LMFDB - Embedded newform 363.2.f.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not 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:	$2.89856959337$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	363.161
Dual form			363.2.f.b.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.690983i) q^{2} +(-1.72982 + 0.0877853i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.224514 + 0.309017i) q^{5} +(1.70582 + 1.11179i) q^{6} +(2.92705 - 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(2.98459 - 0.303706i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.690983i) q^{2} +(-1.72982 + 0.0877853i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.224514 + 0.309017i) q^{5} +(1.70582 + 1.11179i) q^{6} +(2.92705 - 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(2.98459 - 0.303706i) q^{9} -0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +(-0.427051 + 0.587785i) q^{13} +(-3.44095 - 1.11803i) q^{14} +(-0.415497 - 0.514836i) q^{15} +(1.92705 - 1.40008i) q^{16} +(3.44095 - 2.50000i) q^{17} +(-3.04837 - 1.77346i) q^{18} +(-2.50000 - 0.812299i) q^{19} +(0.138757 - 0.190983i) q^{20} +(-4.97980 + 1.90211i) q^{21} -6.23607i q^{23} +(1.38821 - 5.14677i) q^{24} +(1.50000 - 4.61653i) q^{25} +(0.812299 - 0.263932i) q^{26} +(-5.13615 + 0.787361i) q^{27} +(-1.11803 - 1.53884i) q^{28} +(-0.726543 - 2.23607i) q^{29} +(0.0394180 + 0.776740i) q^{30} +(-4.73607 - 3.44095i) q^{31} +3.35520 q^{32} -5.00000 q^{34} +(0.951057 + 0.690983i) q^{35} +(-0.748520 - 1.69629i) q^{36} +(0.927051 + 2.85317i) q^{37} +(1.81636 + 2.50000i) q^{38} +(0.687124 - 1.05425i) q^{39} +(-1.11803 + 0.363271i) q^{40} +(0.224514 - 0.690983i) q^{41} +(6.05040 + 1.63194i) q^{42} -6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +(-4.30902 + 5.93085i) q^{46} +(7.91872 + 2.57295i) q^{47} +(-3.21055 + 2.59107i) q^{48} +(2.00000 - 1.45309i) q^{49} +(-4.61653 + 3.35410i) q^{50} +(-5.73279 + 4.62663i) q^{51} +(0.427051 + 0.138757i) q^{52} +(-1.08981 + 1.50000i) q^{53} +(5.42882 + 2.80017i) q^{54} +9.47214i q^{56} +(4.39587 + 1.18567i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(0.363271 - 0.118034i) q^{59} +(-0.223260 + 0.342548i) q^{60} +(-1.54508 - 2.12663i) q^{61} +(2.12663 + 6.54508i) q^{62} +(8.44720 - 3.72747i) q^{63} +(-7.04508 - 5.11855i) q^{64} -0.277515 q^{65} +7.32624 q^{67} +(-2.12663 - 1.54508i) q^{68} +(0.547435 + 10.7873i) q^{69} +(-0.427051 - 1.31433i) q^{70} +(-3.13068 - 4.30902i) q^{71} +(-1.94955 + 9.02488i) q^{72} +(8.94427 - 2.90617i) q^{73} +(1.08981 - 3.35410i) q^{74} +(-2.18947 + 8.11746i) q^{75} +1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +(-2.33688 + 3.21644i) q^{79} +(0.865300 + 0.281153i) q^{80} +(8.81553 - 1.81288i) q^{81} +(-0.690983 + 0.502029i) q^{82} +(-5.11855 + 3.71885i) q^{83} +(2.06909 + 2.56378i) q^{84} +(1.54508 + 0.502029i) q^{85} +(-4.75528 + 6.54508i) q^{86} +(1.45309 + 3.80423i) q^{87} +0.527864i q^{89} +(-0.136373 - 1.34016i) q^{90} +(-0.690983 + 2.12663i) q^{91} +(-3.66547 + 1.19098i) q^{92} +(8.49463 + 5.53649i) q^{93} +(-5.75329 - 7.91872i) q^{94} +(-0.310271 - 0.954915i) q^{95} +(-5.80390 + 0.294537i) q^{96} +(3.54508 + 2.57565i) q^{97} -2.90617 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	$ 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} + 12 q^{12} + 10 q^{13} - 6 q^{15} + 2 q^{16} - 20 q^{19} + 10 q^{24} + 12 q^{25} - 12 q^{27} + 20 q^{30} - 20 q^{31} - 40 q^{34} - 10 q^{36} - 6 q^{37} - 20 q^{39} + 20 q^{42} + 24 q^{45} - 30 q^{46} + 26 q^{48} + 16 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} + 20 q^{58} + 2 q^{60} + 10 q^{61} + 30 q^{63} - 34 q^{64} - 4 q^{67} - 16 q^{69} + 10 q^{70} + 20 q^{72} + 6 q^{75} - 20 q^{78} - 50 q^{79} - 2 q^{81} - 10 q^{82} - 10 q^{85} - 40 q^{90} - 10 q^{91} + 10 q^{93} + 30 q^{94} - 10 q^{96} + 6 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 + 12 * q^12 + 10 * q^13 - 6 * q^15 + 2 * q^16 - 20 * q^19 + 10 * q^24 + 12 * q^25 - 12 * q^27 + 20 * q^30 - 20 * q^31 - 40 * q^34 - 10 * q^36 - 6 * q^37 - 20 * q^39 + 20 * q^42 + 24 * q^45 - 30 * q^46 + 26 * q^48 + 16 * q^49 - 30 * q^51 - 10 * q^52 + 30 * q^57 + 20 * q^58 + 2 * q^60 + 10 * q^61 + 30 * q^63 - 34 * q^64 - 4 * q^67 - 16 * q^69 + 10 * q^70 + 20 * q^72 + 6 * q^75 - 20 * q^78 - 50 * q^79 - 2 * q^81 - 10 * q^82 - 10 * q^85 - 40 * q^90 - 10 * q^91 + 10 * q^93 + 30 * q^94 - 10 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.690983i	−0.672499	−	0.488599i	0.198362	−	0.980129i	$-0.436438\pi$
$2$	−0.951057	−	0.690983i	−0.672499	−	0.488599i	−0.870861	+	0.491530i	$0.836438\pi$
$3$	−1.72982	+	0.0877853i	−0.998715	+	0.0506828i
$3$	−1.72982	+	0.0877853i	−0.998715	+	0.0506828i
$4$	−0.190983	−	0.587785i	−0.0954915	−	0.293893i
$5$	0.224514	+	0.309017i	0.100406	+	0.138197i	0.856264	−	0.516539i	$-0.172780\pi$
$5$	0.224514	+	0.309017i	0.100406	+	0.138197i	−0.755858	+	0.654736i	$0.772780\pi$
$6$	1.70582	+	1.11179i	0.696398	+	0.453887i
$7$	2.92705	−	0.951057i	1.10632	−	0.359466i	0.301789	−	0.953375i	$-0.402416\pi$
$7$	2.92705	−	0.951057i	1.10632	−	0.359466i	0.804532	+	0.593909i	$0.202416\pi$
$8$	−0.951057	+	2.92705i	−0.336249	+	1.03487i
$9$	2.98459	−	0.303706i	0.994862	−	0.101235i
$10$		−	0.449028i		−	0.141995i
$11$		0			0
$11$		0			0
$12$	0.381966	+	1.00000i	0.110264	+	0.288675i
$13$	−0.427051	+	0.587785i	−0.118443	+	0.163022i	−0.864122	−	0.503283i	$-0.832125\pi$
$13$	−0.427051	+	0.587785i	−0.118443	+	0.163022i	0.745679	+	0.666305i	$0.232125\pi$
$14$	−3.44095	−	1.11803i	−0.919634	−	0.298807i
$15$	−0.415497	−	0.514836i	−0.107281	−	0.132930i
$16$	1.92705	−	1.40008i	0.481763	−	0.350021i
$17$	3.44095	−	2.50000i	0.834554	−	0.606339i	−0.0862900	−	0.996270i	$-0.527501\pi$
$17$	3.44095	−	2.50000i	0.834554	−	0.606339i	0.920844	+	0.389931i	$0.127501\pi$
$18$	−3.04837	−	1.77346i	−0.718507	−	0.418008i
$19$	−2.50000	−	0.812299i	−0.573539	−	0.186354i	0.00786490	−	0.999969i	$-0.497496\pi$
$19$	−2.50000	−	0.812299i	−0.573539	−	0.186354i	−0.581404	+	0.813615i	$0.697496\pi$
$20$	0.138757	−	0.190983i	0.0310271	−	0.0427051i
$21$	−4.97980	+	1.90211i	−1.08668	+	0.415075i
$22$		0			0
$23$		−	6.23607i		−	1.30031i	−0.759802	−	0.650155i	$-0.774704\pi$
$23$		−	6.23607i		−	1.30031i	0.759802	−	0.650155i	$-0.225296\pi$
$24$	1.38821	−	5.14677i	0.283367	−	1.05058i
$25$	1.50000	−	4.61653i	0.300000	−	0.923305i
$26$	0.812299	−	0.263932i	0.159305	−	0.0517613i
$27$	−5.13615	+	0.787361i	−0.988453	+	0.151528i
$28$	−1.11803	−	1.53884i	−0.211289	−	0.290814i
$29$	−0.726543	−	2.23607i	−0.134916	−	0.415227i	0.860661	−	0.509178i	$-0.170050\pi$
$29$	−0.726543	−	2.23607i	−0.134916	−	0.415227i	−0.995577	+	0.0939505i	$0.970050\pi$
$30$	0.0394180	+	0.776740i	0.00719672	+	0.141813i
$31$	−4.73607	−	3.44095i	−0.850623	−	0.618014i	0.0746948	−	0.997206i	$-0.476202\pi$
$31$	−4.73607	−	3.44095i	−0.850623	−	0.618014i	−0.925318	+	0.379193i	$0.876202\pi$
$32$	3.35520			0.593121
$33$		0			0
$34$	−5.00000			−0.857493
$35$	0.951057	+	0.690983i	0.160758	+	0.116797i
$36$	−0.748520	−	1.69629i	−0.124753	−	0.282716i
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	0.997889	−	0.0649448i	$-0.0206871\pi$
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	−0.845483	+	0.534003i	$0.820687\pi$
$38$	1.81636	+	2.50000i	0.294652	+	0.405554i
$39$	0.687124	−	1.05425i	0.110028	−	0.168816i
$40$	−1.11803	+	0.363271i	−0.176777	+	0.0574382i
$41$	0.224514	−	0.690983i	0.0350632	−	0.107913i	−0.931993	−	0.362476i	$-0.881931\pi$
$41$	0.224514	−	0.690983i	0.0350632	−	0.107913i	0.967056	+	0.254563i	$0.0819315\pi$
$42$	6.05040	+	1.63194i	0.933596	+	0.251813i
$43$		−	6.88191i		−	1.04948i	−0.851262	−	0.524741i	$-0.824162\pi$
$43$		−	6.88191i		−	1.04948i	0.851262	−	0.524741i	$-0.175838\pi$
$44$		0			0
$45$	0.763932	+	0.854102i	0.113880	+	0.127322i
$46$	−4.30902	+	5.93085i	−0.635330	+	0.874457i
$47$	7.91872	+	2.57295i	1.15506	+	0.375303i	0.823049	−	0.567971i	$-0.192271\pi$
$47$	7.91872	+	2.57295i	1.15506	+	0.375303i	0.332016	+	0.943274i	$0.392271\pi$
$48$	−3.21055	+	2.59107i	−0.463404	+	0.373988i
$49$	2.00000	−	1.45309i	0.285714	−	0.207584i
$50$	−4.61653	+	3.35410i	−0.652875	+	0.474342i
$51$	−5.73279	+	4.62663i	−0.802751	+	0.647857i
$52$	0.427051	+	0.138757i	0.0592213	+	0.0192422i
$53$	−1.08981	+	1.50000i	−0.149697	+	0.206041i	−0.877280	−	0.479980i	$-0.840644\pi$
$53$	−1.08981	+	1.50000i	−0.149697	+	0.206041i	0.727582	+	0.686021i	$0.240644\pi$
$54$	5.42882	+	2.80017i	0.738769	+	0.381055i
$55$		0			0
$56$			9.47214i			1.26577i
$57$	4.39587	+	1.18567i	0.582247	+	0.157046i
$58$	−0.854102	+	2.62866i	−0.112149	+	0.345159i
$59$	0.363271	−	0.118034i	0.0472939	−	0.0153667i	−0.285275	−	0.958446i	$-0.592085\pi$
$59$	0.363271	−	0.118034i	0.0472939	−	0.0153667i	0.332568	+	0.943079i	$0.392085\pi$
$60$	−0.223260	+	0.342548i	−0.0288228	+	0.0442228i
$61$	−1.54508	−	2.12663i	−0.197828	−	0.272287i	0.698566	−	0.715546i	$-0.253822\pi$
$61$	−1.54508	−	2.12663i	−0.197828	−	0.272287i	−0.896393	+	0.443259i	$0.853822\pi$
$62$	2.12663	+	6.54508i	0.270082	+	0.831227i
$63$	8.44720	−	3.72747i	1.06425	−	0.469618i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−0.277515			−0.0344214
$66$		0			0
$67$	7.32624			0.895042			0.447521	−	0.894273i	$-0.352307\pi$
$67$	7.32624			0.895042			0.447521	+	0.894273i	$0.352307\pi$
$68$	−2.12663	−	1.54508i	−0.257891	−	0.187369i
$69$	0.547435	+	10.7873i	0.0659034	+	1.29864i
$70$	−0.427051	−	1.31433i	−0.0510424	−	0.157092i
$71$	−3.13068	−	4.30902i	−0.371544	−	0.511386i	0.581776	−	0.813349i	$-0.302358\pi$
$71$	−3.13068	−	4.30902i	−0.371544	−	0.511386i	−0.953320	+	0.301963i	$0.902358\pi$
$72$	−1.94955	+	9.02488i	−0.229756	+	1.06359i
$73$	8.94427	−	2.90617i	1.04685	−	0.340141i	0.265417	−	0.964134i	$-0.414490\pi$
$73$	8.94427	−	2.90617i	1.04685	−	0.340141i	0.781431	+	0.623992i	$0.214490\pi$
$74$	1.08981	−	3.35410i	0.126688	−	0.389906i
$75$	−2.18947	+	8.11746i	−0.252819	+	0.937323i
$76$			1.62460i			0.186354i
$77$		0			0
$78$	−1.38197	+	0.527864i	−0.156477	+	0.0597688i
$79$	−2.33688	+	3.21644i	−0.262920	+	0.361878i	−0.919984	−	0.391957i	$-0.871798\pi$
$79$	−2.33688	+	3.21644i	−0.262920	+	0.361878i	0.657064	+	0.753835i	$0.271798\pi$
$80$	0.865300	+	0.281153i	0.0967435	+	0.0314339i
$81$	8.81553	−	1.81288i	0.979503	−	0.201431i
$82$	−0.690983	+	0.502029i	−0.0763063	+	0.0554398i
$83$	−5.11855	+	3.71885i	−0.561834	+	0.408196i	−0.832130	−	0.554581i	$-0.812879\pi$
$83$	−5.11855	+	3.71885i	−0.561834	+	0.408196i	0.270296	+	0.962777i	$0.412879\pi$
$84$	2.06909	+	2.56378i	0.225756	+	0.279731i
$85$	1.54508	+	0.502029i	0.167588	+	0.0544526i
$86$	−4.75528	+	6.54508i	−0.512775	+	0.705775i
$87$	1.45309	+	3.80423i	0.155787	+	0.407856i
$88$		0			0
$89$			0.527864i			0.0559535i	0.999609	+	0.0279767i	$0.00890643\pi$
$89$			0.527864i			0.0559535i	−0.999609	+	0.0279767i	$0.991094\pi$
$90$	−0.136373	−	1.34016i	−0.0143749	−	0.141266i
$91$	−0.690983	+	2.12663i	−0.0724347	+	0.222931i
$92$	−3.66547	+	1.19098i	−0.382152	+	0.124169i
$93$	8.49463	+	5.53649i	0.880852	+	0.574107i
$94$	−5.75329	−	7.91872i	−0.593406	−	0.816754i
$95$	−0.310271	−	0.954915i	−0.0318331	−	0.0979722i
$96$	−5.80390	+	0.294537i	−0.592359	+	0.0300610i
$97$	3.54508	+	2.57565i	0.359949	+	0.261518i	0.753031	−	0.657985i	$-0.228591\pi$
$97$	3.54508	+	2.57565i	0.359949	+	0.261518i	−0.393082	+	0.919503i	$0.628591\pi$
$98$	−2.90617			−0.293568
$99$		0			0
$100$	−3.00000			−0.300000
$101$	12.8985	+	9.37132i	1.28345	+	0.932481i	0.999651	−	0.0264022i	$-0.00840507\pi$
$101$	12.8985	+	9.37132i	1.28345	+	0.932481i	0.283799	+	0.958884i	$0.408405\pi$
$102$	8.64912	−	0.438926i	0.856391	−	0.0434602i
$103$	−3.47214	−	10.6861i	−0.342120	−	1.05294i	−0.963108	−	0.269116i	$-0.913268\pi$
$103$	−3.47214	−	10.6861i	−0.342120	−	1.05294i	0.620988	−	0.783820i	$-0.286732\pi$
$104$	−1.31433	−	1.80902i	−0.128880	−	0.177389i
$105$	−1.70582	−	1.11179i	−0.166471	−	0.108500i
$106$	2.07295	−	0.673542i	0.201343	−	0.0654202i
$107$	4.02874	−	12.3992i	0.389473	−	1.19867i	−0.543710	−	0.839273i	$-0.682981\pi$
$107$	4.02874	−	12.3992i	0.389473	−	1.19867i	0.933183	−	0.359402i	$-0.117019\pi$
$108$	1.44372	+	2.86858i	0.138922	+	0.276029i
$109$			4.70228i			0.450397i	0.974313	+	0.225198i	$0.0723030\pi$
$109$			4.70228i			0.450397i	−0.974313	+	0.225198i	$0.927697\pi$
$110$		0			0
$111$	−1.85410	−	4.85410i	−0.175984	−	0.460731i
$112$	4.30902	−	5.93085i	0.407164	−	0.560413i
$113$	1.95511	+	0.635255i	0.183922	+	0.0597598i	0.399530	−	0.916720i	$-0.369173\pi$
$113$	1.95511	+	0.635255i	0.183922	+	0.0597598i	−0.215608	+	0.976480i	$0.569173\pi$
$114$	−3.36144	−	4.16511i	−0.314828	−	0.390099i
$115$	1.92705	−	1.40008i	0.179698	−	0.130559i
$116$	−1.17557	+	0.854102i	−0.109149	+	0.0793014i
$117$	−1.09606	+	1.88399i	−0.101331	+	0.174175i
$118$	−0.427051	−	0.138757i	−0.0393132	−	0.0127736i
$119$	7.69421	−	10.5902i	0.705327	−	0.970799i
$120$	1.90211	−	0.726543i	0.173638	−	0.0663240i
$121$		0			0
$122$			3.09017i			0.279771i
$123$	−0.327712	+	1.21499i	−0.0295488	+	0.109552i
$124$	−1.11803	+	3.44095i	−0.100402	+	0.309007i
$125$	3.57971	−	1.16312i	0.320179	−	0.104033i
$126$	−10.6094	−	2.29183i	−0.945159	−	0.204173i
$127$	7.56231	+	10.4086i	0.671046	+	0.923616i	0.999784	−	0.0208056i	$-0.00662311\pi$
$127$	7.56231	+	10.4086i	0.671046	+	0.923616i	−0.328737	+	0.944421i	$0.606623\pi$
$128$	1.08981	+	3.35410i	0.0963268	+	0.296464i
$129$	0.604130	+	11.9045i	0.0531907	+	1.04813i
$130$	0.263932	+	0.191758i	0.0231484	+	0.0168183i
$131$	−10.4086			−0.909405			−0.454703	−	0.890643i	$-0.650254\pi$
$131$	−10.4086			−0.909405			−0.454703	+	0.890643i	$0.650254\pi$
$132$		0			0
$133$	−8.09017			−0.701507
$134$	−6.96767	−	5.06231i	−0.601915	−	0.437317i
$135$	−1.39645	−	1.41038i	−0.120187	−	0.121387i
$136$	4.04508	+	12.4495i	0.346863	+	1.06754i
$137$	2.76741	+	3.80902i	0.236436	+	0.325426i	0.910703	−	0.413061i	$-0.135540\pi$
$137$	2.76741	+	3.80902i	0.236436	+	0.325426i	−0.674267	+	0.738487i	$0.735540\pi$
$138$	6.93320	−	10.6376i	0.590193	−	0.905533i
$139$	−13.5172	+	4.39201i	−1.14652	+	0.372526i	−0.819830	−	0.572607i	$-0.805932\pi$
$139$	−13.5172	+	4.39201i	−1.14652	+	0.372526i	−0.326686	+	0.945133i	$0.605932\pi$
$140$	0.224514	−	0.690983i	0.0189749	−	0.0583987i
$141$	−13.9239	−	3.75560i	−1.17260	−	0.316279i
$142$			6.26137i			0.525442i
$143$		0			0
$144$	5.32624	−	4.76393i	0.443853	−	0.396994i
$145$	0.527864	−	0.726543i	0.0438367	−	0.0603361i
$146$	−10.5146	−	3.41641i	−0.870196	−	0.282744i
$147$	−3.33209	+	2.68915i	−0.274826	+	0.221798i
$148$	1.50000	−	1.08981i	0.123299	−	0.0895821i
$149$	10.5474	−	7.66312i	0.864075	−	0.627787i	−0.0649156	−	0.997891i	$-0.520678\pi$
$149$	10.5474	−	7.66312i	0.864075	−	0.627787i	0.928990	+	0.370104i	$0.120678\pi$
$150$	7.69134	−	6.20727i	0.627995	−	0.506822i
$151$	−5.32624	−	1.73060i	−0.433443	−	0.140834i	0.0841654	−	0.996452i	$-0.473178\pi$
$151$	−5.32624	−	1.73060i	−0.433443	−	0.140834i	−0.517608	+	0.855618i	$0.673178\pi$
$152$	4.75528	−	6.54508i	0.385704	−	0.530876i
$153$	9.51057	−	8.50651i	0.768884	−	0.687710i
$154$		0			0
$155$		−	2.23607i		−	0.179605i
$156$	−0.750904	−	0.202537i	−0.0601205	−	0.0162159i
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	4.44501	−	1.44427i	0.353626	−	0.114900i
$159$	1.75351	−	2.69041i	0.139062	−	0.213363i
$160$	0.753289	+	1.03681i	0.0595527	+	0.0819673i
$161$	−5.93085	−	18.2533i	−0.467417	−	1.43856i
$162$	−9.63673	−	4.36723i	−0.757133	−	0.343122i
$163$	11.8262	+	8.59226i	0.926302	+	0.672998i	0.945085	−	0.326825i	$-0.105979\pi$
$163$	11.8262	+	8.59226i	0.926302	+	0.672998i	−0.0187823	+	0.999824i	$0.505979\pi$
$164$	−0.449028			−0.0350632
$165$		0			0
$166$	7.43769			0.577277
$167$	−17.0660	−	12.3992i	−1.32061	−	0.959478i	−0.999924	−	0.0122915i	$-0.996087\pi$
$167$	−17.0660	−	12.3992i	−1.32061	−	0.959478i	−0.320684	−	0.947186i	$-0.603913\pi$
$168$	−0.831514	−	16.3851i	−0.0641527	−	1.26414i
$169$	3.85410	+	11.8617i	0.296469	+	0.912439i
$170$	−1.12257	−	1.54508i	−0.0860972	−	0.118503i
$171$	−7.70817	−	1.66511i	−0.589458	−	0.127334i
$172$	−4.04508	+	1.31433i	−0.308435	+	0.100217i
$173$	−7.13918	+	21.9721i	−0.542782	+	1.67051i	0.183425	+	0.983034i	$0.441282\pi$
$173$	−7.13918	+	21.9721i	−0.542782	+	1.67051i	−0.726206	+	0.687477i	$0.758718\pi$
$174$	1.24669	−	4.62209i	0.0945113	−	0.350400i
$175$		−	14.9394i		−	1.12931i
$176$		0			0
$177$	−0.618034	+	0.236068i	−0.0464543	+	0.0177440i
$178$	0.364745	−	0.502029i	0.0273388	−	0.0376286i
$179$	−13.2618	−	4.30902i	−0.991233	−	0.322071i	−0.231876	−	0.972745i	$-0.574486\pi$
$179$	−13.2618	−	4.30902i	−0.991233	−	0.322071i	−0.759357	+	0.650674i	$0.774486\pi$
$180$	0.356131	−	0.612147i	0.0265444	−	0.0456267i
$181$	−6.28115	+	4.56352i	−0.466874	+	0.339204i	−0.796222	−	0.605005i	$-0.793171\pi$
$181$	−6.28115	+	4.56352i	−0.466874	+	0.339204i	0.329348	+	0.944209i	$0.393171\pi$
$182$	2.12663	−	1.54508i	0.157636	−	0.114529i
$183$	2.85941	+	3.54306i	0.211374	+	0.261910i
$184$	18.2533	+	5.93085i	1.34565	+	0.437228i
$185$	−0.673542	+	0.927051i	−0.0495198	+	0.0681581i
$186$	−4.25325	−	11.1352i	−0.311864	−	0.816470i
$187$		0			0
$188$		−	5.14590i		−	0.375303i
$189$	−14.2850	+	7.18942i	−1.03908	+	0.522953i
$190$	−0.364745	+	1.12257i	−0.0264614	+	0.0814398i
$191$	−23.0499	+	7.48936i	−1.66783	+	0.541911i	−0.982490	−	0.186313i	$-0.940346\pi$
$191$	−23.0499	+	7.48936i	−1.66783	+	0.541911i	−0.685340	+	0.728224i	$0.740346\pi$
$192$	12.6361	+	8.23575i	0.911932	+	0.594364i
$193$	5.79180	+	7.97172i	0.416903	+	0.573817i	0.964885	−	0.262673i	$-0.0846039\pi$
$193$	5.79180	+	7.97172i	0.416903	+	0.573817i	−0.547982	+	0.836490i	$0.684604\pi$
$194$	−1.59184	−	4.89919i	−0.114288	−	0.351741i
$195$	0.480052	−	0.0243617i	0.0343772	−	0.00174458i
$196$	−1.23607	−	0.898056i	−0.0882906	−	0.0641469i
$197$	8.61251			0.613616			0.306808	−	0.951771i	$-0.400739\pi$
$197$	8.61251			0.613616			0.306808	+	0.951771i	$0.400739\pi$
$198$		0			0
$199$	2.23607			0.158511			0.0792553	−	0.996854i	$-0.474746\pi$
$199$	2.23607			0.158511			0.0792553	+	0.996854i	$0.474746\pi$
$200$	12.0862	+	8.78115i	0.854625	+	0.620921i
$201$	−12.6731	+	0.643136i	−0.893892	+	0.0453633i
$202$	−5.79180	−	17.8253i	−0.407509	−	1.25418i
$203$	−4.25325	−	5.85410i	−0.298520	−	0.410877i
$204$	3.81433	+	2.48604i	0.267056	+	0.174058i
$205$	0.263932	−	0.0857567i	0.0184338	−	0.00598951i
$206$	−4.08174	+	12.5623i	−0.284388	+	0.875257i
$207$	−1.89393	−	18.6121i	−0.131637	−	1.29363i
$208$			1.73060i			0.119995i
$209$		0			0
$210$	0.854102	+	2.23607i	0.0589386	+	0.154303i
$211$	11.4443	−	15.7517i	0.787856	−	1.08439i	−0.206516	−	0.978443i	$-0.566212\pi$
$211$	11.4443	−	15.7517i	0.787856	−	1.08439i	0.994372	−	0.105948i	$-0.0337876\pi$
$212$	1.08981	+	0.354102i	0.0748487	+	0.0243198i
$213$	5.79380	+	7.17902i	0.396985	+	0.491898i
$214$	−12.3992	+	9.00854i	−0.847591	+	0.615811i
$215$	2.12663	−	1.54508i	0.145035	−	0.105374i
$216$	2.58012	−	15.7826i	0.175555	−	1.07387i
$217$	−17.1353	−	5.56758i	−1.16322	−	0.377952i
$218$	3.24920	−	4.47214i	0.220063	−	0.302891i
$219$	−15.2169	+	5.81234i	−1.02826	+	0.392762i
$220$		0			0
$221$			3.09017i			0.207867i
$222$	−1.59075	+	5.89768i	−0.106764	+	0.395826i
$223$	0.545085	−	1.67760i	0.0365016	−	0.112340i	−0.931146	−	0.364648i	$-0.881189\pi$
$223$	0.545085	−	1.67760i	0.0365016	−	0.112340i	0.967647	+	0.252307i	$0.0811894\pi$
$224$	9.82084	−	3.19098i	0.656182	−	0.213207i
$225$	3.07481	−	14.2340i	0.204988	−	0.948932i
$226$	−1.42047	−	1.95511i	−0.0944885	−	0.130052i
$227$	4.47777	+	13.7812i	0.297200	+	0.914687i	0.982474	+	0.186402i	$0.0596826\pi$
$227$	4.47777	+	13.7812i	0.297200	+	0.914687i	−0.685274	+	0.728286i	$0.740317\pi$
$228$	−0.142616	−	2.81027i	−0.00944496	−	0.186115i
$229$	12.2361	+	8.89002i	0.808582	+	0.587469i	0.913419	−	0.407020i	$-0.133432\pi$
$229$	12.2361	+	8.89002i	0.808582	+	0.587469i	−0.104837	+	0.994489i	$0.533432\pi$
$230$	−2.80017			−0.184638
$231$		0			0
$232$	7.23607			0.475071
$233$	−7.83297	−	5.69098i	−0.513155	−	0.372829i	0.300864	−	0.953667i	$-0.402725\pi$
$233$	−7.83297	−	5.69098i	−0.513155	−	0.372829i	−0.814019	+	0.580838i	$0.802725\pi$
$234$	2.34422	−	1.03443i	0.153246	−	0.0676227i
$235$	0.982779	+	3.02468i	0.0641094	+	0.197309i
$236$	−0.138757	−	0.190983i	−0.00903233	−	0.0124319i
$237$	3.76004	−	5.76902i	0.244241	−	0.374738i
$238$	−14.6353	+	4.75528i	−0.948663	+	0.308239i
$239$	2.38390	−	7.33688i	0.154201	−	0.474583i	−0.843878	−	0.536536i	$-0.819733\pi$
$239$	2.38390	−	7.33688i	0.154201	−	0.474583i	0.998079	+	0.0619523i	$0.0197327\pi$
$240$	−1.52150	−	0.410385i	−0.0982123	−	0.0264902i
$241$			27.8707i			1.79531i	0.440702	+	0.897654i	$0.354730\pi$
$241$			27.8707i			1.79531i	−0.440702	+	0.897654i	$0.645270\pi$
$242$		0			0
$243$	−15.0902	+	3.90983i	−0.968035	+	0.250816i
$244$	−0.954915	+	1.31433i	−0.0611322	+	0.0841412i
$245$	0.898056	+	0.291796i	0.0573747	+	0.0186422i
$246$	1.15121	−	0.929080i	0.0733984	−	0.0592359i
$247$	1.54508	−	1.12257i	0.0983114	−	0.0714274i
$248$	14.5761	−	10.5902i	0.925584	−	0.672476i
$249$	8.52774	−	6.88229i	0.540424	−	0.436147i
$250$	−4.20820	−	1.36733i	−0.266150	−	0.0864774i
$251$	−11.9475	+	16.4443i	−0.754117	+	1.03795i	0.243563	+	0.969885i	$0.421684\pi$
$251$	−11.9475	+	16.4443i	−0.754117	+	1.03795i	−0.997681	+	0.0680683i	$0.978316\pi$
$252$	−3.80423	−	4.25325i	−0.239644	−	0.267930i
$253$		0			0
$254$		−	15.1246i		−	0.949003i
$255$	−2.71680	−	0.732786i	−0.170132	−	0.0458888i
$256$	−4.10081	+	12.6210i	−0.256301	+	0.788813i
$257$	21.1805	−	6.88197i	1.32120	−	0.429285i	0.438296	−	0.898831i	$-0.355582\pi$
$257$	21.1805	−	6.88197i	1.32120	−	0.429285i	0.882908	+	0.469546i	$0.155582\pi$
$258$	7.65124	−	11.7393i	0.476346	−	0.730857i
$259$	5.42705	+	7.46969i	0.337221	+	0.464144i
$260$	0.0530006	+	0.163119i	0.00328696	+	0.0101162i
$261$	−2.84754	−	6.45309i	−0.176258	−	0.399436i
$262$	9.89919	+	7.19218i	0.611574	+	0.444334i
$263$	9.12705			0.562798			0.281399	−	0.959591i	$-0.409202\pi$
$263$	9.12705			0.562798			0.281399	+	0.959591i	$0.409202\pi$
$264$		0			0
$265$	−0.708204			−0.0435046
$266$	7.69421	+	5.59017i	0.471762	+	0.342755i
$267$	−0.0463387	−	0.913112i	−0.00283588	−	0.0558816i
$268$	−1.39919	−	4.30625i	−0.0854689	−	0.263046i
$269$	11.0292	+	15.1803i	0.672460	+	0.925562i	0.999813	−	0.0193404i	$-0.00615664\pi$
$269$	11.0292	+	15.1803i	0.672460	+	0.925562i	−0.327353	+	0.944902i	$0.606157\pi$
$270$	0.353547	+	2.30628i	0.0215162	+	0.140355i
$271$	16.1180	−	5.23707i	0.979101	−	0.318129i	0.224617	−	0.974447i	$-0.427887\pi$
$271$	16.1180	−	5.23707i	0.979101	−	0.318129i	0.754484	+	0.656318i	$0.227887\pi$
$272$	3.13068	−	9.63525i	0.189826	−	0.584223i
$273$	1.00859	−	3.73935i	0.0610428	−	0.226316i
$274$		−	5.53483i		−	0.334371i
$275$		0			0
$276$	6.23607	−	2.38197i	0.375367	−	0.143378i
$277$	9.53444	−	13.1230i	0.572869	−	0.788487i	−0.420022	−	0.907514i	$-0.637978\pi$
$277$	9.53444	−	13.1230i	0.572869	−	0.788487i	0.992891	+	0.119027i	$0.0379776\pi$
$278$	15.8904	+	5.16312i	0.953046	+	0.309663i
$279$	−15.1802	−	8.83146i	−0.908818	−	0.528726i
$280$	−2.92705	+	2.12663i	−0.174925	+	0.127090i
$281$	−21.5438	+	15.6525i	−1.28519	+	0.933748i	−0.999697	−	0.0246309i	$-0.992159\pi$
$281$	−21.5438	+	15.6525i	−1.28519	+	0.933748i	−0.285498	+	0.958379i	$0.592159\pi$
$282$	10.6473	+	13.1929i	0.634039	+	0.785629i
$283$	20.3262	+	6.60440i	1.20827	+	0.392591i	0.842797	−	0.538232i	$-0.180907\pi$
$283$	20.3262	+	6.60440i	1.20827	+	0.392591i	0.365472	+	0.930822i	$0.380907\pi$
$284$	−1.93487	+	2.66312i	−0.114813	+	0.158027i
$285$	0.620541	+	1.62460i	0.0367577	+	0.0962329i
$286$		0			0
$287$		−	2.23607i		−	0.131991i
$288$	10.0139	−	1.01899i	0.590074	−	0.0600448i
$289$	0.336881	−	1.03681i	0.0198165	−	0.0609890i
$290$	−1.00406	+	0.326238i	−0.0589603	+	0.0191574i
$291$	−6.35848	−	4.14423i	−0.372741	−	0.242939i
$292$	−3.41641	−	4.70228i	−0.199930	−	0.275180i
$293$	4.30625	+	13.2533i	0.251574	+	0.774265i	0.994485	+	0.104876i	$0.0334444\pi$
$293$	4.30625	+	13.2533i	0.251574	+	0.774265i	−0.742911	+	0.669390i	$0.766556\pi$
$294$	5.02717	−	0.255119i	0.293190	−	0.0148788i
$295$	0.118034	+	0.0857567i	0.00687220	+	0.00499295i
$296$	−9.23305			−0.536660
$297$		0			0
$298$	−15.3262			−0.887825
$299$	3.66547	+	2.66312i	0.211980	+	0.154012i
$300$	5.18947	−	0.263356i	0.299614	−	0.0152049i
$301$	−6.54508	−	20.1437i	−0.377252	−	1.16106i
$302$	3.86974	+	5.32624i	0.222678	+	0.306491i
$303$	−23.1348	−	15.0784i	−1.32906	−	0.866234i
$304$	−5.95492	+	1.93487i	−0.341538	+	0.110972i
$305$	0.310271	−	0.954915i	0.0177660	−	0.0546783i
$306$	−14.9229	+	1.51853i	−0.853088	+	0.0868086i
$307$			9.51057i			0.542797i	0.962467	+	0.271398i	$0.0874861\pi$
$307$			9.51057i			0.542797i	−0.962467	+	0.271398i	$0.912514\pi$
$308$		0			0
$309$	6.94427	+	18.1803i	0.395046	+	1.03424i
$310$	−1.54508	+	2.12663i	−0.0877549	+	0.120784i
$311$	4.75528	+	1.54508i	0.269647	+	0.0876137i	0.440720	−	0.897645i	$-0.354723\pi$
$311$	4.75528	+	1.54508i	0.269647	+	0.0876137i	−0.171072	+	0.985258i	$0.554723\pi$
$312$	2.43236	+	3.01390i	0.137705	+	0.170629i
$313$	−8.89919	+	6.46564i	−0.503012	+	0.365459i	−0.810166	−	0.586200i	$-0.800623\pi$
$313$	−8.89919	+	6.46564i	−0.503012	+	0.365459i	0.307154	+	0.951660i	$0.400623\pi$
$314$	−9.23305	+	6.70820i	−0.521051	+	0.378566i
$315$	3.04837	+	1.77346i	0.171756	+	0.0999230i
$316$	2.33688	+	0.759299i	0.131460	+	0.0427139i
$317$	2.48990	−	3.42705i	0.139847	−	0.192482i	−0.733349	−	0.679853i	$-0.762044\pi$
$317$	2.48990	−	3.42705i	0.139847	−	0.192482i	0.873195	+	0.487370i	$0.162044\pi$
$318$	−3.52671	+	1.34708i	−0.197768	+	0.0755407i
$319$		0			0
$320$		−	3.32624i		−	0.185942i
$321$	−5.88055	+	21.8021i	−0.328220	+	1.21687i
$322$	−6.97214	+	21.4580i	−0.388542	+	1.19581i
$323$	−10.6331	+	3.45492i	−0.591643	+	0.192237i
$324$	−2.74920	−	4.83541i	−0.152733	−	0.268634i
$325$	2.07295	+	2.85317i	0.114987	+	0.158265i
$326$	−5.31031	−	16.3435i	−0.294111	−	0.905180i
$327$	−0.412791	−	8.13412i	−0.0228274	−	0.449818i
$328$	1.80902	+	1.31433i	0.0998863	+	0.0725716i
$329$	25.6255			1.41278
$330$		0			0
$331$	12.8885			0.708418			0.354209	−	0.935166i	$-0.384750\pi$
$331$	12.8885			0.708418			0.354209	+	0.935166i	$0.384750\pi$
$332$	3.16344	+	2.29837i	0.173616	+	0.126140i
$333$	3.63339	+	8.23398i	0.199109	+	0.451219i
$334$	7.66312	+	23.5847i	0.419307	+	1.29049i
$335$	1.64484	+	2.26393i	0.0898674	+	0.123692i
$336$	−6.93320	+	10.6376i	−0.378237	+	0.580329i
$337$	−23.9443	+	7.77997i	−1.30433	+	0.423802i	−0.877085	−	0.480335i	$-0.840515\pi$
$337$	−23.9443	+	7.77997i	−1.30433	+	0.423802i	−0.427243	+	0.904137i	$0.640515\pi$
$338$	4.53077	−	13.9443i	0.246441	−	0.758468i
$339$	−3.43777	−	0.927250i	−0.186714	−	0.0503613i
$340$		−	1.00406i		−	0.0544526i
$341$		0			0
$342$	6.18034	+	6.90983i	0.334195	+	0.373641i
$343$	−8.19098	+	11.2739i	−0.442272	+	0.608735i
$344$	20.1437	+	6.54508i	1.08608	+	0.352887i
$345$	−3.21055	+	2.59107i	−0.172850	+	0.139498i
$346$	21.9721	−	15.9637i	1.18123	−	0.858213i
$347$	−5.87785	+	4.27051i	−0.315540	+	0.229253i	−0.734270	−	0.678858i	$-0.762475\pi$
$347$	−5.87785	+	4.27051i	−0.315540	+	0.229253i	0.418730	+	0.908111i	$0.362475\pi$
$348$	1.95855	−	1.58064i	0.104989	−	0.0847314i
$349$	−12.9271	−	4.20025i	−0.691969	−	0.224834i	−0.0581411	−	0.998308i	$-0.518517\pi$
$349$	−12.9271	−	4.20025i	−0.691969	−	0.224834i	−0.633828	+	0.773474i	$0.718517\pi$
$350$	−10.3229	+	14.2082i	−0.551780	+	0.759460i
$351$	1.73060	−	3.35520i	0.0923726	−	0.179087i
$352$		0			0
$353$			33.5967i			1.78817i	0.447893	+	0.894087i	$0.352175\pi$
$353$			33.5967i			1.78817i	−0.447893	+	0.894087i	$0.647825\pi$
$354$	0.750904	+	0.202537i	0.0399101	+	0.0107647i
$355$	0.628677	−	1.93487i	0.0333667	−	0.102692i
$356$	0.310271	−	0.100813i	0.0164443	−	0.00534308i
$357$	−12.3800	+	18.9946i	−0.655218	+	1.00530i
$358$	9.63525	+	13.2618i	0.509239	+	0.700907i
$359$	9.85359	+	30.3262i	0.520053	+	1.60056i	0.773896	+	0.633312i	$0.218305\pi$
$359$	9.85359	+	30.3262i	0.520053	+	1.60056i	−0.253844	+	0.967245i	$0.581695\pi$
$360$	−3.22654	+	1.42377i	−0.170054	+	0.0750392i
$361$	−9.78115	−	7.10642i	−0.514798	−	0.374022i
$362$	9.12705			0.479707
$363$		0			0
$364$	1.38197			0.0724347
$365$	2.90617	+	2.11146i	0.152116	+	0.110519i
$366$	−0.271271	−	5.34545i	−0.0141796	−	0.279411i
$367$	7.40983	+	22.8051i	0.386790	+	1.19042i	0.935173	+	0.354190i	$0.115243\pi$
$367$	7.40983	+	22.8051i	0.386790	+	1.19042i	−0.548383	+	0.836227i	$0.684757\pi$
$368$	−8.73102	−	12.0172i	−0.455136	−	0.626441i
$369$	0.460226	−	2.13049i	0.0239584	−	0.110909i
$370$	1.28115	−	0.416272i	0.0666040	−	0.0216409i
$371$	−1.76336	+	5.42705i	−0.0915489	+	0.281758i
$372$	1.63194	−	6.05040i	0.0846120	−	0.313698i
$373$		−	27.3561i		−	1.41645i	−0.705989	−	0.708223i	$-0.749497\pi$
$373$		−	27.3561i		−	1.41645i	0.705989	−	0.708223i	$-0.250503\pi$
$374$		0			0
$375$	−6.09017	+	2.32624i	−0.314495	+	0.120126i
$376$	−15.0623	+	20.7315i	−0.776779	+	1.06914i
$377$	1.62460	+	0.527864i	0.0836711	+	0.0271864i
$378$	18.5536	+	3.03312i	0.954292	+	0.156007i
$379$	−2.33688	+	1.69784i	−0.120038	+	0.0872124i	−0.646184	−	0.763181i	$-0.723636\pi$
$379$	−2.33688	+	1.69784i	−0.120038	+	0.0872124i	0.526147	+	0.850394i	$0.323636\pi$
$380$	−0.502029	+	0.364745i	−0.0257535	+	0.0187110i
$381$	−13.9952	−	17.3412i	−0.716995	−	0.888418i
$382$	27.0967	+	8.80427i	1.38639	+	0.450465i
$383$	−7.29818	+	10.0451i	−0.372920	+	0.513280i	−0.953691	−	0.300787i	$-0.902751\pi$
$383$	−7.29818	+	10.0451i	−0.372920	+	0.513280i	0.580772	+	0.814066i	$0.302751\pi$
$384$	−2.17963	−	5.70634i	−0.111229	−	0.291200i
$385$		0			0
$386$		−	11.5836i		−	0.589589i
$387$	−2.09008	−	20.5397i	−0.106245	−	1.04409i
$388$	0.836881	−	2.57565i	0.0424862	−	0.130759i
$389$	7.02067	−	2.28115i	0.355962	−	0.115659i	−0.125577	−	0.992084i	$-0.540078\pi$
$389$	7.02067	−	2.28115i	0.355962	−	0.115659i	0.481539	+	0.876425i	$0.340078\pi$
$390$	−0.473390	−	0.308538i	−0.0239710	−	0.0156234i
$391$	−15.5902	−	21.4580i	−0.788429	−	1.08518i
$392$	2.35114	+	7.23607i	0.118751	+	0.365477i
$393$	18.0051	−	0.913723i	0.908237	−	0.0460913i
$394$	−8.19098	−	5.95110i	−0.412656	−	0.299812i
$395$	−1.51860			−0.0764089
$396$		0			0
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	−2.12663	−	1.54508i	−0.106598	−	0.0774481i
$399$	13.9946	−	0.710198i	0.700605	−	0.0355544i
$400$	−3.57295	−	10.9964i	−0.178647	−	0.549820i
$401$	−16.3722	−	22.5344i	−0.817590	−	1.12532i	−0.990108	−	0.140310i	$-0.955190\pi$
$401$	−16.3722	−	22.5344i	−0.817590	−	1.12532i	0.172517	−	0.985006i	$-0.444810\pi$
$402$	12.4972	+	8.14524i	0.623306	+	0.406248i
$403$	4.04508	−	1.31433i	0.201500	−	0.0654713i
$404$	3.04493	−	9.37132i	0.151491	−	0.466241i
$405$	2.53942	+	2.31713i	0.126185	+	0.115139i
$406$			8.50651i			0.422171i
$407$		0			0
$408$	−8.09017	−	21.1803i	−0.400523	−	1.04858i
$409$	12.4377	−	17.1190i	0.615004	−	0.846481i	−0.381973	−	0.924173i	$-0.624755\pi$
$409$	12.4377	−	17.1190i	0.615004	−	0.846481i	0.996977	+	0.0776926i	$0.0247553\pi$
$410$	−0.310271	−	0.100813i	−0.0153232	−	0.00497880i
$411$	−5.12151	−	6.34599i	−0.252626	−	0.313025i
$412$	−5.61803	+	4.08174i	−0.276781	+	0.201093i
$413$	0.951057	−	0.690983i	0.0467984	−	0.0340011i
$414$	−11.0594	+	19.0098i	−0.543540	+	0.934282i
$415$	−2.29837	−	0.746787i	−0.112823	−	0.0366583i
$416$	−1.43284	+	1.97214i	−0.0702508	+	0.0966919i
$417$	22.9969	−	8.78402i	1.12616	−	0.430155i
$418$		0			0
$419$		−	0.854102i		−	0.0417256i	−0.999782	−	0.0208628i	$-0.993359\pi$
$419$		−	0.854102i		−	0.0417256i	0.999782	−	0.0208628i	$-0.00664132\pi$
$420$	−0.327712	+	1.21499i	−0.0159907	+	0.0592854i
$421$	5.91641	−	18.2088i	0.288348	−	0.887444i	−0.697027	−	0.717045i	$-0.745494\pi$
$421$	5.91641	−	18.2088i	0.288348	−	0.887444i	0.985375	−	0.170399i	$-0.0545057\pi$
$422$	−21.7683	+	7.07295i	−1.05966	+	0.344306i
$423$	24.4155	+	5.27423i	1.18712	+	0.256442i
$424$	−3.35410	−	4.61653i	−0.162890	−	0.224198i
$425$	−6.37988	−	19.6353i	−0.309470	−	0.952450i
$426$	−0.549656	−	10.8311i	−0.0266309	−	0.524767i
$427$	−6.54508	−	4.75528i	−0.316739	−	0.230124i
$428$	−8.05748			−0.389473
$429$		0			0
$430$	−3.09017			−0.149021
$431$	4.89404	+	3.55573i	0.235738	+	0.171273i	0.699382	−	0.714748i	$-0.253459\pi$
$431$	4.89404	+	3.55573i	0.235738	+	0.171273i	−0.463645	+	0.886021i	$0.653459\pi$
$432$	−8.79526	+	8.70833i	−0.423162	+	0.418980i
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$	12.4495	+	17.1353i	0.597595	+	0.822519i
$435$	−0.849333	+	1.30313i	−0.0407224	+	0.0624803i
$436$	2.76393	−	0.898056i	0.132368	−	0.0430091i
$437$	−5.06555	+	15.5902i	−0.242318	+	0.745779i
$438$	18.4884	+	4.98676i	0.883408	+	0.238277i
$439$			2.73466i			0.130518i	0.997868	+	0.0652590i	$0.0207874\pi$
$439$			2.73466i			0.130518i	−0.997868	+	0.0652590i	$0.979213\pi$
$440$		0			0
$441$	5.52786	−	4.94427i	0.263232	−	0.235442i
$442$	2.13525	−	2.93893i	0.101564	−	0.139790i
$443$	−1.45309	−	0.472136i	−0.0690382	−	0.0224319i	0.274294	−	0.961646i	$-0.411556\pi$
$443$	−1.45309	−	0.472136i	−0.0690382	−	0.0224319i	−0.343332	+	0.939214i	$0.611556\pi$
$444$	−2.49907	+	2.01686i	−0.118600	+	0.0957162i
$445$	−0.163119	+	0.118513i	−0.00773258	+	0.00561805i
$446$	−1.67760	+	1.21885i	−0.0794366	+	0.0577141i
$447$	−17.5724	+	14.1818i	−0.831146	+	0.670774i
$448$	−25.4894	−	8.28199i	−1.20426	−	0.391287i
$449$	16.3925	−	22.5623i	0.773609	−	1.06478i	−0.222350	−	0.974967i	$-0.571373\pi$
$449$	16.3925	−	22.5623i	0.773609	−	1.06478i	0.995959	−	0.0898141i	$-0.0286273\pi$
$450$	−12.7598	+	11.4127i	−0.601501	+	0.537999i
$451$		0			0
$452$		−	1.27051i		−	0.0597598i
$453$	9.36538	+	2.52607i	0.440024	+	0.118685i
$454$	5.26393	−	16.2007i	0.247049	−	0.760337i
$455$	−0.812299	+	0.263932i	−0.0380812	+	0.0123733i
$456$	−7.65124	+	11.7393i	−0.358302	+	0.549743i
$457$	−14.7361	−	20.2825i	−0.689324	−	0.948773i	0.310674	−	0.950516i	$-0.399445\pi$
$457$	−14.7361	−	20.2825i	−0.689324	−	0.948773i	−0.999998	+	0.00174308i	$0.999445\pi$
$458$	−5.49434	−	16.9098i	−0.256734	−	0.790144i
$459$	−15.7049	+	15.5497i	−0.733040	+	0.725796i
$460$	−1.19098	−	0.865300i	−0.0555299	−	0.0403448i
$461$	−30.7113			−1.43037			−0.715184	−	0.698936i	$-0.753657\pi$
$461$	−30.7113			−1.43037			−0.715184	+	0.698936i	$0.753657\pi$
$462$		0			0
$463$	33.2705			1.54621			0.773106	−	0.634277i	$-0.218702\pi$
$463$	33.2705			1.54621			0.773106	+	0.634277i	$0.218702\pi$
$464$	−4.53077	−	3.29180i	−0.210336	−	0.152818i
$465$	0.196294	+	3.86801i	0.00910291	+	0.179374i
$466$	3.51722	+	10.8249i	0.162932	+	0.501453i
$467$	4.49801	+	6.19098i	0.208143	+	0.286485i	0.900307	−	0.435256i	$-0.143342\pi$
$467$	4.49801	+	6.19098i	0.208143	+	0.286485i	−0.692163	+	0.721741i	$0.743342\pi$
$468$	1.31671	+	0.284435i	0.0608651	+	0.0131480i
$469$	21.4443	−	6.96767i	0.990204	−	0.321737i
$470$	1.15533	−	3.55573i	0.0532912	−	0.164014i
$471$	−4.37895	+	16.2349i	−0.201771	+	0.748065i
$472$			1.17557i			0.0541100i
$473$		0			0
$474$	−7.56231	+	2.88854i	−0.347348	+	0.132675i
$475$	−7.50000	+	10.3229i	−0.344124	+	0.473646i
$476$	−7.69421	−	2.50000i	−0.352663	−	0.114587i
$477$	−2.79709	+	4.80786i	−0.128070	+	0.220137i
$478$	−7.33688	+	5.33056i	−0.335581	+	0.243814i
$479$	16.2007	−	11.7705i	0.740230	−	0.537808i	−0.152553	−	0.988295i	$-0.548750\pi$
$479$	16.2007	−	11.7705i	0.740230	−	0.537808i	0.892783	+	0.450487i	$0.148750\pi$
$480$	−1.39407	−	1.72738i	−0.0636305	−	0.0788436i
$481$	−2.07295	−	0.673542i	−0.0945183	−	0.0307109i
$482$	19.2582	−	26.5066i	0.877185	−	1.20734i
$483$	11.8617	+	31.0543i	0.539726	+	1.41302i
$484$		0			0
$485$			1.67376i			0.0760016i
$486$	17.0532	+	6.70858i	0.773550	+	0.304307i
$487$	0.454915	−	1.40008i	0.0206142	−	0.0634439i	−0.940220	−	0.340567i	$-0.889381\pi$
$487$	0.454915	−	1.40008i	0.0206142	−	0.0634439i	0.960834	+	0.277123i	$0.0893810\pi$
$488$	7.69421	−	2.50000i	0.348300	−	0.113170i
$489$	−21.2116	−	13.8249i	−0.959221	−	0.625186i
$490$	−0.652476	−	0.898056i	−0.0294759	−	0.0405700i
$491$	−5.46158	−	16.8090i	−0.246478	−	0.758580i	−0.995390	−	0.0959111i	$-0.969424\pi$
$491$	−5.46158	−	16.8090i	−0.246478	−	0.758580i	0.748912	−	0.662669i	$-0.230576\pi$
$492$	0.776740	−	0.0394180i	0.0350181	−	0.00177710i
$493$	−8.09017	−	5.87785i	−0.364363	−	0.264725i
$494$	−2.24514			−0.101014
$495$		0			0
$496$	−13.9443			−0.626116
$497$	−13.2618	−	9.63525i	−0.594873	−	0.432200i
$498$	−12.8659	+	0.652920i	−0.576535	+	0.0292580i
$499$	−11.1180	−	34.2178i	−0.497712	−	1.53180i	−0.812688	−	0.582699i	$-0.801997\pi$
$499$	−11.1180	−	34.2178i	−0.497712	−	1.53180i	0.314976	−	0.949100i	$-0.398003\pi$
$500$	−1.36733	−	1.88197i	−0.0611488	−	0.0841641i
$501$	30.6097	+	19.9503i	1.36754	+	0.891313i
$502$	22.7254	−	7.38394i	1.01429	−	0.329561i
$503$	2.62866	−	8.09017i	0.117206	−	0.360723i	−0.875195	−	0.483771i	$-0.839267\pi$
$503$	2.62866	−	8.09017i	0.117206	−	0.360723i	0.992401	+	0.123048i	$0.0392669\pi$
$504$	2.87675	+	28.2704i	0.128140	+	1.25926i
$505$			6.08985i			0.270995i
$506$		0			0
$507$	−7.70820	−	20.1803i	−0.342333	−	0.896240i
$508$	4.67376	−	6.43288i	0.207365	−	0.285413i
$509$	−31.6421	−	10.2812i	−1.40251	−	0.455704i	−0.492510	−	0.870307i	$-0.663921\pi$
$509$	−31.6421	−	10.2812i	−1.40251	−	0.455704i	−0.910003	+	0.414602i	$0.863921\pi$
$510$	2.07748	+	2.57418i	0.0919926	+	0.113987i
$511$	23.4164	−	17.0130i	1.03588	−	0.752612i
$512$	18.3273	−	13.3156i	0.809962	−	0.588472i
$513$	13.4800	+	2.20369i	0.595155	+	0.0972953i
$514$	−24.8992	−	8.09024i	−1.09826	−	0.356845i
$515$	2.52265	−	3.47214i	0.111161	−	0.153001i
$516$	6.88191	−	2.62866i	0.302959	−	0.115720i
$517$		0			0
$518$		−	10.8541i		−	0.476902i
$519$	10.4207	−	38.6347i	0.457418	−	1.69587i
$520$	0.263932	−	0.812299i	0.0115742	−	0.0356217i
$521$	32.0584	−	10.4164i	1.40450	−	0.456351i	0.493860	−	0.869542i	$-0.335586\pi$
$521$	32.0584	−	10.4164i	1.40450	−	0.456351i	0.910645	+	0.413190i	$0.135586\pi$
$522$	−1.75080	+	8.10485i	−0.0766306	+	0.354740i
$523$	11.9721	+	16.4782i	0.523505	+	0.720543i	0.986123	−	0.166015i	$-0.0530900\pi$
$523$	11.9721	+	16.4782i	0.523505	+	0.720543i	−0.462618	+	0.886558i	$0.653090\pi$
$524$	1.98787	+	6.11803i	0.0868405	+	0.267268i
$525$	1.31146	+	25.8425i	0.0572367	+	1.12786i
$526$	−8.68034	−	6.30664i	−0.378481	−	0.274982i
$527$	−24.8990			−1.08462
$528$		0			0
$529$	−15.8885			−0.690806
$530$	0.673542	+	0.489357i	0.0292568	+	0.0212563i
$531$	1.04837	−	0.462611i	0.0454953	−	0.0200756i
$532$	1.54508	+	4.75528i	0.0669879	+	0.206168i
$533$	0.310271	+	0.427051i	0.0134393	+	0.0184976i
$534$	−0.586874	+	0.900441i	−0.0253965	+	0.0389659i
$535$	4.73607	−	1.53884i	0.204758	−	0.0665299i
$536$	−6.96767	+	21.4443i	−0.300957	+	0.926251i
$537$	23.3188	+	6.28965i	1.00628	+	0.271419i
$538$		−	22.0583i		−	0.951002i
$539$		0			0
$540$	−0.562306	+	1.09017i	−0.0241978	+	0.0469134i
$541$	−8.98278	+	12.3637i	−0.386200	+	0.531558i	−0.957214	−	0.289382i	$-0.906550\pi$
$541$	−8.98278	+	12.3637i	−0.386200	+	0.531558i	0.571014	+	0.820940i	$0.306550\pi$
$542$	−18.9479	−	6.15654i	−0.813881	−	0.264446i
$543$	10.4647	−	8.44549i	0.449083	−	0.362431i
$544$	11.5451	−	8.38800i	0.494991	−	0.359632i
$545$	−1.45309	+	1.05573i	−0.0622433	+	0.0452224i
$546$	−3.54306	+	2.85941i	−0.151629	+	0.122372i
$547$	25.5517	+	8.30224i	1.09251	+	0.354978i	0.799216	−	0.601044i	$-0.205248\pi$
$547$	25.5517	+	8.30224i	1.09251	+	0.354978i	0.293294	+	0.956022i	$0.405248\pi$
$548$	1.71036	−	2.35410i	0.0730628	−	0.100562i
$549$	−5.25731	−	5.87785i	−0.224377	−	0.250861i
$550$		0			0
$551$			6.18034i			0.263291i
$552$	−32.0956	−	8.65697i	−1.36608	−	0.368465i
$553$	−3.78115	+	11.6372i	−0.160791	+	0.494864i
$554$	−18.1356	+	5.89261i	−0.770507	+	0.250353i
$555$	1.08373	−	1.66276i	0.0460017	−	0.0705804i
$556$	5.16312	+	7.10642i	0.218965	+	0.301379i
$557$	0.0857567	+	0.263932i	0.00363363	+	0.0111832i	0.952857	−	0.303420i	$-0.0981285\pi$
$557$	0.0857567	+	0.263932i	0.00363363	+	0.0111832i	−0.949223	+	0.314603i	$0.898129\pi$
$558$	8.33489	+	18.8885i	0.352844	+	0.799614i
$559$	4.04508	+	2.93893i	0.171089	+	0.124303i
$560$	2.80017			0.118329
$561$		0			0
$562$	31.3050			1.32052
$563$	−0.865300	−	0.628677i	−0.0364680	−	0.0264956i	0.569402	−	0.822059i	$-0.307175\pi$
$563$	−0.865300	−	0.628677i	−0.0364680	−	0.0264956i	−0.605870	+	0.795564i	$0.707175\pi$
$564$	0.451734	+	8.90150i	0.0190214	+	0.374821i
$565$	0.242646	+	0.746787i	0.0102082	+	0.0314176i
$566$	−14.7679	−	20.3262i	−0.620740	−	0.854376i
$567$	24.0793	−	13.6904i	1.01124	−	0.574945i
$568$	15.5902	−	5.06555i	0.654149	−	0.212546i
$569$	6.43288	−	19.7984i	0.269680	−	0.829991i	−0.720898	−	0.693042i	$-0.756270\pi$
$569$	6.43288	−	19.7984i	0.269680	−	0.829991i	0.990578	−	0.136949i	$-0.0437298\pi$
$570$	0.532400	−	1.97387i	0.0222998	−	0.0826763i
$571$		−	22.5478i		−	0.943598i	−0.881706	−	0.471799i	$-0.843605\pi$
$571$		−	22.5478i		−	0.943598i	0.881706	−	0.471799i	$-0.156395\pi$
$572$		0			0
$573$	39.2148	−	14.9787i	1.63822	−	0.625745i
$574$	−1.54508	+	2.12663i	−0.0644906	+	0.0887637i
$575$	−28.7890	−	9.35410i	−1.20058	−	0.390093i
$576$	−22.5812	−	13.1371i	−0.940884	−	0.547381i
$577$	6.47214	−	4.70228i	0.269439	−	0.195759i	−0.444859	−	0.895601i	$-0.646746\pi$
$577$	6.47214	−	4.70228i	0.269439	−	0.195759i	0.714298	+	0.699842i	$0.246746\pi$
$578$	−1.03681	+	0.753289i	−0.0431257	+	0.0313327i
$579$	−10.7186	−	13.2813i	−0.445449	−	0.551950i
$580$	−0.527864	−	0.171513i	−0.0219184	−	0.00712171i
$581$	−11.4454	+	15.7533i	−0.474837	+	0.653557i
$582$	3.18368	+	8.33499i	0.131968	+	0.345497i
$583$		0			0
$584$			28.9443i			1.19772i
$585$	−0.828266	+	0.0842829i	−0.0342446	+	0.00348467i
$586$	5.06231	−	15.5802i	0.209122	−	0.643611i
$587$	−11.3597	+	3.69098i	−0.468864	+	0.152343i	−0.533914	−	0.845539i	$-0.679279\pi$
$587$	−11.3597	+	3.69098i	−0.468864	+	0.152343i	0.0650498	+	0.997882i	$0.479279\pi$
$588$	2.21702	+	1.44497i	0.0914282	+	0.0595896i
$589$	9.04508	+	12.4495i	0.372696	+	0.512972i
$590$	−0.0530006	−	0.163119i	−0.00218200	−	0.00671550i
$591$	−14.8981	+	0.756051i	−0.612827	+	0.0310998i
$592$	5.78115	+	4.20025i	0.237604	+	0.172629i
$593$	7.33094			0.301046			0.150523	−	0.988607i	$-0.451904\pi$
$593$	7.33094			0.301046			0.150523	+	0.988607i	$0.451904\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$	−6.51864	−	4.73607i	−0.267014	−	0.193997i
$597$	−3.86801	+	0.196294i	−0.158307	+	0.00803377i
$598$	−1.64590	−	5.06555i	−0.0673058	−	0.207146i
$599$	12.7598	+	17.5623i	0.521350	+	0.717576i	0.985781	−	0.168033i	$-0.0537414\pi$
$599$	12.7598	+	17.5623i	0.521350	+	0.717576i	−0.464432	+	0.885609i	$0.653741\pi$
$600$	−21.6779	−	14.1289i	−0.884997	−	0.576808i
$601$	17.7254	−	5.75934i	0.723035	−	0.234928i	0.0756965	−	0.997131i	$-0.475882\pi$
$601$	17.7254	−	5.75934i	0.723035	−	0.234928i	0.647339	+	0.762203i	$0.275882\pi$
$602$	−7.69421	+	23.6803i	−0.313593	+	0.965139i
$603$	21.8658	−	2.22502i	0.890444	−	0.0906100i
$604$			3.46120i			0.140834i
$605$		0			0
$606$	11.5836	+	30.3262i	0.470551	+	1.23192i
$607$	−21.7705	+	29.9645i	−0.883638	+	1.21622i	0.0917623	+	0.995781i	$0.470750\pi$
$607$	−21.7705	+	29.9645i	−0.883638	+	1.21622i	−0.975400	+	0.220442i	$0.929250\pi$
$608$	−8.38800	−	2.72542i	−0.340178	−	0.110531i
$609$	7.87129	+	9.75320i	0.318961	+	0.395220i
$610$	−0.954915	+	0.693786i	−0.0386634	+	0.0280906i
$611$	−4.89404	+	3.55573i	−0.197992	+	0.143849i
$612$	−6.81636	−	3.96557i	−0.275535	−	0.160299i
$613$	−36.1803	−	11.7557i	−1.46131	−	0.474808i	−0.532840	−	0.846216i	$-0.678875\pi$
$613$	−36.1803	−	11.7557i	−1.46131	−	0.474808i	−0.928470	+	0.371407i	$0.878875\pi$
$614$	6.57164	−	9.04508i	0.265210	−	0.365030i
$615$	−0.449028	+	0.171513i	−0.0181066	+	0.00691609i
$616$		0			0
$617$		−	15.7639i		−	0.634632i	−0.948320	−	0.317316i	$-0.897218\pi$
$617$		−	15.7639i		−	0.634632i	0.948320	−	0.317316i	$-0.102782\pi$
$618$	5.95791	−	22.0889i	0.239662	−	0.888546i
$619$	−4.45492	+	13.7108i	−0.179058	+	0.551084i	−0.999796	−	0.0202213i	$-0.993563\pi$
$619$	−4.45492	+	13.7108i	−0.179058	+	0.551084i	0.820737	+	0.571306i	$0.193563\pi$
$620$	−1.31433	+	0.427051i	−0.0527847	+	0.0171508i
$621$	4.91004	+	32.0294i	0.197033	+	1.28530i
$622$	−3.45492	−	4.75528i	−0.138529	−	0.190669i
$623$	0.502029	+	1.54508i	0.0201133	+	0.0619025i
$624$	−0.151921	−	2.99363i	−0.00608171	−	0.119841i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	12.9313			0.516838
$627$		0			0
$628$	−6.00000			−0.239426
$629$	10.3229	+	7.50000i	0.411600	+	0.299045i
$630$	−1.67374	−	3.79303i	−0.0666834	−	0.151118i
$631$	13.4271	+	41.3242i	0.534522	+	1.64509i	0.744679	+	0.667423i	$0.232603\pi$
$631$	13.4271	+	41.3242i	0.534522	+	1.64509i	−0.210156	+	0.977668i	$0.567397\pi$
$632$	−7.19218	−	9.89919i	−0.286090	−	0.393769i
$633$	−18.4138	+	28.2523i	−0.731884	+	1.12293i
$634$	−4.73607	+	1.53884i	−0.188093	+	0.0611152i
$635$	−1.51860	+	4.67376i	−0.0602637	+	0.185473i
$636$	−1.91627	−	0.516865i	−0.0759851	−	0.0204950i
$637$			1.79611i			0.0711645i
$638$		0			0
$639$	−10.6525	−	11.9098i	−0.421405	−	0.471146i
$640$	−0.791796	+	1.08981i	−0.0312985	+	0.0430787i
$641$	10.6004	+	3.44427i	0.418690	+	0.136041i	0.510783	−	0.859710i	$-0.329356\pi$
$641$	10.6004	+	3.44427i	0.418690	+	0.136041i	−0.0920929	+	0.995750i	$0.529356\pi$
$642$	20.6576	−	16.6717i	0.815291	−	0.657978i
$643$	−15.4443	+	11.2209i	−0.609063	+	0.442510i	−0.849084	−	0.528258i	$-0.822846\pi$
$643$	−15.4443	+	11.2209i	−0.609063	+	0.442510i	0.240021	+	0.970768i	$0.422846\pi$
$644$	−9.59632	+	6.97214i	−0.378148	+	0.274741i
$645$	−3.54306	+	2.85941i	−0.139508	+	0.112589i
$646$	12.5000	+	4.06150i	0.491806	+	0.159797i
$647$	14.7881	−	20.3541i	0.581381	−	0.800202i	−0.412465	−	0.910973i	$-0.635332\pi$
$647$	14.7881	−	20.3541i	0.581381	−	0.800202i	0.993846	+	0.110771i	$0.0353321\pi$
$648$	−3.07768	+	27.5276i	−0.120903	+	1.08139i
$649$		0			0
$650$		−	4.14590i		−	0.162615i
$651$	30.1297	+	8.12672i	1.18088	+	0.318511i
$652$	2.79180	−	8.59226i	0.109335	−	0.336499i
$653$	−39.8056	+	12.9336i	−1.55771	+	0.506132i	−0.956196	−	0.292727i	$-0.905437\pi$
$653$	−39.8056	+	12.9336i	−1.55771	+	0.506132i	−0.601518	+	0.798859i	$0.705437\pi$
$654$	−5.22795	+	8.02124i	−0.204429	+	0.313655i
$655$	−2.33688	−	3.21644i	−0.0913095	−	0.125677i
$656$	−0.534785	−	1.64590i	−0.0208798	−	0.0642615i
$657$	25.8123	−	11.3901i	1.00704	−	0.444372i
$658$	−24.3713	−	17.7068i	−0.950093	−	0.690283i
$659$	−3.59222			−0.139933			−0.0699666	−	0.997549i	$-0.522289\pi$
$659$	−3.59222			−0.139933			−0.0699666	+	0.997549i	$0.522289\pi$
$660$		0			0
$661$	−23.4508			−0.912132			−0.456066	−	0.889946i	$-0.650742\pi$
$661$	−23.4508			−0.912132			−0.456066	+	0.889946i	$0.650742\pi$
$662$	−12.2577	−	8.90576i	−0.476410	−	0.346132i
$663$	−0.271271	−	5.34545i	−0.0105353	−	0.207600i
$664$	−6.01722	−	18.5191i	−0.233513	−	0.718681i
$665$	−1.81636	−	2.50000i	−0.0704353	−	0.0969458i
$666$	2.23398	−	10.3416i	0.0865651	−	0.400729i
$667$	−13.9443	+	4.53077i	−0.539924	+	0.175432i
$668$	−4.02874	+	12.3992i	−0.155877	+	0.479739i
$669$	−0.795633	+	2.94980i	−0.0307610	+	0.114046i
$670$		−	3.28969i		−	0.127092i
$671$		0			0
$672$	−16.7082	+	6.38197i	−0.644533	+	0.246190i
$673$	−6.07953	+	8.36775i	−0.234349	+	0.322553i	−0.909953	−	0.414711i	$-0.863883\pi$
$673$	−6.07953	+	8.36775i	−0.234349	+	0.322553i	0.675605	+	0.737264i	$0.263883\pi$
$674$	28.1482	+	9.14590i	1.08423	+	0.352287i
$675$	−4.06936	+	24.8922i	−0.156630	+	0.958102i
$676$	6.23607	−	4.53077i	0.239849	−	0.174260i
$677$	24.0009	−	17.4377i	0.922431	−	0.670185i	−0.0216973	−	0.999765i	$-0.506907\pi$
$677$	24.0009	−	17.4377i	0.922431	−	0.670185i	0.944128	+	0.329580i	$0.106907\pi$
$678$	2.62880	+	3.25731i	0.100958	+	0.125096i
$679$	12.8262	+	4.16750i	0.492226	+	0.159934i
$680$	−2.93893	+	4.04508i	−0.112703	+	0.155122i
$681$	−8.95554	−	23.4459i	−0.343177	−	0.898449i
$682$		0			0
$683$		−	9.00000i		−	0.344375i	−0.985064	−	0.172188i	$-0.944916\pi$
$683$		−	9.00000i		−	0.344375i	0.985064	−	0.172188i	$-0.0550836\pi$
$684$	0.493401	+	4.84876i	0.0188656	+	0.185397i
$685$	−0.555728	+	1.71036i	−0.0212333	+	0.0653493i
$686$	15.5802	−	5.06231i	0.594854	−	0.193280i
$687$	−21.9467	−	14.3040i	−0.837318	−	0.545733i
$688$	−9.63525	−	13.2618i	−0.367341	−	0.505601i
$689$	−0.416272	−	1.28115i	−0.0158587	−	0.0488080i
$690$	4.84380	−	0.245814i	0.184400	−	0.00935796i
$691$	8.38197	+	6.08985i	0.318865	+	0.231669i	0.735691	−	0.677317i	$-0.236858\pi$
$691$	8.38197	+	6.08985i	0.318865	+	0.231669i	−0.416826	+	0.908986i	$0.636858\pi$
$692$	14.2784			0.542782
$693$		0			0
$694$	8.54102			0.324213
$695$	−4.39201	−	3.19098i	−0.166598	−	0.121041i
$696$	−12.5171	+	0.635220i	−0.474461	+	0.0240780i
$697$	−0.954915	−	2.93893i	−0.0361700	−	0.111320i
$698$	9.39205	+	12.9271i	0.355494	+	0.489296i
$699$	14.0492	+	9.15678i	0.531391	+	0.346341i
$700$	−8.78115	+	2.85317i	−0.331896	+	0.107840i
$701$	4.78804	−	14.7361i	0.180842	−	0.556574i	−0.819010	−	0.573779i	$-0.805477\pi$
$701$	4.78804	−	14.7361i	0.180842	−	0.556574i	0.999852	+	0.0172053i	$0.00547688\pi$
$702$	−3.96428	+	1.99517i	−0.149622	+	0.0753028i
$703$		−	7.88597i		−	0.297425i
$704$		0			0
$705$	−1.96556	−	5.14590i	−0.0740272	−	0.193806i
$706$	23.2148	−	31.9524i	0.873700	−	1.20254i
$707$	46.6673	+	15.1631i	1.75510	+	0.570268i
$708$	0.256791	+	0.318186i	0.00965081	+	0.0119582i
$709$	16.5902	−	12.0535i	0.623057	−	0.452677i	−0.230931	−	0.972970i	$-0.574177\pi$
$709$	16.5902	−	12.0535i	0.623057	−	0.452677i	0.853988	+	0.520293i	$0.174177\pi$
$710$	−1.93487	+	1.40576i	−0.0726143	+	0.0527574i
$711$	−5.99777	+	10.3095i	−0.224934	+	0.386635i
$712$	−1.54508	−	0.502029i	−0.0579045	−	0.0188143i
$713$	−21.4580	+	29.5344i	−0.803609	+	1.10607i
$714$	24.8990	−	9.51057i	0.931821	−	0.355924i
$715$		0			0
$716$			8.61803i			0.322071i
$717$	−3.47965	+	12.9008i	−0.129950	+	0.481789i
$718$	11.5836	−	35.6506i	0.432296	−	1.33047i
$719$	28.6502	−	9.30902i	1.06847	−	0.347168i	0.278580	−	0.960413i	$-0.410136\pi$
$719$	28.6502	−	9.30902i	1.06847	−	0.347168i	0.789893	+	0.613245i	$0.210136\pi$
$720$	2.66795	+	0.576329i	0.0994287	+	0.0214785i
$721$	−20.3262	−	27.9767i	−0.756989	−	1.04191i
$722$	4.39201	+	13.5172i	0.163454	+	0.503059i
$723$	−2.44663	−	48.2114i	−0.0909913	−	1.79300i
$724$	3.88197	+	2.82041i	0.144272	+	0.104820i
$725$	−11.4127			−0.423856
$726$		0			0
$727$	−27.8541			−1.03305			−0.516526	−	0.856272i	$-0.672775\pi$
$727$	−27.8541			−1.03305			−0.516526	+	0.856272i	$0.672775\pi$
$728$	−5.56758	−	4.04508i	−0.206348	−	0.149921i
$729$	25.7601	−	8.08802i	0.954079	−	0.299556i
$730$	−1.30495	−	4.01623i	−0.0482984	−	0.148647i
$731$	−17.2048	−	23.6803i	−0.636342	−	0.875849i
$732$	1.53646	−	2.35738i	0.0567891	−	0.0871314i
$733$	−44.7984	+	14.5559i	−1.65467	+	0.537633i	−0.979744	−	0.200256i	$-0.935823\pi$
$733$	−44.7984	+	14.5559i	−1.65467	+	0.537633i	−0.674922	+	0.737889i	$0.735823\pi$
$734$	8.71078	−	26.8090i	0.321521	−	0.989539i
$735$	−1.57909	−	0.425920i	−0.0582458	−	0.0157103i
$736$		−	20.9232i		−	0.771241i
$737$		0			0
$738$	−1.90983	+	1.70820i	−0.0703018	+	0.0628799i
$739$	−7.98936	+	10.9964i	−0.293893	+	0.404509i	−0.930274	−	0.366866i	$-0.880431\pi$
$739$	−7.98936	+	10.9964i	−0.293893	+	0.404509i	0.636381	+	0.771375i	$0.280431\pi$
$740$	0.673542	+	0.218847i	0.0247599	+	0.00804498i
$741$	−2.57418	+	2.07748i	−0.0945649	+	0.0763183i
$742$	5.42705	−	3.94298i	0.199233	−	0.144751i
$743$	−23.7562	+	17.2599i	−0.871529	+	0.633203i	−0.930997	−	0.365027i	$-0.881060\pi$
$743$	−23.7562	+	17.2599i	−0.871529	+	0.633203i	0.0594676	+	0.998230i	$0.481060\pi$
$744$	−24.2845	+	19.5987i	−0.890312	+	0.718523i
$745$	4.73607	+	1.53884i	0.173516	+	0.0563788i
$746$	−18.9026	+	26.0172i	−0.692074	+	0.952558i
$747$	−14.1473	+	12.6538i	−0.517624	+	0.462977i
$748$		0			0
$749$		−	40.1246i		−	1.46612i
$750$	7.39949	+	1.99582i	0.270191	+	0.0728770i
$751$	−4.50000	+	13.8496i	−0.164207	+	0.505378i	−0.998977	−	0.0452211i	$-0.985601\pi$
$751$	−4.50000	+	13.8496i	−0.164207	+	0.505378i	0.834770	+	0.550599i	$0.185601\pi$
$752$	18.8621	−	6.12868i	0.687831	−	0.223490i
$753$	19.2235	−	29.4945i	0.700542	−	1.07484i
$754$	−1.18034	−	1.62460i	−0.0429854	−	0.0591644i
$755$	−0.661030	−	2.03444i	−0.0240574	−	0.0740409i
$756$	6.95402	+	7.02343i	0.252915	+	0.255440i
$757$	−8.80902	−	6.40013i	−0.320169	−	0.232617i	0.416078	−	0.909329i	$-0.363404\pi$
$757$	−8.80902	−	6.40013i	−0.320169	−	0.232617i	−0.736248	+	0.676712i	$0.763404\pi$
$758$	3.39569			0.123337
$759$		0			0
$760$	3.09017			0.112092
$761$	26.8339	+	19.4959i	0.972726	+	0.706727i	0.956071	−	0.293134i	$-0.0946983\pi$
$761$	26.8339	+	19.4959i	0.972726	+	0.706727i	0.0166551	+	0.999861i	$0.494698\pi$
$762$	1.32772	+	26.1629i	0.0480981	+	0.947783i
$763$	4.47214	+	13.7638i	0.161902	+	0.498284i
$764$	8.80427	+	12.1180i	0.318527	+	0.438415i
$765$	4.76391	+	1.02910i	0.172240	+	0.0372071i
$766$	13.8820	−	4.51052i	0.501576	−	0.162972i
$767$	−0.0857567	+	0.263932i	−0.00309650	+	0.00953003i
$768$	5.98575	−	22.1921i	0.215992	−	0.800789i
$769$			30.7113i			1.10748i	0.832690	+	0.553739i	$0.186800\pi$
$769$			30.7113i			1.10748i	−0.832690	+	0.553739i	$0.813200\pi$
$770$		0			0
$771$	−36.0344	+	13.7639i	−1.29775	+	0.495696i
$772$	3.57953	−	4.92680i	0.128830	−	0.177319i
$773$	43.5896	+	14.1631i	1.56781	+	0.509412i	0.958880	−	0.283813i	$-0.0915994\pi$
$773$	43.5896	+	14.1631i	1.56781	+	0.509412i	0.608929	+	0.793225i	$0.291599\pi$
$774$	−12.2048	+	20.9786i	−0.438692	+	0.754060i
$775$	−22.9894	+	16.7027i	−0.825802	+	0.599980i
$776$	−10.9106	+	7.92705i	−0.391669	+	0.284565i
$777$	−10.0436	−	12.4448i	−0.360311	−	0.446456i
$778$	−8.25329	−	2.68166i	−0.295895	−	0.0961420i
$779$	−1.12257	+	1.54508i	−0.0402202	+	0.0553584i
$780$	−0.106001	−	0.277515i	−0.00379545	−	0.00993661i
$781$		0			0
$782$			31.1803i			1.11501i
$783$	5.49223	+	10.9127i	0.196276	+	0.389989i
$784$	1.81966	−	5.60034i	0.0649879	−	0.200012i
$785$	3.52671	−	1.14590i	0.125874	−	0.0408989i
$786$	−17.7552	−	11.5722i	−0.633308	−	0.412767i
$787$	−1.83282	−	2.52265i	−0.0653328	−	0.0899229i	0.775100	−	0.631838i	$-0.217699\pi$
$787$	−1.83282	−	2.52265i	−0.0653328	−	0.0899229i	−0.840433	+	0.541915i	$0.817699\pi$
$788$	−1.64484	−	5.06231i	−0.0585951	−	0.180337i
$789$	−15.7882	+	0.801220i	−0.562075	+	0.0285242i
$790$	1.44427	+	1.04932i	0.0513849	+	0.0373333i
$791$	6.32688			0.224958
$792$		0			0
$793$	1.90983			0.0678201
$794$	21.8743	+	15.8926i	0.776290	+	0.564008i
$795$	1.22507	−	0.0621699i	0.0434487	−	0.00220494i
$796$	−0.427051	−	1.31433i	−0.0151364	−	0.0465851i
$797$	21.2008	+	29.1803i	0.750969	+	1.03362i	0.997912	+	0.0645905i	$0.0205741\pi$
$797$	21.2008	+	29.1803i	0.750969	+	1.03362i	−0.246942	+	0.969030i	$0.579426\pi$
$798$	−13.8004	−	8.99458i	−0.488528	−	0.318405i
$799$	33.6803	−	10.9434i	1.19152	−	0.387150i
$800$	5.03280	−	15.4894i	0.177936	−	0.547631i
$801$	0.160316	+	1.57546i	0.00566447	+	0.0556660i
$802$			32.7445i			1.15625i
$803$		0			0
$804$	2.79837	+	7.32624i	0.0986910	+	0.258376i
$805$	4.30902	−	5.93085i	0.151873	−	0.209035i
$806$	−4.75528	−	1.54508i	−0.167498	−	0.0544233i
$807$	−20.4111	−	25.2911i	−0.718506	−	0.890290i
$808$	−39.6976	+	28.8420i	−1.39656	+	1.01466i
$809$	−17.3435	+	12.6008i	−0.609766	+	0.443021i	−0.849332	−	0.527859i	$-0.822995\pi$
$809$	−17.3435	+	12.6008i	−0.609766	+	0.443021i	0.239566	+	0.970880i	$0.422995\pi$
$810$	−0.814032	−	3.95842i	−0.0286022	−	0.139085i
$811$	19.8992	+	6.46564i	0.698755	+	0.227039i	0.636788	−	0.771039i	$-0.280263\pi$
$811$	19.8992	+	6.46564i	0.698755	+	0.227039i	0.0619670	+	0.998078i	$0.480263\pi$
$812$	−2.62866	+	3.61803i	−0.0922477	+	0.126968i
$813$	−27.4216	+	10.4741i	−0.961719	+	0.367344i
$814$		0			0
$815$			5.58359i			0.195585i
$816$	−4.56970	+	16.9421i	−0.159972	+	0.593093i
$817$	−5.59017	+	17.2048i	−0.195575	+	0.601919i
$818$	−23.6579	+	7.68692i	−0.827179	+	0.268767i
$819$	−1.41643	+	6.55696i	−0.0494940	+	0.229119i
$820$	−0.100813	−	0.138757i	−0.00352054	−	0.00484561i
$821$	14.3718	+	44.2320i	0.501581	+	1.54371i	0.806443	+	0.591311i	$0.201389\pi$
$821$	14.3718	+	44.2320i	0.501581	+	1.54371i	−0.304863	+	0.952396i	$0.598611\pi$
$822$	0.485876	+	9.57428i	0.0169469	+	0.333941i
$823$	−21.1353	−	15.3557i	−0.736729	−	0.535265i	0.154956	−	0.987921i	$-0.450476\pi$
$823$	−21.1353	−	15.3557i	−0.736729	−	0.535265i	−0.891685	+	0.452657i	$0.850476\pi$
$824$	34.5811			1.20469
$825$		0			0
$826$	−1.38197			−0.0480847
$827$	21.0948	+	15.3262i	0.733537	+	0.532946i	0.890680	−	0.454630i	$-0.150229\pi$
$827$	21.0948	+	15.3262i	0.733537	+	0.532946i	−0.157144	+	0.987576i	$0.550229\pi$
$828$	−10.5782	+	4.66782i	−0.367618	+	0.162218i
$829$	−1.62868	−	5.01255i	−0.0565663	−	0.174093i	0.918781	−	0.394767i	$-0.129175\pi$
$829$	−1.62868	−	5.01255i	−0.0565663	−	0.174093i	−0.975348	+	0.220673i	$0.929175\pi$
$830$	1.66987	+	2.29837i	0.0579619	+	0.0797777i
$831$	−15.3409	+	23.5375i	−0.532170	+	0.816508i
$832$	6.01722	−	1.95511i	0.208610	−	0.0677814i
$833$	3.24920	−	10.0000i	0.112578	−	0.346479i
$834$	−27.9409	−	7.53634i	−0.967515	−	0.260962i
$835$		−	8.05748i		−	0.278841i
$836$		0			0
$837$	27.0344	+	13.9443i	0.934447	+	0.481985i
$838$	−0.590170	+	0.812299i	−0.0203871	+	0.0280604i
$839$	−1.57160	−	0.510643i	−0.0542576	−	0.0176294i	0.281762	−	0.959484i	$-0.409081\pi$
$839$	−1.57160	−	0.510643i	−0.0542576	−	0.0176294i	−0.336020	+	0.941855i	$0.609081\pi$
$840$	4.87660	−	3.93564i	0.168259	−	0.135793i
$841$	18.9894	−	13.7966i	0.654805	−	0.475744i
$842$	−18.2088	+	13.2295i	−0.627518	+	0.455918i
$843$	35.8929	−	28.9673i	1.23622	−	0.997686i
$844$	−11.4443	−	3.71847i	−0.393928	−	0.127995i
$845$	−2.80017	+	3.85410i	−0.0963287	+	0.132585i
$846$	−19.5762	−	21.8868i	−0.673042	−	0.752484i
$847$		0			0
$848$			4.41641i			0.151660i
$849$	−35.7406	−	9.64010i	−1.22661	−	0.330847i
$850$	−7.50000	+	23.0826i	−0.257248	+	0.791728i
$851$	17.7926	−	5.78115i	0.609921	−	0.198175i
$852$	3.11320	−	4.77658i	0.106657	−	0.163643i
$853$	0.551663	+	0.759299i	0.0188886	+	0.0259979i	0.818357	−	0.574710i	$-0.194885\pi$
$853$	0.551663	+	0.759299i	0.0188886	+	0.0259979i	−0.799468	+	0.600708i	$0.794885\pi$
$854$	2.93893	+	9.04508i	0.100568	+	0.309516i
$855$	−1.21604	−	2.75580i	−0.0415878	−	0.0942462i
$856$	32.4615	+	23.5847i	1.10951	+	0.806107i
$857$	34.9646			1.19437			0.597184	−	0.802105i	$-0.296286\pi$
$857$	34.9646			1.19437			0.597184	+	0.802105i	$0.296286\pi$
$858$		0			0
$859$	43.4721			1.48325			0.741625	−	0.670815i	$-0.234055\pi$
$859$	43.4721			1.48325			0.741625	+	0.670815i	$0.234055\pi$
$860$	−1.31433	−	0.954915i	−0.0448182	−	0.0325623i
$861$	0.196294	+	3.86801i	0.00668967	+	0.131821i
$862$	−2.19756	−	6.76340i	−0.0748492	−	0.230362i
$863$	−0.661030	−	0.909830i	−0.0225017	−	0.0309710i	0.797618	−	0.603163i	$-0.206093\pi$
$863$	−0.661030	−	0.909830i	−0.0225017	−	0.0309710i	−0.820120	+	0.572192i	$0.806093\pi$
$864$	−17.2328	+	2.64175i	−0.586272	+	0.0898743i
$865$	−8.39261	+	2.72692i	−0.285357	+	0.0927182i
$866$	−2.17963	+	6.70820i	−0.0740668	+	0.227954i
$867$	−0.491728	+	1.82308i	−0.0167000	+	0.0619150i
$868$			11.1352i			0.377952i
$869$		0			0
$870$	1.70820	−	0.652476i	0.0579135	−	0.0221210i
$871$	−3.12868	+	4.30625i	−0.106011	+	0.145912i
$872$	−13.7638	−	4.47214i	−0.466102	−	0.151446i
$873$	11.3629	+	6.61060i	0.384575	+	0.223735i
$874$	15.5902	−	11.3269i	0.527345	−	0.383139i
$875$	9.37181	−	6.80902i	0.316825	−	0.230187i
$876$	6.32258	+	7.83421i	0.213620	+	0.264694i
$877$	32.7254	+	10.6331i	1.10506	+	0.359055i	0.804048	−	0.594565i	$-0.202676\pi$
$877$	32.7254	+	10.6331i	1.10506	+	0.359055i	0.301012	+	0.953620i	$0.402676\pi$
$878$	1.88960	−	2.60081i	0.0637710	−	0.0877732i
$879$	−8.61251	−	22.5478i	−0.290493	−	0.760520i
$880$		0			0
$881$		−	29.9230i		−	1.00813i	−0.863665	−	0.504066i	$-0.831837\pi$
$881$		−	29.9230i		−	1.00813i	0.863665	−	0.504066i	$-0.168163\pi$
$882$	−8.67372	+	0.882622i	−0.292059	+	0.0297194i
$883$	−12.4164	+	38.2138i	−0.417845	+	1.28600i	0.491836	+	0.870688i	$0.336326\pi$
$883$	−12.4164	+	38.2138i	−0.417845	+	1.28600i	−0.909681	+	0.415308i	$0.863674\pi$
$884$	1.81636	−	0.590170i	0.0610907	−	0.0198496i
$885$	−0.211706	−	0.137982i	−0.00711643	−	0.00463823i
$886$	1.05573	+	1.45309i	0.0354679	+	0.0488173i
$887$	−4.30625	−	13.2533i	−0.144590	−	0.445002i	0.852368	−	0.522942i	$-0.175166\pi$
$887$	−4.30625	−	13.2533i	−0.144590	−	0.445002i	−0.996958	+	0.0779403i	$0.975166\pi$
$888$	15.9716	−	0.810526i	0.535970	−	0.0271995i
$889$	32.0344	+	23.2744i	1.07440	+	0.780598i
$890$	0.237026			0.00794512
$891$		0			0
$892$	−1.09017			−0.0365016
$893$	−17.7068	−	12.8647i	−0.592536	−	0.430502i
$894$	26.5117	−	1.34542i	0.886684	−	0.0449975i
$895$	−1.64590	−	5.06555i	−0.0550163	−	0.169323i
$896$	6.37988	+	8.78115i	0.213137	+	0.293358i
$897$	−6.57440	−	4.28496i	−0.219513	−	0.143070i
$898$	−31.1803	+	10.1311i	−1.04050	+	0.338079i
$899$	−4.25325	+	13.0902i	−0.141854	+	0.436582i
$900$	−8.95376	+	0.911119i	−0.298459	+	0.0303706i
$901$			7.88597i			0.262720i
$902$		0			0
$903$	13.0902	+	34.2705i	0.435614	+	1.14045i
$904$	−3.71885	+	5.11855i	−0.123687	+	0.170241i
$905$	−2.82041	−	0.916408i	−0.0937537	−	0.0304624i
$906$	−7.16153	−	8.87375i	−0.237926	−	0.294811i
$907$	25.3992	−	18.4536i	0.843366	−	0.612741i	−0.0799428	−	0.996799i	$-0.525474\pi$
$907$	25.3992	−	18.4536i	0.843366	−	0.612741i	0.923309	+	0.384058i	$0.125474\pi$
$908$	7.24518	−	5.26393i	0.240440	−	0.174690i
$909$	41.3429	+	24.0522i	1.37126	+	0.797760i
$910$	0.954915	+	0.310271i	0.0316551	+	0.0102854i
$911$	−18.6453	+	25.6631i	−0.617748	+	0.850257i	−0.997187	−	0.0749598i	$-0.976117\pi$
$911$	−18.6453	+	25.6631i	−0.617748	+	0.850257i	0.379439	+	0.925217i	$0.376117\pi$
$912$	10.1311	−	3.86974i	0.335474	−	0.128140i
$913$		0			0
$914$			29.4721i			0.974852i
$915$	−0.452886	+	1.67907i	−0.0149720	+	0.0555084i
$916$	2.88854	−	8.89002i	0.0954402	−	0.293735i
$917$	−30.4666	+	9.89919i	−1.00609	+	0.326900i
$918$	25.6808	−	3.93681i	0.847591	−	0.129934i
$919$	27.2599	+	37.5200i	0.899220	+	1.23767i	0.970716	+	0.240229i	$0.0772226\pi$
$919$	27.2599	+	37.5200i	0.899220	+	1.23767i	−0.0714961	+	0.997441i	$0.522777\pi$
$920$	2.26538	+	6.97214i	0.0746875	+	0.229865i
$921$	−0.834887	−	16.4516i	−0.0275105	−	0.542099i
$922$	29.2082	+	21.2210i	0.961921	+	0.698876i
$923$	3.86974			0.127374
$924$		0			0
$925$	14.5623			0.478806
$926$	−31.6421	−	22.9894i	−1.03983	−	0.755477i
$927$	−13.6083	−	30.8392i	−0.446957	−	1.01289i
$928$	−2.43769	−	7.50245i	−0.0800212	−	0.246280i
$929$	−18.9884	−	26.1353i	−0.622988	−	0.857470i	0.374578	−	0.927195i	$-0.377788\pi$
$929$	−18.9884	−	26.1353i	−0.622988	−	0.857470i	−0.997566	+	0.0697256i	$0.977788\pi$
$930$	2.48604	−	3.81433i	0.0815205	−	0.125077i
$931$	−6.18034	+	2.00811i	−0.202552	+	0.0658133i
$932$	−1.84911	+	5.69098i	−0.0605697	+	0.186414i
$933$	−8.36144	−	2.25528i	−0.273741	−	0.0738346i
$934$		−	8.99602i		−	0.294359i
$935$		0			0
$936$	−4.47214	−	5.00000i	−0.146176	−	0.163430i
$937$	21.4828	−	29.5685i	0.701812	−	0.965961i	−0.298123	−	0.954528i	$-0.596361\pi$
$937$	21.4828	−	29.5685i	0.701812	−	0.965961i	0.999935	−	0.0114336i	$-0.00363949\pi$
$938$	−25.2093	−	8.19098i	−0.823111	−	0.267445i
$939$	14.8264	−	11.9656i	0.483843	−	0.390484i
$940$	1.59017	−	1.15533i	0.0518656	−	0.0376826i
$941$	28.9605	−	21.0410i	0.944085	−	0.685918i	−0.00531578	−	0.999986i	$-0.501692\pi$
$941$	28.9605	−	21.0410i	0.944085	−	0.685918i	0.949400	+	0.314068i	$0.101692\pi$
$942$	15.3827	−	12.4145i	0.501195	−	0.404488i
$943$	−4.30902	−	1.40008i	−0.140321	−	0.0455930i
$944$	0.534785	−	0.736068i	0.0174058	−	0.0239570i
$945$	−5.42882	−	2.80017i	−0.176600	−	0.0910895i
$946$		0			0
$947$		−	17.1459i		−	0.557167i	−0.960412	−	0.278583i	$-0.910135\pi$
$947$		−	17.1459i		−	0.557167i	0.960412	−	0.278583i	$-0.0898649\pi$
$948$	−4.10905	−	1.10831i	−0.133456	−	0.0359962i
$949$	−2.11146	+	6.49839i	−0.0685408	+	0.210947i
$950$	14.2658	−	4.63525i	0.462845	−	0.150388i
$951$	−4.00624	+	6.14677i	−0.129911	+	0.199323i
$952$	23.6803	+	32.5932i	0.767484	+	1.05635i
$953$	1.24108	+	3.81966i	0.0402026	+	0.123731i	0.969144	−	0.246497i	$-0.0792796\pi$
$953$	1.24108	+	3.81966i	0.0402026	+	0.123731i	−0.928941	+	0.370228i	$0.879280\pi$
$954$	5.98234	−	2.63981i	0.193685	−	0.0854671i
$955$	−7.48936	−	5.44134i	−0.242350	−	0.176078i
$956$	−4.76779			−0.154201
$957$		0			0
$958$	−23.5410			−0.760576
$959$	11.7229	+	8.51722i	0.378554	+	0.275035i
$960$	0.291995	+	5.75381i	0.00942409	+	0.185703i
$961$	1.01064	+	3.11044i	0.0326014	+	0.100337i
$962$	1.50609	+	2.07295i	0.0485581	+	0.0668346i
$963$	8.25842	−	38.2300i	0.266124	−	1.23194i
$964$	16.3820	−	5.32282i	0.527628	−	0.171437i
$965$	−1.16306	+	3.57953i	−0.0374402	+	0.115229i
$966$	10.1769	−	37.7307i	0.327436	−	1.21396i
$967$		−	12.9313i		−	0.415842i	−0.978146	−	0.207921i	$-0.933330\pi$
$967$		−	12.9313i		−	0.415842i	0.978146	−	0.207921i	$-0.0666697\pi$
$968$		0			0
$969$	18.0902	−	6.90983i	0.581140	−	0.221976i
$970$	1.15654	−	1.59184i	0.0371343	−	0.0511110i
$971$	−7.77997	−	2.52786i	−0.249671	−	0.0811230i	0.181508	−	0.983389i	$-0.441902\pi$
$971$	−7.77997	−	2.52786i	−0.249671	−	0.0811230i	−0.431179	+	0.902266i	$0.641902\pi$
$972$	5.18011	+	8.12307i	0.166152	+	0.260548i
$973$	−35.3885	+	25.7113i	−1.13450	+	0.824266i
$974$	−1.40008	+	1.01722i	−0.0448616	+	0.0325939i
$975$	−3.83630	−	4.75351i	−0.122860	−	0.152234i
$976$	−5.95492	−	1.93487i	−0.190612	−	0.0619337i
$977$	20.0175	−	27.5517i	0.640415	−	0.881456i	−0.358223	−	0.933636i	$-0.616617\pi$
$977$	20.0175	−	27.5517i	0.640415	−	0.881456i	0.998638	+	0.0521804i	$0.0166171\pi$
$978$	10.6206	+	27.8052i	0.339610	+	0.889111i
$979$		0			0
$980$		−	0.583592i		−	0.0186422i
$981$	1.42811	+	14.0344i	0.0455961	+	0.448083i
$982$	−6.42047	+	19.7602i	−0.204886	+	0.630573i
$983$	54.5002	−	17.7082i	1.73829	−	0.564804i	0.743682	−	0.668533i	$-0.233078\pi$
$983$	54.5002	−	17.7082i	1.73829	−	0.564804i	0.994606	+	0.103729i	$0.0330775\pi$
$984$	−3.24466	−	2.11475i	−0.103436	−	0.0674158i
$985$	1.93363	+	2.66141i	0.0616105	+	0.0847996i
$986$	3.63271	+	11.1803i	0.115689	+	0.356055i
$987$	−44.3277	+	2.24954i	−1.41097	+	0.0716037i
$988$	−0.954915	−	0.693786i	−0.0303799	−	0.0220723i
$989$	−42.9161			−1.36465
$990$		0			0
$991$	−12.5623			−0.399055			−0.199527	−	0.979892i	$-0.563941\pi$
$991$	−12.5623			−0.399055			−0.199527	+	0.979892i	$0.563941\pi$
$992$	−15.8904	−	11.5451i	−0.504522	−	0.366557i
$993$	−22.2949	+	1.13142i	−0.707508	+	0.0359047i
$994$	5.95492	+	18.3273i	0.188878	+	0.581308i
$995$	0.502029	+	0.690983i	0.0159154	+	0.0219056i
$996$	−5.67396	−	3.69808i	−0.179786	−	0.117178i
$997$	−14.0066	+	4.55101i	−0.443593	+	0.144132i	−0.522293	−	0.852766i	$-0.674923\pi$
$997$	−14.0066	+	4.55101i	−0.443593	+	0.144132i	0.0786999	+	0.996898i	$0.474923\pi$
$998$	−13.0700	+	40.2254i	−0.413725	+	1.27331i
$999$	−7.00795	−	13.9244i	−0.221722	−	0.440548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.b.161.1		8
3.2	odd	2	inner	363.2.f.b.161.2		8
11.2	odd	10		363.2.f.e.215.1		8
11.3	even	5		33.2.f.a.8.1	✓	8
11.4	even	5		363.2.f.e.233.2		8
11.5	even	5		363.2.d.f.362.5		8
11.6	odd	10		363.2.d.f.362.3		8
11.7	odd	10		363.2.f.d.233.1		8
11.8	odd	10	inner	363.2.f.b.239.2		8
11.9	even	5		363.2.f.d.215.2		8
11.10	odd	2		33.2.f.a.29.2	yes	8
33.2	even	10		363.2.f.e.215.2		8
33.5	odd	10		363.2.d.f.362.4		8
33.8	even	10	inner	363.2.f.b.239.1		8
33.14	odd	10		33.2.f.a.8.2	yes	8
33.17	even	10		363.2.d.f.362.6		8
33.20	odd	10		363.2.f.d.215.1		8
33.26	odd	10		363.2.f.e.233.1		8
33.29	even	10		363.2.f.d.233.2		8
33.32	even	2		33.2.f.a.29.1	yes	8
44.3	odd	10		528.2.bn.c.305.1		8
44.43	even	2		528.2.bn.c.161.2		8
55.3	odd	20		825.2.bs.d.74.2		8
55.14	even	10		825.2.bi.b.701.2		8
55.32	even	4		825.2.bs.a.524.2		8
55.43	even	4		825.2.bs.d.524.1		8
55.47	odd	20		825.2.bs.a.74.1		8
55.54	odd	2		825.2.bi.b.326.1		8
99.14	odd	30		891.2.u.a.107.2		16
99.25	even	15		891.2.u.a.701.2		16
99.32	even	6		891.2.u.a.755.2		16
99.43	odd	6		891.2.u.a.458.2		16
99.47	odd	30		891.2.u.a.701.1		16
99.58	even	15		891.2.u.a.107.1		16
99.65	even	6		891.2.u.a.458.1		16
99.76	odd	6		891.2.u.a.755.1		16
132.47	even	10		528.2.bn.c.305.2		8
132.131	odd	2		528.2.bn.c.161.1		8
165.14	odd	10		825.2.bi.b.701.1		8
165.32	odd	4		825.2.bs.d.524.2		8
165.47	even	20		825.2.bs.d.74.1		8
165.98	odd	4		825.2.bs.a.524.1		8
165.113	even	20		825.2.bs.a.74.2		8
165.164	even	2		825.2.bi.b.326.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.8.1	✓	8	11.3	even	5
33.2.f.a.8.2	yes	8	33.14	odd	10
33.2.f.a.29.1	yes	8	33.32	even	2
33.2.f.a.29.2	yes	8	11.10	odd	2
363.2.d.f.362.3		8	11.6	odd	10
363.2.d.f.362.4		8	33.5	odd	10
363.2.d.f.362.5		8	11.5	even	5
363.2.d.f.362.6		8	33.17	even	10
363.2.f.b.161.1		8	1.1	even	1	trivial
363.2.f.b.161.2		8	3.2	odd	2	inner
363.2.f.b.239.1		8	33.8	even	10	inner
363.2.f.b.239.2		8	11.8	odd	10	inner
363.2.f.d.215.1		8	33.20	odd	10
363.2.f.d.215.2		8	11.9	even	5
363.2.f.d.233.1		8	11.7	odd	10
363.2.f.d.233.2		8	33.29	even	10
363.2.f.e.215.1		8	11.2	odd	10
363.2.f.e.215.2		8	33.2	even	10
363.2.f.e.233.1		8	33.26	odd	10
363.2.f.e.233.2		8	11.4	even	5
528.2.bn.c.161.1		8	132.131	odd	2
528.2.bn.c.161.2		8	44.43	even	2
528.2.bn.c.305.1		8	44.3	odd	10
528.2.bn.c.305.2		8	132.47	even	10
825.2.bi.b.326.1		8	55.54	odd	2
825.2.bi.b.326.2		8	165.164	even	2
825.2.bi.b.701.1		8	165.14	odd	10
825.2.bi.b.701.2		8	55.14	even	10
825.2.bs.a.74.1		8	55.47	odd	20
825.2.bs.a.74.2		8	165.113	even	20
825.2.bs.a.524.1		8	165.98	odd	4
825.2.bs.a.524.2		8	55.32	even	4
825.2.bs.d.74.1		8	165.47	even	20
825.2.bs.d.74.2		8	55.3	odd	20
825.2.bs.d.524.1		8	55.43	even	4
825.2.bs.d.524.2		8	165.32	odd	4
891.2.u.a.107.1		16	99.58	even	15
891.2.u.a.107.2		16	99.14	odd	30
891.2.u.a.458.1		16	99.65	even	6
891.2.u.a.458.2		16	99.43	odd	6
891.2.u.a.701.1		16	99.47	odd	30
891.2.u.a.701.2		16	99.25	even	15
891.2.u.a.755.1		16	99.76	odd	6
891.2.u.a.755.2		16	99.32	even	6

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.690983i) q^{2} +(-1.72982 + 0.0877853i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.224514 + 0.309017i) q^{5} +(1.70582 + 1.11179i) q^{6} +(2.92705 - 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(2.98459 - 0.303706i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.690983i) q^{2} +(-1.72982 + 0.0877853i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.224514 + 0.309017i) q^{5} +(1.70582 + 1.11179i) q^{6} +(2.92705 - 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(2.98459 - 0.303706i) q^{9} -0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +(-0.427051 + 0.587785i) q^{13} +(-3.44095 - 1.11803i) q^{14} +(-0.415497 - 0.514836i) q^{15} +(1.92705 - 1.40008i) q^{16} +(3.44095 - 2.50000i) q^{17} +(-3.04837 - 1.77346i) q^{18} +(-2.50000 - 0.812299i) q^{19} +(0.138757 - 0.190983i) q^{20} +(-4.97980 + 1.90211i) q^{21} -6.23607i q^{23} +(1.38821 - 5.14677i) q^{24} +(1.50000 - 4.61653i) q^{25} +(0.812299 - 0.263932i) q^{26} +(-5.13615 + 0.787361i) q^{27} +(-1.11803 - 1.53884i) q^{28} +(-0.726543 - 2.23607i) q^{29} +(0.0394180 + 0.776740i) q^{30} +(-4.73607 - 3.44095i) q^{31} +3.35520 q^{32} -5.00000 q^{34} +(0.951057 + 0.690983i) q^{35} +(-0.748520 - 1.69629i) q^{36} +(0.927051 + 2.85317i) q^{37} +(1.81636 + 2.50000i) q^{38} +(0.687124 - 1.05425i) q^{39} +(-1.11803 + 0.363271i) q^{40} +(0.224514 - 0.690983i) q^{41} +(6.05040 + 1.63194i) q^{42} -6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +(-4.30902 + 5.93085i) q^{46} +(7.91872 + 2.57295i) q^{47} +(-3.21055 + 2.59107i) q^{48} +(2.00000 - 1.45309i) q^{49} +(-4.61653 + 3.35410i) q^{50} +(-5.73279 + 4.62663i) q^{51} +(0.427051 + 0.138757i) q^{52} +(-1.08981 + 1.50000i) q^{53} +(5.42882 + 2.80017i) q^{54} +9.47214i q^{56} +(4.39587 + 1.18567i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(0.363271 - 0.118034i) q^{59} +(-0.223260 + 0.342548i) q^{60} +(-1.54508 - 2.12663i) q^{61} +(2.12663 + 6.54508i) q^{62} +(8.44720 - 3.72747i) q^{63} +(-7.04508 - 5.11855i) q^{64} -0.277515 q^{65} +7.32624 q^{67} +(-2.12663 - 1.54508i) q^{68} +(0.547435 + 10.7873i) q^{69} +(-0.427051 - 1.31433i) q^{70} +(-3.13068 - 4.30902i) q^{71} +(-1.94955 + 9.02488i) q^{72} +(8.94427 - 2.90617i) q^{73} +(1.08981 - 3.35410i) q^{74} +(-2.18947 + 8.11746i) q^{75} +1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +(-2.33688 + 3.21644i) q^{79} +(0.865300 + 0.281153i) q^{80} +(8.81553 - 1.81288i) q^{81} +(-0.690983 + 0.502029i) q^{82} +(-5.11855 + 3.71885i) q^{83} +(2.06909 + 2.56378i) q^{84} +(1.54508 + 0.502029i) q^{85} +(-4.75528 + 6.54508i) q^{86} +(1.45309 + 3.80423i) q^{87} +0.527864i q^{89} +(-0.136373 - 1.34016i) q^{90} +(-0.690983 + 2.12663i) q^{91} +(-3.66547 + 1.19098i) q^{92} +(8.49463 + 5.53649i) q^{93} +(-5.75329 - 7.91872i) q^{94} +(-0.310271 - 0.954915i) q^{95} +(-5.80390 + 0.294537i) q^{96} +(3.54508 + 2.57565i) q^{97} -2.90617 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	\( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} + 12 q^{12} + 10 q^{13} - 6 q^{15} + 2 q^{16} - 20 q^{19} + 10 q^{24} + 12 q^{25} - 12 q^{27} + 20 q^{30} - 20 q^{31} - 40 q^{34} - 10 q^{36} - 6 q^{37} - 20 q^{39} + 20 q^{42} + 24 q^{45} - 30 q^{46} + 26 q^{48} + 16 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} + 20 q^{58} + 2 q^{60} + 10 q^{61} + 30 q^{63} - 34 q^{64} - 4 q^{67} - 16 q^{69} + 10 q^{70} + 20 q^{72} + 6 q^{75} - 20 q^{78} - 50 q^{79} - 2 q^{81} - 10 q^{82} - 10 q^{85} - 40 q^{90} - 10 q^{91} + 10 q^{93} + 30 q^{94} - 10 q^{96} + 6 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 + 12 * q^12 + 10 * q^13 - 6 * q^15 + 2 * q^16 - 20 * q^19 + 10 * q^24 + 12 * q^25 - 12 * q^27 + 20 * q^30 - 20 * q^31 - 40 * q^34 - 10 * q^36 - 6 * q^37 - 20 * q^39 + 20 * q^42 + 24 * q^45 - 30 * q^46 + 26 * q^48 + 16 * q^49 - 30 * q^51 - 10 * q^52 + 30 * q^57 + 20 * q^58 + 2 * q^60 + 10 * q^61 + 30 * q^63 - 34 * q^64 - 4 * q^67 - 16 * q^69 + 10 * q^70 + 20 * q^72 + 6 * q^75 - 20 * q^78 - 50 * q^79 - 2 * q^81 - 10 * q^82 - 10 * q^85 - 40 * q^90 - 10 * q^91 + 10 * q^93 + 30 * q^94 - 10 * q^96 + 6 * q^97

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