LMFDB - Embedded newform 1560.2.w.f.781.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(781,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))

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

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

chi := DirichletCharacter("1560.781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.w (of order $2$, degree $1$, 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:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 5 x^{16} + 10 x^{15} - 12 x^{14} + 16 x^{13} - 2 x^{12} - 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 5x^16 + 10x^15 - 12x^14 + 16x^13 - 2x^12 - 40x^11 + 72x^10 - 80x^9 - 8x^8 + 128x^7 - 192x^6 + 320x^5 - 320x^4 + 512x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			781.19
Root			$0.288202 - 1.38454i$ of defining polynomial
Character	$\chi$	$=$	1560.781
Dual form			1560.2.w.f.781.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38454 - 0.288202i) q^{2} +1.00000i q^{3} +(1.83388 - 0.798052i) q^{4} -1.00000i q^{5} +(0.288202 + 1.38454i) q^{6} -3.39492 q^{7} +(2.30907 - 1.63346i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.38454 - 0.288202i) q^{2} +1.00000i q^{3} +(1.83388 - 0.798052i) q^{4} -1.00000i q^{5} +(0.288202 + 1.38454i) q^{6} -3.39492 q^{7} +(2.30907 - 1.63346i) q^{8} -1.00000 q^{9} +(-0.288202 - 1.38454i) q^{10} -0.396748i q^{11} +(0.798052 + 1.83388i) q^{12} -1.00000i q^{13} +(-4.70039 + 0.978424i) q^{14} +1.00000 q^{15} +(2.72623 - 2.92706i) q^{16} +4.14322 q^{17} +(-1.38454 + 0.288202i) q^{18} -6.40325i q^{19} +(-0.798052 - 1.83388i) q^{20} -3.39492i q^{21} +(-0.114344 - 0.549312i) q^{22} +7.72529 q^{23} +(1.63346 + 2.30907i) q^{24} -1.00000 q^{25} +(-0.288202 - 1.38454i) q^{26} -1.00000i q^{27} +(-6.22588 + 2.70933i) q^{28} -5.67448i q^{29} +(1.38454 - 0.288202i) q^{30} +4.53959 q^{31} +(2.93097 - 4.83833i) q^{32} +0.396748 q^{33} +(5.73644 - 1.19408i) q^{34} +3.39492i q^{35} +(-1.83388 + 0.798052i) q^{36} +0.138729i q^{37} +(-1.84543 - 8.86553i) q^{38} +1.00000 q^{39} +(-1.63346 - 2.30907i) q^{40} +10.8070 q^{41} +(-0.978424 - 4.70039i) q^{42} -0.00574917i q^{43} +(-0.316626 - 0.727588i) q^{44} +1.00000i q^{45} +(10.6959 - 2.22644i) q^{46} -12.3072 q^{47} +(2.92706 + 2.72623i) q^{48} +4.52551 q^{49} +(-1.38454 + 0.288202i) q^{50} +4.14322i q^{51} +(-0.798052 - 1.83388i) q^{52} -6.40926i q^{53} +(-0.288202 - 1.38454i) q^{54} -0.396748 q^{55} +(-7.83912 + 5.54547i) q^{56} +6.40325 q^{57} +(-1.63539 - 7.85651i) q^{58} +6.11036i q^{59} +(1.83388 - 0.798052i) q^{60} -10.7552i q^{61} +(6.28522 - 1.30832i) q^{62} +3.39492 q^{63} +(2.66362 - 7.54355i) q^{64} -1.00000 q^{65} +(0.549312 - 0.114344i) q^{66} +12.1232i q^{67} +(7.59817 - 3.30650i) q^{68} +7.72529i q^{69} +(0.978424 + 4.70039i) q^{70} -16.2844 q^{71} +(-2.30907 + 1.63346i) q^{72} -4.82153 q^{73} +(0.0399818 + 0.192075i) q^{74} -1.00000i q^{75} +(-5.11013 - 11.7428i) q^{76} +1.34693i q^{77} +(1.38454 - 0.288202i) q^{78} -7.23539 q^{79} +(-2.92706 - 2.72623i) q^{80} +1.00000 q^{81} +(14.9627 - 3.11459i) q^{82} +11.7504i q^{83} +(-2.70933 - 6.22588i) q^{84} -4.14322i q^{85} +(-0.00165692 - 0.00795993i) q^{86} +5.67448 q^{87} +(-0.648072 - 0.916120i) q^{88} -8.53201 q^{89} +(0.288202 + 1.38454i) q^{90} +3.39492i q^{91} +(14.1672 - 6.16518i) q^{92} +4.53959i q^{93} +(-17.0397 + 3.54696i) q^{94} -6.40325 q^{95} +(4.83833 + 2.93097i) q^{96} -1.60886 q^{97} +(6.26573 - 1.30426i) q^{98} +0.396748i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 16 q^{7} - 8 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 16 * q^7 - 8 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 16 q^{7} - 8 q^{8} - 20 q^{9} - 2 q^{10} - 8 q^{12} - 18 q^{14} + 20 q^{15} + 12 q^{16} + 16 q^{17} + 2 q^{18} + 8 q^{20} - 14 q^{22} + 48 q^{23} + 4 q^{24} - 20 q^{25} - 2 q^{26} - 12 q^{28} - 2 q^{30} - 8 q^{31} + 8 q^{32} - 16 q^{33} + 58 q^{34} - 20 q^{38} + 20 q^{39} - 4 q^{40} + 16 q^{41} + 6 q^{42} + 20 q^{44} - 42 q^{46} - 8 q^{47} + 8 q^{48} + 36 q^{49} + 2 q^{50} + 8 q^{52} - 2 q^{54} + 16 q^{55} + 8 q^{56} + 16 q^{57} + 52 q^{58} - 28 q^{62} + 16 q^{63} - 12 q^{64} - 20 q^{65} - 2 q^{66} - 36 q^{68} - 6 q^{70} - 8 q^{71} + 8 q^{72} + 40 q^{73} + 50 q^{74} - 36 q^{76} - 2 q^{78} - 8 q^{79} - 8 q^{80} + 20 q^{81} + 22 q^{82} - 20 q^{84} - 8 q^{86} + 8 q^{87} - 4 q^{88} + 56 q^{89} + 2 q^{90} + 68 q^{92} - 76 q^{94} - 16 q^{95} - 8 q^{96} - 48 q^{97} - 16 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 16 * q^7 - 8 * q^8 - 20 * q^9 - 2 * q^10 - 8 * q^12 - 18 * q^14 + 20 * q^15 + 12 * q^16 + 16 * q^17 + 2 * q^18 + 8 * q^20 - 14 * q^22 + 48 * q^23 + 4 * q^24 - 20 * q^25 - 2 * q^26 - 12 * q^28 - 2 * q^30 - 8 * q^31 + 8 * q^32 - 16 * q^33 + 58 * q^34 - 20 * q^38 + 20 * q^39 - 4 * q^40 + 16 * q^41 + 6 * q^42 + 20 * q^44 - 42 * q^46 - 8 * q^47 + 8 * q^48 + 36 * q^49 + 2 * q^50 + 8 * q^52 - 2 * q^54 + 16 * q^55 + 8 * q^56 + 16 * q^57 + 52 * q^58 - 28 * q^62 + 16 * q^63 - 12 * q^64 - 20 * q^65 - 2 * q^66 - 36 * q^68 - 6 * q^70 - 8 * q^71 + 8 * q^72 + 40 * q^73 + 50 * q^74 - 36 * q^76 - 2 * q^78 - 8 * q^79 - 8 * q^80 + 20 * q^81 + 22 * q^82 - 20 * q^84 - 8 * q^86 + 8 * q^87 - 4 * q^88 + 56 * q^89 + 2 * q^90 + 68 * q^92 - 76 * q^94 - 16 * q^95 - 8 * q^96 - 48 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$1$	$1$

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 $

$2$	1.38454	−	0.288202i	0.979015	−	0.203790i
$2$	1.38454	−	0.288202i	0.979015	−	0.203790i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.83388	−	0.798052i	0.916940	−	0.399026i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.288202	+	1.38454i	0.117658	+	0.565234i
$7$	−3.39492			−1.28316			−0.641580	−	0.767056i	$-0.721721\pi$
$7$	−3.39492			−1.28316			−0.641580	+	0.767056i	$0.721721\pi$
$8$	2.30907	−	1.63346i	0.816380	−	0.577515i
$9$	−1.00000			−0.333333
$10$	−0.288202	−	1.38454i	−0.0911375	−	0.437829i
$11$		−	0.396748i		−	0.119624i	−0.998210	−	0.0598120i	$-0.980950\pi$
$11$		−	0.396748i		−	0.119624i	0.998210	−	0.0598120i	$-0.0190501\pi$
$12$	0.798052	+	1.83388i	0.230378	+	0.529395i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−4.70039	+	0.978424i	−1.25623	+	0.261495i
$15$	1.00000			0.258199
$16$	2.72623	−	2.92706i	0.681557	−	0.731765i
$17$	4.14322			1.00488			0.502439	−	0.864613i	$-0.332436\pi$
$17$	4.14322			1.00488			0.502439	+	0.864613i	$0.332436\pi$
$18$	−1.38454	+	0.288202i	−0.326338	+	0.0679299i
$19$		−	6.40325i		−	1.46901i	−0.678605	−	0.734504i	$-0.737415\pi$
$19$		−	6.40325i		−	1.46901i	0.678605	−	0.734504i	$-0.262585\pi$
$20$	−0.798052	−	1.83388i	−0.178450	−	0.410068i
$21$		−	3.39492i		−	0.740833i
$22$	−0.114344	−	0.549312i	−0.0243781	−	0.117114i
$23$	7.72529			1.61083			0.805417	−	0.592709i	$-0.201941\pi$
$23$	7.72529			1.61083			0.805417	+	0.592709i	$0.201941\pi$
$24$	1.63346	+	2.30907i	0.333428	+	0.471337i
$25$	−1.00000			−0.200000
$26$	−0.288202	−	1.38454i	−0.0565211	−	0.271530i
$27$		−	1.00000i		−	0.192450i
$28$	−6.22588	+	2.70933i	−1.17658	+	0.512014i
$29$		−	5.67448i		−	1.05372i	−0.849951	−	0.526862i	$-0.823369\pi$
$29$		−	5.67448i		−	1.05372i	0.849951	−	0.526862i	$-0.176631\pi$
$30$	1.38454	−	0.288202i	0.252781	−	0.0526182i
$31$	4.53959			0.815334			0.407667	−	0.913131i	$-0.366342\pi$
$31$	4.53959			0.815334			0.407667	+	0.913131i	$0.366342\pi$
$32$	2.93097	−	4.83833i	0.518128	−	0.855303i
$33$	0.396748			0.0690650
$34$	5.73644	−	1.19408i	0.983791	−	0.204784i
$35$			3.39492i			0.573847i
$36$	−1.83388	+	0.798052i	−0.305647	+	0.133009i
$37$			0.138729i			0.0228068i	0.999935	+	0.0114034i	$0.00362990\pi$
$37$			0.138729i			0.0228068i	−0.999935	+	0.0114034i	$0.996370\pi$
$38$	−1.84543	−	8.86553i	−0.299368	−	1.43818i
$39$	1.00000			0.160128
$40$	−1.63346	−	2.30907i	−0.258273	−	0.365096i
$41$	10.8070			1.68777			0.843883	−	0.536527i	$-0.180264\pi$
$41$	10.8070			1.68777			0.843883	+	0.536527i	$0.180264\pi$
$42$	−0.978424	−	4.70039i	−0.150974	−	0.725286i
$43$		−	0.00574917i		−	0.000876740i	−1.00000		0.000438370i	$-0.999860\pi$
$43$		−	0.00574917i		−	0.000876740i	1.00000		0.000438370i	$-0.000139538\pi$
$44$	−0.316626	−	0.727588i	−0.0477331	−	0.109688i
$45$			1.00000i			0.149071i
$46$	10.6959	−	2.22644i	1.57703	−	0.328271i
$47$	−12.3072			−1.79519			−0.897594	−	0.440823i	$-0.854687\pi$
$47$	−12.3072			−1.79519			−0.897594	+	0.440823i	$0.854687\pi$
$48$	2.92706	+	2.72623i	0.422485	+	0.393497i
$49$	4.52551			0.646501
$50$	−1.38454	+	0.288202i	−0.195803	+	0.0407579i
$51$			4.14322i			0.580167i
$52$	−0.798052	−	1.83388i	−0.110670	−	0.254313i
$53$		−	6.40926i		−	0.880380i	−0.897905	−	0.440190i	$-0.854911\pi$
$53$		−	6.40926i		−	0.880380i	0.897905	−	0.440190i	$-0.145089\pi$
$54$	−0.288202	−	1.38454i	−0.0392193	−	0.188411i
$55$	−0.396748			−0.0534975
$56$	−7.83912	+	5.54547i	−1.04755	+	0.741044i
$57$	6.40325			0.848132
$58$	−1.63539	−	7.85651i	−0.214738	−	1.03161i
$59$			6.11036i			0.795502i	0.917493	+	0.397751i	$0.130209\pi$
$59$			6.11036i			0.795502i	−0.917493	+	0.397751i	$0.869791\pi$
$60$	1.83388	−	0.798052i	0.236753	−	0.103028i
$61$		−	10.7552i		−	1.37706i	−0.725207	−	0.688531i	$-0.758256\pi$
$61$		−	10.7552i		−	1.37706i	0.725207	−	0.688531i	$-0.241744\pi$
$62$	6.28522	−	1.30832i	0.798224	−	0.166156i
$63$	3.39492			0.427720
$64$	2.66362	−	7.54355i	0.332953	−	0.942943i
$65$	−1.00000			−0.124035
$66$	0.549312	−	0.114344i	0.0676156	−	0.0140747i
$67$			12.1232i			1.48109i	0.672009	+	0.740543i	$0.265432\pi$
$67$			12.1232i			1.48109i	−0.672009	+	0.740543i	$0.734568\pi$
$68$	7.59817	−	3.30650i	0.921413	−	0.400973i
$69$			7.72529i			0.930015i
$70$	0.978424	+	4.70039i	0.116944	+	0.561804i
$71$	−16.2844			−1.93260			−0.966298	−	0.257424i	$-0.917126\pi$
$71$	−16.2844			−1.93260			−0.966298	+	0.257424i	$0.917126\pi$
$72$	−2.30907	+	1.63346i	−0.272127	+	0.192505i
$73$	−4.82153			−0.564318			−0.282159	−	0.959368i	$-0.591051\pi$
$73$	−4.82153			−0.564318			−0.282159	+	0.959368i	$0.591051\pi$
$74$	0.0399818	+	0.192075i	0.00464779	+	0.0223282i
$75$		−	1.00000i		−	0.115470i
$76$	−5.11013	−	11.7428i	−0.586172	−	1.34699i
$77$			1.34693i			0.153497i
$78$	1.38454	−	0.288202i	0.156768	−	0.0326324i
$79$	−7.23539			−0.814045			−0.407023	−	0.913418i	$-0.633433\pi$
$79$	−7.23539			−0.814045			−0.407023	+	0.913418i	$0.633433\pi$
$80$	−2.92706	−	2.72623i	−0.327255	−	0.304801i
$81$	1.00000			0.111111
$82$	14.9627	−	3.11459i	1.65235	−	0.343949i
$83$			11.7504i			1.28977i	0.764278	+	0.644886i	$0.223095\pi$
$83$			11.7504i			1.28977i	−0.764278	+	0.644886i	$0.776905\pi$
$84$	−2.70933	−	6.22588i	−0.295612	−	0.679299i
$85$		−	4.14322i		−	0.449395i
$86$	−0.00165692	−	0.00795993i	−0.000178670	−	0.000858341i
$87$	5.67448			0.608368
$88$	−0.648072	−	0.916120i	−0.0690847	−	0.0976587i
$89$	−8.53201			−0.904391			−0.452196	−	0.891919i	$-0.649359\pi$
$89$	−8.53201			−0.904391			−0.452196	+	0.891919i	$0.649359\pi$
$90$	0.288202	+	1.38454i	0.0303792	+	0.145943i
$91$			3.39492i			0.355885i
$92$	14.1672	−	6.16518i	1.47704	−	0.642764i
$93$			4.53959i			0.470733i
$94$	−17.0397	+	3.54696i	−1.75752	+	0.365841i
$95$	−6.40325			−0.656960
$96$	4.83833	+	2.93097i	0.493810	+	0.299141i
$97$	−1.60886			−0.163355			−0.0816777	−	0.996659i	$-0.526028\pi$
$97$	−1.60886			−0.163355			−0.0816777	+	0.996659i	$0.526028\pi$
$98$	6.26573	−	1.30426i	0.632934	−	0.131750i
$99$			0.396748i			0.0398747i
$100$	−1.83388	+	0.798052i	−0.183388	+	0.0798052i
$101$			14.9155i			1.48415i	0.670319	+	0.742073i	$0.266157\pi$
$101$			14.9155i			1.48415i	−0.670319	+	0.742073i	$0.733843\pi$
$102$	1.19408	+	5.73644i	0.118232	+	0.567992i
$103$	10.1548			1.00058			0.500290	−	0.865858i	$-0.333227\pi$
$103$	10.1548			1.00058			0.500290	+	0.865858i	$0.333227\pi$
$104$	−1.63346	−	2.30907i	−0.160174	−	0.226423i
$105$	−3.39492			−0.331311
$106$	−1.84716	−	8.87385i	−0.179412	−	0.861905i
$107$		−	1.82095i		−	0.176038i	−0.996119	−	0.0880190i	$-0.971946\pi$
$107$		−	1.82095i		−	0.176038i	0.996119	−	0.0880190i	$-0.0280536\pi$
$108$	−0.798052	−	1.83388i	−0.0767926	−	0.176465i
$109$			10.4131i			0.997390i	0.866777	+	0.498695i	$0.166187\pi$
$109$			10.4131i			0.997390i	−0.866777	+	0.498695i	$0.833813\pi$
$110$	−0.549312	+	0.114344i	−0.0523748	+	0.0109022i
$111$	−0.138729			−0.0131675
$112$	−9.25533	+	9.93715i	−0.874546	+	0.938972i
$113$	7.22500			0.679671			0.339835	−	0.940485i	$-0.389629\pi$
$113$	7.22500			0.679671			0.339835	+	0.940485i	$0.389629\pi$
$114$	8.86553	−	1.84543i	0.830333	−	0.172840i
$115$		−	7.72529i		−	0.720387i
$116$	−4.52853	−	10.4063i	−0.420463	−	0.966201i
$117$			1.00000i			0.0924500i
$118$	1.76102	+	8.46002i	0.162115	+	0.778808i
$119$	−14.0659			−1.28942
$120$	2.30907	−	1.63346i	0.210788	−	0.149114i
$121$	10.8426			0.985690
$122$	−3.09967	−	14.8910i	−0.280631	−	1.34816i
$123$			10.8070i			0.974433i
$124$	8.32505	−	3.62282i	0.747612	−	0.325339i
$125$			1.00000i			0.0894427i
$126$	4.70039	−	0.978424i	0.418744	−	0.0871649i
$127$	10.0781			0.894284			0.447142	−	0.894463i	$-0.352442\pi$
$127$	10.0781			0.894284			0.447142	+	0.894463i	$0.352442\pi$
$128$	1.51382	−	11.2120i	0.133804	−	0.991008i
$129$	0.00574917			0.000506186
$130$	−1.38454	+	0.288202i	−0.121432	+	0.0252770i
$131$		−	15.3388i		−	1.34015i	−0.742292	−	0.670077i	$-0.766261\pi$
$131$		−	15.3388i		−	1.34015i	0.742292	−	0.670077i	$-0.233739\pi$
$132$	0.727588	−	0.316626i	0.0633284	−	0.0275587i
$133$			21.7386i			1.88497i
$134$	3.49393	+	16.7850i	0.301830	+	1.45001i
$135$	−1.00000			−0.0860663
$136$	9.56699	−	6.76778i	0.820363	−	0.580332i
$137$	16.8339			1.43822			0.719110	−	0.694897i	$-0.244550\pi$
$137$	16.8339			1.43822			0.719110	+	0.694897i	$0.244550\pi$
$138$	2.22644	+	10.6959i	0.189527	+	0.910499i
$139$			19.4538i			1.65005i	0.565096	+	0.825025i	$0.308839\pi$
$139$			19.4538i			1.65005i	−0.565096	+	0.825025i	$0.691161\pi$
$140$	2.70933	+	6.22588i	0.228980	+	0.526183i
$141$		−	12.3072i		−	1.03645i
$142$	−22.5463	+	4.69318i	−1.89204	+	0.393843i
$143$	−0.396748			−0.0331777
$144$	−2.72623	+	2.92706i	−0.227186	+	0.243922i
$145$	−5.67448			−0.471240
$146$	−6.67559	+	1.38958i	−0.552476	+	0.115002i
$147$			4.52551i			0.373257i
$148$	0.110713	+	0.254411i	0.00910052	+	0.0209125i
$149$		−	0.699116i		−	0.0572738i	−0.999590	−	0.0286369i	$-0.990883\pi$
$149$		−	0.699116i		−	0.0572738i	0.999590	−	0.0286369i	$-0.00911666\pi$
$150$	−0.288202	−	1.38454i	−0.0235316	−	0.113047i
$151$	−2.67552			−0.217731			−0.108865	−	0.994056i	$-0.534722\pi$
$151$	−2.67552			−0.217731			−0.108865	+	0.994056i	$0.534722\pi$
$152$	−10.4595	−	14.7856i	−0.848374	−	1.19927i
$153$	−4.14322			−0.334959
$154$	0.388188	+	1.86487i	0.0312811	+	0.150276i
$155$		−	4.53959i		−	0.364628i
$156$	1.83388	−	0.798052i	0.146828	−	0.0638953i
$157$		−	11.7388i		−	0.936859i	−0.883501	−	0.468429i	$-0.844820\pi$
$157$		−	11.7388i		−	0.936859i	0.883501	−	0.468429i	$-0.155180\pi$
$158$	−10.0177	+	2.08525i	−0.796962	+	0.165894i
$159$	6.40926			0.508287
$160$	−4.83833	−	2.93097i	−0.382503	−	0.231714i
$161$	−26.2268			−2.06696
$162$	1.38454	−	0.288202i	0.108779	−	0.0226433i
$163$			14.9680i			1.17239i	0.810172	+	0.586193i	$0.199374\pi$
$163$			14.9680i			1.17239i	−0.810172	+	0.586193i	$0.800626\pi$
$164$	19.8187	−	8.62453i	1.54758	−	0.673463i
$165$		−	0.396748i		−	0.0308868i
$166$	3.38649	+	16.2688i	0.262842	+	1.26271i
$167$	−22.4410			−1.73654			−0.868269	−	0.496094i	$-0.834767\pi$
$167$	−22.4410			−1.73654			−0.868269	+	0.496094i	$0.834767\pi$
$168$	−5.54547	−	7.83912i	−0.427842	−	0.604801i
$169$	−1.00000			−0.0769231
$170$	−1.19408	−	5.73644i	−0.0915821	−	0.439965i
$171$			6.40325i			0.489669i
$172$	−0.00458813	−	0.0105433i	−0.000349842	−	0.000803918i
$173$			7.75619i			0.589692i	0.955545	+	0.294846i	$0.0952684\pi$
$173$			7.75619i			0.589692i	−0.955545	+	0.294846i	$0.904732\pi$
$174$	7.85651	−	1.63539i	0.595601	−	0.123979i
$175$	3.39492			0.256632
$176$	−1.16131	−	1.08163i	−0.0875367	−	0.0815306i
$177$	−6.11036			−0.459283
$178$	−11.8129	+	2.45894i	−0.885412	+	0.184305i
$179$		−	17.2528i		−	1.28954i	−0.764378	−	0.644768i	$-0.776954\pi$
$179$		−	17.2528i		−	1.28954i	0.764378	−	0.644768i	$-0.223046\pi$
$180$	0.798052	+	1.83388i	0.0594833	+	0.136689i
$181$		−	7.78316i		−	0.578518i	−0.957251	−	0.289259i	$-0.906591\pi$
$181$		−	7.78316i		−	0.578518i	0.957251	−	0.289259i	$-0.0934089\pi$
$182$	0.978424	+	4.70039i	0.0725256	+	0.348416i
$183$	10.7552			0.795047
$184$	17.8382	−	12.6189i	1.31505	−	0.930281i
$185$	0.138729			0.0101995
$186$	1.30832	+	6.28522i	0.0959305	+	0.460855i
$187$		−	1.64381i		−	0.120208i
$188$	−22.5699	+	9.82178i	−1.64608	+	0.716327i
$189$			3.39492i			0.246944i
$190$	−8.86553	+	1.84543i	−0.643173	+	0.133882i
$191$	6.45160			0.466821			0.233411	−	0.972378i	$-0.425011\pi$
$191$	6.45160			0.466821			0.233411	+	0.972378i	$0.425011\pi$
$192$	7.54355	+	2.66362i	0.544409	+	0.192230i
$193$	19.4499			1.40003			0.700017	−	0.714126i	$-0.253176\pi$
$193$	19.4499			1.40003			0.700017	+	0.714126i	$0.253176\pi$
$194$	−2.22753	+	0.463678i	−0.159927	+	0.0332901i
$195$		−	1.00000i		−	0.0716115i
$196$	8.29923	−	3.61159i	0.592802	−	0.257971i
$197$		−	15.9730i		−	1.13803i	−0.822329	−	0.569013i	$-0.807325\pi$
$197$		−	15.9730i		−	1.13803i	0.822329	−	0.569013i	$-0.192675\pi$
$198$	0.114344	+	0.549312i	0.00812604	+	0.0390379i
$199$	−8.58841			−0.608816			−0.304408	−	0.952542i	$-0.598459\pi$
$199$	−8.58841			−0.608816			−0.304408	+	0.952542i	$0.598459\pi$
$200$	−2.30907	+	1.63346i	−0.163276	+	0.115503i
$201$	−12.1232			−0.855106
$202$	4.29867	+	20.6510i	0.302453	+	1.45300i
$203$			19.2644i			1.35210i
$204$	3.30650	+	7.59817i	0.231502	+	0.531978i
$205$		−	10.8070i		−	0.754792i
$206$	14.0597	−	2.92663i	0.979583	−	0.203908i
$207$	−7.72529			−0.536945
$208$	−2.92706	−	2.72623i	−0.202955	−	0.189030i
$209$	−2.54048			−0.175729
$210$	−4.70039	+	0.978424i	−0.324358	+	0.0675176i
$211$		−	1.87864i		−	0.129331i	−0.997907	−	0.0646656i	$-0.979402\pi$
$211$		−	1.87864i		−	0.129331i	0.997907	−	0.0646656i	$-0.0205981\pi$
$212$	−5.11492	−	11.7538i	−0.351294	−	0.807255i
$213$		−	16.2844i		−	1.11579i
$214$	−0.524802	−	2.52117i	−0.0358747	−	0.172344i
$215$	−0.00574917			−0.000392090
$216$	−1.63346	−	2.30907i	−0.111143	−	0.157112i
$217$	−15.4115			−1.04620
$218$	3.00106	+	14.4173i	0.203258	+	0.976460i
$219$		−	4.82153i		−	0.325809i
$220$	−0.727588	+	0.316626i	−0.0490540	+	0.0213469i
$221$		−	4.14322i		−	0.278703i
$222$	−0.192075	+	0.0399818i	−0.0128912	+	0.00268340i
$223$	17.7336			1.18753			0.593764	−	0.804639i	$-0.297641\pi$
$223$	17.7336			1.18753			0.593764	+	0.804639i	$0.297641\pi$
$224$	−9.95043	+	16.4257i	−0.664841	+	1.09749i
$225$	1.00000			0.0666667
$226$	10.0033	−	2.08226i	0.665408	−	0.138510i
$227$			21.6331i			1.43584i	0.696126	+	0.717919i	$0.254905\pi$
$227$			21.6331i			1.43584i	−0.696126	+	0.717919i	$0.745095\pi$
$228$	11.7428	−	5.11013i	0.777686	−	0.338427i
$229$			17.0379i			1.12590i	0.826492	+	0.562948i	$0.190333\pi$
$229$			17.0379i			1.12590i	−0.826492	+	0.562948i	$0.809667\pi$
$230$	−2.22644	−	10.6959i	−0.146807	−	0.705269i
$231$	−1.34693			−0.0886214
$232$	−9.26902	−	13.1028i	−0.608541	−	0.860239i
$233$	13.8709			0.908714			0.454357	−	0.890820i	$-0.349869\pi$
$233$	13.8709			0.908714			0.454357	+	0.890820i	$0.349869\pi$
$234$	0.288202	+	1.38454i	0.0188404	+	0.0905099i
$235$			12.3072i			0.802832i
$236$	4.87639	+	11.2057i	0.317426	+	0.729427i
$237$		−	7.23539i		−	0.469989i
$238$	−19.4748	+	4.05382i	−1.26236	+	0.262770i
$239$	−18.3021			−1.18386			−0.591932	−	0.805988i	$-0.701635\pi$
$239$	−18.3021			−1.18386			−0.591932	+	0.805988i	$0.701635\pi$
$240$	2.72623	−	2.92706i	0.175977	−	0.188941i
$241$	13.8153			0.889922			0.444961	−	0.895550i	$-0.353218\pi$
$241$	13.8153			0.889922			0.444961	+	0.895550i	$0.353218\pi$
$242$	15.0120	−	3.12486i	0.965005	−	0.200873i
$243$			1.00000i			0.0641500i
$244$	−8.58321	−	19.7237i	−0.549483	−	1.26268i
$245$		−	4.52551i		−	0.289124i
$246$	3.11459	+	14.9627i	0.198579	+	0.953984i
$247$	−6.40325			−0.407429
$248$	10.4822	−	7.41523i	0.665622	−	0.470867i
$249$	−11.7504			−0.744651
$250$	0.288202	+	1.38454i	0.0182275	+	0.0875657i
$251$			14.0408i			0.886249i	0.896460	+	0.443125i	$0.146130\pi$
$251$			14.0408i			0.886249i	−0.896460	+	0.443125i	$0.853870\pi$
$252$	6.22588	−	2.70933i	0.392194	−	0.170671i
$253$		−	3.06499i		−	0.192694i
$254$	13.9534	−	2.90452i	0.875517	−	0.182246i
$255$	4.14322			0.259458
$256$	−1.13538	−	15.9597i	−0.0709613	−	0.997479i
$257$	−17.8821			−1.11545			−0.557727	−	0.830025i	$-0.688326\pi$
$257$	−17.8821			−1.11545			−0.557727	+	0.830025i	$0.688326\pi$
$258$	0.00795993	−	0.00165692i	0.000495564	−	0.000103155i
$259$		−	0.470973i		−	0.0292648i
$260$	−1.83388	+	0.798052i	−0.113732	+	0.0494931i
$261$			5.67448i			0.351241i
$262$	−4.42066	−	21.2371i	−0.273109	−	1.31203i
$263$	26.7434			1.64907			0.824534	−	0.565812i	$-0.191437\pi$
$263$	26.7434			1.64907			0.824534	+	0.565812i	$0.191437\pi$
$264$	0.916120	−	0.648072i	0.0563833	−	0.0398861i
$265$	−6.40926			−0.393718
$266$	6.26509	+	30.0978i	0.384138	+	1.84542i
$267$		−	8.53201i		−	0.522150i
$268$	9.67495	+	22.2325i	0.590992	+	1.35807i
$269$		−	28.9143i		−	1.76294i	−0.472244	−	0.881468i	$-0.656556\pi$
$269$		−	28.9143i		−	1.76294i	0.472244	−	0.881468i	$-0.343444\pi$
$270$	−1.38454	+	0.288202i	−0.0842602	+	0.0175394i
$271$	6.44150			0.391293			0.195647	−	0.980674i	$-0.437319\pi$
$271$	6.44150			0.391293			0.195647	+	0.980674i	$0.437319\pi$
$272$	11.2954	−	12.1275i	0.684882	−	0.735335i
$273$	−3.39492			−0.205470
$274$	23.3072	−	4.85157i	1.40804	−	0.293094i
$275$			0.396748i			0.0239248i
$276$	6.16518	+	14.1672i	0.371100	+	0.852768i
$277$			17.9769i			1.08013i	0.841625	+	0.540063i	$0.181599\pi$
$277$			17.9769i			1.08013i	−0.841625	+	0.540063i	$0.818401\pi$
$278$	5.60663	+	26.9345i	0.336263	+	1.61542i
$279$	−4.53959			−0.271778
$280$	5.54547	+	7.83912i	0.331405	+	0.468477i
$281$	3.10865			0.185447			0.0927233	−	0.995692i	$-0.470443\pi$
$281$	3.10865			0.185447			0.0927233	+	0.995692i	$0.470443\pi$
$282$	−3.54696	−	17.0397i	−0.211218	−	1.01470i
$283$			21.3067i			1.26655i	0.773925	+	0.633277i	$0.218291\pi$
$283$			21.3067i			1.26655i	−0.773925	+	0.633277i	$0.781709\pi$
$284$	−29.8635	+	12.9958i	−1.77207	+	0.771156i
$285$		−	6.40325i		−	0.379296i
$286$	−0.549312	+	0.114344i	−0.0324815	+	0.00676128i
$287$	−36.6889			−2.16568
$288$	−2.93097	+	4.83833i	−0.172709	+	0.285101i
$289$	0.166272			0.00978068
$290$	−7.85651	+	1.63539i	−0.461350	+	0.0960337i
$291$		−	1.60886i		−	0.0943133i
$292$	−8.84211	+	3.84783i	−0.517445	+	0.225177i
$293$			32.3271i			1.88857i	0.329126	+	0.944286i	$0.393246\pi$
$293$			32.3271i			1.88857i	−0.329126	+	0.944286i	$0.606754\pi$
$294$	1.30426	+	6.26573i	0.0760660	+	0.365425i
$295$	6.11036			0.355759
$296$	0.226607	+	0.320334i	0.0131713	+	0.0186190i
$297$	−0.396748			−0.0230217
$298$	−0.201487	−	0.967952i	−0.0116718	−	0.0560719i
$299$		−	7.72529i		−	0.446765i
$300$	−0.798052	−	1.83388i	−0.0460755	−	0.105879i
$301$			0.0195180i			0.00112500i
$302$	−3.70436	+	0.771091i	−0.213162	+	0.0443713i
$303$	−14.9155			−0.856872
$304$	−18.7427	−	17.4567i	−1.07497	−	1.00121i
$305$	−10.7552			−0.615841
$306$	−5.73644	+	1.19408i	−0.327930	+	0.0682612i
$307$		−	12.9514i		−	0.739173i	−0.929196	−	0.369587i	$-0.879499\pi$
$307$		−	12.9514i		−	0.739173i	0.929196	−	0.369587i	$-0.120501\pi$
$308$	1.07492	+	2.47011i	0.0612492	+	0.140747i
$309$			10.1548i			0.577685i
$310$	−1.30832	−	6.28522i	−0.0743074	−	0.356976i
$311$	−16.6519			−0.944240			−0.472120	−	0.881534i	$-0.656511\pi$
$311$	−16.6519			−0.944240			−0.472120	+	0.881534i	$0.656511\pi$
$312$	2.30907	−	1.63346i	0.130725	−	0.0924764i
$313$	−19.1587			−1.08292			−0.541458	−	0.840728i	$-0.682127\pi$
$313$	−19.1587			−1.08292			−0.541458	+	0.840728i	$0.682127\pi$
$314$	−3.38315	−	16.2528i	−0.190922	−	0.917198i
$315$		−	3.39492i		−	0.191282i
$316$	−13.2688	+	5.77422i	−0.746430	+	0.324825i
$317$		−	0.550475i		−	0.0309178i	−0.999881	−	0.0154589i	$-0.995079\pi$
$317$		−	0.550475i		−	0.0309178i	0.999881	−	0.0154589i	$-0.00492091\pi$
$318$	8.87385	−	1.84716i	0.497621	−	0.103584i
$319$	−2.25134			−0.126051
$320$	−7.54355	−	2.66362i	−0.421697	−	0.148901i
$321$	1.82095			0.101636
$322$	−36.3119	+	7.55860i	−2.02358	+	0.421225i
$323$		−	26.5301i		−	1.47617i
$324$	1.83388	−	0.798052i	0.101882	−	0.0443362i
$325$			1.00000i			0.0554700i
$326$	4.31381	+	20.7238i	0.238920	+	1.14778i
$327$	−10.4131			−0.575844
$328$	24.9541	−	17.6528i	1.37786	−	0.974711i
$329$	41.7820			2.30351
$330$	−0.114344	−	0.549312i	−0.00629441	−	0.0302386i
$331$		−	20.2879i		−	1.11513i	−0.830135	−	0.557563i	$-0.811737\pi$
$331$		−	20.2879i		−	1.11513i	0.830135	−	0.557563i	$-0.188263\pi$
$332$	9.37742	+	21.5488i	0.514653	+	1.18264i
$333$		−	0.138729i		−	0.00760228i
$334$	−31.0704	+	6.46754i	−1.70010	+	0.353888i
$335$	12.1232			0.662362
$336$	−9.93715	−	9.25533i	−0.542116	−	0.504920i
$337$	0.423022			0.0230435			0.0115217	−	0.999934i	$-0.496332\pi$
$337$	0.423022			0.0230435			0.0115217	+	0.999934i	$0.496332\pi$
$338$	−1.38454	+	0.288202i	−0.0753088	+	0.0156761i
$339$			7.22500i			0.392408i
$340$	−3.30650	−	7.59817i	−0.179320	−	0.412068i
$341$		−	1.80107i		−	0.0975335i
$342$	1.84543	+	8.86553i	0.0997894	+	0.479393i
$343$	8.40072			0.453596
$344$	−0.00939103	−	0.0132752i	−0.000506330	−	0.000715753i
$345$	7.72529			0.415915
$346$	2.23535	+	10.7387i	0.120173	+	0.577317i
$347$			8.60456i			0.461917i	0.972964	+	0.230959i	$0.0741862\pi$
$347$			8.60456i			0.461917i	−0.972964	+	0.230959i	$0.925814\pi$
$348$	10.4063	−	4.52853i	0.557836	−	0.242754i
$349$		−	22.2219i		−	1.18951i	−0.803908	−	0.594754i	$-0.797249\pi$
$349$		−	22.2219i		−	1.18951i	0.803908	−	0.594754i	$-0.202751\pi$
$350$	4.70039	−	0.978424i	0.251247	−	0.0522989i
$351$	−1.00000			−0.0533761
$352$	−1.91960	−	1.16286i	−0.102315	−	0.0619805i
$353$	−16.7816			−0.893196			−0.446598	−	0.894735i	$-0.647365\pi$
$353$	−16.7816			−0.893196			−0.446598	+	0.894735i	$0.647365\pi$
$354$	−8.46002	+	1.76102i	−0.449645	+	0.0935971i
$355$			16.2844i			0.864284i
$356$	−15.6467	+	6.80899i	−0.829272	+	0.360876i
$357$		−	14.0659i		−	0.744447i
$358$	−4.97230	−	23.8872i	−0.262794	−	1.26248i
$359$	4.32450			0.228239			0.114119	−	0.993467i	$-0.463595\pi$
$359$	4.32450			0.228239			0.114119	+	0.993467i	$0.463595\pi$
$360$	1.63346	+	2.30907i	0.0860909	+	0.121699i
$361$	−22.0017			−1.15798
$362$	−2.24312	−	10.7761i	−0.117896	−	0.566378i
$363$			10.8426i			0.569088i
$364$	2.70933	+	6.22588i	0.142007	+	0.326325i
$365$			4.82153i			0.252371i
$366$	14.8910	−	3.09967i	0.778363	−	0.162022i
$367$	−3.26276			−0.170315			−0.0851574	−	0.996368i	$-0.527139\pi$
$367$	−3.26276			−0.170315			−0.0851574	+	0.996368i	$0.527139\pi$
$368$	21.0609	−	22.6124i	1.09787	−	1.17875i
$369$	−10.8070			−0.562589
$370$	0.192075	−	0.0399818i	0.00998548	−	0.00207856i
$371$			21.7590i			1.12967i
$372$	3.62282	+	8.32505i	0.187835	+	0.431634i
$373$			16.9512i			0.877701i	0.898560	+	0.438851i	$0.144614\pi$
$373$			16.9512i			0.877701i	−0.898560	+	0.438851i	$0.855386\pi$
$374$	−0.473751	−	2.27592i	−0.0244971	−	0.117685i
$375$	−1.00000			−0.0516398
$376$	−28.4182	+	20.1033i	−1.46556	+	1.03675i
$377$	−5.67448			−0.292250
$378$	0.978424	+	4.70039i	0.0503247	+	0.241762i
$379$			33.6603i			1.72902i	0.502620	+	0.864508i	$0.332370\pi$
$379$			33.6603i			1.72902i	−0.502620	+	0.864508i	$0.667630\pi$
$380$	−11.7428	+	5.11013i	−0.602393	+	0.262144i
$381$			10.0781i			0.516315i
$382$	8.93247	−	1.85936i	0.457025	−	0.0951333i
$383$	−30.2431			−1.54535			−0.772676	−	0.634801i	$-0.781082\pi$
$383$	−30.2431			−1.54535			−0.772676	+	0.634801i	$0.781082\pi$
$384$	11.2120	+	1.51382i	0.572159	+	0.0772516i
$385$	1.34693			0.0686459
$386$	26.9291	−	5.60550i	1.37065	−	0.285312i
$387$			0.00574917i			0.000292247i
$388$	−2.95046	+	1.28396i	−0.149787	+	0.0651831i
$389$		−	1.13392i		−	0.0574919i	−0.999587	−	0.0287459i	$-0.990849\pi$
$389$		−	1.13392i		−	0.0574919i	0.999587	−	0.0287459i	$-0.00915138\pi$
$390$	−0.288202	−	1.38454i	−0.0145937	−	0.0701087i
$391$	32.0076			1.61869
$392$	10.4497	−	7.39223i	0.527790	−	0.373364i
$393$	15.3388			0.773738
$394$	−4.60344	−	22.1151i	−0.231918	−	1.11414i
$395$			7.23539i			0.364052i
$396$	0.316626	+	0.727588i	0.0159110	+	0.0365627i
$397$			3.71437i			0.186419i	0.995647	+	0.0932094i	$0.0297126\pi$
$397$			3.71437i			0.186419i	−0.995647	+	0.0932094i	$0.970287\pi$
$398$	−11.8910	+	2.47520i	−0.596040	+	0.124070i
$399$	−21.7386			−1.08829
$400$	−2.72623	+	2.92706i	−0.136311	+	0.146353i
$401$	−14.2660			−0.712411			−0.356206	−	0.934408i	$-0.615930\pi$
$401$	−14.2660			−0.712411			−0.356206	+	0.934408i	$0.615930\pi$
$402$	−16.7850	+	3.49393i	−0.837161	+	0.174262i
$403$		−	4.53959i		−	0.226133i
$404$	11.9033	+	27.3532i	0.592213	+	1.36087i
$405$		−	1.00000i		−	0.0496904i
$406$	5.55204	+	26.6723i	0.275543	+	1.32372i
$407$	0.0550403			0.00272824
$408$	6.76778	+	9.56699i	0.335055	+	0.473637i
$409$	7.42941			0.367361			0.183680	−	0.982986i	$-0.441199\pi$
$409$	7.42941			0.367361			0.183680	+	0.982986i	$0.441199\pi$
$410$	−3.11459	−	14.9627i	−0.153819	−	0.738953i
$411$			16.8339i			0.830356i
$412$	18.6226	−	8.10404i	0.917472	−	0.399257i
$413$		−	20.7442i		−	1.02076i
$414$	−10.6959	+	2.22644i	−0.525677	+	0.109424i
$415$	11.7504			0.576804
$416$	−4.83833	−	2.93097i	−0.237218	−	0.143703i
$417$	−19.4538			−0.952657
$418$	−3.51738	+	0.732171i	−0.172041	+	0.0358116i
$419$		−	4.77450i		−	0.233250i	−0.993176	−	0.116625i	$-0.962792\pi$
$419$		−	4.77450i		−	0.233250i	0.993176	−	0.116625i	$-0.0372075\pi$
$420$	−6.22588	+	2.70933i	−0.303792	+	0.132202i
$421$			14.3349i			0.698639i	0.937004	+	0.349319i	$0.113587\pi$
$421$			14.3349i			0.698639i	−0.937004	+	0.349319i	$0.886413\pi$
$422$	−0.541429	−	2.60105i	−0.0263563	−	0.126617i
$423$	12.3072			0.598396
$424$	−10.4693	−	14.7994i	−0.508433	−	0.718724i
$425$	−4.14322			−0.200976
$426$	−4.69318	−	22.5463i	−0.227385	−	1.09237i
$427$			36.5131i			1.76699i
$428$	−1.45321	−	3.33940i	−0.0702437	−	0.161416i
$429$		−	0.396748i		−	0.0191552i
$430$	−0.00795993	+	0.00165692i	−0.000383862	+	7.99039e-5i
$431$	6.99223			0.336804			0.168402	−	0.985718i	$-0.446139\pi$
$431$	6.99223			0.336804			0.168402	+	0.985718i	$0.446139\pi$
$432$	−2.92706	−	2.72623i	−0.140828	−	0.131166i
$433$	29.2064			1.40357			0.701784	−	0.712390i	$-0.252387\pi$
$433$	29.2064			1.40357			0.701784	+	0.712390i	$0.252387\pi$
$434$	−21.3378	+	4.44164i	−1.02425	+	0.213205i
$435$		−	5.67448i		−	0.272070i
$436$	8.31016	+	19.0963i	0.397985	+	0.914547i
$437$		−	49.4670i		−	2.36633i
$438$	−1.38958	−	6.67559i	−0.0663965	−	0.318972i
$439$	26.0530			1.24344			0.621721	−	0.783239i	$-0.286434\pi$
$439$	26.0530			1.24344			0.621721	+	0.783239i	$0.286434\pi$
$440$	−0.916120	+	0.648072i	−0.0436743	+	0.0308956i
$441$	−4.52551			−0.215500
$442$	−1.19408	−	5.73644i	−0.0567968	−	0.272854i
$443$		−	3.98911i		−	0.189528i	−0.995500	−	0.0947641i	$-0.969790\pi$
$443$		−	3.98911i		−	0.189528i	0.995500	−	0.0947641i	$-0.0302097\pi$
$444$	−0.254411	+	0.110713i	−0.0120738	+	0.00525419i
$445$			8.53201i			0.404456i
$446$	24.5528	−	5.11085i	1.16261	−	0.242006i
$447$	0.699116			0.0330671
$448$	−9.04280	+	25.6098i	−0.427232	+	1.20995i
$449$	−28.6490			−1.35203			−0.676015	−	0.736888i	$-0.736295\pi$
$449$	−28.6490			−1.35203			−0.676015	+	0.736888i	$0.736295\pi$
$450$	1.38454	−	0.288202i	0.0652676	−	0.0135860i
$451$		−	4.28765i		−	0.201897i
$452$	13.2498	−	5.76593i	0.623217	−	0.271206i
$453$		−	2.67552i		−	0.125707i
$454$	6.23470	+	29.9518i	0.292609	+	1.40571i
$455$	3.39492			0.159156
$456$	14.7856	−	10.4595i	0.692398	−	0.489809i
$457$	6.75071			0.315785			0.157892	−	0.987456i	$-0.449530\pi$
$457$	6.75071			0.315785			0.157892	+	0.987456i	$0.449530\pi$
$458$	4.91035	+	23.5896i	0.229446	+	1.10227i
$459$		−	4.14322i		−	0.193389i
$460$	−6.16518	−	14.1672i	−0.287453	−	0.660551i
$461$		−	14.4044i		−	0.670882i	−0.942061	−	0.335441i	$-0.891115\pi$
$461$		−	14.4044i		−	0.670882i	0.942061	−	0.335441i	$-0.108885\pi$
$462$	−1.86487	+	0.388188i	−0.0867617	+	0.0180601i
$463$	16.1305			0.749646			0.374823	−	0.927096i	$-0.377703\pi$
$463$	16.1305			0.749646			0.374823	+	0.927096i	$0.377703\pi$
$464$	−16.6095	−	15.4699i	−0.771079	−	0.718172i
$465$	4.53959			0.210518
$466$	19.2048	−	3.99763i	0.889644	−	0.185186i
$467$			2.95857i			0.136906i	0.997654	+	0.0684530i	$0.0218063\pi$
$467$			2.95857i			0.136906i	−0.997654	+	0.0684530i	$0.978194\pi$
$468$	0.798052	+	1.83388i	0.0368900	+	0.0847711i
$469$		−	41.1574i		−	1.90047i
$470$	3.54696	+	17.0397i	0.163609	+	0.785985i
$471$	11.7388			0.540896
$472$	9.98103	+	14.1093i	0.459414	+	0.649432i
$473$	−0.00228097			−0.000104879
$474$	−2.08525	−	10.0177i	−0.0957789	−	0.460126i
$475$			6.40325i			0.293801i
$476$	−25.7952	+	11.2253i	−1.18232	+	0.514512i
$477$			6.40926i			0.293460i
$478$	−25.3399	+	5.27470i	−1.15902	+	0.241259i
$479$	−15.4082			−0.704017			−0.352008	−	0.935997i	$-0.614501\pi$
$479$	−15.4082			−0.704017			−0.352008	+	0.935997i	$0.614501\pi$
$480$	2.93097	−	4.83833i	0.133780	−	0.220838i
$481$	0.138729			0.00632548
$482$	19.1278	−	3.98160i	0.871246	−	0.181357i
$483$		−	26.2268i		−	1.19336i
$484$	19.8840	−	8.65295i	0.903818	−	0.393316i
$485$			1.60886i			0.0730548i
$486$	0.288202	+	1.38454i	0.0130731	+	0.0628038i
$487$	35.2141			1.59570			0.797851	−	0.602855i	$-0.205970\pi$
$487$	35.2141			1.59570			0.797851	+	0.602855i	$0.205970\pi$
$488$	−17.5682	−	24.8345i	−0.795274	−	1.12421i
$489$	−14.9680			−0.676877
$490$	−1.30426	−	6.26573i	−0.0589205	−	0.283057i
$491$			11.8979i			0.536946i	0.963287	+	0.268473i	$0.0865190\pi$
$491$			11.8979i			0.536946i	−0.963287	+	0.268473i	$0.913481\pi$
$492$	8.62453	+	19.8187i	0.388824	+	0.893496i
$493$		−	23.5106i		−	1.05886i
$494$	−8.86553	+	1.84543i	−0.398879	+	0.0830298i
$495$	0.396748			0.0178325
$496$	12.3759	−	13.2876i	0.555696	−	0.596633i
$497$	55.2841			2.47983
$498$	−16.2688	+	3.38649i	−0.729024	+	0.151752i
$499$		−	21.1824i		−	0.948255i	−0.880456	−	0.474127i	$-0.842764\pi$
$499$		−	21.1824i		−	0.948255i	0.880456	−	0.474127i	$-0.157236\pi$
$500$	0.798052	+	1.83388i	0.0356900	+	0.0820136i
$501$		−	22.4410i		−	1.00259i
$502$	4.04659	+	19.4400i	0.180608	+	0.867651i
$503$	−9.48031			−0.422706			−0.211353	−	0.977410i	$-0.567787\pi$
$503$	−9.48031			−0.422706			−0.211353	+	0.977410i	$0.567787\pi$
$504$	7.83912	−	5.54547i	0.349182	−	0.247015i
$505$	14.9155			0.663730
$506$	−0.883337	−	4.24359i	−0.0392691	−	0.188651i
$507$		−	1.00000i		−	0.0444116i
$508$	18.4820	−	8.04282i	0.820004	−	0.356842i
$509$			2.37660i			0.105341i	0.998612	+	0.0526705i	$0.0167733\pi$
$509$			2.37660i			0.105341i	−0.998612	+	0.0526705i	$0.983227\pi$
$510$	5.73644	−	1.19408i	0.254014	−	0.0528749i
$511$	16.3687			0.724110
$512$	−6.17158	−	21.7695i	−0.272748	−	0.962086i
$513$	−6.40325			−0.282711
$514$	−24.7584	+	5.15365i	−1.09205	+	0.227318i
$515$		−	10.1548i		−	0.447473i
$516$	0.0105433	−	0.00458813i	0.000464142	−	0.000201981i
$517$			4.88285i			0.214748i
$518$	−0.135735	−	0.652079i	−0.00596386	−	0.0286507i
$519$	−7.75619			−0.340459
$520$	−2.30907	+	1.63346i	−0.101259	+	0.0716319i
$521$	−34.5802			−1.51499			−0.757494	−	0.652842i	$-0.773576\pi$
$521$	−34.5802			−1.51499			−0.757494	+	0.652842i	$0.773576\pi$
$522$	1.63539	+	7.85651i	0.0715793	+	0.343870i
$523$		−	1.83692i		−	0.0803228i	−0.999193	−	0.0401614i	$-0.987213\pi$
$523$		−	1.83692i		−	0.0803228i	0.999193	−	0.0401614i	$-0.0127872\pi$
$524$	−12.2411	−	28.1294i	−0.534756	−	1.22884i
$525$			3.39492i			0.148167i
$526$	37.0272	−	7.70750i	1.61446	−	0.336063i
$527$	18.8085			0.819311
$528$	1.08163	−	1.16131i	0.0470717	−	0.0505394i
$529$	36.6801			1.59479
$530$	−8.87385	+	1.84716i	−0.385456	+	0.0802356i
$531$		−	6.11036i		−	0.265167i
$532$	17.3485	+	39.8659i	0.752153	+	1.72841i
$533$		−	10.8070i		−	0.468102i
$534$	−2.45894	−	11.8129i	−0.106409	−	0.511193i
$535$	−1.82095			−0.0787266
$536$	19.8028	+	27.9934i	0.855350	+	1.20913i
$537$	17.2528			0.744514
$538$	−8.33315	−	40.0329i	−0.359268	−	1.72594i
$539$		−	1.79549i		−	0.0773371i
$540$	−1.83388	+	0.798052i	−0.0789176	+	0.0343427i
$541$			19.5442i			0.840269i	0.907462	+	0.420135i	$0.138017\pi$
$541$			19.5442i			0.840269i	−0.907462	+	0.420135i	$0.861983\pi$
$542$	8.91849	−	1.85645i	0.383082	−	0.0797415i
$543$	7.78316			0.334008
$544$	12.1437	−	20.0462i	0.520655	−	0.859476i
$545$	10.4131			0.446047
$546$	−4.70039	+	0.978424i	−0.201158	+	0.0418727i
$547$			36.9621i			1.58038i	0.612860	+	0.790192i	$0.290019\pi$
$547$			36.9621i			1.58038i	−0.612860	+	0.790192i	$0.709981\pi$
$548$	30.8714	−	13.4343i	1.31876	−	0.573887i
$549$			10.7552i			0.459021i
$550$	0.114344	+	0.549312i	0.00487563	+	0.0234227i
$551$	−36.3351			−1.54793
$552$	12.6189	+	17.8382i	0.537098	+	0.759246i
$553$	24.5636			1.04455
$554$	5.18097	+	24.8896i	0.220118	+	1.05746i
$555$			0.138729i			0.00588870i
$556$	15.5252	+	35.6759i	0.658413	+	1.51300i
$557$			30.1003i			1.27539i	0.770289	+	0.637695i	$0.220112\pi$
$557$			30.1003i			1.27539i	−0.770289	+	0.637695i	$0.779888\pi$
$558$	−6.28522	+	1.30832i	−0.266075	+	0.0553855i
$559$	−0.00574917			−0.000243164
$560$	9.93715	+	9.25533i	0.419921	+	0.391109i
$561$	1.64381			0.0694019
$562$	4.30404	−	0.895920i	0.181555	−	0.0377921i
$563$			5.42571i			0.228666i	0.993442	+	0.114333i	$0.0364731\pi$
$563$			5.42571i			0.228666i	−0.993442	+	0.114333i	$0.963527\pi$
$564$	−9.82178	−	22.5699i	−0.413571	−	0.950364i
$565$		−	7.22500i		−	0.303958i
$566$	6.14065	+	29.5000i	0.258111	+	1.23998i
$567$	−3.39492			−0.142573
$568$	−37.6017	+	26.5998i	−1.57773	+	1.11610i
$569$	11.5792			0.485426			0.242713	−	0.970098i	$-0.421963\pi$
$569$	11.5792			0.485426			0.242713	+	0.970098i	$0.421963\pi$
$570$	−1.84543	−	8.86553i	−0.0772966	−	0.371336i
$571$			1.46060i			0.0611243i	0.999533	+	0.0305621i	$0.00972975\pi$
$571$			1.46060i			0.0611243i	−0.999533	+	0.0305621i	$0.990270\pi$
$572$	−0.727588	+	0.316626i	−0.0304220	+	0.0132388i
$573$			6.45160i			0.269519i
$574$	−50.7971	+	10.5738i	−2.12023	+	0.441342i
$575$	−7.72529			−0.322167
$576$	−2.66362	+	7.54355i	−0.110984	+	0.314314i
$577$	−4.03172			−0.167843			−0.0839214	−	0.996472i	$-0.526744\pi$
$577$	−4.03172			−0.167843			−0.0839214	+	0.996472i	$0.526744\pi$
$578$	0.230209	−	0.0479198i	0.00957543	−	0.00199320i
$579$			19.4499i			0.808310i
$580$	−10.4063	+	4.52853i	−0.432098	+	0.188037i
$581$		−	39.8917i		−	1.65499i
$582$	−0.463678	−	2.22753i	−0.0192201	−	0.0923341i
$583$	−2.54286			−0.105315
$584$	−11.1333	+	7.87578i	−0.460698	+	0.325902i
$585$	1.00000			0.0413449
$586$	9.31675	+	44.7581i	0.384871	+	1.84894i
$587$		−	5.86983i		−	0.242274i	−0.992636	−	0.121137i	$-0.961346\pi$
$587$		−	5.86983i		−	0.242274i	0.992636	−	0.121137i	$-0.0386540\pi$
$588$	3.61159	+	8.29923i	0.148939	+	0.342255i
$589$		−	29.0681i		−	1.19773i
$590$	8.46002	−	1.76102i	0.348293	−	0.0725000i
$591$	15.9730			0.657040
$592$	0.406067	+	0.378205i	0.0166892	+	0.0155441i
$593$	28.9942			1.19065			0.595324	−	0.803486i	$-0.297024\pi$
$593$	28.9942			1.19065			0.595324	+	0.803486i	$0.297024\pi$
$594$	−0.549312	+	0.114344i	−0.0225385	+	0.00469157i
$595$			14.0659i			0.576646i
$596$	−0.557931	−	1.28210i	−0.0228538	−	0.0525167i
$597$		−	8.58841i		−	0.351500i
$598$	−2.22644	−	10.6959i	−0.0910460	−	0.437389i
$599$	23.1526			0.945988			0.472994	−	0.881066i	$-0.343173\pi$
$599$	23.1526			0.945988			0.472994	+	0.881066i	$0.343173\pi$
$600$	−1.63346	−	2.30907i	−0.0666857	−	0.0942675i
$601$	−12.0385			−0.491060			−0.245530	−	0.969389i	$-0.578962\pi$
$601$	−12.0385			−0.491060			−0.245530	+	0.969389i	$0.578962\pi$
$602$	0.00562512	+	0.0270234i	0.000229263	+	0.00110139i
$603$		−	12.1232i		−	0.493695i
$604$	−4.90658	+	2.13521i	−0.199646	+	0.0868803i
$605$		−	10.8426i		−	0.440814i
$606$	−20.6510	+	4.29867i	−0.838890	+	0.174622i
$607$	−35.4047			−1.43703			−0.718517	−	0.695509i	$-0.755179\pi$
$607$	−35.4047			−1.43703			−0.718517	+	0.695509i	$0.755179\pi$
$608$	−30.9810	−	18.7678i	−1.25645	−	0.761133i
$609$	−19.2644			−0.780633
$610$	−14.8910	+	3.09967i	−0.602917	+	0.125502i
$611$			12.3072i			0.497896i
$612$	−7.59817	+	3.30650i	−0.307138	+	0.133658i
$613$			20.4475i			0.825868i	0.910761	+	0.412934i	$0.135496\pi$
$613$			20.4475i			0.825868i	−0.910761	+	0.412934i	$0.864504\pi$
$614$	−3.73261	−	17.9316i	−0.150636	−	0.723661i
$615$	10.8070			0.435779
$616$	2.20015	+	3.11016i	0.0886467	+	0.125312i
$617$	6.54022			0.263299			0.131650	−	0.991296i	$-0.457973\pi$
$617$	6.54022			0.263299			0.131650	+	0.991296i	$0.457973\pi$
$618$	2.92663	+	14.0597i	0.117726	+	0.565562i
$619$			8.86767i			0.356422i	0.983992	+	0.178211i	$0.0570309\pi$
$619$			8.86767i			0.356422i	−0.983992	+	0.178211i	$0.942969\pi$
$620$	−3.62282	−	8.32505i	−0.145496	−	0.334342i
$621$		−	7.72529i		−	0.310005i
$622$	−23.0551	+	4.79910i	−0.924425	+	0.192426i
$623$	28.9655			1.16048
$624$	2.72623	−	2.92706i	0.109136	−	0.117176i
$625$	1.00000			0.0400000
$626$	−26.5260	+	5.52159i	−1.06019	+	0.220687i
$627$		−	2.54048i		−	0.101457i
$628$	−9.36818	−	21.5276i	−0.373831	−	0.859043i
$629$			0.574783i			0.0229181i
$630$	−0.978424	−	4.70039i	−0.0389813	−	0.187268i
$631$	23.0301			0.916815			0.458407	−	0.888742i	$-0.348420\pi$
$631$	23.0301			0.916815			0.458407	+	0.888742i	$0.348420\pi$
$632$	−16.7070	+	11.8187i	−0.664570	+	0.470123i
$633$	1.87864			0.0746694
$634$	−0.158648	−	0.762153i	−0.00630072	−	0.0302689i
$635$		−	10.0781i		−	0.399936i
$636$	11.7538	−	5.11492i	0.466069	−	0.202820i
$637$		−	4.52551i		−	0.179307i
$638$	−3.11706	+	0.648840i	−0.123405	+	0.0256878i
$639$	16.2844			0.644199
$640$	−11.2120	−	1.51382i	−0.443192	−	0.0598388i
$641$	−15.5602			−0.614590			−0.307295	−	0.951614i	$-0.599424\pi$
$641$	−15.5602			−0.614590			−0.307295	+	0.951614i	$0.599424\pi$
$642$	2.52117	−	0.524802i	0.0995027	−	0.0207123i
$643$		−	1.70224i		−	0.0671299i	−0.999437	−	0.0335649i	$-0.989314\pi$
$643$		−	1.70224i		−	0.0671299i	0.999437	−	0.0335649i	$-0.0106861\pi$
$644$	−48.0967	+	20.9303i	−1.89528	+	0.824770i
$645$		−	0.00574917i		−	0.000226373i
$646$	−7.64602	−	36.7319i	−0.300829	−	1.44520i
$647$	26.5457			1.04362			0.521810	−	0.853062i	$-0.325257\pi$
$647$	26.5457			1.04362			0.521810	+	0.853062i	$0.325257\pi$
$648$	2.30907	−	1.63346i	0.0907089	−	0.0641683i
$649$	2.42428			0.0951611
$650$	0.288202	+	1.38454i	0.0113042	+	0.0543060i
$651$		−	15.4115i		−	0.604026i
$652$	11.9453	+	27.4495i	0.467812	+	1.07501i
$653$		−	27.0146i		−	1.05716i	−0.848882	−	0.528582i	$-0.822724\pi$
$653$		−	27.0146i		−	1.05716i	0.848882	−	0.528582i	$-0.177276\pi$
$654$	−14.4173	+	3.00106i	−0.563759	+	0.117351i
$655$	−15.3388			−0.599335
$656$	29.4623	−	31.6327i	1.15031	−	1.23505i
$657$	4.82153			0.188106
$658$	57.8486	−	12.0416i	2.25517	−	0.469432i
$659$		−	28.6287i		−	1.11522i	−0.830104	−	0.557608i	$-0.811719\pi$
$659$		−	28.6287i		−	1.11522i	0.830104	−	0.557608i	$-0.188281\pi$
$660$	−0.316626	−	0.727588i	−0.0123246	−	0.0283213i
$661$		−	8.50842i		−	0.330939i	−0.986215	−	0.165470i	$-0.947086\pi$
$661$		−	8.50842i		−	0.330939i	0.986215	−	0.165470i	$-0.0529139\pi$
$662$	−5.84702	−	28.0894i	−0.227251	−	1.09172i
$663$	4.14322			0.160909
$664$	19.1938	+	27.1325i	0.744863	+	1.05294i
$665$	21.7386			0.842985
$666$	−0.0399818	−	0.192075i	−0.00154926	−	0.00744274i
$667$		−	43.8370i		−	1.69737i
$668$	−41.1541	+	17.9091i	−1.59230	+	0.692923i
$669$			17.7336i			0.685620i
$670$	16.7850	−	3.49393i	0.648462	−	0.134982i
$671$	−4.26710			−0.164730
$672$	−16.4257	−	9.95043i	−0.633637	−	0.383846i
$673$	35.9798			1.38692			0.693459	−	0.720496i	$-0.256086\pi$
$673$	35.9798			1.38692			0.693459	+	0.720496i	$0.256086\pi$
$674$	0.585689	−	0.121916i	0.0225599	−	0.00469602i
$675$			1.00000i			0.0384900i
$676$	−1.83388	+	0.798052i	−0.0705338	+	0.0306943i
$677$		−	1.98195i		−	0.0761725i	−0.999274	−	0.0380862i	$-0.987874\pi$
$677$		−	1.98195i		−	0.0761725i	0.999274	−	0.0380862i	$-0.0121262\pi$
$678$	2.08226	+	10.0033i	0.0799687	+	0.384173i
$679$	5.46197			0.209611
$680$	−6.76778	−	9.56699i	−0.259533	−	0.366877i
$681$	−21.6331			−0.828982
$682$	−0.519072	−	2.49365i	−0.0198763	−	0.0954867i
$683$			8.18346i			0.313132i	0.987668	+	0.156566i	$0.0500423\pi$
$683$			8.18346i			0.313132i	−0.987668	+	0.156566i	$0.949958\pi$
$684$	5.11013	+	11.7428i	0.195391	+	0.448997i
$685$		−	16.8339i		−	0.643191i
$686$	11.6311	−	2.42110i	0.444077	−	0.0924381i
$687$	−17.0379			−0.650036
$688$	−0.0168282	−	0.0156735i	−0.000641568	−	0.000597548i
$689$	−6.40926			−0.244173
$690$	10.6959	−	2.22644i	0.407187	−	0.0847592i
$691$		−	18.6051i		−	0.707772i	−0.935289	−	0.353886i	$-0.884860\pi$
$691$		−	18.6051i		−	0.707772i	0.935289	−	0.353886i	$-0.115140\pi$
$692$	6.18984	+	14.2239i	0.235303	+	0.540712i
$693$		−	1.34693i		−	0.0511656i
$694$	2.47985	+	11.9133i	0.0941339	+	0.452224i
$695$	19.4538			0.737925
$696$	13.1028	−	9.26902i	0.496659	−	0.351341i
$697$	44.7757			1.69600
$698$	−6.40438	−	30.7670i	−0.242409	−	1.16455i
$699$			13.8709i			0.524646i
$700$	6.22588	−	2.70933i	0.235316	−	0.102403i
$701$		−	5.69331i		−	0.215033i	−0.994203	−	0.107517i	$-0.965710\pi$
$701$		−	5.69331i		−	0.215033i	0.994203	−	0.107517i	$-0.0342899\pi$
$702$	−1.38454	+	0.288202i	−0.0522559	+	0.0108775i
$703$	0.888314			0.0335034
$704$	−2.99289	−	1.05679i	−0.112799	−	0.0398292i
$705$	−12.3072			−0.463516
$706$	−23.2348	+	4.83650i	−0.874452	+	0.182024i
$707$		−	50.6369i		−	1.90440i
$708$	−11.2057	+	4.87639i	−0.421135	+	0.183266i
$709$		−	6.41637i		−	0.240972i	−0.992715	−	0.120486i	$-0.961555\pi$
$709$		−	6.41637i		−	0.240972i	0.992715	−	0.120486i	$-0.0384453\pi$
$710$	4.69318	+	22.5463i	0.176132	+	0.846146i
$711$	7.23539			0.271348
$712$	−19.7010	+	13.9367i	−0.738327	+	0.522299i
$713$	35.0696			1.31337
$714$	−4.05382	−	19.4748i	−0.151711	−	0.728825i
$715$			0.396748i			0.0148375i
$716$	−13.7687	−	31.6396i	−0.514559	−	1.18243i
$717$		−	18.3021i		−	0.683504i
$718$	5.98743	−	1.24633i	0.223449	−	0.0465126i
$719$	−21.2275			−0.791652			−0.395826	−	0.918326i	$-0.629542\pi$
$719$	−21.2275			−0.791652			−0.395826	+	0.918326i	$0.629542\pi$
$720$	2.92706	+	2.72623i	0.109085	+	0.101600i
$721$	−34.4747			−1.28390
$722$	−30.4621	+	6.34092i	−1.13368	+	0.235985i
$723$			13.8153i			0.513797i
$724$	−6.21137	−	14.2734i	−0.230844	−	0.530466i
$725$			5.67448i			0.210745i
$726$	3.12486	+	15.0120i	0.115974	+	0.557146i
$727$	−48.7583			−1.80835			−0.904173	−	0.427167i	$-0.859512\pi$
$727$	−48.7583			−1.80835			−0.904173	+	0.427167i	$0.859512\pi$
$728$	5.54547	+	7.83912i	0.205529	+	0.290537i
$729$	−1.00000			−0.0370370
$730$	1.38958	+	6.67559i	0.0514305	+	0.247075i
$731$		−	0.0238201i		−	0.000881017i
$732$	19.7237	−	8.58321i	0.729010	−	0.317244i
$733$		−	21.4416i		−	0.791965i	−0.918258	−	0.395982i	$-0.870404\pi$
$733$		−	21.4416i		−	0.791965i	0.918258	−	0.395982i	$-0.129596\pi$
$734$	−4.51741	+	0.940335i	−0.166741	+	0.0347084i
$735$	4.52551			0.166926
$736$	22.6426	−	37.3775i	0.834618	−	1.37775i
$737$	4.80986			0.177174
$738$	−14.9627	+	3.11459i	−0.550783	+	0.114650i
$739$		−	30.7738i		−	1.13203i	−0.824394	−	0.566016i	$-0.808484\pi$
$739$		−	30.7738i		−	1.13203i	0.824394	−	0.566016i	$-0.191516\pi$
$740$	0.254411	−	0.110713i	0.00935235	−	0.00406987i
$741$		−	6.40325i		−	0.235229i
$742$	6.27097	+	30.1261i	0.230215	+	1.10596i
$743$	−44.7693			−1.64243			−0.821214	−	0.570621i	$-0.806703\pi$
$743$	−44.7693			−1.64243			−0.821214	+	0.570621i	$0.806703\pi$
$744$	7.41523	+	10.4822i	0.271855	+	0.384297i
$745$	−0.699116			−0.0256136
$746$	4.88538	+	23.4696i	0.178866	+	0.859282i
$747$		−	11.7504i		−	0.429924i
$748$	−1.31185	−	3.01456i	−0.0479660	−	0.110223i
$749$			6.18199i			0.225885i
$750$	−1.38454	+	0.288202i	−0.0505561	+	0.0105236i
$751$	−14.1338			−0.515750			−0.257875	−	0.966178i	$-0.583022\pi$
$751$	−14.1338			−0.515750			−0.257875	+	0.966178i	$0.583022\pi$
$752$	−33.5522	+	36.0239i	−1.22352	+	1.31366i
$753$	−14.0408			−0.511676
$754$	−7.85651	+	1.63539i	−0.286117	+	0.0595576i
$755$			2.67552i			0.0973722i
$756$	2.70933	+	6.22588i	0.0985372	+	0.226433i
$757$			37.9994i			1.38111i	0.723279	+	0.690556i	$0.242634\pi$
$757$			37.9994i			1.38111i	−0.723279	+	0.690556i	$0.757366\pi$
$758$	9.70097	+	46.6039i	0.352355	+	1.69273i
$759$	3.06499			0.111252
$760$	−14.7856	+	10.4595i	−0.536329	+	0.379404i
$761$	−11.7193			−0.424824			−0.212412	−	0.977180i	$-0.568132\pi$
$761$	−11.7193			−0.424824			−0.212412	+	0.977180i	$0.568132\pi$
$762$	2.90452	+	13.9534i	0.105220	+	0.505480i
$763$		−	35.3515i		−	1.27981i
$764$	11.8314	−	5.14871i	0.428047	−	0.186274i
$765$			4.14322i			0.149798i
$766$	−41.8727	+	8.71613i	−1.51292	+	0.314926i
$767$	6.11036			0.220632
$768$	15.9597	−	1.13538i	0.575895	−	0.0409695i
$769$	−48.3612			−1.74395			−0.871974	−	0.489552i	$-0.837160\pi$
$769$	−48.3612			−1.74395			−0.871974	+	0.489552i	$0.837160\pi$
$770$	1.86487	−	0.388188i	0.0672053	−	0.0139893i
$771$		−	17.8821i		−	0.644007i
$772$	35.6688	−	15.5220i	1.28375	−	0.558650i
$773$			45.4992i			1.63649i	0.574867	+	0.818247i	$0.305054\pi$
$773$			45.4992i			1.63649i	−0.574867	+	0.818247i	$0.694946\pi$
$774$	0.00165692	+	0.00795993i	5.95568e−5	+	0.000286114i
$775$	−4.53959			−0.163067
$776$	−3.71498	+	2.62801i	−0.133360	+	0.0943402i
$777$	0.470973			0.0168961
$778$	−0.326797	−	1.56995i	−0.0117162	−	0.0562854i
$779$		−	69.1998i		−	2.47934i
$780$	−0.798052	−	1.83388i	−0.0285748	−	0.0656634i
$781$			6.46078i			0.231185i
$782$	44.3156	−	9.22464i	1.58472	−	0.329873i
$783$	−5.67448			−0.202789
$784$	12.3376	−	13.2464i	0.440627	−	0.473087i
$785$	−11.7388			−0.418976
$786$	21.2371	−	4.42066i	0.757501	−	0.157680i
$787$			26.3647i			0.939801i	0.882719	+	0.469901i	$0.155710\pi$
$787$			26.3647i			0.939801i	−0.882719	+	0.469901i	$0.844290\pi$
$788$	−12.7472	−	29.2925i	−0.454102	−	1.04350i
$789$			26.7434i			0.952090i
$790$	2.08525	+	10.0177i	0.0741900	+	0.356412i
$791$	−24.5283			−0.872127
$792$	0.648072	+	0.916120i	0.0230282	+	0.0325529i
$793$	−10.7552			−0.381928
$794$	1.07049	+	5.14268i	0.0379902	+	0.182507i
$795$		−	6.40926i		−	0.227313i
$796$	−15.7501	+	6.85399i	−0.558248	+	0.242933i
$797$		−	1.70781i		−	0.0604937i	−0.999542	−	0.0302469i	$-0.990371\pi$
$797$		−	1.70781i		−	0.0604937i	0.999542	−	0.0302469i	$-0.00962934\pi$
$798$	−30.0978	+	6.26509i	−1.06545	+	0.221782i
$799$	−50.9914			−1.80395
$800$	−2.93097	+	4.83833i	−0.103626	+	0.171061i
$801$	8.53201			0.301464
$802$	−19.7518	+	4.11150i	−0.697461	+	0.145182i
$803$			1.91293i			0.0675060i
$804$	−22.2325	+	9.67495i	−0.784080	+	0.341209i
$805$			26.2268i			0.924372i
$806$	−1.30832	−	6.28522i	−0.0460835	−	0.221387i
$807$	28.9143			1.01783
$808$	24.3638	+	34.4409i	0.857116	+	1.21163i
$809$	0.618133			0.0217324			0.0108662	−	0.999941i	$-0.496541\pi$
$809$	0.618133			0.0217324			0.0108662	+	0.999941i	$0.496541\pi$
$810$	−0.288202	−	1.38454i	−0.0101264	−	0.0486476i
$811$			9.02126i			0.316779i	0.987377	+	0.158390i	$0.0506302\pi$
$811$			9.02126i			0.316779i	−0.987377	+	0.158390i	$0.949370\pi$
$812$	15.3740	+	35.3286i	0.539522	+	1.23979i
$813$			6.44150i			0.225913i
$814$	0.0762052	−	0.0158627i	0.00267099	−	0.000555988i
$815$	14.9680			0.524307
$816$	12.1275	+	11.2954i	0.424546	+	0.395417i
$817$	−0.0368134			−0.00128794
$818$	10.2863	−	2.14117i	0.359652	−	0.0748643i
$819$		−	3.39492i		−	0.118628i
$820$	−8.62453	−	19.8187i	−0.301182	−	0.692099i
$821$			9.69790i			0.338459i	0.985577	+	0.169229i	$0.0541279\pi$
$821$			9.69790i			0.338459i	−0.985577	+	0.169229i	$0.945872\pi$
$822$	4.85157	+	23.3072i	0.169218	+	0.812931i
$823$	6.83024			0.238087			0.119044	−	0.992889i	$-0.462017\pi$
$823$	6.83024			0.238087			0.119044	+	0.992889i	$0.462017\pi$
$824$	23.4481	−	16.5874i	0.816854	−	0.577850i
$825$	−0.396748			−0.0138130
$826$	−5.97853	−	28.7211i	−0.208020	−	0.999336i
$827$		−	26.9443i		−	0.936945i	−0.883478	−	0.468472i	$-0.844805\pi$
$827$		−	26.9443i		−	0.936945i	0.883478	−	0.468472i	$-0.155195\pi$
$828$	−14.1672	+	6.16518i	−0.492346	+	0.214255i
$829$			28.2417i			0.980876i	0.871476	+	0.490438i	$0.163163\pi$
$829$			28.2417i			0.980876i	−0.871476	+	0.490438i	$0.836837\pi$
$830$	16.2688	−	3.38649i	0.564700	−	0.117547i
$831$	−17.9769			−0.623611
$832$	−7.54355	−	2.66362i	−0.261525	−	0.0923445i
$833$	18.7502			0.649655
$834$	−26.9345	+	5.60663i	−0.932666	+	0.194142i
$835$			22.4410i			0.776603i
$836$	−4.65893	+	2.02743i	−0.161132	+	0.0701203i
$837$		−	4.53959i		−	0.156911i
$838$	−1.37602	−	6.61047i	−0.0475338	−	0.228355i
$839$	45.0999			1.55702			0.778511	−	0.627631i	$-0.215975\pi$
$839$	45.0999			1.55702			0.778511	+	0.627631i	$0.215975\pi$
$840$	−7.83912	+	5.54547i	−0.270475	+	0.191337i
$841$	−3.19967			−0.110333
$842$	4.13134	+	19.8471i	0.142375	+	0.683977i
$843$			3.10865i			0.107068i
$844$	−1.49926	−	3.44521i	−0.0516065	−	0.118589i
$845$			1.00000i			0.0344010i
$846$	17.0397	−	3.54696i	0.585838	−	0.121947i
$847$	−36.8098			−1.26480
$848$	−18.7603	−	17.4731i	−0.644231	−	0.600029i
$849$	−21.3067			−0.731246
$850$	−5.73644	+	1.19408i	−0.196758	+	0.0409567i
$851$			1.07172i			0.0367380i
$852$	−12.9958	−	29.8635i	−0.445227	−	1.02311i
$853$		−	27.8658i		−	0.954107i	−0.878874	−	0.477054i	$-0.841705\pi$
$853$		−	27.8658i		−	0.954107i	0.878874	−	0.477054i	$-0.158295\pi$
$854$	10.5231	+	50.5537i	0.360094	+	1.72991i
$855$	6.40325			0.218987
$856$	−2.97445	−	4.20471i	−0.101665	−	0.143714i
$857$	−6.54295			−0.223503			−0.111751	−	0.993736i	$-0.535646\pi$
$857$	−6.54295			−0.223503			−0.111751	+	0.993736i	$0.535646\pi$
$858$	−0.114344	−	0.549312i	−0.00390363	−	0.0187532i
$859$		−	22.5237i		−	0.768499i	−0.923229	−	0.384250i	$-0.874460\pi$
$859$		−	22.5237i		−	0.768499i	0.923229	−	0.384250i	$-0.125540\pi$
$860$	−0.0105433	+	0.00458813i	−0.000359523	+	0.000156454i
$861$		−	36.6889i		−	1.25035i
$862$	9.68100	−	2.01518i	0.329736	−	0.0686371i
$863$	39.6856			1.35092			0.675458	−	0.737399i	$-0.263946\pi$
$863$	39.6856			1.35092			0.675458	+	0.737399i	$0.263946\pi$
$864$	−4.83833	−	2.93097i	−0.164603	−	0.0997137i
$865$	7.75619			0.263718
$866$	40.4373	−	8.41733i	1.37411	−	0.286033i
$867$			0.166272i			0.00564688i
$868$	−28.2629	+	12.2992i	−0.959306	+	0.417463i
$869$			2.87063i			0.0973794i
$870$	−1.63539	−	7.85651i	−0.0554451	−	0.266361i
$871$	12.1232			0.410779
$872$	17.0093	+	24.0445i	0.576008	+	0.814250i
$873$	1.60886			0.0544518
$874$	−14.2565	−	68.4888i	−0.482233	−	2.31667i
$875$		−	3.39492i		−	0.114769i
$876$	−3.84783	−	8.84211i	−0.130006	−	0.298747i
$877$		−	39.9136i		−	1.34779i	−0.738829	−	0.673893i	$-0.764621\pi$
$877$		−	39.9136i		−	1.34779i	0.738829	−	0.673893i	$-0.235379\pi$
$878$	36.0713	−	7.50853i	1.21735	−	0.253401i
$879$	−32.3271			−1.09037
$880$	−1.08163	+	1.16131i	−0.0364616	+	0.0391476i
$881$	−17.2027			−0.579572			−0.289786	−	0.957091i	$-0.593584\pi$
$881$	−17.2027			−0.579572			−0.289786	+	0.957091i	$0.593584\pi$
$882$	−6.26573	+	1.30426i	−0.210978	+	0.0439167i
$883$		−	22.1032i		−	0.743830i	−0.928267	−	0.371915i	$-0.878701\pi$
$883$		−	22.1032i		−	0.743830i	0.928267	−	0.371915i	$-0.121299\pi$
$884$	−3.30650	−	7.59817i	−0.111210	−	0.255554i
$885$			6.11036i			0.205398i
$886$	−1.14967	−	5.52306i	−0.0386239	−	0.185551i
$887$	−13.3067			−0.446797			−0.223398	−	0.974727i	$-0.571715\pi$
$887$	−13.3067			−0.446797			−0.223398	+	0.974727i	$0.571715\pi$
$888$	−0.320334	+	0.226607i	−0.0107497	+	0.00760444i
$889$	−34.2143			−1.14751
$890$	2.45894	+	11.8129i	0.0824239	+	0.395968i
$891$		−	0.396748i		−	0.0132916i
$892$	32.5212	−	14.1523i	1.08889	−	0.473855i
$893$			78.8061i			2.63714i
$894$	0.967952	−	0.201487i	0.0323731	−	0.00673872i
$895$	−17.2528			−0.576698
$896$	−5.13929	+	38.0638i	−0.171692	+	1.27162i
$897$	7.72529			0.257940
$898$	−39.6656	+	8.25670i	−1.32366	+	0.275530i
$899$		−	25.7598i		−	0.859136i
$900$	1.83388	−	0.798052i	0.0611293	−	0.0266017i
$901$		−	26.5550i		−	0.884675i
$902$	−1.23571	−	5.93640i	−0.0411446	−	0.197661i
$903$	−0.0195180			−0.000649518
$904$	16.6830	−	11.8017i	0.554870	−	0.392520i
$905$	−7.78316			−0.258721
$906$	−0.771091	−	3.70436i	−0.0256178	−	0.123069i
$907$		−	55.0721i		−	1.82864i	−0.404992	−	0.914320i	$-0.632726\pi$
$907$		−	55.0721i		−	1.82864i	0.404992	−	0.914320i	$-0.367274\pi$
$908$	17.2643	+	39.6725i	0.572937	+	1.31658i
$909$		−	14.9155i		−	0.494715i
$910$	4.70039	−	0.978424i	0.155817	−	0.0324344i
$911$	25.4432			0.842970			0.421485	−	0.906835i	$-0.361509\pi$
$911$	25.4432			0.842970			0.421485	+	0.906835i	$0.361509\pi$
$912$	17.4567	−	18.7427i	0.578050	−	0.620633i
$913$	4.66194			0.154288
$914$	9.34659	−	1.94557i	0.309158	−	0.0643536i
$915$		−	10.7552i		−	0.355556i
$916$	13.5971	+	31.2454i	0.449262	+	1.03238i
$917$			52.0739i			1.71963i
$918$	−1.19408	−	5.73644i	−0.0394106	−	0.189331i
$919$	49.5245			1.63366			0.816831	−	0.576878i	$-0.195729\pi$
$919$	49.5245			1.63366			0.816831	+	0.576878i	$0.195729\pi$
$920$	−12.6189	−	17.8382i	−0.416034	−	0.588109i
$921$	12.9514			0.426762
$922$	−4.15139	−	19.9435i	−0.136719	−	0.656803i
$923$			16.2844i			0.536006i
$924$	−2.47011	+	1.07492i	−0.0812605	+	0.0353623i
$925$		−	0.138729i		−	0.00456137i
$926$	22.3332	−	4.64883i	0.733915	−	0.152770i
$927$	−10.1548			−0.333527
$928$	−27.4550	−	16.6317i	−0.901253	−	0.545963i
$929$	33.9679			1.11445			0.557226	−	0.830361i	$-0.311866\pi$
$929$	33.9679			1.11445			0.557226	+	0.830361i	$0.311866\pi$
$930$	6.28522	−	1.30832i	0.206100	−	0.0429014i
$931$		−	28.9780i		−	0.949714i
$932$	25.4376	−	11.0697i	0.833236	−	0.362600i
$933$		−	16.6519i		−	0.545157i
$934$	0.852664	+	4.09624i	0.0279000	+	0.134033i
$935$	−1.64381			−0.0537585
$936$	1.63346	+	2.30907i	0.0533913	+	0.0754744i
$937$	−24.4041			−0.797248			−0.398624	−	0.917114i	$-0.630512\pi$
$937$	−24.4041			−0.797248			−0.398624	+	0.917114i	$0.630512\pi$
$938$	−11.8616	−	56.9839i	−0.387296	−	1.86059i
$939$		−	19.1587i		−	0.625222i
$940$	9.82178	+	22.5699i	0.320351	+	0.736149i
$941$			30.4557i			0.992828i	0.868086	+	0.496414i	$0.165350\pi$
$941$			30.4557i			0.992828i	−0.868086	+	0.496414i	$0.834650\pi$
$942$	16.2528	−	3.38315i	0.529545	−	0.110229i
$943$	83.4870			2.71871
$944$	17.8854	+	16.6582i	0.582121	+	0.542179i
$945$	3.39492			0.110437
$946$	−0.00315809		0.000657380i	−0.000102678		2.13733e-5i
$947$			10.4726i			0.340313i	0.985417	+	0.170156i	$0.0544273\pi$
$947$			10.4726i			0.340313i	−0.985417	+	0.170156i	$0.945573\pi$
$948$	−5.77422	−	13.2688i	−0.187538	−	0.430952i
$949$			4.82153i			0.156514i
$950$	1.84543	+	8.86553i	0.0598737	+	0.287636i
$951$	0.550475			0.0178504
$952$	−32.4792	+	22.9761i	−1.05266	+	0.744660i
$953$	0.413661			0.0133998			0.00669989	−	0.999978i	$-0.497867\pi$
$953$	0.413661			0.0133998			0.00669989	+	0.999978i	$0.497867\pi$
$954$	1.84716	+	8.87385i	0.0598041	+	0.287302i
$955$		−	6.45160i		−	0.208769i
$956$	−33.5638	+	14.6060i	−1.08553	+	0.472392i
$957$		−	2.25134i		−	0.0727754i
$958$	−21.3331	+	4.44066i	−0.689243	+	0.143471i
$959$	−57.1499			−1.84547
$960$	2.66362	−	7.54355i	0.0859681	−	0.243467i
$961$	−10.3922			−0.335231
$962$	0.192075	−	0.0399818i	0.00619273	−	0.00128907i
$963$			1.82095i			0.0586793i
$964$	25.3356	−	11.0253i	0.816005	−	0.355102i
$965$		−	19.4499i		−	0.626114i
$966$	−7.55860	−	36.3119i	−0.243194	−	1.16832i
$967$	16.9499			0.545073			0.272537	−	0.962145i	$-0.412137\pi$
$967$	16.9499			0.545073			0.272537	+	0.962145i	$0.412137\pi$
$968$	25.0363	−	17.7109i	0.804698	−	0.569251i
$969$	26.5301			0.852269
$970$	0.463678	+	2.22753i	0.0148878	+	0.0715217i
$971$			28.8227i			0.924966i	0.886628	+	0.462483i	$0.153041\pi$
$971$			28.8227i			0.924966i	−0.886628	+	0.462483i	$0.846959\pi$
$972$	0.798052	+	1.83388i	0.0255975	+	0.0588217i
$973$		−	66.0442i		−	2.11728i
$974$	48.7551	−	10.1488i	1.56221	−	0.325187i
$975$	−1.00000			−0.0320256
$976$	−31.4811	−	29.3211i	−1.00769	−	0.938546i
$977$	56.6390			1.81204			0.906020	−	0.423234i	$-0.139105\pi$
$977$	56.6390			1.81204			0.906020	+	0.423234i	$0.139105\pi$
$978$	−20.7238	+	4.31381i	−0.662673	+	0.137941i
$979$			3.38506i			0.108187i
$980$	−3.61159	−	8.29923i	−0.115368	−	0.265109i
$981$		−	10.4131i		−	0.332463i
$982$	3.42901	+	16.4731i	0.109424	+	0.525678i
$983$	−33.4141			−1.06574			−0.532872	−	0.846196i	$-0.678887\pi$
$983$	−33.4141			−1.06574			−0.532872	+	0.846196i	$0.678887\pi$
$984$	17.6528	+	24.9541i	0.562749	+	0.795507i
$985$	−15.9730			−0.508941
$986$	−6.77580	−	32.5513i	−0.215785	−	1.03664i
$987$			41.7820i			1.32993i
$988$	−11.7428	+	5.11013i	−0.373588	+	0.162575i
$989$		−	0.0444140i		−	0.00141228i
$990$	0.549312	−	0.114344i	0.0174583	−	0.00363408i
$991$	32.9225			1.04582			0.522909	−	0.852389i	$-0.324847\pi$
$991$	32.9225			1.04582			0.522909	+	0.852389i	$0.324847\pi$
$992$	13.3054	−	21.9640i	0.422447	−	0.697357i
$993$	20.2879			0.643818
$994$	76.5429	−	15.9330i	2.42779	−	0.505364i
$995$			8.58841i			0.272271i
$996$	−21.5488	+	9.37742i	−0.682800	+	0.297135i
$997$			32.4298i			1.02706i	0.858071	+	0.513531i	$0.171663\pi$
$997$			32.4298i			1.02706i	−0.858071	+	0.513531i	$0.828337\pi$
$998$	−6.10481	−	29.3278i	−0.193244	−	0.928355i
$999$	0.138729			0.00438918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.w.f.781.19	✓	20
4.3	odd	2		6240.2.w.f.3121.8		20
8.3	odd	2		6240.2.w.f.3121.18		20
8.5	even	2	inner	1560.2.w.f.781.20	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.w.f.781.19	✓	20	1.1	even	1	trivial
1560.2.w.f.781.20	yes	20	8.5	even	2	inner
6240.2.w.f.3121.8		20	4.3	odd	2
6240.2.w.f.3121.18		20	8.3	odd	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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.w (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38454 - 0.288202i) q^{2} +1.00000i q^{3} +(1.83388 - 0.798052i) q^{4} -1.00000i q^{5} +(0.288202 + 1.38454i) q^{6} -3.39492 q^{7} +(2.30907 - 1.63346i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.38454 - 0.288202i) q^{2} +1.00000i q^{3} +(1.83388 - 0.798052i) q^{4} -1.00000i q^{5} +(0.288202 + 1.38454i) q^{6} -3.39492 q^{7} +(2.30907 - 1.63346i) q^{8} -1.00000 q^{9} +(-0.288202 - 1.38454i) q^{10} -0.396748i q^{11} +(0.798052 + 1.83388i) q^{12} -1.00000i q^{13} +(-4.70039 + 0.978424i) q^{14} +1.00000 q^{15} +(2.72623 - 2.92706i) q^{16} +4.14322 q^{17} +(-1.38454 + 0.288202i) q^{18} -6.40325i q^{19} +(-0.798052 - 1.83388i) q^{20} -3.39492i q^{21} +(-0.114344 - 0.549312i) q^{22} +7.72529 q^{23} +(1.63346 + 2.30907i) q^{24} -1.00000 q^{25} +(-0.288202 - 1.38454i) q^{26} -1.00000i q^{27} +(-6.22588 + 2.70933i) q^{28} -5.67448i q^{29} +(1.38454 - 0.288202i) q^{30} +4.53959 q^{31} +(2.93097 - 4.83833i) q^{32} +0.396748 q^{33} +(5.73644 - 1.19408i) q^{34} +3.39492i q^{35} +(-1.83388 + 0.798052i) q^{36} +0.138729i q^{37} +(-1.84543 - 8.86553i) q^{38} +1.00000 q^{39} +(-1.63346 - 2.30907i) q^{40} +10.8070 q^{41} +(-0.978424 - 4.70039i) q^{42} -0.00574917i q^{43} +(-0.316626 - 0.727588i) q^{44} +1.00000i q^{45} +(10.6959 - 2.22644i) q^{46} -12.3072 q^{47} +(2.92706 + 2.72623i) q^{48} +4.52551 q^{49} +(-1.38454 + 0.288202i) q^{50} +4.14322i q^{51} +(-0.798052 - 1.83388i) q^{52} -6.40926i q^{53} +(-0.288202 - 1.38454i) q^{54} -0.396748 q^{55} +(-7.83912 + 5.54547i) q^{56} +6.40325 q^{57} +(-1.63539 - 7.85651i) q^{58} +6.11036i q^{59} +(1.83388 - 0.798052i) q^{60} -10.7552i q^{61} +(6.28522 - 1.30832i) q^{62} +3.39492 q^{63} +(2.66362 - 7.54355i) q^{64} -1.00000 q^{65} +(0.549312 - 0.114344i) q^{66} +12.1232i q^{67} +(7.59817 - 3.30650i) q^{68} +7.72529i q^{69} +(0.978424 + 4.70039i) q^{70} -16.2844 q^{71} +(-2.30907 + 1.63346i) q^{72} -4.82153 q^{73} +(0.0399818 + 0.192075i) q^{74} -1.00000i q^{75} +(-5.11013 - 11.7428i) q^{76} +1.34693i q^{77} +(1.38454 - 0.288202i) q^{78} -7.23539 q^{79} +(-2.92706 - 2.72623i) q^{80} +1.00000 q^{81} +(14.9627 - 3.11459i) q^{82} +11.7504i q^{83} +(-2.70933 - 6.22588i) q^{84} -4.14322i q^{85} +(-0.00165692 - 0.00795993i) q^{86} +5.67448 q^{87} +(-0.648072 - 0.916120i) q^{88} -8.53201 q^{89} +(0.288202 + 1.38454i) q^{90} +3.39492i q^{91} +(14.1672 - 6.16518i) q^{92} +4.53959i q^{93} +(-17.0397 + 3.54696i) q^{94} -6.40325 q^{95} +(4.83833 + 2.93097i) q^{96} -1.60886 q^{97} +(6.26573 - 1.30426i) q^{98} +0.396748i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 16 q^{7} - 8 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 16 * q^7 - 8 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 16 q^{7} - 8 q^{8} - 20 q^{9} - 2 q^{10} - 8 q^{12} - 18 q^{14} + 20 q^{15} + 12 q^{16} + 16 q^{17} + 2 q^{18} + 8 q^{20} - 14 q^{22} + 48 q^{23} + 4 q^{24} - 20 q^{25} - 2 q^{26} - 12 q^{28} - 2 q^{30} - 8 q^{31} + 8 q^{32} - 16 q^{33} + 58 q^{34} - 20 q^{38} + 20 q^{39} - 4 q^{40} + 16 q^{41} + 6 q^{42} + 20 q^{44} - 42 q^{46} - 8 q^{47} + 8 q^{48} + 36 q^{49} + 2 q^{50} + 8 q^{52} - 2 q^{54} + 16 q^{55} + 8 q^{56} + 16 q^{57} + 52 q^{58} - 28 q^{62} + 16 q^{63} - 12 q^{64} - 20 q^{65} - 2 q^{66} - 36 q^{68} - 6 q^{70} - 8 q^{71} + 8 q^{72} + 40 q^{73} + 50 q^{74} - 36 q^{76} - 2 q^{78} - 8 q^{79} - 8 q^{80} + 20 q^{81} + 22 q^{82} - 20 q^{84} - 8 q^{86} + 8 q^{87} - 4 q^{88} + 56 q^{89} + 2 q^{90} + 68 q^{92} - 76 q^{94} - 16 q^{95} - 8 q^{96} - 48 q^{97} - 16 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 16 * q^7 - 8 * q^8 - 20 * q^9 - 2 * q^10 - 8 * q^12 - 18 * q^14 + 20 * q^15 + 12 * q^16 + 16 * q^17 + 2 * q^18 + 8 * q^20 - 14 * q^22 + 48 * q^23 + 4 * q^24 - 20 * q^25 - 2 * q^26 - 12 * q^28 - 2 * q^30 - 8 * q^31 + 8 * q^32 - 16 * q^33 + 58 * q^34 - 20 * q^38 + 20 * q^39 - 4 * q^40 + 16 * q^41 + 6 * q^42 + 20 * q^44 - 42 * q^46 - 8 * q^47 + 8 * q^48 + 36 * q^49 + 2 * q^50 + 8 * q^52 - 2 * q^54 + 16 * q^55 + 8 * q^56 + 16 * q^57 + 52 * q^58 - 28 * q^62 + 16 * q^63 - 12 * q^64 - 20 * q^65 - 2 * q^66 - 36 * q^68 - 6 * q^70 - 8 * q^71 + 8 * q^72 + 40 * q^73 + 50 * q^74 - 36 * q^76 - 2 * q^78 - 8 * q^79 - 8 * q^80 + 20 * q^81 + 22 * q^82 - 20 * q^84 - 8 * q^86 + 8 * q^87 - 4 * q^88 + 56 * q^89 + 2 * q^90 + 68 * q^92 - 76 * q^94 - 16 * q^95 - 8 * q^96 - 48 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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