LMFDB - Embedded newform 47.20.a.b.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,20,Mod(1,47)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 20, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	47.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:	$107.543847381$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1378.66 q^{2} -65581.5 q^{3} +1.37642e6 q^{4} +424075. q^{5} -9.04146e7 q^{6} +1.78101e8 q^{7} +1.17480e9 q^{8} +3.13867e9 q^{9} +O(q^{10})$	\(q+1378.66 q^{2} -65581.5 q^{3} +1.37642e6 q^{4} +424075. q^{5} -9.04146e7 q^{6} +1.78101e8 q^{7} +1.17480e9 q^{8} +3.13867e9 q^{9} +5.84655e8 q^{10} +7.30177e9 q^{11} -9.02675e10 q^{12} -1.82024e10 q^{13} +2.45541e11 q^{14} -2.78115e10 q^{15} +8.98006e11 q^{16} +3.33160e11 q^{17} +4.32716e12 q^{18} -1.98748e12 q^{19} +5.83704e11 q^{20} -1.16801e13 q^{21} +1.00667e13 q^{22} +1.72153e12 q^{23} -7.70449e13 q^{24} -1.88936e13 q^{25} -2.50949e13 q^{26} -1.29616e14 q^{27} +2.45141e14 q^{28} +1.44143e14 q^{29} -3.83426e13 q^{30} -4.90667e13 q^{31} +6.22114e14 q^{32} -4.78861e14 q^{33} +4.59314e14 q^{34} +7.55282e13 q^{35} +4.32012e15 q^{36} -4.98837e14 q^{37} -2.74006e15 q^{38} +1.19374e15 q^{39} +4.98201e14 q^{40} +2.69630e15 q^{41} -1.61029e16 q^{42} +4.81541e15 q^{43} +1.00503e16 q^{44} +1.33103e15 q^{45} +2.37341e15 q^{46} -1.11913e15 q^{47} -5.88926e16 q^{48} +2.03211e16 q^{49} -2.60479e16 q^{50} -2.18491e16 q^{51} -2.50540e16 q^{52} -1.00709e16 q^{53} -1.78696e17 q^{54} +3.09650e15 q^{55} +2.09232e17 q^{56} +1.30342e17 q^{57} +1.98725e17 q^{58} -8.64139e15 q^{59} -3.82802e16 q^{60} -1.69693e16 q^{61} -6.76464e16 q^{62} +5.59001e17 q^{63} +3.86870e17 q^{64} -7.71916e15 q^{65} -6.60187e17 q^{66} -1.72013e17 q^{67} +4.58566e17 q^{68} -1.12901e17 q^{69} +1.04128e17 q^{70} +2.86373e17 q^{71} +3.68730e18 q^{72} -3.42186e17 q^{73} -6.87727e17 q^{74} +1.23907e18 q^{75} -2.73560e18 q^{76} +1.30045e18 q^{77} +1.64576e18 q^{78} -2.87821e17 q^{79} +3.80822e17 q^{80} +4.85245e18 q^{81} +3.71729e18 q^{82} +1.55719e18 q^{83} -1.60767e19 q^{84} +1.41285e17 q^{85} +6.63881e18 q^{86} -9.45313e18 q^{87} +8.57809e18 q^{88} -1.18920e18 q^{89} +1.83504e18 q^{90} -3.24186e18 q^{91} +2.36954e18 q^{92} +3.21787e18 q^{93} -1.54290e18 q^{94} -8.42840e17 q^{95} -4.07992e19 q^{96} +4.84689e18 q^{97} +2.80159e19 q^{98} +2.29179e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * q^99

Display 100 coefficients 10 coefficients

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1378.66	1.90402	0.952012	−	0.306061i	$-0.0990112\pi$
$2$	1378.66	1.90402	0.952012	+	0.306061i	$0.0990112\pi$
$3$	−65581.5	−1.92367	−0.961833	−	0.273639i	$-0.911773\pi$
$3$	−65581.5	−1.92367	−0.961833	+	0.273639i	$0.911773\pi$
$4$	1.37642e6	2.62531
$5$	424075.	0.0971019	0.0485509	−	0.998821i	$-0.484540\pi$
$5$	424075.	0.0971019	0.0485509	+	0.998821i	$0.484540\pi$
$6$	−9.04146e7	−3.66270
$7$	1.78101e8	1.66815	0.834075	−	0.551650i	$-0.186002\pi$
$7$	1.78101e8	1.66815	0.834075	+	0.551650i	$0.186002\pi$
$8$	1.17480e9	3.09462
$9$	3.13867e9	2.70049
$10$	5.84655e8	0.184884
$11$	7.30177e9	0.933679	0.466839	−	0.884342i	$-0.345393\pi$
$11$	7.30177e9	0.933679	0.466839	+	0.884342i	$0.345393\pi$
$12$	−9.02675e10	−5.05021
$13$	−1.82024e10	−0.476065	−0.238032	−	0.971257i	$-0.576502\pi$
$13$	−1.82024e10	−0.476065	−0.238032	+	0.971257i	$0.576502\pi$
$14$	2.45541e11	3.17620
$15$	−2.78115e10	−0.186791
$16$	8.98006e11	3.26693
$17$	3.33160e11	0.681377	0.340689	−	0.940176i	$-0.389340\pi$
$17$	3.33160e11	0.681377	0.340689	+	0.940176i	$0.389340\pi$
$18$	4.32716e12	5.14179
$19$	−1.98748e12	−1.41300	−0.706502	−	0.707711i	$-0.749728\pi$
$19$	−1.98748e12	−1.41300	−0.706502	+	0.707711i	$0.749728\pi$
$20$	5.83704e11	0.254922
$21$	−1.16801e13	−3.20896
$22$	1.00667e13	1.77775
$23$	1.72153e12	0.199297	0.0996485	−	0.995023i	$-0.468228\pi$
$23$	1.72153e12	0.199297	0.0996485	+	0.995023i	$0.468228\pi$
$24$	−7.70449e13	−5.95302
$25$	−1.88936e13	−0.990571
$26$	−2.50949e13	−0.906438
$27$	−1.29616e14	−3.27117
$28$	2.45141e14	4.37941
$29$	1.44143e14	1.84507	0.922536	−	0.385911i	$-0.126113\pi$
$29$	1.44143e14	1.84507	0.922536	+	0.385911i	$0.126113\pi$
$30$	−3.83426e13	−0.355655
$31$	−4.90667e13	−0.333312	−0.166656	−	0.986015i	$-0.553297\pi$
$31$	−4.90667e13	−0.333312	−0.166656	+	0.986015i	$0.553297\pi$
$32$	6.22114e14	3.12568
$33$	−4.78861e14	−1.79609
$34$	4.59314e14	1.29736
$35$	7.55282e13	0.161981
$36$	4.32012e15	7.08961
$37$	−4.98837e14	−0.631019	−0.315509	−	0.948922i	$-0.602175\pi$
$37$	−4.98837e14	−0.631019	−0.315509	+	0.948922i	$0.602175\pi$
$38$	−2.74006e15	−2.69039
$39$	1.19374e15	0.915789
$40$	4.98201e14	0.300493
$41$	2.69630e15	1.28624	0.643120	−	0.765765i	$-0.277640\pi$
$41$	2.69630e15	1.28624	0.643120	+	0.765765i	$0.277640\pi$
$42$	−1.61029e16	−6.10994
$43$	4.81541e15	1.46111	0.730554	−	0.682855i	$-0.239262\pi$
$43$	4.81541e15	1.46111	0.730554	+	0.682855i	$0.239262\pi$
$44$	1.00503e16	2.45119
$45$	1.33103e15	0.262222
$46$	2.37341e15	0.379466
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−5.88926e16	−6.28447
$49$	2.03211e16	1.78273
$50$	−2.60479e16	−1.88607
$51$	−2.18491e16	−1.31074
$52$	−2.50540e16	−1.24982
$53$	−1.00709e16	−0.419226	−0.209613	−	0.977784i	$-0.567220\pi$
$53$	−1.00709e16	−0.419226	−0.209613	+	0.977784i	$0.567220\pi$
$54$	−1.78696e17	−6.22838
$55$	3.09650e15	0.0906620
$56$	2.09232e17	5.16230
$57$	1.30342e17	2.71815
$58$	1.98725e17	3.51306
$59$	−8.64139e15	−0.129864	−0.0649321	−	0.997890i	$-0.520683\pi$
$59$	−8.64139e15	−0.129864	−0.0649321	+	0.997890i	$0.520683\pi$
$60$	−3.82802e16	−0.490385
$61$	−1.69693e16	−0.185793	−0.0928966	−	0.995676i	$-0.529613\pi$
$61$	−1.69693e16	−0.185793	−0.0928966	+	0.995676i	$0.529613\pi$
$62$	−6.76464e16	−0.634634
$63$	5.59001e17	4.50482
$64$	3.86870e17	2.68445
$65$	−7.71916e15	−0.0462267
$66$	−6.60187e17	−3.41979
$67$	−1.72013e17	−0.772416	−0.386208	−	0.922412i	$-0.626215\pi$
$67$	−1.72013e17	−0.772416	−0.386208	+	0.922412i	$0.626215\pi$
$68$	4.58566e17	1.78882
$69$	−1.12901e17	−0.383381
$70$	1.04128e17	0.308415
$71$	2.86373e17	0.741273	0.370637	−	0.928778i	$-0.379140\pi$
$71$	2.86373e17	0.741273	0.370637	+	0.928778i	$0.379140\pi$
$72$	3.68730e18	8.35699
$73$	−3.42186e17	−0.680292	−0.340146	−	0.940373i	$-0.610477\pi$
$73$	−3.42186e17	−0.680292	−0.340146	+	0.940373i	$0.610477\pi$
$74$	−6.87727e17	−1.20147
$75$	1.23907e18	1.90553
$76$	−2.73560e18	−3.70957
$77$	1.30045e18	1.55752
$78$	1.64576e18	1.74368
$79$	−2.87821e17	−0.270187	−0.135094	−	0.990833i	$-0.543134\pi$
$79$	−2.87821e17	−0.270187	−0.135094	+	0.990833i	$0.543134\pi$
$80$	3.80822e17	0.317225
$81$	4.85245e18	3.59214
$82$	3.71729e18	2.44903
$83$	1.55719e18	0.914323	0.457162	−	0.889384i	$-0.348866\pi$
$83$	1.55719e18	0.914323	0.457162	+	0.889384i	$0.348866\pi$
$84$	−1.60767e19	−8.42451
$85$	1.41285e17	0.0661630
$86$	6.63881e18	2.78199
$87$	−9.45313e18	−3.54930
$88$	8.57809e18	2.88938
$89$	−1.18920e18	−0.359791	−0.179896	−	0.983686i	$-0.557576\pi$
$89$	−1.18920e18	−0.359791	−0.179896	+	0.983686i	$0.557576\pi$
$90$	1.83504e18	0.499278
$91$	−3.24186e18	−0.794147
$92$	2.36954e18	0.523215
$93$	3.21787e18	0.641181
$94$	−1.54290e18	−0.277730
$95$	−8.42840e17	−0.137205
$96$	−4.07992e19	−6.01277
$97$	4.84689e18	0.647338	0.323669	−	0.946170i	$-0.395084\pi$
$97$	4.84689e18	0.647338	0.323669	+	0.946170i	$0.395084\pi$
$98$	2.80159e19	3.39435
$99$	2.29179e19	2.52139
$100$	−2.60055e19	−2.60055
$101$	−5.38627e18	−0.490044	−0.245022	−	0.969518i	$-0.578795\pi$
$101$	−5.38627e18	−0.490044	−0.245022	+	0.969518i	$0.578795\pi$
$102$	−3.01225e19	−2.49568
$103$	1.01982e19	0.770142	0.385071	−	0.922887i	$-0.374177\pi$
$103$	1.01982e19	0.770142	0.385071	+	0.922887i	$0.374177\pi$
$104$	−2.13841e19	−1.47324
$105$	−4.95325e18	−0.311596
$106$	−1.38844e19	−0.798217
$107$	7.63414e18	0.401434	0.200717	−	0.979649i	$-0.435673\pi$
$107$	7.63414e18	0.401434	0.200717	+	0.979649i	$0.435673\pi$
$108$	−1.78406e20	−8.58782
$109$	−1.29321e19	−0.570319	−0.285160	−	0.958480i	$-0.592047\pi$
$109$	−1.29321e19	−0.570319	−0.285160	+	0.958480i	$0.592047\pi$
$110$	4.26902e18	0.172623
$111$	3.27145e19	1.21387
$112$	1.59936e20	5.44973
$113$	2.14996e19	0.673263	0.336632	−	0.941636i	$-0.390712\pi$
$113$	2.14996e19	0.673263	0.336632	+	0.941636i	$0.390712\pi$
$114$	1.79697e20	5.17542
$115$	7.30058e17	0.0193521
$116$	1.98401e20	4.84388
$117$	−5.71312e19	−1.28561
$118$	−1.19135e19	−0.247264
$119$	5.93361e19	1.13664
$120$	−3.26728e19	−0.578049
$121$	−7.84327e18	−0.128244
$122$	−2.33949e19	−0.353755
$123$	−1.76828e20	−2.47430
$124$	−6.75363e19	−0.875046
$125$	−1.61009e19	−0.193288
$126$	7.70673e20	8.57728
$127$	−5.62458e19	−0.580704	−0.290352	−	0.956920i	$-0.593772\pi$
$127$	−5.62458e19	−0.580704	−0.290352	+	0.956920i	$0.593772\pi$
$128$	2.07195e20	1.98557
$129$	−3.15802e20	−2.81068
$130$	−1.06421e19	−0.0880168
$131$	1.94331e20	1.49439	0.747197	−	0.664602i	$-0.231399\pi$
$131$	1.94331e20	1.49439	0.747197	+	0.664602i	$0.231399\pi$
$132$	−6.59112e20	−4.71527
$133$	−3.53972e20	−2.35710
$134$	−2.37148e20	−1.47070
$135$	−5.49669e19	−0.317636
$136$	3.91395e20	2.10860
$137$	3.80371e20	1.91145	0.955723	−	0.294269i	$-0.0950760\pi$
$137$	3.80371e20	1.91145	0.955723	+	0.294269i	$0.0950760\pi$
$138$	−1.55652e20	−0.729966
$139$	−2.82093e20	−1.23524	−0.617621	−	0.786476i	$-0.711904\pi$
$139$	−2.82093e20	−1.23524	−0.617621	+	0.786476i	$0.711904\pi$
$140$	1.03958e20	0.425248
$141$	7.33943e19	0.280595
$142$	3.94812e20	1.41140
$143$	−1.32909e20	−0.444491
$144$	2.81855e21	8.82229
$145$	6.11275e19	0.179160
$146$	−4.71759e20	−1.29529
$147$	−1.33269e21	−3.42937
$148$	−6.86607e20	−1.65662
$149$	−4.74591e20	−1.07411	−0.537057	−	0.843546i	$-0.680464\pi$
$149$	−4.74591e20	−1.07411	−0.537057	+	0.843546i	$0.680464\pi$
$150$	1.70826e21	3.62817
$151$	3.28121e20	0.654264	0.327132	−	0.944979i	$-0.393918\pi$
$151$	3.28121e20	0.654264	0.327132	+	0.944979i	$0.393918\pi$
$152$	−2.33488e21	−4.37271
$153$	1.04568e21	1.84005
$154$	1.79288e21	2.96555
$155$	−2.08080e19	−0.0323652
$156$	1.64308e21	2.40423
$157$	−4.02932e20	−0.554862	−0.277431	−	0.960746i	$-0.589483\pi$
$157$	−4.02932e20	−0.554862	−0.277431	+	0.960746i	$0.589483\pi$
$158$	−3.96807e20	−0.514443
$159$	6.60466e20	0.806451
$160$	2.63823e20	0.303510
$161$	3.06607e20	0.332457
$162$	6.68989e21	6.83953
$163$	−1.63267e21	−1.57440	−0.787202	−	0.616695i	$-0.788471\pi$
$163$	−1.63267e21	−1.57440	−0.787202	+	0.616695i	$0.788471\pi$
$164$	3.71124e21	3.37678
$165$	−2.03073e20	−0.174403
$166$	2.14684e21	1.74089
$167$	1.76200e21	1.34958	0.674791	−	0.738008i	$-0.264234\pi$
$167$	1.76200e21	1.34958	0.674791	+	0.738008i	$0.264234\pi$
$168$	−1.37218e22	−9.93053
$169$	−1.13059e21	−0.773363
$170$	1.94784e20	0.125976
$171$	−6.23805e21	−3.81580
$172$	6.62800e21	3.83586
$173$	3.17639e21	1.73979	0.869894	−	0.493239i	$-0.164187\pi$
$173$	3.17639e21	1.73979	0.869894	+	0.493239i	$0.164187\pi$
$174$	−1.30327e22	−6.75795
$175$	−3.36498e21	−1.65242
$176$	6.55703e21	3.05026
$177$	5.66715e20	0.249815
$178$	−1.63950e21	−0.685051
$179$	1.10931e21	0.439490	0.219745	−	0.975557i	$-0.429477\pi$
$179$	1.10931e21	0.439490	0.219745	+	0.975557i	$0.429477\pi$
$180$	1.83205e21	0.688414
$181$	−2.93955e20	−0.104794	−0.0523968	−	0.998626i	$-0.516686\pi$
$181$	−2.93955e20	−0.104794	−0.0523968	+	0.998626i	$0.516686\pi$
$182$	−4.46942e21	−1.51208
$183$	1.11287e21	0.357404
$184$	2.02245e21	0.616749
$185$	−2.11544e20	−0.0612731
$186$	4.43635e21	1.22082
$187$	2.43265e21	0.636188
$188$	−1.54039e21	−0.382940
$189$	−2.30848e22	−5.45680
$190$	−1.16199e21	−0.261242
$191$	−4.62523e21	−0.989274	−0.494637	−	0.869100i	$-0.664699\pi$
$191$	−4.62523e21	−0.989274	−0.494637	+	0.869100i	$0.664699\pi$
$192$	−2.53715e22	−5.16398
$193$	2.83579e21	0.549389	0.274695	−	0.961532i	$-0.411423\pi$
$193$	2.83579e21	0.549389	0.274695	+	0.961532i	$0.411423\pi$
$194$	6.68221e21	1.23255
$195$	5.06234e20	0.0889248
$196$	2.79703e22	4.68020
$197$	1.17363e22	1.87112	0.935562	−	0.353163i	$-0.114894\pi$
$197$	1.17363e22	1.87112	0.935562	+	0.353163i	$0.114894\pi$
$198$	3.15959e22	4.80078
$199$	1.42850e21	0.206908	0.103454	−	0.994634i	$-0.467011\pi$
$199$	1.42850e21	0.206908	0.103454	+	0.994634i	$0.467011\pi$
$200$	−2.21962e22	−3.06544
$201$	1.12809e22	1.48587
$202$	−7.42583e21	−0.933055
$203$	2.56721e22	3.07786
$204$	−3.00735e22	−3.44110
$205$	1.14343e21	0.124896
$206$	1.40599e22	1.46637
$207$	5.40332e21	0.538199
$208$	−1.63458e22	−1.55527
$209$	−1.45121e22	−1.31929
$210$	−6.82886e21	−0.593287
$211$	1.06183e22	0.881806	0.440903	−	0.897555i	$-0.354658\pi$
$211$	1.06183e22	0.881806	0.440903	+	0.897555i	$0.354658\pi$
$212$	−1.38618e22	−1.10060
$213$	−1.87808e22	−1.42596
$214$	1.05249e22	0.764340
$215$	2.04209e21	0.141876
$216$	−1.52272e23	−10.1230
$217$	−8.73884e21	−0.556015
$218$	−1.78290e22	−1.08590
$219$	2.24411e22	1.30865
$220$	4.26207e21	0.238015
$221$	−6.06429e21	−0.324380
$222$	4.51022e22	2.31123
$223$	−2.38761e22	−1.17238	−0.586188	−	0.810175i	$-0.699372\pi$
$223$	−2.38761e22	−1.17238	−0.586188	+	0.810175i	$0.699372\pi$
$224$	1.10799e23	5.21411
$225$	−5.93010e22	−2.67503
$226$	2.96406e22	1.28191
$227$	−1.16471e22	−0.483027	−0.241514	−	0.970397i	$-0.577644\pi$
$227$	−1.16471e22	−0.483027	−0.241514	+	0.970397i	$0.577644\pi$
$228$	1.79405e23	7.13597
$229$	3.90770e21	0.149102	0.0745511	−	0.997217i	$-0.476248\pi$
$229$	3.90770e21	0.149102	0.0745511	+	0.997217i	$0.476248\pi$
$230$	1.00650e21	0.0368469
$231$	−8.52857e22	−2.99614
$232$	1.69339e23	5.70980
$233$	−2.65633e22	−0.859805	−0.429903	−	0.902875i	$-0.641452\pi$
$233$	−2.65633e22	−0.859805	−0.429903	+	0.902875i	$0.641452\pi$
$234$	−7.87646e22	−2.44782
$235$	−4.74595e20	−0.0141638
$236$	−1.18941e22	−0.340933
$237$	1.88757e22	0.519750
$238$	8.18044e22	2.16419
$239$	−2.91423e22	−0.740873	−0.370437	−	0.928858i	$-0.620792\pi$
$239$	−2.91423e22	−0.740873	−0.370437	+	0.928858i	$0.620792\pi$
$240$	−2.49749e22	−0.610234
$241$	6.55061e22	1.53858	0.769289	−	0.638900i	$-0.220610\pi$
$241$	6.55061e22	1.53858	0.769289	+	0.638900i	$0.220610\pi$
$242$	−1.08132e22	−0.244179
$243$	−1.67584e23	−3.63891
$244$	−2.33568e22	−0.487764
$245$	8.61768e21	0.173106
$246$	−2.43785e23	−4.71112
$247$	3.61768e22	0.672681
$248$	−5.76434e22	−1.03147
$249$	−1.02123e23	−1.75885
$250$	−2.21977e22	−0.368025
$251$	−9.49502e22	−1.51564	−0.757819	−	0.652464i	$-0.773735\pi$
$251$	−9.49502e22	−1.51564	−0.757819	+	0.652464i	$0.773735\pi$
$252$	7.69418e23	11.8265
$253$	1.25702e22	0.186079
$254$	−7.75439e22	−1.10567
$255$	−9.26566e21	−0.127275
$256$	8.28209e22	1.09613
$257$	4.54967e22	0.580250	0.290125	−	0.956989i	$-0.406303\pi$
$257$	4.54967e22	0.580250	0.290125	+	0.956989i	$0.406303\pi$
$258$	−4.35383e23	−5.35161
$259$	−8.88434e22	−1.05263
$260$	−1.06248e22	−0.121359
$261$	4.52418e23	4.98259
$262$	2.67917e23	2.84536
$263$	−3.09846e21	−0.0317370	−0.0158685	−	0.999874i	$-0.505051\pi$
$263$	−3.09846e21	−0.0317370	−0.0158685	+	0.999874i	$0.505051\pi$
$264$	−5.62564e23	−5.55820
$265$	−4.27083e21	−0.0407077
$266$	−4.88008e23	−4.48798
$267$	7.79896e22	0.692118
$268$	−2.36762e23	−2.02783
$269$	−9.69495e22	−0.801491	−0.400746	−	0.916189i	$-0.631249\pi$
$269$	−9.69495e22	−0.801491	−0.400746	+	0.916189i	$0.631249\pi$
$270$	−7.57807e22	−0.604787
$271$	1.28978e23	0.993816	0.496908	−	0.867803i	$-0.334469\pi$
$271$	1.28978e23	0.993816	0.496908	+	0.867803i	$0.334469\pi$
$272$	2.99179e23	2.22601
$273$	2.12606e23	1.52767
$274$	5.24402e23	3.63944
$275$	−1.37957e23	−0.924875
$276$	−1.55398e23	−1.00649
$277$	−1.23459e23	−0.772617	−0.386309	−	0.922370i	$-0.626250\pi$
$277$	−1.23459e23	−0.772617	−0.386309	+	0.922370i	$0.626250\pi$
$278$	−3.88911e23	−2.35193
$279$	−1.54004e23	−0.900105
$280$	8.87302e22	0.501268
$281$	6.87738e22	0.375589	0.187795	−	0.982208i	$-0.439866\pi$
$281$	6.87738e22	0.375589	0.187795	+	0.982208i	$0.439866\pi$
$282$	1.01186e23	0.534260
$283$	−3.26210e23	−1.66543	−0.832715	−	0.553701i	$-0.813215\pi$
$283$	−3.26210e23	−1.66543	−0.832715	+	0.553701i	$0.813215\pi$
$284$	3.94169e23	1.94607
$285$	5.52747e22	0.263937
$286$	−1.83237e23	−0.846322
$287$	4.80215e23	2.14564
$288$	1.95261e24	8.44087
$289$	−1.28077e23	−0.535725
$290$	8.42741e22	0.341125
$291$	−3.17866e23	−1.24526
$292$	−4.70991e23	−1.78598
$293$	9.79299e22	0.359479	0.179739	−	0.983714i	$-0.442475\pi$
$293$	9.79299e22	0.359479	0.179739	+	0.983714i	$0.442475\pi$
$294$	−1.83733e24	−6.52960
$295$	−3.66459e21	−0.0126100
$296$	−5.86032e23	−1.95276
$297$	−9.46426e23	−3.05422
$298$	−6.54300e23	−2.04514
$299$	−3.13359e22	−0.0948782
$300$	1.70548e24	5.00259
$301$	8.57629e23	2.43735
$302$	4.52367e23	1.24573
$303$	3.53240e23	0.942680
$304$	−1.78477e24	−4.61618
$305$	−7.19624e21	−0.0180409
$306$	1.44164e24	3.50350
$307$	3.78037e23	0.890675	0.445338	−	0.895363i	$-0.353084\pi$
$307$	3.78037e23	0.890675	0.445338	+	0.895363i	$0.353084\pi$
$308$	1.78997e24	4.08896
$309$	−6.68815e23	−1.48150
$310$	−2.86871e22	−0.0616241
$311$	2.25262e23	0.469315	0.234658	−	0.972078i	$-0.424603\pi$
$311$	2.25262e23	0.469315	0.234658	+	0.972078i	$0.424603\pi$
$312$	1.40240e24	2.83402
$313$	−4.89702e23	−0.959976	−0.479988	−	0.877275i	$-0.659359\pi$
$313$	−4.89702e23	−0.959976	−0.479988	+	0.877275i	$0.659359\pi$
$314$	−5.55506e23	−1.05647
$315$	2.37058e23	0.437426
$316$	−3.96161e23	−0.709324
$317$	−2.37564e23	−0.412779	−0.206389	−	0.978470i	$-0.566171\pi$
$317$	−2.37564e23	−0.412779	−0.206389	+	0.978470i	$0.566171\pi$
$318$	9.10559e23	1.53550
$319$	1.05250e24	1.72271
$320$	1.64062e23	0.260665
$321$	−5.00658e23	−0.772224
$322$	4.22707e23	0.633007
$323$	−6.62148e23	−0.962789
$324$	6.67900e24	9.43048
$325$	3.43909e23	0.471576
$326$	−2.25090e24	−2.99770
$327$	8.48108e23	1.09710
$328$	3.16761e24	3.98043
$329$	−1.99318e23	−0.243325
$330$	−2.79969e23	−0.332068
$331$	−6.24781e22	−0.0720049	−0.0360024	−	0.999352i	$-0.511462\pi$
$331$	−6.24781e22	−0.0720049	−0.0360024	+	0.999352i	$0.511462\pi$
$332$	2.14334e24	2.40038
$333$	−1.56569e24	−1.70406
$334$	2.42920e24	2.56964
$335$	−7.29465e22	−0.0750030
$336$	−1.04888e25	−10.4834
$337$	2.56907e23	0.249627	0.124814	−	0.992180i	$-0.460167\pi$
$337$	2.56907e23	0.249627	0.124814	+	0.992180i	$0.460167\pi$
$338$	−1.55871e24	−1.47250
$339$	−1.40998e24	−1.29513
$340$	1.94467e23	0.173698
$341$	−3.58274e23	−0.311206
$342$	−8.60015e24	−7.26537
$343$	1.58906e24	1.30571
$344$	5.65712e24	4.52158
$345$	−4.78783e22	−0.0372270
$346$	4.37917e24	3.31260
$347$	−2.65010e23	−0.195044	−0.0975221	−	0.995233i	$-0.531092\pi$
$347$	−2.65010e23	−0.195044	−0.0975221	+	0.995233i	$0.531092\pi$
$348$	−1.30114e25	−9.31800
$349$	−1.82656e24	−1.27289	−0.636447	−	0.771321i	$-0.719596\pi$
$349$	−1.82656e24	−1.27289	−0.636447	+	0.771321i	$0.719596\pi$
$350$	−4.63916e24	−3.14625
$351$	2.35932e24	1.55729
$352$	4.54253e24	2.91838
$353$	−1.42024e24	−0.888183	−0.444091	−	0.895982i	$-0.646473\pi$
$353$	−1.42024e24	−0.888183	−0.444091	+	0.895982i	$0.646473\pi$
$354$	7.81308e23	0.475654
$355$	1.21444e23	0.0719790
$356$	−1.63684e24	−0.944562
$357$	−3.89135e24	−2.18652
$358$	1.52936e24	0.836800
$359$	−3.12072e24	−1.66287	−0.831434	−	0.555623i	$-0.812480\pi$
$359$	−3.12072e24	−1.66287	−0.831434	+	0.555623i	$0.812480\pi$
$360$	1.56369e24	0.811479
$361$	1.97166e24	0.996581
$362$	−4.05264e23	−0.199529
$363$	5.14373e23	0.246698
$364$	−4.46215e24	−2.08488
$365$	−1.45113e23	−0.0660577
$366$	1.53427e24	0.680505
$367$	−2.56096e24	−1.10681	−0.553407	−	0.832911i	$-0.686672\pi$
$367$	−2.56096e24	−1.10681	−0.553407	+	0.832911i	$0.686672\pi$
$368$	1.54595e24	0.651088
$369$	8.46281e24	3.47348
$370$	−2.91648e23	−0.116665
$371$	−1.79364e24	−0.699333
$372$	4.42913e24	1.68330
$373$	−7.31807e23	−0.271121	−0.135560	−	0.990769i	$-0.543283\pi$
$373$	−7.31807e23	−0.271121	−0.135560	+	0.990769i	$0.543283\pi$
$374$	3.35381e24	1.21132
$375$	1.05592e24	0.371822
$376$	−1.31475e24	−0.451397
$377$	−2.62375e24	−0.878373
$378$	−3.18260e25	−10.3899
$379$	−1.22196e24	−0.389033	−0.194516	−	0.980899i	$-0.562314\pi$
$379$	−1.22196e24	−0.389033	−0.194516	+	0.980899i	$0.562314\pi$
$380$	−1.16010e24	−0.360206
$381$	3.68869e24	1.11708
$382$	−6.37663e24	−1.88360
$383$	6.89589e23	0.198702	0.0993510	−	0.995052i	$-0.468323\pi$
$383$	6.89589e23	0.198702	0.0993510	+	0.995052i	$0.468323\pi$
$384$	−1.35882e25	−3.81957
$385$	5.51490e23	0.151238
$386$	3.90960e24	1.04605
$387$	1.51140e25	3.94571
$388$	6.67133e24	1.69946
$389$	5.49109e23	0.136502	0.0682508	−	0.997668i	$-0.478258\pi$
$389$	5.49109e23	0.136502	0.0682508	+	0.997668i	$0.478258\pi$
$390$	6.97925e23	0.169315
$391$	5.73545e23	0.135796
$392$	2.38732e25	5.51687
$393$	−1.27445e25	−2.87471
$394$	1.61804e25	3.56266
$395$	−1.22058e23	−0.0262357
$396$	3.15445e25	6.61942
$397$	−6.35162e24	−1.30129	−0.650646	−	0.759381i	$-0.725502\pi$
$397$	−6.35162e24	−1.30129	−0.650646	+	0.759381i	$0.725502\pi$
$398$	1.96942e24	0.393957
$399$	2.32140e25	4.53428
$400$	−1.69666e25	−3.23612
$401$	−4.39151e24	−0.817979	−0.408989	−	0.912539i	$-0.634119\pi$
$401$	−4.39151e24	−0.817979	−0.408989	+	0.912539i	$0.634119\pi$
$402$	1.55525e25	2.82913
$403$	8.93130e23	0.158678
$404$	−7.41375e24	−1.28651
$405$	2.05780e24	0.348804
$406$	3.53931e25	5.86032
$407$	−3.64239e24	−0.589169
$408$	−2.56682e25	−4.05625
$409$	4.91173e23	0.0758338	0.0379169	−	0.999281i	$-0.487928\pi$
$409$	4.91173e23	0.0758338	0.0379169	+	0.999281i	$0.487928\pi$
$410$	1.57641e24	0.237806
$411$	−2.49453e25	−3.67698
$412$	1.40370e25	2.02186
$413$	−1.53904e24	−0.216633
$414$	7.44935e24	1.02474
$415$	6.60365e23	0.0887825
$416$	−1.13239e25	−1.48803
$417$	1.85001e25	2.37619
$418$	−2.00073e25	−2.51196
$419$	1.20390e25	1.47760	0.738798	−	0.673927i	$-0.235394\pi$
$419$	1.20390e25	1.47760	0.738798	+	0.673927i	$0.235394\pi$
$420$	−6.81774e24	−0.818036
$421$	−1.52832e25	−1.79281	−0.896407	−	0.443233i	$-0.853832\pi$
$421$	−1.52832e25	−1.79281	−0.896407	+	0.443233i	$0.853832\pi$
$422$	1.46391e25	1.67898
$423$	−3.51258e24	−0.393907
$424$	−1.18313e25	−1.29735
$425$	−6.29460e24	−0.674953
$426$	−2.58923e25	−2.71506
$427$	−3.02225e24	−0.309931
$428$	1.05078e25	1.05389
$429$	8.71640e24	0.855053
$430$	2.81535e24	0.270136
$431$	−4.66679e24	−0.438010	−0.219005	−	0.975724i	$-0.570281\pi$
$431$	−4.66679e24	−0.438010	−0.219005	+	0.975724i	$0.570281\pi$
$432$	−1.16396e26	−10.6867
$433$	1.94677e25	1.74856	0.874279	−	0.485424i	$-0.161335\pi$
$433$	1.94677e25	1.74856	0.874279	+	0.485424i	$0.161335\pi$
$434$	−1.20479e25	−1.05867
$435$	−4.00884e24	−0.344644
$436$	−1.78000e25	−1.49726
$437$	−3.42151e24	−0.281607
$438$	3.09387e25	2.49171
$439$	−1.69229e24	−0.133372	−0.0666858	−	0.997774i	$-0.521242\pi$
$439$	−1.69229e24	−0.133372	−0.0666858	+	0.997774i	$0.521242\pi$
$440$	3.63775e24	0.280564
$441$	6.37813e25	4.81423
$442$	−8.36060e24	−0.617626
$443$	1.48470e25	1.07351	0.536753	−	0.843740i	$-0.319651\pi$
$443$	1.48470e25	1.07351	0.536753	+	0.843740i	$0.319651\pi$
$444$	4.50288e25	3.18678
$445$	−5.04310e23	−0.0349364
$446$	−3.29170e25	−2.23223
$447$	3.11244e25	2.06623
$448$	6.89020e25	4.47807
$449$	6.34486e24	0.403721	0.201861	−	0.979414i	$-0.435301\pi$
$449$	6.34486e24	0.403721	0.201861	+	0.979414i	$0.435301\pi$
$450$	−8.17559e25	−5.09331
$451$	1.96878e25	1.20094
$452$	2.95924e25	1.76752
$453$	−2.15187e25	−1.25858
$454$	−1.60574e25	−0.919695
$455$	−1.37479e24	−0.0771132
$456$	1.53125e26	8.41164
$457$	−5.73236e24	−0.308411	−0.154205	−	0.988039i	$-0.549282\pi$
$457$	−5.73236e24	−0.308411	−0.154205	+	0.988039i	$0.549282\pi$
$458$	5.38739e24	0.283894
$459$	−4.31828e25	−2.22890
$460$	1.00486e24	0.0508052
$461$	2.60643e25	1.29088	0.645441	−	0.763810i	$-0.276674\pi$
$461$	2.60643e25	1.29088	0.645441	+	0.763810i	$0.276674\pi$
$462$	−1.17580e26	−5.70472
$463$	2.40694e25	1.14405	0.572027	−	0.820235i	$-0.306157\pi$
$463$	2.40694e25	1.14405	0.572027	+	0.820235i	$0.306157\pi$
$464$	1.29441e26	6.02771
$465$	1.36462e24	0.0622598
$466$	−3.66217e25	−1.63709
$467$	−1.48507e25	−0.650485	−0.325243	−	0.945631i	$-0.605446\pi$
$467$	−1.48507e25	−0.650485	−0.325243	+	0.945631i	$0.605446\pi$
$468$	−7.86364e25	−3.37511
$469$	−3.06357e25	−1.28851
$470$	−6.54306e23	−0.0269681
$471$	2.64249e25	1.06737
$472$	−1.01519e25	−0.401880
$473$	3.51610e25	1.36421
$474$	2.60232e25	0.989616
$475$	3.75507e25	1.39968
$476$	8.16712e25	2.98403
$477$	−3.16093e25	−1.13212
$478$	−4.01774e25	−1.41064
$479$	−3.18524e25	−1.09636	−0.548181	−	0.836360i	$-0.684680\pi$
$479$	−3.18524e25	−1.09636	−0.548181	+	0.836360i	$0.684680\pi$
$480$	−1.73019e25	−0.583851
$481$	9.08001e24	0.300406
$482$	9.03107e25	2.92949
$483$	−2.01077e25	−0.639537
$484$	−1.07956e25	−0.336679
$485$	2.05544e24	0.0628578
$486$	−2.31041e26	−6.92858
$487$	−4.57196e25	−1.34455	−0.672275	−	0.740302i	$-0.734683\pi$
$487$	−4.57196e25	−1.34455	−0.672275	+	0.740302i	$0.734683\pi$
$488$	−1.99354e25	−0.574959
$489$	1.07073e26	3.02863
$490$	1.18808e25	0.329598
$491$	1.41439e25	0.384854	0.192427	−	0.981311i	$-0.438364\pi$
$491$	1.41439e25	0.384854	0.192427	+	0.981311i	$0.438364\pi$
$492$	−2.43389e26	−6.49578
$493$	4.80227e25	1.25719
$494$	4.98755e25	1.28080
$495$	9.71889e24	0.244831
$496$	−4.40622e25	−1.08891
$497$	5.10034e25	1.23656
$498$	−1.40793e26	−3.34889
$499$	−7.67896e25	−1.79204	−0.896019	−	0.444016i	$-0.853553\pi$
$499$	−7.67896e25	−1.79204	−0.896019	+	0.444016i	$0.853553\pi$
$500$	−2.21616e25	−0.507441
$501$	−1.15555e26	−2.59615
$502$	−1.30904e26	−2.88581
$503$	−2.83756e25	−0.613831	−0.306916	−	0.951737i	$-0.599297\pi$
$503$	−2.83756e25	−0.613831	−0.306916	+	0.951737i	$0.599297\pi$
$504$	6.56712e26	13.9407
$505$	−2.28418e24	−0.0475842
$506$	1.73301e25	0.354300
$507$	7.41461e25	1.48769
$508$	−7.74177e25	−1.52453
$509$	5.41340e25	1.04629	0.523144	−	0.852245i	$-0.324759\pi$
$509$	5.41340e25	1.04629	0.523144	+	0.852245i	$0.324759\pi$
$510$	−1.27742e25	−0.242335
$511$	−6.09438e25	−1.13483
$512$	5.55181e24	0.101478
$513$	2.57609e26	4.62217
$514$	6.27245e25	1.10481
$515$	4.32481e24	0.0747822
$516$	−4.34674e26	−7.37891
$517$	−8.17163e24	−0.136191
$518$	−1.22485e26	−2.00424
$519$	−2.08313e26	−3.34677
$520$	−9.06844e24	−0.143054
$521$	9.97931e25	1.54576	0.772880	−	0.634552i	$-0.218815\pi$
$521$	9.97931e25	1.54576	0.772880	+	0.634552i	$0.218815\pi$
$522$	6.23731e26	9.48698
$523$	−4.72995e24	−0.0706465	−0.0353232	−	0.999376i	$-0.511246\pi$
$523$	−4.72995e24	−0.0706465	−0.0353232	+	0.999376i	$0.511246\pi$
$524$	2.67481e26	3.92324
$525$	2.20680e26	3.17871
$526$	−4.27172e24	−0.0604280
$527$	−1.63471e25	−0.227111
$528$	−4.30020e26	−5.86768
$529$	−7.16518e25	−0.960281
$530$	−5.88802e24	−0.0775083
$531$	−2.71225e25	−0.350696
$532$	−4.87213e26	−6.18812
$533$	−4.90791e25	−0.612333
$534$	1.07521e26	1.31781
$535$	3.23745e24	0.0389800
$536$	−2.02080e26	−2.39033
$537$	−7.27502e25	−0.845432
$538$	−1.33660e26	−1.52606
$539$	1.48380e26	1.66449
$540$	−7.56573e25	−0.833893
$541$	−1.41386e25	−0.153120	−0.0765598	−	0.997065i	$-0.524394\pi$
$541$	−1.41386e25	−0.153120	−0.0765598	+	0.997065i	$0.524394\pi$
$542$	1.77816e26	1.89225
$543$	1.92780e25	0.201588
$544$	2.07263e26	2.12977
$545$	−5.48419e24	−0.0553791
$546$	2.93112e26	2.90873
$547$	−9.33848e25	−0.910744	−0.455372	−	0.890301i	$-0.650494\pi$
$547$	−9.33848e25	−0.910744	−0.455372	+	0.890301i	$0.650494\pi$
$548$	5.23549e26	5.01813
$549$	−5.32610e25	−0.501732
$550$	−1.90196e26	−1.76098
$551$	−2.86482e26	−2.60709
$552$	−1.32635e26	−1.18642
$553$	−5.12612e25	−0.450713
$554$	−1.70208e26	−1.47108
$555$	1.38734e25	0.117869
$556$	−3.88278e26	−3.24289
$557$	5.53939e24	0.0454818	0.0227409	−	0.999741i	$-0.492761\pi$
$557$	5.53939e24	0.0454818	0.0227409	+	0.999741i	$0.492761\pi$
$558$	−2.12320e26	−1.71382
$559$	−8.76517e25	−0.695582
$560$	6.78248e25	0.529178
$561$	−1.59537e26	−1.22381
$562$	9.48157e25	0.715131
$563$	−2.08432e26	−1.54573	−0.772866	−	0.634569i	$-0.781178\pi$
$563$	−2.08432e26	−1.54573	−0.772866	+	0.634569i	$0.781178\pi$
$564$	1.01021e26	0.736649
$565$	9.11744e24	0.0653751
$566$	−4.49733e26	−3.17102
$567$	8.64228e26	5.99224
$568$	3.36430e26	2.29396
$569$	2.41945e26	1.62237	0.811186	−	0.584788i	$-0.198822\pi$
$569$	2.41945e26	1.62237	0.811186	+	0.584788i	$0.198822\pi$
$570$	7.62051e25	0.502542
$571$	1.55190e26	1.00652	0.503258	−	0.864136i	$-0.332135\pi$
$571$	1.55190e26	1.00652	0.503258	+	0.864136i	$0.332135\pi$
$572$	−1.82939e26	−1.16693
$573$	3.03330e26	1.90303
$574$	6.62053e26	4.08536
$575$	−3.25260e25	−0.197418
$576$	1.21426e27	7.24932
$577$	1.53867e26	0.903596	0.451798	−	0.892120i	$-0.350783\pi$
$577$	1.53867e26	0.903596	0.451798	+	0.892120i	$0.350783\pi$
$578$	−1.76575e26	−1.02003
$579$	−1.85976e26	−1.05684
$580$	8.41370e25	0.470350
$581$	2.77337e26	1.52523
$582$	−4.38229e26	−2.37101
$583$	−7.35356e25	−0.391423
$584$	−4.01999e26	−2.10525
$585$	−2.42279e25	−0.124835
$586$	1.35012e26	0.684456
$587$	−1.26587e26	−0.631432	−0.315716	−	0.948854i	$-0.602245\pi$
$587$	−1.26587e26	−0.631432	−0.315716	+	0.948854i	$0.602245\pi$
$588$	−1.83434e27	−9.00315
$589$	9.75191e25	0.470971
$590$	−5.05223e24	−0.0240098
$591$	−7.69685e26	−3.59941
$592$	−4.47959e26	−2.06149
$593$	4.02083e26	1.82094	0.910471	−	0.413572i	$-0.135719\pi$
$593$	4.02083e26	1.82094	0.910471	+	0.413572i	$0.135719\pi$
$594$	−1.30480e27	−5.81531
$595$	2.51630e25	0.110370
$596$	−6.53235e26	−2.81988
$597$	−9.36834e25	−0.398021
$598$	−4.32016e25	−0.180650
$599$	−1.13964e26	−0.469042	−0.234521	−	0.972111i	$-0.575352\pi$
$599$	−1.13964e26	−0.469042	−0.234521	+	0.972111i	$0.575352\pi$
$600$	1.45566e27	5.89689
$601$	−3.48095e25	−0.138800	−0.0694002	−	0.997589i	$-0.522109\pi$
$601$	−3.48095e25	−0.138800	−0.0694002	+	0.997589i	$0.522109\pi$
$602$	1.18238e27	4.64077
$603$	−5.39893e26	−2.08590
$604$	4.51631e26	1.71764
$605$	−3.32613e24	−0.0124527
$606$	4.86997e26	1.79489
$607$	−1.67930e26	−0.609305	−0.304652	−	0.952464i	$-0.598540\pi$
$607$	−1.67930e26	−0.609305	−0.304652	+	0.952464i	$0.598540\pi$
$608$	−1.23644e27	−4.41660
$609$	−1.68361e27	−5.92077
$610$	−9.92117e24	−0.0343502
$611$	2.03708e25	0.0694411
$612$	1.43929e27	4.83070
$613$	−1.05377e25	−0.0348235	−0.0174118	−	0.999848i	$-0.505543\pi$
$613$	−1.05377e25	−0.0348235	−0.0174118	+	0.999848i	$0.505543\pi$
$614$	5.21184e26	1.69587
$615$	−7.49882e25	−0.240259
$616$	1.52777e27	4.81993
$617$	−5.29355e25	−0.164451	−0.0822257	−	0.996614i	$-0.526203\pi$
$617$	−5.29355e25	−0.164451	−0.0822257	+	0.996614i	$0.526203\pi$
$618$	−9.22068e26	−2.82080
$619$	3.39619e26	1.02313	0.511565	−	0.859245i	$-0.329066\pi$
$619$	3.39619e26	1.02313	0.511565	+	0.859245i	$0.329066\pi$
$620$	−2.86404e25	−0.0849686
$621$	−2.23138e26	−0.651934
$622$	3.10560e26	0.893588
$623$	−2.11798e26	−0.600186
$624$	1.07198e27	2.99181
$625$	3.53540e26	0.971803
$626$	−6.75133e26	−1.82782
$627$	9.51726e26	2.53788
$628$	−5.54602e26	−1.45668
$629$	−1.66192e26	−0.429962
$630$	3.26823e26	0.832870
$631$	5.05394e26	1.26868	0.634338	−	0.773055i	$-0.281273\pi$
$631$	5.05394e26	1.26868	0.634338	+	0.773055i	$0.281273\pi$
$632$	−3.38131e26	−0.836127
$633$	−6.96366e26	−1.69630
$634$	−3.27520e26	−0.785940
$635$	−2.38524e25	−0.0563875
$636$	9.09077e26	2.11718
$637$	−3.69892e26	−0.848693
$638$	1.45104e27	3.28007
$639$	8.98832e26	2.00180
$640$	8.78664e25	0.192803
$641$	5.47356e26	1.18337	0.591683	−	0.806171i	$-0.298464\pi$
$641$	5.47356e26	1.18337	0.591683	+	0.806171i	$0.298464\pi$
$642$	−6.90238e26	−1.47033
$643$	−7.71752e26	−1.61984	−0.809922	−	0.586537i	$-0.800491\pi$
$643$	−7.71752e26	−1.61984	−0.809922	+	0.586537i	$0.800491\pi$
$644$	4.22019e26	0.872802
$645$	−1.33924e26	−0.272923
$646$	−9.12877e26	−1.83317
$647$	−4.38955e26	−0.868618	−0.434309	−	0.900764i	$-0.643007\pi$
$647$	−4.38955e26	−0.868618	−0.434309	+	0.900764i	$0.643007\pi$
$648$	5.70064e27	11.1163
$649$	−6.30974e25	−0.121251
$650$	4.74134e26	0.897892
$651$	5.73106e26	1.06959
$652$	−2.24723e27	−4.13329
$653$	−1.04787e27	−1.89947	−0.949737	−	0.313050i	$-0.898649\pi$
$653$	−1.04787e27	−1.89947	−0.949737	+	0.313050i	$0.898649\pi$
$654$	1.16925e27	2.08891
$655$	8.24110e25	0.145108
$656$	2.42130e27	4.20205
$657$	−1.07401e27	−1.83712
$658$	−2.74792e26	−0.463296
$659$	−4.14669e26	−0.689112	−0.344556	−	0.938766i	$-0.611970\pi$
$659$	−4.14669e26	−0.689112	−0.344556	+	0.938766i	$0.611970\pi$
$660$	−2.79513e26	−0.457862
$661$	−8.97174e26	−1.44865	−0.724324	−	0.689459i	$-0.757848\pi$
$661$	−8.97174e26	−1.44865	−0.724324	+	0.689459i	$0.757848\pi$
$662$	−8.61361e25	−0.137099
$663$	3.97705e26	0.623998
$664$	1.82938e27	2.82948
$665$	−1.50111e26	−0.228879
$666$	−2.15855e27	−3.24457
$667$	2.48147e26	0.367717
$668$	2.42525e27	3.54307
$669$	1.56583e27	2.25526
$670$	−1.00568e26	−0.142808
$671$	−1.23906e26	−0.173471
$672$	−7.26638e27	−10.0302
$673$	9.62169e26	1.30951	0.654754	−	0.755842i	$-0.272772\pi$
$673$	9.62169e26	1.30951	0.654754	+	0.755842i	$0.272772\pi$
$674$	3.54188e26	0.475296
$675$	2.44892e27	3.24033
$676$	−1.55617e27	−2.03031
$677$	3.36905e26	0.433426	0.216713	−	0.976235i	$-0.430466\pi$
$677$	3.36905e26	0.433426	0.216713	+	0.976235i	$0.430466\pi$
$678$	−1.94388e27	−2.46596
$679$	8.63236e26	1.07986
$680$	1.65981e26	0.204749
$681$	7.63833e26	0.929182
$682$	−4.93938e26	−0.592544
$683$	−5.70022e26	−0.674365	−0.337183	−	0.941439i	$-0.609474\pi$
$683$	−5.70022e26	−0.674365	−0.337183	+	0.941439i	$0.609474\pi$
$684$	−8.58615e27	−10.0176
$685$	1.61306e26	0.185605
$686$	2.19077e27	2.48610
$687$	−2.56273e26	−0.286823
$688$	4.32426e27	4.77333
$689$	1.83315e26	0.199579
$690$	−6.60080e25	−0.0708810
$691$	−6.14845e26	−0.651215	−0.325607	−	0.945505i	$-0.605569\pi$
$691$	−6.14845e26	−0.651215	−0.325607	+	0.945505i	$0.605569\pi$
$692$	4.37204e27	4.56747
$693$	4.08170e27	4.20606
$694$	−3.65359e26	−0.371369
$695$	−1.19629e26	−0.119944
$696$	−1.11055e28	−10.9837
$697$	8.98300e26	0.876415
$698$	−2.51820e27	−2.42362
$699$	1.74206e27	1.65398
$700$	−4.63161e27	−4.33811
$701$	1.73508e26	0.160324	0.0801618	−	0.996782i	$-0.474456\pi$
$701$	1.73508e26	0.160324	0.0801618	+	0.996782i	$0.474456\pi$
$702$	3.25270e27	2.96511
$703$	9.91428e26	0.891632
$704$	2.82483e27	2.50641
$705$	3.11247e25	0.0272463
$706$	−1.95803e27	−1.69112
$707$	−9.59300e26	−0.817467
$708$	7.80036e26	0.655841
$709$	1.48987e27	1.23597	0.617986	−	0.786189i	$-0.287949\pi$
$709$	1.48987e27	1.23597	0.617986	+	0.786189i	$0.287949\pi$
$710$	1.67430e26	0.137050
$711$	−9.03375e26	−0.729637
$712$	−1.39707e27	−1.11342
$713$	−8.44699e25	−0.0664281
$714$	−5.36485e27	−4.16318
$715$	−5.63635e25	−0.0431609
$716$	1.52687e27	1.15380
$717$	1.91120e27	1.42519
$718$	−4.30242e27	−3.16614
$719$	6.62012e26	0.480774	0.240387	−	0.970677i	$-0.422726\pi$
$719$	6.62012e26	0.480774	0.240387	+	0.970677i	$0.422726\pi$
$720$	1.19527e27	0.856661
$721$	1.81632e27	1.28471
$722$	2.71824e27	1.89751
$723$	−4.29599e27	−2.95971
$724$	−4.04605e26	−0.275115
$725$	−2.72339e27	−1.82768
$726$	7.09146e26	0.469719
$727$	−8.57554e26	−0.560641	−0.280320	−	0.959907i	$-0.590441\pi$
$727$	−8.57554e26	−0.560641	−0.280320	+	0.959907i	$0.590441\pi$
$728$	−3.80852e27	−2.45759
$729$	5.35056e27	3.40791
$730$	−2.00061e26	−0.125775
$731$	1.60430e27	0.995566
$732$	1.53177e27	0.938294
$733$	7.58968e26	0.458918	0.229459	−	0.973318i	$-0.426304\pi$
$733$	7.58968e26	0.458918	0.229459	+	0.973318i	$0.426304\pi$
$734$	−3.53069e27	−2.10740
$735$	−5.65160e26	−0.332998
$736$	1.07099e27	0.622939
$737$	−1.25600e27	−0.721188
$738$	1.16673e28	6.61358
$739$	−1.36364e27	−0.763094	−0.381547	−	0.924349i	$-0.624609\pi$
$739$	−1.36364e27	−0.763094	−0.381547	+	0.924349i	$0.624609\pi$
$740$	−2.91173e26	−0.160861
$741$	−2.37253e27	−1.29401
$742$	−2.47282e27	−1.33155
$743$	−2.59731e27	−1.38080	−0.690399	−	0.723429i	$-0.742565\pi$
$743$	−2.59731e27	−1.38080	−0.690399	+	0.723429i	$0.742565\pi$
$744$	3.78034e27	1.98421
$745$	−2.01262e26	−0.104298
$746$	−1.00891e27	−0.516220
$747$	4.88751e27	2.46912
$748$	3.34835e27	1.67019
$749$	1.35965e27	0.669652
$750$	1.45576e27	0.707957
$751$	1.66466e26	0.0799366	0.0399683	−	0.999201i	$-0.487274\pi$
$751$	1.66466e26	0.0799366	0.0399683	+	0.999201i	$0.487274\pi$
$752$	−1.00499e27	−0.476530
$753$	6.22698e27	2.91558
$754$	−3.61726e27	−1.67244
$755$	1.39148e26	0.0635302
$756$	−3.17742e28	−14.3258
$757$	−2.87768e27	−1.28124	−0.640622	−	0.767856i	$-0.721324\pi$
$757$	−2.87768e27	−1.28124	−0.640622	+	0.767856i	$0.721324\pi$
$758$	−1.68467e27	−0.740727
$759$	−8.24374e26	−0.357954
$760$	−9.90165e26	−0.424599
$761$	−1.08027e27	−0.457486	−0.228743	−	0.973487i	$-0.573462\pi$
$761$	−1.08027e27	−0.457486	−0.228743	+	0.973487i	$0.573462\pi$
$762$	5.08545e27	2.12695
$763$	−2.30323e27	−0.951379
$764$	−6.36625e27	−2.59715
$765$	4.43446e26	0.178672
$766$	9.50710e26	0.378333
$767$	1.57294e26	0.0618237
$768$	−5.43152e27	−2.10858
$769$	1.01279e27	0.388348	0.194174	−	0.980967i	$-0.437797\pi$
$769$	1.01279e27	0.388348	0.194174	+	0.980967i	$0.437797\pi$
$770$	7.60317e26	0.287960
$771$	−2.98374e27	−1.11621
$772$	3.90323e27	1.44231
$773$	6.94060e26	0.253333	0.126666	−	0.991945i	$-0.459572\pi$
$773$	6.94060e26	0.253333	0.126666	+	0.991945i	$0.459572\pi$
$774$	2.08370e28	7.51272
$775$	9.27049e26	0.330169
$776$	5.69410e27	2.00327
$777$	5.82649e27	2.02492
$778$	7.57035e26	0.259902
$779$	−5.35885e27	−1.81746
$780$	6.96789e26	0.233455
$781$	2.09103e27	0.692111
$782$	7.90724e26	0.258560
$783$	−1.86833e28	−6.03554
$784$	1.82485e28	5.82404
$785$	−1.70873e26	−0.0538781
$786$	−1.75704e28	−5.47352
$787$	4.23826e27	1.30445	0.652226	−	0.758025i	$-0.273835\pi$
$787$	4.23826e27	1.30445	0.652226	+	0.758025i	$0.273835\pi$
$788$	1.61541e28	4.91227
$789$	2.03201e26	0.0610513
$790$	−1.68276e26	−0.0499533
$791$	3.82910e27	1.12310
$792$	2.69238e28	7.80274
$793$	3.08881e26	0.0884495
$794$	−8.75673e27	−2.47769
$795$	2.80087e26	0.0783079
$796$	1.96622e27	0.543196
$797$	5.89909e26	0.161039	0.0805195	−	0.996753i	$-0.474342\pi$
$797$	5.89909e26	0.161039	0.0805195	+	0.996753i	$0.474342\pi$
$798$	3.20043e28	8.63337
$799$	−3.72849e26	−0.0993891
$800$	−1.17540e28	−3.09621
$801$	−3.73251e27	−0.971611
$802$	−6.05439e27	−1.55745
$803$	−2.49857e27	−0.635175
$804$	1.55272e28	3.90086
$805$	1.30024e26	0.0322822
$806$	1.23132e27	0.302127
$807$	6.35809e27	1.54180
$808$	−6.32776e27	−1.51650
$809$	−2.77836e27	−0.658078	−0.329039	−	0.944316i	$-0.606725\pi$
$809$	−2.77836e27	−0.658078	−0.329039	+	0.944316i	$0.606725\pi$
$810$	2.83701e27	0.664131
$811$	−6.47250e27	−1.49752	−0.748762	−	0.662839i	$-0.769351\pi$
$811$	−6.47250e27	−1.49752	−0.748762	+	0.662839i	$0.769351\pi$
$812$	3.53355e28	8.08032
$813$	−8.45855e27	−1.91177
$814$	−5.02162e27	−1.12179
$815$	−6.92374e26	−0.152878
$816$	−1.96206e28	−4.28210
$817$	−9.57052e27	−2.06455
$818$	6.77161e26	0.144389
$819$	−1.01751e28	−2.14459
$820$	1.57384e27	0.327891
$821$	1.73022e27	0.356320	0.178160	−	0.984002i	$-0.442986\pi$
$821$	1.73022e27	0.356320	0.178160	+	0.984002i	$0.442986\pi$
$822$	−3.43911e28	−7.00106
$823$	−8.27657e27	−1.66553	−0.832764	−	0.553628i	$-0.813243\pi$
$823$	−8.27657e27	−1.66553	−0.832764	+	0.553628i	$0.813243\pi$
$824$	1.19808e28	2.38330
$825$	9.04743e27	1.77915
$826$	−2.12181e27	−0.412474
$827$	−4.95333e26	−0.0951907	−0.0475953	−	0.998867i	$-0.515156\pi$
$827$	−4.95333e26	−0.0951907	−0.0475953	+	0.998867i	$0.515156\pi$
$828$	7.43723e27	1.41294
$829$	−4.80035e27	−0.901582	−0.450791	−	0.892630i	$-0.648858\pi$
$829$	−4.80035e27	−0.901582	−0.450791	+	0.892630i	$0.648858\pi$
$830$	9.10419e26	0.169044
$831$	8.09662e27	1.48626
$832$	−7.04194e27	−1.27797
$833$	6.77018e27	1.21471
$834$	2.55054e28	4.52433
$835$	7.47220e26	0.131047
$836$	−1.99747e28	−3.46355
$837$	6.35983e27	1.09032
$838$	1.65976e28	2.81338
$839$	−1.07057e28	−1.79422	−0.897109	−	0.441809i	$-0.854337\pi$
$839$	−1.07057e28	−1.79422	−0.897109	+	0.441809i	$0.854337\pi$
$840$	−5.81906e27	−0.964273
$841$	1.46740e28	2.40429
$842$	−2.10704e28	−3.41356
$843$	−4.51029e27	−0.722508
$844$	1.46153e28	2.31501
$845$	−4.79457e26	−0.0750949
$846$	−4.84266e27	−0.750007
$847$	−1.39689e27	−0.213930
$848$	−9.04375e27	−1.36958
$849$	2.13934e28	3.20373
$850$	−8.67812e27	−1.28513
$851$	−8.58764e26	−0.125760
$852$	−2.58502e28	−3.74358
$853$	−5.96444e27	−0.854189	−0.427094	−	0.904207i	$-0.640463\pi$
$853$	−5.96444e27	−0.854189	−0.427094	+	0.904207i	$0.640463\pi$
$854$	−4.16665e27	−0.590116
$855$	−2.64540e27	−0.370521
$856$	8.96855e27	1.24229
$857$	−3.37745e27	−0.462669	−0.231335	−	0.972874i	$-0.574309\pi$
$857$	−3.37745e27	−0.462669	−0.231335	+	0.972874i	$0.574309\pi$
$858$	1.20170e28	1.62804
$859$	−1.36331e28	−1.82667	−0.913335	−	0.407209i	$-0.866502\pi$
$859$	−1.36331e28	−1.82667	−0.913335	+	0.407209i	$0.866502\pi$
$860$	2.81077e27	0.372469
$861$	−3.14932e28	−4.12750
$862$	−6.43392e27	−0.833981
$863$	−1.02469e28	−1.31368	−0.656840	−	0.754030i	$-0.728107\pi$
$863$	−1.02469e28	−1.31368	−0.656840	+	0.754030i	$0.728107\pi$
$864$	−8.06359e28	−10.2246
$865$	1.34703e27	0.168937
$866$	2.68394e28	3.32930
$867$	8.39949e27	1.03056
$868$	−1.20283e28	−1.45971
$869$	−2.10160e27	−0.252268
$870$	−5.52682e27	−0.656210
$871$	3.13105e27	0.367720
$872$	−1.51926e28	−1.76492
$873$	1.52128e28	1.74813
$874$	−4.71710e27	−0.536187
$875$	−2.86759e27	−0.322434
$876$	3.08883e28	3.43562
$877$	1.08654e28	1.19550	0.597752	−	0.801681i	$-0.296061\pi$
$877$	1.08654e28	1.19550	0.597752	+	0.801681i	$0.296061\pi$
$878$	−2.33310e27	−0.253943
$879$	−6.42239e27	−0.691516
$880$	2.78067e27	0.296186
$881$	1.78408e27	0.187993	0.0939966	−	0.995573i	$-0.470036\pi$
$881$	1.78408e27	0.187993	0.0939966	+	0.995573i	$0.470036\pi$
$882$	8.79328e28	9.16641
$883$	−2.99373e27	−0.308735	−0.154368	−	0.988013i	$-0.549334\pi$
$883$	−2.99373e27	−0.308735	−0.154368	+	0.988013i	$0.549334\pi$
$884$	−8.34699e27	−0.851596
$885$	2.40330e26	0.0242575
$886$	2.04690e28	2.04398
$887$	−9.70405e27	−0.958691	−0.479346	−	0.877626i	$-0.659126\pi$
$887$	−9.70405e27	−0.958691	−0.479346	+	0.877626i	$0.659126\pi$
$888$	3.84328e28	3.75646
$889$	−1.00174e28	−0.968702
$890$	−6.95273e26	−0.0665197
$891$	3.54315e28	3.35391
$892$	−3.28634e28	−3.07785
$893$	2.22425e27	0.206108
$894$	4.29100e28	3.93416
$895$	4.70430e26	0.0426753
$896$	3.69017e28	3.31223
$897$	2.05506e27	0.182514
$898$	8.74740e27	0.768695
$899$	−7.07264e27	−0.614985
$900$	−8.16228e28	−7.02276
$901$	−3.35523e27	−0.285651
$902$	2.71428e28	2.28661
$903$	−5.62446e28	−4.68864
$904$	2.52576e28	2.08349
$905$	−1.24659e26	−0.0101756
$906$	−2.96669e28	−2.39638
$907$	1.17294e28	0.937574	0.468787	−	0.883311i	$-0.344691\pi$
$907$	1.17294e28	0.937574	0.468787	+	0.883311i	$0.344691\pi$
$908$	−1.60312e28	−1.26809
$909$	−1.69057e28	−1.32336
$910$	−1.89537e27	−0.146825
$911$	6.81149e26	0.0522177	0.0261088	−	0.999659i	$-0.491688\pi$
$911$	6.81149e26	0.0522177	0.0261088	+	0.999659i	$0.491688\pi$
$912$	1.17048e29	8.87999
$913$	1.13702e28	0.853684
$914$	−7.90298e27	−0.587222
$915$	4.71940e26	0.0347046
$916$	5.37862e27	0.391439
$917$	3.46106e28	2.49288
$918$	−5.95345e28	−4.24388
$919$	−2.62678e28	−1.85322	−0.926608	−	0.376029i	$-0.877289\pi$
$919$	−2.62678e28	−1.85322	−0.926608	+	0.376029i	$0.877289\pi$
$920$	8.57670e26	0.0598874
$921$	−2.47922e28	−1.71336
$922$	3.59338e28	2.45787
$923$	−5.21267e27	−0.352894
$924$	−1.17389e29	−7.86579
$925$	9.42485e27	0.625069
$926$	3.31836e28	2.17831
$927$	3.20089e28	2.07976
$928$	8.96735e28	5.76711
$929$	−1.29802e28	−0.826286	−0.413143	−	0.910666i	$-0.635569\pi$
$929$	−1.29802e28	−0.826286	−0.413143	+	0.910666i	$0.635569\pi$
$930$	1.88134e27	0.118544
$931$	−4.03878e28	−2.51900
$932$	−3.65621e28	−2.25725
$933$	−1.47730e28	−0.902806
$934$	−2.04741e28	−1.23854
$935$	1.03163e27	0.0617750
$936$	−6.71175e28	−3.97846
$937$	6.12727e27	0.359535	0.179767	−	0.983709i	$-0.442466\pi$
$937$	6.12727e27	0.359535	0.179767	+	0.983709i	$0.442466\pi$
$938$	−4.22363e28	−2.45335
$939$	3.21154e28	1.84667
$940$	−6.53241e26	−0.0371842
$941$	−2.89335e28	−1.63042	−0.815209	−	0.579167i	$-0.803378\pi$
$941$	−2.89335e28	−1.63042	−0.815209	+	0.579167i	$0.803378\pi$
$942$	3.64309e28	2.03230
$943$	4.64177e27	0.256344
$944$	−7.76001e27	−0.424257
$945$	−9.78967e27	−0.529866
$946$	4.84750e28	2.59748
$947$	7.77729e27	0.412575	0.206288	−	0.978491i	$-0.433862\pi$
$947$	7.77729e27	0.412575	0.206288	+	0.978491i	$0.433862\pi$
$948$	2.59808e28	1.36450
$949$	6.22860e27	0.323863
$950$	5.17697e28	2.66503
$951$	1.55798e28	0.794048
$952$	6.97078e28	3.51747
$953$	1.50910e28	0.753936	0.376968	−	0.926226i	$-0.376967\pi$
$953$	1.50910e28	0.753936	0.376968	+	0.926226i	$0.376967\pi$
$954$	−4.35785e28	−2.15557
$955$	−1.96145e27	−0.0960603
$956$	−4.01120e28	−1.94502
$957$	−6.90246e28	−3.31391
$958$	−4.39136e28	−2.08750
$959$	6.77445e28	3.18858
$960$	−1.07594e28	−0.501432
$961$	−1.92631e28	−0.888903
$962$	1.25182e28	0.571979
$963$	2.39611e28	1.08407
$964$	9.01637e28	4.03924
$965$	1.20259e27	0.0533467
$966$	−2.77217e28	−1.21769
$967$	2.01830e28	0.877878	0.438939	−	0.898517i	$-0.355354\pi$
$967$	2.01830e28	0.877878	0.438939	+	0.898517i	$0.355354\pi$
$968$	−9.21424e27	−0.396866
$969$	4.34247e28	1.85208
$970$	2.83376e27	0.119683
$971$	−6.82995e27	−0.285650	−0.142825	−	0.989748i	$-0.545619\pi$
$971$	−6.82995e27	−0.285650	−0.142825	+	0.989748i	$0.545619\pi$
$972$	−2.30665e29	−9.55327
$973$	−5.02411e28	−2.06057
$974$	−6.30317e28	−2.56005
$975$	−2.25541e28	−0.907154
$976$	−1.52385e28	−0.606972
$977$	2.33839e28	0.922400	0.461200	−	0.887296i	$-0.347419\pi$
$977$	2.33839e28	0.922400	0.461200	+	0.887296i	$0.347419\pi$
$978$	1.47617e29	5.76658
$979$	−8.68327e27	−0.335929
$980$	1.18615e28	0.454457
$981$	−4.05897e28	−1.54014
$982$	1.94997e28	0.732770
$983$	2.11627e28	0.787614	0.393807	−	0.919193i	$-0.371158\pi$
$983$	2.11627e28	0.787614	0.393807	+	0.919193i	$0.371158\pi$
$984$	−2.07736e29	−7.65701
$985$	4.97707e27	0.181690
$986$	6.62070e28	2.39372
$987$	1.30716e28	0.468075
$988$	4.97944e28	1.76599
$989$	8.28987e27	0.291195
$990$	1.33990e28	0.466165
$991$	7.58589e27	0.261401	0.130700	−	0.991422i	$-0.458277\pi$
$991$	7.58589e27	0.261401	0.130700	+	0.991422i	$0.458277\pi$
$992$	−3.05251e28	−1.04183
$993$	4.09741e27	0.138513
$994$	7.03164e28	2.35443
$995$	6.05792e26	0.0200911
$996$	−1.40564e29	−4.61752
$997$	−5.20024e28	−1.69207	−0.846037	−	0.533123i	$-0.821018\pi$
$997$	−5.20024e28	−1.69207	−0.846037	+	0.533123i	$0.821018\pi$
$998$	−1.05867e29	−3.41208
$999$	6.46573e28	2.06417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.38	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.38	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q+1378.66 q^{2} -65581.5 q^{3} +1.37642e6 q^{4} +424075. q^{5} -9.04146e7 q^{6} +1.78101e8 q^{7} +1.17480e9 q^{8} +3.13867e9 q^{9} +O(q^{10})\)	\(q+1378.66 q^{2} -65581.5 q^{3} +1.37642e6 q^{4} +424075. q^{5} -9.04146e7 q^{6} +1.78101e8 q^{7} +1.17480e9 q^{8} +3.13867e9 q^{9} +5.84655e8 q^{10} +7.30177e9 q^{11} -9.02675e10 q^{12} -1.82024e10 q^{13} +2.45541e11 q^{14} -2.78115e10 q^{15} +8.98006e11 q^{16} +3.33160e11 q^{17} +4.32716e12 q^{18} -1.98748e12 q^{19} +5.83704e11 q^{20} -1.16801e13 q^{21} +1.00667e13 q^{22} +1.72153e12 q^{23} -7.70449e13 q^{24} -1.88936e13 q^{25} -2.50949e13 q^{26} -1.29616e14 q^{27} +2.45141e14 q^{28} +1.44143e14 q^{29} -3.83426e13 q^{30} -4.90667e13 q^{31} +6.22114e14 q^{32} -4.78861e14 q^{33} +4.59314e14 q^{34} +7.55282e13 q^{35} +4.32012e15 q^{36} -4.98837e14 q^{37} -2.74006e15 q^{38} +1.19374e15 q^{39} +4.98201e14 q^{40} +2.69630e15 q^{41} -1.61029e16 q^{42} +4.81541e15 q^{43} +1.00503e16 q^{44} +1.33103e15 q^{45} +2.37341e15 q^{46} -1.11913e15 q^{47} -5.88926e16 q^{48} +2.03211e16 q^{49} -2.60479e16 q^{50} -2.18491e16 q^{51} -2.50540e16 q^{52} -1.00709e16 q^{53} -1.78696e17 q^{54} +3.09650e15 q^{55} +2.09232e17 q^{56} +1.30342e17 q^{57} +1.98725e17 q^{58} -8.64139e15 q^{59} -3.82802e16 q^{60} -1.69693e16 q^{61} -6.76464e16 q^{62} +5.59001e17 q^{63} +3.86870e17 q^{64} -7.71916e15 q^{65} -6.60187e17 q^{66} -1.72013e17 q^{67} +4.58566e17 q^{68} -1.12901e17 q^{69} +1.04128e17 q^{70} +2.86373e17 q^{71} +3.68730e18 q^{72} -3.42186e17 q^{73} -6.87727e17 q^{74} +1.23907e18 q^{75} -2.73560e18 q^{76} +1.30045e18 q^{77} +1.64576e18 q^{78} -2.87821e17 q^{79} +3.80822e17 q^{80} +4.85245e18 q^{81} +3.71729e18 q^{82} +1.55719e18 q^{83} -1.60767e19 q^{84} +1.41285e17 q^{85} +6.63881e18 q^{86} -9.45313e18 q^{87} +8.57809e18 q^{88} -1.18920e18 q^{89} +1.83504e18 q^{90} -3.24186e18 q^{91} +2.36954e18 q^{92} +3.21787e18 q^{93} -1.54290e18 q^{94} -8.42840e17 q^{95} -4.07992e19 q^{96} +4.84689e18 q^{97} +2.80159e19 q^{98} +2.29179e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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