LMFDB - Embedded newform 1274.2.n.m.753.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(753,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.753"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-2,6,0,0,0,0,-24,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 2 x^{10} - 20 x^{9} - 5 x^{8} + 106 x^{7} - 2 x^{6} + 236 x^{5} + 701 x^{4} + \cdots + 4 $ x^12 - 2x^11 + 2x^10 - 20x^9 - 5x^8 + 106x^7 - 2x^6 + 236x^5 + 701x^4 - 282x^3 + 50x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.4
Root			$-1.73868 - 0.465879i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.m.961.4

$q$-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} +(-1.39283 + 2.41246i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.20456 + 1.27280i) q^{5} +2.78567i q^{6} -1.00000i q^{8} +(-2.37997 - 4.12223i) q^{9} +(-1.27280 + 2.20456i) q^{10} +(-2.88497 - 1.66564i) q^{11} +(1.39283 + 2.41246i) q^{12} +(-3.27280 + 1.51286i) q^{13} -7.09122i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.54561 - 6.14117i) q^{17} +(-4.12223 - 2.37997i) q^{18} +(3.93661 - 2.27280i) q^{19} +2.54561i q^{20} -3.33127 q^{22} +(0.879970 + 1.52415i) q^{23} +(2.41246 + 1.39283i) q^{24} +(0.740059 - 1.28182i) q^{25} +(-2.07790 + 2.94658i) q^{26} +4.90261 q^{27} +7.57133 q^{29} +(-3.54561 - 6.14117i) q^{30} +(-2.88497 - 1.66564i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.03656 - 4.63991i) q^{33} -7.09122i q^{34} -4.75994 q^{36} +(-3.25620 + 1.87997i) q^{37} +(2.27280 - 3.93661i) q^{38} +(0.908751 - 10.0027i) q^{39} +(1.27280 + 2.20456i) q^{40} -4.24006i q^{41} +9.09122 q^{43} +(-2.88497 + 1.66564i) q^{44} +(10.4936 + 6.05847i) q^{45} +(1.52415 + 0.879970i) q^{46} +(-9.81317 + 5.66564i) q^{47} +2.78567 q^{48} -1.48012i q^{50} +(9.87688 + 17.1073i) q^{51} +(-0.326224 + 3.59076i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.24578 - 2.45130i) q^{54} +8.48012 q^{55} +12.6625i q^{57} +(6.55697 - 3.78567i) q^{58} +(6.98492 + 4.03274i) q^{59} +(-6.14117 - 3.54561i) q^{60} +(0.392834 + 0.680408i) q^{61} -3.33127 q^{62} -1.00000 q^{64} +(5.28952 - 7.50084i) q^{65} +(4.63991 - 8.03656i) q^{66} +(-4.98825 - 2.87997i) q^{67} +(-3.54561 - 6.14117i) q^{68} -4.90261 q^{69} -11.1427i q^{71} +(-4.12223 + 2.37997i) q^{72} +(-8.08112 - 4.66564i) q^{73} +(-1.87997 + 3.25620i) q^{74} +(2.06156 + 3.57072i) q^{75} -4.54561i q^{76} +(-4.21433 - 9.11694i) q^{78} +(-2.42558 - 4.20122i) q^{79} +(2.20456 + 1.27280i) q^{80} +(0.311393 - 0.539349i) q^{81} +(-2.12003 - 3.67200i) q^{82} -11.2082i q^{83} +18.0515i q^{85} +(7.87322 - 4.54561i) q^{86} +(-10.5456 + 18.2655i) q^{87} +(-1.66564 + 2.88497i) q^{88} +(13.0694 - 7.54561i) q^{89} +12.1169 q^{90} +1.75994 q^{92} +(8.03656 - 4.63991i) q^{93} +(-5.66564 + 9.81317i) q^{94} +(-5.78567 + 10.0211i) q^{95} +(2.41246 - 1.39283i) q^{96} -7.75994i q^{97} +15.8567i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} - 24 q^{9} + 4 q^{10} + 2 q^{12} - 20 q^{13} - 6 q^{16} + 4 q^{17} + 28 q^{22} + 6 q^{23} + 18 q^{25} + 4 q^{26} - 68 q^{27} + 32 q^{29} - 4 q^{30} - 48 q^{36} + 8 q^{38} + 6 q^{39}+ \cdots - 40 q^{95}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 - 24 * q^9 + 4 * q^10 + 2 * q^12 - 20 * q^13 - 6 * q^16 + 4 * q^17 + 28 * q^22 + 6 * q^23 + 18 * q^25 + 4 * q^26 - 68 * q^27 + 32 * q^29 - 4 * q^30 - 48 * q^36 + 8 * q^38 + 6 * q^39 - 4 * q^40 + 32 * q^43 + 4 * q^48 + 12 * q^51 - 10 * q^52 + 36 * q^53 + 120 * q^55 - 10 * q^61 + 28 * q^62 - 12 * q^64 + 20 * q^65 + 42 * q^66 - 4 * q^68 + 68 * q^69 - 18 * q^74 + 78 * q^75 - 80 * q^78 + 14 * q^79 - 46 * q^81 - 30 * q^82 - 88 * q^87 + 14 * q^88 + 48 * q^90 + 12 * q^92 - 34 * q^94 - 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.39283	+	2.41246i	−0.804153	+	1.39283i	0.112709	+	0.993628i	$0.464047\pi$
$3$	−1.39283	+	2.41246i	−0.804153	+	1.39283i	−0.916862	+	0.399205i	$0.869286\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.20456	+	1.27280i	−0.985910	+	0.569215i	−0.904049	−	0.427429i	$-0.859420\pi$
$5$	−2.20456	+	1.27280i	−0.985910	+	0.569215i	−0.0818605	+	0.996644i	$0.526086\pi$
$6$			2.78567i			1.13724i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.37997	−	4.12223i	−0.793323	−	1.37408i
$10$	−1.27280	+	2.20456i	−0.402496	+	0.697143i
$11$	−2.88497	−	1.66564i	−0.869851	−	0.502209i	−0.00255211	−	0.999997i	$-0.500812\pi$
$11$	−2.88497	−	1.66564i	−0.869851	−	0.502209i	−0.867299	+	0.497788i	$0.834146\pi$
$12$	1.39283	+	2.41246i	0.402076	+	0.696417i
$13$	−3.27280	+	1.51286i	−0.907712	+	0.419593i
$13$	−3.27280	+	1.51286i	−0.907712	+	0.419593i
$14$		0			0
$15$		−	7.09122i		−	1.83094i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.54561	−	6.14117i	0.859936	−	1.48945i	−0.0120526	−	0.999927i	$-0.503837\pi$
$17$	3.54561	−	6.14117i	0.859936	−	1.48945i	0.871989	−	0.489526i	$-0.162830\pi$
$18$	−4.12223	−	2.37997i	−0.971619	−	0.560964i
$19$	3.93661	−	2.27280i	0.903121	−	0.521417i	0.0249093	−	0.999690i	$-0.492070\pi$
$19$	3.93661	−	2.27280i	0.903121	−	0.521417i	0.878211	+	0.478273i	$0.158737\pi$
$20$			2.54561i			0.569215i
$21$		0			0
$22$	−3.33127			−0.710230
$23$	0.879970	+	1.52415i	0.183487	+	0.317808i	0.943065	−	0.332607i	$-0.107928\pi$
$23$	0.879970	+	1.52415i	0.183487	+	0.317808i	−0.759579	+	0.650415i	$0.774595\pi$
$24$	2.41246	+	1.39283i	0.492441	+	0.284311i
$25$	0.740059	−	1.28182i	0.148012	−	0.256364i
$26$	−2.07790	+	2.94658i	−0.407510	+	0.577872i
$27$	4.90261			0.943507
$28$		0			0
$29$	7.57133			1.40596			0.702981	−	0.711209i	$-0.251852\pi$
$29$	7.57133			1.40596			0.702981	+	0.711209i	$0.251852\pi$
$30$	−3.54561	−	6.14117i	−0.647336	−	1.12122i
$31$	−2.88497	−	1.66564i	−0.518156	−	0.299157i	0.218024	−	0.975943i	$-0.430039\pi$
$31$	−2.88497	−	1.66564i	−0.518156	−	0.299157i	−0.736180	+	0.676786i	$0.763372\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	8.03656	−	4.63991i	1.39899	−	0.807705i
$34$		−	7.09122i		−	1.21613i
$35$		0			0
$36$	−4.75994			−0.793323
$37$	−3.25620	+	1.87997i	−0.535317	+	0.309065i	−0.743179	−	0.669093i	$-0.766683\pi$
$37$	−3.25620	+	1.87997i	−0.535317	+	0.309065i	0.207862	+	0.978158i	$0.433349\pi$
$38$	2.27280	−	3.93661i	0.368697	−	0.638603i
$39$	0.908751	−	10.0027i	0.145517	−	1.60171i
$40$	1.27280	+	2.20456i	0.201248	+	0.348572i
$41$		−	4.24006i		−	0.662186i	−0.943598	−	0.331093i	$-0.892583\pi$
$41$		−	4.24006i		−	0.662186i	0.943598	−	0.331093i	$-0.107417\pi$
$42$		0			0
$43$	9.09122			1.38640			0.693199	−	0.720747i	$-0.256201\pi$
$43$	9.09122			1.38640			0.693199	+	0.720747i	$0.256201\pi$
$44$	−2.88497	+	1.66564i	−0.434925	+	0.251104i
$45$	10.4936	+	6.05847i	1.56429	+	0.903144i
$46$	1.52415	+	0.879970i	0.224724	+	0.129745i
$47$	−9.81317	+	5.66564i	−1.43140	+	0.826418i	−0.997228	−	0.0744125i	$-0.976292\pi$
$47$	−9.81317	+	5.66564i	−1.43140	+	0.826418i	−0.434171	+	0.900831i	$0.642959\pi$
$48$	2.78567			0.402076
$49$		0			0
$50$		−	1.48012i		−	0.209320i
$51$	9.87688	+	17.1073i	1.38304	+	2.39550i
$52$	−0.326224	+	3.59076i	−0.0452391	+	0.497949i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	4.24578	−	2.45130i	0.577778	−	0.333580i
$55$	8.48012			1.14346
$56$		0			0
$57$			12.6625i			1.67720i
$58$	6.55697	−	3.78567i	0.860972	−	0.497082i
$59$	6.98492	+	4.03274i	0.909359	+	0.525019i	0.880225	−	0.474557i	$-0.157392\pi$
$59$	6.98492	+	4.03274i	0.909359	+	0.525019i	0.0291341	+	0.999576i	$0.490725\pi$
$60$	−6.14117	−	3.54561i	−0.792822	−	0.457736i
$61$	0.392834	+	0.680408i	0.0502972	+	0.0871173i	0.890078	−	0.455809i	$-0.150650\pi$
$61$	0.392834	+	0.680408i	0.0502972	+	0.0871173i	−0.839781	+	0.542926i	$0.817316\pi$
$62$	−3.33127			−0.423072
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.28952	−	7.50084i	0.656084	−	0.930364i
$66$	4.63991	−	8.03656i	0.571134	−	0.989232i
$67$	−4.98825	−	2.87997i	−0.609412	−	0.351844i	0.163323	−	0.986573i	$-0.447779\pi$
$67$	−4.98825	−	2.87997i	−0.609412	−	0.351844i	−0.772735	+	0.634728i	$0.781112\pi$
$68$	−3.54561	−	6.14117i	−0.429968	−	0.744727i
$69$	−4.90261			−0.590205
$70$		0			0
$71$		−	11.1427i		−	1.32239i	−0.750213	−	0.661196i	$-0.770049\pi$
$71$		−	11.1427i		−	1.32239i	0.750213	−	0.661196i	$-0.229951\pi$
$72$	−4.12223	+	2.37997i	−0.485809	+	0.280482i
$73$	−8.08112	−	4.66564i	−0.945824	−	0.546072i	−0.0540426	−	0.998539i	$-0.517211\pi$
$73$	−8.08112	−	4.66564i	−0.945824	−	0.546072i	−0.891781	+	0.452467i	$0.850544\pi$
$74$	−1.87997	+	3.25620i	−0.218542	+	0.378526i
$75$	2.06156	+	3.57072i	0.238048	+	0.412312i
$76$		−	4.54561i		−	0.521417i
$77$		0			0
$78$	−4.21433	−	9.11694i	−0.477179	−	1.03229i
$79$	−2.42558	−	4.20122i	−0.272899	−	0.472675i	0.696704	−	0.717359i	$-0.254649\pi$
$79$	−2.42558	−	4.20122i	−0.272899	−	0.472675i	−0.969603	+	0.244684i	$0.921316\pi$
$80$	2.20456	+	1.27280i	0.246477	+	0.142304i
$81$	0.311393	−	0.539349i	0.0345993	−	0.0599277i
$82$	−2.12003	−	3.67200i	−0.234118	−	0.405504i
$83$		−	11.2082i		−	1.23026i	−0.788428	−	0.615128i	$-0.789105\pi$
$83$		−	11.2082i		−	1.23026i	0.788428	−	0.615128i	$-0.210895\pi$
$84$		0			0
$85$			18.0515i			1.95795i
$86$	7.87322	−	4.54561i	0.848992	−	0.490165i
$87$	−10.5456	+	18.2655i	−1.13061	+	1.95827i
$88$	−1.66564	+	2.88497i	−0.177558	+	0.307539i
$89$	13.0694	−	7.54561i	1.38535	−	0.799833i	0.392564	−	0.919725i	$-0.371588\pi$
$89$	13.0694	−	7.54561i	1.38535	−	0.799833i	0.992787	+	0.119892i	$0.0382548\pi$
$90$	12.1169			1.27724
$91$		0			0
$92$	1.75994			0.183487
$93$	8.03656	−	4.63991i	0.833353	−	0.481136i
$94$	−5.66564	+	9.81317i	−0.584366	+	1.01215i
$95$	−5.78567	+	10.0211i	−0.593597	+	1.02814i
$96$	2.41246	−	1.39283i	0.246221	−	0.142155i
$97$		−	7.75994i		−	0.787903i	−0.919131	−	0.393951i	$-0.871108\pi$
$97$		−	7.75994i		−	0.787903i	0.919131	−	0.393951i	$-0.128892\pi$
$98$		0			0
$99$			15.8567i			1.59366i
$100$	−0.740059	−	1.28182i	−0.0740059	−	0.128182i
$101$	1.84723	−	3.19949i	0.183806	−	0.318361i	−0.759368	−	0.650662i	$-0.774492\pi$
$101$	1.84723	−	3.19949i	0.183806	−	0.318361i	0.943173	+	0.332301i	$0.107825\pi$
$102$	17.1073	+	9.87688i	1.69387	+	0.977957i
$103$	−6.54561	−	11.3373i	−0.644958	−	1.11710i	−0.984311	−	0.176441i	$-0.943542\pi$
$103$	−6.54561	−	11.3373i	−0.644958	−	1.11710i	0.339353	−	0.940659i	$-0.389792\pi$
$104$	1.51286	+	3.27280i	0.148348	+	0.320925i
$105$		0			0
$106$		−	6.00000i		−	0.582772i
$107$	1.75994	+	3.04831i	0.170140	+	0.294691i	0.938469	−	0.345364i	$-0.112245\pi$
$107$	1.75994	+	3.04831i	0.170140	+	0.294691i	−0.768329	+	0.640055i	$0.778911\pi$
$108$	2.45130	−	4.24578i	0.235877	−	0.408551i
$109$	−11.3819	−	6.57133i	−1.09019	−	0.629420i	−0.156561	−	0.987668i	$-0.550041\pi$
$109$	−11.3819	−	6.57133i	−1.09019	−	0.629420i	−0.933626	+	0.358249i	$0.883374\pi$
$110$	7.34400	−	4.24006i	0.700223	−	0.404274i
$111$		−	10.4739i		−	0.994143i
$112$		0			0
$113$	−1.75994			−0.165561			−0.0827806	−	0.996568i	$-0.526380\pi$
$113$	−1.75994			−0.165561			−0.0827806	+	0.996568i	$0.526380\pi$
$114$	6.33127	+	10.9661i	0.592978	+	1.02707i
$115$	−3.87990	−	2.24006i	−0.361802	−	0.208887i
$116$	3.78567	−	6.55697i	0.351490	−	0.608799i
$117$	14.0255	+	9.89068i	1.29666	+	0.914394i
$118$	8.06549			0.742488
$119$		0			0
$120$	−7.09122			−0.647336
$121$	0.0486956	+	0.0843433i	0.00442688	+	0.00766757i
$122$	0.680408	+	0.392834i	0.0616012	+	0.0355655i
$123$	10.2290	+	5.90570i	0.922315	+	0.532499i
$124$	−2.88497	+	1.66564i	−0.259078	+	0.149579i
$125$		−	8.96024i		−	0.801428i
$126$		0			0
$127$	−12.9026			−1.14492			−0.572461	−	0.819932i	$-0.694011\pi$
$127$	−12.9026			−1.14492			−0.572461	+	0.819932i	$0.694011\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−12.6625	+	21.9322i	−1.11488	+	1.93102i
$130$	0.830438	−	9.14067i	0.0728343	−	0.801690i
$131$	8.38975	+	14.5315i	0.733015	+	1.26962i	0.955589	+	0.294704i	$0.0952211\pi$
$131$	8.38975	+	14.5315i	0.733015	+	1.26962i	−0.222573	+	0.974916i	$0.571446\pi$
$132$		−	9.27982i		−	0.807705i
$133$		0			0
$134$	−5.75994			−0.497583
$135$	−10.8081	+	6.24006i	−0.930213	+	0.537059i
$136$	−6.14117	−	3.54561i	−0.526601	−	0.304033i
$137$	−9.64983	−	5.57133i	−0.824441	−	0.475991i	0.0275046	−	0.999622i	$-0.491244\pi$
$137$	−9.64983	−	5.57133i	−0.824441	−	0.475991i	−0.851945	+	0.523630i	$0.824577\pi$
$138$	−4.24578	+	2.45130i	−0.361425	+	0.208669i
$139$	4.54561			0.385553			0.192777	−	0.981243i	$-0.438251\pi$
$139$	4.54561			0.385553			0.192777	+	0.981243i	$0.438251\pi$
$140$		0			0
$141$		−	31.5652i		−	2.65827i
$142$	−5.57133	−	9.64983i	−0.467536	−	0.809796i
$143$	11.9618	+	1.08674i	1.00030	+	0.0908779i
$144$	−2.37997	+	4.12223i	−0.198331	+	0.343519i
$145$	−16.6915	+	9.63682i	−1.38615	+	0.800295i
$146$	−9.33127			−0.772262
$147$		0			0
$148$			3.75994i			0.309065i
$149$	5.03281	−	2.90570i	0.412304	−	0.238044i	−0.279475	−	0.960153i	$-0.590160\pi$
$149$	5.03281	−	2.90570i	0.412304	−	0.238044i	0.691779	+	0.722109i	$0.256827\pi$
$150$	3.57072	+	2.06156i	0.291548	+	0.168326i
$151$	2.67707	+	1.54561i	0.217857	+	0.125780i	0.604958	−	0.796258i	$-0.293190\pi$
$151$	2.67707	+	1.54561i	0.217857	+	0.125780i	−0.387101	+	0.922037i	$0.626523\pi$
$152$	−2.27280	−	3.93661i	−0.184349	−	0.319301i
$153$	−33.7538			−2.72883
$154$		0			0
$155$	8.48012			0.681140
$156$	−8.20819	−	5.78834i	−0.657181	−	0.463438i
$157$	3.96417	−	6.86614i	0.316375	−	0.547978i	−0.663354	−	0.748306i	$-0.730868\pi$
$157$	3.96417	−	6.86614i	0.316375	−	0.547978i	0.979729	+	0.200328i	$0.0642009\pi$
$158$	−4.20122	−	2.42558i	−0.334231	−	0.192969i
$159$	8.35700	+	14.4748i	0.662753	+	1.14792i
$160$	2.54561			0.201248
$161$		0			0
$162$		−	0.622787i		−	0.0489307i
$163$	−8.70481	+	5.02573i	−0.681814	+	0.393645i	−0.800538	−	0.599282i	$-0.795453\pi$
$163$	−8.70481	+	5.02573i	−0.681814	+	0.393645i	0.118724	+	0.992927i	$0.462119\pi$
$164$	−3.67200	−	2.12003i	−0.286735	−	0.165547i
$165$	−11.8114	+	20.4579i	−0.919516	+	1.59265i
$166$	−5.60408	−	9.70655i	−0.434961	−	0.753374i
$167$			24.2339i			1.87527i	0.347616	+	0.937637i	$0.386991\pi$
$167$			24.2339i			1.87527i	−0.347616	+	0.937637i	$0.613009\pi$
$168$		0			0
$169$	8.42249	−	9.90261i	0.647884	−	0.761739i
$170$	9.02573	+	15.6330i	0.692242	+	1.19900i
$171$	−18.7380	−	10.8184i	−1.43293	−	0.827305i
$172$	4.54561	−	7.87322i	0.346599	−	0.600328i
$173$	−10.2985	−	17.8376i	−0.782983	−	1.35617i	−0.930197	−	0.367061i	$-0.880364\pi$
$173$	−10.2985	−	17.8376i	−0.782983	−	1.35617i	0.147214	−	0.989105i	$-0.452969\pi$
$174$			21.0912i			1.59892i
$175$		0			0
$176$			3.33127i			0.251104i
$177$	−19.4577	+	11.2339i	−1.46253	+	0.844390i
$178$	7.54561	−	13.0694i	0.565567	−	0.979591i
$179$	−8.66255	+	15.0040i	−0.647469	+	1.12145i	0.336256	+	0.941771i	$0.390839\pi$
$179$	−8.66255	+	15.0040i	−0.647469	+	1.12145i	−0.983725	+	0.179679i	$0.942494\pi$
$180$	10.4936	−	6.05847i	0.782145	−	0.451572i
$181$	−16.9166			−1.25740			−0.628702	−	0.777646i	$-0.716414\pi$
$181$	−16.9166			−1.25740			−0.628702	+	0.777646i	$0.716414\pi$
$182$		0			0
$183$	−2.18861			−0.161786
$184$	1.52415	−	0.879970i	0.112362	−	0.0648723i
$185$	4.78567	−	8.28902i	0.351849	−	0.609421i
$186$	4.63991	−	8.03656i	0.340215	−	0.589269i
$187$	−20.4579	+	11.8114i	−1.49603	+	0.863735i
$188$			11.3313i			0.826418i
$189$		0			0
$190$			11.5713i			0.839473i
$191$	−2.21433	−	3.83534i	−0.160224	−	0.277515i	0.774725	−	0.632298i	$-0.217888\pi$
$191$	−2.21433	−	3.83534i	−0.160224	−	0.277515i	−0.934949	+	0.354783i	$0.884555\pi$
$192$	1.39283	−	2.41246i	0.100519	−	0.174104i
$193$	2.14785	+	1.24006i	0.154605	+	0.0892614i	0.575307	−	0.817938i	$-0.304883\pi$
$193$	2.14785	+	1.24006i	0.154605	+	0.0892614i	−0.420701	+	0.907199i	$0.638216\pi$
$194$	−3.87997	−	6.72031i	−0.278566	−	0.482490i
$195$	10.7280	+	23.2082i	0.768251	+	1.66197i
$196$		0			0
$197$			8.85116i			0.630619i	0.948989	+	0.315309i	$0.102108\pi$
$197$			8.85116i			0.630619i	−0.948989	+	0.315309i	$0.897892\pi$
$198$	7.92834	+	13.7323i	0.563442	+	0.975911i
$199$	−0.545608	+	0.945020i	−0.0386771	+	0.0669907i	−0.884716	−	0.466131i	$-0.845648\pi$
$199$	−0.545608	+	0.945020i	−0.0386771	+	0.0669907i	0.846039	+	0.533121i	$0.178981\pi$
$200$	−1.28182	−	0.740059i	−0.0906384	−	0.0523301i
$201$	13.8956	−	8.02264i	0.980121	−	0.565873i
$202$		−	3.69445i		−	0.259941i
$203$		0			0
$204$	19.7538			1.38304
$205$	5.39676	+	9.34747i	0.376926	+	0.652856i
$206$	−11.3373	−	6.54561i	−0.789909	−	0.456054i
$207$	4.18861	−	7.25488i	0.291128	−	0.504249i
$208$	2.94658	+	2.07790i	0.204309	+	0.144076i
$209$	−15.1427			−1.04744
$210$		0			0
$211$	15.0398			1.03538			0.517690	−	0.855568i	$-0.326792\pi$
$211$	15.0398			1.03538			0.517690	+	0.855568i	$0.326792\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	26.8812	+	15.5199i	1.84187	+	1.06340i
$214$	3.04831	+	1.75994i	0.208378	+	0.120307i
$215$	−20.0421	+	11.5713i	−1.36686	+	0.789158i
$216$		−	4.90261i		−	0.333580i
$217$		0			0
$218$	−13.1427			−0.890134
$219$	22.5113	−	12.9969i	1.52117	−	0.878250i
$220$	4.24006	−	7.34400i	0.285865	−	0.495132i
$221$	−2.31332	+	25.4629i	−0.155611	+	1.71282i
$222$	−5.23697	−	9.07070i	−0.351483	−	0.608786i
$223$			12.9026i			0.864023i	0.901868	+	0.432011i	$0.142196\pi$
$223$			12.9026i			0.864023i	−0.901868	+	0.432011i	$0.857804\pi$
$224$		0			0
$225$	−7.04528			−0.469685
$226$	−1.52415	+	0.879970i	−0.101385	+	0.0585348i
$227$	7.81651	+	4.51286i	0.518800	+	0.299529i	0.736443	−	0.676499i	$-0.236504\pi$
$227$	7.81651	+	4.51286i	0.518800	+	0.299529i	−0.217644	+	0.976028i	$0.569837\pi$
$228$	10.9661	+	6.33127i	0.726247	+	0.419299i
$229$	−12.2702	+	7.08420i	−0.810837	+	0.468137i	−0.847246	−	0.531200i	$-0.821741\pi$
$229$	−12.2702	+	7.08420i	−0.810837	+	0.468137i	0.0364095	+	0.999337i	$0.488408\pi$
$230$	−4.48012			−0.295410
$231$		0			0
$232$		−	7.57133i		−	0.497082i
$233$	3.69136	+	6.39363i	0.241829	+	0.418861i	0.961235	−	0.275729i	$-0.0889193\pi$
$233$	3.69136	+	6.39363i	0.241829	+	0.418861i	−0.719406	+	0.694590i	$0.755586\pi$
$234$	17.0918	+	1.55281i	1.11733	+	0.101510i
$235$	14.4225	−	24.9805i	0.940820	−	1.62955i
$236$	6.98492	−	4.03274i	0.454679	−	0.262509i
$237$	13.5137			0.877810
$238$		0			0
$239$		−	6.13098i		−	0.396580i	−0.980143	−	0.198290i	$-0.936461\pi$
$239$		−	6.13098i		−	0.396580i	0.980143	−	0.198290i	$-0.0635388\pi$
$240$	−6.14117	+	3.54561i	−0.396411	+	0.228868i
$241$	−23.6642	−	13.6625i	−1.52435	−	0.880082i	−0.999584	−	0.0288337i	$-0.990821\pi$
$241$	−23.6642	−	13.6625i	−1.52435	−	0.880082i	−0.524763	−	0.851248i	$-0.675846\pi$
$242$	0.0843433	+	0.0486956i	0.00542179	+	0.00313027i
$243$	8.22135	+	14.2398i	0.527400	+	0.913483i
$244$	0.785667			0.0502972
$245$		0			0
$246$	11.8114			0.753067
$247$	−9.44532	+	13.3940i	−0.600991	+	0.852240i
$248$	−1.66564	+	2.88497i	−0.105768	+	0.183196i
$249$	27.0392	+	15.6111i	1.71354	+	0.989313i
$250$	−4.48012	−	7.75979i	−0.283348	−	0.490772i
$251$	16.4880			1.04071			0.520356	−	0.853949i	$-0.325799\pi$
$251$	16.4880			1.04071			0.520356	+	0.853949i	$0.325799\pi$
$252$		0			0
$253$		−	5.86285i		−	0.368594i
$254$	−11.1740	+	6.45130i	−0.701118	+	0.404791i
$255$	−43.5484	−	25.1427i	−2.72711	−	1.57449i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.571334	+	0.989580i	0.0356388	+	0.0617283i	0.883295	−	0.468818i	$-0.155320\pi$
$257$	0.571334	+	0.989580i	0.0356388	+	0.0617283i	−0.847656	+	0.530547i	$0.821987\pi$
$258$			25.3251i			1.57667i
$259$		0			0
$260$	−3.85116	−	8.33127i	−0.238839	−	0.516684i
$261$	−18.0196	−	31.2108i	−1.11538	−	1.93190i
$262$	14.5315	+	8.38975i	0.897757	+	0.518320i
$263$	5.30555	−	9.18948i	0.327154	−	0.566648i	−0.654792	−	0.755809i	$-0.727244\pi$
$263$	5.30555	−	9.18948i	0.327154	−	0.566648i	0.981946	+	0.189162i	$0.0605770\pi$
$264$	−4.63991	−	8.03656i	−0.285567	−	0.494616i
$265$			15.2736i			0.938253i
$266$		0			0
$267$			42.0391i			2.57275i
$268$	−4.98825	+	2.87997i	−0.304706	+	0.175922i
$269$	6.02966	−	10.4437i	0.367635	−	0.636762i	−0.621561	−	0.783366i	$-0.713501\pi$
$269$	6.02966	−	10.4437i	0.367635	−	0.636762i	0.989195	+	0.146604i	$0.0468344\pi$
$270$	−6.24006	+	10.8081i	−0.379758	+	0.657760i
$271$	1.19748	−	0.691364i	0.0727415	−	0.0419974i	−0.463188	−	0.886260i	$-0.653295\pi$
$271$	1.19748	−	0.691364i	0.0727415	−	0.0419974i	0.535930	+	0.844263i	$0.319961\pi$
$272$	−7.09122			−0.429968
$273$		0			0
$274$	−11.1427			−0.673153
$275$	−4.27010	+	2.46534i	−0.257496	+	0.148666i
$276$	−2.45130	+	4.24578i	−0.147551	+	0.255566i
$277$	−0.571334	+	0.989580i	−0.0343281	+	0.0594581i	−0.882679	−	0.469976i	$-0.844262\pi$
$277$	−0.571334	+	0.989580i	−0.0343281	+	0.0594581i	0.848351	+	0.529434i	$0.177596\pi$
$278$	3.93661	−	2.27280i	0.236102	−	0.136314i
$279$			15.8567i			0.949314i
$280$		0			0
$281$			7.14267i			0.426096i	0.977042	+	0.213048i	$0.0683390\pi$
$281$			7.14267i			0.426096i	−0.977042	+	0.213048i	$0.931661\pi$
$282$	−15.7826	−	27.3362i	−0.939839	−	1.62785i
$283$	2.41856	−	4.18907i	0.143768	−	0.249014i	−0.785144	−	0.619313i	$-0.787411\pi$
$283$	2.41856	−	4.18907i	0.143768	−	0.249014i	0.928913	+	0.370299i	$0.120745\pi$
$284$	−9.64983	−	5.57133i	−0.572612	−	0.330598i
$285$	−16.1169	−	27.9154i	−0.954685	−	1.65356i
$286$	10.9026	−	5.03976i	0.644685	−	0.298007i
$287$		0			0
$288$			4.75994i			0.280482i
$289$	−16.6427	−	28.8259i	−0.978980	−	1.69564i
$290$	−9.63682	+	16.6915i	−0.565894	+	0.980157i
$291$	18.7205	+	10.8083i	1.09742	+	0.633594i
$292$	−8.08112	+	4.66564i	−0.472912	+	0.273036i
$293$		−	7.63682i		−	0.446148i	−0.974802	−	0.223074i	$-0.928391\pi$
$293$		−	7.63682i		−	0.446148i	0.974802	−	0.223074i	$-0.0716092\pi$
$294$		0			0
$295$	−20.5316			−1.19539
$296$	1.87997	+	3.25620i	0.109271	+	0.189263i
$297$	−14.1439	−	8.16597i	−0.820711	−	0.473838i
$298$	2.90570	−	5.03281i	0.168322	−	0.291543i
$299$	−5.18581	−	3.65698i	−0.299903	−	0.211489i
$300$	4.12312			0.238048
$301$		0			0
$302$	3.09122			0.177879
$303$	5.14576	+	8.91271i	0.295616	+	0.512022i
$304$	−3.93661	−	2.27280i	−0.225780	−	0.130354i
$305$	−1.73205	−	1.00000i	−0.0991769	−	0.0572598i
$306$	−29.2316	+	16.8769i	−1.67106	+	0.964787i
$307$		−	14.3508i		−	0.819045i	−0.912300	−	0.409522i	$-0.865695\pi$
$307$		−	14.3508i		−	0.819045i	0.912300	−	0.409522i	$-0.134305\pi$
$308$		0			0
$309$	36.4678			2.07458
$310$	7.34400	−	4.24006i	0.417111	−	0.240819i
$311$	−1.09122	+	1.89004i	−0.0618771	+	0.107174i	−0.895304	−	0.445455i	$-0.853042\pi$
$311$	−1.09122	+	1.89004i	−0.0618771	+	0.107174i	0.833427	+	0.552629i	$0.186375\pi$
$312$	−10.0027	−	0.908751i	−0.566290	−	0.0514479i
$313$	−7.78567	−	13.4852i	−0.440072	−	0.762227i	0.557622	−	0.830095i	$-0.311714\pi$
$313$	−7.78567	−	13.4852i	−0.440072	−	0.762227i	−0.997694	+	0.0678678i	$0.978380\pi$
$314$		−	7.92834i		−	0.447422i
$315$		0			0
$316$	−4.85116			−0.272899
$317$	−12.2877	+	7.09430i	−0.690146	+	0.398456i	−0.803667	−	0.595080i	$-0.797120\pi$
$317$	−12.2877	+	7.09430i	−0.690146	+	0.398456i	0.113521	+	0.993536i	$0.463787\pi$
$318$	14.4748	+	8.35700i	0.811704	+	0.468637i
$319$	−21.8431	−	12.6111i	−1.22298	−	0.706086i
$320$	2.20456	−	1.27280i	0.123239	−	0.0711519i
$321$	−9.80522			−0.547274
$322$		0			0
$323$		−	32.2339i		−	1.79354i
$324$	−0.311393	−	0.539349i	−0.0172996	−	0.0299638i
$325$	−0.482850	+	5.31475i	−0.0267837	+	0.294810i
$326$	−5.02573	+	8.70481i	−0.278349	+	0.482115i
$327$	31.7061	−	18.3055i	1.75335	−	1.01230i
$328$	−4.24006			−0.234118
$329$		0			0
$330$			23.6228i			1.30039i
$331$	2.46917	−	1.42558i	0.135718	−	0.0783569i	−0.430604	−	0.902541i	$-0.641699\pi$
$331$	2.46917	−	1.42558i	0.135718	−	0.0783569i	0.566322	+	0.824184i	$0.308366\pi$
$332$	−9.70655	−	5.60408i	−0.532716	−	0.307564i
$333$	15.4993	+	8.94855i	0.849359	+	0.490377i
$334$	12.1169	+	20.9872i	0.663010	+	1.14837i
$335$	14.6625			0.801101
$336$		0			0
$337$	−32.5254			−1.77177			−0.885886	−	0.463904i	$-0.846448\pi$
$337$	−32.5254			−1.77177			−0.885886	+	0.463904i	$0.846448\pi$
$338$	2.34279	−	12.7872i	0.127431	−	0.695530i
$339$	2.45130	−	4.24578i	0.133137	−	0.230599i
$340$	15.6330	+	9.02573i	0.847819	+	0.489489i
$341$	5.54870	+	9.61062i	0.300479	+	0.520444i
$342$	−21.6368			−1.16999
$343$		0			0
$344$		−	9.09122i		−	0.490165i
$345$	10.8081	−	6.24006i	0.581889	−	0.335953i
$346$	−17.8376	−	10.2985i	−0.958954	−	0.553652i
$347$	−2.97427	+	5.15159i	−0.159667	+	0.276552i	−0.934749	−	0.355309i	$-0.884376\pi$
$347$	−2.97427	+	5.15159i	−0.159667	+	0.276552i	0.775081	+	0.631861i	$0.217709\pi$
$348$	10.5456	+	18.2655i	0.565304	+	0.979135i
$349$		−	32.9619i		−	1.76441i	−0.470864	−	0.882206i	$-0.656058\pi$
$349$		−	32.9619i		−	1.76441i	0.470864	−	0.882206i	$-0.343942\pi$
$350$		0			0
$351$	−16.0453	+	7.41698i	−0.856434	+	0.395889i
$352$	1.66564	+	2.88497i	0.0887788	+	0.153769i
$353$	−0.737123	−	0.425578i	−0.0392331	−	0.0226512i	0.480255	−	0.877129i	$-0.340544\pi$
$353$	−0.737123	−	0.425578i	−0.0392331	−	0.0226512i	−0.519488	+	0.854478i	$0.673877\pi$
$354$	−11.2339	+	19.4577i	−0.597074	+	1.03416i
$355$	14.1824	+	24.5647i	0.752725	+	1.30376i
$356$		−	15.0912i		−	0.799833i
$357$		0			0
$358$			17.3251i			0.915660i
$359$	24.1935	−	13.9681i	1.27688	−	0.737208i	0.300608	−	0.953748i	$-0.402810\pi$
$359$	24.1935	−	13.9681i	1.27688	−	0.737208i	0.976274	+	0.216540i	$0.0694771\pi$
$360$	6.05847	−	10.4936i	0.319309	−	0.553060i
$361$	0.831275	−	1.43981i	0.0437513	−	0.0757795i
$362$	−14.6502	+	8.45832i	−0.770000	+	0.444560i
$363$	−0.271300			−0.0142395
$364$		0			0
$365$	23.7538			1.24333
$366$	−1.89539	+	1.09430i	−0.0990736	+	0.0572002i
$367$	3.57133	−	6.18573i	0.186422	−	0.322893i	−0.757633	−	0.652681i	$-0.773644\pi$
$367$	3.57133	−	6.18573i	0.186422	−	0.322893i	0.944055	+	0.329789i	$0.106977\pi$
$368$	0.879970	−	1.52415i	0.0458716	−	0.0794520i
$369$	−17.4785	+	10.0912i	−0.909894	+	0.525328i
$370$		−	9.57133i		−	0.497590i
$371$		0			0
$372$		−	9.27982i		−	0.481136i
$373$	16.5713	+	28.7024i	0.858031	+	1.48615i	0.873804	+	0.486278i	$0.161646\pi$
$373$	16.5713	+	28.7024i	0.858031	+	1.48615i	−0.0157730	+	0.999876i	$0.505021\pi$
$374$	−11.8114	+	20.4579i	−0.610753	+	1.05785i
$375$	21.6162	+	12.4801i	1.11626	+	0.644471i
$376$	5.66564	+	9.81317i	0.292183	+	0.506076i
$377$	−24.7795	+	11.4544i	−1.27621	+	0.589931i
$378$		0			0
$379$			35.2736i			1.81189i	0.423400	+	0.905943i	$0.360836\pi$
$379$			35.2736i			1.81189i	−0.423400	+	0.905943i	$0.639164\pi$
$380$	5.78567	+	10.0211i	0.296798	+	0.514070i
$381$	17.9712	−	31.1270i	0.920692	−	1.59468i
$382$	−3.83534	−	2.21433i	−0.196233	−	0.113295i
$383$	6.02239	−	3.47703i	0.307730	−	0.177668i	−0.338180	−	0.941081i	$-0.609811\pi$
$383$	6.02239	−	3.47703i	0.307730	−	0.177668i	0.645910	+	0.763413i	$0.276478\pi$
$384$		−	2.78567i		−	0.142155i
$385$		0			0
$386$	2.48012			0.126235
$387$	−21.6368	−	37.4761i	−1.09986	−	1.90502i
$388$	−6.72031	−	3.87997i	−0.341172	−	0.196976i
$389$	2.63682	−	4.56711i	0.133692	−	0.231562i	−0.791405	−	0.611292i	$-0.790650\pi$
$389$	2.63682	−	4.56711i	0.133692	−	0.231562i	0.925097	+	0.379731i	$0.123983\pi$
$390$	20.8948	+	14.7348i	1.05805	+	0.746127i
$391$	12.4801			0.631147
$392$		0			0
$393$	−46.7421			−2.35783
$394$	4.42558	+	7.66533i	0.222957	+	0.386174i
$395$	10.6947	+	6.17457i	0.538107	+	0.310676i
$396$	13.7323	+	7.92834i	0.690073	+	0.398414i
$397$	−16.1744	+	9.33829i	−0.811770	+	0.468675i	−0.847570	−	0.530683i	$-0.821935\pi$
$397$	−16.1744	+	9.33829i	−0.811770	+	0.468675i	0.0358003	+	0.999359i	$0.488602\pi$
$398$			1.09122i			0.0546977i
$399$		0			0
$400$	−1.48012			−0.0740059
$401$	18.6368	−	10.7599i	0.930676	−	0.537326i	0.0436504	−	0.999047i	$-0.486101\pi$
$401$	18.6368	−	10.7599i	0.930676	−	0.537326i	0.887025	+	0.461721i	$0.152768\pi$
$402$	8.02264	−	13.8956i	0.400133	−	0.693050i
$403$	11.9618	+	1.08674i	0.595861	+	0.0541345i
$404$	−1.84723	−	3.19949i	−0.0919029	−	0.159181i
$405$			1.58537i			0.0787777i
$406$		0			0
$407$	12.5254			0.620861
$408$	17.1073	−	9.87688i	0.846936	−	0.488979i
$409$	16.7360	+	9.66255i	0.827543	+	0.477782i	0.853011	−	0.521893i	$-0.174774\pi$
$409$	16.7360	+	9.66255i	0.827543	+	0.477782i	−0.0254675	+	0.999676i	$0.508107\pi$
$410$	9.34747	+	5.39676i	0.461639	+	0.266527i
$411$	26.8812	−	15.5199i	1.32595	−	0.765539i
$412$	−13.0912			−0.644958
$413$		0			0
$414$		−	8.37721i		−	0.411718i
$415$	14.2658	+	24.7091i	0.700280	+	1.21292i
$416$	3.59076	+	0.326224i	0.176052	+	0.0159944i
$417$	−6.33127	+	10.9661i	−0.310044	+	0.537012i
$418$	−13.1139	+	7.57133i	−0.641424	+	0.370326i
$419$	12.8371			0.627134			0.313567	−	0.949566i	$-0.398476\pi$
$419$	12.8371			0.627134			0.313567	+	0.949566i	$0.398476\pi$
$420$		0			0
$421$			21.3313i			1.03962i	0.854281	+	0.519811i	$0.173998\pi$
$421$			21.3313i			1.03962i	−0.854281	+	0.519811i	$0.826002\pi$
$422$	13.0248	−	7.51988i	0.634038	−	0.366062i
$423$	46.7101	+	26.9681i	2.27112	+	1.31123i
$424$	−5.19615	−	3.00000i	−0.252347	−	0.145693i
$425$	−5.24792	−	9.08966i	−0.254562	−	0.440913i
$426$	31.0398			1.50388
$427$		0			0
$428$	3.51988			0.170140
$429$	−19.2825	+	27.3437i	−0.930970	+	1.32017i
$430$	−11.5713	+	20.0421i	−0.558019	+	0.966518i
$431$	10.0211	+	5.78567i	0.482698	+	0.278686i	0.721540	−	0.692373i	$-0.243435\pi$
$431$	10.0211	+	5.78567i	0.482698	+	0.278686i	−0.238842	+	0.971058i	$0.576768\pi$
$432$	−2.45130	−	4.24578i	−0.117938	−	0.204275i
$433$	29.3766			1.41175			0.705873	−	0.708338i	$-0.250555\pi$
$433$	29.3766			1.41175			0.705873	+	0.708338i	$0.250555\pi$
$434$		0			0
$435$		−	53.6900i		−	2.57424i
$436$	−11.3819	+	6.57133i	−0.545093	+	0.314710i
$437$	6.92820	+	4.00000i	0.331421	+	0.191346i
$438$	12.9969	−	22.5113i	0.621016	−	1.07563i
$439$	−0.0514526	−	0.0891186i	−0.00245570	−	0.00425340i	0.864795	−	0.502125i	$-0.167448\pi$
$439$	−0.0514526	−	0.0891186i	−0.00245570	−	0.00425340i	−0.867251	+	0.497872i	$0.834115\pi$
$440$		−	8.48012i		−	0.404274i
$441$		0			0
$442$	10.7280	+	23.2082i	0.510281	+	1.10390i
$443$	−13.5713	−	23.5062i	−0.644794	−	1.11682i	−0.984349	−	0.176229i	$-0.943610\pi$
$443$	−13.5713	−	23.5062i	−0.644794	−	1.11682i	0.339556	−	0.940586i	$-0.389723\pi$
$444$	−9.07070	−	5.23697i	−0.430476	−	0.248536i
$445$	−19.2082	+	33.2695i	−0.910554	+	1.57713i
$446$	6.45130	+	11.1740i	0.305478	+	0.529104i
$447$			16.1886i			0.765695i
$448$		0			0
$449$		−	9.70231i		−	0.457880i	−0.973440	−	0.228940i	$-0.926474\pi$
$449$		−	9.70231i		−	0.457880i	0.973440	−	0.228940i	$-0.0735260\pi$
$450$	−6.10139	+	3.52264i	−0.287622	+	0.166059i
$451$	−7.06240	+	12.2324i	−0.332555	+	0.576003i
$452$	−0.879970	+	1.52415i	−0.0413903	+	0.0716901i
$453$	−7.45743	+	4.30555i	−0.350381	+	0.202292i
$454$	9.02573			0.423598
$455$		0			0
$456$	12.6625			0.592978
$457$	31.3242	−	18.0850i	1.46528	−	0.845982i	0.466037	−	0.884765i	$-0.345681\pi$
$457$	31.3242	−	18.0850i	1.46528	−	0.845982i	0.999248	+	0.0387828i	$0.0123480\pi$
$458$	−7.08420	+	12.2702i	−0.331023	+	0.573348i
$459$	17.3827	−	30.1078i	0.811356	−	1.40531i
$460$	−3.87990	+	2.24006i	−0.180901	+	0.104443i
$461$			20.9743i			0.976869i	0.872600	+	0.488435i	$0.162432\pi$
$461$			20.9743i			0.976869i	−0.872600	+	0.488435i	$0.837568\pi$
$462$		0			0
$463$			24.8450i			1.15464i	0.816517	+	0.577322i	$0.195902\pi$
$463$			24.8450i			1.15464i	−0.816517	+	0.577322i	$0.804098\pi$
$464$	−3.78567	−	6.55697i	−0.175745	−	0.304400i
$465$	−11.8114	+	20.4579i	−0.547740	+	0.948714i
$466$	6.39363	+	3.69136i	0.296179	+	0.170999i
$467$	−0.635981	−	1.10155i	−0.0294297	−	0.0509737i	0.850935	−	0.525270i	$-0.176036\pi$
$467$	−0.635981	−	1.10155i	−0.0294297	−	0.0509737i	−0.880365	+	0.474297i	$0.842702\pi$
$468$	15.5784	−	7.20114i	0.720110	−	0.332873i
$469$		0			0
$470$		−	28.8450i		−	1.33052i
$471$	11.0429	+	19.1268i	0.508828	+	0.881315i
$472$	4.03274	−	6.98492i	0.185622	−	0.321507i
$473$	−26.2279	−	15.1427i	−1.20596	−	0.696261i
$474$	11.7032	−	6.75685i	0.537546	−	0.310353i
$475$		−	6.72804i		−	0.308704i
$476$		0			0
$477$	−28.5596			−1.30766
$478$	−3.06549	−	5.30958i	−0.140212	−	0.242855i
$479$	−19.0971	−	11.0257i	−0.872570	−	0.503778i	−0.00436831	−	0.999990i	$-0.501390\pi$
$479$	−19.0971	−	11.0257i	−0.872570	−	0.503778i	−0.868201	+	0.496212i	$0.834724\pi$
$480$	−3.54561	+	6.14117i	−0.161834	+	0.280305i
$481$	7.81278	−	11.0790i	0.356232	−	0.505157i
$482$	−27.3251			−1.24462
$483$		0			0
$484$	0.0973913			0.00442688
$485$	9.87688	+	17.1073i	0.448486	+	0.776801i
$486$	14.2398	+	8.22135i	0.645930	+	0.372928i
$487$	3.83534	+	2.21433i	0.173796	+	0.100341i	0.584374	−	0.811484i	$-0.301340\pi$
$487$	3.83534	+	2.21433i	0.173796	+	0.100341i	−0.410579	+	0.911825i	$0.634673\pi$
$488$	0.680408	−	0.392834i	0.0308006	−	0.0177827i
$489$		−	28.0000i		−	1.26620i
$490$		0			0
$491$	−31.0274			−1.40025			−0.700124	−	0.714022i	$-0.746872\pi$
$491$	−31.0274			−1.40025			−0.700124	+	0.714022i	$0.746872\pi$
$492$	10.2290	−	5.90570i	0.461157	−	0.266249i
$493$	26.8450	−	46.4969i	1.20904	−	2.09411i
$494$	−1.48289	+	16.3222i	−0.0667182	+	0.734370i
$495$	−20.1824	−	34.9570i	−0.907133	−	1.57120i
$496$			3.33127i			0.149579i
$497$		0			0
$498$	31.2222			1.39910
$499$	−19.9922	+	11.5425i	−0.894975	+	0.516714i	−0.875567	−	0.483097i	$-0.839512\pi$
$499$	−19.9922	+	11.5425i	−0.894975	+	0.516714i	−0.0194086	+	0.999812i	$0.506178\pi$
$500$	−7.75979	−	4.48012i	−0.347028	−	0.200357i
$501$	−58.4632	−	33.7538i	−2.61194	−	1.50801i
$502$	14.2790	−	8.24399i	0.637303	−	0.367947i
$503$	−17.7023			−0.789307			−0.394654	−	0.918830i	$-0.629135\pi$
$503$	−17.7023			−0.789307			−0.394654	+	0.918830i	$0.629135\pi$
$504$		0			0
$505$			9.40462i			0.418500i
$506$	−2.93142	−	5.07737i	−0.130318	−	0.225717i
$507$	12.1585	+	34.1116i	0.539978	+	1.51495i
$508$	−6.45130	+	11.1740i	−0.286230	+	0.495766i
$509$	21.4151	−	12.3640i	0.949208	−	0.548026i	0.0563732	−	0.998410i	$-0.482046\pi$
$509$	21.4151	−	12.3640i	0.949208	−	0.548026i	0.892835	+	0.450384i	$0.148713\pi$
$510$	−50.2853			−2.22667
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	19.2997	−	11.1427i	0.852101	−	0.491961i
$514$	0.989580	+	0.571334i	0.0436485	+	0.0252005i
$515$	28.8604	+	16.6625i	1.27174	+	0.734240i
$516$	12.6625	+	21.9322i	0.557438	+	0.965510i
$517$	37.7476			1.66014
$518$		0			0
$519$	57.3766			2.51855
$520$	−7.50084	−	5.28952i	−0.328933	−	0.231961i
$521$	10.2143	−	17.6917i	0.447498	−	0.775089i	−0.550724	−	0.834687i	$-0.685648\pi$
$521$	10.2143	−	17.6917i	0.447498	−	0.775089i	0.998222	+	0.0595978i	$0.0189818\pi$
$522$	−31.2108	−	18.0196i	−1.36606	−	0.788694i
$523$	−12.9127	−	22.3655i	−0.564634	−	0.977974i	−0.997084	−	0.0763162i	$-0.975684\pi$
$523$	−12.9127	−	22.3655i	−0.564634	−	0.977974i	0.432450	−	0.901658i	$-0.357649\pi$
$524$	16.7795			0.733015
$525$		0			0
$526$		−	10.6111i		−	0.462666i
$527$	−20.4579	+	11.8114i	−0.891162	+	0.514512i
$528$	−8.03656	−	4.63991i	−0.349746	−	0.201926i
$529$	9.95130	−	17.2362i	0.432665	−	0.749398i
$530$	7.63682	+	13.2274i	0.331722	+	0.574560i
$531$		−	38.3912i		−	1.66604i
$532$		0			0
$533$	6.41463	+	13.8769i	0.277848	+	0.601075i
$534$	21.0196	+	36.4069i	0.909605	+	1.57548i
$535$	−7.75979	−	4.48012i	−0.335485	−	0.193692i
$536$	−2.87997	+	4.98825i	−0.124396	+	0.215460i
$537$	−24.1310	−	41.7961i	−1.04133	−	1.80363i
$538$		−	12.0593i		−	0.519914i
$539$		0			0
$540$			12.4801i			0.537059i
$541$	−24.5201	+	14.1567i	−1.05420	+	0.608644i	−0.923823	−	0.382820i	$-0.874953\pi$
$541$	−24.5201	+	14.1567i	−1.05420	+	0.608644i	−0.130380	+	0.991464i	$0.541620\pi$
$542$	0.691364	−	1.19748i	0.0296966	−	0.0514360i
$543$	23.5621	−	40.8107i	1.01115	−	1.75135i
$544$	−6.14117	+	3.54561i	−0.263301	+	0.152017i
$545$	33.4561			1.43310
$546$		0			0
$547$	25.5713			1.09335			0.546676	−	0.837344i	$-0.315893\pi$
$547$	25.5713			1.09335			0.546676	+	0.837344i	$0.315893\pi$
$548$	−9.64983	+	5.57133i	−0.412220	+	0.237996i
$549$	1.86986	−	3.23870i	0.0798039	−	0.138224i
$550$	−2.46534	+	4.27010i	−0.105122	+	0.182077i
$551$	29.8054	−	17.2082i	1.26975	−	0.733092i
$552$			4.90261i			0.208669i
$553$		0			0
$554$			1.14267i			0.0485473i
$555$	13.3313	+	23.0904i	0.565881	+	0.980135i
$556$	2.27280	−	3.93661i	0.0963884	−	0.166950i
$557$	3.45875	+	1.99691i	0.146552	+	0.0846119i	0.571483	−	0.820614i	$-0.306368\pi$
$557$	3.45875	+	1.99691i	0.146552	+	0.0846119i	−0.424931	+	0.905226i	$0.639702\pi$
$558$	7.92834	+	13.7323i	0.335633	+	0.581334i
$559$	−29.7538	+	13.7538i	−1.25845	+	0.581722i
$560$		0			0
$561$		−	65.8052i		−	2.77830i
$562$	3.57133	+	6.18573i	0.150648	+	0.260929i
$563$	−21.7498	+	37.6718i	−0.916646	+	1.58768i	−0.112173	+	0.993689i	$0.535781\pi$
$563$	−21.7498	+	37.6718i	−0.916646	+	1.58768i	−0.804473	+	0.593989i	$0.797552\pi$
$564$	−27.3362	−	15.7826i	−1.15106	−	0.664566i
$565$	3.87990	−	2.24006i	0.163228	−	0.0942400i
$566$		−	4.83712i		−	0.203319i
$567$		0			0
$568$	−11.1427			−0.467536
$569$	−20.6337	−	35.7387i	−0.865011	−	1.49824i	−0.867036	−	0.498245i	$-0.833978\pi$
$569$	−20.6337	−	35.7387i	−0.865011	−	1.49824i	0.00202490	−	0.999998i	$-0.499355\pi$
$570$	−27.9154	−	16.1169i	−1.16925	−	0.675064i
$571$	−6.96810	+	12.0691i	−0.291606	+	0.505076i	−0.974190	−	0.225731i	$-0.927523\pi$
$571$	−6.96810	+	12.0691i	−0.291606	+	0.505076i	0.682584	+	0.730807i	$0.260856\pi$
$572$	6.92205	−	9.81587i	0.289426	−	0.410422i
$573$	12.3368			0.515377
$574$		0			0
$575$	2.60492			0.108633
$576$	2.37997	+	4.12223i	0.0991654	+	0.171760i
$577$	28.0734	+	16.2082i	1.16871	+	0.674754i	0.953376	−	0.301786i	$-0.0975829\pi$
$577$	28.0734	+	16.2082i	1.16871	+	0.674754i	0.215333	+	0.976541i	$0.430916\pi$
$578$	−28.8259	−	16.6427i	−1.19900	−	0.692244i
$579$	−5.98318	+	3.45439i	−0.248653	+	0.143560i
$580$			19.2736i			0.800295i
$581$		0			0
$582$	21.6166			0.896037
$583$	−17.3098	+	9.99382i	−0.716899	+	0.413902i
$584$	−4.66564	+	8.08112i	−0.193065	+	0.334399i
$585$	−43.5091	−	3.95284i	−1.79888	−	0.163430i
$586$	−3.81841	−	6.61368i	−0.157737	−	0.273209i
$587$			4.03742i			0.166642i	0.996523	+	0.0833210i	$0.0265527\pi$
$587$			4.03742i			0.166642i	−0.996523	+	0.0833210i	$0.973447\pi$
$588$		0			0
$589$	−15.1427			−0.623943
$590$	−17.7809	+	10.2658i	−0.732027	+	0.422636i
$591$	−21.3530	−	12.3282i	−0.878347	−	0.507114i
$592$	3.25620	+	1.87997i	0.133829	+	0.0772663i
$593$	−17.6810	+	10.2082i	−0.726074	+	0.419199i	−0.816984	−	0.576660i	$-0.804356\pi$
$593$	−17.6810	+	10.2082i	−0.726074	+	0.419199i	0.0909105	+	0.995859i	$0.471022\pi$
$594$	−16.3319			−0.670107
$595$		0			0
$596$		−	5.81139i		−	0.238044i
$597$	−1.51988	−	2.63251i	−0.0622046	−	0.107742i
$598$	−6.31953	−	0.574135i	−0.258425	−	0.0234781i
$599$	4.05454	−	7.02267i	0.165664	−	0.286939i	−0.771227	−	0.636560i	$-0.780357\pi$
$599$	4.05454	−	7.02267i	0.165664	−	0.286939i	0.936891	+	0.349622i	$0.113690\pi$
$600$	3.57072	−	2.06156i	0.145774	−	0.0841628i
$601$	−7.70231			−0.314184			−0.157092	−	0.987584i	$-0.550212\pi$
$601$	−7.70231			−0.314184			−0.157092	+	0.987584i	$0.550212\pi$
$602$		0			0
$603$			27.4170i			1.11651i
$604$	2.67707	−	1.54561i	0.108928	−	0.0628899i
$605$	−0.214705	−	0.123960i	−0.00872900	−	0.00503969i
$606$	8.91271	+	5.14576i	0.362054	+	0.209032i
$607$	16.8512	+	29.1871i	0.683967	+	1.18467i	0.973760	+	0.227577i	$0.0730803\pi$
$607$	16.8512	+	29.1871i	0.683967	+	1.18467i	−0.289793	+	0.957089i	$0.593586\pi$
$608$	−4.54561			−0.184349
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	23.5453	−	33.3885i	0.952539	−	1.35075i
$612$	−16.8769	+	29.2316i	−0.682208	+	1.18162i
$613$	20.1502	+	11.6337i	0.813860	+	0.469882i	0.848294	−	0.529525i	$-0.177630\pi$
$613$	20.1502	+	11.6337i	0.813860	+	0.469882i	−0.0344347	+	0.999407i	$0.510963\pi$
$614$	−7.17541	−	12.4282i	−0.289576	−	0.501560i
$615$	−30.0672			−1.21243
$616$		0			0
$617$			1.51988i			0.0611881i	0.999532	+	0.0305941i	$0.00973991\pi$
$617$			1.51988i			0.0611881i	−0.999532	+	0.0305941i	$0.990260\pi$
$618$	31.5820	−	18.2339i	1.27041	−	0.733474i
$619$	0.675059	+	0.389746i	0.0271329	+	0.0156652i	0.513505	−	0.858087i	$-0.328347\pi$
$619$	0.675059	+	0.389746i	0.0271329	+	0.0156652i	−0.486372	+	0.873752i	$0.661680\pi$
$620$	4.24006	−	7.34400i	0.170285	−	0.294942i
$621$	4.31415	+	7.47233i	0.173121	+	0.299854i
$622$			2.18243i			0.0875075i
$623$		0			0
$624$	−9.11694	+	4.21433i	−0.364970	+	0.168708i
$625$	15.1049	+	26.1625i	0.604197	+	1.04650i
$626$	−13.4852	−	7.78567i	−0.538976	−	0.311178i
$627$	21.0912	−	36.5311i	0.842302	−	1.45891i
$628$	−3.96417	−	6.86614i	−0.158188	−	0.273989i
$629$			26.6625i			1.06311i
$630$		0			0
$631$		−	32.4678i		−	1.29252i	−0.763117	−	0.646261i	$-0.776332\pi$
$631$		−	32.4678i		−	1.29252i	0.763117	−	0.646261i	$-0.223668\pi$
$632$	−4.20122	+	2.42558i	−0.167116	+	0.0964843i
$633$	−20.9479	+	36.2828i	−0.832604	+	1.44211i
$634$	−7.09430	+	12.2877i	−0.281751	+	0.488007i
$635$	28.4446	−	16.4225i	1.12879	−	0.651707i
$636$	16.7140			0.662753
$637$		0			0
$638$	−25.2222			−0.998556
$639$	−45.9326	+	26.5192i	−1.81707	+	1.04908i
$640$	1.27280	−	2.20456i	0.0503120	−	0.0871429i
$641$	21.1139	−	36.5703i	0.833947	−	1.44444i	−0.0609377	−	0.998142i	$-0.519409\pi$
$641$	21.1139	−	36.5703i	0.833947	−	1.44444i	0.894885	−	0.446297i	$-0.147258\pi$
$642$	−8.49157	+	4.90261i	−0.335135	+	0.193491i
$643$		−	6.84330i		−	0.269873i	−0.990854	−	0.134937i	$-0.956917\pi$
$643$		−	6.84330i		−	0.269873i	0.990854	−	0.134937i	$-0.0430831\pi$
$644$		0			0
$645$		−	64.4678i		−	2.53842i
$646$	−16.1169	−	27.9154i	−0.634113	−	1.09832i
$647$	1.87688	−	3.25086i	0.0737879	−	0.127804i	−0.826771	−	0.562539i	$-0.809825\pi$
$647$	1.87688	−	3.25086i	0.0737879	−	0.127804i	0.900559	+	0.434735i	$0.143158\pi$
$648$	−0.539349	−	0.311393i	−0.0211876	−	0.0122327i
$649$	−13.4342	−	23.2687i	−0.527338	−	0.913376i
$650$	2.23922	+	4.84414i	0.0878293	+	0.190003i
$651$		0			0
$652$			10.0515i			0.393645i
$653$	−11.9166	−	20.6402i	−0.466334	−	0.807715i	0.532926	−	0.846162i	$-0.321092\pi$
$653$	−11.9166	−	20.6402i	−0.466334	−	0.807715i	−0.999261	+	0.0384469i	$0.987759\pi$
$654$	18.3055	−	31.7061i	0.715804	−	1.23981i
$655$	−36.9914	−	21.3570i	−1.44537	−	0.834487i
$656$	−3.67200	+	2.12003i	−0.143367	+	0.0827733i
$657$			44.4163i			1.73285i
$658$		0			0
$659$	−21.0912			−0.821597			−0.410799	−	0.911726i	$-0.634750\pi$
$659$	−21.0912			−0.821597			−0.410799	+	0.911726i	$0.634750\pi$
$660$	11.8114	+	20.4579i	0.459758	+	0.796324i
$661$	−29.7932	−	17.2011i	−1.15882	−	0.669047i	−0.207801	−	0.978171i	$-0.566631\pi$
$661$	−29.7932	−	17.2011i	−1.15882	−	0.669047i	−0.951022	+	0.309124i	$0.899964\pi$
$662$	1.42558	−	2.46917i	0.0554067	−	0.0959672i
$663$	−58.2060	−	41.0463i	−2.26054	−	1.59411i
$664$	−11.2082			−0.434961
$665$		0			0
$666$	17.8971			0.693498
$667$	6.66255	+	11.5399i	0.257975	+	0.446826i
$668$	20.9872	+	12.1169i	0.812018	+	0.468819i
$669$	−31.1270	−	17.9712i	−1.20344	−	0.694806i
$670$	12.6981	−	7.33127i	0.490572	−	0.283232i
$671$		−	2.61727i		−	0.101039i
$672$		0			0
$673$	10.7997			0.416298			0.208149	−	0.978097i	$-0.433256\pi$
$673$	10.7997			0.416298			0.208149	+	0.978097i	$0.433256\pi$
$674$	−28.1678	+	16.2627i	−1.08498	+	0.626416i
$675$	3.62822	−	6.28426i	0.139650	−	0.241881i
$676$	−4.36467	−	12.2454i	−0.167872	−	0.470977i
$677$	16.8668	+	29.2141i	0.648243	+	1.12279i	0.983542	+	0.180678i	$0.0578292\pi$
$677$	16.8668	+	29.2141i	0.648243	+	1.12279i	−0.335299	+	0.942112i	$0.608837\pi$
$678$		−	4.90261i		−	0.188284i
$679$		0			0
$680$	18.0515			0.692242
$681$	−21.7742	+	12.5713i	−0.834389	+	0.481735i
$682$	9.61062	+	5.54870i	0.368010	+	0.212471i
$683$	18.9338	+	10.9314i	0.724481	+	0.418279i	0.816400	−	0.577487i	$-0.195967\pi$
$683$	18.9338	+	10.9314i	0.724481	+	0.418279i	−0.0919188	+	0.995767i	$0.529300\pi$
$684$	−18.7380	+	10.8184i	−0.716467	+	0.413652i
$685$	28.3649			1.08377
$686$		0			0
$687$		−	39.4684i		−	1.50581i
$688$	−4.54561	−	7.87322i	−0.173300	−	0.300164i
$689$	−1.95734	+	21.5446i	−0.0745689	+	0.820783i
$690$	6.24006	−	10.8081i	0.237555	−	0.411457i
$691$	−9.30145	+	5.37020i	−0.353844	+	0.204292i	−0.666377	−	0.745615i	$-0.732156\pi$
$691$	−9.30145	+	5.37020i	−0.353844	+	0.204292i	0.312533	+	0.949907i	$0.398822\pi$
$692$	−20.5971			−0.782983
$693$		0			0
$694$			5.94855i			0.225804i
$695$	−10.0211	+	5.78567i	−0.380121	+	0.219463i
$696$	18.2655	+	10.5456i	0.692353	+	0.399730i
$697$	−26.0389	−	15.0336i	−0.986295	−	0.569438i
$698$	−16.4810	−	28.5459i	−0.623814	−	1.08048i
$699$	−20.5658			−0.777871
$700$		0			0
$701$	−11.1941			−0.422796			−0.211398	−	0.977400i	$-0.567802\pi$
$701$	−11.1941			−0.422796			−0.211398	+	0.977400i	$0.567802\pi$
$702$	−10.1871	+	14.4459i	−0.384488	+	0.545226i
$703$	−8.54561	+	14.8014i	−0.322304	+	0.558246i
$704$	2.88497	+	1.66564i	0.108731	+	0.0627761i
$705$	40.1763	+	69.5873i	1.51313	+	2.62081i
$706$	−0.851156			−0.0320337
$707$		0			0
$708$			22.4678i			0.844390i
$709$	−4.50359	+	2.60015i	−0.169136	+	0.0976506i	−0.582178	−	0.813061i	$-0.697799\pi$
$709$	−4.50359	+	2.60015i	−0.169136	+	0.0976506i	0.413042	+	0.910712i	$0.364466\pi$
$710$	24.5647	+	14.1824i	0.921896	+	0.532257i
$711$	−11.5456	+	19.9976i	−0.432994	+	0.749968i
$712$	−7.54561	−	13.0694i	−0.282784	−	0.489796i
$713$		−	5.86285i		−	0.219565i
$714$		0			0
$715$	−27.7538	+	12.8293i	−1.03793	+	0.479787i
$716$	8.66255	+	15.0040i	0.323735	+	0.560725i
$717$	14.7907	+	8.53943i	0.552370	+	0.318911i
$718$	13.9681	−	24.1935i	0.521285	−	0.902892i
$719$	19.0257	+	32.9535i	0.709540	+	1.22896i	0.965028	+	0.262147i	$0.0844305\pi$
$719$	19.0257	+	32.9535i	0.709540	+	1.22896i	−0.255488	+	0.966812i	$0.582236\pi$
$720$		−	12.1169i		−	0.451572i
$721$		0			0
$722$		−	1.66255i		−	0.0618737i
$723$	65.9207	−	38.0593i	2.45162	−	1.41544i
$724$	−8.45832	+	14.6502i	−0.314351	+	0.544472i
$725$	5.60324	−	9.70509i	0.208099	−	0.360438i
$726$	−0.234952	+	0.135650i	−0.00871990	+	0.00503444i
$727$	−28.6111			−1.06113			−0.530563	−	0.847645i	$-0.678020\pi$
$727$	−28.6111			−1.06113			−0.530563	+	0.847645i	$0.678020\pi$
$728$		0			0
$729$	−43.9355			−1.62724
$730$	20.5714	−	11.8769i	0.761380	−	0.439583i
$731$	32.2339	−	55.8307i	1.19221	−	2.06497i
$732$	−1.09430	+	1.89539i	−0.0404466	+	0.0700556i
$733$	7.11860	−	4.10992i	0.262931	−	0.151803i	−0.362740	−	0.931891i	$-0.618159\pi$
$733$	7.11860	−	4.10992i	0.262931	−	0.151803i	0.625671	+	0.780087i	$0.284825\pi$
$734$		−	7.14267i		−	0.263641i
$735$		0			0
$736$		−	1.75994i		−	0.0648723i
$737$	9.59397	+	16.6172i	0.353399	+	0.612104i
$738$	−10.0912	+	17.4785i	−0.371463	+	0.643392i
$739$	1.37151	+	0.791843i	0.0504519	+	0.0291284i	0.525014	−	0.851094i	$-0.324060\pi$
$739$	1.37151	+	0.791843i	0.0504519	+	0.0291284i	−0.474562	+	0.880222i	$0.657393\pi$
$740$	−4.78567	−	8.28902i	−0.175925	−	0.304710i
$741$	−19.1567	−	41.4420i	−0.703739	−	1.52241i
$742$		0			0
$743$		−	11.9485i		−	0.438350i	−0.975686	−	0.219175i	$-0.929663\pi$
$743$		−	11.9485i		−	0.438350i	0.975686	−	0.219175i	$-0.0703365\pi$
$744$	−4.63991	−	8.03656i	−0.170107	−	0.294635i
$745$	−7.39676	+	12.8116i	−0.270996	+	0.469380i
$746$	28.7024	+	16.5713i	1.05087	+	0.606720i
$747$	−46.2026	+	26.6751i	−1.69046	+	0.975990i
$748$			23.6228i			0.863735i
$749$		0			0
$750$	24.9602			0.911419
$751$	−13.7826	−	23.8721i	−0.502933	−	0.871106i	−0.999994	−	0.00339058i	$-0.998921\pi$
$751$	−13.7826	−	23.8721i	−0.502933	−	0.871106i	0.497061	−	0.867716i	$-0.334413\pi$
$752$	9.81317	+	5.66564i	0.357850	+	0.206605i
$753$	−22.9650	+	39.7766i	−0.836891	+	1.44954i
$754$	−15.7325	+	22.3095i	−0.572943	+	0.812466i
$755$	−7.86902			−0.286383
$756$		0			0
$757$	−38.2339			−1.38963			−0.694817	−	0.719187i	$-0.744515\pi$
$757$	−38.2339			−1.38963			−0.694817	+	0.719187i	$0.744515\pi$
$758$	17.6368	+	30.5479i	0.640598	+	1.10955i
$759$	14.1439	+	8.16597i	0.513390	+	0.296406i
$760$	10.0211	+	5.78567i	0.363502	+	0.209868i
$761$	44.8147	−	25.8738i	1.62453	−	0.937924i	0.638846	−	0.769334i	$-0.279412\pi$
$761$	44.8147	−	25.8738i	1.62453	−	0.937924i	0.985686	−	0.168590i	$-0.0539214\pi$
$762$		−	35.9424i		−	1.30205i
$763$		0			0
$764$	−4.42867			−0.160224
$765$	74.4122	−	42.9619i	2.69038	−	1.55329i
$766$	3.47703	−	6.02239i	0.125630	−	0.217598i
$767$	−28.9613	−	2.63116i	−1.04573	−	0.0950055i
$768$	−1.39283	−	2.41246i	−0.0502595	−	0.0870521i
$769$		−	24.2401i		−	0.874119i	−0.899433	−	0.437059i	$-0.856020\pi$
$769$		−	24.2401i		−	0.874119i	0.899433	−	0.437059i	$-0.143980\pi$
$770$		0			0
$771$	−3.18309			−0.114636
$772$	2.14785	−	1.24006i	0.0773027	−	0.0446307i
$773$	14.3735	+	8.29853i	0.516978	+	0.298477i	0.735697	−	0.677310i	$-0.236855\pi$
$773$	14.3735	+	8.29853i	0.516978	+	0.298477i	−0.218719	+	0.975788i	$0.570188\pi$
$774$	−37.4761	−	21.6368i	−1.34705	−	0.777720i
$775$	−4.27010	+	2.46534i	−0.153386	+	0.0885577i
$776$	−7.75994			−0.278566
$777$		0			0
$778$		−	5.27365i		−	0.189069i
$779$	−9.63682	−	16.6915i	−0.345275	−	0.598034i
$780$	25.4629	+	2.31332i	0.911717	+	0.0828303i
$781$	−18.5596	+	32.1462i	−0.664116	+	1.15028i
$782$	10.8081	−	6.24006i	0.386497	−	0.223144i
$783$	37.1193			1.32654
$784$		0			0
$785$			20.1824i			0.720342i
$786$	−40.4798	+	23.3710i	−1.44387	+	0.833617i
$787$	7.19816	+	4.15586i	0.256587	+	0.148140i	0.622777	−	0.782400i	$-0.286005\pi$
$787$	7.19816	+	4.15586i	0.256587	+	0.148140i	−0.366190	+	0.930540i	$0.619338\pi$
$788$	7.66533	+	4.42558i	0.273066	+	0.157655i
$789$	14.7795	+	25.5988i	0.526164	+	0.911342i
$790$	12.3491			0.439363
$791$		0			0
$792$	15.8567			0.563442
$793$	−2.31503	−	1.63254i	−0.0822091	−	0.0579731i
$794$	−9.33829	+	16.1744i	−0.331404	+	0.574008i
$795$	−36.8470	−	21.2736i	−1.30683	−	0.754498i
$796$	0.545608	+	0.945020i	0.0193386	+	0.0334954i
$797$	24.3055			0.860947			0.430473	−	0.902603i	$-0.358347\pi$
$797$	24.3055			0.860947			0.430473	+	0.902603i	$0.358347\pi$
$798$		0			0
$799$			80.3525i			2.84267i
$800$	−1.28182	+	0.740059i	−0.0453192	+	0.0261650i
$801$	−62.2095	−	35.9166i	−2.19806	−	1.26905i
$802$	10.7599	−	18.6368i	0.379947	−	0.658087i
$803$	15.5425	+	26.9204i	0.548484	+	0.950001i
$804$		−	16.0453i		−	0.565873i
$805$		0			0
$806$	10.9026	−	5.03976i	0.384028	−	0.177518i
$807$	16.7966	+	29.0926i	0.591269	+	1.02411i
$808$	−3.19949	−	1.84723i	−0.112558	−	0.0649852i
$809$	7.99382	−	13.8457i	0.281048	−	0.486789i	−0.690595	−	0.723241i	$-0.742651\pi$
$809$	7.99382	−	13.8457i	0.281048	−	0.486789i	0.971643	+	0.236452i	$0.0759847\pi$
$810$	0.792685	+	1.37297i	0.0278521	+	0.0482413i
$811$		−	19.7163i		−	0.692335i	−0.938173	−	0.346167i	$-0.887483\pi$
$811$		−	19.7163i		−	0.692335i	0.938173	−	0.346167i	$-0.112517\pi$
$812$		0			0
$813$			3.85182i			0.135089i
$814$	10.8473	−	6.26270i	0.380198	−	0.219507i
$815$	12.7935	−	22.1590i	0.448138	−	0.776197i
$816$	9.87688	−	17.1073i	0.345760	−	0.598874i
$817$	35.7886	−	20.6625i	1.25208	−	0.722891i
$818$	19.3251			0.675686
$819$		0			0
$820$	10.7935			0.376926
$821$	−13.8118	+	7.97427i	−0.482037	+	0.278304i	−0.721265	−	0.692659i	$-0.756439\pi$
$821$	−13.8118	+	7.97427i	−0.482037	+	0.278304i	0.239228	+	0.970963i	$0.423106\pi$
$822$	15.5199	−	26.8812i	0.541318	−	0.937590i
$823$	−11.9969	+	20.7793i	−0.418186	+	0.724320i	−0.995757	−	0.0920209i	$-0.970667\pi$
$823$	−11.9969	+	20.7793i	−0.418186	+	0.724320i	0.577571	+	0.816340i	$0.304001\pi$
$824$	−11.3373	+	6.54561i	−0.394954	+	0.228027i
$825$		−	13.7352i		−	0.478200i
$826$		0			0
$827$		−	49.4280i		−	1.71878i	−0.511321	−	0.859390i	$-0.670844\pi$
$827$		−	49.4280i		−	1.71878i	0.511321	−	0.859390i	$-0.329156\pi$
$828$	−4.18861	−	7.25488i	−0.145564	−	0.252124i
$829$	5.88390	−	10.1912i	0.204356	−	0.353956i	−0.745571	−	0.666426i	$-0.767823\pi$
$829$	5.88390	−	10.1912i	0.204356	−	0.353956i	0.949927	+	0.312471i	$0.101157\pi$
$830$	24.7091	+	14.2658i	0.857664	+	0.495173i
$831$	−1.59155	−	2.75664i	−0.0552101	−	0.0956268i
$832$	3.27280	−	1.51286i	0.113464	−	0.0524491i
$833$		0			0
$834$			12.6625i			0.438468i
$835$	−30.8450	−	53.4251i	−1.06743	−	1.84885i
$836$	−7.57133	+	13.1139i	−0.261860	+	0.453555i
$837$	−14.1439	−	8.16597i	−0.488884	−	0.282257i
$838$	11.1173	−	6.41856i	0.384040	−	0.221725i
$839$		−	16.6687i		−	0.575468i	−0.957710	−	0.287734i	$-0.907098\pi$
$839$		−	16.6687i		−	0.575468i	0.957710	−	0.287734i	$-0.0929020\pi$
$840$		0			0
$841$	28.3251			0.976728
$842$	10.6656	+	18.4734i	0.367562	+	0.636636i
$843$	−17.2314	−	9.94855i	−0.593481	−	0.342646i
$844$	7.51988	−	13.0248i	0.258845	−	0.448333i
$845$	−5.96381	+	32.5511i	−0.205161	+	1.11979i
$846$	53.9362			1.85436
$847$		0			0
$848$	−6.00000			−0.206041
$849$	6.73730	+	11.6693i	0.231224	+	0.400491i
$850$	−9.08966	−	5.24792i	−0.311773	−	0.180002i
$851$	−5.73073	−	3.30864i	−0.196447	−	0.113419i
$852$	26.8812	−	15.5199i	0.920936	−	0.531702i
$853$			23.1286i			0.791909i	0.918270	+	0.395955i	$0.129586\pi$
$853$			23.1286i			0.791909i	−0.918270	+	0.395955i	$0.870414\pi$
$854$		0			0
$855$	55.0789			1.88366
$856$	3.04831	−	1.75994i	0.104189	−	0.0601535i
$857$	−6.82543	+	11.8220i	−0.233152	+	0.403832i	−0.958734	−	0.284304i	$-0.908237\pi$
$857$	−6.82543	+	11.8220i	−0.233152	+	0.403832i	0.725582	+	0.688136i	$0.241571\pi$
$858$	−3.02730	+	33.3216i	−0.103350	+	1.13758i
$859$	6.41856	+	11.1173i	0.218998	+	0.379316i	0.954502	−	0.298204i	$-0.0963877\pi$
$859$	6.41856	+	11.1173i	0.218998	+	0.379316i	−0.735504	+	0.677521i	$0.763054\pi$
$860$			23.1427i			0.789158i
$861$		0			0
$862$	11.5713			0.394121
$863$	34.3143	−	19.8114i	1.16807	−	0.674388i	0.214848	−	0.976647i	$-0.431074\pi$
$863$	34.3143	−	19.8114i	1.16807	−	0.674388i	0.953226	+	0.302260i	$0.0977410\pi$
$864$	−4.24578	−	2.45130i	−0.144444	−	0.0833951i
$865$	45.4075	+	26.2160i	1.54390	+	0.891371i
$866$	25.4408	−	14.6883i	0.864515	−	0.499128i
$867$	92.7219			3.14900
$868$		0			0
$869$			16.1605i			0.548209i
$870$	−26.8450	−	46.4969i	−0.910130	−	1.57639i
$871$	20.6826	+	1.87903i	0.700803	+	0.0636685i
$872$	−6.57133	+	11.3819i	−0.222533	+	0.385439i
$873$	−31.9883	+	18.4684i	−1.08264	+	0.625062i
$874$	8.00000			0.270604
$875$		0			0
$876$		−	25.9938i		−	0.878250i
$877$	−41.0239	+	23.6852i	−1.38528	+	0.799792i	−0.992779	−	0.119959i	$-0.961724\pi$
$877$	−41.0239	+	23.6852i	−1.38528	+	0.799792i	−0.392502	+	0.919751i	$0.628390\pi$
$878$	−0.0891186	−	0.0514526i	−0.00300761	−	0.00173644i
$879$	18.4235	+	10.6368i	0.621410	+	0.358771i
$880$	−4.24006	−	7.34400i	−0.142932	−	0.247566i
$881$	−43.8052			−1.47584			−0.737918	−	0.674891i	$-0.764191\pi$
$881$	−43.8052			−1.47584			−0.737918	+	0.674891i	$0.764191\pi$
$882$		0			0
$883$	−1.81757			−0.0611661			−0.0305830	−	0.999532i	$-0.509736\pi$
$883$	−1.81757			−0.0611661			−0.0305830	+	0.999532i	$0.509736\pi$
$884$	20.8948	+	14.7348i	0.702769	+	0.495586i
$885$	28.5971	−	49.5316i	0.961280	−	1.66499i
$886$	−23.5062	−	13.5713i	−0.789708	−	0.455938i
$887$	−3.63682	−	6.29916i	−0.122113	−	0.211505i	0.798488	−	0.602011i	$-0.205634\pi$
$887$	−3.63682	−	6.29916i	−0.122113	−	0.211505i	−0.920601	+	0.390506i	$0.872300\pi$
$888$	−10.4739			−0.351483
$889$		0			0
$890$			38.4163i			1.28772i
$891$	−1.79672	+	1.03734i	−0.0601924	+	0.0347521i
$892$	11.1740	+	6.45130i	0.374133	+	0.216006i
$893$	−25.7538	+	44.6068i	−0.861817	+	1.49271i
$894$	8.09430	+	14.0197i	0.270714	+	0.468890i
$895$		−	44.1029i		−	1.47420i
$896$		0			0
$897$	16.0453	−	7.41698i	0.535736	−	0.247646i
$898$	−4.85116	−	8.40245i	−0.161885	−	0.280393i
$899$	−21.8431	−	12.6111i	−0.728507	−	0.420604i
$900$	−3.52264	+	6.10139i	−0.117421	+	0.203380i
$901$	−21.2736	−	36.8470i	−0.708728	−	1.22755i
$902$			14.1248i			0.470304i
$903$		0			0
$904$			1.75994i			0.0585348i
$905$	37.2938	−	21.5316i	1.23969	−	0.715734i
$906$	−4.30555	+	7.45743i	−0.143042	+	0.247756i
$907$	6.23388	−	10.7974i	0.206993	−	0.358522i	−0.743773	−	0.668432i	$-0.766966\pi$
$907$	6.23388	−	10.7974i	0.206993	−	0.358522i	0.950766	+	0.309910i	$0.100299\pi$
$908$	7.81651	−	4.51286i	0.259400	−	0.149765i
$909$	−17.5854			−0.583270
$910$		0			0
$911$	1.92047			0.0636282			0.0318141	−	0.999494i	$-0.489872\pi$
$911$	1.92047			0.0636282			0.0318141	+	0.999494i	$0.489872\pi$
$912$	10.9661	−	6.33127i	0.363124	−	0.209649i
$913$	−18.6687	+	32.3352i	−0.617845	+	1.07014i
$914$	18.0850	−	31.3242i	0.598200	−	1.03611i
$915$	4.82492	−	2.78567i	0.159507	−	0.0920913i
$916$			14.1684i			0.468137i
$917$		0			0
$918$		−	34.7655i		−	1.14743i
$919$	6.61418	+	11.4561i	0.218182	+	0.377902i	0.954252	−	0.299003i	$-0.0966541\pi$
$919$	6.61418	+	11.4561i	0.218182	+	0.377902i	−0.736070	+	0.676905i	$0.763321\pi$
$920$	−2.24006	+	3.87990i	−0.0738526	+	0.127916i
$921$	34.6208	+	19.9883i	1.14079	+	0.658637i
$922$	10.4871	+	18.1643i	0.345375	+	0.598208i
$923$	16.8573	+	36.4678i	0.554866	+	1.20035i
$924$		0			0
$925$			5.56516i			0.182981i
$926$	12.4225	+	21.5164i	0.408228	+	0.707072i
$927$	−31.1567	+	53.9650i	−1.02332	+	1.77244i
$928$	−6.55697	−	3.78567i	−0.215243	−	0.124271i
$929$	−1.12861	+	0.651601i	−0.0370284	+	0.0213783i	−0.518400	−	0.855138i	$-0.673472\pi$
$929$	−1.12861	+	0.651601i	−0.0370284	+	0.0213783i	0.481372	+	0.876517i	$0.340139\pi$
$930$			23.6228i			0.774622i
$931$		0			0
$932$	7.38273			0.241829
$933$	−3.03976	−	5.26502i	−0.0995174	−	0.172369i
$934$	−1.10155	−	0.635981i	−0.0360438	−	0.0208099i
$935$	30.0672	−	52.0779i	0.983302	−	1.70313i
$936$	9.89068	−	14.0255i	0.323287	−	0.458439i
$937$	14.9602			0.488730			0.244365	−	0.969683i	$-0.421421\pi$
$937$	14.9602			0.488730			0.244365	+	0.969683i	$0.421421\pi$
$938$		0			0
$939$	43.3766			1.41554
$940$	−14.4225	−	24.9805i	−0.470410	−	0.814774i
$941$	8.60354	+	4.96726i	0.280467	+	0.161928i	0.633635	−	0.773632i	$-0.281562\pi$
$941$	8.60354	+	4.96726i	0.280467	+	0.161928i	−0.353168	+	0.935560i	$0.614895\pi$
$942$	19.1268	+	11.0429i	0.623184	+	0.359796i
$943$	6.46250	−	3.73113i	0.210448	−	0.121502i
$944$		−	8.06549i		−	0.262509i
$945$		0			0
$946$	−30.2853			−0.984661
$947$	−35.0704	+	20.2479i	−1.13964	+	0.657969i	−0.946340	−	0.323172i	$-0.895251\pi$
$947$	−35.0704	+	20.2479i	−1.13964	+	0.657969i	−0.193295	+	0.981141i	$0.561918\pi$
$948$	6.75685	−	11.7032i	0.219452	−	0.380103i
$949$	33.5064	+	3.04409i	1.08766	+	0.0988152i
$950$	−3.36402	−	5.82665i	−0.109143	−	0.189042i
$951$		−	39.5247i		−	1.28168i
$952$		0			0
$953$	−18.9602			−0.614182			−0.307091	−	0.951680i	$-0.599356\pi$
$953$	−18.9602			−0.614182			−0.307091	+	0.951680i	$0.599356\pi$
$954$	−24.7334	+	14.2798i	−0.800773	+	0.462326i
$955$	9.76326	+	5.63682i	0.315932	+	0.182403i
$956$	−5.30958	−	3.06549i	−0.171724	−	0.0991450i
$957$	60.8475	−	35.1303i	1.96692	−	1.13560i
$958$	−22.0515			−0.712450
$959$		0			0
$960$			7.09122i			0.228868i
$961$	−9.95130	−	17.2362i	−0.321010	−	0.556005i
$962$	1.22658	−	13.5011i	0.0395466	−	0.435291i
$963$	8.37721	−	14.5098i	0.269952	−	0.467570i
$964$	−23.6642	+	13.6625i	−0.762174	+	0.440041i
$965$	−6.31341			−0.203236
$966$		0			0
$967$			4.63448i			0.149035i	0.997220	+	0.0745174i	$0.0237416\pi$
$967$			4.63448i			0.149035i	−0.997220	+	0.0745174i	$0.976258\pi$
$968$	0.0843433	−	0.0486956i	0.00271090	−	0.00156514i
$969$	77.7629	+	44.8964i	2.49810	+	1.44228i
$970$	17.1073	+	9.87688i	0.549281	+	0.317128i
$971$	−11.8668	−	20.5539i	−0.380823	−	0.659605i	0.610357	−	0.792126i	$-0.291026\pi$
$971$	−11.8668	−	20.5539i	−0.380823	−	0.659605i	−0.991180	+	0.132522i	$0.957693\pi$
$972$	16.4427			0.527400
$973$		0			0
$974$	4.42867			0.141904
$975$	−12.1491	−	8.56742i	−0.389082	−	0.274377i
$976$	0.392834	−	0.680408i	0.0125743	−	0.0217793i
$977$	−4.10676	−	2.37104i	−0.131387	−	0.0758562i	0.432866	−	0.901458i	$-0.357502\pi$
$977$	−4.10676	−	2.37104i	−0.131387	−	0.0758562i	−0.564253	+	0.825602i	$0.690836\pi$
$978$	−14.0000	−	24.2487i	−0.447671	−	0.775388i
$979$	−50.2730			−1.60673
$980$		0			0
$981$			62.5583i			1.99733i
$982$	−26.8705	+	15.5137i	−0.857473	+	0.495062i
$983$	20.5607	+	11.8707i	0.655783	+	0.378617i	0.790668	−	0.612245i	$-0.209733\pi$
$983$	20.5607	+	11.8707i	0.655783	+	0.378617i	−0.134885	+	0.990861i	$0.543067\pi$
$984$	5.90570	−	10.2290i	0.188267	−	0.326088i
$985$	−11.2658	−	19.5129i	−0.358958	−	0.621733i
$986$		−	53.6900i		−	1.70984i
$987$		0			0
$988$	6.87688	+	14.8769i	0.218783	+	0.473297i
$989$	8.00000	+	13.8564i	0.254385	+	0.440608i
$990$	−34.9570	−	20.1824i	−1.11101	−	0.641440i
$991$	−20.4256	+	35.3781i	−0.648840	+	1.12382i	0.334560	+	0.942374i	$0.391412\pi$
$991$	−20.4256	+	35.3781i	−0.648840	+	1.12382i	−0.983400	+	0.181449i	$0.941921\pi$
$992$	1.66564	+	2.88497i	0.0528840	+	0.0915978i
$993$			7.94237i			0.252044i
$994$		0			0
$995$		−	2.77781i		−	0.0880624i
$996$	27.0392	−	15.6111i	0.856770	−	0.494657i
$997$	2.93844	−	5.08953i	0.0930614	−	0.161187i	−0.815736	−	0.578424i	$-0.803668\pi$
$997$	2.93844	−	5.08953i	0.0930614	−	0.161187i	0.908798	+	0.417237i	$0.137001\pi$
$998$	−11.5425	+	19.9922i	−0.365372	+	0.632843i
$999$	−15.9639	+	9.21676i	−0.505075	+	0.291605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.m.753.4		12
7.2	even	3	inner	1274.2.n.m.961.1		12
7.3	odd	6		1274.2.d.l.883.4		6
7.4	even	3		182.2.d.b.155.6	yes	6
7.5	odd	6		1274.2.n.n.961.3		12
7.6	odd	2		1274.2.n.n.753.6		12
13.12	even	2	inner	1274.2.n.m.753.1		12
21.11	odd	6		1638.2.c.i.883.3		6
28.11	odd	6		1456.2.k.b.337.1		6
91.12	odd	6		1274.2.n.n.961.6		12
91.18	odd	12		2366.2.a.bc.1.3		3
91.25	even	6		182.2.d.b.155.3	✓	6
91.38	odd	6		1274.2.d.l.883.1		6
91.51	even	6	inner	1274.2.n.m.961.4		12
91.60	odd	12		2366.2.a.x.1.3		3
91.90	odd	2		1274.2.n.n.753.3		12
273.116	odd	6		1638.2.c.i.883.4		6
364.207	odd	6		1456.2.k.b.337.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.b.155.3	✓	6	91.25	even	6
182.2.d.b.155.6	yes	6	7.4	even	3
1274.2.d.l.883.1		6	91.38	odd	6
1274.2.d.l.883.4		6	7.3	odd	6
1274.2.n.m.753.1		12	13.12	even	2	inner
1274.2.n.m.753.4		12	1.1	even	1	trivial
1274.2.n.m.961.1		12	7.2	even	3	inner
1274.2.n.m.961.4		12	91.51	even	6	inner
1274.2.n.n.753.3		12	91.90	odd	2
1274.2.n.n.753.6		12	7.6	odd	2
1274.2.n.n.961.3		12	7.5	odd	6
1274.2.n.n.961.6		12	91.12	odd	6
1456.2.k.b.337.1		6	28.11	odd	6
1456.2.k.b.337.2		6	364.207	odd	6
1638.2.c.i.883.3		6	21.11	odd	6
1638.2.c.i.883.4		6	273.116	odd	6
2366.2.a.x.1.3		3	91.60	odd	12
2366.2.a.bc.1.3		3	91.18	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.39283 + 2.41246i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.20456 + 1.27280i) q^{5} +2.78567i q^{6} -1.00000i q^{8} +(-2.37997 - 4.12223i) q^{9} +(-1.27280 + 2.20456i) q^{10} +(-2.88497 - 1.66564i) q^{11} +(1.39283 + 2.41246i) q^{12} +(-3.27280 + 1.51286i) q^{13} -7.09122i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.54561 - 6.14117i) q^{17} +(-4.12223 - 2.37997i) q^{18} +(3.93661 - 2.27280i) q^{19} +2.54561i q^{20} -3.33127 q^{22} +(0.879970 + 1.52415i) q^{23} +(2.41246 + 1.39283i) q^{24} +(0.740059 - 1.28182i) q^{25} +(-2.07790 + 2.94658i) q^{26} +4.90261 q^{27} +7.57133 q^{29} +(-3.54561 - 6.14117i) q^{30} +(-2.88497 - 1.66564i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.03656 - 4.63991i) q^{33} -7.09122i q^{34} -4.75994 q^{36} +(-3.25620 + 1.87997i) q^{37} +(2.27280 - 3.93661i) q^{38} +(0.908751 - 10.0027i) q^{39} +(1.27280 + 2.20456i) q^{40} -4.24006i q^{41} +9.09122 q^{43} +(-2.88497 + 1.66564i) q^{44} +(10.4936 + 6.05847i) q^{45} +(1.52415 + 0.879970i) q^{46} +(-9.81317 + 5.66564i) q^{47} +2.78567 q^{48} -1.48012i q^{50} +(9.87688 + 17.1073i) q^{51} +(-0.326224 + 3.59076i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.24578 - 2.45130i) q^{54} +8.48012 q^{55} +12.6625i q^{57} +(6.55697 - 3.78567i) q^{58} +(6.98492 + 4.03274i) q^{59} +(-6.14117 - 3.54561i) q^{60} +(0.392834 + 0.680408i) q^{61} -3.33127 q^{62} -1.00000 q^{64} +(5.28952 - 7.50084i) q^{65} +(4.63991 - 8.03656i) q^{66} +(-4.98825 - 2.87997i) q^{67} +(-3.54561 - 6.14117i) q^{68} -4.90261 q^{69} -11.1427i q^{71} +(-4.12223 + 2.37997i) q^{72} +(-8.08112 - 4.66564i) q^{73} +(-1.87997 + 3.25620i) q^{74} +(2.06156 + 3.57072i) q^{75} -4.54561i q^{76} +(-4.21433 - 9.11694i) q^{78} +(-2.42558 - 4.20122i) q^{79} +(2.20456 + 1.27280i) q^{80} +(0.311393 - 0.539349i) q^{81} +(-2.12003 - 3.67200i) q^{82} -11.2082i q^{83} +18.0515i q^{85} +(7.87322 - 4.54561i) q^{86} +(-10.5456 + 18.2655i) q^{87} +(-1.66564 + 2.88497i) q^{88} +(13.0694 - 7.54561i) q^{89} +12.1169 q^{90} +1.75994 q^{92} +(8.03656 - 4.63991i) q^{93} +(-5.66564 + 9.81317i) q^{94} +(-5.78567 + 10.0211i) q^{95} +(2.41246 - 1.39283i) q^{96} -7.75994i q^{97} +15.8567i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} - 24 q^{9} + 4 q^{10} + 2 q^{12} - 20 q^{13} - 6 q^{16} + 4 q^{17} + 28 q^{22} + 6 q^{23} + 18 q^{25} + 4 q^{26} - 68 q^{27} + 32 q^{29} - 4 q^{30} - 48 q^{36} + 8 q^{38} + 6 q^{39}+ \cdots - 40 q^{95}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 - 24 * q^9 + 4 * q^10 + 2 * q^12 - 20 * q^13 - 6 * q^16 + 4 * q^17 + 28 * q^22 + 6 * q^23 + 18 * q^25 + 4 * q^26 - 68 * q^27 + 32 * q^29 - 4 * q^30 - 48 * q^36 + 8 * q^38 + 6 * q^39 - 4 * q^40 + 32 * q^43 + 4 * q^48 + 12 * q^51 - 10 * q^52 + 36 * q^53 + 120 * q^55 - 10 * q^61 + 28 * q^62 - 12 * q^64 + 20 * q^65 + 42 * q^66 - 4 * q^68 + 68 * q^69 - 18 * q^74 + 78 * q^75 - 80 * q^78 + 14 * q^79 - 46 * q^81 - 30 * q^82 - 88 * q^87 + 14 * q^88 + 48 * q^90 + 12 * q^92 - 34 * q^94 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

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