Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(25,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.t (of order \(6\), 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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 103.18 | ||
Character | \(\chi\) | \(=\) | 117.103 |
Dual form | 117.4.t.a.25.18 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.916837 | + | 0.529336i | −0.324151 | + | 0.187149i | −0.653241 | − | 0.757150i | \(-0.726591\pi\) |
0.329090 | + | 0.944298i | \(0.393258\pi\) | |||||||
\(3\) | 3.64187 | − | 3.70632i | 0.700877 | − | 0.713282i | ||||
\(4\) | −3.43961 | + | 5.95757i | −0.429951 | + | 0.744697i | ||||
\(5\) | −2.58576 | − | 1.49289i | −0.231277 | − | 0.133528i | 0.379884 | − | 0.925034i | \(-0.375964\pi\) |
−0.611161 | + | 0.791506i | \(0.709297\pi\) | |||||||
\(6\) | −1.37711 | + | 5.32586i | −0.0937003 | + | 0.362379i | ||||
\(7\) | −19.0506 | + | 10.9989i | −1.02864 | + | 0.593883i | −0.916594 | − | 0.399820i | \(-0.869073\pi\) |
−0.112042 | + | 0.993703i | \(0.535739\pi\) | |||||||
\(8\) | − | 15.7522i | − | 0.696156i | ||||||
\(9\) | −0.473631 | − | 26.9958i | −0.0175419 | − | 0.999846i | ||||
\(10\) | 3.16096 | 0.0999582 | ||||||||
\(11\) | −29.0235 | + | 16.7567i | −0.795538 | + | 0.459304i | −0.841908 | − | 0.539620i | \(-0.818568\pi\) |
0.0463707 | + | 0.998924i | \(0.485234\pi\) | |||||||
\(12\) | 9.55409 | + | 34.4450i | 0.229836 | + | 0.828617i | ||||
\(13\) | −44.6088 | − | 14.3893i | −0.951713 | − | 0.306990i | ||||
\(14\) | 11.6442 | − | 20.1683i | 0.222289 | − | 0.385016i | ||||
\(15\) | −14.9501 | + | 4.14675i | −0.257340 | + | 0.0713790i | ||||
\(16\) | −19.1786 | − | 33.2184i | −0.299666 | − | 0.519037i | ||||
\(17\) | 25.4910 | 0.363675 | 0.181838 | − | 0.983329i | \(-0.441795\pi\) | ||||
0.181838 | + | 0.983329i | \(0.441795\pi\) | |||||||
\(18\) | 14.7241 | + | 24.5001i | 0.192806 | + | 0.320818i | ||||
\(19\) | 74.3878i | 0.898196i | 0.893482 | + | 0.449098i | \(0.148255\pi\) | ||||
−0.893482 | + | 0.449098i | \(0.851745\pi\) | |||||||
\(20\) | 17.7880 | − | 10.2699i | 0.198875 | − | 0.114821i | ||||
\(21\) | −28.6144 | + | 110.664i | −0.297342 | + | 1.14995i | ||||
\(22\) | 17.7399 | − | 30.7264i | 0.171916 | − | 0.297768i | ||||
\(23\) | −93.5481 | + | 162.030i | −0.848092 | + | 1.46894i | 0.0348159 | + | 0.999394i | \(0.488916\pi\) |
−0.882908 | + | 0.469545i | \(0.844418\pi\) | |||||||
\(24\) | −58.3827 | − | 57.3674i | −0.496555 | − | 0.487920i | ||||
\(25\) | −58.0426 | − | 100.533i | −0.464341 | − | 0.804262i | ||||
\(26\) | 48.5158 | − | 10.4204i | 0.365951 | − | 0.0786006i | ||||
\(27\) | −101.780 | − | 96.5598i | −0.725467 | − | 0.688257i | ||||
\(28\) | − | 151.327i | − | 1.02136i | ||||||
\(29\) | −12.5886 | − | 21.8040i | −0.0806082 | − | 0.139617i | 0.822903 | − | 0.568182i | \(-0.192353\pi\) |
−0.903511 | + | 0.428564i | \(0.859020\pi\) | |||||||
\(30\) | 11.5118 | − | 11.7155i | 0.0700584 | − | 0.0712984i | ||||
\(31\) | −154.009 | − | 88.9174i | −0.892287 | − | 0.515162i | −0.0175974 | − | 0.999845i | \(-0.505602\pi\) |
−0.874690 | + | 0.484683i | \(0.838935\pi\) | |||||||
\(32\) | 144.302 | + | 83.3127i | 0.797163 | + | 0.460242i | ||||
\(33\) | −43.5939 | + | 168.596i | −0.229961 | + | 0.889358i | ||||
\(34\) | −23.3711 | + | 13.4933i | −0.117886 | + | 0.0680613i | ||||
\(35\) | 65.6803 | 0.317200 | ||||||||
\(36\) | 162.459 | + | 90.0334i | 0.752124 | + | 0.416821i | ||||
\(37\) | − | 252.938i | − | 1.12386i | −0.827186 | − | 0.561928i | \(-0.810060\pi\) | ||
0.827186 | − | 0.561928i | \(-0.189940\pi\) | |||||||
\(38\) | −39.3761 | − | 68.2015i | −0.168096 | − | 0.291151i | ||||
\(39\) | −215.791 | + | 112.931i | −0.886004 | + | 0.463677i | ||||
\(40\) | −23.5163 | + | 40.7314i | −0.0929562 | + | 0.161005i | ||||
\(41\) | 266.236 | + | 153.711i | 1.01412 | + | 0.585504i | 0.912396 | − | 0.409308i | \(-0.134230\pi\) |
0.101727 | + | 0.994812i | \(0.467563\pi\) | |||||||
\(42\) | −32.3438 | − | 116.608i | −0.118827 | − | 0.428403i | ||||
\(43\) | 209.184 | + | 362.317i | 0.741865 | + | 1.28495i | 0.951645 | + | 0.307200i | \(0.0993920\pi\) |
−0.209780 | + | 0.977749i | \(0.567275\pi\) | |||||||
\(44\) | − | 230.546i | − | 0.789912i | ||||||
\(45\) | −39.0770 | + | 70.5117i | −0.129450 | + | 0.233584i | ||||
\(46\) | − | 198.074i | − | 0.634877i | ||||||
\(47\) | 330.941 | − | 191.069i | 1.02708 | − | 0.592983i | 0.110931 | − | 0.993828i | \(-0.464617\pi\) |
0.916146 | + | 0.400845i | \(0.131283\pi\) | |||||||
\(48\) | −192.964 | − | 49.8947i | −0.580249 | − | 0.150035i | ||||
\(49\) | 70.4504 | − | 122.024i | 0.205395 | − | 0.355754i | ||||
\(50\) | 106.431 | + | 61.4481i | 0.301033 | + | 0.173801i | ||||
\(51\) | 92.8348 | − | 94.4779i | 0.254892 | − | 0.259403i | ||||
\(52\) | 239.162 | − | 216.267i | 0.637804 | − | 0.576747i | ||||
\(53\) | −308.496 | −0.799532 | −0.399766 | − | 0.916617i | \(-0.630909\pi\) | ||||
−0.399766 | + | 0.916617i | \(0.630909\pi\) | |||||||
\(54\) | 144.428 | + | 34.6537i | 0.363967 | + | 0.0873291i | ||||
\(55\) | 100.064 | 0.245319 | ||||||||
\(56\) | 173.257 | + | 300.089i | 0.413435 | + | 0.716091i | ||||
\(57\) | 275.705 | + | 270.910i | 0.640667 | + | 0.629525i | ||||
\(58\) | 23.0833 | + | 13.3272i | 0.0522584 | + | 0.0301714i | ||||
\(59\) | 713.867 | + | 412.151i | 1.57521 | + | 0.909449i | 0.995514 | + | 0.0946184i | \(0.0301631\pi\) |
0.579699 | + | 0.814831i | \(0.303170\pi\) | |||||||
\(60\) | 26.7179 | − | 103.329i | 0.0574877 | − | 0.222330i | ||||
\(61\) | −84.3775 | − | 146.146i | −0.177105 | − | 0.306755i | 0.763783 | − | 0.645474i | \(-0.223340\pi\) |
−0.940888 | + | 0.338718i | \(0.890007\pi\) | |||||||
\(62\) | 188.269 | 0.385648 | ||||||||
\(63\) | 305.947 | + | 509.078i | 0.611836 | + | 1.01806i | ||||
\(64\) | 130.456 | 0.254798 | ||||||||
\(65\) | 93.8660 | + | 103.803i | 0.179118 | + | 0.198080i | ||||
\(66\) | −49.2756 | − | 177.651i | −0.0919000 | − | 0.331323i | ||||
\(67\) | −267.380 | − | 154.372i | −0.487548 | − | 0.281486i | 0.236009 | − | 0.971751i | \(-0.424161\pi\) |
−0.723557 | + | 0.690265i | \(0.757494\pi\) | |||||||
\(68\) | −87.6791 | + | 151.865i | −0.156362 | + | 0.270828i | ||||
\(69\) | 259.846 | + | 936.811i | 0.453359 | + | 1.63448i | ||||
\(70\) | −60.2181 | + | 34.7669i | −0.102821 | + | 0.0593635i | ||||
\(71\) | − | 962.451i | − | 1.60876i | −0.594116 | − | 0.804380i | \(-0.702498\pi\) | ||
0.594116 | − | 0.804380i | \(-0.297502\pi\) | |||||||
\(72\) | −425.244 | + | 7.46074i | −0.696049 | + | 0.0122119i | ||||
\(73\) | 128.457i | 0.205955i | 0.994684 | + | 0.102978i | \(0.0328370\pi\) | ||||
−0.994684 | + | 0.102978i | \(0.967163\pi\) | |||||||
\(74\) | 133.889 | + | 231.903i | 0.210328 | + | 0.364299i | ||||
\(75\) | −583.990 | − | 151.002i | −0.899111 | − | 0.232483i | ||||
\(76\) | −443.171 | − | 255.865i | −0.668884 | − | 0.386180i | ||||
\(77\) | 368.610 | − | 638.452i | 0.545546 | − | 0.944913i | ||||
\(78\) | 138.067 | − | 217.765i | 0.200423 | − | 0.316116i | ||||
\(79\) | −420.783 | − | 728.817i | −0.599263 | − | 1.03795i | −0.992930 | − | 0.118701i | \(-0.962127\pi\) |
0.393667 | − | 0.919253i | \(-0.371206\pi\) | |||||||
\(80\) | 114.526i | 0.160055i | ||||||||
\(81\) | −728.551 | + | 25.5722i | −0.999385 | + | 0.0350784i | ||||
\(82\) | −325.460 | −0.438305 | ||||||||
\(83\) | −600.759 | + | 346.848i | −0.794480 | + | 0.458693i | −0.841537 | − | 0.540199i | \(-0.818349\pi\) |
0.0470571 | + | 0.998892i | \(0.485016\pi\) | |||||||
\(84\) | −560.867 | − | 551.113i | −0.728519 | − | 0.715850i | ||||
\(85\) | −65.9135 | − | 38.0552i | −0.0841097 | − | 0.0485608i | ||||
\(86\) | −383.575 | − | 221.457i | −0.480953 | − | 0.277678i | ||||
\(87\) | −126.659 | − | 32.7501i | −0.156083 | − | 0.0403584i | ||||
\(88\) | 263.956 | + | 457.184i | 0.319747 | + | 0.553818i | ||||
\(89\) | 25.2619i | 0.0300872i | 0.999887 | + | 0.0150436i | \(0.00478871\pi\) | ||||
−0.999887 | + | 0.0150436i | \(0.995211\pi\) | |||||||
\(90\) | −1.49713 | − | 85.3327i | −0.00175346 | − | 0.0999428i | ||||
\(91\) | 1008.09 | − | 216.522i | 1.16128 | − | 0.249425i | ||||
\(92\) | −643.537 | − | 1114.64i | −0.729276 | − | 1.26314i | ||||
\(93\) | −890.438 | + | 246.983i | −0.992840 | + | 0.275387i | ||||
\(94\) | −202.279 | + | 350.358i | −0.221952 | + | 0.384432i | ||||
\(95\) | 111.053 | − | 192.349i | 0.119934 | − | 0.207732i | ||||
\(96\) | 834.312 | − | 231.415i | 0.886996 | − | 0.246028i | ||||
\(97\) | −1468.41 | + | 847.785i | −1.53705 | + | 0.887417i | −0.538043 | + | 0.842918i | \(0.680836\pi\) |
−0.999009 | + | 0.0444999i | \(0.985831\pi\) | |||||||
\(98\) | 149.168i | 0.153757i | ||||||||
\(99\) | 466.108 | + | 775.578i | 0.473189 | + | 0.787358i | ||||
\(100\) | 798.575 | 0.798575 | ||||||||
\(101\) | −54.6449 | − | 94.6478i | −0.0538354 | − | 0.0932456i | 0.837852 | − | 0.545898i | \(-0.183811\pi\) |
−0.891687 | + | 0.452652i | \(0.850478\pi\) | |||||||
\(102\) | −35.1039 | + | 135.762i | −0.0340765 | + | 0.131788i | ||||
\(103\) | −356.107 | + | 616.796i | −0.340663 | + | 0.590046i | −0.984556 | − | 0.175070i | \(-0.943985\pi\) |
0.643893 | + | 0.765116i | \(0.277318\pi\) | |||||||
\(104\) | −226.663 | + | 702.688i | −0.213713 | + | 0.662540i | ||||
\(105\) | 239.199 | − | 243.432i | 0.222318 | − | 0.226253i | ||||
\(106\) | 282.841 | − | 163.298i | 0.259169 | − | 0.149631i | ||||
\(107\) | −318.178 | −0.287471 | −0.143736 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143736 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(108\) | 925.346 | − | 274.235i | 0.824458 | − | 0.244336i | ||||
\(109\) | 980.230i | 0.861367i | 0.902503 | + | 0.430684i | \(0.141728\pi\) | ||||
−0.902503 | + | 0.430684i | \(0.858272\pi\) | |||||||
\(110\) | −91.7420 | + | 52.9673i | −0.0795205 | + | 0.0459112i | ||||
\(111\) | −937.468 | − | 921.164i | −0.801626 | − | 0.787685i | ||||
\(112\) | 730.729 | + | 421.887i | 0.616495 | + | 0.355934i | ||||
\(113\) | −147.754 | + | 255.918i | −0.123005 | + | 0.213051i | −0.920951 | − | 0.389678i | \(-0.872586\pi\) |
0.797946 | + | 0.602729i | \(0.205920\pi\) | |||||||
\(114\) | −396.179 | − | 102.440i | −0.325488 | − | 0.0841613i | ||||
\(115\) | 483.785 | − | 279.313i | 0.392289 | − | 0.226488i | ||||
\(116\) | 173.199 | 0.138630 | ||||||||
\(117\) | −367.323 | + | 1211.07i | −0.290248 | + | 0.956952i | ||||
\(118\) | −872.666 | −0.680809 | ||||||||
\(119\) | −485.619 | + | 280.372i | −0.374089 | + | 0.215981i | ||||
\(120\) | 65.3204 | + | 235.497i | 0.0496909 | + | 0.179149i | ||||
\(121\) | −103.924 | + | 180.002i | −0.0780798 | + | 0.135238i | ||||
\(122\) | 154.721 | + | 89.3281i | 0.114818 | + | 0.0662900i | ||||
\(123\) | 1539.30 | − | 426.959i | 1.12841 | − | 0.312989i | ||||
\(124\) | 1059.46 | − | 611.682i | 0.767279 | − | 0.442989i | ||||
\(125\) | 719.826i | 0.515065i | ||||||||
\(126\) | −549.977 | − | 304.793i | −0.388856 | − | 0.215501i | ||||
\(127\) | −588.842 | −0.411427 | −0.205714 | − | 0.978612i | \(-0.565952\pi\) | ||||
−0.205714 | + | 0.978612i | \(0.565952\pi\) | |||||||
\(128\) | −1274.02 | + | 735.557i | −0.879756 | + | 0.507927i | ||||
\(129\) | 2104.68 | + | 544.207i | 1.43649 | + | 0.371432i | ||||
\(130\) | −141.007 | − | 45.4839i | −0.0951315 | − | 0.0306862i | ||||
\(131\) | −240.030 | + | 415.743i | −0.160088 | + | 0.277280i | −0.934900 | − | 0.354911i | \(-0.884511\pi\) |
0.774812 | + | 0.632191i | \(0.217844\pi\) | |||||||
\(132\) | −854.478 | − | 839.618i | −0.563430 | − | 0.553632i | ||||
\(133\) | −818.182 | − | 1417.13i | −0.533424 | − | 0.923917i | ||||
\(134\) | 326.859 | 0.210719 | ||||||||
\(135\) | 119.026 | + | 401.626i | 0.0758823 | + | 0.256048i | ||||
\(136\) | − | 401.540i | − | 0.253175i | ||||||
\(137\) | −620.692 | + | 358.357i | −0.387075 | + | 0.223478i | −0.680892 | − | 0.732384i | \(-0.738408\pi\) |
0.293817 | + | 0.955862i | \(0.405074\pi\) | |||||||
\(138\) | −734.124 | − | 721.357i | −0.452846 | − | 0.444971i | ||||
\(139\) | 1141.18 | − | 1976.58i | 0.696356 | − | 1.20612i | −0.273365 | − | 0.961910i | \(-0.588137\pi\) |
0.969721 | − | 0.244214i | \(-0.0785299\pi\) | |||||||
\(140\) | −225.914 | + | 391.295i | −0.136380 | + | 0.236218i | ||||
\(141\) | 497.079 | − | 1922.42i | 0.296891 | − | 1.14820i | ||||
\(142\) | 509.460 | + | 882.411i | 0.301077 | + | 0.521481i | ||||
\(143\) | 1535.82 | − | 329.871i | 0.898125 | − | 0.192903i | ||||
\(144\) | −887.675 | + | 533.477i | −0.513701 | + | 0.308725i | ||||
\(145\) | 75.1732i | 0.0430538i | ||||||||
\(146\) | −67.9968 | − | 117.774i | −0.0385442 | − | 0.0667606i | ||||
\(147\) | −195.688 | − | 705.506i | −0.109796 | − | 0.395844i | ||||
\(148\) | 1506.89 | + | 870.006i | 0.836932 | + | 0.483203i | ||||
\(149\) | −1206.39 | − | 696.509i | −0.663297 | − | 0.382954i | 0.130235 | − | 0.991483i | \(-0.458427\pi\) |
−0.793532 | + | 0.608529i | \(0.791760\pi\) | |||||||
\(150\) | 615.354 | − | 170.683i | 0.334956 | − | 0.0929078i | ||||
\(151\) | 6.74246 | − | 3.89276i | 0.00363373 | − | 0.00209794i | −0.498182 | − | 0.867072i | \(-0.665999\pi\) |
0.501816 | + | 0.864975i | \(0.332666\pi\) | |||||||
\(152\) | 1171.77 | 0.625285 | ||||||||
\(153\) | −12.0733 | − | 688.151i | −0.00637956 | − | 0.363619i | ||||
\(154\) | 780.475i | 0.408393i | ||||||||
\(155\) | 265.487 | + | 459.837i | 0.137577 | + | 0.238290i | ||||
\(156\) | 69.4413 | − | 1674.03i | 0.0356394 | − | 0.859163i | ||||
\(157\) | −1398.32 | + | 2421.96i | −0.710816 | + | 1.23117i | 0.253735 | + | 0.967274i | \(0.418341\pi\) |
−0.964551 | + | 0.263896i | \(0.914992\pi\) | |||||||
\(158\) | 771.578 | + | 445.471i | 0.388503 | + | 0.224302i | ||||
\(159\) | −1123.50 | + | 1143.39i | −0.560374 | + | 0.570292i | ||||
\(160\) | −248.753 | − | 430.853i | −0.122910 | − | 0.212887i | ||||
\(161\) | − | 4115.69i | − | 2.01467i | ||||||
\(162\) | 654.427 | − | 409.094i | 0.317386 | − | 0.198404i | ||||
\(163\) | 1639.71i | 0.787924i | 0.919127 | + | 0.393962i | \(0.128896\pi\) | ||||
−0.919127 | + | 0.393962i | \(0.871104\pi\) | |||||||
\(164\) | −1831.49 | + | 1057.41i | −0.872046 | + | 0.503476i | ||||
\(165\) | 364.418 | − | 370.868i | 0.171939 | − | 0.174982i | ||||
\(166\) | 367.199 | − | 636.007i | 0.171688 | − | 0.297372i | ||||
\(167\) | 35.1425 | + | 20.2895i | 0.0162839 | + | 0.00940150i | 0.508120 | − | 0.861286i | \(-0.330341\pi\) |
−0.491836 | + | 0.870688i | \(0.663674\pi\) | |||||||
\(168\) | 1743.20 | + | 450.740i | 0.800542 | + | 0.206996i | ||||
\(169\) | 1782.90 | + | 1283.78i | 0.811514 | + | 0.584332i | ||||
\(170\) | 80.5760 | 0.0363523 | ||||||||
\(171\) | 2008.16 | − | 35.2324i | 0.898058 | − | 0.0157561i | ||||
\(172\) | −2878.04 | −1.27586 | ||||||||
\(173\) | −1536.85 | − | 2661.91i | −0.675403 | − | 1.16983i | −0.976351 | − | 0.216192i | \(-0.930636\pi\) |
0.300948 | − | 0.953641i | \(-0.402697\pi\) | |||||||
\(174\) | 133.461 | − | 37.0185i | 0.0581475 | − | 0.0161285i | ||||
\(175\) | 2211.49 | + | 1276.81i | 0.955275 | + | 0.551528i | ||||
\(176\) | 1113.26 | + | 642.742i | 0.476792 | + | 0.275276i | ||||
\(177\) | 4127.37 | − | 1144.82i | 1.75272 | − | 0.486158i | ||||
\(178\) | −13.3721 | − | 23.1611i | −0.00563078 | − | 0.00975279i | ||||
\(179\) | −3216.15 | −1.34294 | −0.671469 | − | 0.741032i | \(-0.734336\pi\) | ||||
−0.671469 | + | 0.741032i | \(0.734336\pi\) | |||||||
\(180\) | −285.669 | − | 475.337i | −0.118292 | − | 0.196831i | ||||
\(181\) | 640.548 | 0.263047 | 0.131524 | − | 0.991313i | \(-0.458013\pi\) | ||||
0.131524 | + | 0.991313i | \(0.458013\pi\) | |||||||
\(182\) | −809.642 | + | 732.135i | −0.329751 | + | 0.298184i | ||||
\(183\) | −848.956 | − | 219.514i | −0.342932 | − | 0.0886719i | ||||
\(184\) | 2552.33 | + | 1473.59i | 1.02261 | + | 0.590405i | ||||
\(185\) | −377.607 | + | 654.035i | −0.150066 | + | 0.259922i | ||||
\(186\) | 685.649 | − | 697.784i | 0.270292 | − | 0.275075i | ||||
\(187\) | −739.839 | + | 427.146i | −0.289317 | + | 0.167037i | ||||
\(188\) | 2628.80i | 1.01981i | ||||||||
\(189\) | 3001.02 | + | 720.056i | 1.15499 | + | 0.277124i | ||||
\(190\) | 235.136i | 0.0897821i | ||||||||
\(191\) | 2473.94 | + | 4284.99i | 0.937216 | + | 1.62331i | 0.770634 | + | 0.637278i | \(0.219940\pi\) |
0.166582 | + | 0.986028i | \(0.446727\pi\) | |||||||
\(192\) | 475.105 | − | 483.513i | 0.178582 | − | 0.181743i | ||||
\(193\) | −1418.12 | − | 818.750i | −0.528903 | − | 0.305362i | 0.211667 | − | 0.977342i | \(-0.432111\pi\) |
−0.740570 | + | 0.671980i | \(0.765444\pi\) | |||||||
\(194\) | 897.526 | − | 1554.56i | 0.332158 | − | 0.575314i | ||||
\(195\) | 726.575 | + | 30.1395i | 0.266826 | + | 0.0110684i | ||||
\(196\) | 484.643 | + | 839.427i | 0.176619 | + | 0.305914i | ||||
\(197\) | − | 4178.99i | − | 1.51137i | −0.654933 | − | 0.755687i | \(-0.727303\pi\) | ||
0.654933 | − | 0.755687i | \(-0.272697\pi\) | |||||||
\(198\) | −837.887 | − | 464.350i | −0.300737 | − | 0.166666i | ||||
\(199\) | −2263.58 | −0.806336 | −0.403168 | − | 0.915126i | \(-0.632091\pi\) | ||||
−0.403168 | + | 0.915126i | \(0.632091\pi\) | |||||||
\(200\) | −1583.61 | + | 914.299i | −0.559891 | + | 0.323253i | ||||
\(201\) | −1545.92 | + | 428.795i | −0.542490 | + | 0.150472i | ||||
\(202\) | 100.201 | + | 57.8511i | 0.0349016 | + | 0.0201504i | ||||
\(203\) | 479.640 | + | 276.920i | 0.165833 | + | 0.0957437i | ||||
\(204\) | 243.544 | + | 878.037i | 0.0835856 | + | 0.301348i | ||||
\(205\) | −458.947 | − | 794.919i | −0.156362 | − | 0.270827i | ||||
\(206\) | − | 754.002i | − | 0.255018i | ||||||
\(207\) | 4418.45 | + | 2448.67i | 1.48359 | + | 0.822194i | ||||
\(208\) | 377.548 | + | 1757.80i | 0.125857 | + | 0.585969i | ||||
\(209\) | −1246.50 | − | 2158.99i | −0.412545 | − | 0.714549i | ||||
\(210\) | −90.4488 | + | 349.804i | −0.0297217 | + | 0.114947i | ||||
\(211\) | 841.449 | − | 1457.43i | 0.274539 | − | 0.475516i | −0.695480 | − | 0.718546i | \(-0.744808\pi\) |
0.970019 | + | 0.243030i | \(0.0781414\pi\) | |||||||
\(212\) | 1061.10 | − | 1837.89i | 0.343759 | − | 0.595409i | ||||
\(213\) | −3567.15 | − | 3505.12i | −1.14750 | − | 1.12754i | ||||
\(214\) | 291.717 | − | 168.423i | 0.0931840 | − | 0.0537998i | ||||
\(215\) | − | 1249.15i | − | 0.396239i | ||||||
\(216\) | −1521.03 | + | 1603.26i | −0.479134 | + | 0.505038i | ||||
\(217\) | 3911.96 | 1.22379 | ||||||||
\(218\) | −518.871 | − | 898.712i | −0.161204 | − | 0.279213i | ||||
\(219\) | 476.102 | + | 467.822i | 0.146904 | + | 0.144349i | ||||
\(220\) | −344.179 | + | 596.136i | −0.105475 | + | 0.182689i | ||||
\(221\) | −1137.12 | − | 366.797i | −0.346114 | − | 0.111645i | ||||
\(222\) | 1347.11 | + | 348.322i | 0.407262 | + | 0.105306i | ||||
\(223\) | −318.826 | + | 184.074i | −0.0957405 | + | 0.0552758i | −0.547106 | − | 0.837063i | \(-0.684270\pi\) |
0.451365 | + | 0.892339i | \(0.350937\pi\) | |||||||
\(224\) | −3665.38 | −1.09332 | ||||||||
\(225\) | −2686.47 | + | 1614.52i | −0.795992 | + | 0.478377i | ||||
\(226\) | − | 312.847i | − | 0.0920809i | ||||||
\(227\) | −493.627 | + | 284.995i | −0.144331 | + | 0.0833296i | −0.570427 | − | 0.821349i | \(-0.693222\pi\) |
0.426096 | + | 0.904678i | \(0.359889\pi\) | |||||||
\(228\) | −2562.28 | + | 710.708i | −0.744261 | + | 0.206438i | ||||
\(229\) | −4250.28 | − | 2453.90i | −1.22649 | − | 0.708114i | −0.260196 | − | 0.965556i | \(-0.583787\pi\) |
−0.966294 | + | 0.257442i | \(0.917120\pi\) | |||||||
\(230\) | −295.701 | + | 512.170i | −0.0847738 | + | 0.146832i | ||||
\(231\) | −1023.88 | − | 3691.34i | −0.291629 | − | 1.05140i | ||||
\(232\) | −343.462 | + | 198.298i | −0.0971955 | + | 0.0561159i | ||||
\(233\) | 4224.22 | 1.18772 | 0.593859 | − | 0.804569i | \(-0.297604\pi\) | ||||
0.593859 | + | 0.804569i | \(0.297604\pi\) | |||||||
\(234\) | −304.287 | − | 1304.79i | −0.0850080 | − | 0.364516i | ||||
\(235\) | −1140.98 | −0.316719 | ||||||||
\(236\) | −4910.84 | + | 2835.28i | −1.35453 | + | 0.782037i | ||||
\(237\) | −4233.66 | − | 1094.70i | −1.16036 | − | 0.300035i | ||||
\(238\) | 296.823 | − | 514.112i | 0.0808409 | − | 0.140021i | ||||
\(239\) | 4878.09 | + | 2816.36i | 1.32024 | + | 0.762241i | 0.983767 | − | 0.179453i | \(-0.0574327\pi\) |
0.336473 | + | 0.941693i | \(0.390766\pi\) | |||||||
\(240\) | 424.471 | + | 417.089i | 0.114164 | + | 0.112179i | ||||
\(241\) | −2999.88 | + | 1731.98i | −0.801824 | + | 0.462933i | −0.844108 | − | 0.536173i | \(-0.819870\pi\) |
0.0422848 | + | 0.999106i | \(0.486536\pi\) | |||||||
\(242\) | − | 220.043i | − | 0.0584501i | ||||||
\(243\) | −2558.51 | + | 2793.38i | −0.675425 | + | 0.737429i | ||||
\(244\) | 1160.90 | 0.304586 | ||||||||
\(245\) | −364.335 | + | 210.349i | −0.0950062 | + | 0.0548518i | ||||
\(246\) | −1185.28 | + | 1206.26i | −0.307198 | + | 0.312635i | ||||
\(247\) | 1070.39 | − | 3318.35i | 0.275737 | − | 0.854825i | ||||
\(248\) | −1400.65 | + | 2425.99i | −0.358633 | + | 0.621171i | ||||
\(249\) | −902.352 | + | 3489.78i | −0.229656 | + | 0.888176i | ||||
\(250\) | −381.030 | − | 659.963i | −0.0963937 | − | 0.166959i | ||||
\(251\) | 2243.83 | 0.564259 | 0.282130 | − | 0.959376i | \(-0.408959\pi\) | ||||
0.282130 | + | 0.959376i | \(0.408959\pi\) | |||||||
\(252\) | −4085.20 | + | 71.6733i | −1.02121 | + | 0.0179166i | ||||
\(253\) | − | 6270.24i | − | 1.55813i | ||||||
\(254\) | 539.872 | − | 311.695i | 0.133364 | − | 0.0769980i | ||||
\(255\) | −381.093 | + | 105.705i | −0.0935881 | + | 0.0259588i | ||||
\(256\) | 256.888 | − | 444.944i | 0.0627169 | − | 0.108629i | ||||
\(257\) | 414.291 | − | 717.573i | 0.100556 | − | 0.174167i | −0.811358 | − | 0.584549i | \(-0.801271\pi\) |
0.911914 | + | 0.410382i | \(0.134605\pi\) | |||||||
\(258\) | −2217.72 | + | 615.134i | −0.535151 | + | 0.148436i | ||||
\(259\) | 2782.03 | + | 4818.61i | 0.667439 | + | 1.15604i | ||||
\(260\) | −941.277 | + | 202.172i | −0.224521 | + | 0.0482237i | ||||
\(261\) | −582.656 | + | 350.166i | −0.138182 | + | 0.0830449i | ||||
\(262\) | − | 508.225i | − | 0.119841i | ||||||
\(263\) | −408.066 | − | 706.792i | −0.0956747 | − | 0.165714i | 0.814215 | − | 0.580563i | \(-0.197168\pi\) |
−0.909890 | + | 0.414850i | \(0.863834\pi\) | |||||||
\(264\) | 2655.76 | + | 686.700i | 0.619132 | + | 0.160089i | ||||
\(265\) | 797.695 | + | 460.550i | 0.184913 | + | 0.106760i | ||||
\(266\) | 1500.28 | + | 866.186i | 0.345820 | + | 0.199659i | ||||
\(267\) | 93.6289 | + | 92.0006i | 0.0214607 | + | 0.0210874i | ||||
\(268\) | 1839.37 | − | 1061.96i | 0.419243 | − | 0.242050i | ||||
\(269\) | 6957.13 | 1.57689 | 0.788445 | − | 0.615105i | \(-0.210886\pi\) | ||||
0.788445 | + | 0.615105i | \(0.210886\pi\) | |||||||
\(270\) | −321.723 | − | 305.221i | −0.0725163 | − | 0.0687969i | ||||
\(271\) | 894.726i | 0.200556i | 0.994959 | + | 0.100278i | \(0.0319733\pi\) | ||||
−0.994959 | + | 0.100278i | \(0.968027\pi\) | |||||||
\(272\) | −488.883 | − | 846.770i | −0.108981 | − | 0.188761i | ||||
\(273\) | 2868.83 | − | 4524.86i | 0.636006 | − | 1.00314i | ||||
\(274\) | 379.382 | − | 657.110i | 0.0836472 | − | 0.144881i | ||||
\(275\) | 3369.20 | + | 1945.21i | 0.738801 | + | 0.426547i | ||||
\(276\) | −6474.89 | − | 1674.21i | −1.41211 | − | 0.365129i | ||||
\(277\) | −2077.04 | − | 3597.54i | −0.450532 | − | 0.780344i | 0.547887 | − | 0.836552i | \(-0.315432\pi\) |
−0.998419 | + | 0.0562082i | \(0.982099\pi\) | |||||||
\(278\) | 2416.27i | 0.521288i | ||||||||
\(279\) | −2327.46 | + | 4199.73i | −0.499431 | + | 0.901187i | ||||
\(280\) | − | 1034.61i | − | 0.220821i | ||||||
\(281\) | 3417.97 | − | 1973.37i | 0.725619 | − | 0.418936i | −0.0911983 | − | 0.995833i | \(-0.529070\pi\) |
0.816817 | + | 0.576896i | \(0.195736\pi\) | |||||||
\(282\) | 561.865 | + | 2025.67i | 0.118647 | + | 0.427754i | ||||
\(283\) | −3241.85 | + | 5615.05i | −0.680947 | + | 1.17943i | 0.293746 | + | 0.955884i | \(0.405098\pi\) |
−0.974692 | + | 0.223551i | \(0.928235\pi\) | |||||||
\(284\) | 5733.87 | + | 3310.45i | 1.19804 | + | 0.691687i | ||||
\(285\) | −308.467 | − | 1112.10i | −0.0641124 | − | 0.231142i | ||||
\(286\) | −1233.49 | + | 1115.40i | −0.255026 | + | 0.230613i | ||||
\(287\) | −6762.60 | −1.39088 | ||||||||
\(288\) | 2180.75 | − | 3935.01i | 0.446188 | − | 0.805114i | ||||
\(289\) | −4263.21 | −0.867740 | ||||||||
\(290\) | −39.7919 | − | 68.9216i | −0.00805745 | − | 0.0139559i | ||||
\(291\) | −2205.58 | + | 8529.90i | −0.444306 | + | 1.71832i | ||||
\(292\) | −765.291 | − | 441.841i | −0.153374 | − | 0.0885506i | ||||
\(293\) | −6713.28 | − | 3875.91i | −1.33855 | − | 0.772810i | −0.351954 | − | 0.936017i | \(-0.614483\pi\) |
−0.986592 | + | 0.163207i | \(0.947816\pi\) | |||||||
\(294\) | 552.864 | + | 543.249i | 0.109672 | + | 0.107765i | ||||
\(295\) | −1230.59 | − | 2131.44i | −0.242874 | − | 0.420669i | ||||
\(296\) | −3984.33 | −0.782379 | ||||||||
\(297\) | 4572.04 | + | 1097.00i | 0.893255 | + | 0.214325i | ||||
\(298\) | 1474.75 | 0.286678 | ||||||||
\(299\) | 6504.57 | − | 5881.88i | 1.25809 | − | 1.13765i | ||||
\(300\) | 2908.30 | − | 2959.77i | 0.559703 | − | 0.569609i | ||||
\(301\) | −7970.15 | − | 4601.57i | −1.52622 | − | 0.881163i | ||||
\(302\) | −4.12116 | + | 7.13806i | −0.000785252 | + | 0.00136010i | ||||
\(303\) | −549.804 | − | 142.163i | −0.104242 | − | 0.0269539i | ||||
\(304\) | 2471.04 | − | 1426.66i | 0.466197 | − | 0.269159i | ||||
\(305\) | 503.864i | 0.0945940i | ||||||||
\(306\) | 375.333 | + | 624.532i | 0.0701188 | + | 0.116674i | ||||
\(307\) | − | 5077.90i | − | 0.944011i | −0.881596 | − | 0.472005i | \(-0.843530\pi\) | ||
0.881596 | − | 0.472005i | \(-0.156470\pi\) | |||||||
\(308\) | 2535.75 | + | 4392.04i | 0.469116 | + | 0.812532i | ||||
\(309\) | 989.149 | + | 3566.14i | 0.182106 | + | 0.656539i | ||||
\(310\) | −486.817 | − | 281.064i | −0.0891914 | − | 0.0514947i | ||||
\(311\) | 759.959 | − | 1316.29i | 0.138564 | − | 0.239999i | −0.788389 | − | 0.615176i | \(-0.789085\pi\) |
0.926953 | + | 0.375177i | \(0.122418\pi\) | |||||||
\(312\) | 1778.91 | + | 3399.18i | 0.322792 | + | 0.616797i | ||||
\(313\) | 1023.94 | + | 1773.51i | 0.184908 | + | 0.320270i | 0.943546 | − | 0.331243i | \(-0.107468\pi\) |
−0.758637 | + | 0.651513i | \(0.774135\pi\) | |||||||
\(314\) | − | 2960.73i | − | 0.532113i | ||||||
\(315\) | −31.1082 | − | 1773.09i | −0.00556429 | − | 0.317151i | ||||
\(316\) | 5789.31 | 1.03061 | ||||||||
\(317\) | 5248.32 | − | 3030.12i | 0.929889 | − | 0.536872i | 0.0431127 | − | 0.999070i | \(-0.486273\pi\) |
0.886777 | + | 0.462198i | \(0.152939\pi\) | |||||||
\(318\) | 424.832 | − | 1643.01i | 0.0749164 | − | 0.289734i | ||||
\(319\) | 730.728 | + | 421.886i | 0.128254 | + | 0.0740473i | ||||
\(320\) | −337.328 | − | 194.757i | −0.0589289 | − | 0.0340226i | ||||
\(321\) | −1158.76 | + | 1179.27i | −0.201482 | + | 0.205048i | ||||
\(322\) | 2178.59 | + | 3773.42i | 0.377043 | + | 0.653058i | ||||
\(323\) | 1896.22i | 0.326652i | ||||||||
\(324\) | 2353.58 | − | 4428.36i | 0.403563 | − | 0.759320i | ||||
\(325\) | 1142.62 | + | 5319.84i | 0.195019 | + | 0.907974i | ||||
\(326\) | −867.955 | − | 1503.34i | −0.147459 | − | 0.255406i | ||||
\(327\) | 3633.05 | + | 3569.87i | 0.614398 | + | 0.603713i | ||||
\(328\) | 2421.29 | − | 4193.80i | 0.407602 | − | 0.705988i | ||||
\(329\) | −4203.08 | + | 7279.95i | −0.704326 | + | 1.21993i | ||||
\(330\) | −137.798 | + | 532.925i | −0.0229865 | + | 0.0888987i | ||||
\(331\) | 203.448 | − | 117.461i | 0.0337840 | − | 0.0195052i | −0.483013 | − | 0.875613i | \(-0.660458\pi\) |
0.516797 | + | 0.856108i | \(0.327124\pi\) | |||||||
\(332\) | − | 4772.09i | − | 0.788863i | ||||||
\(333\) | −6828.26 | + | 119.799i | −1.12368 | + | 0.0197146i | ||||
\(334\) | −42.9599 | −0.00703791 | ||||||||
\(335\) | 460.920 | + | 798.337i | 0.0751724 | + | 0.130202i | ||||
\(336\) | 4224.87 | − | 1171.86i | 0.685968 | − | 0.190269i | ||||
\(337\) | 2012.61 | − | 3485.95i | 0.325323 | − | 0.563477i | −0.656254 | − | 0.754540i | \(-0.727860\pi\) |
0.981578 | + | 0.191063i | \(0.0611935\pi\) | |||||||
\(338\) | −2314.18 | − | 233.264i | −0.372410 | − | 0.0375381i | ||||
\(339\) | 410.413 | + | 1479.65i | 0.0657540 | + | 0.237060i | ||||
\(340\) | 453.433 | − | 261.790i | 0.0723261 | − | 0.0417575i | ||||
\(341\) | 5959.86 | 0.946464 | ||||||||
\(342\) | −1822.51 | + | 1095.29i | −0.288158 | + | 0.173178i | ||||
\(343\) | − | 4445.73i | − | 0.699845i | ||||||
\(344\) | 5707.29 | − | 3295.10i | 0.894524 | − | 0.516454i | ||||
\(345\) | 726.655 | − | 2810.28i | 0.113396 | − | 0.438553i | ||||
\(346\) | 2818.09 | + | 1627.02i | 0.437865 | + | 0.252801i | ||||
\(347\) | 1707.83 | − | 2958.06i | 0.264211 | − | 0.457628i | −0.703145 | − | 0.711046i | \(-0.748222\pi\) |
0.967357 | + | 0.253419i | \(0.0815550\pi\) | |||||||
\(348\) | 630.767 | − | 641.930i | 0.0971628 | − | 0.0988824i | ||||
\(349\) | −1707.06 | + | 985.572i | −0.261825 | + | 0.151165i | −0.625167 | − | 0.780491i | \(-0.714969\pi\) |
0.363342 | + | 0.931656i | \(0.381636\pi\) | |||||||
\(350\) | −2703.44 | −0.412871 | ||||||||
\(351\) | 3150.87 | + | 5771.96i | 0.479148 | + | 0.877734i | ||||
\(352\) | −5584.20 | −0.845564 | ||||||||
\(353\) | 121.306 | − | 70.0361i | 0.0182903 | − | 0.0105599i | −0.490827 | − | 0.871257i | \(-0.663305\pi\) |
0.509117 | + | 0.860697i | \(0.329972\pi\) | |||||||
\(354\) | −3178.13 | + | 3234.38i | −0.477163 | + | 0.485608i | ||||
\(355\) | −1436.83 | + | 2488.66i | −0.214814 | + | 0.372069i | ||||
\(356\) | −150.500 | − | 86.8912i | −0.0224058 | − | 0.0129360i | ||||
\(357\) | −729.410 | + | 2820.94i | −0.108136 | + | 0.418207i | ||||
\(358\) | 2948.68 | − | 1702.42i | 0.435315 | − | 0.251329i | ||||
\(359\) | 11163.7i | 1.64122i | 0.571490 | + | 0.820609i | \(0.306366\pi\) | ||||
−0.571490 | + | 0.820609i | \(0.693634\pi\) | |||||||
\(360\) | 1110.72 | + | 615.550i | 0.162611 | + | 0.0901176i | ||||
\(361\) | 1325.46 | 0.193244 | ||||||||
\(362\) | −587.278 | + | 339.065i | −0.0852670 | + | 0.0492289i | ||||
\(363\) | 288.667 | + | 1040.72i | 0.0417386 | + | 0.150478i | ||||
\(364\) | −2177.49 | + | 6750.53i | −0.313548 | + | 0.972044i | ||||
\(365\) | 191.771 | − | 332.158i | 0.0275008 | − | 0.0476327i | ||||
\(366\) | 894.551 | − | 248.124i | 0.127757 | − | 0.0354362i | ||||
\(367\) | −5484.13 | − | 9498.79i | −0.780025 | − | 1.35104i | −0.931926 | − | 0.362647i | \(-0.881873\pi\) |
0.151901 | − | 0.988396i | \(-0.451460\pi\) | |||||||
\(368\) | 7176.50 | 1.01658 | ||||||||
\(369\) | 4023.47 | − | 7260.06i | 0.567624 | − | 1.02424i | ||||
\(370\) | − | 799.524i | − | 0.112339i | ||||||
\(371\) | 5877.04 | − | 3393.11i | 0.822427 | − | 0.474829i | ||||
\(372\) | 1591.34 | − | 6154.37i | 0.221793 | − | 0.857767i | ||||
\(373\) | 4516.09 | − | 7822.10i | 0.626902 | − | 1.08583i | −0.361268 | − | 0.932462i | \(-0.617656\pi\) |
0.988170 | − | 0.153363i | \(-0.0490105\pi\) | |||||||
\(374\) | 452.208 | − | 783.247i | 0.0625217 | − | 0.108291i | ||||
\(375\) | 2667.90 | + | 2621.51i | 0.367387 | + | 0.360998i | ||||
\(376\) | −3009.75 | − | 5213.04i | −0.412809 | − | 0.715006i | ||||
\(377\) | 247.817 | + | 1153.79i | 0.0338547 | + | 0.157622i | ||||
\(378\) | −3132.60 | + | 928.376i | −0.426253 | + | 0.126324i | ||||
\(379\) | 449.724i | 0.0609519i | 0.999536 | + | 0.0304760i | \(0.00970230\pi\) | ||||
−0.999536 | + | 0.0304760i | \(0.990298\pi\) | |||||||
\(380\) | 763.954 | + | 1323.21i | 0.103132 | + | 0.178629i | ||||
\(381\) | −2144.48 | + | 2182.44i | −0.288360 | + | 0.293463i | ||||
\(382\) | −4536.41 | − | 2619.09i | −0.607599 | − | 0.350797i | ||||
\(383\) | −415.500 | − | 239.889i | −0.0554336 | − | 0.0320046i | 0.472027 | − | 0.881584i | \(-0.343522\pi\) |
−0.527461 | + | 0.849579i | \(0.676856\pi\) | |||||||
\(384\) | −1913.61 | + | 7400.74i | −0.254306 | + | 0.983508i | ||||
\(385\) | −1906.27 | + | 1100.59i | −0.252344 | + | 0.145691i | ||||
\(386\) | 1733.58 | 0.228592 | ||||||||
\(387\) | 9681.97 | − | 5818.69i | 1.27174 | − | 0.764292i | ||||
\(388\) | − | 11664.2i | − | 1.52618i | ||||||
\(389\) | 5126.45 | + | 8879.27i | 0.668178 | + | 1.15732i | 0.978413 | + | 0.206659i | \(0.0662590\pi\) |
−0.310235 | + | 0.950660i | \(0.600408\pi\) | |||||||
\(390\) | −682.105 | + | 356.969i | −0.0885634 | + | 0.0463483i | ||||
\(391\) | −2384.64 | + | 4130.31i | −0.308430 | + | 0.534217i | ||||
\(392\) | −1922.14 | − | 1109.75i | −0.247660 | − | 0.142987i | ||||
\(393\) | 666.723 | + | 2403.71i | 0.0855769 | + | 0.308527i | ||||
\(394\) | 2212.09 | + | 3831.45i | 0.282852 | + | 0.489913i | ||||
\(395\) | 2512.72i | 0.320073i | ||||||||
\(396\) | −6223.79 | + | 109.194i | −0.789791 | + | 0.0138566i | ||||
\(397\) | 8172.25i | 1.03313i | 0.856247 | + | 0.516566i | \(0.172790\pi\) | ||||
−0.856247 | + | 0.516566i | \(0.827210\pi\) | |||||||
\(398\) | 2075.33 | − | 1198.19i | 0.261375 | − | 0.150905i | ||||
\(399\) | −8232.06 | − | 2128.56i | −1.03288 | − | 0.267071i | ||||
\(400\) | −2226.36 | + | 3856.16i | −0.278294 | + | 0.482020i | ||||
\(401\) | −5755.03 | − | 3322.67i | −0.716689 | − | 0.413781i | 0.0968437 | − | 0.995300i | \(-0.469125\pi\) |
−0.813533 | + | 0.581519i | \(0.802459\pi\) | |||||||
\(402\) | 1190.38 | − | 1211.44i | 0.147688 | − | 0.150302i | ||||
\(403\) | 5590.72 | + | 6182.59i | 0.691052 | + | 0.764210i | ||||
\(404\) | 751.828 | 0.0925862 | ||||||||
\(405\) | 1922.03 | + | 1021.52i | 0.235819 | + | 0.125333i | ||||
\(406\) | −586.335 | −0.0716732 | ||||||||
\(407\) | 4238.41 | + | 7341.13i | 0.516192 | + | 0.894070i | ||||
\(408\) | −1488.24 | − | 1462.35i | −0.180585 | − | 0.177444i | ||||
\(409\) | 6611.01 | + | 3816.87i | 0.799250 | + | 0.461447i | 0.843209 | − | 0.537586i | \(-0.180664\pi\) |
−0.0439589 | + | 0.999033i | \(0.513997\pi\) | |||||||
\(410\) | 841.559 | + | 485.874i | 0.101370 | + | 0.0585259i | ||||
\(411\) | −932.292 | + | 3605.57i | −0.111889 | + | 0.432724i | ||||
\(412\) | −2449.74 | − | 4243.07i | −0.292937 | − | 0.507381i | ||||
\(413\) | −18132.8 | −2.16043 | ||||||||
\(414\) | −5347.16 | + | 93.8139i | −0.634780 | + | 0.0111370i | ||||
\(415\) | 2071.22 | 0.244993 | ||||||||
\(416\) | −5238.33 | − | 5792.89i | −0.617380 | − | 0.682739i | ||||
\(417\) | −3169.82 | − | 11428.0i | −0.372246 | − | 1.34204i | ||||
\(418\) | 2285.67 | + | 1319.63i | 0.267454 | + | 0.154414i | ||||
\(419\) | 1404.23 | − | 2432.20i | 0.163726 | − | 0.283581i | −0.772476 | − | 0.635044i | \(-0.780982\pi\) |
0.936202 | + | 0.351462i | \(0.114315\pi\) | |||||||
\(420\) | 627.516 | + | 2262.36i | 0.0729039 | + | 0.262837i | ||||
\(421\) | −1041.73 | + | 601.443i | −0.120596 | + | 0.0696260i | −0.559084 | − | 0.829111i | \(-0.688847\pi\) |
0.438489 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(422\) | 1781.64i | 0.205518i | ||||||||
\(423\) | −5314.80 | − | 8843.52i | −0.610909 | − | 1.01652i | ||||
\(424\) | 4859.49i | 0.556599i | ||||||||
\(425\) | −1479.56 | − | 2562.68i | −0.168869 | − | 0.292490i | ||||
\(426\) | 5125.88 | + | 1325.40i | 0.582981 | + | 0.150741i | ||||
\(427\) | 3214.88 | + | 1856.11i | 0.364354 | + | 0.210360i | ||||
\(428\) | 1094.41 | − | 1895.57i | 0.123598 | − | 0.214079i | ||||
\(429\) | 4370.65 | − | 6893.59i | 0.491881 | − | 0.775818i | ||||
\(430\) | 661.220 | + | 1145.27i | 0.0741555 | + | 0.128441i | ||||
\(431\) | 13530.8i | 1.51219i | 0.654461 | + | 0.756096i | \(0.272895\pi\) | ||||
−0.654461 | + | 0.756096i | \(0.727105\pi\) | |||||||
\(432\) | −1255.55 | + | 5232.86i | −0.139833 | + | 0.582792i | ||||
\(433\) | −12.8820 | −0.00142973 | −0.000714863 | − | 1.00000i | \(-0.500228\pi\) | ||||
−0.000714863 | 1.00000i | \(0.500228\pi\) | ||||||||
\(434\) | −3586.63 | + | 2070.74i | −0.396691 | + | 0.229030i | ||||
\(435\) | 278.616 | + | 273.771i | 0.0307095 | + | 0.0301754i | ||||
\(436\) | −5839.79 | − | 3371.61i | −0.641457 | − | 0.370346i | ||||
\(437\) | −12053.1 | − | 6958.84i | −1.31940 | − | 0.761753i | ||||
\(438\) | −684.143 | − | 176.899i | −0.0746339 | − | 0.0192981i | ||||
\(439\) | 3003.53 | + | 5202.27i | 0.326539 | + | 0.565582i | 0.981823 | − | 0.189801i | \(-0.0607842\pi\) |
−0.655284 | + | 0.755383i | \(0.727451\pi\) | |||||||
\(440\) | − | 1576.22i | − | 0.170781i | ||||||
\(441\) | −3327.50 | − | 1844.07i | −0.359302 | − | 0.199123i | ||||
\(442\) | 1236.72 | − | 265.628i | 0.133087 | − | 0.0285851i | ||||
\(443\) | −5422.30 | − | 9391.70i | −0.581538 | − | 1.00725i | −0.995297 | − | 0.0968671i | \(-0.969118\pi\) |
0.413759 | − | 0.910386i | \(-0.364216\pi\) | |||||||
\(444\) | 8712.42 | − | 2416.59i | 0.931246 | − | 0.258302i | ||||
\(445\) | 37.7132 | − | 65.3212i | 0.00401748 | − | 0.00695848i | ||||
\(446\) | 194.874 | − | 337.532i | 0.0206896 | − | 0.0358354i | ||||
\(447\) | −6974.99 | + | 1934.67i | −0.738044 | + | 0.204713i | ||||
\(448\) | −2485.27 | + | 1434.87i | −0.262094 | + | 0.151320i | ||||
\(449\) | 9498.89i | 0.998397i | 0.866488 | + | 0.499199i | \(0.166372\pi\) | ||||
−0.866488 | + | 0.499199i | \(0.833628\pi\) | |||||||
\(450\) | 1608.43 | − | 2902.30i | 0.168494 | − | 0.304035i | ||||
\(451\) | −10302.8 | −1.07570 | ||||||||
\(452\) | −1016.43 | − | 1760.52i | −0.105772 | − | 0.183203i | ||||
\(453\) | 10.1273 | − | 39.1666i | 0.00105038 | − | 0.00406227i | ||||
\(454\) | 301.717 | − | 522.589i | 0.0311900 | − | 0.0540227i | ||||
\(455\) | −2929.92 | − | 945.092i | −0.301883 | − | 0.0973772i | ||||
\(456\) | 4267.44 | − | 4342.96i | 0.438248 | − | 0.446004i | ||||
\(457\) | −978.386 | + | 564.871i | −0.100147 | + | 0.0578196i | −0.549237 | − | 0.835667i | \(-0.685081\pi\) |
0.449090 | + | 0.893486i | \(0.351748\pi\) | |||||||
\(458\) | 5195.75 | 0.530090 | ||||||||
\(459\) | −2594.48 | − | 2461.41i | −0.263834 | − | 0.250302i | ||||
\(460\) | 3842.91i | 0.389515i | ||||||||
\(461\) | −498.214 | + | 287.644i | −0.0503343 | + | 0.0290605i | −0.524956 | − | 0.851129i | \(-0.675918\pi\) |
0.474622 | + | 0.880190i | \(0.342585\pi\) | |||||||
\(462\) | 2892.69 | + | 2842.38i | 0.291299 | + | 0.286233i | ||||
\(463\) | −8443.82 | − | 4875.04i | −0.847554 | − | 0.489336i | 0.0122708 | − | 0.999925i | \(-0.496094\pi\) |
−0.859825 | + | 0.510589i | \(0.829427\pi\) | |||||||
\(464\) | −482.863 | + | 836.343i | −0.0483111 | + | 0.0836773i | ||||
\(465\) | 2671.17 | + | 690.685i | 0.266393 | + | 0.0688812i | ||||
\(466\) | −3872.93 | + | 2236.03i | −0.385000 | + | 0.222280i | ||||
\(467\) | −19584.4 | −1.94060 | −0.970299 | − | 0.241909i | \(-0.922226\pi\) | ||||
−0.970299 | + | 0.241909i | \(0.922226\pi\) | |||||||
\(468\) | −5951.58 | − | 6353.95i | −0.587846 | − | 0.627589i | ||||
\(469\) | 6791.68 | 0.668679 | ||||||||
\(470\) | 1046.09 | − | 603.959i | 0.102665 | − | 0.0592735i | ||||
\(471\) | 3884.07 | + | 14003.1i | 0.379976 | + | 1.36991i | ||||
\(472\) | 6492.29 | − | 11245.0i | 0.633119 | − | 1.09659i | ||||
\(473\) | −12142.5 | − | 7010.47i | −1.18036 | − | 0.681483i | ||||
\(474\) | 4461.04 | − | 1237.37i | 0.432284 | − | 0.119904i | ||||
\(475\) | 7478.40 | − | 4317.66i | 0.722385 | − | 0.417069i | ||||
\(476\) | − | 3857.48i | − | 0.371444i | ||||||
\(477\) | 146.113 | + | 8328.11i | 0.0140253 | + | 0.799409i | ||||
\(478\) | −5963.21 | −0.570609 | ||||||||
\(479\) | −10864.4 | + | 6272.59i | −1.03634 | + | 0.598334i | −0.918796 | − | 0.394733i | \(-0.870837\pi\) |
−0.117549 | + | 0.993067i | \(0.537504\pi\) | |||||||
\(480\) | −2502.80 | − | 647.149i | −0.237993 | − | 0.0615379i | ||||
\(481\) | −3639.59 | + | 11283.2i | −0.345012 | + | 1.06959i | ||||
\(482\) | 1833.60 | − | 3175.89i | 0.173275 | − | 0.300120i | ||||
\(483\) | −15254.1 | − | 14988.8i | −1.43703 | − | 1.41204i | ||||
\(484\) | −714.916 | − | 1238.27i | −0.0671409 | − | 0.116291i | ||||
\(485\) | 5062.59 | 0.473980 | ||||||||
\(486\) | 867.100 | − | 3915.38i | 0.0809310 | − | 0.365443i | ||||
\(487\) | 17048.7i | 1.58635i | 0.608994 | + | 0.793175i | \(0.291573\pi\) | ||||
−0.608994 | + | 0.793175i | \(0.708427\pi\) | |||||||
\(488\) | −2302.12 | + | 1329.13i | −0.213550 | + | 0.123293i | ||||
\(489\) | 6077.27 | + | 5971.59i | 0.562012 | + | 0.552238i | ||||
\(490\) | 222.691 | − | 385.711i | 0.0205309 | − | 0.0355605i | ||||
\(491\) | 10538.9 | − | 18253.9i | 0.968663 | − | 1.67777i | 0.269229 | − | 0.963076i | \(-0.413231\pi\) |
0.699434 | − | 0.714697i | \(-0.253435\pi\) | |||||||
\(492\) | −2750.94 | + | 10639.1i | −0.252077 | + | 0.974889i | ||||
\(493\) | −320.895 | − | 555.807i | −0.0293152 | − | 0.0507754i | ||||
\(494\) | 775.154 | + | 3608.98i | 0.0705988 | + | 0.328696i | ||||
\(495\) | −47.3933 | − | 2701.30i | −0.00430337 | − | 0.245282i | ||||
\(496\) | 6821.26i | 0.617507i | ||||||||
\(497\) | 10585.9 | + | 18335.3i | 0.955415 | + | 1.65483i | ||||
\(498\) | −1019.96 | − | 3677.21i | −0.0917779 | − | 0.330883i | ||||
\(499\) | 17275.8 | + | 9974.16i | 1.54984 | + | 0.894799i | 0.998153 | + | 0.0607460i | \(0.0193480\pi\) |
0.551684 | + | 0.834053i | \(0.313985\pi\) | |||||||
\(500\) | −4288.41 | − | 2475.92i | −0.383567 | − | 0.221453i | ||||
\(501\) | 203.184 | − | 56.3576i | 0.0181189 | − | 0.00502569i | ||||
\(502\) | −2057.22 | + | 1187.74i | −0.182905 | + | 0.105600i | ||||
\(503\) | 10885.5 | 0.964935 | 0.482467 | − | 0.875914i | \(-0.339741\pi\) | ||||
0.482467 | + | 0.875914i | \(0.339741\pi\) | |||||||
\(504\) | 8019.10 | − | 4819.34i | 0.708728 | − | 0.425933i | ||||
\(505\) | 326.315i | 0.0287541i | ||||||||
\(506\) | 3319.06 | + | 5748.79i | 0.291602 | + | 0.505069i | ||||
\(507\) | 11251.2 | − | 1932.64i | 0.985566 | − | 0.169293i | ||||
\(508\) | 2025.38 | − | 3508.07i | 0.176893 | − | 0.306388i | ||||
\(509\) | 1249.23 | + | 721.245i | 0.108784 | + | 0.0628067i | 0.553405 | − | 0.832912i | \(-0.313328\pi\) |
−0.444621 | + | 0.895719i | \(0.646662\pi\) | |||||||
\(510\) | 293.447 | − | 298.640i | 0.0254785 | − | 0.0259294i | ||||
\(511\) | −1412.88 | − | 2447.18i | −0.122313 | − | 0.211853i | ||||
\(512\) | − | 11225.0i | − | 0.968905i | ||||||
\(513\) | 7182.87 | − | 7571.20i | 0.618190 | − | 0.651612i | ||||
\(514\) | 877.197i | 0.0752753i | ||||||||
\(515\) | 1841.61 | − | 1063.26i | 0.157575 | − | 0.0909760i | ||||
\(516\) | −10481.4 | + | 10666.9i | −0.894223 | + | 0.910049i | ||||
\(517\) | −6403.37 | + | 11091.0i | −0.544719 | + | 0.943481i | ||||
\(518\) | −5101.33 | − | 2945.26i | −0.432702 | − | 0.249821i | ||||
\(519\) | −15462.9 | − | 3998.24i | −1.30779 | − | 0.338156i | ||||
\(520\) | 1635.13 | − | 1478.60i | 0.137894 | − | 0.124694i | ||||
\(521\) | −3947.79 | −0.331969 | −0.165985 | − | 0.986128i | \(-0.553080\pi\) | ||||
−0.165985 | + | 0.986128i | \(0.553080\pi\) | |||||||
\(522\) | 348.845 | − | 629.466i | 0.0292501 | − | 0.0527797i | ||||
\(523\) | 19606.7 | 1.63928 | 0.819638 | − | 0.572882i | \(-0.194175\pi\) | ||||
0.819638 | + | 0.572882i | \(0.194175\pi\) | |||||||
\(524\) | −1651.21 | − | 2859.99i | −0.137660 | − | 0.238433i | ||||
\(525\) | 12786.2 | − | 3546.55i | 1.06293 | − | 0.294827i | ||||
\(526\) | 748.261 | + | 432.009i | 0.0620261 | + | 0.0358108i | ||||
\(527\) | −3925.86 | − | 2266.59i | −0.324503 | − | 0.187352i | ||||
\(528\) | 6436.56 | − | 1785.33i | 0.530522 | − | 0.147152i | ||||
\(529\) | −11419.0 | − | 19778.3i | −0.938521 | − | 1.62557i | ||||
\(530\) | −975.142 | −0.0799198 | ||||||||
\(531\) | 10788.3 | − | 19466.6i | 0.881677 | − | 1.59092i | ||||
\(532\) | 11256.9 | 0.917384 | ||||||||
\(533\) | −9664.67 | − | 10687.8i | −0.785410 | − | 0.868557i | ||||
\(534\) | −134.542 | − | 34.7884i | −0.0109030 | − | 0.00281918i | ||||
\(535\) | 822.730 | + | 475.003i | 0.0664854 | + | 0.0383854i | ||||
\(536\) | −2431.70 | + | 4211.83i | −0.195958 | + | 0.339409i | ||||
\(537\) | −11712.8 | + | 11920.1i | −0.941235 | + | 0.957894i | ||||
\(538\) | −6378.55 | + | 3682.66i | −0.511150 | + | 0.295113i | ||||
\(539\) | 4722.07i | 0.377354i | ||||||||
\(540\) | −2802.12 | − | 672.332i | −0.223304 | − | 0.0535788i | ||||
\(541\) | 6566.67i | 0.521854i | 0.965359 | + | 0.260927i | \(0.0840282\pi\) | ||||
−0.965359 | + | 0.260927i | \(0.915972\pi\) | |||||||
\(542\) | −473.611 | − | 820.318i | −0.0375338 | − | 0.0650105i | ||||
\(543\) | 2332.79 | − | 2374.08i | 0.184364 | − | 0.187627i | ||||
\(544\) | 3678.40 | + | 2123.73i | 0.289908 | + | 0.167379i | ||||
\(545\) | 1463.37 | − | 2534.64i | 0.115017 | − | 0.199214i | ||||
\(546\) | −235.082 | + | 5667.13i | −0.0184259 | + | 0.444196i | ||||
\(547\) | 5901.22 | + | 10221.2i | 0.461276 | + | 0.798954i | 0.999025 | − | 0.0441514i | \(-0.0140584\pi\) |
−0.537749 | + | 0.843105i | \(0.680725\pi\) | |||||||
\(548\) | − | 4930.43i | − | 0.384338i | ||||||
\(549\) | −3905.37 | + | 2347.06i | −0.303602 | + | 0.182459i | ||||
\(550\) | −4118.67 | −0.319311 | ||||||||
\(551\) | 1621.95 | − | 936.435i | 0.125404 | − | 0.0724020i | ||||
\(552\) | 14756.8 | − | 4093.15i | 1.13785 | − | 0.315608i | ||||
\(553\) | 16032.3 | + | 9256.27i | 1.23285 | + | 0.711784i | ||||
\(554\) | 3808.62 | + | 2198.91i | 0.292081 | + | 0.168633i | ||||
\(555\) | 1048.87 | + | 3781.44i | 0.0802198 | + | 0.289213i | ||||
\(556\) | 7850.41 | + | 13597.3i | 0.598798 | + | 1.03715i | ||||
\(557\) | 10027.5i | 0.762798i | 0.924411 | + | 0.381399i | \(0.124558\pi\) | ||||
−0.924411 | + | 0.381399i | \(0.875442\pi\) | |||||||
\(558\) | −89.1700 | − | 5082.47i | −0.00676499 | − | 0.385588i | ||||
\(559\) | −4117.96 | − | 19172.5i | −0.311576 | − | 1.45065i | ||||
\(560\) | −1259.66 | − | 2181.79i | −0.0950541 | − | 0.164638i | ||||
\(561\) | −1111.25 | + | 4297.69i | −0.0836312 | + | 0.323438i | ||||
\(562\) | −2089.15 | + | 3618.51i | −0.156807 | + | 0.271597i | ||||
\(563\) | −6556.24 | + | 11355.7i | −0.490786 | + | 0.850067i | −0.999944 | − | 0.0106064i | \(-0.996624\pi\) |
0.509157 | + | 0.860673i | \(0.329957\pi\) | |||||||
\(564\) | 9743.19 | + | 9573.75i | 0.727415 | + | 0.714765i | ||||
\(565\) | 764.114 | − | 441.161i | 0.0568965 | − | 0.0328492i | ||||
\(566\) | − | 6864.11i | − | 0.509753i | ||||||
\(567\) | 13598.1 | − | 8500.41i | 1.00717 | − | 0.629601i | ||||
\(568\) | −15160.7 | −1.11995 | ||||||||
\(569\) | −11399.5 | − | 19744.5i | −0.839881 | − | 1.45472i | −0.889994 | − | 0.455973i | \(-0.849291\pi\) |
0.0501125 | − | 0.998744i | \(-0.484042\pi\) | |||||||
\(570\) | 871.491 | + | 856.335i | 0.0640399 | + | 0.0629262i | ||||
\(571\) | −5826.85 | + | 10092.4i | −0.427051 | + | 0.739674i | −0.996610 | − | 0.0822769i | \(-0.973781\pi\) |
0.569559 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(572\) | −3317.39 | + | 10284.4i | −0.242495 | + | 0.751770i | ||||
\(573\) | 24891.3 | + | 6436.15i | 1.81475 | + | 0.469239i | ||||
\(574\) | 6200.20 | − | 3579.69i | 0.450856 | − | 0.260302i | ||||
\(575\) | 21719.1 | 1.57522 | ||||||||
\(576\) | −61.7883 | − | 3521.78i | −0.00446964 | − | 0.254759i | ||||
\(577\) | 15037.4i | 1.08495i | 0.840072 | + | 0.542476i | \(0.182513\pi\) | ||||
−0.840072 | + | 0.542476i | \(0.817487\pi\) | |||||||
\(578\) | 3908.67 | − | 2256.67i | 0.281279 | − | 0.162396i | ||||
\(579\) | −8199.14 | + | 2274.22i | −0.588505 | + | 0.163235i | ||||
\(580\) | −447.850 | − | 258.566i | −0.0320620 | − | 0.0185110i | ||||
\(581\) | 7629.88 | − | 13215.3i | 0.544821 | − | 0.943657i | ||||
\(582\) | −2493.03 | − | 8988.02i | −0.177559 | − | 0.640147i | ||||
\(583\) | 8953.64 | − | 5169.38i | 0.636058 | − | 0.367228i | ||||
\(584\) | 2023.48 | 0.143377 | ||||||||
\(585\) | 2757.79 | − | 2583.16i | 0.194907 | − | 0.182565i | ||||
\(586\) | 8206.65 | 0.578521 | ||||||||
\(587\) | 12366.8 | − | 7139.99i | 0.869563 | − | 0.502042i | 0.00235988 | − | 0.999997i | \(-0.499249\pi\) |
0.867203 | + | 0.497955i | \(0.165915\pi\) | |||||||
\(588\) | 4876.19 | + | 1260.84i | 0.341991 | + | 0.0884286i | ||||
\(589\) | 6614.37 | − | 11456.4i | 0.462717 | − | 0.801449i | ||||
\(590\) | 2256.50 | + | 1302.79i | 0.157455 | + | 0.0909069i | ||||
\(591\) | −15488.7 | − | 15219.3i | −1.07804 | − | 1.05929i | ||||
\(592\) | −8402.17 | + | 4851.00i | −0.583323 | + | 0.336782i | ||||
\(593\) | 7062.51i | 0.489077i | 0.969640 | + | 0.244538i | \(0.0786364\pi\) | ||||
−0.969640 | + | 0.244538i | \(0.921364\pi\) | |||||||
\(594\) | −4772.50 | + | 1414.38i | −0.329660 | + | 0.0976979i | ||||
\(595\) | 1674.26 | 0.115358 | ||||||||
\(596\) | 8299.00 | − | 4791.43i | 0.570370 | − | 0.329303i | ||||
\(597\) | −8243.66 | + | 8389.56i | −0.565143 | + | 0.575145i | ||||
\(598\) | −2850.14 | + | 8835.83i | −0.194901 | + | 0.604221i | ||||
\(599\) | −9010.04 | + | 15605.8i | −0.614591 | + | 1.06450i | 0.375865 | + | 0.926675i | \(0.377346\pi\) |
−0.990456 | + | 0.137829i | \(0.955988\pi\) | |||||||
\(600\) | −2378.62 | + | 9199.13i | −0.161844 | + | 0.625921i | ||||
\(601\) | −1335.33 | − | 2312.87i | −0.0906313 | − | 0.156978i | 0.817146 | − | 0.576431i | \(-0.195555\pi\) |
−0.907777 | + | 0.419453i | \(0.862222\pi\) | |||||||
\(602\) | 9743.11 | 0.659634 | ||||||||
\(603\) | −4040.77 | + | 7291.28i | −0.272890 | + | 0.492411i | ||||
\(604\) | 53.5583i | 0.00360804i | ||||||||
\(605\) | 537.445 | − | 310.294i | 0.0361161 | − | 0.0208516i | ||||
\(606\) | 579.333 | − | 160.691i | 0.0388346 | − | 0.0107717i | ||||
\(607\) | 7070.23 | − | 12246.0i | 0.472771 | − | 0.818863i | −0.526744 | − | 0.850024i | \(-0.676587\pi\) |
0.999514 | + | 0.0311613i | \(0.00992056\pi\) | |||||||
\(608\) | −6197.45 | + | 10734.3i | −0.413388 | + | 0.716009i | ||||
\(609\) | 2773.14 | − | 769.193i | 0.184521 | − | 0.0511811i | ||||
\(610\) | −266.713 | − | 461.961i | −0.0177031 | − | 0.0306627i | ||||
\(611\) | −17512.2 | + | 3761.35i | −1.15952 | + | 0.249047i | ||||
\(612\) | 4141.24 | + | 2295.04i | 0.273529 | + | 0.151588i | ||||
\(613\) | 2020.97i | 0.133159i | 0.997781 | + | 0.0665794i | \(0.0212086\pi\) | ||||
−0.997781 | + | 0.0665794i | \(0.978791\pi\) | |||||||
\(614\) | 2687.92 | + | 4655.61i | 0.176670 | + | 0.306002i | ||||
\(615\) | −4617.65 | − | 1193.98i | −0.302767 | − | 0.0782864i | ||||
\(616\) | −10057.0 | − | 5806.43i | −0.657807 | − | 0.379785i | ||||
\(617\) | −16007.4 | − | 9241.85i | −1.04446 | − | 0.603019i | −0.123367 | − | 0.992361i | \(-0.539369\pi\) |
−0.921093 | + | 0.389342i | \(0.872703\pi\) | |||||||
\(618\) | −2794.57 | − | 2745.97i | −0.181900 | − | 0.178737i | ||||
\(619\) | 18080.4 | − | 10438.7i | 1.17401 | − | 0.677817i | 0.219391 | − | 0.975637i | \(-0.429593\pi\) |
0.954622 | + | 0.297820i | \(0.0962596\pi\) | |||||||
\(620\) | −3652.69 | −0.236605 | ||||||||
\(621\) | 25166.9 | − | 7458.46i | 1.62627 | − | 0.481961i | ||||
\(622\) | 1609.10i | 0.103728i | ||||||||
\(623\) | −277.853 | − | 481.255i | −0.0178683 | − | 0.0309488i | ||||
\(624\) | 7889.95 | + | 5002.36i | 0.506171 | + | 0.320921i | ||||
\(625\) | −6180.70 | + | 10705.3i | −0.395565 | + | 0.685139i | ||||
\(626\) | −1877.56 | − | 1084.01i | −0.119876 | − | 0.0692106i | ||||
\(627\) | −12541.5 | − | 3242.85i | −0.798818 | − | 0.206550i | ||||
\(628\) | −9619.35 | − | 16661.2i | −0.611232 | − | 1.05868i | ||||
\(629\) | − | 6447.63i | − | 0.408719i | ||||||
\(630\) | 967.084 | + | 1609.17i | 0.0611580 | + | 0.101763i | ||||
\(631\) | − | 27557.2i | − | 1.73857i | −0.494315 | − | 0.869283i | \(-0.664581\pi\) | ||
0.494315 | − | 0.869283i | \(-0.335419\pi\) | |||||||
\(632\) | −11480.5 | + | 6628.26i | −0.722578 | + | 0.417180i | ||||
\(633\) | −2337.27 | − | 8426.46i | −0.146758 | − | 0.529102i | ||||
\(634\) | −3207.90 | + | 5556.25i | −0.200950 | + | 0.348055i | ||||
\(635\) | 1522.60 | + | 879.074i | 0.0951536 | + | 0.0549370i | ||||
\(636\) | −2947.40 | − | 10626.1i | −0.183761 | − | 0.662506i | ||||
\(637\) | −4898.54 | + | 4429.60i | −0.304690 | + | 0.275522i | ||||
\(638\) | −893.279 | −0.0554314 | ||||||||
\(639\) | −25982.2 | + | 455.847i | −1.60851 | + | 0.0282207i | ||||
\(640\) | 4392.41 | 0.271290 | ||||||||
\(641\) | −3414.43 | − | 5913.96i | −0.210393 | − | 0.364411i | 0.741445 | − | 0.671014i | \(-0.234141\pi\) |
−0.951837 | + | 0.306603i | \(0.900808\pi\) | |||||||
\(642\) | 438.165 | − | 1694.57i | 0.0269361 | − | 0.104174i | ||||
\(643\) | −23813.2 | − | 13748.6i | −1.46050 | − | 0.843220i | −0.461466 | − | 0.887158i | \(-0.652676\pi\) |
−0.999034 | + | 0.0439373i | \(0.986010\pi\) | |||||||
\(644\) | 24519.5 | + | 14156.4i | 1.50032 | + | 0.866210i | ||||
\(645\) | −4629.75 | − | 4549.24i | −0.282630 | − | 0.277715i | ||||
\(646\) | −1003.74 | − | 1738.52i | −0.0611324 | − | 0.105884i | ||||
\(647\) | −10131.7 | −0.615642 | −0.307821 | − | 0.951444i | \(-0.599600\pi\) | ||||
−0.307821 | + | 0.951444i | \(0.599600\pi\) | |||||||
\(648\) | 402.818 | + | 11476.3i | 0.0244200 | + | 0.695727i | ||||
\(649\) | −27625.2 | −1.67085 | ||||||||
\(650\) | −3863.58 | − | 4272.60i | −0.233142 | − | 0.257823i | ||||
\(651\) | 14246.8 | − | 14499.0i | 0.857723 | − | 0.872904i | ||||
\(652\) | −9768.67 | − | 5639.94i | −0.586765 | − | 0.338769i | ||||
\(653\) | 6943.74 | − | 12026.9i | 0.416125 | − | 0.720750i | −0.579421 | − | 0.815029i | \(-0.696721\pi\) |
0.995546 | + | 0.0942789i | \(0.0300545\pi\) | |||||||
\(654\) | −5220.57 | − | 1349.88i | −0.312142 | − | 0.0807104i | ||||
\(655\) | 1241.32 | − | 716.674i | 0.0740492 | − | 0.0427523i | ||||
\(656\) | − | 11791.9i | − | 0.701823i | ||||||
\(657\) | 3467.80 | − | 60.8412i | 0.205924 | − | 0.00361285i | ||||
\(658\) | − | 8899.37i | − | 0.527254i | ||||||
\(659\) | 14739.5 | + | 25529.5i | 0.871272 | + | 1.50909i | 0.860682 | + | 0.509143i | \(0.170038\pi\) |
0.0105903 | + | 0.999944i | \(0.496629\pi\) | |||||||
\(660\) | 956.017 | + | 3446.69i | 0.0563832 | + | 0.203276i | ||||
\(661\) | 5412.48 | + | 3124.90i | 0.318489 | + | 0.183880i | 0.650719 | − | 0.759319i | \(-0.274468\pi\) |
−0.332230 | + | 0.943198i | \(0.607801\pi\) | |||||||
\(662\) | −124.352 | + | 215.385i | −0.00730075 | + | 0.0126453i | ||||
\(663\) | −5500.72 | + | 2878.72i | −0.322218 | + | 0.168628i | ||||
\(664\) | 5463.63 | + | 9463.28i | 0.319322 | + | 0.553082i | ||||
\(665\) | 4885.81i | 0.284908i | ||||||||
\(666\) | 6196.99 | − | 3724.28i | 0.360553 | − | 0.216686i | ||||
\(667\) | 4710.54 | 0.273453 | ||||||||
\(668\) | −241.753 | + | 139.576i | −0.0140025 | + | 0.00808436i | ||||
\(669\) | −478.882 | + | 1852.04i | −0.0276751 | + | 0.107032i | ||||
\(670\) | −845.178 | − | 487.964i | −0.0487344 | − | 0.0281368i | ||||
\(671\) | 4897.86 | + | 2827.78i | 0.281788 | + | 0.162690i | ||||
\(672\) | −13348.8 | + | 13585.1i | −0.766284 | + | 0.779846i | ||||
\(673\) | 12121.5 | + | 20995.1i | 0.694281 | + | 1.20253i | 0.970423 | + | 0.241413i | \(0.0776108\pi\) |
−0.276142 | + | 0.961117i | \(0.589056\pi\) | |||||||
\(674\) | 4261.40i | 0.243535i | ||||||||
\(675\) | −3799.83 | + | 15836.8i | −0.216675 | + | 0.903051i | ||||
\(676\) | −13780.7 | + | 6206.05i | −0.784062 | + | 0.353098i | ||||
\(677\) | 11177.8 | + | 19360.5i | 0.634561 | + | 1.09909i | 0.986608 | + | 0.163110i | \(0.0521526\pi\) |
−0.352047 | + | 0.935983i | \(0.614514\pi\) | |||||||
\(678\) | −1159.51 | − | 1139.35i | −0.0656796 | − | 0.0645374i | ||||
\(679\) | 18649.4 | − | 32301.6i | 1.05404 | − | 1.82566i | ||||
\(680\) | −599.453 | + | 1038.28i | −0.0338059 | + | 0.0585535i | ||||
\(681\) | −741.437 | + | 2867.45i | −0.0417209 | + | 0.161353i | ||||
\(682\) | −5464.22 | + | 3154.77i | −0.306797 | + | 0.177129i | ||||
\(683\) | 21870.4i | 1.22525i | 0.790374 | + | 0.612625i | \(0.209886\pi\) | ||||
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(684\) | −6697.38 | + | 12085.0i | −0.374387 | + | 0.675555i | ||||
\(685\) | 2139.94 | 0.119362 | ||||||||
\(686\) | 2353.28 | + | 4076.01i | 0.130975 | + | 0.226855i | ||||
\(687\) | −24573.9 | + | 6816.12i | −1.36470 | + | 0.378532i | ||||
\(688\) | 8023.71 | − | 13897.5i | 0.444624 | − | 0.770111i | ||||
\(689\) | 13761.7 | + | 4439.04i | 0.760925 | + | 0.245448i | ||||
\(690\) | 821.361 | + | 2961.22i | 0.0453169 | + | 0.163379i | ||||
\(691\) | 14625.0 | − | 8443.76i | 0.805155 | − | 0.464857i | −0.0401154 | − | 0.999195i | \(-0.512773\pi\) |
0.845271 | + | 0.534338i | \(0.179439\pi\) | |||||||
\(692\) | 21144.7 | 1.16156 | ||||||||
\(693\) | −17410.1 | − | 9648.55i | −0.954338 | − | 0.528886i | ||||
\(694\) | 3616.07i | 0.197787i | ||||||||
\(695\) | −5901.62 | + | 3407.30i | −0.322102 | + | 0.185966i | ||||
\(696\) | −515.886 | + | 1995.15i | −0.0280957 | + | 0.108658i | ||||
\(697\) | 6786.62 | + | 3918.26i | 0.368811 | + | 0.212933i | ||||
\(698\) | 1043.40 | − | 1807.22i | 0.0565805 | − | 0.0980003i | ||||
\(699\) | 15384.1 | − | 15656.3i | 0.832444 | − | 0.847177i | ||||
\(700\) | −15213.3 | + | 8783.42i | −0.821443 | + | 0.474260i | ||||
\(701\) | −24493.4 | −1.31969 | −0.659845 | − | 0.751402i | \(-0.729378\pi\) | ||||
−0.659845 | + | 0.751402i | \(0.729378\pi\) | |||||||
\(702\) | −5944.14 | − | 3624.08i | −0.319583 | − | 0.194846i | ||||
\(703\) | 18815.5 | 1.00944 | ||||||||
\(704\) | −3786.30 | + | 2186.02i | −0.202701 | + | 0.117030i | ||||
\(705\) | −4155.28 | + | 4228.82i | −0.221981 | + | 0.225910i | ||||
\(706\) | −74.1453 | + | 128.423i | −0.00395254 | + | 0.00684600i | ||||
\(707\) | 2082.04 | + | 1202.06i | 0.110754 | + | 0.0639439i | ||||
\(708\) | −7376.18 | + | 28526.8i | −0.391545 | + | 1.51427i | ||||
\(709\) | −13980.4 | + | 8071.60i | −0.740544 | + | 0.427553i | −0.822267 | − | 0.569102i | \(-0.807291\pi\) |
0.0817228 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(710\) | − | 3042.26i | − | 0.160809i | ||||||
\(711\) | −19475.7 | + | 11704.6i | −1.02728 | + | 0.617378i | ||||
\(712\) | 397.932 | 0.0209454 | ||||||||
\(713\) | 28814.6 | − | 16636.1i | 1.51348 | − | 0.873811i | ||||
\(714\) | −824.475 | − | 2972.45i | −0.0432146 | − | 0.155800i | ||||
\(715\) | −4463.72 | − | 1439.84i | −0.233474 | − | 0.0753106i | ||||
\(716\) | 11062.3 | − | 19160.4i | 0.577397 | − | 1.00008i | ||||
\(717\) | 28203.7 | − | 7822.93i | 1.46902 | − | 0.407466i | ||||
\(718\) | −5909.35 | − | 10235.3i | −0.307152 | − | 0.532002i | ||||
\(719\) | 8652.54 | 0.448797 | 0.224399 | − | 0.974497i | \(-0.427958\pi\) | ||||
0.224399 | + | 0.974497i | \(0.427958\pi\) | |||||||
\(720\) | 3091.73 | − | 54.2432i | 0.160031 | − | 0.00280767i | ||||
\(721\) | − | 15667.1i | − | 0.809256i | ||||||
\(722\) | −1215.23 | + | 701.613i | −0.0626401 | + | 0.0361653i | ||||
\(723\) | −4505.89 | + | 17426.2i | −0.231778 | + | 0.896385i | ||||
\(724\) | −2203.23 | + | 3816.11i | −0.113097 | + | 0.195891i | ||||
\(725\) | −1461.35 | + | 2531.12i | −0.0748593 | + | 0.129660i | ||||
\(726\) | −815.551 | − | 801.368i | −0.0416914 | − | 0.0409663i | ||||
\(727\) | −3548.36 | − | 6145.94i | −0.181020 | − | 0.313535i | 0.761208 | − | 0.648507i | \(-0.224606\pi\) |
−0.942228 | + | 0.334972i | \(0.891273\pi\) | |||||||
\(728\) | −3410.71 | − | 15879.7i | −0.173639 | − | 0.808434i | ||||
\(729\) | 1035.41 | + | 19655.7i | 0.0526041 | + | 0.998615i | ||||
\(730\) | 406.046i | 0.0205869i | ||||||||
\(731\) | 5332.30 | + | 9235.82i | 0.269798 | + | 0.467304i | ||||
\(732\) | 4227.85 | − | 4302.67i | 0.213478 | − | 0.217256i | ||||
\(733\) | −13381.0 | − | 7725.52i | −0.674268 | − | 0.389289i | 0.123424 | − | 0.992354i | \(-0.460612\pi\) |
−0.797692 | + | 0.603065i | \(0.793946\pi\) | |||||||
\(734\) | 10056.1 | + | 5805.90i | 0.505692 | + | 0.291961i | ||||
\(735\) | −547.238 | + | 2116.40i | −0.0274629 | + | 0.106211i | ||||
\(736\) | −26998.3 | + | 15587.5i | −1.35214 | + | 0.780656i | ||||
\(737\) | 10347.1 | 0.517150 | ||||||||
\(738\) | 154.148 | + | 8786.06i | 0.00768870 | + | 0.438238i | ||||
\(739\) | − | 22224.1i | − | 1.10626i | −0.833095 | − | 0.553130i | \(-0.813433\pi\) | ||
0.833095 | − | 0.553130i | \(-0.186567\pi\) | |||||||
\(740\) | −2597.64 | − | 4499.24i | −0.129042 | − | 0.223507i | ||||
\(741\) | −8400.68 | − | 16052.2i | −0.416473 | − | 0.795806i | ||||
\(742\) | −3592.19 | + | 6221.86i | −0.177727 | + | 0.307832i | ||||
\(743\) | −7680.96 | − | 4434.61i | −0.379256 | − | 0.218964i | 0.298239 | − | 0.954491i | \(-0.403601\pi\) |
−0.677495 | + | 0.735528i | \(0.736934\pi\) | |||||||
\(744\) | 3890.53 | + | 14026.4i | 0.191712 | + | 0.691171i | ||||
\(745\) | 2079.62 | + | 3602.00i | 0.102270 | + | 0.177137i | ||||
\(746\) | 9562.12i | 0.469295i | ||||||||
\(747\) | 9648.00 | + | 16053.7i | 0.472560 | + | 0.786312i | ||||
\(748\) | − | 5876.86i | − | 0.287272i | ||||||
\(749\) | 6061.48 | − | 3499.60i | 0.295703 | − | 0.170724i | ||||
\(750\) | −3833.69 | − | 991.277i | −0.186649 | − | 0.0482618i | ||||
\(751\) | 383.719 | − | 664.620i | 0.0186446 | − | 0.0322934i | −0.856553 | − | 0.516060i | \(-0.827398\pi\) |
0.875197 | + | 0.483766i | \(0.160732\pi\) | |||||||
\(752\) | −12694.0 | − | 7328.87i | −0.615561 | − | 0.355394i | ||||
\(753\) | 8171.72 | − | 8316.34i | 0.395477 | − | 0.402476i | ||||
\(754\) | −837.952 | − | 926.662i | −0.0404727 | − | 0.0447573i | ||||
\(755\) | −23.2458 | −0.00112053 | ||||||||
\(756\) | −14612.1 | + | 15402.1i | −0.702960 | + | 0.740965i | ||||
\(757\) | −17502.4 | −0.840338 | −0.420169 | − | 0.907446i | \(-0.638029\pi\) | ||||
−0.420169 | + | 0.907446i | \(0.638029\pi\) | |||||||
\(758\) | −238.055 | − | 412.324i | −0.0114071 | − | 0.0197576i | ||||
\(759\) | −23239.5 | − | 22835.4i | −1.11138 | − | 1.09206i | ||||
\(760\) | −3029.92 | − | 1749.32i | −0.144614 | − | 0.0834929i | ||||
\(761\) | −10784.3 | − | 6226.29i | −0.513704 | − | 0.296587i | 0.220651 | − | 0.975353i | \(-0.429182\pi\) |
−0.734355 | + | 0.678766i | \(0.762515\pi\) | |||||||
\(762\) | 810.898 | − | 3136.09i | 0.0385508 | − | 0.149093i | ||||
\(763\) | −10781.4 | − | 18674.0i | −0.511552 | − | 0.886034i | ||||
\(764\) | −34037.6 | −1.61183 | ||||||||
\(765\) | −996.113 | + | 1797.42i | −0.0470779 | + | 0.0849486i | ||||
\(766\) | 507.928 | 0.0239585 | ||||||||
\(767\) | −25914.2 | − | 28657.6i | −1.21996 | − | 1.34911i | ||||
\(768\) | −713.551 | − | 2572.53i | −0.0335261 | − | 0.120870i | ||||
\(769\) | −4732.06 | − | 2732.05i | −0.221902 | − | 0.128115i | 0.384929 | − | 0.922946i | \(-0.374226\pi\) |
−0.606830 | + | 0.794831i | \(0.707559\pi\) | |||||||
\(770\) | 1165.16 | − | 2018.12i | 0.0545318 | − | 0.0944518i | ||||
\(771\) | −1150.76 | − | 4148.80i | −0.0537533 | − | 0.193794i | ||||
\(772\) | 9755.52 | − | 5632.35i | 0.454804 | − | 0.262581i | ||||
\(773\) | − | 6462.28i | − | 0.300688i | −0.988634 | − | 0.150344i | \(-0.951962\pi\) | ||
0.988634 | − | 0.150344i | \(-0.0480382\pi\) | |||||||
\(774\) | −5796.74 | + | 10459.8i | −0.269199 | + | 0.485750i | ||||
\(775\) | 20644.0i | 0.956843i | ||||||||
\(776\) | 13354.5 | + | 23130.6i | 0.617781 | + | 1.07003i | ||||
\(777\) | 27991.1 | + | 7237.65i | 1.29237 | + | 0.334169i | ||||
\(778\) | −9400.24 | − | 5427.23i | −0.433181 | − | 0.250097i | ||||
\(779\) | −11434.2 | + | 19804.7i | −0.525898 | + | 0.910881i | ||||
\(780\) | −2678.69 | + | 4224.96i | −0.122965 | + | 0.193946i | ||||
\(781\) | 16127.5 | + | 27933.7i | 0.738910 | + | 1.27983i | ||||
\(782\) | − | 5049.10i | − | 0.230889i | ||||||
\(783\) | −824.127 | + | 3434.77i | −0.0376142 | + | 0.156767i | ||||
\(784\) | −5404.57 | −0.246199 | ||||||||
\(785\) | 7231.43 | − | 4175.07i | 0.328791 | − | 0.189828i | ||||
\(786\) | −1883.65 | − | 1850.89i | −0.0854802 | − | 0.0839936i | ||||
\(787\) | −2077.58 | − | 1199.49i | −0.0941011 | − | 0.0543293i | 0.452211 | − | 0.891911i | \(-0.350635\pi\) |
−0.546312 | + | 0.837582i | \(0.683969\pi\) | |||||||
\(788\) | 24896.6 | + | 14374.1i | 1.12552 | + | 0.649816i | ||||
\(789\) | −4105.72 | − | 1061.62i | −0.185257 | − | 0.0479018i | ||||
\(790\) | −1330.08 | − | 2303.76i | −0.0599012 | − | 0.103752i | ||||
\(791\) | − | 6500.53i | − | 0.292203i | ||||||
\(792\) | 12217.1 | − | 7342.24i | 0.548124 | − | 0.329413i | ||||
\(793\) | 1661.04 | + | 7733.54i | 0.0743826 | + | 0.346313i | ||||
\(794\) | −4325.87 | − | 7492.62i | −0.193349 | − | 0.334891i | ||||
\(795\) | 4612.04 | − | 1279.26i | 0.205751 | − | 0.0570698i | ||||
\(796\) | 7785.83 | − | 13485.4i | 0.346685 | − | 0.600476i | ||||
\(797\) | −6419.66 | + | 11119.2i | −0.285315 | + | 0.494180i | −0.972685 | − | 0.232127i | \(-0.925432\pi\) |
0.687371 | + | 0.726307i | \(0.258765\pi\) | |||||||
\(798\) | 8674.18 | − | 2405.98i | 0.384790 | − | 0.106730i | ||||
\(799\) | 8436.01 | − | 4870.53i | 0.373523 | − | 0.215653i | ||||
\(800\) | − | 19342.7i | − | 0.854837i | ||||||
\(801\) | 681.968 | − | 11.9649i | 0.0300826 | − | 0.000527787i | ||||
\(802\) | 7035.23 | 0.309754 | ||||||||
\(803\) | −2152.52 | − | 3728.27i | −0.0945961 | − | 0.163845i | ||||
\(804\) | 2762.77 | − | 10684.8i | 0.121188 | − | 0.468686i | ||||
\(805\) | −6144.26 | + | 10642.2i | −0.269015 | + | 0.465947i | ||||
\(806\) | −8398.45 | − | 2709.05i | −0.367026 | − | 0.118390i | ||||
\(807\) | 25336.9 | − | 25785.3i | 1.10521 | − | 1.12477i | ||||
\(808\) | −1490.91 | + | 860.778i | −0.0649135 | + | 0.0374778i | ||||
\(809\) | 13578.8 | 0.590118 | 0.295059 | − | 0.955479i | \(-0.404661\pi\) | ||||
0.295059 | + | 0.955479i | \(0.404661\pi\) | |||||||
\(810\) | −2302.92 | + | 80.8325i | −0.0998967 | + | 0.00350637i | ||||
\(811\) | − | 24459.3i | − | 1.05904i | −0.848297 | − | 0.529520i | \(-0.822372\pi\) | ||
0.848297 | − | 0.529520i | \(-0.177628\pi\) | |||||||
\(812\) | −3299.54 | + | 1904.99i | −0.142600 | + | 0.0823302i | ||||
\(813\) | 3316.14 | + | 3258.47i | 0.143053 | + | 0.140565i | ||||
\(814\) | −7771.85 | − | 4487.08i | −0.334648 | − | 0.193209i | ||||
\(815\) | 2447.89 | − | 4239.88i | 0.105210 | − | 0.182229i | ||||
\(816\) | −4918.85 | − | 1271.87i | −0.211022 | − | 0.0545640i | ||||
\(817\) | −26951.9 | + | 15560.7i | −1.15414 | + | 0.666341i | ||||
\(818\) | −8081.62 | −0.345437 | ||||||||
\(819\) | −6322.67 | − | 27111.7i | −0.269758 | − | 1.15673i | ||||
\(820\) | 6314.39 | 0.268912 | ||||||||
\(821\) | 445.705 | − | 257.328i | 0.0189467 | − | 0.0109389i | −0.490497 | − | 0.871443i | \(-0.663185\pi\) |
0.509443 | + | 0.860504i | \(0.329851\pi\) | |||||||
\(822\) | −1053.80 | − | 3799.22i | −0.0447147 | − | 0.161208i | ||||
\(823\) | −9356.12 | + | 16205.3i | −0.396275 | + | 0.686368i | −0.993263 | − | 0.115882i | \(-0.963031\pi\) |
0.596988 | + | 0.802250i | \(0.296364\pi\) | |||||||
\(824\) | 9715.90 | + | 5609.48i | 0.410764 | + | 0.237155i | ||||
\(825\) | 19479.7 | − | 5403.15i | 0.822057 | − | 0.228016i | ||||
\(826\) | 16624.8 | − | 9598.34i | 0.700304 | − | 0.404321i | ||||
\(827\) | − | 34355.1i | − | 1.44455i | −0.691606 | − | 0.722275i | \(-0.743096\pi\) | ||
0.691606 | − | 0.722275i | \(-0.256904\pi\) | |||||||
\(828\) | −29785.8 | + | 17900.8i | −1.25016 | + | 0.751322i | ||||
\(829\) | 21054.6 | 0.882097 | 0.441048 | − | 0.897483i | \(-0.354607\pi\) | ||||
0.441048 | + | 0.897483i | \(0.354607\pi\) | |||||||
\(830\) | −1898.97 | + | 1096.37i | −0.0794148 | + | 0.0458502i | ||||
\(831\) | −20897.9 | − | 5403.58i | −0.872373 | − | 0.225569i | ||||
\(832\) | −5819.51 | − | 1877.17i | −0.242494 | − | 0.0782203i | ||||
\(833\) | 1795.85 | − | 3110.51i | 0.0746970 | − | 0.129379i | ||||
\(834\) | 8955.46 | + | 8799.72i | 0.371825 | + | 0.365359i | ||||
\(835\) | −60.5799 | − | 104.927i | −0.00251072 | − | 0.00434870i | ||||
\(836\) | 17149.8 | 0.709496 | ||||||||
\(837\) | 7089.26 | + | 23921.1i | 0.292761 | + | 0.987856i | ||||
\(838\) | 2973.24i | 0.122564i | ||||||||
\(839\) | 4813.48 | − | 2779.06i | 0.198069 | − | 0.114355i | −0.397686 | − | 0.917522i | \(-0.630186\pi\) |
0.595754 | + | 0.803167i | \(0.296853\pi\) | |||||||
\(840\) | −3834.60 | − | 3767.91i | −0.157507 | − | 0.154768i | ||||
\(841\) | 11877.6 | − | 20572.5i | 0.487005 | − | 0.843517i | ||||
\(842\) | 636.731 | − | 1102.85i | 0.0260608 | − | 0.0451386i | ||||
\(843\) | 5133.86 | − | 19854.8i | 0.209750 | − | 0.811194i | ||||
\(844\) | 5788.51 | + | 10026.0i | 0.236077 | + | 0.408897i | ||||
\(845\) | −2693.60 | − | 5981.20i | −0.109660 | − | 0.243502i | ||||
\(846\) | 9554.00 | + | 5294.75i | 0.388266 | + | 0.215174i | ||||
\(847\) | − | 4572.19i | − | 0.185481i | ||||||
\(848\) | 5916.53 | + | 10247.7i | 0.239593 | + | 0.414987i | ||||
\(849\) | 9004.79 | + | 32464.6i | 0.364009 | + | 1.31235i | ||||
\(850\) | 2713.04 | + | 1566.37i | 0.109478 | + | 0.0632073i | ||||
\(851\) | 40983.5 | + | 23661.8i | 1.65088 | + | 0.953134i | ||||
\(852\) | 33151.6 | − | 9195.35i | 1.33305 | − | 0.369750i | ||||
\(853\) | 41291.1 | − | 23839.4i | 1.65742 | − | 0.956913i | 0.683523 | − | 0.729929i | \(-0.260447\pi\) |
0.973899 | − | 0.226984i | \(-0.0728865\pi\) | |||||||
\(854\) | −3930.03 | −0.157474 | ||||||||
\(855\) | −5245.21 | − | 2906.85i | −0.209804 | − | 0.116272i | ||||
\(856\) | 5012.00i | 0.200125i | ||||||||
\(857\) | −10038.1 | − | 17386.5i | −0.400111 | − | 0.693013i | 0.593628 | − | 0.804740i | \(-0.297695\pi\) |
−0.993739 | + | 0.111727i | \(0.964362\pi\) | |||||||
\(858\) | −358.146 | + | 8633.85i | −0.0142505 | + | 0.343537i | ||||
\(859\) | −2884.88 | + | 4996.76i | −0.114588 | + | 0.198472i | −0.917615 | − | 0.397471i | \(-0.869888\pi\) |
0.803027 | + | 0.595942i | \(0.203221\pi\) | |||||||
\(860\) | 7441.90 | + | 4296.58i | 0.295078 | + | 0.170363i | ||||
\(861\) | −24628.5 | + | 25064.4i | −0.974839 | + | 0.992092i | ||||
\(862\) | −7162.33 | − | 12405.5i | −0.283004 | − | 0.490178i | ||||
\(863\) | 43267.2i | 1.70664i | 0.521384 | + | 0.853322i | \(0.325416\pi\) | ||||
−0.521384 | + | 0.853322i | \(0.674584\pi\) | |||||||
\(864\) | −6642.41 | − | 22413.3i | −0.261550 | − | 0.882543i | ||||
\(865\) | 9177.38i | 0.360740i | ||||||||
\(866\) | 11.8107 | − | 6.81893i | 0.000463447 | − | 0.000267571i | ||||
\(867\) | −15526.0 | + | 15800.8i | −0.608180 | + | 0.618943i | ||||
\(868\) | −13455.6 | + | 23305.8i | −0.526167 | + | 0.911349i | ||||
\(869\) | 24425.2 | + | 14101.9i | 0.953472 | + | 0.550488i | ||||
\(870\) | −400.362 | − | 103.522i | −0.0156018 | − | 0.00403415i | ||||
\(871\) | 9706.23 | + | 10733.8i | 0.377592 | + | 0.417566i | ||||
\(872\) | 15440.8 | 0.599646 | ||||||||
\(873\) | 23582.1 | + | 39239.3i | 0.914244 | + | 1.52125i | ||||
\(874\) | 14734.3 | 0.570244 | ||||||||
\(875\) | −7917.27 | − | 13713.1i | −0.305889 | − | 0.529815i | ||||
\(876\) | −4424.69 | + | 1227.29i | −0.170658 | + | 0.0473359i | ||||
\(877\) | 35632.3 | + | 20572.3i | 1.37197 | + | 0.792106i | 0.991176 | − | 0.132555i | \(-0.0423180\pi\) |
0.380792 | + | 0.924661i | \(0.375651\pi\) | |||||||
\(878\) | −5507.50 | − | 3179.75i | −0.211696 | − | 0.122223i | ||||
\(879\) | −38814.2 | + | 10766.0i | −1.48939 | + | 0.413116i | ||||
\(880\) | −1919.08 | − | 3323.95i | −0.0735140 | − | 0.127330i | ||||
\(881\) | 26874.7 | 1.02773 | 0.513867 | − | 0.857870i | \(-0.328213\pi\) | ||||
0.513867 | + | 0.857870i | \(0.328213\pi\) | |||||||
\(882\) | 4026.91 | − | 70.6505i | 0.153734 | − | 0.00269720i | ||||
\(883\) | −27154.5 | −1.03491 | −0.517454 | − | 0.855711i | \(-0.673120\pi\) | ||||
−0.517454 | + | 0.855711i | \(0.673120\pi\) | |||||||
\(884\) | 6096.48 | − | 5512.86i | 0.231954 | − | 0.209749i | ||||
\(885\) | −12381.5 | − | 3201.47i | −0.470280 | − | 0.121600i | ||||
\(886\) | 9942.74 | + | 5740.44i | 0.377012 | + | 0.217668i | ||||
\(887\) | 1238.16 | − | 2144.56i | 0.0468697 | − | 0.0811807i | −0.841639 | − | 0.540041i | \(-0.818409\pi\) |
0.888508 | + | 0.458860i | \(0.151742\pi\) | |||||||
\(888\) | −14510.4 | + | 14767.2i | −0.548352 | + | 0.558057i | ||||
\(889\) | 11217.8 | − | 6476.59i | 0.423209 | − | 0.244340i | ||||
\(890\) | 79.8519i | 0.00300746i | ||||||||
\(891\) | 20716.6 | − | 12950.3i | 0.778937 | − | 0.486927i | ||||
\(892\) | − | 2532.57i | − | 0.0950635i | ||||||
\(893\) | 14213.2 | + | 24617.9i | 0.532615 | + | 0.922517i | ||||
\(894\) | 5370.84 | − | 5465.89i | 0.200926 | − | 0.204482i | ||||
\(895\) | 8316.17 | + | 4801.34i | 0.310591 | + | 0.179320i | ||||
\(896\) | 16180.6 | − | 28025.6i | 0.603299 | − | 1.04494i | ||||
\(897\) | 1888.62 | − | 45529.0i | 0.0703000 | − | 1.69473i | ||||
\(898\) | −5028.11 | − | 8708.94i | −0.186849 | − | 0.323631i | ||||
\(899\) | 4477.37i | 0.166105i | ||||||||
\(900\) | −378.230 | − | 21558.2i | −0.0140085 | − | 0.798452i | ||||
\(901\) | −7863.88 | −0.290770 | ||||||||
\(902\) | 9445.98 | − | 5453.64i | 0.348688 | − | 0.201315i | ||||
\(903\) | −46081.1 | + | 12781.6i | −1.69821 | + | 0.471037i | ||||
\(904\) | 4031.28 | + | 2327.46i | 0.148317 | + | 0.0856307i | ||||
\(905\) | −1656.30 | − | 956.266i | −0.0608368 | − | 0.0351242i | ||||
\(906\) | 11.4472 | + | 41.2702i | 0.000419767 | + | 0.00151337i | ||||
\(907\) | 8773.74 | + | 15196.6i | 0.321199 | + | 0.556333i | 0.980736 | − | 0.195340i | \(-0.0625809\pi\) |
−0.659537 | + | 0.751672i | \(0.729248\pi\) | |||||||
\(908\) | − | 3921.09i | − | 0.143310i | ||||||
\(909\) | −2529.22 | + | 1520.01i | −0.0922869 | + | 0.0554628i | ||||
\(910\) | 3186.53 | − | 684.418i | 0.116080 | − | 0.0249321i | ||||
\(911\) | −10956.4 | − | 18977.1i | −0.398466 | − | 0.690163i | 0.595071 | − | 0.803673i | \(-0.297124\pi\) |
−0.993537 | + | 0.113510i | \(0.963791\pi\) | |||||||
\(912\) | 3711.55 | − | 14354.2i | 0.134761 | − | 0.521177i | ||||
\(913\) | 11624.1 | − | 20133.5i | 0.421359 | − | 0.729816i | ||||
\(914\) | 598.014 | − | 1035.79i | 0.0216417 | − | 0.0374846i | ||||
\(915\) | 1867.48 | + | 1835.00i | 0.0674722 | + | 0.0662988i | ||||
\(916\) | 29238.6 | − | 16880.9i | 1.05466 | − | 0.608909i | ||||
\(917\) | − | 10560.2i | − | 0.380294i | ||||||
\(918\) | 3681.63 | + | 883.358i | 0.132366 | + | 0.0317594i | ||||
\(919\) | 25117.1 | 0.901564 | 0.450782 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450782 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(920\) | −4399.80 | − | 7620.68i | −0.157671 | − | 0.273094i | ||||
\(921\) | −18820.3 | − | 18493.0i | −0.673346 | − | 0.661636i | ||||
\(922\) | 304.520 | − | 527.445i | 0.0108773 | − | 0.0188400i | ||||
\(923\) | −13849.0 | + | 42933.8i | −0.493873 | + | 1.53108i | ||||
\(924\) | 25513.2 | + | 6596.94i | 0.908357 | + | 0.234874i | ||||
\(925\) | −25428.5 | + | 14681.1i | −0.903874 | + | 0.521852i | ||||
\(926\) | 10322.1 | 0.366314 | ||||||||
\(927\) | 16819.6 | + | 9321.28i | 0.595931 | + | 0.330260i | ||||
\(928\) | − | 4195.15i | − | 0.148397i | ||||||
\(929\) | −36305.4 | + | 20960.9i | −1.28217 | + | 0.740264i | −0.977246 | − | 0.212111i | \(-0.931966\pi\) |
−0.304929 | + | 0.952375i | \(0.598633\pi\) | |||||||
\(930\) | −2814.63 | + | 780.703i | −0.0992425 | + | 0.0275272i | ||||
\(931\) | 9077.07 | + | 5240.65i | 0.319537 | + | 0.184485i | ||||
\(932\) | −14529.7 | + | 25166.1i | −0.510660 | + | 0.884489i | ||||
\(933\) | −2110.92 | − | 7610.39i | −0.0740710 | − | 0.267045i | ||||
\(934\) | 17955.7 | − | 10366.7i | 0.629046 | − | 0.363180i | ||||
\(935\) | 2550.72 | 0.0892166 | ||||||||
\(936\) | 19077.0 | + | 5786.14i | 0.666187 | + | 0.202058i | ||||
\(937\) | −29338.8 | −1.02290 | −0.511449 | − | 0.859314i | \(-0.670891\pi\) | ||||
−0.511449 | + | 0.859314i | \(0.670891\pi\) | |||||||
\(938\) | −6226.86 | + | 3595.08i | −0.216753 | + | 0.125142i | ||||
\(939\) | 10302.2 | + | 2663.84i | 0.358041 | + | 0.0925786i | ||||
\(940\) | 3924.51 | − | 6797.44i | 0.136174 | − | 0.235860i | ||||
\(941\) | −11792.9 | − | 6808.65i | −0.408543 | − | 0.235872i | 0.281621 | − | 0.959526i | \(-0.409128\pi\) |
−0.690163 | + | 0.723654i | \(0.742461\pi\) | |||||||
\(942\) | −10973.4 | − | 10782.6i | −0.379547 | − | 0.372946i | ||||
\(943\) | −49811.7 | + | 28758.8i | −1.72014 | + | 0.993123i | ||||
\(944\) | − | 31618.0i | − | 1.09012i | ||||||
\(945\) | −6684.95 | − | 6342.08i | −0.230118 | − | 0.218315i | ||||
\(946\) | 14843.6 | 0.510155 | ||||||||
\(947\) | −33617.0 | + | 19408.8i | −1.15354 | + | 0.665999i | −0.949748 | − | 0.313014i | \(-0.898661\pi\) |
−0.203796 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(948\) | 21083.9 | − | 21457.0i | 0.722334 | − | 0.735118i | ||||
\(949\) | 1848.40 | − | 5730.31i | 0.0632262 | − | 0.196010i | ||||
\(950\) | −4570.99 | + | 7917.18i | −0.156108 | + | 0.270387i | ||||
\(951\) | 7883.08 | − | 30487.2i | 0.268797 | − | 1.03955i | ||||
\(952\) | 4416.49 | + | 7649.58i | 0.150356 | + | 0.260425i | ||||
\(953\) | 27409.9 | 0.931684 | 0.465842 | − | 0.884868i | \(-0.345752\pi\) | ||||
0.465842 | + | 0.884868i | \(0.345752\pi\) | |||||||
\(954\) | −4542.33 | − | 7558.18i | −0.154155 | − | 0.256504i | ||||
\(955\) | − | 14773.3i | − | 0.500578i | ||||||
\(956\) | −33557.4 | + | 19374.4i | −1.13528 | + | 0.655452i | ||||
\(957\) | 4224.86 | − | 1171.86i | 0.142707 | − | 0.0395830i | ||||
\(958\) | 6640.62 | − | 11501.9i | 0.223955 | − | 0.387901i | ||||
\(959\) | 7883.04 | − | 13653.8i | 0.265440 | − | 0.459755i | ||||
\(960\) | −1950.34 | + | 540.970i | −0.0655696 | + | 0.0181872i | ||||
\(961\) | 917.102 | + | 1588.47i | 0.0307845 | + | 0.0533204i | ||||
\(962\) | −2635.72 | − | 12271.5i | −0.0883358 | − | 0.411277i | ||||
\(963\) | 150.699 | + | 8589.48i | 0.00504279 | + | 0.287427i | ||||
\(964\) | − | 23829.4i | − | 0.796154i | ||||||
\(965\) | 2444.60 | + | 4234.17i | 0.0815487 | + | 0.141247i | ||||
\(966\) | 21919.6 | + | 5667.75i | 0.730075 | + | 0.188775i | ||||
\(967\) | −24181.4 | − | 13961.2i | −0.804160 | − | 0.464282i | 0.0407640 | − | 0.999169i | \(-0.487021\pi\) |
−0.844924 | + | 0.534887i | \(0.820354\pi\) | |||||||
\(968\) | 2835.43 | + | 1637.04i | 0.0941468 | + | 0.0543557i | ||||
\(969\) | 7028.00 | + | 6905.78i | 0.232995 | + | 0.228943i | ||||
\(970\) | −4641.57 | + | 2679.81i | −0.153641 | + | 0.0887046i | ||||
\(971\) | 6448.83 | 0.213134 | 0.106567 | − | 0.994306i | \(-0.466014\pi\) | ||||
0.106567 | + | 0.994306i | \(0.466014\pi\) | |||||||
\(972\) | −7841.48 | − | 24850.6i | −0.258761 | − | 0.820045i | ||||
\(973\) | 50206.7i | 1.65422i | ||||||||
\(974\) | −9024.52 | − | 15630.9i | −0.296883 | − | 0.514217i | ||||
\(975\) | 23878.3 | + | 15139.2i | 0.784325 | + | 0.497275i | ||||
\(976\) | −3236.49 | + | 5605.76i | −0.106145 | + | 0.183848i | ||||
\(977\) | −42803.1 | − | 24712.4i | −1.40163 | − | 0.809231i | −0.407069 | − | 0.913398i | \(-0.633449\pi\) |
−0.994560 | + | 0.104167i | \(0.966782\pi\) | |||||||
\(978\) | −8732.85 | − | 2258.05i | −0.285527 | − | 0.0738287i | ||||
\(979\) | −423.308 | − | 733.190i | −0.0138192 | − | 0.0239355i | ||||
\(980\) | − | 2894.07i | − | 0.0943344i | ||||||
\(981\) | 26462.1 | − | 464.268i | 0.861235 | − | 0.0151100i | ||||
\(982\) | 22314.5i | 0.725136i | ||||||||
\(983\) | −20226.0 | + | 11677.5i | −0.656267 | + | 0.378896i | −0.790853 | − | 0.612006i | \(-0.790363\pi\) |
0.134586 | + | 0.990902i | \(0.457029\pi\) | |||||||
\(984\) | −6725.55 | − | 24247.3i | −0.217889 | − | 0.785546i | ||||
\(985\) | −6238.76 | + | 10805.8i | −0.201811 | + | 0.349546i | ||||
\(986\) | 588.417 | + | 339.723i | 0.0190051 | + | 0.0109726i | ||||
\(987\) | 11674.8 | + | 42090.5i | 0.376507 | + | 1.35740i | ||||
\(988\) | 16087.6 | + | 17790.7i | 0.518032 | + | 0.572873i | ||||
\(989\) | −78274.9 | −2.51668 | ||||||||
\(990\) | 1473.35 | + | 2451.57i | 0.0472991 | + | 0.0787029i | ||||
\(991\) | −24295.3 | −0.778774 | −0.389387 | − | 0.921074i | \(-0.627313\pi\) | ||||
−0.389387 | + | 0.921074i | \(0.627313\pi\) | |||||||
\(992\) | −14815.9 | − | 25661.9i | −0.474199 | − | 0.821337i | ||||
\(993\) | 305.583 | − | 1181.82i | 0.00976574 | − | 0.0377683i | ||||
\(994\) | −19411.0 | − | 11207.0i | −0.619397 | − | 0.357609i | ||||
\(995\) | 5853.07 | + | 3379.27i | 0.186487 | + | 0.107668i | ||||
\(996\) | −17686.9 | − | 17379.3i | −0.562681 | − | 0.552896i | ||||
\(997\) | −27593.8 | − | 47793.8i | −0.876533 | − | 1.51820i | −0.855121 | − | 0.518429i | \(-0.826517\pi\) |
−0.0214124 | − | 0.999771i | \(-0.506816\pi\) | |||||||
\(998\) | −21118.7 | −0.669842 | ||||||||
\(999\) | −24423.6 | + | 25744.0i | −0.773502 | + | 0.815320i |
(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 | 117.4.t.a.103.18 | yes | 80 | |
3.2 | odd | 2 | 351.4.t.a.64.23 | 80 | |||
9.2 | odd | 6 | 351.4.t.a.181.18 | 80 | |||
9.7 | even | 3 | inner | 117.4.t.a.25.23 | yes | 80 | |
13.12 | even | 2 | inner | 117.4.t.a.103.23 | yes | 80 | |
39.38 | odd | 2 | 351.4.t.a.64.18 | 80 | |||
117.25 | even | 6 | inner | 117.4.t.a.25.18 | ✓ | 80 | |
117.38 | odd | 6 | 351.4.t.a.181.23 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.t.a.25.18 | ✓ | 80 | 117.25 | even | 6 | inner | |
117.4.t.a.25.23 | yes | 80 | 9.7 | even | 3 | inner | |
117.4.t.a.103.18 | yes | 80 | 1.1 | even | 1 | trivial | |
117.4.t.a.103.23 | yes | 80 | 13.12 | even | 2 | inner | |
351.4.t.a.64.18 | 80 | 39.38 | odd | 2 | |||
351.4.t.a.64.23 | 80 | 3.2 | odd | 2 | |||
351.4.t.a.181.18 | 80 | 9.2 | odd | 6 | |||
351.4.t.a.181.23 | 80 | 117.38 | odd | 6 |