Properties

Label 225.4.e.g.76.6
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.6
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.g.151.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23192 - 2.13376i) q^{2} +(-4.97325 - 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(-9.62007 - 16.6624i) q^{7} -24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +O(q^{10})\) \(q+(-1.23192 - 2.13376i) q^{2} +(-4.97325 - 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(-9.62007 - 16.6624i) q^{7} -24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +(-19.9274 - 34.5153i) q^{11} +(-7.31354 + 6.85759i) q^{12} +(0.504548 - 0.873903i) q^{13} +(-23.7024 + 41.0538i) q^{14} +(22.4208 + 38.8340i) q^{16} -52.6170 q^{17} +(4.27635 - 66.3864i) q^{18} -49.5371 q^{19} +(22.7565 + 97.3503i) q^{21} +(-49.0982 + 85.0405i) q^{22} +(13.7009 - 23.7307i) q^{23} +(121.669 + 36.8333i) q^{24} -2.48626 q^{26} +(-89.1854 - 108.300i) q^{27} -37.1228 q^{28} +(127.477 + 220.796i) q^{29} +(84.3282 - 146.061i) q^{31} +(-42.6170 + 73.8149i) q^{32} +(47.1388 + 201.656i) q^{33} +(64.8202 + 112.272i) q^{34} +(46.6967 - 23.0935i) q^{36} +419.938 q^{37} +(61.0260 + 105.700i) q^{38} +(-3.82497 + 3.58651i) q^{39} +(-199.285 + 345.172i) q^{41} +(179.687 - 168.485i) q^{42} +(179.414 + 310.754i) q^{43} -76.8977 q^{44} -67.5141 q^{46} +(70.6510 + 122.371i) q^{47} +(-53.0371 - 226.888i) q^{48} +(-13.5915 + 23.5411i) q^{49} +(261.678 + 79.2187i) q^{51} +(-0.973497 - 1.68615i) q^{52} -290.878 q^{53} +(-121.217 + 323.718i) q^{54} +(235.352 + 407.641i) q^{56} +(246.361 + 74.5817i) q^{57} +(314.083 - 544.008i) q^{58} +(-14.3659 + 24.8825i) q^{59} +(-366.364 - 634.561i) q^{61} -415.544 q^{62} +(33.3939 - 518.409i) q^{63} +568.737 q^{64} +(372.212 - 349.007i) q^{66} +(-88.2730 + 152.893i) q^{67} +(-50.7608 + 87.9203i) q^{68} +(-103.866 + 97.3911i) q^{69} -802.814 q^{71} +(-549.635 - 366.363i) q^{72} -512.820 q^{73} +(-517.332 - 896.046i) q^{74} +(-47.7895 + 82.7739i) q^{76} +(-383.406 + 664.079i) q^{77} +(12.3648 + 3.74324i) q^{78} +(-306.174 - 530.309i) q^{79} +(280.488 + 672.880i) q^{81} +982.017 q^{82} +(40.4081 + 69.9889i) q^{83} +(184.621 + 55.8910i) q^{84} +(442.049 - 765.651i) q^{86} +(-301.549 - 1290.00i) q^{87} +(487.518 + 844.405i) q^{88} +24.0097 q^{89} -19.4151 q^{91} +(-26.4352 - 45.7871i) q^{92} +(-639.290 + 599.435i) q^{93} +(174.073 - 301.504i) q^{94} +(323.079 - 302.937i) q^{96} +(683.960 + 1184.65i) q^{97} +66.9747 q^{98} +(69.1736 - 1073.86i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23192 2.13376i −0.435551 0.754397i 0.561789 0.827280i \(-0.310113\pi\)
−0.997340 + 0.0728836i \(0.976780\pi\)
\(3\) −4.97325 1.50557i −0.957103 0.289747i
\(4\) 0.964722 1.67095i 0.120590 0.208869i
\(5\) 0 0
\(6\) 2.91415 + 12.4665i 0.198283 + 0.848235i
\(7\) −9.62007 16.6624i −0.519435 0.899688i −0.999745 0.0225888i \(-0.992809\pi\)
0.480310 0.877099i \(-0.340524\pi\)
\(8\) −24.4647 −1.08120
\(9\) 22.4665 + 14.9752i 0.832093 + 0.554636i
\(10\) 0 0
\(11\) −19.9274 34.5153i −0.546213 0.946069i −0.998529 0.0542113i \(-0.982736\pi\)
0.452316 0.891858i \(-0.350598\pi\)
\(12\) −7.31354 + 6.85759i −0.175936 + 0.164968i
\(13\) 0.504548 0.873903i 0.0107643 0.0186444i −0.860593 0.509293i \(-0.829907\pi\)
0.871357 + 0.490649i \(0.163240\pi\)
\(14\) −23.7024 + 41.0538i −0.452481 + 0.783720i
\(15\) 0 0
\(16\) 22.4208 + 38.8340i 0.350326 + 0.606782i
\(17\) −52.6170 −0.750676 −0.375338 0.926888i \(-0.622473\pi\)
−0.375338 + 0.926888i \(0.622473\pi\)
\(18\) 4.27635 66.3864i 0.0559970 0.869301i
\(19\) −49.5371 −0.598136 −0.299068 0.954232i \(-0.596676\pi\)
−0.299068 + 0.954232i \(0.596676\pi\)
\(20\) 0 0
\(21\) 22.7565 + 97.3503i 0.236471 + 1.01160i
\(22\) −49.0982 + 85.0405i −0.475808 + 0.824123i
\(23\) 13.7009 23.7307i 0.124210 0.215139i −0.797214 0.603697i \(-0.793694\pi\)
0.921424 + 0.388559i \(0.127027\pi\)
\(24\) 121.669 + 36.8333i 1.03482 + 0.313274i
\(25\) 0 0
\(26\) −2.48626 −0.0187537
\(27\) −89.1854 108.300i −0.635694 0.771941i
\(28\) −37.1228 −0.250555
\(29\) 127.477 + 220.796i 0.816269 + 1.41382i 0.908413 + 0.418074i \(0.137295\pi\)
−0.0921441 + 0.995746i \(0.529372\pi\)
\(30\) 0 0
\(31\) 84.3282 146.061i 0.488574 0.846234i −0.511340 0.859379i \(-0.670851\pi\)
0.999914 + 0.0131441i \(0.00418403\pi\)
\(32\) −42.6170 + 73.8149i −0.235428 + 0.407774i
\(33\) 47.1388 + 201.656i 0.248661 + 1.06375i
\(34\) 64.8202 + 112.272i 0.326958 + 0.566308i
\(35\) 0 0
\(36\) 46.6967 23.0935i 0.216188 0.106914i
\(37\) 419.938 1.86588 0.932938 0.360038i \(-0.117236\pi\)
0.932938 + 0.360038i \(0.117236\pi\)
\(38\) 61.0260 + 105.700i 0.260519 + 0.451232i
\(39\) −3.82497 + 3.58651i −0.0157047 + 0.0147257i
\(40\) 0 0
\(41\) −199.285 + 345.172i −0.759100 + 1.31480i 0.184210 + 0.982887i \(0.441027\pi\)
−0.943310 + 0.331913i \(0.892306\pi\)
\(42\) 179.687 168.485i 0.660152 0.618996i
\(43\) 179.414 + 310.754i 0.636288 + 1.10208i 0.986241 + 0.165316i \(0.0528642\pi\)
−0.349953 + 0.936767i \(0.613802\pi\)
\(44\) −76.8977 −0.263472
\(45\) 0 0
\(46\) −67.5141 −0.216400
\(47\) 70.6510 + 122.371i 0.219266 + 0.379780i 0.954584 0.297943i \(-0.0963004\pi\)
−0.735318 + 0.677723i \(0.762967\pi\)
\(48\) −53.0371 226.888i −0.159484 0.682259i
\(49\) −13.5915 + 23.5411i −0.0396253 + 0.0686330i
\(50\) 0 0
\(51\) 261.678 + 79.2187i 0.718475 + 0.217507i
\(52\) −0.973497 1.68615i −0.00259615 0.00449666i
\(53\) −290.878 −0.753872 −0.376936 0.926239i \(-0.623022\pi\)
−0.376936 + 0.926239i \(0.623022\pi\)
\(54\) −121.217 + 323.718i −0.305473 + 0.815785i
\(55\) 0 0
\(56\) 235.352 + 407.641i 0.561611 + 0.972738i
\(57\) 246.361 + 74.5817i 0.572478 + 0.173308i
\(58\) 314.083 544.008i 0.711054 1.23158i
\(59\) −14.3659 + 24.8825i −0.0316998 + 0.0549056i −0.881440 0.472296i \(-0.843425\pi\)
0.849740 + 0.527202i \(0.176759\pi\)
\(60\) 0 0
\(61\) −366.364 634.561i −0.768985 1.33192i −0.938114 0.346327i \(-0.887429\pi\)
0.169129 0.985594i \(-0.445904\pi\)
\(62\) −415.544 −0.851195
\(63\) 33.3939 518.409i 0.0667815 1.03672i
\(64\) 568.737 1.11082
\(65\) 0 0
\(66\) 372.212 349.007i 0.694184 0.650907i
\(67\) −88.2730 + 152.893i −0.160959 + 0.278789i −0.935213 0.354086i \(-0.884792\pi\)
0.774254 + 0.632875i \(0.218125\pi\)
\(68\) −50.7608 + 87.9203i −0.0905243 + 0.156793i
\(69\) −103.866 + 97.3911i −0.181218 + 0.169920i
\(70\) 0 0
\(71\) −802.814 −1.34192 −0.670961 0.741493i \(-0.734118\pi\)
−0.670961 + 0.741493i \(0.734118\pi\)
\(72\) −549.635 366.363i −0.899655 0.599670i
\(73\) −512.820 −0.822205 −0.411103 0.911589i \(-0.634856\pi\)
−0.411103 + 0.911589i \(0.634856\pi\)
\(74\) −517.332 896.046i −0.812684 1.40761i
\(75\) 0 0
\(76\) −47.7895 + 82.7739i −0.0721294 + 0.124932i
\(77\) −383.406 + 664.079i −0.567444 + 0.982842i
\(78\) 12.3648 + 3.74324i 0.0179492 + 0.00543383i
\(79\) −306.174 530.309i −0.436041 0.755246i 0.561339 0.827586i \(-0.310286\pi\)
−0.997380 + 0.0723406i \(0.976953\pi\)
\(80\) 0 0
\(81\) 280.488 + 672.880i 0.384757 + 0.923018i
\(82\) 982.017 1.32251
\(83\) 40.4081 + 69.9889i 0.0534382 + 0.0925576i 0.891507 0.453007i \(-0.149649\pi\)
−0.838069 + 0.545564i \(0.816315\pi\)
\(84\) 184.621 + 55.8910i 0.239807 + 0.0725977i
\(85\) 0 0
\(86\) 442.049 765.651i 0.554272 0.960027i
\(87\) −301.549 1290.00i −0.371603 1.58968i
\(88\) 487.518 + 844.405i 0.590563 + 1.02289i
\(89\) 24.0097 0.0285957 0.0142979 0.999898i \(-0.495449\pi\)
0.0142979 + 0.999898i \(0.495449\pi\)
\(90\) 0 0
\(91\) −19.4151 −0.0223655
\(92\) −26.4352 45.7871i −0.0299572 0.0518873i
\(93\) −639.290 + 599.435i −0.712810 + 0.668371i
\(94\) 174.073 301.504i 0.191003 0.330827i
\(95\) 0 0
\(96\) 323.079 302.937i 0.343480 0.322067i
\(97\) 683.960 + 1184.65i 0.715934 + 1.24003i 0.962598 + 0.270934i \(0.0873324\pi\)
−0.246664 + 0.969101i \(0.579334\pi\)
\(98\) 66.9747 0.0690353
\(99\) 69.1736 1073.86i 0.0702243 1.09017i
\(100\) 0 0
\(101\) −284.206 492.260i −0.279996 0.484967i 0.691387 0.722484i \(-0.257000\pi\)
−0.971383 + 0.237517i \(0.923666\pi\)
\(102\) −153.334 655.948i −0.148846 0.636750i
\(103\) 237.579 411.499i 0.227276 0.393653i −0.729724 0.683742i \(-0.760352\pi\)
0.957000 + 0.290089i \(0.0936849\pi\)
\(104\) −12.3436 + 21.3797i −0.0116384 + 0.0201582i
\(105\) 0 0
\(106\) 358.340 + 620.664i 0.328350 + 0.568719i
\(107\) −1452.60 −1.31242 −0.656208 0.754580i \(-0.727841\pi\)
−0.656208 + 0.754580i \(0.727841\pi\)
\(108\) −267.003 + 44.5444i −0.237893 + 0.0396879i
\(109\) −1962.92 −1.72490 −0.862448 0.506146i \(-0.831070\pi\)
−0.862448 + 0.506146i \(0.831070\pi\)
\(110\) 0 0
\(111\) −2088.46 632.247i −1.78584 0.540633i
\(112\) 431.380 747.172i 0.363943 0.630367i
\(113\) −489.143 + 847.220i −0.407210 + 0.705308i −0.994576 0.104013i \(-0.966832\pi\)
0.587366 + 0.809321i \(0.300165\pi\)
\(114\) −144.359 617.552i −0.118600 0.507360i
\(115\) 0 0
\(116\) 491.918 0.393736
\(117\) 24.4223 12.0778i 0.0192978 0.00954356i
\(118\) 70.7910 0.0552275
\(119\) 506.179 + 876.728i 0.389928 + 0.675374i
\(120\) 0 0
\(121\) −128.704 + 222.923i −0.0966976 + 0.167485i
\(122\) −902.665 + 1563.46i −0.669864 + 1.16024i
\(123\) 1510.78 1416.59i 1.10750 1.03845i
\(124\) −162.706 281.816i −0.117834 0.204095i
\(125\) 0 0
\(126\) −1147.30 + 567.387i −0.811186 + 0.401165i
\(127\) −865.941 −0.605038 −0.302519 0.953143i \(-0.597828\pi\)
−0.302519 + 0.953143i \(0.597828\pi\)
\(128\) −359.705 623.028i −0.248389 0.430222i
\(129\) −424.409 1815.58i −0.289667 1.23917i
\(130\) 0 0
\(131\) 734.478 1272.15i 0.489860 0.848462i −0.510072 0.860132i \(-0.670381\pi\)
0.999932 + 0.0116695i \(0.00371460\pi\)
\(132\) 382.432 + 115.775i 0.252170 + 0.0763403i
\(133\) 476.550 + 825.409i 0.310693 + 0.538136i
\(134\) 434.983 0.280424
\(135\) 0 0
\(136\) 1287.26 0.811628
\(137\) −35.7677 61.9514i −0.0223054 0.0386341i 0.854657 0.519193i \(-0.173767\pi\)
−0.876963 + 0.480559i \(0.840434\pi\)
\(138\) 335.765 + 101.647i 0.207117 + 0.0627014i
\(139\) −114.532 + 198.376i −0.0698886 + 0.121051i −0.898852 0.438252i \(-0.855598\pi\)
0.828964 + 0.559303i \(0.188931\pi\)
\(140\) 0 0
\(141\) −167.127 714.953i −0.0998199 0.427020i
\(142\) 989.006 + 1713.01i 0.584476 + 1.01234i
\(143\) −40.2174 −0.0235185
\(144\) −77.8289 + 1208.22i −0.0450399 + 0.699202i
\(145\) 0 0
\(146\) 631.755 + 1094.23i 0.358113 + 0.620269i
\(147\) 103.037 96.6130i 0.0578117 0.0542075i
\(148\) 405.124 701.695i 0.225006 0.389723i
\(149\) 417.572 723.256i 0.229589 0.397661i −0.728097 0.685474i \(-0.759595\pi\)
0.957686 + 0.287814i \(0.0929283\pi\)
\(150\) 0 0
\(151\) 933.292 + 1616.51i 0.502982 + 0.871190i 0.999994 + 0.00344622i \(0.00109697\pi\)
−0.497013 + 0.867743i \(0.665570\pi\)
\(152\) 1211.91 0.646702
\(153\) −1182.12 787.949i −0.624632 0.416352i
\(154\) 1889.31 0.988604
\(155\) 0 0
\(156\) 2.30283 + 9.85131i 0.00118189 + 0.00505600i
\(157\) 1149.95 1991.78i 0.584563 1.01249i −0.410367 0.911921i \(-0.634599\pi\)
0.994930 0.100572i \(-0.0320673\pi\)
\(158\) −754.367 + 1306.60i −0.379837 + 0.657896i
\(159\) 1446.61 + 437.938i 0.721533 + 0.218432i
\(160\) 0 0
\(161\) −527.215 −0.258077
\(162\) 1090.22 1427.43i 0.528741 0.692281i
\(163\) 44.9023 0.0215768 0.0107884 0.999942i \(-0.496566\pi\)
0.0107884 + 0.999942i \(0.496566\pi\)
\(164\) 384.510 + 665.990i 0.183080 + 0.317104i
\(165\) 0 0
\(166\) 99.5595 172.442i 0.0465501 0.0806272i
\(167\) 588.281 1018.93i 0.272590 0.472140i −0.696934 0.717135i \(-0.745453\pi\)
0.969524 + 0.244995i \(0.0787864\pi\)
\(168\) −556.731 2381.64i −0.255671 1.09374i
\(169\) 1097.99 + 1901.78i 0.499768 + 0.865624i
\(170\) 0 0
\(171\) −1112.93 741.827i −0.497705 0.331748i
\(172\) 692.339 0.306921
\(173\) −534.045 924.994i −0.234698 0.406508i 0.724487 0.689288i \(-0.242077\pi\)
−0.959185 + 0.282780i \(0.908743\pi\)
\(174\) −2381.06 + 2232.61i −1.03740 + 0.972724i
\(175\) 0 0
\(176\) 893.579 1547.72i 0.382705 0.662864i
\(177\) 108.908 102.118i 0.0462487 0.0433654i
\(178\) −29.5781 51.2308i −0.0124549 0.0215725i
\(179\) −2779.66 −1.16068 −0.580339 0.814375i \(-0.697080\pi\)
−0.580339 + 0.814375i \(0.697080\pi\)
\(180\) 0 0
\(181\) −3568.66 −1.46550 −0.732752 0.680496i \(-0.761764\pi\)
−0.732752 + 0.680496i \(0.761764\pi\)
\(182\) 23.9180 + 41.4272i 0.00974132 + 0.0168725i
\(183\) 866.643 + 3707.42i 0.350077 + 1.49760i
\(184\) −335.189 + 580.564i −0.134296 + 0.232607i
\(185\) 0 0
\(186\) 2066.60 + 625.631i 0.814682 + 0.246632i
\(187\) 1048.52 + 1816.09i 0.410029 + 0.710192i
\(188\) 272.634 0.105765
\(189\) −946.579 + 2527.90i −0.364304 + 0.972899i
\(190\) 0 0
\(191\) 1669.31 + 2891.33i 0.632392 + 1.09534i 0.987061 + 0.160344i \(0.0512603\pi\)
−0.354669 + 0.934992i \(0.615406\pi\)
\(192\) −2828.48 856.275i −1.06316 0.321856i
\(193\) −970.433 + 1680.84i −0.361934 + 0.626888i −0.988279 0.152658i \(-0.951217\pi\)
0.626345 + 0.779546i \(0.284550\pi\)
\(194\) 1685.18 2918.81i 0.623652 1.08020i
\(195\) 0 0
\(196\) 26.2240 + 45.4213i 0.00955684 + 0.0165529i
\(197\) −1035.75 −0.374588 −0.187294 0.982304i \(-0.559972\pi\)
−0.187294 + 0.982304i \(0.559972\pi\)
\(198\) −2376.56 + 1175.31i −0.853005 + 0.421847i
\(199\) 1565.53 0.557675 0.278838 0.960338i \(-0.410051\pi\)
0.278838 + 0.960338i \(0.410051\pi\)
\(200\) 0 0
\(201\) 669.196 627.476i 0.234833 0.220193i
\(202\) −700.242 + 1212.85i −0.243905 + 0.422456i
\(203\) 2452.67 4248.14i 0.847997 1.46877i
\(204\) 384.817 360.826i 0.132071 0.123838i
\(205\) 0 0
\(206\) −1170.72 −0.395961
\(207\) 663.184 327.972i 0.222678 0.110124i
\(208\) 45.2496 0.0150841
\(209\) 987.147 + 1709.79i 0.326710 + 0.565878i
\(210\) 0 0
\(211\) −1692.64 + 2931.73i −0.552255 + 0.956534i 0.445856 + 0.895105i \(0.352899\pi\)
−0.998111 + 0.0614294i \(0.980434\pi\)
\(212\) −280.617 + 486.043i −0.0909096 + 0.157460i
\(213\) 3992.60 + 1208.69i 1.28436 + 0.388819i
\(214\) 1789.50 + 3099.50i 0.571624 + 0.990082i
\(215\) 0 0
\(216\) 2181.89 + 2649.53i 0.687310 + 0.834619i
\(217\) −3244.97 −1.01513
\(218\) 2418.17 + 4188.39i 0.751280 + 1.30126i
\(219\) 2550.38 + 772.087i 0.786935 + 0.238232i
\(220\) 0 0
\(221\) −26.5478 + 45.9821i −0.00808054 + 0.0139959i
\(222\) 1223.76 + 5235.14i 0.369971 + 1.58270i
\(223\) −1182.77 2048.62i −0.355176 0.615183i 0.631972 0.774991i \(-0.282246\pi\)
−0.987148 + 0.159808i \(0.948912\pi\)
\(224\) 1639.92 0.489158
\(225\) 0 0
\(226\) 2410.35 0.709443
\(227\) 488.115 + 845.440i 0.142720 + 0.247197i 0.928520 0.371283i \(-0.121082\pi\)
−0.785800 + 0.618480i \(0.787749\pi\)
\(228\) 362.292 339.705i 0.105234 0.0986733i
\(229\) −797.640 + 1381.55i −0.230173 + 0.398671i −0.957859 0.287240i \(-0.907262\pi\)
0.727686 + 0.685910i \(0.240596\pi\)
\(230\) 0 0
\(231\) 2906.60 2725.39i 0.827879 0.776266i
\(232\) −3118.67 5401.70i −0.882546 1.52862i
\(233\) −943.571 −0.265302 −0.132651 0.991163i \(-0.542349\pi\)
−0.132651 + 0.991163i \(0.542349\pi\)
\(234\) −55.8576 37.2322i −0.0156048 0.0104015i
\(235\) 0 0
\(236\) 27.7183 + 48.0095i 0.00764537 + 0.0132422i
\(237\) 724.262 + 3098.33i 0.198506 + 0.849190i
\(238\) 1247.15 2160.13i 0.339667 0.588320i
\(239\) −1365.75 + 2365.54i −0.369635 + 0.640227i −0.989508 0.144475i \(-0.953851\pi\)
0.619873 + 0.784702i \(0.287184\pi\)
\(240\) 0 0
\(241\) −1708.62 2959.41i −0.456687 0.791006i 0.542096 0.840317i \(-0.317631\pi\)
−0.998783 + 0.0493107i \(0.984298\pi\)
\(242\) 634.217 0.168467
\(243\) −381.867 3768.70i −0.100810 0.994906i
\(244\) −1413.76 −0.370928
\(245\) 0 0
\(246\) −4883.82 1478.50i −1.26578 0.383193i
\(247\) −24.9938 + 43.2906i −0.00643854 + 0.0111519i
\(248\) −2063.06 + 3573.32i −0.528244 + 0.914945i
\(249\) −95.5865 408.910i −0.0243275 0.104071i
\(250\) 0 0
\(251\) −3164.50 −0.795782 −0.397891 0.917433i \(-0.630258\pi\)
−0.397891 + 0.917433i \(0.630258\pi\)
\(252\) −834.019 555.920i −0.208485 0.138967i
\(253\) −1092.10 −0.271382
\(254\) 1066.77 + 1847.71i 0.263525 + 0.456439i
\(255\) 0 0
\(256\) 1388.69 2405.28i 0.339036 0.587227i
\(257\) 2774.72 4805.95i 0.673471 1.16649i −0.303442 0.952850i \(-0.598136\pi\)
0.976913 0.213636i \(-0.0685307\pi\)
\(258\) −3351.17 + 3142.24i −0.808661 + 0.758246i
\(259\) −4039.83 6997.20i −0.969201 1.67871i
\(260\) 0 0
\(261\) −442.506 + 6869.50i −0.104944 + 1.62916i
\(262\) −3619.29 −0.853436
\(263\) −2068.82 3583.30i −0.485053 0.840136i 0.514800 0.857311i \(-0.327866\pi\)
−0.999853 + 0.0171742i \(0.994533\pi\)
\(264\) −1153.24 4933.43i −0.268851 1.15012i
\(265\) 0 0
\(266\) 1174.15 2033.68i 0.270645 0.468771i
\(267\) −119.406 36.1483i −0.0273691 0.00828554i
\(268\) 170.318 + 294.999i 0.0388202 + 0.0672386i
\(269\) −1026.74 −0.232719 −0.116359 0.993207i \(-0.537122\pi\)
−0.116359 + 0.993207i \(0.537122\pi\)
\(270\) 0 0
\(271\) 3400.66 0.762270 0.381135 0.924519i \(-0.375533\pi\)
0.381135 + 0.924519i \(0.375533\pi\)
\(272\) −1179.72 2043.33i −0.262981 0.455497i
\(273\) 96.5564 + 29.2309i 0.0214061 + 0.00648035i
\(274\) −88.1261 + 152.639i −0.0194303 + 0.0336542i
\(275\) 0 0
\(276\) 62.5331 + 267.511i 0.0136379 + 0.0583415i
\(277\) −1784.41 3090.68i −0.387056 0.670401i 0.604996 0.796228i \(-0.293175\pi\)
−0.992052 + 0.125828i \(0.959841\pi\)
\(278\) 564.381 0.121760
\(279\) 4081.84 2018.64i 0.875891 0.433165i
\(280\) 0 0
\(281\) 3009.34 + 5212.33i 0.638869 + 1.10655i 0.985681 + 0.168618i \(0.0539306\pi\)
−0.346813 + 0.937934i \(0.612736\pi\)
\(282\) −1319.65 + 1237.38i −0.278666 + 0.261293i
\(283\) −2289.08 + 3964.81i −0.480819 + 0.832803i −0.999758 0.0220082i \(-0.992994\pi\)
0.518939 + 0.854812i \(0.326327\pi\)
\(284\) −774.492 + 1341.46i −0.161823 + 0.280285i
\(285\) 0 0
\(286\) 49.5448 + 85.8141i 0.0102435 + 0.0177423i
\(287\) 7668.55 1.57721
\(288\) −2062.85 + 1020.16i −0.422064 + 0.208728i
\(289\) −2144.45 −0.436485
\(290\) 0 0
\(291\) −1617.93 6921.34i −0.325926 1.39428i
\(292\) −494.729 + 856.895i −0.0991500 + 0.171733i
\(293\) 3239.87 5611.61i 0.645990 1.11889i −0.338082 0.941117i \(-0.609778\pi\)
0.984072 0.177771i \(-0.0568886\pi\)
\(294\) −333.082 100.835i −0.0660739 0.0200028i
\(295\) 0 0
\(296\) −10273.6 −2.01738
\(297\) −1960.78 + 5236.41i −0.383085 + 1.02305i
\(298\) −2057.67 −0.399992
\(299\) −13.8255 23.9466i −0.00267409 0.00463166i
\(300\) 0 0
\(301\) 3451.95 5978.95i 0.661020 1.14492i
\(302\) 2299.49 3982.83i 0.438148 0.758895i
\(303\) 672.298 + 2876.03i 0.127467 + 0.545292i
\(304\) −1110.66 1923.73i −0.209543 0.362938i
\(305\) 0 0
\(306\) −225.009 + 3493.05i −0.0420356 + 0.652564i
\(307\) −708.452 −0.131705 −0.0658526 0.997829i \(-0.520977\pi\)
−0.0658526 + 0.997829i \(0.520977\pi\)
\(308\) 739.761 + 1281.30i 0.136857 + 0.237043i
\(309\) −1801.08 + 1688.80i −0.331586 + 0.310914i
\(310\) 0 0
\(311\) 3117.32 5399.35i 0.568382 0.984467i −0.428344 0.903616i \(-0.640903\pi\)
0.996726 0.0808511i \(-0.0257638\pi\)
\(312\) 93.5765 87.7427i 0.0169799 0.0159213i
\(313\) −1315.71 2278.87i −0.237598 0.411532i 0.722427 0.691448i \(-0.243027\pi\)
−0.960024 + 0.279916i \(0.909693\pi\)
\(314\) −5666.63 −1.01843
\(315\) 0 0
\(316\) −1181.49 −0.210329
\(317\) −251.267 435.207i −0.0445191 0.0771094i 0.842907 0.538059i \(-0.180842\pi\)
−0.887426 + 0.460950i \(0.847509\pi\)
\(318\) −847.663 3626.22i −0.149480 0.639461i
\(319\) 5080.56 8799.79i 0.891714 1.54449i
\(320\) 0 0
\(321\) 7224.17 + 2187.00i 1.25612 + 0.380269i
\(322\) 649.490 + 1124.95i 0.112406 + 0.194692i
\(323\) 2606.49 0.449007
\(324\) 1394.94 + 180.462i 0.239187 + 0.0309434i
\(325\) 0 0
\(326\) −55.3162 95.8105i −0.00939780 0.0162775i
\(327\) 9762.10 + 2955.32i 1.65090 + 0.499784i
\(328\) 4875.44 8444.51i 0.820736 1.42156i
\(329\) 1359.33 2354.44i 0.227789 0.394542i
\(330\) 0 0
\(331\) −1543.57 2673.54i −0.256321 0.443961i 0.708933 0.705276i \(-0.249177\pi\)
−0.965253 + 0.261316i \(0.915844\pi\)
\(332\) 155.930 0.0257765
\(333\) 9434.54 + 6288.65i 1.55258 + 1.03488i
\(334\) −2898.87 −0.474908
\(335\) 0 0
\(336\) −3270.28 + 3066.40i −0.530978 + 0.497875i
\(337\) −2992.90 + 5183.86i −0.483780 + 0.837931i −0.999826 0.0186295i \(-0.994070\pi\)
0.516047 + 0.856560i \(0.327403\pi\)
\(338\) 2705.28 4685.69i 0.435349 0.754047i
\(339\) 3708.18 3477.00i 0.594103 0.557064i
\(340\) 0 0
\(341\) −6721.77 −1.06746
\(342\) −211.838 + 3288.59i −0.0334938 + 0.519960i
\(343\) −6076.36 −0.956539
\(344\) −4389.30 7602.49i −0.687951 1.19157i
\(345\) 0 0
\(346\) −1315.81 + 2279.05i −0.204446 + 0.354110i
\(347\) 503.325 871.784i 0.0778671 0.134870i −0.824462 0.565917i \(-0.808522\pi\)
0.902329 + 0.431047i \(0.141856\pi\)
\(348\) −2446.43 740.618i −0.376846 0.114084i
\(349\) 974.678 + 1688.19i 0.149494 + 0.258931i 0.931040 0.364916i \(-0.118902\pi\)
−0.781547 + 0.623847i \(0.785569\pi\)
\(350\) 0 0
\(351\) −139.642 + 23.2967i −0.0212352 + 0.00354269i
\(352\) 3396.99 0.514376
\(353\) 1295.87 + 2244.50i 0.195388 + 0.338422i 0.947028 0.321152i \(-0.104070\pi\)
−0.751640 + 0.659574i \(0.770737\pi\)
\(354\) −352.062 106.581i −0.0528584 0.0160020i
\(355\) 0 0
\(356\) 23.1627 40.1189i 0.00344837 0.00597275i
\(357\) −1197.38 5122.28i −0.177513 0.759383i
\(358\) 3424.33 + 5931.11i 0.505534 + 0.875611i
\(359\) −605.954 −0.0890837 −0.0445418 0.999008i \(-0.514183\pi\)
−0.0445418 + 0.999008i \(0.514183\pi\)
\(360\) 0 0
\(361\) −4405.08 −0.642233
\(362\) 4396.32 + 7614.64i 0.638302 + 1.10557i
\(363\) 975.706 914.877i 0.141078 0.132283i
\(364\) −18.7302 + 32.4417i −0.00269706 + 0.00467145i
\(365\) 0 0
\(366\) 6843.09 6416.46i 0.977306 0.916377i
\(367\) −4880.13 8452.63i −0.694117 1.20225i −0.970478 0.241191i \(-0.922462\pi\)
0.276361 0.961054i \(-0.410871\pi\)
\(368\) 1228.75 0.174056
\(369\) −9646.25 + 4770.48i −1.36088 + 0.673011i
\(370\) 0 0
\(371\) 2798.27 + 4846.75i 0.391587 + 0.678249i
\(372\) 384.887 + 1646.51i 0.0536436 + 0.229482i
\(373\) −3911.81 + 6775.45i −0.543018 + 0.940535i 0.455711 + 0.890128i \(0.349385\pi\)
−0.998729 + 0.0504071i \(0.983948\pi\)
\(374\) 2583.40 4474.58i 0.357178 0.618650i
\(375\) 0 0
\(376\) −1728.45 2993.77i −0.237069 0.410616i
\(377\) 257.272 0.0351464
\(378\) 6560.05 1094.42i 0.892625 0.148918i
\(379\) 2731.46 0.370200 0.185100 0.982720i \(-0.440739\pi\)
0.185100 + 0.982720i \(0.440739\pi\)
\(380\) 0 0
\(381\) 4306.54 + 1303.74i 0.579084 + 0.175308i
\(382\) 4112.93 7123.80i 0.550879 0.954150i
\(383\) −6299.93 + 10911.8i −0.840500 + 1.45579i 0.0489732 + 0.998800i \(0.484405\pi\)
−0.889473 + 0.456988i \(0.848928\pi\)
\(384\) 850.893 + 3640.04i 0.113078 + 0.483737i
\(385\) 0 0
\(386\) 4782.00 0.630563
\(387\) −622.795 + 9668.32i −0.0818048 + 1.26994i
\(388\) 2639.33 0.345339
\(389\) 2471.73 + 4281.16i 0.322163 + 0.558003i 0.980934 0.194340i \(-0.0622566\pi\)
−0.658771 + 0.752344i \(0.728923\pi\)
\(390\) 0 0
\(391\) −720.902 + 1248.64i −0.0932419 + 0.161500i
\(392\) 332.511 575.925i 0.0428427 0.0742057i
\(393\) −5568.06 + 5220.93i −0.714686 + 0.670130i
\(394\) 1275.96 + 2210.03i 0.163152 + 0.282588i
\(395\) 0 0
\(396\) −1727.62 1151.56i −0.219233 0.146131i
\(397\) −7067.06 −0.893415 −0.446707 0.894680i \(-0.647403\pi\)
−0.446707 + 0.894680i \(0.647403\pi\)
\(398\) −1928.61 3340.46i −0.242896 0.420708i
\(399\) −1127.29 4822.45i −0.141442 0.605074i
\(400\) 0 0
\(401\) 458.792 794.651i 0.0571346 0.0989600i −0.836043 0.548663i \(-0.815137\pi\)
0.893178 + 0.449703i \(0.148470\pi\)
\(402\) −2163.28 654.898i −0.268394 0.0812521i
\(403\) −85.0952 147.389i −0.0105183 0.0182183i
\(404\) −1096.72 −0.135059
\(405\) 0 0
\(406\) −12086.0 −1.47738
\(407\) −8368.28 14494.3i −1.01917 1.76525i
\(408\) −6401.86 1938.06i −0.776812 0.235167i
\(409\) −7367.76 + 12761.3i −0.890739 + 1.54281i −0.0517481 + 0.998660i \(0.516479\pi\)
−0.838991 + 0.544145i \(0.816854\pi\)
\(410\) 0 0
\(411\) 84.6093 + 361.951i 0.0101544 + 0.0434397i
\(412\) −458.396 793.965i −0.0548144 0.0949414i
\(413\) 552.805 0.0658638
\(414\) −1516.80 1011.04i −0.180065 0.120023i
\(415\) 0 0
\(416\) 43.0047 + 74.4863i 0.00506846 + 0.00877883i
\(417\) 868.268 814.137i 0.101965 0.0956078i
\(418\) 2432.18 4212.66i 0.284598 0.492938i
\(419\) 4627.46 8014.99i 0.539537 0.934506i −0.459392 0.888234i \(-0.651932\pi\)
0.998929 0.0462722i \(-0.0147342\pi\)
\(420\) 0 0
\(421\) 5100.98 + 8835.15i 0.590514 + 1.02280i 0.994163 + 0.107886i \(0.0344082\pi\)
−0.403649 + 0.914914i \(0.632258\pi\)
\(422\) 8340.80 0.962142
\(423\) −245.249 + 3807.26i −0.0281901 + 0.437625i
\(424\) 7116.24 0.815083
\(425\) 0 0
\(426\) −2339.52 10008.2i −0.266080 1.13827i
\(427\) −7048.89 + 12209.0i −0.798875 + 1.38369i
\(428\) −1401.36 + 2427.23i −0.158265 + 0.274122i
\(429\) 200.011 + 60.5501i 0.0225096 + 0.00681443i
\(430\) 0 0
\(431\) 8057.20 0.900468 0.450234 0.892911i \(-0.351341\pi\)
0.450234 + 0.892911i \(0.351341\pi\)
\(432\) 2206.13 5891.61i 0.245700 0.656158i
\(433\) 4306.26 0.477935 0.238967 0.971028i \(-0.423191\pi\)
0.238967 + 0.971028i \(0.423191\pi\)
\(434\) 3997.56 + 6923.98i 0.442141 + 0.765810i
\(435\) 0 0
\(436\) −1893.67 + 3279.94i −0.208006 + 0.360276i
\(437\) −678.704 + 1175.55i −0.0742948 + 0.128682i
\(438\) −1494.43 6393.05i −0.163029 0.697424i
\(439\) 2360.90 + 4089.19i 0.256673 + 0.444571i 0.965349 0.260964i \(-0.0840403\pi\)
−0.708676 + 0.705535i \(0.750707\pi\)
\(440\) 0 0
\(441\) −657.885 + 325.352i −0.0710382 + 0.0351314i
\(442\) 130.820 0.0140779
\(443\) −7677.19 13297.3i −0.823373 1.42612i −0.903157 0.429311i \(-0.858756\pi\)
0.0797840 0.996812i \(-0.474577\pi\)
\(444\) −3071.23 + 2879.76i −0.328276 + 0.307810i
\(445\) 0 0
\(446\) −2914.17 + 5047.50i −0.309395 + 0.535888i
\(447\) −3165.60 + 2968.25i −0.334962 + 0.314079i
\(448\) −5471.29 9476.56i −0.576996 0.999387i
\(449\) 5448.64 0.572688 0.286344 0.958127i \(-0.407560\pi\)
0.286344 + 0.958127i \(0.407560\pi\)
\(450\) 0 0
\(451\) 15885.0 1.65852
\(452\) 943.774 + 1634.66i 0.0982111 + 0.170107i
\(453\) −2207.73 9444.45i −0.228980 0.979556i
\(454\) 1202.64 2083.04i 0.124323 0.215334i
\(455\) 0 0
\(456\) −6027.13 1824.62i −0.618961 0.187380i
\(457\) 26.3653 + 45.6661i 0.00269873 + 0.00467433i 0.867372 0.497661i \(-0.165808\pi\)
−0.864673 + 0.502335i \(0.832474\pi\)
\(458\) 3930.53 0.401008
\(459\) 4692.67 + 5698.44i 0.477201 + 0.579478i
\(460\) 0 0
\(461\) 1583.51 + 2742.72i 0.159982 + 0.277096i 0.934862 0.355012i \(-0.115523\pi\)
−0.774880 + 0.632108i \(0.782190\pi\)
\(462\) −9396.03 2844.49i −0.946196 0.286446i
\(463\) −6546.21 + 11338.4i −0.657081 + 1.13810i 0.324287 + 0.945959i \(0.394876\pi\)
−0.981368 + 0.192138i \(0.938458\pi\)
\(464\) −5716.26 + 9900.86i −0.571920 + 0.990594i
\(465\) 0 0
\(466\) 1162.41 + 2013.35i 0.115553 + 0.200143i
\(467\) −13225.4 −1.31049 −0.655246 0.755416i \(-0.727435\pi\)
−0.655246 + 0.755416i \(0.727435\pi\)
\(468\) 3.37928 52.4601i 0.000333776 0.00518156i
\(469\) 3396.77 0.334431
\(470\) 0 0
\(471\) −8717.79 + 8174.29i −0.852854 + 0.799684i
\(472\) 351.458 608.743i 0.0342736 0.0593637i
\(473\) 7150.52 12385.1i 0.695098 1.20394i
\(474\) 5718.84 5362.31i 0.554167 0.519618i
\(475\) 0 0
\(476\) 1953.29 0.188086
\(477\) −6535.02 4355.96i −0.627291 0.418125i
\(478\) 6729.99 0.643981
\(479\) 4279.30 + 7411.96i 0.408196 + 0.707017i 0.994688 0.102939i \(-0.0328246\pi\)
−0.586491 + 0.809955i \(0.699491\pi\)
\(480\) 0 0
\(481\) 211.879 366.985i 0.0200849 0.0347881i
\(482\) −4209.77 + 7291.54i −0.397822 + 0.689047i
\(483\) 2621.98 + 793.761i 0.247006 + 0.0747772i
\(484\) 248.328 + 430.117i 0.0233216 + 0.0403942i
\(485\) 0 0
\(486\) −7571.05 + 5457.56i −0.706646 + 0.509383i
\(487\) 19531.3 1.81735 0.908674 0.417506i \(-0.137096\pi\)
0.908674 + 0.417506i \(0.137096\pi\)
\(488\) 8962.96 + 15524.3i 0.831423 + 1.44007i
\(489\) −223.310 67.6036i −0.0206512 0.00625182i
\(490\) 0 0
\(491\) 9744.11 16877.3i 0.895612 1.55125i 0.0625676 0.998041i \(-0.480071\pi\)
0.833045 0.553206i \(-0.186596\pi\)
\(492\) −909.568 3891.04i −0.0833465 0.356548i
\(493\) −6707.43 11617.6i −0.612754 1.06132i
\(494\) 123.162 0.0112173
\(495\) 0 0
\(496\) 7562.83 0.684640
\(497\) 7723.12 + 13376.8i 0.697041 + 1.20731i
\(498\) −754.759 + 707.705i −0.0679148 + 0.0636807i
\(499\) 169.765 294.042i 0.0152299 0.0263790i −0.858310 0.513132i \(-0.828485\pi\)
0.873540 + 0.486753i \(0.161819\pi\)
\(500\) 0 0
\(501\) −4459.75 + 4181.71i −0.397698 + 0.372904i
\(502\) 3898.42 + 6752.26i 0.346604 + 0.600335i
\(503\) −5550.25 −0.491995 −0.245998 0.969270i \(-0.579116\pi\)
−0.245998 + 0.969270i \(0.579116\pi\)
\(504\) −816.970 + 12682.7i −0.0722039 + 1.12090i
\(505\) 0 0
\(506\) 1345.38 + 2330.27i 0.118201 + 0.204729i
\(507\) −2597.33 11111.1i −0.227517 0.973298i
\(508\) −835.393 + 1446.94i −0.0729617 + 0.126373i
\(509\) −2824.49 + 4892.17i −0.245960 + 0.426015i −0.962401 0.271633i \(-0.912436\pi\)
0.716441 + 0.697647i \(0.245770\pi\)
\(510\) 0 0
\(511\) 4933.36 + 8544.83i 0.427082 + 0.739728i
\(512\) −12598.3 −1.08745
\(513\) 4417.99 + 5364.88i 0.380232 + 0.461726i
\(514\) −13673.0 −1.17332
\(515\) 0 0
\(516\) −3443.18 1042.37i −0.293755 0.0889294i
\(517\) 2815.78 4877.08i 0.239532 0.414882i
\(518\) −9953.54 + 17240.0i −0.844273 + 1.46232i
\(519\) 1263.30 + 5404.27i 0.106845 + 0.457074i
\(520\) 0 0
\(521\) −11159.0 −0.938359 −0.469180 0.883103i \(-0.655450\pi\)
−0.469180 + 0.883103i \(0.655450\pi\)
\(522\) 15203.0 7518.50i 1.27474 0.630414i
\(523\) 9476.61 0.792320 0.396160 0.918182i \(-0.370343\pi\)
0.396160 + 0.918182i \(0.370343\pi\)
\(524\) −1417.13 2454.55i −0.118145 0.204633i
\(525\) 0 0
\(526\) −5097.26 + 8828.72i −0.422531 + 0.731845i
\(527\) −4437.10 + 7685.27i −0.366761 + 0.635248i
\(528\) −6774.21 + 6351.88i −0.558351 + 0.523542i
\(529\) 5708.07 + 9886.67i 0.469144 + 0.812580i
\(530\) 0 0
\(531\) −695.373 + 343.891i −0.0568298 + 0.0281047i
\(532\) 1838.95 0.149866
\(533\) 201.098 + 348.312i 0.0163424 + 0.0283059i
\(534\) 69.9678 + 299.316i 0.00567004 + 0.0242559i
\(535\) 0 0
\(536\) 2159.57 3740.48i 0.174028 0.301426i
\(537\) 13823.9 + 4184.97i 1.11089 + 0.336303i
\(538\) 1264.86 + 2190.81i 0.101361 + 0.175562i
\(539\) 1083.37 0.0865754
\(540\) 0 0
\(541\) 8285.40 0.658442 0.329221 0.944253i \(-0.393214\pi\)
0.329221 + 0.944253i \(0.393214\pi\)
\(542\) −4189.35 7256.17i −0.332008 0.575054i
\(543\) 17747.8 + 5372.87i 1.40264 + 0.424626i
\(544\) 2242.38 3883.92i 0.176730 0.306106i
\(545\) 0 0
\(546\) −56.5787 242.038i −0.00443469 0.0189712i
\(547\) 3459.15 + 5991.42i 0.270389 + 0.468327i 0.968961 0.247212i \(-0.0795145\pi\)
−0.698573 + 0.715539i \(0.746181\pi\)
\(548\) −138.023 −0.0107593
\(549\) 1271.75 19742.7i 0.0988651 1.53479i
\(550\) 0 0
\(551\) −6314.82 10937.6i −0.488240 0.845657i
\(552\) 2541.06 2382.64i 0.195932 0.183717i
\(553\) −5890.83 + 10203.2i −0.452990 + 0.784602i
\(554\) −4396.51 + 7614.97i −0.337165 + 0.583988i
\(555\) 0 0
\(556\) 220.984 + 382.755i 0.0168558 + 0.0291950i
\(557\) 15622.7 1.18843 0.594216 0.804305i \(-0.297462\pi\)
0.594216 + 0.804305i \(0.297462\pi\)
\(558\) −9335.82 6222.84i −0.708274 0.472104i
\(559\) 362.092 0.0273969
\(560\) 0 0
\(561\) −2480.31 10610.5i −0.186664 0.798532i
\(562\) 7414.56 12842.4i 0.556520 0.963921i
\(563\) 4064.65 7040.18i 0.304271 0.527013i −0.672828 0.739799i \(-0.734920\pi\)
0.977099 + 0.212786i \(0.0682538\pi\)
\(564\) −1355.88 410.471i −0.101228 0.0306453i
\(565\) 0 0
\(566\) 11279.9 0.837686
\(567\) 8513.52 11146.8i 0.630572 0.825609i
\(568\) 19640.6 1.45088
\(569\) −4087.84 7080.34i −0.301179 0.521658i 0.675224 0.737613i \(-0.264047\pi\)
−0.976403 + 0.215955i \(0.930714\pi\)
\(570\) 0 0
\(571\) −3939.42 + 6823.27i −0.288721 + 0.500079i −0.973505 0.228667i \(-0.926563\pi\)
0.684784 + 0.728746i \(0.259897\pi\)
\(572\) −38.7986 + 67.2011i −0.00283610 + 0.00491227i
\(573\) −3948.79 16892.6i −0.287894 1.23158i
\(574\) −9447.07 16362.8i −0.686957 1.18984i
\(575\) 0 0
\(576\) 12777.5 + 8516.95i 0.924302 + 0.616099i
\(577\) 16673.4 1.20299 0.601493 0.798878i \(-0.294573\pi\)
0.601493 + 0.798878i \(0.294573\pi\)
\(578\) 2641.80 + 4575.74i 0.190112 + 0.329283i
\(579\) 7356.83 6898.18i 0.528047 0.495127i
\(580\) 0 0
\(581\) 777.458 1346.60i 0.0555153 0.0961553i
\(582\) −12775.3 + 11978.8i −0.909884 + 0.853159i
\(583\) 5796.46 + 10039.8i 0.411775 + 0.713215i
\(584\) 12546.0 0.888965
\(585\) 0 0
\(586\) −15965.1 −1.12545
\(587\) 1506.09 + 2608.63i 0.105900 + 0.183424i 0.914105 0.405477i \(-0.132894\pi\)
−0.808206 + 0.588900i \(0.799561\pi\)
\(588\) −62.0335 265.374i −0.00435071 0.0186119i
\(589\) −4177.37 + 7235.42i −0.292234 + 0.506164i
\(590\) 0 0
\(591\) 5151.03 + 1559.39i 0.358519 + 0.108536i
\(592\) 9415.37 + 16307.9i 0.653664 + 1.13218i
\(593\) −7922.71 −0.548645 −0.274323 0.961638i \(-0.588454\pi\)
−0.274323 + 0.961638i \(0.588454\pi\)
\(594\) 13588.8 2267.03i 0.938642 0.156595i
\(595\) 0 0
\(596\) −805.682 1395.48i −0.0553725 0.0959080i
\(597\) −7785.77 2357.02i −0.533753 0.161585i
\(598\) −34.0641 + 59.0007i −0.00232940 + 0.00403465i
\(599\) 11289.3 19553.6i 0.770061 1.33378i −0.167468 0.985878i \(-0.553559\pi\)
0.937529 0.347907i \(-0.113108\pi\)
\(600\) 0 0
\(601\) −5309.35 9196.07i −0.360354 0.624152i 0.627665 0.778484i \(-0.284011\pi\)
−0.988019 + 0.154332i \(0.950678\pi\)
\(602\) −17010.2 −1.15163
\(603\) −4272.79 + 2113.07i −0.288560 + 0.142705i
\(604\) 3601.47 0.242619
\(605\) 0 0
\(606\) 5308.52 4977.57i 0.355848 0.333663i
\(607\) −6795.28 + 11769.8i −0.454385 + 0.787018i −0.998653 0.0518935i \(-0.983474\pi\)
0.544267 + 0.838912i \(0.316808\pi\)
\(608\) 2111.12 3656.58i 0.140818 0.243904i
\(609\) −18593.6 + 17434.4i −1.23719 + 1.16006i
\(610\) 0 0
\(611\) 142.587 0.00944102
\(612\) −2457.04 + 1215.11i −0.162288 + 0.0802580i
\(613\) 5457.57 0.359591 0.179796 0.983704i \(-0.442456\pi\)
0.179796 + 0.983704i \(0.442456\pi\)
\(614\) 872.760 + 1511.66i 0.0573643 + 0.0993580i
\(615\) 0 0
\(616\) 9379.91 16246.5i 0.613518 1.06264i
\(617\) −2986.05 + 5171.99i −0.194836 + 0.337466i −0.946847 0.321685i \(-0.895751\pi\)
0.752011 + 0.659151i \(0.229084\pi\)
\(618\) 5822.28 + 1762.60i 0.378975 + 0.114729i
\(619\) 419.816 + 727.143i 0.0272598 + 0.0472154i 0.879333 0.476206i \(-0.157989\pi\)
−0.852074 + 0.523422i \(0.824655\pi\)
\(620\) 0 0
\(621\) −3791.97 + 632.617i −0.245034 + 0.0408793i
\(622\) −15361.2 −0.990238
\(623\) −230.975 400.060i −0.0148536 0.0257272i
\(624\) −225.038 68.1265i −0.0144370 0.00437058i
\(625\) 0 0
\(626\) −3241.70 + 5614.79i −0.206972 + 0.358486i
\(627\) −2335.12 9989.43i −0.148733 0.636267i
\(628\) −2218.77 3843.03i −0.140985 0.244194i
\(629\) −22095.9 −1.40067
\(630\) 0 0
\(631\) −13699.4 −0.864284 −0.432142 0.901806i \(-0.642242\pi\)
−0.432142 + 0.901806i \(0.642242\pi\)
\(632\) 7490.44 + 12973.8i 0.471446 + 0.816568i
\(633\) 12831.8 12031.9i 0.805718 0.755487i
\(634\) −619.084 + 1072.29i −0.0387807 + 0.0671702i
\(635\) 0 0
\(636\) 2127.35 1994.72i 0.132634 0.124365i
\(637\) 13.7151 + 23.7552i 0.000853080 + 0.00147758i
\(638\) −25035.5 −1.55355
\(639\) −18036.4 12022.3i −1.11660 0.744279i
\(640\) 0 0
\(641\) 3969.68 + 6875.69i 0.244607 + 0.423671i 0.962021 0.272975i \(-0.0880078\pi\)
−0.717414 + 0.696647i \(0.754674\pi\)
\(642\) −4233.11 18108.8i −0.260230 1.11324i
\(643\) 3817.98 6612.93i 0.234162 0.405581i −0.724867 0.688889i \(-0.758099\pi\)
0.959029 + 0.283308i \(0.0914320\pi\)
\(644\) −508.617 + 880.950i −0.0311216 + 0.0539042i
\(645\) 0 0
\(646\) −3211.00 5561.62i −0.195565 0.338729i
\(647\) −22084.3 −1.34192 −0.670962 0.741491i \(-0.734119\pi\)
−0.670962 + 0.741491i \(0.734119\pi\)
\(648\) −6862.04 16461.8i −0.415997 0.997963i
\(649\) 1145.10 0.0692593
\(650\) 0 0
\(651\) 16138.1 + 4885.54i 0.971583 + 0.294131i
\(652\) 43.3182 75.0294i 0.00260195 0.00450671i
\(653\) −3318.99 + 5748.65i −0.198900 + 0.344506i −0.948172 0.317757i \(-0.897070\pi\)
0.749272 + 0.662263i \(0.230404\pi\)
\(654\) −5720.24 24470.7i −0.342017 1.46312i
\(655\) 0 0
\(656\) −17872.6 −1.06373
\(657\) −11521.3 7679.57i −0.684151 0.456025i
\(658\) −6698.39 −0.396855
\(659\) −11906.1 20622.0i −0.703789 1.21900i −0.967127 0.254295i \(-0.918157\pi\)
0.263338 0.964704i \(-0.415177\pi\)
\(660\) 0 0
\(661\) 499.912 865.873i 0.0294165 0.0509509i −0.850942 0.525259i \(-0.823968\pi\)
0.880359 + 0.474308i \(0.157302\pi\)
\(662\) −3803.12 + 6587.20i −0.223282 + 0.386735i
\(663\) 201.258 188.711i 0.0117892 0.0110542i
\(664\) −988.571 1712.26i −0.0577771 0.100073i
\(665\) 0 0
\(666\) 1795.80 27878.2i 0.104483 1.62201i
\(667\) 6986.19 0.405557
\(668\) −1135.06 1965.97i −0.0657435 0.113871i
\(669\) 2797.88 + 11969.1i 0.161692 + 0.691705i
\(670\) 0 0
\(671\) −14601.4 + 25290.3i −0.840059 + 1.45502i
\(672\) −8155.72 2469.01i −0.468175 0.141732i
\(673\) −5311.03 9198.98i −0.304198 0.526886i 0.672884 0.739748i \(-0.265055\pi\)
−0.977082 + 0.212861i \(0.931722\pi\)
\(674\) 14748.1 0.842843
\(675\) 0 0
\(676\) 4237.02 0.241069
\(677\) −12453.9 21570.8i −0.707005 1.22457i −0.965963 0.258680i \(-0.916713\pi\)
0.258959 0.965888i \(-0.416621\pi\)
\(678\) −11987.3 3628.95i −0.679010 0.205559i
\(679\) 13159.5 22792.9i 0.743763 1.28823i
\(680\) 0 0
\(681\) −1154.65 4939.48i −0.0649725 0.277946i
\(682\) 8280.72 + 14342.6i 0.464934 + 0.805289i
\(683\) 17115.6 0.958874 0.479437 0.877576i \(-0.340841\pi\)
0.479437 + 0.877576i \(0.340841\pi\)
\(684\) −2313.22 + 1143.98i −0.129310 + 0.0639493i
\(685\) 0 0
\(686\) 7485.62 + 12965.5i 0.416622 + 0.721610i
\(687\) 6046.89 5669.91i 0.335813 0.314877i
\(688\) −8045.23 + 13934.7i −0.445816 + 0.772176i
\(689\) −146.762 + 254.199i −0.00811493 + 0.0140555i
\(690\) 0 0
\(691\) −14449.9 25028.0i −0.795514 1.37787i −0.922512 0.385967i \(-0.873868\pi\)
0.126999 0.991903i \(-0.459466\pi\)
\(692\) −2060.82 −0.113209
\(693\) −18558.5 + 9177.96i −1.01729 + 0.503091i
\(694\) −2480.23 −0.135660
\(695\) 0 0
\(696\) 7377.30 + 31559.4i 0.401775 + 1.71876i
\(697\) 10485.8 18161.9i 0.569839 0.986989i
\(698\) 2401.46 4159.45i 0.130224 0.225555i
\(699\) 4692.62 + 1420.61i 0.253921 + 0.0768706i
\(700\) 0 0
\(701\) 576.680 0.0310712 0.0155356 0.999879i \(-0.495055\pi\)
0.0155356 + 0.999879i \(0.495055\pi\)
\(702\) 221.738 + 269.263i 0.0119216 + 0.0144767i
\(703\) −20802.5 −1.11605
\(704\) −11333.5 19630.2i −0.606742 1.05091i
\(705\) 0 0
\(706\) 3192.82 5530.12i 0.170203 0.294800i
\(707\) −5468.17 + 9471.15i −0.290879 + 0.503818i
\(708\) −65.5683 280.495i −0.00348052 0.0148893i
\(709\) −2858.78 4951.55i −0.151430 0.262284i 0.780324 0.625376i \(-0.215054\pi\)
−0.931753 + 0.363092i \(0.881721\pi\)
\(710\) 0 0
\(711\) 1062.81 16499.2i 0.0560600 0.870279i
\(712\) −587.389 −0.0309176
\(713\) −2310.75 4002.33i −0.121372 0.210222i
\(714\) −9454.62 + 8865.18i −0.495560 + 0.464665i
\(715\) 0 0
\(716\) −2681.60 + 4644.66i −0.139966 + 0.242429i
\(717\) 10353.7 9708.22i 0.539284 0.505663i
\(718\) 746.490 + 1292.96i 0.0388005 + 0.0672044i
\(719\) −14799.9 −0.767655 −0.383827 0.923405i \(-0.625394\pi\)
−0.383827 + 0.923405i \(0.625394\pi\)
\(720\) 0 0
\(721\) −9142.12 −0.472219
\(722\) 5426.72 + 9399.36i 0.279725 + 0.484498i
\(723\) 4041.78 + 17290.3i 0.207905 + 0.889398i
\(724\) −3442.76 + 5963.04i −0.176725 + 0.306098i
\(725\) 0 0
\(726\) −3154.12 954.860i −0.161240 0.0488129i
\(727\) −3205.20 5551.57i −0.163513 0.283214i 0.772613 0.634877i \(-0.218949\pi\)
−0.936126 + 0.351664i \(0.885616\pi\)
\(728\) 474.985 0.0241815
\(729\) −3774.92 + 19317.6i −0.191786 + 0.981437i
\(730\) 0 0
\(731\) −9440.23 16351.0i −0.477646 0.827308i
\(732\) 7030.97 + 2128.51i 0.355017 + 0.107476i
\(733\) 8934.62 15475.2i 0.450215 0.779796i −0.548184 0.836358i \(-0.684681\pi\)
0.998399 + 0.0565621i \(0.0180139\pi\)
\(734\) −12023.9 + 20826.0i −0.604647 + 1.04728i
\(735\) 0 0
\(736\) 1167.79 + 2022.66i 0.0584853 + 0.101299i
\(737\) 7036.21 0.351672
\(738\) 22062.5 + 14705.9i 1.10045 + 0.733511i
\(739\) 11099.7 0.552516 0.276258 0.961084i \(-0.410906\pi\)
0.276258 + 0.961084i \(0.410906\pi\)
\(740\) 0 0
\(741\) 189.478 177.665i 0.00939358 0.00880795i
\(742\) 6894.52 11941.7i 0.341113 0.590825i
\(743\) −5428.81 + 9402.97i −0.268053 + 0.464282i −0.968359 0.249561i \(-0.919714\pi\)
0.700306 + 0.713843i \(0.253047\pi\)
\(744\) 15640.0 14665.0i 0.770687 0.722639i
\(745\) 0 0
\(746\) 19276.2 0.946049
\(747\) −140.268 + 2177.53i −0.00687032 + 0.106655i
\(748\) 4046.13 0.197782
\(749\) 13974.1 + 24203.9i 0.681715 + 1.18076i
\(750\) 0 0
\(751\) 16117.0 27915.4i 0.783111 1.35639i −0.147010 0.989135i \(-0.546965\pi\)
0.930121 0.367253i \(-0.119702\pi\)
\(752\) −3168.11 + 5487.33i −0.153629 + 0.266093i
\(753\) 15737.8 + 4764.38i 0.761645 + 0.230576i
\(754\) −316.940 548.956i −0.0153081 0.0265143i
\(755\) 0 0
\(756\) 3310.81 + 4020.41i 0.159276 + 0.193414i
\(757\) −9410.28 −0.451813 −0.225906 0.974149i \(-0.572534\pi\)
−0.225906 + 0.974149i \(0.572534\pi\)
\(758\) −3364.96 5828.27i −0.161241 0.279278i
\(759\) 5431.27 + 1644.23i 0.259740 + 0.0786321i
\(760\) 0 0
\(761\) −17383.6 + 30109.2i −0.828060 + 1.43424i 0.0714983 + 0.997441i \(0.477222\pi\)
−0.899558 + 0.436801i \(0.856111\pi\)
\(762\) −2523.48 10795.2i −0.119969 0.513215i
\(763\) 18883.4 + 32707.0i 0.895971 + 1.55187i
\(764\) 6441.68 0.305042
\(765\) 0 0
\(766\) 31044.2 1.46432
\(767\) 14.4966 + 25.1089i 0.000682454 + 0.00118204i
\(768\) −10527.6 + 9871.30i −0.494640 + 0.463802i
\(769\) 14543.2 25189.6i 0.681980 1.18122i −0.292396 0.956297i \(-0.594452\pi\)
0.974376 0.224927i \(-0.0722143\pi\)
\(770\) 0 0
\(771\) −21035.1 + 19723.7i −0.982568 + 0.921311i
\(772\) 1872.40 + 3243.08i 0.0872915 + 0.151193i
\(773\) −2942.77 −0.136927 −0.0684633 0.997654i \(-0.521810\pi\)
−0.0684633 + 0.997654i \(0.521810\pi\)
\(774\) 21397.1 10581.7i 0.993672 0.491412i
\(775\) 0 0
\(776\) −16732.9 28982.2i −0.774065 1.34072i
\(777\) 9556.33 + 40881.1i 0.441225 + 1.88752i
\(778\) 6089.97 10548.1i 0.280637 0.486078i
\(779\) 9872.01 17098.8i 0.454045 0.786430i
\(780\) 0 0
\(781\) 15998.0 + 27709.4i 0.732975 + 1.26955i
\(782\) 3552.39 0.162446
\(783\) 12543.2 33497.5i 0.572488 1.52887i
\(784\) −1218.93 −0.0555270
\(785\) 0 0
\(786\) 17999.6 + 5449.10i 0.816827 + 0.247281i
\(787\) −16914.6 + 29296.9i −0.766124 + 1.32697i 0.173527 + 0.984829i \(0.444484\pi\)
−0.939650 + 0.342136i \(0.888850\pi\)
\(788\) −999.207 + 1730.68i −0.0451717 + 0.0782397i
\(789\) 4893.85 + 20935.4i 0.220818 + 0.944640i
\(790\) 0 0
\(791\) 18822.4 0.846076
\(792\) −1692.31 + 26271.5i −0.0759262 + 1.17868i
\(793\) −739.392 −0.0331105
\(794\) 8706.09 + 15079.4i 0.389128 + 0.673989i
\(795\) 0 0
\(796\) 1510.30 2615.92i 0.0672502 0.116481i
\(797\) 11452.3 19836.0i 0.508987 0.881591i −0.490959 0.871183i \(-0.663353\pi\)
0.999946 0.0104085i \(-0.00331319\pi\)
\(798\) −8901.20 + 8346.27i −0.394861 + 0.370244i
\(799\) −3717.44 6438.80i −0.164598 0.285092i
\(800\) 0 0
\(801\) 539.413 + 359.549i 0.0237943 + 0.0158602i
\(802\) −2260.79 −0.0995402
\(803\) 10219.2 + 17700.1i 0.449099 + 0.777863i
\(804\) −402.891 1723.53i −0.0176727 0.0756023i
\(805\) 0 0
\(806\) −209.662 + 363.145i −0.00916256 + 0.0158700i
\(807\) 5106.23 + 1545.83i 0.222736 + 0.0674297i
\(808\) 6953.01 + 12043.0i 0.302730 + 0.524344i
\(809\) −30665.7 −1.33269 −0.666347 0.745642i \(-0.732143\pi\)
−0.666347 + 0.745642i \(0.732143\pi\)
\(810\) 0 0
\(811\) −35135.2 −1.52129 −0.760644 0.649169i \(-0.775117\pi\)
−0.760644 + 0.649169i \(0.775117\pi\)
\(812\) −4732.28 8196.56i −0.204520 0.354240i
\(813\) −16912.3 5119.93i −0.729571 0.220866i
\(814\) −20618.2 + 35711.8i −0.887798 + 1.53771i
\(815\) 0 0
\(816\) 2790.65 + 11938.2i 0.119721 + 0.512156i
\(817\) −8887.65 15393.9i −0.380587 0.659196i
\(818\) 36306.1 1.55185
\(819\) −436.190 290.745i −0.0186102 0.0124047i
\(820\) 0 0
\(821\) −17218.5 29823.3i −0.731948 1.26777i −0.956050 0.293205i \(-0.905278\pi\)
0.224102 0.974566i \(-0.428055\pi\)
\(822\) 668.083 626.432i 0.0283480 0.0265807i
\(823\) 21400.9 37067.4i 0.906426 1.56998i 0.0874340 0.996170i \(-0.472133\pi\)
0.818992 0.573805i \(-0.194533\pi\)
\(824\) −5812.30 + 10067.2i −0.245729 + 0.425616i
\(825\) 0 0
\(826\) −681.014 1179.55i −0.0286871 0.0496875i
\(827\) 23589.1 0.991868 0.495934 0.868360i \(-0.334826\pi\)
0.495934 + 0.868360i \(0.334826\pi\)
\(828\) 91.7638 1424.55i 0.00385146 0.0597904i
\(829\) −26766.2 −1.12139 −0.560693 0.828024i \(-0.689465\pi\)
−0.560693 + 0.828024i \(0.689465\pi\)
\(830\) 0 0
\(831\) 4221.06 + 18057.3i 0.176206 + 0.753791i
\(832\) 286.955 497.021i 0.0119572 0.0207105i
\(833\) 715.142 1238.66i 0.0297458 0.0515212i
\(834\) −2806.81 849.717i −0.116537 0.0352797i
\(835\) 0 0
\(836\) 3809.29 0.157592
\(837\) −23339.3 + 3893.71i −0.963826 + 0.160796i
\(838\) −22802.7 −0.939985
\(839\) 15167.2 + 26270.3i 0.624110 + 1.08099i 0.988712 + 0.149827i \(0.0478716\pi\)
−0.364602 + 0.931163i \(0.618795\pi\)
\(840\) 0 0
\(841\) −20306.0 + 35171.1i −0.832590 + 1.44209i
\(842\) 12568.0 21768.5i 0.514398 0.890964i
\(843\) −7118.67 30453.0i −0.290842 1.24420i
\(844\) 3265.85 + 5656.61i 0.133193 + 0.230697i
\(845\) 0 0
\(846\) 8425.90 4166.96i 0.342421 0.169342i
\(847\) 4952.58 0.200912
\(848\) −6521.74 11296.0i −0.264101 0.457436i
\(849\) 17353.5 16271.6i 0.701496 0.657762i
\(850\) 0 0
\(851\) 5753.54 9965.43i 0.231761 0.401422i
\(852\) 5871.41 5505.37i 0.236093 0.221374i
\(853\) 3266.89 + 5658.41i 0.131133 + 0.227128i 0.924113 0.382118i \(-0.124805\pi\)
−0.792981 + 0.609247i \(0.791472\pi\)
\(854\) 34734.8 1.39180
\(855\) 0 0
\(856\) 35537.5 1.41898
\(857\) 18776.5 + 32521.9i 0.748417 + 1.29630i 0.948581 + 0.316534i \(0.102519\pi\)
−0.200164 + 0.979762i \(0.564147\pi\)
\(858\) −117.199 501.368i −0.00466331 0.0199492i
\(859\) −18319.0 + 31729.4i −0.727631 + 1.26029i 0.230251 + 0.973131i \(0.426045\pi\)
−0.957882 + 0.287163i \(0.907288\pi\)
\(860\) 0 0
\(861\) −38137.6 11545.6i −1.50956 0.456993i
\(862\) −9925.86 17192.1i −0.392200 0.679310i
\(863\) −14614.7 −0.576467 −0.288233 0.957560i \(-0.593068\pi\)
−0.288233 + 0.957560i \(0.593068\pi\)
\(864\) 11795.0 1967.77i 0.464437 0.0774826i
\(865\) 0 0
\(866\) −5304.99 9188.52i −0.208165 0.360553i
\(867\) 10664.9 + 3228.62i 0.417761 + 0.126470i
\(868\) −3130.50 + 5422.18i −0.122415 + 0.212028i
\(869\) −12202.5 + 21135.4i −0.476343 + 0.825050i
\(870\) 0 0
\(871\) 89.0759 + 154.284i 0.00346524 + 0.00600197i
\(872\) 48022.2 1.86495
\(873\) −2374.21 + 36857.5i −0.0920446 + 1.42891i
\(874\) 3344.45 0.129437
\(875\) 0 0
\(876\) 3750.53 3516.71i 0.144656 0.135638i
\(877\) 694.282 1202.53i 0.0267323 0.0463017i −0.852350 0.522972i \(-0.824823\pi\)
0.879082 + 0.476670i \(0.158156\pi\)
\(878\) 5816.90 10075.2i 0.223589 0.387267i
\(879\) −24561.4 + 23030.1i −0.942474 + 0.883717i
\(880\) 0 0
\(881\) 23664.2 0.904957 0.452478 0.891775i \(-0.350540\pi\)
0.452478 + 0.891775i \(0.350540\pi\)
\(882\) 1504.69 + 1002.96i 0.0574438 + 0.0382895i
\(883\) −49607.6 −1.89063 −0.945317 0.326152i \(-0.894248\pi\)
−0.945317 + 0.326152i \(0.894248\pi\)
\(884\) 51.2225 + 88.7200i 0.00194887 + 0.00337554i
\(885\) 0 0
\(886\) −18915.4 + 32762.5i −0.717242 + 1.24230i
\(887\) 5738.51 9939.40i 0.217227 0.376248i −0.736732 0.676185i \(-0.763632\pi\)
0.953959 + 0.299936i \(0.0969655\pi\)
\(888\) 51093.4 + 15467.7i 1.93084 + 0.584530i
\(889\) 8330.41 + 14428.7i 0.314278 + 0.544345i
\(890\) 0 0
\(891\) 17635.3 23089.9i 0.663079 0.868171i
\(892\) −4564.19 −0.171323
\(893\) −3499.84 6061.91i −0.131151 0.227160i
\(894\) 10233.3 + 3097.97i 0.382833 + 0.115897i
\(895\) 0 0
\(896\) −6920.78 + 11987.1i −0.258044 + 0.446945i
\(897\) 32.7047 + 139.908i 0.00121737 + 0.00520778i
\(898\) −6712.31 11626.1i −0.249435 0.432034i
\(899\) 42999.4 1.59523
\(900\) 0 0
\(901\) 15305.1 0.565914
\(902\) −19569.1 33894.6i −0.722371 1.25118i
\(903\) −26169.2 + 24537.7i −0.964402 + 0.904278i
\(904\) 11966.7 20727.0i 0.440273 0.762576i
\(905\) 0 0
\(906\) −17432.4 + 16345.6i −0.639241 + 0.599389i
\(907\) −5866.89 10161.8i −0.214782 0.372013i 0.738423 0.674337i \(-0.235571\pi\)
−0.953205 + 0.302325i \(0.902237\pi\)
\(908\) 1883.58 0.0688424
\(909\) 986.558 15315.4i 0.0359979 0.558834i
\(910\) 0 0
\(911\) 17506.7 + 30322.5i 0.636688 + 1.10278i 0.986155 + 0.165827i \(0.0530293\pi\)
−0.349467 + 0.936949i \(0.613637\pi\)
\(912\) 2627.30 + 11239.4i 0.0953933 + 0.408084i
\(913\) 1610.46 2789.40i 0.0583773 0.101112i
\(914\) 64.9602 112.514i 0.00235087 0.00407182i
\(915\) 0 0
\(916\) 1539.00 + 2665.63i 0.0555132 + 0.0961516i
\(917\) −28262.9 −1.01780
\(918\) 6378.07 17033.1i 0.229311 0.612391i
\(919\) 16026.6 0.575264 0.287632 0.957741i \(-0.407132\pi\)
0.287632 + 0.957741i \(0.407132\pi\)
\(920\) 0 0
\(921\) 3523.31 + 1066.63i 0.126055 + 0.0381612i
\(922\) 3901.54 6757.66i 0.139360 0.241379i
\(923\) −405.058 + 701.581i −0.0144449 + 0.0250193i
\(924\) −1749.93 7486.02i −0.0623034 0.266528i
\(925\) 0 0
\(926\) 32257.8 1.14477
\(927\) 11499.9 5687.16i 0.407449 0.201500i
\(928\) −21730.7 −0.768691
\(929\) −12943.4 22418.6i −0.457114 0.791745i 0.541693 0.840577i \(-0.317784\pi\)
−0.998807 + 0.0488314i \(0.984450\pi\)
\(930\) 0 0
\(931\) 673.282 1166.16i 0.0237013 0.0410519i
\(932\) −910.284 + 1576.66i −0.0319929 + 0.0554132i
\(933\) −23632.3 + 22159.0i −0.829247 + 0.777549i
\(934\) 16292.7 + 28219.8i 0.570786 + 0.988631i
\(935\) 0 0
\(936\) −597.483 + 295.480i −0.0208647 + 0.0103185i
\(937\) −6331.15 −0.220736 −0.110368 0.993891i \(-0.535203\pi\)
−0.110368 + 0.993891i \(0.535203\pi\)
\(938\) −4184.56 7247.88i −0.145662 0.252294i
\(939\) 3112.34 + 13314.3i 0.108165 + 0.462721i
\(940\) 0 0
\(941\) 14377.4 24902.3i 0.498075 0.862691i −0.501923 0.864912i \(-0.667374\pi\)
0.999998 + 0.00222173i \(0.000707200\pi\)
\(942\) 28181.6 + 8531.52i 0.974741 + 0.295087i
\(943\) 5460.78 + 9458.35i 0.188576 + 0.326624i
\(944\) −1288.39 −0.0444210
\(945\) 0 0
\(946\) −35235.6 −1.21100
\(947\) −14620.3 25323.2i −0.501687 0.868947i −0.999998 0.00194886i \(-0.999380\pi\)
0.498311 0.866998i \(-0.333954\pi\)
\(948\) 5875.86 + 1778.82i 0.201307 + 0.0609424i
\(949\) −258.742 + 448.154i −0.00885050 + 0.0153295i
\(950\) 0 0
\(951\) 594.379 + 2542.70i 0.0202672 + 0.0867010i
\(952\) −12383.5 21448.9i −0.421588 0.730212i
\(953\) 28758.3 0.977517 0.488758 0.872419i \(-0.337450\pi\)
0.488758 + 0.872419i \(0.337450\pi\)
\(954\) −1243.90 + 19310.4i −0.0422145 + 0.655341i
\(955\) 0 0
\(956\) 2635.13 + 4564.19i 0.0891489 + 0.154410i
\(957\) −38515.6 + 36114.4i −1.30098 + 1.21987i
\(958\) 10543.5 18261.9i 0.355581 0.615884i
\(959\) −688.175 + 1191.95i −0.0231724 + 0.0401358i
\(960\) 0 0
\(961\) 673.025 + 1165.71i 0.0225916 + 0.0391297i
\(962\) −1044.08 −0.0349920
\(963\) −32634.9 21753.0i −1.09205 0.727914i
\(964\) −6593.36 −0.220288
\(965\) 0 0
\(966\) −1536.39 6572.51i −0.0511722 0.218910i
\(967\) −22347.6 + 38707.1i −0.743174 + 1.28721i 0.207869 + 0.978157i \(0.433347\pi\)
−0.951043 + 0.309058i \(0.899986\pi\)
\(968\) 3148.71 5453.73i 0.104549 0.181084i
\(969\) −12962.8 3924.26i −0.429746 0.130099i
\(970\) 0 0
\(971\) −30462.4 −1.00678 −0.503391 0.864059i \(-0.667914\pi\)
−0.503391 + 0.864059i \(0.667914\pi\)
\(972\) −6665.69 2997.67i −0.219961 0.0989200i
\(973\) 4407.24 0.145210
\(974\) −24061.1 41675.1i −0.791548 1.37100i
\(975\) 0 0
\(976\) 16428.4 28454.8i 0.538790 0.933212i
\(977\) −5904.00 + 10226.0i −0.193332 + 0.334861i −0.946353 0.323136i \(-0.895263\pi\)
0.753020 + 0.657997i \(0.228596\pi\)
\(978\) 130.852 + 559.773i 0.00427831 + 0.0183022i
\(979\) −478.451 828.701i −0.0156194 0.0270535i
\(980\) 0 0
\(981\) −44099.9 29395.1i −1.43527 0.956690i
\(982\) −48016.1 −1.56034
\(983\) −12351.5 21393.3i −0.400763 0.694142i 0.593055 0.805162i \(-0.297922\pi\)
−0.993818 + 0.111020i \(0.964588\pi\)
\(984\) −36960.6 + 34656.4i −1.19742 + 1.12277i
\(985\) 0 0
\(986\) −16526.1 + 28624.1i −0.533771 + 0.924519i
\(987\) −10305.1 + 9662.63i −0.332335 + 0.311616i
\(988\) 48.2242 + 83.5268i 0.00155285 + 0.00268962i
\(989\) 9832.55 0.316134
\(990\) 0 0
\(991\) 14443.0 0.462965 0.231482 0.972839i \(-0.425642\pi\)
0.231482 + 0.972839i \(0.425642\pi\)
\(992\) 7187.63 + 12449.3i 0.230048 + 0.398455i
\(993\) 3651.35 + 15620.1i 0.116689 + 0.499184i
\(994\) 19028.6 32958.5i 0.607194 1.05169i
\(995\) 0 0
\(996\) −775.482 234.765i −0.0246708 0.00746867i
\(997\) −23834.7 41282.9i −0.757123 1.31138i −0.944312 0.329051i \(-0.893271\pi\)
0.187189 0.982324i \(-0.440062\pi\)
\(998\) −836.551 −0.0265336
\(999\) −37452.4 45479.4i −1.18613 1.44035i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 225.4.e.g.76.6 32
5.2 odd 4 45.4.j.a.4.11 yes 32
5.3 odd 4 45.4.j.a.4.6 32
5.4 even 2 inner 225.4.e.g.76.11 32
9.4 even 3 2025.4.a.bk.1.11 16
9.5 odd 6 2025.4.a.bl.1.6 16
9.7 even 3 inner 225.4.e.g.151.6 32
15.2 even 4 135.4.j.a.64.6 32
15.8 even 4 135.4.j.a.64.11 32
45.2 even 12 135.4.j.a.19.11 32
45.4 even 6 2025.4.a.bk.1.6 16
45.7 odd 12 45.4.j.a.34.6 yes 32
45.13 odd 12 405.4.b.e.244.6 16
45.14 odd 6 2025.4.a.bl.1.11 16
45.22 odd 12 405.4.b.e.244.11 16
45.23 even 12 405.4.b.f.244.11 16
45.32 even 12 405.4.b.f.244.6 16
45.34 even 6 inner 225.4.e.g.151.11 32
45.38 even 12 135.4.j.a.19.6 32
45.43 odd 12 45.4.j.a.34.11 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.j.a.4.6 32 5.3 odd 4
45.4.j.a.4.11 yes 32 5.2 odd 4
45.4.j.a.34.6 yes 32 45.7 odd 12
45.4.j.a.34.11 yes 32 45.43 odd 12
135.4.j.a.19.6 32 45.38 even 12
135.4.j.a.19.11 32 45.2 even 12
135.4.j.a.64.6 32 15.2 even 4
135.4.j.a.64.11 32 15.8 even 4
225.4.e.g.76.6 32 1.1 even 1 trivial
225.4.e.g.76.11 32 5.4 even 2 inner
225.4.e.g.151.6 32 9.7 even 3 inner
225.4.e.g.151.11 32 45.34 even 6 inner
405.4.b.e.244.6 16 45.13 odd 12
405.4.b.e.244.11 16 45.22 odd 12
405.4.b.f.244.6 16 45.32 even 12
405.4.b.f.244.11 16 45.23 even 12
2025.4.a.bk.1.6 16 45.4 even 6
2025.4.a.bk.1.11 16 9.4 even 3
2025.4.a.bl.1.6 16 9.5 odd 6
2025.4.a.bl.1.11 16 45.14 odd 6