LMFDB - Embedded newform 252.2.bj.b.103.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(103,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("252.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, minimal)

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:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.42
Character	$\chi$	$=$	252.103
Dual form			252.2.bj.b.115.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40573 + 0.154709i) q^{2} +(-0.868676 + 1.49847i) q^{3} +(1.95213 + 0.434957i) q^{4} +(-2.69307 + 1.55484i) q^{5} +(-1.45295 + 1.97204i) q^{6} +(-2.30485 + 1.29911i) q^{7} +(2.67687 + 0.913443i) q^{8} +(-1.49080 - 2.60336i) q^{9} +O(q^{10})$	\(q+(1.40573 + 0.154709i) q^{2} +(-0.868676 + 1.49847i) q^{3} +(1.95213 + 0.434957i) q^{4} +(-2.69307 + 1.55484i) q^{5} +(-1.45295 + 1.97204i) q^{6} +(-2.30485 + 1.29911i) q^{7} +(2.67687 + 0.913443i) q^{8} +(-1.49080 - 2.60336i) q^{9} +(-4.02627 + 1.76904i) q^{10} +(1.94657 + 1.12385i) q^{11} +(-2.34754 + 2.54736i) q^{12} +(3.87442 + 2.23689i) q^{13} +(-3.44097 + 1.46961i) q^{14} +(0.00952410 - 5.38613i) q^{15} +(3.62162 + 1.69819i) q^{16} +(-2.92047 + 1.68614i) q^{17} +(-1.69290 - 3.89026i) q^{18} +(3.28507 - 5.68990i) q^{19} +(-5.93352 + 1.86389i) q^{20} +(0.0554973 - 4.58224i) q^{21} +(2.56248 + 1.88098i) q^{22} +(0.746323 - 0.430890i) q^{23} +(-3.69410 + 3.21771i) q^{24} +(2.33509 - 4.04449i) q^{25} +(5.10030 + 3.74387i) q^{26} +(5.19608 + 0.0275643i) q^{27} +(-5.06442 + 1.53352i) q^{28} +(0.897936 + 1.55527i) q^{29} +(0.846672 - 7.56995i) q^{30} +6.47553 q^{31} +(4.82829 + 2.94748i) q^{32} +(-3.37500 + 1.94061i) q^{33} +(-4.36625 + 1.91842i) q^{34} +(4.18720 - 7.08227i) q^{35} +(-1.77789 - 5.73054i) q^{36} +(-1.93958 + 3.35945i) q^{37} +(5.49818 - 7.49021i) q^{38} +(-6.71752 + 3.86254i) q^{39} +(-8.62926 + 1.70215i) q^{40} +(1.06232 + 0.613333i) q^{41} +(0.786928 - 6.43279i) q^{42} +(-0.846269 + 0.488593i) q^{43} +(3.31113 + 3.04059i) q^{44} +(8.06266 + 4.69308i) q^{45} +(1.11579 - 0.490250i) q^{46} -11.4875 q^{47} +(-5.69070 + 3.95171i) q^{48} +(3.62464 - 5.98849i) q^{49} +(3.90821 - 5.32418i) q^{50} +(0.0103283 - 5.84094i) q^{51} +(6.59041 + 6.05191i) q^{52} +(-0.992739 - 1.71947i) q^{53} +(7.30000 + 0.842629i) q^{54} -6.98968 q^{55} +(-7.35643 + 1.37219i) q^{56} +(5.67247 + 9.86524i) q^{57} +(1.02164 + 2.32520i) q^{58} +6.17823 q^{59} +(2.36133 - 10.5103i) q^{60} -13.1880i q^{61} +(9.10282 + 1.00182i) q^{62} +(6.81812 + 4.06364i) q^{63} +(6.33124 + 4.89033i) q^{64} -13.9121 q^{65} +(-5.04455 + 2.20582i) q^{66} -11.7765i q^{67} +(-6.43454 + 2.02128i) q^{68} +(-0.00263939 + 1.49264i) q^{69} +(6.98175 - 9.30793i) q^{70} +3.55574i q^{71} +(-1.61266 - 8.33063i) q^{72} +(3.89746 - 2.25020i) q^{73} +(-3.24626 + 4.42240i) q^{74} +(4.03209 + 7.01240i) q^{75} +(8.88774 - 9.67856i) q^{76} +(-5.94656 - 0.0615047i) q^{77} +(-10.0406 + 4.39041i) q^{78} +11.2425i q^{79} +(-12.3937 + 1.05773i) q^{80} +(-4.55502 + 7.76221i) q^{81} +(1.39845 + 1.02653i) q^{82} +(1.48263 + 2.56798i) q^{83} +(2.10142 - 8.92099i) q^{84} +(5.24336 - 9.08177i) q^{85} +(-1.26521 + 0.555903i) q^{86} +(-3.11054 - 0.00550025i) q^{87} +(4.18414 + 4.78649i) q^{88} +(-13.1148 - 7.57182i) q^{89} +(10.6078 + 7.84455i) q^{90} +(-11.8359 - 0.122418i) q^{91} +(1.64434 - 0.516534i) q^{92} +(-5.62514 + 9.70337i) q^{93} +(-16.1483 - 1.77723i) q^{94} +20.4311i q^{95} +(-8.61092 + 4.67461i) q^{96} +(-2.86666 + 1.65507i) q^{97} +(6.02172 - 7.85741i) q^{98} +(0.0238472 - 6.74308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.40573	+	0.154709i	0.993998	+	0.109396i
$2$	1.40573	+	0.154709i	0.993998	+	0.109396i
$3$	−0.868676	+	1.49847i	−0.501531	+	0.865140i
$3$	−0.868676	+	1.49847i	−0.501531	+	0.865140i
$4$	1.95213	+	0.434957i	0.976065	+	0.217479i
$5$	−2.69307	+	1.55484i	−1.20438	+	0.695348i	−0.961526	−	0.274715i	$-0.911416\pi$
$5$	−2.69307	+	1.55484i	−1.20438	+	0.695348i	−0.242852	+	0.970063i	$0.578083\pi$
$6$	−1.45295	+	1.97204i	−0.593163	+	0.805082i
$7$	−2.30485	+	1.29911i	−0.871150	+	0.491017i
$7$	−2.30485	+	1.29911i	−0.871150	+	0.491017i
$8$	2.67687	+	0.913443i	0.946416	+	0.322951i
$9$	−1.49080	−	2.60336i	−0.496934	−	0.867788i
$10$	−4.02627	+	1.76904i	−1.27322	+	0.559421i
$11$	1.94657	+	1.12385i	0.586914	+	0.338855i	0.763876	−	0.645363i	$-0.223294\pi$
$11$	1.94657	+	1.12385i	0.586914	+	0.338855i	−0.176962	+	0.984218i	$0.556627\pi$
$12$	−2.34754	+	2.54736i	−0.677676	+	0.735361i
$13$	3.87442	+	2.23689i	1.07457	+	0.620403i	0.929426	−	0.369008i	$-0.120302\pi$
$13$	3.87442	+	2.23689i	1.07457	+	0.620403i	0.145143	+	0.989411i	$0.453636\pi$
$14$	−3.44097	+	1.46961i	−0.919637	+	0.392769i
$15$	0.00952410	−	5.38613i	0.00245911	−	1.39069i
$16$	3.62162	+	1.69819i	0.905406	+	0.424547i
$17$	−2.92047	+	1.68614i	−0.708319	+	0.408948i	−0.810438	−	0.585824i	$-0.800771\pi$
$17$	−2.92047	+	1.68614i	−0.708319	+	0.408948i	0.102119	+	0.994772i	$0.467438\pi$
$18$	−1.69290	−	3.89026i	−0.399019	−	0.916943i
$19$	3.28507	−	5.68990i	0.753646	−	1.30535i	−0.192399	−	0.981317i	$-0.561627\pi$
$19$	3.28507	−	5.68990i	0.753646	−	1.30535i	0.946045	−	0.324036i	$-0.105040\pi$
$20$	−5.93352	+	1.86389i	−1.32677	+	0.416778i
$21$	0.0554973	−	4.58224i	0.0121105	−	0.999927i
$22$	2.56248	+	1.88098i	0.546322	+	0.401027i
$23$	0.746323	−	0.430890i	0.155619	−	0.0898467i	−0.420168	−	0.907446i	$-0.638029\pi$
$23$	0.746323	−	0.430890i	0.155619	−	0.0898467i	0.575787	+	0.817600i	$0.304696\pi$
$24$	−3.69410	+	3.21771i	−0.754054	+	0.656812i
$25$	2.33509	−	4.04449i	0.467017	−	0.808897i
$26$	5.10030	+	3.74387i	1.00025	+	0.734233i
$27$	5.19608	+	0.0275643i	0.999986	+	0.00530476i
$28$	−5.06442	+	1.53352i	−0.957085	+	0.289807i
$29$	0.897936	+	1.55527i	0.166743	+	0.288807i	0.937273	−	0.348597i	$-0.113342\pi$
$29$	0.897936	+	1.55527i	0.166743	+	0.288807i	−0.770530	+	0.637403i	$0.780008\pi$
$30$	0.846672	−	7.56995i	0.154581	−	1.38208i
$31$	6.47553			1.16304			0.581520	−	0.813532i	$-0.302458\pi$
$31$	6.47553			1.16304			0.581520	+	0.813532i	$0.302458\pi$
$32$	4.82829	+	2.94748i	0.853528	+	0.521046i
$33$	−3.37500	+	1.94061i	−0.587512	+	0.337817i
$34$	−4.36625	+	1.91842i	−0.748805	+	0.329007i
$35$	4.18720	−	7.08227i	0.707767	−	1.19712i
$36$	−1.77789	−	5.73054i	−0.296315	−	0.955090i
$37$	−1.93958	+	3.35945i	−0.318865	+	0.552291i	−0.980252	−	0.197755i	$-0.936635\pi$
$37$	−1.93958	+	3.35945i	−0.318865	+	0.552291i	0.661386	+	0.750045i	$0.269968\pi$
$38$	5.49818	−	7.49021i	0.891923	−	1.21507i
$39$	−6.71752	+	3.86254i	−1.07566	+	0.618502i
$40$	−8.62926	+	1.70215i	−1.36441	+	0.269133i
$41$	1.06232	+	0.613333i	0.165907	+	0.0957866i	0.580655	−	0.814150i	$-0.302797\pi$
$41$	1.06232	+	0.613333i	0.165907	+	0.0957866i	−0.414747	+	0.909937i	$0.636130\pi$
$42$	0.786928	−	6.43279i	0.121426	−	0.992601i
$43$	−0.846269	+	0.488593i	−0.129055	+	0.0745098i	−0.563138	−	0.826363i	$-0.690406\pi$
$43$	−0.846269	+	0.488593i	−0.129055	+	0.0745098i	0.434083	+	0.900873i	$0.357073\pi$
$44$	3.31113	+	3.04059i	0.499172	+	0.458386i
$45$	8.06266	+	4.69308i	1.20191	+	0.699603i
$46$	1.11579	−	0.490250i	0.164514	−	0.0722834i
$47$	−11.4875			−1.67563			−0.837815	−	0.545954i	$-0.816167\pi$
$47$	−11.4875			−1.67563			−0.837815	+	0.545954i	$0.816167\pi$
$48$	−5.69070	+	3.95171i	−0.821381	+	0.570380i
$49$	3.62464	−	5.98849i	0.517806	−	0.855498i
$50$	3.90821	−	5.32418i	0.552704	−	0.752953i
$51$	0.0103283	−	5.84094i	0.00144625	−	0.817895i
$52$	6.59041	+	6.05191i	0.913925	+	0.839250i
$53$	−0.992739	−	1.71947i	−0.136363	−	0.236188i	0.789754	−	0.613423i	$-0.210208\pi$
$53$	−0.992739	−	1.71947i	−0.136363	−	0.236188i	−0.926117	+	0.377235i	$0.876875\pi$
$54$	7.30000	+	0.842629i	0.993404	+	0.114667i
$55$	−6.98968			−0.942488
$56$	−7.35643	+	1.37219i	−0.983045	+	0.183367i
$57$	5.67247	+	9.86524i	0.751336	+	1.30668i
$58$	1.02164	+	2.32520i	0.134148	+	0.305314i
$59$	6.17823			0.804336			0.402168	−	0.915566i	$-0.368257\pi$
$59$	6.17823			0.804336			0.402168	+	0.915566i	$0.368257\pi$
$60$	2.36133	−	10.5103i	0.304846	−	1.35687i
$61$		−	13.1880i		−	1.68855i	−0.535911	−	0.844275i	$-0.680032\pi$
$61$		−	13.1880i		−	1.68855i	0.535911	−	0.844275i	$-0.319968\pi$
$62$	9.10282	+	1.00182i	1.15606	+	0.127232i
$63$	6.81812	+	4.06364i	0.859003	+	0.511971i
$64$	6.33124	+	4.89033i	0.791405	+	0.611292i
$65$	−13.9121			−1.72558
$66$	−5.04455	+	2.20582i	−0.620942	+	0.271518i
$67$		−	11.7765i		−	1.43872i	−0.694636	−	0.719362i	$-0.744434\pi$
$67$		−	11.7765i		−	1.43872i	0.694636	−	0.719362i	$-0.255566\pi$
$68$	−6.43454	+	2.02128i	−0.780303	+	0.245116i
$69$	−0.00263939	+	1.49264i	−0.000317745	+	0.179693i
$70$	6.98175	−	9.30793i	0.834479	−	1.11251i
$71$			3.55574i			0.421989i	0.977487	+	0.210994i	$0.0676702\pi$
$71$			3.55574i			0.421989i	−0.977487	+	0.210994i	$0.932330\pi$
$72$	−1.61266	−	8.33063i	−0.190053	−	0.981774i
$73$	3.89746	−	2.25020i	0.456163	−	0.263366i	−0.254267	−	0.967134i	$-0.581834\pi$
$73$	3.89746	−	2.25020i	0.456163	−	0.263366i	0.710429	+	0.703768i	$0.248501\pi$
$74$	−3.24626	+	4.42240i	−0.377370	+	0.514093i
$75$	4.03209	+	7.01240i	0.465586	+	0.809722i
$76$	8.88774	−	9.67856i	1.01949	−	1.11021i
$77$	−5.94656	−	0.0615047i	−0.677673	−	0.00700911i
$78$	−10.0406	+	4.39041i	−1.13687	+	0.497116i
$79$			11.2425i			1.26488i	0.774611	+	0.632438i	$0.217946\pi$
$79$			11.2425i			1.26488i	−0.774611	+	0.632438i	$0.782054\pi$
$80$	−12.3937	+	1.05773i	−1.38566	+	0.118258i
$81$	−4.55502	+	7.76221i	−0.506113	+	0.862467i
$82$	1.39845	+	1.02653i	0.154433	+	0.113361i
$83$	1.48263	+	2.56798i	0.162739	+	0.281873i	0.935850	−	0.352398i	$-0.114634\pi$
$83$	1.48263	+	2.56798i	0.162739	+	0.281873i	−0.773111	+	0.634271i	$0.781300\pi$
$84$	2.10142	−	8.92099i	0.229283	−	0.973360i
$85$	5.24336	−	9.08177i	0.568722	−	0.985056i
$86$	−1.26521	+	0.555903i	−0.136431	+	0.0599445i
$87$	−3.11054	−	0.00550025i	−0.333485	−	0.000589689i
$88$	4.18414	+	4.78649i	0.446031	+	0.510242i
$89$	−13.1148	−	7.57182i	−1.39016	−	0.802611i	−0.396831	−	0.917892i	$-0.629890\pi$
$89$	−13.1148	−	7.57182i	−1.39016	−	0.802611i	−0.993333	+	0.115280i	$0.963223\pi$
$90$	10.6078	+	7.84455i	1.11816	+	0.826888i
$91$	−11.8359	−	0.122418i	−1.24074	−	0.0128329i
$92$	1.64434	−	0.516534i	0.171434	−	0.0538524i
$93$	−5.62514	+	9.70337i	−0.583300	+	1.00619i
$94$	−16.1483	−	1.77723i	−1.66557	−	0.183307i
$95$			20.4311i			2.09618i
$96$	−8.61092	+	4.67461i	−0.878849	+	0.477101i
$97$	−2.86666	+	1.65507i	−0.291066	+	0.168047i	−0.638422	−	0.769686i	$-0.720413\pi$
$97$	−2.86666	+	1.65507i	−0.291066	+	0.168047i	0.347357	+	0.937733i	$0.387079\pi$
$98$	6.02172	−	7.85741i	0.608286	−	0.793718i
$99$	0.0238472	−	6.74308i	0.00239673	−	0.677705i
$100$	6.31757	−	6.87970i	0.631757	−	0.687970i
$101$	9.83018	+	5.67546i	0.978140	+	0.564729i	0.901708	−	0.432346i	$-0.142314\pi$
$101$	9.83018	+	5.67546i	0.978140	+	0.564729i	0.0764318	+	0.997075i	$0.475647\pi$
$102$	0.918165	−	8.20916i	0.0909119	−	0.812828i
$103$	7.44810	+	12.9005i	0.733883	+	1.27112i	0.955212	+	0.295923i	$0.0956273\pi$
$103$	7.44810	+	12.9005i	0.733883	+	1.27112i	−0.221329	+	0.975199i	$0.571039\pi$
$104$	8.32802	+	9.52693i	0.816630	+	0.934192i
$105$	6.97521	+	12.4266i	0.680711	+	1.21271i
$106$	−1.12950	−	2.57070i	−0.109707	−	0.249688i
$107$	−7.24634	−	4.18368i	−0.700531	−	0.404452i	0.107014	−	0.994257i	$-0.465871\pi$
$107$	−7.24634	−	4.18368i	−0.700531	−	0.404452i	−0.807545	+	0.589806i	$0.799204\pi$
$108$	10.1314	+	2.31388i	0.974898	+	0.222653i
$109$	1.40873	+	2.44000i	0.134932	+	0.233709i	0.925572	−	0.378573i	$-0.123585\pi$
$109$	1.40873	+	2.44000i	0.134932	+	0.233709i	−0.790639	+	0.612282i	$0.790252\pi$
$110$	−9.82557	−	1.08137i	−0.936831	−	0.103104i
$111$	−3.34916	−	5.82467i	−0.317888	−	0.552854i
$112$	−10.5534	+	0.790819i	−0.997204	+	0.0747254i
$113$	0.160482	−	0.277962i	0.0150968	−	0.0261485i	−0.858378	−	0.513017i	$-0.828528\pi$
$113$	0.160482	−	0.277962i	0.0150968	−	0.0261485i	0.873475	+	0.486869i	$0.161861\pi$
$114$	6.44769	+	14.7454i	0.603881	+	1.38103i
$115$	−1.33993	+	2.32083i	−0.124949	+	0.216419i
$116$	1.07641	+	3.42665i	0.0999423	+	0.318157i
$117$	0.0474649	−	13.4213i	0.00438813	−	1.24080i
$118$	8.68489	+	0.955828i	0.799509	+	0.0879911i
$119$	4.54077	−	7.68030i	0.416252	−	0.704052i
$120$	4.94542	−	14.4093i	0.451453	−	1.31538i
$121$	−2.97390	−	5.15095i	−0.270355	−	0.468268i
$122$	2.04030	−	18.5387i	0.184720	−	1.67841i
$123$	−1.84188	+	1.05907i	−0.166076	+	0.0954930i
$124$	12.6411	+	2.81658i	1.13520	+	0.252936i
$125$		−	1.02566i		−	0.0917382i
$126$	8.95573	+	6.76720i	0.797840	+	0.602870i
$127$		−	8.00490i		−	0.710320i	−0.934805	−	0.355160i	$-0.884426\pi$
$127$		−	8.00490i		−	0.710320i	0.934805	−	0.355160i	$-0.115574\pi$
$128$	8.14341	+	7.85397i	0.719783	+	0.694199i
$129$	0.00299285	−	1.69253i	0.000263506	−	0.149019i
$130$	−19.5566	−	2.15233i	−1.71523	−	0.188772i
$131$	−2.03383	−	3.52269i	−0.177696	−	0.307779i	0.763395	−	0.645932i	$-0.223531\pi$
$131$	−2.03383	−	3.52269i	−0.177696	−	0.307779i	−0.941091	+	0.338153i	$0.890198\pi$
$132$	−7.43252	+	2.32034i	−0.646918	+	0.201960i
$133$	−0.179780	+	17.3820i	−0.0155889	+	1.50721i
$134$	1.82193	−	16.5545i	0.157390	−	1.43009i
$135$	−14.0363	+	8.00487i	−1.20805	+	0.688949i
$136$	−9.35791	+	1.84588i	−0.802434	+	0.158283i
$137$	7.54147	−	13.0622i	0.644311	−	1.11598i	−0.340149	−	0.940372i	$-0.610477\pi$
$137$	7.54147	−	13.0622i	0.644311	−	1.11598i	0.984460	−	0.175608i	$-0.0561892\pi$
$138$	−0.234636	+	2.09784i	−0.0199735	+	0.178580i
$139$	−4.06208	+	7.03573i	−0.344541	+	0.596762i	−0.985270	−	0.171004i	$-0.945299\pi$
$139$	−4.06208	+	7.03573i	−0.344541	+	0.596762i	0.640729	+	0.767767i	$0.278632\pi$
$140$	11.2545	−	12.0043i	0.951175	−	1.01454i
$141$	9.97896	−	17.2137i	0.840380	−	1.44966i
$142$	−0.550106	+	4.99840i	−0.0461638	+	0.419456i
$143$	5.02789	+	8.70856i	0.420453	+	0.728246i
$144$	−0.978127	−	11.9601i	−0.0815106	−	0.996672i
$145$	−4.83641	−	2.79230i	−0.401642	−	0.231888i
$146$	5.82688	−	2.56019i	0.482236	−	0.211883i
$147$	5.82491	+	10.6335i	0.480430	+	0.877033i
$148$	−5.24753	+	5.71445i	−0.431345	+	0.469725i
$149$	9.17992	+	15.9001i	0.752048	+	1.30259i	0.946828	+	0.321739i	$0.104267\pi$
$149$	9.17992	+	15.9001i	0.752048	+	1.30259i	−0.194780	+	0.980847i	$0.562399\pi$
$150$	4.58314	+	10.4813i	0.374211	+	0.855795i
$151$	−12.3120	−	7.10833i	−1.00193	−	0.578467i	−0.0931147	−	0.995655i	$-0.529682\pi$
$151$	−12.3120	−	7.10833i	−1.00193	−	0.578467i	−0.908820	+	0.417188i	$0.863016\pi$
$152$	13.9911	−	12.2304i	1.13483	−	0.992016i
$153$	8.74348	+	5.08936i	0.706868	+	0.411451i
$154$	−8.34972	−	1.00645i	−0.672839	−	0.0811017i
$155$	−17.4391	+	10.0684i	−1.40074	+	0.808717i
$156$	−14.7935	+	4.61835i	−1.18443	+	0.369764i
$157$			8.40391i			0.670705i	0.942093	+	0.335352i	$0.108855\pi$
$157$			8.40391i			0.670705i	−0.942093	+	0.335352i	$0.891145\pi$
$158$	−1.73931	+	15.8038i	−0.138372	+	1.25728i
$159$	3.43894	+	0.00608096i	0.272726	+	0.000482251i
$160$	−17.5858	−	0.430545i	−1.39028	−	0.0340376i
$161$	−1.16039	+	1.96269i	−0.0914514	+	0.154681i
$162$	−7.60399	+	10.2068i	−0.597426	+	0.801924i
$163$	19.0039	+	10.9719i	1.48850	+	0.859384i	0.999914	−	0.0131335i	$-0.00418066\pi$
$163$	19.0039	+	10.9719i	1.48850	+	0.859384i	0.488583	+	0.872517i	$0.337514\pi$
$164$	1.80702	+	1.65937i	0.141105	+	0.129575i
$165$	6.07177	−	10.4738i	0.472687	−	0.815384i
$166$	1.68688	+	3.83926i	0.130927	+	0.297984i
$167$	−1.89367	+	3.27994i	−0.146537	+	0.253809i	−0.929945	−	0.367698i	$-0.880146\pi$
$167$	−1.89367	+	3.27994i	−0.146537	+	0.253809i	0.783408	+	0.621507i	$0.213479\pi$
$168$	4.33417	−	12.2154i	0.334389	−	0.942435i
$169$	3.50739	+	6.07499i	0.269800	+	0.467307i
$170$	8.77576	−	11.9553i	0.673070	−	0.916928i
$171$	−19.7103	−	0.0697061i	−1.50728	−	0.00533056i
$172$	−1.86454	+	0.585707i	−0.142170	+	0.0446598i
$173$		−	2.83127i		−	0.215257i	−0.994191	−	0.107629i	$-0.965674\pi$
$173$		−	2.83127i		−	0.215257i	0.994191	−	0.107629i	$-0.0343257\pi$
$174$	−4.37171	−	0.488960i	−0.331419	−	0.0370680i
$175$	−0.127791	+	12.3555i	−0.00966011	+	0.933984i
$176$	5.14124	+	7.37582i	0.387536	+	0.555974i
$177$	−5.36688	+	9.25786i	−0.403399	+	0.695864i
$178$	−17.2644	−	12.6729i	−1.29402	−	0.949873i
$179$	8.30663	−	4.79584i	0.620867	−	0.358458i	−0.156340	−	0.987703i	$-0.549969\pi$
$179$	8.30663	−	4.79584i	0.620867	−	0.358458i	0.777206	+	0.629246i	$0.216636\pi$
$180$	13.6981	+	12.6684i	1.02099	+	0.944248i
$181$		−	7.07527i		−	0.525901i	−0.964809	−	0.262950i	$-0.915304\pi$
$181$		−	7.07527i		−	0.525901i	0.964809	−	0.262950i	$-0.0846955\pi$
$182$	−16.6191	−	2.00321i	−1.23189	−	0.148488i
$183$	19.7618	+	11.4561i	1.46083	+	0.846859i
$184$	2.39140	−	0.471711i	0.176296	−	0.0347750i
$185$		−	12.0630i		−	0.886889i
$186$	−9.40861	+	12.7700i	−0.689873	+	0.936343i
$187$	−7.57989			−0.554296
$188$	−22.4252	−	4.99659i	−1.63552	−	0.364414i
$189$	−12.0120	+	6.68673i	−0.873743	+	0.486388i
$190$	−3.16087	+	28.7205i	−0.229314	+	2.08360i
$191$		−	17.8697i		−	1.29301i	−0.762912	−	0.646503i	$-0.776231\pi$
$191$		−	17.8697i		−	1.29301i	0.762912	−	0.646503i	$-0.223769\pi$
$192$	−12.8278	+	5.23904i	−0.925767	+	0.378095i
$193$	−13.3943			−0.964141			−0.482071	−	0.876132i	$-0.660115\pi$
$193$	−13.3943			−0.964141			−0.482071	+	0.876132i	$0.660115\pi$
$194$	−4.28580	+	1.88307i	−0.307702	+	0.135197i
$195$	12.0851	−	20.8468i	0.865433	−	1.49287i
$196$	9.68050	−	10.1137i	0.691465	−	0.722410i
$197$	7.63734			0.544138			0.272069	−	0.962278i	$-0.412292\pi$
$197$	7.63734			0.544138			0.272069	+	0.962278i	$0.412292\pi$
$198$	1.07674	−	9.47524i	0.0765206	−	0.673376i
$199$	−12.0186	−	20.8169i	−0.851978	−	1.47567i	−0.879420	−	0.476046i	$-0.842070\pi$
$199$	−12.0186	−	20.8169i	−0.851978	−	1.47567i	0.0274425	−	0.999623i	$-0.491264\pi$
$200$	9.94513	−	8.69359i	0.703227	−	0.614730i
$201$	17.6466	+	10.2299i	1.24470	+	0.721564i
$202$	12.9405	+	9.49896i	0.910490	+	0.668344i
$203$	−4.09007	−	2.41815i	−0.287067	−	0.169721i
$204$	2.56072	−	11.3978i	0.179286	−	0.798004i
$205$	−3.81455			−0.266420
$206$	8.47416	+	19.2868i	0.590423	+	1.34378i
$207$	−2.23438	−	1.30058i	−0.155300	−	0.0903965i
$208$	10.2330	+	14.6807i	0.709532	+	1.01792i
$209$	12.7892	−	7.38387i	0.884650	−	0.510753i
$210$	7.88273	+	18.5475i	0.543960	+	1.27990i
$211$	8.06636	+	4.65711i	0.555311	+	0.320609i	0.751261	−	0.660005i	$-0.229446\pi$
$211$	8.06636	+	4.65711i	0.555311	+	0.320609i	−0.195950	+	0.980614i	$0.562779\pi$
$212$	−1.19006	−	3.78844i	−0.0817335	−	0.260191i
$213$	−5.32816	−	3.08879i	−0.365079	−	0.211640i
$214$	−9.53912	−	7.00218i	−0.652081	−	0.478659i
$215$	1.51937	−	2.63163i	0.103620	−	0.179476i
$216$	13.8840	+	4.82011i	0.944689	+	0.327967i
$217$	−14.9251	+	8.41241i	−1.01318	+	0.571072i
$218$	1.60280	+	3.64791i	0.108556	+	0.247068i
$219$	−0.0137834	+	7.79490i	−0.000931399	+	0.526731i
$220$	−13.6448	−	3.04021i	−0.919930	−	0.204971i
$221$	−15.0868			−1.01485
$222$	−3.80687	−	8.70604i	−0.255500	−	0.584311i
$223$	4.36816	+	7.56588i	0.292514	+	0.506649i	0.974403	−	0.224806i	$-0.0721750\pi$
$223$	4.36816	+	7.56588i	0.292514	+	0.506649i	−0.681890	+	0.731455i	$0.738842\pi$
$224$	−14.9576	−	0.521036i	−0.999394	−	0.0348132i
$225$	−14.0104	−	0.0495484i	−0.934028	−	0.00330323i
$226$	0.268597	−	0.365911i	0.0178668	−	0.0243400i
$227$	10.8912	−	18.8641i	0.722873	−	1.25205i	−0.236970	−	0.971517i	$-0.576154\pi$
$227$	10.8912	−	18.8641i	0.722873	−	1.25205i	0.959844	−	0.280536i	$-0.0905122\pi$
$228$	6.78243	+	21.7255i	0.449177	+	1.43881i
$229$	−7.36146	+	4.25014i	−0.486459	+	0.280857i	−0.723104	−	0.690739i	$-0.757285\pi$
$229$	−7.36146	+	4.25014i	−0.486459	+	0.280857i	0.236645	+	0.971596i	$0.423952\pi$
$230$	−2.24263	+	3.05515i	−0.147875	+	0.201451i
$231$	5.25780	−	8.85729i	0.345938	−	0.582767i
$232$	0.983004	+	4.98347i	0.0645374	+	0.327181i
$233$	9.13727	−	15.8262i	0.598602	−	1.03681i	−0.394425	−	0.918928i	$-0.629056\pi$
$233$	9.13727	−	15.8262i	0.598602	−	1.03681i	0.993028	−	0.117882i	$-0.0376103\pi$
$234$	2.14312	−	18.8593i	0.140100	−	1.23287i
$235$	30.9368	−	17.8614i	2.01809	−	1.16515i
$236$	12.0607	+	2.68726i	0.785085	+	0.174926i
$237$	−16.8465	−	9.76607i	−1.09429	−	0.634374i
$238$	7.57129	−	10.0939i	0.490774	−	0.654290i
$239$	−18.8702	−	10.8947i	−1.22061	−	0.704721i	−0.255564	−	0.966792i	$-0.582261\pi$
$239$	−18.8702	−	10.8947i	−1.22061	−	0.704721i	−0.965048	+	0.262072i	$0.915594\pi$
$240$	9.18115	−	19.4904i	0.592641	−	1.25810i
$241$	−4.20079	−	2.42533i	−0.270597	−	0.156229i	0.358562	−	0.933506i	$-0.383267\pi$
$241$	−4.20079	−	2.42533i	−0.270597	−	0.156229i	−0.629159	+	0.777277i	$0.716601\pi$
$242$	−3.38359	−	7.70091i	−0.217506	−	0.495033i
$243$	−7.67457	−	13.5684i	−0.492324	−	0.870412i
$244$	5.73621	−	25.7447i	0.367223	−	1.64813i
$245$	−0.450237	+	21.7632i	−0.0287646	+	1.39040i
$246$	−2.75302	+	1.20381i	−0.175526	+	0.0767519i
$247$	25.4554	−	14.6967i	1.61969	−	0.935128i
$248$	17.3341	+	5.91503i	1.10072	+	0.375605i
$249$	−5.13596	−	0.00908173i	−0.325478	−	0.000575531i
$250$	0.158680	−	1.44180i	0.0100358	−	0.0911876i
$251$	15.0188			0.947977			0.473988	−	0.880531i	$-0.342814\pi$
$251$	15.0188			0.947977			0.473988	+	0.880531i	$0.342814\pi$
$252$	11.5424	+	10.8984i	0.727100	+	0.686532i
$253$	1.93703			0.121780
$254$	1.23843	−	11.2527i	0.0777061	−	0.706057i
$255$	9.05394	+	15.7461i	0.566980	+	0.986060i
$256$	10.2323	+	12.3004i	0.639520	+	0.768774i
$257$	20.6963	−	11.9490i	1.29100	−	0.745358i	0.312167	−	0.950027i	$-0.398945\pi$
$257$	20.6963	−	11.9490i	1.29100	−	0.745358i	0.978831	+	0.204669i	$0.0656119\pi$
$258$	0.266058	−	2.37878i	0.0165640	−	0.148096i
$259$	0.106147	−	10.2628i	0.00659563	−	0.637696i
$260$	−27.1582	−	6.05117i	−1.68428	−	0.375278i
$261$	2.71029	−	4.65626i	0.167763	−	0.288215i
$262$	−2.31401	−	5.26659i	−0.142960	−	0.325371i
$263$	4.31868	+	2.49339i	0.266301	+	0.153749i	0.627206	−	0.778854i	$-0.284199\pi$
$263$	4.31868	+	2.49339i	0.266301	+	0.153749i	−0.360904	+	0.932603i	$0.617532\pi$
$264$	−10.8071	+	2.11188i	−0.665129	+	0.129977i
$265$	5.34703	+	3.08711i	0.328466	+	0.189640i
$266$	−2.94188	+	24.4065i	−0.180378	+	1.49646i
$267$	22.7386	−	13.0746i	1.39158	−	0.800152i
$268$	5.12226	−	22.9892i	0.312892	−	1.40429i
$269$	6.44486	−	3.72094i	0.392950	−	0.226870i	−0.290487	−	0.956879i	$-0.593817\pi$
$269$	6.44486	−	3.72094i	0.392950	−	0.226870i	0.683438	+	0.730009i	$0.260484\pi$
$270$	−20.9696	+	9.08111i	−1.27617	+	0.552659i
$271$	1.27225	−	2.20361i	0.0772839	−	0.133860i	−0.824793	−	0.565434i	$-0.808709\pi$
$271$	1.27225	−	2.20361i	0.0772839	−	0.133860i	0.902077	+	0.431575i	$0.142042\pi$
$272$	−13.4402	+	1.14704i	−0.814934	+	0.0695496i
$273$	10.4650	−	17.6294i	0.633371	−	1.06698i
$274$	12.6221	−	17.1951i	0.762528	−	1.03880i
$275$	9.09083	−	5.24859i	0.548198	−	0.316502i
$276$	−0.654389	+	2.91269i	−0.0393896	+	0.175323i
$277$	−5.95389	+	10.3124i	−0.357735	+	0.619615i	−0.987582	−	0.157104i	$-0.949784\pi$
$277$	−5.95389	+	10.3124i	−0.357735	+	0.619615i	0.629847	+	0.776719i	$0.283117\pi$
$278$	−6.79866	+	9.26186i	−0.407756	+	0.555489i
$279$	−9.65374	−	16.8582i	−0.577954	−	1.00927i
$280$	17.6778	−	15.1335i	1.05645	−	0.904401i
$281$	1.85332	+	3.21004i	0.110560	+	0.191495i	0.915996	−	0.401187i	$-0.131402\pi$
$281$	1.85332	+	3.21004i	0.110560	+	0.191495i	−0.805436	+	0.592682i	$0.798069\pi$
$282$	16.6908	−	22.6539i	0.993923	−	1.34902i
$283$	−14.8737			−0.884149			−0.442075	−	0.896978i	$-0.645757\pi$
$283$	−14.8737			−0.884149			−0.442075	+	0.896978i	$0.645757\pi$
$284$	−1.54660	+	6.94127i	−0.0917736	+	0.411888i
$285$	−30.6153	−	17.7480i	−1.81349	−	1.05130i
$286$	5.72054	+	13.0197i	0.338262	+	0.769871i
$287$	−3.24528	−	0.0335656i	−0.191563	−	0.00198132i
$288$	0.475354	−	16.9639i	0.0280105	−	0.999608i
$289$	−2.81389	+	4.87380i	−0.165523	+	0.286694i
$290$	−6.36667	−	4.67345i	−0.373864	−	0.274434i
$291$	0.0101380	−	5.73332i	0.000594301	−	0.336093i
$292$	8.58708	−	2.69745i	0.502521	−	0.157856i
$293$	−4.33341	−	2.50189i	−0.253160	−	0.146162i	0.368050	−	0.929806i	$-0.380025\pi$
$293$	−4.33341	−	2.50189i	−0.253160	−	0.146162i	−0.621210	+	0.783644i	$0.713359\pi$
$294$	6.54313	+	15.8489i	0.381603	+	0.924326i
$295$	−16.6384	+	9.60618i	−0.968725	+	0.559294i
$296$	−8.26067	+	7.22111i	−0.480142	+	0.419719i
$297$	10.0836	+	5.89329i	0.585108	+	0.341964i
$298$	10.4446	+	23.7714i	0.605037	+	1.37704i
$299$	3.85542			0.222965
$300$	4.82108	+	15.4429i	0.278345	+	0.891596i
$301$	1.31578	−	2.22553i	0.0758405	−	0.128277i
$302$	−16.2075	−	11.8971i	−0.932640	−	0.684603i
$303$	−17.0437	+	9.80006i	−0.979137	+	0.562999i
$304$	21.5598	−	15.0280i	1.23654	−	0.861916i
$305$	20.5053	+	35.5162i	1.17413	+	2.03365i
$306$	11.5036	+	8.50694i	0.657615	+	0.486310i
$307$	−21.7954			−1.24393			−0.621963	−	0.783046i	$-0.713665\pi$
$307$	−21.7954			−1.24393			−0.621963	+	0.783046i	$0.713665\pi$
$308$	−11.5817	−	2.70657i	−0.659929	−	0.154221i
$309$	−25.8009	−	0.0456228i	−1.46776	−	0.00259539i
$310$	−26.0722	+	11.4555i	−1.48080	+	0.650628i
$311$	2.43653			0.138163			0.0690816	−	0.997611i	$-0.477993\pi$
$311$	2.43653			0.138163			0.0690816	+	0.997611i	$0.477993\pi$
$312$	−21.5101	+	4.20344i	−1.21777	+	0.237973i
$313$			0.317830i			0.0179648i	0.999960	+	0.00898241i	$0.00285923\pi$
$313$			0.317830i			0.0179648i	−0.999960	+	0.00898241i	$0.997141\pi$
$314$	−1.30016	+	11.8136i	−0.0733724	+	0.666680i
$315$	−24.6800	−	0.342557i	−1.39056	−	0.0193009i
$316$	−4.88999	+	21.9468i	−0.275084	+	1.23460i
$317$	−34.6247			−1.94472			−0.972360	−	0.233488i	$-0.924986\pi$
$317$	−34.6247			−1.94472			−0.972360	+	0.233488i	$0.924986\pi$
$318$	4.83327	+	0.540584i	0.271036	+	0.0303145i
$319$			4.03660i			0.226006i
$320$	−24.6542	−	3.32591i	−1.37821	−	0.185924i
$321$	12.5638	−	7.22414i	0.701245	−	0.403212i
$322$	−1.93483	+	2.57948i	−0.107824	+	0.143749i
$323$			22.1563i			1.23281i
$324$	−12.2682	+	13.1716i	−0.681567	+	0.731755i
$325$	18.0942	−	10.4467i	1.00368	−	0.579478i
$326$	25.0168	+	18.3635i	1.38555	+	1.01706i
$327$	−4.87999	−	0.00862911i	−0.269864	−	0.000477191i
$328$	2.28346	+	2.61219i	0.126083	+	0.144234i
$329$	26.4770	−	14.9236i	1.45973	−	0.822762i
$330$	10.1556	−	13.7839i	0.559049	−	0.758780i
$331$		−	2.97190i		−	0.163350i	−0.996659	−	0.0816751i	$-0.973973\pi$
$331$		−	2.97190i		−	0.163350i	0.996659	−	0.0816751i	$-0.0260270\pi$
$332$	1.77732	+	5.65792i	0.0975429	+	0.310519i
$333$	11.6374	+	0.0411562i	0.637726	+	0.00225534i
$334$	−3.16942	+	4.31773i	−0.173423	+	0.236256i
$335$	18.3106	+	31.7148i	1.00041	+	1.73277i
$336$	7.98249	−	16.5009i	0.435480	−	0.900198i
$337$	−16.0847	+	27.8595i	−0.876190	+	1.51760i	−0.0206995	+	0.999786i	$0.506589\pi$
$337$	−16.0847	+	27.8595i	−0.876190	+	1.51760i	−0.855490	+	0.517819i	$0.826744\pi$
$338$	3.99058	+	9.08239i	0.217059	+	0.494017i
$339$	0.277111	+	0.481936i	0.0150506	+	0.0261752i
$340$	14.1859	−	15.4482i	0.769339	−	0.837794i
$341$	12.6051	+	7.27756i	0.682604	+	0.394102i
$342$	−27.6965	−	3.14735i	−1.49765	−	0.170189i
$343$	−0.574547	+	18.5113i	−0.0310226	+	0.999519i
$344$	−2.71165	+	0.534882i	−0.146202	+	0.0288389i
$345$	−2.31372	−	4.02390i	−0.124567	−	0.216639i
$346$	0.438023	−	3.97998i	0.0235483	−	0.213965i
$347$		−	10.9556i		−	0.588125i	−0.955786	−	0.294063i	$-0.904993\pi$
$347$		−	10.9556i		−	0.588125i	0.955786	−	0.294063i	$-0.0950074\pi$
$348$	−6.06978	−	1.36369i	−0.325374	−	0.0731013i
$349$	3.99503	−	2.30653i	0.213849	−	0.123466i	−0.389250	−	0.921132i	$-0.627266\pi$
$349$	3.99503	−	2.30653i	0.213849	−	0.123466i	0.603099	+	0.797666i	$0.293932\pi$
$350$	−2.09114	+	17.3486i	−0.111776	+	0.927322i
$351$	20.0701	+	11.7299i	1.07126	+	0.626095i
$352$	6.08607	+	11.1638i	0.324388	+	0.595032i
$353$	−5.48109	−	3.16451i	−0.291729	−	0.168430i	0.346992	−	0.937868i	$-0.387203\pi$
$353$	−5.48109	−	3.16451i	−0.291729	−	0.168430i	−0.638721	+	0.769438i	$0.720536\pi$
$354$	−8.97664	+	12.1837i	−0.477103	+	0.647557i
$355$	−5.52862	−	9.57586i	−0.293429	−	0.508234i
$356$	−22.3083	−	20.4855i	−1.18234	−	1.08573i
$357$	7.56420	+	13.4759i	0.400340	+	0.713220i
$358$	12.4188	−	5.45652i	0.656354	−	0.288386i
$359$	−5.17029	−	2.98507i	−0.272878	−	0.157546i	0.357317	−	0.933983i	$-0.383692\pi$
$359$	−5.17029	−	2.98507i	−0.272878	−	0.157546i	−0.630195	+	0.776437i	$0.717025\pi$
$360$	17.2958	+	19.9275i	0.911570	+	1.05027i
$361$	−12.0833	−	20.9289i	−0.635964	−	1.10152i
$362$	1.09461	−	9.94589i	0.0575314	−	0.522744i
$363$	10.3019	+	0.0182164i	0.540709	+	0.000956116i
$364$	−23.0520	−	5.38709i	−1.20825	−	0.282360i
$365$	−6.99742	+	12.1199i	−0.366262	+	0.634384i
$366$	26.0073	+	19.1615i	1.35942	+	1.00159i
$367$	−2.61563	+	4.53040i	−0.136535	+	0.236485i	−0.926183	−	0.377075i	$-0.876930\pi$
$367$	−2.61563	+	4.53040i	−0.136535	+	0.236485i	0.789648	+	0.613560i	$0.210263\pi$
$368$	3.43463	−	0.293125i	0.179043	−	0.0152802i
$369$	0.0130144	−	3.67998i	0.000677502	−	0.191572i
$370$	1.86626	−	16.9573i	0.0970220	−	0.881566i
$371$	4.52189	+	2.67345i	0.234765	+	0.138799i
$372$	−15.2016	+	16.4955i	−0.788164	+	0.855254i
$373$	−5.78658	−	10.0226i	−0.299618	−	0.518953i	0.676431	−	0.736506i	$-0.263526\pi$
$373$	−5.78658	−	10.0226i	−0.299618	−	0.518953i	−0.976048	+	0.217553i	$0.930192\pi$
$374$	−10.6552	−	1.17268i	−0.550969	−	0.0606377i
$375$	1.53692	+	0.890970i	0.0793664	+	0.0460095i
$376$	−30.7506	−	10.4932i	−1.58584	−	0.541147i
$377$			8.03435i			0.413790i
$378$	−17.9200	+	7.54135i	−0.921708	+	0.387885i
$379$		−	7.65108i		−	0.393009i	−0.980503	−	0.196505i	$-0.937041\pi$
$379$		−	7.65108i		−	0.393009i	0.980503	−	0.196505i	$-0.0629591\pi$
$380$	−8.88665	+	39.8841i	−0.455875	+	2.04601i
$381$	11.9951	+	6.95367i	0.614527	+	0.356247i
$382$	2.76460	−	25.1199i	0.141449	−	1.28524i
$383$	−4.69924	−	8.13932i	−0.240120	−	0.415900i	0.720628	−	0.693322i	$-0.243853\pi$
$383$	−4.69924	−	8.13932i	−0.240120	−	0.415900i	−0.960748	+	0.277422i	$0.910520\pi$
$384$	−18.8429	+	5.38007i	−0.961573	+	0.274551i
$385$	16.1101	−	9.08034i	0.821049	−	0.462777i
$386$	−18.8287	−	2.07222i	−0.958355	−	0.105473i
$387$	2.53361	+	1.47475i	0.128790	+	0.0749657i
$388$	−6.31598	+	1.98403i	−0.320645	+	0.100724i
$389$	5.77972	−	10.0108i	0.293043	−	0.507566i	−0.681484	−	0.731833i	$-0.738665\pi$
$389$	5.77972	−	10.0108i	0.293043	−	0.507566i	0.974528	+	0.224266i	$0.0719986\pi$
$390$	20.2135	−	27.4352i	1.02355	−	1.38924i
$391$	−1.45308	+	2.51680i	−0.0734853	+	0.127280i
$392$	15.1728	−	12.7195i	0.766343	−	0.642431i
$393$	7.04537	+	0.0124581i	0.355392	+	0.000628427i
$394$	10.7360	+	1.18157i	0.540872	+	0.0595264i
$395$	−17.4803	−	30.2768i	−0.879529	−	1.52339i
$396$	2.97951	−	13.1530i	0.149726	−	0.660963i
$397$	24.9433	+	14.4010i	1.25187	+	0.722765i	0.971480	−	0.237122i	$-0.0762042\pi$
$397$	24.9433	+	14.4010i	1.25187	+	0.722765i	0.280386	+	0.959887i	$0.409538\pi$
$398$	−13.6743	−	31.1222i	−0.685432	−	1.56002i
$399$	−25.8902	−	15.3687i	−1.29613	−	0.769399i
$400$	15.3251	−	10.6822i	0.766255	−	0.534110i
$401$	1.14117	+	1.97656i	0.0569871	+	0.0987045i	0.893112	−	0.449835i	$-0.148517\pi$
$401$	1.14117	+	1.97656i	0.0569871	+	0.0987045i	−0.836124	+	0.548540i	$0.815184\pi$
$402$	23.2237	+	17.1106i	1.15829	+	0.853398i
$403$	25.0889	+	14.4851i	1.24977	+	0.721553i
$404$	16.7212	+	15.3549i	0.831912	+	0.763937i
$405$	0.197953	−	27.9865i	0.00983637	−	1.39066i
$406$	−5.37541	−	4.03202i	−0.266777	−	0.200106i
$407$	−7.55107	+	4.35961i	−0.374293	+	0.216098i
$408$	5.36301	−	15.6260i	0.265509	−	0.773602i
$409$			25.5722i			1.26447i	0.774779	+	0.632233i	$0.217861\pi$
$409$			25.5722i			1.26447i	−0.774779	+	0.632233i	$0.782139\pi$
$410$	−5.36221	−	0.590146i	−0.264821	−	0.0291452i
$411$	13.0222	+	22.6475i	0.642337	+	1.11712i
$412$	8.92850	+	28.4230i	0.439875	+	1.40030i
$413$	−14.2399	+	8.02618i	−0.700698	+	0.394942i
$414$	−2.93972	−	2.17394i	−0.144479	−	0.106843i
$415$	−7.98563	−	4.61051i	−0.391999	−	0.226321i
$416$	12.1136	+	22.2201i	0.593917	+	1.08943i
$417$	−7.01417	−	12.1987i	−0.343485	−	0.597371i
$418$	19.1205	−	8.40109i	0.935215	−	0.410911i
$419$	−8.09827	+	14.0266i	−0.395626	+	0.685245i	−0.993181	−	0.116584i	$-0.962806\pi$
$419$	−8.09827	+	14.0266i	−0.395626	+	0.685245i	0.597555	+	0.801828i	$0.296139\pi$
$420$	8.21149	+	27.2922i	0.400680	+	1.33172i
$421$	7.05042	+	12.2117i	0.343616	+	0.595161i	0.985101	−	0.171975i	$-0.0550147\pi$
$421$	7.05042	+	12.2117i	0.343616	+	0.595161i	−0.641485	+	0.767135i	$0.721681\pi$
$422$	10.6186	+	7.79456i	0.516905	+	0.379433i
$423$	17.1257	+	29.9063i	0.832678	+	1.45409i
$424$	−1.08679	−	5.50962i	−0.0527791	−	0.267571i
$425$			15.7491i			0.763943i
$426$	−7.01206	−	5.16630i	−0.339736	−	0.250308i
$427$	17.1326	+	30.3963i	0.829105	+	1.47098i
$428$	−12.3261	−	11.3189i	−0.595804	−	0.547121i
$429$	−17.4171	−	0.0307980i	−0.840905	−	0.00148694i
$430$	2.54296	−	3.46429i	0.122632	−	0.167063i
$431$	−34.1956	+	19.7428i	−1.64714	+	0.950978i	−0.668942	+	0.743314i	$0.733253\pi$
$431$	−34.1956	+	19.7428i	−1.64714	+	0.950978i	−0.978200	+	0.207664i	$0.933414\pi$
$432$	18.7714	+	8.92374i	0.903141	+	0.429344i
$433$		−	9.21684i		−	0.442933i	−0.975168	−	0.221466i	$-0.928916\pi$
$433$		−	9.21684i		−	0.442933i	0.975168	−	0.221466i	$-0.0710843\pi$
$434$	−22.2821	+	9.51649i	−1.06957	+	0.456806i
$435$	8.38545	−	4.82159i	0.402051	−	0.231178i
$436$	1.68874	+	5.37593i	0.0808758	+	0.257460i
$437$		−	5.66200i		−	0.270850i
$438$	−1.22532	+	10.9554i	−0.0585480	+	0.523468i
$439$	−0.0764266			−0.00364764			−0.00182382	−	0.999998i	$-0.500581\pi$
$439$	−0.0764266			−0.00364764			−0.00182382	+	0.999998i	$0.500581\pi$
$440$	−18.7104	−	6.38467i	−0.891985	−	0.304377i
$441$	−20.9938	−	0.508604i	−0.999707	−	0.0242192i
$442$	−21.2080	−	2.33407i	−1.00876	−	0.111020i
$443$			32.7993i			1.55834i	0.626811	+	0.779171i	$0.284360\pi$
$443$			32.7993i			1.55834i	−0.626811	+	0.779171i	$0.715640\pi$
$444$	−4.00451	−	12.8273i	−0.190046	−	0.608755i
$445$	47.0920			2.23238
$446$	4.96993	+	11.3113i	0.235333	+	0.535608i
$447$	−31.8001	−	0.0562310i	−1.50409	−	0.00265964i
$448$	−20.9456	−	3.04650i	−0.989587	−	0.143934i
$449$	−4.56654			−0.215508			−0.107754	−	0.994178i	$-0.534366\pi$
$449$	−4.56654			−0.215508			−0.107754	+	0.994178i	$0.534366\pi$
$450$	−19.6872	−	2.23719i	−0.928061	−	0.105462i
$451$	1.37859	+	2.38780i	0.0649155	+	0.112437i
$452$	0.434183	−	0.472816i	0.0204222	−	0.0222394i
$453$	21.3467	−	12.2743i	1.00296	−	0.576695i
$454$	18.2285	−	24.8328i	0.855504	−	1.16546i
$455$	32.0653	−	18.0733i	1.50324	−	0.847290i
$456$	6.17310	+	31.5894i	0.289082	+	1.47931i
$457$	12.7046			0.594297			0.297148	−	0.954831i	$-0.403964\pi$
$457$	12.7046			0.594297			0.297148	+	0.954831i	$0.403964\pi$
$458$	−11.0057	+	4.83565i	−0.514264	+	0.225955i
$459$	−15.2215	+	8.68080i	−0.710478	+	0.405185i
$460$	−3.62519	+	3.94775i	−0.169025	+	0.184065i
$461$	−5.25347	+	3.03309i	−0.244679	+	0.141265i	−0.617325	−	0.786708i	$-0.711784\pi$
$461$	−5.25347	+	3.03309i	−0.244679	+	0.141265i	0.372647	+	0.927973i	$0.378450\pi$
$462$	8.76133	−	11.6375i	0.407614	−	0.541425i
$463$	−22.5045	−	12.9930i	−1.04587	−	0.603835i	−0.124382	−	0.992234i	$-0.539695\pi$
$463$	−22.5045	−	12.9930i	−1.04587	−	0.603835i	−0.921491	+	0.388399i	$0.873028\pi$
$464$	0.610846	+	7.15747i	0.0283578	+	0.332277i
$465$	0.0616736	−	34.8781i	0.00286005	−	1.61743i
$466$	15.2930	−	20.8337i	0.708432	−	0.965102i
$467$	−5.64144	+	9.77126i	−0.261055	+	0.452160i	−0.966522	−	0.256582i	$-0.917404\pi$
$467$	−5.64144	+	9.77126i	−0.261055	+	0.452160i	0.705468	+	0.708742i	$0.250737\pi$
$468$	5.93034	−	26.1794i	0.274130	−	1.21015i
$469$	15.2989	+	27.1429i	0.706437	+	1.25334i
$470$	46.2519	−	20.3220i	2.13344	−	0.937382i
$471$	−12.5930	−	7.30028i	−0.580254	−	0.336379i
$472$	16.5383	+	5.64346i	0.761237	+	0.259761i
$473$	−2.19643			−0.100992
$474$	−22.1706	−	16.3347i	−1.01833	−	0.750278i
$475$	−15.3418	−	26.5728i	−0.703931	−	1.21924i
$476$	12.2048	−	13.0179i	0.559405	−	0.596674i
$477$	−2.99644	+	5.14786i	−0.137198	+	0.235704i
$478$	−24.8408	−	18.2344i	−1.13619	−	0.834021i
$479$	7.94418	−	13.7597i	0.362979	−	0.628698i	−0.625471	−	0.780248i	$-0.715093\pi$
$479$	7.94418	−	13.7597i	0.362979	−	0.628698i	0.988450	+	0.151550i	$0.0484263\pi$
$480$	15.9215	−	25.9777i	0.726715	−	1.18571i
$481$	−15.0295	+	8.67728i	−0.685286	+	0.395650i
$482$	−5.52994	−	4.05925i	−0.251882	−	0.184894i
$483$	−1.93302	−	3.44374i	−0.0879555	−	0.156696i
$484$	−3.56500	−	11.3488i	−0.162045	−	0.515857i
$485$	5.14675	−	8.91443i	0.233702	−	0.404784i
$486$	−8.68918	−	20.2608i	−0.394149	−	0.919046i
$487$	−4.87135	+	2.81247i	−0.220742	+	0.127445i	−0.606294	−	0.795241i	$-0.707344\pi$
$487$	−4.87135	+	2.81247i	−0.220742	+	0.127445i	0.385552	+	0.922686i	$0.374011\pi$
$488$	12.0465	−	35.3025i	0.545319	−	1.59807i
$489$	−32.9492	+	18.9456i	−1.49001	+	0.856751i
$490$	−3.99987	+	30.5234i	−0.180696	+	1.37891i
$491$	8.97587	+	5.18222i	0.405075	+	0.233870i	0.688672	−	0.725073i	$-0.258194\pi$
$491$	8.97587	+	5.18222i	0.405075	+	0.233870i	−0.283596	+	0.958944i	$0.591528\pi$
$492$	−4.05623	+	1.26630i	−0.182869	+	0.0570894i
$493$	−5.24480	−	3.02808i	−0.236214	−	0.136378i
$494$	38.0570	−	16.7213i	1.71227	−	0.752328i
$495$	10.4202	+	18.1967i	0.468354	+	0.817880i
$496$	23.4519	+	10.9967i	1.05302	+	0.493765i
$497$	−4.61929	−	8.19544i	−0.207203	−	0.367616i
$498$	−7.21835	−	0.807347i	−0.323462	−	0.0361781i
$499$	9.99521	−	5.77074i	0.447447	−	0.258334i	−0.259304	−	0.965796i	$-0.583493\pi$
$499$	9.99521	−	5.77074i	0.447447	−	0.258334i	0.706751	+	0.707462i	$0.250160\pi$
$500$	0.446120	−	2.00223i	0.0199511	−	0.0895424i
$501$	−3.26989	−	5.68681i	−0.146088	−	0.254068i
$502$	21.1123	+	2.32354i	0.942287	+	0.103705i
$503$	11.7098			0.522114			0.261057	−	0.965323i	$-0.415929\pi$
$503$	11.7098			0.522114			0.261057	+	0.965323i	$0.415929\pi$
$504$	14.5393	+	17.1058i	0.647632	+	0.761953i
$505$	−35.2978			−1.57073
$506$	2.72293	+	0.299676i	0.121049	+	0.0133222i
$507$	−12.1500	−	0.0214843i	−0.539598	−	0.000954152i
$508$	3.48179	−	15.6266i	0.154480	−	0.693319i
$509$	−24.2423	+	13.9963i	−1.07452	+	0.620376i	−0.929414	−	0.369040i	$-0.879687\pi$
$509$	−24.2423	+	13.9963i	−1.07452	+	0.620376i	−0.145109	+	0.989416i	$0.546353\pi$
$510$	10.2913	+	23.5355i	0.455706	+	1.04217i
$511$	−6.05979	+	10.2496i	−0.268069	+	0.453415i
$512$	12.4809	+	18.8740i	0.551581	+	0.834121i
$513$	17.2263	−	29.4746i	0.760560	−	1.30134i
$514$	30.9419	−	13.5951i	1.36479	−	0.599655i
$515$	−40.1165	−	23.1613i	−1.76774	−	1.02061i
$516$	0.742023	−	3.30275i	0.0326657	−	0.145395i
$517$	−22.3613	−	12.9103i	−0.983451	−	0.567796i
$518$	1.73695	−	14.4102i	0.0763174	−	0.633147i
$519$	4.24256	+	2.45945i	0.186228	+	0.107958i
$520$	−37.2408	−	12.7079i	−1.63312	−	0.557279i
$521$	−11.9117	+	6.87723i	−0.521862	+	0.301297i	−0.737696	−	0.675133i	$-0.764086\pi$
$521$	−11.9117	+	6.87723i	−0.521862	+	0.301297i	0.215834	+	0.976430i	$0.430753\pi$
$522$	4.53029	−	6.12611i	0.198286	−	0.268133i
$523$	−5.47135	+	9.47665i	−0.239245	+	0.414385i	−0.960498	−	0.278287i	$-0.910233\pi$
$523$	−5.47135	+	9.47665i	−0.239245	+	0.414385i	0.721253	+	0.692672i	$0.243567\pi$
$524$	−2.43808	−	7.76138i	−0.106508	−	0.339058i
$525$	−18.4032	−	10.9244i	−0.803182	−	0.476779i
$526$	5.68513	+	4.17316i	0.247883	+	0.181959i
$527$	−18.9116	+	10.9186i	−0.823803	+	0.475623i
$528$	−15.5185	+	1.29677i	−0.675356	+	0.0564348i
$529$	−11.1287	+	19.2754i	−0.483855	+	0.838062i
$530$	7.03886	+	5.16687i	0.305748	+	0.224434i
$531$	−9.21051	−	16.0842i	−0.399702	−	0.697994i
$532$	−7.91139	+	33.8537i	−0.343002	+	1.46775i
$533$	2.74392	+	4.75262i	0.118853	+	0.205859i
$534$	33.9870	−	14.8614i	1.47076	−	0.643116i
$535$	26.0199			1.12494
$536$	10.7571	−	31.5240i	0.464637	−	1.36163i
$537$	−0.0293766	+	16.6132i	−0.00126769	+	0.716914i
$538$	9.63538	−	4.23355i	0.415411	−	0.182521i
$539$	13.7858	−	7.58346i	0.593797	−	0.326643i
$540$	−30.8824	+	9.52136i	−1.32897	+	0.409734i
$541$	0.448496	−	0.776818i	0.0192824	−	0.0333980i	−0.856223	−	0.516606i	$-0.827195\pi$
$541$	0.448496	−	0.776818i	0.0192824	−	0.0333980i	0.875506	+	0.483208i	$0.160529\pi$
$542$	2.12936	−	2.90084i	0.0914638	−	0.124602i
$543$	10.6021	+	6.14612i	0.454978	+	0.263755i
$544$	−19.0707	−	0.466901i	−0.817651	−	0.0200182i
$545$	−7.58764	−	4.38072i	−0.325019	−	0.187650i
$546$	17.4384	−	23.1630i	0.746293	−	0.991285i
$547$	28.3909	−	16.3915i	1.21391	−	0.700849i	0.250298	−	0.968169i	$-0.419471\pi$
$547$	28.3909	−	16.3915i	1.21391	−	0.700849i	0.963608	+	0.267320i	$0.0861379\pi$
$548$	20.4034	−	22.2189i	0.871592	−	0.949145i
$549$	−34.3331	+	19.6607i	−1.46530	+	0.839098i
$550$	13.5912	−	5.97165i	0.579532	−	0.254632i
$551$	11.7991			0.502659
$552$	−1.37051	+	3.99320i	−0.0583328	+	0.169962i
$553$	−14.6052	−	25.9122i	−0.621075	−	1.10190i
$554$	−9.96497	+	13.5753i	−0.423371	+	0.576761i
$555$	18.0760	+	10.4788i	0.767283	+	0.444802i
$556$	−10.9899	+	11.9678i	−0.466078	+	0.507549i
$557$	−3.85227	−	6.67232i	−0.163226	−	0.282715i	0.772798	−	0.634652i	$-0.218857\pi$
$557$	−3.85227	−	6.67232i	−0.163226	−	0.282715i	−0.936024	+	0.351937i	$0.885523\pi$
$558$	−10.9624	−	25.1915i	−0.464075	−	1.06644i
$559$	−4.37173			−0.184904
$560$	27.1915	−	18.5387i	1.14905	−	0.783401i
$561$	6.58447	−	11.3582i	0.277996	−	0.479544i
$562$	2.10863	+	4.79916i	0.0889473	+	0.202440i
$563$	26.1423			1.10177			0.550883	−	0.834582i	$-0.314291\pi$
$563$	26.1423			1.10177			0.550883	+	0.834582i	$0.314291\pi$
$564$	26.9675	−	29.2630i	1.13553	−	1.23219i
$565$			0.998097i			0.0419902i
$566$	−20.9083	−	2.30110i	−0.878843	−	0.0967223i
$567$	0.414675	−	23.8082i	0.0174147	−	0.999848i
$568$	−3.24797	+	9.51825i	−0.136282	+	0.399377i
$569$	34.8933			1.46280			0.731402	−	0.681947i	$-0.238866\pi$
$569$	34.8933			1.46280			0.731402	+	0.681947i	$0.238866\pi$
$570$	−40.2909	−	29.6853i	−1.68760	−	1.24338i
$571$		−	1.24825i		−	0.0522377i	−0.999659	−	0.0261188i	$-0.991685\pi$
$571$		−	1.24825i		−	0.0522377i	0.999659	−	0.0261188i	$-0.00831483\pi$
$572$	6.02724	+	19.1872i	0.252012	+	0.802255i
$573$	26.7771	+	15.5230i	1.11863	+	0.648482i
$574$	−4.55678	−	0.549259i	−0.190196	−	0.0229256i
$575$		−	4.02466i		−	0.167840i
$576$	3.29269	−	23.7731i	0.137195	−	0.990544i
$577$	−17.3046	+	9.99080i	−0.720399	+	0.415923i	−0.814900	−	0.579602i	$-0.803208\pi$
$577$	−17.3046	+	9.99080i	−0.720399	+	0.415923i	0.0945005	+	0.995525i	$0.469875\pi$
$578$	−4.70958	+	6.41589i	−0.195893	+	0.266866i
$579$	11.6353	−	20.0709i	0.483546	−	0.834117i
$580$	−8.22677	−	7.55457i	−0.341598	−	0.313686i
$581$	−6.75331	−	3.99272i	−0.280175	−	0.165646i
$582$	0.901248	−	8.05790i	0.0373579	−	0.334011i
$583$		−	4.46278i		−	0.184829i
$584$	12.4884	−	2.46338i	0.516774	−	0.101935i
$585$	20.7402	+	36.2183i	0.857501	+	1.49744i
$586$	−5.70451	−	4.18739i	−0.235651	−	0.172980i
$587$	12.2337	+	21.1895i	0.504940	+	0.874582i	0.999984	+	0.00571398i	$0.00181883\pi$
$587$	12.2337	+	21.1895i	0.504940	+	0.874582i	−0.495043	+	0.868868i	$0.664848\pi$
$588$	6.74588	+	23.2915i	0.278195	+	0.960524i
$589$	21.2725	−	36.8451i	0.876520	−	1.51818i
$590$	−24.8752	+	10.9295i	−1.02410	+	0.449962i
$591$	−6.63438	+	11.4443i	−0.272902	+	0.470755i
$592$	−12.7294	+	8.87291i	−0.523176	+	0.364674i
$593$	34.1540	+	19.7188i	1.40254	+	0.809755i	0.994653	−	0.103278i	$-0.0329331\pi$
$593$	34.1540	+	19.7188i	1.40254	+	0.809755i	0.407885	+	0.913033i	$0.366266\pi$
$594$	13.2630	+	9.84437i	0.544187	+	0.403920i
$595$	−0.286951	+	27.7438i	−0.0117639	+	1.13738i
$596$	11.0045	+	35.0319i	0.450763	+	1.43496i
$597$	41.6337	+	0.0736193i	1.70395	+	0.00301304i
$598$	5.41966	+	0.596469i	0.221626	+	0.0243914i
$599$		−	22.7169i		−	0.928187i	−0.885786	−	0.464094i	$-0.846380\pi$
$599$		−	22.7169i		−	0.928187i	0.885786	−	0.464094i	$-0.153620\pi$
$600$	4.38795	+	22.4544i	0.179137	+	0.916695i
$601$	−4.60939	+	2.66123i	−0.188021	+	0.108554i	−0.591056	−	0.806631i	$-0.701289\pi$
$601$	−4.60939	+	2.66123i	−0.188021	+	0.108554i	0.403035	+	0.915185i	$0.367955\pi$
$602$	2.19394	−	2.92492i	0.0894184	−	0.119211i
$603$	−30.6584	+	17.5564i	−1.24851	+	0.714951i
$604$	−20.9428	−	19.2316i	−0.852149	−	0.782521i
$605$	16.0179	+	9.24791i	0.651219	+	0.375981i
$606$	−25.4750	+	11.1394i	−1.03485	+	0.452506i
$607$	−12.4527	−	21.5687i	−0.505440	−	0.875447i	−0.999980	−	0.00629282i	$-0.997997\pi$
$607$	−12.4527	−	21.5687i	−0.505440	−	0.875447i	0.494540	−	0.869155i	$-0.335336\pi$
$608$	32.6321	−	17.7898i	1.32341	−	0.721471i
$609$	7.17646	−	4.02824i	0.290805	−	0.163233i
$610$	23.3301	+	53.0984i	0.944609	+	2.14989i
$611$	−44.5075	−	25.6964i	−1.80058	−	1.03957i
$612$	14.8547	+	13.7381i	0.600468	+	0.555331i
$613$	−12.0689	−	20.9039i	−0.487457	−	0.844300i	0.512439	−	0.858724i	$-0.328742\pi$
$613$	−12.0689	−	20.9039i	−0.487457	−	0.844300i	−0.999896	+	0.0144232i	$0.995409\pi$
$614$	−30.6383	−	3.37194i	−1.23646	−	0.136080i
$615$	3.31361	−	5.71598i	0.133618	−	0.230490i
$616$	−15.8620	−	5.59649i	−0.639097	−	0.225489i
$617$	12.0546	−	20.8792i	0.485301	−	0.840567i	−0.514556	−	0.857457i	$-0.672043\pi$
$617$	12.0546	−	20.8792i	0.485301	−	0.840567i	0.999857	+	0.0168900i	$0.00537652\pi$
$618$	−36.2620	−	4.05577i	−1.45867	−	0.163147i
$619$	−17.7628	+	30.7660i	−0.713946	+	1.23659i	0.249419	+	0.968396i	$0.419760\pi$
$619$	−17.7628	+	30.7660i	−0.713946	+	1.23659i	−0.963365	+	0.268194i	$0.913573\pi$
$620$	−38.4227	+	12.0697i	−1.54309	+	0.484730i
$621$	3.88983	−	2.21836i	0.156093	−	0.0890199i
$622$	3.42510	+	0.376954i	0.137334	+	0.0151145i
$623$	40.0642	+	0.414380i	1.60514	+	0.0166018i
$624$	−30.8877	+	2.58107i	−1.23650	+	0.103325i
$625$	13.2702	+	22.9846i	0.530807	+	0.919385i
$626$	−0.0491712	+	0.446782i	−0.00196528	+	0.0178570i
$627$	−0.0452294	+	25.5784i	−0.00180629	+	1.02150i
$628$	−3.65534	+	16.4055i	−0.145864	+	0.654652i
$629$		−	13.0816i		−	0.521597i
$630$	−34.6403	−	4.29977i	−1.38010	−	0.171307i
$631$		−	29.1706i		−	1.16126i	−0.814166	−	0.580632i	$-0.802806\pi$
$631$		−	29.1706i		−	1.16126i	0.814166	−	0.580632i	$-0.197194\pi$
$632$	−10.2694	+	30.0946i	−0.408493	+	1.19710i
$633$	−13.9856	+	8.04164i	−0.555877	+	0.319626i
$634$	−48.6729	−	5.35677i	−1.93305	−	0.212744i
$635$	12.4464	+	21.5578i	0.493920	+	0.855494i
$636$	6.71062	+	1.50766i	0.266093	+	0.0597828i
$637$	27.4390	−	15.0940i	1.08717	−	0.598044i
$638$	−0.624499	+	5.67435i	−0.0247241	+	0.224650i
$639$	9.25689	−	5.30091i	0.366197	−	0.209701i
$640$	−34.1425	−	8.48955i	−1.34960	−	0.335579i
$641$	−1.13191	+	1.96052i	−0.0447077	+	0.0774360i	−0.887513	−	0.460782i	$-0.847569\pi$
$641$	−1.13191	+	1.96052i	−0.0447077	+	0.0774360i	0.842806	+	0.538218i	$0.180902\pi$
$642$	18.7789	−	8.21142i	0.741146	−	0.324079i
$643$	−5.41789	+	9.38406i	−0.213661	+	0.370071i	−0.952857	−	0.303418i	$-0.901872\pi$
$643$	−5.41789	+	9.38406i	−0.213661	+	0.370071i	0.739197	+	0.673489i	$0.235205\pi$
$644$	−3.11891	+	3.32670i	−0.122902	+	0.131090i
$645$	2.62357	+	4.56277i	0.103303	+	0.179659i
$646$	−3.42778	+	31.1456i	−0.134864	+	1.22541i
$647$	11.2094	+	19.4153i	0.440687	+	0.763293i	0.997741	−	0.0671839i	$-0.0214014\pi$
$647$	11.2094	+	19.4153i	0.440687	+	0.763293i	−0.557053	+	0.830477i	$0.688068\pi$
$648$	−19.2835	+	16.6176i	−0.757528	+	0.652803i
$649$	12.0264	+	6.94343i	0.472076	+	0.272553i
$650$	27.0517	−	11.8858i	1.06105	−	0.466201i
$651$	0.359375	−	29.6724i	0.0140850	−	1.16295i
$652$	32.3257	+	29.6844i	1.26597	+	1.16253i
$653$	16.2140	+	28.0834i	0.634502	+	1.09899i	0.986621	+	0.163034i	$0.0521279\pi$
$653$	16.2140	+	28.0834i	0.634502	+	1.09899i	−0.352119	+	0.935955i	$0.614539\pi$
$654$	−6.85859	−	0.767109i	−0.268192	−	0.0299963i
$655$	10.9545	+	6.32457i	0.428027	+	0.247122i
$656$	2.80579	+	4.02529i	0.109548	+	0.157161i
$657$	−11.6684	−	6.79190i	−0.455229	−	0.264977i
$658$	39.5283	−	16.8822i	1.54097	−	0.658136i
$659$	−27.6786	+	15.9802i	−1.07820	+	0.622502i	−0.930411	−	0.366517i	$-0.880550\pi$
$659$	−27.6786	+	15.9802i	−1.07820	+	0.622502i	−0.147793	+	0.989018i	$0.547217\pi$
$660$	16.4085	−	17.8053i	0.638701	−	0.693069i
$661$		−	11.9087i		−	0.463195i	−0.972812	−	0.231598i	$-0.925605\pi$
$661$		−	11.9087i		−	0.463195i	0.972812	−	0.231598i	$-0.0743953\pi$
$662$	0.459780	−	4.17767i	0.0178698	−	0.162370i
$663$	13.1056	−	22.6071i	0.508979	−	0.877988i
$664$	1.62309	+	8.22845i	0.0629880	+	0.319326i
$665$	−26.5422	−	47.0905i	−1.02926	−	1.82609i
$666$	16.3526	+	1.85827i	0.633652	+	0.0720065i
$667$	1.34030	+	0.773823i	0.0518966	+	0.0299625i
$668$	−5.12333	+	5.57920i	−0.198228	+	0.215866i
$669$	−15.1317	−	0.0267569i	−0.585026	−	0.00103448i
$670$	20.8331	+	47.4152i	0.804851	+	1.83181i
$671$	14.8214	−	25.6714i	0.572173	−	0.991033i
$672$	13.7740	−	21.9608i	0.531345	−	0.847156i
$673$	−17.3361	−	30.0270i	−0.668257	−	1.15745i	−0.978391	−	0.206762i	$-0.933707\pi$
$673$	−17.3361	−	30.0270i	−0.668257	−	1.15745i	0.310134	−	0.950693i	$-0.399626\pi$
$674$	−26.9208	+	36.6744i	−1.03695	+	1.41265i
$675$	12.2448	−	20.9511i	0.471302	−	0.806409i
$676$	4.20453	+	13.3847i	0.161713	+	0.514797i
$677$		−	40.3262i		−	1.54986i	−0.632045	−	0.774931i	$-0.717784\pi$
$677$		−	40.3262i		−	1.54986i	0.632045	−	0.774931i	$-0.282216\pi$
$678$	0.314982	+	0.720341i	0.0120968	+	0.0276645i
$679$	4.45711	−	7.53878i	0.171048	−	0.289312i
$680$	22.3315	−	19.5212i	0.856373	−	0.748603i
$681$	18.8063	+	32.7068i	0.720658	+	1.25333i
$682$	16.5934	+	12.1804i	0.635394	+	0.466411i
$683$	−13.6413	+	7.87579i	−0.521968	+	0.301359i	−0.737740	−	0.675085i	$-0.764107\pi$
$683$	−13.6413	+	7.87579i	−0.521968	+	0.301359i	0.215771	+	0.976444i	$0.430773\pi$
$684$	−38.4467	−	8.70920i	−1.47005	−	0.333005i
$685$			46.9033i			1.79208i
$686$	−3.67153	+	25.9330i	−0.140180	+	0.990126i
$687$	0.0260340	−	14.7229i	0.000993258	−	0.561714i
$688$	−3.89459	+	0.332380i	−0.148480	+	0.0126719i
$689$		−	8.88261i		−	0.338400i
$690$	−2.62992	−	6.01445i	−0.100119	−	0.228966i
$691$	−13.8708			−0.527672			−0.263836	−	0.964568i	$-0.584988\pi$
$691$	−13.8708			−0.527672			−0.263836	+	0.964568i	$0.584988\pi$
$692$	1.23148	−	5.52700i	0.0468139	−	0.210105i
$693$	8.70503	+	15.5728i	0.330677	+	0.591560i
$694$	1.69493	−	15.4005i	0.0643385	−	0.584595i
$695$		−	25.2636i		−	0.958303i
$696$	−8.32147	−	2.85602i	−0.315425	−	0.108257i
$697$	−4.13665			−0.156687
$698$	5.97276	−	2.62428i	0.226072	−	0.0993306i
$699$	15.7777	+	27.4397i	0.596768	+	1.03787i
$700$	−5.62356	+	24.0639i	−0.212551	+	0.909529i
$701$	−18.9982			−0.717551			−0.358776	−	0.933424i	$-0.616806\pi$
$701$	−18.9982			−0.717551			−0.358776	+	0.933424i	$0.616806\pi$
$702$	26.3984	+	19.5940i	0.996342	+	0.739529i
$703$	12.7433	+	22.0720i	0.480623	+	0.832463i
$704$	6.82820	+	16.6348i	0.257348	+	0.626947i
$705$	−0.109409	+	61.8734i	−0.00412057	+	2.33029i
$706$	−7.21532	−	5.29640i	−0.271552	−	0.199333i
$707$	−30.0301	−	0.310598i	−1.12940	−	0.0116813i
$708$	−14.5036	+	15.7382i	−0.545079	+	0.591477i
$709$	−7.95474			−0.298746			−0.149373	−	0.988781i	$-0.547726\pi$
$709$	−7.95474			−0.298746			−0.149373	+	0.988781i	$0.547726\pi$
$710$	−6.29026	−	14.3164i	−0.236069	−	0.537283i
$711$	29.2682	−	16.7603i	1.09764	−	0.628560i
$712$	−28.1901	−	32.2484i	−1.05647	−	1.20856i
$713$	4.83284	−	2.79024i	0.180991	−	0.104495i
$714$	8.54835	+	20.1137i	0.319914	+	0.752735i
$715$	−27.0809	−	15.6352i	−1.01277	−	0.584722i
$716$	18.3016	−	5.74906i	0.683963	−	0.214853i
$717$	32.7175	−	18.8124i	1.22186	−	0.702561i
$718$	−6.80620	−	4.99608i	−0.254005	−	0.186452i
$719$	−3.08870	+	5.34978i	−0.115189	+	0.199513i	−0.917855	−	0.396915i	$-0.870081\pi$
$719$	−3.08870	+	5.34978i	−0.115189	+	0.199513i	0.802666	+	0.596428i	$0.203414\pi$
$720$	21.2302	+	30.6885i	0.791204	+	1.14369i
$721$	−33.9258	−	20.0578i	−1.26346	−	0.746990i
$722$	−13.7479	−	31.2897i	−0.511645	−	1.16448i
$723$	7.28340	−	4.18792i	0.270873	−	0.155750i
$724$	3.07744	−	13.8118i	0.114372	−	0.513313i
$725$	8.38703			0.311486
$726$	14.4788	+	1.61940i	0.537359	+	0.0601017i
$727$	13.6339	+	23.6147i	0.505655	+	0.875819i	0.999979	+	0.00654173i	$0.00208231\pi$
$727$	13.6339	+	23.6147i	0.505655	+	0.875819i	−0.494324	+	0.869278i	$0.664584\pi$
$728$	−31.5713	−	11.1391i	−1.17011	−	0.412843i
$729$	26.9985	+	0.286453i	0.999944	+	0.0106094i
$730$	−11.7115	+	15.9547i	−0.433462	+	0.590509i
$731$	1.64767	−	2.85385i	0.0609413	−	0.105553i
$732$	33.5946	+	30.9593i	1.24169	+	1.14429i
$733$	9.47896	−	5.47268i	0.350113	−	0.202138i	−0.314622	−	0.949217i	$-0.601878\pi$
$733$	9.47896	−	5.47268i	0.350113	−	0.202138i	0.664735	+	0.747079i	$0.268544\pi$
$734$	−4.37775	+	5.96384i	−0.161586	+	0.220129i
$735$	−32.2203	−	19.5798i	−1.18846	−	0.722213i
$736$	4.87350	+	0.119316i	0.179640	+	0.00439804i
$737$	13.2350	−	22.9237i	0.487518	−	0.844407i
$738$	0.587621	−	5.17102i	0.0216306	−	0.190348i
$739$	−5.56689	+	3.21404i	−0.204781	+	0.118230i	−0.598884	−	0.800836i	$-0.704389\pi$
$739$	−5.56689	+	3.21404i	−0.204781	+	0.118230i	0.394102	+	0.919067i	$0.371056\pi$
$740$	5.24689	−	23.5485i	0.192879	−	0.865661i
$741$	−0.0900236	+	50.9108i	−0.00330710	+	1.87025i
$742$	5.94293	+	4.45772i	0.218172	+	0.163648i
$743$	−25.1981	−	14.5481i	−0.924427	−	0.533718i	−0.0393825	−	0.999224i	$-0.512539\pi$
$743$	−25.1981	−	14.5481i	−0.924427	−	0.533718i	−0.885045	+	0.465506i	$0.845872\pi$
$744$	−23.9212	+	20.8364i	−0.876995	+	0.763899i
$745$	−49.4443	−	28.5467i	−1.81150	−	1.04587i
$746$	−6.58375	−	14.9843i	−0.241048	−	0.548615i
$747$	4.47510	−	7.68817i	0.163735	−	0.281296i
$748$	−14.7969	−	3.29693i	−0.541029	−	0.120548i
$749$	22.1368	+	0.228958i	0.808860	+	0.00836596i
$750$	2.02265	+	1.49024i	0.0738568	+	0.0544157i
$751$	−10.0086	+	5.77846i	−0.365219	+	0.210859i	−0.671368	−	0.741125i	$-0.734293\pi$
$751$	−10.0086	+	5.77846i	−0.365219	+	0.210859i	0.306149	+	0.951984i	$0.400959\pi$
$752$	−41.6036	−	19.5080i	−1.51713	−	0.711384i
$753$	−13.0465	+	22.5051i	−0.475439	+	0.820133i
$754$	−1.24299	+	11.2941i	−0.0452670	+	0.411307i
$755$	44.2094			1.60894
$756$	−26.3574	+	7.82868i	−0.958609	+	0.284726i
$757$	10.5542			0.383600			0.191800	−	0.981434i	$-0.438567\pi$
$757$	10.5542			0.383600			0.191800	+	0.981434i	$0.438567\pi$
$758$	1.18369	−	10.7553i	0.0429936	−	0.390651i
$759$	−1.68265	+	2.90257i	−0.0610764	+	0.105357i
$760$	−18.6626	+	54.6913i	−0.676965	+	1.98386i
$761$	−31.3515	+	18.1008i	−1.13649	+	0.656153i	−0.945559	−	0.325450i	$-0.894484\pi$
$761$	−31.3515	+	18.1008i	−1.13649	+	0.656153i	−0.190931	+	0.981603i	$0.561151\pi$
$762$	15.7860	+	11.6307i	0.571866	+	0.421336i
$763$	−6.41674	−	3.79373i	−0.232301	−	0.137342i
$764$	7.77255	−	34.8840i	0.281201	−	1.26206i
$765$	−31.4600	−	0.111259i	−1.13744	−	0.00402259i
$766$	−5.34662	−	12.1687i	−0.193181	−	0.439672i
$767$	23.9370	+	13.8200i	0.864315	+	0.499013i
$768$	−27.3203	+	4.64773i	−0.985836	+	0.167711i
$769$	−11.0469	−	6.37795i	−0.398363	−	0.229995i	0.287415	−	0.957806i	$-0.407204\pi$
$769$	−11.0469	−	6.37795i	−0.398363	−	0.229995i	−0.685777	+	0.727812i	$0.740538\pi$
$770$	24.0512	−	10.2721i	0.866747	−	0.370180i
$771$	−0.0731928	+	41.3925i	−0.00263598	+	1.49071i
$772$	−26.1474	−	5.82594i	−0.941065	−	0.209680i
$773$	−43.1258	+	24.8987i	−1.55113	+	0.895543i	−0.553075	+	0.833131i	$0.686546\pi$
$773$	−43.1258	+	24.8987i	−1.55113	+	0.895543i	−0.998051	+	0.0624114i	$0.980121\pi$
$774$	3.33340	+	2.46507i	0.119817	+	0.0886050i
$775$	15.1209	−	26.1902i	0.543160	−	0.940780i
$776$	−9.18549	+	1.81187i	−0.329740	+	0.0650422i
$777$	15.2862	+	9.07407i	0.548389	+	0.325530i
$778$	9.67346	−	13.1782i	0.346810	−	0.472462i
$779$	6.97961	−	4.02968i	0.250071	−	0.144378i
$780$	32.6592	−	35.4392i	1.16939	−	1.26893i
$781$	−3.99613	+	6.92151i	−0.142993	+	0.247671i
$782$	−2.43200	+	3.31313i	−0.0869682	+	0.118477i
$783$	4.62288	+	8.10606i	0.165208	+	0.289687i
$784$	23.2967	−	15.5327i	0.832023	−	0.554741i
$785$	−13.0668	−	22.6323i	−0.466373	−	0.807782i
$786$	9.90194	+	1.10750i	0.353190	+	0.0395031i
$787$	−10.6193			−0.378537			−0.189268	−	0.981925i	$-0.560612\pi$
$787$	−10.6193			−0.378537			−0.189268	+	0.981925i	$0.560612\pi$
$788$	14.9091	+	3.32192i	0.531114	+	0.118338i
$789$	−7.48780	+	4.30545i	−0.266573	+	0.153278i
$790$	−19.8884	−	45.2652i	−0.707598	−	1.61046i
$791$	−0.00878261	+	0.849144i	−0.000312274	+	0.0301921i
$792$	6.22326	−	18.0286i	0.221134	−	0.640617i
$793$	29.5001	−	51.0957i	1.04758	−	1.81446i
$794$	32.8354	+	24.1028i	1.16528	+	0.855376i
$795$	−9.27077	+	5.33065i	−0.328800	+	0.189059i
$796$	−14.4075	−	45.8648i	−0.510659	−	1.62564i
$797$	−25.9905	−	15.0056i	−0.920629	−	0.531526i	−0.0367937	−	0.999323i	$-0.511714\pi$
$797$	−25.9905	−	15.0056i	−0.920629	−	0.531526i	−0.883836	+	0.467797i	$0.845048\pi$
$798$	−34.0168	−	25.6097i	−1.20418	−	0.906573i
$799$	33.5491	−	19.3696i	1.18688	−	0.685246i
$800$	23.1955	−	12.6453i	0.820085	−	0.447079i
$801$	−0.160667	+	45.4306i	−0.00567690	+	1.60521i
$802$	1.29837	+	2.95505i	0.0458472	+	0.104346i
$803$	10.1156			0.356971
$804$	29.9989	+	27.6457i	1.05798	+	0.974988i
$805$	0.0733300	−	7.08988i	0.00258454	−	0.249885i
$806$	33.0271	+	24.2435i	1.16333	+	0.853942i
$807$	−0.0227924	+	12.8897i	−0.000802331	+	0.453739i
$808$	21.1299	+	24.1718i	0.743347	+	0.850360i
$809$	−25.8662	−	44.8015i	−0.909405	−	1.57514i	−0.814892	−	0.579613i	$-0.803204\pi$
$809$	−25.8662	−	44.8015i	−0.909405	−	1.57514i	−0.0945135	−	0.995524i	$-0.530130\pi$
$810$	4.60804	−	39.3107i	0.161910	−	1.38124i
$811$	−27.3735			−0.961213			−0.480607	−	0.876936i	$-0.659584\pi$
$811$	−27.3735			−0.961213			−0.480607	+	0.876936i	$0.659584\pi$
$812$	−6.93256	−	6.49954i	−0.243285	−	0.228089i
$813$	2.19686	+	3.82065i	0.0770471	+	0.133996i
$814$	−11.2892	+	4.96020i	−0.395687	+	0.173855i
$815$	−68.2383			−2.39028
$816$	9.95641	−	21.1361i	0.348544	−	0.739913i
$817$			6.42025i			0.224616i
$818$	−3.95626	+	35.9475i	−0.138327	+	1.25688i
$819$	17.3263	+	30.9957i	0.605430	+	1.08308i
$820$	−7.44650	−	1.65917i	−0.260043	−	0.0579406i
$821$	−11.9881			−0.418386			−0.209193	−	0.977874i	$-0.567084\pi$
$821$	−11.9881			−0.418386			−0.209193	+	0.977874i	$0.567084\pi$
$822$	14.8018	+	33.8508i	0.516274	+	1.18068i
$823$		−	21.8368i		−	0.761184i	−0.924743	−	0.380592i	$-0.875720\pi$
$823$		−	21.8368i		−	0.761184i	0.924743	−	0.380592i	$-0.124280\pi$
$824$	8.15371	+	41.3363i	0.284048	+	1.44002i
$825$	−0.0321499	+	18.1816i	−0.00111932	+	0.633003i
$826$	−21.2591	+	9.07957i	−0.739698	+	0.315919i
$827$			20.0823i			0.698331i	0.937061	+	0.349166i	$0.113535\pi$
$827$			20.0823i			0.698331i	−0.937061	+	0.349166i	$0.886465\pi$
$828$	−3.79611	−	3.51076i	−0.131924	−	0.122007i
$829$	48.8320	−	28.1931i	1.69600	−	0.979188i	0.746525	−	0.665357i	$-0.231721\pi$
$829$	48.8320	−	28.1931i	1.69600	−	0.979188i	0.949479	−	0.313831i	$-0.101613\pi$
$830$	−10.5123	−	7.71656i	−0.364888	−	0.267846i
$831$	−10.2808	−	17.8799i	−0.356638	−	0.620246i
$832$	13.5907	+	33.1095i	0.471173	+	1.14787i
$833$	−0.488255	+	23.6009i	−0.0169170	+	0.817721i
$834$	−7.97275	−	18.2331i	−0.276074	−	0.631361i
$835$		−	11.7775i		−	0.407576i
$836$	28.1779	−	8.85150i	0.974554	−	0.306136i
$837$	33.6474	+	0.178494i	1.16302	+	0.00616965i
$838$	−13.5540	+	18.4647i	−0.468215	+	0.637852i
$839$	−27.0448	−	46.8430i	−0.933691	−	1.61720i	−0.776951	−	0.629561i	$-0.783235\pi$
$839$	−27.0448	−	46.8430i	−0.933691	−	1.61720i	−0.156740	−	0.987640i	$-0.550098\pi$
$840$	7.32075	+	39.6358i	0.252590	+	1.36756i
$841$	12.8874	−	22.3217i	0.444394	−	0.769713i
$842$	8.02169	+	18.2570i	0.276446	+	0.629179i
$843$	−6.42007	−	0.0113524i	−0.221119	−	0.000390996i
$844$	13.7209	+	12.5998i	0.472294	+	0.433703i
$845$	−18.8913	−	10.9069i	−0.649881	−	0.375209i
$846$	19.4472	+	44.6895i	0.668609	+	1.53646i
$847$	13.5460	+	8.00873i	0.465447	+	0.275183i
$848$	−0.675339	−	7.91315i	−0.0231912	−	0.271739i
$849$	12.9204	−	22.2877i	0.443428	−	0.764913i
$850$	−2.43653	+	22.1389i	−0.0835722	+	0.759358i
$851$			3.34298i			0.114596i
$852$	−9.05776	−	8.34724i	−0.310314	−	0.285972i
$853$	24.2820	−	14.0192i	0.831398	−	0.480008i	−0.0229329	−	0.999737i	$-0.507300\pi$
$853$	24.2820	−	14.0192i	0.831398	−	0.480008i	0.854331	+	0.519729i	$0.173967\pi$
$854$	19.3812	+	45.3794i	0.663210	+	1.55285i
$855$	53.1895	−	30.4587i	1.81904	−	1.04167i
$856$	−15.5760	−	17.8183i	−0.532375	−	0.609016i
$857$	−37.2473	−	21.5047i	−1.27234	−	0.734587i	−0.296914	−	0.954904i	$-0.595957\pi$
$857$	−37.2473	−	21.5047i	−1.27234	−	0.734587i	−0.975428	+	0.220317i	$0.929291\pi$
$858$	−24.4789	−	2.73788i	−0.835695	−	0.0934696i
$859$	6.52507	+	11.3018i	0.222632	+	0.385611i	0.955607	−	0.294646i	$-0.0952017\pi$
$859$	6.52507	+	11.3018i	0.222632	+	0.385611i	−0.732974	+	0.680257i	$0.761868\pi$
$860$	4.11066	−	4.47643i	0.140172	−	0.152645i
$861$	2.86940	−	4.83379i	0.0977888	−	0.164735i
$862$	−51.1240	+	22.4626i	−1.74129	+	0.765080i
$863$	44.0479	+	25.4311i	1.49941	+	0.865684i	1.00000		0.000682608i	$-0.000217281\pi$
$863$	44.0479	+	25.4311i	1.49941	+	0.865684i	0.499409	+	0.866367i	$0.333551\pi$
$864$	25.0069	+	15.4484i	0.850752	+	0.525567i
$865$	4.40218	+	7.62480i	0.149679	+	0.259251i
$866$	1.42593	−	12.9563i	0.0484550	−	0.440275i
$867$	−4.85886	−	8.45027i	−0.165016	−	0.286986i
$868$	−32.7948	+	9.93034i	−1.11313	+	0.337058i
$869$	−12.6349	+	21.8843i	−0.428609	+	0.742373i
$870$	12.5336	−	5.48053i	0.424928	−	0.185807i
$871$	26.3427	−	45.6269i	0.892588	−	1.54601i
$872$	1.54219	+	7.81835i	0.0522253	+	0.264763i
$873$	8.58238	+	4.99559i	0.290469	+	0.169075i
$874$	0.875964	−	7.95922i	0.0296299	−	0.269225i
$875$	1.33245	+	2.36400i	0.0450450	+	0.0799178i
$876$	−3.41736	+	15.2107i	−0.115462	+	0.513921i
$877$	−5.40219	−	9.35687i	−0.182419	−	0.315959i	0.760285	−	0.649590i	$-0.225059\pi$
$877$	−5.40219	−	9.35687i	−0.182419	−	0.315959i	−0.942704	+	0.333631i	$0.891726\pi$
$878$	−0.107435	−	0.0118239i	−0.00362575	−	0.000399037i
$879$	7.51333	−	4.32013i	0.253418	−	0.145714i
$880$	−25.3140	−	11.8698i	−0.853334	−	0.400130i
$881$			43.3115i			1.45920i	0.683873	+	0.729601i	$0.260294\pi$
$881$			43.3115i			1.45920i	−0.683873	+	0.729601i	$0.739706\pi$
$882$	−29.4329	−	3.96290i	−0.991057	−	0.133438i
$883$		−	18.6655i		−	0.628143i	−0.949399	−	0.314072i	$-0.898307\pi$
$883$		−	18.6655i		−	0.628143i	0.949399	−	0.314072i	$-0.101693\pi$
$884$	−29.4515	−	6.56213i	−0.990560	−	0.220708i
$885$	0.0588421	−	33.2767i	0.00197795	−	1.11859i
$886$	−5.07435	+	46.1068i	−0.170476	+	1.54899i
$887$	−1.40376	−	2.43138i	−0.0471336	−	0.0816379i	0.841496	−	0.540263i	$-0.181675\pi$
$887$	−1.40376	−	2.43138i	−0.0471336	−	0.0816379i	−0.888630	+	0.458625i	$0.848342\pi$
$888$	−3.64475	−	18.6512i	−0.122310	−	0.625892i
$889$	10.3992	+	18.4501i	0.348779	+	0.618796i
$890$	66.1985	+	7.28557i	2.21898	+	0.244213i
$891$	−17.5903	+	9.99052i	−0.589296	+	0.334695i
$892$	5.23638	+	16.6695i	0.175327	+	0.558137i
$893$	−37.7373	+	65.3630i	−1.26283	+	2.18729i
$894$	−44.6936	−	4.99882i	−1.49478	−	0.167185i
$895$	−14.9136	+	25.8310i	−0.498505	+	0.863437i
$896$	−28.9725	−	7.52303i	−0.967902	−	0.251327i
$897$	−3.34911	+	5.77721i	−0.111824	+	0.192896i
$898$	−6.41930	−	0.706485i	−0.214215	−	0.0235757i
$899$	5.81461	+	10.0712i	0.193928	+	0.335894i
$900$	−27.3286	−	6.19066i	−0.910954	−	0.206355i
$901$	5.79854	+	3.34779i	0.193177	+	0.111531i
$902$	1.56851	+	3.56987i	0.0522257	+	0.118864i
$903$	2.19189	+	3.90492i	0.0729414	+	0.129948i
$904$	0.683491	−	0.597478i	0.0227326	−	0.0198718i
$905$	11.0009	+	19.0542i	0.365684	+	0.633383i
$906$	31.9066	−	13.9517i	1.06002	−	0.463514i
$907$	20.8642	+	12.0460i	0.692784	+	0.399979i	0.804654	−	0.593744i	$-0.202351\pi$
$907$	20.8642	+	12.0460i	0.692784	+	0.399979i	−0.111870	+	0.993723i	$0.535684\pi$
$908$	29.4661	−	32.0879i	0.977866	−	1.06488i
$909$	0.120428	−	34.0525i	0.00399435	−	1.12945i
$910$	47.8711	−	20.4453i	1.58691	−	0.677756i
$911$	2.87372	−	1.65914i	0.0952107	−	0.0549699i	−0.451639	−	0.892201i	$-0.649160\pi$
$911$	2.87372	−	1.65914i	0.0952107	−	0.0549699i	0.546849	+	0.837231i	$0.315827\pi$
$912$	3.79051	+	45.3611i	0.125516	+	1.50206i
$913$			6.66502i			0.220580i
$914$	17.8592	+	1.96552i	0.590730	+	0.0650136i
$915$	−71.0323	−	0.125604i	−2.34825	−	0.00415233i
$916$	−16.2192	+	5.09491i	−0.535896	+	0.168341i
$917$	9.26402	+	5.47711i	0.305925	+	0.180870i
$918$	−22.7402	+	9.84792i	−0.750540	+	0.325030i
$919$	38.9661	+	22.4971i	1.28537	+	0.742110i	0.977825	−	0.209422i	$-0.0671583\pi$
$919$	38.9661	+	22.4971i	1.28537	+	0.742110i	0.307548	+	0.951533i	$0.400492\pi$
$920$	−5.70677	+	4.98861i	−0.188147	+	0.164470i
$921$	18.9331	−	32.6596i	0.623867	−	1.07617i
$922$	−7.85419	+	3.45094i	−0.258664	+	0.113651i
$923$	−7.95382	+	13.7764i	−0.261803	+	0.453456i
$924$	14.1165	−	15.0037i	0.464397	−	0.493584i
$925$	9.05818	+	15.6892i	0.297831	+	0.515858i
$926$	−29.6250	−	21.7462i	−0.973539	−	0.714625i
$927$	22.4810	−	38.6222i	0.738374	−	1.26852i
$928$	−0.248643	+	10.1559i	−0.00816212	+	0.333385i
$929$		−	20.0843i		−	0.658945i	−0.944165	−	0.329473i	$-0.893129\pi$
$929$		−	20.0843i		−	0.658945i	0.944165	−	0.329473i	$-0.106871\pi$
$930$	5.48265	−	49.0195i	0.179783	−	1.60741i
$931$	−22.1667	−	40.2964i	−0.726485	−	1.32066i
$932$	24.7209	−	26.9205i	0.809759	−	0.881810i
$933$	−2.11656	+	3.65106i	−0.0692930	+	0.119530i
$934$	−9.44202	+	12.8629i	−0.308952	+	0.420888i
$935$	20.4132	−	11.7855i	0.667582	−	0.385429i
$936$	12.3866	−	35.8836i	0.404870	−	1.17289i
$937$			52.5195i			1.71574i	0.513868	+	0.857869i	$0.328212\pi$
$937$			52.5195i			1.71574i	−0.513868	+	0.857869i	$0.671788\pi$
$938$	17.3068	+	40.5224i	0.565086	+	1.32310i
$939$	−0.476258	−	0.276092i	−0.0155421	−	0.00900991i
$940$	68.1615	−	21.4115i	2.22318	−	0.698366i
$941$			17.8776i			0.582794i	0.956602	+	0.291397i	$0.0941201\pi$
$941$			17.8776i			0.582794i	−0.956602	+	0.291397i	$0.905880\pi$
$942$	−16.5728	−	12.2104i	−0.539973	−	0.397838i
$943$	1.05712			0.0344244
$944$	22.3752	+	10.4918i	0.728251	+	0.341478i
$945$	21.9523	−	36.6846i	0.714107	−	1.19335i
$946$	−3.08758	−	0.339808i	−0.100386	−	0.0110481i
$947$		−	59.9199i		−	1.94714i	−0.228399	−	0.973568i	$-0.573349\pi$
$947$		−	59.9199i		−	1.94714i	0.228399	−	0.973568i	$-0.426651\pi$
$948$	−28.6387	−	26.3921i	−0.930140	−	0.857176i
$949$	20.1338			0.653572
$950$	−17.4553	−	39.7276i	−0.566326	−	1.28893i
$951$	30.0777	−	51.8840i	0.975336	−	1.68245i
$952$	19.1706	−	16.4114i	0.621321	−	0.531896i
$953$	11.2404			0.364111			0.182056	−	0.983288i	$-0.441725\pi$
$953$	11.2404			0.364111			0.182056	+	0.983288i	$0.441725\pi$
$954$	−5.00860	+	6.77290i	−0.162159	+	0.219281i
$955$	27.7846	+	48.1243i	0.899088	+	1.55727i
$956$	−32.0984	−	29.4756i	−1.03814	−	0.953310i
$957$	−6.04870	−	3.50650i	−0.195527	−	0.113349i
$958$	13.2961	−	18.1134i	0.429578	−	0.585216i
$959$	−0.412719	+	39.9036i	−0.0133274	+	1.28855i
$960$	26.4003	−	34.0543i	0.852066	−	1.09910i
$961$	10.9325			0.352662
$962$	−22.4698	+	9.87267i	−0.724455	+	0.318308i
$963$	−0.0887739	+	25.1019i	−0.00286070	+	0.808898i
$964$	−7.14558	−	6.56172i	−0.230144	−	0.211339i
$965$	36.0717	−	20.8260i	1.16119	−	0.670413i
$966$	−2.18452	−	5.14001i	−0.0702857	−	0.165377i
$967$	−28.0105	−	16.1719i	−0.900756	−	0.520052i	−0.0233107	−	0.999728i	$-0.507421\pi$
$967$	−28.0105	−	16.1719i	−0.900756	−	0.520052i	−0.877445	+	0.479676i	$0.840754\pi$
$968$	−3.25564	−	16.5049i	−0.104640	−	0.530488i
$969$	−33.2004	−	19.2466i	−1.06655	−	0.618291i
$970$	8.61406	−	11.7350i	0.276581	−	0.376788i
$971$	4.19734	−	7.27001i	0.134699	−	0.233306i	−0.790783	−	0.612096i	$-0.790327\pi$
$971$	4.19734	−	7.27001i	0.134699	−	0.233306i	0.925483	+	0.378790i	$0.123660\pi$
$972$	−9.08009	−	29.8254i	−0.291244	−	0.956649i
$973$	0.222304	−	21.4933i	0.00712673	−	0.689045i
$974$	−7.28289	+	3.19992i	−0.233359	+	0.102532i
$975$	−0.0639905	+	36.1883i	−0.00204934	+	1.15895i
$976$	22.3957	−	47.7619i	0.716868	−	1.52882i
$977$	−11.3855			−0.364254			−0.182127	−	0.983275i	$-0.558298\pi$
$977$	−11.3855			−0.364254			−0.182127	+	0.983275i	$0.558298\pi$
$978$	−49.2486	+	21.5348i	−1.57480	+	0.688607i
$979$	−17.0192	−	29.4782i	−0.543938	−	0.942127i
$980$	−10.3450	+	42.2887i	−0.330458	+	1.35086i
$981$	4.25206	−	7.30500i	0.135758	−	0.233231i
$982$	11.8159	+	8.67343i	0.377060	+	0.276780i
$983$	−20.2073	+	35.0001i	−0.644514	+	1.11633i	0.339900	+	0.940462i	$0.389607\pi$
$983$	−20.2073	+	35.0001i	−0.644514	+	1.11633i	−0.984414	+	0.175869i	$0.943726\pi$
$984$	−5.89786	+	1.15254i	−0.188017	+	0.0367416i
$985$	−20.5679	+	11.8749i	−0.655347	+	0.378365i
$986$	−6.90427	−	5.06807i	−0.219877	−	0.161400i
$987$	−0.637528	+	52.6387i	−0.0202927	+	1.67551i
$988$	56.0847	−	17.6178i	1.78429	−	0.560498i
$989$	−0.421060	+	0.729297i	−0.0133889	+	0.0231903i
$990$	11.8328	+	27.1916i	0.376071	+	0.864207i
$991$	−41.5797	+	24.0060i	−1.32082	+	0.762577i	−0.983860	−	0.178941i	$-0.942733\pi$
$991$	−41.5797	+	24.0060i	−1.32082	+	0.762577i	−0.336962	+	0.941518i	$0.609399\pi$
$992$	31.2657	+	19.0865i	0.992688	+	0.605998i
$993$	4.45329	+	2.58162i	0.141321	+	0.0819251i
$994$	−5.22554	−	12.2352i	−0.165744	−	0.388076i
$995$	64.7340	+	37.3742i	2.05221	+	1.18484i
$996$	−10.0221	−	2.25165i	−0.317563	−	0.0713463i
$997$	−25.0034	−	14.4357i	−0.791866	−	0.457184i	0.0487532	−	0.998811i	$-0.484475\pi$
$997$	−25.0034	−	14.4357i	−0.791866	−	0.457184i	−0.840619	+	0.541627i	$0.817809\pi$
$998$	14.9433	−	6.56572i	0.473022	−	0.207834i
$999$	−10.1708	+	17.4025i	−0.321790	+	0.550591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.103.42	yes	84
3.2	odd	2		756.2.bj.b.523.1		84
4.3	odd	2	inner	252.2.bj.b.103.41	yes	84
7.3	odd	6		252.2.n.b.31.14	✓	84
9.2	odd	6		756.2.n.b.19.27		84
9.7	even	3		252.2.n.b.187.16	yes	84
12.11	even	2		756.2.bj.b.523.2		84
21.17	even	6		756.2.n.b.199.29		84
28.3	even	6		252.2.n.b.31.16	yes	84
36.7	odd	6		252.2.n.b.187.14	yes	84
36.11	even	6		756.2.n.b.19.29		84
63.38	even	6		756.2.bj.b.451.1		84
63.52	odd	6	inner	252.2.bj.b.115.42	yes	84
84.59	odd	6		756.2.n.b.199.27		84
252.115	even	6	inner	252.2.bj.b.115.41	yes	84
252.227	odd	6		756.2.bj.b.451.2		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.14	✓	84	7.3	odd	6
252.2.n.b.31.16	yes	84	28.3	even	6
252.2.n.b.187.14	yes	84	36.7	odd	6
252.2.n.b.187.16	yes	84	9.7	even	3
252.2.bj.b.103.41	yes	84	4.3	odd	2	inner
252.2.bj.b.103.42	yes	84	1.1	even	1	trivial
252.2.bj.b.115.41	yes	84	252.115	even	6	inner
252.2.bj.b.115.42	yes	84	63.52	odd	6	inner
756.2.n.b.19.27		84	9.2	odd	6
756.2.n.b.19.29		84	36.11	even	6
756.2.n.b.199.27		84	84.59	odd	6
756.2.n.b.199.29		84	21.17	even	6
756.2.bj.b.451.1		84	63.38	even	6
756.2.bj.b.451.2		84	252.227	odd	6
756.2.bj.b.523.1		84	3.2	odd	2
756.2.bj.b.523.2		84	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40573 + 0.154709i) q^{2} +(-0.868676 + 1.49847i) q^{3} +(1.95213 + 0.434957i) q^{4} +(-2.69307 + 1.55484i) q^{5} +(-1.45295 + 1.97204i) q^{6} +(-2.30485 + 1.29911i) q^{7} +(2.67687 + 0.913443i) q^{8} +(-1.49080 - 2.60336i) q^{9} +O(q^{10})\)	\(q+(1.40573 + 0.154709i) q^{2} +(-0.868676 + 1.49847i) q^{3} +(1.95213 + 0.434957i) q^{4} +(-2.69307 + 1.55484i) q^{5} +(-1.45295 + 1.97204i) q^{6} +(-2.30485 + 1.29911i) q^{7} +(2.67687 + 0.913443i) q^{8} +(-1.49080 - 2.60336i) q^{9} +(-4.02627 + 1.76904i) q^{10} +(1.94657 + 1.12385i) q^{11} +(-2.34754 + 2.54736i) q^{12} +(3.87442 + 2.23689i) q^{13} +(-3.44097 + 1.46961i) q^{14} +(0.00952410 - 5.38613i) q^{15} +(3.62162 + 1.69819i) q^{16} +(-2.92047 + 1.68614i) q^{17} +(-1.69290 - 3.89026i) q^{18} +(3.28507 - 5.68990i) q^{19} +(-5.93352 + 1.86389i) q^{20} +(0.0554973 - 4.58224i) q^{21} +(2.56248 + 1.88098i) q^{22} +(0.746323 - 0.430890i) q^{23} +(-3.69410 + 3.21771i) q^{24} +(2.33509 - 4.04449i) q^{25} +(5.10030 + 3.74387i) q^{26} +(5.19608 + 0.0275643i) q^{27} +(-5.06442 + 1.53352i) q^{28} +(0.897936 + 1.55527i) q^{29} +(0.846672 - 7.56995i) q^{30} +6.47553 q^{31} +(4.82829 + 2.94748i) q^{32} +(-3.37500 + 1.94061i) q^{33} +(-4.36625 + 1.91842i) q^{34} +(4.18720 - 7.08227i) q^{35} +(-1.77789 - 5.73054i) q^{36} +(-1.93958 + 3.35945i) q^{37} +(5.49818 - 7.49021i) q^{38} +(-6.71752 + 3.86254i) q^{39} +(-8.62926 + 1.70215i) q^{40} +(1.06232 + 0.613333i) q^{41} +(0.786928 - 6.43279i) q^{42} +(-0.846269 + 0.488593i) q^{43} +(3.31113 + 3.04059i) q^{44} +(8.06266 + 4.69308i) q^{45} +(1.11579 - 0.490250i) q^{46} -11.4875 q^{47} +(-5.69070 + 3.95171i) q^{48} +(3.62464 - 5.98849i) q^{49} +(3.90821 - 5.32418i) q^{50} +(0.0103283 - 5.84094i) q^{51} +(6.59041 + 6.05191i) q^{52} +(-0.992739 - 1.71947i) q^{53} +(7.30000 + 0.842629i) q^{54} -6.98968 q^{55} +(-7.35643 + 1.37219i) q^{56} +(5.67247 + 9.86524i) q^{57} +(1.02164 + 2.32520i) q^{58} +6.17823 q^{59} +(2.36133 - 10.5103i) q^{60} -13.1880i q^{61} +(9.10282 + 1.00182i) q^{62} +(6.81812 + 4.06364i) q^{63} +(6.33124 + 4.89033i) q^{64} -13.9121 q^{65} +(-5.04455 + 2.20582i) q^{66} -11.7765i q^{67} +(-6.43454 + 2.02128i) q^{68} +(-0.00263939 + 1.49264i) q^{69} +(6.98175 - 9.30793i) q^{70} +3.55574i q^{71} +(-1.61266 - 8.33063i) q^{72} +(3.89746 - 2.25020i) q^{73} +(-3.24626 + 4.42240i) q^{74} +(4.03209 + 7.01240i) q^{75} +(8.88774 - 9.67856i) q^{76} +(-5.94656 - 0.0615047i) q^{77} +(-10.0406 + 4.39041i) q^{78} +11.2425i q^{79} +(-12.3937 + 1.05773i) q^{80} +(-4.55502 + 7.76221i) q^{81} +(1.39845 + 1.02653i) q^{82} +(1.48263 + 2.56798i) q^{83} +(2.10142 - 8.92099i) q^{84} +(5.24336 - 9.08177i) q^{85} +(-1.26521 + 0.555903i) q^{86} +(-3.11054 - 0.00550025i) q^{87} +(4.18414 + 4.78649i) q^{88} +(-13.1148 - 7.57182i) q^{89} +(10.6078 + 7.84455i) q^{90} +(-11.8359 - 0.122418i) q^{91} +(1.64434 - 0.516534i) q^{92} +(-5.62514 + 9.70337i) q^{93} +(-16.1483 - 1.77723i) q^{94} +20.4311i q^{95} +(-8.61092 + 4.67461i) q^{96} +(-2.86666 + 1.65507i) q^{97} +(6.02172 - 7.85741i) q^{98} +(0.0238472 - 6.74308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more