | −2.37568 | ||||||||
\(790\) | −3901.22 | + | 29609.9i | −0.175695 | + | 1.33351i | ||||
\(791\) | −26626.8 | −1.19689 | ||||||||
\(792\) | 1199.10 | − | 1199.10i | 0.0537982 | − | 0.0537982i | ||||
\(793\) | −1767.15 | − | 1767.15i | −0.0791340 | − | 0.0791340i | ||||
\(794\) | − | 1080.46i | − | 0.0482923i | ||||||
\(795\) | 20517.9 | + | 26744.9i | 0.915338 | + | 1.19314i | ||||
\(796\) | − | 14123.7i | − | 0.628896i | ||||||
\(797\) | 13843.6 | − | 13843.6i | 0.615264 | − | 0.615264i | −0.329049 | − | 0.944313i | \(-0.606728\pi\) |
0.944313 | + | 0.329049i | \(0.106728\pi\) | |||||||
\(798\) | 17028.5 | − | 17028.5i | 0.755393 | − | 0.755393i | ||||
\(799\) | 9748.23 | 0.431624 | ||||||||
\(800\) | −3464.50 | + | 1999.31i | −0.153111 | + | 0.0883579i | ||||
\(801\) | 8501.40i | 0.375009i | ||||||||
\(802\) | −16569.7 | + | 16569.7i | −0.729547 | + | 0.729547i | ||||
\(803\) | −1277.25 | − | 1277.25i | −0.0561308 | − | 0.0561308i | ||||
\(804\) | −12776.8 | −0.560449 | ||||||||
\(805\) | −19142.2 | + | 3406.64i | −0.838104 | + | 0.149153i | ||||
\(806\) | −10007.8 | −0.437356 | ||||||||
\(807\) | −39107.9 | − | 39107.9i | −1.70590 | − | 1.70590i | ||||
\(808\) | 5832.33 | − | 5832.33i | 0.253937 | − | 0.253937i | ||||
\(809\) | 13373.0i | 0.581174i | 0.956849 | + | 0.290587i | \(0.0938506\pi\) | ||||
−0.956849 | + | 0.290587i | \(0.906149\pi\) | |||||||
\(810\) | 2357.29 | − | 17891.7i | 0.102255 | − | 0.776110i | ||||
\(811\) | −21869.8 | −0.946920 | −0.473460 | − | 0.880815i | \(-0.656995\pi\) | ||||
−0.473460 | + | 0.880815i | \(0.656995\pi\) | |||||||
\(812\) | −1146.05 | + | 1146.05i | −0.0495299 | + | 0.0495299i | ||||
\(813\) | −37590.1 | + | 37590.1i | −1.62158 | + | 1.62158i | ||||
\(814\) | − | 2775.04i | − | 0.119490i | ||||||
\(815\) | 7879.30 | + | 1038.13i | 0.338650 | + | 0.0446184i | ||||
\(816\) | 5339.74i | 0.229079i | ||||||||
\(817\) | −9767.72 | − | 9767.72i | −0.418273 | − | 0.418273i | ||||
\(818\) | −19702.5 | + | 19702.5i | −0.842155 | + | 0.842155i | ||||
\(819\) | 23077.2 | 0.984592 | ||||||||
\(820\) | 9827.68 | − | 7539.49i | 0.418534 | − | 0.321086i | ||||
\(821\) | −19840.0 | −0.843385 | −0.421693 | − | 0.906739i | \(-0.638564\pi\) | ||||
−0.421693 | + | 0.906739i | \(0.638564\pi\) | |||||||
\(822\) | 21014.6 | − | 21014.6i | 0.891689 | − | 0.891689i | ||||
\(823\) | 29859.6 | − | 29859.6i | 1.26469 | − | 1.26469i | 0.315897 | − | 0.948794i | \(-0.397695\pi\) |
0.948794 | − | 0.315897i | \(-0.102305\pi\) | |||||||
\(824\) | −11507.8 | −0.486523 | ||||||||
\(825\) | −6893.18 | + | 3977.95i | −0.290897 | + | 0.167872i | ||||
\(826\) | − | 19339.0i | − | 0.814635i | ||||||
\(827\) | 32427.4 | − | 32427.4i | 1.36349 | − | 1.36349i | 0.494074 | − | 0.869420i | \(-0.335507\pi\) |
0.869420 | − | 0.494074i | \(-0.164493\pi\) | |||||||
\(828\) | 9970.75 | − | 3162.28i | 0.418487 | − | 0.132725i | ||||
\(829\) | 24497.6i | 1.02634i | 0.858286 | + | 0.513171i | \(0.171529\pi\) | ||||
−0.858286 | + | 0.513171i | \(0.828471\pi\) | |||||||
\(830\) | −758.489 | + | 581.889i | −0.0317199 | + | 0.0243345i | ||||
\(831\) | −13119.3 | −0.547659 | ||||||||
\(832\) | −2794.11 | − | 2794.11i | −0.116428 | − | 0.116428i | ||||
\(833\) | 3129.71 | + | 3129.71i | 0.130178 | + | 0.130178i | ||||
\(834\) | 17418.3i | 0.723198i | ||||||||
\(835\) | 1250.93 | − | 9494.42i | 0.0518444 | − | 0.393494i | ||||
\(836\) | −3835.85 | −0.158691 | ||||||||
\(837\) | 1343.56 | + | 1343.56i | 0.0554843 | + | 0.0554843i | ||||
\(838\) | 1131.12 | + | 1131.12i | 0.0466275 | + | 0.0466275i | ||||
\(839\) | 26598.5 | 1.09449 | 0.547247 | − | 0.836971i | \(-0.315676\pi\) | ||||
0.547247 | + | 0.836971i | \(0.315676\pi\) | |||||||
\(840\) | −1311.67 | + | 9955.43i | −0.0538771 | + | 0.408923i | ||||
\(841\) | 23728.5 | 0.972918 | ||||||||
\(842\) | 23101.0 | − | 23101.0i | 0.945503 | − | 0.945503i | ||||
\(843\) | 39599.5 | + | 39599.5i | 1.61789 | + | 1.61789i | ||||
\(844\) | − | 4149.06i | − | 0.169214i | ||||||
\(845\) | 14326.4 | − | 10990.7i | 0.583245 | − | 0.447447i | ||||
\(846\) | −9862.36 | −0.400798 | ||||||||
\(847\) | −13946.9 | + | 13946.9i | −0.565786 | + | 0.565786i | ||||
\(848\) | −4790.21 | − | 4790.21i | −0.193982 | − | 0.193982i | ||||
\(849\) | 9336.65 | 0.377424 | ||||||||
\(850\) | 3034.74 | − | 11316.8i | 0.122460 | − | 0.456662i | ||||
\(851\) | 7878.31 | − | 15196.7i | 0.317350 | − | 0.612144i | ||||
\(852\) | −15078.8 | − | 15078.8i | −0.606326 | − | 0.606326i | ||||
\(853\) | 34394.3 | − | 34394.3i | 1.38058 | − | 1.38058i | 0.537003 | − | 0.843580i | \(-0.319556\pi\) |
0.843580 | − | 0.537003i | \(-0.180444\pi\) | |||||||
\(854\) | − | 1276.31i | − | 0.0511409i | ||||||
\(855\) | 22555.5 | − | 17303.9i | 0.902202 | − | 0.692141i | ||||
\(856\) | 10220.4i | 0.408090i | ||||||||
\(857\) | −537.863 | − | 537.863i | −0.0214388 | − | 0.0214388i | 0.696306 | − | 0.717745i | \(-0.254826\pi\) |
−0.717745 | + | 0.696306i | \(0.754826\pi\) | |||||||
\(858\) | −5559.33 | − | 5559.33i | −0.221203 | − | 0.221203i | ||||
\(859\) | − | 42120.1i | − | 1.67301i | −0.547957 | − | 0.836507i | \(-0.684594\pi\) | ||
0.547957 | − | 0.836507i | \(-0.315406\pi\) | |||||||
\(860\) | 5710.53 | + | 752.384i | 0.226427 | + | 0.0298326i | ||||
\(861\) | − | 31094.9i | − | 1.23079i | ||||||
\(862\) | 9614.51 | − | 9614.51i | 0.379897 | − | 0.379897i | ||||
\(863\) | −4664.16 | + | 4664.16i | −0.183974 | + | 0.183974i | −0.793085 | − | 0.609111i | \(-0.791526\pi\) |
0.609111 | + | 0.793085i | \(0.291526\pi\) | |||||||
\(864\) | 750.230i | 0.0295409i | ||||||||
\(865\) | 24308.3 | + | 3202.71i | 0.955499 | + | 0.125891i | ||||
\(866\) | − | 7987.42i | − | 0.313422i | ||||||
\(867\) | 13678.4 | + | 13678.4i | 0.535805 | + | 0.535805i | ||||
\(868\) | −3614.01 | − | 3614.01i | −0.141322 | − | 0.141322i | ||||
\(869\) | − | 11942.1i | − | 0.466178i | ||||||
\(870\) | −3246.85 | + | 2490.88i | −0.126527 | + | 0.0970677i | ||||
\(871\) | 27695.1i | 1.07740i | ||||||||
\(872\) | −6852.84 | + | 6852.84i | −0.266131 | + | 0.266131i | ||||
\(873\) | 16099.3 | + | 16099.3i | 0.624145 | + | 0.624145i | ||||
\(874\) | −21005.9 | − | 10890.0i | −0.812969 | − | 0.421462i | ||||
\(875\) | 8437.88 | − | 20353.6i | 0.326003 | − | 0.786376i | ||||
\(876\) | −5754.32 | −0.221941 | ||||||||
\(877\) | 1732.23 | + | 1732.23i | 0.0666968 | + | 0.0666968i | 0.739668 | − | 0.672972i | \(-0.234982\pi\) |
−0.672972 | + | 0.739668i | \(0.734982\pi\) | |||||||
\(878\) | 8447.16 | − | 8447.16i | 0.324690 | − | 0.324690i | ||||
\(879\) | 48114.5 | 1.84626 | ||||||||
\(880\) | 1269.02 | − | 973.550i | 0.0486120 | − | 0.0372936i | ||||
\(881\) | 20113.1i | 0.769157i | 0.923092 | + | 0.384579i | \(0.125653\pi\) | ||||
−0.923092 | + | 0.384579i | \(0.874347\pi\) | |||||||
\(882\) | −3166.35 | − | 3166.35i | −0.120880 | − | 0.120880i | ||||
\(883\) | −8519.50 | + | 8519.50i | −0.324693 | + | 0.324693i | −0.850564 | − | 0.525871i | \(-0.823739\pi\) |
0.525871 | + | 0.850564i | \(0.323739\pi\) | |||||||
\(884\) | 11574.5 | 0.440375 | ||||||||
\(885\) | 6378.31 | − | 48410.8i | 0.242265 | − | 1.83877i | ||||
\(886\) | −10318.6 | −0.391264 | ||||||||
\(887\) | −11579.2 | − | 11579.2i | −0.438322 | − | 0.438322i | 0.453125 | − | 0.891447i | \(-0.350309\pi\) |
−0.891447 | + | 0.453125i | \(0.850309\pi\) | |||||||
\(888\) | −6251.13 | − | 6251.13i | −0.236232 | − | 0.236232i | ||||
\(889\) | 24212.7 | 0.913462 | ||||||||
\(890\) | −1047.40 | + | 7949.69i | −0.0394483 | + | 0.299409i | ||||
\(891\) | 7215.98i | 0.271318i | ||||||||
\(892\) | −14044.2 | − | 14044.2i | −0.527167 | − | 0.527167i | ||||
\(893\) | 15774.6 | + | 15774.6i | 0.591126 | + | 0.591126i | ||||
\(894\) | −45169.0 | −1.68980 | ||||||||
\(895\) | 3499.07 | − | 2684.38i | 0.130683 | − | 0.100256i | ||||
\(896\) | − | 2018.02i | − | 0.0752426i | ||||||
\(897\) | −14661.1 | − | 46226.9i | −0.545730 | − | 1.72070i | ||||
\(898\) | 8644.51 | − | 8644.51i | 0.321237 | − | 0.321237i | ||||
\(899\) | − | 2082.91i | − | 0.0772735i | ||||||
\(900\) | −3070.27 | + | 11449.3i | −0.113714 | + | 0.424048i | ||||
\(901\) | 19843.3 | 0.733712 | ||||||||
\(902\) | −3502.22 | + | 3502.22i | −0.129281 | + | 0.129281i | ||||
\(903\) | 10224.4 | − | 10224.4i | 0.376794 | − | 0.376794i | ||||
\(904\) | 13511.2 | 0.497096 | ||||||||
\(905\) | 5177.15 | − | 3971.75i | 0.190160 | − | 0.145884i | ||||
\(906\) | 3423.42 | 0.125536 | ||||||||
\(907\) | 2613.75 | − | 2613.75i | 0.0956869 | − | 0.0956869i | −0.657643 | − | 0.753330i | \(-0.728446\pi\) |
0.753330 | + | 0.657643i | \(0.228446\pi\) | |||||||
\(908\) | 13147.3 | + | 13147.3i | 0.480515 | + | 0.480515i | ||||
\(909\) | − | 24443.1i | − | 0.891887i | ||||||
\(910\) | 21579.5 | + | 2843.18i | 0.786104 | + | 0.103572i | ||||
\(911\) | − | 30173.3i | − | 1.09735i | −0.836036 | − | 0.548675i | \(-0.815133\pi\) | ||
0.836036 | − | 0.548675i | \(-0.184867\pi\) | |||||||
\(912\) | −8640.75 | + | 8640.75i | −0.313732 | + | 0.313732i | ||||
\(913\) | 270.297 | − | 270.297i | 0.00979796 | − | 0.00979796i | ||||
\(914\) | 1773.01 | 0.0641640 | ||||||||
\(915\) | 420.947 | − | 3194.95i | 0.0152088 | − | 0.115434i | ||||
\(916\) | − | 26102.3i | − | 0.941534i | ||||||
\(917\) | −14909.6 | + | 14909.6i | −0.536921 | + | 0.536921i | ||||
\(918\) | −1553.90 | − | 1553.90i | −0.0558674 | − | 0.0558674i | ||||
\(919\) | 26983.4 | 0.968553 | 0.484276 | − | 0.874915i | \(-0.339083\pi\) | ||||
0.484276 | + | 0.874915i | \(0.339083\pi\) | |||||||
\(920\) | 9713.28 | − | 1728.62i | 0.348084 | − | 0.0619468i | ||||
\(921\) | 23163.6 | 0.828739 | ||||||||
\(922\) | −1012.48 | − | 1012.48i | −0.0361650 | − | 0.0361650i | ||||
\(923\) | −32684.9 | + | 32684.9i | −1.16559 | + | 1.16559i | ||||
\(924\) | − | 4015.18i | − | 0.142954i | ||||||
\(925\) | 9695.65 | + | 16801.1i | 0.344639 | + | 0.597207i | ||||
\(926\) | −4037.27 | −0.143275 | ||||||||
\(927\) | −24114.4 | + | 24114.4i | −0.854393 | + | 0.854393i | ||||
\(928\) | 581.535 | − | 581.535i | 0.0205709 | − | 0.0205709i | ||||
\(929\) | − | 42125.9i | − | 1.48774i | −0.668327 | − | 0.743868i | \(-0.732989\pi\) | ||
0.668327 | − | 0.743868i | \(-0.267011\pi\) | |||||||
\(930\) | −7854.91 | − | 10238.8i | −0.276960 | − | 0.361016i | ||||
\(931\) | 10129.0i | 0.356567i | ||||||||
\(932\) | −8290.32 | − | 8290.32i | −0.291372 | − | 0.291372i | ||||
\(933\) | −50561.2 | + | 50561.2i | −1.77417 | + | 1.77417i | ||||
\(934\) | 18282.3 | 0.640488 | ||||||||
\(935\) | −611.979 | + | 4644.87i | −0.0214052 | + | 0.162464i | ||||
\(936\) | −11710.0 | −0.408924 | ||||||||
\(937\) | 14100.5 | − | 14100.5i | 0.491616 | − | 0.491616i | −0.417199 | − | 0.908815i | \(-0.636988\pi\) |
0.908815 | + | 0.417199i | \(0.136988\pi\) | |||||||
\(938\) | −10001.3 | + | 10001.3i | −0.348137 | + | 0.348137i | ||||
\(939\) | −6385.52 | −0.221921 | ||||||||
\(940\) | −9222.33 | − | 1215.08i | −0.319999 | − | 0.0421611i | ||||
\(941\) | 20561.8i | 0.712324i | 0.934424 | + | 0.356162i | \(0.115915\pi\) | ||||
−0.934424 | + | 0.356162i | \(0.884085\pi\) | |||||||
\(942\) | −21039.8 | + | 21039.8i | −0.727721 | + | 0.727721i | ||||
\(943\) | −29121.6 | + | 9236.08i | −1.00565 | + | 0.318948i | ||||
\(944\) | 9813.13i | 0.338337i | ||||||||
\(945\) | −2515.39 | − | 3278.80i | −0.0865881 | − | 0.112867i | ||||
\(946\) | −2303.14 | −0.0791561 | ||||||||
\(947\) | 31271.9 | + | 31271.9i | 1.07307 | + | 1.07307i | 0.997111 | + | 0.0759641i | \(0.0242034\pi\) |
0.0759641 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(948\) | −26901.2 | − | 26901.2i | −0.921634 | − | 0.921634i | ||||
\(949\) | 12473.1i | 0.426654i | ||||||||
\(950\) | 23223.6 | − | 13402.0i | 0.793131 | − | 0.457704i | ||||
\(951\) | 78837.7 | 2.68821 | ||||||||
\(952\) | 4179.78 | + | 4179.78i | 0.142298 | + | 0.142298i | ||||
\(953\) | 37454.1 | + | 37454.1i | 1.27309 | + | 1.27309i | 0.944456 | + | 0.328638i | \(0.106590\pi\) |
0.328638 | + | 0.944456i | \(0.393410\pi\) | |||||||
\(954\) | −20075.6 | −0.681311 | ||||||||
\(955\) | 26757.5 | − | 20527.5i | 0.906650 | − | 0.695554i | ||||
\(956\) | 249.722 | 0.00844831 | ||||||||
\(957\) | 1157.06 | − | 1157.06i | 0.0390830 | − | 0.0390830i | ||||
\(958\) | −19122.4 | − | 19122.4i | −0.644902 | − | 0.644902i | ||||
\(959\) | − | 32899.2i | − | 1.10779i | ||||||
\(960\) | 665.576 | − | 5051.66i | 0.0223764 | − | 0.169835i | ||||
\(961\) | −23222.6 | −0.779518 | ||||||||
\(962\) | −13550.0 | + | 13550.0i | −0.454127 | + | 0.454127i | ||||
\(963\) | 21416.6 | + | 21416.6i | 0.716656 | + | 0.716656i | ||||
\(964\) | 11795.7 | 0.394102 | ||||||||
\(965\) | −7334.88 | − | 966.399i | −0.244682 | − | 0.0322378i | ||||
\(966\) | 11399.1 | − | 21987.9i | 0.379667 | − | 0.732349i | ||||
\(967\) | −24154.7 | − | 24154.7i | −0.803272 | − | 0.803272i | 0.180334 | − | 0.983605i | \(-0.442282\pi\) |
−0.983605 | + | 0.180334i | \(0.942282\pi\) | |||||||
\(968\) | 7077.04 | − | 7077.04i | 0.234984 | − | 0.234984i | ||||
\(969\) | − | 35793.9i | − | 1.18665i | ||||||
\(970\) | 13071.0 | + | 17038.0i | 0.432665 | + | 0.563976i | ||||
\(971\) | − | 29666.4i | − | 0.980473i | −0.871589 | − | 0.490237i | \(-0.836910\pi\) | ||
0.871589 | − | 0.490237i | \(-0.163090\pi\) | |||||||
\(972\) | 14464.5 | + | 14464.5i | 0.477313 | + | 0.477313i | ||||
\(973\) | 13634.5 | + | 13634.5i | 0.449232 | + | 0.449232i | ||||
\(974\) | − | 35614.8i | − | 1.17163i | ||||||
\(975\) | 53081.8 | + | 14234.6i | 1.74357 | + | 0.467560i | ||||
\(976\) | 647.634i | 0.0212400i | ||||||||
\(977\) | 10267.1 | − | 10267.1i | 0.336207 | − | 0.336207i | −0.518731 | − | 0.854938i | \(-0.673595\pi\) |
0.854938 | + | 0.518731i | \(0.173595\pi\) | |||||||
\(978\) | −7158.49 | + | 7158.49i | −0.234052 | + | 0.234052i | ||||
\(979\) | − | 3206.23i | − | 0.104670i | ||||||
\(980\) | −2570.76 | − | 3350.97i | −0.0837958 | − | 0.109227i | ||||
\(981\) | 28720.0i | 0.934718i | ||||||||
\(982\) | −17617.0 | − | 17617.0i | −0.572486 | − | 0.572486i | ||||
\(983\) | 15831.6 | + | 15831.6i | 0.513681 | + | 0.513681i | 0.915652 | − | 0.401971i | \(-0.131675\pi\) |
−0.401971 | + | 0.915652i | \(0.631675\pi\) | |||||||
\(984\) | 15778.4i | 0.511176i | ||||||||
\(985\) | −4418.53 | + | 33536.3i | −0.142930 | + | 1.08483i | ||||
\(986\) | 2408.99i | 0.0778070i | ||||||||
\(987\) | −16512.0 | + | 16512.0i | −0.532506 | + | 0.532506i | ||||
\(988\) | 18729.8 | + | 18729.8i | 0.603111 | + | 0.603111i | ||||
\(989\) | −12612.5 | − | 6538.60i | −0.405514 | − | 0.210228i | ||||
\(990\) | 619.144 | − | 4699.25i | 0.0198765 | − | 0.150861i | ||||
\(991\) | 20195.0 | 0.647342 | 0.323671 | − | 0.946170i | \(-0.395083\pi\) | ||||
0.323671 | + | 0.946170i | \(0.395083\pi\) | |||||||
\(992\) | 1833.85 | + | 1833.85i | 0.0586944 | + | 0.0586944i | ||||
\(993\) | −48310.1 | + | 48310.1i | −1.54388 | + | 1.54388i | ||||
\(994\) | −23606.4 | −0.753269 | ||||||||
\(995\) | −24028.9 | − | 31321.5i | −0.765596 | − | 0.997949i | ||||
\(996\) | − | 1217.76i | − | 0.0387411i | ||||||
\(997\) | −6704.33 | − | 6704.33i | −0.212967 | − | 0.212967i | 0.592560 | − | 0.805527i | \(-0.298117\pi\) |
−0.805527 | + | 0.592560i | \(0.798117\pi\) | |||||||
\(998\) | 25243.6 | − | 25243.6i | 0.800675 | − | 0.800675i | ||||
\(999\) | 3638.24 | 0.115224 |
(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 | 230.4.e.a.137.16 | yes | 72 | |
5.3 | odd | 4 | inner | 230.4.e.a.183.15 | yes | 72 | |
23.22 | odd | 2 | inner | 230.4.e.a.137.15 | ✓ | 72 | |
115.68 | even | 4 | inner | 230.4.e.a.183.16 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.e.a.137.15 | ✓ | 72 | 23.22 | odd | 2 | inner | |
230.4.e.a.137.16 | yes | 72 | 1.1 | even | 1 | trivial | |
230.4.e.a.183.15 | yes | 72 | 5.3 | odd | 4 | inner | |
230.4.e.a.183.16 | yes | 72 | 115.68 | even | 4 | inner |