LMFDB - Embedded newform 1274.2.n.m.753.1

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			753.1
Root			$0.465879 - 1.73868i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.m.961.1

$q$-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} +(3.59076 - 0.326224i) 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} +(8.20819 - 5.78834i) 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} +(-2.94658 + 2.07790i) 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} +(-9.14067 + 0.830438i) 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	0.0818605	−	0.996644i	$-0.473914\pi$
$5$	2.20456	−	1.27280i	0.985910	−	0.569215i	0.904049	+	0.427429i	$0.140580\pi$
$6$		−	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	0.867299	−	0.497788i	$-0.165854\pi$
$11$	2.88497	+	1.66564i	0.869851	+	0.502209i	0.00255211	+	0.999997i	$0.499188\pi$
$12$	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	−0.878211	−	0.478273i	$-0.841263\pi$
$19$	−3.93661	+	2.27280i	−0.903121	+	0.521417i	−0.0249093	+	0.999690i	$0.507930\pi$
$20$		−	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
$26$	3.59076	−	0.326224i	0.704207	−	0.0639778i
$27$	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	0.736180	−	0.676786i	$-0.236628\pi$
$31$	2.88497	+	1.66564i	0.518156	+	0.299157i	−0.218024	+	0.975943i	$0.569961\pi$
$32$	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	−0.207862	−	0.978158i	$-0.566651\pi$
$37$	3.25620	−	1.87997i	0.535317	−	0.309065i	0.743179	+	0.669093i	$0.233317\pi$
$38$	2.27280	−	3.93661i	0.368697	−	0.638603i
$39$	8.20819	−	5.78834i	1.31436	−	0.926876i
$40$	1.27280	+	2.20456i	0.201248	+	0.348572i
$41$			4.24006i			0.662186i	0.943598	+	0.331093i	$0.107417\pi$
$41$			4.24006i			0.662186i	−0.943598	+	0.331093i	$0.892583\pi$
$42$		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	0.434171	−	0.900831i	$-0.357041\pi$
$47$	9.81317	−	5.66564i	1.43140	−	0.826418i	0.997228	+	0.0744125i	$0.0237081\pi$
$48$	2.78567			0.402076
$49$		0			0
$50$			1.48012i			0.209320i
$51$	9.87688	+	17.1073i	1.38304	+	2.39550i
$52$	−2.94658	+	2.07790i	−0.408617	+	0.288153i
$53$	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	−0.0291341	−	0.999576i	$-0.509275\pi$
$59$	−6.98492	−	4.03274i	−0.909359	−	0.525019i	−0.880225	+	0.474557i	$0.842608\pi$
$60$	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
$65$	−9.14067	+	0.830438i	−1.13376	+	0.103003i
$66$	4.63991	−	8.03656i	0.571134	−	0.989232i
$67$	4.98825	+	2.87997i	0.609412	+	0.351844i	0.772735	−	0.634728i	$-0.218888\pi$
$67$	4.98825	+	2.87997i	0.609412	+	0.351844i	−0.163323	+	0.986573i	$0.552221\pi$
$68$	−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	$0.229951\pi$
$71$			11.1427i			1.32239i	−0.750213	+	0.661196i	$0.770049\pi$
$72$	4.12223	−	2.37997i	0.485809	−	0.280482i
$73$	8.08112	+	4.66564i	0.945824	+	0.546072i	0.891781	−	0.452467i	$-0.149456\pi$
$73$	8.08112	+	4.66564i	0.945824	+	0.546072i	0.0540426	+	0.998539i	$0.482789\pi$
$74$	−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	$0.210895\pi$
$83$			11.2082i			1.23026i	−0.788428	+	0.615128i	$0.789105\pi$
$84$		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	−0.992787	−	0.119892i	$-0.961745\pi$
$89$	−13.0694	+	7.54561i	−1.38535	+	0.799833i	−0.392564	+	0.919725i	$0.628412\pi$
$90$	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	$0.128892\pi$
$97$			7.75994i			0.787903i	−0.919131	+	0.393951i	$0.871108\pi$
$98$		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	0.933626	−	0.358249i	$-0.116626\pi$
$109$	11.3819	+	6.57133i	1.09019	+	0.629420i	0.156561	+	0.987668i	$0.449959\pi$
$110$	−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
$117$	1.55281	+	17.0918i	0.143557	+	1.58014i
$118$	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
$130$	7.50084	−	5.28952i	0.657867	−	0.463921i
$131$	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	0.851945	−	0.523630i	$-0.175423\pi$
$137$	9.64983	+	5.57133i	0.824441	+	0.475991i	−0.0275046	+	0.999622i	$0.508756\pi$
$138$	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
$143$	−6.92205	−	9.81587i	−0.578851	−	0.820844i
$144$	−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	−0.691779	−	0.722109i	$-0.743173\pi$
$149$	−5.03281	+	2.90570i	−0.412304	+	0.238044i	0.279475	+	0.960153i	$0.409840\pi$
$150$	−3.57072	−	2.06156i	−0.291548	−	0.168326i
$151$	−2.67707	−	1.54561i	−0.217857	−	0.125780i	0.387101	−	0.922037i	$-0.373477\pi$
$151$	−2.67707	−	1.54561i	−0.217857	−	0.125780i	−0.604958	+	0.796258i	$0.706810\pi$
$152$	−2.27280	−	3.93661i	−0.184349	−	0.319301i
$153$	−33.7538			−2.72883
$154$		0			0
$155$	8.48012			0.681140
$156$	−0.908751	−	10.0027i	−0.0727583	−	0.800855i
$157$	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	−0.118724	−	0.992927i	$-0.537881\pi$
$163$	8.70481	−	5.02573i	0.681814	−	0.393645i	0.800538	+	0.599282i	$0.204547\pi$
$164$	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	$-0.613009\pi$
$167$		−	24.2339i		−	1.87527i	0.347616	−	0.937637i	$-0.386991\pi$
$168$		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	0.420701	−	0.907199i	$-0.361784\pi$
$193$	−2.14785	−	1.24006i	−0.154605	−	0.0892614i	−0.575307	+	0.817938i	$0.695117\pi$
$194$	−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	$-0.897892\pi$
$197$		−	8.85116i		−	0.630619i	0.948989	−	0.315309i	$-0.102108\pi$
$198$	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
$208$	0.326224	+	3.59076i	0.0226196	+	0.248975i
$209$	−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
$221$	−20.8948	+	14.7348i	−1.40554	+	0.991172i
$222$	−5.23697	−	9.07070i	−0.351483	−	0.608786i
$223$		−	12.9026i		−	0.864023i	−0.901868	−	0.432011i	$-0.857804\pi$
$223$		−	12.9026i		−	0.864023i	0.901868	−	0.432011i	$-0.142196\pi$
$224$		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	0.217644	−	0.976028i	$-0.430163\pi$
$227$	−7.81651	−	4.51286i	−0.518800	−	0.299529i	−0.736443	+	0.676499i	$0.763496\pi$
$228$	−10.9661	−	6.33127i	−0.726247	−	0.419299i
$229$	12.2702	−	7.08420i	0.810837	−	0.468137i	−0.0364095	−	0.999337i	$-0.511592\pi$
$229$	12.2702	−	7.08420i	0.810837	−	0.468137i	0.847246	+	0.531200i	$0.178259\pi$
$230$	−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	$0.755586\pi$
$234$	−9.89068	−	14.0255i	−0.646574	−	0.916879i
$235$	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	$0.0635388\pi$
$239$			6.13098i			0.396580i	−0.980143	+	0.198290i	$0.936461\pi$
$240$	6.14117	−	3.54561i	0.396411	−	0.228868i
$241$	23.6642	+	13.6625i	1.52435	+	0.880082i	0.999584	+	0.0288337i	$0.00917932\pi$
$241$	23.6642	+	13.6625i	1.52435	+	0.880082i	0.524763	+	0.851248i	$0.324154\pi$
$242$	−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
$247$	16.3222	−	1.48289i	1.03856	−	0.0943538i
$248$	−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	−0.535930	−	0.844263i	$-0.680039\pi$
$271$	−1.19748	+	0.691364i	−0.0727415	+	0.0419974i	0.463188	+	0.886260i	$0.346705\pi$
$272$	−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	$-0.931661\pi$
$281$		−	7.14267i		−	0.426096i	0.977042	−	0.213048i	$-0.0683390\pi$
$282$	−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	$0.0716092\pi$
$293$			7.63682i			0.446148i	−0.974802	+	0.223074i	$0.928391\pi$
$294$		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
$299$	−0.574135	−	6.31953i	−0.0332031	−	0.365468i
$300$	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	$0.134305\pi$
$307$			14.3508i			0.819045i	−0.912300	+	0.409522i	$0.865695\pi$
$308$		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	$0.186375\pi$
$312$	5.78834	+	8.20819i	0.327700	+	0.464697i
$313$	−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	−0.113521	−	0.993536i	$-0.536213\pi$
$317$	12.2877	−	7.09430i	0.690146	−	0.398456i	0.803667	+	0.595080i	$0.202880\pi$
$318$	−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
$325$	−4.36129	+	3.07554i	−0.241921	+	0.170600i
$326$	−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	−0.566322	−	0.824184i	$-0.691634\pi$
$331$	−2.46917	+	1.42558i	−0.135718	+	0.0783569i	0.430604	+	0.902541i	$0.358301\pi$
$332$	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	$0.846448\pi$
$338$	−12.2454	−	4.36467i	−0.666062	−	0.237407i
$339$	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	$0.343942\pi$
$349$			32.9619i			1.76441i	−0.470864	+	0.882206i	$0.656058\pi$
$350$		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	0.519488	−	0.854478i	$-0.326123\pi$
$353$	0.737123	+	0.425578i	0.0392331	+	0.0226512i	−0.480255	+	0.877129i	$0.659456\pi$
$354$	−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	−0.976274	−	0.216540i	$-0.930523\pi$
$359$	−24.1935	+	13.9681i	−1.27688	+	0.737208i	−0.300608	+	0.953748i	$0.597190\pi$
$360$	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	$-0.639164\pi$
$379$		−	35.2736i		−	1.81189i	0.423400	−	0.905943i	$-0.360836\pi$
$380$	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	−0.645910	−	0.763413i	$-0.723522\pi$
$383$	−6.02239	+	3.47703i	−0.307730	+	0.177668i	0.338180	+	0.941081i	$0.390189\pi$
$384$			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	$0.123983\pi$
$390$	2.31332	+	25.4629i	0.117140	+	1.28936i
$391$	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	−0.0358003	−	0.999359i	$-0.511398\pi$
$397$	16.1744	−	9.33829i	0.811770	−	0.468675i	0.847570	+	0.530683i	$0.178065\pi$
$398$		−	1.09122i		−	0.0546977i
$399$		0			0
$400$	−1.48012			−0.0740059
$401$	−18.6368	+	10.7599i	−0.930676	+	0.537326i	−0.887025	−	0.461721i	$-0.847232\pi$
$401$	−18.6368	+	10.7599i	−0.930676	+	0.537326i	−0.0436504	+	0.999047i	$0.513899\pi$
$402$	8.02264	−	13.8956i	0.400133	−	0.693050i
$403$	−6.92205	−	9.81587i	−0.344812	−	0.488963i
$404$	−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	0.0254675	−	0.999676i	$-0.491893\pi$
$409$	−16.7360	−	9.66255i	−0.827543	−	0.477782i	−0.853011	+	0.521893i	$0.825226\pi$
$410$	−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
$416$	−2.07790	−	2.94658i	−0.101877	−	0.144468i
$417$	−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	$-0.826002\pi$
$421$		−	21.3313i		−	1.03962i	0.854281	−	0.519811i	$-0.173998\pi$
$422$	−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
$429$	33.3216	−	3.02730i	1.60878	−	0.146159i
$430$	−11.5713	+	20.0421i	−0.558019	+	0.966518i
$431$	−10.0211	−	5.78567i	−0.482698	−	0.278686i	0.238842	−	0.971058i	$-0.423232\pi$
$431$	−10.0211	−	5.78567i	−0.482698	−	0.278686i	−0.721540	+	0.692373i	$0.756565\pi$
$432$	−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	$0.0735260\pi$
$449$			9.70231i			0.457880i	−0.973440	+	0.228940i	$0.926474\pi$
$450$	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	−0.999248	−	0.0387828i	$-0.987652\pi$
$457$	−31.3242	+	18.0850i	−1.46528	+	0.845982i	−0.466037	+	0.884765i	$0.654319\pi$
$458$	−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	$-0.837568\pi$
$461$		−	20.9743i		−	0.976869i	0.872600	−	0.488435i	$-0.162432\pi$
$462$		0			0
$463$		−	24.8450i		−	1.15464i	−0.816517	−	0.577322i	$-0.804098\pi$
$463$		−	24.8450i		−	1.15464i	0.816517	−	0.577322i	$-0.195902\pi$
$464$	−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	0.868201	−	0.496212i	$-0.165276\pi$
$479$	19.0971	+	11.0257i	0.872570	+	0.503778i	0.00436831	+	0.999990i	$0.498610\pi$
$480$	−3.54561	+	6.14117i	−0.161834	+	0.280305i
$481$	−13.5011	+	1.22658i	−0.615595	+	0.0559274i
$482$	−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	0.410579	−	0.911825i	$-0.365327\pi$
$487$	−3.83534	−	2.21433i	−0.173796	−	0.100341i	−0.584374	+	0.811484i	$0.698660\pi$
$488$	−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
$494$	−13.3940	+	9.44532i	−0.602624	+	0.424965i
$495$	−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	0.0194086	−	0.999812i	$-0.493822\pi$
$499$	19.9922	−	11.5425i	0.894975	−	0.516714i	0.875567	+	0.483097i	$0.160488\pi$
$500$	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
$507$	−35.6208	+	6.52622i	−1.58197	+	0.289840i
$508$	−6.45130	+	11.1740i	−0.286230	+	0.495766i
$509$	−21.4151	+	12.3640i	−0.949208	+	0.548026i	−0.892835	−	0.450384i	$-0.851287\pi$
$509$	−21.4151	+	12.3640i	−0.949208	+	0.548026i	−0.0563732	+	0.998410i	$0.517954\pi$
$510$	−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
$520$	−0.830438	−	9.14067i	−0.0364171	−	0.400845i
$521$	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	0.130380	−	0.991464i	$-0.458380\pi$
$541$	24.5201	−	14.1567i	1.05420	−	0.608644i	0.923823	+	0.382820i	$0.125047\pi$
$542$	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	0.424931	−	0.905226i	$-0.360298\pi$
$557$	−3.45875	−	1.99691i	−0.146552	−	0.0846119i	−0.571483	+	0.820614i	$0.693632\pi$
$558$	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	$0.260856\pi$
$572$	−11.9618	+	1.08674i	−0.500149	+	0.0454390i
$573$	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	−0.215333	−	0.976541i	$-0.569084\pi$
$577$	−28.0734	−	16.2082i	−1.16871	−	0.674754i	−0.953376	+	0.301786i	$0.902417\pi$
$578$	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
$585$	25.1778	+	35.7035i	1.04097	+	1.47616i
$586$	−3.81841	−	6.61368i	−0.157737	−	0.273209i
$587$		−	4.03742i		−	0.166642i	−0.996523	−	0.0833210i	$-0.973447\pi$
$587$		−	4.03742i		−	0.166642i	0.996523	−	0.0833210i	$-0.0265527\pi$
$588$		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	−0.0909105	−	0.995859i	$-0.528978\pi$
$593$	17.6810	−	10.2082i	0.726074	−	0.419199i	0.816984	+	0.576660i	$0.195644\pi$
$594$	−16.3319			−0.670107
$595$		0			0
$596$			5.81139i			0.238044i
$597$	−1.51988	−	2.63251i	−0.0622046	−	0.107742i
$598$	3.65698	+	5.18581i	0.149545	+	0.212063i
$599$	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
$611$	−40.6879	+	3.69653i	−1.64606	+	0.149546i
$612$	−16.8769	+	29.2316i	−0.682208	+	1.18162i
$613$	−20.1502	−	11.6337i	−0.813860	−	0.469882i	0.0344347	−	0.999407i	$-0.489037\pi$
$613$	−20.1502	−	11.6337i	−0.813860	−	0.469882i	−0.848294	+	0.529525i	$0.822370\pi$
$614$	−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	$-0.990260\pi$
$617$		−	1.51988i		−	0.0611881i	0.999532	−	0.0305941i	$-0.00973991\pi$
$618$	−31.5820	+	18.2339i	−1.27041	+	0.733474i
$619$	−0.675059	−	0.389746i	−0.0271329	−	0.0156652i	0.486372	−	0.873752i	$-0.338320\pi$
$619$	−0.675059	−	0.389746i	−0.0271329	−	0.0156652i	−0.513505	+	0.858087i	$0.671653\pi$
$620$	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	$0.223668\pi$
$631$			32.4678i			1.29252i	−0.763117	+	0.646261i	$0.776332\pi$
$632$	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	$0.0430831\pi$
$643$			6.84330i			0.269873i	−0.990854	+	0.134937i	$0.956917\pi$
$644$		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	0.951022	−	0.309124i	$-0.100036\pi$
$661$	29.7932	+	17.2011i	1.15882	+	0.669047i	0.207801	+	0.978171i	$0.433369\pi$
$662$	1.42558	−	2.46917i	0.0554067	−	0.0959672i
$663$	−6.44415	−	70.9311i	−0.250270	−	2.75474i
$664$	−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
$676$	12.7872	−	2.34279i	0.491814	−	0.0901072i
$677$	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	0.0919188	−	0.995767i	$-0.470700\pi$
$683$	−18.9338	−	10.9314i	−0.724481	−	0.418279i	−0.816400	+	0.577487i	$0.804033\pi$
$684$	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
$689$	−17.6795	+	12.4674i	−0.673535	+	0.474970i
$690$	6.24006	−	10.8081i	0.237555	−	0.411457i
$691$	9.30145	−	5.37020i	0.353844	−	0.204292i	−0.312533	−	0.949907i	$-0.601178\pi$
$691$	9.30145	−	5.37020i	0.353844	−	0.204292i	0.666377	+	0.745615i	$0.267844\pi$
$692$	−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	$0.567802\pi$
$702$	17.6041	−	1.59935i	0.664424	−	0.0603635i
$703$	−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	−0.413042	−	0.910712i	$-0.635534\pi$
$709$	4.50359	−	2.60015i	0.169136	−	0.0976506i	0.582178	+	0.813061i	$0.302201\pi$
$710$	−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	−0.625671	−	0.780087i	$-0.715175\pi$
$733$	−7.11860	+	4.10992i	−0.262931	+	0.151803i	0.362740	+	0.931891i	$0.381841\pi$
$734$			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	0.474562	−	0.880222i	$-0.342607\pi$
$739$	−1.37151	−	0.791843i	−0.0504519	−	0.0291284i	−0.525014	+	0.851094i	$0.675940\pi$
$740$	−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	$0.0703365\pi$
$743$			11.9485i			0.438350i	−0.975686	+	0.219175i	$0.929663\pi$
$744$	−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
$754$	27.1869	−	2.46995i	0.990087	−	0.0899503i
$755$	−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	$0.720588\pi$
$761$	−44.8147	+	25.8738i	−1.62453	+	0.937924i	−0.985686	+	0.168590i	$0.946079\pi$
$762$			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
$767$	16.7593	+	23.7656i	0.605142	+	0.858126i
$768$	−1.39283	−	2.41246i	−0.0502595	−	0.0870521i
$769$			24.2401i			0.874119i	0.899433	+	0.437059i	$0.143980\pi$
$769$			24.2401i			0.874119i	−0.899433	+	0.437059i	$0.856020\pi$
$770$		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	0.218719	−	0.975788i	$-0.429812\pi$
$773$	−14.3735	−	8.29853i	−0.516978	−	0.298477i	−0.735697	+	0.677310i	$0.763145\pi$
$774$	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
$780$	−14.7348	−	20.8948i	−0.527592	−	0.748155i
$781$	−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	0.366190	−	0.930540i	$-0.380662\pi$
$787$	−7.19816	−	4.15586i	−0.256587	−	0.148140i	−0.622777	+	0.782400i	$0.713995\pi$
$788$	−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
$793$	−0.256303	−	2.82114i	−0.00910160	−	0.100182i
$794$	−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	$0.112517\pi$
$811$			19.7163i			0.692335i	−0.938173	+	0.346167i	$0.887483\pi$
$812$		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	−0.239228	−	0.970963i	$-0.576894\pi$
$821$	13.8118	−	7.97427i	0.482037	−	0.278304i	0.721265	+	0.692659i	$0.243561\pi$
$822$	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	$0.329156\pi$
$827$			49.4280i			1.71878i	−0.511321	+	0.859390i	$0.670844\pi$
$828$	−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	$0.0929020\pi$
$839$			16.6687i			0.575468i	−0.957710	+	0.287734i	$0.907098\pi$
$840$		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
$845$	31.1720	+	11.1107i	1.07235	+	0.382221i
$846$	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	$-0.870414\pi$
$853$		−	23.1286i		−	0.791909i	0.918270	−	0.395955i	$-0.129586\pi$
$854$		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	$0.241571\pi$
$858$	−27.3437	+	19.2825i	−0.933500	+	0.658295i
$859$	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	−0.953226	−	0.302260i	$-0.902259\pi$
$863$	−34.3143	+	19.8114i	−1.16807	+	0.674388i	−0.214848	+	0.976647i	$0.568926\pi$
$864$	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
$871$	−11.9686	−	16.9721i	−0.405540	−	0.575079i
$872$	−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	0.392502	−	0.919751i	$-0.371610\pi$
$877$	41.0239	−	23.6852i	1.38528	−	0.799792i	0.992779	+	0.119959i	$0.0382764\pi$
$878$	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	$0.509736\pi$
$884$	2.31332	+	25.4629i	0.0778055	+	0.856409i
$885$	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	−0.481372	−	0.876517i	$-0.659861\pi$
$929$	1.12861	−	0.651601i	0.0370284	−	0.0213783i	0.518400	+	0.855138i	$0.326528\pi$
$930$		−	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
$936$	−17.0918	+	1.55281i	−0.558664	+	0.0507551i
$937$	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	0.353168	−	0.935560i	$-0.385105\pi$
$941$	−8.60354	−	4.96726i	−0.280467	−	0.161928i	−0.633635	+	0.773632i	$0.718438\pi$
$942$	−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	0.193295	−	0.981141i	$-0.438082\pi$
$947$	35.0704	−	20.2479i	1.13964	−	0.657969i	0.946340	+	0.323172i	$0.104749\pi$
$948$	6.75685	−	11.7032i	0.219452	−	0.380103i
$949$	−19.3895	−	27.4953i	−0.629408	−	0.892537i
$950$	−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
$962$	11.0790	−	7.81278i	0.357200	−	0.251894i
$963$	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	$-0.976258\pi$
$967$		−	4.63448i		−	0.149035i	0.997220	−	0.0745174i	$-0.0237416\pi$
$968$	−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
$975$	−1.34506	−	14.8051i	−0.0430764	−	0.474144i
$976$	0.392834	−	0.680408i	0.0125743	−	0.0217793i
$977$	4.10676	+	2.37104i	0.131387	+	0.0758562i	0.564253	−	0.825602i	$-0.309164\pi$
$977$	4.10676	+	2.37104i	0.131387	+	0.0758562i	−0.432866	+	0.901458i	$0.642498\pi$
$978$	−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	0.134885	−	0.990861i	$-0.456933\pi$
$983$	−20.5607	−	11.8707i	−0.655783	−	0.378617i	−0.790668	+	0.612245i	$0.790267\pi$
$984$	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.753.1		12
7.2	even	3	inner	1274.2.n.m.961.4		12
7.3	odd	6		1274.2.d.l.883.1		6
7.4	even	3		182.2.d.b.155.3	✓	6
7.5	odd	6		1274.2.n.n.961.6		12
7.6	odd	2		1274.2.n.n.753.3		12
13.12	even	2	inner	1274.2.n.m.753.4		12
21.11	odd	6		1638.2.c.i.883.4		6
28.11	odd	6		1456.2.k.b.337.2		6
91.12	odd	6		1274.2.n.n.961.3		12
91.18	odd	12		2366.2.a.x.1.3		3
91.25	even	6		182.2.d.b.155.6	yes	6
91.38	odd	6		1274.2.d.l.883.4		6
91.51	even	6	inner	1274.2.n.m.961.1		12
91.60	odd	12		2366.2.a.bc.1.3		3
91.90	odd	2		1274.2.n.n.753.6		12
273.116	odd	6		1638.2.c.i.883.3		6
364.207	odd	6		1456.2.k.b.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.b.155.3	✓	6	7.4	even	3
182.2.d.b.155.6	yes	6	91.25	even	6
1274.2.d.l.883.1		6	7.3	odd	6
1274.2.d.l.883.4		6	91.38	odd	6
1274.2.n.m.753.1		12	1.1	even	1	trivial
1274.2.n.m.753.4		12	13.12	even	2	inner
1274.2.n.m.961.1		12	91.51	even	6	inner
1274.2.n.m.961.4		12	7.2	even	3	inner
1274.2.n.n.753.3		12	7.6	odd	2
1274.2.n.n.753.6		12	91.90	odd	2
1274.2.n.n.961.3		12	91.12	odd	6
1274.2.n.n.961.6		12	7.5	odd	6
1456.2.k.b.337.1		6	364.207	odd	6
1456.2.k.b.337.2		6	28.11	odd	6
1638.2.c.i.883.3		6	273.116	odd	6
1638.2.c.i.883.4		6	21.11	odd	6
2366.2.a.x.1.3		3	91.18	odd	12
2366.2.a.bc.1.3		3	91.60	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} +(3.59076 - 0.326224i) 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} +(8.20819 - 5.78834i) 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} +(-2.94658 + 2.07790i) 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} +(-9.14067 + 0.830438i) 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

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