Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(8,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.8");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.j (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: | \(6.19520055060\) |
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 | 8.9 | ||
Character | \(\chi\) | \(=\) | 105.8 |
Dual form | 105.4.j.a.92.9 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42501 | − | 2.42501i | −0.857369 | − | 0.857369i | 0.133658 | − | 0.991027i | \(-0.457327\pi\) |
−0.991027 | + | 0.133658i | \(0.957327\pi\) | |||||||
\(3\) | −0.644450 | − | 5.15603i | −0.124024 | − | 0.992279i | ||||
\(4\) | 3.76131i | 0.470163i | ||||||||
\(5\) | 4.31658 | + | 10.3134i | 0.386087 | + | 0.922463i | ||||
\(6\) | −10.9406 | + | 14.0662i | −0.744415 | + | 0.957084i | ||||
\(7\) | −4.94975 | + | 4.94975i | −0.267261 | + | 0.267261i | ||||
\(8\) | −10.2789 | + | 10.2789i | −0.454266 | + | 0.454266i | ||||
\(9\) | −26.1694 | + | 6.64561i | −0.969236 | + | 0.246134i | ||||
\(10\) | 14.5424 | − | 35.4779i | 0.459872 | − | 1.12191i | ||||
\(11\) | 64.4965i | 1.76786i | 0.467622 | + | 0.883929i | \(0.345111\pi\) | ||||
−0.467622 | + | 0.883929i | \(0.654889\pi\) | |||||||
\(12\) | 19.3934 | − | 2.42397i | 0.466533 | − | 0.0583117i | ||||
\(13\) | −33.2786 | − | 33.2786i | −0.709986 | − | 0.709986i | 0.256546 | − | 0.966532i | \(-0.417415\pi\) |
−0.966532 | + | 0.256546i | \(0.917415\pi\) | |||||||
\(14\) | 24.0063 | 0.458283 | ||||||||
\(15\) | 50.3946 | − | 28.9029i | 0.867456 | − | 0.497514i | ||||
\(16\) | 79.9430 | 1.24911 | ||||||||
\(17\) | 14.1115 | + | 14.1115i | 0.201326 | + | 0.201326i | 0.800568 | − | 0.599242i | \(-0.204531\pi\) |
−0.599242 | + | 0.800568i | \(0.704531\pi\) | |||||||
\(18\) | 79.5765 | + | 47.3452i | 1.04202 | + | 0.619965i | ||||
\(19\) | 28.7961i | 0.347699i | 0.984772 | + | 0.173850i | \(0.0556207\pi\) | ||||
−0.984772 | + | 0.173850i | \(0.944379\pi\) | |||||||
\(20\) | −38.7920 | + | 16.2360i | −0.433708 | + | 0.181524i | ||||
\(21\) | 28.7109 | + | 22.3312i | 0.298345 | + | 0.232051i | ||||
\(22\) | 156.404 | − | 156.404i | 1.51571 | − | 1.51571i | ||||
\(23\) | 52.0749 | − | 52.0749i | 0.472103 | − | 0.472103i | −0.430491 | − | 0.902595i | \(-0.641660\pi\) |
0.902595 | + | 0.430491i | \(0.141660\pi\) | |||||||
\(24\) | 59.6223 | + | 46.3739i | 0.507098 | + | 0.394418i | ||||
\(25\) | −87.7343 | + | 89.0376i | −0.701874 | + | 0.712301i | ||||
\(26\) | 161.401i | 1.21744i | ||||||||
\(27\) | 51.1298 | + | 130.647i | 0.364442 | + | 0.931226i | ||||
\(28\) | −18.6175 | − | 18.6175i | −0.125656 | − | 0.125656i | ||||
\(29\) | −128.946 | −0.825680 | −0.412840 | − | 0.910804i | \(-0.635463\pi\) | ||||
−0.412840 | + | 0.910804i | \(0.635463\pi\) | |||||||
\(30\) | −192.297 | − | 52.1175i | −1.17028 | − | 0.317177i | ||||
\(31\) | −149.658 | −0.867074 | −0.433537 | − | 0.901136i | \(-0.642735\pi\) | ||||
−0.433537 | + | 0.901136i | \(0.642735\pi\) | |||||||
\(32\) | −111.631 | − | 111.631i | −0.616682 | − | 0.616682i | ||||
\(33\) | 332.546 | − | 41.5648i | 1.75421 | − | 0.219258i | ||||
\(34\) | − | 68.4410i | − | 0.345222i | ||||||
\(35\) | −72.4149 | − | 29.6830i | −0.349724 | − | 0.143352i | ||||
\(36\) | −24.9962 | − | 98.4310i | −0.115723 | − | 0.455699i | ||||
\(37\) | 39.6793 | − | 39.6793i | 0.176304 | − | 0.176304i | −0.613439 | − | 0.789742i | \(-0.710214\pi\) |
0.789742 | + | 0.613439i | \(0.210214\pi\) | |||||||
\(38\) | 69.8308 | − | 69.8308i | 0.298107 | − | 0.298107i | ||||
\(39\) | −150.139 | + | 193.032i | −0.616448 | + | 0.792560i | ||||
\(40\) | −150.380 | − | 61.6409i | −0.594429 | − | 0.243657i | ||||
\(41\) | 347.833i | 1.32494i | 0.749090 | + | 0.662468i | \(0.230491\pi\) | ||||
−0.749090 | + | 0.662468i | \(0.769509\pi\) | |||||||
\(42\) | −15.4709 | − | 123.777i | −0.0568383 | − | 0.454745i | ||||
\(43\) | −8.50132 | − | 8.50132i | −0.0301497 | − | 0.0301497i | 0.691871 | − | 0.722021i | \(-0.256787\pi\) |
−0.722021 | + | 0.691871i | \(0.756787\pi\) | |||||||
\(44\) | −242.591 | −0.831181 | ||||||||
\(45\) | −181.501 | − | 241.210i | −0.601258 | − | 0.799055i | ||||
\(46\) | −252.564 | −0.809533 | ||||||||
\(47\) | −157.345 | − | 157.345i | −0.488323 | − | 0.488323i | 0.419453 | − | 0.907777i | \(-0.362222\pi\) |
−0.907777 | + | 0.419453i | \(0.862222\pi\) | |||||||
\(48\) | −51.5193 | − | 412.189i | −0.154920 | − | 1.23947i | ||||
\(49\) | − | 49.0000i | − | 0.142857i | ||||||
\(50\) | 428.673 | − | 3.16064i | 1.21247 | − | 0.00893965i | ||||
\(51\) | 63.6653 | − | 81.8536i | 0.174802 | − | 0.224741i | ||||
\(52\) | 125.171 | − | 125.171i | 0.333809 | − | 0.333809i | ||||
\(53\) | −177.993 | + | 177.993i | −0.461307 | + | 0.461307i | −0.899084 | − | 0.437777i | \(-0.855766\pi\) |
0.437777 | + | 0.899084i | \(0.355766\pi\) | |||||||
\(54\) | 192.830 | − | 440.811i | 0.485943 | − | 1.11087i | ||||
\(55\) | −665.181 | + | 278.404i | −1.63078 | + | 0.682546i | ||||
\(56\) | − | 101.755i | − | 0.242815i | ||||||
\(57\) | 148.474 | − | 18.5577i | 0.345015 | − | 0.0431232i | ||||
\(58\) | 312.696 | + | 312.696i | 0.707913 | + | 0.707913i | ||||
\(59\) | −739.310 | −1.63136 | −0.815678 | − | 0.578506i | \(-0.803636\pi\) | ||||
−0.815678 | + | 0.578506i | \(0.803636\pi\) | |||||||
\(60\) | 108.713 | + | 189.550i | 0.233913 | + | 0.407846i | ||||
\(61\) | 749.659 | 1.57351 | 0.786754 | − | 0.617266i | \(-0.211760\pi\) | ||||
0.786754 | + | 0.617266i | \(0.211760\pi\) | |||||||
\(62\) | 362.921 | + | 362.921i | 0.743403 | + | 0.743403i | ||||
\(63\) | 96.6377 | − | 162.426i | 0.193257 | − | 0.324821i | ||||
\(64\) | − | 98.1305i | − | 0.191661i | ||||||
\(65\) | 199.567 | − | 486.866i | 0.380819 | − | 0.929051i | ||||
\(66\) | −907.221 | − | 705.632i | −1.69199 | − | 1.31602i | ||||
\(67\) | −636.068 | + | 636.068i | −1.15982 | + | 1.15982i | −0.175308 | + | 0.984514i | \(0.556092\pi\) |
−0.984514 | + | 0.175308i | \(0.943908\pi\) | |||||||
\(68\) | −53.0777 | + | 53.0777i | −0.0946562 | + | 0.0946562i | ||||
\(69\) | −302.060 | − | 234.940i | −0.527011 | − | 0.409906i | ||||
\(70\) | 103.625 | + | 247.588i | 0.176937 | + | 0.422749i | ||||
\(71\) | 385.792i | 0.644860i | 0.946593 | + | 0.322430i | \(0.104500\pi\) | ||||
−0.946593 | + | 0.322430i | \(0.895500\pi\) | |||||||
\(72\) | 200.682 | − | 337.301i | 0.328480 | − | 0.552101i | ||||
\(73\) | 791.037 | + | 791.037i | 1.26827 | + | 1.26827i | 0.946981 | + | 0.321291i | \(0.104117\pi\) |
0.321291 | + | 0.946981i | \(0.395883\pi\) | |||||||
\(74\) | −192.445 | −0.302314 | ||||||||
\(75\) | 515.621 | + | 394.981i | 0.793851 | + | 0.608112i | ||||
\(76\) | −108.311 | −0.163475 | ||||||||
\(77\) | −319.241 | − | 319.241i | −0.472480 | − | 0.472480i | ||||
\(78\) | 832.191 | − | 104.015i | 1.20804 | − | 0.150992i | ||||
\(79\) | 364.787i | 0.519515i | 0.965674 | + | 0.259758i | \(0.0836427\pi\) | ||||
−0.965674 | + | 0.259758i | \(0.916357\pi\) | |||||||
\(80\) | 345.080 | + | 824.488i | 0.482265 | + | 1.15226i | ||||
\(81\) | 640.672 | − | 347.823i | 0.878836 | − | 0.477123i | ||||
\(82\) | 843.497 | − | 843.497i | 1.13596 | − | 1.13596i | ||||
\(83\) | 171.525 | − | 171.525i | 0.226835 | − | 0.226835i | −0.584534 | − | 0.811369i | \(-0.698723\pi\) |
0.811369 | + | 0.584534i | \(0.198723\pi\) | |||||||
\(84\) | −83.9945 | + | 107.991i | −0.109102 | + | 0.140271i | ||||
\(85\) | −84.6249 | + | 206.452i | −0.107987 | + | 0.263445i | ||||
\(86\) | 41.2315i | 0.0516989i | ||||||||
\(87\) | 83.0994 | + | 664.851i | 0.102405 | + | 0.819305i | ||||
\(88\) | −662.950 | − | 662.950i | −0.803077 | − | 0.803077i | ||||
\(89\) | 861.079 | 1.02555 | 0.512776 | − | 0.858522i | \(-0.328617\pi\) | ||||
0.512776 | + | 0.858522i | \(0.328617\pi\) | |||||||
\(90\) | −144.794 | + | 1025.08i | −0.169585 | + | 1.20058i | ||||
\(91\) | 329.441 | 0.379503 | ||||||||
\(92\) | 195.870 | + | 195.870i | 0.221966 | + | 0.221966i | ||||
\(93\) | 96.4469 | + | 771.640i | 0.107538 | + | 0.860380i | ||||
\(94\) | 763.127i | 0.837347i | ||||||||
\(95\) | −296.987 | + | 124.301i | −0.320740 | + | 0.134242i | ||||
\(96\) | −503.635 | + | 647.516i | −0.535437 | + | 0.688405i | ||||
\(97\) | 614.348 | − | 614.348i | 0.643068 | − | 0.643068i | −0.308240 | − | 0.951308i | \(-0.599740\pi\) |
0.951308 | + | 0.308240i | \(0.0997401\pi\) | |||||||
\(98\) | −118.825 | + | 118.825i | −0.122481 | + | 0.122481i | ||||
\(99\) | −428.619 | − | 1687.83i | −0.435129 | − | 1.71347i | ||||
\(100\) | −334.898 | − | 329.995i | −0.334898 | − | 0.329995i | ||||
\(101\) | 777.575i | 0.766055i | 0.923737 | + | 0.383028i | \(0.125119\pi\) | ||||
−0.923737 | + | 0.383028i | \(0.874881\pi\) | |||||||
\(102\) | −352.884 | + | 44.1068i | −0.342556 | + | 0.0428159i | ||||
\(103\) | −948.506 | − | 948.506i | −0.907370 | − | 0.907370i | 0.0886896 | − | 0.996059i | \(-0.471732\pi\) |
−0.996059 | + | 0.0886896i | \(0.971732\pi\) | |||||||
\(104\) | 684.131 | 0.645044 | ||||||||
\(105\) | −106.379 | + | 392.503i | −0.0988713 | + | 0.364804i | ||||
\(106\) | 863.270 | 0.791021 | ||||||||
\(107\) | −1355.08 | − | 1355.08i | −1.22430 | − | 1.22430i | −0.966087 | − | 0.258216i | \(-0.916865\pi\) |
−0.258216 | − | 0.966087i | \(-0.583135\pi\) | |||||||
\(108\) | −491.405 | + | 192.315i | −0.437828 | + | 0.171347i | ||||
\(109\) | − | 2159.23i | − | 1.89740i | −0.316171 | − | 0.948702i | \(-0.602397\pi\) | ||
0.316171 | − | 0.948702i | \(-0.397603\pi\) | |||||||
\(110\) | 2288.20 | + | 937.936i | 1.98338 | + | 0.812988i | ||||
\(111\) | −230.159 | − | 179.016i | −0.196808 | − | 0.153076i | ||||
\(112\) | −395.698 | + | 395.698i | −0.333839 | + | 0.333839i | ||||
\(113\) | −660.464 | + | 660.464i | −0.549834 | + | 0.549834i | −0.926393 | − | 0.376559i | \(-0.877107\pi\) |
0.376559 | + | 0.926393i | \(0.377107\pi\) | |||||||
\(114\) | −405.052 | − | 315.048i | −0.332778 | − | 0.258832i | ||||
\(115\) | 761.858 | + | 312.286i | 0.617770 | + | 0.253225i | ||||
\(116\) | − | 485.006i | − | 0.388204i | ||||||
\(117\) | 1092.04 | + | 649.723i | 0.862895 | + | 0.513392i | ||||
\(118\) | 1792.83 | + | 1792.83i | 1.39867 | + | 1.39867i | ||||
\(119\) | −139.697 | −0.107613 | ||||||||
\(120\) | −220.910 | + | 815.089i | −0.168052 | + | 0.620059i | ||||
\(121\) | −2828.80 | −2.12532 | ||||||||
\(122\) | −1817.93 | − | 1817.93i | −1.34908 | − | 1.34908i | ||||
\(123\) | 1793.44 | − | 224.161i | 1.31471 | − | 0.164325i | ||||
\(124\) | − | 562.908i | − | 0.407667i | ||||||
\(125\) | −1297.00 | − | 520.504i | −0.928055 | − | 0.372443i | ||||
\(126\) | −628.231 | + | 159.537i | −0.444184 | + | 0.112799i | ||||
\(127\) | −84.0040 | + | 84.0040i | −0.0586941 | + | 0.0586941i | −0.735845 | − | 0.677150i | \(-0.763215\pi\) |
0.677150 | + | 0.735845i | \(0.263215\pi\) | |||||||
\(128\) | −1131.02 | + | 1131.02i | −0.781007 | + | 0.781007i | ||||
\(129\) | −38.3544 | + | 49.3118i | −0.0261777 | + | 0.0336563i | ||||
\(130\) | −1664.60 | + | 696.702i | −1.12304 | + | 0.470037i | ||||
\(131\) | 30.0047i | 0.0200116i | 0.999950 | + | 0.0100058i | \(0.00318501\pi\) | ||||
−0.999950 | + | 0.0100058i | \(0.996815\pi\) | |||||||
\(132\) | 156.338 | + | 1250.81i | 0.103087 | + | 0.824764i | ||||
\(133\) | −142.534 | − | 142.534i | −0.0929266 | − | 0.0929266i | ||||
\(134\) | 3084.94 | 1.98879 | ||||||||
\(135\) | −1126.72 | + | 1091.27i | −0.718315 | + | 0.695718i | ||||
\(136\) | −290.101 | −0.182911 | ||||||||
\(137\) | −743.783 | − | 743.783i | −0.463837 | − | 0.463837i | 0.436074 | − | 0.899911i | \(-0.356369\pi\) |
−0.899911 | + | 0.436074i | \(0.856369\pi\) | |||||||
\(138\) | 162.765 | + | 1302.23i | 0.100402 | + | 0.803283i | ||||
\(139\) | 467.679i | 0.285382i | 0.989767 | + | 0.142691i | \(0.0455755\pi\) | ||||
−0.989767 | + | 0.142691i | \(0.954425\pi\) | |||||||
\(140\) | 111.647 | − | 272.375i | 0.0673991 | − | 0.164428i | ||||
\(141\) | −709.877 | + | 912.680i | −0.423989 | + | 0.545117i | ||||
\(142\) | 935.547 | − | 935.547i | 0.552883 | − | 0.552883i | ||||
\(143\) | 2146.35 | − | 2146.35i | 1.25515 | − | 1.25515i | ||||
\(144\) | −2092.06 | + | 531.270i | −1.21068 | + | 0.307448i | ||||
\(145\) | −556.607 | − | 1329.88i | −0.318784 | − | 0.761659i | ||||
\(146\) | − | 3836.54i | − | 2.17475i | ||||||
\(147\) | −252.646 | + | 31.5781i | −0.141754 | + | 0.0177178i | ||||
\(148\) | 149.246 | + | 149.246i | 0.0828914 | + | 0.0828914i | ||||
\(149\) | 2989.37 | 1.64361 | 0.821807 | − | 0.569767i | \(-0.192966\pi\) | ||||
0.821807 | + | 0.569767i | \(0.192966\pi\) | |||||||
\(150\) | −292.555 | − | 2208.21i | −0.159247 | − | 1.20200i | ||||
\(151\) | 784.335 | 0.422704 | 0.211352 | − | 0.977410i | \(-0.432213\pi\) | ||||
0.211352 | + | 0.977410i | \(0.432213\pi\) | |||||||
\(152\) | −295.991 | − | 295.991i | −0.157948 | − | 0.157948i | ||||
\(153\) | −463.069 | − | 275.510i | −0.244686 | − | 0.145579i | ||||
\(154\) | 1548.32i | 0.810179i | ||||||||
\(155\) | −646.009 | − | 1543.49i | −0.334766 | − | 0.799844i | ||||
\(156\) | −726.052 | − | 564.719i | −0.372632 | − | 0.289831i | ||||
\(157\) | −180.490 | + | 180.490i | −0.0917496 | + | 0.0917496i | −0.751492 | − | 0.659742i | \(-0.770665\pi\) |
0.659742 | + | 0.751492i | \(0.270665\pi\) | |||||||
\(158\) | 884.610 | − | 884.610i | 0.445416 | − | 0.445416i | ||||
\(159\) | 1032.45 | + | 803.032i | 0.514959 | + | 0.400532i | ||||
\(160\) | 669.439 | − | 1633.17i | 0.330774 | − | 0.806959i | ||||
\(161\) | 515.516i | 0.252350i | ||||||||
\(162\) | −2397.11 | − | 710.160i | −1.16256 | − | 0.344416i | ||||
\(163\) | 26.7139 | + | 26.7139i | 0.0128368 | + | 0.0128368i | 0.713496 | − | 0.700659i | \(-0.247111\pi\) |
−0.700659 | + | 0.713496i | \(0.747111\pi\) | |||||||
\(164\) | −1308.31 | −0.622936 | ||||||||
\(165\) | 1864.14 | + | 3250.28i | 0.879533 | + | 1.53354i | ||||
\(166\) | −831.899 | −0.388963 | ||||||||
\(167\) | 996.283 | + | 996.283i | 0.461645 | + | 0.461645i | 0.899194 | − | 0.437549i | \(-0.144154\pi\) |
−0.437549 | + | 0.899194i | \(0.644154\pi\) | |||||||
\(168\) | −524.655 | + | 65.5763i | −0.240940 | + | 0.0301150i | ||||
\(169\) | 17.9257i | 0.00815917i | ||||||||
\(170\) | 705.863 | − | 295.431i | 0.318454 | − | 0.133286i | ||||
\(171\) | −191.368 | − | 753.577i | −0.0855806 | − | 0.337003i | ||||
\(172\) | 31.9761 | − | 31.9761i | 0.0141753 | − | 0.0141753i | ||||
\(173\) | 698.793 | − | 698.793i | 0.307100 | − | 0.307100i | −0.536684 | − | 0.843783i | \(-0.680323\pi\) |
0.843783 | + | 0.536684i | \(0.180323\pi\) | |||||||
\(174\) | 1410.75 | − | 1813.79i | 0.614648 | − | 0.790245i | ||||
\(175\) | −6.45128 | − | 874.976i | −0.00278669 | − | 0.377954i | ||||
\(176\) | 5156.05i | 2.20825i | ||||||||
\(177\) | 476.448 | + | 3811.91i | 0.202328 | + | 1.61876i | ||||
\(178\) | −2088.12 | − | 2088.12i | −0.879277 | − | 0.879277i | ||||
\(179\) | −1735.43 | −0.724648 | −0.362324 | − | 0.932052i | \(-0.618017\pi\) | ||||
−0.362324 | + | 0.932052i | \(0.618017\pi\) | |||||||
\(180\) | 907.265 | − | 682.682i | 0.375686 | − | 0.282690i | ||||
\(181\) | 4167.77 | 1.71154 | 0.855768 | − | 0.517360i | \(-0.173085\pi\) | ||||
0.855768 | + | 0.517360i | \(0.173085\pi\) | |||||||
\(182\) | −798.896 | − | 798.896i | −0.325374 | − | 0.325374i | ||||
\(183\) | −483.118 | − | 3865.27i | −0.195154 | − | 1.56136i | ||||
\(184\) | 1070.54i | 0.428921i | ||||||||
\(185\) | 580.509 | + | 237.951i | 0.230702 | + | 0.0945650i | ||||
\(186\) | 1637.35 | − | 2105.12i | 0.645463 | − | 0.829863i | ||||
\(187\) | −910.144 | + | 910.144i | −0.355916 | + | 0.355916i | ||||
\(188\) | 591.825 | − | 591.825i | 0.229592 | − | 0.229592i | ||||
\(189\) | −899.751 | − | 393.592i | −0.346282 | − | 0.151479i | ||||
\(190\) | 1021.63 | + | 418.766i | 0.390087 | + | 0.159897i | ||||
\(191\) | − | 1900.21i | − | 0.719868i | −0.932978 | − | 0.359934i | \(-0.882799\pi\) | ||
0.932978 | − | 0.359934i | \(-0.117201\pi\) | |||||||
\(192\) | −505.964 | + | 63.2402i | −0.190181 | + | 0.0237707i | ||||
\(193\) | −2303.99 | − | 2303.99i | −0.859301 | − | 0.859301i | 0.131954 | − | 0.991256i | \(-0.457875\pi\) |
−0.991256 | + | 0.131954i | \(0.957875\pi\) | |||||||
\(194\) | −2979.60 | −1.10269 | ||||||||
\(195\) | −2638.91 | − | 715.213i | −0.969109 | − | 0.262654i | ||||
\(196\) | 184.304 | 0.0671662 | ||||||||
\(197\) | 2269.23 | + | 2269.23i | 0.820690 | + | 0.820690i | 0.986207 | − | 0.165517i | \(-0.0529293\pi\) |
−0.165517 | + | 0.986207i | \(0.552929\pi\) | |||||||
\(198\) | −3053.60 | + | 5132.41i | −1.09601 | + | 1.84214i | ||||
\(199\) | 3805.04i | 1.35544i | 0.735320 | + | 0.677720i | \(0.237032\pi\) | ||||
−0.735320 | + | 0.677720i | \(0.762968\pi\) | |||||||
\(200\) | −13.3970 | − | 1817.01i | −0.00473655 | − | 0.642411i | ||||
\(201\) | 3689.50 | + | 2869.67i | 1.29471 | + | 1.00702i | ||||
\(202\) | 1885.62 | − | 1885.62i | 0.656792 | − | 0.656792i | ||||
\(203\) | 638.252 | − | 638.252i | 0.220672 | − | 0.220672i | ||||
\(204\) | 307.877 | + | 239.465i | 0.105665 | + | 0.0821857i | ||||
\(205\) | −3587.36 | + | 1501.45i | −1.22220 | + | 0.511540i | ||||
\(206\) | 4600.27i | 1.55590i | ||||||||
\(207\) | −1016.70 | + | 1708.84i | −0.341379 | + | 0.573780i | ||||
\(208\) | −2660.39 | − | 2660.39i | −0.886850 | − | 0.886850i | ||||
\(209\) | −1857.25 | −0.614683 | ||||||||
\(210\) | 1209.79 | − | 693.853i | 0.397540 | − | 0.228002i | ||||
\(211\) | −1628.37 | −0.531286 | −0.265643 | − | 0.964071i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964071i | \(0.585584\pi\) | |||||||
\(212\) | −669.488 | − | 669.488i | −0.216890 | − | 0.216890i | ||||
\(213\) | 1989.15 | − | 248.623i | 0.639881 | − | 0.0799784i | ||||
\(214\) | 6572.15i | 2.09936i | ||||||||
\(215\) | 50.9813 | − | 124.375i | 0.0161716 | − | 0.0394524i | ||||
\(216\) | −1868.46 | − | 817.349i | −0.588578 | − | 0.257470i | ||||
\(217\) | 740.768 | − | 740.768i | 0.231735 | − | 0.231735i | ||||
\(218\) | −5236.15 | + | 5236.15i | −1.62678 | + | 1.62678i | ||||
\(219\) | 3568.83 | − | 4588.39i | 1.10118 | − | 1.41578i | ||||
\(220\) | −1047.16 | − | 2501.95i | −0.320908 | − | 0.766734i | ||||
\(221\) | − | 939.222i | − | 0.285877i | ||||||
\(222\) | 124.021 | + | 992.252i | 0.0374944 | + | 0.299980i | ||||
\(223\) | 1989.12 | + | 1989.12i | 0.597315 | + | 0.597315i | 0.939597 | − | 0.342282i | \(-0.111200\pi\) |
−0.342282 | + | 0.939597i | \(0.611200\pi\) | |||||||
\(224\) | 1105.09 | 0.329631 | ||||||||
\(225\) | 1704.24 | − | 2913.11i | 0.504960 | − | 0.863143i | ||||
\(226\) | 3203.26 | 0.942821 | ||||||||
\(227\) | 2922.00 | + | 2922.00i | 0.854360 | + | 0.854360i | 0.990667 | − | 0.136306i | \(-0.0435231\pi\) |
−0.136306 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(228\) | 69.8011 | + | 558.456i | 0.0202750 | + | 0.162213i | ||||
\(229\) | 3297.71i | 0.951610i | 0.879551 | + | 0.475805i | \(0.157843\pi\) | ||||
−0.879551 | + | 0.475805i | \(0.842157\pi\) | |||||||
\(230\) | −1090.21 | − | 2604.81i | −0.312550 | − | 0.746764i | ||||
\(231\) | −1440.28 | + | 1851.75i | −0.410233 | + | 0.527431i | ||||
\(232\) | 1325.42 | − | 1325.42i | 0.375078 | − | 0.375078i | ||||
\(233\) | −3389.26 | + | 3389.26i | −0.952951 | + | 0.952951i | −0.998942 | − | 0.0459912i | \(-0.985355\pi\) |
0.0459912 | + | 0.998942i | \(0.485355\pi\) | |||||||
\(234\) | −1072.61 | − | 4223.77i | −0.299653 | − | 1.17999i | ||||
\(235\) | 943.579 | − | 2301.97i | 0.261925 | − | 0.638995i | ||||
\(236\) | − | 2780.77i | − | 0.767004i | ||||||
\(237\) | 1880.85 | − | 235.087i | 0.515504 | − | 0.0644326i | ||||
\(238\) | 338.766 | + | 338.766i | 0.0922644 | + | 0.0922644i | ||||
\(239\) | 28.4146 | 0.00769033 | 0.00384517 | − | 0.999993i | \(-0.498776\pi\) | ||||
0.00384517 | + | 0.999993i | \(0.498776\pi\) | |||||||
\(240\) | 4028.70 | − | 2310.59i | 1.08355 | − | 0.621449i | ||||
\(241\) | 5848.65 | 1.56326 | 0.781628 | − | 0.623745i | \(-0.214390\pi\) | ||||
0.781628 | + | 0.623745i | \(0.214390\pi\) | |||||||
\(242\) | 6859.86 | + | 6859.86i | 1.82218 | + | 1.82218i | ||||
\(243\) | −2206.27 | − | 3079.17i | −0.582437 | − | 0.812876i | ||||
\(244\) | 2819.70i | 0.739806i | ||||||||
\(245\) | 505.359 | − | 211.512i | 0.131780 | − | 0.0551552i | ||||
\(246\) | −4892.69 | − | 3805.51i | −1.26808 | − | 0.986302i | ||||
\(247\) | 958.294 | − | 958.294i | 0.246862 | − | 0.246862i | ||||
\(248\) | 1538.31 | − | 1538.31i | 0.393882 | − | 0.393882i | ||||
\(249\) | −994.929 | − | 773.850i | −0.253217 | − | 0.196951i | ||||
\(250\) | 1883.00 | + | 4407.45i | 0.476365 | + | 1.11501i | ||||
\(251\) | 92.4335i | 0.0232444i | 0.999932 | + | 0.0116222i | \(0.00369955\pi\) | ||||
−0.999932 | + | 0.0116222i | \(0.996300\pi\) | |||||||
\(252\) | 610.933 | + | 363.484i | 0.152719 | + | 0.0908624i | ||||
\(253\) | 3358.65 | + | 3358.65i | 0.834611 | + | 0.834611i | ||||
\(254\) | 407.420 | 0.100645 | ||||||||
\(255\) | 1119.01 | + | 303.281i | 0.274804 | + | 0.0744791i | ||||
\(256\) | 4700.41 | 1.14756 | ||||||||
\(257\) | −2809.64 | − | 2809.64i | −0.681947 | − | 0.681947i | 0.278491 | − | 0.960439i | \(-0.410166\pi\) |
−0.960439 | + | 0.278491i | \(0.910166\pi\) | |||||||
\(258\) | 212.591 | − | 26.5716i | 0.0512998 | − | 0.00641193i | ||||
\(259\) | 392.805i | 0.0942382i | ||||||||
\(260\) | 1831.25 | + | 750.633i | 0.436806 | + | 0.179047i | ||||
\(261\) | 3374.44 | − | 856.927i | 0.800279 | − | 0.203228i | ||||
\(262\) | 72.7617 | − | 72.7617i | 0.0171574 | − | 0.0171574i | ||||
\(263\) | −2822.90 | + | 2822.90i | −0.661853 | + | 0.661853i | −0.955817 | − | 0.293964i | \(-0.905025\pi\) |
0.293964 | + | 0.955817i | \(0.405025\pi\) | |||||||
\(264\) | −2990.96 | + | 3845.43i | −0.697275 | + | 0.896477i | ||||
\(265\) | −2604.05 | − | 1067.40i | −0.603643 | − | 0.247434i | ||||
\(266\) | 691.290i | 0.159345i | ||||||||
\(267\) | −554.922 | − | 4439.75i | −0.127194 | − | 1.01763i | ||||
\(268\) | −2392.45 | − | 2392.45i | −0.545305 | − | 0.545305i | ||||
\(269\) | −436.688 | −0.0989789 | −0.0494895 | − | 0.998775i | \(-0.515759\pi\) | ||||
−0.0494895 | + | 0.998775i | \(0.515759\pi\) | |||||||
\(270\) | 5378.65 | + | 85.9510i | 1.21235 | + | 0.0193734i | ||||
\(271\) | 2711.07 | 0.607697 | 0.303849 | − | 0.952720i | \(-0.401728\pi\) | ||||
0.303849 | + | 0.952720i | \(0.401728\pi\) | |||||||
\(272\) | 1128.12 | + | 1128.12i | 0.251479 | + | 0.251479i | ||||
\(273\) | −212.308 | − | 1698.61i | −0.0470677 | − | 0.376573i | ||||
\(274\) | 3607.36i | 0.795359i | ||||||||
\(275\) | −5742.62 | − | 5658.55i | −1.25925 | − | 1.24081i | ||||
\(276\) | 883.683 | − | 1136.14i | 0.192723 | − | 0.247781i | ||||
\(277\) | −648.071 | + | 648.071i | −0.140573 | + | 0.140573i | −0.773892 | − | 0.633318i | \(-0.781692\pi\) |
0.633318 | + | 0.773892i | \(0.281692\pi\) | |||||||
\(278\) | 1134.13 | − | 1134.13i | 0.244677 | − | 0.244677i | ||||
\(279\) | 3916.45 | − | 994.567i | 0.840400 | − | 0.213416i | ||||
\(280\) | 1049.45 | − | 439.236i | 0.223988 | − | 0.0937477i | ||||
\(281\) | − | 6658.36i | − | 1.41354i | −0.707444 | − | 0.706769i | \(-0.750152\pi\) | ||
0.707444 | − | 0.706769i | \(-0.249848\pi\) | |||||||
\(282\) | 3934.71 | − | 491.797i | 0.830882 | − | 0.103851i | ||||
\(283\) | −2883.94 | − | 2883.94i | −0.605767 | − | 0.605767i | 0.336070 | − | 0.941837i | \(-0.390902\pi\) |
−0.941837 | + | 0.336070i | \(0.890902\pi\) | |||||||
\(284\) | −1451.08 | −0.303189 | ||||||||
\(285\) | 832.293 | + | 1451.17i | 0.172985 | + | 0.301614i | ||||
\(286\) | −10409.8 | −2.15226 | ||||||||
\(287\) | −1721.69 | − | 1721.69i | −0.354104 | − | 0.354104i | ||||
\(288\) | 3663.18 | + | 2179.46i | 0.749497 | + | 0.445924i | ||||
\(289\) | − | 4514.73i | − | 0.918936i | ||||||
\(290\) | −1875.19 | + | 4574.74i | −0.379707 | + | 0.926339i | ||||
\(291\) | −3563.52 | − | 2771.68i | −0.717859 | − | 0.558347i | ||||
\(292\) | −2975.33 | + | 2975.33i | −0.596295 | + | 0.596295i | ||||
\(293\) | −1362.70 | + | 1362.70i | −0.271707 | + | 0.271707i | −0.829787 | − | 0.558080i | \(-0.811538\pi\) |
0.558080 | + | 0.829787i | \(0.311538\pi\) | |||||||
\(294\) | 689.244 | + | 536.090i | 0.136726 | + | 0.106345i | ||||
\(295\) | −3191.29 | − | 7624.84i | −0.629845 | − | 1.50486i | ||||
\(296\) | 815.715i | 0.160177i | ||||||||
\(297\) | −8426.30 | + | 3297.70i | −1.64627 | + | 0.644282i | ||||
\(298\) | −7249.23 | − | 7249.23i | −1.40918 | − | 1.40918i | ||||
\(299\) | −3465.96 | −0.670373 | ||||||||
\(300\) | −1485.64 | + | 1939.41i | −0.285912 | + | 0.373240i | ||||
\(301\) | 84.1588 | 0.0161157 | ||||||||
\(302\) | −1902.02 | − | 1902.02i | −0.362413 | − | 0.362413i | ||||
\(303\) | 4009.20 | − | 501.108i | 0.760141 | − | 0.0950096i | ||||
\(304\) | 2302.05i | 0.434315i | ||||||||
\(305\) | 3235.96 | + | 7731.57i | 0.607511 | + | 1.45150i | ||||
\(306\) | 454.832 | + | 1791.06i | 0.0849707 | + | 0.334601i | ||||
\(307\) | −4547.73 | + | 4547.73i | −0.845448 | + | 0.845448i | −0.989561 | − | 0.144113i | \(-0.953967\pi\) |
0.144113 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(308\) | 1200.76 | − | 1200.76i | 0.222143 | − | 0.222143i | ||||
\(309\) | −4279.26 | + | 5501.79i | −0.787828 | + | 1.01290i | ||||
\(310\) | −2176.39 | + | 5309.54i | −0.398743 | + | 0.972779i | ||||
\(311\) | 2073.47i | 0.378056i | 0.981972 | + | 0.189028i | \(0.0605337\pi\) | ||||
−0.981972 | + | 0.189028i | \(0.939466\pi\) | |||||||
\(312\) | −440.888 | − | 3527.40i | −0.0800013 | − | 0.640064i | ||||
\(313\) | −1239.08 | − | 1239.08i | −0.223760 | − | 0.223760i | 0.586320 | − | 0.810080i | \(-0.300576\pi\) |
−0.810080 | + | 0.586320i | \(0.800576\pi\) | |||||||
\(314\) | 875.379 | 0.157326 | ||||||||
\(315\) | 2092.31 | + | 295.543i | 0.374249 | + | 0.0528633i | ||||
\(316\) | −1372.07 | −0.244257 | ||||||||
\(317\) | 4665.96 | + | 4665.96i | 0.826708 | + | 0.826708i | 0.987060 | − | 0.160352i | \(-0.0512628\pi\) |
−0.160352 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(318\) | −556.334 | − | 4451.05i | −0.0981059 | − | 0.784913i | ||||
\(319\) | − | 8316.59i | − | 1.45968i | ||||||
\(320\) | 1012.06 | − | 423.588i | 0.176800 | − | 0.0739978i | ||||
\(321\) | −6113.55 | + | 7860.12i | −1.06301 | + | 1.36669i | ||||
\(322\) | 1250.13 | − | 1250.13i | 0.216357 | − | 0.216357i | ||||
\(323\) | −406.357 | + | 406.357i | −0.0700010 | + | 0.0700010i | ||||
\(324\) | 1308.27 | + | 2409.76i | 0.224326 | + | 0.413197i | ||||
\(325\) | 5882.71 | − | 43.3738i | 1.00404 | − | 0.00740290i | ||||
\(326\) | − | 129.563i | − | 0.0220117i | ||||||
\(327\) | −11133.1 | + | 1391.52i | −1.88275 | + | 0.235325i | ||||
\(328\) | −3575.33 | − | 3575.33i | −0.601873 | − | 0.601873i | ||||
\(329\) | 1557.64 | 0.261020 | ||||||||
\(330\) | 3361.40 | − | 12402.5i | 0.560724 | − | 2.06889i | ||||
\(331\) | 3368.62 | 0.559384 | 0.279692 | − | 0.960090i | \(-0.409768\pi\) | ||||
0.279692 | + | 0.960090i | \(0.409768\pi\) | |||||||
\(332\) | 645.158 | + | 645.158i | 0.106650 | + | 0.106650i | ||||
\(333\) | −774.688 | + | 1302.07i | −0.127485 | + | 0.214274i | ||||
\(334\) | − | 4831.98i | − | 0.791600i | ||||||
\(335\) | −9305.69 | − | 3814.41i | −1.51768 | − | 0.622100i | ||||
\(336\) | 2295.24 | + | 1785.22i | 0.372665 | + | 0.289857i | ||||
\(337\) | 1833.78 | − | 1833.78i | 0.296417 | − | 0.296417i | −0.543192 | − | 0.839609i | \(-0.682784\pi\) |
0.839609 | + | 0.543192i | \(0.182784\pi\) | |||||||
\(338\) | 43.4699 | − | 43.4699i | 0.00699542 | − | 0.00699542i | ||||
\(339\) | 3831.01 | + | 2979.74i | 0.613782 | + | 0.477396i | ||||
\(340\) | −776.529 | − | 318.300i | −0.123862 | − | 0.0507713i | ||||
\(341\) | − | 9652.40i | − | 1.53286i | ||||||
\(342\) | −1363.36 | + | 2291.50i | −0.215562 | + | 0.362310i | ||||
\(343\) | 242.538 | + | 242.538i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 174.768 | 0.0273920 | ||||||||
\(345\) | 1119.18 | − | 4129.42i | 0.174651 | − | 0.644407i | ||||
\(346\) | −3389.15 | −0.526595 | ||||||||
\(347\) | −153.526 | − | 153.526i | −0.0237514 | − | 0.0237514i | 0.695131 | − | 0.718883i | \(-0.255346\pi\) |
−0.718883 | + | 0.695131i | \(0.755346\pi\) | |||||||
\(348\) | −2500.71 | + | 312.562i | −0.385207 | + | 0.0481469i | ||||
\(349\) | 5414.15i | 0.830409i | 0.909728 | + | 0.415204i | \(0.136290\pi\) | ||||
−0.909728 | + | 0.415204i | \(0.863710\pi\) | |||||||
\(350\) | −2106.18 | + | 2137.47i | −0.321657 | + | 0.326435i | ||||
\(351\) | 2646.23 | − | 6049.29i | 0.402408 | − | 0.919906i | ||||
\(352\) | 7199.84 | − | 7199.84i | 1.09021 | − | 1.09021i | ||||
\(353\) | −1171.64 | + | 1171.64i | −0.176657 | + | 0.176657i | −0.789897 | − | 0.613240i | \(-0.789866\pi\) |
0.613240 | + | 0.789897i | \(0.289866\pi\) | |||||||
\(354\) | 8088.51 | − | 10399.3i | 1.21441 | − | 1.56134i | ||||
\(355\) | −3978.84 | + | 1665.30i | −0.594859 | + | 0.248972i | ||||
\(356\) | 3238.78i | 0.482177i | ||||||||
\(357\) | 90.0277 | + | 720.282i | 0.0133467 | + | 0.106783i | ||||
\(358\) | 4208.42 | + | 4208.42i | 0.621291 | + | 0.621291i | ||||
\(359\) | 12471.9 | 1.83354 | 0.916772 | − | 0.399412i | \(-0.130786\pi\) | ||||
0.916772 | + | 0.399412i | \(0.130786\pi\) | |||||||
\(360\) | 4344.99 | + | 613.737i | 0.636114 | + | 0.0898522i | ||||
\(361\) | 6029.78 | 0.879105 | ||||||||
\(362\) | −10106.9 | − | 10106.9i | −1.46742 | − | 1.46742i | ||||
\(363\) | 1823.02 | + | 14585.4i | 0.263592 | + | 2.10891i | ||||
\(364\) | 1239.13i | 0.178428i | ||||||||
\(365\) | −4743.74 | + | 11572.9i | −0.680270 | + | 1.65960i | ||||
\(366\) | −8201.73 | + | 10544.9i | −1.17134 | + | 1.50598i | ||||
\(367\) | 2603.02 | − | 2603.02i | 0.370235 | − | 0.370235i | −0.497328 | − | 0.867563i | \(-0.665685\pi\) |
0.867563 | + | 0.497328i | \(0.165685\pi\) | |||||||
\(368\) | 4163.03 | − | 4163.03i | 0.589709 | − | 0.589709i | ||||
\(369\) | −2311.56 | − | 9102.57i | −0.326112 | − | 1.28418i | ||||
\(370\) | −830.704 | − | 1984.77i | −0.116720 | − | 0.278874i | ||||
\(371\) | − | 1762.04i | − | 0.246579i | ||||||
\(372\) | −2902.37 | + | 362.766i | −0.404519 | + | 0.0505606i | ||||
\(373\) | 6486.49 | + | 6486.49i | 0.900423 | + | 0.900423i | 0.995473 | − | 0.0950492i | \(-0.0303008\pi\) |
−0.0950492 | + | 0.995473i | \(0.530301\pi\) | |||||||
\(374\) | 4414.21 | 0.610303 | ||||||||
\(375\) | −1847.89 | + | 7022.80i | −0.254466 | + | 0.967082i | ||||
\(376\) | 3234.66 | 0.443657 | ||||||||
\(377\) | 4291.15 | + | 4291.15i | 0.586221 | + | 0.586221i | ||||
\(378\) | 1227.44 | + | 3136.36i | 0.167018 | + | 0.426765i | ||||
\(379\) | 3726.36i | 0.505040i | 0.967592 | + | 0.252520i | \(0.0812594\pi\) | ||||
−0.967592 | + | 0.252520i | \(0.918741\pi\) | |||||||
\(380\) | −467.534 | − | 1117.06i | −0.0631157 | − | 0.150800i | ||||
\(381\) | 487.264 | + | 378.991i | 0.0655204 | + | 0.0509614i | ||||
\(382\) | −4608.03 | + | 4608.03i | −0.617192 | + | 0.617192i | ||||
\(383\) | 2525.20 | − | 2525.20i | 0.336897 | − | 0.336897i | −0.518301 | − | 0.855198i | \(-0.673435\pi\) |
0.855198 | + | 0.518301i | \(0.173435\pi\) | |||||||
\(384\) | 6560.45 | + | 5102.68i | 0.871841 | + | 0.678113i | ||||
\(385\) | 1914.45 | − | 4670.51i | 0.253427 | − | 0.618263i | ||||
\(386\) | 11174.4i | 1.47348i | ||||||||
\(387\) | 278.971 | + | 165.978i | 0.0366431 | + | 0.0218013i | ||||
\(388\) | 2310.75 | + | 2310.75i | 0.302347 | + | 0.302347i | ||||
\(389\) | −6573.93 | −0.856842 | −0.428421 | − | 0.903579i | \(-0.640930\pi\) | ||||
−0.428421 | + | 0.903579i | \(0.640930\pi\) | |||||||
\(390\) | 4664.97 | + | 8133.77i | 0.605693 | + | 1.05608i | ||||
\(391\) | 1469.71 | 0.190094 | ||||||||
\(392\) | 503.664 | + | 503.664i | 0.0648951 | + | 0.0648951i | ||||
\(393\) | 154.705 | − | 19.3366i | 0.0198571 | − | 0.00248193i | ||||
\(394\) | − | 11005.8i | − | 1.40727i | ||||||
\(395\) | −3762.21 | + | 1574.63i | −0.479233 | + | 0.200578i | ||||
\(396\) | 6348.46 | − | 1612.17i | 0.805611 | − | 0.204582i | ||||
\(397\) | 1839.24 | − | 1839.24i | 0.232516 | − | 0.232516i | −0.581226 | − | 0.813742i | \(-0.697427\pi\) |
0.813742 | + | 0.581226i | \(0.197427\pi\) | |||||||
\(398\) | 9227.26 | − | 9227.26i | 1.16211 | − | 1.16211i | ||||
\(399\) | −643.052 | + | 826.764i | −0.0806839 | + | 0.103734i | ||||
\(400\) | −7013.74 | + | 7117.94i | −0.876718 | + | 0.889742i | ||||
\(401\) | − | 14811.1i | − | 1.84446i | −0.386640 | − | 0.922231i | \(-0.626364\pi\) | ||
0.386640 | − | 0.922231i | \(-0.373636\pi\) | |||||||
\(402\) | −1988.09 | − | 15906.0i | −0.246659 | − | 1.97343i | ||||
\(403\) | 4980.39 | + | 4980.39i | 0.615610 | + | 0.615610i | ||||
\(404\) | −2924.70 | −0.360171 | ||||||||
\(405\) | 6352.76 | + | 5106.13i | 0.779435 | + | 0.626483i | ||||
\(406\) | −3095.53 | −0.378395 | ||||||||
\(407\) | 2559.17 | + | 2559.17i | 0.311679 | + | 0.311679i | ||||
\(408\) | 186.955 | + | 1495.77i | 0.0226855 | + | 0.181499i | ||||
\(409\) | 1635.74i | 0.197756i | 0.995100 | + | 0.0988781i | \(0.0315254\pi\) | ||||
−0.995100 | + | 0.0988781i | \(0.968475\pi\) | |||||||
\(410\) | 12340.4 | + | 5058.34i | 1.48646 | + | 0.609301i | ||||
\(411\) | −3355.64 | + | 4314.30i | −0.402729 | + | 0.517783i | ||||
\(412\) | 3567.62 | − | 3567.62i | 0.426612 | − | 0.426612i | ||||
\(413\) | 3659.40 | − | 3659.40i | 0.435998 | − | 0.435998i | ||||
\(414\) | 6609.44 | − | 1678.44i | 0.784629 | − | 0.199254i | ||||
\(415\) | 2509.42 | + | 1028.61i | 0.296825 | + | 0.121669i | ||||
\(416\) | 7429.87i | 0.875671i | ||||||||
\(417\) | 2411.37 | − | 301.396i | 0.283178 | − | 0.0353943i | ||||
\(418\) | 4503.84 | + | 4503.84i | 0.527010 | + | 0.527010i | ||||
\(419\) | −8667.85 | −1.01063 | −0.505313 | − | 0.862936i | \(-0.668623\pi\) | ||||
−0.505313 | + | 0.862936i | \(0.668623\pi\) | |||||||
\(420\) | −1476.32 | − | 400.122i | −0.171517 | − | 0.0464856i | ||||
\(421\) | −7264.93 | −0.841023 | −0.420512 | − | 0.907287i | \(-0.638149\pi\) | ||||
−0.420512 | + | 0.907287i | \(0.638149\pi\) | |||||||
\(422\) | 3948.80 | + | 3948.80i | 0.455508 | + | 0.455508i | ||||
\(423\) | 5163.29 | + | 3071.97i | 0.593493 | + | 0.353108i | ||||
\(424\) | − | 3659.14i | − | 0.419112i | ||||||
\(425\) | −2494.52 | + | 18.3923i | −0.284711 | + | 0.00209920i | ||||
\(426\) | −5426.63 | − | 4220.80i | −0.617185 | − | 0.480043i | ||||
\(427\) | −3710.62 | + | 3710.62i | −0.420538 | + | 0.420538i | ||||
\(428\) | 5096.87 | − | 5096.87i | 0.575622 | − | 0.575622i | ||||
\(429\) | −12449.9 | − | 9683.44i | −1.40113 | − | 1.08979i | ||||
\(430\) | −425.239 | + | 177.979i | −0.0476903 | + | 0.0199603i | ||||
\(431\) | 4531.28i | 0.506413i | 0.967412 | + | 0.253206i | \(0.0814852\pi\) | ||||
−0.967412 | + | 0.253206i | \(0.918515\pi\) | |||||||
\(432\) | 4087.47 | + | 10444.3i | 0.455229 | + | 1.16320i | ||||
\(433\) | 6817.22 | + | 6817.22i | 0.756616 | + | 0.756616i | 0.975705 | − | 0.219089i | \(-0.0703084\pi\) |
−0.219089 | + | 0.975705i | \(0.570308\pi\) | |||||||
\(434\) | −3592.73 | −0.397366 | ||||||||
\(435\) | −6498.20 | + | 3726.93i | −0.716241 | + | 0.410787i | ||||
\(436\) | 8121.54 | 0.892090 | ||||||||
\(437\) | 1499.56 | + | 1499.56i | 0.164150 | + | 0.164150i | ||||
\(438\) | −19781.3 | + | 2472.46i | −2.15796 | + | 0.269723i | ||||
\(439\) | 9765.07i | 1.06164i | 0.847484 | + | 0.530821i | \(0.178116\pi\) | ||||
−0.847484 | + | 0.530821i | \(0.821884\pi\) | |||||||
\(440\) | 3975.62 | − | 9698.98i | 0.430751 | − | 1.05087i | ||||
\(441\) | 325.635 | + | 1282.30i | 0.0351620 | + | 0.138462i | ||||
\(442\) | −2277.62 | + | 2277.62i | −0.245102 | + | 0.245102i | ||||
\(443\) | −4984.49 | + | 4984.49i | −0.534583 | + | 0.534583i | −0.921933 | − | 0.387350i | \(-0.873390\pi\) |
0.387350 | + | 0.921933i | \(0.373390\pi\) | |||||||
\(444\) | 673.335 | − | 865.698i | 0.0719709 | − | 0.0925320i | ||||
\(445\) | 3716.91 | + | 8880.69i | 0.395952 | + | 0.946033i | ||||
\(446\) | − | 9647.25i | − | 1.02424i | ||||||
\(447\) | −1926.50 | − | 15413.3i | −0.203848 | − | 1.63092i | ||||
\(448\) | 485.721 | + | 485.721i | 0.0512236 | + | 0.0512236i | ||||
\(449\) | 5432.39 | 0.570981 | 0.285491 | − | 0.958382i | \(-0.407843\pi\) | ||||
0.285491 | + | 0.958382i | \(0.407843\pi\) | |||||||
\(450\) | −11197.1 | + | 2931.51i | −1.17297 | + | 0.307094i | ||||
\(451\) | −22434.0 | −2.34230 | ||||||||
\(452\) | −2484.21 | − | 2484.21i | −0.258512 | − | 0.258512i | ||||
\(453\) | −505.465 | − | 4044.06i | −0.0524256 | − | 0.419440i | ||||
\(454\) | − | 14171.7i | − | 1.46500i | ||||||
\(455\) | 1422.06 | + | 3397.67i | 0.146521 | + | 0.350078i | ||||
\(456\) | −1335.39 | + | 1716.89i | −0.137139 | + | 0.176318i | ||||
\(457\) | −4503.81 | + | 4503.81i | −0.461005 | + | 0.461005i | −0.898985 | − | 0.437980i | \(-0.855694\pi\) |
0.437980 | + | 0.898985i | \(0.355694\pi\) | |||||||
\(458\) | 7996.96 | − | 7996.96i | 0.815881 | − | 0.815881i | ||||
\(459\) | −1122.11 | + | 2565.15i | −0.114108 | + | 0.260852i | ||||
\(460\) | −1174.60 | + | 2865.58i | −0.119057 | + | 0.290453i | ||||
\(461\) | 6214.48i | 0.627846i | 0.949448 | + | 0.313923i | \(0.101643\pi\) | ||||
−0.949448 | + | 0.313923i | \(0.898357\pi\) | |||||||
\(462\) | 7983.21 | − | 997.818i | 0.803924 | − | 0.100482i | ||||
\(463\) | −7606.78 | − | 7606.78i | −0.763536 | − | 0.763536i | 0.213424 | − | 0.976960i | \(-0.431538\pi\) |
−0.976960 | + | 0.213424i | \(0.931538\pi\) | |||||||
\(464\) | −10308.4 | −1.03137 | ||||||||
\(465\) | −7541.94 | + | 4325.55i | −0.752149 | + | 0.431381i | ||||
\(466\) | 16437.9 | 1.63406 | ||||||||
\(467\) | 9790.21 | + | 9790.21i | 0.970101 | + | 0.970101i | 0.999566 | − | 0.0294650i | \(-0.00938034\pi\) |
−0.0294650 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(468\) | −2443.81 | + | 4107.48i | −0.241378 | + | 0.405701i | ||||
\(469\) | − | 6296.75i | − | 0.619951i | ||||||
\(470\) | −7870.47 | + | 3294.10i | −0.772421 | + | 0.323288i | ||||
\(471\) | 1046.93 | + | 814.296i | 0.102420 | + | 0.0796620i | ||||
\(472\) | 7599.26 | − | 7599.26i | 0.741069 | − | 0.741069i | ||||
\(473\) | 548.305 | − | 548.305i | 0.0533004 | − | 0.0533004i | ||||
\(474\) | −5131.16 | − | 3990.99i | −0.497220 | − | 0.386735i | ||||
\(475\) | −2563.94 | − | 2526.41i | −0.247667 | − | 0.244041i | ||||
\(476\) | − | 525.443i | − | 0.0505959i | ||||||
\(477\) | 3475.10 | − | 5840.85i | 0.333572 | − | 0.560658i | ||||
\(478\) | −68.9056 | − | 68.9056i | −0.00659345 | − | 0.00659345i | ||||
\(479\) | 8524.16 | 0.813108 | 0.406554 | − | 0.913627i | \(-0.366730\pi\) | ||||
0.406554 | + | 0.913627i | \(0.366730\pi\) | |||||||
\(480\) | −8852.10 | − | 2399.15i | −0.841753 | − | 0.228137i | ||||
\(481\) | −2640.94 | −0.250346 | ||||||||
\(482\) | −14183.0 | − | 14183.0i | −1.34029 | − | 1.34029i | ||||
\(483\) | 2658.02 | − | 332.224i | 0.250401 | − | 0.0312975i | ||||
\(484\) | − | 10640.0i | − | 0.999247i | ||||||
\(485\) | 8987.93 | + | 3684.16i | 0.841486 | + | 0.344926i | ||||
\(486\) | −2116.79 | + | 12817.2i | −0.197571 | + | 1.19630i | ||||
\(487\) | −5184.97 | + | 5184.97i | −0.482450 | + | 0.482450i | −0.905913 | − | 0.423463i | \(-0.860814\pi\) |
0.423463 | + | 0.905913i | \(0.360814\pi\) | |||||||
\(488\) | −7705.64 | + | 7705.64i | −0.714791 | + | 0.714791i | ||||
\(489\) | 120.522 | − | 154.953i | 0.0111456 | − | 0.0143297i | ||||
\(490\) | −1738.42 | − | 712.579i | −0.160273 | − | 0.0656960i | ||||
\(491\) | 2689.92i | 0.247239i | 0.992330 | + | 0.123620i | \(0.0394502\pi\) | ||||
−0.992330 | + | 0.123620i | \(0.960550\pi\) | |||||||
\(492\) | 843.138 | + | 6745.67i | 0.0772594 | + | 0.618127i | ||||
\(493\) | −1819.63 | − | 1819.63i | −0.166231 | − | 0.166231i | ||||
\(494\) | −4647.74 | −0.423303 | ||||||||
\(495\) | 15557.2 | − | 11706.2i | 1.41261 | − | 1.06294i | ||||
\(496\) | −11964.1 | −1.08307 | ||||||||
\(497\) | −1909.57 | − | 1909.57i | −0.172346 | − | 0.172346i | ||||
\(498\) | 536.117 | + | 4289.30i | 0.0482409 | + | 0.385960i | ||||
\(499\) | 9788.18i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(500\) | 1957.78 | − | 4878.40i | 0.175109 | − | 0.436337i | ||||
\(501\) | 4494.81 | − | 5778.92i | 0.400825 | − | 0.515336i | ||||
\(502\) | 224.152 | − | 224.152i | 0.0199290 | − | 0.0199290i | ||||
\(503\) | 5673.30 | − | 5673.30i | 0.502903 | − | 0.502903i | −0.409436 | − | 0.912339i | \(-0.634275\pi\) |
0.912339 | + | 0.409436i | \(0.134275\pi\) | |||||||
\(504\) | 676.228 | + | 2662.88i | 0.0597650 | + | 0.235345i | ||||
\(505\) | −8019.47 | + | 3356.46i | −0.706657 | + | 0.295764i | ||||
\(506\) | − | 16289.5i | − | 1.43114i | ||||||
\(507\) | 92.4255 | − | 11.5522i | 0.00809617 | − | 0.00101194i | ||||
\(508\) | −315.965 | − | 315.965i | −0.0275958 | − | 0.0275958i | ||||
\(509\) | −6952.13 | −0.605398 | −0.302699 | − | 0.953086i | \(-0.597888\pi\) | ||||
−0.302699 | + | 0.953086i | \(0.597888\pi\) | |||||||
\(510\) | −1978.15 | − | 3449.06i | −0.171753 | − | 0.299465i | ||||
\(511\) | −7830.86 | −0.677920 | ||||||||
\(512\) | −2350.37 | − | 2350.37i | −0.202876 | − | 0.202876i | ||||
\(513\) | −3762.14 | + | 1472.34i | −0.323787 | + | 0.126716i | ||||
\(514\) | 13626.8i | 1.16936i | ||||||||
\(515\) | 5688.06 | − | 13876.7i | 0.486691 | − | 1.18734i | ||||
\(516\) | −185.477 | − | 144.263i | −0.0158239 | − | 0.0123078i | ||||
\(517\) | 10148.2 | − | 10148.2i | 0.863286 | − | 0.863286i | ||||
\(518\) | 952.554 | − | 952.554i | 0.0807969 | − | 0.0807969i | ||||
\(519\) | −4053.33 | − | 3152.66i | −0.342816 | − | 0.266641i | ||||
\(520\) | 2953.11 | + | 7055.75i | 0.249043 | + | 0.595029i | ||||
\(521\) | − | 843.078i | − | 0.0708943i | −0.999372 | − | 0.0354471i | \(-0.988714\pi\) | ||
0.999372 | − | 0.0354471i | \(-0.0112855\pi\) | |||||||
\(522\) | −10261.1 | − | 6104.99i | −0.860376 | − | 0.511893i | ||||
\(523\) | 7617.41 | + | 7617.41i | 0.636876 | + | 0.636876i | 0.949784 | − | 0.312908i | \(-0.101303\pi\) |
−0.312908 | + | 0.949784i | \(0.601303\pi\) | |||||||
\(524\) | −112.857 | −0.00940874 | ||||||||
\(525\) | −4507.25 | + | 597.141i | −0.374690 | + | 0.0496407i | ||||
\(526\) | 13691.1 | 1.13490 | ||||||||
\(527\) | −2111.90 | − | 2111.90i | −0.174565 | − | 0.174565i | ||||
\(528\) | 26584.7 | − | 3322.81i | 2.19120 | − | 0.273877i | ||||
\(529\) | 6743.40i | 0.554237i | ||||||||
\(530\) | 3726.37 | + | 8903.29i | 0.305403 | + | 0.729687i | ||||
\(531\) | 19347.3 | − | 4913.17i | 1.58117 | − | 0.401532i | ||||
\(532\) | 536.113 | − | 536.113i | 0.0436907 | − | 0.0436907i | ||||
\(533\) | 11575.4 | − | 11575.4i | 0.940686 | − | 0.940686i | ||||
\(534\) | −9420.73 | + | 12112.1i | −0.763436 | + | 0.981540i | ||||
\(535\) | 8126.23 | − | 19824.8i | 0.656687 | − | 1.60206i | ||||
\(536\) | − | 13076.1i | − | 1.05373i | ||||||
\(537\) | 1118.40 | + | 8947.93i | 0.0898741 | + | 0.719053i | ||||
\(538\) | 1058.97 | + | 1058.97i | 0.0848615 | + | 0.0848615i | ||||
\(539\) | 3160.33 | 0.252551 | ||||||||
\(540\) | −4104.62 | − | 4237.93i | −0.327101 | − | 0.337725i | ||||
\(541\) | −20352.3 | −1.61740 | −0.808699 | − | 0.588223i | \(-0.799828\pi\) | ||||
−0.808699 | + | 0.588223i | \(0.799828\pi\) | |||||||
\(542\) | −6574.37 | − | 6574.37i | −0.521021 | − | 0.521021i | ||||
\(543\) | −2685.92 | − | 21489.2i | −0.212272 | − | 1.69832i | ||||
\(544\) | − | 3150.58i | − | 0.248309i | ||||||
\(545\) | 22269.1 | − | 9320.50i | 1.75028 | − | 0.732563i | ||||
\(546\) | −3604.29 | + | 4633.98i | −0.282508 | + | 0.363217i | ||||
\(547\) | 2555.31 | − | 2555.31i | 0.199739 | − | 0.199739i | −0.600149 | − | 0.799888i | \(-0.704892\pi\) |
0.799888 | + | 0.600149i | \(0.204892\pi\) | |||||||
\(548\) | 2797.60 | − | 2797.60i | 0.218079 | − | 0.218079i | ||||
\(549\) | −19618.1 | + | 4981.94i | −1.52510 | + | 0.387294i | ||||
\(550\) | 203.850 | + | 27647.9i | 0.0158040 | + | 2.14347i | ||||
\(551\) | − | 3713.16i | − | 0.287088i | ||||||
\(552\) | 5519.75 | − | 689.911i | 0.425609 | − | 0.0531966i | ||||
\(553\) | −1805.60 | − | 1805.60i | −0.138846 | − | 0.138846i | ||||
\(554\) | 3143.15 | 0.241047 | ||||||||
\(555\) | 852.775 | − | 3146.47i | 0.0652222 | − | 0.240649i | ||||
\(556\) | −1759.09 | −0.134176 | ||||||||
\(557\) | 2195.78 | + | 2195.78i | 0.167035 | + | 0.167035i | 0.785675 | − | 0.618640i | \(-0.212316\pi\) |
−0.618640 | + | 0.785675i | \(0.712316\pi\) | |||||||
\(558\) | −11909.2 | − | 7085.58i | −0.903509 | − | 0.537556i | ||||
\(559\) | 565.823i | 0.0428118i | ||||||||
\(560\) | −5789.07 | − | 2372.95i | −0.436844 | − | 0.179063i | ||||
\(561\) | 5279.27 | + | 4106.19i | 0.397310 | + | 0.309026i | ||||
\(562\) | −16146.6 | + | 16146.6i | −1.21192 | + | 1.21192i | ||||
\(563\) | −17800.8 | + | 17800.8i | −1.33253 | + | 1.33253i | −0.429434 | + | 0.903098i | \(0.641287\pi\) |
−0.903098 | + | 0.429434i | \(0.858713\pi\) | |||||||
\(564\) | −3432.87 | − | 2670.07i | −0.256294 | − | 0.199344i | ||||
\(565\) | −9662.61 | − | 3960.71i | −0.719485 | − | 0.294918i | ||||
\(566\) | 13987.1i | 1.03873i | ||||||||
\(567\) | −1449.53 | + | 4892.80i | −0.107362 | + | 0.362395i | ||||
\(568\) | −3965.50 | − | 3965.50i | −0.292938 | − | 0.292938i | ||||
\(569\) | 8272.60 | 0.609500 | 0.304750 | − | 0.952432i | \(-0.401427\pi\) | ||||
0.304750 | + | 0.952432i | \(0.401427\pi\) | |||||||
\(570\) | 1500.78 | − | 5537.41i | 0.110282 | − | 0.406907i | ||||
\(571\) | 24911.1 | 1.82574 | 0.912869 | − | 0.408253i | \(-0.133862\pi\) | ||||
0.912869 | + | 0.408253i | \(0.133862\pi\) | |||||||
\(572\) | 8073.08 | + | 8073.08i | 0.590127 | + | 0.590127i | ||||
\(573\) | −9797.57 | + | 1224.59i | −0.714310 | + | 0.0892812i | ||||
\(574\) | 8350.20i | 0.607196i | ||||||||
\(575\) | 67.8721 | + | 9205.38i | 0.00492254 | + | 0.667637i | ||||
\(576\) | 652.137 | + | 2568.01i | 0.0471743 | + | 0.185765i | ||||
\(577\) | 4880.24 | − | 4880.24i | 0.352109 | − | 0.352109i | −0.508785 | − | 0.860894i | \(-0.669905\pi\) |
0.860894 | + | 0.508785i | \(0.169905\pi\) | |||||||
\(578\) | −10948.2 | + | 10948.2i | −0.787867 | + | 0.787867i | ||||
\(579\) | −10394.7 | + | 13364.3i | −0.746092 | + | 0.959241i | ||||
\(580\) | 5002.09 | − | 2093.57i | 0.358104 | − | 0.149881i | ||||
\(581\) | 1698.01i | 0.121249i | ||||||||
\(582\) | 1920.20 | + | 15362.9i | 0.136761 | + | 1.09418i | ||||
\(583\) | −11480.0 | − | 11480.0i | −0.815525 | − | 0.815525i | ||||
\(584\) | −16261.9 | −1.15226 | ||||||||
\(585\) | −1987.02 | + | 14067.2i | −0.140433 | + | 0.994202i | ||||
\(586\) | 6609.13 | 0.465906 | ||||||||
\(587\) | −2950.14 | − | 2950.14i | −0.207437 | − | 0.207437i | 0.595740 | − | 0.803177i | \(-0.296859\pi\) |
−0.803177 | + | 0.595740i | \(0.796859\pi\) | |||||||
\(588\) | −118.775 | − | 950.278i | −0.00833025 | − | 0.0666476i | ||||
\(589\) | − | 4309.56i | − | 0.301481i | ||||||
\(590\) | −10751.4 | + | 26229.2i | −0.750215 | + | 1.83023i | ||||
\(591\) | 10237.8 | − | 13162.6i | 0.712568 | − | 0.916139i | ||||
\(592\) | 3172.08 | − | 3172.08i | 0.220222 | − | 0.220222i | ||||
\(593\) | 4336.37 | − | 4336.37i | 0.300292 | − | 0.300292i | −0.540836 | − | 0.841128i | \(-0.681892\pi\) |
0.841128 | + | 0.540836i | \(0.181892\pi\) | |||||||
\(594\) | 28430.8 | + | 12436.9i | 1.96385 | + | 0.859077i | ||||
\(595\) | −603.013 | − | 1440.76i | −0.0415481 | − | 0.0992693i | ||||
\(596\) | 11243.9i | 0.772766i | ||||||||
\(597\) | 19618.9 | − | 2452.16i | 1.34497 | − | 0.168108i | ||||
\(598\) | 8404.97 | + | 8404.97i | 0.574757 | + | 0.574757i | ||||
\(599\) | −27716.3 | −1.89058 | −0.945289 | − | 0.326234i | \(-0.894220\pi\) | ||||
−0.945289 | + | 0.326234i | \(0.894220\pi\) | |||||||
\(600\) | −9359.95 | + | 1240.05i | −0.636864 | + | 0.0843747i | ||||
\(601\) | −12187.0 | −0.827153 | −0.413576 | − | 0.910469i | \(-0.635721\pi\) | ||||
−0.413576 | + | 0.910469i | \(0.635721\pi\) | |||||||
\(602\) | −204.085 | − | 204.085i | −0.0138171 | − | 0.0138171i | ||||
\(603\) | 12418.4 | − | 20872.5i | 0.838669 | − | 1.40961i | ||||
\(604\) | 2950.13i | 0.198740i | ||||||||
\(605\) | −12210.7 | − | 29174.7i | −0.820557 | − | 1.96053i | ||||
\(606\) | −10937.5 | − | 8507.15i | −0.733179 | − | 0.570263i | ||||
\(607\) | 11510.6 | − | 11510.6i | 0.769691 | − | 0.769691i | −0.208361 | − | 0.978052i | \(-0.566813\pi\) |
0.978052 | + | 0.208361i | \(0.0668129\pi\) | |||||||
\(608\) | 3214.55 | − | 3214.55i | 0.214420 | − | 0.214420i | ||||
\(609\) | −3702.17 | − | 2879.53i | −0.246337 | − | 0.191600i | ||||
\(610\) | 10901.9 | − | 26596.3i | 0.723613 | − | 1.76533i | ||||
\(611\) | 10472.5i | 0.693405i | ||||||||
\(612\) | 1036.28 | − | 1741.74i | 0.0684461 | − | 0.115042i | ||||
\(613\) | 6228.42 | + | 6228.42i | 0.410381 | + | 0.410381i | 0.881871 | − | 0.471490i | \(-0.156284\pi\) |
−0.471490 | + | 0.881871i | \(0.656284\pi\) | |||||||
\(614\) | 22056.5 | 1.44972 | ||||||||
\(615\) | 10053.4 | + | 17528.9i | 0.659174 | + | 1.14932i | ||||
\(616\) | 6562.87 | 0.429263 | ||||||||
\(617\) | 8196.21 | + | 8196.21i | 0.534793 | + | 0.534793i | 0.921995 | − | 0.387202i | \(-0.126558\pi\) |
−0.387202 | + | 0.921995i | \(0.626558\pi\) | |||||||
\(618\) | 23719.1 | − | 2964.64i | 1.54389 | − | 0.192970i | ||||
\(619\) | − | 17512.8i | − | 1.13716i | −0.822629 | − | 0.568579i | \(-0.807494\pi\) | ||
0.822629 | − | 0.568579i | \(-0.192506\pi\) | |||||||
\(620\) | 5805.52 | − | 2429.84i | 0.376057 | − | 0.157395i | ||||
\(621\) | 9466.04 | + | 4140.87i | 0.611689 | + | 0.267580i | ||||
\(622\) | 5028.17 | − | 5028.17i | 0.324134 | − | 0.324134i | ||||
\(623\) | −4262.12 | + | 4262.12i | −0.274090 | + | 0.274090i | ||||
\(624\) | −12002.6 | + | 15431.5i | −0.770012 | + | 0.989994i | ||||
\(625\) | −230.396 | − | 15623.3i | −0.0147454 | − | 0.999891i | ||||
\(626\) | 6009.55i | 0.383690i | ||||||||
\(627\) | 1196.91 | + | 9576.05i | 0.0762357 | + | 0.609937i | ||||
\(628\) | −678.879 | − | 678.879i | −0.0431373 | − | 0.0431373i | ||||
\(629\) | 1119.87 | 0.0709891 | ||||||||
\(630\) | −4357.18 | − | 5790.57i | −0.275546 | − | 0.366193i | ||||
\(631\) | −15834.8 | −0.999006 | −0.499503 | − | 0.866312i | \(-0.666484\pi\) | ||||
−0.499503 | + | 0.866312i | \(0.666484\pi\) | |||||||
\(632\) | −3749.59 | − | 3749.59i | −0.235998 | − | 0.235998i | ||||
\(633\) | 1049.40 | + | 8395.92i | 0.0658925 | + | 0.527184i | ||||
\(634\) | − | 22630.0i | − | 1.41759i | ||||||
\(635\) | −1228.98 | − | 503.760i | −0.0768041 | − | 0.0314821i | ||||
\(636\) | −3020.45 | + | 3883.35i | −0.188315 | + | 0.242115i | ||||
\(637\) | −1630.65 | + | 1630.65i | −0.101427 | + | 0.101427i | ||||
\(638\) | −20167.8 | + | 20167.8i | −1.25149 | + | 1.25149i | ||||
\(639\) | −2563.82 | − | 10095.9i | −0.158722 | − | 0.625021i | ||||
\(640\) | −16546.8 | − | 6782.56i | −1.02199 | − | 0.418913i | ||||
\(641\) | 2960.57i | 0.182426i | 0.995831 | + | 0.0912132i | \(0.0290745\pi\) | ||||
−0.995831 | + | 0.0912132i | \(0.970926\pi\) | |||||||
\(642\) | 33886.2 | − | 4235.42i | 2.08315 | − | 0.260372i | ||||
\(643\) | 6111.30 | + | 6111.30i | 0.374815 | + | 0.374815i | 0.869227 | − | 0.494412i | \(-0.164617\pi\) |
−0.494412 | + | 0.869227i | \(0.664617\pi\) | |||||||
\(644\) | −1939.01 | −0.118646 | ||||||||
\(645\) | −674.134 | − | 182.708i | −0.0411535 | − | 0.0111537i | ||||
\(646\) | 1970.84 | 0.120033 | ||||||||
\(647\) | 13851.7 | + | 13851.7i | 0.841677 | + | 0.841677i | 0.989077 | − | 0.147400i | \(-0.0470905\pi\) |
−0.147400 | + | 0.989077i | \(0.547090\pi\) | |||||||
\(648\) | −3010.15 | + | 10160.6i | −0.182484 | + | 0.615966i | ||||
\(649\) | − | 47682.9i | − | 2.88400i | ||||||
\(650\) | −14370.8 | − | 14160.4i | −0.867183 | − | 0.854489i | ||||
\(651\) | −4296.81 | − | 3342.04i | −0.258687 | − | 0.201205i | ||||
\(652\) | −100.479 | + | 100.479i | −0.00603537 | + | 0.00603537i | ||||
\(653\) | −1322.00 | + | 1322.00i | −0.0792248 | + | 0.0792248i | −0.745609 | − | 0.666384i | \(-0.767841\pi\) |
0.666384 | + | 0.745609i | \(0.267841\pi\) | |||||||
\(654\) | 30372.2 | + | 23623.3i | 1.81598 | + | 1.41246i | ||||
\(655\) | −309.452 | + | 129.518i | −0.0184600 | + | 0.00772623i | ||||
\(656\) | 27806.8i | 1.65499i | ||||||||
\(657\) | −25957.8 | − | 15444.0i | −1.54142 | − | 0.917090i | ||||
\(658\) | −3777.29 | − | 3777.29i | −0.223790 | − | 0.223790i | ||||
\(659\) | 21863.2 | 1.29237 | 0.646183 | − | 0.763183i | \(-0.276364\pi\) | ||||
0.646183 | + | 0.763183i | \(0.276364\pi\) | |||||||
\(660\) | −12225.3 | + | 7011.59i | −0.721013 | + | 0.413524i | ||||
\(661\) | −21335.2 | −1.25543 | −0.627717 | − | 0.778442i | \(-0.716010\pi\) | ||||
−0.627717 | + | 0.778442i | \(0.716010\pi\) | |||||||
\(662\) | −8168.93 | − | 8168.93i | −0.479599 | − | 0.479599i | ||||
\(663\) | −4842.66 | + | 605.282i | −0.283670 | + | 0.0354558i | ||||
\(664\) | 3526.16i | 0.206087i | ||||||||
\(665\) | 854.755 | − | 2085.27i | 0.0498436 | − | 0.121599i | ||||
\(666\) | 5036.16 | − | 1278.91i | 0.293014 | − | 0.0744098i | ||||
\(667\) | −6714.87 | + | 6714.87i | −0.389806 | + | 0.389806i | ||||
\(668\) | −3747.33 | + | 3747.33i | −0.217048 | + | 0.217048i | ||||
\(669\) | 8974.08 | − | 11537.9i | 0.518622 | − | 0.666785i | ||||
\(670\) | 13316.4 | + | 31816.3i | 0.767845 | + | 1.83458i | ||||
\(671\) | 48350.4i | 2.78174i | ||||||||
\(672\) | −712.178 | − | 5697.91i | −0.0408823 | − | 0.327086i | ||||
\(673\) | 20720.1 | + | 20720.1i | 1.18678 | + | 1.18678i | 0.977953 | + | 0.208826i | \(0.0669643\pi\) |
0.208826 | + | 0.977953i | \(0.433036\pi\) | |||||||
\(674\) | −8893.87 | −0.508278 | ||||||||
\(675\) | −16118.4 | − | 6909.77i | −0.919106 | − | 0.394011i | ||||
\(676\) | −67.4240 | −0.00383614 | ||||||||
\(677\) | 5089.70 | + | 5089.70i | 0.288941 | + | 0.288941i | 0.836661 | − | 0.547720i | \(-0.184504\pi\) |
−0.547720 | + | 0.836661i | \(0.684504\pi\) | |||||||
\(678\) | −2064.34 | − | 16516.1i | −0.116933 | − | 0.935542i | ||||
\(679\) | 6081.74i | 0.343734i | ||||||||
\(680\) | −1252.24 | − | 2991.94i | −0.0706196 | − | 0.168729i | ||||
\(681\) | 13182.8 | − | 16949.0i | 0.741803 | − | 0.953726i | ||||
\(682\) | −23407.1 | + | 23407.1i | −1.31423 | + | 1.31423i | ||||
\(683\) | −17464.4 | + | 17464.4i | −0.978415 | + | 0.978415i | −0.999772 | − | 0.0213568i | \(-0.993201\pi\) |
0.0213568 | + | 0.999772i | \(0.493201\pi\) | |||||||
\(684\) | 2834.43 | − | 719.793i | 0.158446 | − | 0.0402368i | ||||
\(685\) | 4460.37 | − | 10881.6i | 0.248791 | − | 0.606954i | ||||
\(686\) | − | 1176.31i | − | 0.0654690i | ||||||
\(687\) | 17003.1 | − | 2125.21i | 0.944263 | − | 0.118023i | ||||
\(688\) | −679.621 | − | 679.621i | −0.0376603 | − | 0.0376603i | ||||
\(689\) | 11846.7 | 0.655043 | ||||||||
\(690\) | −12727.9 | + | 7299.84i | −0.702235 | + | 0.402754i | ||||
\(691\) | 12449.0 | 0.685355 | 0.342678 | − | 0.939453i | \(-0.388666\pi\) | ||||
0.342678 | + | 0.939453i | \(0.388666\pi\) | |||||||
\(692\) | 2628.37 | + | 2628.37i | 0.144387 | + | 0.144387i | ||||
\(693\) | 10475.9 | + | 6232.79i | 0.574238 | + | 0.341651i | ||||
\(694\) | 744.604i | 0.0407274i | ||||||||
\(695\) | −4823.39 | + | 2018.78i | −0.263254 | + | 0.110182i | ||||
\(696\) | −7688.08 | − | 5979.75i | −0.418701 | − | 0.325663i | ||||
\(697\) | −4908.45 | + | 4908.45i | −0.266744 | + | 0.266744i | ||||
\(698\) | 13129.3 | − | 13129.3i | 0.711967 | − | 0.711967i | ||||
\(699\) | 19659.3 | + | 15290.9i | 1.06378 | + | 0.827404i | ||||
\(700\) | 3291.05 | − | 24.2652i | 0.177700 | − | 0.00131020i | ||||
\(701\) | − | 16136.2i | − | 0.869408i | −0.900573 | − | 0.434704i | \(-0.856853\pi\) | ||
0.900573 | − | 0.434704i | \(-0.143147\pi\) | |||||||
\(702\) | −21086.7 | + | 8252.43i | −1.13371 | + | 0.443686i | ||||
\(703\) | 1142.61 | + | 1142.61i | 0.0613006 | + | 0.0613006i | ||||
\(704\) | 6329.07 | 0.338829 | ||||||||
\(705\) | −12477.1 | − | 3381.62i | −0.666547 | − | 0.180652i | ||||
\(706\) | 5682.46 | 0.302921 | ||||||||
\(707\) | −3848.80 | − | 3848.80i | −0.204737 | − | 0.204737i | ||||
\(708\) | −14337.8 | + | 1792.07i | −0.761082 | + | 0.0951272i | ||||
\(709\) | 30039.6i | 1.59120i | 0.605822 | + | 0.795600i | \(0.292844\pi\) | ||||
−0.605822 | + | 0.795600i | \(0.707156\pi\) | |||||||
\(710\) | 13687.1 | + | 5610.35i | 0.723474 | + | 0.296553i | ||||
\(711\) | −2424.23 | − | 9546.23i | −0.127870 | − | 0.503533i | ||||
\(712\) | −8850.90 | + | 8850.90i | −0.465873 | + | 0.465873i | ||||
\(713\) | −7793.41 | + | 7793.41i | −0.409349 | + | 0.409349i | ||||
\(714\) | 1528.37 | − | 1965.01i | 0.0801090 | − | 0.102995i | ||||
\(715\) | 31401.2 | + | 12871.4i | 1.64243 | + | 0.673234i | ||||
\(716\) | − | 6527.48i | − | 0.340703i | ||||||
\(717\) | −18.3118 | − | 146.507i | −0.000953789 | − | 0.00763096i | ||||
\(718\) | −30244.4 | − | 30244.4i | −1.57202 | − | 1.57202i | ||||
\(719\) | 23798.4 | 1.23439 | 0.617197 | − | 0.786809i | \(-0.288268\pi\) | ||||
0.617197 | + | 0.786809i | \(0.288268\pi\) | |||||||
\(720\) | −14509.8 | − | 19283.1i | −0.751038 | − | 0.998107i | ||||
\(721\) | 9389.73 | 0.485010 | ||||||||
\(722\) | −14622.3 | − | 14622.3i | −0.753718 | − | 0.753718i | ||||
\(723\) | −3769.16 | − | 30155.8i | −0.193882 | − | 1.55119i | ||||
\(724\) | 15676.3i | 0.804701i | ||||||||
\(725\) | 11313.0 | − | 11481.1i | 0.579524 | − | 0.588133i | ||||
\(726\) | 30948.8 | − | 39790.5i | 1.58212 | − | 2.03411i | ||||
\(727\) | −22339.4 | + | 22339.4i | −1.13964 | + | 1.13964i | −0.151130 | + | 0.988514i | \(0.548291\pi\) |
−0.988514 | + | 0.151130i | \(0.951709\pi\) | |||||||
\(728\) | −3386.28 | + | 3386.28i | −0.172395 | + | 0.172395i | ||||
\(729\) | −14454.5 | + | 13360.0i | −0.734364 | + | 0.678756i | ||||
\(730\) | 39567.9 | − | 16560.7i | 2.00613 | − | 0.839643i | ||||
\(731\) | − | 239.933i | − | 0.0121399i | ||||||
\(732\) | 14538.5 | − | 1817.15i | 0.734094 | − | 0.0917540i | ||||
\(733\) | −8364.93 | − | 8364.93i | −0.421509 | − | 0.421509i | 0.464214 | − | 0.885723i | \(-0.346337\pi\) |
−0.885723 | + | 0.464214i | \(0.846337\pi\) | |||||||
\(734\) | −12624.7 | −0.634856 | ||||||||
\(735\) | −1416.24 | − | 2469.34i | −0.0710734 | − | 0.123922i | ||||
\(736\) | −11626.4 | −0.582276 | ||||||||
\(737\) | −41024.1 | − | 41024.1i | −2.05040 | − | 2.05040i | ||||
\(738\) | −16468.2 | + | 27679.3i | −0.821415 | + | 1.38061i | ||||
\(739\) | 20172.5i | 1.00413i | 0.864829 | + | 0.502067i | \(0.167427\pi\) | ||||
−0.864829 | + | 0.502067i | \(0.832573\pi\) | |||||||
\(740\) | −895.007 | + | 2183.47i | −0.0444610 | + | 0.108468i | ||||
\(741\) | −5558.57 | − | 4323.42i | −0.275572 | − | 0.214339i | ||||
\(742\) | −4272.97 | + | 4272.97i | −0.211409 | + | 0.211409i | ||||
\(743\) | 13733.0 | − | 13733.0i | 0.678080 | − | 0.678080i | −0.281485 | − | 0.959566i | \(-0.590827\pi\) |
0.959566 | + | 0.281485i | \(0.0908271\pi\) | |||||||
\(744\) | −8922.94 | − | 6940.21i | −0.439692 | − | 0.341990i | ||||
\(745\) | 12903.8 | + | 30830.7i | 0.634577 | + | 1.51617i | ||||
\(746\) | − | 31459.6i | − | 1.54399i | ||||||
\(747\) | −3348.81 | + | 5628.59i | −0.164025 | + | 0.275689i | ||||
\(748\) | −3423.33 | − | 3423.33i | −0.167339 | − | 0.167339i | ||||
\(749\) | 13414.6 | 0.654418 | ||||||||
\(750\) | 21511.5 | − | 12549.2i | 1.04732 | − | 0.610975i | ||||
\(751\) | 29245.7 | 1.42102 | 0.710512 | − | 0.703685i | \(-0.248463\pi\) | ||||
0.710512 | + | 0.703685i | \(0.248463\pi\) | |||||||
\(752\) | −12578.7 | − | 12578.7i | −0.609969 | − | 0.609969i | ||||
\(753\) | 476.590 | − | 59.5688i | 0.0230650 | − | 0.00288288i | ||||
\(754\) | − | 20812.1i | − | 1.00522i | ||||||
\(755\) | 3385.65 | + | 8089.20i | 0.163200 | + | 0.389929i | ||||
\(756\) | 1480.42 | − | 3384.24i | 0.0712200 | − | 0.162809i | ||||
\(757\) | −12461.1 | + | 12461.1i | −0.598292 | + | 0.598292i | −0.939858 | − | 0.341566i | \(-0.889043\pi\) |
0.341566 | + | 0.939858i | \(0.389043\pi\) | |||||||
\(758\) | 9036.44 | − | 9036.44i | 0.433006 | − | 0.433006i | ||||
\(759\) | 15152.8 | − | 19481.8i | 0.724655 | − | 0.931679i | ||||
\(760\) | 1775.02 | − | 4330.36i | 0.0847194 | − | 0.206683i | ||||
\(761\) | − | 6494.66i | − | 0.309371i | −0.987964 | − | 0.154685i | \(-0.950564\pi\) | ||
0.987964 | − | 0.154685i | \(-0.0494364\pi\) | |||||||
\(762\) | −262.562 | − | 2100.67i | −0.0124824 | − | 0.0998679i | ||||
\(763\) | 10687.7 | + | 10687.7i | 0.507103 | + | 0.507103i | ||||
\(764\) | 7147.29 | 0.338455 | ||||||||
\(765\) | 842.580 | − | 5965.10i | 0.0398216 | − | 0.281920i | ||||
\(766\) | −12247.2 | −0.577690 | ||||||||
\(767\) | 24603.2 | + | 24603.2i | 1.15824 | + | 1.15824i | ||||
\(768\) | −3029.18 | − | 24235.5i | −0.142326 | − | 1.13870i | ||||
\(769\) | 9399.14i | 0.440756i | 0.975415 | + | 0.220378i | \(0.0707291\pi\) | ||||
−0.975415 | + | 0.220378i | \(0.929271\pi\) | |||||||
\(770\) | −15968.6 | + | 6683.47i | −0.747360 | + | 0.312799i | ||||
\(771\) | −12675.9 | + | 16297.3i | −0.592104 | + | 0.761260i | ||||
\(772\) | 8666.03 | − | 8666.03i | 0.404012 | − | 0.404012i | ||||
\(773\) | 7432.94 | − | 7432.94i | 0.345853 | − | 0.345853i | −0.512709 | − | 0.858562i | \(-0.671358\pi\) |
0.858562 | + | 0.512709i | \(0.171358\pi\) | |||||||
\(774\) | −274.009 | − | 1079.00i | −0.0127248 | − | 0.0501084i | ||||
\(775\) | 13130.1 | − | 13325.2i | 0.608577 | − | 0.617618i | ||||
\(776\) | 12629.6i | 0.584247i | ||||||||
\(777\) | 2025.31 | − | 253.143i | 0.0935106 | − | 0.0116878i | ||||
\(778\) | 15941.8 | + | 15941.8i | 0.734630 | + | 0.734630i | ||||
\(779\) | −10016.2 | −0.460680 | ||||||||
\(780\) | 2690.14 | − | 9925.75i | 0.123490 | − | 0.455639i | ||||
\(781\) | −24882.2 | −1.14002 | ||||||||
\(782\) | −3564.06 | − | 3564.06i | −0.162980 | − | 0.162980i | ||||
\(783\) | −6593.00 | − | 16846.5i | −0.300913 | − | 0.768895i | ||||
\(784\) | − | 3917.21i | − | 0.178444i | ||||||
\(785\) | −2640.58 | − | 1082.37i | −0.120059 | − | 0.0492122i | ||||
\(786\) | −422.053 | − | 328.270i | −0.0191528 | − | 0.0148970i | ||||
\(787\) | 11601.7 | − | 11601.7i | 0.525485 | − | 0.525485i | −0.393738 | − | 0.919223i | \(-0.628818\pi\) |
0.919223 | + | 0.393738i | \(0.128818\pi\) | |||||||
\(788\) | −8535.27 | + | 8535.27i | −0.385858 | + | 0.385858i | ||||
\(789\) | 16374.2 | + | 12735.7i | 0.738828 | + | 0.574657i | ||||
\(790\) | 12941.9 | + | 5304.88i | 0.582849 | + | 0.238910i | ||||
\(791\) | − | 6538.26i | − | 0.293899i | ||||||
\(792\) | 21754.7 | + | 12943.3i | 0.976035 | + | 0.580706i | ||||
\(793\) | −24947.6 | − | 24947.6i | −1.11717 | − | 1.11717i | ||||
\(794\) | −8920.32 | −0.398703 | ||||||||
\(795\) | −3825.38 | + | 14114.4i | −0.170657 | + | 0.629670i | ||||
\(796\) | −14311.9 | −0.637278 | ||||||||
\(797\) | 5475.46 | + | 5475.46i | 0.243351 | + | 0.243351i | 0.818235 | − | 0.574884i | \(-0.194953\pi\) |
−0.574884 | + | 0.818235i | \(0.694953\pi\) | |||||||
\(798\) | 3564.31 | − | 445.502i | 0.158114 | − | 0.0197626i | ||||
\(799\) | − | 4440.77i | − | 0.196625i | ||||||
\(800\) | 19733.3 | − | 145.495i | 0.872097 | − | 0.00643005i | ||||
\(801\) | −22533.9 | + | 5722.39i | −0.994002 | + | 0.252423i | ||||
\(802\) | −35916.9 | + | 35916.9i | −1.58138 | + | 1.58138i | ||||
\(803\) | −51019.1 | + | 51019.1i | −2.24212 | + | 2.24212i | ||||
\(804\) | −10793.7 | + | 13877.3i | −0.473464 | + | 0.608726i | ||||
\(805\) | −5316.74 | + | 2225.26i | −0.232783 | + | 0.0974289i | ||||
\(806\) | − | 24155.0i | − | 1.05561i | ||||||
\(807\) | 281.424 | + | 2251.58i | 0.0122758 | + | 0.0982147i | ||||
\(808\) | −7992.58 | − | 7992.58i | −0.347993 | − | 0.347993i | ||||
\(809\) | 1410.65 | 0.0613051 | 0.0306525 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306525 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(810\) | −3023.10 | − | 27787.9i | −0.131137 | − | 1.20539i | ||||
\(811\) | −20555.4 | −0.890007 | −0.445004 | − | 0.895529i | \(-0.646798\pi\) | ||||
−0.445004 | + | 0.895529i | \(0.646798\pi\) | |||||||
\(812\) | 2400.66 | + | 2400.66i | 0.103752 | + | 0.103752i | ||||
\(813\) | −1747.15 | − | 13978.4i | −0.0753693 | − | 0.603005i | ||||
\(814\) | − | 12412.0i | − | 0.534449i | ||||||
\(815\) | −160.199 | + | 390.824i | −0.00688532 | + | 0.0167975i | ||||
\(816\) | 5089.60 | − | 6543.63i | 0.218347 | − | 0.280726i | ||||
\(817\) | 244.805 | − | 244.805i | 0.0104830 | − | 0.0104830i | ||||
\(818\) | 3966.69 | − | 3966.69i | 0.169550 | − | 0.169550i | ||||
\(819\) | −8621.26 | + | 2189.34i | −0.367828 | + | 0.0934086i | ||||
\(820\) | −5647.41 | − | 13493.1i | −0.240507 | − | 0.574635i | ||||
\(821\) | − | 7612.82i | − | 0.323617i | −0.986822 | − | 0.161808i | \(-0.948267\pi\) | ||
0.986822 | − | 0.161808i | \(-0.0517326\pi\) | |||||||
\(822\) | 18599.7 | − | 2324.76i | 0.789218 | − | 0.0986440i | ||||
\(823\) | −20915.2 | − | 20915.2i | −0.885854 | − | 0.885854i | 0.108268 | − | 0.994122i | \(-0.465470\pi\) |
−0.994122 | + | 0.108268i | \(0.965470\pi\) | |||||||
\(824\) | 19499.1 | 0.824374 | ||||||||
\(825\) | −25474.9 | + | 33255.8i | −1.07506 | + | 1.40342i | ||||
\(826\) | −17748.1 | −0.747623 | ||||||||
\(827\) | −23583.9 | − | 23583.9i | −0.991646 | − | 0.991646i | 0.00831923 | − | 0.999965i | \(-0.497352\pi\) |
−0.999965 | + | 0.00831923i | \(0.997352\pi\) | |||||||
\(828\) | −6427.46 | − | 3824.11i | −0.269770 | − | 0.160504i | ||||
\(829\) | 145.682i | 0.00610344i | 0.999995 | + | 0.00305172i | \(0.000971395\pi\) | ||||
−0.999995 | + | 0.00305172i | \(0.999029\pi\) | |||||||
\(830\) | −3590.96 | − | 8579.74i | −0.150173 | − | 0.358804i | ||||
\(831\) | 3759.13 | + | 2923.83i | 0.156923 | + | 0.122054i | ||||
\(832\) | −3265.64 | + | 3265.64i | −0.136077 | + | 0.136077i | ||||
\(833\) | 691.464 | − | 691.464i | 0.0287609 | − | 0.0287609i | ||||
\(834\) | −6578.48 | − | 5116.70i | −0.273134 | − | 0.212442i | ||||
\(835\) | −5974.57 | + | 14575.6i | −0.247615 | + | 0.604085i | ||||
\(836\) | − | 6985.69i | − | 0.289001i | ||||||
\(837\) | −7651.97 | − | 19552.4i | −0.315999 | − | 0.807442i | ||||
\(838\) | 21019.6 | + | 21019.6i | 0.866480 | + | 0.866480i | ||||
\(839\) | 8354.60 | 0.343782 | 0.171891 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171891 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(840\) | −2941.03 | − | 5127.93i | −0.120804 | − | 0.210632i | ||||
\(841\) | −7761.85 | −0.318252 | ||||||||
\(842\) | 17617.5 | + | 17617.5i | 0.721067 | + | 0.721067i | ||||
\(843\) | −34330.7 | + | 4290.98i | −1.40262 | + | 0.175313i | ||||
\(844\) | − | 6124.79i | − | 0.249791i | ||||||
\(845\) | −184.876 | + | 77.3777i | −0.00752653 | + | 0.00315015i | ||||
\(846\) | −5071.45 | − | 19970.6i | −0.206099 | − | 0.811586i | ||||
\(847\) | 14001.8 | − | 14001.8i | 0.568015 | − | 0.568015i | ||||
\(848\) | −14229.3 | + | 14229.3i | −0.576223 | + | 0.576223i | ||||
\(849\) | −13011.1 | + | 16728.2i | −0.525960 | + | 0.676220i | ||||
\(850\) | 6093.83 | + | 6004.62i | 0.245902 | + | 0.242302i | ||||
\(851\) | − | 4132.59i | − | 0.166467i | ||||||
\(852\) | 935.149 | + | 7481.82i | 0.0376029 | + | 0.300848i | ||||
\(853\) | 15191.1 | + | 15191.1i | 0.609771 | + | 0.609771i | 0.942886 | − | 0.333115i | \(-0.108100\pi\) |
−0.333115 | + | 0.942886i | \(0.608100\pi\) | |||||||
\(854\) | 17996.6 | 0.721112 | ||||||||
\(855\) | 6945.92 | − | 5226.54i | 0.277831 | − | 0.209057i | ||||
\(856\) | 27857.3 | 1.11232 | ||||||||
\(857\) | −16843.7 | − | 16843.7i | −0.671378 | − | 0.671378i | 0.286655 | − | 0.958034i | \(-0.407457\pi\) |
−0.958034 | + | 0.286655i | \(0.907457\pi\) | |||||||
\(858\) | 6708.61 | + | 53673.4i | 0.266933 | + | 2.13564i | ||||
\(859\) | − | 14875.3i | − | 0.590850i | −0.955366 | − | 0.295425i | \(-0.904539\pi\) | ||
0.955366 | − | 0.295425i | \(-0.0954612\pi\) | |||||||
\(860\) | 467.811 | + | 191.756i | 0.0185491 | + | 0.00760329i | ||||
\(861\) | −7767.53 | + | 9986.61i | −0.307453 | + | 0.395288i | ||||
\(862\) | 10988.4 | − | 10988.4i | 0.434183 | − | 0.434183i | ||||
\(863\) | −6883.68 | + | 6883.68i | −0.271522 | + | 0.271522i | −0.829713 | − | 0.558191i | \(-0.811496\pi\) |
0.558191 | + | 0.829713i | \(0.311496\pi\) | |||||||
\(864\) | 8876.66 | − | 20292.1i | 0.349525 | − | 0.799016i | ||||
\(865\) | 10223.4 | + | 4190.56i | 0.401855 | + | 0.164721i | ||||
\(866\) | − | 33063.6i | − | 1.29740i | ||||||
\(867\) | −23278.1 | + | 2909.52i | −0.911841 | + | 0.113970i | ||||
\(868\) | 2786.25 | + | 2786.25i | 0.108953 | + | 0.108953i | ||||
\(869\) | −23527.5 | −0.918429 | ||||||||
\(870\) | 24796.0 | + | 6720.36i | 0.966279 | + | 0.261887i | ||||
\(871\) | 42334.8 | 1.64691 | ||||||||
\(872\) | 22194.5 | + | 22194.5i | 0.861926 | + | 0.861926i | ||||
\(873\) | −11994.4 | + | 20159.8i | −0.465004 | + | 0.781565i | ||||
\(874\) | − | 7272.87i | − | 0.281474i | ||||||
\(875\) | 8996.17 | − | 3843.44i | 0.347573 | − | 0.148494i | ||||
\(876\) | 17258.4 | + | 13423.5i | 0.665646 | + | 0.517736i | ||||
\(877\) | −22144.5 | + | 22144.5i | −0.852642 | + | 0.852642i | −0.990458 | − | 0.137816i | \(-0.955992\pi\) |
0.137816 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(878\) | 23680.3 | − | 23680.3i | 0.910220 | − | 0.910220i | ||||
\(879\) | 7904.34 | + | 6147.95i | 0.303307 | + | 0.235911i | ||||
\(880\) | −53176.6 | + | 22256.5i | −2.03703 | + | 0.852575i | ||||
\(881\) | − | 12710.1i | − | 0.486055i | −0.970019 | − | 0.243028i | \(-0.921859\pi\) | ||
0.970019 | − | 0.243028i | \(-0.0781405\pi\) | |||||||
\(882\) | 2319.92 | − | 3899.25i | 0.0885665 | − | 0.148860i | ||||
\(883\) | −6187.03 | − | 6187.03i | −0.235798 | − | 0.235798i | 0.579309 | − | 0.815108i | \(-0.303322\pi\) |
−0.815108 | + | 0.579309i | \(0.803322\pi\) | |||||||
\(884\) | 3532.70 | 0.134409 | ||||||||
\(885\) | −37257.3 | + | 21368.2i | −1.41513 | + | 0.811622i | ||||
\(886\) | 24174.8 | 0.916669 | ||||||||
\(887\) | −12565.3 | − | 12565.3i | −0.475649 | − | 0.475649i | 0.428088 | − | 0.903737i | \(-0.359187\pi\) |
−0.903737 | + | 0.428088i | \(0.859187\pi\) | |||||||
\(888\) | 4205.85 | − | 525.688i | 0.158941 | − | 0.0198659i | ||||
\(889\) | − | 831.597i | − | 0.0313733i | ||||||
\(890\) | 12522.2 | − | 30549.3i | 0.471623 | − | 1.15058i | ||||
\(891\) | 22433.4 | + | 41321.1i | 0.843486 | + | 1.55366i | ||||
\(892\) | −7481.69 | + | 7481.69i | −0.280836 | + | 0.280836i | ||||
\(893\) | 4530.94 | − | 4530.94i | 0.169790 | − | 0.169790i | ||||
\(894\) | −32705.5 | + | 42049.0i | −1.22353 | + | 1.57308i | ||||
\(895\) | −7491.11 | − | 17898.2i | −0.279777 | − | 0.668461i | ||||
\(896\) | − | 11196.5i | − | 0.417466i | ||||||
\(897\) | 2233.64 | + | 17870.6i | 0.0831427 | + | 0.665197i | ||||
\(898\) | −13173.6 | − | 13173.6i | −0.489541 | − | 0.489541i | ||||
\(899\) | 19297.8 | 0.715926 | ||||||||
\(900\) | 10957.1 | + | 6410.17i | 0.405818 | + | 0.237414i | ||||
\(901\) | −5023.51 | −0.185746 | ||||||||
\(902\) | 54402.6 | + | 54402.6i | 2.00821 | + | 2.00821i | ||||
\(903\) | −54.2361 | − | 433.925i | −0.00199874 | − | 0.0159913i | ||||
\(904\) | − | 13577.6i | − | 0.499541i | ||||||
\(905\) | 17990.5 | + | 42984.1i | 0.660801 | + | 1.57883i | ||||
\(906\) | −8581.11 | + | 11032.6i | −0.314667 | + | 0.404563i | ||||
\(907\) | 16133.5 | − | 16133.5i | 0.590635 | − | 0.590635i | −0.347168 | − | 0.937803i | \(-0.612857\pi\) |
0.937803 | + | 0.347168i | \(0.112857\pi\) | |||||||
\(908\) | −10990.5 | + | 10990.5i | −0.401689 | + | 0.401689i | ||||
\(909\) | −5167.46 | − | 20348.6i | −0.188552 | − | 0.742488i | ||||
\(910\) | 4790.87 | − | 11687.9i | 0.174523 | − | 0.425768i | ||||
\(911\) | − | 13345.2i | − | 0.485343i | −0.970108 | − | 0.242672i | \(-0.921976\pi\) | ||
0.970108 | − | 0.242672i | \(-0.0780238\pi\) | |||||||
\(912\) | 11869.5 | − | 1483.56i | 0.430961 | − | 0.0538656i | ||||
\(913\) | 11062.8 | + | 11062.8i | 0.401012 | + | 0.401012i | ||||
\(914\) | 21843.5 | 0.790503 | ||||||||
\(915\) | 37778.8 | − | 21667.4i | 1.36495 | − | 0.782842i | ||||
\(916\) | −12403.7 | −0.447412 | ||||||||
\(917\) | −148.516 | − | 148.516i | −0.00534834 | − | 0.00534834i | ||||
\(918\) | 8941.64 | − | 3499.38i | 0.321479 | − | 0.125813i | ||||
\(919\) | 20941.3i | 0.751674i | 0.926686 | + | 0.375837i | \(0.122645\pi\) | ||||
−0.926686 | + | 0.375837i | \(0.877355\pi\) | |||||||
\(920\) | −11041.0 | + | 4621.08i | −0.395663 | + | 0.165601i | ||||
\(921\) | 26379.0 | + | 20517.5i | 0.943777 | + | 0.734064i | ||||
\(922\) | 15070.1 | − | 15070.1i | 0.538296 | − | 0.538296i | ||||
\(923\) | 12838.6 | − | 12838.6i | 0.457841 | − | 0.457841i | ||||
\(924\) | −6965.02 | − | 5417.35i | −0.247979 | − | 0.192876i | ||||
\(925\) | 51.7162 | + | 7014.18i | 0.00183829 | + | 0.249324i | ||||
\(926\) | 36893.0i | 1.30926i | ||||||||
\(927\) | 31125.2 | + | 18518.4i | 1.10279 | + | 0.656121i | ||||
\(928\) | 14394.5 | + | 14394.5i | 0.509182 | + | 0.509182i | ||||
\(929\) | 8836.82 | 0.312085 | 0.156042 | − | 0.987750i | \(-0.450126\pi\) | ||||
0.156042 | + | 0.987750i | \(0.450126\pi\) | |||||||
\(930\) | 28778.7 | + | 7799.79i | 1.01472 | + | 0.275016i | ||||
\(931\) | 1411.01 | 0.0496713 | ||||||||
\(932\) | −12748.0 | − | 12748.0i | −0.448042 | − | 0.448042i | ||||
\(933\) | 10690.9 | − | 1336.24i | 0.375137 | − | 0.0468882i | ||||
\(934\) | − | 47482.7i | − | 1.66347i | ||||||
\(935\) | −13315.4 | − | 5458.01i | −0.465734 | − | 0.190905i | ||||
\(936\) | −17903.3 | + | 4546.47i | −0.625200 | + | 0.158767i | ||||
\(937\) | 25647.4 | − | 25647.4i | 0.894198 | − | 0.894198i | −0.100717 | − | 0.994915i | \(-0.532114\pi\) |
0.994915 | + | 0.100717i | \(0.0321136\pi\) | |||||||
\(938\) | −15269.7 | + | 15269.7i | −0.531526 | + | 0.531526i | ||||
\(939\) | −5590.21 | + | 7187.26i | −0.194281 | + | 0.249784i | ||||
\(940\) | 8658.41 | + | 3549.09i | 0.300432 | + | 0.123147i | ||||
\(941\) | 29254.4i | 1.01346i | 0.862104 | + | 0.506731i | \(0.169146\pi\) | ||||
−0.862104 | + | 0.506731i | \(0.830854\pi\) | |||||||
\(942\) | −564.138 | − | 4513.49i | −0.0195123 | − | 0.156112i | ||||
\(943\) | 18113.4 | + | 18113.4i | 0.625507 | + | 0.625507i | ||||
\(944\) | −59102.7 | −2.03774 | ||||||||
\(945\) | 175.437 | − | 10978.5i | 0.00603912 | − | 0.377916i | ||||
\(946\) | −2659.29 | −0.0913963 | ||||||||
\(947\) | 175.686 | + | 175.686i | 0.00602855 | + | 0.00602855i | 0.710115 | − | 0.704086i | \(-0.248643\pi\) |
−0.704086 | + | 0.710115i | \(0.748643\pi\) | |||||||
\(948\) | 884.233 | + | 7074.46i | 0.0302938 | + | 0.242371i | ||||
\(949\) | − | 52649.1i | − | 1.80091i | ||||||
\(950\) | 91.0143 | + | 12344.1i | 0.00310831 | + | 0.421575i | ||||
\(951\) | 21050.9 | − | 27064.8i | 0.717793 | − | 0.922857i | ||||
\(952\) | 1435.92 | − | 1435.92i | 0.0488851 | − | 0.0488851i | ||||
\(953\) | 33607.7 | − | 33607.7i | 1.14235 | − | 1.14235i | 0.154331 | − | 0.988019i | \(-0.450678\pi\) |
0.988019 | − | 0.154331i | \(-0.0493224\pi\) | |||||||
\(954\) | −22591.2 | + | 5736.96i | −0.766686 | + | 0.194697i | ||||
\(955\) | 19597.8 | − | 8202.43i | 0.664051 | − | 0.277931i | ||||
\(956\) | 106.876i | 0.00361571i | ||||||||
\(957\) | −42880.6 | + | 5359.62i | −1.44841 | + | 0.181037i | ||||
\(958\) | −20671.1 | − | 20671.1i | −0.697134 | − | 0.697134i | ||||
\(959\) | 7363.08 | 0.247931 | ||||||||
\(960\) | −2836.26 | − | 4945.25i | −0.0953540 | − | 0.166258i | ||||
\(961\) | −7393.58 | −0.248182 | ||||||||
\(962\) | 6404.29 | + | 6404.29i | 0.214639 | + | 0.214639i | ||||
\(963\) | 44466.9 | + | 26456.2i | 1.48798 | + | 0.885296i | ||||
\(964\) | 21998.6i | 0.734985i | ||||||||
\(965\) | 13816.7 | − | 33707.5i | 0.460908 | − | 1.12444i | ||||
\(966\) | −7251.35 | − | 5640.06i | −0.241520 | − | 0.187853i | ||||
\(967\) | 20966.3 | − | 20966.3i | 0.697241 | − | 0.697241i | −0.266574 | − | 0.963814i | \(-0.585892\pi\) |
0.963814 | + | 0.266574i | \(0.0858916\pi\) | |||||||
\(968\) | 29076.8 | − | 29076.8i | 0.965459 | − | 0.965459i | ||||
\(969\) | 2357.07 | + | 1833.31i | 0.0781424 | + | 0.0607787i | ||||
\(970\) | −12861.7 | − | 30729.9i | −0.425735 | − | 1.01719i | ||||
\(971\) | 6714.76i | 0.221923i | 0.993825 | + | 0.110961i | \(0.0353930\pi\) | ||||
−0.993825 | + | 0.110961i | \(0.964607\pi\) | |||||||
\(972\) | 11581.7 | − | 8298.45i | 0.382184 | − | 0.273840i | ||||
\(973\) | −2314.90 | − | 2314.90i | −0.0762715 | − | 0.0762715i | ||||
\(974\) | 25147.2 | 0.827276 | ||||||||
\(975\) | −4014.75 | − | 30303.5i | −0.131872 | − | 0.995374i | ||||
\(976\) | 59930.0 | 1.96549 | ||||||||
\(977\) | −27247.7 | − | 27247.7i | −0.892253 | − | 0.892253i | 0.102482 | − | 0.994735i | \(-0.467322\pi\) |
−0.994735 | + | 0.102482i | \(0.967322\pi\) | |||||||
\(978\) | −668.029 | + | 83.4966i | −0.0218417 | + | 0.00272999i | ||||
\(979\) | 55536.6i | 1.81303i | ||||||||
\(980\) | 795.563 | + | 1900.81i | 0.0259320 | + | 0.0619583i | ||||
\(981\) | 14349.4 | + | 56505.8i | 0.467015 | + | 1.83903i | ||||
\(982\) | 6523.07 | − | 6523.07i | 0.211975 | − | 0.211975i | ||||
\(983\) | 12779.7 | − | 12779.7i | 0.414660 | − | 0.414660i | −0.468699 | − | 0.883358i | \(-0.655277\pi\) |
0.883358 | + | 0.468699i | \(0.155277\pi\) | |||||||
\(984\) | −16130.4 | + | 20738.6i | −0.522579 | + | 0.671873i | ||||
\(985\) | −13608.3 | + | 33198.9i | −0.440198 | + | 1.07391i | ||||
\(986\) | 8825.22i | 0.285043i | ||||||||
\(987\) | −1003.82 | − | 8031.25i | −0.0323728 | − | 0.259005i | ||||
\(988\) | 3604.44 | + | 3604.44i | 0.116065 | + | 0.116065i | ||||
\(989\) | −885.411 | −0.0284676 | ||||||||
\(990\) | −66113.9 | − | 9338.70i | −2.12246 | − | 0.299801i | ||||
\(991\) | −42783.0 | −1.37139 | −0.685694 | − | 0.727890i | \(-0.740501\pi\) | ||||
−0.685694 | + | 0.727890i | \(0.740501\pi\) | |||||||
\(992\) | 16706.5 | + | 16706.5i | 0.534710 | + | 0.534710i | ||||
\(993\) | −2170.91 | − | 17368.7i | −0.0693773 | − | 0.555065i | ||||
\(994\) | 9261.44i | 0.295528i | ||||||||
\(995\) | −39243.1 | + | 16424.8i | −1.25034 | + | 0.523317i | ||||
\(996\) | 2910.69 | − | 3742.23i | 0.0925990 | − | 0.119053i | ||||
\(997\) | 7352.58 | − | 7352.58i | 0.233559 | − | 0.233559i | −0.580617 | − | 0.814177i | \(-0.697189\pi\) |
0.814177 | + | 0.580617i | \(0.197189\pi\) | |||||||
\(998\) | 23736.4 | − | 23736.4i | 0.752868 | − | 0.752868i | ||||
\(999\) | 7212.79 | + | 3155.20i | 0.228431 | + | 0.0999260i |
(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 | 105.4.j.a.8.9 | ✓ | 72 | |
3.2 | odd | 2 | inner | 105.4.j.a.8.28 | yes | 72 | |
5.2 | odd | 4 | inner | 105.4.j.a.92.28 | yes | 72 | |
15.2 | even | 4 | inner | 105.4.j.a.92.9 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.j.a.8.9 | ✓ | 72 | 1.1 | even | 1 | trivial | |
105.4.j.a.8.28 | yes | 72 | 3.2 | odd | 2 | inner | |
105.4.j.a.92.9 | yes | 72 | 15.2 | even | 4 | inner | |
105.4.j.a.92.28 | yes | 72 | 5.2 | odd | 4 | inner |