LMFDB - Embedded newform 990.2.n.e.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	990.631
Dual form			990.2.n.e.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.00000 - 3.07768i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.00000 - 3.07768i) q^{7} +(-0.309017 + 0.951057i) q^{8} -1.00000 q^{10} +(-3.04508 - 1.31433i) q^{11} +(-2.73607 - 1.98787i) q^{13} +(1.00000 - 3.07768i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-4.92705 + 3.57971i) q^{17} +(0.381966 - 1.17557i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-1.69098 - 2.85317i) q^{22} -6.85410 q^{23} +(0.309017 - 0.951057i) q^{25} +(-1.04508 - 3.21644i) q^{26} +(2.61803 - 1.90211i) q^{28} +(0.809017 + 2.48990i) q^{29} +(1.11803 + 0.812299i) q^{31} -1.00000 q^{32} -6.09017 q^{34} +(2.61803 + 1.90211i) q^{35} +(-1.97214 - 6.06961i) q^{37} +(1.00000 - 0.726543i) q^{38} +(-0.309017 - 0.951057i) q^{40} +(-0.381966 + 1.17557i) q^{41} -0.0901699 q^{43} +(0.309017 - 3.30220i) q^{44} +(-5.54508 - 4.02874i) q^{46} +(1.33688 - 4.11450i) q^{47} +(-2.80902 + 2.04087i) q^{49} +(0.809017 - 0.587785i) q^{50} +(1.04508 - 3.21644i) q^{52} +(6.85410 + 4.97980i) q^{53} +(3.23607 - 0.726543i) q^{55} +3.23607 q^{56} +(-0.809017 + 2.48990i) q^{58} +(-4.35410 - 13.4005i) q^{59} +(0.427051 + 1.31433i) q^{62} +(-0.809017 - 0.587785i) q^{64} +3.38197 q^{65} -5.09017 q^{67} +(-4.92705 - 3.57971i) q^{68} +(1.00000 + 3.07768i) q^{70} +(8.47214 - 6.15537i) q^{71} +(4.14590 + 12.7598i) q^{73} +(1.97214 - 6.06961i) q^{74} +1.23607 q^{76} +(-1.00000 + 10.6861i) q^{77} +(3.30902 + 2.40414i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-1.00000 + 0.726543i) q^{82} +(3.23607 - 2.35114i) q^{83} +(1.88197 - 5.79210i) q^{85} +(-0.0729490 - 0.0530006i) q^{86} +(2.19098 - 2.48990i) q^{88} -17.2361 q^{89} +(-3.38197 + 10.4086i) q^{91} +(-2.11803 - 6.51864i) q^{92} +(3.50000 - 2.54290i) q^{94} +(0.381966 + 1.17557i) q^{95} +(-15.0902 - 10.9637i) q^{97} -3.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8	$ 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8} - 4 q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 13 q^{17} + 6 q^{19} - q^{20} - 9 q^{22} - 14 q^{23} - q^{25} + 7 q^{26} + 6 q^{28} + q^{29} - 4 q^{32} - 2 q^{34} + 6 q^{35} + 10 q^{37} + 4 q^{38} + q^{40} - 6 q^{41} + 22 q^{43} - q^{44} - 11 q^{46} + 21 q^{47} - 9 q^{49} + q^{50} - 7 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} - q^{58} - 4 q^{59} - 5 q^{62} - q^{64} + 18 q^{65} + 2 q^{67} - 13 q^{68} + 4 q^{70} + 16 q^{71} + 30 q^{73} - 10 q^{74} - 4 q^{76} - 4 q^{77} + 11 q^{79} - q^{80} - 4 q^{82} + 4 q^{83} + 12 q^{85} - 7 q^{86} + 11 q^{88} - 60 q^{89} - 18 q^{91} - 4 q^{92} + 14 q^{94} + 6 q^{95} - 38 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8 - 4 * q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 13 * q^17 + 6 * q^19 - q^20 - 9 * q^22 - 14 * q^23 - q^25 + 7 * q^26 + 6 * q^28 + q^29 - 4 * q^32 - 2 * q^34 + 6 * q^35 + 10 * q^37 + 4 * q^38 + q^40 - 6 * q^41 + 22 * q^43 - q^44 - 11 * q^46 + 21 * q^47 - 9 * q^49 + q^50 - 7 * q^52 + 14 * q^53 + 4 * q^55 + 4 * q^56 - q^58 - 4 * q^59 - 5 * q^62 - q^64 + 18 * q^65 + 2 * q^67 - 13 * q^68 + 4 * q^70 + 16 * q^71 + 30 * q^73 - 10 * q^74 - 4 * q^76 - 4 * q^77 + 11 * q^79 - q^80 - 4 * q^82 + 4 * q^83 + 12 * q^85 - 7 * q^86 + 11 * q^88 - 60 * q^89 - 18 * q^91 - 4 * q^92 + 14 * q^94 + 6 * q^95 - 38 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−1.00000	−	3.07768i	−0.377964	−	1.16326i	−0.941457	−	0.337134i	$-0.890543\pi$
$7$	−1.00000	−	3.07768i	−0.377964	−	1.16326i	0.563492	−	0.826121i	$-0.309457\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$12$		0			0
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	0.139708	−	0.990193i	$-0.455384\pi$
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	−0.898557	+	0.438857i	$0.855384\pi$
$14$	1.00000	−	3.07768i	0.267261	−	0.822546i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.92705	+	3.57971i	−1.19499	+	0.868208i	−0.993782	−	0.111342i	$-0.964485\pi$
$17$	−4.92705	+	3.57971i	−1.19499	+	0.868208i	−0.201203	+	0.979550i	$0.564485\pi$
$18$		0			0
$19$	0.381966	−	1.17557i	0.0876290	−	0.269694i	−0.897634	−	0.440742i	$-0.854715\pi$
$19$	0.381966	−	1.17557i	0.0876290	−	0.269694i	0.985263	+	0.171048i	$0.0547153\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$		0			0
$22$	−1.69098	−	2.85317i	−0.360519	−	0.608298i
$23$	−6.85410			−1.42918			−0.714590	−	0.699544i	$-0.753386\pi$
$23$	−6.85410			−1.42918			−0.714590	+	0.699544i	$0.753386\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−1.04508	−	3.21644i	−0.204958	−	0.630796i
$27$		0			0
$28$	2.61803	−	1.90211i	0.494762	−	0.359466i
$29$	0.809017	+	2.48990i	0.150231	+	0.462363i	0.997646	−	0.0685673i	$-0.0218428\pi$
$29$	0.809017	+	2.48990i	0.150231	+	0.462363i	−0.847416	+	0.530930i	$0.821843\pi$
$30$		0			0
$31$	1.11803	+	0.812299i	0.200805	+	0.145893i	0.683644	−	0.729816i	$-0.260394\pi$
$31$	1.11803	+	0.812299i	0.200805	+	0.145893i	−0.482839	+	0.875709i	$0.660394\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−6.09017			−1.04446
$35$	2.61803	+	1.90211i	0.442529	+	0.321516i
$36$		0			0
$37$	−1.97214	−	6.06961i	−0.324217	−	0.997838i	−0.971793	−	0.235837i	$-0.924217\pi$
$37$	−1.97214	−	6.06961i	−0.324217	−	0.997838i	0.647576	−	0.762001i	$-0.275783\pi$
$38$	1.00000	−	0.726543i	0.162221	−	0.117861i
$39$		0			0
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	−0.381966	+	1.17557i	−0.0596531	+	0.183593i	−0.976443	−	0.215778i	$-0.930771\pi$
$41$	−0.381966	+	1.17557i	−0.0596531	+	0.183593i	0.916789	+	0.399371i	$0.130771\pi$
$42$		0			0
$43$	−0.0901699			−0.0137508			−0.00687539	−	0.999976i	$-0.502189\pi$
$43$	−0.0901699			−0.0137508			−0.00687539	+	0.999976i	$0.502189\pi$
$44$	0.309017	−	3.30220i	0.0465861	−	0.497825i
$45$		0			0
$46$	−5.54508	−	4.02874i	−0.817578	−	0.594005i
$47$	1.33688	−	4.11450i	0.195004	−	0.600161i	−0.804972	−	0.593312i	$-0.797820\pi$
$47$	1.33688	−	4.11450i	0.195004	−	0.600161i	0.999977	−	0.00684879i	$-0.00218005\pi$
$48$		0			0
$49$	−2.80902	+	2.04087i	−0.401288	+	0.291553i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$		0			0
$52$	1.04508	−	3.21644i	0.144927	−	0.446040i
$53$	6.85410	+	4.97980i	0.941483	+	0.684028i	0.948777	−	0.315946i	$-0.102322\pi$
$53$	6.85410	+	4.97980i	0.941483	+	0.684028i	−0.00729395	+	0.999973i	$0.502322\pi$
$54$		0			0
$55$	3.23607	−	0.726543i	0.436351	−	0.0979670i
$56$	3.23607			0.432438
$57$		0			0
$58$	−0.809017	+	2.48990i	−0.106229	+	0.326940i
$59$	−4.35410	−	13.4005i	−0.566856	−	1.74460i	−0.662372	−	0.749175i	$-0.730450\pi$
$59$	−4.35410	−	13.4005i	−0.566856	−	1.74460i	0.0955164	−	0.995428i	$-0.469550\pi$
$60$		0			0
$61$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$61$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$62$	0.427051	+	1.31433i	0.0542355	+	0.166920i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.38197			0.419481
$66$		0			0
$67$	−5.09017			−0.621863			−0.310932	−	0.950432i	$-0.600641\pi$
$67$	−5.09017			−0.621863			−0.310932	+	0.950432i	$0.600641\pi$
$68$	−4.92705	−	3.57971i	−0.597493	−	0.434104i
$69$		0			0
$70$	1.00000	+	3.07768i	0.119523	+	0.367854i
$71$	8.47214	−	6.15537i	1.00546	−	0.730508i	0.0422061	−	0.999109i	$-0.486561\pi$
$71$	8.47214	−	6.15537i	1.00546	−	0.730508i	0.963251	+	0.268601i	$0.0865614\pi$
$72$		0			0
$73$	4.14590	+	12.7598i	0.485241	+	1.49342i	0.831632	+	0.555327i	$0.187407\pi$
$73$	4.14590	+	12.7598i	0.485241	+	1.49342i	−0.346391	+	0.938090i	$0.612593\pi$
$74$	1.97214	−	6.06961i	0.229256	−	0.705578i
$75$		0			0
$76$	1.23607			0.141787
$77$	−1.00000	+	10.6861i	−0.113961	+	1.21780i
$78$		0			0
$79$	3.30902	+	2.40414i	0.372293	+	0.270487i	0.758161	−	0.652067i	$-0.226098\pi$
$79$	3.30902	+	2.40414i	0.372293	+	0.270487i	−0.385868	+	0.922554i	$0.626098\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$		0			0
$82$	−1.00000	+	0.726543i	−0.110432	+	0.0802332i
$83$	3.23607	−	2.35114i	0.355205	−	0.258071i	−0.395845	−	0.918318i	$-0.629548\pi$
$83$	3.23607	−	2.35114i	0.355205	−	0.258071i	0.751049	+	0.660246i	$0.229548\pi$
$84$		0			0
$85$	1.88197	−	5.79210i	0.204128	−	0.628241i
$86$	−0.0729490	−	0.0530006i	−0.00786629	−	0.00571520i
$87$		0			0
$88$	2.19098	−	2.48990i	0.233560	−	0.265424i
$89$	−17.2361			−1.82702			−0.913510	−	0.406817i	$-0.866639\pi$
$89$	−17.2361			−1.82702			−0.913510	+	0.406817i	$0.866639\pi$
$90$		0			0
$91$	−3.38197	+	10.4086i	−0.354526	+	1.09112i
$92$	−2.11803	−	6.51864i	−0.220820	−	0.679615i
$93$		0			0
$94$	3.50000	−	2.54290i	0.360997	−	0.262280i
$95$	0.381966	+	1.17557i	0.0391889	+	0.120611i
$96$		0			0
$97$	−15.0902	−	10.9637i	−1.53217	−	1.11319i	−0.955015	−	0.296559i	$-0.904161\pi$
$97$	−15.0902	−	10.9637i	−1.53217	−	1.11319i	−0.577160	−	0.816631i	$-0.695839\pi$
$98$	−3.47214			−0.350739
$99$		0			0
$100$	1.00000			0.100000
$101$	12.6353	+	9.18005i	1.25725	+	0.913449i	0.998620	−	0.0525259i	$-0.0167272\pi$
$101$	12.6353	+	9.18005i	1.25725	+	0.913449i	0.258635	+	0.965975i	$0.416727\pi$
$102$		0			0
$103$	2.09017	+	6.43288i	0.205951	+	0.633851i	0.999673	+	0.0255706i	$0.00814025\pi$
$103$	2.09017	+	6.43288i	0.205951	+	0.633851i	−0.793722	+	0.608280i	$0.791860\pi$
$104$	2.73607	−	1.98787i	0.268294	−	0.194927i
$105$		0			0
$106$	2.61803	+	8.05748i	0.254286	+	0.782612i
$107$	−1.94427	+	5.98385i	−0.187960	+	0.578481i	−0.999987	−	0.00513899i	$-0.998364\pi$
$107$	−1.94427	+	5.98385i	−0.187960	+	0.578481i	0.812027	+	0.583620i	$0.198364\pi$
$108$		0			0
$109$	−2.47214			−0.236788			−0.118394	−	0.992967i	$-0.537775\pi$
$109$	−2.47214			−0.236788			−0.118394	+	0.992967i	$0.537775\pi$
$110$	3.04508	+	1.31433i	0.290337	+	0.125316i
$111$		0			0
$112$	2.61803	+	1.90211i	0.247381	+	0.179733i
$113$	6.04508	−	18.6049i	0.568674	−	1.75020i	−0.0881015	−	0.996112i	$-0.528080\pi$
$113$	6.04508	−	18.6049i	0.568674	−	1.75020i	0.656775	−	0.754086i	$-0.271920\pi$
$114$		0			0
$115$	5.54508	−	4.02874i	0.517082	−	0.375682i
$116$	−2.11803	+	1.53884i	−0.196655	+	0.142878i
$117$		0			0
$118$	4.35410	−	13.4005i	0.400828	−	1.23362i
$119$	15.9443	+	11.5842i	1.46161	+	1.06192i
$120$		0			0
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$		0			0
$123$		0			0
$124$	−0.427051	+	1.31433i	−0.0383503	+	0.118030i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	−11.8541	+	8.61251i	−1.05188	+	0.764237i	−0.972569	−	0.232613i	$-0.925272\pi$
$127$	−11.8541	+	8.61251i	−1.05188	+	0.764237i	−0.0793121	+	0.996850i	$0.525272\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	2.73607	+	1.98787i	0.239969	+	0.174348i
$131$	3.38197			0.295484			0.147742	−	0.989026i	$-0.452800\pi$
$131$	3.38197			0.295484			0.147742	+	0.989026i	$0.452800\pi$
$132$		0			0
$133$	−4.00000			−0.346844
$134$	−4.11803	−	2.99193i	−0.355744	−	0.258463i
$135$		0			0
$136$	−1.88197	−	5.79210i	−0.161377	−	0.496668i
$137$	−10.3541	+	7.52270i	−0.884611	+	0.642707i	−0.934467	−	0.356049i	$-0.884124\pi$
$137$	−10.3541	+	7.52270i	−0.884611	+	0.642707i	0.0498566	+	0.998756i	$0.484124\pi$
$138$		0			0
$139$	2.70820	+	8.33499i	0.229707	+	0.706965i	0.997780	+	0.0666024i	$0.0212159\pi$
$139$	2.70820	+	8.33499i	0.229707	+	0.706965i	−0.768073	+	0.640363i	$0.778784\pi$
$140$	−1.00000	+	3.07768i	−0.0845154	+	0.260112i
$141$		0			0
$142$	10.4721			0.878802
$143$	5.71885	+	9.64932i	0.478234	+	0.806917i
$144$		0			0
$145$	−2.11803	−	1.53884i	−0.175893	−	0.127794i
$146$	−4.14590	+	12.7598i	−0.343117	+	1.05601i
$147$		0			0
$148$	5.16312	−	3.75123i	0.424406	−	0.308349i
$149$	−6.16312	+	4.47777i	−0.504902	+	0.366833i	−0.810886	−	0.585204i	$-0.801015\pi$
$149$	−6.16312	+	4.47777i	−0.504902	+	0.366833i	0.305984	+	0.952037i	$0.401015\pi$
$150$		0			0
$151$	6.47214	−	19.9192i	0.526695	−	1.62100i	−0.234245	−	0.972178i	$-0.575262\pi$
$151$	6.47214	−	19.9192i	0.526695	−	1.62100i	0.760940	−	0.648823i	$-0.224738\pi$
$152$	1.00000	+	0.726543i	0.0811107	+	0.0589304i
$153$		0			0
$154$	−7.09017	+	8.05748i	−0.571342	+	0.649290i
$155$	−1.38197			−0.111002
$156$		0			0
$157$	−2.86475	+	8.81678i	−0.228632	+	0.703656i	0.769271	+	0.638923i	$0.220620\pi$
$157$	−2.86475	+	8.81678i	−0.228632	+	0.703656i	−0.997903	+	0.0647330i	$0.979380\pi$
$158$	1.26393	+	3.88998i	0.100553	+	0.309470i
$159$		0			0
$160$	0.809017	−	0.587785i	0.0639584	−	0.0464685i
$161$	6.85410	+	21.0948i	0.540179	+	1.66250i
$162$		0			0
$163$	−0.690983	−	0.502029i	−0.0541220	−	0.0393219i	0.560395	−	0.828225i	$-0.310649\pi$
$163$	−0.690983	−	0.502029i	−0.0541220	−	0.0393219i	−0.614517	+	0.788903i	$0.710649\pi$
$164$	−1.23607			−0.0965207
$165$		0			0
$166$	4.00000			0.310460
$167$	−10.7361	−	7.80021i	−0.830782	−	0.603598i	0.0889985	−	0.996032i	$-0.471633\pi$
$167$	−10.7361	−	7.80021i	−0.830782	−	0.603598i	−0.919780	+	0.392433i	$0.871633\pi$
$168$		0			0
$169$	−0.482779	−	1.48584i	−0.0371369	−	0.114295i
$170$	4.92705	−	3.57971i	0.377888	−	0.274551i
$171$		0			0
$172$	−0.0278640	−	0.0857567i	−0.00212461	−	0.00653889i
$173$	2.94427	−	9.06154i	0.223849	−	0.688936i	−0.774558	−	0.632503i	$-0.782027\pi$
$173$	2.94427	−	9.06154i	0.223849	−	0.688936i	0.998406	−	0.0564325i	$-0.0179726\pi$
$174$		0			0
$175$	−3.23607			−0.244624
$176$	3.23607	−	0.726543i	0.243928	−	0.0547652i
$177$		0			0
$178$	−13.9443	−	10.1311i	−1.04517	−	0.759359i
$179$	−5.60739	+	17.2578i	−0.419116	+	1.28991i	0.489401	+	0.872059i	$0.337215\pi$
$179$	−5.60739	+	17.2578i	−0.419116	+	1.28991i	−0.908517	+	0.417848i	$0.862785\pi$
$180$		0			0
$181$	−17.7082	+	12.8658i	−1.31624	+	0.956305i	−0.316270	+	0.948669i	$0.602430\pi$
$181$	−17.7082	+	12.8658i	−1.31624	+	0.956305i	−0.999971	+	0.00763529i	$0.997570\pi$
$182$	−8.85410	+	6.43288i	−0.656310	+	0.476837i
$183$		0			0
$184$	2.11803	−	6.51864i	0.156144	−	0.480560i
$185$	5.16312	+	3.75123i	0.379600	+	0.275796i
$186$		0			0
$187$	19.7082	−	4.42477i	1.44121	−	0.323571i
$188$	4.32624			0.315523
$189$		0			0
$190$	−0.381966	+	1.17557i	−0.0277107	+	0.0852848i
$191$	−2.85410	−	8.78402i	−0.206516	−	0.635590i	−0.999648	−	0.0265400i	$-0.991551\pi$
$191$	−2.85410	−	8.78402i	−0.206516	−	0.635590i	0.793132	−	0.609050i	$-0.208449\pi$
$192$		0			0
$193$	16.9443	−	12.3107i	1.21968	−	0.886146i	0.223602	−	0.974680i	$-0.428218\pi$
$193$	16.9443	−	12.3107i	1.21968	−	0.886146i	0.996073	+	0.0885344i	$0.0282183\pi$
$194$	−5.76393	−	17.7396i	−0.413826	−	1.27363i
$195$		0			0
$196$	−2.80902	−	2.04087i	−0.200644	−	0.145776i
$197$	−10.9443			−0.779747			−0.389874	−	0.920868i	$-0.627481\pi$
$197$	−10.9443			−0.779747			−0.389874	+	0.920868i	$0.627481\pi$
$198$		0			0
$199$	25.9787			1.84158			0.920791	−	0.390056i	$-0.127544\pi$
$199$	25.9787			1.84158			0.920791	+	0.390056i	$0.127544\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$		0			0
$202$	4.82624	+	14.8536i	0.339573	+	1.04510i
$203$	6.85410	−	4.97980i	0.481064	−	0.349513i
$204$		0			0
$205$	−0.381966	−	1.17557i	−0.0266777	−	0.0821054i
$206$	−2.09017	+	6.43288i	−0.145629	+	0.448200i
$207$		0			0
$208$	3.38197			0.234497
$209$	−2.70820	+	3.07768i	−0.187330	+	0.212888i
$210$		0			0
$211$	20.4164	+	14.8334i	1.40552	+	1.02117i	0.993954	+	0.109794i	$0.0350191\pi$
$211$	20.4164	+	14.8334i	1.40552	+	1.02117i	0.411569	+	0.911379i	$0.364981\pi$
$212$	−2.61803	+	8.05748i	−0.179807	+	0.553390i
$213$		0			0
$214$	−5.09017	+	3.69822i	−0.347957	+	0.252805i
$215$	0.0729490	−	0.0530006i	0.00497508	−	0.00361461i
$216$		0			0
$217$	1.38197	−	4.25325i	0.0938140	−	0.288730i
$218$	−2.00000	−	1.45309i	−0.135457	−	0.0984153i
$219$		0			0
$220$	1.69098	+	2.85317i	0.114006	+	0.192361i
$221$	20.5967			1.38549
$222$		0			0
$223$	2.23607	−	6.88191i	0.149738	−	0.460847i	−0.847852	−	0.530234i	$-0.822104\pi$
$223$	2.23607	−	6.88191i	0.149738	−	0.460847i	0.997590	+	0.0693868i	$0.0221043\pi$
$224$	1.00000	+	3.07768i	0.0668153	+	0.205636i
$225$		0			0
$226$	15.8262	−	11.4984i	1.05275	−	0.764865i
$227$	−6.29180	−	19.3642i	−0.417601	−	1.28524i	−0.909904	−	0.414820i	$-0.863845\pi$
$227$	−6.29180	−	19.3642i	−0.417601	−	1.28524i	0.492302	−	0.870424i	$-0.336155\pi$
$228$		0			0
$229$	−0.618034	−	0.449028i	−0.0408408	−	0.0296726i	0.567178	−	0.823596i	$-0.308035\pi$
$229$	−0.618034	−	0.449028i	−0.0408408	−	0.0296726i	−0.608018	+	0.793923i	$0.708035\pi$
$230$	6.85410			0.451946
$231$		0			0
$232$	−2.61803			−0.171882
$233$	−3.59017	−	2.60841i	−0.235200	−	0.170883i	0.463942	−	0.885865i	$-0.346435\pi$
$233$	−3.59017	−	2.60841i	−0.235200	−	0.170883i	−0.699142	+	0.714983i	$0.746435\pi$
$234$		0			0
$235$	1.33688	+	4.11450i	0.0872085	+	0.268400i
$236$	11.3992	−	8.28199i	0.742024	−	0.539112i
$237$		0			0
$238$	6.09017	+	18.7436i	0.394767	+	1.21497i
$239$	1.00000	−	3.07768i	0.0646846	−	0.199079i	−0.913491	−	0.406859i	$-0.866624\pi$
$239$	1.00000	−	3.07768i	0.0646846	−	0.199079i	0.978175	+	0.207780i	$0.0666240\pi$
$240$		0			0
$241$	−23.8885			−1.53880			−0.769398	−	0.638769i	$-0.779444\pi$
$241$	−23.8885			−1.53880			−0.769398	+	0.638769i	$0.779444\pi$
$242$	1.39919	+	10.9106i	0.0899431	+	0.701363i
$243$		0			0
$244$		0			0
$245$	1.07295	−	3.30220i	0.0685482	−	0.210970i
$246$		0			0
$247$	−3.38197	+	2.45714i	−0.215189	+	0.156344i
$248$	−1.11803	+	0.812299i	−0.0709952	+	0.0515811i
$249$		0			0
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	6.78115	+	4.92680i	0.428023	+	0.310977i	0.780858	−	0.624709i	$-0.214782\pi$
$251$	6.78115	+	4.92680i	0.428023	+	0.310977i	−0.352835	+	0.935685i	$0.614782\pi$
$252$		0			0
$253$	20.8713	+	9.00854i	1.31217	+	0.566362i
$254$	−14.6525			−0.919378
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−9.38197	−	28.8747i	−0.585231	−	1.80116i	−0.598341	−	0.801242i	$-0.704173\pi$
$257$	−9.38197	−	28.8747i	−0.585231	−	1.80116i	0.0131100	−	0.999914i	$-0.495827\pi$
$258$		0			0
$259$	−16.7082	+	12.1392i	−1.03820	+	0.754294i
$260$	1.04508	+	3.21644i	0.0648134	+	0.199475i
$261$		0			0
$262$	2.73607	+	1.98787i	0.169035	+	0.122811i
$263$	−6.85410			−0.422642			−0.211321	−	0.977417i	$-0.567777\pi$
$263$	−6.85410			−0.422642			−0.211321	+	0.977417i	$0.567777\pi$
$264$		0			0
$265$	−8.47214			−0.520439
$266$	−3.23607	−	2.35114i	−0.198416	−	0.144158i
$267$		0			0
$268$	−1.57295	−	4.84104i	−0.0960832	−	0.295714i
$269$	2.59017	−	1.88187i	0.157925	−	0.114740i	−0.506016	−	0.862524i	$-0.668882\pi$
$269$	2.59017	−	1.88187i	0.157925	−	0.114740i	0.663942	+	0.747784i	$0.268882\pi$
$270$		0			0
$271$	−1.97214	−	6.06961i	−0.119799	−	0.368703i	0.873119	−	0.487507i	$-0.162094\pi$
$271$	−1.97214	−	6.06961i	−0.119799	−	0.368703i	−0.992918	+	0.118805i	$0.962094\pi$
$272$	1.88197	−	5.79210i	0.114111	−	0.351197i
$273$		0			0
$274$	−12.7984			−0.773178
$275$	−2.19098	+	2.48990i	−0.132121	+	0.150147i
$276$		0			0
$277$	19.0172	+	13.8168i	1.14263	+	0.830172i	0.987484	−	0.157719i	$-0.0504139\pi$
$277$	19.0172	+	13.8168i	1.14263	+	0.830172i	0.155150	+	0.987891i	$0.450414\pi$
$278$	−2.70820	+	8.33499i	−0.162427	+	0.499900i
$279$		0			0
$280$	−2.61803	+	1.90211i	−0.156457	+	0.113673i
$281$	−6.09017	+	4.42477i	−0.363309	+	0.263959i	−0.754431	−	0.656379i	$-0.772087\pi$
$281$	−6.09017	+	4.42477i	−0.363309	+	0.263959i	0.391122	+	0.920339i	$0.372087\pi$
$282$		0			0
$283$	−6.89919	+	21.2335i	−0.410114	+	1.26220i	0.506435	+	0.862278i	$0.330963\pi$
$283$	−6.89919	+	21.2335i	−0.410114	+	1.26220i	−0.916549	+	0.399923i	$0.869037\pi$
$284$	8.47214	+	6.15537i	0.502729	+	0.365254i
$285$		0			0
$286$	−1.04508	+	11.1679i	−0.0617972	+	0.660373i
$287$	4.00000			0.236113
$288$		0			0
$289$	6.20820	−	19.1069i	0.365188	−	1.12393i
$290$	−0.809017	−	2.48990i	−0.0475071	−	0.146212i
$291$		0			0
$292$	−10.8541	+	7.88597i	−0.635188	+	0.461491i
$293$	6.18034	+	19.0211i	0.361059	+	1.11123i	0.952412	+	0.304813i	$0.0985941\pi$
$293$	6.18034	+	19.0211i	0.361059	+	1.11123i	−0.591353	+	0.806413i	$0.701406\pi$
$294$		0			0
$295$	11.3992	+	8.28199i	0.663686	+	0.482196i
$296$	6.38197			0.370944
$297$		0			0
$298$	−7.61803			−0.441301
$299$	18.7533	+	13.6251i	1.08453	+	0.787958i
$300$		0			0
$301$	0.0901699	+	0.277515i	0.00519731	+	0.0159957i
$302$	16.9443	−	12.3107i	0.975033	−	0.708403i
$303$		0			0
$304$	0.381966	+	1.17557i	0.0219073	+	0.0674236i
$305$		0			0
$306$		0			0
$307$	−33.4508			−1.90914			−0.954570	−	0.297985i	$-0.903685\pi$
$307$	−33.4508			−1.90914			−0.954570	+	0.297985i	$0.903685\pi$
$308$	−10.4721	+	2.35114i	−0.596705	+	0.133969i
$309$		0			0
$310$	−1.11803	−	0.812299i	−0.0635001	−	0.0461355i
$311$	−2.85410	+	8.78402i	−0.161841	+	0.498096i	−0.998790	−	0.0491856i	$-0.984337\pi$
$311$	−2.85410	+	8.78402i	−0.161841	+	0.498096i	0.836948	+	0.547282i	$0.184337\pi$
$312$		0			0
$313$	−6.85410	+	4.97980i	−0.387417	+	0.281475i	−0.764396	−	0.644747i	$-0.776963\pi$
$313$	−6.85410	+	4.97980i	−0.387417	+	0.281475i	0.376979	+	0.926222i	$0.376963\pi$
$314$	−7.50000	+	5.44907i	−0.423249	+	0.307509i
$315$		0			0
$316$	−1.26393	+	3.88998i	−0.0711017	+	0.218829i
$317$	−22.1803	−	16.1150i	−1.24577	−	0.905106i	−0.247803	−	0.968810i	$-0.579709\pi$
$317$	−22.1803	−	16.1150i	−1.24577	−	0.905106i	−0.997969	+	0.0637041i	$0.979709\pi$
$318$		0			0
$319$	0.809017	−	8.64527i	0.0452963	−	0.484042i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−6.85410	+	21.0948i	−0.381964	+	1.17556i
$323$	2.32624	+	7.15942i	0.129435	+	0.398361i
$324$		0			0
$325$	−2.73607	+	1.98787i	−0.151770	+	0.110267i
$326$	−0.263932	−	0.812299i	−0.0146178	−	0.0449891i
$327$		0			0
$328$	−1.00000	−	0.726543i	−0.0552158	−	0.0401166i
$329$	−14.0000			−0.771845
$330$		0			0
$331$	9.23607			0.507660			0.253830	−	0.967249i	$-0.418310\pi$
$331$	9.23607			0.507660			0.253830	+	0.967249i	$0.418310\pi$
$332$	3.23607	+	2.35114i	0.177602	+	0.129036i
$333$		0			0
$334$	−4.10081	−	12.6210i	−0.224387	−	0.690591i
$335$	4.11803	−	2.99193i	0.224992	−	0.163466i
$336$		0			0
$337$	−4.70820	−	14.4904i	−0.256472	−	0.789340i	−0.993536	−	0.113517i	$-0.963788\pi$
$337$	−4.70820	−	14.4904i	−0.256472	−	0.789340i	0.737064	−	0.675823i	$-0.236212\pi$
$338$	0.482779	−	1.48584i	0.0262597	−	0.0808191i
$339$		0			0
$340$	6.09017			0.330286
$341$	−2.33688	−	3.94298i	−0.126549	−	0.213525i
$342$		0			0
$343$	−9.23607	−	6.71040i	−0.498701	−	0.362327i
$344$	0.0278640	−	0.0857567i	0.00150233	−	0.00462369i
$345$		0			0
$346$	7.70820	−	5.60034i	0.414396	−	0.301076i
$347$	29.0344	−	21.0948i	1.55865	−	1.13243i	0.621546	−	0.783378i	$-0.286505\pi$
$347$	29.0344	−	21.0948i	1.55865	−	1.13243i	0.937105	−	0.349048i	$-0.113495\pi$
$348$		0			0
$349$	−3.52786	+	10.8576i	−0.188842	+	0.581197i	−0.999993	−	0.00363995i	$-0.998841\pi$
$349$	−3.52786	+	10.8576i	−0.188842	+	0.581197i	0.811151	+	0.584837i	$0.198841\pi$
$350$	−2.61803	−	1.90211i	−0.139940	−	0.101672i
$351$		0			0
$352$	3.04508	+	1.31433i	0.162304	+	0.0700539i
$353$	−23.6180			−1.25706			−0.628531	−	0.777785i	$-0.716343\pi$
$353$	−23.6180			−1.25706			−0.628531	+	0.777785i	$0.716343\pi$
$354$		0			0
$355$	−3.23607	+	9.95959i	−0.171753	+	0.528600i
$356$	−5.32624	−	16.3925i	−0.282290	−	0.868799i
$357$		0			0
$358$	−14.6803	+	10.6659i	−0.775880	+	0.563710i
$359$	3.76393	+	11.5842i	0.198653	+	0.611390i	0.999915	+	0.0130763i	$0.00416243\pi$
$359$	3.76393	+	11.5842i	0.198653	+	0.611390i	−0.801262	+	0.598314i	$0.795838\pi$
$360$		0			0
$361$	14.1353	+	10.2699i	0.743961	+	0.540519i
$362$	−21.8885			−1.15044
$363$		0			0
$364$	−10.9443			−0.573636
$365$	−10.8541	−	7.88597i	−0.568130	−	0.412770i
$366$		0			0
$367$	−8.27051	−	25.4540i	−0.431717	−	1.32869i	−0.896414	−	0.443219i	$-0.853837\pi$
$367$	−8.27051	−	25.4540i	−0.431717	−	1.32869i	0.464696	−	0.885470i	$-0.346163\pi$
$368$	5.54508	−	4.02874i	0.289058	−	0.210013i
$369$		0			0
$370$	1.97214	+	6.06961i	0.102526	+	0.315544i
$371$	8.47214	−	26.0746i	0.439851	−	1.35372i
$372$		0			0
$373$	−11.5279			−0.596890			−0.298445	−	0.954427i	$-0.596468\pi$
$373$	−11.5279			−0.596890			−0.298445	+	0.954427i	$0.596468\pi$
$374$	18.5451	+	8.00448i	0.958944	+	0.413902i
$375$		0			0
$376$	3.50000	+	2.54290i	0.180499	+	0.131140i
$377$	2.73607	−	8.42075i	0.140915	−	0.433691i
$378$		0			0
$379$	10.0000	−	7.26543i	0.513665	−	0.373200i	−0.300547	−	0.953767i	$-0.597169\pi$
$379$	10.0000	−	7.26543i	0.513665	−	0.373200i	0.814212	+	0.580567i	$0.197169\pi$
$380$	−1.00000	+	0.726543i	−0.0512989	+	0.0372708i
$381$		0			0
$382$	2.85410	−	8.78402i	0.146029	−	0.449430i
$383$	−0.263932	−	0.191758i	−0.0134863	−	0.00979837i	0.581022	−	0.813888i	$-0.302653\pi$
$383$	−0.263932	−	0.191758i	−0.0134863	−	0.00979837i	−0.594508	+	0.804090i	$0.702653\pi$
$384$		0			0
$385$	−5.47214	−	9.23305i	−0.278886	−	0.470560i
$386$	20.9443			1.06604
$387$		0			0
$388$	5.76393	−	17.7396i	0.292619	−	0.900590i
$389$	−2.11803	−	6.51864i	−0.107389	−	0.330508i	0.882895	−	0.469570i	$-0.155591\pi$
$389$	−2.11803	−	6.51864i	−0.107389	−	0.330508i	−0.990284	+	0.139062i	$0.955591\pi$
$390$		0			0
$391$	33.7705	−	24.5357i	1.70785	−	1.24082i
$392$	−1.07295	−	3.30220i	−0.0541921	−	0.166786i
$393$		0			0
$394$	−8.85410	−	6.43288i	−0.446063	−	0.324084i
$395$	−4.09017			−0.205799
$396$		0			0
$397$	2.20163			0.110496			0.0552482	−	0.998473i	$-0.482405\pi$
$397$	2.20163			0.110496			0.0552482	+	0.998473i	$0.482405\pi$
$398$	21.0172	+	15.2699i	1.05350	+	0.765411i
$399$		0			0
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	17.8541	−	12.9718i	0.891591	−	0.647779i	−0.0447011	−	0.999000i	$-0.514234\pi$
$401$	17.8541	−	12.9718i	0.891591	−	0.647779i	0.936292	+	0.351221i	$0.114234\pi$
$402$		0			0
$403$	−1.44427	−	4.44501i	−0.0719443	−	0.221422i
$404$	−4.82624	+	14.8536i	−0.240114	+	0.738996i
$405$		0			0
$406$	8.47214			0.420465
$407$	−1.97214	+	21.0745i	−0.0977551	+	1.04462i
$408$		0			0
$409$	−10.5000	−	7.62870i	−0.519192	−	0.377215i	0.297108	−	0.954844i	$-0.403978\pi$
$409$	−10.5000	−	7.62870i	−0.519192	−	0.377215i	−0.816299	+	0.577629i	$0.803978\pi$
$410$	0.381966	−	1.17557i	0.0188640	−	0.0580573i
$411$		0			0
$412$	−5.47214	+	3.97574i	−0.269593	+	0.195871i
$413$	−36.8885	+	26.8011i	−1.81517	+	1.31880i
$414$		0			0
$415$	−1.23607	+	3.80423i	−0.0606762	+	0.186742i
$416$	2.73607	+	1.98787i	0.134147	+	0.0974633i
$417$		0			0
$418$	−4.00000	+	0.898056i	−0.195646	+	0.0439254i
$419$	−22.8541			−1.11650			−0.558248	−	0.829674i	$-0.688526\pi$
$419$	−22.8541			−1.11650			−0.558248	+	0.829674i	$0.688526\pi$
$420$		0			0
$421$	−0.763932	+	2.35114i	−0.0372318	+	0.114588i	−0.967945	−	0.251162i	$-0.919187\pi$
$421$	−0.763932	+	2.35114i	−0.0372318	+	0.114588i	0.930713	+	0.365750i	$0.119187\pi$
$422$	7.79837	+	24.0009i	0.379619	+	1.16835i
$423$		0			0
$424$	−6.85410	+	4.97980i	−0.332865	+	0.241840i
$425$	1.88197	+	5.79210i	0.0912888	+	0.280958i
$426$		0			0
$427$		0			0
$428$	−6.29180			−0.304125
$429$		0			0
$430$	0.0901699			0.00434838
$431$	18.0902	+	13.1433i	0.871373	+	0.633089i	0.930955	−	0.365134i	$-0.118977\pi$
$431$	18.0902	+	13.1433i	0.871373	+	0.633089i	−0.0595822	+	0.998223i	$0.518977\pi$
$432$		0			0
$433$	−7.05573	−	21.7153i	−0.339077	−	1.04357i	−0.964679	−	0.263428i	$-0.915147\pi$
$433$	−7.05573	−	21.7153i	−0.339077	−	1.04357i	0.625602	−	0.780142i	$-0.284853\pi$
$434$	3.61803	−	2.62866i	0.173671	−	0.126180i
$435$		0			0
$436$	−0.763932	−	2.35114i	−0.0365857	−	0.112599i
$437$	−2.61803	+	8.05748i	−0.125238	+	0.385442i
$438$		0			0
$439$	1.67376			0.0798843			0.0399422	−	0.999202i	$-0.487283\pi$
$439$	1.67376			0.0798843			0.0399422	+	0.999202i	$0.487283\pi$
$440$	−0.309017	+	3.30220i	−0.0147318	+	0.157426i
$441$		0			0
$442$	16.6631	+	12.1065i	0.792584	+	0.575846i
$443$	5.76393	−	17.7396i	0.273853	−	0.842832i	−0.715668	−	0.698441i	$-0.753878\pi$
$443$	5.76393	−	17.7396i	0.273853	−	0.842832i	0.989521	−	0.144391i	$-0.0461224\pi$
$444$		0			0
$445$	13.9443	−	10.1311i	0.661022	−	0.480261i
$446$	5.85410	−	4.25325i	0.277200	−	0.201397i
$447$		0			0
$448$	−1.00000	+	3.07768i	−0.0472456	+	0.145407i
$449$	−9.00000	−	6.53888i	−0.424736	−	0.308589i	0.354804	−	0.934941i	$-0.384547\pi$
$449$	−9.00000	−	6.53888i	−0.424736	−	0.308589i	−0.779541	+	0.626352i	$0.784547\pi$
$450$		0			0
$451$	2.70820	−	3.07768i	0.127524	−	0.144922i
$452$	19.5623			0.920133
$453$		0			0
$454$	6.29180	−	19.3642i	0.295289	−	0.908805i
$455$	−3.38197	−	10.4086i	−0.158549	−	0.487964i
$456$		0			0
$457$	−3.76393	+	2.73466i	−0.176069	+	0.127922i	−0.672330	−	0.740252i	$-0.734706\pi$
$457$	−3.76393	+	2.73466i	−0.176069	+	0.127922i	0.496260	+	0.868174i	$0.334706\pi$
$458$	−0.236068	−	0.726543i	−0.0110307	−	0.0339491i
$459$		0			0
$460$	5.54508	+	4.02874i	0.258541	+	0.187841i
$461$	−23.2148			−1.08122			−0.540610	−	0.841273i	$-0.681807\pi$
$461$	−23.2148			−1.08122			−0.540610	+	0.841273i	$0.681807\pi$
$462$		0			0
$463$	11.8885			0.552507			0.276254	−	0.961085i	$-0.410907\pi$
$463$	11.8885			0.552507			0.276254	+	0.961085i	$0.410907\pi$
$464$	−2.11803	−	1.53884i	−0.0983273	−	0.0714389i
$465$		0			0
$466$	−1.37132	−	4.22050i	−0.0635253	−	0.195511i
$467$	23.0902	−	16.7760i	1.06849	−	0.776300i	0.0928462	−	0.995680i	$-0.470404\pi$
$467$	23.0902	−	16.7760i	1.06849	−	0.776300i	0.975639	+	0.219380i	$0.0704035\pi$
$468$		0			0
$469$	5.09017	+	15.6659i	0.235042	+	0.723386i
$470$	−1.33688	+	4.11450i	−0.0616657	+	0.189788i
$471$		0			0
$472$	14.0902			0.648553
$473$	0.274575	+	0.118513i	0.0126250	+	0.00544923i
$474$		0			0
$475$	−1.00000	−	0.726543i	−0.0458831	−	0.0333361i
$476$	−6.09017	+	18.7436i	−0.279142	+	0.859112i
$477$		0			0
$478$	2.61803	−	1.90211i	0.119746	−	0.0870006i
$479$	10.3262	−	7.50245i	0.471818	−	0.342796i	−0.326331	−	0.945255i	$-0.605813\pi$
$479$	10.3262	−	7.50245i	0.471818	−	0.342796i	0.798149	+	0.602460i	$0.205813\pi$
$480$		0			0
$481$	−6.66970	+	20.5272i	−0.304112	+	0.935960i
$482$	−19.3262	−	14.0413i	−0.880286	−	0.639565i
$483$		0			0
$484$	−5.28115	+	9.64932i	−0.240052	+	0.438606i
$485$	18.6525			0.846965
$486$		0			0
$487$	3.52786	−	10.8576i	0.159863	−	0.492007i	−0.838758	−	0.544504i	$-0.816718\pi$
$487$	3.52786	−	10.8576i	0.159863	−	0.492007i	0.998621	+	0.0524969i	$0.0167180\pi$
$488$		0			0
$489$		0			0
$490$	2.80902	−	2.04087i	0.126898	−	0.0921971i
$491$	−8.66312	−	26.6623i	−0.390961	−	1.20325i	−0.932063	−	0.362297i	$-0.881993\pi$
$491$	−8.66312	−	26.6623i	−0.390961	−	1.20325i	0.541102	−	0.840957i	$-0.318007\pi$
$492$		0			0
$493$	−12.8992	−	9.37181i	−0.580950	−	0.422085i
$494$	−4.18034			−0.188082
$495$		0			0
$496$	−1.38197			−0.0620521
$497$	−27.4164	−	19.9192i	−1.22979	−	0.893498i
$498$		0			0
$499$	−10.0344	−	30.8828i	−0.449203	−	1.38251i	−0.877808	−	0.479013i	$-0.840995\pi$
$499$	−10.0344	−	30.8828i	−0.449203	−	1.38251i	0.428604	−	0.903492i	$-0.359005\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$		0			0
$502$	2.59017	+	7.97172i	0.115605	+	0.355795i
$503$	7.51722	−	23.1356i	0.335176	−	1.03157i	−0.631459	−	0.775409i	$-0.717544\pi$
$503$	7.51722	−	23.1356i	0.335176	−	1.03157i	0.966635	−	0.256157i	$-0.0824565\pi$
$504$		0			0
$505$	−15.6180			−0.694993
$506$	11.5902	+	19.5559i	0.515246	+	0.869366i
$507$		0			0
$508$	−11.8541	−	8.61251i	−0.525941	−	0.382118i
$509$	−2.71885	+	8.36775i	−0.120511	+	0.370894i	−0.993056	−	0.117638i	$-0.962468\pi$
$509$	−2.71885	+	8.36775i	−0.120511	+	0.370894i	0.872546	+	0.488532i	$0.162468\pi$
$510$		0			0
$511$	35.1246	−	25.5195i	1.55382	−	1.12892i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	9.38197	−	28.8747i	0.413821	−	1.27361i
$515$	−5.47214	−	3.97574i	−0.241131	−	0.175192i
$516$		0			0
$517$	−9.47871	+	10.7719i	−0.416873	+	0.473747i
$518$	−20.6525			−0.907418
$519$		0			0
$520$	−1.04508	+	3.21644i	−0.0458300	+	0.141050i
$521$	0.729490	+	2.24514i	0.0319595	+	0.0983614i	0.965764	−	0.259423i	$-0.0835323\pi$
$521$	0.729490	+	2.24514i	0.0319595	+	0.0983614i	−0.933804	+	0.357784i	$0.883532\pi$
$522$		0			0
$523$	−31.4164	+	22.8254i	−1.37374	+	0.998083i	−0.376309	+	0.926494i	$0.622807\pi$
$523$	−31.4164	+	22.8254i	−1.37374	+	0.998083i	−0.997434	+	0.0715891i	$0.977193\pi$
$524$	1.04508	+	3.21644i	0.0456547	+	0.140511i
$525$		0			0
$526$	−5.54508	−	4.02874i	−0.241777	−	0.175661i
$527$	−8.41641			−0.366624
$528$		0			0
$529$	23.9787			1.04255
$530$	−6.85410	−	4.97980i	−0.297723	−	0.216309i
$531$		0			0
$532$	−1.23607	−	3.80423i	−0.0535903	−	0.164934i
$533$	3.38197	−	2.45714i	0.146489	−	0.106431i
$534$		0			0
$535$	−1.94427	−	5.98385i	−0.0840582	−	0.258705i
$536$	1.57295	−	4.84104i	0.0679410	−	0.209101i
$537$		0			0
$538$	3.20163			0.138032
$539$	11.2361	−	2.52265i	0.483972	−	0.108658i
$540$		0			0
$541$	−21.0902	−	15.3229i	−0.906737	−	0.658783i	0.0334503	−	0.999440i	$-0.489350\pi$
$541$	−21.0902	−	15.3229i	−0.906737	−	0.658783i	−0.940188	+	0.340657i	$0.889350\pi$
$542$	1.97214	−	6.06961i	0.0847105	−	0.260712i
$543$		0			0
$544$	4.92705	−	3.57971i	0.211246	−	0.153479i
$545$	2.00000	−	1.45309i	0.0856706	−	0.0622433i
$546$		0			0
$547$	10.6074	−	32.6462i	0.453539	−	1.39585i	−0.419302	−	0.907847i	$-0.637725\pi$
$547$	10.6074	−	32.6462i	0.453539	−	1.39585i	0.872842	−	0.488004i	$-0.162275\pi$
$548$	−10.3541	−	7.52270i	−0.442305	−	0.321354i
$549$		0			0
$550$	−3.23607	+	0.726543i	−0.137986	+	0.0309799i
$551$	3.23607			0.137861
$552$		0			0
$553$	4.09017	−	12.5882i	0.173932	−	0.535307i
$554$	7.26393	+	22.3561i	0.308615	+	0.949819i
$555$		0			0
$556$	−7.09017	+	5.15131i	−0.300690	+	0.218464i
$557$	10.8541	+	33.4055i	0.459903	+	1.41544i	0.865281	+	0.501287i	$0.167140\pi$
$557$	10.8541	+	33.4055i	0.459903	+	1.41544i	−0.405378	+	0.914149i	$0.632860\pi$
$558$		0			0
$559$	0.246711	+	0.179246i	0.0104348	+	0.00758130i
$560$	−3.23607			−0.136749
$561$		0			0
$562$	−7.52786			−0.317544
$563$	13.7984	+	10.0251i	0.581532	+	0.422508i	0.839276	−	0.543705i	$-0.182979\pi$
$563$	13.7984	+	10.0251i	0.581532	+	0.422508i	−0.257744	+	0.966213i	$0.582979\pi$
$564$		0			0
$565$	6.04508	+	18.6049i	0.254319	+	0.782712i
$566$	−18.0623	+	13.1230i	−0.759215	+	0.551602i
$567$		0			0
$568$	3.23607	+	9.95959i	0.135782	+	0.417895i
$569$	7.85410	−	24.1724i	0.329261	−	1.01336i	−0.640219	−	0.768192i	$-0.721156\pi$
$569$	7.85410	−	24.1724i	0.329261	−	1.01336i	0.969480	−	0.245169i	$-0.0788435\pi$
$570$		0			0
$571$	−28.3607			−1.18686			−0.593429	−	0.804887i	$-0.702226\pi$
$571$	−28.3607			−1.18686			−0.593429	+	0.804887i	$0.702226\pi$
$572$	−7.40983	+	8.42075i	−0.309821	+	0.352089i
$573$		0			0
$574$	3.23607	+	2.35114i	0.135071	+	0.0981347i
$575$	−2.11803	+	6.51864i	−0.0883281	+	0.271846i
$576$		0			0
$577$	−13.7984	+	10.0251i	−0.574434	+	0.417351i	−0.836713	−	0.547641i	$-0.815526\pi$
$577$	−13.7984	+	10.0251i	−0.574434	+	0.417351i	0.262279	+	0.964992i	$0.415526\pi$
$578$	16.2533	−	11.8087i	0.676048	−	0.491177i
$579$		0			0
$580$	0.809017	−	2.48990i	0.0335926	−	0.103387i
$581$	−10.4721	−	7.60845i	−0.434457	−	0.315652i
$582$		0			0
$583$	−14.3262	−	24.1724i	−0.593332	−	1.00112i
$584$	−13.4164			−0.555175
$585$		0			0
$586$	−6.18034	+	19.0211i	−0.255307	+	0.785756i
$587$	8.12461	+	25.0050i	0.335339	+	1.03207i	0.966555	+	0.256459i	$0.0825560\pi$
$587$	8.12461	+	25.0050i	0.335339	+	1.03207i	−0.631216	+	0.775607i	$0.717444\pi$
$588$		0			0
$589$	1.38197	−	1.00406i	0.0569429	−	0.0413715i
$590$	4.35410	+	13.4005i	0.179256	+	0.551692i
$591$		0			0
$592$	5.16312	+	3.75123i	0.212203	+	0.154174i
$593$	17.6738			0.725774			0.362887	−	0.931833i	$-0.381791\pi$
$593$	17.6738			0.725774			0.362887	+	0.931833i	$0.381791\pi$
$594$		0			0
$595$	−19.7082			−0.807958
$596$	−6.16312	−	4.47777i	−0.252451	−	0.183417i
$597$		0			0
$598$	7.16312	+	22.0458i	0.292922	+	0.901520i
$599$	14.7082	−	10.6861i	0.600961	−	0.436624i	−0.245259	−	0.969458i	$-0.578873\pi$
$599$	14.7082	−	10.6861i	0.600961	−	0.436624i	0.846220	+	0.532834i	$0.178873\pi$
$600$		0			0
$601$	−5.85410	−	18.0171i	−0.238794	−	0.734932i	−0.996595	−	0.0824468i	$-0.973727\pi$
$601$	−5.85410	−	18.0171i	−0.238794	−	0.734932i	0.757802	−	0.652485i	$-0.226273\pi$
$602$	−0.0901699	+	0.277515i	−0.00367505	+	0.0113106i
$603$		0			0
$604$	20.9443			0.852210
$605$	−10.8090	−	2.04087i	−0.439449	−	0.0829732i
$606$		0			0
$607$	3.61803	+	2.62866i	0.146851	+	0.106694i	0.658785	−	0.752331i	$-0.271071\pi$
$607$	3.61803	+	2.62866i	0.146851	+	0.106694i	−0.511934	+	0.859025i	$0.671071\pi$
$608$	−0.381966	+	1.17557i	−0.0154908	+	0.0476757i
$609$		0			0
$610$		0			0
$611$	−11.8369	+	8.60000i	−0.478869	+	0.347919i
$612$		0			0
$613$	1.85410	−	5.70634i	0.0748865	−	0.230477i	−0.906606	−	0.421979i	$-0.861336\pi$
$613$	1.85410	−	5.70634i	0.0748865	−	0.230477i	0.981492	+	0.191502i	$0.0613357\pi$
$614$	−27.0623	−	19.6619i	−1.09215	−	0.793490i
$615$		0			0
$616$	−9.85410	−	4.25325i	−0.397033	−	0.171368i
$617$	−26.3607			−1.06124			−0.530621	−	0.847610i	$-0.678041\pi$
$617$	−26.3607			−1.06124			−0.530621	+	0.847610i	$0.678041\pi$
$618$		0			0
$619$	2.94427	−	9.06154i	0.118340	−	0.364214i	−0.874289	−	0.485406i	$-0.838672\pi$
$619$	2.94427	−	9.06154i	0.118340	−	0.364214i	0.992629	+	0.121192i	$0.0386717\pi$
$620$	−0.427051	−	1.31433i	−0.0171508	−	0.0527847i
$621$		0			0
$622$	−7.47214	+	5.42882i	−0.299605	+	0.217676i
$623$	17.2361	+	53.0472i	0.690548	+	2.12529i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−8.47214			−0.338615
$627$		0			0
$628$	−9.27051			−0.369934
$629$	31.4443	+	22.8456i	1.25377	+	0.910914i
$630$		0			0
$631$	−1.75329	−	5.39607i	−0.0697973	−	0.214814i	0.910073	−	0.414447i	$-0.136025\pi$
$631$	−1.75329	−	5.39607i	−0.0697973	−	0.214814i	−0.979871	+	0.199633i	$0.936025\pi$
$632$	−3.30902	+	2.40414i	−0.131626	+	0.0956316i
$633$		0			0
$634$	−8.47214	−	26.0746i	−0.336472	−	1.03555i
$635$	4.52786	−	13.9353i	0.179683	−	0.553007i
$636$		0			0
$637$	11.7426			0.465261
$638$	5.73607	−	6.51864i	0.227093	−	0.258075i
$639$		0			0
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	−3.76393	+	11.5842i	−0.148666	+	0.457548i	−0.997464	−	0.0711694i	$-0.977327\pi$
$641$	−3.76393	+	11.5842i	−0.148666	+	0.457548i	0.848798	+	0.528717i	$0.177327\pi$
$642$		0			0
$643$	3.88197	−	2.82041i	0.153090	−	0.111226i	−0.508604	−	0.861001i	$-0.669838\pi$
$643$	3.88197	−	2.82041i	0.153090	−	0.111226i	0.661693	+	0.749775i	$0.269838\pi$
$644$	−17.9443	+	13.0373i	−0.707103	+	0.513741i
$645$		0			0
$646$	−2.32624	+	7.15942i	−0.0915246	+	0.281684i
$647$	−10.0172	−	7.27794i	−0.393818	−	0.286125i	0.373200	−	0.927751i	$-0.378260\pi$
$647$	−10.0172	−	7.27794i	−0.393818	−	0.286125i	−0.767018	+	0.641625i	$0.778260\pi$
$648$		0			0
$649$	−4.35410	+	46.5285i	−0.170913	+	1.82640i
$650$	−3.38197			−0.132652
$651$		0			0
$652$	0.263932	−	0.812299i	0.0103364	−	0.0318121i
$653$	−7.58359	−	23.3399i	−0.296769	−	0.913361i	−0.982622	−	0.185620i	$-0.940571\pi$
$653$	−7.58359	−	23.3399i	−0.296769	−	0.913361i	0.685853	−	0.727740i	$-0.259429\pi$
$654$		0			0
$655$	−2.73607	+	1.98787i	−0.106907	+	0.0776725i
$656$	−0.381966	−	1.17557i	−0.0149133	−	0.0458983i
$657$		0			0
$658$	−11.3262	−	8.22899i	−0.441543	−	0.320800i
$659$	15.4164			0.600538			0.300269	−	0.953855i	$-0.402924\pi$
$659$	15.4164			0.600538			0.300269	+	0.953855i	$0.402924\pi$
$660$		0			0
$661$	8.36068			0.325193			0.162596	−	0.986693i	$-0.448013\pi$
$661$	8.36068			0.325193			0.162596	+	0.986693i	$0.448013\pi$
$662$	7.47214	+	5.42882i	0.290413	+	0.210997i
$663$		0			0
$664$	1.23607	+	3.80423i	0.0479687	+	0.147633i
$665$	3.23607	−	2.35114i	0.125489	−	0.0911733i
$666$		0			0
$667$	−5.54508	−	17.0660i	−0.214707	−	0.660799i
$668$	4.10081	−	12.6210i	0.158665	−	0.488321i
$669$		0			0
$670$	5.09017			0.196650
$671$		0			0
$672$		0			0
$673$	12.7082	+	9.23305i	0.489865	+	0.355908i	0.805132	−	0.593095i	$-0.202094\pi$
$673$	12.7082	+	9.23305i	0.489865	+	0.355908i	−0.315267	+	0.949003i	$0.602094\pi$
$674$	4.70820	−	14.4904i	0.181353	−	0.558148i
$675$		0			0
$676$	1.26393	−	0.918300i	0.0486128	−	0.0353192i
$677$	22.0344	−	16.0090i	0.846852	−	0.615274i	−0.0774240	−	0.996998i	$-0.524670\pi$
$677$	22.0344	−	16.0090i	0.846852	−	0.615274i	0.924276	+	0.381724i	$0.124670\pi$
$678$		0			0
$679$	−18.6525	+	57.4064i	−0.715816	+	2.20306i
$680$	4.92705	+	3.57971i	0.188944	+	0.137276i
$681$		0			0
$682$	0.427051	−	4.56352i	0.0163526	−	0.174746i
$683$	−21.1246			−0.808311			−0.404155	−	0.914690i	$-0.632435\pi$
$683$	−21.1246			−0.808311			−0.404155	+	0.914690i	$0.632435\pi$
$684$		0			0
$685$	3.95492	−	12.1720i	0.151110	−	0.465067i
$686$	−3.52786	−	10.8576i	−0.134694	−	0.414547i
$687$		0			0
$688$	0.0729490	−	0.0530006i	0.00278116	−	0.00202063i
$689$	−8.85410	−	27.2501i	−0.337314	−	1.03815i
$690$		0			0
$691$	16.7082	+	12.1392i	0.635610	+	0.461798i	0.858339	−	0.513083i	$-0.171497\pi$
$691$	16.7082	+	12.1392i	0.635610	+	0.461798i	−0.222729	+	0.974880i	$0.571497\pi$
$692$	9.52786			0.362195
$693$		0			0
$694$	35.8885			1.36231
$695$	−7.09017	−	5.15131i	−0.268945	−	0.195400i
$696$		0			0
$697$	−2.32624	−	7.15942i	−0.0881125	−	0.271183i
$698$	−9.23607	+	6.71040i	−0.349590	+	0.253992i
$699$		0			0
$700$	−1.00000	−	3.07768i	−0.0377964	−	0.116326i
$701$	1.09017	−	3.35520i	0.0411752	−	0.126724i	−0.928356	−	0.371692i	$-0.878778\pi$
$701$	1.09017	−	3.35520i	0.0411752	−	0.126724i	0.969531	+	0.244968i	$0.0787776\pi$
$702$		0			0
$703$	−7.88854			−0.297522
$704$	1.69098	+	2.85317i	0.0637313	+	0.107533i
$705$		0			0
$706$	−19.1074	−	13.8823i	−0.719116	−	0.522468i
$707$	15.6180	−	48.0674i	0.587377	−	1.80776i
$708$		0			0
$709$	8.56231	−	6.22088i	0.321564	−	0.233630i	−0.415278	−	0.909694i	$-0.636316\pi$
$709$	8.56231	−	6.22088i	0.321564	−	0.233630i	0.736843	+	0.676064i	$0.236316\pi$
$710$	−8.47214	+	6.15537i	−0.317954	+	0.231007i
$711$		0			0
$712$	5.32624	−	16.3925i	0.199609	−	0.614334i
$713$	−7.66312	−	5.56758i	−0.286986	−	0.208508i
$714$		0			0
$715$	−10.2984	−	4.44501i	−0.385137	−	0.166234i
$716$	−18.1459			−0.678144
$717$		0			0
$718$	−3.76393	+	11.5842i	−0.140469	+	0.432318i
$719$	−12.5623	−	38.6628i	−0.468495	−	1.44188i	−0.854533	−	0.519397i	$-0.826157\pi$
$719$	−12.5623	−	38.6628i	−0.468495	−	1.44188i	0.386038	−	0.922483i	$-0.373843\pi$
$720$		0			0
$721$	17.7082	−	12.8658i	0.659488	−	0.479146i
$722$	5.39919	+	16.6170i	0.200937	+	0.618420i
$723$		0			0
$724$	−17.7082	−	12.8658i	−0.658120	−	0.478152i
$725$	2.61803			0.0972313
$726$		0			0
$727$	−50.1803			−1.86109			−0.930543	−	0.366183i	$-0.880664\pi$
$727$	−50.1803			−1.86109			−0.930543	+	0.366183i	$0.880664\pi$
$728$	−8.85410	−	6.43288i	−0.328155	−	0.238418i
$729$		0			0
$730$	−4.14590	−	12.7598i	−0.153447	−	0.472260i
$731$	0.444272	−	0.322782i	0.0164320	−	0.0119385i
$732$		0			0
$733$	15.8607	+	48.8142i	0.585828	+	1.80299i	0.595921	+	0.803043i	$0.296787\pi$
$733$	15.8607	+	48.8142i	0.585828	+	1.80299i	−0.0100937	+	0.999949i	$0.503213\pi$
$734$	8.27051	−	25.4540i	0.305270	−	0.939525i
$735$		0			0
$736$	6.85410			0.252646
$737$	15.5000	+	6.69015i	0.570950	+	0.246435i
$738$		0			0
$739$	−21.8541	−	15.8779i	−0.803916	−	0.584079i	0.108144	−	0.994135i	$-0.465509\pi$
$739$	−21.8541	−	15.8779i	−0.803916	−	0.584079i	−0.912060	+	0.410056i	$0.865509\pi$
$740$	−1.97214	+	6.06961i	−0.0724972	+	0.223123i
$741$		0			0
$742$	22.1803	−	16.1150i	0.814266	−	0.591599i
$743$	8.73607	−	6.34712i	0.320495	−	0.232853i	−0.415892	−	0.909414i	$-0.636530\pi$
$743$	8.73607	−	6.34712i	0.320495	−	0.232853i	0.736387	+	0.676561i	$0.236530\pi$
$744$		0			0
$745$	2.35410	−	7.24518i	0.0862476	−	0.265443i
$746$	−9.32624	−	6.77591i	−0.341458	−	0.248084i
$747$		0			0
$748$	10.2984	+	17.3763i	0.376546	+	0.635340i
$749$	20.3607			0.743963
$750$		0			0
$751$	−8.97214	+	27.6134i	−0.327398	+	1.00763i	0.642949	+	0.765909i	$0.277711\pi$
$751$	−8.97214	+	27.6134i	−0.327398	+	1.00763i	−0.970347	+	0.241718i	$0.922289\pi$
$752$	1.33688	+	4.11450i	0.0487510	+	0.150040i
$753$		0			0
$754$	7.16312	−	5.20431i	0.260865	−	0.189530i
$755$	6.47214	+	19.9192i	0.235545	+	0.724933i
$756$		0			0
$757$	43.5689	+	31.6546i	1.58354	+	1.15051i	0.912494	+	0.409090i	$0.134154\pi$
$757$	43.5689	+	31.6546i	1.58354	+	1.15051i	0.671044	+	0.741417i	$0.265846\pi$
$758$	12.3607			0.448960
$759$		0			0
$760$	−1.23607			−0.0448369
$761$	−8.09017	−	5.87785i	−0.293268	−	0.213072i	0.431416	−	0.902153i	$-0.358014\pi$
$761$	−8.09017	−	5.87785i	−0.293268	−	0.213072i	−0.724684	+	0.689081i	$0.758014\pi$
$762$		0			0
$763$	2.47214	+	7.60845i	0.0894973	+	0.275444i
$764$	7.47214	−	5.42882i	0.270332	−	0.196408i
$765$		0			0
$766$	−0.100813	−	0.310271i	−0.00364252	−	0.0112105i
$767$	−14.7254	+	45.3202i	−0.531704	+	1.63642i
$768$		0			0
$769$	−24.4508			−0.881720			−0.440860	−	0.897576i	$-0.645327\pi$
$769$	−24.4508			−0.881720			−0.440860	+	0.897576i	$0.645327\pi$
$770$	1.00000	−	10.6861i	0.0360375	−	0.385102i
$771$		0			0
$772$	16.9443	+	12.3107i	0.609838	+	0.443073i
$773$	−6.05573	+	18.6376i	−0.217809	+	0.670348i	0.781133	+	0.624365i	$0.214642\pi$
$773$	−6.05573	+	18.6376i	−0.217809	+	0.670348i	−0.998942	+	0.0459835i	$0.985358\pi$
$774$		0			0
$775$	1.11803	−	0.812299i	0.0401610	−	0.0291787i
$776$	15.0902	−	10.9637i	0.541706	−	0.393572i
$777$		0			0
$778$	2.11803	−	6.51864i	0.0759352	−	0.233705i
$779$	1.23607	+	0.898056i	0.0442867	+	0.0321762i
$780$		0			0
$781$	−33.8885	+	7.60845i	−1.21263	+	0.272252i
$782$	41.7426			1.49271
$783$		0			0
$784$	1.07295	−	3.30220i	0.0383196	−	0.117936i
$785$	−2.86475	−	8.81678i	−0.102247	−	0.314684i
$786$		0			0
$787$	−17.0172	+	12.3637i	−0.606598	+	0.440720i	−0.848215	−	0.529652i	$-0.822322\pi$
$787$	−17.0172	+	12.3637i	−0.606598	+	0.440720i	0.241616	+	0.970372i	$0.422322\pi$
$788$	−3.38197	−	10.4086i	−0.120478	−	0.370792i
$789$		0			0
$790$	−3.30902	−	2.40414i	−0.117730	−	0.0855355i
$791$	−63.3050			−2.25086
$792$		0			0
$793$		0			0
$794$	1.78115	+	1.29408i	0.0632108	+	0.0459253i
$795$		0			0
$796$	8.02786	+	24.7072i	0.284540	+	0.875724i
$797$	−17.5623	+	12.7598i	−0.622089	+	0.451974i	−0.853651	−	0.520846i	$-0.825616\pi$
$797$	−17.5623	+	12.7598i	−0.622089	+	0.451974i	0.231562	+	0.972820i	$0.425616\pi$
$798$		0			0
$799$	8.14183	+	25.0580i	0.288037	+	0.886488i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$		0			0
$802$	22.0689			0.779279
$803$	4.14590	−	44.3036i	0.146306	−	1.56344i
$804$		0			0
$805$	−17.9443	−	13.0373i	−0.632452	−	0.459504i
$806$	1.44427	−	4.44501i	0.0508723	−	0.156569i
$807$		0			0
$808$	−12.6353	+	9.18005i	−0.444507	+	0.322953i
$809$	−2.14590	+	1.55909i	−0.0754458	+	0.0548146i	−0.624869	−	0.780730i	$-0.714848\pi$
$809$	−2.14590	+	1.55909i	−0.0754458	+	0.0548146i	0.549423	+	0.835544i	$0.314848\pi$
$810$		0			0
$811$	−1.41641	+	4.35926i	−0.0497368	+	0.153074i	−0.972840	−	0.231478i	$-0.925644\pi$
$811$	−1.41641	+	4.35926i	−0.0497368	+	0.153074i	0.923103	+	0.384552i	$0.125644\pi$
$812$	6.85410	+	4.97980i	0.240532	+	0.174757i
$813$		0			0
$814$	−13.9828	+	15.8904i	−0.490096	+	0.556960i
$815$	0.854102			0.0299179
$816$		0			0
$817$	−0.0344419	+	0.106001i	−0.00120497	+	0.00370851i
$818$	−4.01064	−	12.3435i	−0.140229	−	0.431580i
$819$		0			0
$820$	1.00000	−	0.726543i	0.0349215	−	0.0253720i
$821$	13.3820	+	41.1855i	0.467034	+	1.43738i	0.856407	+	0.516302i	$0.172692\pi$
$821$	13.3820	+	41.1855i	0.467034	+	1.43738i	−0.389373	+	0.921080i	$0.627308\pi$
$822$		0			0
$823$	10.3262	+	7.50245i	0.359950	+	0.261519i	0.753031	−	0.657985i	$-0.228591\pi$
$823$	10.3262	+	7.50245i	0.359950	+	0.261519i	−0.393081	+	0.919504i	$0.628591\pi$
$824$	−6.76393			−0.235633
$825$		0			0
$826$	−45.5967			−1.58651
$827$	24.5066	+	17.8051i	0.852177	+	0.619143i	0.925745	−	0.378147i	$-0.123439\pi$
$827$	24.5066	+	17.8051i	0.852177	+	0.619143i	−0.0735683	+	0.997290i	$0.523439\pi$
$828$		0			0
$829$	11.0000	+	33.8545i	0.382046	+	1.17582i	0.938601	+	0.345005i	$0.112123\pi$
$829$	11.0000	+	33.8545i	0.382046	+	1.17582i	−0.556555	+	0.830811i	$0.687877\pi$
$830$	−3.23607	+	2.35114i	−0.112326	+	0.0816093i
$831$		0			0
$832$	1.04508	+	3.21644i	0.0362318	+	0.111510i
$833$	6.53444	−	20.1109i	0.226405	−	0.696803i
$834$		0			0
$835$	13.2705			0.459245
$836$	−3.76393	−	1.62460i	−0.130178	−	0.0561879i
$837$		0			0
$838$	−18.4894	−	13.4333i	−0.638704	−	0.464046i
$839$	7.21478	−	22.2048i	0.249082	−	0.766595i	−0.745856	−	0.666107i	$-0.767959\pi$
$839$	7.21478	−	22.2048i	0.249082	−	0.766595i	0.994938	−	0.100488i	$-0.0320405\pi$
$840$		0			0
$841$	17.9164	−	13.0170i	0.617807	−	0.448863i
$842$	−2.00000	+	1.45309i	−0.0689246	+	0.0500766i
$843$		0			0
$844$	−7.79837	+	24.0009i	−0.268431	+	0.826146i
$845$	1.26393	+	0.918300i	0.0434806	+	0.0315905i
$846$		0			0
$847$	17.0902	−	31.2259i	0.587225	−	1.07293i
$848$	−8.47214			−0.290934
$849$		0			0
$850$	−1.88197	+	5.79210i	−0.0645509	+	0.198667i
$851$	13.5172	+	41.6017i	0.463364	+	1.42609i
$852$		0			0
$853$	22.2705	−	16.1805i	0.762528	−	0.554009i	−0.137157	−	0.990549i	$-0.543796\pi$
$853$	22.2705	−	16.1805i	0.762528	−	0.554009i	0.899685	+	0.436541i	$0.143796\pi$
$854$		0			0
$855$		0			0
$856$	−5.09017	−	3.69822i	−0.173978	−	0.126403i
$857$	−24.1591			−0.825258			−0.412629	−	0.910899i	$-0.635389\pi$
$857$	−24.1591			−0.825258			−0.412629	+	0.910899i	$0.635389\pi$
$858$		0			0
$859$	−19.1246			−0.652523			−0.326262	−	0.945279i	$-0.605789\pi$
$859$	−19.1246			−0.652523			−0.326262	+	0.945279i	$0.605789\pi$
$860$	0.0729490	+	0.0530006i	0.00248754	+	0.00180730i
$861$		0			0
$862$	6.90983	+	21.2663i	0.235350	+	0.724332i
$863$	−35.8713	+	26.0620i	−1.22107	+	0.887162i	−0.996189	−	0.0872230i	$-0.972201\pi$
$863$	−35.8713	+	26.0620i	−1.22107	+	0.887162i	−0.224885	+	0.974385i	$0.572201\pi$
$864$		0			0
$865$	2.94427	+	9.06154i	0.100108	+	0.308102i
$866$	7.05573	−	21.7153i	0.239763	−	0.737916i
$867$		0			0
$868$	4.47214			0.151794
$869$	−6.91641	−	11.6699i	−0.234623	−	0.395876i
$870$		0			0
$871$	13.9271	+	10.1186i	0.471900	+	0.342856i
$872$	0.763932	−	2.35114i	0.0258700	−	0.0796197i
$873$		0			0
$874$	−6.85410	+	4.97980i	−0.231843	+	0.168444i
$875$	2.61803	−	1.90211i	0.0885057	−	0.0643032i
$876$		0			0
$877$	5.86068	−	18.0373i	0.197901	−	0.609077i	−0.802029	−	0.597285i	$-0.796246\pi$
$877$	5.86068	−	18.0373i	0.197901	−	0.609077i	0.999930	−	0.0117923i	$-0.00375371\pi$
$878$	1.35410	+	0.983813i	0.0456987	+	0.0332021i
$879$		0			0
$880$	−2.19098	+	2.48990i	−0.0738580	+	0.0839345i
$881$	−8.00000			−0.269527			−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000			−0.269527			−0.134763	+	0.990878i	$0.543027\pi$
$882$		0			0
$883$	−1.44427	+	4.44501i	−0.0486036	+	0.149587i	−0.972413	−	0.233267i	$-0.925058\pi$
$883$	−1.44427	+	4.44501i	−0.0486036	+	0.149587i	0.923809	+	0.382853i	$0.125058\pi$
$884$	6.36475	+	19.5887i	0.214070	+	0.658838i
$885$		0			0
$886$	15.0902	−	10.9637i	0.506964	−	0.368331i
$887$	13.1180	+	40.3732i	0.440460	+	1.35560i	0.887386	+	0.461027i	$0.152519\pi$
$887$	13.1180	+	40.3732i	0.440460	+	1.35560i	−0.446926	+	0.894571i	$0.647481\pi$
$888$		0			0
$889$	38.3607	+	27.8707i	1.28658	+	0.934752i
$890$	17.2361			0.577754
$891$		0			0
$892$	7.23607			0.242281
$893$	−4.32624	−	3.14320i	−0.144772	−	0.105183i
$894$		0			0
$895$	−5.60739	−	17.2578i	−0.187434	−	0.576864i
$896$	−2.61803	+	1.90211i	−0.0874624	+	0.0635451i
$897$		0			0
$898$	−3.43769	−	10.5801i	−0.114717	−	0.353064i
$899$	−1.11803	+	3.44095i	−0.0372885	+	0.114762i
$900$		0			0
$901$	−51.5967			−1.71894
$902$	4.00000	−	0.898056i	0.133185	−	0.0299020i
$903$		0			0
$904$	15.8262	+	11.4984i	0.526373	+	0.382432i
$905$	6.76393	−	20.8172i	0.224841	−	0.691989i
$906$		0			0
$907$	19.0172	−	13.8168i	0.631456	−	0.458780i	−0.225448	−	0.974255i	$-0.572385\pi$
$907$	19.0172	−	13.8168i	0.631456	−	0.458780i	0.856904	+	0.515475i	$0.172385\pi$
$908$	16.4721	−	11.9677i	0.546647	−	0.397162i
$909$		0			0
$910$	3.38197	−	10.4086i	0.112111	−	0.345042i
$911$	2.85410	+	2.07363i	0.0945606	+	0.0687023i	0.634061	−	0.773283i	$-0.281387\pi$
$911$	2.85410	+	2.07363i	0.0945606	+	0.0687023i	−0.539500	+	0.841985i	$0.681387\pi$
$912$		0			0
$913$	−12.9443	+	2.90617i	−0.428393	+	0.0961802i
$914$	−4.65248			−0.153890
$915$		0			0
$916$	0.236068	−	0.726543i	0.00779991	−	0.0240056i
$917$	−3.38197	−	10.4086i	−0.111682	−	0.343723i
$918$		0			0
$919$	−37.4894	+	27.2376i	−1.23666	+	0.898486i	−0.997371	−	0.0724626i	$-0.976914\pi$
$919$	−37.4894	+	27.2376i	−1.23666	+	0.898486i	−0.239289	+	0.970948i	$0.576914\pi$
$920$	2.11803	+	6.51864i	0.0698295	+	0.214913i
$921$		0			0
$922$	−18.7812	−	13.6453i	−0.618524	−	0.449384i
$923$	−35.4164			−1.16575
$924$		0			0
$925$	−6.38197			−0.209838
$926$	9.61803	+	6.98791i	0.316068	+	0.229637i
$927$		0			0
$928$	−0.809017	−	2.48990i	−0.0265573	−	0.0817349i
$929$	−24.6525	+	17.9111i	−0.808821	+	0.587643i	−0.913489	−	0.406864i	$-0.866622\pi$
$929$	−24.6525	+	17.9111i	−0.808821	+	0.587643i	0.104667	+	0.994507i	$0.466622\pi$
$930$		0			0
$931$	1.32624	+	4.08174i	0.0434657	+	0.133774i
$932$	1.37132	−	4.22050i	0.0449192	−	0.138247i
$933$		0			0
$934$	28.5410			0.933891
$935$	−13.3435	+	15.1639i	−0.436378	+	0.495913i
$936$		0			0
$937$	34.5066	+	25.0705i	1.12728	+	0.819017i	0.985297	−	0.170852i	$-0.0546519\pi$
$937$	34.5066	+	25.0705i	1.12728	+	0.819017i	0.141984	+	0.989869i	$0.454652\pi$
$938$	−5.09017	+	15.6659i	−0.166200	+	0.511511i
$939$		0			0
$940$	−3.50000	+	2.54290i	−0.114157	+	0.0829402i
$941$	0.826238	−	0.600297i	0.0269346	−	0.0195691i	−0.574237	−	0.818689i	$-0.694701\pi$
$941$	0.826238	−	0.600297i	0.0269346	−	0.0195691i	0.601171	+	0.799120i	$0.294701\pi$
$942$		0			0
$943$	2.61803	−	8.05748i	0.0852549	−	0.262388i
$944$	11.3992	+	8.28199i	0.371012	+	0.269556i
$945$		0			0
$946$	0.152476	+	0.257270i	0.00495742	+	0.00836457i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	14.0213	−	43.1531i	0.455150	−	1.40081i
$950$	−0.381966	−	1.17557i	−0.0123926	−	0.0381405i
$951$		0			0
$952$	−15.9443	+	11.5842i	−0.516757	+	0.375446i
$953$	18.2984	+	56.3166i	0.592742	+	1.82427i	0.565657	+	0.824641i	$0.308623\pi$
$953$	18.2984	+	56.3166i	0.592742	+	1.82427i	0.0270855	+	0.999633i	$0.491377\pi$
$954$		0			0
$955$	7.47214	+	5.42882i	0.241793	+	0.175673i
$956$	3.23607			0.104662
$957$		0			0
$958$	12.7639			0.412384
$959$	33.5066	+	24.3440i	1.08198	+	0.786107i
$960$		0			0
$961$	−8.98936	−	27.6664i	−0.289979	−	0.892464i
$962$	−17.4615	+	12.6865i	−0.562981	+	0.409030i
$963$		0			0
$964$	−7.38197	−	22.7194i	−0.237757	−	0.731741i
$965$	−6.47214	+	19.9192i	−0.208345	+	0.641221i
$966$		0			0
$967$	53.3050			1.71417			0.857086	−	0.515174i	$-0.172273\pi$
$967$	53.3050			1.71417			0.857086	+	0.515174i	$0.172273\pi$
$968$	−9.94427	+	4.70228i	−0.319621	+	0.151137i
$969$		0			0
$970$	15.0902	+	10.9637i	0.484516	+	0.352022i
$971$	−2.58359	+	7.95148i	−0.0829114	+	0.255175i	−0.983915	−	0.178636i	$-0.942832\pi$
$971$	−2.58359	+	7.95148i	−0.0829114	+	0.255175i	0.901004	+	0.433811i	$0.142832\pi$
$972$		0			0
$973$	22.9443	−	16.6700i	0.735560	−	0.534415i
$974$	9.23607	−	6.71040i	0.295943	−	0.215015i
$975$		0			0
$976$		0			0
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	0.894669	−	0.446729i	$-0.147411\pi$
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	−0.148397	+	0.988928i	$0.547411\pi$
$978$		0			0
$979$	52.4853	+	22.6538i	1.67744	+	0.724020i
$980$	3.47214			0.110913
$981$		0			0
$982$	8.66312	−	26.6623i	0.276451	−	0.850829i
$983$	15.8197	+	48.6879i	0.504569	+	1.55290i	0.801494	+	0.598002i	$0.204039\pi$
$983$	15.8197	+	48.6879i	0.504569	+	1.55290i	−0.296925	+	0.954901i	$0.595961\pi$
$984$		0			0
$985$	8.85410	−	6.43288i	0.282115	−	0.204969i
$986$	−4.92705	−	15.1639i	−0.156909	−	0.482917i
$987$		0			0
$988$	−3.38197	−	2.45714i	−0.107595	−	0.0781721i
$989$	0.618034			0.0196523
$990$		0			0
$991$	54.5197			1.73188			0.865938	−	0.500151i	$-0.166722\pi$
$991$	54.5197			1.73188			0.865938	+	0.500151i	$0.166722\pi$
$992$	−1.11803	−	0.812299i	−0.0354976	−	0.0257905i
$993$		0			0
$994$	−10.4721	−	32.2299i	−0.332156	−	1.02227i
$995$	−21.0172	+	15.2699i	−0.666291	+	0.484089i
$996$		0			0
$997$	−7.73607	−	23.8092i	−0.245004	−	0.754044i	−0.995636	−	0.0933236i	$-0.970251\pi$
$997$	−7.73607	−	23.8092i	−0.245004	−	0.754044i	0.750632	−	0.660720i	$-0.229749\pi$
$998$	10.0344	−	30.8828i	0.317635	−	0.977579i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.e.631.1		4
3.2	odd	2		330.2.m.b.301.1	yes	4
11.3	even	5	inner	990.2.n.e.91.1		4
33.5	odd	10		3630.2.a.bj.1.1		2
33.14	odd	10		330.2.m.b.91.1	✓	4
33.17	even	10		3630.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.91.1	✓	4	33.14	odd	10
330.2.m.b.301.1	yes	4	3.2	odd	2
990.2.n.e.91.1		4	11.3	even	5	inner
990.2.n.e.631.1		4	1.1	even	1	trivial
3630.2.a.bb.1.2		2	33.17	even	10
3630.2.a.bj.1.1		2	33.5	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.00000 - 3.07768i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.00000 - 3.07768i) q^{7} +(-0.309017 + 0.951057i) q^{8} -1.00000 q^{10} +(-3.04508 - 1.31433i) q^{11} +(-2.73607 - 1.98787i) q^{13} +(1.00000 - 3.07768i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-4.92705 + 3.57971i) q^{17} +(0.381966 - 1.17557i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-1.69098 - 2.85317i) q^{22} -6.85410 q^{23} +(0.309017 - 0.951057i) q^{25} +(-1.04508 - 3.21644i) q^{26} +(2.61803 - 1.90211i) q^{28} +(0.809017 + 2.48990i) q^{29} +(1.11803 + 0.812299i) q^{31} -1.00000 q^{32} -6.09017 q^{34} +(2.61803 + 1.90211i) q^{35} +(-1.97214 - 6.06961i) q^{37} +(1.00000 - 0.726543i) q^{38} +(-0.309017 - 0.951057i) q^{40} +(-0.381966 + 1.17557i) q^{41} -0.0901699 q^{43} +(0.309017 - 3.30220i) q^{44} +(-5.54508 - 4.02874i) q^{46} +(1.33688 - 4.11450i) q^{47} +(-2.80902 + 2.04087i) q^{49} +(0.809017 - 0.587785i) q^{50} +(1.04508 - 3.21644i) q^{52} +(6.85410 + 4.97980i) q^{53} +(3.23607 - 0.726543i) q^{55} +3.23607 q^{56} +(-0.809017 + 2.48990i) q^{58} +(-4.35410 - 13.4005i) q^{59} +(0.427051 + 1.31433i) q^{62} +(-0.809017 - 0.587785i) q^{64} +3.38197 q^{65} -5.09017 q^{67} +(-4.92705 - 3.57971i) q^{68} +(1.00000 + 3.07768i) q^{70} +(8.47214 - 6.15537i) q^{71} +(4.14590 + 12.7598i) q^{73} +(1.97214 - 6.06961i) q^{74} +1.23607 q^{76} +(-1.00000 + 10.6861i) q^{77} +(3.30902 + 2.40414i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-1.00000 + 0.726543i) q^{82} +(3.23607 - 2.35114i) q^{83} +(1.88197 - 5.79210i) q^{85} +(-0.0729490 - 0.0530006i) q^{86} +(2.19098 - 2.48990i) q^{88} -17.2361 q^{89} +(-3.38197 + 10.4086i) q^{91} +(-2.11803 - 6.51864i) q^{92} +(3.50000 - 2.54290i) q^{94} +(0.381966 + 1.17557i) q^{95} +(-15.0902 - 10.9637i) q^{97} -3.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8	\( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8} - 4 q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 13 q^{17} + 6 q^{19} - q^{20} - 9 q^{22} - 14 q^{23} - q^{25} + 7 q^{26} + 6 q^{28} + q^{29} - 4 q^{32} - 2 q^{34} + 6 q^{35} + 10 q^{37} + 4 q^{38} + q^{40} - 6 q^{41} + 22 q^{43} - q^{44} - 11 q^{46} + 21 q^{47} - 9 q^{49} + q^{50} - 7 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} - q^{58} - 4 q^{59} - 5 q^{62} - q^{64} + 18 q^{65} + 2 q^{67} - 13 q^{68} + 4 q^{70} + 16 q^{71} + 30 q^{73} - 10 q^{74} - 4 q^{76} - 4 q^{77} + 11 q^{79} - q^{80} - 4 q^{82} + 4 q^{83} + 12 q^{85} - 7 q^{86} + 11 q^{88} - 60 q^{89} - 18 q^{91} - 4 q^{92} + 14 q^{94} + 6 q^{95} - 38 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8 - 4 * q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 13 * q^17 + 6 * q^19 - q^20 - 9 * q^22 - 14 * q^23 - q^25 + 7 * q^26 + 6 * q^28 + q^29 - 4 * q^32 - 2 * q^34 + 6 * q^35 + 10 * q^37 + 4 * q^38 + q^40 - 6 * q^41 + 22 * q^43 - q^44 - 11 * q^46 + 21 * q^47 - 9 * q^49 + q^50 - 7 * q^52 + 14 * q^53 + 4 * q^55 + 4 * q^56 - q^58 - 4 * q^59 - 5 * q^62 - q^64 + 18 * q^65 + 2 * q^67 - 13 * q^68 + 4 * q^70 + 16 * q^71 + 30 * q^73 - 10 * q^74 - 4 * q^76 - 4 * q^77 + 11 * q^79 - q^80 - 4 * q^82 + 4 * q^83 + 12 * q^85 - 7 * q^86 + 11 * q^88 - 60 * q^89 - 18 * q^91 - 4 * q^92 + 14 * q^94 + 6 * q^95 - 38 * q^97 + 4 * q^98

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