LMFDB - Embedded newform 47.20.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-429.582 q^{2} -11787.5 q^{3} -339747. q^{4} -3.89489e6 q^{5} +5.06369e6 q^{6} +6.69387e7 q^{7} +3.71174e8 q^{8} -1.02332e9 q^{9} +O(q^{10})$	\(q-429.582 q^{2} -11787.5 q^{3} -339747. q^{4} -3.89489e6 q^{5} +5.06369e6 q^{6} +6.69387e7 q^{7} +3.71174e8 q^{8} -1.02332e9 q^{9} +1.67317e9 q^{10} +1.31057e10 q^{11} +4.00477e9 q^{12} +1.57011e10 q^{13} -2.87557e10 q^{14} +4.59109e10 q^{15} +1.86758e10 q^{16} +4.58068e11 q^{17} +4.39598e11 q^{18} -2.23727e12 q^{19} +1.32328e12 q^{20} -7.89039e11 q^{21} -5.62999e12 q^{22} +9.93761e12 q^{23} -4.37521e12 q^{24} -3.90333e12 q^{25} -6.74491e12 q^{26} +2.57625e13 q^{27} -2.27422e13 q^{28} -7.69100e13 q^{29} -1.97225e13 q^{30} -1.88206e14 q^{31} -2.02625e14 q^{32} -1.54484e14 q^{33} -1.96778e14 q^{34} -2.60719e14 q^{35} +3.47669e14 q^{36} +3.45723e14 q^{37} +9.61089e14 q^{38} -1.85077e14 q^{39} -1.44568e15 q^{40} +2.56857e15 q^{41} +3.38957e14 q^{42} +5.26243e14 q^{43} -4.45264e15 q^{44} +3.98570e15 q^{45} -4.26902e15 q^{46} -1.11913e15 q^{47} -2.20141e14 q^{48} -6.91811e15 q^{49} +1.67680e15 q^{50} -5.39947e15 q^{51} -5.33441e15 q^{52} +1.33774e16 q^{53} -1.10671e16 q^{54} -5.10454e16 q^{55} +2.48459e16 q^{56} +2.63717e16 q^{57} +3.30392e16 q^{58} +3.84661e16 q^{59} -1.55981e16 q^{60} -1.36846e17 q^{61} +8.08497e16 q^{62} -6.84995e16 q^{63} +7.72525e16 q^{64} -6.11541e16 q^{65} +6.63633e16 q^{66} -4.10728e17 q^{67} -1.55627e17 q^{68} -1.17139e17 q^{69} +1.12000e17 q^{70} +7.27096e17 q^{71} -3.79829e17 q^{72} -7.34252e17 q^{73} -1.48516e17 q^{74} +4.60104e16 q^{75} +7.60106e17 q^{76} +8.77281e17 q^{77} +7.95055e16 q^{78} +8.15449e17 q^{79} -7.27403e16 q^{80} +8.85687e17 q^{81} -1.10341e18 q^{82} -2.50994e18 q^{83} +2.68074e17 q^{84} -1.78412e18 q^{85} -2.26065e17 q^{86} +9.06575e17 q^{87} +4.86451e18 q^{88} -3.71704e18 q^{89} -1.71219e18 q^{90} +1.05101e18 q^{91} -3.37628e18 q^{92} +2.21847e18 q^{93} +4.80758e17 q^{94} +8.71390e18 q^{95} +2.38844e18 q^{96} -4.05704e17 q^{97} +2.97189e18 q^{98} -1.34113e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−429.582	−0.593282	−0.296641	−	0.954989i	$-0.595866\pi$
$2$	−429.582	−0.593282	−0.296641	+	0.954989i	$0.595866\pi$
$3$	−11787.5	−0.345755	−0.172878	−	0.984943i	$-0.555307\pi$
$3$	−11787.5	−0.345755	−0.172878	+	0.984943i	$0.555307\pi$
$4$	−339747.	−0.648017
$5$	−3.89489e6	−0.891826	−0.445913	−	0.895076i	$-0.647121\pi$
$5$	−3.89489e6	−0.891826	−0.445913	+	0.895076i	$0.647121\pi$
$6$	5.06369e6	0.205130
$7$	6.69387e7	0.626969	0.313484	−	0.949593i	$-0.398504\pi$
$7$	6.69387e7	0.626969	0.313484	+	0.949593i	$0.398504\pi$
$8$	3.71174e8	0.977738
$9$	−1.02332e9	−0.880453
$10$	1.67317e9	0.529104
$11$	1.31057e10	1.67583	0.837917	−	0.545798i	$-0.183773\pi$
$11$	1.31057e10	1.67583	0.837917	+	0.545798i	$0.183773\pi$
$12$	4.00477e9	0.224055
$13$	1.57011e10	0.410647	0.205323	−	0.978694i	$-0.434175\pi$
$13$	1.57011e10	0.410647	0.205323	+	0.978694i	$0.434175\pi$
$14$	−2.87557e10	−0.371969
$15$	4.59109e10	0.308354
$16$	1.86758e10	0.0679423
$17$	4.58068e11	0.936840	0.468420	−	0.883506i	$-0.344823\pi$
$17$	4.58068e11	0.936840	0.468420	+	0.883506i	$0.344823\pi$
$18$	4.39598e11	0.522357
$19$	−2.23727e12	−1.59059	−0.795296	−	0.606222i	$-0.792684\pi$
$19$	−2.23727e12	−1.59059	−0.795296	+	0.606222i	$0.792684\pi$
$20$	1.32328e12	0.577918
$21$	−7.89039e11	−0.216778
$22$	−5.62999e12	−0.994241
$23$	9.93761e12	1.15045	0.575225	−	0.817995i	$-0.304915\pi$
$23$	9.93761e12	1.15045	0.575225	+	0.817995i	$0.304915\pi$
$24$	−4.37521e12	−0.338058
$25$	−3.90333e12	−0.204647
$26$	−6.74491e12	−0.243629
$27$	2.57625e13	0.650177
$28$	−2.27422e13	−0.406286
$29$	−7.69100e13	−0.984469	−0.492234	−	0.870463i	$-0.663820\pi$
$29$	−7.69100e13	−0.984469	−0.492234	+	0.870463i	$0.663820\pi$
$30$	−1.97225e13	−0.182941
$31$	−1.88206e14	−1.27849	−0.639243	−	0.769004i	$-0.720752\pi$
$31$	−1.88206e14	−1.27849	−0.639243	+	0.769004i	$0.720752\pi$
$32$	−2.02625e14	−1.01805
$33$	−1.54484e14	−0.579428
$34$	−1.96778e14	−0.555810
$35$	−2.60719e14	−0.559147
$36$	3.47669e14	0.570548
$37$	3.45723e14	0.437333	0.218666	−	0.975800i	$-0.429829\pi$
$37$	3.45723e14	0.437333	0.218666	+	0.975800i	$0.429829\pi$
$38$	9.61089e14	0.943669
$39$	−1.85077e14	−0.141983
$40$	−1.44568e15	−0.871972
$41$	2.56857e15	1.22531	0.612653	−	0.790352i	$-0.290102\pi$
$41$	2.56857e15	1.22531	0.612653	+	0.790352i	$0.290102\pi$
$42$	3.38957e14	0.128610
$43$	5.26243e14	0.159675	0.0798374	−	0.996808i	$-0.474560\pi$
$43$	5.26243e14	0.159675	0.0798374	+	0.996808i	$0.474560\pi$
$44$	−4.45264e15	−1.08597
$45$	3.98570e15	0.785211
$46$	−4.26902e15	−0.682541
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−2.20141e14	−0.0234914
$49$	−6.91811e15	−0.606910
$50$	1.67680e15	0.121413
$51$	−5.39947e15	−0.323917
$52$	−5.33441e15	−0.266106
$53$	1.33774e16	0.556865	0.278432	−	0.960456i	$-0.410185\pi$
$53$	1.33774e16	0.556865	0.278432	+	0.960456i	$0.410185\pi$
$54$	−1.10671e16	−0.385738
$55$	−5.10454e16	−1.49455
$56$	2.48459e16	0.613011
$57$	2.63717e16	0.549956
$58$	3.30392e16	0.584068
$59$	3.84661e16	0.578074	0.289037	−	0.957318i	$-0.406665\pi$
$59$	3.84661e16	0.578074	0.289037	+	0.957318i	$0.406665\pi$
$60$	−1.55981e16	−0.199818
$61$	−1.36846e17	−1.49830	−0.749148	−	0.662403i	$-0.769537\pi$
$61$	−1.36846e17	−1.49830	−0.749148	+	0.662403i	$0.769537\pi$
$62$	8.08497e16	0.758503
$63$	−6.84995e16	−0.552017
$64$	7.72525e16	0.536047
$65$	−6.11541e16	−0.366226
$66$	6.63633e16	0.343764
$67$	−4.10728e17	−1.84435	−0.922176	−	0.386770i	$-0.873591\pi$
$67$	−4.10728e17	−1.84435	−0.922176	+	0.386770i	$0.873591\pi$
$68$	−1.55627e17	−0.607088
$69$	−1.17139e17	−0.397774
$70$	1.12000e17	0.331732
$71$	7.27096e17	1.88208	0.941039	−	0.338299i	$-0.109852\pi$
$71$	7.27096e17	1.88208	0.941039	+	0.338299i	$0.109852\pi$
$72$	−3.79829e17	−0.860853
$73$	−7.34252e17	−1.45975	−0.729874	−	0.683581i	$-0.760421\pi$
$73$	−7.34252e17	−1.45975	−0.729874	+	0.683581i	$0.760421\pi$
$74$	−1.48516e17	−0.259461
$75$	4.60104e16	0.0707578
$76$	7.60106e17	1.03073
$77$	8.77281e17	1.05070
$78$	7.95055e16	0.0842362
$79$	8.15449e17	0.765490	0.382745	−	0.923854i	$-0.374979\pi$
$79$	8.15449e17	0.765490	0.382745	+	0.923854i	$0.374979\pi$
$80$	−7.27403e16	−0.0605927
$81$	8.85687e17	0.655651
$82$	−1.10341e18	−0.726952
$83$	−2.50994e18	−1.47374	−0.736872	−	0.676032i	$-0.763698\pi$
$83$	−2.50994e18	−1.47374	−0.736872	+	0.676032i	$0.763698\pi$
$84$	2.68074e17	0.140476
$85$	−1.78412e18	−0.835498
$86$	−2.26065e17	−0.0947321
$87$	9.06575e17	0.340385
$88$	4.86451e18	1.63853
$89$	−3.71704e18	−1.12458	−0.562292	−	0.826938i	$-0.690080\pi$
$89$	−3.71704e18	−1.12458	−0.562292	+	0.826938i	$0.690080\pi$
$90$	−1.71219e18	−0.465851
$91$	1.05101e18	0.257463
$92$	−3.37628e18	−0.745511
$93$	2.21847e18	0.442044
$94$	4.80758e17	0.0865390
$95$	8.71390e18	1.41853
$96$	2.38844e18	0.351995
$97$	−4.05704e17	−0.0541848	−0.0270924	−	0.999633i	$-0.508625\pi$
$97$	−4.05704e17	−0.0541848	−0.0270924	+	0.999633i	$0.508625\pi$
$98$	2.97189e18	0.360069
$99$	−1.34113e19	−1.47549
$100$	1.32615e18	0.132615
$101$	8.00427e18	0.728230	0.364115	−	0.931354i	$-0.381372\pi$
$101$	8.00427e18	0.728230	0.364115	+	0.931354i	$0.381372\pi$
$102$	2.31951e18	0.192174
$103$	1.87327e19	1.41464	0.707322	−	0.706891i	$-0.249903\pi$
$103$	1.87327e19	1.41464	0.707322	+	0.706891i	$0.249903\pi$
$104$	5.82784e18	0.401505
$105$	3.07322e18	0.193328
$106$	−5.74667e18	−0.330378
$107$	2.09133e19	1.09971	0.549854	−	0.835261i	$-0.314684\pi$
$107$	2.09133e19	1.09971	0.549854	+	0.835261i	$0.314684\pi$
$108$	−8.75273e18	−0.421325
$109$	3.79734e19	1.67467	0.837333	−	0.546694i	$-0.184114\pi$
$109$	3.79734e19	1.67467	0.837333	+	0.546694i	$0.184114\pi$
$110$	2.19282e19	0.886690
$111$	−4.07520e18	−0.151210
$112$	1.25014e18	0.0425977
$113$	−2.78462e19	−0.872008	−0.436004	−	0.899945i	$-0.643607\pi$
$113$	−2.78462e19	−0.872008	−0.436004	+	0.899945i	$0.643607\pi$
$114$	−1.13288e19	−0.326279
$115$	−3.87059e19	−1.02600
$116$	2.61300e19	0.637952
$117$	−1.60672e19	−0.361555
$118$	−1.65243e19	−0.342961
$119$	3.06625e19	0.587369
$120$	1.70409e19	0.301489
$121$	1.10601e20	1.80842
$122$	5.87864e19	0.888911
$123$	−3.02770e19	−0.423657
$124$	6.39423e19	0.828481
$125$	8.94921e19	1.07434
$126$	2.94261e19	0.327501
$127$	−9.46665e19	−0.977375	−0.488687	−	0.872459i	$-0.662524\pi$
$127$	−9.46665e19	−0.977375	−0.488687	+	0.872459i	$0.662524\pi$
$128$	7.30475e19	0.700021
$129$	−6.20308e18	−0.0552084
$130$	2.62707e19	0.217275
$131$	−1.09676e20	−0.843404	−0.421702	−	0.906734i	$-0.638567\pi$
$131$	−1.09676e20	−0.843404	−0.421702	+	0.906734i	$0.638567\pi$
$132$	5.24854e19	0.375479
$133$	−1.49760e20	−0.997251
$134$	1.76441e20	1.09422
$135$	−1.00342e20	−0.579844
$136$	1.70023e20	0.915984
$137$	2.39218e20	1.20212	0.601062	−	0.799202i	$-0.294744\pi$
$137$	2.39218e20	1.20212	0.601062	+	0.799202i	$0.294744\pi$
$138$	5.03210e19	0.235992
$139$	1.61415e20	0.706809	0.353405	−	0.935471i	$-0.385024\pi$
$139$	1.61415e20	0.706809	0.353405	+	0.935471i	$0.385024\pi$
$140$	8.85785e19	0.362336
$141$	1.31917e19	0.0504336
$142$	−3.12347e20	−1.11660
$143$	2.05775e20	0.688176
$144$	−1.91113e19	−0.0598200
$145$	2.99556e20	0.877975
$146$	3.15421e20	0.866042
$147$	8.15470e19	0.209843
$148$	−1.17458e20	−0.283399
$149$	−1.62099e20	−0.366868	−0.183434	−	0.983032i	$-0.558721\pi$
$149$	−1.62099e20	−0.366868	−0.183434	+	0.983032i	$0.558721\pi$
$150$	−1.97652e19	−0.0419793
$151$	1.31371e20	0.261950	0.130975	−	0.991386i	$-0.458189\pi$
$151$	1.31371e20	0.261950	0.130975	+	0.991386i	$0.458189\pi$
$152$	−8.30415e20	−1.55518
$153$	−4.68749e20	−0.824843
$154$	−3.76864e20	−0.623358
$155$	7.33040e20	1.14019
$156$	6.28793e19	0.0920076
$157$	8.14937e20	1.12222	0.561109	−	0.827742i	$-0.310375\pi$
$157$	8.14937e20	1.12222	0.561109	+	0.827742i	$0.310375\pi$
$158$	−3.50302e20	−0.454151
$159$	−1.57685e20	−0.192539
$160$	7.89201e20	0.907921
$161$	6.65211e20	0.721296
$162$	−3.80475e20	−0.388986
$163$	3.93930e20	0.379871	0.189936	−	0.981797i	$-0.439172\pi$
$163$	3.93930e20	0.379871	0.189936	+	0.981797i	$0.439172\pi$
$164$	−8.72665e20	−0.794019
$165$	6.01696e20	0.516749
$166$	1.07823e21	0.874346
$167$	3.15749e19	0.0241844	0.0120922	−	0.999927i	$-0.496151\pi$
$167$	3.15749e19	0.0241844	0.0120922	+	0.999927i	$0.496151\pi$
$168$	−2.92871e20	−0.211952
$169$	−1.21540e21	−0.831369
$170$	7.66427e20	0.495686
$171$	2.28943e21	1.40044
$172$	−1.78790e20	−0.103472
$173$	−2.07435e21	−1.13617	−0.568085	−	0.822970i	$-0.692316\pi$
$173$	−2.07435e21	−1.13617	−0.568085	+	0.822970i	$0.692316\pi$
$174$	−3.89448e20	−0.201945
$175$	−2.61284e20	−0.128307
$176$	2.44761e20	0.113860
$177$	−4.53418e20	−0.199872
$178$	1.59677e21	0.667196
$179$	1.98656e21	0.787041	0.393520	−	0.919316i	$-0.371257\pi$
$179$	1.98656e21	0.787041	0.393520	+	0.919316i	$0.371257\pi$
$180$	−1.35413e21	−0.508830
$181$	4.18892e20	0.149333	0.0746664	−	0.997209i	$-0.476211\pi$
$181$	4.18892e20	0.149333	0.0746664	+	0.997209i	$0.476211\pi$
$182$	−4.51496e20	−0.152748
$183$	1.61306e21	0.518044
$184$	3.68858e21	1.12484
$185$	−1.34655e21	−0.390024
$186$	−9.53014e20	−0.262257
$187$	6.00332e21	1.56999
$188$	3.80222e20	0.0945229
$189$	1.72451e21	0.407641
$190$	−3.74334e21	−0.841588
$191$	4.70651e21	1.00666	0.503329	−	0.864095i	$-0.332109\pi$
$191$	4.70651e21	1.00666	0.503329	+	0.864095i	$0.332109\pi$
$192$	−9.10612e20	−0.185341
$193$	−4.88481e21	−0.946352	−0.473176	−	0.880968i	$-0.656893\pi$
$193$	−4.88481e21	−0.946352	−0.473176	+	0.880968i	$0.656893\pi$
$194$	1.74283e20	0.0321469
$195$	7.20853e20	0.126624
$196$	2.35041e21	0.393288
$197$	−9.61462e21	−1.53286	−0.766431	−	0.642327i	$-0.777969\pi$
$197$	−9.61462e21	−1.53286	−0.766431	+	0.642327i	$0.777969\pi$
$198$	5.76126e21	0.875383
$199$	−2.71215e21	−0.392834	−0.196417	−	0.980520i	$-0.562931\pi$
$199$	−2.71215e21	−0.392834	−0.196417	+	0.980520i	$0.562931\pi$
$200$	−1.44881e21	−0.200091
$201$	4.84145e21	0.637695
$202$	−3.43849e21	−0.432046
$203$	−5.14826e21	−0.617231
$204$	1.83446e21	0.209904
$205$	−1.00043e22	−1.09276
$206$	−8.04724e21	−0.839283
$207$	−1.01693e22	−1.01292
$208$	2.93232e20	0.0279003
$209$	−2.93210e22	−2.66557
$210$	−1.32020e21	−0.114698
$211$	−8.13748e21	−0.675782	−0.337891	−	0.941185i	$-0.609714\pi$
$211$	−8.13748e21	−0.675782	−0.337891	+	0.941185i	$0.609714\pi$
$212$	−4.54492e21	−0.360858
$213$	−8.57063e21	−0.650738
$214$	−8.98398e21	−0.652436
$215$	−2.04966e21	−0.142402
$216$	9.56235e21	0.635703
$217$	−1.25982e22	−0.801571
$218$	−1.63127e22	−0.993548
$219$	8.65498e21	0.504716
$220$	1.73425e22	0.968494
$221$	7.19218e21	0.384710
$222$	1.75063e21	0.0897102
$223$	2.07653e22	1.01963	0.509813	−	0.860285i	$-0.329714\pi$
$223$	2.07653e22	1.01963	0.509813	+	0.860285i	$0.329714\pi$
$224$	−1.35634e22	−0.638284
$225$	3.99434e21	0.180182
$226$	1.19622e22	0.517346
$227$	2.41381e22	1.00105	0.500527	−	0.865721i	$-0.333139\pi$
$227$	2.41381e22	1.00105	0.500527	+	0.865721i	$0.333139\pi$
$228$	−8.95973e21	−0.356380
$229$	−4.19321e22	−1.59996	−0.799982	−	0.600025i	$-0.795157\pi$
$229$	−4.19321e22	−1.59996	−0.799982	+	0.600025i	$0.795157\pi$
$230$	1.66274e22	0.608707
$231$	−1.03409e22	−0.363284
$232$	−2.85470e22	−0.962553
$233$	3.68882e22	1.19400	0.597002	−	0.802239i	$-0.296358\pi$
$233$	3.68882e22	1.19400	0.597002	+	0.802239i	$0.296358\pi$
$234$	6.90218e21	0.214504
$235$	4.35889e21	0.130086
$236$	−1.30687e22	−0.374602
$237$	−9.61209e21	−0.264672
$238$	−1.31720e22	−0.348475
$239$	3.62234e22	0.920893	0.460446	−	0.887688i	$-0.347689\pi$
$239$	3.62234e22	0.920893	0.460446	+	0.887688i	$0.347689\pi$
$240$	8.57425e20	0.0209503
$241$	−2.73262e22	−0.641825	−0.320913	−	0.947109i	$-0.603990\pi$
$241$	−2.73262e22	−0.641825	−0.320913	+	0.947109i	$0.603990\pi$
$242$	−4.75123e22	−1.07290
$243$	−4.03827e22	−0.876872
$244$	4.64929e22	0.970920
$245$	2.69453e22	0.541258
$246$	1.30064e22	0.251348
$247$	−3.51276e22	−0.653171
$248$	−6.98570e22	−1.25003
$249$	2.95859e22	0.509555
$250$	−3.84442e22	−0.637383
$251$	−3.58460e22	−0.572190	−0.286095	−	0.958201i	$-0.592357\pi$
$251$	−3.58460e22	−0.572190	−0.286095	+	0.958201i	$0.592357\pi$
$252$	2.32725e22	0.357716
$253$	1.30240e23	1.92796
$254$	4.06670e22	0.579859
$255$	2.10303e22	0.288878
$256$	−7.18824e22	−0.951356
$257$	−8.44816e22	−1.07745	−0.538725	−	0.842482i	$-0.681094\pi$
$257$	−8.44816e22	−1.07745	−0.538725	+	0.842482i	$0.681094\pi$
$258$	2.66473e21	0.0327541
$259$	2.31422e22	0.274194
$260$	2.07769e22	0.237320
$261$	7.87033e22	0.866779
$262$	4.71150e22	0.500376
$263$	3.19947e22	0.327717	0.163858	−	0.986484i	$-0.447606\pi$
$263$	3.19947e22	0.327717	0.163858	+	0.986484i	$0.447606\pi$
$264$	−5.73403e22	−0.566529
$265$	−5.21033e22	−0.496626
$266$	6.43341e22	0.591651
$267$	4.38145e22	0.388831
$268$	1.39544e23	1.19517
$269$	−8.78802e22	−0.726515	−0.363257	−	0.931689i	$-0.618335\pi$
$269$	−8.78802e22	−0.726515	−0.363257	+	0.931689i	$0.618335\pi$
$270$	4.31051e22	0.344011
$271$	1.69840e23	1.30868	0.654338	−	0.756202i	$-0.272947\pi$
$271$	1.69840e23	1.30868	0.654338	+	0.756202i	$0.272947\pi$
$272$	8.55481e21	0.0636511
$273$	−1.23888e22	−0.0890192
$274$	−1.02764e23	−0.713198
$275$	−5.11560e22	−0.342954
$276$	3.97978e22	0.257764
$277$	−1.15124e23	−0.720456	−0.360228	−	0.932864i	$-0.617301\pi$
$277$	−1.15124e23	−0.720456	−0.360228	+	0.932864i	$0.617301\pi$
$278$	−6.93408e22	−0.419337
$279$	1.92594e23	1.12565
$280$	−9.67720e22	−0.546699
$281$	3.25649e23	1.77844	0.889220	−	0.457480i	$-0.151248\pi$
$281$	3.25649e23	1.77844	0.889220	+	0.457480i	$0.151248\pi$
$282$	−5.66693e21	−0.0299213
$283$	3.90469e23	1.99350	0.996749	−	0.0805672i	$-0.0256732\pi$
$283$	3.90469e23	1.99350	0.996749	+	0.0805672i	$0.0256732\pi$
$284$	−2.47029e23	−1.21962
$285$	−1.02715e23	−0.490464
$286$	−8.83971e22	−0.408282
$287$	1.71937e23	0.768229
$288$	2.07349e23	0.896343
$289$	−2.92461e22	−0.122331
$290$	−1.28684e23	−0.520886
$291$	4.78222e21	0.0187347
$292$	2.49460e23	0.945942
$293$	−8.27445e22	−0.303736	−0.151868	−	0.988401i	$-0.548529\pi$
$293$	−8.27445e22	−0.303736	−0.151868	+	0.988401i	$0.548529\pi$
$294$	−3.50311e22	−0.124496
$295$	−1.49821e23	−0.515541
$296$	1.28323e23	0.427597
$297$	3.37636e23	1.08959
$298$	6.96346e22	0.217656
$299$	1.56032e23	0.472429
$300$	−1.56319e22	−0.0458522
$301$	3.52260e22	0.100111
$302$	−5.64345e22	−0.155410
$303$	−9.43501e22	−0.251789
$304$	−4.17828e22	−0.108068
$305$	5.32998e23	1.33622
$306$	2.01366e23	0.489365
$307$	2.33501e23	0.550141	0.275070	−	0.961424i	$-0.411299\pi$
$307$	2.33501e23	0.550141	0.275070	+	0.961424i	$0.411299\pi$
$308$	−2.98054e23	−0.680868
$309$	−2.20812e23	−0.489121
$310$	−3.14901e23	−0.676453
$311$	4.84331e23	1.00906	0.504531	−	0.863393i	$-0.331665\pi$
$311$	4.84331e23	1.00906	0.504531	+	0.863393i	$0.331665\pi$
$312$	−6.86956e22	−0.138823
$313$	−4.60383e22	−0.0902502	−0.0451251	−	0.998981i	$-0.514369\pi$
$313$	−4.60383e22	−0.0902502	−0.0451251	+	0.998981i	$0.514369\pi$
$314$	−3.50082e23	−0.665791
$315$	2.66798e23	0.492303
$316$	−2.77047e23	−0.496050
$317$	7.07895e23	1.23000	0.615001	−	0.788526i	$-0.289156\pi$
$317$	7.07895e23	1.23000	0.615001	+	0.788526i	$0.289156\pi$
$318$	6.77388e22	0.114230
$319$	−1.00796e24	−1.64981
$320$	−3.00890e23	−0.478060
$321$	−2.46515e23	−0.380230
$322$	−2.85763e23	−0.427932
$323$	−1.02482e24	−1.49013
$324$	−3.00910e23	−0.424873
$325$	−6.12866e22	−0.0840376
$326$	−1.69225e23	−0.225371
$327$	−4.47611e23	−0.579025
$328$	9.53387e23	1.19803
$329$	−7.49131e22	−0.0914528
$330$	−2.58478e23	−0.306578
$331$	9.93323e23	1.14479	0.572394	−	0.819979i	$-0.306015\pi$
$331$	9.93323e23	1.14479	0.572394	+	0.819979i	$0.306015\pi$
$332$	8.52747e23	0.955011
$333$	−3.53784e23	−0.385051
$334$	−1.35640e22	−0.0143482
$335$	1.59974e24	1.64484
$336$	−1.47360e22	−0.0147284
$337$	−1.22836e24	−1.19355	−0.596776	−	0.802408i	$-0.703552\pi$
$337$	−1.22836e24	−1.19355	−0.596776	+	0.802408i	$0.703552\pi$
$338$	5.22112e23	0.493236
$339$	3.28236e23	0.301501
$340$	6.06151e23	0.541416
$341$	−2.46657e24	−2.14253
$342$	−9.83499e23	−0.830856
$343$	−1.22612e24	−1.00748
$344$	1.95328e23	0.156120
$345$	4.56245e23	0.354745
$346$	8.91102e23	0.674069
$347$	2.38077e24	1.75222	0.876108	−	0.482114i	$-0.160131\pi$
$347$	2.38077e24	1.75222	0.876108	+	0.482114i	$0.160131\pi$
$348$	−3.08007e23	−0.220575
$349$	−7.86368e23	−0.548004	−0.274002	−	0.961729i	$-0.588348\pi$
$349$	−7.86368e23	−0.548004	−0.274002	+	0.961729i	$0.588348\pi$
$350$	1.12243e23	0.0761223
$351$	4.04499e23	0.266993
$352$	−2.65555e24	−1.70608
$353$	−6.28619e22	−0.0393123	−0.0196561	−	0.999807i	$-0.506257\pi$
$353$	−6.28619e22	−0.0393123	−0.0196561	+	0.999807i	$0.506257\pi$
$354$	1.94780e23	0.118581
$355$	−2.83196e24	−1.67848
$356$	1.26285e24	0.728750
$357$	−3.61433e23	−0.203086
$358$	−8.53389e23	−0.466937
$359$	−5.45910e23	−0.290887	−0.145443	−	0.989367i	$-0.546461\pi$
$359$	−5.45910e23	−0.290887	−0.145443	+	0.989367i	$0.546461\pi$
$360$	1.47939e24	0.767731
$361$	3.02694e24	1.52998
$362$	−1.79948e23	−0.0885965
$363$	−1.30371e24	−0.625270
$364$	−3.57079e23	−0.166840
$365$	2.85983e24	1.30184
$366$	−6.92943e23	−0.307346
$367$	1.08427e24	0.468609	0.234305	−	0.972163i	$-0.424719\pi$
$367$	1.08427e24	0.468609	0.234305	+	0.972163i	$0.424719\pi$
$368$	1.85593e23	0.0781642
$369$	−2.62846e24	−1.07883
$370$	5.78455e23	0.231394
$371$	8.95463e23	0.349137
$372$	−7.53719e23	−0.286452
$373$	3.34704e24	1.24001	0.620007	−	0.784596i	$-0.287130\pi$
$373$	3.34704e24	1.24001	0.620007	+	0.784596i	$0.287130\pi$
$374$	−2.57892e24	−0.931445
$375$	−1.05489e24	−0.371457
$376$	−4.15392e23	−0.142618
$377$	−1.20757e24	−0.404269
$378$	−7.40816e23	−0.241846
$379$	−4.63688e24	−1.47623	−0.738115	−	0.674675i	$-0.764284\pi$
$379$	−4.63688e24	−1.47623	−0.738115	+	0.674675i	$0.764284\pi$
$380$	−2.96053e24	−0.919231
$381$	1.11588e24	0.337933
$382$	−2.02183e24	−0.597231
$383$	−1.51218e24	−0.435727	−0.217864	−	0.975979i	$-0.569909\pi$
$383$	−1.51218e24	−0.435727	−0.217864	+	0.975979i	$0.569909\pi$
$384$	−8.61046e23	−0.242036
$385$	−3.41691e24	−0.937037
$386$	2.09842e24	0.561454
$387$	−5.38513e23	−0.140586
$388$	1.37837e23	0.0351126
$389$	6.18324e23	0.153708	0.0768538	−	0.997042i	$-0.475513\pi$
$389$	6.18324e23	0.153708	0.0768538	+	0.997042i	$0.475513\pi$
$390$	−3.09665e23	−0.0751240
$391$	4.55210e24	1.07779
$392$	−2.56782e24	−0.593399
$393$	1.29281e24	0.291612
$394$	4.13027e24	0.909419
$395$	−3.17608e24	−0.682684
$396$	4.55646e24	0.956144
$397$	−4.48832e24	−0.919548	−0.459774	−	0.888036i	$-0.652070\pi$
$397$	−4.48832e24	−0.919548	−0.459774	+	0.888036i	$0.652070\pi$
$398$	1.16509e24	0.233062
$399$	1.76529e24	0.344805
$400$	−7.28980e22	−0.0139042
$401$	−3.16173e24	−0.588916	−0.294458	−	0.955664i	$-0.595139\pi$
$401$	−3.16173e24	−0.588916	−0.294458	+	0.955664i	$0.595139\pi$
$402$	−2.07980e24	−0.378333
$403$	−2.95504e24	−0.525007
$404$	−2.71943e24	−0.471905
$405$	−3.44965e24	−0.584726
$406$	2.21160e24	0.366192
$407$	4.53095e24	0.732896
$408$	−2.00414e24	−0.316706
$409$	4.03605e24	0.623139	0.311570	−	0.950223i	$-0.399145\pi$
$409$	4.03605e24	0.623139	0.311570	+	0.950223i	$0.399145\pi$
$410$	4.29766e24	0.648315
$411$	−2.81978e24	−0.415641
$412$	−6.36439e24	−0.916713
$413$	2.57487e24	0.362434
$414$	4.36856e24	0.600945
$415$	9.77595e24	1.31432
$416$	−3.18144e24	−0.418058
$417$	−1.90267e24	−0.244383
$418$	1.25958e25	1.58143
$419$	6.31941e24	0.775610	0.387805	−	0.921742i	$-0.373233\pi$
$419$	6.31941e24	0.775610	0.387805	+	0.921742i	$0.373233\pi$
$420$	−1.04412e24	−0.125280
$421$	−1.95552e24	−0.229394	−0.114697	−	0.993401i	$-0.536590\pi$
$421$	−1.95552e24	−0.229394	−0.114697	+	0.993401i	$0.536590\pi$
$422$	3.49571e24	0.400929
$423$	1.14523e24	0.128427
$424$	4.96533e24	0.544468
$425$	−1.78799e24	−0.191721
$426$	3.68179e24	0.386071
$427$	−9.16027e24	−0.939384
$428$	−7.10524e24	−0.712629
$429$	−2.42556e24	−0.237941
$430$	8.80496e23	0.0844845
$431$	1.80412e25	1.69329	0.846647	−	0.532154i	$-0.178617\pi$
$431$	1.80412e25	1.69329	0.846647	+	0.532154i	$0.178617\pi$
$432$	4.81136e23	0.0441745
$433$	−5.45985e24	−0.490394	−0.245197	−	0.969473i	$-0.578853\pi$
$433$	−5.45985e24	−0.490394	−0.245197	+	0.969473i	$0.578853\pi$
$434$	5.41197e24	0.475558
$435$	−3.53101e24	−0.303565
$436$	−1.29014e25	−1.08521
$437$	−2.22331e25	−1.82990
$438$	−3.71802e24	−0.299439
$439$	1.95748e25	1.54271	0.771355	−	0.636406i	$-0.219580\pi$
$439$	1.95748e25	1.54271	0.771355	+	0.636406i	$0.219580\pi$
$440$	−1.89467e25	−1.46128
$441$	7.07941e24	0.534356
$442$	−3.08963e24	−0.228242
$443$	−2.46532e25	−1.78253	−0.891266	−	0.453481i	$-0.850182\pi$
$443$	−2.46532e25	−1.78253	−0.891266	+	0.453481i	$0.850182\pi$
$444$	1.38454e24	0.0979867
$445$	1.44775e25	1.00293
$446$	−8.92038e24	−0.604926
$447$	1.91073e24	0.126847
$448$	5.17118e24	0.336084
$449$	1.83771e25	1.16933	0.584663	−	0.811276i	$-0.301227\pi$
$449$	1.83771e25	1.16933	0.584663	+	0.811276i	$0.301227\pi$
$450$	−1.71590e24	−0.106899
$451$	3.36630e25	2.05341
$452$	9.46066e24	0.565075
$453$	−1.54853e24	−0.0905705
$454$	−1.03693e25	−0.593908
$455$	−4.09358e24	−0.229612
$456$	9.78850e24	0.537713
$457$	2.03812e25	1.09654	0.548272	−	0.836300i	$-0.315286\pi$
$457$	2.03812e25	1.09654	0.548272	+	0.836300i	$0.315286\pi$
$458$	1.80133e25	0.949229
$459$	1.18010e25	0.609112
$460$	1.31502e25	0.664865
$461$	1.74421e25	0.863856	0.431928	−	0.901908i	$-0.357834\pi$
$461$	1.74421e25	0.863856	0.431928	+	0.901908i	$0.357834\pi$
$462$	4.44228e24	0.215530
$463$	3.13889e25	1.49196	0.745980	−	0.665969i	$-0.231982\pi$
$463$	3.13889e25	1.49196	0.745980	+	0.665969i	$0.231982\pi$
$464$	−1.43636e24	−0.0668871
$465$	−8.64069e24	−0.394226
$466$	−1.58465e25	−0.708381
$467$	1.54628e25	0.677297	0.338648	−	0.940913i	$-0.390030\pi$
$467$	1.54628e25	0.677297	0.338648	+	0.940913i	$0.390030\pi$
$468$	5.45879e24	0.234294
$469$	−2.74936e25	−1.15635
$470$	−1.87250e24	−0.0771777
$471$	−9.60605e24	−0.388013
$472$	1.42776e25	0.565205
$473$	6.89680e24	0.267588
$474$	4.12918e24	0.157025
$475$	8.73279e24	0.325510
$476$	−1.04175e25	−0.380625
$477$	−1.36893e25	−0.490293
$478$	−1.55609e25	−0.546349
$479$	3.89908e25	1.34207	0.671034	−	0.741426i	$-0.265850\pi$
$479$	3.89908e25	1.34207	0.671034	+	0.741426i	$0.265850\pi$
$480$	−9.30269e24	−0.313919
$481$	5.42824e24	0.179589
$482$	1.17388e25	0.380783
$483$	−7.84116e24	−0.249392
$484$	−3.75764e25	−1.17188
$485$	1.58017e24	0.0483234
$486$	1.73477e25	0.520232
$487$	−2.03685e24	−0.0599010	−0.0299505	−	0.999551i	$-0.509535\pi$
$487$	−2.03685e24	−0.0599010	−0.0299505	+	0.999551i	$0.509535\pi$
$488$	−5.07935e25	−1.46494
$489$	−4.64344e24	−0.131343
$490$	−1.15752e25	−0.321119
$491$	4.75307e23	0.0129330	0.00646651	−	0.999979i	$-0.497942\pi$
$491$	4.75307e23	0.0129330	0.00646651	+	0.999979i	$0.497942\pi$
$492$	1.02865e25	0.274537
$493$	−3.52300e25	−0.922290
$494$	1.50902e25	0.387515
$495$	5.22356e25	1.31588
$496$	−3.51490e24	−0.0868634
$497$	4.86709e25	1.18000
$498$	−1.27096e25	−0.302310
$499$	3.68588e25	0.860173	0.430086	−	0.902788i	$-0.358483\pi$
$499$	3.68588e25	0.860173	0.430086	+	0.902788i	$0.358483\pi$
$500$	−3.04047e25	−0.696187
$501$	−3.72189e23	−0.00836189
$502$	1.53988e25	0.339470
$503$	−3.95045e25	−0.854577	−0.427289	−	0.904115i	$-0.640531\pi$
$503$	−3.95045e25	−0.854577	−0.427289	+	0.904115i	$0.640531\pi$
$504$	−2.54252e25	−0.539728
$505$	−3.11757e25	−0.649454
$506$	−5.59486e25	−1.14382
$507$	1.43264e25	0.287450
$508$	3.21627e25	0.633355
$509$	6.83174e24	0.132042	0.0660210	−	0.997818i	$-0.478970\pi$
$509$	6.83174e24	0.132042	0.0660210	+	0.997818i	$0.478970\pi$
$510$	−9.03425e24	−0.171386
$511$	−4.91499e25	−0.915217
$512$	−7.41855e24	−0.135598
$513$	−5.76375e25	−1.03417
$514$	3.62917e25	0.639232
$515$	−7.29619e25	−1.26162
$516$	2.10748e24	0.0357760
$517$	−1.46670e25	−0.244445
$518$	−9.94149e24	−0.162674
$519$	2.44513e25	0.392837
$520$	−2.26988e25	−0.358073
$521$	1.01010e26	1.56461	0.782304	−	0.622897i	$-0.214044\pi$
$521$	1.01010e26	1.56461	0.782304	+	0.622897i	$0.214044\pi$
$522$	−3.38095e25	−0.514244
$523$	−8.44459e25	−1.26128	−0.630642	−	0.776074i	$-0.717208\pi$
$523$	−8.44459e25	−1.26128	−0.630642	+	0.776074i	$0.717208\pi$
$524$	3.72623e25	0.546540
$525$	3.07988e24	0.0443629
$526$	−1.37443e25	−0.194428
$527$	−8.62110e25	−1.19774
$528$	−2.88511e24	−0.0393677
$529$	2.41407e25	0.323534
$530$	2.23826e25	0.294639
$531$	−3.93630e25	−0.508967
$532$	5.08805e25	0.646235
$533$	4.03294e25	0.503169
$534$	−1.88219e25	−0.230687
$535$	−8.14550e25	−0.980747
$536$	−1.52452e26	−1.80329
$537$	−2.34165e25	−0.272124
$538$	3.77518e25	0.431028
$539$	−9.06668e25	−1.01708
$540$	3.40909e25	0.375749
$541$	1.37578e26	1.48996	0.744978	−	0.667089i	$-0.232460\pi$
$541$	1.37578e26	1.48996	0.744978	+	0.667089i	$0.232460\pi$
$542$	−7.29603e25	−0.776414
$543$	−4.93768e24	−0.0516327
$544$	−9.28160e25	−0.953747
$545$	−1.47902e26	−1.49351
$546$	5.32200e24	0.0528135
$547$	−1.40085e25	−0.136620	−0.0683098	−	0.997664i	$-0.521761\pi$
$547$	−1.40085e25	−0.136620	−0.0683098	+	0.997664i	$0.521761\pi$
$548$	−8.12738e25	−0.778997
$549$	1.40036e26	1.31918
$550$	2.19757e25	0.203468
$551$	1.72068e26	1.56589
$552$	−4.34791e25	−0.388919
$553$	5.45851e25	0.479938
$554$	4.94551e25	0.427434
$555$	1.58725e25	0.134853
$556$	−5.48402e25	−0.458024
$557$	4.39700e25	0.361020	0.180510	−	0.983573i	$-0.442225\pi$
$557$	4.39700e25	0.361020	0.180510	+	0.983573i	$0.442225\pi$
$558$	−8.27349e25	−0.667826
$559$	8.26260e24	0.0655699
$560$	−4.86914e24	−0.0379897
$561$	−7.07640e25	−0.542832
$562$	−1.39893e26	−1.05512
$563$	−4.37775e25	−0.324654	−0.162327	−	0.986737i	$-0.551900\pi$
$563$	−4.37775e25	−0.324654	−0.162327	+	0.986737i	$0.551900\pi$
$564$	−4.48185e24	−0.0326818
$565$	1.08458e26	0.777679
$566$	−1.67739e26	−1.18271
$567$	5.92868e25	0.411073
$568$	2.69879e26	1.84018
$569$	−7.45487e25	−0.499889	−0.249944	−	0.968260i	$-0.580412\pi$
$569$	−7.45487e25	−0.499889	−0.249944	+	0.968260i	$0.580412\pi$
$570$	4.41245e25	0.290984
$571$	2.59631e26	1.68389	0.841945	−	0.539564i	$-0.181411\pi$
$571$	2.59631e26	1.68389	0.841945	+	0.539564i	$0.181411\pi$
$572$	−6.99114e25	−0.445949
$573$	−5.54778e25	−0.348057
$574$	−7.38609e25	−0.455776
$575$	−3.87898e25	−0.235436
$576$	−7.90537e25	−0.471964
$577$	1.66984e26	0.980630	0.490315	−	0.871545i	$-0.336882\pi$
$577$	1.66984e26	0.980630	0.490315	+	0.871545i	$0.336882\pi$
$578$	1.25636e25	0.0725770
$579$	5.75796e25	0.327206
$580$	−1.01773e26	−0.568942
$581$	−1.68012e26	−0.923992
$582$	−2.05436e24	−0.0111149
$583$	1.75320e26	0.933212
$584$	−2.72535e26	−1.42725
$585$	6.25800e25	0.322444
$586$	3.55455e25	0.180201
$587$	5.70304e25	0.284475	0.142238	−	0.989833i	$-0.454570\pi$
$587$	5.70304e25	0.284475	0.142238	+	0.989833i	$0.454570\pi$
$588$	−2.77054e25	−0.135981
$589$	4.21066e26	2.03355
$590$	6.43604e25	0.305861
$591$	1.13332e26	0.529995
$592$	6.45667e24	0.0297134
$593$	2.56600e26	1.16208	0.581042	−	0.813873i	$-0.302645\pi$
$593$	2.56600e26	1.16208	0.581042	+	0.813873i	$0.302645\pi$
$594$	−1.45042e26	−0.646433
$595$	−1.19427e26	−0.523831
$596$	5.50726e25	0.237737
$597$	3.19694e25	0.135825
$598$	−6.70283e25	−0.280283
$599$	2.85962e26	1.17694	0.588470	−	0.808519i	$-0.299731\pi$
$599$	2.85962e26	1.17694	0.588470	+	0.808519i	$0.299731\pi$
$600$	1.70779e25	0.0691826
$601$	3.76214e26	1.50012	0.750062	−	0.661368i	$-0.230024\pi$
$601$	3.76214e26	1.50012	0.750062	+	0.661368i	$0.230024\pi$
$602$	−1.51325e25	−0.0593941
$603$	4.20305e26	1.62387
$604$	−4.46329e25	−0.169748
$605$	−4.30779e26	−1.61279
$606$	4.05311e25	0.149382
$607$	−4.66226e26	−1.69162	−0.845812	−	0.533482i	$-0.820883\pi$
$607$	−4.66226e26	−1.69162	−0.845812	+	0.533482i	$0.820883\pi$
$608$	4.53326e26	1.61930
$609$	6.06850e25	0.213411
$610$	−2.28966e26	−0.792754
$611$	−1.75716e25	−0.0598990
$612$	1.59256e26	0.534512
$613$	2.34476e25	0.0774862	0.0387431	−	0.999249i	$-0.487665\pi$
$613$	2.34476e25	0.0774862	0.0387431	+	0.999249i	$0.487665\pi$
$614$	−1.00308e26	−0.326388
$615$	1.17925e26	0.377828
$616$	3.25624e26	1.02730
$617$	−2.35692e26	−0.732211	−0.366105	−	0.930573i	$-0.619309\pi$
$617$	−2.35692e26	−0.732211	−0.366105	+	0.930573i	$0.619309\pi$
$618$	9.48567e25	0.290187
$619$	3.29904e26	0.993861	0.496931	−	0.867790i	$-0.334460\pi$
$619$	3.29904e26	0.993861	0.496931	+	0.867790i	$0.334460\pi$
$620$	−2.49048e26	−0.738861
$621$	2.56017e26	0.747996
$622$	−2.08060e26	−0.598659
$623$	−2.48814e26	−0.705080
$624$	−3.45646e24	−0.00964668
$625$	−2.74112e26	−0.753473
$626$	1.97772e25	0.0535438
$627$	3.45621e26	0.921634
$628$	−2.76873e26	−0.727216
$629$	1.58365e26	0.409711
$630$	−1.14612e26	−0.292074
$631$	−3.53475e26	−0.887319	−0.443660	−	0.896195i	$-0.646320\pi$
$631$	−3.53475e26	−0.887319	−0.443660	+	0.896195i	$0.646320\pi$
$632$	3.02674e26	0.748449
$633$	9.59204e25	0.233655
$634$	−3.04099e26	−0.729738
$635$	3.68715e26	0.871648
$636$	5.35732e25	0.124768
$637$	−1.08622e26	−0.249226
$638$	4.33002e26	0.978800
$639$	−7.44050e26	−1.65708
$640$	−2.84512e26	−0.624296
$641$	−8.98587e26	−1.94271	−0.971357	−	0.237625i	$-0.923631\pi$
$641$	−8.98587e26	−1.94271	−0.971357	+	0.237625i	$0.923631\pi$
$642$	1.05899e26	0.225583
$643$	−2.99700e24	−0.00629046	−0.00314523	−	0.999995i	$-0.501001\pi$
$643$	−2.99700e24	−0.00629046	−0.00314523	+	0.999995i	$0.501001\pi$
$644$	−2.26004e26	−0.467412
$645$	2.41603e25	0.0492363
$646$	4.40244e26	0.884066
$647$	4.84943e26	0.959622	0.479811	−	0.877372i	$-0.340705\pi$
$647$	4.84943e26	0.959622	0.479811	+	0.877372i	$0.340705\pi$
$648$	3.28744e26	0.641055
$649$	5.04126e26	0.968756
$650$	2.63276e25	0.0498580
$651$	1.48501e26	0.277148
$652$	−1.33837e26	−0.246163
$653$	4.12659e26	0.748026	0.374013	−	0.927424i	$-0.377982\pi$
$653$	4.12659e26	0.748026	0.374013	+	0.927424i	$0.377982\pi$
$654$	1.92286e26	0.343525
$655$	4.27177e26	0.752170
$656$	4.79702e25	0.0832502
$657$	7.51373e26	1.28524
$658$	3.21813e25	0.0542573
$659$	5.85015e26	0.972199	0.486100	−	0.873903i	$-0.338419\pi$
$659$	5.85015e26	0.972199	0.486100	+	0.873903i	$0.338419\pi$
$660$	−2.04425e26	−0.334862
$661$	−3.20511e26	−0.517522	−0.258761	−	0.965941i	$-0.583314\pi$
$661$	−3.20511e26	−0.517522	−0.258761	+	0.965941i	$0.583314\pi$
$662$	−4.26714e26	−0.679181
$663$	−8.47777e25	−0.133016
$664$	−9.31626e26	−1.44094
$665$	5.83297e26	0.889374
$666$	1.51979e26	0.228444
$667$	−7.64302e26	−1.13258
$668$	−1.07275e25	−0.0156719
$669$	−2.44770e26	−0.352542
$670$	−6.87220e26	−0.975854
$671$	−1.79346e27	−2.51089
$672$	1.59879e26	0.220690
$673$	5.22448e26	0.711049	0.355525	−	0.934667i	$-0.384302\pi$
$673$	5.22448e26	0.711049	0.355525	+	0.934667i	$0.384302\pi$
$674$	5.27681e26	0.708113
$675$	−1.00559e26	−0.133057
$676$	4.12927e26	0.538741
$677$	−1.27178e26	−0.163613	−0.0818066	−	0.996648i	$-0.526069\pi$
$677$	−1.27178e26	−0.163613	−0.0818066	+	0.996648i	$0.526069\pi$
$678$	−1.41004e26	−0.178875
$679$	−2.71573e25	−0.0339722
$680$	−6.62220e26	−0.816898
$681$	−2.84528e26	−0.346120
$682$	1.05959e27	1.27112
$683$	1.12855e27	1.33513	0.667565	−	0.744551i	$-0.267337\pi$
$683$	1.12855e27	1.33513	0.667565	+	0.744551i	$0.267337\pi$
$684$	−7.77829e26	−0.907509
$685$	−9.31729e26	−1.07209
$686$	5.26717e26	0.597721
$687$	4.94274e26	0.553196
$688$	9.82804e24	0.0108487
$689$	2.10039e26	0.228675
$690$	−1.95995e26	−0.210464
$691$	8.01870e26	0.849302	0.424651	−	0.905357i	$-0.360397\pi$
$691$	8.01870e26	0.849302	0.424651	+	0.905357i	$0.360397\pi$
$692$	7.04754e26	0.736258
$693$	−8.97736e26	−0.925088
$694$	−1.02274e27	−1.03956
$695$	−6.28692e26	−0.630351
$696$	3.36497e26	0.332808
$697$	1.17658e27	1.14792
$698$	3.37809e26	0.325121
$699$	−4.34819e26	−0.412834
$700$	8.87705e25	0.0831452
$701$	1.26249e27	1.16656	0.583281	−	0.812271i	$-0.301769\pi$
$701$	1.26249e27	1.16656	0.583281	+	0.812271i	$0.301769\pi$
$702$	−1.73766e26	−0.158402
$703$	−7.73474e26	−0.695617
$704$	1.01245e27	0.898325
$705$	−5.13803e25	−0.0449780
$706$	2.70043e25	0.0233232
$707$	5.35795e26	0.456577
$708$	1.54048e26	0.129521
$709$	1.09031e27	0.904508	0.452254	−	0.891889i	$-0.350620\pi$
$709$	1.09031e27	0.904508	0.452254	+	0.891889i	$0.350620\pi$
$710$	1.21656e27	0.995815
$711$	−8.34463e26	−0.673978
$712$	−1.37967e27	−1.09955
$713$	−1.87031e27	−1.47083
$714$	1.55265e26	0.120487
$715$	−8.01469e26	−0.613733
$716$	−6.74928e26	−0.510016
$717$	−4.26982e26	−0.318404
$718$	2.34513e26	0.172578
$719$	−2.66581e27	−1.93600	−0.968000	−	0.250949i	$-0.919257\pi$
$719$	−2.66581e27	−1.93600	−0.968000	+	0.250949i	$0.919257\pi$
$720$	7.44364e25	0.0533490
$721$	1.25394e27	0.886938
$722$	−1.30032e27	−0.907709
$723$	3.22107e26	0.221915
$724$	−1.42317e26	−0.0967702
$725$	3.00205e26	0.201469
$726$	5.60050e26	0.370961
$727$	−4.20902e26	−0.275172	−0.137586	−	0.990490i	$-0.543934\pi$
$727$	−4.20902e26	−0.275172	−0.137586	+	0.990490i	$0.543934\pi$
$728$	3.90108e26	0.251731
$729$	−5.53390e26	−0.352468
$730$	−1.22853e27	−0.772359
$731$	2.41055e26	0.149590
$732$	−5.48035e26	−0.335701
$733$	3.98135e26	0.240737	0.120368	−	0.992729i	$-0.461592\pi$
$733$	3.98135e26	0.240737	0.120368	+	0.992729i	$0.461592\pi$
$734$	−4.65784e26	−0.278017
$735$	−3.17617e26	−0.187143
$736$	−2.01361e27	−1.17121
$737$	−5.38289e27	−3.09083
$738$	1.12914e27	0.640047
$739$	−2.87795e27	−1.61050	−0.805250	−	0.592936i	$-0.797969\pi$
$739$	−2.87795e27	−1.61050	−0.805250	+	0.592936i	$0.797969\pi$
$740$	4.57488e26	0.252742
$741$	4.14066e26	0.225838
$742$	−3.84675e26	−0.207136
$743$	2.24152e27	1.19165	0.595825	−	0.803114i	$-0.296825\pi$
$743$	2.24152e27	1.19165	0.595825	+	0.803114i	$0.296825\pi$
$744$	8.23438e26	0.432203
$745$	6.31356e26	0.327182
$746$	−1.43783e27	−0.735678
$747$	2.56847e27	1.29756
$748$	−2.03961e27	−1.01738
$749$	1.39991e27	0.689482
$750$	4.53160e26	0.220379
$751$	−2.33908e27	−1.12322	−0.561611	−	0.827401i	$-0.689818\pi$
$751$	−2.33908e27	−1.12322	−0.561611	+	0.827401i	$0.689818\pi$
$752$	−2.09007e25	−0.00991041
$753$	4.22534e26	0.197838
$754$	5.18752e26	0.239846
$755$	−5.11675e26	−0.233613
$756$	−5.85896e26	−0.264158
$757$	1.35938e27	0.605245	0.302623	−	0.953110i	$-0.402138\pi$
$757$	1.35938e27	0.605245	0.302623	+	0.953110i	$0.402138\pi$
$758$	1.99192e27	0.875820
$759$	−1.53520e27	−0.666603
$760$	3.23437e27	1.38695
$761$	−3.71255e27	−1.57224	−0.786119	−	0.618075i	$-0.787913\pi$
$761$	−3.71255e27	−1.57224	−0.786119	+	0.618075i	$0.787913\pi$
$762$	−4.79362e26	−0.200489
$763$	2.54189e27	1.04996
$764$	−1.59902e27	−0.652331
$765$	1.82572e27	0.735617
$766$	6.49604e26	0.258509
$767$	6.03960e26	0.237384
$768$	8.47313e26	0.328937
$769$	4.14692e27	1.59010	0.795052	−	0.606541i	$-0.207444\pi$
$769$	4.14692e27	1.59010	0.795052	+	0.606541i	$0.207444\pi$
$770$	1.46784e27	0.555927
$771$	9.95825e26	0.372534
$772$	1.65960e27	0.613252
$773$	−1.24453e27	−0.454257	−0.227129	−	0.973865i	$-0.572934\pi$
$773$	−1.24453e27	−0.454257	−0.227129	+	0.973865i	$0.572934\pi$
$774$	2.31336e26	0.0834072
$775$	7.34628e26	0.261638
$776$	−1.50587e26	−0.0529785
$777$	−2.72789e26	−0.0948040
$778$	−2.65621e26	−0.0911919
$779$	−5.74658e27	−1.94896
$780$	−2.44908e26	−0.0820548
$781$	9.52913e27	3.15405
$782$	−1.95550e27	−0.639431
$783$	−1.98139e27	−0.640079
$784$	−1.29201e26	−0.0412349
$785$	−3.17409e27	−1.00082
$786$	−5.55367e26	−0.173008
$787$	3.75162e27	1.15467	0.577337	−	0.816506i	$-0.304092\pi$
$787$	3.75162e27	1.15467	0.577337	+	0.816506i	$0.304092\pi$
$788$	3.26654e27	0.993320
$789$	−3.77137e26	−0.113310
$790$	1.36439e27	0.405024
$791$	−1.86399e27	−0.546722
$792$	−4.97793e27	−1.44265
$793$	−2.14863e27	−0.615270
$794$	1.92810e27	0.545551
$795$	6.14167e26	0.171711
$796$	9.21446e26	0.254563
$797$	−2.10331e27	−0.574180	−0.287090	−	0.957904i	$-0.592688\pi$
$797$	−2.10331e27	−0.574180	−0.287090	+	0.957904i	$0.592688\pi$
$798$	−7.58337e26	−0.204566
$799$	−5.12638e26	−0.136652
$800$	7.90912e26	0.208340
$801$	3.80371e27	0.990144
$802$	1.35822e27	0.349393
$803$	−9.62291e27	−2.44630
$804$	−1.64487e27	−0.413237
$805$	−2.59092e27	−0.643270
$806$	1.26943e27	0.311477
$807$	1.03589e27	0.251196
$808$	2.97098e27	0.712018
$809$	1.87906e27	0.445071	0.222535	−	0.974925i	$-0.428567\pi$
$809$	1.87906e27	0.445071	0.222535	+	0.974925i	$0.428567\pi$
$810$	1.48191e27	0.346908
$811$	−4.80796e26	−0.111240	−0.0556202	−	0.998452i	$-0.517714\pi$
$811$	−4.80796e26	−0.111240	−0.0556202	+	0.998452i	$0.517714\pi$
$812$	1.74911e27	0.399976
$813$	−2.00199e27	−0.452482
$814$	−1.94642e27	−0.434814
$815$	−1.53431e27	−0.338779
$816$	−1.00840e26	−0.0220077
$817$	−1.17735e27	−0.253977
$818$	−1.73381e27	−0.369697
$819$	−1.07552e27	−0.226684
$820$	3.39893e27	0.708127
$821$	4.98351e27	1.02630	0.513151	−	0.858298i	$-0.328478\pi$
$821$	4.98351e27	1.02630	0.513151	+	0.858298i	$0.328478\pi$
$822$	1.21133e27	0.246592
$823$	1.22050e27	0.245607	0.122803	−	0.992431i	$-0.460812\pi$
$823$	1.22050e27	0.245607	0.122803	+	0.992431i	$0.460812\pi$
$824$	6.95310e27	1.38315
$825$	6.03000e26	0.118578
$826$	−1.10612e27	−0.215026
$827$	6.61986e26	0.127217	0.0636087	−	0.997975i	$-0.479739\pi$
$827$	6.61986e26	0.127217	0.0636087	+	0.997975i	$0.479739\pi$
$828$	3.45500e27	0.656387
$829$	2.33217e27	0.438019	0.219010	−	0.975723i	$-0.429717\pi$
$829$	2.33217e27	0.438019	0.219010	+	0.975723i	$0.429717\pi$
$830$	−4.19957e27	−0.779764
$831$	1.35702e27	0.249102
$832$	1.21295e27	0.220126
$833$	−3.16896e27	−0.568578
$834$	8.17353e26	0.144988
$835$	−1.22981e26	−0.0215683
$836$	9.96174e27	1.72733
$837$	−4.84864e27	−0.831243
$838$	−2.71470e27	−0.460155
$839$	3.89844e27	0.653359	0.326680	−	0.945135i	$-0.394070\pi$
$839$	3.89844e27	0.653359	0.326680	+	0.945135i	$0.394070\pi$
$840$	1.14070e27	0.189024
$841$	−1.88108e26	−0.0308209
$842$	8.40055e26	0.136095
$843$	−3.83858e27	−0.614905
$844$	2.76469e27	0.437918
$845$	4.73383e27	0.741436
$846$	−4.91968e26	−0.0761936
$847$	7.40350e27	1.13382
$848$	2.49833e26	0.0378347
$849$	−4.60265e27	−0.689263
$850$	7.68089e26	0.113745
$851$	3.43566e27	0.503129
$852$	2.91185e27	0.421689
$853$	1.33883e27	0.191738	0.0958692	−	0.995394i	$-0.469437\pi$
$853$	1.33883e27	0.191738	0.0958692	+	0.995394i	$0.469437\pi$
$854$	3.93509e27	0.557320
$855$	−8.91709e27	−1.24895
$856$	7.76248e27	1.07523
$857$	−1.39952e28	−1.91717	−0.958586	−	0.284804i	$-0.908071\pi$
$857$	−1.39952e28	−1.91717	−0.958586	+	0.284804i	$0.908071\pi$
$858$	1.04198e27	0.141166
$859$	4.94681e27	0.662811	0.331406	−	0.943488i	$-0.392477\pi$
$859$	4.94681e27	0.662811	0.331406	+	0.943488i	$0.392477\pi$
$860$	6.96366e26	0.0922789
$861$	−2.02670e27	−0.265619
$862$	−7.75019e27	−1.00460
$863$	−5.67023e27	−0.726939	−0.363469	−	0.931606i	$-0.618408\pi$
$863$	−5.67023e27	−0.726939	−0.363469	+	0.931606i	$0.618408\pi$
$864$	−5.22011e27	−0.661911
$865$	8.07935e27	1.01327
$866$	2.34545e27	0.290942
$867$	3.44737e26	0.0422967
$868$	4.28022e27	0.519432
$869$	1.06871e28	1.28283
$870$	1.51686e27	0.180099
$871$	−6.44889e27	−0.757378
$872$	1.40947e28	1.63738
$873$	4.15163e26	0.0477072
$874$	9.55093e27	1.08564
$875$	5.99049e27	0.673574
$876$	−2.94051e27	−0.327064
$877$	−6.34245e27	−0.697849	−0.348924	−	0.937151i	$-0.613453\pi$
$877$	−6.34245e27	−0.697849	−0.348924	+	0.937151i	$0.613453\pi$
$878$	−8.40897e27	−0.915261
$879$	9.75349e26	0.105018
$880$	−9.53315e26	−0.101543
$881$	−1.47178e25	−0.00155086	−0.000775428	−	1.00000i	$-0.500247\pi$
$881$	−1.47178e25	−0.00155086	−0.000775428		1.00000i	$0.500247\pi$
$882$	−3.04119e27	−0.317024
$883$	−1.03828e28	−1.07075	−0.535374	−	0.844615i	$-0.679829\pi$
$883$	−1.03828e28	−1.07075	−0.535374	+	0.844615i	$0.679829\pi$
$884$	−2.44352e27	−0.249299
$885$	1.76601e27	0.178251
$886$	1.05906e28	1.05754
$887$	1.64598e28	1.62611	0.813054	−	0.582188i	$-0.197803\pi$
$887$	1.64598e28	1.62611	0.813054	+	0.582188i	$0.197803\pi$
$888$	−1.51261e27	−0.147844
$889$	−6.33685e27	−0.612783
$890$	−6.21925e27	−0.595022
$891$	1.16076e28	1.09876
$892$	−7.05494e27	−0.660735
$893$	2.50379e27	0.232012
$894$	−8.20817e26	−0.0752558
$895$	−7.73742e27	−0.701903
$896$	4.88971e27	0.438891
$897$	−1.83922e27	−0.163345
$898$	−7.89446e27	−0.693740
$899$	1.44749e28	1.25863
$900$	−1.35707e27	−0.116761
$901$	6.12774e27	0.521693
$902$	−1.44610e28	−1.21825
$903$	−4.15226e26	−0.0346139
$904$	−1.03358e28	−0.852595
$905$	−1.63154e27	−0.133179
$906$	6.65221e26	0.0537339
$907$	1.48590e28	1.18774	0.593869	−	0.804562i	$-0.297600\pi$
$907$	1.48590e28	1.18774	0.593869	+	0.804562i	$0.297600\pi$
$908$	−8.20087e27	−0.648700
$909$	−8.19090e27	−0.641172
$910$	1.75853e27	0.136225
$911$	−4.67734e27	−0.358571	−0.179285	−	0.983797i	$-0.557379\pi$
$911$	−4.67734e27	−0.358571	−0.179285	+	0.983797i	$0.557379\pi$
$912$	4.92514e26	0.0373653
$913$	−3.28947e28	−2.46975
$914$	−8.75540e27	−0.650560
$915$	−6.28271e27	−0.462005
$916$	1.42463e28	1.03680
$917$	−7.34159e27	−0.528788
$918$	−5.06948e27	−0.361375
$919$	−1.41375e28	−0.997414	−0.498707	−	0.866771i	$-0.666192\pi$
$919$	−1.41375e28	−0.997414	−0.498707	+	0.866771i	$0.666192\pi$
$920$	−1.43666e28	−1.00316
$921$	−2.75239e27	−0.190214
$922$	−7.49283e27	−0.512510
$923$	1.14162e28	0.772869
$924$	3.51330e27	0.235414
$925$	−1.34947e27	−0.0894988
$926$	−1.34841e28	−0.885152
$927$	−1.91695e28	−1.24553
$928$	1.55839e28	1.00224
$929$	−1.09575e27	−0.0697527	−0.0348763	−	0.999392i	$-0.511104\pi$
$929$	−1.09575e27	−0.0697527	−0.0348763	+	0.999392i	$0.511104\pi$
$930$	3.71188e27	0.233887
$931$	1.54776e28	0.965346
$932$	−1.25327e28	−0.773735
$933$	−5.70904e27	−0.348889
$934$	−6.64256e27	−0.401828
$935$	−2.33823e28	−1.40015
$936$	−5.96373e27	−0.353507
$937$	−1.02241e28	−0.599930	−0.299965	−	0.953950i	$-0.596975\pi$
$937$	−1.02241e28	−0.599930	−0.299965	+	0.953950i	$0.596975\pi$
$938$	1.18108e28	0.686042
$939$	5.42676e26	0.0312045
$940$	−1.48092e27	−0.0842980
$941$	−2.63416e28	−1.48437	−0.742184	−	0.670196i	$-0.766210\pi$
$941$	−2.63416e28	−1.48437	−0.742184	+	0.670196i	$0.766210\pi$
$942$	4.12658e27	0.230201
$943$	2.55255e28	1.40965
$944$	7.18386e26	0.0392757
$945$	−6.71676e27	−0.363544
$946$	−2.96274e27	−0.158755
$947$	1.29415e28	0.686529	0.343264	−	0.939239i	$-0.388467\pi$
$947$	1.29415e28	0.686529	0.343264	+	0.939239i	$0.388467\pi$
$948$	3.26568e27	0.171512
$949$	−1.15286e28	−0.599441
$950$	−3.75145e27	−0.193119
$951$	−8.34430e27	−0.425280
$952$	1.13811e28	0.574293
$953$	2.65879e28	1.32832	0.664159	−	0.747592i	$-0.268790\pi$
$953$	2.65879e28	1.32832	0.664159	+	0.747592i	$0.268790\pi$
$954$	5.88066e27	0.290882
$955$	−1.83313e28	−0.897763
$956$	−1.23068e28	−0.596754
$957$	1.18813e28	0.570429
$958$	−1.67497e28	−0.796225
$959$	1.60130e28	0.753694
$960$	3.54673e27	0.165292
$961$	1.37507e28	0.634529
$962$	−2.33187e27	−0.106547
$963$	−2.14009e28	−0.968241
$964$	9.28399e27	0.415913
$965$	1.90258e28	0.843981
$966$	3.36842e27	0.147960
$967$	−1.90360e28	−0.827988	−0.413994	−	0.910280i	$-0.635867\pi$
$967$	−1.90360e28	−0.827988	−0.413994	+	0.910280i	$0.635867\pi$
$968$	4.10523e28	1.76816
$969$	1.20801e28	0.515220
$970$	−6.78813e26	−0.0286694
$971$	−2.23397e28	−0.934316	−0.467158	−	0.884174i	$-0.654722\pi$
$971$	−2.23397e28	−0.934316	−0.467158	+	0.884174i	$0.654722\pi$
$972$	1.37199e28	0.568228
$973$	1.08049e28	0.443147
$974$	8.74994e26	0.0355381
$975$	7.22415e26	0.0290565
$976$	−2.55571e27	−0.101798
$977$	−5.39572e27	−0.212839	−0.106419	−	0.994321i	$-0.533939\pi$
$977$	−5.39572e27	−0.212839	−0.106419	+	0.994321i	$0.533939\pi$
$978$	1.99474e27	0.0779232
$979$	−4.87145e28	−1.88462
$980$	−9.15458e27	−0.350744
$981$	−3.88588e28	−1.47446
$982$	−2.04183e26	−0.00767292
$983$	3.94164e28	1.46696	0.733480	−	0.679711i	$-0.237895\pi$
$983$	3.94164e28	1.46696	0.733480	+	0.679711i	$0.237895\pi$
$984$	−1.12380e28	−0.414225
$985$	3.74479e28	1.36705
$986$	1.51342e28	0.547178
$987$	8.83037e26	0.0316203
$988$	1.19345e28	0.423266
$989$	5.22960e27	0.183698
$990$	−2.24395e28	−0.780689
$991$	−2.19326e28	−0.755770	−0.377885	−	0.925852i	$-0.623349\pi$
$991$	−2.19326e28	−0.755770	−0.377885	+	0.925852i	$0.623349\pi$
$992$	3.81351e28	1.30156
$993$	−1.17088e28	−0.395816
$994$	−2.09081e28	−0.700075
$995$	1.05635e28	0.350340
$996$	−1.00517e28	−0.330200
$997$	3.62265e28	1.17875	0.589375	−	0.807859i	$-0.299374\pi$
$997$	3.62265e28	1.17875	0.589375	+	0.807859i	$0.299374\pi$
$998$	−1.58339e28	−0.510325
$999$	8.90667e27	0.284344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.14	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-429.582 q^{2} -11787.5 q^{3} -339747. q^{4} -3.89489e6 q^{5} +5.06369e6 q^{6} +6.69387e7 q^{7} +3.71174e8 q^{8} -1.02332e9 q^{9} +O(q^{10})\)	\(q-429.582 q^{2} -11787.5 q^{3} -339747. q^{4} -3.89489e6 q^{5} +5.06369e6 q^{6} +6.69387e7 q^{7} +3.71174e8 q^{8} -1.02332e9 q^{9} +1.67317e9 q^{10} +1.31057e10 q^{11} +4.00477e9 q^{12} +1.57011e10 q^{13} -2.87557e10 q^{14} +4.59109e10 q^{15} +1.86758e10 q^{16} +4.58068e11 q^{17} +4.39598e11 q^{18} -2.23727e12 q^{19} +1.32328e12 q^{20} -7.89039e11 q^{21} -5.62999e12 q^{22} +9.93761e12 q^{23} -4.37521e12 q^{24} -3.90333e12 q^{25} -6.74491e12 q^{26} +2.57625e13 q^{27} -2.27422e13 q^{28} -7.69100e13 q^{29} -1.97225e13 q^{30} -1.88206e14 q^{31} -2.02625e14 q^{32} -1.54484e14 q^{33} -1.96778e14 q^{34} -2.60719e14 q^{35} +3.47669e14 q^{36} +3.45723e14 q^{37} +9.61089e14 q^{38} -1.85077e14 q^{39} -1.44568e15 q^{40} +2.56857e15 q^{41} +3.38957e14 q^{42} +5.26243e14 q^{43} -4.45264e15 q^{44} +3.98570e15 q^{45} -4.26902e15 q^{46} -1.11913e15 q^{47} -2.20141e14 q^{48} -6.91811e15 q^{49} +1.67680e15 q^{50} -5.39947e15 q^{51} -5.33441e15 q^{52} +1.33774e16 q^{53} -1.10671e16 q^{54} -5.10454e16 q^{55} +2.48459e16 q^{56} +2.63717e16 q^{57} +3.30392e16 q^{58} +3.84661e16 q^{59} -1.55981e16 q^{60} -1.36846e17 q^{61} +8.08497e16 q^{62} -6.84995e16 q^{63} +7.72525e16 q^{64} -6.11541e16 q^{65} +6.63633e16 q^{66} -4.10728e17 q^{67} -1.55627e17 q^{68} -1.17139e17 q^{69} +1.12000e17 q^{70} +7.27096e17 q^{71} -3.79829e17 q^{72} -7.34252e17 q^{73} -1.48516e17 q^{74} +4.60104e16 q^{75} +7.60106e17 q^{76} +8.77281e17 q^{77} +7.95055e16 q^{78} +8.15449e17 q^{79} -7.27403e16 q^{80} +8.85687e17 q^{81} -1.10341e18 q^{82} -2.50994e18 q^{83} +2.68074e17 q^{84} -1.78412e18 q^{85} -2.26065e17 q^{86} +9.06575e17 q^{87} +4.86451e18 q^{88} -3.71704e18 q^{89} -1.71219e18 q^{90} +1.05101e18 q^{91} -3.37628e18 q^{92} +2.21847e18 q^{93} +4.80758e17 q^{94} +8.71390e18 q^{95} +2.38844e18 q^{96} -4.05704e17 q^{97} +2.97189e18 q^{98} -1.34113e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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

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