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 | 103.11 | ||
Character | \(\chi\) | \(=\) | 117.103 |
Dual form | 117.4.t.a.25.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63673 | + | 1.52232i | −0.932224 | + | 0.538220i | −0.887514 | − | 0.460780i | \(-0.847570\pi\) |
−0.0447100 | + | 0.999000i | \(0.514236\pi\) | |||||||
\(3\) | 0.490546 | + | 5.17295i | 0.0944055 | + | 0.995534i | ||||
\(4\) | 0.634892 | − | 1.09966i | 0.0793615 | − | 0.137458i | ||||
\(5\) | −4.80701 | − | 2.77533i | −0.429952 | − | 0.248233i | 0.269374 | − | 0.963036i | \(-0.413183\pi\) |
−0.699326 | + | 0.714802i | \(0.746517\pi\) | |||||||
\(6\) | −9.16829 | − | 12.8929i | −0.623823 | − | 0.877250i | ||||
\(7\) | −8.73788 | + | 5.04482i | −0.471801 | + | 0.272395i | −0.716993 | − | 0.697080i | \(-0.754482\pi\) |
0.245192 | + | 0.969474i | \(0.421149\pi\) | |||||||
\(8\) | − | 20.4910i | − | 0.905584i | ||||||
\(9\) | −26.5187 | + | 5.07513i | −0.982175 | + | 0.187968i | ||||
\(10\) | 16.8997 | 0.534416 | ||||||||
\(11\) | 13.9366 | − | 8.04628i | 0.382003 | − | 0.220549i | −0.296686 | − | 0.954975i | \(-0.595882\pi\) |
0.678689 | + | 0.734425i | \(0.262548\pi\) | |||||||
\(12\) | 5.99995 | + | 2.74482i | 0.144336 | + | 0.0660302i | ||||
\(13\) | −46.8593 | − | 1.09731i | −0.999726 | − | 0.0234106i | ||||
\(14\) | 15.3596 | − | 26.6036i | 0.293216 | − | 0.507866i | ||||
\(15\) | 11.9986 | − | 26.2279i | 0.206535 | − | 0.451467i | ||||
\(16\) | 36.2730 | + | 62.8266i | 0.566765 | + | 0.981666i | ||||
\(17\) | 68.7556 | 0.980923 | 0.490461 | − | 0.871463i | \(-0.336828\pi\) | ||||
0.490461 | + | 0.871463i | \(0.336828\pi\) | |||||||
\(18\) | 62.1967 | − | 53.7516i | 0.814440 | − | 0.703854i | ||||
\(19\) | 7.26478i | 0.0877187i | 0.999038 | + | 0.0438593i | \(0.0139653\pi\) | ||||
−0.999038 | + | 0.0438593i | \(0.986035\pi\) | |||||||
\(20\) | −6.10387 | + | 3.52407i | −0.0682433 | + | 0.0394003i | ||||
\(21\) | −30.3829 | − | 42.7259i | −0.315719 | − | 0.443978i | ||||
\(22\) | −24.4980 | + | 42.4317i | −0.237408 | + | 0.411203i | ||||
\(23\) | 59.2055 | − | 102.547i | 0.536748 | − | 0.929674i | −0.462329 | − | 0.886709i | \(-0.652986\pi\) |
0.999077 | − | 0.0429658i | \(-0.0136806\pi\) | |||||||
\(24\) | 105.999 | − | 10.0518i | 0.901540 | − | 0.0854922i | ||||
\(25\) | −47.0951 | − | 81.5711i | −0.376761 | − | 0.652568i | ||||
\(26\) | 125.226 | − | 68.4414i | 0.944569 | − | 0.516249i | ||||
\(27\) | −39.2620 | − | 134.690i | −0.279851 | − | 0.960043i | ||||
\(28\) | 12.8116i | 0.0864705i | ||||||||
\(29\) | −69.2119 | − | 119.879i | −0.443184 | − | 0.767617i | 0.554740 | − | 0.832024i | \(-0.312818\pi\) |
−0.997924 | + | 0.0644070i | \(0.979484\pi\) | |||||||
\(30\) | 8.29009 | + | 87.4214i | 0.0504519 | + | 0.532029i | ||||
\(31\) | −5.73632 | − | 3.31187i | −0.0332346 | − | 0.0191880i | 0.483291 | − | 0.875460i | \(-0.339441\pi\) |
−0.516525 | + | 0.856272i | \(0.672775\pi\) | |||||||
\(32\) | −49.3179 | − | 28.4737i | −0.272445 | − | 0.157296i | ||||
\(33\) | 48.4595 | + | 68.1460i | 0.255628 | + | 0.359476i | ||||
\(34\) | −181.290 | + | 104.668i | −0.914440 | + | 0.527952i | ||||
\(35\) | 56.0042 | 0.270469 | ||||||||
\(36\) | −11.2556 | + | 32.3839i | −0.0521092 | + | 0.149925i | ||||
\(37\) | 228.565i | 1.01556i | 0.861485 | + | 0.507782i | \(0.169535\pi\) | ||||
−0.861485 | + | 0.507782i | \(0.830465\pi\) | |||||||
\(38\) | −11.0593 | − | 19.1553i | −0.0472119 | − | 0.0817735i | ||||
\(39\) | −17.3103 | − | 242.939i | −0.0710736 | − | 0.997471i | ||||
\(40\) | −56.8694 | + | 98.5007i | −0.224796 | + | 0.389358i | ||||
\(41\) | −213.771 | − | 123.421i | −0.814280 | − | 0.470125i | 0.0341602 | − | 0.999416i | \(-0.489124\pi\) |
−0.848440 | + | 0.529292i | \(0.822458\pi\) | |||||||
\(42\) | 145.154 | + | 66.4041i | 0.533279 | + | 0.243961i | ||||
\(43\) | −48.2284 | − | 83.5341i | −0.171041 | − | 0.296252i | 0.767743 | − | 0.640758i | \(-0.221380\pi\) |
−0.938784 | + | 0.344506i | \(0.888046\pi\) | |||||||
\(44\) | − | 20.4341i | − | 0.0700125i | ||||||
\(45\) | 141.561 | + | 49.2020i | 0.468949 | + | 0.162991i | ||||
\(46\) | 360.518i | 1.15555i | ||||||||
\(47\) | −245.615 | + | 141.806i | −0.762268 | + | 0.440096i | −0.830110 | − | 0.557600i | \(-0.811722\pi\) |
0.0678412 | + | 0.997696i | \(0.478389\pi\) | |||||||
\(48\) | −307.205 | + | 218.457i | −0.923776 | + | 0.656908i | ||||
\(49\) | −120.600 | + | 208.885i | −0.351602 | + | 0.608993i | ||||
\(50\) | 248.354 | + | 143.387i | 0.702451 | + | 0.405560i | ||||
\(51\) | 33.7278 | + | 355.669i | 0.0926046 | + | 0.976542i | ||||
\(52\) | −30.9573 | + | 50.8329i | −0.0825577 | + | 0.135563i | ||||
\(53\) | −214.638 | −0.556279 | −0.278140 | − | 0.960541i | \(-0.589718\pi\) | ||||
−0.278140 | + | 0.960541i | \(0.589718\pi\) | |||||||
\(54\) | 308.565 | + | 295.373i | 0.777599 | + | 0.744354i | ||||
\(55\) | −89.3244 | −0.218991 | ||||||||
\(56\) | 103.374 | + | 179.048i | 0.246676 | + | 0.427256i | ||||
\(57\) | −37.5803 | + | 3.56371i | −0.0873269 | + | 0.00828113i | ||||
\(58\) | 364.986 | + | 210.725i | 0.826293 | + | 0.477061i | ||||
\(59\) | −356.106 | − | 205.598i | −0.785782 | − | 0.453671i | 0.0526937 | − | 0.998611i | \(-0.483219\pi\) |
−0.838475 | + | 0.544939i | \(0.816553\pi\) | |||||||
\(60\) | −21.2240 | − | 29.8463i | −0.0456669 | − | 0.0642189i | ||||
\(61\) | −156.839 | − | 271.653i | −0.329199 | − | 0.570190i | 0.653154 | − | 0.757225i | \(-0.273445\pi\) |
−0.982353 | + | 0.187035i | \(0.940112\pi\) | |||||||
\(62\) | 20.1668 | 0.0413095 | ||||||||
\(63\) | 206.114 | − | 178.128i | 0.412190 | − | 0.356223i | ||||
\(64\) | −406.984 | −0.794890 | ||||||||
\(65\) | 222.208 | + | 135.325i | 0.424023 | + | 0.258231i | ||||
\(66\) | −231.514 | − | 105.912i | −0.431779 | − | 0.197528i | ||||
\(67\) | −164.887 | − | 95.1974i | −0.300659 | − | 0.173585i | 0.342080 | − | 0.939671i | \(-0.388869\pi\) |
−0.642739 | + | 0.766085i | \(0.722202\pi\) | |||||||
\(68\) | 43.6524 | − | 75.6081i | 0.0778475 | − | 0.134836i | ||||
\(69\) | 559.513 | + | 255.963i | 0.976194 | + | 0.446584i | ||||
\(70\) | −147.668 | + | 85.2560i | −0.252138 | + | 0.145572i | ||||
\(71\) | − | 671.025i | − | 1.12163i | −0.827940 | − | 0.560817i | \(-0.810487\pi\) | ||
0.827940 | − | 0.560817i | \(-0.189513\pi\) | |||||||
\(72\) | 103.995 | + | 543.396i | 0.170221 | + | 0.889442i | ||||
\(73\) | 734.644i | 1.17786i | 0.808185 | + | 0.588929i | \(0.200450\pi\) | ||||
−0.808185 | + | 0.588929i | \(0.799550\pi\) | |||||||
\(74\) | −347.948 | − | 602.664i | −0.546597 | − | 0.946734i | ||||
\(75\) | 398.860 | − | 283.635i | 0.614086 | − | 0.436684i | ||||
\(76\) | 7.98882 | + | 4.61235i | 0.0120576 | + | 0.00696148i | ||||
\(77\) | −81.1840 | + | 140.615i | −0.120153 | + | 0.208111i | ||||
\(78\) | 415.473 | + | 614.212i | 0.603115 | + | 0.891614i | ||||
\(79\) | −623.091 | − | 1079.23i | −0.887382 | − | 1.53699i | −0.842958 | − | 0.537979i | \(-0.819188\pi\) |
−0.0444239 | − | 0.999013i | \(-0.514145\pi\) | |||||||
\(80\) | − | 402.678i | − | 0.562759i | ||||||
\(81\) | 677.486 | − | 269.172i | 0.929336 | − | 0.369235i | ||||
\(82\) | 751.542 | 1.01212 | ||||||||
\(83\) | −1145.07 | + | 661.105i | −1.51431 | + | 0.874285i | −0.514447 | + | 0.857522i | \(0.672003\pi\) |
−0.999859 | + | 0.0167636i | \(0.994664\pi\) | |||||||
\(84\) | −66.2740 | + | 6.28470i | −0.0860843 | + | 0.00816329i | ||||
\(85\) | −330.509 | − | 190.820i | −0.421750 | − | 0.243498i | ||||
\(86\) | 254.331 | + | 146.838i | 0.318897 | + | 0.184115i | ||||
\(87\) | 586.174 | − | 416.835i | 0.722350 | − | 0.513672i | ||||
\(88\) | −164.877 | − | 285.575i | −0.199726 | − | 0.345936i | ||||
\(89\) | − | 720.654i | − | 0.858306i | −0.903232 | − | 0.429153i | \(-0.858812\pi\) | ||
0.903232 | − | 0.429153i | \(-0.141188\pi\) | |||||||
\(90\) | −448.159 | + | 85.7683i | −0.524890 | + | 0.100453i | ||||
\(91\) | 414.987 | − | 226.809i | 0.478049 | − | 0.261275i | ||||
\(92\) | −75.1781 | − | 130.212i | −0.0851942 | − | 0.147561i | ||||
\(93\) | 14.3182 | − | 31.2983i | 0.0159648 | − | 0.0348977i | ||||
\(94\) | 431.747 | − | 747.807i | 0.473737 | − | 0.820536i | ||||
\(95\) | 20.1622 | − | 34.9219i | 0.0217747 | − | 0.0377149i | ||||
\(96\) | 123.100 | − | 269.086i | 0.130873 | − | 0.286078i | ||||
\(97\) | 1418.86 | − | 819.178i | 1.48519 | − | 0.857473i | 0.485329 | − | 0.874331i | \(-0.338700\pi\) |
0.999858 | + | 0.0168582i | \(0.00536639\pi\) | |||||||
\(98\) | − | 734.363i | − | 0.756958i | ||||||
\(99\) | −328.744 | + | 284.107i | −0.333738 | + | 0.288422i | ||||
\(100\) | −119.601 | −0.119601 | ||||||||
\(101\) | 99.7602 | + | 172.790i | 0.0982822 | + | 0.170230i | 0.910974 | − | 0.412464i | \(-0.135332\pi\) |
−0.812691 | + | 0.582694i | \(0.801999\pi\) | |||||||
\(102\) | −630.372 | − | 886.459i | −0.611923 | − | 0.860515i | ||||
\(103\) | −422.503 | + | 731.796i | −0.404179 | + | 0.700059i | −0.994226 | − | 0.107311i | \(-0.965776\pi\) |
0.590046 | + | 0.807369i | \(0.299109\pi\) | |||||||
\(104\) | −22.4849 | + | 960.196i | −0.0212003 | + | 0.905336i | ||||
\(105\) | 27.4726 | + | 289.706i | 0.0255338 | + | 0.269261i | ||||
\(106\) | 565.942 | − | 326.747i | 0.518577 | − | 0.299401i | ||||
\(107\) | 1347.30 | 1.21728 | 0.608638 | − | 0.793448i | \(-0.291716\pi\) | ||||
0.608638 | + | 0.793448i | \(0.291716\pi\) | |||||||
\(108\) | −173.041 | − | 42.3387i | −0.154175 | − | 0.0377226i | ||||
\(109\) | − | 768.628i | − | 0.675424i | −0.941249 | − | 0.337712i | \(-0.890347\pi\) | ||
0.941249 | − | 0.337712i | \(-0.109653\pi\) | |||||||
\(110\) | 235.524 | − | 135.980i | 0.204149 | − | 0.117865i | ||||
\(111\) | −1182.36 | + | 112.122i | −1.01103 | + | 0.0958749i | ||||
\(112\) | −633.897 | − | 365.981i | −0.534801 | − | 0.308767i | ||||
\(113\) | −883.548 | + | 1530.35i | −0.735550 | + | 1.27401i | 0.218931 | + | 0.975740i | \(0.429743\pi\) |
−0.954481 | + | 0.298270i | \(0.903590\pi\) | |||||||
\(114\) | 93.6640 | − | 66.6056i | 0.0769512 | − | 0.0547210i | ||||
\(115\) | −569.203 | + | 328.630i | −0.461552 | + | 0.266477i | ||||
\(116\) | −175.768 | −0.140687 | ||||||||
\(117\) | 1248.22 | − | 208.718i | 0.986306 | − | 0.164923i | ||||
\(118\) | 1251.94 | 0.976700 | ||||||||
\(119\) | −600.778 | + | 346.860i | −0.462801 | + | 0.267198i | ||||
\(120\) | −537.436 | − | 245.863i | −0.408841 | − | 0.187035i | ||||
\(121\) | −536.015 | + | 928.405i | −0.402716 | + | 0.697524i | ||||
\(122\) | 827.083 | + | 477.517i | 0.613775 | + | 0.354363i | ||||
\(123\) | 533.585 | − | 1166.37i | 0.391152 | − | 0.855025i | ||||
\(124\) | −7.28389 | + | 4.20535i | −0.00527510 | + | 0.00304558i | ||||
\(125\) | 1216.65i | 0.870564i | ||||||||
\(126\) | −272.300 | + | 783.446i | −0.192527 | + | 0.553928i | ||||
\(127\) | 677.641 | 0.473472 | 0.236736 | − | 0.971574i | \(-0.423922\pi\) | ||||
0.236736 | + | 0.971574i | \(0.423922\pi\) | |||||||
\(128\) | 1467.65 | − | 847.347i | 1.01346 | − | 0.585122i | ||||
\(129\) | 408.459 | − | 290.460i | 0.278781 | − | 0.198245i | ||||
\(130\) | −791.910 | − | 18.5442i | −0.534270 | − | 0.0125110i | ||||
\(131\) | 629.841 | − | 1090.92i | 0.420072 | − | 0.727586i | −0.575874 | − | 0.817539i | \(-0.695338\pi\) |
0.995946 | + | 0.0899522i | \(0.0286714\pi\) | |||||||
\(132\) | 105.704 | − | 10.0238i | 0.0696998 | − | 0.00660957i | ||||
\(133\) | −36.6495 | − | 63.4788i | −0.0238941 | − | 0.0413858i | ||||
\(134\) | 579.682 | 0.373708 | ||||||||
\(135\) | −185.077 | + | 756.424i | −0.117992 | + | 0.482241i | ||||
\(136\) | − | 1408.87i | − | 0.888308i | ||||||
\(137\) | −1504.23 | + | 868.469i | −0.938068 | + | 0.541594i | −0.889354 | − | 0.457219i | \(-0.848846\pi\) |
−0.0487139 | + | 0.998813i | \(0.515512\pi\) | |||||||
\(138\) | −1864.94 | + | 176.850i | −1.15039 | + | 0.109091i | ||||
\(139\) | −1164.46 | + | 2016.90i | −0.710560 | + | 1.23073i | 0.254087 | + | 0.967181i | \(0.418225\pi\) |
−0.964647 | + | 0.263545i | \(0.915108\pi\) | |||||||
\(140\) | 35.5566 | − | 61.5858i | 0.0214648 | − | 0.0371782i | ||||
\(141\) | −854.039 | − | 1200.99i | −0.510093 | − | 0.717316i | ||||
\(142\) | 1021.51 | + | 1769.31i | 0.603686 | + | 1.04561i | ||||
\(143\) | −661.887 | + | 361.750i | −0.387061 | + | 0.211546i | ||||
\(144\) | −1280.77 | − | 1481.99i | −0.741184 | − | 0.857634i | ||||
\(145\) | 768.344i | 0.440052i | ||||||||
\(146\) | −1118.36 | − | 1937.06i | −0.633946 | − | 1.09803i | ||||
\(147\) | −1139.71 | − | 521.388i | −0.639467 | − | 0.292540i | ||||
\(148\) | 251.345 | + | 145.114i | 0.139598 | + | 0.0805967i | ||||
\(149\) | 654.032 | + | 377.606i | 0.359600 | + | 0.207615i | 0.668905 | − | 0.743348i | \(-0.266763\pi\) |
−0.309305 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(150\) | −619.905 | + | 1355.06i | −0.337434 | + | 0.737601i | ||||
\(151\) | −1186.51 | + | 685.030i | −0.639447 | + | 0.369185i | −0.784401 | − | 0.620253i | \(-0.787030\pi\) |
0.144955 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(152\) | 148.863 | 0.0794367 | ||||||||
\(153\) | −1823.31 | + | 348.944i | −0.963438 | + | 0.184382i | ||||
\(154\) | − | 494.351i | − | 0.258675i | ||||||
\(155\) | 18.3831 | + | 31.8404i | 0.00952621 | + | 0.0164999i | ||||
\(156\) | −278.142 | − | 135.204i | −0.142751 | − | 0.0693911i | ||||
\(157\) | 573.034 | − | 992.524i | 0.291294 | − | 0.504535i | −0.682822 | − | 0.730584i | \(-0.739248\pi\) |
0.974116 | + | 0.226049i | \(0.0725810\pi\) | |||||||
\(158\) | 3285.84 | + | 1897.08i | 1.65448 | + | 0.955214i | ||||
\(159\) | −105.290 | − | 1110.31i | −0.0525159 | − | 0.553795i | ||||
\(160\) | 158.048 | + | 273.747i | 0.0780923 | + | 0.135260i | ||||
\(161\) | 1194.72i | 0.584829i | ||||||||
\(162\) | −1376.58 | + | 1741.08i | −0.667620 | + | 0.844397i | ||||
\(163\) | 36.6388i | 0.0176060i | 0.999961 | + | 0.00880299i | \(0.00280211\pi\) | ||||
−0.999961 | + | 0.00880299i | \(0.997198\pi\) | |||||||
\(164\) | −271.443 | + | 156.718i | −0.129245 | + | 0.0746195i | ||||
\(165\) | −43.8177 | − | 462.070i | −0.0206739 | − | 0.218013i | ||||
\(166\) | 2012.82 | − | 3486.31i | 0.941116 | − | 1.63006i | ||||
\(167\) | 2701.70 | + | 1559.83i | 1.25188 | + | 0.722773i | 0.971482 | − | 0.237112i | \(-0.0762007\pi\) |
0.280397 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(168\) | −875.497 | + | 622.577i | −0.402060 | + | 0.285910i | ||||
\(169\) | 2194.59 | + | 102.838i | 0.998904 | + | 0.0468084i | ||||
\(170\) | 1161.95 | 0.524221 | ||||||||
\(171\) | −36.8697 | − | 192.653i | −0.0164883 | − | 0.0861551i | ||||
\(172\) | −122.479 | −0.0542963 | ||||||||
\(173\) | −567.113 | − | 982.269i | −0.249230 | − | 0.431679i | 0.714082 | − | 0.700062i | \(-0.246844\pi\) |
−0.963312 | + | 0.268382i | \(0.913511\pi\) | |||||||
\(174\) | −911.026 | + | 1991.42i | −0.396923 | + | 0.867640i | ||||
\(175\) | 823.022 | + | 475.172i | 0.355512 | + | 0.205255i | ||||
\(176\) | 1011.04 | + | 583.725i | 0.433012 | + | 0.249999i | ||||
\(177\) | 888.862 | − | 1942.97i | 0.377463 | − | 0.825101i | ||||
\(178\) | 1097.06 | + | 1900.17i | 0.461957 | + | 0.800133i | ||||
\(179\) | −1008.31 | −0.421031 | −0.210516 | − | 0.977590i | \(-0.567514\pi\) | ||||
−0.210516 | + | 0.977590i | \(0.567514\pi\) | |||||||
\(180\) | 143.982 | − | 124.432i | 0.0596209 | − | 0.0515255i | ||||
\(181\) | −125.169 | −0.0514019 | −0.0257009 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257009 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(182\) | −748.933 | + | 1229.77i | −0.305025 | + | 0.500862i | ||||
\(183\) | 1328.31 | − | 944.577i | 0.536565 | − | 0.381558i | ||||
\(184\) | −2101.29 | − | 1213.18i | −0.841898 | − | 0.486070i | ||||
\(185\) | 634.344 | − | 1098.72i | 0.252097 | − | 0.436644i | ||||
\(186\) | 9.89275 | + | 104.322i | 0.00389985 | + | 0.0411250i | ||||
\(187\) | 958.217 | − | 553.227i | 0.374715 | − | 0.216342i | ||||
\(188\) | 360.125i | 0.139707i | ||||||||
\(189\) | 1022.56 | + | 978.838i | 0.393545 | + | 0.376720i | ||||
\(190\) | 122.773i | 0.0468783i | ||||||||
\(191\) | 207.194 | + | 358.870i | 0.0784922 | + | 0.135952i | 0.902600 | − | 0.430481i | \(-0.141656\pi\) |
−0.824107 | + | 0.566434i | \(0.808323\pi\) | |||||||
\(192\) | −199.644 | − | 2105.30i | −0.0750420 | − | 0.791340i | ||||
\(193\) | 3565.53 | + | 2058.56i | 1.32980 | + | 0.767763i | 0.985269 | − | 0.171010i | \(-0.0547031\pi\) |
0.344535 | + | 0.938773i | \(0.388036\pi\) | |||||||
\(194\) | −2494.09 | + | 4319.90i | −0.923018 | + | 1.59871i | ||||
\(195\) | −591.025 | + | 1215.85i | −0.217047 | + | 0.446508i | ||||
\(196\) | 153.135 | + | 265.238i | 0.0558074 | + | 0.0966612i | ||||
\(197\) | − | 1699.68i | − | 0.614708i | −0.951595 | − | 0.307354i | \(-0.900557\pi\) | ||
0.951595 | − | 0.307354i | \(-0.0994435\pi\) | |||||||
\(198\) | 434.308 | − | 1249.57i | 0.155884 | − | 0.448499i | ||||
\(199\) | −4121.82 | −1.46828 | −0.734141 | − | 0.678997i | \(-0.762415\pi\) | ||||
−0.734141 | + | 0.678997i | \(0.762415\pi\) | |||||||
\(200\) | −1671.48 | + | 965.027i | −0.590956 | + | 0.341188i | ||||
\(201\) | 411.567 | − | 899.649i | 0.144426 | − | 0.315703i | ||||
\(202\) | −526.081 | − | 303.733i | −0.183242 | − | 0.105795i | ||||
\(203\) | 1209.53 | + | 698.323i | 0.418189 | + | 0.241442i | ||||
\(204\) | 412.530 | + | 188.722i | 0.141583 | + | 0.0647706i | ||||
\(205\) | 685.068 | + | 1186.57i | 0.233401 | + | 0.404262i | ||||
\(206\) | − | 2572.73i | − | 0.870149i | ||||||
\(207\) | −1049.62 | + | 3019.89i | −0.352431 | + | 1.01399i | ||||
\(208\) | −1630.79 | − | 2983.81i | −0.543628 | − | 0.994665i | ||||
\(209\) | 58.4544 | + | 101.246i | 0.0193463 | + | 0.0335088i | ||||
\(210\) | −513.462 | − | 722.055i | −0.168725 | − | 0.237269i | ||||
\(211\) | 881.180 | − | 1526.25i | 0.287502 | − | 0.497968i | −0.685711 | − | 0.727874i | \(-0.740509\pi\) |
0.973213 | + | 0.229906i | \(0.0738418\pi\) | |||||||
\(212\) | −136.272 | + | 236.030i | −0.0441471 | + | 0.0764651i | ||||
\(213\) | 3471.18 | − | 329.168i | 1.11662 | − | 0.105888i | ||||
\(214\) | −3552.47 | + | 2051.02i | −1.13477 | + | 0.655162i | ||||
\(215\) | 535.399i | 0.169832i | ||||||||
\(216\) | −2759.94 | + | 804.519i | −0.869400 | + | 0.253429i | ||||
\(217\) | 66.8310 | 0.0209069 | ||||||||
\(218\) | 1170.09 | + | 2026.66i | 0.363527 | + | 0.629647i | ||||
\(219\) | −3800.27 | + | 360.376i | −1.17260 | + | 0.111196i | ||||
\(220\) | −56.7113 | + | 98.2268i | −0.0173794 | + | 0.0301021i | ||||
\(221\) | −3221.84 | − | 75.4460i | −0.980654 | − | 0.0229640i | ||||
\(222\) | 2946.87 | − | 2095.55i | 0.890904 | − | 0.633533i | ||||
\(223\) | −747.181 | + | 431.385i | −0.224372 | + | 0.129541i | −0.607973 | − | 0.793958i | \(-0.708017\pi\) |
0.383601 | + | 0.923499i | \(0.374684\pi\) | |||||||
\(224\) | 574.578 | 0.171387 | ||||||||
\(225\) | 1662.89 | + | 1924.15i | 0.492707 | + | 0.570118i | ||||
\(226\) | − | 5380.16i | − | 1.58355i | ||||||
\(227\) | −474.461 | + | 273.930i | −0.138727 | + | 0.0800942i | −0.567757 | − | 0.823196i | \(-0.692189\pi\) |
0.429030 | + | 0.903290i | \(0.358855\pi\) | |||||||
\(228\) | −19.9405 | + | 43.5883i | −0.00579208 | + | 0.0126610i | ||||
\(229\) | 773.852 | + | 446.784i | 0.223308 | + | 0.128927i | 0.607481 | − | 0.794334i | \(-0.292180\pi\) |
−0.384173 | + | 0.923261i | \(0.625513\pi\) | |||||||
\(230\) | 1000.56 | − | 1733.01i | 0.286847 | − | 0.496833i | ||||
\(231\) | −767.217 | − | 350.982i | −0.218525 | − | 0.0999695i | ||||
\(232\) | −2456.44 | + | 1418.22i | −0.695142 | + | 0.401340i | ||||
\(233\) | 2144.64 | 0.603004 | 0.301502 | − | 0.953466i | \(-0.402512\pi\) | ||||
0.301502 | + | 0.953466i | \(0.402512\pi\) | |||||||
\(234\) | −2973.48 | + | 2450.52i | −0.830694 | + | 0.684595i | ||||
\(235\) | 1574.23 | 0.436986 | ||||||||
\(236\) | −452.178 | + | 261.065i | −0.124722 | + | 0.0720080i | ||||
\(237\) | 5277.12 | − | 3752.62i | 1.44635 | − | 1.02852i | ||||
\(238\) | 1056.06 | − | 1829.15i | 0.287623 | − | 0.498177i | ||||
\(239\) | −4217.95 | − | 2435.23i | −1.14157 | − | 0.659088i | −0.194754 | − | 0.980852i | \(-0.562391\pi\) |
−0.946820 | + | 0.321764i | \(0.895724\pi\) | |||||||
\(240\) | 2083.03 | − | 197.532i | 0.560246 | − | 0.0531276i | ||||
\(241\) | 4509.67 | − | 2603.66i | 1.20537 | − | 0.695919i | 0.243624 | − | 0.969870i | \(-0.421664\pi\) |
0.961744 | + | 0.273950i | \(0.0883304\pi\) | |||||||
\(242\) | − | 3263.94i | − | 0.866999i | ||||||
\(243\) | 1724.75 | + | 3372.56i | 0.455320 | + | 0.890328i | ||||
\(244\) | −398.303 | −0.104503 | ||||||||
\(245\) | 1159.45 | − | 669.408i | 0.302345 | − | 0.174559i | ||||
\(246\) | 368.666 | + | 3887.69i | 0.0955499 | + | 1.00760i | ||||
\(247\) | 7.97169 | − | 340.423i | 0.00205355 | − | 0.0876946i | ||||
\(248\) | −67.8636 | + | 117.543i | −0.0173764 | + | 0.0300968i | ||||
\(249\) | −3981.57 | − | 5599.07i | −1.01334 | − | 1.42501i | ||||
\(250\) | −1852.13 | − | 3207.98i | −0.468555 | − | 0.811561i | ||||
\(251\) | −4539.47 | −1.14155 | −0.570775 | − | 0.821107i | \(-0.693357\pi\) | ||||
−0.570775 | + | 0.821107i | \(0.693357\pi\) | |||||||
\(252\) | −65.0208 | − | 339.749i | −0.0162537 | − | 0.0849292i | ||||
\(253\) | − | 1905.54i | − | 0.473518i | ||||||
\(254\) | −1786.76 | + | 1031.58i | −0.441382 | + | 0.254832i | ||||
\(255\) | 824.970 | − | 1803.31i | 0.202595 | − | 0.442854i | ||||
\(256\) | −951.925 | + | 1648.78i | −0.232404 | + | 0.402535i | ||||
\(257\) | −383.653 | + | 664.507i | −0.0931192 | + | 0.161287i | −0.908822 | − | 0.417184i | \(-0.863017\pi\) |
0.815703 | + | 0.578471i | \(0.196350\pi\) | |||||||
\(258\) | −634.823 | + | 1387.67i | −0.153187 | + | 0.334855i | ||||
\(259\) | −1153.07 | − | 1997.17i | −0.276634 | − | 0.479144i | ||||
\(260\) | 289.890 | − | 158.438i | 0.0691470 | − | 0.0377919i | ||||
\(261\) | 2443.81 | + | 2827.77i | 0.579571 | + | 0.670630i | ||||
\(262\) | 3835.27i | 0.904365i | ||||||||
\(263\) | −4038.50 | − | 6994.89i | −0.946862 | − | 1.64001i | −0.751979 | − | 0.659187i | \(-0.770901\pi\) |
−0.194883 | − | 0.980826i | \(-0.562433\pi\) | |||||||
\(264\) | 1396.38 | − | 992.985i | 0.325536 | − | 0.231492i | ||||
\(265\) | 1031.77 | + | 595.692i | 0.239174 | + | 0.138087i | ||||
\(266\) | 193.269 | + | 111.584i | 0.0445493 | + | 0.0257205i | ||||
\(267\) | 3727.90 | − | 353.514i | 0.854472 | − | 0.0810288i | ||||
\(268\) | −209.371 | + | 120.880i | −0.0477214 | + | 0.0275520i | ||||
\(269\) | −1646.88 | −0.373280 | −0.186640 | − | 0.982428i | \(-0.559760\pi\) | ||||
−0.186640 | + | 0.982428i | \(0.559760\pi\) | |||||||
\(270\) | −663.517 | − | 2276.23i | −0.149557 | − | 0.513063i | ||||
\(271\) | 7310.53i | 1.63868i | 0.573306 | + | 0.819342i | \(0.305661\pi\) | ||||
−0.573306 | + | 0.819342i | \(0.694339\pi\) | |||||||
\(272\) | 2493.97 | + | 4319.68i | 0.555953 | + | 0.962938i | ||||
\(273\) | 1376.84 | + | 2035.44i | 0.305238 | + | 0.451248i | ||||
\(274\) | 2644.17 | − | 4579.84i | 0.582993 | − | 1.00977i | ||||
\(275\) | −1312.69 | − | 757.880i | −0.287847 | − | 0.166189i | ||||
\(276\) | 636.703 | − | 452.768i | 0.138859 | − | 0.0987442i | ||||
\(277\) | 207.100 | + | 358.707i | 0.0449220 | + | 0.0778073i | 0.887612 | − | 0.460592i | \(-0.152363\pi\) |
−0.842690 | + | 0.538399i | \(0.819029\pi\) | |||||||
\(278\) | − | 7090.68i | − | 1.52975i | ||||||
\(279\) | 168.928 | + | 58.7139i | 0.0362490 | + | 0.0125990i | ||||
\(280\) | − | 1147.58i | − | 0.244933i | ||||||
\(281\) | 7224.62 | − | 4171.13i | 1.53375 | − | 0.885513i | 0.534569 | − | 0.845125i | \(-0.320474\pi\) |
0.999184 | − | 0.0403875i | \(-0.0128592\pi\) | |||||||
\(282\) | 4080.16 | + | 1866.57i | 0.861595 | + | 0.394158i | ||||
\(283\) | 626.340 | − | 1084.85i | 0.131562 | − | 0.227872i | −0.792717 | − | 0.609590i | \(-0.791334\pi\) |
0.924279 | + | 0.381718i | \(0.124667\pi\) | |||||||
\(284\) | −737.903 | − | 426.028i | −0.154178 | − | 0.0890145i | ||||
\(285\) | 190.540 | + | 87.1670i | 0.0396021 | + | 0.0181169i | ||||
\(286\) | 1194.52 | − | 1961.44i | 0.246970 | − | 0.405533i | ||||
\(287\) | 2490.54 | 0.512237 | ||||||||
\(288\) | 1452.35 | + | 504.791i | 0.297156 | + | 0.103282i | ||||
\(289\) | −185.663 | −0.0377901 | ||||||||
\(290\) | −1169.66 | − | 2025.91i | −0.236845 | − | 0.410227i | ||||
\(291\) | 4933.58 | + | 6937.83i | 0.993854 | + | 1.39760i | ||||
\(292\) | 807.862 | + | 466.419i | 0.161906 | + | 0.0934765i | ||||
\(293\) | −3473.26 | − | 2005.29i | −0.692526 | − | 0.399830i | 0.112032 | − | 0.993705i | \(-0.464264\pi\) |
−0.804557 | + | 0.593875i | \(0.797597\pi\) | |||||||
\(294\) | 3798.82 | − | 360.239i | 0.753577 | − | 0.0714610i | ||||
\(295\) | 1141.21 | + | 1976.63i | 0.225233 | + | 0.390114i | ||||
\(296\) | 4683.54 | 0.919679 | ||||||||
\(297\) | −1630.93 | − | 1561.21i | −0.318641 | − | 0.305018i | ||||
\(298\) | −2299.34 | −0.446971 | ||||||||
\(299\) | −2886.85 | + | 4740.31i | −0.558365 | + | 0.916854i | ||||
\(300\) | −58.6698 | − | 618.690i | −0.0112910 | − | 0.119067i | ||||
\(301\) | 842.828 | + | 486.607i | 0.161395 | + | 0.0931813i | ||||
\(302\) | 2085.66 | − | 3612.47i | 0.397405 | − | 0.688326i | ||||
\(303\) | −844.895 | + | 600.815i | −0.160191 | + | 0.113914i | ||||
\(304\) | −456.422 | + | 263.515i | −0.0861104 | + | 0.0497159i | ||||
\(305\) | 1741.12i | 0.326873i | ||||||||
\(306\) | 4276.38 | − | 3695.73i | 0.798902 | − | 0.690427i | ||||
\(307\) | 8610.90i | 1.60081i | 0.599456 | + | 0.800407i | \(0.295383\pi\) | ||||
−0.599456 | + | 0.800407i | \(0.704617\pi\) | |||||||
\(308\) | 103.086 | + | 178.550i | 0.0190710 | + | 0.0330320i | ||||
\(309\) | −3992.80 | − | 1826.60i | −0.735089 | − | 0.336285i | ||||
\(310\) | −96.9422 | − | 55.9696i | −0.0177611 | − | 0.0102544i | ||||
\(311\) | 609.721 | − | 1056.07i | 0.111171 | − | 0.192553i | −0.805072 | − | 0.593177i | \(-0.797873\pi\) |
0.916243 | + | 0.400624i | \(0.131207\pi\) | |||||||
\(312\) | −4978.07 | + | 354.706i | −0.903294 | + | 0.0643631i | ||||
\(313\) | −419.508 | − | 726.609i | −0.0757571 | − | 0.131215i | 0.825658 | − | 0.564171i | \(-0.190804\pi\) |
−0.901415 | + | 0.432956i | \(0.857471\pi\) | |||||||
\(314\) | 3489.36i | 0.627120i | ||||||||
\(315\) | −1485.16 | + | 284.228i | −0.265648 | + | 0.0508395i | ||||
\(316\) | −1582.38 | −0.281696 | ||||||||
\(317\) | −6136.85 | + | 3543.11i | −1.08732 | + | 0.627764i | −0.932861 | − | 0.360236i | \(-0.882696\pi\) |
−0.154457 | + | 0.987999i | \(0.549363\pi\) | |||||||
\(318\) | 1967.86 | + | 2767.30i | 0.347020 | + | 0.487996i | ||||
\(319\) | −1929.15 | − | 1113.80i | −0.338595 | − | 0.195488i | ||||
\(320\) | 1956.38 | + | 1129.51i | 0.341765 | + | 0.197318i | ||||
\(321\) | 660.913 | + | 6969.51i | 0.114918 | + | 1.21184i | ||||
\(322\) | −1818.75 | − | 3150.16i | −0.314766 | − | 0.545191i | ||||
\(323\) | 499.495i | 0.0860453i | ||||||||
\(324\) | 134.131 | − | 915.903i | 0.0229992 | − | 0.157048i | ||||
\(325\) | 2117.33 | + | 3874.04i | 0.361380 | + | 0.661210i | ||||
\(326\) | −55.7759 | − | 96.6066i | −0.00947589 | − | 0.0164127i | ||||
\(327\) | 3976.07 | − | 377.047i | 0.672407 | − | 0.0637638i | ||||
\(328\) | −2529.02 | + | 4380.39i | −0.425737 | + | 0.737399i | ||||
\(329\) | 1430.77 | − | 2478.16i | 0.239759 | − | 0.415275i | ||||
\(330\) | 818.952 | + | 1151.65i | 0.136612 | + | 0.192110i | ||||
\(331\) | −8243.80 | + | 4759.56i | −1.36894 | + | 0.790360i | −0.990793 | − | 0.135385i | \(-0.956773\pi\) |
−0.378150 | + | 0.925744i | \(0.623440\pi\) | |||||||
\(332\) | 1678.92i | 0.277538i | ||||||||
\(333\) | −1160.00 | − | 6061.26i | −0.190893 | − | 0.997462i | ||||
\(334\) | −9498.20 | −1.55604 | ||||||||
\(335\) | 528.409 | + | 915.231i | 0.0861793 | + | 0.149267i | ||||
\(336\) | 1582.24 | − | 3458.65i | 0.256900 | − | 0.561562i | ||||
\(337\) | −3634.69 | + | 6295.47i | −0.587520 | + | 1.01761i | 0.407036 | + | 0.913412i | \(0.366562\pi\) |
−0.994556 | + | 0.104202i | \(0.966771\pi\) | |||||||
\(338\) | −5943.10 | + | 3069.71i | −0.956396 | + | 0.493994i | ||||
\(339\) | −8349.84 | − | 3819.84i | −1.33776 | − | 0.611992i | ||||
\(340\) | −419.675 | + | 242.300i | −0.0669414 | + | 0.0386487i | ||||
\(341\) | −106.593 | −0.0169276 | ||||||||
\(342\) | 390.494 | + | 451.846i | 0.0617412 | + | 0.0714416i | ||||
\(343\) | − | 5894.36i | − | 0.927887i | ||||||
\(344\) | −1711.70 | + | 988.250i | −0.268281 | + | 0.154892i | ||||
\(345\) | −1979.20 | − | 2783.25i | −0.308860 | − | 0.434334i | ||||
\(346\) | 2990.65 | + | 1726.65i | 0.464677 | + | 0.268281i | ||||
\(347\) | 3266.00 | − | 5656.88i | 0.505269 | − | 0.875151i | −0.494713 | − | 0.869057i | \(-0.664727\pi\) |
0.999981 | − | 0.00609457i | \(-0.00193998\pi\) | |||||||
\(348\) | −86.2224 | − | 909.240i | −0.0132816 | − | 0.140059i | ||||
\(349\) | −9407.97 | + | 5431.70i | −1.44297 | + | 0.833100i | −0.998047 | − | 0.0624674i | \(-0.980103\pi\) |
−0.444925 | + | 0.895568i | \(0.646770\pi\) | |||||||
\(350\) | −2893.45 | −0.441889 | ||||||||
\(351\) | 1692.00 | + | 6354.58i | 0.257299 | + | 0.966332i | ||||
\(352\) | −916.429 | −0.138766 | ||||||||
\(353\) | 4848.14 | − | 2799.07i | 0.730993 | − | 0.422039i | −0.0877925 | − | 0.996139i | \(-0.527981\pi\) |
0.818785 | + | 0.574100i | \(0.194648\pi\) | |||||||
\(354\) | 614.134 | + | 6476.23i | 0.0922059 | + | 0.972338i | ||||
\(355\) | −1862.32 | + | 3225.63i | −0.278427 | + | 0.482249i | ||||
\(356\) | −792.478 | − | 457.537i | −0.117981 | − | 0.0681164i | ||||
\(357\) | −2088.99 | − | 2937.64i | −0.309696 | − | 0.435509i | ||||
\(358\) | 2658.64 | − | 1534.97i | 0.392496 | − | 0.226607i | ||||
\(359\) | − | 1568.61i | − | 0.230607i | −0.993330 | − | 0.115304i | \(-0.963216\pi\) | ||
0.993330 | − | 0.115304i | \(-0.0367841\pi\) | |||||||
\(360\) | 1008.20 | − | 2900.73i | 0.147602 | − | 0.424672i | ||||
\(361\) | 6806.22 | 0.992305 | ||||||||
\(362\) | 330.037 | − | 190.547i | 0.0479181 | − | 0.0276655i | ||||
\(363\) | −5065.53 | − | 2317.35i | −0.732428 | − | 0.335067i | ||||
\(364\) | 14.0583 | − | 600.345i | 0.00202433 | − | 0.0864468i | ||||
\(365\) | 2038.88 | − | 3531.45i | 0.292383 | − | 0.506423i | ||||
\(366\) | −2064.45 | + | 4512.70i | −0.294837 | + | 0.644488i | ||||
\(367\) | 967.532 | + | 1675.81i | 0.137615 | + | 0.238356i | 0.926593 | − | 0.376065i | \(-0.122723\pi\) |
−0.788978 | + | 0.614421i | \(0.789390\pi\) | |||||||
\(368\) | 8590.23 | 1.21684 | ||||||||
\(369\) | 6295.32 | + | 2188.05i | 0.888134 | + | 0.308686i | ||||
\(370\) | 3862.69i | 0.542734i | ||||||||
\(371\) | 1875.48 | − | 1082.81i | 0.262453 | − | 0.151527i | ||||
\(372\) | −25.3271 | − | 35.6162i | −0.00352998 | − | 0.00496402i | ||||
\(373\) | −4269.79 | + | 7395.49i | −0.592711 | + | 1.02661i | 0.401154 | + | 0.916011i | \(0.368609\pi\) |
−0.993865 | + | 0.110596i | \(0.964724\pi\) | |||||||
\(374\) | −1684.37 | + | 2917.42i | −0.232879 | + | 0.403359i | ||||
\(375\) | −6293.67 | + | 596.823i | −0.866676 | + | 0.0821861i | ||||
\(376\) | 2905.75 | + | 5032.90i | 0.398544 | + | 0.690298i | ||||
\(377\) | 3111.68 | + | 5693.37i | 0.425092 | + | 0.777782i | ||||
\(378\) | −4186.30 | − | 1024.28i | −0.569630 | − | 0.139374i | ||||
\(379\) | 8878.52i | 1.20332i | 0.798752 | + | 0.601661i | \(0.205494\pi\) | ||||
−0.798752 | + | 0.601661i | \(0.794506\pi\) | |||||||
\(380\) | −25.6016 | − | 44.3433i | −0.00345614 | − | 0.00598621i | ||||
\(381\) | 332.414 | + | 3505.40i | 0.0446984 | + | 0.471357i | ||||
\(382\) | −1092.63 | − | 630.829i | −0.146345 | − | 0.0844921i | ||||
\(383\) | −7825.32 | − | 4517.95i | −1.04401 | − | 0.602759i | −0.123043 | − | 0.992401i | \(-0.539265\pi\) |
−0.920966 | + | 0.389643i | \(0.872599\pi\) | |||||||
\(384\) | 5103.23 | + | 7176.40i | 0.678185 | + | 0.953696i | ||||
\(385\) | 780.505 | − | 450.625i | 0.103320 | − | 0.0596519i | ||||
\(386\) | −12535.1 | −1.65290 | ||||||||
\(387\) | 1702.90 | + | 1970.45i | 0.223678 | + | 0.258821i | ||||
\(388\) | − | 2080.36i | − | 0.272201i | ||||||
\(389\) | −3023.10 | − | 5236.17i | −0.394029 | − | 0.682479i | 0.598947 | − | 0.800788i | \(-0.295586\pi\) |
−0.992977 | + | 0.118310i | \(0.962252\pi\) | |||||||
\(390\) | −292.540 | − | 4105.60i | −0.0379829 | − | 0.533065i | ||||
\(391\) | 4070.71 | − | 7050.68i | 0.526508 | − | 0.911939i | ||||
\(392\) | 4280.26 | + | 2471.21i | 0.551495 | + | 0.318406i | ||||
\(393\) | 5952.22 | + | 2722.99i | 0.763994 | + | 0.349508i | ||||
\(394\) | 2587.45 | + | 4481.60i | 0.330848 | + | 0.573045i | ||||
\(395\) | 6917.14i | 0.881111i | ||||||||
\(396\) | 103.706 | + | 541.885i | 0.0131601 | + | 0.0687646i | ||||
\(397\) | − | 12540.8i | − | 1.58540i | −0.609614 | − | 0.792698i | \(-0.708676\pi\) | ||
0.609614 | − | 0.792698i | \(-0.291324\pi\) | |||||||
\(398\) | 10868.1 | − | 6274.71i | 1.36877 | − | 0.790259i | ||||
\(399\) | 310.394 | − | 220.725i | 0.0389452 | − | 0.0276944i | ||||
\(400\) | 3416.56 | − | 5917.65i | 0.427069 | − | 0.739706i | ||||
\(401\) | 5478.90 | + | 3163.24i | 0.682302 | + | 0.393927i | 0.800722 | − | 0.599036i | \(-0.204450\pi\) |
−0.118420 | + | 0.992964i | \(0.537783\pi\) | |||||||
\(402\) | 284.361 | + | 2998.67i | 0.0352801 | + | 0.372039i | ||||
\(403\) | 265.166 | + | 161.486i | 0.0327763 | + | 0.0199608i | ||||
\(404\) | 253.348 | 0.0311993 | ||||||||
\(405\) | −4003.73 | − | 586.334i | −0.491227 | − | 0.0719387i | ||||
\(406\) | −4252.27 | −0.519795 | ||||||||
\(407\) | 1839.10 | + | 3185.41i | 0.223982 | + | 0.387949i | ||||
\(408\) | 7288.03 | − | 691.117i | 0.884341 | − | 0.0838612i | ||||
\(409\) | −3293.82 | − | 1901.69i | −0.398212 | − | 0.229908i | 0.287500 | − | 0.957781i | \(-0.407176\pi\) |
−0.685712 | + | 0.727873i | \(0.740509\pi\) | |||||||
\(410\) | −3612.68 | − | 2085.78i | −0.435164 | − | 0.251242i | ||||
\(411\) | −5230.44 | − | 7355.29i | −0.627734 | − | 0.882749i | ||||
\(412\) | 536.487 | + | 929.223i | 0.0641525 | + | 0.111115i | ||||
\(413\) | 4148.82 | 0.494310 | ||||||||
\(414\) | −1829.68 | − | 9560.47i | −0.217207 | − | 1.13496i | ||||
\(415\) | 7339.14 | 0.868107 | ||||||||
\(416\) | 2279.76 | + | 1388.37i | 0.268688 | + | 0.163631i | ||||
\(417\) | −11004.5 | − | 5034.29i | −1.29231 | − | 0.591199i | ||||
\(418\) | −308.257 | − | 177.972i | −0.0360702 | − | 0.0208251i | ||||
\(419\) | 5461.79 | − | 9460.10i | 0.636816 | − | 1.10300i | −0.349311 | − | 0.937007i | \(-0.613584\pi\) |
0.986127 | − | 0.165991i | \(-0.0530822\pi\) | |||||||
\(420\) | 336.022 | + | 153.722i | 0.0390386 | + | 0.0178592i | ||||
\(421\) | 10331.6 | − | 5964.94i | 1.19603 | − | 0.690531i | 0.236366 | − | 0.971664i | \(-0.424044\pi\) |
0.959669 | + | 0.281133i | \(0.0907103\pi\) | |||||||
\(422\) | 5365.74i | 0.618957i | ||||||||
\(423\) | 5793.71 | − | 5007.04i | 0.665957 | − | 0.575533i | ||||
\(424\) | 4398.16i | 0.503758i | ||||||||
\(425\) | −3238.05 | − | 5608.47i | −0.369573 | − | 0.640119i | ||||
\(426\) | −8651.45 | + | 6152.15i | −0.983953 | + | 0.699702i | ||||
\(427\) | 2740.88 | + | 1582.45i | 0.310633 | + | 0.179344i | ||||
\(428\) | 855.390 | − | 1481.58i | 0.0966048 | − | 0.167324i | ||||
\(429\) | −2196.00 | − | 3246.45i | −0.247142 | − | 0.365362i | ||||
\(430\) | −815.047 | − | 1411.70i | −0.0914071 | − | 0.158322i | ||||
\(431\) | − | 9244.15i | − | 1.03312i | −0.856251 | − | 0.516560i | \(-0.827212\pi\) | ||
0.856251 | − | 0.516560i | \(-0.172788\pi\) | |||||||
\(432\) | 7037.99 | − | 7352.32i | 0.783832 | − | 0.818839i | ||||
\(433\) | 6503.71 | 0.721821 | 0.360910 | − | 0.932601i | \(-0.382466\pi\) | ||||
0.360910 | + | 0.932601i | \(0.382466\pi\) | |||||||
\(434\) | −176.215 | + | 101.738i | −0.0194899 | + | 0.0112525i | ||||
\(435\) | −3974.60 | + | 376.908i | −0.438086 | + | 0.0415433i | ||||
\(436\) | −845.233 | − | 487.996i | −0.0928425 | − | 0.0536026i | ||||
\(437\) | 744.981 | + | 430.115i | 0.0815498 | + | 0.0470828i | ||||
\(438\) | 9471.69 | − | 6735.43i | 1.03328 | − | 0.734775i | ||||
\(439\) | −5129.20 | − | 8884.03i | −0.557638 | − | 0.965858i | −0.997693 | − | 0.0678871i | \(-0.978374\pi\) |
0.440055 | − | 0.897971i | \(-0.354959\pi\) | |||||||
\(440\) | 1830.35i | 0.198315i | ||||||||
\(441\) | 2138.03 | − | 6151.42i | 0.230864 | − | 0.664228i | ||||
\(442\) | 8609.98 | − | 4705.73i | 0.926549 | − | 0.506400i | ||||
\(443\) | 7887.01 | + | 13660.7i | 0.845877 | + | 1.46510i | 0.884858 | + | 0.465861i | \(0.154255\pi\) |
−0.0389811 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(444\) | −627.371 | + | 1371.38i | −0.0670579 | + | 0.146583i | ||||
\(445\) | −2000.05 | + | 3464.20i | −0.213060 | + | 0.369031i | ||||
\(446\) | 1313.41 | − | 2274.89i | 0.139443 | − | 0.241523i | ||||
\(447\) | −1632.50 | + | 3568.51i | −0.172740 | + | 0.377594i | ||||
\(448\) | 3556.17 | − | 2053.16i | 0.375030 | − | 0.216524i | ||||
\(449\) | 6797.23i | 0.714435i | 0.934021 | + | 0.357218i | \(0.116275\pi\) | ||||
−0.934021 | + | 0.357218i | \(0.883725\pi\) | |||||||
\(450\) | −7313.74 | − | 2542.02i | −0.766162 | − | 0.266293i | ||||
\(451\) | −3972.32 | −0.414743 | ||||||||
\(452\) | 1121.91 | + | 1943.21i | 0.116749 | + | 0.202215i | ||||
\(453\) | −4125.66 | − | 5801.69i | −0.427903 | − | 0.601738i | ||||
\(454\) | 834.017 | − | 1444.56i | 0.0862166 | − | 0.149332i | ||||
\(455\) | −2624.32 | − | 61.4537i | −0.270395 | − | 0.00633186i | ||||
\(456\) | 73.0240 | + | 770.059i | 0.00749926 | + | 0.0790819i | ||||
\(457\) | 12008.3 | − | 6933.00i | 1.22916 | − | 0.709654i | 0.262303 | − | 0.964986i | \(-0.415518\pi\) |
0.966854 | + | 0.255332i | \(0.0821846\pi\) | |||||||
\(458\) | −2720.58 | −0.277565 | ||||||||
\(459\) | −2699.49 | − | 9260.72i | −0.274512 | − | 0.941729i | ||||
\(460\) | 834.577i | 0.0845921i | ||||||||
\(461\) | 835.055 | − | 482.119i | 0.0843653 | − | 0.0487083i | −0.457224 | − | 0.889352i | \(-0.651156\pi\) |
0.541589 | + | 0.840643i | \(0.317823\pi\) | |||||||
\(462\) | 2557.25 | − | 242.502i | 0.257520 | − | 0.0244203i | ||||
\(463\) | −10382.6 | − | 5994.39i | −1.04216 | − | 0.601691i | −0.121715 | − | 0.992565i | \(-0.538839\pi\) |
−0.920444 | + | 0.390874i | \(0.872173\pi\) | |||||||
\(464\) | 5021.04 | − | 8696.70i | 0.502362 | − | 0.870117i | ||||
\(465\) | −155.691 | + | 110.714i | −0.0155269 | + | 0.0110413i | ||||
\(466\) | −5654.83 | + | 3264.82i | −0.562135 | + | 0.324549i | ||||
\(467\) | −9189.77 | −0.910604 | −0.455302 | − | 0.890337i | \(-0.650469\pi\) | ||||
−0.455302 | + | 0.890337i | \(0.650469\pi\) | |||||||
\(468\) | 562.964 | − | 1505.14i | 0.0556047 | − | 0.148664i | ||||
\(469\) | 1921.01 | 0.189135 | ||||||||
\(470\) | −4150.82 | + | 2396.48i | −0.407369 | + | 0.235194i | ||||
\(471\) | 5415.37 | + | 2477.40i | 0.529782 | + | 0.242362i | ||||
\(472\) | −4212.92 | + | 7296.99i | −0.410838 | + | 0.711591i | ||||
\(473\) | −1344.28 | − | 776.119i | −0.130676 | − | 0.0754460i | ||||
\(474\) | −8201.65 | + | 17928.1i | −0.794756 | + | 1.73727i | ||||
\(475\) | 592.596 | − | 342.135i | 0.0572424 | − | 0.0330489i | ||||
\(476\) | 880.873i | 0.0848209i | ||||||||
\(477\) | 5691.93 | − | 1089.32i | 0.546364 | − | 0.104563i | ||||
\(478\) | 14828.8 | 1.41894 | ||||||||
\(479\) | 14232.2 | − | 8216.96i | 1.35759 | − | 0.783805i | 0.368291 | − | 0.929711i | \(-0.379943\pi\) |
0.989298 | + | 0.145906i | \(0.0466097\pi\) | |||||||
\(480\) | −1338.55 | + | 951.858i | −0.127283 | + | 0.0905128i | ||||
\(481\) | 250.806 | − | 10710.4i | 0.0237750 | − | 1.01529i | ||||
\(482\) | −7927.19 | + | 13730.3i | −0.749115 | + | 1.29751i | ||||
\(483\) | −6180.24 | + | 586.066i | −0.582217 | + | 0.0552111i | ||||
\(484\) | 680.623 | + | 1178.87i | 0.0639202 | + | 0.110713i | ||||
\(485\) | −9093.96 | −0.851413 | ||||||||
\(486\) | −9681.80 | − | 6266.90i | −0.903653 | − | 0.584923i | ||||
\(487\) | − | 20083.2i | − | 1.86870i | −0.356360 | − | 0.934349i | \(-0.615982\pi\) | ||
0.356360 | − | 0.934349i | \(-0.384018\pi\) | |||||||
\(488\) | −5566.45 | + | 3213.79i | −0.516355 | + | 0.298118i | ||||
\(489\) | −189.531 | + | 17.9730i | −0.0175273 | + | 0.00166210i | ||||
\(490\) | −2038.10 | + | 3530.09i | −0.187902 | + | 0.325456i | ||||
\(491\) | −9870.08 | + | 17095.5i | −0.907190 | + | 1.57130i | −0.0892407 | + | 0.996010i | \(0.528444\pi\) |
−0.817950 | + | 0.575290i | \(0.804889\pi\) | |||||||
\(492\) | −943.848 | − | 1327.28i | −0.0864877 | − | 0.121623i | ||||
\(493\) | −4758.71 | − | 8242.33i | −0.434729 | − | 0.752973i | ||||
\(494\) | 497.212 | + | 909.738i | 0.0452846 | + | 0.0828563i | ||||
\(495\) | 2368.77 | − | 453.333i | 0.215087 | − | 0.0411632i | ||||
\(496\) | − | 480.525i | − | 0.0435004i | ||||||
\(497\) | 3385.20 | + | 5863.34i | 0.305527 | + | 0.529188i | ||||
\(498\) | 19021.9 | + | 8702.02i | 1.71163 | + | 0.783026i | ||||
\(499\) | −9242.05 | − | 5335.90i | −0.829121 | − | 0.478693i | 0.0244309 | − | 0.999702i | \(-0.492223\pi\) |
−0.853551 | + | 0.521009i | \(0.825556\pi\) | |||||||
\(500\) | 1337.91 | + | 772.441i | 0.119666 | + | 0.0690893i | ||||
\(501\) | −6743.59 | + | 14740.9i | −0.601360 | + | 1.31452i | ||||
\(502\) | 11969.4 | − | 6910.51i | 1.06418 | − | 0.614405i | ||||
\(503\) | 4278.25 | 0.379240 | 0.189620 | − | 0.981858i | \(-0.439274\pi\) | ||||
0.189620 | + | 0.981858i | \(0.439274\pi\) | |||||||
\(504\) | −3650.03 | − | 4223.50i | −0.322590 | − | 0.373273i | ||||
\(505\) | − | 1107.47i | − | 0.0975877i | ||||||
\(506\) | 2900.83 | + | 5024.38i | 0.254857 | + | 0.441425i | ||||
\(507\) | 544.572 | + | 11403.0i | 0.0477027 | + | 0.998862i | ||||
\(508\) | 430.229 | − | 745.178i | 0.0375754 | − | 0.0650825i | ||||
\(509\) | −8144.34 | − | 4702.14i | −0.709217 | − | 0.409467i | 0.101554 | − | 0.994830i | \(-0.467619\pi\) |
−0.810771 | + | 0.585363i | \(0.800952\pi\) | |||||||
\(510\) | 569.990 | + | 6010.71i | 0.0494894 | + | 0.521880i | ||||
\(511\) | −3706.15 | − | 6419.23i | −0.320842 | − | 0.555715i | ||||
\(512\) | 7761.03i | 0.669907i | ||||||||
\(513\) | 978.496 | − | 285.230i | 0.0842137 | − | 0.0245482i | ||||
\(514\) | − | 2336.17i | − | 0.200474i | ||||||
\(515\) | 4061.96 | − | 2345.17i | 0.347556 | − | 0.200661i | ||||
\(516\) | −60.0817 | − | 633.579i | −0.00512587 | − | 0.0540538i | ||||
\(517\) | −2282.02 | + | 3952.57i | −0.194126 | + | 0.336236i | ||||
\(518\) | 6080.66 | + | 3510.67i | 0.515770 | + | 0.297780i | ||||
\(519\) | 4803.03 | − | 3415.49i | 0.406223 | − | 0.288870i | ||||
\(520\) | 2772.95 | − | 4553.27i | 0.233850 | − | 0.383989i | ||||
\(521\) | −22802.4 | −1.91745 | −0.958725 | − | 0.284336i | \(-0.908227\pi\) | ||||
−0.958725 | + | 0.284336i | \(0.908227\pi\) | |||||||
\(522\) | −10748.4 | − | 3735.80i | −0.901237 | − | 0.313241i | ||||
\(523\) | −5214.23 | −0.435951 | −0.217975 | − | 0.975954i | \(-0.569945\pi\) | ||||
−0.217975 | + | 0.975954i | \(0.569945\pi\) | |||||||
\(524\) | −799.762 | − | 1385.23i | −0.0666751 | − | 0.115485i | ||||
\(525\) | −2054.31 | + | 4490.54i | −0.170776 | + | 0.373302i | ||||
\(526\) | 21296.9 | + | 12295.8i | 1.76538 | + | 1.01924i | ||||
\(527\) | −394.404 | − | 227.709i | −0.0326006 | − | 0.0188220i | ||||
\(528\) | −2523.61 | + | 5516.40i | −0.208004 | + | 0.454679i | ||||
\(529\) | −927.079 | − | 1605.75i | −0.0761962 | − | 0.131976i | ||||
\(530\) | −3627.32 | −0.297285 | ||||||||
\(531\) | 10486.9 | + | 3644.92i | 0.857051 | + | 0.297883i | ||||
\(532\) | −93.0738 | −0.00758508 | ||||||||
\(533\) | 9881.75 | + | 6017.99i | 0.803051 | + | 0.489059i | ||||
\(534\) | −9291.31 | + | 6607.17i | −0.752948 | + | 0.535431i | ||||
\(535\) | −6476.50 | − | 3739.21i | −0.523371 | − | 0.302168i | ||||
\(536\) | −1950.69 | + | 3378.70i | −0.157196 | + | 0.272272i | ||||
\(537\) | −494.622 | − | 5215.93i | −0.0397477 | − | 0.419151i | ||||
\(538\) | 4342.39 | − | 2507.08i | 0.347981 | − | 0.200907i | ||||
\(539\) | 3881.51i | 0.310183i | ||||||||
\(540\) | 714.308 | + | 683.770i | 0.0569240 | + | 0.0544903i | ||||
\(541\) | 10389.1i | 0.825620i | 0.910817 | + | 0.412810i | \(0.135453\pi\) | ||||
−0.910817 | + | 0.412810i | \(0.864547\pi\) | |||||||
\(542\) | −11128.9 | − | 19275.9i | −0.881972 | − | 1.52762i | ||||
\(543\) | −61.4011 | − | 647.493i | −0.00485262 | − | 0.0511723i | ||||
\(544\) | −3390.88 | − | 1957.73i | −0.267248 | − | 0.154296i | ||||
\(545\) | −2133.20 | + | 3694.81i | −0.167663 | + | 0.290400i | ||||
\(546\) | −6728.94 | − | 3270.93i | −0.527421 | − | 0.256379i | ||||
\(547\) | −3395.32 | − | 5880.87i | −0.265400 | − | 0.459685i | 0.702269 | − | 0.711912i | \(-0.252171\pi\) |
−0.967668 | + | 0.252227i | \(0.918837\pi\) | |||||||
\(548\) | 2205.54i | 0.171927i | ||||||||
\(549\) | 5537.84 | + | 6407.91i | 0.430509 | + | 0.498148i | ||||
\(550\) | 4614.93 | 0.357784 | ||||||||
\(551\) | 870.891 | − | 502.809i | 0.0673343 | − | 0.0388755i | ||||
\(552\) | 5244.94 | − | 11465.0i | 0.404420 | − | 0.884026i | ||||
\(553\) | 10889.0 | + | 6286.76i | 0.837336 | + | 0.483436i | ||||
\(554\) | −1092.13 | − | 630.542i | −0.0837548 | − | 0.0483559i | ||||
\(555\) | 5994.77 | + | 2742.46i | 0.458494 | + | 0.209749i | ||||
\(556\) | 1478.61 | + | 2561.02i | 0.112782 | + | 0.195344i | ||||
\(557\) | 17044.7i | 1.29660i | 0.761384 | + | 0.648301i | \(0.224520\pi\) | ||||
−0.761384 | + | 0.648301i | \(0.775480\pi\) | |||||||
\(558\) | −534.799 | + | 102.349i | −0.0405732 | + | 0.00776486i | ||||
\(559\) | 2168.29 | + | 3967.27i | 0.164059 | + | 0.300175i | ||||
\(560\) | 2031.44 | + | 3518.55i | 0.153293 | + | 0.265511i | ||||
\(561\) | 3331.86 | + | 4685.42i | 0.250751 | + | 0.352618i | ||||
\(562\) | −12699.6 | + | 21996.3i | −0.953201 | + | 1.65099i | ||||
\(563\) | −1451.41 | + | 2513.91i | −0.108649 | + | 0.188186i | −0.915223 | − | 0.402947i | \(-0.867986\pi\) |
0.806574 | + | 0.591133i | \(0.201319\pi\) | |||||||
\(564\) | −1862.91 | + | 176.658i | −0.139083 | + | 0.0131891i | ||||
\(565\) | 8494.46 | − | 4904.28i | 0.632504 | − | 0.365176i | ||||
\(566\) | 3813.95i | 0.283237i | ||||||||
\(567\) | −4561.87 | + | 5769.79i | −0.337884 | + | 0.427351i | ||||
\(568\) | −13750.0 | −1.01573 | ||||||||
\(569\) | 10399.5 | + | 18012.5i | 0.766204 | + | 1.32710i | 0.939608 | + | 0.342253i | \(0.111190\pi\) |
−0.173404 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(570\) | −635.097 | + | 60.2257i | −0.0466689 | + | 0.00442557i | ||||
\(571\) | 13115.3 | − | 22716.3i | 0.961220 | − | 1.66488i | 0.241776 | − | 0.970332i | \(-0.422270\pi\) |
0.719445 | − | 0.694550i | \(-0.244396\pi\) | |||||||
\(572\) | −22.4224 | + | 957.526i | −0.00163904 | + | 0.0699933i | ||||
\(573\) | −1754.78 | + | 1247.84i | −0.127935 | + | 0.0909763i | ||||
\(574\) | −6566.89 | + | 3791.39i | −0.477520 | + | 0.275696i | ||||
\(575\) | −11153.1 | −0.808902 | ||||||||
\(576\) | 10792.7 | − | 2065.50i | 0.780721 | − | 0.149414i | ||||
\(577\) | − | 797.699i | − | 0.0575540i | −0.999586 | − | 0.0287770i | \(-0.990839\pi\) | ||
0.999586 | − | 0.0287770i | \(-0.00916126\pi\) | |||||||
\(578\) | 489.543 | − | 282.638i | 0.0352289 | − | 0.0203394i | ||||
\(579\) | −8899.76 | + | 19454.1i | −0.638793 | + | 1.39635i | ||||
\(580\) | 844.921 | + | 487.815i | 0.0604887 | + | 0.0349231i | ||||
\(581\) | 6670.31 | − | 11553.3i | 0.476301 | − | 0.824978i | ||||
\(582\) | −23570.1 | − | 10782.7i | −1.67871 | − | 0.767969i | ||||
\(583\) | −2991.32 | + | 1727.04i | −0.212500 | + | 0.122687i | ||||
\(584\) | 15053.6 | 1.06665 | ||||||||
\(585\) | −6579.47 | − | 2460.91i | −0.465004 | − | 0.173925i | ||||
\(586\) | 12210.7 | 0.860786 | ||||||||
\(587\) | 16577.8 | − | 9571.22i | 1.16566 | − | 0.672992i | 0.213004 | − | 0.977051i | \(-0.431675\pi\) |
0.952653 | + | 0.304059i | \(0.0983420\pi\) | |||||||
\(588\) | −1296.94 | + | 922.273i | −0.0909610 | + | 0.0646835i | ||||
\(589\) | 24.0600 | − | 41.6731i | 0.00168315 | − | 0.00291530i | ||||
\(590\) | −6018.10 | − | 3474.55i | −0.419934 | − | 0.242449i | ||||
\(591\) | 8792.37 | − | 833.772i | 0.611962 | − | 0.0580318i | ||||
\(592\) | −14360.0 | + | 8290.73i | −0.996945 | + | 0.575586i | ||||
\(593\) | 17283.4i | 1.19687i | 0.801171 | + | 0.598436i | \(0.204211\pi\) | ||||
−0.801171 | + | 0.598436i | \(0.795789\pi\) | |||||||
\(594\) | 6676.98 | + | 1633.68i | 0.461212 | + | 0.112847i | ||||
\(595\) | 3850.60 | 0.265310 | ||||||||
\(596\) | 830.480 | − | 479.478i | 0.0570768 | − | 0.0329533i | ||||
\(597\) | −2021.94 | − | 21322.0i | −0.138614 | − | 1.46172i | ||||
\(598\) | 395.599 | − | 16893.6i | 0.0270522 | − | 1.15524i | ||||
\(599\) | 3756.18 | − | 6505.90i | 0.256216 | − | 0.443779i | −0.709009 | − | 0.705199i | \(-0.750857\pi\) |
0.965225 | + | 0.261420i | \(0.0841908\pi\) | |||||||
\(600\) | −5811.96 | − | 8173.06i | −0.395454 | − | 0.556106i | ||||
\(601\) | 10384.5 | + | 17986.6i | 0.704816 | + | 1.22078i | 0.966758 | + | 0.255694i | \(0.0823039\pi\) |
−0.261941 | + | 0.965084i | \(0.584363\pi\) | |||||||
\(602\) | −2963.08 | −0.200608 | ||||||||
\(603\) | 4855.73 | + | 1687.69i | 0.327928 | + | 0.113977i | ||||
\(604\) | 1739.68i | 0.117196i | ||||||||
\(605\) | 5153.26 | − | 2975.24i | 0.346297 | − | 0.199935i | ||||
\(606\) | 1313.13 | − | 2870.38i | 0.0880234 | − | 0.192411i | ||||
\(607\) | −9778.44 | + | 16936.8i | −0.653863 | + | 1.13252i | 0.328315 | + | 0.944568i | \(0.393519\pi\) |
−0.982178 | + | 0.187955i | \(0.939814\pi\) | |||||||
\(608\) | 206.855 | − | 358.283i | 0.0137978 | − | 0.0238985i | ||||
\(609\) | −3019.06 | + | 6599.40i | −0.200884 | + | 0.439115i | ||||
\(610\) | −2650.53 | − | 4590.86i | −0.175929 | − | 0.304719i | ||||
\(611\) | 11665.0 | − | 6375.41i | 0.772362 | − | 0.422130i | ||||
\(612\) | −773.884 | + | 2226.57i | −0.0511151 | + | 0.147065i | ||||
\(613\) | 1142.33i | 0.0752662i | 0.999292 | + | 0.0376331i | \(0.0119818\pi\) | ||||
−0.999292 | + | 0.0376331i | \(0.988018\pi\) | |||||||
\(614\) | −13108.5 | − | 22704.6i | −0.861590 | − | 1.49232i | ||||
\(615\) | −5802.02 | + | 4125.89i | −0.380423 | + | 0.270523i | ||||
\(616\) | 2881.34 | + | 1663.54i | 0.188462 | + | 0.108809i | ||||
\(617\) | 3394.09 | + | 1959.58i | 0.221460 | + | 0.127860i | 0.606626 | − | 0.794987i | \(-0.292522\pi\) |
−0.385166 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(618\) | 13308.6 | − | 1262.04i | 0.866263 | − | 0.0821469i | ||||
\(619\) | −8523.92 | + | 4921.28i | −0.553482 | + | 0.319553i | −0.750525 | − | 0.660842i | \(-0.770199\pi\) |
0.197043 | + | 0.980395i | \(0.436866\pi\) | |||||||
\(620\) | 46.6850 | 0.00302406 | ||||||||
\(621\) | −16136.6 | − | 3948.21i | −1.04274 | − | 0.255131i | ||||
\(622\) | 3712.75i | 0.239337i | ||||||||
\(623\) | 3635.57 | + | 6296.99i | 0.233798 | + | 0.404950i | ||||
\(624\) | 14635.1 | − | 9899.67i | 0.938901 | − | 0.635102i | ||||
\(625\) | −2510.28 | + | 4347.92i | −0.160658 | + | 0.278267i | ||||
\(626\) | 2212.26 | + | 1277.25i | 0.141245 | + | 0.0815480i | ||||
\(627\) | −495.066 | + | 352.047i | −0.0315327 | + | 0.0224233i | ||||
\(628\) | −727.629 | − | 1260.29i | −0.0462350 | − | 0.0800813i | ||||
\(629\) | 15715.1i | 0.996190i | ||||||||
\(630\) | 3483.28 | − | 3010.31i | 0.220281 | − | 0.190371i | ||||
\(631\) | − | 7460.17i | − | 0.470657i | −0.971916 | − | 0.235329i | \(-0.924383\pi\) | ||
0.971916 | − | 0.235329i | \(-0.0756166\pi\) | |||||||
\(632\) | −22114.4 | + | 12767.8i | −1.39188 | + | 0.803600i | ||||
\(633\) | 8327.46 | + | 3809.60i | 0.522886 | + | 0.239207i | ||||
\(634\) | 10787.5 | − | 18684.5i | 0.675750 | − | 1.17043i | ||||
\(635\) | −3257.43 | − | 1880.68i | −0.203570 | − | 0.117531i | ||||
\(636\) | −1287.82 | − | 589.144i | −0.0802913 | − | 0.0367312i | ||||
\(637\) | 5880.43 | − | 9655.86i | 0.365763 | − | 0.600595i | ||||
\(638\) | 6782.20 | 0.420862 | ||||||||
\(639\) | 3405.54 | + | 17794.7i | 0.210831 | + | 1.10164i | ||||
\(640\) | −9406.68 | −0.580987 | ||||||||
\(641\) | −14122.2 | − | 24460.4i | −0.870195 | − | 1.50722i | −0.861794 | − | 0.507258i | \(-0.830659\pi\) |
−0.00840076 | − | 0.999965i | \(-0.502674\pi\) | |||||||
\(642\) | −12352.5 | − | 17370.6i | −0.759365 | − | 1.06786i | ||||
\(643\) | −7915.00 | − | 4569.73i | −0.485439 | − | 0.280268i | 0.237241 | − | 0.971451i | \(-0.423757\pi\) |
−0.722680 | + | 0.691183i | \(0.757090\pi\) | |||||||
\(644\) | 1313.79 | + | 758.520i | 0.0803894 | + | 0.0464128i | ||||
\(645\) | −2769.59 | + | 262.638i | −0.169074 | + | 0.0160331i | ||||
\(646\) | −760.389 | − | 1317.03i | −0.0463113 | − | 0.0802135i | ||||
\(647\) | 13312.8 | 0.808933 | 0.404466 | − | 0.914553i | \(-0.367457\pi\) | ||||
0.404466 | + | 0.914553i | \(0.367457\pi\) | |||||||
\(648\) | −5515.61 | − | 13882.4i | −0.334373 | − | 0.841592i | ||||
\(649\) | −6617.20 | −0.400228 | ||||||||
\(650\) | −11480.4 | − | 6991.55i | −0.692764 | − | 0.421894i | ||||
\(651\) | 32.7837 | + | 345.713i | 0.00197372 | + | 0.0208135i | ||||
\(652\) | 40.2904 | + | 23.2617i | 0.00242008 | + | 0.00139724i | ||||
\(653\) | −4591.45 | + | 7952.62i | −0.275156 | + | 0.476585i | −0.970175 | − | 0.242407i | \(-0.922063\pi\) |
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(654\) | −9909.83 | + | 7047.01i | −0.592516 | + | 0.421345i | ||||
\(655\) | −6055.31 | + | 3496.03i | −0.361222 | + | 0.208552i | ||||
\(656\) | − | 17907.4i | − | 1.06580i | ||||||
\(657\) | −3728.42 | − | 19481.8i | −0.221399 | − | 1.15686i | ||||
\(658\) | 8712.33i | 0.516173i | ||||||||
\(659\) | 587.895 | + | 1018.26i | 0.0347514 | + | 0.0601911i | 0.882878 | − | 0.469602i | \(-0.155603\pi\) |
−0.848127 | + | 0.529794i | \(0.822269\pi\) | |||||||
\(660\) | −535.942 | − | 245.180i | −0.0316083 | − | 0.0144600i | ||||
\(661\) | 17964.1 | + | 10371.6i | 1.05707 | + | 0.610300i | 0.924620 | − | 0.380890i | \(-0.124382\pi\) |
0.132450 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(662\) | 14491.1 | − | 25099.3i | 0.850775 | − | 1.47358i | ||||
\(663\) | −1190.18 | − | 16703.4i | −0.0697177 | − | 0.978442i | ||||
\(664\) | 13546.7 | + | 23463.6i | 0.791739 | + | 1.37133i | ||||
\(665\) | 406.858i | 0.0237252i | ||||||||
\(666\) | 12285.8 | + | 14216.0i | 0.714810 | + | 0.827116i | ||||
\(667\) | −16390.9 | −0.951512 | ||||||||
\(668\) | 3430.57 | − | 1980.64i | 0.198702 | − | 0.114721i | ||||
\(669\) | −2598.06 | − | 3653.51i | −0.150145 | − | 0.211140i | ||||
\(670\) | −2786.54 | − | 1608.81i | −0.160677 | − | 0.0927668i | ||||
\(671\) | −4371.59 | − | 2523.94i | −0.251510 | − | 0.145210i | ||||
\(672\) | 281.857 | + | 2972.26i | 0.0161798 | + | 0.170621i | ||||
\(673\) | 8580.99 | + | 14862.7i | 0.491490 | + | 0.851286i | 0.999952 | − | 0.00979839i | \(-0.00311897\pi\) |
−0.508462 | + | 0.861085i | \(0.669786\pi\) | |||||||
\(674\) | − | 22132.6i | − | 1.26486i | ||||||
\(675\) | −9137.79 | + | 9545.90i | −0.521057 | + | 0.544329i | ||||
\(676\) | 1506.42 | − | 2348.02i | 0.0857087 | − | 0.133593i | ||||
\(677\) | 16289.3 | + | 28213.9i | 0.924739 | + | 1.60169i | 0.791980 | + | 0.610546i | \(0.209050\pi\) |
0.132758 | + | 0.991148i | \(0.457617\pi\) | |||||||
\(678\) | 27831.3 | − | 2639.21i | 1.57648 | − | 0.149496i | ||||
\(679\) | −8265.20 | + | 14315.8i | −0.467142 | + | 0.809114i | ||||
\(680\) | −3910.09 | + | 6772.48i | −0.220508 | + | 0.381930i | ||||
\(681\) | −1649.77 | − | 2319.99i | −0.0928331 | − | 0.130546i | ||||
\(682\) | 281.056 | − | 162.268i | 0.0157804 | − | 0.00911079i | ||||
\(683\) | − | 22612.1i | − | 1.26681i | −0.773822 | − | 0.633404i | \(-0.781657\pi\) | ||
0.773822 | − | 0.633404i | \(-0.218343\pi\) | |||||||
\(684\) | −235.262 | − | 81.7693i | −0.0131513 | − | 0.00457095i | ||||
\(685\) | 9641.16 | 0.537766 | ||||||||
\(686\) | 8973.07 | + | 15541.8i | 0.499407 | + | 0.864999i | ||||
\(687\) | −1931.58 | + | 4222.26i | −0.107270 | + | 0.234482i | ||||
\(688\) | 3498.78 | − | 6060.06i | 0.193880 | − | 0.335810i | ||||
\(689\) | 10057.8 | + | 235.524i | 0.556127 | + | 0.0130228i | ||||
\(690\) | 9455.61 | + | 4325.70i | 0.521694 | + | 0.238662i | ||||
\(691\) | 804.889 | − | 464.703i | 0.0443118 | − | 0.0255834i | −0.477680 | − | 0.878534i | \(-0.658522\pi\) |
0.521992 | + | 0.852950i | \(0.325189\pi\) | |||||||
\(692\) | −1440.22 | −0.0791171 | ||||||||
\(693\) | 1439.26 | − | 4140.95i | 0.0788931 | − | 0.226986i | ||||
\(694\) | 19887.6i | 1.08778i | ||||||||
\(695\) | 11195.1 | − | 6463.50i | 0.611014 | − | 0.352769i | ||||
\(696\) | −8541.39 | − | 12011.3i | −0.465173 | − | 0.654148i | ||||
\(697\) | −14698.0 | − | 8485.88i | −0.798746 | − | 0.461156i | ||||
\(698\) | 16537.5 | − | 28643.8i | 0.896782 | − | 1.55327i | ||||
\(699\) | 1052.04 | + | 11094.1i | 0.0569269 | + | 0.600311i | ||||
\(700\) | 1045.06 | − | 603.366i | 0.0564279 | − | 0.0325787i | ||||
\(701\) | −6586.37 | −0.354870 | −0.177435 | − | 0.984133i | \(-0.556780\pi\) | ||||
−0.177435 | + | 0.984133i | \(0.556780\pi\) | |||||||
\(702\) | −14135.0 | − | 14179.6i | −0.759960 | − | 0.762354i | ||||
\(703\) | −1660.48 | −0.0890840 | ||||||||
\(704\) | −5671.95 | + | 3274.70i | −0.303650 | + | 0.175313i | ||||
\(705\) | 772.233 | + | 8143.42i | 0.0412539 | + | 0.435034i | ||||
\(706\) | −8522.15 | + | 14760.8i | −0.454299 | + | 0.786870i | ||||
\(707\) | −1743.38 | − | 1006.54i | −0.0927393 | − | 0.0535431i | ||||
\(708\) | −1572.29 | − | 2211.03i | −0.0834608 | − | 0.117367i | ||||
\(709\) | −30479.9 | + | 17597.6i | −1.61452 | + | 0.932144i | −0.626216 | + | 0.779650i | \(0.715397\pi\) |
−0.988304 | + | 0.152494i | \(0.951269\pi\) | |||||||
\(710\) | − | 11340.1i | − | 0.599419i | ||||||
\(711\) | 22000.8 | + | 25457.4i | 1.16047 | + | 1.34280i | ||||
\(712\) | −14766.9 | −0.777268 | ||||||||
\(713\) | −679.243 | + | 392.161i | −0.0356772 | + | 0.0205983i | ||||
\(714\) | 9980.13 | + | 4565.66i | 0.523105 | + | 0.239307i | ||||
\(715\) | 4185.68 | + | 98.0162i | 0.218931 | + | 0.00512671i | ||||
\(716\) | −640.167 | + | 1108.80i | −0.0334137 | + | 0.0578741i | ||||
\(717\) | 10528.2 | − | 23013.8i | 0.548374 | − | 1.19870i | ||||
\(718\) | 2387.92 | + | 4135.99i | 0.124117 | + | 0.214978i | ||||
\(719\) | 30432.2 | 1.57848 | 0.789241 | − | 0.614083i | \(-0.210474\pi\) | ||||
0.789241 | + | 0.614083i | \(0.210474\pi\) | |||||||
\(720\) | 2043.64 | + | 10678.5i | 0.105781 | + | 0.552728i | ||||
\(721\) | − | 8525.80i | − | 0.440385i | ||||||
\(722\) | −17946.2 | + | 10361.2i | −0.925051 | + | 0.534079i | ||||
\(723\) | 15680.8 | + | 22051.1i | 0.806605 | + | 1.13429i | ||||
\(724\) | −79.4688 | + | 137.644i | −0.00407933 | + | 0.00706560i | ||||
\(725\) | −6519.08 | + | 11291.4i | −0.333948 | + | 0.578416i | ||||
\(726\) | 16884.2 | − | 1601.11i | 0.863127 | − | 0.0818495i | ||||
\(727\) | 6261.40 | + | 10845.1i | 0.319425 | + | 0.553261i | 0.980368 | − | 0.197175i | \(-0.0631768\pi\) |
−0.660943 | + | 0.750436i | \(0.729843\pi\) | |||||||
\(728\) | −4647.54 | − | 8503.51i | −0.236606 | − | 0.432913i | ||||
\(729\) | −16600.0 | + | 10576.4i | −0.843367 | + | 0.537338i | ||||
\(730\) | 12415.3i | 0.629466i | ||||||||
\(731\) | −3315.98 | − | 5743.44i | −0.167778 | − | 0.290600i | ||||
\(732\) | −195.386 | − | 2060.40i | −0.00986566 | − | 0.104036i | ||||
\(733\) | −9955.67 | − | 5747.91i | −0.501666 | − | 0.289637i | 0.227735 | − | 0.973723i | \(-0.426868\pi\) |
−0.729401 | + | 0.684086i | \(0.760201\pi\) | |||||||
\(734\) | −5102.24 | − | 2945.78i | −0.256576 | − | 0.148134i | ||||
\(735\) | 4031.57 | + | 5669.39i | 0.202322 | + | 0.284515i | ||||
\(736\) | −5839.78 | + | 3371.60i | −0.292469 | + | 0.168857i | ||||
\(737\) | −3063.94 | −0.153137 | ||||||||
\(738\) | −19930.0 | + | 3814.18i | −0.994081 | + | 0.190246i | ||||
\(739\) | − | 33163.0i | − | 1.65077i | −0.564569 | − | 0.825386i | \(-0.690958\pi\) | ||
0.564569 | − | 0.825386i | \(-0.309042\pi\) | |||||||
\(740\) | −805.480 | − | 1395.13i | −0.0400135 | − | 0.0693055i | ||||
\(741\) | 1764.90 | − | 125.756i | 0.0874968 | − | 0.00623448i | ||||
\(742\) | −3296.76 | + | 5710.15i | −0.163110 | + | 0.282515i | ||||
\(743\) | 269.186 | + | 155.415i | 0.0132914 | + | 0.00767377i | 0.506631 | − | 0.862163i | \(-0.330891\pi\) |
−0.493340 | + | 0.869837i | \(0.664224\pi\) | |||||||
\(744\) | −641.334 | − | 293.394i | −0.0316028 | − | 0.0144575i | ||||
\(745\) | −2095.96 | − | 3630.31i | −0.103074 | − | 0.178529i | ||||
\(746\) | − | 25999.9i | − | 1.27604i | ||||||
\(747\) | 27010.5 | − | 23343.0i | 1.32298 | − | 1.14334i | ||||
\(748\) | − | 1404.96i | − | 0.0686769i | ||||||
\(749\) | −11772.6 | + | 6796.89i | −0.574312 | + | 0.331579i | ||||
\(750\) | 15686.1 | − | 11154.6i | 0.763702 | − | 0.543078i | ||||
\(751\) | 19054.8 | − | 33003.9i | 0.925859 | − | 1.60363i | 0.135685 | − | 0.990752i | \(-0.456676\pi\) |
0.790174 | − | 0.612883i | \(-0.209990\pi\) | |||||||
\(752\) | −17818.4 | − | 10287.4i | −0.864054 | − | 0.498862i | ||||
\(753\) | −2226.82 | − | 23482.4i | −0.107769 | − | 1.13645i | ||||
\(754\) | −16871.8 | − | 10274.9i | −0.814899 | − | 0.496274i | ||||
\(755\) | 7604.74 | 0.366576 | ||||||||
\(756\) | 1725.61 | − | 503.011i | 0.0830154 | − | 0.0241989i | ||||
\(757\) | −38423.1 | −1.84480 | −0.922399 | − | 0.386238i | \(-0.873774\pi\) | ||||
−0.922399 | + | 0.386238i | \(0.873774\pi\) | |||||||
\(758\) | −13515.9 | − | 23410.2i | −0.647651 | − | 1.12177i | ||||
\(759\) | 9857.23 | − | 934.752i | 0.471403 | − | 0.0447027i | ||||
\(760\) | −715.586 | − | 413.144i | −0.0341540 | − | 0.0197188i | ||||
\(761\) | −12394.9 | − | 7156.21i | −0.590427 | − | 0.340883i | 0.174839 | − | 0.984597i | \(-0.444059\pi\) |
−0.765266 | + | 0.643714i | \(0.777393\pi\) | |||||||
\(762\) | −6212.81 | − | 8736.75i | −0.295363 | − | 0.415353i | ||||
\(763\) | 3877.59 | + | 6716.18i | 0.183982 | + | 0.318666i | ||||
\(764\) | 526.182 | 0.0249170 | ||||||||
\(765\) | 9733.12 | + | 3382.92i | 0.460002 | + | 0.159882i | ||||
\(766\) | 27511.0 | 1.29767 | ||||||||
\(767\) | 16461.3 | + | 10024.9i | 0.774946 | + | 0.471943i | ||||
\(768\) | −8996.03 | − | 4115.45i | −0.422677 | − | 0.193364i | ||||
\(769\) | 2405.24 | + | 1388.67i | 0.112790 | + | 0.0651191i | 0.555334 | − | 0.831628i | \(-0.312591\pi\) |
−0.442544 | + | 0.896747i | \(0.645924\pi\) | |||||||
\(770\) | −1371.99 | + | 2376.35i | −0.0642117 | + | 0.111218i | ||||
\(771\) | −3625.66 | − | 1658.65i | −0.169358 | − | 0.0774769i | ||||
\(772\) | 4527.45 | − | 2613.92i | 0.211070 | − | 0.121862i | ||||
\(773\) | 3486.85i | 0.162242i | 0.996704 | + | 0.0811211i | \(0.0258501\pi\) | ||||
−0.996704 | + | 0.0811211i | \(0.974150\pi\) | |||||||
\(774\) | −7489.74 | − | 2603.19i | −0.347821 | − | 0.120891i | ||||
\(775\) | 623.890i | 0.0289172i | ||||||||
\(776\) | −16785.8 | − | 29073.9i | −0.776514 | − | 1.34496i | ||||
\(777\) | 9765.64 | − | 6944.47i | 0.450889 | − | 0.320633i | ||||
\(778\) | 15942.2 | + | 9204.24i | 0.734647 | + | 0.424149i | ||||
\(779\) | 896.626 | − | 1553.00i | 0.0412387 | − | 0.0714275i | ||||
\(780\) | 961.794 | + | 1421.86i | 0.0441510 | + | 0.0652704i | ||||
\(781\) | −5399.25 | − | 9351.78i | −0.247376 | − | 0.428468i | ||||
\(782\) | 24787.6i | 1.13351i | ||||||||
\(783\) | −13429.1 | + | 14028.9i | −0.612920 | + | 0.640294i | ||||
\(784\) | −17498.0 | −0.797104 | ||||||||
\(785\) | −5509.17 | + | 3180.72i | −0.250485 | + | 0.144617i | ||||
\(786\) | −19839.6 | + | 1881.37i | −0.900326 | + | 0.0853771i | ||||
\(787\) | 30317.0 | + | 17503.5i | 1.37317 | + | 0.792799i | 0.991326 | − | 0.131428i | \(-0.0419562\pi\) |
0.381843 | + | 0.924227i | \(0.375290\pi\) | |||||||
\(788\) | −1869.08 | − | 1079.11i | −0.0844965 | − | 0.0487841i | ||||
\(789\) | 34203.1 | − | 24322.3i | 1.54330 | − | 1.09746i | ||||
\(790\) | −10530.1 | − | 18238.6i | −0.474232 | − | 0.821393i | ||||
\(791\) | − | 17829.4i | − | 0.801440i | ||||||
\(792\) | 5821.65 | + | 6736.30i | 0.261191 | + | 0.302227i | ||||
\(793\) | 7051.28 | + | 12901.6i | 0.315761 | + | 0.577741i | ||||
\(794\) | 19091.0 | + | 33066.6i | 0.853292 | + | 1.47794i | ||||
\(795\) | −2575.35 | + | 5629.49i | −0.114891 | + | 0.251142i | ||||
\(796\) | −2616.91 | + | 4532.62i | −0.116525 | + | 0.201827i | ||||
\(797\) | 7551.67 | − | 13079.9i | 0.335626 | − | 0.581321i | −0.647979 | − | 0.761658i | \(-0.724386\pi\) |
0.983605 | + | 0.180337i | \(0.0577189\pi\) | |||||||
\(798\) | −482.411 | + | 1054.51i | −0.0214000 | + | 0.0467785i | ||||
\(799\) | −16887.4 | + | 9749.95i | −0.747727 | + | 0.431700i | ||||
\(800\) | 5363.88i | 0.237052i | ||||||||
\(801\) | 3657.41 | + | 19110.8i | 0.161334 | + | 0.843006i | ||||
\(802\) | −19261.8 | −0.848078 | ||||||||
\(803\) | 5911.15 | + | 10238.4i | 0.259776 | + | 0.449945i | ||||
\(804\) | −728.012 | − | 1023.77i | −0.0319341 | − | 0.0449072i | ||||
\(805\) | 3315.75 | − | 5743.05i | 0.145174 | − | 0.251448i | ||||
\(806\) | −945.004 | − | 22.1292i | −0.0412982 | − | 0.000967081i | ||||
\(807\) | −807.872 | − | 8519.24i | −0.0352397 | − | 0.371613i | ||||
\(808\) | 3540.64 | − | 2044.19i | 0.154157 | − | 0.0890029i | ||||
\(809\) | 1284.09 | 0.0558048 | 0.0279024 | − | 0.999611i | \(-0.491117\pi\) | ||||
0.0279024 | + | 0.999611i | \(0.491117\pi\) | |||||||
\(810\) | 11449.3 | − | 4548.93i | 0.496652 | − | 0.197325i | ||||
\(811\) | 23107.7i | 1.00052i | 0.865876 | + | 0.500259i | \(0.166762\pi\) | ||||
−0.865876 | + | 0.500259i | \(0.833238\pi\) | |||||||
\(812\) | 1535.84 | − | 886.719i | 0.0663762 | − | 0.0383223i | ||||
\(813\) | −37817.0 | + | 3586.15i | −1.63136 | + | 0.154701i | ||||
\(814\) | −9698.41 | − | 5599.38i | −0.417603 | − | 0.241103i | ||||
\(815\) | 101.685 | − | 176.123i | 0.00437039 | − | 0.00756973i | ||||
\(816\) | −21122.1 | + | 15020.2i | −0.906153 | + | 0.644377i | ||||
\(817\) | 606.857 | − | 350.369i | 0.0259868 | − | 0.0150035i | ||||
\(818\) | 11579.9 | 0.494964 | ||||||||
\(819\) | −9853.84 | + | 8120.79i | −0.420416 | + | 0.346475i | ||||
\(820\) | 1739.78 | 0.0740922 | ||||||||
\(821\) | −19528.2 | + | 11274.6i | −0.830133 | + | 0.479278i | −0.853898 | − | 0.520440i | \(-0.825768\pi\) |
0.0237652 | + | 0.999718i | \(0.492435\pi\) | |||||||
\(822\) | 24988.3 | + | 11431.5i | 1.06030 | + | 0.485061i | ||||
\(823\) | 8724.29 | − | 15110.9i | 0.369514 | − | 0.640016i | −0.619976 | − | 0.784621i | \(-0.712858\pi\) |
0.989490 | + | 0.144604i | \(0.0461910\pi\) | |||||||
\(824\) | 14995.3 | + | 8657.52i | 0.633962 | + | 0.366018i | ||||
\(825\) | 3276.54 | − | 7162.23i | 0.138272 | − | 0.302251i | ||||
\(826\) | −10939.3 | + | 6315.82i | −0.460808 | + | 0.266048i | ||||
\(827\) | 2792.22i | 0.117406i | 0.998275 | + | 0.0587031i | \(0.0186965\pi\) | ||||
−0.998275 | + | 0.0587031i | \(0.981303\pi\) | |||||||
\(828\) | 2654.47 | + | 3071.53i | 0.111412 | + | 0.128917i | ||||
\(829\) | 11254.3 | 0.471507 | 0.235753 | − | 0.971813i | \(-0.424244\pi\) | ||||
0.235753 | + | 0.971813i | \(0.424244\pi\) | |||||||
\(830\) | −19351.3 | + | 11172.5i | −0.809270 | + | 0.467232i | ||||
\(831\) | −1753.98 | + | 1247.28i | −0.0732189 | + | 0.0520669i | ||||
\(832\) | 19071.0 | + | 446.586i | 0.794672 | + | 0.0186089i | ||||
\(833\) | −8291.91 | + | 14362.0i | −0.344895 | + | 0.597376i | ||||
\(834\) | 36679.7 | − | 3478.30i | 1.52292 | − | 0.144417i | ||||
\(835\) | −8658.07 | − | 14996.2i | −0.358832 | − | 0.621516i | ||||
\(836\) | 148.449 | 0.00614141 | ||||||||
\(837\) | −220.857 | + | 902.658i | −0.00912059 | + | 0.0372765i | ||||
\(838\) | 33258.3i | 1.37099i | ||||||||
\(839\) | 31822.0 | − | 18372.4i | 1.30943 | − | 0.756003i | 0.327433 | − | 0.944874i | \(-0.393816\pi\) |
0.982002 | + | 0.188872i | \(0.0604831\pi\) | |||||||
\(840\) | 5936.38 | − | 562.942i | 0.243839 | − | 0.0231230i | ||||
\(841\) | 2613.92 | − | 4527.45i | 0.107176 | − | 0.185635i | ||||
\(842\) | −18161.1 | + | 31455.9i | −0.743315 | + | 1.28746i | ||||
\(843\) | 25121.1 | + | 35326.4i | 1.02635 | + | 1.44331i | ||||
\(844\) | −1118.91 | − | 1938.01i | −0.0456332 | − | 0.0790390i | ||||
\(845\) | −10264.0 | − | 6585.06i | −0.417862 | − | 0.268086i | ||||
\(846\) | −7654.15 | + | 22022.1i | −0.311058 | + | 0.894957i | ||||
\(847\) | − | 10816.4i | − | 0.438790i | ||||||
\(848\) | −7785.56 | − | 13485.0i | −0.315280 | − | 0.546080i | ||||
\(849\) | 5919.13 | + | 2707.85i | 0.239274 | + | 0.109462i | ||||
\(850\) | 17075.7 | + | 9858.67i | 0.689050 | + | 0.397823i | ||||
\(851\) | 23438.7 | + | 13532.3i | 0.944144 | + | 0.545102i | ||||
\(852\) | 1841.85 | − | 4026.12i | 0.0740617 | − | 0.161893i | ||||
\(853\) | 29266.7 | − | 16897.2i | 1.17476 | − | 0.678251i | 0.219967 | − | 0.975507i | \(-0.429405\pi\) |
0.954798 | + | 0.297257i | \(0.0960717\pi\) | |||||||
\(854\) | −9635.94 | −0.386107 | ||||||||
\(855\) | −357.442 | + | 1028.41i | −0.0142974 | + | 0.0411355i | ||||
\(856\) | − | 27607.6i | − | 1.10235i | ||||||
\(857\) | −21122.0 | − | 36584.3i | −0.841905 | − | 1.45822i | −0.888282 | − | 0.459299i | \(-0.848101\pi\) |
0.0463765 | − | 0.998924i | \(-0.485233\pi\) | |||||||
\(858\) | 10732.4 | + | 5217.00i | 0.427037 | + | 0.207582i | ||||
\(859\) | 6753.29 | − | 11697.0i | 0.268241 | − | 0.464607i | −0.700167 | − | 0.713980i | \(-0.746891\pi\) |
0.968408 | + | 0.249372i | \(0.0802243\pi\) | |||||||
\(860\) | 588.760 | + | 339.921i | 0.0233448 | + | 0.0134781i | ||||
\(861\) | 1221.73 | + | 12883.4i | 0.0483581 | + | 0.509950i | ||||
\(862\) | 14072.5 | + | 24374.3i | 0.556046 | + | 0.963100i | ||||
\(863\) | − | 21666.9i | − | 0.854634i | −0.904102 | − | 0.427317i | \(-0.859459\pi\) | ||
0.904102 | − | 0.427317i | \(-0.140541\pi\) | |||||||
\(864\) | −1898.81 | + | 7760.57i | −0.0747672 | + | 0.305579i | ||||
\(865\) | 6295.71i | 0.247469i | ||||||||
\(866\) | −17148.5 | + | 9900.70i | −0.672899 | + | 0.388498i | ||||
\(867\) | −91.0761 | − | 960.424i | −0.00356760 | − | 0.0376213i | ||||
\(868\) | 42.4305 | − | 73.4917i | 0.00165920 | − | 0.00287382i | ||||
\(869\) | −17367.5 | − | 10027.1i | −0.677965 | − | 0.391423i | ||||
\(870\) | 9906.17 | − | 7044.40i | 0.386035 | − | 0.274515i | ||||
\(871\) | 7622.02 | + | 4641.82i | 0.296513 | + | 0.180576i | ||||
\(872\) | −15750.0 | −0.611653 | ||||||||
\(873\) | −33468.9 | + | 28924.4i | −1.29754 | + | 1.12136i | ||||
\(874\) | −2619.08 | −0.101364 | ||||||||
\(875\) | −6137.78 | − | 10630.9i | −0.237137 | − | 0.410733i | ||||
\(876\) | −2016.47 | + | 4407.83i | −0.0777742 | + | 0.170008i | ||||
\(877\) | 534.486 | + | 308.586i | 0.0205796 | + | 0.0118816i | 0.510255 | − | 0.860023i | \(-0.329551\pi\) |
−0.489675 | + | 0.871905i | \(0.662885\pi\) | |||||||
\(878\) | 27048.6 | + | 15616.5i | 1.03969 | + | 0.600264i | ||||
\(879\) | 8669.45 | − | 18950.7i | 0.332666 | − | 0.727179i | ||||
\(880\) | −3240.06 | − | 5611.95i | −0.124116 | − | 0.214976i | ||||
\(881\) | −17158.0 | −0.656148 | −0.328074 | − | 0.944652i | \(-0.606400\pi\) | ||||
−0.328074 | + | 0.944652i | \(0.606400\pi\) | |||||||
\(882\) | 3726.99 | + | 19474.4i | 0.142284 | + | 0.743465i | ||||
\(883\) | −31380.3 | −1.19596 | −0.597979 | − | 0.801512i | \(-0.704029\pi\) | ||||
−0.597979 | + | 0.801512i | \(0.704029\pi\) | |||||||
\(884\) | −2128.49 | + | 3495.05i | −0.0809827 | + | 0.132976i | ||||
\(885\) | −9665.17 | + | 6873.02i | −0.367109 | + | 0.261056i | ||||
\(886\) | −41591.8 | − | 24013.1i | −1.57709 | − | 0.910535i | ||||
\(887\) | −4133.17 | + | 7158.87i | −0.156458 | + | 0.270993i | −0.933589 | − | 0.358346i | \(-0.883341\pi\) |
0.777131 | + | 0.629339i | \(0.216674\pi\) | |||||||
\(888\) | 2297.49 | + | 24227.7i | 0.0868228 | + | 0.915572i | ||||
\(889\) | −5921.15 | + | 3418.58i | −0.223385 | + | 0.128971i | ||||
\(890\) | − | 12178.9i | − | 0.458692i | ||||||
\(891\) | 7275.99 | − | 9202.58i | 0.273575 | − | 0.346013i | ||||
\(892\) | 1095.53i | 0.0411223i | ||||||||
\(893\) | −1030.19 | − | 1784.34i | −0.0386046 | − | 0.0668652i | ||||
\(894\) | −1127.93 | − | 11894.4i | −0.0421965 | − | 0.444974i | ||||
\(895\) | 4846.96 | + | 2798.39i | 0.181023 | + | 0.104514i | ||||
\(896\) | −8549.42 | + | 14808.0i | −0.318768 | + | 0.552122i | ||||
\(897\) | −25937.5 | − | 12608.2i | −0.965472 | − | 0.469315i | ||||
\(898\) | −10347.5 | − | 17922.5i | −0.384523 | − | 0.666014i | ||||
\(899\) | 916.882i | 0.0340153i | ||||||||
\(900\) | 3171.67 | − | 606.991i | 0.117469 | − | 0.0224812i | ||||
\(901\) | −14757.6 | −0.545667 | ||||||||
\(902\) | 10473.9 | − | 6047.12i | 0.386633 | − | 0.223223i | ||||
\(903\) | −2103.75 | + | 4598.61i | −0.0775286 | + | 0.169471i | ||||
\(904\) | 31358.5 | + | 18104.8i | 1.15372 | + | 0.666103i | ||||
\(905\) | 601.689 | + | 347.386i | 0.0221004 | + | 0.0127597i | ||||
\(906\) | 19710.2 | + | 9016.94i | 0.722769 | + | 0.330649i | ||||
\(907\) | 15791.7 | + | 27352.0i | 0.578120 | + | 1.00133i | 0.995695 | + | 0.0926903i | \(0.0295467\pi\) |
−0.417575 | + | 0.908642i | \(0.637120\pi\) | |||||||
\(908\) | 695.664i | 0.0254256i | ||||||||
\(909\) | −3522.44 | − | 4075.87i | −0.128528 | − | 0.148722i | ||||
\(910\) | 7013.16 | − | 3833.00i | 0.255477 | − | 0.139629i | ||||
\(911\) | −3394.35 | − | 5879.18i | −0.123446 | − | 0.213816i | 0.797678 | − | 0.603083i | \(-0.206061\pi\) |
−0.921125 | + | 0.389268i | \(0.872728\pi\) | |||||||
\(912\) | −1587.04 | − | 2231.78i | −0.0576231 | − | 0.0810324i | ||||
\(913\) | −10638.9 | + | 18427.1i | −0.385646 | + | 0.667959i | ||||
\(914\) | −21108.4 | + | 36560.9i | −0.763900 | + | 1.32311i | ||||
\(915\) | −9006.72 | + | 854.099i | −0.325413 | + | 0.0308586i | ||||
\(916\) | 982.625 | − | 567.319i | 0.0354441 | − | 0.0204637i | ||||
\(917\) | 12709.7i | 0.457701i | ||||||||
\(918\) | 21215.6 | + | 20308.5i | 0.762764 | + | 0.730154i | ||||
\(919\) | −15161.2 | −0.544201 | −0.272100 | − | 0.962269i | \(-0.587718\pi\) | ||||
−0.272100 | + | 0.962269i | \(0.587718\pi\) | |||||||
\(920\) | 6733.96 | + | 11663.6i | 0.241318 | + | 0.417974i | ||||
\(921\) | −44543.7 | + | 4224.04i | −1.59367 | + | 0.151126i | ||||
\(922\) | −1467.88 | + | 2542.44i | −0.0524316 | + | 0.0908142i | ||||
\(923\) | −736.320 | + | 31443.8i | −0.0262581 | + | 1.12133i | ||||
\(924\) | −873.063 | + | 620.846i | −0.0310840 | + | 0.0221043i | ||||
\(925\) | 18644.3 | − | 10764.3i | 0.662725 | − | 0.382625i | ||||
\(926\) | 36501.4 | 1.29537 | ||||||||
\(927\) | 7490.28 | − | 21550.6i | 0.265386 | − | 0.763553i | ||||
\(928\) | 7882.87i | 0.278845i | ||||||||
\(929\) | −23237.3 | + | 13416.1i | −0.820658 | + | 0.473807i | −0.850643 | − | 0.525743i | \(-0.823787\pi\) |
0.0299855 | + | 0.999550i | \(0.490454\pi\) | |||||||
\(930\) | 241.973 | − | 528.933i | 0.00853185 | − | 0.0186499i | ||||
\(931\) | −1517.50 | − | 876.130i | −0.0534201 | − | 0.0308421i | ||||
\(932\) | 1361.61 | − | 2358.38i | 0.0478553 | − | 0.0828878i | ||||
\(933\) | 5762.08 | + | 2636.00i | 0.202189 | + | 0.0924962i | ||||
\(934\) | 24230.9 | − | 13989.7i | 0.848887 | − | 0.490105i | ||||
\(935\) | −6141.55 | −0.214813 | ||||||||
\(936\) | −4276.85 | − | 25577.3i | −0.149352 | − | 0.893184i | ||||
\(937\) | 36211.6 | 1.26252 | 0.631261 | − | 0.775571i | \(-0.282538\pi\) | ||||
0.631261 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(938\) | −5065.19 | + | 2924.39i | −0.176316 | + | 0.101796i | ||||
\(939\) | 3552.92 | − | 2526.53i | 0.123477 | − | 0.0878062i | ||||
\(940\) | 999.467 | − | 1731.13i | 0.0346798 | − | 0.0600672i | ||||
\(941\) | 16812.0 | + | 9706.43i | 0.582419 | + | 0.336260i | 0.762094 | − | 0.647466i | \(-0.224171\pi\) |
−0.179675 | + | 0.983726i | \(0.557505\pi\) | |||||||
\(942\) | −18050.2 | + | 1711.69i | −0.624319 | + | 0.0592036i | ||||
\(943\) | −25312.9 | + | 14614.4i | −0.874125 | + | 0.504677i | ||||
\(944\) | − | 29830.6i | − | 1.02850i | ||||||
\(945\) | −2198.84 | − | 7543.22i | −0.0756912 | − | 0.259662i | ||||
\(946\) | 4725.99 | 0.162426 | ||||||||
\(947\) | −37558.0 | + | 21684.1i | −1.28878 | + | 0.744076i | −0.978436 | − | 0.206550i | \(-0.933776\pi\) |
−0.310341 | + | 0.950625i | \(0.600443\pi\) | |||||||
\(948\) | −776.230 | − | 8185.57i | −0.0265937 | − | 0.280438i | ||||
\(949\) | 806.130 | − | 34424.9i | 0.0275744 | − | 1.17753i | ||||
\(950\) | −1041.68 | + | 1804.24i | −0.0355752 | + | 0.0616181i | ||||
\(951\) | −21338.7 | − | 30007.5i | −0.727609 | − | 1.02320i | ||||
\(952\) | 7107.51 | + | 12310.6i | 0.241970 | + | 0.419105i | ||||
\(953\) | 4804.73 | 0.163316 | 0.0816581 | − | 0.996660i | \(-0.473978\pi\) | ||||
0.0816581 | + | 0.996660i | \(0.473978\pi\) | |||||||
\(954\) | −13349.8 | + | 11537.1i | −0.453056 | + | 0.391540i | ||||
\(955\) | − | 2300.13i | − | 0.0779375i | ||||||
\(956\) | −5355.88 | + | 3092.22i | −0.181194 | + | 0.104612i | ||||
\(957\) | 4815.27 | − | 10525.8i | 0.162650 | − | 0.355538i | ||||
\(958\) | −25017.6 | + | 43331.8i | −0.843718 | + | 1.46136i | ||||
\(959\) | 8762.54 | − | 15177.2i | 0.295054 | − | 0.511049i | ||||
\(960\) | −4883.22 | + | 10674.3i | −0.164172 | + | 0.358866i | ||||
\(961\) | −14873.6 | − | 25761.8i | −0.499264 | − | 0.864750i | ||||
\(962\) | 15643.3 | + | 28622.2i | 0.524284 | + | 0.959271i | ||||
\(963\) | −35728.7 | + | 6837.73i | −1.19558 | + | 0.228809i | ||||
\(964\) | − | 6612.17i | − | 0.220917i | ||||||
\(965\) | −11426.4 | − | 19791.0i | −0.381169 | − | 0.660203i | ||||
\(966\) | 15403.4 | − | 10953.6i | 0.513041 | − | 0.364830i | ||||
\(967\) | −28427.6 | − | 16412.7i | −0.945368 | − | 0.545809i | −0.0537292 | − | 0.998556i | \(-0.517111\pi\) |
−0.891639 | + | 0.452747i | \(0.850444\pi\) | |||||||
\(968\) | 19024.0 | + | 10983.5i | 0.631667 | + | 0.364693i | ||||
\(969\) | −2583.86 | + | 245.025i | −0.0856610 | + | 0.00812315i | ||||
\(970\) | 23978.3 | − | 13843.9i | 0.793708 | − | 0.458248i | ||||
\(971\) | −11347.9 | −0.375049 | −0.187524 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187524 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(972\) | 4803.71 | + | 244.562i | 0.158518 | + | 0.00807029i | ||||
\(973\) | − | 23497.9i | − | 0.774211i | ||||||
\(974\) | 30572.9 | + | 52953.9i | 1.00577 | + | 1.74205i | ||||
\(975\) | −19001.6 | + | 12853.3i | −0.624140 | + | 0.422188i | ||||
\(976\) | 11378.0 | − | 19707.3i | 0.373157 | − | 0.646328i | ||||
\(977\) | −16759.9 | − | 9676.31i | −0.548818 | − | 0.316860i | 0.199827 | − | 0.979831i | \(-0.435962\pi\) |
−0.748645 | + | 0.662971i | \(0.769295\pi\) | |||||||
\(978\) | 472.380 | − | 335.915i | 0.0154448 | − | 0.0109830i | ||||
\(979\) | −5798.58 | − | 10043.4i | −0.189299 | − | 0.327875i | ||||
\(980\) | − | 1700.01i | − | 0.0554130i | ||||||
\(981\) | 3900.89 | + | 20383.0i | 0.126958 | + | 0.663385i | ||||
\(982\) | − | 60101.5i | − | 1.95307i | ||||||
\(983\) | −182.802 | + | 105.541i | −0.00593131 | + | 0.00342444i | −0.502963 | − | 0.864308i | \(-0.667757\pi\) |
0.497031 | + | 0.867733i | \(0.334423\pi\) | |||||||
\(984\) | −23900.1 | − | 10933.7i | −0.774297 | − | 0.354221i | ||||
\(985\) | −4717.18 | + | 8170.40i | −0.152591 | + | 0.264295i | ||||
\(986\) | 25094.8 | + | 14488.5i | 0.810530 | + | 0.467960i | ||||
\(987\) | 13521.3 | + | 6185.64i | 0.436055 | + | 0.199484i | ||||
\(988\) | −369.290 | − | 224.898i | −0.0118914 | − | 0.00724185i | ||||
\(989\) | −11421.6 | −0.367224 | ||||||||
\(990\) | −5555.68 | + | 4801.33i | −0.178355 | + | 0.154138i | ||||
\(991\) | 20810.5 | 0.667070 | 0.333535 | − | 0.942738i | \(-0.391758\pi\) | ||||
0.333535 | + | 0.942738i | \(0.391758\pi\) | |||||||
\(992\) | 188.602 | + | 326.668i | 0.00603641 | + | 0.0104554i | ||||
\(993\) | −28664.9 | − | 40309.9i | −0.916066 | − | 1.28821i | ||||
\(994\) | −17851.7 | − | 10306.7i | −0.569639 | − | 0.328881i | ||||
\(995\) | 19813.7 | + | 11439.4i | 0.631291 | + | 0.364476i | ||||
\(996\) | −8684.96 | + | 823.587i | −0.276299 | + | 0.0262012i | ||||
\(997\) | 20607.5 | + | 35693.3i | 0.654611 | + | 1.13382i | 0.981991 | + | 0.188926i | \(0.0605008\pi\) |
−0.327381 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(998\) | 32491.7 | 1.03057 | ||||||||
\(999\) | 30785.5 | − | 8973.93i | 0.974986 | − | 0.284207i |
(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.103.11 | yes | 80 | |
3.2 | odd | 2 | 351.4.t.a.64.30 | 80 | |||
9.2 | odd | 6 | 351.4.t.a.181.11 | 80 | |||
9.7 | even | 3 | inner | 117.4.t.a.25.30 | yes | 80 | |
13.12 | even | 2 | inner | 117.4.t.a.103.30 | yes | 80 | |
39.38 | odd | 2 | 351.4.t.a.64.11 | 80 | |||
117.25 | even | 6 | inner | 117.4.t.a.25.11 | ✓ | 80 | |
117.38 | odd | 6 | 351.4.t.a.181.30 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.t.a.25.11 | ✓ | 80 | 117.25 | even | 6 | inner | |
117.4.t.a.25.30 | yes | 80 | 9.7 | even | 3 | inner | |
117.4.t.a.103.11 | yes | 80 | 1.1 | even | 1 | trivial | |
117.4.t.a.103.30 | yes | 80 | 13.12 | even | 2 | inner | |
351.4.t.a.64.11 | 80 | 39.38 | odd | 2 | |||
351.4.t.a.64.30 | 80 | 3.2 | odd | 2 | |||
351.4.t.a.181.11 | 80 | 9.2 | odd | 6 | |||
351.4.t.a.181.30 | 80 | 117.38 | odd | 6 |