Properties

Label 39.5.g.a.31.3
Level $39$
Weight $5$
Character 39.31
Analytic conductor $4.031$
Analytic rank $0$
Dimension $20$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,5,Mod(31,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.31");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 39.g (of order \(4\), 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: \(4.03142856027\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.3
Root \(4.05053 - 4.05053i\) of defining polynomial
Character \(\chi\) \(=\) 39.31
Dual form 39.5.g.a.34.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.05053 + 4.05053i) q^{2} +5.19615 q^{3} -16.8136i q^{4} +(33.5573 - 33.5573i) q^{5} +(-21.0472 + 21.0472i) q^{6} +(23.7132 + 23.7132i) q^{7} +(3.29565 + 3.29565i) q^{8} +27.0000 q^{9} +271.850i q^{10} +(32.2545 + 32.2545i) q^{11} -87.3662i q^{12} +(72.8001 + 152.516i) q^{13} -192.102 q^{14} +(174.369 - 174.369i) q^{15} +242.320 q^{16} -354.222i q^{17} +(-109.364 + 109.364i) q^{18} +(-168.478 + 168.478i) q^{19} +(-564.221 - 564.221i) q^{20} +(123.217 + 123.217i) q^{21} -261.296 q^{22} +182.161i q^{23} +(17.1247 + 17.1247i) q^{24} -1627.19i q^{25} +(-912.650 - 322.892i) q^{26} +140.296 q^{27} +(398.704 - 398.704i) q^{28} +913.769 q^{29} +1412.58i q^{30} +(-876.095 + 876.095i) q^{31} +(-1034.25 + 1034.25i) q^{32} +(167.599 + 167.599i) q^{33} +(1434.79 + 1434.79i) q^{34} +1591.50 q^{35} -453.968i q^{36} +(112.687 + 112.687i) q^{37} -1364.85i q^{38} +(378.280 + 792.497i) q^{39} +221.186 q^{40} +(-1133.48 + 1133.48i) q^{41} -998.190 q^{42} -411.247i q^{43} +(542.315 - 542.315i) q^{44} +(906.048 - 906.048i) q^{45} +(-737.848 - 737.848i) q^{46} +(-3000.97 - 3000.97i) q^{47} +1259.13 q^{48} -1276.37i q^{49} +(6590.99 + 6590.99i) q^{50} -1840.59i q^{51} +(2564.35 - 1224.03i) q^{52} -4228.78 q^{53} +(-568.274 + 568.274i) q^{54} +2164.75 q^{55} +156.301i q^{56} +(-875.438 + 875.438i) q^{57} +(-3701.25 + 3701.25i) q^{58} +(1690.19 + 1690.19i) q^{59} +(-2931.78 - 2931.78i) q^{60} -3760.65 q^{61} -7097.31i q^{62} +(640.255 + 640.255i) q^{63} -4501.45i q^{64} +(7561.01 + 2675.06i) q^{65} -1357.73 q^{66} +(-2631.54 + 2631.54i) q^{67} -5955.76 q^{68} +946.535i q^{69} +(-6446.43 + 6446.43i) q^{70} +(297.661 - 297.661i) q^{71} +(88.9825 + 88.9825i) q^{72} +(2616.29 + 2616.29i) q^{73} -912.887 q^{74} -8455.13i q^{75} +(2832.73 + 2832.73i) q^{76} +1529.71i q^{77} +(-4742.27 - 1677.80i) q^{78} +7885.52 q^{79} +(8131.61 - 8131.61i) q^{80} +729.000 q^{81} -9182.36i q^{82} +(-4078.45 + 4078.45i) q^{83} +(2071.73 - 2071.73i) q^{84} +(-11886.7 - 11886.7i) q^{85} +(1665.77 + 1665.77i) q^{86} +4748.08 q^{87} +212.599i q^{88} +(1722.86 + 1722.86i) q^{89} +7339.96i q^{90} +(-1890.32 + 5342.96i) q^{91} +3062.78 q^{92} +(-4552.33 + 4552.33i) q^{93} +24311.0 q^{94} +11307.4i q^{95} +(-5374.15 + 5374.15i) q^{96} +(1560.33 - 1560.33i) q^{97} +(5169.99 + 5169.99i) q^{98} +(870.871 + 870.871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.05053 + 4.05053i −1.01263 + 1.01263i −0.0127141 + 0.999919i \(0.504047\pi\)
−0.999919 + 0.0127141i \(0.995953\pi\)
\(3\) 5.19615 0.577350
\(4\) 16.8136i 1.05085i
\(5\) 33.5573 33.5573i 1.34229 1.34229i 0.448521 0.893772i \(-0.351951\pi\)
0.893772 0.448521i \(-0.148049\pi\)
\(6\) −21.0472 + 21.0472i −0.584644 + 0.584644i
\(7\) 23.7132 + 23.7132i 0.483942 + 0.483942i 0.906388 0.422446i \(-0.138828\pi\)
−0.422446 + 0.906388i \(0.638828\pi\)
\(8\) 3.29565 + 3.29565i 0.0514945 + 0.0514945i
\(9\) 27.0000 0.333333
\(10\) 271.850i 2.71850i
\(11\) 32.2545 + 32.2545i 0.266566 + 0.266566i 0.827715 0.561149i \(-0.189641\pi\)
−0.561149 + 0.827715i \(0.689641\pi\)
\(12\) 87.3662i 0.606710i
\(13\) 72.8001 + 152.516i 0.430770 + 0.902462i
\(14\) −192.102 −0.980111
\(15\) 174.369 174.369i 0.774974 0.774974i
\(16\) 242.320 0.946562
\(17\) 354.222i 1.22568i −0.790206 0.612841i \(-0.790027\pi\)
0.790206 0.612841i \(-0.209973\pi\)
\(18\) −109.364 + 109.364i −0.337544 + 0.337544i
\(19\) −168.478 + 168.478i −0.466699 + 0.466699i −0.900843 0.434145i \(-0.857051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(20\) −564.221 564.221i −1.41055 1.41055i
\(21\) 123.217 + 123.217i 0.279404 + 0.279404i
\(22\) −261.296 −0.539867
\(23\) 182.161i 0.344349i 0.985066 + 0.172175i \(0.0550793\pi\)
−0.985066 + 0.172175i \(0.944921\pi\)
\(24\) 17.1247 + 17.1247i 0.0297304 + 0.0297304i
\(25\) 1627.19i 2.60350i
\(26\) −912.650 322.892i −1.35007 0.477651i
\(27\) 140.296 0.192450
\(28\) 398.704 398.704i 0.508551 0.508551i
\(29\) 913.769 1.08653 0.543264 0.839562i \(-0.317188\pi\)
0.543264 + 0.839562i \(0.317188\pi\)
\(30\) 1412.58i 1.56953i
\(31\) −876.095 + 876.095i −0.911650 + 0.911650i −0.996402 0.0847522i \(-0.972990\pi\)
0.0847522 + 0.996402i \(0.472990\pi\)
\(32\) −1034.25 + 1034.25i −1.01001 + 1.01001i
\(33\) 167.599 + 167.599i 0.153902 + 0.153902i
\(34\) 1434.79 + 1434.79i 1.24117 + 1.24117i
\(35\) 1591.50 1.29918
\(36\) 453.968i 0.350284i
\(37\) 112.687 + 112.687i 0.0823135 + 0.0823135i 0.747065 0.664751i \(-0.231462\pi\)
−0.664751 + 0.747065i \(0.731462\pi\)
\(38\) 1364.85i 0.945189i
\(39\) 378.280 + 792.497i 0.248705 + 0.521037i
\(40\) 221.186 0.138242
\(41\) −1133.48 + 1133.48i −0.674287 + 0.674287i −0.958701 0.284415i \(-0.908201\pi\)
0.284415 + 0.958701i \(0.408201\pi\)
\(42\) −998.190 −0.565868
\(43\) 411.247i 0.222416i −0.993797 0.111208i \(-0.964528\pi\)
0.993797 0.111208i \(-0.0354720\pi\)
\(44\) 542.315 542.315i 0.280121 0.280121i
\(45\) 906.048 906.048i 0.447431 0.447431i
\(46\) −737.848 737.848i −0.348700 0.348700i
\(47\) −3000.97 3000.97i −1.35852 1.35852i −0.875746 0.482772i \(-0.839630\pi\)
−0.482772 0.875746i \(-0.660370\pi\)
\(48\) 1259.13 0.546498
\(49\) 1276.37i 0.531600i
\(50\) 6590.99 + 6590.99i 2.63639 + 2.63639i
\(51\) 1840.59i 0.707648i
\(52\) 2564.35 1224.03i 0.948354 0.452675i
\(53\) −4228.78 −1.50544 −0.752720 0.658341i \(-0.771259\pi\)
−0.752720 + 0.658341i \(0.771259\pi\)
\(54\) −568.274 + 568.274i −0.194881 + 0.194881i
\(55\) 2164.75 0.715619
\(56\) 156.301i 0.0498407i
\(57\) −875.438 + 875.438i −0.269449 + 0.269449i
\(58\) −3701.25 + 3701.25i −1.10025 + 1.10025i
\(59\) 1690.19 + 1690.19i 0.485547 + 0.485547i 0.906898 0.421350i \(-0.138444\pi\)
−0.421350 + 0.906898i \(0.638444\pi\)
\(60\) −2931.78 2931.78i −0.814383 0.814383i
\(61\) −3760.65 −1.01066 −0.505328 0.862928i \(-0.668628\pi\)
−0.505328 + 0.862928i \(0.668628\pi\)
\(62\) 7097.31i 1.84633i
\(63\) 640.255 + 640.255i 0.161314 + 0.161314i
\(64\) 4501.45i 1.09899i
\(65\) 7561.01 + 2675.06i 1.78959 + 0.633149i
\(66\) −1357.73 −0.311692
\(67\) −2631.54 + 2631.54i −0.586219 + 0.586219i −0.936605 0.350386i \(-0.886050\pi\)
0.350386 + 0.936605i \(0.386050\pi\)
\(68\) −5955.76 −1.28801
\(69\) 946.535i 0.198810i
\(70\) −6446.43 + 6446.43i −1.31560 + 1.31560i
\(71\) 297.661 297.661i 0.0590479 0.0590479i −0.676966 0.736014i \(-0.736706\pi\)
0.736014 + 0.676966i \(0.236706\pi\)
\(72\) 88.9825 + 88.9825i 0.0171648 + 0.0171648i
\(73\) 2616.29 + 2616.29i 0.490953 + 0.490953i 0.908606 0.417653i \(-0.137147\pi\)
−0.417653 + 0.908606i \(0.637147\pi\)
\(74\) −912.887 −0.166707
\(75\) 8455.13i 1.50313i
\(76\) 2832.73 + 2832.73i 0.490431 + 0.490431i
\(77\) 1529.71i 0.258005i
\(78\) −4742.27 1677.80i −0.779466 0.275772i
\(79\) 7885.52 1.26350 0.631752 0.775171i \(-0.282336\pi\)
0.631752 + 0.775171i \(0.282336\pi\)
\(80\) 8131.61 8131.61i 1.27056 1.27056i
\(81\) 729.000 0.111111
\(82\) 9182.36i 1.36561i
\(83\) −4078.45 + 4078.45i −0.592024 + 0.592024i −0.938178 0.346154i \(-0.887488\pi\)
0.346154 + 0.938178i \(0.387488\pi\)
\(84\) 2071.73 2071.73i 0.293612 0.293612i
\(85\) −11886.7 11886.7i −1.64522 1.64522i
\(86\) 1665.77 + 1665.77i 0.225226 + 0.225226i
\(87\) 4748.08 0.627307
\(88\) 212.599i 0.0274534i
\(89\) 1722.86 + 1722.86i 0.217505 + 0.217505i 0.807446 0.589941i \(-0.200849\pi\)
−0.589941 + 0.807446i \(0.700849\pi\)
\(90\) 7339.96i 0.906167i
\(91\) −1890.32 + 5342.96i −0.228272 + 0.645207i
\(92\) 3062.78 0.361860
\(93\) −4552.33 + 4552.33i −0.526341 + 0.526341i
\(94\) 24311.0 2.75136
\(95\) 11307.4i 1.25289i
\(96\) −5374.15 + 5374.15i −0.583132 + 0.583132i
\(97\) 1560.33 1560.33i 0.165834 0.165834i −0.619311 0.785146i \(-0.712588\pi\)
0.785146 + 0.619311i \(0.212588\pi\)
\(98\) 5169.99 + 5169.99i 0.538316 + 0.538316i
\(99\) 870.871 + 870.871i 0.0888553 + 0.0888553i
\(100\) −27359.0 −2.73590
\(101\) 9982.36i 0.978567i 0.872125 + 0.489283i \(0.162742\pi\)
−0.872125 + 0.489283i \(0.837258\pi\)
\(102\) 7455.38 + 7455.38i 0.716587 + 0.716587i
\(103\) 6.56148i 0.000618483i −1.00000 0.000309241i \(-0.999902\pi\)
1.00000 0.000309241i \(-9.84346e-5\pi\)
\(104\) −262.716 + 742.563i −0.0242896 + 0.0686541i
\(105\) 8269.68 0.750084
\(106\) 17128.8 17128.8i 1.52446 1.52446i
\(107\) −6183.10 −0.540056 −0.270028 0.962853i \(-0.587033\pi\)
−0.270028 + 0.962853i \(0.587033\pi\)
\(108\) 2358.89i 0.202237i
\(109\) 3694.46 3694.46i 0.310956 0.310956i −0.534324 0.845280i \(-0.679434\pi\)
0.845280 + 0.534324i \(0.179434\pi\)
\(110\) −8768.39 + 8768.39i −0.724660 + 0.724660i
\(111\) 585.540 + 585.540i 0.0475238 + 0.0475238i
\(112\) 5746.17 + 5746.17i 0.458081 + 0.458081i
\(113\) −21267.9 −1.66559 −0.832794 0.553583i \(-0.813260\pi\)
−0.832794 + 0.553583i \(0.813260\pi\)
\(114\) 7091.98i 0.545705i
\(115\) 6112.83 + 6112.83i 0.462218 + 0.462218i
\(116\) 15363.8i 1.14178i
\(117\) 1965.60 + 4117.93i 0.143590 + 0.300821i
\(118\) −13692.3 −0.983363
\(119\) 8399.72 8399.72i 0.593159 0.593159i
\(120\) 1149.32 0.0798138
\(121\) 12560.3i 0.857885i
\(122\) 15232.6 15232.6i 1.02342 1.02342i
\(123\) −5889.71 + 5889.71i −0.389300 + 0.389300i
\(124\) 14730.3 + 14730.3i 0.958009 + 0.958009i
\(125\) −33630.8 33630.8i −2.15237 2.15237i
\(126\) −5186.75 −0.326704
\(127\) 26466.7i 1.64094i 0.571693 + 0.820468i \(0.306287\pi\)
−0.571693 + 0.820468i \(0.693713\pi\)
\(128\) 1685.19 + 1685.19i 0.102856 + 0.102856i
\(129\) 2136.90i 0.128412i
\(130\) −41461.5 + 19790.7i −2.45334 + 1.17105i
\(131\) 21491.7 1.25236 0.626178 0.779680i \(-0.284618\pi\)
0.626178 + 0.779680i \(0.284618\pi\)
\(132\) 2817.95 2817.95i 0.161728 0.161728i
\(133\) −7990.30 −0.451710
\(134\) 21318.3i 1.18725i
\(135\) 4707.96 4707.96i 0.258325 0.258325i
\(136\) 1167.39 1167.39i 0.0631159 0.0631159i
\(137\) −5030.14 5030.14i −0.268002 0.268002i 0.560292 0.828295i \(-0.310689\pi\)
−0.828295 + 0.560292i \(0.810689\pi\)
\(138\) −3833.97 3833.97i −0.201322 0.201322i
\(139\) 12182.9 0.630554 0.315277 0.949000i \(-0.397903\pi\)
0.315277 + 0.949000i \(0.397903\pi\)
\(140\) 26758.9i 1.36525i
\(141\) −15593.5 15593.5i −0.784341 0.784341i
\(142\) 2411.37i 0.119588i
\(143\) −2571.20 + 7267.45i −0.125737 + 0.355394i
\(144\) 6542.64 0.315521
\(145\) 30663.7 30663.7i 1.45844 1.45844i
\(146\) −21194.7 −0.994311
\(147\) 6632.23i 0.306920i
\(148\) 1894.68 1894.68i 0.0864994 0.0864994i
\(149\) −10032.3 + 10032.3i −0.451887 + 0.451887i −0.895980 0.444094i \(-0.853526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(150\) 34247.8 + 34247.8i 1.52212 + 1.52212i
\(151\) 10057.5 + 10057.5i 0.441098 + 0.441098i 0.892381 0.451283i \(-0.149033\pi\)
−0.451283 + 0.892381i \(0.649033\pi\)
\(152\) −1110.49 −0.0480649
\(153\) 9563.99i 0.408561i
\(154\) −6196.14 6196.14i −0.261264 0.261264i
\(155\) 58798.9i 2.44740i
\(156\) 13324.7 6360.27i 0.547532 0.261352i
\(157\) 8554.44 0.347050 0.173525 0.984829i \(-0.444484\pi\)
0.173525 + 0.984829i \(0.444484\pi\)
\(158\) −31940.6 + 31940.6i −1.27947 + 1.27947i
\(159\) −21973.4 −0.869166
\(160\) 69413.7i 2.71147i
\(161\) −4319.61 + 4319.61i −0.166645 + 0.166645i
\(162\) −2952.84 + 2952.84i −0.112515 + 0.112515i
\(163\) −1164.17 1164.17i −0.0438170 0.0438170i 0.684859 0.728676i \(-0.259864\pi\)
−0.728676 + 0.684859i \(0.759864\pi\)
\(164\) 19057.8 + 19057.8i 0.708576 + 0.708576i
\(165\) 11248.4 0.413163
\(166\) 33039.8i 1.19901i
\(167\) 7534.77 + 7534.77i 0.270170 + 0.270170i 0.829169 0.558999i \(-0.188814\pi\)
−0.558999 + 0.829169i \(0.688814\pi\)
\(168\) 812.161i 0.0287756i
\(169\) −17961.3 + 22206.4i −0.628875 + 0.777506i
\(170\) 96295.3 3.33202
\(171\) −4548.91 + 4548.91i −0.155566 + 0.155566i
\(172\) −6914.56 −0.233726
\(173\) 39158.0i 1.30836i −0.756337 0.654182i \(-0.773013\pi\)
0.756337 0.654182i \(-0.226987\pi\)
\(174\) −19232.3 + 19232.3i −0.635232 + 0.635232i
\(175\) 38585.8 38585.8i 1.25994 1.25994i
\(176\) 7815.90 + 7815.90i 0.252321 + 0.252321i
\(177\) 8782.49 + 8782.49i 0.280331 + 0.280331i
\(178\) −13957.0 −0.440505
\(179\) 37765.1i 1.17865i −0.807897 0.589324i \(-0.799394\pi\)
0.807897 0.589324i \(-0.200606\pi\)
\(180\) −15234.0 15234.0i −0.470184 0.470184i
\(181\) 9590.57i 0.292744i −0.989230 0.146372i \(-0.953240\pi\)
0.989230 0.146372i \(-0.0467596\pi\)
\(182\) −13985.0 29298.6i −0.422202 0.884513i
\(183\) −19540.9 −0.583502
\(184\) −600.338 + 600.338i −0.0177321 + 0.0177321i
\(185\) 7562.97 0.220978
\(186\) 36878.7i 1.06598i
\(187\) 11425.2 11425.2i 0.326725 0.326725i
\(188\) −50457.2 + 50457.2i −1.42760 + 1.42760i
\(189\) 3326.86 + 3326.86i 0.0931347 + 0.0931347i
\(190\) −45800.8 45800.8i −1.26872 1.26872i
\(191\) 46392.7 1.27170 0.635848 0.771814i \(-0.280651\pi\)
0.635848 + 0.771814i \(0.280651\pi\)
\(192\) 23390.2i 0.634500i
\(193\) 9357.45 + 9357.45i 0.251213 + 0.251213i 0.821468 0.570255i \(-0.193155\pi\)
−0.570255 + 0.821468i \(0.693155\pi\)
\(194\) 12640.4i 0.335858i
\(195\) 39288.2 + 13900.0i 1.03322 + 0.365549i
\(196\) −21460.5 −0.558633
\(197\) −4463.00 + 4463.00i −0.114999 + 0.114999i −0.762265 0.647266i \(-0.775912\pi\)
0.647266 + 0.762265i \(0.275912\pi\)
\(198\) −7054.98 −0.179956
\(199\) 71326.4i 1.80113i −0.434726 0.900563i \(-0.643155\pi\)
0.434726 0.900563i \(-0.356845\pi\)
\(200\) 5362.65 5362.65i 0.134066 0.134066i
\(201\) −13673.9 + 13673.9i −0.338454 + 0.338454i
\(202\) −40433.9 40433.9i −0.990929 0.990929i
\(203\) 21668.4 + 21668.4i 0.525816 + 0.525816i
\(204\) −30947.0 −0.743633
\(205\) 76072.9i 1.81018i
\(206\) 26.5775 + 26.5775i 0.000626296 + 0.000626296i
\(207\) 4918.34i 0.114783i
\(208\) 17640.9 + 36957.7i 0.407750 + 0.854236i
\(209\) −10868.4 −0.248812
\(210\) −33496.6 + 33496.6i −0.759560 + 0.759560i
\(211\) −45146.1 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(212\) 71101.2i 1.58199i
\(213\) 1546.69 1546.69i 0.0340913 0.0340913i
\(214\) 25044.8 25044.8i 0.546878 0.546878i
\(215\) −13800.4 13800.4i −0.298548 0.298548i
\(216\) 462.367 + 462.367i 0.00991013 + 0.00991013i
\(217\) −41550.0 −0.882371
\(218\) 29929.1i 0.629768i
\(219\) 13594.6 + 13594.6i 0.283452 + 0.283452i
\(220\) 36397.3i 0.752010i
\(221\) 54024.5 25787.4i 1.10613 0.527986i
\(222\) −4743.50 −0.0962483
\(223\) 22521.9 22521.9i 0.452892 0.452892i −0.443421 0.896313i \(-0.646235\pi\)
0.896313 + 0.443421i \(0.146235\pi\)
\(224\) −49050.9 −0.977577
\(225\) 43934.1i 0.867835i
\(226\) 86146.3 86146.3i 1.68663 1.68663i
\(227\) 33678.9 33678.9i 0.653592 0.653592i −0.300264 0.953856i \(-0.597075\pi\)
0.953856 + 0.300264i \(0.0970749\pi\)
\(228\) 14719.3 + 14719.3i 0.283151 + 0.283151i
\(229\) 55067.0 + 55067.0i 1.05008 + 1.05008i 0.998678 + 0.0513970i \(0.0163674\pi\)
0.0513970 + 0.998678i \(0.483633\pi\)
\(230\) −49520.4 −0.936114
\(231\) 7948.61i 0.148959i
\(232\) 3011.46 + 3011.46i 0.0559502 + 0.0559502i
\(233\) 6668.81i 0.122839i 0.998112 + 0.0614195i \(0.0195627\pi\)
−0.998112 + 0.0614195i \(0.980437\pi\)
\(234\) −24641.6 8718.09i −0.450025 0.159217i
\(235\) −201409. −3.64706
\(236\) 28418.2 28418.2i 0.510239 0.510239i
\(237\) 40974.4 0.729484
\(238\) 68046.7i 1.20130i
\(239\) −24924.8 + 24924.8i −0.436350 + 0.436350i −0.890782 0.454431i \(-0.849842\pi\)
0.454431 + 0.890782i \(0.349842\pi\)
\(240\) 42253.1 42253.1i 0.733560 0.733560i
\(241\) 4314.21 + 4314.21i 0.0742792 + 0.0742792i 0.743270 0.668991i \(-0.233274\pi\)
−0.668991 + 0.743270i \(0.733274\pi\)
\(242\) 50875.9 + 50875.9i 0.868723 + 0.868723i
\(243\) 3788.00 0.0641500
\(244\) 63230.2i 1.06205i
\(245\) −42831.7 42831.7i −0.713564 0.713564i
\(246\) 47713.0i 0.788435i
\(247\) −37960.9 13430.4i −0.622217 0.220138i
\(248\) −5774.61 −0.0938900
\(249\) −21192.3 + 21192.3i −0.341805 + 0.341805i
\(250\) 272445. 4.35913
\(251\) 100235.i 1.59100i 0.605954 + 0.795500i \(0.292791\pi\)
−0.605954 + 0.795500i \(0.707209\pi\)
\(252\) 10765.0 10765.0i 0.169517 0.169517i
\(253\) −5875.50 + 5875.50i −0.0917918 + 0.0917918i
\(254\) −107204. 107204.i −1.66167 1.66167i
\(255\) −61765.3 61765.3i −0.949871 0.949871i
\(256\) 58371.4 0.890676
\(257\) 14954.5i 0.226415i −0.993571 0.113208i \(-0.963887\pi\)
0.993571 0.113208i \(-0.0361125\pi\)
\(258\) 8655.60 + 8655.60i 0.130034 + 0.130034i
\(259\) 5344.34i 0.0796700i
\(260\) 44977.4 127128.i 0.665346 1.88059i
\(261\) 24671.8 0.362176
\(262\) −87052.7 + 87052.7i −1.26818 + 1.26818i
\(263\) −7574.07 −0.109501 −0.0547505 0.998500i \(-0.517436\pi\)
−0.0547505 + 0.998500i \(0.517436\pi\)
\(264\) 1104.70i 0.0158502i
\(265\) −141907. + 141907.i −2.02074 + 2.02074i
\(266\) 32365.0 32365.0i 0.457417 0.457417i
\(267\) 8952.22 + 8952.22i 0.125576 + 0.125576i
\(268\) 44245.7 + 44245.7i 0.616030 + 0.616030i
\(269\) 100457. 1.38827 0.694136 0.719844i \(-0.255787\pi\)
0.694136 + 0.719844i \(0.255787\pi\)
\(270\) 38139.5i 0.523176i
\(271\) 66620.4 + 66620.4i 0.907128 + 0.907128i 0.996040 0.0889115i \(-0.0283388\pi\)
−0.0889115 + 0.996040i \(0.528339\pi\)
\(272\) 85835.0i 1.16018i
\(273\) −9822.38 + 27762.8i −0.131793 + 0.372510i
\(274\) 40749.5 0.542776
\(275\) 52484.2 52484.2i 0.694005 0.694005i
\(276\) 15914.7 0.208920
\(277\) 70180.3i 0.914652i −0.889299 0.457326i \(-0.848807\pi\)
0.889299 0.457326i \(-0.151193\pi\)
\(278\) −49347.3 + 49347.3i −0.638519 + 0.638519i
\(279\) −23654.6 + 23654.6i −0.303883 + 0.303883i
\(280\) 5245.03 + 5245.03i 0.0669009 + 0.0669009i
\(281\) −20515.7 20515.7i −0.259820 0.259820i 0.565161 0.824981i \(-0.308814\pi\)
−0.824981 + 0.565161i \(0.808814\pi\)
\(282\) 126324. 1.58850
\(283\) 30170.2i 0.376708i 0.982101 + 0.188354i \(0.0603153\pi\)
−0.982101 + 0.188354i \(0.939685\pi\)
\(284\) −5004.76 5004.76i −0.0620507 0.0620507i
\(285\) 58754.8i 0.723358i
\(286\) −19022.3 39851.8i −0.232558 0.487209i
\(287\) −53756.6 −0.652631
\(288\) −27924.9 + 27924.9i −0.336672 + 0.336672i
\(289\) −41952.2 −0.502295
\(290\) 248408.i 2.95373i
\(291\) 8107.73 8107.73i 0.0957444 0.0957444i
\(292\) 43989.3 43989.3i 0.515919 0.515919i
\(293\) −67660.9 67660.9i −0.788139 0.788139i 0.193050 0.981189i \(-0.438162\pi\)
−0.981189 + 0.193050i \(0.938162\pi\)
\(294\) 26864.0 + 26864.0i 0.310797 + 0.310797i
\(295\) 113437. 1.30349
\(296\) 742.755i 0.00847739i
\(297\) 4525.18 + 4525.18i 0.0513006 + 0.0513006i
\(298\) 81272.6i 0.915191i
\(299\) −27782.4 + 13261.3i −0.310762 + 0.148335i
\(300\) −142161. −1.57957
\(301\) 9751.97 9751.97i 0.107636 0.107636i
\(302\) −81476.3 −0.893341
\(303\) 51869.9i 0.564976i
\(304\) −40825.6 + 40825.6i −0.441759 + 0.441759i
\(305\) −126197. + 126197.i −1.35660 + 1.35660i
\(306\) 38739.3 + 38739.3i 0.413722 + 0.413722i
\(307\) −96671.1 96671.1i −1.02570 1.02570i −0.999661 0.0260377i \(-0.991711\pi\)
−0.0260377 0.999661i \(-0.508289\pi\)
\(308\) 25720.0 0.271125
\(309\) 34.0945i 0.000357081i
\(310\) −238167. 238167.i −2.47832 2.47832i
\(311\) 70642.4i 0.730373i −0.930934 0.365186i \(-0.881005\pi\)
0.930934 0.365186i \(-0.118995\pi\)
\(312\) −1365.11 + 3858.47i −0.0140236 + 0.0396375i
\(313\) 68524.0 0.699446 0.349723 0.936853i \(-0.386276\pi\)
0.349723 + 0.936853i \(0.386276\pi\)
\(314\) −34650.0 + 34650.0i −0.351435 + 0.351435i
\(315\) 42970.5 0.433061
\(316\) 132584.i 1.32775i
\(317\) 140417. 140417.i 1.39734 1.39734i 0.589760 0.807578i \(-0.299222\pi\)
0.807578 0.589760i \(-0.200778\pi\)
\(318\) 89003.9 89003.9i 0.880147 0.880147i
\(319\) 29473.2 + 29473.2i 0.289631 + 0.289631i
\(320\) −151057. 151057.i −1.47516 1.47516i
\(321\) −32128.3 −0.311801
\(322\) 34993.4i 0.337501i
\(323\) 59678.7 + 59678.7i 0.572024 + 0.572024i
\(324\) 12257.1i 0.116761i
\(325\) 248173. 118460.i 2.34956 1.12151i
\(326\) 9431.05 0.0887411
\(327\) 19197.0 19197.0i 0.179530 0.179530i
\(328\) −7471.08 −0.0694441
\(329\) 142325.i 1.31489i
\(330\) −45561.9 + 45561.9i −0.418383 + 0.418383i
\(331\) −73424.6 + 73424.6i −0.670171 + 0.670171i −0.957755 0.287585i \(-0.907148\pi\)
0.287585 + 0.957755i \(0.407148\pi\)
\(332\) 68573.6 + 68573.6i 0.622130 + 0.622130i
\(333\) 3042.56 + 3042.56i 0.0274378 + 0.0274378i
\(334\) −61039.7 −0.547166
\(335\) 176615.i 1.57376i
\(336\) 29858.0 + 29858.0i 0.264473 + 0.264473i
\(337\) 14312.2i 0.126022i 0.998013 + 0.0630111i \(0.0200703\pi\)
−0.998013 + 0.0630111i \(0.979930\pi\)
\(338\) −17194.8 162700.i −0.150509 1.42415i
\(339\) −110511. −0.961628
\(340\) −199859. + 199859.i −1.72889 + 1.72889i
\(341\) −56516.0 −0.486030
\(342\) 36851.0i 0.315063i
\(343\) 87202.1 87202.1i 0.741206 0.741206i
\(344\) 1355.33 1355.33i 0.0114532 0.0114532i
\(345\) 31763.2 + 31763.2i 0.266862 + 0.266862i
\(346\) 158611. + 158611.i 1.32489 + 1.32489i
\(347\) 216160. 1.79521 0.897607 0.440797i \(-0.145304\pi\)
0.897607 + 0.440797i \(0.145304\pi\)
\(348\) 79832.6i 0.659207i
\(349\) −20673.5 20673.5i −0.169732 0.169732i 0.617130 0.786862i \(-0.288295\pi\)
−0.786862 + 0.617130i \(0.788295\pi\)
\(350\) 312586.i 2.55172i
\(351\) 10213.6 + 21397.4i 0.0829017 + 0.173679i
\(352\) −66718.7 −0.538471
\(353\) −70477.9 + 70477.9i −0.565592 + 0.565592i −0.930890 0.365298i \(-0.880967\pi\)
0.365298 + 0.930890i \(0.380967\pi\)
\(354\) −71147.5 −0.567745
\(355\) 19977.4i 0.158519i
\(356\) 28967.5 28967.5i 0.228565 0.228565i
\(357\) 43646.2 43646.2i 0.342460 0.342460i
\(358\) 152969. + 152969.i 1.19354 + 1.19354i
\(359\) −90432.4 90432.4i −0.701674 0.701674i 0.263096 0.964770i \(-0.415256\pi\)
−0.964770 + 0.263096i \(0.915256\pi\)
\(360\) 5972.03 0.0460805
\(361\) 73551.2i 0.564385i
\(362\) 38846.9 + 38846.9i 0.296442 + 0.296442i
\(363\) 65265.2i 0.495300i
\(364\) 89834.5 + 31783.1i 0.678017 + 0.239880i
\(365\) 175591. 1.31801
\(366\) 79151.1 79151.1i 0.590874 0.590874i
\(367\) −156339. −1.16074 −0.580369 0.814354i \(-0.697091\pi\)
−0.580369 + 0.814354i \(0.697091\pi\)
\(368\) 44141.2i 0.325948i
\(369\) −30603.8 + 30603.8i −0.224762 + 0.224762i
\(370\) −30634.1 + 30634.1i −0.223770 + 0.223770i
\(371\) −100278. 100278.i −0.728546 0.728546i
\(372\) 76541.1 + 76541.1i 0.553107 + 0.553107i
\(373\) 12154.0 0.0873580 0.0436790 0.999046i \(-0.486092\pi\)
0.0436790 + 0.999046i \(0.486092\pi\)
\(374\) 92556.7i 0.661705i
\(375\) −174751. 174751.i −1.24267 1.24267i
\(376\) 19780.3i 0.139913i
\(377\) 66522.5 + 139364.i 0.468043 + 0.980549i
\(378\) −26951.1 −0.188623
\(379\) 56764.9 56764.9i 0.395186 0.395186i −0.481345 0.876531i \(-0.659852\pi\)
0.876531 + 0.481345i \(0.159852\pi\)
\(380\) 190118. 1.31661
\(381\) 137525.i 0.947395i
\(382\) −187915. + 187915.i −1.28776 + 1.28776i
\(383\) 14158.7 14158.7i 0.0965218 0.0965218i −0.657197 0.753719i \(-0.728258\pi\)
0.753719 + 0.657197i \(0.228258\pi\)
\(384\) 8756.51 + 8756.51i 0.0593839 + 0.0593839i
\(385\) 51333.0 + 51333.0i 0.346318 + 0.346318i
\(386\) −75805.3 −0.508774
\(387\) 11103.7i 0.0741387i
\(388\) −26234.9 26234.9i −0.174267 0.174267i
\(389\) 14487.6i 0.0957405i 0.998854 + 0.0478703i \(0.0152434\pi\)
−0.998854 + 0.0478703i \(0.984757\pi\)
\(390\) −215440. + 102836.i −1.41644 + 0.676105i
\(391\) 64525.4 0.422063
\(392\) 4206.48 4206.48i 0.0273745 0.0273745i
\(393\) 111674. 0.723048
\(394\) 36155.0i 0.232904i
\(395\) 264617. 264617.i 1.69599 1.69599i
\(396\) 14642.5 14642.5i 0.0933738 0.0933738i
\(397\) 120415. + 120415.i 0.764013 + 0.764013i 0.977045 0.213032i \(-0.0683339\pi\)
−0.213032 + 0.977045i \(0.568334\pi\)
\(398\) 288910. + 288910.i 1.82388 + 1.82388i
\(399\) −41518.8 −0.260795
\(400\) 394300.i 2.46438i
\(401\) 31598.4 + 31598.4i 0.196506 + 0.196506i 0.798500 0.601994i \(-0.205627\pi\)
−0.601994 + 0.798500i \(0.705627\pi\)
\(402\) 110773.i 0.685459i
\(403\) −197398. 69838.8i −1.21544 0.430018i
\(404\) 167840. 1.02833
\(405\) 24463.3 24463.3i 0.149144 0.149144i
\(406\) −175537. −1.06492
\(407\) 7269.34i 0.0438840i
\(408\) 6065.94 6065.94i 0.0364400 0.0364400i
\(409\) 16690.9 16690.9i 0.0997776 0.0997776i −0.655456 0.755233i \(-0.727523\pi\)
0.755233 + 0.655456i \(0.227523\pi\)
\(410\) −308136. 308136.i −1.83305 1.83305i
\(411\) −26137.4 26137.4i −0.154731 0.154731i
\(412\) −110.322 −0.000649934
\(413\) 80159.5i 0.469954i
\(414\) −19921.9 19921.9i −0.116233 0.116233i
\(415\) 273724.i 1.58934i
\(416\) −233034. 82446.6i −1.34658 0.476416i
\(417\) 63304.3 0.364050
\(418\) 44022.6 44022.6i 0.251955 0.251955i
\(419\) −45247.7 −0.257732 −0.128866 0.991662i \(-0.541134\pi\)
−0.128866 + 0.991662i \(0.541134\pi\)
\(420\) 139043.i 0.788228i
\(421\) 95387.7 95387.7i 0.538181 0.538181i −0.384814 0.922994i \(-0.625734\pi\)
0.922994 + 0.384814i \(0.125734\pi\)
\(422\) 182866. 182866.i 1.02685 1.02685i
\(423\) −81026.1 81026.1i −0.452839 0.452839i
\(424\) −13936.6 13936.6i −0.0775219 0.0775219i
\(425\) −576386. −3.19107
\(426\) 12529.8i 0.0690441i
\(427\) −89176.8 89176.8i −0.489098 0.489098i
\(428\) 103960.i 0.567519i
\(429\) −13360.3 + 37762.8i −0.0725943 + 0.205187i
\(430\) 111798. 0.604639
\(431\) −120110. + 120110.i −0.646582 + 0.646582i −0.952165 0.305583i \(-0.901149\pi\)
0.305583 + 0.952165i \(0.401149\pi\)
\(432\) 33996.5 0.182166
\(433\) 104909.i 0.559549i −0.960066 0.279774i \(-0.909740\pi\)
0.960066 0.279774i \(-0.0902596\pi\)
\(434\) 168300. 168300.i 0.893518 0.893518i
\(435\) 159333. 159333.i 0.842030 0.842030i
\(436\) −62117.4 62117.4i −0.326768 0.326768i
\(437\) −30690.1 30690.1i −0.160707 0.160707i
\(438\) −110131. −0.574066
\(439\) 189251.i 0.981997i −0.871160 0.490998i \(-0.836632\pi\)
0.871160 0.490998i \(-0.163368\pi\)
\(440\) 7134.25 + 7134.25i 0.0368505 + 0.0368505i
\(441\) 34462.1i 0.177200i
\(442\) −114376. + 323281.i −0.585448 + 1.65476i
\(443\) −154643. −0.787995 −0.393998 0.919111i \(-0.628908\pi\)
−0.393998 + 0.919111i \(0.628908\pi\)
\(444\) 9845.06 9845.06i 0.0499404 0.0499404i
\(445\) 115629. 0.583910
\(446\) 182451.i 0.917227i
\(447\) −52129.6 + 52129.6i −0.260897 + 0.260897i
\(448\) 106744. 106744.i 0.531846 0.531846i
\(449\) 54131.2 + 54131.2i 0.268507 + 0.268507i 0.828498 0.559992i \(-0.189196\pi\)
−0.559992 + 0.828498i \(0.689196\pi\)
\(450\) 177957. + 177957.i 0.878798 + 0.878798i
\(451\) −73119.3 −0.359484
\(452\) 357591.i 1.75029i
\(453\) 52260.2 + 52260.2i 0.254668 + 0.254668i
\(454\) 272835.i 1.32370i
\(455\) 115861. + 242729.i 0.559649 + 1.17246i
\(456\) −5770.28 −0.0277503
\(457\) −44160.2 + 44160.2i −0.211446 + 0.211446i −0.804881 0.593436i \(-0.797771\pi\)
0.593436 + 0.804881i \(0.297771\pi\)
\(458\) −446101. −2.12668
\(459\) 49696.0i 0.235883i
\(460\) 102779. 102779.i 0.485723 0.485723i
\(461\) −145494. + 145494.i −0.684610 + 0.684610i −0.961035 0.276425i \(-0.910850\pi\)
0.276425 + 0.961035i \(0.410850\pi\)
\(462\) −32196.1 32196.1i −0.150841 0.150841i
\(463\) −168589. 168589.i −0.786443 0.786443i 0.194467 0.980909i \(-0.437702\pi\)
−0.980909 + 0.194467i \(0.937702\pi\)
\(464\) 221424. 1.02847
\(465\) 305528.i 1.41301i
\(466\) −27012.2 27012.2i −0.124391 0.124391i
\(467\) 164176.i 0.752793i −0.926459 0.376397i \(-0.877163\pi\)
0.926459 0.376397i \(-0.122837\pi\)
\(468\) 69237.4 33048.9i 0.316118 0.150892i
\(469\) −124804. −0.567392
\(470\) 815813. 815813.i 3.69313 3.69313i
\(471\) 44450.2 0.200369
\(472\) 11140.6i 0.0500061i
\(473\) 13264.6 13264.6i 0.0592885 0.0592885i
\(474\) −165968. + 165968.i −0.738700 + 0.738700i
\(475\) 274146. + 274146.i 1.21505 + 1.21505i
\(476\) −141230. 141230.i −0.623322 0.623322i
\(477\) −114177. −0.501813
\(478\) 201917.i 0.883726i
\(479\) 10906.2 + 10906.2i 0.0475337 + 0.0475337i 0.730474 0.682940i \(-0.239299\pi\)
−0.682940 + 0.730474i \(0.739299\pi\)
\(480\) 360684.i 1.56547i
\(481\) −8982.97 + 25390.3i −0.0388267 + 0.109743i
\(482\) −34949.7 −0.150435
\(483\) −22445.3 + 22445.3i −0.0962126 + 0.0962126i
\(484\) −211184. −0.901510
\(485\) 104721.i 0.445196i
\(486\) −15343.4 + 15343.4i −0.0649605 + 0.0649605i
\(487\) 225502. 225502.i 0.950808 0.950808i −0.0480379 0.998846i \(-0.515297\pi\)
0.998846 + 0.0480379i \(0.0152968\pi\)
\(488\) −12393.8 12393.8i −0.0520432 0.0520432i
\(489\) −6049.23 6049.23i −0.0252978 0.0252978i
\(490\) 346982. 1.44516
\(491\) 311585.i 1.29245i 0.763147 + 0.646225i \(0.223653\pi\)
−0.763147 + 0.646225i \(0.776347\pi\)
\(492\) 99027.5 + 99027.5i 0.409096 + 0.409096i
\(493\) 323677.i 1.33174i
\(494\) 208162. 99361.4i 0.852997 0.407159i
\(495\) 58448.2 0.238540
\(496\) −212295. + 212295.i −0.862933 + 0.862933i
\(497\) 14116.9 0.0571516
\(498\) 171680.i 0.692247i
\(499\) 1928.12 1928.12i 0.00774341 0.00774341i −0.703224 0.710968i \(-0.748257\pi\)
0.710968 + 0.703224i \(0.248257\pi\)
\(500\) −565456. + 565456.i −2.26183 + 2.26183i
\(501\) 39151.8 + 39151.8i 0.155983 + 0.155983i
\(502\) −406003. 406003.i −1.61110 1.61110i
\(503\) −185299. −0.732382 −0.366191 0.930540i \(-0.619338\pi\)
−0.366191 + 0.930540i \(0.619338\pi\)
\(504\) 4220.11i 0.0166136i
\(505\) 334981. + 334981.i 1.31352 + 1.31352i
\(506\) 47597.8i 0.185903i
\(507\) −93329.6 + 115388.i −0.363081 + 0.448894i
\(508\) 445001. 1.72438
\(509\) 103850. 103850.i 0.400841 0.400841i −0.477688 0.878529i \(-0.658525\pi\)
0.878529 + 0.477688i \(0.158525\pi\)
\(510\) 500365. 1.92374
\(511\) 124081.i 0.475186i
\(512\) −263398. + 263398.i −1.00478 + 1.00478i
\(513\) −23636.8 + 23636.8i −0.0898162 + 0.0898162i
\(514\) 60573.7 + 60573.7i 0.229276 + 0.229276i
\(515\) −220.186 220.186i −0.000830185 0.000830185i
\(516\) −35929.1 −0.134942
\(517\) 193589.i 0.724269i
\(518\) −21647.4 21647.4i −0.0806765 0.0806765i
\(519\) 203471.i 0.755384i
\(520\) 16102.4 + 33734.5i 0.0595503 + 0.124758i
\(521\) 200788. 0.739712 0.369856 0.929089i \(-0.379407\pi\)
0.369856 + 0.929089i \(0.379407\pi\)
\(522\) −99933.8 + 99933.8i −0.366751 + 0.366751i
\(523\) −9411.84 −0.0344089 −0.0172045 0.999852i \(-0.505477\pi\)
−0.0172045 + 0.999852i \(0.505477\pi\)
\(524\) 361353.i 1.31604i
\(525\) 200498. 200498.i 0.727429 0.727429i
\(526\) 30679.0 30679.0i 0.110884 0.110884i
\(527\) 310332. + 310332.i 1.11739 + 1.11739i
\(528\) 40612.6 + 40612.6i 0.145678 + 0.145678i
\(529\) 246658. 0.881424
\(530\) 1.14959e6i 4.09254i
\(531\) 45635.1 + 45635.1i 0.161849 + 0.161849i
\(532\) 134346.i 0.474681i
\(533\) −255390. 90356.1i −0.898980 0.318056i
\(534\) −72522.5 −0.254326
\(535\) −207488. + 207488.i −0.724913 + 0.724913i
\(536\) −17345.3 −0.0603742
\(537\) 196233.i 0.680493i
\(538\) −406904. + 406904.i −1.40581 + 1.40581i
\(539\) 41168.7 41168.7i 0.141707 0.141707i
\(540\) −79158.0 79158.0i −0.271461 0.271461i
\(541\) −16197.1 16197.1i −0.0553406 0.0553406i 0.678895 0.734235i \(-0.262459\pi\)
−0.734235 + 0.678895i \(0.762459\pi\)
\(542\) −539696. −1.83718
\(543\) 49834.1i 0.169016i
\(544\) 366356. + 366356.i 1.23796 + 1.23796i
\(545\) 247953.i 0.834788i
\(546\) −72668.3 152240.i −0.243759 0.510674i
\(547\) −211628. −0.707292 −0.353646 0.935379i \(-0.615058\pi\)
−0.353646 + 0.935379i \(0.615058\pi\)
\(548\) −84574.9 + 84574.9i −0.281631 + 0.281631i
\(549\) −101537. −0.336885
\(550\) 425178.i 1.40555i
\(551\) −153950. + 153950.i −0.507081 + 0.507081i
\(552\) −3119.45 + 3119.45i −0.0102376 + 0.0102376i
\(553\) 186991. + 186991.i 0.611462 + 0.611462i
\(554\) 284268. + 284268.i 0.926207 + 0.926207i
\(555\) 39298.3 0.127582
\(556\) 204839.i 0.662619i
\(557\) −143135. 143135.i −0.461354 0.461354i 0.437745 0.899099i \(-0.355777\pi\)
−0.899099 + 0.437745i \(0.855777\pi\)
\(558\) 191627.i 0.615445i
\(559\) 62721.8 29938.8i 0.200722 0.0958101i
\(560\) 385652. 1.22976
\(561\) 59367.3 59367.3i 0.188635 0.188635i
\(562\) 166199. 0.526206
\(563\) 230941.i 0.728592i 0.931283 + 0.364296i \(0.118690\pi\)
−0.931283 + 0.364296i \(0.881310\pi\)
\(564\) −262183. + 262183.i −0.824226 + 0.824226i
\(565\) −713694. + 713694.i −2.23571 + 2.23571i
\(566\) −122205. 122205.i −0.381467 0.381467i
\(567\) 17286.9 + 17286.9i 0.0537713 + 0.0537713i
\(568\) 1961.97 0.00608129
\(569\) 243018.i 0.750609i 0.926902 + 0.375305i \(0.122462\pi\)
−0.926902 + 0.375305i \(0.877538\pi\)
\(570\) −237988. 237988.i −0.732497 0.732497i
\(571\) 229921.i 0.705189i 0.935776 + 0.352595i \(0.114701\pi\)
−0.935776 + 0.352595i \(0.885299\pi\)
\(572\) 122192. + 43231.2i 0.373467 + 0.132131i
\(573\) 241064. 0.734214
\(574\) 217743. 217743.i 0.660876 0.660876i
\(575\) 296410. 0.896515
\(576\) 121539.i 0.366329i
\(577\) −45748.5 + 45748.5i −0.137412 + 0.137412i −0.772467 0.635055i \(-0.780977\pi\)
0.635055 + 0.772467i \(0.280977\pi\)
\(578\) 169929. 169929.i 0.508641 0.508641i
\(579\) 48622.7 + 48622.7i 0.145038 + 0.145038i
\(580\) −515568. 515568.i −1.53260 1.53260i
\(581\) −193426. −0.573010
\(582\) 65681.3i 0.193908i
\(583\) −136397. 136397.i −0.401299 0.401299i
\(584\) 17244.7i 0.0505628i
\(585\) 204147. + 72226.5i 0.596529 + 0.211050i
\(586\) 548126. 1.59619
\(587\) −183355. + 183355.i −0.532127 + 0.532127i −0.921205 0.389078i \(-0.872794\pi\)
0.389078 + 0.921205i \(0.372794\pi\)
\(588\) −111512. −0.322527
\(589\) 295206.i 0.850931i
\(590\) −459479. + 459479.i −1.31996 + 1.31996i
\(591\) −23190.4 + 23190.4i −0.0663947 + 0.0663947i
\(592\) 27306.4 + 27306.4i 0.0779149 + 0.0779149i
\(593\) −83397.8 83397.8i −0.237162 0.237162i 0.578512 0.815674i \(-0.303634\pi\)
−0.815674 + 0.578512i \(0.803634\pi\)
\(594\) −36658.8 −0.103897
\(595\) 563745.i 1.59239i
\(596\) 168680. + 168680.i 0.474866 + 0.474866i
\(597\) 370623.i 1.03988i
\(598\) 58818.3 166249.i 0.164479 0.464897i
\(599\) −217649. −0.606601 −0.303300 0.952895i \(-0.598089\pi\)
−0.303300 + 0.952895i \(0.598089\pi\)
\(600\) 27865.1 27865.1i 0.0774031 0.0774031i
\(601\) −441379. −1.22197 −0.610987 0.791640i \(-0.709227\pi\)
−0.610987 + 0.791640i \(0.709227\pi\)
\(602\) 79001.4i 0.217993i
\(603\) −71051.5 + 71051.5i −0.195406 + 0.195406i
\(604\) 169103. 169103.i 0.463529 0.463529i
\(605\) −421490. 421490.i −1.15153 1.15153i
\(606\) −210101. 210101.i −0.572113 0.572113i
\(607\) −283335. −0.768993 −0.384497 0.923126i \(-0.625625\pi\)
−0.384497 + 0.923126i \(0.625625\pi\)
\(608\) 348499.i 0.942745i
\(609\) 112592. + 112592.i 0.303580 + 0.303580i
\(610\) 1.02233e6i 2.74747i
\(611\) 239225. 676166.i 0.640802 1.81122i
\(612\) −160805. −0.429337
\(613\) 482403. 482403.i 1.28377 1.28377i 0.345272 0.938503i \(-0.387787\pi\)
0.938503 0.345272i \(-0.112213\pi\)
\(614\) 783139. 2.07731
\(615\) 395286.i 1.04511i
\(616\) −5041.39 + 5041.39i −0.0132858 + 0.0132858i
\(617\) 136398. 136398.i 0.358293 0.358293i −0.504890 0.863184i \(-0.668467\pi\)
0.863184 + 0.504890i \(0.168467\pi\)
\(618\) 138.101 + 138.101i 0.000361592 + 0.000361592i
\(619\) 130340. + 130340.i 0.340170 + 0.340170i 0.856431 0.516261i \(-0.172677\pi\)
−0.516261 + 0.856431i \(0.672677\pi\)
\(620\) 988623. 2.57186
\(621\) 25556.5i 0.0662701i
\(622\) 286139. + 286139.i 0.739600 + 0.739600i
\(623\) 81708.7i 0.210519i
\(624\) 91664.8 + 192038.i 0.235415 + 0.493193i
\(625\) −1.24013e6 −3.17473
\(626\) −277559. + 277559.i −0.708282 + 0.708282i
\(627\) −56473.6 −0.143652
\(628\) 143831.i 0.364698i
\(629\) 39916.3 39916.3i 0.100890 0.100890i
\(630\) −174054. + 174054.i −0.438532 + 0.438532i
\(631\) −145847. 145847.i −0.366302 0.366302i 0.499825 0.866127i \(-0.333398\pi\)
−0.866127 + 0.499825i \(0.833398\pi\)
\(632\) 25987.9 + 25987.9i 0.0650635 + 0.0650635i
\(633\) −234586. −0.585456
\(634\) 1.13753e6i 2.82998i
\(635\) 888150. + 888150.i 2.20262 + 2.20262i
\(636\) 369453.i 0.913365i
\(637\) 194667. 92920.0i 0.479749 0.228997i
\(638\) −238764. −0.586580
\(639\) 8036.84 8036.84i 0.0196826 0.0196826i
\(640\) 113101. 0.276126
\(641\) 207974.i 0.506165i 0.967445 + 0.253083i \(0.0814445\pi\)
−0.967445 + 0.253083i \(0.918556\pi\)
\(642\) 130137. 130137.i 0.315740 0.315740i
\(643\) −30795.0 + 30795.0i −0.0744831 + 0.0744831i −0.743367 0.668884i \(-0.766772\pi\)
0.668884 + 0.743367i \(0.266772\pi\)
\(644\) 72628.3 + 72628.3i 0.175119 + 0.175119i
\(645\) −71708.8 71708.8i −0.172367 0.172367i
\(646\) −483461. −1.15850
\(647\) 216754.i 0.517795i 0.965905 + 0.258898i \(0.0833592\pi\)
−0.965905 + 0.258898i \(0.916641\pi\)
\(648\) 2402.53 + 2402.53i 0.00572161 + 0.00572161i
\(649\) 109032.i 0.258861i
\(650\) −525407. + 1.48506e6i −1.24357 + 3.51492i
\(651\) −215900. −0.509437
\(652\) −19574.0 + 19574.0i −0.0460452 + 0.0460452i
\(653\) 622399. 1.45963 0.729815 0.683645i \(-0.239606\pi\)
0.729815 + 0.683645i \(0.239606\pi\)
\(654\) 155516.i 0.363597i
\(655\) 721203. 721203.i 1.68103 1.68103i
\(656\) −274664. + 274664.i −0.638254 + 0.638254i
\(657\) 70639.8 + 70639.8i 0.163651 + 0.163651i
\(658\) 576491. + 576491.i 1.33150 + 1.33150i
\(659\) 127164. 0.292814 0.146407 0.989224i \(-0.453229\pi\)
0.146407 + 0.989224i \(0.453229\pi\)
\(660\) 189126.i 0.434173i
\(661\) 512043. + 512043.i 1.17194 + 1.17194i 0.981748 + 0.190187i \(0.0609095\pi\)
0.190187 + 0.981748i \(0.439091\pi\)
\(662\) 594817.i 1.35727i
\(663\) 280720. 133995.i 0.638625 0.304833i
\(664\) −26882.3 −0.0609720
\(665\) −268133. + 268133.i −0.606328 + 0.606328i
\(666\) −24647.9 −0.0555690
\(667\) 166453.i 0.374145i
\(668\) 126687. 126687.i 0.283909 0.283909i
\(669\) 117027. 117027.i 0.261477 0.261477i
\(670\) −715384. 715384.i −1.59364 1.59364i
\(671\) −121298. 121298.i −0.269406 0.269406i
\(672\) −254876. −0.564404
\(673\) 70363.7i 0.155353i −0.996979 0.0776763i \(-0.975250\pi\)
0.996979 0.0776763i \(-0.0247501\pi\)
\(674\) −57972.1 57972.1i −0.127614 0.127614i
\(675\) 228288.i 0.501045i
\(676\) 373370. + 301995.i 0.817044 + 0.660855i
\(677\) 289817. 0.632334 0.316167 0.948704i \(-0.397604\pi\)
0.316167 + 0.948704i \(0.397604\pi\)
\(678\) 447629. 447629.i 0.973776 0.973776i
\(679\) 74000.9 0.160508
\(680\) 78349.1i 0.169440i
\(681\) 175001. 175001.i 0.377351 0.377351i
\(682\) 228920. 228920.i 0.492170 0.492170i
\(683\) 126812. + 126812.i 0.271844 + 0.271844i 0.829842 0.557998i \(-0.188430\pi\)
−0.557998 + 0.829842i \(0.688430\pi\)
\(684\) 76483.7 + 76483.7i 0.163477 + 0.163477i
\(685\) −337596. −0.719476
\(686\) 706430.i 1.50114i
\(687\) 286137. + 286137.i 0.606261 + 0.606261i
\(688\) 99653.4i 0.210531i
\(689\) −307856. 644957.i −0.648498 1.35860i
\(690\) −257316. −0.540466
\(691\) 512067. 512067.i 1.07243 1.07243i 0.0752718 0.997163i \(-0.476018\pi\)
0.997163 0.0752718i \(-0.0239824\pi\)
\(692\) −658388. −1.37490
\(693\) 41302.2i 0.0860016i
\(694\) −875563. + 875563.i −1.81789 + 1.81789i
\(695\) 408827. 408827.i 0.846388 0.846388i
\(696\) 15648.0 + 15648.0i 0.0323029 + 0.0323029i
\(697\) 401502. + 401502.i 0.826461 + 0.826461i
\(698\) 167478. 0.343753
\(699\) 34652.1i 0.0709211i
\(700\) −648768. 648768.i −1.32402 1.32402i
\(701\) 718609.i 1.46237i 0.682181 + 0.731184i \(0.261032\pi\)
−0.682181 + 0.731184i \(0.738968\pi\)
\(702\) −128041. 45300.5i −0.259822 0.0919240i
\(703\) −37970.7 −0.0768312
\(704\) 145192. 145192.i 0.292952 0.292952i
\(705\) −1.04655e6 −2.10563
\(706\) 570946.i 1.14547i
\(707\) −236713. + 236713.i −0.473570 + 0.473570i
\(708\) 147666. 147666.i 0.294586 0.294586i
\(709\) −360756. 360756.i −0.717664 0.717664i 0.250462 0.968126i \(-0.419417\pi\)
−0.968126 + 0.250462i \(0.919417\pi\)
\(710\) 80919.1 + 80919.1i 0.160522 + 0.160522i
\(711\) 212909. 0.421168
\(712\) 11355.9i 0.0224006i
\(713\) −159590. 159590.i −0.313926 0.313926i
\(714\) 353581.i 0.693573i
\(715\) 157594. + 330159.i 0.308267 + 0.645819i
\(716\) −634968. −1.23858
\(717\) −129513. + 129513.i −0.251927 + 0.251927i
\(718\) 732599. 1.42108
\(719\) 756213.i 1.46280i −0.681946 0.731402i \(-0.738866\pi\)
0.681946 0.731402i \(-0.261134\pi\)
\(720\) 219553. 219553.i 0.423521 0.423521i
\(721\) 155.593 155.593i 0.000299310 0.000299310i
\(722\) −297921. 297921.i −0.571515 0.571515i
\(723\) 22417.3 + 22417.3i 0.0428851 + 0.0428851i
\(724\) −161252. −0.307630
\(725\) 1.48688e6i 2.82878i
\(726\) 264359. + 264359.i 0.501557 + 0.501557i
\(727\) 2488.50i 0.00470835i 0.999997 + 0.00235417i \(0.000749357\pi\)
−0.999997 + 0.00235417i \(0.999251\pi\)
\(728\) −23838.3 + 11378.7i −0.0449794 + 0.0214699i
\(729\) 19683.0 0.0370370
\(730\) −711239. + 711239.i −1.33466 + 1.33466i
\(731\) −145673. −0.272611
\(732\) 328554.i 0.613174i
\(733\) 269312. 269312.i 0.501243 0.501243i −0.410581 0.911824i \(-0.634674\pi\)
0.911824 + 0.410581i \(0.134674\pi\)
\(734\) 633254. 633254.i 1.17540 1.17540i
\(735\) −222560. 222560.i −0.411976 0.411976i
\(736\) −188401. 188401.i −0.347798 0.347798i
\(737\) −169758. −0.312532
\(738\) 247924.i 0.455203i
\(739\) −710849. 710849.i −1.30163 1.30163i −0.927291 0.374342i \(-0.877869\pi\)
−0.374342 0.927291i \(-0.622131\pi\)
\(740\) 127161.i 0.232215i
\(741\) −197250. 69786.4i −0.359237 0.127097i
\(742\) 812357. 1.47550
\(743\) −516575. + 516575.i −0.935741 + 0.935741i −0.998057 0.0623154i \(-0.980152\pi\)
0.0623154 + 0.998057i \(0.480152\pi\)
\(744\) −30005.7 −0.0542074
\(745\) 673317.i 1.21313i
\(746\) −49230.3 + 49230.3i −0.0884616 + 0.0884616i
\(747\) −110118. + 110118.i −0.197341 + 0.197341i
\(748\) −192100. 192100.i −0.343340 0.343340i
\(749\) −146621. 146621.i −0.261356 0.261356i
\(750\) 1.41567e6 2.51674
\(751\) 628582.i 1.11450i 0.830343 + 0.557252i \(0.188144\pi\)
−0.830343 + 0.557252i \(0.811856\pi\)
\(752\) −727194. 727194.i −1.28592 1.28592i
\(753\) 520834.i 0.918564i
\(754\) −833952. 295049.i −1.46689 0.518981i
\(755\) 675004. 1.18417
\(756\) 55936.7 55936.7i 0.0978708 0.0978708i
\(757\) 874918. 1.52678 0.763389 0.645940i \(-0.223534\pi\)
0.763389 + 0.645940i \(0.223534\pi\)
\(758\) 459856.i 0.800357i
\(759\) −30530.0 + 30530.0i −0.0529960 + 0.0529960i
\(760\) −37265.1 + 37265.1i −0.0645171 + 0.0645171i
\(761\) 176909. + 176909.i 0.305479 + 0.305479i 0.843153 0.537674i \(-0.180697\pi\)
−0.537674 + 0.843153i \(0.680697\pi\)
\(762\) −557049. 557049.i −0.959363 0.959363i
\(763\) 175215. 0.300969
\(764\) 780031.i 1.33636i
\(765\) −320942. 320942.i −0.548408 0.548408i
\(766\) 114700.i 0.195482i
\(767\) −134735. + 380827.i −0.229029 + 0.647347i
\(768\) 303306. 0.514232
\(769\) 64761.1 64761.1i 0.109512 0.109512i −0.650228 0.759740i \(-0.725326\pi\)
0.759740 + 0.650228i \(0.225326\pi\)
\(770\) −415852. −0.701387
\(771\) 77705.8i 0.130721i
\(772\) 157333. 157333.i 0.263988 0.263988i
\(773\) 65728.0 65728.0i 0.110000 0.110000i −0.649965 0.759964i \(-0.725216\pi\)
0.759964 + 0.649965i \(0.225216\pi\)
\(774\) 44975.8 + 44975.8i 0.0750753 + 0.0750753i
\(775\) 1.42557e6 + 1.42557e6i 2.37348 + 2.37348i
\(776\) 10284.6 0.0170791
\(777\) 27770.0i 0.0459975i
\(778\) −58682.3 58682.3i −0.0969501 0.0969501i
\(779\) 381932.i 0.629377i
\(780\) 233709. 660577.i 0.384138 1.08576i
\(781\) 19201.8 0.0314803
\(782\) −261362. + 261362.i −0.427395 + 0.427395i
\(783\) 128198. 0.209102
\(784\) 309290.i 0.503193i
\(785\) 287064. 287064.i 0.465843 0.465843i
\(786\) −452339. + 452339.i −0.732182 + 0.732182i
\(787\) 853121. + 853121.i 1.37740 + 1.37740i 0.848983 + 0.528420i \(0.177215\pi\)
0.528420 + 0.848983i \(0.322785\pi\)
\(788\) 75039.2 + 75039.2i 0.120847 + 0.120847i
\(789\) −39356.0 −0.0632204
\(790\) 2.14368e6i 3.43484i
\(791\) −504329. 504329.i −0.806048 0.806048i
\(792\) 5740.17i 0.00915112i
\(793\) −273775. 573559.i −0.435360 0.912078i
\(794\) −975493. −1.54733
\(795\) −737369. + 737369.i −1.16668 + 1.16668i
\(796\) −1.19926e6 −1.89272
\(797\) 264563.i 0.416498i 0.978076 + 0.208249i \(0.0667765\pi\)
−0.978076 + 0.208249i \(0.933224\pi\)
\(798\) 168173. 168173.i 0.264090 0.264090i
\(799\) −1.06301e6 + 1.06301e6i −1.66511 + 1.66511i
\(800\) 1.68293e6 + 1.68293e6i 2.62958 + 2.62958i
\(801\) 46517.1 + 46517.1i 0.0725016 + 0.0725016i
\(802\) −255980. −0.397977
\(803\) 168774.i 0.261743i
\(804\) 229908. + 229908.i 0.355665 + 0.355665i
\(805\) 289909.i 0.447373i
\(806\) 1.08245e6 516685.i 1.66625 0.795345i
\(807\) 521989. 0.801520
\(808\) −32898.4 + 32898.4i −0.0503908 + 0.0503908i
\(809\) −903066. −1.37982 −0.689910 0.723895i \(-0.742350\pi\)
−0.689910 + 0.723895i \(0.742350\pi\)
\(810\) 198179.i 0.302056i
\(811\) 158801. 158801.i 0.241442 0.241442i −0.576005 0.817446i \(-0.695389\pi\)
0.817446 + 0.576005i \(0.195389\pi\)
\(812\) 364324. 364324.i 0.552555 0.552555i
\(813\) 346170. + 346170.i 0.523731 + 0.523731i
\(814\) −29444.7 29444.7i −0.0444384 0.0444384i
\(815\) −78133.2 −0.117631
\(816\) 446012.i 0.669832i
\(817\) 69286.2 + 69286.2i 0.103801 + 0.103801i
\(818\) 135214.i 0.202076i
\(819\) −51038.6 + 144260.i −0.0760905 + 0.215069i
\(820\) 1.27906e6 1.90223
\(821\) 566290. 566290.i 0.840142 0.840142i −0.148735 0.988877i \(-0.547520\pi\)
0.988877 + 0.148735i \(0.0475203\pi\)
\(822\) 211740. 0.313372
\(823\) 664034.i 0.980371i −0.871618 0.490186i \(-0.836929\pi\)
0.871618 0.490186i \(-0.163071\pi\)
\(824\) 21.6244 21.6244i 3.18485e−5 3.18485e-5i
\(825\) 272716. 272716.i 0.400684 0.400684i
\(826\) −324689. 324689.i −0.475891 0.475891i
\(827\) −694781. 694781.i −1.01587 1.01587i −0.999872 0.0159954i \(-0.994908\pi\)
−0.0159954 0.999872i \(-0.505092\pi\)
\(828\) 82695.2 0.120620
\(829\) 1.07123e6i 1.55874i −0.626564 0.779370i \(-0.715539\pi\)
0.626564 0.779370i \(-0.284461\pi\)
\(830\) −1.10873e6 1.10873e6i −1.60942 1.60942i
\(831\) 364668.i 0.528074i
\(832\) 686543. 327706.i 0.991794 0.473410i
\(833\) −452119. −0.651573
\(834\) −256416. + 256416.i −0.368649 + 0.368649i
\(835\) 505694. 0.725295
\(836\) 182737.i 0.261465i
\(837\) −122913. + 122913.i −0.175447 + 0.175447i
\(838\) 183277. 183277.i 0.260988 0.260988i
\(839\) 710646. + 710646.i 1.00955 + 1.00955i 0.999954 + 0.00959972i \(0.00305573\pi\)
0.00959972 + 0.999954i \(0.496944\pi\)
\(840\) 27254.0 + 27254.0i 0.0386252 + 0.0386252i
\(841\) 127693. 0.180541
\(842\) 772742.i 1.08996i
\(843\) −106603. 106603.i −0.150007 0.150007i
\(844\) 759070.i 1.06561i
\(845\) 142453. + 1.34792e6i 0.199507 + 1.88778i
\(846\) 656398. 0.917120
\(847\) 297844. 297844.i 0.415167 0.415167i
\(848\) −1.02472e6 −1.42499
\(849\) 156769.i 0.217493i
\(850\) 2.33467e6 2.33467e6i 3.23138 3.23138i
\(851\) −20527.2 + 20527.2i −0.0283446 + 0.0283446i
\(852\) −26005.5 26005.5i −0.0358250 0.0358250i
\(853\) −719087. 719087.i −0.988288 0.988288i 0.0116445 0.999932i \(-0.496293\pi\)
−0.999932 + 0.0116445i \(0.996293\pi\)
\(854\) 722427. 0.990555
\(855\) 305299.i 0.417631i
\(856\) −20377.3 20377.3i −0.0278099 0.0278099i
\(857\) 625779.i 0.852038i 0.904714 + 0.426019i \(0.140084\pi\)
−0.904714 + 0.426019i \(0.859916\pi\)
\(858\) −98843.0 207076.i −0.134268 0.281290i
\(859\) −1.38660e6 −1.87917 −0.939585 0.342315i \(-0.888789\pi\)
−0.939585 + 0.342315i \(0.888789\pi\)
\(860\) −232034. + 232034.i −0.313729 + 0.313729i
\(861\) −279327. −0.376797
\(862\) 973017.i 1.30950i
\(863\) −251871. + 251871.i −0.338187 + 0.338187i −0.855685 0.517497i \(-0.826864\pi\)
0.517497 + 0.855685i \(0.326864\pi\)
\(864\) −145102. + 145102.i −0.194377 + 0.194377i
\(865\) −1.31404e6 1.31404e6i −1.75621 1.75621i
\(866\) 424938. + 424938.i 0.566618 + 0.566618i
\(867\) −217990. −0.290000
\(868\) 698606.i 0.927242i
\(869\) 254343. + 254343.i 0.336807 + 0.336807i
\(870\) 1.29077e6i 1.70533i
\(871\) −592928. 209776.i −0.781566 0.276515i
\(872\) 24351.3 0.0320250
\(873\) 42129.0 42129.0i 0.0552781 0.0552781i
\(874\) 248623. 0.325475
\(875\) 1.59499e6i 2.08325i
\(876\) 228575. 228575.i 0.297866 0.297866i
\(877\) 248488. 248488.i 0.323077 0.323077i −0.526869 0.849946i \(-0.676634\pi\)
0.849946 + 0.526869i \(0.176634\pi\)
\(878\) 766569. + 766569.i 0.994403 + 0.994403i
\(879\) −351577. 351577.i −0.455032 0.455032i
\(880\) 524562. 0.677378
\(881\) 1.01415e6i 1.30662i 0.757089 + 0.653312i \(0.226621\pi\)
−0.757089 + 0.653312i \(0.773379\pi\)
\(882\) 139590. + 139590.i 0.179439 + 0.179439i
\(883\) 1.21924e6i 1.56375i 0.623433 + 0.781877i \(0.285737\pi\)
−0.623433 + 0.781877i \(0.714263\pi\)
\(884\) −433580. 908349.i −0.554836 1.16238i
\(885\) 589434. 0.752573
\(886\) 626388. 626388.i 0.797950 0.797950i
\(887\) 904300. 1.14938 0.574692 0.818370i \(-0.305122\pi\)
0.574692 + 0.818370i \(0.305122\pi\)
\(888\) 3859.47i 0.00489443i
\(889\) −627608. + 627608.i −0.794118 + 0.794118i
\(890\) −468359. + 468359.i −0.591287 + 0.591287i
\(891\) 23513.5 + 23513.5i 0.0296184 + 0.0296184i
\(892\) −378674. 378674.i −0.475923 0.475923i
\(893\) 1.01120e6 1.26804
\(894\) 422305.i 0.528386i
\(895\) −1.26729e6 1.26729e6i −1.58209 1.58209i
\(896\) 79922.4i 0.0995526i
\(897\) −144362. + 68907.8i −0.179419 + 0.0856414i
\(898\) −438520. −0.543797
\(899\) −800549. + 800549.i −0.990532 + 0.990532i
\(900\) −738692. −0.911966
\(901\) 1.49793e6i 1.84519i
\(902\) 296172. 296172.i 0.364025 0.364025i
\(903\) 50672.7 50672.7i 0.0621439 0.0621439i
\(904\) −70091.5 70091.5i −0.0857687 0.0857687i
\(905\) −321834. 321834.i −0.392948 0.392948i
\(906\) −423363. −0.515771
\(907\) 1.40623e6i 1.70940i 0.519124 + 0.854699i \(0.326258\pi\)
−0.519124 + 0.854699i \(0.673742\pi\)
\(908\) −566265. 566265.i −0.686828 0.686828i
\(909\) 269524.i 0.326189i
\(910\) −1.45248e6 513883.i −1.75400 0.620557i
\(911\) −320928. −0.386697 −0.193348 0.981130i \(-0.561935\pi\)
−0.193348 + 0.981130i \(0.561935\pi\)
\(912\) −212136. + 212136.i −0.255050 + 0.255050i
\(913\) −263097. −0.315627
\(914\) 357745.i 0.428234i
\(915\) −655741. + 655741.i −0.783231 + 0.783231i
\(916\) 925876. 925876.i 1.10347 1.10347i
\(917\) 509635. + 509635.i 0.606067 + 0.606067i
\(918\) 201295. + 201295.i 0.238862 + 0.238862i
\(919\) −824931. −0.976757 −0.488378 0.872632i \(-0.662411\pi\)
−0.488378 + 0.872632i \(0.662411\pi\)
\(920\) 40291.5i 0.0476034i
\(921\) −502318. 502318.i −0.592187 0.592187i
\(922\) 1.17866e6i 1.38652i
\(923\) 67067.8 + 23728.3i 0.0787246 + 0.0278525i
\(924\) 133645. 0.156534
\(925\) 183364. 183364.i 0.214304 0.214304i
\(926\) 1.36575e6 1.59276
\(927\) 177.160i 0.000206161i
\(928\) −945070. + 945070.i −1.09741 + 1.09741i
\(929\) 678405. 678405.i 0.786064 0.786064i −0.194783 0.980846i \(-0.562400\pi\)
0.980846 + 0.194783i \(0.0624001\pi\)
\(930\) −1.23755e6 1.23755e6i −1.43086 1.43086i
\(931\) 215041. + 215041.i 0.248097 + 0.248097i
\(932\) 112127. 0.129086
\(933\) 367069.i 0.421681i
\(934\) 665000. + 665000.i 0.762303 + 0.762303i
\(935\) 766802.i 0.877122i
\(936\) −7093.33 + 20049.2i −0.00809652 + 0.0228847i
\(937\) 1.11931e6 1.27488 0.637441 0.770499i \(-0.279993\pi\)
0.637441 + 0.770499i \(0.279993\pi\)
\(938\) 505523. 505523.i 0.574560 0.574560i
\(939\) 356061. 0.403825
\(940\) 3.38642e6i 3.83252i
\(941\) 498975. 498975.i 0.563507 0.563507i −0.366795 0.930302i \(-0.619545\pi\)
0.930302 + 0.366795i \(0.119545\pi\)
\(942\) −180047. + 180047.i −0.202901 + 0.202901i
\(943\) −206475. 206475.i −0.232190 0.232190i
\(944\) 409567. + 409567.i 0.459601 + 0.459601i
\(945\) 223281. 0.250028
\(946\) 107457.i 0.120075i
\(947\) −672812. 672812.i −0.750228 0.750228i 0.224293 0.974522i \(-0.427993\pi\)
−0.974522 + 0.224293i \(0.927993\pi\)
\(948\) 688928.i 0.766580i
\(949\) −208560. + 589492.i −0.231579 + 0.654554i
\(950\) −2.22087e6 −2.46080
\(951\) 729629. 729629.i 0.806754 0.806754i
\(952\) 55365.1 0.0610889
\(953\) 226250.i 0.249117i 0.992212 + 0.124558i \(0.0397514\pi\)
−0.992212 + 0.124558i \(0.960249\pi\)
\(954\) 462478. 462478.i 0.508153 0.508153i
\(955\) 1.55682e6 1.55682e6i 1.70699 1.70699i
\(956\) 419076. + 419076.i 0.458540 + 0.458540i
\(957\) 153147. + 153147.i 0.167219 + 0.167219i
\(958\) −88351.7 −0.0962684
\(959\) 238561.i 0.259395i
\(960\) −784913. 784913.i −0.851686 0.851686i
\(961\) 611566.i 0.662211i
\(962\) −66458.2 139230.i −0.0718123 0.150447i
\(963\) −166944. −0.180019
\(964\) 72537.6 72537.6i 0.0780565 0.0780565i
\(965\) 628022. 0.674404
\(966\) 181831.i 0.194856i
\(967\) −652291. + 652291.i −0.697571 + 0.697571i −0.963886 0.266315i \(-0.914194\pi\)
0.266315 + 0.963886i \(0.414194\pi\)
\(968\) 41394.3 41394.3i 0.0441764 0.0441764i
\(969\) 310100. + 310100.i 0.330258 + 0.330258i
\(970\) 424177. + 424177.i 0.450821 + 0.450821i
\(971\) 330964. 0.351028 0.175514 0.984477i \(-0.443841\pi\)
0.175514 + 0.984477i \(0.443841\pi\)
\(972\) 63690.0i 0.0674122i
\(973\) 288896. + 288896.i 0.305151 + 0.305151i
\(974\) 1.82681e6i 1.92564i
\(975\) 1.28954e6 615534.i 1.35652 0.647504i
\(976\) −911280. −0.956648
\(977\) −812569. + 812569.i −0.851278 + 0.851278i −0.990291 0.139013i \(-0.955607\pi\)
0.139013 + 0.990291i \(0.455607\pi\)
\(978\) 49005.2 0.0512347
\(979\) 111140.i 0.115959i
\(980\) −720156. + 720156.i −0.749850 + 0.749850i
\(981\) 99750.5 99750.5i 0.103652 0.103652i
\(982\) −1.26209e6 1.26209e6i −1.30878 1.30878i
\(983\) 1.32394e6 + 1.32394e6i 1.37013 + 1.37013i 0.860235 + 0.509898i \(0.170317\pi\)
0.509898 + 0.860235i \(0.329683\pi\)
\(984\) −38820.9 −0.0400936
\(985\) 299533.i 0.308725i
\(986\) 1.31107e6 + 1.31107e6i 1.34856 + 1.34856i
\(987\) 739541.i 0.759151i
\(988\) −225814. + 638260.i −0.231333 + 0.653858i
\(989\) 74913.1 0.0765888
\(990\) −236746. + 236746.i −0.241553 + 0.241553i
\(991\) −424185. −0.431925 −0.215962 0.976402i \(-0.569289\pi\)
−0.215962 + 0.976402i \(0.569289\pi\)
\(992\) 1.81221e6i 1.84156i
\(993\) −381525. + 381525.i −0.386923 + 0.386923i
\(994\) −57181.2 + 57181.2i −0.0578736 + 0.0578736i
\(995\) −2.39352e6 2.39352e6i −2.41764 2.41764i
\(996\) 356319. + 356319.i 0.359187 + 0.359187i
\(997\) 1.53487e6 1.54412 0.772060 0.635549i \(-0.219226\pi\)
0.772060 + 0.635549i \(0.219226\pi\)
\(998\) 15619.8i 0.0156825i
\(999\) 15809.6 + 15809.6i 0.0158413 + 0.0158413i
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 39.5.g.a.31.3 20
3.2 odd 2 117.5.j.b.109.8 20
13.8 odd 4 inner 39.5.g.a.34.3 yes 20
39.8 even 4 117.5.j.b.73.8 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.5.g.a.31.3 20 1.1 even 1 trivial
39.5.g.a.34.3 yes 20 13.8 odd 4 inner
117.5.j.b.73.8 20 39.8 even 4
117.5.j.b.109.8 20 3.2 odd 2