Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.4 | ||
Root | \(2.21837 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.f.147.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.21837 | − | 1.28078i | 0.784312 | − | 0.452823i | −0.0536442 | − | 0.998560i | \(-0.517084\pi\) |
0.837956 | + | 0.545737i | \(0.183750\pi\) | |||||||
\(3\) | 1.84233 | + | 3.19101i | 0.354556 | + | 0.614110i | 0.987042 | − | 0.160462i | \(-0.0512985\pi\) |
−0.632486 | + | 0.774572i | \(0.717965\pi\) | |||||||
\(4\) | −0.719224 | + | 1.24573i | −0.0899029 | + | 0.155716i | ||||
\(5\) | 0.561553i | 0.0502268i | 0.999685 | + | 0.0251134i | \(0.00799469\pi\) | ||||
−0.999685 | + | 0.0251134i | \(0.992005\pi\) | |||||||
\(6\) | 8.17394 | + | 4.71922i | 0.556166 | + | 0.321102i | ||||
\(7\) | 15.7418 | + | 9.08854i | 0.849978 | + | 0.490735i | 0.860643 | − | 0.509208i | \(-0.170062\pi\) |
−0.0106654 | + | 0.999943i | \(0.503395\pi\) | |||||||
\(8\) | 24.1771i | 1.06849i | ||||||||
\(9\) | 6.71165 | − | 11.6249i | 0.248579 | − | 0.430552i | ||||
\(10\) | 0.719224 | + | 1.24573i | 0.0227438 | + | 0.0393935i | ||||
\(11\) | −56.0653 | + | 32.3693i | −1.53676 | + | 0.887247i | −0.537731 | + | 0.843116i | \(0.680718\pi\) |
−0.999026 | + | 0.0441305i | \(0.985948\pi\) | |||||||
\(12\) | −5.30019 | −0.127503 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 46.5616 | 0.888864 | ||||||||
\(15\) | −1.79192 | + | 1.03457i | −0.0308448 | + | 0.0178082i | ||||
\(16\) | 25.2116 | + | 43.6679i | 0.393932 | + | 0.682310i | ||||
\(17\) | −12.7732 | + | 22.1238i | −0.182233 | + | 0.315636i | −0.942641 | − | 0.333810i | \(-0.891666\pi\) |
0.760408 | + | 0.649446i | \(0.224999\pi\) | |||||||
\(18\) | − | 34.3845i | − | 0.450250i | ||||||
\(19\) | 93.5045 | + | 53.9848i | 1.12902 | + | 0.651841i | 0.943689 | − | 0.330835i | \(-0.107330\pi\) |
0.185333 | + | 0.982676i | \(0.440664\pi\) | |||||||
\(20\) | −0.699544 | − | 0.403882i | −0.00782114 | − | 0.00451554i | ||||
\(21\) | 66.9763i | 0.695973i | ||||||||
\(22\) | −82.9157 | + | 143.614i | −0.803531 | + | 1.39176i | ||||
\(23\) | 36.6307 | + | 63.4462i | 0.332088 | + | 0.575193i | 0.982921 | − | 0.184027i | \(-0.0589135\pi\) |
−0.650833 | + | 0.759221i | \(0.725580\pi\) | |||||||
\(24\) | −77.1493 | + | 44.5421i | −0.656168 | + | 0.378839i | ||||
\(25\) | 124.685 | 0.997477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.946 | 1.06165 | ||||||||
\(28\) | −22.6438 | + | 13.0734i | −0.152831 | + | 0.0882371i | ||||
\(29\) | −87.9545 | − | 152.342i | −0.563198 | − | 0.975488i | −0.997215 | − | 0.0745830i | \(-0.976237\pi\) |
0.434017 | − | 0.900905i | \(-0.357096\pi\) | |||||||
\(30\) | −2.65009 | + | 4.59010i | −0.0161280 | + | 0.0279344i | ||||
\(31\) | − | 113.093i | − | 0.655228i | −0.944812 | − | 0.327614i | \(-0.893755\pi\) | ||
0.944812 | − | 0.327614i | \(-0.106245\pi\) | |||||||
\(32\) | −55.6462 | − | 32.1274i | −0.307405 | − | 0.177480i | ||||
\(33\) | −206.581 | − | 119.270i | −1.08973 | − | 0.629158i | ||||
\(34\) | 65.4384i | 0.330077i | ||||||||
\(35\) | −5.10370 | + | 8.83986i | −0.0246481 | + | 0.0426917i | ||||
\(36\) | 9.65435 | + | 16.7218i | 0.0446961 | + | 0.0774158i | ||||
\(37\) | −99.4264 | + | 57.4039i | −0.441773 | + | 0.255058i | −0.704349 | − | 0.709853i | \(-0.748761\pi\) |
0.262576 | + | 0.964911i | \(0.415428\pi\) | |||||||
\(38\) | 276.570 | 1.18067 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.5767 | −0.0536666 | ||||||||
\(41\) | −60.3151 | + | 34.8229i | −0.229747 | + | 0.132645i | −0.610455 | − | 0.792051i | \(-0.709014\pi\) |
0.380708 | + | 0.924695i | \(0.375680\pi\) | |||||||
\(42\) | 85.7817 | + | 148.578i | 0.315153 | + | 0.545860i | ||||
\(43\) | 219.151 | − | 379.581i | 0.777214 | − | 1.34617i | −0.156327 | − | 0.987705i | \(-0.549965\pi\) |
0.933541 | − | 0.358469i | \(-0.116701\pi\) | |||||||
\(44\) | − | 93.1231i | − | 0.319064i | ||||||
\(45\) | 6.52800 | + | 3.76894i | 0.0216253 | + | 0.0124854i | ||||
\(46\) | 162.521 | + | 93.8314i | 0.520921 | + | 0.300754i | ||||
\(47\) | 31.9479i | 0.0991506i | 0.998770 | + | 0.0495753i | \(0.0157868\pi\) | ||||
−0.998770 | + | 0.0495753i | \(0.984213\pi\) | |||||||
\(48\) | −92.8963 | + | 160.901i | −0.279342 | + | 0.483835i | ||||
\(49\) | −6.29686 | − | 10.9065i | −0.0183582 | − | 0.0317973i | ||||
\(50\) | 276.597 | − | 159.693i | 0.782334 | − | 0.451680i | ||||
\(51\) | −94.1298 | −0.258447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.84658 | 0.00737752 | 0.00368876 | − | 0.999993i | \(-0.498826\pi\) | ||||
0.00368876 | + | 0.999993i | \(0.498826\pi\) | |||||||
\(54\) | 330.417 | − | 190.767i | 0.832669 | − | 0.480741i | ||||
\(55\) | −18.1771 | − | 31.4836i | −0.0445636 | − | 0.0771864i | ||||
\(56\) | −219.734 | + | 380.591i | −0.524344 | + | 0.908190i | ||||
\(57\) | 397.831i | 0.924457i | ||||||||
\(58\) | −390.231 | − | 225.300i | −0.883446 | − | 0.510058i | ||||
\(59\) | 62.0356 | + | 35.8163i | 0.136887 | + | 0.0790319i | 0.566880 | − | 0.823801i | \(-0.308150\pi\) |
−0.429992 | + | 0.902832i | \(0.641484\pi\) | |||||||
\(60\) | − | 2.97633i | − | 0.00640405i | ||||||
\(61\) | 460.348 | − | 797.345i | 0.966253 | − | 1.67360i | 0.260044 | − | 0.965597i | \(-0.416263\pi\) |
0.706209 | − | 0.708003i | \(-0.250404\pi\) | |||||||
\(62\) | −144.847 | − | 250.882i | −0.296702 | − | 0.513903i | ||||
\(63\) | 211.307 | − | 121.998i | 0.422574 | − | 0.243973i | ||||
\(64\) | −567.978 | −1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −611.032 | −1.13959 | ||||||||
\(67\) | −384.758 | + | 222.140i | −0.701577 | + | 0.405056i | −0.807935 | − | 0.589272i | \(-0.799415\pi\) |
0.106357 | + | 0.994328i | \(0.466081\pi\) | |||||||
\(68\) | −18.3736 | − | 31.8240i | −0.0327665 | − | 0.0567533i | ||||
\(69\) | −134.972 | + | 233.778i | −0.235488 | + | 0.407877i | ||||
\(70\) | 26.1468i | 0.0446448i | ||||||||
\(71\) | 469.142 | + | 270.859i | 0.784182 | + | 0.452748i | 0.837910 | − | 0.545808i | \(-0.183777\pi\) |
−0.0537283 | + | 0.998556i | \(0.517110\pi\) | |||||||
\(72\) | 281.056 | + | 162.268i | 0.460039 | + | 0.265604i | ||||
\(73\) | − | 764.004i | − | 1.22493i | −0.790498 | − | 0.612465i | \(-0.790178\pi\) | ||
0.790498 | − | 0.612465i | \(-0.209822\pi\) | |||||||
\(74\) | −147.043 | + | 254.686i | −0.230992 | + | 0.400090i | ||||
\(75\) | 229.710 | + | 397.870i | 0.353662 | + | 0.612561i | ||||
\(76\) | −134.501 | + | 77.6543i | −0.203005 | + | 0.117205i | ||||
\(77\) | −1176.76 | −1.74161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421.538 | −0.600338 | −0.300169 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300169 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(80\) | −24.5218 | + | 14.1577i | −0.0342703 | + | 0.0197859i | ||||
\(81\) | 93.1932 | + | 161.415i | 0.127837 | + | 0.221420i | ||||
\(82\) | −89.2007 | + | 154.500i | −0.120129 | + | 0.208069i | ||||
\(83\) | 603.797i | 0.798498i | 0.916842 | + | 0.399249i | \(0.130729\pi\) | ||||
−0.916842 | + | 0.399249i | \(0.869271\pi\) | |||||||
\(84\) | −83.4346 | − | 48.1710i | −0.108374 | − | 0.0625700i | ||||
\(85\) | −12.4237 | − | 7.17283i | −0.0158534 | − | 0.00915297i | ||||
\(86\) | − | 1122.73i | − | 1.40776i | ||||||
\(87\) | 324.082 | − | 561.327i | 0.399371 | − | 0.691731i | ||||
\(88\) | −782.596 | − | 1355.50i | −0.948011 | − | 1.64200i | ||||
\(89\) | 1004.49 | − | 579.941i | 1.19635 | − | 0.690715i | 0.236613 | − | 0.971604i | \(-0.423963\pi\) |
0.959740 | + | 0.280889i | \(0.0906292\pi\) | |||||||
\(90\) | 19.3087 | 0.0226146 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −105.383 | −0.119423 | ||||||||
\(93\) | 360.880 | − | 208.354i | 0.402382 | − | 0.232315i | ||||
\(94\) | 40.9181 | + | 70.8722i | 0.0448977 | + | 0.0777650i | ||||
\(95\) | −30.3153 | + | 52.5077i | −0.0327399 | + | 0.0567071i | ||||
\(96\) | − | 236.757i | − | 0.251707i | ||||||
\(97\) | −505.126 | − | 291.634i | −0.528740 | − | 0.305268i | 0.211763 | − | 0.977321i | \(-0.432079\pi\) |
−0.740503 | + | 0.672053i | \(0.765413\pi\) | |||||||
\(98\) | −27.9375 | − | 16.1298i | −0.0287971 | − | 0.0166260i | ||||
\(99\) | 869.006i | 0.882206i | ||||||||
\(100\) | −89.6761 | + | 155.324i | −0.0896761 | + | 0.155324i | ||||
\(101\) | 460.870 | + | 798.251i | 0.454043 | + | 0.786425i | 0.998633 | − | 0.0522775i | \(-0.0166480\pi\) |
−0.544590 | + | 0.838702i | \(0.683315\pi\) | |||||||
\(102\) | −208.815 | + | 120.559i | −0.202703 | + | 0.117031i | ||||
\(103\) | 930.712 | 0.890347 | 0.445174 | − | 0.895444i | \(-0.353142\pi\) | ||||
0.445174 | + | 0.895444i | \(0.353142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −37.6107 | −0.0349565 | ||||||||
\(106\) | 6.31478 | − | 3.64584i | 0.00578628 | − | 0.00334071i | ||||
\(107\) | −428.691 | − | 742.515i | −0.387319 | − | 0.670857i | 0.604769 | − | 0.796401i | \(-0.293266\pi\) |
−0.992088 | + | 0.125545i | \(0.959932\pi\) | |||||||
\(108\) | −107.125 | + | 185.547i | −0.0954459 | + | 0.165317i | ||||
\(109\) | 671.853i | 0.590384i | 0.955438 | + | 0.295192i | \(0.0953836\pi\) | ||||
−0.955438 | + | 0.295192i | \(0.904616\pi\) | |||||||
\(110\) | −80.6470 | − | 46.5616i | −0.0699035 | − | 0.0403588i | ||||
\(111\) | −366.352 | − | 211.514i | −0.313267 | − | 0.180865i | ||||
\(112\) | 916.548i | 0.773265i | ||||||||
\(113\) | −320.737 | + | 555.532i | −0.267012 | + | 0.462479i | −0.968089 | − | 0.250607i | \(-0.919370\pi\) |
0.701077 | + | 0.713086i | \(0.252703\pi\) | |||||||
\(114\) | 509.533 | + | 882.537i | 0.418615 | + | 0.725063i | ||||
\(115\) | −35.6284 | + | 20.5701i | −0.0288901 | + | 0.0166797i | ||||
\(116\) | 253.036 | 0.202533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 183.491 | 0.143150 | ||||||||
\(119\) | −402.147 | + | 232.179i | −0.309788 | + | 0.178856i | ||||
\(120\) | −25.0128 | − | 43.3234i | −0.0190279 | − | 0.0329572i | ||||
\(121\) | 1430.05 | − | 2476.91i | 1.07441 | − | 1.86094i | ||||
\(122\) | − | 2358.41i | − | 1.75017i | ||||||
\(123\) | −222.240 | − | 128.311i | −0.162917 | − | 0.0940599i | ||||
\(124\) | 140.883 | + | 81.3390i | 0.102030 | + | 0.0589069i | ||||
\(125\) | 140.211i | 0.100327i | ||||||||
\(126\) | 312.505 | − | 541.274i | 0.220953 | − | 0.382703i | ||||
\(127\) | −276.587 | − | 479.063i | −0.193253 | − | 0.334724i | 0.753073 | − | 0.657937i | \(-0.228570\pi\) |
−0.946326 | + | 0.323212i | \(0.895237\pi\) | |||||||
\(128\) | −814.816 | + | 470.434i | −0.562658 | + | 0.324851i | ||||
\(129\) | 1614.99 | 1.10227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2056.40 | 1.37152 | 0.685758 | − | 0.727830i | \(-0.259471\pi\) | ||||
0.685758 | + | 0.727830i | \(0.259471\pi\) | |||||||
\(132\) | 297.157 | − | 171.563i | 0.195941 | − | 0.113126i | ||||
\(133\) | 981.287 | + | 1699.64i | 0.639762 | + | 1.10810i | ||||
\(134\) | −569.024 | + | 985.578i | −0.366837 | + | 0.635380i | ||||
\(135\) | 83.6411i | 0.0533235i | ||||||||
\(136\) | −534.890 | − | 308.819i | −0.337253 | − | 0.194713i | ||||
\(137\) | −1566.26 | − | 904.283i | −0.976752 | − | 0.563928i | −0.0754639 | − | 0.997149i | \(-0.524044\pi\) |
−0.901288 | + | 0.433221i | \(0.857377\pi\) | |||||||
\(138\) | 691.474i | 0.426537i | ||||||||
\(139\) | −746.818 | + | 1293.53i | −0.455714 | + | 0.789320i | −0.998729 | − | 0.0504032i | \(-0.983949\pi\) |
0.543015 | + | 0.839723i | \(0.317283\pi\) | |||||||
\(140\) | −7.34140 | − | 12.7157i | −0.00443187 | − | 0.00767622i | ||||
\(141\) | −101.946 | + | 58.8585i | −0.0608894 | + | 0.0351545i | ||||
\(142\) | 1387.64 | 0.820058 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 676.847 | 0.391694 | ||||||||
\(145\) | 85.5479 | − | 49.3911i | 0.0489956 | − | 0.0282876i | ||||
\(146\) | −978.518 | − | 1694.84i | −0.554676 | − | 0.960727i | ||||
\(147\) | 23.2018 | − | 40.1867i | 0.0130180 | − | 0.0225479i | ||||
\(148\) | − | 165.145i | − | 0.0917218i | ||||||
\(149\) | 2389.38 | + | 1379.51i | 1.31373 | + | 0.758482i | 0.982712 | − | 0.185143i | \(-0.0592747\pi\) |
0.331018 | + | 0.943625i | \(0.392608\pi\) | |||||||
\(150\) | 1019.16 | + | 588.415i | 0.554763 | + | 0.320292i | ||||
\(151\) | 976.355i | 0.526190i | 0.964770 | + | 0.263095i | \(0.0847432\pi\) | ||||
−0.964770 | + | 0.263095i | \(0.915257\pi\) | |||||||
\(152\) | −1305.20 | + | 2260.67i | −0.696483 | + | 1.20634i | ||||
\(153\) | 171.458 | + | 296.975i | 0.0905986 | + | 0.156921i | ||||
\(154\) | −2610.49 | + | 1507.17i | −1.36597 | + | 0.788642i | ||||
\(155\) | 63.5076 | 0.0329100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −564.875 | −0.287146 | −0.143573 | − | 0.989640i | \(-0.545859\pi\) | ||||
−0.143573 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(158\) | −935.127 | + | 539.896i | −0.470853 | + | 0.271847i | ||||
\(159\) | 5.24435 | + | 9.08347i | 0.00261575 | + | 0.00453061i | ||||
\(160\) | 18.0412 | − | 31.2483i | 0.00891427 | − | 0.0154400i | ||||
\(161\) | 1331.68i | 0.651869i | ||||||||
\(162\) | 413.474 | + | 238.719i | 0.200528 | + | 0.115775i | ||||
\(163\) | 1306.43 | + | 754.266i | 0.627775 | + | 0.362446i | 0.779890 | − | 0.625917i | \(-0.215275\pi\) |
−0.152115 | + | 0.988363i | \(0.548608\pi\) | |||||||
\(164\) | − | 100.182i | − | 0.0477005i | ||||||
\(165\) | 66.9763 | − | 116.006i | 0.0316006 | − | 0.0547339i | ||||
\(166\) | 773.329 | + | 1339.45i | 0.361578 | + | 0.626272i | ||||
\(167\) | −513.138 | + | 296.260i | −0.237771 | + | 0.137277i | −0.614152 | − | 0.789188i | \(-0.710502\pi\) |
0.376381 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(168\) | −1619.29 | −0.743638 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −36.7471 | −0.0165787 | ||||||||
\(171\) | 1255.14 | − | 724.654i | 0.561303 | − | 0.324068i | ||||
\(172\) | 315.237 | + | 546.007i | 0.139748 | + | 0.242050i | ||||
\(173\) | −2247.78 | + | 3893.28i | −0.987838 | + | 1.71099i | −0.359262 | + | 0.933237i | \(0.616972\pi\) |
−0.628576 | + | 0.777748i | \(0.716362\pi\) | |||||||
\(174\) | − | 1660.31i | − | 0.723377i | ||||||
\(175\) | 1962.76 | + | 1133.20i | 0.847834 | + | 0.489497i | ||||
\(176\) | −2827.00 | − | 1632.17i | −1.21076 | − | 0.699030i | ||||
\(177\) | 263.941i | 0.112085i | ||||||||
\(178\) | 1485.55 | − | 2573.05i | 0.625543 | − | 1.08347i | ||||
\(179\) | −77.1425 | − | 133.615i | −0.0322117 | − | 0.0557924i | 0.849470 | − | 0.527637i | \(-0.176922\pi\) |
−0.881682 | + | 0.471844i | \(0.843588\pi\) | |||||||
\(180\) | −9.39019 | + | 5.42143i | −0.00388835 | + | 0.00224494i | ||||
\(181\) | −1071.35 | −0.439959 | −0.219979 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219979 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3392.45 | 1.37037 | ||||||||
\(184\) | −1533.94 | + | 885.623i | −0.614586 | + | 0.354831i | ||||
\(185\) | −32.2353 | − | 55.8332i | −0.0128107 | − | 0.0221889i | ||||
\(186\) | 533.710 | − | 924.413i | 0.210395 | − | 0.364415i | ||||
\(187\) | − | 1653.84i | − | 0.646742i | ||||||
\(188\) | −39.7985 | − | 22.9777i | −0.0154394 | − | 0.00891393i | ||||
\(189\) | 2344.68 | + | 1353.70i | 0.902383 | + | 0.520991i | ||||
\(190\) | 155.309i | 0.0593015i | ||||||||
\(191\) | −338.601 | + | 586.475i | −0.128274 | + | 0.222177i | −0.923008 | − | 0.384781i | \(-0.874277\pi\) |
0.794734 | + | 0.606958i | \(0.207610\pi\) | |||||||
\(192\) | −1046.40 | − | 1812.42i | −0.393321 | − | 0.681252i | ||||
\(193\) | −1144.61 | + | 660.840i | −0.426895 | + | 0.246468i | −0.698023 | − | 0.716075i | \(-0.745937\pi\) |
0.271128 | + | 0.962543i | \(0.412603\pi\) | |||||||
\(194\) | −1494.07 | −0.552929 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.1154 | 0.00660183 | ||||||||
\(197\) | 1097.57 | − | 633.683i | 0.396948 | − | 0.229178i | −0.288218 | − | 0.957565i | \(-0.593063\pi\) |
0.685166 | + | 0.728387i | \(0.259730\pi\) | |||||||
\(198\) | 1113.00 | + | 1927.78i | 0.399483 | + | 0.691925i | ||||
\(199\) | 1198.12 | − | 2075.21i | 0.426796 | − | 0.739233i | −0.569790 | − | 0.821790i | \(-0.692975\pi\) |
0.996586 | + | 0.0825573i | \(0.0263088\pi\) | |||||||
\(200\) | 3014.51i | 1.06579i | ||||||||
\(201\) | −1417.70 | − | 818.510i | −0.497497 | − | 0.287230i | ||||
\(202\) | 2044.76 | + | 1180.54i | 0.712222 | + | 0.411202i | ||||
\(203\) | − | 3197.51i | − | 1.10552i | ||||||
\(204\) | 67.7003 | − | 117.260i | 0.0232352 | − | 0.0402445i | ||||
\(205\) | −19.5549 | − | 33.8701i | −0.00666231 | − | 0.0115395i | ||||
\(206\) | 2064.66 | − | 1192.03i | 0.698310 | − | 0.403170i | ||||
\(207\) | 983.409 | 0.330201 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6989.81 | −2.31337 | ||||||||
\(210\) | −83.4346 | + | 48.1710i | −0.0274168 | + | 0.0158291i | ||||
\(211\) | 45.7769 | + | 79.2880i | 0.0149356 | + | 0.0258692i | 0.873397 | − | 0.487010i | \(-0.161912\pi\) |
−0.858461 | + | 0.512879i | \(0.828579\pi\) | |||||||
\(212\) | −2.04733 | + | 3.54608i | −0.000663261 | + | 0.00114880i | ||||
\(213\) | 1996.05i | 0.642099i | ||||||||
\(214\) | −1901.99 | − | 1098.12i | −0.607558 | − | 0.350774i | ||||
\(215\) | 213.155 | + | 123.065i | 0.0676141 | + | 0.0390370i | ||||
\(216\) | 3601.08i | 1.13436i | ||||||||
\(217\) | 1027.85 | − | 1780.29i | 0.321543 | − | 0.556929i | ||||
\(218\) | 860.494 | + | 1490.42i | 0.267339 | + | 0.463045i | ||||
\(219\) | 2437.94 | − | 1407.55i | 0.752241 | − | 0.434307i | ||||
\(220\) | 52.2935 | 0.0160256 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1083.61 | −0.327599 | ||||||||
\(223\) | 1069.90 | − | 617.709i | 0.321282 | − | 0.185493i | −0.330682 | − | 0.943742i | \(-0.607279\pi\) |
0.651964 | + | 0.758250i | \(0.273945\pi\) | |||||||
\(224\) | −583.982 | − | 1011.49i | −0.174192 | − | 0.301709i | ||||
\(225\) | 836.839 | − | 1449.45i | 0.247952 | − | 0.429466i | ||||
\(226\) | 1643.17i | 0.483637i | ||||||||
\(227\) | −2859.32 | − | 1650.83i | −0.836035 | − | 0.482685i | 0.0198797 | − | 0.999802i | \(-0.493672\pi\) |
−0.855914 | + | 0.517118i | \(0.827005\pi\) | |||||||
\(228\) | −495.591 | − | 286.130i | −0.143953 | − | 0.0831114i | ||||
\(229\) | − | 211.283i | − | 0.0609694i | −0.999535 | − | 0.0304847i | \(-0.990295\pi\) | ||
0.999535 | − | 0.0304847i | \(-0.00970508\pi\) | |||||||
\(230\) | −52.6913 | + | 91.2640i | −0.0151059 | + | 0.0261642i | ||||
\(231\) | −2167.98 | − | 3755.05i | −0.617500 | − | 1.06954i | ||||
\(232\) | 3683.18 | − | 2126.48i | 1.04230 | − | 0.601769i | ||||
\(233\) | 256.724 | 0.0721827 | 0.0360913 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360913 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.9404 | −0.00498002 | ||||||||
\(236\) | −89.2349 | + | 51.5198i | −0.0246131 | + | 0.0142104i | ||||
\(237\) | −776.612 | − | 1345.13i | −0.212854 | − | 0.368674i | ||||
\(238\) | −594.740 | + | 1030.12i | −0.161980 | + | 0.280558i | ||||
\(239\) | − | 3549.62i | − | 0.960694i | −0.877078 | − | 0.480347i | \(-0.840511\pi\) | ||
0.877078 | − | 0.480347i | \(-0.159489\pi\) | |||||||
\(240\) | −90.3545 | − | 52.1662i | −0.0243015 | − | 0.0140305i | ||||
\(241\) | −4356.19 | − | 2515.05i | −1.16434 | − | 0.672235i | −0.212003 | − | 0.977269i | \(-0.567999\pi\) |
−0.952341 | + | 0.305034i | \(0.901332\pi\) | |||||||
\(242\) | − | 7326.27i | − | 1.94608i | ||||||
\(243\) | 1667.39 | − | 2888.00i | 0.440176 | − | 0.762408i | ||||
\(244\) | 662.186 | + | 1146.94i | 0.173738 | + | 0.300923i | ||||
\(245\) | 6.12457 | − | 3.53602i | 0.00159708 | − | 0.000922074i | ||||
\(246\) | −657.349 | −0.170370 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2734.25 | 0.700102 | ||||||||
\(249\) | −1926.72 | + | 1112.39i | −0.490366 | + | 0.283113i | ||||
\(250\) | 179.579 | + | 311.040i | 0.0454303 | + | 0.0786876i | ||||
\(251\) | −359.392 | + | 622.485i | −0.0903770 | + | 0.156538i | −0.907670 | − | 0.419685i | \(-0.862141\pi\) |
0.817293 | + | 0.576223i | \(0.195474\pi\) | |||||||
\(252\) | 350.976i | 0.0877357i | ||||||||
\(253\) | −4107.42 | − | 2371.42i | −1.02068 | − | 0.589288i | ||||
\(254\) | −1227.14 | − | 708.492i | −0.303141 | − | 0.175019i | ||||
\(255\) | − | 52.8588i | − | 0.0129810i | ||||||
\(256\) | 1066.87 | − | 1847.87i | 0.260466 | − | 0.451141i | ||||
\(257\) | 640.397 | + | 1109.20i | 0.155435 | + | 0.269222i | 0.933217 | − | 0.359312i | \(-0.116989\pi\) |
−0.777782 | + | 0.628534i | \(0.783655\pi\) | |||||||
\(258\) | 3582.65 | − | 2068.45i | 0.864520 | − | 0.499131i | ||||
\(259\) | −2086.87 | −0.500663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2361.28 | −0.559998 | ||||||||
\(262\) | 4561.86 | − | 2633.79i | 1.07570 | − | 0.621054i | ||||
\(263\) | −2612.77 | − | 4525.46i | −0.612587 | − | 1.06103i | −0.990803 | − | 0.135315i | \(-0.956795\pi\) |
0.378215 | − | 0.925718i | \(-0.376538\pi\) | |||||||
\(264\) | 2883.60 | − | 4994.54i | 0.672247 | − | 1.16437i | ||||
\(265\) | 1.59851i | 0.000370549i | ||||||||
\(266\) | 4353.71 | + | 2513.62i | 1.00355 | + | 0.579398i | ||||
\(267\) | 3701.19 | + | 2136.89i | 0.848350 | + | 0.489795i | ||||
\(268\) | − | 639.074i | − | 0.145663i | ||||||
\(269\) | −3221.90 | + | 5580.50i | −0.730270 | + | 1.26487i | 0.226497 | + | 0.974012i | \(0.427273\pi\) |
−0.956768 | + | 0.290854i | \(0.906061\pi\) | |||||||
\(270\) | 107.125 | + | 185.547i | 0.0241461 | + | 0.0418223i | ||||
\(271\) | 3403.42 | − | 1964.97i | 0.762890 | − | 0.440455i | −0.0674426 | − | 0.997723i | \(-0.521484\pi\) |
0.830332 | + | 0.557269i | \(0.188151\pi\) | |||||||
\(272\) | −1288.13 | −0.287149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4632.74 | −1.02144 | ||||||||
\(275\) | −6990.48 | + | 4035.96i | −1.53288 | + | 0.885009i | ||||
\(276\) | −194.149 | − | 336.277i | −0.0423421 | − | 0.0733387i | ||||
\(277\) | −2942.20 | + | 5096.04i | −0.638194 | + | 1.10538i | 0.347635 | + | 0.937630i | \(0.386985\pi\) |
−0.985829 | + | 0.167754i | \(0.946348\pi\) | |||||||
\(278\) | 3826.03i | 0.825431i | ||||||||
\(279\) | −1314.69 | − | 759.039i | −0.282110 | − | 0.162876i | ||||
\(280\) | −213.722 | − | 123.392i | −0.0456155 | − | 0.0263361i | ||||
\(281\) | − | 3529.79i | − | 0.749358i | −0.927155 | − | 0.374679i | \(-0.877753\pi\) | ||
0.927155 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(282\) | −150.769 | + | 261.140i | −0.0318375 | + | 0.0551442i | ||||
\(283\) | −1305.50 | − | 2261.19i | −0.274219 | − | 0.474961i | 0.695719 | − | 0.718314i | \(-0.255086\pi\) |
−0.969938 | + | 0.243353i | \(0.921753\pi\) | |||||||
\(284\) | −674.836 | + | 389.617i | −0.141001 | + | 0.0814067i | ||||
\(285\) | −223.403 | −0.0464325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1265.96 | −0.260373 | ||||||||
\(288\) | −746.955 | + | 431.255i | −0.152829 | + | 0.0882359i | ||||
\(289\) | 2130.19 | + | 3689.60i | 0.433582 | + | 0.750987i | ||||
\(290\) | 126.518 | − | 219.136i | 0.0256186 | − | 0.0443727i | ||||
\(291\) | − | 2149.15i | − | 0.432939i | ||||||
\(292\) | 951.744 | + | 549.490i | 0.190742 | + | 0.110125i | ||||
\(293\) | −4755.37 | − | 2745.51i | −0.948163 | − | 0.547422i | −0.0556531 | − | 0.998450i | \(-0.517724\pi\) |
−0.892510 | + | 0.451028i | \(0.851057\pi\) | |||||||
\(294\) | − | 118.865i | − | 0.0235795i | ||||||
\(295\) | −20.1127 | + | 34.8363i | −0.00396952 | + | 0.00687541i | ||||
\(296\) | −1387.86 | − | 2403.84i | −0.272526 | − | 0.472028i | ||||
\(297\) | −8350.70 | + | 4821.28i | −1.63150 | + | 0.941950i | ||||
\(298\) | 7067.37 | 1.37383 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −660.852 | −0.127181 | ||||||||
\(301\) | 6899.67 | − | 3983.53i | 1.32123 | − | 0.762813i | ||||
\(302\) | 1250.49 | + | 2165.92i | 0.238271 | + | 0.412697i | ||||
\(303\) | −1698.15 | + | 2941.28i | −0.321967 | + | 0.557664i | ||||
\(304\) | 5444.19i | 1.02712i | ||||||||
\(305\) | 447.751 | + | 258.509i | 0.0840596 | + | 0.0485318i | ||||
\(306\) | 760.716 | + | 439.200i | 0.142115 | + | 0.0820502i | ||||
\(307\) | 7307.59i | 1.35852i | 0.733897 | + | 0.679261i | \(0.237700\pi\) | ||||
−0.733897 | + | 0.679261i | \(0.762300\pi\) | |||||||
\(308\) | 846.353 | − | 1465.93i | 0.156576 | − | 0.271198i | ||||
\(309\) | 1714.68 | + | 2969.91i | 0.315678 | + | 0.546771i | ||||
\(310\) | 140.883 | − | 81.3390i | 0.0258117 | − | 0.0149024i | ||||
\(311\) | −7904.92 | −1.44131 | −0.720654 | − | 0.693295i | \(-0.756158\pi\) | ||||
−0.720654 | + | 0.693295i | \(0.756158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10002.4 | 1.80629 | 0.903145 | − | 0.429336i | \(-0.141252\pi\) | ||||
0.903145 | + | 0.429336i | \(0.141252\pi\) | |||||||
\(314\) | −1253.10 | + | 723.478i | −0.225212 | + | 0.130026i | ||||
\(315\) | 68.5084 | + | 118.660i | 0.0122540 | + | 0.0212246i | ||||
\(316\) | 303.180 | − | 525.123i | 0.0539722 | − | 0.0934825i | ||||
\(317\) | − | 6230.81i | − | 1.10397i | −0.833856 | − | 0.551983i | \(-0.813871\pi\) | ||
0.833856 | − | 0.551983i | \(-0.186129\pi\) | |||||||
\(318\) | 23.2678 | + | 13.4337i | 0.00410312 | + | 0.00236894i | ||||
\(319\) | 9862.40 | + | 5694.06i | 1.73100 | + | 0.999392i | ||||
\(320\) | − | 318.950i | − | 0.0557182i | ||||||
\(321\) | 1579.58 | − | 2735.91i | 0.274653 | − | 0.475713i | ||||
\(322\) | 1705.58 | + | 2954.15i | 0.295181 | + | 0.511269i | ||||
\(323\) | −2388.70 | + | 1379.12i | −0.411489 | + | 0.237573i | ||||
\(324\) | −268.107 | −0.0459717 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3864.19 | 0.656495 | ||||||||
\(327\) | −2143.89 | + | 1237.77i | −0.362561 | + | 0.209324i | ||||
\(328\) | −841.917 | − | 1458.24i | −0.141729 | − | 0.245482i | ||||
\(329\) | −290.360 | + | 502.918i | −0.0486567 | + | 0.0842758i | ||||
\(330\) | − | 343.127i | − | 0.0572379i | ||||||
\(331\) | 4013.60 | + | 2317.25i | 0.666488 | + | 0.384797i | 0.794745 | − | 0.606944i | \(-0.207605\pi\) |
−0.128257 | + | 0.991741i | \(0.540938\pi\) | |||||||
\(332\) | −752.170 | − | 434.265i | −0.124339 | − | 0.0717874i | ||||
\(333\) | 1541.10i | 0.253609i | ||||||||
\(334\) | −758.886 | + | 1314.43i | −0.124325 | + | 0.215337i | ||||
\(335\) | −124.743 | − | 216.062i | −0.0203447 | − | 0.0352380i | ||||
\(336\) | −2924.71 | + | 1688.58i | −0.474870 | + | 0.274166i | ||||
\(337\) | −3029.82 | −0.489747 | −0.244874 | − | 0.969555i | \(-0.578746\pi\) | ||||
−0.244874 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2363.61 | −0.378684 | ||||||||
\(340\) | 17.8708 | − | 10.3177i | 0.00285054 | − | 0.00164576i | ||||
\(341\) | 3660.74 | + | 6340.58i | 0.581349 | + | 1.00693i | ||||
\(342\) | 1856.24 | − | 3215.10i | 0.293491 | − | 0.508342i | ||||
\(343\) | − | 6463.66i | − | 1.01751i | ||||||
\(344\) | 9177.15 | + | 5298.43i | 1.43837 | + | 0.830443i | ||||
\(345\) | −131.278 | − | 75.7937i | −0.0204864 | − | 0.0118278i | ||||
\(346\) | 11515.6i | 1.78926i | ||||||||
\(347\) | −1420.80 | + | 2460.90i | −0.219805 | + | 0.380714i | −0.954748 | − | 0.297415i | \(-0.903876\pi\) |
0.734943 | + | 0.678129i | \(0.237209\pi\) | |||||||
\(348\) | 466.175 | + | 807.440i | 0.0718093 | + | 0.124377i | ||||
\(349\) | −6552.07 | + | 3782.84i | −1.00494 | + | 0.580202i | −0.909706 | − | 0.415252i | \(-0.863693\pi\) |
−0.0952339 | + | 0.995455i | \(0.530360\pi\) | |||||||
\(350\) | 5805.51 | 0.886622 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4159.76 | 0.629875 | ||||||||
\(353\) | −2026.01 | + | 1169.72i | −0.305478 | + | 0.176368i | −0.644901 | − | 0.764266i | \(-0.723101\pi\) |
0.339423 | + | 0.940634i | \(0.389768\pi\) | |||||||
\(354\) | 338.050 | + | 585.520i | 0.0507547 | + | 0.0879097i | ||||
\(355\) | −152.102 | + | 263.448i | −0.0227401 | + | 0.0393870i | ||||
\(356\) | 1668.43i | 0.248389i | ||||||||
\(357\) | −1481.77 | − | 855.502i | −0.219674 | − | 0.126829i | ||||
\(358\) | −342.261 | − | 197.605i | −0.0505281 | − | 0.0291724i | ||||
\(359\) | 2531.68i | 0.372192i | 0.982532 | + | 0.186096i | \(0.0595835\pi\) | ||||
−0.982532 | + | 0.186096i | \(0.940417\pi\) | |||||||
\(360\) | −91.1221 | + | 157.828i | −0.0133404 | + | 0.0231063i | ||||
\(361\) | 2399.23 | + | 4155.58i | 0.349793 | + | 0.605858i | ||||
\(362\) | −2376.64 | + | 1372.16i | −0.345065 | + | 0.199223i | ||||
\(363\) | 10538.5 | 1.52376 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 429.028 | 0.0615243 | ||||||||
\(366\) | 7525.70 | − | 4344.97i | 1.07479 | − | 0.620533i | ||||
\(367\) | −3288.91 | − | 5696.55i | −0.467792 | − | 0.810239i | 0.531531 | − | 0.847039i | \(-0.321617\pi\) |
−0.999323 | + | 0.0368000i | \(0.988284\pi\) | |||||||
\(368\) | −1847.04 | + | 3199.17i | −0.261640 | + | 0.453174i | ||||
\(369\) | 934.876i | 0.131891i | ||||||||
\(370\) | −143.020 | − | 82.5725i | −0.0200952 | − | 0.0116020i | ||||
\(371\) | 44.8104 | + | 25.8713i | 0.00627073 | + | 0.00362041i | ||||
\(372\) | 599.413i | 0.0835433i | ||||||||
\(373\) | −1451.36 | + | 2513.83i | −0.201471 | + | 0.348958i | −0.949003 | − | 0.315268i | \(-0.897905\pi\) |
0.747532 | + | 0.664226i | \(0.231239\pi\) | |||||||
\(374\) | −2118.20 | − | 3668.83i | −0.292859 | − | 0.507247i | ||||
\(375\) | −447.415 | + | 258.315i | −0.0616117 | + | 0.0355716i | ||||
\(376\) | −772.407 | −0.105941 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6935.16 | 0.943667 | ||||||||
\(379\) | −1615.77 | + | 932.867i | −0.218989 | + | 0.126433i | −0.605482 | − | 0.795859i | \(-0.707020\pi\) |
0.386493 | + | 0.922292i | \(0.373686\pi\) | |||||||
\(380\) | −43.6070 | − | 75.5296i | −0.00588682 | − | 0.0101963i | ||||
\(381\) | 1019.13 | − | 1765.18i | 0.137038 | − | 0.237357i | ||||
\(382\) | 1734.69i | 0.232342i | ||||||||
\(383\) | −9384.24 | − | 5417.99i | −1.25199 | − | 0.722837i | −0.280486 | − | 0.959858i | \(-0.590496\pi\) |
−0.971504 | + | 0.237021i | \(0.923829\pi\) | |||||||
\(384\) | −3002.32 | − | 1733.39i | −0.398988 | − | 0.230356i | ||||
\(385\) | − | 660.813i | − | 0.0874757i | ||||||
\(386\) | −1692.78 | + | 2931.97i | −0.223213 | + | 0.386616i | ||||
\(387\) | −2941.73 | − | 5095.22i | −0.386399 | − | 0.669263i | ||||
\(388\) | 726.597 | − | 419.501i | 0.0950705 | − | 0.0548890i | ||||
\(389\) | 9520.34 | 1.24088 | 0.620438 | − | 0.784256i | \(-0.286955\pi\) | ||||
0.620438 | + | 0.784256i | \(0.286955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1871.56 | −0.242069 | ||||||||
\(392\) | 263.687 | − | 152.240i | 0.0339750 | − | 0.0196155i | ||||
\(393\) | 3788.57 | + | 6561.99i | 0.486280 | + | 0.842261i | ||||
\(394\) | 1623.21 | − | 2811.49i | 0.207554 | − | 0.359494i | ||||
\(395\) | − | 236.716i | − | 0.0301531i | ||||||
\(396\) | −1082.55 | − | 625.009i | −0.137374 | − | 0.0793129i | ||||
\(397\) | −8754.51 | − | 5054.42i | −1.10674 | − | 0.638978i | −0.168758 | − | 0.985657i | \(-0.553976\pi\) |
−0.937983 | + | 0.346680i | \(0.887309\pi\) | |||||||
\(398\) | − | 6138.10i | − | 0.773053i | ||||||
\(399\) | −3615.71 | + | 6262.59i | −0.453664 | + | 0.785768i | ||||
\(400\) | 3143.51 | + | 5444.71i | 0.392938 | + | 0.680589i | ||||
\(401\) | −1805.12 | + | 1042.19i | −0.224797 | + | 0.129787i | −0.608169 | − | 0.793807i | \(-0.708096\pi\) |
0.383373 | + | 0.923594i | \(0.374763\pi\) | |||||||
\(402\) | −4193.32 | −0.520258 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1325.88 | −0.163279 | ||||||||
\(405\) | −90.6432 | + | 52.3329i | −0.0111212 | + | 0.00642084i | ||||
\(406\) | −4095.30 | − | 7093.27i | −0.500607 | − | 0.867076i | ||||
\(407\) | 3716.25 | − | 6436.73i | 0.452599 | − | 0.783924i | ||||
\(408\) | − | 2275.78i | − | 0.276147i | ||||||
\(409\) | 8414.76 | + | 4858.26i | 1.01732 | + | 0.587349i | 0.913326 | − | 0.407229i | \(-0.133505\pi\) |
0.103992 | + | 0.994578i | \(0.466838\pi\) | |||||||
\(410\) | −86.7600 | − | 50.0909i | −0.0104507 | − | 0.00603369i | ||||
\(411\) | − | 6663.95i | − | 0.799777i | ||||||
\(412\) | −669.390 | + | 1159.42i | −0.0800449 | + | 0.138642i | ||||
\(413\) | 651.035 | + | 1127.63i | 0.0775674 | + | 0.134351i | ||||
\(414\) | 2181.56 | − | 1259.53i | 0.258981 | − | 0.149523i | ||||
\(415\) | −339.064 | −0.0401060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5503.54 | −0.646305 | ||||||||
\(418\) | −15506.0 | + | 8952.38i | −1.81441 | + | 1.04755i | ||||
\(419\) | −6690.94 | − | 11589.1i | −0.780129 | − | 1.35122i | −0.931866 | − | 0.362802i | \(-0.881820\pi\) |
0.151737 | − | 0.988421i | \(-0.451513\pi\) | |||||||
\(420\) | 27.0505 | − | 46.8529i | 0.00314269 | − | 0.00544330i | ||||
\(421\) | − | 9463.37i | − | 1.09553i | −0.836633 | − | 0.547763i | \(-0.815479\pi\) | ||
0.836633 | − | 0.547763i | \(-0.184521\pi\) | |||||||
\(422\) | 203.100 | + | 117.260i | 0.0234284 | + | 0.0135264i | ||||
\(423\) | 371.391 | + | 214.423i | 0.0426895 | + | 0.0246468i | ||||
\(424\) | 68.8221i | 0.00788278i | ||||||||
\(425\) | −1592.62 | + | 2758.50i | −0.181773 | + | 0.314840i | ||||
\(426\) | 2556.49 | + | 4427.97i | 0.290757 | + | 0.503606i | ||||
\(427\) | 14493.4 | − | 8367.77i | 1.64259 | − | 0.948349i | ||||
\(428\) | 1233.30 | 0.139285 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 630.474 | 0.0707074 | ||||||||
\(431\) | 4202.20 | − | 2426.14i | 0.469635 | − | 0.271144i | −0.246452 | − | 0.969155i | \(-0.579265\pi\) |
0.716087 | + | 0.698011i | \(0.245931\pi\) | |||||||
\(432\) | 3755.17 | + | 6504.15i | 0.418220 | + | 0.724378i | ||||
\(433\) | −4104.00 | + | 7108.33i | −0.455486 | + | 0.788925i | −0.998716 | − | 0.0506587i | \(-0.983868\pi\) |
0.543230 | + | 0.839584i | \(0.317201\pi\) | |||||||
\(434\) | − | 5265.78i | − | 0.582409i | ||||||
\(435\) | 315.215 | + | 181.989i | 0.0347434 | + | 0.0200591i | ||||
\(436\) | −836.949 | − | 483.213i | −0.0919325 | − | 0.0530773i | ||||
\(437\) | 7910.01i | 0.865874i | ||||||||
\(438\) | 3605.50 | − | 6244.92i | 0.393328 | − | 0.681264i | ||||
\(439\) | −1496.90 | − | 2592.71i | −0.162741 | − | 0.281875i | 0.773110 | − | 0.634272i | \(-0.218700\pi\) |
−0.935851 | + | 0.352397i | \(0.885367\pi\) | |||||||
\(440\) | 761.182 | − | 439.469i | 0.0824726 | − | 0.0476156i | ||||
\(441\) | −169.049 | −0.0182539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9743.67 | 1.04500 | 0.522501 | − | 0.852639i | \(-0.324999\pi\) | ||||
0.522501 | + | 0.852639i | \(0.324999\pi\) | |||||||
\(444\) | 526.979 | − | 304.251i | 0.0563273 | − | 0.0325206i | ||||
\(445\) | 325.668 | + | 564.073i | 0.0346924 | + | 0.0600890i | ||||
\(446\) | 1582.29 | − | 2740.61i | 0.167990 | − | 0.290968i | ||||
\(447\) | 10166.0i | 1.07570i | ||||||||
\(448\) | −8941.01 | − | 5162.09i | −0.942908 | − | 0.544388i | ||||
\(449\) | −486.237 | − | 280.729i | −0.0511068 | − | 0.0295065i | 0.474229 | − | 0.880402i | \(-0.342727\pi\) |
−0.525336 | + | 0.850895i | \(0.676060\pi\) | |||||||
\(450\) | − | 4287.22i | − | 0.449114i | ||||||
\(451\) | 2254.39 | − | 3904.71i | 0.235377 | − | 0.407685i | ||||
\(452\) | −461.363 | − | 799.104i | −0.0480104 | − | 0.0831564i | ||||
\(453\) | −3115.56 | + | 1798.77i | −0.323138 | + | 0.186564i | ||||
\(454\) | −8457.38 | −0.874283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9618.40 | −0.987770 | ||||||||
\(457\) | 11915.1 | − | 6879.20i | 1.21962 | − | 0.704148i | 0.254783 | − | 0.966998i | \(-0.417996\pi\) |
0.964837 | + | 0.262851i | \(0.0846627\pi\) | |||||||
\(458\) | −270.606 | − | 468.704i | −0.0276083 | − | 0.0478190i | ||||
\(459\) | −1902.52 | + | 3295.26i | −0.193468 | + | 0.335097i | ||||
\(460\) | − | 59.1779i | − | 0.00599823i | ||||||
\(461\) | −10400.3 | − | 6004.62i | −1.05074 | − | 0.606644i | −0.127882 | − | 0.991789i | \(-0.540818\pi\) |
−0.922856 | + | 0.385145i | \(0.874151\pi\) | |||||||
\(462\) | −9618.75 | − | 5553.39i | −0.968625 | − | 0.559236i | ||||
\(463\) | − | 13635.7i | − | 1.36870i | −0.729156 | − | 0.684348i | \(-0.760087\pi\) | ||
0.729156 | − | 0.684348i | \(-0.239913\pi\) | |||||||
\(464\) | 4434.96 | − | 7681.57i | 0.443724 | − | 0.768552i | ||||
\(465\) | 117.002 | + | 202.653i | 0.0116685 | + | 0.0202104i | ||||
\(466\) | 569.509 | − | 328.806i | 0.0566138 | − | 0.0326860i | ||||
\(467\) | −8821.95 | −0.874157 | −0.437079 | − | 0.899423i | \(-0.643987\pi\) | ||||
−0.437079 | + | 0.899423i | \(0.643987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8075.72 | −0.795100 | ||||||||
\(470\) | −39.7985 | + | 22.9777i | −0.00390589 | + | 0.00225507i | ||||
\(471\) | −1040.69 | − | 1802.52i | −0.101809 | − | 0.176339i | ||||
\(472\) | −865.933 | + | 1499.84i | −0.0844445 | + | 0.146262i | ||||
\(473\) | 28375.1i | 2.75832i | ||||||||
\(474\) | −3445.62 | − | 1989.33i | −0.333888 | − | 0.192770i | ||||
\(475\) | 11658.6 | + | 6731.08i | 1.12617 | + | 0.650196i | ||||
\(476\) | − | 667.956i | − | 0.0643187i | ||||||
\(477\) | 19.1053 | − | 33.0913i | 0.00183390 | − | 0.00317641i | ||||
\(478\) | −4546.27 | − | 7874.37i | −0.435024 | − | 0.753484i | ||||
\(479\) | 12661.3 | − | 7310.02i | 1.20775 | − | 0.697293i | 0.245480 | − | 0.969402i | \(-0.421054\pi\) |
0.962267 | + | 0.272109i | \(0.0877210\pi\) | |||||||
\(480\) | 132.951 | 0.0126424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12884.9 | −1.21761 | ||||||||
\(483\) | −4249.39 | + | 2453.39i | −0.400319 | + | 0.231124i | ||||
\(484\) | 2057.04 | + | 3562.91i | 0.193186 | + | 0.334608i | ||||
\(485\) | 163.768 | − | 283.655i | 0.0153326 | − | 0.0265569i | ||||
\(486\) | − | 8542.20i | − | 0.797288i | ||||||
\(487\) | 8486.06 | + | 4899.43i | 0.789610 | + | 0.455882i | 0.839825 | − | 0.542857i | \(-0.182657\pi\) |
−0.0502150 | + | 0.998738i | \(0.515991\pi\) | |||||||
\(488\) | 19277.5 | + | 11129.9i | 1.78822 | + | 1.03243i | ||||
\(489\) | 5558.43i | 0.514030i | ||||||||
\(490\) | 9.05771 | − | 15.6884i | 0.000835072 | − | 0.00144639i | ||||
\(491\) | −5418.03 | − | 9384.31i | −0.497989 | − | 0.862542i | 0.502009 | − | 0.864863i | \(-0.332595\pi\) |
−0.999997 | + | 0.00232091i | \(0.999261\pi\) | |||||||
\(492\) | 319.681 | − | 184.568i | 0.0292934 | − | 0.0169125i | ||||
\(493\) | 4493.84 | 0.410532 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −487.993 | −0.0443104 | ||||||||
\(496\) | 4938.52 | − | 2851.26i | 0.447069 | − | 0.258115i | ||||
\(497\) | 4923.43 | + | 8527.63i | 0.444358 | + | 0.769651i | ||||
\(498\) | −2849.45 | + | 4935.40i | −0.256400 | + | 0.444098i | ||||
\(499\) | 2589.96i | 0.232349i | 0.993229 | + | 0.116175i | \(0.0370633\pi\) | ||||
−0.993229 | + | 0.116175i | \(0.962937\pi\) | |||||||
\(500\) | −174.665 | − | 100.843i | −0.0156226 | − | 0.00901969i | ||||
\(501\) | −1890.74 | − | 1091.62i | −0.168607 | − | 0.0973451i | ||||
\(502\) | 1841.20i | 0.163699i | ||||||||
\(503\) | 8533.73 | − | 14780.9i | 0.756462 | − | 1.31023i | −0.188183 | − | 0.982134i | \(-0.560260\pi\) |
0.944644 | − | 0.328096i | \(-0.106407\pi\) | |||||||
\(504\) | 2949.56 | + | 5108.79i | 0.260682 | + | 0.451515i | ||||
\(505\) | −448.260 | + | 258.803i | −0.0394996 | + | 0.0228051i | ||||
\(506\) | −12149.0 | −1.06737 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 795.712 | 0.0694961 | ||||||||
\(509\) | −877.192 | + | 506.447i | −0.0763867 | + | 0.0441019i | −0.537707 | − | 0.843132i | \(-0.680709\pi\) |
0.461320 | + | 0.887234i | \(0.347376\pi\) | |||||||
\(510\) | −67.7003 | − | 117.260i | −0.00587808 | − | 0.0101811i | ||||
\(511\) | 6943.68 | − | 12026.8i | 0.601116 | − | 1.04116i | ||||
\(512\) | − | 12992.6i | − | 1.12148i | ||||||
\(513\) | 13927.1 | + | 8040.83i | 1.19863 | + | 0.692030i | ||||
\(514\) | 2841.28 | + | 1640.41i | 0.243820 | + | 0.140769i | ||||
\(515\) | 522.644i | 0.0447193i | ||||||||
\(516\) | −1161.54 | + | 2011.85i | −0.0990969 | + | 0.171641i | ||||
\(517\) | −1034.13 | − | 1791.17i | −0.0879711 | − | 0.152370i | ||||
\(518\) | −4629.45 | + | 2672.81i | −0.392676 | + | 0.226712i | ||||
\(519\) | −16564.6 | −1.40098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14367.7 | −1.20818 | −0.604089 | − | 0.796917i | \(-0.706463\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(522\) | −5238.19 | + | 3024.27i | −0.439213 | + | 0.253580i | ||||
\(523\) | 8109.96 | + | 14046.9i | 0.678057 | + | 1.17443i | 0.975565 | + | 0.219709i | \(0.0705109\pi\) |
−0.297509 | + | 0.954719i | \(0.596156\pi\) | |||||||
\(524\) | −1479.01 | + | 2561.72i | −0.123303 | + | 0.213568i | ||||
\(525\) | 8350.92i | 0.694217i | ||||||||
\(526\) | −11592.2 | − | 6692.76i | −0.960919 | − | 0.554787i | ||||
\(527\) | 2502.05 | + | 1444.56i | 0.206814 | + | 0.119404i | ||||
\(528\) | − | 12028.0i | − | 0.991382i | ||||||
\(529\) | 3399.89 | − | 5888.78i | 0.279435 | − | 0.483996i | ||||
\(530\) | 2.04733 | + | 3.54608i | 0.000167793 | + | 0.000290626i | ||||
\(531\) | 832.722 | − | 480.772i | 0.0680547 | − | 0.0392914i | ||||
\(532\) | −2823.06 | −0.230066 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10947.5 | 0.887161 | ||||||||
\(535\) | 416.961 | − | 240.733i | 0.0336950 | − | 0.0194538i | ||||
\(536\) | −5370.70 | − | 9302.32i | −0.432796 | − | 0.749625i | ||||
\(537\) | 284.244 | − | 492.325i | 0.0228418 | − | 0.0395631i | ||||
\(538\) | 16506.1i | 1.32273i | ||||||||
\(539\) | 706.071 | + | 407.650i | 0.0564242 | + | 0.0325765i | ||||
\(540\) | −104.194 | − | 60.1566i | −0.00830335 | − | 0.00479394i | ||||
\(541\) | − | 17592.2i | − | 1.39806i | −0.715094 | − | 0.699029i | \(-0.753616\pi\) | ||
0.715094 | − | 0.699029i | \(-0.246384\pi\) | |||||||
\(542\) | 5033.36 | − | 8718.04i | 0.398896 | − | 0.690908i | ||||
\(543\) | −1973.77 | − | 3418.67i | −0.155990 | − | 0.270183i | ||||
\(544\) | 1421.56 | − | 820.738i | 0.112038 | − | 0.0646854i | ||||
\(545\) | −377.281 | −0.0296531 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10504.6 | 0.821103 | 0.410552 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410552 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(548\) | 2252.99 | − | 1300.76i | 0.175626 | − | 0.101398i | ||||
\(549\) | −6179.38 | − | 10703.0i | −0.480382 | − | 0.832045i | ||||
\(550\) | −10338.3 | + | 17906.5i | −0.801504 | + | 1.38825i | ||||
\(551\) | − | 18992.8i | − | 1.46846i | ||||||
\(552\) | −5652.06 | − | 3263.22i | −0.435811 | − | 0.251616i | ||||
\(553\) | −6635.77 | − | 3831.16i | −0.510274 | − | 0.294607i | ||||
\(554\) | 15073.2i | 1.15596i | ||||||||
\(555\) | 118.776 | − | 205.726i | 0.00908426 | − | 0.0157344i | ||||
\(556\) | −1074.26 | − | 1860.67i | −0.0819401 | − | 0.141924i | ||||
\(557\) | 439.558 | − | 253.779i | 0.0334375 | − | 0.0193051i | −0.483188 | − | 0.875517i | \(-0.660521\pi\) |
0.516626 | + | 0.856211i | \(0.327188\pi\) | |||||||
\(558\) | −3888.64 | −0.295016 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −514.690 | −0.0388386 | ||||||||
\(561\) | 5277.41 | − | 3046.92i | 0.397170 | − | 0.229306i | ||||
\(562\) | −4520.87 | − | 7830.38i | −0.339327 | − | 0.587731i | ||||
\(563\) | −1721.57 | + | 2981.85i | −0.128873 | + | 0.223215i | −0.923240 | − | 0.384223i | \(-0.874469\pi\) |
0.794367 | + | 0.607438i | \(0.207803\pi\) | |||||||
\(564\) | − | 169.330i | − | 0.0126420i | ||||||
\(565\) | −311.961 | − | 180.111i | −0.0232288 | − | 0.0134112i | ||||
\(566\) | −5792.16 | − | 3344.11i | −0.430146 | − | 0.248345i | ||||
\(567\) | 3387.96i | 0.250936i | ||||||||
\(568\) | −6548.59 | + | 11342.5i | −0.483755 | + | 0.837888i | ||||
\(569\) | 11986.1 | + | 20760.5i | 0.883098 | + | 1.52957i | 0.847879 | + | 0.530190i | \(0.177879\pi\) |
0.0352188 | + | 0.999380i | \(0.488787\pi\) | |||||||
\(570\) | −495.591 | + | 286.130i | −0.0364176 | + | 0.0210257i | ||||
\(571\) | 7458.32 | 0.546622 | 0.273311 | − | 0.961926i | \(-0.411881\pi\) | ||||
0.273311 | + | 0.961926i | \(0.411881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2495.26 | −0.181922 | ||||||||
\(574\) | −2808.36 | + | 1621.41i | −0.204214 | + | 0.117903i | ||||
\(575\) | 4567.28 | + | 7910.77i | 0.331250 | + | 0.573742i | ||||
\(576\) | −3812.07 | + | 6602.70i | −0.275757 | + | 0.477626i | ||||
\(577\) | 5669.57i | 0.409059i | 0.978860 | + | 0.204530i | \(0.0655665\pi\) | ||||
−0.978860 | + | 0.204530i | \(0.934434\pi\) | |||||||
\(578\) | 9451.10 | + | 5456.60i | 0.680128 | + | 0.392672i | ||||
\(579\) | −4217.49 | − | 2434.97i | −0.302717 | − | 0.174774i | ||||
\(580\) | 142.093i | 0.0101726i | ||||||||
\(581\) | −5487.64 | + | 9504.87i | −0.391851 | + | 0.678706i | ||||
\(582\) | −2752.58 | − | 4767.60i | −0.196045 | − | 0.339559i | ||||
\(583\) | −159.595 | + | 92.1420i | −0.0113375 | + | 0.00654568i | ||||
\(584\) | 18471.4 | 1.30882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14065.6 | −0.991541 | ||||||||
\(587\) | 881.087 | − | 508.696i | 0.0619529 | − | 0.0357685i | −0.468704 | − | 0.883355i | \(-0.655279\pi\) |
0.530657 | + | 0.847587i | \(0.321945\pi\) | |||||||
\(588\) | 33.3746 | + | 57.8064i | 0.00234072 | + | 0.00405425i | ||||
\(589\) | 6105.30 | − | 10574.7i | 0.427104 | − | 0.739766i | ||||
\(590\) | 103.040i | 0.00718996i | ||||||||
\(591\) | 4044.18 | + | 2334.91i | 0.281481 | + | 0.162513i | ||||
\(592\) | −5013.41 | − | 2894.49i | −0.348057 | − | 0.200951i | ||||
\(593\) | 10198.2i | 0.706221i | 0.935582 | + | 0.353111i | \(0.114876\pi\) | ||||
−0.935582 | + | 0.353111i | \(0.885124\pi\) | |||||||
\(594\) | −12350.0 | + | 21390.8i | −0.853073 | + | 1.47757i | ||||
\(595\) | −130.381 | − | 225.827i | −0.00898336 | − | 0.0155596i | ||||
\(596\) | −3437.00 | + | 1984.35i | −0.236216 | + | 0.136380i | ||||
\(597\) | 8829.33 | 0.605294 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12516.3 | 0.853763 | 0.426881 | − | 0.904308i | \(-0.359612\pi\) | ||||
0.426881 | + | 0.904308i | \(0.359612\pi\) | |||||||
\(600\) | −9619.33 | + | 5553.72i | −0.654512 | + | 0.377883i | ||||
\(601\) | −4813.73 | − | 8337.63i | −0.326716 | − | 0.565888i | 0.655142 | − | 0.755505i | \(-0.272609\pi\) |
−0.981858 | + | 0.189617i | \(0.939275\pi\) | |||||||
\(602\) | 10204.0 | − | 17673.9i | 0.690838 | − | 1.19657i | ||||
\(603\) | 5963.70i | 0.402754i | ||||||||
\(604\) | −1216.28 | − | 702.218i | −0.0819364 | − | 0.0473060i | ||||
\(605\) | 1390.92 | + | 803.046i | 0.0934691 | + | 0.0539644i | ||||
\(606\) | 8699.80i | 0.583177i | ||||||||
\(607\) | −3333.60 | + | 5773.96i | −0.222910 | + | 0.386092i | −0.955690 | − | 0.294373i | \(-0.904889\pi\) |
0.732780 | + | 0.680466i | \(0.238222\pi\) | |||||||
\(608\) | −3468.78 | − | 6008.11i | −0.231378 | − | 0.400758i | ||||
\(609\) | 10203.3 | − | 5890.87i | 0.678913 | − | 0.391971i | ||||
\(610\) | 1324.37 | 0.0879053 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −493.268 | −0.0325803 | ||||||||
\(613\) | −19992.5 | + | 11542.7i | −1.31728 | + | 0.760530i | −0.983290 | − | 0.182047i | \(-0.941728\pi\) |
−0.333987 | + | 0.942578i | \(0.608394\pi\) | |||||||
\(614\) | 9359.39 | + | 16210.9i | 0.615170 | + | 1.06551i | ||||
\(615\) | 72.0532 | − | 124.800i | 0.00472433 | − | 0.00818278i | ||||
\(616\) | − | 28450.6i | − | 1.86089i | ||||||
\(617\) | −2640.72 | − | 1524.62i | −0.172304 | − | 0.0994796i | 0.411368 | − | 0.911469i | \(-0.365051\pi\) |
−0.583672 | + | 0.811990i | \(0.698384\pi\) | |||||||
\(618\) | 7607.58 | + | 4392.24i | 0.495181 | + | 0.285893i | ||||
\(619\) | − | 7296.58i | − | 0.473787i | −0.971536 | − | 0.236894i | \(-0.923871\pi\) | ||
0.971536 | − | 0.236894i | \(-0.0761293\pi\) | |||||||
\(620\) | −45.6761 | + | 79.1134i | −0.00295871 | + | 0.00512463i | ||||
\(621\) | 5455.99 | + | 9450.06i | 0.352563 | + | 0.610657i | ||||
\(622\) | −17536.0 | + | 10124.4i | −1.13044 | + | 0.652657i | ||||
\(623\) | 21083.3 | 1.35583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15506.8 | 0.992438 | ||||||||
\(626\) | 22189.0 | − | 12810.8i | 1.41670 | − | 0.817929i | ||||
\(627\) | −12877.5 | − | 22304.5i | −0.820222 | − | 1.42067i | ||||
\(628\) | 406.271 | − | 703.683i | 0.0258153 | − | 0.0447134i | ||||
\(629\) | − | 2932.92i | − | 0.185920i | ||||||
\(630\) | 303.954 | + | 175.488i | 0.0192219 | + | 0.0110978i | ||||
\(631\) | −20637.0 | − | 11914.8i | −1.30197 | − | 0.751694i | −0.321230 | − | 0.947001i | \(-0.604096\pi\) |
−0.980742 | + | 0.195307i | \(0.937430\pi\) | |||||||
\(632\) | − | 10191.6i | − | 0.641453i | ||||||
\(633\) | −168.672 | + | 292.149i | −0.0105910 | + | 0.0183442i | ||||
\(634\) | −7980.27 | − | 13822.2i | −0.499901 | − | 0.865853i | ||||
\(635\) | 269.019 | − | 155.318i | 0.0168121 | − | 0.00970648i | ||||
\(636\) | −15.0874 | −0.000940653 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29171.3 | 1.81019 | ||||||||
\(639\) | 6297.43 | − | 3635.82i | 0.389863 | − | 0.225088i | ||||
\(640\) | −264.174 | − | 457.562i | −0.0163162 | − | 0.0282605i | ||||
\(641\) | 6702.63 | − | 11609.3i | 0.413008 | − | 0.715351i | −0.582209 | − | 0.813039i | \(-0.697812\pi\) |
0.995217 | + | 0.0976883i | \(0.0311448\pi\) | |||||||
\(642\) | − | 8092.36i | − | 0.497477i | ||||||
\(643\) | −4547.94 | − | 2625.76i | −0.278932 | − | 0.161042i | 0.354008 | − | 0.935243i | \(-0.384819\pi\) |
−0.632940 | + | 0.774201i | \(0.718152\pi\) | |||||||
\(644\) | −1658.91 | − | 957.774i | −0.101507 | − | 0.0586049i | ||||
\(645\) | 906.904i | 0.0553633i | ||||||||
\(646\) | −3532.68 | + | 6118.79i | −0.215157 | + | 0.372663i | ||||
\(647\) | 10805.7 | + | 18716.1i | 0.656595 | + | 1.13726i | 0.981492 | + | 0.191506i | \(0.0613370\pi\) |
−0.324897 | + | 0.945749i | \(0.605330\pi\) | |||||||
\(648\) | −3902.55 | + | 2253.14i | −0.236584 | + | 0.136592i | ||||
\(649\) | −4637.39 | −0.280483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7574.54 | 0.456021 | ||||||||
\(652\) | −1879.23 | + | 1084.97i | −0.112878 | + | 0.0651699i | ||||
\(653\) | 10797.9 | + | 18702.6i | 0.647099 | + | 1.12081i | 0.983813 | + | 0.179201i | \(0.0573512\pi\) |
−0.336714 | + | 0.941607i | \(0.609316\pi\) | |||||||
\(654\) | −3170.63 | + | 5491.68i | −0.189574 | + | 0.328351i | ||||
\(655\) | 1154.78i | 0.0688869i | ||||||||
\(656\) | −3041.28 | − | 1755.89i | −0.181009 | − | 0.104506i | ||||
\(657\) | −8881.48 | − | 5127.72i | −0.527396 | − | 0.304492i | ||||
\(658\) | 1487.54i | 0.0881314i | ||||||||
\(659\) | 8321.30 | − | 14412.9i | 0.491884 | − | 0.851968i | −0.508072 | − | 0.861315i | \(-0.669642\pi\) |
0.999956 | + | 0.00934609i | \(0.00297500\pi\) | |||||||
\(660\) | 96.3419 | + | 166.869i | 0.00568198 | + | 0.00984147i | ||||
\(661\) | −23366.3 | + | 13490.6i | −1.37495 | + | 0.793831i | −0.991547 | − | 0.129748i | \(-0.958583\pi\) |
−0.383408 | + | 0.923579i | \(0.625250\pi\) | |||||||
\(662\) | 11871.5 | 0.696980 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14598.1 | −0.853185 | ||||||||
\(665\) | −954.437 | + | 551.044i | −0.0556564 | + | 0.0321332i | ||||
\(666\) | 1973.80 | + | 3418.73i | 0.114840 | + | 0.198908i | ||||
\(667\) | 6443.67 | − | 11160.8i | 0.374063 | − | 0.647896i | ||||
\(668\) | − | 852.310i | − | 0.0493665i | ||||||
\(669\) | 3942.23 | + | 2276.05i | 0.227826 | + | 0.131535i | ||||
\(670\) | −553.454 | − | 319.537i | −0.0319131 | − | 0.0184251i | ||||
\(671\) | 59604.5i | 3.42922i | ||||||||
\(672\) | 2151.77 | − | 3726.98i | 0.123521 | − | 0.213945i | ||||
\(673\) | 5574.62 | + | 9655.53i | 0.319296 | + | 0.553036i | 0.980341 | − | 0.197309i | \(-0.0632204\pi\) |
−0.661046 | + | 0.750346i | \(0.729887\pi\) | |||||||
\(674\) | −6721.26 | + | 3880.52i | −0.384115 | + | 0.221769i | ||||
\(675\) | 18571.3 | 1.05898 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3314.33 | 0.188154 | 0.0940769 | − | 0.995565i | \(-0.470010\pi\) | ||||
0.0940769 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(678\) | −5243.36 | + | 3027.26i | −0.297006 | + | 0.171477i | ||||
\(679\) | −5301.06 | − | 9181.71i | −0.299611 | − | 0.518942i | ||||
\(680\) | 173.418 | − | 300.369i | 0.00977982 | − | 0.0169391i | ||||
\(681\) | − | 12165.5i | − | 0.684556i | ||||||
\(682\) | 16241.7 | + | 9377.17i | 0.911918 | + | 0.526496i | ||||
\(683\) | 21222.2 | + | 12252.6i | 1.18894 | + | 0.686433i | 0.958065 | − | 0.286552i | \(-0.0925090\pi\) |
0.230872 | + | 0.972984i | \(0.425842\pi\) | |||||||
\(684\) | 2084.75i | 0.116539i | ||||||||
\(685\) | 507.803 | − | 879.540i | 0.0283243 | − | 0.0490591i | ||||
\(686\) | −8278.50 | − | 14338.8i | −0.460750 | − | 0.798042i | ||||
\(687\) | 674.206 | − | 389.253i | 0.0374419 | − | 0.0216171i | ||||
\(688\) | 22100.6 | 1.22468 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −388.299 | −0.0214236 | ||||||||
\(691\) | −18838.5 | + | 10876.4i | −1.03712 | + | 0.598782i | −0.919017 | − | 0.394219i | \(-0.871015\pi\) |
−0.118105 | + | 0.993001i | \(0.537682\pi\) | |||||||
\(692\) | −3233.32 | − | 5600.27i | −0.177619 | − | 0.307645i | ||||
\(693\) | −7897.99 | + | 13679.7i | −0.432929 | + | 0.749855i | ||||
\(694\) | 7278.90i | 0.398132i | ||||||||
\(695\) | −726.383 | − | 419.378i | −0.0396450 | − | 0.0228891i | ||||
\(696\) | 13571.3 | + | 7835.37i | 0.739105 | + | 0.426722i | ||||
\(697\) | − | 1779.20i | − | 0.0966887i | ||||||
\(698\) | −9689.94 | + | 16783.5i | −0.525458 | + | 0.910120i | ||||
\(699\) | 472.971 | + | 819.209i | 0.0255928 | + | 0.0443281i | ||||
\(700\) | −2823.33 | + | 1630.05i | −0.152446 | + | 0.0880145i | ||||
\(701\) | −34250.9 | −1.84542 | −0.922709 | − | 0.385496i | \(-0.874030\pi\) | ||||
−0.922709 | + | 0.385496i | \(0.874030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12395.8 | −0.665028 | ||||||||
\(704\) | 31843.9 | − | 18385.1i | 1.70477 | − | 0.984252i | ||||
\(705\) | −33.0522 | − | 57.2480i | −0.00176570 | − | 0.00305828i | ||||
\(706\) | −2996.30 | + | 5189.74i | −0.159727 | + | 0.276655i | ||||
\(707\) | 16754.6i | 0.891259i | ||||||||
\(708\) | −328.800 | − | 189.833i | −0.0174535 | − | 0.0100768i | ||||
\(709\) | −4786.62 | − | 2763.56i | −0.253548 | − | 0.146386i | 0.367840 | − | 0.929889i | \(-0.380097\pi\) |
−0.621388 | + | 0.783503i | \(0.713431\pi\) | |||||||
\(710\) | 779.234i | 0.0411889i | ||||||||
\(711\) | −2829.21 | + | 4900.34i | −0.149232 | + | 0.258477i | ||||
\(712\) | 14021.3 | + | 24285.6i | 0.738020 | + | 1.27829i | ||||
\(713\) | 7175.31 | − | 4142.67i | 0.376883 | − | 0.217593i | ||||
\(714\) | −4382.83 | −0.229724 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 221.931 | 0.0115837 | ||||||||
\(717\) | 11326.9 | − | 6539.57i | 0.589972 | − | 0.340620i | ||||
\(718\) | 3242.51 | + | 5616.19i | 0.168537 | + | 0.291914i | ||||
\(719\) | −1888.89 | + | 3271.65i | −0.0979745 | + | 0.169697i | −0.910846 | − | 0.412746i | \(-0.864570\pi\) |
0.812872 | + | 0.582443i | \(0.197903\pi\) | |||||||
\(720\) | 380.085i | 0.0196735i | ||||||||
\(721\) | 14651.1 | + | 8458.81i | 0.756776 | + | 0.436925i | ||||
\(722\) | 10644.7 | + | 6145.75i | 0.548693 | + | 0.316788i | ||||
\(723\) | − | 18534.2i | − | 0.953380i | ||||||
\(724\) | 770.538 | − | 1334.61i | 0.0395536 | − | 0.0685088i | ||||
\(725\) | −10966.6 | − | 18994.7i | −0.561777 | − | 0.973027i | ||||
\(726\) | 23378.2 | − | 13497.4i | 1.19510 | − | 0.689994i | ||||
\(727\) | −19076.8 | −0.973204 | −0.486602 | − | 0.873624i | \(-0.661764\pi\) | ||||
−0.486602 | + | 0.873624i | \(0.661764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17319.9 | 0.879944 | ||||||||
\(730\) | 951.744 | − | 549.490i | 0.0482543 | − | 0.0278596i | ||||
\(731\) | 5598.52 | + | 9696.92i | 0.283268 | + | 0.490634i | ||||
\(732\) | −2439.93 | + | 4226.08i | −0.123200 | + | 0.213388i | ||||
\(733\) | 7997.30i | 0.402984i | 0.979490 | + | 0.201492i | \(0.0645790\pi\) | ||||
−0.979490 | + | 0.201492i | \(0.935421\pi\) | |||||||
\(734\) | −14592.0 | − | 8424.71i | −0.733789 | − | 0.423653i | ||||
\(735\) | 22.5669 | + | 13.0290i | 0.00113251 | + | 0.000653855i | ||||
\(736\) | − | 4707.39i | − | 0.235756i | ||||||
\(737\) | 14381.0 | − | 24908.7i | 0.718769 | − | 1.24494i | ||||
\(738\) | 1197.37 | + | 2073.90i | 0.0597232 | + | 0.103444i | ||||
\(739\) | −25100.6 | + | 14491.8i | −1.24944 | + | 0.721367i | −0.970998 | − | 0.239086i | \(-0.923152\pi\) |
−0.278445 | + | 0.960452i | \(0.589819\pi\) | |||||||
\(740\) | 92.7376 | 0.00460689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 132.541 | 0.00655761 | ||||||||
\(743\) | −16580.4 | + | 9572.69i | −0.818674 | + | 0.472662i | −0.849959 | − | 0.526849i | \(-0.823373\pi\) |
0.0312847 | + | 0.999511i | \(0.490040\pi\) | |||||||
\(744\) | 5037.40 | + | 8725.02i | 0.248226 | + | 0.429939i | ||||
\(745\) | −774.667 | + | 1341.76i | −0.0380961 | + | 0.0659844i | ||||
\(746\) | 7435.47i | 0.364922i | ||||||||
\(747\) | 7019.09 | + | 4052.47i | 0.343795 | + | 0.198490i | ||||
\(748\) | 2060.24 | + | 1189.48i | 0.100708 | + | 0.0581440i | ||||
\(749\) | − | 15584.7i | − | 0.760284i | ||||||
\(750\) | −661.688 | + | 1146.08i | −0.0322152 | + | 0.0557984i | ||||
\(751\) | −12758.4 | − | 22098.3i | −0.619923 | − | 1.07374i | −0.989499 | − | 0.144538i | \(-0.953830\pi\) |
0.369576 | − | 0.929200i | \(-0.379503\pi\) | |||||||
\(752\) | −1395.10 | + | 805.459i | −0.0676515 | + | 0.0390586i | ||||
\(753\) | −2648.47 | −0.128175 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −548.275 | −0.0264288 | ||||||||
\(756\) | −3372.70 | + | 1947.23i | −0.162254 | + | 0.0936773i | ||||
\(757\) | 8615.31 | + | 14922.2i | 0.413645 | + | 0.716453i | 0.995285 | − | 0.0969925i | \(-0.0309223\pi\) |
−0.581641 | + | 0.813446i | \(0.697589\pi\) | |||||||
\(758\) | −2389.59 | + | 4138.89i | −0.114504 | + | 0.198326i | ||||
\(759\) | − | 17475.7i | − | 0.835744i | ||||||
\(760\) | −1269.48 | − | 732.936i | −0.0605908 | − | 0.0349821i | ||||
\(761\) | −2029.15 | − | 1171.53i | −0.0966576 | − | 0.0558053i | 0.450892 | − | 0.892579i | \(-0.351106\pi\) |
−0.547550 | + | 0.836773i | \(0.684439\pi\) | |||||||
\(762\) | − | 5221.11i | − | 0.248216i | ||||||
\(763\) | −6106.17 | + | 10576.2i | −0.289722 | + | 0.501814i | ||||
\(764\) | −487.060 | − | 843.613i | −0.0230644 | − | 0.0399488i | ||||
\(765\) | −166.767 | + | 96.2829i | −0.00788166 | + | 0.00455048i | ||||
\(766\) | −27756.9 | −1.30927 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 7862.11 | 0.369400 | ||||||||
\(769\) | −6148.93 | + | 3550.09i | −0.288344 | + | 0.166475i | −0.637195 | − | 0.770703i | \(-0.719905\pi\) |
0.348851 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(770\) | −846.353 | − | 1465.93i | −0.0396110 | − | 0.0686082i | ||||
\(771\) | −2359.65 | + | 4087.03i | −0.110221 | + | 0.190909i | ||||
\(772\) | − | 1901.17i | − | 0.0886328i | ||||||
\(773\) | −10626.5 | − | 6135.22i | −0.494449 | − | 0.285470i | 0.231969 | − | 0.972723i | \(-0.425483\pi\) |
−0.726418 | + | 0.687253i | \(0.758816\pi\) | |||||||
\(774\) | −13051.7 | − | 7535.39i | −0.606115 | − | 0.349941i | ||||
\(775\) | − | 14100.9i | − | 0.653575i | ||||||
\(776\) | 7050.87 | − | 12212.5i | 0.326175 | − | 0.564951i | ||||
\(777\) | −3844.70 | − | 6659.22i | −0.177513 | − | 0.307462i | ||||
\(778\) | 21119.6 | − | 12193.4i | 0.973233 | − | 0.561897i | ||||
\(779\) | −7519.64 | −0.345852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35070.1 | −1.60680 | ||||||||
\(782\) | −4151.82 | + | 2397.06i | −0.189858 | + | 0.109614i | ||||
\(783\) | −13100.5 | − | 22690.7i | −0.597922 | − | 1.03563i | ||||
\(784\) | 317.509 | − | 549.941i | 0.0144638 | − | 0.0250520i | ||||
\(785\) | − | 317.207i | − | 0.0144224i | ||||||
\(786\) | 16808.9 | + | 9704.61i | 0.762790 | + | 0.440397i | ||||
\(787\) | 2966.17 | + | 1712.52i | 0.134349 | + | 0.0775663i | 0.565668 | − | 0.824633i | \(-0.308618\pi\) |
−0.431319 | + | 0.902199i | \(0.641952\pi\) | |||||||
\(788\) | 1823.04i | 0.0824151i | ||||||||
\(789\) | 9627.17 | − | 16674.8i | 0.434394 | − | 0.752392i | ||||
\(790\) | −303.180 | − | 525.123i | −0.0136540 | − | 0.0236494i | ||||
\(791\) | −10098.0 | + | 5830.06i | −0.453909 | + | 0.262064i | ||||
\(792\) | −21010.0 | −0.942624 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25894.3 | −1.15737 | ||||||||
\(795\) | −5.10085 | + | 2.94498i | −0.000227558 | + | 0.000131381i | ||||
\(796\) | 1723.43 | + | 2985.07i | 0.0767405 | + | 0.132918i | ||||
\(797\) | −5890.57 | + | 10202.8i | −0.261800 | + | 0.453451i | −0.966720 | − | 0.255836i | \(-0.917649\pi\) |
0.704920 | + | 0.709286i | \(0.250983\pi\) | |||||||
\(798\) | 18523.6i | 0.821717i | ||||||||
\(799\) | −706.810 | − | 408.077i | −0.0312955 | − | 0.0180685i | ||||
\(800\) | −6938.23 | − | 4005.79i | −0.306629 | − | 0.177033i | ||||
\(801\) | − | 15569.4i | − | 0.686790i | ||||||
\(802\) | −2669.62 | + | 4623.92i | −0.117541 | + | 0.203586i | ||||
\(803\) | 24730.3 | + | 42834.1i | 1.08682 | + | 1.88242i | ||||
\(804\) | 2039.29 | − | 1177.38i | 0.0894530 | − | 0.0516457i | ||||
\(805\) | −747.807 | −0.0327413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23743.2 | −1.03569 | ||||||||
\(808\) | −19299.4 | + | 11142.5i | −0.840284 | + | 0.485138i | ||||
\(809\) | −9455.06 | − | 16376.7i | −0.410905 | − | 0.711709i | 0.584084 | − | 0.811693i | \(-0.301454\pi\) |
−0.994989 | + | 0.0999847i | \(0.968121\pi\) | |||||||
\(810\) | −134.053 | + | 232.187i | −0.00581501 | + | 0.0100719i | ||||
\(811\) | 12803.3i | 0.554359i | 0.960818 | + | 0.277180i | \(0.0893997\pi\) | ||||
−0.960818 | + | 0.277180i | \(0.910600\pi\) | |||||||
\(812\) | 3983.24 | + | 2299.73i | 0.172148 | + | 0.0993899i | ||||
\(813\) | 12540.4 | + | 7240.23i | 0.540975 | + | 0.312332i | ||||
\(814\) | − | 19038.7i | − | 0.819788i | ||||||
\(815\) | −423.560 | + | 733.628i | −0.0182045 | + | 0.0315311i | ||||
\(816\) | −2373.17 | − | 4110.44i | −0.101811 | − | 0.176341i | ||||
\(817\) | 40983.2 | − | 23661.7i | 1.75498 | − | 1.01324i | ||||
\(818\) | 24889.4 | 1.06386 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56.2574 | 0.00239585 | ||||||||
\(821\) | 16744.7 | − | 9667.54i | 0.711806 | − | 0.410962i | −0.0999231 | − | 0.994995i | \(-0.531860\pi\) |
0.811730 | + | 0.584033i | \(0.198526\pi\) | |||||||
\(822\) | −8535.03 | − | 14783.1i | −0.362157 | − | 0.627275i | ||||
\(823\) | −1062.95 | + | 1841.09i | −0.0450209 | + | 0.0779784i | −0.887658 | − | 0.460504i | \(-0.847669\pi\) |
0.842637 | + | 0.538482i | \(0.181002\pi\) | |||||||
\(824\) | 22501.9i | 0.951324i | ||||||||
\(825\) | −25757.5 | − | 14871.1i | −1.08698 | − | 0.627571i | ||||
\(826\) | 2888.47 | + | 1667.66i | 0.121674 | + | 0.0702486i | ||||
\(827\) | 6989.24i | 0.293881i | 0.989145 | + | 0.146941i | \(0.0469426\pi\) | ||||
−0.989145 | + | 0.146941i | \(0.953057\pi\) | |||||||
\(828\) | −707.291 | + | 1225.06i | −0.0296861 | + | 0.0514178i | ||||
\(829\) | −16324.8 | − | 28275.4i | −0.683938 | − | 1.18462i | −0.973769 | − | 0.227538i | \(-0.926932\pi\) |
0.289831 | − | 0.957078i | \(-0.406401\pi\) | |||||||
\(830\) | −752.170 | + | 434.265i | −0.0314556 | + | 0.0181609i | ||||
\(831\) | −21682.0 | −0.905103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 321.724 | 0.0133819 | ||||||||
\(834\) | −12208.9 | + | 7048.80i | −0.506905 | + | 0.292662i | ||||
\(835\) | −166.366 | − | 288.154i | −0.00689500 | − | 0.0119425i | ||||
\(836\) | 5027.24 | − | 8707.43i | 0.207979 | − | 0.360231i | ||||
\(837\) | − | 16844.7i | − | 0.695626i | ||||||
\(838\) | −29686.0 | − | 17139.2i | −1.22373 | − | 0.706520i | ||||
\(839\) | −3497.21 | − | 2019.12i | −0.143906 | − | 0.0830841i | 0.426318 | − | 0.904573i | \(-0.359810\pi\) |
−0.570224 | + | 0.821489i | \(0.693144\pi\) | |||||||
\(840\) | − | 909.318i | − | 0.0373505i | ||||||
\(841\) | −3277.50 | + | 5676.80i | −0.134384 | + | 0.232761i | ||||
\(842\) | −12120.5 | − | 20993.3i | −0.496079 | − | 0.859235i | ||||
\(843\) | 11263.6 | − | 6503.04i | 0.460188 | − | 0.265690i | ||||
\(844\) | −131.695 | −0.00537102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1098.51 | 0.0446426 | ||||||||
\(847\) | 45023.0 | − | 25994.1i | 1.82646 | − | 1.05451i | ||||
\(848\) | 71.7671 | + | 124.304i | 0.00290624 | + | 0.00503376i | ||||
\(849\) | 4810.32 | − | 8331.72i | 0.194452 | − | 0.336801i | ||||
\(850\) | 8159.17i | 0.329244i | ||||||||
\(851\) | −7284.12 | − | 4205.49i | −0.293415 | − | 0.169403i | ||||
\(852\) | −2486.54 | − | 1435.61i | −0.0999853 | − | 0.0577265i | ||||
\(853\) | − | 8114.12i | − | 0.325700i | −0.986651 | − | 0.162850i | \(-0.947931\pi\) | ||
0.986651 | − | 0.162850i | \(-0.0520687\pi\) | |||||||
\(854\) | 21434.5 | − | 37125.6i | 0.858868 | − | 1.48760i | ||||
\(855\) | 406.932 | + | 704.826i | 0.0162769 | + | 0.0281925i | ||||
\(856\) | 17951.8 | − | 10364.5i | 0.716801 | − | 0.413845i | ||||
\(857\) | 22298.1 | 0.888786 | 0.444393 | − | 0.895832i | \(-0.353419\pi\) | ||||
0.444393 | + | 0.895832i | \(0.353419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33550.5 | 1.33263 | 0.666315 | − | 0.745670i | \(-0.267870\pi\) | ||||
0.666315 | + | 0.745670i | \(0.267870\pi\) | |||||||
\(860\) | −306.612 | + | 177.022i | −0.0121574 | + | 0.00701908i | ||||
\(861\) | −2332.31 | − | 4039.68i | −0.0923170 | − | 0.159898i | ||||
\(862\) | 6214.69 | − | 10764.2i | 0.245560 | − | 0.425323i | ||||
\(863\) | − | 14120.5i | − | 0.556972i | −0.960440 | − | 0.278486i | \(-0.910167\pi\) | ||
0.960440 | − | 0.278486i | \(-0.0898326\pi\) | |||||||
\(864\) | −8288.28 | − | 4785.24i | −0.326358 | − | 0.188423i | ||||
\(865\) | −2186.28 | − | 1262.25i | −0.0859373 | − | 0.0496159i | ||||
\(866\) | 21025.2i | 0.825018i | ||||||||
\(867\) | −7849.03 | + | 13594.9i | −0.307459 | + | 0.532534i | ||||
\(868\) | 1478.51 | + | 2560.85i | 0.0578154 | + | 0.100139i | ||||
\(869\) | 23633.6 | − | 13644.9i | 0.922574 | − | 0.532648i | ||||
\(870\) | 932.351 | 0.0363329 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16243.4 | −0.630817 | ||||||||
\(873\) | −6780.45 | + | 3914.69i | −0.262868 | + | 0.151767i | ||||
\(874\) | 10131.0 | + | 17547.3i | 0.392088 | + | 0.679116i | ||||
\(875\) | −1274.31 | + | 2207.18i | −0.0492339 | + | 0.0852757i | ||||
\(876\) | 4049.36i | 0.156182i | ||||||||
\(877\) | 1681.55 | + | 970.844i | 0.0647457 | + | 0.0373809i | 0.532023 | − | 0.846730i | \(-0.321432\pi\) |
−0.467278 | + | 0.884111i | \(0.654765\pi\) | |||||||
\(878\) | −6641.36 | − | 3834.39i | −0.255279 | − | 0.147385i | ||||
\(879\) | − | 20232.6i | − | 0.776368i | ||||||
\(880\) | 916.548 | − | 1587.51i | 0.0351100 | − | 0.0608124i | ||||
\(881\) | −395.116 | − | 684.360i | −0.0151099 | − | 0.0261710i | 0.858372 | − | 0.513028i | \(-0.171476\pi\) |
−0.873481 | + | 0.486857i | \(0.838143\pi\) | |||||||
\(882\) | −375.014 | + | 216.514i | −0.0143167 | + | 0.00826578i | ||||
\(883\) | 36638.6 | 1.39636 | 0.698180 | − | 0.715922i | \(-0.253993\pi\) | ||||
0.698180 | + | 0.715922i | \(0.253993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −148.217 | −0.00562968 | ||||||||
\(886\) | 21615.1 | − | 12479.5i | 0.819607 | − | 0.473201i | ||||
\(887\) | 20343.2 | + | 35235.4i | 0.770075 | + | 1.33381i | 0.937522 | + | 0.347927i | \(0.113114\pi\) |
−0.167447 | + | 0.985881i | \(0.553552\pi\) | |||||||
\(888\) | 5113.78 | − | 8857.33i | 0.193252 | − | 0.334721i | ||||
\(889\) | − | 10055.1i | − | 0.379344i | ||||||
\(890\) | 1444.90 | + | 834.215i | 0.0544194 | + | 0.0314190i | ||||
\(891\) | −10449.8 | − | 6033.20i | −0.392909 | − | 0.226846i | ||||
\(892\) | 1777.08i | 0.0667053i | ||||||||
\(893\) | −1724.70 | + | 2987.27i | −0.0646304 | + | 0.111943i | ||||
\(894\) | 13020.4 | + | 22552.0i | 0.487101 | + | 0.843684i | ||||
\(895\) | 75.0317 | − | 43.3196i | 0.00280227 | − | 0.00161789i | ||||
\(896\) | −17102.2 | −0.637663 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1438.21 | −0.0534449 | ||||||||
\(899\) | −17228.8 | + | 9947.02i | −0.639167 | + | 0.369023i | ||||
\(900\) | 1203.75 | + | 2084.95i | 0.0445833 | + | 0.0772205i | ||||
\(901\) | −36.3600 | + | 62.9773i | −0.00134442 | + | 0.00232861i | ||||
\(902\) | − | 11549.5i | − | 0.426336i | ||||||
\(903\) | 25422.9 | + | 14677.9i | 0.936901 | + | 0.540920i | ||||
\(904\) | −13431.2 | − | 7754.48i | −0.494152 | − | 0.285299i | ||||
\(905\) | − | 601.618i | − | 0.0220977i | ||||||
\(906\) | −4607.64 | + | 7980.66i | −0.168961 | + | 0.292649i | ||||
\(907\) | −5232.22 | − | 9062.46i | −0.191547 | − | 0.331769i | 0.754216 | − | 0.656626i | \(-0.228017\pi\) |
−0.945763 | + | 0.324857i | \(0.894684\pi\) | |||||||
\(908\) | 4112.98 | − | 2374.63i | 0.150324 | − | 0.0867896i | ||||
\(909\) | 12372.8 | 0.451463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35611.5 | −1.29513 | −0.647563 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647563 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(912\) | −17372.4 | + | 10030.0i | −0.630767 | + | 0.364173i | ||||
\(913\) | −19544.5 | − | 33852.1i | −0.708465 | − | 1.22710i | ||||
\(914\) | 17621.4 | − | 30521.2i | 0.637708 | − | 1.10454i | ||||
\(915\) | 1905.04i | 0.0688291i | ||||||||
\(916\) | 263.202 | + | 151.960i | 0.00949393 | + | 0.00548133i | ||||
\(917\) | 32371.5 | + | 18689.7i | 1.16576 | + | 0.673051i | ||||
\(918\) | 9746.80i | 0.350427i | ||||||||
\(919\) | −538.627 | + | 932.930i | −0.0193337 | + | 0.0334870i | −0.875530 | − | 0.483163i | \(-0.839488\pi\) |
0.856197 | + | 0.516650i | \(0.172821\pi\) | |||||||
\(920\) | −497.324 | − | 861.391i | −0.0178221 | − | 0.0308687i | ||||
\(921\) | −23318.6 | + | 13463.0i | −0.834282 | + | 0.481673i | ||||
\(922\) | −30762.3 | −1.09881 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6237.04 | 0.222060 | ||||||||
\(925\) | −12397.0 | + | 7157.38i | −0.440659 | + | 0.254414i | ||||
\(926\) | −17464.3 | − | 30249.1i | −0.619777 | − | 1.07348i | ||||
\(927\) | 6246.61 | − | 10819.4i | 0.221322 | − | 0.383341i | ||||
\(928\) | 11303.0i | 0.399826i | ||||||||
\(929\) | −48266.9 | − | 27866.9i | −1.70461 | − | 0.984159i | −0.940951 | − | 0.338542i | \(-0.890066\pi\) |
−0.763661 | − | 0.645617i | \(-0.776600\pi\) | |||||||
\(930\) | 519.107 | + | 299.706i | 0.0183034 | + | 0.0105675i | ||||
\(931\) | − | 1359.74i | − | 0.0478665i | ||||||
\(932\) | −184.642 | + | 319.810i | −0.00648944 | + | 0.0112400i | ||||
\(933\) | −14563.5 | − | 25224.7i | −0.511025 | − | 0.885121i | ||||
\(934\) | −19570.4 | + | 11299.0i | −0.685612 | + | 0.395838i | ||||
\(935\) | 928.718 | 0.0324838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3198.60 | −0.111519 | −0.0557596 | − | 0.998444i | \(-0.517758\pi\) | ||||
−0.0557596 | + | 0.998444i | \(0.517758\pi\) | |||||||
\(938\) | −17914.9 | + | 10343.2i | −0.623607 | + | 0.360040i | ||||
\(939\) | 18427.7 | + | 31917.7i | 0.640432 | + | 1.10926i | ||||
\(940\) | 12.9032 | − | 22.3490i | 0.000447718 | − | 0.000775471i | ||||
\(941\) | 8823.35i | 0.305667i | 0.988252 | + | 0.152834i | \(0.0488399\pi\) | ||||
−0.988252 | + | 0.152834i | \(0.951160\pi\) | |||||||
\(942\) | −4617.25 | − | 2665.77i | −0.159701 | − | 0.0922033i | ||||
\(943\) | −4418.76 | − | 2551.17i | −0.152593 | − | 0.0880993i | ||||
\(944\) | 3611.95i | 0.124533i | ||||||||
\(945\) | −760.175 | + | 1316.66i | −0.0261677 | + | 0.0453238i | ||||
\(946\) | 36342.1 | + | 62946.4i | 1.24903 | + | 2.16339i | ||||
\(947\) | −24500.2 | + | 14145.2i | −0.840708 | + | 0.485383i | −0.857505 | − | 0.514476i | \(-0.827987\pi\) |
0.0167965 | + | 0.999859i | \(0.494653\pi\) | |||||||
\(948\) | 2234.23 | 0.0765447 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 34484.0 | 1.17769 | ||||||||
\(951\) | 19882.6 | − | 11479.2i | 0.677956 | − | 0.391418i | ||||
\(952\) | −5613.42 | − | 9722.73i | −0.191105 | − | 0.331004i | ||||
\(953\) | −6199.52 | + | 10737.9i | −0.210726 | + | 0.364988i | −0.951942 | − | 0.306278i | \(-0.900916\pi\) |
0.741216 | + | 0.671267i | \(0.234250\pi\) | |||||||
\(954\) | − | 97.8783i | − | 0.00332173i | ||||||
\(955\) | −329.337 | − | 190.143i | −0.0111592 | − | 0.00644280i | ||||
\(956\) | 4421.88 | + | 2552.97i | 0.149596 | + | 0.0863693i | ||||
\(957\) | 41961.3i | 1.41736i | ||||||||
\(958\) | 18725.0 | − | 32432.7i | 0.631500 | − | 1.09379i | ||||
\(959\) | −16437.2 | − | 28470.1i | −0.553478 | − | 0.958653i | ||||
\(960\) | 1017.77 | − | 587.610i | 0.0342171 | − | 0.0197553i | ||||
\(961\) | 17001.0 | 0.570676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11508.9 | −0.385118 | ||||||||
\(964\) | 6266.15 | − | 3617.77i | 0.209356 | − | 0.120872i | ||||
\(965\) | −371.097 | − | 642.758i | −0.0123793 | − | 0.0214416i | ||||
\(966\) | −6284.49 | + | 10885.0i | −0.209317 | + | 0.362547i | ||||
\(967\) | − | 26667.1i | − | 0.886820i | −0.896319 | − | 0.443410i | \(-0.853769\pi\) | ||
0.896319 | − | 0.443410i | \(-0.146231\pi\) | |||||||
\(968\) | 59884.5 | + | 34574.3i | 1.98839 | + | 1.14800i | ||||
\(969\) | −8801.55 | − | 5081.58i | −0.291792 | − | 0.168466i | ||||
\(970\) | − | 839.001i | − | 0.0277719i | ||||||
\(971\) | −24710.3 | + | 42799.6i | −0.816676 | + | 1.41453i | 0.0914414 | + | 0.995810i | \(0.470853\pi\) |
−0.908118 | + | 0.418715i | \(0.862481\pi\) | |||||||
\(972\) | 2398.45 | + | 4154.23i | 0.0791463 | + | 0.137085i | ||||
\(973\) | −23512.5 | + | 13575.0i | −0.774694 | + | 0.447270i | ||||
\(974\) | 25100.3 | 0.825735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46424.5 | 1.52255 | ||||||||
\(977\) | 674.425 | − | 389.380i | 0.0220847 | − | 0.0127506i | −0.488917 | − | 0.872330i | \(-0.662608\pi\) |
0.511002 | + | 0.859580i | \(0.329275\pi\) | |||||||
\(978\) | 7119.10 | + | 12330.6i | 0.232765 | + | 0.403160i | ||||
\(979\) | −37544.6 | + | 65029.2i | −1.22567 | + | 2.12292i | ||||
\(980\) | 10.1728i | 0.000331589i | ||||||||
\(981\) | 7810.23 | + | 4509.24i | 0.254191 | + | 0.146757i | ||||
\(982\) | −24038.4 | − | 13878.6i | −0.781157 | − | 0.451001i | ||||
\(983\) | − | 5997.90i | − | 0.194612i | −0.995255 | − | 0.0973059i | \(-0.968977\pi\) | ||
0.995255 | − | 0.0973059i | \(-0.0310225\pi\) | |||||||
\(984\) | 3102.17 | − | 5373.12i | 0.100502 | − | 0.174074i | ||||
\(985\) | 355.847 | + | 616.344i | 0.0115109 | + | 0.0199374i | ||||
\(986\) | 9969.01 | − | 5755.61i | 0.321986 | − | 0.185898i | ||||
\(987\) | −2139.75 | −0.0690062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32110.6 | 1.03241 | ||||||||
\(990\) | −1082.55 | + | 625.009i | −0.0347532 | + | 0.0200647i | ||||
\(991\) | −4487.47 | − | 7772.53i | −0.143844 | − | 0.249145i | 0.785097 | − | 0.619373i | \(-0.212613\pi\) |
−0.928941 | + | 0.370228i | \(0.879280\pi\) | |||||||
\(992\) | −3633.37 | + | 6293.19i | −0.116290 | + | 0.201420i | ||||
\(993\) | 17076.6i | 0.545729i | ||||||||
\(994\) | 21844.0 | + | 12611.6i | 0.697031 | + | 0.402431i | ||||
\(995\) | 1165.34 | + | 672.808i | 0.0371293 | + | 0.0214366i | ||||
\(996\) | − | 3200.24i | − | 0.101811i | ||||||
\(997\) | −14265.1 | + | 24707.9i | −0.453140 | + | 0.784861i | −0.998579 | − | 0.0532892i | \(-0.983029\pi\) |
0.545439 | + | 0.838150i | \(0.316363\pi\) | |||||||
\(998\) | 3317.16 | + | 5745.48i | 0.105213 | + | 0.182234i | ||||
\(999\) | −14809.2 | + | 8550.08i | −0.469011 | + | 0.270783i |
(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 | 169.4.e.f.23.4 | 8 | ||
13.2 | odd | 12 | 13.4.a.b.1.2 | ✓ | 2 | ||
13.3 | even | 3 | 169.4.b.f.168.4 | 4 | |||
13.4 | even | 6 | inner | 169.4.e.f.147.4 | 8 | ||
13.5 | odd | 4 | 169.4.c.g.146.1 | 4 | |||
13.6 | odd | 12 | 169.4.c.g.22.1 | 4 | |||
13.7 | odd | 12 | 169.4.c.j.22.2 | 4 | |||
13.8 | odd | 4 | 169.4.c.j.146.2 | 4 | |||
13.9 | even | 3 | inner | 169.4.e.f.147.1 | 8 | ||
13.10 | even | 6 | 169.4.b.f.168.1 | 4 | |||
13.11 | odd | 12 | 169.4.a.g.1.1 | 2 | |||
13.12 | even | 2 | inner | 169.4.e.f.23.1 | 8 | ||
39.2 | even | 12 | 117.4.a.d.1.1 | 2 | |||
39.11 | even | 12 | 1521.4.a.r.1.2 | 2 | |||
52.15 | even | 12 | 208.4.a.h.1.2 | 2 | |||
65.2 | even | 12 | 325.4.b.e.274.4 | 4 | |||
65.28 | even | 12 | 325.4.b.e.274.1 | 4 | |||
65.54 | odd | 12 | 325.4.a.f.1.1 | 2 | |||
91.41 | even | 12 | 637.4.a.b.1.2 | 2 | |||
104.67 | even | 12 | 832.4.a.z.1.1 | 2 | |||
104.93 | odd | 12 | 832.4.a.s.1.2 | 2 | |||
143.54 | even | 12 | 1573.4.a.b.1.1 | 2 | |||
156.119 | odd | 12 | 1872.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.2 | ✓ | 2 | 13.2 | odd | 12 | ||
117.4.a.d.1.1 | 2 | 39.2 | even | 12 | |||
169.4.a.g.1.1 | 2 | 13.11 | odd | 12 | |||
169.4.b.f.168.1 | 4 | 13.10 | even | 6 | |||
169.4.b.f.168.4 | 4 | 13.3 | even | 3 | |||
169.4.c.g.22.1 | 4 | 13.6 | odd | 12 | |||
169.4.c.g.146.1 | 4 | 13.5 | odd | 4 | |||
169.4.c.j.22.2 | 4 | 13.7 | odd | 12 | |||
169.4.c.j.146.2 | 4 | 13.8 | odd | 4 | |||
169.4.e.f.23.1 | 8 | 13.12 | even | 2 | inner | ||
169.4.e.f.23.4 | 8 | 1.1 | even | 1 | trivial | ||
169.4.e.f.147.1 | 8 | 13.9 | even | 3 | inner | ||
169.4.e.f.147.4 | 8 | 13.4 | even | 6 | inner | ||
208.4.a.h.1.2 | 2 | 52.15 | even | 12 | |||
325.4.a.f.1.1 | 2 | 65.54 | odd | 12 | |||
325.4.b.e.274.1 | 4 | 65.28 | even | 12 | |||
325.4.b.e.274.4 | 4 | 65.2 | even | 12 | |||
637.4.a.b.1.2 | 2 | 91.41 | even | 12 | |||
832.4.a.s.1.2 | 2 | 104.93 | odd | 12 | |||
832.4.a.z.1.1 | 2 | 104.67 | even | 12 | |||
1521.4.a.r.1.2 | 2 | 39.11 | even | 12 | |||
1573.4.a.b.1.1 | 2 | 143.54 | even | 12 | |||
1872.4.a.bb.1.1 | 2 | 156.119 | odd | 12 |