LMFDB - Embedded newform 47.20.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-350.911 q^{2} +55855.4 q^{3} -401150. q^{4} +2.41892e6 q^{5} -1.96003e7 q^{6} +9.44084e7 q^{7} +3.24746e8 q^{8} +1.95756e9 q^{9} +O(q^{10})$	\(q-350.911 q^{2} +55855.4 q^{3} -401150. q^{4} +2.41892e6 q^{5} -1.96003e7 q^{6} +9.44084e7 q^{7} +3.24746e8 q^{8} +1.95756e9 q^{9} -8.48826e8 q^{10} +1.32182e10 q^{11} -2.24064e10 q^{12} +7.42221e10 q^{13} -3.31289e10 q^{14} +1.35110e11 q^{15} +9.63609e10 q^{16} +8.03160e11 q^{17} -6.86930e11 q^{18} +8.34528e11 q^{19} -9.70349e11 q^{20} +5.27322e12 q^{21} -4.63840e12 q^{22} -1.72649e13 q^{23} +1.81388e13 q^{24} -1.32223e13 q^{25} -2.60453e13 q^{26} +4.44219e13 q^{27} -3.78719e13 q^{28} -3.50480e13 q^{29} -4.74115e13 q^{30} +1.81634e14 q^{31} -2.04075e14 q^{32} +7.38306e14 q^{33} -2.81838e14 q^{34} +2.28366e14 q^{35} -7.85276e14 q^{36} -6.44566e13 q^{37} -2.92845e14 q^{38} +4.14570e15 q^{39} +7.85535e14 q^{40} -5.90434e14 q^{41} -1.85043e15 q^{42} -4.36598e14 q^{43} -5.30246e15 q^{44} +4.73519e15 q^{45} +6.05844e15 q^{46} -1.11913e15 q^{47} +5.38228e15 q^{48} -2.48596e15 q^{49} +4.63985e15 q^{50} +4.48608e16 q^{51} -2.97742e16 q^{52} -3.01680e15 q^{53} -1.55881e16 q^{54} +3.19737e16 q^{55} +3.06588e16 q^{56} +4.66129e16 q^{57} +1.22987e16 q^{58} -8.65481e16 q^{59} -5.41992e16 q^{60} +6.02495e16 q^{61} -6.37375e16 q^{62} +1.84810e17 q^{63} +2.10911e16 q^{64} +1.79537e17 q^{65} -2.59079e17 q^{66} -1.13708e17 q^{67} -3.22187e17 q^{68} -9.64337e17 q^{69} -8.01362e16 q^{70} -2.40293e17 q^{71} +6.35711e17 q^{72} -6.22889e17 q^{73} +2.26185e16 q^{74} -7.38537e17 q^{75} -3.34770e17 q^{76} +1.24791e18 q^{77} -1.45477e18 q^{78} -9.82397e16 q^{79} +2.33089e17 q^{80} +2.06002e17 q^{81} +2.07190e17 q^{82} -9.34152e17 q^{83} -2.11535e18 q^{84} +1.94278e18 q^{85} +1.53207e17 q^{86} -1.95762e18 q^{87} +4.29255e18 q^{88} +2.59940e18 q^{89} -1.66163e18 q^{90} +7.00719e18 q^{91} +6.92580e18 q^{92} +1.01453e19 q^{93} +3.92715e17 q^{94} +2.01866e18 q^{95} -1.13987e19 q^{96} +8.91807e18 q^{97} +8.72349e17 q^{98} +2.58754e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−350.911	−0.484632	−0.242316	−	0.970197i	$-0.577907\pi$
$2$	−350.911	−0.484632	−0.242316	+	0.970197i	$0.577907\pi$
$3$	55855.4	1.63837	0.819187	−	0.573526i	$-0.194425\pi$
$3$	55855.4	1.63837	0.819187	+	0.573526i	$0.194425\pi$
$4$	−401150.	−0.765132
$5$	2.41892e6	0.553868	0.276934	−	0.960889i	$-0.410682\pi$
$5$	2.41892e6	0.553868	0.276934	+	0.960889i	$0.410682\pi$
$6$	−1.96003e7	−0.794008
$7$	9.44084e7	0.884258	0.442129	−	0.896951i	$-0.354223\pi$
$7$	9.44084e7	0.884258	0.442129	+	0.896951i	$0.354223\pi$
$8$	3.24746e8	0.855439
$9$	1.95756e9	1.68427
$10$	−8.48826e8	−0.268422
$11$	1.32182e10	1.69021	0.845105	−	0.534601i	$-0.179538\pi$
$11$	1.32182e10	1.69021	0.845105	+	0.534601i	$0.179538\pi$
$12$	−2.24064e10	−1.25357
$13$	7.42221e10	1.94120	0.970602	−	0.240689i	$-0.0773733\pi$
$13$	7.42221e10	1.94120	0.970602	+	0.240689i	$0.0773733\pi$
$14$	−3.31289e10	−0.428540
$15$	1.35110e11	0.907444
$16$	9.63609e10	0.350559
$17$	8.03160e11	1.64262	0.821310	−	0.570482i	$-0.193243\pi$
$17$	8.03160e11	1.64262	0.821310	+	0.570482i	$0.193243\pi$
$18$	−6.86930e11	−0.816251
$19$	8.34528e11	0.593310	0.296655	−	0.954985i	$-0.404129\pi$
$19$	8.34528e11	0.593310	0.296655	+	0.954985i	$0.404129\pi$
$20$	−9.70349e11	−0.423782
$21$	5.27322e12	1.44875
$22$	−4.63840e12	−0.819129
$23$	−1.72649e13	−1.99871	−0.999354	−	0.0359486i	$-0.988555\pi$
$23$	−1.72649e13	−1.99871	−0.999354	+	0.0359486i	$0.988555\pi$
$24$	1.81388e13	1.40153
$25$	−1.32223e13	−0.693230
$26$	−2.60453e13	−0.940770
$27$	4.44219e13	1.12109
$28$	−3.78719e13	−0.676574
$29$	−3.50480e13	−0.448623	−0.224312	−	0.974517i	$-0.572013\pi$
$29$	−3.50480e13	−0.448623	−0.224312	+	0.974517i	$0.572013\pi$
$30$	−4.74115e13	−0.439776
$31$	1.81634e14	1.23385	0.616925	−	0.787022i	$-0.288378\pi$
$31$	1.81634e14	1.23385	0.616925	+	0.787022i	$0.288378\pi$
$32$	−2.04075e14	−1.02533
$33$	7.38306e14	2.76920
$34$	−2.81838e14	−0.796066
$35$	2.28366e14	0.489763
$36$	−7.85276e14	−1.28869
$37$	−6.44566e13	−0.0815364	−0.0407682	−	0.999169i	$-0.512981\pi$
$37$	−6.44566e13	−0.0815364	−0.0407682	+	0.999169i	$0.512981\pi$
$38$	−2.92845e14	−0.287537
$39$	4.14570e15	3.18042
$40$	7.85535e14	0.473801
$41$	−5.90434e14	−0.281660	−0.140830	−	0.990034i	$-0.544977\pi$
$41$	−5.90434e14	−0.281660	−0.140830	+	0.990034i	$0.544977\pi$
$42$	−1.85043e15	−0.702109
$43$	−4.36598e14	−0.132474	−0.0662371	−	0.997804i	$-0.521099\pi$
$43$	−4.36598e14	−0.132474	−0.0662371	+	0.997804i	$0.521099\pi$
$44$	−5.30246e15	−1.29323
$45$	4.73519e15	0.932864
$46$	6.05844e15	0.968637
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	5.38228e15	0.574347
$49$	−2.48596e15	−0.218087
$50$	4.63985e15	0.335961
$51$	4.48608e16	2.69123
$52$	−2.97742e16	−1.48528
$53$	−3.01680e15	−0.125581	−0.0627907	−	0.998027i	$-0.520000\pi$
$53$	−3.01680e15	−0.125581	−0.0627907	+	0.998027i	$0.520000\pi$
$54$	−1.55881e16	−0.543317
$55$	3.19737e16	0.936154
$56$	3.06588e16	0.756429
$57$	4.66129e16	0.972064
$58$	1.22987e16	0.217417
$59$	−8.65481e16	−1.30066	−0.650329	−	0.759653i	$-0.725369\pi$
$59$	−8.65481e16	−1.30066	−0.650329	+	0.759653i	$0.725369\pi$
$60$	−5.41992e16	−0.694314
$61$	6.02495e16	0.659659	0.329830	−	0.944040i	$-0.393009\pi$
$61$	6.02495e16	0.659659	0.329830	+	0.944040i	$0.393009\pi$
$62$	−6.37375e16	−0.597963
$63$	1.84810e17	1.48933
$64$	2.10911e16	0.146349
$65$	1.79537e17	1.07517
$66$	−2.59079e17	−1.34204
$67$	−1.13708e17	−0.510598	−0.255299	−	0.966862i	$-0.582174\pi$
$67$	−1.13708e17	−0.510598	−0.255299	+	0.966862i	$0.582174\pi$
$68$	−3.22187e17	−1.25682
$69$	−9.64337e17	−3.27463
$70$	−8.01362e16	−0.237355
$71$	−2.40293e17	−0.621995	−0.310998	−	0.950411i	$-0.600663\pi$
$71$	−2.40293e17	−0.621995	−0.310998	+	0.950411i	$0.600663\pi$
$72$	6.35711e17	1.44079
$73$	−6.22889e17	−1.23835	−0.619175	−	0.785253i	$-0.712533\pi$
$73$	−6.22889e17	−1.23835	−0.619175	+	0.785253i	$0.712533\pi$
$74$	2.26185e16	0.0395151
$75$	−7.38537e17	−1.13577
$76$	−3.34770e17	−0.453960
$77$	1.24791e18	1.49458
$78$	−1.45477e18	−1.54133
$79$	−9.82397e16	−0.0922209	−0.0461105	−	0.998936i	$-0.514683\pi$
$79$	−9.82397e16	−0.0922209	−0.0461105	+	0.998936i	$0.514683\pi$
$80$	2.33089e17	0.194163
$81$	2.06002e17	0.152498
$82$	2.07190e17	0.136501
$83$	−9.34152e17	−0.548499	−0.274249	−	0.961659i	$-0.588429\pi$
$83$	−9.34152e17	−0.548499	−0.274249	+	0.961659i	$0.588429\pi$
$84$	−2.11535e18	−1.10848
$85$	1.94278e18	0.909796
$86$	1.53207e17	0.0642012
$87$	−1.95762e18	−0.735013
$88$	4.29255e18	1.44587
$89$	2.59940e18	0.786446	0.393223	−	0.919443i	$-0.371360\pi$
$89$	2.59940e18	0.786446	0.393223	+	0.919443i	$0.371360\pi$
$90$	−1.66163e18	−0.452096
$91$	7.00719e18	1.71653
$92$	6.92580e18	1.52927
$93$	1.01453e19	2.02151
$94$	3.92715e17	0.0706908
$95$	2.01866e18	0.328616
$96$	−1.13987e19	−1.67988
$97$	8.91807e18	1.19108	0.595538	−	0.803327i	$-0.296939\pi$
$97$	8.91807e18	1.19108	0.595538	+	0.803327i	$0.296939\pi$
$98$	8.72349e17	0.105692
$99$	2.58754e19	2.84677
$100$	5.30412e18	0.530412
$101$	−8.39659e18	−0.763924	−0.381962	−	0.924178i	$-0.624751\pi$
$101$	−8.39659e18	−0.763924	−0.381962	+	0.924178i	$0.624751\pi$
$102$	−1.57421e19	−1.30425
$103$	−1.94943e19	−1.47216	−0.736079	−	0.676896i	$-0.763325\pi$
$103$	−1.94943e19	−1.47216	−0.736079	+	0.676896i	$0.763325\pi$
$104$	2.41033e19	1.66058
$105$	1.27555e19	0.802415
$106$	1.05863e18	0.0608607
$107$	−1.22568e19	−0.644513	−0.322256	−	0.946652i	$-0.604441\pi$
$107$	−1.22568e19	−0.644513	−0.322256	+	0.946652i	$0.604441\pi$
$108$	−1.78198e19	−0.857783
$109$	−1.42366e19	−0.627846	−0.313923	−	0.949448i	$-0.601643\pi$
$109$	−1.42366e19	−0.627846	−0.313923	+	0.949448i	$0.601643\pi$
$110$	−1.12199e19	−0.453690
$111$	−3.60025e18	−0.133587
$112$	9.09727e18	0.309985
$113$	2.74857e18	0.0860718	0.0430359	−	0.999074i	$-0.486297\pi$
$113$	2.74857e18	0.0860718	0.0430359	+	0.999074i	$0.486297\pi$
$114$	−1.63570e19	−0.471093
$115$	−4.17624e19	−1.10702
$116$	1.40595e19	0.343256
$117$	1.45294e20	3.26951
$118$	3.03707e19	0.630340
$119$	7.58250e19	1.45250
$120$	4.38764e19	0.776263
$121$	1.13561e20	1.85681
$122$	−2.11422e19	−0.319692
$123$	−3.29789e19	−0.461464
$124$	−7.28626e19	−0.944057
$125$	−7.81210e19	−0.937826
$126$	−6.48520e19	−0.721777
$127$	−5.41106e18	−0.0558659	−0.0279330	−	0.999610i	$-0.508892\pi$
$127$	−5.41106e18	−0.0558659	−0.0279330	+	0.999610i	$0.508892\pi$
$128$	9.95928e19	0.954406
$129$	−2.43863e19	−0.217042
$130$	−6.30016e19	−0.521063
$131$	−2.70907e19	−0.208326	−0.104163	−	0.994560i	$-0.533216\pi$
$131$	−2.70907e19	−0.208326	−0.104163	+	0.994560i	$0.533216\pi$
$132$	−2.96171e20	−2.11880
$133$	7.87864e19	0.524639
$134$	3.99013e19	0.247452
$135$	1.07453e20	0.620937
$136$	2.60823e20	1.40516
$137$	2.00820e20	1.00916	0.504581	−	0.863364i	$-0.331647\pi$
$137$	2.00820e20	1.00916	0.504581	+	0.863364i	$0.331647\pi$
$138$	3.38396e20	1.58699
$139$	−2.99967e20	−1.31351	−0.656755	−	0.754104i	$-0.728071\pi$
$139$	−2.99967e20	−1.31351	−0.656755	+	0.754104i	$0.728071\pi$
$140$	−9.16090e19	−0.374733
$141$	−6.25095e19	−0.238981
$142$	8.43215e19	0.301439
$143$	9.81080e20	3.28104
$144$	1.88633e20	0.590436
$145$	−8.47782e19	−0.248478
$146$	2.18579e20	0.600144
$147$	−1.38854e20	−0.357309
$148$	2.58568e19	0.0623861
$149$	1.94952e20	0.441223	0.220611	−	0.975362i	$-0.429195\pi$
$149$	1.94952e20	0.441223	0.220611	+	0.975362i	$0.429195\pi$
$150$	2.59161e20	0.550430
$151$	−1.85061e20	−0.369007	−0.184504	−	0.982832i	$-0.559068\pi$
$151$	−1.85061e20	−0.369007	−0.184504	+	0.982832i	$0.559068\pi$
$152$	2.71010e20	0.507541
$153$	1.57224e21	2.76662
$154$	−4.37904e20	−0.724322
$155$	4.39359e20	0.683390
$156$	−1.66305e21	−2.43344
$157$	−3.19534e20	−0.440018	−0.220009	−	0.975498i	$-0.570609\pi$
$157$	−3.19534e20	−0.440018	−0.220009	+	0.975498i	$0.570609\pi$
$158$	3.44734e19	0.0446932
$159$	−1.68504e20	−0.205749
$160$	−4.93640e20	−0.567899
$161$	−1.62995e21	−1.76737
$162$	−7.22882e19	−0.0739052
$163$	−2.36176e19	−0.0227748	−0.0113874	−	0.999935i	$-0.503625\pi$
$163$	−2.36176e19	−0.0227748	−0.0113874	+	0.999935i	$0.503625\pi$
$164$	2.36853e20	0.215507
$165$	1.78590e21	1.53377
$166$	3.27804e20	0.265820
$167$	1.67565e21	1.28344	0.641721	−	0.766938i	$-0.278221\pi$
$167$	1.67565e21	1.28344	0.641721	+	0.766938i	$0.278221\pi$
$168$	1.71246e21	1.23931
$169$	4.04700e21	2.76828
$170$	−6.81743e20	−0.440916
$171$	1.63364e21	0.999295
$172$	1.75141e20	0.101360
$173$	−2.82682e21	−1.54832	−0.774158	−	0.632992i	$-0.781827\pi$
$173$	−2.82682e21	−1.54832	−0.774158	+	0.632992i	$0.781827\pi$
$174$	6.86949e20	0.356211
$175$	−1.24830e21	−0.612994
$176$	1.27371e21	0.592518
$177$	−4.83418e21	−2.13097
$178$	−9.12159e20	−0.381137
$179$	−4.33909e21	−1.71908	−0.859538	−	0.511072i	$-0.829249\pi$
$179$	−4.33909e21	−1.71908	−0.859538	+	0.511072i	$0.829249\pi$
$180$	−1.89952e21	−0.713764
$181$	−3.03617e21	−1.08238	−0.541190	−	0.840900i	$-0.682026\pi$
$181$	−3.03617e21	−1.08238	−0.541190	+	0.840900i	$0.682026\pi$
$182$	−2.45890e21	−0.831883
$183$	3.36526e21	1.08077
$184$	−5.60670e21	−1.70977
$185$	−1.55916e20	−0.0451604
$186$	−3.56008e21	−0.979687
$187$	1.06163e22	2.77637
$188$	4.48939e20	0.111606
$189$	4.19380e21	0.991335
$190$	−7.08369e20	−0.159258
$191$	−3.62225e21	−0.774750	−0.387375	−	0.921922i	$-0.626618\pi$
$191$	−3.62225e21	−0.774750	−0.387375	+	0.921922i	$0.626618\pi$
$192$	1.17805e21	0.239775
$193$	6.47868e21	1.25514	0.627570	−	0.778561i	$-0.284050\pi$
$193$	6.47868e21	1.25514	0.627570	+	0.778561i	$0.284050\pi$
$194$	−3.12945e21	−0.577233
$195$	1.00281e22	1.76153
$196$	9.97240e20	0.166866
$197$	6.94614e21	1.10742	0.553712	−	0.832708i	$-0.313211\pi$
$197$	6.94614e21	1.10742	0.553712	+	0.832708i	$0.313211\pi$
$198$	−9.07996e21	−1.37964
$199$	1.31280e22	1.90150	0.950749	−	0.309963i	$-0.100317\pi$
$199$	1.31280e22	1.90150	0.950749	+	0.309963i	$0.100317\pi$
$200$	−4.29389e21	−0.593016
$201$	−6.35119e21	−0.836551
$202$	2.94646e21	0.370222
$203$	−3.30882e21	−0.396699
$204$	−1.79959e22	−2.05914
$205$	−1.42821e21	−0.156003
$206$	6.84077e21	0.713454
$207$	−3.37971e22	−3.36636
$208$	7.15211e21	0.680507
$209$	1.10309e22	1.00282
$210$	−4.47604e21	−0.388876
$211$	−1.17402e22	−0.974975	−0.487488	−	0.873130i	$-0.662087\pi$
$211$	−1.17402e22	−0.974975	−0.487488	+	0.873130i	$0.662087\pi$
$212$	1.21019e21	0.0960863
$213$	−1.34217e22	−1.01906
$214$	4.30105e21	0.312351
$215$	−1.05610e21	−0.0733733
$216$	1.44258e22	0.959026
$217$	1.71478e22	1.09104
$218$	4.99576e21	0.304274
$219$	−3.47917e22	−2.02888
$220$	−1.28262e22	−0.716281
$221$	5.96122e22	3.18866
$222$	1.26337e21	0.0647406
$223$	−2.83647e22	−1.39278	−0.696389	−	0.717664i	$-0.745211\pi$
$223$	−2.83647e22	−1.39278	−0.696389	+	0.717664i	$0.745211\pi$
$224$	−1.92664e22	−0.906658
$225$	−2.58835e22	−1.16759
$226$	−9.64502e20	−0.0417131
$227$	−2.90866e22	−1.20628	−0.603139	−	0.797636i	$-0.706084\pi$
$227$	−2.90866e22	−1.20628	−0.603139	+	0.797636i	$0.706084\pi$
$228$	−1.86987e22	−0.743757
$229$	−1.63809e21	−0.0625031	−0.0312515	−	0.999512i	$-0.509949\pi$
$229$	−1.63809e21	−0.0625031	−0.0312515	+	0.999512i	$0.509949\pi$
$230$	1.46549e22	0.536498
$231$	6.97022e22	2.44868
$232$	−1.13817e22	−0.383770
$233$	−2.19684e22	−0.711078	−0.355539	−	0.934661i	$-0.615703\pi$
$233$	−2.19684e22	−0.711078	−0.355539	+	0.934661i	$0.615703\pi$
$234$	−5.09854e22	−1.58451
$235$	−2.70709e21	−0.0807900
$236$	3.47187e22	0.995175
$237$	−5.48721e21	−0.151092
$238$	−2.66078e22	−0.703928
$239$	−1.86968e22	−0.475321	−0.237660	−	0.971348i	$-0.576380\pi$
$239$	−1.86968e22	−0.475321	−0.237660	+	0.971348i	$0.576380\pi$
$240$	1.30193e22	0.318113
$241$	−2.11947e22	−0.497812	−0.248906	−	0.968528i	$-0.580071\pi$
$241$	−2.11947e22	−0.497812	−0.248906	+	0.968528i	$0.580071\pi$
$242$	−3.98497e22	−0.899868
$243$	−4.01235e22	−0.871244
$244$	−2.41690e22	−0.504726
$245$	−6.01333e21	−0.120792
$246$	1.15727e22	0.223640
$247$	6.19404e22	1.15174
$248$	5.89851e22	1.05548
$249$	−5.21774e22	−0.898646
$250$	2.74135e22	0.454501
$251$	1.05281e23	1.68054	0.840272	−	0.542164i	$-0.182395\pi$
$251$	1.05281e23	1.68054	0.840272	+	0.542164i	$0.182395\pi$
$252$	−7.41366e22	−1.13953
$253$	−2.28210e23	−3.37823
$254$	1.89880e21	0.0270744
$255$	1.08515e23	1.49059
$256$	−4.60060e22	−0.608885
$257$	8.96137e22	1.14290	0.571452	−	0.820635i	$-0.306380\pi$
$257$	8.96137e22	1.14290	0.571452	+	0.820635i	$0.306380\pi$
$258$	8.55744e21	0.105186
$259$	−6.08525e21	−0.0720992
$260$	−7.20213e22	−0.822648
$261$	−6.86086e22	−0.755603
$262$	9.50644e21	0.100961
$263$	6.38991e22	0.654508	0.327254	−	0.944936i	$-0.393877\pi$
$263$	6.38991e22	0.654508	0.327254	+	0.944936i	$0.393877\pi$
$264$	2.39762e23	2.36888
$265$	−7.29739e21	−0.0695556
$266$	−2.76470e22	−0.254257
$267$	1.45191e23	1.28849
$268$	4.56138e22	0.390675
$269$	4.64626e22	0.384111	0.192056	−	0.981384i	$-0.438485\pi$
$269$	4.64626e22	0.384111	0.192056	+	0.981384i	$0.438485\pi$
$270$	−3.77064e22	−0.300926
$271$	−1.32803e23	−1.02329	−0.511645	−	0.859197i	$-0.670964\pi$
$271$	−1.32803e23	−1.02329	−0.511645	+	0.859197i	$0.670964\pi$
$272$	7.73932e22	0.575835
$273$	3.91389e23	2.81231
$274$	−7.04698e22	−0.489072
$275$	−1.74775e23	−1.17170
$276$	3.86843e23	2.50552
$277$	−1.01783e23	−0.636970	−0.318485	−	0.947928i	$-0.603174\pi$
$277$	−1.01783e23	−0.636970	−0.318485	+	0.947928i	$0.603174\pi$
$278$	1.05262e23	0.636569
$279$	3.55561e23	2.07814
$280$	7.41611e22	0.418962
$281$	−1.45470e23	−0.794444	−0.397222	−	0.917723i	$-0.630026\pi$
$281$	−1.45470e23	−0.794444	−0.397222	+	0.917723i	$0.630026\pi$
$282$	2.19353e22	0.115818
$283$	−7.50857e22	−0.383342	−0.191671	−	0.981459i	$-0.561391\pi$
$283$	−7.50857e22	−0.383342	−0.191671	+	0.981459i	$0.561391\pi$
$284$	9.63935e22	0.475909
$285$	1.12753e23	0.538395
$286$	−3.44272e23	−1.59010
$287$	−5.57420e22	−0.249060
$288$	−3.99489e23	−1.72694
$289$	4.05993e23	1.69820
$290$	2.97496e22	0.120420
$291$	4.98122e23	1.95143
$292$	2.49872e23	0.947502
$293$	2.69366e23	0.988782	0.494391	−	0.869240i	$-0.335391\pi$
$293$	2.69366e23	0.988782	0.494391	+	0.869240i	$0.335391\pi$
$294$	4.87254e22	0.173163
$295$	−2.09353e23	−0.720394
$296$	−2.09320e22	−0.0697494
$297$	5.87176e23	1.89488
$298$	−6.84108e22	−0.213831
$299$	−1.28144e24	−3.87990
$300$	2.96264e23	0.869014
$301$	−4.12185e22	−0.117141
$302$	6.49401e22	0.178833
$303$	−4.68995e23	−1.25159
$304$	8.04158e22	0.207990
$305$	1.45739e23	0.365364
$306$	−5.51715e23	−1.34079
$307$	2.98750e23	0.703872	0.351936	−	0.936024i	$-0.385523\pi$
$307$	2.98750e23	0.703872	0.351936	+	0.936024i	$0.385523\pi$
$308$	−5.00596e23	−1.14355
$309$	−1.08886e24	−2.41195
$310$	−1.54176e23	−0.331193
$311$	−2.28578e23	−0.476224	−0.238112	−	0.971238i	$-0.576529\pi$
$311$	−2.28578e23	−0.476224	−0.238112	+	0.971238i	$0.576529\pi$
$312$	1.34630e24	2.72066
$313$	4.15851e22	0.0815204	0.0407602	−	0.999169i	$-0.487022\pi$
$313$	4.15851e22	0.0815204	0.0407602	+	0.999169i	$0.487022\pi$
$314$	1.12128e23	0.213247
$315$	4.47042e23	0.824893
$316$	3.94088e22	0.0705612
$317$	8.31972e23	1.44559	0.722796	−	0.691062i	$-0.242857\pi$
$317$	8.31972e23	1.44559	0.722796	+	0.691062i	$0.242857\pi$
$318$	5.91300e22	0.0997127
$319$	−4.63270e23	−0.758267
$320$	5.10178e22	0.0810582
$321$	−6.84609e23	−1.05595
$322$	5.71967e23	0.856525
$323$	6.70259e23	0.974583
$324$	−8.26374e22	−0.116681
$325$	−9.81387e23	−1.34570
$326$	8.28768e21	0.0110374
$327$	−7.95188e23	−1.02865
$328$	−1.91741e23	−0.240943
$329$	−1.05655e23	−0.128982
$330$	−6.26693e23	−0.743314
$331$	1.88075e23	0.216753	0.108377	−	0.994110i	$-0.465435\pi$
$331$	1.88075e23	0.216753	0.108377	+	0.994110i	$0.465435\pi$
$332$	3.74734e23	0.419674
$333$	−1.26178e23	−0.137329
$334$	−5.88003e23	−0.621997
$335$	−2.75050e23	−0.282804
$336$	5.08132e23	0.507871
$337$	3.50044e23	0.340125	0.170063	−	0.985433i	$-0.445603\pi$
$337$	3.50044e23	0.340125	0.170063	+	0.985433i	$0.445603\pi$
$338$	−1.42014e24	−1.34159
$339$	1.53522e23	0.141018
$340$	−7.79345e23	−0.696114
$341$	2.40087e24	2.08546
$342$	−5.73262e23	−0.484290
$343$	−1.31085e24	−1.07710
$344$	−1.41783e23	−0.113324
$345$	−2.33265e24	−1.81371
$346$	9.91961e23	0.750364
$347$	2.46629e24	1.81516	0.907578	−	0.419884i	$-0.137929\pi$
$347$	2.46629e24	1.81516	0.907578	+	0.419884i	$0.137929\pi$
$348$	7.85297e23	0.562382
$349$	−1.39722e24	−0.973695	−0.486848	−	0.873487i	$-0.661853\pi$
$349$	−1.39722e24	−0.973695	−0.486848	+	0.873487i	$0.661853\pi$
$350$	4.38041e23	0.297077
$351$	3.29709e24	2.17627
$352$	−2.69749e24	−1.73302
$353$	2.48310e21	0.00155287	0.000776435	−	1.00000i	$-0.499753\pi$
$353$	2.48310e21	0.00155287	0.000776435		1.00000i	$0.499753\pi$
$354$	1.69637e24	1.03273
$355$	−5.81250e23	−0.344504
$356$	−1.04275e24	−0.601735
$357$	4.23524e24	2.37974
$358$	1.52263e24	0.833119
$359$	−2.24441e24	−1.19593	−0.597963	−	0.801524i	$-0.704023\pi$
$359$	−2.24441e24	−1.19593	−0.597963	+	0.801524i	$0.704023\pi$
$360$	1.53773e24	0.798009
$361$	−1.28198e24	−0.647983
$362$	1.06543e24	0.524556
$363$	6.34298e24	3.04215
$364$	−2.81093e24	−1.31337
$365$	−1.50672e24	−0.685883
$366$	−1.18091e24	−0.523775
$367$	1.56645e24	0.676998	0.338499	−	0.940967i	$-0.390081\pi$
$367$	1.56645e24	0.676998	0.338499	+	0.940967i	$0.390081\pi$
$368$	−1.66366e24	−0.700665
$369$	−1.15581e24	−0.474392
$370$	5.47125e22	0.0218862
$371$	−2.84811e23	−0.111046
$372$	−4.06977e24	−1.54672
$373$	2.91217e24	1.07890	0.539451	−	0.842017i	$-0.318632\pi$
$373$	2.91217e24	1.07890	0.539451	+	0.842017i	$0.318632\pi$
$374$	−3.72537e24	−1.34552
$375$	−4.36348e24	−1.53651
$376$	−3.63433e23	−0.124779
$377$	−2.60133e24	−0.870870
$378$	−1.47165e24	−0.480432
$379$	1.20883e24	0.384851	0.192425	−	0.981312i	$-0.438365\pi$
$379$	1.20883e24	0.384851	0.192425	+	0.981312i	$0.438365\pi$
$380$	−8.09783e23	−0.251434
$381$	−3.02237e23	−0.0915293
$382$	1.27109e24	0.375468
$383$	−4.65357e23	−0.134090	−0.0670452	−	0.997750i	$-0.521357\pi$
$383$	−4.65357e23	−0.134090	−0.0670452	+	0.997750i	$0.521357\pi$
$384$	5.56279e24	1.56367
$385$	3.01858e24	0.827802
$386$	−2.27344e24	−0.608280
$387$	−8.54668e23	−0.223122
$388$	−3.57748e24	−0.911330
$389$	1.34802e24	0.335100	0.167550	−	0.985864i	$-0.446415\pi$
$389$	1.34802e24	0.335100	0.167550	+	0.985864i	$0.446415\pi$
$390$	−3.51898e24	−0.853696
$391$	−1.38665e25	−3.28312
$392$	−8.07304e23	−0.186560
$393$	−1.51316e24	−0.341316
$394$	−2.43747e24	−0.536693
$395$	−2.37634e23	−0.0510783
$396$	−1.03799e25	−2.17816
$397$	−4.42630e24	−0.906842	−0.453421	−	0.891297i	$-0.649797\pi$
$397$	−4.42630e24	−0.906842	−0.453421	+	0.891297i	$0.649797\pi$
$398$	−4.60677e24	−0.921526
$399$	4.40065e24	0.859555
$400$	−1.27411e24	−0.243018
$401$	−3.18941e24	−0.594072	−0.297036	−	0.954866i	$-0.595998\pi$
$401$	−3.18941e24	−0.594072	−0.297036	+	0.954866i	$0.595998\pi$
$402$	2.22870e24	0.405419
$403$	1.34813e25	2.39515
$404$	3.36829e24	0.584502
$405$	4.98302e23	0.0844636
$406$	1.16110e24	0.192253
$407$	−8.51998e23	−0.137814
$408$	1.45684e25	2.30218
$409$	6.83093e24	1.05465	0.527325	−	0.849664i	$-0.323195\pi$
$409$	6.83093e24	1.05465	0.527325	+	0.849664i	$0.323195\pi$
$410$	5.01176e23	0.0756038
$411$	1.12169e25	1.65339
$412$	7.82013e24	1.12639
$413$	−8.17086e24	−1.15012
$414$	1.18598e25	1.63145
$415$	−2.25964e24	−0.303796
$416$	−1.51468e25	−1.99038
$417$	−1.67548e25	−2.15202
$418$	−3.87087e24	−0.485998
$419$	9.87324e24	1.21179	0.605894	−	0.795545i	$-0.292816\pi$
$419$	9.87324e24	1.21179	0.605894	+	0.795545i	$0.292816\pi$
$420$	−5.11686e24	−0.613953
$421$	−5.85393e24	−0.686700	−0.343350	−	0.939207i	$-0.611562\pi$
$421$	−5.85393e24	−0.686700	−0.343350	+	0.939207i	$0.611562\pi$
$422$	4.11978e24	0.472504
$423$	−2.19077e24	−0.245676
$424$	−9.79693e23	−0.107427
$425$	−1.06196e25	−1.13871
$426$	4.70981e24	0.493870
$427$	5.68805e24	0.583309
$428$	4.91681e24	0.493137
$429$	5.47986e25	5.37558
$430$	3.70596e23	0.0355590
$431$	−5.12109e24	−0.480650	−0.240325	−	0.970693i	$-0.577254\pi$
$431$	−5.12109e24	−0.480650	−0.240325	+	0.970693i	$0.577254\pi$
$432$	4.28053e24	0.393009
$433$	7.70068e24	0.691662	0.345831	−	0.938297i	$-0.387597\pi$
$433$	7.70068e24	0.691662	0.345831	+	0.938297i	$0.387597\pi$
$434$	−6.01735e24	−0.528753
$435$	−4.73532e24	−0.407100
$436$	5.71099e24	0.480385
$437$	−1.44080e25	−1.18585
$438$	1.22088e25	0.983261
$439$	1.06113e25	0.836291	0.418146	−	0.908380i	$-0.362680\pi$
$439$	1.06113e25	0.836291	0.418146	+	0.908380i	$0.362680\pi$
$440$	1.03833e25	0.800822
$441$	−4.86641e24	−0.367318
$442$	−2.09186e25	−1.54533
$443$	−2.06970e25	−1.49648	−0.748241	−	0.663427i	$-0.769101\pi$
$443$	−2.06970e25	−1.49648	−0.748241	+	0.663427i	$0.769101\pi$
$444$	1.44424e24	0.102212
$445$	6.28775e24	0.435587
$446$	9.95348e24	0.674985
$447$	1.08891e25	0.722888
$448$	1.99118e24	0.129411
$449$	5.64424e24	0.359141	0.179571	−	0.983745i	$-0.442529\pi$
$449$	5.64424e24	0.359141	0.179571	+	0.983745i	$0.442529\pi$
$450$	9.08281e24	0.565850
$451$	−7.80446e24	−0.476064
$452$	−1.10259e24	−0.0658563
$453$	−1.03367e25	−0.604572
$454$	1.02068e25	0.584601
$455$	1.69498e25	0.950730
$456$	1.51374e25	0.831541
$457$	−5.63469e24	−0.303156	−0.151578	−	0.988445i	$-0.548435\pi$
$457$	−5.63469e24	−0.303156	−0.151578	+	0.988445i	$0.548435\pi$
$458$	5.74824e23	0.0302910
$459$	3.56779e25	1.84153
$460$	1.67530e25	0.847017
$461$	2.90461e25	1.43856	0.719281	−	0.694719i	$-0.244471\pi$
$461$	2.90461e25	1.43856	0.719281	+	0.694719i	$0.244471\pi$
$462$	−2.44593e25	−1.18671
$463$	3.33811e25	1.58665	0.793325	−	0.608798i	$-0.208348\pi$
$463$	3.33811e25	1.58665	0.793325	+	0.608798i	$0.208348\pi$
$464$	−3.37725e24	−0.157269
$465$	2.45406e25	1.11965
$466$	7.70896e24	0.344611
$467$	−2.83443e25	−1.24153	−0.620763	−	0.783998i	$-0.713177\pi$
$467$	−2.83443e25	−1.24153	−0.620763	+	0.783998i	$0.713177\pi$
$468$	−5.82848e25	−2.50161
$469$	−1.07350e25	−0.451501
$470$	9.49947e23	0.0391534
$471$	−1.78477e25	−0.720914
$472$	−2.81062e25	−1.11263
$473$	−5.77102e24	−0.223909
$474$	1.92552e24	0.0732242
$475$	−1.10344e25	−0.411300
$476$	−3.04172e25	−1.11135
$477$	−5.90557e24	−0.211513
$478$	6.56090e24	0.230355
$479$	4.24690e25	1.46179	0.730894	−	0.682491i	$-0.239103\pi$
$479$	4.24690e25	1.46179	0.730894	+	0.682491i	$0.239103\pi$
$480$	−2.75725e25	−0.930430
$481$	−4.78411e24	−0.158279
$482$	7.43745e24	0.241255
$483$	−9.10415e25	−2.89562
$484$	−4.55548e25	−1.42070
$485$	2.15721e25	0.659699
$486$	1.40798e25	0.422233
$487$	1.69321e25	0.497949	0.248975	−	0.968510i	$-0.419906\pi$
$487$	1.69321e25	0.497949	0.248975	+	0.968510i	$0.419906\pi$
$488$	1.95658e25	0.564298
$489$	−1.31917e24	−0.0373136
$490$	2.11014e24	0.0585395
$491$	−6.80207e25	−1.85083	−0.925415	−	0.378955i	$-0.876284\pi$
$491$	−6.80207e25	−1.85083	−0.925415	+	0.378955i	$0.876284\pi$
$492$	1.32295e25	0.353081
$493$	−2.81491e25	−0.736918
$494$	−2.17356e25	−0.558168
$495$	6.25905e25	1.57674
$496$	1.75025e25	0.432537
$497$	−2.26857e25	−0.550005
$498$	1.83096e25	0.435513
$499$	−1.55874e25	−0.363762	−0.181881	−	0.983321i	$-0.558219\pi$
$499$	−1.55874e25	−0.363762	−0.181881	+	0.983321i	$0.558219\pi$
$500$	3.13382e25	0.717561
$501$	9.35940e25	2.10276
$502$	−3.69443e25	−0.814446
$503$	−4.78224e25	−1.03451	−0.517255	−	0.855831i	$-0.673046\pi$
$503$	−4.78224e25	−1.03451	−0.517255	+	0.855831i	$0.673046\pi$
$504$	6.00164e25	1.27403
$505$	−2.03107e25	−0.423113
$506$	8.00814e25	1.63720
$507$	2.26047e26	4.53547
$508$	2.17064e24	0.0427448
$509$	−4.69474e25	−0.907386	−0.453693	−	0.891158i	$-0.649894\pi$
$509$	−4.69474e25	−0.907386	−0.453693	+	0.891158i	$0.649894\pi$
$510$	−3.80790e25	−0.722385
$511$	−5.88059e25	−1.09502
$512$	−3.60713e25	−0.659321
$513$	3.70713e25	0.665155
$514$	−3.14464e25	−0.553888
$515$	−4.71552e25	−0.815381
$516$	9.78257e24	0.166066
$517$	−1.47928e25	−0.246542
$518$	2.13538e24	0.0349416
$519$	−1.57893e26	−2.53672
$520$	5.83041e25	0.919744
$521$	5.39631e25	0.835869	0.417935	−	0.908477i	$-0.362754\pi$
$521$	5.39631e25	0.835869	0.417935	+	0.908477i	$0.362754\pi$
$522$	2.40755e25	0.366189
$523$	−2.69612e25	−0.402693	−0.201346	−	0.979520i	$-0.564532\pi$
$523$	−2.69612e25	−0.402693	−0.201346	+	0.979520i	$0.564532\pi$
$524$	1.08674e25	0.159397
$525$	−6.97241e25	−1.00431
$526$	−2.24229e25	−0.317195
$527$	1.45881e26	2.02675
$528$	7.11438e25	0.970766
$529$	2.23461e26	2.99483
$530$	2.56073e24	0.0337088
$531$	−1.69423e26	−2.19066
$532$	−3.16051e25	−0.401418
$533$	−4.38233e25	−0.546760
$534$	−5.09490e25	−0.624445
$535$	−2.96482e25	−0.356975
$536$	−3.69262e25	−0.436786
$537$	−2.42362e26	−2.81649
$538$	−1.63042e25	−0.186153
$539$	−3.28598e25	−0.368613
$540$	−4.31047e25	−0.475099
$541$	−1.96146e25	−0.212425	−0.106212	−	0.994343i	$-0.533872\pi$
$541$	−1.96146e25	−0.212425	−0.106212	+	0.994343i	$0.533872\pi$
$542$	4.66019e25	0.495919
$543$	−1.69587e26	−1.77334
$544$	−1.63905e26	−1.68423
$545$	−3.44371e25	−0.347744
$546$	−1.37343e26	−1.36294
$547$	1.24919e26	1.21828	0.609142	−	0.793061i	$-0.291514\pi$
$547$	1.24919e26	1.21828	0.609142	+	0.793061i	$0.291514\pi$
$548$	−8.05587e25	−0.772142
$549$	1.17942e26	1.11105
$550$	6.13303e25	0.567845
$551$	−2.92485e25	−0.266173
$552$	−3.13165e26	−2.80125
$553$	−9.27465e24	−0.0815471
$554$	3.57169e25	0.308696
$555$	−8.70872e24	−0.0739897
$556$	1.20332e26	1.00501
$557$	−7.83082e25	−0.642958	−0.321479	−	0.946917i	$-0.604180\pi$
$557$	−7.83082e25	−0.642958	−0.321479	+	0.946917i	$0.604180\pi$
$558$	−1.24770e26	−1.00713
$559$	−3.24052e25	−0.257160
$560$	2.20056e25	0.171691
$561$	5.92977e26	4.54874
$562$	5.10470e25	0.385013
$563$	7.00337e25	0.519371	0.259685	−	0.965693i	$-0.416381\pi$
$563$	7.00337e25	0.519371	0.259685	+	0.965693i	$0.416381\pi$
$564$	2.50756e25	0.182852
$565$	6.64856e24	0.0476724
$566$	2.63484e25	0.185780
$567$	1.94483e25	0.134847
$568$	−7.80343e25	−0.532079
$569$	2.33827e26	1.56794	0.783969	−	0.620800i	$-0.213192\pi$
$569$	2.33827e26	1.56794	0.783969	+	0.620800i	$0.213192\pi$
$570$	−3.95662e25	−0.260924
$571$	5.13318e25	0.332923	0.166461	−	0.986048i	$-0.446766\pi$
$571$	5.13318e25	0.332923	0.166461	+	0.986048i	$0.446766\pi$
$572$	−3.93560e26	−2.51043
$573$	−2.02322e26	−1.26933
$574$	1.95605e25	0.120702
$575$	2.28282e26	1.38556
$576$	4.12873e25	0.246492
$577$	−2.43365e26	−1.42918	−0.714591	−	0.699542i	$-0.753387\pi$
$577$	−2.43365e26	−1.42918	−0.714591	+	0.699542i	$0.753387\pi$
$578$	−1.42467e26	−0.823003
$579$	3.61869e26	2.05639
$580$	3.40088e25	0.190119
$581$	−8.81917e25	−0.485014
$582$	−1.74797e26	−0.945724
$583$	−3.98765e25	−0.212259
$584$	−2.02281e26	−1.05933
$585$	3.51456e26	1.81088
$586$	−9.45235e25	−0.479195
$587$	−3.21574e26	−1.60405	−0.802026	−	0.597289i	$-0.796244\pi$
$587$	−3.21574e26	−1.60405	−0.802026	+	0.597289i	$0.796244\pi$
$588$	5.57012e25	0.273388
$589$	1.51579e26	0.732055
$590$	7.34642e25	0.349126
$591$	3.87979e26	1.81438
$592$	−6.21110e24	−0.0285833
$593$	−2.30951e26	−1.04592	−0.522962	−	0.852356i	$-0.675173\pi$
$593$	−2.30951e26	−1.04592	−0.522962	+	0.852356i	$0.675173\pi$
$594$	−2.06046e26	−0.918319
$595$	1.83415e26	0.804494
$596$	−7.82049e25	−0.337594
$597$	7.33272e26	3.11536
$598$	4.49670e26	1.88032
$599$	−4.42135e25	−0.181970	−0.0909850	−	0.995852i	$-0.529002\pi$
$599$	−4.42135e25	−0.181970	−0.0909850	+	0.995852i	$0.529002\pi$
$600$	−2.39837e26	−0.971582
$601$	4.20018e26	1.67479	0.837395	−	0.546599i	$-0.184078\pi$
$601$	4.20018e26	1.67479	0.837395	+	0.546599i	$0.184078\pi$
$602$	1.44640e25	0.0567705
$603$	−2.22590e26	−0.859986
$604$	7.42373e25	0.282339
$605$	2.74694e26	1.02843
$606$	1.64575e26	0.606562
$607$	4.38890e26	1.59244	0.796220	−	0.605007i	$-0.206830\pi$
$607$	4.38890e26	1.59244	0.796220	+	0.605007i	$0.206830\pi$
$608$	−1.70306e26	−0.608339
$609$	−1.84815e26	−0.649941
$610$	−5.11413e25	−0.177067
$611$	−8.30642e25	−0.283154
$612$	−6.30702e26	−2.11683
$613$	−4.68650e26	−1.54872	−0.774362	−	0.632743i	$-0.781929\pi$
$613$	−4.68650e26	−1.54872	−0.774362	+	0.632743i	$0.781929\pi$
$614$	−1.04835e26	−0.341119
$615$	−7.97735e25	−0.255591
$616$	4.05252e26	1.27852
$617$	2.97937e26	0.925584	0.462792	−	0.886467i	$-0.346848\pi$
$617$	2.97937e26	0.925584	0.462792	+	0.886467i	$0.346848\pi$
$618$	3.82094e26	1.16891
$619$	5.57902e26	1.68073	0.840363	−	0.542024i	$-0.182342\pi$
$619$	5.57902e26	1.68073	0.840363	+	0.542024i	$0.182342\pi$
$620$	−1.76249e26	−0.522884
$621$	−7.66939e26	−2.24073
$622$	8.02106e25	0.230793
$623$	2.45405e26	0.695421
$624$	3.99484e26	1.11492
$625$	6.32271e25	0.173797
$626$	−1.45927e25	−0.0395074
$627$	6.16137e26	1.64299
$628$	1.28181e26	0.336672
$629$	−5.17690e25	−0.133933
$630$	−1.56872e26	−0.399769
$631$	2.21937e26	0.557122	0.278561	−	0.960418i	$-0.410143\pi$
$631$	2.21937e26	0.557122	0.278561	+	0.960418i	$0.410143\pi$
$632$	−3.19029e25	−0.0788894
$633$	−6.55756e26	−1.59737
$634$	−2.91948e26	−0.700580
$635$	−1.30889e25	−0.0309424
$636$	6.75954e25	0.157425
$637$	−1.84513e26	−0.423352
$638$	1.62566e26	0.367481
$639$	−4.70389e26	−1.04761
$640$	2.40907e26	0.528615
$641$	8.44295e25	0.182534	0.0912668	−	0.995826i	$-0.470908\pi$
$641$	8.44295e25	0.182534	0.0912668	+	0.995826i	$0.470908\pi$
$642$	2.40237e26	0.511749
$643$	3.30007e26	0.692659	0.346329	−	0.938113i	$-0.387428\pi$
$643$	3.30007e26	0.692659	0.346329	+	0.938113i	$0.387428\pi$
$644$	6.53853e26	1.35227
$645$	−5.89886e25	−0.120213
$646$	−2.35201e26	−0.472314
$647$	6.15440e26	1.21785	0.608927	−	0.793226i	$-0.291600\pi$
$647$	6.15440e26	1.21785	0.608927	+	0.793226i	$0.291600\pi$
$648$	6.68982e25	0.130452
$649$	−1.14401e27	−2.19839
$650$	3.44380e26	0.652170
$651$	9.57798e26	1.78753
$652$	9.47420e24	0.0174257
$653$	−5.30942e26	−0.962436	−0.481218	−	0.876601i	$-0.659805\pi$
$653$	−5.30942e26	−0.962436	−0.481218	+	0.876601i	$0.659805\pi$
$654$	2.79040e26	0.498515
$655$	−6.55303e25	−0.115385
$656$	−5.68948e25	−0.0987384
$657$	−1.21934e27	−2.08572
$658$	3.70756e25	0.0625089
$659$	5.22132e26	0.867699	0.433850	−	0.900985i	$-0.357155\pi$
$659$	5.22132e26	0.867699	0.433850	+	0.900985i	$0.357155\pi$
$660$	−7.16414e26	−1.17354
$661$	−6.26794e26	−1.01207	−0.506036	−	0.862513i	$-0.668890\pi$
$661$	−6.26794e26	−1.01207	−0.506036	+	0.862513i	$0.668890\pi$
$662$	−6.59976e25	−0.105045
$663$	3.32966e27	5.22422
$664$	−3.03362e26	−0.469207
$665$	1.90578e26	0.290581
$666$	4.42772e25	0.0665542
$667$	6.05099e26	0.896667
$668$	−6.72186e26	−0.982003
$669$	−1.58432e27	−2.28189
$670$	9.65181e25	0.137056
$671$	7.96387e26	1.11496
$672$	−1.07613e27	−1.48544
$673$	−7.20655e26	−0.980808	−0.490404	−	0.871495i	$-0.663151\pi$
$673$	−7.20655e26	−0.980808	−0.490404	+	0.871495i	$0.663151\pi$
$674$	−1.22834e26	−0.164835
$675$	−5.87360e26	−0.777174
$676$	−1.62345e27	−2.11810
$677$	−7.52230e26	−0.967739	−0.483869	−	0.875140i	$-0.660769\pi$
$677$	−7.52230e26	−0.967739	−0.483869	+	0.875140i	$0.660769\pi$
$678$	−5.38726e25	−0.0683417
$679$	8.41941e26	1.05322
$680$	6.30910e26	0.778275
$681$	−1.62464e27	−1.97634
$682$	−8.42493e26	−1.01068
$683$	1.18730e27	1.40464	0.702319	−	0.711862i	$-0.252148\pi$
$683$	1.18730e27	1.40464	0.702319	+	0.711862i	$0.252148\pi$
$684$	−6.55334e26	−0.764592
$685$	4.85767e26	0.558943
$686$	4.59990e26	0.521999
$687$	−9.14963e25	−0.102403
$688$	−4.20710e25	−0.0464400
$689$	−2.23913e26	−0.243779
$690$	8.18554e26	0.878984
$691$	−9.58932e26	−1.01566	−0.507828	−	0.861459i	$-0.669551\pi$
$691$	−9.58932e26	−1.01566	−0.507828	+	0.861459i	$0.669551\pi$
$692$	1.13398e27	1.18467
$693$	2.44285e27	2.51728
$694$	−8.65448e26	−0.879682
$695$	−7.25597e26	−0.727512
$696$	−6.35729e26	−0.628759
$697$	−4.74213e26	−0.462660
$698$	4.90300e26	0.471884
$699$	−1.22705e27	−1.16501
$700$	5.00754e26	0.469021
$701$	−8.87686e26	−0.820235	−0.410118	−	0.912033i	$-0.634512\pi$
$701$	−8.87686e26	−0.820235	−0.410118	+	0.912033i	$0.634512\pi$
$702$	−1.15698e27	−1.05469
$703$	−5.37909e25	−0.0483763
$704$	2.78786e26	0.247361
$705$	−1.51205e26	−0.132364
$706$	−8.71348e23	−0.000752570 0
$707$	−7.92709e26	−0.675506
$708$	1.93923e27	1.63047
$709$	1.93468e27	1.60498	0.802489	−	0.596667i	$-0.203509\pi$
$709$	1.93468e27	1.60498	0.802489	+	0.596667i	$0.203509\pi$
$710$	2.03967e26	0.166957
$711$	−1.92310e26	−0.155325
$712$	8.44146e26	0.672756
$713$	−3.13590e27	−2.46610
$714$	−1.48619e27	−1.15330
$715$	2.37315e27	1.81727
$716$	1.74062e27	1.31532
$717$	−1.04432e27	−0.778753
$718$	7.87586e26	0.579584
$719$	−1.54253e26	−0.112024	−0.0560119	−	0.998430i	$-0.517838\pi$
$719$	−1.54253e26	−0.112024	−0.0560119	+	0.998430i	$0.517838\pi$
$720$	4.56287e26	0.327024
$721$	−1.84043e27	−1.30177
$722$	4.49862e26	0.314033
$723$	−1.18384e27	−0.815602
$724$	1.21796e27	0.828164
$725$	4.63415e26	0.310999
$726$	−2.22582e27	−1.47432
$727$	2.58884e27	1.69250	0.846249	−	0.532788i	$-0.178856\pi$
$727$	2.58884e27	1.69250	0.846249	+	0.532788i	$0.178856\pi$
$728$	2.27556e27	1.46838
$729$	−2.48054e27	−1.57992
$730$	5.28724e26	0.332401
$731$	−3.50658e26	−0.217605
$732$	−1.34997e27	−0.826931
$733$	−1.85454e27	−1.12137	−0.560685	−	0.828029i	$-0.689462\pi$
$733$	−1.85454e27	−1.12137	−0.560685	+	0.828029i	$0.689462\pi$
$734$	−5.49683e26	−0.328095
$735$	−3.35877e26	−0.197902
$736$	3.52332e27	2.04934
$737$	−1.50301e27	−0.863018
$738$	4.05587e26	0.229905
$739$	2.18142e27	1.22072	0.610361	−	0.792123i	$-0.291024\pi$
$739$	2.18142e27	1.22072	0.610361	+	0.792123i	$0.291024\pi$
$740$	6.25454e25	0.0345537
$741$	3.45971e27	1.88697
$742$	9.99432e25	0.0538166
$743$	−2.62421e27	−1.39510	−0.697548	−	0.716538i	$-0.745726\pi$
$743$	−2.62421e27	−1.39510	−0.697548	+	0.716538i	$0.745726\pi$
$744$	3.29463e27	1.72928
$745$	4.71573e26	0.244379
$746$	−1.02191e27	−0.522871
$747$	−1.82866e27	−0.923820
$748$	−4.25872e27	−2.12429
$749$	−1.15715e27	−0.569916
$750$	1.53119e27	0.744642
$751$	2.83660e27	1.36213	0.681065	−	0.732223i	$-0.261517\pi$
$751$	2.83660e27	1.36213	0.681065	+	0.732223i	$0.261517\pi$
$752$	−1.07840e26	−0.0511343
$753$	5.88052e27	2.75336
$754$	9.12836e26	0.422051
$755$	−4.47649e26	−0.204381
$756$	−1.68234e27	−0.758502
$757$	2.02816e26	0.0903007	0.0451503	−	0.998980i	$-0.485623\pi$
$757$	2.02816e26	0.0903007	0.0451503	+	0.998980i	$0.485623\pi$
$758$	−4.24192e26	−0.186511
$759$	−1.27468e28	−5.53481
$760$	6.55551e26	0.281111
$761$	1.14720e27	0.485832	0.242916	−	0.970047i	$-0.421896\pi$
$761$	1.14720e27	0.485832	0.242916	+	0.970047i	$0.421896\pi$
$762$	1.06058e26	0.0443580
$763$	−1.34405e27	−0.555178
$764$	1.45306e27	0.592786
$765$	3.80311e27	1.53234
$766$	1.63299e26	0.0649845
$767$	−6.42378e27	−2.52484
$768$	−2.56968e27	−0.997581
$769$	−1.46988e27	−0.563615	−0.281808	−	0.959471i	$-0.590934\pi$
$769$	−1.46988e27	−0.563615	−0.281808	+	0.959471i	$0.590934\pi$
$770$	−1.05925e27	−0.401179
$771$	5.00541e27	1.87250
$772$	−2.59892e27	−0.960347
$773$	−3.29168e27	−1.20147	−0.600734	−	0.799449i	$-0.705125\pi$
$773$	−3.29168e27	−1.20147	−0.600734	+	0.799449i	$0.705125\pi$
$774$	2.99912e26	0.108132
$775$	−2.40163e27	−0.855341
$776$	2.89611e27	1.01889
$777$	−3.39894e26	−0.118125
$778$	−4.73034e26	−0.162400
$779$	−4.92734e26	−0.167112
$780$	−4.02278e27	−1.34781
$781$	−3.17623e27	−1.05130
$782$	4.86589e27	1.59110
$783$	−1.55690e27	−0.502948
$784$	−2.39549e26	−0.0764525
$785$	−7.72927e26	−0.243712
$786$	5.30986e26	0.165413
$787$	2.45350e27	0.755137	0.377569	−	0.925982i	$-0.376760\pi$
$787$	2.45350e27	0.755137	0.377569	+	0.925982i	$0.376760\pi$
$788$	−2.78644e27	−0.847326
$789$	3.56911e27	1.07233
$790$	8.33883e25	0.0247541
$791$	2.59488e26	0.0761097
$792$	8.40293e27	2.43524
$793$	4.47184e27	1.28053
$794$	1.55324e27	0.439484
$795$	−4.07599e26	−0.113958
$796$	−5.26631e27	−1.45490
$797$	2.62470e27	0.716515	0.358258	−	0.933623i	$-0.383371\pi$
$797$	2.62470e27	0.716515	0.358258	+	0.933623i	$0.383371\pi$
$798$	−1.54423e27	−0.416568
$799$	−8.98841e26	−0.239601
$800$	2.69834e27	0.710790
$801$	5.08850e27	1.32459
$802$	1.11920e27	0.287906
$803$	−8.23345e27	−2.09307
$804$	2.54778e27	0.640072
$805$	−3.94272e27	−0.978892
$806$	−4.73073e27	−1.16077
$807$	2.59519e27	0.629318
$808$	−2.72676e27	−0.653490
$809$	6.31288e27	1.49526	0.747630	−	0.664116i	$-0.231192\pi$
$809$	6.31288e27	1.49526	0.747630	+	0.664116i	$0.231192\pi$
$810$	−1.74859e26	−0.0409337
$811$	8.41281e27	1.94645	0.973225	−	0.229855i	$-0.0738252\pi$
$811$	8.41281e27	1.94645	0.973225	+	0.229855i	$0.0738252\pi$
$812$	1.32733e27	0.303527
$813$	−7.41775e27	−1.67653
$814$	2.98976e26	0.0667888
$815$	−5.71291e25	−0.0126142
$816$	4.32283e27	0.943434
$817$	−3.64353e26	−0.0785983
$818$	−2.39705e27	−0.511117
$819$	1.37170e28	2.89110
$820$	5.72927e26	0.119363
$821$	6.80012e26	0.140042	0.0700208	−	0.997546i	$-0.477693\pi$
$821$	6.80012e26	0.140042	0.0700208	+	0.997546i	$0.477693\pi$
$822$	−3.93612e27	−0.801283
$823$	−2.51830e27	−0.506768	−0.253384	−	0.967366i	$-0.581544\pi$
$823$	−2.51830e27	−0.506768	−0.253384	+	0.967366i	$0.581544\pi$
$824$	−6.33070e27	−1.25934
$825$	−9.76210e27	−1.91969
$826$	2.86724e27	0.557384
$827$	5.88697e27	1.13133	0.565665	−	0.824635i	$-0.308619\pi$
$827$	5.88697e27	1.13133	0.565665	+	0.824635i	$0.308619\pi$
$828$	1.35577e28	2.57571
$829$	2.85708e27	0.536605	0.268302	−	0.963335i	$-0.413537\pi$
$829$	2.85708e27	0.536605	0.268302	+	0.963335i	$0.413537\pi$
$830$	7.92932e26	0.147229
$831$	−5.68515e27	−1.04359
$832$	1.56543e27	0.284094
$833$	−1.99662e27	−0.358235
$834$	5.87944e27	1.04294
$835$	4.05326e27	0.710858
$836$	−4.42505e27	−0.767288
$837$	8.06854e27	1.38326
$838$	−3.46463e27	−0.587271
$839$	3.84359e26	0.0644167	0.0322084	−	0.999481i	$-0.489746\pi$
$839$	3.84359e26	0.0644167	0.0322084	+	0.999481i	$0.489746\pi$
$840$	4.14230e27	0.686417
$841$	−4.87490e27	−0.798737
$842$	2.05421e27	0.332797
$843$	−8.12528e27	−1.30160
$844$	4.70959e27	0.745985
$845$	9.78937e27	1.53326
$846$	7.68765e26	0.119062
$847$	1.07211e28	1.64190
$848$	−2.90701e26	−0.0440237
$849$	−4.19394e27	−0.628057
$850$	3.72654e27	0.551857
$851$	1.11284e27	0.162967
$852$	5.38410e27	0.779717
$853$	8.23464e27	1.17931	0.589656	−	0.807655i	$-0.299263\pi$
$853$	8.23464e27	1.17931	0.589656	+	0.807655i	$0.299263\pi$
$854$	−1.99600e27	−0.282690
$855$	3.95165e27	0.553478
$856$	−3.98035e27	−0.551342
$857$	−4.73865e27	−0.649138	−0.324569	−	0.945862i	$-0.605219\pi$
$857$	−4.73865e27	−0.649138	−0.324569	+	0.945862i	$0.605219\pi$
$858$	−1.92294e28	−2.60518
$859$	6.58280e27	0.882015	0.441007	−	0.897503i	$-0.354621\pi$
$859$	6.58280e27	0.882015	0.441007	+	0.897503i	$0.354621\pi$
$860$	4.23652e26	0.0561402
$861$	−3.11349e27	−0.408054
$862$	1.79705e27	0.232938
$863$	6.46142e27	0.828372	0.414186	−	0.910192i	$-0.364066\pi$
$863$	6.46142e27	0.828372	0.414186	+	0.910192i	$0.364066\pi$
$864$	−9.06538e27	−1.14949
$865$	−6.83785e27	−0.857564
$866$	−2.70225e27	−0.335201
$867$	2.26769e28	2.78229
$868$	−6.87883e27	−0.834790
$869$	−1.29855e27	−0.155873
$870$	1.66168e27	0.197294
$871$	−8.43963e27	−0.991176
$872$	−4.62327e27	−0.537084
$873$	1.74577e28	2.00609
$874$	5.05593e27	0.574702
$875$	−7.37527e27	−0.829281
$876$	1.39567e28	1.55236
$877$	−1.05263e28	−1.15819	−0.579094	−	0.815260i	$-0.696594\pi$
$877$	−1.05263e28	−1.15819	−0.579094	+	0.815260i	$0.696594\pi$
$878$	−3.72364e27	−0.405293
$879$	1.50455e28	1.61999
$880$	3.08101e27	0.328177
$881$	1.79429e28	1.89069	0.945346	−	0.326069i	$-0.105724\pi$
$881$	1.79429e28	1.89069	0.945346	+	0.326069i	$0.105724\pi$
$882$	1.70768e27	0.178014
$883$	−1.37598e27	−0.141901	−0.0709504	−	0.997480i	$-0.522603\pi$
$883$	−1.37598e27	−0.141901	−0.0709504	+	0.997480i	$0.522603\pi$
$884$	−2.39134e28	−2.43975
$885$	−1.16935e28	−1.18027
$886$	7.26280e27	0.725243
$887$	1.87612e27	0.185347	0.0926736	−	0.995697i	$-0.470459\pi$
$887$	1.87612e27	0.185347	0.0926736	+	0.995697i	$0.470459\pi$
$888$	−1.16917e27	−0.114276
$889$	−5.10849e26	−0.0493999
$890$	−2.20644e27	−0.211100
$891$	2.72296e27	0.257753
$892$	1.13785e28	1.06566
$893$	−9.33946e26	−0.0865431
$894$	−3.82111e27	−0.350335
$895$	−1.04959e28	−0.952142
$896$	9.40239e27	0.843941
$897$	−7.15751e28	−6.35673
$898$	−1.98062e27	−0.174051
$899$	−6.36592e27	−0.553533
$900$	1.03832e28	0.893358
$901$	−2.42297e27	−0.206283
$902$	2.73867e27	0.230716
$903$	−2.30228e27	−0.191921
$904$	8.92586e26	0.0736292
$905$	−7.34426e27	−0.599496
$906$	3.62725e27	0.292995
$907$	6.23403e27	0.498310	0.249155	−	0.968464i	$-0.419847\pi$
$907$	6.23403e27	0.498310	0.249155	+	0.968464i	$0.419847\pi$
$908$	1.16681e28	0.922962
$909$	−1.64369e28	−1.28665
$910$	−5.94788e27	−0.460754
$911$	−1.11348e27	−0.0853610	−0.0426805	−	0.999089i	$-0.513590\pi$
$911$	−1.11348e27	−0.0853610	−0.0426805	+	0.999089i	$0.513590\pi$
$912$	4.49166e27	0.340766
$913$	−1.23478e28	−0.927077
$914$	1.97727e27	0.146919
$915$	8.14029e27	0.598604
$916$	6.57120e26	0.0478231
$917$	−2.55759e27	−0.184214
$918$	−1.25198e28	−0.892463
$919$	−1.98954e28	−1.40364	−0.701820	−	0.712355i	$-0.747629\pi$
$919$	−1.98954e28	−1.40364	−0.701820	+	0.712355i	$0.747629\pi$
$920$	−1.35622e28	−0.946989
$921$	1.66868e28	1.15321
$922$	−1.01926e28	−0.697173
$923$	−1.78351e28	−1.20742
$924$	−2.79610e28	−1.87357
$925$	8.52266e26	0.0565234
$926$	−1.17138e28	−0.768941
$927$	−3.81613e28	−2.47951
$928$	7.15240e27	0.459987
$929$	1.21686e28	0.774626	0.387313	−	0.921948i	$-0.373403\pi$
$929$	1.21686e28	0.774626	0.387313	+	0.921948i	$0.373403\pi$
$930$	−8.61156e27	−0.542617
$931$	−2.07460e27	−0.129393
$932$	8.81262e27	0.544069
$933$	−1.27673e28	−0.780233
$934$	9.94634e27	0.601683
$935$	2.56800e28	1.53775
$936$	4.71838e28	2.79687
$937$	1.87935e28	1.10276	0.551381	−	0.834253i	$-0.314101\pi$
$937$	1.87935e28	1.10276	0.551381	+	0.834253i	$0.314101\pi$
$938$	3.76702e27	0.218812
$939$	2.32275e27	0.133561
$940$	1.08595e27	0.0618150
$941$	−3.21063e28	−1.80921	−0.904604	−	0.426254i	$-0.859833\pi$
$941$	−3.21063e28	−1.80921	−0.904604	+	0.426254i	$0.859833\pi$
$942$	6.26295e27	0.349378
$943$	1.01938e28	0.562956
$944$	−8.33985e27	−0.455957
$945$	1.01445e28	0.549069
$946$	2.02511e27	0.108514
$947$	−1.40411e28	−0.744860	−0.372430	−	0.928060i	$-0.621475\pi$
$947$	−1.40411e28	−0.744860	−0.372430	+	0.928060i	$0.621475\pi$
$948$	2.20119e27	0.115606
$949$	−4.62321e28	−2.40389
$950$	3.87209e27	0.199329
$951$	4.64701e28	2.36842
$952$	2.46239e28	1.24253
$953$	4.12838e27	0.206251	0.103126	−	0.994668i	$-0.467116\pi$
$953$	4.12838e27	0.206251	0.103126	+	0.994668i	$0.467116\pi$
$954$	2.07233e27	0.102506
$955$	−8.76194e27	−0.429109
$956$	7.50020e27	0.363683
$957$	−2.58761e28	−1.24233
$958$	−1.49028e28	−0.708429
$959$	1.89591e28	0.892360
$960$	2.84962e27	0.132804
$961$	1.13204e28	0.522383
$962$	1.67880e27	0.0767069
$963$	−2.39935e28	−1.08553
$964$	8.50224e27	0.380892
$965$	1.56714e28	0.695182
$966$	3.19474e28	1.40331
$967$	−2.09092e28	−0.909464	−0.454732	−	0.890628i	$-0.650265\pi$
$967$	−2.09092e28	−0.909464	−0.454732	+	0.890628i	$0.650265\pi$
$968$	3.68784e28	1.58839
$969$	3.74376e28	1.59673
$970$	−7.56989e27	−0.319711
$971$	3.48526e27	0.145765	0.0728824	−	0.997341i	$-0.476780\pi$
$971$	3.48526e27	0.145765	0.0728824	+	0.997341i	$0.476780\pi$
$972$	1.60955e28	0.666617
$973$	−2.83194e28	−1.16148
$974$	−5.94165e27	−0.241322
$975$	−5.48158e28	−2.20476
$976$	5.80569e27	0.231249
$977$	−8.29741e27	−0.327299	−0.163649	−	0.986519i	$-0.552327\pi$
$977$	−8.29741e27	−0.327299	−0.163649	+	0.986519i	$0.552327\pi$
$978$	4.62912e26	0.0180834
$979$	3.43593e28	1.32926
$980$	2.41224e27	0.0924216
$981$	−2.78690e28	−1.05746
$982$	2.38692e28	0.896971
$983$	−5.07343e28	−1.88818	−0.944089	−	0.329691i	$-0.893055\pi$
$983$	−5.07343e28	−1.88818	−0.944089	+	0.329691i	$0.893055\pi$
$984$	−1.07098e28	−0.394755
$985$	1.68022e28	0.613367
$986$	9.87783e27	0.357134
$987$	−5.90142e27	−0.211321
$988$	−2.48474e28	−0.881230
$989$	7.53781e27	0.264777
$990$	−2.19637e28	−0.764137
$991$	3.35646e28	1.15660	0.578298	−	0.815826i	$-0.303717\pi$
$991$	3.35646e28	1.15660	0.578298	+	0.815826i	$0.303717\pi$
$992$	−3.70670e28	−1.26510
$993$	1.05050e28	0.355123
$994$	7.96066e27	0.266550
$995$	3.17557e28	1.05318
$996$	2.09309e28	0.687583
$997$	4.21086e28	1.37014	0.685072	−	0.728475i	$-0.259771\pi$
$997$	4.21086e28	1.37014	0.685072	+	0.728475i	$0.259771\pi$
$998$	5.46977e27	0.176291
$999$	−2.86329e27	−0.0914098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.15	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-350.911 q^{2} +55855.4 q^{3} -401150. q^{4} +2.41892e6 q^{5} -1.96003e7 q^{6} +9.44084e7 q^{7} +3.24746e8 q^{8} +1.95756e9 q^{9} +O(q^{10})\)	\(q-350.911 q^{2} +55855.4 q^{3} -401150. q^{4} +2.41892e6 q^{5} -1.96003e7 q^{6} +9.44084e7 q^{7} +3.24746e8 q^{8} +1.95756e9 q^{9} -8.48826e8 q^{10} +1.32182e10 q^{11} -2.24064e10 q^{12} +7.42221e10 q^{13} -3.31289e10 q^{14} +1.35110e11 q^{15} +9.63609e10 q^{16} +8.03160e11 q^{17} -6.86930e11 q^{18} +8.34528e11 q^{19} -9.70349e11 q^{20} +5.27322e12 q^{21} -4.63840e12 q^{22} -1.72649e13 q^{23} +1.81388e13 q^{24} -1.32223e13 q^{25} -2.60453e13 q^{26} +4.44219e13 q^{27} -3.78719e13 q^{28} -3.50480e13 q^{29} -4.74115e13 q^{30} +1.81634e14 q^{31} -2.04075e14 q^{32} +7.38306e14 q^{33} -2.81838e14 q^{34} +2.28366e14 q^{35} -7.85276e14 q^{36} -6.44566e13 q^{37} -2.92845e14 q^{38} +4.14570e15 q^{39} +7.85535e14 q^{40} -5.90434e14 q^{41} -1.85043e15 q^{42} -4.36598e14 q^{43} -5.30246e15 q^{44} +4.73519e15 q^{45} +6.05844e15 q^{46} -1.11913e15 q^{47} +5.38228e15 q^{48} -2.48596e15 q^{49} +4.63985e15 q^{50} +4.48608e16 q^{51} -2.97742e16 q^{52} -3.01680e15 q^{53} -1.55881e16 q^{54} +3.19737e16 q^{55} +3.06588e16 q^{56} +4.66129e16 q^{57} +1.22987e16 q^{58} -8.65481e16 q^{59} -5.41992e16 q^{60} +6.02495e16 q^{61} -6.37375e16 q^{62} +1.84810e17 q^{63} +2.10911e16 q^{64} +1.79537e17 q^{65} -2.59079e17 q^{66} -1.13708e17 q^{67} -3.22187e17 q^{68} -9.64337e17 q^{69} -8.01362e16 q^{70} -2.40293e17 q^{71} +6.35711e17 q^{72} -6.22889e17 q^{73} +2.26185e16 q^{74} -7.38537e17 q^{75} -3.34770e17 q^{76} +1.24791e18 q^{77} -1.45477e18 q^{78} -9.82397e16 q^{79} +2.33089e17 q^{80} +2.06002e17 q^{81} +2.07190e17 q^{82} -9.34152e17 q^{83} -2.11535e18 q^{84} +1.94278e18 q^{85} +1.53207e17 q^{86} -1.95762e18 q^{87} +4.29255e18 q^{88} +2.59940e18 q^{89} -1.66163e18 q^{90} +7.00719e18 q^{91} +6.92580e18 q^{92} +1.01453e19 q^{93} +3.92715e17 q^{94} +2.01866e18 q^{95} -1.13987e19 q^{96} +8.91807e18 q^{97} +8.72349e17 q^{98} +2.58754e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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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