LMFDB - Embedded newform 363.2.f.f.239.2

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			239.2
Root			$1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	363.239
Dual form			363.2.f.f.161.2

$q$-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} +(1.65401 + 0.514040i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.66251 + 2.28825i) q^{5} +(1.64027 - 0.556338i) q^{6} +(-1.34500 - 0.437016i) q^{7} +(0.927051 + 2.85317i) q^{8} +(2.47152 + 1.70046i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 - 3.43237i) q^{13} +(-1.34500 + 0.437016i) q^{14} +(-3.92606 + 2.93019i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(2.99901 - 0.0770245i) q^{18} +(4.03499 - 1.31105i) q^{19} +(-1.66251 - 2.28825i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(0.0667106 + 5.19572i) q^{24} +(-0.927051 - 2.85317i) q^{25} +(-4.03499 - 1.31105i) q^{26} +(3.21383 + 4.08305i) q^{27} +(0.831254 - 1.14412i) q^{28} +(0.618034 - 1.90211i) q^{29} +(-1.45393 + 4.67826i) q^{30} +(1.61803 - 1.17557i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(-2.38098 + 1.82509i) q^{36} +(2.47214 - 7.60845i) q^{37} +(2.49376 - 3.43237i) q^{38} +(-2.36034 - 6.95908i) q^{39} +(-8.06998 - 2.62210i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-2.44929 + 0.0314477i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(2.68999 - 0.874032i) q^{47} +(1.03598 + 1.38807i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(6.21588 + 8.32844i) q^{51} +(4.03499 - 1.31105i) q^{52} +(3.32502 + 4.57649i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(7.34786 - 0.0943431i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(10.7600 + 3.49613i) q^{59} +(-1.57356 - 4.63939i) q^{60} +(-5.81878 + 8.00886i) q^{61} +(0.618034 - 1.90211i) q^{62} +(-2.58107 - 3.36721i) 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} +(-2.56047 + 8.62809i) q^{72} +(-1.34500 - 0.437016i) q^{73} +(-2.47214 - 7.60845i) q^{74} +(-0.0667106 - 5.19572i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-2.49376 - 3.43237i) q^{79} +(-2.68999 + 0.874032i) q^{80} +(3.21687 + 8.40546i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-12.9443 - 9.40456i) q^{83} +(1.96303 - 1.46510i) q^{84} +(-16.1400 + 5.24419i) q^{85} +(-2.49376 - 3.43237i) q^{86} +(2.00000 - 2.82843i) q^{87} +(-4.80963 + 6.99053i) q^{90} +(1.85410 + 5.70634i) q^{91} +(3.28054 - 1.11268i) q^{93} +(1.66251 - 2.28825i) q^{94} +(-3.70820 + 11.4127i) q^{95} +(-8.27007 - 2.57020i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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	$-0.584973\pi$
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	0.835853	+	0.548953i	$0.184973\pi$
$3$	1.65401	+	0.514040i	0.954945	+	0.296781i
$3$	1.65401	+	0.514040i	0.954945	+	0.296781i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.66251	+	2.28825i	−0.743496	+	1.02333i	0.254914	+	0.966964i	$0.417953\pi$
$5$	−1.66251	+	2.28825i	−0.743496	+	1.02333i	−0.998410	+	0.0563708i	$0.982047\pi$
$6$	1.64027	−	0.556338i	0.669638	−	0.227124i
$7$	−1.34500	−	0.437016i	−0.508361	−	0.165177i	0.0435957	−	0.999049i	$-0.486119\pi$
$7$	−1.34500	−	0.437016i	−0.508361	−	0.165177i	−0.551957	+	0.833873i	$0.686119\pi$
$8$	0.927051	+	2.85317i	0.327762	+	1.00875i
$9$	2.47152	+	1.70046i	0.823842	+	0.566820i
$10$			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	−1.00000		0.000696272i	$-0.999778\pi$
$13$	−2.49376	−	3.43237i	−0.691645	−	0.951968i	0.308355	−	0.951271i	$-0.400222\pi$
$14$	−1.34500	+	0.437016i	−0.359466	+	0.116797i
$15$	−3.92606	+	2.93019i	−1.01370	+	0.756573i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	4.85410	+	3.52671i	1.17729	+	0.855353i	0.991864	−	0.127304i	$-0.0406325\pi$
$17$	4.85410	+	3.52671i	1.17729	+	0.855353i	0.185429	+	0.982658i	$0.440633\pi$
$18$	2.99901	−	0.0770245i	0.706874	−	0.0181548i
$19$	4.03499	−	1.31105i	0.925690	−	0.300775i	0.192891	−	0.981220i	$-0.438214\pi$
$19$	4.03499	−	1.31105i	0.925690	−	0.300775i	0.732799	+	0.680445i	$0.238214\pi$
$20$	−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			$\pi$
$24$	0.0667106	+	5.19572i	0.0136173	+	1.06057i
$25$	−0.927051	−	2.85317i	−0.185410	−	0.570634i
$26$	−4.03499	−	1.31105i	−0.791327	−	0.257118i
$27$	3.21383	+	4.08305i	0.618502	+	0.785783i
$28$	0.831254	−	1.14412i	0.157092	−	0.216219i
$29$	0.618034	−	1.90211i	0.114766	−	0.353214i	−0.877132	−	0.480249i	$-0.840546\pi$
$29$	0.618034	−	1.90211i	0.114766	−	0.353214i	0.991898	+	0.127036i	$0.0405463\pi$
$30$	−1.45393	+	4.67826i	−0.265449	+	0.854129i
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	−0.432923	−	0.901431i	$-0.642518\pi$
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	0.723531	+	0.690292i	$0.242518\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$	3.23607	−	2.35114i	0.546995	−	0.397415i
$36$	−2.38098	+	1.82509i	−0.396830	+	0.304181i
$37$	2.47214	−	7.60845i	0.406417	−	1.25082i	−0.513290	−	0.858215i	$-0.671573\pi$
$37$	2.47214	−	7.60845i	0.406417	−	1.25082i	0.919707	−	0.392607i	$-0.128427\pi$
$38$	2.49376	−	3.43237i	0.404542	−	0.556804i
$39$	−2.36034	−	6.95908i	−0.377957	−	1.11434i
$40$	−8.06998	−	2.62210i	−1.27598	−	0.414590i
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	−0.984994	−	0.172588i	$-0.944787\pi$
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	0.695432	−	0.718592i	$-0.255213\pi$
$42$	−2.44929	+	0.0314477i	−0.377933	+	0.00485249i
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$		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	$-0.533863\pi$
$47$	2.68999	−	0.874032i	0.392376	−	0.127491i	0.498559	+	0.866856i	$0.333863\pi$
$48$	1.03598	+	1.38807i	0.149531	+	0.200351i
$49$	−4.04508	−	2.93893i	−0.577869	−	0.419847i
$50$	−2.42705	−	1.76336i	−0.343237	−	0.249376i
$51$	6.21588	+	8.32844i	0.870397	+	1.16621i
$52$	4.03499	−	1.31105i	0.559553	−	0.181810i
$53$	3.32502	+	4.57649i	0.456726	+	0.628629i	0.973826	−	0.227296i	$-0.0729884\pi$
$53$	3.32502	+	4.57649i	0.456726	+	0.628629i	−0.517100	+	0.855925i	$0.672988\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$	7.34786	−	0.0943431i	0.973248	−	0.0124960i
$58$	−0.618034	−	1.90211i	−0.0811518	−	0.249760i
$59$	10.7600	+	3.49613i	1.40083	+	0.455157i	0.909459	−	0.415794i	$-0.136496\pi$
$59$	10.7600	+	3.49613i	1.40083	+	0.455157i	0.491371	+	0.870951i	$0.336496\pi$
$60$	−1.57356	−	4.63939i	−0.203146	−	0.598942i
$61$	−5.81878	+	8.00886i	−0.745018	+	1.02543i	0.253296	+	0.967389i	$0.418485\pi$
$61$	−5.81878	+	8.00886i	−0.745018	+	1.02543i	−0.998314	+	0.0580406i	$0.981515\pi$
$62$	0.618034	−	1.90211i	0.0784904	−	0.241569i
$63$	−2.58107	−	3.36721i	−0.325184	−	0.424229i
$64$	−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	$-0.853678\pi$
$71$	−1.66251	+	2.28825i	−0.197303	+	0.271565i	0.698889	+	0.715230i	$0.253678\pi$
$72$	−2.56047	+	8.62809i	−0.301755	+	1.01683i
$73$	−1.34500	−	0.437016i	−0.157420	−	0.0511489i	0.229247	−	0.973368i	$-0.426374\pi$
$73$	−1.34500	−	0.437016i	−0.157420	−	0.0511489i	−0.386667	+	0.922219i	$0.626374\pi$
$74$	−2.47214	−	7.60845i	−0.287380	−	0.884465i
$75$	−0.0667106	−	5.19572i	−0.00770308	−	0.599951i
$76$			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	0.645353	−	0.763885i	$-0.276710\pi$
$79$	−2.49376	−	3.43237i	−0.280570	−	0.386172i	−0.925923	+	0.377713i	$0.876710\pi$
$80$	−2.68999	+	0.874032i	−0.300750	+	0.0977198i
$81$	3.21687	+	8.40546i	0.357430	+	0.933940i
$82$	−4.85410	−	3.52671i	−0.536046	−	0.389460i
$83$	−12.9443	−	9.40456i	−1.42082	−	1.03229i	−0.991636	−	0.129067i	$-0.958802\pi$
$83$	−12.9443	−	9.40456i	−1.42082	−	1.03229i	−0.429183	−	0.903218i	$-0.641198\pi$
$84$	1.96303	−	1.46510i	0.214184	−	0.159855i
$85$	−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			$\pi$
$90$	−4.80963	+	6.99053i	−0.506979	+	0.736866i
$91$	1.85410	+	5.70634i	0.194363	+	0.598187i
$92$		0			0
$93$	3.28054	−	1.11268i	0.340176	−	0.115379i
$94$	1.66251	−	2.28825i	0.171475	−	0.236015i
$95$	−3.70820	+	11.4127i	−0.380454	+	1.17092i
$96$	−8.27007	−	2.57020i	−0.844060	−	0.262320i
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	−0.502604	−	0.864517i	$-0.667625\pi$
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	0.666891	+	0.745155i	$0.267625\pi$
$98$	−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	$-0.865755\pi$
$101$	−8.09017	+	5.87785i	−0.805002	+	0.584868i	0.107375	+	0.994219i	$0.465755\pi$
$102$	9.92408	+	3.08424i	0.982631	+	0.305386i
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	−0.752279	−	0.658845i	$-0.771045\pi$
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	0.995866	−	0.0908382i	$-0.0289546\pi$
$104$	7.48128	−	10.2971i	0.733600	−	1.00971i
$105$	6.56108	−	2.22535i	0.640296	−	0.217172i
$106$	5.37999	+	1.74806i	0.522551	+	0.169787i
$107$	4.94427	+	15.2169i	0.477981	+	1.47107i	0.841895	+	0.539641i	$0.181440\pi$
$107$	4.94427	+	15.2169i	0.477981	+	1.47107i	−0.363914	+	0.931432i	$0.618560\pi$
$108$	−4.87634	+	1.79480i	−0.469226	+	0.172705i
$109$		−	4.24264i		−	0.406371i	−0.979140	−	0.203186i	$-0.934871\pi$
$109$		−	4.24264i		−	0.406371i	0.979140	−	0.203186i	$-0.0651295\pi$
$110$		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	$-0.557527\pi$
$113$	2.68999	−	0.874032i	0.253053	−	0.0822220i	0.432797	+	0.901492i	$0.357527\pi$
$114$	5.88909	−	4.39529i	0.551564	−	0.411657i
$115$		0			0
$116$	1.61803	+	1.17557i	0.150231	+	0.109149i
$117$	−0.326787	−	12.7237i	−0.0302115	−	1.17631i
$118$	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
$123$	−0.133421	−	10.3914i	−0.0120302	−	0.936965i
$124$	0.618034	+	1.90211i	0.0555011	+	0.170815i
$125$	−5.37999	−	1.74806i	−0.481201	−	0.156352i
$126$	−4.06732	−	1.20702i	−0.362346	−	0.107530i
$127$	−5.81878	+	8.00886i	−0.516333	+	0.710671i	−0.984971	−	0.172719i	$-0.944745\pi$
$127$	−5.81878	+	8.00886i	−0.516333	+	0.710671i	0.468638	+	0.883390i	$0.344745\pi$
$128$	0.927051	−	2.85317i	0.0819405	−	0.252187i
$129$	2.18089	−	7.01739i	0.192017	−	0.617846i
$130$	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
$135$	−14.6860	+	0.565934i	−1.26397	+	0.0487079i
$136$	−5.56231	+	17.1190i	−0.476964	+	1.46794i
$137$	−1.66251	+	2.28825i	−0.142038	+	0.195498i	−0.874109	−	0.485730i	$-0.838554\pi$
$137$	−1.66251	+	2.28825i	−0.142038	+	0.195498i	0.732071	+	0.681228i	$0.238554\pi$
$138$		0			0
$139$	−1.34500	−	0.437016i	−0.114081	−	0.0370672i	0.251420	−	0.967878i	$-0.419102\pi$
$139$	−1.34500	−	0.437016i	−0.114081	−	0.0370672i	−0.365501	+	0.930811i	$0.619102\pi$
$140$	1.23607	+	3.80423i	0.104467	+	0.321516i
$141$	4.89858	−	0.0628954i	0.412534	−	0.00529675i
$142$			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
$147$	−5.17990	−	6.94036i	−0.427231	−	0.572431i
$148$	6.47214	+	4.70228i	0.532006	+	0.386525i
$149$	4.85410	+	3.52671i	0.397664	+	0.288919i	0.768589	−	0.639743i	$-0.220959\pi$
$149$	4.85410	+	3.52671i	0.397664	+	0.288919i	−0.370925	+	0.928663i	$0.620959\pi$
$150$	−3.10794	−	4.16422i	−0.253762	−	0.340007i
$151$	4.03499	−	1.31105i	0.328363	−	0.106692i	−0.140196	−	0.990124i	$-0.544773\pi$
$151$	4.03499	−	1.31105i	0.328363	−	0.106692i	0.468559	+	0.883432i	$0.344773\pi$
$152$	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
$156$	7.34786	−	0.0943431i	0.588300	−	0.00755349i
$157$	−6.18034	−	19.0211i	−0.493245	−	1.51805i	−0.819674	−	0.572830i	$-0.805846\pi$
$157$	−6.18034	−	19.0211i	−0.493245	−	1.51805i	0.326429	−	0.945222i	$-0.394154\pi$
$158$	−4.03499	−	1.31105i	−0.321007	−	0.104301i
$159$	3.14712	+	9.27877i	0.249583	+	0.735855i
$160$	8.31254	−	11.4412i	0.657164	−	0.904508i
$161$		0			0
$162$	7.54311	+	4.90933i	0.592642	+	0.385714i
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.999093	−	0.0425718i	$-0.986445\pi$
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.268249	+	0.963350i	$0.586445\pi$
$164$	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	$-0.546308\pi$
$167$	9.70820	−	7.05342i	0.751243	−	0.545810i	0.896212	+	0.443626i	$0.146308\pi$
$168$	2.18089	−	7.01739i	0.168259	−	0.541403i
$169$	−1.54508	+	4.75528i	−0.118853	+	0.365791i
$170$	−9.97505	+	13.7295i	−0.765051	+	1.05300i
$171$	12.2020	+	3.62105i	0.933108	+	0.276909i
$172$	4.03499	+	1.31105i	0.307665	+	0.0999665i
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	0.855505	−	0.517794i	$-0.173247\pi$
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	−0.996470	+	0.0839492i	$0.973247\pi$
$174$	−0.0444738	−	3.46382i	−0.00337155	−	0.262591i
$175$			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	$-0.566291\pi$
$179$	2.68999	−	0.874032i	0.201060	−	0.0653282i	0.407816	+	0.913064i	$0.366291\pi$
$180$	−0.217858	−	8.48248i	−0.0162382	−	0.632247i
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	0.846353	−	0.532622i	$-0.178793\pi$
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	−0.245016	+	0.969519i	$0.578793\pi$
$182$	4.85410	+	3.52671i	0.359810	+	0.261417i
$183$	−13.7412	+	10.2557i	−1.01578	+	0.758122i
$184$		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
$189$	−2.53824	−	6.89618i	−0.184629	−	0.501624i
$190$	3.70820	+	11.4127i	0.269021	+	0.827963i
$191$	−18.8300	−	6.11822i	−1.36249	−	0.442699i	−0.465615	−	0.884987i	$-0.654167\pi$
$191$	−18.8300	−	6.11822i	−1.36249	−	0.442699i	−0.896873	+	0.442288i	$0.854167\pi$
$192$	−11.4819	+	3.89436i	−0.828634	+	0.281051i
$193$	12.4688	−	17.1618i	0.897524	−	1.23534i	−0.0737265	−	0.997278i	$-0.523489\pi$
$193$	12.4688	−	17.1618i	0.897524	−	1.23534i	0.971251	−	0.238058i	$-0.0765108\pi$
$194$	0.618034	−	1.90211i	0.0443723	−	0.136564i
$195$	19.8482	+	6.16849i	1.42136	+	0.441734i
$196$	4.04508	−	2.93893i	0.288935	−	0.209923i
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		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
$201$	3.30803	+	1.02808i	0.233330	+	0.0725152i
$202$	−3.09017	+	9.51057i	−0.217424	+	0.669161i
$203$	−1.66251	+	2.28825i	−0.116685	+	0.160603i
$204$	−9.84163	+	3.33803i	−0.689052	+	0.233709i
$205$	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	0.851232	+	0.524790i	$0.175856\pi$
$211$	15.7938	+	21.7383i	1.08729	+	1.49653i	0.236060	+	0.971738i	$0.424144\pi$
$212$	−5.37999	+	1.74806i	−0.369499	+	0.120058i
$213$	−3.92606	+	2.93019i	−0.269009	+	0.200774i
$214$	12.9443	+	9.40456i	0.884852	+	0.642883i
$215$	9.70820	+	7.05342i	0.662094	+	0.481039i
$216$	−8.67025	+	12.9548i	−0.589936	+	0.881462i
$217$	−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
$222$	−0.177895	−	13.8553i	−0.0119395	−	0.929904i
$223$	7.41641	+	22.8254i	0.496639	+	1.52850i	0.814386	+	0.580323i	$0.197074\pi$
$223$	7.41641	+	22.8254i	0.496639	+	1.52850i	−0.317747	+	0.948176i	$0.602926\pi$
$224$	6.72499	+	2.18508i	0.449332	+	0.145997i
$225$	2.56047	−	8.62809i	0.170698	−	0.575206i
$226$	1.66251	−	2.28825i	0.110588	−	0.152212i
$227$	7.41641	−	22.8254i	0.492244	−	1.51497i	−0.328963	−	0.944343i	$-0.606699\pi$
$227$	7.41641	−	22.8254i	0.492244	−	1.51497i	0.821208	−	0.570629i	$-0.193301\pi$
$228$	−2.18089	+	7.01739i	−0.144433	+	0.464738i
$229$	19.4164	−	14.1068i	1.28307	−	0.932207i	0.283431	−	0.958993i	$-0.408527\pi$
$229$	19.4164	−	14.1068i	1.28307	−	0.932207i	0.999641	+	0.0267860i	$0.00852726\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	−8.09017	+	5.87785i	−0.530005	+	0.385071i	−0.820360	−	0.571848i	$-0.806227\pi$
$233$	−8.09017	+	5.87785i	−0.530005	+	0.385071i	0.290355	+	0.956919i	$0.406227\pi$
$234$	−7.74320	−	10.1016i	−0.506188	−	0.660364i
$235$	−2.47214	+	7.60845i	−0.161264	+	0.496321i
$236$	−6.65003	+	9.15298i	−0.432880	+	0.595808i
$237$	−2.36034	−	6.95908i	−0.153321	−	0.452041i
$238$	−8.06998	−	2.62210i	−0.523099	−	0.169965i
$239$	4.94427	+	15.2169i	0.319818	+	0.984300i	0.973726	+	0.227725i	$0.0731287\pi$
$239$	4.94427	+	15.2169i	0.319818	+	0.984300i	−0.653907	+	0.756575i	$0.726871\pi$
$240$	−4.89858	+	0.0628954i	−0.316202	+	0.00405988i
$241$		−	4.24264i		−	0.273293i	−0.990620	−	0.136646i	$-0.956368\pi$
$241$		−	4.24264i		−	0.273293i	0.990620	−	0.136646i	$-0.0436324\pi$
$242$		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
$246$	−6.21588	−	8.32844i	−0.396310	−	0.531002i
$247$	−14.5623	−	10.5801i	−0.926577	−	0.673198i
$248$	4.85410	+	3.52671i	0.308236	+	0.223946i
$249$	−16.5757	−	22.2092i	−1.05044	−	1.40745i
$250$	−5.37999	+	1.74806i	−0.340260	+	0.110557i
$251$	−14.9626	−	20.5942i	−0.944429	−	1.29990i	−0.953958	−	0.299940i	$-0.903033\pi$
$251$	−14.9626	−	20.5942i	−0.944429	−	1.29990i	0.00952890	−	0.999955i	$-0.496967\pi$
$252$	4.00000	−	1.41421i	0.251976	−	0.0890871i
$253$		0			0
$254$			9.89949i			0.621150i
$255$	−29.3915	+	0.377372i	−1.84056	+	0.0236320i
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	10.7600	+	3.49613i	0.671189	+	0.218082i	0.624734	−	0.780838i	$-0.285208\pi$
$257$	10.7600	+	3.49613i	0.671189	+	0.218082i	0.0464552	+	0.998920i	$0.485208\pi$
$258$	−2.36034	−	6.95908i	−0.146948	−	0.433253i
$259$	−6.65003	+	9.15298i	−0.413213	+	0.568739i
$260$	−3.70820	+	11.4127i	−0.229973	+	0.707784i
$261$	4.76195	−	3.65018i	0.294758	−	0.225940i
$262$		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	0.0970866	−	0.995276i	$-0.469048\pi$
$269$	16.6251	−	22.8825i	1.01365	−	1.39517i	0.916562	−	0.399892i	$-0.130952\pi$
$270$	−11.5486	+	9.09009i	−0.702826	+	0.553205i
$271$	28.2449	+	9.17734i	1.71576	+	0.557483i	0.991275	−	0.131809i	$-0.0420787\pi$
$271$	28.2449	+	9.17734i	1.71576	+	0.557483i	0.724483	+	0.689293i	$0.242079\pi$
$272$	1.85410	+	5.70634i	0.112421	+	0.345998i
$273$	0.133421	+	10.3914i	0.00807502	+	0.628919i
$274$			2.82843i			0.170872i
$275$		0			0
$276$		0			0
$277$	−2.49376	−	3.43237i	−0.149836	−	0.206231i	0.727501	−	0.686107i	$-0.240682\pi$
$277$	−2.49376	−	3.43237i	−0.149836	−	0.206231i	−0.877336	+	0.479876i	$0.840682\pi$
$278$	−1.34500	+	0.437016i	−0.0806676	+	0.0262105i
$279$	5.99802	−	0.154049i	0.359092	−	0.00922267i
$280$	9.70820	+	7.05342i	0.580176	+	0.421523i
$281$	4.85410	+	3.52671i	0.289571	+	0.210386i	0.723081	−	0.690763i	$-0.242725\pi$
$281$	4.85410	+	3.52671i	0.289571	+	0.210386i	−0.433510	+	0.901149i	$0.642725\pi$
$282$	3.92606	−	2.93019i	0.233794	−	0.174491i
$283$	−25.5549	+	8.30330i	−1.51908	+	0.493580i	−0.945515	−	0.325577i	$-0.894441\pi$
$283$	−25.5549	+	8.30330i	−1.51908	+	0.493580i	−0.573568	+	0.819158i	$0.694441\pi$
$284$	−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
$288$	−12.3576	−	8.50230i	−0.728180	−	0.501003i
$289$	5.87132	+	18.0701i	0.345372	+	1.06295i
$290$	5.37999	+	1.74806i	0.315924	+	0.102650i
$291$	3.28054	−	1.11268i	0.192309	−	0.0652262i
$292$	0.831254	−	1.14412i	0.0486455	−	0.0669547i
$293$	0.618034	−	1.90211i	0.0361059	−	0.111123i	−0.931379	−	0.364051i	$-0.881394\pi$
$293$	0.618034	−	1.90211i	0.0361059	−	0.111123i	0.967485	+	0.252928i	$0.0813935\pi$
$294$	−8.27007	−	2.57020i	−0.482320	−	0.149897i
$295$	−25.8885	+	18.8091i	−1.50729	+	1.09511i
$296$	24.0000			1.39497
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	4.96204	+	1.54212i	0.286484	+	0.0890344i
$301$	−1.85410	+	5.70634i	−0.106869	+	0.328908i
$302$	2.49376	−	3.43237i	0.143500	−	0.197511i
$303$	−16.4027	+	5.56338i	−0.942311	+	0.319608i
$304$	4.03499	+	1.31105i	0.231423	+	0.0751938i
$305$	−8.65248	−	26.6296i	−0.495439	−	1.52481i
$306$	14.8291	+	10.2028i	0.847726	+	0.583253i
$307$		−	4.24264i		−	0.242140i	−0.992644	−	0.121070i	$-0.961367\pi$
$307$		−	4.24264i		−	0.242140i	0.992644	−	0.121070i	$-0.0386326\pi$
$308$		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	$-0.896192\pi$
$311$	−26.8999	+	8.74032i	−1.52536	+	0.495618i	−0.578064	+	0.815991i	$0.696192\pi$
$312$	17.6673	−	13.1859i	1.00021	−	0.746503i
$313$	−9.70820	−	7.05342i	−0.548740	−	0.398683i	0.278581	−	0.960413i	$-0.410136\pi$
$313$	−9.70820	−	7.05342i	−0.548740	−	0.398683i	−0.827321	+	0.561730i	$0.810136\pi$
$314$	−16.1803	−	11.7557i	−0.913109	−	0.663413i
$315$	11.9960	−	0.308098i	0.675901	−	0.0173593i
$316$	4.03499	−	1.31105i	0.226986	−	0.0737522i
$317$	−14.9626	−	20.5942i	−0.840382	−	1.15669i	−0.985901	−	0.167331i	$-0.946485\pi$
$317$	−14.9626	−	20.5942i	−0.840382	−	1.15669i	0.145519	−	0.989355i	$-0.453515\pi$
$318$	8.00000	+	5.65685i	0.448618	+	0.317221i
$319$		0			0
$320$		−	19.7990i		−	1.10680i
$321$	0.355790	+	27.7105i	0.0198583	+	1.54665i
$322$		0			0
$323$	24.2099	+	7.86629i	1.34708	+	0.437692i
$324$	−8.98813	+	0.461994i	−0.499341	+	0.0256664i
$325$	−7.48128	+	10.2971i	−0.414987	+	0.571181i
$326$	−6.18034	+	19.0211i	−0.342297	+	1.05348i
$327$	2.18089	−	7.01739i	0.120603	−	0.388062i
$328$	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
$333$	19.0478	−	14.6007i	1.04381	−	0.800114i
$334$	3.70820	−	11.4127i	0.202904	−	0.624474i
$335$	−3.32502	+	4.57649i	−0.181665	+	0.250040i
$336$	−0.786780	−	2.31969i	−0.0429224	−	0.126550i
$337$	−30.9349	−	10.0514i	−1.68513	−	0.547533i	−0.699237	−	0.714890i	$-0.746477\pi$
$337$	−30.9349	−	10.0514i	−1.68513	−	0.547533i	−0.985896	+	0.167357i	$0.946477\pi$
$338$	1.54508	+	4.75528i	0.0840415	+	0.258653i
$339$	4.89858	−	0.0628954i	0.266054	−	0.00341601i
$340$		−	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	$-0.441297\pi$
$347$	−12.9443	−	9.40456i	−0.694885	−	0.504863i	−0.878262	+	0.478179i	$0.841297\pi$
$348$	2.07196	+	2.77615i	0.111069	+	0.148817i
$349$	4.03499	−	1.31105i	0.215988	−	0.0701788i	−0.199024	−	0.979995i	$-0.563777\pi$
$349$	4.03499	−	1.31105i	0.215988	−	0.0701788i	0.415012	+	0.909816i	$0.363777\pi$
$350$	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			$\pi$
$354$	19.5943	−	0.251582i	1.04143	−	0.0133714i
$355$	−2.47214	−	7.60845i	−0.131207	−	0.403815i
$356$		0			0
$357$	−4.72068	−	13.9182i	−0.249845	−	0.736627i
$358$	1.66251	−	2.28825i	0.0878663	−	0.120938i
$359$	−6.18034	+	19.0211i	−0.326186	+	1.00390i	0.644717	+	0.764422i	$0.276975\pi$
$359$	−6.18034	+	19.0211i	−0.326186	+	1.00390i	−0.970902	+	0.239475i	$0.923025\pi$
$360$	−15.4864	−	20.2033i	−0.816204	−	1.06481i
$361$	−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
$366$	−5.08874	+	16.3739i	−0.265993	+	0.855878i
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	2.47214	−	7.60845i	0.129044	−	0.397158i	0.994616	+	0.103627i	$0.0330448\pi$
$368$		0			0
$369$	5.12094	−	17.2562i	0.266586	−	0.898321i
$370$	21.5200	+	6.99226i	1.11877	+	0.363510i
$371$	−2.47214	−	7.60845i	−0.128347	−	0.395011i
$372$	0.0444738	+	3.46382i	0.00230586	+	0.179590i
$373$		−	4.24264i		−	0.219676i	−0.993950	−	0.109838i	$-0.964967\pi$
$373$		−	4.24264i		−	0.219676i	0.993950	−	0.109838i	$-0.0350331\pi$
$374$		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
$378$	−6.10695	−	4.08719i	−0.314108	−	0.210223i
$379$	−9.70820	−	7.05342i	−0.498677	−	0.362310i	0.309834	−	0.950791i	$-0.399726\pi$
$379$	−9.70820	−	7.05342i	−0.498677	−	0.362310i	−0.808511	+	0.588481i	$0.799726\pi$
$380$	−9.70820	−	7.05342i	−0.498020	−	0.361833i
$381$	−13.7412	+	10.2557i	−0.703984	+	0.525414i
$382$	−18.8300	+	6.11822i	−0.963424	+	0.313036i
$383$	3.32502	+	4.57649i	0.169900	+	0.233848i	0.885473	−	0.464690i	$-0.153834\pi$
$383$	3.32502	+	4.57649i	0.169900	+	0.233848i	−0.715573	+	0.698538i	$0.753834\pi$
$384$	3.00000	−	4.24264i	0.153093	−	0.216506i
$385$		0			0
$386$		−	21.2132i		−	1.07972i
$387$	7.21444	−	10.4858i	0.366731	−	0.533023i
$388$	0.618034	+	1.90211i	0.0313759	+	0.0965652i
$389$	−18.8300	−	6.11822i	−0.954717	−	0.310206i	−0.210086	−	0.977683i	$-0.567374\pi$
$389$	−18.8300	−	6.11822i	−0.954717	−	0.310206i	−0.744631	+	0.667477i	$0.767374\pi$
$390$	19.6833	−	6.67605i	0.996700	−	0.338055i
$391$		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
$399$	−9.92408	−	3.08424i	−0.496826	−	0.154405i
$400$	0.927051	−	2.85317i	0.0463525	−	0.142658i
$401$	−1.66251	+	2.28825i	−0.0830217	+	0.114270i	−0.848508	−	0.529183i	$-0.822499\pi$
$401$	−1.66251	+	2.28825i	−0.0830217	+	0.114270i	0.765486	+	0.643452i	$0.222499\pi$
$402$	3.28054	−	1.11268i	0.163619	−	0.0554952i
$403$	−8.06998	−	2.62210i	−0.401994	−	0.130616i
$404$	−3.09017	−	9.51057i	−0.153742	−	0.473168i
$405$	−24.5818	−	6.61316i	−1.22148	−	0.328610i
$406$			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	0.742900	−	0.669403i	$-0.233450\pi$
$409$	−2.49376	−	3.43237i	−0.123309	−	0.169720i	−0.866208	+	0.499683i	$0.833450\pi$
$410$	16.1400	−	5.24419i	0.797096	−	0.258992i
$411$	−3.92606	+	2.93019i	−0.193658	+	0.144536i
$412$	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	$0.725210\pi$
$420$	0.0889475	+	6.92763i	0.00434019	+	0.338034i
$421$	−6.18034	−	19.0211i	−0.301211	−	0.927033i	−0.981064	−	0.193684i	$-0.937956\pi$
$421$	−6.18034	−	19.0211i	−0.301211	−	0.927033i	0.679853	−	0.733349i	$-0.262044\pi$
$422$	25.5549	+	8.30330i	1.24400	+	0.404199i
$423$	8.13464	+	2.41404i	0.395520	+	0.117374i
$424$	−9.97505	+	13.7295i	−0.484431	+	0.666762i
$425$	5.56231	−	17.1190i	0.269811	−	0.830394i
$426$	−1.45393	+	4.67826i	−0.0704429	+	0.226662i
$427$	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	$-0.980090\pi$
$431$	−25.8885	+	18.8091i	−1.24701	+	0.906004i	−0.248963	+	0.968513i	$0.580090\pi$
$432$	0.200088	+	5.19230i	0.00962674	+	0.249815i
$433$	9.27051	−	28.5317i	0.445512	−	1.37115i	−0.436409	−	0.899749i	$-0.643750\pi$
$433$	9.27051	−	28.5317i	0.445512	−	1.37115i	0.881921	−	0.471397i	$-0.156250\pi$
$434$	−1.66251	+	2.28825i	−0.0798029	+	0.109839i
$435$	3.14712	+	9.27877i	0.150893	+	0.444883i
$436$	4.03499	+	1.31105i	0.193241	+	0.0627878i
$437$		0			0
$438$	−2.44929	+	0.0314477i	−0.117032	+	0.00150263i
$439$			26.8701i			1.28244i	0.767358	+	0.641219i	$0.221571\pi$
$439$			26.8701i			1.28244i	−0.767358	+	0.641219i	$0.778429\pi$
$440$		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	$-0.834527\pi$
$443$	−26.8999	+	8.74032i	−1.27805	+	0.415265i	−0.410160	+	0.912014i	$0.634527\pi$
$444$	8.28784	+	11.1046i	0.393323	+	0.527000i
$445$		0			0
$446$	19.4164	+	14.1068i	0.919394	+	0.667979i
$447$	6.21588	+	8.32844i	0.294001	+	0.393921i
$448$	9.41498	−	3.05911i	0.444816	−	0.144529i
$449$	3.32502	+	4.57649i	0.156917	+	0.215978i	0.880236	−	0.474536i	$-0.157384\pi$
$449$	3.32502	+	4.57649i	0.156917	+	0.215978i	−0.723319	+	0.690514i	$0.757384\pi$
$450$	−3.00000	−	8.48528i	−0.141421	−	0.400000i
$451$		0			0
$452$			2.82843i			0.133038i
$453$	7.34786	−	0.0943431i	0.345233	−	0.00443263i
$454$	−7.41641	−	22.8254i	−0.348069	−	1.07125i
$455$	−16.1400	−	5.24419i	−0.756653	−	0.245852i
$456$	7.08102	+	20.8772i	0.331599	+	0.977666i
$457$	−5.81878	+	8.00886i	−0.272191	+	0.374639i	−0.923128	−	0.384493i	$-0.874376\pi$
$457$	−5.81878	+	8.00886i	−0.272191	+	0.374639i	0.650937	+	0.759132i	$0.274376\pi$
$458$	7.41641	−	22.8254i	0.346546	−	1.06656i
$459$	1.20053	+	31.1538i	0.0560358	+	1.45413i
$460$		0			0
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		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
$465$	−2.90785	+	9.35652i	−0.134848	+	0.433898i
$466$	−3.09017	+	9.51057i	−0.143149	+	0.440568i
$467$	16.6251	−	22.8825i	0.769317	−	1.05887i	−0.227065	−	0.973880i	$-0.572913\pi$
$467$	16.6251	−	22.8825i	0.769317	−	1.05887i	0.996381	−	0.0849941i	$-0.0270871\pi$
$468$	12.2020	+	3.62105i	0.564036	+	0.167383i
$469$	−2.68999	−	0.874032i	−0.124212	−	0.0403591i
$470$	2.47214	+	7.60845i	0.114031	+	0.350952i
$471$	−0.444738	−	34.6382i	−0.0204924	−	1.59604i
$472$			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
$477$	0.435716	+	16.9650i	0.0199501	+	0.776773i
$478$	12.9443	+	9.40456i	0.592057	+	0.430155i
$479$	22.6525	+	16.4580i	1.03502	+	0.751985i	0.969307	−	0.245854i	$-0.0790684\pi$
$479$	22.6525	+	16.4580i	1.03502	+	0.751985i	0.0657112	+	0.997839i	$0.479068\pi$
$480$	19.6303	−	14.6510i	0.895997	−	0.668722i
$481$	−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
$486$	9.95281	+	11.9976i	0.451469	+	0.544221i
$487$	0.618034	+	1.90211i	0.0280058	+	0.0861930i	0.964082	−	0.265603i	$-0.0855711\pi$
$487$	0.618034	+	1.90211i	0.0280058	+	0.0861930i	−0.936077	+	0.351796i	$0.885571\pi$
$488$	−28.2449	−	9.17734i	−1.27859	−	0.415439i
$489$	−32.8054	+	11.1268i	−1.48351	+	0.503169i
$490$	8.31254	−	11.4412i	0.375522	−	0.516862i
$491$	−6.18034	+	19.0211i	−0.278915	+	0.858412i	0.709242	+	0.704965i	$0.249037\pi$
$491$	−6.18034	+	19.0211i	−0.278915	+	0.858412i	−0.988157	+	0.153447i	$0.950963\pi$
$492$	9.92408	+	3.08424i	0.447412	+	0.139048i
$493$	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
$498$	−26.4642	−	8.22465i	−1.18589	−	0.368555i
$499$	−4.32624	+	13.3148i	−0.193669	+	0.596052i	0.806321	+	0.591479i	$0.201456\pi$
$499$	−4.32624	+	13.3148i	−0.193669	+	0.596052i	−0.999990	+	0.00457310i	$0.998544\pi$
$500$	3.32502	−	4.57649i	0.148699	−	0.204667i
$501$	19.6833	−	6.67605i	0.879383	−	0.298264i
$502$	−24.2099	−	7.86629i	−1.08054	−	0.351090i
$503$	4.94427	+	15.2169i	0.220454	+	0.678488i	0.998721	+	0.0505549i	$0.0160990\pi$
$503$	4.94427	+	15.2169i	0.220454	+	0.678488i	−0.778267	+	0.627933i	$0.783901\pi$
$504$	7.21444	−	10.4858i	0.321357	−	0.467074i
$505$		−	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	$-0.328989\pi$
$509$	32.2799	−	10.4884i	1.43078	−	0.464889i	0.919011	+	0.394232i	$0.128989\pi$
$510$	−23.5564	+	17.5812i	−1.04309	+	0.778507i
$511$	1.61803	+	1.17557i	0.0715776	+	0.0520042i
$512$	−8.89919	−	6.46564i	−0.393292	−	0.285744i
$513$	18.3209	+	12.2616i	0.808885	+	0.541362i
$514$	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
$519$	−0.133421	−	10.3914i	−0.00585654	−	0.456134i
$520$	11.1246	+	34.2380i	0.487846	+	1.50144i
$521$	−18.8300	−	6.11822i	−0.824955	−	0.268044i	−0.134036	−	0.990976i	$-0.542794\pi$
$521$	−18.8300	−	6.11822i	−0.824955	−	0.268044i	−0.690919	+	0.722932i	$0.742794\pi$
$522$	1.70698	−	5.75206i	0.0747126	−	0.251761i
$523$	12.4688	−	17.1618i	0.545223	−	0.750435i	−0.444131	−	0.895962i	$-0.646488\pi$
$523$	12.4688	−	17.1618i	0.545223	−	0.750435i	0.989354	+	0.145527i	$0.0464877\pi$
$524$		0			0
$525$	−2.18089	+	7.01739i	−0.0951818	+	0.306264i
$526$		0			0
$527$	12.0000			0.522728
$528$		0			0
$529$	23.0000			1.00000
$530$	−12.9443	+	9.40456i	−0.562263	+	0.408508i
$531$	20.6485	+	26.9377i	0.896069	+	1.16900i
$532$	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
$537$	4.89858	−	0.0628954i	0.211389	−	0.00271414i
$538$		−	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	−0.972508	−	0.232871i	$-0.925188\pi$
$541$	−20.7813	−	28.6031i	−0.893460	−	1.22974i	0.0790477	−	0.996871i	$-0.474812\pi$
$542$	28.2449	−	9.17734i	1.21322	−	0.394200i
$543$	10.3598	+	13.8807i	0.444582	+	0.595679i
$544$	−24.2705	−	17.6336i	−1.04059	−	0.756033i
$545$	9.70820	+	7.05342i	0.415854	+	0.302135i
$546$	6.21588	+	8.32844i	0.266015	+	0.356424i
$547$	33.6249	−	10.9254i	1.43770	−	0.467136i	0.516519	−	0.856276i	$-0.327228\pi$
$547$	33.6249	−	10.9254i	1.43770	−	0.467136i	0.921179	+	0.389139i	$0.127228\pi$
$548$	−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
$555$	12.5885	+	37.1151i	0.534351	+	1.57545i
$556$	0.831254	−	1.14412i	0.0352530	−	0.0485216i
$557$	0.618034	−	1.90211i	0.0261869	−	0.0805951i	−0.937109	−	0.349037i	$-0.886509\pi$
$557$	0.618034	−	1.90211i	0.0261869	−	0.0805951i	0.963296	+	0.268442i	$0.0865087\pi$
$558$	4.76195	−	3.65018i	0.201590	−	0.154524i
$559$	−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	$-0.618626\pi$
$563$	9.70820	−	7.05342i	0.409152	−	0.297266i	0.773258	+	0.634091i	$0.218626\pi$
$564$	−1.45393	+	4.67826i	−0.0612213	+	0.196990i
$565$	−2.47214	+	7.60845i	−0.104004	+	0.320090i
$566$	−15.7938	+	21.7383i	−0.663864	+	0.913730i
$567$	−0.653359	−	12.7111i	−0.0274385	−	0.533818i
$568$	−8.06998	−	2.62210i	−0.338609	−	0.110021i
$569$	11.7426	+	36.1401i	0.492277	+	1.51507i	0.821157	+	0.570702i	$0.193329\pi$
$569$	11.7426	+	36.1401i	0.492277	+	1.51507i	−0.328880	+	0.944372i	$0.606671\pi$
$570$	0.266843	+	20.7829i	0.0111768	+	0.870500i
$571$			26.8701i			1.12448i	0.826975	+	0.562238i	$0.190060\pi$
$571$			26.8701i			1.12448i	−0.826975	+	0.562238i	$0.809940\pi$
$572$		0			0
$573$	−28.0000	−	19.7990i	−1.16972	−	0.827115i
$574$	4.98752	+	6.86474i	0.208175	+	0.286529i
$575$		0			0
$576$	−20.9931	+	0.539171i	−0.874712	+	0.0224655i
$577$	25.8885	+	18.8091i	1.07775	+	0.783034i	0.977290	−	0.211906i	$-0.0679672\pi$
$577$	25.8885	+	18.8091i	1.07775	+	0.783034i	0.100464	+	0.994941i	$0.467967\pi$
$578$	15.3713	+	11.1679i	0.639363	+	0.464524i
$579$	29.4455	−	21.9765i	1.22371	−	0.913310i
$580$	−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
$585$	29.6583	+	20.4055i	1.22622	+	0.843665i
$586$	−0.618034	−	1.90211i	−0.0255307	−	0.0785756i
$587$	10.7600	+	3.49613i	0.444112	+	0.144301i	0.522532	−	0.852620i	$-0.324988\pi$
$587$	10.7600	+	3.49613i	0.444112	+	0.144301i	−0.0784201	+	0.996920i	$0.524988\pi$
$588$	8.20135	−	2.78169i	0.338218	−	0.114715i
$589$	4.98752	−	6.86474i	0.205507	−	0.282857i
$590$	−9.88854	+	30.4338i	−0.407105	+	1.25294i
$591$	−36.3883	−	11.3089i	−1.49681	−	0.465186i
$592$	6.47214	−	4.70228i	0.266003	−	0.193263i
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$		0			0
$595$	24.0000			0.983904
$596$	−4.85410	+	3.52671i	−0.198832	+	0.144460i
$597$	3.30803	+	1.02808i	0.135389	+	0.0420766i
$598$		0			0
$599$	−19.9501	+	27.4589i	−0.815139	+	1.12194i	0.175371	+	0.984502i	$0.443887\pi$
$599$	−19.9501	+	27.4589i	−0.815139	+	1.12194i	−0.990510	+	0.137440i	$0.956113\pi$
$600$	14.7624	−	5.00704i	0.602674	−	0.204411i
$601$	28.2449	+	9.17734i	1.15214	+	0.374351i	0.821947	−	0.569564i	$-0.192888\pi$
$601$	28.2449	+	9.17734i	1.15214	+	0.374351i	0.330188	+	0.943915i	$0.392888\pi$
$602$	1.85410	+	5.70634i	0.0755676	+	0.232573i
$603$	4.94305	+	3.40092i	0.201297	+	0.138496i
$604$			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	0.755403	−	0.655260i	$-0.227441\pi$
$607$	−2.49376	−	3.43237i	−0.101219	−	0.139316i	−0.856622	+	0.515945i	$0.827441\pi$
$608$	−20.1750	+	6.55524i	−0.818202	+	0.265850i
$609$	−3.92606	+	2.93019i	−0.159092	+	0.118737i
$610$	−22.6525	−	16.4580i	−0.917172	−	0.666364i
$611$	−9.70820	−	7.05342i	−0.392752	−	0.285351i
$612$	−17.9941	+	0.462147i	−0.727367	+	0.0186812i
$613$	4.03499	−	1.31105i	0.162972	−	0.0529527i	−0.226395	−	0.974036i	$-0.572694\pi$
$613$	4.03499	−	1.31105i	0.162972	−	0.0529527i	0.389367	+	0.921083i	$0.372694\pi$
$614$	−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	$0.784579\pi$
$618$	−0.177895	−	13.8553i	−0.00715599	−	0.557340i
$619$	−6.18034	−	19.0211i	−0.248409	−	0.764524i	−0.995057	−	0.0993047i	$-0.968338\pi$
$619$	−6.18034	−	19.0211i	−0.248409	−	0.764524i	0.746648	−	0.665219i	$-0.231662\pi$
$620$	−5.37999	−	1.74806i	−0.216066	−	0.0702039i
$621$		0			0
$622$	−16.6251	+	22.8825i	−0.666605	+	0.917503i
$623$		0			0
$624$	2.18089	−	7.01739i	0.0873054	−	0.280920i
$625$	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
$630$	9.52391	−	7.30035i	0.379442	−	0.290853i
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	−0.999496	−	0.0317495i	$-0.989892\pi$
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	0.827271	+	0.561803i	$0.189892\pi$
$632$	7.48128	−	10.2971i	0.297590	−	0.409597i
$633$	14.9488	+	44.0742i	0.594162	+	1.75179i
$634$	−24.2099	−	7.86629i	−0.961500	−	0.312410i
$635$	−8.65248	−	26.6296i	−0.343363	−	1.05676i
$636$	−9.79715	+	0.125791i	−0.388482	+	0.00498793i
$637$			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	$-0.788654\pi$
$641$	−26.8999	+	8.74032i	−1.06248	+	0.345222i	−0.274928	+	0.961465i	$0.588654\pi$
$642$	16.5757	+	22.2092i	0.654190	+	0.876526i
$643$	−9.70820	−	7.05342i	−0.382854	−	0.278160i	0.379667	−	0.925123i	$-0.376039\pi$
$643$	−9.70820	−	7.05342i	−0.382854	−	0.278160i	−0.762521	+	0.646963i	$0.776039\pi$
$644$		0			0
$645$	12.4318	+	16.6569i	0.489500	+	0.655864i
$646$	24.2099	−	7.86629i	0.952528	−	0.309495i
$647$	3.32502	+	4.57649i	0.130720	+	0.179920i	0.869360	−	0.494180i	$-0.164532\pi$
$647$	3.32502	+	4.57649i	0.130720	+	0.179920i	−0.738640	+	0.674100i	$0.764532\pi$
$648$	−21.0000	+	16.9706i	−0.824958	+	0.666667i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	−4.89858	+	0.0628954i	−0.191990	+	0.00246506i
$652$	−6.18034	−	19.0211i	−0.242041	−	0.744925i
$653$	10.7600	+	3.49613i	0.421070	+	0.136814i	0.511885	−	0.859054i	$-0.328947\pi$
$653$	10.7600	+	3.49613i	0.421070	+	0.136814i	−0.0908151	+	0.995868i	$0.528947\pi$
$654$	−2.36034	−	6.95908i	−0.0922966	−	0.272122i
$655$		0			0
$656$	1.85410	−	5.70634i	0.0723905	−	0.222795i
$657$	−2.58107	−	3.36721i	−0.100697	−	0.131367i
$658$	−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
$663$	13.0853	−	42.1043i	0.508192	−	1.63520i
$664$	14.8328	−	45.6507i	0.575625	−	1.77159i
$665$	9.97505	−	13.7295i	0.386816	−	0.532406i
$666$	6.82793	−	23.0082i	0.264577	−	0.891551i
$667$		0			0
$668$	3.70820	+	11.4127i	0.143475	+	0.441570i
$669$	0.533685	+	41.5658i	0.0206335	+	1.60703i
$670$			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	0.758244	−	0.651971i	$-0.226058\pi$
$673$	−2.49376	−	3.43237i	−0.0961274	−	0.132308i	−0.854371	+	0.519663i	$0.826058\pi$
$674$	−30.9349	+	10.0514i	−1.19157	+	0.387164i
$675$	8.67025	−	12.9548i	0.333718	−	0.498630i
$676$	−4.04508	−	2.93893i	−0.155580	−	0.113036i
$677$	−30.7426	−	22.3358i	−1.18154	−	0.858436i	−0.189192	−	0.981940i	$-0.560587\pi$
$677$	−30.7426	−	22.3358i	−1.18154	−	0.858436i	−0.992344	+	0.123504i	$0.960587\pi$
$678$	3.92606	−	2.93019i	0.150780	−	0.112533i
$679$	−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	$-0.202946\pi$
$684$	−7.21444	+	10.4858i	−0.275851	+	0.400934i
$685$	−2.47214	−	7.60845i	−0.0944555	−	0.290704i
$686$	16.1400	+	5.24419i	0.616227	+	0.200224i
$687$	39.3665	−	13.3521i	1.50193	−	0.509414i
$688$	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	−0.851357	−	0.524587i	$-0.824220\pi$
$691$	−16.1803	+	11.7557i	−0.615529	+	0.447208i	0.235828	+	0.971795i	$0.424220\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−16.0000			−0.607352
$695$	3.23607	−	2.35114i	0.122751	−	0.0891839i
$696$	9.92408	+	3.08424i	0.376171	+	0.116908i
$697$	11.1246	−	34.2380i	0.421375	−	1.29686i
$698$	2.49376	−	3.43237i	0.0943903	−	0.129917i
$699$	−16.4027	+	5.56338i	−0.620407	+	0.210426i
$700$	−4.03499	−	1.31105i	−0.152508	−	0.0495530i
$701$	−1.85410	−	5.70634i	−0.0700285	−	0.215525i	0.909917	−	0.414790i	$-0.136145\pi$
$701$	−1.85410	−	5.70634i	−0.0700285	−	0.215525i	−0.979946	+	0.199264i	$0.936145\pi$
$702$	−7.61471	−	20.6886i	−0.287399	−	0.780839i
$703$		−	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
$708$	−15.7042	+	11.7208i	−0.590202	+	0.440494i
$709$	25.8885	+	18.8091i	0.972265	+	0.706392i	0.955967	−	0.293476i	$-0.0948119\pi$
$709$	25.8885	+	18.8091i	0.972265	+	0.706392i	0.0162981	+	0.999867i	$0.494812\pi$
$710$	−6.47214	−	4.70228i	−0.242895	−	0.176473i
$711$	−0.326787	−	12.7237i	−0.0122555	−	0.477177i
$712$		0			0
$713$		0			0
$714$	−12.0000	−	8.48528i	−0.449089	−	0.317554i
$715$		0			0
$716$			2.82843i			0.105703i
$717$	0.355790	+	27.7105i	0.0132872	+	1.03487i
$718$	6.18034	+	19.0211i	0.230648	+	0.709862i
$719$	−18.8300	−	6.11822i	−0.702239	−	0.228171i	−0.0639332	−	0.997954i	$-0.520364\pi$
$719$	−18.8300	−	6.11822i	−0.702239	−	0.228171i	−0.638306	+	0.769783i	$0.720364\pi$
$720$	−8.13464	−	2.41404i	−0.303160	−	0.0899658i
$721$	−6.65003	+	9.15298i	−0.247660	+	0.340875i
$722$	−0.309017	+	0.951057i	−0.0115004	+	0.0353947i
$723$	2.18089	−	7.01739i	0.0811081	−	0.260979i
$724$	−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
$729$	−6.34258	+	26.2445i	−0.234910	+	0.972017i
$730$	1.23607	−	3.80423i	0.0457489	−	0.140801i
$731$	14.9626	−	20.5942i	0.553411	−	0.761704i
$732$	−5.50746	−	16.2379i	−0.203562	−	0.600168i
$733$	−1.34500	−	0.437016i	−0.0496786	−	0.0161416i	0.284072	−	0.958803i	$-0.408314\pi$
$733$	−1.34500	−	0.437016i	−0.0496786	−	0.0161416i	−0.333751	+	0.942661i	$0.608314\pi$
$734$	−2.47214	−	7.60845i	−0.0912482	−	0.280833i
$735$	24.4929	−	0.314477i	0.903433	−	0.0115997i
$736$		0			0
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$	−2.49376	−	3.43237i	−0.0917345	−	0.126262i	0.760683	−	0.649124i	$-0.224864\pi$
$739$	−2.49376	−	3.43237i	−0.0917345	−	0.126262i	−0.852417	+	0.522862i	$0.824864\pi$
$740$	−21.5200	+	6.99226i	−0.791089	+	0.257040i
$741$	−18.6476	−	24.9853i	−0.685038	−	0.917858i
$742$	−6.47214	−	4.70228i	−0.237600	−	0.172626i
$743$	−12.9443	−	9.40456i	−0.474879	−	0.345020i	0.324461	−	0.945899i	$-0.394817\pi$
$743$	−12.9443	−	9.40456i	−0.474879	−	0.345020i	−0.799340	+	0.600879i	$0.794817\pi$
$744$	6.21588	+	8.32844i	0.227885	+	0.305335i
$745$	−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
$750$	−9.79715	+	0.125791i	−0.357741	+	0.00459323i
$751$	0.618034	+	1.90211i	0.0225524	+	0.0694091i	0.961699	−	0.274107i	$-0.0883821\pi$
$751$	0.618034	+	1.90211i	0.0225524	+	0.0694091i	−0.939147	+	0.343516i	$0.888382\pi$
$752$	2.68999	+	0.874032i	0.0980940	+	0.0318727i
$753$	−14.1620	−	41.7545i	−0.516094	−	1.52162i
$754$	−4.98752	+	6.86474i	−0.181635	+	0.249999i
$755$	−3.70820	+	11.4127i	−0.134955	+	0.415350i
$756$	7.34302	−	0.282967i	0.267063	−	0.0102914i
$757$	−16.1803	+	11.7557i	−0.588084	+	0.427268i	−0.841630	−	0.540055i	$-0.818403\pi$
$757$	−16.1803	+	11.7557i	−0.588084	+	0.427268i	0.253545	+	0.967324i	$0.418403\pi$
$758$	−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	$-0.758014\pi$
$761$	−8.09017	+	5.87785i	−0.293268	+	0.213072i	0.431416	+	0.902153i	$0.358014\pi$
$762$	−5.08874	+	16.3739i	−0.184346	+	0.593164i
$763$	−1.85410	+	5.70634i	−0.0671230	+	0.206583i
$764$	11.6376	−	16.0177i	0.421032	−	0.579501i
$765$	−48.8079	−	14.4842i	−1.76465	−	0.523678i
$766$	5.37999	+	1.74806i	0.194387	+	0.0631601i
$767$	−14.8328	−	45.6507i	−0.535582	−	1.64835i
$768$	−0.378027	−	29.4424i	−0.0136409	−	1.06241i
$769$		−	35.3553i		−	1.27495i	−0.770473	−	0.637473i	$-0.779980\pi$
$769$		−	35.3553i		−	1.27495i	0.770473	−	0.637473i	$-0.220020\pi$
$770$		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	$-0.391013\pi$
$773$	32.2799	−	10.4884i	1.16103	−	0.377241i	0.825287	+	0.564713i	$0.191013\pi$
$774$	−0.326787	−	12.7237i	−0.0117461	−	0.457345i
$775$	−4.85410	−	3.52671i	−0.174364	−	0.126683i
$776$	4.85410	+	3.52671i	0.174252	+	0.126602i
$777$	−15.7042	+	11.7208i	−0.563387	+	0.420480i
$778$	−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
$783$	9.75268	−	3.58961i	0.348532	−	0.128282i
$784$	−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	−0.526732	−	0.850031i	$-0.676583\pi$
$787$	12.4688	−	17.1618i	0.444465	−	0.611754i	0.971197	+	0.238278i	$0.0765829\pi$
$788$	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
$795$	−26.4642	−	8.22465i	−0.938589	−	0.291698i
$796$	−0.618034	+	1.90211i	−0.0219056	+	0.0674186i
$797$	−1.66251	+	2.28825i	−0.0588890	+	0.0810538i	−0.837446	−	0.546520i	$-0.815952\pi$
$797$	−1.66251	+	2.28825i	−0.0588890	+	0.0810538i	0.778557	+	0.627574i	$0.215952\pi$
$798$	−9.84163	+	3.33803i	−0.348390	+	0.118165i
$799$	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
$807$	39.2606	−	29.3019i	1.38204	−	1.03148i
$808$	−24.2705	−	17.6336i	−0.853834	−	0.620346i
$809$	40.4508	+	29.3893i	1.42218	+	1.03327i	0.991408	+	0.130809i	$0.0417575\pi$
$809$	40.4508	+	29.3893i	1.42218	+	1.03327i	0.430769	+	0.902462i	$0.358243\pi$
$810$	−23.7742	+	9.09868i	−0.835341	+	0.319695i
$811$	−25.5549	+	8.30330i	−0.897355	+	0.291568i	−0.721145	−	0.692784i	$-0.756384\pi$
$811$	−25.5549	+	8.30330i	−0.897355	+	0.291568i	−0.176210	+	0.984353i	$0.556384\pi$
$812$	−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
$816$	0.133421	+	10.3914i	0.00467068	+	0.363773i
$817$	−5.56231	−	17.1190i	−0.194600	−	0.598919i
$818$	−4.03499	−	1.31105i	−0.141080	−	0.0458397i
$819$	−5.12094	+	17.2562i	−0.178940	+	0.602980i
$820$	−9.97505	+	13.7295i	−0.348344	+	0.479454i
$821$	−12.9787	+	39.9444i	−0.452960	+	1.39407i	0.420553	+	0.907268i	$0.361836\pi$
$821$	−12.9787	+	39.9444i	−0.452960	+	1.39407i	−0.873513	+	0.486800i	$0.838164\pi$
$822$	−1.45393	+	4.67826i	−0.0507115	+	0.163173i
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	−0.195486	−	0.980707i	$-0.562628\pi$
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	0.872299	+	0.488973i	$0.162628\pi$
$824$	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	$-0.633096\pi$
$827$	9.70820	−	7.05342i	0.337587	−	0.245272i	0.743643	+	0.668577i	$0.233096\pi$
$828$		0			0
$829$	−4.32624	+	13.3148i	−0.150256	+	0.462442i	−0.997649	−	0.0685244i	$-0.978171\pi$
$829$	−4.32624	+	13.3148i	−0.150256	+	0.462442i	0.847393	+	0.530966i	$0.178171\pi$
$830$	26.6001	−	36.6119i	0.923304	−	1.27082i
$831$	−2.36034	−	6.95908i	−0.0818793	−	0.241408i
$832$	28.2449	+	9.17734i	0.979217	+	0.318167i
$833$	−9.27051	−	28.5317i	−0.321204	−	0.988565i
$834$	−2.44929	+	0.0314477i	−0.0848119	+	0.00108894i
$835$			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	$-0.400745\pi$
$839$	32.2799	−	10.4884i	1.11443	−	0.362099i	0.807638	+	0.589678i	$0.200745\pi$
$840$	12.4318	+	16.6569i	0.428936	+	0.574717i
$841$	20.2254	+	14.6946i	0.697428	+	0.506711i
$842$	−16.1803	−	11.7557i	−0.557611	−	0.405128i
$843$	6.21588	+	8.32844i	0.214086	+	0.286847i
$844$	−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
$849$	−46.5365	+	0.597506i	−1.59713	+	0.0205064i
$850$	−5.56231	−	17.1190i	−0.190786	−	0.587177i
$851$		0			0
$852$	−1.57356	−	4.63939i	−0.0539093	−	0.158943i
$853$	−24.1064	+	33.1796i	−0.825386	+	1.13605i	0.163378	+	0.986564i	$0.447761\pi$
$853$	−24.1064	+	33.1796i	−0.825386	+	1.13605i	−0.988764	+	0.149483i	$0.952239\pi$
$854$	4.32624	−	13.3148i	0.148041	−	0.455623i
$855$	−28.5717	+	21.9011i	−0.977132	+	0.749001i
$856$	−38.8328	+	28.2137i	−1.32728	+	0.964324i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		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
$861$	−4.36178	+	14.0348i	−0.148649	+	0.478304i
$862$	−9.88854	+	30.4338i	−0.336805	+	1.03658i
$863$	−19.9501	+	27.4589i	−0.679109	+	0.934713i	−0.999923	−	0.0124289i	$-0.996044\pi$
$863$	−19.9501	+	27.4589i	−0.679109	+	0.934713i	0.320814	+	0.947142i	$0.396044\pi$
$864$	−16.0692	−	20.4152i	−0.546684	−	0.694541i
$865$	16.1400	+	5.24419i	0.548775	+	0.178308i
$866$	−9.27051	−	28.5317i	−0.315025	−	0.969546i
$867$	0.422501	+	32.9063i	0.0143489	+	1.11755i
$868$		−	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
$873$	5.99802	−	0.154049i	0.203002	−	0.00521377i
$874$		0			0
$875$	6.47214	+	4.70228i	0.218798	+	0.158966i
$876$	1.96303	−	1.46510i	0.0663247	−	0.0495010i
$877$	33.6249	−	10.9254i	1.13543	−	0.368925i	0.319795	−	0.947487i	$-0.396386\pi$
$877$	33.6249	−	10.9254i	1.13543	−	0.368925i	0.815638	+	0.578562i	$0.196386\pi$
$878$	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	$0.824399\pi$
$882$	−12.3576	−	8.50230i	−0.416103	−	0.286287i
$883$	14.2148	+	43.7486i	0.478365	+	1.47226i	0.841365	+	0.540468i	$0.181753\pi$
$883$	14.2148	+	43.7486i	0.478365	+	1.47226i	−0.362999	+	0.931790i	$0.618247\pi$
$884$	24.2099	+	7.86629i	0.814269	+	0.264572i
$885$	−52.4887	+	17.8028i	−1.76439	+	0.598435i
$886$	−16.6251	+	22.8825i	−0.558530	+	0.768751i
$887$	7.41641	−	22.8254i	0.249019	−	0.766400i	−0.745931	−	0.666023i	$-0.767995\pi$
$887$	7.41641	−	22.8254i	0.249019	−	0.766400i	0.994949	−	0.100377i	$-0.0320049\pi$
$888$	39.6963	+	12.3370i	1.33212	+	0.414002i
$889$	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
$894$	9.92408	+	3.08424i	0.331911	+	0.103153i
$895$	−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
$900$	7.41457	+	5.10138i	0.247152	+	0.170046i
$901$			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
$906$	5.88909	−	4.39529i	0.195652	−	0.146024i
$907$	−9.70820	−	7.05342i	−0.322356	−	0.234205i	0.414824	−	0.909902i	$-0.363843\pi$
$907$	−9.70820	−	7.05342i	−0.322356	−	0.234205i	−0.737180	+	0.675696i	$0.763843\pi$
$908$	19.4164	+	14.1068i	0.644356	+	0.468152i
$909$	−29.9901	+	0.770245i	−0.994709	+	0.0255474i
$910$	−16.1400	+	5.24419i	−0.535035	+	0.173843i
$911$	21.6126	+	29.7472i	0.716057	+	0.985568i	0.999646	+	0.0266223i	$0.00847514\pi$
$911$	21.6126	+	29.7472i	0.716057	+	0.985568i	−0.283588	+	0.958946i	$0.591525\pi$
$912$	6.00000	+	4.24264i	0.198680	+	0.140488i
$913$		0			0
$914$			9.89949i			0.327446i
$915$	−0.622633	−	48.4934i	−0.0205836	−	1.60314i
$916$	7.41641	+	22.8254i	0.245045	+	0.754171i
$917$		0			0
$918$	19.2830	+	24.4983i	0.636433	+	0.808564i
$919$	12.4688	−	17.1618i	0.411308	−	0.566117i	−0.552229	−	0.833693i	$-0.686223\pi$
$919$	12.4688	−	17.1618i	0.411308	−	0.566117i	0.963537	+	0.267576i	$0.0862225\pi$
$920$		0			0
$921$	2.18089	−	7.01739i	0.0718627	−	0.231231i
$922$	−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
$927$	19.0478	−	14.6007i	0.625612	−	0.479550i
$928$	−3.09017	+	9.51057i	−0.101440	+	0.312200i
$929$	−1.66251	+	2.28825i	−0.0545451	+	0.0750749i	−0.835418	−	0.549615i	$-0.814775\pi$
$929$	−1.66251	+	2.28825i	−0.0545451	+	0.0750749i	0.780873	+	0.624690i	$0.214775\pi$
$930$	3.14712	+	9.27877i	0.103198	+	0.304263i
$931$	−20.1750	−	6.55524i	−0.661207	−	0.214839i
$932$	−3.09017	−	9.51057i	−0.101222	−	0.311529i
$933$	−48.9858	+	0.628954i	−1.60372	+	0.0205910i
$934$		−	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	0.321023	−	0.947071i	$-0.395973\pi$
$937$	−20.7813	−	28.6031i	−0.678897	−	0.934422i	−0.999920	+	0.0126498i	$0.995973\pi$
$938$	−2.68999	+	0.874032i	−0.0878314	+	0.0285382i
$939$	−12.4318	−	16.6569i	−0.405695	−	0.543576i
$940$	−6.47214	−	4.70228i	−0.211098	−	0.153372i
$941$	−30.7426	−	22.3358i	−1.00218	−	0.728128i	−0.0396268	−	0.999215i	$-0.512617\pi$
$941$	−30.7426	−	22.3358i	−1.00218	−	0.728128i	−0.962555	+	0.271087i	$0.912617\pi$
$942$	−20.7196	−	27.7615i	−0.675081	−	0.904517i
$943$		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	$-0.168697\pi$
$948$	7.34786	−	0.0943431i	0.238648	−	0.00306412i
$949$	1.85410	+	5.70634i	0.0601867	+	0.185236i
$950$	−12.1050	−	3.93314i	−0.392737	−	0.127608i
$951$	−14.1620	−	41.7545i	−0.459236	−	1.35398i
$952$	14.9626	−	20.5942i	0.484940	−	0.667462i
$953$	0.618034	−	1.90211i	0.0200201	−	0.0616155i	−0.940547	−	0.339663i	$-0.889687\pi$
$953$	0.618034	−	1.90211i	0.0200201	−	0.0616155i	0.960567	+	0.278047i	$0.0896871\pi$
$954$	10.3243	+	13.4688i	0.334260	+	0.436070i
$955$	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
$960$	10.1775	−	32.7478i	0.328477	−	1.05693i
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$	−19.9501	+	27.4589i	−0.643217	+	0.885312i
$963$	−13.6559	+	46.0165i	−0.440054	+	1.48286i
$964$	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	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		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	$-0.416677\pi$
$971$	32.2799	−	10.4884i	1.03591	−	0.336588i	0.777125	+	0.629346i	$0.216677\pi$
$972$	−15.1040	−	3.85612i	−0.484461	−	0.123685i
$973$	1.61803	+	1.17557i	0.0518718	+	0.0376871i
$974$	1.61803	+	1.17557i	0.0518452	+	0.0376677i
$975$	−17.6673	+	13.1859i	−0.565806	+	0.422286i
$976$	−9.41498	+	3.05911i	−0.301366	+	0.0979198i
$977$	−14.9626	−	20.5942i	−0.478695	−	0.658867i	0.499558	−	0.866280i	$-0.333496\pi$
$977$	−14.9626	−	20.5942i	−0.478695	−	0.658867i	−0.978253	+	0.207413i	$0.933496\pi$
$978$	−20.0000	+	28.2843i	−0.639529	+	0.904431i
$979$		0			0
$980$			14.1421i			0.451754i
$981$	7.21444	−	10.4858i	0.230339	−	0.334786i
$982$	6.18034	+	19.0211i	0.197223	+	0.606989i
$983$	10.7600	+	3.49613i	0.343190	+	0.111509i	0.475541	−	0.879694i	$-0.342252\pi$
$983$	10.7600	+	3.49613i	0.343190	+	0.111509i	−0.132351	+	0.991203i	$0.542252\pi$
$984$	29.5249	−	10.0141i	0.941219	−	0.319237i
$985$	36.5752	−	50.3414i	1.16538	−	1.60401i
$986$	3.70820	−	11.4127i	0.118093	−	0.363454i
$987$	−6.61606	−	2.05616i	−0.210591	−	0.0654484i
$988$	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
$993$	−33.0803	−	10.2808i	−1.04977	−	0.326252i
$994$	1.23607	−	3.80423i	0.0392057	−	0.120663i
$995$	−3.32502	+	4.57649i	−0.105410	+	0.145085i
$996$	26.2443	−	8.90140i	0.831584	−	0.282052i
$997$	28.2449	+	9.17734i	0.894526	+	0.290649i	0.719976	−	0.693999i	$-0.244153\pi$
$997$	28.2449	+	9.17734i	0.894526	+	0.290649i	0.174550	+	0.984648i	$0.444153\pi$
$998$	4.32624	+	13.3148i	0.136945	+	0.421472i
$999$	39.0107	−	14.3584i	1.23424	−	0.454281i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(1.65401 + 0.514040i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.66251 + 2.28825i) q^{5} +(1.64027 - 0.556338i) q^{6} +(-1.34500 - 0.437016i) q^{7} +(0.927051 + 2.85317i) q^{8} +(2.47152 + 1.70046i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 - 3.43237i) q^{13} +(-1.34500 + 0.437016i) q^{14} +(-3.92606 + 2.93019i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(2.99901 - 0.0770245i) q^{18} +(4.03499 - 1.31105i) q^{19} +(-1.66251 - 2.28825i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(0.0667106 + 5.19572i) q^{24} +(-0.927051 - 2.85317i) q^{25} +(-4.03499 - 1.31105i) q^{26} +(3.21383 + 4.08305i) q^{27} +(0.831254 - 1.14412i) q^{28} +(0.618034 - 1.90211i) q^{29} +(-1.45393 + 4.67826i) q^{30} +(1.61803 - 1.17557i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(-2.38098 + 1.82509i) q^{36} +(2.47214 - 7.60845i) q^{37} +(2.49376 - 3.43237i) q^{38} +(-2.36034 - 6.95908i) q^{39} +(-8.06998 - 2.62210i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-2.44929 + 0.0314477i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(2.68999 - 0.874032i) q^{47} +(1.03598 + 1.38807i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(6.21588 + 8.32844i) q^{51} +(4.03499 - 1.31105i) q^{52} +(3.32502 + 4.57649i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(7.34786 - 0.0943431i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(10.7600 + 3.49613i) q^{59} +(-1.57356 - 4.63939i) q^{60} +(-5.81878 + 8.00886i) q^{61} +(0.618034 - 1.90211i) q^{62} +(-2.58107 - 3.36721i) 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} +(-2.56047 + 8.62809i) q^{72} +(-1.34500 - 0.437016i) q^{73} +(-2.47214 - 7.60845i) q^{74} +(-0.0667106 - 5.19572i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-2.49376 - 3.43237i) q^{79} +(-2.68999 + 0.874032i) q^{80} +(3.21687 + 8.40546i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-12.9443 - 9.40456i) q^{83} +(1.96303 - 1.46510i) q^{84} +(-16.1400 + 5.24419i) q^{85} +(-2.49376 - 3.43237i) q^{86} +(2.00000 - 2.82843i) q^{87} +(-4.80963 + 6.99053i) q^{90} +(1.85410 + 5.70634i) q^{91} +(3.28054 - 1.11268i) q^{93} +(1.66251 - 2.28825i) q^{94} +(-3.70820 + 11.4127i) q^{95} +(-8.27007 - 2.57020i) q^{96} +(1.61803 - 1.17557i) q^{97} -5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} - 16 q^{21} - 6 q^{24} + 6 q^{25} + 10 q^{27} - 4 q^{29} - 8 q^{30} + 4 q^{31} - 40 q^{32}+ \cdots - 40 q^{98}+O(q^{100}) \) 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

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