LMFDB - Embedded newform 450.2.j.g.349.4

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			349.4
Root			$0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	450.349
Dual form			450.2.j.g.49.4

$q$-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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.65831	−	0.500000i	0.957427	−	0.288675i
$3$	1.65831	−	0.500000i	0.957427	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.68614	+	0.396143i	0.688364	+	0.161725i
$7$	2.05446	+	1.18614i	0.776511	+	0.448319i	0.835192	−	0.549958i	$-0.185356\pi$
$7$	2.05446	+	1.18614i	0.776511	+	0.448319i	−0.0586811	+	0.998277i	$0.518690\pi$
$8$			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	−0.950730	−	0.310021i	$-0.899664\pi$
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	0.743851	+	0.668346i	$0.232997\pi$
$12$	1.26217	+	1.18614i	0.364357	+	0.342409i
$13$	−4.10891	+	2.37228i	−1.13961	+	0.657952i	−0.946333	−	0.323192i	$-0.895244\pi$
$13$	−4.10891	+	2.37228i	−1.13961	+	0.657952i	−0.193274	+	0.981145i	$0.561911\pi$
$14$	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	$-0.647873\pi$
$17$		−	7.37228i		−	1.78804i	0.448026	−	0.894020i	$-0.352127\pi$
$18$	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	−0.0502598	−	0.998736i	$-0.516005\pi$
$23$	3.78651	−	2.18614i	0.789541	−	0.455842i	0.839801	+	0.542894i	$0.182672\pi$
$24$	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	−0.994432	−	0.105378i	$-0.966395\pi$
$29$	−2.18614	+	3.78651i	−0.405956	+	0.703137i	0.588476	+	0.808515i	$0.299728\pi$
$30$		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	$0.626235\pi$
$32$	−0.866025	+	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	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	−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	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	2.99422	+	2.81386i	0.462018	+	0.434188i
$43$	−9.84868	−	5.68614i	−1.50191	−	0.867128i	−0.999998	−	0.00221007i	$-0.999297\pi$
$43$	−9.84868	−	5.68614i	−1.50191	−	0.867128i	−0.501913	−	0.864918i	$-0.667370\pi$
$44$	−1.37228			−0.206879
$45$		0			0
$46$	4.37228			0.644658
$47$	1.40965	+	0.813859i	0.205618	+	0.118714i	0.599273	−	0.800545i	$-0.295456\pi$
$47$	1.40965	+	0.813859i	0.205618	+	0.118714i	−0.393655	+	0.919258i	$0.628790\pi$
$48$	−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	$-0.710560\pi$
$53$		−	11.4891i		−	1.57815i	0.614295	−	0.789076i	$-0.289440\pi$
$54$	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	0.817899	−	0.575361i	$-0.195139\pi$
$59$	−0.686141	−	1.18843i	−0.0893279	−	0.154720i	−0.907227	+	0.420641i	$0.861805\pi$
$60$		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	$0.968292\pi$
$62$			6.74456i			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	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	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	$0.309460\pi$
$73$			14.1168i			1.65225i	−0.563486	+	0.826126i	$0.690540\pi$
$74$	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	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$			3.00000i			0.331295i
$83$	1.40965	+	0.813859i	0.154729	+	0.0893327i	0.575365	−	0.817897i	$-0.304860\pi$
$83$	1.40965	+	0.813859i	0.154729	+	0.0893327i	−0.420637	+	0.907229i	$0.638193\pi$
$84$	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	0.611061	−	0.791584i	$-0.290743\pi$
$97$	2.27567	+	1.31386i	0.231059	+	0.133402i	−0.380001	+	0.924986i	$0.624076\pi$
$98$		−	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	−0.562242	−	0.826973i	$-0.690061\pi$
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	0.997300	+	0.0734297i	$0.0233944\pi$
$102$	2.92048	−	12.4307i	0.289171	−	1.23082i
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.374987	−	0.927030i	$-0.377647\pi$
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.990325	+	0.138767i	$0.0443138\pi$
$104$	−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	$-0.753024\pi$
$107$		−	14.4891i		−	1.40072i	0.713791	−	0.700358i	$-0.246976\pi$
$108$	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	−0.960827	−	0.277149i	$-0.910610\pi$
$113$	−12.7692	+	7.37228i	−1.20122	+	0.693526i	−0.240395	+	0.970675i	$0.577277\pi$
$114$	−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	$0.132553\pi$
$127$			9.11684i			0.808989i	−0.914540	+	0.404495i	$0.867447\pi$
$128$	−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	0.609341	−	0.792908i	$-0.291434\pi$
$131$	−4.37228	−	7.57301i	−0.382008	−	0.661657i	−0.991349	+	0.131251i	$0.958101\pi$
$132$	−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	0.568046	−	0.822996i	$-0.307699\pi$
$137$	1.63086	+	0.941578i	0.139334	+	0.0804444i	−0.428713	+	0.903441i	$0.641033\pi$
$138$	7.25061	−	2.18614i	0.617213	−	0.186097i
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	0.938470	+	0.345359i	$0.112243\pi$
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	−0.170145	+	0.985419i	$0.554424\pi$
$140$		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	0.930153	+	0.367171i	$0.119674\pi$
$149$	9.55842	+	16.5557i	0.783056	+	1.35629i	−0.147097	+	0.989122i	$0.546993\pi$
$150$		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	$0.0332784\pi$
$152$		−	3.37228i		−	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	−0.326993	−	0.945027i	$-0.606036\pi$
$157$	4.10891	−	2.37228i	0.327927	−	0.189329i	0.654920	+	0.755698i	$0.272702\pi$
$158$	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	$-0.981426\pi$
$163$		−	1.48913i		−	0.116637i	0.998298	−	0.0583186i	$-0.0185739\pi$
$164$	−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	−0.222143	−	0.975014i	$-0.571305\pi$
$167$	6.60580	−	3.81386i	0.511172	−	0.295125i	0.733315	+	0.679889i	$0.237972\pi$
$168$	−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	0.772732	−	0.634733i	$-0.218890\pi$
$173$	8.01544	+	4.62772i	0.609403	+	0.351839i	−0.163329	+	0.986572i	$0.552223\pi$
$174$	−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	−0.749482	−	0.662025i	$-0.769697\pi$
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	0.948071	+	0.318058i	$0.103031\pi$
$192$	−1.65831	+	0.500000i	−0.119678	+	0.0360844i
$193$	−3.36291	+	1.94158i	−0.242068	+	0.139758i	−0.616127	−	0.787647i	$-0.711299\pi$
$193$	−3.36291	+	1.94158i	−0.242068	+	0.139758i	0.374059	+	0.927405i	$0.377966\pi$
$194$	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	$0.214096\pi$
$197$			17.4891i			1.24605i	−0.782202	+	0.623024i	$0.785904\pi$
$198$	−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	0.963454	−	0.267873i	$-0.0863207\pi$
$211$	3.62772	+	6.28339i	0.249742	+	0.432567i	−0.713712	+	0.700439i	$0.752987\pi$
$212$	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	0.813836	−	0.581095i	$-0.197376\pi$
$223$	10.7147	+	6.18614i	0.717510	+	0.414255i	−0.0963255	+	0.995350i	$0.530709\pi$
$224$	−2.37228			−0.158505
$225$		0			0
$226$	−14.7446			−0.980794
$227$	−1.63086	−	0.941578i	−0.108244	−	0.0624947i	0.444901	−	0.895580i	$-0.353239\pi$
$227$	−1.63086	−	0.941578i	−0.108244	−	0.0624947i	−0.553145	+	0.833085i	$0.686572\pi$
$228$	−4.25639	−	4.00000i	−0.281886	−	0.264906i
$229$	9.18614	+	15.9109i	0.607037	+	1.05142i	0.991726	+	0.128373i	$0.0409755\pi$
$229$	9.18614	+	15.9109i	0.607037	+	1.05142i	−0.384689	+	0.923046i	$0.625691\pi$
$230$		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	$0.107517\pi$
$233$			10.1168i			0.662776i	−0.943494	+	0.331388i	$0.892483\pi$
$234$	−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	0.522776	−	0.852470i	$-0.324897\pi$
$239$	−7.37228	−	12.7692i	−0.476873	−	0.825969i	−0.999649	+	0.0265017i	$0.991563\pi$
$240$		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	$0.276360\pi$
$242$			9.11684i			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	−0.536608	−	0.843832i	$-0.680295\pi$
$257$	−1.18843	+	0.686141i	−0.0741323	+	0.0428003i	0.462476	+	0.886632i	$0.346961\pi$
$258$	−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	0.639351	−	0.768915i	$-0.279203\pi$
$263$	4.75372	+	2.74456i	0.293127	+	0.169237i	−0.346224	+	0.938152i	$0.612536\pi$
$264$	−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	0.356997	−	0.934106i	$-0.383801\pi$
$277$	−4.55134	−	2.62772i	−0.273464	−	0.157884i	−0.630461	+	0.776221i	$0.717134\pi$
$278$			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	−0.923836	−	0.382788i	$-0.874964\pi$
$281$	−2.18614	+	3.78651i	−0.130414	+	0.225884i	0.793422	+	0.608672i	$0.208297\pi$
$282$	2.05446	+	1.93070i	0.122341	+	0.114972i
$283$	27.5928	−	15.9307i	1.64022	−	0.946982i	0.659467	−	0.751733i	$-0.270782\pi$
$283$	27.5928	−	15.9307i	1.64022	−	0.946982i	0.980754	−	0.195249i	$-0.0625514\pi$
$284$	−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	−0.277037	−	0.960859i	$-0.589352\pi$
$293$	7.13058	−	4.11684i	0.416573	−	0.240509i	0.693610	+	0.720351i	$0.256019\pi$
$294$	−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	$-0.602728\pi$
$307$		−	33.2337i		−	1.89675i	0.317156	−	0.948373i	$-0.397272\pi$
$308$	−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	0.966883	−	0.255221i	$-0.0821481\pi$
$311$	4.62772	+	8.01544i	0.262414	+	0.454514i	−0.704469	+	0.709735i	$0.748815\pi$
$312$	−5.98844	−	5.62772i	−0.339029	−	0.318607i
$313$	8.11663	+	4.68614i	0.458779	+	0.264876i	0.711531	−	0.702655i	$-0.248002\pi$
$313$	8.11663	+	4.68614i	0.458779	+	0.264876i	−0.252752	+	0.967531i	$0.581336\pi$
$314$	4.74456			0.267751
$315$		0			0
$316$	2.00000			0.112509
$317$	7.57301	+	4.37228i	0.425343	+	0.245572i	0.697361	−	0.716720i	$-0.254358\pi$
$317$	7.57301	+	4.37228i	0.425343	+	0.245572i	−0.272018	+	0.962292i	$0.587691\pi$
$318$	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	−0.498892	−	0.866664i	$-0.666260\pi$
$331$	9.11684	−	15.7908i	0.501107	−	0.867943i	0.999999	−	0.00127880i	$-0.000407055\pi$
$332$			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	−0.418342	−	0.908290i	$-0.637389\pi$
$337$	2.92048	−	1.68614i	0.159089	−	0.0918499i	0.577431	+	0.816440i	$0.304055\pi$
$338$	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	−0.916476	−	0.400089i	$-0.868979\pi$
$347$	−19.1537	+	11.0584i	−1.02823	+	0.593647i	−0.111751	+	0.993736i	$0.535646\pi$
$348$	−7.25061	+	2.18614i	−0.388673	+	0.117189i
$349$	0.441578	−	0.764836i	0.0236371	−	0.0409407i	−0.853965	−	0.520331i	$-0.825809\pi$
$349$	0.441578	−	0.764836i	0.0236371	−	0.0409407i	0.877602	+	0.479390i	$0.159142\pi$
$350$		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	0.994285	−	0.106757i	$-0.0340466\pi$
$353$	26.2843	+	15.1753i	1.39897	+	0.807698i	0.404689	+	0.914455i	$0.367380\pi$
$354$	−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	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$			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	−0.658422	−	0.752649i	$-0.728776\pi$
$373$	−6.48577	+	3.74456i	−0.335821	+	0.193886i	0.322602	+	0.946535i	$0.395443\pi$
$374$	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	−0.913184	−	0.407547i	$-0.866384\pi$
$383$	−19.8997	+	11.4891i	−1.01683	+	0.587067i	−0.103646	+	0.994614i	$0.533051\pi$
$384$	−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	−0.967024	−	0.254686i	$-0.918028\pi$
$389$	−5.18614	+	8.98266i	−0.262948	+	0.455439i	0.704076	+	0.710124i	$0.251361\pi$
$390$		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	$0.0911462\pi$
$397$			11.2554i			0.564894i	−0.959283	+	0.282447i	$0.908854\pi$
$398$	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	0.591599	−	0.806232i	$-0.298497\pi$
$401$	−8.05842	−	13.9576i	−0.402418	−	0.697009i	−0.994017	+	0.109223i	$0.965164\pi$
$402$	−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	0.699952	−	0.714190i	$-0.253205\pi$
$409$	−5.43070	−	9.40625i	−0.268531	−	0.465109i	−0.968483	+	0.249081i	$0.919872\pi$
$410$		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	−0.934862	−	0.355012i	$-0.884477\pi$
$419$	−15.8614	−	27.4728i	−0.774880	−	1.34213i	0.159981	−	0.987120i	$-0.448857\pi$
$420$		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	$-0.220101\pi$
$422$			7.25544i			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	$-0.995199\pi$
$433$		−	0.627719i		−	0.0301662i	0.999886	−	0.0150831i	$-0.00480129\pi$
$434$	−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	−0.604703	−	0.796451i	$-0.706708\pi$
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	0.992098	+	0.125462i	$0.0400414\pi$
$440$		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	−0.156368	−	0.987699i	$-0.549979\pi$
$443$	−22.9403	−	13.2446i	−1.08992	−	0.629268i	−0.933556	+	0.358431i	$0.883312\pi$
$444$	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	−0.255131	−	0.966906i	$-0.582119\pi$
$457$	−26.0820	−	15.0584i	−1.22006	−	0.704403i	−0.964931	+	0.262503i	$0.915452\pi$
$458$			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	−0.998065	−	0.0621833i	$-0.980194\pi$
$461$	−9.55842	+	16.5557i	−0.445180	+	0.771075i	0.552885	+	0.833258i	$0.313527\pi$
$462$	−5.39853	+	1.62772i	−0.251162	+	0.0757283i
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	0.0402476	+	0.999190i	$0.487185\pi$
$464$	−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	$0.204381\pi$
$467$			25.8832i			1.19773i	−0.800850	+	0.598865i	$0.795619\pi$
$468$	−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	0.462460	+	0.886640i	$0.346967\pi$
$479$	−11.7446	+	20.3422i	−0.536623	+	0.929458i	−0.999083	+	0.0428178i	$0.986366\pi$
$480$		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	$-0.990945\pi$
$487$		−	1.25544i		−	0.0568893i	0.999595	−	0.0284446i	$-0.00905543\pi$
$488$	−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	0.822470	−	0.568808i	$-0.192595\pi$
$491$	−1.80298	−	3.12286i	−0.0813676	−	0.140933i	−0.903838	+	0.427876i	$0.859262\pi$
$492$	−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	0.841362	−	0.540472i	$-0.181754\pi$
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	−0.888743	+	0.458405i	$0.848421\pi$
$500$		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	$-0.837954\pi$
$503$		−	21.8614i		−	0.974752i	0.873192	−	0.487376i	$-0.162046\pi$
$504$	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	0.950840	−	0.309682i	$-0.100223\pi$
$509$	4.67527	+	8.09780i	0.207228	+	0.358929i	−0.743613	+	0.668611i	$0.766889\pi$
$510$		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	$0.0781488\pi$
$523$			11.1168i			0.486106i	−0.970013	+	0.243053i	$0.921851\pi$
$524$	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	−0.462343	−	0.886701i	$-0.652991\pi$
$547$	−34.1798	−	19.7337i	−1.46142	−	0.843752i	−0.999077	+	0.0429494i	$0.986325\pi$
$548$			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	$-0.933661\pi$
$557$		−	9.76631i		−	0.413812i	0.978361	−	0.206906i	$-0.0663394\pi$
$558$	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	−0.773106	−	0.634277i	$-0.781298\pi$
$563$	−14.4824	+	8.36141i	−0.610360	+	0.352391i	0.162747	+	0.986668i	$0.447965\pi$
$564$	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	−0.747613	−	0.664135i	$-0.768800\pi$
$569$	4.80298	−	8.31901i	0.201352	−	0.348751i	0.948964	+	0.315384i	$0.102133\pi$
$570$		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	$0.603324\pi$
$572$	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	$-0.834386\pi$
$577$		−	23.8832i		−	0.994269i	0.867674	−	0.497134i	$-0.165614\pi$
$578$	−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	−0.0673658	−	0.997728i	$-0.521459\pi$
$587$	−23.3827	−	13.5000i	−0.965107	−	0.557205i	−0.897741	+	0.440524i	$0.854793\pi$
$588$	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	$-0.717979\pi$
$593$		−	37.7228i		−	1.54909i	0.632519	−	0.774545i	$-0.282021\pi$
$594$	−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	−0.931305	−	0.364239i	$-0.881329\pi$
$599$	−19.1168	−	33.1113i	−0.781093	−	1.35289i	0.150212	−	0.988654i	$-0.452004\pi$
$600$		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	$0.982113\pi$
$602$		−	26.9783i		−	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	−0.484398	−	0.874848i	$-0.660961\pi$
$607$	0.764836	−	0.441578i	0.0310437	−	0.0179231i	0.515442	+	0.856925i	$0.327628\pi$
$608$	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	$0.00150220\pi$
$613$			0.233688i			0.00943857i	−0.999989	+	0.00471928i	$0.998498\pi$
$614$	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	−0.833267	−	0.552870i	$-0.813532\pi$
$617$	−19.1537	+	11.0584i	−0.771101	+	0.445195i	0.0621663	+	0.998066i	$0.480199\pi$
$618$	26.5330	−	8.00000i	1.06731	−	0.321807i
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	0.173682	+	0.984802i	$0.444434\pi$
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	−0.939704	+	0.341988i	$0.888900\pi$
$620$		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	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$	5.73977	−	24.4307i	0.226531	−	0.964203i
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	−0.675937	−	0.736959i	$-0.736261\pi$
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	0.300257	+	0.953858i	$0.402928\pi$
$644$	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	$0.157059\pi$
$647$			24.0951i			0.947276i	−0.880720	+	0.473638i	$0.842941\pi$
$648$	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	0.301873	−	0.953348i	$-0.402388\pi$
$653$	32.6689	−	18.8614i	1.27843	−	0.738104i	0.976560	+	0.215244i	$0.0690548\pi$
$654$	−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	−0.914518	−	0.404545i	$-0.867430\pi$
$659$	−2.74456	+	4.75372i	−0.106913	+	0.185179i	0.807605	+	0.589724i	$0.200763\pi$
$660$		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	$0.975665\pi$
$662$	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	0.323711	−	0.946156i	$-0.395069\pi$
$673$	−8.66025	−	5.00000i	−0.333828	−	0.192736i	−0.657539	+	0.753420i	$0.728403\pi$
$674$	3.37228			0.129895
$675$		0			0
$676$	9.51087			0.365803
$677$	37.8651	+	21.8614i	1.45527	+	0.840202i	0.998773	−	0.0495215i	$-0.0157696\pi$
$677$	37.8651	+	21.8614i	1.45527	+	0.840202i	0.456500	+	0.889724i	$0.349103\pi$
$678$	−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	$-0.781752\pi$
$683$		−	33.0951i		−	1.26635i	0.774009	−	0.633174i	$-0.218248\pi$
$684$	−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	−0.848738	−	0.528813i	$-0.822637\pi$
$691$	0.883156	−	1.52967i	0.0335968	−	0.0581914i	0.882335	+	0.470622i	$0.155970\pi$
$692$			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	−0.999863	−	0.0165226i	$-0.994740\pi$
$709$	−12.9307	+	22.3966i	−0.485623	+	0.841123i	0.514241	+	0.857646i	$0.328074\pi$
$710$		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	0.485750	−	0.874098i	$-0.338547\pi$
$727$	−0.764836	−	0.441578i	−0.0283662	−	0.0163772i	−0.514116	+	0.857721i	$0.671880\pi$
$728$		−	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	−0.934915	−	0.354871i	$-0.884525\pi$
$733$	−29.6472	+	17.1168i	−1.09505	+	0.632225i	−0.160131	+	0.987096i	$0.551192\pi$
$734$	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	−0.842770	−	0.538273i	$-0.819077\pi$
$743$	−21.7518	+	12.5584i	−0.797997	+	0.460724i	0.0447732	+	0.998997i	$0.485743\pi$
$744$	−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	0.983036	−	0.183412i	$-0.0587143\pi$
$751$	9.11684	+	15.7908i	0.332678	+	0.576216i	−0.650358	+	0.759628i	$0.725381\pi$
$752$	−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	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	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	0.735347	−	0.677690i	$-0.237019\pi$
$761$	−6.04755	−	10.4747i	−0.219223	−	0.379706i	−0.954571	+	0.297984i	$0.903686\pi$
$762$	−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	0.654877	−	0.755735i	$-0.272720\pi$
$769$	−9.06930	−	15.7085i	−0.327047	−	0.566462i	−0.981925	+	0.189273i	$0.939387\pi$
$770$		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	$-0.914574\pi$
$773$		−	14.7446i		−	0.530325i	0.964204	−	0.265163i	$-0.0854256\pi$
$774$	−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	−0.865474	−	0.500953i	$-0.832983\pi$
$787$	−24.2487	+	14.0000i	−0.864373	+	0.499046i	0.00110111	+	0.999999i	$0.499650\pi$
$788$	−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	−0.449236	−	0.893413i	$-0.648304\pi$
$797$	2.81929	−	1.62772i	0.0998644	−	0.0576568i	0.549100	+	0.835756i	$0.314970\pi$
$798$	−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	−0.0439382	+	0.999034i	$0.513990\pi$
$821$	−25.4198	+	44.0284i	−0.887158	+	1.53660i	−0.843220	+	0.537569i	$0.819343\pi$
$822$	2.37686	+	2.23369i	0.0829025	+	0.0779088i
$823$	−32.9913	+	19.0475i	−1.15001	+	0.663956i	−0.948888	−	0.315612i	$-0.897790\pi$
$823$	−32.9913	+	19.0475i	−1.15001	+	0.663956i	−0.201117	+	0.979567i	$0.564457\pi$
$824$	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	$0.0451936\pi$
$827$			8.13859i			0.283007i	−0.989938	+	0.141503i	$0.954806\pi$
$828$	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	−0.177447	−	0.984130i	$-0.556784\pi$
$839$	22.1168	−	38.3075i	0.763558	−	1.32252i	0.941005	−	0.338391i	$-0.109883\pi$
$840$		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	0.473584	−	0.880749i	$-0.342960\pi$
$853$	−1.52967	−	0.883156i	−0.0523749	−	0.0302387i	−0.525959	+	0.850510i	$0.676293\pi$
$854$	−21.6277			−0.740085
$855$		0			0
$856$	14.4891			0.495228
$857$	−20.3422	−	11.7446i	−0.694876	−	0.401187i	0.110560	−	0.993869i	$-0.464735\pi$
$857$	−20.3422	−	11.7446i	−0.694876	−	0.401187i	−0.805436	+	0.592683i	$0.798069\pi$
$858$	2.57924	−	10.9783i	0.0880538	−	0.374791i
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	0.867020	−	0.498273i	$-0.166032\pi$
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	−0.865027	+	0.501725i	$0.832699\pi$
$860$		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	$0.258235\pi$
$863$			42.6060i			1.45032i	−0.688578	+	0.725162i	$0.741765\pi$
$864$	−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	−0.654301	+	0.756234i	$0.727037\pi$
$877$	−48.4598	+	27.9783i	−1.63637	+	0.944758i	−0.982069	+	0.188524i	$0.939630\pi$
$878$	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	$-0.931325\pi$
$883$		−	12.7228i		−	0.428157i	0.976816	−	0.214078i	$-0.0686748\pi$
$884$	−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	−0.935409	−	0.353568i	$-0.884968\pi$
$887$	−32.6689	+	18.8614i	−1.09691	+	0.633304i	−0.161506	+	0.986872i	$0.551635\pi$
$888$	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	0.597258	−	0.802049i	$-0.296257\pi$
$907$	6.06218	+	3.50000i	0.201291	+	0.116216i	−0.395966	+	0.918265i	$0.629590\pi$
$908$		−	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	−0.274162	−	0.961683i	$-0.588401\pi$
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	0.969923	−	0.243410i	$-0.0782661\pi$
$912$	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	0.326312	+	0.945262i	$0.394194\pi$
$929$	−19.9783	+	34.6033i	−0.655465	+	1.13530i	−0.981777	+	0.190037i	$0.939139\pi$
$930$		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	$-0.906514\pi$
$937$		−	17.7228i		−	0.578979i	0.957181	−	0.289490i	$-0.0934855\pi$
$938$	−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	−0.990678	−	0.136226i	$-0.956503\pi$
$941$	−18.8139	−	32.5866i	−0.613314	−	1.06229i	0.377363	−	0.926065i	$-0.376831\pi$
$942$	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	0.144943	−	0.989440i	$-0.453700\pi$
$947$	−19.6785	−	11.3614i	−0.639466	−	0.369196i	−0.784409	+	0.620244i	$0.787034\pi$
$948$	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	$-0.833389\pi$
$953$		−	30.8614i		−	0.999699i	0.866112	−	0.499850i	$-0.166611\pi$
$954$	−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	−0.213453	−	0.976953i	$-0.568471\pi$
$967$	16.3533	−	9.44158i	0.525886	−	0.303621i	0.739340	+	0.673333i	$0.235138\pi$
$968$	−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	−0.939218	−	0.343322i	$-0.888448\pi$
$977$	−34.7422	+	20.0584i	−1.11150	+	0.641726i	−0.172284	+	0.985047i	$0.555115\pi$
$978$	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	0.702801	−	0.711387i	$-0.251932\pi$
$983$	13.7364	+	7.93070i	0.438123	+	0.252950i	−0.264678	+	0.964337i	$0.585266\pi$
$984$	−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	0.295567	−	0.955322i	$-0.404491\pi$
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$998$		−	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.349.4		8
3.2	odd	2		1350.2.j.f.1099.2		8
5.2	odd	4		450.2.e.j.151.1		4
5.3	odd	4		90.2.e.c.61.2	yes	4
5.4	even	2	inner	450.2.j.g.349.1		8
9.2	odd	6		4050.2.c.ba.649.3		4
9.4	even	3	inner	450.2.j.g.49.1		8
9.5	odd	6		1350.2.j.f.199.3		8
9.7	even	3		4050.2.c.v.649.1		4
15.2	even	4		1350.2.e.l.451.1		4
15.8	even	4		270.2.e.c.181.2		4
15.14	odd	2		1350.2.j.f.1099.3		8
20.3	even	4		720.2.q.f.241.1		4
45.2	even	12		4050.2.a.bo.1.2		2
45.4	even	6	inner	450.2.j.g.49.4		8
45.7	odd	12		4050.2.a.bw.1.2		2
45.13	odd	12		90.2.e.c.31.1	✓	4
45.14	odd	6		1350.2.j.f.199.2		8
45.22	odd	12		450.2.e.j.301.2		4
45.23	even	12		270.2.e.c.91.2		4
45.29	odd	6		4050.2.c.ba.649.2		4
45.32	even	12		1350.2.e.l.901.1		4
45.34	even	6		4050.2.c.v.649.4		4
45.38	even	12		810.2.a.k.1.1		2
45.43	odd	12		810.2.a.i.1.1		2
60.23	odd	4		2160.2.q.f.721.1		4
180.23	odd	12		2160.2.q.f.1441.1		4
180.43	even	12		6480.2.a.be.1.2		2
180.83	odd	12		6480.2.a.bn.1.2		2
180.103	even	12		720.2.q.f.481.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	45.13	odd	12
90.2.e.c.61.2	yes	4	5.3	odd	4
270.2.e.c.91.2		4	45.23	even	12
270.2.e.c.181.2		4	15.8	even	4
450.2.e.j.151.1		4	5.2	odd	4
450.2.e.j.301.2		4	45.22	odd	12
450.2.j.g.49.1		8	9.4	even	3	inner
450.2.j.g.49.4		8	45.4	even	6	inner
450.2.j.g.349.1		8	5.4	even	2	inner
450.2.j.g.349.4		8	1.1	even	1	trivial
720.2.q.f.241.1		4	20.3	even	4
720.2.q.f.481.2		4	180.103	even	12
810.2.a.i.1.1		2	45.43	odd	12
810.2.a.k.1.1		2	45.38	even	12
1350.2.e.l.451.1		4	15.2	even	4
1350.2.e.l.901.1		4	45.32	even	12
1350.2.j.f.199.2		8	45.14	odd	6
1350.2.j.f.199.3		8	9.5	odd	6
1350.2.j.f.1099.2		8	3.2	odd	2
1350.2.j.f.1099.3		8	15.14	odd	2
2160.2.q.f.721.1		4	60.23	odd	4
2160.2.q.f.1441.1		4	180.23	odd	12
4050.2.a.bo.1.2		2	45.2	even	12
4050.2.a.bw.1.2		2	45.7	odd	12
4050.2.c.v.649.1		4	9.7	even	3
4050.2.c.v.649.4		4	45.34	even	6
4050.2.c.ba.649.2		4	45.29	odd	6
4050.2.c.ba.649.3		4	9.2	odd	6
6480.2.a.be.1.2		2	180.43	even	12
6480.2.a.bn.1.2		2	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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