LMFDB - Embedded newform 639.2.z.a.53.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			53.14
Character	$\chi$	$=$	639.53
Dual form			639.2.z.a.422.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0324280 + 0.360305i) q^{2} +(1.83909 - 0.333746i) q^{4} +(0.370233 - 0.509581i) q^{5} +(2.04417 + 3.42136i) q^{7} +(0.372372 + 1.34926i) q^{8} +O(q^{10})$	\(q+(0.0324280 + 0.360305i) q^{2} +(1.83909 - 0.333746i) q^{4} +(0.370233 - 0.509581i) q^{5} +(2.04417 + 3.42136i) q^{7} +(0.372372 + 1.34926i) q^{8} +(0.195610 + 0.116872i) q^{10} +(-3.34100 + 5.06140i) q^{11} +(-3.55362 + 2.34573i) q^{13} +(-1.16644 + 0.847471i) q^{14} +(3.02582 - 1.13561i) q^{16} +(-0.290435 + 0.893867i) q^{17} +(0.441948 + 0.462241i) q^{19} +(0.510821 - 1.06073i) q^{20} +(-1.93199 - 1.03965i) q^{22} +(-1.88112 - 8.24173i) q^{23} +(1.42248 + 4.37796i) q^{25} +(-0.960412 - 1.20432i) q^{26} +(4.90128 + 5.60996i) q^{28} +(2.87644 - 1.54788i) q^{29} +(2.14293 - 5.70981i) q^{31} +(1.72190 + 3.57556i) q^{32} +(-0.331483 - 0.0756588i) q^{34} +(2.50028 + 0.225029i) q^{35} +(1.17473 - 5.14681i) q^{37} +(-0.152216 + 0.174225i) q^{38} +(0.825421 + 0.309786i) q^{40} +(-1.68304 + 2.11047i) q^{41} +(4.26422 - 3.72554i) q^{43} +(-4.45518 + 10.4234i) q^{44} +(2.90853 - 0.945039i) q^{46} +(-0.399187 - 2.94692i) q^{47} +(-4.21001 + 7.82351i) q^{49} +(-1.53127 + 0.654496i) q^{50} +(-5.75256 + 5.50001i) q^{52} +(5.65661 + 1.02652i) q^{53} +(1.34225 + 3.57641i) q^{55} +(-3.85511 + 4.03213i) q^{56} +(0.650984 + 0.986199i) q^{58} +(0.216618 + 4.82338i) q^{59} +(4.04714 - 6.77376i) q^{61} +(2.12676 + 0.586949i) q^{62} +(4.31639 - 2.57892i) q^{64} +(-0.120329 + 2.67932i) q^{65} +(-0.301019 - 1.65875i) q^{67} +(-0.235812 + 1.74084i) q^{68} +0.908160i q^{70} +(2.48147 - 8.05247i) q^{71} +(-14.4101 + 1.29693i) q^{73} +(1.89251 + 0.256358i) q^{74} +(0.967053 + 0.702605i) q^{76} +(-24.1464 - 1.08442i) q^{77} +(8.91301 - 2.45983i) q^{79} +(0.541572 - 1.96234i) q^{80} +(-0.814989 - 0.537970i) q^{82} +(11.4479 - 0.514127i) q^{83} +(0.347970 + 0.478939i) q^{85} +(1.48061 + 1.41561i) q^{86} +(-8.07323 - 2.62315i) q^{88} +(1.04708 - 5.76988i) q^{89} +(-15.2898 - 7.36317i) q^{91} +(-6.21020 - 14.5295i) q^{92} +(1.04884 - 0.239392i) q^{94} +(0.399173 - 0.0540717i) q^{95} +(-10.3600 + 8.26184i) q^{97} +(-2.95537 - 1.26319i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{23}{70}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0324280	+	0.360305i	0.0229301	+	0.254774i	0.999259	+	0.0384838i	$0.0122528\pi$
$2$	0.0324280	+	0.360305i	0.0229301	+	0.254774i	−0.976329	+	0.216290i	$0.930604\pi$
$3$		0			0
$3$		0			0
$4$	1.83909	−	0.333746i	0.919546	−	0.166873i
$5$	0.370233	−	0.509581i	0.165573	−	0.227892i	−0.718166	−	0.695872i	$-0.755018\pi$
$5$	0.370233	−	0.509581i	0.165573	−	0.227892i	0.883739	+	0.467980i	$0.155018\pi$
$6$		0			0
$7$	2.04417	+	3.42136i	0.772623	+	1.29315i	0.951000	+	0.309191i	$0.100058\pi$
$7$	2.04417	+	3.42136i	0.772623	+	1.29315i	−0.178377	+	0.983962i	$0.557085\pi$
$8$	0.372372	+	1.34926i	0.131653	+	0.477035i
$9$		0			0
$10$	0.195610	+	0.116872i	0.0618575	+	0.0369581i
$11$	−3.34100	+	5.06140i	−1.00735	+	1.52607i	−0.165605	+	0.986192i	$0.552958\pi$
$11$	−3.34100	+	5.06140i	−1.00735	+	1.52607i	−0.841744	+	0.539877i	$0.818471\pi$
$12$		0			0
$13$	−3.55362	+	2.34573i	−0.985597	+	0.650587i	−0.937401	−	0.348251i	$-0.886776\pi$
$13$	−3.55362	+	2.34573i	−0.985597	+	0.650587i	−0.0481960	+	0.998838i	$0.515347\pi$
$14$	−1.16644	+	0.847471i	−0.311745	+	0.226496i
$15$		0			0
$16$	3.02582	−	1.13561i	0.756455	−	0.283902i
$17$	−0.290435	+	0.893867i	−0.0704409	+	0.216795i	−0.980079	−	0.198606i	$-0.936359\pi$
$17$	−0.290435	+	0.893867i	−0.0704409	+	0.216795i	0.909639	+	0.415401i	$0.136359\pi$
$18$		0			0
$19$	0.441948	+	0.462241i	0.101390	+	0.106045i	0.771542	−	0.636178i	$-0.219486\pi$
$19$	0.441948	+	0.462241i	0.101390	+	0.106045i	−0.670153	+	0.742223i	$0.733771\pi$
$20$	0.510821	−	1.06073i	0.114223	−	0.237187i
$21$		0			0
$22$	−1.93199	−	1.03965i	−0.411901	−	0.221653i
$23$	−1.88112	−	8.24173i	−0.392241	−	1.71852i	−0.656725	−	0.754130i	$-0.728059\pi$
$23$	−1.88112	−	8.24173i	−0.392241	−	1.71852i	0.264485	−	0.964390i	$-0.414798\pi$
$24$		0			0
$25$	1.42248	+	4.37796i	0.284497	+	0.875591i
$26$	−0.960412	−	1.20432i	−0.188352	−	0.236186i
$27$		0			0
$28$	4.90128	+	5.60996i	0.926254	+	1.06018i
$29$	2.87644	−	1.54788i	0.534141	−	0.287433i	−0.184479	−	0.982836i	$-0.559060\pi$
$29$	2.87644	−	1.54788i	0.534141	−	0.287433i	0.718620	+	0.695403i	$0.244774\pi$
$30$		0			0
$31$	2.14293	−	5.70981i	0.384881	−	1.02551i	−0.590896	−	0.806748i	$-0.701226\pi$
$31$	2.14293	−	5.70981i	0.384881	−	1.02551i	0.975778	−	0.218765i	$-0.0702029\pi$
$32$	1.72190	+	3.57556i	0.304392	+	0.632076i
$33$		0			0
$34$	−0.331483	−	0.0756588i	−0.0568488	−	0.0129754i
$35$	2.50028	+	0.225029i	0.422625	+	0.0380369i
$36$		0			0
$37$	1.17473	−	5.14681i	0.193124	−	0.846130i	−0.781789	−	0.623543i	$-0.785693\pi$
$37$	1.17473	−	5.14681i	0.193124	−	0.846130i	0.974913	−	0.222587i	$-0.0714502\pi$
$38$	−0.152216	+	0.174225i	−0.0246927	+	0.0282631i
$39$		0			0
$40$	0.825421	+	0.309786i	0.130511	+	0.0489814i
$41$	−1.68304	+	2.11047i	−0.262847	+	0.329600i	−0.895689	−	0.444681i	$-0.853317\pi$
$41$	−1.68304	+	2.11047i	−0.262847	+	0.329600i	0.632842	+	0.774281i	$0.281888\pi$
$42$		0			0
$43$	4.26422	−	3.72554i	0.650288	−	0.568139i	−0.268310	−	0.963333i	$-0.586465\pi$
$43$	4.26422	−	3.72554i	0.650288	−	0.568139i	0.918598	+	0.395193i	$0.129322\pi$
$44$	−4.45518	+	10.4234i	−0.671644	+	1.57139i
$45$		0			0
$46$	2.90853	−	0.945039i	0.428840	−	0.139338i
$47$	−0.399187	−	2.94692i	−0.0582274	−	0.429852i	−0.996475	−	0.0838881i	$-0.973266\pi$
$47$	−0.399187	−	2.94692i	−0.0582274	−	0.429852i	0.938248	−	0.345964i	$-0.112448\pi$
$48$		0			0
$49$	−4.21001	+	7.82351i	−0.601430	+	1.11764i
$50$	−1.53127	+	0.654496i	−0.216554	+	0.0925597i
$51$		0			0
$52$	−5.75256	+	5.50001i	−0.797736	+	0.762714i
$53$	5.65661	+	1.02652i	0.776995	+	0.141004i	0.552547	−	0.833482i	$-0.313656\pi$
$53$	5.65661	+	1.02652i	0.776995	+	0.141004i	0.224449	+	0.974486i	$0.427942\pi$
$54$		0			0
$55$	1.34225	+	3.57641i	0.180989	+	0.482243i
$56$	−3.85511	+	4.03213i	−0.515161	+	0.538816i
$57$		0			0
$58$	0.650984	+	0.986199i	0.0854784	+	0.129494i
$59$	0.216618	+	4.82338i	0.0282013	+	0.627951i	0.962471	+	0.271384i	$0.0874814\pi$
$59$	0.216618	+	4.82338i	0.0282013	+	0.627951i	−0.934270	+	0.356567i	$0.883947\pi$
$60$		0			0
$61$	4.04714	−	6.77376i	0.518183	−	0.867292i	−0.481777	−	0.876294i	$-0.660008\pi$
$61$	4.04714	−	6.77376i	0.518183	−	0.867292i	0.999959	+	0.00900230i	$0.00286556\pi$
$62$	2.12676	+	0.586949i	0.270099	+	0.0745426i
$63$		0			0
$64$	4.31639	−	2.57892i	0.539549	−	0.322365i
$65$	−0.120329	+	2.67932i	−0.0149249	+	0.332329i
$66$		0			0
$67$	−0.301019	−	1.65875i	−0.0367753	−	0.202649i	0.960311	−	0.278932i	$-0.0899804\pi$
$67$	−0.301019	−	1.65875i	−0.0367753	−	0.202649i	−0.997086	+	0.0762833i	$0.975695\pi$
$68$	−0.235812	+	1.74084i	−0.0285964	+	0.211107i
$69$		0			0
$70$			0.908160i			0.108546i
$71$	2.48147	−	8.05247i	0.294496	−	0.955653i
$71$	2.48147	−	8.05247i	0.294496	−	0.955653i
$72$		0			0
$73$	−14.4101	+	1.29693i	−1.68657	+	0.151794i	−0.890981	−	0.454040i	$-0.849982\pi$
$73$	−14.4101	+	1.29693i	−1.68657	+	0.151794i	−0.795591	+	0.605834i	$0.792840\pi$
$74$	1.89251	+	0.256358i	0.220000	+	0.0298010i
$75$		0			0
$76$	0.967053	+	0.702605i	0.110929	+	0.0805944i
$77$	−24.1464	−	1.08442i	−2.75174	−	0.123581i
$78$		0			0
$79$	8.91301	−	2.45983i	1.00279	−	0.276753i	0.274179	−	0.961679i	$-0.411594\pi$
$79$	8.91301	−	2.45983i	1.00279	−	0.276753i	0.728613	+	0.684926i	$0.240165\pi$
$80$	0.541572	−	1.96234i	0.0605496	−	0.219396i
$81$		0			0
$82$	−0.814989	−	0.537970i	−0.0900005	−	0.0594088i
$83$	11.4479	−	0.514127i	1.25657	−	0.0564327i	0.593405	−	0.804904i	$-0.297783\pi$
$83$	11.4479	−	0.514127i	1.25657	−	0.0564327i	0.663167	+	0.748471i	$0.269212\pi$
$84$		0			0
$85$	0.347970	+	0.478939i	0.0377426	+	0.0519483i
$86$	1.48061	+	1.41561i	0.159658	+	0.152649i
$87$		0			0
$88$	−8.07323	−	2.62315i	−0.860609	−	0.279629i
$89$	1.04708	−	5.76988i	0.110990	−	0.611606i	−0.879707	−	0.475517i	$-0.842261\pi$
$89$	1.04708	−	5.76988i	0.110990	−	0.611606i	0.990697	−	0.136089i	$-0.0434532\pi$
$90$		0			0
$91$	−15.2898	−	7.36317i	−1.60280	−	0.771870i
$92$	−6.21020	−	14.5295i	−0.647458	−	1.51480i
$93$		0			0
$94$	1.04884	−	0.239392i	0.108180	−	0.0246914i
$95$	0.399173	−	0.0540717i	0.0409543	−	0.00554764i
$96$		0			0
$97$	−10.3600	+	8.26184i	−1.05190	+	0.838863i	−0.987271	−	0.159046i	$-0.949158\pi$
$97$	−10.3600	+	8.26184i	−1.05190	+	0.838863i	−0.0646300	+	0.997909i	$0.520587\pi$
$98$	−2.95537	−	1.26319i	−0.298537	−	0.127601i
$99$		0			0
$100$	4.07720	+	7.57671i	0.407720	+	0.757671i
$101$	13.6464	+	10.8827i	1.35787	+	1.08287i	0.988111	+	0.153740i	$0.0491317\pi$
$101$	13.6464	+	10.8827i	1.35787	+	1.08287i	0.369760	+	0.929127i	$0.379440\pi$
$102$		0			0
$103$	6.70469	−	3.22881i	0.660633	−	0.318144i	−0.0733559	−	0.997306i	$-0.523371\pi$
$103$	6.70469	−	3.22881i	0.660633	−	0.318144i	0.733988	+	0.679162i	$0.237657\pi$
$104$	−4.48826	−	3.92127i	−0.440110	−	0.384512i
$105$		0			0
$106$	−0.186429	+	2.07139i	−0.0181075	+	0.201191i
$107$	0.394852	−	4.38717i	0.0381718	−	0.424124i	−0.954051	−	0.299646i	$-0.903132\pi$
$107$	0.394852	−	4.38717i	0.0381718	−	0.424124i	0.992222	−	0.124478i	$-0.0397256\pi$
$108$		0			0
$109$	13.3381	+	11.6532i	1.27756	+	1.11617i	0.987239	+	0.159243i	$0.0509053\pi$
$109$	13.3381	+	11.6532i	1.27756	+	1.11617i	0.290322	+	0.956929i	$0.406238\pi$
$110$	−1.24507	+	0.599594i	−0.118713	+	0.0571690i
$111$		0			0
$112$	10.0706	+	8.03105i	0.951583	+	0.758862i
$113$	−0.570571	−	1.06030i	−0.0536748	−	0.0997445i	0.852345	−	0.522980i	$-0.175180\pi$
$113$	−0.570571	−	1.06030i	−0.0536748	−	0.0997445i	−0.906020	+	0.423236i	$0.860894\pi$
$114$		0			0
$115$	−4.89629	−	2.09277i	−0.456581	−	0.195152i
$116$	4.77343	−	3.80669i	0.443202	−	0.353442i
$117$		0			0
$118$	−1.73086	+	0.234461i	−0.159339	+	0.0215839i
$119$	−3.65194	+	0.833532i	−0.334773	+	0.0764097i
$120$		0			0
$121$	−10.1322	−	23.7055i	−0.921109	−	2.15504i
$122$	2.57186	+	1.23854i	0.232845	+	0.112132i
$123$		0			0
$124$	2.03542	−	11.2161i	0.182786	−	1.00723i
$125$	5.75282	+	1.86920i	0.514548	+	0.167187i
$126$		0			0
$127$	−13.8357	−	13.2283i	−1.22772	−	1.17382i	−0.978694	−	0.205326i	$-0.934175\pi$
$127$	−13.8357	−	13.2283i	−1.22772	−	1.17382i	−0.249028	−	0.968496i	$-0.580111\pi$
$128$	5.73451	+	7.89287i	0.506864	+	0.697638i
$129$		0			0
$130$	−0.969275	+	0.0435302i	−0.0850110	+	0.00381785i
$131$	8.34472	+	5.50830i	0.729081	+	0.481262i	0.860105	−	0.510117i	$-0.170398\pi$
$131$	8.34472	+	5.50830i	0.729081	+	0.481262i	−0.131024	+	0.991379i	$0.541826\pi$
$132$		0			0
$133$	−0.678078	+	2.45696i	−0.0587969	+	0.213046i
$134$	0.587894	−	0.162248i	0.0507863	−	0.0140161i
$135$		0			0
$136$	−1.31421	−	0.0590211i	−0.112692	−	0.00506102i
$137$	1.10034	+	0.799441i	0.0940081	+	0.0683009i	0.633796	−	0.773500i	$-0.281496\pi$
$137$	1.10034	+	0.799441i	0.0940081	+	0.0683009i	−0.539788	+	0.841801i	$0.681496\pi$
$138$		0			0
$139$	−12.5474	−	1.69967i	−1.06426	−	0.144164i	−0.418893	−	0.908036i	$-0.637582\pi$
$139$	−12.5474	−	1.69967i	−1.06426	−	0.144164i	−0.645368	+	0.763872i	$0.723296\pi$
$140$	4.67335	−	0.420609i	0.394970	−	0.0355479i
$141$		0			0
$142$	2.98181	+	0.632958i	0.250228	+	0.0531167i
$143$		−	25.8234i		−	2.15946i
$144$		0			0
$145$	0.276181	−	2.03885i	0.0229356	−	0.169318i
$146$	−0.934580	−	5.14996i	−0.0773464	−	0.426214i
$147$		0			0
$148$	0.442701	−	9.85751i	0.0363898	−	0.810282i
$149$	−3.44803	+	2.06010i	−0.282473	+	0.168770i	−0.647147	−	0.762366i	$-0.724038\pi$
$149$	−3.44803	+	2.06010i	−0.282473	+	0.168770i	0.364673	+	0.931136i	$0.381181\pi$
$150$		0			0
$151$	−9.55483	−	2.63697i	−0.777561	−	0.214593i	−0.145341	−	0.989382i	$-0.546428\pi$
$151$	−9.55483	−	2.63697i	−0.777561	−	0.214593i	−0.632221	+	0.774788i	$0.717856\pi$
$152$	−0.459114	+	0.768427i	−0.0372391	+	0.0623277i
$153$		0			0
$154$	−0.392300	−	8.73524i	−0.0316124	−	0.703905i
$155$	−2.11623	−	3.20596i	−0.169980	−	0.257509i
$156$		0			0
$157$	0.588579	−	0.615605i	0.0469737	−	0.0491306i	−0.698890	−	0.715229i	$-0.746323\pi$
$157$	0.588579	−	0.615605i	0.0469737	−	0.0491306i	0.745864	+	0.666098i	$0.232037\pi$
$158$	1.17532	+	3.13163i	0.0935034	+	0.249139i
$159$		0			0
$160$	2.45954	+	0.446341i	0.194444	+	0.0352864i
$161$	24.3526	−	23.2835i	1.91925	−	1.83500i
$162$		0			0
$163$	−7.00514	+	2.99414i	−0.548685	+	0.234519i	−0.649468	−	0.760389i	$-0.725008\pi$
$163$	−7.00514	+	2.99414i	−0.548685	+	0.234519i	0.100783	+	0.994908i	$0.467865\pi$
$164$	−2.39091	+	4.44305i	−0.186699	+	0.346944i
$165$		0			0
$166$	0.556475	+	4.10807i	0.0431909	+	0.318848i
$167$	15.3094	−	4.97432i	1.18468	−	0.384925i	0.350574	−	0.936535i	$-0.385986\pi$
$167$	15.3094	−	4.97432i	1.18468	−	0.384925i	0.834102	+	0.551610i	$0.185986\pi$
$168$		0			0
$169$	2.01648	−	4.71778i	0.155114	−	0.362906i
$170$	−0.161280	+	0.140906i	−0.0123696	+	0.0108070i
$171$		0			0
$172$	6.59891	−	8.27477i	0.503162	−	0.630945i
$173$	−19.0849	−	7.16268i	−1.45100	−	0.544568i	−0.503405	−	0.864051i	$-0.667920\pi$
$173$	−19.0849	−	7.16268i	−1.45100	−	0.544568i	−0.947592	+	0.319482i	$0.896491\pi$
$174$		0			0
$175$	−12.0708	+	13.8161i	−0.912465	+	1.04440i
$176$	−4.36149	+	19.1089i	−0.328760	+	1.44039i
$177$		0			0
$178$	2.11287	+	0.190161i	0.158366	+	0.0142532i
$179$	12.8141	+	2.92473i	0.957770	+	0.218605i	0.672711	−	0.739905i	$-0.265130\pi$
$179$	12.8141	+	2.92473i	0.957770	+	0.218605i	0.285059	+	0.958510i	$0.407987\pi$
$180$		0			0
$181$	1.03752	+	2.15444i	0.0771186	+	0.160138i	0.935963	−	0.352098i	$-0.114532\pi$
$181$	1.03752	+	2.15444i	0.0771186	+	0.160138i	−0.858845	+	0.512236i	$0.828817\pi$
$182$	2.15717	−	5.74775i	0.159900	−	0.426051i
$183$		0			0
$184$	10.4197	−	5.60711i	0.768154	−	0.413361i
$185$	−2.18780	−	2.50413i	−0.160850	−	0.184108i
$186$		0			0
$187$	−3.55388	−	4.45642i	−0.259885	−	0.325886i
$188$	−1.71766	−	5.28643i	−0.125274	−	0.385552i
$189$		0			0
$190$	0.0324266	+	0.142070i	0.00235248	+	0.0103069i
$191$	−22.6989	−	12.2148i	−1.64243	−	0.883831i	−0.992279	−	0.124029i	$-0.960418\pi$
$191$	−22.6989	−	12.2148i	−1.64243	−	0.883831i	−0.650155	−	0.759802i	$-0.725296\pi$
$192$		0			0
$193$	3.58069	−	7.43538i	0.257744	−	0.535210i	−0.731438	−	0.681908i	$-0.761150\pi$
$193$	3.58069	−	7.43538i	0.257744	−	0.535210i	0.989181	+	0.146698i	$0.0468646\pi$
$194$	−3.31273	−	3.46485i	−0.237841	−	0.248762i
$195$		0			0
$196$	−5.13153	+	15.7932i	−0.366538	+	1.12809i
$197$	−6.78219	+	2.54540i	−0.483211	+	0.181352i	−0.581079	−	0.813847i	$-0.697369\pi$
$197$	−6.78219	+	2.54540i	−0.483211	+	0.181352i	0.0978677	+	0.995199i	$0.468798\pi$
$198$		0			0
$199$	−18.4860	+	13.4308i	−1.31044	+	0.952087i	−0.310437	+	0.950594i	$0.600475\pi$
$199$	−18.4860	+	13.4308i	−1.31044	+	0.952087i	−0.999999	+	0.00149299i	$0.999525\pi$
$200$	−5.37730	+	3.54952i	−0.380233	+	0.250989i
$201$		0			0
$202$	−3.47855	+	5.26978i	−0.244750	+	0.370780i
$203$	11.1758	+	6.67721i	0.784385	+	0.468648i
$204$		0			0
$205$	0.452339	+	1.63901i	0.0315927	+	0.114474i
$206$	1.38077	+	2.31103i	0.0962031	+	0.161017i
$207$		0			0
$208$	−8.08879	+	11.1333i	−0.560857	+	0.771953i
$209$	−3.81613	+	0.692526i	−0.263967	+	0.0479030i
$210$		0			0
$211$	0.255874	+	2.84299i	0.0176151	+	0.195719i	0.999963	+	0.00865417i	$0.00275474\pi$
$211$	0.255874	+	2.84299i	0.0176151	+	0.195719i	−0.982347	+	0.187065i	$0.940102\pi$
$212$	10.7456			0.738012
$213$		0			0
$214$	1.59352			0.108931
$215$	−0.319711	−	3.55228i	−0.0218041	−	0.242264i
$216$		0			0
$217$	23.9158	−	4.34009i	1.62351	−	0.294624i
$218$	−3.76616	+	5.18368i	−0.255077	+	0.351083i
$219$		0			0
$220$	3.66213	+	6.12937i	0.246901	+	0.413242i
$221$	−1.06467	−	3.85775i	−0.0716175	−	0.259500i
$222$		0			0
$223$	−22.5614	−	13.4798i	−1.51082	−	0.902675i	−0.999051	−	0.0435534i	$-0.986132\pi$
$223$	−22.5614	−	13.4798i	−1.51082	−	0.902675i	−0.511772	−	0.859121i	$-0.671011\pi$
$224$	−8.71344	+	13.2003i	−0.582191	+	0.881982i
$225$		0			0
$226$	0.363528	−	0.239963i	0.0241815	−	0.0159621i
$227$	−13.8876	+	10.0899i	−0.921752	+	0.669692i	−0.943959	−	0.330062i	$-0.892930\pi$
$227$	−13.8876	+	10.0899i	−0.921752	+	0.669692i	0.0222078	+	0.999753i	$0.492930\pi$
$228$		0			0
$229$	−6.82065	+	2.55983i	−0.450721	+	0.169159i	−0.566404	−	0.824128i	$-0.691666\pi$
$229$	−6.82065	+	2.55983i	−0.450721	+	0.169159i	0.115683	+	0.993286i	$0.463094\pi$
$230$	0.595259	−	1.83202i	0.0392502	−	0.120800i
$231$		0			0
$232$	3.15959	+	3.30467i	0.207437	+	0.216962i
$233$	0.461608	−	0.958538i	0.0302409	−	0.0627959i	−0.885301	−	0.465018i	$-0.846048\pi$
$233$	0.461608	−	0.958538i	0.0302409	−	0.0627959i	0.915542	+	0.402222i	$0.131762\pi$
$234$		0			0
$235$	−1.64949	−	0.887627i	−0.107601	−	0.0579024i
$236$	2.00817	+	8.79835i	0.130720	+	0.572724i
$237$		0			0
$238$	−0.418750	−	1.28878i	−0.0271436	−	0.0835393i
$239$	10.1816	+	12.7673i	0.658593	+	0.825849i	0.993189	−	0.116512i	$-0.0371715\pi$
$239$	10.1816	+	12.7673i	0.658593	+	0.825849i	−0.334597	+	0.942361i	$0.608600\pi$
$240$		0			0
$241$	2.73574	+	3.13130i	0.176224	+	0.201705i	0.834400	−	0.551160i	$-0.185814\pi$
$241$	2.73574	+	3.13130i	0.176224	+	0.201705i	−0.658176	+	0.752864i	$0.728672\pi$
$242$	8.21262	−	4.41940i	0.527927	−	0.284090i
$243$		0			0
$244$	5.18234	−	13.8083i	0.331765	−	0.883985i
$245$	2.42803	+	5.04186i	0.155121	+	0.322113i
$246$		0			0
$247$	−2.65481	−	0.605942i	−0.168921	−	0.0385552i
$248$	8.50198	+	0.765192i	0.539876	+	0.0485897i
$249$		0			0
$250$	−0.486930	+	2.13338i	−0.0307962	+	0.134927i
$251$	12.6124	−	14.4361i	0.796089	−	0.911197i	−0.201578	−	0.979473i	$-0.564607\pi$
$251$	12.6124	−	14.4361i	0.796089	−	0.911197i	0.997666	+	0.0682756i	$0.0217497\pi$
$252$		0			0
$253$	47.9995	+	18.0145i	3.01770	+	1.13256i
$254$	4.31755	−	5.41404i	0.270907	−	0.339707i
$255$		0			0
$256$	4.91520	−	4.29428i	0.307200	−	0.268393i
$257$	−9.22907	+	21.5925i	−0.575694	+	1.34690i	0.338248	+	0.941057i	$0.390166\pi$
$257$	−9.22907	+	21.5925i	−0.575694	+	1.34690i	−0.913942	+	0.405846i	$0.866977\pi$
$258$		0			0
$259$	20.0104	−	6.50178i	1.24339	−	0.404001i
$260$	0.672918	+	4.96768i	0.0417326	+	0.308082i
$261$		0			0
$262$	−1.71406	+	3.18526i	−0.105895	+	0.196786i
$263$	−24.2083	+	10.3471i	−1.49275	+	0.638031i	−0.975934	−	0.218066i	$-0.930025\pi$
$263$	−24.2083	+	10.3471i	−1.49275	+	0.638031i	−0.516814	+	0.856098i	$0.672882\pi$
$264$		0			0
$265$	2.61736	−	2.50245i	0.160783	−	0.153724i
$266$	−0.907243	−	0.164640i	−0.0556267	−	0.0100947i
$267$		0			0
$268$	−1.10720	−	2.95013i	−0.0676331	−	0.180208i
$269$	16.6061	−	17.3686i	1.01249	−	1.05898i	0.0142395	−	0.999899i	$-0.495467\pi$
$269$	16.6061	−	17.3686i	1.01249	−	1.05898i	0.998253	−	0.0590855i	$-0.0188184\pi$
$270$		0			0
$271$	7.18218	+	10.8805i	0.436286	+	0.660946i	0.984498	−	0.175394i	$-0.0561199\pi$
$271$	7.18218	+	10.8805i	0.436286	+	0.660946i	−0.548212	+	0.836339i	$0.684691\pi$
$272$	0.136280	+	3.03450i	0.00826317	+	0.183994i
$273$		0			0
$274$	−0.252361	+	0.422380i	−0.0152457	+	0.0255169i
$275$	−26.9111	−	7.42699i	−1.62280	−	0.447864i
$276$		0			0
$277$	7.63789	−	4.56343i	0.458916	−	0.274190i	−0.264779	−	0.964309i	$-0.585299\pi$
$277$	7.63789	−	4.56343i	0.458916	−	0.274190i	0.723696	+	0.690119i	$0.242442\pi$
$278$	0.205509	−	4.57602i	0.0123256	−	0.274451i
$279$		0			0
$280$	0.627411	+	3.45732i	0.0374950	+	0.206614i
$281$	−1.81777	+	13.4193i	−0.108439	+	0.800528i	0.852296	+	0.523060i	$0.175210\pi$
$281$	−1.81777	+	13.4193i	−0.108439	+	0.800528i	−0.960735	+	0.277468i	$0.910505\pi$
$282$		0			0
$283$		−	5.37645i		−	0.319597i	−0.987150	−	0.159798i	$-0.948916\pi$
$283$		−	5.37645i		−	0.319597i	0.987150	−	0.159798i	$-0.0510844\pi$
$284$	1.87616	−	15.6374i	0.111330	−	0.927910i
$285$		0			0
$286$	9.30428	−	0.837400i	0.550173	−	0.0495165i
$287$	−10.6611	−	1.44414i	−0.629305	−	0.0852451i
$288$		0			0
$289$	13.0386	+	9.47313i	0.766979	+	0.557243i
$290$	0.743564	+	0.0333935i	0.0436636	+	0.00196093i
$291$		0			0
$292$	−26.0686	+	7.19448i	−1.52555	+	0.421025i
$293$	−8.13399	+	29.4728i	−0.475193	+	1.72182i	0.196058	+	0.980592i	$0.437186\pi$
$293$	−8.13399	+	29.4728i	−0.475193	+	1.72182i	−0.671251	+	0.741230i	$0.734243\pi$
$294$		0			0
$295$	2.53811	+	1.67539i	0.147774	+	0.0975449i
$296$	7.38181	−	0.331517i	0.429059	−	0.0192691i
$297$		0			0
$298$	−0.854076	−	1.17553i	−0.0494753	−	0.0680969i
$299$	26.0176	+	24.8754i	1.50464	+	1.43858i
$300$		0			0
$301$	21.4632	+	6.97382i	1.23712	+	0.401964i
$302$	0.640267	−	3.52816i	0.0368432	−	0.203023i
$303$		0			0
$304$	1.86218	+	0.896778i	0.106803	+	0.0514338i
$305$	−1.95340	−	4.57021i	−0.111852	−	0.261690i
$306$		0			0
$307$	−7.76550	+	1.77242i	−0.443200	+	0.101158i	−0.438297	−	0.898830i	$-0.644418\pi$
$307$	−7.76550	+	1.77242i	−0.443200	+	0.101158i	−0.00490368	+	0.999988i	$0.501561\pi$
$308$	−44.7694	+	6.06443i	−2.55097	+	0.345553i
$309$		0			0
$310$	1.08650	−	0.866451i	0.0617088	−	0.0492111i
$311$	−29.6970	−	12.6931i	−1.68396	−	0.719761i	−0.684011	−	0.729472i	$-0.739766\pi$
$311$	−29.6970	−	12.6931i	−1.68396	−	0.719761i	−0.999953	+	0.00971131i	$0.996909\pi$
$312$		0			0
$313$	0.434345	+	0.807148i	0.0245506	+	0.0456227i	0.892575	−	0.450898i	$-0.148896\pi$
$313$	0.434345	+	0.807148i	0.0245506	+	0.0456227i	−0.868025	+	0.496521i	$0.834611\pi$
$314$	0.240892	+	0.192105i	0.0135943	+	0.0108411i
$315$		0			0
$316$	15.5709	−	7.49854i	0.875930	−	0.421826i
$317$	5.95766	+	5.20505i	0.334615	+	0.292345i	0.808804	−	0.588079i	$-0.200116\pi$
$317$	5.95766	+	5.20505i	0.334615	+	0.292345i	−0.474188	+	0.880424i	$0.657258\pi$
$318$		0			0
$319$	−1.77575	+	19.7302i	−0.0994231	+	1.10468i
$320$	0.283897	−	3.15435i	0.0158703	−	0.176334i
$321$		0			0
$322$	9.17885	+	8.01932i	0.511517	+	0.446899i
$323$	−0.541539	+	0.260792i	−0.0301321	+	0.0145108i
$324$		0			0
$325$	−15.3245	−	12.2208i	−0.850048	−	0.677890i
$326$	−1.30597	−	2.42689i	−0.0723307	−	0.134413i
$327$		0			0
$328$	−3.47429	−	1.48498i	−0.191835	−	0.0819943i
$329$	9.26647	−	7.38976i	0.510877	−	0.407411i
$330$		0			0
$331$	−9.61312	+	1.30219i	−0.528385	+	0.0715746i	−0.393567	−	0.919296i	$-0.628759\pi$
$331$	−9.61312	+	1.30219i	−0.528385	+	0.0715746i	−0.134818	+	0.990870i	$0.543045\pi$
$332$	20.8822	−	4.76622i	1.14606	−	0.261580i
$333$		0			0
$334$	2.28872	+	5.35474i	0.125233	+	0.292998i
$335$	−0.956715	−	0.460730i	−0.0522709	−	0.0251724i
$336$		0			0
$337$	1.89152	−	10.4231i	0.103038	−	0.567785i	−0.890565	−	0.454855i	$-0.849691\pi$
$337$	1.89152	−	10.4231i	0.103038	−	0.567785i	0.993603	−	0.112929i	$-0.0360234\pi$
$338$	1.76523	+	0.573557i	0.0960158	+	0.0311974i
$339$		0			0
$340$	0.799792	+	0.764680i	0.0433748	+	0.0414706i
$341$	21.7401	+	29.9227i	1.17729	+	1.62041i
$342$		0			0
$343$	−7.50251	+	0.336938i	−0.405097	+	0.0181929i
$344$	6.61459	+	4.36625i	0.356635	+	0.235413i
$345$		0			0
$346$	1.96186	−	7.10864i	0.105470	−	0.382163i
$347$	13.4016	−	3.69860i	0.719435	−	0.198551i	0.112898	−	0.993607i	$-0.463987\pi$
$347$	13.4016	−	3.69860i	0.719435	−	0.198551i	0.606537	+	0.795055i	$0.292558\pi$
$348$		0			0
$349$	−4.07805	−	0.183145i	−0.218293	−	0.00980355i	−0.0645502	−	0.997914i	$-0.520561\pi$
$349$	−4.07805	−	0.183145i	−0.218293	−	0.00980355i	−0.153743	+	0.988111i	$0.549133\pi$
$350$	−5.36944	−	3.90113i	−0.287009	−	0.208524i
$351$		0			0
$352$	−23.8502	−	3.23073i	−1.27122	−	0.172199i
$353$	−28.7271	+	2.58549i	−1.52899	+	0.137612i	−0.821949	−	0.569561i	$-0.807113\pi$
$353$	−28.7271	+	2.58549i	−1.52899	+	0.137612i	−0.707041	+	0.707173i	$0.749970\pi$
$354$		0			0
$355$	−3.18467	−	4.24580i	−0.169025	−	0.225344i
$356$		−	10.9608i		−	0.580921i
$357$		0			0
$358$	−0.638259	+	4.71182i	−0.0337330	+	0.249027i
$359$	−0.0288163	−	0.158791i	−0.00152087	−	0.00838066i	0.983160	−	0.182746i	$-0.0584985\pi$
$359$	−0.0288163	−	0.158791i	−0.00152087	−	0.00838066i	−0.984681	+	0.174365i	$0.944213\pi$
$360$		0			0
$361$	0.834083	−	18.5723i	0.0438991	−	0.977489i
$362$	−0.742611	+	0.443689i	−0.0390308	+	0.0233198i
$363$		0			0
$364$	−30.5767	−	8.43864i	−1.60266	−	0.442305i
$365$	−4.67419	+	7.82328i	−0.244658	+	0.409489i
$366$		0			0
$367$	1.44067	+	32.0790i	0.0752024	+	1.67451i	0.582569	+	0.812781i	$0.302048\pi$
$367$	1.44067	+	32.0790i	0.0752024	+	1.67451i	−0.507366	+	0.861730i	$0.669381\pi$
$368$	−15.0513	−	22.8018i	−0.784604	−	1.18862i
$369$		0			0
$370$	0.831305	−	0.869477i	0.0432175	−	0.0452020i
$371$	8.05096	+	21.4517i	0.417985	+	1.11372i
$372$		0			0
$373$	15.7221	+	2.85315i	0.814062	+	0.147730i	0.569593	−	0.821927i	$-0.307101\pi$
$373$	15.7221	+	2.85315i	0.814062	+	0.147730i	0.244469	+	0.969657i	$0.421387\pi$
$374$	1.49042	−	1.42499i	0.0770679	−	0.0736845i
$375$		0			0
$376$	3.82751	−	1.63596i	0.197389	−	0.0843680i
$377$	−6.59087	+	12.2479i	−0.339447	+	0.630799i
$378$		0			0
$379$	−2.14382	−	15.8263i	−0.110121	−	0.812944i	−0.958809	−	0.284051i	$-0.908322\pi$
$379$	−2.14382	−	15.8263i	−0.110121	−	0.812944i	0.848688	−	0.528893i	$-0.177393\pi$
$380$	0.716069	−	0.232665i	0.0367336	−	0.0119355i
$381$		0			0
$382$	3.66496	−	8.57461i	0.187516	−	0.438715i
$383$	4.47751	−	3.91188i	0.228790	−	0.199888i	−0.535909	−	0.844276i	$-0.680031\pi$
$383$	4.47751	−	3.91188i	0.228790	−	0.199888i	0.764698	+	0.644388i	$0.222888\pi$
$384$		0			0
$385$	−9.49240	+	11.9031i	−0.483777	+	0.606638i
$386$	2.79512	+	1.04902i	0.142268	+	0.0533939i
$387$		0			0
$388$	−16.2957	+	18.6519i	−0.827288	+	0.946907i
$389$	1.39754	−	6.12302i	0.0708581	−	0.310450i	−0.927062	−	0.374907i	$-0.877675\pi$
$389$	1.39754	−	6.12302i	0.0708581	−	0.310450i	0.997920	+	0.0644576i	$0.0205317\pi$
$390$		0			0
$391$	7.91336	+	0.712215i	0.400196	+	0.0360183i
$392$	−12.1236	−	2.76714i	−0.612336	−	0.139762i
$393$		0			0
$394$	−1.13705	−	2.36111i	−0.0572838	−	0.118951i
$395$	2.04640	−	5.45261i	0.102966	−	0.274351i
$396$		0			0
$397$	5.56051	−	2.99224i	0.279074	−	0.150176i	−0.328345	−	0.944558i	$-0.606491\pi$
$397$	5.56051	−	2.99224i	0.279074	−	0.150176i	0.607419	+	0.794382i	$0.292205\pi$
$398$	−5.43866	−	6.22504i	−0.272615	−	0.312033i
$399$		0			0
$400$	9.27582	+	11.6315i	0.463791	+	0.581576i
$401$	−1.41241	−	4.34694i	−0.0705322	−	0.217076i	0.909577	−	0.415536i	$-0.136406\pi$
$401$	−1.41241	−	4.34694i	−0.0705322	−	0.217076i	−0.980109	+	0.198460i	$0.936406\pi$
$402$		0			0
$403$	5.77850	+	25.3172i	0.287847	+	1.26114i
$404$	28.7291	+	15.4598i	1.42933	+	0.769153i
$405$		0			0
$406$	−2.04342	+	4.24321i	−0.101413	+	0.210587i
$407$	22.1253	+	23.1412i	1.09671	+	1.14707i
$408$		0			0
$409$	0.638952	−	1.96649i	0.0315942	−	0.0972368i	−0.934016	−	0.357231i	$-0.883721\pi$
$409$	0.638952	−	1.96649i	0.0315942	−	0.0972368i	0.965610	+	0.259995i	$0.0837208\pi$
$410$	−0.575875	+	0.216130i	−0.0284404	+	0.0106739i
$411$		0			0
$412$	11.2529	−	8.17573i	0.554392	−	0.402790i
$413$	−16.0597	+	10.6009i	−0.790248	+	0.521638i
$414$		0			0
$415$	3.97640	−	6.02400i	0.195194	−	0.295706i
$416$	−14.5063	−	8.66709i	−0.711228	−	0.424939i
$417$		0			0
$418$	−0.373270	−	1.35251i	−0.0182572	−	0.0661536i
$419$	−9.96493	−	16.6785i	−0.486818	−	0.814797i	0.512210	−	0.858860i	$-0.328827\pi$
$419$	−9.96493	−	16.6785i	−0.486818	−	0.814797i	−0.999029	+	0.0440632i	$0.985970\pi$
$420$		0			0
$421$	10.0475	−	13.8292i	0.489685	−	0.673993i	−0.490645	−	0.871360i	$-0.663239\pi$
$421$	10.0475	−	13.8292i	0.489685	−	0.673993i	0.980330	+	0.197366i	$0.0632388\pi$
$422$	−1.01604	+	0.184385i	−0.0494603	+	0.00897572i
$423$		0			0
$424$	0.721316	+	8.01448i	0.0350302	+	0.389217i
$425$	−4.32645			−0.209864
$426$		0			0
$427$	31.4485			1.52190
$428$	−0.738030	−	8.20019i	−0.0356740	−	0.396371i
$429$		0			0
$430$	1.26954	−	0.230387i	0.0612225	−	0.0111102i
$431$	10.3354	−	14.2255i	0.497841	−	0.685219i	−0.483969	−	0.875085i	$-0.660805\pi$
$431$	10.3354	−	14.2255i	0.497841	−	0.685219i	0.981810	+	0.189866i	$0.0608054\pi$
$432$		0			0
$433$	8.04733	+	13.4690i	0.386730	+	0.647277i	0.988470	−	0.151415i	$-0.0483830\pi$
$433$	8.04733	+	13.4690i	0.386730	+	0.647277i	−0.601741	+	0.798692i	$0.705526\pi$
$434$	2.33930	+	8.47625i	0.112290	+	0.406873i
$435$		0			0
$436$	28.4192	+	16.9797i	1.36104	+	0.813181i
$437$	2.97831	−	4.51195i	0.142472	−	0.215836i
$438$		0			0
$439$	22.9855	−	15.1726i	1.09704	−	0.724150i	0.133322	−	0.991073i	$-0.457436\pi$
$439$	22.9855	−	15.1726i	1.09704	−	0.724150i	0.963718	+	0.266923i	$0.0860070\pi$
$440$	−4.32568	+	3.14279i	−0.206219	+	0.149827i
$441$		0			0
$442$	1.35544	−	0.508705i	0.0644717	−	0.0241966i
$443$	5.78486	−	17.8040i	0.274847	−	0.845892i	−0.714413	−	0.699724i	$-0.753306\pi$
$443$	5.78486	−	17.8040i	0.274847	−	0.845892i	0.989260	−	0.146167i	$-0.0466938\pi$
$444$		0			0
$445$	−2.55256	−	2.66977i	−0.121003	−	0.126559i
$446$	4.12522	−	8.56610i	0.195335	−	0.405616i
$447$		0			0
$448$	17.6469	+	9.49618i	0.833736	+	0.448652i
$449$	7.14752	+	31.3153i	0.337312	+	1.47786i	0.804633	+	0.593773i	$0.202362\pi$
$449$	7.14752	+	31.3153i	0.337312	+	1.47786i	−0.467320	+	0.884088i	$0.654781\pi$
$450$		0			0
$451$	−5.05888	−	15.5696i	−0.238213	−	0.733145i
$452$	−1.40320	−	1.75956i	−0.0660011	−	0.0827628i
$453$		0			0
$454$	−4.08579	−	4.67656i	−0.191756	−	0.219482i
$455$	−9.41291	+	5.06530i	−0.441284	+	0.237465i
$456$		0			0
$457$	−1.38218	+	3.68281i	−0.0646557	+	0.172275i	−0.964592	−	0.263747i	$-0.915042\pi$
$457$	−1.38218	+	3.68281i	−0.0646557	+	0.172275i	0.899936	+	0.436022i	$0.143613\pi$
$458$	−1.14350	−	2.37450i	−0.0534322	−	0.110953i
$459$		0			0
$460$	−9.70317	−	2.21469i	−0.452413	−	0.103260i
$461$	−9.78523	−	0.880686i	−0.455743	−	0.0410176i	−0.140610	−	0.990065i	$-0.544906\pi$
$461$	−9.78523	−	0.880686i	−0.455743	−	0.0410176i	−0.315133	+	0.949047i	$0.602049\pi$
$462$		0			0
$463$	−7.25278	+	31.7765i	−0.337065	+	1.47678i	0.468072	+	0.883690i	$0.344949\pi$
$463$	−7.25278	+	31.7765i	−0.337065	+	1.47678i	−0.805137	+	0.593088i	$0.797908\pi$
$464$	6.94579	−	7.95010i	0.322450	−	0.369074i
$465$		0			0
$466$	0.360335	+	0.135236i	0.0166922	+	0.00626468i
$467$	5.10046	−	6.39578i	0.236021	−	0.295961i	−0.649689	−	0.760200i	$-0.725101\pi$
$467$	5.10046	−	6.39578i	0.236021	−	0.295961i	0.885710	+	0.464239i	$0.153672\pi$
$468$		0			0
$469$	5.05985	−	4.42066i	0.233642	−	0.204127i
$470$	0.266326	−	0.623102i	0.0122847	−	0.0287415i
$471$		0			0
$472$	−6.42733	+	2.08837i	−0.295842	+	0.0961248i
$473$	4.60967	+	34.0299i	0.211953	+	1.56470i
$474$		0			0
$475$	−1.39501	+	2.59236i	−0.0640073	+	0.118946i
$476$	−6.43807	+	2.75176i	−0.295088	+	0.126127i
$477$		0			0
$478$	−4.26995	+	4.08249i	−0.195303	+	0.186729i
$479$	−20.2686	−	3.67822i	−0.926098	−	0.168062i	−0.305501	−	0.952192i	$-0.598824\pi$
$479$	−20.2686	−	3.67822i	−0.926098	−	0.168062i	−0.620597	+	0.784130i	$0.713110\pi$
$480$		0			0
$481$	7.89847	+	21.0454i	0.360139	+	0.959587i
$482$	−1.03951	+	1.08724i	−0.0473483	+	0.0495224i
$483$		0			0
$484$	−26.5456	−	40.2149i	−1.20662	−	1.82795i
$485$	0.374464	+	8.33808i	0.0170035	+	0.378613i
$486$		0			0
$487$	8.09828	−	13.5542i	0.366968	−	0.614201i	−0.618154	−	0.786057i	$-0.712119\pi$
$487$	8.09828	−	13.5542i	0.366968	−	0.614201i	0.985122	+	0.171856i	$0.0549763\pi$
$488$	10.6466	+	2.93827i	0.481949	+	0.133009i
$489$		0			0
$490$	−1.73787	+	1.03833i	−0.0785089	+	0.0469069i
$491$	1.33675	−	29.7651i	0.0603268	−	1.34328i	−0.709354	−	0.704852i	$-0.751013\pi$
$491$	1.33675	−	29.7651i	0.0603268	−	1.34328i	0.769681	−	0.638429i	$-0.220415\pi$
$492$		0			0
$493$	0.548178	+	3.02071i	0.0246887	+	0.136046i
$494$	0.132234	−	0.976188i	0.00594947	−	0.0439208i
$495$		0			0
$496$		−	19.7104i		−	0.885023i
$497$	32.6230	−	7.97062i	1.46334	−	0.357531i
$498$		0			0
$499$	17.0848	−	1.53766i	0.764822	−	0.0688352i	0.299642	−	0.954052i	$-0.403133\pi$
$499$	17.0848	−	1.53766i	0.764822	−	0.0688352i	0.465180	+	0.885216i	$0.345990\pi$
$500$	11.2038	+	1.51766i	0.501049	+	0.0678717i
$501$		0			0
$502$	5.61038	+	4.07618i	0.250403	+	0.181929i
$503$	−34.6762	−	1.55731i	−1.54614	−	0.0694370i	−0.744652	−	0.667453i	$-0.767384\pi$
$503$	−34.6762	−	1.55731i	−1.54614	−	0.0694370i	−0.801484	+	0.598016i	$0.795956\pi$
$504$		0			0
$505$	10.5980	−	2.92485i	0.471603	−	0.130154i
$506$	−4.93418	+	17.8786i	−0.219351	+	0.794801i
$507$		0			0
$508$	−29.8601	−	19.7104i	−1.32483	−	0.874510i
$509$	−27.3622	+	1.22884i	−1.21281	+	0.0544672i	−0.642057	−	0.766657i	$-0.721919\pi$
$509$	−27.3622	+	1.22884i	−1.21281	+	0.0544672i	−0.570749	+	0.821124i	$0.693347\pi$
$510$		0			0
$511$	−33.8939	−	46.6510i	−1.49938	−	2.06372i
$512$	15.8100	+	15.1159i	0.698710	+	0.668035i
$513$		0			0
$514$	−8.07915	−	2.62508i	−0.356356	−	0.115787i
$515$	0.836954	−	4.61199i	0.0368806	−	0.203229i
$516$		0			0
$517$	16.2492	+	7.82521i	0.714640	+	0.344152i
$518$	2.99152	+	6.99901i	0.131440	+	0.307519i
$519$		0			0
$520$	−3.65991	+	0.835350i	−0.160498	+	0.0366325i
$521$	29.8056	−	4.03744i	1.30581	−	0.176884i	0.551925	−	0.833894i	$-0.313893\pi$
$521$	29.8056	−	4.03744i	1.30581	−	0.176884i	0.753882	+	0.657010i	$0.228179\pi$
$522$		0			0
$523$	−27.2724	+	21.7490i	−1.19254	+	0.951019i	−0.999544	−	0.0301810i	$-0.990392\pi$
$523$	−27.2724	+	21.7490i	−1.19254	+	0.951019i	−0.192995	+	0.981200i	$0.561820\pi$
$524$	17.1851	+	7.34525i	0.750733	+	0.320879i
$525$		0			0
$526$	−4.51314	−	8.38683i	−0.196782	−	0.365683i
$527$	4.48143	+	3.57382i	0.195214	+	0.155678i
$528$		0			0
$529$	−43.6652	+	21.0281i	−1.89849	+	0.914264i
$530$	0.986520	+	0.861897i	0.0428517	+	0.0374384i
$531$		0			0
$532$	−0.427047	+	4.74488i	−0.0185148	+	0.205717i
$533$	1.03032	−	11.4478i	0.0446280	−	0.495858i
$534$		0			0
$535$	−2.08943	−	1.82548i	−0.0903341	−	0.0789225i
$536$	2.12599	−	1.02382i	0.0918288	−	0.0442224i
$537$		0			0
$538$	6.79650	+	5.42003i	0.293018	+	0.233674i
$539$	−25.5323	−	47.4469i	−1.09975	−	2.04368i
$540$		0			0
$541$	−11.0923	−	4.74107i	−0.476895	−	0.203834i	0.141133	−	0.989991i	$-0.454925\pi$
$541$	−11.0923	−	4.74107i	−0.476895	−	0.203834i	−0.618028	+	0.786156i	$0.712068\pi$
$542$	−3.68740	+	2.94061i	−0.158388	+	0.126310i
$543$		0			0
$544$	−3.69618	+	0.500681i	−0.158472	+	0.0214665i
$545$	10.8765	−	2.48248i	0.465896	−	0.106338i
$546$		0			0
$547$	2.09517	+	4.90190i	0.0895832	+	0.209590i	0.958328	−	0.285669i	$-0.0922159\pi$
$547$	2.09517	+	4.90190i	0.0895832	+	0.209590i	−0.868745	+	0.495259i	$0.835073\pi$
$548$	2.29043	+	1.10301i	0.0978423	+	0.0471184i
$549$		0			0
$550$	1.80331	−	9.93703i	0.0768932	−	0.423716i
$551$	1.98673	+	0.645527i	0.0846374	+	0.0275004i
$552$		0			0
$553$	26.6357	+	25.4663i	1.13266	+	1.08294i
$554$	1.89190	+	2.60398i	0.0803793	+	0.110633i
$555$		0			0
$556$	−23.6432	+	1.06182i	−1.00269	+	0.0450310i
$557$	−12.7144	−	8.39272i	−0.538727	−	0.355611i	0.252050	−	0.967714i	$-0.418895\pi$
$557$	−12.7144	−	8.39272i	−0.538727	−	0.355611i	−0.790778	+	0.612103i	$0.790324\pi$
$558$		0			0
$559$	−6.41434	+	23.2418i	−0.271298	+	0.983025i
$560$	7.82094	−	2.15844i	0.330495	−	0.0912108i
$561$		0			0
$562$	−4.89398	−	0.219789i	−0.206440	−	0.00927123i
$563$	−22.3586	−	16.2445i	−0.942301	−	0.684622i	0.00667208	−	0.999978i	$-0.497876\pi$
$563$	−22.3586	−	16.2445i	−0.942301	−	0.684622i	−0.948974	+	0.315356i	$0.897876\pi$
$564$		0			0
$565$	−0.751553	−	0.101805i	−0.0316181	−	0.00428296i
$566$	1.93716	−	0.174348i	0.0814249	−	0.00732838i
$567$		0			0
$568$	11.7889	+	0.349627i	0.494651	+	0.0146700i
$569$		−	34.3987i		−	1.44207i	−0.692900	−	0.721033i	$-0.743667\pi$
$569$		−	34.3987i		−	1.44207i	0.692900	−	0.721033i	$-0.256333\pi$
$570$		0			0
$571$	3.03977	−	22.4405i	0.127210	−	0.939104i	−0.809036	−	0.587759i	$-0.800010\pi$
$571$	3.03977	−	22.4405i	0.127210	−	0.939104i	0.936246	−	0.351345i	$-0.114276\pi$
$572$	−8.61844	−	47.4915i	−0.360355	−	1.98572i
$573$		0			0
$574$	0.174614	−	3.88807i	0.00728823	−	0.162285i
$575$	33.4061	−	19.9592i	1.39313	−	0.832356i
$576$		0			0
$577$	−16.8607	−	4.65326i	−0.701921	−	0.193718i	−0.103182	−	0.994662i	$-0.532903\pi$
$577$	−16.8607	−	4.65326i	−0.701921	−	0.193718i	−0.598738	+	0.800945i	$0.704331\pi$
$578$	−2.99039	+	5.00508i	−0.124384	+	0.208184i
$579$		0			0
$580$	−0.172536	−	3.84181i	−0.00716417	−	0.159523i
$581$	25.1605	+	38.1165i	1.04383	+	1.58134i
$582$		0			0
$583$	−24.0944	+	25.2007i	−0.997887	+	1.04371i
$584$	−7.11580	−	18.9600i	−0.294454	−	0.784570i
$585$		0			0
$586$	−10.8830	−	1.97497i	−0.449571	−	0.0815852i
$587$	6.65640	−	6.36417i	0.274739	−	0.262678i	−0.541098	−	0.840960i	$-0.681991\pi$
$587$	6.65640	−	6.36417i	0.274739	−	0.262678i	0.815837	+	0.578282i	$0.196277\pi$
$588$		0			0
$589$	3.58637	−	1.53289i	0.147774	−	0.0631616i
$590$	−0.521345	+	0.968821i	−0.0214634	+	0.0398857i
$591$		0			0
$592$	−2.29025	−	16.9073i	−0.0941289	−	0.694887i
$593$	−10.9179	+	3.54745i	−0.448346	+	0.145676i	−0.524483	−	0.851421i	$-0.675741\pi$
$593$	−10.9179	+	3.54745i	−0.448346	+	0.145676i	0.0761370	+	0.997097i	$0.475741\pi$
$594$		0			0
$595$	−0.927316	+	2.16956i	−0.0380162	+	0.0889434i
$596$	−5.65369	+	4.93948i	−0.231584	+	0.202329i
$597$		0			0
$598$	−8.11902	+	10.1809i	−0.332011	+	0.416329i
$599$	24.5774	+	9.22405i	1.00421	+	0.376885i	0.798673	−	0.601766i	$-0.205536\pi$
$599$	24.5774	+	9.22405i	1.00421	+	0.376885i	0.205533	+	0.978650i	$0.434107\pi$
$600$		0			0
$601$	16.1373	−	18.4706i	0.658252	−	0.753430i	−0.322949	−	0.946416i	$-0.604674\pi$
$601$	16.1373	−	18.4706i	0.658252	−	0.753430i	0.981202	+	0.192986i	$0.0618172\pi$
$602$	−1.81669	+	7.95944i	−0.0740427	+	0.324402i
$603$		0			0
$604$	−18.4523	−	1.66074i	−0.750813	−	0.0675744i
$605$	−15.8311	−	3.61335i	−0.643627	−	0.146904i
$606$		0			0
$607$	−4.76969	−	9.90436i	−0.193596	−	0.402006i	0.781463	−	0.623951i	$-0.214474\pi$
$607$	−4.76969	−	9.90436i	−0.193596	−	0.402006i	−0.975059	+	0.221946i	$0.928759\pi$
$608$	−0.891782	+	2.37614i	−0.0361665	+	0.0963654i
$609$		0			0
$610$	1.58332	−	0.852023i	0.0641069	−	0.0344974i
$611$	8.33122	+	9.53585i	0.337045	+	0.385779i
$612$		0			0
$613$	−1.31481	−	1.64872i	−0.0531046	−	0.0665910i	0.754570	−	0.656220i	$-0.227846\pi$
$613$	−1.31481	−	1.64872i	−0.0531046	−	0.0665910i	−0.807674	+	0.589629i	$0.799274\pi$
$614$	−0.890432	−	2.74047i	−0.0359349	−	0.110596i
$615$		0			0
$616$	−7.52829	−	32.9836i	−0.303323	−	1.32895i
$617$	−3.05199	−	1.64235i	−0.122868	−	0.0661183i	0.411280	−	0.911509i	$-0.365082\pi$
$617$	−3.05199	−	1.64235i	−0.122868	−	0.0661183i	−0.534148	+	0.845391i	$0.679368\pi$
$618$		0			0
$619$	11.3044	−	23.4739i	0.454364	−	0.943497i	−0.540411	−	0.841401i	$-0.681731\pi$
$619$	11.3044	−	23.4739i	0.454364	−	0.943497i	0.994775	−	0.102095i	$-0.0325546\pi$
$620$	−4.96192	−	5.18976i	−0.199276	−	0.208426i
$621$		0			0
$622$	3.61037	−	11.1116i	0.144763	−	0.445534i
$623$	21.8812	−	8.21217i	0.876653	−	0.329013i
$624$		0			0
$625$	−15.5382	+	11.2891i	−0.621526	+	0.451565i
$626$	−0.276734	+	0.182671i	−0.0110605	+	0.00730099i
$627$		0			0
$628$	0.876994	−	1.32859i	0.0349959	−	0.0530165i
$629$	4.25938	+	2.54486i	0.169833	+	0.101470i
$630$		0			0
$631$	1.85974	+	6.73862i	0.0740351	+	0.268260i	0.991603	−	0.129319i	$-0.0412791\pi$
$631$	1.85974	+	6.73862i	0.0740351	+	0.268260i	−0.917568	+	0.397579i	$0.869850\pi$
$632$	6.63790	+	11.1100i	0.264042	+	0.441931i
$633$		0			0
$634$	−1.68221	+	2.31536i	−0.0668090	+	0.0919547i
$635$	−11.8633	+	2.15288i	−0.470782	+	0.0854344i
$636$		0			0
$637$	−3.39102	−	37.6773i	−0.134357	−	1.49283i
$638$	−7.16648			−0.283724
$639$		0			0
$640$	6.14517			0.242909
$641$	−2.08607	−	23.1781i	−0.0823947	−	0.915480i	−0.925753	−	0.378129i	$-0.876568\pi$
$641$	−2.08607	−	23.1781i	−0.0823947	−	0.915480i	0.843358	−	0.537351i	$-0.180575\pi$
$642$		0			0
$643$	0.579678	−	0.105196i	0.0228603	−	0.00414853i	−0.167115	−	0.985937i	$-0.553445\pi$
$643$	0.579678	−	0.105196i	0.0228603	−	0.00414853i	0.189975	+	0.981789i	$0.439159\pi$
$644$	37.0159	−	50.9480i	1.45863	−	2.00763i
$645$		0			0
$646$	−0.111525	−	0.186662i	−0.00438791	−	0.00734412i
$647$	−2.34337	−	8.49100i	−0.0921272	−	0.333815i	0.903339	−	0.428926i	$-0.141108\pi$
$647$	−2.34337	−	8.49100i	−0.0921272	−	0.333815i	−0.995467	+	0.0951109i	$0.969679\pi$
$648$		0			0
$649$	−25.1368	−	15.0185i	−0.986705	−	0.589529i
$650$	3.90628	−	5.91777i	0.153217	−	0.232114i
$651$		0			0
$652$	−11.8838	+	7.84443i	−0.465406	+	0.307212i
$653$	−11.7075	+	8.50598i	−0.458149	+	0.332865i	−0.792805	−	0.609476i	$-0.791380\pi$
$653$	−11.7075	+	8.50598i	−0.458149	+	0.332865i	0.334656	+	0.942340i	$0.391380\pi$
$654$		0			0
$655$	5.89641	−	2.21296i	0.230392	−	0.0864676i
$656$	−2.69592	+	8.29717i	−0.105258	+	0.323950i
$657$		0			0
$658$	2.96306	+	3.09912i	0.115512	+	0.120816i
$659$	−7.89992	+	16.4044i	−0.307737	+	0.639023i	−0.996280	−	0.0861724i	$-0.972536\pi$
$659$	−7.89992	+	16.4044i	−0.307737	+	0.639023i	0.688543	+	0.725196i	$0.258251\pi$
$660$		0			0
$661$	18.5004	+	9.95549i	0.719582	+	0.387224i	0.792302	−	0.610129i	$-0.208882\pi$
$661$	18.5004	+	9.95549i	0.719582	+	0.387224i	−0.0727203	+	0.997352i	$0.523168\pi$
$662$	−0.780918	−	3.42142i	−0.0303512	−	0.132977i
$663$		0			0
$664$	4.95657	+	15.2548i	0.192352	+	0.591999i
$665$	1.00098	+	1.25518i	0.0388162	+	0.0486739i
$666$		0			0
$667$	−18.1681	−	20.7951i	−0.703472	−	0.805188i
$668$	26.4952	−	14.2577i	1.02513	−	0.551646i
$669$		0			0
$670$	0.134979	−	0.359649i	0.00521468	−	0.0138945i
$671$	20.7632	+	43.1153i	0.801556	+	1.66445i
$672$		0			0
$673$	5.05991	+	1.15489i	0.195045	+	0.0445178i	0.318927	−	0.947779i	$-0.396677\pi$
$673$	5.05991	+	1.15489i	0.195045	+	0.0445178i	−0.123882	+	0.992297i	$0.539534\pi$
$674$	3.81684	+	0.343522i	0.147019	+	0.0132320i
$675$		0			0
$676$	2.13394	−	9.34942i	0.0820748	−	0.359593i
$677$	14.9452	−	17.1062i	0.574391	−	0.657444i	−0.390343	−	0.920670i	$-0.627644\pi$
$677$	14.9452	−	17.1062i	0.574391	−	0.657444i	0.964734	+	0.263226i	$0.0847864\pi$
$678$		0			0
$679$	−49.4444	−	18.5568i	−1.89750	−	0.712144i
$680$	−0.516639	+	0.647844i	−0.0198122	+	0.0248437i
$681$		0			0
$682$	−10.0763	+	8.80340i	−0.385841	+	0.337099i
$683$	0.982294	−	2.29819i	0.0375864	−	0.0879379i	−0.899683	−	0.436544i	$-0.856202\pi$
$683$	0.982294	−	2.29819i	0.0375864	−	0.0879379i	0.937269	+	0.348607i	$0.113345\pi$
$684$		0			0
$685$	0.814761	−	0.264732i	0.0311304	−	0.0101149i
$686$	−0.364692	−	2.69226i	−0.0139240	−	0.102791i
$687$		0			0
$688$	8.67201	−	16.1153i	0.330617	−	0.614390i
$689$	−22.5094	+	9.62098i	−0.857540	+	0.366530i
$690$		0			0
$691$	32.2718	−	30.8550i	1.22768	−	1.17378i	0.248969	−	0.968511i	$-0.419908\pi$
$691$	32.2718	−	30.8550i	1.22768	−	1.17378i	0.978706	−	0.205266i	$-0.0658061\pi$
$692$	−37.4894	−	6.80332i	−1.42513	−	0.258623i
$693$		0			0
$694$	1.76721	+	4.70872i	0.0670824	+	0.178740i
$695$	−5.51159	+	5.76467i	−0.209067	+	0.218667i
$696$		0			0
$697$	−1.39766	−	2.11737i	−0.0529403	−	0.0802012i
$698$	−0.0662548	−	1.47528i	−0.00250778	−	0.0558401i
$699$		0			0
$700$	−17.5882	+	29.4377i	−0.664771	+	1.11264i
$701$	46.9850	+	12.9670i	1.77460	+	0.489758i	0.991270	−	0.131850i	$-0.0420917\pi$
$701$	46.9850	+	12.9670i	1.77460	+	0.489758i	0.783328	+	0.621608i	$0.213520\pi$
$702$		0			0
$703$	2.89823	−	1.73161i	0.109309	−	0.0653091i
$704$	−1.36810	+	30.4632i	−0.0515623	+	1.14812i
$705$		0			0
$706$	−1.86312	−	10.2667i	−0.0701196	−	0.386391i
$707$	−9.33794	+	68.9354i	−0.351189	+	2.59258i
$708$		0			0
$709$			17.4348i			0.654778i	0.944890	+	0.327389i	$0.106169\pi$
$709$			17.4348i			0.654778i	−0.944890	+	0.327389i	$0.893831\pi$
$710$	1.42651	−	1.28513i	0.0535359	−	0.0482302i
$711$		0			0
$712$	8.17496	−	0.735759i	0.306369	−	0.0275737i
$713$	−51.0899	−	6.92059i	−1.91333	−	0.259178i
$714$		0			0
$715$	−13.1591	−	9.56065i	−0.492123	−	0.357548i
$716$	24.5424	+	1.10220i	0.917193	+	0.0411912i
$717$		0			0
$718$	0.0562786	−	0.0155319i	0.00210030	−	0.000579646i
$719$	−9.12983	+	33.0812i	−0.340485	+	1.23372i	0.570505	+	0.821294i	$0.306747\pi$
$719$	−9.12983	+	33.0812i	−0.340485	+	1.23372i	−0.910991	+	0.412427i	$0.864681\pi$
$720$		0			0
$721$	24.7524	+	16.3389i	0.921829	+	0.608494i
$722$	6.71873	−	0.301739i	0.250045	−	0.0112295i
$723$		0			0
$724$	2.62714	+	3.61595i	0.0976369	+	0.134386i
$725$	10.8682	+	10.3911i	0.403636	+	0.385915i
$726$		0			0
$727$	−17.0423	−	5.53739i	−0.632065	−	0.205370i	−0.0245752	−	0.999698i	$-0.507823\pi$
$727$	−17.0423	−	5.53739i	−0.632065	−	0.205370i	−0.607490	+	0.794328i	$0.707823\pi$
$728$	4.24134	−	23.3717i	0.157194	−	0.866213i
$729$		0			0
$730$	−2.97034	−	1.43044i	−0.109937	−	0.0529429i
$731$	2.09166	+	4.89368i	0.0773627	+	0.180999i
$732$		0			0
$733$	−11.2232	+	2.56162i	−0.414538	+	0.0946156i	−0.424703	−	0.905333i	$-0.639621\pi$
$733$	−11.2232	+	2.56162i	−0.414538	+	0.0946156i	0.0101650	+	0.999948i	$0.496764\pi$
$734$	−11.5115	+	1.55934i	−0.424897	+	0.0575563i
$735$		0			0
$736$	26.2297	−	20.9175i	0.966840	−	0.771029i
$737$	9.40130	+	4.01831i	0.346301	+	0.148016i
$738$		0			0
$739$	8.75612	+	16.2716i	0.322099	+	0.598561i	0.989228	−	0.146382i	$-0.0467627\pi$
$739$	8.75612	+	16.2716i	0.322099	+	0.598561i	−0.667129	+	0.744942i	$0.732477\pi$
$740$	−4.85930	−	3.87516i	−0.178632	−	0.142454i
$741$		0			0
$742$	−7.46807	+	3.59643i	−0.274161	+	0.132029i
$743$	28.0295	+	24.4887i	1.02830	+	0.898402i	0.994882	−	0.101040i	$-0.0322169\pi$
$743$	28.0295	+	24.4887i	1.02830	+	0.898402i	0.0334211	+	0.999441i	$0.489360\pi$
$744$		0			0
$745$	−0.226783	+	2.51977i	−0.00830869	+	0.0923171i
$746$	−0.518165	+	5.75728i	−0.0189714	+	0.210789i
$747$		0			0
$748$	−8.02321	−	7.00967i	−0.293358	−	0.256299i
$749$	15.8172	−	7.61718i	0.577949	−	0.278326i
$750$		0			0
$751$	−28.0775	−	22.3911i	−1.02456	−	0.817062i	−0.0412808	−	0.999148i	$-0.513144\pi$
$751$	−28.0775	−	22.3911i	−1.02456	−	0.817062i	−0.983283	+	0.182085i	$0.941715\pi$
$752$	−4.55442	−	8.46352i	−0.166082	−	0.308633i
$753$		0			0
$754$	−4.62670	−	1.97755i	−0.168495	−	0.0720180i
$755$	−4.88126	+	3.89267i	−0.177647	+	0.141669i
$756$		0			0
$757$	34.7603	−	4.70860i	1.26338	−	0.171137i	0.528267	−	0.849078i	$-0.322842\pi$
$757$	34.7603	−	4.70860i	1.26338	−	0.171137i	0.735116	+	0.677941i	$0.237128\pi$
$758$	5.63278	−	1.28565i	0.204592	−	0.0466967i
$759$		0			0
$760$	0.221597	+	0.518453i	0.00803818	+	0.0188063i
$761$	−41.6342	−	20.0500i	−1.50924	−	0.726811i	−0.517572	−	0.855640i	$-0.673164\pi$
$761$	−41.6342	−	20.0500i	−1.50924	−	0.726811i	−0.991667	+	0.128828i	$0.958878\pi$
$762$		0			0
$763$	−12.6043	+	69.4556i	−0.456308	+	2.51446i
$764$	−45.8219	−	14.8885i	−1.65778	−	0.538645i
$765$		0			0
$766$	1.55466	+	1.48641i	0.0561723	+	0.0537062i
$767$	−12.0841	−	16.6324i	−0.436332	−	0.600560i
$768$		0			0
$769$	23.4856	−	1.05474i	0.846912	−	0.0380349i	0.382821	−	0.923822i	$-0.374953\pi$
$769$	23.4856	−	1.05474i	0.846912	−	0.0380349i	0.464091	+	0.885788i	$0.346381\pi$
$770$	−4.59656	−	3.03416i	−0.165648	−	0.109344i
$771$		0			0
$772$	4.10369	−	14.8694i	0.147695	−	0.535161i
$773$	−21.0779	+	5.81712i	−0.758118	+	0.209227i	−0.623664	−	0.781693i	$-0.714357\pi$
$773$	−21.0779	+	5.81712i	−0.758118	+	0.209227i	−0.134454	+	0.990920i	$0.542928\pi$
$774$		0			0
$775$	28.0456	+	1.25953i	1.00743	+	0.0452436i
$776$	−15.0051	−	10.9019i	−0.538653	−	0.391354i
$777$		0			0
$778$	2.25147	+	0.304983i	0.0807192	+	0.0109342i
$779$	−1.71936	+	0.154745i	−0.0616026	+	0.00554433i
$780$		0			0
$781$	32.4662	+	39.4630i	1.16173	+	1.41210i
$782$			2.87431i			0.102785i
$783$		0			0
$784$	−3.85428	+	28.4535i	−0.137653	+	1.01619i
$785$	−0.0957899	−	0.527846i	−0.00341889	−	0.0188396i
$786$		0			0
$787$	1.35393	−	30.1476i	0.0482624	−	1.07465i	−0.818051	−	0.575146i	$-0.804945\pi$
$787$	1.35393	−	30.1476i	0.0482624	−	1.07465i	0.866313	−	0.499501i	$-0.166483\pi$
$788$	−11.6236	+	6.94475i	−0.414072	+	0.247397i
$789$		0			0
$790$	2.03096	+	0.560510i	0.0722584	+	0.0199420i
$791$	2.46132	−	4.11956i	0.0875146	−	0.146475i
$792$		0			0
$793$	1.50740	+	33.5649i	0.0535293	+	1.19192i
$794$	1.25843	+	1.90645i	0.0446601	+	0.0676572i
$795$		0			0
$796$	−29.5149	+	30.8702i	−1.04613	+	1.09416i
$797$	−17.9672	−	47.8734i	−0.636430	−	1.69576i	−0.715246	−	0.698873i	$-0.753685\pi$
$797$	−17.9672	−	47.8734i	−0.636430	−	1.69576i	0.0788158	−	0.996889i	$-0.474886\pi$
$798$		0			0
$799$	2.75009	+	0.499068i	0.0972913	+	0.0176558i
$800$	−13.2043	+	12.6246i	−0.466842	+	0.446346i
$801$		0			0
$802$	1.52042	−	0.649859i	0.0536879	−	0.0229473i
$803$	41.5798	−	77.2682i	1.46732	−	2.72674i
$804$		0			0
$805$	−2.84870	−	21.0299i	−0.100403	−	0.741208i
$806$	−8.93453	+	2.90301i	−0.314705	+	0.102254i
$807$		0			0
$808$	−9.60199	+	22.4650i	−0.337797	+	0.790315i
$809$	−3.71565	+	3.24626i	−0.130635	+	0.114132i	−0.720777	−	0.693167i	$-0.756215\pi$
$809$	−3.71565	+	3.24626i	−0.130635	+	0.114132i	0.590142	+	0.807300i	$0.299072\pi$
$810$		0			0
$811$	12.4327	−	15.5901i	0.436570	−	0.547442i	−0.514065	−	0.857751i	$-0.671861\pi$
$811$	12.4327	−	15.5901i	0.436570	−	0.547442i	0.950636	+	0.310309i	$0.100433\pi$
$812$	22.7817	+	8.55013i	0.799483	+	0.300051i
$813$		0			0
$814$	−7.62042	+	8.72227i	−0.267095	+	0.305715i
$815$	−1.06777	+	4.67822i	−0.0374024	+	0.163871i
$816$		0			0
$817$	3.60666	+	0.324605i	0.126181	+	0.0113565i
$818$	0.729256	+	0.166448i	0.0254978	+	0.00581972i
$819$		0			0
$820$	1.37891	+	2.86333i	0.0481535	+	0.0999917i
$821$	1.47085	−	3.91905i	0.0513329	−	0.136776i	−0.908067	−	0.418824i	$-0.862442\pi$
$821$	1.47085	−	3.91905i	0.0513329	−	0.136776i	0.959400	+	0.282048i	$0.0910138\pi$
$822$		0			0
$823$	−5.58489	+	3.00536i	−0.194677	+	0.104760i	−0.568303	−	0.822819i	$-0.692400\pi$
$823$	−5.58489	+	3.00536i	−0.194677	+	0.104760i	0.373626	+	0.927579i	$0.378114\pi$
$824$	6.85313	+	7.84404i	0.238740	+	0.273260i
$825$		0			0
$826$	−4.34035	−	5.44263i	−0.151020	−	0.189373i
$827$	3.66078	+	11.2667i	0.127298	+	0.391783i	0.994313	−	0.106500i	$-0.0339643\pi$
$827$	3.66078	+	11.2667i	0.127298	+	0.391783i	−0.867015	+	0.498282i	$0.833964\pi$
$828$		0			0
$829$	8.44116	+	36.9831i	0.293174	+	1.28448i	0.880081	+	0.474823i	$0.157488\pi$
$829$	8.44116	+	36.9831i	0.293174	+	1.28448i	−0.586908	+	0.809654i	$0.699655\pi$
$830$	2.29942	+	1.23737i	0.0798140	+	0.0429498i
$831$		0			0
$832$	−9.28937	+	19.2896i	−0.322051	+	0.668746i
$833$	−5.77045	−	6.03541i	−0.199934	−	0.209115i
$834$		0			0
$835$	3.13321	−	9.64304i	0.108429	−	0.333711i
$836$	−6.78709	+	2.54724i	−0.234736	+	0.0880981i
$837$		0			0
$838$	5.68619	−	4.13126i	0.196426	−	0.142712i
$839$	44.7833	−	29.5612i	1.54609	−	1.02057i	0.565445	−	0.824786i	$-0.308704\pi$
$839$	44.7833	−	29.5612i	1.54609	−	1.02057i	0.980648	−	0.195781i	$-0.0627242\pi$
$840$		0			0
$841$	−10.0980	+	15.2979i	−0.348209	+	0.527513i
$842$	5.30854	+	3.17170i	0.182944	+	0.109304i
$843$		0			0
$844$	1.41941	+	5.14312i	0.0488581	+	0.177034i
$845$	−1.65753	−	2.77424i	−0.0570207	−	0.0954366i
$846$		0			0
$847$	60.3930	−	83.1238i	2.07513	−	2.85617i
$848$	18.2816	−	3.31762i	0.627793	−	0.113928i
$849$		0			0
$850$	−0.140298	−	1.55884i	−0.00481219	−	0.0534678i
$851$	−44.6284			−1.52984
$852$		0			0
$853$	12.5769			0.430625			0.215312	−	0.976545i	$-0.430923\pi$
$853$	12.5769			0.430625			0.215312	+	0.976545i	$0.430923\pi$
$854$	1.01981	+	11.3310i	0.0348973	+	0.387740i
$855$		0			0
$856$	6.06646	−	1.10090i	0.207347	−	0.0376280i
$857$	−11.3197	+	15.5803i	−0.386675	+	0.532213i	−0.957337	−	0.288972i	$-0.906686\pi$
$857$	−11.3197	+	15.5803i	−0.386675	+	0.532213i	0.570662	+	0.821185i	$0.306686\pi$
$858$		0			0
$859$	15.9546	+	26.7035i	0.544364	+	0.911111i	0.999783	+	0.0208343i	$0.00663223\pi$
$859$	15.9546	+	26.7035i	0.544364	+	0.911111i	−0.455419	+	0.890277i	$0.650511\pi$
$860$	−1.77354	−	6.42627i	−0.0604772	−	0.219134i
$861$		0			0
$862$	5.46067	+	3.26260i	0.185991	+	0.111125i
$863$	24.8952	−	37.7147i	0.847444	−	1.28382i	−0.109628	−	0.993973i	$-0.534966\pi$
$863$	24.8952	−	37.7147i	0.847444	−	1.28382i	0.957072	−	0.289850i	$-0.0936055\pi$
$864$		0			0
$865$	−10.7158	+	7.07345i	−0.364349	+	0.240504i
$866$	−4.59197	+	3.33626i	−0.156041	+	0.113371i
$867$		0			0
$868$	42.5349	−	15.9636i	1.44373	−	0.541841i
$869$	−17.3282	+	53.3306i	−0.587817	+	1.80912i
$870$		0			0
$871$	4.96068	+	5.18846i	0.168086	+	0.175804i
$872$	−10.7564	+	22.3359i	−0.364258	+	0.756389i
$873$		0			0
$874$	1.72226	+	0.926785i	0.0582562	+	0.0313490i
$875$	5.36451	+	23.5034i	0.181353	+	0.794561i
$876$		0			0
$877$	14.2965	+	44.0002i	0.482759	+	1.48578i	0.835200	+	0.549946i	$0.185352\pi$
$877$	14.2965	+	44.0002i	0.482759	+	1.48578i	−0.352441	+	0.935834i	$0.614648\pi$
$878$	6.21214	+	7.78978i	0.209650	+	0.262892i
$879$		0			0
$880$	8.12280	+	9.29729i	0.273819	+	0.313412i
$881$	−10.4635	+	5.63066i	−0.352525	+	0.189702i	−0.640541	−	0.767924i	$-0.721290\pi$
$881$	−10.4635	+	5.63066i	−0.352525	+	0.189702i	0.288016	+	0.957626i	$0.407004\pi$
$882$		0			0
$883$	−12.7092	+	33.8636i	−0.427700	+	1.13960i	0.529025	+	0.848606i	$0.322558\pi$
$883$	−12.7092	+	33.8636i	−0.427700	+	1.13960i	−0.956724	+	0.290996i	$0.906014\pi$
$884$	−3.24553	−	6.73942i	−0.109159	−	0.226671i
$885$		0			0
$886$	6.60244	+	1.50696i	0.221813	+	0.0506274i
$887$	39.9046	+	3.59148i	1.33987	+	0.120590i	0.736264	−	0.676695i	$-0.236588\pi$
$887$	39.9046	+	3.59148i	1.33987	+	0.120590i	0.603603	+	0.797285i	$0.293731\pi$
$888$		0			0
$889$	16.9763	−	74.3779i	0.569366	−	2.49455i
$890$	0.879155	−	1.00627i	0.0294693	−	0.0337304i
$891$		0			0
$892$	−45.9913	−	17.2608i	−1.53990	−	0.577935i
$893$	1.18577	−	1.48690i	0.0396802	−	0.0497574i
$894$		0			0
$895$	6.23458	−	5.44699i	0.208399	−	0.182073i
$896$	−15.2821	+	35.7542i	−0.510538	+	1.19446i
$897$		0			0
$898$	−11.0513	+	3.59078i	−0.368786	+	0.119826i
$899$	−2.67409	−	19.7409i	−0.0891858	−	0.658396i
$900$		0			0
$901$	−2.56045	+	4.75812i	−0.0853011	+	0.158516i
$902$	5.44576	−	2.32763i	0.181324	−	0.0775015i
$903$		0			0
$904$	1.21815	−	1.16467i	0.0405152	−	0.0387365i
$905$	1.48199	+	0.268941i	0.0492630	+	0.00893992i
$906$		0			0
$907$	−16.1227	−	42.9588i	−0.535345	−	1.42642i	−0.874192	−	0.485581i	$-0.838608\pi$
$907$	−16.1227	−	42.9588i	−0.535345	−	1.42642i	0.338847	−	0.940842i	$-0.389963\pi$
$908$	−22.1731	+	23.1912i	−0.735839	+	0.769628i
$909$		0			0
$910$	−2.13029	−	3.22726i	−0.0706185	−	0.106983i
$911$	2.01054	+	44.7682i	0.0666123	+	1.48324i	0.702626	+	0.711559i	$0.252011\pi$
$911$	2.01054	+	44.7682i	0.0666123	+	1.48324i	−0.636014	+	0.771678i	$0.719418\pi$
$912$		0			0
$913$	−35.6453	+	59.6602i	−1.17969	+	1.97446i
$914$	−1.37175	−	0.378580i	−0.0453736	−	0.0125223i
$915$		0			0
$916$	−11.6895	+	6.98413i	−0.386231	+	0.230762i
$917$	−1.78788	+	39.8102i	−0.0590409	+	1.31465i
$918$		0			0
$919$	6.20368	+	34.1851i	0.204640	+	1.12766i	0.908678	+	0.417499i	$0.137093\pi$
$919$	6.20368	+	34.1851i	0.204640	+	1.12766i	−0.704037	+	0.710163i	$0.748621\pi$
$920$	1.00045	−	7.38564i	0.0329840	−	0.243497i
$921$		0			0
$922$		−	3.55422i		−	0.117052i
$923$	10.0707	+	34.4363i	0.331481	+	1.13348i
$924$		0			0
$925$	24.2035	−	2.17836i	0.795807	−	0.0716239i
$926$	−11.6844	−	1.58276i	−0.383973	−	0.0520127i
$927$		0			0
$928$	10.4875	+	7.61959i	0.344268	+	0.250125i
$929$	−25.8246	−	1.15978i	−0.847276	−	0.0380512i	−0.383007	−	0.923745i	$-0.625112\pi$
$929$	−25.8246	−	1.15978i	−0.847276	−	0.0380512i	−0.464269	+	0.885694i	$0.653683\pi$
$930$		0			0
$931$	−5.47695	+	1.51154i	−0.179500	+	0.0495388i
$932$	0.529031	−	1.91690i	0.0173290	−	0.0627901i
$933$		0			0
$934$	2.46983	+	1.63032i	0.0808152	+	0.0533456i
$935$	−3.58667	+	0.161077i	−0.117297	+	0.00526780i
$936$		0			0
$937$	−9.29855	−	12.7983i	−0.303770	−	0.418104i	0.629656	−	0.776874i	$-0.283196\pi$
$937$	−9.29855	−	12.7983i	−0.303770	−	0.418104i	−0.933426	+	0.358771i	$0.883196\pi$
$938$	1.75686	+	1.67973i	0.0573636	+	0.0548453i
$939$		0			0
$940$	−3.32980	−	1.08192i	−0.108606	−	0.0352883i
$941$	1.03298	−	5.69221i	0.0336743	−	0.185561i	−0.962708	−	0.270542i	$-0.912797\pi$
$941$	1.03298	−	5.69221i	0.0336743	−	0.185561i	0.996383	+	0.0849808i	$0.0270829\pi$
$942$		0			0
$943$	20.5599	+	9.90114i	0.669523	+	0.322425i
$944$	6.13293	+	14.3487i	0.199610	+	0.467010i
$945$		0			0
$946$	−12.1117	+	2.76441i	−0.393784	+	0.0898787i
$947$	−2.23225	+	0.302378i	−0.0725382	+	0.00982597i	−0.170412	−	0.985373i	$-0.554510\pi$
$947$	−2.23225	+	0.302378i	−0.0725382	+	0.00982597i	0.0978742	+	0.995199i	$0.468796\pi$
$948$		0			0
$949$	48.1657	−	38.4109i	1.56353	−	1.24687i
$950$	−0.979276	−	0.418563i	−0.0317719	−	0.0135800i
$951$		0			0
$952$	−2.48453	−	4.61703i	−0.0805241	−	0.149639i
$953$	−21.2235	−	16.9252i	−0.687497	−	0.548261i	0.216245	−	0.976339i	$-0.430619\pi$
$953$	−21.2235	−	16.9252i	−0.687497	−	0.548261i	−0.903741	+	0.428079i	$0.859191\pi$
$954$		0			0
$955$	−14.6283	+	7.04462i	−0.473361	+	0.227958i
$956$	22.9859	+	20.0822i	0.743418	+	0.649505i
$957$		0			0
$958$	0.668006	−	7.42216i	0.0215823	−	0.239799i
$959$	−0.485904	+	5.39884i	−0.0156907	+	0.174338i
$960$		0			0
$961$	−4.66461	−	4.07535i	−0.150471	−	0.131463i
$962$	−7.32662	+	3.52831i	−0.236220	+	0.113757i
$963$		0			0
$964$	6.07633	+	4.84571i	0.195705	+	0.156070i
$965$	−2.46324	−	4.57747i	−0.0792946	−	0.147354i
$966$		0			0
$967$	26.1023	+	11.1567i	0.839394	+	0.358774i	0.769395	−	0.638773i	$-0.220558\pi$
$967$	26.1023	+	11.1567i	0.839394	+	0.358774i	0.0699985	+	0.997547i	$0.477701\pi$
$968$	28.2118	−	22.4982i	0.906763	−	0.723119i
$969$		0			0
$970$	−2.99211	+	0.405308i	−0.0960707	+	0.0130137i
$971$	−36.4825	+	8.32690i	−1.17078	+	0.267223i	−0.763333	−	0.646006i	$-0.776438\pi$
$971$	−36.4825	+	8.32690i	−1.17078	+	0.267223i	−0.407447	+	0.913229i	$0.633581\pi$
$972$		0			0
$973$	−19.8339	−	46.4038i	−0.635846	−	1.48764i
$974$	5.14627	+	2.47831i	0.164897	+	0.0794102i
$975$		0			0
$976$	4.55355	−	25.0921i	0.145756	−	0.803180i
$977$	22.7752	+	7.40010i	0.728642	+	0.236750i	0.649766	−	0.760134i	$-0.274867\pi$
$977$	22.7752	+	7.40010i	0.728642	+	0.236750i	0.0788759	+	0.996884i	$0.474867\pi$
$978$		0			0
$979$	25.7054	+	24.5768i	0.821547	+	0.785479i
$980$	6.14808	+	8.46210i	0.196393	+	0.270312i
$981$		0			0
$982$	10.7679	−	0.483585i	0.343616	−	0.0154318i
$983$	−6.34256	−	4.18669i	−0.202296	−	0.133535i	0.445688	−	0.895188i	$-0.352959\pi$
$983$	−6.34256	−	4.18669i	−0.202296	−	0.133535i	−0.647984	+	0.761654i	$0.724388\pi$
$984$		0			0
$985$	−1.21390	+	4.39847i	−0.0386781	+	0.140147i
$986$	−1.07060	+	0.295467i	−0.0340948	+	0.00940958i
$987$		0			0
$988$	−5.08466	−	0.228352i	−0.161765	−	0.00726486i
$989$	−38.7264	−	28.1364i	−1.23143	−	0.894685i
$990$		0			0
$991$	12.7338	+	1.72491i	0.404503	+	0.0547937i	0.333659	−	0.942694i	$-0.391717\pi$
$991$	12.7338	+	1.72491i	0.404503	+	0.0547937i	0.0708438	+	0.997487i	$0.477431\pi$
$992$	24.1057	−	2.16955i	0.765357	−	0.0688834i
$993$		0			0
$994$	3.92975	+	11.4957i	0.124644	+	0.364622i
$995$			14.3926i			0.456277i
$996$		0			0
$997$	−4.73319	+	34.9418i	−0.149902	+	1.10662i	0.747138	+	0.664669i	$0.231427\pi$
$997$	−4.73319	+	34.9418i	−0.149902	+	1.10662i	−0.897040	+	0.441950i	$0.854287\pi$
$998$	1.10805	+	6.10588i	0.0350748	+	0.193278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.53.14	yes	576
3.2	odd	2	inner	639.2.z.a.53.11	✓	576
71.67	odd	70	inner	639.2.z.a.422.11	yes	576
213.209	even	70	inner	639.2.z.a.422.14	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.53.11	✓	576	3.2	odd	2	inner
639.2.z.a.53.14	yes	576	1.1	even	1	trivial
639.2.z.a.422.11	yes	576	71.67	odd	70	inner
639.2.z.a.422.14	yes	576	213.209	even	70	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0324280 + 0.360305i) q^{2} +(1.83909 - 0.333746i) q^{4} +(0.370233 - 0.509581i) q^{5} +(2.04417 + 3.42136i) q^{7} +(0.372372 + 1.34926i) q^{8} +O(q^{10})\)	\(q+(0.0324280 + 0.360305i) q^{2} +(1.83909 - 0.333746i) q^{4} +(0.370233 - 0.509581i) q^{5} +(2.04417 + 3.42136i) q^{7} +(0.372372 + 1.34926i) q^{8} +(0.195610 + 0.116872i) q^{10} +(-3.34100 + 5.06140i) q^{11} +(-3.55362 + 2.34573i) q^{13} +(-1.16644 + 0.847471i) q^{14} +(3.02582 - 1.13561i) q^{16} +(-0.290435 + 0.893867i) q^{17} +(0.441948 + 0.462241i) q^{19} +(0.510821 - 1.06073i) q^{20} +(-1.93199 - 1.03965i) q^{22} +(-1.88112 - 8.24173i) q^{23} +(1.42248 + 4.37796i) q^{25} +(-0.960412 - 1.20432i) q^{26} +(4.90128 + 5.60996i) q^{28} +(2.87644 - 1.54788i) q^{29} +(2.14293 - 5.70981i) q^{31} +(1.72190 + 3.57556i) q^{32} +(-0.331483 - 0.0756588i) q^{34} +(2.50028 + 0.225029i) q^{35} +(1.17473 - 5.14681i) q^{37} +(-0.152216 + 0.174225i) q^{38} +(0.825421 + 0.309786i) q^{40} +(-1.68304 + 2.11047i) q^{41} +(4.26422 - 3.72554i) q^{43} +(-4.45518 + 10.4234i) q^{44} +(2.90853 - 0.945039i) q^{46} +(-0.399187 - 2.94692i) q^{47} +(-4.21001 + 7.82351i) q^{49} +(-1.53127 + 0.654496i) q^{50} +(-5.75256 + 5.50001i) q^{52} +(5.65661 + 1.02652i) q^{53} +(1.34225 + 3.57641i) q^{55} +(-3.85511 + 4.03213i) q^{56} +(0.650984 + 0.986199i) q^{58} +(0.216618 + 4.82338i) q^{59} +(4.04714 - 6.77376i) q^{61} +(2.12676 + 0.586949i) q^{62} +(4.31639 - 2.57892i) q^{64} +(-0.120329 + 2.67932i) q^{65} +(-0.301019 - 1.65875i) q^{67} +(-0.235812 + 1.74084i) q^{68} +0.908160i q^{70} +(2.48147 - 8.05247i) q^{71} +(-14.4101 + 1.29693i) q^{73} +(1.89251 + 0.256358i) q^{74} +(0.967053 + 0.702605i) q^{76} +(-24.1464 - 1.08442i) q^{77} +(8.91301 - 2.45983i) q^{79} +(0.541572 - 1.96234i) q^{80} +(-0.814989 - 0.537970i) q^{82} +(11.4479 - 0.514127i) q^{83} +(0.347970 + 0.478939i) q^{85} +(1.48061 + 1.41561i) q^{86} +(-8.07323 - 2.62315i) q^{88} +(1.04708 - 5.76988i) q^{89} +(-15.2898 - 7.36317i) q^{91} +(-6.21020 - 14.5295i) q^{92} +(1.04884 - 0.239392i) q^{94} +(0.399173 - 0.0540717i) q^{95} +(-10.3600 + 8.26184i) q^{97} +(-2.95537 - 1.26319i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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