Properties

Label 60.5.c.a.31.5
Level $60$
Weight $5$
Character 60.31
Analytic conductor $6.202$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,5,Mod(31,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.31");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), 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: \(6.20219778503\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + 25296 x^{8} - 6656 x^{7} - 110848 x^{6} - 227328 x^{5} + 1077248 x^{4} + \cdots + 16777216 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.5
Root \(1.85226 - 2.13755i\) of defining polynomial
Character \(\chi\) \(=\) 60.31
Dual form 60.5.c.a.31.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.34902 - 2.18726i) q^{2} +5.19615i q^{3} +(6.43181 + 14.6503i) q^{4} -11.1803 q^{5} +(11.3653 - 17.4020i) q^{6} -1.39605i q^{7} +(10.5038 - 63.1322i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-3.34902 - 2.18726i) q^{2} +5.19615i q^{3} +(6.43181 + 14.6503i) q^{4} -11.1803 q^{5} +(11.3653 - 17.4020i) q^{6} -1.39605i q^{7} +(10.5038 - 63.1322i) q^{8} -27.0000 q^{9} +(37.4431 + 24.4543i) q^{10} -164.588i q^{11} +(-76.1253 + 33.4207i) q^{12} -158.663 q^{13} +(-3.05352 + 4.67540i) q^{14} -58.0948i q^{15} +(-173.264 + 188.456i) q^{16} -548.214 q^{17} +(90.4234 + 59.0560i) q^{18} -25.6686i q^{19} +(-71.9098 - 163.796i) q^{20} +7.25409 q^{21} +(-359.996 + 551.208i) q^{22} -730.150i q^{23} +(328.044 + 54.5793i) q^{24} +125.000 q^{25} +(531.364 + 347.036i) q^{26} -140.296i q^{27} +(20.4526 - 8.97913i) q^{28} +773.909 q^{29} +(-127.068 + 194.560i) q^{30} -194.974i q^{31} +(992.465 - 252.170i) q^{32} +855.224 q^{33} +(1835.98 + 1199.09i) q^{34} +15.6083i q^{35} +(-173.659 - 395.559i) q^{36} -1373.19 q^{37} +(-56.1439 + 85.9646i) q^{38} -824.435i q^{39} +(-117.436 + 705.839i) q^{40} -647.851 q^{41} +(-24.2941 - 15.8666i) q^{42} +1502.44i q^{43} +(2411.27 - 1058.60i) q^{44} +301.869 q^{45} +(-1597.03 + 2445.28i) q^{46} +647.613i q^{47} +(-979.247 - 900.305i) q^{48} +2399.05 q^{49} +(-418.627 - 273.407i) q^{50} -2848.61i q^{51} +(-1020.49 - 2324.46i) q^{52} -4407.11 q^{53} +(-306.864 + 469.854i) q^{54} +1840.15i q^{55} +(-88.1357 - 14.6638i) q^{56} +133.378 q^{57} +(-2591.83 - 1692.74i) q^{58} +5978.96i q^{59} +(851.107 - 373.654i) q^{60} -560.288 q^{61} +(-426.459 + 652.971i) q^{62} +37.6934i q^{63} +(-3875.34 - 1326.26i) q^{64} +1773.90 q^{65} +(-2864.16 - 1870.60i) q^{66} -2986.47i q^{67} +(-3526.01 - 8031.52i) q^{68} +3793.97 q^{69} +(34.1394 - 52.2725i) q^{70} -2673.19i q^{71} +(-283.603 + 1704.57i) q^{72} +2649.09 q^{73} +(4598.82 + 3003.51i) q^{74} +649.519i q^{75} +(376.053 - 165.096i) q^{76} -229.773 q^{77} +(-1803.25 + 2761.05i) q^{78} -3158.78i q^{79} +(1937.15 - 2107.00i) q^{80} +729.000 q^{81} +(2169.66 + 1417.02i) q^{82} +13095.0i q^{83} +(46.6569 + 106.275i) q^{84} +6129.22 q^{85} +(3286.22 - 5031.69i) q^{86} +4021.35i q^{87} +(-10390.8 - 1728.80i) q^{88} -7112.37 q^{89} +(-1010.96 - 660.266i) q^{90} +221.501i q^{91} +(10696.9 - 4696.19i) q^{92} +1013.12 q^{93} +(1416.50 - 2168.87i) q^{94} +286.984i q^{95} +(1310.31 + 5157.00i) q^{96} +5310.91 q^{97} +(-8034.46 - 5247.34i) q^{98} +4443.88i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.34902 2.18726i −0.837254 0.546814i
\(3\) 5.19615i 0.577350i
\(4\) 6.43181 + 14.6503i 0.401988 + 0.915645i
\(5\) −11.1803 −0.447214
\(6\) 11.3653 17.4020i 0.315703 0.483389i
\(7\) 1.39605i 0.0284908i −0.999899 0.0142454i \(-0.995465\pi\)
0.999899 0.0142454i \(-0.00453461\pi\)
\(8\) 10.5038 63.1322i 0.164122 0.986440i
\(9\) −27.0000 −0.333333
\(10\) 37.4431 + 24.4543i 0.374431 + 0.244543i
\(11\) 164.588i 1.36023i −0.733105 0.680116i \(-0.761930\pi\)
0.733105 0.680116i \(-0.238070\pi\)
\(12\) −76.1253 + 33.4207i −0.528648 + 0.232088i
\(13\) −158.663 −0.938832 −0.469416 0.882977i \(-0.655536\pi\)
−0.469416 + 0.882977i \(0.655536\pi\)
\(14\) −3.05352 + 4.67540i −0.0155792 + 0.0238541i
\(15\) 58.0948i 0.258199i
\(16\) −173.264 + 188.456i −0.676811 + 0.736157i
\(17\) −548.214 −1.89694 −0.948468 0.316873i \(-0.897367\pi\)
−0.948468 + 0.316873i \(0.897367\pi\)
\(18\) 90.4234 + 59.0560i 0.279085 + 0.182271i
\(19\) 25.6686i 0.0711042i −0.999368 0.0355521i \(-0.988681\pi\)
0.999368 0.0355521i \(-0.0113190\pi\)
\(20\) −71.9098 163.796i −0.179774 0.409489i
\(21\) 7.25409 0.0164492
\(22\) −359.996 + 551.208i −0.743794 + 1.13886i
\(23\) 730.150i 1.38025i −0.723692 0.690123i \(-0.757556\pi\)
0.723692 0.690123i \(-0.242444\pi\)
\(24\) 328.044 + 54.5793i 0.569521 + 0.0947558i
\(25\) 125.000 0.200000
\(26\) 531.364 + 347.036i 0.786041 + 0.513367i
\(27\) 140.296i 0.192450i
\(28\) 20.4526 8.97913i 0.0260875 0.0114530i
\(29\) 773.909 0.920225 0.460112 0.887861i \(-0.347809\pi\)
0.460112 + 0.887861i \(0.347809\pi\)
\(30\) −127.068 + 194.560i −0.141187 + 0.216178i
\(31\) 194.974i 0.202887i −0.994841 0.101443i \(-0.967654\pi\)
0.994841 0.101443i \(-0.0323461\pi\)
\(32\) 992.465 252.170i 0.969204 0.246260i
\(33\) 855.224 0.785330
\(34\) 1835.98 + 1199.09i 1.58822 + 1.03727i
\(35\) 15.6083i 0.0127415i
\(36\) −173.659 395.559i −0.133996 0.305215i
\(37\) −1373.19 −1.00306 −0.501529 0.865141i \(-0.667229\pi\)
−0.501529 + 0.865141i \(0.667229\pi\)
\(38\) −56.1439 + 85.9646i −0.0388808 + 0.0595323i
\(39\) 824.435i 0.542035i
\(40\) −117.436 + 705.839i −0.0733975 + 0.441149i
\(41\) −647.851 −0.385396 −0.192698 0.981258i \(-0.561724\pi\)
−0.192698 + 0.981258i \(0.561724\pi\)
\(42\) −24.2941 15.8666i −0.0137721 0.00899465i
\(43\) 1502.44i 0.812568i 0.913747 + 0.406284i \(0.133176\pi\)
−0.913747 + 0.406284i \(0.866824\pi\)
\(44\) 2411.27 1058.60i 1.24549 0.546797i
\(45\) 301.869 0.149071
\(46\) −1597.03 + 2445.28i −0.754738 + 1.15562i
\(47\) 647.613i 0.293170i 0.989198 + 0.146585i \(0.0468282\pi\)
−0.989198 + 0.146585i \(0.953172\pi\)
\(48\) −979.247 900.305i −0.425020 0.390757i
\(49\) 2399.05 0.999188
\(50\) −418.627 273.407i −0.167451 0.109363i
\(51\) 2848.61i 1.09520i
\(52\) −1020.49 2324.46i −0.377399 0.859637i
\(53\) −4407.11 −1.56892 −0.784462 0.620177i \(-0.787061\pi\)
−0.784462 + 0.620177i \(0.787061\pi\)
\(54\) −306.864 + 469.854i −0.105234 + 0.161130i
\(55\) 1840.15i 0.608314i
\(56\) −88.1357 14.6638i −0.0281045 0.00467597i
\(57\) 133.378 0.0410520
\(58\) −2591.83 1692.74i −0.770462 0.503192i
\(59\) 5978.96i 1.71760i 0.512311 + 0.858800i \(0.328789\pi\)
−0.512311 + 0.858800i \(0.671211\pi\)
\(60\) 851.107 373.654i 0.236419 0.103793i
\(61\) −560.288 −0.150575 −0.0752873 0.997162i \(-0.523987\pi\)
−0.0752873 + 0.997162i \(0.523987\pi\)
\(62\) −426.459 + 652.971i −0.110941 + 0.169868i
\(63\) 37.6934i 0.00949694i
\(64\) −3875.34 1326.26i −0.946128 0.323793i
\(65\) 1773.90 0.419859
\(66\) −2864.16 1870.60i −0.657521 0.429430i
\(67\) 2986.47i 0.665286i −0.943053 0.332643i \(-0.892060\pi\)
0.943053 0.332643i \(-0.107940\pi\)
\(68\) −3526.01 8031.52i −0.762545 1.73692i
\(69\) 3793.97 0.796885
\(70\) 34.1394 52.2725i 0.00696723 0.0106679i
\(71\) 2673.19i 0.530290i −0.964209 0.265145i \(-0.914580\pi\)
0.964209 0.265145i \(-0.0854198\pi\)
\(72\) −283.603 + 1704.57i −0.0547073 + 0.328813i
\(73\) 2649.09 0.497108 0.248554 0.968618i \(-0.420045\pi\)
0.248554 + 0.968618i \(0.420045\pi\)
\(74\) 4598.82 + 3003.51i 0.839815 + 0.548487i
\(75\) 649.519i 0.115470i
\(76\) 376.053 165.096i 0.0651062 0.0285830i
\(77\) −229.773 −0.0387541
\(78\) −1803.25 + 2761.05i −0.296393 + 0.453821i
\(79\) 3158.78i 0.506134i −0.967449 0.253067i \(-0.918561\pi\)
0.967449 0.253067i \(-0.0814393\pi\)
\(80\) 1937.15 2107.00i 0.302679 0.329219i
\(81\) 729.000 0.111111
\(82\) 2169.66 + 1417.02i 0.322675 + 0.210740i
\(83\) 13095.0i 1.90085i 0.310952 + 0.950426i \(0.399352\pi\)
−0.310952 + 0.950426i \(0.600648\pi\)
\(84\) 46.6569 + 106.275i 0.00661238 + 0.0150616i
\(85\) 6129.22 0.848336
\(86\) 3286.22 5031.69i 0.444324 0.680325i
\(87\) 4021.35i 0.531292i
\(88\) −10390.8 1728.80i −1.34179 0.223244i
\(89\) −7112.37 −0.897913 −0.448956 0.893554i \(-0.648204\pi\)
−0.448956 + 0.893554i \(0.648204\pi\)
\(90\) −1010.96 660.266i −0.124810 0.0815143i
\(91\) 221.501i 0.0267481i
\(92\) 10696.9 4696.19i 1.26382 0.554842i
\(93\) 1013.12 0.117137
\(94\) 1416.50 2168.87i 0.160310 0.245458i
\(95\) 286.984i 0.0317988i
\(96\) 1310.31 + 5157.00i 0.142178 + 0.559570i
\(97\) 5310.91 0.564450 0.282225 0.959348i \(-0.408927\pi\)
0.282225 + 0.959348i \(0.408927\pi\)
\(98\) −8034.46 5247.34i −0.836574 0.546371i
\(99\) 4443.88i 0.453410i
\(100\) 803.976 + 1831.29i 0.0803976 + 0.183129i
\(101\) −17042.8 −1.67070 −0.835348 0.549721i \(-0.814734\pi\)
−0.835348 + 0.549721i \(0.814734\pi\)
\(102\) −6230.64 + 9540.03i −0.598869 + 0.916957i
\(103\) 3359.31i 0.316647i −0.987387 0.158323i \(-0.949391\pi\)
0.987387 0.158323i \(-0.0506089\pi\)
\(104\) −1666.56 + 10016.7i −0.154083 + 0.926102i
\(105\) −81.1032 −0.00735630
\(106\) 14759.5 + 9639.48i 1.31359 + 0.857910i
\(107\) 6655.05i 0.581278i −0.956833 0.290639i \(-0.906132\pi\)
0.956833 0.290639i \(-0.0938678\pi\)
\(108\) 2055.38 902.358i 0.176216 0.0773626i
\(109\) 10400.1 0.875355 0.437677 0.899132i \(-0.355801\pi\)
0.437677 + 0.899132i \(0.355801\pi\)
\(110\) 4024.88 6162.69i 0.332635 0.509313i
\(111\) 7135.29i 0.579116i
\(112\) 263.094 + 241.885i 0.0209737 + 0.0192829i
\(113\) 11224.7 0.879056 0.439528 0.898229i \(-0.355146\pi\)
0.439528 + 0.898229i \(0.355146\pi\)
\(114\) −446.685 291.732i −0.0343710 0.0224478i
\(115\) 8163.33i 0.617265i
\(116\) 4977.63 + 11338.0i 0.369919 + 0.842599i
\(117\) 4283.89 0.312944
\(118\) 13077.5 20023.6i 0.939208 1.43807i
\(119\) 765.335i 0.0540453i
\(120\) −3667.65 610.216i −0.254698 0.0423761i
\(121\) −12448.2 −0.850229
\(122\) 1876.41 + 1225.50i 0.126069 + 0.0823364i
\(123\) 3366.33i 0.222509i
\(124\) 2856.43 1254.04i 0.185772 0.0815580i
\(125\) −1397.54 −0.0894427
\(126\) 82.4451 126.236i 0.00519307 0.00795135i
\(127\) 25607.7i 1.58768i −0.608128 0.793839i \(-0.708079\pi\)
0.608128 0.793839i \(-0.291921\pi\)
\(128\) 10077.7 + 12918.0i 0.615095 + 0.788453i
\(129\) −7806.89 −0.469136
\(130\) −5940.83 3879.98i −0.351528 0.229585i
\(131\) 16564.8i 0.965256i −0.875825 0.482628i \(-0.839682\pi\)
0.875825 0.482628i \(-0.160318\pi\)
\(132\) 5500.64 + 12529.3i 0.315693 + 0.719083i
\(133\) −35.8347 −0.00202582
\(134\) −6532.18 + 10001.7i −0.363788 + 0.557013i
\(135\) 1568.56i 0.0860663i
\(136\) −5758.33 + 34610.0i −0.311329 + 1.87121i
\(137\) −5619.61 −0.299409 −0.149705 0.988731i \(-0.547832\pi\)
−0.149705 + 0.988731i \(0.547832\pi\)
\(138\) −12706.1 8298.39i −0.667195 0.435748i
\(139\) 33597.0i 1.73888i −0.494036 0.869442i \(-0.664479\pi\)
0.494036 0.869442i \(-0.335521\pi\)
\(140\) −228.667 + 100.390i −0.0116667 + 0.00512193i
\(141\) −3365.10 −0.169262
\(142\) −5846.96 + 8952.55i −0.289970 + 0.443987i
\(143\) 26114.0i 1.27703i
\(144\) 4678.12 5088.31i 0.225604 0.245386i
\(145\) −8652.57 −0.411537
\(146\) −8871.84 5794.24i −0.416206 0.271826i
\(147\) 12465.8i 0.576882i
\(148\) −8832.08 20117.6i −0.403217 0.918445i
\(149\) −19602.3 −0.882946 −0.441473 0.897275i \(-0.645544\pi\)
−0.441473 + 0.897275i \(0.645544\pi\)
\(150\) 1420.67 2175.25i 0.0631407 0.0966777i
\(151\) 9340.31i 0.409645i −0.978799 0.204822i \(-0.934338\pi\)
0.978799 0.204822i \(-0.0656617\pi\)
\(152\) −1620.52 269.618i −0.0701400 0.0116698i
\(153\) 14801.8 0.632312
\(154\) 769.514 + 502.573i 0.0324470 + 0.0211913i
\(155\) 2179.88i 0.0907337i
\(156\) 12078.2 5302.61i 0.496312 0.217892i
\(157\) −34913.2 −1.41642 −0.708208 0.706004i \(-0.750496\pi\)
−0.708208 + 0.706004i \(0.750496\pi\)
\(158\) −6909.07 + 10578.8i −0.276761 + 0.423763i
\(159\) 22900.0i 0.905818i
\(160\) −11096.1 + 2819.35i −0.433441 + 0.110131i
\(161\) −1019.33 −0.0393244
\(162\) −2441.43 1594.51i −0.0930282 0.0607572i
\(163\) 49700.0i 1.87060i 0.353853 + 0.935301i \(0.384871\pi\)
−0.353853 + 0.935301i \(0.615129\pi\)
\(164\) −4166.85 9491.23i −0.154925 0.352886i
\(165\) −9561.70 −0.351210
\(166\) 28642.1 43855.2i 1.03941 1.59149i
\(167\) 51638.7i 1.85158i −0.378038 0.925790i \(-0.623401\pi\)
0.378038 0.925790i \(-0.376599\pi\)
\(168\) 76.1955 457.967i 0.00269967 0.0162261i
\(169\) −3387.16 −0.118594
\(170\) −20526.9 13406.2i −0.710272 0.463882i
\(171\) 693.053i 0.0237014i
\(172\) −22011.2 + 9663.39i −0.744023 + 0.326642i
\(173\) 48824.2 1.63133 0.815667 0.578522i \(-0.196370\pi\)
0.815667 + 0.578522i \(0.196370\pi\)
\(174\) 8795.73 13467.6i 0.290518 0.444826i
\(175\) 174.506i 0.00569817i
\(176\) 31017.6 + 28517.1i 1.00134 + 0.920620i
\(177\) −31067.6 −0.991657
\(178\) 23819.4 + 15556.6i 0.751781 + 0.490992i
\(179\) 51061.1i 1.59362i 0.604233 + 0.796808i \(0.293480\pi\)
−0.604233 + 0.796808i \(0.706520\pi\)
\(180\) 1941.56 + 4422.48i 0.0599248 + 0.136496i
\(181\) 16788.0 0.512438 0.256219 0.966619i \(-0.417523\pi\)
0.256219 + 0.966619i \(0.417523\pi\)
\(182\) 484.480 741.811i 0.0146263 0.0223950i
\(183\) 2911.34i 0.0869343i
\(184\) −46096.0 7669.35i −1.36153 0.226529i
\(185\) 15352.7 0.448581
\(186\) −3392.94 2215.94i −0.0980732 0.0640520i
\(187\) 90229.5i 2.58027i
\(188\) −9487.74 + 4165.32i −0.268440 + 0.117851i
\(189\) −195.861 −0.00548306
\(190\) 627.708 961.113i 0.0173880 0.0266236i
\(191\) 34310.5i 0.940504i −0.882532 0.470252i \(-0.844163\pi\)
0.882532 0.470252i \(-0.155837\pi\)
\(192\) 6891.42 20136.9i 0.186942 0.546247i
\(193\) 33325.8 0.894675 0.447338 0.894365i \(-0.352372\pi\)
0.447338 + 0.894365i \(0.352372\pi\)
\(194\) −17786.3 11616.3i −0.472588 0.308650i
\(195\) 9217.47i 0.242405i
\(196\) 15430.2 + 35146.9i 0.401662 + 0.914902i
\(197\) 53779.0 1.38573 0.692867 0.721065i \(-0.256347\pi\)
0.692867 + 0.721065i \(0.256347\pi\)
\(198\) 9719.90 14882.6i 0.247931 0.379620i
\(199\) 7992.31i 0.201821i −0.994896 0.100910i \(-0.967824\pi\)
0.994896 0.100910i \(-0.0321755\pi\)
\(200\) 1312.97 7891.52i 0.0328244 0.197288i
\(201\) 15518.2 0.384103
\(202\) 57076.5 + 37276.9i 1.39880 + 0.913561i
\(203\) 1080.42i 0.0262180i
\(204\) 41733.0 18321.7i 1.00281 0.440256i
\(205\) 7243.20 0.172354
\(206\) −7347.67 + 11250.4i −0.173147 + 0.265114i
\(207\) 19714.1i 0.460082i
\(208\) 27490.5 29900.9i 0.635412 0.691128i
\(209\) −4224.75 −0.0967182
\(210\) 271.616 + 177.394i 0.00615909 + 0.00402253i
\(211\) 23096.8i 0.518785i 0.965772 + 0.259393i \(0.0835224\pi\)
−0.965772 + 0.259393i \(0.916478\pi\)
\(212\) −28345.7 64565.5i −0.630688 1.43658i
\(213\) 13890.3 0.306163
\(214\) −14556.3 + 22287.9i −0.317851 + 0.486677i
\(215\) 16797.8i 0.363391i
\(216\) −8857.20 1473.64i −0.189840 0.0315853i
\(217\) −272.194 −0.00578041
\(218\) −34830.1 22747.7i −0.732894 0.478657i
\(219\) 13765.1i 0.287006i
\(220\) −26958.8 + 11835.5i −0.557000 + 0.244535i
\(221\) 86981.2 1.78090
\(222\) −15606.7 + 23896.2i −0.316669 + 0.484867i
\(223\) 46059.3i 0.926206i 0.886305 + 0.463103i \(0.153264\pi\)
−0.886305 + 0.463103i \(0.846736\pi\)
\(224\) −352.042 1385.53i −0.00701615 0.0276134i
\(225\) −3375.00 −0.0666667
\(226\) −37591.6 24551.2i −0.735993 0.480681i
\(227\) 49636.5i 0.963274i −0.876371 0.481637i \(-0.840042\pi\)
0.876371 0.481637i \(-0.159958\pi\)
\(228\) 857.862 + 1954.03i 0.0165024 + 0.0375891i
\(229\) −8900.38 −0.169722 −0.0848609 0.996393i \(-0.527045\pi\)
−0.0848609 + 0.996393i \(0.527045\pi\)
\(230\) 17855.3 27339.1i 0.337529 0.516807i
\(231\) 1193.94i 0.0223747i
\(232\) 8128.98 48858.5i 0.151029 0.907747i
\(233\) −13357.8 −0.246050 −0.123025 0.992404i \(-0.539260\pi\)
−0.123025 + 0.992404i \(0.539260\pi\)
\(234\) −14346.8 9369.98i −0.262014 0.171122i
\(235\) 7240.54i 0.131110i
\(236\) −87593.7 + 38455.5i −1.57271 + 0.690454i
\(237\) 16413.5 0.292217
\(238\) 1673.99 2563.12i 0.0295527 0.0452496i
\(239\) 40201.8i 0.703801i −0.936037 0.351900i \(-0.885536\pi\)
0.936037 0.351900i \(-0.114464\pi\)
\(240\) 10948.3 + 10065.7i 0.190075 + 0.174752i
\(241\) −91284.7 −1.57168 −0.785840 0.618430i \(-0.787769\pi\)
−0.785840 + 0.618430i \(0.787769\pi\)
\(242\) 41689.2 + 27227.4i 0.711858 + 0.464918i
\(243\) 3788.00i 0.0641500i
\(244\) −3603.67 8208.40i −0.0605292 0.137873i
\(245\) −26822.2 −0.446851
\(246\) −7363.04 + 11273.9i −0.121671 + 0.186296i
\(247\) 4072.65i 0.0667549i
\(248\) −12309.1 2047.97i −0.200136 0.0332981i
\(249\) −68043.4 −1.09746
\(250\) 4680.39 + 3056.79i 0.0748863 + 0.0489086i
\(251\) 85298.2i 1.35392i 0.736021 + 0.676959i \(0.236703\pi\)
−0.736021 + 0.676959i \(0.763297\pi\)
\(252\) −552.220 + 242.437i −0.00869583 + 0.00381766i
\(253\) −120174. −1.87745
\(254\) −56010.6 + 85760.5i −0.868166 + 1.32929i
\(255\) 31848.4i 0.489787i
\(256\) −5495.39 65305.2i −0.0838529 0.996478i
\(257\) 23409.7 0.354429 0.177214 0.984172i \(-0.443291\pi\)
0.177214 + 0.984172i \(0.443291\pi\)
\(258\) 26145.4 + 17075.7i 0.392786 + 0.256530i
\(259\) 1917.04i 0.0285780i
\(260\) 11409.4 + 25988.2i 0.168778 + 0.384441i
\(261\) −20895.5 −0.306742
\(262\) −36231.4 + 55475.6i −0.527816 + 0.808164i
\(263\) 88925.7i 1.28563i −0.766021 0.642815i \(-0.777766\pi\)
0.766021 0.642815i \(-0.222234\pi\)
\(264\) 8983.10 53992.2i 0.128890 0.774681i
\(265\) 49272.9 0.701644
\(266\) 120.011 + 78.3797i 0.00169612 + 0.00110775i
\(267\) 36956.9i 0.518410i
\(268\) 43752.7 19208.4i 0.609166 0.267437i
\(269\) −78384.1 −1.08324 −0.541619 0.840624i \(-0.682188\pi\)
−0.541619 + 0.840624i \(0.682188\pi\)
\(270\) 3430.84 5253.13i 0.0470623 0.0720593i
\(271\) 79821.4i 1.08688i −0.839449 0.543439i \(-0.817122\pi\)
0.839449 0.543439i \(-0.182878\pi\)
\(272\) 94985.7 103314.i 1.28387 1.39644i
\(273\) −1150.95 −0.0154430
\(274\) 18820.2 + 12291.5i 0.250682 + 0.163721i
\(275\) 20573.5i 0.272046i
\(276\) 24402.1 + 55582.9i 0.320338 + 0.729664i
\(277\) −13987.6 −0.182299 −0.0911494 0.995837i \(-0.529054\pi\)
−0.0911494 + 0.995837i \(0.529054\pi\)
\(278\) −73485.2 + 112517.i −0.950847 + 1.45589i
\(279\) 5264.30i 0.0676289i
\(280\) 985.387 + 163.947i 0.0125687 + 0.00209116i
\(281\) −14451.9 −0.183026 −0.0915132 0.995804i \(-0.529170\pi\)
−0.0915132 + 0.995804i \(0.529170\pi\)
\(282\) 11269.8 + 7360.33i 0.141715 + 0.0925549i
\(283\) 117174.i 1.46305i −0.681817 0.731523i \(-0.738810\pi\)
0.681817 0.731523i \(-0.261190\pi\)
\(284\) 39163.1 17193.4i 0.485557 0.213170i
\(285\) −1491.21 −0.0183590
\(286\) 57118.0 87456.1i 0.698298 1.06920i
\(287\) 904.433i 0.0109803i
\(288\) −26796.5 + 6808.59i −0.323068 + 0.0820866i
\(289\) 217018. 2.59837
\(290\) 28977.6 + 18925.4i 0.344561 + 0.225034i
\(291\) 27596.3i 0.325885i
\(292\) 17038.4 + 38810.0i 0.199832 + 0.455175i
\(293\) −29064.0 −0.338548 −0.169274 0.985569i \(-0.554142\pi\)
−0.169274 + 0.985569i \(0.554142\pi\)
\(294\) 27266.0 41748.3i 0.315447 0.482996i
\(295\) 66846.8i 0.768134i
\(296\) −14423.7 + 86692.3i −0.164624 + 0.989457i
\(297\) −23091.1 −0.261777
\(298\) 65648.3 + 42875.2i 0.739250 + 0.482808i
\(299\) 115848.i 1.29582i
\(300\) −9515.66 + 4177.58i −0.105730 + 0.0464176i
\(301\) 2097.48 0.0231507
\(302\) −20429.7 + 31280.8i −0.224000 + 0.342977i
\(303\) 88556.8i 0.964577i
\(304\) 4837.41 + 4447.44i 0.0523438 + 0.0481241i
\(305\) 6264.21 0.0673390
\(306\) −49571.4 32375.3i −0.529406 0.345757i
\(307\) 35059.6i 0.371989i 0.982551 + 0.185995i \(0.0595507\pi\)
−0.982551 + 0.185995i \(0.940449\pi\)
\(308\) −1477.86 3366.25i −0.0155787 0.0354850i
\(309\) 17455.5 0.182816
\(310\) 4767.95 7300.44i 0.0496145 0.0759671i
\(311\) 52153.5i 0.539216i 0.962970 + 0.269608i \(0.0868942\pi\)
−0.962970 + 0.269608i \(0.913106\pi\)
\(312\) −52048.4 8659.70i −0.534685 0.0889598i
\(313\) −120087. −1.22577 −0.612885 0.790172i \(-0.709991\pi\)
−0.612885 + 0.790172i \(0.709991\pi\)
\(314\) 116925. + 76364.2i 1.18590 + 0.774516i
\(315\) 421.425i 0.00424716i
\(316\) 46277.2 20316.7i 0.463439 0.203460i
\(317\) 16118.8 0.160404 0.0802018 0.996779i \(-0.474444\pi\)
0.0802018 + 0.996779i \(0.474444\pi\)
\(318\) −50088.2 + 76692.4i −0.495314 + 0.758400i
\(319\) 127376.i 1.25172i
\(320\) 43327.6 + 14828.0i 0.423121 + 0.144805i
\(321\) 34580.6 0.335601
\(322\) 3413.74 + 2229.53i 0.0329245 + 0.0215031i
\(323\) 14071.9i 0.134880i
\(324\) 4688.79 + 10680.1i 0.0446653 + 0.101738i
\(325\) −19832.8 −0.187766
\(326\) 108707. 166446.i 1.02287 1.56617i
\(327\) 54040.4i 0.505386i
\(328\) −6804.90 + 40900.3i −0.0632520 + 0.380170i
\(329\) 904.101 0.00835267
\(330\) 32022.3 + 20913.9i 0.294052 + 0.192047i
\(331\) 7678.94i 0.0700882i −0.999386 0.0350441i \(-0.988843\pi\)
0.999386 0.0350441i \(-0.0111572\pi\)
\(332\) −191845. + 84224.3i −1.74050 + 0.764119i
\(333\) 37076.1 0.334353
\(334\) −112947. + 172939.i −1.01247 + 1.55024i
\(335\) 33389.7i 0.297525i
\(336\) −1256.87 + 1367.08i −0.0111330 + 0.0121092i
\(337\) 68133.9 0.599934 0.299967 0.953950i \(-0.403024\pi\)
0.299967 + 0.953950i \(0.403024\pi\)
\(338\) 11343.7 + 7408.59i 0.0992932 + 0.0648489i
\(339\) 58325.1i 0.507523i
\(340\) 39422.0 + 89795.1i 0.341021 + 0.776774i
\(341\) −32090.4 −0.275973
\(342\) 1515.88 2321.04i 0.0129603 0.0198441i
\(343\) 6701.12i 0.0569585i
\(344\) 94852.1 + 15781.3i 0.801549 + 0.133360i
\(345\) −42417.9 −0.356378
\(346\) −163513. 106791.i −1.36584 0.892037i
\(347\) 33524.6i 0.278423i −0.990263 0.139212i \(-0.955543\pi\)
0.990263 0.139212i \(-0.0444568\pi\)
\(348\) −58914.0 + 25864.5i −0.486475 + 0.213573i
\(349\) 178271. 1.46362 0.731811 0.681508i \(-0.238676\pi\)
0.731811 + 0.681508i \(0.238676\pi\)
\(350\) −381.690 + 584.424i −0.00311584 + 0.00477081i
\(351\) 22259.8i 0.180678i
\(352\) −41504.1 163348.i −0.334970 1.31834i
\(353\) −80952.7 −0.649654 −0.324827 0.945773i \(-0.605306\pi\)
−0.324827 + 0.945773i \(0.605306\pi\)
\(354\) 104046. + 67952.9i 0.830268 + 0.542252i
\(355\) 29887.2i 0.237153i
\(356\) −45745.4 104198.i −0.360950 0.822169i
\(357\) −3976.80 −0.0312031
\(358\) 111684. 171004.i 0.871412 1.33426i
\(359\) 95946.6i 0.744459i 0.928141 + 0.372229i \(0.121407\pi\)
−0.928141 + 0.372229i \(0.878593\pi\)
\(360\) 3170.77 19057.7i 0.0244658 0.147050i
\(361\) 129662. 0.994944
\(362\) −56223.2 36719.7i −0.429041 0.280209i
\(363\) 64682.8i 0.490880i
\(364\) −3245.06 + 1424.65i −0.0244918 + 0.0107524i
\(365\) −29617.7 −0.222314
\(366\) −6367.86 + 9750.14i −0.0475369 + 0.0727861i
\(367\) 36711.3i 0.272564i 0.990670 + 0.136282i \(0.0435153\pi\)
−0.990670 + 0.136282i \(0.956485\pi\)
\(368\) 137601. + 126509.i 1.01608 + 0.934166i
\(369\) 17492.0 0.128465
\(370\) −51416.4 33580.3i −0.375577 0.245291i
\(371\) 6152.54i 0.0446999i
\(372\) 6516.16 + 14842.5i 0.0470876 + 0.107256i
\(373\) −234487. −1.68539 −0.842696 0.538390i \(-0.819033\pi\)
−0.842696 + 0.538390i \(0.819033\pi\)
\(374\) 197355. 302180.i 1.41093 2.16034i
\(375\) 7261.84i 0.0516398i
\(376\) 40885.2 + 6802.40i 0.289195 + 0.0481157i
\(377\) −122790. −0.863937
\(378\) 655.940 + 428.397i 0.00459072 + 0.00299822i
\(379\) 25997.1i 0.180987i −0.995897 0.0904933i \(-0.971156\pi\)
0.995897 0.0904933i \(-0.0288444\pi\)
\(380\) −4204.40 + 1845.83i −0.0291164 + 0.0127827i
\(381\) 133061. 0.916647
\(382\) −75046.0 + 114906.i −0.514281 + 0.787441i
\(383\) 135973.i 0.926948i −0.886110 0.463474i \(-0.846603\pi\)
0.886110 0.463474i \(-0.153397\pi\)
\(384\) −67124.0 + 52365.3i −0.455214 + 0.355125i
\(385\) 2568.94 0.0173314
\(386\) −111609. 72892.0i −0.749070 0.489221i
\(387\) 40565.8i 0.270856i
\(388\) 34158.8 + 77806.6i 0.226902 + 0.516836i
\(389\) 104895. 0.693196 0.346598 0.938014i \(-0.387337\pi\)
0.346598 + 0.938014i \(0.387337\pi\)
\(390\) 20161.0 30869.4i 0.132551 0.202955i
\(391\) 400279.i 2.61824i
\(392\) 25199.1 151457.i 0.163989 0.985639i
\(393\) 86073.0 0.557291
\(394\) −180107. 117628.i −1.16021 0.757740i
\(395\) 35316.3i 0.226350i
\(396\) −65104.2 + 28582.2i −0.415163 + 0.182266i
\(397\) 4591.59 0.0291328 0.0145664 0.999894i \(-0.495363\pi\)
0.0145664 + 0.999894i \(0.495363\pi\)
\(398\) −17481.2 + 26766.4i −0.110359 + 0.168975i
\(399\) 186.203i 0.00116961i
\(400\) −21658.0 + 23557.0i −0.135362 + 0.147231i
\(401\) −108079. −0.672128 −0.336064 0.941839i \(-0.609096\pi\)
−0.336064 + 0.941839i \(0.609096\pi\)
\(402\) −51970.5 33942.2i −0.321592 0.210033i
\(403\) 30935.1i 0.190477i
\(404\) −109616. 249682.i −0.671600 1.52976i
\(405\) −8150.47 −0.0496904
\(406\) −2363.15 + 3618.33i −0.0143364 + 0.0219511i
\(407\) 226010.i 1.36439i
\(408\) −179839. 29921.2i −1.08035 0.179746i
\(409\) 94485.1 0.564829 0.282414 0.959293i \(-0.408865\pi\)
0.282414 + 0.959293i \(0.408865\pi\)
\(410\) −24257.6 15842.7i −0.144304 0.0942459i
\(411\) 29200.4i 0.172864i
\(412\) 49214.9 21606.4i 0.289936 0.127288i
\(413\) 8346.94 0.0489358
\(414\) 43119.7 66022.7i 0.251579 0.385205i
\(415\) 146406.i 0.850086i
\(416\) −157467. + 40010.0i −0.909920 + 0.231197i
\(417\) 174575. 1.00394
\(418\) 14148.7 + 9240.61i 0.0809777 + 0.0528869i
\(419\) 33591.5i 0.191338i 0.995413 + 0.0956691i \(0.0304991\pi\)
−0.995413 + 0.0956691i \(0.969501\pi\)
\(420\) −521.640 1188.19i −0.00295714 0.00673576i
\(421\) −187912. −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(422\) 50518.7 77351.7i 0.283679 0.434355i
\(423\) 17485.6i 0.0977234i
\(424\) −46291.3 + 278230.i −0.257495 + 1.54765i
\(425\) −68526.8 −0.379387
\(426\) −46518.8 30381.7i −0.256336 0.167414i
\(427\) 782.191i 0.00429000i
\(428\) 97498.6 42804.0i 0.532244 0.233667i
\(429\) −135692. −0.737293
\(430\) −36741.0 + 56256.0i −0.198708 + 0.304251i
\(431\) 59456.6i 0.320070i 0.987111 + 0.160035i \(0.0511608\pi\)
−0.987111 + 0.160035i \(0.948839\pi\)
\(432\) 26439.7 + 24308.2i 0.141673 + 0.130252i
\(433\) 199941. 1.06641 0.533206 0.845985i \(-0.320987\pi\)
0.533206 + 0.845985i \(0.320987\pi\)
\(434\) 911.581 + 595.358i 0.00483967 + 0.00316081i
\(435\) 44960.0i 0.237601i
\(436\) 66891.4 + 152365.i 0.351882 + 0.801514i
\(437\) −18741.9 −0.0981413
\(438\) 30107.8 46099.4i 0.156939 0.240297i
\(439\) 12289.2i 0.0637670i −0.999492 0.0318835i \(-0.989849\pi\)
0.999492 0.0318835i \(-0.0101505\pi\)
\(440\) 116173. + 19328.6i 0.600065 + 0.0998376i
\(441\) −64774.4 −0.333063
\(442\) −291301. 190250.i −1.49107 0.973824i
\(443\) 294620.i 1.50125i −0.660726 0.750627i \(-0.729751\pi\)
0.660726 0.750627i \(-0.270249\pi\)
\(444\) 104534. 45892.8i 0.530265 0.232798i
\(445\) 79518.7 0.401559
\(446\) 100744. 154253.i 0.506463 0.775469i
\(447\) 101856.i 0.509769i
\(448\) −1851.52 + 5410.17i −0.00922512 + 0.0269560i
\(449\) −301030. −1.49320 −0.746599 0.665274i \(-0.768315\pi\)
−0.746599 + 0.665274i \(0.768315\pi\)
\(450\) 11302.9 + 7381.99i 0.0558169 + 0.0364543i
\(451\) 106629.i 0.524228i
\(452\) 72194.9 + 164445.i 0.353370 + 0.804903i
\(453\) 48533.7 0.236508
\(454\) −108568. + 166234.i −0.526732 + 0.806505i
\(455\) 2476.46i 0.0119621i
\(456\) 1400.98 8420.44i 0.00673753 0.0404954i
\(457\) −65670.5 −0.314440 −0.157220 0.987564i \(-0.550253\pi\)
−0.157220 + 0.987564i \(0.550253\pi\)
\(458\) 29807.5 + 19467.4i 0.142100 + 0.0928063i
\(459\) 76912.4i 0.365065i
\(460\) −119595. + 52504.9i −0.565195 + 0.248133i
\(461\) 330337. 1.55437 0.777187 0.629270i \(-0.216646\pi\)
0.777187 + 0.629270i \(0.216646\pi\)
\(462\) −2611.45 + 3998.51i −0.0122348 + 0.0187333i
\(463\) 212356.i 0.990609i 0.868719 + 0.495304i \(0.164943\pi\)
−0.868719 + 0.495304i \(0.835057\pi\)
\(464\) −134090. + 145848.i −0.622818 + 0.677429i
\(465\) −11327.0 −0.0523851
\(466\) 44735.6 + 29217.0i 0.206007 + 0.134544i
\(467\) 275863.i 1.26491i 0.774596 + 0.632456i \(0.217953\pi\)
−0.774596 + 0.632456i \(0.782047\pi\)
\(468\) 27553.2 + 62760.4i 0.125800 + 0.286546i
\(469\) −4169.26 −0.0189546
\(470\) −15836.9 + 24248.7i −0.0716927 + 0.109772i
\(471\) 181414.i 0.817768i
\(472\) 377465. + 62801.8i 1.69431 + 0.281896i
\(473\) 247283. 1.10528
\(474\) −54969.1 35900.6i −0.244660 0.159788i
\(475\) 3208.58i 0.0142208i
\(476\) −11212.4 + 4922.49i −0.0494863 + 0.0217256i
\(477\) 118992. 0.522974
\(478\) −87931.7 + 134636.i −0.384848 + 0.589260i
\(479\) 129251.i 0.563329i −0.959513 0.281664i \(-0.909114\pi\)
0.959513 0.281664i \(-0.0908865\pi\)
\(480\) −14649.8 57657.0i −0.0635840 0.250247i
\(481\) 217874. 0.941704
\(482\) 305714. + 199663.i 1.31589 + 0.859417i
\(483\) 5296.58i 0.0227039i
\(484\) −80064.5 182370.i −0.341782 0.778508i
\(485\) −59377.8 −0.252430
\(486\) 8285.32 12686.1i 0.0350782 0.0537099i
\(487\) 296541.i 1.25034i −0.780490 0.625168i \(-0.785031\pi\)
0.780490 0.625168i \(-0.214969\pi\)
\(488\) −5885.16 + 35372.2i −0.0247126 + 0.148533i
\(489\) −258249. −1.07999
\(490\) 89828.0 + 58667.1i 0.374127 + 0.244344i
\(491\) 340038.i 1.41047i −0.708972 0.705236i \(-0.750841\pi\)
0.708972 0.705236i \(-0.249159\pi\)
\(492\) 49317.9 21651.6i 0.203739 0.0894458i
\(493\) −424268. −1.74561
\(494\) 8907.94 13639.4i 0.0365026 0.0558908i
\(495\) 49684.0i 0.202771i
\(496\) 36744.1 + 33781.9i 0.149356 + 0.137316i
\(497\) −3731.91 −0.0151084
\(498\) 227878. + 148828.i 0.918850 + 0.600105i
\(499\) 146808.i 0.589587i −0.955561 0.294794i \(-0.904749\pi\)
0.955561 0.294794i \(-0.0952509\pi\)
\(500\) −8988.72 20474.4i −0.0359549 0.0818978i
\(501\) 268323. 1.06901
\(502\) 186569. 285665.i 0.740342 1.13357i
\(503\) 410402.i 1.62208i 0.584989 + 0.811041i \(0.301099\pi\)
−0.584989 + 0.811041i \(0.698901\pi\)
\(504\) 2379.66 + 395.924i 0.00936817 + 0.00155866i
\(505\) 190544. 0.747158
\(506\) 402464. + 262851.i 1.57191 + 1.02662i
\(507\) 17600.2i 0.0684702i
\(508\) 375161. 164704.i 1.45375 0.638228i
\(509\) −170171. −0.656825 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(510\) 69660.6 106661.i 0.267822 0.410076i
\(511\) 3698.26i 0.0141630i
\(512\) −124435. + 230728.i −0.474682 + 0.880157i
\(513\) −3601.21 −0.0136840
\(514\) −78399.3 51202.9i −0.296747 0.193807i
\(515\) 37558.2i 0.141609i
\(516\) −50212.4 114373.i −0.188587 0.429562i
\(517\) 106589. 0.398779
\(518\) 4193.06 6420.19i 0.0156268 0.0239270i
\(519\) 253698.i 0.941851i
\(520\) 18632.7 111990.i 0.0689080 0.414165i
\(521\) 64423.8 0.237340 0.118670 0.992934i \(-0.462137\pi\)
0.118670 + 0.992934i \(0.462137\pi\)
\(522\) 69979.5 + 45703.9i 0.256821 + 0.167731i
\(523\) 108085.i 0.395150i −0.980288 0.197575i \(-0.936693\pi\)
0.980288 0.197575i \(-0.0633066\pi\)
\(524\) 242679. 106541.i 0.883832 0.388021i
\(525\) 906.762 0.00328984
\(526\) −194504. + 297814.i −0.703001 + 1.07640i
\(527\) 106888.i 0.384863i
\(528\) −148179. + 161172.i −0.531520 + 0.578126i
\(529\) −253278. −0.905079
\(530\) −165016. 107773.i −0.587454 0.383669i
\(531\) 161432.i 0.572533i
\(532\) −230.482 524.990i −0.000814354 0.00185493i
\(533\) 102790. 0.361823
\(534\) −80834.4 + 123769.i −0.283474 + 0.434041i
\(535\) 74405.7i 0.259955i
\(536\) −188542. 31369.3i −0.656265 0.109188i
\(537\) −265321. −0.920075
\(538\) 262510. + 171446.i 0.906945 + 0.592330i
\(539\) 394855.i 1.35913i
\(540\) −22979.9 + 10088.7i −0.0788062 + 0.0345976i
\(541\) −343195. −1.17259 −0.586295 0.810098i \(-0.699414\pi\)
−0.586295 + 0.810098i \(0.699414\pi\)
\(542\) −174590. + 267323.i −0.594321 + 0.909993i
\(543\) 87233.0i 0.295856i
\(544\) −544084. + 138243.i −1.83852 + 0.467139i
\(545\) −116277. −0.391471
\(546\) 3854.56 + 2517.43i 0.0129297 + 0.00844447i
\(547\) 310047.i 1.03622i −0.855313 0.518111i \(-0.826635\pi\)
0.855313 0.518111i \(-0.173365\pi\)
\(548\) −36144.3 82329.1i −0.120359 0.274153i
\(549\) 15127.8 0.0501916
\(550\) −44999.5 + 68901.0i −0.148759 + 0.227772i
\(551\) 19865.2i 0.0654318i
\(552\) 39851.1 239522.i 0.130786 0.786080i
\(553\) −4409.82 −0.0144202
\(554\) 46844.7 + 30594.5i 0.152630 + 0.0996836i
\(555\) 79775.0i 0.258989i
\(556\) 492206. 216089.i 1.59220 0.699010i
\(557\) 1815.28 0.00585104 0.00292552 0.999996i \(-0.499069\pi\)
0.00292552 + 0.999996i \(0.499069\pi\)
\(558\) 11514.4 17630.2i 0.0369805 0.0566226i
\(559\) 238381.i 0.762865i
\(560\) −2941.48 2704.36i −0.00937973 0.00862358i
\(561\) −468846. −1.48972
\(562\) 48399.8 + 31610.1i 0.153240 + 0.100081i
\(563\) 240858.i 0.759878i −0.925012 0.379939i \(-0.875945\pi\)
0.925012 0.379939i \(-0.124055\pi\)
\(564\) −21643.7 49299.7i −0.0680413 0.154984i
\(565\) −125496. −0.393126
\(566\) −256289. + 392417.i −0.800014 + 1.22494i
\(567\) 1017.72i 0.00316565i
\(568\) −168764. 28078.6i −0.523099 0.0870321i
\(569\) −240114. −0.741639 −0.370820 0.928705i \(-0.620923\pi\)
−0.370820 + 0.928705i \(0.620923\pi\)
\(570\) 4994.09 + 3261.66i 0.0153712 + 0.0100390i
\(571\) 301943.i 0.926090i −0.886335 0.463045i \(-0.846757\pi\)
0.886335 0.463045i \(-0.153243\pi\)
\(572\) −382578. + 167960.i −1.16931 + 0.513350i
\(573\) 178283. 0.543000
\(574\) 1978.23 3028.96i 0.00600417 0.00919327i
\(575\) 91268.8i 0.276049i
\(576\) 104634. + 35808.9i 0.315376 + 0.107931i
\(577\) −67660.1 −0.203227 −0.101613 0.994824i \(-0.532400\pi\)
−0.101613 + 0.994824i \(0.532400\pi\)
\(578\) −726797. 474675.i −2.17549 1.42082i
\(579\) 173166.i 0.516541i
\(580\) −55651.6 126763.i −0.165433 0.376822i
\(581\) 18281.2 0.0541568
\(582\) 60360.2 92420.5i 0.178199 0.272849i
\(583\) 725357.i 2.13410i
\(584\) 27825.5 167243.i 0.0815863 0.490367i
\(585\) −47895.4 −0.139953
\(586\) 97335.7 + 63570.4i 0.283450 + 0.185123i
\(587\) 204755.i 0.594235i −0.954841 0.297117i \(-0.903975\pi\)
0.954841 0.297117i \(-0.0960253\pi\)
\(588\) −182628. + 80177.9i −0.528219 + 0.231899i
\(589\) −5004.72 −0.0144261
\(590\) −146211. + 223871.i −0.420027 + 0.643123i
\(591\) 279444.i 0.800054i
\(592\) 237923. 258785.i 0.678881 0.738408i
\(593\) 361586. 1.02826 0.514129 0.857713i \(-0.328115\pi\)
0.514129 + 0.857713i \(0.328115\pi\)
\(594\) 77332.3 + 50506.1i 0.219174 + 0.143143i
\(595\) 8556.71i 0.0241698i
\(596\) −126078. 287180.i −0.354934 0.808465i
\(597\) 41529.2 0.116521
\(598\) 253388. 387975.i 0.708573 1.08493i
\(599\) 314411.i 0.876284i −0.898906 0.438142i \(-0.855637\pi\)
0.898906 0.438142i \(-0.144363\pi\)
\(600\) 41005.5 + 6822.42i 0.113904 + 0.0189512i
\(601\) 4980.63 0.0137891 0.00689454 0.999976i \(-0.497805\pi\)
0.00689454 + 0.999976i \(0.497805\pi\)
\(602\) −7024.49 4587.73i −0.0193830 0.0126592i
\(603\) 80634.7i 0.221762i
\(604\) 136838. 60075.1i 0.375089 0.164672i
\(605\) 139175. 0.380234
\(606\) −193697. + 296578.i −0.527445 + 0.807596i
\(607\) 224016.i 0.607998i 0.952672 + 0.303999i \(0.0983219\pi\)
−0.952672 + 0.303999i \(0.901678\pi\)
\(608\) −6472.85 25475.2i −0.0175101 0.0689145i
\(609\) 5614.01 0.0151370
\(610\) −20979.0 13701.5i −0.0563799 0.0368220i
\(611\) 102752.i 0.275238i
\(612\) 95202.3 + 216851.i 0.254182 + 0.578973i
\(613\) 606099. 1.61296 0.806478 0.591264i \(-0.201371\pi\)
0.806478 + 0.591264i \(0.201371\pi\)
\(614\) 76684.4 117415.i 0.203409 0.311449i
\(615\) 37636.8i 0.0995089i
\(616\) −2413.49 + 14506.1i −0.00636040 + 0.0382286i
\(617\) 223682. 0.587571 0.293786 0.955871i \(-0.405085\pi\)
0.293786 + 0.955871i \(0.405085\pi\)
\(618\) −58458.6 38179.6i −0.153064 0.0999665i
\(619\) 218632.i 0.570602i 0.958438 + 0.285301i \(0.0920936\pi\)
−0.958438 + 0.285301i \(0.907906\pi\)
\(620\) −31935.9 + 14020.6i −0.0830799 + 0.0364739i
\(621\) −102437. −0.265628
\(622\) 114073. 174663.i 0.294851 0.451461i
\(623\) 9929.23i 0.0255823i
\(624\) 155370. + 142845.i 0.399023 + 0.366855i
\(625\) 15625.0 0.0400000
\(626\) 402175. + 262662.i 1.02628 + 0.670269i
\(627\) 21952.4i 0.0558403i
\(628\) −224555. 511490.i −0.569382 1.29693i
\(629\) 752801. 1.90274
\(630\) −921.764 + 1411.36i −0.00232241 + 0.00355595i
\(631\) 57752.6i 0.145048i 0.997367 + 0.0725242i \(0.0231054\pi\)
−0.997367 + 0.0725242i \(0.976895\pi\)
\(632\) −199421. 33179.2i −0.499271 0.0830677i
\(633\) −120015. −0.299521
\(634\) −53982.1 35255.9i −0.134298 0.0877110i
\(635\) 286302.i 0.710031i
\(636\) 335492. 147288.i 0.829408 0.364128i
\(637\) −380640. −0.938070
\(638\) −278604. + 426585.i −0.684458 + 1.04801i
\(639\) 72176.1i 0.176763i
\(640\) −112672. 144428.i −0.275079 0.352607i
\(641\) −239533. −0.582974 −0.291487 0.956575i \(-0.594150\pi\)
−0.291487 + 0.956575i \(0.594150\pi\)
\(642\) −115811. 75636.8i −0.280983 0.183511i
\(643\) 131015.i 0.316884i 0.987368 + 0.158442i \(0.0506471\pi\)
−0.987368 + 0.158442i \(0.949353\pi\)
\(644\) −6556.11 14933.5i −0.0158079 0.0360071i
\(645\) 87283.7 0.209804
\(646\) 30778.9 47127.0i 0.0737544 0.112929i
\(647\) 227917.i 0.544464i 0.962232 + 0.272232i \(0.0877618\pi\)
−0.962232 + 0.272232i \(0.912238\pi\)
\(648\) 7657.27 46023.3i 0.0182358 0.109604i
\(649\) 984066. 2.33633
\(650\) 66420.5 + 43379.5i 0.157208 + 0.102673i
\(651\) 1414.36i 0.00333732i
\(652\) −728121. + 319661.i −1.71281 + 0.751960i
\(653\) 334292. 0.783970 0.391985 0.919972i \(-0.371789\pi\)
0.391985 + 0.919972i \(0.371789\pi\)
\(654\) 118200. 180982.i 0.276352 0.423137i
\(655\) 185200.i 0.431676i
\(656\) 112249. 122092.i 0.260841 0.283712i
\(657\) −71525.4 −0.165703
\(658\) −3027.85 1977.50i −0.00699330 0.00456736i
\(659\) 820031.i 1.88825i 0.329588 + 0.944125i \(0.393090\pi\)
−0.329588 + 0.944125i \(0.606910\pi\)
\(660\) −61499.0 140082.i −0.141182 0.321584i
\(661\) −368205. −0.842727 −0.421363 0.906892i \(-0.638448\pi\)
−0.421363 + 0.906892i \(0.638448\pi\)
\(662\) −16795.8 + 25716.9i −0.0383253 + 0.0586816i
\(663\) 451967.i 1.02821i
\(664\) 826713. + 137547.i 1.87508 + 0.311971i
\(665\) 400.644 0.000905973
\(666\) −124168. 81094.9i −0.279938 0.182829i
\(667\) 565070.i 1.27014i
\(668\) 756524. 332130.i 1.69539 0.744313i
\(669\) −239331. −0.534745
\(670\) 73032.0 111823.i 0.162691 0.249104i
\(671\) 92216.7i 0.204816i
\(672\) 7199.43 1829.26i 0.0159426 0.00405077i
\(673\) −272051. −0.600649 −0.300325 0.953837i \(-0.597095\pi\)
−0.300325 + 0.953837i \(0.597095\pi\)
\(674\) −228181. 149026.i −0.502297 0.328053i
\(675\) 17537.0i 0.0384900i
\(676\) −21785.6 49623.0i −0.0476733 0.108590i
\(677\) −348582. −0.760549 −0.380275 0.924874i \(-0.624171\pi\)
−0.380275 + 0.924874i \(0.624171\pi\)
\(678\) 127572. 195332.i 0.277521 0.424926i
\(679\) 7414.30i 0.0160817i
\(680\) 64380.1 386951.i 0.139230 0.836832i
\(681\) 257919. 0.556147
\(682\) 107471. + 70190.0i 0.231059 + 0.150906i
\(683\) 146496.i 0.314040i −0.987595 0.157020i \(-0.949811\pi\)
0.987595 0.157020i \(-0.0501887\pi\)
\(684\) −10153.4 + 4457.58i −0.0217021 + 0.00952768i
\(685\) 62829.2 0.133900
\(686\) −14657.1 + 22442.1i −0.0311458 + 0.0476888i
\(687\) 46247.7i 0.0979889i
\(688\) −283143. 260318.i −0.598177 0.549955i
\(689\) 699243. 1.47296
\(690\) 142058. + 92778.9i 0.298379 + 0.194873i
\(691\) 79772.8i 0.167070i −0.996505 0.0835350i \(-0.973379\pi\)
0.996505 0.0835350i \(-0.0266211\pi\)
\(692\) 314028. + 715290.i 0.655776 + 1.49372i
\(693\) 6203.88 0.0129180
\(694\) −73327.0 + 112275.i −0.152246 + 0.233111i
\(695\) 375626.i 0.777652i
\(696\) 253876. + 42239.4i 0.524088 + 0.0871966i
\(697\) 355161. 0.731072
\(698\) −597031. 389924.i −1.22542 0.800329i
\(699\) 69409.3i 0.142057i
\(700\) 2556.57 1122.39i 0.00521750 0.00229059i
\(701\) −1418.50 −0.00288665 −0.00144332 0.999999i \(-0.500459\pi\)
−0.00144332 + 0.999999i \(0.500459\pi\)
\(702\) 48687.8 74548.3i 0.0987975 0.151274i
\(703\) 35247.8i 0.0713217i
\(704\) −218286. + 637835.i −0.440433 + 1.28695i
\(705\) 37622.9 0.0756963
\(706\) 271112. + 177064.i 0.543925 + 0.355240i
\(707\) 23792.6i 0.0475995i
\(708\) −199821. 455150.i −0.398634 0.908005i
\(709\) −794794. −1.58111 −0.790555 0.612391i \(-0.790208\pi\)
−0.790555 + 0.612391i \(0.790208\pi\)
\(710\) 65370.9 100093.i 0.129679 0.198557i
\(711\) 85287.1i 0.168711i
\(712\) −74706.9 + 449019.i −0.147367 + 0.885737i
\(713\) −142360. −0.280034
\(714\) 13318.4 + 8698.28i 0.0261249 + 0.0170623i
\(715\) 291963.i 0.571105i
\(716\) −748061. + 328415.i −1.45919 + 0.640615i
\(717\) 208895. 0.406339
\(718\) 209860. 321327.i 0.407081 0.623301i
\(719\) 713193.i 1.37959i −0.724006 0.689794i \(-0.757701\pi\)
0.724006 0.689794i \(-0.242299\pi\)
\(720\) −52303.0 + 56889.1i −0.100893 + 0.109740i
\(721\) −4689.76 −0.00902153
\(722\) −434240. 283604.i −0.833021 0.544050i
\(723\) 474329.i 0.907410i
\(724\) 107977. + 245949.i 0.205994 + 0.469212i
\(725\) 96738.6 0.184045
\(726\) −141478. + 216624.i −0.268420 + 0.410991i
\(727\) 886306.i 1.67693i 0.544955 + 0.838465i \(0.316547\pi\)
−0.544955 + 0.838465i \(0.683453\pi\)
\(728\) 13983.8 + 2326.60i 0.0263854 + 0.00438995i
\(729\) −19683.0 −0.0370370
\(730\) 99190.2 + 64781.6i 0.186133 + 0.121564i
\(731\) 823658.i 1.54139i
\(732\) 42652.1 18725.2i 0.0796010 0.0349466i
\(733\) −267035. −0.497005 −0.248502 0.968631i \(-0.579938\pi\)
−0.248502 + 0.968631i \(0.579938\pi\)
\(734\) 80297.2 122947.i 0.149042 0.228205i
\(735\) 139372.i 0.257989i
\(736\) −184122. 724648.i −0.339899 1.33774i
\(737\) −491537. −0.904943
\(738\) −58580.9 38259.5i −0.107558 0.0702468i
\(739\) 706999.i 1.29458i 0.762242 + 0.647292i \(0.224099\pi\)
−0.762242 + 0.647292i \(0.775901\pi\)
\(740\) 98745.6 + 224922.i 0.180324 + 0.410741i
\(741\) −21162.1 −0.0385410
\(742\) 13457.2 20605.0i 0.0244426 0.0374252i
\(743\) 990710.i 1.79461i 0.441416 + 0.897303i \(0.354476\pi\)
−0.441416 + 0.897303i \(0.645524\pi\)
\(744\) 10641.6 63960.2i 0.0192247 0.115548i
\(745\) 219160. 0.394865
\(746\) 785300. + 512883.i 1.41110 + 0.921596i
\(747\) 353564.i 0.633617i
\(748\) −1.32189e6 + 580339.i −2.36261 + 1.03724i
\(749\) −9290.78 −0.0165611
\(750\) −15883.5 + 24320.0i −0.0282374 + 0.0432356i
\(751\) 629696.i 1.11648i −0.829679 0.558240i \(-0.811477\pi\)
0.829679 0.558240i \(-0.188523\pi\)
\(752\) −122047. 112208.i −0.215819 0.198421i
\(753\) −443222. −0.781685
\(754\) 411227. + 268574.i 0.723334 + 0.472413i
\(755\) 104428.i 0.183199i
\(756\) −1259.74 2869.42i −0.00220413 0.00502054i
\(757\) −14822.4 −0.0258658 −0.0129329 0.999916i \(-0.504117\pi\)
−0.0129329 + 0.999916i \(0.504117\pi\)
\(758\) −56862.4 + 87064.7i −0.0989661 + 0.151532i
\(759\) 624442.i 1.08395i
\(760\) 18117.9 + 3014.42i 0.0313676 + 0.00521887i
\(761\) −458988. −0.792559 −0.396280 0.918130i \(-0.629699\pi\)
−0.396280 + 0.918130i \(0.629699\pi\)
\(762\) −445625. 291039.i −0.767466 0.501236i
\(763\) 14519.1i 0.0249396i
\(764\) 502660. 220679.i 0.861168 0.378071i
\(765\) −165489. −0.282779
\(766\) −297408. + 455376.i −0.506869 + 0.776091i
\(767\) 948638.i 1.61254i
\(768\) 339336. 28554.9i 0.575317 0.0484125i
\(769\) 179362. 0.303304 0.151652 0.988434i \(-0.451541\pi\)
0.151652 + 0.988434i \(0.451541\pi\)
\(770\) −8603.43 5618.94i −0.0145108 0.00947704i
\(771\) 121640.i 0.204629i
\(772\) 214345. + 488233.i 0.359649 + 0.819205i
\(773\) −129744. −0.217134 −0.108567 0.994089i \(-0.534626\pi\)
−0.108567 + 0.994089i \(0.534626\pi\)
\(774\) −88727.9 + 135856.i −0.148108 + 0.226775i
\(775\) 24371.8i 0.0405773i
\(776\) 55784.8 335289.i 0.0926386 0.556796i
\(777\) −9961.23 −0.0164995
\(778\) −351295. 229433.i −0.580381 0.379050i
\(779\) 16629.4i 0.0274033i
\(780\) −135039. + 59285.0i −0.221957 + 0.0974441i
\(781\) −439975. −0.721317
\(782\) 875513. 1.34054e6i 1.43169 2.19213i
\(783\) 108576.i 0.177097i
\(784\) −415668. + 452116.i −0.676262 + 0.735559i
\(785\) 390342. 0.633440
\(786\) −288260. 188264.i −0.466594 0.304735i
\(787\) 293979.i 0.474643i 0.971431 + 0.237322i \(0.0762695\pi\)
−0.971431 + 0.237322i \(0.923730\pi\)
\(788\) 345896. + 787879.i 0.557049 + 1.26884i
\(789\) 462072. 0.742259
\(790\) 77245.8 118275.i 0.123771 0.189512i
\(791\) 15670.2i 0.0250450i
\(792\) 280552. + 46677.6i 0.447262 + 0.0744146i
\(793\) 88896.9 0.141364
\(794\) −15377.3 10043.0i −0.0243915 0.0159302i
\(795\) 256030.i 0.405094i
\(796\) 117090. 51405.0i 0.184796 0.0811295i
\(797\) 281322. 0.442881 0.221441 0.975174i \(-0.428924\pi\)
0.221441 + 0.975174i \(0.428924\pi\)
\(798\) −407.273 + 623.595i −0.000639558 + 0.000979258i
\(799\) 355031.i 0.556125i
\(800\) 124058. 31521.2i 0.193841 0.0492519i
\(801\) 192034. 0.299304
\(802\) 361958. + 236396.i 0.562742 + 0.367529i
\(803\) 436008.i 0.676182i
\(804\) 99809.8 + 227346.i 0.154405 + 0.351702i
\(805\) 11396.4 0.0175864
\(806\) 67663.1 103602.i 0.104155 0.159477i
\(807\) 407296.i 0.625407i
\(808\) −179014. + 1.07595e6i −0.274198 + 1.64804i
\(809\) −1.00560e6 −1.53648 −0.768239 0.640163i \(-0.778867\pi\)
−0.768239 + 0.640163i \(0.778867\pi\)
\(810\) 27296.0 + 17827.2i 0.0416035 + 0.0271714i
\(811\) 669583.i 1.01804i −0.860756 0.509018i \(-0.830009\pi\)
0.860756 0.509018i \(-0.169991\pi\)
\(812\) 15828.4 6949.03i 0.0240064 0.0105393i
\(813\) 414764. 0.627509
\(814\) 494342. 756911.i 0.746069 1.14234i
\(815\) 555663.i 0.836559i
\(816\) 536837. + 493560.i 0.806236 + 0.741241i
\(817\) 38565.5 0.0577770
\(818\) −316432. 206663.i −0.472905 0.308856i
\(819\) 5980.53i 0.00891604i
\(820\) 46586.9 + 106115.i 0.0692844 + 0.157816i
\(821\) −706530. −1.04820 −0.524100 0.851657i \(-0.675598\pi\)
−0.524100 + 0.851657i \(0.675598\pi\)
\(822\) −63868.7 + 97792.5i −0.0945246 + 0.144731i
\(823\) 925866.i 1.36694i −0.729980 0.683468i \(-0.760471\pi\)
0.729980 0.683468i \(-0.239529\pi\)
\(824\) −212080. 35285.5i −0.312353 0.0519687i
\(825\) 106903. 0.157066
\(826\) −27954.0 18256.9i −0.0409717 0.0267588i
\(827\) 639584.i 0.935162i −0.883950 0.467581i \(-0.845126\pi\)
0.883950 0.467581i \(-0.154874\pi\)
\(828\) −288817. + 126797.i −0.421272 + 0.184947i
\(829\) −458584. −0.667283 −0.333642 0.942700i \(-0.608278\pi\)
−0.333642 + 0.942700i \(0.608278\pi\)
\(830\) −320228. + 490316.i −0.464840 + 0.711738i
\(831\) 72681.7i 0.105250i
\(832\) 614872. + 210427.i 0.888256 + 0.303987i
\(833\) −1.31519e6 −1.89540
\(834\) −584654. 381840.i −0.840557 0.548971i
\(835\) 577338.i 0.828052i
\(836\) −27172.8 61893.9i −0.0388795 0.0885595i
\(837\) −27354.1 −0.0390456
\(838\) 73473.3 112499.i 0.104626 0.160199i
\(839\) 734005.i 1.04274i 0.853331 + 0.521369i \(0.174579\pi\)
−0.853331 + 0.521369i \(0.825421\pi\)
\(840\) −851.892 + 5120.22i −0.00120733 + 0.00725655i
\(841\) −108346. −0.153186
\(842\) 629321. + 411013.i 0.887663 + 0.579737i
\(843\) 75094.5i 0.105670i
\(844\) −338376. + 148554.i −0.475023 + 0.208545i
\(845\) 37869.6 0.0530368
\(846\) −38245.4 + 58559.4i −0.0534366 + 0.0818193i
\(847\) 17378.3i 0.0242237i
\(848\) 763591. 830546.i 1.06186 1.15497i
\(849\) 608853. 0.844690
\(850\) 229497. + 149886.i 0.317643 + 0.207454i
\(851\) 1.00263e6i 1.38447i
\(852\) 89339.8 + 203497.i 0.123074 + 0.280336i
\(853\) −144945. −0.199208 −0.0996039 0.995027i \(-0.531758\pi\)
−0.0996039 + 0.995027i \(0.531758\pi\)
\(854\) 1710.85 2619.57i 0.00234583 0.00359182i
\(855\) 7748.56i 0.0105996i
\(856\) −420148. 69903.3i −0.573396 0.0954004i
\(857\) 749831. 1.02094 0.510472 0.859894i \(-0.329471\pi\)
0.510472 + 0.859894i \(0.329471\pi\)
\(858\) 454435. + 296794.i 0.617302 + 0.403163i
\(859\) 991769.i 1.34408i 0.740516 + 0.672038i \(0.234581\pi\)
−0.740516 + 0.672038i \(0.765419\pi\)
\(860\) 246093. 108040.i 0.332737 0.146079i
\(861\) −4699.57 −0.00633946
\(862\) 130047. 199121.i 0.175019 0.267980i
\(863\) 254191.i 0.341301i 0.985332 + 0.170651i \(0.0545870\pi\)
−0.985332 + 0.170651i \(0.945413\pi\)
\(864\) −35378.5 139239.i −0.0473927 0.186523i
\(865\) −545871. −0.729554
\(866\) −669604. 437322.i −0.892858 0.583130i
\(867\) 1.12766e6i 1.50017i
\(868\) −1750.70 3987.73i −0.00232366 0.00529280i
\(869\) −519898. −0.688460
\(870\) −98339.2 + 150572.i −0.129924 + 0.198932i
\(871\) 473841.i 0.624592i
\(872\) 109240. 656580.i 0.143665 0.863485i
\(873\) −143395. −0.188150
\(874\) 62767.1 + 40993.5i 0.0821692 + 0.0536651i
\(875\) 1951.04i 0.00254830i
\(876\) −201663. + 88534.3i −0.262795 + 0.115373i
\(877\) −378981. −0.492740 −0.246370 0.969176i \(-0.579238\pi\)
−0.246370 + 0.969176i \(0.579238\pi\)
\(878\) −26879.7 + 41156.8i −0.0348687 + 0.0533891i
\(879\) 151021.i 0.195461i
\(880\) −346787. 318831.i −0.447814 0.411714i
\(881\) 1.18545e6 1.52733 0.763665 0.645613i \(-0.223398\pi\)
0.763665 + 0.645613i \(0.223398\pi\)
\(882\) 216930. + 141678.i 0.278858 + 0.182124i
\(883\) 161617.i 0.207284i −0.994615 0.103642i \(-0.966950\pi\)
0.994615 0.103642i \(-0.0330496\pi\)
\(884\) 559446. + 1.27430e6i 0.715902 + 1.63068i
\(885\) 347346. 0.443482
\(886\) −644409. + 986686.i −0.820908 + 1.25693i
\(887\) 185284.i 0.235499i 0.993043 + 0.117750i \(0.0375680\pi\)
−0.993043 + 0.117750i \(0.962432\pi\)
\(888\) −450466. 74947.6i −0.571263 0.0950456i
\(889\) −35749.6 −0.0452343
\(890\) −266309. 173928.i −0.336207 0.219578i
\(891\) 119985.i 0.151137i
\(892\) −674783. + 296244.i −0.848076 + 0.372324i
\(893\) 16623.3 0.0208456
\(894\) −222786. + 341119.i −0.278749 + 0.426806i
\(895\) 570880.i 0.712687i
\(896\) 18034.2 14069.0i 0.0224637 0.0175246i
\(897\) −601962. −0.748142
\(898\) 1.00816e6 + 658431.i 1.25019 + 0.816502i
\(899\) 150892.i 0.186701i
\(900\) −21707.4 49444.8i −0.0267992 0.0610430i
\(901\) 2.41604e6 2.97615
\(902\) 233224. 357101.i 0.286656 0.438912i
\(903\) 10898.8i 0.0133661i
\(904\) 117902. 708638.i 0.144272 0.867136i
\(905\) −187695. −0.229169
\(906\) −162540. 106156.i −0.198018 0.129326i
\(907\) 81044.4i 0.0985163i −0.998786 0.0492582i \(-0.984314\pi\)
0.998786 0.0492582i \(-0.0156857\pi\)
\(908\) 727191. 319253.i 0.882017 0.387225i
\(909\) 460155. 0.556899
\(910\) −5416.65 + 8293.70i −0.00654106 + 0.0100153i
\(911\) 990859.i 1.19392i 0.802271 + 0.596960i \(0.203625\pi\)
−0.802271 + 0.596960i \(0.796375\pi\)
\(912\) −23109.6 + 25135.9i −0.0277845 + 0.0302207i
\(913\) 2.15527e6 2.58560
\(914\) 219932. + 143638.i 0.263266 + 0.171940i
\(915\) 32549.8i 0.0388782i
\(916\) −57245.5 130393.i −0.0682261 0.155405i
\(917\) −23125.2 −0.0275009
\(918\) 168227. 257581.i 0.199623 0.305652i
\(919\) 1.33459e6i 1.58021i −0.612969 0.790107i \(-0.710025\pi\)
0.612969 0.790107i \(-0.289975\pi\)
\(920\) 515368. + 85745.9i 0.608895 + 0.101307i
\(921\) −182175. −0.214768
\(922\) −1.10630e6 722532.i −1.30141 0.849954i
\(923\) 424135.i 0.497853i
\(924\) 17491.6 7679.17i 0.0204873 0.00899436i
\(925\) −171648. −0.200612
\(926\) 464477. 711183.i 0.541679 0.829391i
\(927\) 90701.3i 0.105549i
\(928\) 768077. 195157.i 0.891885 0.226614i
\(929\) −264841. −0.306870 −0.153435 0.988159i \(-0.549034\pi\)
−0.153435 + 0.988159i \(0.549034\pi\)
\(930\) 37934.2 + 24775.0i 0.0438596 + 0.0286449i
\(931\) 61580.3i 0.0710465i
\(932\) −85915.0 195696.i −0.0989093 0.225295i
\(933\) −270998. −0.311317
\(934\) 603384. 923871.i 0.691672 1.05905i
\(935\) 1.00880e6i 1.15393i
\(936\) 44997.1 270451.i 0.0513610 0.308701i
\(937\) 1.27942e6 1.45724 0.728622 0.684916i \(-0.240161\pi\)
0.728622 + 0.684916i \(0.240161\pi\)
\(938\) 13962.9 + 9119.25i 0.0158698 + 0.0103646i
\(939\) 623993.i 0.707698i
\(940\) 106076. 46569.7i 0.120050 0.0527045i
\(941\) −117710. −0.132934 −0.0664668 0.997789i \(-0.521173\pi\)
−0.0664668 + 0.997789i \(0.521173\pi\)
\(942\) −396800. + 607560.i −0.447167 + 0.684679i
\(943\) 473029.i 0.531942i
\(944\) −1.12677e6 1.03594e6i −1.26442 1.16249i
\(945\) 2189.79 0.00245210
\(946\) −828155. 540872.i −0.925400 0.604383i
\(947\) 1.42125e6i 1.58479i 0.610011 + 0.792393i \(0.291165\pi\)
−0.610011 + 0.792393i \(0.708835\pi\)
\(948\) 105569. + 240463.i 0.117468 + 0.267567i
\(949\) −420312. −0.466701
\(950\) −7017.98 + 10745.6i −0.00777616 + 0.0119065i
\(951\) 83755.7i 0.0926090i
\(952\) 48317.3 + 8038.93i 0.0533124 + 0.00887001i
\(953\) −544751. −0.599808 −0.299904 0.953969i \(-0.596955\pi\)
−0.299904 + 0.953969i \(0.596955\pi\)
\(954\) −398506. 260266.i −0.437862 0.285970i
\(955\) 383603.i 0.420606i
\(956\) 588969. 258570.i 0.644431 0.282919i
\(957\) 661866. 0.722680
\(958\) −282705. + 432863.i −0.308036 + 0.471649i
\(959\) 7845.27i 0.00853042i
\(960\) −77048.5 + 225137.i −0.0836029 + 0.244289i
\(961\) 885506. 0.958837
\(962\) −729662. 476546.i −0.788445 0.514937i
\(963\) 179686.i 0.193759i
\(964\) −587126. 1.33735e6i −0.631796 1.43910i
\(965\) −372593. −0.400111
\(966\) −11585.0 + 17738.3i −0.0124148 + 0.0190090i
\(967\) 369389.i 0.395031i 0.980300 + 0.197516i \(0.0632873\pi\)
−0.980300 + 0.197516i \(0.936713\pi\)
\(968\) −130753. + 785882.i −0.139541 + 0.838700i
\(969\) −73119.8 −0.0778731
\(970\) 198857. + 129875.i 0.211348 + 0.138032i
\(971\) 750410.i 0.795903i 0.917406 + 0.397952i \(0.130279\pi\)
−0.917406 + 0.397952i \(0.869721\pi\)
\(972\) −55495.3 + 24363.7i −0.0587386 + 0.0257875i
\(973\) −46903.1 −0.0495422
\(974\) −648611. + 993120.i −0.683702 + 1.04685i
\(975\) 103054.i 0.108407i
\(976\) 97077.6 105590.i 0.101911 0.110847i
\(977\) −1.18852e6 −1.24513 −0.622566 0.782567i \(-0.713910\pi\)
−0.622566 + 0.782567i \(0.713910\pi\)
\(978\) 864880. + 564857.i 0.904228 + 0.590556i
\(979\) 1.17061e6i 1.22137i
\(980\) −172515. 392954.i −0.179629 0.409156i
\(981\) −280802. −0.291785
\(982\) −743751. + 1.13879e6i −0.771267 + 1.18092i
\(983\) 144516.i 0.149558i −0.997200 0.0747789i \(-0.976175\pi\)
0.997200 0.0747789i \(-0.0238251\pi\)
\(984\) −212524. 35359.3i −0.219491 0.0365185i
\(985\) −601267. −0.619719
\(986\) 1.42088e6 + 927984.i 1.46152 + 0.954523i
\(987\) 4697.85i 0.00482241i
\(988\) −59665.6 + 26194.5i −0.0611238 + 0.0268347i
\(989\) 1.09700e6 1.12154
\(990\) −108672. + 166393.i −0.110878 + 0.169771i
\(991\) 382181.i 0.389154i −0.980887 0.194577i \(-0.937667\pi\)
0.980887 0.194577i \(-0.0623334\pi\)
\(992\) −49166.6 193505.i −0.0499628 0.196639i
\(993\) 39900.9 0.0404655
\(994\) 12498.2 + 8162.65i 0.0126496 + 0.00826149i
\(995\) 89356.7i 0.0902570i
\(996\) −437642. 996858.i −0.441164 1.00488i
\(997\) −1.03299e6 −1.03921 −0.519607 0.854406i \(-0.673921\pi\)
−0.519607 + 0.854406i \(0.673921\pi\)
\(998\) −321106. + 491662.i −0.322395 + 0.493634i
\(999\) 192653.i 0.193039i
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 60.5.c.a.31.5 16
3.2 odd 2 180.5.c.c.91.12 16
4.3 odd 2 inner 60.5.c.a.31.6 yes 16
5.2 odd 4 300.5.f.b.199.23 32
5.3 odd 4 300.5.f.b.199.10 32
5.4 even 2 300.5.c.d.151.12 16
8.3 odd 2 960.5.e.f.511.15 16
8.5 even 2 960.5.e.f.511.6 16
12.11 even 2 180.5.c.c.91.11 16
20.3 even 4 300.5.f.b.199.24 32
20.7 even 4 300.5.f.b.199.9 32
20.19 odd 2 300.5.c.d.151.11 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.5.c.a.31.5 16 1.1 even 1 trivial
60.5.c.a.31.6 yes 16 4.3 odd 2 inner
180.5.c.c.91.11 16 12.11 even 2
180.5.c.c.91.12 16 3.2 odd 2
300.5.c.d.151.11 16 20.19 odd 2
300.5.c.d.151.12 16 5.4 even 2
300.5.f.b.199.9 32 20.7 even 4
300.5.f.b.199.10 32 5.3 odd 4
300.5.f.b.199.23 32 5.2 odd 4
300.5.f.b.199.24 32 20.3 even 4
960.5.e.f.511.6 16 8.5 even 2
960.5.e.f.511.15 16 8.3 odd 2