LMFDB - Embedded newform 450.2.e.j.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(151,450)] 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([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.151"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,-2,-2,0,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	450.151
Dual form			450.2.e.j.301.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68614 + 0.396143i) q^{6} +(-1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +(-0.686141 + 1.18843i) q^{11} +(-1.18614 + 1.26217i) q^{12} +(2.37228 + 4.10891i) q^{13} +(-1.18614 - 2.05446i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.37228 q^{17} +(-0.186141 - 2.99422i) q^{18} +3.37228 q^{19} +(4.00000 + 0.939764i) q^{21} +(-0.686141 - 1.18843i) q^{22} +(-2.18614 - 3.78651i) q^{23} +(-0.500000 - 1.65831i) q^{24} -4.74456 q^{26} +(4.00000 + 3.31662i) q^{27} +2.37228 q^{28} +(2.18614 - 3.78651i) q^{29} +(3.37228 + 5.84096i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.31386 + 0.543620i) q^{33} +(-3.68614 + 6.38458i) q^{34} +(2.68614 + 1.33591i) q^{36} +4.00000 q^{37} +(-1.68614 + 2.92048i) q^{38} +(5.62772 - 5.98844i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-2.81386 + 2.99422i) q^{42} +(-5.68614 + 9.84868i) q^{43} +1.37228 q^{44} +4.37228 q^{46} +(-0.813859 + 1.40965i) q^{47} +(1.68614 + 0.396143i) q^{48} +(0.686141 + 1.18843i) q^{49} +(-3.68614 - 12.2255i) q^{51} +(2.37228 - 4.10891i) q^{52} -11.4891 q^{53} +(-4.87228 + 1.80579i) q^{54} +(-1.18614 + 2.05446i) q^{56} +(-1.68614 - 5.59230i) q^{57} +(2.18614 + 3.78651i) q^{58} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} -6.74456 q^{62} +(-0.441578 - 7.10313i) q^{63} +1.00000 q^{64} +(-1.62772 + 1.73205i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-3.68614 - 6.38458i) q^{68} +(-5.18614 + 5.51856i) q^{69} -6.00000 q^{71} +(-2.50000 + 1.65831i) q^{72} +14.1168 q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.68614 - 2.92048i) q^{76} +(-1.62772 - 2.81929i) q^{77} +(2.37228 + 7.86797i) q^{78} +(-1.00000 + 1.73205i) q^{79} +(3.50000 - 8.29156i) q^{81} -3.00000 q^{82} +(0.813859 - 1.40965i) q^{83} +(-1.18614 - 3.93398i) q^{84} +(-5.68614 - 9.84868i) q^{86} +(-7.37228 - 1.73205i) q^{87} +(-0.686141 + 1.18843i) q^{88} -1.11684 q^{89} -11.2554 q^{91} +(-2.18614 + 3.78651i) q^{92} +(8.00000 - 8.51278i) q^{93} +(-0.813859 - 1.40965i) q^{94} +(-1.18614 + 1.26217i) q^{96} +(-1.31386 + 2.27567i) q^{97} -1.37228 q^{98} +(-0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{6} + q^{7} + 4 q^{8} - 10 q^{9} + 3 q^{11} + q^{12} - 2 q^{13} + q^{14} - 2 q^{16} + 18 q^{17} + 5 q^{18} + 2 q^{19} + 16 q^{21} + 3 q^{22} - 3 q^{23} - 2 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^6 + q^7 + 4 * q^8 - 10 * q^9 + 3 * q^11 + q^12 - 2 * q^13 + q^14 - 2 * q^16 + 18 * q^17 + 5 * q^18 + 2 * q^19 + 16 * q^21 + 3 * q^22 - 3 * q^23 - 2 * q^24 + 4 * q^26 + 16 * q^27 - 2 * q^28 + 3 * q^29 + 2 * q^31 - 2 * q^32 + 15 * q^33 - 9 * q^34 + 5 * q^36 + 16 * q^37 - q^38 + 34 * q^39 + 6 * q^41 - 17 * q^42 - 17 * q^43 - 6 * q^44 + 6 * q^46 - 9 * q^47 + q^48 - 3 * q^49 - 9 * q^51 - 2 * q^52 - 8 * q^54 + q^56 - q^57 + 3 * q^58 - 3 * q^59 - q^61 - 4 * q^62 - 19 * q^63 + 4 * q^64 - 18 * q^66 - 14 * q^67 - 9 * q^68 - 15 * q^69 - 24 * q^71 - 10 * q^72 + 22 * q^73 - 8 * q^74 - q^76 - 18 * q^77 - 2 * q^78 - 4 * q^79 + 14 * q^81 - 12 * q^82 + 9 * q^83 + q^84 - 17 * q^86 - 18 * q^87 + 3 * q^88 + 30 * q^89 - 68 * q^91 - 3 * q^92 + 32 * q^93 - 9 * q^94 + q^96 - 11 * q^97 + 6 * q^98 - 24 * 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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	1.65831i	−0.288675	−	0.957427i
$3$	−0.500000	−	1.65831i	−0.288675	−	0.957427i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.68614	+	0.396143i	0.688364	+	0.161725i
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	−0.998277	−	0.0586811i	$-0.981310\pi$
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	0.549958	+	0.835192i	$0.314644\pi$
$8$	1.00000			0.353553
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$		0			0
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	−0.950730	−	0.310021i	$-0.899664\pi$
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	0.743851	+	0.668346i	$0.232997\pi$
$12$	−1.18614	+	1.26217i	−0.342409	+	0.364357i
$13$	2.37228	+	4.10891i	0.657952	+	1.13961i	0.981145	+	0.193274i	$0.0619106\pi$
$13$	2.37228	+	4.10891i	0.657952	+	1.13961i	−0.323192	+	0.946333i	$0.604756\pi$
$14$	−1.18614	−	2.05446i	−0.317009	−	0.549076i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.37228			1.78804			0.894020	−	0.448026i	$-0.147873\pi$
$17$	7.37228			1.78804			0.894020	+	0.448026i	$0.147873\pi$
$18$	−0.186141	−	2.99422i	−0.0438738	−	0.705744i
$19$	3.37228			0.773654			0.386827	−	0.922152i	$-0.373571\pi$
$19$	3.37228			0.773654			0.386827	+	0.922152i	$0.373571\pi$
$20$		0			0
$21$	4.00000	+	0.939764i	0.872872	+	0.205073i
$22$	−0.686141	−	1.18843i	−0.146286	−	0.253374i
$23$	−2.18614	−	3.78651i	−0.455842	−	0.789541i	0.542894	−	0.839801i	$-0.317328\pi$
$23$	−2.18614	−	3.78651i	−0.455842	−	0.789541i	−0.998736	+	0.0502598i	$0.983995\pi$
$24$	−0.500000	−	1.65831i	−0.102062	−	0.338502i
$25$		0			0
$26$	−4.74456			−0.930485
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$	2.37228			0.448319
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	−0.588476	−	0.808515i	$-0.700272\pi$
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	0.994432	+	0.105378i	$0.0336052\pi$
$30$		0			0
$31$	3.37228	+	5.84096i	0.605680	+	1.04907i	0.991944	+	0.126680i	$0.0404320\pi$
$31$	3.37228	+	5.84096i	0.605680	+	1.04907i	−0.386264	+	0.922388i	$0.626235\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.31386	+	0.543620i	0.402791	+	0.0946322i
$34$	−3.68614	+	6.38458i	−0.632168	+	1.09495i
$35$		0			0
$36$	2.68614	+	1.33591i	0.447690	+	0.222651i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−1.68614	+	2.92048i	−0.273528	+	0.473765i
$39$	5.62772	−	5.98844i	0.901156	−	0.958918i
$40$		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	$0.758066\pi$
$42$	−2.81386	+	2.99422i	−0.434188	+	0.462018i
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.00221007	+	0.999998i	$0.500703\pi$
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.864918	+	0.501913i	$0.832630\pi$
$44$	1.37228			0.206879
$45$		0			0
$46$	4.37228			0.644658
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	−0.919258	−	0.393655i	$-0.871210\pi$
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	0.800545	+	0.599273i	$0.204544\pi$
$48$	1.68614	+	0.396143i	0.243373	+	0.0571784i
$49$	0.686141	+	1.18843i	0.0980201	+	0.169776i
$50$		0			0
$51$	−3.68614	−	12.2255i	−0.516163	−	1.71192i
$52$	2.37228	−	4.10891i	0.328976	−	0.569804i
$53$	−11.4891			−1.57815			−0.789076	−	0.614295i	$-0.789440\pi$
$53$	−11.4891			−1.57815			−0.789076	+	0.614295i	$0.789440\pi$
$54$	−4.87228	+	1.80579i	−0.663034	+	0.245737i
$55$		0			0
$56$	−1.18614	+	2.05446i	−0.158505	+	0.274538i
$57$	−1.68614	−	5.59230i	−0.223335	−	0.740718i
$58$	2.18614	+	3.78651i	0.287054	+	0.497193i
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	0.907227	−	0.420641i	$-0.138195\pi$
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	−0.817899	+	0.575361i	$0.804861\pi$
$60$		0			0
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	0.411397	+	0.911456i	$0.365041\pi$
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	−0.995043	+	0.0994483i	$0.968292\pi$
$62$	−6.74456			−0.856560
$63$	−0.441578	−	7.10313i	−0.0556336	−	0.894910i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.62772	+	1.73205i	−0.200358	+	0.213201i
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$	−3.68614	−	6.38458i	−0.447010	−	0.774244i
$69$	−5.18614	+	5.51856i	−0.624338	+	0.664356i
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−2.50000	+	1.65831i	−0.294628	+	0.195434i
$73$	14.1168			1.65225			0.826126	−	0.563486i	$-0.190540\pi$
$73$	14.1168			1.65225			0.826126	+	0.563486i	$0.190540\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−1.68614	−	2.92048i	−0.193414	−	0.335002i
$77$	−1.62772	−	2.81929i	−0.185496	−	0.321288i
$78$	2.37228	+	7.86797i	0.268608	+	0.890872i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$		0			0
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$	−3.00000			−0.331295
$83$	0.813859	−	1.40965i	0.0893327	−	0.154729i	−0.817897	−	0.575365i	$-0.804860\pi$
$83$	0.813859	−	1.40965i	0.0893327	−	0.154729i	0.907229	+	0.420637i	$0.138193\pi$
$84$	−1.18614	−	3.93398i	−0.129419	−	0.429233i
$85$		0			0
$86$	−5.68614	−	9.84868i	−0.613152	−	1.06201i
$87$	−7.37228	−	1.73205i	−0.790392	−	0.185695i
$88$	−0.686141	+	1.18843i	−0.0731428	+	0.126687i
$89$	−1.11684			−0.118385			−0.0591926	−	0.998247i	$-0.518853\pi$
$89$	−1.11684			−0.118385			−0.0591926	+	0.998247i	$0.518853\pi$
$90$		0			0
$91$	−11.2554			−1.17989
$92$	−2.18614	+	3.78651i	−0.227921	+	0.394771i
$93$	8.00000	−	8.51278i	0.829561	−	0.882734i
$94$	−0.813859	−	1.40965i	−0.0839432	−	0.145394i
$95$		0			0
$96$	−1.18614	+	1.26217i	−0.121060	+	0.128820i
$97$	−1.31386	+	2.27567i	−0.133402	+	0.231059i	−0.924986	−	0.380001i	$-0.875924\pi$
$97$	−1.31386	+	2.27567i	−0.133402	+	0.231059i	0.791584	+	0.611061i	$0.209257\pi$
$98$	−1.37228			−0.138621
$99$	−0.255437	−	4.10891i	−0.0256724	−	0.412961i
$100$		0			0
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	−0.562242	−	0.826973i	$-0.690061\pi$
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	0.997300	+	0.0734297i	$0.0233944\pi$
$102$	12.4307	+	2.92048i	1.23082	+	0.289171i
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$	2.37228	+	4.10891i	0.232621	+	0.402912i
$105$		0			0
$106$	5.74456	−	9.94987i	0.557961	−	0.966417i
$107$	14.4891			1.40072			0.700358	−	0.713791i	$-0.253024\pi$
$107$	14.4891			1.40072			0.700358	+	0.713791i	$0.253024\pi$
$108$	0.872281	−	5.12241i	0.0839353	−	0.492905i
$109$	9.62772			0.922168			0.461084	−	0.887356i	$-0.347461\pi$
$109$	9.62772			0.922168			0.461084	+	0.887356i	$0.347461\pi$
$110$		0			0
$111$	−2.00000	−	6.63325i	−0.189832	−	0.629600i
$112$	−1.18614	−	2.05446i	−0.112080	−	0.194128i
$113$	7.37228	+	12.7692i	0.693526	+	1.20122i	0.970675	+	0.240395i	$0.0772770\pi$
$113$	7.37228	+	12.7692i	0.693526	+	1.20122i	−0.277149	+	0.960827i	$0.589390\pi$
$114$	5.68614	+	1.33591i	0.532556	+	0.125119i
$115$		0			0
$116$	−4.37228			−0.405956
$117$	−12.7446	−	6.33830i	−1.17824	−	0.585976i
$118$	−1.37228			−0.126329
$119$	−8.74456	+	15.1460i	−0.801613	+	1.38843i
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$	−4.55842	−	7.89542i	−0.412700	−	0.714818i
$123$	3.55842	−	3.78651i	0.320852	−	0.341418i
$124$	3.37228	−	5.84096i	0.302840	−	0.524534i
$125$		0			0
$126$	6.37228	+	3.16915i	0.567688	+	0.282330i
$127$	−9.11684			−0.808989			−0.404495	−	0.914540i	$-0.632553\pi$
$127$	−9.11684			−0.808989			−0.404495	+	0.914540i	$0.632553\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	19.1753	+	4.50506i	1.68829	+	0.396648i
$130$		0			0
$131$	−4.37228	−	7.57301i	−0.382008	−	0.661657i	0.609341	−	0.792908i	$-0.291434\pi$
$131$	−4.37228	−	7.57301i	−0.382008	−	0.661657i	−0.991349	+	0.131251i	$0.958101\pi$
$132$	−0.686141	−	2.27567i	−0.0597209	−	0.198072i
$133$	−4.00000	+	6.92820i	−0.346844	+	0.600751i
$134$	7.00000			0.604708
$135$		0			0
$136$	7.37228			0.632168
$137$	−0.941578	+	1.63086i	−0.0804444	+	0.139334i	−0.903441	−	0.428713i	$-0.858967\pi$
$137$	−0.941578	+	1.63086i	−0.0804444	+	0.139334i	0.822996	+	0.568046i	$0.192301\pi$
$138$	−2.18614	−	7.25061i	−0.186097	−	0.617213i
$139$	−9.05842	−	15.6896i	−0.768325	−	1.33078i	−0.938470	−	0.345359i	$-0.887757\pi$
$139$	−9.05842	−	15.6896i	−0.768325	−	1.33078i	0.170145	−	0.985419i	$-0.445576\pi$
$140$		0			0
$141$	2.74456	+	0.644810i	0.231134	+	0.0543028i
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	−6.51087			−0.544467
$144$	−0.186141	−	2.99422i	−0.0155117	−	0.249518i
$145$		0			0
$146$	−7.05842	+	12.2255i	−0.584159	+	1.01179i
$147$	1.62772	−	1.73205i	0.134252	−	0.142857i
$148$	−2.00000	−	3.46410i	−0.164399	−	0.284747i
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	−0.930153	−	0.367171i	$-0.880326\pi$
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	0.147097	−	0.989122i	$-0.453007\pi$
$150$		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	$0.0332784\pi$
$152$	3.37228			0.273528
$153$	−18.4307	+	12.2255i	−1.49003	+	0.988377i
$154$	3.25544			0.262331
$155$		0			0
$156$	−8.00000	−	1.87953i	−0.640513	−	0.150483i
$157$	2.37228	+	4.10891i	0.189329	+	0.327927i	0.945027	−	0.326993i	$-0.106036\pi$
$157$	2.37228	+	4.10891i	0.189329	+	0.327927i	−0.755698	+	0.654920i	$0.772702\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	5.74456	+	19.0526i	0.455573	+	1.51097i
$160$		0			0
$161$	10.3723			0.817450
$162$	5.43070	+	7.17687i	0.426676	+	0.563868i
$163$	−1.48913			−0.116637			−0.0583186	−	0.998298i	$-0.518574\pi$
$163$	−1.48913			−0.116637			−0.0583186	+	0.998298i	$0.518574\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	0.813859	+	1.40965i	0.0631677	+	0.109410i
$167$	3.81386	+	6.60580i	0.295125	+	0.511172i	0.975014	−	0.222143i	$-0.0713053\pi$
$167$	3.81386	+	6.60580i	0.295125	+	0.511172i	−0.679889	+	0.733315i	$0.737972\pi$
$168$	4.00000	+	0.939764i	0.308607	+	0.0725044i
$169$	−4.75544	+	8.23666i	−0.365803	+	0.633589i
$170$		0			0
$171$	−8.43070	+	5.59230i	−0.644712	+	0.427654i
$172$	11.3723			0.867128
$173$	4.62772	−	8.01544i	0.351839	−	0.609403i	−0.634733	−	0.772732i	$-0.718890\pi$
$173$	4.62772	−	8.01544i	0.351839	−	0.609403i	0.986572	+	0.163329i	$0.0522231\pi$
$174$	5.18614	−	5.51856i	0.393160	−	0.418361i
$175$		0			0
$176$	−0.686141	−	1.18843i	−0.0517198	−	0.0895813i
$177$	1.62772	−	1.73205i	0.122347	−	0.130189i
$178$	0.558422	−	0.967215i	0.0418555	−	0.0724958i
$179$	−3.25544			−0.243323			−0.121661	−	0.992572i	$-0.538822\pi$
$179$	−3.25544			−0.243323			−0.121661	+	0.992572i	$0.538822\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$	5.62772	−	9.74749i	0.417154	−	0.722532i
$183$	15.3723	+	3.61158i	1.13635	+	0.266976i
$184$	−2.18614	−	3.78651i	−0.161164	−	0.279145i
$185$		0			0
$186$	3.37228	+	11.1846i	0.247268	+	0.820094i
$187$	−5.05842	+	8.76144i	−0.369908	+	0.640700i
$188$	1.62772			0.118714
$189$	−11.5584	+	4.28384i	−0.840751	+	0.311604i
$190$		0			0
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	−0.749482	−	0.662025i	$-0.769697\pi$
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	0.948071	+	0.318058i	$0.103031\pi$
$192$	−0.500000	−	1.65831i	−0.0360844	−	0.119678i
$193$	1.94158	+	3.36291i	0.139758	+	0.242068i	0.927405	−	0.374059i	$-0.122034\pi$
$193$	1.94158	+	3.36291i	0.139758	+	0.242068i	−0.787647	+	0.616127i	$0.788701\pi$
$194$	−1.31386	−	2.27567i	−0.0943296	−	0.163384i
$195$		0			0
$196$	0.686141	−	1.18843i	0.0490100	−	0.0848879i
$197$	−17.4891			−1.24605			−0.623024	−	0.782202i	$-0.714096\pi$
$197$	−17.4891			−1.24605			−0.623024	+	0.782202i	$0.714096\pi$
$198$	3.68614	+	1.83324i	0.261963	+	0.130283i
$199$	−9.48913			−0.672666			−0.336333	−	0.941743i	$-0.609187\pi$
$199$	−9.48913			−0.672666			−0.336333	+	0.941743i	$0.609187\pi$
$200$		0			0
$201$	−8.30298	+	8.83518i	−0.585647	+	0.623186i
$202$	4.37228	+	7.57301i	0.307633	+	0.532835i
$203$	5.18614	+	8.98266i	0.363996	+	0.630459i
$204$	−8.74456	+	9.30506i	−0.612242	+	0.651485i
$205$		0			0
$206$	16.0000			1.11477
$207$	11.7446	+	5.84096i	0.816304	+	0.405975i
$208$	−4.74456			−0.328976
$209$	−2.31386	+	4.00772i	−0.160053	+	0.277220i
$210$		0			0
$211$	3.62772	+	6.28339i	0.249742	+	0.432567i	0.963454	−	0.267873i	$-0.0863207\pi$
$211$	3.62772	+	6.28339i	0.249742	+	0.432567i	−0.713712	+	0.700439i	$0.752987\pi$
$212$	5.74456	+	9.94987i	0.394538	+	0.683360i
$213$	3.00000	+	9.94987i	0.205557	+	0.681754i
$214$	−7.24456	+	12.5480i	−0.495228	+	0.857760i
$215$		0			0
$216$	4.00000	+	3.31662i	0.272166	+	0.225668i
$217$	−16.0000			−1.08615
$218$	−4.81386	+	8.33785i	−0.326036	+	0.564710i
$219$	−7.05842	−	23.4101i	−0.476964	−	1.58191i
$220$		0			0
$221$	17.4891	+	30.2921i	1.17645	+	2.03766i
$222$	6.74456	+	1.58457i	0.452665	+	0.106350i
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	−0.581095	−	0.813836i	$-0.697376\pi$
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	0.995350	+	0.0963255i	$0.0307090\pi$
$224$	2.37228			0.158505
$225$		0			0
$226$	−14.7446			−0.980794
$227$	0.941578	−	1.63086i	0.0624947	−	0.108244i	−0.833085	−	0.553145i	$-0.813428\pi$
$227$	0.941578	−	1.63086i	0.0624947	−	0.108244i	0.895580	+	0.444901i	$0.146761\pi$
$228$	−4.00000	+	4.25639i	−0.264906	+	0.281886i
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	−0.991726	−	0.128373i	$-0.959025\pi$
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	0.384689	−	0.923046i	$-0.374309\pi$
$230$		0			0
$231$	−3.86141	+	4.10891i	−0.254062	+	0.270347i
$232$	2.18614	−	3.78651i	0.143527	−	0.248596i
$233$	10.1168			0.662776			0.331388	−	0.943494i	$-0.392483\pi$
$233$	10.1168			0.662776			0.331388	+	0.943494i	$0.392483\pi$
$234$	11.8614	−	7.86797i	0.775404	−	0.514345i
$235$		0			0
$236$	0.686141	−	1.18843i	0.0446640	−	0.0773602i
$237$	3.37228	+	0.792287i	0.219053	+	0.0514646i
$238$	−8.74456	−	15.1460i	−0.566826	−	0.981771i
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	0.999649	−	0.0265017i	$-0.00843674\pi$
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	−0.522776	+	0.852470i	$0.675103\pi$
$240$		0			0
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	−0.984025	−	0.178032i	$-0.943027\pi$
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	0.646193	+	0.763174i	$0.276360\pi$
$242$	−9.11684			−0.586053
$243$	−15.5000	−	1.65831i	−0.994325	−	0.106381i
$244$	9.11684			0.583646
$245$		0			0
$246$	1.50000	+	4.97494i	0.0956365	+	0.317190i
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$	3.37228	+	5.84096i	0.214140	+	0.370901i
$249$	−2.74456	−	0.644810i	−0.173930	−	0.0408632i
$250$		0			0
$251$	15.6060			0.985040			0.492520	−	0.870301i	$-0.336076\pi$
$251$	15.6060			0.985040			0.492520	+	0.870301i	$0.336076\pi$
$252$	−5.93070	+	3.93398i	−0.373599	+	0.247818i
$253$	6.00000			0.377217
$254$	4.55842	−	7.89542i	0.286021	−	0.495403i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.686141	−	1.18843i	−0.0428003	−	0.0741323i	0.843832	−	0.536608i	$-0.180295\pi$
$257$	−0.686141	−	1.18843i	−0.0428003	−	0.0741323i	−0.886632	+	0.462476i	$0.846961\pi$
$258$	−13.4891	+	14.3537i	−0.839796	+	0.893625i
$259$	−4.74456	+	8.21782i	−0.294813	+	0.510631i
$260$		0			0
$261$	0.813859	+	13.0916i	0.0503766	+	0.810348i
$262$	8.74456			0.540241
$263$	2.74456	−	4.75372i	0.169237	−	0.293127i	−0.768915	−	0.639351i	$-0.779203\pi$
$263$	2.74456	−	4.75372i	0.169237	−	0.293127i	0.938152	+	0.346224i	$0.112536\pi$
$264$	2.31386	+	0.543620i	0.142408	+	0.0334575i
$265$		0			0
$266$	−4.00000	−	6.92820i	−0.245256	−	0.424795i
$267$	0.558422	+	1.85208i	0.0341749	+	0.113345i
$268$	−3.50000	+	6.06218i	−0.213797	+	0.370306i
$269$	4.37228			0.266583			0.133291	−	0.991077i	$-0.457445\pi$
$269$	4.37228			0.266583			0.133291	+	0.991077i	$0.457445\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−3.68614	+	6.38458i	−0.223505	+	0.387122i
$273$	5.62772	+	18.6650i	0.340605	+	1.12966i
$274$	−0.941578	−	1.63086i	−0.0568828	−	0.0985239i
$275$		0			0
$276$	7.37228	+	1.73205i	0.443759	+	0.104257i
$277$	2.62772	−	4.55134i	0.157884	−	0.273464i	−0.776221	−	0.630461i	$-0.782866\pi$
$277$	2.62772	−	4.55134i	0.157884	−	0.273464i	0.934106	+	0.356997i	$0.116199\pi$
$278$	18.1168			1.08658
$279$	−18.1168	−	9.01011i	−1.08463	−	0.539421i
$280$		0			0
$281$	−2.18614	+	3.78651i	−0.130414	+	0.225884i	−0.923836	−	0.382788i	$-0.874964\pi$
$281$	−2.18614	+	3.78651i	−0.130414	+	0.225884i	0.793422	+	0.608672i	$0.208297\pi$
$282$	−1.93070	+	2.05446i	−0.114972	+	0.122341i
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.751733	−	0.659467i	$-0.770782\pi$
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.195249	−	0.980754i	$-0.562551\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	3.25544	−	5.63858i	0.192498	−	0.333416i
$287$	−7.11684			−0.420094
$288$	2.68614	+	1.33591i	0.158282	+	0.0787191i
$289$	37.3505			2.19709
$290$		0			0
$291$	4.43070	+	1.04095i	0.259732	+	0.0610218i
$292$	−7.05842	−	12.2255i	−0.413063	−	0.715446i
$293$	−4.11684	−	7.13058i	−0.240509	−	0.416573i	0.720351	−	0.693610i	$-0.243981\pi$
$293$	−4.11684	−	7.13058i	−0.240509	−	0.416573i	−0.960859	+	0.277037i	$0.910648\pi$
$294$	0.686141	+	2.27567i	0.0400165	+	0.132720i
$295$		0			0
$296$	4.00000			0.232495
$297$	−6.68614	+	2.47805i	−0.387969	+	0.143791i
$298$	19.1168			1.10741
$299$	10.3723	−	17.9653i	0.599845	−	1.03896i
$300$		0			0
$301$	−13.4891	−	23.3639i	−0.777500	−	1.34667i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	−14.7446	−	3.46410i	−0.847053	−	0.199007i
$304$	−1.68614	+	2.92048i	−0.0967068	+	0.167501i
$305$		0			0
$306$	−1.37228	−	22.0742i	−0.0784481	−	1.26190i
$307$	33.2337			1.89675			0.948373	−	0.317156i	$-0.102728\pi$
$307$	33.2337			1.89675			0.948373	+	0.317156i	$0.102728\pi$
$308$	−1.62772	+	2.81929i	−0.0927479	+	0.160644i
$309$	−18.9783	+	20.1947i	−1.07963	+	1.14884i
$310$		0			0
$311$	4.62772	+	8.01544i	0.262414	+	0.454514i	0.966883	−	0.255221i	$-0.0821481\pi$
$311$	4.62772	+	8.01544i	0.262414	+	0.454514i	−0.704469	+	0.709735i	$0.748815\pi$
$312$	5.62772	−	5.98844i	0.318607	−	0.339029i
$313$	4.68614	−	8.11663i	0.264876	−	0.458779i	−0.702655	−	0.711531i	$-0.748002\pi$
$313$	4.68614	−	8.11663i	0.264876	−	0.458779i	0.967531	+	0.252752i	$0.0813355\pi$
$314$	−4.74456			−0.267751
$315$		0			0
$316$	2.00000			0.112509
$317$	−4.37228	+	7.57301i	−0.245572	+	0.425343i	−0.962292	−	0.272018i	$-0.912309\pi$
$317$	−4.37228	+	7.57301i	−0.245572	+	0.425343i	0.716720	+	0.697361i	$0.245642\pi$
$318$	−19.3723	−	4.55134i	−1.08634	−	0.255227i
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	−7.24456	−	24.0275i	−0.404352	−	1.34108i
$322$	−5.18614	+	8.98266i	−0.289012	+	0.500584i
$323$	24.8614			1.38333
$324$	−8.93070	+	1.11469i	−0.496150	+	0.0619273i
$325$		0			0
$326$	0.744563	−	1.28962i	0.0412375	−	0.0714255i
$327$	−4.81386	−	15.9658i	−0.266207	−	0.882909i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−1.93070	−	3.34408i	−0.106443	−	0.184365i
$330$		0			0
$331$	9.11684	−	15.7908i	0.501107	−	0.867943i	−0.498892	−	0.866664i	$-0.666260\pi$
$331$	9.11684	−	15.7908i	0.501107	−	0.867943i	0.999999	−	0.00127880i	$-0.000407055\pi$
$332$	−1.62772			−0.0893327
$333$	−10.0000	+	6.63325i	−0.547997	+	0.363500i
$334$	−7.62772			−0.417370
$335$		0			0
$336$	−2.81386	+	2.99422i	−0.153509	+	0.163348i
$337$	1.68614	+	2.92048i	0.0918499	+	0.159089i	0.908290	−	0.418342i	$-0.137389\pi$
$337$	1.68614	+	2.92048i	0.0918499	+	0.159089i	−0.816440	+	0.577431i	$0.804055\pi$
$338$	−4.75544	−	8.23666i	−0.258662	−	0.448015i
$339$	17.4891	−	18.6101i	0.949879	−	1.01076i
$340$		0			0
$341$	−9.25544			−0.501210
$342$	−0.627719	−	10.0974i	−0.0339431	−	0.546002i
$343$	−19.8614			−1.07242
$344$	−5.68614	+	9.84868i	−0.306576	+	0.531005i
$345$		0			0
$346$	4.62772	+	8.01544i	0.248788	+	0.430913i
$347$	−11.0584	−	19.1537i	−0.593647	−	1.02823i	−0.993736	−	0.111751i	$-0.964354\pi$
$347$	−11.0584	−	19.1537i	−0.593647	−	1.02823i	0.400089	−	0.916476i	$-0.368979\pi$
$348$	2.18614	+	7.25061i	0.117189	+	0.388673i
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	−0.877602	−	0.479390i	$-0.840858\pi$
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	0.853965	+	0.520331i	$0.174191\pi$
$350$		0			0
$351$	−4.13859	+	24.3036i	−0.220902	+	1.29723i
$352$	1.37228			0.0731428
$353$	15.1753	−	26.2843i	0.807698	−	1.39897i	−0.106757	−	0.994285i	$-0.534047\pi$
$353$	15.1753	−	26.2843i	0.807698	−	1.39897i	0.914455	−	0.404689i	$-0.132620\pi$
$354$	0.686141	+	2.27567i	0.0364680	+	0.120951i
$355$		0			0
$356$	0.558422	+	0.967215i	0.0295963	+	0.0512623i
$357$	29.4891	+	6.92820i	1.56073	+	0.366679i
$358$	1.62772	−	2.81929i	0.0860276	−	0.149004i
$359$	5.48913			0.289705			0.144852	−	0.989453i	$-0.453729\pi$
$359$	5.48913			0.289705			0.144852	+	0.989453i	$0.453729\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$	3.93070	−	6.80818i	0.206593	−	0.357830i
$363$	10.8139	−	11.5070i	0.567580	−	0.603961i
$364$	5.62772	+	9.74749i	0.294973	+	0.510908i
$365$		0			0
$366$	−10.8139	+	11.5070i	−0.565249	+	0.601480i
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	4.37228			0.227921
$369$	−8.05842	−	4.00772i	−0.419505	−	0.208634i
$370$		0			0
$371$	13.6277	−	23.6039i	0.707516	−	1.22545i
$372$	−11.3723	−	2.67181i	−0.589625	−	0.138527i
$373$	3.74456	+	6.48577i	0.193886	+	0.335821i	0.946535	−	0.322602i	$-0.104557\pi$
$373$	3.74456	+	6.48577i	0.193886	+	0.335821i	−0.752649	+	0.658422i	$0.771224\pi$
$374$	−5.05842	−	8.76144i	−0.261565	−	0.453043i
$375$		0			0
$376$	−0.813859	+	1.40965i	−0.0419716	+	0.0726969i
$377$	20.7446			1.06840
$378$	2.06930	−	12.1518i	0.106433	−	0.625022i
$379$	−10.8614			−0.557913			−0.278956	−	0.960304i	$-0.589989\pi$
$379$	−10.8614			−0.557913			−0.278956	+	0.960304i	$0.589989\pi$
$380$		0			0
$381$	4.55842	+	15.1186i	0.233535	+	0.774548i
$382$	2.74456	+	4.75372i	0.140424	+	0.243222i
$383$	11.4891	+	19.8997i	0.587067	+	1.01683i	0.994614	+	0.103646i	$0.0330508\pi$
$383$	11.4891	+	19.8997i	0.587067	+	1.01683i	−0.407547	+	0.913184i	$0.633616\pi$
$384$	1.68614	+	0.396143i	0.0860455	+	0.0202156i
$385$		0			0
$386$	−3.88316			−0.197647
$387$	−2.11684	−	34.0511i	−0.107605	−	1.73092i
$388$	2.62772			0.133402
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	−0.704076	−	0.710124i	$-0.748639\pi$
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	0.967024	+	0.254686i	$0.0819720\pi$
$390$		0			0
$391$	−16.1168	−	27.9152i	−0.815064	−	1.41173i
$392$	0.686141	+	1.18843i	0.0346553	+	0.0600248i
$393$	−10.3723	+	11.0371i	−0.523212	+	0.556749i
$394$	8.74456	−	15.1460i	0.440545	−	0.763046i
$395$		0			0
$396$	−3.43070	+	2.27567i	−0.172399	+	0.114357i
$397$	−11.2554			−0.564894			−0.282447	−	0.959283i	$-0.591146\pi$
$397$	−11.2554			−0.564894			−0.282447	+	0.959283i	$0.591146\pi$
$398$	4.74456	−	8.21782i	0.237823	−	0.411922i
$399$	13.4891	+	3.16915i	0.675301	+	0.158656i
$400$		0			0
$401$	−8.05842	−	13.9576i	−0.402418	−	0.697009i	0.591599	−	0.806232i	$-0.298497\pi$
$401$	−8.05842	−	13.9576i	−0.402418	−	0.697009i	−0.994017	+	0.109223i	$0.965164\pi$
$402$	−3.50000	−	11.6082i	−0.174564	−	0.578964i
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$	−8.74456			−0.435058
$405$		0			0
$406$	−10.3723			−0.514768
$407$	−2.74456	+	4.75372i	−0.136043	+	0.235633i
$408$	−3.68614	−	12.2255i	−0.182491	−	0.605255i
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	0.968483	−	0.249081i	$-0.0801285\pi$
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	−0.699952	+	0.714190i	$0.746795\pi$
$410$		0			0
$411$	3.17527	+	0.746000i	0.156624	+	0.0367975i
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	−3.25544			−0.160190
$414$	−10.9307	+	7.25061i	−0.537215	+	0.356348i
$415$		0			0
$416$	2.37228	−	4.10891i	0.116311	−	0.201456i
$417$	−21.4891	+	22.8665i	−1.05233	+	1.11978i
$418$	−2.31386	−	4.00772i	−0.113175	−	0.196024i
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	0.934862	+	0.355012i	$0.115523\pi$
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	−0.159981	+	0.987120i	$0.551143\pi$
$420$		0			0
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.167082	−	0.985943i	$-0.446566\pi$
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.770311	−	0.637669i	$-0.220101\pi$
$422$	−7.25544			−0.353189
$423$	−0.302985	−	4.87375i	−0.0147316	−	0.236970i
$424$	−11.4891			−0.557961
$425$		0			0
$426$	−10.1168	−	2.37686i	−0.490163	−	0.115159i
$427$	−10.8139	−	18.7302i	−0.523319	−	0.906416i
$428$	−7.24456	−	12.5480i	−0.350179	−	0.606528i
$429$	3.25544	+	10.7971i	0.157174	+	0.521287i
$430$		0			0
$431$	−26.2337			−1.26363			−0.631816	−	0.775118i	$-0.717690\pi$
$431$	−26.2337			−1.26363			−0.631816	+	0.775118i	$0.717690\pi$
$432$	−4.87228	+	1.80579i	−0.234418	+	0.0868811i
$433$	−0.627719			−0.0301662			−0.0150831	−	0.999886i	$-0.504801\pi$
$433$	−0.627719			−0.0301662			−0.0150831	+	0.999886i	$0.504801\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$		0			0
$436$	−4.81386	−	8.33785i	−0.230542	−	0.399311i
$437$	−7.37228	−	12.7692i	−0.352664	−	0.610832i
$438$	23.8030	+	5.59230i	1.13735	+	0.267210i
$439$	−8.11684	+	14.0588i	−0.387396	+	0.670989i	−0.992098	−	0.125462i	$-0.959959\pi$
$439$	−8.11684	+	14.0588i	−0.387396	+	0.670989i	0.604703	+	0.796451i	$0.293292\pi$
$440$		0			0
$441$	−3.68614	−	1.83324i	−0.175531	−	0.0872972i
$442$	−34.9783			−1.66375
$443$	−13.2446	+	22.9403i	−0.629268	+	1.08992i	0.358431	+	0.933556i	$0.383312\pi$
$443$	−13.2446	+	22.9403i	−0.629268	+	1.08992i	−0.987699	+	0.156368i	$0.950021\pi$
$444$	−4.74456	+	5.04868i	−0.225167	+	0.239600i
$445$		0			0
$446$	6.18614	+	10.7147i	0.292922	+	0.507356i
$447$	−22.6753	+	24.1287i	−1.07250	+	1.14125i
$448$	−1.18614	+	2.05446i	−0.0560399	+	0.0970639i
$449$	−18.8614			−0.890125			−0.445062	−	0.895500i	$-0.646819\pi$
$449$	−18.8614			−0.890125			−0.445062	+	0.895500i	$0.646819\pi$
$450$		0			0
$451$	−4.11684			−0.193855
$452$	7.37228	−	12.7692i	0.346763	−	0.600611i
$453$	−16.8614	−	3.96143i	−0.792218	−	0.186124i
$454$	0.941578	+	1.63086i	0.0441904	+	0.0765401i
$455$		0			0
$456$	−1.68614	−	5.59230i	−0.0789608	−	0.261883i
$457$	15.0584	−	26.0820i	0.704403	−	1.22006i	−0.262503	−	0.964931i	$-0.584548\pi$
$457$	15.0584	−	26.0820i	0.704403	−	1.22006i	0.966906	−	0.255131i	$-0.0821186\pi$
$458$	18.3723			0.858480
$459$	29.4891	+	24.4511i	1.37643	+	1.14128i
$460$		0			0
$461$	−9.55842	+	16.5557i	−0.445180	+	0.771075i	−0.998065	−	0.0621833i	$-0.980194\pi$
$461$	−9.55842	+	16.5557i	−0.445180	+	0.771075i	0.552885	+	0.833258i	$0.313527\pi$
$462$	−1.62772	−	5.39853i	−0.0757283	−	0.251162i
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	−0.534450	+	0.845200i	$0.679481\pi$
$464$	2.18614	+	3.78651i	0.101489	+	0.175784i
$465$		0			0
$466$	−5.05842	+	8.76144i	−0.234327	+	0.405866i
$467$	−25.8832			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$467$	−25.8832			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$468$	0.883156	+	14.2063i	0.0408239	+	0.656685i
$469$	16.6060			0.766792
$470$		0			0
$471$	5.62772	−	5.98844i	0.259312	−	0.275933i
$472$	0.686141	+	1.18843i	0.0315822	+	0.0547019i
$473$	−7.80298	−	13.5152i	−0.358782	−	0.621428i
$474$	−2.37228	+	2.52434i	−0.108962	+	0.115947i
$475$		0			0
$476$	17.4891			0.801613
$477$	28.7228	−	19.0526i	1.31513	−	0.872357i
$478$	−14.7446			−0.674401
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	−0.462460	−	0.886640i	$-0.653033\pi$
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	0.999083	−	0.0428178i	$-0.0136335\pi$
$480$		0			0
$481$	9.48913	+	16.4356i	0.432667	+	0.749401i
$482$	−5.24456	−	9.08385i	−0.238883	−	0.413758i
$483$	−5.18614	−	17.2005i	−0.235978	−	0.782649i
$484$	4.55842	−	7.89542i	0.207201	−	0.358883i
$485$		0			0
$486$	9.18614	−	12.5942i	0.416692	−	0.571286i
$487$	1.25544			0.0568893			0.0284446	−	0.999595i	$-0.490945\pi$
$487$	1.25544			0.0568893			0.0284446	+	0.999595i	$0.490945\pi$
$488$	−4.55842	+	7.89542i	−0.206350	+	0.357409i
$489$	0.744563	+	2.46943i	0.0336703	+	0.111672i
$490$		0			0
$491$	−1.80298	−	3.12286i	−0.0813676	−	0.140933i	0.822470	−	0.568808i	$-0.192595\pi$
$491$	−1.80298	−	3.12286i	−0.0813676	−	0.140933i	−0.903838	+	0.427876i	$0.859262\pi$
$492$	−5.05842	−	1.18843i	−0.228051	−	0.0535786i
$493$	16.1168	−	27.9152i	0.725866	−	1.25724i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	−6.74456			−0.302840
$497$	7.11684	−	12.3267i	0.319234	−	0.552930i
$498$	1.93070	−	2.05446i	0.0865169	−	0.0920624i
$499$	1.05842	+	1.83324i	0.0473815	+	0.0820671i	0.888743	−	0.458405i	$-0.151579\pi$
$499$	1.05842	+	1.83324i	0.0473815	+	0.0820671i	−0.841362	+	0.540472i	$0.818246\pi$
$500$		0			0
$501$	9.04755	−	9.62747i	0.404215	−	0.430124i
$502$	−7.80298	+	13.5152i	−0.348264	+	0.603211i
$503$	−21.8614			−0.974752			−0.487376	−	0.873192i	$-0.662046\pi$
$503$	−21.8614			−0.974752			−0.487376	+	0.873192i	$0.662046\pi$
$504$	−0.441578	−	7.10313i	−0.0196694	−	0.316399i
$505$		0			0
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$	16.0367	+	3.76767i	0.712214	+	0.167328i
$508$	4.55842	+	7.89542i	0.202247	+	0.350303i
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	0.743613	−	0.668611i	$-0.233111\pi$
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	−0.950840	+	0.309682i	$0.899777\pi$
$510$		0			0
$511$	−16.7446	+	29.0024i	−0.740736	+	1.28299i
$512$	1.00000			0.0441942
$513$	13.4891	+	11.1846i	0.595559	+	0.493812i
$514$	1.37228			0.0605287
$515$		0			0
$516$	−5.68614	−	18.8588i	−0.250318	−	0.830212i
$517$	−1.11684	−	1.93443i	−0.0491187	−	0.0850762i
$518$	−4.74456	−	8.21782i	−0.208464	−	0.361070i
$519$	−15.6060	−	3.66648i	−0.685026	−	0.160941i
$520$		0			0
$521$	−41.2337			−1.80648			−0.903240	−	0.429135i	$-0.858818\pi$
$521$	−41.2337			−1.80648			−0.903240	+	0.429135i	$0.858818\pi$
$522$	−11.7446	−	5.84096i	−0.514046	−	0.255652i
$523$	11.1168			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$523$	11.1168			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$524$	−4.37228	+	7.57301i	−0.191004	+	0.330829i
$525$		0			0
$526$	2.74456	+	4.75372i	0.119669	+	0.207272i
$527$	24.8614	+	43.0612i	1.08298	+	1.87578i
$528$	−1.62772	+	1.73205i	−0.0708374	+	0.0753778i
$529$	1.94158	−	3.36291i	0.0844164	−	0.146214i
$530$		0			0
$531$	−3.68614	−	1.83324i	−0.159965	−	0.0795559i
$532$	8.00000			0.346844
$533$	−7.11684	+	12.3267i	−0.308265	+	0.533930i
$534$	−1.88316	−	0.442430i	−0.0814921	−	0.0191458i
$535$		0			0
$536$	−3.50000	−	6.06218i	−0.151177	−	0.261846i
$537$	1.62772	+	5.39853i	0.0702412	+	0.232964i
$538$	−2.18614	+	3.78651i	−0.0942512	+	0.163248i
$539$	−1.88316			−0.0811133
$540$		0			0
$541$	21.6277			0.929848			0.464924	−	0.885351i	$-0.346082\pi$
$541$	21.6277			0.929848			0.464924	+	0.885351i	$0.346082\pi$
$542$	−4.00000	+	6.92820i	−0.171815	+	0.297592i
$543$	3.93070	+	13.0367i	0.168683	+	0.559457i
$544$	−3.68614	−	6.38458i	−0.158042	−	0.273737i
$545$		0			0
$546$	−18.9783	−	4.45877i	−0.812194	−	0.190818i
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	−0.0429494	−	0.999077i	$-0.513675\pi$
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	0.886701	−	0.462343i	$-0.152991\pi$
$548$	1.88316			0.0804444
$549$	−1.69702	−	27.2978i	−0.0724269	−	1.16504i
$550$		0			0
$551$	7.37228	−	12.7692i	0.314070	−	0.543985i
$552$	−5.18614	+	5.51856i	−0.220737	+	0.234885i
$553$	−2.37228	−	4.10891i	−0.100880	−	0.174729i
$554$	2.62772	+	4.55134i	0.111641	+	0.193368i
$555$		0			0
$556$	−9.05842	+	15.6896i	−0.384163	+	0.665389i
$557$	9.76631			0.413812			0.206906	−	0.978361i	$-0.433661\pi$
$557$	9.76631			0.413812			0.206906	+	0.978361i	$0.433661\pi$
$558$	16.8614	−	11.1846i	0.713800	−	0.473482i
$559$	−53.9565			−2.28212
$560$		0			0
$561$	17.0584	+	4.00772i	0.720207	+	0.169206i
$562$	−2.18614	−	3.78651i	−0.0922168	−	0.159724i
$563$	8.36141	+	14.4824i	0.352391	+	0.610360i	0.986668	−	0.162747i	$-0.0520353\pi$
$563$	8.36141	+	14.4824i	0.352391	+	0.610360i	−0.634277	+	0.773106i	$0.718702\pi$
$564$	−0.813859	−	2.69927i	−0.0342697	−	0.113660i
$565$		0			0
$566$	31.8614			1.33923
$567$	12.8832	+	17.0256i	0.541042	+	0.715006i
$568$	−6.00000			−0.251754
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	−0.948964	−	0.315384i	$-0.897867\pi$
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	0.747613	+	0.664135i	$0.231200\pi$
$570$		0			0
$571$	15.8030	+	27.3716i	0.661334	+	1.14546i	0.980265	+	0.197687i	$0.0633429\pi$
$571$	15.8030	+	27.3716i	0.661334	+	1.14546i	−0.318931	+	0.947778i	$0.603324\pi$
$572$	3.25544	+	5.63858i	0.136117	+	0.235761i
$573$	−9.25544	−	2.17448i	−0.386651	−	0.0908403i
$574$	3.55842	−	6.16337i	0.148526	−	0.257254i
$575$		0			0
$576$	−2.50000	+	1.65831i	−0.104167	+	0.0690963i
$577$	23.8832			0.994269			0.497134	−	0.867674i	$-0.334386\pi$
$577$	23.8832			0.994269			0.497134	+	0.867674i	$0.334386\pi$
$578$	−18.6753	+	32.3465i	−0.776789	+	1.34544i
$579$	4.60597	−	4.90120i	0.191418	−	0.203687i
$580$		0			0
$581$	1.93070	+	3.34408i	0.0800991	+	0.138736i
$582$	−3.11684	+	3.31662i	−0.129197	+	0.137479i
$583$	7.88316	−	13.6540i	0.326487	−	0.565492i
$584$	14.1168			0.584159
$585$		0			0
$586$	8.23369			0.340131
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	−0.440524	−	0.897741i	$-0.645207\pi$
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	0.997728	−	0.0673658i	$-0.0214594\pi$
$588$	−2.31386	−	0.543620i	−0.0954220	−	0.0224185i
$589$	11.3723	+	19.6974i	0.468587	+	0.811616i
$590$		0			0
$591$	8.74456	+	29.0024i	0.359703	+	1.19300i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	−37.7228			−1.54909			−0.774545	−	0.632519i	$-0.782021\pi$
$593$	−37.7228			−1.54909			−0.774545	+	0.632519i	$0.782021\pi$
$594$	1.19702	−	7.02939i	0.0491141	−	0.288419i
$595$		0			0
$596$	−9.55842	+	16.5557i	−0.391528	+	0.678147i
$597$	4.74456	+	15.7359i	0.194182	+	0.644029i
$598$	10.3723	+	17.9653i	0.424154	+	0.734656i
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	0.931305	+	0.364239i	$0.118671\pi$
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	−0.150212	+	0.988654i	$0.547996\pi$
$600$		0			0
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	0.450572	+	0.892740i	$0.351220\pi$
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	−0.998422	+	0.0561635i	$0.982113\pi$
$602$	26.9783			1.09955
$603$	18.8030	+	9.35135i	0.765717	+	0.380816i
$604$	−10.0000			−0.406894
$605$		0			0
$606$	10.3723	−	11.0371i	0.421345	−	0.448352i
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	0.874848	−	0.484398i	$-0.160961\pi$
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	−0.856925	+	0.515442i	$0.827628\pi$
$608$	−1.68614	−	2.92048i	−0.0683820	−	0.118441i
$609$	12.3030	−	13.0916i	0.498542	−	0.530497i
$610$		0			0
$611$	−7.72281			−0.312432
$612$	19.8030	+	9.84868i	0.800488	+	0.398109i
$613$	0.233688			0.00943857			0.00471928	−	0.999989i	$-0.498498\pi$
$613$	0.233688			0.00943857			0.00471928	+	0.999989i	$0.498498\pi$
$614$	−16.6168	+	28.7812i	−0.670601	+	1.16152i
$615$		0			0
$616$	−1.62772	−	2.81929i	−0.0655827	−	0.113592i
$617$	−11.0584	−	19.1537i	−0.445195	−	0.771101i	0.552870	−	0.833267i	$-0.313532\pi$
$617$	−11.0584	−	19.1537i	−0.445195	−	0.771101i	−0.998066	+	0.0621663i	$0.980199\pi$
$618$	−8.00000	−	26.5330i	−0.321807	−	1.06731i
$619$	19.0584	−	33.0102i	0.766023	−	1.32679i	−0.173682	−	0.984802i	$-0.555566\pi$
$619$	19.0584	−	33.0102i	0.766023	−	1.32679i	0.939704	−	0.341988i	$-0.111100\pi$
$620$		0			0
$621$	3.81386	−	22.3966i	0.153045	−	0.898746i
$622$	−9.25544			−0.371109
$623$	1.32473	−	2.29451i	0.0530743	−	0.0919275i
$624$	2.37228	+	7.86797i	0.0949673	+	0.314971i
$625$		0			0
$626$	4.68614	+	8.11663i	0.187296	+	0.324406i
$627$	7.80298	+	1.83324i	0.311621	+	0.0732126i
$628$	2.37228	−	4.10891i	0.0946643	−	0.163963i
$629$	29.4891			1.17581
$630$		0			0
$631$	33.7228			1.34248			0.671242	−	0.741238i	$-0.265761\pi$
$631$	33.7228			1.34248			0.671242	+	0.741238i	$0.265761\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$	8.60597	−	9.15759i	0.342057	−	0.363981i
$634$	−4.37228	−	7.57301i	−0.173645	−	0.300763i
$635$		0			0
$636$	13.6277	−	14.5012i	0.540374	−	0.575011i
$637$	−3.25544	+	5.63858i	−0.128985	+	0.223409i
$638$	−6.00000			−0.237542
$639$	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	$-0.113179\pi$
$642$	24.4307	+	5.73977i	0.964203	+	0.226531i
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$	−5.18614	−	8.98266i	−0.204363	−	0.353966i
$645$		0			0
$646$	−12.4307	+	21.5306i	−0.489079	+	0.847111i
$647$	−24.0951			−0.947276			−0.473638	−	0.880720i	$-0.657059\pi$
$647$	−24.0951			−0.947276			−0.473638	+	0.880720i	$0.657059\pi$
$648$	3.50000	−	8.29156i	0.137493	−	0.325723i
$649$	−1.88316			−0.0739203
$650$		0			0
$651$	8.00000	+	26.5330i	0.313545	+	1.03991i
$652$	0.744563	+	1.28962i	0.0291593	+	0.0505054i
$653$	−18.8614	−	32.6689i	−0.738104	−	1.27843i	−0.953348	−	0.301873i	$-0.902388\pi$
$653$	−18.8614	−	32.6689i	−0.738104	−	1.27843i	0.215244	−	0.976560i	$-0.430945\pi$
$654$	16.2337	+	3.81396i	0.634787	+	0.149138i
$655$		0			0
$656$	−3.00000			−0.117130
$657$	−35.2921	+	23.4101i	−1.37688	+	0.913316i
$658$	3.86141			0.150533
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	−0.807605	−	0.589724i	$-0.799237\pi$
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	0.914518	+	0.404545i	$0.132570\pi$
$660$		0			0
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	0.564684	−	0.825307i	$-0.308998\pi$
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	−0.997079	+	0.0763770i	$0.975665\pi$
$662$	9.11684	+	15.7908i	0.354336	+	0.613728i
$663$	41.4891	−	44.1485i	1.61130	−	1.71458i
$664$	0.813859	−	1.40965i	0.0315839	−	0.0547049i
$665$		0			0
$666$	−0.744563	−	11.9769i	−0.0288512	−	0.464095i
$667$	−19.1168			−0.740207
$668$	3.81386	−	6.60580i	0.147563	−	0.255586i
$669$	−20.8614	−	4.90120i	−0.806549	−	0.189491i
$670$		0			0
$671$	−6.25544	−	10.8347i	−0.241488	−	0.418270i
$672$	−1.18614	−	3.93398i	−0.0457564	−	0.151757i
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	−0.946156	−	0.323711i	$-0.895069\pi$
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	0.753420	+	0.657539i	$0.228403\pi$
$674$	−3.37228			−0.129895
$675$		0			0
$676$	9.51087			0.365803
$677$	−21.8614	+	37.8651i	−0.840202	+	1.45527i	0.0495215	+	0.998773i	$0.484230\pi$
$677$	−21.8614	+	37.8651i	−0.840202	+	1.45527i	−0.889724	+	0.456500i	$0.849103\pi$
$678$	7.37228	+	24.4511i	0.283131	+	0.939038i
$679$	−3.11684	−	5.39853i	−0.119613	−	0.207177i
$680$		0			0
$681$	−3.17527	−	0.746000i	−0.121676	−	0.0285868i
$682$	4.62772	−	8.01544i	0.177205	−	0.306927i
$683$	−33.0951			−1.26635			−0.633174	−	0.774009i	$-0.718248\pi$
$683$	−33.0951			−1.26635			−0.633174	+	0.774009i	$0.718248\pi$
$684$	9.05842	+	4.50506i	0.346357	+	0.172255i
$685$		0			0
$686$	9.93070	−	17.2005i	0.379156	−	0.656717i
$687$	−21.7921	+	23.1889i	−0.831421	+	0.884713i
$688$	−5.68614	−	9.84868i	−0.216782	−	0.375478i
$689$	−27.2554	−	47.2078i	−1.03835	−	1.79847i
$690$		0			0
$691$	0.883156	−	1.52967i	0.0335968	−	0.0581914i	−0.848738	−	0.528813i	$-0.822637\pi$
$691$	0.883156	−	1.52967i	0.0335968	−	0.0581914i	0.882335	+	0.470622i	$0.155970\pi$
$692$	−9.25544			−0.351839
$693$	8.74456	+	4.34896i	0.332178	+	0.165203i
$694$	22.1168			0.839544
$695$		0			0
$696$	−7.37228	−	1.73205i	−0.279446	−	0.0656532i
$697$	11.0584	+	19.1537i	0.418868	+	0.725500i
$698$	−0.441578	−	0.764836i	−0.0167140	−	0.0289495i
$699$	−5.05842	−	16.7769i	−0.191327	−	0.634560i
$700$		0			0
$701$	14.1386			0.534007			0.267004	−	0.963696i	$-0.413966\pi$
$701$	14.1386			0.534007			0.267004	+	0.963696i	$0.413966\pi$
$702$	−18.9783	−	15.7359i	−0.716288	−	0.593915i
$703$	13.4891			0.508752
$704$	−0.686141	+	1.18843i	−0.0258599	+	0.0447907i
$705$		0			0
$706$	15.1753	+	26.2843i	0.571129	+	0.989224i
$707$	10.3723	+	17.9653i	0.390090	+	0.675655i
$708$	−2.31386	−	0.543620i	−0.0869602	−	0.0204305i
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	−0.514241	−	0.857646i	$-0.671926\pi$
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	0.999863	+	0.0165226i	$0.00525955\pi$
$710$		0			0
$711$	−0.372281	−	5.98844i	−0.0139616	−	0.224584i
$712$	−1.11684			−0.0418555
$713$	14.7446	−	25.5383i	0.552188	−	0.956418i
$714$	−20.7446	+	22.0742i	−0.776346	+	0.826107i
$715$		0			0
$716$	1.62772	+	2.81929i	0.0608307	+	0.105362i
$717$	17.4891	−	18.6101i	0.653143	−	0.695008i
$718$	−2.74456	+	4.75372i	−0.102426	+	0.177407i
$719$	−38.2337			−1.42588			−0.712938	−	0.701227i	$-0.752636\pi$
$719$	−38.2337			−1.42588			−0.712938	+	0.701227i	$0.752636\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$	3.81386	−	6.60580i	0.141937	−	0.245842i
$723$	17.6861	+	4.15520i	0.657755	+	0.154534i
$724$	3.93070	+	6.80818i	0.146083	+	0.253024i
$725$		0			0
$726$	4.55842	+	15.1186i	0.169179	+	0.561103i
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	−0.857721	−	0.514116i	$-0.828120\pi$
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	0.874098	+	0.485750i	$0.161453\pi$
$728$	−11.2554			−0.417154
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	−41.9198	+	72.6073i	−1.55046	+	2.68548i
$732$	−4.55842	−	15.1186i	−0.168484	−	0.558799i
$733$	17.1168	+	29.6472i	0.632225	+	1.09505i	0.987096	+	0.160131i	$0.0511915\pi$
$733$	17.1168	+	29.6472i	0.632225	+	1.09505i	−0.354871	+	0.934915i	$0.615475\pi$
$734$	−8.00000	−	13.8564i	−0.295285	−	0.511449i
$735$		0			0
$736$	−2.18614	+	3.78651i	−0.0805822	+	0.139572i
$737$	9.60597			0.353840
$738$	7.50000	−	4.97494i	0.276079	−	0.183130i
$739$	−23.8832			−0.878556			−0.439278	−	0.898351i	$-0.644766\pi$
$739$	−23.8832			−0.878556			−0.439278	+	0.898351i	$0.644766\pi$
$740$		0			0
$741$	18.9783	−	20.1947i	0.697183	−	0.741871i
$742$	13.6277	+	23.6039i	0.500289	+	0.866526i
$743$	12.5584	+	21.7518i	0.460724	+	0.797997i	0.998997	−	0.0447732i	$-0.0142565\pi$
$743$	12.5584	+	21.7518i	0.460724	+	0.797997i	−0.538273	+	0.842770i	$0.680923\pi$
$744$	8.00000	−	8.51278i	0.293294	−	0.312094i
$745$		0			0
$746$	−7.48913			−0.274196
$747$	0.302985	+	4.87375i	0.0110856	+	0.178321i
$748$	10.1168			0.369908
$749$	−17.1861	+	29.7673i	−0.627968	+	1.08767i
$750$		0			0
$751$	9.11684	+	15.7908i	0.332678	+	0.576216i	0.983036	−	0.183412i	$-0.0587143\pi$
$751$	9.11684	+	15.7908i	0.332678	+	0.576216i	−0.650358	+	0.759628i	$0.725381\pi$
$752$	−0.813859	−	1.40965i	−0.0296784	−	0.0514045i
$753$	−7.80298	−	25.8796i	−0.284357	−	0.943104i
$754$	−10.3723	+	17.9653i	−0.377736	+	0.654258i
$755$		0			0
$756$	9.48913	+	7.86797i	0.345116	+	0.286155i
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	5.43070	−	9.40625i	0.197252	−	0.341651i
$759$	−3.00000	−	9.94987i	−0.108893	−	0.361158i
$760$		0			0
$761$	−6.04755	−	10.4747i	−0.219223	−	0.379706i	0.735347	−	0.677690i	$-0.237019\pi$
$761$	−6.04755	−	10.4747i	−0.219223	−	0.379706i	−0.954571	+	0.297984i	$0.903686\pi$
$762$	−15.3723	−	3.61158i	−0.556879	−	0.130834i
$763$	−11.4198	+	19.7797i	−0.413426	+	0.716074i
$764$	−5.48913			−0.198590
$765$		0			0
$766$	−22.9783			−0.830238
$767$	−3.25544	+	5.63858i	−0.117547	+	0.203597i
$768$	−1.18614	+	1.26217i	−0.0428012	+	0.0455446i
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	0.981925	−	0.189273i	$-0.0606131\pi$
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	−0.654877	+	0.755735i	$0.727280\pi$
$770$		0			0
$771$	−1.62772	+	1.73205i	−0.0586209	+	0.0623783i
$772$	1.94158	−	3.36291i	0.0698789	−	0.121034i
$773$	−14.7446			−0.530325			−0.265163	−	0.964204i	$-0.585426\pi$
$773$	−14.7446			−0.530325			−0.265163	+	0.964204i	$0.585426\pi$
$774$	30.5475	+	15.1923i	1.09801	+	0.546076i
$775$		0			0
$776$	−1.31386	+	2.27567i	−0.0471648	+	0.0816918i
$777$	16.0000	+	3.75906i	0.573997	+	0.134855i
$778$	5.18614	+	8.98266i	0.185932	+	0.322044i
$779$	5.05842	+	8.76144i	0.181237	+	0.313911i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$	32.2337			1.15267
$783$	21.3030	−	7.89542i	0.761307	−	0.282159i
$784$	−1.37228			−0.0490100
$785$		0			0
$786$	−4.37228	−	14.5012i	−0.155954	−	0.517241i
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	8.74456	+	15.1460i	0.311512	+	0.539555i
$789$	−9.25544	−	2.17448i	−0.329502	−	0.0774136i
$790$		0			0
$791$	−34.9783			−1.24368
$792$	−0.255437	−	4.10891i	−0.00907657	−	0.146004i
$793$	−43.2554			−1.53605
$794$	5.62772	−	9.74749i	0.199720	−	0.345926i
$795$		0			0
$796$	4.74456	+	8.21782i	0.168167	+	0.291273i
$797$	1.62772	+	2.81929i	0.0576568	+	0.0998644i	0.893413	−	0.449236i	$-0.148304\pi$
$797$	1.62772	+	2.81929i	0.0576568	+	0.0998644i	−0.835756	+	0.549100i	$0.814970\pi$
$798$	−9.48913	+	10.0974i	−0.335911	+	0.357442i
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$		0			0
$801$	2.79211	−	1.85208i	0.0986544	−	0.0654399i
$802$	16.1168			0.569106
$803$	−9.68614	+	16.7769i	−0.341816	+	0.592044i
$804$	11.8030	+	2.77300i	0.416259	+	0.0977963i
$805$		0			0
$806$	−16.0000	−	27.7128i	−0.563576	−	0.976142i
$807$	−2.18614	−	7.25061i	−0.0769558	−	0.255234i
$808$	4.37228	−	7.57301i	0.153816	−	0.266418i
$809$	−12.3505			−0.434222			−0.217111	−	0.976147i	$-0.569663\pi$
$809$	−12.3505			−0.434222			−0.217111	+	0.976147i	$0.569663\pi$
$810$		0			0
$811$	9.37228			0.329105			0.164553	−	0.986368i	$-0.447382\pi$
$811$	9.37228			0.329105			0.164553	+	0.986368i	$0.447382\pi$
$812$	5.18614	−	8.98266i	0.181998	−	0.315230i
$813$	−4.00000	−	13.2665i	−0.140286	−	0.465276i
$814$	−2.74456	−	4.75372i	−0.0961969	−	0.166618i
$815$		0			0
$816$	12.4307	+	2.92048i	0.435162	+	0.102237i
$817$	−19.1753	+	33.2125i	−0.670858	+	1.16196i
$818$	−10.8614			−0.379760
$819$	28.1386	−	18.6650i	0.983242	−	0.652209i
$820$		0			0
$821$	−25.4198	+	44.0284i	−0.887158	+	1.53660i	−0.0439382	+	0.999034i	$0.513990\pi$
$821$	−25.4198	+	44.0284i	−0.887158	+	1.53660i	−0.843220	+	0.537569i	$0.819343\pi$
$822$	−2.23369	+	2.37686i	−0.0779088	+	0.0829025i
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	0.979567	+	0.201117i	$0.0644570\pi$
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	−0.315612	+	0.948888i	$0.602210\pi$
$824$	−8.00000	−	13.8564i	−0.278693	−	0.482711i
$825$		0			0
$826$	1.62772	−	2.81929i	0.0566356	−	0.0980957i
$827$	−8.13859			−0.283007			−0.141503	−	0.989938i	$-0.545194\pi$
$827$	−8.13859			−0.283007			−0.141503	+	0.989938i	$0.545194\pi$
$828$	−0.813859	−	13.0916i	−0.0282836	−	0.454964i
$829$	−32.8832			−1.14208			−0.571040	−	0.820923i	$-0.693460\pi$
$829$	−32.8832			−1.14208			−0.571040	+	0.820923i	$0.693460\pi$
$830$		0			0
$831$	−8.86141	−	2.08191i	−0.307399	−	0.0722206i
$832$	2.37228	+	4.10891i	0.0822441	+	0.142451i
$833$	5.05842	+	8.76144i	0.175264	+	0.303566i
$834$	−9.05842	−	30.0434i	−0.313668	−	1.04032i
$835$		0			0
$836$	4.62772			0.160053
$837$	−5.88316	+	34.5484i	−0.203352	+	1.19417i
$838$	−31.7228			−1.09585
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	0.177447	+	0.984130i	$0.443216\pi$
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	−0.941005	+	0.338391i	$0.890117\pi$
$840$		0			0
$841$	4.94158	+	8.55906i	0.170399	+	0.295140i
$842$	19.2337	+	33.3137i	0.662837	+	1.14807i
$843$	7.37228	+	1.73205i	0.253915	+	0.0596550i
$844$	3.62772	−	6.28339i	0.124871	−	0.216283i
$845$		0			0
$846$	4.37228	+	2.17448i	0.150322	+	0.0747602i
$847$	−21.6277			−0.743137
$848$	5.74456	−	9.94987i	0.197269	−	0.341680i
$849$	−37.7921	+	40.2145i	−1.29702	+	1.38016i
$850$		0			0
$851$	−8.74456	−	15.1460i	−0.299760	−	0.519199i
$852$	7.11684	−	7.57301i	0.243819	−	0.259447i
$853$	−0.883156	+	1.52967i	−0.0302387	+	0.0523749i	−0.880749	−	0.473584i	$-0.842960\pi$
$853$	−0.883156	+	1.52967i	−0.0302387	+	0.0523749i	0.850510	+	0.525959i	$0.176293\pi$
$854$	21.6277			0.740085
$855$		0			0
$856$	14.4891			0.495228
$857$	11.7446	−	20.3422i	0.401187	−	0.694876i	−0.592683	−	0.805436i	$-0.701931\pi$
$857$	11.7446	−	20.3422i	0.401187	−	0.694876i	0.993869	+	0.110560i	$0.0352646\pi$
$858$	−10.9783	−	2.57924i	−0.374791	−	0.0880538i
$859$	−0.0584220	−	0.101190i	−0.00199333	−	0.00345255i	0.865027	−	0.501725i	$-0.167301\pi$
$859$	−0.0584220	−	0.101190i	−0.00199333	−	0.00345255i	−0.867020	+	0.498273i	$0.833968\pi$
$860$		0			0
$861$	3.55842	+	11.8020i	0.121271	+	0.402209i
$862$	13.1168	−	22.7190i	0.446761	−	0.773814i
$863$	42.6060			1.45032			0.725162	−	0.688578i	$-0.241765\pi$
$863$	42.6060			1.45032			0.725162	+	0.688578i	$0.241765\pi$
$864$	0.872281	−	5.12241i	0.0296756	−	0.174268i
$865$		0			0
$866$	0.313859	−	0.543620i	0.0106654	−	0.0184730i
$867$	−18.6753	−	61.9389i	−0.634245	−	2.10355i
$868$	8.00000	+	13.8564i	0.271538	+	0.470317i
$869$	−1.37228	−	2.37686i	−0.0465515	−	0.0806295i
$870$		0			0
$871$	16.6060	−	28.7624i	0.562672	−	0.974576i
$872$	9.62772			0.326036
$873$	−0.489125	−	7.86797i	−0.0165544	−	0.266290i
$874$	14.7446			0.498742
$875$		0			0
$876$	−16.7446	+	17.8178i	−0.565746	+	0.602009i
$877$	−27.9783	−	48.4598i	−0.944758	−	1.63637i	−0.756234	−	0.654301i	$-0.772963\pi$
$877$	−27.9783	−	48.4598i	−0.944758	−	1.63637i	−0.188524	−	0.982069i	$-0.560370\pi$
$878$	−8.11684	−	14.0588i	−0.273930	−	0.474461i
$879$	−9.76631	+	10.3923i	−0.329410	+	0.350524i
$880$		0			0
$881$	27.3505			0.921463			0.460731	−	0.887540i	$-0.347587\pi$
$881$	27.3505			0.921463			0.460731	+	0.887540i	$0.347587\pi$
$882$	3.43070	−	2.27567i	0.115518	−	0.0766258i
$883$	−12.7228			−0.428157			−0.214078	−	0.976816i	$-0.568675\pi$
$883$	−12.7228			−0.428157			−0.214078	+	0.976816i	$0.568675\pi$
$884$	17.4891	−	30.2921i	0.588223	−	1.01883i
$885$		0			0
$886$	−13.2446	−	22.9403i	−0.444960	−	0.770693i
$887$	−18.8614	−	32.6689i	−0.633304	−	1.09691i	−0.986872	−	0.161506i	$-0.948365\pi$
$887$	−18.8614	−	32.6689i	−0.633304	−	1.09691i	0.353568	−	0.935409i	$-0.384968\pi$
$888$	−2.00000	−	6.63325i	−0.0671156	−	0.222597i
$889$	10.8139	−	18.7302i	0.362685	−	0.628189i
$890$		0			0
$891$	7.45245	+	9.84868i	0.249667	+	0.329943i
$892$	−12.3723			−0.414255
$893$	−2.74456	+	4.75372i	−0.0918433	+	0.159077i
$894$	−9.55842	−	31.7017i	−0.319681	−	1.06026i
$895$		0			0
$896$	−1.18614	−	2.05446i	−0.0396262	−	0.0686346i
$897$	−34.9783	−	8.21782i	−1.16789	−	0.274385i
$898$	9.43070	−	16.3345i	0.314707	−	0.545088i
$899$	29.4891			0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$	2.05842	−	3.56529i	0.0685380	−	0.118711i
$903$	−32.0000	+	34.0511i	−1.06489	+	1.13315i
$904$	7.37228	+	12.7692i	0.245198	+	0.424696i
$905$		0			0
$906$	11.8614	−	12.6217i	0.394069	−	0.419328i
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$	−1.88316			−0.0624947
$909$	1.62772	+	26.1831i	0.0539880	+	0.868440i
$910$		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	$-0.0782661\pi$
$912$	5.68614	+	1.33591i	0.188287	+	0.0442363i
$913$	1.11684	+	1.93443i	0.0369621	+	0.0640203i
$914$	15.0584	+	26.0820i	0.498088	+	0.862714i
$915$		0			0
$916$	−9.18614	+	15.9109i	−0.303519	+	0.525710i
$917$	20.7446			0.685046
$918$	−35.9198	+	13.3128i	−1.18553	+	0.439387i
$919$	42.4674			1.40087			0.700435	−	0.713716i	$-0.252989\pi$
$919$	42.4674			1.40087			0.700435	+	0.713716i	$0.252989\pi$
$920$		0			0
$921$	−16.6168	−	55.1118i	−0.547544	−	1.81600i
$922$	−9.55842	−	16.5557i	−0.314790	−	0.545232i
$923$	−14.2337	−	24.6535i	−0.468508	−	0.811479i
$924$	5.48913	+	1.28962i	0.180579	+	0.0424254i
$925$		0			0
$926$	−20.0000			−0.657241
$927$	42.9783	+	21.3745i	1.41159	+	0.702031i
$928$	−4.37228			−0.143527
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	−0.326312	−	0.945262i	$-0.605806\pi$
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	0.981777	−	0.190037i	$-0.0608607\pi$
$930$		0			0
$931$	2.31386	+	4.00772i	0.0758337	+	0.131348i
$932$	−5.05842	−	8.76144i	−0.165694	−	0.286991i
$933$	10.9783	−	11.6819i	0.359412	−	0.382449i
$934$	12.9416	−	22.4155i	0.423461	−	0.733457i
$935$		0			0
$936$	−12.7446	−	6.33830i	−0.416569	−	0.207174i
$937$	17.7228			0.578979			0.289490	−	0.957181i	$-0.406514\pi$
$937$	17.7228			0.578979			0.289490	+	0.957181i	$0.406514\pi$
$938$	−8.30298	+	14.3812i	−0.271102	+	0.469563i
$939$	−15.8030	−	3.71277i	−0.515711	−	0.121162i
$940$		0			0
$941$	−18.8139	−	32.5866i	−0.613314	−	1.06229i	−0.990678	−	0.136226i	$-0.956503\pi$
$941$	−18.8139	−	32.5866i	−0.613314	−	1.06229i	0.377363	−	0.926065i	$-0.376831\pi$
$942$	2.37228	+	7.86797i	0.0772931	+	0.256352i
$943$	6.55842	−	11.3595i	0.213572	−	0.369917i
$944$	−1.37228			−0.0446640
$945$		0			0
$946$	15.6060			0.507394
$947$	11.3614	−	19.6785i	0.369196	−	0.639466i	−0.620244	−	0.784409i	$-0.712966\pi$
$947$	11.3614	−	19.6785i	0.369196	−	0.639466i	0.989440	+	0.144943i	$0.0462997\pi$
$948$	−1.00000	−	3.31662i	−0.0324785	−	0.107719i
$949$	33.4891	+	58.0049i	1.08710	+	1.88292i
$950$		0			0
$951$	14.7446	+	3.46410i	0.478125	+	0.112331i
$952$	−8.74456	+	15.1460i	−0.283413	+	0.490886i
$953$	−30.8614			−0.999699			−0.499850	−	0.866112i	$-0.666611\pi$
$953$	−30.8614			−0.999699			−0.499850	+	0.866112i	$0.666611\pi$
$954$	2.13859	+	34.4010i	0.0692395	+	1.11377i
$955$		0			0
$956$	7.37228	−	12.7692i	0.238437	−	0.412984i
$957$	7.11684	−	7.57301i	0.230055	−	0.244801i
$958$	11.7446	+	20.3422i	0.379450	+	0.657226i
$959$	−2.23369	−	3.86886i	−0.0721295	−	0.124932i
$960$		0			0
$961$	−7.24456	+	12.5480i	−0.233696	+	0.404773i
$962$	−18.9783			−0.611883
$963$	−36.2228	+	24.0275i	−1.16726	+	0.774275i
$964$	10.4891			0.337832
$965$		0			0
$966$	17.4891	+	4.10891i	0.562703	+	0.132202i
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	0.976953	−	0.213453i	$-0.0684711\pi$
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	−0.673333	+	0.739340i	$0.735138\pi$
$968$	4.55842	+	7.89542i	0.146513	+	0.253768i
$969$	−12.4307	−	41.2280i	−0.399332	−	1.32443i
$970$		0			0
$971$	22.9783			0.737407			0.368704	−	0.929547i	$-0.379802\pi$
$971$	22.9783			0.737407			0.368704	+	0.929547i	$0.379802\pi$
$972$	6.31386	+	14.2525i	0.202517	+	0.457151i
$973$	42.9783			1.37782
$974$	−0.627719	+	1.08724i	−0.0201134	+	0.0348374i
$975$		0			0
$976$	−4.55842	−	7.89542i	−0.145912	−	0.252726i
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	−0.985047	−	0.172284i	$-0.944885\pi$
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	0.343322	−	0.939218i	$-0.388448\pi$
$978$	−2.51087	−	0.589907i	−0.0802889	−	0.0188632i
$979$	0.766312	−	1.32729i	0.0244914	−	0.0424204i
$980$		0			0
$981$	−24.0693	+	15.9658i	−0.768474	+	0.509748i
$982$	3.60597			0.115071
$983$	7.93070	−	13.7364i	0.252950	−	0.438123i	−0.711387	−	0.702801i	$-0.751932\pi$
$983$	7.93070	−	13.7364i	0.252950	−	0.438123i	0.964337	+	0.264678i	$0.0852658\pi$
$984$	3.55842	−	3.78651i	0.113438	−	0.120709i
$985$		0			0
$986$	16.1168	+	27.9152i	0.513265	+	0.889001i
$987$	−4.58017	+	4.87375i	−0.145788	+	0.155133i
$988$	8.00000	−	13.8564i	0.254514	−	0.440831i
$989$	49.7228			1.58109
$990$		0			0
$991$	−18.2337			−0.579212			−0.289606	−	0.957146i	$-0.593524\pi$
$991$	−18.2337			−0.579212			−0.289606	+	0.957146i	$0.593524\pi$
$992$	3.37228	−	5.84096i	0.107070	−	0.185451i
$993$	−30.7446	−	7.22316i	−0.975649	−	0.229220i
$994$	7.11684	+	12.3267i	0.225733	+	0.390980i
$995$		0			0
$996$	0.813859	+	2.69927i	0.0257881	+	0.0855295i
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	−2.11684			−0.0670075
$999$	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.e.j.151.1		4
3.2	odd	2		1350.2.e.l.451.1		4
5.2	odd	4		450.2.j.g.349.1		8
5.3	odd	4		450.2.j.g.349.4		8
5.4	even	2		90.2.e.c.61.2	yes	4
9.2	odd	6		4050.2.a.bo.1.2		2
9.4	even	3	inner	450.2.e.j.301.2		4
9.5	odd	6		1350.2.e.l.901.1		4
9.7	even	3		4050.2.a.bw.1.2		2
15.2	even	4		1350.2.j.f.1099.3		8
15.8	even	4		1350.2.j.f.1099.2		8
15.14	odd	2		270.2.e.c.181.2		4
20.19	odd	2		720.2.q.f.241.1		4
45.2	even	12		4050.2.c.ba.649.2		4
45.4	even	6		90.2.e.c.31.1	✓	4
45.7	odd	12		4050.2.c.v.649.4		4
45.13	odd	12		450.2.j.g.49.1		8
45.14	odd	6		270.2.e.c.91.2		4
45.22	odd	12		450.2.j.g.49.4		8
45.23	even	12		1350.2.j.f.199.3		8
45.29	odd	6		810.2.a.k.1.1		2
45.32	even	12		1350.2.j.f.199.2		8
45.34	even	6		810.2.a.i.1.1		2
45.38	even	12		4050.2.c.ba.649.3		4
45.43	odd	12		4050.2.c.v.649.1		4
60.59	even	2		2160.2.q.f.721.1		4
180.59	even	6		2160.2.q.f.1441.1		4
180.79	odd	6		6480.2.a.be.1.2		2
180.119	even	6		6480.2.a.bn.1.2		2
180.139	odd	6		720.2.q.f.481.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	45.4	even	6
90.2.e.c.61.2	yes	4	5.4	even	2
270.2.e.c.91.2		4	45.14	odd	6
270.2.e.c.181.2		4	15.14	odd	2
450.2.e.j.151.1		4	1.1	even	1	trivial
450.2.e.j.301.2		4	9.4	even	3	inner
450.2.j.g.49.1		8	45.13	odd	12
450.2.j.g.49.4		8	45.22	odd	12
450.2.j.g.349.1		8	5.2	odd	4
450.2.j.g.349.4		8	5.3	odd	4
720.2.q.f.241.1		4	20.19	odd	2
720.2.q.f.481.2		4	180.139	odd	6
810.2.a.i.1.1		2	45.34	even	6
810.2.a.k.1.1		2	45.29	odd	6
1350.2.e.l.451.1		4	3.2	odd	2
1350.2.e.l.901.1		4	9.5	odd	6
1350.2.j.f.199.2		8	45.32	even	12
1350.2.j.f.199.3		8	45.23	even	12
1350.2.j.f.1099.2		8	15.8	even	4
1350.2.j.f.1099.3		8	15.2	even	4
2160.2.q.f.721.1		4	60.59	even	2
2160.2.q.f.1441.1		4	180.59	even	6
4050.2.a.bo.1.2		2	9.2	odd	6
4050.2.a.bw.1.2		2	9.7	even	3
4050.2.c.v.649.1		4	45.43	odd	12
4050.2.c.v.649.4		4	45.7	odd	12
4050.2.c.ba.649.2		4	45.2	even	12
4050.2.c.ba.649.3		4	45.38	even	12
6480.2.a.be.1.2		2	180.79	odd	6
6480.2.a.bn.1.2		2	180.119	even	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 1.65831i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68614 + 0.396143i) q^{6} +(-1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +(-0.686141 + 1.18843i) q^{11} +(-1.18614 + 1.26217i) q^{12} +(2.37228 + 4.10891i) q^{13} +(-1.18614 - 2.05446i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.37228 q^{17} +(-0.186141 - 2.99422i) q^{18} +3.37228 q^{19} +(4.00000 + 0.939764i) q^{21} +(-0.686141 - 1.18843i) q^{22} +(-2.18614 - 3.78651i) q^{23} +(-0.500000 - 1.65831i) q^{24} -4.74456 q^{26} +(4.00000 + 3.31662i) q^{27} +2.37228 q^{28} +(2.18614 - 3.78651i) q^{29} +(3.37228 + 5.84096i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.31386 + 0.543620i) q^{33} +(-3.68614 + 6.38458i) q^{34} +(2.68614 + 1.33591i) q^{36} +4.00000 q^{37} +(-1.68614 + 2.92048i) q^{38} +(5.62772 - 5.98844i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-2.81386 + 2.99422i) q^{42} +(-5.68614 + 9.84868i) q^{43} +1.37228 q^{44} +4.37228 q^{46} +(-0.813859 + 1.40965i) q^{47} +(1.68614 + 0.396143i) q^{48} +(0.686141 + 1.18843i) q^{49} +(-3.68614 - 12.2255i) q^{51} +(2.37228 - 4.10891i) q^{52} -11.4891 q^{53} +(-4.87228 + 1.80579i) q^{54} +(-1.18614 + 2.05446i) q^{56} +(-1.68614 - 5.59230i) q^{57} +(2.18614 + 3.78651i) q^{58} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} -6.74456 q^{62} +(-0.441578 - 7.10313i) q^{63} +1.00000 q^{64} +(-1.62772 + 1.73205i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-3.68614 - 6.38458i) q^{68} +(-5.18614 + 5.51856i) q^{69} -6.00000 q^{71} +(-2.50000 + 1.65831i) q^{72} +14.1168 q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.68614 - 2.92048i) q^{76} +(-1.62772 - 2.81929i) q^{77} +(2.37228 + 7.86797i) q^{78} +(-1.00000 + 1.73205i) q^{79} +(3.50000 - 8.29156i) q^{81} -3.00000 q^{82} +(0.813859 - 1.40965i) q^{83} +(-1.18614 - 3.93398i) q^{84} +(-5.68614 - 9.84868i) q^{86} +(-7.37228 - 1.73205i) q^{87} +(-0.686141 + 1.18843i) q^{88} -1.11684 q^{89} -11.2554 q^{91} +(-2.18614 + 3.78651i) q^{92} +(8.00000 - 8.51278i) q^{93} +(-0.813859 - 1.40965i) q^{94} +(-1.18614 + 1.26217i) q^{96} +(-1.31386 + 2.27567i) q^{97} -1.37228 q^{98} +(-0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{6} + q^{7} + 4 q^{8} - 10 q^{9} + 3 q^{11} + q^{12} - 2 q^{13} + q^{14} - 2 q^{16} + 18 q^{17} + 5 q^{18} + 2 q^{19} + 16 q^{21} + 3 q^{22} - 3 q^{23} - 2 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^6 + q^7 + 4 * q^8 - 10 * q^9 + 3 * q^11 + q^12 - 2 * q^13 + q^14 - 2 * q^16 + 18 * q^17 + 5 * q^18 + 2 * q^19 + 16 * q^21 + 3 * q^22 - 3 * q^23 - 2 * q^24 + 4 * q^26 + 16 * q^27 - 2 * q^28 + 3 * q^29 + 2 * q^31 - 2 * q^32 + 15 * q^33 - 9 * q^34 + 5 * q^36 + 16 * q^37 - q^38 + 34 * q^39 + 6 * q^41 - 17 * q^42 - 17 * q^43 - 6 * q^44 + 6 * q^46 - 9 * q^47 + q^48 - 3 * q^49 - 9 * q^51 - 2 * q^52 - 8 * q^54 + q^56 - q^57 + 3 * q^58 - 3 * q^59 - q^61 - 4 * q^62 - 19 * q^63 + 4 * q^64 - 18 * q^66 - 14 * q^67 - 9 * q^68 - 15 * q^69 - 24 * q^71 - 10 * q^72 + 22 * q^73 - 8 * q^74 - q^76 - 18 * q^77 - 2 * q^78 - 4 * q^79 + 14 * q^81 - 12 * q^82 + 9 * q^83 + q^84 - 17 * q^86 - 18 * q^87 + 3 * q^88 + 30 * q^89 - 68 * q^91 - 3 * q^92 + 32 * q^93 - 9 * q^94 + q^96 - 11 * q^97 + 6 * q^98 - 24 * q^99

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