Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(68,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.68");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.g (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.3 | ||
Root | \(-2.23014 - 2.00661i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.80 |
Dual form | 147.4.g.d.68.3 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.65310 | + | 0.954416i | −0.584458 | + | 0.337437i | −0.762903 | − | 0.646513i | \(-0.776227\pi\) |
0.178445 | + | 0.983950i | \(0.442893\pi\) | |||||||
\(3\) | 3.47555 | − | 3.86271i | 0.668870 | − | 0.743380i | ||||
\(4\) | −2.17818 | + | 3.77272i | −0.272273 | + | 0.471590i | ||||
\(5\) | −0.623706 | − | 1.08029i | −0.0557859 | − | 0.0966240i | 0.836784 | − | 0.547533i | \(-0.184433\pi\) |
−0.892570 | + | 0.450909i | \(0.851100\pi\) | |||||||
\(6\) | −2.05878 | + | 9.70256i | −0.140082 | + | 0.660175i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 23.5862i | − | 1.04237i | ||||||
\(9\) | −2.84113 | − | 26.8501i | −0.105227 | − | 0.994448i | ||||
\(10\) | 2.06209 | + | 1.19055i | 0.0652090 | + | 0.0376484i | ||||
\(11\) | 35.2392 | + | 20.3453i | 0.965910 | + | 0.557668i | 0.897987 | − | 0.440022i | \(-0.145029\pi\) |
0.0679230 | + | 0.997691i | \(0.478363\pi\) | |||||||
\(12\) | 7.00257 | + | 21.5260i | 0.168456 | + | 0.517834i | ||||
\(13\) | − | 19.5973i | − | 0.418101i | −0.977905 | − | 0.209050i | \(-0.932963\pi\) | ||
0.977905 | − | 0.209050i | \(-0.0670373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.34057 | − | 1.34540i | −0.109142 | − | 0.0231588i | ||||
\(16\) | 5.08559 | + | 8.80850i | 0.0794623 | + | 0.137633i | ||||
\(17\) | 52.3592 | − | 90.6889i | 0.746999 | − | 1.29384i | −0.202256 | − | 0.979333i | \(-0.564827\pi\) |
0.949255 | − | 0.314507i | \(-0.101839\pi\) | |||||||
\(18\) | 30.3228 | + | 41.6742i | 0.397064 | + | 0.545706i | ||||
\(19\) | −35.0345 | + | 20.2272i | −0.423025 | + | 0.244234i | −0.696371 | − | 0.717682i | \(-0.745203\pi\) |
0.273346 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(20\) | 5.43418 | 0.0607559 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −77.6716 | −0.752711 | ||||||||
\(23\) | 69.6324 | − | 40.2023i | 0.631276 | − | 0.364467i | −0.149970 | − | 0.988691i | \(-0.547918\pi\) |
0.781246 | + | 0.624223i | \(0.214584\pi\) | |||||||
\(24\) | −91.1068 | − | 81.9750i | −0.774879 | − | 0.697212i | ||||
\(25\) | 61.7220 | − | 106.906i | 0.493776 | − | 0.855245i | ||||
\(26\) | 18.7040 | + | 32.3962i | 0.141083 | + | 0.244362i | ||||
\(27\) | −113.589 | − | 82.3444i | −0.809636 | − | 0.586933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 211.712i | − | 1.35565i | −0.735222 | − | 0.677827i | \(-0.762922\pi\) | ||
0.735222 | − | 0.677827i | \(-0.237078\pi\) | |||||||
\(30\) | 11.7656 | − | 3.82746i | 0.0716034 | − | 0.0232932i | ||||
\(31\) | 86.6242 | + | 50.0125i | 0.501876 | + | 0.289758i | 0.729488 | − | 0.683994i | \(-0.239758\pi\) |
−0.227612 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(32\) | 146.596 | + | 84.6373i | 0.809837 | + | 0.467560i | ||||
\(33\) | 201.064 | − | 65.4076i | 1.06063 | − | 0.345030i | ||||
\(34\) | 199.890i | 1.00826i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 107.486 | + | 47.7656i | 0.497622 | + | 0.221137i | ||||
\(37\) | 94.9875 | + | 164.523i | 0.422050 | + | 0.731012i | 0.996140 | − | 0.0877801i | \(-0.0279773\pi\) |
−0.574090 | + | 0.818792i | \(0.694644\pi\) | |||||||
\(38\) | 38.6103 | − | 66.8750i | 0.164827 | − | 0.285488i | ||||
\(39\) | −75.6987 | − | 68.1113i | −0.310808 | − | 0.279655i | ||||
\(40\) | −25.4799 | + | 14.7109i | −0.100718 | + | 0.0581497i | ||||
\(41\) | 186.753 | 0.711362 | 0.355681 | − | 0.934607i | \(-0.384249\pi\) | ||||
0.355681 | + | 0.934607i | \(0.384249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 158.618 | 0.562536 | 0.281268 | − | 0.959629i | \(-0.409245\pi\) | ||||
0.281268 | + | 0.959629i | \(0.409245\pi\) | |||||||
\(44\) | −153.515 | + | 88.6317i | −0.525982 | + | 0.303676i | ||||
\(45\) | −27.2339 | + | 19.8158i | −0.0902174 | + | 0.0656437i | ||||
\(46\) | −76.7393 | + | 132.916i | −0.245969 | + | 0.426032i | ||||
\(47\) | −179.034 | − | 310.097i | −0.555635 | − | 0.962388i | −0.997854 | − | 0.0654808i | \(-0.979142\pi\) |
0.442219 | − | 0.896907i | \(-0.354191\pi\) | |||||||
\(48\) | 51.6999 | + | 10.9702i | 0.155463 | + | 0.0329877i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 235.634i | 0.666473i | ||||||||
\(51\) | −168.328 | − | 517.442i | −0.462170 | − | 1.42071i | ||||
\(52\) | 73.9351 | + | 42.6865i | 0.197172 | + | 0.113837i | ||||
\(53\) | −366.460 | − | 211.576i | −0.949758 | − | 0.548343i | −0.0567521 | − | 0.998388i | \(-0.518074\pi\) |
−0.893006 | + | 0.450045i | \(0.851408\pi\) | |||||||
\(54\) | 266.364 | + | 27.7123i | 0.671251 | + | 0.0698364i | ||||
\(55\) | − | 50.7580i | − | 0.124440i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.6323 | + | 205.629i | −0.101390 | + | 0.477829i | ||||
\(58\) | 202.061 | + | 349.980i | 0.457447 | + | 0.792322i | ||||
\(59\) | −312.781 | + | 541.753i | −0.690180 | + | 1.19543i | 0.281599 | + | 0.959532i | \(0.409135\pi\) |
−0.971779 | + | 0.235895i | \(0.924198\pi\) | |||||||
\(60\) | 18.8867 | − | 20.9907i | 0.0406378 | − | 0.0451647i | ||||
\(61\) | −699.575 | + | 403.900i | −1.46838 | + | 0.847772i | −0.999372 | − | 0.0354209i | \(-0.988723\pi\) |
−0.469011 | + | 0.883192i | \(0.655389\pi\) | |||||||
\(62\) | −190.931 | −0.391101 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −404.486 | −0.790012 | ||||||||
\(65\) | −21.1708 | + | 12.2229i | −0.0403986 | + | 0.0233241i | ||||
\(66\) | −269.952 | + | 300.023i | −0.503466 | + | 0.559550i | ||||
\(67\) | −149.272 | + | 258.547i | −0.272187 | + | 0.471441i | −0.969421 | − | 0.245402i | \(-0.921080\pi\) |
0.697235 | + | 0.716843i | \(0.254413\pi\) | |||||||
\(68\) | 228.096 | + | 395.074i | 0.406775 | + | 0.704555i | ||||
\(69\) | 86.7208 | − | 408.695i | 0.151304 | − | 0.713059i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 455.386i | 0.761189i | 0.924742 | + | 0.380594i | \(0.124281\pi\) | ||||
−0.924742 | + | 0.380594i | \(0.875719\pi\) | |||||||
\(72\) | −633.292 | + | 67.0114i | −1.03659 | + | 0.109686i | ||||
\(73\) | 434.467 | + | 250.840i | 0.696582 | + | 0.402172i | 0.806073 | − | 0.591816i | \(-0.201589\pi\) |
−0.109491 | + | 0.993988i | \(0.534922\pi\) | |||||||
\(74\) | −314.047 | − | 181.315i | −0.493341 | − | 0.284831i | ||||
\(75\) | −198.428 | − | 609.970i | −0.305500 | − | 0.939110i | ||||
\(76\) | − | 176.234i | − | 0.265993i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 190.144 | + | 40.3465i | 0.276020 | + | 0.0585685i | ||||
\(79\) | 30.9561 | + | 53.6176i | 0.0440865 | + | 0.0763601i | 0.887227 | − | 0.461334i | \(-0.152629\pi\) |
−0.843140 | + | 0.537694i | \(0.819296\pi\) | |||||||
\(80\) | 6.34382 | − | 10.9878i | 0.00886576 | − | 0.0153559i | ||||
\(81\) | −712.856 | + | 152.569i | −0.977855 | + | 0.209285i | ||||
\(82\) | −308.720 | + | 178.240i | −0.415761 | + | 0.240040i | ||||
\(83\) | 73.1180 | 0.0966957 | 0.0483478 | − | 0.998831i | \(-0.484604\pi\) | ||||
0.0483478 | + | 0.998831i | \(0.484604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.627 | −0.166688 | ||||||||
\(86\) | −262.211 | + | 151.388i | −0.328779 | + | 0.189820i | ||||
\(87\) | −817.783 | − | 735.816i | −1.00777 | − | 0.906755i | ||||
\(88\) | 479.870 | − | 831.158i | 0.581298 | − | 1.00684i | ||||
\(89\) | −57.3723 | − | 99.3717i | −0.0683309 | − | 0.118353i | 0.829836 | − | 0.558008i | \(-0.188434\pi\) |
−0.898167 | + | 0.439655i | \(0.855101\pi\) | |||||||
\(90\) | 26.1077 | − | 58.7498i | 0.0305777 | − | 0.0688086i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 350.271i | 0.396938i | ||||||||
\(93\) | 494.251 | − | 160.784i | 0.551090 | − | 0.179274i | ||||
\(94\) | 591.922 | + | 341.746i | 0.649490 | + | 0.374983i | ||||
\(95\) | 43.7025 | + | 25.2316i | 0.0471977 | + | 0.0272496i | ||||
\(96\) | 836.432 | − | 272.098i | 0.889250 | − | 0.289280i | ||||
\(97\) | 1416.51i | 1.48273i | 0.671101 | + | 0.741366i | \(0.265822\pi\) | ||||
−0.671101 | + | 0.741366i | \(0.734178\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 446.156 | − | 1003.98i | 0.452933 | − | 1.01923i | ||||
\(100\) | 268.883 | + | 465.720i | 0.268883 | + | 0.465720i | ||||
\(101\) | −120.406 | + | 208.549i | −0.118622 | + | 0.205459i | −0.919222 | − | 0.393740i | \(-0.871181\pi\) |
0.800600 | + | 0.599199i | \(0.204514\pi\) | |||||||
\(102\) | 772.117 | + | 694.727i | 0.749520 | + | 0.674394i | ||||
\(103\) | 960.453 | − | 554.518i | 0.918799 | − | 0.530469i | 0.0355471 | − | 0.999368i | \(-0.488683\pi\) |
0.883252 | + | 0.468899i | \(0.155349\pi\) | |||||||
\(104\) | −462.226 | −0.435817 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 807.725 | 0.740124 | ||||||||
\(107\) | 924.644 | − | 533.843i | 0.835408 | − | 0.482323i | −0.0202926 | − | 0.999794i | \(-0.506460\pi\) |
0.855701 | + | 0.517471i | \(0.173126\pi\) | |||||||
\(108\) | 558.079 | − | 249.178i | 0.497233 | − | 0.222011i | ||||
\(109\) | −5.04376 | + | 8.73604i | −0.00443215 | + | 0.00767671i | −0.868233 | − | 0.496157i | \(-0.834744\pi\) |
0.863801 | + | 0.503833i | \(0.168077\pi\) | |||||||
\(110\) | 48.4442 | + | 83.9079i | 0.0419907 | + | 0.0727300i | ||||
\(111\) | 965.640 | + | 204.899i | 0.825716 | + | 0.175208i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 884.294i | − | 0.736171i | −0.929792 | − | 0.368086i | \(-0.880013\pi\) | ||
0.929792 | − | 0.368086i | \(-0.119987\pi\) | |||||||
\(114\) | −124.127 | − | 381.568i | −0.101979 | − | 0.313484i | ||||
\(115\) | −86.8602 | − | 50.1487i | −0.0704326 | − | 0.0406643i | ||||
\(116\) | 798.731 | + | 461.148i | 0.639313 | + | 0.369108i | ||||
\(117\) | −526.189 | + | 55.6784i | −0.415780 | + | 0.0439954i | ||||
\(118\) | − | 1194.09i | − | 0.931569i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −31.7330 | + | 149.550i | −0.0241401 | + | 0.113767i | ||||
\(121\) | 162.366 | + | 281.226i | 0.121988 | + | 0.211289i | ||||
\(122\) | 770.976 | − | 1335.37i | 0.572139 | − | 0.990973i | ||||
\(123\) | 649.067 | − | 721.372i | 0.475808 | − | 0.528812i | ||||
\(124\) | −377.366 | + | 217.873i | −0.273294 | + | 0.157787i | ||||
\(125\) | −309.912 | −0.221755 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −840.132 | −0.587005 | −0.293503 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293503 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(128\) | −504.115 | + | 291.051i | −0.348108 | + | 0.200980i | ||||
\(129\) | 551.285 | − | 612.697i | 0.376263 | − | 0.418178i | ||||
\(130\) | 23.3315 | − | 40.4114i | 0.0157408 | − | 0.0272639i | ||||
\(131\) | 258.951 | + | 448.517i | 0.172707 | + | 0.299138i | 0.939366 | − | 0.342918i | \(-0.111415\pi\) |
−0.766658 | + | 0.642056i | \(0.778082\pi\) | |||||||
\(132\) | −191.189 | + | 901.027i | −0.126067 | + | 0.594124i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 569.871i | − | 0.367383i | ||||||
\(135\) | −18.1098 | + | 174.067i | −0.0115455 | + | 0.110973i | ||||
\(136\) | −2139.01 | − | 1234.96i | −1.34866 | − | 0.778651i | ||||
\(137\) | 950.957 | + | 549.035i | 0.593034 | + | 0.342389i | 0.766296 | − | 0.642487i | \(-0.222097\pi\) |
−0.173262 | + | 0.984876i | \(0.555431\pi\) | |||||||
\(138\) | 246.707 | + | 758.380i | 0.152182 | + | 0.467808i | ||||
\(139\) | − | 828.268i | − | 0.505416i | −0.967543 | − | 0.252708i | \(-0.918679\pi\) | ||
0.967543 | − | 0.252708i | \(-0.0813212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1820.06 | − | 386.197i | −1.08707 | − | 0.230664i | ||||
\(142\) | −434.628 | − | 752.797i | −0.256853 | − | 0.444883i | ||||
\(143\) | 398.714 | − | 690.592i | 0.233162 | − | 0.403848i | ||||
\(144\) | 222.060 | − | 161.575i | 0.128507 | − | 0.0935039i | ||||
\(145\) | −228.710 | + | 132.046i | −0.130989 | + | 0.0756264i | ||||
\(146\) | −957.621 | −0.542830 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −827.601 | −0.459651 | ||||||||
\(149\) | 773.007 | − | 446.296i | 0.425015 | − | 0.245382i | −0.272206 | − | 0.962239i | \(-0.587753\pi\) |
0.697221 | + | 0.716857i | \(0.254420\pi\) | |||||||
\(150\) | 910.186 | + | 818.956i | 0.495442 | + | 0.445783i | ||||
\(151\) | −712.518 | + | 1234.12i | −0.383999 | + | 0.665106i | −0.991630 | − | 0.129113i | \(-0.958787\pi\) |
0.607630 | + | 0.794220i | \(0.292120\pi\) | |||||||
\(152\) | 477.083 | + | 826.332i | 0.254583 | + | 0.440950i | ||||
\(153\) | −2583.76 | − | 1148.19i | −1.36526 | − | 0.606705i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 124.772i | − | 0.0646577i | ||||||
\(156\) | 421.851 | − | 137.231i | 0.216507 | − | 0.0704314i | ||||
\(157\) | 244.872 | + | 141.377i | 0.124477 | + | 0.0718670i | 0.560946 | − | 0.827853i | \(-0.310438\pi\) |
−0.436468 | + | 0.899720i | \(0.643771\pi\) | |||||||
\(158\) | −102.347 | − | 59.0900i | −0.0515334 | − | 0.0297528i | ||||
\(159\) | −2090.91 | + | 680.189i | −1.04289 | + | 0.339261i | ||||
\(160\) | − | 211.155i | − | 0.104333i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1032.81 | − | 932.572i | 0.500894 | − | 0.452283i | ||||
\(163\) | −1158.07 | − | 2005.83i | −0.556484 | − | 0.963858i | −0.997786 | − | 0.0664997i | \(-0.978817\pi\) |
0.441303 | − | 0.897358i | \(-0.354516\pi\) | |||||||
\(164\) | −406.781 | + | 704.565i | −0.193685 | + | 0.335471i | ||||
\(165\) | −196.064 | − | 176.412i | −0.0925063 | − | 0.0832342i | ||||
\(166\) | −120.871 | + | 69.7849i | −0.0565145 | + | 0.0326287i | ||||
\(167\) | 2344.70 | 1.08646 | 0.543229 | − | 0.839585i | \(-0.317202\pi\) | ||||
0.543229 | + | 0.839585i | \(0.317202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1812.95 | 0.825192 | ||||||||
\(170\) | 215.939 | − | 124.672i | 0.0974221 | − | 0.0562467i | ||||
\(171\) | 642.640 | + | 883.213i | 0.287391 | + | 0.394977i | ||||
\(172\) | −345.499 | + | 598.423i | −0.153163 | + | 0.265287i | ||||
\(173\) | −516.901 | − | 895.298i | −0.227163 | − | 0.393458i | 0.729803 | − | 0.683657i | \(-0.239612\pi\) |
−0.956966 | + | 0.290199i | \(0.906278\pi\) | |||||||
\(174\) | 2054.15 | + | 435.869i | 0.894969 | + | 0.189903i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 413.872i | 0.177255i | ||||||||
\(177\) | 1005.55 | + | 3091.07i | 0.427016 | + | 1.31265i | ||||
\(178\) | 189.684 | + | 109.514i | 0.0798730 | + | 0.0461147i | ||||
\(179\) | −125.472 | − | 72.4412i | −0.0523922 | − | 0.0302486i | 0.473575 | − | 0.880753i | \(-0.342963\pi\) |
−0.525967 | + | 0.850505i | \(0.676297\pi\) | |||||||
\(180\) | −15.4392 | − | 145.908i | −0.00639316 | − | 0.0604186i | ||||
\(181\) | 2057.17i | 0.844797i | 0.906410 | + | 0.422398i | \(0.138812\pi\) | ||||
−0.906410 | + | 0.422398i | \(0.861188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −871.257 | + | 4106.03i | −0.351941 | + | 1.65862i | ||||
\(184\) | −948.219 | − | 1642.36i | −0.379911 | − | 0.658025i | ||||
\(185\) | 118.489 | − | 205.228i | 0.0470889 | − | 0.0815604i | ||||
\(186\) | −663.589 | + | 737.511i | −0.261595 | + | 0.290736i | ||||
\(187\) | 3690.19 | − | 2130.53i | 1.44307 | − | 0.833155i | ||||
\(188\) | 1559.88 | 0.605137 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −96.3259 | −0.0367801 | ||||||||
\(191\) | −2553.66 | + | 1474.36i | −0.967417 | + | 0.558538i | −0.898448 | − | 0.439080i | \(-0.855304\pi\) |
−0.0689690 | + | 0.997619i | \(0.521971\pi\) | |||||||
\(192\) | −1405.81 | + | 1562.41i | −0.528415 | + | 0.587279i | ||||
\(193\) | 1135.40 | − | 1966.57i | 0.423460 | − | 0.733455i | −0.572815 | − | 0.819685i | \(-0.694149\pi\) |
0.996275 | + | 0.0862300i | \(0.0274820\pi\) | |||||||
\(194\) | −1351.94 | − | 2341.63i | −0.500329 | − | 0.866594i | ||||
\(195\) | −26.3662 | + | 124.258i | −0.00968270 | + | 0.0456323i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 495.849i | − | 0.179329i | −0.995972 | − | 0.0896645i | \(-0.971421\pi\) | ||
0.995972 | − | 0.0896645i | \(-0.0285795\pi\) | |||||||
\(198\) | 220.675 | + | 2085.49i | 0.0792055 | + | 0.748532i | ||||
\(199\) | −727.207 | − | 419.853i | −0.259047 | − | 0.149561i | 0.364853 | − | 0.931065i | \(-0.381119\pi\) |
−0.623900 | + | 0.781504i | \(0.714453\pi\) | |||||||
\(200\) | −2521.50 | − | 1455.79i | −0.891484 | − | 0.514699i | ||||
\(201\) | 479.890 | + | 1475.19i | 0.168402 | + | 0.517670i | ||||
\(202\) | − | 459.668i | − | 0.160109i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2318.81 | + | 492.028i | 0.795831 | + | 0.168867i | ||||
\(205\) | −116.479 | − | 201.747i | −0.0396840 | − | 0.0687347i | ||||
\(206\) | −1058.48 | + | 1833.34i | −0.357999 | + | 0.620073i | ||||
\(207\) | −1277.27 | − | 1755.42i | −0.428871 | − | 0.589420i | ||||
\(208\) | 172.623 | − | 99.6638i | 0.0575444 | − | 0.0332233i | ||||
\(209\) | −1646.12 | −0.544805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4001.71 | 1.30564 | 0.652818 | − | 0.757514i | \(-0.273586\pi\) | ||||
0.652818 | + | 0.757514i | \(0.273586\pi\) | |||||||
\(212\) | 1596.43 | − | 921.701i | 0.517186 | − | 0.298598i | ||||
\(213\) | 1759.03 | + | 1582.72i | 0.565852 | + | 0.509136i | ||||
\(214\) | −1019.02 | + | 1764.99i | −0.325507 | + | 0.563795i | ||||
\(215\) | −98.9311 | − | 171.354i | −0.0313816 | − | 0.0543545i | ||||
\(216\) | −1942.19 | + | 2679.13i | −0.611803 | + | 0.843943i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 19.2554i | − | 0.00598228i | ||||||
\(219\) | 2478.93 | − | 806.416i | 0.764889 | − | 0.248825i | ||||
\(220\) | 191.496 | + | 110.560i | 0.0586848 | + | 0.0338817i | ||||
\(221\) | −1777.26 | − | 1026.10i | −0.540955 | − | 0.312321i | ||||
\(222\) | −1791.85 | + | 582.905i | −0.541718 | + | 0.176225i | ||||
\(223\) | − | 3040.54i | − | 0.913047i | −0.889711 | − | 0.456523i | \(-0.849095\pi\) | ||
0.889711 | − | 0.456523i | \(-0.150905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3045.79 | − | 1353.51i | −0.902455 | − | 0.401040i | ||||
\(226\) | 843.984 | + | 1461.82i | 0.248411 | + | 0.430261i | ||||
\(227\) | −2198.24 | + | 3807.46i | −0.642741 | + | 1.11326i | 0.342078 | + | 0.939672i | \(0.388869\pi\) |
−0.984818 | + | 0.173588i | \(0.944464\pi\) | |||||||
\(228\) | −680.742 | − | 612.510i | −0.197734 | − | 0.177914i | ||||
\(229\) | 1717.81 | − | 991.778i | 0.495703 | − | 0.286194i | −0.231234 | − | 0.972898i | \(-0.574276\pi\) |
0.726937 | + | 0.686704i | \(0.240943\pi\) | |||||||
\(230\) | 191.451 | 0.0548865 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4993.49 | −1.41310 | ||||||||
\(233\) | −3787.78 | + | 2186.87i | −1.06500 | + | 0.614879i | −0.926812 | − | 0.375526i | \(-0.877462\pi\) |
−0.138191 | + | 0.990406i | \(0.544129\pi\) | |||||||
\(234\) | 816.701 | − | 594.245i | 0.228160 | − | 0.166013i | ||||
\(235\) | −223.329 | + | 386.818i | −0.0619932 | + | 0.107375i | ||||
\(236\) | −1362.59 | − | 2360.07i | −0.375834 | − | 0.650964i | ||||
\(237\) | 314.699 | + | 66.7758i | 0.0862527 | + | 0.0183019i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3826.41i | 1.03561i | 0.855500 | + | 0.517803i | \(0.173250\pi\) | ||||
−0.855500 | + | 0.517803i | \(0.826750\pi\) | |||||||
\(240\) | −20.3946 | − | 62.6931i | −0.00548526 | − | 0.0168618i | ||||
\(241\) | −2979.03 | − | 1719.94i | −0.796250 | − | 0.459715i | 0.0459083 | − | 0.998946i | \(-0.485382\pi\) |
−0.842158 | + | 0.539231i | \(0.818715\pi\) | |||||||
\(242\) | −536.813 | − | 309.929i | −0.142594 | − | 0.0823264i | ||||
\(243\) | −1888.24 | + | 3283.82i | −0.498479 | + | 0.866902i | ||||
\(244\) | − | 3519.07i | − | 0.923300i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −384.483 | + | 1811.98i | −0.0996493 | + | 0.469624i | ||||
\(247\) | 396.398 | + | 686.582i | 0.102114 | + | 0.176867i | ||||
\(248\) | 1179.61 | − | 2043.14i | 0.302036 | − | 0.523142i | ||||
\(249\) | 254.125 | − | 282.434i | 0.0646768 | − | 0.0718816i | ||||
\(250\) | 512.314 | − | 295.785i | 0.129606 | − | 0.0748282i | ||||
\(251\) | 2046.61 | 0.514664 | 0.257332 | − | 0.966323i | \(-0.417157\pi\) | ||||
0.257332 | + | 0.966323i | \(0.417157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3271.72 | 0.813008 | ||||||||
\(254\) | 1388.82 | − | 801.835i | 0.343080 | − | 0.198077i | ||||
\(255\) | −454.000 | + | 504.575i | −0.111493 | + | 0.123913i | ||||
\(256\) | 2173.51 | − | 3764.63i | 0.530642 | − | 0.919099i | ||||
\(257\) | 3025.57 | + | 5240.44i | 0.734357 | + | 1.27194i | 0.955005 | + | 0.296590i | \(0.0958496\pi\) |
−0.220648 | + | 0.975354i | \(0.570817\pi\) | |||||||
\(258\) | −326.560 | + | 1539.00i | −0.0788014 | + | 0.371372i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 106.495i | − | 0.0254021i | ||||||
\(261\) | −5684.49 | + | 601.501i | −1.34813 | + | 0.142651i | ||||
\(262\) | −856.143 | − | 494.294i | −0.201880 | − | 0.116556i | ||||
\(263\) | 5433.69 | + | 3137.14i | 1.27398 | + | 0.735530i | 0.975734 | − | 0.218960i | \(-0.0702665\pi\) |
0.298242 | + | 0.954490i | \(0.403600\pi\) | |||||||
\(264\) | −1542.72 | − | 4742.33i | −0.359650 | − | 1.10557i | ||||
\(265\) | 527.844i | 0.122359i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −583.245 | − | 123.758i | −0.133685 | − | 0.0283666i | ||||
\(268\) | −650.284 | − | 1126.32i | −0.148218 | − | 0.256721i | ||||
\(269\) | 1668.18 | − | 2889.37i | 0.378106 | − | 0.654899i | −0.612681 | − | 0.790331i | \(-0.709909\pi\) |
0.990787 | + | 0.135432i | \(0.0432421\pi\) | |||||||
\(270\) | −136.195 | − | 305.034i | −0.0306985 | − | 0.0687548i | ||||
\(271\) | −2462.26 | + | 1421.59i | −0.551925 | + | 0.318654i | −0.749898 | − | 0.661553i | \(-0.769897\pi\) |
0.197973 | + | 0.980207i | \(0.436564\pi\) | |||||||
\(272\) | 1065.11 | 0.237433 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2096.03 | −0.462138 | ||||||||
\(275\) | 4350.06 | − | 2511.51i | 0.953886 | − | 0.550726i | ||||
\(276\) | 1353.00 | + | 1217.39i | 0.295076 | + | 0.265500i | ||||
\(277\) | −3174.17 | + | 5497.82i | −0.688510 | + | 1.19253i | 0.283809 | + | 0.958881i | \(0.408402\pi\) |
−0.972320 | + | 0.233654i | \(0.924932\pi\) | |||||||
\(278\) | 790.512 | + | 1369.21i | 0.170546 | + | 0.295394i | ||||
\(279\) | 1096.73 | − | 2467.96i | 0.235339 | − | 0.529580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3735.88i | − | 0.793110i | −0.918011 | − | 0.396555i | \(-0.870206\pi\) | ||
0.918011 | − | 0.396555i | \(-0.129794\pi\) | |||||||
\(282\) | 3377.32 | − | 1098.67i | 0.713179 | − | 0.232003i | ||||
\(283\) | 4777.96 | + | 2758.56i | 1.00361 | + | 0.579432i | 0.909313 | − | 0.416112i | \(-0.136608\pi\) |
0.0942927 | + | 0.995545i | \(0.469941\pi\) | |||||||
\(284\) | −1718.05 | − | 991.914i | −0.358969 | − | 0.207251i | ||||
\(285\) | 249.353 | − | 81.1164i | 0.0518259 | − | 0.0168594i | ||||
\(286\) | 1522.15i | 0.314709i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1856.02 | − | 4176.59i | 0.379747 | − | 0.854541i | ||||
\(289\) | −3026.48 | − | 5242.01i | −0.616014 | − | 1.06697i | ||||
\(290\) | 252.054 | − | 436.570i | 0.0510383 | − | 0.0884008i | ||||
\(291\) | 5471.58 | + | 4923.16i | 1.10223 | + | 0.991755i | ||||
\(292\) | −1892.70 | + | 1092.75i | −0.379321 | + | 0.219001i | ||||
\(293\) | −7574.50 | −1.51026 | −0.755131 | − | 0.655574i | \(-0.772427\pi\) | ||||
−0.755131 | + | 0.655574i | \(0.772427\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 780.333 | 0.154009 | ||||||||
\(296\) | 3880.48 | − | 2240.40i | 0.761988 | − | 0.439934i | ||||
\(297\) | −2327.45 | − | 5212.75i | −0.454721 | − | 1.01843i | ||||
\(298\) | −851.904 | + | 1475.54i | −0.165602 | + | 0.286831i | ||||
\(299\) | −787.855 | − | 1364.61i | −0.152384 | − | 0.263937i | ||||
\(300\) | 2733.46 | + | 580.012i | 0.526055 | + | 0.111623i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 2720.15i | − | 0.518302i | ||||||
\(303\) | 387.088 | + | 1189.91i | 0.0733915 | + | 0.225606i | ||||
\(304\) | −356.343 | − | 205.735i | −0.0672291 | − | 0.0388148i | ||||
\(305\) | 872.657 | + | 503.829i | 0.163830 | + | 0.0945874i | ||||
\(306\) | 5367.06 | − | 567.912i | 1.00266 | − | 0.106096i | ||||
\(307\) | 10635.6i | 1.97723i | 0.150480 | + | 0.988613i | \(0.451918\pi\) | ||||
−0.150480 | + | 0.988613i | \(0.548082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1196.16 | − | 5637.21i | 0.220217 | − | 1.03783i | ||||
\(310\) | 119.085 | + | 206.261i | 0.0218179 | + | 0.0377897i | ||||
\(311\) | 2885.59 | − | 4997.99i | 0.526132 | − | 0.911287i | −0.473405 | − | 0.880845i | \(-0.656975\pi\) |
0.999537 | − | 0.0304419i | \(-0.00969146\pi\) | |||||||
\(312\) | −1606.49 | + | 1785.45i | −0.291505 | + | 0.323978i | ||||
\(313\) | 2030.41 | − | 1172.26i | 0.366664 | − | 0.211694i | −0.305336 | − | 0.952245i | \(-0.598769\pi\) |
0.672000 | + | 0.740551i | \(0.265435\pi\) | |||||||
\(314\) | −539.730 | −0.0970023 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −269.712 | −0.0480142 | ||||||||
\(317\) | −6852.10 | + | 3956.06i | −1.21405 | + | 0.700929i | −0.963638 | − | 0.267211i | \(-0.913898\pi\) |
−0.250407 | + | 0.968141i | \(0.580565\pi\) | |||||||
\(318\) | 2807.29 | − | 3120.01i | 0.495047 | − | 0.550193i | ||||
\(319\) | 4307.36 | − | 7460.56i | 0.756005 | − | 1.30944i | ||||
\(320\) | 252.280 | + | 436.962i | 0.0440715 | + | 0.0763341i | ||||
\(321\) | 1151.56 | − | 5427.03i | 0.200230 | − | 0.943637i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4236.32i | 0.729769i | ||||||||
\(324\) | 977.130 | − | 3021.73i | 0.167546 | − | 0.518129i | ||||
\(325\) | −2095.06 | − | 1209.58i | −0.357579 | − | 0.206448i | ||||
\(326\) | 3828.79 | + | 2210.55i | 0.650482 | + | 0.375556i | ||||
\(327\) | 16.2150 | + | 49.8451i | 0.00274218 | + | 0.00842949i | ||||
\(328\) | − | 4404.78i | − | 0.741505i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 492.482 | + | 104.500i | 0.0821523 | + | 0.0174319i | ||||
\(331\) | 2440.02 | + | 4226.23i | 0.405182 | + | 0.701797i | 0.994343 | − | 0.106220i | \(-0.0338747\pi\) |
−0.589160 | + | 0.808016i | \(0.700541\pi\) | |||||||
\(332\) | −159.264 | + | 275.854i | −0.0263276 | + | 0.0456007i | ||||
\(333\) | 4147.59 | − | 3017.86i | 0.682543 | − | 0.496629i | ||||
\(334\) | −3876.02 | + | 2237.82i | −0.634989 | + | 0.366611i | ||||
\(335\) | 372.407 | 0.0607367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4136.39 | −0.668616 | −0.334308 | − | 0.942464i | \(-0.608503\pi\) | ||||
−0.334308 | + | 0.942464i | \(0.608503\pi\) | |||||||
\(338\) | −2996.97 | + | 1730.30i | −0.482290 | + | 0.278450i | ||||
\(339\) | −3415.77 | − | 3073.41i | −0.547255 | − | 0.492403i | ||||
\(340\) | 284.529 | − | 492.819i | 0.0453846 | − | 0.0786085i | ||||
\(341\) | 2035.04 | + | 3524.80i | 0.323178 | + | 0.559761i | ||||
\(342\) | −1905.30 | − | 846.691i | −0.301248 | − | 0.133871i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3741.20i | − | 0.586373i | ||||||
\(345\) | −495.597 | + | 161.222i | −0.0773393 | + | 0.0251591i | ||||
\(346\) | 1708.97 | + | 986.676i | 0.265535 | + | 0.153306i | ||||
\(347\) | 2009.83 | + | 1160.38i | 0.310933 | + | 0.179517i | 0.647344 | − | 0.762198i | \(-0.275880\pi\) |
−0.336411 | + | 0.941715i | \(0.609213\pi\) | |||||||
\(348\) | 4557.31 | − | 1482.53i | 0.702004 | − | 0.228368i | ||||
\(349\) | 226.795i | 0.0347853i | 0.999849 | + | 0.0173926i | \(0.00553653\pi\) | ||||
−0.999849 | + | 0.0173926i | \(0.994463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1613.73 | + | 2226.03i | −0.245397 | + | 0.338509i | ||||
\(352\) | 3443.95 | + | 5965.10i | 0.521486 | + | 0.903241i | ||||
\(353\) | −742.854 | + | 1286.66i | −0.112006 | + | 0.194000i | −0.916579 | − | 0.399854i | \(-0.869061\pi\) |
0.804573 | + | 0.593854i | \(0.202394\pi\) | |||||||
\(354\) | −4612.44 | − | 4150.13i | −0.692509 | − | 0.623098i | ||||
\(355\) | 491.949 | − | 284.027i | 0.0735491 | − | 0.0424636i | ||||
\(356\) | 499.869 | 0.0744185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 276.556 | 0.0408280 | ||||||||
\(359\) | 9419.94 | − | 5438.60i | 1.38486 | − | 0.799550i | 0.392131 | − | 0.919909i | \(-0.371738\pi\) |
0.992730 | + | 0.120359i | \(0.0384045\pi\) | |||||||
\(360\) | 467.380 | + | 642.344i | 0.0684252 | + | 0.0940402i | ||||
\(361\) | −2611.22 | + | 4522.77i | −0.380700 | + | 0.659392i | ||||
\(362\) | −1963.39 | − | 3400.70i | −0.285066 | − | 0.493748i | ||||
\(363\) | 1650.61 | + | 350.241i | 0.238662 | + | 0.0506416i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 625.800i | − | 0.0897421i | ||||||
\(366\) | −2478.59 | − | 7619.21i | −0.353983 | − | 1.08815i | ||||
\(367\) | 3299.69 | + | 1905.08i | 0.469325 | + | 0.270965i | 0.715957 | − | 0.698144i | \(-0.245991\pi\) |
−0.246632 | + | 0.969109i | \(0.579324\pi\) | |||||||
\(368\) | 708.243 | + | 408.904i | 0.100325 | + | 0.0579229i | ||||
\(369\) | −530.587 | − | 5014.32i | −0.0748544 | − | 0.707413i | ||||
\(370\) | 452.349i | 0.0635581i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −469.976 | + | 2214.89i | −0.0655030 | + | 0.308700i | ||||
\(373\) | 4869.55 | + | 8434.30i | 0.675967 | + | 1.17081i | 0.976185 | + | 0.216938i | \(0.0696070\pi\) |
−0.300219 | + | 0.953870i | \(0.597060\pi\) | |||||||
\(374\) | −4066.83 | + | 7043.95i | −0.562274 | + | 0.973888i | ||||
\(375\) | −1077.11 | + | 1197.10i | −0.148325 | + | 0.164848i | ||||
\(376\) | −7314.00 | + | 4222.74i | −1.00317 | + | 0.579179i | ||||
\(377\) | −4148.98 | −0.566800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 320.171 | 0.0433933 | 0.0216967 | − | 0.999765i | \(-0.493093\pi\) | ||||
0.0216967 | + | 0.999765i | \(0.493093\pi\) | |||||||
\(380\) | −190.384 | + | 109.918i | −0.0257013 | + | 0.0148386i | ||||
\(381\) | −2919.92 | + | 3245.19i | −0.392630 | + | 0.436368i | ||||
\(382\) | 2814.30 | − | 4874.51i | 0.376943 | − | 0.652884i | ||||
\(383\) | 2185.13 | + | 3784.75i | 0.291527 | + | 0.504939i | 0.974171 | − | 0.225812i | \(-0.0725034\pi\) |
−0.682644 | + | 0.730751i | \(0.739170\pi\) | |||||||
\(384\) | −627.829 | + | 2958.81i | −0.0834343 | + | 0.393206i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4334.57i | 0.571564i | ||||||||
\(387\) | −450.654 | − | 4258.92i | −0.0591939 | − | 0.559413i | ||||
\(388\) | −5344.11 | − | 3085.42i | −0.699242 | − | 0.403708i | ||||
\(389\) | −11877.4 | − | 6857.42i | −1.54809 | − | 0.893791i | −0.998288 | − | 0.0584981i | \(-0.981369\pi\) |
−0.549805 | − | 0.835293i | \(-0.685298\pi\) | |||||||
\(390\) | −75.0078 | − | 230.575i | −0.00973889 | − | 0.0299375i | ||||
\(391\) | − | 8419.84i | − | 1.08903i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2632.49 | + | 558.587i | 0.337892 | + | 0.0716971i | ||||
\(394\) | 473.246 | + | 819.687i | 0.0605122 | + | 0.104810i | ||||
\(395\) | 38.6150 | − | 66.8832i | 0.00491882 | − | 0.00851964i | ||||
\(396\) | 2815.93 | + | 3870.07i | 0.357337 | + | 0.491107i | ||||
\(397\) | 2181.61 | − | 1259.55i | 0.275798 | − | 0.159232i | −0.355722 | − | 0.934592i | \(-0.615765\pi\) |
0.631520 | + | 0.775360i | \(0.282432\pi\) | |||||||
\(398\) | 1602.86 | 0.201869 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1255.57 | 0.156946 | ||||||||
\(401\) | −2268.96 | + | 1309.98i | −0.282560 | + | 0.163136i | −0.634582 | − | 0.772856i | \(-0.718828\pi\) |
0.352022 | + | 0.935992i | \(0.385494\pi\) | |||||||
\(402\) | −2201.25 | − | 1980.61i | −0.273105 | − | 0.245731i | ||||
\(403\) | 980.109 | − | 1697.60i | 0.121148 | − | 0.209835i | ||||
\(404\) | −524.530 | − | 908.513i | −0.0645950 | − | 0.111882i | ||||
\(405\) | 609.431 | + | 674.933i | 0.0747725 | + | 0.0828091i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7730.22i | 0.941456i | ||||||||
\(408\) | −12204.5 | + | 3970.22i | −1.48091 | + | 0.481753i | ||||
\(409\) | 12058.7 | + | 6962.09i | 1.45786 | + | 0.841694i | 0.998906 | − | 0.0467669i | \(-0.0148918\pi\) |
0.458952 | + | 0.888461i | \(0.348225\pi\) | |||||||
\(410\) | 385.101 | + | 222.338i | 0.0463872 | + | 0.0267817i | ||||
\(411\) | 5425.86 | − | 1765.08i | 0.651187 | − | 0.211836i | ||||
\(412\) | 4831.36i | 0.577729i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3786.85 | + | 1682.83i | 0.449549 | + | 0.199774i | ||||
\(415\) | −45.6041 | − | 78.9886i | −0.00539426 | − | 0.00934313i | ||||
\(416\) | 1658.66 | − | 2872.89i | 0.195487 | − | 0.338593i | ||||
\(417\) | −3199.36 | − | 2878.69i | −0.375716 | − | 0.338057i | ||||
\(418\) | 2721.19 | − | 1571.08i | 0.318416 | − | 0.183837i | ||||
\(419\) | 15171.1 | 1.76887 | 0.884433 | − | 0.466666i | \(-0.154545\pi\) | ||||
0.884433 | + | 0.466666i | \(0.154545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1052.53 | −0.121846 | −0.0609228 | − | 0.998142i | \(-0.519404\pi\) | ||||
−0.0609228 | + | 0.998142i | \(0.519404\pi\) | |||||||
\(422\) | −6615.22 | + | 3819.30i | −0.763090 | + | 0.440570i | ||||
\(423\) | −7817.47 | + | 5688.11i | −0.898577 | + | 0.653819i | ||||
\(424\) | −4990.27 | + | 8643.40i | −0.571578 | + | 0.990002i | ||||
\(425\) | −6463.43 | − | 11195.0i | −0.737700 | − | 1.27773i | ||||
\(426\) | −4418.41 | − | 937.541i | −0.502518 | − | 0.106629i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4651.23i | 0.525294i | ||||||||
\(429\) | −1281.81 | − | 3940.30i | −0.144258 | − | 0.443449i | ||||
\(430\) | 327.085 | + | 188.843i | 0.0366824 | + | 0.0211786i | ||||
\(431\) | −6923.58 | − | 3997.33i | −0.773776 | − | 0.446740i | 0.0604442 | − | 0.998172i | \(-0.480748\pi\) |
−0.834220 | + | 0.551432i | \(0.814082\pi\) | |||||||
\(432\) | 147.665 | − | 1419.32i | 0.0164456 | − | 0.158072i | ||||
\(433\) | 12889.4i | 1.43055i | 0.698845 | + | 0.715273i | \(0.253697\pi\) | ||||
−0.698845 | + | 0.715273i | \(0.746303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −284.838 | + | 1342.38i | −0.0313953 | + | 0.147959i | ||||
\(436\) | −21.9724 | − | 38.0574i | −0.00241351 | − | 0.00418032i | ||||
\(437\) | −1626.36 | + | 2816.94i | −0.178030 | + | 0.308358i | ||||
\(438\) | −3328.26 | + | 3699.02i | −0.363083 | + | 0.403529i | ||||
\(439\) | −12456.7 | + | 7191.89i | −1.35427 | + | 0.781891i | −0.988845 | − | 0.148948i | \(-0.952411\pi\) |
−0.365430 | + | 0.930839i | \(0.619078\pi\) | |||||||
\(440\) | −1197.19 | −0.129713 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3917.30 | 0.421554 | ||||||||
\(443\) | −3432.16 | + | 1981.56i | −0.368097 | + | 0.212521i | −0.672627 | − | 0.739982i | \(-0.734834\pi\) |
0.304530 | + | 0.952503i | \(0.401501\pi\) | |||||||
\(444\) | −2876.37 | + | 3196.79i | −0.307447 | + | 0.341695i | ||||
\(445\) | −71.5668 | + | 123.957i | −0.00762380 | + | 0.0132048i | ||||
\(446\) | 2901.94 | + | 5026.30i | 0.308096 | + | 0.533637i | ||||
\(447\) | 962.710 | − | 4537.03i | 0.101867 | − | 0.480076i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13479.1i | − | 1.41675i | −0.705838 | − | 0.708373i | \(-0.749430\pi\) | ||
0.705838 | − | 0.708373i | \(-0.250570\pi\) | |||||||
\(450\) | 6326.79 | − | 669.465i | 0.662773 | − | 0.0701308i | ||||
\(451\) | 6581.00 | + | 3799.54i | 0.687112 | + | 0.396704i | ||||
\(452\) | 3336.19 | + | 1926.15i | 0.347171 | + | 0.200439i | ||||
\(453\) | 2290.65 | + | 7041.49i | 0.237581 | + | 0.730327i | ||||
\(454\) | − | 8392.13i | − | 0.867538i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4850.01 | + | 1029.12i | 0.498076 | + | 0.105686i | ||||
\(457\) | −1989.79 | − | 3446.42i | −0.203673 | − | 0.352772i | 0.746036 | − | 0.665905i | \(-0.231955\pi\) |
−0.949709 | + | 0.313134i | \(0.898621\pi\) | |||||||
\(458\) | −1893.14 | + | 3279.01i | −0.193145 | + | 0.334537i | ||||
\(459\) | −13415.1 | + | 5989.74i | −1.36419 | + | 0.609101i | ||||
\(460\) | 378.395 | − | 218.466i | 0.0383538 | − | 0.0221436i | ||||
\(461\) | −9053.72 | −0.914694 | −0.457347 | − | 0.889288i | \(-0.651200\pi\) | ||||
−0.457347 | + | 0.889288i | \(0.651200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5736.10 | −0.575764 | −0.287882 | − | 0.957666i | \(-0.592951\pi\) | ||||
−0.287882 | + | 0.957666i | \(0.592951\pi\) | |||||||
\(464\) | 1864.87 | − | 1076.68i | 0.186582 | − | 0.107723i | ||||
\(465\) | −481.960 | − | 433.652i | −0.0480653 | − | 0.0432476i | ||||
\(466\) | 4174.37 | − | 7230.23i | 0.414966 | − | 0.718742i | ||||
\(467\) | −6196.30 | − | 10732.3i | −0.613984 | − | 1.06345i | −0.990562 | − | 0.137067i | \(-0.956232\pi\) |
0.376578 | − | 0.926385i | \(-0.377101\pi\) | |||||||
\(468\) | 936.077 | − | 2106.44i | 0.0924576 | − | 0.208056i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 852.596i | − | 0.0836752i | ||||||
\(471\) | 1397.17 | − | 454.509i | 0.136684 | − | 0.0444643i | ||||
\(472\) | 12777.9 | + | 7377.32i | 1.24608 | + | 0.719425i | ||||
\(473\) | 5589.57 | + | 3227.14i | 0.543359 | + | 0.313709i | ||||
\(474\) | −583.959 | + | 189.967i | −0.0565868 | + | 0.0184081i | ||||
\(475\) | 4993.85i | 0.482387i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4639.67 | + | 10440.6i | −0.445359 | + | 1.00219i | ||||
\(478\) | −3651.98 | − | 6325.42i | −0.349452 | − | 0.605268i | ||||
\(479\) | −4133.87 | + | 7160.07i | −0.394324 | + | 0.682989i | −0.993015 | − | 0.117991i | \(-0.962355\pi\) |
0.598691 | + | 0.800980i | \(0.295688\pi\) | |||||||
\(480\) | −815.632 | − | 733.880i | −0.0775590 | − | 0.0697851i | ||||
\(481\) | 3224.21 | − | 1861.50i | 0.305637 | − | 0.176460i | ||||
\(482\) | 6566.17 | 0.620499 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1414.65 | −0.132856 | ||||||||
\(485\) | 1530.24 | − | 883.487i | 0.143268 | − | 0.0827156i | ||||
\(486\) | −12.6949 | − | 7230.63i | −0.00118488 | − | 0.674873i | ||||
\(487\) | −470.075 | + | 814.194i | −0.0437395 | + | 0.0757590i | −0.887066 | − | 0.461642i | \(-0.847260\pi\) |
0.843327 | + | 0.537401i | \(0.180594\pi\) | |||||||
\(488\) | 9526.46 | + | 16500.3i | 0.883694 | + | 1.53060i | ||||
\(489\) | −11772.9 | − | 2498.08i | −1.08873 | − | 0.231017i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1057.30i | 0.0971801i | 0.998819 | + | 0.0485900i | \(0.0154728\pi\) | ||||
−0.998819 | + | 0.0485900i | \(0.984527\pi\) | |||||||
\(492\) | 1307.75 | + | 4020.03i | 0.119833 | + | 0.368368i | ||||
\(493\) | −19199.9 | − | 11085.1i | −1.75400 | − | 1.01267i | ||||
\(494\) | −1310.57 | − | 756.658i | −0.119363 | − | 0.0689142i | ||||
\(495\) | −1362.86 | + | 144.210i | −0.123749 | + | 0.0130944i | ||||
\(496\) | 1017.37i | 0.0920995i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −150.534 | + | 709.431i | −0.0135454 | + | 0.0638361i | ||||
\(499\) | 3086.65 | + | 5346.23i | 0.276909 | + | 0.479620i | 0.970615 | − | 0.240638i | \(-0.0773568\pi\) |
−0.693706 | + | 0.720258i | \(0.744023\pi\) | |||||||
\(500\) | 675.044 | − | 1169.21i | 0.0603778 | − | 0.104577i | ||||
\(501\) | 8149.12 | − | 9056.91i | 0.726699 | − | 0.807651i | ||||
\(502\) | −3383.24 | + | 1953.31i | −0.300800 | + | 0.173667i | ||||
\(503\) | 4284.28 | 0.379775 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 300.390 | 0.0264697 | ||||||||
\(506\) | −5408.46 | + | 3122.58i | −0.475169 | + | 0.274339i | ||||
\(507\) | 6300.98 | − | 7002.89i | 0.551946 | − | 0.613431i | ||||
\(508\) | 1829.96 | − | 3169.58i | 0.159826 | − | 0.276826i | ||||
\(509\) | −7550.52 | − | 13077.9i | −0.657507 | − | 1.13884i | −0.981259 | − | 0.192693i | \(-0.938278\pi\) |
0.323752 | − | 0.946142i | \(-0.395056\pi\) | |||||||
\(510\) | 268.932 | − | 1267.42i | 0.0233500 | − | 0.110043i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3640.92i | 0.314272i | ||||||||
\(513\) | 5645.13 | + | 587.315i | 0.485845 | + | 0.0505470i | ||||
\(514\) | −10003.1 | − | 5775.30i | −0.858401 | − | 0.495598i | ||||
\(515\) | −1198.08 | − | 691.712i | −0.102512 | − | 0.0591854i | ||||
\(516\) | 1110.74 | + | 3414.41i | 0.0947624 | + | 0.291301i | ||||
\(517\) | − | 14570.1i | − | 1.23944i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5254.79 | − | 1115.01i | −0.444431 | − | 0.0943037i | ||||
\(520\) | 288.293 | + | 499.338i | 0.0243125 | + | 0.0421104i | ||||
\(521\) | 6894.00 | − | 11940.8i | 0.579715 | − | 1.00410i | −0.415796 | − | 0.909458i | \(-0.636497\pi\) |
0.995512 | − | 0.0946385i | \(-0.0301695\pi\) | |||||||
\(522\) | 8822.93 | − | 6419.71i | 0.739788 | − | 0.538281i | ||||
\(523\) | 832.513 | − | 480.652i | 0.0696047 | − | 0.0401863i | −0.464794 | − | 0.885419i | \(-0.653872\pi\) |
0.534398 | + | 0.845233i | \(0.320538\pi\) | |||||||
\(524\) | −2256.17 | −0.188094 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11976.5 | −0.992780 | ||||||||
\(527\) | 9071.15 | − | 5237.23i | 0.749802 | − | 0.432898i | ||||
\(528\) | 1598.67 | + | 1438.43i | 0.131767 | + | 0.118560i | ||||
\(529\) | −2851.06 | + | 4938.17i | −0.234327 | + | 0.405866i | ||||
\(530\) | −503.783 | − | 872.577i | −0.0412885 | − | 0.0715138i | ||||
\(531\) | 15434.8 | + | 6859.02i | 1.26142 | + | 0.560557i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3659.84i | − | 0.297421i | ||||||
\(534\) | 1082.28 | − | 352.073i | 0.0877054 | − | 0.0285313i | ||||
\(535\) | −1153.41 | − | 665.922i | −0.0932080 | − | 0.0538137i | ||||
\(536\) | 6098.14 | + | 3520.76i | 0.491417 | + | 0.283720i | ||||
\(537\) | −715.903 | + | 232.889i | −0.0575298 | + | 0.0187149i | ||||
\(538\) | 6368.54i | 0.510348i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −617.261 | − | 447.474i | −0.0491902 | − | 0.0356596i | ||||
\(541\) | 597.846 | + | 1035.50i | 0.0475109 | + | 0.0822913i | 0.888803 | − | 0.458290i | \(-0.151538\pi\) |
−0.841292 | + | 0.540581i | \(0.818204\pi\) | |||||||
\(542\) | 2713.57 | − | 4700.04i | 0.215051 | − | 0.372480i | ||||
\(543\) | 7946.26 | + | 7149.79i | 0.628005 | + | 0.565059i | ||||
\(544\) | 15351.3 | − | 8863.09i | 1.20989 | − | 0.698533i | ||||
\(545\) | 12.5833 | 0.000989006 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18601.8 | 1.45403 | 0.727014 | − | 0.686622i | \(-0.240907\pi\) | ||||
0.727014 | + | 0.686622i | \(0.240907\pi\) | |||||||
\(548\) | −4142.71 | + | 2391.80i | −0.322934 | + | 0.186446i | ||||
\(549\) | 12832.3 | + | 17636.1i | 0.997578 | + | 1.37102i | ||||
\(550\) | −4794.05 | + | 8303.53i | −0.371671 | + | 0.643753i | ||||
\(551\) | 4282.34 | + | 7417.24i | 0.331096 | + | 0.573475i | ||||
\(552\) | −9639.56 | − | 2045.41i | −0.743274 | − | 0.157715i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 12117.9i | − | 0.929315i | ||||||
\(555\) | −380.925 | − | 1170.97i | −0.0291340 | − | 0.0895582i | ||||
\(556\) | 3124.83 | + | 1804.12i | 0.238349 | + | 0.137611i | ||||
\(557\) | 5908.09 | + | 3411.04i | 0.449432 | + | 0.259480i | 0.707590 | − | 0.706623i | \(-0.249782\pi\) |
−0.258158 | + | 0.966103i | \(0.583116\pi\) | |||||||
\(558\) | 542.458 | + | 5126.51i | 0.0411543 | + | 0.388929i | ||||
\(559\) | − | 3108.49i | − | 0.235197i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4595.80 | − | 21658.9i | 0.345873 | − | 1.63002i | ||||
\(562\) | 3565.58 | + | 6175.77i | 0.267624 | + | 0.463539i | ||||
\(563\) | 5679.80 | − | 9837.71i | 0.425178 | − | 0.736430i | −0.571259 | − | 0.820770i | \(-0.693545\pi\) |
0.996437 | + | 0.0843399i | \(0.0268782\pi\) | |||||||
\(564\) | 5421.43 | − | 6025.36i | 0.404758 | − | 0.449847i | ||||
\(565\) | −955.293 | + | 551.539i | −0.0711318 | + | 0.0410680i | ||||
\(566\) | −10531.2 | −0.782087 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10740.8 | 0.793443 | ||||||||
\(569\) | 18467.2 | − | 10662.1i | 1.36061 | − | 0.785549i | 0.370905 | − | 0.928671i | \(-0.379047\pi\) |
0.989705 | + | 0.143122i | \(0.0457141\pi\) | |||||||
\(570\) | −334.785 | + | 372.079i | −0.0246011 | + | 0.0273416i | ||||
\(571\) | 7384.00 | − | 12789.5i | 0.541175 | − | 0.937343i | −0.457662 | − | 0.889126i | \(-0.651313\pi\) |
0.998837 | − | 0.0482163i | \(-0.0153537\pi\) | |||||||
\(572\) | 1736.94 | + | 3008.47i | 0.126967 | + | 0.219913i | ||||
\(573\) | −3180.36 | + | 14988.3i | −0.231870 | + | 1.09275i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9925.45i | − | 0.719861i | ||||||
\(576\) | 1149.20 | + | 10860.5i | 0.0831305 | + | 0.785626i | ||||
\(577\) | −16718.5 | − | 9652.44i | −1.20624 | − | 0.696424i | −0.244305 | − | 0.969698i | \(-0.578560\pi\) |
−0.961936 | + | 0.273275i | \(0.911893\pi\) | |||||||
\(578\) | 10006.1 | + | 5777.04i | 0.720069 | + | 0.415732i | ||||
\(579\) | −3650.16 | − | 11220.6i | −0.261996 | − | 0.805377i | ||||
\(580\) | − | 1150.48i | − | 0.0823640i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13743.8 | − | 2916.29i | −0.978863 | − | 0.207705i | ||||
\(583\) | −8609.17 | − | 14911.5i | −0.611587 | − | 1.05930i | ||||
\(584\) | 5916.35 | − | 10247.4i | 0.419213 | − | 0.726099i | ||||
\(585\) | 388.336 | + | 533.710i | 0.0274457 | + | 0.0377200i | ||||
\(586\) | 12521.4 | − | 7229.22i | 0.882684 | − | 0.509618i | ||||
\(587\) | −4397.46 | −0.309204 | −0.154602 | − | 0.987977i | \(-0.549410\pi\) | ||||
−0.154602 | + | 0.987977i | \(0.549410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4046.45 | −0.283075 | ||||||||
\(590\) | −1289.97 | + | 744.762i | −0.0900119 | + | 0.0519684i | ||||
\(591\) | −1915.32 | − | 1723.35i | −0.133310 | − | 0.119948i | ||||
\(592\) | −966.135 | + | 1673.40i | −0.0670742 | + | 0.116176i | ||||
\(593\) | 10970.1 | + | 19000.8i | 0.759677 | + | 1.31580i | 0.943015 | + | 0.332749i | \(0.107976\pi\) |
−0.183339 | + | 0.983050i | \(0.558691\pi\) | |||||||
\(594\) | 8822.62 | + | 6395.82i | 0.609422 | + | 0.441791i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3888.46i | 0.267244i | ||||||||
\(597\) | −4149.21 | + | 1349.77i | −0.284449 | + | 0.0925335i | ||||
\(598\) | 2604.80 | + | 1503.88i | 0.178124 | + | 0.102840i | ||||
\(599\) | −4765.07 | − | 2751.12i | −0.325034 | − | 0.187659i | 0.328600 | − | 0.944469i | \(-0.393423\pi\) |
−0.653634 | + | 0.756810i | \(0.726757\pi\) | |||||||
\(600\) | −14386.9 | + | 4680.17i | −0.978903 | + | 0.318445i | ||||
\(601\) | 5814.58i | 0.394645i | 0.980339 | + | 0.197322i | \(0.0632246\pi\) | ||||
−0.980339 | + | 0.197322i | \(0.936775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7366.11 | + | 3273.41i | 0.497465 | + | 0.221067i | ||||
\(604\) | −3103.99 | − | 5376.27i | −0.209105 | − | 0.362181i | ||||
\(605\) | 202.537 | − | 350.804i | 0.0136104 | − | 0.0235739i | ||||
\(606\) | −1775.56 | − | 1597.60i | −0.119022 | − | 0.107092i | ||||
\(607\) | 11510.7 | − | 6645.69i | 0.769693 | − | 0.444382i | −0.0630721 | − | 0.998009i | \(-0.520090\pi\) |
0.832765 | + | 0.553627i | \(0.186756\pi\) | |||||||
\(608\) | −6847.90 | −0.456775 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1923.45 | −0.127669 | ||||||||
\(611\) | −6077.05 | + | 3508.59i | −0.402375 | + | 0.232311i | ||||
\(612\) | 9959.72 | − | 7246.85i | 0.657839 | − | 0.478655i | ||||
\(613\) | −9797.17 | + | 16969.2i | −0.645520 | + | 1.11807i | 0.338661 | + | 0.940909i | \(0.390026\pi\) |
−0.984181 | + | 0.177166i | \(0.943307\pi\) | |||||||
\(614\) | −10150.8 | − | 17581.7i | −0.667189 | − | 1.15561i | ||||
\(615\) | −1184.12 | − | 251.257i | −0.0776394 | − | 0.0164743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 348.388i | 0.0227319i | 0.999935 | + | 0.0113660i | \(0.00361797\pi\) | ||||
−0.999935 | + | 0.0113660i | \(0.996382\pi\) | |||||||
\(618\) | 3402.88 | + | 10460.5i | 0.221495 | + | 0.680878i | ||||
\(619\) | −5867.68 | − | 3387.71i | −0.381005 | − | 0.219973i | 0.297251 | − | 0.954799i | \(-0.403930\pi\) |
−0.678255 | + | 0.734826i | \(0.737264\pi\) | |||||||
\(620\) | 470.731 | + | 271.777i | 0.0304920 | + | 0.0176045i | ||||
\(621\) | −11219.9 | − | 1167.31i | −0.725022 | − | 0.0754307i | ||||
\(622\) | 11016.2i | 0.710145i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 214.986 | − | 1013.18i | 0.0137922 | − | 0.0649994i | ||||
\(625\) | −7521.95 | − | 13028.4i | −0.481405 | − | 0.833818i | ||||
\(626\) | −2237.65 | + | 3875.72i | −0.142866 | + | 0.247452i | ||||
\(627\) | −5721.16 | + | 6358.48i | −0.364404 | + | 0.404997i | ||||
\(628\) | −1066.75 | + | 615.890i | −0.0677836 | + | 0.0391349i | ||||
\(629\) | 19893.9 | 1.26108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7326.82 | −0.462244 | −0.231122 | − | 0.972925i | \(-0.574240\pi\) | ||||
−0.231122 | + | 0.972925i | \(0.574240\pi\) | |||||||
\(632\) | 1264.64 | − | 730.138i | 0.0795957 | − | 0.0459546i | ||||
\(633\) | 13908.2 | − | 15457.5i | 0.873301 | − | 0.970584i | ||||
\(634\) | 7551.46 | − | 13079.5i | 0.473039 | − | 0.819327i | ||||
\(635\) | 523.995 | + | 907.586i | 0.0327466 | + | 0.0567188i | ||||
\(636\) | 1988.21 | − | 9369.98i | 0.123959 | − | 0.584189i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16444.0i | 1.02042i | ||||||||
\(639\) | 12227.2 | − | 1293.81i | 0.756963 | − | 0.0800975i | ||||
\(640\) | 628.838 | + | 363.060i | 0.0388391 | + | 0.0224238i | ||||
\(641\) | −2433.38 | − | 1404.91i | −0.149942 | − | 0.0865689i | 0.423152 | − | 0.906059i | \(-0.360924\pi\) |
−0.573094 | + | 0.819490i | \(0.694257\pi\) | |||||||
\(642\) | 3276.01 | + | 10070.5i | 0.201392 | + | 0.619081i | ||||
\(643\) | − | 27485.5i | − | 1.68573i | −0.538128 | − | 0.842863i | \(-0.680868\pi\) | ||
0.538128 | − | 0.842863i | \(-0.319132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1005.73 | − | 213.405i | −0.0613962 | − | 0.0130276i | ||||
\(646\) | −4043.21 | − | 7003.05i | −0.246251 | − | 0.426519i | ||||
\(647\) | −14659.9 | + | 25391.7i | −0.890790 | + | 1.54289i | −0.0518595 | + | 0.998654i | \(0.516515\pi\) |
−0.838930 | + | 0.544239i | \(0.816819\pi\) | |||||||
\(648\) | 3598.53 | + | 16813.6i | 0.218153 | + | 1.01929i | ||||
\(649\) | −22044.3 | + | 12727.3i | −1.33330 | + | 0.769783i | ||||
\(650\) | 4617.78 | 0.278653 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10089.9 | 0.606061 | ||||||||
\(653\) | −14500.6 | + | 8371.91i | −0.868992 | + | 0.501713i | −0.867013 | − | 0.498285i | \(-0.833963\pi\) |
−0.00197863 | + | 0.999998i | \(0.500630\pi\) | |||||||
\(654\) | −74.3780 | − | 66.9229i | −0.00444711 | − | 0.00400137i | ||||
\(655\) | 323.019 | − | 559.485i | 0.0192693 | − | 0.0333754i | ||||
\(656\) | 949.747 | + | 1645.01i | 0.0565265 | + | 0.0979068i | ||||
\(657\) | 5500.69 | − | 12378.1i | 0.326640 | − | 0.735034i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9520.47i | 0.562769i | 0.959595 | + | 0.281385i | \(0.0907937\pi\) | ||||
−0.959595 | + | 0.281385i | \(0.909206\pi\) | |||||||
\(660\) | 1092.62 | − | 355.437i | 0.0644394 | − | 0.0209626i | ||||
\(661\) | 20217.5 | + | 11672.6i | 1.18966 | + | 0.686853i | 0.958230 | − | 0.285998i | \(-0.0923250\pi\) |
0.231434 | + | 0.972851i | \(0.425658\pi\) | |||||||
\(662\) | −8067.16 | − | 4657.58i | −0.473624 | − | 0.273447i | ||||
\(663\) | −10140.5 | + | 3298.77i | −0.594002 | + | 0.193233i | ||||
\(664\) | − | 1724.58i | − | 0.100793i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3976.08 | + | 8947.34i | −0.231337 | + | 0.520574i | ||||
\(667\) | −8511.31 | − | 14742.0i | −0.494092 | − | 0.855792i | ||||
\(668\) | −5107.19 | + | 8845.91i | −0.295813 | + | 0.512363i | ||||
\(669\) | −11744.7 | − | 10567.5i | −0.678740 | − | 0.610709i | ||||
\(670\) | −615.625 | + | 355.431i | −0.0354980 | + | 0.0204948i | ||||
\(671\) | −32869.9 | −1.89110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12283.5 | −0.703559 | −0.351780 | − | 0.936083i | \(-0.614423\pi\) | ||||
−0.351780 | + | 0.936083i | \(0.614423\pi\) | |||||||
\(674\) | 6837.85 | − | 3947.84i | 0.390778 | − | 0.225616i | ||||
\(675\) | −15814.0 | + | 7060.82i | −0.901750 | + | 0.402624i | ||||
\(676\) | −3948.93 | + | 6839.74i | −0.224677 | + | 0.389152i | ||||
\(677\) | 6495.88 | + | 11251.2i | 0.368769 | + | 0.638727i | 0.989373 | − | 0.145397i | \(-0.0464459\pi\) |
−0.620604 | + | 0.784124i | \(0.713113\pi\) | |||||||
\(678\) | 8579.91 | + | 1820.57i | 0.486002 | + | 0.103125i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3081.00i | 0.173751i | ||||||||
\(681\) | 7067.05 | + | 21724.2i | 0.397665 | + | 1.22243i | ||||
\(682\) | −6728.24 | − | 3884.55i | −0.377768 | − | 0.218104i | ||||
\(683\) | 7366.62 | + | 4253.12i | 0.412703 | + | 0.238274i | 0.691950 | − | 0.721945i | \(-0.256752\pi\) |
−0.279248 | + | 0.960219i | \(0.590085\pi\) | |||||||
\(684\) | −4731.90 | + | 500.703i | −0.264516 | + | 0.0279896i | ||||
\(685\) | − | 1369.74i | − | 0.0764018i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2139.38 | − | 10082.4i | 0.118810 | − | 0.559923i | ||||
\(688\) | 806.667 | + | 1397.19i | 0.0447004 | + | 0.0774234i | ||||
\(689\) | −4146.31 | + | 7181.62i | −0.229263 | + | 0.397095i | ||||
\(690\) | 665.397 | − | 739.520i | 0.0367119 | − | 0.0408015i | ||||
\(691\) | 22372.0 | − | 12916.5i | 1.23165 | − | 0.711093i | 0.264276 | − | 0.964447i | \(-0.414867\pi\) |
0.967374 | + | 0.253354i | \(0.0815336\pi\) | |||||||
\(692\) | 4503.61 | 0.247401 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4429.93 | −0.242303 | ||||||||
\(695\) | −894.770 | + | 516.595i | −0.0488353 | + | 0.0281951i | ||||
\(696\) | −17355.1 | + | 19288.4i | −0.945177 | + | 1.05047i | ||||
\(697\) | 9778.22 | − | 16936.4i | 0.531387 | − | 0.920389i | ||||
\(698\) | −216.457 | − | 374.914i | −0.0117378 | − | 0.0203305i | ||||
\(699\) | −4717.33 | + | 22231.7i | −0.255259 | + | 1.20298i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22607.8i | 1.21810i | 0.793134 | + | 0.609048i | \(0.208448\pi\) | ||||
−0.793134 | + | 0.609048i | \(0.791552\pi\) | |||||||
\(702\) | 543.086 | − | 5220.01i | 0.0291987 | − | 0.280650i | ||||
\(703\) | −6655.69 | − | 3842.67i | −0.357076 | − | 0.206158i | ||||
\(704\) | −14253.8 | − | 8229.41i | −0.763080 | − | 0.440565i | ||||
\(705\) | 717.975 | + | 2207.06i | 0.0383553 | + | 0.117905i | ||||
\(706\) | − | 2835.96i | − | 0.151180i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13852.0 | − | 2939.26i | −0.735298 | − | 0.156023i | ||||
\(709\) | 5472.41 | + | 9478.50i | 0.289874 | + | 0.502077i | 0.973779 | − | 0.227494i | \(-0.0730532\pi\) |
−0.683905 | + | 0.729571i | \(0.739720\pi\) | |||||||
\(710\) | −542.159 | + | 939.048i | −0.0286576 | + | 0.0496364i | ||||
\(711\) | 1351.69 | − | 983.509i | 0.0712971 | − | 0.0518769i | ||||
\(712\) | −2343.80 | + | 1353.19i | −0.123368 | + | 0.0712263i | ||||
\(713\) | 8042.46 | 0.422430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −994.720 | −0.0520285 | ||||||||
\(716\) | 546.601 | − | 315.580i | 0.0285299 | − | 0.0164718i | ||||
\(717\) | 14780.3 | + | 13298.9i | 0.769849 | + | 0.692685i | ||||
\(718\) | −10381.4 | + | 17981.1i | −0.539595 | + | 0.934607i | ||||
\(719\) | −12885.3 | − | 22317.9i | −0.668344 | − | 1.15761i | −0.978367 | − | 0.206877i | \(-0.933670\pi\) |
0.310023 | − | 0.950729i | \(-0.399663\pi\) | |||||||
\(720\) | −313.048 | − | 139.114i | −0.0162036 | − | 0.00720068i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 9968.76i | − | 0.513849i | ||||||
\(723\) | −16997.4 | + | 5529.40i | −0.874330 | + | 0.284427i | ||||
\(724\) | −7761.13 | − | 4480.89i | −0.398398 | − | 0.230015i | ||||
\(725\) | −22633.2 | − | 13067.3i | −1.15942 | − | 0.669389i | ||||
\(726\) | −3062.89 | + | 996.381i | −0.156576 | + | 0.0509355i | ||||
\(727\) | − | 15593.1i | − | 0.795485i | −0.917497 | − | 0.397742i | \(-0.869794\pi\) | ||
0.917497 | − | 0.397742i | \(-0.130206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6121.81 | + | 18706.8i | 0.311020 | + | 0.950403i | ||||
\(730\) | 597.273 | + | 1034.51i | 0.0302823 | + | 0.0524505i | ||||
\(731\) | 8305.13 | − | 14384.9i | 0.420214 | − | 0.727832i | ||||
\(732\) | −13593.2 | − | 12230.7i | −0.686363 | − | 0.617568i | ||||
\(733\) | −692.858 | + | 400.022i | −0.0349131 | + | 0.0201571i | −0.517355 | − | 0.855771i | \(-0.673083\pi\) |
0.482442 | + | 0.875928i | \(0.339750\pi\) | |||||||
\(734\) | −7272.94 | −0.365734 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13610.4 | 0.681641 | ||||||||
\(737\) | −10520.5 | + | 6073.99i | −0.525815 | + | 0.303580i | ||||
\(738\) | 5662.86 | + | 7782.76i | 0.282456 | + | 0.388194i | ||||
\(739\) | 454.445 | − | 787.122i | 0.0226211 | − | 0.0391810i | −0.854493 | − | 0.519463i | \(-0.826132\pi\) |
0.877114 | + | 0.480282i | \(0.159466\pi\) | |||||||
\(740\) | 516.179 | + | 894.048i | 0.0256421 | + | 0.0444133i | ||||
\(741\) | 4029.77 | + | 855.076i | 0.199781 | + | 0.0423914i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8109.00i | 0.400391i | 0.979756 | + | 0.200195i | \(0.0641577\pi\) | ||||
−0.979756 | + | 0.200195i | \(0.935842\pi\) | |||||||
\(744\) | −3792.28 | − | 11657.5i | −0.186870 | − | 0.574442i | ||||
\(745\) | −964.258 | − | 556.715i | −0.0474197 | − | 0.0273778i | ||||
\(746\) | −16099.7 | − | 9295.14i | −0.790148 | − | 0.456192i | ||||
\(747\) | −207.737 | − | 1963.22i | −0.0101750 | − | 0.0961588i | ||||
\(748\) | 18562.8i | 0.907382i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 638.041 | − | 3006.94i | 0.0310639 | − | 0.146397i | ||||
\(751\) | 10382.2 | + | 17982.5i | 0.504463 | + | 0.873756i | 0.999987 | + | 0.00516122i | \(0.00164288\pi\) |
−0.495524 | + | 0.868594i | \(0.665024\pi\) | |||||||
\(752\) | 1820.99 | − | 3154.05i | 0.0883041 | − | 0.152947i | ||||
\(753\) | 7113.09 | − | 7905.46i | 0.344243 | − | 0.382591i | ||||
\(754\) | 6858.67 | − | 3959.85i | 0.331271 | − | 0.191259i | ||||
\(755\) | 1777.61 | 0.0856870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23295.6 | 1.11848 | 0.559242 | − | 0.829005i | \(-0.311092\pi\) | ||||
0.559242 | + | 0.829005i | \(0.311092\pi\) | |||||||
\(758\) | −529.273 | + | 305.576i | −0.0253616 | + | 0.0146425i | ||||
\(759\) | 11371.0 | − | 12637.7i | 0.543796 | − | 0.604374i | ||||
\(760\) | 595.119 | − | 1030.78i | 0.0284042 | − | 0.0491976i | ||||
\(761\) | −5014.38 | − | 8685.16i | −0.238858 | − | 0.413715i | 0.721529 | − | 0.692385i | \(-0.243440\pi\) |
−0.960387 | + | 0.278670i | \(0.910106\pi\) | |||||||
\(762\) | 1729.65 | − | 8151.43i | 0.0822290 | − | 0.387526i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 12845.7i | − | 0.608299i | ||||||
\(765\) | 371.128 | + | 3507.35i | 0.0175401 | + | 0.165763i | ||||
\(766\) | −7224.45 | − | 4171.04i | −0.340770 | − | 0.196744i | ||||
\(767\) | 10616.9 | + | 6129.66i | 0.499809 | + | 0.288565i | ||||
\(768\) | −6987.55 | − | 21479.8i | −0.328309 | − | 1.00923i | ||||
\(769\) | 13500.3i | 0.633074i | 0.948580 | + | 0.316537i | \(0.102520\pi\) | ||||
−0.948580 | + | 0.316537i | \(0.897480\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30757.8 | + | 6526.49i | 1.43673 | + | 0.304858i | ||||
\(772\) | 4946.21 | + | 8567.09i | 0.230593 | + | 0.399399i | ||||
\(773\) | −11644.9 | + | 20169.5i | −0.541833 | + | 0.938482i | 0.456966 | + | 0.889484i | \(0.348936\pi\) |
−0.998799 | + | 0.0489979i | \(0.984397\pi\) | |||||||
\(774\) | 4809.75 | + | 6610.29i | 0.223363 | + | 0.306979i | ||||
\(775\) | 10693.2 | − | 6173.74i | 0.495629 | − | 0.286151i | ||||
\(776\) | 33410.2 | 1.54556 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26179.3 | 1.20639 | ||||||||
\(779\) | −6542.79 | + | 3777.48i | −0.300924 | + | 0.173739i | ||||
\(780\) | −411.360 | − | 370.129i | −0.0188834 | − | 0.0169907i | ||||
\(781\) | −9264.99 | + | 16047.4i | −0.424491 | + | 0.735240i | ||||
\(782\) | 8036.02 | + | 13918.8i | 0.367478 | + | 0.636490i | ||||
\(783\) | −17433.3 | + | 24048.1i | −0.795677 | + | 1.09759i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 352.711i | − | 0.0160367i | ||||||
\(786\) | −4884.88 | + | 1589.09i | −0.221677 | + | 0.0721132i | ||||
\(787\) | 20635.4 | + | 11913.8i | 0.934653 | + | 0.539622i | 0.888280 | − | 0.459302i | \(-0.151901\pi\) |
0.0463726 | + | 0.998924i | \(0.485234\pi\) | |||||||
\(788\) | 1870.70 | + | 1080.05i | 0.0845698 | + | 0.0488264i | ||||
\(789\) | 31002.9 | − | 10085.5i | 1.39890 | − | 0.455074i | ||||
\(790\) | 147.419i | 0.00663916i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −23680.1 | − | 10523.1i | −1.06242 | − | 0.472125i | ||||
\(793\) | 7915.34 | + | 13709.8i | 0.354454 | + | 0.613932i | ||||
\(794\) | −2404.27 | + | 4164.32i | −0.107461 | + | 0.186129i | ||||
\(795\) | 2038.91 | + | 1834.55i | 0.0909594 | + | 0.0818424i | ||||
\(796\) | 3167.98 | − | 1829.03i | 0.141063 | − | 0.0814426i | ||||
\(797\) | 12609.3 | 0.560406 | 0.280203 | − | 0.959941i | \(-0.409598\pi\) | ||||
0.280203 | + | 0.959941i | \(0.409598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37496.4 | −1.66023 | ||||||||
\(800\) | 18096.4 | − | 10448.0i | 0.799756 | − | 0.461739i | ||||
\(801\) | −2505.14 | + | 1822.78i | −0.110505 | + | 0.0804054i | ||||
\(802\) | 2500.54 | − | 4331.06i | 0.110096 | − | 0.190692i | ||||
\(803\) | 10206.8 | + | 17678.8i | 0.448557 | + | 0.776924i | ||||
\(804\) | −6610.76 | − | 1402.74i | −0.289980 | − | 0.0615307i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3741.73i | 0.163519i | ||||||||
\(807\) | −5362.97 | − | 16485.8i | −0.233935 | − | 0.719118i | ||||
\(808\) | 4918.87 | + | 2839.91i | 0.214165 | + | 0.123648i | ||||
\(809\) | 30281.4 | + | 17483.0i | 1.31599 | + | 0.759789i | 0.983082 | − | 0.183169i | \(-0.0586354\pi\) |
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(810\) | −1651.61 | − | 534.079i | −0.0716442 | − | 0.0231674i | ||||
\(811\) | − | 5691.42i | − | 0.246428i | −0.992380 | − | 0.123214i | \(-0.960680\pi\) | ||
0.992380 | − | 0.123214i | \(-0.0393201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3066.52 | + | 14451.8i | −0.132285 | + | 0.623428i | ||||
\(814\) | −7377.84 | − | 12778.8i | −0.317682 | − | 0.550241i | ||||
\(815\) | −1444.59 | + | 2502.10i | −0.0620879 | + | 0.107539i | ||||
\(816\) | 3701.84 | − | 4114.22i | 0.158812 | − | 0.176503i | ||||
\(817\) | −5557.12 | + | 3208.40i | −0.237967 | + | 0.137390i | ||||
\(818\) | −26578.9 | −1.13607 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1014.85 | 0.0432195 | ||||||||
\(821\) | 10487.0 | − | 6054.70i | 0.445798 | − | 0.257382i | −0.260256 | − | 0.965540i | \(-0.583807\pi\) |
0.706054 | + | 0.708158i | \(0.250474\pi\) | |||||||
\(822\) | −7284.86 | + | 8096.37i | −0.309110 | + | 0.343544i | ||||
\(823\) | 15861.0 | − | 27472.0i | 0.671784 | − | 1.16356i | −0.305614 | − | 0.952155i | \(-0.598862\pi\) |
0.977398 | − | 0.211408i | \(-0.0678049\pi\) | |||||||
\(824\) | −13079.0 | − | 22653.5i | −0.552946 | − | 0.957731i | ||||
\(825\) | 5417.61 | − | 25531.9i | 0.228627 | − | 1.07746i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36401.9i | − | 1.53061i | −0.643666 | − | 0.765307i | \(-0.722587\pi\) | ||
0.643666 | − | 0.765307i | \(-0.277413\pi\) | |||||||
\(828\) | 9404.82 | − | 995.165i | 0.394735 | − | 0.0417686i | ||||
\(829\) | −27287.8 | − | 15754.6i | −1.14324 | − | 0.660049i | −0.196007 | − | 0.980602i | \(-0.562798\pi\) |
−0.947230 | + | 0.320554i | \(0.896131\pi\) | |||||||
\(830\) | 150.776 | + | 87.0505i | 0.00630543 | + | 0.00364044i | ||||
\(831\) | 10204.5 | + | 31368.9i | 0.425983 | + | 1.30948i | ||||
\(832\) | 7926.83i | 0.330305i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8036.32 | + | 1705.22i | 0.333663 | + | 0.0707998i | ||||
\(835\) | −1462.40 | − | 2532.96i | −0.0606090 | − | 0.104978i | ||||
\(836\) | 3585.54 | − | 6210.34i | 0.148336 | − | 0.256925i | ||||
\(837\) | −5721.28 | − | 12813.9i | −0.236268 | − | 0.529166i | ||||
\(838\) | −25079.2 | + | 14479.5i | −1.03383 | + | 0.596881i | ||||
\(839\) | 13781.4 | 0.567090 | 0.283545 | − | 0.958959i | \(-0.408490\pi\) | ||||
0.283545 | + | 0.958959i | \(0.408490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20433.0 | −0.837796 | ||||||||
\(842\) | 1739.93 | − | 1004.55i | 0.0712136 | − | 0.0411152i | ||||
\(843\) | −14430.6 | − | 12984.2i | −0.589582 | − | 0.530487i | ||||
\(844\) | −8716.46 | + | 15097.4i | −0.355489 | + | 0.615726i | ||||
\(845\) | −1130.74 | − | 1958.51i | −0.0460341 | − | 0.0797334i | ||||
\(846\) | 7494.20 | − | 16864.1i | 0.304558 | − | 0.685343i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4303.95i | − | 0.174290i | ||||||
\(849\) | 27261.6 | − | 8868.40i | 1.10202 | − | 0.358496i | ||||
\(850\) | 21369.3 | + | 12337.6i | 0.862309 | + | 0.497854i | ||||
\(851\) | 13228.4 | + | 7637.43i | 0.532860 | + | 0.307647i | ||||
\(852\) | −9802.63 | + | 3188.87i | −0.394170 | + | 0.128227i | ||||
\(853\) | 11376.3i | 0.456645i | 0.973586 | + | 0.228322i | \(0.0733240\pi\) | ||||
−0.973586 | + | 0.228322i | \(0.926676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 553.308 | − | 1245.10i | 0.0221318 | − | 0.0498030i | ||||
\(856\) | −12591.3 | − | 21808.8i | −0.502761 | − | 0.870807i | ||||
\(857\) | 21559.6 | − | 37342.3i | 0.859349 | − | 1.48844i | −0.0132022 | − | 0.999913i | \(-0.504203\pi\) |
0.872551 | − | 0.488523i | \(-0.162464\pi\) | |||||||
\(858\) | 5879.65 | + | 5290.32i | 0.233948 | + | 0.210499i | ||||
\(859\) | −32325.9 | + | 18663.4i | −1.28399 | + | 0.741311i | −0.977575 | − | 0.210588i | \(-0.932462\pi\) |
−0.306413 | + | 0.951899i | \(0.599129\pi\) | |||||||
\(860\) | 861.960 | 0.0341774 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15260.5 | 0.602986 | ||||||||
\(863\) | −30262.7 | + | 17472.2i | −1.19369 | + | 0.689176i | −0.959141 | − | 0.282929i | \(-0.908694\pi\) |
−0.234547 | + | 0.972105i | \(0.575361\pi\) | |||||||
\(864\) | −9682.26 | − | 21685.2i | −0.381247 | − | 0.853873i | ||||
\(865\) | −644.788 | + | 1116.80i | −0.0253450 | + | 0.0438988i | ||||
\(866\) | −12301.9 | − | 21307.5i | −0.482719 | − | 0.836093i | ||||
\(867\) | −30767.1 | − | 6528.45i | −1.20520 | − | 0.255730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2519.25i | 0.0983426i | ||||||||
\(870\) | −810.319 | − | 2490.93i | −0.0315775 | − | 0.0970694i | ||||
\(871\) | 5066.82 | + | 2925.33i | 0.197110 | + | 0.113801i | ||||
\(872\) | 206.050 | + | 118.963i | 0.00800200 | + | 0.00461995i | ||||
\(873\) | 38033.5 | − | 4024.49i | 1.47450 | − | 0.156023i | ||||
\(874\) | − | 6208.89i | − | 0.240296i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2357.18 | + | 11108.8i | −0.0909152 | + | 0.428462i | ||||
\(877\) | −2054.59 | − | 3558.66i | −0.0791092 | − | 0.137021i | 0.823757 | − | 0.566944i | \(-0.191874\pi\) |
−0.902866 | + | 0.429922i | \(0.858541\pi\) | |||||||
\(878\) | 13728.1 | − | 23777.8i | 0.527678 | − | 0.913964i | ||||
\(879\) | −26325.5 | + | 29258.1i | −1.01017 | + | 1.12270i | ||||
\(880\) | 447.102 | − | 258.134i | 0.0171271 | − | 0.00988831i | ||||
\(881\) | −15697.6 | −0.600301 | −0.300151 | − | 0.953892i | \(-0.597037\pi\) | ||||
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44102.6 | −1.68083 | −0.840413 | − | 0.541946i | \(-0.817688\pi\) | ||||
−0.840413 | + | 0.541946i | \(0.817688\pi\) | |||||||
\(884\) | 7742.37 | − | 4470.06i | 0.294575 | − | 0.170073i | ||||
\(885\) | 2712.09 | − | 3014.20i | 0.103012 | − | 0.114487i | ||||
\(886\) | 3782.46 | − | 6551.42i | 0.143425 | − | 0.248419i | ||||
\(887\) | 14164.5 | + | 24533.5i | 0.536185 | + | 0.928699i | 0.999105 | + | 0.0422991i | \(0.0134682\pi\) |
−0.462920 | + | 0.886400i | \(0.653198\pi\) | |||||||
\(888\) | 4832.79 | − | 22775.8i | 0.182633 | − | 0.860704i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 273.218i | − | 0.0102902i | ||||||
\(891\) | −28224.5 | − | 9126.89i | −1.06123 | − | 0.343168i | ||||
\(892\) | 11471.1 | + | 6622.84i | 0.430584 | + | 0.248598i | ||||
\(893\) | 12544.8 | + | 7242.73i | 0.470095 | + | 0.271409i | ||||
\(894\) | 2738.76 | + | 8418.97i | 0.102458 | + | 0.314958i | ||||
\(895\) | 180.728i | 0.00674979i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8009.31 | − | 1699.49i | −0.298131 | − | 0.0632602i | ||||
\(898\) | 12864.7 | + | 22282.3i | 0.478062 | + | 0.828028i | ||||
\(899\) | 10588.3 | − | 18339.4i | 0.392812 | − | 0.680370i | ||||
\(900\) | 11740.7 | − | 8542.72i | 0.434840 | − | 0.316397i | ||||
\(901\) | −38375.1 | + | 22155.9i | −1.41894 | + | 0.819223i | ||||
\(902\) | −14505.4 | −0.535450 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20857.1 | −0.767365 | ||||||||
\(905\) | 2222.34 | − | 1283.07i | 0.0816277 | − | 0.0471278i | ||||
\(906\) | −10507.2 | − | 9454.03i | −0.385295 | − | 0.346677i | ||||
\(907\) | −7102.79 | + | 12302.4i | −0.260027 | + | 0.450380i | −0.966249 | − | 0.257611i | \(-0.917065\pi\) |
0.706222 | + | 0.707991i | \(0.250398\pi\) | |||||||
\(908\) | −9576.32 | − | 16586.7i | −0.350002 | − | 0.606220i | ||||
\(909\) | 5941.64 | + | 2640.39i | 0.216800 | + | 0.0963434i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 17955.9i | − | 0.653025i | −0.945193 | − | 0.326512i | \(-0.894127\pi\) | ||
0.945193 | − | 0.326512i | \(-0.105873\pi\) | |||||||
\(912\) | −2033.18 | + | 661.410i | −0.0738216 | + | 0.0240148i | ||||
\(913\) | 2576.62 | + | 1487.61i | 0.0933993 | + | 0.0539241i | ||||
\(914\) | 6578.63 | + | 3798.17i | 0.238076 | + | 0.137453i | ||||
\(915\) | 4979.11 | − | 1619.74i | 0.179895 | − | 0.0585214i | ||||
\(916\) | 8641.09i | 0.311692i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 16459.8 | − | 22705.2i | 0.591781 | − | 0.816323i | ||||
\(919\) | 21121.3 | + | 36583.1i | 0.758135 | + | 1.31313i | 0.943800 | + | 0.330516i | \(0.107223\pi\) |
−0.185665 | + | 0.982613i | \(0.559444\pi\) | |||||||
\(920\) | −1182.82 | + | 2048.70i | −0.0423874 | + | 0.0734171i | ||||
\(921\) | 41082.5 | + | 36964.7i | 1.46983 | + | 1.32251i | ||||
\(922\) | 14966.7 | − | 8641.01i | 0.534600 | − | 0.308651i | ||||
\(923\) | 8924.34 | 0.318254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23451.3 | 0.833593 | ||||||||
\(926\) | 9482.32 | − | 5474.62i | 0.336510 | − | 0.194284i | ||||
\(927\) | −17617.6 | − | 24212.8i | −0.624206 | − | 0.857878i | ||||
\(928\) | 17918.7 | − | 31036.2i | 0.633849 | − | 1.09786i | ||||
\(929\) | 22338.1 | + | 38690.6i | 0.788900 | + | 1.36641i | 0.926642 | + | 0.375946i | \(0.122682\pi\) |
−0.137742 | + | 0.990468i | \(0.543984\pi\) | |||||||
\(930\) | 1210.61 | + | 256.879i | 0.0426854 | + | 0.00905741i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 19053.6i | − | 0.669660i | ||||||
\(933\) | −9276.80 | − | 28517.0i | −0.325519 | − | 1.00065i | ||||
\(934\) | 20486.2 | + | 11827.7i | 0.717696 | + | 0.414362i | ||||
\(935\) | −4603.19 | − | 2657.65i | −0.161006 | − | 0.0929566i | ||||
\(936\) | 1313.24 | + | 12410.8i | 0.0458597 | + | 0.433398i | ||||
\(937\) | 15309.3i | 0.533761i | 0.963730 | + | 0.266880i | \(0.0859929\pi\) | ||||
−0.963730 | + | 0.266880i | \(0.914007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2528.70 | − | 11917.2i | 0.0878817 | − | 0.414166i | ||||
\(940\) | −972.904 | − | 1685.12i | −0.0337581 | − | 0.0584708i | ||||
\(941\) | −21192.2 | + | 36706.0i | −0.734162 | + | 1.27161i | 0.220928 | + | 0.975290i | \(0.429091\pi\) |
−0.955090 | + | 0.296316i | \(0.904242\pi\) | |||||||
\(942\) | −1875.86 | + | 2084.82i | −0.0648819 | + | 0.0721096i | ||||
\(943\) | 13004.0 | − | 7507.87i | 0.449066 | − | 0.259268i | ||||
\(944\) | −6362.70 | −0.219373 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12320.1 | −0.423427 | ||||||||
\(947\) | 10648.1 | − | 6147.69i | 0.365383 | − | 0.210954i | −0.306057 | − | 0.952013i | \(-0.599010\pi\) |
0.671439 | + | 0.741060i | \(0.265676\pi\) | |||||||
\(948\) | −937.398 | + | 1041.82i | −0.0321153 | + | 0.0356928i | ||||
\(949\) | 4915.78 | − | 8514.37i | 0.168148 | − | 0.291242i | ||||
\(950\) | −4766.21 | − | 8255.32i | −0.162775 | − | 0.281935i | ||||
\(951\) | −8533.67 | + | 40217.2i | −0.290981 | + | 1.37133i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1322.78i | 0.0449621i | 0.999747 | + | 0.0224811i | \(0.00715655\pi\) | ||||
−0.999747 | + | 0.0224811i | \(0.992843\pi\) | |||||||
\(954\) | −2294.85 | − | 21687.5i | −0.0778810 | − | 0.736015i | ||||
\(955\) | 3185.47 | + | 1839.13i | 0.107936 | + | 0.0623171i | ||||
\(956\) | −14436.0 | − | 8334.62i | −0.488382 | − | 0.281967i | ||||
\(957\) | −13847.6 | − | 42567.6i | −0.467742 | − | 1.43784i | ||||
\(958\) | − | 15781.7i | − | 0.532238i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2564.67 | + | 544.197i | 0.0862234 | + | 0.0182957i | ||||
\(961\) | −9893.00 | − | 17135.2i | −0.332080 | − | 0.575180i | ||||
\(962\) | −3553.29 | + | 6154.47i | −0.119088 | + | 0.206266i | ||||
\(963\) | −16960.8 | − | 23310.1i | −0.567553 | − | 0.780017i | ||||
\(964\) | 12977.7 | − | 7492.70i | 0.433594 | − | 0.250336i | ||||
\(965\) | −2832.62 | −0.0944925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36887.2 | 1.22669 | 0.613346 | − | 0.789814i | \(-0.289823\pi\) | ||||
0.613346 | + | 0.789814i | \(0.289823\pi\) | |||||||
\(968\) | 6633.06 | − | 3829.60i | 0.220242 | − | 0.127157i | ||||
\(969\) | 16363.7 | + | 14723.5i | 0.542495 | + | 0.488120i | ||||
\(970\) | −1686.43 | + | 2920.98i | −0.0558226 | + | 0.0966875i | ||||
\(971\) | −3409.79 | − | 5905.93i | −0.112693 | − | 0.195191i | 0.804162 | − | 0.594410i | \(-0.202614\pi\) |
−0.916855 | + | 0.399220i | \(0.869281\pi\) | |||||||
\(972\) | −8276.02 | − | 14276.5i | −0.273100 | − | 0.471111i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 1794.59i | − | 0.0590373i | ||||||
\(975\) | −11953.8 | + | 3888.65i | −0.392643 | + | 0.127730i | ||||
\(976\) | −7115.50 | − | 4108.14i | −0.233362 | − | 0.134732i | ||||
\(977\) | 42700.8 | + | 24653.3i | 1.39828 | + | 0.807298i | 0.994213 | − | 0.107431i | \(-0.0342624\pi\) |
0.404068 | + | 0.914729i | \(0.367596\pi\) | |||||||
\(978\) | 21845.9 | − | 7106.65i | 0.714269 | − | 0.232357i | ||||
\(979\) | − | 4669.03i | − | 0.152424i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 248.894 | + | 110.605i | 0.00810047 | + | 0.00359975i | ||||
\(982\) | −1009.11 | − | 1747.82i | −0.0327921 | − | 0.0567977i | ||||
\(983\) | 9765.55 | − | 16914.4i | 0.316859 | − | 0.548816i | −0.662972 | − | 0.748644i | \(-0.730705\pi\) |
0.979831 | + | 0.199828i | \(0.0640384\pi\) | |||||||
\(984\) | −17014.4 | − | 15309.0i | −0.551220 | − | 0.495970i | ||||
\(985\) | −535.661 | + | 309.264i | −0.0173275 | + | 0.0100040i | ||||
\(986\) | 42319.1 | 1.36685 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3453.71 | −0.111212 | ||||||||
\(989\) | 11045.0 | − | 6376.81i | 0.355116 | − | 0.205026i | ||||
\(990\) | 2115.30 | − | 1539.13i | 0.0679077 | − | 0.0494107i | ||||
\(991\) | −9285.39 | + | 16082.8i | −0.297639 | + | 0.515526i | −0.975595 | − | 0.219576i | \(-0.929533\pi\) |
0.677956 | + | 0.735102i | \(0.262866\pi\) | |||||||
\(992\) | 8465.85 | + | 14663.3i | 0.270959 | + | 0.469314i | ||||
\(993\) | 24805.1 | + | 5263.39i | 0.792716 | + | 0.168206i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1047.46i | 0.0333735i | ||||||||
\(996\) | 512.014 | + | 1573.94i | 0.0162889 | + | 0.0500723i | ||||
\(997\) | −19389.3 | − | 11194.4i | −0.615913 | − | 0.355598i | 0.159363 | − | 0.987220i | \(-0.449056\pi\) |
−0.775276 | + | 0.631622i | \(0.782389\pi\) | |||||||
\(998\) | −10205.1 | − | 5891.89i | −0.323683 | − | 0.186878i | ||||
\(999\) | 2758.05 | − | 26509.7i | 0.0873481 | − | 0.839569i |
(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 | 147.4.g.d.80.3 | 12 | ||
3.2 | odd | 2 | inner | 147.4.g.d.80.4 | 12 | ||
7.2 | even | 3 | 21.4.g.a.5.4 | yes | 12 | ||
7.3 | odd | 6 | 147.4.c.a.146.6 | 12 | |||
7.4 | even | 3 | 147.4.c.a.146.5 | 12 | |||
7.5 | odd | 6 | inner | 147.4.g.d.68.4 | 12 | ||
7.6 | odd | 2 | 21.4.g.a.17.3 | yes | 12 | ||
21.2 | odd | 6 | 21.4.g.a.5.3 | ✓ | 12 | ||
21.5 | even | 6 | inner | 147.4.g.d.68.3 | 12 | ||
21.11 | odd | 6 | 147.4.c.a.146.8 | 12 | |||
21.17 | even | 6 | 147.4.c.a.146.7 | 12 | |||
21.20 | even | 2 | 21.4.g.a.17.4 | yes | 12 | ||
28.23 | odd | 6 | 336.4.bc.d.257.3 | 12 | |||
28.27 | even | 2 | 336.4.bc.d.17.5 | 12 | |||
84.23 | even | 6 | 336.4.bc.d.257.5 | 12 | |||
84.83 | odd | 2 | 336.4.bc.d.17.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.3 | ✓ | 12 | 21.2 | odd | 6 | ||
21.4.g.a.5.4 | yes | 12 | 7.2 | even | 3 | ||
21.4.g.a.17.3 | yes | 12 | 7.6 | odd | 2 | ||
21.4.g.a.17.4 | yes | 12 | 21.20 | even | 2 | ||
147.4.c.a.146.5 | 12 | 7.4 | even | 3 | |||
147.4.c.a.146.6 | 12 | 7.3 | odd | 6 | |||
147.4.c.a.146.7 | 12 | 21.17 | even | 6 | |||
147.4.c.a.146.8 | 12 | 21.11 | odd | 6 | |||
147.4.g.d.68.3 | 12 | 21.5 | even | 6 | inner | ||
147.4.g.d.68.4 | 12 | 7.5 | odd | 6 | inner | ||
147.4.g.d.80.3 | 12 | 1.1 | even | 1 | trivial | ||
147.4.g.d.80.4 | 12 | 3.2 | odd | 2 | inner | ||
336.4.bc.d.17.3 | 12 | 84.83 | odd | 2 | |||
336.4.bc.d.17.5 | 12 | 28.27 | even | 2 | |||
336.4.bc.d.257.3 | 12 | 28.23 | odd | 6 | |||
336.4.bc.d.257.5 | 12 | 84.23 | even | 6 |