LMFDB - Embedded newform 363.2.f.f.215.1

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			215.1
Root			$-0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.f.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.64027 + 0.556338i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.68999 - 0.874032i) q^{5} +(1.03598 + 1.38807i) q^{6} +(0.831254 + 1.14412i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(2.38098 - 1.82509i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-4.03499 + 1.31105i) q^{13} +(0.831254 - 1.14412i) q^{14} +(4.89858 - 0.0628954i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.85410 + 5.70634i) q^{17} +(-2.47152 - 1.70046i) q^{18} +(-2.49376 + 3.43237i) q^{19} +(-2.68999 + 0.874032i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(4.96204 + 1.54212i) q^{24} +(2.42705 + 1.76336i) q^{25} +(2.49376 + 3.43237i) q^{26} +(-2.89008 + 4.31827i) q^{27} +(1.34500 + 0.437016i) q^{28} +(-1.61803 + 1.17557i) q^{29} +(-1.57356 - 4.63939i) q^{30} +(-0.618034 - 1.90211i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(-1.23607 - 3.80423i) q^{35} +(0.853491 - 2.87603i) q^{36} +(-6.47214 + 4.70228i) q^{37} +(4.03499 + 1.31105i) q^{38} +(5.88909 - 4.39529i) q^{39} +(4.98752 + 6.86474i) q^{40} +(4.85410 + 3.52671i) q^{41} +(-0.726963 + 2.33913i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(-1.66251 + 2.28825i) q^{47} +(-0.0222369 - 1.73191i) q^{48} +(1.54508 - 4.75528i) q^{49} +(0.927051 - 2.85317i) q^{50} +(-0.133421 - 10.3914i) q^{51} +(-2.49376 + 3.43237i) q^{52} +(5.37999 - 1.74806i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(2.18089 - 7.01739i) q^{57} +(1.61803 + 1.17557i) q^{58} +(-6.65003 - 9.15298i) q^{59} +(3.92606 - 2.93019i) q^{60} +(-9.41498 - 3.05911i) q^{61} +(-1.61803 + 1.17557i) q^{62} +(4.06732 + 1.20702i) q^{63} +(2.16312 + 6.65740i) q^{64} +12.0000 q^{65} +2.00000 q^{67} +(1.85410 + 5.70634i) q^{68} +(-3.23607 + 2.35114i) q^{70} +(-2.68999 - 0.874032i) q^{71} +(-8.99703 + 0.231073i) q^{72} +(0.831254 + 1.14412i) q^{73} +(6.47214 + 4.70228i) q^{74} +(-4.96204 - 1.54212i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-4.03499 + 1.31105i) q^{79} +(1.66251 - 2.28825i) q^{80} +(2.33810 - 8.69099i) q^{81} +(1.85410 - 5.70634i) q^{82} +(4.94427 - 15.2169i) q^{83} +(-2.44929 + 0.0314477i) q^{84} +(9.97505 - 13.7295i) q^{85} +(-4.03499 + 1.31105i) q^{86} +(2.00000 - 2.82843i) q^{87} +(5.16213 + 6.73442i) q^{90} +(-4.85410 - 3.52671i) q^{91} +(2.07196 + 2.77615i) q^{93} +(2.68999 + 0.874032i) q^{94} +(9.70820 - 7.05342i) q^{95} +(8.20135 - 2.78169i) q^{96} +(-0.618034 - 1.90211i) 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	−0.998886	−	0.0471903i	$-0.984973\pi$
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	0.780378	−	0.625308i	$-0.215027\pi$
$3$	−1.64027	+	0.556338i	−0.947011	+	0.321202i
$3$	−1.64027	+	0.556338i	−0.947011	+	0.321202i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.68999	−	0.874032i	−1.20300	−	0.390879i	−0.362137	−	0.932125i	$-0.617953\pi$
$5$	−2.68999	−	0.874032i	−1.20300	−	0.390879i	−0.840864	+	0.541246i	$0.817953\pi$
$6$	1.03598	+	1.38807i	0.422937	+	0.566678i
$7$	0.831254	+	1.14412i	0.314184	+	0.432438i	0.936680	−	0.350185i	$-0.113881\pi$
$7$	0.831254	+	1.14412i	0.314184	+	0.432438i	−0.622496	+	0.782623i	$0.713881\pi$
$8$	−2.42705	−	1.76336i	−0.858092	−	0.623440i
$9$	2.38098	−	1.82509i	0.793659	−	0.608363i
$10$			2.82843i			0.894427i
$11$		0			0
$11$		0			0
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.809426	−	0.587222i	$-0.800222\pi$
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.309679	+	0.950841i	$0.600222\pi$
$14$	0.831254	−	1.14412i	0.222162	−	0.305780i
$15$	4.89858	−	0.0628954i	1.26481	−	0.0162395i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	0.427576	+	0.903979i	$0.359367\pi$
$17$	−1.85410	+	5.70634i	−0.449686	+	1.38399i	−0.877262	+	0.480011i	$0.840633\pi$
$18$	−2.47152	−	1.70046i	−0.582544	−	0.400802i
$19$	−2.49376	+	3.43237i	−0.572108	+	0.787439i	−0.992802	−	0.119763i	$-0.961786\pi$
$19$	−2.49376	+	3.43237i	−0.572108	+	0.787439i	0.420694	+	0.907202i	$0.361786\pi$
$20$	−2.68999	+	0.874032i	−0.601501	+	0.195440i
$21$	−2.00000	−	1.41421i	−0.436436	−	0.308607i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	4.96204	+	1.54212i	1.01287	+	0.314784i
$25$	2.42705	+	1.76336i	0.485410	+	0.352671i
$26$	2.49376	+	3.43237i	0.489067	+	0.673143i
$27$	−2.89008	+	4.31827i	−0.556197	+	0.831051i
$28$	1.34500	+	0.437016i	0.254181	+	0.0825883i
$29$	−1.61803	+	1.17557i	−0.300461	+	0.218298i	−0.727793	−	0.685797i	$-0.759454\pi$
$29$	−1.61803	+	1.17557i	−0.300461	+	0.218298i	0.427331	+	0.904095i	$0.359454\pi$
$30$	−1.57356	−	4.63939i	−0.287291	−	0.847032i
$31$	−0.618034	−	1.90211i	−0.111002	−	0.341630i	0.880090	−	0.474807i	$-0.157482\pi$
$31$	−0.618034	−	1.90211i	−0.111002	−	0.341630i	−0.991092	+	0.133177i	$0.957482\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$	−1.23607	−	3.80423i	−0.208934	−	0.643032i
$36$	0.853491	−	2.87603i	0.142248	−	0.479338i
$37$	−6.47214	+	4.70228i	−1.06401	+	0.773050i	−0.974827	−	0.222965i	$-0.928427\pi$
$37$	−6.47214	+	4.70228i	−1.06401	+	0.773050i	−0.0891861	+	0.996015i	$0.528427\pi$
$38$	4.03499	+	1.31105i	0.654562	+	0.212680i
$39$	5.88909	−	4.39529i	0.943010	−	0.703810i
$40$	4.98752	+	6.86474i	0.788597	+	1.08541i
$41$	4.85410	+	3.52671i	0.758083	+	0.550780i	0.898322	−	0.439338i	$-0.144787\pi$
$41$	4.85410	+	3.52671i	0.758083	+	0.550780i	−0.140238	+	0.990118i	$0.544787\pi$
$42$	−0.726963	+	2.33913i	−0.112173	+	0.360935i
$43$		−	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
$47$	−1.66251	+	2.28825i	−0.242502	+	0.333775i	−0.912868	−	0.408256i	$-0.866137\pi$
$47$	−1.66251	+	2.28825i	−0.242502	+	0.333775i	0.670366	+	0.742031i	$0.266137\pi$
$48$	−0.0222369	−	1.73191i	−0.00320962	−	0.249979i
$49$	1.54508	−	4.75528i	0.220726	−	0.679326i
$50$	0.927051	−	2.85317i	0.131105	−	0.403499i
$51$	−0.133421	−	10.3914i	−0.0186827	−	1.45509i
$52$	−2.49376	+	3.43237i	−0.345823	+	0.475984i
$53$	5.37999	−	1.74806i	0.738998	−	0.240115i	0.0847577	−	0.996402i	$-0.472988\pi$
$53$	5.37999	−	1.74806i	0.738998	−	0.240115i	0.654241	+	0.756287i	$0.272988\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$	2.18089	−	7.01739i	0.288866	−	0.929476i
$58$	1.61803	+	1.17557i	0.212458	+	0.154360i
$59$	−6.65003	−	9.15298i	−0.865760	−	1.19162i	−0.980165	−	0.198183i	$-0.936496\pi$
$59$	−6.65003	−	9.15298i	−0.865760	−	1.19162i	0.114405	−	0.993434i	$-0.463504\pi$
$60$	3.92606	−	2.93019i	0.506852	−	0.378286i
$61$	−9.41498	−	3.05911i	−1.20546	−	0.391679i	−0.363696	−	0.931518i	$-0.618485\pi$
$61$	−9.41498	−	3.05911i	−1.20546	−	0.391679i	−0.841769	+	0.539839i	$0.818485\pi$
$62$	−1.61803	+	1.17557i	−0.205491	+	0.149298i
$63$	4.06732	+	1.20702i	0.512434	+	0.152070i
$64$	2.16312	+	6.65740i	0.270390	+	0.832174i
$65$	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	$0.461015\pi$
$68$	1.85410	+	5.70634i	0.224843	+	0.691995i
$69$		0			0
$70$	−3.23607	+	2.35114i	−0.386784	+	0.281015i
$71$	−2.68999	−	0.874032i	−0.319244	−	0.103729i	0.145012	−	0.989430i	$-0.453678\pi$
$71$	−2.68999	−	0.874032i	−0.319244	−	0.103729i	−0.464255	+	0.885701i	$0.653678\pi$
$72$	−8.99703	+	0.231073i	−1.06031	+	0.0272323i
$73$	0.831254	+	1.14412i	0.0972909	+	0.133909i	0.854887	−	0.518814i	$-0.173626\pi$
$73$	0.831254	+	1.14412i	0.0972909	+	0.133909i	−0.757596	+	0.652724i	$0.773626\pi$
$74$	6.47214	+	4.70228i	0.752371	+	0.546629i
$75$	−4.96204	−	1.54212i	−0.572967	−	0.178069i
$76$			4.24264i			0.486664i
$77$		0			0
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$	−4.03499	+	1.31105i	−0.453972	+	0.147504i	−0.527073	−	0.849820i	$-0.676710\pi$
$79$	−4.03499	+	1.31105i	−0.453972	+	0.147504i	0.0731009	+	0.997325i	$0.476710\pi$
$80$	1.66251	−	2.28825i	0.185874	−	0.255834i
$81$	2.33810	−	8.69099i	0.259789	−	0.965665i
$82$	1.85410	−	5.70634i	0.204751	−	0.630160i
$83$	4.94427	−	15.2169i	0.542704	−	1.67027i	−0.183682	−	0.982986i	$-0.558802\pi$
$83$	4.94427	−	15.2169i	0.542704	−	1.67027i	0.726386	−	0.687287i	$-0.241198\pi$
$84$	−2.44929	+	0.0314477i	−0.267239	+	0.00343123i
$85$	9.97505	−	13.7295i	1.08195	−	1.48917i
$86$	−4.03499	+	1.31105i	−0.435104	+	0.141374i
$87$	2.00000	−	2.82843i	0.214423	−	0.303239i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	5.16213	+	6.73442i	0.544136	+	0.709870i
$91$	−4.85410	−	3.52671i	−0.508848	−	0.369700i
$92$		0			0
$93$	2.07196	+	2.77615i	0.214852	+	0.287873i
$94$	2.68999	+	0.874032i	0.277452	+	0.0901495i
$95$	9.70820	−	7.05342i	0.996041	−	0.723666i
$96$	8.20135	−	2.78169i	0.837047	−	0.283905i
$97$	−0.618034	−	1.90211i	−0.0627518	−	0.193130i	0.914766	−	0.403985i	$-0.132375\pi$
$97$	−0.618034	−	1.90211i	−0.0627518	−	0.193130i	−0.977517	+	0.210855i	$0.932375\pi$
$98$	−5.00000			−0.505076
$99$		0			0
$100$	3.00000			0.300000
$101$	3.09017	+	9.51057i	0.307483	+	0.946337i	0.978739	+	0.205110i	$0.0657554\pi$
$101$	3.09017	+	9.51057i	0.307483	+	0.946337i	−0.671255	+	0.741226i	$0.734245\pi$
$102$	−9.84163	+	3.33803i	−0.974466	+	0.330514i
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	−0.859066	−	0.511865i	$-0.828955\pi$
$103$	−6.47214	+	4.70228i	−0.637719	+	0.463330i	0.221347	+	0.975195i	$0.428955\pi$
$104$	12.1050	+	3.93314i	1.18699	+	0.385677i
$105$	4.14392	+	5.55229i	0.404405	+	0.541848i
$106$	−3.32502	−	4.57649i	−0.322954	−	0.444508i
$107$	−12.9443	−	9.40456i	−1.25137	−	0.909174i	−0.253069	−	0.967448i	$-0.581440\pi$
$107$	−12.9443	−	9.40456i	−1.25137	−	0.909174i	−0.998301	+	0.0582746i	$0.981440\pi$
$108$	0.200088	+	5.19230i	0.0192535	+	0.499629i
$109$		−	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
$112$	−1.34500	+	0.437016i	−0.127090	+	0.0412941i
$113$	−1.66251	+	2.28825i	−0.156396	+	0.215260i	−0.880023	−	0.474930i	$-0.842473\pi$
$113$	−1.66251	+	2.28825i	−0.156396	+	0.215260i	0.723628	+	0.690190i	$0.242473\pi$
$114$	−7.34786	+	0.0943431i	−0.688190	+	0.00883604i
$115$		0			0
$116$	−0.618034	+	1.90211i	−0.0573830	+	0.176607i
$117$	−7.21444	+	10.4858i	−0.666975	+	0.969412i
$118$	−6.65003	+	9.15298i	−0.612185	+	0.842600i
$119$	−8.06998	+	2.62210i	−0.739774	+	0.240367i
$120$	−12.0000	−	8.48528i	−1.09545	−	0.774597i
$121$		0			0
$122$			9.89949i			0.896258i
$123$	−9.92408	−	3.08424i	−0.894825	−	0.278097i
$124$	−1.61803	−	1.17557i	−0.145304	−	0.105569i
$125$	3.32502	+	4.57649i	0.297398	+	0.409334i
$126$	−0.108929	−	4.24124i	−0.00970417	−	0.377840i
$127$	−9.41498	−	3.05911i	−0.835444	−	0.271452i	−0.140107	−	0.990136i	$-0.544745\pi$
$127$	−9.41498	−	3.05911i	−0.835444	−	0.271452i	−0.695337	+	0.718684i	$0.744745\pi$
$128$	−2.42705	+	1.76336i	−0.214523	+	0.155860i
$129$	2.36034	+	6.95908i	0.207816	+	0.612713i
$130$	−3.70820	−	11.4127i	−0.325231	−	1.00096i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$	−0.618034	−	1.90211i	−0.0533900	−	0.164318i
$135$	11.5486	−	9.09009i	0.993946	−	0.782350i
$136$	14.5623	−	10.5801i	1.24871	−	0.907239i
$137$	−2.68999	−	0.874032i	−0.229822	−	0.0746736i	0.191842	−	0.981426i	$-0.438554\pi$
$137$	−2.68999	−	0.874032i	−0.229822	−	0.0746736i	−0.421664	+	0.906752i	$0.638554\pi$
$138$		0			0
$139$	0.831254	+	1.14412i	0.0705060	+	0.0970432i	0.842814	−	0.538206i	$-0.180898\pi$
$139$	0.831254	+	1.14412i	0.0705060	+	0.0970432i	−0.772308	+	0.635249i	$0.780898\pi$
$140$	−3.23607	−	2.35114i	−0.273498	−	0.198708i
$141$	1.45393	−	4.67826i	0.122443	−	0.393980i
$142$			2.82843i			0.237356i
$143$		0			0
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	5.37999	−	1.74806i	0.446784	−	0.145169i
$146$	0.831254	−	1.14412i	0.0687951	−	0.0946883i
$147$	0.111184	+	8.65954i	0.00917034	+	0.714227i
$148$	−2.47214	+	7.60845i	−0.203208	+	0.625411i
$149$	−1.85410	+	5.70634i	−0.151894	+	0.467482i	−0.997833	−	0.0657982i	$-0.979041\pi$
$149$	−1.85410	+	5.70634i	−0.151894	+	0.467482i	0.845939	+	0.533280i	$0.179041\pi$
$150$	0.0667106	+	5.19572i	0.00544690	+	0.424229i
$151$	−2.49376	+	3.43237i	−0.202939	+	0.279322i	−0.898341	−	0.439300i	$-0.855227\pi$
$151$	−2.49376	+	3.43237i	−0.202939	+	0.279322i	0.695401	+	0.718622i	$0.255227\pi$
$152$	12.1050	−	3.93314i	0.981843	−	0.319020i
$153$	6.00000	+	16.9706i	0.485071	+	1.37199i
$154$		0			0
$155$			5.65685i			0.454369i
$156$	2.18089	−	7.01739i	0.174611	−	0.561841i
$157$	16.1803	+	11.7557i	1.29133	+	0.938207i	0.999831	−	0.0183633i	$-0.00584556\pi$
$157$	16.1803	+	11.7557i	1.29133	+	0.938207i	0.291500	+	0.956571i	$0.405846\pi$
$158$	2.49376	+	3.43237i	0.198393	+	0.273065i
$159$	−7.85212	+	5.86039i	−0.622714	+	0.464759i
$160$	13.4500	+	4.37016i	1.06331	+	0.345492i
$161$		0			0
$162$	−8.98813	+	0.461994i	−0.706175	+	0.0362977i
$163$	6.18034	+	19.0211i	0.484082	+	1.48985i	0.833307	+	0.552811i	$0.186445\pi$
$163$	6.18034	+	19.0211i	0.484082	+	1.48985i	−0.349225	+	0.937039i	$0.613555\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	−16.0000			−1.24184
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	−0.985808	−	0.167879i	$-0.946308\pi$
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	0.698858	−	0.715260i	$-0.253692\pi$
$168$	2.36034	+	6.95908i	0.182104	+	0.536905i
$169$	4.04508	−	2.93893i	0.311160	−	0.226071i
$170$	−16.1400	−	5.24419i	−1.23788	−	0.402211i
$171$	0.326787	+	12.7237i	0.0249900	+	0.973008i
$172$	−2.49376	−	3.43237i	−0.190148	−	0.261716i
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	0.756817	−	0.653627i	$-0.226753\pi$
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	−0.387767	+	0.921758i	$0.626753\pi$
$174$	−3.30803	−	1.02808i	−0.250781	−	0.0779386i
$175$			4.24264i			0.320713i
$176$		0			0
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$		0			0
$179$	−1.66251	+	2.28825i	−0.124262	+	0.171032i	−0.866615	−	0.498977i	$-0.833709\pi$
$179$	−1.66251	+	2.28825i	−0.124262	+	0.171032i	0.742354	+	0.670008i	$0.233709\pi$
$180$	−4.80963	+	6.99053i	−0.358489	+	0.521043i
$181$	−3.09017	+	9.51057i	−0.229691	+	0.706915i	0.768091	+	0.640341i	$0.221207\pi$
$181$	−3.09017	+	9.51057i	−0.229691	+	0.706915i	−0.997781	+	0.0665740i	$0.978793\pi$
$182$	−1.85410	+	5.70634i	−0.137435	+	0.422982i
$183$	17.1450	−	0.220134i	1.26740	−	0.0162728i
$184$		0			0
$185$	21.5200	−	6.99226i	1.58218	−	0.514081i
$186$	2.00000	−	2.82843i	0.146647	−	0.207390i
$187$		0			0
$188$			2.82843i			0.206284i
$189$	−7.34302	+	0.282967i	−0.534126	+	0.0205828i
$190$	−9.70820	−	7.05342i	−0.704307	−	0.511709i
$191$	11.6376	+	16.0177i	0.842064	+	1.15900i	0.985556	+	0.169350i	$0.0541668\pi$
$191$	11.6376	+	16.0177i	0.842064	+	1.15900i	−0.143492	+	0.989651i	$0.545833\pi$
$192$	−7.25186	−	9.71651i	−0.523358	−	0.701229i
$193$	20.1750	+	6.55524i	1.45223	+	0.471857i	0.925685	−	0.378294i	$-0.123489\pi$
$193$	20.1750	+	6.55524i	1.45223	+	0.471857i	0.526540	+	0.850151i	$0.323489\pi$
$194$	−1.61803	+	1.17557i	−0.116168	+	0.0844010i
$195$	−19.6833	+	6.67605i	−1.40955	+	0.478082i
$196$	−1.54508	−	4.75528i	−0.110363	−	0.339663i
$197$	−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	$0.477417\pi$
$200$	−2.78115	−	8.55951i	−0.196657	−	0.605249i
$201$	−3.28054	+	1.11268i	−0.231392	+	0.0784821i
$202$	8.09017	−	5.87785i	0.569222	−	0.413564i
$203$	−2.68999	−	0.874032i	−0.188801	−	0.0613450i
$204$	−6.21588	−	8.32844i	−0.435199	−	0.583107i
$205$	−9.97505	−	13.7295i	−0.696687	−	0.958908i
$206$	6.47214	+	4.70228i	0.450935	+	0.327624i
$207$		0			0
$208$		−	4.24264i		−	0.294174i
$209$		0			0
$210$	4.00000	−	5.65685i	0.276026	−	0.390360i
$211$	25.5549	−	8.30330i	1.75927	−	0.571623i	0.762150	−	0.647400i	$-0.224144\pi$
$211$	25.5549	−	8.30330i	1.75927	−	0.571623i	0.997125	+	0.0757773i	$0.0241438\pi$
$212$	3.32502	−	4.57649i	0.228363	−	0.314315i
$213$	4.89858	−	0.0628954i	0.335645	−	0.00430952i
$214$	−4.94427	+	15.2169i	−0.337983	+	1.04021i
$215$	−3.70820	+	11.4127i	−0.252897	+	0.778338i
$216$	14.6290	−	5.38441i	0.995378	−	0.366363i
$217$	1.66251	−	2.28825i	0.112858	−	0.155336i
$218$	−4.03499	+	1.31105i	−0.273284	+	0.0887954i
$219$	−2.00000	−	1.41421i	−0.135147	−	0.0955637i
$220$		0			0
$221$		−	25.4558i		−	1.71235i
$222$	−13.2321	−	4.11232i	−0.888081	−	0.276001i
$223$	−19.4164	−	14.1068i	−1.30022	−	0.944664i	−0.300261	−	0.953857i	$-0.597074\pi$
$223$	−19.4164	−	14.1068i	−1.30022	−	0.944664i	−0.999958	+	0.00919277i	$0.997074\pi$
$224$	−4.15627	−	5.72061i	−0.277702	−	0.382225i
$225$	8.99703	−	0.231073i	0.599802	−	0.0154049i
$226$	2.68999	+	0.874032i	0.178936	+	0.0581397i
$227$	−19.4164	+	14.1068i	−1.28871	+	0.936304i	−0.999779	−	0.0210448i	$-0.993301\pi$
$227$	−19.4164	+	14.1068i	−1.28871	+	0.936304i	−0.288934	+	0.957349i	$0.593301\pi$
$228$	−2.36034	−	6.95908i	−0.156317	−	0.460876i
$229$	−7.41641	−	22.8254i	−0.490090	−	1.50834i	−0.824471	−	0.565904i	$-0.808527\pi$
$229$	−7.41641	−	22.8254i	−0.490090	−	1.50834i	0.334381	−	0.942438i	$-0.391473\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	3.09017	+	9.51057i	0.202444	+	0.623058i	0.999809	+	0.0195604i	$0.00622666\pi$
$233$	3.09017	+	9.51057i	0.202444	+	0.623058i	−0.797365	+	0.603497i	$0.793773\pi$
$234$	12.2020	+	3.62105i	0.797667	+	0.236716i
$235$	6.47214	−	4.70228i	0.422196	−	0.306743i
$236$	−10.7600	−	3.49613i	−0.700415	−	0.227579i
$237$	5.88909	−	4.39529i	0.382538	−	0.285505i
$238$	4.98752	+	6.86474i	0.323293	+	0.444975i
$239$	−12.9443	−	9.40456i	−0.837295	−	0.608331i	0.0843185	−	0.996439i	$-0.473129\pi$
$239$	−12.9443	−	9.40456i	−0.837295	−	0.608331i	−0.921614	+	0.388108i	$0.873129\pi$
$240$	−1.45393	+	4.67826i	−0.0938505	+	0.301980i
$241$		−	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
$244$	−9.41498	+	3.05911i	−0.602732	+	0.195840i
$245$	−8.31254	+	11.4412i	−0.531069	+	0.730953i
$246$	0.133421	+	10.3914i	0.00850663	+	0.662535i
$247$	5.56231	−	17.1190i	0.353921	−	1.08926i
$248$	−1.85410	+	5.70634i	−0.117736	+	0.362353i
$249$	0.355790	+	27.7105i	0.0225473	+	1.75608i
$250$	3.32502	−	4.57649i	0.210292	−	0.289443i
$251$	−24.2099	+	7.86629i	−1.52812	+	0.496516i	−0.948069	−	0.318065i	$-0.896967\pi$
$251$	−24.2099	+	7.86629i	−1.52812	+	0.496516i	−0.580050	+	0.814581i	$0.696967\pi$
$252$	4.00000	−	1.41421i	0.251976	−	0.0890871i
$253$		0			0
$254$			9.89949i			0.621150i
$255$	−8.72356	+	28.0695i	−0.546290	+	1.75778i
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	−6.65003	−	9.15298i	−0.414818	−	0.570947i	0.549568	−	0.835449i	$-0.314792\pi$
$257$	−6.65003	−	9.15298i	−0.414818	−	0.570947i	−0.964385	+	0.264502i	$0.914792\pi$
$258$	5.88909	−	4.39529i	0.366639	−	0.273639i
$259$	−10.7600	−	3.49613i	−0.668592	−	0.217239i
$260$	9.70820	−	7.05342i	0.602077	−	0.437435i
$261$	−1.70698	+	5.75206i	−0.105660	+	0.356044i
$262$		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
$266$	1.85410	+	5.70634i	0.113682	+	0.349878i
$267$		0			0
$268$	1.61803	−	1.17557i	0.0988372	−	0.0718094i
$269$	26.8999	+	8.74032i	1.64012	+	0.532907i	0.976565	−	0.215222i	$-0.0690476\pi$
$269$	26.8999	+	8.74032i	1.64012	+	0.532907i	0.663553	+	0.748129i	$0.269048\pi$
$270$	−12.2139	−	8.17439i	−0.743314	−	0.497477i
$271$	−17.4563	−	24.0266i	−1.06040	−	1.45951i	−0.879434	−	0.476021i	$-0.842079\pi$
$271$	−17.4563	−	24.0266i	−1.06040	−	1.45951i	−0.180963	−	0.983490i	$-0.557921\pi$
$272$	−4.85410	−	3.52671i	−0.294323	−	0.213838i
$273$	9.92408	+	3.08424i	0.600633	+	0.186667i
$274$			2.82843i			0.170872i
$275$		0			0
$276$		0			0
$277$	−4.03499	+	1.31105i	−0.242439	+	0.0787732i	−0.427716	−	0.903913i	$-0.640682\pi$
$277$	−4.03499	+	1.31105i	−0.242439	+	0.0787732i	0.185277	+	0.982686i	$0.440682\pi$
$278$	0.831254	−	1.14412i	0.0498553	−	0.0686199i
$279$	−4.94305	−	3.40092i	−0.295933	−	0.203608i
$280$	−3.70820	+	11.4127i	−0.221608	+	0.682038i
$281$	−1.85410	+	5.70634i	−0.110606	+	0.340412i	−0.991005	−	0.133822i	$-0.957275\pi$
$281$	−1.85410	+	5.70634i	−0.110606	+	0.340412i	0.880399	+	0.474234i	$0.157275\pi$
$282$	−4.89858	+	0.0628954i	−0.291706	+	0.00374537i
$283$	15.7938	−	21.7383i	0.938845	−	1.29221i	−0.0174623	−	0.999848i	$-0.505559\pi$
$283$	15.7938	−	21.7383i	0.938845	−	1.29221i	0.956308	−	0.292362i	$-0.0944413\pi$
$284$	−2.68999	+	0.874032i	−0.159622	+	0.0518643i
$285$	−12.0000	+	16.9706i	−0.710819	+	1.00525i
$286$		0			0
$287$			8.48528i			0.500870i
$288$	−11.9049	+	9.12544i	−0.701502	+	0.537722i
$289$	−15.3713	−	11.1679i	−0.904195	−	0.656936i
$290$	−3.32502	−	4.57649i	−0.195252	−	0.268741i
$291$	2.07196	+	2.77615i	0.121460	+	0.162741i
$292$	1.34500	+	0.437016i	0.0787100	+	0.0255744i
$293$	−1.61803	+	1.17557i	−0.0945266	+	0.0686776i	−0.634045	−	0.773296i	$-0.718606\pi$
$293$	−1.61803	+	1.17557i	−0.0945266	+	0.0686776i	0.539518	+	0.841974i	$0.318606\pi$
$294$	8.20135	−	2.78169i	0.478313	−	0.162231i
$295$	9.88854	+	30.4338i	0.575733	+	1.77192i
$296$	24.0000			1.39497
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	−4.92081	+	1.66901i	−0.284103	+	0.0963605i
$301$	4.85410	−	3.52671i	0.279786	−	0.203276i
$302$	4.03499	+	1.31105i	0.232188	+	0.0754423i
$303$	−10.3598	−	13.8807i	−0.595155	−	0.797427i
$304$	−2.49376	−	3.43237i	−0.143027	−	0.196860i
$305$	22.6525	+	16.4580i	1.29708	+	0.942382i
$306$	14.2859	−	10.9505i	0.816668	−	0.626000i
$307$		−	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
$310$	5.37999	−	1.74806i	0.305563	−	0.0992834i
$311$	16.6251	−	22.8825i	0.942722	−	1.29755i	−0.0119638	−	0.999928i	$-0.503808\pi$
$311$	16.6251	−	22.8825i	0.942722	−	1.29755i	0.954685	−	0.297617i	$-0.0961917\pi$
$312$	−22.0436	+	0.283029i	−1.24797	+	0.0160234i
$313$	3.70820	−	11.4127i	0.209600	−	0.645083i	−0.789893	−	0.613245i	$-0.789864\pi$
$313$	3.70820	−	11.4127i	0.209600	−	0.645083i	0.999493	−	0.0318380i	$-0.0101361\pi$
$314$	6.18034	−	19.0211i	0.348777	−	1.07342i
$315$	−9.88610	−	6.80184i	−0.557019	−	0.383240i
$316$	−2.49376	+	3.43237i	−0.140285	+	0.193086i
$317$	−24.2099	+	7.86629i	−1.35977	+	0.441815i	−0.895965	−	0.444125i	$-0.853515\pi$
$317$	−24.2099	+	7.86629i	−1.35977	+	0.441815i	−0.463801	+	0.885939i	$0.653515\pi$
$318$	8.00000	+	5.65685i	0.448618	+	0.317221i
$319$		0			0
$320$		−	19.7990i		−	1.10680i
$321$	26.4642	+	8.22465i	1.47709	+	0.459055i
$322$		0			0
$323$	−14.9626	−	20.5942i	−0.832540	−	1.14589i
$324$	−3.21687	−	8.40546i	−0.178715	−	0.466970i
$325$	−12.1050	−	3.93314i	−0.671463	−	0.218172i
$326$	16.1803	−	11.7557i	0.896146	−	0.651088i
$327$	2.36034	+	6.95908i	0.130527	+	0.384838i
$328$	−5.56231	−	17.1190i	−0.307127	−	0.945240i
$329$	−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	$0.685239\pi$
$332$	−4.94427	−	15.2169i	−0.271352	−	0.835136i
$333$	−6.82793	+	23.0082i	−0.374168	+	1.26084i
$334$	−9.70820	+	7.05342i	−0.531209	+	0.385946i
$335$	−5.37999	−	1.74806i	−0.293940	−	0.0955069i
$336$	1.96303	−	1.46510i	0.107092	−	0.0799276i
$337$	19.1188	+	26.3148i	1.04147	+	1.43346i	0.895977	+	0.444100i	$0.146477\pi$
$337$	19.1188	+	26.3148i	1.04147	+	1.43346i	0.145493	+	0.989359i	$0.453523\pi$
$338$	−4.04508	−	2.93893i	−0.220024	−	0.159857i
$339$	1.45393	−	4.67826i	0.0789664	−	0.254088i
$340$		−	16.9706i		−	0.920358i
$341$		0			0
$342$	12.0000	−	4.24264i	0.648886	−	0.229416i
$343$	16.1400	−	5.24419i	0.871476	−	0.283160i
$344$	−7.48128	+	10.2971i	−0.403364	+	0.555183i
$345$		0			0
$346$	1.85410	−	5.70634i	0.0996771	−	0.306775i
$347$	4.94427	−	15.2169i	0.265422	−	0.816886i	−0.726173	−	0.687512i	$-0.758703\pi$
$347$	4.94427	−	15.2169i	0.265422	−	0.816886i	0.991596	−	0.129375i	$-0.0412970\pi$
$348$	−0.0444738	−	3.46382i	−0.00238404	−	0.185680i
$349$	−2.49376	+	3.43237i	−0.133488	+	0.183730i	−0.870528	−	0.492118i	$-0.836223\pi$
$349$	−2.49376	+	3.43237i	−0.133488	+	0.183730i	0.737040	+	0.675849i	$0.236223\pi$
$350$	4.03499	−	1.31105i	0.215679	−	0.0700785i
$351$	6.00000	−	21.2132i	0.320256	−	1.13228i
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	5.81570	−	18.7130i	0.309101	−	0.994586i
$355$	6.47214	+	4.70228i	0.343505	+	0.249571i
$356$		0			0
$357$	11.7782	−	8.79058i	0.623368	−	0.465247i
$358$	2.68999	+	0.874032i	0.142171	+	0.0461940i
$359$	16.1803	−	11.7557i	0.853966	−	0.620442i	−0.0722709	−	0.997385i	$-0.523025\pi$
$359$	16.1803	−	11.7557i	0.853966	−	0.620442i	0.926237	+	0.376943i	$0.123025\pi$
$360$	24.4039	+	7.24211i	1.28620	+	0.381693i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	10.0000			0.525588
$363$		0			0
$364$	−6.00000			−0.314485
$365$	−1.23607	−	3.80423i	−0.0646988	−	0.199122i
$366$	−5.50746	−	16.2379i	−0.287880	−	0.848766i
$367$	−6.47214	+	4.70228i	−0.337843	+	0.245457i	−0.743751	−	0.668457i	$-0.766955\pi$
$367$	−6.47214	+	4.70228i	−0.337843	+	0.245457i	0.405908	+	0.913914i	$0.366955\pi$
$368$		0			0
$369$	17.9941	−	0.462147i	0.936734	−	0.0240584i
$370$	−13.3001	−	18.3060i	−0.691437	−	0.951682i
$371$	6.47214	+	4.70228i	0.336017	+	0.244130i
$372$	3.30803	+	1.02808i	0.171513	+	0.0533035i
$373$		−	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
$376$	8.06998	−	2.62210i	0.416178	−	0.135224i
$377$	4.98752	−	6.86474i	0.256871	−	0.353552i
$378$	2.53824	+	6.89618i	0.130553	+	0.354701i
$379$	3.70820	−	11.4127i	0.190478	−	0.586230i	−0.809522	−	0.587090i	$-0.800274\pi$
$379$	3.70820	−	11.4127i	0.190478	−	0.586230i	1.00000		0.000859657i	$0.000273637\pi$
$380$	3.70820	−	11.4127i	0.190227	−	0.585458i
$381$	17.1450	−	0.220134i	0.878366	−	0.0112778i
$382$	11.6376	−	16.0177i	0.595429	−	0.819538i
$383$	5.37999	−	1.74806i	0.274905	−	0.0893219i	−0.168320	−	0.985732i	$-0.553834\pi$
$383$	5.37999	−	1.74806i	0.274905	−	0.0893219i	0.443225	+	0.896410i	$0.353834\pi$
$384$	3.00000	−	4.24264i	0.153093	−	0.216506i
$385$		0			0
$386$		−	21.2132i		−	1.07972i
$387$	−7.74320	−	10.1016i	−0.393609	−	0.513495i
$388$	−1.61803	−	1.17557i	−0.0821432	−	0.0596806i
$389$	11.6376	+	16.0177i	0.590047	+	0.812131i	0.994752	−	0.102317i	$-0.0326256\pi$
$389$	11.6376	+	16.0177i	0.590047	+	0.812131i	−0.404704	+	0.914448i	$0.632626\pi$
$390$	12.4318	+	16.6569i	0.629507	+	0.843453i
$391$		0			0
$392$	−12.1353	+	8.81678i	−0.612923	+	0.445315i
$393$		0			0
$394$	6.79837	+	20.9232i	0.342497	+	1.05410i
$395$	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	$0.484018\pi$
$398$	−0.618034	−	1.90211i	−0.0309792	−	0.0953443i
$399$	9.84163	−	3.33803i	0.492698	−	0.167110i
$400$	−2.42705	+	1.76336i	−0.121353	+	0.0881678i
$401$	−2.68999	−	0.874032i	−0.134332	−	0.0436471i	0.241079	−	0.970505i	$-0.422499\pi$
$401$	−2.68999	−	0.874032i	−0.134332	−	0.0436471i	−0.375411	+	0.926858i	$0.622499\pi$
$402$	2.07196	+	2.77615i	0.103340	+	0.138462i
$403$	4.98752	+	6.86474i	0.248446	+	0.341957i
$404$	8.09017	+	5.87785i	0.402501	+	0.292434i
$405$	−13.8857	+	21.3351i	−0.689985	+	1.06015i
$406$			2.82843i			0.140372i
$407$		0			0
$408$	−18.0000	+	25.4558i	−0.891133	+	1.26025i
$409$	−4.03499	+	1.31105i	−0.199517	+	0.0648272i	−0.407071	−	0.913396i	$-0.633450\pi$
$409$	−4.03499	+	1.31105i	−0.199517	+	0.0648272i	0.207554	+	0.978224i	$0.433450\pi$
$410$	−9.97505	+	13.7295i	−0.492632	+	0.678050i
$411$	4.89858	−	0.0628954i	0.241629	−	0.00310240i
$412$	−2.47214	+	7.60845i	−0.121793	+	0.374842i
$413$	4.94427	−	15.2169i	0.243292	−	0.748775i
$414$		0			0
$415$	−26.6001	+	36.6119i	−1.30575	+	1.79721i
$416$	20.1750	−	6.55524i	0.989159	−	0.321397i
$417$	−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	$0.725210\pi$
$420$	6.61606	+	2.05616i	0.322830	+	0.100330i
$421$	16.1803	+	11.7557i	0.788582	+	0.572938i	0.907542	−	0.419961i	$-0.137956\pi$
$421$	16.1803	+	11.7557i	0.788582	+	0.572938i	−0.118961	+	0.992899i	$0.537956\pi$
$422$	−15.7938	−	21.7383i	−0.768831	−	1.05821i
$423$	0.217858	+	8.48248i	0.0105926	+	0.412432i
$424$	−16.1400	−	5.24419i	−0.783826	−	0.254680i
$425$	−14.5623	+	10.5801i	−0.706376	+	0.513212i
$426$	−1.57356	−	4.63939i	−0.0762392	−	0.224779i
$427$	−4.32624	−	13.3148i	−0.209361	−	0.644348i
$428$	−16.0000			−0.773389
$429$		0			0
$430$	12.0000			0.578691
$431$	9.88854	+	30.4338i	0.476314	+	1.46594i	0.844177	+	0.536065i	$0.180090\pi$
$431$	9.88854	+	30.4338i	0.476314	+	1.46594i	−0.367862	+	0.929880i	$0.619910\pi$
$432$	−3.21383	−	4.08305i	−0.154626	−	0.196446i
$433$	−24.2705	+	17.6336i	−1.16637	+	0.847415i	−0.990569	−	0.137012i	$-0.956250\pi$
$433$	−24.2705	+	17.6336i	−1.16637	+	0.847415i	−0.175797	+	0.984426i	$0.556250\pi$
$434$	−2.68999	−	0.874032i	−0.129124	−	0.0419549i
$435$	−7.85212	+	5.86039i	−0.376481	+	0.280984i
$436$	−2.49376	−	3.43237i	−0.119430	−	0.164381i
$437$		0			0
$438$	−0.726963	+	2.33913i	−0.0347356	+	0.111768i
$439$			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
$442$	−24.2099	+	7.86629i	−1.15155	+	0.374161i
$443$	16.6251	−	22.8825i	0.789881	−	1.08718i	−0.204242	−	0.978921i	$-0.565473\pi$
$443$	16.6251	−	22.8825i	0.789881	−	1.08718i	0.994123	−	0.108258i	$-0.0345272\pi$
$444$	−0.177895	−	13.8553i	−0.00844253	−	0.657542i
$445$		0			0
$446$	−7.41641	+	22.8254i	−0.351177	+	1.08081i
$447$	−0.133421	−	10.3914i	−0.00631061	−	0.491499i
$448$	−5.81878	+	8.00886i	−0.274911	+	0.378383i
$449$	5.37999	−	1.74806i	0.253897	−	0.0824962i	−0.179303	−	0.983794i	$-0.557384\pi$
$449$	5.37999	−	1.74806i	0.253897	−	0.0824962i	0.433200	+	0.901298i	$0.357384\pi$
$450$	−3.00000	−	8.48528i	−0.141421	−	0.400000i
$451$		0			0
$452$			2.82843i			0.133038i
$453$	2.18089	−	7.01739i	0.102467	−	0.329706i
$454$	19.4164	+	14.1068i	0.911257	+	0.662067i
$455$	9.97505	+	13.7295i	0.467637	+	0.643648i
$456$	−17.6673	+	13.1859i	−0.827346	+	0.617485i
$457$	−9.41498	−	3.05911i	−0.440414	−	0.143099i	0.0804125	−	0.996762i	$-0.474376\pi$
$457$	−9.41498	−	3.05911i	−0.440414	−	0.143099i	−0.520827	+	0.853662i	$0.674376\pi$
$458$	−19.4164	+	14.1068i	−0.907269	+	0.659170i
$459$	−19.2830	−	24.4983i	−0.900053	−	1.14348i
$460$		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	$0.311689\pi$
$464$	−0.618034	−	1.90211i	−0.0286915	−	0.0883034i
$465$	−3.14712	−	9.27877i	−0.145944	−	0.430293i
$466$	8.09017	−	5.87785i	0.374770	−	0.272286i
$467$	26.8999	+	8.74032i	1.24478	+	0.404454i	0.856048	−	0.516897i	$-0.172913\pi$
$467$	26.8999	+	8.74032i	1.24478	+	0.404454i	0.388733	+	0.921350i	$0.372913\pi$
$468$	0.326787	+	12.7237i	0.0151057	+	0.588154i
$469$	1.66251	+	2.28825i	0.0767675	+	0.105661i
$470$	−6.47214	−	4.70228i	−0.298537	−	0.216900i
$471$	−33.0803	−	10.2808i	−1.52426	−	0.473715i
$472$			33.9411i			1.56227i
$473$		0			0
$474$	−6.00000	−	4.24264i	−0.275589	−	0.194871i
$475$	−12.1050	+	3.93314i	−0.555414	+	0.180465i
$476$	−4.98752	+	6.86474i	−0.228603	+	0.314645i
$477$	9.61926	−	13.9811i	0.440435	−	0.640149i
$478$	−4.94427	+	15.2169i	−0.226146	+	0.696005i
$479$	−8.65248	+	26.6296i	−0.395342	+	1.21674i	0.533353	+	0.845893i	$0.320932\pi$
$479$	−8.65248	+	26.6296i	−0.395342	+	1.21674i	−0.928695	+	0.370844i	$0.879068\pi$
$480$	−24.4929	+	0.314477i	−1.11794	+	0.0143538i
$481$	19.9501	−	27.4589i	0.909646	−	1.25202i
$482$	−4.03499	+	1.31105i	−0.183789	+	0.0597166i
$483$		0			0
$484$		0			0
$485$			5.65685i			0.256865i
$486$	14.4860	−	5.75823i	0.657096	−	0.261199i
$487$	−1.61803	−	1.17557i	−0.0733201	−	0.0532702i	0.550521	−	0.834821i	$-0.314429\pi$
$487$	−1.61803	−	1.17557i	−0.0733201	−	0.0532702i	−0.623842	+	0.781551i	$0.714429\pi$
$488$	17.4563	+	24.0266i	0.790211	+	1.08763i
$489$	−20.7196	−	27.7615i	−0.936973	−	1.25542i
$490$	13.4500	+	4.37016i	0.607608	+	0.197424i
$491$	16.1803	−	11.7557i	0.730209	−	0.530528i	−0.159421	−	0.987211i	$-0.550963\pi$
$491$	16.1803	−	11.7557i	0.730209	−	0.530528i	0.889629	+	0.456683i	$0.150963\pi$
$492$	−9.84163	+	3.33803i	−0.443695	+	0.150490i
$493$	−3.70820	−	11.4127i	−0.167009	−	0.514001i
$494$	−18.0000			−0.809858
$495$		0			0
$496$	2.00000			0.0898027
$497$	−1.23607	−	3.80423i	−0.0554452	−	0.170643i
$498$	26.2443	−	8.90140i	1.17604	−	0.398881i
$499$	11.3262	−	8.22899i	0.507032	−	0.368380i	−0.304664	−	0.952460i	$-0.598544\pi$
$499$	11.3262	−	8.22899i	0.507032	−	0.368380i	0.811697	+	0.584079i	$0.198544\pi$
$500$	5.37999	+	1.74806i	0.240600	+	0.0781758i
$501$	12.4318	+	16.6569i	0.555410	+	0.744174i
$502$	14.9626	+	20.5942i	0.667812	+	0.919165i
$503$	−12.9443	−	9.40456i	−0.577157	−	0.419329i	0.260541	−	0.965463i	$-0.416099\pi$
$503$	−12.9443	−	9.40456i	−0.577157	−	0.419329i	−0.837698	+	0.546134i	$0.816099\pi$
$504$	−7.74320	−	10.1016i	−0.344909	−	0.449962i
$505$		−	28.2843i		−	1.25863i
$506$		0			0
$507$	−5.00000	+	7.07107i	−0.222058	+	0.314037i
$508$	−9.41498	+	3.05911i	−0.417722	+	0.135726i
$509$	−19.9501	+	27.4589i	−0.884272	+	1.21710i	0.0909469	+	0.995856i	$0.471011\pi$
$509$	−19.9501	+	27.4589i	−0.884272	+	1.21710i	−0.975219	+	0.221241i	$0.928989\pi$
$510$	29.3915	−	0.377372i	1.30148	−	0.0167103i
$511$	−0.618034	+	1.90211i	−0.0273402	+	0.0841445i
$512$	3.39919	−	10.4616i	0.150224	−	0.462343i
$513$	−7.61471	−	20.6886i	−0.336197	−	0.913422i
$514$	−6.65003	+	9.15298i	−0.293320	+	0.403721i
$515$	21.5200	−	6.99226i	0.948282	−	0.308116i
$516$	6.00000	+	4.24264i	0.264135	+	0.186772i
$517$		0			0
$518$			11.3137i			0.497096i
$519$	−9.92408	−	3.08424i	−0.435619	−	0.135383i
$520$	−29.1246	−	21.1603i	−1.27720	−	0.927939i
$521$	11.6376	+	16.0177i	0.509851	+	0.701749i	0.983894	−	0.178752i	$-0.0572061\pi$
$521$	11.6376	+	16.0177i	0.509851	+	0.701749i	−0.474044	+	0.880501i	$0.657206\pi$
$522$	5.99802	−	0.154049i	0.262526	−	0.00674254i
$523$	20.1750	+	6.55524i	0.882189	+	0.286641i	0.714866	−	0.699261i	$-0.246488\pi$
$523$	20.1750	+	6.55524i	0.882189	+	0.286641i	0.167323	+	0.985902i	$0.446488\pi$
$524$		0			0
$525$	−2.36034	−	6.95908i	−0.103014	−	0.303719i
$526$		0			0
$527$	12.0000			0.522728
$528$		0			0
$529$	23.0000			1.00000
$530$	4.94427	+	15.2169i	0.214765	+	0.660980i
$531$	−32.5386	−	9.65615i	−1.41205	−	0.419041i
$532$	−4.85410	+	3.52671i	−0.210452	+	0.152902i
$533$	−24.2099	−	7.86629i	−1.04865	−	0.340727i
$534$		0			0
$535$	26.6001	+	36.6119i	1.15002	+	1.58287i
$536$	−4.85410	−	3.52671i	−0.209665	−	0.152331i
$537$	1.45393	−	4.67826i	0.0627415	−	0.201882i
$538$		−	28.2843i		−	1.21942i
$539$		0			0
$540$	4.00000	−	14.1421i	0.172133	−	0.608581i
$541$	−33.6249	+	10.9254i	−1.44565	+	0.469720i	−0.923653	−	0.383229i	$-0.874812\pi$
$541$	−33.6249	+	10.9254i	−1.44565	+	0.469720i	−0.521995	+	0.852949i	$0.674812\pi$
$542$	−17.4563	+	24.0266i	−0.749814	+	1.03203i
$543$	−0.222369	−	17.3191i	−0.00954276	−	0.743233i
$544$	9.27051	−	28.5317i	0.397470	−	1.22329i
$545$	−3.70820	+	11.4127i	−0.158842	+	0.488865i
$546$	−0.133421	−	10.3914i	−0.00570990	−	0.444713i
$547$	−20.7813	+	28.6031i	−0.888546	+	1.22298i	0.0854335	+	0.996344i	$0.472772\pi$
$547$	−20.7813	+	28.6031i	−0.888546	+	1.22298i	−0.973980	+	0.226635i	$0.927228\pi$
$548$	−2.68999	+	0.874032i	−0.114911	+	0.0373368i
$549$	−28.0000	+	9.89949i	−1.19501	+	0.422500i
$550$		0			0
$551$		−	8.48528i		−	0.361485i
$552$		0			0
$553$	−4.85410	−	3.52671i	−0.206417	−	0.149971i
$554$	2.49376	+	3.43237i	0.105950	+	0.145827i
$555$	−31.4085	+	23.4416i	−1.33322	+	0.995038i
$556$	1.34500	+	0.437016i	0.0570406	+	0.0185336i
$557$	−1.61803	+	1.17557i	−0.0685583	+	0.0498105i	−0.621537	−	0.783385i	$-0.713491\pi$
$557$	−1.61803	+	1.17557i	−0.0685583	+	0.0498105i	0.552978	+	0.833196i	$0.313491\pi$
$558$	−1.70698	+	5.75206i	−0.0722623	+	0.243504i
$559$	5.56231	+	17.1190i	0.235260	+	0.724057i
$560$	4.00000			0.169031
$561$		0			0
$562$	6.00000			0.253095
$563$	−3.70820	−	11.4127i	−0.156282	−	0.480987i	0.842006	−	0.539468i	$-0.181374\pi$
$563$	−3.70820	−	11.4127i	−0.156282	−	0.480987i	−0.998289	+	0.0584805i	$0.981374\pi$
$564$	−1.57356	−	4.63939i	−0.0662588	−	0.195353i
$565$	6.47214	−	4.70228i	0.272285	−	0.197826i
$566$	−25.5549	−	8.30330i	−1.07415	−	0.349014i
$567$	11.8871	−	4.54934i	0.499212	−	0.191054i
$568$	4.98752	+	6.86474i	0.209272	+	0.288038i
$569$	−30.7426	−	22.3358i	−1.28880	−	0.936367i	−0.289018	−	0.957324i	$-0.593329\pi$
$569$	−30.7426	−	22.3358i	−1.28880	−	0.936367i	−0.999780	+	0.0209564i	$0.993329\pi$
$570$	19.8482	+	6.16849i	0.831348	+	0.258369i
$571$			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
$574$	8.06998	−	2.62210i	0.336835	−	0.109444i
$575$		0			0
$576$	17.3007	+	11.9032i	0.720861	+	0.495968i
$577$	−9.88854	+	30.4338i	−0.411665	+	1.26698i	0.503534	+	0.863975i	$0.332033\pi$
$577$	−9.88854	+	30.4338i	−0.411665	+	1.26698i	−0.915200	+	0.403001i	$0.867967\pi$
$578$	−5.87132	+	18.0701i	−0.244215	+	0.751616i
$579$	−36.7393	+	0.471715i	−1.52683	+	0.0196038i
$580$	3.32502	−	4.57649i	0.138064	−	0.190028i
$581$	21.5200	−	6.99226i	0.892798	−	0.290088i
$582$	2.00000	−	2.82843i	0.0829027	−	0.117242i
$583$		0			0
$584$		−	4.24264i		−	0.175562i
$585$	28.5717	−	21.9011i	1.18130	−	0.905498i
$586$	1.61803	+	1.17557i	0.0668404	+	0.0485624i
$587$	−6.65003	−	9.15298i	−0.274476	−	0.377784i	0.649418	−	0.760431i	$-0.275012\pi$
$587$	−6.65003	−	9.15298i	−0.274476	−	0.377784i	−0.923894	+	0.382647i	$0.875012\pi$
$588$	5.17990	+	6.94036i	0.213615	+	0.286216i
$589$	8.06998	+	2.62210i	0.332518	+	0.108042i
$590$	25.8885	−	18.8091i	1.06581	−	0.774360i
$591$	36.0860	−	12.2394i	1.48438	−	0.503463i
$592$	−2.47214	−	7.60845i	−0.101604	−	0.312705i
$593$	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
$596$	1.85410	+	5.70634i	0.0759470	+	0.233741i
$597$	−3.28054	+	1.11268i	−0.134264	+	0.0455388i
$598$		0			0
$599$	−32.2799	−	10.4884i	−1.31892	−	0.428544i	−0.436798	−	0.899560i	$-0.643887\pi$
$599$	−32.2799	−	10.4884i	−1.31892	−	0.428544i	−0.882125	+	0.471016i	$0.843887\pi$
$600$	9.32382	+	12.4927i	0.380643	+	0.510010i
$601$	−17.4563	−	24.0266i	−0.712059	−	0.980065i	−0.999750	−	0.0223415i	$-0.992888\pi$
$601$	−17.4563	−	24.0266i	−0.712059	−	0.980065i	0.287692	−	0.957723i	$-0.407112\pi$
$602$	−4.85410	−	3.52671i	−0.197838	−	0.143738i
$603$	4.76195	−	3.65018i	0.193922	−	0.148647i
$604$			4.24264i			0.172631i
$605$		0			0
$606$	−10.0000	+	14.1421i	−0.406222	+	0.574485i
$607$	−4.03499	+	1.31105i	−0.163775	+	0.0532138i	−0.389757	−	0.920918i	$-0.627441\pi$
$607$	−4.03499	+	1.31105i	−0.163775	+	0.0532138i	0.225982	+	0.974132i	$0.427441\pi$
$608$	12.4688	−	17.1618i	0.505677	−	0.696005i
$609$	4.89858	−	0.0628954i	0.198500	−	0.00254865i
$610$	8.65248	−	26.6296i	0.350329	−	1.07820i
$611$	3.70820	−	11.4127i	0.150018	−	0.461708i
$612$	14.8291	+	10.2028i	0.599433	+	0.412422i
$613$	−2.49376	+	3.43237i	−0.100722	+	0.138632i	−0.856403	−	0.516308i	$-0.827306\pi$
$613$	−2.49376	+	3.43237i	−0.100722	+	0.138632i	0.755681	+	0.654940i	$0.227306\pi$
$614$	−4.03499	+	1.31105i	−0.162839	+	0.0529096i
$615$	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	$0.784579\pi$
$618$	−13.2321	−	4.11232i	−0.532274	−	0.165422i
$619$	16.1803	+	11.7557i	0.650343	+	0.472502i	0.863388	−	0.504541i	$-0.168338\pi$
$619$	16.1803	+	11.7557i	0.650343	+	0.472502i	−0.213045	+	0.977042i	$0.568338\pi$
$620$	3.32502	+	4.57649i	0.133536	+	0.183796i
$621$		0			0
$622$	−26.8999	−	8.74032i	−1.07859	−	0.350455i
$623$		0			0
$624$	2.36034	+	6.95908i	0.0944892	+	0.278586i
$625$	−9.57953	−	29.4828i	−0.383181	−	1.17931i
$626$	−12.0000			−0.479616
$627$		0			0
$628$	20.0000			0.798087
$629$	−14.8328	−	45.6507i	−0.591423	−	1.82021i
$630$	−3.41396	+	11.5041i	−0.136016	+	0.458335i
$631$	11.3262	−	8.22899i	0.450890	−	0.327591i	−0.339057	−	0.940766i	$-0.610108\pi$
$631$	11.3262	−	8.22899i	0.450890	−	0.327591i	0.789947	+	0.613175i	$0.210108\pi$
$632$	12.1050	+	3.93314i	0.481510	+	0.156452i
$633$	−37.2976	+	27.8368i	−1.48245	+	1.10642i
$634$	14.9626	+	20.5942i	0.594240	+	0.817901i
$635$	22.6525	+	16.4580i	0.898936	+	0.653115i
$636$	−2.90785	+	9.35652i	−0.115304	+	0.371010i
$637$			21.2132i			0.840498i
$638$		0			0
$639$	−8.00000	+	2.82843i	−0.316475	+	0.111891i
$640$	8.06998	−	2.62210i	0.318994	−	0.103647i
$641$	16.6251	−	22.8825i	0.656651	−	0.903803i	−0.342714	−	0.939440i	$-0.611346\pi$
$641$	16.6251	−	22.8825i	0.656651	−	0.903803i	0.999365	+	0.0356372i	$0.0113461\pi$
$642$	−0.355790	−	27.7105i	−0.0140419	−	1.09365i
$643$	3.70820	−	11.4127i	0.146237	−	0.450072i	−0.850931	−	0.525278i	$-0.823961\pi$
$643$	3.70820	−	11.4127i	0.146237	−	0.450072i	0.997168	+	0.0752058i	$0.0239614\pi$
$644$		0			0
$645$	−0.266843	−	20.7829i	−0.0105069	−	0.818326i
$646$	−14.9626	+	20.5942i	−0.588694	+	0.810268i
$647$	5.37999	−	1.74806i	0.211509	−	0.0687235i	−0.201346	−	0.979520i	$-0.564532\pi$
$647$	5.37999	−	1.74806i	0.211509	−	0.0687235i	0.412855	+	0.910797i	$0.364532\pi$
$648$	−21.0000	+	16.9706i	−0.824958	+	0.666667i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	−1.45393	+	4.67826i	−0.0569839	+	0.183355i
$652$	16.1803	+	11.7557i	0.633671	+	0.460389i
$653$	−6.65003	−	9.15298i	−0.260236	−	0.358184i	0.658827	−	0.752294i	$-0.271053\pi$
$653$	−6.65003	−	9.15298i	−0.260236	−	0.358184i	−0.919063	+	0.394110i	$0.871053\pi$
$654$	5.88909	−	4.39529i	0.230282	−	0.171869i
$655$		0			0
$656$	−4.85410	+	3.52671i	−0.189521	+	0.137695i
$657$	4.06732	+	1.20702i	0.158681	+	0.0470903i
$658$	1.23607	+	3.80423i	0.0481869	+	0.148304i
$659$		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	$0.627164\pi$
$662$	6.18034	+	19.0211i	0.240206	+	0.739277i
$663$	14.1620	+	41.7545i	0.550008	+	1.62161i
$664$	−38.8328	+	28.2137i	−1.50701	+	1.09490i
$665$	16.1400	+	5.24419i	0.625881	+	0.203361i
$666$	23.9921	−	0.616196i	0.929675	−	0.0238771i
$667$		0			0
$668$	−9.70820	−	7.05342i	−0.375622	−	0.272905i
$669$	39.6963	+	12.3370i	1.53475	+	0.476975i
$670$			5.65685i			0.218543i
$671$		0			0
$672$	10.0000	+	7.07107i	0.385758	+	0.272772i
$673$	−4.03499	+	1.31105i	−0.155537	+	0.0505372i	−0.385751	−	0.922603i	$-0.626058\pi$
$673$	−4.03499	+	1.31105i	−0.155537	+	0.0505372i	0.230213	+	0.973140i	$0.426058\pi$
$674$	19.1188	−	26.3148i	0.736430	−	1.01361i
$675$	−14.6290	+	5.38441i	−0.563071	+	0.207246i
$676$	1.54508	−	4.75528i	0.0594263	−	0.182895i
$677$	11.7426	−	36.1401i	0.451307	−	1.38898i	−0.424111	−	0.905610i	$-0.639413\pi$
$677$	11.7426	−	36.1401i	0.451307	−	1.38898i	0.875417	−	0.483368i	$-0.160587\pi$
$678$	−4.89858	+	0.0628954i	−0.188129	+	0.00241548i
$679$	1.66251	−	2.28825i	0.0638012	−	0.0878148i
$680$	−48.4199	+	15.7326i	−1.85682	+	0.603317i
$681$	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	$-0.202946\pi$
$684$	7.74320	+	10.1016i	0.296068	+	0.386245i
$685$	6.47214	+	4.70228i	0.247288	+	0.179665i
$686$	−9.97505	−	13.7295i	−0.380849	−	0.524194i
$687$	24.8635	+	33.3137i	0.948602	+	1.27100i
$688$	4.03499	+	1.31105i	0.153833	+	0.0499832i
$689$	−19.4164	+	14.1068i	−0.739706	+	0.537428i
$690$		0			0
$691$	6.18034	+	19.0211i	0.235111	+	0.723598i	0.997107	+	0.0760155i	$0.0242198\pi$
$691$	6.18034	+	19.0211i	0.235111	+	0.723598i	−0.761995	+	0.647582i	$0.775780\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−16.0000			−0.607352
$695$	−1.23607	−	3.80423i	−0.0468867	−	0.144303i
$696$	−9.84163	+	3.33803i	−0.373046	+	0.126528i
$697$	−29.1246	+	21.1603i	−1.10317	+	0.801502i
$698$	4.03499	+	1.31105i	0.152727	+	0.0496239i
$699$	−10.3598	−	13.8807i	−0.391844	−	0.525017i
$700$	2.49376	+	3.43237i	0.0942553	+	0.129731i
$701$	4.85410	+	3.52671i	0.183337	+	0.133202i	0.675668	−	0.737206i	$-0.263855\pi$
$701$	4.85410	+	3.52671i	0.183337	+	0.133202i	−0.492331	+	0.870408i	$0.663855\pi$
$702$	−22.0291	+	0.848901i	−0.831433	+	0.0320397i
$703$		−	33.9411i		−	1.28011i
$704$		0			0
$705$	−8.00000	+	11.3137i	−0.301297	+	0.426099i
$706$		0			0
$707$	−8.31254	+	11.4412i	−0.312625	+	0.430292i
$708$	19.5943	−	0.251582i	0.736399	−	0.00945502i
$709$	−9.88854	+	30.4338i	−0.371372	+	1.14297i	0.574522	+	0.818489i	$0.305188\pi$
$709$	−9.88854	+	30.4338i	−0.371372	+	1.14297i	−0.945894	+	0.324476i	$0.894812\pi$
$710$	2.47214	−	7.60845i	0.0927776	−	0.285540i
$711$	−7.21444	+	10.4858i	−0.270563	+	0.393248i
$712$		0			0
$713$		0			0
$714$	−12.0000	−	8.48528i	−0.449089	−	0.317554i
$715$		0			0
$716$			2.82843i			0.105703i
$717$	26.4642	+	8.22465i	0.988325	+	0.307155i
$718$	−16.1803	−	11.7557i	−0.603845	−	0.438719i
$719$	11.6376	+	16.0177i	0.434008	+	0.597360i	0.968867	−	0.247581i	$-0.0796355\pi$
$719$	11.6376	+	16.0177i	0.434008	+	0.597360i	−0.534860	+	0.844941i	$0.679636\pi$
$720$	−0.217858	−	8.48248i	−0.00811909	−	0.316124i
$721$	−10.7600	−	3.49613i	−0.400722	−	0.130203i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	2.36034	+	6.95908i	0.0877820	+	0.258811i
$724$	3.09017	+	9.51057i	0.114845	+	0.353457i
$725$	−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	$0.488192\pi$
$728$	5.56231	+	17.1190i	0.206153	+	0.634473i
$729$	−10.2949	−	24.9603i	−0.381291	−	0.924455i
$730$	−3.23607	+	2.35114i	−0.119772	+	0.0870196i
$731$	24.2099	+	7.86629i	0.895437	+	0.290945i
$732$	13.7412	−	10.2557i	0.507890	−	0.379061i
$733$	0.831254	+	1.14412i	0.0307031	+	0.0422591i	0.824093	−	0.566455i	$-0.191686\pi$
$733$	0.831254	+	1.14412i	0.0307031	+	0.0422591i	−0.793389	+	0.608714i	$0.791686\pi$
$734$	6.47214	+	4.70228i	0.238891	+	0.173564i
$735$	7.26963	−	23.3913i	0.268144	−	0.862801i
$736$		0			0
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$	−4.03499	+	1.31105i	−0.148430	+	0.0482277i	−0.382289	−	0.924043i	$-0.624864\pi$
$739$	−4.03499	+	1.31105i	−0.148430	+	0.0482277i	0.233860	+	0.972270i	$0.424864\pi$
$740$	13.3001	−	18.3060i	0.488920	−	0.672941i
$741$	0.400264	+	31.1743i	0.0147041	+	1.14522i
$742$	2.47214	−	7.60845i	0.0907550	−	0.279315i
$743$	4.94427	−	15.2169i	0.181388	−	0.558254i	−0.818480	−	0.574535i	$-0.805183\pi$
$743$	4.94427	−	15.2169i	0.181388	−	0.558254i	0.999867	+	0.0162814i	$0.00518275\pi$
$744$	−0.133421	−	10.3914i	−0.00489146	−	0.380969i
$745$	9.97505	−	13.7295i	0.365457	−	0.503009i
$746$	−4.03499	+	1.31105i	−0.147732	+	0.0480009i
$747$	−16.0000	−	45.2548i	−0.585409	−	1.65579i
$748$		0			0
$749$		−	22.6274i		−	0.826788i
$750$	−2.90785	+	9.35652i	−0.106180	+	0.341652i
$751$	−1.61803	−	1.17557i	−0.0590429	−	0.0428972i	0.557872	−	0.829927i	$-0.311618\pi$
$751$	−1.61803	−	1.17557i	−0.0590429	−	0.0428972i	−0.616915	+	0.787030i	$0.711618\pi$
$752$	−1.66251	−	2.28825i	−0.0606254	−	0.0834437i
$753$	35.3346	−	26.3717i	1.28766	−	0.961040i
$754$	−8.06998	−	2.62210i	−0.293891	−	0.0954911i
$755$	9.70820	−	7.05342i	0.353318	−	0.256700i
$756$	−5.77430	+	4.54504i	−0.210009	+	0.165302i
$757$	6.18034	+	19.0211i	0.224628	+	0.691335i	0.998329	+	0.0577836i	$0.0184034\pi$
$757$	6.18034	+	19.0211i	0.224628	+	0.691335i	−0.773701	+	0.633551i	$0.781597\pi$
$758$	−12.0000			−0.435860
$759$		0			0
$760$	−36.0000			−1.30586
$761$	3.09017	+	9.51057i	0.112019	+	0.344758i	0.991314	−	0.131520i	$-0.0419857\pi$
$761$	3.09017	+	9.51057i	0.112019	+	0.344758i	−0.879295	+	0.476278i	$0.841986\pi$
$762$	−5.50746	−	16.2379i	−0.199514	−	0.588235i
$763$	4.85410	−	3.52671i	0.175730	−	0.127676i
$764$	18.8300	+	6.11822i	0.681244	+	0.221350i
$765$	−1.30715	−	50.8949i	−0.0472601	−	1.84011i
$766$	−3.32502	−	4.57649i	−0.120138	−	0.165355i
$767$	38.8328	+	28.2137i	1.40217	+	1.01874i
$768$	−28.1182	−	8.73869i	−1.01463	−	0.315330i
$769$		−	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
$772$	20.1750	−	6.55524i	0.726113	−	0.235928i
$773$	−19.9501	+	27.4589i	−0.717555	+	0.987630i	0.282047	+	0.959401i	$0.408987\pi$
$773$	−19.9501	+	27.4589i	−0.717555	+	0.987630i	−0.999601	+	0.0282290i	$0.991013\pi$
$774$	−7.21444	+	10.4858i	−0.259318	+	0.376904i
$775$	1.85410	−	5.70634i	0.0666013	−	0.204978i
$776$	−1.85410	+	5.70634i	−0.0665584	+	0.204846i
$777$	19.5943	−	0.251582i	0.702942	−	0.00902544i
$778$	11.6376	−	16.0177i	0.417227	−	0.574263i
$779$	−24.2099	+	7.86629i	−0.867411	+	0.281839i
$780$	−12.0000	+	16.9706i	−0.429669	+	0.607644i
$781$		0			0
$782$		0			0
$783$	−0.400176	−	10.3846i	−0.0143011	−	0.371115i
$784$	4.04508	+	2.93893i	0.144467	+	0.104962i
$785$	−33.2502	−	45.7649i	−1.18675	−	1.63342i
$786$		0			0
$787$	20.1750	+	6.55524i	0.719159	+	0.233669i	0.645659	−	0.763626i	$-0.276583\pi$
$787$	20.1750	+	6.55524i	0.719159	+	0.233669i	0.0735007	+	0.997295i	$0.476583\pi$
$788$	−17.7984	+	12.9313i	−0.634041	+	0.460658i
$789$		0			0
$790$	−3.70820	−	11.4127i	−0.131932	−	0.406045i
$791$	−4.00000			−0.142224
$792$		0			0
$793$	42.0000			1.49146
$794$	−0.618034	−	1.90211i	−0.0219332	−	0.0675035i
$795$	26.2443	−	8.90140i	0.930791	−	0.315700i
$796$	1.61803	−	1.17557i	0.0573497	−	0.0416670i
$797$	−2.68999	−	0.874032i	−0.0952845	−	0.0309598i	0.260987	−	0.965342i	$-0.415952\pi$
$797$	−2.68999	−	0.874032i	−0.0952845	−	0.0309598i	−0.356271	+	0.934383i	$0.615952\pi$
$798$	−6.21588	−	8.32844i	−0.220040	−	0.294823i
$799$	−9.97505	−	13.7295i	−0.352892	−	0.485714i
$800$	−12.1353	−	8.81678i	−0.429046	−	0.311720i
$801$		0			0
$802$			2.82843i			0.0998752i
$803$		0			0
$804$	−2.00000	+	2.82843i	−0.0705346	+	0.0997509i
$805$		0			0
$806$	4.98752	−	6.86474i	0.175678	−	0.241800i
$807$	−48.9858	+	0.628954i	−1.72438	+	0.0221402i
$808$	9.27051	−	28.5317i	0.326135	−	1.00374i
$809$	−15.4508	+	47.5528i	−0.543223	+	1.67187i	0.181955	+	0.983307i	$0.441757\pi$
$809$	−15.4508	+	47.5528i	−0.543223	+	1.67187i	−0.725178	+	0.688561i	$0.758243\pi$
$810$	24.5818	+	6.61316i	0.863717	+	0.232363i
$811$	15.7938	−	21.7383i	0.554596	−	0.763336i	−0.436031	−	0.899932i	$-0.643616\pi$
$811$	15.7938	−	21.7383i	0.554596	−	0.763336i	0.990627	+	0.136596i	$0.0436161\pi$
$812$	−2.68999	+	0.874032i	−0.0944003	+	0.0306725i
$813$	42.0000	+	29.6985i	1.47300	+	1.04157i
$814$		0			0
$815$		−	56.5685i		−	1.98151i
$816$	9.92408	+	3.08424i	0.347412	+	0.107970i
$817$	14.5623	+	10.5801i	0.509471	+	0.370152i
$818$	2.49376	+	3.43237i	0.0871923	+	0.120010i
$819$	−17.9941	+	0.462147i	−0.628764	+	0.0161487i
$820$	−16.1400	−	5.24419i	−0.563632	−	0.183135i
$821$	33.9787	−	24.6870i	1.18587	−	0.861582i	0.193044	−	0.981190i	$-0.438164\pi$
$821$	33.9787	−	24.6870i	1.18587	−	0.861582i	0.992821	+	0.119609i	$0.0381639\pi$
$822$	−1.57356	−	4.63939i	−0.0548842	−	0.161817i
$823$	−7.41641	−	22.8254i	−0.258520	−	0.795642i	−0.993116	−	0.117137i	$-0.962628\pi$
$823$	−7.41641	−	22.8254i	−0.258520	−	0.795642i	0.734596	−	0.678505i	$-0.237372\pi$
$824$	24.0000			0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	−3.70820	−	11.4127i	−0.128947	−	0.396858i	0.865653	−	0.500645i	$-0.166904\pi$
$827$	−3.70820	−	11.4127i	−0.128947	−	0.396858i	−0.994600	+	0.103787i	$0.966904\pi$
$828$		0			0
$829$	11.3262	−	8.22899i	0.393377	−	0.285805i	−0.373461	−	0.927646i	$-0.621829\pi$
$829$	11.3262	−	8.22899i	0.393377	−	0.285805i	0.766838	+	0.641841i	$0.221829\pi$
$830$	43.0399	+	13.9845i	1.49394	+	0.485410i
$831$	5.88909	−	4.39529i	0.204290	−	0.152471i
$832$	−17.4563	−	24.0266i	−0.605189	−	0.832972i
$833$	24.2705	+	17.6336i	0.840923	+	0.610967i
$834$	−0.726963	+	2.33913i	−0.0251727	+	0.0809974i
$835$			33.9411i			1.17458i
$836$		0			0
$837$	10.0000	+	2.82843i	0.345651	+	0.0977647i
$838$	29.5899	−	9.61435i	1.02217	−	0.332122i
$839$	−19.9501	+	27.4589i	−0.688754	+	0.947988i	−0.999997	−	0.00234204i	$-0.999255\pi$
$839$	−19.9501	+	27.4589i	−0.688754	+	0.947988i	0.311244	+	0.950330i	$0.399255\pi$
$840$	−0.266843	−	20.7829i	−0.00920694	−	0.717078i
$841$	−7.72542	+	23.7764i	−0.266394	+	0.819876i
$842$	6.18034	−	19.0211i	0.212989	−	0.655511i
$843$	−0.133421	−	10.3914i	−0.00459527	−	0.357900i
$844$	15.7938	−	21.7383i	0.543646	−	0.748264i
$845$	−13.4500	+	4.37016i	−0.462693	+	0.150338i
$846$	8.00000	−	2.82843i	0.275046	−	0.0972433i
$847$		0			0
$848$			5.65685i			0.194257i
$849$	−13.8123	+	44.4435i	−0.474037	+	1.52530i
$850$	14.5623	+	10.5801i	0.499483	+	0.362896i
$851$		0			0
$852$	3.92606	−	2.93019i	0.134505	−	0.100387i
$853$	−39.0049	−	12.6735i	−1.33550	−	0.433931i	−0.447712	−	0.894178i	$-0.647761\pi$
$853$	−39.0049	−	12.6735i	−1.33550	−	0.433931i	−0.887791	+	0.460247i	$0.847761\pi$
$854$	−11.3262	+	8.22899i	−0.387576	+	0.281590i
$855$	10.2419	−	34.5124i	0.350265	−	1.18030i
$856$	14.8328	+	45.6507i	0.506975	+	1.56031i
$857$	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	$0.610832\pi$
$860$	3.70820	+	11.4127i	0.126449	+	0.389169i
$861$	−4.72068	−	13.9182i	−0.160880	−	0.474330i
$862$	25.8885	−	18.8091i	0.881767	−	0.640641i
$863$	−32.2799	−	10.4884i	−1.09882	−	0.357029i	−0.297173	−	0.954824i	$-0.596044\pi$
$863$	−32.2799	−	10.4884i	−1.09882	−	0.357029i	−0.801649	+	0.597795i	$0.796044\pi$
$864$	14.4504	−	21.5913i	0.491613	−	0.734552i
$865$	−9.97505	−	13.7295i	−0.339162	−	0.466816i
$866$	24.2705	+	17.6336i	0.824745	+	0.599213i
$867$	31.4263	+	9.76677i	1.06729	+	0.331697i
$868$		−	2.82843i		−	0.0960031i
$869$		0			0
$870$	8.00000	+	5.65685i	0.271225	+	0.191785i
$871$	−8.06998	+	2.62210i	−0.273441	+	0.0888463i
$872$	−7.48128	+	10.2971i	−0.253348	+	0.348704i
$873$	−4.94305	−	3.40092i	−0.167297	−	0.115104i
$874$		0			0
$875$	−2.47214	+	7.60845i	−0.0835734	+	0.257213i
$876$	−2.44929	+	0.0314477i	−0.0827538	+	0.00106252i
$877$	−20.7813	+	28.6031i	−0.701736	+	0.965857i	0.298199	+	0.954504i	$0.403614\pi$
$877$	−20.7813	+	28.6031i	−0.701736	+	0.965857i	−0.999936	+	0.0113534i	$0.996386\pi$
$878$	25.5549	−	8.30330i	0.862438	−	0.280223i
$879$	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	$0.824399\pi$
$882$	−11.9049	+	9.12544i	−0.400858	+	0.307270i
$883$	−37.2148	−	27.0381i	−1.25238	−	0.909905i	−0.254020	−	0.967199i	$-0.581753\pi$
$883$	−37.2148	−	27.0381i	−1.25238	−	0.909905i	−0.998357	+	0.0572938i	$0.981753\pi$
$884$	−14.9626	−	20.5942i	−0.503246	−	0.692658i
$885$	−33.1514	−	44.4183i	−1.11437	−	1.49311i
$886$	−26.8999	−	8.74032i	−0.903721	−	0.293637i
$887$	−19.4164	+	14.1068i	−0.651939	+	0.473662i	−0.863931	−	0.503610i	$-0.832005\pi$
$887$	−19.4164	+	14.1068i	−0.651939	+	0.473662i	0.211992	+	0.977271i	$0.432005\pi$
$888$	−39.3665	+	13.3521i	−1.32105	+	0.448067i
$889$	−4.32624	−	13.3148i	−0.145097	−	0.446564i
$890$		0			0
$891$		0			0
$892$	−24.0000			−0.803579
$893$	−3.70820	−	11.4127i	−0.124090	−	0.381911i
$894$	−9.84163	+	3.33803i	−0.329153	+	0.111640i
$895$	6.47214	−	4.70228i	0.216340	−	0.157180i
$896$	−4.03499	−	1.31105i	−0.134800	−	0.0437990i
$897$		0			0
$898$	−3.32502	−	4.57649i	−0.110957	−	0.152719i
$899$	3.23607	+	2.35114i	0.107929	+	0.0784149i
$900$	7.14293	−	5.47527i	0.238098	−	0.182509i
$901$			33.9411i			1.13074i
$902$		0			0
$903$	−6.00000	+	8.48528i	−0.199667	+	0.282372i
$904$	8.06998	−	2.62210i	0.268404	−	0.0872096i
$905$	16.6251	−	22.8825i	0.552636	−	0.760639i
$906$	−7.34786	+	0.0943431i	−0.244116	+	0.00313434i
$907$	3.70820	−	11.4127i	0.123129	−	0.378952i	−0.870427	−	0.492298i	$-0.836157\pi$
$907$	3.70820	−	11.4127i	0.123129	−	0.378952i	0.993556	+	0.113346i	$0.0361570\pi$
$908$	−7.41641	+	22.8254i	−0.246122	+	0.757486i
$909$	24.7152	+	17.0046i	0.819753	+	0.564007i
$910$	9.97505	−	13.7295i	0.330670	−	0.455128i
$911$	34.9699	−	11.3624i	1.15861	−	0.376454i	0.334227	−	0.942493i	$-0.391525\pi$
$911$	34.9699	−	11.3624i	1.15861	−	0.376454i	0.824378	+	0.566039i	$0.191525\pi$
$912$	6.00000	+	4.24264i	0.198680	+	0.140488i
$913$		0			0
$914$			9.89949i			0.327446i
$915$	−46.3124	−	14.3931i	−1.53104	−	0.475822i
$916$	−19.4164	−	14.1068i	−0.641536	−	0.466103i
$917$		0			0
$918$	−17.3405	+	25.9096i	−0.572322	+	0.855144i
$919$	20.1750	+	6.55524i	0.665510	+	0.216237i	0.622241	−	0.782826i	$-0.286223\pi$
$919$	20.1750	+	6.55524i	0.665510	+	0.216237i	0.0432697	+	0.999063i	$0.486223\pi$
$920$		0			0
$921$	2.36034	+	6.95908i	0.0777759	+	0.229309i
$922$	6.79837	+	20.9232i	0.223893	+	0.689070i
$923$	12.0000			0.394985
$924$		0			0
$925$	−24.0000			−0.789115
$926$	−7.41641	−	22.8254i	−0.243718	−	0.750088i
$927$	−6.82793	+	23.0082i	−0.224259	+	0.755690i
$928$	8.09017	−	5.87785i	0.265573	−	0.192950i
$929$	−2.68999	−	0.874032i	−0.0882558	−	0.0286761i	0.264556	−	0.964370i	$-0.414775\pi$
$929$	−2.68999	−	0.874032i	−0.0882558	−	0.0286761i	−0.352812	+	0.935694i	$0.614775\pi$
$930$	−7.85212	+	5.86039i	−0.257481	+	0.192170i
$931$	12.4688	+	17.1618i	0.408649	+	0.562457i
$932$	8.09017	+	5.87785i	0.265002	+	0.192535i
$933$	−14.5393	+	46.7826i	−0.475994	+	1.53159i
$934$		−	28.2843i		−	0.925490i
$935$		0			0
$936$	36.0000	−	12.7279i	1.17670	−	0.416025i
$937$	−33.6249	+	10.9254i	−1.09848	+	0.356917i	−0.801517	−	0.597972i	$-0.795973\pi$
$937$	−33.6249	+	10.9254i	−1.09848	+	0.356917i	−0.296962	+	0.954889i	$0.595973\pi$
$938$	1.66251	−	2.28825i	0.0542828	−	0.0747139i
$939$	0.266843	+	20.7829i	0.00870808	+	0.678224i
$940$	2.47214	−	7.60845i	0.0806322	−	0.248160i
$941$	11.7426	−	36.1401i	0.382799	−	1.17814i	−0.555265	−	0.831674i	$-0.687383\pi$
$941$	11.7426	−	36.1401i	0.382799	−	1.17814i	0.938064	−	0.346462i	$-0.112617\pi$
$942$	0.444738	+	34.6382i	0.0144903	+	1.12857i
$943$		0			0
$944$	10.7600	−	3.49613i	0.350207	−	0.113789i
$945$	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	$-0.168697\pi$
$948$	2.18089	−	7.01739i	0.0708320	−	0.227914i
$949$	−4.85410	−	3.52671i	−0.157571	−	0.114482i
$950$	7.48128	+	10.2971i	0.242725	+	0.334082i
$951$	35.3346	−	26.3717i	1.14580	−	0.855162i
$952$	24.2099	+	7.86629i	0.784649	+	0.254948i
$953$	−1.61803	+	1.17557i	−0.0524133	+	0.0380805i	−0.613683	−	0.789552i	$-0.710313\pi$
$953$	−1.61803	+	1.17557i	−0.0524133	+	0.0380805i	0.561270	+	0.827633i	$0.310313\pi$
$954$	−16.2693	−	4.82807i	−0.526738	−	0.156315i
$955$	−17.3050	−	53.2592i	−0.559975	−	1.72343i
$956$	−16.0000			−0.517477
$957$		0			0
$958$	28.0000			0.904639
$959$	−1.23607	−	3.80423i	−0.0399147	−	0.122845i
$960$	11.0149	+	32.4757i	0.355505	+	1.04815i
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	−32.2799	−	10.4884i	−1.04075	−	0.338159i
$963$	−47.9842	+	1.23239i	−1.54627	+	0.0397133i
$964$	−2.49376	−	3.43237i	−0.0803187	−	0.110549i
$965$	−48.5410	−	35.2671i	−1.56259	−	1.13529i
$966$		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
$970$	5.37999	−	1.74806i	0.172741	−	0.0561270i
$971$	−19.9501	+	27.4589i	−0.640229	+	0.881200i	−0.998628	−	0.0523690i	$-0.983323\pi$
$971$	−19.9501	+	27.4589i	−0.640229	+	0.881200i	0.358399	+	0.933569i	$0.383323\pi$
$972$	9.95281	+	11.9976i	0.319237	+	0.384822i
$973$	−0.618034	+	1.90211i	−0.0198133	+	0.0609789i
$974$	−0.618034	+	1.90211i	−0.0198031	+	0.0609476i
$975$	22.0436	−	0.283029i	0.705960	−	0.00906419i
$976$	5.81878	−	8.00886i	0.186255	−	0.256357i
$977$	−24.2099	+	7.86629i	−0.774545	+	0.251665i	−0.669509	−	0.742804i	$-0.733496\pi$
$977$	−24.2099	+	7.86629i	−0.774545	+	0.251665i	−0.105035	+	0.994468i	$0.533496\pi$
$978$	−20.0000	+	28.2843i	−0.639529	+	0.904431i
$979$		0			0
$980$			14.1421i			0.451754i
$981$	−7.74320	−	10.1016i	−0.247221	−	0.322520i
$982$	−16.1803	−	11.7557i	−0.516335	−	0.375140i
$983$	−6.65003	−	9.15298i	−0.212103	−	0.291935i	0.689688	−	0.724106i	$-0.257748\pi$
$983$	−6.65003	−	9.15298i	−0.212103	−	0.291935i	−0.901791	+	0.432171i	$0.857748\pi$
$984$	18.6476	+	24.9853i	0.594465	+	0.796502i
$985$	59.1799	+	19.2287i	1.88563	+	0.612677i
$986$	−9.70820	+	7.05342i	−0.309172	+	0.224627i
$987$	6.56108	−	2.22535i	0.208842	−	0.0708337i
$988$	−5.56231	−	17.1190i	−0.176961	−	0.544628i
$989$		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	$0.732459\pi$
$992$	3.09017	+	9.51057i	0.0981130	+	0.301961i
$993$	32.8054	−	11.1268i	1.04105	−	0.353097i
$994$	−3.23607	+	2.35114i	−0.102642	+	0.0745737i
$995$	−5.37999	−	1.74806i	−0.170557	−	0.0554174i
$996$	16.5757	+	22.2092i	0.525221	+	0.703724i
$997$	−17.4563	−	24.0266i	−0.552848	−	0.760929i	0.437548	−	0.899195i	$-0.355847\pi$
$997$	−17.4563	−	24.0266i	−0.552848	−	0.760929i	−0.990395	+	0.138266i	$0.955847\pi$
$998$	−11.3262	−	8.22899i	−0.358526	−	0.260484i
$999$	−1.60070	−	41.5384i	−0.0506440	−	1.31422i

Twists

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

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

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+(-0.309017 - 0.951057i) q^{2} +(-1.64027 + 0.556338i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.68999 - 0.874032i) q^{5} +(1.03598 + 1.38807i) q^{6} +(0.831254 + 1.14412i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(2.38098 - 1.82509i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-4.03499 + 1.31105i) q^{13} +(0.831254 - 1.14412i) q^{14} +(4.89858 - 0.0628954i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.85410 + 5.70634i) q^{17} +(-2.47152 - 1.70046i) q^{18} +(-2.49376 + 3.43237i) q^{19} +(-2.68999 + 0.874032i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(4.96204 + 1.54212i) q^{24} +(2.42705 + 1.76336i) q^{25} +(2.49376 + 3.43237i) q^{26} +(-2.89008 + 4.31827i) q^{27} +(1.34500 + 0.437016i) q^{28} +(-1.61803 + 1.17557i) q^{29} +(-1.57356 - 4.63939i) q^{30} +(-0.618034 - 1.90211i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(-1.23607 - 3.80423i) q^{35} +(0.853491 - 2.87603i) q^{36} +(-6.47214 + 4.70228i) q^{37} +(4.03499 + 1.31105i) q^{38} +(5.88909 - 4.39529i) q^{39} +(4.98752 + 6.86474i) q^{40} +(4.85410 + 3.52671i) q^{41} +(-0.726963 + 2.33913i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(-1.66251 + 2.28825i) q^{47} +(-0.0222369 - 1.73191i) q^{48} +(1.54508 - 4.75528i) q^{49} +(0.927051 - 2.85317i) q^{50} +(-0.133421 - 10.3914i) q^{51} +(-2.49376 + 3.43237i) q^{52} +(5.37999 - 1.74806i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(2.18089 - 7.01739i) q^{57} +(1.61803 + 1.17557i) q^{58} +(-6.65003 - 9.15298i) q^{59} +(3.92606 - 2.93019i) q^{60} +(-9.41498 - 3.05911i) q^{61} +(-1.61803 + 1.17557i) q^{62} +(4.06732 + 1.20702i) q^{63} +(2.16312 + 6.65740i) q^{64} +12.0000 q^{65} +2.00000 q^{67} +(1.85410 + 5.70634i) q^{68} +(-3.23607 + 2.35114i) q^{70} +(-2.68999 - 0.874032i) q^{71} +(-8.99703 + 0.231073i) q^{72} +(0.831254 + 1.14412i) q^{73} +(6.47214 + 4.70228i) q^{74} +(-4.96204 - 1.54212i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-4.03499 + 1.31105i) q^{79} +(1.66251 - 2.28825i) q^{80} +(2.33810 - 8.69099i) q^{81} +(1.85410 - 5.70634i) q^{82} +(4.94427 - 15.2169i) q^{83} +(-2.44929 + 0.0314477i) q^{84} +(9.97505 - 13.7295i) q^{85} +(-4.03499 + 1.31105i) q^{86} +(2.00000 - 2.82843i) q^{87} +(5.16213 + 6.73442i) q^{90} +(-4.85410 - 3.52671i) q^{91} +(2.07196 + 2.77615i) q^{93} +(2.68999 + 0.874032i) q^{94} +(9.70820 - 7.05342i) q^{95} +(8.20135 - 2.78169i) q^{96} +(-0.618034 - 1.90211i) 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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