LMFDB - Embedded newform 363.2.f.a.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:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
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			161.1
Root			$-0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	363.161
Dual form			363.2.f.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.03598 - 1.38807i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.66251 + 2.28825i) q^{5} +(0.0222369 + 1.73191i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.853491 + 2.87603i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.03598 - 1.38807i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.66251 + 2.28825i) q^{5} +(0.0222369 + 1.73191i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.853491 + 2.87603i) q^{9} -2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 + 3.43237i) q^{13} +(1.34500 + 0.437016i) q^{14} +(1.45393 - 4.67826i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.85410 + 3.52671i) q^{17} +(2.38098 - 1.82509i) q^{18} +(4.03499 + 1.31105i) q^{19} +(1.66251 - 2.28825i) q^{20} +(2.00000 + 1.41421i) q^{21} +(4.92081 - 1.66901i) q^{24} +(-0.927051 + 2.85317i) q^{25} +(4.03499 - 1.31105i) q^{26} +(4.87634 - 1.79480i) q^{27} +(0.831254 + 1.14412i) q^{28} +(-0.618034 - 1.90211i) q^{29} +(-3.92606 + 2.93019i) q^{30} +(1.61803 + 1.17557i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(-3.23607 - 2.35114i) q^{35} +(2.99901 - 0.0770245i) q^{36} +(2.47214 + 7.60845i) q^{37} +(-2.49376 - 3.43237i) q^{38} +(7.34786 - 0.0943431i) q^{39} +(-8.06998 + 2.62210i) q^{40} +(1.85410 - 5.70634i) q^{41} +(-0.786780 - 2.31969i) q^{42} +4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(-2.68999 - 0.874032i) q^{47} +(-1.65401 - 0.514040i) q^{48} +(-4.04508 + 2.93893i) q^{49} +(2.42705 - 1.76336i) q^{50} +(9.92408 + 3.08424i) q^{51} +(4.03499 + 1.31105i) q^{52} +(-3.32502 + 4.57649i) q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(-2.36034 - 6.95908i) q^{57} +(-0.618034 + 1.90211i) q^{58} +(-10.7600 + 3.49613i) q^{59} +(-4.89858 + 0.0628954i) q^{60} +(-5.81878 - 8.00886i) q^{61} +(-0.618034 - 1.90211i) q^{62} +(-0.108929 - 4.24124i) q^{63} +(-5.66312 - 4.11450i) q^{64} -12.0000 q^{65} +2.00000 q^{67} +(4.85410 + 3.52671i) q^{68} +(1.23607 + 3.80423i) q^{70} +(1.66251 + 2.28825i) q^{71} +(-7.41457 - 5.10138i) q^{72} +(-1.34500 + 0.437016i) q^{73} +(2.47214 - 7.60845i) q^{74} +(4.92081 - 1.66901i) q^{75} -4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-2.49376 + 3.43237i) q^{79} +(2.68999 + 0.874032i) q^{80} +(-7.54311 - 4.90933i) q^{81} +(-4.85410 + 3.52671i) q^{82} +(12.9443 - 9.40456i) q^{83} +(0.726963 - 2.33913i) q^{84} +(-16.1400 - 5.24419i) q^{85} +(2.49376 - 3.43237i) q^{86} +(-2.00000 + 2.82843i) q^{87} +(8.13464 + 2.41404i) q^{90} +(1.85410 - 5.70634i) q^{91} +(-0.0444738 - 3.46382i) q^{93} +(1.66251 + 2.28825i) q^{94} +(3.70820 + 11.4127i) q^{95} +(-5.17990 - 6.94036i) q^{96} +(1.61803 + 1.17557i) q^{97} +5.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} + 16 q^{21} + 6 q^{24} + 6 q^{25} + 10 q^{27} + 4 q^{29} + 8 q^{30} + 4 q^{31} + 40 q^{32} + 48 q^{34} - 8 q^{35} - 2 q^{36} - 16 q^{37} + 12 q^{39} - 12 q^{41} - 4 q^{42} - 64 q^{45} + 2 q^{48} - 10 q^{49} + 6 q^{50} - 12 q^{51} - 40 q^{54} - 12 q^{57} + 4 q^{58} - 8 q^{60} + 4 q^{62} - 8 q^{63} - 14 q^{64} - 96 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} - 6 q^{72} - 16 q^{74} + 6 q^{75} - 48 q^{78} + 14 q^{81} - 12 q^{82} + 32 q^{83} + 4 q^{84} - 16 q^{87} + 16 q^{90} - 12 q^{91} + 4 q^{93} - 24 q^{95} - 10 q^{96} + 4 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 + 16 * q^21 + 6 * q^24 + 6 * q^25 + 10 * q^27 + 4 * q^29 + 8 * q^30 + 4 * q^31 + 40 * q^32 + 48 * q^34 - 8 * q^35 - 2 * q^36 - 16 * q^37 + 12 * q^39 - 12 * q^41 - 4 * q^42 - 64 * q^45 + 2 * q^48 - 10 * q^49 + 6 * q^50 - 12 * q^51 - 40 * q^54 - 12 * q^57 + 4 * q^58 - 8 * q^60 + 4 * q^62 - 8 * q^63 - 14 * q^64 - 96 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 - 6 * q^72 - 16 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 32 * q^83 + 4 * q^84 - 16 * q^87 + 16 * q^90 - 12 * q^91 + 4 * q^93 - 24 * q^95 - 10 * q^96 + 4 * q^97 + 40 * q^98

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	0.263792	−	0.964580i	$-0.415027\pi$
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	−0.835853	+	0.548953i	$0.815027\pi$
$3$	−1.03598	−	1.38807i	−0.598123	−	0.801404i
$3$	−1.03598	−	1.38807i	−0.598123	−	0.801404i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.66251	+	2.28825i	0.743496	+	1.02333i	0.998410	+	0.0563708i	$0.0179529\pi$
$5$	1.66251	+	2.28825i	0.743496	+	1.02333i	−0.254914	+	0.966964i	$0.582047\pi$
$6$	0.0222369	+	1.73191i	0.00907817	+	0.707049i
$7$	−1.34500	+	0.437016i	−0.508361	+	0.165177i	−0.551957	−	0.833873i	$-0.686119\pi$
$7$	−1.34500	+	0.437016i	−0.508361	+	0.165177i	0.0435957	+	0.999049i	$0.486119\pi$
$8$	−0.927051	+	2.85317i	−0.327762	+	1.00875i
$9$	−0.853491	+	2.87603i	−0.284497	+	0.958677i
$10$		−	2.82843i		−	0.894427i
$11$		0			0
$11$		0			0
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−2.49376	+	3.43237i	−0.691645	+	0.951968i	0.308355	+	0.951271i	$0.400222\pi$
$13$	−2.49376	+	3.43237i	−0.691645	+	0.951968i	−1.00000		0.000696272i	$0.999778\pi$
$14$	1.34500	+	0.437016i	0.359466	+	0.116797i
$15$	1.45393	−	4.67826i	0.375402	−	1.20792i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−4.85410	+	3.52671i	−1.17729	+	0.855353i	−0.991864	−	0.127304i	$-0.959367\pi$
$17$	−4.85410	+	3.52671i	−1.17729	+	0.855353i	−0.185429	+	0.982658i	$0.559367\pi$
$18$	2.38098	−	1.82509i	0.561202	−	0.430178i
$19$	4.03499	+	1.31105i	0.925690	+	0.300775i	0.732799	−	0.680445i	$-0.238214\pi$
$19$	4.03499	+	1.31105i	0.925690	+	0.300775i	0.192891	+	0.981220i	$0.438214\pi$
$20$	1.66251	−	2.28825i	0.371748	−	0.511667i
$21$	2.00000	+	1.41421i	0.436436	+	0.308607i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	4.92081	−	1.66901i	1.00446	−	0.340686i
$25$	−0.927051	+	2.85317i	−0.185410	+	0.570634i
$26$	4.03499	−	1.31105i	0.791327	−	0.257118i
$27$	4.87634	−	1.79480i	0.938452	−	0.345410i
$28$	0.831254	+	1.14412i	0.157092	+	0.216219i
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	0.877132	−	0.480249i	$-0.159454\pi$
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	−0.991898	+	0.127036i	$0.959454\pi$
$30$	−3.92606	+	2.93019i	−0.716798	+	0.534978i
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	0.723531	−	0.690292i	$-0.242518\pi$
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	−0.432923	+	0.901431i	$0.642518\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$	−3.23607	−	2.35114i	−0.546995	−	0.397415i
$36$	2.99901	−	0.0770245i	0.499835	−	0.0128374i
$37$	2.47214	+	7.60845i	0.406417	+	1.25082i	0.919707	+	0.392607i	$0.128427\pi$
$37$	2.47214	+	7.60845i	0.406417	+	1.25082i	−0.513290	+	0.858215i	$0.671573\pi$
$38$	−2.49376	−	3.43237i	−0.404542	−	0.556804i
$39$	7.34786	−	0.0943431i	1.17660	−	0.0151070i
$40$	−8.06998	+	2.62210i	−1.27598	+	0.414590i
$41$	1.85410	−	5.70634i	0.289562	−	0.891180i	−0.695432	−	0.718592i	$-0.744787\pi$
$41$	1.85410	−	5.70634i	0.289562	−	0.891180i	0.984994	−	0.172588i	$-0.0552131\pi$
$42$	−0.786780	−	2.31969i	−0.121403	−	0.357936i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	−8.00000	+	2.82843i	−1.19257	+	0.421637i
$46$		0			0
$47$	−2.68999	−	0.874032i	−0.392376	−	0.127491i	0.106183	−	0.994347i	$-0.466137\pi$
$47$	−2.68999	−	0.874032i	−0.392376	−	0.127491i	−0.498559	+	0.866856i	$0.666137\pi$
$48$	−1.65401	−	0.514040i	−0.238736	−	0.0741954i
$49$	−4.04508	+	2.93893i	−0.577869	+	0.419847i
$50$	2.42705	−	1.76336i	0.343237	−	0.249376i
$51$	9.92408	+	3.08424i	1.38965	+	0.431880i
$52$	4.03499	+	1.31105i	0.559553	+	0.181810i
$53$	−3.32502	+	4.57649i	−0.456726	+	0.628629i	−0.973826	−	0.227296i	$-0.927012\pi$
$53$	−3.32502	+	4.57649i	−0.456726	+	0.628629i	0.517100	+	0.855925i	$0.327012\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$	−2.36034	−	6.95908i	−0.312635	−	0.921753i
$58$	−0.618034	+	1.90211i	−0.0811518	+	0.249760i
$59$	−10.7600	+	3.49613i	−1.40083	+	0.455157i	−0.909459	−	0.415794i	$-0.863504\pi$
$59$	−10.7600	+	3.49613i	−1.40083	+	0.455157i	−0.491371	+	0.870951i	$0.663504\pi$
$60$	−4.89858	+	0.0628954i	−0.632403	+	0.00811976i
$61$	−5.81878	−	8.00886i	−0.745018	−	1.02543i	−0.998314	−	0.0580406i	$-0.981515\pi$
$61$	−5.81878	−	8.00886i	−0.745018	−	1.02543i	0.253296	−	0.967389i	$-0.418485\pi$
$62$	−0.618034	−	1.90211i	−0.0784904	−	0.241569i
$63$	−0.108929	−	4.24124i	−0.0137238	−	0.534346i
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−12.0000			−1.48842
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	4.85410	+	3.52671i	0.588646	+	0.427677i
$69$		0			0
$70$	1.23607	+	3.80423i	0.147738	+	0.454692i
$71$	1.66251	+	2.28825i	0.197303	+	0.271565i	0.896193	−	0.443665i	$-0.146322\pi$
$71$	1.66251	+	2.28825i	0.197303	+	0.271565i	−0.698889	+	0.715230i	$0.746322\pi$
$72$	−7.41457	−	5.10138i	−0.873816	−	0.601204i
$73$	−1.34500	+	0.437016i	−0.157420	+	0.0511489i	−0.386667	−	0.922219i	$-0.626374\pi$
$73$	−1.34500	+	0.437016i	−0.157420	+	0.0511489i	0.229247	+	0.973368i	$0.426374\pi$
$74$	2.47214	−	7.60845i	0.287380	−	0.884465i
$75$	4.92081	−	1.66901i	0.568206	−	0.192721i
$76$		−	4.24264i		−	0.486664i
$77$		0			0
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$	−2.49376	+	3.43237i	−0.280570	+	0.386172i	−0.925923	−	0.377713i	$-0.876710\pi$
$79$	−2.49376	+	3.43237i	−0.280570	+	0.386172i	0.645353	+	0.763885i	$0.276710\pi$
$80$	2.68999	+	0.874032i	0.300750	+	0.0977198i
$81$	−7.54311	−	4.90933i	−0.838123	−	0.545481i
$82$	−4.85410	+	3.52671i	−0.536046	+	0.389460i
$83$	12.9443	−	9.40456i	1.42082	−	1.03229i	0.429183	−	0.903218i	$-0.358802\pi$
$83$	12.9443	−	9.40456i	1.42082	−	1.03229i	0.991636	−	0.129067i	$-0.0411983\pi$
$84$	0.726963	−	2.33913i	0.0793182	−	0.255220i
$85$	−16.1400	−	5.24419i	−1.75062	−	0.568813i
$86$	2.49376	−	3.43237i	0.268909	−	0.370122i
$87$	−2.00000	+	2.82843i	−0.214423	+	0.303239i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	8.13464	+	2.41404i	0.857467	+	0.254462i
$91$	1.85410	−	5.70634i	0.194363	−	0.598187i
$92$		0			0
$93$	−0.0444738	−	3.46382i	−0.00461171	−	0.359181i
$94$	1.66251	+	2.28825i	0.171475	+	0.236015i
$95$	3.70820	+	11.4127i	0.380454	+	1.17092i
$96$	−5.17990	−	6.94036i	−0.528671	−	0.708348i
$97$	1.61803	+	1.17557i	0.164286	+	0.119361i	0.666891	−	0.745155i	$-0.267625\pi$
$97$	1.61803	+	1.17557i	0.164286	+	0.119361i	−0.502604	+	0.864517i	$0.667625\pi$
$98$	5.00000			0.505076
$99$		0			0
$100$	3.00000			0.300000
$101$	8.09017	+	5.87785i	0.805002	+	0.584868i	0.912377	−	0.409350i	$-0.134245\pi$
$101$	8.09017	+	5.87785i	0.805002	+	0.584868i	−0.107375	+	0.994219i	$0.534245\pi$
$102$	−6.21588	−	8.32844i	−0.615464	−	0.824638i
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	0.995866	+	0.0908382i	$0.0289546\pi$
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	−0.752279	+	0.658845i	$0.771045\pi$
$104$	−7.48128	−	10.2971i	−0.733600	−	1.00971i
$105$	0.0889475	+	6.92763i	0.00868039	+	0.676068i
$106$	5.37999	−	1.74806i	0.522551	−	0.169787i
$107$	−4.94427	+	15.2169i	−0.477981	+	1.47107i	0.363914	+	0.931432i	$0.381440\pi$
$107$	−4.94427	+	15.2169i	−0.477981	+	1.47107i	−0.841895	+	0.539641i	$0.818560\pi$
$108$	−3.21383	−	4.08305i	−0.309251	−	0.392892i
$109$			4.24264i			0.406371i	0.979140	+	0.203186i	$0.0651295\pi$
$109$			4.24264i			0.406371i	−0.979140	+	0.203186i	$0.934871\pi$
$110$		0			0
$111$	8.00000	−	11.3137i	0.759326	−	1.07385i
$112$	−0.831254	+	1.14412i	−0.0785461	+	0.108109i
$113$	−2.68999	−	0.874032i	−0.253053	−	0.0822220i	0.179743	−	0.983714i	$-0.442473\pi$
$113$	−2.68999	−	0.874032i	−0.253053	−	0.0822220i	−0.432797	+	0.901492i	$0.642473\pi$
$114$	−2.18089	+	7.01739i	−0.204259	+	0.657239i
$115$		0			0
$116$	−1.61803	+	1.17557i	−0.150231	+	0.109149i
$117$	−7.74320	−	10.1016i	−0.715859	−	0.933896i
$118$	10.7600	+	3.49613i	0.990536	+	0.321845i
$119$	4.98752	−	6.86474i	0.457206	−	0.629289i
$120$	12.0000	+	8.48528i	1.09545	+	0.774597i
$121$		0			0
$122$			9.89949i			0.896258i
$123$	−9.84163	+	3.33803i	−0.887389	+	0.300980i
$124$	0.618034	−	1.90211i	0.0555011	−	0.170815i
$125$	5.37999	−	1.74806i	0.481201	−	0.156352i
$126$	−2.40481	+	3.49526i	−0.214238	+	0.311383i
$127$	−5.81878	−	8.00886i	−0.516333	−	0.710671i	0.468638	−	0.883390i	$-0.344745\pi$
$127$	−5.81878	−	8.00886i	−0.516333	−	0.710671i	−0.984971	+	0.172719i	$0.944745\pi$
$128$	−0.927051	−	2.85317i	−0.0819405	−	0.252187i
$129$	5.88909	−	4.39529i	0.518506	−	0.386984i
$130$	9.70820	+	7.05342i	0.851466	+	0.618626i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$	−1.61803	−	1.17557i	−0.139777	−	0.101554i
$135$	12.2139	+	8.17439i	1.05121	+	0.703539i
$136$	−5.56231	−	17.1190i	−0.476964	−	1.46794i
$137$	1.66251	+	2.28825i	0.142038	+	0.195498i	0.874109	−	0.485730i	$-0.161446\pi$
$137$	1.66251	+	2.28825i	0.142038	+	0.195498i	−0.732071	+	0.681228i	$0.761446\pi$
$138$		0			0
$139$	−1.34500	+	0.437016i	−0.114081	+	0.0370672i	−0.365501	−	0.930811i	$-0.619102\pi$
$139$	−1.34500	+	0.437016i	−0.114081	+	0.0370672i	0.251420	+	0.967878i	$0.419102\pi$
$140$	−1.23607	+	3.80423i	−0.104467	+	0.321516i
$141$	1.57356	+	4.63939i	0.132518	+	0.390707i
$142$		−	2.82843i		−	0.237356i
$143$		0			0
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	3.32502	−	4.57649i	0.276128	−	0.380057i
$146$	1.34500	+	0.437016i	0.111313	+	0.0361677i
$147$	8.27007	+	2.57020i	0.682104	+	0.211987i
$148$	6.47214	−	4.70228i	0.532006	−	0.386525i
$149$	−4.85410	+	3.52671i	−0.397664	+	0.288919i	−0.768589	−	0.639743i	$-0.779041\pi$
$149$	−4.85410	+	3.52671i	−0.397664	+	0.288919i	0.370925	+	0.928663i	$0.379041\pi$
$150$	−4.96204	−	1.54212i	−0.405149	−	0.125914i
$151$	4.03499	+	1.31105i	0.328363	+	0.106692i	0.468559	−	0.883432i	$-0.344773\pi$
$151$	4.03499	+	1.31105i	0.328363	+	0.106692i	−0.140196	+	0.990124i	$0.544773\pi$
$152$	−7.48128	+	10.2971i	−0.606812	+	0.835206i
$153$	−6.00000	−	16.9706i	−0.485071	−	1.37199i
$154$		0			0
$155$			5.65685i			0.454369i
$156$	−2.36034	−	6.95908i	−0.188978	−	0.557172i
$157$	−6.18034	+	19.0211i	−0.493245	+	1.51805i	0.326429	+	0.945222i	$0.394154\pi$
$157$	−6.18034	+	19.0211i	−0.493245	+	1.51805i	−0.819674	+	0.572830i	$0.805846\pi$
$158$	4.03499	−	1.31105i	0.321007	−	0.104301i
$159$	9.79715	−	0.125791i	0.776965	−	0.00997586i
$160$	8.31254	+	11.4412i	0.657164	+	0.904508i
$161$		0			0
$162$	3.21687	+	8.40546i	0.252741	+	0.660395i
$163$	−16.1803	−	11.7557i	−1.26734	−	0.920778i	−0.268249	−	0.963350i	$-0.586445\pi$
$163$	−16.1803	−	11.7557i	−1.26734	−	0.920778i	−0.999093	+	0.0425718i	$0.986445\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−16.0000			−1.24184
$167$	−9.70820	−	7.05342i	−0.751243	−	0.545810i	0.144969	−	0.989436i	$-0.453692\pi$
$167$	−9.70820	−	7.05342i	−0.751243	−	0.545810i	−0.896212	+	0.443626i	$0.853692\pi$
$168$	−5.88909	+	4.39529i	−0.454353	+	0.339104i
$169$	−1.54508	−	4.75528i	−0.118853	−	0.365791i
$170$	9.97505	+	13.7295i	0.765051	+	1.05300i
$171$	−7.21444	+	10.4858i	−0.551702	+	0.801869i
$172$	4.03499	−	1.31105i	0.307665	−	0.0999665i
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	−0.855505	−	0.517794i	$-0.826753\pi$
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	0.996470	+	0.0839492i	$0.0267533\pi$
$174$	3.28054	−	1.11268i	0.248697	−	0.0843517i
$175$		−	4.24264i		−	0.320713i
$176$		0			0
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$		0			0
$179$	−2.68999	−	0.874032i	−0.201060	−	0.0653282i	0.206756	−	0.978393i	$-0.433709\pi$
$179$	−2.68999	−	0.874032i	−0.201060	−	0.0653282i	−0.407816	+	0.913064i	$0.633709\pi$
$180$	5.16213	+	6.73442i	0.384762	+	0.501954i
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	−0.245016	−	0.969519i	$-0.578793\pi$
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	0.846353	+	0.532622i	$0.178793\pi$
$182$	−4.85410	+	3.52671i	−0.359810	+	0.261417i
$183$	−5.08874	+	16.3739i	−0.376171	+	1.21039i
$184$		0			0
$185$	−13.3001	+	18.3060i	−0.977840	+	1.34588i
$186$	−2.00000	+	2.82843i	−0.146647	+	0.207390i
$187$		0			0
$188$			2.82843i			0.206284i
$189$	−5.77430	+	4.54504i	−0.420019	+	0.330603i
$190$	3.70820	−	11.4127i	0.269021	−	0.827963i
$191$	18.8300	−	6.11822i	1.36249	−	0.442699i	0.465615	−	0.884987i	$-0.345833\pi$
$191$	18.8300	−	6.11822i	1.36249	−	0.442699i	0.896873	+	0.442288i	$0.145833\pi$
$192$	0.155658	+	12.1234i	0.0112337	+	0.874928i
$193$	12.4688	+	17.1618i	0.897524	+	1.23534i	0.971251	+	0.238058i	$0.0765108\pi$
$193$	12.4688	+	17.1618i	0.897524	+	1.23534i	−0.0737265	+	0.997278i	$0.523489\pi$
$194$	−0.618034	−	1.90211i	−0.0443723	−	0.136564i
$195$	12.4318	+	16.6569i	0.890257	+	1.19282i
$196$	4.04508	+	2.93893i	0.288935	+	0.209923i
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	−7.28115	−	5.29007i	−0.514855	−	0.374064i
$201$	−2.07196	−	2.77615i	−0.146145	−	0.195814i
$202$	−3.09017	−	9.51057i	−0.217424	−	0.669161i
$203$	1.66251	+	2.28825i	0.116685	+	0.160603i
$204$	−0.133421	−	10.3914i	−0.00934136	−	0.727547i
$205$	16.1400	−	5.24419i	1.12726	−	0.366270i
$206$	2.47214	−	7.60845i	0.172242	−	0.530106i
$207$		0			0
$208$			4.24264i			0.294174i
$209$		0			0
$210$	4.00000	−	5.65685i	0.276026	−	0.390360i
$211$	15.7938	−	21.7383i	1.08729	−	1.49653i	0.236060	−	0.971738i	$-0.424144\pi$
$211$	15.7938	−	21.7383i	1.08729	−	1.49653i	0.851232	−	0.524790i	$-0.175856\pi$
$212$	5.37999	+	1.74806i	0.369499	+	0.120058i
$213$	1.45393	−	4.67826i	0.0996214	−	0.320549i
$214$	12.9443	−	9.40456i	0.884852	−	0.642883i
$215$	−9.70820	+	7.05342i	−0.662094	+	0.481039i
$216$	0.600264	+	15.5769i	0.0408428	+	1.05987i
$217$	−2.68999	−	0.874032i	−0.182609	−	0.0593332i
$218$	2.49376	−	3.43237i	0.168899	−	0.232469i
$219$	2.00000	+	1.41421i	0.135147	+	0.0955637i
$220$		0			0
$221$		−	25.4558i		−	1.71235i
$222$	−13.1222	+	4.45070i	−0.880702	+	0.298711i
$223$	7.41641	−	22.8254i	0.496639	−	1.52850i	−0.317747	−	0.948176i	$-0.602926\pi$
$223$	7.41641	−	22.8254i	0.496639	−	1.52850i	0.814386	−	0.580323i	$-0.197074\pi$
$224$	−6.72499	+	2.18508i	−0.449332	+	0.145997i
$225$	−7.41457	−	5.10138i	−0.494305	−	0.340092i
$226$	1.66251	+	2.28825i	0.110588	+	0.152212i
$227$	−7.41641	−	22.8254i	−0.492244	−	1.51497i	−0.821208	−	0.570629i	$-0.806699\pi$
$227$	−7.41641	−	22.8254i	−0.492244	−	1.51497i	0.328963	−	0.944343i	$-0.393301\pi$
$228$	−5.88909	+	4.39529i	−0.390015	+	0.291085i
$229$	19.4164	+	14.1068i	1.28307	+	0.932207i	0.999641	−	0.0267860i	$-0.00852726\pi$
$229$	19.4164	+	14.1068i	1.28307	+	0.932207i	0.283431	+	0.958993i	$0.408527\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	8.09017	+	5.87785i	0.530005	+	0.385071i	0.820360	−	0.571848i	$-0.193773\pi$
$233$	8.09017	+	5.87785i	0.530005	+	0.385071i	−0.290355	+	0.956919i	$0.593773\pi$
$234$	0.326787	+	12.7237i	0.0213627	+	0.831776i
$235$	−2.47214	−	7.60845i	−0.161264	−	0.496321i
$236$	6.65003	+	9.15298i	0.432880	+	0.595808i
$237$	7.34786	−	0.0943431i	0.477295	−	0.00612824i
$238$	−8.06998	+	2.62210i	−0.523099	+	0.169965i
$239$	−4.94427	+	15.2169i	−0.319818	+	0.984300i	0.653907	+	0.756575i	$0.273129\pi$
$239$	−4.94427	+	15.2169i	−0.319818	+	0.984300i	−0.973726	+	0.227725i	$0.926871\pi$
$240$	−1.57356	−	4.63939i	−0.101573	−	0.299471i
$241$			4.24264i			0.273293i	0.990620	+	0.136646i	$0.0436324\pi$
$241$			4.24264i			0.273293i	−0.990620	+	0.136646i	$0.956368\pi$
$242$		0			0
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	−5.81878	+	8.00886i	−0.372509	+	0.512715i
$245$	−13.4500	−	4.37016i	−0.859287	−	0.279199i
$246$	9.92408	+	3.08424i	0.632736	+	0.196644i
$247$	−14.5623	+	10.5801i	−0.926577	+	0.673198i
$248$	−4.85410	+	3.52671i	−0.308236	+	0.223946i
$249$	−26.4642	−	8.22465i	−1.67710	−	0.521216i
$250$	−5.37999	−	1.74806i	−0.340260	−	0.110557i
$251$	14.9626	−	20.5942i	0.944429	−	1.29990i	−0.00952890	−	0.999955i	$-0.503033\pi$
$251$	14.9626	−	20.5942i	0.944429	−	1.29990i	0.953958	−	0.299940i	$-0.0969668\pi$
$252$	−4.00000	+	1.41421i	−0.251976	+	0.0890871i
$253$		0			0
$254$			9.89949i			0.621150i
$255$	9.44136	+	27.8363i	0.591241	+	1.74318i
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−10.7600	+	3.49613i	−0.671189	+	0.218082i	−0.624734	−	0.780838i	$-0.714792\pi$
$257$	−10.7600	+	3.49613i	−0.671189	+	0.218082i	−0.0464552	+	0.998920i	$0.514792\pi$
$258$	−7.34786	+	0.0943431i	−0.457458	+	0.00587354i
$259$	−6.65003	−	9.15298i	−0.413213	−	0.568739i
$260$	3.70820	+	11.4127i	0.229973	+	0.707784i
$261$	5.99802	−	0.154049i	0.371268	−	0.00953539i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−16.0000			−0.982872
$266$	4.85410	+	3.52671i	0.297624	+	0.216237i
$267$		0			0
$268$	−0.618034	−	1.90211i	−0.0377524	−	0.116190i
$269$	−16.6251	−	22.8825i	−1.01365	−	1.39517i	−0.916562	−	0.399892i	$-0.869048\pi$
$269$	−16.6251	−	22.8825i	−1.01365	−	1.39517i	−0.0970866	−	0.995276i	$-0.530952\pi$
$270$	−5.07647	−	13.7924i	−0.308944	−	0.839377i
$271$	28.2449	−	9.17734i	1.71576	−	0.557483i	0.724483	−	0.689293i	$-0.242079\pi$
$271$	28.2449	−	9.17734i	1.71576	−	0.557483i	0.991275	+	0.131809i	$0.0420787\pi$
$272$	−1.85410	+	5.70634i	−0.112421	+	0.345998i
$273$	−9.84163	+	3.33803i	−0.595642	+	0.202026i
$274$		−	2.82843i		−	0.170872i
$275$		0			0
$276$		0			0
$277$	−2.49376	+	3.43237i	−0.149836	+	0.206231i	−0.877336	−	0.479876i	$-0.840682\pi$
$277$	−2.49376	+	3.43237i	−0.149836	+	0.206231i	0.727501	+	0.686107i	$0.240682\pi$
$278$	1.34500	+	0.437016i	0.0806676	+	0.0262105i
$279$	−4.76195	+	3.65018i	−0.285091	+	0.218530i
$280$	9.70820	−	7.05342i	0.580176	−	0.421523i
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	−0.723081	−	0.690763i	$-0.757275\pi$
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	0.433510	+	0.901149i	$0.357275\pi$
$282$	1.45393	−	4.67826i	0.0865800	−	0.278586i
$283$	−25.5549	−	8.30330i	−1.51908	−	0.493580i	−0.573568	−	0.819158i	$-0.694441\pi$
$283$	−25.5549	−	8.30330i	−1.51908	−	0.493580i	−0.945515	+	0.325577i	$0.894441\pi$
$284$	1.66251	−	2.28825i	0.0986517	−	0.135782i
$285$	12.0000	−	16.9706i	0.710819	−	1.00525i
$286$		0			0
$287$			8.48528i			0.500870i
$288$	−4.26745	+	14.3802i	−0.251462	+	0.847359i
$289$	5.87132	−	18.0701i	0.345372	−	1.06295i
$290$	−5.37999	+	1.74806i	−0.315924	+	0.102650i
$291$	−0.0444738	−	3.46382i	−0.00260710	−	0.203052i
$292$	0.831254	+	1.14412i	0.0486455	+	0.0669547i
$293$	−0.618034	−	1.90211i	−0.0361059	−	0.111123i	0.931379	−	0.364051i	$-0.118606\pi$
$293$	−0.618034	−	1.90211i	−0.0361059	−	0.111123i	−0.967485	+	0.252928i	$0.918606\pi$
$294$	−5.17990	−	6.94036i	−0.302098	−	0.404770i
$295$	−25.8885	−	18.8091i	−1.50729	−	1.09511i
$296$	−24.0000			−1.39497
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	−3.10794	−	4.16422i	−0.179437	−	0.240421i
$301$	−1.85410	−	5.70634i	−0.106869	−	0.328908i
$302$	−2.49376	−	3.43237i	−0.143500	−	0.197511i
$303$	−0.222369	−	17.3191i	−0.0127748	−	0.994955i
$304$	4.03499	−	1.31105i	0.231423	−	0.0751938i
$305$	8.65248	−	26.6296i	0.495439	−	1.52481i
$306$	−5.12094	+	17.2562i	−0.292745	+	0.986470i
$307$			4.24264i			0.242140i	0.992644	+	0.121070i	$0.0386326\pi$
$307$			4.24264i			0.242140i	−0.992644	+	0.121070i	$0.961367\pi$
$308$		0			0
$309$	8.00000	−	11.3137i	0.455104	−	0.643614i
$310$	3.32502	−	4.57649i	0.188848	−	0.259927i
$311$	26.8999	+	8.74032i	1.52536	+	0.495618i	0.947291	−	0.320373i	$-0.103808\pi$
$311$	26.8999	+	8.74032i	1.52536	+	0.495618i	0.578064	+	0.815991i	$0.303808\pi$
$312$	−6.54267	+	21.0522i	−0.370406	+	1.19184i
$313$	−9.70820	+	7.05342i	−0.548740	+	0.398683i	−0.827321	−	0.561730i	$-0.810136\pi$
$313$	−9.70820	+	7.05342i	−0.548740	+	0.398683i	0.278581	+	0.960413i	$0.410136\pi$
$314$	16.1803	−	11.7557i	0.913109	−	0.663413i
$315$	9.52391	−	7.30035i	0.536611	−	0.411328i
$316$	4.03499	+	1.31105i	0.226986	+	0.0737522i
$317$	14.9626	−	20.5942i	0.840382	−	1.15669i	−0.145519	−	0.989355i	$-0.546485\pi$
$317$	14.9626	−	20.5942i	0.840382	−	1.15669i	0.985901	−	0.167331i	$-0.0535147\pi$
$318$	−8.00000	−	5.65685i	−0.448618	−	0.317221i
$319$		0			0
$320$		−	19.7990i		−	1.10680i
$321$	26.2443	−	8.90140i	1.46482	−	0.496828i
$322$		0			0
$323$	−24.2099	+	7.86629i	−1.34708	+	0.437692i
$324$	−2.33810	+	8.69099i	−0.129895	+	0.482833i
$325$	−7.48128	−	10.2971i	−0.414987	−	0.571181i
$326$	6.18034	+	19.0211i	0.342297	+	1.05348i
$327$	5.88909	−	4.39529i	0.325668	−	0.243060i
$328$	14.5623	+	10.5801i	0.804069	+	0.584190i
$329$	4.00000			0.220527
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	−12.9443	−	9.40456i	−0.710409	−	0.516143i
$333$	−23.9921	+	0.616196i	−1.31476	+	0.0337673i
$334$	3.70820	+	11.4127i	0.202904	+	0.624474i
$335$	3.32502	+	4.57649i	0.181665	+	0.250040i
$336$	2.44929	−	0.0314477i	0.133620	−	0.00171561i
$337$	−30.9349	+	10.0514i	−1.68513	+	0.547533i	−0.985896	−	0.167357i	$-0.946477\pi$
$337$	−30.9349	+	10.0514i	−1.68513	+	0.547533i	−0.699237	+	0.714890i	$0.746477\pi$
$338$	−1.54508	+	4.75528i	−0.0840415	+	0.258653i
$339$	1.57356	+	4.63939i	0.0854641	+	0.251977i
$340$			16.9706i			0.920358i
$341$		0			0
$342$	12.0000	−	4.24264i	0.648886	−	0.229416i
$343$	9.97505	−	13.7295i	0.538602	−	0.741322i
$344$	−12.1050	−	3.93314i	−0.652656	−	0.212061i
$345$		0			0
$346$	−4.85410	+	3.52671i	−0.260958	+	0.189597i
$347$	12.9443	−	9.40456i	0.694885	−	0.504863i	−0.183377	−	0.983043i	$-0.558703\pi$
$347$	12.9443	−	9.40456i	0.694885	−	0.504863i	0.878262	+	0.478179i	$0.158703\pi$
$348$	3.30803	+	1.02808i	0.177329	+	0.0551109i
$349$	4.03499	+	1.31105i	0.215988	+	0.0701788i	0.415012	−	0.909816i	$-0.363777\pi$
$349$	4.03499	+	1.31105i	0.215988	+	0.0701788i	−0.199024	+	0.979995i	$0.563777\pi$
$350$	−2.49376	+	3.43237i	−0.133297	+	0.183468i
$351$	−6.00000	+	21.2132i	−0.320256	+	1.13228i
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	−6.29424	−	18.5575i	−0.334535	−	0.986322i
$355$	−2.47214	+	7.60845i	−0.131207	+	0.403815i
$356$		0			0
$357$	−14.6957	+	0.188686i	−0.777780	+	0.00998633i
$358$	1.66251	+	2.28825i	0.0878663	+	0.120938i
$359$	6.18034	+	19.0211i	0.326186	+	1.00390i	0.970902	+	0.239475i	$0.0769754\pi$
$359$	6.18034	+	19.0211i	0.326186	+	1.00390i	−0.644717	+	0.764422i	$0.723025\pi$
$360$	−0.653574	−	25.4475i	−0.0344464	−	1.34120i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−10.0000			−0.525588
$363$		0			0
$364$	−6.00000			−0.314485
$365$	−3.23607	−	2.35114i	−0.169384	−	0.123064i
$366$	13.7412	−	10.2557i	0.718265	−	0.536073i
$367$	2.47214	+	7.60845i	0.129044	+	0.397158i	0.994616	−	0.103627i	$-0.0330448\pi$
$367$	2.47214	+	7.60845i	0.129044	+	0.397158i	−0.865572	+	0.500785i	$0.833045\pi$
$368$		0			0
$369$	14.8291	+	10.2028i	0.771975	+	0.531135i
$370$	21.5200	−	6.99226i	1.11877	−	0.363510i
$371$	2.47214	−	7.60845i	0.128347	−	0.395011i
$372$	−3.28054	+	1.11268i	−0.170088	+	0.0576895i
$373$			4.24264i			0.219676i	0.993950	+	0.109838i	$0.0350331\pi$
$373$			4.24264i			0.219676i	−0.993950	+	0.109838i	$0.964967\pi$
$374$		0			0
$375$	−8.00000	−	5.65685i	−0.413118	−	0.292119i
$376$	4.98752	−	6.86474i	0.257212	−	0.354022i
$377$	8.06998	+	2.62210i	0.415625	+	0.135045i
$378$	7.34302	−	0.282967i	0.377684	−	0.0145543i
$379$	−9.70820	+	7.05342i	−0.498677	+	0.362310i	−0.808511	−	0.588481i	$-0.799726\pi$
$379$	−9.70820	+	7.05342i	−0.498677	+	0.362310i	0.309834	+	0.950791i	$0.399726\pi$
$380$	9.70820	−	7.05342i	0.498020	−	0.361833i
$381$	−5.08874	+	16.3739i	−0.260704	+	0.838860i
$382$	−18.8300	−	6.11822i	−0.963424	−	0.313036i
$383$	−3.32502	+	4.57649i	−0.169900	+	0.233848i	−0.885473	−	0.464690i	$-0.846166\pi$
$383$	−3.32502	+	4.57649i	−0.169900	+	0.233848i	0.715573	+	0.698538i	$0.246166\pi$
$384$	−3.00000	+	4.24264i	−0.153093	+	0.216506i
$385$		0			0
$386$		−	21.2132i		−	1.07972i
$387$	−12.2020	−	3.62105i	−0.620261	−	0.184069i
$388$	0.618034	−	1.90211i	0.0313759	−	0.0965652i
$389$	18.8300	−	6.11822i	0.954717	−	0.310206i	0.210086	−	0.977683i	$-0.432626\pi$
$389$	18.8300	−	6.11822i	0.954717	−	0.310206i	0.744631	+	0.667477i	$0.232626\pi$
$390$	−0.266843	−	20.7829i	−0.0135121	−	1.05238i
$391$		0			0
$392$	−4.63525	−	14.2658i	−0.234116	−	0.720534i
$393$		0			0
$394$	−17.7984	−	12.9313i	−0.896669	−	0.651468i
$395$	−12.0000			−0.603786
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−1.61803	−	1.17557i	−0.0811047	−	0.0589260i
$399$	6.21588	+	8.32844i	0.311183	+	0.416943i
$400$	0.927051	+	2.85317i	0.0463525	+	0.142658i
$401$	1.66251	+	2.28825i	0.0830217	+	0.114270i	0.848508	−	0.529183i	$-0.177501\pi$
$401$	1.66251	+	2.28825i	0.0830217	+	0.114270i	−0.765486	+	0.643452i	$0.777501\pi$
$402$	0.0444738	+	3.46382i	0.00221815	+	0.172759i
$403$	−8.06998	+	2.62210i	−0.401994	+	0.130616i
$404$	3.09017	−	9.51057i	0.153742	−	0.473168i
$405$	−1.30672	−	25.4223i	−0.0649313	−	1.26324i
$406$		−	2.82843i		−	0.140372i
$407$		0			0
$408$	−18.0000	+	25.4558i	−0.891133	+	1.26025i
$409$	−2.49376	+	3.43237i	−0.123309	+	0.169720i	−0.866208	−	0.499683i	$-0.833450\pi$
$409$	−2.49376	+	3.43237i	−0.123309	+	0.169720i	0.742900	+	0.669403i	$0.233450\pi$
$410$	−16.1400	−	5.24419i	−0.797096	−	0.258992i
$411$	1.45393	−	4.67826i	0.0717169	−	0.230761i
$412$	6.47214	−	4.70228i	0.318859	−	0.231665i
$413$	12.9443	−	9.40456i	0.636946	−	0.462768i
$414$		0			0
$415$	43.0399	+	13.9845i	2.11275	+	0.686473i
$416$	−12.4688	+	17.1618i	−0.611334	+	0.841429i
$417$	2.00000	+	1.41421i	0.0979404	+	0.0692543i
$418$		0			0
$419$			31.1127i			1.51995i	0.649950	+	0.759977i	$0.274790\pi$
$419$			31.1127i			1.51995i	−0.649950	+	0.759977i	$0.725210\pi$
$420$	6.56108	−	2.22535i	0.320148	−	0.108586i
$421$	−6.18034	+	19.0211i	−0.301211	+	0.927033i	0.679853	+	0.733349i	$0.262044\pi$
$421$	−6.18034	+	19.0211i	−0.301211	+	0.927033i	−0.981064	+	0.193684i	$0.937956\pi$
$422$	−25.5549	+	8.30330i	−1.24400	+	0.404199i
$423$	4.80963	−	6.99053i	0.233852	−	0.339891i
$424$	−9.97505	−	13.7295i	−0.484431	−	0.666762i
$425$	−5.56231	−	17.1190i	−0.269811	−	0.830394i
$426$	−3.92606	+	2.93019i	−0.190218	+	0.141968i
$427$	11.3262	+	8.22899i	0.548115	+	0.398229i
$428$	16.0000			0.773389
$429$		0			0
$430$	12.0000			0.578691
$431$	25.8885	+	18.8091i	1.24701	+	0.906004i	0.998044	−	0.0625092i	$-0.0199103\pi$
$431$	25.8885	+	18.8091i	1.24701	+	0.906004i	0.248963	+	0.968513i	$0.419910\pi$
$432$	2.89008	−	4.31827i	0.139049	−	0.207763i
$433$	9.27051	+	28.5317i	0.445512	+	1.37115i	0.881921	+	0.471397i	$0.156250\pi$
$433$	9.27051	+	28.5317i	0.445512	+	1.37115i	−0.436409	+	0.899749i	$0.643750\pi$
$434$	1.66251	+	2.28825i	0.0798029	+	0.109839i
$435$	−9.79715	+	0.125791i	−0.469737	+	0.00603121i
$436$	4.03499	−	1.31105i	0.193241	−	0.0627878i
$437$		0			0
$438$	−0.786780	−	2.31969i	−0.0375938	−	0.110839i
$439$		−	26.8701i		−	1.28244i	−0.767358	−	0.641219i	$-0.778429\pi$
$439$		−	26.8701i		−	1.28244i	0.767358	−	0.641219i	$-0.221571\pi$
$440$		0			0
$441$	−5.00000	−	14.1421i	−0.238095	−	0.673435i
$442$	−14.9626	+	20.5942i	−0.711697	+	0.979567i
$443$	26.8999	+	8.74032i	1.27805	+	0.415265i	0.867895	−	0.496748i	$-0.165473\pi$
$443$	26.8999	+	8.74032i	1.27805	+	0.415265i	0.410160	+	0.912014i	$0.365473\pi$
$444$	−13.2321	−	4.11232i	−0.627968	−	0.195162i
$445$		0			0
$446$	−19.4164	+	14.1068i	−0.919394	+	0.667979i
$447$	9.92408	+	3.08424i	0.469393	+	0.145880i
$448$	9.41498	+	3.05911i	0.444816	+	0.144529i
$449$	−3.32502	+	4.57649i	−0.156917	+	0.215978i	−0.880236	−	0.474536i	$-0.842616\pi$
$449$	−3.32502	+	4.57649i	−0.156917	+	0.215978i	0.723319	+	0.690514i	$0.242616\pi$
$450$	3.00000	+	8.48528i	0.141421	+	0.400000i
$451$		0			0
$452$			2.82843i			0.133038i
$453$	−2.36034	−	6.95908i	−0.110898	−	0.326966i
$454$	−7.41641	+	22.8254i	−0.348069	+	1.07125i
$455$	16.1400	−	5.24419i	0.756653	−	0.245852i
$456$	22.0436	−	0.283029i	1.03229	−	0.0132541i
$457$	−5.81878	−	8.00886i	−0.272191	−	0.374639i	0.650937	−	0.759132i	$-0.274376\pi$
$457$	−5.81878	−	8.00886i	−0.272191	−	0.374639i	−0.923128	+	0.384493i	$0.874376\pi$
$458$	−7.41641	−	22.8254i	−0.346546	−	1.06656i
$459$	−17.3405	+	25.9096i	−0.809385	+	1.20936i
$460$		0			0
$461$	22.0000			1.02464			0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	−1.61803	−	1.17557i	−0.0751153	−	0.0545745i
$465$	7.85212	−	5.86039i	0.364134	−	0.271769i
$466$	−3.09017	−	9.51057i	−0.143149	−	0.440568i
$467$	−16.6251	−	22.8825i	−0.769317	−	1.05887i	−0.996381	−	0.0849941i	$-0.972913\pi$
$467$	−16.6251	−	22.8825i	−0.769317	−	1.05887i	0.227065	−	0.973880i	$-0.427087\pi$
$468$	−7.21444	+	10.4858i	−0.333488	+	0.484706i
$469$	−2.68999	+	0.874032i	−0.124212	+	0.0403591i
$470$	−2.47214	+	7.60845i	−0.114031	+	0.350952i
$471$	32.8054	−	11.1268i	1.51159	−	0.512694i
$472$		−	33.9411i		−	1.56227i
$473$		0			0
$474$	−6.00000	−	4.24264i	−0.275589	−	0.194871i
$475$	−7.48128	+	10.2971i	−0.343265	+	0.472464i
$476$	−8.06998	−	2.62210i	−0.369887	−	0.120184i
$477$	−10.3243	−	13.4688i	−0.472715	−	0.616696i
$478$	12.9443	−	9.40456i	0.592057	−	0.430155i
$479$	−22.6525	+	16.4580i	−1.03502	+	0.751985i	−0.969307	−	0.245854i	$-0.920932\pi$
$479$	−22.6525	+	16.4580i	−1.03502	+	0.751985i	−0.0657112	+	0.997839i	$0.520932\pi$
$480$	7.26963	−	23.3913i	0.331812	−	1.06766i
$481$	−32.2799	−	10.4884i	−1.47184	−	0.478229i
$482$	2.49376	−	3.43237i	0.113588	−	0.156340i
$483$		0			0
$484$		0			0
$485$			5.65685i			0.256865i
$486$	8.33478	−	13.1731i	0.378073	−	0.597546i
$487$	0.618034	−	1.90211i	0.0280058	−	0.0861930i	−0.936077	−	0.351796i	$-0.885571\pi$
$487$	0.618034	−	1.90211i	0.0280058	−	0.0861930i	0.964082	+	0.265603i	$0.0855711\pi$
$488$	28.2449	−	9.17734i	1.27859	−	0.415439i
$489$	0.444738	+	34.6382i	0.0201117	+	1.56639i
$490$	8.31254	+	11.4412i	0.375522	+	0.516862i
$491$	6.18034	+	19.0211i	0.278915	+	0.858412i	0.988157	+	0.153447i	$0.0490373\pi$
$491$	6.18034	+	19.0211i	0.278915	+	0.858412i	−0.709242	+	0.704965i	$0.750963\pi$
$492$	6.21588	+	8.32844i	0.280234	+	0.375475i
$493$	9.70820	+	7.05342i	0.437236	+	0.317670i
$494$	18.0000			0.809858
$495$		0			0
$496$	2.00000			0.0898027
$497$	−3.23607	−	2.35114i	−0.145157	−	0.105463i
$498$	16.5757	+	22.2092i	0.742774	+	0.995216i
$499$	−4.32624	−	13.3148i	−0.193669	−	0.596052i	−0.999990	−	0.00457310i	$-0.998544\pi$
$499$	−4.32624	−	13.3148i	−0.193669	−	0.596052i	0.806321	−	0.591479i	$-0.201456\pi$
$500$	−3.32502	−	4.57649i	−0.148699	−	0.204667i
$501$	0.266843	+	20.7829i	0.0119216	+	0.928511i
$502$	−24.2099	+	7.86629i	−1.08054	+	0.351090i
$503$	−4.94427	+	15.2169i	−0.220454	+	0.678488i	0.778267	+	0.627933i	$0.216099\pi$
$503$	−4.94427	+	15.2169i	−0.220454	+	0.678488i	−0.998721	+	0.0505549i	$0.983901\pi$
$504$	12.2020	+	3.62105i	0.543519	+	0.161295i
$505$			28.2843i			1.25863i
$506$		0			0
$507$	−5.00000	+	7.07107i	−0.222058	+	0.314037i
$508$	−5.81878	+	8.00886i	−0.258166	+	0.355336i
$509$	−32.2799	−	10.4884i	−1.43078	−	0.464889i	−0.511772	−	0.859121i	$-0.671011\pi$
$509$	−32.2799	−	10.4884i	−1.43078	−	0.464889i	−0.919011	+	0.394232i	$0.871011\pi$
$510$	8.72356	−	28.0695i	0.386286	−	1.24294i
$511$	1.61803	−	1.17557i	0.0715776	−	0.0520042i
$512$	8.89919	−	6.46564i	0.393292	−	0.285744i
$513$	22.0291	−	0.848901i	0.972607	−	0.0374799i
$514$	10.7600	+	3.49613i	0.474602	+	0.154208i
$515$	−13.3001	+	18.3060i	−0.586071	+	0.806657i
$516$	−6.00000	−	4.24264i	−0.264135	−	0.186772i
$517$		0			0
$518$			11.3137i			0.497096i
$519$	−9.84163	+	3.33803i	−0.431999	+	0.146523i
$520$	11.1246	−	34.2380i	0.487846	−	1.50144i
$521$	18.8300	−	6.11822i	0.824955	−	0.268044i	0.134036	−	0.990976i	$-0.457206\pi$
$521$	18.8300	−	6.11822i	0.824955	−	0.268044i	0.690919	+	0.722932i	$0.257206\pi$
$522$	−4.94305	−	3.40092i	−0.216351	−	0.148854i
$523$	12.4688	+	17.1618i	0.545223	+	0.750435i	0.989354	−	0.145527i	$-0.0464877\pi$
$523$	12.4688	+	17.1618i	0.545223	+	0.750435i	−0.444131	+	0.895962i	$0.646488\pi$
$524$		0			0
$525$	−5.88909	+	4.39529i	−0.257021	+	0.191826i
$526$		0			0
$527$	−12.0000			−0.522728
$528$		0			0
$529$	23.0000			1.00000
$530$	12.9443	+	9.40456i	0.562263	+	0.408508i
$531$	−0.871432	−	33.9299i	−0.0378169	−	1.47243i
$532$	1.85410	+	5.70634i	0.0803855	+	0.247401i
$533$	14.9626	+	20.5942i	0.648101	+	0.892034i
$534$		0			0
$535$	−43.0399	+	13.9845i	−1.86078	+	0.604603i
$536$	−1.85410	+	5.70634i	−0.0800850	+	0.246476i
$537$	1.57356	+	4.63939i	0.0679041	+	0.200204i
$538$			28.2843i			1.21942i
$539$		0			0
$540$	4.00000	−	14.1421i	0.172133	−	0.608581i
$541$	−20.7813	+	28.6031i	−0.893460	+	1.22974i	0.0790477	+	0.996871i	$0.474812\pi$
$541$	−20.7813	+	28.6031i	−0.893460	+	1.22974i	−0.972508	+	0.232871i	$0.925188\pi$
$542$	−28.2449	−	9.17734i	−1.21322	−	0.394200i
$543$	−16.5401	−	5.14040i	−0.709805	−	0.220596i
$544$	−24.2705	+	17.6336i	−1.04059	+	0.756033i
$545$	−9.70820	+	7.05342i	−0.415854	+	0.302135i
$546$	9.92408	+	3.08424i	0.424712	+	0.131993i
$547$	33.6249	+	10.9254i	1.43770	+	0.467136i	0.921179	−	0.389139i	$-0.127228\pi$
$547$	33.6249	+	10.9254i	1.43770	+	0.467136i	0.516519	+	0.856276i	$0.327228\pi$
$548$	1.66251	−	2.28825i	0.0710188	−	0.0977490i
$549$	28.0000	−	9.89949i	1.19501	−	0.422500i
$550$		0			0
$551$		−	8.48528i		−	0.361485i
$552$		0			0
$553$	1.85410	−	5.70634i	0.0788444	−	0.242658i
$554$	4.03499	−	1.31105i	0.171430	−	0.0557011i
$555$	39.1886	−	0.503163i	1.66346	−	0.0213581i
$556$	0.831254	+	1.14412i	0.0352530	+	0.0485216i
$557$	−0.618034	−	1.90211i	−0.0261869	−	0.0805951i	0.937109	−	0.349037i	$-0.113491\pi$
$557$	−0.618034	−	1.90211i	−0.0261869	−	0.0805951i	−0.963296	+	0.268442i	$0.913491\pi$
$558$	5.99802	−	0.154049i	0.253917	−	0.00652141i
$559$	−14.5623	−	10.5801i	−0.615920	−	0.447492i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	6.00000			0.253095
$563$	−9.70820	−	7.05342i	−0.409152	−	0.297266i	0.364106	−	0.931357i	$-0.381374\pi$
$563$	−9.70820	−	7.05342i	−0.409152	−	0.297266i	−0.773258	+	0.634091i	$0.781374\pi$
$564$	3.92606	−	2.93019i	0.165317	−	0.123383i
$565$	−2.47214	−	7.60845i	−0.104004	−	0.320090i
$566$	15.7938	+	21.7383i	0.663864	+	0.913730i
$567$	12.2909	+	3.30658i	0.516170	+	0.138863i
$568$	−8.06998	+	2.62210i	−0.338609	+	0.110021i
$569$	−11.7426	+	36.1401i	−0.492277	+	1.51507i	0.328880	+	0.944372i	$0.393329\pi$
$569$	−11.7426	+	36.1401i	−0.492277	+	1.51507i	−0.821157	+	0.570702i	$0.806671\pi$
$570$	−19.6833	+	6.67605i	−0.824441	+	0.279629i
$571$		−	26.8701i		−	1.12448i	−0.826975	−	0.562238i	$-0.809940\pi$
$571$		−	26.8701i		−	1.12448i	0.826975	−	0.562238i	$-0.190060\pi$
$572$		0			0
$573$	−28.0000	−	19.7990i	−1.16972	−	0.827115i
$574$	4.98752	−	6.86474i	0.208175	−	0.286529i
$575$		0			0
$576$	16.6668	−	12.7756i	0.694452	−	0.532317i
$577$	25.8885	−	18.8091i	1.07775	−	0.783034i	0.100464	−	0.994941i	$-0.467967\pi$
$577$	25.8885	−	18.8091i	1.07775	−	0.783034i	0.977290	+	0.211906i	$0.0679672\pi$
$578$	−15.3713	+	11.1679i	−0.639363	+	0.464524i
$579$	10.9044	−	35.0869i	0.453173	−	1.45816i
$580$	−5.37999	−	1.74806i	−0.223392	−	0.0725844i
$581$	−13.3001	+	18.3060i	−0.551780	+	0.759459i
$582$	−2.00000	+	2.82843i	−0.0829027	+	0.117242i
$583$		0			0
$584$		−	4.24264i		−	0.175562i
$585$	10.2419	−	34.5124i	0.423450	−	1.42691i
$586$	−0.618034	+	1.90211i	−0.0255307	+	0.0785756i
$587$	−10.7600	+	3.49613i	−0.444112	+	0.144301i	−0.522532	−	0.852620i	$-0.675012\pi$
$587$	−10.7600	+	3.49613i	−0.444112	+	0.144301i	0.0784201	+	0.996920i	$0.475012\pi$
$588$	−0.111184	−	8.65954i	−0.00458517	−	0.357113i
$589$	4.98752	+	6.86474i	0.205507	+	0.282857i
$590$	9.88854	+	30.4338i	0.407105	+	1.25294i
$591$	−22.7916	−	30.5376i	−0.937520	−	1.25615i
$592$	6.47214	+	4.70228i	0.266003	+	0.193263i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$		0			0
$595$	24.0000			0.983904
$596$	4.85410	+	3.52671i	0.198832	+	0.144460i
$597$	−2.07196	−	2.77615i	−0.0847997	−	0.113620i
$598$		0			0
$599$	19.9501	+	27.4589i	0.815139	+	1.12194i	0.990510	+	0.137440i	$0.0438874\pi$
$599$	19.9501	+	27.4589i	0.815139	+	1.12194i	−0.175371	+	0.984502i	$0.556113\pi$
$600$	0.200132	+	15.5872i	0.00817035	+	0.636344i
$601$	28.2449	−	9.17734i	1.15214	−	0.374351i	0.330188	−	0.943915i	$-0.392888\pi$
$601$	28.2449	−	9.17734i	1.15214	−	0.374351i	0.821947	+	0.569564i	$0.192888\pi$
$602$	−1.85410	+	5.70634i	−0.0755676	+	0.232573i
$603$	−1.70698	+	5.75206i	−0.0695137	+	0.234242i
$604$		−	4.24264i		−	0.172631i
$605$		0			0
$606$	−10.0000	+	14.1421i	−0.406222	+	0.574485i
$607$	−2.49376	+	3.43237i	−0.101219	+	0.139316i	−0.856622	−	0.515945i	$-0.827441\pi$
$607$	−2.49376	+	3.43237i	−0.101219	+	0.139316i	0.755403	+	0.655260i	$0.227441\pi$
$608$	20.1750	+	6.55524i	0.818202	+	0.265850i
$609$	1.45393	−	4.67826i	0.0589161	−	0.189573i
$610$	−22.6525	+	16.4580i	−0.917172	+	0.666364i
$611$	9.70820	−	7.05342i	0.392752	−	0.285351i
$612$	−14.2859	+	10.9505i	−0.577472	+	0.442649i
$613$	4.03499	+	1.31105i	0.162972	+	0.0529527i	0.389367	−	0.921083i	$-0.372694\pi$
$613$	4.03499	+	1.31105i	0.162972	+	0.0529527i	−0.226395	+	0.974036i	$0.572694\pi$
$614$	2.49376	−	3.43237i	0.100640	−	0.138519i
$615$	−24.0000	−	16.9706i	−0.967773	−	0.684319i
$616$		0			0
$617$			31.1127i			1.25255i	0.779602	+	0.626275i	$0.215421\pi$
$617$			31.1127i			1.25255i	−0.779602	+	0.626275i	$0.784579\pi$
$618$	−13.1222	+	4.45070i	−0.527851	+	0.179033i
$619$	−6.18034	+	19.0211i	−0.248409	+	0.764524i	0.746648	+	0.665219i	$0.231662\pi$
$619$	−6.18034	+	19.0211i	−0.248409	+	0.764524i	−0.995057	+	0.0993047i	$0.968338\pi$
$620$	5.37999	−	1.74806i	0.216066	−	0.0702039i
$621$		0			0
$622$	−16.6251	−	22.8825i	−0.666605	−	0.917503i
$623$		0			0
$624$	5.88909	−	4.39529i	0.235752	−	0.175952i
$625$	25.0795	+	18.2213i	1.00318	+	0.728854i
$626$	12.0000			0.479616
$627$		0			0
$628$	20.0000			0.798087
$629$	−38.8328	−	28.2137i	−1.54837	−	1.12495i
$630$	−11.9960	+	0.308098i	−0.477934	+	0.0122749i
$631$	−4.32624	−	13.3148i	−0.172225	−	0.530053i	0.827271	−	0.561803i	$-0.189892\pi$
$631$	−4.32624	−	13.3148i	−0.172225	−	0.530053i	−0.999496	+	0.0317495i	$0.989892\pi$
$632$	−7.48128	−	10.2971i	−0.297590	−	0.409597i
$633$	−46.5365	+	0.597506i	−1.84966	+	0.0237487i
$634$	−24.2099	+	7.86629i	−0.961500	+	0.312410i
$635$	8.65248	−	26.6296i	0.343363	−	1.05676i
$636$	−3.14712	−	9.27877i	−0.124791	−	0.367927i
$637$		−	21.2132i		−	0.840498i
$638$		0			0
$639$	−8.00000	+	2.82843i	−0.316475	+	0.111891i
$640$	4.98752	−	6.86474i	0.197149	−	0.271353i
$641$	26.8999	+	8.74032i	1.06248	+	0.345222i	0.787556	−	0.616243i	$-0.211346\pi$
$641$	26.8999	+	8.74032i	1.06248	+	0.345222i	0.274928	+	0.961465i	$0.411346\pi$
$642$	−26.4642	−	8.22465i	−1.04446	−	0.324601i
$643$	−9.70820	+	7.05342i	−0.382854	+	0.278160i	−0.762521	−	0.646963i	$-0.776039\pi$
$643$	−9.70820	+	7.05342i	−0.382854	+	0.278160i	0.379667	+	0.925123i	$0.376039\pi$
$644$		0			0
$645$	19.8482	+	6.16849i	0.781521	+	0.242884i
$646$	24.2099	+	7.86629i	0.952528	+	0.309495i
$647$	−3.32502	+	4.57649i	−0.130720	+	0.179920i	−0.869360	−	0.494180i	$-0.835468\pi$
$647$	−3.32502	+	4.57649i	−0.130720	+	0.179920i	0.738640	+	0.674100i	$0.235468\pi$
$648$	21.0000	−	16.9706i	0.824958	−	0.666667i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	1.57356	+	4.63939i	0.0616727	+	0.181832i
$652$	−6.18034	+	19.0211i	−0.242041	+	0.744925i
$653$	−10.7600	+	3.49613i	−0.421070	+	0.136814i	−0.511885	−	0.859054i	$-0.671053\pi$
$653$	−10.7600	+	3.49613i	−0.421070	+	0.136814i	0.0908151	+	0.995868i	$0.471053\pi$
$654$	−7.34786	+	0.0943431i	−0.287324	+	0.00368911i
$655$		0			0
$656$	−1.85410	−	5.70634i	−0.0723905	−	0.222795i
$657$	−0.108929	−	4.24124i	−0.00424973	−	0.165467i
$658$	−3.23607	−	2.35114i	−0.126155	−	0.0916570i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−20.0000			−0.777910			−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000			−0.777910			−0.388955	+	0.921257i	$0.627164\pi$
$662$	16.1803	+	11.7557i	0.628867	+	0.456898i
$663$	−35.3346	+	26.3717i	−1.37228	+	1.02419i
$664$	14.8328	+	45.6507i	0.575625	+	1.77159i
$665$	−9.97505	−	13.7295i	−0.386816	−	0.532406i
$666$	19.7722	+	13.6037i	0.766157	+	0.527132i
$667$		0			0
$668$	−3.70820	+	11.4127i	−0.143475	+	0.441570i
$669$	−39.3665	+	13.3521i	−1.52200	+	0.516222i
$670$		−	5.65685i		−	0.218543i
$671$		0			0
$672$	10.0000	+	7.07107i	0.385758	+	0.272772i
$673$	−2.49376	+	3.43237i	−0.0961274	+	0.132308i	−0.854371	−	0.519663i	$-0.826058\pi$
$673$	−2.49376	+	3.43237i	−0.0961274	+	0.132308i	0.758244	+	0.651971i	$0.226058\pi$
$674$	30.9349	+	10.0514i	1.19157	+	0.387164i
$675$	0.600264	+	15.5769i	0.0231042	+	0.599555i
$676$	−4.04508	+	2.93893i	−0.155580	+	0.113036i
$677$	30.7426	−	22.3358i	1.18154	−	0.858436i	0.189192	−	0.981940i	$-0.439413\pi$
$677$	30.7426	−	22.3358i	1.18154	−	0.858436i	0.992344	+	0.123504i	$0.0394132\pi$
$678$	1.45393	−	4.67826i	0.0558377	−	0.179667i
$679$	−2.68999	−	0.874032i	−0.103232	−	0.0335423i
$680$	29.9251	−	41.1884i	1.14758	−	1.57950i
$681$	−24.0000	+	33.9411i	−0.919682	+	1.30063i
$682$		0			0
$683$		−	31.1127i		−	1.19049i	−0.803543	−	0.595247i	$-0.797054\pi$
$683$		−	31.1127i		−	1.19049i	0.803543	−	0.595247i	$-0.202946\pi$
$684$	12.2020	+	3.62105i	0.466554	+	0.138454i
$685$	−2.47214	+	7.60845i	−0.0944555	+	0.290704i
$686$	−16.1400	+	5.24419i	−0.616227	+	0.200224i
$687$	−0.533685	−	41.5658i	−0.0203614	−	1.58583i
$688$	2.49376	+	3.43237i	0.0950738	+	0.130858i
$689$	−7.41641	−	22.8254i	−0.282543	−	0.869577i
$690$		0			0
$691$	−16.1803	−	11.7557i	−0.615529	−	0.447208i	0.235828	−	0.971795i	$-0.424220\pi$
$691$	−16.1803	−	11.7557i	−0.615529	−	0.447208i	−0.851357	+	0.524587i	$0.824220\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−16.0000			−0.607352
$695$	−3.23607	−	2.35114i	−0.122751	−	0.0891839i
$696$	−6.21588	−	8.32844i	−0.235612	−	0.315689i
$697$	11.1246	+	34.2380i	0.421375	+	1.29686i
$698$	−2.49376	−	3.43237i	−0.0943903	−	0.129917i
$699$	−0.222369	−	17.3191i	−0.00841076	−	0.655068i
$700$	−4.03499	+	1.31105i	−0.152508	+	0.0495530i
$701$	1.85410	−	5.70634i	0.0700285	−	0.215525i	−0.909917	−	0.414790i	$-0.863855\pi$
$701$	1.85410	−	5.70634i	0.0700285	−	0.215525i	0.979946	+	0.199264i	$0.0638552\pi$
$702$	17.3229	−	13.6351i	0.653811	−	0.514625i
$703$			33.9411i			1.28011i
$704$		0			0
$705$	−8.00000	+	11.3137i	−0.301297	+	0.426099i
$706$		0			0
$707$	−13.4500	−	4.37016i	−0.505838	−	0.164357i
$708$	5.81570	−	18.7130i	0.218568	−	0.703279i
$709$	25.8885	−	18.8091i	0.972265	−	0.706392i	0.0162981	−	0.999867i	$-0.494812\pi$
$709$	25.8885	−	18.8091i	0.972265	−	0.706392i	0.955967	+	0.293476i	$0.0948119\pi$
$710$	6.47214	−	4.70228i	0.242895	−	0.176473i
$711$	−7.74320	−	10.1016i	−0.290393	−	0.378841i
$712$		0			0
$713$		0			0
$714$	12.0000	+	8.48528i	0.449089	+	0.317554i
$715$		0			0
$716$			2.82843i			0.105703i
$717$	26.2443	−	8.90140i	0.980113	−	0.332429i
$718$	6.18034	−	19.0211i	0.230648	−	0.709862i
$719$	18.8300	−	6.11822i	0.702239	−	0.228171i	0.0639332	−	0.997954i	$-0.479636\pi$
$719$	18.8300	−	6.11822i	0.702239	−	0.228171i	0.638306	+	0.769783i	$0.279636\pi$
$720$	−4.80963	+	6.99053i	−0.179244	+	0.260522i
$721$	−6.65003	−	9.15298i	−0.247660	−	0.340875i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	5.88909	−	4.39529i	0.219018	−	0.163463i
$724$	−8.09017	−	5.87785i	−0.300669	−	0.218449i
$725$	6.00000			0.222834
$726$		0			0
$727$	2.00000			0.0741759			0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000			0.0741759			0.0370879	+	0.999312i	$0.488192\pi$
$728$	14.5623	+	10.5801i	0.539715	+	0.392126i
$729$	20.5574	−	17.5041i	0.761384	−	0.648301i
$730$	1.23607	+	3.80423i	0.0457489	+	0.140801i
$731$	−14.9626	−	20.5942i	−0.553411	−	0.761704i
$732$	17.1450	−	0.220134i	0.633698	−	0.00813638i
$733$	−1.34500	+	0.437016i	−0.0496786	+	0.0161416i	−0.333751	−	0.942661i	$-0.608314\pi$
$733$	−1.34500	+	0.437016i	−0.0496786	+	0.0161416i	0.284072	+	0.958803i	$0.408314\pi$
$734$	2.47214	−	7.60845i	0.0912482	−	0.280833i
$735$	7.86780	+	23.1969i	0.290208	+	0.855632i
$736$		0			0
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$	−2.49376	+	3.43237i	−0.0917345	+	0.126262i	−0.852417	−	0.522862i	$-0.824864\pi$
$739$	−2.49376	+	3.43237i	−0.0917345	+	0.126262i	0.760683	+	0.649124i	$0.224864\pi$
$740$	21.5200	+	6.99226i	0.791089	+	0.257040i
$741$	29.7723	+	9.25273i	1.09371	+	0.339907i
$742$	−6.47214	+	4.70228i	−0.237600	+	0.172626i
$743$	12.9443	−	9.40456i	0.474879	−	0.345020i	−0.324461	−	0.945899i	$-0.605183\pi$
$743$	12.9443	−	9.40456i	0.474879	−	0.345020i	0.799340	+	0.600879i	$0.205183\pi$
$744$	9.92408	+	3.08424i	0.363835	+	0.113074i
$745$	−16.1400	−	5.24419i	−0.591323	−	0.192132i
$746$	2.49376	−	3.43237i	0.0913031	−	0.125668i
$747$	16.0000	+	45.2548i	0.585409	+	1.65579i
$748$		0			0
$749$		−	22.6274i		−	0.826788i
$750$	3.14712	+	9.27877i	0.114917	+	0.338813i
$751$	0.618034	−	1.90211i	0.0225524	−	0.0694091i	−0.939147	−	0.343516i	$-0.888382\pi$
$751$	0.618034	−	1.90211i	0.0225524	−	0.0694091i	0.961699	+	0.274107i	$0.0883821\pi$
$752$	−2.68999	+	0.874032i	−0.0980940	+	0.0318727i
$753$	−44.0872	+	0.566059i	−1.60663	+	0.0206283i
$754$	−4.98752	−	6.86474i	−0.181635	−	0.249999i
$755$	3.70820	+	11.4127i	0.134955	+	0.415350i
$756$	6.10695	+	4.08719i	0.222108	+	0.148650i
$757$	−16.1803	−	11.7557i	−0.588084	−	0.427268i	0.253545	−	0.967324i	$-0.418403\pi$
$757$	−16.1803	−	11.7557i	−0.588084	−	0.427268i	−0.841630	+	0.540055i	$0.818403\pi$
$758$	12.0000			0.435860
$759$		0			0
$760$	−36.0000			−1.30586
$761$	8.09017	+	5.87785i	0.293268	+	0.213072i	0.724684	−	0.689081i	$-0.241986\pi$
$761$	8.09017	+	5.87785i	0.293268	+	0.213072i	−0.431416	+	0.902153i	$0.641986\pi$
$762$	13.7412	−	10.2557i	0.497792	−	0.371524i
$763$	−1.85410	−	5.70634i	−0.0671230	−	0.206583i
$764$	−11.6376	−	16.0177i	−0.421032	−	0.579501i
$765$	28.8578	−	41.9432i	1.04335	−	1.51646i
$766$	5.37999	−	1.74806i	0.194387	−	0.0631601i
$767$	14.8328	−	45.6507i	0.535582	−	1.64835i
$768$	27.8846	−	9.45774i	1.00620	−	0.341277i
$769$			35.3553i			1.27495i	0.770473	+	0.637473i	$0.220020\pi$
$769$			35.3553i			1.27495i	−0.770473	+	0.637473i	$0.779980\pi$
$770$		0			0
$771$	16.0000	+	11.3137i	0.576226	+	0.407453i
$772$	12.4688	−	17.1618i	0.448762	−	0.617668i
$773$	−32.2799	−	10.4884i	−1.16103	−	0.377241i	−0.335741	−	0.941954i	$-0.608987\pi$
$773$	−32.2799	−	10.4884i	−1.16103	−	0.377241i	−0.825287	+	0.564713i	$0.808987\pi$
$774$	7.74320	+	10.1016i	0.278323	+	0.363096i
$775$	−4.85410	+	3.52671i	−0.174364	+	0.126683i
$776$	−4.85410	+	3.52671i	−0.174252	+	0.126602i
$777$	−5.81570	+	18.7130i	−0.208637	+	0.671326i
$778$	−18.8300	−	6.11822i	−0.675087	−	0.219349i
$779$	14.9626	−	20.5942i	0.536090	−	0.737864i
$780$	12.0000	−	16.9706i	0.429669	−	0.607644i
$781$		0			0
$782$		0			0
$783$	−6.42766	−	8.16610i	−0.229706	−	0.291833i
$784$	−1.54508	+	4.75528i	−0.0551816	+	0.169832i
$785$	−53.7999	+	17.4806i	−1.92020	+	0.623911i
$786$		0			0
$787$	12.4688	+	17.1618i	0.444465	+	0.611754i	0.971197	−	0.238278i	$-0.0765829\pi$
$787$	12.4688	+	17.1618i	0.444465	+	0.611754i	−0.526732	+	0.850031i	$0.676583\pi$
$788$	−6.79837	−	20.9232i	−0.242182	−	0.745360i
$789$		0			0
$790$	9.70820	+	7.05342i	0.345402	+	0.250950i
$791$	4.00000			0.142224
$792$		0			0
$793$	42.0000			1.49146
$794$	−1.61803	−	1.17557i	−0.0574219	−	0.0417194i
$795$	16.5757	+	22.2092i	0.587879	+	0.787678i
$796$	−0.618034	−	1.90211i	−0.0219056	−	0.0674186i
$797$	1.66251	+	2.28825i	0.0588890	+	0.0810538i	0.837446	−	0.546520i	$-0.184048\pi$
$797$	1.66251	+	2.28825i	0.0588890	+	0.0810538i	−0.778557	+	0.627574i	$0.784048\pi$
$798$	−0.133421	−	10.3914i	−0.00472306	−	0.367853i
$799$	16.1400	−	5.24419i	0.570991	−	0.185526i
$800$	−4.63525	+	14.2658i	−0.163881	+	0.504374i
$801$		0			0
$802$		−	2.82843i		−	0.0998752i
$803$		0			0
$804$	−2.00000	+	2.82843i	−0.0705346	+	0.0997509i
$805$		0			0
$806$	8.06998	+	2.62210i	0.284253	+	0.0923594i
$807$	−14.5393	+	46.7826i	−0.511806	+	1.64682i
$808$	−24.2705	+	17.6336i	−0.853834	+	0.620346i
$809$	−40.4508	+	29.3893i	−1.42218	+	1.03327i	−0.430769	+	0.902462i	$0.641757\pi$
$809$	−40.4508	+	29.3893i	−1.42218	+	1.03327i	−0.991408	+	0.130809i	$0.958243\pi$
$810$	−13.8857	+	21.3351i	−0.487893	+	0.749640i
$811$	−25.5549	−	8.30330i	−0.897355	−	0.291568i	−0.176210	−	0.984353i	$-0.556384\pi$
$811$	−25.5549	−	8.30330i	−0.897355	−	0.291568i	−0.721145	+	0.692784i	$0.756384\pi$
$812$	1.66251	−	2.28825i	0.0583426	−	0.0803017i
$813$	−42.0000	−	29.6985i	−1.47300	−	1.04157i
$814$		0			0
$815$		−	56.5685i		−	1.98151i
$816$	9.84163	−	3.33803i	0.344526	−	0.116854i
$817$	−5.56231	+	17.1190i	−0.194600	+	0.598919i
$818$	4.03499	−	1.31105i	0.141080	−	0.0458397i
$819$	14.8291	+	10.2028i	0.518172	+	0.356513i
$820$	−9.97505	−	13.7295i	−0.348344	−	0.479454i
$821$	12.9787	+	39.9444i	0.452960	+	1.39407i	0.873513	+	0.486800i	$0.161836\pi$
$821$	12.9787	+	39.9444i	0.452960	+	1.39407i	−0.420553	+	0.907268i	$0.638164\pi$
$822$	−3.92606	+	2.93019i	−0.136937	+	0.102202i
$823$	19.4164	+	14.1068i	0.676813	+	0.491734i	0.872299	−	0.488973i	$-0.162628\pi$
$823$	19.4164	+	14.1068i	0.676813	+	0.491734i	−0.195486	+	0.980707i	$0.562628\pi$
$824$	−24.0000			−0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	−9.70820	−	7.05342i	−0.337587	−	0.245272i	0.406056	−	0.913848i	$-0.366904\pi$
$827$	−9.70820	−	7.05342i	−0.337587	−	0.245272i	−0.743643	+	0.668577i	$0.766904\pi$
$828$		0			0
$829$	−4.32624	−	13.3148i	−0.150256	−	0.462442i	0.847393	−	0.530966i	$-0.178171\pi$
$829$	−4.32624	−	13.3148i	−0.150256	−	0.462442i	−0.997649	+	0.0685244i	$0.978171\pi$
$830$	−26.6001	−	36.6119i	−0.923304	−	1.27082i
$831$	7.34786	−	0.0943431i	0.254895	−	0.00327273i
$832$	28.2449	−	9.17734i	0.979217	−	0.318167i
$833$	9.27051	−	28.5317i	0.321204	−	0.988565i
$834$	−0.786780	−	2.31969i	−0.0272440	−	0.0803244i
$835$		−	33.9411i		−	1.17458i
$836$		0			0
$837$	10.0000	+	2.82843i	0.345651	+	0.0977647i
$838$	18.2876	−	25.1707i	0.631734	−	0.869507i
$839$	−32.2799	−	10.4884i	−1.11443	−	0.362099i	−0.306789	−	0.951778i	$-0.599255\pi$
$839$	−32.2799	−	10.4884i	−1.11443	−	0.362099i	−0.807638	+	0.589678i	$0.799255\pi$
$840$	−19.8482	−	6.16849i	−0.684827	−	0.212833i
$841$	20.2254	−	14.6946i	0.697428	−	0.506711i
$842$	16.1803	−	11.7557i	0.557611	−	0.405128i
$843$	9.92408	+	3.08424i	0.341804	+	0.106227i
$844$	−25.5549	−	8.30330i	−0.879637	−	0.285812i
$845$	8.31254	−	11.4412i	0.285960	−	0.393590i
$846$	−8.00000	+	2.82843i	−0.275046	+	0.0972433i
$847$		0			0
$848$			5.65685i			0.194257i
$849$	14.9488	+	44.0742i	0.513042	+	1.51262i
$850$	−5.56231	+	17.1190i	−0.190786	+	0.587177i
$851$		0			0
$852$	−4.89858	+	0.0628954i	−0.167822	+	0.00215476i
$853$	−24.1064	−	33.1796i	−0.825386	−	1.13605i	−0.988764	−	0.149483i	$-0.952239\pi$
$853$	−24.1064	−	33.1796i	−0.825386	−	1.13605i	0.163378	−	0.986564i	$-0.447761\pi$
$854$	−4.32624	−	13.3148i	−0.148041	−	0.455623i
$855$	−35.9881	+	0.924294i	−1.23077	+	0.0316102i
$856$	−38.8328	−	28.2137i	−1.32728	−	0.964324i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	9.70820	+	7.05342i	0.331047	+	0.240520i
$861$	11.7782	−	8.79058i	0.401400	−	0.299582i
$862$	−9.88854	−	30.4338i	−0.336805	−	1.03658i
$863$	19.9501	+	27.4589i	0.679109	+	0.934713i	0.999923	−	0.0124289i	$-0.00395634\pi$
$863$	19.9501	+	27.4589i	0.679109	+	0.934713i	−0.320814	+	0.947142i	$0.603956\pi$
$864$	24.3817	−	8.97402i	0.829482	−	0.305302i
$865$	16.1400	−	5.24419i	0.548775	−	0.178308i
$866$	9.27051	−	28.5317i	0.315025	−	0.969546i
$867$	−31.1651	+	10.5704i	−1.05842	+	0.358990i
$868$			2.82843i			0.0960031i
$869$		0			0
$870$	8.00000	+	5.65685i	0.271225	+	0.191785i
$871$	−4.98752	+	6.86474i	−0.168996	+	0.232603i
$872$	−12.1050	−	3.93314i	−0.409926	−	0.133193i
$873$	−4.76195	+	3.65018i	−0.161168	+	0.123540i
$874$		0			0
$875$	−6.47214	+	4.70228i	−0.218798	+	0.158966i
$876$	0.726963	−	2.33913i	0.0245618	−	0.0790318i
$877$	33.6249	+	10.9254i	1.13543	+	0.368925i	0.815638	−	0.578562i	$-0.196386\pi$
$877$	33.6249	+	10.9254i	1.13543	+	0.368925i	0.319795	+	0.947487i	$0.396386\pi$
$878$	−15.7938	+	21.7383i	−0.533016	+	0.733633i
$879$	−2.00000	+	2.82843i	−0.0674583	+	0.0954005i
$880$		0			0
$881$			31.1127i			1.04821i	0.851653	+	0.524107i	$0.175601\pi$
$881$			31.1127i			1.04821i	−0.851653	+	0.524107i	$0.824399\pi$
$882$	−4.26745	+	14.3802i	−0.143693	+	0.484205i
$883$	14.2148	−	43.7486i	0.478365	−	1.47226i	−0.362999	−	0.931790i	$-0.618247\pi$
$883$	14.2148	−	43.7486i	0.478365	−	1.47226i	0.841365	−	0.540468i	$-0.181753\pi$
$884$	−24.2099	+	7.86629i	−0.814269	+	0.264572i
$885$	0.711580	+	55.4211i	0.0239195	+	1.86296i
$886$	−16.6251	−	22.8825i	−0.558530	−	0.768751i
$887$	−7.41641	−	22.8254i	−0.249019	−	0.766400i	−0.994949	−	0.100377i	$-0.967995\pi$
$887$	−7.41641	−	22.8254i	−0.249019	−	0.766400i	0.745931	−	0.666023i	$-0.232005\pi$
$888$	24.8635	+	33.3137i	0.834365	+	1.11794i
$889$	11.3262	+	8.22899i	0.379870	+	0.275992i
$890$		0			0
$891$		0			0
$892$	−24.0000			−0.803579
$893$	−9.70820	−	7.05342i	−0.324873	−	0.236034i
$894$	−6.21588	−	8.32844i	−0.207890	−	0.278545i
$895$	−2.47214	−	7.60845i	−0.0826344	−	0.254323i
$896$	2.49376	+	3.43237i	0.0833107	+	0.114667i
$897$		0			0
$898$	5.37999	−	1.74806i	0.179533	−	0.0583337i
$899$	1.23607	−	3.80423i	0.0412252	−	0.126878i
$900$	−2.56047	+	8.62809i	−0.0853491	+	0.287603i
$901$		−	33.9411i		−	1.13074i
$902$		0			0
$903$	−6.00000	+	8.48528i	−0.199667	+	0.282372i
$904$	4.98752	−	6.86474i	0.165883	−	0.228318i
$905$	26.8999	+	8.74032i	0.894184	+	0.290538i
$906$	−2.18089	+	7.01739i	−0.0724552	+	0.233137i
$907$	−9.70820	+	7.05342i	−0.322356	+	0.234205i	−0.737180	−	0.675696i	$-0.763843\pi$
$907$	−9.70820	+	7.05342i	−0.322356	+	0.234205i	0.414824	+	0.909902i	$0.363843\pi$
$908$	−19.4164	+	14.1068i	−0.644356	+	0.468152i
$909$	−23.8098	+	18.2509i	−0.789720	+	0.605344i
$910$	−16.1400	−	5.24419i	−0.535035	−	0.173843i
$911$	−21.6126	+	29.7472i	−0.716057	+	0.985568i	0.283588	+	0.958946i	$0.408475\pi$
$911$	−21.6126	+	29.7472i	−0.716057	+	0.985568i	−0.999646	+	0.0266223i	$0.991525\pi$
$912$	−6.00000	−	4.24264i	−0.198680	−	0.140488i
$913$		0			0
$914$			9.89949i			0.327446i
$915$	−45.9276	+	15.5775i	−1.51832	+	0.514975i
$916$	7.41641	−	22.8254i	0.245045	−	0.754171i
$917$		0			0
$918$	29.2580	−	10.7688i	0.965659	−	0.355424i
$919$	12.4688	+	17.1618i	0.411308	+	0.566117i	0.963537	−	0.267576i	$-0.0862225\pi$
$919$	12.4688	+	17.1618i	0.411308	+	0.566117i	−0.552229	+	0.833693i	$0.686223\pi$
$920$		0			0
$921$	5.88909	−	4.39529i	0.194052	−	0.144830i
$922$	−17.7984	−	12.9313i	−0.586158	−	0.425869i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−24.0000			−0.789115
$926$	−19.4164	−	14.1068i	−0.638063	−	0.463580i
$927$	−23.9921	+	0.616196i	−0.788004	+	0.0202385i
$928$	−3.09017	−	9.51057i	−0.101440	−	0.312200i
$929$	1.66251	+	2.28825i	0.0545451	+	0.0750749i	0.835418	−	0.549615i	$-0.185225\pi$
$929$	1.66251	+	2.28825i	0.0545451	+	0.0750749i	−0.780873	+	0.624690i	$0.785225\pi$
$930$	−9.79715	+	0.125791i	−0.321261	+	0.00412484i
$931$	−20.1750	+	6.55524i	−0.661207	+	0.214839i
$932$	3.09017	−	9.51057i	0.101222	−	0.311529i
$933$	−15.7356	−	46.3939i	−0.515160	−	1.51887i
$934$			28.2843i			0.925490i
$935$		0			0
$936$	36.0000	−	12.7279i	1.17670	−	0.416025i
$937$	−20.7813	+	28.6031i	−0.678897	+	0.934422i	−0.999920	−	0.0126498i	$-0.995973\pi$
$937$	−20.7813	+	28.6031i	−0.678897	+	0.934422i	0.321023	+	0.947071i	$0.395973\pi$
$938$	2.68999	+	0.874032i	0.0878314	+	0.0285382i
$939$	19.8482	+	6.16849i	0.647720	+	0.201301i
$940$	−6.47214	+	4.70228i	−0.211098	+	0.153372i
$941$	30.7426	−	22.3358i	1.00218	−	0.728128i	0.0396268	−	0.999215i	$-0.487383\pi$
$941$	30.7426	−	22.3358i	1.00218	−	0.728128i	0.962555	+	0.271087i	$0.0873831\pi$
$942$	−33.0803	−	10.2808i	−1.07781	−	0.334967i
$943$		0			0
$944$	−6.65003	+	9.15298i	−0.216440	+	0.297904i
$945$	−20.0000	−	5.65685i	−0.650600	−	0.184017i
$946$		0			0
$947$		−	31.1127i		−	1.01103i	−0.862819	−	0.505513i	$-0.831303\pi$
$947$		−	31.1127i		−	1.01103i	0.862819	−	0.505513i	$-0.168697\pi$
$948$	−2.36034	−	6.95908i	−0.0766603	−	0.226020i
$949$	1.85410	−	5.70634i	0.0601867	−	0.185236i
$950$	12.1050	−	3.93314i	0.392737	−	0.127608i
$951$	−44.0872	+	0.566059i	−1.42962	+	0.0183557i
$952$	14.9626	+	20.5942i	0.484940	+	0.667462i
$953$	−0.618034	−	1.90211i	−0.0200201	−	0.0616155i	0.940547	−	0.339663i	$-0.110313\pi$
$953$	−0.618034	−	1.90211i	−0.0200201	−	0.0616155i	−0.960567	+	0.278047i	$0.910313\pi$
$954$	0.435716	+	16.9650i	0.0141068	+	0.549261i
$955$	45.3050	+	32.9160i	1.46603	+	1.06514i
$956$	16.0000			0.517477
$957$		0			0
$958$	28.0000			0.904639
$959$	−3.23607	−	2.35114i	−0.104498	−	0.0759223i
$960$	−27.4824	+	20.5114i	−0.886992	+	0.662001i
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	19.9501	+	27.4589i	0.643217	+	0.885312i
$963$	−39.5444	−	27.2074i	−1.27430	−	0.876745i
$964$	4.03499	−	1.31105i	0.129958	−	0.0422260i
$965$	−18.5410	+	57.0634i	−0.596857	+	1.83694i
$966$		0			0
$967$			4.24264i			0.136434i	0.997671	+	0.0682171i	$0.0217310\pi$
$967$			4.24264i			0.136434i	−0.997671	+	0.0682171i	$0.978269\pi$
$968$		0			0
$969$	36.0000	+	25.4558i	1.15649	+	0.817760i
$970$	3.32502	−	4.57649i	0.106760	−	0.146942i
$971$	−32.2799	−	10.4884i	−1.03591	−	0.336588i	−0.258787	−	0.965934i	$-0.583323\pi$
$971$	−32.2799	−	10.4884i	−1.03591	−	0.336588i	−0.777125	+	0.629346i	$0.783323\pi$
$972$	14.4860	−	5.75823i	0.464637	−	0.184695i
$973$	1.61803	−	1.17557i	0.0518718	−	0.0376871i
$974$	−1.61803	+	1.17557i	−0.0518452	+	0.0376677i
$975$	−6.54267	+	21.0522i	−0.209533	+	0.674209i
$976$	−9.41498	−	3.05911i	−0.301366	−	0.0979198i
$977$	14.9626	−	20.5942i	0.478695	−	0.658867i	−0.499558	−	0.866280i	$-0.666504\pi$
$977$	14.9626	−	20.5942i	0.478695	−	0.658867i	0.978253	+	0.207413i	$0.0665044\pi$
$978$	20.0000	−	28.2843i	0.639529	−	0.904431i
$979$		0			0
$980$			14.1421i			0.451754i
$981$	−12.2020	−	3.62105i	−0.389579	−	0.115611i
$982$	6.18034	−	19.0211i	0.197223	−	0.606989i
$983$	−10.7600	+	3.49613i	−0.343190	+	0.111509i	−0.475541	−	0.879694i	$-0.657748\pi$
$983$	−10.7600	+	3.49613i	−0.343190	+	0.111509i	0.132351	+	0.991203i	$0.457748\pi$
$984$	−0.400264	−	31.1743i	−0.0127599	−	0.993802i
$985$	36.5752	+	50.3414i	1.16538	+	1.60401i
$986$	−3.70820	−	11.4127i	−0.118093	−	0.363454i
$987$	−4.14392	−	5.55229i	−0.131902	−	0.176731i
$988$	14.5623	+	10.5801i	0.463289	+	0.336599i
$989$		0			0
$990$		0			0
$991$	−42.0000			−1.33417			−0.667087	−	0.744980i	$-0.732459\pi$
$991$	−42.0000			−1.33417			−0.667087	+	0.744980i	$0.732459\pi$
$992$	8.09017	+	5.87785i	0.256863	+	0.186622i
$993$	20.7196	+	27.7615i	0.657517	+	0.880983i
$994$	1.23607	+	3.80423i	0.0392057	+	0.120663i
$995$	3.32502	+	4.57649i	0.105410	+	0.145085i
$996$	0.355790	+	27.7105i	0.0112736	+	0.878042i
$997$	28.2449	−	9.17734i	0.894526	−	0.290649i	0.174550	−	0.984648i	$-0.444153\pi$
$997$	28.2449	−	9.17734i	0.894526	−	0.290649i	0.719976	+	0.693999i	$0.244153\pi$
$998$	−4.32624	+	13.3148i	−0.136945	+	0.421472i
$999$	25.7106	+	32.6644i	0.813449	+	1.03346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.a.161.1		8
3.2	odd	2		363.2.f.f.161.2		8
11.2	odd	10		363.2.f.f.215.1		8
11.3	even	5	inner	363.2.f.a.239.2		8
11.4	even	5	inner	363.2.f.a.233.2		8
11.5	even	5		363.2.d.b.362.1	yes	2
11.6	odd	10		363.2.d.a.362.1	✓	2
11.7	odd	10		363.2.f.f.233.2		8
11.8	odd	10		363.2.f.f.239.2		8
11.9	even	5	inner	363.2.f.a.215.1		8
11.10	odd	2		363.2.f.f.161.1		8
33.2	even	10	inner	363.2.f.a.215.2		8
33.5	odd	10		363.2.d.a.362.2	yes	2
33.8	even	10	inner	363.2.f.a.239.1		8
33.14	odd	10		363.2.f.f.239.1		8
33.17	even	10		363.2.d.b.362.2	yes	2
33.20	odd	10		363.2.f.f.215.2		8
33.26	odd	10		363.2.f.f.233.1		8
33.29	even	10	inner	363.2.f.a.233.1		8
33.32	even	2	inner	363.2.f.a.161.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.a.362.1	✓	2	11.6	odd	10
363.2.d.a.362.2	yes	2	33.5	odd	10
363.2.d.b.362.1	yes	2	11.5	even	5
363.2.d.b.362.2	yes	2	33.17	even	10
363.2.f.a.161.1		8	1.1	even	1	trivial
363.2.f.a.161.2		8	33.32	even	2	inner
363.2.f.a.215.1		8	11.9	even	5	inner
363.2.f.a.215.2		8	33.2	even	10	inner
363.2.f.a.233.1		8	33.29	even	10	inner
363.2.f.a.233.2		8	11.4	even	5	inner
363.2.f.a.239.1		8	33.8	even	10	inner
363.2.f.a.239.2		8	11.3	even	5	inner
363.2.f.f.161.1		8	11.10	odd	2
363.2.f.f.161.2		8	3.2	odd	2
363.2.f.f.215.1		8	11.2	odd	10
363.2.f.f.215.2		8	33.20	odd	10
363.2.f.f.233.1		8	33.26	odd	10
363.2.f.f.233.2		8	11.7	odd	10
363.2.f.f.239.1		8	33.14	odd	10
363.2.f.f.239.2		8	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.03598 - 1.38807i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.66251 + 2.28825i) q^{5} +(0.0222369 + 1.73191i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.853491 + 2.87603i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.03598 - 1.38807i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.66251 + 2.28825i) q^{5} +(0.0222369 + 1.73191i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.853491 + 2.87603i) q^{9} -2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 + 3.43237i) q^{13} +(1.34500 + 0.437016i) q^{14} +(1.45393 - 4.67826i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.85410 + 3.52671i) q^{17} +(2.38098 - 1.82509i) q^{18} +(4.03499 + 1.31105i) q^{19} +(1.66251 - 2.28825i) q^{20} +(2.00000 + 1.41421i) q^{21} +(4.92081 - 1.66901i) q^{24} +(-0.927051 + 2.85317i) q^{25} +(4.03499 - 1.31105i) q^{26} +(4.87634 - 1.79480i) q^{27} +(0.831254 + 1.14412i) q^{28} +(-0.618034 - 1.90211i) q^{29} +(-3.92606 + 2.93019i) q^{30} +(1.61803 + 1.17557i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(-3.23607 - 2.35114i) q^{35} +(2.99901 - 0.0770245i) q^{36} +(2.47214 + 7.60845i) q^{37} +(-2.49376 - 3.43237i) q^{38} +(7.34786 - 0.0943431i) q^{39} +(-8.06998 + 2.62210i) q^{40} +(1.85410 - 5.70634i) q^{41} +(-0.786780 - 2.31969i) q^{42} +4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(-2.68999 - 0.874032i) q^{47} +(-1.65401 - 0.514040i) q^{48} +(-4.04508 + 2.93893i) q^{49} +(2.42705 - 1.76336i) q^{50} +(9.92408 + 3.08424i) q^{51} +(4.03499 + 1.31105i) q^{52} +(-3.32502 + 4.57649i) q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(-2.36034 - 6.95908i) q^{57} +(-0.618034 + 1.90211i) q^{58} +(-10.7600 + 3.49613i) q^{59} +(-4.89858 + 0.0628954i) q^{60} +(-5.81878 - 8.00886i) q^{61} +(-0.618034 - 1.90211i) q^{62} +(-0.108929 - 4.24124i) q^{63} +(-5.66312 - 4.11450i) q^{64} -12.0000 q^{65} +2.00000 q^{67} +(4.85410 + 3.52671i) q^{68} +(1.23607 + 3.80423i) q^{70} +(1.66251 + 2.28825i) q^{71} +(-7.41457 - 5.10138i) q^{72} +(-1.34500 + 0.437016i) q^{73} +(2.47214 - 7.60845i) q^{74} +(4.92081 - 1.66901i) q^{75} -4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-2.49376 + 3.43237i) q^{79} +(2.68999 + 0.874032i) q^{80} +(-7.54311 - 4.90933i) q^{81} +(-4.85410 + 3.52671i) q^{82} +(12.9443 - 9.40456i) q^{83} +(0.726963 - 2.33913i) q^{84} +(-16.1400 - 5.24419i) q^{85} +(2.49376 - 3.43237i) q^{86} +(-2.00000 + 2.82843i) q^{87} +(8.13464 + 2.41404i) q^{90} +(1.85410 - 5.70634i) q^{91} +(-0.0444738 - 3.46382i) q^{93} +(1.66251 + 2.28825i) q^{94} +(3.70820 + 11.4127i) q^{95} +(-5.17990 - 6.94036i) q^{96} +(1.61803 + 1.17557i) q^{97} +5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} + 16 q^{21} + 6 q^{24} + 6 q^{25} + 10 q^{27} + 4 q^{29} + 8 q^{30} + 4 q^{31} + 40 q^{32} + 48 q^{34} - 8 q^{35} - 2 q^{36} - 16 q^{37} + 12 q^{39} - 12 q^{41} - 4 q^{42} - 64 q^{45} + 2 q^{48} - 10 q^{49} + 6 q^{50} - 12 q^{51} - 40 q^{54} - 12 q^{57} + 4 q^{58} - 8 q^{60} + 4 q^{62} - 8 q^{63} - 14 q^{64} - 96 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} - 6 q^{72} - 16 q^{74} + 6 q^{75} - 48 q^{78} + 14 q^{81} - 12 q^{82} + 32 q^{83} + 4 q^{84} - 16 q^{87} + 16 q^{90} - 12 q^{91} + 4 q^{93} - 24 q^{95} - 10 q^{96} + 4 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 + 16 * q^21 + 6 * q^24 + 6 * q^25 + 10 * q^27 + 4 * q^29 + 8 * q^30 + 4 * q^31 + 40 * q^32 + 48 * q^34 - 8 * q^35 - 2 * q^36 - 16 * q^37 + 12 * q^39 - 12 * q^41 - 4 * q^42 - 64 * q^45 + 2 * q^48 - 10 * q^49 + 6 * q^50 - 12 * q^51 - 40 * q^54 - 12 * q^57 + 4 * q^58 - 8 * q^60 + 4 * q^62 - 8 * q^63 - 14 * q^64 - 96 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 - 6 * q^72 - 16 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 32 * q^83 + 4 * q^84 - 16 * q^87 + 16 * q^90 - 12 * q^91 + 4 * q^93 - 24 * q^95 - 10 * q^96 + 4 * q^97 + 40 * q^98

Introduction

L-functions

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