LMFDB - Embedded newform 23.14.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,14,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	23.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:	$24.6631136589$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 91997 x^{12} + 766599 x^{11} + 3278769040 x^{10} - 30986318669 x^{9} + \cdots - 45\!\cdots\!18 $ x^14 - 6x^13 - 91997x^12 + 766599x^11 + 3278769040x^10 - 30986318669x^9 - 56829440072404x^8 + 496745885608086x^7 + 489413218263943745x^6 - 2739731727714726112x^5 - 1876344541617480126605x^4 + 570635039214955094451x^3 + 2228700241007939520815870x^2 - 899908554608774434140317*x - 453423216458424113690611218
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{4}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-110.794$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+115.794 q^{2} +1474.58 q^{3} +5216.18 q^{4} -8934.12 q^{5} +170747. q^{6} +359817. q^{7} -344581. q^{8} +580071. q^{9} +O(q^{10})$	\(q+115.794 q^{2} +1474.58 q^{3} +5216.18 q^{4} -8934.12 q^{5} +170747. q^{6} +359817. q^{7} -344581. q^{8} +580071. q^{9} -1.03451e6 q^{10} +8.79534e6 q^{11} +7.69169e6 q^{12} +1.88074e7 q^{13} +4.16645e7 q^{14} -1.31741e7 q^{15} -8.26313e7 q^{16} +1.96122e8 q^{17} +6.71685e7 q^{18} -3.51419e8 q^{19} -4.66020e7 q^{20} +5.30580e8 q^{21} +1.01845e9 q^{22} +1.48036e8 q^{23} -5.08113e8 q^{24} -1.14088e9 q^{25} +2.17778e9 q^{26} -1.49560e9 q^{27} +1.87687e9 q^{28} +1.90841e9 q^{29} -1.52548e9 q^{30} -4.51567e9 q^{31} -6.74537e9 q^{32} +1.29695e10 q^{33} +2.27097e10 q^{34} -3.21465e9 q^{35} +3.02575e9 q^{36} +5.38185e9 q^{37} -4.06921e10 q^{38} +2.77331e10 q^{39} +3.07853e9 q^{40} +2.24962e10 q^{41} +6.14378e10 q^{42} -3.14488e10 q^{43} +4.58781e10 q^{44} -5.18242e9 q^{45} +1.71416e10 q^{46} +7.79049e10 q^{47} -1.21847e11 q^{48} +3.25793e10 q^{49} -1.32107e11 q^{50} +2.89198e11 q^{51} +9.81030e10 q^{52} -2.64318e11 q^{53} -1.73181e11 q^{54} -7.85787e10 q^{55} -1.23986e11 q^{56} -5.18197e11 q^{57} +2.20982e11 q^{58} -5.25257e11 q^{59} -6.87185e10 q^{60} -6.11472e11 q^{61} -5.22886e11 q^{62} +2.08719e11 q^{63} -1.04156e11 q^{64} -1.68028e11 q^{65} +1.50178e12 q^{66} +7.65177e10 q^{67} +1.02301e12 q^{68} +2.18291e11 q^{69} -3.72236e11 q^{70} +8.12094e11 q^{71} -1.99881e11 q^{72} +8.00860e11 q^{73} +6.23185e11 q^{74} -1.68233e12 q^{75} -1.83307e12 q^{76} +3.16471e12 q^{77} +3.21132e12 q^{78} -9.80638e11 q^{79} +7.38238e11 q^{80} -3.13020e12 q^{81} +2.60491e12 q^{82} -1.77592e12 q^{83} +2.76760e12 q^{84} -1.75218e12 q^{85} -3.64157e12 q^{86} +2.81411e12 q^{87} -3.03071e12 q^{88} -5.17476e12 q^{89} -6.00092e11 q^{90} +6.76724e12 q^{91} +7.72182e11 q^{92} -6.65872e12 q^{93} +9.02090e12 q^{94} +3.13962e12 q^{95} -9.94661e12 q^{96} +8.73956e12 q^{97} +3.77248e12 q^{98} +5.10192e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) $ 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * 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 $

$2$	115.794	1.27935	0.639676	−	0.768645i	$-0.279069\pi$
$2$	115.794	1.27935	0.639676	+	0.768645i	$0.279069\pi$
$3$	1474.58	1.16783	0.583917	−	0.811814i	$-0.301519\pi$
$3$	1474.58	1.16783	0.583917	+	0.811814i	$0.301519\pi$
$4$	5216.18	0.636741
$5$	−8934.12	−0.255709	−0.127855	−	0.991793i	$-0.540809\pi$
$5$	−8934.12	−0.255709	−0.127855	+	0.991793i	$0.540809\pi$
$6$	170747.	1.49407
$7$	359817.	1.15596	0.577982	−	0.816049i	$-0.303840\pi$
$7$	359817.	1.15596	0.577982	+	0.816049i	$0.303840\pi$
$8$	−344581.	−0.464736
$9$	580071.	0.363835
$10$	−1.03451e6	−0.327142
$11$	8.79534e6	1.49693	0.748463	−	0.663177i	$-0.230792\pi$
$11$	8.79534e6	1.49693	0.748463	+	0.663177i	$0.230792\pi$
$12$	7.69169e6	0.743607
$13$	1.88074e7	1.08068	0.540341	−	0.841446i	$-0.318295\pi$
$13$	1.88074e7	1.08068	0.540341	+	0.841446i	$0.318295\pi$
$14$	4.16645e7	1.47889
$15$	−1.31741e7	−0.298626
$16$	−8.26313e7	−1.23130
$17$	1.96122e8	1.97065	0.985323	−	0.170701i	$-0.0546032\pi$
$17$	1.96122e8	1.97065	0.985323	+	0.170701i	$0.0546032\pi$
$18$	6.71685e7	0.465473
$19$	−3.51419e8	−1.71367	−0.856835	−	0.515591i	$-0.827572\pi$
$19$	−3.51419e8	−1.71367	−0.856835	+	0.515591i	$0.827572\pi$
$20$	−4.66020e7	−0.162821
$21$	5.30580e8	1.34997
$22$	1.01845e9	1.91509
$23$	1.48036e8	0.208514
$23$	1.48036e8	0.208514
$24$	−5.08113e8	−0.542735
$25$	−1.14088e9	−0.934613
$26$	2.17778e9	1.38257
$27$	−1.49560e9	−0.742935
$28$	1.87687e9	0.736050
$29$	1.90841e9	0.595779	0.297889	−	0.954600i	$-0.403717\pi$
$29$	1.90841e9	0.595779	0.297889	+	0.954600i	$0.403717\pi$
$30$	−1.52548e9	−0.382048
$31$	−4.51567e9	−0.913842	−0.456921	−	0.889507i	$-0.651048\pi$
$31$	−4.51567e9	−0.913842	−0.456921	+	0.889507i	$0.651048\pi$
$32$	−6.74537e9	−1.11053
$33$	1.29695e10	1.74816
$34$	2.27097e10	2.52115
$35$	−3.21465e9	−0.295591
$36$	3.02575e9	0.231669
$37$	5.38185e9	0.344842	0.172421	−	0.985023i	$-0.444841\pi$
$37$	5.38185e9	0.344842	0.172421	+	0.985023i	$0.444841\pi$
$38$	−4.06921e10	−2.19239
$39$	2.77331e10	1.26206
$40$	3.07853e9	0.118837
$41$	2.24962e10	0.739628	0.369814	−	0.929106i	$-0.379421\pi$
$41$	2.24962e10	0.739628	0.369814	+	0.929106i	$0.379421\pi$
$42$	6.14378e10	1.72709
$43$	−3.14488e10	−0.758681	−0.379340	−	0.925257i	$-0.623849\pi$
$43$	−3.14488e10	−0.758681	−0.379340	+	0.925257i	$0.623849\pi$
$44$	4.58781e10	0.953154
$45$	−5.18242e9	−0.0930361
$46$	1.71416e10	0.266763
$47$	7.79049e10	1.05421	0.527107	−	0.849799i	$-0.323277\pi$
$47$	7.79049e10	1.05421	0.527107	+	0.849799i	$0.323277\pi$
$48$	−1.21847e11	−1.43796
$49$	3.25793e10	0.336254
$50$	−1.32107e11	−1.19570
$51$	2.89198e11	2.30139
$52$	9.81030e10	0.688114
$53$	−2.64318e11	−1.63807	−0.819036	−	0.573742i	$-0.805491\pi$
$53$	−2.64318e11	−1.63807	−0.819036	+	0.573742i	$0.805491\pi$
$54$	−1.73181e11	−0.950475
$55$	−7.85787e10	−0.382778
$56$	−1.23986e11	−0.537219
$57$	−5.18197e11	−2.00128
$58$	2.20982e11	0.762211
$59$	−5.25257e11	−1.62119	−0.810595	−	0.585608i	$-0.800856\pi$
$59$	−5.25257e11	−1.62119	−0.810595	+	0.585608i	$0.800856\pi$
$60$	−6.87185e10	−0.190147
$61$	−6.11472e11	−1.51961	−0.759806	−	0.650149i	$-0.774706\pi$
$61$	−6.11472e11	−1.51961	−0.759806	+	0.650149i	$0.774706\pi$
$62$	−5.22886e11	−1.16912
$63$	2.08719e11	0.420581
$64$	−1.04156e11	−0.189459
$65$	−1.68028e11	−0.276341
$66$	1.50178e12	2.23651
$67$	7.65177e10	0.103342	0.0516709	−	0.998664i	$-0.483545\pi$
$67$	7.65177e10	0.103342	0.0516709	+	0.998664i	$0.483545\pi$
$68$	1.02301e12	1.25479
$69$	2.18291e11	0.243510
$70$	−3.72236e11	−0.378165
$71$	8.12094e11	0.752362	0.376181	−	0.926546i	$-0.377237\pi$
$71$	8.12094e11	0.752362	0.376181	+	0.926546i	$0.377237\pi$
$72$	−1.99881e11	−0.169087
$73$	8.00860e11	0.619381	0.309691	−	0.950837i	$-0.399774\pi$
$73$	8.00860e11	0.619381	0.309691	+	0.950837i	$0.399774\pi$
$74$	6.23185e11	0.441175
$75$	−1.68233e12	−1.09147
$76$	−1.83307e12	−1.09116
$77$	3.16471e12	1.73039
$78$	3.21132e12	1.61461
$79$	−9.80638e11	−0.453871	−0.226936	−	0.973910i	$-0.572871\pi$
$79$	−9.80638e11	−0.453871	−0.226936	+	0.973910i	$0.572871\pi$
$80$	7.38238e11	0.314856
$81$	−3.13020e12	−1.23146
$82$	2.60491e12	0.946244
$83$	−1.77592e12	−0.596232	−0.298116	−	0.954530i	$-0.596358\pi$
$83$	−1.77592e12	−0.596232	−0.298116	+	0.954530i	$0.596358\pi$
$84$	2.76760e12	0.859583
$85$	−1.75218e12	−0.503913
$86$	−3.64157e12	−0.970620
$87$	2.81411e12	0.695771
$88$	−3.03071e12	−0.695676
$89$	−5.17476e12	−1.10371	−0.551855	−	0.833940i	$-0.686080\pi$
$89$	−5.17476e12	−1.10371	−0.551855	+	0.833940i	$0.686080\pi$
$90$	−6.00092e11	−0.119026
$91$	6.76724e12	1.24923
$92$	7.72182e11	0.132770
$93$	−6.65872e12	−1.06721
$94$	9.02090e12	1.34871
$95$	3.13962e12	0.438202
$96$	−9.94661e12	−1.29692
$97$	8.73956e12	1.06530	0.532652	−	0.846334i	$-0.321195\pi$
$97$	8.73956e12	1.06530	0.532652	+	0.846334i	$0.321195\pi$
$98$	3.77248e12	0.430187
$99$	5.10192e12	0.544634
$100$	−5.95106e12	−0.595106
$101$	3.81869e12	0.357953	0.178976	−	0.983853i	$-0.442721\pi$
$101$	3.81869e12	0.357953	0.178976	+	0.983853i	$0.442721\pi$
$102$	3.34873e13	2.94428
$103$	−2.95322e12	−0.243699	−0.121850	−	0.992549i	$-0.538883\pi$
$103$	−2.95322e12	−0.243699	−0.121850	+	0.992549i	$0.538883\pi$
$104$	−6.48069e12	−0.502232
$105$	−4.74027e12	−0.345201
$106$	−3.06063e13	−2.09567
$107$	1.53573e12	0.0989285	0.0494642	−	0.998776i	$-0.484249\pi$
$107$	1.53573e12	0.0989285	0.0494642	+	0.998776i	$0.484249\pi$
$108$	−7.80131e12	−0.473057
$109$	2.40302e13	1.37241	0.686207	−	0.727407i	$-0.259275\pi$
$109$	2.40302e13	1.37241	0.686207	+	0.727407i	$0.259275\pi$
$110$	−9.09891e12	−0.489708
$111$	7.93599e12	0.402718
$112$	−2.97321e13	−1.42334
$113$	−1.56399e13	−0.706682	−0.353341	−	0.935495i	$-0.614954\pi$
$113$	−1.56399e13	−0.706682	−0.353341	+	0.935495i	$0.614954\pi$
$114$	−6.00039e13	−2.56034
$115$	−1.32257e12	−0.0533191
$116$	9.95462e12	0.379357
$117$	1.09096e13	0.393190
$118$	−6.08214e13	−2.07407
$119$	7.05681e13	2.27800
$120$	4.53955e12	0.138782
$121$	4.28354e13	1.24079
$122$	−7.08047e13	−1.94412
$123$	3.31724e13	0.863762
$124$	−2.35545e13	−0.581880
$125$	2.10987e13	0.494699
$126$	2.41684e13	0.538070
$127$	−4.74283e12	−0.100303	−0.0501514	−	0.998742i	$-0.515970\pi$
$127$	−4.74283e12	−0.100303	−0.0501514	+	0.998742i	$0.515970\pi$
$128$	4.31975e13	0.868147
$129$	−4.63739e13	−0.886013
$130$	−1.94566e13	−0.353537
$131$	−3.81675e13	−0.659827	−0.329913	−	0.944011i	$-0.607020\pi$
$131$	−3.81675e13	−0.659827	−0.329913	+	0.944011i	$0.607020\pi$
$132$	6.76510e13	1.11312
$133$	−1.26447e14	−1.98094
$134$	8.86027e12	0.132210
$135$	1.33619e13	0.189975
$136$	−6.75800e13	−0.915831
$137$	1.28319e14	1.65809	0.829043	−	0.559185i	$-0.188886\pi$
$137$	1.28319e14	1.65809	0.829043	+	0.559185i	$0.188886\pi$
$138$	2.52767e13	0.311535
$139$	1.04327e13	0.122687	0.0613437	−	0.998117i	$-0.480461\pi$
$139$	1.04327e13	0.122687	0.0613437	+	0.998117i	$0.480461\pi$
$140$	−1.67682e13	−0.188215
$141$	1.14877e14	1.23115
$142$	9.40353e13	0.962536
$143$	1.65418e14	1.61770
$144$	−4.79320e13	−0.447991
$145$	−1.70500e13	−0.152346
$146$	9.27346e13	0.792407
$147$	4.80409e13	0.392689
$148$	2.80727e13	0.219575
$149$	−1.00168e14	−0.749924	−0.374962	−	0.927040i	$-0.622344\pi$
$149$	−1.00168e14	−0.749924	−0.374962	+	0.927040i	$0.622344\pi$
$150$	−1.94803e14	−1.39638
$151$	−4.80124e13	−0.329612	−0.164806	−	0.986326i	$-0.552700\pi$
$151$	−4.80124e13	−0.329612	−0.164806	+	0.986326i	$0.552700\pi$
$152$	1.21092e14	0.796405
$153$	1.13765e14	0.716990
$154$	3.66454e14	2.21378
$155$	4.03435e13	0.233678
$156$	1.44661e14	0.803603
$157$	−2.47875e14	−1.32095	−0.660473	−	0.750850i	$-0.729644\pi$
$157$	−2.47875e14	−1.32095	−0.660473	+	0.750850i	$0.729644\pi$
$158$	−1.13552e14	−0.580661
$159$	−3.89758e14	−1.91300
$160$	6.02640e13	0.283974
$161$	5.32658e13	0.241035
$162$	−3.62458e14	−1.57547
$163$	3.09645e14	1.29314	0.646569	−	0.762855i	$-0.276203\pi$
$163$	3.09645e14	1.29314	0.646569	+	0.762855i	$0.276203\pi$
$164$	1.17344e14	0.470951
$165$	−1.15871e14	−0.447021
$166$	−2.05640e14	−0.762790
$167$	2.00625e14	0.715694	0.357847	−	0.933780i	$-0.383511\pi$
$167$	2.00625e14	0.715694	0.357847	+	0.933780i	$0.383511\pi$
$168$	−1.82828e14	−0.627382
$169$	5.08445e13	0.167873
$170$	−2.02891e14	−0.644682
$171$	−2.03848e14	−0.623493
$172$	−1.64043e14	−0.483083
$173$	5.37359e14	1.52393	0.761965	−	0.647618i	$-0.224235\pi$
$173$	5.37359e14	1.52393	0.761965	+	0.647618i	$0.224235\pi$
$174$	3.25856e14	0.890135
$175$	−4.10510e14	−1.08038
$176$	−7.26770e14	−1.84317
$177$	−7.74535e14	−1.89328
$178$	−5.99205e14	−1.41203
$179$	3.25786e14	0.740265	0.370133	−	0.928979i	$-0.379312\pi$
$179$	3.25786e14	0.740265	0.370133	+	0.928979i	$0.379312\pi$
$180$	−2.70325e13	−0.0592399
$181$	−6.58139e13	−0.139126	−0.0695628	−	0.997578i	$-0.522160\pi$
$181$	−6.58139e13	−0.139126	−0.0695628	+	0.997578i	$0.522160\pi$
$182$	7.83603e14	1.59820
$183$	−9.01667e14	−1.77465
$184$	−5.10104e13	−0.0969042
$185$	−4.80821e13	−0.0881795
$186$	−7.71038e14	−1.36534
$187$	1.72496e15	2.94991
$188$	4.06366e14	0.671261
$189$	−5.38142e14	−0.858806
$190$	3.63548e14	0.560614
$191$	4.05996e13	0.0605069	0.0302534	−	0.999542i	$-0.490369\pi$
$191$	4.05996e13	0.0605069	0.0302534	+	0.999542i	$0.490369\pi$
$192$	−1.53587e14	−0.221256
$193$	8.43913e14	1.17537	0.587685	−	0.809089i	$-0.300039\pi$
$193$	8.43913e14	1.17537	0.587685	+	0.809089i	$0.300039\pi$
$194$	1.01199e15	1.36290
$195$	−2.47771e14	−0.322720
$196$	1.69940e14	0.214107
$197$	−1.28670e15	−1.56836	−0.784182	−	0.620530i	$-0.786917\pi$
$197$	−1.28670e15	−1.56836	−0.784182	+	0.620530i	$0.786917\pi$
$198$	5.90770e14	0.696779
$199$	1.28960e15	1.47201	0.736007	−	0.676974i	$-0.236709\pi$
$199$	1.28960e15	1.47201	0.736007	+	0.676974i	$0.236709\pi$
$200$	3.93127e14	0.434348
$201$	1.12832e14	0.120686
$202$	4.42181e14	0.457948
$203$	6.86679e14	0.688699
$204$	1.50851e15	1.46539
$205$	−2.00983e14	−0.189130
$206$	−3.41965e14	−0.311777
$207$	8.58713e13	0.0758649
$208$	−1.55408e15	−1.33065
$209$	−3.09085e15	−2.56524
$210$	−5.48893e14	−0.441634
$211$	5.80158e14	0.452595	0.226298	−	0.974058i	$-0.427338\pi$
$211$	5.80158e14	0.452595	0.226298	+	0.974058i	$0.427338\pi$
$212$	−1.37873e15	−1.04303
$213$	1.19750e15	0.878634
$214$	1.77828e14	0.126564
$215$	2.80967e14	0.194002
$216$	5.15355e14	0.345269
$217$	−1.62481e15	−1.05637
$218$	2.78254e15	1.75580
$219$	1.18093e15	0.723334
$220$	−4.09880e14	−0.243730
$221$	3.68855e15	2.12964
$222$	9.18937e14	0.515219
$223$	6.46443e14	0.352005	0.176002	−	0.984390i	$-0.443683\pi$
$223$	6.46443e14	0.352005	0.176002	+	0.984390i	$0.443683\pi$
$224$	−2.42710e15	−1.28374
$225$	−6.61794e14	−0.340045
$226$	−1.81100e15	−0.904095
$227$	−3.53538e15	−1.71501	−0.857507	−	0.514473i	$-0.827988\pi$
$227$	−3.53538e15	−1.71501	−0.857507	+	0.514473i	$0.827988\pi$
$228$	−2.70301e15	−1.27430
$229$	−1.57475e14	−0.0721574	−0.0360787	−	0.999349i	$-0.511487\pi$
$229$	−1.57475e14	−0.0721574	−0.0360787	+	0.999349i	$0.511487\pi$
$230$	−1.53145e14	−0.0682139
$231$	4.66663e15	2.02081
$232$	−6.57603e14	−0.276880
$233$	−2.53001e15	−1.03588	−0.517939	−	0.855418i	$-0.673301\pi$
$233$	−2.53001e15	−1.03588	−0.517939	+	0.855418i	$0.673301\pi$
$234$	1.26327e15	0.503028
$235$	−6.96012e14	−0.269573
$236$	−2.73983e15	−1.03228
$237$	−1.44603e15	−0.530046
$238$	8.17134e15	2.91436
$239$	−3.24606e15	−1.12660	−0.563301	−	0.826251i	$-0.690469\pi$
$239$	−3.24606e15	−1.12660	−0.563301	+	0.826251i	$0.690469\pi$
$240$	1.08859e15	0.367699
$241$	4.01832e15	1.32109	0.660546	−	0.750785i	$-0.270325\pi$
$241$	4.01832e15	1.32109	0.660546	+	0.750785i	$0.270325\pi$
$242$	4.96006e15	1.58740
$243$	−2.23128e15	−0.695205
$244$	−3.18955e15	−0.967599
$245$	−2.91068e14	−0.0859833
$246$	3.84116e15	1.10506
$247$	−6.60929e15	−1.85193
$248$	1.55601e15	0.424695
$249$	−2.61874e15	−0.696299
$250$	2.44310e15	0.632894
$251$	5.64724e14	0.142547	0.0712734	−	0.997457i	$-0.477294\pi$
$251$	5.64724e14	0.142547	0.0712734	+	0.997457i	$0.477294\pi$
$252$	1.08872e15	0.267801
$253$	1.30203e15	0.312131
$254$	−5.49190e14	−0.128323
$255$	−2.58373e15	−0.588486
$256$	5.85524e15	1.30012
$257$	−8.90957e14	−0.192882	−0.0964409	−	0.995339i	$-0.530746\pi$
$257$	−8.90957e14	−0.192882	−0.0964409	+	0.995339i	$0.530746\pi$
$258$	−5.36980e15	−1.13352
$259$	1.93648e15	0.398626
$260$	−8.76464e14	−0.175957
$261$	1.10701e15	0.216765
$262$	−4.41955e15	−0.844151
$263$	2.31266e15	0.430924	0.215462	−	0.976512i	$-0.430874\pi$
$263$	2.31266e15	0.430924	0.215462	+	0.976512i	$0.430874\pi$
$264$	−4.46903e15	−0.812434
$265$	2.36145e15	0.418871
$266$	−1.46417e16	−2.53432
$267$	−7.63061e15	−1.28895
$268$	3.99130e14	0.0658019
$269$	−6.96302e15	−1.12049	−0.560244	−	0.828327i	$-0.689293\pi$
$269$	−6.96302e15	−1.12049	−0.560244	+	0.828327i	$0.689293\pi$
$270$	1.54722e15	0.243045
$271$	−2.95068e15	−0.452504	−0.226252	−	0.974069i	$-0.572647\pi$
$271$	−2.95068e15	−0.452504	−0.226252	+	0.974069i	$0.572647\pi$
$272$	−1.62058e16	−2.42646
$273$	9.97885e15	1.45889
$274$	1.48585e16	2.12127
$275$	−1.00345e16	−1.39905
$276$	1.13865e15	0.155053
$277$	3.06395e14	0.0407533	0.0203767	−	0.999792i	$-0.493513\pi$
$277$	3.06395e14	0.0407533	0.0203767	+	0.999792i	$0.493513\pi$
$278$	1.20804e15	0.156960
$279$	−2.61941e15	−0.332488
$280$	1.10771e15	0.137372
$281$	3.21254e15	0.389276	0.194638	−	0.980875i	$-0.437647\pi$
$281$	3.21254e15	0.389276	0.194638	+	0.980875i	$0.437647\pi$
$282$	1.33021e16	1.57507
$283$	−9.24749e15	−1.07007	−0.535035	−	0.844830i	$-0.679702\pi$
$283$	−9.24749e15	−1.07007	−0.535035	+	0.844830i	$0.679702\pi$
$284$	4.23603e15	0.479060
$285$	4.62963e15	0.511747
$286$	1.91543e16	2.06961
$287$	8.09450e15	0.854983
$288$	−3.91279e15	−0.404051
$289$	2.85593e16	2.88344
$290$	−1.97428e15	−0.194905
$291$	1.28872e16	1.24410
$292$	4.17743e15	0.394385
$293$	−7.38903e15	−0.682257	−0.341128	−	0.940017i	$-0.610809\pi$
$293$	−7.38903e15	−0.682257	−0.341128	+	0.940017i	$0.610809\pi$
$294$	5.56283e15	0.502387
$295$	4.69271e15	0.414553
$296$	−1.85449e15	−0.160261
$297$	−1.31543e16	−1.11212
$298$	−1.15988e16	−0.959416
$299$	2.78418e15	0.225338
$300$	−8.77533e15	−0.694985
$301$	−1.13158e16	−0.877008
$302$	−5.55953e15	−0.421690
$303$	5.63098e15	0.418029
$304$	2.90382e16	2.11004
$305$	5.46297e15	0.388579
$306$	1.31732e16	0.917283
$307$	−1.36142e15	−0.0928097	−0.0464049	−	0.998923i	$-0.514776\pi$
$307$	−1.36142e15	−0.0928097	−0.0464049	+	0.998923i	$0.514776\pi$
$308$	1.65077e16	1.10181
$309$	−4.35477e15	−0.284600
$310$	4.67153e15	0.298956
$311$	1.59904e16	1.00211	0.501055	−	0.865415i	$-0.332945\pi$
$311$	1.59904e16	1.00211	0.501055	+	0.865415i	$0.332945\pi$
$312$	−9.55631e15	−0.586523
$313$	−1.52467e16	−0.916510	−0.458255	−	0.888821i	$-0.651525\pi$
$313$	−1.52467e16	−0.916510	−0.458255	+	0.888821i	$0.651525\pi$
$314$	−2.87024e16	−1.68995
$315$	−1.86472e15	−0.107546
$316$	−5.11519e15	−0.288998
$317$	4.63939e15	0.256788	0.128394	−	0.991723i	$-0.459018\pi$
$317$	4.63939e15	0.256788	0.128394	+	0.991723i	$0.459018\pi$
$318$	−4.51316e16	−2.44739
$319$	1.67851e16	0.891837
$320$	9.30543e14	0.0484464
$321$	2.26457e15	0.115532
$322$	6.16785e15	0.308369
$323$	−6.89211e16	−3.37704
$324$	−1.63277e16	−0.784120
$325$	−2.14571e16	−1.01002
$326$	3.58550e16	1.65438
$327$	3.54345e16	1.60275
$328$	−7.75175e15	−0.343732
$329$	2.80315e16	1.21863
$330$	−1.34171e16	−0.571897
$331$	−7.13138e15	−0.298052	−0.149026	−	0.988833i	$-0.547614\pi$
$331$	−7.13138e15	−0.298052	−0.149026	+	0.988833i	$0.547614\pi$
$332$	−9.26350e15	−0.379645
$333$	3.12186e15	0.125466
$334$	2.32311e16	0.915624
$335$	−6.83618e14	−0.0264255
$336$	−4.38425e16	−1.66223
$337$	1.83180e16	0.681214	0.340607	−	0.940206i	$-0.389367\pi$
$337$	1.83180e16	0.681214	0.340607	+	0.940206i	$0.389367\pi$
$338$	5.88748e15	0.214769
$339$	−2.30623e16	−0.825287
$340$	−9.13968e15	−0.320862
$341$	−3.97168e16	−1.36795
$342$	−2.36043e16	−0.797667
$343$	−2.31397e16	−0.767267
$344$	1.08367e16	0.352587
$345$	−1.95024e15	−0.0622678
$346$	6.22228e16	1.94964
$347$	4.00799e16	1.23249	0.616247	−	0.787553i	$-0.288652\pi$
$347$	4.00799e16	1.23249	0.616247	+	0.787553i	$0.288652\pi$
$348$	1.46789e16	0.443025
$349$	4.35252e16	1.28936	0.644682	−	0.764451i	$-0.276990\pi$
$349$	4.35252e16	1.28936	0.644682	+	0.764451i	$0.276990\pi$
$350$	−4.75344e16	−1.38218
$351$	−2.81284e16	−0.802876
$352$	−5.93279e16	−1.66238
$353$	1.75037e16	0.481498	0.240749	−	0.970587i	$-0.422607\pi$
$353$	1.75037e16	0.481498	0.240749	+	0.970587i	$0.422607\pi$
$354$	−8.96862e16	−2.42217
$355$	−7.25534e15	−0.192386
$356$	−2.69925e16	−0.702778
$357$	1.04058e17	2.66032
$358$	3.77239e16	0.947059
$359$	2.24779e15	0.0554169	0.0277084	−	0.999616i	$-0.491179\pi$
$359$	2.24779e15	0.0554169	0.0277084	+	0.999616i	$0.491179\pi$
$360$	1.78577e15	0.0432373
$361$	8.14425e16	1.93666
$362$	−7.62083e15	−0.177990
$363$	6.31643e16	1.44903
$364$	3.52991e16	0.795435
$365$	−7.15498e15	−0.158382
$366$	−1.04407e17	−2.27041
$367$	−2.63158e16	−0.562196	−0.281098	−	0.959679i	$-0.590699\pi$
$367$	−2.63158e16	−0.562196	−0.281098	+	0.959679i	$0.590699\pi$
$368$	−1.22324e16	−0.256744
$369$	1.30494e16	0.269103
$370$	−5.56761e15	−0.112813
$371$	−9.51060e16	−1.89355
$372$	−3.47331e16	−0.679539
$373$	5.78616e16	1.11246	0.556228	−	0.831030i	$-0.312248\pi$
$373$	5.78616e16	1.11246	0.556228	+	0.831030i	$0.312248\pi$
$374$	1.99740e17	3.77397
$375$	3.11118e16	0.577726
$376$	−2.68446e16	−0.489932
$377$	3.58923e16	0.643847
$378$	−6.23134e16	−1.09871
$379$	−1.07954e16	−0.187105	−0.0935526	−	0.995614i	$-0.529822\pi$
$379$	−1.07954e16	−0.187105	−0.0935526	+	0.995614i	$0.529822\pi$
$380$	1.63768e16	0.279021
$381$	−6.99369e15	−0.117137
$382$	4.70118e15	0.0774096
$383$	1.49750e16	0.242423	0.121211	−	0.992627i	$-0.461322\pi$
$383$	1.49750e16	0.242423	0.121211	+	0.992627i	$0.461322\pi$
$384$	6.36982e16	1.01385
$385$	−2.82739e16	−0.442478
$386$	9.77198e16	1.50371
$387$	−1.82425e16	−0.276035
$388$	4.55871e16	0.678322
$389$	5.37904e16	0.787105	0.393552	−	0.919302i	$-0.371246\pi$
$389$	5.37904e16	0.787105	0.393552	+	0.919302i	$0.371246\pi$
$390$	−2.86903e16	−0.412872
$391$	2.90331e16	0.410908
$392$	−1.12262e16	−0.156269
$393$	−5.62811e16	−0.770568
$394$	−1.48992e17	−2.00649
$395$	8.76114e15	0.116059
$396$	2.66125e16	0.346791
$397$	−3.74346e16	−0.479883	−0.239941	−	0.970787i	$-0.577128\pi$
$397$	−3.74346e16	−0.479883	−0.239941	+	0.970787i	$0.577128\pi$
$398$	1.49328e17	1.88322
$399$	−1.86456e17	−2.31341
$400$	9.42728e16	1.15079
$401$	−2.54596e16	−0.305783	−0.152892	−	0.988243i	$-0.548859\pi$
$401$	−2.54596e16	−0.305783	−0.152892	+	0.988243i	$0.548859\pi$
$402$	1.30652e16	0.154400
$403$	−8.49281e16	−0.987572
$404$	1.99190e16	0.227923
$405$	2.79656e16	0.314896
$406$	7.95131e16	0.881089
$407$	4.73352e16	0.516203
$408$	−9.96523e16	−1.06954
$409$	−6.34252e15	−0.0669977	−0.0334989	−	0.999439i	$-0.510665\pi$
$409$	−6.34252e15	−0.0669977	−0.0334989	+	0.999439i	$0.510665\pi$
$410$	−2.32726e16	−0.241964
$411$	1.89217e17	1.93637
$412$	−1.54045e16	−0.155173
$413$	−1.88996e17	−1.87404
$414$	9.94335e15	0.0970579
$415$	1.58663e16	0.152462
$416$	−1.26863e17	−1.20013
$417$	1.53839e16	0.143279
$418$	−3.57901e17	−3.28184
$419$	2.42510e16	0.218947	0.109473	−	0.993990i	$-0.465084\pi$
$419$	2.42510e16	0.218947	0.109473	+	0.993990i	$0.465084\pi$
$420$	−2.47261e16	−0.219804
$421$	9.14680e16	0.800637	0.400319	−	0.916376i	$-0.368899\pi$
$421$	9.14680e16	0.800637	0.400319	+	0.916376i	$0.368899\pi$
$422$	6.71786e16	0.579029
$423$	4.51904e16	0.383560
$424$	9.10789e16	0.761272
$425$	−2.23753e17	−1.84179
$426$	1.38663e17	1.12408
$427$	−2.20018e17	−1.75662
$428$	8.01066e15	0.0629918
$429$	2.43922e17	1.88921
$430$	3.25343e16	0.248197
$431$	9.54687e15	0.0717395	0.0358698	−	0.999356i	$-0.488580\pi$
$431$	9.54687e15	0.0717395	0.0358698	+	0.999356i	$0.488580\pi$
$432$	1.23583e17	0.914777
$433$	−2.46247e17	−1.79556	−0.897778	−	0.440447i	$-0.854820\pi$
$433$	−2.46247e17	−1.79556	−0.897778	+	0.440447i	$0.854820\pi$
$434$	−1.88143e17	−1.35147
$435$	−2.51416e16	−0.177915
$436$	1.25346e17	0.873871
$437$	−5.20227e16	−0.357325
$438$	1.36745e17	0.925399
$439$	−7.00966e16	−0.467388	−0.233694	−	0.972310i	$-0.575081\pi$
$439$	−7.00966e16	−0.467388	−0.233694	+	0.972310i	$0.575081\pi$
$440$	2.70767e16	0.177891
$441$	1.88983e16	0.122341
$442$	4.27111e17	2.72456
$443$	6.65551e16	0.418367	0.209183	−	0.977876i	$-0.432919\pi$
$443$	6.65551e16	0.418367	0.209183	+	0.977876i	$0.432919\pi$
$444$	4.13955e16	0.256427
$445$	4.62319e16	0.282229
$446$	7.48540e16	0.450338
$447$	−1.47706e17	−0.875786
$448$	−3.74771e16	−0.219008
$449$	1.43607e17	0.827132	0.413566	−	0.910474i	$-0.364283\pi$
$449$	1.43607e17	0.827132	0.413566	+	0.910474i	$0.364283\pi$
$450$	−7.66316e16	−0.435037
$451$	1.97861e17	1.10717
$452$	−8.15805e16	−0.449973
$453$	−7.07982e16	−0.384932
$454$	−4.09374e17	−2.19411
$455$	−6.04593e16	−0.319440
$456$	1.78561e17	0.930068
$457$	−1.90187e17	−0.976619	−0.488310	−	0.872670i	$-0.662386\pi$
$457$	−1.90187e17	−0.976619	−0.488310	+	0.872670i	$0.662386\pi$
$458$	−1.82346e16	−0.0923147
$459$	−2.93320e17	−1.46406
$460$	−6.89877e15	−0.0339505
$461$	−1.00329e17	−0.486823	−0.243411	−	0.969923i	$-0.578267\pi$
$461$	−1.00329e17	−0.486823	−0.243411	+	0.969923i	$0.578267\pi$
$462$	5.40367e17	2.58533
$463$	−3.28734e17	−1.55084	−0.775422	−	0.631444i	$-0.782463\pi$
$463$	−3.28734e17	−1.55084	−0.775422	+	0.631444i	$0.782463\pi$
$464$	−1.57695e17	−0.733584
$465$	5.94899e16	0.272897
$466$	−2.92959e17	−1.32525
$467$	1.20748e17	0.538668	0.269334	−	0.963047i	$-0.413196\pi$
$467$	1.20748e17	0.538668	0.269334	+	0.963047i	$0.413196\pi$
$468$	5.69067e16	0.250360
$469$	2.75324e16	0.119459
$470$	−8.05938e16	−0.344878
$471$	−3.65512e17	−1.54264
$472$	1.80994e17	0.753426
$473$	−2.76603e17	−1.13569
$474$	−1.67441e17	−0.678116
$475$	4.00929e17	1.60162
$476$	3.68096e17	1.45049
$477$	−1.53323e17	−0.595988
$478$	−3.75874e17	−1.44132
$479$	3.46361e17	1.31023	0.655117	−	0.755528i	$-0.272619\pi$
$479$	3.46361e17	1.31023	0.655117	+	0.755528i	$0.272619\pi$
$480$	8.88642e16	0.331634
$481$	1.01219e17	0.372665
$482$	4.65296e17	1.69014
$483$	7.85449e16	0.281489
$484$	2.23437e17	0.790060
$485$	−7.80803e16	−0.272408
$486$	−2.58368e17	−0.889411
$487$	6.36333e16	0.216146	0.108073	−	0.994143i	$-0.465532\pi$
$487$	6.36333e16	0.216146	0.108073	+	0.994143i	$0.465532\pi$
$488$	2.10702e17	0.706219
$489$	4.56598e17	1.51017
$490$	−3.37038e16	−0.110003
$491$	−1.74587e17	−0.562317	−0.281159	−	0.959661i	$-0.590719\pi$
$491$	−1.74587e17	−0.562317	−0.281159	+	0.959661i	$0.590719\pi$
$492$	1.73033e17	0.549992
$493$	3.74282e17	1.17407
$494$	−7.65315e17	−2.36927
$495$	−4.55812e16	−0.139268
$496$	3.73135e17	1.12522
$497$	2.92205e17	0.869704
$498$	−3.03233e17	−0.890811
$499$	8.20153e16	0.237816	0.118908	−	0.992905i	$-0.462061\pi$
$499$	8.20153e16	0.237816	0.118908	+	0.992905i	$0.462061\pi$
$500$	1.10055e17	0.314995
$501$	2.95838e17	0.835812
$502$	6.53915e16	0.182367
$503$	−6.27244e17	−1.72681	−0.863405	−	0.504511i	$-0.831673\pi$
$503$	−6.27244e17	−1.72681	−0.863405	+	0.504511i	$0.831673\pi$
$504$	−7.19208e16	−0.195459
$505$	−3.41167e16	−0.0915319
$506$	1.50766e17	0.399325
$507$	7.49745e16	0.196048
$508$	−2.47394e16	−0.0638669
$509$	−1.59761e17	−0.407198	−0.203599	−	0.979054i	$-0.565264\pi$
$509$	−1.59761e17	−0.407198	−0.203599	+	0.979054i	$0.565264\pi$
$510$	−2.99180e17	−0.752881
$511$	2.88163e17	0.715983
$512$	3.24126e17	0.795169
$513$	5.25582e17	1.27314
$514$	−1.03167e17	−0.246764
$515$	2.63845e16	0.0623162
$516$	−2.41894e17	−0.564161
$517$	6.85201e17	1.57808
$518$	2.24232e17	0.509982
$519$	7.92380e17	1.77970
$520$	5.78993e16	0.128426
$521$	2.07578e17	0.454711	0.227355	−	0.973812i	$-0.426992\pi$
$521$	2.07578e17	0.454711	0.227355	+	0.973812i	$0.426992\pi$
$522$	1.28185e17	0.277319
$523$	3.27785e17	0.700371	0.350186	−	0.936680i	$-0.386119\pi$
$523$	3.27785e17	0.700371	0.350186	+	0.936680i	$0.386119\pi$
$524$	−1.99088e17	−0.420139
$525$	−6.05331e17	−1.26170
$526$	2.67792e17	0.551303
$527$	−8.85622e17	−1.80086
$528$	−1.07168e18	−2.15251
$529$	2.19146e16	0.0434783
$530$	2.73441e17	0.535883
$531$	−3.04686e17	−0.589846
$532$	−6.59568e17	−1.26135
$533$	4.23095e17	0.799302
$534$	−8.83577e17	−1.64902
$535$	−1.37204e16	−0.0252970
$536$	−2.63666e16	−0.0480267
$537$	4.80398e17	0.864506
$538$	−8.06273e17	−1.43350
$539$	2.86546e17	0.503347
$540$	6.96979e16	0.120965
$541$	−1.03281e18	−1.77109	−0.885544	−	0.464555i	$-0.846214\pi$
$541$	−1.03281e18	−1.77109	−0.885544	+	0.464555i	$0.846214\pi$
$542$	−3.41670e17	−0.578911
$543$	−9.70480e16	−0.162475
$544$	−1.32292e18	−2.18846
$545$	−2.14689e17	−0.350939
$546$	1.15549e18	1.86644
$547$	−5.36214e15	−0.00855894	−0.00427947	−	0.999991i	$-0.501362\pi$
$547$	−5.36214e15	−0.00855894	−0.00427947	+	0.999991i	$0.501362\pi$
$548$	6.69334e17	1.05577
$549$	−3.54697e17	−0.552889
$550$	−1.16193e18	−1.78987
$551$	−6.70653e17	−1.02097
$552$	−7.52190e16	−0.113168
$553$	−3.52850e17	−0.524659
$554$	3.54786e16	0.0521378
$555$	−7.09011e16	−0.102979
$556$	5.44188e16	0.0781201
$557$	−2.53397e17	−0.359536	−0.179768	−	0.983709i	$-0.557535\pi$
$557$	−2.53397e17	−0.359536	−0.179768	+	0.983709i	$0.557535\pi$
$558$	−3.03311e17	−0.425369
$559$	−5.91471e17	−0.819893
$560$	2.65631e17	0.363962
$561$	2.54360e18	3.44500
$562$	3.71992e17	0.498021
$563$	−7.05800e17	−0.934064	−0.467032	−	0.884240i	$-0.654677\pi$
$563$	−7.05800e17	−0.934064	−0.467032	+	0.884240i	$0.654677\pi$
$564$	5.99220e17	0.783921
$565$	1.39729e17	0.180705
$566$	−1.07080e18	−1.36900
$567$	−1.12630e18	−1.42352
$568$	−2.79832e17	−0.349650
$569$	−4.66184e15	−0.00575874	−0.00287937	−	0.999996i	$-0.500917\pi$
$569$	−4.66184e15	−0.00575874	−0.00287937	+	0.999996i	$0.500917\pi$
$570$	5.36082e17	0.654704
$571$	−3.99353e17	−0.482194	−0.241097	−	0.970501i	$-0.577507\pi$
$571$	−3.99353e17	−0.482194	−0.241097	+	0.970501i	$0.577507\pi$
$572$	8.62849e17	1.03006
$573$	5.98674e16	0.0706619
$574$	9.37292e17	1.09382
$575$	−1.68892e17	−0.194880
$576$	−6.04179e16	−0.0689318
$577$	1.46581e18	1.65362	0.826809	−	0.562482i	$-0.190154\pi$
$577$	1.46581e18	1.65362	0.826809	+	0.562482i	$0.190154\pi$
$578$	3.30699e18	3.68894
$579$	1.24442e18	1.37264
$580$	−8.89358e16	−0.0970051
$581$	−6.39005e17	−0.689222
$582$	1.49226e18	1.59164
$583$	−2.32477e18	−2.45207
$584$	−2.75961e17	−0.287849
$585$	−9.74681e16	−0.100542
$586$	−8.55603e17	−0.872846
$587$	1.86559e18	1.88221	0.941106	−	0.338111i	$-0.109788\pi$
$587$	1.86559e18	1.88221	0.941106	+	0.338111i	$0.109788\pi$
$588$	2.50590e17	0.250041
$589$	1.58689e18	1.56602
$590$	5.43386e17	0.530360
$591$	−1.89735e18	−1.83159
$592$	−4.44709e17	−0.424605
$593$	3.87877e17	0.366302	0.183151	−	0.983085i	$-0.441370\pi$
$593$	3.87877e17	0.366302	0.183151	+	0.983085i	$0.441370\pi$
$594$	−1.52319e18	−1.42279
$595$	−6.30464e17	−0.582505
$596$	−5.22493e17	−0.477507
$597$	1.90163e18	1.71907
$598$	3.22390e17	0.288286
$599$	−8.15657e16	−0.0721495	−0.0360748	−	0.999349i	$-0.511485\pi$
$599$	−8.15657e16	−0.0721495	−0.0360748	+	0.999349i	$0.511485\pi$
$600$	5.79699e17	0.507247
$601$	4.17703e17	0.361562	0.180781	−	0.983523i	$-0.442137\pi$
$601$	4.17703e17	0.361562	0.180781	+	0.983523i	$0.442137\pi$
$602$	−1.31030e18	−1.12200
$603$	4.43857e16	0.0375993
$604$	−2.50441e17	−0.209877
$605$	−3.82696e17	−0.317281
$606$	6.52032e17	0.534806
$607$	−1.07455e18	−0.871971	−0.435986	−	0.899954i	$-0.643600\pi$
$607$	−1.07455e18	−0.871971	−0.435986	+	0.899954i	$0.643600\pi$
$608$	2.37045e18	1.90308
$609$	1.01257e18	0.804286
$610$	6.32577e17	0.497130
$611$	1.46519e18	1.13927
$612$	5.93417e17	0.456537
$613$	−7.21506e17	−0.549221	−0.274610	−	0.961556i	$-0.588549\pi$
$613$	−7.21506e17	−0.549221	−0.274610	+	0.961556i	$0.588549\pi$
$614$	−1.57644e17	−0.118736
$615$	−2.96367e17	−0.220872
$616$	−1.09050e18	−0.804177
$617$	−1.55016e18	−1.13116	−0.565578	−	0.824695i	$-0.691347\pi$
$617$	−1.55016e18	−1.13116	−0.565578	+	0.824695i	$0.691347\pi$
$618$	−5.04255e17	−0.364104
$619$	2.33367e18	1.66744	0.833719	−	0.552190i	$-0.186208\pi$
$619$	2.33367e18	1.66744	0.833719	+	0.552190i	$0.186208\pi$
$620$	2.10439e17	0.148792
$621$	−2.21402e17	−0.154913
$622$	1.85158e18	1.28205
$623$	−1.86197e18	−1.27585
$624$	−2.29162e18	−1.55397
$625$	1.20418e18	0.808113
$626$	−1.76547e18	−1.17254
$627$	−4.55772e18	−2.99577
$628$	−1.29296e18	−0.841100
$629$	1.05550e18	0.679562
$630$	−2.15923e17	−0.137590
$631$	2.06531e17	0.130255	0.0651274	−	0.997877i	$-0.479255\pi$
$631$	2.06531e17	0.130255	0.0651274	+	0.997877i	$0.479255\pi$
$632$	3.37910e17	0.210931
$633$	8.55491e17	0.528556
$634$	5.37212e17	0.328523
$635$	4.23730e16	0.0256484
$636$	−2.03305e18	−1.21808
$637$	6.12733e17	0.363383
$638$	1.94361e18	1.14097
$639$	4.71072e17	0.273736
$640$	−3.85931e17	−0.221994
$641$	1.79676e18	1.02309	0.511543	−	0.859257i	$-0.329074\pi$
$641$	1.79676e18	1.02309	0.511543	+	0.859257i	$0.329074\pi$
$642$	2.62223e17	0.147806
$643$	4.29294e17	0.239543	0.119771	−	0.992801i	$-0.461784\pi$
$643$	4.29294e17	0.239543	0.119771	+	0.992801i	$0.461784\pi$
$644$	2.77844e17	0.153477
$645$	4.14310e17	0.226562
$646$	−7.98063e18	−4.32042
$647$	1.69173e18	0.906677	0.453338	−	0.891339i	$-0.350233\pi$
$647$	1.69173e18	0.906677	0.453338	+	0.891339i	$0.350233\pi$
$648$	1.07861e18	0.572304
$649$	−4.61981e18	−2.42680
$650$	−2.48460e18	−1.29217
$651$	−2.39592e18	−1.23366
$652$	1.61517e18	0.823394
$653$	2.54748e18	1.28581	0.642903	−	0.765948i	$-0.277730\pi$
$653$	2.54748e18	1.28581	0.642903	+	0.765948i	$0.277730\pi$
$654$	4.10309e18	2.05048
$655$	3.40993e17	0.168724
$656$	−1.85889e18	−0.910705
$657$	4.64556e17	0.225353
$658$	3.24587e18	1.55906
$659$	−2.31572e17	−0.110136	−0.0550681	−	0.998483i	$-0.517538\pi$
$659$	−2.31572e17	−0.110136	−0.0550681	+	0.998483i	$0.517538\pi$
$660$	−6.04403e17	−0.284637
$661$	2.41845e18	1.12779	0.563893	−	0.825848i	$-0.309303\pi$
$661$	2.41845e18	1.12779	0.563893	+	0.825848i	$0.309303\pi$
$662$	−8.25768e17	−0.381313
$663$	5.43908e18	2.48707
$664$	6.11947e17	0.277090
$665$	1.12969e18	0.506546
$666$	3.61491e17	0.160515
$667$	2.82513e17	0.124228
$668$	1.04649e18	0.455712
$669$	9.53233e17	0.411083
$670$	−7.91587e16	−0.0338075
$671$	−5.37811e18	−2.27475
$672$	−3.57896e18	−1.49919
$673$	−4.16389e18	−1.72743	−0.863717	−	0.503977i	$-0.831870\pi$
$673$	−4.16389e18	−1.72743	−0.863717	+	0.503977i	$0.831870\pi$
$674$	2.12111e18	0.871512
$675$	1.70631e18	0.694356
$676$	2.65214e17	0.106892
$677$	2.15033e18	0.858377	0.429188	−	0.903215i	$-0.358800\pi$
$677$	2.15033e18	0.858377	0.429188	+	0.903215i	$0.358800\pi$
$678$	−2.67047e18	−1.05583
$679$	3.14464e18	1.23145
$680$	6.03768e17	0.234187
$681$	−5.21320e18	−2.00285
$682$	−4.59896e18	−1.75009
$683$	−4.63815e18	−1.74828	−0.874138	−	0.485677i	$-0.838573\pi$
$683$	−4.63815e18	−1.74828	−0.874138	+	0.485677i	$0.838573\pi$
$684$	−1.06331e18	−0.397004
$685$	−1.14642e18	−0.423988
$686$	−2.67943e18	−0.981604
$687$	−2.32210e17	−0.0842678
$688$	2.59865e18	0.934165
$689$	−4.97114e18	−1.77024
$690$	−2.25825e17	−0.0796625
$691$	4.32696e18	1.51208	0.756041	−	0.654524i	$-0.227131\pi$
$691$	4.32696e18	1.51208	0.756041	+	0.654524i	$0.227131\pi$
$692$	2.80296e18	0.970348
$693$	1.83576e18	0.629578
$694$	4.64100e18	1.57679
$695$	−9.32070e16	−0.0313724
$696$	−9.69690e17	−0.323350
$697$	4.41199e18	1.45754
$698$	5.03995e18	1.64955
$699$	−3.73071e18	−1.20973
$700$	−2.14129e18	−0.687921
$701$	3.01089e18	0.958358	0.479179	−	0.877717i	$-0.340934\pi$
$701$	3.01089e18	0.958358	0.479179	+	0.877717i	$0.340934\pi$
$702$	−3.25709e18	−1.02716
$703$	−1.89129e18	−0.590946
$704$	−9.16089e17	−0.283606
$705$	−1.02633e18	−0.314816
$706$	2.02682e18	0.616005
$707$	1.37403e18	0.413781
$708$	−4.04011e18	−1.20553
$709$	−3.53619e17	−0.104553	−0.0522763	−	0.998633i	$-0.516648\pi$
$709$	−3.53619e17	−0.104553	−0.0522763	+	0.998633i	$0.516648\pi$
$710$	−8.40123e17	−0.246130
$711$	−5.68840e17	−0.165134
$712$	1.78313e18	0.512935
$713$	−6.68481e17	−0.190549
$714$	1.20493e19	3.40349
$715$	−1.47786e18	−0.413661
$716$	1.69936e18	0.471357
$717$	−4.78659e18	−1.31568
$718$	2.60280e17	0.0708977
$719$	−5.90911e17	−0.159509	−0.0797544	−	0.996815i	$-0.525414\pi$
$719$	−5.90911e17	−0.159509	−0.0797544	+	0.996815i	$0.525414\pi$
$720$	4.28230e17	0.114556
$721$	−1.06262e18	−0.281708
$722$	9.43053e18	2.47767
$723$	5.92534e18	1.54282
$724$	−3.43297e17	−0.0885869
$725$	−2.17728e18	−0.556823
$726$	7.31402e18	1.85382
$727$	4.15661e18	1.04416	0.522079	−	0.852897i	$-0.325157\pi$
$727$	4.15661e18	1.04416	0.522079	+	0.852897i	$0.325157\pi$
$728$	−2.33186e18	−0.580562
$729$	1.70035e18	0.419576
$730$	−8.28502e17	−0.202626
$731$	−6.16781e18	−1.49509
$732$	−4.70326e18	−1.13000
$733$	3.28499e17	0.0782272	0.0391136	−	0.999235i	$-0.487547\pi$
$733$	3.28499e17	0.0782272	0.0391136	+	0.999235i	$0.487547\pi$
$734$	−3.04721e18	−0.719246
$735$	−4.29203e17	−0.100414
$736$	−9.98557e17	−0.231562
$737$	6.72999e17	0.154695
$738$	1.51103e18	0.344277
$739$	1.99452e18	0.450454	0.225227	−	0.974306i	$-0.427688\pi$
$739$	1.99452e18	0.450454	0.225227	+	0.974306i	$0.427688\pi$
$740$	−2.50805e17	−0.0561475
$741$	−9.74595e18	−2.16275
$742$	−1.10127e19	−2.42252
$743$	−2.40286e18	−0.523964	−0.261982	−	0.965073i	$-0.584376\pi$
$743$	−2.40286e18	−0.523964	−0.261982	+	0.965073i	$0.584376\pi$
$744$	2.29447e18	0.495974
$745$	8.94911e17	0.191763
$746$	6.70001e18	1.42322
$747$	−1.03016e18	−0.216930
$748$	8.99771e18	1.87833
$749$	5.52583e17	0.114358
$750$	3.60255e18	0.739115
$751$	−2.08124e18	−0.423315	−0.211657	−	0.977344i	$-0.567886\pi$
$751$	−2.08124e18	−0.423315	−0.211657	+	0.977344i	$0.567886\pi$
$752$	−6.43738e18	−1.29806
$753$	8.32733e17	0.166471
$754$	4.15611e18	0.823707
$755$	4.28948e17	0.0842849
$756$	−2.80705e18	−0.546837
$757$	−7.67951e18	−1.48324	−0.741618	−	0.670822i	$-0.765941\pi$
$757$	−7.67951e18	−1.48324	−0.741618	+	0.670822i	$0.765941\pi$
$758$	−1.25004e18	−0.239373
$759$	1.91995e18	0.364517
$760$	−1.08185e18	−0.203648
$761$	7.40621e18	1.38228	0.691140	−	0.722721i	$-0.257109\pi$
$761$	7.40621e18	1.38228	0.691140	+	0.722721i	$0.257109\pi$
$762$	−8.09825e17	−0.149859
$763$	8.64647e18	1.58646
$764$	2.11775e17	0.0385272
$765$	−1.01639e18	−0.183341
$766$	1.73401e18	0.310144
$767$	−9.87874e18	−1.75199
$768$	8.63404e18	1.51833
$769$	3.71498e18	0.647792	0.323896	−	0.946093i	$-0.395007\pi$
$769$	3.71498e18	0.647792	0.323896	+	0.946093i	$0.395007\pi$
$770$	−3.27394e18	−0.566085
$771$	−1.31379e18	−0.225254
$772$	4.40200e18	0.748407
$773$	2.67292e18	0.450630	0.225315	−	0.974286i	$-0.427659\pi$
$773$	2.67292e18	0.450630	0.225315	+	0.974286i	$0.427659\pi$
$774$	−2.11237e18	−0.353146
$775$	5.15186e18	0.854088
$776$	−3.01149e18	−0.495085
$777$	2.85550e18	0.465528
$778$	6.22859e18	1.00698
$779$	−7.90558e18	−1.26748
$780$	−1.29242e18	−0.205489
$781$	7.14264e18	1.12623
$782$	3.36185e18	0.525696
$783$	−2.85422e18	−0.442625
$784$	−2.69207e18	−0.414030
$785$	2.21455e18	0.337778
$786$	−6.51700e18	−0.985827
$787$	2.50050e18	0.375138	0.187569	−	0.982251i	$-0.439939\pi$
$787$	2.50050e18	0.375138	0.187569	+	0.982251i	$0.439939\pi$
$788$	−6.71166e18	−0.998642
$789$	3.41022e18	0.503247
$790$	1.01449e18	0.148481
$791$	−5.62750e18	−0.816900
$792$	−1.75803e18	−0.253111
$793$	−1.15002e19	−1.64222
$794$	−4.33469e18	−0.613939
$795$	3.48215e18	0.489171
$796$	6.72681e18	0.937291
$797$	−1.29217e19	−1.78583	−0.892914	−	0.450227i	$-0.851343\pi$
$797$	−1.29217e19	−1.78583	−0.892914	+	0.450227i	$0.851343\pi$
$798$	−2.15904e19	−2.95966
$799$	1.52789e19	2.07748
$800$	7.69569e18	1.03792
$801$	−3.00173e18	−0.401569
$802$	−2.94806e18	−0.391204
$803$	7.04384e18	0.927168
$804$	5.88550e17	0.0768456
$805$	−4.75883e17	−0.0616350
$806$	−9.83414e18	−1.26345
$807$	−1.02675e19	−1.30854
$808$	−1.31585e18	−0.166354
$809$	−2.04187e18	−0.256073	−0.128036	−	0.991769i	$-0.540867\pi$
$809$	−2.04187e18	−0.256073	−0.128036	+	0.991769i	$0.540867\pi$
$810$	3.23824e18	0.402862
$811$	3.56895e18	0.440458	0.220229	−	0.975448i	$-0.429320\pi$
$811$	3.56895e18	0.440458	0.220229	+	0.975448i	$0.429320\pi$
$812$	3.58184e18	0.438523
$813$	−4.35102e18	−0.528449
$814$	5.48112e18	0.660406
$815$	−2.76641e18	−0.330668
$816$	−2.38968e19	−2.83370
$817$	1.10517e19	1.30013
$818$	−7.34423e17	−0.0857137
$819$	3.92548e18	0.454514
$820$	−1.04837e18	−0.120427
$821$	−1.63793e18	−0.186666	−0.0933328	−	0.995635i	$-0.529752\pi$
$821$	−1.63793e18	−0.186666	−0.0933328	+	0.995635i	$0.529752\pi$
$822$	2.19101e19	2.47730
$823$	−8.00155e18	−0.897584	−0.448792	−	0.893636i	$-0.648146\pi$
$823$	−8.00155e18	−0.897584	−0.448792	+	0.893636i	$0.648146\pi$
$824$	1.01763e18	0.113256
$825$	−1.47967e19	−1.63385
$826$	−2.18846e19	−2.39755
$827$	8.38310e18	0.911211	0.455605	−	0.890182i	$-0.349423\pi$
$827$	8.38310e18	0.911211	0.455605	+	0.890182i	$0.349423\pi$
$828$	4.47920e17	0.0483063
$829$	7.49194e18	0.801659	0.400830	−	0.916153i	$-0.368722\pi$
$829$	7.49194e18	0.801659	0.400830	+	0.916153i	$0.368722\pi$
$830$	1.83721e18	0.195053
$831$	4.51805e17	0.0475931
$832$	−1.95891e18	−0.204745
$833$	6.38952e18	0.662637
$834$	1.78136e18	0.183304
$835$	−1.79241e18	−0.183010
$836$	−1.61224e19	−1.63339
$837$	6.75363e18	0.678925
$838$	2.80811e18	0.280110
$839$	−1.45313e19	−1.43831	−0.719154	−	0.694851i	$-0.755470\pi$
$839$	−1.45313e19	−1.43831	−0.719154	+	0.694851i	$0.755470\pi$
$840$	1.63341e18	0.160428
$841$	−6.61859e18	−0.645047
$842$	1.05914e19	1.02430
$843$	4.73716e18	0.454609
$844$	3.02621e18	0.288186
$845$	−4.54251e17	−0.0429267
$846$	5.23276e18	0.490708
$847$	1.54129e19	1.43431
$848$	2.18409e19	2.01696
$849$	−1.36362e19	−1.24966
$850$	−2.59092e19	−2.35630
$851$	7.96707e17	0.0719046
$852$	6.24637e18	0.559462
$853$	2.15630e19	1.91664	0.958319	−	0.285702i	$-0.0922267\pi$
$853$	2.15630e19	1.91664	0.958319	+	0.285702i	$0.0922267\pi$
$854$	−2.54767e19	−2.24733
$855$	1.82120e18	0.159433
$856$	−5.29185e17	−0.0459757
$857$	1.70303e19	1.46841	0.734204	−	0.678929i	$-0.237555\pi$
$857$	1.70303e19	1.46841	0.734204	+	0.678929i	$0.237555\pi$
$858$	2.82447e19	2.41696
$859$	1.19837e19	1.01773	0.508867	−	0.860845i	$-0.330064\pi$
$859$	1.19837e19	1.01773	0.508867	+	0.860845i	$0.330064\pi$
$860$	1.46558e18	0.123529
$861$	1.19360e19	0.998478
$862$	1.10547e18	0.0917801
$863$	2.18027e19	1.79655	0.898277	−	0.439429i	$-0.144819\pi$
$863$	2.18027e19	1.79655	0.898277	+	0.439429i	$0.144819\pi$
$864$	1.00884e19	0.825053
$865$	−4.80083e18	−0.389683
$866$	−2.85138e19	−2.29715
$867$	4.21131e19	3.36738
$868$	−8.47532e18	−0.672633
$869$	−8.62505e18	−0.679412
$870$	−2.91124e18	−0.227616
$871$	1.43910e18	0.111679
$872$	−8.28035e18	−0.637810
$873$	5.06957e18	0.387595
$874$	−6.02390e18	−0.457144
$875$	7.59168e18	0.571854
$876$	6.15997e18	0.460576
$877$	−6.04433e18	−0.448591	−0.224296	−	0.974521i	$-0.572008\pi$
$877$	−6.04433e18	−0.448591	−0.224296	+	0.974521i	$0.572008\pi$
$878$	−8.11674e18	−0.597953
$879$	−1.08957e19	−0.796762
$880$	6.49306e18	0.471316
$881$	−1.97013e17	−0.0141955	−0.00709775	−	0.999975i	$-0.502259\pi$
$881$	−1.97013e17	−0.0141955	−0.00709775	+	0.999975i	$0.502259\pi$
$882$	2.18830e18	0.156517
$883$	2.65558e19	1.88545	0.942724	−	0.333575i	$-0.108255\pi$
$883$	2.65558e19	1.88545	0.942724	+	0.333575i	$0.108255\pi$
$884$	1.92402e19	1.35603
$885$	6.91979e18	0.484129
$886$	7.70666e18	0.535238
$887$	1.17993e19	0.813493	0.406746	−	0.913541i	$-0.366663\pi$
$887$	1.17993e19	0.813493	0.406746	+	0.913541i	$0.366663\pi$
$888$	−2.73459e18	−0.187158
$889$	−1.70655e18	−0.115947
$890$	5.35337e18	0.361071
$891$	−2.75312e19	−1.84340
$892$	3.37196e18	0.224136
$893$	−2.73773e19	−1.80657
$894$	−1.71034e19	−1.12044
$895$	−2.91061e18	−0.189293
$896$	1.55432e19	1.00355
$897$	4.10550e18	0.263157
$898$	1.66288e19	1.05819
$899$	−8.61775e18	−0.544448
$900$	−3.45204e18	−0.216520
$901$	−5.18385e19	−3.22806
$902$	2.29111e19	1.41646
$903$	−1.66861e19	−1.02420
$904$	5.38922e18	0.328421
$905$	5.87989e17	0.0355757
$906$	−8.19799e18	−0.492463
$907$	−1.92867e19	−1.15030	−0.575148	−	0.818049i	$-0.695056\pi$
$907$	−1.92867e19	−1.15030	−0.575148	+	0.818049i	$0.695056\pi$
$908$	−1.84412e19	−1.09202
$909$	2.21511e18	0.130236
$910$	−7.00081e18	−0.408676
$911$	−5.10818e18	−0.296071	−0.148036	−	0.988982i	$-0.547295\pi$
$911$	−5.10818e18	−0.296071	−0.148036	+	0.988982i	$0.547295\pi$
$912$	4.28193e19	2.46418
$913$	−1.56198e19	−0.892514
$914$	−2.20224e19	−1.24944
$915$	8.05560e18	0.453796
$916$	−8.21418e17	−0.0459456
$917$	−1.37333e19	−0.762736
$918$	−3.39646e19	−1.87305
$919$	−2.22959e19	−1.22088	−0.610442	−	0.792061i	$-0.709008\pi$
$919$	−2.22959e19	−1.22088	−0.610442	+	0.792061i	$0.709008\pi$
$920$	4.55733e17	0.0247793
$921$	−2.00753e18	−0.108386
$922$	−1.16175e19	−0.622817
$923$	1.52734e19	0.813064
$924$	2.43420e19	1.28673
$925$	−6.14007e18	−0.322294
$926$	−3.80653e19	−1.98407
$927$	−1.71308e18	−0.0886664
$928$	−1.28729e19	−0.661631
$929$	3.69170e19	1.88419	0.942094	−	0.335348i	$-0.108854\pi$
$929$	3.69170e19	1.88419	0.942094	+	0.335348i	$0.108854\pi$
$930$	6.88855e18	0.349131
$931$	−1.14490e19	−0.576228
$932$	−1.31970e19	−0.659585
$933$	2.35791e19	1.17030
$934$	1.39819e19	0.689146
$935$	−1.54110e19	−0.754320
$936$	−3.75926e18	−0.182730
$937$	1.36044e19	0.656707	0.328354	−	0.944555i	$-0.393506\pi$
$937$	1.36044e19	0.656707	0.328354	+	0.944555i	$0.393506\pi$
$938$	3.18808e18	0.152831
$939$	−2.24825e19	−1.07033
$940$	−3.63052e18	−0.171648
$941$	2.54846e19	1.19659	0.598294	−	0.801277i	$-0.295845\pi$
$941$	2.54846e19	1.19659	0.598294	+	0.801277i	$0.295845\pi$
$942$	−4.23240e19	−1.97359
$943$	3.33024e18	0.154223
$944$	4.34026e19	1.99617
$945$	4.80783e18	0.219605
$946$	−3.20289e19	−1.45295
$947$	6.54918e18	0.295061	0.147531	−	0.989058i	$-0.452868\pi$
$947$	6.54918e18	0.295061	0.147531	+	0.989058i	$0.452868\pi$
$948$	−7.54277e18	−0.337502
$949$	1.50621e19	0.669354
$950$	4.64250e19	2.04903
$951$	6.84116e18	0.299886
$952$	−2.43164e19	−1.05867
$953$	−3.84692e19	−1.66345	−0.831724	−	0.555189i	$-0.812646\pi$
$953$	−3.84692e19	−1.66345	−0.831724	+	0.555189i	$0.812646\pi$
$954$	−1.77538e19	−0.762479
$955$	−3.62722e17	−0.0154722
$956$	−1.69321e19	−0.717354
$957$	2.47511e19	1.04152
$958$	4.01065e19	1.67625
$959$	4.61713e19	1.91669
$960$	1.37216e18	0.0565774
$961$	−4.02629e18	−0.164893
$962$	1.17205e19	0.476769
$963$	8.90834e17	0.0359937
$964$	2.09603e19	0.841193
$965$	−7.53962e18	−0.300554
$966$	9.09500e18	0.360124
$967$	2.65206e19	1.04307	0.521533	−	0.853231i	$-0.325360\pi$
$967$	2.65206e19	1.04307	0.521533	+	0.853231i	$0.325360\pi$
$968$	−1.47603e19	−0.576639
$969$	−1.01630e20	−3.94382
$970$	−9.04121e18	−0.348506
$971$	4.27835e19	1.63814	0.819070	−	0.573693i	$-0.194490\pi$
$971$	4.27835e19	1.63814	0.819070	+	0.573693i	$0.194490\pi$
$972$	−1.16387e19	−0.442665
$973$	3.75386e18	0.141822
$974$	7.36834e18	0.276526
$975$	−3.16403e19	−1.17953
$976$	5.05267e19	1.87110
$977$	5.79495e18	0.213175	0.106587	−	0.994303i	$-0.466008\pi$
$977$	5.79495e18	0.213175	0.106587	+	0.994303i	$0.466008\pi$
$978$	5.28711e19	1.93204
$979$	−4.55138e19	−1.65217
$980$	−1.51826e18	−0.0547491
$981$	1.39392e19	0.499332
$982$	−2.02160e19	−0.719402
$983$	−1.31844e19	−0.466082	−0.233041	−	0.972467i	$-0.574868\pi$
$983$	−1.31844e19	−0.466082	−0.233041	+	0.972467i	$0.574868\pi$
$984$	−1.14306e19	−0.401422
$985$	1.14955e19	0.401046
$986$	4.33395e19	1.50205
$987$	4.13348e19	1.42316
$988$	−3.44753e19	−1.17920
$989$	−4.65555e18	−0.158196
$990$	−5.27801e18	−0.178173
$991$	−3.43112e19	−1.15069	−0.575343	−	0.817912i	$-0.695132\pi$
$991$	−3.43112e19	−1.15069	−0.575343	+	0.817912i	$0.695132\pi$
$992$	3.04599e19	1.01485
$993$	−1.05158e19	−0.348075
$994$	3.38355e19	1.11266
$995$	−1.15215e19	−0.376408
$996$	−1.36598e19	−0.443362
$997$	−1.11562e18	−0.0359748	−0.0179874	−	0.999838i	$-0.505726\pi$
$997$	−1.11562e18	−0.0359748	−0.0179874	+	0.999838i	$0.505726\pi$
$998$	9.49685e18	0.304250
$999$	−8.04909e18	−0.256195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.a.b.1.11	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.a.b.1.11	✓	14	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q+115.794 q^{2} +1474.58 q^{3} +5216.18 q^{4} -8934.12 q^{5} +170747. q^{6} +359817. q^{7} -344581. q^{8} +580071. q^{9} +O(q^{10})\)	\(q+115.794 q^{2} +1474.58 q^{3} +5216.18 q^{4} -8934.12 q^{5} +170747. q^{6} +359817. q^{7} -344581. q^{8} +580071. q^{9} -1.03451e6 q^{10} +8.79534e6 q^{11} +7.69169e6 q^{12} +1.88074e7 q^{13} +4.16645e7 q^{14} -1.31741e7 q^{15} -8.26313e7 q^{16} +1.96122e8 q^{17} +6.71685e7 q^{18} -3.51419e8 q^{19} -4.66020e7 q^{20} +5.30580e8 q^{21} +1.01845e9 q^{22} +1.48036e8 q^{23} -5.08113e8 q^{24} -1.14088e9 q^{25} +2.17778e9 q^{26} -1.49560e9 q^{27} +1.87687e9 q^{28} +1.90841e9 q^{29} -1.52548e9 q^{30} -4.51567e9 q^{31} -6.74537e9 q^{32} +1.29695e10 q^{33} +2.27097e10 q^{34} -3.21465e9 q^{35} +3.02575e9 q^{36} +5.38185e9 q^{37} -4.06921e10 q^{38} +2.77331e10 q^{39} +3.07853e9 q^{40} +2.24962e10 q^{41} +6.14378e10 q^{42} -3.14488e10 q^{43} +4.58781e10 q^{44} -5.18242e9 q^{45} +1.71416e10 q^{46} +7.79049e10 q^{47} -1.21847e11 q^{48} +3.25793e10 q^{49} -1.32107e11 q^{50} +2.89198e11 q^{51} +9.81030e10 q^{52} -2.64318e11 q^{53} -1.73181e11 q^{54} -7.85787e10 q^{55} -1.23986e11 q^{56} -5.18197e11 q^{57} +2.20982e11 q^{58} -5.25257e11 q^{59} -6.87185e10 q^{60} -6.11472e11 q^{61} -5.22886e11 q^{62} +2.08719e11 q^{63} -1.04156e11 q^{64} -1.68028e11 q^{65} +1.50178e12 q^{66} +7.65177e10 q^{67} +1.02301e12 q^{68} +2.18291e11 q^{69} -3.72236e11 q^{70} +8.12094e11 q^{71} -1.99881e11 q^{72} +8.00860e11 q^{73} +6.23185e11 q^{74} -1.68233e12 q^{75} -1.83307e12 q^{76} +3.16471e12 q^{77} +3.21132e12 q^{78} -9.80638e11 q^{79} +7.38238e11 q^{80} -3.13020e12 q^{81} +2.60491e12 q^{82} -1.77592e12 q^{83} +2.76760e12 q^{84} -1.75218e12 q^{85} -3.64157e12 q^{86} +2.81411e12 q^{87} -3.03071e12 q^{88} -5.17476e12 q^{89} -6.00092e11 q^{90} +6.76724e12 q^{91} +7.72182e11 q^{92} -6.65872e12 q^{93} +9.02090e12 q^{94} +3.13962e12 q^{95} -9.94661e12 q^{96} +8.73956e12 q^{97} +3.77248e12 q^{98} +5.10192e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9	\( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) 14 * q + 64 * q^2 + 2056 * q^3 + 69632 * q^4 + 52182 * q^5 + 311167 * q^6 + 190602 * q^7 + 2356809 * q^8 + 12050784 * q^9 + 3585670 * q^10 + 1070730 * q^11 - 8508331 * q^12 + 23949638 * q^13 - 119280968 * q^14 - 44834930 * q^15 + 256829072 * q^16 + 69487470 * q^17 + 92449927 * q^18 + 111438548 * q^19 + 1129282316 * q^20 + 621345174 * q^21 + 2278933028 * q^22 + 2072502446 * q^23 + 8776950724 * q^24 + 5548551686 * q^25 - 925154105 * q^26 - 2006600744 * q^27 + 10886499970 * q^28 + 6082889362 * q^29 + 33591682946 * q^30 + 15979895560 * q^31 + 39045677992 * q^32 + 48341340746 * q^33 + 26300859414 * q^34 + 71251965504 * q^35 + 134660338135 * q^36 + 52356093690 * q^37 + 96969962716 * q^38 + 35694630240 * q^39 + 30337594230 * q^40 + 116782373266 * q^41 + 47161428352 * q^42 + 551363512 * q^43 - 18191926218 * q^44 + 66956385060 * q^45 + 9474296896 * q^46 - 89763073312 * q^47 + 7373438519 * q^48 + 198965141586 * q^49 - 353559739256 * q^50 - 849385907902 * q^51 + 290946305159 * q^52 - 255252512096 * q^53 - 20138610103 * q^54 - 308239853444 * q^55 - 1741462242990 * q^56 - 373036556464 * q^57 - 2063171638367 * q^58 - 844368470500 * q^59 - 3864457510716 * q^60 - 660411924036 * q^61 - 3066592203813 * q^62 - 2044550744028 * q^63 - 149179140181 * q^64 + 25563523898 * q^65 - 3128765504558 * q^66 + 343438236966 * q^67 - 687566878740 * q^68 + 304361787784 * q^69 + 2831163146300 * q^70 + 525250335580 * q^71 - 1782771811281 * q^72 + 6080256001118 * q^73 + 1193156509458 * q^74 + 3035968085076 * q^75 + 11140697506136 * q^76 - 905513956696 * q^77 + 15392222627509 * q^78 + 2029462022780 * q^79 + 6389606776510 * q^80 + 11017226960590 * q^81 + 5032544493407 * q^82 + 1645588044714 * q^83 - 8835767120594 * q^84 + 8689341605448 * q^85 - 5028664556794 * q^86 + 14107817502696 * q^87 + 35486297142892 * q^88 + 3557834996156 * q^89 - 20611184383708 * q^90 + 20574193795614 * q^91 + 10308035022848 * q^92 + 32845521705562 * q^93 - 4653170522585 * q^94 + 35338742719324 * q^95 + 44121425602615 * q^96 + 20411381883630 * q^97 - 10415391287228 * q^98 - 9767188111540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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