LMFDB - Embedded newform 450.2.j.g.349.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(49,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,2,0,0,20,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	450.349
Dual form			450.2.j.g.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.65831 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.18614 - 1.26217i) q^{6} +(-2.92048 - 1.68614i) q^{7} +1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(2.18614 - 3.78651i) q^{11} +(-0.396143 - 1.68614i) q^{12} +(5.84096 - 3.37228i) q^{13} +(-1.68614 - 2.92048i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.62772i q^{17} +(1.33591 + 2.68614i) q^{18} +2.37228 q^{19} +(4.00000 + 4.25639i) q^{21} +(3.78651 - 2.18614i) q^{22} +(-1.18843 + 0.686141i) q^{23} +(0.500000 - 1.65831i) q^{24} +6.74456 q^{26} +(-3.31662 - 4.00000i) q^{27} -3.37228i q^{28} +(0.686141 - 1.18843i) q^{29} +(-2.37228 - 4.10891i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.51856 + 5.18614i) q^{33} +(0.813859 - 1.40965i) q^{34} +(-0.186141 + 2.99422i) q^{36} -4.00000i q^{37} +(2.05446 + 1.18614i) q^{38} +(-11.3723 + 2.67181i) q^{39} +(1.50000 + 2.59808i) q^{41} +(1.33591 + 5.68614i) q^{42} +(-4.87375 - 2.81386i) q^{43} +4.37228 q^{44} -1.37228 q^{46} +(6.38458 + 3.68614i) q^{47} +(1.26217 - 1.18614i) q^{48} +(2.18614 + 3.78651i) q^{49} +(-0.813859 + 2.69927i) q^{51} +(5.84096 + 3.37228i) q^{52} +11.4891i q^{53} +(-0.872281 - 5.12241i) q^{54} +(1.68614 - 2.92048i) q^{56} +(-3.93398 - 1.18614i) q^{57} +(1.18843 - 0.686141i) q^{58} +(2.18614 + 3.78651i) q^{59} +(4.05842 - 7.02939i) q^{61} -4.74456i q^{62} +(-4.50506 - 9.05842i) q^{63} -1.00000 q^{64} +(-7.37228 + 1.73205i) q^{66} +(-6.06218 + 3.50000i) q^{67} +(1.40965 - 0.813859i) q^{68} +(2.31386 - 0.543620i) q^{69} -6.00000 q^{71} +(-1.65831 + 2.50000i) q^{72} -3.11684i q^{73} +(2.00000 - 3.46410i) q^{74} +(1.18614 + 2.05446i) q^{76} +(-12.7692 + 7.37228i) q^{77} +(-11.1846 - 3.37228i) q^{78} +(1.00000 - 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} +3.00000i q^{82} +(6.38458 + 3.68614i) q^{83} +(-1.68614 + 5.59230i) q^{84} +(-2.81386 - 4.87375i) q^{86} +(-1.73205 + 1.62772i) q^{87} +(3.78651 + 2.18614i) q^{88} -16.1168 q^{89} -22.7446 q^{91} +(-1.18843 - 0.686141i) q^{92} +(1.87953 + 8.00000i) q^{93} +(3.68614 + 6.38458i) q^{94} +(1.68614 - 0.396143i) q^{96} +(7.25061 + 4.18614i) q^{97} +4.37228i q^{98} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9} + 6 q^{11} - 2 q^{14} - 4 q^{16} - 4 q^{19} + 32 q^{21} + 4 q^{24} + 8 q^{26} - 6 q^{29} + 4 q^{31} + 18 q^{34} + 10 q^{36} - 68 q^{39} + 12 q^{41} + 12 q^{44} + 12 q^{46}+ \cdots + 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9 + 6 * q^11 - 2 * q^14 - 4 * q^16 - 4 * q^19 + 32 * q^21 + 4 * q^24 + 8 * q^26 - 6 * q^29 + 4 * q^31 + 18 * q^34 + 10 * q^36 - 68 * q^39 + 12 * q^41 + 12 * q^44 + 12 * q^46 + 6 * q^49 - 18 * q^51 + 16 * q^54 + 2 * q^56 + 6 * q^59 - 2 * q^61 - 8 * q^64 - 36 * q^66 + 30 * q^69 - 48 * q^71 + 16 * q^74 - 2 * q^76 + 8 * q^79 + 28 * q^81 - 2 * q^84 - 34 * q^86 - 60 * q^89 - 136 * q^91 + 18 * q^94 + 2 * q^96 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.65831	−	0.500000i	−0.957427	−	0.288675i
$3$	−1.65831	−	0.500000i	−0.957427	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.18614	−	1.26217i	−0.484240	−	0.515278i
$7$	−2.92048	−	1.68614i	−1.10384	−	0.637301i	−0.166612	−	0.986023i	$-0.553283\pi$
$7$	−2.92048	−	1.68614i	−1.10384	−	0.637301i	−0.937226	+	0.348721i	$0.886616\pi$
$8$			1.00000i			0.353553i
$9$	2.50000	+	1.65831i	0.833333	+	0.552771i
$10$		0			0
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	−0.321691	−	0.946845i	$-0.604251\pi$
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	0.980837	−	0.194830i	$-0.0624155\pi$
$12$	−0.396143	−	1.68614i	−0.114357	−	0.486747i
$13$	5.84096	−	3.37228i	1.61999	−	0.935303i	0.633071	−	0.774094i	$-0.281794\pi$
$13$	5.84096	−	3.37228i	1.61999	−	0.935303i	0.986920	−	0.161209i	$-0.0515393\pi$
$14$	−1.68614	−	2.92048i	−0.450640	−	0.780531i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	1.62772i		−	0.394780i	−0.980325	−	0.197390i	$-0.936754\pi$
$17$		−	1.62772i		−	0.394780i	0.980325	−	0.197390i	$-0.0632465\pi$
$18$	1.33591	+	2.68614i	0.314876	+	0.633129i
$19$	2.37228			0.544239			0.272119	−	0.962264i	$-0.412275\pi$
$19$	2.37228			0.544239			0.272119	+	0.962264i	$0.412275\pi$
$20$		0			0
$21$	4.00000	+	4.25639i	0.872872	+	0.928820i
$22$	3.78651	−	2.18614i	0.807286	−	0.466087i
$23$	−1.18843	+	0.686141i	−0.247805	+	0.143070i	−0.618759	−	0.785581i	$-0.712364\pi$
$23$	−1.18843	+	0.686141i	−0.247805	+	0.143070i	0.370954	+	0.928651i	$0.379031\pi$
$24$	0.500000	−	1.65831i	0.102062	−	0.338502i
$25$		0			0
$26$	6.74456			1.32272
$27$	−3.31662	−	4.00000i	−0.638285	−	0.769800i
$28$		−	3.37228i		−	0.637301i
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	−0.795261	−	0.606268i	$-0.792666\pi$
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	0.922674	+	0.385582i	$0.125999\pi$
$30$		0			0
$31$	−2.37228	−	4.10891i	−0.426074	−	0.737982i	0.570446	−	0.821335i	$-0.306770\pi$
$31$	−2.37228	−	4.10891i	−0.426074	−	0.737982i	−0.996520	+	0.0833529i	$0.973437\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.51856	+	5.18614i	−0.960658	+	0.902791i
$34$	0.813859	−	1.40965i	0.139576	−	0.241752i
$35$		0			0
$36$	−0.186141	+	2.99422i	−0.0310234	+	0.499037i
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	2.05446	+	1.18614i	0.333277	+	0.192417i
$39$	−11.3723	+	2.67181i	−1.82102	+	0.427833i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	1.33591	+	5.68614i	0.206135	+	0.877391i
$43$	−4.87375	−	2.81386i	−0.743240	−	0.429110i	0.0800065	−	0.996794i	$-0.474506\pi$
$43$	−4.87375	−	2.81386i	−0.743240	−	0.429110i	−0.823246	+	0.567685i	$0.807839\pi$
$44$	4.37228			0.659146
$45$		0			0
$46$	−1.37228			−0.202332
$47$	6.38458	+	3.68614i	0.931287	+	0.537679i	0.887218	−	0.461350i	$-0.152635\pi$
$47$	6.38458	+	3.68614i	0.931287	+	0.537679i	0.0440687	+	0.999029i	$0.485968\pi$
$48$	1.26217	−	1.18614i	0.182178	−	0.171205i
$49$	2.18614	+	3.78651i	0.312306	+	0.540930i
$50$		0			0
$51$	−0.813859	+	2.69927i	−0.113963	+	0.377973i
$52$	5.84096	+	3.37228i	0.809996	+	0.467651i
$53$			11.4891i			1.57815i	0.614295	+	0.789076i	$0.289440\pi$
$53$			11.4891i			1.57815i	−0.614295	+	0.789076i	$0.710560\pi$
$54$	−0.872281	−	5.12241i	−0.118702	−	0.697072i
$55$		0			0
$56$	1.68614	−	2.92048i	0.225320	−	0.390266i
$57$	−3.93398	−	1.18614i	−0.521069	−	0.157108i
$58$	1.18843	−	0.686141i	0.156049	−	0.0900947i
$59$	2.18614	+	3.78651i	0.284611	+	0.492961i	0.972515	−	0.232841i	$-0.0748021\pi$
$59$	2.18614	+	3.78651i	0.284611	+	0.492961i	−0.687904	+	0.725802i	$0.741469\pi$
$60$		0			0
$61$	4.05842	−	7.02939i	0.519628	−	0.900022i	−0.480112	−	0.877207i	$-0.659404\pi$
$61$	4.05842	−	7.02939i	0.519628	−	0.900022i	0.999740	−	0.0228144i	$-0.00726267\pi$
$62$		−	4.74456i		−	0.602560i
$63$	−4.50506	−	9.05842i	−0.567584	−	1.14125i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−7.37228	+	1.73205i	−0.907465	+	0.213201i
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	1.40965	−	0.813859i	0.170945	−	0.0986949i
$69$	2.31386	−	0.543620i	0.278556	−	0.0654442i
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.65831	+	2.50000i	−0.195434	+	0.294628i
$73$		−	3.11684i		−	0.364799i	−0.983225	−	0.182399i	$-0.941614\pi$
$73$		−	3.11684i		−	0.364799i	0.983225	−	0.182399i	$-0.0583864\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	1.18614	+	2.05446i	0.136060	+	0.235662i
$77$	−12.7692	+	7.37228i	−1.45518	+	0.840149i
$78$	−11.1846	−	3.37228i	−1.26641	−	0.381836i
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$			3.00000i			0.331295i
$83$	6.38458	+	3.68614i	0.700799	+	0.404607i	0.807645	−	0.589669i	$-0.200742\pi$
$83$	6.38458	+	3.68614i	0.700799	+	0.404607i	−0.106846	+	0.994276i	$0.534075\pi$
$84$	−1.68614	+	5.59230i	−0.183973	+	0.610170i
$85$		0			0
$86$	−2.81386	−	4.87375i	−0.303426	−	0.525550i
$87$	−1.73205	+	1.62772i	−0.185695	+	0.174510i
$88$	3.78651	+	2.18614i	0.403643	+	0.233043i
$89$	−16.1168			−1.70838			−0.854191	−	0.519959i	$-0.825947\pi$
$89$	−16.1168			−1.70838			−0.854191	+	0.519959i	$0.825947\pi$
$90$		0			0
$91$	−22.7446			−2.38428
$92$	−1.18843	−	0.686141i	−0.123902	−	0.0715351i
$93$	1.87953	+	8.00000i	0.194898	+	0.829561i
$94$	3.68614	+	6.38458i	0.380196	+	0.658519i
$95$		0			0
$96$	1.68614	−	0.396143i	0.172091	−	0.0404312i
$97$	7.25061	+	4.18614i	0.736188	+	0.425038i	0.820682	−	0.571386i	$-0.193594\pi$
$97$	7.25061	+	4.18614i	0.736188	+	0.425038i	−0.0844938	+	0.996424i	$0.526927\pi$
$98$			4.37228i			0.441667i
$99$	11.7446	−	5.84096i	1.18037	−	0.587039i
$100$		0			0
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	−0.926187	−	0.377064i	$-0.876934\pi$
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	0.789640	+	0.613570i	$0.210267\pi$
$102$	−2.05446	+	1.93070i	−0.203421	+	0.191168i
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.374987	−	0.927030i	$-0.377647\pi$
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.990325	+	0.138767i	$0.0443138\pi$
$104$	3.37228	+	5.84096i	0.330679	+	0.572754i
$105$		0			0
$106$	−5.74456	+	9.94987i	−0.557961	+	0.966417i
$107$			8.48913i			0.820675i	0.911934	+	0.410337i	$0.134589\pi$
$107$			8.48913i			0.820675i	−0.911934	+	0.410337i	$0.865411\pi$
$108$	1.80579	−	4.87228i	0.173762	−	0.468835i
$109$	−15.3723			−1.47240			−0.736199	−	0.676765i	$-0.763381\pi$
$109$	−15.3723			−1.47240			−0.736199	+	0.676765i	$0.763381\pi$
$110$		0			0
$111$	−2.00000	+	6.63325i	−0.189832	+	0.629600i
$112$	2.92048	−	1.68614i	0.275960	−	0.159325i
$113$	−2.81929	+	1.62772i	−0.265217	+	0.153123i	−0.626712	−	0.779251i	$-0.715600\pi$
$113$	−2.81929	+	1.62772i	−0.265217	+	0.153123i	0.361495	+	0.932374i	$0.382266\pi$
$114$	−2.81386	−	2.99422i	−0.263542	−	0.280434i
$115$		0			0
$116$	1.37228			0.127413
$117$	20.1947	+	1.25544i	1.86700	+	0.116065i
$118$			4.37228i			0.402501i
$119$	−2.74456	+	4.75372i	−0.251594	+	0.435773i
$120$		0			0
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$	7.02939	−	4.05842i	0.636411	−	0.367432i
$123$	−1.18843	−	5.05842i	−0.107157	−	0.456103i
$124$	2.37228	−	4.10891i	0.213037	−	0.368991i
$125$		0			0
$126$	0.627719	−	10.0974i	0.0559216	−	0.899544i
$127$		−	8.11684i		−	0.720253i	−0.932903	−	0.360127i	$-0.882733\pi$
$127$		−	8.11684i		−	0.720253i	0.932903	−	0.360127i	$-0.117267\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	6.67527	+	7.10313i	0.587724	+	0.625396i
$130$		0			0
$131$	1.37228	+	2.37686i	0.119897	+	0.207667i	0.919727	−	0.392560i	$-0.128410\pi$
$131$	1.37228	+	2.37686i	0.119897	+	0.207667i	−0.799830	+	0.600227i	$0.795077\pi$
$132$	−7.25061	−	2.18614i	−0.631084	−	0.190279i
$133$	−6.92820	−	4.00000i	−0.600751	−	0.346844i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	1.62772			0.139576
$137$	16.5557	+	9.55842i	1.41445	+	0.816631i	0.995803	−	0.0915197i	$-0.0291724\pi$
$137$	16.5557	+	9.55842i	1.41445	+	0.816631i	0.418643	+	0.908151i	$0.362506\pi$
$138$	2.27567	+	0.686141i	0.193718	+	0.0584082i
$139$	0.441578	+	0.764836i	0.0374542	+	0.0648725i	0.884145	−	0.467213i	$-0.154742\pi$
$139$	0.441578	+	0.764836i	0.0374542	+	0.0648725i	−0.846691	+	0.532085i	$0.821409\pi$
$140$		0			0
$141$	−8.74456	−	9.30506i	−0.736425	−	0.783628i
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$		−	29.4891i		−	2.46600i
$144$	−2.68614	+	1.33591i	−0.223845	+	0.111326i
$145$		0			0
$146$	1.55842	−	2.69927i	0.128976	−	0.223393i
$147$	−1.73205	−	7.37228i	−0.142857	−	0.608056i
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$	0.941578	+	1.63086i	0.0771371	+	0.133605i	0.902014	−	0.431708i	$-0.142089\pi$
$149$	0.941578	+	1.63086i	0.0771371	+	0.133605i	−0.824877	+	0.565313i	$0.808755\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$			2.37228i			0.192417i
$153$	2.69927	−	4.06930i	0.218223	−	0.328983i
$154$	−14.7446			−1.18815
$155$		0			0
$156$	−8.00000	−	8.51278i	−0.640513	−	0.681568i
$157$	−5.84096	+	3.37228i	−0.466160	+	0.269137i	−0.714631	−	0.699502i	$-0.753405\pi$
$157$	−5.84096	+	3.37228i	−0.466160	+	0.269137i	0.248471	+	0.968639i	$0.420072\pi$
$158$	1.73205	−	1.00000i	0.137795	−	0.0795557i
$159$	5.74456	−	19.0526i	0.455573	−	1.51097i
$160$		0			0
$161$	4.62772			0.364715
$162$	−1.11469	+	8.93070i	−0.0875785	+	0.701662i
$163$			21.4891i			1.68316i	0.540134	+	0.841579i	$0.318374\pi$
$163$			21.4891i			1.68316i	−0.540134	+	0.841579i	$0.681626\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$		0			0
$166$	3.68614	+	6.38458i	0.286100	+	0.495540i
$167$	11.5807	−	6.68614i	0.896144	−	0.517389i	0.0201970	−	0.999796i	$-0.493571\pi$
$167$	11.5807	−	6.68614i	0.896144	−	0.517389i	0.875947	+	0.482407i	$0.160237\pi$
$168$	−4.25639	+	4.00000i	−0.328388	+	0.308607i
$169$	16.2446	−	28.1364i	1.24958	−	2.16434i
$170$		0			0
$171$	5.93070	+	3.93398i	0.453532	+	0.300839i
$172$		−	5.62772i		−	0.429110i
$173$	17.9653	+	10.3723i	1.36588	+	0.788590i	0.990399	−	0.138241i	$-0.0441448\pi$
$173$	17.9653	+	10.3723i	1.36588	+	0.788590i	0.375479	+	0.926831i	$0.377478\pi$
$174$	−2.31386	+	0.543620i	−0.175413	+	0.0412118i
$175$		0			0
$176$	2.18614	+	3.78651i	0.164787	+	0.285419i
$177$	−1.73205	−	7.37228i	−0.130189	−	0.554135i
$178$	−13.9576	−	8.05842i	−1.04617	−	0.604004i
$179$	14.7446			1.10206			0.551030	−	0.834485i	$-0.314235\pi$
$179$	14.7446			1.10206			0.551030	+	0.834485i	$0.314235\pi$
$180$		0			0
$181$	20.8614			1.55062			0.775308	−	0.631583i	$-0.217595\pi$
$181$	20.8614			1.55062			0.775308	+	0.631583i	$0.217595\pi$
$182$	−19.6974	−	11.3723i	−1.46007	−	0.842970i
$183$	−10.2448	+	9.62772i	−0.757319	+	0.711701i
$184$	−0.686141	−	1.18843i	−0.0505830	−	0.0876123i
$185$		0			0
$186$	−2.37228	+	7.86797i	−0.173944	+	0.576907i
$187$	−6.16337	−	3.55842i	−0.450710	−	0.260218i
$188$			7.37228i			0.537679i
$189$	2.94158	+	17.2742i	0.213968	+	1.25651i
$190$		0			0
$191$	−8.74456	+	15.1460i	−0.632734	+	1.09593i	0.354256	+	0.935148i	$0.384734\pi$
$191$	−8.74456	+	15.1460i	−0.632734	+	1.09593i	−0.986990	+	0.160780i	$0.948599\pi$
$192$	1.65831	+	0.500000i	0.119678	+	0.0360844i
$193$	−18.2877	+	10.5584i	−1.31638	+	0.760012i	−0.983144	−	0.182832i	$-0.941474\pi$
$193$	−18.2877	+	10.5584i	−1.31638	+	0.760012i	−0.333235	+	0.942844i	$0.608140\pi$
$194$	4.18614	+	7.25061i	0.300547	+	0.520563i
$195$		0			0
$196$	−2.18614	+	3.78651i	−0.156153	+	0.270465i
$197$		−	5.48913i		−	0.391084i	−0.980695	−	0.195542i	$-0.937353\pi$
$197$		−	5.48913i		−	0.391084i	0.980695	−	0.195542i	$-0.0626466\pi$
$198$	13.0916	+	0.813859i	0.930377	+	0.0578385i
$199$	−13.4891			−0.956219			−0.478109	−	0.878300i	$-0.658678\pi$
$199$	−13.4891			−0.956219			−0.478109	+	0.878300i	$0.658678\pi$
$200$		0			0
$201$	11.8030	−	2.77300i	0.832518	−	0.195593i
$202$	−2.37686	+	1.37228i	−0.167235	+	0.0965534i
$203$	−4.00772	+	2.31386i	−0.281287	+	0.162401i
$204$	−2.74456	+	0.644810i	−0.192158	+	0.0451457i
$205$		0			0
$206$	16.0000			1.11477
$207$	−4.10891	−	0.255437i	−0.285589	−	0.0177541i
$208$			6.74456i			0.467651i
$209$	5.18614	−	8.98266i	0.358733	−	0.621344i
$210$		0			0
$211$	9.37228	+	16.2333i	0.645214	+	1.11754i	0.984252	+	0.176771i	$0.0565653\pi$
$211$	9.37228	+	16.2333i	0.645214	+	1.11754i	−0.339037	+	0.940773i	$0.610101\pi$
$212$	−9.94987	+	5.74456i	−0.683360	+	0.394538i
$213$	9.94987	+	3.00000i	0.681754	+	0.205557i
$214$	−4.24456	+	7.35180i	−0.290152	+	0.502559i
$215$		0			0
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$			16.0000i			1.08615i
$218$	−13.3128	−	7.68614i	−0.901656	−	0.520571i
$219$	−1.55842	+	5.16870i	−0.105308	+	0.349268i
$220$		0			0
$221$	−5.48913	−	9.50744i	−0.369239	−	0.639540i
$222$	−5.04868	+	4.74456i	−0.338845	+	0.318434i
$223$	5.73977	+	3.31386i	0.384364	+	0.221912i	0.679715	−	0.733476i	$-0.262103\pi$
$223$	5.73977	+	3.31386i	0.384364	+	0.221912i	−0.295351	+	0.955389i	$0.595437\pi$
$224$	3.37228			0.225320
$225$		0			0
$226$	−3.25544			−0.216548
$227$	−16.5557	−	9.55842i	−1.09884	−	0.634415i	−0.162923	−	0.986639i	$-0.552092\pi$
$227$	−16.5557	−	9.55842i	−1.09884	−	0.634415i	−0.935916	+	0.352224i	$0.885426\pi$
$228$	−0.939764	−	4.00000i	−0.0622374	−	0.264906i
$229$	6.31386	+	10.9359i	0.417232	+	0.722666i	0.995660	−	0.0930670i	$-0.0296671\pi$
$229$	6.31386	+	10.9359i	0.417232	+	0.722666i	−0.578428	+	0.815733i	$0.696334\pi$
$230$		0			0
$231$	24.8614	−	5.84096i	1.63576	−	0.384307i
$232$	1.18843	+	0.686141i	0.0780243	+	0.0450473i
$233$		−	7.11684i		−	0.466240i	−0.972448	−	0.233120i	$-0.925107\pi$
$233$		−	7.11684i		−	0.466240i	0.972448	−	0.233120i	$-0.0748935\pi$
$234$	16.8614	+	11.1846i	1.10226	+	0.731160i
$235$		0			0
$236$	−2.18614	+	3.78651i	−0.142306	+	0.246481i
$237$	−2.52434	+	2.37228i	−0.163973	+	0.154096i
$238$	−4.75372	+	2.74456i	−0.308138	+	0.177904i
$239$	−1.62772	−	2.81929i	−0.105288	−	0.182365i	0.808568	−	0.588403i	$-0.200243\pi$
$239$	−1.62772	−	2.81929i	−0.105288	−	0.182365i	−0.913856	+	0.406038i	$0.866910\pi$
$240$		0			0
$241$	6.24456	−	10.8159i	0.402248	−	0.696713i	−0.591749	−	0.806122i	$-0.701562\pi$
$241$	6.24456	−	10.8159i	0.402248	−	0.696713i	0.993997	+	0.109409i	$0.0348958\pi$
$242$		−	8.11684i		−	0.521770i
$243$	−1.65831	−	15.5000i	−0.106381	−	0.994325i
$244$	8.11684			0.519628
$245$		0			0
$246$	1.50000	−	4.97494i	0.0956365	−	0.317190i
$247$	13.8564	−	8.00000i	0.881662	−	0.509028i
$248$	4.10891	−	2.37228i	0.260916	−	0.150640i
$249$	−8.74456	−	9.30506i	−0.554164	−	0.589684i
$250$		0			0
$251$	−24.6060			−1.55312			−0.776558	−	0.630046i	$-0.783036\pi$
$251$	−24.6060			−1.55312			−0.776558	+	0.630046i	$0.783036\pi$
$252$	5.59230	−	8.43070i	0.352282	−	0.531084i
$253$			6.00000i			0.377217i
$254$	4.05842	−	7.02939i	0.254648	−	0.441063i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.78651	−	2.18614i	0.236196	−	0.136368i	−0.377231	−	0.926119i	$-0.623124\pi$
$257$	3.78651	−	2.18614i	0.236196	−	0.136368i	0.613427	+	0.789751i	$0.289790\pi$
$258$	2.22938	+	9.48913i	0.138795	+	0.590767i
$259$	−6.74456	+	11.6819i	−0.419087	+	0.725880i
$260$		0			0
$261$	3.68614	−	1.83324i	0.228166	−	0.113475i
$262$			2.74456i			0.169560i
$263$	−15.1460	−	8.74456i	−0.933944	−	0.539213i	−0.0458872	−	0.998947i	$-0.514611\pi$
$263$	−15.1460	−	8.74456i	−0.933944	−	0.539213i	−0.888057	+	0.459734i	$0.847945\pi$
$264$	−5.18614	−	5.51856i	−0.319185	−	0.339644i
$265$		0			0
$266$	−4.00000	−	6.92820i	−0.245256	−	0.424795i
$267$	26.7268	+	8.05842i	1.63565	+	0.493167i
$268$	−6.06218	−	3.50000i	−0.370306	−	0.213797i
$269$	1.37228			0.0836695			0.0418347	−	0.999125i	$-0.486680\pi$
$269$	1.37228			0.0836695			0.0418347	+	0.999125i	$0.486680\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	1.40965	+	0.813859i	0.0854723	+	0.0493475i
$273$	37.7176	+	11.3723i	2.28277	+	0.688282i
$274$	9.55842	+	16.5557i	0.577445	+	1.00016i
$275$		0			0
$276$	1.62772	+	1.73205i	0.0979772	+	0.104257i
$277$	−14.5012	−	8.37228i	−0.871294	−	0.503042i	−0.00351574	−	0.999994i	$-0.501119\pi$
$277$	−14.5012	−	8.37228i	−0.871294	−	0.503042i	−0.867778	+	0.496952i	$0.834452\pi$
$278$			0.883156i			0.0529682i
$279$	0.883156	−	14.2063i	0.0528732	−	0.850507i
$280$		0			0
$281$	0.686141	−	1.18843i	0.0409317	−	0.0708958i	−0.844834	−	0.535029i	$-0.820301\pi$
$281$	0.686141	−	1.18843i	0.0409317	−	0.0708958i	0.885765	+	0.464133i	$0.153634\pi$
$282$	−2.92048	−	12.4307i	−0.173912	−	0.740238i
$283$	2.71810	−	1.56930i	0.161574	−	0.0932850i	−0.417033	−	0.908892i	$-0.636930\pi$
$283$	2.71810	−	1.56930i	0.161574	−	0.0932850i	0.578607	+	0.815607i	$0.303597\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	14.7446	−	25.5383i	0.871864	−	1.51011i
$287$		−	10.1168i		−	0.597178i
$288$	−2.99422	−	0.186141i	−0.176436	−	0.0109684i
$289$	14.3505			0.844149
$290$		0			0
$291$	−9.93070	−	10.5672i	−0.582148	−	0.619462i
$292$	2.69927	−	1.55842i	0.157963	−	0.0911997i
$293$	−22.7190	+	13.1168i	−1.32726	+	0.766294i	−0.984875	−	0.173265i	$-0.944568\pi$
$293$	−22.7190	+	13.1168i	−1.32726	+	0.766294i	−0.342385	+	0.939560i	$0.611235\pi$
$294$	2.18614	−	7.25061i	0.127498	−	0.422864i
$295$		0			0
$296$	4.00000			0.232495
$297$	−22.3966	+	3.81386i	−1.29958	+	0.221303i
$298$			1.88316i			0.109088i
$299$	−4.62772	+	8.01544i	−0.267628	+	0.463545i
$300$		0			0
$301$	9.48913	+	16.4356i	0.546944	+	0.947335i
$302$	8.66025	−	5.00000i	0.498342	−	0.287718i
$303$	3.46410	−	3.25544i	0.199007	−	0.187020i
$304$	−1.18614	+	2.05446i	−0.0680298	+	0.117831i
$305$		0			0
$306$	4.37228	−	2.17448i	0.249947	−	0.124307i
$307$			1.23369i			0.0704103i	0.999380	+	0.0352051i	$0.0112085\pi$
$307$			1.23369i			0.0704103i	−0.999380	+	0.0352051i	$0.988792\pi$
$308$	−12.7692	−	7.37228i	−0.727591	−	0.420075i
$309$	−26.9783	+	6.33830i	−1.53474	+	0.360573i
$310$		0			0
$311$	10.3723	+	17.9653i	0.588158	+	1.01872i	0.994474	+	0.104987i	$0.0334801\pi$
$311$	10.3723	+	17.9653i	0.588158	+	1.01872i	−0.406315	+	0.913733i	$0.633187\pi$
$312$	−2.67181	−	11.3723i	−0.151262	−	0.643829i
$313$	3.14170	+	1.81386i	0.177579	+	0.102525i	0.586155	−	0.810199i	$-0.300641\pi$
$313$	3.14170	+	1.81386i	0.177579	+	0.102525i	−0.408576	+	0.912724i	$0.633974\pi$
$314$	−6.74456			−0.380618
$315$		0			0
$316$	2.00000			0.112509
$317$	−2.37686	−	1.37228i	−0.133498	−	0.0770750i	0.431764	−	0.901987i	$-0.357891\pi$
$317$	−2.37686	−	1.37228i	−0.133498	−	0.0770750i	−0.565262	+	0.824912i	$0.691225\pi$
$318$	14.5012	−	13.6277i	0.813188	−	0.764205i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	4.24456	−	14.0776i	0.236908	−	0.785736i
$322$	4.00772	+	2.31386i	0.223342	+	0.128946i
$323$		−	3.86141i		−	0.214854i
$324$	−5.43070	+	7.17687i	−0.301706	+	0.398715i
$325$		0			0
$326$	−10.7446	+	18.6101i	−0.595086	+	1.03072i
$327$	25.4920	+	7.68614i	1.40971	+	0.425045i
$328$	−2.59808	+	1.50000i	−0.143455	+	0.0828236i
$329$	−12.4307	−	21.5306i	−0.685327	−	1.18702i
$330$		0			0
$331$	−8.11684	+	14.0588i	−0.446142	+	0.772741i	−0.998131	−	0.0611107i	$-0.980536\pi$
$331$	−8.11684	+	14.0588i	−0.446142	+	0.772741i	0.551989	+	0.833851i	$0.313869\pi$
$332$			7.37228i			0.404607i
$333$	6.63325	−	10.0000i	0.363500	−	0.547997i
$334$	13.3723			0.731699
$335$		0			0
$336$	−5.68614	+	1.33591i	−0.310204	+	0.0728797i
$337$	−2.05446	+	1.18614i	−0.111913	+	0.0646132i	−0.554912	−	0.831909i	$-0.687248\pi$
$337$	−2.05446	+	1.18614i	−0.111913	+	0.0646132i	0.442999	+	0.896522i	$0.353915\pi$
$338$	28.1364	−	16.2446i	1.53042	−	0.883588i
$339$	5.48913	−	1.28962i	0.298128	−	0.0700426i
$340$		0			0
$341$	−20.7446			−1.12338
$342$	3.16915	+	6.37228i	0.171368	+	0.344574i
$343$			8.86141i			0.478471i
$344$	2.81386	−	4.87375i	0.151713	−	0.262775i
$345$		0			0
$346$	10.3723	+	17.9653i	0.557617	+	0.965821i
$347$	−4.22894	+	2.44158i	−0.227021	+	0.131071i	−0.609197	−	0.793019i	$-0.708508\pi$
$347$	−4.22894	+	2.44158i	−0.227021	+	0.131071i	0.382176	+	0.924090i	$0.375175\pi$
$348$	−2.27567	−	0.686141i	−0.121989	−	0.0367810i
$349$	9.05842	−	15.6896i	0.484886	−	0.839848i	−0.514963	−	0.857212i	$-0.672194\pi$
$349$	9.05842	−	15.6896i	0.484886	−	0.839848i	0.999849	+	0.0173648i	$0.00552768\pi$
$350$		0			0
$351$	−32.8614	−	12.1793i	−1.75401	−	0.650081i
$352$			4.37228i			0.233043i
$353$	−18.4901	−	10.6753i	−0.984129	−	0.568187i	−0.0806147	−	0.996745i	$-0.525688\pi$
$353$	−18.4901	−	10.6753i	−0.984129	−	0.568187i	−0.903514	+	0.428558i	$0.859022\pi$
$354$	2.18614	−	7.25061i	0.116192	−	0.385365i
$355$		0			0
$356$	−8.05842	−	13.9576i	−0.427096	−	0.739751i
$357$	6.92820	−	6.51087i	0.366679	−	0.344592i
$358$	12.7692	+	7.37228i	0.674871	+	0.389637i
$359$	17.4891			0.923041			0.461520	−	0.887130i	$-0.347304\pi$
$359$	17.4891			0.923041			0.461520	+	0.887130i	$0.347304\pi$
$360$		0			0
$361$	−13.3723			−0.703804
$362$	18.0665	+	10.4307i	0.949555	+	0.548226i
$363$	3.21543	+	13.6861i	0.168767	+	0.718336i
$364$	−11.3723	−	19.6974i	−0.596070	−	1.03242i
$365$		0			0
$366$	−13.6861	+	3.21543i	−0.715386	+	0.168073i
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$		−	1.37228i		−	0.0715351i
$369$	−0.558422	+	8.98266i	−0.0290703	+	0.467619i
$370$		0			0
$371$	19.3723	−	33.5538i	1.00576	−	1.74203i
$372$	−5.98844	+	5.62772i	−0.310486	+	0.291784i
$373$	13.4140	−	7.74456i	0.694549	−	0.400998i	−0.110765	−	0.993847i	$-0.535330\pi$
$373$	13.4140	−	7.74456i	0.694549	−	0.400998i	0.805314	+	0.592848i	$0.201997\pi$
$374$	−3.55842	−	6.16337i	−0.184002	−	0.318700i
$375$		0			0
$376$	−3.68614	+	6.38458i	−0.190098	+	0.329260i
$377$		−	9.25544i		−	0.476679i
$378$	−6.08963	+	16.4307i	−0.313217	+	0.845104i
$379$	−17.8614			−0.917479			−0.458739	−	0.888571i	$-0.651699\pi$
$379$	−17.8614			−0.917479			−0.458739	+	0.888571i	$0.651699\pi$
$380$		0			0
$381$	−4.05842	+	13.4603i	−0.207919	+	0.689590i
$382$	−15.1460	+	8.74456i	−0.774938	+	0.447411i
$383$	19.8997	−	11.4891i	1.01683	−	0.587067i	0.103646	−	0.994614i	$-0.466949\pi$
$383$	19.8997	−	11.4891i	1.01683	−	0.587067i	0.913184	+	0.407547i	$0.133616\pi$
$384$	1.18614	+	1.26217i	0.0605300	+	0.0644098i
$385$		0			0
$386$	−21.1168			−1.07482
$387$	−7.51811	−	15.1168i	−0.382167	−	0.768432i
$388$			8.37228i			0.425038i
$389$	−2.31386	+	4.00772i	−0.117317	+	0.203200i	−0.918704	−	0.394947i	$-0.870763\pi$
$389$	−2.31386	+	4.00772i	−0.117317	+	0.203200i	0.801386	+	0.598147i	$0.204096\pi$
$390$		0			0
$391$	1.11684	+	1.93443i	0.0564812	+	0.0978284i
$392$	−3.78651	+	2.18614i	−0.191247	+	0.110417i
$393$	−1.08724	−	4.62772i	−0.0548440	−	0.233438i
$394$	2.74456	−	4.75372i	0.138269	−	0.239489i
$395$		0			0
$396$	10.9307	+	7.25061i	0.549289	+	0.364357i
$397$			22.7446i			1.14152i	0.821118	+	0.570758i	$0.193351\pi$
$397$			22.7446i			1.14152i	−0.821118	+	0.570758i	$0.806649\pi$
$398$	−11.6819	−	6.74456i	−0.585562	−	0.338074i
$399$	9.48913	+	10.0974i	0.475050	+	0.505500i
$400$		0			0
$401$	0.558422	+	0.967215i	0.0278863	+	0.0483004i	0.879632	−	0.475655i	$-0.157789\pi$
$401$	0.558422	+	0.967215i	0.0278863	+	0.0483004i	−0.851745	+	0.523956i	$0.824456\pi$
$402$	11.6082	+	3.50000i	0.578964	+	0.174564i
$403$	−27.7128	−	16.0000i	−1.38047	−	0.797017i
$404$	−2.74456			−0.136547
$405$		0			0
$406$	−4.62772			−0.229670
$407$	−15.1460	−	8.74456i	−0.750761	−	0.433452i
$408$	−2.69927	−	0.813859i	−0.133634	−	0.0402920i
$409$	8.93070	+	15.4684i	0.441595	+	0.764865i	0.997808	−	0.0661749i	$-0.0210795\pi$
$409$	8.93070	+	15.4684i	0.441595	+	0.764865i	−0.556213	+	0.831040i	$0.687746\pi$
$410$		0			0
$411$	−22.6753	−	24.1287i	−1.11849	−	1.19018i
$412$	13.8564	+	8.00000i	0.682656	+	0.394132i
$413$		−	14.7446i		−	0.725532i
$414$	−3.43070	−	2.27567i	−0.168610	−	0.111843i
$415$		0			0
$416$	−3.37228	+	5.84096i	−0.165340	+	0.286377i
$417$	−0.349857	−	1.48913i	−0.0171325	−	0.0729228i
$418$	8.98266	−	5.18614i	0.439356	−	0.253662i
$419$	12.8614	+	22.2766i	0.628321	+	1.08828i	0.987889	+	0.155165i	$0.0495908\pi$
$419$	12.8614	+	22.2766i	0.628321	+	1.08828i	−0.359568	+	0.933119i	$0.617076\pi$
$420$		0			0
$421$	−15.2337	+	26.3855i	−0.742445	+	1.28595i	0.208935	+	0.977930i	$0.433000\pi$
$421$	−15.2337	+	26.3855i	−0.742445	+	1.28595i	−0.951379	+	0.308022i	$0.900333\pi$
$422$			18.7446i			0.912471i
$423$	9.84868	+	19.8030i	0.478859	+	0.962854i
$424$	−11.4891			−0.557961
$425$		0			0
$426$	7.11684	+	7.57301i	0.344812	+	0.366914i
$427$	−23.7051	+	13.6861i	−1.14717	+	0.662319i
$428$	−7.35180	+	4.24456i	−0.355363	+	0.205169i
$429$	−14.7446	+	48.9022i	−0.711874	+	2.36102i
$430$		0			0
$431$	8.23369			0.396603			0.198301	−	0.980141i	$-0.436458\pi$
$431$	8.23369			0.396603			0.198301	+	0.980141i	$0.436458\pi$
$432$	5.12241	−	0.872281i	0.246452	−	0.0419677i
$433$		−	6.37228i		−	0.306232i	−0.988208	−	0.153116i	$-0.951069\pi$
$433$		−	6.37228i		−	0.306232i	0.988208	−	0.153116i	$-0.0489309\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$		0			0
$436$	−7.68614	−	13.3128i	−0.368099	−	0.637567i
$437$	−2.81929	+	1.62772i	−0.134865	+	0.0778643i
$438$	−3.93398	+	3.69702i	−0.187973	+	0.176650i
$439$	−9.11684	+	15.7908i	−0.435123	+	0.753656i	−0.997306	−	0.0733577i	$-0.976629\pi$
$439$	−9.11684	+	15.7908i	−0.435123	+	0.753656i	0.562182	+	0.827013i	$0.309962\pi$
$440$		0			0
$441$	−0.813859	+	13.0916i	−0.0387552	+	0.623408i
$442$		−	10.9783i		−	0.522182i
$443$	−3.04051	−	1.75544i	−0.144459	−	0.0834033i	0.426029	−	0.904710i	$-0.359912\pi$
$443$	−3.04051	−	1.75544i	−0.144459	−	0.0834033i	−0.570487	+	0.821306i	$0.693246\pi$
$444$	−6.74456	+	1.58457i	−0.320083	+	0.0752006i
$445$		0			0
$446$	3.31386	+	5.73977i	0.156916	+	0.271786i
$447$	−0.746000	−	3.17527i	−0.0352846	−	0.150185i
$448$	2.92048	+	1.68614i	0.137980	+	0.0796627i
$449$	−9.86141			−0.465389			−0.232694	−	0.972550i	$-0.574754\pi$
$449$	−9.86141			−0.465389			−0.232694	+	0.972550i	$0.574754\pi$
$450$		0			0
$451$	13.1168			0.617648
$452$	−2.81929	−	1.62772i	−0.132608	−	0.0765614i
$453$	−12.6217	+	11.8614i	−0.593019	+	0.557297i
$454$	−9.55842	−	16.5557i	−0.448599	−	0.776996i
$455$		0			0
$456$	1.18614	−	3.93398i	0.0555461	−	0.184226i
$457$	−11.1571	−	6.44158i	−0.521909	−	0.301324i	0.215806	−	0.976436i	$-0.430762\pi$
$457$	−11.1571	−	6.44158i	−0.521909	−	0.301324i	−0.737715	+	0.675112i	$0.764095\pi$
$458$			12.6277i			0.590055i
$459$	−6.51087	+	5.39853i	−0.303902	+	0.251982i
$460$		0			0
$461$	−0.941578	+	1.63086i	−0.0438537	+	0.0759568i	−0.887119	−	0.461541i	$-0.847297\pi$
$461$	−0.941578	+	1.63086i	−0.0438537	+	0.0759568i	0.843265	+	0.537497i	$0.180630\pi$
$462$	24.4511	+	7.37228i	1.13757	+	0.342990i
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	0.0402476	+	0.999190i	$0.487185\pi$
$464$	0.686141	+	1.18843i	0.0318533	+	0.0551715i
$465$		0			0
$466$	3.55842	−	6.16337i	0.164841	−	0.285512i
$467$			43.1168i			1.99521i	0.0691713	+	0.997605i	$0.477964\pi$
$467$			43.1168i			1.99521i	−0.0691713	+	0.997605i	$0.522036\pi$
$468$	9.01011	+	18.1168i	0.416493	+	0.837451i
$469$	23.6060			1.09002
$470$		0			0
$471$	11.3723	−	2.67181i	0.524007	−	0.123111i
$472$	−3.78651	+	2.18614i	−0.174288	+	0.100625i
$473$	−21.3094	+	12.3030i	−0.979807	+	0.565692i
$474$	−3.37228	+	0.792287i	−0.154894	+	0.0363909i
$475$		0			0
$476$	−5.48913			−0.251594
$477$	−19.0526	+	28.7228i	−0.872357	+	1.31513i
$478$		−	3.25544i		−	0.148900i
$479$	−0.255437	+	0.442430i	−0.0116712	+	0.0202152i	−0.871802	−	0.489858i	$-0.837048\pi$
$479$	−0.255437	+	0.442430i	−0.0116712	+	0.0202152i	0.860131	+	0.510074i	$0.170382\pi$
$480$		0			0
$481$	−13.4891	−	23.3639i	−0.615051	−	1.06530i
$482$	10.8159	−	6.24456i	0.492651	−	0.284432i
$483$	−7.67420	−	2.31386i	−0.349188	−	0.105284i
$484$	4.05842	−	7.02939i	0.184474	−	0.319518i
$485$		0			0
$486$	6.31386	−	14.2525i	0.286402	−	0.646509i
$487$		−	12.7446i		−	0.577511i	−0.957403	−	0.288756i	$-0.906758\pi$
$487$		−	12.7446i		−	0.577511i	0.957403	−	0.288756i	$-0.0932415\pi$
$488$	7.02939	+	4.05842i	0.318206	+	0.183716i
$489$	10.7446	−	35.6357i	0.485886	−	1.61150i
$490$		0			0
$491$	18.3030	+	31.7017i	0.826002	+	1.43068i	0.901151	+	0.433505i	$0.142723\pi$
$491$	18.3030	+	31.7017i	0.826002	+	1.43068i	−0.0751489	+	0.997172i	$0.523943\pi$
$492$	3.78651	−	3.55842i	0.170709	−	0.160426i
$493$	−1.93443	−	1.11684i	−0.0871224	−	0.0503001i
$494$	16.0000			0.719874
$495$		0			0
$496$	4.74456			0.213037
$497$	17.5229	+	10.1168i	0.786009	+	0.453802i
$498$	−2.92048	−	12.4307i	−0.130870	−	0.557033i
$499$	7.55842	+	13.0916i	0.338361	+	0.586059i	0.984125	−	0.177479i	$-0.0567940\pi$
$499$	7.55842	+	13.0916i	0.338361	+	0.586059i	−0.645763	+	0.763538i	$0.723461\pi$
$500$		0			0
$501$	−22.5475	+	5.29734i	−1.00735	+	0.236668i
$502$	−21.3094	−	12.3030i	−0.951085	−	0.549109i
$503$			6.86141i			0.305935i	0.988231	+	0.152967i	$0.0488830\pi$
$503$			6.86141i			0.305935i	−0.988231	+	0.152967i	$0.951117\pi$
$504$	9.05842	−	4.50506i	0.403494	−	0.200671i
$505$		0			0
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$	−41.0068	+	38.5367i	−1.82117	+	1.71147i
$508$	7.02939	−	4.05842i	0.311879	−	0.180063i
$509$	−21.1753	−	36.6766i	−0.938577	−	1.62566i	−0.768127	−	0.640297i	$-0.778811\pi$
$509$	−21.1753	−	36.6766i	−0.938577	−	1.62566i	−0.170450	−	0.985366i	$-0.554522\pi$
$510$		0			0
$511$	−5.25544	+	9.10268i	−0.232487	+	0.402679i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.86797	−	9.48913i	−0.347379	−	0.418955i
$514$	4.37228			0.192853
$515$		0			0
$516$	−2.81386	+	9.33252i	−0.123873	+	0.410841i
$517$	27.9152	−	16.1168i	1.22771	−	0.708818i
$518$	−11.6819	+	6.74456i	−0.513274	+	0.296339i
$519$	−24.6060	−	26.1831i	−1.08008	−	1.14931i
$520$		0			0
$521$	−6.76631			−0.296438			−0.148219	−	0.988955i	$-0.547354\pi$
$521$	−6.76631			−0.296438			−0.148219	+	0.988955i	$0.547354\pi$
$522$	4.10891	+	0.255437i	0.179842	+	0.0111802i
$523$		−	6.11684i		−	0.267471i	−0.991017	−	0.133735i	$-0.957303\pi$
$523$		−	6.11684i		−	0.267471i	0.991017	−	0.133735i	$-0.0426972\pi$
$524$	−1.37228	+	2.37686i	−0.0599484	+	0.103834i
$525$		0			0
$526$	−8.74456	−	15.1460i	−0.381281	−	0.660398i
$527$	−6.68815	+	3.86141i	−0.291340	+	0.168206i
$528$	−1.73205	−	7.37228i	−0.0753778	−	0.320837i
$529$	−10.5584	+	18.2877i	−0.459062	+	0.795118i
$530$		0			0
$531$	−0.813859	+	13.0916i	−0.0353185	+	0.568126i
$532$		−	8.00000i		−	0.346844i
$533$	17.5229	+	10.1168i	0.759001	+	0.438209i
$534$	19.1168	+	20.3422i	0.827267	+	0.880292i
$535$		0			0
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$	−24.4511	−	7.37228i	−1.05514	−	0.318137i
$538$	1.18843	+	0.686141i	0.0512369	+	0.0295816i
$539$	19.1168			0.823421
$540$		0			0
$541$	27.3723			1.17683			0.588413	−	0.808560i	$-0.299753\pi$
$541$	27.3723			1.17683			0.588413	+	0.808560i	$0.299753\pi$
$542$	6.92820	+	4.00000i	0.297592	+	0.171815i
$543$	−34.5947	−	10.4307i	−1.48460	−	0.447624i
$544$	0.813859	+	1.40965i	0.0348939	+	0.0604381i
$545$		0			0
$546$	26.9783	+	28.7075i	1.15456	+	1.22857i
$547$	25.5195	+	14.7337i	1.09113	+	0.629967i	0.933878	−	0.357591i	$-0.116402\pi$
$547$	25.5195	+	14.7337i	1.09113	+	0.629967i	0.157256	+	0.987558i	$0.449735\pi$
$548$			19.1168i			0.816631i
$549$	21.8030	−	10.8434i	0.930529	−	0.462783i
$550$		0			0
$551$	1.62772	−	2.81929i	0.0693431	−	0.120106i
$552$	0.543620	+	2.31386i	0.0231380	+	0.0984844i
$553$	−5.84096	+	3.37228i	−0.248383	+	0.143404i
$554$	−8.37228	−	14.5012i	−0.355704	−	0.616098i
$555$		0			0
$556$	−0.441578	+	0.764836i	−0.0187271	+	0.0324363i
$557$		−	44.2337i		−	1.87424i	−0.349005	−	0.937121i	$-0.613480\pi$
$557$		−	44.2337i		−	1.87424i	0.349005	−	0.937121i	$-0.386520\pi$
$558$	7.86797	−	11.8614i	0.333078	−	0.502133i
$559$	−37.9565			−1.60539
$560$		0			0
$561$	8.44158	+	8.98266i	0.356404	+	0.379248i
$562$	1.18843	−	0.686141i	0.0501309	−	0.0289431i
$563$	35.2670	−	20.3614i	1.48633	−	0.858131i	0.486448	−	0.873710i	$-0.338292\pi$
$563$	35.2670	−	20.3614i	1.48633	−	0.858131i	0.999879	+	0.0155787i	$0.00495904\pi$
$564$	3.68614	−	12.2255i	0.155215	−	0.514788i
$565$		0			0
$566$	3.13859			0.131925
$567$	3.75906	−	30.1168i	0.157865	−	1.26479i
$568$		−	6.00000i		−	0.251754i
$569$	−15.3030	+	26.5055i	−0.641534	+	1.11117i	0.343556	+	0.939132i	$0.388369\pi$
$569$	−15.3030	+	26.5055i	−0.641534	+	1.11117i	−0.985090	+	0.172038i	$0.944965\pi$
$570$		0			0
$571$	−4.30298	−	7.45299i	−0.180074	−	0.311898i	0.761831	−	0.647775i	$-0.224300\pi$
$571$	−4.30298	−	7.45299i	−0.180074	−	0.311898i	−0.941906	+	0.335878i	$0.890967\pi$
$572$	25.5383	−	14.7446i	1.06781	−	0.616501i
$573$	22.0742	−	20.7446i	0.922164	−	0.866617i
$574$	5.05842	−	8.76144i	0.211134	−	0.365696i
$575$		0			0
$576$	−2.50000	−	1.65831i	−0.104167	−	0.0690963i
$577$		−	41.1168i		−	1.71172i	−0.517210	−	0.855858i	$-0.673030\pi$
$577$		−	41.1168i		−	1.71172i	0.517210	−	0.855858i	$-0.326970\pi$
$578$	12.4279	+	7.17527i	0.516934	+	0.298452i
$579$	35.6060	−	8.36530i	1.47973	−	0.347650i
$580$		0			0
$581$	−12.4307	−	21.5306i	−0.515712	−	0.893240i
$582$	−3.31662	−	14.1168i	−0.137479	−	0.585162i
$583$	43.5036	+	25.1168i	1.80174	+	1.04023i
$584$	3.11684			0.128976
$585$		0			0
$586$	−26.2337			−1.08370
$587$	−23.3827	−	13.5000i	−0.965107	−	0.557205i	−0.0673658	−	0.997728i	$-0.521459\pi$
$587$	−23.3827	−	13.5000i	−0.965107	−	0.557205i	−0.897741	+	0.440524i	$0.854793\pi$
$588$	5.51856	−	5.18614i	0.227581	−	0.213873i
$589$	−5.62772	−	9.74749i	−0.231886	−	0.401639i
$590$		0			0
$591$	−2.74456	+	9.10268i	−0.112896	+	0.374434i
$592$	3.46410	+	2.00000i	0.142374	+	0.0821995i
$593$			19.7228i			0.809919i	0.914335	+	0.404959i	$0.132714\pi$
$593$			19.7228i			0.809919i	−0.914335	+	0.404959i	$0.867286\pi$
$594$	−21.3030	−	7.89542i	−0.874072	−	0.323953i
$595$		0			0
$596$	−0.941578	+	1.63086i	−0.0385685	+	0.0668027i
$597$	22.3692	+	6.74456i	0.915510	+	0.276037i
$598$	−8.01544	+	4.62772i	−0.327776	+	0.189241i
$599$	−1.88316	−	3.26172i	−0.0769437	−	0.133270i	0.824986	−	0.565153i	$-0.191183\pi$
$599$	−1.88316	−	3.26172i	−0.0769437	−	0.133270i	−0.901930	+	0.431883i	$0.857849\pi$
$600$		0			0
$601$	0.930703	−	1.61203i	0.0379642	−	0.0657559i	−0.846419	−	0.532517i	$-0.821246\pi$
$601$	0.930703	−	1.61203i	0.0379642	−	0.0657559i	0.884383	+	0.466762i	$0.154579\pi$
$602$			18.9783i			0.773496i
$603$	−20.9595	−	1.30298i	−0.853538	−	0.0530616i
$604$	10.0000			0.406894
$605$		0			0
$606$	4.62772	−	1.08724i	0.187988	−	0.0441661i
$607$	15.6896	−	9.05842i	0.636823	−	0.367670i	−0.146567	−	0.989201i	$-0.546822\pi$
$607$	15.6896	−	9.05842i	0.636823	−	0.367670i	0.783390	+	0.621531i	$0.213489\pi$
$608$	−2.05446	+	1.18614i	−0.0833192	+	0.0481044i
$609$	7.80298	−	1.83324i	0.316193	−	0.0742867i
$610$		0			0
$611$	49.7228			2.01157
$612$	4.87375	+	0.302985i	0.197010	+	0.0122474i
$613$		−	34.2337i		−	1.38269i	−0.722527	−	0.691343i	$-0.757019\pi$
$613$		−	34.2337i		−	1.38269i	0.722527	−	0.691343i	$-0.242981\pi$
$614$	−0.616844	+	1.06841i	−0.0248938	+	0.0431173i
$615$		0			0
$616$	−7.37228	−	12.7692i	−0.297038	−	0.514484i
$617$	−4.22894	+	2.44158i	−0.170251	+	0.0982942i	−0.582704	−	0.812684i	$-0.698005\pi$
$617$	−4.22894	+	2.44158i	−0.170251	+	0.0982942i	0.412453	+	0.910979i	$0.364672\pi$
$618$	−26.5330	−	8.00000i	−1.06731	−	0.321807i
$619$	−10.4416	+	18.0853i	−0.419682	+	0.726911i	−0.995907	−	0.0903798i	$-0.971192\pi$
$619$	−10.4416	+	18.0853i	−0.419682	+	0.726911i	0.576225	+	0.817291i	$0.304525\pi$
$620$		0			0
$621$	6.68614	+	2.47805i	0.268306	+	0.0994408i
$622$			20.7446i			0.831781i
$623$	47.0689	+	27.1753i	1.88578	+	1.08875i
$624$	3.37228	−	11.1846i	0.134999	−	0.447742i
$625$		0			0
$626$	1.81386	+	3.14170i	0.0724964	+	0.125567i
$627$	−13.0916	+	12.3030i	−0.522827	+	0.491334i
$628$	−5.84096	−	3.37228i	−0.233080	−	0.134569i
$629$	−6.51087			−0.259606
$630$		0			0
$631$	−23.7228			−0.944390			−0.472195	−	0.881494i	$-0.656538\pi$
$631$	−23.7228			−0.944390			−0.472195	+	0.881494i	$0.656538\pi$
$632$	1.73205	+	1.00000i	0.0688973	+	0.0397779i
$633$	−7.42554	−	31.6060i	−0.295139	−	1.25622i
$634$	−1.37228	−	2.37686i	−0.0545003	−	0.0943972i
$635$		0			0
$636$	19.3723	−	4.55134i	0.768161	−	0.180472i
$637$	25.5383	+	14.7446i	1.01187	+	0.584201i
$638$		−	6.00000i		−	0.237542i
$639$	−15.0000	−	9.94987i	−0.593391	−	0.393611i
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$	10.7147	−	10.0693i	0.422876	−	0.397403i
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	−0.675937	−	0.736959i	$-0.736261\pi$
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	0.300257	+	0.953858i	$0.402928\pi$
$644$	2.31386	+	4.00772i	0.0911788	+	0.157926i
$645$		0			0
$646$	1.93070	−	3.34408i	0.0759625	−	0.131571i
$647$		−	39.0951i		−	1.53699i	−0.639858	−	0.768493i	$-0.721007\pi$
$647$		−	39.0951i		−	1.53699i	0.639858	−	0.768493i	$-0.278993\pi$
$648$	−8.29156	+	3.50000i	−0.325723	+	0.137493i
$649$	19.1168			0.750402
$650$		0			0
$651$	8.00000	−	26.5330i	0.313545	−	1.03991i
$652$	−18.6101	+	10.7446i	−0.728829	+	0.420790i
$653$	−17.0805	+	9.86141i	−0.668410	+	0.385907i	−0.795474	−	0.605988i	$-0.792778\pi$
$653$	−17.0805	+	9.86141i	−0.668410	+	0.385907i	0.127064	+	0.991895i	$0.459445\pi$
$654$	18.2337	+	19.4024i	0.712994	+	0.758694i
$655$		0			0
$656$	−3.00000			−0.117130
$657$	5.16870	−	7.79211i	0.201650	−	0.303999i
$658$		−	24.8614i		−	0.969199i
$659$	8.74456	−	15.1460i	0.340640	−	0.590005i	−0.643912	−	0.765100i	$-0.722690\pi$
$659$	8.74456	−	15.1460i	0.340640	−	0.590005i	0.984552	+	0.175094i	$0.0560230\pi$
$660$		0			0
$661$	6.11684	+	10.5947i	0.237918	+	0.412085i	0.960117	−	0.279600i	$-0.0902018\pi$
$661$	6.11684	+	10.5947i	0.237918	+	0.412085i	−0.722199	+	0.691685i	$0.756868\pi$
$662$	−14.0588	+	8.11684i	−0.546410	+	0.315470i
$663$	4.34896	+	18.5109i	0.168900	+	0.718903i
$664$	−3.68614	+	6.38458i	−0.143050	+	0.247770i
$665$		0			0
$666$	10.7446	−	5.34363i	0.416343	−	0.207061i
$667$			1.88316i			0.0729161i
$668$	11.5807	+	6.68614i	0.448072	+	0.258695i
$669$	−7.86141	−	8.36530i	−0.303940	−	0.323421i
$670$		0			0
$671$	−17.7446	−	30.7345i	−0.685021	−	1.18649i
$672$	−5.59230	−	1.68614i	−0.215727	−	0.0650443i
$673$	−8.66025	−	5.00000i	−0.333828	−	0.192736i	0.323711	−	0.946156i	$-0.395069\pi$
$673$	−8.66025	−	5.00000i	−0.333828	−	0.192736i	−0.657539	+	0.753420i	$0.728403\pi$
$674$	−2.37228			−0.0913769
$675$		0			0
$676$	32.4891			1.24958
$677$	−11.8843	−	6.86141i	−0.456751	−	0.263705i	0.253926	−	0.967224i	$-0.418278\pi$
$677$	−11.8843	−	6.86141i	−0.456751	−	0.263705i	−0.710677	+	0.703518i	$0.751611\pi$
$678$	5.39853	+	1.62772i	0.207329	+	0.0625122i
$679$	−14.1168	−	24.4511i	−0.541755	−	0.938347i
$680$		0			0
$681$	22.6753	+	24.1287i	0.868918	+	0.924613i
$682$	−17.9653	−	10.3723i	−0.687928	−	0.397175i
$683$			30.0951i			1.15156i	0.817606	+	0.575778i	$0.195301\pi$
$683$			30.0951i			1.15156i	−0.817606	+	0.575778i	$0.804699\pi$
$684$	−0.441578	+	7.10313i	−0.0168842	+	0.271595i
$685$		0			0
$686$	−4.43070	+	7.67420i	−0.169165	+	0.293002i
$687$	−5.00239	−	21.2921i	−0.190853	−	0.812345i
$688$	4.87375	−	2.81386i	0.185810	−	0.107277i
$689$	38.7446	+	67.1076i	1.47605	+	2.55659i
$690$		0			0
$691$	18.1168	−	31.3793i	0.689197	−	1.19372i	−0.282901	−	0.959149i	$-0.591297\pi$
$691$	18.1168	−	31.3793i	0.689197	−	1.19372i	0.972098	−	0.234575i	$-0.0753700\pi$
$692$			20.7446i			0.788590i
$693$	−44.1485	−	2.74456i	−1.67706	−	0.104257i
$694$	−4.88316			−0.185362
$695$		0			0
$696$	−1.62772	−	1.73205i	−0.0616985	−	0.0656532i
$697$	4.22894	−	2.44158i	0.160182	−	0.0924814i
$698$	15.6896	−	9.05842i	0.593862	−	0.342866i
$699$	−3.55842	+	11.8020i	−0.134592	+	0.446391i
$700$		0			0
$701$	42.8614			1.61885			0.809426	−	0.587221i	$-0.199778\pi$
$701$	42.8614			1.61885			0.809426	+	0.587221i	$0.199778\pi$
$702$	−22.3692	−	26.9783i	−0.844270	−	1.01823i
$703$		−	9.48913i		−	0.357889i
$704$	−2.18614	+	3.78651i	−0.0823933	+	0.142709i
$705$		0			0
$706$	−10.6753	−	18.4901i	−0.401769	−	0.695884i
$707$	8.01544	−	4.62772i	0.301452	−	0.174043i
$708$	5.51856	−	5.18614i	0.207400	−	0.194907i
$709$	1.43070	−	2.47805i	0.0537312	−	0.0930652i	−0.837909	−	0.545810i	$-0.816222\pi$
$709$	1.43070	−	2.47805i	0.0537312	−	0.0930652i	0.891640	+	0.452745i	$0.149555\pi$
$710$		0			0
$711$	5.37228	−	2.67181i	0.201476	−	0.100201i
$712$		−	16.1168i		−	0.604004i
$713$	5.63858	+	3.25544i	0.211167	+	0.121917i
$714$	9.25544	−	2.17448i	0.346376	−	0.0813779i
$715$		0			0
$716$	7.37228	+	12.7692i	0.275515	+	0.477206i
$717$	1.28962	+	5.48913i	0.0481618	+	0.204995i
$718$	15.1460	+	8.74456i	0.565245	+	0.326344i
$719$	3.76631			0.140460			0.0702299	−	0.997531i	$-0.477627\pi$
$719$	3.76631			0.140460			0.0702299	+	0.997531i	$0.477627\pi$
$720$		0			0
$721$	−53.9565			−2.00945
$722$	−11.5807	−	6.68614i	−0.430990	−	0.248832i
$723$	−15.7634	+	14.8139i	−0.586247	+	0.550933i
$724$	10.4307	+	18.0665i	0.387654	+	0.671436i
$725$		0			0
$726$	−4.05842	+	13.4603i	−0.150622	+	0.499557i
$727$	−15.6896	−	9.05842i	−0.581897	−	0.335958i	0.179990	−	0.983668i	$-0.442393\pi$
$727$	−15.6896	−	9.05842i	−0.581897	−	0.335958i	−0.761887	+	0.647710i	$0.775727\pi$
$728$		−	22.7446i		−	0.842970i
$729$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$730$		0			0
$731$	−4.58017	+	7.93309i	−0.169404	+	0.293416i
$732$	−13.4603	−	4.05842i	−0.497506	−	0.150004i
$733$	0.202380	−	0.116844i	0.00747506	−	0.00431573i	−0.496258	−	0.868175i	$-0.665293\pi$
$733$	0.202380	−	0.116844i	0.00747506	−	0.00431573i	0.503733	+	0.863859i	$0.331960\pi$
$734$	8.00000	+	13.8564i	0.295285	+	0.511449i
$735$		0			0
$736$	0.686141	−	1.18843i	0.0252915	−	0.0438061i
$737$			30.6060i			1.12739i
$738$	−4.97494	+	7.50000i	−0.183130	+	0.276079i
$739$	41.1168			1.51251			0.756254	−	0.654278i	$-0.227028\pi$
$739$	41.1168			1.51251			0.756254	+	0.654278i	$0.227028\pi$
$740$		0			0
$741$	−26.9783	+	6.33830i	−0.991071	+	0.232843i
$742$	33.5538	−	19.3723i	1.23180	−	0.711179i
$743$	−6.82701	+	3.94158i	−0.250459	+	0.144602i	−0.619974	−	0.784622i	$-0.712857\pi$
$743$	−6.82701	+	3.94158i	−0.250459	+	0.144602i	0.369516	+	0.929225i	$0.379524\pi$
$744$	−8.00000	+	1.87953i	−0.293294	+	0.0689068i
$745$		0			0
$746$	15.4891			0.567097
$747$	9.84868	+	19.8030i	0.360345	+	0.724553i
$748$		−	7.11684i		−	0.260218i
$749$	14.3139	−	24.7923i	0.523017	−	0.905892i
$750$		0			0
$751$	−8.11684	−	14.0588i	−0.296188	−	0.513012i	0.679073	−	0.734071i	$-0.262382\pi$
$751$	−8.11684	−	14.0588i	−0.296188	−	0.513012i	−0.975261	+	0.221059i	$0.929049\pi$
$752$	−6.38458	+	3.68614i	−0.232822	+	0.134420i
$753$	40.8044	+	12.3030i	1.48699	+	0.448346i
$754$	4.62772	−	8.01544i	0.168532	−	0.291905i
$755$		0			0
$756$	−13.4891	+	11.1846i	−0.490595	+	0.406780i
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−15.4684	−	8.93070i	−0.561839	−	0.324378i
$759$	3.00000	−	9.94987i	0.108893	−	0.361158i
$760$		0			0
$761$	25.5475	+	44.2496i	0.926098	+	1.60405i	0.789786	+	0.613383i	$0.210192\pi$
$761$	25.5475	+	44.2496i	0.926098	+	1.60405i	0.136312	+	0.990666i	$0.456475\pi$
$762$	−10.2448	+	9.62772i	−0.371131	+	0.348775i
$763$	44.8945	+	25.9198i	1.62529	+	0.938361i
$764$	−17.4891			−0.632734
$765$		0			0
$766$	22.9783			0.830238
$767$	25.5383	+	14.7446i	0.922136	+	0.532395i
$768$	0.396143	+	1.68614i	0.0142946	+	0.0608434i
$769$	−23.4307	−	40.5832i	−0.844933	−	1.46347i	−0.885680	−	0.464297i	$-0.846307\pi$
$769$	−23.4307	−	40.5832i	−0.844933	−	1.46347i	0.0407468	−	0.999170i	$-0.487026\pi$
$770$		0			0
$771$	−7.37228	+	1.73205i	−0.265506	+	0.0623783i
$772$	−18.2877	−	10.5584i	−0.658190	−	0.380006i
$773$		−	3.25544i		−	0.117090i	−0.998285	−	0.0585450i	$-0.981354\pi$
$773$		−	3.25544i		−	0.117090i	0.998285	−	0.0585450i	$-0.0186461\pi$
$774$	1.04755	−	16.8506i	0.0376533	−	0.605683i
$775$		0			0
$776$	−4.18614	+	7.25061i	−0.150274	+	0.260282i
$777$	17.0256	−	16.0000i	0.610788	−	0.573997i
$778$	−4.00772	+	2.31386i	−0.143684	+	0.0829559i
$779$	3.55842	+	6.16337i	0.127494	+	0.220826i
$780$		0			0
$781$	−13.1168	+	22.7190i	−0.469358	+	0.812951i
$782$			2.23369i			0.0798765i
$783$	−7.02939	+	1.19702i	−0.251210	+	0.0427778i
$784$	−4.37228			−0.156153
$785$		0			0
$786$	1.37228	−	4.55134i	0.0489477	−	0.162341i
$787$	−24.2487	+	14.0000i	−0.864373	+	0.499046i	−0.865474	−	0.500953i	$-0.832983\pi$
$787$	−24.2487	+	14.0000i	−0.864373	+	0.499046i	0.00110111	+	0.999999i	$0.499650\pi$
$788$	4.75372	−	2.74456i	0.169344	−	0.0977710i
$789$	20.7446	+	22.0742i	0.738526	+	0.785863i
$790$		0			0
$791$	10.9783			0.390342
$792$	5.84096	+	11.7446i	0.207550	+	0.417325i
$793$		−	54.7446i		−	1.94404i
$794$	−11.3723	+	19.6974i	−0.403587	+	0.699033i
$795$		0			0
$796$	−6.74456	−	11.6819i	−0.239055	−	0.414055i
$797$	12.7692	−	7.37228i	0.452307	−	0.261140i	−0.256497	−	0.966545i	$-0.582568\pi$
$797$	12.7692	−	7.37228i	0.452307	−	0.261140i	0.708804	+	0.705405i	$0.249235\pi$
$798$	3.16915	+	13.4891i	0.112187	+	0.477510i
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$		0			0
$801$	−40.2921	−	26.7268i	−1.42365	−	0.944344i
$802$			1.11684i			0.0394371i
$803$	−11.8020	−	6.81386i	−0.416482	−	0.240456i
$804$	8.30298	+	8.83518i	0.292824	+	0.311593i
$805$		0			0
$806$	−16.0000	−	27.7128i	−0.563576	−	0.976142i
$807$	−2.27567	−	0.686141i	−0.0801074	−	0.0241533i
$808$	−2.37686	−	1.37228i	−0.0836177	−	0.0482767i
$809$	−39.3505			−1.38349			−0.691746	−	0.722141i	$-0.743158\pi$
$809$	−39.3505			−1.38349			−0.691746	+	0.722141i	$0.743158\pi$
$810$		0			0
$811$	3.62772			0.127386			0.0636932	−	0.997970i	$-0.479712\pi$
$811$	3.62772			0.127386			0.0636932	+	0.997970i	$0.479712\pi$
$812$	−4.00772	−	2.31386i	−0.140643	−	0.0812005i
$813$	−13.2665	−	4.00000i	−0.465276	−	0.140286i
$814$	−8.74456	−	15.1460i	−0.306497	−	0.530868i
$815$		0			0
$816$	−1.93070	−	2.05446i	−0.0675881	−	0.0719203i
$817$	−11.5619	−	6.67527i	−0.404500	−	0.233538i
$818$			17.8614i			0.624509i
$819$	−56.8614	−	37.7176i	−1.98690	−	1.31796i
$820$		0			0
$821$	11.9198	−	20.6457i	0.416005	−	0.720542i	−0.579528	−	0.814952i	$-0.696763\pi$
$821$	11.9198	−	20.6457i	0.416005	−	0.720542i	0.995533	+	0.0944104i	$0.0300966\pi$
$822$	−7.57301	−	32.2337i	−0.264139	−	1.12428i
$823$	21.7330	−	12.5475i	0.757564	−	0.437380i	−0.0708562	−	0.997487i	$-0.522573\pi$
$823$	21.7330	−	12.5475i	0.757564	−	0.437380i	0.828421	+	0.560107i	$0.189240\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$	7.37228	−	12.7692i	0.256514	−	0.444296i
$827$			36.8614i			1.28180i	0.767626	+	0.640898i	$0.221438\pi$
$827$			36.8614i			1.28180i	−0.767626	+	0.640898i	$0.778562\pi$
$828$	−1.83324	−	3.68614i	−0.0637095	−	0.128102i
$829$	50.1168			1.74063			0.870315	−	0.492496i	$-0.163915\pi$
$829$	50.1168			1.74063			0.870315	+	0.492496i	$0.163915\pi$
$830$		0			0
$831$	19.8614	+	21.1345i	0.688985	+	0.733147i
$832$	−5.84096	+	3.37228i	−0.202499	+	0.116913i
$833$	6.16337	−	3.55842i	0.213548	−	0.123292i
$834$	0.441578	−	1.46455i	0.0152906	−	0.0507132i
$835$		0			0
$836$	10.3723			0.358733
$837$	−8.56768	+	23.1168i	−0.296142	+	0.799035i
$838$			25.7228i			0.888580i
$839$	4.88316	−	8.45787i	0.168585	−	0.291998i	−0.769337	−	0.638843i	$-0.779413\pi$
$839$	4.88316	−	8.45787i	0.168585	−	0.291998i	0.937923	+	0.346844i	$0.112747\pi$
$840$		0			0
$841$	13.5584	+	23.4839i	0.467532	+	0.809789i
$842$	−26.3855	+	15.2337i	−0.909305	+	0.524988i
$843$	−1.73205	+	1.62772i	−0.0596550	+	0.0560616i
$844$	−9.37228	+	16.2333i	−0.322607	+	0.558772i
$845$		0			0
$846$	−1.37228	+	22.0742i	−0.0471800	+	0.758928i
$847$			27.3723i			0.940523i
$848$	−9.94987	−	5.74456i	−0.341680	−	0.197269i
$849$	−5.29211	+	1.24333i	−0.181625	+	0.0426711i
$850$		0			0
$851$	2.74456	+	4.75372i	0.0940824	+	0.162955i
$852$	2.37686	+	10.1168i	0.0814299	+	0.346597i
$853$	−31.3793	−	18.1168i	−1.07441	−	0.620309i	−0.145024	−	0.989428i	$-0.546326\pi$
$853$	−31.3793	−	18.1168i	−1.07441	−	0.620309i	−0.929382	+	0.369119i	$0.879659\pi$
$854$	−27.3723			−0.936660
$855$		0			0
$856$	−8.48913			−0.290152
$857$	−0.442430	−	0.255437i	−0.0151131	−	0.00872557i	0.492424	−	0.870355i	$-0.336111\pi$
$857$	−0.442430	−	0.255437i	−0.0151131	−	0.00872557i	−0.507538	+	0.861630i	$0.669444\pi$
$858$	−37.2203	+	34.9783i	−1.27068	+	1.19414i
$859$	−8.55842	−	14.8236i	−0.292010	−	0.505775i	0.682275	−	0.731095i	$-0.260991\pi$
$859$	−8.55842	−	14.8236i	−0.292010	−	0.505775i	−0.974285	+	0.225320i	$0.927657\pi$
$860$		0			0
$861$	−5.05842	+	16.7769i	−0.172391	+	0.571755i
$862$	7.13058	+	4.11684i	0.242869	+	0.140220i
$863$			2.39403i			0.0814938i	0.999170	+	0.0407469i	$0.0129737\pi$
$863$			2.39403i			0.0814938i	−0.999170	+	0.0407469i	$0.987026\pi$
$864$	4.87228	+	1.80579i	0.165758	+	0.0614342i
$865$		0			0
$866$	3.18614	−	5.51856i	0.108269	−	0.187528i
$867$	−23.7977	−	7.17527i	−0.808211	−	0.243685i
$868$	−13.8564	+	8.00000i	−0.470317	+	0.271538i
$869$	−4.37228	−	7.57301i	−0.148319	−	0.256897i
$870$		0			0
$871$	−23.6060	+	40.8867i	−0.799858	+	1.38539i
$872$		−	15.3723i		−	0.520571i
$873$	11.1846	+	22.4891i	0.378541	+	0.761142i
$874$	−3.25544			−0.110117
$875$		0			0
$876$	−5.25544	+	1.23472i	−0.177565	+	0.0417172i
$877$	31.1392	−	17.9783i	1.05150	−	0.607082i	0.128429	−	0.991719i	$-0.459006\pi$
$877$	31.1392	−	17.9783i	1.05150	−	0.607082i	0.923068	+	0.384636i	$0.125673\pi$
$878$	−15.7908	+	9.11684i	−0.532915	+	0.307679i
$879$	44.2337	−	10.3923i	1.49197	−	0.350524i
$880$		0			0
$881$	−24.3505			−0.820390			−0.410195	−	0.911998i	$-0.634539\pi$
$881$	−24.3505			−0.820390			−0.410195	+	0.911998i	$0.634539\pi$
$882$	−7.25061	+	10.9307i	−0.244141	+	0.368056i
$883$			44.7228i			1.50504i	0.658568	+	0.752521i	$0.271163\pi$
$883$			44.7228i			1.50504i	−0.658568	+	0.752521i	$0.728837\pi$
$884$	5.48913	−	9.50744i	0.184619	−	0.319770i
$885$		0			0
$886$	−1.75544	−	3.04051i	−0.0589751	−	0.102148i
$887$	17.0805	−	9.86141i	0.573506	−	0.331114i	−0.185043	−	0.982730i	$-0.559242\pi$
$887$	17.0805	−	9.86141i	0.573506	−	0.331114i	0.758548	+	0.651617i	$0.225909\pi$
$888$	−6.63325	−	2.00000i	−0.222597	−	0.0671156i
$889$	−13.6861	+	23.7051i	−0.459018	+	0.795043i
$890$		0			0
$891$	39.0475	+	4.87375i	1.30814	+	0.163277i
$892$			6.62772i			0.221912i
$893$	15.1460	+	8.74456i	0.506842	+	0.292626i
$894$	0.941578	−	3.12286i	0.0314911	−	0.104444i
$895$		0			0
$896$	1.68614	+	2.92048i	0.0563300	+	0.0975664i
$897$	11.6819	−	10.9783i	0.390048	−	0.366553i
$898$	−8.54023	−	4.93070i	−0.284991	−	0.164540i
$899$	−6.51087			−0.217150
$900$		0			0
$901$	18.7011			0.623023
$902$	11.3595	+	6.55842i	0.378231	+	0.218372i
$903$	−7.51811	−	32.0000i	−0.250187	−	1.06489i
$904$	−1.62772	−	2.81929i	−0.0541371	−	0.0937682i
$905$		0			0
$906$	−16.8614	+	3.96143i	−0.560183	+	0.131610i
$907$	6.06218	+	3.50000i	0.201291	+	0.116216i	0.597258	−	0.802049i	$-0.296257\pi$
$907$	6.06218	+	3.50000i	0.201291	+	0.116216i	−0.395966	+	0.918265i	$0.629590\pi$
$908$		−	19.1168i		−	0.634415i
$909$	−7.37228	+	3.66648i	−0.244523	+	0.121610i
$910$		0			0
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	−0.274162	−	0.961683i	$-0.588401\pi$
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	0.969923	−	0.243410i	$-0.0782661\pi$
$912$	2.99422	−	2.81386i	0.0991485	−	0.0931762i
$913$	27.9152	−	16.1168i	0.923858	−	0.533390i
$914$	−6.44158	−	11.1571i	−0.213068	−	0.369045i
$915$		0			0
$916$	−6.31386	+	10.9359i	−0.208616	+	0.361333i
$917$		−	9.25544i		−	0.305641i
$918$	−8.33785	+	1.41983i	−0.275190	+	0.0468613i
$919$	26.4674			0.873078			0.436539	−	0.899685i	$-0.356204\pi$
$919$	26.4674			0.873078			0.436539	+	0.899685i	$0.356204\pi$
$920$		0			0
$921$	0.616844	−	2.04584i	0.0203257	−	0.0674127i
$922$	−1.63086	+	0.941578i	−0.0537095	+	0.0310092i
$923$	−35.0458	+	20.2337i	−1.15355	+	0.666000i
$924$	17.4891	+	18.6101i	0.575350	+	0.612228i
$925$		0			0
$926$	−20.0000			−0.657241
$927$	47.9075	+	2.97825i	1.57349	+	0.0978186i
$928$			1.37228i			0.0450473i
$929$	25.9783	−	44.9956i	0.852319	−	1.47626i	−0.0267916	−	0.999641i	$-0.508529\pi$
$929$	25.9783	−	44.9956i	0.852319	−	1.47626i	0.879110	−	0.476618i	$-0.158138\pi$
$930$		0			0
$931$	5.18614	+	8.98266i	0.169969	+	0.294395i
$932$	6.16337	−	3.55842i	0.201888	−	0.116560i
$933$	−8.21782	−	34.9783i	−0.269039	−	1.14514i
$934$	−21.5584	+	37.3403i	−0.705413	+	1.22181i
$935$		0			0
$936$	−1.25544	+	20.1947i	−0.0410353	+	0.660084i
$937$			39.7228i			1.29769i	0.760922	+	0.648844i	$0.224747\pi$
$937$			39.7228i			1.29769i	−0.760922	+	0.648844i	$0.775253\pi$
$938$	20.4434	+	11.8030i	0.667500	+	0.385381i
$939$	−4.30298	−	4.57879i	−0.140423	−	0.149423i
$940$		0			0
$941$	−21.6861	−	37.5615i	−0.706948	−	1.22447i	−0.965984	−	0.258602i	$-0.916738\pi$
$941$	−21.6861	−	37.5615i	−0.706948	−	1.22447i	0.259036	−	0.965868i	$-0.416595\pi$
$942$	11.1846	+	3.37228i	0.364414	+	0.109875i
$943$	−3.56529	−	2.05842i	−0.116102	−	0.0670314i
$944$	−4.37228			−0.142306
$945$		0			0
$946$	−24.6060			−0.800009
$947$	30.0708	+	17.3614i	0.977171	+	0.564170i	0.901415	−	0.432956i	$-0.142530\pi$
$947$	30.0708	+	17.3614i	0.977171	+	0.564170i	0.0757561	+	0.997126i	$0.475863\pi$
$948$	−3.31662	−	1.00000i	−0.107719	−	0.0324785i
$949$	−10.5109	−	18.2054i	−0.341197	−	0.590971i
$950$		0			0
$951$	3.25544	+	3.46410i	0.105565	+	0.112331i
$952$	−4.75372	−	2.74456i	−0.154069	−	0.0889518i
$953$		−	2.13859i		−	0.0692758i	−0.999400	−	0.0346379i	$-0.988972\pi$
$953$		−	2.13859i		−	0.0692758i	0.999400	−	0.0346379i	$-0.0110278\pi$
$954$	−30.8614	+	15.3484i	−0.999175	+	0.496923i
$955$		0			0
$956$	1.62772	−	2.81929i	0.0526442	−	0.0911824i
$957$	2.37686	+	10.1168i	0.0768330	+	0.327031i
$958$	−0.442430	+	0.255437i	−0.0142943	+	0.00825281i
$959$	−32.2337	−	55.8304i	−1.04088	−	1.80286i
$960$		0			0
$961$	4.24456	−	7.35180i	0.136921	−	0.237155i
$962$		−	26.9783i		−	0.869814i
$963$	−14.0776	+	21.2228i	−0.453645	+	0.683896i
$964$	12.4891			0.402248
$965$		0			0
$966$	−5.48913	−	5.84096i	−0.176610	−	0.187930i
$967$	31.2781	−	18.0584i	1.00584	−	0.580720i	0.0958662	−	0.995394i	$-0.469438\pi$
$967$	31.2781	−	18.0584i	1.00584	−	0.580720i	0.909970	+	0.414675i	$0.136105\pi$
$968$	7.02939	−	4.05842i	0.225933	−	0.130443i
$969$	−1.93070	+	6.40342i	−0.0620231	+	0.205707i
$970$		0			0
$971$	−22.9783			−0.737407			−0.368704	−	0.929547i	$-0.620198\pi$
$971$	−22.9783			−0.737407			−0.368704	+	0.929547i	$0.620198\pi$
$972$	12.5942	−	9.18614i	0.403960	−	0.294646i
$973$		−	2.97825i		−	0.0954783i
$974$	6.37228	−	11.0371i	0.204181	−	0.353652i
$975$		0			0
$976$	4.05842	+	7.02939i	0.129907	+	0.225005i
$977$	−19.8174	+	11.4416i	−0.634015	+	0.366049i	−0.782305	−	0.622895i	$-0.785956\pi$
$977$	−19.8174	+	11.4416i	−0.634015	+	0.366049i	0.148291	+	0.988944i	$0.452623\pi$
$978$	27.1229	−	25.4891i	0.867295	−	0.815052i
$979$	−35.2337	+	61.0265i	−1.12607	+	1.95042i
$980$		0			0
$981$	−38.4307	−	25.4920i	−1.22700	−	0.813898i
$982$			36.6060i			1.16814i
$983$	−11.1383	−	6.43070i	−0.355257	−	0.205108i	0.311741	−	0.950167i	$-0.399088\pi$
$983$	−11.1383	−	6.43070i	−0.355257	−	0.205108i	−0.666998	+	0.745059i	$0.732421\pi$
$984$	5.05842	−	1.18843i	0.161257	−	0.0378858i
$985$		0			0
$986$	−1.11684	−	1.93443i	−0.0355676	−	0.0616048i
$987$	9.84868	+	41.9198i	0.313487	+	1.33432i
$988$	13.8564	+	8.00000i	0.440831	+	0.254514i
$989$	7.72281			0.245571
$990$		0			0
$991$	16.2337			0.515680			0.257840	−	0.966188i	$-0.416989\pi$
$991$	16.2337			0.515680			0.257840	+	0.966188i	$0.416989\pi$
$992$	4.10891	+	2.37228i	0.130458	+	0.0753200i
$993$	20.4897	−	19.2554i	0.650220	−	0.611053i
$994$	10.1168	+	17.5229i	0.320887	+	0.555792i
$995$		0			0
$996$	3.68614	−	12.2255i	0.116800	−	0.387381i
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$998$			15.1168i			0.478515i
$999$	−16.0000	+	13.2665i	−0.506218	+	0.419733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.j.g.349.3		8
3.2	odd	2		1350.2.j.f.1099.1		8
5.2	odd	4		450.2.e.j.151.2		4
5.3	odd	4		90.2.e.c.61.1	yes	4
5.4	even	2	inner	450.2.j.g.349.2		8
9.2	odd	6		4050.2.c.ba.649.4		4
9.4	even	3	inner	450.2.j.g.49.2		8
9.5	odd	6		1350.2.j.f.199.4		8
9.7	even	3		4050.2.c.v.649.2		4
15.2	even	4		1350.2.e.l.451.2		4
15.8	even	4		270.2.e.c.181.1		4
15.14	odd	2		1350.2.j.f.1099.4		8
20.3	even	4		720.2.q.f.241.2		4
45.2	even	12		4050.2.a.bo.1.1		2
45.4	even	6	inner	450.2.j.g.49.3		8
45.7	odd	12		4050.2.a.bw.1.1		2
45.13	odd	12		90.2.e.c.31.2	✓	4
45.14	odd	6		1350.2.j.f.199.1		8
45.22	odd	12		450.2.e.j.301.1		4
45.23	even	12		270.2.e.c.91.1		4
45.29	odd	6		4050.2.c.ba.649.1		4
45.32	even	12		1350.2.e.l.901.2		4
45.34	even	6		4050.2.c.v.649.3		4
45.38	even	12		810.2.a.k.1.2		2
45.43	odd	12		810.2.a.i.1.2		2
60.23	odd	4		2160.2.q.f.721.2		4
180.23	odd	12		2160.2.q.f.1441.2		4
180.43	even	12		6480.2.a.be.1.1		2
180.83	odd	12		6480.2.a.bn.1.1		2
180.103	even	12		720.2.q.f.481.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.2	✓	4	45.13	odd	12
90.2.e.c.61.1	yes	4	5.3	odd	4
270.2.e.c.91.1		4	45.23	even	12
270.2.e.c.181.1		4	15.8	even	4
450.2.e.j.151.2		4	5.2	odd	4
450.2.e.j.301.1		4	45.22	odd	12
450.2.j.g.49.2		8	9.4	even	3	inner
450.2.j.g.49.3		8	45.4	even	6	inner
450.2.j.g.349.2		8	5.4	even	2	inner
450.2.j.g.349.3		8	1.1	even	1	trivial
720.2.q.f.241.2		4	20.3	even	4
720.2.q.f.481.1		4	180.103	even	12
810.2.a.i.1.2		2	45.43	odd	12
810.2.a.k.1.2		2	45.38	even	12
1350.2.e.l.451.2		4	15.2	even	4
1350.2.e.l.901.2		4	45.32	even	12
1350.2.j.f.199.1		8	45.14	odd	6
1350.2.j.f.199.4		8	9.5	odd	6
1350.2.j.f.1099.1		8	3.2	odd	2
1350.2.j.f.1099.4		8	15.14	odd	2
2160.2.q.f.721.2		4	60.23	odd	4
2160.2.q.f.1441.2		4	180.23	odd	12
4050.2.a.bo.1.1		2	45.2	even	12
4050.2.a.bw.1.1		2	45.7	odd	12
4050.2.c.v.649.2		4	9.7	even	3
4050.2.c.v.649.3		4	45.34	even	6
4050.2.c.ba.649.1		4	45.29	odd	6
4050.2.c.ba.649.4		4	9.2	odd	6
6480.2.a.be.1.1		2	180.43	even	12
6480.2.a.bn.1.1		2	180.83	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.65831 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.18614 - 1.26217i) q^{6} +(-2.92048 - 1.68614i) q^{7} +1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(2.18614 - 3.78651i) q^{11} +(-0.396143 - 1.68614i) q^{12} +(5.84096 - 3.37228i) q^{13} +(-1.68614 - 2.92048i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.62772i q^{17} +(1.33591 + 2.68614i) q^{18} +2.37228 q^{19} +(4.00000 + 4.25639i) q^{21} +(3.78651 - 2.18614i) q^{22} +(-1.18843 + 0.686141i) q^{23} +(0.500000 - 1.65831i) q^{24} +6.74456 q^{26} +(-3.31662 - 4.00000i) q^{27} -3.37228i q^{28} +(0.686141 - 1.18843i) q^{29} +(-2.37228 - 4.10891i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.51856 + 5.18614i) q^{33} +(0.813859 - 1.40965i) q^{34} +(-0.186141 + 2.99422i) q^{36} -4.00000i q^{37} +(2.05446 + 1.18614i) q^{38} +(-11.3723 + 2.67181i) q^{39} +(1.50000 + 2.59808i) q^{41} +(1.33591 + 5.68614i) q^{42} +(-4.87375 - 2.81386i) q^{43} +4.37228 q^{44} -1.37228 q^{46} +(6.38458 + 3.68614i) q^{47} +(1.26217 - 1.18614i) q^{48} +(2.18614 + 3.78651i) q^{49} +(-0.813859 + 2.69927i) q^{51} +(5.84096 + 3.37228i) q^{52} +11.4891i q^{53} +(-0.872281 - 5.12241i) q^{54} +(1.68614 - 2.92048i) q^{56} +(-3.93398 - 1.18614i) q^{57} +(1.18843 - 0.686141i) q^{58} +(2.18614 + 3.78651i) q^{59} +(4.05842 - 7.02939i) q^{61} -4.74456i q^{62} +(-4.50506 - 9.05842i) q^{63} -1.00000 q^{64} +(-7.37228 + 1.73205i) q^{66} +(-6.06218 + 3.50000i) q^{67} +(1.40965 - 0.813859i) q^{68} +(2.31386 - 0.543620i) q^{69} -6.00000 q^{71} +(-1.65831 + 2.50000i) q^{72} -3.11684i q^{73} +(2.00000 - 3.46410i) q^{74} +(1.18614 + 2.05446i) q^{76} +(-12.7692 + 7.37228i) q^{77} +(-11.1846 - 3.37228i) q^{78} +(1.00000 - 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} +3.00000i q^{82} +(6.38458 + 3.68614i) q^{83} +(-1.68614 + 5.59230i) q^{84} +(-2.81386 - 4.87375i) q^{86} +(-1.73205 + 1.62772i) q^{87} +(3.78651 + 2.18614i) q^{88} -16.1168 q^{89} -22.7446 q^{91} +(-1.18843 - 0.686141i) q^{92} +(1.87953 + 8.00000i) q^{93} +(3.68614 + 6.38458i) q^{94} +(1.68614 - 0.396143i) q^{96} +(7.25061 + 4.18614i) q^{97} +4.37228i q^{98} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9} + 6 q^{11} - 2 q^{14} - 4 q^{16} - 4 q^{19} + 32 q^{21} + 4 q^{24} + 8 q^{26} - 6 q^{29} + 4 q^{31} + 18 q^{34} + 10 q^{36} - 68 q^{39} + 12 q^{41} + 12 q^{44} + 12 q^{46}+ \cdots + 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9 + 6 * q^11 - 2 * q^14 - 4 * q^16 - 4 * q^19 + 32 * q^21 + 4 * q^24 + 8 * q^26 - 6 * q^29 + 4 * q^31 + 18 * q^34 + 10 * q^36 - 68 * q^39 + 12 * q^41 + 12 * q^44 + 12 * q^46 + 6 * q^49 - 18 * q^51 + 16 * q^54 + 2 * q^56 + 6 * q^59 - 2 * q^61 - 8 * q^64 - 36 * q^66 + 30 * q^69 - 48 * q^71 + 16 * q^74 - 2 * q^76 + 8 * q^79 + 28 * q^81 - 2 * q^84 - 34 * q^86 - 60 * q^89 - 136 * q^91 + 18 * q^94 + 2 * q^96 + 48 * q^99

Introduction

L-functions

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