Properties

Label 197.10.a.b.1.6
Level $197$
Weight $10$
Character 197.1
Self dual yes
Analytic conductor $101.462$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,10,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)

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: yes
Analytic conductor: \(101.462059724\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-39.0491 q^{2} -79.6019 q^{3} +1012.83 q^{4} -1275.42 q^{5} +3108.38 q^{6} +8453.17 q^{7} -19557.0 q^{8} -13346.5 q^{9} +O(q^{10})\) \(q-39.0491 q^{2} -79.6019 q^{3} +1012.83 q^{4} -1275.42 q^{5} +3108.38 q^{6} +8453.17 q^{7} -19557.0 q^{8} -13346.5 q^{9} +49804.1 q^{10} -89247.0 q^{11} -80623.3 q^{12} -15037.6 q^{13} -330088. q^{14} +101526. q^{15} +245114. q^{16} -142485. q^{17} +521170. q^{18} +600806. q^{19} -1.29179e6 q^{20} -672888. q^{21} +3.48502e6 q^{22} -2.40992e6 q^{23} +1.55677e6 q^{24} -326424. q^{25} +587205. q^{26} +2.62921e6 q^{27} +8.56163e6 q^{28} -1.26844e6 q^{29} -3.96450e6 q^{30} +3.18354e6 q^{31} +441726. q^{32} +7.10423e6 q^{33} +5.56390e6 q^{34} -1.07814e7 q^{35} -1.35178e7 q^{36} +1.60137e6 q^{37} -2.34609e7 q^{38} +1.19702e6 q^{39} +2.49434e7 q^{40} -1.15907e7 q^{41} +2.62757e7 q^{42} -1.10757e7 q^{43} -9.03922e7 q^{44} +1.70225e7 q^{45} +9.41051e7 q^{46} -1.71311e7 q^{47} -1.95115e7 q^{48} +3.11024e7 q^{49} +1.27466e7 q^{50} +1.13421e7 q^{51} -1.52306e7 q^{52} -4.36131e7 q^{53} -1.02668e8 q^{54} +1.13828e8 q^{55} -1.65319e8 q^{56} -4.78253e7 q^{57} +4.95316e7 q^{58} +9.68517e7 q^{59} +1.02829e8 q^{60} -1.42632e8 q^{61} -1.24314e8 q^{62} -1.12821e8 q^{63} -1.42747e8 q^{64} +1.91793e7 q^{65} -2.77414e8 q^{66} -2.80649e8 q^{67} -1.44313e8 q^{68} +1.91834e8 q^{69} +4.21002e8 q^{70} -3.55491e8 q^{71} +2.61018e8 q^{72} -2.25622e8 q^{73} -6.25321e7 q^{74} +2.59840e7 q^{75} +6.08515e8 q^{76} -7.54420e8 q^{77} -4.67426e7 q^{78} -1.66304e8 q^{79} -3.12623e8 q^{80} +5.34094e7 q^{81} +4.52606e8 q^{82} -3.45602e8 q^{83} -6.81522e8 q^{84} +1.81728e8 q^{85} +4.32495e8 q^{86} +1.00971e8 q^{87} +1.74540e9 q^{88} +3.49116e8 q^{89} -6.64712e8 q^{90} -1.27115e8 q^{91} -2.44084e9 q^{92} -2.53416e8 q^{93} +6.68953e8 q^{94} -7.66281e8 q^{95} -3.51623e7 q^{96} -1.34695e9 q^{97} -1.21452e9 q^{98} +1.19114e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −39.0491 −1.72574 −0.862871 0.505424i \(-0.831336\pi\)
−0.862871 + 0.505424i \(0.831336\pi\)
\(3\) −79.6019 −0.567385 −0.283692 0.958915i \(-0.591559\pi\)
−0.283692 + 0.958915i \(0.591559\pi\)
\(4\) 1012.83 1.97819
\(5\) −1275.42 −0.912618 −0.456309 0.889822i \(-0.650829\pi\)
−0.456309 + 0.889822i \(0.650829\pi\)
\(6\) 3108.38 0.979160
\(7\) 8453.17 1.33069 0.665347 0.746534i \(-0.268284\pi\)
0.665347 + 0.746534i \(0.268284\pi\)
\(8\) −19557.0 −1.68810
\(9\) −13346.5 −0.678074
\(10\) 49804.1 1.57494
\(11\) −89247.0 −1.83792 −0.918960 0.394350i \(-0.870970\pi\)
−0.918960 + 0.394350i \(0.870970\pi\)
\(12\) −80623.3 −1.12239
\(13\) −15037.6 −0.146027 −0.0730136 0.997331i \(-0.523262\pi\)
−0.0730136 + 0.997331i \(0.523262\pi\)
\(14\) −330088. −2.29644
\(15\) 101526. 0.517805
\(16\) 245114. 0.935034
\(17\) −142485. −0.413760 −0.206880 0.978366i \(-0.566331\pi\)
−0.206880 + 0.978366i \(0.566331\pi\)
\(18\) 521170. 1.17018
\(19\) 600806. 1.05765 0.528826 0.848730i \(-0.322632\pi\)
0.528826 + 0.848730i \(0.322632\pi\)
\(20\) −1.29179e6 −1.80533
\(21\) −672888. −0.755016
\(22\) 3.48502e6 3.17178
\(23\) −2.40992e6 −1.79567 −0.897836 0.440331i \(-0.854861\pi\)
−0.897836 + 0.440331i \(0.854861\pi\)
\(24\) 1.55677e6 0.957801
\(25\) −326424. −0.167129
\(26\) 587205. 0.252005
\(27\) 2.62921e6 0.952114
\(28\) 8.56163e6 2.63236
\(29\) −1.26844e6 −0.333028 −0.166514 0.986039i \(-0.553251\pi\)
−0.166514 + 0.986039i \(0.553251\pi\)
\(30\) −3.96450e6 −0.893599
\(31\) 3.18354e6 0.619132 0.309566 0.950878i \(-0.399816\pi\)
0.309566 + 0.950878i \(0.399816\pi\)
\(32\) 441726. 0.0744695
\(33\) 7.10423e6 1.04281
\(34\) 5.56390e6 0.714042
\(35\) −1.07814e7 −1.21441
\(36\) −1.35178e7 −1.34136
\(37\) 1.60137e6 0.140470 0.0702352 0.997530i \(-0.477625\pi\)
0.0702352 + 0.997530i \(0.477625\pi\)
\(38\) −2.34609e7 −1.82523
\(39\) 1.19702e6 0.0828536
\(40\) 2.49434e7 1.54059
\(41\) −1.15907e7 −0.640593 −0.320297 0.947317i \(-0.603783\pi\)
−0.320297 + 0.947317i \(0.603783\pi\)
\(42\) 2.62757e7 1.30296
\(43\) −1.10757e7 −0.494040 −0.247020 0.969010i \(-0.579451\pi\)
−0.247020 + 0.969010i \(0.579451\pi\)
\(44\) −9.03922e7 −3.63575
\(45\) 1.70225e7 0.618822
\(46\) 9.41051e7 3.09887
\(47\) −1.71311e7 −0.512088 −0.256044 0.966665i \(-0.582419\pi\)
−0.256044 + 0.966665i \(0.582419\pi\)
\(48\) −1.95115e7 −0.530524
\(49\) 3.11024e7 0.770747
\(50\) 1.27466e7 0.288422
\(51\) 1.13421e7 0.234761
\(52\) −1.52306e7 −0.288869
\(53\) −4.36131e7 −0.759234 −0.379617 0.925144i \(-0.623944\pi\)
−0.379617 + 0.925144i \(0.623944\pi\)
\(54\) −1.02668e8 −1.64310
\(55\) 1.13828e8 1.67732
\(56\) −1.65319e8 −2.24634
\(57\) −4.78253e7 −0.600096
\(58\) 4.95316e7 0.574720
\(59\) 9.68517e7 1.04057 0.520287 0.853991i \(-0.325825\pi\)
0.520287 + 0.853991i \(0.325825\pi\)
\(60\) 1.02829e8 1.02432
\(61\) −1.42632e8 −1.31897 −0.659483 0.751720i \(-0.729225\pi\)
−0.659483 + 0.751720i \(0.729225\pi\)
\(62\) −1.24314e8 −1.06846
\(63\) −1.12821e8 −0.902310
\(64\) −1.42747e8 −1.06355
\(65\) 1.91793e7 0.133267
\(66\) −2.77414e8 −1.79962
\(67\) −2.80649e8 −1.70148 −0.850741 0.525585i \(-0.823846\pi\)
−0.850741 + 0.525585i \(0.823846\pi\)
\(68\) −1.44313e8 −0.818493
\(69\) 1.91834e8 1.01884
\(70\) 4.21002e8 2.09577
\(71\) −3.55491e8 −1.66022 −0.830111 0.557598i \(-0.811723\pi\)
−0.830111 + 0.557598i \(0.811723\pi\)
\(72\) 2.61018e8 1.14466
\(73\) −2.25622e8 −0.929883 −0.464941 0.885341i \(-0.653925\pi\)
−0.464941 + 0.885341i \(0.653925\pi\)
\(74\) −6.25321e7 −0.242416
\(75\) 2.59840e7 0.0948266
\(76\) 6.08515e8 2.09223
\(77\) −7.54420e8 −2.44571
\(78\) −4.67426e7 −0.142984
\(79\) −1.66304e8 −0.480376 −0.240188 0.970726i \(-0.577209\pi\)
−0.240188 + 0.970726i \(0.577209\pi\)
\(80\) −3.12623e8 −0.853328
\(81\) 5.34094e7 0.137859
\(82\) 4.52606e8 1.10550
\(83\) −3.45602e8 −0.799328 −0.399664 0.916662i \(-0.630873\pi\)
−0.399664 + 0.916662i \(0.630873\pi\)
\(84\) −6.81522e8 −1.49356
\(85\) 1.81728e8 0.377604
\(86\) 4.32495e8 0.852585
\(87\) 1.00971e8 0.188955
\(88\) 1.74540e9 3.10259
\(89\) 3.49116e8 0.589814 0.294907 0.955526i \(-0.404711\pi\)
0.294907 + 0.955526i \(0.404711\pi\)
\(90\) −6.64712e8 −1.06793
\(91\) −1.27115e8 −0.194318
\(92\) −2.44084e9 −3.55217
\(93\) −2.53416e8 −0.351286
\(94\) 6.68953e8 0.883731
\(95\) −7.66281e8 −0.965232
\(96\) −3.51623e7 −0.0422529
\(97\) −1.34695e9 −1.54482 −0.772412 0.635122i \(-0.780950\pi\)
−0.772412 + 0.635122i \(0.780950\pi\)
\(98\) −1.21452e9 −1.33011
\(99\) 1.19114e9 1.24625
\(100\) −3.30613e8 −0.330613
\(101\) −5.32171e8 −0.508868 −0.254434 0.967090i \(-0.581889\pi\)
−0.254434 + 0.967090i \(0.581889\pi\)
\(102\) −4.42897e8 −0.405137
\(103\) 4.01519e8 0.351511 0.175756 0.984434i \(-0.443763\pi\)
0.175756 + 0.984434i \(0.443763\pi\)
\(104\) 2.94091e8 0.246508
\(105\) 8.58216e8 0.689041
\(106\) 1.70305e9 1.31024
\(107\) −4.67531e8 −0.344813 −0.172407 0.985026i \(-0.555154\pi\)
−0.172407 + 0.985026i \(0.555154\pi\)
\(108\) 2.66295e9 1.88346
\(109\) −1.54398e9 −1.04766 −0.523831 0.851822i \(-0.675498\pi\)
−0.523831 + 0.851822i \(0.675498\pi\)
\(110\) −4.44486e9 −2.89462
\(111\) −1.27472e8 −0.0797007
\(112\) 2.07199e9 1.24424
\(113\) 2.09523e9 1.20887 0.604433 0.796656i \(-0.293400\pi\)
0.604433 + 0.796656i \(0.293400\pi\)
\(114\) 1.86753e9 1.03561
\(115\) 3.07366e9 1.63876
\(116\) −1.28472e9 −0.658791
\(117\) 2.00700e8 0.0990173
\(118\) −3.78197e9 −1.79576
\(119\) −1.20445e9 −0.550588
\(120\) −1.98554e9 −0.874106
\(121\) 5.60708e9 2.37795
\(122\) 5.56966e9 2.27619
\(123\) 9.22642e8 0.363463
\(124\) 3.22439e9 1.22476
\(125\) 2.90739e9 1.06514
\(126\) 4.40554e9 1.55715
\(127\) −2.22074e9 −0.757499 −0.378749 0.925499i \(-0.623646\pi\)
−0.378749 + 0.925499i \(0.623646\pi\)
\(128\) 5.34798e9 1.76094
\(129\) 8.81644e8 0.280311
\(130\) −7.48934e8 −0.229984
\(131\) 1.42085e9 0.421530 0.210765 0.977537i \(-0.432405\pi\)
0.210765 + 0.977537i \(0.432405\pi\)
\(132\) 7.19539e9 2.06287
\(133\) 5.07871e9 1.40741
\(134\) 1.09591e10 2.93632
\(135\) −3.35336e9 −0.868916
\(136\) 2.78657e9 0.698466
\(137\) −1.19961e9 −0.290936 −0.145468 0.989363i \(-0.546469\pi\)
−0.145468 + 0.989363i \(0.546469\pi\)
\(138\) −7.49094e9 −1.75825
\(139\) −2.22400e9 −0.505322 −0.252661 0.967555i \(-0.581306\pi\)
−0.252661 + 0.967555i \(0.581306\pi\)
\(140\) −1.09197e10 −2.40234
\(141\) 1.36367e9 0.290551
\(142\) 1.38816e10 2.86511
\(143\) 1.34206e9 0.268386
\(144\) −3.27142e9 −0.634022
\(145\) 1.61780e9 0.303927
\(146\) 8.81033e9 1.60474
\(147\) −2.47581e9 −0.437310
\(148\) 1.62192e9 0.277876
\(149\) 4.96037e9 0.824473 0.412236 0.911077i \(-0.364748\pi\)
0.412236 + 0.911077i \(0.364748\pi\)
\(150\) −1.01465e9 −0.163646
\(151\) −1.90705e9 −0.298515 −0.149257 0.988798i \(-0.547688\pi\)
−0.149257 + 0.988798i \(0.547688\pi\)
\(152\) −1.17500e10 −1.78542
\(153\) 1.90168e9 0.280560
\(154\) 2.94594e10 4.22067
\(155\) −4.06036e9 −0.565030
\(156\) 1.21238e9 0.163900
\(157\) 3.66831e7 0.00481857 0.00240928 0.999997i \(-0.499233\pi\)
0.00240928 + 0.999997i \(0.499233\pi\)
\(158\) 6.49402e9 0.829004
\(159\) 3.47169e9 0.430778
\(160\) −5.63387e8 −0.0679622
\(161\) −2.03714e10 −2.38949
\(162\) −2.08559e9 −0.237909
\(163\) −1.53611e9 −0.170443 −0.0852213 0.996362i \(-0.527160\pi\)
−0.0852213 + 0.996362i \(0.527160\pi\)
\(164\) −1.17394e10 −1.26721
\(165\) −9.06089e9 −0.951685
\(166\) 1.34954e10 1.37943
\(167\) −8.96869e9 −0.892288 −0.446144 0.894961i \(-0.647203\pi\)
−0.446144 + 0.894961i \(0.647203\pi\)
\(168\) 1.31597e10 1.27454
\(169\) −1.03784e10 −0.978676
\(170\) −7.09632e9 −0.651648
\(171\) −8.01868e9 −0.717167
\(172\) −1.12178e10 −0.977302
\(173\) −5.25118e9 −0.445707 −0.222854 0.974852i \(-0.571537\pi\)
−0.222854 + 0.974852i \(0.571537\pi\)
\(174\) −3.94281e9 −0.326087
\(175\) −2.75932e9 −0.222398
\(176\) −2.18757e10 −1.71852
\(177\) −7.70958e9 −0.590406
\(178\) −1.36327e10 −1.01787
\(179\) −4.79868e9 −0.349368 −0.174684 0.984625i \(-0.555890\pi\)
−0.174684 + 0.984625i \(0.555890\pi\)
\(180\) 1.72409e10 1.22415
\(181\) −1.53526e10 −1.06323 −0.531615 0.846986i \(-0.678415\pi\)
−0.531615 + 0.846986i \(0.678415\pi\)
\(182\) 4.96374e9 0.335342
\(183\) 1.13538e10 0.748361
\(184\) 4.71308e10 3.03127
\(185\) −2.04243e9 −0.128196
\(186\) 9.89566e9 0.606229
\(187\) 1.27163e10 0.760457
\(188\) −1.73509e10 −1.01300
\(189\) 2.22252e10 1.26697
\(190\) 2.99226e10 1.66574
\(191\) 1.87145e10 1.01748 0.508742 0.860919i \(-0.330111\pi\)
0.508742 + 0.860919i \(0.330111\pi\)
\(192\) 1.13629e10 0.603442
\(193\) 1.45956e10 0.757206 0.378603 0.925559i \(-0.376405\pi\)
0.378603 + 0.925559i \(0.376405\pi\)
\(194\) 5.25972e10 2.66597
\(195\) −1.52671e9 −0.0756137
\(196\) 3.15015e10 1.52468
\(197\) 1.50614e9 0.0712470
\(198\) −4.65129e10 −2.15070
\(199\) −1.01298e10 −0.457893 −0.228947 0.973439i \(-0.573528\pi\)
−0.228947 + 0.973439i \(0.573528\pi\)
\(200\) 6.38388e9 0.282130
\(201\) 2.23402e10 0.965395
\(202\) 2.07808e10 0.878175
\(203\) −1.07224e10 −0.443158
\(204\) 1.14876e10 0.464401
\(205\) 1.47830e10 0.584616
\(206\) −1.56790e10 −0.606618
\(207\) 3.21640e10 1.21760
\(208\) −3.68592e9 −0.136540
\(209\) −5.36201e10 −1.94388
\(210\) −3.35126e10 −1.18911
\(211\) 2.35402e10 0.817596 0.408798 0.912625i \(-0.365948\pi\)
0.408798 + 0.912625i \(0.365948\pi\)
\(212\) −4.41727e10 −1.50191
\(213\) 2.82978e10 0.941985
\(214\) 1.82567e10 0.595059
\(215\) 1.41261e10 0.450869
\(216\) −5.14195e10 −1.60726
\(217\) 2.69110e10 0.823875
\(218\) 6.02908e10 1.80799
\(219\) 1.79599e10 0.527602
\(220\) 1.15288e11 3.31805
\(221\) 2.14263e9 0.0604201
\(222\) 4.97768e9 0.137543
\(223\) −5.35567e10 −1.45025 −0.725123 0.688619i \(-0.758217\pi\)
−0.725123 + 0.688619i \(0.758217\pi\)
\(224\) 3.73399e9 0.0990961
\(225\) 4.35663e9 0.113326
\(226\) −8.18167e10 −2.08619
\(227\) 1.59083e10 0.397655 0.198828 0.980034i \(-0.436287\pi\)
0.198828 + 0.980034i \(0.436287\pi\)
\(228\) −4.84389e10 −1.18710
\(229\) −7.41530e10 −1.78184 −0.890920 0.454160i \(-0.849939\pi\)
−0.890920 + 0.454160i \(0.849939\pi\)
\(230\) −1.20024e11 −2.82808
\(231\) 6.00533e10 1.38766
\(232\) 2.48070e10 0.562183
\(233\) 4.29576e10 0.954857 0.477428 0.878671i \(-0.341569\pi\)
0.477428 + 0.878671i \(0.341569\pi\)
\(234\) −7.83715e9 −0.170878
\(235\) 2.18493e10 0.467340
\(236\) 9.80944e10 2.05845
\(237\) 1.32381e10 0.272558
\(238\) 4.70326e10 0.950172
\(239\) −9.42540e10 −1.86857 −0.934285 0.356527i \(-0.883961\pi\)
−0.934285 + 0.356527i \(0.883961\pi\)
\(240\) 2.48854e10 0.484166
\(241\) 2.19180e10 0.418528 0.209264 0.977859i \(-0.432893\pi\)
0.209264 + 0.977859i \(0.432893\pi\)
\(242\) −2.18952e11 −4.10373
\(243\) −5.60023e10 −1.03033
\(244\) −1.44462e11 −2.60916
\(245\) −3.96687e10 −0.703397
\(246\) −3.60283e10 −0.627243
\(247\) −9.03468e9 −0.154446
\(248\) −6.22605e10 −1.04515
\(249\) 2.75106e10 0.453527
\(250\) −1.13531e11 −1.83816
\(251\) 5.15861e10 0.820354 0.410177 0.912006i \(-0.365467\pi\)
0.410177 + 0.912006i \(0.365467\pi\)
\(252\) −1.14268e11 −1.78494
\(253\) 2.15078e11 3.30030
\(254\) 8.67181e10 1.30725
\(255\) −1.44659e10 −0.214247
\(256\) −1.35747e11 −1.97538
\(257\) 1.40209e10 0.200482 0.100241 0.994963i \(-0.468039\pi\)
0.100241 + 0.994963i \(0.468039\pi\)
\(258\) −3.44274e10 −0.483744
\(259\) 1.35367e10 0.186923
\(260\) 1.94254e10 0.263627
\(261\) 1.69293e10 0.225817
\(262\) −5.54830e10 −0.727452
\(263\) 1.36610e11 1.76068 0.880341 0.474341i \(-0.157314\pi\)
0.880341 + 0.474341i \(0.157314\pi\)
\(264\) −1.38938e11 −1.76036
\(265\) 5.56251e10 0.692890
\(266\) −1.98319e11 −2.42883
\(267\) −2.77903e10 −0.334652
\(268\) −2.84250e11 −3.36585
\(269\) −1.41052e11 −1.64246 −0.821230 0.570597i \(-0.806712\pi\)
−0.821230 + 0.570597i \(0.806712\pi\)
\(270\) 1.30946e11 1.49953
\(271\) 4.91664e10 0.553740 0.276870 0.960907i \(-0.410703\pi\)
0.276870 + 0.960907i \(0.410703\pi\)
\(272\) −3.49249e10 −0.386879
\(273\) 1.01186e10 0.110253
\(274\) 4.68437e10 0.502081
\(275\) 2.91324e10 0.307170
\(276\) 1.94295e11 2.01545
\(277\) 2.96882e10 0.302988 0.151494 0.988458i \(-0.451592\pi\)
0.151494 + 0.988458i \(0.451592\pi\)
\(278\) 8.68451e10 0.872055
\(279\) −4.24893e10 −0.419817
\(280\) 2.10851e11 2.05005
\(281\) 1.85410e11 1.77400 0.887000 0.461769i \(-0.152785\pi\)
0.887000 + 0.461769i \(0.152785\pi\)
\(282\) −5.32499e10 −0.501416
\(283\) 1.87000e11 1.73302 0.866509 0.499162i \(-0.166359\pi\)
0.866509 + 0.499162i \(0.166359\pi\)
\(284\) −3.60052e11 −3.28423
\(285\) 6.09974e10 0.547658
\(286\) −5.24063e10 −0.463166
\(287\) −9.79781e10 −0.852433
\(288\) −5.89552e9 −0.0504958
\(289\) −9.82860e10 −0.828803
\(290\) −6.31736e10 −0.524499
\(291\) 1.07220e11 0.876510
\(292\) −2.28517e11 −1.83948
\(293\) 1.63221e11 1.29381 0.646906 0.762570i \(-0.276063\pi\)
0.646906 + 0.762570i \(0.276063\pi\)
\(294\) 9.66782e10 0.754685
\(295\) −1.23527e11 −0.949647
\(296\) −3.13180e10 −0.237127
\(297\) −2.34650e11 −1.74991
\(298\) −1.93698e11 −1.42283
\(299\) 3.62394e10 0.262217
\(300\) 2.63174e10 0.187585
\(301\) −9.36245e10 −0.657416
\(302\) 7.44685e10 0.515159
\(303\) 4.23619e10 0.288724
\(304\) 1.47266e11 0.988941
\(305\) 1.81916e11 1.20371
\(306\) −7.42588e10 −0.484174
\(307\) −2.46455e11 −1.58349 −0.791744 0.610853i \(-0.790826\pi\)
−0.791744 + 0.610853i \(0.790826\pi\)
\(308\) −7.64100e11 −4.83807
\(309\) −3.19617e10 −0.199442
\(310\) 1.58553e11 0.975097
\(311\) −6.07495e10 −0.368231 −0.184116 0.982905i \(-0.558942\pi\)
−0.184116 + 0.982905i \(0.558942\pi\)
\(312\) −2.34102e10 −0.139865
\(313\) −1.06777e10 −0.0628820 −0.0314410 0.999506i \(-0.510010\pi\)
−0.0314410 + 0.999506i \(0.510010\pi\)
\(314\) −1.43244e9 −0.00831560
\(315\) 1.43894e11 0.823464
\(316\) −1.68438e11 −0.950272
\(317\) 4.35923e9 0.0242462 0.0121231 0.999927i \(-0.496141\pi\)
0.0121231 + 0.999927i \(0.496141\pi\)
\(318\) −1.35566e11 −0.743412
\(319\) 1.13205e11 0.612078
\(320\) 1.82063e11 0.970613
\(321\) 3.72164e10 0.195642
\(322\) 7.95486e11 4.12364
\(323\) −8.56056e10 −0.437614
\(324\) 5.40947e10 0.272711
\(325\) 4.90864e9 0.0244054
\(326\) 5.99837e10 0.294140
\(327\) 1.22903e11 0.594428
\(328\) 2.26679e11 1.08138
\(329\) −1.44812e11 −0.681432
\(330\) 3.53820e11 1.64236
\(331\) −1.15879e11 −0.530614 −0.265307 0.964164i \(-0.585473\pi\)
−0.265307 + 0.964164i \(0.585473\pi\)
\(332\) −3.50037e11 −1.58122
\(333\) −2.13728e10 −0.0952493
\(334\) 3.50219e11 1.53986
\(335\) 3.57946e11 1.55280
\(336\) −1.64934e11 −0.705965
\(337\) 3.02194e11 1.27630 0.638148 0.769914i \(-0.279701\pi\)
0.638148 + 0.769914i \(0.279701\pi\)
\(338\) 4.05266e11 1.68894
\(339\) −1.66784e11 −0.685892
\(340\) 1.84060e11 0.746971
\(341\) −2.84122e11 −1.13791
\(342\) 3.13122e11 1.23764
\(343\) −7.82017e10 −0.305065
\(344\) 2.16607e11 0.833987
\(345\) −2.44669e11 −0.929808
\(346\) 2.05054e11 0.769176
\(347\) 2.99477e11 1.10887 0.554436 0.832226i \(-0.312934\pi\)
0.554436 + 0.832226i \(0.312934\pi\)
\(348\) 1.02266e11 0.373788
\(349\) 3.11765e11 1.12490 0.562448 0.826832i \(-0.309859\pi\)
0.562448 + 0.826832i \(0.309859\pi\)
\(350\) 1.07749e11 0.383802
\(351\) −3.95371e10 −0.139035
\(352\) −3.94228e10 −0.136869
\(353\) 2.58265e11 0.885278 0.442639 0.896700i \(-0.354042\pi\)
0.442639 + 0.896700i \(0.354042\pi\)
\(354\) 3.01052e11 1.01889
\(355\) 4.53401e11 1.51515
\(356\) 3.53596e11 1.16676
\(357\) 9.58763e10 0.312395
\(358\) 1.87384e11 0.602919
\(359\) −2.60364e11 −0.827286 −0.413643 0.910439i \(-0.635744\pi\)
−0.413643 + 0.910439i \(0.635744\pi\)
\(360\) −3.32908e11 −1.04463
\(361\) 3.82798e10 0.118628
\(362\) 5.99503e11 1.83486
\(363\) −4.46335e11 −1.34921
\(364\) −1.28746e11 −0.384396
\(365\) 2.87763e11 0.848627
\(366\) −4.43355e11 −1.29148
\(367\) 1.77047e10 0.0509439 0.0254719 0.999676i \(-0.491891\pi\)
0.0254719 + 0.999676i \(0.491891\pi\)
\(368\) −5.90703e11 −1.67901
\(369\) 1.54696e11 0.434370
\(370\) 7.97548e10 0.221233
\(371\) −3.68669e11 −1.01031
\(372\) −2.56668e11 −0.694909
\(373\) −2.31864e11 −0.620218 −0.310109 0.950701i \(-0.600365\pi\)
−0.310109 + 0.950701i \(0.600365\pi\)
\(374\) −4.96561e11 −1.31235
\(375\) −2.31434e11 −0.604346
\(376\) 3.35032e11 0.864453
\(377\) 1.90744e10 0.0486311
\(378\) −8.67873e11 −2.18647
\(379\) −3.15074e11 −0.784397 −0.392199 0.919881i \(-0.628285\pi\)
−0.392199 + 0.919881i \(0.628285\pi\)
\(380\) −7.76113e11 −1.90941
\(381\) 1.76776e11 0.429793
\(382\) −7.30783e11 −1.75591
\(383\) −5.19998e11 −1.23483 −0.617415 0.786638i \(-0.711820\pi\)
−0.617415 + 0.786638i \(0.711820\pi\)
\(384\) −4.25710e11 −0.999132
\(385\) 9.62204e11 2.23200
\(386\) −5.69945e11 −1.30674
\(387\) 1.47822e11 0.334996
\(388\) −1.36423e12 −3.05595
\(389\) 7.66921e11 1.69816 0.849078 0.528267i \(-0.177158\pi\)
0.849078 + 0.528267i \(0.177158\pi\)
\(390\) 5.96166e10 0.130490
\(391\) 3.43376e11 0.742976
\(392\) −6.08270e11 −1.30110
\(393\) −1.13103e11 −0.239170
\(394\) −5.88133e10 −0.122954
\(395\) 2.12108e11 0.438399
\(396\) 1.20642e12 2.46531
\(397\) 3.62638e11 0.732682 0.366341 0.930481i \(-0.380610\pi\)
0.366341 + 0.930481i \(0.380610\pi\)
\(398\) 3.95561e11 0.790205
\(399\) −4.04275e11 −0.798544
\(400\) −8.00110e10 −0.156272
\(401\) 3.57307e11 0.690068 0.345034 0.938590i \(-0.387867\pi\)
0.345034 + 0.938590i \(0.387867\pi\)
\(402\) −8.72365e11 −1.66602
\(403\) −4.78728e10 −0.0904100
\(404\) −5.39000e11 −1.00664
\(405\) −6.81195e10 −0.125813
\(406\) 4.18699e11 0.764776
\(407\) −1.42918e11 −0.258173
\(408\) −2.21817e11 −0.396299
\(409\) 9.49530e11 1.67785 0.838926 0.544245i \(-0.183184\pi\)
0.838926 + 0.544245i \(0.183184\pi\)
\(410\) −5.77264e11 −1.00890
\(411\) 9.54914e10 0.165073
\(412\) 4.06671e11 0.695354
\(413\) 8.18704e11 1.38469
\(414\) −1.25598e12 −2.10126
\(415\) 4.40788e11 0.729480
\(416\) −6.64251e9 −0.0108746
\(417\) 1.77035e11 0.286712
\(418\) 2.09382e12 3.35464
\(419\) −4.72730e11 −0.749291 −0.374645 0.927168i \(-0.622236\pi\)
−0.374645 + 0.927168i \(0.622236\pi\)
\(420\) 8.69228e11 1.36305
\(421\) −5.33072e11 −0.827021 −0.413511 0.910499i \(-0.635698\pi\)
−0.413511 + 0.910499i \(0.635698\pi\)
\(422\) −9.19223e11 −1.41096
\(423\) 2.28640e11 0.347233
\(424\) 8.52942e11 1.28166
\(425\) 4.65105e10 0.0691513
\(426\) −1.10500e12 −1.62562
\(427\) −1.20569e12 −1.75514
\(428\) −4.73530e11 −0.682105
\(429\) −1.06831e11 −0.152278
\(430\) −5.51613e11 −0.778084
\(431\) −9.22826e11 −1.28817 −0.644084 0.764955i \(-0.722761\pi\)
−0.644084 + 0.764955i \(0.722761\pi\)
\(432\) 6.44456e11 0.890259
\(433\) 1.08108e12 1.47795 0.738976 0.673731i \(-0.235309\pi\)
0.738976 + 0.673731i \(0.235309\pi\)
\(434\) −1.05085e12 −1.42180
\(435\) −1.28780e11 −0.172444
\(436\) −1.56379e12 −2.07247
\(437\) −1.44789e12 −1.89920
\(438\) −7.01319e11 −0.910504
\(439\) 4.65455e11 0.598119 0.299059 0.954235i \(-0.403327\pi\)
0.299059 + 0.954235i \(0.403327\pi\)
\(440\) −2.22613e12 −2.83148
\(441\) −4.15110e11 −0.522624
\(442\) −8.36677e10 −0.104270
\(443\) 8.59536e11 1.06034 0.530172 0.847890i \(-0.322127\pi\)
0.530172 + 0.847890i \(0.322127\pi\)
\(444\) −1.29108e11 −0.157663
\(445\) −4.45271e11 −0.538275
\(446\) 2.09134e12 2.50275
\(447\) −3.94855e11 −0.467793
\(448\) −1.20667e12 −1.41526
\(449\) 9.10060e11 1.05672 0.528362 0.849019i \(-0.322807\pi\)
0.528362 + 0.849019i \(0.322807\pi\)
\(450\) −1.70123e11 −0.195572
\(451\) 1.03444e12 1.17736
\(452\) 2.12211e12 2.39136
\(453\) 1.51805e11 0.169373
\(454\) −6.21204e11 −0.686250
\(455\) 1.62126e11 0.177338
\(456\) 9.35319e11 1.01302
\(457\) 4.94571e11 0.530403 0.265201 0.964193i \(-0.414562\pi\)
0.265201 + 0.964193i \(0.414562\pi\)
\(458\) 2.89561e12 3.07500
\(459\) −3.74623e11 −0.393946
\(460\) 3.11310e12 3.24177
\(461\) 1.03892e12 1.07134 0.535670 0.844428i \(-0.320059\pi\)
0.535670 + 0.844428i \(0.320059\pi\)
\(462\) −2.34503e12 −2.39474
\(463\) −5.14038e11 −0.519853 −0.259926 0.965628i \(-0.583698\pi\)
−0.259926 + 0.965628i \(0.583698\pi\)
\(464\) −3.10913e11 −0.311392
\(465\) 3.23212e11 0.320590
\(466\) −1.67745e12 −1.64784
\(467\) 8.14302e11 0.792245 0.396123 0.918198i \(-0.370355\pi\)
0.396123 + 0.918198i \(0.370355\pi\)
\(468\) 2.03275e11 0.195875
\(469\) −2.37238e12 −2.26415
\(470\) −8.53197e11 −0.806508
\(471\) −2.92005e9 −0.00273398
\(472\) −1.89413e12 −1.75659
\(473\) 9.88470e11 0.908006
\(474\) −5.16936e11 −0.470365
\(475\) −1.96118e11 −0.176765
\(476\) −1.21990e12 −1.08916
\(477\) 5.82084e11 0.514817
\(478\) 3.68053e12 3.22467
\(479\) 1.58296e12 1.37391 0.686956 0.726699i \(-0.258946\pi\)
0.686956 + 0.726699i \(0.258946\pi\)
\(480\) 4.48467e10 0.0385607
\(481\) −2.40808e10 −0.0205125
\(482\) −8.55878e11 −0.722271
\(483\) 1.62160e12 1.35576
\(484\) 5.67903e12 4.70403
\(485\) 1.71793e12 1.40983
\(486\) 2.18684e12 1.77809
\(487\) −1.51814e12 −1.22302 −0.611508 0.791238i \(-0.709437\pi\)
−0.611508 + 0.791238i \(0.709437\pi\)
\(488\) 2.78946e12 2.22654
\(489\) 1.22277e11 0.0967065
\(490\) 1.54903e12 1.21388
\(491\) −2.12449e12 −1.64963 −0.824817 0.565400i \(-0.808722\pi\)
−0.824817 + 0.565400i \(0.808722\pi\)
\(492\) 9.34480e11 0.718997
\(493\) 1.80734e11 0.137793
\(494\) 3.52796e11 0.266534
\(495\) −1.51920e12 −1.13735
\(496\) 7.80329e11 0.578909
\(497\) −3.00503e12 −2.20925
\(498\) −1.07426e12 −0.782670
\(499\) 1.94053e12 1.40109 0.700547 0.713606i \(-0.252939\pi\)
0.700547 + 0.713606i \(0.252939\pi\)
\(500\) 2.94469e12 2.10705
\(501\) 7.13925e11 0.506271
\(502\) −2.01439e12 −1.41572
\(503\) −3.37063e11 −0.234777 −0.117388 0.993086i \(-0.537452\pi\)
−0.117388 + 0.993086i \(0.537452\pi\)
\(504\) 2.20643e12 1.52319
\(505\) 6.78743e11 0.464402
\(506\) −8.39860e12 −5.69547
\(507\) 8.26138e11 0.555286
\(508\) −2.24924e12 −1.49847
\(509\) −1.68624e12 −1.11350 −0.556748 0.830681i \(-0.687951\pi\)
−0.556748 + 0.830681i \(0.687951\pi\)
\(510\) 5.64880e11 0.369735
\(511\) −1.90722e12 −1.23739
\(512\) 2.56264e12 1.64806
\(513\) 1.57965e12 1.00701
\(514\) −5.47502e11 −0.345981
\(515\) −5.12107e11 −0.320795
\(516\) 8.92957e11 0.554507
\(517\) 1.52890e12 0.941176
\(518\) −5.28595e11 −0.322581
\(519\) 4.18004e11 0.252888
\(520\) −3.75089e11 −0.224968
\(521\) 1.78643e12 1.06223 0.531113 0.847301i \(-0.321774\pi\)
0.531113 + 0.847301i \(0.321774\pi\)
\(522\) −6.61075e11 −0.389703
\(523\) −2.70264e11 −0.157954 −0.0789769 0.996876i \(-0.525165\pi\)
−0.0789769 + 0.996876i \(0.525165\pi\)
\(524\) 1.43908e12 0.833865
\(525\) 2.19647e11 0.126185
\(526\) −5.33449e12 −3.03848
\(527\) −4.53606e11 −0.256172
\(528\) 1.74134e12 0.975061
\(529\) 4.00655e12 2.22444
\(530\) −2.17211e12 −1.19575
\(531\) −1.29263e12 −0.705587
\(532\) 5.14388e12 2.78412
\(533\) 1.74296e11 0.0935440
\(534\) 1.08519e12 0.577522
\(535\) 5.96300e11 0.314683
\(536\) 5.48866e12 2.87227
\(537\) 3.81984e11 0.198226
\(538\) 5.50797e12 2.83446
\(539\) −2.77580e12 −1.41657
\(540\) −3.39638e12 −1.71888
\(541\) 2.30383e12 1.15628 0.578139 0.815938i \(-0.303779\pi\)
0.578139 + 0.815938i \(0.303779\pi\)
\(542\) −1.91990e12 −0.955613
\(543\) 1.22209e12 0.603261
\(544\) −6.29392e10 −0.0308125
\(545\) 1.96922e12 0.956114
\(546\) −3.95123e11 −0.190268
\(547\) 3.70350e12 1.76876 0.884380 0.466767i \(-0.154581\pi\)
0.884380 + 0.466767i \(0.154581\pi\)
\(548\) −1.21500e12 −0.575526
\(549\) 1.90365e12 0.894357
\(550\) −1.13759e12 −0.530097
\(551\) −7.62088e11 −0.352227
\(552\) −3.75170e12 −1.71990
\(553\) −1.40580e12 −0.639233
\(554\) −1.15930e12 −0.522878
\(555\) 1.62581e11 0.0727363
\(556\) −2.25254e12 −0.999621
\(557\) −8.74013e11 −0.384742 −0.192371 0.981322i \(-0.561618\pi\)
−0.192371 + 0.981322i \(0.561618\pi\)
\(558\) 1.65917e12 0.724496
\(559\) 1.66552e11 0.0721432
\(560\) −2.64266e12 −1.13552
\(561\) −1.01224e12 −0.431472
\(562\) −7.24007e12 −3.06147
\(563\) −1.02727e12 −0.430921 −0.215461 0.976513i \(-0.569125\pi\)
−0.215461 + 0.976513i \(0.569125\pi\)
\(564\) 1.38116e12 0.574763
\(565\) −2.67230e12 −1.10323
\(566\) −7.30218e12 −2.99074
\(567\) 4.51479e11 0.183448
\(568\) 6.95234e12 2.80261
\(569\) −1.21328e12 −0.485238 −0.242619 0.970122i \(-0.578006\pi\)
−0.242619 + 0.970122i \(0.578006\pi\)
\(570\) −2.38189e12 −0.945117
\(571\) −8.45365e11 −0.332799 −0.166399 0.986058i \(-0.553214\pi\)
−0.166399 + 0.986058i \(0.553214\pi\)
\(572\) 1.35928e12 0.530918
\(573\) −1.48971e12 −0.577305
\(574\) 3.82596e12 1.47108
\(575\) 7.86656e11 0.300109
\(576\) 1.90518e12 0.721165
\(577\) 7.88912e11 0.296304 0.148152 0.988965i \(-0.452668\pi\)
0.148152 + 0.988965i \(0.452668\pi\)
\(578\) 3.83798e12 1.43030
\(579\) −1.16184e12 −0.429627
\(580\) 1.63856e12 0.601224
\(581\) −2.92143e12 −1.06366
\(582\) −4.18684e12 −1.51263
\(583\) 3.89234e12 1.39541
\(584\) 4.41249e12 1.56973
\(585\) −2.55977e11 −0.0903649
\(586\) −6.37362e12 −2.23279
\(587\) −3.62250e12 −1.25932 −0.629661 0.776870i \(-0.716806\pi\)
−0.629661 + 0.776870i \(0.716806\pi\)
\(588\) −2.50758e12 −0.865081
\(589\) 1.91269e12 0.654826
\(590\) 4.82361e12 1.63885
\(591\) −1.19891e11 −0.0404245
\(592\) 3.92518e11 0.131344
\(593\) −3.87408e12 −1.28654 −0.643269 0.765640i \(-0.722422\pi\)
−0.643269 + 0.765640i \(0.722422\pi\)
\(594\) 9.16285e12 3.01989
\(595\) 1.53618e12 0.502476
\(596\) 5.02402e12 1.63096
\(597\) 8.06355e11 0.259802
\(598\) −1.41511e12 −0.452519
\(599\) 2.34043e12 0.742805 0.371402 0.928472i \(-0.378877\pi\)
0.371402 + 0.928472i \(0.378877\pi\)
\(600\) −5.08169e11 −0.160077
\(601\) −4.41644e12 −1.38082 −0.690410 0.723418i \(-0.742570\pi\)
−0.690410 + 0.723418i \(0.742570\pi\)
\(602\) 3.65595e12 1.13453
\(603\) 3.74570e12 1.15373
\(604\) −1.93152e12 −0.590518
\(605\) −7.15140e12 −2.17016
\(606\) −1.65419e12 −0.498264
\(607\) 1.79254e12 0.535943 0.267972 0.963427i \(-0.413647\pi\)
0.267972 + 0.963427i \(0.413647\pi\)
\(608\) 2.65392e11 0.0787628
\(609\) 8.53521e11 0.251441
\(610\) −7.10366e12 −2.07729
\(611\) 2.57610e11 0.0747787
\(612\) 1.92608e12 0.554999
\(613\) 8.04928e11 0.230242 0.115121 0.993351i \(-0.463274\pi\)
0.115121 + 0.993351i \(0.463274\pi\)
\(614\) 9.62384e12 2.73269
\(615\) −1.17676e12 −0.331703
\(616\) 1.47542e13 4.12860
\(617\) −6.31640e12 −1.75463 −0.877317 0.479911i \(-0.840669\pi\)
−0.877317 + 0.479911i \(0.840669\pi\)
\(618\) 1.24808e12 0.344186
\(619\) −5.48930e12 −1.50283 −0.751413 0.659832i \(-0.770628\pi\)
−0.751413 + 0.659832i \(0.770628\pi\)
\(620\) −4.11246e12 −1.11773
\(621\) −6.33619e12 −1.70968
\(622\) 2.37221e12 0.635473
\(623\) 2.95114e12 0.784862
\(624\) 2.93406e11 0.0774709
\(625\) −3.07060e12 −0.804939
\(626\) 4.16953e11 0.108518
\(627\) 4.26826e12 1.10293
\(628\) 3.71538e10 0.00953202
\(629\) −2.28171e11 −0.0581209
\(630\) −5.61892e12 −1.42109
\(631\) −3.02802e12 −0.760373 −0.380186 0.924910i \(-0.624140\pi\)
−0.380186 + 0.924910i \(0.624140\pi\)
\(632\) 3.25241e12 0.810920
\(633\) −1.87384e12 −0.463892
\(634\) −1.70224e11 −0.0418427
\(635\) 2.83239e12 0.691307
\(636\) 3.51623e12 0.852159
\(637\) −4.67706e11 −0.112550
\(638\) −4.42055e12 −1.05629
\(639\) 4.74457e12 1.12575
\(640\) −6.82093e12 −1.60707
\(641\) −7.28464e12 −1.70430 −0.852152 0.523294i \(-0.824703\pi\)
−0.852152 + 0.523294i \(0.824703\pi\)
\(642\) −1.45327e12 −0.337627
\(643\) 4.15435e12 0.958415 0.479207 0.877702i \(-0.340924\pi\)
0.479207 + 0.877702i \(0.340924\pi\)
\(644\) −2.06328e13 −4.72685
\(645\) −1.12447e12 −0.255816
\(646\) 3.34282e12 0.755208
\(647\) 4.98496e12 1.11839 0.559194 0.829037i \(-0.311111\pi\)
0.559194 + 0.829037i \(0.311111\pi\)
\(648\) −1.04453e12 −0.232719
\(649\) −8.64373e12 −1.91249
\(650\) −1.91678e11 −0.0421174
\(651\) −2.14217e12 −0.467454
\(652\) −1.55582e12 −0.337167
\(653\) 2.92509e12 0.629550 0.314775 0.949166i \(-0.398071\pi\)
0.314775 + 0.949166i \(0.398071\pi\)
\(654\) −4.79926e12 −1.02583
\(655\) −1.81219e12 −0.384696
\(656\) −2.84104e12 −0.598976
\(657\) 3.01127e12 0.630530
\(658\) 5.65477e12 1.17598
\(659\) 8.90371e11 0.183902 0.0919510 0.995764i \(-0.470690\pi\)
0.0919510 + 0.995764i \(0.470690\pi\)
\(660\) −9.17716e12 −1.88261
\(661\) −4.27530e12 −0.871084 −0.435542 0.900168i \(-0.643443\pi\)
−0.435542 + 0.900168i \(0.643443\pi\)
\(662\) 4.52497e12 0.915703
\(663\) −1.70557e11 −0.0342815
\(664\) 6.75894e12 1.34934
\(665\) −6.47750e12 −1.28443
\(666\) 8.34587e11 0.164376
\(667\) 3.05684e12 0.598008
\(668\) −9.08377e12 −1.76511
\(669\) 4.26321e12 0.822848
\(670\) −1.39775e13 −2.67974
\(671\) 1.27295e13 2.42415
\(672\) −2.97232e11 −0.0562257
\(673\) 3.41372e12 0.641445 0.320723 0.947173i \(-0.396074\pi\)
0.320723 + 0.947173i \(0.396074\pi\)
\(674\) −1.18004e13 −2.20256
\(675\) −8.58239e11 −0.159126
\(676\) −1.05115e13 −1.93600
\(677\) 4.27690e11 0.0782492 0.0391246 0.999234i \(-0.487543\pi\)
0.0391246 + 0.999234i \(0.487543\pi\)
\(678\) 6.51277e12 1.18367
\(679\) −1.13860e13 −2.05569
\(680\) −3.55406e12 −0.637433
\(681\) −1.26633e12 −0.225624
\(682\) 1.10947e13 1.96375
\(683\) 8.79939e12 1.54725 0.773623 0.633647i \(-0.218443\pi\)
0.773623 + 0.633647i \(0.218443\pi\)
\(684\) −8.12156e12 −1.41869
\(685\) 1.53001e12 0.265514
\(686\) 3.05371e12 0.526464
\(687\) 5.90272e12 1.01099
\(688\) −2.71480e12 −0.461944
\(689\) 6.55837e11 0.110869
\(690\) 9.55411e12 1.60461
\(691\) −6.74731e12 −1.12585 −0.562924 0.826509i \(-0.690324\pi\)
−0.562924 + 0.826509i \(0.690324\pi\)
\(692\) −5.31856e12 −0.881692
\(693\) 1.00689e13 1.65837
\(694\) −1.16943e13 −1.91363
\(695\) 2.83654e12 0.461166
\(696\) −1.97468e12 −0.318974
\(697\) 1.65150e12 0.265052
\(698\) −1.21741e13 −1.94128
\(699\) −3.41951e12 −0.541772
\(700\) −2.79472e12 −0.439945
\(701\) −8.83497e12 −1.38189 −0.690946 0.722907i \(-0.742806\pi\)
−0.690946 + 0.722907i \(0.742806\pi\)
\(702\) 1.54389e12 0.239938
\(703\) 9.62114e11 0.148569
\(704\) 1.27398e13 1.95472
\(705\) −1.73925e12 −0.265162
\(706\) −1.00850e13 −1.52776
\(707\) −4.49853e12 −0.677148
\(708\) −7.80850e12 −1.16793
\(709\) 7.92256e12 1.17749 0.588745 0.808318i \(-0.299622\pi\)
0.588745 + 0.808318i \(0.299622\pi\)
\(710\) −1.77049e13 −2.61475
\(711\) 2.21958e12 0.325730
\(712\) −6.82767e12 −0.995663
\(713\) −7.67207e12 −1.11176
\(714\) −3.74388e12 −0.539113
\(715\) −1.71169e12 −0.244934
\(716\) −4.86025e12 −0.691115
\(717\) 7.50280e12 1.06020
\(718\) 1.01670e13 1.42768
\(719\) −7.51488e12 −1.04868 −0.524339 0.851510i \(-0.675687\pi\)
−0.524339 + 0.851510i \(0.675687\pi\)
\(720\) 4.17244e12 0.578620
\(721\) 3.39411e12 0.467754
\(722\) −1.49479e12 −0.204721
\(723\) −1.74472e12 −0.237466
\(724\) −1.55495e13 −2.10327
\(725\) 4.14051e11 0.0556587
\(726\) 1.74290e13 2.32840
\(727\) −1.01859e13 −1.35237 −0.676185 0.736732i \(-0.736368\pi\)
−0.676185 + 0.736732i \(0.736368\pi\)
\(728\) 2.48600e12 0.328027
\(729\) 3.40663e12 0.446737
\(730\) −1.12369e13 −1.46451
\(731\) 1.57811e12 0.204414
\(732\) 1.14995e13 1.48040
\(733\) 2.12333e12 0.271675 0.135837 0.990731i \(-0.456628\pi\)
0.135837 + 0.990731i \(0.456628\pi\)
\(734\) −6.91354e11 −0.0879160
\(735\) 3.15771e12 0.399097
\(736\) −1.06452e12 −0.133723
\(737\) 2.50471e13 3.12719
\(738\) −6.04072e12 −0.749610
\(739\) 3.80150e12 0.468873 0.234436 0.972131i \(-0.424676\pi\)
0.234436 + 0.972131i \(0.424676\pi\)
\(740\) −2.06863e12 −0.253595
\(741\) 7.19178e11 0.0876303
\(742\) 1.43962e13 1.74353
\(743\) −5.70236e12 −0.686444 −0.343222 0.939254i \(-0.611518\pi\)
−0.343222 + 0.939254i \(0.611518\pi\)
\(744\) 4.95606e12 0.593005
\(745\) −6.32657e12 −0.752428
\(746\) 9.05409e12 1.07034
\(747\) 4.61259e12 0.542004
\(748\) 1.28795e13 1.50433
\(749\) −3.95212e12 −0.458841
\(750\) 9.03727e12 1.04295
\(751\) 1.51873e13 1.74221 0.871103 0.491100i \(-0.163405\pi\)
0.871103 + 0.491100i \(0.163405\pi\)
\(752\) −4.19906e12 −0.478819
\(753\) −4.10635e12 −0.465456
\(754\) −7.44836e11 −0.0839247
\(755\) 2.43229e12 0.272430
\(756\) 2.25104e13 2.50631
\(757\) −5.88356e12 −0.651192 −0.325596 0.945509i \(-0.605565\pi\)
−0.325596 + 0.945509i \(0.605565\pi\)
\(758\) 1.23033e13 1.35367
\(759\) −1.71206e13 −1.87254
\(760\) 1.49862e13 1.62940
\(761\) −1.54838e12 −0.167358 −0.0836791 0.996493i \(-0.526667\pi\)
−0.0836791 + 0.996493i \(0.526667\pi\)
\(762\) −6.90292e12 −0.741713
\(763\) −1.30515e13 −1.39412
\(764\) 1.89546e13 2.01277
\(765\) −2.42544e12 −0.256044
\(766\) 2.03054e13 2.13100
\(767\) −1.45642e12 −0.151952
\(768\) 1.08057e13 1.12080
\(769\) −1.67793e13 −1.73024 −0.865119 0.501567i \(-0.832757\pi\)
−0.865119 + 0.501567i \(0.832757\pi\)
\(770\) −3.75732e13 −3.85185
\(771\) −1.11609e12 −0.113751
\(772\) 1.47829e13 1.49789
\(773\) 1.30862e13 1.31827 0.659135 0.752025i \(-0.270923\pi\)
0.659135 + 0.752025i \(0.270923\pi\)
\(774\) −5.77231e12 −0.578116
\(775\) −1.03919e12 −0.103475
\(776\) 2.63423e13 2.60781
\(777\) −1.07754e12 −0.106057
\(778\) −2.99476e13 −2.93058
\(779\) −6.96376e12 −0.677525
\(780\) −1.54630e12 −0.149578
\(781\) 3.17265e13 3.05136
\(782\) −1.34085e13 −1.28219
\(783\) −3.33501e12 −0.317080
\(784\) 7.62363e12 0.720675
\(785\) −4.67865e10 −0.00439751
\(786\) 4.41656e12 0.412745
\(787\) 1.29789e13 1.20601 0.603007 0.797736i \(-0.293969\pi\)
0.603007 + 0.797736i \(0.293969\pi\)
\(788\) 1.52546e12 0.140940
\(789\) −1.08744e13 −0.998985
\(790\) −8.28262e12 −0.756564
\(791\) 1.77113e13 1.60863
\(792\) −2.32951e13 −2.10378
\(793\) 2.14485e12 0.192605
\(794\) −1.41607e13 −1.26442
\(795\) −4.42786e12 −0.393135
\(796\) −1.02598e13 −0.905798
\(797\) −1.21803e13 −1.06929 −0.534643 0.845078i \(-0.679554\pi\)
−0.534643 + 0.845078i \(0.679554\pi\)
\(798\) 1.57866e13 1.37808
\(799\) 2.44092e12 0.211881
\(800\) −1.44190e11 −0.0124460
\(801\) −4.65949e12 −0.399938
\(802\) −1.39525e13 −1.19088
\(803\) 2.01361e13 1.70905
\(804\) 2.26269e13 1.90973
\(805\) 2.59822e13 2.18069
\(806\) 1.86939e12 0.156024
\(807\) 1.12280e13 0.931908
\(808\) 1.04077e13 0.859019
\(809\) −2.09872e13 −1.72260 −0.861301 0.508094i \(-0.830350\pi\)
−0.861301 + 0.508094i \(0.830350\pi\)
\(810\) 2.66001e12 0.217120
\(811\) 1.43158e12 0.116204 0.0581022 0.998311i \(-0.481495\pi\)
0.0581022 + 0.998311i \(0.481495\pi\)
\(812\) −1.08599e13 −0.876649
\(813\) −3.91374e12 −0.314184
\(814\) 5.58081e12 0.445540
\(815\) 1.95919e12 0.155549
\(816\) 2.78009e12 0.219509
\(817\) −6.65432e12 −0.522522
\(818\) −3.70783e13 −2.89554
\(819\) 1.69655e12 0.131762
\(820\) 1.49727e13 1.15648
\(821\) 1.83664e13 1.41085 0.705424 0.708786i \(-0.250757\pi\)
0.705424 + 0.708786i \(0.250757\pi\)
\(822\) −3.72885e12 −0.284873
\(823\) 1.70966e13 1.29900 0.649501 0.760361i \(-0.274978\pi\)
0.649501 + 0.760361i \(0.274978\pi\)
\(824\) −7.85252e12 −0.593385
\(825\) −2.31899e12 −0.174284
\(826\) −3.19696e13 −2.38961
\(827\) −1.72326e12 −0.128108 −0.0640541 0.997946i \(-0.520403\pi\)
−0.0640541 + 0.997946i \(0.520403\pi\)
\(828\) 3.25767e13 2.40864
\(829\) −5.63109e12 −0.414093 −0.207046 0.978331i \(-0.566385\pi\)
−0.207046 + 0.978331i \(0.566385\pi\)
\(830\) −1.72124e13 −1.25890
\(831\) −2.36324e12 −0.171911
\(832\) 2.14658e12 0.155307
\(833\) −4.43162e12 −0.318904
\(834\) −6.91304e12 −0.494791
\(835\) 1.14389e13 0.814318
\(836\) −5.43081e13 −3.84536
\(837\) 8.37021e12 0.589484
\(838\) 1.84597e13 1.29308
\(839\) 4.57522e12 0.318775 0.159387 0.987216i \(-0.449048\pi\)
0.159387 + 0.987216i \(0.449048\pi\)
\(840\) −1.67841e13 −1.16317
\(841\) −1.28982e13 −0.889093
\(842\) 2.08160e13 1.42723
\(843\) −1.47590e13 −1.00654
\(844\) 2.38422e13 1.61736
\(845\) 1.32368e13 0.893157
\(846\) −8.92820e12 −0.599235
\(847\) 4.73976e13 3.16433
\(848\) −1.06902e13 −0.709909
\(849\) −1.48856e13 −0.983288
\(850\) −1.81619e12 −0.119337
\(851\) −3.85917e12 −0.252238
\(852\) 2.86609e13 1.86342
\(853\) 2.11280e13 1.36643 0.683216 0.730217i \(-0.260581\pi\)
0.683216 + 0.730217i \(0.260581\pi\)
\(854\) 4.70813e13 3.02892
\(855\) 1.02272e13 0.654499
\(856\) 9.14351e12 0.582078
\(857\) −2.25888e13 −1.43047 −0.715236 0.698883i \(-0.753681\pi\)
−0.715236 + 0.698883i \(0.753681\pi\)
\(858\) 4.17164e12 0.262793
\(859\) 4.85641e12 0.304331 0.152165 0.988355i \(-0.451375\pi\)
0.152165 + 0.988355i \(0.451375\pi\)
\(860\) 1.43074e13 0.891903
\(861\) 7.79924e12 0.483658
\(862\) 3.60355e13 2.22304
\(863\) −1.98231e13 −1.21653 −0.608265 0.793734i \(-0.708134\pi\)
−0.608265 + 0.793734i \(0.708134\pi\)
\(864\) 1.16139e12 0.0709035
\(865\) 6.69747e12 0.406760
\(866\) −4.22150e13 −2.55057
\(867\) 7.82375e12 0.470250
\(868\) 2.72563e13 1.62978
\(869\) 1.48421e13 0.882892
\(870\) 5.02874e12 0.297593
\(871\) 4.22029e12 0.248463
\(872\) 3.01955e13 1.76855
\(873\) 1.79771e13 1.04751
\(874\) 5.65389e13 3.27752
\(875\) 2.45766e13 1.41738
\(876\) 1.81904e13 1.04369
\(877\) 2.66447e13 1.52094 0.760470 0.649373i \(-0.224968\pi\)
0.760470 + 0.649373i \(0.224968\pi\)
\(878\) −1.81756e13 −1.03220
\(879\) −1.29927e13 −0.734089
\(880\) 2.79007e13 1.56835
\(881\) −1.95120e13 −1.09121 −0.545606 0.838042i \(-0.683701\pi\)
−0.545606 + 0.838042i \(0.683701\pi\)
\(882\) 1.62097e13 0.901914
\(883\) −2.04432e13 −1.13169 −0.565843 0.824513i \(-0.691449\pi\)
−0.565843 + 0.824513i \(0.691449\pi\)
\(884\) 2.17012e12 0.119522
\(885\) 9.83297e12 0.538815
\(886\) −3.35641e13 −1.82988
\(887\) 1.17863e13 0.639327 0.319663 0.947531i \(-0.396430\pi\)
0.319663 + 0.947531i \(0.396430\pi\)
\(888\) 2.49298e12 0.134543
\(889\) −1.87723e13 −1.00800
\(890\) 1.73874e13 0.928923
\(891\) −4.76663e12 −0.253374
\(892\) −5.42439e13 −2.86886
\(893\) −1.02924e13 −0.541610
\(894\) 1.54187e13 0.807291
\(895\) 6.12034e12 0.318839
\(896\) 4.52074e13 2.34328
\(897\) −2.88472e12 −0.148778
\(898\) −3.55370e13 −1.82363
\(899\) −4.03814e12 −0.206188
\(900\) 4.41254e12 0.224180
\(901\) 6.21420e12 0.314140
\(902\) −4.03938e13 −2.03182
\(903\) 7.45269e12 0.373008
\(904\) −4.09764e13 −2.04068
\(905\) 1.95810e13 0.970322
\(906\) −5.92784e12 −0.292294
\(907\) 1.15261e13 0.565521 0.282761 0.959191i \(-0.408750\pi\)
0.282761 + 0.959191i \(0.408750\pi\)
\(908\) 1.61124e13 0.786636
\(909\) 7.10265e12 0.345050
\(910\) −6.33086e12 −0.306039
\(911\) −2.35555e13 −1.13308 −0.566539 0.824035i \(-0.691718\pi\)
−0.566539 + 0.824035i \(0.691718\pi\)
\(912\) −1.17226e13 −0.561110
\(913\) 3.08440e13 1.46910
\(914\) −1.93125e13 −0.915338
\(915\) −1.44809e13 −0.682968
\(916\) −7.51044e13 −3.52481
\(917\) 1.20107e13 0.560928
\(918\) 1.46287e13 0.679850
\(919\) 2.09257e13 0.967744 0.483872 0.875139i \(-0.339230\pi\)
0.483872 + 0.875139i \(0.339230\pi\)
\(920\) −6.01116e13 −2.76639
\(921\) 1.96183e13 0.898447
\(922\) −4.05688e13 −1.84886
\(923\) 5.34573e12 0.242437
\(924\) 6.08238e13 2.74505
\(925\) −5.22727e11 −0.0234767
\(926\) 2.00727e13 0.897132
\(927\) −5.35889e12 −0.238351
\(928\) −5.60305e11 −0.0248004
\(929\) −3.80942e13 −1.67799 −0.838993 0.544143i \(-0.816855\pi\)
−0.838993 + 0.544143i \(0.816855\pi\)
\(930\) −1.26211e13 −0.553255
\(931\) 1.86865e13 0.815183
\(932\) 4.35088e13 1.88888
\(933\) 4.83578e12 0.208929
\(934\) −3.17978e13 −1.36721
\(935\) −1.62187e13 −0.694007
\(936\) −3.92509e12 −0.167151
\(937\) −4.31602e13 −1.82917 −0.914587 0.404390i \(-0.867484\pi\)
−0.914587 + 0.404390i \(0.867484\pi\)
\(938\) 9.26391e13 3.90734
\(939\) 8.49962e11 0.0356783
\(940\) 2.21297e13 0.924486
\(941\) −4.21804e13 −1.75371 −0.876853 0.480758i \(-0.840362\pi\)
−0.876853 + 0.480758i \(0.840362\pi\)
\(942\) 1.14025e11 0.00471815
\(943\) 2.79326e13 1.15029
\(944\) 2.37397e13 0.972972
\(945\) −2.83465e13 −1.15626
\(946\) −3.85989e13 −1.56698
\(947\) 3.96137e13 1.60055 0.800277 0.599631i \(-0.204686\pi\)
0.800277 + 0.599631i \(0.204686\pi\)
\(948\) 1.34080e13 0.539170
\(949\) 3.39281e12 0.135788
\(950\) 7.65821e12 0.305050
\(951\) −3.47003e11 −0.0137569
\(952\) 2.35554e13 0.929445
\(953\) −4.14491e13 −1.62778 −0.813892 0.581016i \(-0.802655\pi\)
−0.813892 + 0.581016i \(0.802655\pi\)
\(954\) −2.27298e13 −0.888441
\(955\) −2.38688e13 −0.928573
\(956\) −9.54634e13 −3.69638
\(957\) −9.01132e12 −0.347284
\(958\) −6.18130e13 −2.37102
\(959\) −1.01405e13 −0.387148
\(960\) −1.44925e13 −0.550711
\(961\) −1.63047e13 −0.616676
\(962\) 9.40334e11 0.0353993
\(963\) 6.23993e12 0.233809
\(964\) 2.21992e13 0.827926
\(965\) −1.86155e13 −0.691039
\(966\) −6.33222e13 −2.33969
\(967\) −1.93142e13 −0.710326 −0.355163 0.934804i \(-0.615575\pi\)
−0.355163 + 0.934804i \(0.615575\pi\)
\(968\) −1.09658e14 −4.01421
\(969\) 6.81437e12 0.248295
\(970\) −6.70836e13 −2.43301
\(971\) −8.57087e12 −0.309413 −0.154706 0.987960i \(-0.549443\pi\)
−0.154706 + 0.987960i \(0.549443\pi\)
\(972\) −5.67209e13 −2.03819
\(973\) −1.87998e13 −0.672429
\(974\) 5.92821e13 2.11061
\(975\) −3.90737e11 −0.0138473
\(976\) −3.49611e13 −1.23328
\(977\) −1.39653e13 −0.490373 −0.245186 0.969476i \(-0.578849\pi\)
−0.245186 + 0.969476i \(0.578849\pi\)
\(978\) −4.77482e12 −0.166891
\(979\) −3.11576e13 −1.08403
\(980\) −4.01777e13 −1.39145
\(981\) 2.06067e13 0.710392
\(982\) 8.29593e13 2.84684
\(983\) −1.91478e13 −0.654074 −0.327037 0.945011i \(-0.606050\pi\)
−0.327037 + 0.945011i \(0.606050\pi\)
\(984\) −1.80441e13 −0.613561
\(985\) −1.92096e12 −0.0650213
\(986\) −7.05749e12 −0.237796
\(987\) 1.15273e13 0.386634
\(988\) −9.15061e12 −0.305523
\(989\) 2.66914e13 0.887133
\(990\) 5.93235e13 1.96277
\(991\) 3.97256e12 0.130840 0.0654199 0.997858i \(-0.479161\pi\)
0.0654199 + 0.997858i \(0.479161\pi\)
\(992\) 1.40625e12 0.0461064
\(993\) 9.22419e12 0.301062
\(994\) 1.17343e14 3.81259
\(995\) 1.29198e13 0.417881
\(996\) 2.78636e13 0.897160
\(997\) 4.96779e13 1.59234 0.796169 0.605074i \(-0.206857\pi\)
0.796169 + 0.605074i \(0.206857\pi\)
\(998\) −7.57759e13 −2.41793
\(999\) 4.21035e12 0.133744
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 197.10.a.b.1.6 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.b.1.6 76 1.1 even 1 trivial