LMFDB - Embedded newform 3234.2.e.d.2155.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.10
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.d.2155.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.98215i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.98215i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +1.98215 q^{10} +(2.62367 + 2.02888i) q^{11} -1.00000i q^{12} -3.67261 q^{13} -1.98215 q^{15} +1.00000 q^{16} -5.16068 q^{17} +1.00000i q^{18} -0.193339 q^{19} -1.98215i q^{20} +(2.02888 - 2.62367i) q^{22} -7.53092 q^{23} -1.00000 q^{24} +1.07108 q^{25} +3.67261i q^{26} -1.00000i q^{27} -4.29083i q^{29} +1.98215i q^{30} -4.34968i q^{31} -1.00000i q^{32} +(-2.02888 + 2.62367i) q^{33} +5.16068i q^{34} +1.00000 q^{36} +3.62086 q^{37} +0.193339i q^{38} -3.67261i q^{39} -1.98215 q^{40} -10.3366 q^{41} -3.78649i q^{43} +(-2.62367 - 2.02888i) q^{44} -1.98215i q^{45} +7.53092i q^{46} -2.69500i q^{47} +1.00000i q^{48} -1.07108i q^{50} -5.16068i q^{51} +3.67261 q^{52} +12.2295 q^{53} -1.00000 q^{54} +(-4.02154 + 5.20051i) q^{55} -0.193339i q^{57} -4.29083 q^{58} -2.76294i q^{59} +1.98215 q^{60} -11.4514 q^{61} -4.34968 q^{62} -1.00000 q^{64} -7.27967i q^{65} +(2.62367 + 2.02888i) q^{66} +8.97778 q^{67} +5.16068 q^{68} -7.53092i q^{69} -0.605004 q^{71} -1.00000i q^{72} +2.49221 q^{73} -3.62086i q^{74} +1.07108i q^{75} +0.193339 q^{76} -3.67261 q^{78} -1.40671i q^{79} +1.98215i q^{80} +1.00000 q^{81} +10.3366i q^{82} +9.45312 q^{83} -10.2292i q^{85} -3.78649 q^{86} +4.29083 q^{87} +(-2.02888 + 2.62367i) q^{88} +5.62367i q^{89} -1.98215 q^{90} +7.53092 q^{92} +4.34968 q^{93} -2.69500 q^{94} -0.383226i q^{95} +1.00000 q^{96} -9.63113i q^{97} +(-2.62367 - 2.02888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9} + 24 q^{16} - 16 q^{17} + 32 q^{19} - 8 q^{22} - 24 q^{24} - 8 q^{25} + 8 q^{33} + 24 q^{36} + 16 q^{37} + 16 q^{41} - 24 q^{54} - 16 q^{55} + 16 q^{62} - 24 q^{64} - 64 q^{67} + 16 q^{68} + 64 q^{71} - 32 q^{76} + 24 q^{81} + 16 q^{83} + 8 q^{88} - 16 q^{93} - 64 q^{94} + 24 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9 + 24 * q^16 - 16 * q^17 + 32 * q^19 - 8 * q^22 - 24 * q^24 - 8 * q^25 + 8 * q^33 + 24 * q^36 + 16 * q^37 + 16 * q^41 - 24 * q^54 - 16 * q^55 + 16 * q^62 - 24 * q^64 - 64 * q^67 + 16 * q^68 + 64 * q^71 - 32 * q^76 + 24 * q^81 + 16 * q^83 + 8 * q^88 - 16 * q^93 - 64 * q^94 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$			1.98215i			0.886444i	0.896412	+	0.443222i	$0.146165\pi$
$5$			1.98215i			0.886444i	−0.896412	+	0.443222i	$0.853835\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	1.98215			0.626811
$11$	2.62367	+	2.02888i	0.791067	+	0.611730i
$11$	2.62367	+	2.02888i	0.791067	+	0.611730i
$12$		−	1.00000i		−	0.288675i
$13$	−3.67261			−1.01860			−0.509300	−	0.860589i	$-0.670096\pi$
$13$	−3.67261			−1.01860			−0.509300	+	0.860589i	$0.670096\pi$
$14$		0			0
$15$	−1.98215			−0.511789
$16$	1.00000			0.250000
$17$	−5.16068			−1.25165			−0.625825	−	0.779964i	$-0.715238\pi$
$17$	−5.16068			−1.25165			−0.625825	+	0.779964i	$0.715238\pi$
$18$			1.00000i			0.235702i
$19$	−0.193339			−0.0443549			−0.0221775	−	0.999754i	$-0.507060\pi$
$19$	−0.193339			−0.0443549			−0.0221775	+	0.999754i	$0.507060\pi$
$20$		−	1.98215i		−	0.443222i
$21$		0			0
$22$	2.02888	−	2.62367i	0.432558	−	0.559369i
$23$	−7.53092			−1.57031			−0.785153	−	0.619302i	$-0.787416\pi$
$23$	−7.53092			−1.57031			−0.785153	+	0.619302i	$0.787416\pi$
$24$	−1.00000			−0.204124
$25$	1.07108			0.214216
$26$			3.67261i			0.720259i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	4.29083i		−	0.796787i	−0.917215	−	0.398393i	$-0.869568\pi$
$29$		−	4.29083i		−	0.796787i	0.917215	−	0.398393i	$-0.130432\pi$
$30$			1.98215i			0.361889i
$31$		−	4.34968i		−	0.781225i	−0.920555	−	0.390613i	$-0.872263\pi$
$31$		−	4.34968i		−	0.781225i	0.920555	−	0.390613i	$-0.127737\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.02888	+	2.62367i	−0.353183	+	0.456722i
$34$			5.16068i			0.885050i
$35$		0			0
$36$	1.00000			0.166667
$37$	3.62086			0.595265			0.297633	−	0.954681i	$-0.403803\pi$
$37$	3.62086			0.595265			0.297633	+	0.954681i	$0.403803\pi$
$38$			0.193339i			0.0313637i
$39$		−	3.67261i		−	0.588089i
$40$	−1.98215			−0.313405
$41$	−10.3366			−1.61430			−0.807150	−	0.590347i	$-0.798991\pi$
$41$	−10.3366			−1.61430			−0.807150	+	0.590347i	$0.798991\pi$
$42$		0			0
$43$		−	3.78649i		−	0.577434i	−0.957414	−	0.288717i	$-0.906771\pi$
$43$		−	3.78649i		−	0.577434i	0.957414	−	0.288717i	$-0.0932287\pi$
$44$	−2.62367	−	2.02888i	−0.395533	−	0.305865i
$45$		−	1.98215i		−	0.295481i
$46$			7.53092i			1.11037i
$47$		−	2.69500i		−	0.393105i	−0.980493	−	0.196553i	$-0.937025\pi$
$47$		−	2.69500i		−	0.393105i	0.980493	−	0.196553i	$-0.0629747\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	1.07108i		−	0.151474i
$51$		−	5.16068i		−	0.722640i
$52$	3.67261			0.509300
$53$	12.2295			1.67985			0.839925	−	0.542702i	$-0.182599\pi$
$53$	12.2295			1.67985			0.839925	+	0.542702i	$0.182599\pi$
$54$	−1.00000			−0.136083
$55$	−4.02154	+	5.20051i	−0.542265	+	0.701237i
$56$		0			0
$57$		−	0.193339i		−	0.0256083i
$58$	−4.29083			−0.563413
$59$		−	2.76294i		−	0.359705i	−0.983694	−	0.179852i	$-0.942438\pi$
$59$		−	2.76294i		−	0.359705i	0.983694	−	0.179852i	$-0.0575620\pi$
$60$	1.98215			0.255894
$61$	−11.4514			−1.46620			−0.733098	−	0.680123i	$-0.761926\pi$
$61$	−11.4514			−1.46620			−0.733098	+	0.680123i	$0.761926\pi$
$62$	−4.34968			−0.552410
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	7.27967i		−	0.902932i
$66$	2.62367	+	2.02888i	0.322952	+	0.249738i
$67$	8.97778			1.09681			0.548405	−	0.836213i	$-0.315235\pi$
$67$	8.97778			1.09681			0.548405	+	0.836213i	$0.315235\pi$
$68$	5.16068			0.625825
$69$		−	7.53092i		−	0.906616i
$70$		0			0
$71$	−0.605004			−0.0718007			−0.0359004	−	0.999355i	$-0.511430\pi$
$71$	−0.605004			−0.0718007			−0.0359004	+	0.999355i	$0.511430\pi$
$72$		−	1.00000i		−	0.117851i
$73$	2.49221			0.291691			0.145846	−	0.989307i	$-0.453410\pi$
$73$	2.49221			0.291691			0.145846	+	0.989307i	$0.453410\pi$
$74$		−	3.62086i		−	0.420916i
$75$			1.07108i			0.123678i
$76$	0.193339			0.0221775
$77$		0			0
$78$	−3.67261			−0.415842
$79$		−	1.40671i		−	0.158268i	−0.996864	−	0.0791339i	$-0.974785\pi$
$79$		−	1.40671i		−	0.158268i	0.996864	−	0.0791339i	$-0.0252155\pi$
$80$			1.98215i			0.221611i
$81$	1.00000			0.111111
$82$			10.3366i			1.14148i
$83$	9.45312			1.03761			0.518807	−	0.854891i	$-0.326376\pi$
$83$	9.45312			1.03761			0.518807	+	0.854891i	$0.326376\pi$
$84$		0			0
$85$		−	10.2292i		−	1.10952i
$86$	−3.78649			−0.408308
$87$	4.29083			0.460025
$88$	−2.02888	+	2.62367i	−0.216279	+	0.279684i
$89$			5.62367i			0.596107i	0.954549	+	0.298054i	$0.0963375\pi$
$89$			5.62367i			0.596107i	−0.954549	+	0.298054i	$0.903663\pi$
$90$	−1.98215			−0.208937
$91$		0			0
$92$	7.53092			0.785153
$93$	4.34968			0.451041
$94$	−2.69500			−0.277968
$95$		−	0.383226i		−	0.0393182i
$96$	1.00000			0.102062
$97$		−	9.63113i		−	0.977893i	−0.872314	−	0.488947i	$-0.837381\pi$
$97$		−	9.63113i		−	0.977893i	0.872314	−	0.488947i	$-0.162619\pi$
$98$		0			0
$99$	−2.62367	−	2.02888i	−0.263689	−	0.203910i
$100$	−1.07108			−0.107108
$101$	12.3926			1.23310			0.616552	−	0.787314i	$-0.288529\pi$
$101$	12.3926			1.23310			0.616552	+	0.787314i	$0.288529\pi$
$102$	−5.16068			−0.510984
$103$			6.69759i			0.659933i	0.943993	+	0.329966i	$0.107037\pi$
$103$			6.69759i			0.659933i	−0.943993	+	0.329966i	$0.892963\pi$
$104$		−	3.67261i		−	0.360130i
$105$		0			0
$106$		−	12.2295i		−	1.18783i
$107$		−	14.1241i		−	1.36543i	−0.730683	−	0.682716i	$-0.760798\pi$
$107$		−	14.1241i		−	1.36543i	0.730683	−	0.682716i	$-0.239202\pi$
$108$			1.00000i			0.0962250i
$109$		−	1.75960i		−	0.168539i	−0.996443	−	0.0842695i	$-0.973144\pi$
$109$		−	1.75960i		−	0.168539i	0.996443	−	0.0842695i	$-0.0268557\pi$
$110$	5.20051	+	4.02154i	0.495849	+	0.383439i
$111$			3.62086i			0.343676i
$112$		0			0
$113$	−16.4564			−1.54809			−0.774045	−	0.633130i	$-0.781770\pi$
$113$	−16.4564			−1.54809			−0.774045	+	0.633130i	$0.781770\pi$
$114$	−0.193339			−0.0181078
$115$		−	14.9274i		−	1.39199i
$116$			4.29083i			0.398393i
$117$	3.67261			0.339533
$118$	−2.76294			−0.254350
$119$		0			0
$120$		−	1.98215i		−	0.180945i
$121$	2.76730	+	10.6462i	0.251573	+	0.967838i
$122$			11.4514i			1.03676i
$123$		−	10.3366i		−	0.932016i
$124$			4.34968i			0.390613i
$125$			12.0338i			1.07634i
$126$		0			0
$127$		−	3.28996i		−	0.291937i	−0.989289	−	0.145969i	$-0.953370\pi$
$127$		−	3.28996i		−	0.291937i	0.989289	−	0.145969i	$-0.0466298\pi$
$128$			1.00000i			0.0883883i
$129$	3.78649			0.333382
$130$	−7.27967			−0.638470
$131$	−2.45475			−0.214473			−0.107236	−	0.994234i	$-0.534200\pi$
$131$	−2.45475			−0.214473			−0.107236	+	0.994234i	$0.534200\pi$
$132$	2.02888	−	2.62367i	0.176591	−	0.228361i
$133$		0			0
$134$		−	8.97778i		−	0.775562i
$135$	1.98215			0.170596
$136$		−	5.16068i		−	0.442525i
$137$	−14.8479			−1.26854			−0.634269	−	0.773113i	$-0.718699\pi$
$137$	−14.8479			−1.26854			−0.634269	+	0.773113i	$0.718699\pi$
$138$	−7.53092			−0.641074
$139$	10.1921			0.864483			0.432241	−	0.901758i	$-0.357723\pi$
$139$	10.1921			0.864483			0.432241	+	0.901758i	$0.357723\pi$
$140$		0			0
$141$	2.69500			0.226960
$142$			0.605004i			0.0507708i
$143$	−9.63573	−	7.45129i	−0.805780	−	0.623108i
$144$	−1.00000			−0.0833333
$145$	8.50506			0.706307
$146$		−	2.49221i		−	0.206257i
$147$		0			0
$148$	−3.62086			−0.297633
$149$		−	21.3790i		−	1.75144i	−0.482820	−	0.875720i	$-0.660387\pi$
$149$		−	21.3790i		−	1.75144i	0.482820	−	0.875720i	$-0.339613\pi$
$150$	1.07108			0.0874535
$151$		−	9.79712i		−	0.797278i	−0.917108	−	0.398639i	$-0.869483\pi$
$151$		−	9.79712i		−	0.797278i	0.917108	−	0.398639i	$-0.130517\pi$
$152$		−	0.193339i		−	0.0156818i
$153$	5.16068			0.417217
$154$		0			0
$155$	8.62171			0.692513
$156$			3.67261i			0.294045i
$157$		−	16.1094i		−	1.28567i	−0.766006	−	0.642833i	$-0.777759\pi$
$157$		−	16.1094i		−	1.28567i	0.766006	−	0.642833i	$-0.222241\pi$
$158$	−1.40671			−0.111912
$159$			12.2295i			0.969862i
$160$	1.98215			0.156703
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−22.8989			−1.79358			−0.896790	−	0.442457i	$-0.854107\pi$
$163$	−22.8989			−1.79358			−0.896790	+	0.442457i	$0.854107\pi$
$164$	10.3366			0.807150
$165$	−5.20051	−	4.02154i	−0.404859	−	0.313077i
$166$		−	9.45312i		−	0.733705i
$167$	−3.92850			−0.303997			−0.151998	−	0.988381i	$-0.548571\pi$
$167$	−3.92850			−0.303997			−0.151998	+	0.988381i	$0.548571\pi$
$168$		0			0
$169$	0.488099			0.0375461
$170$	−10.2292			−0.784548
$171$	0.193339			0.0147850
$172$			3.78649i			0.288717i
$173$	−23.2365			−1.76664			−0.883321	−	0.468769i	$-0.844698\pi$
$173$	−23.2365			−1.76664			−0.883321	+	0.468769i	$0.844698\pi$
$174$		−	4.29083i		−	0.325287i
$175$		0			0
$176$	2.62367	+	2.02888i	0.197767	+	0.152933i
$177$	2.76294			0.207676
$178$	5.62367			0.421512
$179$	−9.12111			−0.681744			−0.340872	−	0.940110i	$-0.610722\pi$
$179$	−9.12111			−0.681744			−0.340872	+	0.940110i	$0.610722\pi$
$180$			1.98215i			0.147741i
$181$		−	3.80895i		−	0.283117i	−0.989930	−	0.141559i	$-0.954789\pi$
$181$		−	3.80895i		−	0.283117i	0.989930	−	0.141559i	$-0.0452113\pi$
$182$		0			0
$183$		−	11.4514i		−	0.846509i
$184$		−	7.53092i		−	0.555187i
$185$			7.17708i			0.527669i
$186$		−	4.34968i		−	0.318934i
$187$	−13.5399	−	10.4704i	−0.990138	−	0.765672i
$188$			2.69500i			0.196553i
$189$		0			0
$190$	−0.383226			−0.0278022
$191$	−3.81784			−0.276249			−0.138125	−	0.990415i	$-0.544107\pi$
$191$	−3.81784			−0.276249			−0.138125	+	0.990415i	$0.544107\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			14.1400i			1.01782i	0.860819	+	0.508911i	$0.169952\pi$
$193$			14.1400i			1.01782i	−0.860819	+	0.508911i	$0.830048\pi$
$194$	−9.63113			−0.691475
$195$	7.27967			0.521308
$196$		0			0
$197$			19.8023i			1.41086i	0.708780	+	0.705429i	$0.249246\pi$
$197$			19.8023i			1.41086i	−0.708780	+	0.705429i	$0.750754\pi$
$198$	−2.02888	+	2.62367i	−0.144186	+	0.186456i
$199$		−	15.6034i		−	1.10610i	−0.833149	−	0.553049i	$-0.813464\pi$
$199$		−	15.6034i		−	1.10610i	0.833149	−	0.553049i	$-0.186536\pi$
$200$			1.07108i			0.0757369i
$201$			8.97778i			0.633244i
$202$		−	12.3926i		−	0.871937i
$203$		0			0
$204$			5.16068i			0.361320i
$205$		−	20.4886i		−	1.43099i
$206$	6.69759			0.466643
$207$	7.53092			0.523435
$208$	−3.67261			−0.254650
$209$	−0.507257	−	0.392261i	−0.0350877	−	0.0271333i
$210$		0			0
$211$			1.61475i			0.111164i	0.998454	+	0.0555818i	$0.0177014\pi$
$211$			1.61475i			0.111164i	−0.998454	+	0.0555818i	$0.982299\pi$
$212$	−12.2295			−0.839925
$213$		−	0.605004i		−	0.0414542i
$214$	−14.1241			−0.965507
$215$	7.50539			0.511863
$216$	1.00000			0.0680414
$217$		0			0
$218$	−1.75960			−0.119175
$219$			2.49221i			0.168408i
$220$	4.02154	−	5.20051i	0.271132	−	0.350618i
$221$	18.9532			1.27493
$222$	3.62086			0.243016
$223$		−	13.7495i		−	0.920732i	−0.887729	−	0.460366i	$-0.847718\pi$
$223$		−	13.7495i		−	0.920732i	0.887729	−	0.460366i	$-0.152282\pi$
$224$		0			0
$225$	−1.07108			−0.0714055
$226$			16.4564i			1.09467i
$227$	−12.3129			−0.817235			−0.408617	−	0.912706i	$-0.633989\pi$
$227$	−12.3129			−0.817235			−0.408617	+	0.912706i	$0.633989\pi$
$228$			0.193339i			0.0128042i
$229$		−	11.3303i		−	0.748724i	−0.927283	−	0.374362i	$-0.877862\pi$
$229$		−	11.3303i		−	0.748724i	0.927283	−	0.374362i	$-0.122138\pi$
$230$	−14.9274			−0.984284
$231$		0			0
$232$	4.29083			0.281707
$233$		−	24.9153i		−	1.63226i	−0.577870	−	0.816129i	$-0.696116\pi$
$233$		−	24.9153i		−	1.63226i	0.577870	−	0.816129i	$-0.303884\pi$
$234$		−	3.67261i		−	0.240086i
$235$	5.34188			0.348466
$236$			2.76294i			0.179852i
$237$	1.40671			0.0913759
$238$		0			0
$239$		−	5.39548i		−	0.349005i	−0.984657	−	0.174502i	$-0.944168\pi$
$239$		−	5.39548i		−	0.349005i	0.984657	−	0.174502i	$-0.0558317\pi$
$240$	−1.98215			−0.127947
$241$	19.0210			1.22525			0.612624	−	0.790374i	$-0.290114\pi$
$241$	19.0210			1.22525			0.612624	+	0.790374i	$0.290114\pi$
$242$	10.6462	−	2.76730i	0.684365	−	0.177889i
$243$			1.00000i			0.0641500i
$244$	11.4514			0.733098
$245$		0			0
$246$	−10.3366			−0.659035
$247$	0.710059			0.0451799
$248$	4.34968			0.276205
$249$			9.45312i			0.599067i
$250$	12.0338			0.761084
$251$			31.4849i			1.98731i	0.112467	+	0.993655i	$0.464125\pi$
$251$			31.4849i			1.98731i	−0.112467	+	0.993655i	$0.535875\pi$
$252$		0			0
$253$	−19.7587	−	15.2793i	−1.24222	−	0.960603i
$254$	−3.28996			−0.206431
$255$	10.2292			0.640580
$256$	1.00000			0.0625000
$257$			1.06081i			0.0661718i	0.999453	+	0.0330859i	$0.0105335\pi$
$257$			1.06081i			0.0661718i	−0.999453	+	0.0330859i	$0.989467\pi$
$258$		−	3.78649i		−	0.235736i
$259$		0			0
$260$			7.27967i			0.451466i
$261$			4.29083i			0.265596i
$262$			2.45475i			0.151655i
$263$		−	0.158801i		−	0.00979211i	−0.999988	−	0.00489606i	$-0.998442\pi$
$263$		−	0.158801i		−	0.00979211i	0.999988	−	0.00489606i	$-0.00155847\pi$
$264$	−2.62367	−	2.02888i	−0.161476	−	0.124869i
$265$			24.2407i			1.48909i
$266$		0			0
$267$	−5.62367			−0.344163
$268$	−8.97778			−0.548405
$269$			8.62477i			0.525861i	0.964815	+	0.262931i	$0.0846891\pi$
$269$			8.62477i			0.525861i	−0.964815	+	0.262931i	$0.915311\pi$
$270$		−	1.98215i		−	0.120630i
$271$	−23.1509			−1.40632			−0.703159	−	0.711033i	$-0.748228\pi$
$271$	−23.1509			−1.40632			−0.703159	+	0.711033i	$0.748228\pi$
$272$	−5.16068			−0.312912
$273$		0			0
$274$			14.8479i			0.896992i
$275$	2.81017	+	2.17310i	0.169459	+	0.131043i
$276$			7.53092i			0.453308i
$277$		−	23.7066i		−	1.42439i	−0.701980	−	0.712197i	$-0.747700\pi$
$277$		−	23.7066i		−	1.42439i	0.701980	−	0.712197i	$-0.252300\pi$
$278$		−	10.1921i		−	0.611282i
$279$			4.34968i			0.260408i
$280$		0			0
$281$			26.6628i			1.59057i	0.606235	+	0.795285i	$0.292679\pi$
$281$			26.6628i			1.59057i	−0.606235	+	0.795285i	$0.707321\pi$
$282$		−	2.69500i		−	0.160485i
$283$	−6.91406			−0.410998			−0.205499	−	0.978657i	$-0.565882\pi$
$283$	−6.91406			−0.410998			−0.205499	+	0.978657i	$0.565882\pi$
$284$	0.605004			0.0359004
$285$	0.383226			0.0227004
$286$	−7.45129	+	9.63573i	−0.440604	+	0.569773i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	9.63266			0.566627
$290$		−	8.50506i		−	0.499435i
$291$	9.63113			0.564587
$292$	−2.49221			−0.145846
$293$	−21.4874			−1.25531			−0.627655	−	0.778492i	$-0.715985\pi$
$293$	−21.4874			−1.25531			−0.627655	+	0.778492i	$0.715985\pi$
$294$		0			0
$295$	5.47657			0.318858
$296$			3.62086i			0.210458i
$297$	2.02888	−	2.62367i	0.117728	−	0.152241i
$298$	−21.3790			−1.23845
$299$	27.6582			1.59951
$300$		−	1.07108i		−	0.0618389i
$301$		0			0
$302$	−9.79712			−0.563761
$303$			12.3926i			0.711933i
$304$	−0.193339			−0.0110887
$305$		−	22.6983i		−	1.29970i
$306$		−	5.16068i		−	0.295017i
$307$	−8.43081			−0.481171			−0.240586	−	0.970628i	$-0.577340\pi$
$307$	−8.43081			−0.481171			−0.240586	+	0.970628i	$0.577340\pi$
$308$		0			0
$309$	−6.69759			−0.381012
$310$		−	8.62171i		−	0.489680i
$311$			28.6048i			1.62203i	0.585026	+	0.811014i	$0.301084\pi$
$311$			28.6048i			1.62203i	−0.585026	+	0.811014i	$0.698916\pi$
$312$	3.67261			0.207921
$313$		−	19.5248i		−	1.10361i	−0.833974	−	0.551803i	$-0.813940\pi$
$313$		−	19.5248i		−	1.10361i	0.833974	−	0.551803i	$-0.186060\pi$
$314$	−16.1094			−0.909104
$315$		0			0
$316$			1.40671i			0.0791339i
$317$	1.94148			0.109044			0.0545221	−	0.998513i	$-0.482636\pi$
$317$	1.94148			0.109044			0.0545221	+	0.998513i	$0.482636\pi$
$318$	12.2295			0.685796
$319$	8.70557	−	11.2577i	0.487418	−	0.630311i
$320$		−	1.98215i		−	0.110806i
$321$	14.1241			0.788333
$322$		0			0
$323$	0.997760			0.0555169
$324$	−1.00000			−0.0555556
$325$	−3.93367			−0.218201
$326$			22.8989i			1.26825i
$327$	1.75960			0.0973060
$328$		−	10.3366i		−	0.570741i
$329$		0			0
$330$	−4.02154	+	5.20051i	−0.221379	+	0.286279i
$331$	4.24442			0.233294			0.116647	−	0.993173i	$-0.462785\pi$
$331$	4.24442			0.233294			0.116647	+	0.993173i	$0.462785\pi$
$332$	−9.45312			−0.518807
$333$	−3.62086			−0.198422
$334$			3.92850i			0.214958i
$335$			17.7953i			0.972262i
$336$		0			0
$337$		−	10.3153i		−	0.561908i	−0.959721	−	0.280954i	$-0.909349\pi$
$337$		−	10.3153i		−	0.561908i	0.959721	−	0.280954i	$-0.0906509\pi$
$338$		−	0.488099i		−	0.0265491i
$339$		−	16.4564i		−	0.893791i
$340$			10.2292i			0.554759i
$341$	8.82497	−	11.4121i	0.477899	−	0.618001i
$342$		−	0.193339i		−	0.0104546i
$343$		0			0
$344$	3.78649			0.204154
$345$	14.9274			0.803665
$346$			23.2365i			1.24920i
$347$			34.0404i			1.82738i	0.406408	+	0.913692i	$0.366781\pi$
$347$			34.0404i			1.82738i	−0.406408	+	0.913692i	$0.633219\pi$
$348$	−4.29083			−0.230013
$349$	7.18549			0.384630			0.192315	−	0.981333i	$-0.438400\pi$
$349$	7.18549			0.384630			0.192315	+	0.981333i	$0.438400\pi$
$350$		0			0
$351$			3.67261i			0.196030i
$352$	2.02888	−	2.62367i	0.108140	−	0.139842i
$353$		−	17.0747i		−	0.908796i	−0.890799	−	0.454398i	$-0.849854\pi$
$353$		−	17.0747i		−	0.908796i	0.890799	−	0.454398i	$-0.150146\pi$
$354$		−	2.76294i		−	0.146849i
$355$		−	1.19921i		−	0.0636474i
$356$		−	5.62367i		−	0.298054i
$357$		0			0
$358$			9.12111i			0.482066i
$359$		−	2.60274i		−	0.137368i	−0.997638	−	0.0686838i	$-0.978120\pi$
$359$		−	2.60274i		−	0.137368i	0.997638	−	0.0686838i	$-0.0218799\pi$
$360$	1.98215			0.104468
$361$	−18.9626			−0.998033
$362$	−3.80895			−0.200194
$363$	−10.6462	+	2.76730i	−0.558782	+	0.145246i
$364$		0			0
$365$			4.93994i			0.258568i
$366$	−11.4514			−0.598572
$367$		−	0.373015i		−	0.0194713i	−0.999953	−	0.00973563i	$-0.996901\pi$
$367$		−	0.373015i		−	0.0194713i	0.999953	−	0.00973563i	$-0.00309899\pi$
$368$	−7.53092			−0.392576
$369$	10.3366			0.538100
$370$	7.17708			0.373119
$371$		0			0
$372$	−4.34968			−0.225520
$373$		−	17.8927i		−	0.926449i	−0.886241	−	0.463225i	$-0.846692\pi$
$373$		−	17.8927i		−	0.926449i	0.886241	−	0.463225i	$-0.153308\pi$
$374$	−10.4704	+	13.5399i	−0.541412	+	0.700134i
$375$	−12.0338			−0.621422
$376$	2.69500			0.138984
$377$			15.7586i			0.811607i
$378$		0			0
$379$	−0.192125			−0.00986881			−0.00493440	−	0.999988i	$-0.501571\pi$
$379$	−0.192125			−0.00986881			−0.00493440	+	0.999988i	$0.501571\pi$
$380$			0.383226i			0.0196591i
$381$	3.28996			0.168550
$382$			3.81784i			0.195338i
$383$			25.1572i			1.28547i	0.766087	+	0.642737i	$0.222201\pi$
$383$			25.1572i			1.28547i	−0.766087	+	0.642737i	$0.777799\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	14.1400			0.719709
$387$			3.78649i			0.192478i
$388$			9.63113i			0.488947i
$389$	26.0702			1.32181			0.660906	−	0.750469i	$-0.270172\pi$
$389$	26.0702			1.32181			0.660906	+	0.750469i	$0.270172\pi$
$390$		−	7.27967i		−	0.368621i
$391$	38.8647			1.96547
$392$		0			0
$393$		−	2.45475i		−	0.123826i
$394$	19.8023			0.997628
$395$	2.78832			0.140296
$396$	2.62367	+	2.02888i	0.131844	+	0.101955i
$397$			7.59366i			0.381115i	0.981676	+	0.190557i	$0.0610295\pi$
$397$			7.59366i			0.381115i	−0.981676	+	0.190557i	$0.938970\pi$
$398$	−15.6034			−0.782130
$399$		0			0
$400$	1.07108			0.0535541
$401$	5.02065			0.250719			0.125360	−	0.992111i	$-0.459992\pi$
$401$	5.02065			0.250719			0.125360	+	0.992111i	$0.459992\pi$
$402$	8.97778			0.447771
$403$			15.9747i			0.795756i
$404$	−12.3926			−0.616552
$405$			1.98215i			0.0984938i
$406$		0			0
$407$	9.49994	+	7.34628i	0.470894	+	0.364142i
$408$	5.16068			0.255492
$409$	−23.8802			−1.18080			−0.590400	−	0.807111i	$-0.701030\pi$
$409$	−23.8802			−1.18080			−0.590400	+	0.807111i	$0.701030\pi$
$410$	−20.4886			−1.01186
$411$		−	14.8479i		−	0.732391i
$412$		−	6.69759i		−	0.329966i
$413$		0			0
$414$		−	7.53092i		−	0.370125i
$415$			18.7375i			0.919788i
$416$			3.67261i			0.180065i
$417$			10.1921i			0.499109i
$418$	−0.392261	+	0.507257i	−0.0191861	+	0.0248108i
$419$			26.3584i			1.28769i	0.765156	+	0.643845i	$0.222662\pi$
$419$			26.3584i			1.28769i	−0.765156	+	0.643845i	$0.777338\pi$
$420$		0			0
$421$	22.7183			1.10722			0.553610	−	0.832776i	$-0.313250\pi$
$421$	22.7183			1.10722			0.553610	+	0.832776i	$0.313250\pi$
$422$	1.61475			0.0786046
$423$			2.69500i			0.131035i
$424$			12.2295i			0.593917i
$425$	−5.52752			−0.268124
$426$	−0.605004			−0.0293125
$427$		0			0
$428$			14.1241i			0.682716i
$429$	7.45129	−	9.63573i	0.359752	−	0.465218i
$430$		−	7.50539i		−	0.361942i
$431$		−	8.78327i		−	0.423075i	−0.977370	−	0.211538i	$-0.932153\pi$
$431$		−	8.78327i		−	0.423075i	0.977370	−	0.211538i	$-0.0678471\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	17.3328i		−	0.832959i	−0.909145	−	0.416480i	$-0.863264\pi$
$433$		−	17.3328i		−	0.832959i	0.909145	−	0.416480i	$-0.136736\pi$
$434$		0			0
$435$			8.50506i			0.407787i
$436$			1.75960i			0.0842695i
$437$	1.45602			0.0696508
$438$	2.49221			0.119082
$439$	−20.1587			−0.962124			−0.481062	−	0.876686i	$-0.659749\pi$
$439$	−20.1587			−0.962124			−0.481062	+	0.876686i	$0.659749\pi$
$440$	−5.20051	−	4.02154i	−0.247925	−	0.191720i
$441$		0			0
$442$		−	18.9532i		−	0.901512i
$443$	−31.5575			−1.49934			−0.749670	−	0.661811i	$-0.769788\pi$
$443$	−31.5575			−1.49934			−0.749670	+	0.661811i	$0.769788\pi$
$444$		−	3.62086i		−	0.171838i
$445$	−11.1469			−0.528416
$446$	−13.7495			−0.651056
$447$	21.3790			1.01119
$448$		0			0
$449$	8.72510			0.411763			0.205882	−	0.978577i	$-0.433994\pi$
$449$	8.72510			0.411763			0.205882	+	0.978577i	$0.433994\pi$
$450$			1.07108i			0.0504913i
$451$	−27.1197	−	20.9716i	−1.27702	−	0.987516i
$452$	16.4564			0.774045
$453$	9.79712			0.460309
$454$			12.3129i			0.577872i
$455$		0			0
$456$	0.193339			0.00905391
$457$			20.4099i			0.954734i	0.878704	+	0.477367i	$0.158409\pi$
$457$			20.4099i			0.954734i	−0.878704	+	0.477367i	$0.841591\pi$
$458$	−11.3303			−0.529428
$459$			5.16068i			0.240880i
$460$			14.9274i			0.695994i
$461$	17.5256			0.816248			0.408124	−	0.912927i	$-0.366183\pi$
$461$	17.5256			0.816248			0.408124	+	0.912927i	$0.366183\pi$
$462$		0			0
$463$	−39.8665			−1.85275			−0.926377	−	0.376596i	$-0.877094\pi$
$463$	−39.8665			−1.85275			−0.926377	+	0.376596i	$0.877094\pi$
$464$		−	4.29083i		−	0.199197i
$465$			8.62171i			0.399822i
$466$	−24.9153			−1.15418
$467$		−	11.0065i		−	0.509319i	−0.967031	−	0.254659i	$-0.918037\pi$
$467$		−	11.0065i		−	0.509319i	0.967031	−	0.254659i	$-0.0819634\pi$
$468$	−3.67261			−0.169767
$469$		0			0
$470$		−	5.34188i		−	0.246403i
$471$	16.1094			0.742280
$472$	2.76294			0.127175
$473$	7.68233	−	9.93450i	0.353234	−	0.456789i
$474$		−	1.40671i		−	0.0646125i
$475$	−0.207082			−0.00950155
$476$		0			0
$477$	−12.2295			−0.559950
$478$	−5.39548			−0.246784
$479$	1.36913			0.0625571			0.0312786	−	0.999511i	$-0.490042\pi$
$479$	1.36913			0.0625571			0.0312786	+	0.999511i	$0.490042\pi$
$480$			1.98215i			0.0904723i
$481$	−13.2980			−0.606337
$482$		−	19.0210i		−	0.866382i
$483$		0			0
$484$	−2.76730	−	10.6462i	−0.125786	−	0.483919i
$485$	19.0903			0.866848
$486$	1.00000			0.0453609
$487$	−12.9287			−0.585856			−0.292928	−	0.956134i	$-0.594630\pi$
$487$	−12.9287			−0.585856			−0.292928	+	0.956134i	$0.594630\pi$
$488$		−	11.4514i		−	0.518378i
$489$		−	22.8989i		−	1.03552i
$490$		0			0
$491$			6.08579i			0.274648i	0.990526	+	0.137324i	$0.0438501\pi$
$491$			6.08579i			0.274648i	−0.990526	+	0.137324i	$0.956150\pi$
$492$			10.3366i			0.466008i
$493$			22.1436i			0.997298i
$494$		−	0.710059i		−	0.0319470i
$495$	4.02154	−	5.20051i	0.180755	−	0.233746i
$496$		−	4.34968i		−	0.195306i
$497$		0			0
$498$	9.45312			0.423605
$499$	−3.58565			−0.160516			−0.0802578	−	0.996774i	$-0.525574\pi$
$499$	−3.58565			−0.160516			−0.0802578	+	0.996774i	$0.525574\pi$
$500$		−	12.0338i		−	0.538168i
$501$		−	3.92850i		−	0.175513i
$502$	31.4849			1.40524
$503$	−29.4875			−1.31478			−0.657392	−	0.753549i	$-0.728340\pi$
$503$	−29.4875			−1.31478			−0.657392	+	0.753549i	$0.728340\pi$
$504$		0			0
$505$			24.5639i			1.09308i
$506$	−15.2793	+	19.7587i	−0.679249	+	0.878379i
$507$			0.488099i			0.0216772i
$508$			3.28996i			0.145969i
$509$		−	8.59337i		−	0.380894i	−0.981697	−	0.190447i	$-0.939006\pi$
$509$		−	8.59337i		−	0.380894i	0.981697	−	0.190447i	$-0.0609938\pi$
$510$		−	10.2292i		−	0.452959i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			0.193339i			0.00853611i
$514$	1.06081			0.0467905
$515$	−13.2756			−0.584994
$516$	−3.78649			−0.166691
$517$	5.46782	−	7.07078i	0.240474	−	0.310973i
$518$		0			0
$519$		−	23.2365i		−	1.01997i
$520$	7.27967			0.319235
$521$			9.45996i			0.414449i	0.978293	+	0.207224i	$0.0664430\pi$
$521$			9.45996i			0.414449i	−0.978293	+	0.207224i	$0.933557\pi$
$522$	4.29083			0.187804
$523$	−10.7676			−0.470835			−0.235417	−	0.971894i	$-0.575646\pi$
$523$	−10.7676			−0.470835			−0.235417	+	0.971894i	$0.575646\pi$
$524$	2.45475			0.107236
$525$		0			0
$526$	−0.158801			−0.00692407
$527$			22.4473i			0.977821i
$528$	−2.02888	+	2.62367i	−0.0882956	+	0.114181i
$529$	33.7148			1.46586
$530$	24.2407			1.05295
$531$			2.76294i			0.119902i
$532$		0			0
$533$	37.9622			1.64433
$534$			5.62367i			0.243360i
$535$	27.9962			1.21038
$536$			8.97778i			0.387781i
$537$		−	9.12111i		−	0.393605i
$538$	8.62477			0.371840
$539$		0			0
$540$	−1.98215			−0.0852981
$541$			19.5235i			0.839382i	0.907667	+	0.419691i	$0.137862\pi$
$541$			19.5235i			0.839382i	−0.907667	+	0.419691i	$0.862138\pi$
$542$			23.1509i			0.994416i
$543$	3.80895			0.163458
$544$			5.16068i			0.221263i
$545$	3.48779			0.149400
$546$		0			0
$547$			27.4404i			1.17327i	0.809853	+	0.586634i	$0.199547\pi$
$547$			27.4404i			1.17327i	−0.809853	+	0.586634i	$0.800453\pi$
$548$	14.8479			0.634269
$549$	11.4514			0.488732
$550$	2.17310	−	2.81017i	0.0926611	−	0.119826i
$551$			0.829583i			0.0353414i
$552$	7.53092			0.320537
$553$		0			0
$554$	−23.7066			−1.00720
$555$	−7.17708			−0.304650
$556$	−10.1921			−0.432241
$557$			25.8344i			1.09464i	0.836923	+	0.547320i	$0.184352\pi$
$557$			25.8344i			1.09464i	−0.836923	+	0.547320i	$0.815648\pi$
$558$	4.34968			0.184137
$559$			13.9063i			0.588174i
$560$		0			0
$561$	10.4704	−	13.5399i	0.442061	−	0.571657i
$562$	26.6628			1.12470
$563$	−23.3907			−0.985800			−0.492900	−	0.870086i	$-0.664063\pi$
$563$	−23.3907			−0.985800			−0.492900	+	0.870086i	$0.664063\pi$
$564$	−2.69500			−0.113480
$565$		−	32.6191i		−	1.37230i
$566$			6.91406i			0.290620i
$567$		0			0
$568$		−	0.605004i		−	0.0253854i
$569$		−	6.18017i		−	0.259086i	−0.991574	−	0.129543i	$-0.958649\pi$
$569$		−	6.18017i		−	0.259086i	0.991574	−	0.129543i	$-0.0413511\pi$
$570$		−	0.383226i		−	0.0160516i
$571$		−	18.9348i		−	0.792397i	−0.918165	−	0.396199i	$-0.870329\pi$
$571$		−	18.9348i		−	0.792397i	0.918165	−	0.396199i	$-0.129671\pi$
$572$	9.63573	+	7.45129i	0.402890	+	0.311554i
$573$		−	3.81784i		−	0.159493i
$574$		0			0
$575$	−8.06623			−0.336385
$576$	1.00000			0.0416667
$577$			27.2082i			1.13269i	0.824167	+	0.566347i	$0.191644\pi$
$577$			27.2082i			1.13269i	−0.824167	+	0.566347i	$0.808356\pi$
$578$		−	9.63266i		−	0.400666i
$579$	−14.1400			−0.587640
$580$	−8.50506			−0.353154
$581$		0			0
$582$		−	9.63113i		−	0.399223i
$583$	32.0862	+	24.8122i	1.32887	+	1.02762i
$584$			2.49221i			0.103128i
$585$			7.27967i			0.300977i
$586$			21.4874i			0.887638i
$587$			15.3386i			0.633091i	0.948577	+	0.316545i	$0.102523\pi$
$587$			15.3386i			0.633091i	−0.948577	+	0.316545i	$0.897477\pi$
$588$		0			0
$589$			0.840961i			0.0346512i
$590$		−	5.47657i		−	0.225467i
$591$	−19.8023			−0.814560
$592$	3.62086			0.148816
$593$	22.0540			0.905649			0.452825	−	0.891600i	$-0.350416\pi$
$593$	22.0540			0.905649			0.452825	+	0.891600i	$0.350416\pi$
$594$	−2.62367	−	2.02888i	−0.107651	−	0.0832459i
$595$		0			0
$596$			21.3790i			0.875720i
$597$	15.6034			0.638606
$598$		−	27.6582i		−	1.13103i
$599$	19.8303			0.810245			0.405123	−	0.914262i	$-0.367229\pi$
$599$	19.8303			0.810245			0.405123	+	0.914262i	$0.367229\pi$
$600$	−1.07108			−0.0437267
$601$	27.2296			1.11072			0.555360	−	0.831610i	$-0.312581\pi$
$601$	27.2296			1.11072			0.555360	+	0.831610i	$0.312581\pi$
$602$		0			0
$603$	−8.97778			−0.365604
$604$			9.79712i			0.398639i
$605$	−21.1024	+	5.48520i	−0.857935	+	0.223005i
$606$	12.3926			0.503413
$607$	39.7167			1.61205			0.806025	−	0.591882i	$-0.201615\pi$
$607$	39.7167			1.61205			0.806025	+	0.591882i	$0.201615\pi$
$608$			0.193339i			0.00784092i
$609$		0			0
$610$	−22.6983			−0.919027
$611$			9.89768i			0.400417i
$612$	−5.16068			−0.208608
$613$		−	31.7463i		−	1.28222i	−0.767449	−	0.641110i	$-0.778474\pi$
$613$		−	31.7463i		−	1.28222i	0.767449	−	0.641110i	$-0.221526\pi$
$614$			8.43081i			0.340240i
$615$	20.4886			0.826181
$616$		0			0
$617$	0.714255			0.0287548			0.0143774	−	0.999897i	$-0.495423\pi$
$617$	0.714255			0.0287548			0.0143774	+	0.999897i	$0.495423\pi$
$618$			6.69759i			0.269416i
$619$			3.39964i			0.136643i	0.997663	+	0.0683215i	$0.0217644\pi$
$619$			3.39964i			0.136643i	−0.997663	+	0.0683215i	$0.978236\pi$
$620$	−8.62171			−0.346256
$621$			7.53092i			0.302205i
$622$	28.6048			1.14695
$623$		0			0
$624$		−	3.67261i		−	0.147022i
$625$	−18.4974			−0.739895
$626$	−19.5248			−0.780368
$627$	0.392261	−	0.507257i	0.0156654	−	0.0202579i
$628$			16.1094i			0.642833i
$629$	−18.6861			−0.745063
$630$		0			0
$631$	7.71388			0.307085			0.153542	−	0.988142i	$-0.450932\pi$
$631$	7.71388			0.307085			0.153542	+	0.988142i	$0.450932\pi$
$632$	1.40671			0.0559561
$633$	−1.61475			−0.0641804
$634$		−	1.94148i		−	0.0771059i
$635$	6.52120			0.258786
$636$		−	12.2295i		−	0.484931i
$637$		0			0
$638$	−11.2577	−	8.70557i	−0.445697	−	0.344657i
$639$	0.605004			0.0239336
$640$	−1.98215			−0.0783514
$641$	−0.711305			−0.0280949			−0.0140474	−	0.999901i	$-0.504472\pi$
$641$	−0.711305			−0.0280949			−0.0140474	+	0.999901i	$0.504472\pi$
$642$		−	14.1241i		−	0.557436i
$643$		−	25.1356i		−	0.991252i	−0.868536	−	0.495626i	$-0.834939\pi$
$643$		−	25.1356i		−	0.991252i	0.868536	−	0.495626i	$-0.165061\pi$
$644$		0			0
$645$			7.50539i			0.295524i
$646$		−	0.997760i		−	0.0392563i
$647$			4.81750i			0.189395i	0.995506	+	0.0946977i	$0.0301884\pi$
$647$			4.81750i			0.189395i	−0.995506	+	0.0946977i	$0.969812\pi$
$648$			1.00000i			0.0392837i
$649$	5.60568	−	7.24906i	0.220042	−	0.284550i
$650$			3.93367i			0.154291i
$651$		0			0
$652$	22.8989			0.896790
$653$	48.9607			1.91598			0.957990	−	0.286803i	$-0.0925926\pi$
$653$	48.9607			1.91598			0.957990	+	0.286803i	$0.0925926\pi$
$654$		−	1.75960i		−	0.0688057i
$655$		−	4.86569i		−	0.190118i
$656$	−10.3366			−0.403575
$657$	−2.49221			−0.0972304
$658$		0			0
$659$			46.0081i			1.79222i	0.443830	+	0.896111i	$0.353620\pi$
$659$			46.0081i			1.79222i	−0.443830	+	0.896111i	$0.646380\pi$
$660$	5.20051	+	4.02154i	0.202430	+	0.156538i
$661$			9.59131i			0.373059i	0.982449	+	0.186529i	$0.0597239\pi$
$661$			9.59131i			0.373059i	−0.982449	+	0.186529i	$0.940276\pi$
$662$		−	4.24442i		−	0.164964i
$663$			18.9532i			0.736081i
$664$			9.45312i			0.366852i
$665$		0			0
$666$			3.62086i			0.140305i
$667$			32.3139i			1.25120i
$668$	3.92850			0.151998
$669$	13.7495			0.531585
$670$	17.7953			0.687493
$671$	−30.0446	−	23.2334i	−1.15986	−	0.896916i
$672$		0			0
$673$		−	31.8983i		−	1.22959i	−0.788688	−	0.614794i	$-0.789239\pi$
$673$		−	31.8983i		−	1.22959i	0.788688	−	0.614794i	$-0.210761\pi$
$674$	−10.3153			−0.397329
$675$		−	1.07108i		−	0.0412260i
$676$	−0.488099			−0.0187730
$677$	−38.5354			−1.48104			−0.740518	−	0.672036i	$-0.765420\pi$
$677$	−38.5354			−1.48104			−0.740518	+	0.672036i	$0.765420\pi$
$678$	−16.4564			−0.632005
$679$		0			0
$680$	10.2292			0.392274
$681$		−	12.3129i		−	0.471831i
$682$	−11.4121	−	8.82497i	−0.436993	−	0.337926i
$683$	−18.0800			−0.691811			−0.345905	−	0.938269i	$-0.612428\pi$
$683$	−18.0800			−0.691811			−0.345905	+	0.938269i	$0.612428\pi$
$684$	−0.193339			−0.00739249
$685$		−	29.4307i		−	1.12449i
$686$		0			0
$687$	11.3303			0.432276
$688$		−	3.78649i		−	0.144359i
$689$	−44.9142			−1.71110
$690$		−	14.9274i		−	0.568277i
$691$		−	15.1907i		−	0.577882i	−0.957347	−	0.288941i	$-0.906697\pi$
$691$		−	15.1907i		−	0.577882i	0.957347	−	0.288941i	$-0.0933032\pi$
$692$	23.2365			0.883321
$693$		0			0
$694$	34.0404			1.29216
$695$			20.2023i			0.766316i
$696$			4.29083i			0.162643i
$697$	53.3437			2.02054
$698$		−	7.18549i		−	0.271975i
$699$	24.9153			0.942385
$700$		0			0
$701$		−	38.5800i		−	1.45715i	−0.684968	−	0.728573i	$-0.740184\pi$
$701$		−	38.5800i		−	1.45715i	0.684968	−	0.728573i	$-0.259816\pi$
$702$	3.67261			0.138614
$703$	−0.700052			−0.0264029
$704$	−2.62367	−	2.02888i	−0.0988833	−	0.0764663i
$705$			5.34188i			0.201187i
$706$	−17.0747			−0.642616
$707$		0			0
$708$	−2.76294			−0.103838
$709$	−23.9070			−0.897848			−0.448924	−	0.893570i	$-0.648193\pi$
$709$	−23.9070			−0.897848			−0.448924	+	0.893570i	$0.648193\pi$
$710$	−1.19921			−0.0450055
$711$			1.40671i			0.0527559i
$712$	−5.62367			−0.210756
$713$			32.7571i			1.22676i
$714$		0			0
$715$	14.7696	−	19.0995i	0.552351	−	0.714280i
$716$	9.12111			0.340872
$717$	5.39548			0.201498
$718$	−2.60274			−0.0971335
$719$			16.3168i			0.608516i	0.952590	+	0.304258i	$0.0984084\pi$
$719$			16.3168i			0.608516i	−0.952590	+	0.304258i	$0.901592\pi$
$720$		−	1.98215i		−	0.0738704i
$721$		0			0
$722$			18.9626i			0.705716i
$723$			19.0210i			0.707398i
$724$			3.80895i			0.141559i
$725$		−	4.59583i		−	0.170685i
$726$	2.76730	+	10.6462i	0.102704	+	0.395118i
$727$		−	33.8359i		−	1.25491i	−0.778655	−	0.627453i	$-0.784098\pi$
$727$		−	33.8359i		−	1.25491i	0.778655	−	0.627453i	$-0.215902\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	4.93994			0.182835
$731$			19.5409i			0.722745i
$732$			11.4514i			0.423254i
$733$	31.1261			1.14967			0.574834	−	0.818270i	$-0.305066\pi$
$733$	31.1261			1.14967			0.574834	+	0.818270i	$0.305066\pi$
$734$	−0.373015			−0.0137683
$735$		0			0
$736$			7.53092i			0.277593i
$737$	23.5547	+	18.2148i	0.867650	+	0.670952i
$738$		−	10.3366i		−	0.380494i
$739$			4.01173i			0.147574i	0.997274	+	0.0737869i	$0.0235085\pi$
$739$			4.01173i			0.147574i	−0.997274	+	0.0737869i	$0.976492\pi$
$740$		−	7.17708i		−	0.263835i
$741$			0.710059i			0.0260847i
$742$		0			0
$743$			47.7092i			1.75028i	0.483869	+	0.875140i	$0.339231\pi$
$743$			47.7092i			1.75028i	−0.483869	+	0.875140i	$0.660769\pi$
$744$			4.34968i			0.159467i
$745$	42.3765			1.55255
$746$	−17.8927			−0.655099
$747$	−9.45312			−0.345872
$748$	13.5399	+	10.4704i	0.495069	+	0.382836i
$749$		0			0
$750$			12.0338i			0.439412i
$751$	−17.3297			−0.632369			−0.316185	−	0.948698i	$-0.602402\pi$
$751$	−17.3297			−0.632369			−0.316185	+	0.948698i	$0.602402\pi$
$752$		−	2.69500i		−	0.0982764i
$753$	−31.4849			−1.14737
$754$	15.7586			0.573893
$755$	19.4194			0.706743
$756$		0			0
$757$	3.43161			0.124724			0.0623620	−	0.998054i	$-0.480137\pi$
$757$	3.43161			0.124724			0.0623620	+	0.998054i	$0.480137\pi$
$758$			0.192125i			0.00697830i
$759$	15.2793	−	19.7587i	0.554604	−	0.717194i
$760$	0.383226			0.0139011
$761$	13.4794			0.488629			0.244314	−	0.969696i	$-0.421437\pi$
$761$	13.4794			0.488629			0.244314	+	0.969696i	$0.421437\pi$
$762$		−	3.28996i		−	0.119183i
$763$		0			0
$764$	3.81784			0.138125
$765$			10.2292i			0.369839i
$766$	25.1572			0.908968
$767$			10.1472i			0.366395i
$768$			1.00000i			0.0360844i
$769$	15.1578			0.546606			0.273303	−	0.961928i	$-0.411884\pi$
$769$	15.1578			0.546606			0.273303	+	0.961928i	$0.411884\pi$
$770$		0			0
$771$	−1.06081			−0.0382043
$772$		−	14.1400i		−	0.508911i
$773$			22.9744i			0.826331i	0.910656	+	0.413166i	$0.135577\pi$
$773$			22.9744i			0.826331i	−0.910656	+	0.413166i	$0.864423\pi$
$774$	3.78649			0.136103
$775$		−	4.65886i		−	0.167351i
$776$	9.63113			0.345738
$777$		0			0
$778$		−	26.0702i		−	0.934662i
$779$	1.99846			0.0716022
$780$	−7.27967			−0.260654
$781$	−1.58733	−	1.22748i	−0.0567992	−	0.0439227i
$782$		−	38.8647i		−	1.38980i
$783$	−4.29083			−0.153342
$784$		0			0
$785$	31.9312			1.13967
$786$	−2.45475			−0.0875581
$787$	−38.9313			−1.38775			−0.693876	−	0.720095i	$-0.744098\pi$
$787$	−38.9313			−1.38775			−0.693876	+	0.720095i	$0.744098\pi$
$788$		−	19.8023i		−	0.705429i
$789$	0.158801			0.00565348
$790$		−	2.78832i		−	0.0992039i
$791$		0			0
$792$	2.02888	−	2.62367i	0.0720931	−	0.0932281i
$793$	42.0564			1.49347
$794$	7.59366			0.269489
$795$	−24.2407			−0.859729
$796$			15.6034i			0.553049i
$797$		−	19.7227i		−	0.698612i	−0.937009	−	0.349306i	$-0.886417\pi$
$797$		−	19.7227i		−	0.698612i	0.937009	−	0.349306i	$-0.113583\pi$
$798$		0			0
$799$			13.9080i			0.492030i
$800$		−	1.07108i		−	0.0378685i
$801$		−	5.62367i		−	0.198702i
$802$		−	5.02065i		−	0.177285i
$803$	6.53874	+	5.05640i	0.230747	+	0.178436i
$804$		−	8.97778i		−	0.316622i
$805$		0			0
$806$	15.9747			0.562685
$807$	−8.62477			−0.303606
$808$			12.3926i			0.435968i
$809$		−	8.29777i		−	0.291734i	−0.989304	−	0.145867i	$-0.953403\pi$
$809$		−	8.29777i		−	0.291734i	0.989304	−	0.145867i	$-0.0465972\pi$
$810$	1.98215			0.0696456
$811$	−37.4151			−1.31382			−0.656910	−	0.753969i	$-0.728137\pi$
$811$	−37.4151			−1.31382			−0.656910	+	0.753969i	$0.728137\pi$
$812$		0			0
$813$		−	23.1509i		−	0.811938i
$814$	7.34628	−	9.49994i	0.257487	−	0.332973i
$815$		−	45.3890i		−	1.58991i
$816$		−	5.16068i		−	0.180660i
$817$			0.732075i			0.0256121i
$818$			23.8802i			0.834952i
$819$		0			0
$820$			20.4886i			0.715493i
$821$		−	40.3027i		−	1.40657i	−0.710907	−	0.703286i	$-0.751715\pi$
$821$		−	40.3027i		−	1.40657i	0.710907	−	0.703286i	$-0.248285\pi$
$822$	−14.8479			−0.517878
$823$	2.04557			0.0713040			0.0356520	−	0.999364i	$-0.488649\pi$
$823$	2.04557			0.0713040			0.0356520	+	0.999364i	$0.488649\pi$
$824$	−6.69759			−0.233322
$825$	−2.17310	+	2.81017i	−0.0756575	+	0.0978374i
$826$		0			0
$827$		−	50.2951i		−	1.74893i	−0.485088	−	0.874465i	$-0.661212\pi$
$827$		−	50.2951i		−	1.74893i	0.485088	−	0.874465i	$-0.338788\pi$
$828$	−7.53092			−0.261718
$829$			52.8837i			1.83673i	0.395736	+	0.918364i	$0.370489\pi$
$829$			52.8837i			1.83673i	−0.395736	+	0.918364i	$0.629511\pi$
$830$	18.7375			0.650388
$831$	23.7066			0.822374
$832$	3.67261			0.127325
$833$		0			0
$834$	10.1921			0.352924
$835$		−	7.78688i		−	0.269476i
$836$	0.507257	+	0.392261i	0.0175439	+	0.0135666i
$837$	−4.34968			−0.150347
$838$	26.3584			0.910535
$839$		−	43.1151i		−	1.48850i	−0.667902	−	0.744249i	$-0.732808\pi$
$839$		−	43.1151i		−	1.48850i	0.667902	−	0.744249i	$-0.267192\pi$
$840$		0			0
$841$	10.5888			0.365131
$842$		−	22.7183i		−	0.782923i
$843$	−26.6628			−0.918316
$844$		−	1.61475i		−	0.0555818i
$845$			0.967486i			0.0332825i
$846$	2.69500			0.0926558
$847$		0			0
$848$	12.2295			0.419963
$849$		−	6.91406i		−	0.237290i
$850$			5.52752i			0.189592i
$851$	−27.2684			−0.934748
$852$			0.605004i			0.0207271i
$853$	0.279234			0.00956079			0.00478039	−	0.999989i	$-0.498478\pi$
$853$	0.279234			0.00956079			0.00478039	+	0.999989i	$0.498478\pi$
$854$		0			0
$855$			0.383226i			0.0131061i
$856$	14.1241			0.482753
$857$	−34.3123			−1.17209			−0.586044	−	0.810280i	$-0.699315\pi$
$857$	−34.3123			−1.17209			−0.586044	+	0.810280i	$0.699315\pi$
$858$	−9.63573	−	7.45129i	−0.328958	−	0.254383i
$859$		−	39.6022i		−	1.35121i	−0.737265	−	0.675604i	$-0.763883\pi$
$859$		−	39.6022i		−	1.35121i	0.737265	−	0.675604i	$-0.236117\pi$
$860$	−7.50539			−0.255932
$861$		0			0
$862$	−8.78327			−0.299159
$863$	−51.4451			−1.75121			−0.875607	−	0.483025i	$-0.839538\pi$
$863$	−51.4451			−1.75121			−0.875607	+	0.483025i	$0.839538\pi$
$864$	−1.00000			−0.0340207
$865$		−	46.0583i		−	1.56603i
$866$	−17.3328			−0.588991
$867$			9.63266i			0.327142i
$868$		0			0
$869$	2.85405	−	3.69076i	0.0968171	−	0.125200i
$870$	8.50506			0.288349
$871$	−32.9719			−1.11721
$872$	1.75960			0.0595875
$873$			9.63113i			0.325964i
$874$		−	1.45602i		−	0.0492506i
$875$		0			0
$876$		−	2.49221i		−	0.0842040i
$877$			45.0427i			1.52098i	0.649348	+	0.760492i	$0.275042\pi$
$877$			45.0427i			1.52098i	−0.649348	+	0.760492i	$0.724958\pi$
$878$			20.1587i			0.680325i
$879$		−	21.4874i		−	0.724754i
$880$	−4.02154	+	5.20051i	−0.135566	+	0.175309i
$881$		−	37.8658i		−	1.27573i	−0.770148	−	0.637865i	$-0.779818\pi$
$881$		−	37.8658i		−	1.27573i	0.770148	−	0.637865i	$-0.220182\pi$
$882$		0			0
$883$	−44.1505			−1.48578			−0.742891	−	0.669412i	$-0.766546\pi$
$883$	−44.1505			−1.48578			−0.742891	+	0.669412i	$0.766546\pi$
$884$	−18.9532			−0.637465
$885$			5.47657i			0.184093i
$886$			31.5575i			1.06019i
$887$	47.4459			1.59308			0.796538	−	0.604588i	$-0.206662\pi$
$887$	47.4459			1.59308			0.796538	+	0.604588i	$0.206662\pi$
$888$	−3.62086			−0.121508
$889$		0			0
$890$			11.1469i			0.373647i
$891$	2.62367	+	2.02888i	0.0878963	+	0.0679700i
$892$			13.7495i			0.460366i
$893$			0.521047i			0.0174362i
$894$		−	21.3790i		−	0.715022i
$895$		−	18.0794i		−	0.604328i
$896$		0			0
$897$			27.6582i			0.923479i
$898$		−	8.72510i		−	0.291160i
$899$	−18.6637			−0.622470
$900$	1.07108			0.0357027
$901$	−63.1126			−2.10259
$902$	−20.9716	+	27.1197i	−0.698279	+	0.902989i
$903$		0			0
$904$		−	16.4564i		−	0.547333i
$905$	7.54991			0.250968
$906$		−	9.79712i		−	0.325487i
$907$	8.47059			0.281261			0.140631	−	0.990062i	$-0.455087\pi$
$907$	8.47059			0.281261			0.140631	+	0.990062i	$0.455087\pi$
$908$	12.3129			0.408617
$909$	−12.3926			−0.411035
$910$		0			0
$911$	32.7926			1.08647			0.543234	−	0.839581i	$-0.317200\pi$
$911$	32.7926			1.08647			0.543234	+	0.839581i	$0.317200\pi$
$912$		−	0.193339i		−	0.00640208i
$913$	24.8019	+	19.1792i	0.820822	+	0.634740i
$914$	20.4099			0.675099
$915$	22.6983			0.750383
$916$			11.3303i			0.374362i
$917$		0			0
$918$	5.16068			0.170328
$919$		−	4.17690i		−	0.137783i	−0.997624	−	0.0688916i	$-0.978054\pi$
$919$		−	4.17690i		−	0.137783i	0.997624	−	0.0688916i	$-0.0219462\pi$
$920$	14.9274			0.492142
$921$		−	8.43081i		−	0.277804i
$922$		−	17.5256i		−	0.577174i
$923$	2.22195			0.0731362
$924$		0			0
$925$	3.87823			0.127516
$926$			39.8665i			1.31010i
$927$		−	6.69759i		−	0.219978i
$928$	−4.29083			−0.140853
$929$		−	6.15740i		−	0.202018i	−0.994886	−	0.101009i	$-0.967793\pi$
$929$		−	6.15740i		−	0.202018i	0.994886	−	0.101009i	$-0.0322071\pi$
$930$	8.62171			0.282717
$931$		0			0
$932$			24.9153i			0.816129i
$933$	−28.6048			−0.936479
$934$	−11.0065			−0.360143
$935$	20.7539	−	26.8382i	0.678725	−	0.877703i
$936$			3.67261i			0.120043i
$937$	−55.3499			−1.80820			−0.904101	−	0.427318i	$-0.859458\pi$
$937$	−55.3499			−1.80820			−0.904101	+	0.427318i	$0.859458\pi$
$938$		0			0
$939$	19.5248			0.637168
$940$	−5.34188			−0.174233
$941$	30.9504			1.00895			0.504477	−	0.863425i	$-0.331685\pi$
$941$	30.9504			1.00895			0.504477	+	0.863425i	$0.331685\pi$
$942$		−	16.1094i		−	0.524871i
$943$	77.8438			2.53494
$944$		−	2.76294i		−	0.0899262i
$945$		0			0
$946$	−9.93450	−	7.68233i	−0.322998	−	0.249774i
$947$	−38.0669			−1.23701			−0.618504	−	0.785782i	$-0.712261\pi$
$947$	−38.0669			−1.23701			−0.618504	+	0.785782i	$0.712261\pi$
$948$	−1.40671			−0.0456880
$949$	−9.15293			−0.297117
$950$			0.207082i			0.00671861i
$951$			1.94148i			0.0629567i
$952$		0			0
$953$		−	22.3796i		−	0.724946i	−0.931994	−	0.362473i	$-0.881933\pi$
$953$		−	22.3796i		−	0.724946i	0.931994	−	0.362473i	$-0.118067\pi$
$954$			12.2295i			0.395945i
$955$		−	7.56753i		−	0.244879i
$956$			5.39548i			0.174502i
$957$	11.2577	+	8.70557i	0.363910	+	0.281411i
$958$		−	1.36913i		−	0.0442346i
$959$		0			0
$960$	1.98215			0.0639736
$961$	12.0803			0.389687
$962$			13.2980i			0.428745i
$963$			14.1241i			0.455144i
$964$	−19.0210			−0.612624
$965$	−28.0277			−0.902242
$966$		0			0
$967$			51.6214i			1.66003i	0.557740	+	0.830016i	$0.311669\pi$
$967$			51.6214i			1.66003i	−0.557740	+	0.830016i	$0.688331\pi$
$968$	−10.6462	+	2.76730i	−0.342183	+	0.0889444i
$969$			0.997760i			0.0320527i
$970$		−	19.0903i		−	0.612954i
$971$			33.8484i			1.08625i	0.839652	+	0.543124i	$0.182759\pi$
$971$			33.8484i			1.08625i	−0.839652	+	0.543124i	$0.817241\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$			12.9287i			0.414263i
$975$		−	3.93367i		−	0.125978i
$976$	−11.4514			−0.366549
$977$	−32.9519			−1.05422			−0.527112	−	0.849796i	$-0.676725\pi$
$977$	−32.9519			−1.05422			−0.527112	+	0.849796i	$0.676725\pi$
$978$	−22.8989			−0.732226
$979$	−11.4097	+	14.7547i	−0.364657	+	0.471561i
$980$		0			0
$981$			1.75960i			0.0561796i
$982$	6.08579			0.194205
$983$			24.1769i			0.771122i	0.922682	+	0.385561i	$0.125992\pi$
$983$			24.1769i			0.771122i	−0.922682	+	0.385561i	$0.874008\pi$
$984$	10.3366			0.329518
$985$	−39.2512			−1.25065
$986$	22.1436			0.705196
$987$		0			0
$988$	−0.710059			−0.0225900
$989$			28.5157i			0.906748i
$990$	−5.20051	−	4.02154i	−0.165283	−	0.127813i
$991$	54.2033			1.72182			0.860912	−	0.508753i	$-0.169893\pi$
$991$	54.2033			1.72182			0.860912	+	0.508753i	$0.169893\pi$
$992$	−4.34968			−0.138102
$993$			4.24442i			0.134692i
$994$		0			0
$995$	30.9284			0.980495
$996$		−	9.45312i		−	0.299534i
$997$	41.2983			1.30793			0.653965	−	0.756525i	$-0.273104\pi$
$997$	41.2983			1.30793			0.653965	+	0.756525i	$0.273104\pi$
$998$			3.58565i			0.113502i
$999$		−	3.62086i		−	0.114559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.d.2155.10	yes	24
7.6	odd	2		3234.2.e.c.2155.3	✓	24
11.10	odd	2		3234.2.e.c.2155.22	yes	24
77.76	even	2	inner	3234.2.e.d.2155.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.3	✓	24	7.6	odd	2
3234.2.e.c.2155.22	yes	24	11.10	odd	2
3234.2.e.d.2155.10	yes	24	1.1	even	1	trivial
3234.2.e.d.2155.15	yes	24	77.76	even	2	inner

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.98215i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.98215i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +1.98215 q^{10} +(2.62367 + 2.02888i) q^{11} -1.00000i q^{12} -3.67261 q^{13} -1.98215 q^{15} +1.00000 q^{16} -5.16068 q^{17} +1.00000i q^{18} -0.193339 q^{19} -1.98215i q^{20} +(2.02888 - 2.62367i) q^{22} -7.53092 q^{23} -1.00000 q^{24} +1.07108 q^{25} +3.67261i q^{26} -1.00000i q^{27} -4.29083i q^{29} +1.98215i q^{30} -4.34968i q^{31} -1.00000i q^{32} +(-2.02888 + 2.62367i) q^{33} +5.16068i q^{34} +1.00000 q^{36} +3.62086 q^{37} +0.193339i q^{38} -3.67261i q^{39} -1.98215 q^{40} -10.3366 q^{41} -3.78649i q^{43} +(-2.62367 - 2.02888i) q^{44} -1.98215i q^{45} +7.53092i q^{46} -2.69500i q^{47} +1.00000i q^{48} -1.07108i q^{50} -5.16068i q^{51} +3.67261 q^{52} +12.2295 q^{53} -1.00000 q^{54} +(-4.02154 + 5.20051i) q^{55} -0.193339i q^{57} -4.29083 q^{58} -2.76294i q^{59} +1.98215 q^{60} -11.4514 q^{61} -4.34968 q^{62} -1.00000 q^{64} -7.27967i q^{65} +(2.62367 + 2.02888i) q^{66} +8.97778 q^{67} +5.16068 q^{68} -7.53092i q^{69} -0.605004 q^{71} -1.00000i q^{72} +2.49221 q^{73} -3.62086i q^{74} +1.07108i q^{75} +0.193339 q^{76} -3.67261 q^{78} -1.40671i q^{79} +1.98215i q^{80} +1.00000 q^{81} +10.3366i q^{82} +9.45312 q^{83} -10.2292i q^{85} -3.78649 q^{86} +4.29083 q^{87} +(-2.02888 + 2.62367i) q^{88} +5.62367i q^{89} -1.98215 q^{90} +7.53092 q^{92} +4.34968 q^{93} -2.69500 q^{94} -0.383226i q^{95} +1.00000 q^{96} -9.63113i q^{97} +(-2.62367 - 2.02888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9} + 24 q^{16} - 16 q^{17} + 32 q^{19} - 8 q^{22} - 24 q^{24} - 8 q^{25} + 8 q^{33} + 24 q^{36} + 16 q^{37} + 16 q^{41} - 24 q^{54} - 16 q^{55} + 16 q^{62} - 24 q^{64} - 64 q^{67} + 16 q^{68} + 64 q^{71} - 32 q^{76} + 24 q^{81} + 16 q^{83} + 8 q^{88} - 16 q^{93} - 64 q^{94} + 24 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9 + 24 * q^16 - 16 * q^17 + 32 * q^19 - 8 * q^22 - 24 * q^24 - 8 * q^25 + 8 * q^33 + 24 * q^36 + 16 * q^37 + 16 * q^41 - 24 * q^54 - 16 * q^55 + 16 * q^62 - 24 * q^64 - 64 * q^67 + 16 * q^68 + 64 * q^71 - 32 * q^76 + 24 * q^81 + 16 * q^83 + 8 * q^88 - 16 * q^93 - 64 * q^94 + 24 * q^96

Introduction

L-functions

Modular forms

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