LMFDB - Embedded newform 990.2.ba.c.829.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(289,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			829.2
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	990.829
Dual form			990.2.ba.c.289.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.366554 + 2.20582i) q^{5} +(-1.17557 + 0.381966i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.00000 + 1.00000i) q^{10} +(-2.80902 + 1.76336i) q^{11} +(-0.363271 + 0.500000i) q^{13} +(-0.381966 + 1.17557i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.951057 + 1.30902i) q^{17} +(-0.763932 + 2.35114i) q^{19} +(1.98459 - 1.03025i) q^{20} +(-0.224514 + 3.30902i) q^{22} +1.61803i q^{23} +(-4.73128 + 1.61710i) q^{25} +(0.190983 + 0.587785i) q^{26} +(0.726543 + 1.00000i) q^{28} +(2.19098 + 6.74315i) q^{29} +(-0.118034 - 0.0857567i) q^{31} +1.00000i q^{32} +1.61803 q^{34} +(-1.27346 - 2.45309i) q^{35} +(-6.06961 + 1.97214i) q^{37} +(1.45309 + 2.00000i) q^{38} +(0.333023 - 2.21113i) q^{40} +(-3.38197 + 10.4086i) q^{41} -9.61803i q^{43} +(2.54508 + 2.12663i) q^{44} +(1.30902 + 0.951057i) q^{46} +(6.01661 + 1.95492i) q^{47} +(-4.42705 + 3.21644i) q^{49} +(-1.47271 + 4.77819i) q^{50} +(0.587785 + 0.190983i) q^{52} +(3.97574 - 5.47214i) q^{53} +(-4.91930 - 5.54982i) q^{55} +1.23607 q^{56} +(6.74315 + 2.19098i) q^{58} +(2.20820 + 6.79615i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(-0.138757 + 0.0450850i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-1.23607 - 0.618034i) q^{65} -1.38197i q^{67} +(0.951057 - 1.30902i) q^{68} +(-2.73311 - 0.411638i) q^{70} +(1.38197 - 1.00406i) q^{71} +(7.77997 - 2.52786i) q^{73} +(-1.97214 + 6.06961i) q^{74} +2.47214 q^{76} +(2.62866 - 3.14590i) q^{77} +(-7.78115 - 5.65334i) q^{79} +(-1.59310 - 1.56909i) q^{80} +(6.43288 + 8.85410i) q^{82} +(1.62460 + 2.23607i) q^{83} +(-2.53884 + 2.57768i) q^{85} +(-7.78115 - 5.65334i) q^{86} +(3.21644 - 0.809017i) q^{88} +8.47214 q^{89} +(0.236068 - 0.726543i) q^{91} +(1.53884 - 0.500000i) q^{92} +(5.11803 - 3.71847i) q^{94} +(-5.46621 - 0.823277i) q^{95} +(-1.90211 + 2.61803i) q^{97} +5.47214i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 2 q^{5} + 16 q^{10} - 18 q^{11} - 12 q^{14} - 2 q^{16} - 24 q^{19} + 2 q^{20} + 6 q^{25} + 6 q^{26} + 22 q^{29} + 8 q^{31} + 4 q^{34} - 16 q^{35} + 4 q^{40} - 36 q^{41} - 2 q^{44} + 6 q^{46}+ \cdots - 24 q^{95}+O(q^{100}) $ 8 * q + 2 * q^4 - 2 * q^5 + 16 * q^10 - 18 * q^11 - 12 * q^14 - 2 * q^16 - 24 * q^19 + 2 * q^20 + 6 * q^25 + 6 * q^26 + 22 * q^29 + 8 * q^31 + 4 * q^34 - 16 * q^35 + 4 * q^40 - 36 * q^41 - 2 * q^44 + 6 * q^46 - 22 * q^49 - 8 * q^50 - 8 * q^55 - 8 * q^56 - 36 * q^59 + 2 * q^64 + 8 * q^65 - 12 * q^70 + 20 * q^71 + 20 * q^74 - 16 * q^76 - 22 * q^79 - 2 * q^80 - 8 * q^85 - 22 * q^86 + 32 * q^89 - 16 * q^91 + 32 * q^94 - 24 * q^95

Character values

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

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

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	0.366554	+	2.20582i	0.163928	+	0.986472i
$5$	0.366554	+	2.20582i	0.163928	+	0.986472i
$6$		0			0
$7$	−1.17557	+	0.381966i	−0.444324	+	0.144370i	−0.522630	−	0.852560i	$-0.675049\pi$
$7$	−1.17557	+	0.381966i	−0.444324	+	0.144370i	0.0783058	+	0.996929i	$0.475049\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$		0			0
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$12$		0			0
$13$	−0.363271	+	0.500000i	−0.100753	+	0.138675i	−0.856417	−	0.516285i	$-0.827315\pi$
$13$	−0.363271	+	0.500000i	−0.100753	+	0.138675i	0.755664	+	0.654960i	$0.227315\pi$
$14$	−0.381966	+	1.17557i	−0.102085	+	0.314184i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.951057	+	1.30902i	0.230665	+	0.317483i	0.908623	−	0.417618i	$-0.137135\pi$
$17$	0.951057	+	1.30902i	0.230665	+	0.317483i	−0.677958	+	0.735101i	$0.737135\pi$
$18$		0			0
$19$	−0.763932	+	2.35114i	−0.175258	+	0.539389i	−0.999645	−	0.0266376i	$-0.991520\pi$
$19$	−0.763932	+	2.35114i	−0.175258	+	0.539389i	0.824387	+	0.566026i	$0.191520\pi$
$20$	1.98459	−	1.03025i	0.443767	−	0.230371i
$21$		0			0
$22$	−0.224514	+	3.30902i	−0.0478665	+	0.705485i
$23$			1.61803i			0.337383i	0.985669	+	0.168692i	$0.0539542\pi$
$23$			1.61803i			0.337383i	−0.985669	+	0.168692i	$0.946046\pi$
$24$		0			0
$25$	−4.73128	+	1.61710i	−0.946255	+	0.323420i
$26$	0.190983	+	0.587785i	0.0374548	+	0.115274i
$27$		0			0
$28$	0.726543	+	1.00000i	0.137304	+	0.188982i
$29$	2.19098	+	6.74315i	0.406855	+	1.25217i	0.919336	+	0.393473i	$0.128727\pi$
$29$	2.19098	+	6.74315i	0.406855	+	1.25217i	−0.512481	+	0.858699i	$0.671273\pi$
$30$		0			0
$31$	−0.118034	−	0.0857567i	−0.0211995	−	0.0154024i	0.577135	−	0.816649i	$-0.304171\pi$
$31$	−0.118034	−	0.0857567i	−0.0211995	−	0.0154024i	−0.598335	+	0.801246i	$0.704171\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	1.61803			0.277491
$35$	−1.27346	−	2.45309i	−0.215254	−	0.414647i
$36$		0			0
$37$	−6.06961	+	1.97214i	−0.997838	+	0.324217i	−0.762001	−	0.647576i	$-0.775783\pi$
$37$	−6.06961	+	1.97214i	−0.997838	+	0.324217i	−0.235837	+	0.971793i	$0.575783\pi$
$38$	1.45309	+	2.00000i	0.235722	+	0.324443i
$39$		0			0
$40$	0.333023	−	2.21113i	0.0526555	−	0.349610i
$41$	−3.38197	+	10.4086i	−0.528174	+	1.62555i	0.229778	+	0.973243i	$0.426200\pi$
$41$	−3.38197	+	10.4086i	−0.528174	+	1.62555i	−0.757952	+	0.652310i	$0.773800\pi$
$42$		0			0
$43$		−	9.61803i		−	1.46674i	−0.679832	−	0.733368i	$-0.737947\pi$
$43$		−	9.61803i		−	1.46674i	0.679832	−	0.733368i	$-0.262053\pi$
$44$	2.54508	+	2.12663i	0.383686	+	0.320601i
$45$		0			0
$46$	1.30902	+	0.951057i	0.193004	+	0.140226i
$47$	6.01661	+	1.95492i	0.877613	+	0.285154i	0.712966	−	0.701199i	$-0.247352\pi$
$47$	6.01661	+	1.95492i	0.877613	+	0.285154i	0.164647	+	0.986353i	$0.447352\pi$
$48$		0			0
$49$	−4.42705	+	3.21644i	−0.632436	+	0.459492i
$50$	−1.47271	+	4.77819i	−0.208273	+	0.675738i
$51$		0			0
$52$	0.587785	+	0.190983i	0.0815111	+	0.0264846i
$53$	3.97574	−	5.47214i	0.546110	−	0.751656i	−0.443368	−	0.896340i	$-0.646217\pi$
$53$	3.97574	−	5.47214i	0.546110	−	0.751656i	0.989478	+	0.144684i	$0.0462165\pi$
$54$		0			0
$55$	−4.91930	−	5.54982i	−0.663318	−	0.748338i
$56$	1.23607			0.165177
$57$		0			0
$58$	6.74315	+	2.19098i	0.885419	+	0.287690i
$59$	2.20820	+	6.79615i	0.287484	+	0.884784i	0.985643	+	0.168842i	$0.0540026\pi$
$59$	2.20820	+	6.79615i	0.287484	+	0.884784i	−0.698160	+	0.715942i	$0.745997\pi$
$60$		0			0
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	−0.721660	−	0.692247i	$-0.756621\pi$
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	0.435361	+	0.900256i	$0.356621\pi$
$62$	−0.138757	+	0.0450850i	−0.0176222	+	0.00572580i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.23607	−	0.618034i	−0.153315	−	0.0766577i
$66$		0			0
$67$		−	1.38197i		−	0.168834i	−0.996431	−	0.0844170i	$-0.973097\pi$
$67$		−	1.38197i		−	0.168834i	0.996431	−	0.0844170i	$-0.0269028\pi$
$68$	0.951057	−	1.30902i	0.115333	−	0.158742i
$69$		0			0
$70$	−2.73311	−	0.411638i	−0.326669	−	0.0492002i
$71$	1.38197	−	1.00406i	0.164009	−	0.119160i	−0.502753	−	0.864430i	$-0.667680\pi$
$71$	1.38197	−	1.00406i	0.164009	−	0.119160i	0.666762	+	0.745270i	$0.267680\pi$
$72$		0			0
$73$	7.77997	−	2.52786i	0.910576	−	0.295864i	0.183981	−	0.982930i	$-0.441102\pi$
$73$	7.77997	−	2.52786i	0.910576	−	0.295864i	0.726595	+	0.687066i	$0.241102\pi$
$74$	−1.97214	+	6.06961i	−0.229256	+	0.705578i
$75$		0			0
$76$	2.47214			0.283573
$77$	2.62866	−	3.14590i	0.299563	−	0.358508i
$78$		0			0
$79$	−7.78115	−	5.65334i	−0.875448	−	0.636050i	0.0565952	−	0.998397i	$-0.481976\pi$
$79$	−7.78115	−	5.65334i	−0.875448	−	0.636050i	−0.932043	+	0.362347i	$0.881976\pi$
$80$	−1.59310	−	1.56909i	−0.178114	−	0.175430i
$81$		0			0
$82$	6.43288	+	8.85410i	0.710393	+	0.977772i
$83$	1.62460	+	2.23607i	0.178323	+	0.245440i	0.888817	−	0.458263i	$-0.151528\pi$
$83$	1.62460	+	2.23607i	0.178323	+	0.245440i	−0.710494	+	0.703704i	$0.751528\pi$
$84$		0			0
$85$	−2.53884	+	2.57768i	−0.275376	+	0.279589i
$86$	−7.78115	−	5.65334i	−0.839063	−	0.609615i
$87$		0			0
$88$	3.21644	−	0.809017i	0.342874	−	0.0862415i
$89$	8.47214			0.898045			0.449022	−	0.893521i	$-0.351772\pi$
$89$	8.47214			0.898045			0.449022	+	0.893521i	$0.351772\pi$
$90$		0			0
$91$	0.236068	−	0.726543i	0.0247466	−	0.0761624i
$92$	1.53884	−	0.500000i	0.160435	−	0.0521286i
$93$		0			0
$94$	5.11803	−	3.71847i	0.527885	−	0.383531i
$95$	−5.46621	−	0.823277i	−0.560822	−	0.0844664i
$96$		0			0
$97$	−1.90211	+	2.61803i	−0.193130	+	0.265821i	−0.894590	−	0.446888i	$-0.852532\pi$
$97$	−1.90211	+	2.61803i	−0.193130	+	0.265821i	0.701459	+	0.712709i	$0.252532\pi$
$98$			5.47214i			0.552769i
$99$		0			0
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	−0.690983	−	0.502029i	−0.0687554	−	0.0499537i	0.552877	−	0.833263i	$-0.313530\pi$
$101$	−0.690983	−	0.502029i	−0.0687554	−	0.0499537i	−0.621632	+	0.783309i	$0.713530\pi$
$102$		0			0
$103$	16.5640	−	5.38197i	1.63210	−	0.530301i	0.657346	−	0.753589i	$-0.271679\pi$
$103$	16.5640	−	5.38197i	1.63210	−	0.530301i	0.974752	+	0.223288i	$0.0716791\pi$
$104$	0.500000	−	0.363271i	0.0490290	−	0.0356217i
$105$		0			0
$106$	−2.09017	−	6.43288i	−0.203015	−	0.624817i
$107$	−16.8415	−	5.47214i	−1.62813	−	0.529011i	−0.654289	−	0.756244i	$-0.727032\pi$
$107$	−16.8415	−	5.47214i	−1.62813	−	0.529011i	−0.973840	+	0.227233i	$0.927032\pi$
$108$		0			0
$109$	12.9443			1.23984			0.619918	−	0.784666i	$-0.287166\pi$
$109$	12.9443			1.23984			0.619918	+	0.784666i	$0.287166\pi$
$110$	−7.38139	+	0.717695i	−0.703788	+	0.0684295i
$111$		0			0
$112$	0.726543	−	1.00000i	0.0686518	−	0.0944911i
$113$	9.37181	+	3.04508i	0.881626	+	0.286457i	0.714632	−	0.699501i	$-0.246594\pi$
$113$	9.37181	+	3.04508i	0.881626	+	0.286457i	0.166993	+	0.985958i	$0.446594\pi$
$114$		0			0
$115$	−3.56909	+	0.593096i	−0.332819	+	0.0553065i
$116$	5.73607	−	4.16750i	0.532581	−	0.386942i
$117$		0			0
$118$	6.79615	+	2.20820i	0.625637	+	0.203282i
$119$	−1.61803	−	1.17557i	−0.148325	−	0.107764i
$120$		0			0
$121$	4.78115	−	9.90659i	0.434650	−	0.900599i
$122$			2.76393i			0.250235i
$123$		0			0
$124$	−0.0450850	+	0.138757i	−0.00404875	+	0.0124608i
$125$	−5.30130	−	9.84359i	−0.474163	−	0.880437i
$126$		0			0
$127$	−4.70228	−	6.47214i	−0.417260	−	0.574309i	0.547710	−	0.836668i	$-0.315500\pi$
$127$	−4.70228	−	6.47214i	−0.417260	−	0.574309i	−0.964970	+	0.262359i	$0.915500\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$		0			0
$130$	−1.22654	+	0.636729i	−0.107575	+	0.0558448i
$131$	−3.85410			−0.336734			−0.168367	−	0.985724i	$-0.553849\pi$
$131$	−3.85410			−0.336734			−0.168367	+	0.985724i	$0.553849\pi$
$132$		0			0
$133$		−	3.05573i		−	0.264965i
$134$	−1.11803	−	0.812299i	−0.0965834	−	0.0701720i
$135$		0			0
$136$	−0.500000	−	1.53884i	−0.0428746	−	0.131955i
$137$	5.62058	+	7.73607i	0.480199	+	0.660937i	0.978543	−	0.206042i	$-0.0660585\pi$
$137$	5.62058	+	7.73607i	0.480199	+	0.660937i	−0.498344	+	0.866979i	$0.666058\pi$
$138$		0			0
$139$	−2.09017	−	6.43288i	−0.177286	−	0.545630i	0.822445	−	0.568845i	$-0.192610\pi$
$139$	−2.09017	−	6.43288i	−0.177286	−	0.545630i	−0.999730	+	0.0232153i	$0.992610\pi$
$140$	−1.93950	+	1.96917i	−0.163918	+	0.166426i
$141$		0			0
$142$		−	1.70820i		−	0.143349i
$143$	0.138757	−	2.04508i	0.0116035	−	0.171019i
$144$		0			0
$145$	−14.0711	+	7.30464i	−1.16854	+	0.606617i
$146$	2.52786	−	7.77997i	0.209208	−	0.643875i
$147$		0			0
$148$	3.75123	+	5.16312i	0.308349	+	0.424406i
$149$	5.78115	−	4.20025i	0.473611	−	0.344098i	−0.325236	−	0.945633i	$-0.605444\pi$
$149$	5.78115	−	4.20025i	0.473611	−	0.344098i	0.798847	+	0.601535i	$0.205444\pi$
$150$		0			0
$151$	−4.76393	+	14.6619i	−0.387683	+	1.19317i	0.546832	+	0.837243i	$0.315834\pi$
$151$	−4.76393	+	14.6619i	−0.387683	+	1.19317i	−0.934515	+	0.355924i	$0.884166\pi$
$152$	1.45309	−	2.00000i	0.117861	−	0.162221i
$153$		0			0
$154$	−1.00000	−	3.97574i	−0.0805823	−	0.320374i
$155$	0.145898	−	0.291796i	0.0117188	−	0.0234376i
$156$		0			0
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	0.0663350	−	0.997797i	$-0.478869\pi$
$157$	−5.84510	−	1.89919i	−0.466489	−	0.151572i	−0.532824	+	0.846226i	$0.678869\pi$
$158$	−9.14729	+	2.97214i	−0.727720	+	0.236450i
$159$		0			0
$160$	−2.20582	+	0.366554i	−0.174385	+	0.0289786i
$161$	−0.618034	−	1.90211i	−0.0487079	−	0.149908i
$162$		0			0
$163$	11.9147	−	16.3992i	0.933232	−	1.28448i	−0.0253536	−	0.999679i	$-0.508071\pi$
$163$	11.9147	−	16.3992i	0.933232	−	1.28448i	0.958586	−	0.284805i	$-0.0919288\pi$
$164$	10.9443			0.854604
$165$		0			0
$166$	2.76393			0.214523
$167$	−5.34307	+	7.35410i	−0.413459	+	0.569077i	−0.964058	−	0.265692i	$-0.914399\pi$
$167$	−5.34307	+	7.35410i	−0.413459	+	0.569077i	0.550599	+	0.834770i	$0.314399\pi$
$168$		0			0
$169$	3.89919	+	12.0005i	0.299937	+	0.923113i
$170$	0.593096	+	3.56909i	0.0454884	+	0.273737i
$171$		0			0
$172$	−9.14729	+	2.97214i	−0.697475	+	0.226623i
$173$	−18.4661	−	6.00000i	−1.40395	−	0.456172i	−0.493485	−	0.869754i	$-0.664277\pi$
$173$	−18.4661	−	6.00000i	−1.40395	−	0.456172i	−0.910467	+	0.413583i	$0.864277\pi$
$174$		0			0
$175$	4.94427	−	3.70820i	0.373752	−	0.280314i
$176$	1.23607	−	3.07768i	0.0931721	−	0.231989i
$177$		0			0
$178$	4.97980	−	6.85410i	0.373252	−	0.513737i
$179$	4.71885	−	14.5231i	0.352703	−	1.08551i	−0.604626	−	0.796509i	$-0.706677\pi$
$179$	4.71885	−	14.5231i	0.352703	−	1.08551i	0.957329	−	0.288999i	$-0.0933225\pi$
$180$		0			0
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.993883	−	0.110442i	$-0.964773\pi$
$181$	−16.0902	+	11.6902i	−1.19597	+	0.868925i	−0.202090	+	0.979367i	$0.564773\pi$
$182$	−0.449028	−	0.618034i	−0.0332842	−	0.0458117i
$183$		0			0
$184$	0.500000	−	1.53884i	0.0368605	−	0.113445i
$185$	−6.57501	−	12.6656i	−0.483405	−	0.931191i
$186$		0			0
$187$	−4.97980	−	2.00000i	−0.364159	−	0.146254i
$188$		−	6.32624i		−	0.461388i
$189$		0			0
$190$	−3.87901	+	3.93835i	−0.281413	+	0.285718i
$191$	−1.38197	−	4.25325i	−0.0999956	−	0.307755i	0.888528	−	0.458823i	$-0.151729\pi$
$191$	−1.38197	−	4.25325i	−0.0999956	−	0.307755i	−0.988523	+	0.151068i	$0.951729\pi$
$192$		0			0
$193$	4.14725	+	5.70820i	0.298526	+	0.410886i	0.931760	−	0.363075i	$-0.118273\pi$
$193$	4.14725	+	5.70820i	0.298526	+	0.410886i	−0.633234	+	0.773960i	$0.718273\pi$
$194$	1.00000	+	3.07768i	0.0717958	+	0.220965i
$195$		0			0
$196$	4.42705	+	3.21644i	0.316218	+	0.229746i
$197$		−	10.7639i		−	0.766898i	−0.923562	−	0.383449i	$-0.874736\pi$
$197$		−	10.7639i		−	0.766898i	0.923562	−	0.383449i	$-0.125264\pi$
$198$		0			0
$199$	−9.03444			−0.640435			−0.320217	−	0.947344i	$-0.603756\pi$
$199$	−9.03444			−0.640435			−0.320217	+	0.947344i	$0.603756\pi$
$200$	4.99942	−	0.0759100i	0.353513	−	0.00536765i
$201$		0			0
$202$	−0.812299	+	0.263932i	−0.0571532	+	0.0185702i
$203$	−5.15131	−	7.09017i	−0.361551	−	0.497632i
$204$		0			0
$205$	−24.1992	−	3.64469i	−1.69015	−	0.254556i
$206$	5.38197	−	16.5640i	0.374979	−	1.15407i
$207$		0			0
$208$		−	0.618034i		−	0.0428529i
$209$	−2.00000	−	7.95148i	−0.138343	−	0.550015i
$210$		0			0
$211$	−9.85410	−	7.15942i	−0.678384	−	0.492875i	0.194437	−	0.980915i	$-0.437712\pi$
$211$	−9.85410	−	7.15942i	−0.678384	−	0.492875i	−0.872821	+	0.488040i	$0.837712\pi$
$212$	−6.43288	−	2.09017i	−0.441812	−	0.143553i
$213$		0			0
$214$	−14.3262	+	10.4086i	−0.979321	+	0.711519i
$215$	21.2156	−	3.52552i	1.44689	−	0.240439i
$216$		0			0
$217$	0.171513	+	0.0557281i	0.0116431	+	0.00378307i
$218$	7.60845	−	10.4721i	0.515309	−	0.709263i
$219$		0			0
$220$	−3.75804	+	6.39352i	−0.253367	+	0.431051i
$221$	−1.00000			−0.0672673
$222$		0			0
$223$	3.63271	+	1.18034i	0.243264	+	0.0790414i	0.428112	−	0.903726i	$-0.359179\pi$
$223$	3.63271	+	1.18034i	0.243264	+	0.0790414i	−0.184847	+	0.982767i	$0.559179\pi$
$224$	−0.381966	−	1.17557i	−0.0255212	−	0.0785461i
$225$		0			0
$226$	7.97214	−	5.79210i	0.530299	−	0.385284i
$227$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$227$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$228$		0			0
$229$	15.8541	+	11.5187i	1.04767	+	0.761176i	0.971768	−	0.235940i	$-0.0758168\pi$
$229$	15.8541	+	11.5187i	1.04767	+	0.761176i	0.0759008	+	0.997115i	$0.475817\pi$
$230$	−1.61803	+	3.23607i	−0.106690	+	0.213380i
$231$		0			0
$232$		−	7.09017i		−	0.465492i
$233$	−12.8455	+	17.6803i	−0.841538	+	1.15828i	0.144126	+	0.989559i	$0.453963\pi$
$233$	−12.8455	+	17.6803i	−0.841538	+	1.15828i	−0.985664	+	0.168718i	$0.946037\pi$
$234$		0			0
$235$	−2.10678	+	13.9881i	−0.137431	+	0.912485i
$236$	5.78115	−	4.20025i	0.376321	−	0.273413i
$237$		0			0
$238$	−1.90211	+	0.618034i	−0.123296	+	0.0400612i
$239$	−1.79837	+	5.53483i	−0.116327	+	0.358018i	−0.992222	−	0.124485i	$-0.960272\pi$
$239$	−1.79837	+	5.53483i	−0.116327	+	0.358018i	0.875894	+	0.482503i	$0.160272\pi$
$240$		0			0
$241$	14.9443			0.962645			0.481323	−	0.876544i	$-0.340157\pi$
$241$	14.9443			0.962645			0.481323	+	0.876544i	$0.340157\pi$
$242$	−5.20431	−	9.69098i	−0.334546	−	0.622960i
$243$		0			0
$244$	2.23607	+	1.62460i	0.143150	+	0.104004i
$245$	−8.71764	−	8.58628i	−0.556949	−	0.548557i
$246$		0			0
$247$	−0.898056	−	1.23607i	−0.0571419	−	0.0786491i
$248$	0.0857567	+	0.118034i	0.00544556	+	0.00749517i
$249$		0			0
$250$	−11.0797	−	1.49707i	−0.700739	−	0.0946833i
$251$	5.92705	+	4.30625i	0.374112	+	0.271808i	0.758914	−	0.651191i	$-0.225730\pi$
$251$	5.92705	+	4.30625i	0.374112	+	0.271808i	−0.384802	+	0.922999i	$0.625730\pi$
$252$		0			0
$253$	−2.85317	−	4.54508i	−0.179377	−	0.285747i
$254$	−8.00000			−0.501965
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.15942	−	2.32624i	0.446593	−	0.145107i	−0.0770826	−	0.997025i	$-0.524561\pi$
$257$	7.15942	−	2.32624i	0.446593	−	0.145107i	0.523675	+	0.851918i	$0.324561\pi$
$258$		0			0
$259$	6.38197	−	4.63677i	0.396556	−	0.288115i
$260$	−0.205819	+	1.36655i	−0.0127644	+	0.0847501i
$261$		0			0
$262$	−2.26538	+	3.11803i	−0.139956	+	0.192633i
$263$			6.56231i			0.404649i	0.979319	+	0.202325i	$0.0648496\pi$
$263$			6.56231i			0.404649i	−0.979319	+	0.202325i	$0.935150\pi$
$264$		0			0
$265$	13.5279	+	6.76393i	0.831010	+	0.415505i
$266$	−2.47214	−	1.79611i	−0.151576	−	0.110127i
$267$		0			0
$268$	−1.31433	+	0.427051i	−0.0802853	+	0.0260863i
$269$	21.4443	−	15.5802i	1.30748	−	0.949940i	0.307482	−	0.951554i	$-0.400514\pi$
$269$	21.4443	−	15.5802i	1.30748	−	0.949940i	0.999999	+	0.00161395i	$0.000513736\pi$
$270$		0			0
$271$	−5.20820	−	16.0292i	−0.316376	−	0.973705i	−0.975184	−	0.221394i	$-0.928939\pi$
$271$	−5.20820	−	16.0292i	−0.316376	−	0.973705i	0.658809	−	0.752311i	$-0.271061\pi$
$272$	−1.53884	−	0.500000i	−0.0933060	−	0.0303170i
$273$		0			0
$274$	9.56231			0.577680
$275$	10.4387	−	12.8854i	0.629478	−	0.777018i
$276$		0			0
$277$	−17.5150	+	24.1074i	−1.05238	+	1.44847i	−0.165647	+	0.986185i	$0.552971\pi$
$277$	−17.5150	+	24.1074i	−1.05238	+	1.44847i	−0.886730	+	0.462288i	$0.847029\pi$
$278$	−6.43288	−	2.09017i	−0.385819	−	0.125360i
$279$		0			0
$280$	0.453085	+	2.72654i	0.0270770	+	0.162942i
$281$	−4.23607	+	3.07768i	−0.252703	+	0.183599i	−0.706924	−	0.707290i	$-0.749918\pi$
$281$	−4.23607	+	3.07768i	−0.252703	+	0.183599i	0.454221	+	0.890889i	$0.349918\pi$
$282$		0			0
$283$	27.1114	+	8.80902i	1.61160	+	0.523642i	0.969940	−	0.243345i	$-0.0782446\pi$
$283$	27.1114	+	8.80902i	1.61160	+	0.523642i	0.641664	+	0.766986i	$0.278245\pi$
$284$	−1.38197	−	1.00406i	−0.0820046	−	0.0595798i
$285$		0			0
$286$	−1.57295	−	1.31433i	−0.0930104	−	0.0777178i
$287$		−	13.5279i		−	0.798525i
$288$		0			0
$289$	4.44427	−	13.6781i	0.261428	−	0.804592i
$290$	−2.36119	+	15.6773i	−0.138654	+	0.920602i
$291$		0			0
$292$	−4.80828	−	6.61803i	−0.281383	−	0.387291i
$293$	2.45714	−	0.798374i	0.143548	−	0.0466415i	−0.236362	−	0.971665i	$-0.575955\pi$
$293$	2.45714	−	0.798374i	0.143548	−	0.0466415i	0.379910	+	0.925024i	$0.375955\pi$
$294$		0			0
$295$	−14.1817	+	7.36205i	−0.825688	+	0.428635i
$296$	6.38197			0.370944
$297$		0			0
$298$		−	7.14590i		−	0.413951i
$299$	−0.809017	−	0.587785i	−0.0467867	−	0.0339925i
$300$		0			0
$301$	3.67376	+	11.3067i	0.211752	+	0.651706i
$302$	9.06154	+	12.4721i	0.521433	+	0.717691i
$303$		0			0
$304$	−0.763932	−	2.35114i	−0.0438145	−	0.134847i
$305$	−4.40321	−	4.33686i	−0.252127	−	0.248328i
$306$		0			0
$307$		−	9.74265i		−	0.556042i	−0.960575	−	0.278021i	$-0.910321\pi$
$307$		−	9.74265i		−	0.556042i	0.960575	−	0.278021i	$-0.0896785\pi$
$308$	−3.80423	−	1.52786i	−0.216766	−	0.0870581i
$309$		0			0
$310$	−0.150311	−	0.289547i	−0.00853711	−	0.0164452i
$311$	−6.14590	+	18.9151i	−0.348502	+	1.07258i	0.611180	+	0.791491i	$0.290695\pi$
$311$	−6.14590	+	18.9151i	−0.348502	+	1.07258i	−0.959682	+	0.281087i	$0.909305\pi$
$312$		0			0
$313$	15.2169	+	20.9443i	0.860110	+	1.18384i	0.981543	+	0.191241i	$0.0612511\pi$
$313$	15.2169	+	20.9443i	0.860110	+	1.18384i	−0.121433	+	0.992600i	$0.538749\pi$
$314$	−4.97214	+	3.61247i	−0.280594	+	0.203863i
$315$		0			0
$316$	−2.97214	+	9.14729i	−0.167196	+	0.514575i
$317$	−12.8658	+	17.7082i	−0.722613	+	0.994592i	0.276820	+	0.960922i	$0.410720\pi$
$317$	−12.8658	+	17.7082i	−0.722613	+	0.994592i	−0.999433	+	0.0336700i	$0.989280\pi$
$318$		0			0
$319$	−18.0451	−	15.0781i	−1.01033	−	0.844214i
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$		0			0
$322$	−1.90211	−	0.618034i	−0.106001	−	0.0344417i
$323$	−3.80423	+	1.23607i	−0.211673	+	0.0687767i
$324$		0			0
$325$	0.910186	−	2.95309i	0.0504880	−	0.163808i
$326$	−6.26393	−	19.2784i	−0.346927	−	1.06773i
$327$		0			0
$328$	6.43288	−	8.85410i	0.355196	−	0.488886i
$329$	−7.81966			−0.431112
$330$		0			0
$331$	26.4721			1.45504			0.727520	−	0.686086i	$-0.240673\pi$
$331$	26.4721			1.45504			0.727520	+	0.686086i	$0.240673\pi$
$332$	1.62460	−	2.23607i	0.0891614	−	0.122720i
$333$		0			0
$334$	2.80902	+	8.64527i	0.153703	+	0.473048i
$335$	3.04837	−	0.506564i	0.166550	−	0.0276766i
$336$		0			0
$337$	−12.3107	+	4.00000i	−0.670608	+	0.217894i	−0.624479	−	0.781042i	$-0.714689\pi$
$337$	−12.3107	+	4.00000i	−0.670608	+	0.217894i	−0.0461294	+	0.998935i	$0.514689\pi$
$338$	12.0005	+	3.89919i	0.652739	+	0.212088i
$339$		0			0
$340$	3.23607	+	1.61803i	0.175500	+	0.0877502i
$341$	0.482779	+	0.0327561i	0.0261440	+	0.00177384i
$342$		0			0
$343$	9.06154	−	12.4721i	0.489277	−	0.673432i
$344$	−2.97214	+	9.14729i	−0.160247	+	0.493189i
$345$		0			0
$346$	−15.7082	+	11.4127i	−0.844478	+	0.613549i
$347$	4.25325	+	5.85410i	0.228327	+	0.314265i	0.907774	−	0.419460i	$-0.137780\pi$
$347$	4.25325	+	5.85410i	0.228327	+	0.314265i	−0.679447	+	0.733724i	$0.737780\pi$
$348$		0			0
$349$	−0.0557281	+	0.171513i	−0.00298306	+	0.00918090i	−0.952537	−	0.304423i	$-0.901536\pi$
$349$	−0.0557281	+	0.171513i	−0.00298306	+	0.00918090i	0.949554	+	0.313604i	$0.101536\pi$
$350$	−0.0938299	−	6.17963i	−0.00501542	−	0.330315i
$351$		0			0
$352$	−1.76336	−	2.80902i	−0.0939872	−	0.149721i
$353$		−	10.5623i		−	0.562175i	−0.959682	−	0.281087i	$-0.909305\pi$
$353$		−	10.5623i		−	0.562175i	0.959682	−	0.281087i	$-0.0906951\pi$
$354$		0			0
$355$	2.72133	+	2.68033i	0.144433	+	0.142257i
$356$	−2.61803	−	8.05748i	−0.138756	−	0.427046i
$357$		0			0
$358$	−8.97578	−	12.3541i	−0.474385	−	0.652935i
$359$	−5.27051	−	16.2210i	−0.278167	−	0.856110i	−0.988364	−	0.152107i	$-0.951394\pi$
$359$	−5.27051	−	16.2210i	−0.278167	−	0.856110i	0.710197	−	0.704003i	$-0.248606\pi$
$360$		0			0
$361$	10.4271	+	7.57570i	0.548792	+	0.398721i
$362$			19.8885i			1.04532i
$363$		0			0
$364$	−0.763932			−0.0400409
$365$	8.42778	+	16.2346i	0.441130	+	0.849758i
$366$		0			0
$367$	27.0786	−	8.79837i	1.41349	−	0.459271i	0.499964	−	0.866046i	$-0.333347\pi$
$367$	27.0786	−	8.79837i	1.41349	−	0.459271i	0.913528	+	0.406775i	$0.133347\pi$
$368$	−0.951057	−	1.30902i	−0.0495772	−	0.0682372i
$369$		0			0
$370$	−14.1114	−	2.12534i	−0.733615	−	0.110491i
$371$	−2.58359	+	7.95148i	−0.134133	+	0.412820i
$372$		0			0
$373$			9.41641i			0.487563i	0.969830	+	0.243782i	$0.0783880\pi$
$373$			9.41641i			0.487563i	−0.969830	+	0.243782i	$0.921612\pi$
$374$	−4.54508	+	2.85317i	−0.235021	+	0.147534i
$375$		0			0
$376$	−5.11803	−	3.71847i	−0.263942	−	0.191765i
$377$	−4.16750	−	1.35410i	−0.214637	−	0.0697398i
$378$		0			0
$379$	−26.4164	+	19.1926i	−1.35692	+	0.985860i	−0.358286	+	0.933612i	$0.616639\pi$
$379$	−26.4164	+	19.1926i	−1.35692	+	0.985860i	−0.998634	+	0.0522478i	$0.983361\pi$
$380$	0.906170	+	5.45309i	0.0464855	+	0.279737i
$381$		0			0
$382$	−4.25325	−	1.38197i	−0.217615	−	0.0707075i
$383$	10.6004	−	14.5902i	0.541654	−	0.745523i	−0.447196	−	0.894436i	$-0.647577\pi$
$383$	10.6004	−	14.5902i	0.541654	−	0.745523i	0.988850	+	0.148913i	$0.0475774\pi$
$384$		0			0
$385$	7.90283	+	4.64520i	0.402765	+	0.236741i
$386$	7.05573			0.359127
$387$		0			0
$388$	3.07768	+	1.00000i	0.156246	+	0.0507673i
$389$	−0.972136	−	2.99193i	−0.0492892	−	0.151697i	0.923383	−	0.383881i	$-0.125413\pi$
$389$	−0.972136	−	2.99193i	−0.0492892	−	0.151697i	−0.972672	+	0.232184i	$0.925413\pi$
$390$		0			0
$391$	−2.11803	+	1.53884i	−0.107114	+	0.0778226i
$392$	5.20431	−	1.69098i	0.262857	−	0.0854075i
$393$		0			0
$394$	−8.70820	−	6.32688i	−0.438713	−	0.318744i
$395$	9.61803	−	19.2361i	0.483936	−	0.967872i
$396$		0			0
$397$		−	5.61803i		−	0.281961i	−0.990012	−	0.140981i	$-0.954975\pi$
$397$		−	5.61803i		−	0.281961i	0.990012	−	0.140981i	$-0.0450255\pi$
$398$	−5.31031	+	7.30902i	−0.266182	+	0.366368i
$399$		0			0
$400$	2.87718	−	4.08924i	0.143859	−	0.204462i
$401$	−24.5623	+	17.8456i	−1.22658	+	0.891165i	−0.996629	−	0.0820368i	$-0.973857\pi$
$401$	−24.5623	+	17.8456i	−1.22658	+	0.891165i	−0.229954	+	0.973202i	$0.573857\pi$
$402$		0			0
$403$	0.0857567	−	0.0278640i	0.00427185	−	0.00138801i
$404$	−0.263932	+	0.812299i	−0.0131311	+	0.0404134i
$405$		0			0
$406$	−8.76393			−0.434947
$407$	13.5721	−	16.2426i	0.672742	−	0.805118i
$408$		0			0
$409$	−17.6803	−	12.8455i	−0.874237	−	0.635170i	0.0574839	−	0.998346i	$-0.481692\pi$
$409$	−17.6803	−	12.8455i	−0.874237	−	0.635170i	−0.931720	+	0.363176i	$0.881692\pi$
$410$	−17.1726	+	17.4353i	−0.848092	+	0.861067i
$411$		0			0
$412$	−10.2371	−	14.0902i	−0.504346	−	0.694173i
$413$	−5.19180	−	7.14590i	−0.255472	−	0.351627i
$414$		0			0
$415$	−4.33686	+	4.40321i	−0.212888	+	0.216145i
$416$	−0.500000	−	0.363271i	−0.0245145	−	0.0178108i
$417$		0			0
$418$	−7.60845	−	3.05573i	−0.372142	−	0.149461i
$419$	−34.5623			−1.68848			−0.844240	−	0.535966i	$-0.819948\pi$
$419$	−34.5623			−1.68848			−0.844240	+	0.535966i	$0.819948\pi$
$420$		0			0
$421$	2.03444	−	6.26137i	0.0991526	−	0.305160i	−0.889161	−	0.457594i	$-0.848711\pi$
$421$	2.03444	−	6.26137i	0.0991526	−	0.305160i	0.988314	+	0.152434i	$0.0487112\pi$
$422$	−11.5842	+	3.76393i	−0.563910	+	0.183225i
$423$		0			0
$424$	−5.47214	+	3.97574i	−0.265750	+	0.193079i
$425$	−6.61653	−	4.65537i	−0.320949	−	0.225818i
$426$		0			0
$427$	2.00811	−	2.76393i	0.0971795	−	0.133756i
$428$			17.7082i			0.855958i
$429$		0			0
$430$	9.61803	−	19.2361i	0.463823	−	0.927646i
$431$	29.8885	+	21.7153i	1.43968	+	1.04599i	0.988109	+	0.153754i	$0.0491364\pi$
$431$	29.8885	+	21.7153i	1.43968	+	1.04599i	0.451571	+	0.892235i	$0.350864\pi$
$432$		0			0
$433$	24.1724	−	7.85410i	1.16165	−	0.377444i	0.336132	−	0.941815i	$-0.390881\pi$
$433$	24.1724	−	7.85410i	1.16165	−	0.377444i	0.825521	+	0.564371i	$0.190881\pi$
$434$	0.145898	−	0.106001i	0.00700333	−	0.00508822i
$435$		0			0
$436$	−4.00000	−	12.3107i	−0.191565	−	0.589577i
$437$	−3.80423	−	1.23607i	−0.181981	−	0.0591292i
$438$		0			0
$439$	37.1591			1.77350			0.886752	−	0.462245i	$-0.152956\pi$
$439$	37.1591			1.77350			0.886752	+	0.462245i	$0.152956\pi$
$440$	2.96354	+	6.79834i	0.141281	+	0.324098i
$441$		0			0
$442$	−0.587785	+	0.809017i	−0.0279581	+	0.0384810i
$443$	38.1078	+	12.3820i	1.81055	+	0.588285i	0.999997	+	0.00262712i	$0.000836238\pi$
$443$	38.1078	+	12.3820i	1.81055	+	0.588285i	0.810558	+	0.585658i	$0.199164\pi$
$444$		0			0
$445$	3.10549	+	18.6880i	0.147214	+	0.885896i
$446$	3.09017	−	2.24514i	0.146324	−	0.106310i
$447$		0			0
$448$	−1.17557	−	0.381966i	−0.0555405	−	0.0180462i
$449$	10.1803	+	7.39645i	0.480440	+	0.349060i	0.801496	−	0.598000i	$-0.204038\pi$
$449$	10.1803	+	7.39645i	0.480440	+	0.349060i	−0.321056	+	0.947060i	$0.604038\pi$
$450$		0			0
$451$	−8.85410	−	35.2016i	−0.416923	−	1.65758i
$452$		−	9.85410i		−	0.463498i
$453$		0			0
$454$		0			0
$455$	1.68915	+	0.254407i	0.0791887	+	0.0119268i
$456$		0			0
$457$	18.0826	+	24.8885i	0.845868	+	1.16424i	0.984758	+	0.173929i	$0.0556464\pi$
$457$	18.0826	+	24.8885i	0.845868	+	1.16424i	−0.138890	+	0.990308i	$0.544354\pi$
$458$	18.6376	−	6.05573i	0.870879	−	0.282966i
$459$		0			0
$460$	1.66698	+	3.21113i	0.0777232	+	0.149720i
$461$	−9.43769			−0.439557			−0.219779	−	0.975550i	$-0.570534\pi$
$461$	−9.43769			−0.439557			−0.219779	+	0.975550i	$0.570534\pi$
$462$		0			0
$463$		−	22.9443i		−	1.06631i	−0.846017	−	0.533155i	$-0.821006\pi$
$463$		−	22.9443i		−	1.06631i	0.846017	−	0.533155i	$-0.178994\pi$
$464$	−5.73607	−	4.16750i	−0.266290	−	0.193471i
$465$		0			0
$466$	6.75329	+	20.7845i	0.312840	+	0.962823i
$467$	5.32282	+	7.32624i	0.246311	+	0.339018i	0.914215	−	0.405229i	$-0.132808\pi$
$467$	5.32282	+	7.32624i	0.246311	+	0.339018i	−0.667904	+	0.744247i	$0.732808\pi$
$468$		0			0
$469$	0.527864	+	1.62460i	0.0243745	+	0.0750170i
$470$	10.0783	+	9.92644i	0.464878	+	0.457873i
$471$		0			0
$472$		−	7.14590i		−	0.328917i
$473$	16.9600	+	27.0172i	0.779822	+	1.24225i
$474$		0			0
$475$	−0.187660	−	12.3593i	−0.00861042	−	0.567082i
$476$	−0.618034	+	1.90211i	−0.0283275	+	0.0871832i
$477$		0			0
$478$	3.42071	+	4.70820i	0.156460	+	0.215348i
$479$	−25.0344	+	18.1886i	−1.14385	+	0.831058i	−0.987651	−	0.156667i	$-0.949925\pi$
$479$	−25.0344	+	18.1886i	−1.14385	+	0.831058i	−0.156201	+	0.987725i	$0.549925\pi$
$480$		0			0
$481$	1.21885	−	3.75123i	0.0555746	−	0.171041i
$482$	8.78402	−	12.0902i	0.400101	−	0.550692i
$483$		0			0
$484$	−10.8992	−	1.48584i	−0.495418	−	0.0675382i
$485$	−6.47214	−	3.23607i	−0.293885	−	0.146942i
$486$		0			0
$487$	−1.17557	−	0.381966i	−0.0532702	−	0.0173085i	0.282261	−	0.959338i	$-0.408916\pi$
$487$	−1.17557	−	0.381966i	−0.0532702	−	0.0173085i	−0.335531	+	0.942029i	$0.608916\pi$
$488$	2.62866	−	0.854102i	0.118994	−	0.0386634i
$489$		0			0
$490$	−12.0705	+	2.00583i	−0.545292	+	0.0906142i
$491$	12.0451	+	37.0710i	0.543587	+	1.67299i	0.724326	+	0.689458i	$0.242151\pi$
$491$	12.0451	+	37.0710i	0.543587	+	1.67299i	−0.180739	+	0.983531i	$0.557849\pi$
$492$		0			0
$493$	−6.74315	+	9.28115i	−0.303696	+	0.418002i
$494$	−1.52786			−0.0687419
$495$		0			0
$496$	0.145898			0.00655102
$497$	−1.24108	+	1.70820i	−0.0556702	+	0.0766234i
$498$		0			0
$499$	5.09017	+	15.6659i	0.227867	+	0.701303i	0.997988	+	0.0634051i	$0.0201960\pi$
$499$	5.09017	+	15.6659i	0.227867	+	0.701303i	−0.770121	+	0.637898i	$0.779804\pi$
$500$	−7.72362	+	8.08367i	−0.345411	+	0.361513i
$501$		0			0
$502$	6.96767	−	2.26393i	0.310982	−	0.101044i
$503$	−1.65735	−	0.538507i	−0.0738978	−	0.0240108i	0.271835	−	0.962344i	$-0.412370\pi$
$503$	−1.65735	−	0.538507i	−0.0738978	−	0.0240108i	−0.345733	+	0.938333i	$0.612370\pi$
$504$		0			0
$505$	0.854102	−	1.70820i	0.0380070	−	0.0760141i
$506$	−5.35410	−	0.363271i	−0.238019	−	0.0161494i
$507$		0			0
$508$	−4.70228	+	6.47214i	−0.208630	+	0.287155i
$509$	−0.392609	+	1.20833i	−0.0174021	+	0.0535581i	−0.959380	−	0.282115i	$-0.908964\pi$
$509$	−0.392609	+	1.20833i	−0.0174021	+	0.0535581i	0.941978	+	0.335674i	$0.108964\pi$
$510$		0			0
$511$	−8.18034	+	5.94336i	−0.361877	+	0.262919i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$		0			0
$514$	2.32624	−	7.15942i	0.102606	−	0.315789i
$515$	17.9432	+	34.5644i	0.790673	+	1.52309i
$516$		0			0
$517$	−20.3480	+	5.11803i	−0.894903	+	0.225091i
$518$		−	7.88854i		−	0.346603i
$519$		0			0
$520$	0.984587	+	0.969751i	0.0431770	+	0.0425264i
$521$	10.8197	+	33.2995i	0.474018	+	1.45888i	0.847278	+	0.531150i	$0.178240\pi$
$521$	10.8197	+	33.2995i	0.474018	+	1.45888i	−0.373260	+	0.927727i	$0.621760\pi$
$522$		0			0
$523$	6.71040	+	9.23607i	0.293425	+	0.403865i	0.930123	−	0.367248i	$-0.119700\pi$
$523$	6.71040	+	9.23607i	0.293425	+	0.403865i	−0.636698	+	0.771113i	$0.719700\pi$
$524$	1.19098	+	3.66547i	0.0520283	+	0.160127i
$525$		0			0
$526$	5.30902	+	3.85723i	0.231484	+	0.168183i
$527$		−	0.236068i		−	0.0102833i
$528$		0			0
$529$	20.3820			0.886172
$530$	13.4236	−	6.96853i	0.583085	−	0.302694i
$531$		0			0
$532$	−2.90617	+	0.944272i	−0.125998	+	0.0409394i
$533$	−3.97574	−	5.47214i	−0.172208	−	0.237025i
$534$		0			0
$535$	5.89723	−	39.1551i	0.254960	−	1.69282i
$536$	−0.427051	+	1.31433i	−0.0184458	+	0.0567703i
$537$		0			0
$538$		−	26.5066i		−	1.14278i
$539$	6.76393	−	16.8415i	0.291343	−	0.725415i
$540$		0			0
$541$	1.76393	+	1.28157i	0.0758374	+	0.0550991i	0.625058	−	0.780578i	$-0.285075\pi$
$541$	1.76393	+	1.28157i	0.0758374	+	0.0550991i	−0.549221	+	0.835677i	$0.685075\pi$
$542$	−16.0292	−	5.20820i	−0.688513	−	0.223712i
$543$		0			0
$544$	−1.30902	+	0.951057i	−0.0561236	+	0.0407762i
$545$	4.74477	+	28.5527i	0.203244	+	1.22306i
$546$		0			0
$547$	27.6664	+	8.98936i	1.18293	+	0.384357i	0.833454	−	0.552588i	$-0.186360\pi$
$547$	27.6664	+	8.98936i	1.18293	+	0.384357i	0.349475	+	0.936946i	$0.386360\pi$
$548$	5.62058	−	7.73607i	0.240099	−	0.330468i
$549$		0			0
$550$	−4.28878	−	16.0189i	−0.182874	−	0.683050i
$551$	−17.5279			−0.746712
$552$		0			0
$553$	11.3067	+	3.67376i	0.480809	+	0.156224i
$554$	9.20820	+	28.3399i	0.391219	+	1.20405i
$555$		0			0
$556$	−5.47214	+	3.97574i	−0.232070	+	0.168609i
$557$	26.6296	−	8.65248i	1.12833	−	0.366617i	0.315390	−	0.948962i	$-0.397865\pi$
$557$	26.6296	−	8.65248i	1.12833	−	0.366617i	0.812942	+	0.582345i	$0.197865\pi$
$558$		0			0
$559$	4.80902	+	3.49396i	0.203400	+	0.147779i
$560$	2.47214	+	1.23607i	0.104467	+	0.0522334i
$561$		0			0
$562$			5.23607i			0.220870i
$563$	−20.1967	+	27.7984i	−0.851189	+	1.17156i	0.132410	+	0.991195i	$0.457728\pi$
$563$	−20.1967	+	27.7984i	−0.851189	+	1.17156i	−0.983599	+	0.180367i	$0.942272\pi$
$564$		0			0
$565$	−3.28164	+	21.7887i	−0.138060	+	0.916658i
$566$	23.0623	−	16.7557i	0.969381	−	0.704297i
$567$		0			0
$568$	−1.62460	+	0.527864i	−0.0681666	+	0.0221487i
$569$	0.618034	−	1.90211i	0.0259093	−	0.0797407i	−0.937266	−	0.348616i	$-0.886652\pi$
$569$	0.618034	−	1.90211i	0.0259093	−	0.0797407i	0.963175	+	0.268875i	$0.0866518\pi$
$570$		0			0
$571$	−0.583592			−0.0244226			−0.0122113	−	0.999925i	$-0.503887\pi$
$571$	−0.583592			−0.0244226			−0.0122113	+	0.999925i	$0.503887\pi$
$572$	−1.98787	+	0.500000i	−0.0831170	+	0.0209061i
$573$		0			0
$574$	−10.9443	−	7.95148i	−0.456805	−	0.331888i
$575$	−2.61653	−	7.65537i	−0.109117	−	0.319251i
$576$		0			0
$577$	19.5357	+	26.8885i	0.813281	+	1.11938i	0.990809	+	0.135269i	$0.0431899\pi$
$577$	19.5357	+	26.8885i	0.813281	+	1.11938i	−0.177528	+	0.984116i	$0.556810\pi$
$578$	−8.45351	−	11.6353i	−0.351620	−	0.483963i
$579$		0			0
$580$	11.2953	+	11.1251i	0.469013	+	0.461945i
$581$	−2.76393	−	2.00811i	−0.114667	−	0.0833106i
$582$		0			0
$583$	−1.51860	+	22.3820i	−0.0628939	+	0.926966i
$584$	−8.18034			−0.338505
$585$		0			0
$586$	0.798374	−	2.45714i	0.0329805	−	0.101504i
$587$	14.7679	−	4.79837i	0.609535	−	0.198050i	0.0120468	−	0.999927i	$-0.496165\pi$
$587$	14.7679	−	4.79837i	0.609535	−	0.198050i	0.597489	+	0.801877i	$0.296165\pi$
$588$		0			0
$589$	0.291796	−	0.212002i	0.0120232	−	0.00873540i
$590$	−2.37975	+	15.8005i	−0.0979726	+	0.650497i
$591$		0			0
$592$	3.75123	−	5.16312i	0.154174	−	0.212203i
$593$		−	26.5066i		−	1.08849i	−0.838925	−	0.544247i	$-0.816815\pi$
$593$		−	26.5066i		−	1.08849i	0.838925	−	0.544247i	$-0.183185\pi$
$594$		0			0
$595$	2.00000	−	4.00000i	0.0819920	−	0.163984i
$596$	−5.78115	−	4.20025i	−0.236805	−	0.172049i
$597$		0			0
$598$	−0.951057	+	0.309017i	−0.0388916	+	0.0126366i
$599$	−27.4164	+	19.9192i	−1.12020	+	0.813876i	−0.984240	−	0.176838i	$-0.943413\pi$
$599$	−27.4164	+	19.9192i	−1.12020	+	0.813876i	−0.135964	+	0.990714i	$0.543413\pi$
$600$		0			0
$601$	−6.32624	−	19.4702i	−0.258053	−	0.794204i	−0.993213	−	0.116311i	$-0.962893\pi$
$601$	−6.32624	−	19.4702i	−0.258053	−	0.794204i	0.735160	−	0.677893i	$-0.237107\pi$
$602$	11.3067	+	3.67376i	0.460826	+	0.149731i
$603$		0			0
$604$	15.4164			0.627285
$605$	23.6047	+	6.91506i	0.959668	+	0.281137i
$606$		0			0
$607$	0.726543	−	1.00000i	0.0294895	−	0.0405887i	−0.794018	−	0.607895i	$-0.792014\pi$
$607$	0.726543	−	1.00000i	0.0294895	−	0.0405887i	0.823507	+	0.567306i	$0.192014\pi$
$608$	−2.35114	−	0.763932i	−0.0953514	−	0.0309815i
$609$		0			0
$610$	−6.09673	+	1.01313i	−0.246850	+	0.0410204i
$611$	−3.16312	+	2.29814i	−0.127966	+	0.0929728i
$612$		0			0
$613$	−35.5851	−	11.5623i	−1.43727	−	0.466997i	−0.516224	−	0.856453i	$-0.672663\pi$
$613$	−35.5851	−	11.5623i	−1.43727	−	0.466997i	−0.921045	+	0.389456i	$0.872663\pi$
$614$	−7.88197	−	5.72658i	−0.318090	−	0.231106i
$615$		0			0
$616$	−3.47214	+	2.17963i	−0.139896	+	0.0878197i
$617$			19.3050i			0.777188i	0.921409	+	0.388594i	$0.127039\pi$
$617$			19.3050i			0.777188i	−0.921409	+	0.388594i	$0.872961\pi$
$618$		0			0
$619$	11.3820	−	35.0301i	0.457480	−	1.40798i	−0.410719	−	0.911762i	$-0.634722\pi$
$619$	11.3820	−	35.0301i	0.457480	−	1.40798i	0.868199	−	0.496216i	$-0.165278\pi$
$620$	−0.322600	−	0.0485873i	−0.0129559	−	0.00195131i
$621$		0			0
$622$	11.6902	+	16.0902i	0.468734	+	0.645157i
$623$	−9.95959	+	3.23607i	−0.399023	+	0.129650i
$624$		0			0
$625$	19.7700	−	15.3019i	0.790799	−	0.612076i
$626$	25.8885			1.03471
$627$		0			0
$628$			6.14590i			0.245248i
$629$	−8.35410	−	6.06961i	−0.333100	−	0.242011i
$630$		0			0
$631$	5.95492	+	18.3273i	0.237061	+	0.729600i	0.996841	+	0.0794196i	$0.0253067\pi$
$631$	5.95492	+	18.3273i	0.237061	+	0.729600i	−0.759780	+	0.650180i	$0.774693\pi$
$632$	5.65334	+	7.78115i	0.224878	+	0.309518i
$633$		0			0
$634$	6.76393	+	20.8172i	0.268630	+	0.826758i
$635$	12.5527	−	12.7448i	0.498140	−	0.505761i
$636$		0			0
$637$		−	3.38197i		−	0.133998i
$638$	−22.8051	+	5.73607i	−0.902863	+	0.227093i
$639$		0			0
$640$	1.03025	+	1.98459i	0.0407242	+	0.0784477i
$641$	0.145898	−	0.449028i	0.00576263	−	0.0177355i	−0.948134	−	0.317871i	$-0.897032\pi$
$641$	0.145898	−	0.449028i	0.00576263	−	0.0177355i	0.953896	+	0.300136i	$0.0970320\pi$
$642$		0			0
$643$	−9.49032	−	13.0623i	−0.374262	−	0.515127i	0.579791	−	0.814765i	$-0.303134\pi$
$643$	−9.49032	−	13.0623i	−0.374262	−	0.515127i	−0.954053	+	0.299638i	$0.903134\pi$
$644$	−1.61803	+	1.17557i	−0.0637595	+	0.0463240i
$645$		0			0
$646$	−1.23607	+	3.80423i	−0.0486324	+	0.149675i
$647$	−26.2336	+	36.1074i	−1.03135	+	1.41953i	−0.127417	+	0.991849i	$0.540669\pi$
$647$	−26.2336	+	36.1074i	−1.03135	+	1.41953i	−0.903931	+	0.427679i	$0.859331\pi$
$648$		0			0
$649$	−18.1869	−	15.1967i	−0.713899	−	0.596521i
$650$	−1.85410	−	2.47214i	−0.0727239	−	0.0969651i
$651$		0			0
$652$	−19.2784	−	6.26393i	−0.755000	−	0.245315i
$653$	3.69822	−	1.20163i	0.144723	−	0.0470233i	−0.235760	−	0.971811i	$-0.575758\pi$
$653$	3.69822	−	1.20163i	0.144723	−	0.0470233i	0.380483	+	0.924788i	$0.375758\pi$
$654$		0			0
$655$	−1.41273	−	8.50145i	−0.0552001	−	0.332179i
$656$	−3.38197	−	10.4086i	−0.132044	−	0.406388i
$657$		0			0
$658$	−4.59628	+	6.32624i	−0.179182	+	0.246622i
$659$	−9.88854			−0.385203			−0.192601	−	0.981277i	$-0.561692\pi$
$659$	−9.88854			−0.385203			−0.192601	+	0.981277i	$0.561692\pi$
$660$		0			0
$661$	40.3607			1.56985			0.784924	−	0.619592i	$-0.212702\pi$
$661$	40.3607			1.56985			0.784924	+	0.619592i	$0.212702\pi$
$662$	15.5599	−	21.4164i	0.604754	−	0.832372i
$663$		0			0
$664$	−0.854102	−	2.62866i	−0.0331456	−	0.102012i
$665$	6.74038	−	1.12009i	0.261381	−	0.0434351i
$666$		0			0
$667$	−10.9106	+	3.54508i	−0.422462	+	0.137266i
$668$	8.64527	+	2.80902i	0.334495	+	0.108684i
$669$		0			0
$670$	1.38197	−	2.76393i	0.0533900	−	0.106780i
$671$	3.41641	−	8.50651i	0.131889	−	0.328390i
$672$		0			0
$673$	−15.3229	+	21.0902i	−0.590655	+	0.812966i	−0.994813	−	0.101723i	$-0.967565\pi$
$673$	−15.3229	+	21.0902i	−0.590655	+	0.812966i	0.404158	+	0.914689i	$0.367565\pi$
$674$	−4.00000	+	12.3107i	−0.154074	+	0.474192i
$675$		0			0
$676$	10.2082	−	7.41669i	0.392623	−	0.285257i
$677$	−13.1433	−	18.0902i	−0.505137	−	0.695262i	0.477953	−	0.878386i	$-0.341379\pi$
$677$	−13.1433	−	18.0902i	−0.505137	−	0.695262i	−0.983090	+	0.183124i	$0.941379\pi$
$678$		0			0
$679$	1.23607	−	3.80423i	0.0474359	−	0.145993i
$680$	3.21113	−	1.66698i	0.123141	−	0.0639257i
$681$		0			0
$682$	0.310271	−	0.371323i	0.0118809	−	0.0142187i
$683$		−	20.0689i		−	0.767914i	−0.923351	−	0.383957i	$-0.874561\pi$
$683$		−	20.0689i		−	0.767914i	0.923351	−	0.383957i	$-0.125439\pi$
$684$		0			0
$685$	−15.0041	+	15.2337i	−0.573278	+	0.582049i
$686$	−4.76393	−	14.6619i	−0.181888	−	0.559793i
$687$		0			0
$688$	5.65334	+	7.78115i	0.215532	+	0.296654i
$689$	1.29180	+	3.97574i	0.0492135	+	0.151464i
$690$		0			0
$691$	−14.0344	−	10.1966i	−0.533895	−	0.387898i	0.287918	−	0.957655i	$-0.407037\pi$
$691$	−14.0344	−	10.1966i	−0.533895	−	0.387898i	−0.821813	+	0.569758i	$0.807037\pi$
$692$			19.4164i			0.738101i
$693$		0			0
$694$	7.23607			0.274677
$695$	13.4236	−	6.96853i	0.509187	−	0.264332i
$696$		0			0
$697$	−16.8415	+	5.47214i	−0.637917	+	0.207272i
$698$	0.106001	+	0.145898i	0.00401220	+	0.00552232i
$699$		0			0
$700$	−5.05458	−	3.55638i	−0.191045	−	0.134419i
$701$	−8.03444	+	24.7275i	−0.303457	+	0.933944i	0.676792	+	0.736174i	$0.263370\pi$
$701$	−8.03444	+	24.7275i	−0.303457	+	0.933944i	−0.980249	+	0.197769i	$0.936630\pi$
$702$		0			0
$703$		−	15.7771i		−	0.595044i
$704$	−3.30902	−	0.224514i	−0.124713	−	0.00846169i
$705$		0			0
$706$	−8.54508	−	6.20837i	−0.321599	−	0.233655i
$707$	1.00406	+	0.326238i	0.0377615	+	0.0122694i
$708$		0			0
$709$	−36.8885	+	26.8011i	−1.38538	+	1.00654i	−0.389024	+	0.921228i	$0.627188\pi$
$709$	−36.8885	+	26.8011i	−1.38538	+	1.00654i	−0.996355	+	0.0853086i	$0.972812\pi$
$710$	3.76799	−	0.626148i	0.141410	−	0.0234989i
$711$		0			0
$712$	−8.05748	−	2.61803i	−0.301967	−	0.0981150i
$713$	0.138757	−	0.190983i	0.00519650	−	0.00715237i
$714$		0			0
$715$	4.56195	−	0.443560i	0.170607	−	0.0165882i
$716$	−15.2705			−0.570686
$717$		0			0
$718$	−16.2210	−	5.27051i	−0.605361	−	0.196694i
$719$	−8.61803	−	26.5236i	−0.321398	−	0.989163i	−0.973040	−	0.230636i	$-0.925919\pi$
$719$	−8.61803	−	26.5236i	−0.321398	−	0.989163i	0.651642	−	0.758527i	$-0.274081\pi$
$720$		0			0
$721$	−17.4164	+	12.6538i	−0.648621	+	0.471251i
$722$	12.2577	−	3.98278i	0.456186	−	0.148224i
$723$		0			0
$724$	16.0902	+	11.6902i	0.597986	+	0.434463i
$725$	−21.2705	−	28.3607i	−0.789967	−	1.05329i
$726$		0			0
$727$			2.18034i			0.0808643i	0.999182	+	0.0404322i	$0.0128735\pi$
$727$			2.18034i			0.0808643i	−0.999182	+	0.0404322i	$0.987127\pi$
$728$	−0.449028	+	0.618034i	−0.0166421	+	0.0229059i
$729$		0			0
$730$	18.0878	+	2.72424i	0.669459	+	0.100829i
$731$	12.5902	−	9.14729i	0.465664	−	0.338325i
$732$		0			0
$733$	−42.1038	+	13.6803i	−1.55514	+	0.505295i	−0.955504	−	0.294979i	$-0.904687\pi$
$733$	−42.1038	+	13.6803i	−1.55514	+	0.505295i	−0.599634	+	0.800274i	$0.704687\pi$
$734$	8.79837	−	27.0786i	0.324754	−	0.999490i
$735$		0			0
$736$	−1.61803			−0.0596415
$737$	2.43690	+	3.88197i	0.0897643	+	0.142994i
$738$		0			0
$739$	17.4721	+	12.6942i	0.642723	+	0.466966i	0.860785	−	0.508969i	$-0.169973\pi$
$739$	17.4721	+	12.6942i	0.642723	+	0.466966i	−0.218062	+	0.975935i	$0.569973\pi$
$740$	−10.0139	+	10.1671i	−0.368118	+	0.373749i
$741$		0			0
$742$	4.91428	+	6.76393i	0.180409	+	0.248312i
$743$	−16.5842	−	22.8262i	−0.608416	−	0.837413i	0.388030	−	0.921647i	$-0.373156\pi$
$743$	−16.5842	−	22.8262i	−0.608416	−	0.837413i	−0.996446	+	0.0842335i	$0.973156\pi$
$744$		0			0
$745$	11.3841	+	11.2126i	0.417081	+	0.410796i
$746$	7.61803	+	5.53483i	0.278916	+	0.202644i
$747$		0			0
$748$	−0.363271	+	5.35410i	−0.0132825	+	0.195765i
$749$	21.8885			0.799790
$750$		0			0
$751$	−10.5000	+	32.3157i	−0.383150	+	1.17922i	0.554663	+	0.832075i	$0.312847\pi$
$751$	−10.5000	+	32.3157i	−0.383150	+	1.17922i	−0.937813	+	0.347141i	$0.887153\pi$
$752$	−6.01661	+	1.95492i	−0.219403	+	0.0712884i
$753$		0			0
$754$	−3.54508	+	2.57565i	−0.129104	+	0.0937998i
$755$	−34.0877	−	5.13401i	−1.24058	−	0.186846i
$756$		0			0
$757$	12.1595	−	16.7361i	0.441943	−	0.608283i	−0.528699	−	0.848809i	$-0.677320\pi$
$757$	12.1595	−	16.7361i	0.441943	−	0.608283i	0.970643	+	0.240526i	$0.0773201\pi$
$758$			32.6525i			1.18599i
$759$		0			0
$760$	4.94427	+	2.47214i	0.179348	+	0.0896738i
$761$	1.23607	+	0.898056i	0.0448074	+	0.0325545i	0.609964	−	0.792429i	$-0.291184\pi$
$761$	1.23607	+	0.898056i	0.0448074	+	0.0325545i	−0.565156	+	0.824984i	$0.691184\pi$
$762$		0			0
$763$	−15.2169	+	4.94427i	−0.550889	+	0.178995i
$764$	−3.61803	+	2.62866i	−0.130896	+	0.0951014i
$765$		0			0
$766$	−5.57295	−	17.1518i	−0.201359	−	0.619719i
$767$	−4.20025	−	1.36475i	−0.151662	−	0.0492781i
$768$		0			0
$769$	13.0344			0.470034			0.235017	−	0.971991i	$-0.424485\pi$
$769$	13.0344			0.470034			0.235017	+	0.971991i	$0.424485\pi$
$770$	8.40321	−	3.66314i	0.302831	−	0.132010i
$771$		0			0
$772$	4.14725	−	5.70820i	0.149263	−	0.205443i
$773$	41.1199	+	13.3607i	1.47898	+	0.480550i	0.933808	−	0.357773i	$-0.116464\pi$
$773$	41.1199	+	13.3607i	1.47898	+	0.480550i	0.545173	+	0.838323i	$0.316464\pi$
$774$		0			0
$775$	0.697129	+	0.214866i	0.0250416	+	0.00771821i
$776$	2.61803	−	1.90211i	0.0939819	−	0.0682819i
$777$		0			0
$778$	−2.99193	−	0.972136i	−0.107266	−	0.0348528i
$779$	−21.8885	−	15.9030i	−0.784238	−	0.569783i
$780$		0			0
$781$	−2.11146	+	5.25731i	−0.0755538	+	0.188121i
$782$			2.61803i			0.0936207i
$783$		0			0
$784$	1.69098	−	5.20431i	0.0603923	−	0.185868i
$785$	2.04672	−	13.5894i	0.0730507	−	0.485026i
$786$		0			0
$787$	−29.2707	−	40.2877i	−1.04339	−	1.43610i	−0.894402	−	0.447263i	$-0.852399\pi$
$787$	−29.2707	−	40.2877i	−1.04339	−	1.43610i	−0.148987	−	0.988839i	$-0.547601\pi$
$788$	−10.2371	+	3.32624i	−0.364682	+	0.118492i
$789$		0			0
$790$	−9.90897	−	19.0878i	−0.352545	−	0.679115i
$791$	−12.1803			−0.433083
$792$		0			0
$793$		−	1.70820i		−	0.0606601i
$794$	−4.54508	−	3.30220i	−0.161299	−	0.117191i
$795$		0			0
$796$	2.79180	+	8.59226i	0.0989526	+	0.304545i
$797$	1.79611	+	2.47214i	0.0636215	+	0.0875675i	0.839642	−	0.543140i	$-0.182765\pi$
$797$	1.79611	+	2.47214i	0.0636215	+	0.0875675i	−0.776021	+	0.630708i	$0.782765\pi$
$798$		0			0
$799$	3.16312	+	9.73508i	0.111903	+	0.344402i
$800$	−1.61710	−	4.73128i	−0.0571732	−	0.167276i
$801$		0			0
$802$			30.3607i			1.07207i
$803$	−17.3965	+	20.8197i	−0.613910	+	0.734710i
$804$		0			0
$805$	3.96917	−	2.06050i	0.139895	−	0.0726230i
$806$	0.0278640	−	0.0857567i	0.000981469	−	0.00302065i
$807$		0			0
$808$	0.502029	+	0.690983i	0.0176613	+	0.0243087i
$809$	33.2705	−	24.1724i	1.16973	−	0.849858i	0.178752	−	0.983894i	$-0.442794\pi$
$809$	33.2705	−	24.1724i	1.16973	−	0.849858i	0.990976	+	0.134036i	$0.0427939\pi$
$810$		0			0
$811$	−5.20163	+	16.0090i	−0.182654	+	0.562151i	−0.999900	−	0.0141380i	$-0.995500\pi$
$811$	−5.20163	+	16.0090i	−0.182654	+	0.562151i	0.817246	+	0.576289i	$0.195500\pi$
$812$	−5.15131	+	7.09017i	−0.180776	+	0.248816i
$813$		0			0
$814$	−5.16312	−	20.5272i	−0.180967	−	0.719479i
$815$	40.5410	+	20.2705i	1.42009	+	0.710045i
$816$		0			0
$817$	22.6134	+	7.34752i	0.791141	+	0.257057i
$818$	−20.7845	+	6.75329i	−0.726713	+	0.236123i
$819$		0			0
$820$	4.01166	+	24.1411i	0.140093	+	0.843043i
$821$	−8.61803	−	26.5236i	−0.300771	−	0.925679i	−0.981221	−	0.192885i	$-0.938216\pi$
$821$	−8.61803	−	26.5236i	−0.300771	−	0.925679i	0.680450	−	0.732795i	$-0.261784\pi$
$822$		0			0
$823$	−20.0252	+	27.5623i	−0.698034	+	0.960762i	0.301938	+	0.953327i	$0.402366\pi$
$823$	−20.0252	+	27.5623i	−0.698034	+	0.960762i	−0.999972	+	0.00743409i	$0.997634\pi$
$824$	−17.4164			−0.606729
$825$		0			0
$826$	−8.83282			−0.307333
$827$	17.9516	−	24.7082i	0.624237	−	0.859188i	−0.373416	−	0.927664i	$-0.621814\pi$
$827$	17.9516	−	24.7082i	0.624237	−	0.859188i	0.997653	+	0.0684756i	$0.0218135\pi$
$828$		0			0
$829$	3.03444	+	9.33905i	0.105391	+	0.324359i	0.989822	−	0.142312i	$-0.0454535\pi$
$829$	3.03444	+	9.33905i	0.105391	+	0.324359i	−0.884431	+	0.466670i	$0.845453\pi$
$830$	1.01313	+	6.09673i	0.0351662	+	0.211621i
$831$		0			0
$832$	−0.587785	+	0.190983i	−0.0203778	+	0.00662114i
$833$	−8.42075	−	2.73607i	−0.291762	−	0.0947991i
$834$		0			0
$835$	−18.1803	−	9.09017i	−0.629157	−	0.314578i
$836$	−6.94427	+	4.35926i	−0.240173	+	0.150768i
$837$		0			0
$838$	−20.3152	+	27.9615i	−0.701777	+	0.965914i
$839$	6.38197	−	19.6417i	0.220330	−	0.678106i	−0.778402	−	0.627766i	$-0.783970\pi$
$839$	6.38197	−	19.6417i	0.220330	−	0.678106i	0.998732	−	0.0503399i	$-0.0160305\pi$
$840$		0			0
$841$	−17.2082	+	12.5025i	−0.593386	+	0.431120i
$842$	−3.86974	−	5.32624i	−0.133360	−	0.183554i
$843$		0			0
$844$	−3.76393	+	11.5842i	−0.129560	+	0.398744i
$845$	−25.0416	+	12.9997i	−0.861457	+	0.447204i
$846$		0			0
$847$	−1.83660	+	13.4721i	−0.0631063	+	0.462908i
$848$			6.76393i			0.232274i
$849$		0			0
$850$	−7.65537	+	2.61653i	−0.262577	+	0.0897461i
$851$	−3.19098	−	9.82084i	−0.109385	−	0.336654i
$852$		0			0
$853$	−15.2824	−	21.0344i	−0.523260	−	0.720206i	0.462825	−	0.886450i	$-0.346836\pi$
$853$	−15.2824	−	21.0344i	−0.523260	−	0.720206i	−0.986085	+	0.166244i	$0.946836\pi$
$854$	−1.05573	−	3.24920i	−0.0361263	−	0.111185i
$855$		0			0
$856$	14.3262	+	10.4086i	0.489661	+	0.355759i
$857$		−	32.4508i		−	1.10850i	−0.832350	−	0.554250i	$-0.813005\pi$
$857$		−	32.4508i		−	1.10850i	0.832350	−	0.554250i	$-0.186995\pi$
$858$		0			0
$859$	−18.7639			−0.640217			−0.320109	−	0.947381i	$-0.603719\pi$
$859$	−18.7639			−0.640217			−0.320109	+	0.947381i	$0.603719\pi$
$860$	−9.90897	−	19.0878i	−0.337893	−	0.650890i
$861$		0			0
$862$	35.1361	−	11.4164i	1.19674	−	0.388844i
$863$	−31.1729	−	42.9058i	−1.06114	−	1.46053i	−0.878738	−	0.477305i	$-0.841614\pi$
$863$	−31.1729	−	42.9058i	−1.06114	−	1.46053i	−0.182399	−	0.983225i	$-0.558386\pi$
$864$		0			0
$865$	6.46610	−	42.9322i	0.219854	−	1.45974i
$866$	7.85410	−	24.1724i	0.266893	−	0.821413i
$867$		0			0
$868$		−	0.180340i		−	0.00612113i
$869$	31.8262	+	2.15938i	1.07963	+	0.0732521i
$870$		0			0
$871$	0.690983	+	0.502029i	0.0234131	+	0.0170106i
$872$	−12.3107	−	4.00000i	−0.416894	−	0.135457i
$873$		0			0
$874$	−3.23607	+	2.35114i	−0.109462	+	0.0795285i
$875$	9.99197	+	9.54691i	0.337790	+	0.322745i
$876$		0			0
$877$	−38.6426	−	12.5557i	−1.30487	−	0.423977i	−0.427595	−	0.903971i	$-0.640639\pi$
$877$	−38.6426	−	12.5557i	−1.30487	−	0.423977i	−0.877272	+	0.479994i	$0.840639\pi$
$878$	21.8415	−	30.0623i	0.737116	−	1.01455i
$879$		0			0
$880$	7.24190	+	1.59841i	0.244124	+	0.0538823i
$881$	20.6525			0.695800			0.347900	−	0.937532i	$-0.386895\pi$
$881$	20.6525			0.695800			0.347900	+	0.937532i	$0.386895\pi$
$882$		0			0
$883$	−36.6749	−	11.9164i	−1.23421	−	0.401019i	−0.381972	−	0.924174i	$-0.624755\pi$
$883$	−36.6749	−	11.9164i	−1.23421	−	0.401019i	−0.852238	+	0.523155i	$0.824755\pi$
$884$	0.309017	+	0.951057i	0.0103934	+	0.0319875i
$885$		0			0
$886$	32.4164	−	23.5519i	1.08905	−	0.791242i
$887$	−50.0552	+	16.2639i	−1.68069	+	0.546089i	−0.985045	−	0.172296i	$-0.944881\pi$
$887$	−50.0552	+	16.2639i	−1.68069	+	0.546089i	−0.695645	+	0.718386i	$0.744881\pi$
$888$		0			0
$889$	8.00000	+	5.81234i	0.268311	+	0.194940i
$890$	16.9443	+	8.47214i	0.567973	+	0.283987i
$891$		0			0
$892$		−	3.81966i		−	0.127892i
$893$	−9.19256	+	12.6525i	−0.307617	+	0.423399i
$894$		0			0
$895$	33.7651	+	5.08542i	1.12864	+	0.169987i
$896$	−1.00000	+	0.726543i	−0.0334077	+	0.0242721i
$897$		0			0
$898$	11.9677	−	3.88854i	0.399368	−	0.129762i
$899$	0.319660	−	0.983813i	0.0106613	−	0.0328120i
$900$		0			0
$901$	10.9443			0.364607
$902$	−33.6830	−	13.5279i	−1.12152	−	0.450429i
$903$		0			0
$904$	−7.97214	−	5.79210i	−0.265149	−	0.192642i
$905$	−31.6844	−	31.2069i	−1.05322	−	1.03735i
$906$		0			0
$907$	22.5604	+	31.0517i	0.749104	+	1.03105i	0.998043	+	0.0625343i	$0.0199183\pi$
$907$	22.5604	+	31.0517i	0.749104	+	1.03105i	−0.248939	+	0.968519i	$0.580082\pi$
$908$		0			0
$909$		0			0
$910$	1.19868	−	1.21702i	0.0397358	−	0.0403437i
$911$	15.8541	+	11.5187i	0.525270	+	0.381631i	0.818585	−	0.574385i	$-0.194759\pi$
$911$	15.8541	+	11.5187i	0.525270	+	0.381631i	−0.293316	+	0.956016i	$0.594759\pi$
$912$		0			0
$913$	−8.50651	−	3.41641i	−0.281524	−	0.113067i
$914$	30.7639			1.01758
$915$		0			0
$916$	6.05573	−	18.6376i	0.200087	−	0.615804i
$917$	4.53077	−	1.47214i	0.149619	−	0.0486142i
$918$		0			0
$919$	17.3090	−	12.5757i	0.570972	−	0.414835i	−0.264486	−	0.964389i	$-0.585202\pi$
$919$	17.3090	−	12.5757i	0.570972	−	0.414835i	0.835458	+	0.549554i	$0.185202\pi$
$920$	3.57768	+	0.538842i	0.117953	+	0.0177651i
$921$		0			0
$922$	−5.54734	+	7.63525i	−0.182692	+	0.251454i
$923$			1.05573i			0.0347497i
$924$		0			0
$925$	25.5279	−	19.1459i	0.839351	−	0.629513i
$926$	−18.5623	−	13.4863i	−0.609995	−	0.443187i
$927$		0			0
$928$	−6.74315	+	2.19098i	−0.221355	+	0.0719225i
$929$	16.7984	−	12.2047i	0.551137	−	0.400424i	−0.277068	−	0.960850i	$-0.589363\pi$
$929$	16.7984	−	12.2047i	0.551137	−	0.400424i	0.828204	+	0.560426i	$0.189363\pi$
$930$		0			0
$931$	−4.18034	−	12.8658i	−0.137005	−	0.421658i
$932$	20.7845	+	6.75329i	0.680818	+	0.221211i
$933$		0			0
$934$	9.05573			0.296312
$935$	2.58628	−	11.7176i	0.0845803	−	0.383208i
$936$		0			0
$937$	31.9524	−	43.9787i	1.04384	−	1.43672i	0.149810	−	0.988715i	$-0.452134\pi$
$937$	31.9524	−	43.9787i	1.04384	−	1.43672i	0.894030	−	0.448007i	$-0.147866\pi$
$938$	1.62460	+	0.527864i	0.0530450	+	0.0172354i
$939$		0			0
$940$	13.9545	−	2.31890i	0.455147	−	0.0756343i
$941$	−3.02786	+	2.19987i	−0.0987055	+	0.0717138i	−0.636043	−	0.771653i	$-0.719430\pi$
$941$	−3.02786	+	2.19987i	−0.0987055	+	0.0717138i	0.537338	+	0.843367i	$0.319430\pi$
$942$		0			0
$943$	−16.8415	−	5.47214i	−0.548435	−	0.178197i
$944$	−5.78115	−	4.20025i	−0.188161	−	0.136707i
$945$		0			0
$946$	31.8262	+	2.15938i	1.03476	+	0.0702076i
$947$			3.12461i			0.101536i	0.998710	+	0.0507681i	$0.0161669\pi$
$947$			3.12461i			0.101536i	−0.998710	+	0.0507681i	$0.983833\pi$
$948$		0			0
$949$	−1.56231	+	4.80828i	−0.0507146	+	0.156083i
$950$	−10.1092	−	7.11277i	−0.327984	−	0.230769i
$951$		0			0
$952$	1.17557	+	1.61803i	0.0381005	+	0.0524408i
$953$	26.5033	−	8.61146i	0.858527	−	0.278952i	0.153514	−	0.988146i	$-0.450941\pi$
$953$	26.5033	−	8.61146i	0.858527	−	0.278952i	0.705013	+	0.709194i	$0.250941\pi$
$954$		0			0
$955$	8.87535	−	4.60741i	0.287199	−	0.149092i
$956$	5.81966			0.188221
$957$		0			0
$958$			30.9443i			0.999764i
$959$	−9.56231	−	6.94742i	−0.308783	−	0.224344i
$960$		0			0
$961$	−9.57295	−	29.4625i	−0.308805	−	0.950403i
$962$	−2.31838	−	3.19098i	−0.0747477	−	0.102881i
$963$		0			0
$964$	−4.61803	−	14.2128i	−0.148737	−	0.457765i
$965$	−11.0711	+	11.2405i	−0.356391	+	0.361843i
$966$		0			0
$967$		−	26.2918i		−	0.845487i	−0.906249	−	0.422744i	$-0.861067\pi$
$967$		−	26.2918i		−	0.845487i	0.906249	−	0.422744i	$-0.138933\pi$
$968$	−7.60845	+	7.94427i	−0.244545	+	0.255339i
$969$		0			0
$970$	−6.42226	+	3.33395i	−0.206206	+	0.107047i
$971$	11.4164	−	35.1361i	0.366370	−	1.12757i	−0.582749	−	0.812652i	$-0.698023\pi$
$971$	11.4164	−	35.1361i	0.366370	−	1.12757i	0.949119	−	0.314918i	$-0.101977\pi$
$972$		0			0
$973$	4.91428	+	6.76393i	0.157545	+	0.216842i
$974$	−1.00000	+	0.726543i	−0.0320421	+	0.0232799i
$975$		0			0
$976$	0.854102	−	2.62866i	0.0273391	−	0.0841412i
$977$	−7.88597	+	10.8541i	−0.252294	+	0.347253i	−0.916313	−	0.400462i	$-0.868849\pi$
$977$	−7.88597	+	10.8541i	−0.252294	+	0.347253i	0.664019	+	0.747716i	$0.268849\pi$
$978$		0			0
$979$	−23.7984	+	14.9394i	−0.760599	+	0.477465i
$980$	−5.47214	+	10.9443i	−0.174801	+	0.349602i
$981$		0			0
$982$	37.0710	+	12.0451i	1.18298	+	0.384374i
$983$	26.4176	−	8.58359i	0.842590	−	0.273774i	0.144251	−	0.989541i	$-0.453923\pi$
$983$	26.4176	−	8.58359i	0.842590	−	0.273774i	0.698339	+	0.715767i	$0.253923\pi$
$984$		0			0
$985$	23.7433	−	3.94556i	0.756524	−	0.125716i
$986$	3.54508	+	10.9106i	0.112899	+	0.347466i
$987$		0			0
$988$	−0.898056	+	1.23607i	−0.0285710	+	0.0393246i
$989$	15.5623			0.494853
$990$		0			0
$991$	−5.03444			−0.159924			−0.0799622	−	0.996798i	$-0.525480\pi$
$991$	−5.03444			−0.159924			−0.0799622	+	0.996798i	$0.525480\pi$
$992$	0.0857567	−	0.118034i	0.00272278	−	0.00374758i
$993$		0			0
$994$	0.652476	+	2.00811i	0.0206953	+	0.0636935i
$995$	−3.31161	−	19.9283i	−0.104985	−	0.631771i
$996$		0			0
$997$	21.6295	−	7.02786i	0.685014	−	0.222575i	0.0542250	−	0.998529i	$-0.482731\pi$
$997$	21.6295	−	7.02786i	0.685014	−	0.222575i	0.630789	+	0.775954i	$0.282731\pi$
$998$	15.6659	+	5.09017i	0.495896	+	0.161127i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.c.829.2	yes	8
3.2	odd	2		990.2.ba.e.829.1	yes	8
5.4	even	2	inner	990.2.ba.c.829.1	yes	8
11.3	even	5	inner	990.2.ba.c.289.1	✓	8
15.14	odd	2		990.2.ba.e.829.2	yes	8
33.14	odd	10		990.2.ba.e.289.2	yes	8
55.14	even	10	inner	990.2.ba.c.289.2	yes	8
165.14	odd	10		990.2.ba.e.289.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.ba.c.289.1	✓	8	11.3	even	5	inner
990.2.ba.c.289.2	yes	8	55.14	even	10	inner
990.2.ba.c.829.1	yes	8	5.4	even	2	inner
990.2.ba.c.829.2	yes	8	1.1	even	1	trivial
990.2.ba.e.289.1	yes	8	165.14	odd	10
990.2.ba.e.289.2	yes	8	33.14	odd	10
990.2.ba.e.829.1	yes	8	3.2	odd	2
990.2.ba.e.829.2	yes	8	15.14	odd	2

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.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(0.366554 + 2.20582i) q^{5} +(-1.17557 + 0.381966i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.00000 + 1.00000i) q^{10} +(-2.80902 + 1.76336i) q^{11} +(-0.363271 + 0.500000i) q^{13} +(-0.381966 + 1.17557i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.951057 + 1.30902i) q^{17} +(-0.763932 + 2.35114i) q^{19} +(1.98459 - 1.03025i) q^{20} +(-0.224514 + 3.30902i) q^{22} +1.61803i q^{23} +(-4.73128 + 1.61710i) q^{25} +(0.190983 + 0.587785i) q^{26} +(0.726543 + 1.00000i) q^{28} +(2.19098 + 6.74315i) q^{29} +(-0.118034 - 0.0857567i) q^{31} +1.00000i q^{32} +1.61803 q^{34} +(-1.27346 - 2.45309i) q^{35} +(-6.06961 + 1.97214i) q^{37} +(1.45309 + 2.00000i) q^{38} +(0.333023 - 2.21113i) q^{40} +(-3.38197 + 10.4086i) q^{41} -9.61803i q^{43} +(2.54508 + 2.12663i) q^{44} +(1.30902 + 0.951057i) q^{46} +(6.01661 + 1.95492i) q^{47} +(-4.42705 + 3.21644i) q^{49} +(-1.47271 + 4.77819i) q^{50} +(0.587785 + 0.190983i) q^{52} +(3.97574 - 5.47214i) q^{53} +(-4.91930 - 5.54982i) q^{55} +1.23607 q^{56} +(6.74315 + 2.19098i) q^{58} +(2.20820 + 6.79615i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(-0.138757 + 0.0450850i) q^{62} +(0.809017 + 0.587785i) q^{64} +(-1.23607 - 0.618034i) q^{65} -1.38197i q^{67} +(0.951057 - 1.30902i) q^{68} +(-2.73311 - 0.411638i) q^{70} +(1.38197 - 1.00406i) q^{71} +(7.77997 - 2.52786i) q^{73} +(-1.97214 + 6.06961i) q^{74} +2.47214 q^{76} +(2.62866 - 3.14590i) q^{77} +(-7.78115 - 5.65334i) q^{79} +(-1.59310 - 1.56909i) q^{80} +(6.43288 + 8.85410i) q^{82} +(1.62460 + 2.23607i) q^{83} +(-2.53884 + 2.57768i) q^{85} +(-7.78115 - 5.65334i) q^{86} +(3.21644 - 0.809017i) q^{88} +8.47214 q^{89} +(0.236068 - 0.726543i) q^{91} +(1.53884 - 0.500000i) q^{92} +(5.11803 - 3.71847i) q^{94} +(-5.46621 - 0.823277i) q^{95} +(-1.90211 + 2.61803i) q^{97} +5.47214i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 2 q^{5} + 16 q^{10} - 18 q^{11} - 12 q^{14} - 2 q^{16} - 24 q^{19} + 2 q^{20} + 6 q^{25} + 6 q^{26} + 22 q^{29} + 8 q^{31} + 4 q^{34} - 16 q^{35} + 4 q^{40} - 36 q^{41} - 2 q^{44} + 6 q^{46}+ \cdots - 24 q^{95}+O(q^{100}) \) 8 * q + 2 * q^4 - 2 * q^5 + 16 * q^10 - 18 * q^11 - 12 * q^14 - 2 * q^16 - 24 * q^19 + 2 * q^20 + 6 * q^25 + 6 * q^26 + 22 * q^29 + 8 * q^31 + 4 * q^34 - 16 * q^35 + 4 * q^40 - 36 * q^41 - 2 * q^44 + 6 * q^46 - 22 * q^49 - 8 * q^50 - 8 * q^55 - 8 * q^56 - 36 * q^59 + 2 * q^64 + 8 * q^65 - 12 * q^70 + 20 * q^71 + 20 * q^74 - 16 * q^76 - 22 * q^79 - 2 * q^80 - 8 * q^85 - 22 * q^86 + 32 * q^89 - 16 * q^91 + 32 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more