LMFDB - Embedded newform 990.2.ba.c.289.1

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			289.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	990.289
Dual form			990.2.ba.c.829.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.98459 + 1.03025i) q^{5} +(1.17557 + 0.381966i) q^{7} +(0.951057 - 0.309017i) q^{8} +(2.00000 + 1.00000i) q^{10} +(-2.80902 - 1.76336i) q^{11} +(0.363271 + 0.500000i) q^{13} +(-0.381966 - 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.951057 + 1.30902i) q^{17} +(-0.763932 - 2.35114i) q^{19} +(-0.366554 - 2.20582i) q^{20} +(0.224514 + 3.30902i) q^{22} +1.61803i q^{23} +(2.87718 - 4.08924i) q^{25} +(0.190983 - 0.587785i) q^{26} +(-0.726543 + 1.00000i) q^{28} +(2.19098 - 6.74315i) q^{29} +(-0.118034 + 0.0857567i) q^{31} +1.00000i q^{32} +1.61803 q^{34} +(-2.72654 + 0.453085i) q^{35} +(6.06961 + 1.97214i) q^{37} +(-1.45309 + 2.00000i) q^{38} +(-1.56909 + 1.59310i) q^{40} +(-3.38197 - 10.4086i) q^{41} -9.61803i q^{43} +(2.54508 - 2.12663i) q^{44} +(1.30902 - 0.951057i) q^{46} +(-6.01661 + 1.95492i) q^{47} +(-4.42705 - 3.21644i) q^{49} +(-4.99942 + 0.0759100i) q^{50} +(-0.587785 + 0.190983i) q^{52} +(-3.97574 - 5.47214i) q^{53} +(7.39144 + 0.605548i) q^{55} +1.23607 q^{56} +(-6.74315 + 2.19098i) q^{58} +(2.20820 - 6.79615i) q^{59} +(-2.23607 - 1.62460i) q^{61} +(0.138757 + 0.0450850i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-1.23607 - 0.618034i) q^{65} -1.38197i q^{67} +(-0.951057 - 1.30902i) q^{68} +(1.96917 + 1.93950i) q^{70} +(1.38197 + 1.00406i) q^{71} +(-7.77997 - 2.52786i) q^{73} +(-1.97214 - 6.06961i) q^{74} +2.47214 q^{76} +(-2.62866 - 3.14590i) q^{77} +(-7.78115 + 5.65334i) q^{79} +(2.21113 + 0.333023i) q^{80} +(-6.43288 + 8.85410i) q^{82} +(-1.62460 + 2.23607i) q^{83} +(0.538842 - 3.57768i) q^{85} +(-7.78115 + 5.65334i) q^{86} +(-3.21644 - 0.809017i) q^{88} +8.47214 q^{89} +(0.236068 + 0.726543i) q^{91} +(-1.53884 - 0.500000i) q^{92} +(5.11803 + 3.71847i) q^{94} +(3.93835 + 3.87901i) q^{95} +(1.90211 + 2.61803i) q^{97} +5.47214i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.587785	−	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
$5$	−1.98459	+	1.03025i	−0.887535	+	0.460741i
$5$	−1.98459	+	1.03025i	−0.887535	+	0.460741i
$6$		0			0
$7$	1.17557	+	0.381966i	0.444324	+	0.144370i	0.522630	−	0.852560i	$-0.324951\pi$
$7$	1.17557	+	0.381966i	0.444324	+	0.144370i	−0.0783058	+	0.996929i	$0.524951\pi$
$8$	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	$-0.172685\pi$
$13$	0.363271	+	0.500000i	0.100753	+	0.138675i	−0.755664	+	0.654960i	$0.772685\pi$
$14$	−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	$-0.862865\pi$
$17$	−0.951057	+	1.30902i	−0.230665	+	0.317483i	0.677958	+	0.735101i	$0.262865\pi$
$18$		0			0
$19$	−0.763932	−	2.35114i	−0.175258	−	0.539389i	0.824387	−	0.566026i	$-0.191520\pi$
$19$	−0.763932	−	2.35114i	−0.175258	−	0.539389i	−0.999645	+	0.0266376i	$0.991520\pi$
$20$	−0.366554	−	2.20582i	−0.0819639	−	0.493236i
$21$		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
$25$	2.87718	−	4.08924i	0.575435	−	0.817848i
$26$	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	−0.512481	−	0.858699i	$-0.671273\pi$
$29$	2.19098	−	6.74315i	0.406855	−	1.25217i	0.919336	−	0.393473i	$-0.128727\pi$
$30$		0			0
$31$	−0.118034	+	0.0857567i	−0.0211995	+	0.0154024i	−0.598335	−	0.801246i	$-0.704171\pi$
$31$	−0.118034	+	0.0857567i	−0.0211995	+	0.0154024i	0.577135	+	0.816649i	$0.304171\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	1.61803			0.277491
$35$	−2.72654	+	0.453085i	−0.460870	+	0.0765854i
$36$		0			0
$37$	6.06961	+	1.97214i	0.997838	+	0.324217i	0.762001	−	0.647576i	$-0.224217\pi$
$37$	6.06961	+	1.97214i	0.997838	+	0.324217i	0.235837	+	0.971793i	$0.424217\pi$
$38$	−1.45309	+	2.00000i	−0.235722	+	0.324443i
$39$		0			0
$40$	−1.56909	+	1.59310i	−0.248095	+	0.251891i
$41$	−3.38197	−	10.4086i	−0.528174	−	1.62555i	−0.757952	−	0.652310i	$-0.773800\pi$
$41$	−3.38197	−	10.4086i	−0.528174	−	1.62555i	0.229778	−	0.973243i	$-0.426200\pi$
$42$		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	$-0.752648\pi$
$47$	−6.01661	+	1.95492i	−0.877613	+	0.285154i	−0.164647	+	0.986353i	$0.552648\pi$
$48$		0			0
$49$	−4.42705	−	3.21644i	−0.632436	−	0.459492i
$50$	−4.99942	+	0.0759100i	−0.707025	+	0.0107353i
$51$		0			0
$52$	−0.587785	+	0.190983i	−0.0815111	+	0.0264846i
$53$	−3.97574	−	5.47214i	−0.546110	−	0.751656i	0.443368	−	0.896340i	$-0.353783\pi$
$53$	−3.97574	−	5.47214i	−0.546110	−	0.751656i	−0.989478	+	0.144684i	$0.953783\pi$
$54$		0			0
$55$	7.39144	+	0.605548i	0.996661	+	0.0816520i
$56$	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	−0.698160	−	0.715942i	$-0.745997\pi$
$59$	2.20820	−	6.79615i	0.287484	−	0.884784i	0.985643	−	0.168842i	$-0.0540026\pi$
$60$		0			0
$61$	−2.23607	−	1.62460i	−0.286299	−	0.208009i	0.435361	−	0.900256i	$-0.356621\pi$
$61$	−2.23607	−	1.62460i	−0.286299	−	0.208009i	−0.721660	+	0.692247i	$0.756621\pi$
$62$	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
$70$	1.96917	+	1.93950i	0.235361	+	0.231815i
$71$	1.38197	+	1.00406i	0.164009	+	0.119160i	0.666762	−	0.745270i	$-0.267680\pi$
$71$	1.38197	+	1.00406i	0.164009	+	0.119160i	−0.502753	+	0.864430i	$0.667680\pi$
$72$		0			0
$73$	−7.77997	−	2.52786i	−0.910576	−	0.295864i	−0.183981	−	0.982930i	$-0.558898\pi$
$73$	−7.77997	−	2.52786i	−0.910576	−	0.295864i	−0.726595	+	0.687066i	$0.758898\pi$
$74$	−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	−0.932043	−	0.362347i	$-0.881976\pi$
$79$	−7.78115	+	5.65334i	−0.875448	+	0.636050i	0.0565952	+	0.998397i	$0.481976\pi$
$80$	2.21113	+	0.333023i	0.247212	+	0.0372331i
$81$		0			0
$82$	−6.43288	+	8.85410i	−0.710393	+	0.977772i
$83$	−1.62460	+	2.23607i	−0.178323	+	0.245440i	−0.888817	−	0.458263i	$-0.848472\pi$
$83$	−1.62460	+	2.23607i	−0.178323	+	0.245440i	0.710494	+	0.703704i	$0.248472\pi$
$84$		0			0
$85$	0.538842	−	3.57768i	0.0584456	−	0.388054i
$86$	−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
$95$	3.93835	+	3.87901i	0.404066	+	0.397978i
$96$		0			0
$97$	1.90211	+	2.61803i	0.193130	+	0.265821i	0.894590	−	0.446888i	$-0.147468\pi$
$97$	1.90211	+	2.61803i	0.193130	+	0.265821i	−0.701459	+	0.712709i	$0.747468\pi$
$98$			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	−0.621632	−	0.783309i	$-0.713530\pi$
$101$	−0.690983	+	0.502029i	−0.0687554	+	0.0499537i	0.552877	+	0.833263i	$0.313530\pi$
$102$		0			0
$103$	−16.5640	−	5.38197i	−1.63210	−	0.530301i	−0.657346	−	0.753589i	$-0.728321\pi$
$103$	−16.5640	−	5.38197i	−1.63210	−	0.530301i	−0.974752	+	0.223288i	$0.928321\pi$
$104$	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	$-0.272968\pi$
$107$	16.8415	−	5.47214i	1.62813	−	0.529011i	0.973840	+	0.227233i	$0.0729679\pi$
$108$		0			0
$109$	12.9443			1.23984			0.619918	−	0.784666i	$-0.287166\pi$
$109$	12.9443			1.23984			0.619918	+	0.784666i	$0.287166\pi$
$110$	−3.85468	−	6.33573i	−0.367529	−	0.604088i
$111$		0			0
$112$	−0.726543	−	1.00000i	−0.0686518	−	0.0944911i
$113$	−9.37181	+	3.04508i	−0.881626	+	0.286457i	−0.714632	−	0.699501i	$-0.753406\pi$
$113$	−9.37181	+	3.04508i	−0.881626	+	0.286457i	−0.166993	+	0.985958i	$0.553406\pi$
$114$		0			0
$115$	−1.66698	−	3.21113i	−0.155446	−	0.299439i
$116$	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
$125$	−1.49707	+	11.0797i	−0.133902	+	0.990995i
$126$		0			0
$127$	4.70228	−	6.47214i	0.417260	−	0.574309i	−0.547710	−	0.836668i	$-0.684500\pi$
$127$	4.70228	−	6.47214i	0.417260	−	0.574309i	0.964970	+	0.262359i	$0.0845004\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$		0			0
$130$	0.226543	+	1.36327i	0.0198691	+	0.119567i
$131$	−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	$-0.933942\pi$
$137$	−5.62058	+	7.73607i	−0.480199	+	0.660937i	0.498344	+	0.866979i	$0.333942\pi$
$138$		0			0
$139$	−2.09017	+	6.43288i	−0.177286	+	0.545630i	−0.999730	−	0.0232153i	$-0.992610\pi$
$139$	−2.09017	+	6.43288i	−0.177286	+	0.545630i	0.822445	+	0.568845i	$0.192610\pi$
$140$	0.411638	−	2.73311i	0.0347898	−	0.230990i
$141$		0			0
$142$		−	1.70820i		−	0.143349i
$143$	−0.138757	−	2.04508i	−0.0116035	−	0.171019i
$144$		0			0
$145$	2.59893	+	15.6396i	0.215829	+	1.29880i
$146$	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	0.798847	−	0.601535i	$-0.205444\pi$
$149$	5.78115	+	4.20025i	0.473611	+	0.344098i	−0.325236	+	0.945633i	$0.605444\pi$
$150$		0			0
$151$	−4.76393	−	14.6619i	−0.387683	−	1.19317i	−0.934515	−	0.355924i	$-0.884166\pi$
$151$	−4.76393	−	14.6619i	−0.387683	−	1.19317i	0.546832	−	0.837243i	$-0.315834\pi$
$152$	−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	$-0.521131\pi$
$157$	5.84510	−	1.89919i	0.466489	−	0.151572i	0.532824	+	0.846226i	$0.321131\pi$
$158$	9.14729	+	2.97214i	0.727720	+	0.236450i
$159$		0			0
$160$	−1.03025	−	1.98459i	−0.0814483	−	0.156895i
$161$	−0.618034	+	1.90211i	−0.0487079	+	0.149908i
$162$		0			0
$163$	−11.9147	−	16.3992i	−0.933232	−	1.28448i	−0.958586	−	0.284805i	$-0.908071\pi$
$163$	−11.9147	−	16.3992i	−0.933232	−	1.28448i	0.0253536	−	0.999679i	$-0.491929\pi$
$164$	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	$-0.0856006\pi$
$167$	5.34307	+	7.35410i	0.413459	+	0.569077i	−0.550599	+	0.834770i	$0.685601\pi$
$168$		0			0
$169$	3.89919	−	12.0005i	0.299937	−	0.923113i
$170$	−3.21113	+	1.66698i	−0.246282	+	0.127851i
$171$		0			0
$172$	9.14729	+	2.97214i	0.697475	+	0.226623i
$173$	18.4661	−	6.00000i	1.40395	−	0.456172i	0.493485	−	0.869754i	$-0.335723\pi$
$173$	18.4661	−	6.00000i	1.40395	−	0.456172i	0.910467	+	0.413583i	$0.135723\pi$
$174$		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	0.957329	+	0.288999i	$0.0933225\pi$
$179$	4.71885	+	14.5231i	0.352703	+	1.08551i	−0.604626	+	0.796509i	$0.706677\pi$
$180$		0			0
$181$	−16.0902	−	11.6902i	−1.19597	−	0.868925i	−0.202090	−	0.979367i	$-0.564773\pi$
$181$	−16.0902	−	11.6902i	−1.19597	−	0.868925i	−0.993883	+	0.110442i	$0.964773\pi$
$182$	0.449028	−	0.618034i	0.0332842	−	0.0458117i
$183$		0			0
$184$	0.500000	+	1.53884i	0.0368605	+	0.113445i
$185$	−14.0775	+	2.33933i	−1.03500	+	0.171991i
$186$		0			0
$187$	4.97980	−	2.00000i	0.364159	−	0.146254i
$188$		−	6.32624i		−	0.461388i
$189$		0			0
$190$	0.823277	−	5.46621i	0.0597268	−	0.396561i
$191$	−1.38197	+	4.25325i	−0.0999956	+	0.307755i	−0.988523	−	0.151068i	$-0.951729\pi$
$191$	−1.38197	+	4.25325i	−0.0999956	+	0.307755i	0.888528	+	0.458823i	$0.151729\pi$
$192$		0			0
$193$	−4.14725	+	5.70820i	−0.298526	+	0.410886i	−0.931760	−	0.363075i	$-0.881727\pi$
$193$	−4.14725	+	5.70820i	−0.298526	+	0.410886i	0.633234	+	0.773960i	$0.281727\pi$
$194$	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	$0.603756\pi$
$200$	1.47271	−	4.77819i	0.104136	−	0.337869i
$201$		0			0
$202$	0.812299	+	0.263932i	0.0571532	+	0.0185702i
$203$	5.15131	−	7.09017i	0.361551	−	0.497632i
$204$		0			0
$205$	17.4353	+	17.1726i	1.21773	+	1.19938i
$206$	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	−0.872821	−	0.488040i	$-0.837712\pi$
$211$	−9.85410	+	7.15942i	−0.678384	+	0.492875i	0.194437	+	0.980915i	$0.437712\pi$
$212$	6.43288	−	2.09017i	0.441812	−	0.143553i
$213$		0			0
$214$	−14.3262	−	10.4086i	−0.979321	−	0.711519i
$215$	9.90897	+	19.0878i	0.675786	+	1.30178i
$216$		0			0
$217$	−0.171513	+	0.0557281i	−0.0116431	+	0.00378307i
$218$	−7.60845	−	10.4721i	−0.515309	−	0.709263i
$219$		0			0
$220$	−2.85999	+	6.84255i	−0.192820	+	0.461324i
$221$	−1.00000			−0.0672673
$222$		0			0
$223$	−3.63271	+	1.18034i	−0.243264	+	0.0790414i	−0.428112	−	0.903726i	$-0.640821\pi$
$223$	−3.63271	+	1.18034i	−0.243264	+	0.0790414i	0.184847	+	0.982767i	$0.440821\pi$
$224$	−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	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$	15.8541	−	11.5187i	1.04767	−	0.761176i	0.0759008	−	0.997115i	$-0.475817\pi$
$229$	15.8541	−	11.5187i	1.04767	−	0.761176i	0.971768	+	0.235940i	$0.0758168\pi$
$230$	−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	0.985664	+	0.168718i	$0.0539628\pi$
$233$	12.8455	+	17.6803i	0.841538	+	1.15828i	−0.144126	+	0.989559i	$0.546037\pi$
$234$		0			0
$235$	9.92644	−	10.0783i	0.647530	−	0.657436i
$236$	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	0.875894	−	0.482503i	$-0.160272\pi$
$239$	−1.79837	−	5.53483i	−0.116327	−	0.358018i	−0.992222	+	0.124485i	$0.960272\pi$
$240$		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
$245$	12.0996	+	1.82234i	0.773015	+	0.116425i
$246$		0			0
$247$	0.898056	−	1.23607i	0.0571419	−	0.0786491i
$248$	−0.0857567	+	0.118034i	−0.00544556	+	0.00749517i
$249$		0			0
$250$	9.84359	−	5.30130i	0.622563	−	0.335284i
$251$	5.92705	−	4.30625i	0.374112	−	0.271808i	−0.384802	−	0.922999i	$-0.625730\pi$
$251$	5.92705	−	4.30625i	0.374112	−	0.271808i	0.758914	+	0.651191i	$0.225730\pi$
$252$		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	$-0.475439\pi$
$257$	−7.15942	−	2.32624i	−0.446593	−	0.145107i	−0.523675	+	0.851918i	$0.675439\pi$
$258$		0			0
$259$	6.38197	+	4.63677i	0.396556	+	0.288115i
$260$	0.969751	−	0.984587i	0.0601414	−	0.0610615i
$261$		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	0.999999	−	0.00161395i	$-0.000513736\pi$
$269$	21.4443	+	15.5802i	1.30748	+	0.949940i	0.307482	+	0.951554i	$0.400514\pi$
$270$		0			0
$271$	−5.20820	+	16.0292i	−0.316376	+	0.973705i	0.658809	+	0.752311i	$0.271061\pi$
$271$	−5.20820	+	16.0292i	−0.316376	+	0.973705i	−0.975184	+	0.221394i	$0.928939\pi$
$272$	1.53884	−	0.500000i	0.0933060	−	0.0303170i
$273$		0			0
$274$	9.56231			0.577680
$275$	−15.2928	+	6.41325i	−0.922191	+	0.386734i
$276$		0			0
$277$	17.5150	+	24.1074i	1.05238	+	1.44847i	0.886730	+	0.462288i	$0.152971\pi$
$277$	17.5150	+	24.1074i	1.05238	+	1.44847i	0.165647	+	0.986185i	$0.447029\pi$
$278$	6.43288	−	2.09017i	0.385819	−	0.125360i
$279$		0			0
$280$	−2.45309	+	1.27346i	−0.146600	+	0.0761036i
$281$	−4.23607	−	3.07768i	−0.252703	−	0.183599i	0.454221	−	0.890889i	$-0.349918\pi$
$281$	−4.23607	−	3.07768i	−0.252703	−	0.183599i	−0.706924	+	0.707290i	$0.749918\pi$
$282$		0			0
$283$	−27.1114	+	8.80902i	−1.61160	+	0.523642i	−0.969940	−	0.243345i	$-0.921755\pi$
$283$	−27.1114	+	8.80902i	−1.61160	+	0.523642i	−0.641664	+	0.766986i	$0.721755\pi$
$284$	−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
$290$	11.1251	−	11.2953i	0.653289	−	0.663284i
$291$		0			0
$292$	4.80828	−	6.61803i	0.281383	−	0.387291i
$293$	−2.45714	−	0.798374i	−0.143548	−	0.0466415i	0.236362	−	0.971665i	$-0.424045\pi$
$293$	−2.45714	−	0.798374i	−0.143548	−	0.0466415i	−0.379910	+	0.925024i	$0.624045\pi$
$294$		0			0
$295$	2.61935	+	15.7626i	0.152505	+	0.917732i
$296$	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
$305$	6.11141	+	0.920452i	0.349938	+	0.0527049i
$306$		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
$310$	−0.321825	+	0.0534794i	−0.0182784	+	0.00303743i
$311$	−6.14590	−	18.9151i	−0.348502	−	1.07258i	−0.959682	−	0.281087i	$-0.909305\pi$
$311$	−6.14590	−	18.9151i	−0.348502	−	1.07258i	0.611180	−	0.791491i	$-0.290695\pi$
$312$		0			0
$313$	−15.2169	+	20.9443i	−0.860110	+	1.18384i	0.121433	+	0.992600i	$0.461251\pi$
$313$	−15.2169	+	20.9443i	−0.860110	+	1.18384i	−0.981543	+	0.191241i	$0.938749\pi$
$314$	−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	0.999433	+	0.0336700i	$0.0107195\pi$
$317$	12.8658	+	17.7082i	0.722613	+	0.994592i	−0.276820	+	0.960922i	$0.589280\pi$
$318$		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
$325$	3.08981	−	0.0469149i	0.171392	−	0.00260237i
$326$	−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
$335$	1.42377	+	2.74263i	0.0777888	+	0.149846i
$336$		0			0
$337$	12.3107	+	4.00000i	0.670608	+	0.217894i	0.624479	−	0.781042i	$-0.285311\pi$
$337$	12.3107	+	4.00000i	0.670608	+	0.217894i	0.0461294	+	0.998935i	$0.485311\pi$
$338$	−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	$-0.862220\pi$
$347$	−4.25325	+	5.85410i	−0.228327	+	0.314265i	0.679447	+	0.733724i	$0.262220\pi$
$348$		0			0
$349$	−0.0557281	−	0.171513i	−0.00298306	−	0.00918090i	0.949554	−	0.313604i	$-0.101536\pi$
$349$	−0.0557281	−	0.171513i	−0.00298306	−	0.00918090i	−0.952537	+	0.304423i	$0.901536\pi$
$350$	−5.90617	−	1.82037i	−0.315698	−	0.0973030i
$351$		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
$355$	−3.77706	−	0.568870i	−0.200466	−	0.0301925i
$356$	−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	0.710197	+	0.704003i	$0.248606\pi$
$359$	−5.27051	+	16.2210i	−0.278167	+	0.856110i	−0.988364	+	0.152107i	$0.951394\pi$
$360$		0			0
$361$	10.4271	−	7.57570i	0.548792	−	0.398721i
$362$			19.8885i			1.04532i
$363$		0			0
$364$	−0.763932			−0.0400409
$365$	18.0444	−	2.99853i	0.944485	−	0.156950i
$366$		0			0
$367$	−27.0786	−	8.79837i	−1.41349	−	0.459271i	−0.499964	−	0.866046i	$-0.666653\pi$
$367$	−27.0786	−	8.79837i	−1.41349	−	0.459271i	−0.913528	+	0.406775i	$0.866653\pi$
$368$	0.951057	−	1.30902i	0.0495772	−	0.0682372i
$369$		0			0
$370$	10.1671	+	10.0139i	0.528562	+	0.520597i
$371$	−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	−0.998634	−	0.0522478i	$-0.983361\pi$
$379$	−26.4164	−	19.1926i	−1.35692	−	0.985860i	−0.358286	−	0.933612i	$-0.616639\pi$
$380$	−4.90617	+	2.54691i	−0.251681	+	0.130654i
$381$		0			0
$382$	4.25325	−	1.38197i	0.217615	−	0.0707075i
$383$	−10.6004	−	14.5902i	−0.541654	−	0.745523i	0.447196	−	0.894436i	$-0.352423\pi$
$383$	−10.6004	−	14.5902i	−0.541654	−	0.745523i	−0.988850	+	0.148913i	$0.952423\pi$
$384$		0			0
$385$	8.45785	+	3.53514i	0.431052	+	0.180167i
$386$	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	−0.972672	−	0.232184i	$-0.925413\pi$
$389$	−0.972136	+	2.99193i	−0.0492892	+	0.151697i	0.923383	+	0.383881i	$0.125413\pi$
$390$		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
$400$	−4.73128	+	1.61710i	−0.236564	+	0.0808551i
$401$	−24.5623	−	17.8456i	−1.22658	−	0.891165i	−0.229954	−	0.973202i	$-0.573857\pi$
$401$	−24.5623	−	17.8456i	−1.22658	−	0.891165i	−0.996629	+	0.0820368i	$0.973857\pi$
$402$		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	−0.931720	−	0.363176i	$-0.881692\pi$
$409$	−17.6803	+	12.8455i	−0.874237	+	0.635170i	0.0574839	+	0.998346i	$0.481692\pi$
$410$	3.64469	−	24.1992i	0.179998	−	1.19511i
$411$		0			0
$412$	10.2371	−	14.0902i	0.504346	−	0.694173i
$413$	5.19180	−	7.14590i	0.255472	−	0.351627i
$414$		0			0
$415$	0.920452	−	6.11141i	0.0451832	−	0.299997i
$416$	−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	0.988314	−	0.152434i	$-0.0487112\pi$
$421$	2.03444	+	6.26137i	0.0991526	+	0.305160i	−0.889161	+	0.457594i	$0.848711\pi$
$422$	11.5842	+	3.76393i	0.563910	+	0.183225i
$423$		0			0
$424$	−5.47214	−	3.97574i	−0.265750	−	0.193079i
$425$	2.61653	+	7.65537i	0.126920	+	0.371340i
$426$		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	0.451571	−	0.892235i	$-0.350864\pi$
$431$	29.8885	−	21.7153i	1.43968	−	1.04599i	0.988109	−	0.153754i	$-0.0491364\pi$
$432$		0			0
$433$	−24.1724	−	7.85410i	−1.16165	−	0.377444i	−0.336132	−	0.941815i	$-0.609119\pi$
$433$	−24.1724	−	7.85410i	−1.16165	−	0.377444i	−0.825521	+	0.564371i	$0.809119\pi$
$434$	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	$0.152956\pi$
$440$	7.21680	−	1.70817i	0.344047	−	0.0814338i
$441$		0			0
$442$	0.587785	+	0.809017i	0.0279581	+	0.0384810i
$443$	−38.1078	+	12.3820i	−1.81055	+	0.588285i	−0.810558	+	0.585658i	$0.800836\pi$
$443$	−38.1078	+	12.3820i	−1.81055	+	0.588285i	−0.999997	+	0.00262712i	$0.999164\pi$
$444$		0			0
$445$	−16.8137	+	8.72841i	−0.797046	+	0.413766i
$446$	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	−0.321056	−	0.947060i	$-0.604038\pi$
$449$	10.1803	−	7.39645i	0.480440	−	0.349060i	0.801496	+	0.598000i	$0.204038\pi$
$450$		0			0
$451$	−8.85410	+	35.2016i	−0.416923	+	1.65758i
$452$		−	9.85410i		−	0.463498i
$453$		0			0
$454$		0			0
$455$	−1.21702	−	1.19868i	−0.0570546	−	0.0561949i
$456$		0			0
$457$	−18.0826	+	24.8885i	−0.845868	+	1.16424i	0.138890	+	0.990308i	$0.455646\pi$
$457$	−18.0826	+	24.8885i	−0.845868	+	1.16424i	−0.984758	+	0.173929i	$0.944354\pi$
$458$	−18.6376	−	6.05573i	−0.870879	−	0.282966i
$459$		0			0
$460$	3.56909	−	0.593096i	0.166410	−	0.0276532i
$461$	−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	$-0.867192\pi$
$467$	−5.32282	+	7.32624i	−0.246311	+	0.339018i	0.667904	+	0.744247i	$0.267192\pi$
$468$		0			0
$469$	0.527864	−	1.62460i	0.0243745	−	0.0750170i
$470$	−13.9881	−	2.10678i	−0.645225	−	0.0971785i
$471$		0			0
$472$		−	7.14590i		−	0.328917i
$473$	−16.9600	+	27.0172i	−0.779822	+	1.24225i
$474$		0			0
$475$	−11.8123	−	3.64074i	−0.541987	−	0.167049i
$476$	−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	−0.156201	−	0.987725i	$-0.549925\pi$
$479$	−25.0344	−	18.1886i	−1.14385	−	0.831058i	−0.987651	+	0.156667i	$0.949925\pi$
$480$		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	$-0.591084\pi$
$487$	1.17557	−	0.381966i	0.0532702	−	0.0173085i	0.335531	+	0.942029i	$0.391084\pi$
$488$	−2.62866	−	0.854102i	−0.118994	−	0.0386634i
$489$		0			0
$490$	−5.63766	−	10.8599i	−0.254684	−	0.490602i
$491$	12.0451	−	37.0710i	0.543587	−	1.67299i	−0.180739	−	0.983531i	$-0.557849\pi$
$491$	12.0451	−	37.0710i	0.543587	−	1.67299i	0.724326	−	0.689458i	$-0.242151\pi$
$492$		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	−0.770121	−	0.637898i	$-0.779804\pi$
$499$	5.09017	−	15.6659i	0.227867	−	0.701303i	0.997988	−	0.0634051i	$-0.0201960\pi$
$500$	−10.0748	−	4.84760i	−0.450557	−	0.216791i
$501$		0			0
$502$	−6.96767	−	2.26393i	−0.310982	−	0.101044i
$503$	1.65735	−	0.538507i	0.0738978	−	0.0240108i	−0.271835	−	0.962344i	$-0.587630\pi$
$503$	1.65735	−	0.538507i	0.0738978	−	0.0240108i	0.345733	+	0.938333i	$0.387630\pi$
$504$		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	0.941978	−	0.335674i	$-0.108964\pi$
$509$	−0.392609	−	1.20833i	−0.0174021	−	0.0535581i	−0.959380	+	0.282115i	$0.908964\pi$
$510$		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
$515$	38.4174	−	6.38405i	1.69288	−	0.281315i
$516$		0			0
$517$	20.3480	+	5.11803i	0.894903	+	0.225091i
$518$		−	7.88854i		−	0.346603i
$519$		0			0
$520$	−1.36655	−	0.205819i	−0.0599273	−	0.00902577i
$521$	10.8197	−	33.2995i	0.474018	−	1.45888i	−0.373260	−	0.927727i	$-0.621760\pi$
$521$	10.8197	−	33.2995i	0.474018	−	1.45888i	0.847278	−	0.531150i	$-0.178240\pi$
$522$		0			0
$523$	−6.71040	+	9.23607i	−0.293425	+	0.403865i	−0.930123	−	0.367248i	$-0.880300\pi$
$523$	−6.71040	+	9.23607i	−0.293425	+	0.403865i	0.636698	+	0.771113i	$0.280300\pi$
$524$	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
$530$	−2.47934	−	14.9200i	−0.107696	−	0.648084i
$531$		0			0
$532$	2.90617	+	0.944272i	0.125998	+	0.0409394i
$533$	3.97574	−	5.47214i	0.172208	−	0.237025i
$534$		0			0
$535$	−27.7858	+	28.2109i	−1.20128	+	1.21966i
$536$	−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	−0.549221	−	0.835677i	$-0.685075\pi$
$541$	1.76393	−	1.28157i	0.0758374	−	0.0550991i	0.625058	+	0.780578i	$0.285075\pi$
$542$	16.0292	−	5.20820i	0.688513	−	0.223712i
$543$		0			0
$544$	−1.30902	−	0.951057i	−0.0561236	−	0.0407762i
$545$	−25.6890	+	13.3358i	−1.10040	+	0.571244i
$546$		0			0
$547$	−27.6664	+	8.98936i	−1.18293	+	0.384357i	−0.833454	−	0.552588i	$-0.813640\pi$
$547$	−27.6664	+	8.98936i	−1.18293	+	0.384357i	−0.349475	+	0.936946i	$0.613640\pi$
$548$	−5.62058	−	7.73607i	−0.240099	−	0.330468i
$549$		0			0
$550$	14.1773	+	8.60253i	0.604523	+	0.366813i
$551$	−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	$-0.602135\pi$
$557$	−26.6296	−	8.65248i	−1.12833	−	0.366617i	−0.812942	+	0.582345i	$0.802135\pi$
$558$		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	0.983599	+	0.180367i	$0.0577285\pi$
$563$	20.1967	+	27.7984i	0.851189	+	1.17156i	−0.132410	+	0.991195i	$0.542272\pi$
$564$		0			0
$565$	15.4620	−	15.6985i	0.650490	−	0.660442i
$566$	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	0.963175	−	0.268875i	$-0.0866518\pi$
$569$	0.618034	+	1.90211i	0.0259093	+	0.0797407i	−0.937266	+	0.348616i	$0.886652\pi$
$570$		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
$575$	6.61653	+	4.65537i	0.275928	+	0.194142i
$576$		0			0
$577$	−19.5357	+	26.8885i	−0.813281	+	1.11938i	0.177528	+	0.984116i	$0.443190\pi$
$577$	−19.5357	+	26.8885i	−0.813281	+	1.11938i	−0.990809	+	0.135269i	$0.956810\pi$
$578$	8.45351	−	11.6353i	0.351620	−	0.483963i
$579$		0			0
$580$	−15.6773	−	2.36119i	−0.650964	−	0.0980429i
$581$	−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	$-0.503835\pi$
$587$	−14.7679	−	4.79837i	−0.609535	−	0.198050i	−0.597489	+	0.801877i	$0.703835\pi$
$588$		0			0
$589$	0.291796	+	0.212002i	0.0120232	+	0.00873540i
$590$	11.2126	−	11.3841i	0.461614	−	0.468676i
$591$		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	−0.135964	−	0.990714i	$-0.543413\pi$
$599$	−27.4164	−	19.9192i	−1.12020	−	0.813876i	−0.984240	+	0.176838i	$0.943413\pi$
$600$		0			0
$601$	−6.32624	+	19.4702i	−0.258053	+	0.794204i	0.735160	+	0.677893i	$0.237107\pi$
$601$	−6.32624	+	19.4702i	−0.258053	+	0.794204i	−0.993213	+	0.116311i	$0.962893\pi$
$602$	−11.3067	+	3.67376i	−0.460826	+	0.149731i
$603$		0			0
$604$	15.4164			0.627285
$605$	−19.6949	−	14.7347i	−0.800710	−	0.599052i
$606$		0			0
$607$	−0.726543	−	1.00000i	−0.0294895	−	0.0405887i	0.794018	−	0.607895i	$-0.207986\pi$
$607$	−0.726543	−	1.00000i	−0.0294895	−	0.0405887i	−0.823507	+	0.567306i	$0.807986\pi$
$608$	2.35114	−	0.763932i	0.0953514	−	0.0309815i
$609$		0			0
$610$	−2.84754	−	5.48526i	−0.115293	−	0.222092i
$611$	−3.16312	−	2.29814i	−0.127966	−	0.0929728i
$612$		0			0
$613$	35.5851	−	11.5623i	1.43727	−	0.466997i	0.516224	−	0.856453i	$-0.327337\pi$
$613$	35.5851	−	11.5623i	1.43727	−	0.466997i	0.921045	+	0.389456i	$0.127337\pi$
$614$	−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	0.868199	+	0.496216i	$0.165278\pi$
$619$	11.3820	+	35.0301i	0.457480	+	1.40798i	−0.410719	+	0.911762i	$0.634722\pi$
$620$	0.232430	+	0.228927i	0.00933460	+	0.00919394i
$621$		0			0
$622$	−11.6902	+	16.0902i	−0.468734	+	0.645157i
$623$	9.95959	+	3.23607i	0.399023	+	0.129650i
$624$		0			0
$625$	−8.44373	−	23.5309i	−0.337749	−	0.941236i
$626$	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	−0.759780	−	0.650180i	$-0.774693\pi$
$631$	5.95492	−	18.3273i	0.237061	−	0.729600i	0.996841	−	0.0794196i	$-0.0253067\pi$
$632$	−5.65334	+	7.78115i	−0.224878	+	0.309518i
$633$		0			0
$634$	6.76393	−	20.8172i	0.268630	−	0.826758i
$635$	−2.66418	+	17.6890i	−0.105725	+	0.701968i
$636$		0			0
$637$		−	3.38197i		−	0.133998i
$638$	22.8051	+	5.73607i	0.902863	+	0.227093i
$639$		0			0
$640$	2.20582	−	0.366554i	0.0871927	−	0.0144893i
$641$	0.145898	+	0.449028i	0.00576263	+	0.0177355i	0.953896	−	0.300136i	$-0.0970320\pi$
$641$	0.145898	+	0.449028i	0.00576263	+	0.0177355i	−0.948134	+	0.317871i	$0.897032\pi$
$642$		0			0
$643$	9.49032	−	13.0623i	0.374262	−	0.515127i	−0.579791	−	0.814765i	$-0.696866\pi$
$643$	9.49032	−	13.0623i	0.374262	−	0.515127i	0.954053	+	0.299638i	$0.0968659\pi$
$644$	−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	0.903931	+	0.427679i	$0.140669\pi$
$647$	26.2336	+	36.1074i	1.03135	+	1.41953i	0.127417	+	0.991849i	$0.459331\pi$
$648$		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	$-0.424242\pi$
$653$	−3.69822	−	1.20163i	−0.144723	−	0.0470233i	−0.380483	+	0.924788i	$0.624242\pi$
$654$		0			0
$655$	7.64880	−	3.97068i	0.298863	−	0.155147i
$656$	−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
$665$	3.14816	+	6.06436i	0.122080	+	0.235166i
$666$		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	$-0.0324355\pi$
$673$	15.3229	+	21.0902i	0.590655	+	0.812966i	−0.404158	+	0.914689i	$0.632435\pi$
$674$	−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	$-0.658621\pi$
$677$	13.1433	−	18.0902i	0.505137	−	0.695262i	0.983090	+	0.183124i	$0.0586210\pi$
$678$		0			0
$679$	1.23607	+	3.80423i	0.0474359	+	0.145993i
$680$	−0.593096	−	3.56909i	−0.0227442	−	0.136868i
$681$		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
$685$	3.18446	−	21.1435i	0.121672	−	0.807852i
$686$	−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	−0.821813	−	0.569758i	$-0.807037\pi$
$691$	−14.0344	+	10.1966i	−0.533895	+	0.387898i	0.287918	+	0.957655i	$0.407037\pi$
$692$			19.4164i			0.738101i
$693$		0			0
$694$	7.23607			0.274677
$695$	−2.47934	−	14.9200i	−0.0940468	−	0.565948i
$696$		0			0
$697$	16.8415	+	5.47214i	0.637917	+	0.207272i
$698$	−0.106001	+	0.145898i	−0.00401220	+	0.00552232i
$699$		0			0
$700$	1.99885	+	5.84818i	0.0755493	+	0.221040i
$701$	−8.03444	−	24.7275i	−0.303457	−	0.933944i	−0.980249	−	0.197769i	$-0.936630\pi$
$701$	−8.03444	−	24.7275i	−0.303457	−	0.933944i	0.676792	−	0.736174i	$-0.263370\pi$
$702$		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	−0.996355	−	0.0853086i	$-0.972812\pi$
$709$	−36.8885	−	26.8011i	−1.38538	−	1.00654i	−0.389024	−	0.921228i	$-0.627188\pi$
$710$	1.75987	+	3.39008i	0.0660469	+	0.127227i
$711$		0			0
$712$	8.05748	−	2.61803i	0.301967	−	0.0981150i
$713$	−0.138757	−	0.190983i	−0.00519650	−	0.00715237i
$714$		0			0
$715$	2.38232	+	3.91570i	0.0890938	+	0.146439i
$716$	−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	0.651642	+	0.758527i	$0.274081\pi$
$719$	−8.61803	+	26.5236i	−0.321398	+	0.989163i	−0.973040	+	0.230636i	$0.925919\pi$
$720$		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
$730$	−13.0321	−	12.8357i	−0.482338	−	0.475070i
$731$	12.5902	+	9.14729i	0.465664	+	0.338325i
$732$		0			0
$733$	42.1038	+	13.6803i	1.55514	+	0.505295i	0.955504	−	0.294979i	$-0.0953128\pi$
$733$	42.1038	+	13.6803i	1.55514	+	0.505295i	0.599634	+	0.800274i	$0.295313\pi$
$734$	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	−0.218062	−	0.975935i	$-0.569973\pi$
$739$	17.4721	−	12.6942i	0.642723	−	0.466966i	0.860785	+	0.508969i	$0.169973\pi$
$740$	2.12534	−	14.1114i	0.0781290	−	0.518744i
$741$		0			0
$742$	−4.91428	+	6.76393i	−0.180409	+	0.248312i
$743$	16.5842	−	22.8262i	0.608416	−	0.837413i	−0.388030	−	0.921647i	$-0.626844\pi$
$743$	16.5842	−	22.8262i	0.608416	−	0.837413i	0.996446	+	0.0842335i	$0.0268442\pi$
$744$		0			0
$745$	−15.8005	−	2.37975i	−0.578886	−	0.0871871i
$746$	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	−0.937813	−	0.347141i	$-0.887153\pi$
$751$	−10.5000	−	32.3157i	−0.383150	−	1.17922i	0.554663	−	0.832075i	$-0.312847\pi$
$752$	6.01661	+	1.95492i	0.219403	+	0.0712884i
$753$		0			0
$754$	−3.54508	−	2.57565i	−0.129104	−	0.0937998i
$755$	24.5598	+	24.1897i	0.893823	+	0.880355i
$756$		0			0
$757$	−12.1595	−	16.7361i	−0.441943	−	0.608283i	0.528699	−	0.848809i	$-0.322680\pi$
$757$	−12.1595	−	16.7361i	−0.441943	−	0.608283i	−0.970643	+	0.240526i	$0.922680\pi$
$758$			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	−0.565156	−	0.824984i	$-0.691184\pi$
$761$	1.23607	−	0.898056i	0.0448074	−	0.0325545i	0.609964	+	0.792429i	$0.291184\pi$
$762$		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	$0.424485\pi$
$770$	−2.11141	−	8.92045i	−0.0760900	−	0.321471i
$771$		0			0
$772$	−4.14725	−	5.70820i	−0.149263	−	0.205443i
$773$	−41.1199	+	13.3607i	−1.47898	+	0.480550i	−0.933808	−	0.357773i	$-0.883536\pi$
$773$	−41.1199	+	13.3607i	−1.47898	+	0.480550i	−0.545173	+	0.838323i	$0.683536\pi$
$774$		0			0
$775$	0.0110751	+	0.729406i	0.000397830	+	0.0262010i
$776$	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
$785$	−9.64347	+	9.79101i	−0.344190	+	0.349456i
$786$		0			0
$787$	29.2707	−	40.2877i	1.04339	−	1.43610i	0.148987	−	0.988839i	$-0.452399\pi$
$787$	29.2707	−	40.2877i	1.04339	−	1.43610i	0.894402	−	0.447263i	$-0.147601\pi$
$788$	10.2371	+	3.32624i	0.364682	+	0.118492i
$789$		0			0
$790$	−21.2156	+	3.52552i	−0.754819	+	0.125433i
$791$	−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	$-0.817235\pi$
$797$	−1.79611	+	2.47214i	−0.0636215	+	0.0875675i	0.776021	+	0.630708i	$0.217235\pi$
$798$		0			0
$799$	3.16312	−	9.73508i	0.111903	−	0.344402i
$800$	4.08924	+	2.87718i	0.144576	+	0.101724i
$801$		0			0
$802$			30.3607i			1.07207i
$803$	17.3965	+	20.8197i	0.613910	+	0.734710i
$804$		0			0
$805$	−0.733107	−	4.41164i	−0.0258386	−	0.155490i
$806$	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	0.990976	−	0.134036i	$-0.0427939\pi$
$809$	33.2705	+	24.1724i	1.16973	+	0.849858i	0.178752	+	0.983894i	$0.442794\pi$
$810$		0			0
$811$	−5.20163	−	16.0090i	−0.182654	−	0.562151i	0.817246	−	0.576289i	$-0.195500\pi$
$811$	−5.20163	−	16.0090i	−0.182654	−	0.562151i	−0.999900	+	0.0141380i	$0.995500\pi$
$812$	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
$820$	−21.7199	+	11.2753i	−0.758491	+	0.393751i
$821$	−8.61803	+	26.5236i	−0.300771	+	0.925679i	0.680450	+	0.732795i	$0.261784\pi$
$821$	−8.61803	+	26.5236i	−0.300771	+	0.925679i	−0.981221	+	0.192885i	$0.938216\pi$
$822$		0			0
$823$	20.0252	+	27.5623i	0.698034	+	0.960762i	0.999972	+	0.00743409i	$0.00236637\pi$
$823$	20.0252	+	27.5623i	0.698034	+	0.960762i	−0.301938	+	0.953327i	$0.597634\pi$
$824$	−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	$-0.378186\pi$
$827$	−17.9516	−	24.7082i	−0.624237	−	0.859188i	−0.997653	+	0.0684756i	$0.978186\pi$
$828$		0			0
$829$	3.03444	−	9.33905i	0.105391	−	0.324359i	−0.884431	−	0.466670i	$-0.845453\pi$
$829$	3.03444	−	9.33905i	0.105391	−	0.324359i	0.989822	+	0.142312i	$0.0454535\pi$
$830$	−5.48526	+	2.84754i	−0.190396	+	0.0988395i
$831$		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	0.998732	+	0.0503399i	$0.0160305\pi$
$839$	6.38197	+	19.6417i	0.220330	+	0.678106i	−0.778402	+	0.627766i	$0.783970\pi$
$840$		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
$845$	4.62518	+	27.8331i	0.159111	+	0.957488i
$846$		0			0
$847$	1.83660	+	13.4721i	0.0631063	+	0.462908i
$848$			6.76393i			0.232274i
$849$		0			0
$850$	4.65537	−	6.61653i	0.159678	−	0.226945i
$851$	−3.19098	+	9.82084i	−0.109385	+	0.336654i
$852$		0			0
$853$	15.2824	−	21.0344i	0.523260	−	0.720206i	−0.462825	−	0.886450i	$-0.653164\pi$
$853$	15.2824	−	21.0344i	0.523260	−	0.720206i	0.986085	+	0.166244i	$0.0531640\pi$
$854$	−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	$0.603719\pi$
$860$	−21.2156	+	3.52552i	−0.723447	+	0.120219i
$861$		0			0
$862$	−35.1361	−	11.4164i	−1.19674	−	0.388844i
$863$	31.1729	−	42.9058i	1.06114	−	1.46053i	0.182399	−	0.983225i	$-0.441614\pi$
$863$	31.1729	−	42.9058i	1.06114	−	1.46053i	0.878738	−	0.477305i	$-0.158386\pi$
$864$		0			0
$865$	−30.4661	+	30.9322i	−1.03588	+	1.05173i
$866$	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
$875$	−5.99197	+	12.4531i	−0.202565	+	0.420991i
$876$		0			0
$877$	38.6426	−	12.5557i	1.30487	−	0.423977i	0.427595	−	0.903971i	$-0.359361\pi$
$877$	38.6426	−	12.5557i	1.30487	−	0.423977i	0.877272	+	0.479994i	$0.159361\pi$
$878$	−21.8415	−	30.0623i	−0.737116	−	1.01455i
$879$		0			0
$880$	−5.62386	−	4.83447i	−0.189580	−	0.162970i
$881$	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	$-0.375245\pi$
$883$	36.6749	−	11.9164i	1.23421	−	0.401019i	0.852238	+	0.523155i	$0.175245\pi$
$884$	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	$-0.0551186\pi$
$887$	50.0552	+	16.2639i	1.68069	+	0.546089i	0.695645	+	0.718386i	$0.255119\pi$
$888$		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
$895$	−24.3274	−	23.9608i	−0.813175	−	0.800922i
$896$	−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
$905$	43.9762	+	6.62333i	1.46182	+	0.220167i
$906$		0			0
$907$	−22.5604	+	31.0517i	−0.749104	+	1.03105i	0.248939	+	0.968519i	$0.419918\pi$
$907$	−22.5604	+	31.0517i	−0.749104	+	1.03105i	−0.998043	+	0.0625343i	$0.980082\pi$
$908$		0			0
$909$		0			0
$910$	−0.254407	+	1.68915i	−0.00843350	+	0.0559949i
$911$	15.8541	−	11.5187i	0.525270	−	0.381631i	−0.293316	−	0.956016i	$-0.594759\pi$
$911$	15.8541	−	11.5187i	0.525270	−	0.381631i	0.818585	+	0.574385i	$0.194759\pi$
$912$		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	0.835458	−	0.549554i	$-0.185202\pi$
$919$	17.3090	+	12.5757i	0.570972	+	0.414835i	−0.264486	+	0.964389i	$0.585202\pi$
$920$	−2.57768	−	2.53884i	−0.0849837	−	0.0837031i
$921$		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	0.828204	−	0.560426i	$-0.189363\pi$
$929$	16.7984	+	12.2047i	0.551137	+	0.400424i	−0.277068	+	0.960850i	$0.589363\pi$
$930$		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
$935$	−7.82234	+	9.09960i	−0.255818	+	0.297589i
$936$		0			0
$937$	−31.9524	−	43.9787i	−1.04384	−	1.43672i	−0.894030	−	0.448007i	$-0.852134\pi$
$937$	−31.9524	−	43.9787i	−1.04384	−	1.43672i	−0.149810	−	0.988715i	$-0.547866\pi$
$938$	−1.62460	+	0.527864i	−0.0530450	+	0.0172354i
$939$		0			0
$940$	6.51760	+	12.5550i	0.212581	+	0.409498i
$941$	−3.02786	−	2.19987i	−0.0987055	−	0.0717138i	0.537338	−	0.843367i	$-0.319430\pi$
$941$	−3.02786	−	2.19987i	−0.0987055	−	0.0717138i	−0.636043	+	0.771653i	$0.719430\pi$
$942$		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
$950$	3.99769	+	11.6964i	0.129702	+	0.379480i
$951$		0			0
$952$	−1.17557	+	1.61803i	−0.0381005	+	0.0524408i
$953$	−26.5033	−	8.61146i	−0.858527	−	0.278952i	−0.153514	−	0.988146i	$-0.549059\pi$
$953$	−26.5033	−	8.61146i	−0.858527	−	0.278952i	−0.705013	+	0.709194i	$0.749059\pi$
$954$		0			0
$955$	−1.63928	−	9.86472i	−0.0530458	−	0.319215i
$956$	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
$965$	2.34972	−	15.6011i	0.0756400	−	0.502218i
$966$		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
$970$	1.18619	+	7.13818i	0.0380863	+	0.229193i
$971$	11.4164	+	35.1361i	0.366370	+	1.12757i	0.949119	+	0.314918i	$0.101977\pi$
$971$	11.4164	+	35.1361i	0.366370	+	1.12757i	−0.582749	+	0.812652i	$0.698023\pi$
$972$		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	$-0.131151\pi$
$977$	7.88597	+	10.8541i	0.252294	+	0.347253i	−0.664019	+	0.747716i	$0.731151\pi$
$978$		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	$-0.546077\pi$
$983$	−26.4176	−	8.58359i	−0.842590	−	0.273774i	−0.698339	+	0.715767i	$0.746077\pi$
$984$		0			0
$985$	11.0895	+	21.3620i	0.353342	+	0.680649i
$986$	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
$995$	17.9296	−	9.30772i	0.568408	−	0.295075i
$996$		0			0
$997$	−21.6295	−	7.02786i	−0.685014	−	0.222575i	−0.0542250	−	0.998529i	$-0.517269\pi$
$997$	−21.6295	−	7.02786i	−0.685014	−	0.222575i	−0.630789	+	0.775954i	$0.717269\pi$
$998$	−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.289.1	✓	8
3.2	odd	2		990.2.ba.e.289.2	yes	8
5.4	even	2	inner	990.2.ba.c.289.2	yes	8
11.4	even	5	inner	990.2.ba.c.829.2	yes	8
15.14	odd	2		990.2.ba.e.289.1	yes	8
33.26	odd	10		990.2.ba.e.829.1	yes	8
55.4	even	10	inner	990.2.ba.c.829.1	yes	8
165.59	odd	10		990.2.ba.e.829.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.ba.c.289.1	✓	8	1.1	even	1	trivial
990.2.ba.c.289.2	yes	8	5.4	even	2	inner
990.2.ba.c.829.1	yes	8	55.4	even	10	inner
990.2.ba.c.829.2	yes	8	11.4	even	5	inner
990.2.ba.e.289.1	yes	8	15.14	odd	2
990.2.ba.e.289.2	yes	8	3.2	odd	2
990.2.ba.e.829.1	yes	8	33.26	odd	10
990.2.ba.e.829.2	yes	8	165.59	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.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.98459 + 1.03025i) q^{5} +(1.17557 + 0.381966i) q^{7} +(0.951057 - 0.309017i) q^{8} +(2.00000 + 1.00000i) q^{10} +(-2.80902 - 1.76336i) q^{11} +(0.363271 + 0.500000i) q^{13} +(-0.381966 - 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.951057 + 1.30902i) q^{17} +(-0.763932 - 2.35114i) q^{19} +(-0.366554 - 2.20582i) q^{20} +(0.224514 + 3.30902i) q^{22} +1.61803i q^{23} +(2.87718 - 4.08924i) q^{25} +(0.190983 - 0.587785i) q^{26} +(-0.726543 + 1.00000i) q^{28} +(2.19098 - 6.74315i) q^{29} +(-0.118034 + 0.0857567i) q^{31} +1.00000i q^{32} +1.61803 q^{34} +(-2.72654 + 0.453085i) q^{35} +(6.06961 + 1.97214i) q^{37} +(-1.45309 + 2.00000i) q^{38} +(-1.56909 + 1.59310i) q^{40} +(-3.38197 - 10.4086i) q^{41} -9.61803i q^{43} +(2.54508 - 2.12663i) q^{44} +(1.30902 - 0.951057i) q^{46} +(-6.01661 + 1.95492i) q^{47} +(-4.42705 - 3.21644i) q^{49} +(-4.99942 + 0.0759100i) q^{50} +(-0.587785 + 0.190983i) q^{52} +(-3.97574 - 5.47214i) q^{53} +(7.39144 + 0.605548i) q^{55} +1.23607 q^{56} +(-6.74315 + 2.19098i) q^{58} +(2.20820 - 6.79615i) q^{59} +(-2.23607 - 1.62460i) q^{61} +(0.138757 + 0.0450850i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-1.23607 - 0.618034i) q^{65} -1.38197i q^{67} +(-0.951057 - 1.30902i) q^{68} +(1.96917 + 1.93950i) q^{70} +(1.38197 + 1.00406i) q^{71} +(-7.77997 - 2.52786i) q^{73} +(-1.97214 - 6.06961i) q^{74} +2.47214 q^{76} +(-2.62866 - 3.14590i) q^{77} +(-7.78115 + 5.65334i) q^{79} +(2.21113 + 0.333023i) q^{80} +(-6.43288 + 8.85410i) q^{82} +(-1.62460 + 2.23607i) q^{83} +(0.538842 - 3.57768i) q^{85} +(-7.78115 + 5.65334i) q^{86} +(-3.21644 - 0.809017i) q^{88} +8.47214 q^{89} +(0.236068 + 0.726543i) q^{91} +(-1.53884 - 0.500000i) q^{92} +(5.11803 + 3.71847i) q^{94} +(3.93835 + 3.87901i) q^{95} +(1.90211 + 2.61803i) q^{97} +5.47214i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 2 q^{5} + 16 q^{10} - 18 q^{11} - 12 q^{14} - 2 q^{16} - 24 q^{19} + 2 q^{20} + 6 q^{25} + 6 q^{26} + 22 q^{29} + 8 q^{31} + 4 q^{34} - 16 q^{35} + 4 q^{40} - 36 q^{41} - 2 q^{44} + 6 q^{46}+ \cdots - 24 q^{95}+O(q^{100}) \) 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

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