LMFDB - Embedded newform 450.2.j.g.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(49,450)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			49.4
Root			$0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	450.49
Dual form			450.2.j.g.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(2.05446 - 1.18614i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(2.05446 - 1.18614i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(-0.686141 - 1.18843i) q^{11} +(1.26217 - 1.18614i) q^{12} +(-4.10891 - 2.37228i) q^{13} +(1.18614 - 2.05446i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.37228i q^{17} +(2.99422 + 0.186141i) q^{18} -3.37228 q^{19} +(4.00000 - 0.939764i) q^{21} +(-1.18843 - 0.686141i) q^{22} +(3.78651 + 2.18614i) q^{23} +(0.500000 - 1.65831i) q^{24} -4.74456 q^{26} +(3.31662 + 4.00000i) q^{27} -2.37228i q^{28} +(-2.18614 - 3.78651i) q^{29} +(3.37228 - 5.84096i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.543620 - 2.31386i) q^{33} +(3.68614 + 6.38458i) q^{34} +(2.68614 - 1.33591i) q^{36} +4.00000i q^{37} +(-2.92048 + 1.68614i) q^{38} +(-5.62772 - 5.98844i) q^{39} +(1.50000 - 2.59808i) q^{41} +(2.99422 - 2.81386i) q^{42} +(-9.84868 + 5.68614i) q^{43} -1.37228 q^{44} +4.37228 q^{46} +(1.40965 - 0.813859i) q^{47} +(-0.396143 - 1.68614i) q^{48} +(-0.686141 + 1.18843i) q^{49} +(-3.68614 + 12.2255i) q^{51} +(-4.10891 + 2.37228i) q^{52} +11.4891i q^{53} +(4.87228 + 1.80579i) q^{54} +(-1.18614 - 2.05446i) q^{56} +(-5.59230 - 1.68614i) q^{57} +(-3.78651 - 2.18614i) q^{58} +(-0.686141 + 1.18843i) q^{59} +(-4.55842 - 7.89542i) q^{61} -6.74456i q^{62} +(7.10313 + 0.441578i) q^{63} -1.00000 q^{64} +(-1.62772 - 1.73205i) q^{66} +(-6.06218 - 3.50000i) q^{67} +(6.38458 + 3.68614i) q^{68} +(5.18614 + 5.51856i) q^{69} -6.00000 q^{71} +(1.65831 - 2.50000i) q^{72} -14.1168i q^{73} +(2.00000 + 3.46410i) q^{74} +(-1.68614 + 2.92048i) q^{76} +(-2.81929 - 1.62772i) q^{77} +(-7.86797 - 2.37228i) q^{78} +(1.00000 + 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} -3.00000i q^{82} +(1.40965 - 0.813859i) q^{83} +(1.18614 - 3.93398i) q^{84} +(-5.68614 + 9.84868i) q^{86} +(-1.73205 - 7.37228i) q^{87} +(-1.18843 + 0.686141i) q^{88} +1.11684 q^{89} -11.2554 q^{91} +(3.78651 - 2.18614i) q^{92} +(8.51278 - 8.00000i) q^{93} +(0.813859 - 1.40965i) q^{94} +(-1.18614 - 1.26217i) q^{96} +(2.27567 - 1.31386i) q^{97} +1.37228i q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$6$	1.68614	−	0.396143i	0.688364	−	0.161725i
$7$	2.05446	−	1.18614i	0.776511	−	0.448319i	−0.0586811	−	0.998277i	$-0.518690\pi$
$7$	2.05446	−	1.18614i	0.776511	−	0.448319i	0.835192	+	0.549958i	$0.185356\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.50000	+	1.65831i	0.833333	+	0.552771i
$10$		0			0
$11$	−0.686141	−	1.18843i	−0.206879	−	0.358325i	0.743851	−	0.668346i	$-0.232997\pi$
$11$	−0.686141	−	1.18843i	−0.206879	−	0.358325i	−0.950730	+	0.310021i	$0.899664\pi$
$12$	1.26217	−	1.18614i	0.364357	−	0.342409i
$13$	−4.10891	−	2.37228i	−1.13961	−	0.657952i	−0.193274	−	0.981145i	$-0.561911\pi$
$13$	−4.10891	−	2.37228i	−1.13961	−	0.657952i	−0.946333	+	0.323192i	$0.895244\pi$
$14$	1.18614	−	2.05446i	0.317009	−	0.549076i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			7.37228i			1.78804i	0.448026	+	0.894020i	$0.352127\pi$
$17$			7.37228i			1.78804i	−0.448026	+	0.894020i	$0.647873\pi$
$18$	2.99422	+	0.186141i	0.705744	+	0.0438738i
$19$	−3.37228			−0.773654			−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228			−0.773654			−0.386827	+	0.922152i	$0.626429\pi$
$20$		0			0
$21$	4.00000	−	0.939764i	0.872872	−	0.205073i
$22$	−1.18843	−	0.686141i	−0.253374	−	0.146286i
$23$	3.78651	+	2.18614i	0.789541	+	0.455842i	0.839801	−	0.542894i	$-0.182672\pi$
$23$	3.78651	+	2.18614i	0.789541	+	0.455842i	−0.0502598	+	0.998736i	$0.516005\pi$
$24$	0.500000	−	1.65831i	0.102062	−	0.338502i
$25$		0			0
$26$	−4.74456			−0.930485
$27$	3.31662	+	4.00000i	0.638285	+	0.769800i
$28$		−	2.37228i		−	0.448319i
$29$	−2.18614	−	3.78651i	−0.405956	−	0.703137i	0.588476	−	0.808515i	$-0.299728\pi$
$29$	−2.18614	−	3.78651i	−0.405956	−	0.703137i	−0.994432	+	0.105378i	$0.966395\pi$
$30$		0			0
$31$	3.37228	−	5.84096i	0.605680	−	1.04907i	−0.386264	−	0.922388i	$-0.626235\pi$
$31$	3.37228	−	5.84096i	0.605680	−	1.04907i	0.991944	−	0.126680i	$-0.0404320\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.543620	−	2.31386i	−0.0946322	−	0.402791i
$34$	3.68614	+	6.38458i	0.632168	+	1.09495i
$35$		0			0
$36$	2.68614	−	1.33591i	0.447690	−	0.222651i
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	−2.92048	+	1.68614i	−0.473765	+	0.273528i
$39$	−5.62772	−	5.98844i	−0.901156	−	0.958918i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	2.99422	−	2.81386i	0.462018	−	0.434188i
$43$	−9.84868	+	5.68614i	−1.50191	+	0.867128i	−0.501913	+	0.864918i	$0.667370\pi$
$43$	−9.84868	+	5.68614i	−1.50191	+	0.867128i	−0.999998	+	0.00221007i	$0.999297\pi$
$44$	−1.37228			−0.206879
$45$		0			0
$46$	4.37228			0.644658
$47$	1.40965	−	0.813859i	0.205618	−	0.118714i	−0.393655	−	0.919258i	$-0.628790\pi$
$47$	1.40965	−	0.813859i	0.205618	−	0.118714i	0.599273	+	0.800545i	$0.295456\pi$
$48$	−0.396143	−	1.68614i	−0.0571784	−	0.243373i
$49$	−0.686141	+	1.18843i	−0.0980201	+	0.169776i
$50$		0			0
$51$	−3.68614	+	12.2255i	−0.516163	+	1.71192i
$52$	−4.10891	+	2.37228i	−0.569804	+	0.328976i
$53$			11.4891i			1.57815i	0.614295	+	0.789076i	$0.289440\pi$
$53$			11.4891i			1.57815i	−0.614295	+	0.789076i	$0.710560\pi$
$54$	4.87228	+	1.80579i	0.663034	+	0.245737i
$55$		0			0
$56$	−1.18614	−	2.05446i	−0.158505	−	0.274538i
$57$	−5.59230	−	1.68614i	−0.740718	−	0.223335i
$58$	−3.78651	−	2.18614i	−0.497193	−	0.287054i
$59$	−0.686141	+	1.18843i	−0.0893279	+	0.154720i	−0.907227	−	0.420641i	$-0.861805\pi$
$59$	−0.686141	+	1.18843i	−0.0893279	+	0.154720i	0.817899	+	0.575361i	$0.195139\pi$
$60$		0			0
$61$	−4.55842	−	7.89542i	−0.583646	−	1.01090i	−0.995043	−	0.0994483i	$-0.968292\pi$
$61$	−4.55842	−	7.89542i	−0.583646	−	1.01090i	0.411397	−	0.911456i	$-0.365041\pi$
$62$		−	6.74456i		−	0.856560i
$63$	7.10313	+	0.441578i	0.894910	+	0.0556336i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.62772	−	1.73205i	−0.200358	−	0.213201i
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	0.0816792	−	0.996659i	$-0.473972\pi$
$67$	−6.06218	−	3.50000i	−0.740613	−	0.427593i	−0.822292	+	0.569066i	$0.807305\pi$
$68$	6.38458	+	3.68614i	0.774244	+	0.447010i
$69$	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	$0.615871\pi$
$72$	1.65831	−	2.50000i	0.195434	−	0.294628i
$73$		−	14.1168i		−	1.65225i	−0.563486	−	0.826126i	$-0.690540\pi$
$73$		−	14.1168i		−	1.65225i	0.563486	−	0.826126i	$-0.309460\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	−1.68614	+	2.92048i	−0.193414	+	0.335002i
$77$	−2.81929	−	1.62772i	−0.321288	−	0.185496i
$78$	−7.86797	−	2.37228i	−0.890872	−	0.268608i
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$		−	3.00000i		−	0.331295i
$83$	1.40965	−	0.813859i	0.154729	−	0.0893327i	−0.420637	−	0.907229i	$-0.638193\pi$
$83$	1.40965	−	0.813859i	0.154729	−	0.0893327i	0.575365	+	0.817897i	$0.304860\pi$
$84$	1.18614	−	3.93398i	0.129419	−	0.429233i
$85$		0			0
$86$	−5.68614	+	9.84868i	−0.613152	+	1.06201i
$87$	−1.73205	−	7.37228i	−0.185695	−	0.790392i
$88$	−1.18843	+	0.686141i	−0.126687	+	0.0731428i
$89$	1.11684			0.118385			0.0591926	−	0.998247i	$-0.481147\pi$
$89$	1.11684			0.118385			0.0591926	+	0.998247i	$0.481147\pi$
$90$		0			0
$91$	−11.2554			−1.17989
$92$	3.78651	−	2.18614i	0.394771	−	0.227921i
$93$	8.51278	−	8.00000i	0.882734	−	0.829561i
$94$	0.813859	−	1.40965i	0.0839432	−	0.145394i
$95$		0			0
$96$	−1.18614	−	1.26217i	−0.121060	−	0.128820i
$97$	2.27567	−	1.31386i	0.231059	−	0.133402i	−0.380001	−	0.924986i	$-0.624076\pi$
$97$	2.27567	−	1.31386i	0.231059	−	0.133402i	0.611061	+	0.791584i	$0.290743\pi$
$98$			1.37228i			0.138621i
$99$	0.255437	−	4.10891i	0.0256724	−	0.412961i
$100$		0			0
$101$	4.37228	+	7.57301i	0.435058	+	0.753543i	0.997300	−	0.0734297i	$-0.0233944\pi$
$101$	4.37228	+	7.57301i	0.435058	+	0.753543i	−0.562242	+	0.826973i	$0.690061\pi$
$102$	2.92048	+	12.4307i	0.289171	+	1.23082i
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.990325	−	0.138767i	$-0.0443138\pi$
$103$	13.8564	+	8.00000i	1.36531	+	0.788263i	0.374987	+	0.927030i	$0.377647\pi$
$104$	−2.37228	+	4.10891i	−0.232621	+	0.402912i
$105$		0			0
$106$	5.74456	+	9.94987i	0.557961	+	0.966417i
$107$			14.4891i			1.40072i	0.713791	+	0.700358i	$0.246976\pi$
$107$			14.4891i			1.40072i	−0.713791	+	0.700358i	$0.753024\pi$
$108$	5.12241	−	0.872281i	0.492905	−	0.0839353i
$109$	−9.62772			−0.922168			−0.461084	−	0.887356i	$-0.652539\pi$
$109$	−9.62772			−0.922168			−0.461084	+	0.887356i	$0.652539\pi$
$110$		0			0
$111$	−2.00000	+	6.63325i	−0.189832	+	0.629600i
$112$	−2.05446	−	1.18614i	−0.194128	−	0.112080i
$113$	−12.7692	−	7.37228i	−1.20122	−	0.693526i	−0.240395	−	0.970675i	$-0.577277\pi$
$113$	−12.7692	−	7.37228i	−1.20122	−	0.693526i	−0.960827	+	0.277149i	$0.910610\pi$
$114$	−5.68614	+	1.33591i	−0.532556	+	0.125119i
$115$		0			0
$116$	−4.37228			−0.405956
$117$	−6.33830	−	12.7446i	−0.585976	−	1.17824i
$118$			1.37228i			0.126329i
$119$	8.74456	+	15.1460i	0.801613	+	1.38843i
$120$		0			0
$121$	4.55842	−	7.89542i	0.414402	−	0.717765i
$122$	−7.89542	−	4.55842i	−0.714818	−	0.412700i
$123$	3.78651	−	3.55842i	0.341418	−	0.320852i
$124$	−3.37228	−	5.84096i	−0.302840	−	0.524534i
$125$		0			0
$126$	6.37228	−	3.16915i	0.567688	−	0.282330i
$127$		−	9.11684i		−	0.808989i	−0.914540	−	0.404495i	$-0.867447\pi$
$127$		−	9.11684i		−	0.808989i	0.914540	−	0.404495i	$-0.132553\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−19.1753	+	4.50506i	−1.68829	+	0.396648i
$130$		0			0
$131$	−4.37228	+	7.57301i	−0.382008	+	0.661657i	−0.991349	−	0.131251i	$-0.958101\pi$
$131$	−4.37228	+	7.57301i	−0.382008	+	0.661657i	0.609341	+	0.792908i	$0.291434\pi$
$132$	−2.27567	−	0.686141i	−0.198072	−	0.0597209i
$133$	−6.92820	+	4.00000i	−0.600751	+	0.346844i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	7.37228			0.632168
$137$	1.63086	−	0.941578i	0.139334	−	0.0804444i	−0.428713	−	0.903441i	$-0.641033\pi$
$137$	1.63086	−	0.941578i	0.139334	−	0.0804444i	0.568046	+	0.822996i	$0.307699\pi$
$138$	7.25061	+	2.18614i	0.617213	+	0.186097i
$139$	9.05842	−	15.6896i	0.768325	−	1.33078i	−0.170145	−	0.985419i	$-0.554424\pi$
$139$	9.05842	−	15.6896i	0.768325	−	1.33078i	0.938470	−	0.345359i	$-0.112243\pi$
$140$		0			0
$141$	2.74456	−	0.644810i	0.231134	−	0.0543028i
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$			6.51087i			0.544467i
$144$	0.186141	−	2.99422i	0.0155117	−	0.249518i
$145$		0			0
$146$	−7.05842	−	12.2255i	−0.584159	−	1.01179i
$147$	−1.73205	+	1.62772i	−0.142857	+	0.134252i
$148$	3.46410	+	2.00000i	0.284747	+	0.164399i
$149$	9.55842	−	16.5557i	0.783056	−	1.35629i	−0.147097	−	0.989122i	$-0.546993\pi$
$149$	9.55842	−	16.5557i	0.783056	−	1.35629i	0.930153	−	0.367171i	$-0.119674\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$			3.37228i			0.273528i
$153$	−12.2255	+	18.4307i	−0.988377	+	1.49003i
$154$	−3.25544			−0.262331
$155$		0			0
$156$	−8.00000	+	1.87953i	−0.640513	+	0.150483i
$157$	4.10891	+	2.37228i	0.327927	+	0.189329i	0.654920	−	0.755698i	$-0.272702\pi$
$157$	4.10891	+	2.37228i	0.327927	+	0.189329i	−0.326993	+	0.945027i	$0.606036\pi$
$158$	1.73205	+	1.00000i	0.137795	+	0.0795557i
$159$	−5.74456	+	19.0526i	−0.455573	+	1.51097i
$160$		0			0
$161$	10.3723			0.817450
$162$	7.17687	+	5.43070i	0.563868	+	0.426676i
$163$			1.48913i			0.116637i	0.998298	+	0.0583186i	$0.0185739\pi$
$163$			1.48913i			0.116637i	−0.998298	+	0.0583186i	$0.981426\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	0.813859	−	1.40965i	0.0631677	−	0.109410i
$167$	6.60580	+	3.81386i	0.511172	+	0.295125i	0.733315	−	0.679889i	$-0.237972\pi$
$167$	6.60580	+	3.81386i	0.511172	+	0.295125i	−0.222143	+	0.975014i	$0.571305\pi$
$168$	−0.939764	−	4.00000i	−0.0725044	−	0.308607i
$169$	4.75544	+	8.23666i	0.365803	+	0.633589i
$170$		0			0
$171$	−8.43070	−	5.59230i	−0.644712	−	0.427654i
$172$			11.3723i			0.867128i
$173$	8.01544	−	4.62772i	0.609403	−	0.351839i	−0.163329	−	0.986572i	$-0.552223\pi$
$173$	8.01544	−	4.62772i	0.609403	−	0.351839i	0.772732	+	0.634733i	$0.218890\pi$
$174$	−5.18614	−	5.51856i	−0.393160	−	0.418361i
$175$		0			0
$176$	−0.686141	+	1.18843i	−0.0517198	+	0.0895813i
$177$	−1.73205	+	1.62772i	−0.130189	+	0.122347i
$178$	0.967215	−	0.558422i	0.0724958	−	0.0418555i
$179$	3.25544			0.243323			0.121661	−	0.992572i	$-0.461178\pi$
$179$	3.25544			0.243323			0.121661	+	0.992572i	$0.461178\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$	−9.74749	+	5.62772i	−0.722532	+	0.417154i
$183$	−3.61158	−	15.3723i	−0.266976	−	1.13635i
$184$	2.18614	−	3.78651i	0.161164	−	0.279145i
$185$		0			0
$186$	3.37228	−	11.1846i	0.247268	−	0.820094i
$187$	8.76144	−	5.05842i	0.640700	−	0.369908i
$188$		−	1.62772i		−	0.118714i
$189$	11.5584	+	4.28384i	0.840751	+	0.311604i
$190$		0			0
$191$	2.74456	+	4.75372i	0.198590	+	0.343967i	0.948071	−	0.318058i	$-0.103031\pi$
$191$	2.74456	+	4.75372i	0.198590	+	0.343967i	−0.749482	+	0.662025i	$0.769697\pi$
$192$	−1.65831	−	0.500000i	−0.119678	−	0.0360844i
$193$	−3.36291	−	1.94158i	−0.242068	−	0.139758i	0.374059	−	0.927405i	$-0.377966\pi$
$193$	−3.36291	−	1.94158i	−0.242068	−	0.139758i	−0.616127	+	0.787647i	$0.711299\pi$
$194$	1.31386	−	2.27567i	0.0943296	−	0.163384i
$195$		0			0
$196$	0.686141	+	1.18843i	0.0490100	+	0.0848879i
$197$		−	17.4891i		−	1.24605i	−0.782202	−	0.623024i	$-0.785904\pi$
$197$		−	17.4891i		−	1.24605i	0.782202	−	0.623024i	$-0.214096\pi$
$198$	−1.83324	−	3.68614i	−0.130283	−	0.261963i
$199$	9.48913			0.672666			0.336333	−	0.941743i	$-0.390813\pi$
$199$	9.48913			0.672666			0.336333	+	0.941743i	$0.390813\pi$
$200$		0			0
$201$	−8.30298	−	8.83518i	−0.585647	−	0.623186i
$202$	7.57301	+	4.37228i	0.532835	+	0.307633i
$203$	−8.98266	−	5.18614i	−0.630459	−	0.363996i
$204$	8.74456	+	9.30506i	0.612242	+	0.651485i
$205$		0			0
$206$	16.0000			1.11477
$207$	5.84096	+	11.7446i	0.405975	+	0.816304i
$208$			4.74456i			0.328976i
$209$	2.31386	+	4.00772i	0.160053	+	0.277220i
$210$		0			0
$211$	3.62772	−	6.28339i	0.249742	−	0.432567i	−0.713712	−	0.700439i	$-0.752987\pi$
$211$	3.62772	−	6.28339i	0.249742	−	0.432567i	0.963454	+	0.267873i	$0.0863207\pi$
$212$	9.94987	+	5.74456i	0.683360	+	0.394538i
$213$	−9.94987	−	3.00000i	−0.681754	−	0.205557i
$214$	7.24456	+	12.5480i	0.495228	+	0.857760i
$215$		0			0
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$		−	16.0000i		−	1.08615i
$218$	−8.33785	+	4.81386i	−0.564710	+	0.326036i
$219$	7.05842	−	23.4101i	0.476964	−	1.58191i
$220$		0			0
$221$	17.4891	−	30.2921i	1.17645	−	2.03766i
$222$	1.58457	+	6.74456i	0.106350	+	0.452665i
$223$	10.7147	−	6.18614i	0.717510	−	0.414255i	−0.0963255	−	0.995350i	$-0.530709\pi$
$223$	10.7147	−	6.18614i	0.717510	−	0.414255i	0.813836	+	0.581095i	$0.197376\pi$
$224$	−2.37228			−0.158505
$225$		0			0
$226$	−14.7446			−0.980794
$227$	−1.63086	+	0.941578i	−0.108244	+	0.0624947i	−0.553145	−	0.833085i	$-0.686572\pi$
$227$	−1.63086	+	0.941578i	−0.108244	+	0.0624947i	0.444901	+	0.895580i	$0.353239\pi$
$228$	−4.25639	+	4.00000i	−0.281886	+	0.264906i
$229$	9.18614	−	15.9109i	0.607037	−	1.05142i	−0.384689	−	0.923046i	$-0.625691\pi$
$229$	9.18614	−	15.9109i	0.607037	−	1.05142i	0.991726	−	0.128373i	$-0.0409755\pi$
$230$		0			0
$231$	−3.86141	−	4.10891i	−0.254062	−	0.270347i
$232$	−3.78651	+	2.18614i	−0.248596	+	0.143527i
$233$		−	10.1168i		−	0.662776i	−0.943494	−	0.331388i	$-0.892483\pi$
$233$		−	10.1168i		−	0.662776i	0.943494	−	0.331388i	$-0.107517\pi$
$234$	−11.8614	−	7.86797i	−0.775404	−	0.514345i
$235$		0			0
$236$	0.686141	+	1.18843i	0.0446640	+	0.0773602i
$237$	0.792287	+	3.37228i	0.0514646	+	0.219053i
$238$	15.1460	+	8.74456i	0.981771	+	0.566826i
$239$	−7.37228	+	12.7692i	−0.476873	+	0.825969i	−0.999649	−	0.0265017i	$-0.991563\pi$
$239$	−7.37228	+	12.7692i	−0.476873	+	0.825969i	0.522776	+	0.852470i	$0.324897\pi$
$240$		0			0
$241$	−5.24456	−	9.08385i	−0.337832	−	0.585142i	0.646193	−	0.763174i	$-0.276360\pi$
$241$	−5.24456	−	9.08385i	−0.337832	−	0.585142i	−0.984025	+	0.178032i	$0.943027\pi$
$242$		−	9.11684i		−	0.586053i
$243$	1.65831	+	15.5000i	0.106381	+	0.994325i
$244$	−9.11684			−0.583646
$245$		0			0
$246$	1.50000	−	4.97494i	0.0956365	−	0.317190i
$247$	13.8564	+	8.00000i	0.881662	+	0.509028i
$248$	−5.84096	−	3.37228i	−0.370901	−	0.214140i
$249$	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	$0.336076\pi$
$252$	3.93398	−	5.93070i	0.247818	−	0.373599i
$253$		−	6.00000i		−	0.377217i
$254$	−4.55842	−	7.89542i	−0.286021	−	0.495403i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.18843	−	0.686141i	−0.0741323	−	0.0428003i	0.462476	−	0.886632i	$-0.346961\pi$
$257$	−1.18843	−	0.686141i	−0.0741323	−	0.0428003i	−0.536608	+	0.843832i	$0.680295\pi$
$258$	−14.3537	+	13.4891i	−0.893625	+	0.839796i
$259$	4.74456	+	8.21782i	0.294813	+	0.510631i
$260$		0			0
$261$	0.813859	−	13.0916i	0.0503766	−	0.810348i
$262$			8.74456i			0.540241i
$263$	4.75372	−	2.74456i	0.293127	−	0.169237i	−0.346224	−	0.938152i	$-0.612536\pi$
$263$	4.75372	−	2.74456i	0.293127	−	0.169237i	0.639351	+	0.768915i	$0.279203\pi$
$264$	−2.31386	+	0.543620i	−0.142408	+	0.0334575i
$265$		0			0
$266$	−4.00000	+	6.92820i	−0.245256	+	0.424795i
$267$	1.85208	+	0.558422i	0.113345	+	0.0341749i
$268$	−6.06218	+	3.50000i	−0.370306	+	0.213797i
$269$	−4.37228			−0.266583			−0.133291	−	0.991077i	$-0.542555\pi$
$269$	−4.37228			−0.266583			−0.133291	+	0.991077i	$0.542555\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	6.38458	−	3.68614i	0.387122	−	0.223505i
$273$	−18.6650	−	5.62772i	−1.12966	−	0.340605i
$274$	0.941578	−	1.63086i	0.0568828	−	0.0985239i
$275$		0			0
$276$	7.37228	−	1.73205i	0.443759	−	0.104257i
$277$	−4.55134	+	2.62772i	−0.273464	+	0.157884i	−0.630461	−	0.776221i	$-0.717134\pi$
$277$	−4.55134	+	2.62772i	−0.273464	+	0.157884i	0.356997	+	0.934106i	$0.383801\pi$
$278$		−	18.1168i		−	1.08658i
$279$	18.1168	−	9.01011i	1.08463	−	0.539421i
$280$		0			0
$281$	−2.18614	−	3.78651i	−0.130414	−	0.225884i	0.793422	−	0.608672i	$-0.208297\pi$
$281$	−2.18614	−	3.78651i	−0.130414	−	0.225884i	−0.923836	+	0.382788i	$0.874964\pi$
$282$	2.05446	−	1.93070i	0.122341	−	0.114972i
$283$	27.5928	+	15.9307i	1.64022	+	0.946982i	0.980754	+	0.195249i	$0.0625514\pi$
$283$	27.5928	+	15.9307i	1.64022	+	0.946982i	0.659467	+	0.751733i	$0.270782\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	3.25544	+	5.63858i	0.192498	+	0.333416i
$287$		−	7.11684i		−	0.420094i
$288$	−1.33591	−	2.68614i	−0.0787191	−	0.158282i
$289$	−37.3505			−2.19709
$290$		0			0
$291$	4.43070	−	1.04095i	0.259732	−	0.0610218i
$292$	−12.2255	−	7.05842i	−0.715446	−	0.413063i
$293$	7.13058	+	4.11684i	0.416573	+	0.240509i	0.693610	−	0.720351i	$-0.256019\pi$
$293$	7.13058	+	4.11684i	0.416573	+	0.240509i	−0.277037	+	0.960859i	$0.589352\pi$
$294$	−0.686141	+	2.27567i	−0.0400165	+	0.132720i
$295$		0			0
$296$	4.00000			0.232495
$297$	2.47805	−	6.68614i	0.143791	−	0.387969i
$298$		−	19.1168i		−	1.10741i
$299$	−10.3723	−	17.9653i	−0.599845	−	1.03896i
$300$		0			0
$301$	−13.4891	+	23.3639i	−0.777500	+	1.34667i
$302$	8.66025	+	5.00000i	0.498342	+	0.287718i
$303$	3.46410	+	14.7446i	0.199007	+	0.847053i
$304$	1.68614	+	2.92048i	0.0967068	+	0.167501i
$305$		0			0
$306$	−1.37228	+	22.0742i	−0.0784481	+	1.26190i
$307$			33.2337i			1.89675i	0.317156	+	0.948373i	$0.397272\pi$
$307$			33.2337i			1.89675i	−0.317156	+	0.948373i	$0.602728\pi$
$308$	−2.81929	+	1.62772i	−0.160644	+	0.0927479i
$309$	18.9783	+	20.1947i	1.07963	+	1.14884i
$310$		0			0
$311$	4.62772	−	8.01544i	0.262414	−	0.454514i	−0.704469	−	0.709735i	$-0.748815\pi$
$311$	4.62772	−	8.01544i	0.262414	−	0.454514i	0.966883	+	0.255221i	$0.0821481\pi$
$312$	−5.98844	+	5.62772i	−0.339029	+	0.318607i
$313$	8.11663	−	4.68614i	0.458779	−	0.264876i	−0.252752	−	0.967531i	$-0.581336\pi$
$313$	8.11663	−	4.68614i	0.458779	−	0.264876i	0.711531	+	0.702655i	$0.248002\pi$
$314$	4.74456			0.267751
$315$		0			0
$316$	2.00000			0.112509
$317$	7.57301	−	4.37228i	0.425343	−	0.245572i	−0.272018	−	0.962292i	$-0.587691\pi$
$317$	7.57301	−	4.37228i	0.425343	−	0.245572i	0.697361	+	0.716720i	$0.254358\pi$
$318$	4.55134	+	19.3723i	0.255227	+	1.08634i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$		0			0
$321$	−7.24456	+	24.0275i	−0.404352	+	1.34108i
$322$	8.98266	−	5.18614i	0.500584	−	0.289012i
$323$		−	24.8614i		−	1.38333i
$324$	8.93070	+	1.11469i	0.496150	+	0.0619273i
$325$		0			0
$326$	0.744563	+	1.28962i	0.0412375	+	0.0714255i
$327$	−15.9658	−	4.81386i	−0.882909	−	0.266207i
$328$	−2.59808	−	1.50000i	−0.143455	−	0.0828236i
$329$	1.93070	−	3.34408i	0.106443	−	0.184365i
$330$		0			0
$331$	9.11684	+	15.7908i	0.501107	+	0.867943i	0.999999	+	0.00127880i	$0.000407055\pi$
$331$	9.11684	+	15.7908i	0.501107	+	0.867943i	−0.498892	+	0.866664i	$0.666260\pi$
$332$		−	1.62772i		−	0.0893327i
$333$	−6.63325	+	10.0000i	−0.363500	+	0.547997i
$334$	7.62772			0.417370
$335$		0			0
$336$	−2.81386	−	2.99422i	−0.153509	−	0.163348i
$337$	2.92048	+	1.68614i	0.159089	+	0.0918499i	0.577431	−	0.816440i	$-0.304055\pi$
$337$	2.92048	+	1.68614i	0.159089	+	0.0918499i	−0.418342	+	0.908290i	$0.637389\pi$
$338$	8.23666	+	4.75544i	0.448015	+	0.258662i
$339$	−17.4891	−	18.6101i	−0.949879	−	1.01076i
$340$		0			0
$341$	−9.25544			−0.501210
$342$	−10.0974	−	0.627719i	−0.546002	−	0.0339431i
$343$			19.8614i			1.07242i
$344$	5.68614	+	9.84868i	0.306576	+	0.531005i
$345$		0			0
$346$	4.62772	−	8.01544i	0.248788	−	0.430913i
$347$	−19.1537	−	11.0584i	−1.02823	−	0.593647i	−0.111751	−	0.993736i	$-0.535646\pi$
$347$	−19.1537	−	11.0584i	−1.02823	−	0.593647i	−0.916476	+	0.400089i	$0.868979\pi$
$348$	−7.25061	−	2.18614i	−0.388673	−	0.117189i
$349$	0.441578	+	0.764836i	0.0236371	+	0.0409407i	0.877602	−	0.479390i	$-0.159142\pi$
$349$	0.441578	+	0.764836i	0.0236371	+	0.0409407i	−0.853965	+	0.520331i	$0.825809\pi$
$350$		0			0
$351$	−4.13859	−	24.3036i	−0.220902	−	1.29723i
$352$			1.37228i			0.0731428i
$353$	26.2843	−	15.1753i	1.39897	−	0.807698i	0.404689	−	0.914455i	$-0.367380\pi$
$353$	26.2843	−	15.1753i	1.39897	−	0.807698i	0.994285	+	0.106757i	$0.0340466\pi$
$354$	−0.686141	+	2.27567i	−0.0364680	+	0.120951i
$355$		0			0
$356$	0.558422	−	0.967215i	0.0295963	−	0.0512623i
$357$	6.92820	+	29.4891i	0.366679	+	1.56073i
$358$	2.81929	−	1.62772i	0.149004	−	0.0860276i
$359$	−5.48913			−0.289705			−0.144852	−	0.989453i	$-0.546271\pi$
$359$	−5.48913			−0.289705			−0.144852	+	0.989453i	$0.546271\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$	−6.80818	+	3.93070i	−0.357830	+	0.206593i
$363$	11.5070	−	10.8139i	0.603961	−	0.567580i
$364$	−5.62772	+	9.74749i	−0.294973	+	0.510908i
$365$		0			0
$366$	−10.8139	−	11.5070i	−0.565249	−	0.601480i
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	−0.0926670	−	0.995697i	$-0.529539\pi$
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	0.815966	+	0.578101i	$0.196206\pi$
$368$		−	4.37228i		−	0.227921i
$369$	8.05842	−	4.00772i	0.419505	−	0.208634i
$370$		0			0
$371$	13.6277	+	23.6039i	0.707516	+	1.22545i
$372$	−2.67181	−	11.3723i	−0.138527	−	0.589625i
$373$	−6.48577	−	3.74456i	−0.335821	−	0.193886i	0.322602	−	0.946535i	$-0.395443\pi$
$373$	−6.48577	−	3.74456i	−0.335821	−	0.193886i	−0.658422	+	0.752649i	$0.728776\pi$
$374$	5.05842	−	8.76144i	0.261565	−	0.453043i
$375$		0			0
$376$	−0.813859	−	1.40965i	−0.0419716	−	0.0726969i
$377$			20.7446i			1.06840i
$378$	12.1518	−	2.06930i	0.625022	−	0.106433i
$379$	10.8614			0.557913			0.278956	−	0.960304i	$-0.410011\pi$
$379$	10.8614			0.557913			0.278956	+	0.960304i	$0.410011\pi$
$380$		0			0
$381$	4.55842	−	15.1186i	0.233535	−	0.774548i
$382$	4.75372	+	2.74456i	0.243222	+	0.140424i
$383$	−19.8997	−	11.4891i	−1.01683	−	0.587067i	−0.103646	−	0.994614i	$-0.533051\pi$
$383$	−19.8997	−	11.4891i	−1.01683	−	0.587067i	−0.913184	+	0.407547i	$0.866384\pi$
$384$	−1.68614	+	0.396143i	−0.0860455	+	0.0202156i
$385$		0			0
$386$	−3.88316			−0.197647
$387$	−34.0511	−	2.11684i	−1.73092	−	0.107605i
$388$		−	2.62772i		−	0.133402i
$389$	−5.18614	−	8.98266i	−0.262948	−	0.455439i	0.704076	−	0.710124i	$-0.251361\pi$
$389$	−5.18614	−	8.98266i	−0.262948	−	0.455439i	−0.967024	+	0.254686i	$0.918028\pi$
$390$		0			0
$391$	−16.1168	+	27.9152i	−0.815064	+	1.41173i
$392$	1.18843	+	0.686141i	0.0600248	+	0.0346553i
$393$	−11.0371	+	10.3723i	−0.556749	+	0.523212i
$394$	−8.74456	−	15.1460i	−0.440545	−	0.763046i
$395$		0			0
$396$	−3.43070	−	2.27567i	−0.172399	−	0.114357i
$397$		−	11.2554i		−	0.564894i	−0.959283	−	0.282447i	$-0.908854\pi$
$397$		−	11.2554i		−	0.564894i	0.959283	−	0.282447i	$-0.0911462\pi$
$398$	8.21782	−	4.74456i	0.411922	−	0.237823i
$399$	−13.4891	+	3.16915i	−0.675301	+	0.158656i
$400$		0			0
$401$	−8.05842	+	13.9576i	−0.402418	+	0.697009i	−0.994017	−	0.109223i	$-0.965164\pi$
$401$	−8.05842	+	13.9576i	−0.402418	+	0.697009i	0.591599	+	0.806232i	$0.298497\pi$
$402$	−11.6082	−	3.50000i	−0.578964	−	0.174564i
$403$	−27.7128	+	16.0000i	−1.38047	+	0.797017i
$404$	8.74456			0.435058
$405$		0			0
$406$	−10.3723			−0.514768
$407$	4.75372	−	2.74456i	0.235633	−	0.136043i
$408$	12.2255	+	3.68614i	0.605255	+	0.182491i
$409$	−5.43070	+	9.40625i	−0.268531	+	0.465109i	−0.968483	−	0.249081i	$-0.919872\pi$
$409$	−5.43070	+	9.40625i	−0.268531	+	0.465109i	0.699952	+	0.714190i	$0.253205\pi$
$410$		0			0
$411$	3.17527	−	0.746000i	0.156624	−	0.0367975i
$412$	13.8564	−	8.00000i	0.682656	−	0.394132i
$413$			3.25544i			0.160190i
$414$	10.9307	+	7.25061i	0.537215	+	0.356348i
$415$		0			0
$416$	2.37228	+	4.10891i	0.116311	+	0.201456i
$417$	22.8665	−	21.4891i	1.11978	−	1.05233i
$418$	4.00772	+	2.31386i	0.196024	+	0.113175i
$419$	−15.8614	+	27.4728i	−0.774880	+	1.34213i	0.159981	+	0.987120i	$0.448857\pi$
$419$	−15.8614	+	27.4728i	−0.774880	+	1.34213i	−0.934862	+	0.355012i	$0.884477\pi$
$420$		0			0
$421$	19.2337	+	33.3137i	0.937393	+	1.62361i	0.770311	+	0.637669i	$0.220101\pi$
$421$	19.2337	+	33.3137i	0.937393	+	1.62361i	0.167082	+	0.985943i	$0.446566\pi$
$422$		−	7.25544i		−	0.353189i
$423$	4.87375	+	0.302985i	0.236970	+	0.0147316i
$424$	11.4891			0.557961
$425$		0			0
$426$	−10.1168	+	2.37686i	−0.490163	+	0.115159i
$427$	−18.7302	−	10.8139i	−0.906416	−	0.523319i
$428$	12.5480	+	7.24456i	0.606528	+	0.350179i
$429$	−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	$0.717690\pi$
$432$	1.80579	−	4.87228i	0.0868811	−	0.234418i
$433$			0.627719i			0.0301662i	0.999886	+	0.0150831i	$0.00480129\pi$
$433$			0.627719i			0.0301662i	−0.999886	+	0.0150831i	$0.995199\pi$
$434$	−8.00000	−	13.8564i	−0.384012	−	0.665129i
$435$		0			0
$436$	−4.81386	+	8.33785i	−0.230542	+	0.399311i
$437$	−12.7692	−	7.37228i	−0.610832	−	0.352664i
$438$	−5.59230	−	23.8030i	−0.267210	−	1.13735i
$439$	8.11684	+	14.0588i	0.387396	+	0.670989i	0.992098	−	0.125462i	$-0.0400414\pi$
$439$	8.11684	+	14.0588i	0.387396	+	0.670989i	−0.604703	+	0.796451i	$0.706708\pi$
$440$		0			0
$441$	−3.68614	+	1.83324i	−0.175531	+	0.0872972i
$442$		−	34.9783i		−	1.66375i
$443$	−22.9403	+	13.2446i	−1.08992	+	0.629268i	−0.933556	−	0.358431i	$-0.883312\pi$
$443$	−22.9403	+	13.2446i	−1.08992	+	0.629268i	−0.156368	+	0.987699i	$0.549979\pi$
$444$	4.74456	+	5.04868i	0.225167	+	0.239600i
$445$		0			0
$446$	6.18614	−	10.7147i	0.292922	−	0.507356i
$447$	24.1287	−	22.6753i	1.14125	−	1.07250i
$448$	−2.05446	+	1.18614i	−0.0970639	+	0.0560399i
$449$	18.8614			0.890125			0.445062	−	0.895500i	$-0.353181\pi$
$449$	18.8614			0.890125			0.445062	+	0.895500i	$0.353181\pi$
$450$		0			0
$451$	−4.11684			−0.193855
$452$	−12.7692	+	7.37228i	−0.600611	+	0.346763i
$453$	3.96143	+	16.8614i	0.186124	+	0.792218i
$454$	−0.941578	+	1.63086i	−0.0441904	+	0.0765401i
$455$		0			0
$456$	−1.68614	+	5.59230i	−0.0789608	+	0.261883i
$457$	−26.0820	+	15.0584i	−1.22006	+	0.704403i	−0.964931	−	0.262503i	$-0.915452\pi$
$457$	−26.0820	+	15.0584i	−1.22006	+	0.704403i	−0.255131	+	0.966906i	$0.582119\pi$
$458$		−	18.3723i		−	0.858480i
$459$	−29.4891	+	24.4511i	−1.37643	+	1.14128i
$460$		0			0
$461$	−9.55842	−	16.5557i	−0.445180	−	0.771075i	0.552885	−	0.833258i	$-0.313527\pi$
$461$	−9.55842	−	16.5557i	−0.445180	−	0.771075i	−0.998065	+	0.0621833i	$0.980194\pi$
$462$	−5.39853	−	1.62772i	−0.251162	−	0.0757283i
$463$	−17.3205	−	10.0000i	−0.804952	−	0.464739i	0.0402476	−	0.999190i	$-0.487185\pi$
$463$	−17.3205	−	10.0000i	−0.804952	−	0.464739i	−0.845200	+	0.534450i	$0.820519\pi$
$464$	−2.18614	+	3.78651i	−0.101489	+	0.175784i
$465$		0			0
$466$	−5.05842	−	8.76144i	−0.234327	−	0.405866i
$467$		−	25.8832i		−	1.19773i	−0.800850	−	0.598865i	$-0.795619\pi$
$467$		−	25.8832i		−	1.19773i	0.800850	−	0.598865i	$-0.204381\pi$
$468$	−14.2063	−	0.883156i	−0.656685	−	0.0408239i
$469$	−16.6060			−0.766792
$470$		0			0
$471$	5.62772	+	5.98844i	0.259312	+	0.275933i
$472$	1.18843	+	0.686141i	0.0547019	+	0.0315822i
$473$	13.5152	+	7.80298i	0.621428	+	0.358782i
$474$	2.37228	+	2.52434i	0.108962	+	0.115947i
$475$		0			0
$476$	17.4891			0.801613
$477$	−19.0526	+	28.7228i	−0.872357	+	1.31513i
$478$			14.7446i			0.674401i
$479$	−11.7446	−	20.3422i	−0.536623	−	0.929458i	−0.999083	−	0.0428178i	$-0.986366\pi$
$479$	−11.7446	−	20.3422i	−0.536623	−	0.929458i	0.462460	−	0.886640i	$-0.346967\pi$
$480$		0			0
$481$	9.48913	−	16.4356i	0.432667	−	0.749401i
$482$	−9.08385	−	5.24456i	−0.413758	−	0.238883i
$483$	17.2005	+	5.18614i	0.782649	+	0.235978i
$484$	−4.55842	−	7.89542i	−0.207201	−	0.358883i
$485$		0			0
$486$	9.18614	+	12.5942i	0.416692	+	0.571286i
$487$			1.25544i			0.0568893i	0.999595	+	0.0284446i	$0.00905543\pi$
$487$			1.25544i			0.0568893i	−0.999595	+	0.0284446i	$0.990945\pi$
$488$	−7.89542	+	4.55842i	−0.357409	+	0.206350i
$489$	−0.744563	+	2.46943i	−0.0336703	+	0.111672i
$490$		0			0
$491$	−1.80298	+	3.12286i	−0.0813676	+	0.140933i	−0.903838	−	0.427876i	$-0.859262\pi$
$491$	−1.80298	+	3.12286i	−0.0813676	+	0.140933i	0.822470	+	0.568808i	$0.192595\pi$
$492$	−1.18843	−	5.05842i	−0.0535786	−	0.228051i
$493$	27.9152	−	16.1168i	1.25724	−	0.725866i
$494$	16.0000			0.719874
$495$		0			0
$496$	−6.74456			−0.302840
$497$	−12.3267	+	7.11684i	−0.552930	+	0.319234i
$498$	2.05446	−	1.93070i	0.0920624	−	0.0865169i
$499$	−1.05842	+	1.83324i	−0.0473815	+	0.0820671i	−0.888743	−	0.458405i	$-0.848421\pi$
$499$	−1.05842	+	1.83324i	−0.0473815	+	0.0820671i	0.841362	+	0.540472i	$0.181754\pi$
$500$		0			0
$501$	9.04755	+	9.62747i	0.404215	+	0.430124i
$502$	13.5152	−	7.80298i	0.603211	−	0.348264i
$503$			21.8614i			0.974752i	0.873192	+	0.487376i	$0.162046\pi$
$503$			21.8614i			0.974752i	−0.873192	+	0.487376i	$0.837954\pi$
$504$	0.441578	−	7.10313i	0.0196694	−	0.316399i
$505$		0			0
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$	3.76767	+	16.0367i	0.167328	+	0.712214i
$508$	−7.89542	−	4.55842i	−0.350303	−	0.202247i
$509$	4.67527	−	8.09780i	0.207228	−	0.358929i	−0.743613	−	0.668611i	$-0.766889\pi$
$509$	4.67527	−	8.09780i	0.207228	−	0.358929i	0.950840	+	0.309682i	$0.100223\pi$
$510$		0			0
$511$	−16.7446	−	29.0024i	−0.740736	−	1.28299i
$512$			1.00000i			0.0441942i
$513$	−11.1846	−	13.4891i	−0.493812	−	0.595559i
$514$	−1.37228			−0.0605287
$515$		0			0
$516$	−5.68614	+	18.8588i	−0.250318	+	0.830212i
$517$	−1.93443	−	1.11684i	−0.0850762	−	0.0491187i
$518$	8.21782	+	4.74456i	0.361070	+	0.208464i
$519$	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	$0.858818\pi$
$522$	−5.84096	−	11.7446i	−0.255652	−	0.514046i
$523$		−	11.1168i		−	0.486106i	−0.970013	−	0.243053i	$-0.921851\pi$
$523$		−	11.1168i		−	0.486106i	0.970013	−	0.243053i	$-0.0781488\pi$
$524$	4.37228	+	7.57301i	0.191004	+	0.330829i
$525$		0			0
$526$	2.74456	−	4.75372i	0.119669	−	0.207272i
$527$	43.0612	+	24.8614i	1.87578	+	1.08298i
$528$	−1.73205	+	1.62772i	−0.0753778	+	0.0708374i
$529$	−1.94158	−	3.36291i	−0.0844164	−	0.146214i
$530$		0			0
$531$	−3.68614	+	1.83324i	−0.159965	+	0.0795559i
$532$			8.00000i			0.346844i
$533$	−12.3267	+	7.11684i	−0.533930	+	0.308265i
$534$	1.88316	−	0.442430i	0.0814921	−	0.0191458i
$535$		0			0
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$	5.39853	+	1.62772i	0.232964	+	0.0702412i
$538$	−3.78651	+	2.18614i	−0.163248	+	0.0942512i
$539$	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	$0.346082\pi$
$542$	6.92820	−	4.00000i	0.297592	−	0.171815i
$543$	−13.0367	−	3.93070i	−0.559457	−	0.168683i
$544$	3.68614	−	6.38458i	0.158042	−	0.273737i
$545$		0			0
$546$	−18.9783	+	4.45877i	−0.812194	+	0.190818i
$547$	−34.1798	+	19.7337i	−1.46142	+	0.843752i	−0.999077	−	0.0429494i	$-0.986325\pi$
$547$	−34.1798	+	19.7337i	−1.46142	+	0.843752i	−0.462343	+	0.886701i	$0.652991\pi$
$548$		−	1.88316i		−	0.0804444i
$549$	1.69702	−	27.2978i	0.0724269	−	1.16504i
$550$		0			0
$551$	7.37228	+	12.7692i	0.314070	+	0.543985i
$552$	5.51856	−	5.18614i	0.234885	−	0.220737i
$553$	4.10891	+	2.37228i	0.174729	+	0.100880i
$554$	−2.62772	+	4.55134i	−0.111641	+	0.193368i
$555$		0			0
$556$	−9.05842	−	15.6896i	−0.384163	−	0.665389i
$557$			9.76631i			0.413812i	0.978361	+	0.206906i	$0.0663394\pi$
$557$			9.76631i			0.413812i	−0.978361	+	0.206906i	$0.933661\pi$
$558$	11.1846	−	16.8614i	0.473482	−	0.713800i
$559$	53.9565			2.28212
$560$		0			0
$561$	17.0584	−	4.00772i	0.720207	−	0.169206i
$562$	−3.78651	−	2.18614i	−0.159724	−	0.0922168i
$563$	−14.4824	−	8.36141i	−0.610360	−	0.352391i	0.162747	−	0.986668i	$-0.447965\pi$
$563$	−14.4824	−	8.36141i	−0.610360	−	0.352391i	−0.773106	+	0.634277i	$0.781298\pi$
$564$	0.813859	−	2.69927i	0.0342697	−	0.113660i
$565$		0			0
$566$	31.8614			1.33923
$567$	17.0256	+	12.8832i	0.715006	+	0.541042i
$568$			6.00000i			0.251754i
$569$	4.80298	+	8.31901i	0.201352	+	0.348751i	0.948964	−	0.315384i	$-0.102133\pi$
$569$	4.80298	+	8.31901i	0.201352	+	0.348751i	−0.747613	+	0.664135i	$0.768800\pi$
$570$		0			0
$571$	15.8030	−	27.3716i	0.661334	−	1.14546i	−0.318931	−	0.947778i	$-0.603324\pi$
$571$	15.8030	−	27.3716i	0.661334	−	1.14546i	0.980265	−	0.197687i	$-0.0633429\pi$
$572$	5.63858	+	3.25544i	0.235761	+	0.136117i
$573$	2.17448	+	9.25544i	0.0908403	+	0.386651i
$574$	−3.55842	−	6.16337i	−0.148526	−	0.257254i
$575$		0			0
$576$	−2.50000	−	1.65831i	−0.104167	−	0.0690963i
$577$			23.8832i			0.994269i	0.867674	+	0.497134i	$0.165614\pi$
$577$			23.8832i			0.994269i	−0.867674	+	0.497134i	$0.834386\pi$
$578$	−32.3465	+	18.6753i	−1.34544	+	0.776789i
$579$	−4.60597	−	4.90120i	−0.191418	−	0.203687i
$580$		0			0
$581$	1.93070	−	3.34408i	0.0800991	−	0.138736i
$582$	3.31662	−	3.11684i	0.137479	−	0.129197i
$583$	13.6540	−	7.88316i	0.565492	−	0.326487i
$584$	−14.1168			−0.584159
$585$		0			0
$586$	8.23369			0.340131
$587$	−23.3827	+	13.5000i	−0.965107	+	0.557205i	−0.897741	−	0.440524i	$-0.854793\pi$
$587$	−23.3827	+	13.5000i	−0.965107	+	0.557205i	−0.0673658	+	0.997728i	$0.521459\pi$
$588$	0.543620	+	2.31386i	0.0224185	+	0.0954220i
$589$	−11.3723	+	19.6974i	−0.468587	+	0.811616i
$590$		0			0
$591$	8.74456	−	29.0024i	0.359703	−	1.19300i
$592$	3.46410	−	2.00000i	0.142374	−	0.0821995i
$593$			37.7228i			1.54909i	0.632519	+	0.774545i	$0.282021\pi$
$593$			37.7228i			1.54909i	−0.632519	+	0.774545i	$0.717979\pi$
$594$	−1.19702	−	7.02939i	−0.0491141	−	0.288419i
$595$		0			0
$596$	−9.55842	−	16.5557i	−0.391528	−	0.678147i
$597$	15.7359	+	4.74456i	0.644029	+	0.194182i
$598$	−17.9653	−	10.3723i	−0.734656	−	0.424154i
$599$	−19.1168	+	33.1113i	−0.781093	+	1.35289i	0.150212	+	0.988654i	$0.452004\pi$
$599$	−19.1168	+	33.1113i	−0.781093	+	1.35289i	−0.931305	+	0.364239i	$0.881329\pi$
$600$		0			0
$601$	−13.4307	−	23.2627i	−0.547850	−	0.948904i	−0.998422	−	0.0561635i	$-0.982113\pi$
$601$	−13.4307	−	23.2627i	−0.547850	−	0.948904i	0.450572	−	0.892740i	$-0.351220\pi$
$602$			26.9783i			1.09955i
$603$	−9.35135	−	18.8030i	−0.380816	−	0.765717i
$604$	10.0000			0.406894
$605$		0			0
$606$	10.3723	+	11.0371i	0.421345	+	0.448352i
$607$	0.764836	+	0.441578i	0.0310437	+	0.0179231i	0.515442	−	0.856925i	$-0.327628\pi$
$607$	0.764836	+	0.441578i	0.0310437	+	0.0179231i	−0.484398	+	0.874848i	$0.660961\pi$
$608$	2.92048	+	1.68614i	0.118441	+	0.0683820i
$609$	−12.3030	−	13.0916i	−0.498542	−	0.530497i
$610$		0			0
$611$	−7.72281			−0.312432
$612$	9.84868	+	19.8030i	0.398109	+	0.800488i
$613$		−	0.233688i		−	0.00943857i	−0.999989	−	0.00471928i	$-0.998498\pi$
$613$		−	0.233688i		−	0.00943857i	0.999989	−	0.00471928i	$-0.00150220\pi$
$614$	16.6168	+	28.7812i	0.670601	+	1.16152i
$615$		0			0
$616$	−1.62772	+	2.81929i	−0.0655827	+	0.113592i
$617$	−19.1537	−	11.0584i	−0.771101	−	0.445195i	0.0621663	−	0.998066i	$-0.480199\pi$
$617$	−19.1537	−	11.0584i	−0.771101	−	0.445195i	−0.833267	+	0.552870i	$0.813532\pi$
$618$	26.5330	+	8.00000i	1.06731	+	0.321807i
$619$	−19.0584	−	33.0102i	−0.766023	−	1.32679i	−0.939704	−	0.341988i	$-0.888900\pi$
$619$	−19.0584	−	33.0102i	−0.766023	−	1.32679i	0.173682	−	0.984802i	$-0.444434\pi$
$620$		0			0
$621$	3.81386	+	22.3966i	0.153045	+	0.898746i
$622$		−	9.25544i		−	0.371109i
$623$	2.29451	−	1.32473i	0.0919275	−	0.0530743i
$624$	−2.37228	+	7.86797i	−0.0949673	+	0.314971i
$625$		0			0
$626$	4.68614	−	8.11663i	0.187296	−	0.324406i
$627$	1.83324	+	7.80298i	0.0732126	+	0.311621i
$628$	4.10891	−	2.37228i	0.163963	−	0.0946643i
$629$	−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	$0.265761\pi$
$632$	1.73205	−	1.00000i	0.0688973	−	0.0397779i
$633$	9.15759	−	8.60597i	0.363981	−	0.342057i
$634$	4.37228	−	7.57301i	0.173645	−	0.300763i
$635$		0			0
$636$	13.6277	+	14.5012i	0.540374	+	0.575011i
$637$	5.63858	−	3.25544i	0.223409	−	0.128985i
$638$			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	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$	5.73977	+	24.4307i	0.226531	+	0.964203i
$643$	−9.52628	−	5.50000i	−0.375680	−	0.216899i	0.300257	−	0.953858i	$-0.402928\pi$
$643$	−9.52628	−	5.50000i	−0.375680	−	0.216899i	−0.675937	+	0.736959i	$0.736261\pi$
$644$	5.18614	−	8.98266i	0.204363	−	0.353966i
$645$		0			0
$646$	−12.4307	−	21.5306i	−0.489079	−	0.847111i
$647$		−	24.0951i		−	0.947276i	−0.880720	−	0.473638i	$-0.842941\pi$
$647$		−	24.0951i		−	0.947276i	0.880720	−	0.473638i	$-0.157059\pi$
$648$	8.29156	−	3.50000i	0.325723	−	0.137493i
$649$	1.88316			0.0739203
$650$		0			0
$651$	8.00000	−	26.5330i	0.313545	−	1.03991i
$652$	1.28962	+	0.744563i	0.0505054	+	0.0291593i
$653$	32.6689	+	18.8614i	1.27843	+	0.738104i	0.976560	−	0.215244i	$-0.0690548\pi$
$653$	32.6689	+	18.8614i	1.27843	+	0.738104i	0.301873	+	0.953348i	$0.402388\pi$
$654$	−16.2337	+	3.81396i	−0.634787	+	0.149138i
$655$		0			0
$656$	−3.00000			−0.117130
$657$	23.4101	−	35.2921i	0.913316	−	1.37688i
$658$		−	3.86141i		−	0.150533i
$659$	−2.74456	−	4.75372i	−0.106913	−	0.185179i	0.807605	−	0.589724i	$-0.200763\pi$
$659$	−2.74456	−	4.75372i	−0.106913	−	0.185179i	−0.914518	+	0.404545i	$0.867430\pi$
$660$		0			0
$661$	−11.1168	+	19.2549i	−0.432395	+	0.748930i	−0.997079	−	0.0763770i	$-0.975665\pi$
$661$	−11.1168	+	19.2549i	−0.432395	+	0.748930i	0.564684	+	0.825307i	$0.308998\pi$
$662$	15.7908	+	9.11684i	0.613728	+	0.354336i
$663$	44.1485	−	41.4891i	1.71458	−	1.61130i
$664$	−0.813859	−	1.40965i	−0.0315839	−	0.0547049i
$665$		0			0
$666$	−0.744563	+	11.9769i	−0.0288512	+	0.464095i
$667$		−	19.1168i		−	0.740207i
$668$	6.60580	−	3.81386i	0.255586	−	0.147563i
$669$	20.8614	−	4.90120i	0.806549	−	0.189491i
$670$		0			0
$671$	−6.25544	+	10.8347i	−0.241488	+	0.418270i
$672$	−3.93398	−	1.18614i	−0.151757	−	0.0457564i
$673$	−8.66025	+	5.00000i	−0.333828	+	0.192736i	−0.657539	−	0.753420i	$-0.728403\pi$
$673$	−8.66025	+	5.00000i	−0.333828	+	0.192736i	0.323711	+	0.946156i	$0.395069\pi$
$674$	3.37228			0.129895
$675$		0			0
$676$	9.51087			0.365803
$677$	37.8651	−	21.8614i	1.45527	−	0.840202i	0.456500	−	0.889724i	$-0.349103\pi$
$677$	37.8651	−	21.8614i	1.45527	−	0.840202i	0.998773	+	0.0495215i	$0.0157696\pi$
$678$	−24.4511	−	7.37228i	−0.939038	−	0.283131i
$679$	3.11684	−	5.39853i	0.119613	−	0.207177i
$680$		0			0
$681$	−3.17527	+	0.746000i	−0.121676	+	0.0285868i
$682$	−8.01544	+	4.62772i	−0.306927	+	0.177205i
$683$			33.0951i			1.26635i	0.774009	+	0.633174i	$0.218248\pi$
$683$			33.0951i			1.26635i	−0.774009	+	0.633174i	$0.781752\pi$
$684$	−9.05842	+	4.50506i	−0.346357	+	0.172255i
$685$		0			0
$686$	9.93070	+	17.2005i	0.379156	+	0.656717i
$687$	23.1889	−	21.7921i	0.884713	−	0.831421i
$688$	9.84868	+	5.68614i	0.375478	+	0.216782i
$689$	27.2554	−	47.2078i	1.03835	−	1.79847i
$690$		0			0
$691$	0.883156	+	1.52967i	0.0335968	+	0.0581914i	0.882335	−	0.470622i	$-0.155970\pi$
$691$	0.883156	+	1.52967i	0.0335968	+	0.0581914i	−0.848738	+	0.528813i	$0.822637\pi$
$692$		−	9.25544i		−	0.351839i
$693$	−4.34896	−	8.74456i	−0.165203	−	0.332178i
$694$	−22.1168			−0.839544
$695$		0			0
$696$	−7.37228	+	1.73205i	−0.279446	+	0.0656532i
$697$	19.1537	+	11.0584i	0.725500	+	0.418868i
$698$	0.764836	+	0.441578i	0.0289495	+	0.0167140i
$699$	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	$0.413966\pi$
$702$	−15.7359	−	18.9783i	−0.593915	−	0.716288i
$703$		−	13.4891i		−	0.508752i
$704$	0.686141	+	1.18843i	0.0258599	+	0.0447907i
$705$		0			0
$706$	15.1753	−	26.2843i	0.571129	−	0.989224i
$707$	17.9653	+	10.3723i	0.675655	+	0.390090i
$708$	0.543620	+	2.31386i	0.0204305	+	0.0869602i
$709$	−12.9307	−	22.3966i	−0.485623	−	0.841123i	0.514241	−	0.857646i	$-0.328074\pi$
$709$	−12.9307	−	22.3966i	−0.485623	−	0.841123i	−0.999863	+	0.0165226i	$0.994740\pi$
$710$		0			0
$711$	−0.372281	+	5.98844i	−0.0139616	+	0.224584i
$712$		−	1.11684i		−	0.0418555i
$713$	25.5383	−	14.7446i	0.956418	−	0.552188i
$714$	20.7446	+	22.0742i	0.776346	+	0.826107i
$715$		0			0
$716$	1.62772	−	2.81929i	0.0608307	−	0.105362i
$717$	−18.6101	+	17.4891i	−0.695008	+	0.653143i
$718$	−4.75372	+	2.74456i	−0.177407	+	0.102426i
$719$	38.2337			1.42588			0.712938	−	0.701227i	$-0.247364\pi$
$719$	38.2337			1.42588			0.712938	+	0.701227i	$0.247364\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$	−6.60580	+	3.81386i	−0.245842	+	0.141937i
$723$	−4.15520	−	17.6861i	−0.154534	−	0.657755i
$724$	−3.93070	+	6.80818i	−0.146083	+	0.253024i
$725$		0			0
$726$	4.55842	−	15.1186i	0.169179	−	0.561103i
$727$	−0.764836	+	0.441578i	−0.0283662	+	0.0163772i	−0.514116	−	0.857721i	$-0.671880\pi$
$727$	−0.764836	+	0.441578i	−0.0283662	+	0.0163772i	0.485750	+	0.874098i	$0.338547\pi$
$728$			11.2554i			0.417154i
$729$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$730$		0			0
$731$	−41.9198	−	72.6073i	−1.55046	−	2.68548i
$732$	−15.1186	−	4.55842i	−0.558799	−	0.168484i
$733$	−29.6472	−	17.1168i	−1.09505	−	0.632225i	−0.160131	−	0.987096i	$-0.551192\pi$
$733$	−29.6472	−	17.1168i	−1.09505	−	0.632225i	−0.934915	+	0.354871i	$0.884525\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	−2.18614	−	3.78651i	−0.0805822	−	0.139572i
$737$			9.60597i			0.353840i
$738$	4.97494	−	7.50000i	0.183130	−	0.276079i
$739$	23.8832			0.878556			0.439278	−	0.898351i	$-0.355234\pi$
$739$	23.8832			0.878556			0.439278	+	0.898351i	$0.355234\pi$
$740$		0			0
$741$	18.9783	+	20.1947i	0.697183	+	0.741871i
$742$	23.6039	+	13.6277i	0.866526	+	0.500289i
$743$	−21.7518	−	12.5584i	−0.797997	−	0.460724i	0.0447732	−	0.998997i	$-0.485743\pi$
$743$	−21.7518	−	12.5584i	−0.797997	−	0.460724i	−0.842770	+	0.538273i	$0.819077\pi$
$744$	−8.00000	−	8.51278i	−0.293294	−	0.312094i
$745$		0			0
$746$	−7.48913			−0.274196
$747$	4.87375	+	0.302985i	0.178321	+	0.0110856i
$748$		−	10.1168i		−	0.369908i
$749$	17.1861	+	29.7673i	0.627968	+	1.08767i
$750$		0			0
$751$	9.11684	−	15.7908i	0.332678	−	0.576216i	−0.650358	−	0.759628i	$-0.725381\pi$
$751$	9.11684	−	15.7908i	0.332678	−	0.576216i	0.983036	+	0.183412i	$0.0587143\pi$
$752$	−1.40965	−	0.813859i	−0.0514045	−	0.0296784i
$753$	25.8796	+	7.80298i	0.943104	+	0.284357i
$754$	10.3723	+	17.9653i	0.377736	+	0.654258i
$755$		0			0
$756$	9.48913	−	7.86797i	0.345116	−	0.286155i
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	9.40625	−	5.43070i	0.341651	−	0.197252i
$759$	3.00000	−	9.94987i	0.108893	−	0.361158i
$760$		0			0
$761$	−6.04755	+	10.4747i	−0.219223	+	0.379706i	−0.954571	−	0.297984i	$-0.903686\pi$
$761$	−6.04755	+	10.4747i	−0.219223	+	0.379706i	0.735347	+	0.677690i	$0.237019\pi$
$762$	−3.61158	−	15.3723i	−0.130834	−	0.556879i
$763$	−19.7797	+	11.4198i	−0.716074	+	0.413426i
$764$	5.48913			0.198590
$765$		0			0
$766$	−22.9783			−0.830238
$767$	5.63858	−	3.25544i	0.203597	−	0.117547i
$768$	−1.26217	+	1.18614i	−0.0455446	+	0.0428012i
$769$	−9.06930	+	15.7085i	−0.327047	+	0.566462i	−0.981925	−	0.189273i	$-0.939387\pi$
$769$	−9.06930	+	15.7085i	−0.327047	+	0.566462i	0.654877	+	0.755735i	$0.272720\pi$
$770$		0			0
$771$	−1.62772	−	1.73205i	−0.0586209	−	0.0623783i
$772$	−3.36291	+	1.94158i	−0.121034	+	0.0698789i
$773$			14.7446i			0.530325i	0.964204	+	0.265163i	$0.0854256\pi$
$773$			14.7446i			0.530325i	−0.964204	+	0.265163i	$0.914574\pi$
$774$	−30.5475	+	15.1923i	−1.09801	+	0.546076i
$775$		0			0
$776$	−1.31386	−	2.27567i	−0.0471648	−	0.0816918i
$777$	3.75906	+	16.0000i	0.134855	+	0.573997i
$778$	−8.98266	−	5.18614i	−0.322044	−	0.185932i
$779$	−5.05842	+	8.76144i	−0.181237	+	0.313911i
$780$		0			0
$781$	4.11684	+	7.13058i	0.147312	+	0.255152i
$782$			32.2337i			1.15267i
$783$	7.89542	−	21.3030i	0.282159	−	0.761307i
$784$	1.37228			0.0490100
$785$		0			0
$786$	−4.37228	+	14.5012i	−0.155954	+	0.517241i
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$	−15.1460	−	8.74456i	−0.539555	−	0.311512i
$789$	9.25544	−	2.17448i	0.329502	−	0.0774136i
$790$		0			0
$791$	−34.9783			−1.24368
$792$	−4.10891	−	0.255437i	−0.146004	−	0.00907657i
$793$			43.2554i			1.53605i
$794$	−5.62772	−	9.74749i	−0.199720	−	0.345926i
$795$		0			0
$796$	4.74456	−	8.21782i	0.168167	−	0.291273i
$797$	2.81929	+	1.62772i	0.0998644	+	0.0576568i	0.549100	−	0.835756i	$-0.314970\pi$
$797$	2.81929	+	1.62772i	0.0998644	+	0.0576568i	−0.449236	+	0.893413i	$0.648304\pi$
$798$	−10.0974	+	9.48913i	−0.357442	+	0.335911i
$799$	6.00000	+	10.3923i	0.212265	+	0.367653i
$800$		0			0
$801$	2.79211	+	1.85208i	0.0986544	+	0.0654399i
$802$			16.1168i			0.569106i
$803$	−16.7769	+	9.68614i	−0.592044	+	0.341816i
$804$	−11.8030	+	2.77300i	−0.416259	+	0.0977963i
$805$		0			0
$806$	−16.0000	+	27.7128i	−0.563576	+	0.976142i
$807$	−7.25061	−	2.18614i	−0.255234	−	0.0769558i
$808$	7.57301	−	4.37228i	0.266418	−	0.153816i
$809$	12.3505			0.434222			0.217111	−	0.976147i	$-0.430337\pi$
$809$	12.3505			0.434222			0.217111	+	0.976147i	$0.430337\pi$
$810$		0			0
$811$	9.37228			0.329105			0.164553	−	0.986368i	$-0.447382\pi$
$811$	9.37228			0.329105			0.164553	+	0.986368i	$0.447382\pi$
$812$	−8.98266	+	5.18614i	−0.315230	+	0.181998i
$813$	13.2665	+	4.00000i	0.465276	+	0.140286i
$814$	2.74456	−	4.75372i	0.0961969	−	0.166618i
$815$		0			0
$816$	12.4307	−	2.92048i	0.435162	−	0.102237i
$817$	33.2125	−	19.1753i	1.16196	−	0.670858i
$818$			10.8614i			0.379760i
$819$	−28.1386	−	18.6650i	−0.983242	−	0.652209i
$820$		0			0
$821$	−25.4198	−	44.0284i	−0.887158	−	1.53660i	−0.843220	−	0.537569i	$-0.819343\pi$
$821$	−25.4198	−	44.0284i	−0.887158	−	1.53660i	−0.0439382	−	0.999034i	$-0.513990\pi$
$822$	2.37686	−	2.23369i	0.0829025	−	0.0779088i
$823$	−32.9913	−	19.0475i	−1.15001	−	0.663956i	−0.201117	−	0.979567i	$-0.564457\pi$
$823$	−32.9913	−	19.0475i	−1.15001	−	0.663956i	−0.948888	+	0.315612i	$0.897790\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	1.62772	+	2.81929i	0.0566356	+	0.0980957i
$827$		−	8.13859i		−	0.283007i	−0.989938	−	0.141503i	$-0.954806\pi$
$827$		−	8.13859i		−	0.283007i	0.989938	−	0.141503i	$-0.0451936\pi$
$828$	13.0916	+	0.813859i	0.454964	+	0.0282836i
$829$	32.8832			1.14208			0.571040	−	0.820923i	$-0.306540\pi$
$829$	32.8832			1.14208			0.571040	+	0.820923i	$0.306540\pi$
$830$		0			0
$831$	−8.86141	+	2.08191i	−0.307399	+	0.0722206i
$832$	4.10891	+	2.37228i	0.142451	+	0.0822441i
$833$	−8.76144	−	5.05842i	−0.303566	−	0.175264i
$834$	9.05842	−	30.0434i	0.313668	−	1.04032i
$835$		0			0
$836$	4.62772			0.160053
$837$	34.5484	−	5.88316i	1.19417	−	0.203352i
$838$			31.7228i			1.09585i
$839$	22.1168	+	38.3075i	0.763558	+	1.32252i	0.941005	+	0.338391i	$0.109883\pi$
$839$	22.1168	+	38.3075i	0.763558	+	1.32252i	−0.177447	+	0.984130i	$0.556784\pi$
$840$		0			0
$841$	4.94158	−	8.55906i	0.170399	−	0.295140i
$842$	33.3137	+	19.2337i	1.14807	+	0.662837i
$843$	−1.73205	−	7.37228i	−0.0596550	−	0.253915i
$844$	−3.62772	−	6.28339i	−0.124871	−	0.216283i
$845$		0			0
$846$	4.37228	−	2.17448i	0.150322	−	0.0747602i
$847$		−	21.6277i		−	0.743137i
$848$	9.94987	−	5.74456i	0.341680	−	0.197269i
$849$	37.7921	+	40.2145i	1.29702	+	1.38016i
$850$		0			0
$851$	−8.74456	+	15.1460i	−0.299760	+	0.519199i
$852$	−7.57301	+	7.11684i	−0.259447	+	0.243819i
$853$	−1.52967	+	0.883156i	−0.0523749	+	0.0302387i	−0.525959	−	0.850510i	$-0.676293\pi$
$853$	−1.52967	+	0.883156i	−0.0523749	+	0.0302387i	0.473584	+	0.880749i	$0.342960\pi$
$854$	−21.6277			−0.740085
$855$		0			0
$856$	14.4891			0.495228
$857$	−20.3422	+	11.7446i	−0.694876	+	0.401187i	−0.805436	−	0.592683i	$-0.798069\pi$
$857$	−20.3422	+	11.7446i	−0.694876	+	0.401187i	0.110560	+	0.993869i	$0.464735\pi$
$858$	2.57924	+	10.9783i	0.0880538	+	0.374791i
$859$	0.0584220	−	0.101190i	0.00199333	−	0.00345255i	−0.865027	−	0.501725i	$-0.832699\pi$
$859$	0.0584220	−	0.101190i	0.00199333	−	0.00345255i	0.867020	+	0.498273i	$0.166032\pi$
$860$		0			0
$861$	3.55842	−	11.8020i	0.121271	−	0.402209i
$862$	−22.7190	+	13.1168i	−0.773814	+	0.446761i
$863$		−	42.6060i		−	1.45032i	−0.688578	−	0.725162i	$-0.741765\pi$
$863$		−	42.6060i		−	1.45032i	0.688578	−	0.725162i	$-0.258235\pi$
$864$	−0.872281	−	5.12241i	−0.0296756	−	0.174268i
$865$		0			0
$866$	0.313859	+	0.543620i	0.0106654	+	0.0184730i
$867$	−61.9389	−	18.6753i	−2.10355	−	0.634245i
$868$	−13.8564	−	8.00000i	−0.470317	−	0.271538i
$869$	1.37228	−	2.37686i	0.0465515	−	0.0806295i
$870$		0			0
$871$	16.6060	+	28.7624i	0.562672	+	0.974576i
$872$			9.62772i			0.326036i
$873$	7.86797	+	0.489125i	0.266290	+	0.0165544i
$874$	−14.7446			−0.498742
$875$		0			0
$876$	−16.7446	−	17.8178i	−0.565746	−	0.602009i
$877$	−48.4598	−	27.9783i	−1.63637	−	0.944758i	−0.982069	−	0.188524i	$-0.939630\pi$
$877$	−48.4598	−	27.9783i	−1.63637	−	0.944758i	−0.654301	−	0.756234i	$-0.727037\pi$
$878$	14.0588	+	8.11684i	0.474461	+	0.273930i
$879$	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	$0.347587\pi$
$882$	−2.27567	+	3.43070i	−0.0766258	+	0.115518i
$883$			12.7228i			0.428157i	0.976816	+	0.214078i	$0.0686748\pi$
$883$			12.7228i			0.428157i	−0.976816	+	0.214078i	$0.931325\pi$
$884$	−17.4891	−	30.2921i	−0.588223	−	1.01883i
$885$		0			0
$886$	−13.2446	+	22.9403i	−0.444960	+	0.770693i
$887$	−32.6689	−	18.8614i	−1.09691	−	0.633304i	−0.161506	−	0.986872i	$-0.551635\pi$
$887$	−32.6689	−	18.8614i	−1.09691	−	0.633304i	−0.935409	+	0.353568i	$0.884968\pi$
$888$	6.63325	+	2.00000i	0.222597	+	0.0671156i
$889$	−10.8139	−	18.7302i	−0.362685	−	0.628189i
$890$		0			0
$891$	7.45245	−	9.84868i	0.249667	−	0.329943i
$892$		−	12.3723i		−	0.414255i
$893$	−4.75372	+	2.74456i	−0.159077	+	0.0918433i
$894$	9.55842	−	31.7017i	0.319681	−	1.06026i
$895$		0			0
$896$	−1.18614	+	2.05446i	−0.0396262	+	0.0686346i
$897$	−8.21782	−	34.9783i	−0.274385	−	1.16789i
$898$	16.3345	−	9.43070i	0.545088	−	0.314707i
$899$	−29.4891			−0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$	−3.56529	+	2.05842i	−0.118711	+	0.0685380i
$903$	−34.0511	+	32.0000i	−1.13315	+	1.06489i
$904$	−7.37228	+	12.7692i	−0.245198	+	0.424696i
$905$		0			0
$906$	11.8614	+	12.6217i	0.394069	+	0.419328i
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	−0.395966	−	0.918265i	$-0.629590\pi$
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	0.597258	+	0.802049i	$0.296257\pi$
$908$			1.88316i			0.0624947i
$909$	−1.62772	+	26.1831i	−0.0539880	+	0.868440i
$910$		0			0
$911$	21.0000	+	36.3731i	0.695761	+	1.20509i	0.969923	+	0.243410i	$0.0782661\pi$
$911$	21.0000	+	36.3731i	0.695761	+	1.20509i	−0.274162	+	0.961683i	$0.588401\pi$
$912$	1.33591	+	5.68614i	0.0442363	+	0.188287i
$913$	−1.93443	−	1.11684i	−0.0640203	−	0.0369621i
$914$	−15.0584	+	26.0820i	−0.498088	+	0.862714i
$915$		0			0
$916$	−9.18614	−	15.9109i	−0.303519	−	0.525710i
$917$			20.7446i			0.685046i
$918$	−13.3128	+	35.9198i	−0.439387	+	1.18553i
$919$	−42.4674			−1.40087			−0.700435	−	0.713716i	$-0.747011\pi$
$919$	−42.4674			−1.40087			−0.700435	+	0.713716i	$0.747011\pi$
$920$		0			0
$921$	−16.6168	+	55.1118i	−0.547544	+	1.81600i
$922$	−16.5557	−	9.55842i	−0.545232	−	0.314790i
$923$	24.6535	+	14.2337i	0.811479	+	0.468508i
$924$	−5.48913	+	1.28962i	−0.180579	+	0.0424254i
$925$		0			0
$926$	−20.0000			−0.657241
$927$	21.3745	+	42.9783i	0.702031	+	1.41159i
$928$			4.37228i			0.143527i
$929$	−19.9783	−	34.6033i	−0.655465	−	1.13530i	−0.981777	−	0.190037i	$-0.939139\pi$
$929$	−19.9783	−	34.6033i	−0.655465	−	1.13530i	0.326312	−	0.945262i	$-0.394194\pi$
$930$		0			0
$931$	2.31386	−	4.00772i	0.0758337	−	0.131348i
$932$	−8.76144	−	5.05842i	−0.286991	−	0.165694i
$933$	11.6819	−	10.9783i	0.382449	−	0.359412i
$934$	−12.9416	−	22.4155i	−0.423461	−	0.733457i
$935$		0			0
$936$	−12.7446	+	6.33830i	−0.416569	+	0.207174i
$937$			17.7228i			0.578979i	0.957181	+	0.289490i	$0.0934855\pi$
$937$			17.7228i			0.578979i	−0.957181	+	0.289490i	$0.906514\pi$
$938$	−14.3812	+	8.30298i	−0.469563	+	0.271102i
$939$	15.8030	−	3.71277i	0.515711	−	0.121162i
$940$		0			0
$941$	−18.8139	+	32.5866i	−0.613314	+	1.06229i	0.377363	+	0.926065i	$0.376831\pi$
$941$	−18.8139	+	32.5866i	−0.613314	+	1.06229i	−0.990678	+	0.136226i	$0.956503\pi$
$942$	7.86797	+	2.37228i	0.256352	+	0.0772931i
$943$	11.3595	−	6.55842i	0.369917	−	0.213572i
$944$	1.37228			0.0446640
$945$		0			0
$946$	15.6060			0.507394
$947$	−19.6785	+	11.3614i	−0.639466	+	0.369196i	−0.784409	−	0.620244i	$-0.787034\pi$
$947$	−19.6785	+	11.3614i	−0.639466	+	0.369196i	0.144943	+	0.989440i	$0.453700\pi$
$948$	3.31662	+	1.00000i	0.107719	+	0.0324785i
$949$	−33.4891	+	58.0049i	−1.08710	+	1.88292i
$950$		0			0
$951$	14.7446	−	3.46410i	0.478125	−	0.112331i
$952$	15.1460	−	8.74456i	0.490886	−	0.283413i
$953$			30.8614i			0.999699i	0.866112	+	0.499850i	$0.166611\pi$
$953$			30.8614i			0.999699i	−0.866112	+	0.499850i	$0.833389\pi$
$954$	−2.13859	+	34.4010i	−0.0692395	+	1.11377i
$955$		0			0
$956$	7.37228	+	12.7692i	0.238437	+	0.412984i
$957$	−7.57301	+	7.11684i	−0.244801	+	0.230055i
$958$	−20.3422	−	11.7446i	−0.657226	−	0.379450i
$959$	2.23369	−	3.86886i	0.0721295	−	0.124932i
$960$		0			0
$961$	−7.24456	−	12.5480i	−0.233696	−	0.404773i
$962$		−	18.9783i		−	0.611883i
$963$	−24.0275	+	36.2228i	−0.774275	+	1.16726i
$964$	−10.4891			−0.337832
$965$		0			0
$966$	17.4891	−	4.10891i	0.562703	−	0.132202i
$967$	16.3533	+	9.44158i	0.525886	+	0.303621i	0.739340	−	0.673333i	$-0.235138\pi$
$967$	16.3533	+	9.44158i	0.525886	+	0.303621i	−0.213453	+	0.976953i	$0.568471\pi$
$968$	−7.89542	−	4.55842i	−0.253768	−	0.146513i
$969$	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	$0.379802\pi$
$972$	14.2525	+	6.31386i	0.457151	+	0.202517i
$973$		−	42.9783i		−	1.37782i
$974$	0.627719	+	1.08724i	0.0201134	+	0.0348374i
$975$		0			0
$976$	−4.55842	+	7.89542i	−0.145912	+	0.252726i
$977$	−34.7422	−	20.0584i	−1.11150	−	0.641726i	−0.172284	−	0.985047i	$-0.555115\pi$
$977$	−34.7422	−	20.0584i	−1.11150	−	0.641726i	−0.939218	+	0.343322i	$0.888448\pi$
$978$	0.589907	+	2.51087i	0.0188632	+	0.0802889i
$979$	−0.766312	−	1.32729i	−0.0244914	−	0.0424204i
$980$		0			0
$981$	−24.0693	−	15.9658i	−0.768474	−	0.509748i
$982$			3.60597i			0.115071i
$983$	13.7364	−	7.93070i	0.438123	−	0.252950i	−0.264678	−	0.964337i	$-0.585266\pi$
$983$	13.7364	−	7.93070i	0.438123	−	0.252950i	0.702801	+	0.711387i	$0.251932\pi$
$984$	−3.55842	−	3.78651i	−0.113438	−	0.120709i
$985$		0			0
$986$	16.1168	−	27.9152i	0.513265	−	0.889001i
$987$	4.87375	−	4.58017i	0.155133	−	0.145788i
$988$	13.8564	−	8.00000i	0.440831	−	0.254514i
$989$	−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	$0.593524\pi$
$992$	−5.84096	+	3.37228i	−0.185451	+	0.107070i
$993$	7.22316	+	30.7446i	0.229220	+	0.975649i
$994$	−7.11684	+	12.3267i	−0.225733	+	0.390980i
$995$		0			0
$996$	0.813859	−	2.69927i	0.0257881	−	0.0855295i
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	−0.679549	−	0.733630i	$-0.737825\pi$
$997$	−12.1244	+	7.00000i	−0.383982	+	0.221692i	0.295567	+	0.955322i	$0.404491\pi$
$998$			2.11684i			0.0670075i
$999$	−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.49.4		8
3.2	odd	2		1350.2.j.f.199.2		8
5.2	odd	4		90.2.e.c.31.1	✓	4
5.3	odd	4		450.2.e.j.301.2		4
5.4	even	2	inner	450.2.j.g.49.1		8
9.2	odd	6		1350.2.j.f.1099.3		8
9.4	even	3		4050.2.c.v.649.4		4
9.5	odd	6		4050.2.c.ba.649.2		4
9.7	even	3	inner	450.2.j.g.349.1		8
15.2	even	4		270.2.e.c.91.2		4
15.8	even	4		1350.2.e.l.901.1		4
15.14	odd	2		1350.2.j.f.199.3		8
20.7	even	4		720.2.q.f.481.2		4
45.2	even	12		270.2.e.c.181.2		4
45.4	even	6		4050.2.c.v.649.1		4
45.7	odd	12		90.2.e.c.61.2	yes	4
45.13	odd	12		4050.2.a.bw.1.2		2
45.14	odd	6		4050.2.c.ba.649.3		4
45.22	odd	12		810.2.a.i.1.1		2
45.23	even	12		4050.2.a.bo.1.2		2
45.29	odd	6		1350.2.j.f.1099.2		8
45.32	even	12		810.2.a.k.1.1		2
45.34	even	6	inner	450.2.j.g.349.4		8
45.38	even	12		1350.2.e.l.451.1		4
45.43	odd	12		450.2.e.j.151.1		4
60.47	odd	4		2160.2.q.f.1441.1		4
180.7	even	12		720.2.q.f.241.1		4
180.47	odd	12		2160.2.q.f.721.1		4
180.67	even	12		6480.2.a.be.1.2		2
180.167	odd	12		6480.2.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	5.2	odd	4
90.2.e.c.61.2	yes	4	45.7	odd	12
270.2.e.c.91.2		4	15.2	even	4
270.2.e.c.181.2		4	45.2	even	12
450.2.e.j.151.1		4	45.43	odd	12
450.2.e.j.301.2		4	5.3	odd	4
450.2.j.g.49.1		8	5.4	even	2	inner
450.2.j.g.49.4		8	1.1	even	1	trivial
450.2.j.g.349.1		8	9.7	even	3	inner
450.2.j.g.349.4		8	45.34	even	6	inner
720.2.q.f.241.1		4	180.7	even	12
720.2.q.f.481.2		4	20.7	even	4
810.2.a.i.1.1		2	45.22	odd	12
810.2.a.k.1.1		2	45.32	even	12
1350.2.e.l.451.1		4	45.38	even	12
1350.2.e.l.901.1		4	15.8	even	4
1350.2.j.f.199.2		8	3.2	odd	2
1350.2.j.f.199.3		8	15.14	odd	2
1350.2.j.f.1099.2		8	45.29	odd	6
1350.2.j.f.1099.3		8	9.2	odd	6
2160.2.q.f.721.1		4	180.47	odd	12
2160.2.q.f.1441.1		4	60.47	odd	4
4050.2.a.bo.1.2		2	45.23	even	12
4050.2.a.bw.1.2		2	45.13	odd	12
4050.2.c.v.649.1		4	45.4	even	6
4050.2.c.v.649.4		4	9.4	even	3
4050.2.c.ba.649.2		4	9.5	odd	6
4050.2.c.ba.649.3		4	45.14	odd	6
6480.2.a.be.1.2		2	180.67	even	12
6480.2.a.bn.1.2		2	180.167	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(2.05446 - 1.18614i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.65831 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.68614 - 0.396143i) q^{6} +(2.05446 - 1.18614i) q^{7} -1.00000i q^{8} +(2.50000 + 1.65831i) q^{9} +(-0.686141 - 1.18843i) q^{11} +(1.26217 - 1.18614i) q^{12} +(-4.10891 - 2.37228i) q^{13} +(1.18614 - 2.05446i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.37228i q^{17} +(2.99422 + 0.186141i) q^{18} -3.37228 q^{19} +(4.00000 - 0.939764i) q^{21} +(-1.18843 - 0.686141i) q^{22} +(3.78651 + 2.18614i) q^{23} +(0.500000 - 1.65831i) q^{24} -4.74456 q^{26} +(3.31662 + 4.00000i) q^{27} -2.37228i q^{28} +(-2.18614 - 3.78651i) q^{29} +(3.37228 - 5.84096i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.543620 - 2.31386i) q^{33} +(3.68614 + 6.38458i) q^{34} +(2.68614 - 1.33591i) q^{36} +4.00000i q^{37} +(-2.92048 + 1.68614i) q^{38} +(-5.62772 - 5.98844i) q^{39} +(1.50000 - 2.59808i) q^{41} +(2.99422 - 2.81386i) q^{42} +(-9.84868 + 5.68614i) q^{43} -1.37228 q^{44} +4.37228 q^{46} +(1.40965 - 0.813859i) q^{47} +(-0.396143 - 1.68614i) q^{48} +(-0.686141 + 1.18843i) q^{49} +(-3.68614 + 12.2255i) q^{51} +(-4.10891 + 2.37228i) q^{52} +11.4891i q^{53} +(4.87228 + 1.80579i) q^{54} +(-1.18614 - 2.05446i) q^{56} +(-5.59230 - 1.68614i) q^{57} +(-3.78651 - 2.18614i) q^{58} +(-0.686141 + 1.18843i) q^{59} +(-4.55842 - 7.89542i) q^{61} -6.74456i q^{62} +(7.10313 + 0.441578i) q^{63} -1.00000 q^{64} +(-1.62772 - 1.73205i) q^{66} +(-6.06218 - 3.50000i) q^{67} +(6.38458 + 3.68614i) q^{68} +(5.18614 + 5.51856i) q^{69} -6.00000 q^{71} +(1.65831 - 2.50000i) q^{72} -14.1168i q^{73} +(2.00000 + 3.46410i) q^{74} +(-1.68614 + 2.92048i) q^{76} +(-2.81929 - 1.62772i) q^{77} +(-7.86797 - 2.37228i) q^{78} +(1.00000 + 1.73205i) q^{79} +(3.50000 + 8.29156i) q^{81} -3.00000i q^{82} +(1.40965 - 0.813859i) q^{83} +(1.18614 - 3.93398i) q^{84} +(-5.68614 + 9.84868i) q^{86} +(-1.73205 - 7.37228i) q^{87} +(-1.18843 + 0.686141i) q^{88} +1.11684 q^{89} -11.2554 q^{91} +(3.78651 - 2.18614i) q^{92} +(8.51278 - 8.00000i) q^{93} +(0.813859 - 1.40965i) q^{94} +(-1.18614 - 1.26217i) q^{96} +(2.27567 - 1.31386i) q^{97} +1.37228i q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 2 * q^6 + 20 * q^9	\( 8 q + 4 q^{4} + 2 q^{6} + 20 q^{9} + 6 q^{11} - 2 q^{14} - 4 q^{16} - 4 q^{19} + 32 q^{21} + 4 q^{24} + 8 q^{26} - 6 q^{29} + 4 q^{31} + 18 q^{34} + 10 q^{36} - 68 q^{39} + 12 q^{41} + 12 q^{44} + 12 q^{46} + 6 q^{49} - 18 q^{51} + 16 q^{54} + 2 q^{56} + 6 q^{59} - 2 q^{61} - 8 q^{64} - 36 q^{66} + 30 q^{69} - 48 q^{71} + 16 q^{74} - 2 q^{76} + 8 q^{79} + 28 q^{81} - 2 q^{84} - 34 q^{86} - 60 q^{89} - 136 q^{91} + 18 q^{94} + 2 q^{96} + 48 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

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Representations

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Database

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