LMFDB - Embedded newform 33.2.f.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,2,Mod(2,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("33.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	33.f (of order $10$, 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:	$0.263506326670$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	33.29
Dual form			33.2.f.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.690983i) q^{2} +(1.34786 + 1.08779i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-0.224514 - 0.309017i) q^{5} +(-0.530249 - 1.96589i) q^{6} +(-2.92705 + 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(0.633446 + 2.93236i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.690983i) q^{2} +(1.34786 + 1.08779i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-0.224514 - 0.309017i) q^{5} +(-0.530249 - 1.96589i) q^{6} +(-2.92705 + 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(0.633446 + 2.93236i) q^{9} +0.449028i q^{10} +(-1.31433 - 3.04508i) q^{11} +(0.381966 - 1.00000i) q^{12} +(0.427051 - 0.587785i) q^{13} +(3.44095 + 1.11803i) q^{14} +(0.0335310 - 0.660734i) q^{15} +(1.92705 - 1.40008i) q^{16} +(3.44095 - 2.50000i) q^{17} +(1.42377 - 3.22654i) q^{18} +(2.50000 + 0.812299i) q^{19} +(-0.138757 + 0.190983i) q^{20} +(-4.97980 - 1.90211i) q^{21} +(-0.854102 + 3.80423i) q^{22} +6.23607i q^{23} +(-4.46589 + 2.91071i) q^{24} +(1.50000 - 4.61653i) q^{25} +(-0.812299 + 0.263932i) q^{26} +(-2.33598 + 4.64146i) q^{27} +(1.11803 + 1.53884i) q^{28} +(-0.726543 - 2.23607i) q^{29} +(-0.488446 + 0.605226i) q^{30} +(-4.73607 - 3.44095i) q^{31} +3.35520 q^{32} +(1.54087 - 5.53405i) q^{33} -5.00000 q^{34} +(0.951057 + 0.690983i) q^{35} +(1.60262 - 0.932362i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-1.81636 - 2.50000i) q^{38} +(1.21499 - 0.327712i) q^{39} +(1.11803 - 0.363271i) q^{40} +(0.224514 - 0.690983i) q^{41} +(3.42174 + 5.24997i) q^{42} +6.88191i q^{43} +(-1.53884 + 1.35410i) q^{44} +(0.763932 - 0.854102i) q^{45} +(4.30902 - 5.93085i) q^{46} +(-7.91872 - 2.57295i) q^{47} +(4.12038 + 0.209101i) q^{48} +(2.00000 - 1.45309i) q^{49} +(-4.61653 + 3.35410i) q^{50} +(7.35738 + 0.373373i) q^{51} +(-0.427051 - 0.138757i) q^{52} +(1.08981 - 1.50000i) q^{53} +(5.42882 - 2.80017i) q^{54} +(-0.645898 + 1.08981i) q^{55} -9.47214i q^{56} +(2.48604 + 3.81433i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(-0.363271 + 0.118034i) q^{59} +(-0.394774 + 0.106480i) q^{60} +(1.54508 + 2.12663i) q^{61} +(2.12663 + 6.54508i) q^{62} +(-4.64297 - 7.98073i) q^{63} +(-7.04508 - 5.11855i) q^{64} -0.277515 q^{65} +(-5.28939 + 4.19848i) q^{66} +7.32624 q^{67} +(-2.12663 - 1.54508i) q^{68} +(-6.78350 + 8.40534i) q^{69} +(-0.427051 - 1.31433i) q^{70} +(3.13068 + 4.30902i) q^{71} +(-9.18562 - 0.934712i) q^{72} +(-8.94427 + 2.90617i) q^{73} +(1.08981 - 3.35410i) q^{74} +(7.04358 - 4.59075i) q^{75} -1.62460i q^{76} +(6.74315 + 7.66312i) q^{77} +(-1.38197 - 0.527864i) q^{78} +(2.33688 - 3.21644i) q^{79} +(-0.865300 - 0.281153i) q^{80} +(-8.19749 + 3.71499i) q^{81} +(-0.690983 + 0.502029i) q^{82} +(-5.11855 + 3.71885i) q^{83} +(-0.166977 + 3.29032i) q^{84} +(-1.54508 - 0.502029i) q^{85} +(4.75528 - 6.54508i) q^{86} +(1.45309 - 3.80423i) q^{87} +(10.1631 - 0.951057i) q^{88} -0.527864i q^{89} +(-1.31671 + 0.284435i) q^{90} +(-0.690983 + 2.12663i) q^{91} +(3.66547 - 1.19098i) q^{92} +(-2.64053 - 9.78975i) q^{93} +(5.75329 + 7.91872i) q^{94} +(-0.310271 - 0.954915i) q^{95} +(4.52233 + 3.64973i) q^{96} +(3.54508 + 2.57565i) q^{97} -2.90617 q^{98} +(8.09673 - 5.78298i) q^{99} +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} + 20 q^{22} - 10 q^{24} + 12 q^{25} - 12 q^{27} - 20 q^{30} - 20 q^{31} - 4 q^{33} - 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} - 32 q^{55} - 30 q^{57} + 20 q^{58} + 2 q^{60} - 10 q^{61} - 30 q^{63} - 34 q^{64} - 30 q^{66} - 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} + 50 q^{88} + 40 q^{90} - 10 q^{91} + 10 q^{93} - 30 q^{94} + 10 q^{96} + 6 q^{97} + 16 q^{99}+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 + 20 * q^22 - 10 * q^24 + 12 * q^25 - 12 * q^27 - 20 * q^30 - 20 * q^31 - 4 * q^33 - 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 - 32 * q^55 - 30 * q^57 + 20 * q^58 + 2 * q^60 - 10 * q^61 - 30 * q^63 - 34 * q^64 - 30 * q^66 - 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 + 50 * q^88 + 40 * q^90 - 10 * q^91 + 10 * q^93 - 30 * q^94 + 10 * q^96 + 6 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.951057	−	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	$0.836438\pi$
$3$	1.34786	+	1.08779i	0.778187	+	0.628033i
$3$	1.34786	+	1.08779i	0.778187	+	0.628033i
$4$	−0.190983	−	0.587785i	−0.0954915	−	0.293893i
$5$	−0.224514	−	0.309017i	−0.100406	−	0.138197i	0.755858	−	0.654736i	$-0.227220\pi$
$5$	−0.224514	−	0.309017i	−0.100406	−	0.138197i	−0.856264	+	0.516539i	$0.827220\pi$
$6$	−0.530249	−	1.96589i	−0.216473	−	0.802572i
$7$	−2.92705	+	0.951057i	−1.10632	+	0.359466i	−0.804532	−	0.593909i	$-0.797584\pi$
$7$	−2.92705	+	0.951057i	−1.10632	+	0.359466i	−0.301789	+	0.953375i	$0.597584\pi$
$8$	−0.951057	+	2.92705i	−0.336249	+	1.03487i
$9$	0.633446	+	2.93236i	0.211149	+	0.977454i
$10$			0.449028i			0.141995i
$11$	−1.31433	−	3.04508i	−0.396285	−	0.918128i
$11$	−1.31433	−	3.04508i	−0.396285	−	0.918128i
$12$	0.381966	−	1.00000i	0.110264	−	0.288675i
$13$	0.427051	−	0.587785i	0.118443	−	0.163022i	−0.745679	−	0.666305i	$-0.767875\pi$
$13$	0.427051	−	0.587785i	0.118443	−	0.163022i	0.864122	+	0.503283i	$0.167875\pi$
$14$	3.44095	+	1.11803i	0.919634	+	0.298807i
$15$	0.0335310	−	0.660734i	0.00865766	−	0.170601i
$16$	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	$0.127501\pi$
$18$	1.42377	−	3.22654i	0.335586	−	0.760503i
$19$	2.50000	+	0.812299i	0.573539	+	0.186354i	0.581404	−	0.813615i	$-0.302504\pi$
$19$	2.50000	+	0.812299i	0.573539	+	0.186354i	−0.00786490	+	0.999969i	$0.502504\pi$
$20$	−0.138757	+	0.190983i	−0.0310271	+	0.0427051i
$21$	−4.97980	−	1.90211i	−1.08668	−	0.415075i
$22$	−0.854102	+	3.80423i	−0.182095	+	0.811064i
$23$			6.23607i			1.30031i	0.759802	+	0.650155i	$0.225296\pi$
$23$			6.23607i			1.30031i	−0.759802	+	0.650155i	$0.774704\pi$
$24$	−4.46589	+	2.91071i	−0.911597	+	0.594145i
$25$	1.50000	−	4.61653i	0.300000	−	0.923305i
$26$	−0.812299	+	0.263932i	−0.159305	+	0.0517613i
$27$	−2.33598	+	4.64146i	−0.449560	+	0.893250i
$28$	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	$0.970050\pi$
$30$	−0.488446	+	0.605226i	−0.0891776	+	0.110499i
$31$	−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
$33$	1.54087	−	5.53405i	0.268231	−	0.963355i
$34$	−5.00000			−0.857493
$35$	0.951057	+	0.690983i	0.160758	+	0.116797i
$36$	1.60262	−	0.932362i	0.267104	−	0.155394i
$37$	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
$39$	1.21499	−	0.327712i	0.194554	−	0.0524759i
$40$	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	$0.0819315\pi$
$42$	3.42174	+	5.24997i	0.527986	+	0.810088i
$43$			6.88191i			1.04948i	0.851262	+	0.524741i	$0.175838\pi$
$43$			6.88191i			1.04948i	−0.851262	+	0.524741i	$0.824162\pi$
$44$	−1.53884	+	1.35410i	−0.231989	+	0.204139i
$45$	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	−0.332016	−	0.943274i	$-0.607729\pi$
$47$	−7.91872	−	2.57295i	−1.15506	−	0.375303i	−0.823049	+	0.567971i	$0.807729\pi$
$48$	4.12038	+	0.209101i	0.594726	+	0.0301812i
$49$	2.00000	−	1.45309i	0.285714	−	0.207584i
$50$	−4.61653	+	3.35410i	−0.652875	+	0.474342i
$51$	7.35738	+	0.373373i	1.03024	+	0.0522827i
$52$	−0.427051	−	0.138757i	−0.0592213	−	0.0192422i
$53$	1.08981	−	1.50000i	0.149697	−	0.206041i	−0.727582	−	0.686021i	$-0.759356\pi$
$53$	1.08981	−	1.50000i	0.149697	−	0.206041i	0.877280	+	0.479980i	$0.159356\pi$
$54$	5.42882	−	2.80017i	0.738769	−	0.381055i
$55$	−0.645898	+	1.08981i	−0.0870929	+	0.146950i
$56$		−	9.47214i		−	1.26577i
$57$	2.48604	+	3.81433i	0.329284	+	0.505220i
$58$	−0.854102	+	2.62866i	−0.112149	+	0.345159i
$59$	−0.363271	+	0.118034i	−0.0472939	+	0.0153667i	−0.332568	−	0.943079i	$-0.607915\pi$
$59$	−0.363271	+	0.118034i	−0.0472939	+	0.0153667i	0.285275	+	0.958446i	$0.407915\pi$
$60$	−0.394774	+	0.106480i	−0.0509651	+	0.0137465i
$61$	1.54508	+	2.12663i	0.197828	+	0.272287i	0.896393	−	0.443259i	$-0.146178\pi$
$61$	1.54508	+	2.12663i	0.197828	+	0.272287i	−0.698566	+	0.715546i	$0.746178\pi$
$62$	2.12663	+	6.54508i	0.270082	+	0.831227i
$63$	−4.64297	−	7.98073i	−0.584959	−	1.00548i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−0.277515			−0.0344214
$66$	−5.28939	+	4.19848i	−0.651079	+	0.516797i
$67$	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
$69$	−6.78350	+	8.40534i	−0.816638	+	1.01188i
$70$	−0.427051	−	1.31433i	−0.0510424	−	0.157092i
$71$	3.13068	+	4.30902i	0.371544	+	0.511386i	0.953320	−	0.301963i	$-0.0976419\pi$
$71$	3.13068	+	4.30902i	0.371544	+	0.511386i	−0.581776	+	0.813349i	$0.697642\pi$
$72$	−9.18562	−	0.934712i	−1.08254	−	0.110157i
$73$	−8.94427	+	2.90617i	−1.04685	+	0.340141i	−0.781431	−	0.623992i	$-0.785510\pi$
$73$	−8.94427	+	2.90617i	−1.04685	+	0.340141i	−0.265417	+	0.964134i	$0.585510\pi$
$74$	1.08981	−	3.35410i	0.126688	−	0.389906i
$75$	7.04358	−	4.59075i	0.813322	−	0.530094i
$76$		−	1.62460i		−	0.186354i
$77$	6.74315	+	7.66312i	0.768454	+	0.873293i
$78$	−1.38197	−	0.527864i	−0.156477	−	0.0597688i
$79$	2.33688	−	3.21644i	0.262920	−	0.361878i	−0.657064	−	0.753835i	$-0.728202\pi$
$79$	2.33688	−	3.21644i	0.262920	−	0.361878i	0.919984	+	0.391957i	$0.128202\pi$
$80$	−0.865300	−	0.281153i	−0.0967435	−	0.0314339i
$81$	−8.19749	+	3.71499i	−0.910832	+	0.412777i
$82$	−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	$0.412879\pi$
$84$	−0.166977	+	3.29032i	−0.0182187	+	0.359004i
$85$	−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
$88$	10.1631	−	0.951057i	1.08339	−	0.101383i
$89$		−	0.527864i		−	0.0559535i	−0.999609	−	0.0279767i	$-0.991094\pi$
$89$		−	0.527864i		−	0.0559535i	0.999609	−	0.0279767i	$-0.00890643\pi$
$90$	−1.31671	+	0.284435i	−0.138794	+	0.0299821i
$91$	−0.690983	+	2.12663i	−0.0724347	+	0.222931i
$92$	3.66547	−	1.19098i	0.382152	−	0.124169i
$93$	−2.64053	−	9.78975i	−0.273810	−	1.01515i
$94$	5.75329	+	7.91872i	0.593406	+	0.816754i
$95$	−0.310271	−	0.954915i	−0.0318331	−	0.0979722i
$96$	4.52233	+	3.64973i	0.461559	+	0.372500i
$97$	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
$99$	8.09673	−	5.78298i	0.813752	−	0.581212i
$100$	−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	$0.408405\pi$
$102$	−6.73929	−	5.43893i	−0.667290	−	0.538534i
$103$	−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
$105$	0.530249	+	1.96589i	0.0517470	+	0.191851i
$106$	−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	$-0.117019\pi$
$108$	3.17432	+	0.486616i	0.305449	+	0.0468247i
$109$		−	4.70228i		−	0.450397i	−0.974313	−	0.225198i	$-0.927697\pi$
$109$		−	4.70228i		−	0.450397i	0.974313	−	0.225198i	$-0.0723030\pi$
$110$	1.36733	−	0.590170i	0.130370	−	0.0562705i
$111$	−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	0.215608	−	0.976480i	$-0.430827\pi$
$113$	−1.95511	−	0.635255i	−0.183922	−	0.0597598i	−0.399530	+	0.916720i	$0.630827\pi$
$114$	0.271271	−	5.34545i	0.0254069	−	0.500647i
$115$	1.92705	−	1.40008i	0.179698	−	0.130559i
$116$	−1.17557	+	0.854102i	−0.109149	+	0.0793014i
$117$	1.99411	+	0.879937i	0.184356	+	0.0813502i
$118$	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
$121$	−7.54508	+	8.00448i	−0.685917	+	0.727680i
$122$		−	3.09017i		−	0.279771i
$123$	1.05425	−	0.687124i	0.0950589	−	0.0619559i
$124$	−1.11803	+	3.44095i	−0.100402	+	0.309007i
$125$	−3.57971	+	1.16312i	−0.320179	+	0.104033i
$126$	−1.09882	+	10.7983i	−0.0978906	+	0.961992i
$127$	−7.56231	−	10.4086i	−0.671046	−	0.923616i	0.328737	−	0.944421i	$-0.393377\pi$
$127$	−7.56231	−	10.4086i	−0.671046	−	0.923616i	−0.999784	+	0.0208056i	$0.993377\pi$
$128$	1.08981	+	3.35410i	0.0963268	+	0.296464i
$129$	−7.48604	+	9.27584i	−0.659109	+	0.816692i
$130$	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	$0.650254\pi$
$132$	−3.54711	+	0.151209i	−0.308737	+	0.0131610i
$133$	−8.09017			−0.701507
$134$	−6.96767	−	5.06231i	−0.601915	−	0.437317i
$135$	1.95875	−	0.320215i	0.168583	−	0.0275597i
$136$	4.04508	+	12.4495i	0.346863	+	1.06754i
$137$	−2.76741	−	3.80902i	−0.236436	−	0.325426i	0.674267	−	0.738487i	$-0.264460\pi$
$137$	−2.76741	−	3.80902i	−0.236436	−	0.325426i	−0.910703	+	0.413061i	$0.864460\pi$
$138$	12.2594	−	3.30667i	1.04359	−	0.281482i
$139$	13.5172	−	4.39201i	1.14652	−	0.372526i	0.326686	−	0.945133i	$-0.394068\pi$
$139$	13.5172	−	4.39201i	1.14652	−	0.372526i	0.819830	+	0.572607i	$0.194068\pi$
$140$	0.224514	−	0.690983i	0.0189749	−	0.0583987i
$141$	−7.87450	−	12.0818i	−0.663153	−	1.01747i
$142$		−	6.26137i		−	0.525442i
$143$	−2.35114	−	0.527864i	−0.196612	−	0.0441422i
$144$	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
$147$	4.27636	+	0.217017i	0.352708	+	0.0178993i
$148$	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	$0.120678\pi$
$150$	−9.87097	−	0.500932i	−0.805961	−	0.0409010i
$151$	5.32624	+	1.73060i	0.433443	+	0.140834i	0.517608	−	0.855618i	$-0.326822\pi$
$151$	5.32624	+	1.73060i	0.433443	+	0.140834i	−0.0841654	+	0.996452i	$0.526822\pi$
$152$	−4.75528	+	6.54508i	−0.385704	+	0.530876i
$153$	9.51057	+	8.50651i	0.768884	+	0.687710i
$154$	−1.11803	−	11.9475i	−0.0900937	−	0.962754i
$155$			2.23607i			0.179605i
$156$	−0.424666	−	0.651565i	−0.0340005	−	0.0521669i
$157$	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
$159$	3.10059	−	0.836305i	0.245893	−	0.0663233i
$160$	−0.753289	−	1.03681i	−0.0595527	−	0.0819673i
$161$	−5.93085	−	18.2533i	−0.467417	−	1.43856i
$162$	10.3633	+	2.13116i	0.814215	+	0.167440i
$163$	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
$165$	−2.05606	+	0.766317i	−0.160064	+	0.0596577i
$166$	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	$-0.603913\pi$
$168$	10.3036	−	12.7671i	0.794944	−	0.985003i
$169$	3.85410	+	11.8617i	0.296469	+	0.912439i
$170$	1.12257	+	1.54508i	0.0860972	+	0.118503i
$171$	−0.798339	+	7.84545i	−0.0610505	+	0.599957i
$172$	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	$0.758718\pi$
$174$	−4.01062	+	2.61398i	−0.304044	+	0.198165i
$175$			14.9394i			1.12931i
$176$	−6.79615	−	4.02786i	−0.512279	−	0.303612i
$177$	−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	0.759357	−	0.650674i	$-0.225514\pi$
$179$	13.2618	+	4.30902i	0.991233	+	0.322071i	0.231876	+	0.972745i	$0.425514\pi$
$180$	−0.647927	−	0.285909i	−0.0482936	−	0.0213104i
$181$	−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
$183$	−0.230757	+	4.54711i	−0.0170581	+	0.336132i
$184$	−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
$187$	−12.1353	−	7.19218i	−0.887418	−	0.525944i
$188$			5.14590i			0.375303i
$189$	2.42325	−	15.8075i	0.176265	−	1.14982i
$190$	−0.364745	+	1.12257i	−0.0264614	+	0.0814398i
$191$	23.0499	−	7.48936i	1.66783	−	0.541911i	0.685340	−	0.728224i	$-0.259654\pi$
$191$	23.0499	−	7.48936i	1.66783	−	0.541911i	0.982490	+	0.186313i	$0.0596538\pi$
$192$	−3.92789	−	14.5626i	−0.283471	−	1.05097i
$193$	−5.79180	−	7.97172i	−0.416903	−	0.573817i	0.547982	−	0.836490i	$-0.315396\pi$
$193$	−5.79180	−	7.97172i	−0.416903	−	0.573817i	−0.964885	+	0.262673i	$0.915396\pi$
$194$	−1.59184	−	4.89919i	−0.114288	−	0.351741i
$195$	−0.374050	−	0.301876i	−0.0267863	−	0.0216178i
$196$	−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	$0.400739\pi$
$198$	−11.6964	−	0.0947623i	−0.831227	−	0.00673446i
$199$	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
$201$	9.87473	+	7.96937i	0.696510	+	0.562116i
$202$	−5.79180	−	17.8253i	−0.407509	−	1.25418i
$203$	4.25325	+	5.85410i	0.298520	+	0.410877i
$204$	−1.18567	−	4.39587i	−0.0830137	−	0.307772i
$205$	−0.263932	+	0.0857567i	−0.0184338	+	0.00598951i
$206$	−4.08174	+	12.5623i	−0.284388	+	0.875257i
$207$	−18.2864	+	3.95022i	−1.27099	+	0.274559i
$208$		−	1.73060i		−	0.119995i
$209$	−0.812299	−	8.68034i	−0.0561879	−	0.600432i
$210$	0.854102	−	2.23607i	0.0589386	−	0.154303i
$211$	−11.4443	+	15.7517i	−0.787856	+	1.08439i	0.206516	+	0.978443i	$0.433788\pi$
$211$	−11.4443	+	15.7517i	−0.787856	+	1.08439i	−0.994372	+	0.105948i	$0.966212\pi$
$212$	−1.08981	−	0.354102i	−0.0748487	−	0.0243198i
$213$	−0.467565	+	9.21346i	−0.0320370	+	0.631296i
$214$	−12.3992	+	9.00854i	−0.847591	+	0.615811i
$215$	2.12663	−	1.54508i	0.145035	−	0.105374i
$216$	−11.3641	−	11.2518i	−0.773232	−	0.765591i
$217$	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
$220$	0.763932	+	0.171513i	0.0515043	+	0.0115634i
$221$		−	3.09017i		−	0.207867i
$222$	5.11746	−	3.33537i	0.343461	−	0.223856i
$223$	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
$225$	14.4875	+	1.47422i	0.965833	+	0.0982814i
$226$	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	$0.740317\pi$
$228$	1.76721	−	2.18973i	0.117037	−	0.145018i
$229$	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
$231$	0.752989	+	17.6639i	0.0495430	+	1.16220i
$232$	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	$0.802725\pi$
$234$	−1.28849	−	2.21477i	−0.0842314	−	0.144784i
$235$	0.982779	+	3.02468i	0.0641094	+	0.197309i
$236$	0.138757	+	0.190983i	0.00903233	+	0.0124319i
$237$	6.64858	−	1.79328i	0.431872	−	0.116486i
$238$	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	$0.0197327\pi$
$240$	−0.860468	−	1.32021i	−0.0555430	−	0.0852195i
$241$		−	27.8707i		−	1.79531i	−0.440702	−	0.897654i	$-0.645270\pi$
$241$		−	27.8707i		−	1.79531i	0.440702	−	0.897654i	$-0.354730\pi$
$242$	12.7068	−	2.39919i	0.816822	−	0.154226i
$243$	−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
$246$	−1.47745	−	0.0749776i	−0.0941986	−	0.00478039i
$247$	1.54508	−	1.12257i	0.0983114	−	0.0714274i
$248$	14.5761	−	10.5902i	0.925584	−	0.672476i
$249$	−10.9444	−	0.555407i	−0.693573	−	0.0351975i
$250$	4.20820	+	1.36733i	0.266150	+	0.0864774i
$251$	11.9475	−	16.4443i	0.754117	−	1.03795i	−0.243563	−	0.969885i	$-0.578316\pi$
$251$	11.9475	−	16.4443i	0.754117	−	1.03795i	0.997681	−	0.0680683i	$-0.0216836\pi$
$252$	−3.80423	+	4.25325i	−0.239644	+	0.267930i
$253$	18.9894	−	8.19624i	1.19385	−	0.515293i
$254$			15.1246i			0.949003i
$255$	−1.53646	−	2.35738i	−0.0962167	−	0.147625i
$256$	−4.10081	+	12.6210i	−0.256301	+	0.788813i
$257$	−21.1805	+	6.88197i	−1.32120	+	0.429285i	−0.882908	−	0.469546i	$-0.844418\pi$
$257$	−21.1805	+	6.88197i	−1.32120	+	0.429285i	−0.438296	+	0.898831i	$0.644418\pi$
$258$	13.5291	−	3.64912i	0.842285	−	0.227185i
$259$	−5.42705	−	7.46969i	−0.337221	−	0.464144i
$260$	0.0530006	+	0.163119i	0.00328696	+	0.0101162i
$261$	6.09673	−	3.54691i	0.377378	−	0.219549i
$262$	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	$0.409202\pi$
$264$	14.7330	+	9.77340i	0.906753	+	0.601511i
$265$	−0.708204			−0.0435046
$266$	7.69421	+	5.59017i	0.471762	+	0.342755i
$267$	0.574203	−	0.711486i	0.0351406	−	0.0435422i
$268$	−1.39919	−	4.30625i	−0.0854689	−	0.263046i
$269$	−11.0292	−	15.1803i	−0.672460	−	0.925562i	0.327353	−	0.944902i	$-0.393843\pi$
$269$	−11.0292	−	15.1803i	−0.672460	−	0.925562i	−0.999813	+	0.0193404i	$0.993843\pi$
$270$	−2.08415	−	1.04892i	−0.126837	−	0.0638354i
$271$	−16.1180	+	5.23707i	−0.979101	+	0.318129i	−0.754484	−	0.656318i	$-0.772113\pi$
$271$	−16.1180	+	5.23707i	−0.979101	+	0.318129i	−0.224617	+	0.974447i	$0.572113\pi$
$272$	3.13068	−	9.63525i	0.189826	−	0.584223i
$273$	−3.24466	+	2.11475i	−0.196376	+	0.127991i
$274$			5.53483i			0.334371i
$275$	−16.0292	+	1.50000i	−0.966597	+	0.0904534i
$276$	6.23607	+	2.38197i	0.375367	+	0.143378i
$277$	−9.53444	+	13.1230i	−0.572869	+	0.788487i	−0.992891	−	0.119027i	$-0.962022\pi$
$277$	−9.53444	+	13.1230i	−0.572869	+	0.788487i	0.420022	+	0.907514i	$0.362022\pi$
$278$	−15.8904	−	5.16312i	−0.953046	−	0.309663i
$279$	7.09008	−	16.0675i	0.424472	−	0.961938i
$280$	−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	$0.592159\pi$
$282$	−0.859249	+	16.9317i	−0.0511675	+	1.00827i
$283$	−20.3262	−	6.60440i	−1.20827	−	0.392591i	−0.365472	−	0.930822i	$-0.619093\pi$
$283$	−20.3262	−	6.60440i	−1.20827	−	0.392591i	−0.842797	+	0.538232i	$0.819093\pi$
$284$	1.93487	−	2.66312i	0.114813	−	0.158027i
$285$	0.620541	−	1.62460i	0.0367577	−	0.0962329i
$286$	1.87132	+	2.12663i	0.110654	+	0.125750i
$287$			2.23607i			0.131991i
$288$	2.12534	+	9.83865i	0.125237	+	0.579748i
$289$	0.336881	−	1.03681i	0.0198165	−	0.0609890i
$290$	1.00406	−	0.326238i	0.0589603	−	0.0191574i
$291$	1.97651	+	7.32791i	0.115865	+	0.429570i
$292$	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	$0.766556\pi$
$294$	−3.91711	−	3.16129i	−0.228450	−	0.184370i
$295$	0.118034	+	0.0857567i	0.00687220	+	0.00499295i
$296$	−9.23305			−0.536660
$297$	17.2039	+	1.01286i	0.998271	+	0.0587723i
$298$	−15.3262			−0.887825
$299$	3.66547	+	2.66312i	0.211980	+	0.154012i
$300$	−4.04358	−	3.26336i	−0.233456	−	0.188410i
$301$	−6.54508	−	20.1437i	−0.377252	−	1.16106i
$302$	−3.86974	−	5.32624i	−0.222678	−	0.306491i
$303$	7.19140	+	26.6620i	0.413135	+	1.53169i
$304$	5.95492	−	1.93487i	0.341538	−	0.110972i
$305$	0.310271	−	0.954915i	0.0177660	−	0.0546783i
$306$	−3.16723	−	14.6618i	−0.181059	−	0.838160i
$307$		−	9.51057i		−	0.542797i	−0.962467	−	0.271398i	$-0.912514\pi$
$307$		−	9.51057i		−	0.542797i	0.962467	−	0.271398i	$-0.0874861\pi$
$308$	3.21644	−	5.42705i	0.183274	−	0.309235i
$309$	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	0.171072	−	0.985258i	$-0.445277\pi$
$311$	−4.75528	−	1.54508i	−0.269647	−	0.0876137i	−0.440720	+	0.897645i	$0.645277\pi$
$312$	−0.196294	+	3.86801i	−0.0111129	+	0.218983i
$313$	−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
$315$	−1.42377	+	3.22654i	−0.0802203	+	0.181795i
$316$	−2.33688	−	0.759299i	−0.131460	−	0.0427139i
$317$	−2.48990	+	3.42705i	−0.139847	+	0.192482i	−0.873195	−	0.487370i	$-0.837956\pi$
$317$	−2.48990	+	3.42705i	−0.139847	+	0.192482i	0.733349	+	0.679853i	$0.237956\pi$
$318$	−3.52671	−	1.34708i	−0.197768	−	0.0755407i
$319$	−5.85410	+	5.15131i	−0.327767	+	0.288418i
$320$			3.32624i			0.185942i
$321$	18.9178	−	12.3299i	1.05589	−	0.688191i
$322$	−6.97214	+	21.4580i	−0.388542	+	1.19581i
$323$	10.6331	−	3.45492i	0.591643	−	0.192237i
$324$	3.74920	+	4.10886i	0.208289	+	0.228270i
$325$	−2.07295	−	2.85317i	−0.114987	−	0.158265i
$326$	−5.31031	−	16.3435i	−0.294111	−	0.905180i
$327$	5.11507	−	6.33801i	0.282864	−	0.350493i
$328$	1.80902	+	1.31433i	0.0998863	+	0.0725716i
$329$	25.6255			1.41278
$330$	2.48494	+	0.691894i	0.136792	+	0.0380875i
$331$	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
$333$	−7.77929	+	4.52578i	−0.426302	+	0.248011i
$334$	7.66312	+	23.5847i	0.419307	+	1.29049i
$335$	−1.64484	−	2.26393i	−0.0898674	−	0.123692i
$336$	−12.2594	+	3.30667i	−0.668807	+	0.180393i
$337$	23.9443	−	7.77997i	1.30433	−	0.423802i	0.427243	−	0.904137i	$-0.359485\pi$
$337$	23.9443	−	7.77997i	1.30433	−	0.423802i	0.877085	+	0.480335i	$0.159485\pi$
$338$	4.53077	−	13.9443i	0.246441	−	0.758468i
$339$	−1.94420	−	2.98298i	−0.105594	−	0.162013i
$340$			1.00406i			0.0544526i
$341$	−4.25325	+	18.9443i	−0.230327	+	1.02589i
$342$	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
$345$	4.12038	+	0.209101i	0.221834	+	0.0112576i
$346$	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	$0.362475\pi$
$348$	−2.51358	−	0.127559i	−0.134742	−	0.00683790i
$349$	12.9271	+	4.20025i	0.691969	+	0.224834i	0.633828	−	0.773474i	$-0.281483\pi$
$349$	12.9271	+	4.20025i	0.691969	+	0.224834i	0.0581411	+	0.998308i	$0.481483\pi$
$350$	10.3229	−	14.2082i	0.551780	−	0.759460i
$351$	1.73060	+	3.35520i	0.0923726	+	0.179087i
$352$	−4.40983	−	10.2169i	−0.235045	−	0.544561i
$353$		−	33.5967i		−	1.78817i	−0.447893	−	0.894087i	$-0.647825\pi$
$353$		−	33.5967i		−	1.78817i	0.447893	−	0.894087i	$-0.352175\pi$
$354$	0.424666	+	0.651565i	0.0225708	+	0.0346303i
$355$	0.628677	−	1.93487i	0.0333667	−	0.102692i
$356$	−0.310271	+	0.100813i	−0.0164443	+	0.00534308i
$357$	−21.8905	+	5.90441i	−1.15857	+	0.312494i
$358$	−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	$0.581695\pi$
$360$	1.77346	+	3.04837i	0.0934694	+	0.160663i
$361$	−9.78115	−	7.10642i	−0.514798	−	0.374022i
$362$	9.12705			0.479707
$363$	−18.8769	+	2.58148i	−0.990778	+	0.135492i
$364$	1.38197			0.0724347
$365$	2.90617	+	2.11146i	0.152116	+	0.110519i
$366$	3.36144	−	4.16511i	0.175705	−	0.217714i
$367$	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
$369$	2.16843	+	0.220655i	0.112884	+	0.0114869i
$370$	−1.28115	+	0.416272i	−0.0666040	+	0.0216409i
$371$	−1.76336	+	5.42705i	−0.0915489	+	0.281758i
$372$	−5.24997	+	3.42174i	−0.272198	+	0.177409i
$373$			27.3561i			1.41645i	0.705989	+	0.708223i	$0.250503\pi$
$373$			27.3561i			1.41645i	−0.705989	+	0.708223i	$0.749497\pi$
$374$	6.57164	+	15.2254i	0.339811	+	0.787288i
$375$	−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
$378$	−13.2273	+	13.3594i	−0.680340	+	0.687131i
$379$	−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
$381$	1.12942	−	22.2555i	0.0578622	−	1.14018i
$382$	−27.0967	−	8.80427i	−1.38639	−	0.450465i
$383$	7.29818	−	10.0451i	0.372920	−	0.513280i	−0.580772	−	0.814066i	$-0.697249\pi$
$383$	7.29818	−	10.0451i	0.372920	−	0.513280i	0.953691	+	0.300787i	$0.0972492\pi$
$384$	−2.17963	+	5.70634i	−0.111229	+	0.291200i
$385$	0.854102	−	3.80423i	0.0435291	−	0.193881i
$386$			11.5836i			0.589589i
$387$	−20.1802	+	4.35932i	−1.02582	+	0.221597i
$388$	0.836881	−	2.57565i	0.0424862	−	0.130759i
$389$	−7.02067	+	2.28115i	−0.355962	+	0.115659i	−0.481539	−	0.876425i	$-0.659922\pi$
$389$	−7.02067	+	2.28115i	−0.355962	+	0.115659i	0.125577	+	0.992084i	$0.459922\pi$
$390$	0.147152	+	0.545564i	0.00745132	+	0.0276257i
$391$	15.5902	+	21.4580i	0.788429	+	1.08518i
$392$	2.35114	+	7.23607i	0.118751	+	0.365477i
$393$	−14.0294	−	11.3223i	−0.707687	−	0.571137i
$394$	−8.19098	−	5.95110i	−0.412656	−	0.299812i
$395$	−1.51860			−0.0764089
$396$	−4.94549	−	3.65469i	−0.248520	−	0.183655i
$397$	−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
$399$	−10.9044	−	8.80037i	−0.545903	−	0.440569i
$400$	−3.57295	−	10.9964i	−0.178647	−	0.549820i
$401$	16.3722	+	22.5344i	0.817590	+	1.12532i	0.990108	+	0.140310i	$0.0448099\pi$
$401$	16.3722	+	22.5344i	0.817590	+	1.12532i	−0.172517	+	0.985006i	$0.555190\pi$
$402$	−3.88473	−	14.4026i	−0.193753	−	0.718336i
$403$	−4.04508	+	1.31433i	−0.201500	+	0.0654713i
$404$	3.04493	−	9.37132i	0.151491	−	0.466241i
$405$	2.98845	+	1.69910i	0.148497	+	0.0844288i
$406$		−	8.50651i		−	0.422171i
$407$	7.46969	−	6.57295i	0.370259	−	0.325809i
$408$	−8.09017	+	21.1803i	−0.400523	+	1.04858i
$409$	−12.4377	+	17.1190i	−0.615004	+	0.846481i	−0.996977	−	0.0776926i	$-0.975245\pi$
$409$	−12.4377	+	17.1190i	−0.615004	+	0.846481i	0.381973	+	0.924173i	$0.375245\pi$
$410$	0.310271	+	0.100813i	0.0153232	+	0.00497880i
$411$	0.413311	−	8.14437i	0.0203871	−	0.401732i
$412$	−5.61803	+	4.08174i	−0.276781	+	0.201093i
$413$	0.951057	−	0.690983i	0.0467984	−	0.0340011i
$414$	20.1209	+	8.87872i	0.988890	+	0.436365i
$415$	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
$418$	−5.22542	+	8.81678i	−0.255584	+	0.431243i
$419$			0.854102i			0.0417256i	0.999782	+	0.0208628i	$0.00664132\pi$
$419$			0.854102i			0.0417256i	−0.999782	+	0.0208628i	$0.993359\pi$
$420$	1.05425	−	0.687124i	0.0514423	−	0.0335282i
$421$	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
$423$	2.52873	−	24.8504i	0.122951	−	1.20827i
$424$	3.35410	+	4.61653i	0.162890	+	0.224198i
$425$	−6.37988	−	19.6353i	−0.309470	−	0.952450i
$426$	6.81102	−	8.43944i	0.329995	−	0.408892i
$427$	−6.54508	−	4.75528i	−0.316739	−	0.230124i
$428$	−8.05748			−0.389473
$429$	−2.59480	−	3.26902i	−0.125278	−	0.157830i
$430$	−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	$0.653459\pi$
$432$	1.99688	+	12.2149i	0.0960750	+	0.587690i
$433$	−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
$435$	−1.50181	+	0.405074i	−0.0720062	+	0.0194218i
$436$	−2.76393	+	0.898056i	−0.132368	+	0.0430091i
$437$	−5.06555	+	15.5902i	−0.242318	+	0.745779i
$438$	10.4559	+	16.0425i	0.499603	+	0.766540i
$439$		−	2.73466i		−	0.130518i	−0.997868	−	0.0652590i	$-0.979213\pi$
$439$		−	2.73466i		−	0.130518i	0.997868	−	0.0652590i	$-0.0207874\pi$
$440$	−2.57565	−	2.92705i	−0.122790	−	0.139542i
$441$	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	0.343332	−	0.939214i	$-0.388444\pi$
$443$	1.45309	+	0.472136i	0.0690382	+	0.0224319i	−0.274294	+	0.961646i	$0.588444\pi$
$444$	3.20727	+	0.162763i	0.152210	+	0.00772438i
$445$	−0.163119	+	0.118513i	−0.00773258	+	0.00561805i
$446$	−1.67760	+	1.21885i	−0.0794366	+	0.0577141i
$447$	22.5522	+	1.14448i	1.06668	+	0.0541321i
$448$	25.4894	+	8.28199i	1.20426	+	0.391287i
$449$	−16.3925	+	22.5623i	−0.773609	+	1.06478i	0.222350	+	0.974967i	$0.428627\pi$
$449$	−16.3925	+	22.5623i	−0.773609	+	1.06478i	−0.995959	+	0.0898141i	$0.971373\pi$
$450$	−12.7598	−	11.4127i	−0.601501	−	0.537999i
$451$	−2.39919	+	0.224514i	−0.112973	+	0.0105720i
$452$			1.27051i			0.0597598i
$453$	5.29650	+	8.12641i	0.248851	+	0.381812i
$454$	5.26393	−	16.2007i	0.247049	−	0.760337i
$455$	0.812299	−	0.263932i	0.0380812	−	0.0123733i
$456$	−13.5291	+	3.64912i	−0.633558	+	0.170886i
$457$	14.7361	+	20.2825i	0.689324	+	0.948773i	0.999998	−	0.00174308i	$-0.000554841\pi$
$457$	14.7361	+	20.2825i	0.689324	+	0.948773i	−0.310674	+	0.950516i	$0.600555\pi$
$458$	−5.49434	−	16.9098i	−0.256734	−	0.790144i
$459$	3.56564	+	21.8110i	0.166430	+	1.01805i
$460$	−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	$0.753657\pi$
$462$	11.4893	−	17.3197i	0.534532	−	0.805784i
$463$	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
$465$	−2.43236	+	3.01390i	−0.112798	+	0.139766i
$466$	3.51722	+	10.8249i	0.162932	+	0.501453i
$467$	−4.49801	−	6.19098i	−0.208143	−	0.286485i	0.692163	−	0.721741i	$-0.256658\pi$
$467$	−4.49801	−	6.19098i	−0.208143	−	0.286485i	−0.900307	+	0.435256i	$0.856658\pi$
$468$	0.136373	−	1.34016i	0.00630382	−	0.0619491i
$469$	−21.4443	+	6.96767i	−0.990204	+	0.321737i
$470$	1.15533	−	3.55573i	0.0532912	−	0.164014i
$471$	14.0872	−	9.18149i	0.649102	−	0.423061i
$472$		−	1.17557i		−	0.0541100i
$473$	20.9560	−	9.04508i	0.963558	−	0.415893i
$474$	−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
$477$	5.08888	+	2.24556i	0.233004	+	0.102817i
$478$	−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	$0.148750\pi$
$480$	0.112503	−	2.21689i	0.00513504	−	0.101187i
$481$	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
$484$	6.14590	+	2.90617i	0.279359	+	0.132099i
$485$		−	1.67376i		−	0.0760016i
$486$	11.6500	+	14.1455i	0.528454	+	0.641654i
$487$	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
$489$	6.59356	+	24.4456i	0.298171	+	1.10547i
$490$	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	$-0.230576\pi$
$492$	−0.605226	−	0.488446i	−0.0272857	−	0.0220208i
$493$	−8.09017	−	5.87785i	−0.364363	−	0.264725i
$494$	−2.24514			−0.101014
$495$	−3.60487	−	1.20367i	−0.162027	−	0.0541009i
$496$	−13.9443			−0.626116
$497$	−13.2618	−	9.63525i	−0.594873	−	0.432200i
$498$	10.0250	+	8.09061i	0.449229	+	0.362549i
$499$	−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
$501$	−9.51493	−	35.2765i	−0.425096	−	1.57604i
$502$	−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	$0.0392669\pi$
$504$	27.7757	−	6.00009i	1.23723	−	0.267265i
$505$		−	6.08985i		−	0.270995i
$506$	−23.7234	−	5.32624i	−1.05463	−	0.236780i
$507$	−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	0.910003	−	0.414602i	$-0.136079\pi$
$509$	31.6421	+	10.2812i	1.40251	+	0.455704i	0.492510	+	0.870307i	$0.336079\pi$
$510$	−0.167655	+	3.30367i	−0.00742388	+	0.146289i
$511$	23.4164	−	17.0130i	1.03588	−	0.752612i
$512$	18.3273	−	13.3156i	0.809962	−	0.588472i
$513$	−9.61022	+	9.70614i	−0.424301	+	0.428537i
$514$	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
$517$	2.57295	+	27.4949i	0.113158	+	1.20922i
$518$			10.8541i			0.476902i
$519$	−33.5236	+	21.8494i	−1.47152	+	0.959084i
$520$	0.263932	−	0.812299i	0.0115742	−	0.0356217i
$521$	−32.0584	+	10.4164i	−1.40450	+	0.456351i	−0.910645	−	0.413190i	$-0.864414\pi$
$521$	−32.0584	+	10.4164i	−1.40450	+	0.456351i	−0.493860	+	0.869542i	$0.664414\pi$
$522$	−8.24920	−	0.839423i	−0.361058	−	0.0367406i
$523$	−11.9721	−	16.4782i	−0.523505	−	0.720543i	0.462618	−	0.886558i	$-0.346910\pi$
$523$	−11.9721	−	16.4782i	−0.523505	−	0.720543i	−0.986123	+	0.166015i	$0.946910\pi$
$524$	1.98787	+	6.11803i	0.0868405	+	0.267268i
$525$	−16.2508	+	20.1362i	−0.709245	+	0.878815i
$526$	−8.68034	−	6.30664i	−0.378481	−	0.274982i
$527$	−24.8990			−1.08462
$528$	−4.77880	−	12.8217i	−0.207971	−	0.557995i
$529$	−15.8885			−0.690806
$530$	0.673542	+	0.489357i	0.0292568	+	0.0212563i
$531$	−0.576231	−	0.990475i	−0.0250063	−	0.0429829i
$532$	1.54508	+	4.75528i	0.0669879	+	0.206168i
$533$	−0.310271	−	0.427051i	−0.0134393	−	0.0184976i
$534$	−1.03772	+	0.279899i	−0.0449067	+	0.0121124i
$535$	−4.73607	+	1.53884i	−0.204758	+	0.0665299i
$536$	−6.96767	+	21.4443i	−0.300957	+	0.926251i
$537$	13.1877	+	20.2339i	0.569093	+	0.873158i
$538$			22.0583i			0.951002i
$539$	−7.05342	−	4.18034i	−0.303812	−	0.180060i
$540$	−0.562306	−	1.09017i	−0.0241978	−	0.0469134i
$541$	8.98278	−	12.3637i	0.386200	−	0.531558i	−0.571014	−	0.820940i	$-0.693450\pi$
$541$	8.98278	−	12.3637i	0.386200	−	0.531558i	0.957214	+	0.289382i	$0.0934498\pi$
$542$	18.9479	+	6.15654i	0.813881	+	0.264446i
$543$	−13.4302	−	0.681559i	−0.576347	−	0.0292485i
$544$	11.5451	−	8.38800i	0.494991	−	0.359632i
$545$	−1.45309	+	1.05573i	−0.0622433	+	0.0452224i
$546$	4.54711	+	0.230757i	0.194598	+	0.00987550i
$547$	−25.5517	−	8.30224i	−1.09251	−	0.354978i	−0.293294	−	0.956022i	$-0.594752\pi$
$547$	−25.5517	−	8.30224i	−1.09251	−	0.354978i	−0.799216	+	0.601044i	$0.794752\pi$
$548$	−1.71036	+	2.35410i	−0.0730628	+	0.100562i
$549$	−5.25731	+	5.87785i	−0.224377	+	0.250861i
$550$	16.2812	+	9.64932i	0.694231	+	0.411448i
$551$		−	6.18034i		−	0.263291i
$552$	−18.1514	−	27.8496i	−0.772573	−	1.18536i
$553$	−3.78115	+	11.6372i	−0.160791	+	0.494864i
$554$	18.1356	−	5.89261i	0.770507	−	0.250353i
$555$	1.91627	−	0.516865i	0.0813412	−	0.0219397i
$556$	−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	$0.898129\pi$
$558$	−17.8455	+	10.3820i	−0.755458	+	0.439505i
$559$	4.04508	+	2.93893i	0.171089	+	0.124303i
$560$	2.80017			0.118329
$561$	−8.53306	−	22.8946i	−0.360266	−	0.966611i
$562$	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	$0.707175\pi$
$564$	−5.59763	+	6.93594i	−0.235703	+	0.292056i
$565$	0.242646	+	0.746787i	0.0102082	+	0.0314176i
$566$	14.7679	+	20.3262i	0.620740	+	0.854376i
$567$	20.4613	−	18.6702i	0.859294	−	0.784076i
$568$	−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	$-0.0437298\pi$
$570$	−1.71274	+	1.11630i	−0.0717388	+	0.0467567i
$571$			22.5478i			0.943598i	0.881706	+	0.471799i	$0.156395\pi$
$571$			22.5478i			0.943598i	−0.881706	+	0.471799i	$0.843605\pi$
$572$	0.138757	+	1.48278i	0.00580173	+	0.0619981i
$573$	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
$576$	10.5468	−	23.9011i	0.439449	−	0.995878i
$577$	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
$579$	0.865000	−	17.0450i	0.0359482	−	0.708366i
$580$	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
$583$	−6.00000	−	1.34708i	−0.248495	−	0.0557905i
$584$		−	28.9443i		−	1.19772i
$585$	−0.175791	−	0.813773i	−0.00726805	−	0.0336454i
$586$	5.06231	−	15.5802i	0.209122	−	0.643611i
$587$	11.3597	−	3.69098i	0.468864	−	0.152343i	−0.0650498	−	0.997882i	$-0.520721\pi$
$587$	11.3597	−	3.69098i	0.468864	−	0.152343i	0.533914	+	0.845539i	$0.320721\pi$
$588$	−0.689153	−	2.55503i	−0.0284202	−	0.105368i
$589$	−9.04508	−	12.4495i	−0.372696	−	0.512972i
$590$	−0.0530006	−	0.163119i	−0.00218200	−	0.00671550i
$591$	11.6084	+	9.36856i	0.477508	+	0.385371i
$592$	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	$0.451904\pi$
$594$	−15.6620	−	12.8509i	−0.642620	−	0.527278i
$595$	5.00000			0.204980
$596$	−6.51864	−	4.73607i	−0.267014	−	0.193997i
$597$	3.01390	+	2.43236i	0.123351	+	0.0995499i
$598$	−1.64590	−	5.06555i	−0.0673058	−	0.207146i
$599$	−12.7598	−	17.5623i	−0.521350	−	0.717576i	0.464432	−	0.885609i	$-0.346259\pi$
$599$	−12.7598	−	17.5623i	−0.521350	−	0.717576i	−0.985781	+	0.168033i	$0.946259\pi$
$600$	6.73851	+	24.9830i	0.275098	+	1.01993i
$601$	−17.7254	+	5.75934i	−0.723035	+	0.234928i	−0.647339	−	0.762203i	$-0.724118\pi$
$601$	−17.7254	+	5.75934i	−0.723035	+	0.234928i	−0.0756965	+	0.997131i	$0.524118\pi$
$602$	−7.69421	+	23.6803i	−0.313593	+	0.965139i
$603$	4.64078	+	21.4832i	0.188987	+	0.874863i
$604$		−	3.46120i		−	0.140834i
$605$	4.16750	+	0.534442i	0.169433	+	0.0217282i
$606$	11.5836	−	30.3262i	0.470551	−	1.23192i
$607$	21.7705	−	29.9645i	0.883638	−	1.21622i	−0.0917623	−	0.995781i	$-0.529250\pi$
$607$	21.7705	−	29.9645i	0.883638	−	1.21622i	0.975400	−	0.220442i	$-0.0707500\pi$
$608$	8.38800	+	2.72542i	0.340178	+	0.110531i
$609$	−0.635220	+	12.5171i	−0.0257404	+	0.507220i
$610$	−0.954915	+	0.693786i	−0.0386634	+	0.0280906i
$611$	−4.89404	+	3.55573i	−0.197992	+	0.143849i
$612$	3.18364	−	7.21477i	0.128691	−	0.291640i
$613$	36.1803	+	11.7557i	1.46131	+	0.474808i	0.928470	−	0.371407i	$-0.121125\pi$
$613$	36.1803	+	11.7557i	1.46131	+	0.474808i	0.532840	+	0.846216i	$0.321125\pi$
$614$	−6.57164	+	9.04508i	−0.265210	+	0.365030i
$615$	−0.449028	−	0.171513i	−0.0181066	−	0.00691609i
$616$	−28.8435	+	12.4495i	−1.16214	+	0.501604i
$617$			15.7639i			0.634632i	0.948320	+	0.317316i	$0.102782\pi$
$617$			15.7639i			0.634632i	−0.948320	+	0.317316i	$0.897218\pi$
$618$	−19.1667	+	12.4922i	−0.770998	+	0.502508i
$619$	−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
$621$	−28.9445	−	14.5674i	−1.16150	−	0.584568i
$622$	3.45492	+	4.75528i	0.138529	+	0.190669i
$623$	0.502029	+	1.54508i	0.0201133	+	0.0619025i
$624$	1.88252	−	2.33260i	0.0753611	−	0.0933789i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	12.9313			0.516838
$627$	8.34748	−	12.5835i	0.333366	−	0.502536i
$628$	−6.00000			−0.239426
$629$	10.3229	+	7.50000i	0.411600	+	0.299045i
$630$	3.58357	−	2.08482i	0.142773	−	0.0830614i
$631$	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
$633$	−32.5597	+	8.78214i	−1.29413	+	0.349059i
$634$	4.73607	−	1.53884i	0.188093	−	0.0611152i
$635$	−1.51860	+	4.67376i	−0.0602637	+	0.185473i
$636$	−1.08373	−	1.66276i	−0.0429726	−	0.0659328i
$637$		−	1.79611i		−	0.0711645i
$638$	9.12705	−	0.854102i	0.361343	−	0.0338142i
$639$	−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	0.0920929	−	0.995750i	$-0.470644\pi$
$641$	−10.6004	−	3.44427i	−0.418690	−	0.136041i	−0.510783	+	0.859710i	$0.670644\pi$
$642$	−26.5117	−	1.34542i	−1.04633	−	0.0530994i
$643$	−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
$645$	4.54711	+	0.230757i	0.179042	+	0.00908606i
$646$	−12.5000	−	4.06150i	−0.491806	−	0.159797i
$647$	−14.7881	+	20.3541i	−0.581381	+	0.800202i	−0.993846	−	0.110771i	$-0.964668\pi$
$647$	−14.7881	+	20.3541i	−0.581381	+	0.800202i	0.412465	+	0.910973i	$0.364668\pi$
$648$	−3.07768	−	27.5276i	−0.120903	−	1.08139i
$649$	0.836881	+	0.951057i	0.0328505	+	0.0373322i
$650$			4.14590i			0.162615i
$651$	17.0396	+	26.1438i	0.667833	+	1.02466i
$652$	2.79180	−	8.59226i	0.109335	−	0.336499i
$653$	39.8056	−	12.9336i	1.55771	−	0.506132i	0.601518	−	0.798859i	$-0.294563\pi$
$653$	39.8056	−	12.9336i	1.55771	−	0.506132i	0.956196	+	0.292727i	$0.0945628\pi$
$654$	−9.24418	+	2.49338i	−0.361476	+	0.0974988i
$655$	2.33688	+	3.21644i	0.0913095	+	0.125677i
$656$	−0.534785	−	1.64590i	−0.0208798	−	0.0642615i
$657$	−14.1877	−	24.3869i	−0.553513	−	0.951425i
$658$	−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	$0.522289\pi$
$660$	0.843103	+	1.06217i	0.0328177	+	0.0413449i
$661$	−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
$663$	3.36144	−	4.16511i	0.130548	−	0.161760i
$664$	−6.01722	−	18.5191i	−0.233513	−	0.718681i
$665$	1.81636	+	2.50000i	0.0704353	+	0.0969458i
$666$	10.5258	+	1.07108i	0.407866	+	0.0415037i
$667$	13.9443	−	4.53077i	0.539924	−	0.175432i
$668$	−4.02874	+	12.3992i	−0.155877	+	0.479739i
$669$	2.55957	−	1.66823i	0.0989585	−	0.0644975i
$670$			3.28969i			0.127092i
$671$	4.44501	−	7.50000i	0.171598	−	0.289534i
$672$	−16.7082	−	6.38197i	−0.644533	−	0.246190i
$673$	6.07953	−	8.36775i	0.234349	−	0.322553i	−0.675605	−	0.737264i	$-0.736117\pi$
$673$	6.07953	−	8.36775i	0.234349	−	0.322553i	0.909953	+	0.414711i	$0.136117\pi$
$674$	−28.1482	−	9.14590i	−1.08423	−	0.352287i
$675$	17.9235	+	17.7463i	0.689874	+	0.683056i
$676$	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	$0.106907\pi$
$678$	−0.212147	+	4.18039i	−0.00814744	+	0.160547i
$679$	−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
$682$	17.1353	−	15.0781i	0.656143	−	0.577372i
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$	4.76391	−	1.02910i	0.182153	−	0.0393485i
$685$	−0.555728	+	1.71036i	−0.0212333	+	0.0653493i
$686$	−15.5802	+	5.06231i	−0.594854	+	0.193280i
$687$	6.82205	+	25.2927i	0.260278	+	0.964977i
$688$	9.63525	+	13.2618i	0.367341	+	0.505601i
$689$	−0.416272	−	1.28115i	−0.0158587	−	0.0488080i
$690$	−3.77423	−	3.04598i	−0.143683	−	0.115959i
$691$	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
$693$	−18.1996	+	24.6275i	−0.691346	+	0.935523i
$694$	8.54102			0.324213
$695$	−4.39201	−	3.19098i	−0.166598	−	0.121041i
$696$	9.75320	+	7.87129i	0.369694	+	0.298360i
$697$	−0.954915	−	2.93893i	−0.0361700	−	0.111320i
$698$	−9.39205	−	12.9271i	−0.355494	−	0.489296i
$699$	−4.36716	−	16.1912i	−0.165181	−	0.612408i
$700$	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	$0.00547688\pi$
$702$	0.672487	−	4.38680i	0.0253814	−	0.165569i
$703$			7.88597i			0.297425i
$704$	−6.32688	+	28.1803i	−0.238453	+	1.06209i
$705$	−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
$708$	−0.0207233	+	0.408356i	−0.000778829	+	0.0153470i
$709$	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
$711$	10.9121	+	4.81514i	0.409234	+	0.180582i
$712$	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
$715$	0.364745	+	0.845055i	0.0136407	+	0.0316033i
$716$		−	8.61803i		−	0.322071i
$717$	11.1941	−	7.29591i	0.418052	−	0.272471i
$718$	11.5836	−	35.6506i	0.432296	−	1.33047i
$719$	−28.6502	+	9.30902i	−1.06847	+	0.347168i	−0.789893	−	0.613245i	$-0.789864\pi$
$719$	−28.6502	+	9.30902i	−1.06847	+	0.347168i	−0.278580	+	0.960413i	$0.589864\pi$
$720$	0.276321	−	2.71547i	0.0102979	−	0.101199i
$721$	20.3262	+	27.9767i	0.756989	+	1.04191i
$722$	4.39201	+	13.5172i	0.163454	+	0.503059i
$723$	30.3173	−	37.5657i	1.12751	−	1.39708i
$724$	3.88197	+	2.82041i	0.144272	+	0.104820i
$725$	−11.4127			−0.423856
$726$	19.7367	+	10.5885i	0.732498	+	0.392975i
$727$	−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
$729$	−16.0864	−	21.6848i	−0.595791	−	0.803139i
$730$	−1.30495	−	4.01623i	−0.0482984	−	0.148647i
$731$	17.2048	+	23.6803i	0.636342	+	0.875849i
$732$	2.71680	−	0.732786i	0.100416	−	0.0270845i
$733$	44.7984	−	14.5559i	1.65467	−	0.537633i	0.674922	−	0.737889i	$-0.264177\pi$
$733$	44.7984	−	14.5559i	1.65467	−	0.537633i	0.979744	+	0.200256i	$0.0641773\pi$
$734$	8.71078	−	26.8090i	0.321521	−	0.989539i
$735$	−0.893041	−	1.37019i	−0.0329403	−	0.0505403i
$736$			20.9232i			0.771241i
$737$	−9.62908	−	22.3090i	−0.354692	−	0.821763i
$738$	−1.90983	−	1.70820i	−0.0703018	−	0.0628799i
$739$	7.98936	−	10.9964i	0.293893	−	0.404509i	−0.636381	−	0.771375i	$-0.719569\pi$
$739$	7.98936	−	10.9964i	0.293893	−	0.404509i	0.930274	+	0.366866i	$0.119569\pi$
$740$	−0.673542	−	0.218847i	−0.0247599	−	0.00804498i
$741$	3.30367	+	0.167655i	0.121363	+	0.00615896i
$742$	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	$0.481060\pi$
$744$	31.1664	+	1.58163i	1.14261	+	0.0579855i
$745$	−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
$748$	−1.90983	+	8.50651i	−0.0698303	+	0.311029i
$749$			40.1246i			1.46612i
$750$	4.18470	+	6.42059i	0.152804	+	0.234447i
$751$	−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
$753$	33.9913	−	9.16828i	1.23871	−	0.334111i
$754$	1.18034	+	1.62460i	0.0429854	+	0.0591644i
$755$	−0.661030	−	2.03444i	−0.0240574	−	0.0740409i
$756$	−9.75419	+	1.59460i	−0.354756	+	0.0579952i
$757$	−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
$759$	34.5107	+	9.60897i	1.25266	+	0.348784i
$760$	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	$0.494698\pi$
$762$	−16.4523	+	20.3858i	−0.596005	+	0.738501i
$763$	4.47214	+	13.7638i	0.161902	+	0.498284i
$764$	−8.80427	−	12.1180i	−0.318527	−	0.438415i
$765$	0.493401	−	4.84876i	0.0178389	−	0.175307i
$766$	−13.8820	+	4.51052i	−0.501576	+	0.162972i
$767$	−0.0857567	+	0.263932i	−0.00309650	+	0.00953003i
$768$	−19.2563	+	12.5505i	−0.694850	+	0.452878i
$769$		−	30.7113i		−	1.10748i	−0.832690	−	0.553739i	$-0.813200\pi$
$769$		−	30.7113i		−	1.10748i	0.832690	−	0.553739i	$-0.186800\pi$
$770$	−3.44095	+	3.02786i	−0.124003	+	0.109117i
$771$	−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	−0.608929	−	0.793225i	$-0.708401\pi$
$773$	−43.5896	−	14.1631i	−1.56781	−	0.509412i	−0.958880	+	0.283813i	$0.908401\pi$
$774$	22.2048	+	9.79825i	0.798134	+	0.352191i
$775$	−22.9894	+	16.7027i	−0.825802	+	0.599980i
$776$	−10.9106	+	7.92705i	−0.391669	+	0.284565i
$777$	0.810526	−	15.9716i	0.0290774	−	0.572977i
$778$	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
$781$	9.00658	−	15.1967i	0.322281	−	0.543779i
$782$		−	31.1803i		−	1.11501i
$783$	12.0758	+	1.85120i	0.431555	+	0.0661564i
$784$	1.81966	−	5.60034i	0.0649879	−	0.200012i
$785$	−3.52671	+	1.14590i	−0.125874	+	0.0408989i
$786$	5.51916	+	20.4622i	0.196862	+	0.729864i
$787$	1.83282	+	2.52265i	0.0653328	+	0.0899229i	0.840433	−	0.541915i	$-0.182301\pi$
$787$	1.83282	+	2.52265i	0.0653328	+	0.0899229i	−0.775100	+	0.631838i	$0.782301\pi$
$788$	−1.64484	−	5.06231i	−0.0585951	−	0.180337i
$789$	12.3020	+	9.92827i	0.437962	+	0.353456i
$790$	1.44427	+	1.04932i	0.0513849	+	0.0373333i
$791$	6.32688			0.224958
$792$	9.22663	+	29.1995i	0.327854	+	1.03756i
$793$	1.90983			0.0678201
$794$	21.8743	+	15.8926i	0.776290	+	0.564008i
$795$	−0.954559	−	0.770374i	−0.0338547	−	0.0273223i
$796$	−0.427051	−	1.31433i	−0.0151364	−	0.0465851i
$797$	−21.2008	−	29.1803i	−0.750969	−	1.03362i	−0.997912	−	0.0645905i	$-0.979426\pi$
$797$	−21.2008	−	29.1803i	−0.750969	−	1.03362i	0.246942	−	0.969030i	$-0.420574\pi$
$798$	4.28980	+	15.9044i	0.151857	+	0.563010i
$799$	−33.6803	+	10.9434i	−1.19152	+	0.387150i
$800$	5.03280	−	15.4894i	0.177936	−	0.547631i
$801$	1.54789	−	0.334374i	0.0546919	−	0.0118145i
$802$		−	32.7445i		−	1.15625i
$803$	20.6052	+	23.4164i	0.727143	+	0.826347i
$804$	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
$807$	1.64720	−	32.4583i	0.0579841	−	1.14259i
$808$	−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	$0.422995\pi$
$810$	−1.66813	−	3.68090i	−0.0586122	−	0.129334i
$811$	−19.8992	−	6.46564i	−0.698755	−	0.227039i	−0.0619670	−	0.998078i	$-0.519737\pi$
$811$	−19.8992	−	6.46564i	−0.698755	−	0.227039i	−0.636788	+	0.771039i	$0.719737\pi$
$812$	2.62866	−	3.61803i	0.0922477	−	0.126968i
$813$	−27.4216	−	10.4741i	−0.961719	−	0.367344i
$814$	−11.6459	+	1.08981i	−0.408189	+	0.0381980i
$815$		−	5.58359i		−	0.195585i
$816$	14.7008	−	9.58145i	0.514631	−	0.335418i
$817$	−5.59017	+	17.2048i	−0.195575	+	0.601919i
$818$	23.6579	−	7.68692i	0.827179	−	0.268767i
$819$	−6.67374	−	0.679108i	−0.233199	−	0.0237299i
$820$	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	$0.598611\pi$
$822$	−6.02070	+	7.46016i	−0.209996	+	0.260203i
$823$	−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
$825$	−23.2368	−	15.4145i	−0.809001	−	0.536666i
$826$	−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	$0.550229\pi$
$828$	5.81427	+	9.99406i	0.202060	+	0.347317i
$829$	−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
$831$	−27.1261	+	7.31657i	−0.940995	+	0.253809i
$832$	−6.01722	+	1.95511i	−0.208610	+	0.0677814i
$833$	3.24920	−	10.0000i	0.112578	−	0.346479i
$834$	−15.8017	−	24.2445i	−0.547169	−	0.839520i
$835$			8.05748i			0.278841i
$836$	−4.94704	+	2.13525i	−0.171097	+	0.0738493i
$837$	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	0.336020	−	0.941855i	$-0.390919\pi$
$839$	1.57160	+	0.510643i	0.0542576	+	0.0176294i	−0.281762	+	0.959484i	$0.590919\pi$
$840$	−6.25856	−	0.317610i	−0.215941	−	0.0109586i
$841$	18.9894	−	13.7966i	0.654805	−	0.475744i
$842$	−18.2088	+	13.2295i	−0.627518	+	0.455918i
$843$	−46.0645	−	2.33768i	−1.58655	−	0.0805141i
$844$	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
$847$	14.4721	−	30.6053i	0.497268	−	1.05161i
$848$		−	4.41641i		−	0.151660i
$849$	−20.2127	−	31.0124i	−0.693699	−	1.06434i
$850$	−7.50000	+	23.0826i	−0.257248	+	0.791728i
$851$	−17.7926	+	5.78115i	−0.609921	+	0.198175i
$852$	5.50483	−	1.48479i	0.188592	−	0.0508679i
$853$	−0.551663	−	0.759299i	−0.0188886	−	0.0259979i	0.799468	−	0.600708i	$-0.205115\pi$
$853$	−0.551663	−	0.759299i	−0.0188886	−	0.0259979i	−0.818357	+	0.574710i	$0.805115\pi$
$854$	2.93893	+	9.04508i	0.100568	+	0.309516i
$855$	2.60362	−	1.51471i	0.0890418	−	0.0518021i
$856$	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	$0.296286\pi$
$858$	0.208965	+	4.90199i	0.00713396	+	0.167351i
$859$	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
$861$	−2.43236	+	3.01390i	−0.0828947	+	0.102714i
$862$	−2.19756	−	6.76340i	−0.0748492	−	0.230362i
$863$	0.661030	+	0.909830i	0.0225017	+	0.0309710i	0.820120	−	0.572192i	$-0.193907\pi$
$863$	0.661030	+	0.909830i	0.0225017	+	0.0309710i	−0.797618	+	0.603163i	$0.793907\pi$
$864$	−7.83769	+	15.5730i	−0.266644	+	0.529805i
$865$	8.39261	−	2.72692i	0.285357	−	0.0927182i
$866$	−2.17963	+	6.70820i	−0.0740668	+	0.227954i
$867$	1.58190	−	1.03102i	0.0537241	−	0.0350154i
$868$		−	11.1352i		−	0.377952i
$869$	−12.8658	−	2.88854i	−0.436441	−	0.0979871i
$870$	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
$873$	−5.30713	+	12.0270i	−0.179619	+	0.407053i
$874$	15.5902	−	11.3269i	0.527345	−	0.383139i
$875$	9.37181	−	6.80902i	0.316825	−	0.230187i
$876$	−0.510238	+	10.0543i	−0.0172393	+	0.339704i
$877$	−32.7254	−	10.6331i	−1.10506	−	0.359055i	−0.301012	−	0.953620i	$-0.597324\pi$
$877$	−32.7254	−	10.6331i	−1.10506	−	0.359055i	−0.804048	+	0.594565i	$0.797324\pi$
$878$	−1.88960	+	2.60081i	−0.0637710	+	0.0877732i
$879$	−8.61251	+	22.5478i	−0.290493	+	0.760520i
$880$	0.281153	+	3.00444i	0.00947766	+	0.101280i
$881$			29.9230i			1.00813i	0.863665	+	0.504066i	$0.168163\pi$
$881$			29.9230i			1.00813i	−0.863665	+	0.504066i	$0.831837\pi$
$882$	−1.84090	−	8.52194i	−0.0619864	−	0.286949i
$883$	−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
$885$	0.0658083	+	0.243984i	0.00221212	+	0.00820142i
$886$	−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	$0.975166\pi$
$888$	−12.4448	−	10.0436i	−0.417622	−	0.337040i
$889$	32.0344	+	23.2744i	1.07440	+	0.780598i
$890$	0.237026			0.00794512
$891$	22.0866	+	20.0793i	0.739930	+	0.672683i
$892$	−1.09017			−0.0365016
$893$	−17.7068	−	12.8647i	−0.592536	−	0.430502i
$894$	−20.6576	−	16.6717i	−0.690894	−	0.557584i
$895$	−1.64590	−	5.06555i	−0.0550163	−	0.169323i
$896$	−6.37988	−	8.78115i	−0.213137	−	0.293358i
$897$	2.04363	+	7.57675i	0.0682349	+	0.252980i
$898$	31.1803	−	10.1311i	1.04050	−	0.338079i
$899$	−4.25325	+	13.0902i	−0.141854	+	0.436582i
$900$	−1.90034	−	8.79709i	−0.0633446	−	0.293236i
$901$		−	7.88597i		−	0.262720i
$902$	2.43690	+	1.44427i	0.0811398	+	0.0480890i
$903$	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
$906$	0.577942	−	11.3885i	0.0192008	−	0.378356i
$907$	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
$909$	−19.3096	+	43.7594i	−0.640459	+	1.45141i
$910$	−0.954915	−	0.310271i	−0.0316551	−	0.0102854i
$911$	18.6453	−	25.6631i	0.617748	−	0.850257i	−0.379439	−	0.925217i	$-0.623883\pi$
$911$	18.6453	−	25.6631i	0.617748	−	0.850257i	0.997187	+	0.0749598i	$0.0238829\pi$
$912$	10.1311	+	3.86974i	0.335474	+	0.128140i
$913$	18.0517	+	10.6986i	0.597423	+	0.354074i
$914$		−	29.4721i		−	0.974852i
$915$	1.45694	−	0.949583i	0.0481651	−	0.0313922i
$916$	2.88854	−	8.89002i	0.0954402	−	0.293735i
$917$	30.4666	−	9.89919i	1.00609	−	0.326900i
$918$	11.6799	−	23.2073i	0.385495	−	0.765956i
$919$	−27.2599	−	37.5200i	−0.899220	−	1.23767i	−0.970716	−	0.240229i	$-0.922777\pi$
$919$	−27.2599	−	37.5200i	−0.899220	−	1.23767i	0.0714961	−	0.997441i	$-0.477223\pi$
$920$	2.26538	+	6.97214i	0.0746875	+	0.229865i
$921$	10.3455	−	12.8189i	0.340894	−	0.422397i
$922$	29.2082	+	21.2210i	0.961921	+	0.698876i
$923$	3.86974			0.127374
$924$	10.2388	−	3.81610i	0.336831	−	0.125541i
$925$	14.5623			0.478806
$926$	−31.6421	−	22.9894i	−1.03983	−	0.755477i
$927$	29.1362	−	16.9507i	0.956958	−	0.556733i
$928$	−2.43769	−	7.50245i	−0.0800212	−	0.246280i
$929$	18.9884	+	26.1353i	0.622988	+	0.857470i	0.997566	−	0.0697256i	$-0.0222124\pi$
$929$	18.9884	+	26.1353i	0.622988	+	0.857470i	−0.374578	+	0.927195i	$0.622212\pi$
$930$	4.39587	−	1.18567i	0.144146	−	0.0388797i
$931$	6.18034	−	2.00811i	0.202552	−	0.0658133i
$932$	−1.84911	+	5.69098i	−0.0605697	+	0.186414i
$933$	−4.72873	−	7.25528i	−0.154812	−	0.237527i
$934$			8.99602i			0.294359i
$935$	0.502029	+	5.36475i	0.0164181	+	0.175446i
$936$	−4.47214	+	5.00000i	−0.146176	+	0.163430i
$937$	−21.4828	+	29.5685i	−0.701812	+	0.965961i	0.298123	+	0.954528i	$0.403639\pi$
$937$	−21.4828	+	29.5685i	−0.701812	+	0.965961i	−0.999935	+	0.0114336i	$0.996361\pi$
$938$	25.2093	+	8.19098i	0.823111	+	0.267445i
$939$	−19.0281	−	0.965638i	−0.620958	−	0.0315124i
$940$	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	$0.101692\pi$
$942$	−19.7419	−	1.00186i	−0.643227	−	0.0326425i
$943$	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
$946$	−26.1803	−	5.87785i	−0.851196	−	0.191105i
$947$			17.1459i			0.557167i	0.960412	+	0.278583i	$0.0898649\pi$
$947$			17.1459i			0.557167i	−0.960412	+	0.278583i	$0.910135\pi$
$948$	−2.32383	−	3.56545i	−0.0754745	−	0.115801i
$949$	−2.11146	+	6.49839i	−0.0685408	+	0.210947i
$950$	−14.2658	+	4.63525i	−0.462845	+	0.150388i
$951$	−7.08393	+	1.91071i	−0.229712	+	0.0619589i
$952$	−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	$0.879280\pi$
$954$	−3.28817	−	5.65198i	−0.106458	−	0.182990i
$955$	−7.48936	−	5.44134i	−0.242350	−	0.176078i
$956$	−4.76779			−0.154201
$957$	−13.4940	+	0.575233i	−0.436200	+	0.0185946i
$958$	−23.5410			−0.760576
$959$	11.7229	+	8.51722i	0.378554	+	0.275035i
$960$	−3.61823	+	4.48330i	−0.116778	+	0.144698i
$961$	1.01064	+	3.11044i	0.0326014	+	0.100337i
$962$	−1.50609	−	2.07295i	−0.0485581	−	0.0668346i
$963$	38.9109	+	3.95950i	1.25389	+	0.127593i
$964$	−16.3820	+	5.32282i	−0.527628	+	0.171437i
$965$	−1.16306	+	3.57953i	−0.0374402	+	0.115229i
$966$	−32.7392	+	21.3382i	−1.05337	+	0.686545i
$967$			12.9313i			0.415842i	0.978146	+	0.207921i	$0.0666697\pi$
$967$			12.9313i			0.415842i	−0.978146	+	0.207921i	$0.933330\pi$
$968$	−16.2537	−	29.6976i	−0.522414	−	0.954516i
$969$	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	0.431179	−	0.902266i	$-0.358098\pi$
$971$	7.77997	+	2.52786i	0.249671	+	0.0811230i	−0.181508	+	0.983389i	$0.558098\pi$
$972$	0.583826	+	9.61649i	0.0187262	+	0.308449i
$973$	−35.3885	+	25.7113i	−1.13450	+	0.824266i
$974$	−1.40008	+	1.01722i	−0.0448616	+	0.0325939i
$975$	0.309593	−	6.10059i	0.00991492	−	0.195375i
$976$	5.95492	+	1.93487i	0.190612	+	0.0619337i
$977$	−20.0175	+	27.5517i	−0.640415	+	0.881456i	−0.998638	−	0.0521804i	$-0.983383\pi$
$977$	−20.0175	+	27.5517i	−0.640415	+	0.881456i	0.358223	+	0.933636i	$0.383383\pi$
$978$	10.6206	−	27.8052i	0.339610	−	0.889111i
$979$	−1.60739	+	0.693786i	−0.0513724	+	0.0221735i
$980$			0.583592i			0.0186422i
$981$	13.7888	−	2.97864i	0.440242	−	0.0951008i
$982$	−6.42047	+	19.7602i	−0.204886	+	0.630573i
$983$	−54.5002	+	17.7082i	−1.73829	+	0.564804i	−0.994606	−	0.103729i	$-0.966922\pi$
$983$	−54.5002	+	17.7082i	−1.73829	+	0.564804i	−0.743682	+	0.668533i	$0.766922\pi$
$984$	1.00859	+	3.73935i	0.0321528	+	0.119206i
$985$	−1.93363	−	2.66141i	−0.0616105	−	0.0847996i
$986$	3.63271	+	11.1803i	0.115689	+	0.356055i
$987$	34.5396	+	27.8751i	1.09941	+	0.887273i
$988$	−0.954915	−	0.693786i	−0.0303799	−	0.0220723i
$989$	−42.9161			−1.36465
$990$	2.59672	+	3.63566i	0.0825292	+	0.115549i
$991$	−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
$993$	17.3719	+	14.0200i	0.551282	+	0.444910i
$994$	5.95492	+	18.3273i	0.188878	+	0.581308i
$995$	−0.502029	−	0.690983i	−0.0159154	−	0.0219056i
$996$	1.76373	+	6.53903i	0.0558860	+	0.207197i
$997$	14.0066	−	4.55101i	0.443593	−	0.144132i	−0.0786999	−	0.996898i	$-0.525077\pi$
$997$	14.0066	−	4.55101i	0.443593	−	0.144132i	0.522293	+	0.852766i	$0.325077\pi$
$998$	−13.0700	+	40.2254i	−0.413725	+	1.27331i
$999$	−15.4085	−	2.36208i	−0.487502	−	0.0747330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.2.f.a.29.1	yes	8
3.2	odd	2	inner	33.2.f.a.29.2	yes	8
4.3	odd	2		528.2.bn.c.161.1		8
5.2	odd	4		825.2.bs.d.524.2		8
5.3	odd	4		825.2.bs.a.524.1		8
5.4	even	2		825.2.bi.b.326.2		8
9.2	odd	6		891.2.u.a.458.2		16
9.4	even	3		891.2.u.a.755.2		16
9.5	odd	6		891.2.u.a.755.1		16
9.7	even	3		891.2.u.a.458.1		16
11.2	odd	10		363.2.f.d.215.1		8
11.3	even	5		363.2.f.b.239.1		8
11.4	even	5		363.2.f.d.233.2		8
11.5	even	5		363.2.d.f.362.6		8
11.6	odd	10		363.2.d.f.362.4		8
11.7	odd	10		363.2.f.e.233.1		8
11.8	odd	10	inner	33.2.f.a.8.2	yes	8
11.9	even	5		363.2.f.e.215.2		8
11.10	odd	2		363.2.f.b.161.2		8
12.11	even	2		528.2.bn.c.161.2		8
15.2	even	4		825.2.bs.a.524.2		8
15.8	even	4		825.2.bs.d.524.1		8
15.14	odd	2		825.2.bi.b.326.1		8
33.2	even	10		363.2.f.d.215.2		8
33.5	odd	10		363.2.d.f.362.3		8
33.8	even	10	inner	33.2.f.a.8.1	✓	8
33.14	odd	10		363.2.f.b.239.2		8
33.17	even	10		363.2.d.f.362.5		8
33.20	odd	10		363.2.f.e.215.1		8
33.26	odd	10		363.2.f.d.233.1		8
33.29	even	10		363.2.f.e.233.2		8
33.32	even	2		363.2.f.b.161.1		8
44.19	even	10		528.2.bn.c.305.2		8
55.8	even	20		825.2.bs.a.74.2		8
55.19	odd	10		825.2.bi.b.701.1		8
55.52	even	20		825.2.bs.d.74.1		8
99.41	even	30		891.2.u.a.107.1		16
99.52	odd	30		891.2.u.a.701.1		16
99.74	even	30		891.2.u.a.701.2		16
99.85	odd	30		891.2.u.a.107.2		16
132.107	odd	10		528.2.bn.c.305.1		8
165.8	odd	20		825.2.bs.d.74.2		8
165.74	even	10		825.2.bi.b.701.2		8
165.107	odd	20		825.2.bs.a.74.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.8.1	✓	8	33.8	even	10	inner
33.2.f.a.8.2	yes	8	11.8	odd	10	inner
33.2.f.a.29.1	yes	8	1.1	even	1	trivial
33.2.f.a.29.2	yes	8	3.2	odd	2	inner
363.2.d.f.362.3		8	33.5	odd	10
363.2.d.f.362.4		8	11.6	odd	10
363.2.d.f.362.5		8	33.17	even	10
363.2.d.f.362.6		8	11.5	even	5
363.2.f.b.161.1		8	33.32	even	2
363.2.f.b.161.2		8	11.10	odd	2
363.2.f.b.239.1		8	11.3	even	5
363.2.f.b.239.2		8	33.14	odd	10
363.2.f.d.215.1		8	11.2	odd	10
363.2.f.d.215.2		8	33.2	even	10
363.2.f.d.233.1		8	33.26	odd	10
363.2.f.d.233.2		8	11.4	even	5
363.2.f.e.215.1		8	33.20	odd	10
363.2.f.e.215.2		8	11.9	even	5
363.2.f.e.233.1		8	11.7	odd	10
363.2.f.e.233.2		8	33.29	even	10
528.2.bn.c.161.1		8	4.3	odd	2
528.2.bn.c.161.2		8	12.11	even	2
528.2.bn.c.305.1		8	132.107	odd	10
528.2.bn.c.305.2		8	44.19	even	10
825.2.bi.b.326.1		8	15.14	odd	2
825.2.bi.b.326.2		8	5.4	even	2
825.2.bi.b.701.1		8	55.19	odd	10
825.2.bi.b.701.2		8	165.74	even	10
825.2.bs.a.74.1		8	165.107	odd	20
825.2.bs.a.74.2		8	55.8	even	20
825.2.bs.a.524.1		8	5.3	odd	4
825.2.bs.a.524.2		8	15.2	even	4
825.2.bs.d.74.1		8	55.52	even	20
825.2.bs.d.74.2		8	165.8	odd	20
825.2.bs.d.524.1		8	15.8	even	4
825.2.bs.d.524.2		8	5.2	odd	4
891.2.u.a.107.1		16	99.41	even	30
891.2.u.a.107.2		16	99.85	odd	30
891.2.u.a.458.1		16	9.7	even	3
891.2.u.a.458.2		16	9.2	odd	6
891.2.u.a.701.1		16	99.52	odd	30
891.2.u.a.701.2		16	99.74	even	30
891.2.u.a.755.1		16	9.5	odd	6
891.2.u.a.755.2		16	9.4	even	3

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.690983i) q^{2} +(1.34786 + 1.08779i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-0.224514 - 0.309017i) q^{5} +(-0.530249 - 1.96589i) q^{6} +(-2.92705 + 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(0.633446 + 2.93236i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.690983i) q^{2} +(1.34786 + 1.08779i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-0.224514 - 0.309017i) q^{5} +(-0.530249 - 1.96589i) q^{6} +(-2.92705 + 0.951057i) q^{7} +(-0.951057 + 2.92705i) q^{8} +(0.633446 + 2.93236i) q^{9} +0.449028i q^{10} +(-1.31433 - 3.04508i) q^{11} +(0.381966 - 1.00000i) q^{12} +(0.427051 - 0.587785i) q^{13} +(3.44095 + 1.11803i) q^{14} +(0.0335310 - 0.660734i) q^{15} +(1.92705 - 1.40008i) q^{16} +(3.44095 - 2.50000i) q^{17} +(1.42377 - 3.22654i) q^{18} +(2.50000 + 0.812299i) q^{19} +(-0.138757 + 0.190983i) q^{20} +(-4.97980 - 1.90211i) q^{21} +(-0.854102 + 3.80423i) q^{22} +6.23607i q^{23} +(-4.46589 + 2.91071i) q^{24} +(1.50000 - 4.61653i) q^{25} +(-0.812299 + 0.263932i) q^{26} +(-2.33598 + 4.64146i) q^{27} +(1.11803 + 1.53884i) q^{28} +(-0.726543 - 2.23607i) q^{29} +(-0.488446 + 0.605226i) q^{30} +(-4.73607 - 3.44095i) q^{31} +3.35520 q^{32} +(1.54087 - 5.53405i) q^{33} -5.00000 q^{34} +(0.951057 + 0.690983i) q^{35} +(1.60262 - 0.932362i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-1.81636 - 2.50000i) q^{38} +(1.21499 - 0.327712i) q^{39} +(1.11803 - 0.363271i) q^{40} +(0.224514 - 0.690983i) q^{41} +(3.42174 + 5.24997i) q^{42} +6.88191i q^{43} +(-1.53884 + 1.35410i) q^{44} +(0.763932 - 0.854102i) q^{45} +(4.30902 - 5.93085i) q^{46} +(-7.91872 - 2.57295i) q^{47} +(4.12038 + 0.209101i) q^{48} +(2.00000 - 1.45309i) q^{49} +(-4.61653 + 3.35410i) q^{50} +(7.35738 + 0.373373i) q^{51} +(-0.427051 - 0.138757i) q^{52} +(1.08981 - 1.50000i) q^{53} +(5.42882 - 2.80017i) q^{54} +(-0.645898 + 1.08981i) q^{55} -9.47214i q^{56} +(2.48604 + 3.81433i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(-0.363271 + 0.118034i) q^{59} +(-0.394774 + 0.106480i) q^{60} +(1.54508 + 2.12663i) q^{61} +(2.12663 + 6.54508i) q^{62} +(-4.64297 - 7.98073i) q^{63} +(-7.04508 - 5.11855i) q^{64} -0.277515 q^{65} +(-5.28939 + 4.19848i) q^{66} +7.32624 q^{67} +(-2.12663 - 1.54508i) q^{68} +(-6.78350 + 8.40534i) q^{69} +(-0.427051 - 1.31433i) q^{70} +(3.13068 + 4.30902i) q^{71} +(-9.18562 - 0.934712i) q^{72} +(-8.94427 + 2.90617i) q^{73} +(1.08981 - 3.35410i) q^{74} +(7.04358 - 4.59075i) q^{75} -1.62460i q^{76} +(6.74315 + 7.66312i) q^{77} +(-1.38197 - 0.527864i) q^{78} +(2.33688 - 3.21644i) q^{79} +(-0.865300 - 0.281153i) q^{80} +(-8.19749 + 3.71499i) q^{81} +(-0.690983 + 0.502029i) q^{82} +(-5.11855 + 3.71885i) q^{83} +(-0.166977 + 3.29032i) q^{84} +(-1.54508 - 0.502029i) q^{85} +(4.75528 - 6.54508i) q^{86} +(1.45309 - 3.80423i) q^{87} +(10.1631 - 0.951057i) q^{88} -0.527864i q^{89} +(-1.31671 + 0.284435i) q^{90} +(-0.690983 + 2.12663i) q^{91} +(3.66547 - 1.19098i) q^{92} +(-2.64053 - 9.78975i) q^{93} +(5.75329 + 7.91872i) q^{94} +(-0.310271 - 0.954915i) q^{95} +(4.52233 + 3.64973i) q^{96} +(3.54508 + 2.57565i) q^{97} -2.90617 q^{98} +(8.09673 - 5.78298i) q^{99} +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	\( 8 q - 6 q^{3} - 6 q^{4} - 10 q^{7} + 10 q^{9} + 12 q^{12} - 10 q^{13} - 6 q^{15} + 2 q^{16} + 20 q^{19} + 20 q^{22} - 10 q^{24} + 12 q^{25} - 12 q^{27} - 20 q^{30} - 20 q^{31} - 4 q^{33} - 40 q^{34} - 10 q^{36} - 6 q^{37} + 20 q^{39} + 20 q^{42} + 24 q^{45} + 30 q^{46} + 26 q^{48} + 16 q^{49} + 30 q^{51} + 10 q^{52} - 32 q^{55} - 30 q^{57} + 20 q^{58} + 2 q^{60} - 10 q^{61} - 30 q^{63} - 34 q^{64} - 30 q^{66} - 4 q^{67} - 16 q^{69} + 10 q^{70} - 20 q^{72} + 6 q^{75} - 20 q^{78} + 50 q^{79} - 2 q^{81} - 10 q^{82} + 10 q^{85} + 50 q^{88} + 40 q^{90} - 10 q^{91} + 10 q^{93} - 30 q^{94} + 10 q^{96} + 6 q^{97} + 16 q^{99}+O(q^{100}) \) 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 + 20 * q^22 - 10 * q^24 + 12 * q^25 - 12 * q^27 - 20 * q^30 - 20 * q^31 - 4 * q^33 - 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 - 32 * q^55 - 30 * q^57 + 20 * q^58 + 2 * q^60 - 10 * q^61 - 30 * q^63 - 34 * q^64 - 30 * q^66 - 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 + 50 * q^88 + 40 * q^90 - 10 * q^91 + 10 * q^93 - 30 * q^94 + 10 * q^96 + 6 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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