LMFDB - Embedded newform 552.2.f.d.277.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (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:	$4.40774219157$
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} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.17
Root			$-1.14290 + 0.832928i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14290 - 0.832928i) q^{2} -1.00000i q^{3} +(0.612462 - 1.90391i) q^{4} -1.03589i q^{5} +(-0.832928 - 1.14290i) q^{6} -3.71260 q^{7} +(-0.885838 - 2.68613i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.14290 - 0.832928i) q^{2} -1.00000i q^{3} +(0.612462 - 1.90391i) q^{4} -1.03589i q^{5} +(-0.832928 - 1.14290i) q^{6} -3.71260 q^{7} +(-0.885838 - 2.68613i) q^{8} -1.00000 q^{9} +(-0.862822 - 1.18392i) q^{10} +1.98292i q^{11} +(-1.90391 - 0.612462i) q^{12} -4.05749i q^{13} +(-4.24315 + 3.09233i) q^{14} -1.03589 q^{15} +(-3.24978 - 2.33215i) q^{16} +0.0352924 q^{17} +(-1.14290 + 0.832928i) q^{18} +0.839050i q^{19} +(-1.97225 - 0.634443i) q^{20} +3.71260i q^{21} +(1.65163 + 2.26629i) q^{22} +1.00000 q^{23} +(-2.68613 + 0.885838i) q^{24} +3.92693 q^{25} +(-3.37959 - 4.63732i) q^{26} +1.00000i q^{27} +(-2.27383 + 7.06847i) q^{28} -8.98442i q^{29} +(-1.18392 + 0.862822i) q^{30} +5.65271 q^{31} +(-5.65670 + 0.0414082i) q^{32} +1.98292 q^{33} +(0.0403358 - 0.0293960i) q^{34} +3.84584i q^{35} +(-0.612462 + 1.90391i) q^{36} +1.63184i q^{37} +(0.698868 + 0.958954i) q^{38} -4.05749 q^{39} +(-2.78253 + 0.917631i) q^{40} -1.65181 q^{41} +(3.09233 + 4.24315i) q^{42} +2.17414i q^{43} +(3.77531 + 1.21446i) q^{44} +1.03589i q^{45} +(1.14290 - 0.832928i) q^{46} +9.26034 q^{47} +(-2.33215 + 3.24978i) q^{48} +6.78340 q^{49} +(4.48811 - 3.27085i) q^{50} -0.0352924i q^{51} +(-7.72511 - 2.48506i) q^{52} -9.53235i q^{53} +(0.832928 + 1.14290i) q^{54} +2.05409 q^{55} +(3.28876 + 9.97253i) q^{56} +0.839050 q^{57} +(-7.48337 - 10.2683i) q^{58} +0.521307i q^{59} +(-0.634443 + 1.97225i) q^{60} +1.08170i q^{61} +(6.46050 - 4.70830i) q^{62} +3.71260 q^{63} +(-6.43058 + 4.75895i) q^{64} -4.20311 q^{65} +(2.26629 - 1.65163i) q^{66} +3.82606i q^{67} +(0.0216152 - 0.0671936i) q^{68} -1.00000i q^{69} +(3.20331 + 4.39543i) q^{70} -0.0570741 q^{71} +(0.885838 + 2.68613i) q^{72} +2.11118 q^{73} +(1.35920 + 1.86503i) q^{74} -3.92693i q^{75} +(1.59748 + 0.513886i) q^{76} -7.36179i q^{77} +(-4.63732 + 3.37959i) q^{78} -10.6052 q^{79} +(-2.41585 + 3.36641i) q^{80} +1.00000 q^{81} +(-1.88786 + 1.37584i) q^{82} -12.9986i q^{83} +(7.06847 + 2.27383i) q^{84} -0.0365590i q^{85} +(1.81090 + 2.48484i) q^{86} -8.98442 q^{87} +(5.32638 - 1.75655i) q^{88} -8.32127 q^{89} +(0.862822 + 1.18392i) q^{90} +15.0638i q^{91} +(0.612462 - 1.90391i) q^{92} -5.65271i q^{93} +(10.5837 - 7.71320i) q^{94} +0.869163 q^{95} +(0.0414082 + 5.65670i) q^{96} +17.4131 q^{97} +(7.75278 - 5.65009i) q^{98} -1.98292i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	1.14290	−	0.832928i	0.808156	−	0.588969i
$2$	1.14290	−	0.832928i	0.808156	−	0.588969i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.612462	−	1.90391i	0.306231	−	0.951957i
$5$		−	1.03589i		−	0.463264i	−0.972803	−	0.231632i	$-0.925593\pi$
$5$		−	1.03589i		−	0.463264i	0.972803	−	0.231632i	$-0.0744065\pi$
$6$	−0.832928	−	1.14290i	−0.340041	−	0.466589i
$7$	−3.71260			−1.40323			−0.701616	−	0.712556i	$-0.747538\pi$
$7$	−3.71260			−1.40323			−0.701616	+	0.712556i	$0.747538\pi$
$8$	−0.885838	−	2.68613i	−0.313191	−	0.949690i
$9$	−1.00000			−0.333333
$10$	−0.862822	−	1.18392i	−0.272848	−	0.374389i
$11$			1.98292i			0.597873i	0.954273	+	0.298936i	$0.0966319\pi$
$11$			1.98292i			0.597873i	−0.954273	+	0.298936i	$0.903368\pi$
$12$	−1.90391	−	0.612462i	−0.549613	−	0.176803i
$13$		−	4.05749i		−	1.12534i	−0.826680	−	0.562672i	$-0.809773\pi$
$13$		−	4.05749i		−	1.12534i	0.826680	−	0.562672i	$-0.190227\pi$
$14$	−4.24315	+	3.09233i	−1.13403	+	0.826460i
$15$	−1.03589			−0.267466
$16$	−3.24978	−	2.33215i	−0.812445	−	0.583038i
$17$	0.0352924			0.00855966			0.00427983	−	0.999991i	$-0.498638\pi$
$17$	0.0352924			0.00855966			0.00427983	+	0.999991i	$0.498638\pi$
$18$	−1.14290	+	0.832928i	−0.269385	+	0.196323i
$19$			0.839050i			0.192491i	0.995358	+	0.0962456i	$0.0306834\pi$
$19$			0.839050i			0.192491i	−0.995358	+	0.0962456i	$0.969317\pi$
$20$	−1.97225	−	0.634443i	−0.441007	−	0.141866i
$21$			3.71260i			0.810156i
$22$	1.65163	+	2.26629i	0.352129	+	0.483174i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−2.68613	+	0.885838i	−0.548304	+	0.180821i
$25$	3.92693			0.785386
$26$	−3.37959	−	4.63732i	−0.662793	−	0.909453i
$27$			1.00000i			0.192450i
$28$	−2.27383	+	7.06847i	−0.429713	+	1.33582i
$29$		−	8.98442i		−	1.66836i	−0.551489	−	0.834182i	$-0.685940\pi$
$29$		−	8.98442i		−	1.66836i	0.551489	−	0.834182i	$-0.314060\pi$
$30$	−1.18392	+	0.862822i	−0.216154	+	0.157529i
$31$	5.65271			1.01526			0.507628	−	0.861576i	$-0.330522\pi$
$31$	5.65271			1.01526			0.507628	+	0.861576i	$0.330522\pi$
$32$	−5.65670	+	0.0414082i	−0.999973	+	0.00732001i
$33$	1.98292			0.345182
$34$	0.0403358	−	0.0293960i	0.00691753	−	0.00504137i
$35$			3.84584i			0.650066i
$36$	−0.612462	+	1.90391i	−0.102077	+	0.317319i
$37$			1.63184i			0.268272i	0.990963	+	0.134136i	$0.0428260\pi$
$37$			1.63184i			0.268272i	−0.990963	+	0.134136i	$0.957174\pi$
$38$	0.698868	+	0.958954i	0.113371	+	0.155563i
$39$	−4.05749			−0.649718
$40$	−2.78253	+	0.917631i	−0.439957	+	0.145090i
$41$	−1.65181			−0.257969			−0.128984	−	0.991647i	$-0.541172\pi$
$41$	−1.65181			−0.257969			−0.128984	+	0.991647i	$0.541172\pi$
$42$	3.09233	+	4.24315i	0.477157	+	0.654732i
$43$			2.17414i			0.331554i	0.986163	+	0.165777i	$0.0530131\pi$
$43$			2.17414i			0.331554i	−0.986163	+	0.165777i	$0.946987\pi$
$44$	3.77531	+	1.21446i	0.569149	+	0.183087i
$45$			1.03589i			0.154421i
$46$	1.14290	−	0.832928i	0.168512	−	0.122809i
$47$	9.26034			1.35076			0.675380	−	0.737470i	$-0.263980\pi$
$47$	9.26034			1.35076			0.675380	+	0.737470i	$0.263980\pi$
$48$	−2.33215	+	3.24978i	−0.336617	+	0.469065i
$49$	6.78340			0.969058
$50$	4.48811	−	3.27085i	0.634714	−	0.462568i
$51$		−	0.0352924i		−	0.00494192i
$52$	−7.72511	−	2.48506i	−1.07128	−	0.344615i
$53$		−	9.53235i		−	1.30937i	−0.755902	−	0.654684i	$-0.772802\pi$
$53$		−	9.53235i		−	1.30937i	0.755902	−	0.654684i	$-0.227198\pi$
$54$	0.832928	+	1.14290i	0.113347	+	0.155530i
$55$	2.05409			0.276973
$56$	3.28876	+	9.97253i	0.439479	+	1.33263i
$57$	0.839050			0.111135
$58$	−7.48337	−	10.2683i	−0.982615	−	1.34830i
$59$			0.521307i			0.0678684i	0.999424	+	0.0339342i	$0.0108037\pi$
$59$			0.521307i			0.0678684i	−0.999424	+	0.0339342i	$0.989196\pi$
$60$	−0.634443	+	1.97225i	−0.0819062	+	0.254616i
$61$			1.08170i			0.138498i	0.997599	+	0.0692488i	$0.0220602\pi$
$61$			1.08170i			0.138498i	−0.997599	+	0.0692488i	$0.977940\pi$
$62$	6.46050	−	4.70830i	0.820485	−	0.597954i
$63$	3.71260			0.467744
$64$	−6.43058	+	4.75895i	−0.803823	+	0.594869i
$65$	−4.20311			−0.521331
$66$	2.26629	−	1.65163i	0.278961	−	0.203302i
$67$			3.82606i			0.467427i	0.972305	+	0.233714i	$0.0750878\pi$
$67$			3.82606i			0.467427i	−0.972305	+	0.233714i	$0.924912\pi$
$68$	0.0216152	−	0.0671936i	0.00262123	−	0.00814843i
$69$		−	1.00000i		−	0.120386i
$70$	3.20331	+	4.39543i	0.382869	+	0.525355i
$71$	−0.0570741			−0.00677345			−0.00338673	−	0.999994i	$-0.501078\pi$
$71$	−0.0570741			−0.00677345			−0.00338673	+	0.999994i	$0.501078\pi$
$72$	0.885838	+	2.68613i	0.104397	+	0.316563i
$73$	2.11118			0.247095			0.123548	−	0.992339i	$-0.460573\pi$
$73$	2.11118			0.247095			0.123548	+	0.992339i	$0.460573\pi$
$74$	1.35920	+	1.86503i	0.158004	+	0.216806i
$75$		−	3.92693i		−	0.453443i
$76$	1.59748	+	0.513886i	0.183243	+	0.0589468i
$77$		−	7.36179i		−	0.838954i
$78$	−4.63732	+	3.37959i	−0.525073	+	0.382664i
$79$	−10.6052			−1.19318			−0.596590	−	0.802546i	$-0.703478\pi$
$79$	−10.6052			−1.19318			−0.596590	+	0.802546i	$0.703478\pi$
$80$	−2.41585	+	3.36641i	−0.270100	+	0.376377i
$81$	1.00000			0.111111
$82$	−1.88786	+	1.37584i	−0.208479	+	0.151936i
$83$		−	12.9986i		−	1.42678i	−0.700766	−	0.713391i	$-0.747158\pi$
$83$		−	12.9986i		−	1.42678i	0.700766	−	0.713391i	$-0.252842\pi$
$84$	7.06847	+	2.27383i	0.771234	+	0.248095i
$85$		−	0.0365590i		−	0.00396538i
$86$	1.81090	+	2.48484i	0.195275	+	0.267947i
$87$	−8.98442			−0.963231
$88$	5.32638	−	1.75655i	0.567794	−	0.187248i
$89$	−8.32127			−0.882053			−0.441026	−	0.897494i	$-0.645385\pi$
$89$	−8.32127			−0.882053			−0.441026	+	0.897494i	$0.645385\pi$
$90$	0.862822	+	1.18392i	0.0909494	+	0.124796i
$91$			15.0638i			1.57912i
$92$	0.612462	−	1.90391i	0.0638536	−	0.198497i
$93$		−	5.65271i		−	0.586158i
$94$	10.5837	−	7.71320i	1.09162	−	0.795556i
$95$	0.869163			0.0891742
$96$	0.0414082	+	5.65670i	0.00422621	+	0.577335i
$97$	17.4131			1.76803			0.884016	−	0.467456i	$-0.154829\pi$
$97$	17.4131			1.76803			0.884016	+	0.467456i	$0.154829\pi$
$98$	7.75278	−	5.65009i	0.783149	−	0.570745i
$99$		−	1.98292i		−	0.199291i
$100$	2.40510	−	7.47654i	0.240510	−	0.747654i
$101$			3.74361i			0.372503i	0.982502	+	0.186252i	$0.0596340\pi$
$101$			3.74361i			0.372503i	−0.982502	+	0.186252i	$0.940366\pi$
$102$	−0.0293960	−	0.0403358i	−0.00291064	−	0.00399384i
$103$	13.8609			1.36575			0.682877	−	0.730533i	$-0.260728\pi$
$103$	13.8609			1.36575			0.682877	+	0.730533i	$0.260728\pi$
$104$	−10.8989	+	3.59428i	−1.06873	+	0.352448i
$105$	3.84584			0.375316
$106$	−7.93976	−	10.8946i	−0.771178	−	1.05817i
$107$		−	0.628866i		−	0.0607947i	−0.999538	−	0.0303974i	$-0.990323\pi$
$107$		−	0.628866i		−	0.0607947i	0.999538	−	0.0303974i	$-0.00967727\pi$
$108$	1.90391	+	0.612462i	0.183204	+	0.0589342i
$109$			17.4967i			1.67588i	0.545763	+	0.837939i	$0.316240\pi$
$109$			17.4967i			1.67588i	−0.545763	+	0.837939i	$0.683760\pi$
$110$	2.34763	−	1.71091i	0.223837	−	0.163129i
$111$	1.63184			0.154887
$112$	12.0651	+	8.65834i	1.14005	+	0.818136i
$113$	18.6143			1.75108			0.875541	−	0.483144i	$-0.160505\pi$
$113$	18.6143			1.75108			0.875541	+	0.483144i	$0.160505\pi$
$114$	0.958954	−	0.698868i	0.0898142	−	0.0654550i
$115$		−	1.03589i		−	0.0965972i
$116$	−17.1056	−	5.50261i	−1.58821	−	0.510905i
$117$			4.05749i			0.375115i
$118$	0.434211	+	0.595804i	0.0399724	+	0.0548482i
$119$	−0.131026			−0.0120112
$120$	0.917631	+	2.78253i	0.0837678	+	0.254009i
$121$	7.06803			0.642548
$122$	0.900979	+	1.23628i	0.0815708	+	0.111928i
$123$			1.65181i			0.148938i
$124$	3.46207	−	10.7623i	0.310903	−	0.966480i
$125$		−	9.24732i		−	0.827105i
$126$	4.24315	−	3.09233i	0.378010	−	0.275487i
$127$	−17.9648			−1.59412			−0.797060	−	0.603900i	$-0.793613\pi$
$127$	−17.9648			−1.59412			−0.797060	+	0.603900i	$0.793613\pi$
$128$	−3.38568	+	10.7952i	−0.299254	+	0.954173i
$129$	2.17414			0.191423
$130$	−4.80375	+	3.50089i	−0.421317	+	0.307048i
$131$			11.4395i			0.999475i	0.866177	+	0.499737i	$0.166570\pi$
$131$			11.4395i			0.999475i	−0.866177	+	0.499737i	$0.833430\pi$
$132$	1.21446	−	3.77531i	0.105705	−	0.328599i
$133$		−	3.11506i		−	0.270110i
$134$	3.18683	+	4.37282i	0.275300	+	0.377754i
$135$	1.03589			0.0891552
$136$	−0.0312633	−	0.0947999i	−0.00268081	−	0.00812902i
$137$	−1.46165			−0.124877			−0.0624387	−	0.998049i	$-0.519888\pi$
$137$	−1.46165			−0.124877			−0.0624387	+	0.998049i	$0.519888\pi$
$138$	−0.832928	−	1.14290i	−0.0709035	−	0.0972905i
$139$			18.8020i			1.59477i	0.603473	+	0.797383i	$0.293783\pi$
$139$			18.8020i			1.59477i	−0.603473	+	0.797383i	$0.706217\pi$
$140$	7.32216	+	2.35543i	0.618835	+	0.199070i
$141$		−	9.26034i		−	0.779862i
$142$	−0.0652303	+	0.0475386i	−0.00547400	+	0.00398935i
$143$	8.04567			0.672813
$144$	3.24978	+	2.33215i	0.270815	+	0.194346i
$145$	−9.30687			−0.772893
$146$	2.41288	−	1.75846i	0.199691	−	0.145531i
$147$		−	6.78340i		−	0.559486i
$148$	3.10688	+	0.999438i	0.255384	+	0.0821533i
$149$		−	7.30712i		−	0.598622i	−0.954156	−	0.299311i	$-0.903243\pi$
$149$		−	7.30712i		−	0.598622i	0.954156	−	0.299311i	$-0.0967568\pi$
$150$	−3.27085	−	4.48811i	−0.267064	−	0.366453i
$151$	6.67219			0.542975			0.271488	−	0.962442i	$-0.412484\pi$
$151$	6.67219			0.542975			0.271488	+	0.962442i	$0.412484\pi$
$152$	2.25380	−	0.743262i	0.182807	−	0.0602865i
$153$	−0.0352924			−0.00285322
$154$	−6.13184	−	8.41382i	−0.494118	−	0.678005i
$155$		−	5.85558i		−	0.470332i
$156$	−2.48506	+	7.72511i	−0.198964	+	0.618503i
$157$		−	4.12484i		−	0.329198i	−0.986361	−	0.164599i	$-0.947367\pi$
$157$		−	4.12484i		−	0.329198i	0.986361	−	0.164599i	$-0.0526330\pi$
$158$	−12.1208	+	8.83338i	−0.964275	+	0.702746i
$159$	−9.53235			−0.755964
$160$	0.0428944	+	5.85972i	0.00339110	+	0.463252i
$161$	−3.71260			−0.292594
$162$	1.14290	−	0.832928i	0.0897951	−	0.0654410i
$163$			13.7415i			1.07632i	0.842842	+	0.538160i	$0.180881\pi$
$163$			13.7415i			1.07632i	−0.842842	+	0.538160i	$0.819119\pi$
$164$	−1.01167	+	3.14490i	−0.0789980	+	0.245575i
$165$		−	2.05409i		−	0.159910i
$166$	−10.8269	−	14.8562i	−0.840331	−	1.15306i
$167$	3.23975			0.250699			0.125350	−	0.992113i	$-0.459995\pi$
$167$	3.23975			0.250699			0.125350	+	0.992113i	$0.459995\pi$
$168$	9.97253	−	3.28876i	0.769397	−	0.253734i
$169$	−3.46319			−0.266399
$170$	−0.0304510	−	0.0417834i	−0.00233549	−	0.00320464i
$171$		−	0.839050i		−	0.0641637i
$172$	4.13938	+	1.33158i	0.315625	+	0.101532i
$173$		−	18.1261i		−	1.37810i	−0.724713	−	0.689051i	$-0.758028\pi$
$173$		−	18.1261i		−	1.37810i	0.724713	−	0.689051i	$-0.241972\pi$
$174$	−10.2683	+	7.48337i	−0.778440	+	0.567313i
$175$	−14.5791			−1.10208
$176$	4.62447	−	6.44406i	0.348582	−	0.485739i
$177$	0.521307			0.0391838
$178$	−9.51041	+	6.93102i	−0.712836	+	0.519502i
$179$		−	6.25406i		−	0.467450i	−0.972303	−	0.233725i	$-0.924908\pi$
$179$		−	6.25406i		−	0.467450i	0.972303	−	0.233725i	$-0.0750916\pi$
$180$	1.97225	+	0.634443i	0.147002	+	0.0472886i
$181$			12.6374i			0.939330i	0.882845	+	0.469665i	$0.155625\pi$
$181$			12.6374i			0.939330i	−0.882845	+	0.469665i	$0.844375\pi$
$182$	12.5471	+	17.2165i	0.930051	+	1.27617i
$183$	1.08170			0.0799616
$184$	−0.885838	−	2.68613i	−0.0653049	−	0.198024i
$185$	1.69040			0.124281
$186$	−4.70830	−	6.46050i	−0.345229	−	0.473707i
$187$			0.0699819i			0.00511759i
$188$	5.67161	−	17.6309i	0.413645	−	1.28587i
$189$		−	3.71260i		−	0.270052i
$190$	0.993370	−	0.723950i	0.0720666	−	0.0525209i
$191$	−17.8806			−1.29380			−0.646898	−	0.762576i	$-0.723934\pi$
$191$	−17.8806			−1.29380			−0.646898	+	0.762576i	$0.723934\pi$
$192$	4.75895	+	6.43058i	0.343448	+	0.464087i
$193$	−2.56140			−0.184374			−0.0921870	−	0.995742i	$-0.529386\pi$
$193$	−2.56140			−0.184374			−0.0921870	+	0.995742i	$0.529386\pi$
$194$	19.9015	−	14.5039i	1.42885	−	1.04132i
$195$			4.20311i			0.300991i
$196$	4.15458	−	12.9150i	0.296755	−	0.922501i
$197$			8.36352i			0.595876i	0.954585	+	0.297938i	$0.0962989\pi$
$197$			8.36352i			0.595876i	−0.954585	+	0.297938i	$0.903701\pi$
$198$	−1.65163	−	2.26629i	−0.117376	−	0.161058i
$199$	−4.24697			−0.301059			−0.150530	−	0.988605i	$-0.548098\pi$
$199$	−4.24697			−0.301059			−0.150530	+	0.988605i	$0.548098\pi$
$200$	−3.47863	−	10.5482i	−0.245976	−	0.745874i
$201$	3.82606			0.269869
$202$	3.11816	+	4.27859i	0.219393	+	0.301041i
$203$			33.3556i			2.34110i
$204$	−0.0671936	−	0.0216152i	−0.00470450	−	0.00151337i
$205$			1.71109i			0.119508i
$206$	15.8417	−	11.5451i	1.10374	−	0.804387i
$207$	−1.00000			−0.0695048
$208$	−9.46267	+	13.1859i	−0.656118	+	0.914280i
$209$	−1.66377			−0.115085
$210$	4.39543	−	3.20331i	0.303314	−	0.221050i
$211$		−	23.2483i		−	1.60048i	−0.599680	−	0.800240i	$-0.704705\pi$
$211$		−	23.2483i		−	1.60048i	0.599680	−	0.800240i	$-0.295295\pi$
$212$	−18.1488	−	5.83820i	−1.24646	−	0.400969i
$213$			0.0570741i			0.00391065i
$214$	−0.523800	−	0.718733i	−0.0358062	−	0.0491316i
$215$	2.25217			0.153597
$216$	2.68613	−	0.885838i	0.182768	−	0.0602737i
$217$	−20.9862			−1.42464
$218$	14.5735	+	19.9970i	0.987041	+	1.35437i
$219$		−	2.11118i		−	0.142660i
$220$	1.25805	−	3.91081i	0.0848177	−	0.263666i
$221$		−	0.143198i		−	0.00963256i
$222$	1.86503	−	1.35920i	0.125173	−	0.0912237i
$223$	−27.1897			−1.82075			−0.910377	−	0.413779i	$-0.864209\pi$
$223$	−27.1897			−1.82075			−0.910377	+	0.413779i	$0.864209\pi$
$224$	21.0011	−	0.153732i	1.40319	−	0.0102717i
$225$	−3.92693			−0.261795
$226$	21.2743	−	15.5043i	1.41515	−	1.03133i
$227$		−	8.83046i		−	0.586098i	−0.956097	−	0.293049i	$-0.905330\pi$
$227$		−	8.83046i		−	0.586098i	0.956097	−	0.293049i	$-0.0946700\pi$
$228$	0.513886	−	1.59748i	0.0340329	−	0.105796i
$229$			25.0163i			1.65313i	0.562844	+	0.826563i	$0.309707\pi$
$229$			25.0163i			1.65313i	−0.562844	+	0.826563i	$0.690293\pi$
$230$	−0.862822	−	1.18392i	−0.0568928	−	0.0780656i
$231$	−7.36179			−0.484370
$232$	−24.1333	+	7.95874i	−1.58443	+	0.522517i
$233$	22.2640			1.45856			0.729282	−	0.684213i	$-0.239854\pi$
$233$	22.2640			1.45856			0.729282	+	0.684213i	$0.239854\pi$
$234$	3.37959	+	4.63732i	0.220931	+	0.303151i
$235$		−	9.59270i		−	0.625758i
$236$	0.992524	+	0.319281i	0.0646078	+	0.0207834i
$237$			10.6052i			0.688883i
$238$	−0.149751	+	0.109136i	−0.00970690	+	0.00707421i
$239$	−4.66752			−0.301917			−0.150958	−	0.988540i	$-0.548236\pi$
$239$	−4.66752			−0.301917			−0.150958	+	0.988540i	$0.548236\pi$
$240$	3.36641	+	2.41585i	0.217301	+	0.155942i
$241$	17.6837			1.13911			0.569555	−	0.821953i	$-0.307116\pi$
$241$	17.6837			1.13911			0.569555	+	0.821953i	$0.307116\pi$
$242$	8.07808	−	5.88716i	0.519279	−	0.378441i
$243$		−	1.00000i		−	0.0641500i
$244$	2.05947	+	0.662500i	0.131844	+	0.0424122i
$245$		−	7.02686i		−	0.448930i
$246$	1.37584	+	1.88786i	0.0877200	+	0.120365i
$247$	3.40443			0.216619
$248$	−5.00738	−	15.1839i	−0.317969	−	0.964179i
$249$	−12.9986			−0.823753
$250$	−7.70235	−	10.5688i	−0.487139	−	0.668430i
$251$			4.11640i			0.259825i	0.991525	+	0.129912i	$0.0414696\pi$
$251$			4.11640i			0.259825i	−0.991525	+	0.129912i	$0.958530\pi$
$252$	2.27383	−	7.06847i	0.143238	−	0.445272i
$253$			1.98292i			0.124665i
$254$	−20.5321	+	14.9634i	−1.28830	+	0.938888i
$255$	−0.0365590			−0.00228941
$256$	5.12215	+	15.1580i	0.320134	+	0.947372i
$257$	−19.7060			−1.22923			−0.614614	−	0.788828i	$-0.710688\pi$
$257$	−19.7060			−1.22923			−0.614614	+	0.788828i	$0.710688\pi$
$258$	2.48484	−	1.81090i	0.154699	−	0.112742i
$259$		−	6.05836i		−	0.376448i
$260$	−2.57424	+	8.00236i	−0.159648	+	0.496285i
$261$			8.98442i			0.556122i
$262$	9.52829	+	13.0743i	0.588660	+	0.807731i
$263$	−12.1168			−0.747155			−0.373577	−	0.927599i	$-0.621869\pi$
$263$	−12.1168			−0.747155			−0.373577	+	0.927599i	$0.621869\pi$
$264$	−1.75655	−	5.32638i	−0.108108	−	0.327816i
$265$	−9.87446			−0.606583
$266$	−2.59462	−	3.56021i	−0.159086	−	0.218291i
$267$			8.32127i			0.509253i
$268$	7.28449	+	2.34331i	0.444971	+	0.143141i
$269$			16.2608i			0.991441i	0.868482	+	0.495720i	$0.165096\pi$
$269$			16.2608i			0.991441i	−0.868482	+	0.495720i	$0.834904\pi$
$270$	1.18392	−	0.862822i	0.0720513	−	0.0525096i
$271$	15.3045			0.929685			0.464843	−	0.885393i	$-0.346111\pi$
$271$	15.3045			0.929685			0.464843	+	0.885393i	$0.346111\pi$
$272$	−0.114692	−	0.0823071i	−0.00695425	−	0.00499060i
$273$	15.0638			0.911704
$274$	−1.67053	+	1.21745i	−0.100920	+	0.0735489i
$275$			7.78679i			0.469561i
$276$	−1.90391	−	0.612462i	−0.114602	−	0.0368659i
$277$		−	11.1209i		−	0.668188i	−0.942540	−	0.334094i	$-0.891570\pi$
$277$		−	11.1209i		−	0.668188i	0.942540	−	0.334094i	$-0.108430\pi$
$278$	15.6607	+	21.4889i	0.939268	+	1.28882i
$279$	−5.65271			−0.338419
$280$	10.3304	−	3.40680i	0.617362	−	0.203595i
$281$	−31.5006			−1.87917			−0.939584	−	0.342317i	$-0.888788\pi$
$281$	−31.5006			−1.87917			−0.939584	+	0.342317i	$0.888788\pi$
$282$	−7.71320	−	10.5837i	−0.459314	−	0.630250i
$283$			19.1846i			1.14041i	0.821504	+	0.570203i	$0.193135\pi$
$283$			19.1846i			1.14041i	−0.821504	+	0.570203i	$0.806865\pi$
$284$	−0.0349557	+	0.108664i	−0.00207424	+	0.00644804i
$285$		−	0.869163i		−	0.0514848i
$286$	9.19543	−	6.70146i	0.543737	−	0.396266i
$287$	6.13249			0.361990
$288$	5.65670	−	0.0414082i	0.333324	−	0.00244000i
$289$	−16.9988			−0.999927
$290$	−10.6369	+	7.75195i	−0.624618	+	0.455210i
$291$		−	17.4131i		−	1.02077i
$292$	1.29302	−	4.01951i	0.0756682	−	0.235224i
$293$			29.1881i			1.70519i	0.522574	+	0.852594i	$0.324972\pi$
$293$			29.1881i			1.70519i	−0.522574	+	0.852594i	$0.675028\pi$
$294$	−5.65009	−	7.75278i	−0.329520	−	0.452152i
$295$	0.540017			0.0314410
$296$	4.38333	−	1.44554i	0.254776	−	0.0840205i
$297$	−1.98292			−0.115061
$298$	−6.08630	−	8.35134i	−0.352570	−	0.483780i
$299$		−	4.05749i		−	0.234650i
$300$	−7.47654	−	2.40510i	−0.431658	−	0.138858i
$301$		−	8.07172i		−	0.465246i
$302$	7.62568	−	5.55745i	0.438808	−	0.319796i
$303$	3.74361			0.215065
$304$	1.95679	−	2.72673i	0.112230	−	0.156389i
$305$	1.12052			0.0641609
$306$	−0.0403358	+	0.0293960i	−0.00230584	+	0.00168046i
$307$		−	15.3866i		−	0.878160i	−0.898448	−	0.439080i	$-0.855304\pi$
$307$		−	15.3866i		−	0.878160i	0.898448	−	0.439080i	$-0.144696\pi$
$308$	−14.0162	−	4.50882i	−0.798648	−	0.256914i
$309$		−	13.8609i		−	0.788519i
$310$	−4.87728	−	6.69237i	−0.277011	−	0.380101i
$311$	−22.4890			−1.27523			−0.637616	−	0.770354i	$-0.720079\pi$
$311$	−22.4890			−1.27523			−0.637616	+	0.770354i	$0.720079\pi$
$312$	3.59428	+	10.8989i	0.203486	+	0.617030i
$313$	24.1804			1.36676			0.683379	−	0.730064i	$-0.260510\pi$
$313$	24.1804			1.36676			0.683379	+	0.730064i	$0.260510\pi$
$314$	−3.43570	−	4.71430i	−0.193888	−	0.266043i
$315$		−	3.84584i		−	0.216689i
$316$	−6.49529	+	20.1914i	−0.365389	+	1.13586i
$317$		−	8.16834i		−	0.458780i	−0.973335	−	0.229390i	$-0.926327\pi$
$317$		−	8.16834i		−	0.458780i	0.973335	−	0.229390i	$-0.0736731\pi$
$318$	−10.8946	+	7.93976i	−0.610937	+	0.445240i
$319$	17.8154			0.997470
$320$	4.92975	+	6.66137i	0.275581	+	0.372382i
$321$	−0.628866			−0.0350998
$322$	−4.24315	+	3.09233i	−0.236461	+	0.172329i
$323$			0.0296120i			0.00164766i
$324$	0.612462	−	1.90391i	0.0340257	−	0.105773i
$325$		−	15.9335i		−	0.883830i
$326$	11.4457	+	15.7053i	0.633920	+	0.869835i
$327$	17.4967			0.967569
$328$	1.46323	+	4.43696i	0.0807935	+	0.244990i
$329$	−34.3800			−1.89543
$330$	−1.71091	−	2.34763i	−0.0941823	−	0.129233i
$331$		−	26.7727i		−	1.47156i	−0.677220	−	0.735781i	$-0.736815\pi$
$331$		−	26.7727i		−	1.47156i	0.677220	−	0.735781i	$-0.263185\pi$
$332$	−24.7482	−	7.96115i	−1.35824	−	0.436925i
$333$		−	1.63184i		−	0.0894241i
$334$	3.70272	−	2.69848i	0.202604	−	0.147654i
$335$	3.96337			0.216542
$336$	8.65834	−	12.0651i	0.472351	−	0.658207i
$337$	−33.0578			−1.80077			−0.900386	−	0.435092i	$-0.856716\pi$
$337$	−33.0578			−1.80077			−0.900386	+	0.435092i	$0.856716\pi$
$338$	−3.95809	+	2.88459i	−0.215292	+	0.156901i
$339$		−	18.6143i		−	1.01099i
$340$	−0.0696052	−	0.0223910i	−0.00377487	−	0.00121432i
$341$			11.2089i			0.606994i
$342$	−0.698868	−	0.958954i	−0.0377904	−	0.0518543i
$343$	0.804135			0.0434192
$344$	5.84003	−	1.92594i	0.314873	−	0.103840i
$345$	−1.03589			−0.0557704
$346$	−15.0977	−	20.7164i	−0.811659	−	1.11372i
$347$		−	21.8355i		−	1.17219i	−0.810242	−	0.586095i	$-0.800664\pi$
$347$		−	21.8355i		−	1.17219i	0.810242	−	0.586095i	$-0.199336\pi$
$348$	−5.50261	+	17.1056i	−0.294971	+	0.916954i
$349$			26.5464i			1.42099i	0.703700	+	0.710497i	$0.251530\pi$
$349$			26.5464i			1.42099i	−0.703700	+	0.710497i	$0.748470\pi$
$350$	−16.6626	+	12.1434i	−0.890651	+	0.649090i
$351$	4.05749			0.216573
$352$	−0.0821092	−	11.2168i	−0.00437644	−	0.597857i
$353$	−1.79765			−0.0956794			−0.0478397	−	0.998855i	$-0.515234\pi$
$353$	−1.79765			−0.0956794			−0.0478397	+	0.998855i	$0.515234\pi$
$354$	0.595804	−	0.434211i	0.0316666	−	0.0230781i
$355$			0.0591225i			0.00313790i
$356$	−5.09646	+	15.8430i	−0.270112	+	0.839676i
$357$			0.131026i			0.00693466i
$358$	−5.20918	−	7.14780i	−0.275314	−	0.377773i
$359$	29.4648			1.55509			0.777547	−	0.628824i	$-0.216464\pi$
$359$	29.4648			1.55509			0.777547	+	0.628824i	$0.216464\pi$
$360$	2.78253	−	0.917631i	0.146652	−	0.0483634i
$361$	18.2960			0.962947
$362$	10.5260	+	14.4433i	0.553236	+	0.759125i
$363$		−	7.06803i		−	0.370975i
$364$	28.6802	+	9.22602i	1.50325	+	0.483575i
$365$		−	2.18695i		−	0.114470i
$366$	1.23628	−	0.900979i	0.0646214	−	0.0470949i
$367$	−4.47265			−0.233470			−0.116735	−	0.993163i	$-0.537243\pi$
$367$	−4.47265			−0.233470			−0.116735	+	0.993163i	$0.537243\pi$
$368$	−3.24978	−	2.33215i	−0.169407	−	0.121572i
$369$	1.65181			0.0859896
$370$	1.93197	−	1.40798i	0.100438	−	0.0731976i
$371$			35.3898i			1.83735i
$372$	−10.7623	−	3.46207i	−0.557998	−	0.179500i
$373$		−	9.38766i		−	0.486075i	−0.970017	−	0.243037i	$-0.921856\pi$
$373$		−	9.38766i		−	0.486075i	0.970017	−	0.243037i	$-0.0781438\pi$
$374$	0.0582899	+	0.0799827i	0.00301410	+	0.00413581i
$375$	−9.24732			−0.477529
$376$	−8.20317	−	24.8745i	−0.423046	−	1.28280i
$377$	−36.4541			−1.87748
$378$	−3.09233	−	4.24315i	−0.159052	−	0.218244i
$379$			9.91274i			0.509183i	0.967049	+	0.254592i	$0.0819410\pi$
$379$			9.91274i			0.509183i	−0.967049	+	0.254592i	$0.918059\pi$
$380$	0.532329	−	1.65481i	0.0273079	−	0.0848900i
$381$			17.9648i			0.920366i
$382$	−20.4358	+	14.8933i	−1.04559	+	0.762006i
$383$	34.2745			1.75134			0.875672	−	0.482907i	$-0.160419\pi$
$383$	34.2745			1.75134			0.875672	+	0.482907i	$0.160419\pi$
$384$	10.7952	+	3.38568i	0.550892	+	0.172775i
$385$	−7.62600			−0.388657
$386$	−2.92744	+	2.13347i	−0.149003	+	0.108591i
$387$		−	2.17414i		−	0.110518i
$388$	10.6649	−	33.1531i	0.541426	−	1.68309i
$389$		−	17.0908i		−	0.866539i	−0.901264	−	0.433269i	$-0.857360\pi$
$389$		−	17.0908i		−	0.866539i	0.901264	−	0.433269i	$-0.142640\pi$
$390$	3.50089	+	4.80375i	0.177274	+	0.243247i
$391$	0.0352924			0.00178481
$392$	−6.00900	−	18.2211i	−0.303500	−	0.920305i
$393$	11.4395			0.577047
$394$	6.96621	+	9.55871i	0.350953	+	0.481561i
$395$			10.9858i			0.552757i
$396$	−3.77531	−	1.21446i	−0.189716	−	0.0610291i
$397$			14.1217i			0.708750i	0.935103	+	0.354375i	$0.115306\pi$
$397$			14.1217i			0.708750i	−0.935103	+	0.354375i	$0.884694\pi$
$398$	−4.85388	+	3.53742i	−0.243303	+	0.177315i
$399$	−3.11506			−0.155948
$400$	−12.7617	−	9.15820i	−0.638083	−	0.457910i
$401$	−20.8984			−1.04362			−0.521808	−	0.853063i	$-0.674742\pi$
$401$	−20.8984			−1.04362			−0.521808	+	0.853063i	$0.674742\pi$
$402$	4.37282	−	3.18683i	0.218096	−	0.158945i
$403$		−	22.9358i		−	1.14251i
$404$	7.12752	+	2.29282i	0.354607	+	0.114072i
$405$		−	1.03589i		−	0.0514738i
$406$	27.7828	+	38.1222i	1.37884	+	1.89197i
$407$	−3.23580			−0.160393
$408$	−0.0947999	+	0.0312633i	−0.00469329	+	0.00154777i
$409$	20.5558			1.01642			0.508209	−	0.861234i	$-0.330308\pi$
$409$	20.5558			1.01642			0.508209	+	0.861234i	$0.330308\pi$
$410$	1.42521	+	1.95561i	0.0703863	+	0.0965807i
$411$			1.46165i			0.0720980i
$412$	8.48927	−	26.3900i	0.418236	−	1.30014i
$413$		−	1.93541i		−	0.0952351i
$414$	−1.14290	+	0.832928i	−0.0561707	+	0.0409362i
$415$	−13.4651			−0.660977
$416$	0.168013	+	22.9520i	0.00823753	+	1.12531i
$417$	18.8020			0.920739
$418$	−1.90153	+	1.38580i	−0.0930068	+	0.0677817i
$419$			16.3140i			0.796990i	0.917171	+	0.398495i	$0.130467\pi$
$419$			16.3140i			0.796990i	−0.917171	+	0.398495i	$0.869533\pi$
$420$	2.35543	−	7.32216i	0.114933	−	0.357285i
$421$		−	19.9773i		−	0.973636i	−0.873503	−	0.486818i	$-0.838157\pi$
$421$		−	19.9773i		−	0.973636i	0.873503	−	0.486818i	$-0.161843\pi$
$422$	−19.3642	−	26.5706i	−0.942633	−	1.29344i
$423$	−9.26034			−0.450253
$424$	−25.6051	+	8.44412i	−1.24349	+	0.410083i
$425$	0.138591			0.00672264
$426$	0.0475386	+	0.0652303i	0.00230325	+	0.00316042i
$427$		−	4.01592i		−	0.194344i
$428$	−1.19731	−	0.385156i	−0.0578740	−	0.0186172i
$429$		−	8.04567i		−	0.388449i
$430$	2.57402	−	1.87590i	0.124130	−	0.0904638i
$431$	6.28068			0.302530			0.151265	−	0.988493i	$-0.451665\pi$
$431$	6.28068			0.302530			0.151265	+	0.988493i	$0.451665\pi$
$432$	2.33215	−	3.24978i	0.112206	−	0.156355i
$433$	16.6871			0.801929			0.400964	−	0.916094i	$-0.368675\pi$
$433$	16.6871			0.801929			0.400964	+	0.916094i	$0.368675\pi$
$434$	−23.9853	+	17.4800i	−1.15133	+	0.839068i
$435$			9.30687i			0.446230i
$436$	33.3122	+	10.7161i	1.59536	+	0.513206i
$437$			0.839050i			0.0401372i
$438$	−1.75846	−	2.41288i	−0.0840226	−	0.115292i
$439$	10.5597			0.503985			0.251993	−	0.967729i	$-0.418914\pi$
$439$	10.5597			0.503985			0.251993	+	0.967729i	$0.418914\pi$
$440$	−1.81959	−	5.51754i	−0.0867455	−	0.263039i
$441$	−6.78340			−0.323019
$442$	−0.119274	−	0.163662i	−0.00567328	−	0.00778461i
$443$		−	2.31761i		−	0.110113i	−0.998483	−	0.0550564i	$-0.982466\pi$
$443$		−	2.31761i		−	0.110113i	0.998483	−	0.0550564i	$-0.0175339\pi$
$444$	0.999438	−	3.10688i	0.0474312	−	0.147446i
$445$			8.61992i			0.408623i
$446$	−31.0752	+	22.6470i	−1.47145	+	1.07237i
$447$	−7.30712			−0.345615
$448$	23.8742	−	17.6681i	1.12795	−	0.834739i
$449$	−8.86194			−0.418221			−0.209111	−	0.977892i	$-0.567057\pi$
$449$	−8.86194			−0.418221			−0.209111	+	0.977892i	$0.567057\pi$
$450$	−4.48811	+	3.27085i	−0.211571	+	0.154189i
$451$		−	3.27540i		−	0.154232i
$452$	11.4005	−	35.4399i	0.536235	−	1.66695i
$453$		−	6.67219i		−	0.313487i
$454$	−7.35514	−	10.0924i	−0.345194	−	0.473659i
$455$	15.6045			0.731548
$456$	−0.743262	−	2.25380i	−0.0348064	−	0.105544i
$457$	−11.1767			−0.522823			−0.261411	−	0.965228i	$-0.584188\pi$
$457$	−11.1767			−0.522823			−0.261411	+	0.965228i	$0.584188\pi$
$458$	20.8368	+	28.5913i	0.973640	+	1.33598i
$459$			0.0352924i			0.00164731i
$460$	−1.97225	−	0.634443i	−0.0919564	−	0.0295811i
$461$		−	14.5453i		−	0.677443i	−0.940887	−	0.338722i	$-0.890005\pi$
$461$		−	14.5453i		−	0.677443i	0.940887	−	0.338722i	$-0.109995\pi$
$462$	−8.41382	+	6.13184i	−0.391447	+	0.285279i
$463$	13.3702			0.621366			0.310683	−	0.950514i	$-0.399442\pi$
$463$	13.3702			0.621366			0.310683	+	0.950514i	$0.399442\pi$
$464$	−20.9530	+	29.1974i	−0.972719	+	1.35545i
$465$	−5.85558			−0.271546
$466$	25.4457	−	18.5443i	1.17875	−	0.859049i
$467$		−	21.0042i		−	0.971960i	−0.873970	−	0.485980i	$-0.838463\pi$
$467$		−	21.0042i		−	0.971960i	0.873970	−	0.485980i	$-0.161537\pi$
$468$	7.72511	+	2.48506i	0.357093	+	0.114872i
$469$		−	14.2046i		−	0.655909i
$470$	−7.99002	−	10.9635i	−0.368552	−	0.505710i
$471$	−4.12484			−0.190063
$472$	1.40030	−	0.461794i	0.0644540	−	0.0212558i
$473$	−4.31115			−0.198227
$474$	8.83338	+	12.1208i	0.405731	+	0.556725i
$475$			3.29489i			0.151180i
$476$	−0.0802487	+	0.249463i	−0.00367819	+	0.0114341i
$477$			9.53235i			0.436456i
$478$	−5.33453	+	3.88770i	−0.243996	+	0.177819i
$479$	6.39527			0.292207			0.146104	−	0.989269i	$-0.453327\pi$
$479$	6.39527			0.292207			0.146104	+	0.989269i	$0.453327\pi$
$480$	5.85972	−	0.0428944i	0.267458	−	0.00195785i
$481$	6.62116			0.301899
$482$	20.2108	−	14.7293i	0.920578	−	0.670900i
$483$			3.71260i			0.168929i
$484$	4.32890	−	13.4569i	0.196768	−	0.611678i
$485$		−	18.0381i		−	0.819066i
$486$	−0.832928	−	1.14290i	−0.0377824	−	0.0518432i
$487$	25.2354			1.14352			0.571762	−	0.820420i	$-0.306260\pi$
$487$	25.2354			1.14352			0.571762	+	0.820420i	$0.306260\pi$
$488$	2.90559	−	0.958212i	0.131530	−	0.0433762i
$489$	13.7415			0.621414
$490$	−5.85287	−	8.03103i	−0.264406	−	0.362805i
$491$			38.6086i			1.74238i	0.490945	+	0.871191i	$0.336652\pi$
$491$			38.6086i			1.74238i	−0.490945	+	0.871191i	$0.663348\pi$
$492$	3.14490	+	1.01167i	0.141783	+	0.0456095i
$493$		−	0.317081i		−	0.0142806i
$494$	3.89094	−	2.83565i	0.175062	−	0.127582i
$495$	−2.05409			−0.0923243
$496$	−18.3701	−	13.1830i	−0.824840	−	0.591932i
$497$	0.211893			0.00950472
$498$	−14.8562	+	10.8269i	−0.665721	+	0.485165i
$499$		−	42.0927i		−	1.88433i	−0.335153	−	0.942164i	$-0.608788\pi$
$499$		−	42.0927i		−	1.88433i	0.335153	−	0.942164i	$-0.391212\pi$
$500$	−17.6061	−	5.66363i	−0.787369	−	0.253285i
$501$		−	3.23975i		−	0.144741i
$502$	3.42866	+	4.70465i	0.153029	+	0.209979i
$503$	37.8332			1.68690			0.843449	−	0.537210i	$-0.180522\pi$
$503$	37.8332			1.68690			0.843449	+	0.537210i	$0.180522\pi$
$504$	−3.28876	−	9.97253i	−0.146493	−	0.444212i
$505$	3.87797			0.172567
$506$	1.65163	+	2.26629i	0.0734239	+	0.100749i
$507$			3.46319i			0.153806i
$508$	−11.0028	+	34.2035i	−0.488169	+	1.51753i
$509$			19.8782i			0.881088i	0.897731	+	0.440544i	$0.145214\pi$
$509$			19.8782i			0.881088i	−0.897731	+	0.440544i	$0.854786\pi$
$510$	−0.0417834	+	0.0304510i	−0.00185020	+	0.00134839i
$511$	−7.83798			−0.346732
$512$	18.4796	+	13.0577i	0.816691	+	0.577075i
$513$	−0.839050			−0.0370449
$514$	−22.5221	+	16.4137i	−0.993407	+	0.723977i
$515$		−	14.3584i		−	0.632705i
$516$	1.33158	−	4.13938i	0.0586195	−	0.182226i
$517$			18.3625i			0.807583i
$518$	−5.04618	−	6.92413i	−0.221716	−	0.304229i
$519$	−18.1261			−0.795647
$520$	3.72327	+	11.2901i	0.163276	+	0.495103i
$521$	24.0911			1.05545			0.527726	−	0.849415i	$-0.323045\pi$
$521$	24.0911			1.05545			0.527726	+	0.849415i	$0.323045\pi$
$522$	7.48337	+	10.2683i	0.327538	+	0.449433i
$523$		−	6.89987i		−	0.301710i	−0.988556	−	0.150855i	$-0.951797\pi$
$523$		−	6.89987i		−	0.301710i	0.988556	−	0.150855i	$-0.0482027\pi$
$524$	21.7798	+	7.00626i	0.951457	+	0.306070i
$525$			14.5791i			0.636285i
$526$	−13.8484	+	10.0924i	−0.603817	+	0.440051i
$527$	0.199497			0.00869024
$528$	−6.44406	−	4.62447i	−0.280442	−	0.201254i
$529$	1.00000			0.0434783
$530$	−11.2856	+	8.22471i	−0.490214	+	0.357259i
$531$		−	0.521307i		−	0.0226228i
$532$	−5.93080	−	1.90785i	−0.257133	−	0.0827159i
$533$			6.70218i			0.290304i
$534$	6.93102	+	9.51041i	0.299934	+	0.411556i
$535$	−0.651435			−0.0281640
$536$	10.2773	−	3.38927i	0.443911	−	0.146394i
$537$	−6.25406			−0.269883
$538$	13.5441	+	18.5846i	0.583928	+	0.801238i
$539$			13.4509i			0.579373i
$540$	0.634443	−	1.97225i	0.0273021	−	0.0848719i
$541$			31.7799i			1.36633i	0.730266	+	0.683163i	$0.239396\pi$
$541$			31.7799i			1.36633i	−0.730266	+	0.683163i	$0.760604\pi$
$542$	17.4916	−	12.7476i	0.751330	−	0.547556i
$543$	12.6374			0.542323
$544$	−0.199638	+	0.00146139i	−0.00855943	+	6.26568e-5i
$545$	18.1246			0.776374
$546$	17.2165	−	12.5471i	0.736799	−	0.536965i
$547$		−	3.03957i		−	0.129963i	−0.997886	−	0.0649814i	$-0.979301\pi$
$547$		−	3.03957i		−	0.129963i	0.997886	−	0.0649814i	$-0.0206988\pi$
$548$	−0.895206	+	2.78286i	−0.0382413	+	0.118878i
$549$		−	1.08170i		−	0.0461659i
$550$	6.48584	+	8.89956i	0.276557	+	0.379479i
$551$	7.53837			0.321145
$552$	−2.68613	+	0.885838i	−0.114329	+	0.0377038i
$553$	39.3729			1.67431
$554$	−9.26288	−	12.7101i	−0.393542	−	0.540000i
$555$		−	1.69040i		−	0.0717536i
$556$	35.7974	+	11.5155i	1.51815	+	0.488367i
$557$		−	1.27269i		−	0.0539258i	−0.999636	−	0.0269629i	$-0.991416\pi$
$557$		−	1.27269i		−	0.0539258i	0.999636	−	0.0269629i	$-0.00858360\pi$
$558$	−6.46050	+	4.70830i	−0.273495	+	0.199318i
$559$	8.82155			0.373112
$560$	8.96909	−	12.4982i	0.379013	−	0.528143i
$561$	0.0699819			0.00295464
$562$	−36.0022	+	26.2377i	−1.51866	+	1.10677i
$563$		−	28.3319i		−	1.19405i	−0.802223	−	0.597024i	$-0.796350\pi$
$563$		−	28.3319i		−	1.19405i	0.802223	−	0.597024i	$-0.203650\pi$
$564$	−17.6309	−	5.67161i	−0.742395	−	0.238818i
$565$		−	19.2823i		−	0.811213i
$566$	15.9794	+	21.9262i	0.671664	+	0.921625i
$567$	−3.71260			−0.155915
$568$	0.0505584	+	0.153308i	0.00212138	+	0.00643268i
$569$	−22.2098			−0.931082			−0.465541	−	0.885026i	$-0.654140\pi$
$569$	−22.2098			−0.931082			−0.465541	+	0.885026i	$0.654140\pi$
$570$	−0.723950	−	0.993370i	−0.0303229	−	0.0416077i
$571$			5.60588i			0.234599i	0.993097	+	0.117299i	$0.0374237\pi$
$571$			5.60588i			0.234599i	−0.993097	+	0.117299i	$0.962576\pi$
$572$	4.92767	−	15.3183i	0.206036	−	0.640489i
$573$			17.8806i			0.746974i
$574$	7.00886	−	5.10793i	0.292544	−	0.213201i
$575$	3.92693			0.163764
$576$	6.43058	−	4.75895i	0.267941	−	0.198290i
$577$	8.63486			0.359474			0.179737	−	0.983715i	$-0.442475\pi$
$577$	8.63486			0.359474			0.179737	+	0.983715i	$0.442475\pi$
$578$	−19.4280	+	14.1587i	−0.808096	+	0.588926i
$579$			2.56140i			0.106448i
$580$	−5.70010	+	17.7195i	−0.236684	+	0.735761i
$581$			48.2586i			2.00211i
$582$	−14.5039	−	19.9015i	−0.601204	−	0.824944i
$583$	18.9019			0.782836
$584$	−1.87017	−	5.67091i	−0.0773880	−	0.234664i
$585$	4.20311			0.173777
$586$	24.3116	+	33.3592i	1.00430	+	1.37806i
$587$			5.46776i			0.225679i	0.993613	+	0.112839i	$0.0359946\pi$
$587$			5.46776i			0.225679i	−0.993613	+	0.112839i	$0.964005\pi$
$588$	−12.9150	−	4.15458i	−0.532606	−	0.171332i
$589$			4.74290i			0.195428i
$590$	0.617188	−	0.449795i	0.0254092	−	0.0185178i
$591$	8.36352			0.344029
$592$	3.80569	−	5.30311i	0.156413	−	0.217957i
$593$	40.5175			1.66385			0.831927	−	0.554884i	$-0.187238\pi$
$593$	40.5175			1.66385			0.831927	+	0.554884i	$0.187238\pi$
$594$	−2.26629	+	1.65163i	−0.0929869	+	0.0677672i
$595$			0.135729i			0.00556435i
$596$	−13.9121	−	4.47533i	−0.569863	−	0.183317i
$597$			4.24697i			0.173817i
$598$	−3.37959	−	4.63732i	−0.138202	−	0.189634i
$599$	−4.37851			−0.178901			−0.0894505	−	0.995991i	$-0.528511\pi$
$599$	−4.37851			−0.178901			−0.0894505	+	0.995991i	$0.528511\pi$
$600$	−10.5482	+	3.47863i	−0.430630	+	0.142014i
$601$	3.04134			0.124059			0.0620294	−	0.998074i	$-0.480243\pi$
$601$	3.04134			0.124059			0.0620294	+	0.998074i	$0.480243\pi$
$602$	−6.72317	−	9.22521i	−0.274016	−	0.375992i
$603$		−	3.82606i		−	0.155809i
$604$	4.08646	−	12.7033i	0.166276	−	0.516889i
$605$		−	7.32170i		−	0.297669i
$606$	4.27859	−	3.11816i	0.173806	−	0.126667i
$607$	14.2779			0.579520			0.289760	−	0.957099i	$-0.406424\pi$
$607$	14.2779			0.579520			0.289760	+	0.957099i	$0.406424\pi$
$608$	−0.0347436	−	4.74625i	−0.00140904	−	0.192486i
$609$	33.3556			1.35164
$610$	1.28065	−	0.933315i	0.0518520	−	0.0377888i
$611$		−	37.5737i		−	1.52007i
$612$	−0.0216152	+	0.0671936i	−0.000873744	+	0.00271614i
$613$		−	2.22906i		−	0.0900308i	−0.998986	−	0.0450154i	$-0.985666\pi$
$613$		−	2.22906i		−	0.0900308i	0.998986	−	0.0450154i	$-0.0143337\pi$
$614$	−12.8159	−	17.5854i	−0.517209	−	0.709690i
$615$	1.71109			0.0689977
$616$	−19.7747	+	6.52136i	−0.796746	+	0.262753i
$617$	9.07230			0.365237			0.182618	−	0.983184i	$-0.441543\pi$
$617$	9.07230			0.365237			0.182618	+	0.983184i	$0.441543\pi$
$618$	−11.5451	−	15.8417i	−0.464413	−	0.637246i
$619$			3.24295i			0.130345i	0.997874	+	0.0651726i	$0.0207598\pi$
$619$			3.24295i			0.130345i	−0.997874	+	0.0651726i	$0.979240\pi$
$620$	−11.1485	−	3.58632i	−0.447735	−	0.144030i
$621$			1.00000i			0.0401286i
$622$	−25.7027	+	18.7317i	−1.03059	+	0.751072i
$623$	30.8935			1.23772
$624$	13.1859	+	9.46267i	0.527860	+	0.378810i
$625$	10.0555			0.402218
$626$	27.6359	−	20.1405i	1.10455	−	0.804978i
$627$			1.66377i			0.0664445i
$628$	−7.85334	−	2.52631i	−0.313383	−	0.100811i
$629$			0.0575914i			0.00229632i
$630$	−3.20331	−	4.39543i	−0.127623	−	0.175118i
$631$	5.73771			0.228415			0.114207	−	0.993457i	$-0.463567\pi$
$631$	5.73771			0.228415			0.114207	+	0.993457i	$0.463567\pi$
$632$	9.39451	+	28.4870i	0.373693	+	1.13315i
$633$	−23.2483			−0.924038
$634$	−6.80364	−	9.33564i	−0.270207	−	0.370766i
$635$			18.6096i			0.738499i
$636$	−5.83820	+	18.1488i	−0.231500	+	0.719646i
$637$		−	27.5236i		−	1.09052i
$638$	20.3613	−	14.8389i	0.806111	−	0.587479i
$639$	0.0570741			0.00225782
$640$	11.1827	+	3.50719i	0.442034	+	0.138634i
$641$	44.4992			1.75761			0.878807	−	0.477178i	$-0.158340\pi$
$641$	44.4992			1.75761			0.878807	+	0.477178i	$0.158340\pi$
$642$	−0.718733	+	0.523800i	−0.0283661	+	0.0206727i
$643$			13.4068i			0.528714i	0.964425	+	0.264357i	$0.0851598\pi$
$643$			13.4068i			0.528714i	−0.964425	+	0.264357i	$0.914840\pi$
$644$	−2.27383	+	7.06847i	−0.0896013	+	0.278537i
$645$		−	2.25217i		−	0.0886792i
$646$	0.0246647	+	0.0338437i	0.000970420	+	0.00133156i
$647$	18.2256			0.716521			0.358261	−	0.933622i	$-0.383370\pi$
$647$	18.2256			0.716521			0.358261	+	0.933622i	$0.383370\pi$
$648$	−0.885838	−	2.68613i	−0.0347990	−	0.105521i
$649$	−1.03371			−0.0405767
$650$	−13.2714	−	18.2104i	−0.520548	−	0.714272i
$651$			20.9862i			0.822516i
$652$	26.1627	+	8.41617i	1.02461	+	0.329603i
$653$			49.1873i			1.92485i	0.271551	+	0.962424i	$0.412463\pi$
$653$			49.1873i			1.92485i	−0.271551	+	0.962424i	$0.587537\pi$
$654$	19.9970	−	14.5735i	0.781946	−	0.569868i
$655$	11.8501			0.463021
$656$	5.36801	+	3.85226i	0.209585	+	0.150405i
$657$	−2.11118			−0.0823651
$658$	−39.2930	+	28.6360i	−1.53180	+	1.11635i
$659$		−	11.5711i		−	0.450746i	−0.974273	−	0.225373i	$-0.927640\pi$
$659$		−	11.5711i		−	0.450746i	0.974273	−	0.225373i	$-0.0723601\pi$
$660$	−3.91081	−	1.25805i	−0.152228	−	0.0489695i
$661$			12.5878i			0.489609i	0.969572	+	0.244804i	$0.0787237\pi$
$661$			12.5878i			0.489609i	−0.969572	+	0.244804i	$0.921276\pi$
$662$	−22.2997	−	30.5987i	−0.866704	−	1.18925i
$663$	−0.143198			−0.00556136
$664$	−34.9159	+	11.5147i	−1.35500	+	0.446856i
$665$	−3.22685			−0.125132
$666$	−1.35920	−	1.86503i	−0.0526680	−	0.0722686i
$667$		−	8.98442i		−	0.347878i
$668$	1.98422	−	6.16820i	0.0767718	−	0.238655i
$669$			27.1897i			1.05121i
$670$	4.52976	−	3.30121i	0.175000	−	0.127537i
$671$	−2.14493			−0.0828039
$672$	−0.153732	−	21.0011i	−0.00593035	−	0.810134i
$673$	−27.6053			−1.06411			−0.532054	−	0.846710i	$-0.678580\pi$
$673$	−27.6053			−1.06411			−0.532054	+	0.846710i	$0.678580\pi$
$674$	−37.7819	+	27.5347i	−1.45530	+	1.06060i
$675$			3.92693i			0.151148i
$676$	−2.12107	+	6.59362i	−0.0815797	+	0.253601i
$677$			4.67781i			0.179783i	0.995952	+	0.0898914i	$0.0286520\pi$
$677$			4.67781i			0.179783i	−0.995952	+	0.0898914i	$0.971348\pi$
$678$	−15.5043	−	21.2743i	−0.595440	−	0.817035i
$679$	−64.6479			−2.48096
$680$	−0.0982022	+	0.0323854i	−0.00376588	+	0.00124192i
$681$	−8.83046			−0.338384
$682$	9.33618	+	12.8107i	0.357501	+	0.490546i
$683$			17.8023i			0.681185i	0.940211	+	0.340592i	$0.110628\pi$
$683$			17.8023i			0.681185i	−0.940211	+	0.340592i	$0.889372\pi$
$684$	−1.59748	−	0.513886i	−0.0610811	−	0.0196489i
$685$			1.51411i			0.0578512i
$686$	0.919050	−	0.669787i	0.0350895	−	0.0255726i
$687$	25.0163			0.954433
$688$	5.07043	−	7.06549i	0.193308	−	0.269369i
$689$	−38.6774			−1.47349
$690$	−1.18392	+	0.862822i	−0.0450712	+	0.0328471i
$691$		−	29.6148i		−	1.12660i	−0.826253	−	0.563300i	$-0.809532\pi$
$691$		−	29.6148i		−	1.12660i	0.826253	−	0.563300i	$-0.190468\pi$
$692$	−34.5105	−	11.1015i	−1.31189	−	0.422017i
$693$			7.36179i			0.279651i
$694$	−18.1874	−	24.9559i	−0.690384	−	0.947312i
$695$	19.4768			0.738798
$696$	7.95874	+	24.1333i	0.301675	+	0.914771i
$697$	−0.0582961			−0.00220812
$698$	22.1112	+	30.3400i	0.836922	+	1.14838i
$699$		−	22.2640i		−	0.842103i
$700$	−8.92916	+	27.7574i	−0.337491	+	1.04913i
$701$		−	16.2594i		−	0.614109i	−0.951692	−	0.307054i	$-0.900657\pi$
$701$		−	16.2594i		−	0.614109i	0.951692	−	0.307054i	$-0.0993433\pi$
$702$	4.63732	−	3.37959i	0.175024	−	0.127555i
$703$	−1.36919			−0.0516401
$704$	−9.43662	−	12.7513i	−0.355656	−	0.480584i
$705$	−9.59270			−0.361282
$706$	−2.05455	+	1.49731i	−0.0773238	+	0.0563522i
$707$		−	13.8985i		−	0.522708i
$708$	0.319281	−	0.992524i	0.0119993	−	0.0373013i
$709$			4.30800i			0.161790i	0.996723	+	0.0808952i	$0.0257779\pi$
$709$			4.30800i			0.161790i	−0.996723	+	0.0808952i	$0.974222\pi$
$710$	0.0492448	+	0.0675714i	0.00184812	+	0.00253591i
$711$	10.6052			0.397727
$712$	7.37130	+	22.3520i	0.276251	+	0.837677i
$713$	5.65271			0.211696
$714$	0.109136	+	0.149751i	0.00408430	+	0.00560428i
$715$		−	8.33443i		−	0.311690i
$716$	−11.9072	−	3.83037i	−0.444993	−	0.143148i
$717$			4.66752i			0.174312i
$718$	33.6755	−	24.5421i	1.25676	−	0.915903i
$719$	12.9861			0.484301			0.242150	−	0.970239i	$-0.422147\pi$
$719$	12.9861			0.484301			0.242150	+	0.970239i	$0.422147\pi$
$720$	2.41585	−	3.36641i	0.0900334	−	0.125459i
$721$	−51.4600			−1.91647
$722$	20.9106	−	15.2392i	0.778211	−	0.567146i
$723$		−	17.6837i		−	0.657665i
$724$	24.0605	+	7.73992i	0.894202	+	0.287652i
$725$		−	35.2812i		−	1.31031i
$726$	−5.88716	−	8.07808i	−0.218493	−	0.299806i
$727$	−32.5529			−1.20732			−0.603660	−	0.797242i	$-0.706291\pi$
$727$	−32.5529			−1.20732			−0.603660	+	0.797242i	$0.706291\pi$
$728$	40.4634	−	13.3441i	1.49967	−	0.494566i
$729$	−1.00000			−0.0370370
$730$	−1.82157	−	2.49948i	−0.0674195	−	0.0925098i
$731$			0.0767306i			0.00283799i
$732$	0.662500	−	2.05947i	0.0244867	−	0.0761200i
$733$		−	27.4265i		−	1.01302i	−0.862233	−	0.506511i	$-0.830935\pi$
$733$		−	27.4265i		−	1.01302i	0.862233	−	0.506511i	$-0.169065\pi$
$734$	−5.11181	+	3.72539i	−0.188680	+	0.137507i
$735$	−7.02686			−0.259190
$736$	−5.65670	+	0.0414082i	−0.208509	+	0.00152633i
$737$	−7.58677			−0.279462
$738$	1.88786	−	1.37584i	0.0694929	−	0.0506452i
$739$		−	21.1976i		−	0.779767i	−0.920864	−	0.389884i	$-0.872515\pi$
$739$		−	21.1976i		−	0.779767i	0.920864	−	0.389884i	$-0.127485\pi$
$740$	1.03531	−	3.21838i	0.0380587	−	0.118310i
$741$		−	3.40443i		−	0.125065i
$742$	29.4772	+	40.4472i	1.08214	+	1.48486i
$743$	−28.4918			−1.04526			−0.522631	−	0.852559i	$-0.675049\pi$
$743$	−28.4918			−1.04526			−0.522631	+	0.852559i	$0.675049\pi$
$744$	−15.1839	+	5.00738i	−0.556669	+	0.183580i
$745$	−7.56937			−0.277320
$746$	−7.81925	−	10.7292i	−0.286283	−	0.392824i
$747$			12.9986i			0.475594i
$748$	0.133240	+	0.0428613i	0.00487172	+	0.00156716i
$749$			2.33473i			0.0853091i
$750$	−10.5688	+	7.70235i	−0.385918	+	0.281250i
$751$	−43.8582			−1.60041			−0.800205	−	0.599727i	$-0.795276\pi$
$751$	−43.8582			−1.60041			−0.800205	+	0.599727i	$0.795276\pi$
$752$	−30.0941	−	21.5965i	−1.09742	−	0.787544i
$753$	4.11640			0.150010
$754$	−41.6636	+	30.3637i	−1.51730	+	1.10578i
$755$		−	6.91165i		−	0.251541i
$756$	−7.06847	−	2.27383i	−0.257078	−	0.0826983i
$757$		−	23.8058i		−	0.865238i	−0.901577	−	0.432619i	$-0.857589\pi$
$757$		−	23.8058i		−	0.865238i	0.901577	−	0.432619i	$-0.142411\pi$
$758$	8.25660	+	11.3293i	0.299893	+	0.411499i
$759$	1.98292			0.0719754
$760$	−0.769938	−	2.33468i	−0.0279286	−	0.0846879i
$761$	51.1304			1.85348			0.926738	−	0.375709i	$-0.122601\pi$
$761$	51.1304			1.85348			0.926738	+	0.375709i	$0.122601\pi$
$762$	14.9634	+	20.5321i	0.542067	+	0.743799i
$763$		−	64.9582i		−	2.35165i
$764$	−10.9512	+	34.0432i	−0.396201	+	1.23164i
$765$			0.0365590i			0.00132179i
$766$	39.1724	−	28.5482i	1.41536	−	1.03149i
$767$	2.11520			0.0763753
$768$	15.1580	−	5.12215i	0.546966	−	0.184830i
$769$	−39.8744			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$769$	−39.8744			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$770$	−8.71579	+	6.35191i	−0.314095	+	0.228907i
$771$			19.7060i			0.709695i
$772$	−1.56876	+	4.87669i	−0.0564610	+	0.175516i
$773$		−	28.3459i		−	1.01953i	−0.860314	−	0.509765i	$-0.829732\pi$
$773$		−	28.3459i		−	1.01953i	0.860314	−	0.509765i	$-0.170268\pi$
$774$	−1.81090	−	2.48484i	−0.0650916	−	0.0893157i
$775$	22.1978			0.797368
$776$	−15.4252	−	46.7738i	−0.553732	−	1.67908i
$777$	−6.05836			−0.217342
$778$	−14.2354	−	19.5332i	−0.510364	−	0.700298i
$779$		−	1.38595i		−	0.0496567i
$780$	8.00236	+	2.57424i	0.286530	+	0.0921727i
$781$		−	0.113173i		−	0.00404966i
$782$	0.0403358	−	0.0293960i	0.00144241	−	0.00105120i
$783$	8.98442			0.321077
$784$	−22.0446	−	15.8199i	−0.787306	−	0.564997i
$785$	−4.27288			−0.152506
$786$	13.0743	−	9.52829i	0.466344	−	0.339863i
$787$		−	21.7598i		−	0.775653i	−0.921732	−	0.387827i	$-0.873226\pi$
$787$		−	21.7598i		−	0.775653i	0.921732	−	0.387827i	$-0.126774\pi$
$788$	15.9234	+	5.12234i	0.567249	+	0.182476i
$789$			12.1168i			0.431370i
$790$	9.15041	+	12.5558i	0.325557	+	0.446714i
$791$	−69.1073			−2.45717
$792$	−5.32638	+	1.75655i	−0.189265	+	0.0624162i
$793$	4.38898			0.155857
$794$	11.7624	+	16.1398i	0.417432	+	0.572780i
$795$			9.87446i			0.350211i
$796$	−2.60110	+	8.08586i	−0.0921937	+	0.286596i
$797$			28.2980i			1.00237i	0.865341	+	0.501184i	$0.167102\pi$
$797$			28.2980i			1.00237i	−0.865341	+	0.501184i	$0.832898\pi$
$798$	−3.56021	+	2.59462i	−0.126030	+	0.0918485i
$799$	0.326819			0.0115620
$800$	−22.2135	+	0.162607i	−0.785365	+	0.00574904i
$801$	8.32127			0.294018
$802$	−23.8849	+	17.4069i	−0.843404	+	0.614658i
$803$			4.18631i			0.147732i
$804$	2.34331	−	7.28449i	0.0826423	−	0.256904i
$805$			3.84584i			0.135548i
$806$	−19.1038	−	26.2134i	−0.672904	−	0.923328i
$807$	16.2608			0.572409
$808$	10.0558	−	3.31623i	0.353763	−	0.116665i
$809$	−14.9378			−0.525186			−0.262593	−	0.964907i	$-0.584578\pi$
$809$	−14.9378			−0.525186			−0.262593	+	0.964907i	$0.584578\pi$
$810$	−0.862822	−	1.18392i	−0.0303165	−	0.0415988i
$811$			52.6398i			1.84843i	0.381868	+	0.924217i	$0.375281\pi$
$811$			52.6398i			1.84843i	−0.381868	+	0.924217i	$0.624719\pi$
$812$	63.5061	+	20.4290i	2.22863	+	0.716918i
$813$		−	15.3045i		−	0.536754i
$814$	−3.69821	+	2.69519i	−0.129622	+	0.0944664i
$815$	14.2347			0.498621
$816$	−0.0823071	+	0.114692i	−0.00288132	+	0.00401504i
$817$	−1.82421			−0.0638212
$818$	23.4933	−	17.1215i	0.821423	−	0.598638i
$819$		−	15.0638i		−	0.526373i
$820$	3.25777	+	1.04798i	0.113766	+	0.0365969i
$821$			7.88739i			0.275272i	0.990483	+	0.137636i	$0.0439504\pi$
$821$			7.88739i			0.275272i	−0.990483	+	0.137636i	$0.956050\pi$
$822$	1.21745	+	1.67053i	0.0424635	+	0.0582664i
$823$	−13.2341			−0.461313			−0.230657	−	0.973035i	$-0.574087\pi$
$823$	−13.2341			−0.461313			−0.230657	+	0.973035i	$0.574087\pi$
$824$	−12.2785	−	37.2322i	−0.427742	−	1.29704i
$825$	7.78679			0.271101
$826$	−1.61205	−	2.21198i	−0.0560905	−	0.0769648i
$827$		−	36.3427i		−	1.26376i	−0.775066	−	0.631880i	$-0.782283\pi$
$827$		−	36.3427i		−	1.26376i	0.775066	−	0.631880i	$-0.217717\pi$
$828$	−0.612462	+	1.90391i	−0.0212845	+	0.0661656i
$829$		−	24.4887i		−	0.850528i	−0.905069	−	0.425264i	$-0.860181\pi$
$829$		−	24.4887i		−	0.850528i	0.905069	−	0.425264i	$-0.139819\pi$
$830$	−15.3894	+	11.2155i	−0.534172	+	0.389295i
$831$	−11.1209			−0.385779
$832$	19.3094	+	26.0920i	0.669432	+	0.904577i
$833$	0.239402			0.00829480
$834$	21.4889	−	15.6607i	0.744100	−	0.542287i
$835$		−	3.35602i		−	0.116140i
$836$	−1.01899	+	3.16767i	−0.0352427	+	0.109556i
$837$			5.65271i			0.195386i
$838$	13.5884	+	18.6453i	0.469402	+	0.644092i
$839$	−38.1236			−1.31617			−0.658087	−	0.752942i	$-0.728634\pi$
$839$	−38.1236			−1.31617			−0.658087	+	0.752942i	$0.728634\pi$
$840$	−3.40680	−	10.3304i	−0.117546	−	0.356434i
$841$	−51.7198			−1.78344
$842$	−16.6397	−	22.8322i	−0.573442	−	0.786850i
$843$			31.5006i			1.08494i
$844$	−44.2628	−	14.2387i	−1.52359	−	0.490116i
$845$			3.58748i			0.123413i
$846$	−10.5837	+	7.71320i	−0.363875	+	0.265185i
$847$	−26.2408			−0.901643
$848$	−22.2309	+	30.9780i	−0.763411	+	1.06379i
$849$	19.1846			0.658414
$850$	0.158396	−	0.115436i	0.00543294	−	0.00395943i
$851$			1.63184i			0.0559387i
$852$	0.108664	+	0.0349557i	0.00372278	+	0.00119756i
$853$			28.3191i			0.969627i	0.874618	+	0.484813i	$0.161113\pi$
$853$			28.3191i			0.969627i	−0.874618	+	0.484813i	$0.838887\pi$
$854$	−3.34497	−	4.58982i	−0.114463	−	0.157060i
$855$	−0.869163			−0.0297247
$856$	−1.68921	+	0.557073i	−0.0577361	+	0.0190404i
$857$	−5.00409			−0.170937			−0.0854683	−	0.996341i	$-0.527239\pi$
$857$	−5.00409			−0.170937			−0.0854683	+	0.996341i	$0.527239\pi$
$858$	−6.70146	−	9.19543i	−0.228784	−	0.313927i
$859$			43.3989i			1.48075i	0.672194	+	0.740375i	$0.265352\pi$
$859$			43.3989i			1.48075i	−0.672194	+	0.740375i	$0.734648\pi$
$860$	1.37937	−	4.28794i	0.0470361	−	0.146218i
$861$		−	6.13249i		−	0.208995i
$862$	7.17822	−	5.23135i	0.244491	−	0.178181i
$863$	−56.3132			−1.91692			−0.958462	−	0.285220i	$-0.907933\pi$
$863$	−56.3132			−1.91692			−0.958462	+	0.285220i	$0.907933\pi$
$864$	−0.0414082	−	5.65670i	−0.00140874	−	0.192445i
$865$	−18.7766			−0.638425
$866$	19.0717	−	13.8991i	0.648083	−	0.472311i
$867$			16.9988i			0.577308i
$868$	−12.8533	+	39.9560i	−0.436269	+	1.35620i
$869$		−	21.0293i		−	0.713370i
$870$	7.75195	+	10.6369i	0.262816	+	0.360623i
$871$	15.5242			0.526017
$872$	46.9984	−	15.4992i	1.59157	−	0.524870i
$873$	−17.4131			−0.589344
$874$	0.698868	+	0.958954i	0.0236396	+	0.0324371i
$875$			34.3316i			1.16062i
$876$	−4.01951	−	1.29302i	−0.135807	−	0.0436871i
$877$		−	36.0118i		−	1.21603i	−0.793924	−	0.608017i	$-0.791965\pi$
$877$		−	36.0118i		−	1.21603i	0.793924	−	0.608017i	$-0.208035\pi$
$878$	12.0687	−	8.79544i	0.407298	−	0.296832i
$879$	29.1881			0.984491
$880$	−6.67533	−	4.79044i	−0.225025	−	0.161486i
$881$	−7.27238			−0.245013			−0.122506	−	0.992468i	$-0.539093\pi$
$881$	−7.27238			−0.245013			−0.122506	+	0.992468i	$0.539093\pi$
$882$	−7.75278	+	5.65009i	−0.261050	+	0.190248i
$883$			53.3083i			1.79397i	0.442065	+	0.896983i	$0.354246\pi$
$883$			53.3083i			1.79397i	−0.442065	+	0.896983i	$0.645754\pi$
$884$	−0.272637	−	0.0877035i	−0.00916978	−	0.00294979i
$885$		−	0.540017i		−	0.0181525i
$886$	−1.93040	−	2.64880i	−0.0648530	−	0.0889883i
$887$	9.02645			0.303079			0.151539	−	0.988451i	$-0.451577\pi$
$887$	9.02645			0.303079			0.151539	+	0.988451i	$0.451577\pi$
$888$	−1.44554	−	4.38333i	−0.0485093	−	0.147095i
$889$	66.6962			2.23692
$890$	7.17977	+	9.85174i	0.240666	+	0.330231i
$891$			1.98292i			0.0664303i
$892$	−16.6526	+	51.7668i	−0.557571	+	1.73328i
$893$			7.76989i			0.260009i
$894$	−8.35134	+	6.08630i	−0.279310	+	0.203556i
$895$	−6.47852			−0.216553
$896$	12.5697	−	40.0784i	0.419923	−	1.33893i
$897$	−4.05749			−0.135475
$898$	−10.1284	+	7.38136i	−0.337988	+	0.246319i
$899$		−	50.7863i		−	1.69382i
$900$	−2.40510	+	7.47654i	−0.0801699	+	0.249218i
$901$		−	0.336419i		−	0.0112077i
$902$	−2.72817	−	3.74347i	−0.0908382	−	0.124644i
$903$	−8.07172			−0.268610
$904$	−16.4892	−	50.0003i	−0.548423	−	1.66298i
$905$	13.0909			0.435158
$906$	−5.55745	−	7.62568i	−0.184634	−	0.253346i
$907$			18.6291i			0.618568i	0.950970	+	0.309284i	$0.100089\pi$
$907$			18.6291i			0.618568i	−0.950970	+	0.309284i	$0.899911\pi$
$908$	−16.8124	−	5.40832i	−0.557941	−	0.179481i
$909$		−	3.74361i		−	0.124168i
$910$	17.8344	−	12.9974i	0.591205	−	0.430859i
$911$	−19.8933			−0.659094			−0.329547	−	0.944139i	$-0.606896\pi$
$911$	−19.8933			−0.659094			−0.329547	+	0.944139i	$0.606896\pi$
$912$	−2.72673	−	1.95679i	−0.0902910	−	0.0647958i
$913$	25.7752			0.853035
$914$	−12.7739	+	9.30936i	−0.422522	+	0.307926i
$915$		−	1.12052i		−	0.0370433i
$916$	47.6290	+	15.3216i	1.57371	+	0.506239i
$917$		−	42.4703i		−	1.40249i
$918$	0.0293960	+	0.0403358i	0.000970213	+	0.00133128i
$919$	−44.6518			−1.47293			−0.736463	−	0.676477i	$-0.763506\pi$
$919$	−44.6518			−1.47293			−0.736463	+	0.676477i	$0.763506\pi$
$920$	−2.78253	+	0.917631i	−0.0917374	+	0.0302534i
$921$	−15.3866			−0.507006
$922$	−12.1152	−	16.6239i	−0.398993	−	0.547480i
$923$			0.231577i			0.00762246i
$924$	−4.50882	+	14.0162i	−0.148329	+	0.461100i
$925$			6.40812i			0.210698i
$926$	15.2809	−	11.1364i	0.502161	−	0.365966i
$927$	−13.8609			−0.455252
$928$	0.372029	+	50.8222i	0.0122124	+	1.66832i
$929$	45.7107			1.49972			0.749860	−	0.661597i	$-0.230121\pi$
$929$	45.7107			1.49972			0.749860	+	0.661597i	$0.230121\pi$
$930$	−6.69237	+	4.87728i	−0.219451	+	0.159932i
$931$			5.69161i			0.186535i
$932$	13.6359	−	42.3888i	0.446658	−	1.38849i
$933$			22.4890i			0.736255i
$934$	−17.4950	−	24.0058i	−0.572455	−	0.785495i
$935$	0.0724936			0.00237079
$936$	10.8989	−	3.59428i	0.356243	−	0.117483i
$937$	−54.7330			−1.78805			−0.894024	−	0.448018i	$-0.852130\pi$
$937$	−54.7330			−1.78805			−0.894024	+	0.448018i	$0.852130\pi$
$938$	−11.8314	−	16.2345i	−0.386310	−	0.530076i
$939$		−	24.1804i		−	0.789098i
$940$	−18.2637	−	5.87516i	−0.595695	−	0.191627i
$941$		−	36.7184i		−	1.19699i	−0.801128	−	0.598493i	$-0.795767\pi$
$941$		−	36.7184i		−	1.19699i	0.801128	−	0.598493i	$-0.204233\pi$
$942$	−4.71430	+	3.43570i	−0.153600	+	0.111941i
$943$	−1.65181			−0.0537902
$944$	1.21577	−	1.69413i	0.0395698	−	0.0551394i
$945$	−3.84584			−0.125105
$946$	−4.92724	+	3.59088i	−0.160198	+	0.116750i
$947$		−	26.4766i		−	0.860374i	−0.902740	−	0.430187i	$-0.858448\pi$
$947$		−	26.4766i		−	0.860374i	0.902740	−	0.430187i	$-0.141552\pi$
$948$	20.1914	+	6.49529i	0.655787	+	0.210957i
$949$		−	8.56609i		−	0.278067i
$950$	2.74441	+	3.76575i	0.0890403	+	0.122177i
$951$	−8.16834			−0.264877
$952$	0.116068	+	0.351954i	0.00376179	+	0.0114069i
$953$	−5.66869			−0.183627			−0.0918134	−	0.995776i	$-0.529266\pi$
$953$	−5.66869			−0.183627			−0.0918134	+	0.995776i	$0.529266\pi$
$954$	7.93976	+	10.8946i	0.257059	+	0.352725i
$955$			18.5224i			0.599369i
$956$	−2.85868	+	8.88655i	−0.0924562	+	0.287412i
$957$		−	17.8154i		−	0.575890i
$958$	7.30918	−	5.32680i	0.236149	−	0.172101i
$959$	5.42653			0.175232
$960$	6.66137	−	4.92975i	0.214995	−	0.159107i
$961$	0.953085			0.0307447
$962$	7.56735	−	5.51495i	0.243981	−	0.177809i
$963$			0.628866i			0.0202649i
$964$	10.8306	−	33.6683i	0.348831	−	1.08438i
$965$			2.65333i			0.0854138i
$966$	3.09233	+	4.24315i	0.0994941	+	0.136521i
$967$	3.36120			0.108089			0.0540445	−	0.998539i	$-0.482789\pi$
$967$	3.36120			0.108089			0.0540445	+	0.998539i	$0.482789\pi$
$968$	−6.26113	−	18.9856i	−0.201240	−	0.610221i
$969$	0.0296120			0.000951276
$970$	−15.0244	−	20.6158i	−0.482404	−	0.661933i
$971$		−	9.91531i		−	0.318197i	−0.987263	−	0.159099i	$-0.949141\pi$
$971$		−	9.91531i		−	0.318197i	0.987263	−	0.159099i	$-0.0508588\pi$
$972$	−1.90391	−	0.612462i	−0.0610681	−	0.0196447i
$973$		−	69.8044i		−	2.23783i
$974$	28.8416	−	21.0193i	0.924145	−	0.673500i
$975$	−15.9335			−0.510279
$976$	2.52269	−	3.51529i	0.0807493	−	0.112522i
$977$	27.2308			0.871191			0.435596	−	0.900142i	$-0.356538\pi$
$977$	27.2308			0.871191			0.435596	+	0.900142i	$0.356538\pi$
$978$	15.7053	−	11.4457i	0.502199	−	0.365994i
$979$		−	16.5004i		−	0.527355i
$980$	−13.3785	−	4.30368i	−0.427362	−	0.137476i
$981$		−	17.4967i		−	0.558626i
$982$	32.1582	+	44.1259i	1.02621	+	1.40812i
$983$	−12.7325			−0.406103			−0.203051	−	0.979168i	$-0.565086\pi$
$983$	−12.7325			−0.406103			−0.203051	+	0.979168i	$0.565086\pi$
$984$	4.43696	−	1.46323i	0.141445	−	0.0466461i
$985$	8.66369			0.276048
$986$	−0.264106	−	0.362394i	−0.00841085	−	0.0115410i
$987$			34.3800i			1.09433i
$988$	2.08508	−	6.48175i	0.0663354	−	0.206212i
$989$			2.17414i			0.0691337i
$990$	−2.34763	+	1.71091i	−0.0746124	+	0.0543762i
$991$	56.1787			1.78458			0.892288	−	0.451467i	$-0.149099\pi$
$991$	56.1787			1.78458			0.892288	+	0.451467i	$0.149099\pi$
$992$	−31.9757	+	0.234069i	−1.01523	+	0.00743168i
$993$	−26.7727			−0.849606
$994$	0.242174	−	0.176492i	0.00768129	−	0.00559799i
$995$			4.39939i			0.139470i
$996$	−7.96115	+	24.7482i	−0.252259	+	0.784178i
$997$		−	1.37812i		−	0.0436456i	−0.999762	−	0.0218228i	$-0.993053\pi$
$997$		−	1.37812i		−	0.0436456i	0.999762	−	0.0218228i	$-0.00694696\pi$
$998$	−35.0602	−	48.1079i	−1.10981	−	1.52283i
$999$	−1.63184			−0.0516290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.17	✓	20
4.3	odd	2		2208.2.f.d.1105.15		20
8.3	odd	2		2208.2.f.d.1105.6		20
8.5	even	2	inner	552.2.f.d.277.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.17	✓	20	1.1	even	1	trivial
552.2.f.d.277.18	yes	20	8.5	even	2	inner
2208.2.f.d.1105.6		20	8.3	odd	2
2208.2.f.d.1105.15		20	4.3	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14290 - 0.832928i) q^{2} -1.00000i q^{3} +(0.612462 - 1.90391i) q^{4} -1.03589i q^{5} +(-0.832928 - 1.14290i) q^{6} -3.71260 q^{7} +(-0.885838 - 2.68613i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.14290 - 0.832928i) q^{2} -1.00000i q^{3} +(0.612462 - 1.90391i) q^{4} -1.03589i q^{5} +(-0.832928 - 1.14290i) q^{6} -3.71260 q^{7} +(-0.885838 - 2.68613i) q^{8} -1.00000 q^{9} +(-0.862822 - 1.18392i) q^{10} +1.98292i q^{11} +(-1.90391 - 0.612462i) q^{12} -4.05749i q^{13} +(-4.24315 + 3.09233i) q^{14} -1.03589 q^{15} +(-3.24978 - 2.33215i) q^{16} +0.0352924 q^{17} +(-1.14290 + 0.832928i) q^{18} +0.839050i q^{19} +(-1.97225 - 0.634443i) q^{20} +3.71260i q^{21} +(1.65163 + 2.26629i) q^{22} +1.00000 q^{23} +(-2.68613 + 0.885838i) q^{24} +3.92693 q^{25} +(-3.37959 - 4.63732i) q^{26} +1.00000i q^{27} +(-2.27383 + 7.06847i) q^{28} -8.98442i q^{29} +(-1.18392 + 0.862822i) q^{30} +5.65271 q^{31} +(-5.65670 + 0.0414082i) q^{32} +1.98292 q^{33} +(0.0403358 - 0.0293960i) q^{34} +3.84584i q^{35} +(-0.612462 + 1.90391i) q^{36} +1.63184i q^{37} +(0.698868 + 0.958954i) q^{38} -4.05749 q^{39} +(-2.78253 + 0.917631i) q^{40} -1.65181 q^{41} +(3.09233 + 4.24315i) q^{42} +2.17414i q^{43} +(3.77531 + 1.21446i) q^{44} +1.03589i q^{45} +(1.14290 - 0.832928i) q^{46} +9.26034 q^{47} +(-2.33215 + 3.24978i) q^{48} +6.78340 q^{49} +(4.48811 - 3.27085i) q^{50} -0.0352924i q^{51} +(-7.72511 - 2.48506i) q^{52} -9.53235i q^{53} +(0.832928 + 1.14290i) q^{54} +2.05409 q^{55} +(3.28876 + 9.97253i) q^{56} +0.839050 q^{57} +(-7.48337 - 10.2683i) q^{58} +0.521307i q^{59} +(-0.634443 + 1.97225i) q^{60} +1.08170i q^{61} +(6.46050 - 4.70830i) q^{62} +3.71260 q^{63} +(-6.43058 + 4.75895i) q^{64} -4.20311 q^{65} +(2.26629 - 1.65163i) q^{66} +3.82606i q^{67} +(0.0216152 - 0.0671936i) q^{68} -1.00000i q^{69} +(3.20331 + 4.39543i) q^{70} -0.0570741 q^{71} +(0.885838 + 2.68613i) q^{72} +2.11118 q^{73} +(1.35920 + 1.86503i) q^{74} -3.92693i q^{75} +(1.59748 + 0.513886i) q^{76} -7.36179i q^{77} +(-4.63732 + 3.37959i) q^{78} -10.6052 q^{79} +(-2.41585 + 3.36641i) q^{80} +1.00000 q^{81} +(-1.88786 + 1.37584i) q^{82} -12.9986i q^{83} +(7.06847 + 2.27383i) q^{84} -0.0365590i q^{85} +(1.81090 + 2.48484i) q^{86} -8.98442 q^{87} +(5.32638 - 1.75655i) q^{88} -8.32127 q^{89} +(0.862822 + 1.18392i) q^{90} +15.0638i q^{91} +(0.612462 - 1.90391i) q^{92} -5.65271i q^{93} +(10.5837 - 7.71320i) q^{94} +0.869163 q^{95} +(0.0414082 + 5.65670i) q^{96} +17.4131 q^{97} +(7.75278 - 5.65009i) q^{98} -1.98292i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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