LMFDB - Embedded newform 990.2.n.b.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(91,990)] 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("990.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,0,-1,-1,0,0,-1,0,4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	990.91
Dual form			990.2.n.b.631.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.309017 + 0.951057i) q^{8} +1.00000 q^{10} +(-3.04508 + 1.31433i) q^{11} +(1.11803 - 0.812299i) q^{13} +(-0.809017 - 0.587785i) q^{16} +(1.30902 + 0.951057i) q^{17} +(0.618034 + 1.90211i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(1.69098 - 2.85317i) q^{22} -4.85410 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.427051 + 1.31433i) q^{26} +(-2.04508 + 6.29412i) q^{29} +(3.35410 - 2.43690i) q^{31} +1.00000 q^{32} -1.61803 q^{34} +(-2.11803 + 6.51864i) q^{37} +(-1.61803 - 1.17557i) q^{38} +(0.309017 - 0.951057i) q^{40} +(1.14590 + 3.52671i) q^{41} -2.85410 q^{43} +(0.309017 + 3.30220i) q^{44} +(3.92705 - 2.85317i) q^{46} +(0.336881 + 1.03681i) q^{47} +(5.66312 + 4.11450i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.427051 - 1.31433i) q^{52} +(-8.85410 + 6.43288i) q^{53} +(3.23607 + 0.726543i) q^{55} +(-2.04508 - 6.29412i) q^{58} +(-0.354102 + 1.08981i) q^{59} +(6.23607 + 4.53077i) q^{61} +(-1.28115 + 3.94298i) q^{62} +(-0.809017 + 0.587785i) q^{64} -1.38197 q^{65} -12.6180 q^{67} +(1.30902 - 0.951057i) q^{68} +(8.85410 + 6.43288i) q^{71} +(-2.11803 - 6.51864i) q^{74} +2.00000 q^{76} +(-9.78115 + 7.10642i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-3.00000 - 2.17963i) q^{82} +(0.618034 + 0.449028i) q^{83} +(-0.500000 - 1.53884i) q^{85} +(2.30902 - 1.67760i) q^{86} +(-2.19098 - 2.48990i) q^{88} -4.47214 q^{89} +(-1.50000 + 4.61653i) q^{92} +(-0.881966 - 0.640786i) q^{94} +(0.618034 - 1.90211i) q^{95} +(-7.47214 + 5.42882i) q^{97} -7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - q^{5} - q^{8} + 4 q^{10} - q^{11} - q^{16} + 3 q^{17} - 2 q^{19} - q^{20} + 9 q^{22} - 6 q^{23} - q^{25} + 5 q^{26} + 3 q^{29} + 4 q^{32} - 2 q^{34} - 4 q^{37} - 2 q^{38} - q^{40}+ \cdots - 28 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - q^5 - q^8 + 4 * q^10 - q^11 - q^16 + 3 * q^17 - 2 * q^19 - q^20 + 9 * q^22 - 6 * q^23 - q^25 + 5 * q^26 + 3 * q^29 + 4 * q^32 - 2 * q^34 - 4 * q^37 - 2 * q^38 - q^40 + 18 * q^41 + 2 * q^43 - q^44 + 9 * q^46 + 17 * q^47 + 7 * q^49 - q^50 + 5 * q^52 - 22 * q^53 + 4 * q^55 + 3 * q^58 + 12 * q^59 + 16 * q^61 + 15 * q^62 - q^64 - 10 * q^65 - 46 * q^67 + 3 * q^68 + 22 * q^71 - 4 * q^74 + 8 * q^76 - 19 * q^79 - q^80 - 12 * q^82 - 2 * q^83 - 2 * q^85 + 7 * q^86 - 11 * q^88 - 6 * q^92 - 8 * q^94 - 2 * q^95 - 12 * q^97 - 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$7$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$11$	−3.04508	+	1.31433i	−0.918128	+	0.396285i
$12$		0			0
$13$	1.11803	−	0.812299i	0.310087	−	0.225291i	−0.421847	−	0.906667i	$-0.638618\pi$
$13$	1.11803	−	0.812299i	0.310087	−	0.225291i	0.731934	+	0.681376i	$0.238618\pi$
$14$		0			0
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.30902	+	0.951057i	0.317483	+	0.230665i	0.735101	−	0.677958i	$-0.237135\pi$
$17$	1.30902	+	0.951057i	0.317483	+	0.230665i	−0.417618	+	0.908623i	$0.637135\pi$
$18$		0			0
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	0.996584	−	0.0825877i	$-0.0263185\pi$
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	−0.854797	+	0.518962i	$0.826318\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$		0			0
$22$	1.69098	−	2.85317i	0.360519	−	0.608298i
$23$	−4.85410			−1.01215			−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410			−1.01215			−0.506075	+	0.862489i	$0.668904\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.427051	+	1.31433i	−0.0837516	+	0.257761i
$27$		0			0
$28$		0			0
$29$	−2.04508	+	6.29412i	−0.379763	+	1.16879i	0.560446	+	0.828191i	$0.310630\pi$
$29$	−2.04508	+	6.29412i	−0.379763	+	1.16879i	−0.940209	+	0.340599i	$0.889370\pi$
$30$		0			0
$31$	3.35410	−	2.43690i	0.602414	−	0.437680i	−0.244321	−	0.969695i	$-0.578565\pi$
$31$	3.35410	−	2.43690i	0.602414	−	0.437680i	0.846735	+	0.532015i	$0.178565\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.61803			−0.277491
$35$		0			0
$36$		0			0
$37$	−2.11803	+	6.51864i	−0.348203	+	1.07166i	0.611644	+	0.791133i	$0.290508\pi$
$37$	−2.11803	+	6.51864i	−0.348203	+	1.07166i	−0.959847	+	0.280525i	$0.909492\pi$
$38$	−1.61803	−	1.17557i	−0.262480	−	0.190703i
$39$		0			0
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	1.14590	+	3.52671i	0.178959	+	0.550780i	0.999792	−	0.0203886i	$-0.00649033\pi$
$41$	1.14590	+	3.52671i	0.178959	+	0.550780i	−0.820833	+	0.571168i	$0.806490\pi$
$42$		0			0
$43$	−2.85410			−0.435246			−0.217623	−	0.976033i	$-0.569830\pi$
$43$	−2.85410			−0.435246			−0.217623	+	0.976033i	$0.569830\pi$
$44$	0.309017	+	3.30220i	0.0465861	+	0.497825i
$45$		0			0
$46$	3.92705	−	2.85317i	0.579012	−	0.420677i
$47$	0.336881	+	1.03681i	0.0491391	+	0.151235i	0.972615	−	0.232421i	$-0.0746648\pi$
$47$	0.336881	+	1.03681i	0.0491391	+	0.151235i	−0.923476	+	0.383656i	$0.874665\pi$
$48$		0			0
$49$	5.66312	+	4.11450i	0.809017	+	0.587785i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$		0			0
$52$	−0.427051	−	1.31433i	−0.0592213	−	0.182264i
$53$	−8.85410	+	6.43288i	−1.21620	+	0.883624i	−0.995779	−	0.0917797i	$-0.970744\pi$
$53$	−8.85410	+	6.43288i	−1.21620	+	0.883624i	−0.220425	+	0.975404i	$0.570744\pi$
$54$		0			0
$55$	3.23607	+	0.726543i	0.436351	+	0.0979670i
$56$		0			0
$57$		0			0
$58$	−2.04508	−	6.29412i	−0.268533	−	0.826459i
$59$	−0.354102	+	1.08981i	−0.0461001	+	0.141882i	−0.971457	−	0.237215i	$-0.923765\pi$
$59$	−0.354102	+	1.08981i	−0.0461001	+	0.141882i	0.925357	+	0.379097i	$0.123765\pi$
$60$		0			0
$61$	6.23607	+	4.53077i	0.798447	+	0.580105i	0.910458	−	0.413601i	$-0.135729\pi$
$61$	6.23607	+	4.53077i	0.798447	+	0.580105i	−0.112011	+	0.993707i	$0.535729\pi$
$62$	−1.28115	+	3.94298i	−0.162707	+	0.500759i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.38197			−0.171412
$66$		0			0
$67$	−12.6180			−1.54154			−0.770769	−	0.637115i	$-0.780128\pi$
$67$	−12.6180			−1.54154			−0.770769	+	0.637115i	$0.780128\pi$
$68$	1.30902	−	0.951057i	0.158742	−	0.115333i
$69$		0			0
$70$		0			0
$71$	8.85410	+	6.43288i	1.05079	+	0.763443i	0.972362	−	0.233477i	$-0.0750105\pi$
$71$	8.85410	+	6.43288i	1.05079	+	0.763443i	0.0784263	+	0.996920i	$0.475010\pi$
$72$		0			0
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$	−2.11803	−	6.51864i	−0.246216	−	0.757776i
$75$		0			0
$76$	2.00000			0.229416
$77$		0			0
$78$		0			0
$79$	−9.78115	+	7.10642i	−1.10047	+	0.799535i	−0.981136	−	0.193320i	$-0.938075\pi$
$79$	−9.78115	+	7.10642i	−1.10047	+	0.799535i	−0.119330	+	0.992855i	$0.538075\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$		0			0
$82$	−3.00000	−	2.17963i	−0.331295	−	0.240700i
$83$	0.618034	+	0.449028i	0.0678380	+	0.0492872i	0.621187	−	0.783662i	$-0.286651\pi$
$83$	0.618034	+	0.449028i	0.0678380	+	0.0492872i	−0.553349	+	0.832949i	$0.686651\pi$
$84$		0			0
$85$	−0.500000	−	1.53884i	−0.0542326	−	0.166911i
$86$	2.30902	−	1.67760i	0.248988	−	0.180900i
$87$		0			0
$88$	−2.19098	−	2.48990i	−0.233560	−	0.265424i
$89$	−4.47214			−0.474045			−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214			−0.474045			−0.237023	+	0.971504i	$0.576172\pi$
$90$		0			0
$91$		0			0
$92$	−1.50000	+	4.61653i	−0.156386	+	0.481306i
$93$		0			0
$94$	−0.881966	−	0.640786i	−0.0909678	−	0.0660920i
$95$	0.618034	−	1.90211i	0.0634089	−	0.195153i
$96$		0			0
$97$	−7.47214	+	5.42882i	−0.758680	+	0.551214i	−0.898505	−	0.438963i	$-0.855346\pi$
$97$	−7.47214	+	5.42882i	−0.758680	+	0.551214i	0.139825	+	0.990176i	$0.455346\pi$
$98$	−7.00000			−0.707107
$99$		0			0
$100$	1.00000			0.100000
$101$	4.30902	−	3.13068i	0.428763	−	0.311515i	−0.352391	−	0.935853i	$-0.614631\pi$
$101$	4.30902	−	3.13068i	0.428763	−	0.311515i	0.781154	+	0.624338i	$0.214631\pi$
$102$		0			0
$103$	−3.00000	+	9.23305i	−0.295599	+	0.909760i	0.687421	+	0.726259i	$0.258743\pi$
$103$	−3.00000	+	9.23305i	−0.295599	+	0.909760i	−0.983020	+	0.183500i	$0.941257\pi$
$104$	1.11803	+	0.812299i	0.109632	+	0.0796525i
$105$		0			0
$106$	3.38197	−	10.4086i	0.328486	−	1.01097i
$107$	−0.909830	−	2.80017i	−0.0879566	−	0.270703i	0.897398	−	0.441223i	$-0.145455\pi$
$107$	−0.909830	−	2.80017i	−0.0879566	−	0.270703i	−0.985354	+	0.170520i	$0.945455\pi$
$108$		0			0
$109$	−5.70820			−0.546747			−0.273373	−	0.961908i	$-0.588139\pi$
$109$	−5.70820			−0.546747			−0.273373	+	0.961908i	$0.588139\pi$
$110$	−3.04508	+	1.31433i	−0.290337	+	0.125316i
$111$		0			0
$112$		0			0
$113$	−3.80902	−	11.7229i	−0.358322	−	1.10280i	−0.954058	−	0.299622i	$-0.903139\pi$
$113$	−3.80902	−	11.7229i	−0.358322	−	1.10280i	0.595736	−	0.803180i	$-0.296861\pi$
$114$		0			0
$115$	3.92705	+	2.85317i	0.366199	+	0.266059i
$116$	5.35410	+	3.88998i	0.497116	+	0.361176i
$117$		0			0
$118$	−0.354102	−	1.08981i	−0.0325977	−	0.100325i
$119$		0			0
$120$		0			0
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	−7.70820			−0.697868
$123$		0			0
$124$	−1.28115	−	3.94298i	−0.115051	−	0.354090i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−7.61803	−	5.53483i	−0.675991	−	0.491136i	0.196034	−	0.980597i	$-0.437194\pi$
$127$	−7.61803	−	5.53483i	−0.675991	−	0.491136i	−0.872025	+	0.489461i	$0.837194\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	1.11803	−	0.812299i	0.0980581	−	0.0712434i
$131$	1.85410			0.161994			0.0809968	−	0.996714i	$-0.474190\pi$
$131$	1.85410			0.161994			0.0809968	+	0.996714i	$0.474190\pi$
$132$		0			0
$133$		0			0
$134$	10.2082	−	7.41669i	0.881855	−	0.640705i
$135$		0			0
$136$	−0.500000	+	1.53884i	−0.0428746	+	0.131955i
$137$	0.500000	+	0.363271i	0.0427179	+	0.0310364i	0.608939	−	0.793217i	$-0.291595\pi$
$137$	0.500000	+	0.363271i	0.0427179	+	0.0310364i	−0.566221	+	0.824253i	$0.691595\pi$
$138$		0			0
$139$	2.70820	−	8.33499i	0.229707	−	0.706965i	−0.768073	−	0.640363i	$-0.778784\pi$
$139$	2.70820	−	8.33499i	0.229707	−	0.706965i	0.997780	−	0.0666024i	$-0.0212159\pi$
$140$		0			0
$141$		0			0
$142$	−10.9443			−0.918423
$143$	−2.33688	+	3.94298i	−0.195420	+	0.329729i
$144$		0			0
$145$	5.35410	−	3.88998i	0.444634	−	0.323045i
$146$		0			0
$147$		0			0
$148$	5.54508	+	4.02874i	0.455803	+	0.331160i
$149$	−1.07295	−	0.779543i	−0.0878994	−	0.0638627i	0.542968	−	0.839754i	$-0.317301\pi$
$149$	−1.07295	−	0.779543i	−0.0878994	−	0.0638627i	−0.630867	+	0.775891i	$0.717301\pi$
$150$		0			0
$151$	1.70820	+	5.25731i	0.139012	+	0.427834i	0.996192	−	0.0871818i	$-0.0277861\pi$
$151$	1.70820	+	5.25731i	0.139012	+	0.427834i	−0.857181	+	0.515016i	$0.827786\pi$
$152$	−1.61803	+	1.17557i	−0.131240	+	0.0953514i
$153$		0			0
$154$		0			0
$155$	−4.14590			−0.333007
$156$		0			0
$157$	3.48278	+	10.7189i	0.277956	+	0.855461i	0.988422	+	0.151729i	$0.0484842\pi$
$157$	3.48278	+	10.7189i	0.277956	+	0.855461i	−0.710466	+	0.703731i	$0.751516\pi$
$158$	3.73607	−	11.4984i	0.297226	−	0.914766i
$159$		0			0
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$		0			0
$162$		0			0
$163$	−8.92705	+	6.48588i	−0.699221	+	0.508014i	−0.879678	−	0.475569i	$-0.842242\pi$
$163$	−8.92705	+	6.48588i	−0.699221	+	0.508014i	0.180458	+	0.983583i	$0.442242\pi$
$164$	3.70820			0.289562
$165$		0			0
$166$	−0.763932			−0.0592926
$167$	13.5902	−	9.87384i	1.05164	−	0.764060i	0.0791155	−	0.996865i	$-0.474790\pi$
$167$	13.5902	−	9.87384i	1.05164	−	0.764060i	0.972523	+	0.232805i	$0.0747904\pi$
$168$		0			0
$169$	−3.42705	+	10.5474i	−0.263619	+	0.811337i
$170$	1.30902	+	0.951057i	0.100397	+	0.0729427i
$171$		0			0
$172$	−0.881966	+	2.71441i	−0.0672493	+	0.206972i
$173$	−3.00000	−	9.23305i	−0.228086	−	0.701976i	−0.997964	−	0.0637846i	$-0.979683\pi$
$173$	−3.00000	−	9.23305i	−0.228086	−	0.701976i	0.769878	−	0.638191i	$-0.220317\pi$
$174$		0			0
$175$		0			0
$176$	3.23607	+	0.726543i	0.243928	+	0.0547652i
$177$		0			0
$178$	3.61803	−	2.62866i	0.271183	−	0.197026i
$179$	2.57295	+	7.91872i	0.192311	+	0.591873i	0.999997	+	0.00226056i	$0.000719558\pi$
$179$	2.57295	+	7.91872i	0.192311	+	0.591873i	−0.807686	+	0.589613i	$0.799280\pi$
$180$		0			0
$181$	18.7082	+	13.5923i	1.39057	+	1.01031i	0.995803	+	0.0915270i	$0.0291748\pi$
$181$	18.7082	+	13.5923i	1.39057	+	1.01031i	0.394767	+	0.918781i	$0.370825\pi$
$182$		0			0
$183$		0			0
$184$	−1.50000	−	4.61653i	−0.110581	−	0.340335i
$185$	5.54508	−	4.02874i	0.407683	−	0.296199i
$186$		0			0
$187$	−5.23607	−	1.17557i	−0.382899	−	0.0859662i
$188$	1.09017			0.0795088
$189$		0			0
$190$	0.618034	+	1.90211i	0.0448369	+	0.137994i
$191$	4.00000	−	12.3107i	0.289430	−	0.890773i	−0.695606	−	0.718424i	$-0.744864\pi$
$191$	4.00000	−	12.3107i	0.289430	−	0.890773i	0.985036	−	0.172350i	$-0.0551360\pi$
$192$		0			0
$193$	−1.14590	−	0.832544i	−0.0824835	−	0.0599278i	0.545779	−	0.837929i	$-0.316234\pi$
$193$	−1.14590	−	0.832544i	−0.0824835	−	0.0599278i	−0.628263	+	0.778001i	$0.716234\pi$
$194$	2.85410	−	8.78402i	0.204913	−	0.630656i
$195$		0			0
$196$	5.66312	−	4.11450i	0.404508	−	0.293893i
$197$	24.3607			1.73563			0.867813	−	0.496890i	$-0.165525\pi$
$197$	24.3607			1.73563			0.867813	+	0.496890i	$0.165525\pi$
$198$		0			0
$199$	−20.0902			−1.42415			−0.712077	−	0.702101i	$-0.752245\pi$
$199$	−20.0902			−1.42415			−0.712077	+	0.702101i	$0.752245\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$		0			0
$202$	−1.64590	+	5.06555i	−0.115805	+	0.356411i
$203$		0			0
$204$		0			0
$205$	1.14590	−	3.52671i	0.0800330	−	0.246316i
$206$	−3.00000	−	9.23305i	−0.209020	−	0.643297i
$207$		0			0
$208$	−1.38197			−0.0958221
$209$	−4.38197	−	4.97980i	−0.303107	−	0.344460i
$210$		0			0
$211$	14.5623	−	10.5801i	1.00251	−	0.728366i	0.0398855	−	0.999204i	$-0.487301\pi$
$211$	14.5623	−	10.5801i	1.00251	−	0.728366i	0.962625	+	0.270838i	$0.0873007\pi$
$212$	3.38197	+	10.4086i	0.232274	+	0.714867i
$213$		0			0
$214$	2.38197	+	1.73060i	0.162828	+	0.118301i
$215$	2.30902	+	1.67760i	0.157474	+	0.114411i
$216$		0			0
$217$		0			0
$218$	4.61803	−	3.35520i	0.312773	−	0.227243i
$219$		0			0
$220$	1.69098	−	2.85317i	0.114006	−	0.192361i
$221$	2.23607			0.150414
$222$		0			0
$223$	−3.61803	−	11.1352i	−0.242281	−	0.745666i	−0.996072	−	0.0885506i	$-0.971777\pi$
$223$	−3.61803	−	11.1352i	−0.242281	−	0.745666i	0.753790	−	0.657115i	$-0.228223\pi$
$224$		0			0
$225$		0			0
$226$	9.97214	+	7.24518i	0.663337	+	0.481942i
$227$	3.94427	−	12.1392i	0.261791	−	0.805708i	−0.730625	−	0.682779i	$-0.760771\pi$
$227$	3.94427	−	12.1392i	0.261791	−	0.805708i	0.992415	−	0.122929i	$-0.0392288\pi$
$228$		0			0
$229$	−4.00000	+	2.90617i	−0.264327	+	0.192045i	−0.712053	−	0.702126i	$-0.752234\pi$
$229$	−4.00000	+	2.90617i	−0.264327	+	0.192045i	0.447725	+	0.894171i	$0.352234\pi$
$230$	−4.85410			−0.320070
$231$		0			0
$232$	−6.61803			−0.434495
$233$	−2.73607	+	1.98787i	−0.179246	+	0.130230i	−0.673790	−	0.738923i	$-0.735335\pi$
$233$	−2.73607	+	1.98787i	−0.179246	+	0.130230i	0.494545	+	0.869152i	$0.335335\pi$
$234$		0			0
$235$	0.336881	−	1.03681i	0.0219757	−	0.0676342i
$236$	0.927051	+	0.673542i	0.0603459	+	0.0438438i
$237$		0			0
$238$		0			0
$239$	−3.47214	−	10.6861i	−0.224594	−	0.691229i	−0.998333	−	0.0577239i	$-0.981616\pi$
$239$	−3.47214	−	10.6861i	−0.224594	−	0.691229i	0.773739	−	0.633505i	$-0.218384\pi$
$240$		0			0
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	−1.39919	+	10.9106i	−0.0899431	+	0.701363i
$243$		0			0
$244$	6.23607	−	4.53077i	0.399223	−	0.290053i
$245$	−2.16312	−	6.65740i	−0.138197	−	0.425325i
$246$		0			0
$247$	2.23607	+	1.62460i	0.142278	+	0.103371i
$248$	3.35410	+	2.43690i	0.212986	+	0.154743i
$249$		0			0
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−8.16312	+	5.93085i	−0.515251	+	0.374352i	−0.814812	−	0.579725i	$-0.803160\pi$
$251$	−8.16312	+	5.93085i	−0.515251	+	0.374352i	0.299561	+	0.954077i	$0.403160\pi$
$252$		0			0
$253$	14.7812	−	6.37988i	0.929283	−	0.401100i
$254$	9.41641			0.590838
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	8.79837	−	27.0786i	0.548827	−	1.68912i	−0.162884	−	0.986645i	$-0.552080\pi$
$257$	8.79837	−	27.0786i	0.548827	−	1.68912i	0.711711	−	0.702472i	$-0.247920\pi$
$258$		0			0
$259$		0			0
$260$	−0.427051	+	1.31433i	−0.0264846	+	0.0815111i
$261$		0			0
$262$	−1.50000	+	1.08981i	−0.0926703	+	0.0673289i
$263$	17.0344			1.05039			0.525194	−	0.850982i	$-0.323993\pi$
$263$	17.0344			1.05039			0.525194	+	0.850982i	$0.323993\pi$
$264$		0			0
$265$	10.9443			0.672301
$266$		0			0
$267$		0			0
$268$	−3.89919	+	12.0005i	−0.238181	+	0.733045i
$269$	14.3541	+	10.4289i	0.875185	+	0.635859i	0.931973	−	0.362527i	$-0.118086\pi$
$269$	14.3541	+	10.4289i	0.875185	+	0.635859i	−0.0567882	+	0.998386i	$0.518086\pi$
$270$		0			0
$271$	8.73607	−	26.8869i	0.530678	−	1.63326i	−0.222128	−	0.975018i	$-0.571300\pi$
$271$	8.73607	−	26.8869i	0.530678	−	1.63326i	0.752806	−	0.658242i	$-0.228700\pi$
$272$	−0.500000	−	1.53884i	−0.0303170	−	0.0933060i
$273$		0			0
$274$	−0.618034			−0.0373368
$275$	−2.19098	−	2.48990i	−0.132121	−	0.150147i
$276$		0			0
$277$	0.454915	−	0.330515i	0.0273332	−	0.0198587i	−0.574035	−	0.818831i	$-0.694623\pi$
$277$	0.454915	−	0.330515i	0.0273332	−	0.0198587i	0.601368	+	0.798972i	$0.294623\pi$
$278$	2.70820	+	8.33499i	0.162427	+	0.499900i
$279$		0			0
$280$		0			0
$281$	14.7082	+	10.6861i	0.877418	+	0.637481i	0.932567	−	0.360997i	$-0.117563\pi$
$281$	14.7082	+	10.6861i	0.877418	+	0.637481i	−0.0551492	+	0.998478i	$0.517563\pi$
$282$		0			0
$283$	0.954915	+	2.93893i	0.0567638	+	0.174701i	0.975419	−	0.220360i	$-0.0707233\pi$
$283$	0.954915	+	2.93893i	0.0567638	+	0.174701i	−0.918655	+	0.395061i	$0.870723\pi$
$284$	8.85410	−	6.43288i	0.525394	−	0.381721i
$285$		0			0
$286$	−0.427051	−	4.56352i	−0.0252521	−	0.269847i
$287$		0			0
$288$		0			0
$289$	−4.44427	−	13.6781i	−0.261428	−	0.804592i
$290$	−2.04508	+	6.29412i	−0.120092	+	0.369604i
$291$		0			0
$292$		0			0
$293$	−0.472136	+	1.45309i	−0.0275825	+	0.0848901i	−0.963900	−	0.266264i	$-0.914211\pi$
$293$	−0.472136	+	1.45309i	−0.0275825	+	0.0848901i	0.936318	+	0.351154i	$0.114211\pi$
$294$		0			0
$295$	0.927051	−	0.673542i	0.0539750	−	0.0392151i
$296$	−6.85410			−0.398387
$297$		0			0
$298$	1.32624			0.0768269
$299$	−5.42705	+	3.94298i	−0.313854	+	0.228029i
$300$		0			0
$301$		0			0
$302$	−4.47214	−	3.24920i	−0.257343	−	0.186970i
$303$		0			0
$304$	0.618034	−	1.90211i	0.0354467	−	0.109094i
$305$	−2.38197	−	7.33094i	−0.136391	−	0.419768i
$306$		0			0
$307$	−32.9787			−1.88219			−0.941097	−	0.338136i	$-0.890204\pi$
$307$	−32.9787			−1.88219			−0.941097	+	0.338136i	$0.890204\pi$
$308$		0			0
$309$		0			0
$310$	3.35410	−	2.43690i	0.190500	−	0.138406i
$311$	−9.56231	−	29.4298i	−0.542229	−	1.66881i	−0.727490	−	0.686119i	$-0.759313\pi$
$311$	−9.56231	−	29.4298i	−0.542229	−	1.66881i	0.185261	−	0.982689i	$-0.440687\pi$
$312$		0			0
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.996871	+	0.0790445i	$0.0251869\pi$
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.383226	+	0.923655i	$0.374813\pi$
$314$	−9.11803	−	6.62464i	−0.514560	−	0.373850i
$315$		0			0
$316$	3.73607	+	11.4984i	0.210170	+	0.646837i
$317$	−13.3262	+	9.68208i	−0.748476	+	0.543800i	−0.895354	−	0.445355i	$-0.853078\pi$
$317$	−13.3262	+	9.68208i	−0.748476	+	0.543800i	0.146878	+	0.989155i	$0.453078\pi$
$318$		0			0
$319$	−2.04508	−	21.8541i	−0.114503	−	1.22359i
$320$	1.00000			0.0559017
$321$		0			0
$322$		0			0
$323$	−1.00000	+	3.07768i	−0.0556415	+	0.171247i
$324$		0			0
$325$	1.11803	+	0.812299i	0.0620174	+	0.0450583i
$326$	3.40983	−	10.4944i	0.188853	−	0.581230i
$327$		0			0
$328$	−3.00000	+	2.17963i	−0.165647	+	0.120350i
$329$		0			0
$330$		0			0
$331$	−4.58359			−0.251937			−0.125969	−	0.992034i	$-0.540204\pi$
$331$	−4.58359			−0.251937			−0.125969	+	0.992034i	$0.540204\pi$
$332$	0.618034	−	0.449028i	0.0339190	−	0.0246436i
$333$		0			0
$334$	−5.19098	+	15.9762i	−0.284038	+	0.874179i
$335$	10.2082	+	7.41669i	0.557734	+	0.405217i
$336$		0			0
$337$	7.94427	−	24.4500i	0.432752	−	1.33187i	−0.462621	−	0.886556i	$-0.653091\pi$
$337$	7.94427	−	24.4500i	0.432752	−	1.33187i	0.895373	−	0.445318i	$-0.146909\pi$
$338$	−3.42705	−	10.5474i	−0.186407	−	0.573702i
$339$		0			0
$340$	−1.61803			−0.0877502
$341$	−7.01064	+	11.8290i	−0.379648	+	0.640574i
$342$		0			0
$343$		0			0
$344$	−0.881966	−	2.71441i	−0.0475524	−	0.146351i
$345$		0			0
$346$	7.85410	+	5.70634i	0.422239	+	0.306775i
$347$	−3.00000	−	2.17963i	−0.161048	−	0.117009i	0.504342	−	0.863504i	$-0.331735\pi$
$347$	−3.00000	−	2.17963i	−0.161048	−	0.117009i	−0.665391	+	0.746495i	$0.731735\pi$
$348$		0			0
$349$	4.20163	+	12.9313i	0.224908	+	0.692195i	0.998301	+	0.0582685i	$0.0185580\pi$
$349$	4.20163	+	12.9313i	0.224908	+	0.692195i	−0.773393	+	0.633927i	$0.781442\pi$
$350$		0			0
$351$		0			0
$352$	−3.04508	+	1.31433i	−0.162304	+	0.0700539i
$353$	−0.270510			−0.0143978			−0.00719889	−	0.999974i	$-0.502291\pi$
$353$	−0.270510			−0.0143978			−0.00719889	+	0.999974i	$0.502291\pi$
$354$		0			0
$355$	−3.38197	−	10.4086i	−0.179496	−	0.552432i
$356$	−1.38197	+	4.25325i	−0.0732441	+	0.225422i
$357$		0			0
$358$	−6.73607	−	4.89404i	−0.356012	−	0.258658i
$359$	−8.76393	+	26.9726i	−0.462543	+	1.42356i	0.399504	+	0.916731i	$0.369182\pi$
$359$	−8.76393	+	26.9726i	−0.462543	+	1.42356i	−0.862047	+	0.506829i	$0.830818\pi$
$360$		0			0
$361$	12.1353	−	8.81678i	0.638698	−	0.464041i
$362$	−23.1246			−1.21540
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.14590	+	21.9928i	−0.373013	+	1.14802i	0.571797	+	0.820395i	$0.306247\pi$
$367$	−7.14590	+	21.9928i	−0.373013	+	1.14802i	−0.944810	+	0.327620i	$0.893753\pi$
$368$	3.92705	+	2.85317i	0.204712	+	0.148732i
$369$		0			0
$370$	−2.11803	+	6.51864i	−0.110111	+	0.338888i
$371$		0			0
$372$		0			0
$373$	−28.8328			−1.49291			−0.746453	−	0.665438i	$-0.768245\pi$
$373$	−28.8328			−1.49291			−0.746453	+	0.665438i	$0.768245\pi$
$374$	4.92705	−	2.12663i	0.254772	−	0.109965i
$375$		0			0
$376$	−0.881966	+	0.640786i	−0.0454839	+	0.0330460i
$377$	2.82624	+	8.69827i	0.145559	+	0.447983i
$378$		0			0
$379$	4.47214	+	3.24920i	0.229718	+	0.166900i	0.696690	−	0.717372i	$-0.254655\pi$
$379$	4.47214	+	3.24920i	0.229718	+	0.166900i	−0.466972	+	0.884272i	$0.654655\pi$
$380$	−1.61803	−	1.17557i	−0.0830034	−	0.0603055i
$381$		0			0
$382$	4.00000	+	12.3107i	0.204658	+	0.629872i
$383$	−17.0623	+	12.3965i	−0.871843	+	0.633431i	−0.931081	−	0.364813i	$-0.881133\pi$
$383$	−17.0623	+	12.3965i	−0.871843	+	0.633431i	0.0592378	+	0.998244i	$0.481133\pi$
$384$		0			0
$385$		0			0
$386$	1.41641			0.0720933
$387$		0			0
$388$	2.85410	+	8.78402i	0.144895	+	0.445941i
$389$	−0.0623059	+	0.191758i	−0.00315903	+	0.00972251i	−0.952624	−	0.304152i	$-0.901627\pi$
$389$	−0.0623059	+	0.191758i	−0.00315903	+	0.00972251i	0.949465	+	0.313874i	$0.101627\pi$
$390$		0			0
$391$	−6.35410	−	4.61653i	−0.321341	−	0.233468i
$392$	−2.16312	+	6.65740i	−0.109254	+	0.336249i
$393$		0			0
$394$	−19.7082	+	14.3188i	−0.992885	+	0.721373i
$395$	12.0902			0.608322
$396$		0			0
$397$	−18.8541			−0.946260			−0.473130	−	0.880993i	$-0.656876\pi$
$397$	−18.8541			−0.946260			−0.473130	+	0.880993i	$0.656876\pi$
$398$	16.2533	−	11.8087i	0.814704	−	0.591917i
$399$		0			0
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	3.70820	+	2.69417i	0.185179	+	0.134540i	0.676513	−	0.736431i	$-0.263490\pi$
$401$	3.70820	+	2.69417i	0.185179	+	0.134540i	−0.491334	+	0.870971i	$0.663490\pi$
$402$		0			0
$403$	1.77051	−	5.44907i	0.0881954	−	0.271437i
$404$	−1.64590	−	5.06555i	−0.0818865	−	0.252021i
$405$		0			0
$406$		0			0
$407$	−2.11803	−	22.6336i	−0.104987	−	1.12191i
$408$		0			0
$409$	22.4443	−	16.3067i	1.10980	−	0.806315i	0.127166	−	0.991881i	$-0.459412\pi$
$409$	22.4443	−	16.3067i	1.10980	−	0.806315i	0.982632	+	0.185566i	$0.0594119\pi$
$410$	1.14590	+	3.52671i	0.0565919	+	0.174172i
$411$		0			0
$412$	7.85410	+	5.70634i	0.386944	+	0.281131i
$413$		0			0
$414$		0			0
$415$	−0.236068	−	0.726543i	−0.0115881	−	0.0356646i
$416$	1.11803	−	0.812299i	0.0548161	−	0.0398262i
$417$		0			0
$418$	6.47214	+	1.45309i	0.316563	+	0.0710727i
$419$	−16.7426			−0.817932			−0.408966	−	0.912550i	$-0.634110\pi$
$419$	−16.7426			−0.817932			−0.408966	+	0.912550i	$0.634110\pi$
$420$		0			0
$421$	6.05573	+	18.6376i	0.295138	+	0.908342i	0.983175	+	0.182666i	$0.0584727\pi$
$421$	6.05573	+	18.6376i	0.295138	+	0.908342i	−0.688037	+	0.725676i	$0.741527\pi$
$422$	−5.56231	+	17.1190i	−0.270769	+	0.833341i
$423$		0			0
$424$	−8.85410	−	6.43288i	−0.429993	−	0.312408i
$425$	−0.500000	+	1.53884i	−0.0242536	+	0.0746448i
$426$		0			0
$427$		0			0
$428$	−2.94427			−0.142317
$429$		0			0
$430$	−2.85410			−0.137637
$431$	−30.6525	+	22.2703i	−1.47648	+	1.07272i	−0.497807	+	0.867288i	$0.665861\pi$
$431$	−30.6525	+	22.2703i	−1.47648	+	1.07272i	−0.978670	+	0.205436i	$0.934139\pi$
$432$		0			0
$433$	5.14590	−	15.8374i	0.247296	−	0.761099i	−0.747954	−	0.663750i	$-0.768964\pi$
$433$	5.14590	−	15.8374i	0.247296	−	0.761099i	0.995250	−	0.0973488i	$-0.0310362\pi$
$434$		0			0
$435$		0			0
$436$	−1.76393	+	5.42882i	−0.0844770	+	0.259994i
$437$	−3.00000	−	9.23305i	−0.143509	−	0.441677i
$438$		0			0
$439$	−24.5066			−1.16964			−0.584818	−	0.811165i	$-0.698834\pi$
$439$	−24.5066			−1.16964			−0.584818	+	0.811165i	$0.698834\pi$
$440$	0.309017	+	3.30220i	0.0147318	+	0.157426i
$441$		0			0
$442$	−1.80902	+	1.31433i	−0.0860462	+	0.0625162i
$443$	7.90983	+	24.3440i	0.375807	+	1.15662i	0.942932	+	0.332984i	$0.108056\pi$
$443$	7.90983	+	24.3440i	0.375807	+	1.15662i	−0.567125	+	0.823632i	$0.691944\pi$
$444$		0			0
$445$	3.61803	+	2.62866i	0.171511	+	0.124610i
$446$	9.47214	+	6.88191i	0.448519	+	0.325868i
$447$		0			0
$448$		0			0
$449$	−24.1803	+	17.5680i	−1.14114	+	0.829087i	−0.987278	−	0.159005i	$-0.949171\pi$
$449$	−24.1803	+	17.5680i	−1.14114	+	0.829087i	−0.153863	+	0.988092i	$0.549171\pi$
$450$		0			0
$451$	−8.12461	−	9.23305i	−0.382573	−	0.434767i
$452$	−12.3262			−0.579777
$453$		0			0
$454$	3.94427	+	12.1392i	0.185114	+	0.569722i
$455$		0			0
$456$		0			0
$457$	−0.145898	−	0.106001i	−0.00682482	−	0.00495852i	0.584368	−	0.811489i	$-0.301343\pi$
$457$	−0.145898	−	0.106001i	−0.00682482	−	0.00495852i	−0.591192	+	0.806531i	$0.701343\pi$
$458$	1.52786	−	4.70228i	0.0713924	−	0.219723i
$459$		0			0
$460$	3.92705	−	2.85317i	0.183100	−	0.133030i
$461$	−10.0902			−0.469946			−0.234973	−	0.972002i	$-0.575500\pi$
$461$	−10.0902			−0.469946			−0.234973	+	0.972002i	$0.575500\pi$
$462$		0			0
$463$	−7.41641			−0.344670			−0.172335	−	0.985038i	$-0.555131\pi$
$463$	−7.41641			−0.344670			−0.172335	+	0.985038i	$0.555131\pi$
$464$	5.35410	−	3.88998i	0.248558	−	0.180588i
$465$		0			0
$466$	1.04508	−	3.21644i	0.0484126	−	0.148999i
$467$	−3.32624	−	2.41665i	−0.153920	−	0.111829i	0.508160	−	0.861263i	$-0.330326\pi$
$467$	−3.32624	−	2.41665i	−0.153920	−	0.111829i	−0.662080	+	0.749433i	$0.730326\pi$
$468$		0			0
$469$		0			0
$470$	0.336881	+	1.03681i	0.0155392	+	0.0478246i
$471$		0			0
$472$	−1.14590			−0.0527442
$473$	8.69098	−	3.75123i	0.399612	−	0.172482i
$474$		0			0
$475$	−1.61803	+	1.17557i	−0.0742405	+	0.0539389i
$476$		0			0
$477$		0			0
$478$	9.09017	+	6.60440i	0.415775	+	0.302078i
$479$	−3.32624	−	2.41665i	−0.151980	−	0.110420i	0.509197	−	0.860650i	$-0.329943\pi$
$479$	−3.32624	−	2.41665i	−0.151980	−	0.110420i	−0.661176	+	0.750230i	$0.729943\pi$
$480$		0			0
$481$	2.92705	+	9.00854i	0.133462	+	0.410754i
$482$	−14.5623	+	10.5801i	−0.663295	+	0.481912i
$483$		0			0
$484$	−5.28115	−	9.64932i	−0.240052	−	0.438606i
$485$	9.23607			0.419388
$486$		0			0
$487$	−5.38197	−	16.5640i	−0.243880	−	0.750586i	−0.995819	−	0.0913526i	$-0.970881\pi$
$487$	−5.38197	−	16.5640i	−0.243880	−	0.750586i	0.751938	−	0.659233i	$-0.229119\pi$
$488$	−2.38197	+	7.33094i	−0.107827	+	0.331856i
$489$		0			0
$490$	5.66312	+	4.11450i	0.255834	+	0.185874i
$491$	6.10081	−	18.7764i	0.275326	−	0.847366i	−0.713807	−	0.700342i	$-0.753031\pi$
$491$	6.10081	−	18.7764i	0.275326	−	0.847366i	0.989133	−	0.147024i	$-0.0469693\pi$
$492$		0			0
$493$	−8.66312	+	6.29412i	−0.390167	+	0.283473i
$494$	−2.76393			−0.124355
$495$		0			0
$496$	−4.14590			−0.186156
$497$		0			0
$498$		0			0
$499$	3.18034	−	9.78808i	0.142372	−	0.438175i	−0.854292	−	0.519793i	$-0.826009\pi$
$499$	3.18034	−	9.78808i	0.142372	−	0.438175i	0.996664	+	0.0816187i	$0.0260090\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$		0			0
$502$	3.11803	−	9.59632i	0.139165	−	0.428305i
$503$	11.5729	+	35.6179i	0.516012	+	1.58812i	0.781433	+	0.623990i	$0.214489\pi$
$503$	11.5729	+	35.6179i	0.516012	+	1.58812i	−0.265420	+	0.964133i	$0.585511\pi$
$504$		0			0
$505$	−5.32624			−0.237014
$506$	−8.20820	+	13.8496i	−0.364899	+	0.615689i
$507$		0			0
$508$	−7.61803	+	5.53483i	−0.337996	+	0.245568i
$509$	3.01064	+	9.26581i	0.133444	+	0.410700i	0.995345	−	0.0963779i	$-0.0307257\pi$
$509$	3.01064	+	9.26581i	0.133444	+	0.410700i	−0.861900	+	0.507078i	$0.830726\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	8.79837	+	27.0786i	0.388080	+	1.19439i
$515$	7.85410	−	5.70634i	0.346093	−	0.251451i
$516$		0			0
$517$	−2.38854	−	2.71441i	−0.105048	−	0.119380i
$518$		0			0
$519$		0			0
$520$	−0.427051	−	1.31433i	−0.0187274	−	0.0576371i
$521$	−6.94427	+	21.3723i	−0.304234	+	0.936336i	0.675728	+	0.737151i	$0.263829\pi$
$521$	−6.94427	+	21.3723i	−0.304234	+	0.936336i	−0.979962	+	0.199185i	$0.936171\pi$
$522$		0			0
$523$	−21.7082	−	15.7719i	−0.949233	−	0.689658i	0.00139197	−	0.999999i	$-0.499557\pi$
$523$	−21.7082	−	15.7719i	−0.949233	−	0.689658i	−0.950625	+	0.310341i	$0.899557\pi$
$524$	0.572949	−	1.76336i	0.0250294	−	0.0770326i
$525$		0			0
$526$	−13.7812	+	10.0126i	−0.600887	+	0.436570i
$527$	6.70820			0.292214
$528$		0			0
$529$	0.562306			0.0244481
$530$	−8.85410	+	6.43288i	−0.384598	+	0.279427i
$531$		0			0
$532$		0			0
$533$	4.14590	+	3.01217i	0.179579	+	0.130472i
$534$		0			0
$535$	−0.909830	+	2.80017i	−0.0393354	+	0.121062i
$536$	−3.89919	−	12.0005i	−0.168419	−	0.518341i
$537$		0			0
$538$	−17.7426			−0.764940
$539$	−22.6525	−	5.08580i	−0.975711	−	0.219061i
$540$		0			0
$541$	7.61803	−	5.53483i	0.327525	−	0.237961i	−0.411855	−	0.911249i	$-0.635119\pi$
$541$	7.61803	−	5.53483i	0.327525	−	0.237961i	0.739380	+	0.673289i	$0.235119\pi$
$542$	8.73607	+	26.8869i	0.375246	+	1.15489i
$543$		0			0
$544$	1.30902	+	0.951057i	0.0561236	+	0.0407762i
$545$	4.61803	+	3.35520i	0.197815	+	0.143721i
$546$		0			0
$547$	0.572949	+	1.76336i	0.0244975	+	0.0753956i	0.962558	−	0.271076i	$-0.0873796\pi$
$547$	0.572949	+	1.76336i	0.0244975	+	0.0753956i	−0.938060	+	0.346472i	$0.887380\pi$
$548$	0.500000	−	0.363271i	0.0213589	−	0.0155182i
$549$		0			0
$550$	3.23607	+	0.726543i	0.137986	+	0.0309799i
$551$	−13.2361			−0.563875
$552$		0			0
$553$		0			0
$554$	−0.173762	+	0.534785i	−0.00738244	+	0.0227208i
$555$		0			0
$556$	−7.09017	−	5.15131i	−0.300690	−	0.218464i
$557$	−5.14590	+	15.8374i	−0.218039	+	0.671054i	0.780885	+	0.624675i	$0.214768\pi$
$557$	−5.14590	+	15.8374i	−0.218039	+	0.671054i	−0.998924	+	0.0463795i	$0.985232\pi$
$558$		0			0
$559$	−3.19098	+	2.31838i	−0.134964	+	0.0980572i
$560$		0			0
$561$		0			0
$562$	−18.1803			−0.766891
$563$	−1.09017	+	0.792055i	−0.0459452	+	0.0333811i	−0.610521	−	0.792000i	$-0.709040\pi$
$563$	−1.09017	+	0.792055i	−0.0459452	+	0.0333811i	0.564576	+	0.825381i	$0.309040\pi$
$564$		0			0
$565$	−3.80902	+	11.7229i	−0.160247	+	0.493188i
$566$	−2.50000	−	1.81636i	−0.105083	−	0.0763472i
$567$		0			0
$568$	−3.38197	+	10.4086i	−0.141904	+	0.436736i
$569$	2.76393	+	8.50651i	0.115870	+	0.356611i	0.992128	−	0.125232i	$-0.0399675\pi$
$569$	2.76393	+	8.50651i	0.115870	+	0.356611i	−0.876257	+	0.481843i	$0.839967\pi$
$570$		0			0
$571$	−21.7082			−0.908460			−0.454230	−	0.890884i	$-0.650086\pi$
$571$	−21.7082			−0.908460			−0.454230	+	0.890884i	$0.650086\pi$
$572$	3.02786	+	3.44095i	0.126601	+	0.143874i
$573$		0			0
$574$		0			0
$575$	−1.50000	−	4.61653i	−0.0625543	−	0.192522i
$576$		0			0
$577$	20.3262	+	14.7679i	0.846192	+	0.614795i	0.924094	−	0.382166i	$-0.124822\pi$
$577$	20.3262	+	14.7679i	0.846192	+	0.614795i	−0.0779012	+	0.996961i	$0.524822\pi$
$578$	11.6353	+	8.45351i	0.483963	+	0.351620i
$579$		0			0
$580$	−2.04508	−	6.29412i	−0.0849175	−	0.261349i
$581$		0			0
$582$		0			0
$583$	18.5066	−	31.2259i	0.766464	−	1.29324i
$584$		0			0
$585$		0			0
$586$	−0.472136	−	1.45309i	−0.0195038	−	0.0600264i
$587$	−1.58359	+	4.87380i	−0.0653618	+	0.201163i	−0.978404	−	0.206702i	$-0.933727\pi$
$587$	−1.58359	+	4.87380i	−0.0653618	+	0.201163i	0.913042	+	0.407866i	$0.133727\pi$
$588$		0			0
$589$	6.70820	+	4.87380i	0.276407	+	0.200821i
$590$	−0.354102	+	1.08981i	−0.0145781	+	0.0448669i
$591$		0			0
$592$	5.54508	−	4.02874i	0.227902	−	0.165580i
$593$	−16.6869			−0.685250			−0.342625	−	0.939472i	$-0.611316\pi$
$593$	−16.6869			−0.685250			−0.342625	+	0.939472i	$0.611316\pi$
$594$		0			0
$595$		0			0
$596$	−1.07295	+	0.779543i	−0.0439497	+	0.0319313i
$597$		0			0
$598$	2.07295	−	6.37988i	0.0847692	−	0.260893i
$599$	−10.3262	−	7.50245i	−0.421919	−	0.306542i	0.356491	−	0.934299i	$-0.383973\pi$
$599$	−10.3262	−	7.50245i	−0.421919	−	0.306542i	−0.778409	+	0.627757i	$0.783973\pi$
$600$		0			0
$601$	13.7426	−	42.2955i	0.560574	−	1.72527i	−0.120174	−	0.992753i	$-0.538345\pi$
$601$	13.7426	−	42.2955i	0.560574	−	1.72527i	0.680749	−	0.732517i	$-0.261655\pi$
$602$		0			0
$603$		0			0
$604$	5.52786			0.224926
$605$	−10.8090	+	2.04087i	−0.439449	+	0.0829732i
$606$		0			0
$607$	3.85410	−	2.80017i	0.156433	−	0.113655i	−0.506815	−	0.862055i	$-0.669177\pi$
$607$	3.85410	−	2.80017i	0.156433	−	0.113655i	0.663248	+	0.748399i	$0.269177\pi$
$608$	0.618034	+	1.90211i	0.0250646	+	0.0771409i
$609$		0			0
$610$	6.23607	+	4.53077i	0.252491	+	0.183445i
$611$	1.21885	+	0.885544i	0.0493093	+	0.0358253i
$612$		0			0
$613$	−2.03444	−	6.26137i	−0.0821703	−	0.252894i	0.901528	−	0.432721i	$-0.142446\pi$
$613$	−2.03444	−	6.26137i	−0.0821703	−	0.252894i	−0.983698	+	0.179826i	$0.942446\pi$
$614$	26.6803	−	19.3844i	1.07673	−	0.782291i
$615$		0			0
$616$		0			0
$617$	13.0557			0.525604			0.262802	−	0.964850i	$-0.415353\pi$
$617$	13.0557			0.525604			0.262802	+	0.964850i	$0.415353\pi$
$618$		0			0
$619$	7.76393	+	23.8949i	0.312059	+	0.960418i	0.976948	+	0.213476i	$0.0684786\pi$
$619$	7.76393	+	23.8949i	0.312059	+	0.960418i	−0.664889	+	0.746942i	$0.731521\pi$
$620$	−1.28115	+	3.94298i	−0.0514523	+	0.158354i
$621$		0			0
$622$	25.0344	+	18.1886i	1.00379	+	0.729296i
$623$		0			0
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−30.1803			−1.20625
$627$		0			0
$628$	11.2705			0.449742
$629$	−8.97214	+	6.51864i	−0.357742	+	0.259915i
$630$		0			0
$631$	−7.19098	+	22.1316i	−0.286269	+	0.881044i	0.699747	+	0.714391i	$0.253296\pi$
$631$	−7.19098	+	22.1316i	−0.286269	+	0.881044i	−0.986016	+	0.166653i	$0.946704\pi$
$632$	−9.78115	−	7.10642i	−0.389073	−	0.282678i
$633$		0			0
$634$	5.09017	−	15.6659i	0.202156	−	0.622174i
$635$	2.90983	+	8.95554i	0.115473	+	0.355390i
$636$		0			0
$637$	9.67376			0.383288
$638$	14.5000	+	16.4782i	0.574060	+	0.652379i
$639$		0			0
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−9.90983	−	30.4993i	−0.391415	−	1.20465i	−0.931719	−	0.363181i	$-0.881691\pi$
$641$	−9.90983	−	30.4993i	−0.391415	−	1.20465i	0.540304	−	0.841470i	$-0.318309\pi$
$642$		0			0
$643$	17.9721	+	13.0575i	0.708752	+	0.514938i	0.882771	−	0.469804i	$-0.155675\pi$
$643$	17.9721	+	13.0575i	0.708752	+	0.514938i	−0.174019	+	0.984742i	$0.555675\pi$
$644$		0			0
$645$		0			0
$646$	−1.00000	−	3.07768i	−0.0393445	−	0.121090i
$647$	−7.45492	+	5.41631i	−0.293083	+	0.212937i	−0.724604	−	0.689166i	$-0.757977\pi$
$647$	−7.45492	+	5.41631i	−0.293083	+	0.212937i	0.431521	+	0.902103i	$0.357977\pi$
$648$		0			0
$649$	−0.354102	−	3.78398i	−0.0138997	−	0.148534i
$650$	−1.38197			−0.0542052
$651$		0			0
$652$	3.40983	+	10.4944i	0.133539	+	0.410992i
$653$	6.85410	−	21.0948i	0.268222	−	0.825502i	−0.722712	−	0.691149i	$-0.757105\pi$
$653$	6.85410	−	21.0948i	0.268222	−	0.825502i	0.990934	−	0.134352i	$-0.0428954\pi$
$654$		0			0
$655$	−1.50000	−	1.08981i	−0.0586098	−	0.0425825i
$656$	1.14590	−	3.52671i	0.0447398	−	0.137695i
$657$		0			0
$658$		0			0
$659$	48.3607			1.88386			0.941932	−	0.335803i	$-0.109008\pi$
$659$	48.3607			1.88386			0.941932	+	0.335803i	$0.109008\pi$
$660$		0			0
$661$	−40.8328			−1.58821			−0.794106	−	0.607779i	$-0.792061\pi$
$661$	−40.8328			−1.58821			−0.794106	+	0.607779i	$0.792061\pi$
$662$	3.70820	−	2.69417i	0.144123	−	0.104712i
$663$		0			0
$664$	−0.236068	+	0.726543i	−0.00916121	+	0.0281953i
$665$		0			0
$666$		0			0
$667$	9.92705	−	30.5523i	0.384377	−	1.18299i
$668$	−5.19098	−	15.9762i	−0.200845	−	0.618138i
$669$		0			0
$670$	−12.6180			−0.487477
$671$	−24.9443	−	5.60034i	−0.962963	−	0.216199i
$672$		0			0
$673$	27.5066	−	19.9847i	1.06030	−	0.770354i	0.0861567	−	0.996282i	$-0.472541\pi$
$673$	27.5066	−	19.9847i	1.06030	−	0.770354i	0.974144	+	0.225928i	$0.0725414\pi$
$674$	7.94427	+	24.4500i	0.306002	+	0.941777i
$675$		0			0
$676$	8.97214	+	6.51864i	0.345082	+	0.250717i
$677$	−27.7082	−	20.1312i	−1.06491	−	0.773704i	−0.0899218	−	0.995949i	$-0.528662\pi$
$677$	−27.7082	−	20.1312i	−1.06491	−	0.773704i	−0.974991	+	0.222244i	$0.928662\pi$
$678$		0			0
$679$		0			0
$680$	1.30902	−	0.951057i	0.0501985	−	0.0364714i
$681$		0			0
$682$	−1.28115	−	13.6906i	−0.0490579	−	0.524239i
$683$	20.6525			0.790245			0.395123	−	0.918628i	$-0.370702\pi$
$683$	20.6525			0.790245			0.395123	+	0.918628i	$0.370702\pi$
$684$		0			0
$685$	−0.190983	−	0.587785i	−0.00729709	−	0.0224581i
$686$		0			0
$687$		0			0
$688$	2.30902	+	1.67760i	0.0880304	+	0.0639579i
$689$	−4.67376	+	14.3844i	−0.178056	+	0.548000i
$690$		0			0
$691$	−2.61803	+	1.90211i	−0.0995947	+	0.0723598i	−0.636468	−	0.771303i	$-0.719605\pi$
$691$	−2.61803	+	1.90211i	−0.0995947	+	0.0723598i	0.536873	+	0.843663i	$0.319605\pi$
$692$	−9.70820			−0.369051
$693$		0			0
$694$	3.70820			0.140761
$695$	−7.09017	+	5.15131i	−0.268945	+	0.195400i
$696$		0			0
$697$	−1.85410	+	5.70634i	−0.0702291	+	0.216143i
$698$	−11.0000	−	7.99197i	−0.416356	−	0.302500i
$699$		0			0
$700$		0			0
$701$	3.67376	+	11.3067i	0.138756	+	0.427047i	0.996155	−	0.0876045i	$-0.0279212\pi$
$701$	3.67376	+	11.3067i	0.138756	+	0.427047i	−0.857399	+	0.514652i	$0.827921\pi$
$702$		0			0
$703$	−13.7082			−0.517015
$704$	1.69098	−	2.85317i	0.0637313	−	0.107533i
$705$		0			0
$706$	0.218847	−	0.159002i	0.00823642	−	0.00598411i
$707$		0			0
$708$		0			0
$709$	23.5623	+	17.1190i	0.884901	+	0.642918i	0.934544	−	0.355849i	$-0.115808\pi$
$709$	23.5623	+	17.1190i	0.884901	+	0.642918i	−0.0496425	+	0.998767i	$0.515808\pi$
$710$	8.85410	+	6.43288i	0.332289	+	0.241422i
$711$		0			0
$712$	−1.38197	−	4.25325i	−0.0517914	−	0.159397i
$713$	−16.2812	+	11.8290i	−0.609734	+	0.442998i
$714$		0			0
$715$	4.20820	−	1.81636i	0.157378	−	0.0679279i
$716$	8.32624			0.311166
$717$		0			0
$718$	−8.76393	−	26.9726i	−0.327067	−	1.00661i
$719$	−3.90983	+	12.0332i	−0.145812	+	0.448763i	−0.997115	−	0.0759119i	$-0.975813\pi$
$719$	−3.90983	+	12.0332i	−0.145812	+	0.448763i	0.851302	+	0.524675i	$0.175813\pi$
$720$		0			0
$721$		0			0
$722$	−4.63525	+	14.2658i	−0.172506	+	0.530920i
$723$		0			0
$724$	18.7082	−	13.5923i	0.695285	−	0.505154i
$725$	−6.61803			−0.245788
$726$		0			0
$727$	46.7214			1.73280			0.866400	−	0.499351i	$-0.166428\pi$
$727$	46.7214			1.73280			0.866400	+	0.499351i	$0.166428\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.73607	−	2.71441i	−0.138183	−	0.100396i
$732$		0			0
$733$	−13.4787	+	41.4832i	−0.497848	+	1.53222i	0.314624	+	0.949216i	$0.398122\pi$
$733$	−13.4787	+	41.4832i	−0.497848	+	1.53222i	−0.812471	+	0.583001i	$0.801878\pi$
$734$	−7.14590	−	21.9928i	−0.263760	−	0.811770i
$735$		0			0
$736$	−4.85410			−0.178925
$737$	38.4230	−	16.5842i	1.41533	−	0.610888i
$738$		0			0
$739$	6.70820	−	4.87380i	0.246765	−	0.179285i	−0.457527	−	0.889196i	$-0.651265\pi$
$739$	6.70820	−	4.87380i	0.246765	−	0.179285i	0.704292	+	0.709910i	$0.251265\pi$
$740$	−2.11803	−	6.51864i	−0.0778605	−	0.239630i
$741$		0			0
$742$		0			0
$743$	33.5344	+	24.3642i	1.23026	+	0.893836i	0.996910	−	0.0785571i	$-0.0250313\pi$
$743$	33.5344	+	24.3642i	1.23026	+	0.893836i	0.233350	+	0.972393i	$0.425031\pi$
$744$		0			0
$745$	0.409830	+	1.26133i	0.0150150	+	0.0462115i
$746$	23.3262	−	16.9475i	0.854034	−	0.620492i
$747$		0			0
$748$	−2.73607	+	4.61653i	−0.100041	+	0.168797i
$749$		0			0
$750$		0			0
$751$	4.79180	+	14.7476i	0.174855	+	0.538149i	0.999627	−	0.0273171i	$-0.00869640\pi$
$751$	4.79180	+	14.7476i	0.174855	+	0.538149i	−0.824772	+	0.565466i	$0.808696\pi$
$752$	0.336881	−	1.03681i	0.0122848	−	0.0378087i
$753$		0			0
$754$	−7.39919	−	5.37582i	−0.269462	−	0.195776i
$755$	1.70820	−	5.25731i	0.0621679	−	0.191333i
$756$		0			0
$757$	7.06231	−	5.13107i	0.256684	−	0.186492i	−0.452000	−	0.892018i	$-0.649289\pi$
$757$	7.06231	−	5.13107i	0.256684	−	0.186492i	0.708684	+	0.705526i	$0.249289\pi$
$758$	−5.52786			−0.200781
$759$		0			0
$760$	2.00000			0.0725476
$761$	−16.4164	+	11.9272i	−0.595094	+	0.432361i	−0.844134	−	0.536132i	$-0.819885\pi$
$761$	−16.4164	+	11.9272i	−0.595094	+	0.432361i	0.249040	+	0.968493i	$0.419885\pi$
$762$		0			0
$763$		0			0
$764$	−10.4721	−	7.60845i	−0.378869	−	0.275264i
$765$		0			0
$766$	6.51722	−	20.0579i	0.235477	−	0.724723i
$767$	0.489357	+	1.50609i	0.0176697	+	0.0543816i
$768$		0			0
$769$	13.2148			0.476537			0.238269	−	0.971199i	$-0.423420\pi$
$769$	13.2148			0.476537			0.238269	+	0.971199i	$0.423420\pi$
$770$		0			0
$771$		0			0
$772$	−1.14590	+	0.832544i	−0.0412418	+	0.0299639i
$773$	−11.7639	−	36.2057i	−0.423119	−	1.30223i	−0.904784	−	0.425871i	$-0.859968\pi$
$773$	−11.7639	−	36.2057i	−0.423119	−	1.30223i	0.481664	−	0.876356i	$-0.340032\pi$
$774$		0			0
$775$	3.35410	+	2.43690i	0.120483	+	0.0875360i
$776$	−7.47214	−	5.42882i	−0.268234	−	0.194883i
$777$		0			0
$778$	−0.0623059	−	0.191758i	−0.00223377	−	0.00687485i
$779$	−6.00000	+	4.35926i	−0.214972	+	0.156187i
$780$		0			0
$781$	−35.4164	−	7.95148i	−1.26730	−	0.284526i
$782$	7.85410			0.280862
$783$		0			0
$784$	−2.16312	−	6.65740i	−0.0772542	−	0.237764i
$785$	3.48278	−	10.7189i	0.124306	−	0.382574i
$786$		0			0
$787$	−12.4894	−	9.07405i	−0.445197	−	0.323455i	0.342499	−	0.939518i	$-0.388727\pi$
$787$	−12.4894	−	9.07405i	−0.445197	−	0.323455i	−0.787697	+	0.616063i	$0.788727\pi$
$788$	7.52786	−	23.1684i	0.268169	−	0.825339i
$789$		0			0
$790$	−9.78115	+	7.10642i	−0.347998	+	0.252835i
$791$		0			0
$792$		0			0
$793$	10.6525			0.378281
$794$	15.2533	−	11.0822i	0.541319	−	0.393291i
$795$		0			0
$796$	−6.20820	+	19.1069i	−0.220044	+	0.677226i
$797$	−7.00000	−	5.08580i	−0.247953	−	0.180148i	0.456866	−	0.889535i	$-0.348972\pi$
$797$	−7.00000	−	5.08580i	−0.247953	−	0.180148i	−0.704819	+	0.709387i	$0.748972\pi$
$798$		0			0
$799$	−0.545085	+	1.67760i	−0.0192837	+	0.0593492i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$		0			0
$802$	−4.58359			−0.161852
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.77051	+	5.44907i	0.0623635	+	0.191935i
$807$		0			0
$808$	4.30902	+	3.13068i	0.151591	+	0.110137i
$809$	−41.7426	−	30.3278i	−1.46759	−	1.06627i	−0.981302	−	0.192472i	$-0.938350\pi$
$809$	−41.7426	−	30.3278i	−1.46759	−	1.06627i	−0.486291	−	0.873797i	$-0.661650\pi$
$810$		0			0
$811$	10.8541	+	33.4055i	0.381139	+	1.17303i	0.939243	+	0.343254i	$0.111529\pi$
$811$	10.8541	+	33.4055i	0.381139	+	1.17303i	−0.558104	+	0.829771i	$0.688471\pi$
$812$		0			0
$813$		0			0
$814$	15.0172	+	17.0660i	0.526353	+	0.598164i
$815$	11.0344			0.386520
$816$		0			0
$817$	−1.76393	−	5.42882i	−0.0617122	−	0.189931i
$818$	−8.57295	+	26.3848i	−0.299746	+	0.922524i
$819$		0			0
$820$	−3.00000	−	2.17963i	−0.104765	−	0.0761159i
$821$	−6.72949	+	20.7112i	−0.234861	+	0.722827i	0.762279	+	0.647249i	$0.224080\pi$
$821$	−6.72949	+	20.7112i	−0.234861	+	0.722827i	−0.997140	+	0.0755787i	$0.975920\pi$
$822$		0			0
$823$	−18.8541	+	13.6983i	−0.657213	+	0.477493i	−0.865720	−	0.500528i	$-0.833139\pi$
$823$	−18.8541	+	13.6983i	−0.657213	+	0.477493i	0.208508	+	0.978021i	$0.433139\pi$
$824$	−9.70820			−0.338201
$825$		0			0
$826$		0			0
$827$	38.7426	−	28.1482i	1.34721	−	0.978808i	0.348069	−	0.937469i	$-0.386838\pi$
$827$	38.7426	−	28.1482i	1.34721	−	0.978808i	0.999145	−	0.0413391i	$-0.0131624\pi$
$828$		0			0
$829$	0.965558	−	2.97168i	0.0335352	−	0.103211i	−0.932888	−	0.360167i	$-0.882720\pi$
$829$	0.965558	−	2.97168i	0.0335352	−	0.103211i	0.966423	+	0.256956i	$0.0827197\pi$
$830$	0.618034	+	0.449028i	0.0214523	+	0.0155860i
$831$		0			0
$832$	−0.427051	+	1.31433i	−0.0148053	+	0.0455661i
$833$	3.50000	+	10.7719i	0.121268	+	0.373224i
$834$		0			0
$835$	−16.7984			−0.581332
$836$	−6.09017	+	2.62866i	−0.210633	+	0.0909140i
$837$		0			0
$838$	13.5451	−	9.84108i	0.467907	−	0.339954i
$839$	−1.03444	−	3.18368i	−0.0357129	−	0.109913i	0.931611	−	0.363457i	$-0.118404\pi$
$839$	−1.03444	−	3.18368i	−0.0357129	−	0.109913i	−0.967324	+	0.253544i	$0.918404\pi$
$840$		0			0
$841$	−11.9721	−	8.69827i	−0.412832	−	0.299940i
$842$	−15.8541	−	11.5187i	−0.546368	−	0.396960i
$843$		0			0
$844$	−5.56231	−	17.1190i	−0.191462	−	0.589261i
$845$	8.97214	−	6.51864i	0.308651	−	0.224248i
$846$		0			0
$847$		0			0
$848$	10.9443			0.375828
$849$		0			0
$850$	−0.500000	−	1.53884i	−0.0171499	−	0.0527818i
$851$	10.2812	−	31.6421i	0.352433	−	1.08468i
$852$		0			0
$853$	33.9787	+	24.6870i	1.16341	+	0.845266i	0.990205	−	0.139620i	$-0.0445881\pi$
$853$	33.9787	+	24.6870i	1.16341	+	0.845266i	0.173204	+	0.984886i	$0.444588\pi$
$854$		0			0
$855$		0			0
$856$	2.38197	−	1.73060i	0.0814139	−	0.0591507i
$857$	37.7984			1.29117			0.645584	−	0.763689i	$-0.276614\pi$
$857$	37.7984			1.29117			0.645584	+	0.763689i	$0.276614\pi$
$858$		0			0
$859$	−8.76393			−0.299022			−0.149511	−	0.988760i	$-0.547770\pi$
$859$	−8.76393			−0.299022			−0.149511	+	0.988760i	$0.547770\pi$
$860$	2.30902	−	1.67760i	0.0787368	−	0.0572057i
$861$		0			0
$862$	11.7082	−	36.0341i	0.398783	−	1.22733i
$863$	−8.07295	−	5.86534i	−0.274806	−	0.199659i	0.441843	−	0.897093i	$-0.354325\pi$
$863$	−8.07295	−	5.86534i	−0.274806	−	0.199659i	−0.716649	+	0.697434i	$0.754325\pi$
$864$		0			0
$865$	−3.00000	+	9.23305i	−0.102003	+	0.313933i
$866$	5.14590	+	15.8374i	0.174865	+	0.538178i
$867$		0			0
$868$		0			0
$869$	20.4443	−	34.4953i	0.693524	−	1.17017i
$870$		0			0
$871$	−14.1074	+	10.2496i	−0.478011	+	0.347295i
$872$	−1.76393	−	5.42882i	−0.0597343	−	0.183843i
$873$		0			0
$874$	7.85410	+	5.70634i	0.265669	+	0.193020i
$875$		0			0
$876$		0			0
$877$	15.7148	+	48.3651i	0.530650	+	1.63317i	0.752864	+	0.658176i	$0.228672\pi$
$877$	15.7148	+	48.3651i	0.530650	+	1.63317i	−0.222213	+	0.974998i	$0.571328\pi$
$878$	19.8262	−	14.4046i	0.669103	−	0.486132i
$879$		0			0
$880$	−2.19098	−	2.48990i	−0.0738580	−	0.0839345i
$881$	35.4853			1.19553			0.597765	−	0.801671i	$-0.296056\pi$
$881$	35.4853			1.19553			0.597765	+	0.801671i	$0.296056\pi$
$882$		0			0
$883$	−7.64590	−	23.5317i	−0.257305	−	0.791903i	−0.993367	−	0.114989i	$-0.963317\pi$
$883$	−7.64590	−	23.5317i	−0.257305	−	0.791903i	0.736062	−	0.676914i	$-0.236683\pi$
$884$	0.690983	−	2.12663i	0.0232403	−	0.0715262i
$885$		0			0
$886$	−20.7082	−	15.0454i	−0.695706	−	0.505460i
$887$	1.44427	−	4.44501i	0.0484939	−	0.149249i	−0.923877	−	0.382689i	$-0.874998\pi$
$887$	1.44427	−	4.44501i	0.0484939	−	0.149249i	0.972371	+	0.233440i	$0.0749982\pi$
$888$		0			0
$889$		0			0
$890$	−4.47214			−0.149906
$891$		0			0
$892$	−11.7082			−0.392020
$893$	−1.76393	+	1.28157i	−0.0590277	+	0.0428862i
$894$		0			0
$895$	2.57295	−	7.91872i	0.0860042	−	0.264694i
$896$		0			0
$897$		0			0
$898$	9.23607	−	28.4257i	0.308212	−	0.948578i
$899$	8.47871	+	26.0948i	0.282781	+	0.870310i
$900$		0			0
$901$	−17.7082			−0.589946
$902$	12.0000	+	2.69417i	0.399556	+	0.0897060i
$903$		0			0
$904$	9.97214	−	7.24518i	0.331668	−	0.240971i
$905$	−7.14590	−	21.9928i	−0.237538	−	0.731066i
$906$		0			0
$907$	15.5451	+	11.2942i	0.516166	+	0.375017i	0.815158	−	0.579239i	$-0.196650\pi$
$907$	15.5451	+	11.2942i	0.516166	+	0.375017i	−0.298992	+	0.954256i	$0.596650\pi$
$908$	−10.3262	−	7.50245i	−0.342688	−	0.248978i
$909$		0			0
$910$		0			0
$911$	43.9787	−	31.9524i	1.45708	−	1.05863i	0.472968	−	0.881080i	$-0.343183\pi$
$911$	43.9787	−	31.9524i	1.45708	−	1.05863i	0.984112	−	0.177551i	$-0.0568174\pi$
$912$		0			0
$913$	−2.47214	−	0.555029i	−0.0818158	−	0.0183688i
$914$	0.180340			0.00596511
$915$		0			0
$916$	1.52786	+	4.70228i	0.0504820	+	0.155368i
$917$		0			0
$918$		0			0
$919$	15.0172	+	10.9106i	0.495372	+	0.359909i	0.807247	−	0.590214i	$-0.200957\pi$
$919$	15.0172	+	10.9106i	0.495372	+	0.359909i	−0.311874	+	0.950123i	$0.600957\pi$
$920$	−1.50000	+	4.61653i	−0.0494535	+	0.152202i
$921$		0			0
$922$	8.16312	−	5.93085i	0.268838	−	0.195322i
$923$	15.1246			0.497833
$924$		0			0
$925$	−6.85410			−0.225361
$926$	6.00000	−	4.35926i	0.197172	−	0.143254i
$927$		0			0
$928$	−2.04508	+	6.29412i	−0.0671332	+	0.206615i
$929$	19.7984	+	14.3844i	0.649564	+	0.471936i	0.863122	−	0.504995i	$-0.168506\pi$
$929$	19.7984	+	14.3844i	0.649564	+	0.471936i	−0.213559	+	0.976930i	$0.568506\pi$
$930$		0			0
$931$	−4.32624	+	13.3148i	−0.141787	+	0.436375i
$932$	1.04508	+	3.21644i	0.0342329	+	0.105358i
$933$		0			0
$934$	4.11146			0.134531
$935$	3.54508	+	4.02874i	0.115937	+	0.131754i
$936$		0			0
$937$	45.7426	−	33.2340i	1.49435	−	1.08571i	0.521781	−	0.853079i	$-0.325268\pi$
$937$	45.7426	−	33.2340i	1.49435	−	1.08571i	0.972566	−	0.232627i	$-0.0747322\pi$
$938$		0			0
$939$		0			0
$940$	−0.881966	−	0.640786i	−0.0287666	−	0.0209001i
$941$	48.0066	+	34.8788i	1.56497	+	1.13702i	0.931782	+	0.363019i	$0.118254\pi$
$941$	48.0066	+	34.8788i	1.56497	+	1.13702i	0.633188	+	0.773998i	$0.281746\pi$
$942$		0			0
$943$	−5.56231	−	17.1190i	−0.181134	−	0.557472i
$944$	0.927051	−	0.673542i	0.0301729	−	0.0219219i
$945$		0			0
$946$	−4.82624	+	8.14324i	−0.156915	+	0.264759i
$947$	−38.7214			−1.25828			−0.629138	−	0.777294i	$-0.716592\pi$
$947$	−38.7214			−1.25828			−0.629138	+	0.777294i	$0.716592\pi$
$948$		0			0
$949$		0			0
$950$	0.618034	−	1.90211i	0.0200517	−	0.0617127i
$951$		0			0
$952$		0			0
$953$	6.68034	−	20.5600i	0.216397	−	0.666003i	−0.782654	−	0.622457i	$-0.786135\pi$
$953$	6.68034	−	20.5600i	0.216397	−	0.666003i	0.999051	−	0.0435458i	$-0.0138654\pi$
$954$		0			0
$955$	−10.4721	+	7.60845i	−0.338870	+	0.246204i
$956$	−11.2361			−0.363400
$957$		0			0
$958$	4.11146			0.132835
$959$		0			0
$960$		0			0
$961$	−4.26800	+	13.1355i	−0.137677	+	0.423727i
$962$	−7.66312	−	5.56758i	−0.247069	−	0.179506i
$963$		0			0
$964$	5.56231	−	17.1190i	0.179150	−	0.551366i
$965$	0.437694	+	1.34708i	0.0140899	+	0.0433642i
$966$		0			0
$967$	44.7639			1.43951			0.719756	−	0.694228i	$-0.244254\pi$
$967$	44.7639			1.43951			0.719756	+	0.694228i	$0.244254\pi$
$968$	9.94427	+	4.70228i	0.319621	+	0.151137i
$969$		0			0
$970$	−7.47214	+	5.42882i	−0.239916	+	0.174309i
$971$	−15.7082	−	48.3449i	−0.504100	−	1.55146i	−0.802278	−	0.596951i	$-0.796379\pi$
$971$	−15.7082	−	48.3449i	−0.504100	−	1.55146i	0.298178	−	0.954510i	$-0.403621\pi$
$972$		0			0
$973$		0			0
$974$	14.0902	+	10.2371i	0.451478	+	0.328018i
$975$		0			0
$976$	−2.38197	−	7.33094i	−0.0762449	−	0.234658i
$977$	−1.90983	+	1.38757i	−0.0611009	+	0.0443924i	−0.617916	−	0.786244i	$-0.712023\pi$
$977$	−1.90983	+	1.38757i	−0.0611009	+	0.0443924i	0.556816	+	0.830636i	$0.312023\pi$
$978$		0			0
$979$	13.6180	−	5.87785i	0.435234	−	0.187857i
$980$	−7.00000			−0.223607
$981$		0			0
$982$	6.10081	+	18.7764i	0.194685	+	0.599178i
$983$	8.36068	−	25.7315i	0.266664	−	0.820708i	−0.724641	−	0.689127i	$-0.757994\pi$
$983$	8.36068	−	25.7315i	0.266664	−	0.820708i	0.991305	−	0.131582i	$-0.0420056\pi$
$984$		0			0
$985$	−19.7082	−	14.3188i	−0.627956	−	0.456236i
$986$	3.30902	−	10.1841i	0.105381	−	0.324328i
$987$		0			0
$988$	2.23607	−	1.62460i	0.0711388	−	0.0516854i
$989$	13.8541			0.440535
$990$		0			0
$991$	−52.2705			−1.66043			−0.830214	−	0.557445i	$-0.811782\pi$
$991$	−52.2705			−1.66043			−0.830214	+	0.557445i	$0.811782\pi$
$992$	3.35410	−	2.43690i	0.106493	−	0.0773716i
$993$		0			0
$994$		0			0
$995$	16.2533	+	11.8087i	0.515264	+	0.374361i
$996$		0			0
$997$	4.11803	−	12.6740i	0.130419	−	0.401390i	−0.864430	−	0.502753i	$-0.832320\pi$
$997$	4.11803	−	12.6740i	0.130419	−	0.401390i	0.994849	+	0.101363i	$0.0323205\pi$
$998$	3.18034	+	9.78808i	0.100672	+	0.309836i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.b.91.1	✓	4
3.2	odd	2		990.2.n.g.91.1	yes	4
11.4	even	5	inner	990.2.n.b.631.1	yes	4
33.26	odd	10		990.2.n.g.631.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.n.b.91.1	✓	4	1.1	even	1	trivial
990.2.n.b.631.1	yes	4	11.4	even	5	inner
990.2.n.g.91.1	yes	4	3.2	odd	2
990.2.n.g.631.1	yes	4	33.26	odd	10

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.309017 + 0.951057i) q^{8} +1.00000 q^{10} +(-3.04508 + 1.31433i) q^{11} +(1.11803 - 0.812299i) q^{13} +(-0.809017 - 0.587785i) q^{16} +(1.30902 + 0.951057i) q^{17} +(0.618034 + 1.90211i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(1.69098 - 2.85317i) q^{22} -4.85410 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.427051 + 1.31433i) q^{26} +(-2.04508 + 6.29412i) q^{29} +(3.35410 - 2.43690i) q^{31} +1.00000 q^{32} -1.61803 q^{34} +(-2.11803 + 6.51864i) q^{37} +(-1.61803 - 1.17557i) q^{38} +(0.309017 - 0.951057i) q^{40} +(1.14590 + 3.52671i) q^{41} -2.85410 q^{43} +(0.309017 + 3.30220i) q^{44} +(3.92705 - 2.85317i) q^{46} +(0.336881 + 1.03681i) q^{47} +(5.66312 + 4.11450i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.427051 - 1.31433i) q^{52} +(-8.85410 + 6.43288i) q^{53} +(3.23607 + 0.726543i) q^{55} +(-2.04508 - 6.29412i) q^{58} +(-0.354102 + 1.08981i) q^{59} +(6.23607 + 4.53077i) q^{61} +(-1.28115 + 3.94298i) q^{62} +(-0.809017 + 0.587785i) q^{64} -1.38197 q^{65} -12.6180 q^{67} +(1.30902 - 0.951057i) q^{68} +(8.85410 + 6.43288i) q^{71} +(-2.11803 - 6.51864i) q^{74} +2.00000 q^{76} +(-9.78115 + 7.10642i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-3.00000 - 2.17963i) q^{82} +(0.618034 + 0.449028i) q^{83} +(-0.500000 - 1.53884i) q^{85} +(2.30902 - 1.67760i) q^{86} +(-2.19098 - 2.48990i) q^{88} -4.47214 q^{89} +(-1.50000 + 4.61653i) q^{92} +(-0.881966 - 0.640786i) q^{94} +(0.618034 - 1.90211i) q^{95} +(-7.47214 + 5.42882i) q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - q^{5} - q^{8} + 4 q^{10} - q^{11} - q^{16} + 3 q^{17} - 2 q^{19} - q^{20} + 9 q^{22} - 6 q^{23} - q^{25} + 5 q^{26} + 3 q^{29} + 4 q^{32} - 2 q^{34} - 4 q^{37} - 2 q^{38} - q^{40}+ \cdots - 28 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - q^5 - q^8 + 4 * q^10 - q^11 - q^16 + 3 * q^17 - 2 * q^19 - q^20 + 9 * q^22 - 6 * q^23 - q^25 + 5 * q^26 + 3 * q^29 + 4 * q^32 - 2 * q^34 - 4 * q^37 - 2 * q^38 - q^40 + 18 * q^41 + 2 * q^43 - q^44 + 9 * q^46 + 17 * q^47 + 7 * q^49 - q^50 + 5 * q^52 - 22 * q^53 + 4 * q^55 + 3 * q^58 + 12 * q^59 + 16 * q^61 + 15 * q^62 - q^64 - 10 * q^65 - 46 * q^67 + 3 * q^68 + 22 * q^71 - 4 * q^74 + 8 * q^76 - 19 * q^79 - q^80 - 12 * q^82 - 2 * q^83 - 2 * q^85 + 7 * q^86 - 11 * q^88 - 6 * q^92 - 8 * q^94 - 2 * q^95 - 12 * q^97 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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