LMFDB - Embedded newform 363.2.f.a.215.2

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			215.2
Root			$-1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.a.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.0222369 - 1.73191i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.68999 + 0.874032i) q^{5} +(1.65401 - 0.514040i) q^{6} +(0.831254 + 1.14412i) q^{7} +(2.42705 + 1.76336i) q^{8} +(-2.99901 - 0.0770245i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.0222369 - 1.73191i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.68999 + 0.874032i) q^{5} +(1.65401 - 0.514040i) q^{6} +(0.831254 + 1.14412i) q^{7} +(2.42705 + 1.76336i) q^{8} +(-2.99901 - 0.0770245i) q^{9} +2.82843i q^{10} +(-1.00000 - 1.41421i) q^{12} +(-4.03499 + 1.31105i) q^{13} +(-0.831254 + 1.14412i) q^{14} +(1.57356 - 4.63939i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.85410 - 5.70634i) q^{17} +(-0.853491 - 2.87603i) q^{18} +(-2.49376 + 3.43237i) q^{19} +(2.68999 - 0.874032i) q^{20} +(2.00000 - 1.41421i) q^{21} +(3.10794 - 4.16422i) q^{24} +(2.42705 + 1.76336i) q^{25} +(-2.49376 - 3.43237i) q^{26} +(-0.200088 + 5.19230i) q^{27} +(1.34500 + 0.437016i) q^{28} +(1.61803 - 1.17557i) q^{29} +(4.89858 + 0.0628954i) q^{30} +(-0.618034 - 1.90211i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(1.23607 + 3.80423i) q^{35} +(-2.47152 + 1.70046i) q^{36} +(-6.47214 + 4.70228i) q^{37} +(-4.03499 - 1.31105i) q^{38} +(2.18089 + 7.01739i) q^{39} +(4.98752 + 6.86474i) q^{40} +(-4.85410 - 3.52671i) q^{41} +(1.96303 + 1.46510i) q^{42} -4.24264i q^{43} +(-8.00000 - 2.82843i) q^{45} +(1.66251 - 2.28825i) q^{47} +(1.64027 + 0.556338i) q^{48} +(1.54508 - 4.75528i) q^{49} +(-0.927051 + 2.85317i) q^{50} +(-9.84163 - 3.33803i) q^{51} +(-2.49376 + 3.43237i) q^{52} +(-5.37999 + 1.74806i) q^{53} +(-5.00000 + 1.41421i) q^{54} +4.24264i q^{56} +(5.88909 + 4.39529i) q^{57} +(1.61803 + 1.17557i) q^{58} +(6.65003 + 9.15298i) q^{59} +(-1.45393 - 4.67826i) q^{60} +(-9.41498 - 3.05911i) q^{61} +(1.61803 - 1.17557i) q^{62} +(-2.40481 - 3.49526i) 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} +(-7.14293 - 5.47527i) q^{72} +(0.831254 + 1.14412i) q^{73} +(-6.47214 - 4.70228i) q^{74} +(3.10794 - 4.16422i) q^{75} +4.24264i q^{76} +(-6.00000 + 4.24264i) q^{78} +(-4.03499 + 1.31105i) q^{79} +(-1.66251 + 2.28825i) q^{80} +(8.98813 + 0.461994i) q^{81} +(1.85410 - 5.70634i) q^{82} +(-4.94427 + 15.2169i) q^{83} +(0.786780 - 2.31969i) q^{84} +(9.97505 - 13.7295i) q^{85} +(4.03499 - 1.31105i) q^{86} +(-2.00000 - 2.82843i) q^{87} +(0.217858 - 8.48248i) q^{90} +(-4.85410 - 3.52671i) q^{91} +(-3.30803 + 1.02808i) q^{93} +(2.68999 + 0.874032i) q^{94} +(-9.70820 + 7.05342i) q^{95} +(0.111184 - 8.65954i) 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}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} + 16 q^{21} + 6 q^{24} + 6 q^{25} + 10 q^{27} + 4 q^{29} + 8 q^{30} + 4 q^{31} + 40 q^{32} + 48 q^{34} - 8 q^{35} - 2 q^{36} - 16 q^{37} + 12 q^{39} - 12 q^{41} - 4 q^{42} - 64 q^{45} + 2 q^{48} - 10 q^{49} + 6 q^{50} - 12 q^{51} - 40 q^{54} - 12 q^{57} + 4 q^{58} - 8 q^{60} + 4 q^{62} - 8 q^{63} - 14 q^{64} - 96 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} - 6 q^{72} - 16 q^{74} + 6 q^{75} - 48 q^{78} + 14 q^{81} - 12 q^{82} + 32 q^{83} + 4 q^{84} - 16 q^{87} + 16 q^{90} - 12 q^{91} + 4 q^{93} - 24 q^{95} - 10 q^{96} + 4 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 + 16 * q^21 + 6 * q^24 + 6 * q^25 + 10 * q^27 + 4 * q^29 + 8 * q^30 + 4 * q^31 + 40 * q^32 + 48 * q^34 - 8 * q^35 - 2 * q^36 - 16 * q^37 + 12 * q^39 - 12 * q^41 - 4 * q^42 - 64 * q^45 + 2 * q^48 - 10 * q^49 + 6 * q^50 - 12 * q^51 - 40 * q^54 - 12 * q^57 + 4 * q^58 - 8 * q^60 + 4 * q^62 - 8 * q^63 - 14 * q^64 - 96 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 - 6 * q^72 - 16 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 32 * q^83 + 4 * q^84 - 16 * q^87 + 16 * q^90 - 12 * q^91 + 4 * q^93 - 24 * q^95 - 10 * q^96 + 4 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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	$0.0150267\pi$
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i	−0.780378	+	0.625308i	$0.784973\pi$
$3$	0.0222369	−	1.73191i	0.0128385	−	0.999918i
$3$	0.0222369	−	1.73191i	0.0128385	−	0.999918i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	2.68999	+	0.874032i	1.20300	+	0.390879i	0.840864	−	0.541246i	$-0.182047\pi$
$5$	2.68999	+	0.874032i	1.20300	+	0.390879i	0.362137	+	0.932125i	$0.382047\pi$
$6$	1.65401	−	0.514040i	0.675248	−	0.209856i
$7$	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
$9$	−2.99901	−	0.0770245i	−0.999670	−	0.0256748i
$10$			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
$15$	1.57356	−	4.63939i	0.406292	−	1.19788i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.85410	−	5.70634i	0.449686	−	1.38399i	−0.427576	−	0.903979i	$-0.640633\pi$
$17$	1.85410	−	5.70634i	0.449686	−	1.38399i	0.877262	−	0.480011i	$-0.159367\pi$
$18$	−0.853491	−	2.87603i	−0.201170	−	0.677887i
$19$	−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			$\pi$
$24$	3.10794	−	4.16422i	0.634406	−	0.850017i
$25$	2.42705	+	1.76336i	0.485410	+	0.352671i
$26$	−2.49376	−	3.43237i	−0.489067	−	0.673143i
$27$	−0.200088	+	5.19230i	−0.0385069	+	0.999258i
$28$	1.34500	+	0.437016i	0.254181	+	0.0825883i
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	−0.427331	−	0.904095i	$-0.640546\pi$
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	0.727793	+	0.685797i	$0.240546\pi$
$30$	4.89858	+	0.0628954i	0.894353	+	0.0114831i
$31$	−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
$36$	−2.47152	+	1.70046i	−0.411921	+	0.283410i
$37$	−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
$39$	2.18089	+	7.01739i	0.349222	+	1.12368i
$40$	4.98752	+	6.86474i	0.788597	+	1.08541i
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	0.140238	−	0.990118i	$-0.455213\pi$
$41$	−4.85410	−	3.52671i	−0.758083	−	0.550780i	−0.898322	+	0.439338i	$0.855213\pi$
$42$	1.96303	+	1.46510i	0.302902	+	0.226069i
$43$		−	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	−0.670366	−	0.742031i	$-0.733863\pi$
$47$	1.66251	−	2.28825i	0.242502	−	0.333775i	0.912868	+	0.408256i	$0.133863\pi$
$48$	1.64027	+	0.556338i	0.236753	+	0.0803004i
$49$	1.54508	−	4.75528i	0.220726	−	0.679326i
$50$	−0.927051	+	2.85317i	−0.131105	+	0.403499i
$51$	−9.84163	−	3.33803i	−1.37810	−	0.467417i
$52$	−2.49376	+	3.43237i	−0.345823	+	0.475984i
$53$	−5.37999	+	1.74806i	−0.738998	+	0.240115i	−0.654241	−	0.756287i	$-0.727012\pi$
$53$	−5.37999	+	1.74806i	−0.738998	+	0.240115i	−0.0847577	+	0.996402i	$0.527012\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$		0			0
$56$			4.24264i			0.566947i
$57$	5.88909	+	4.39529i	0.780029	+	0.582171i
$58$	1.61803	+	1.17557i	0.212458	+	0.154360i
$59$	6.65003	+	9.15298i	0.865760	+	1.19162i	0.980165	+	0.198183i	$0.0635039\pi$
$59$	6.65003	+	9.15298i	0.865760	+	1.19162i	−0.114405	+	0.993434i	$0.536496\pi$
$60$	−1.45393	−	4.67826i	−0.187701	−	0.603961i
$61$	−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
$63$	−2.40481	−	3.49526i	−0.302978	−	0.440362i
$64$	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	0.464255	−	0.885701i	$-0.346322\pi$
$71$	2.68999	+	0.874032i	0.319244	+	0.103729i	−0.145012	+	0.989430i	$0.546322\pi$
$72$	−7.14293	−	5.47527i	−0.841803	−	0.645266i
$73$	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
$75$	3.10794	−	4.16422i	0.358874	−	0.480842i
$76$			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
$81$	8.98813	+	0.461994i	0.998682	+	0.0513327i
$82$	1.85410	−	5.70634i	0.204751	−	0.630160i
$83$	−4.94427	+	15.2169i	−0.542704	+	1.67027i	0.183682	+	0.982986i	$0.441198\pi$
$83$	−4.94427	+	15.2169i	−0.542704	+	1.67027i	−0.726386	+	0.687287i	$0.758802\pi$
$84$	0.786780	−	2.31969i	0.0858447	−	0.253099i
$85$	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			$\pi$
$90$	0.217858	−	8.48248i	0.0229643	−	0.894132i
$91$	−4.85410	−	3.52671i	−0.508848	−	0.369700i
$92$		0			0
$93$	−3.30803	+	1.02808i	−0.343027	+	0.106607i
$94$	2.68999	+	0.874032i	0.277452	+	0.0901495i
$95$	−9.70820	+	7.05342i	−0.996041	+	0.723666i
$96$	0.111184	−	8.65954i	0.0113477	−	0.883811i
$97$	−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	$-0.934245\pi$
$101$	−3.09017	−	9.51057i	−0.307483	−	0.946337i	0.671255	−	0.741226i	$-0.265755\pi$
$102$	0.133421	−	10.3914i	0.0132107	−	1.02891i
$103$	−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
$105$	6.61606	−	2.05616i	0.645661	−	0.200661i
$106$	−3.32502	−	4.57649i	−0.322954	−	0.444508i
$107$	12.9443	+	9.40456i	1.25137	+	0.909174i	0.998301	−	0.0582746i	$-0.0185599\pi$
$107$	12.9443	+	9.40456i	1.25137	+	0.909174i	0.253069	+	0.967448i	$0.418560\pi$
$108$	2.89008	+	4.31827i	0.278098	+	0.415525i
$109$		−	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	−0.723628	−	0.690190i	$-0.757527\pi$
$113$	1.66251	−	2.28825i	0.156396	−	0.215260i	0.880023	+	0.474930i	$0.157527\pi$
$114$	−2.36034	+	6.95908i	−0.221066	+	0.651778i
$115$		0			0
$116$	0.618034	−	1.90211i	0.0573830	−	0.176607i
$117$	12.2020	−	3.62105i	1.12807	−	0.334767i
$118$	−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
$123$	−6.21588	+	8.32844i	−0.560467	+	0.750950i
$124$	−1.61803	−	1.17557i	−0.145304	−	0.105569i
$125$	−3.32502	−	4.57649i	−0.297398	−	0.409334i
$126$	2.58107	−	3.36721i	0.229940	−	0.299975i
$127$	−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
$129$	−7.34786	−	0.0943431i	−0.646943	−	0.00830645i
$130$	−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
$135$	−5.07647	+	13.7924i	−0.436913	+	1.18706i
$136$	14.5623	−	10.5801i	1.24871	−	0.907239i
$137$	2.68999	+	0.874032i	0.229822	+	0.0746736i	0.421664	−	0.906752i	$-0.361446\pi$
$137$	2.68999	+	0.874032i	0.229822	+	0.0746736i	−0.191842	+	0.981426i	$0.561446\pi$
$138$		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
$141$	−3.92606	−	2.93019i	−0.330634	−	0.246767i
$142$			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
$147$	−8.20135	−	2.78169i	−0.676436	−	0.229430i
$148$	−2.47214	+	7.60845i	−0.203208	+	0.625411i
$149$	1.85410	−	5.70634i	0.151894	−	0.467482i	−0.845939	−	0.533280i	$-0.820959\pi$
$149$	1.85410	−	5.70634i	0.151894	−	0.467482i	0.997833	+	0.0657982i	$0.0209593\pi$
$150$	4.92081	+	1.66901i	0.401783	+	0.136274i
$151$	−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
$156$	5.88909	+	4.39529i	0.471505	+	0.351905i
$157$	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
$159$	2.90785	+	9.35652i	0.230608	+	0.742020i
$160$	13.4500	+	4.37016i	1.06331	+	0.345492i
$161$		0			0
$162$	2.33810	+	8.69099i	0.183699	+	0.682829i
$163$	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	$0.0536919\pi$
$167$	3.70820	+	11.4127i	0.286949	+	0.883140i	−0.698858	+	0.715260i	$0.746308\pi$
$168$	7.34786	+	0.0943431i	0.566900	+	0.00727873i
$169$	4.04508	−	2.93893i	0.311160	−	0.226071i
$170$	16.1400	+	5.24419i	1.23788	+	0.402211i
$171$	7.74320	−	10.1016i	0.592137	−	0.772491i
$172$	−2.49376	−	3.43237i	−0.190148	−	0.261716i
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	0.387767	−	0.921758i	$-0.373247\pi$
$173$	−4.85410	−	3.52671i	−0.369051	−	0.268131i	−0.756817	+	0.653627i	$0.773247\pi$
$174$	2.07196	−	2.77615i	0.157075	−	0.210459i
$175$			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	−0.742354	−	0.670008i	$-0.766291\pi$
$179$	1.66251	−	2.28825i	0.124262	−	0.171032i	0.866615	+	0.498977i	$0.166291\pi$
$180$	−8.13464	+	2.41404i	−0.606321	+	0.179932i
$181$	−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
$183$	−5.50746	+	16.2379i	−0.407123	+	1.20034i
$184$		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
$189$	−6.10695	+	4.08719i	−0.444215	+	0.297300i
$190$	−9.70820	−	7.05342i	−0.704307	−	0.511709i
$191$	−11.6376	−	16.0177i	−0.842064	−	1.15900i	−0.985556	−	0.169350i	$-0.945833\pi$
$191$	−11.6376	−	16.0177i	−0.842064	−	1.15900i	0.143492	−	0.989651i	$-0.454167\pi$
$192$	11.5781	−	3.59828i	0.835577	−	0.259684i
$193$	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
$195$	−0.266843	+	20.7829i	−0.0191090	+	1.48829i
$196$	−1.54508	−	4.75528i	−0.110363	−	0.339663i
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	2.78115	+	8.55951i	0.196657	+	0.605249i
$201$	0.0444738	−	3.46382i	0.00313694	−	0.244319i
$202$	8.09017	−	5.87785i	0.569222	−	0.413564i
$203$	2.68999	+	0.874032i	0.188801	+	0.0613450i
$204$	−9.92408	+	3.08424i	−0.694825	+	0.215940i
$205$	−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
$213$	1.57356	−	4.63939i	0.107819	−	0.317886i
$214$	−4.94427	+	15.2169i	−0.337983	+	1.04021i
$215$	3.70820	−	11.4127i	0.252897	−	0.778338i
$216$	−9.64149	+	12.2491i	−0.656021	+	0.833449i
$217$	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
$222$	−8.28784	+	11.1046i	−0.556243	+	0.745291i
$223$	−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
$225$	−7.14293	−	5.47527i	−0.476195	−	0.365018i
$226$	2.68999	+	0.874032i	0.178936	+	0.0581397i
$227$	19.4164	−	14.1068i	1.28871	−	0.936304i	0.288934	−	0.957349i	$-0.406699\pi$
$227$	19.4164	−	14.1068i	1.28871	−	0.936304i	0.999779	+	0.0210448i	$0.00669928\pi$
$228$	7.34786	+	0.0943431i	0.486624	+	0.00624802i
$229$	−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	$-0.993773\pi$
$233$	−3.09017	−	9.51057i	−0.202444	−	0.623058i	0.797365	−	0.603497i	$-0.206227\pi$
$234$	7.21444	+	10.4858i	0.471623	+	0.685478i
$235$	6.47214	−	4.70228i	0.422196	−	0.306743i
$236$	10.7600	+	3.49613i	0.700415	+	0.227579i
$237$	2.18089	+	7.01739i	0.141664	+	0.455828i
$238$	4.98752	+	6.86474i	0.323293	+	0.444975i
$239$	12.9443	+	9.40456i	0.837295	+	0.608331i	0.921614	−	0.388108i	$-0.126871\pi$
$239$	12.9443	+	9.40456i	0.837295	+	0.608331i	−0.0843185	+	0.996439i	$0.526871\pi$
$240$	3.92606	+	2.93019i	0.253426	+	0.189143i
$241$		−	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
$246$	−9.84163	−	3.33803i	−0.627479	−	0.212825i
$247$	5.56231	−	17.1190i	0.353921	−	1.08926i
$248$	1.85410	−	5.70634i	0.117736	−	0.362353i
$249$	26.2443	+	8.90140i	1.66317	+	0.564103i
$250$	3.32502	−	4.57649i	0.210292	−	0.289443i
$251$	24.2099	−	7.86629i	1.52812	−	0.496516i	0.580050	−	0.814581i	$-0.303033\pi$
$251$	24.2099	−	7.86629i	1.52812	−	0.496516i	0.948069	+	0.318065i	$0.103033\pi$
$252$	−4.00000	−	1.41421i	−0.251976	−	0.0890871i
$253$		0			0
$254$		−	9.89949i		−	0.621150i
$255$	−23.5564	−	17.5812i	−1.47516	−	1.10098i
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	6.65003	+	9.15298i	0.414818	+	0.570947i	0.964385	−	0.264502i	$-0.0852075\pi$
$257$	6.65003	+	9.15298i	0.414818	+	0.570947i	−0.549568	+	0.835449i	$0.685208\pi$
$258$	−2.18089	−	7.01739i	−0.135776	−	0.436883i
$259$	−10.7600	−	3.49613i	−0.668592	−	0.217239i
$260$	−9.70820	+	7.05342i	−0.602077	+	0.437435i
$261$	−4.94305	+	3.40092i	−0.305967	+	0.210512i
$262$		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	−0.663553	−	0.748129i	$-0.730952\pi$
$269$	−26.8999	−	8.74032i	−1.64012	−	0.532907i	−0.976565	+	0.215222i	$0.930952\pi$
$270$	−14.6860	−	0.565934i	−0.893764	−	0.0344417i
$271$	−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
$273$	−6.21588	+	8.32844i	−0.376202	+	0.504060i
$274$			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
$279$	1.70698	+	5.75206i	0.102194	+	0.344367i
$280$	−3.70820	+	11.4127i	−0.221608	+	0.682038i
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	−0.880399	−	0.474234i	$-0.842725\pi$
$281$	1.85410	−	5.70634i	0.110606	−	0.340412i	0.991005	+	0.133822i	$0.0427251\pi$
$282$	1.57356	−	4.63939i	0.0937041	−	0.276271i
$283$	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
$288$	−14.9951	−	0.385122i	−0.883592	−	0.0226936i
$289$	−15.3713	−	11.1679i	−0.904195	−	0.656936i
$290$	3.32502	+	4.57649i	0.195252	+	0.268741i
$291$	−3.30803	+	1.02808i	−0.193920	+	0.0602672i
$292$	1.34500	+	0.437016i	0.0787100	+	0.0255744i
$293$	1.61803	−	1.17557i	0.0945266	−	0.0686776i	−0.539518	−	0.841974i	$-0.681394\pi$
$293$	1.61803	−	1.17557i	0.0945266	−	0.0686776i	0.634045	+	0.773296i	$0.281394\pi$
$294$	0.111184	−	8.65954i	0.00648441	−	0.505035i
$295$	9.88854	+	30.4338i	0.575733	+	1.77192i
$296$	−24.0000			−1.39497
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	0.0667106	−	5.19572i	0.00385154	−	0.299975i
$301$	4.85410	−	3.52671i	0.279786	−	0.203276i
$302$	−4.03499	−	1.31105i	−0.232188	−	0.0754423i
$303$	−16.5401	+	5.14040i	−0.950206	+	0.295309i
$304$	−2.49376	−	3.43237i	−0.143027	−	0.196860i
$305$	−22.6525	−	16.4580i	−1.29708	−	0.942382i
$306$	−17.9941	−	0.462147i	−1.02865	−	0.0264192i
$307$		−	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	$0.496192\pi$
$311$	−16.6251	+	22.8825i	−0.942722	+	1.29755i	−0.954685	+	0.297617i	$0.903808\pi$
$312$	−7.08102	+	20.8772i	−0.400884	+	1.18194i
$313$	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
$315$	−3.41396	−	11.5041i	−0.192355	−	0.648184i
$316$	−2.49376	+	3.43237i	−0.140285	+	0.193086i
$317$	24.2099	−	7.86629i	1.35977	−	0.441815i	0.463801	−	0.885939i	$-0.346485\pi$
$317$	24.2099	−	7.86629i	1.35977	−	0.441815i	0.895965	+	0.444125i	$0.146485\pi$
$318$	−8.00000	+	5.65685i	−0.448618	+	0.317221i
$319$		0			0
$320$			19.7990i			1.10680i
$321$	16.5757	−	22.2092i	0.925164	−	1.23959i
$322$		0			0
$323$	14.9626	+	20.5942i	0.832540	+	1.14589i
$324$	7.54311	−	4.90933i	0.419062	−	0.272741i
$325$	−12.1050	−	3.93314i	−0.671463	−	0.218172i
$326$	−16.1803	+	11.7557i	−0.896146	+	0.651088i
$327$	−7.34786	−	0.0943431i	−0.406338	−	0.00521719i
$328$	−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
$333$	19.7722	−	13.6037i	1.08351	−	0.745477i
$334$	−9.70820	+	7.05342i	−0.531209	+	0.385946i
$335$	5.37999	+	1.74806i	0.293940	+	0.0955069i
$336$	0.726963	+	2.33913i	0.0396591	+	0.127610i
$337$	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
$339$	−3.92606	−	2.93019i	−0.213234	−	0.159146i
$340$		−	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	$0.241297\pi$
$347$	−4.94427	+	15.2169i	−0.265422	+	0.816886i	−0.991596	+	0.129375i	$0.958703\pi$
$348$	−3.28054	−	1.11268i	−0.175855	−	0.0596456i
$349$	−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			$\pi$
$354$	15.7042	+	11.7208i	0.834671	+	0.622952i
$355$	6.47214	+	4.70228i	0.343505	+	0.249571i
$356$		0			0
$357$	−4.36178	−	14.0348i	−0.230850	−	0.742799i
$358$	2.68999	+	0.874032i	0.142171	+	0.0461940i
$359$	−16.1803	+	11.7557i	−0.853966	+	0.620442i	−0.926237	−	0.376943i	$-0.876975\pi$
$359$	−16.1803	+	11.7557i	−0.853966	+	0.620442i	0.0722709	+	0.997385i	$0.476975\pi$
$360$	−14.4289	−	20.9716i	−0.760469	−	1.10530i
$361$	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
$366$	−17.1450	−	0.220134i	−0.896184	−	0.0115066i
$367$	−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
$369$	14.2859	+	10.9505i	0.743692	+	0.570062i
$370$	−13.3001	−	18.3060i	−0.691437	−	0.951682i
$371$	−6.47214	−	4.70228i	−0.336017	−	0.244130i
$372$	−2.07196	+	2.77615i	−0.107426	+	0.143936i
$373$		−	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
$378$	−5.77430	−	4.54504i	−0.296998	−	0.233772i
$379$	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
$381$	−5.50746	+	16.2379i	−0.282156	+	0.831890i
$382$	11.6376	−	16.0177i	0.595429	−	0.819538i
$383$	−5.37999	+	1.74806i	−0.274905	+	0.0893219i	−0.443225	−	0.896410i	$-0.646166\pi$
$383$	−5.37999	+	1.74806i	−0.274905	+	0.0893219i	0.168320	+	0.985732i	$0.446166\pi$
$384$	−3.00000	−	4.24264i	−0.153093	−	0.216506i
$385$		0			0
$386$			21.2132i			1.07972i
$387$	−0.326787	+	12.7237i	−0.0166115	+	0.646783i
$388$	−1.61803	−	1.17557i	−0.0821432	−	0.0596806i
$389$	−11.6376	−	16.0177i	−0.590047	−	0.812131i	0.404704	−	0.914448i	$-0.367374\pi$
$389$	−11.6376	−	16.0177i	−0.590047	−	0.812131i	−0.994752	+	0.102317i	$0.967374\pi$
$390$	−19.8482	+	6.16849i	−1.00505	+	0.312353i
$391$		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
$399$	−0.133421	+	10.3914i	−0.00667942	+	0.520223i
$400$	−2.42705	+	1.76336i	−0.121353	+	0.0881678i
$401$	2.68999	+	0.874032i	0.134332	+	0.0436471i	0.375411	−	0.926858i	$-0.377501\pi$
$401$	2.68999	+	0.874032i	0.134332	+	0.0436471i	−0.241079	+	0.970505i	$0.577501\pi$
$402$	3.30803	−	1.02808i	0.164989	−	0.0512760i
$403$	4.98752	+	6.86474i	0.248446	+	0.341957i
$404$	−8.09017	−	5.87785i	−0.402501	−	0.292434i
$405$	23.7742	+	9.09868i	1.18135	+	0.452117i
$406$			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
$411$	1.57356	−	4.63939i	0.0776180	−	0.228844i
$412$	−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	$-0.725210\pi$
$419$		−	31.1127i		−	1.51995i	0.649950	−	0.759977i	$-0.274790\pi$
$420$	4.14392	−	5.55229i	0.202203	−	0.270924i
$421$	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
$423$	−5.16213	+	6.73442i	−0.250991	+	0.327439i
$424$	−16.1400	−	5.24419i	−0.783826	−	0.254680i
$425$	14.5623	−	10.5801i	0.706376	−	0.513212i
$426$	4.89858	+	0.0628954i	0.237337	+	0.00304729i
$427$	−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	$-0.819910\pi$
$431$	−9.88854	−	30.4338i	−0.476314	−	1.46594i	0.367862	−	0.929880i	$-0.380090\pi$
$432$	−4.87634	−	1.79480i	−0.234613	−	0.0863525i
$433$	−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
$435$	−2.90785	−	9.35652i	−0.139421	−	0.448611i
$436$	−2.49376	−	3.43237i	−0.119430	−	0.164381i
$437$		0			0
$438$	1.96303	+	1.46510i	0.0937972	+	0.0700050i
$439$			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	$0.434527\pi$
$443$	−16.6251	+	22.8825i	−0.789881	+	1.08718i	−0.994123	+	0.108258i	$0.965473\pi$
$444$	13.1222	+	4.45070i	0.622750	+	0.211221i
$445$		0			0
$446$	7.41641	−	22.8254i	0.351177	−	1.08081i
$447$	−9.84163	−	3.33803i	−0.465493	−	0.157883i
$448$	−5.81878	+	8.00886i	−0.274911	+	0.378383i
$449$	−5.37999	+	1.74806i	−0.253897	+	0.0824962i	−0.433200	−	0.901298i	$-0.642616\pi$
$449$	−5.37999	+	1.74806i	−0.253897	+	0.0824962i	0.179303	+	0.983794i	$0.442616\pi$
$450$	3.00000	−	8.48528i	0.141421	−	0.400000i
$451$		0			0
$452$		−	2.82843i		−	0.133038i
$453$	5.88909	+	4.39529i	0.276694	+	0.206509i
$454$	19.4164	+	14.1068i	0.911257	+	0.662067i
$455$	−9.97505	−	13.7295i	−0.467637	−	0.643648i
$456$	6.54267	+	21.0522i	0.306388	+	0.985858i
$457$	−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
$459$	29.2580	+	10.7688i	1.36565	+	0.502646i
$460$		0			0
$461$	22.0000			1.02464			0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	0.618034	+	1.90211i	0.0286915	+	0.0883034i
$465$	−9.79715	−	0.125791i	−0.454332	−	0.00583341i
$466$	8.09017	−	5.87785i	0.374770	−	0.272286i
$467$	−26.8999	−	8.74032i	−1.24478	−	0.404454i	−0.388733	−	0.921350i	$-0.627087\pi$
$467$	−26.8999	−	8.74032i	−1.24478	−	0.404454i	−0.856048	+	0.516897i	$0.827087\pi$
$468$	7.74320	−	10.1016i	0.357929	−	0.466948i
$469$	1.66251	+	2.28825i	0.0767675	+	0.105661i
$470$	6.47214	+	4.70228i	0.298537	+	0.216900i
$471$	20.7196	−	27.7615i	0.954709	−	1.27918i
$472$			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
$477$	16.2693	−	4.82807i	0.744919	−	0.221062i
$478$	−4.94427	+	15.2169i	−0.226146	+	0.696005i
$479$	8.65248	−	26.6296i	0.395342	−	1.21674i	−0.533353	−	0.845893i	$-0.679068\pi$
$479$	8.65248	−	26.6296i	0.395342	−	1.21674i	0.928695	−	0.370844i	$-0.120932\pi$
$480$	7.86780	−	23.1969i	0.359114	−	1.05879i
$481$	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
$486$	15.1040	−	3.85612i	0.685131	−	0.174917i
$487$	−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
$489$	33.0803	−	10.2808i	1.49594	−	0.464914i
$490$	13.4500	+	4.37016i	0.607608	+	0.197424i
$491$	−16.1803	+	11.7557i	−0.730209	+	0.530528i	−0.889629	−	0.456683i	$-0.849037\pi$
$491$	−16.1803	+	11.7557i	−0.730209	+	0.530528i	0.159421	+	0.987211i	$0.449037\pi$
$492$	−0.133421	+	10.3914i	−0.00601510	+	0.468483i
$493$	−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
$498$	−0.355790	+	27.7105i	−0.0159433	+	1.24174i
$499$	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
$501$	19.8482	−	6.16849i	0.886751	−	0.275588i
$502$	14.9626	+	20.5942i	0.667812	+	0.919165i
$503$	12.9443	+	9.40456i	0.577157	+	0.419329i	0.837698	−	0.546134i	$-0.183901\pi$
$503$	12.9443	+	9.40456i	0.577157	+	0.419329i	−0.260541	+	0.965463i	$0.583901\pi$
$504$	0.326787	−	12.7237i	0.0145563	−	0.566760i
$505$		−	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	$-0.528989\pi$
$509$	19.9501	−	27.4589i	0.884272	−	1.21710i	0.975219	−	0.221241i	$-0.0710106\pi$
$510$	9.44136	−	27.8363i	0.418071	−	1.23261i
$511$	−0.618034	+	1.90211i	−0.0273402	+	0.0841445i
$512$	−3.39919	+	10.4616i	−0.150224	+	0.462343i
$513$	−17.3229	−	13.6351i	−0.764825	−	0.602006i
$514$	−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
$519$	−6.21588	+	8.32844i	−0.272847	+	0.365578i
$520$	−29.1246	−	21.1603i	−1.27720	−	0.927939i
$521$	−11.6376	−	16.0177i	−0.509851	−	0.701749i	0.474044	−	0.880501i	$-0.342794\pi$
$521$	−11.6376	−	16.0177i	−0.509851	−	0.701749i	−0.983894	+	0.178752i	$0.942794\pi$
$522$	−4.76195	−	3.65018i	−0.208425	−	0.159764i
$523$	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
$525$	7.34786	+	0.0943431i	0.320687	+	0.00411747i
$526$		0			0
$527$	−12.0000			−0.522728
$528$		0			0
$529$	23.0000			1.00000
$530$	−4.94427	−	15.2169i	−0.214765	−	0.660980i
$531$	−19.2385	−	27.9621i	−0.834880	−	1.21345i
$532$	−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
$537$	−3.92606	−	2.93019i	−0.169422	−	0.126447i
$538$		−	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
$543$	16.4027	+	5.56338i	0.703908	+	0.238747i
$544$	9.27051	−	28.5317i	0.397470	−	1.22329i
$545$	3.70820	−	11.4127i	0.158842	−	0.488865i
$546$	−9.84163	−	3.33803i	−0.421183	−	0.142854i
$547$	−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
$555$	11.6314	+	37.4261i	0.493726	+	1.58865i
$556$	1.34500	+	0.437016i	0.0570406	+	0.0185336i
$557$	1.61803	−	1.17557i	0.0685583	−	0.0498105i	−0.552978	−	0.833196i	$-0.686509\pi$
$557$	1.61803	−	1.17557i	0.0685583	−	0.0498105i	0.621537	+	0.783385i	$0.286509\pi$
$558$	−4.94305	+	3.40092i	−0.209256	+	0.143972i
$559$	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	0.998289	−	0.0584805i	$-0.0186256\pi$
$563$	3.70820	+	11.4127i	0.156282	+	0.480987i	−0.842006	+	0.539468i	$0.818626\pi$
$564$	−4.89858	−	0.0628954i	−0.206267	−	0.00264837i
$565$	6.47214	−	4.70228i	0.272285	−	0.197826i
$566$	25.5549	+	8.30330i	1.07415	+	0.349014i
$567$	6.94284	+	10.6676i	0.291572	+	0.447996i
$568$	4.98752	+	6.86474i	0.209272	+	0.288038i
$569$	30.7426	+	22.3358i	1.28880	+	0.936367i	0.999780	−	0.0209564i	$-0.00667113\pi$
$569$	30.7426	+	22.3358i	1.28880	+	0.936367i	0.289018	+	0.957324i	$0.406671\pi$
$570$	−12.4318	+	16.6569i	−0.520709	+	0.697680i
$571$			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
$576$	−5.97444	−	20.1322i	−0.248935	−	0.838842i
$577$	−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
$579$	11.8017	−	34.7954i	0.490462	−	1.44605i
$580$	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
$585$	35.9881	+	0.924294i	1.48793	+	0.0382148i
$586$	1.61803	+	1.17557i	0.0668404	+	0.0485624i
$587$	6.65003	+	9.15298i	0.274476	+	0.377784i	0.923894	−	0.382647i	$-0.124988\pi$
$587$	6.65003	+	9.15298i	0.274476	+	0.377784i	−0.649418	+	0.760431i	$0.724988\pi$
$588$	−8.27007	+	2.57020i	−0.341052	+	0.105993i
$589$	8.06998	+	2.62210i	0.332518	+	0.108042i
$590$	−25.8885	+	18.8091i	−1.06581	+	0.774360i
$591$	0.489211	−	38.1020i	0.0201235	−	1.56731i
$592$	−2.47214	−	7.60845i	−0.101604	−	0.312705i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$		0			0
$595$	24.0000			0.983904
$596$	−1.85410	−	5.70634i	−0.0759470	−	0.233741i
$597$	0.0444738	−	3.46382i	0.00182019	−	0.141765i
$598$		0			0
$599$	32.2799	+	10.4884i	1.31892	+	0.428544i	0.882125	−	0.471016i	$-0.156113\pi$
$599$	32.2799	+	10.4884i	1.31892	+	0.428544i	0.436798	+	0.899560i	$0.356113\pi$
$600$	14.8861	−	4.62636i	0.607724	−	0.188871i
$601$	−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
$603$	−5.99802	−	0.154049i	−0.244258	−	0.00627336i
$604$			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
$609$	1.57356	−	4.63939i	0.0637639	−	0.187997i
$610$	8.65248	−	26.6296i	0.350329	−	1.07820i
$611$	−3.70820	+	11.4127i	−0.150018	+	0.461708i
$612$	5.12094	+	17.2562i	0.207002	+	0.697540i
$613$	−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	$-0.784579\pi$
$617$		−	31.1127i		−	1.25255i	0.779602	−	0.626275i	$-0.215421\pi$
$618$	−8.28784	+	11.1046i	−0.333386	+	0.446692i
$619$	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
$624$	−7.34786	−	0.0943431i	−0.294150	−	0.00377675i
$625$	−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
$630$	9.88610	−	6.80184i	0.393872	−	0.270992i
$631$	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
$633$	−13.8123	−	44.4435i	−0.548990	−	1.76647i
$634$	14.9626	+	20.5942i	0.594240	+	0.817901i
$635$	−22.6525	−	16.4580i	−0.898936	−	0.653115i
$636$	7.85212	+	5.86039i	0.311357	+	0.232380i
$637$			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	−0.999365	−	0.0356372i	$-0.988654\pi$
$641$	−16.6251	+	22.8825i	−0.656651	+	0.903803i	0.342714	+	0.939440i	$0.388654\pi$
$642$	26.2443	+	8.90140i	1.03578	+	0.351310i
$643$	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
$645$	−19.6833	−	6.67605i	−0.775027	−	0.262869i
$646$	−14.9626	+	20.5942i	−0.588694	+	0.810268i
$647$	−5.37999	+	1.74806i	−0.211509	+	0.0687235i	−0.412855	−	0.910797i	$-0.635468\pi$
$647$	−5.37999	+	1.74806i	−0.211509	+	0.0687235i	0.201346	+	0.979520i	$0.435468\pi$
$648$	21.0000	+	16.9706i	0.824958	+	0.666667i
$649$		0			0
$650$		−	12.7279i		−	0.499230i
$651$	−3.92606	−	2.93019i	−0.153875	−	0.114843i
$652$	16.1803	+	11.7557i	0.633671	+	0.460389i
$653$	6.65003	+	9.15298i	0.260236	+	0.358184i	0.919063	−	0.394110i	$-0.128947\pi$
$653$	6.65003	+	9.15298i	0.260236	+	0.358184i	−0.658827	+	0.752294i	$0.728947\pi$
$654$	−2.18089	−	7.01739i	−0.0852795	−	0.274402i
$655$		0			0
$656$	4.85410	−	3.52671i	0.189521	−	0.137695i
$657$	−2.40481	−	3.49526i	−0.0938207	−	0.136363i
$658$	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
$663$	44.0872	+	0.566059i	1.71220	+	0.0219839i
$664$	−38.8328	+	28.2137i	−1.50701	+	1.09490i
$665$	−16.1400	−	5.24419i	−0.625881	−	0.203361i
$666$	19.0478	+	14.6007i	0.738088	+	0.565766i
$667$		0			0
$668$	9.70820	+	7.05342i	0.375622	+	0.272905i
$669$	−24.8635	+	33.3137i	−0.961279	+	1.28798i
$670$			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
$675$	−9.64149	+	12.2491i	−0.371101	+	0.471470i
$676$	1.54508	−	4.75528i	0.0594263	−	0.182895i
$677$	−11.7426	+	36.1401i	−0.451307	+	1.38898i	0.424111	+	0.905610i	$0.360587\pi$
$677$	−11.7426	+	36.1401i	−0.451307	+	1.38898i	−0.875417	+	0.483368i	$0.839413\pi$
$678$	1.57356	−	4.63939i	0.0604322	−	0.178175i
$679$	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	$0.202946\pi$
$683$			31.1127i			1.19049i	−0.803543	+	0.595247i	$0.797054\pi$
$684$	0.326787	−	12.7237i	0.0124950	−	0.486504i
$685$	6.47214	+	4.70228i	0.247288	+	0.179665i
$686$	9.97505	+	13.7295i	0.380849	+	0.524194i
$687$	−39.6963	+	12.3370i	−1.51451	+	0.470685i
$688$	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
$696$	0.133421	−	10.3914i	0.00505732	−	0.393887i
$697$	−29.1246	+	21.1603i	−1.10317	+	0.801502i
$698$	−4.03499	−	1.31105i	−0.152727	−	0.0496239i
$699$	−16.5401	+	5.14040i	−0.625606	+	0.194428i
$700$	2.49376	+	3.43237i	0.0942553	+	0.129731i
$701$	−4.85410	−	3.52671i	−0.183337	−	0.133202i	0.492331	−	0.870408i	$-0.336145\pi$
$701$	−4.85410	−	3.52671i	−0.183337	−	0.133202i	−0.675668	+	0.737206i	$0.736145\pi$
$702$	18.3209	−	12.2616i	0.691476	−	0.462783i
$703$		−	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
$708$	6.29424	−	18.5575i	0.236552	−	0.697435i
$709$	−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
$711$	12.2020	−	3.62105i	0.457609	−	0.135800i
$712$		0			0
$713$		0			0
$714$	12.0000	−	8.48528i	0.449089	−	0.317554i
$715$		0			0
$716$		−	2.82843i		−	0.105703i
$717$	16.5757	−	22.2092i	0.619030	−	0.829416i
$718$	−16.1803	−	11.7557i	−0.603845	−	0.438719i
$719$	−11.6376	−	16.0177i	−0.434008	−	0.597360i	0.534860	−	0.844941i	$-0.320364\pi$
$719$	−11.6376	−	16.0177i	−0.434008	−	0.597360i	−0.968867	+	0.247581i	$0.920364\pi$
$720$	5.16213	−	6.73442i	0.192381	−	0.250977i
$721$	−10.7600	−	3.49613i	−0.400722	−	0.130203i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$	−7.34786	−	0.0943431i	−0.273270	−	0.00350866i
$724$	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
$729$	−26.9199	−	2.07783i	−0.997034	−	0.0769568i
$730$	−3.23607	+	2.35114i	−0.119772	+	0.0870196i
$731$	−24.2099	−	7.86629i	−0.895437	−	0.290945i
$732$	5.08874	+	16.3739i	0.188085	+	0.605197i
$733$	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
$735$	−19.6303	−	14.6510i	−0.724075	−	0.540409i
$736$		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
$741$	−29.5249	−	10.0141i	−1.08462	−	0.367876i
$742$	2.47214	−	7.60845i	0.0907550	−	0.279315i
$743$	−4.94427	+	15.2169i	−0.181388	+	0.558254i	−0.999867	−	0.0162814i	$-0.994817\pi$
$743$	−4.94427	+	15.2169i	−0.181388	+	0.558254i	0.818480	+	0.574535i	$0.194817\pi$
$744$	−9.84163	−	3.33803i	−0.360811	−	0.122378i
$745$	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
$750$	−7.85212	−	5.86039i	−0.286719	−	0.213991i
$751$	−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
$753$	−13.0853	−	42.1043i	−0.476856	−	1.53437i
$754$	−8.06998	−	2.62210i	−0.293891	−	0.0954911i
$755$	−9.70820	+	7.05342i	−0.353318	+	0.256700i
$756$	−2.53824	+	6.89618i	−0.0923147	+	0.250812i
$757$	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	0.879295	−	0.476278i	$-0.158014\pi$
$761$	−3.09017	−	9.51057i	−0.112019	−	0.344758i	−0.991314	+	0.131520i	$0.958014\pi$
$762$	−17.1450	−	0.220134i	−0.621098	−	0.00797461i
$763$	4.85410	−	3.52671i	0.175730	−	0.127676i
$764$	−18.8300	−	6.11822i	−0.681244	−	0.221350i
$765$	−30.9728	+	40.4065i	−1.11982	+	1.46090i
$766$	−3.32502	−	4.57649i	−0.120138	−	0.165355i
$767$	−38.8328	−	28.2137i	−1.40217	−	1.01874i
$768$	17.6117	−	23.5972i	0.635506	−	0.851492i
$769$		−	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	$-0.591013\pi$
$773$	19.9501	−	27.4589i	0.717555	−	0.987630i	0.999601	−	0.0282290i	$-0.00898675\pi$
$774$	−12.2020	+	3.62105i	−0.438591	+	0.130156i
$775$	1.85410	−	5.70634i	0.0666013	−	0.204978i
$776$	1.85410	−	5.70634i	0.0665584	−	0.204846i
$777$	−6.29424	+	18.5575i	−0.225805	+	0.665748i
$778$	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
$783$	5.78016	+	8.63653i	0.206566	+	0.308645i
$784$	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
$795$	−0.355790	+	27.7105i	−0.0126186	+	0.982791i
$796$	1.61803	−	1.17557i	0.0573497	−	0.0416670i
$797$	2.68999	+	0.874032i	0.0952845	+	0.0309598i	0.356271	−	0.934383i	$-0.384048\pi$
$797$	2.68999	+	0.874032i	0.0952845	+	0.0309598i	−0.260987	+	0.965342i	$0.584048\pi$
$798$	−9.92408	+	3.08424i	−0.351309	+	0.109181i
$799$	−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
$807$	−15.7356	+	46.3939i	−0.553919	+	1.63314i
$808$	9.27051	−	28.5317i	0.326135	−	1.00374i
$809$	15.4508	−	47.5528i	0.543223	−	1.67187i	−0.181955	−	0.983307i	$-0.558243\pi$
$809$	15.4508	−	47.5528i	0.543223	−	1.67187i	0.725178	−	0.688561i	$-0.241757\pi$
$810$	−1.30672	+	25.4223i	−0.0459134	+	0.893248i
$811$	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
$816$	6.21588	−	8.32844i	0.217599	−	0.291554i
$817$	14.5623	+	10.5801i	0.509471	+	0.370152i
$818$	−2.49376	−	3.43237i	−0.0871923	−	0.120010i
$819$	14.2859	+	10.9505i	0.499188	+	0.382643i
$820$	−16.1400	−	5.24419i	−0.563632	−	0.183135i
$821$	−33.9787	+	24.6870i	−1.18587	+	0.861582i	−0.992821	−	0.119609i	$-0.961836\pi$
$821$	−33.9787	+	24.6870i	−1.18587	+	0.861582i	−0.193044	+	0.981190i	$0.561836\pi$
$822$	4.89858	+	0.0628954i	0.170857	+	0.00219373i
$823$	−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	0.994600	−	0.103787i	$-0.0330962\pi$
$827$	3.70820	+	11.4127i	0.128947	+	0.396858i	−0.865653	+	0.500645i	$0.833096\pi$
$828$		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
$831$	2.18089	+	7.01739i	0.0756542	+	0.243430i
$832$	−17.4563	−	24.0266i	−0.605189	−	0.832972i
$833$	−24.2705	−	17.6336i	−0.840923	−	0.610967i
$834$	1.96303	+	1.46510i	0.0679742	+	0.0507322i
$835$			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	−0.311244	−	0.950330i	$-0.600745\pi$
$839$	19.9501	−	27.4589i	0.688754	−	0.947988i	0.999997	+	0.00234204i	$0.000745495\pi$
$840$	19.6833	+	6.67605i	0.679137	+	0.230346i
$841$	−7.72542	+	23.7764i	−0.266394	+	0.819876i
$842$	−6.18034	+	19.0211i	−0.212989	+	0.655511i
$843$	−9.84163	−	3.33803i	−0.338964	−	0.114968i
$844$	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
$849$	−37.2976	−	27.8368i	−1.28005	−	0.955358i
$850$	14.5623	+	10.5801i	0.499483	+	0.362896i
$851$		0			0
$852$	−1.45393	−	4.67826i	−0.0498107	−	0.160274i
$853$	−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
$855$	29.6583	−	20.4055i	1.01429	−	0.697854i
$856$	14.8328	+	45.6507i	0.506975	+	1.56031i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−3.70820	−	11.4127i	−0.126449	−	0.389169i
$861$	−14.6957	−	0.188686i	−0.500829	−	0.00643041i
$862$	25.8885	−	18.8091i	0.881767	−	0.640641i
$863$	32.2799	+	10.4884i	1.09882	+	0.357029i	0.801649	−	0.597795i	$-0.203956\pi$
$863$	32.2799	+	10.4884i	1.09882	+	0.357029i	0.297173	+	0.954824i	$0.403956\pi$
$864$	−1.00044	+	25.9615i	−0.0340357	+	0.883228i
$865$	−9.97505	−	13.7295i	−0.339162	−	0.466816i
$866$	−24.2705	−	17.6336i	−0.824745	−	0.599213i
$867$	−19.6836	+	26.3734i	−0.668491	+	0.895687i
$868$		−	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
$873$	1.70698	+	5.75206i	0.0577726	+	0.194678i
$874$		0			0
$875$	2.47214	−	7.60845i	0.0835734	−	0.257213i
$876$	0.786780	−	2.31969i	0.0265828	−	0.0783752i
$877$	−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	$-0.824399\pi$
$881$		−	31.1127i		−	1.04821i	0.851653	−	0.524107i	$-0.175601\pi$
$882$	−14.9951	−	0.385122i	−0.504910	−	0.0129677i
$883$	−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
$885$	52.9284	−	16.4493i	1.77917	−	0.552937i
$886$	−26.8999	−	8.74032i	−0.903721	−	0.293637i
$887$	19.4164	−	14.1068i	0.651939	−	0.473662i	−0.211992	−	0.977271i	$-0.567995\pi$
$887$	19.4164	−	14.1068i	0.651939	−	0.473662i	0.863931	+	0.503610i	$0.167995\pi$
$888$	−0.533685	+	41.5658i	−0.0179093	+	1.39486i
$889$	−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
$894$	0.133421	−	10.3914i	0.00446228	−	0.347542i
$895$	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
$900$	−8.99703	−	0.231073i	−0.299901	−	0.00770245i
$901$			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
$906$	−2.36034	+	6.95908i	−0.0784171	+	0.231200i
$907$	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
$909$	8.53491	+	28.7603i	0.283085	+	0.953919i
$910$	9.97505	−	13.7295i	0.330670	−	0.455128i
$911$	−34.9699	+	11.3624i	−1.15861	+	0.376454i	−0.824378	−	0.566039i	$-0.808475\pi$
$911$	−34.9699	+	11.3624i	−1.15861	+	0.376454i	−0.334227	+	0.942493i	$0.608475\pi$
$912$	−6.00000	+	4.24264i	−0.198680	+	0.140488i
$913$		0			0
$914$		−	9.89949i		−	0.327446i
$915$	−29.0074	+	38.8660i	−0.958956	+	1.28487i
$916$	−19.4164	−	14.1068i	−0.641536	−	0.466103i
$917$		0			0
$918$	−1.20053	+	31.1538i	−0.0396233	+	1.02823i
$919$	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
$921$	−7.34786	−	0.0943431i	−0.242120	−	0.00310871i
$922$	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
$927$	19.7722	−	13.6037i	0.649404	−	0.446804i
$928$	8.09017	−	5.87785i	0.265573	−	0.192950i
$929$	2.68999	+	0.874032i	0.0882558	+	0.0286761i	0.352812	−	0.935694i	$-0.385225\pi$
$929$	2.68999	+	0.874032i	0.0882558	+	0.0286761i	−0.264556	+	0.964370i	$0.585225\pi$
$930$	−2.90785	−	9.35652i	−0.0953522	−	0.306812i
$931$	12.4688	+	17.1618i	0.408649	+	0.562457i
$932$	−8.09017	−	5.87785i	−0.265002	−	0.192535i
$933$	39.2606	+	29.3019i	1.28534	+	0.959302i
$934$		−	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
$939$	−19.6833	−	6.67605i	−0.642339	−	0.217865i
$940$	2.47214	−	7.60845i	0.0806322	−	0.248160i
$941$	−11.7426	+	36.1401i	−0.382799	+	1.17814i	0.555265	+	0.831674i	$0.312617\pi$
$941$	−11.7426	+	36.1401i	−0.382799	+	1.17814i	−0.938064	+	0.346462i	$0.887383\pi$
$942$	32.8054	+	11.1268i	1.06886	+	0.362529i
$943$		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	$0.168697\pi$
$947$			31.1127i			1.01103i	−0.862819	+	0.505513i	$0.831303\pi$
$948$	5.88909	+	4.39529i	0.191269	+	0.142752i
$949$	−4.85410	−	3.52671i	−0.157571	−	0.114482i
$950$	−7.48128	−	10.2971i	−0.242725	−	0.334082i
$951$	−13.0853	−	42.1043i	−0.424321	−	1.36533i
$952$	24.2099	+	7.86629i	0.784649	+	0.254948i
$953$	1.61803	−	1.17557i	0.0524133	−	0.0380805i	−0.561270	−	0.827633i	$-0.689687\pi$
$953$	1.61803	−	1.17557i	0.0524133	−	0.0380805i	0.613683	+	0.789552i	$0.289687\pi$
$954$	9.61926	+	13.9811i	0.311435	+	0.452653i
$955$	−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
$960$	34.2900	+	0.440268i	1.10671	+	0.0142096i
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	32.2799	+	10.4884i	1.04075	+	0.338159i
$963$	−38.0956	−	29.2014i	−1.22761	−	0.941003i
$964$	−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	−0.358399	−	0.933569i	$-0.616677\pi$
$971$	19.9501	−	27.4589i	0.640229	−	0.881200i	0.998628	+	0.0523690i	$0.0166772\pi$
$972$	−8.33478	−	13.1731i	−0.267338	−	0.422529i
$973$	−0.618034	+	1.90211i	−0.0198133	+	0.0609789i
$974$	0.618034	−	1.90211i	0.0198031	−	0.0609476i
$975$	−7.08102	+	20.8772i	−0.226774	+	0.668607i
$976$	5.81878	−	8.00886i	0.186255	−	0.256357i
$977$	24.2099	−	7.86629i	0.774545	−	0.251665i	0.105035	−	0.994468i	$-0.466504\pi$
$977$	24.2099	−	7.86629i	0.774545	−	0.251665i	0.669509	+	0.742804i	$0.266504\pi$
$978$	20.0000	+	28.2843i	0.639529	+	0.904431i
$979$		0			0
$980$		−	14.1421i		−	0.451754i
$981$	−0.326787	+	12.7237i	−0.0104335	+	0.406237i
$982$	−16.1803	−	11.7557i	−0.516335	−	0.375140i
$983$	6.65003	+	9.15298i	0.212103	+	0.291935i	0.901791	−	0.432171i	$-0.142252\pi$
$983$	6.65003	+	9.15298i	0.212103	+	0.291935i	−0.689688	+	0.724106i	$0.742252\pi$
$984$	−29.7723	+	9.25273i	−0.949105	+	0.294966i
$985$	59.1799	+	19.2287i	1.88563	+	0.612677i
$986$	9.70820	−	7.05342i	0.309172	−	0.224627i
$987$	0.0889475	−	6.92763i	0.00283123	−	0.220509i
$988$	−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
$993$	−0.444738	+	34.6382i	−0.0141133	+	1.09921i
$994$	−3.23607	+	2.35114i	−0.102642	+	0.0745737i
$995$	5.37999	+	1.74806i	0.170557	+	0.0554174i
$996$	26.4642	−	8.22465i	0.838551	−	0.260608i
$997$	−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
$999$	−23.1207	−	34.5461i	−0.731505	−	1.09299i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.0222369 - 1.73191i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.68999 + 0.874032i) q^{5} +(1.65401 - 0.514040i) q^{6} +(0.831254 + 1.14412i) q^{7} +(2.42705 + 1.76336i) q^{8} +(-2.99901 - 0.0770245i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.0222369 - 1.73191i) q^{3} +(0.809017 - 0.587785i) q^{4} +(2.68999 + 0.874032i) q^{5} +(1.65401 - 0.514040i) q^{6} +(0.831254 + 1.14412i) q^{7} +(2.42705 + 1.76336i) q^{8} +(-2.99901 - 0.0770245i) q^{9} +2.82843i q^{10} +(-1.00000 - 1.41421i) q^{12} +(-4.03499 + 1.31105i) q^{13} +(-0.831254 + 1.14412i) q^{14} +(1.57356 - 4.63939i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.85410 - 5.70634i) q^{17} +(-0.853491 - 2.87603i) q^{18} +(-2.49376 + 3.43237i) q^{19} +(2.68999 - 0.874032i) q^{20} +(2.00000 - 1.41421i) q^{21} +(3.10794 - 4.16422i) q^{24} +(2.42705 + 1.76336i) q^{25} +(-2.49376 - 3.43237i) q^{26} +(-0.200088 + 5.19230i) q^{27} +(1.34500 + 0.437016i) q^{28} +(1.61803 - 1.17557i) q^{29} +(4.89858 + 0.0628954i) q^{30} +(-0.618034 - 1.90211i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(1.23607 + 3.80423i) q^{35} +(-2.47152 + 1.70046i) q^{36} +(-6.47214 + 4.70228i) q^{37} +(-4.03499 - 1.31105i) q^{38} +(2.18089 + 7.01739i) q^{39} +(4.98752 + 6.86474i) q^{40} +(-4.85410 - 3.52671i) q^{41} +(1.96303 + 1.46510i) q^{42} -4.24264i q^{43} +(-8.00000 - 2.82843i) q^{45} +(1.66251 - 2.28825i) q^{47} +(1.64027 + 0.556338i) q^{48} +(1.54508 - 4.75528i) q^{49} +(-0.927051 + 2.85317i) q^{50} +(-9.84163 - 3.33803i) q^{51} +(-2.49376 + 3.43237i) q^{52} +(-5.37999 + 1.74806i) q^{53} +(-5.00000 + 1.41421i) q^{54} +4.24264i q^{56} +(5.88909 + 4.39529i) q^{57} +(1.61803 + 1.17557i) q^{58} +(6.65003 + 9.15298i) q^{59} +(-1.45393 - 4.67826i) q^{60} +(-9.41498 - 3.05911i) q^{61} +(1.61803 - 1.17557i) q^{62} +(-2.40481 - 3.49526i) 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} +(-7.14293 - 5.47527i) q^{72} +(0.831254 + 1.14412i) q^{73} +(-6.47214 - 4.70228i) q^{74} +(3.10794 - 4.16422i) q^{75} +4.24264i q^{76} +(-6.00000 + 4.24264i) q^{78} +(-4.03499 + 1.31105i) q^{79} +(-1.66251 + 2.28825i) q^{80} +(8.98813 + 0.461994i) q^{81} +(1.85410 - 5.70634i) q^{82} +(-4.94427 + 15.2169i) q^{83} +(0.786780 - 2.31969i) q^{84} +(9.97505 - 13.7295i) q^{85} +(4.03499 - 1.31105i) q^{86} +(-2.00000 - 2.82843i) q^{87} +(0.217858 - 8.48248i) q^{90} +(-4.85410 - 3.52671i) q^{91} +(-3.30803 + 1.02808i) q^{93} +(2.68999 + 0.874032i) q^{94} +(-9.70820 + 7.05342i) q^{95} +(0.111184 - 8.65954i) q^{96} +(-0.618034 - 1.90211i) q^{97} +5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} + 16 q^{21} + 6 q^{24} + 6 q^{25} + 10 q^{27} + 4 q^{29} + 8 q^{30} + 4 q^{31} + 40 q^{32} + 48 q^{34} - 8 q^{35} - 2 q^{36} - 16 q^{37} + 12 q^{39} - 12 q^{41} - 4 q^{42} - 64 q^{45} + 2 q^{48} - 10 q^{49} + 6 q^{50} - 12 q^{51} - 40 q^{54} - 12 q^{57} + 4 q^{58} - 8 q^{60} + 4 q^{62} - 8 q^{63} - 14 q^{64} - 96 q^{65} + 16 q^{67} + 12 q^{68} - 8 q^{70} - 6 q^{72} - 16 q^{74} + 6 q^{75} - 48 q^{78} + 14 q^{81} - 12 q^{82} + 32 q^{83} + 4 q^{84} - 16 q^{87} + 16 q^{90} - 12 q^{91} + 4 q^{93} - 24 q^{95} - 10 q^{96} + 4 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 8 * q^12 + 8 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 + 16 * q^21 + 6 * q^24 + 6 * q^25 + 10 * q^27 + 4 * q^29 + 8 * q^30 + 4 * q^31 + 40 * q^32 + 48 * q^34 - 8 * q^35 - 2 * q^36 - 16 * q^37 + 12 * q^39 - 12 * q^41 - 4 * q^42 - 64 * q^45 + 2 * q^48 - 10 * q^49 + 6 * q^50 - 12 * q^51 - 40 * q^54 - 12 * q^57 + 4 * q^58 - 8 * q^60 + 4 * q^62 - 8 * q^63 - 14 * q^64 - 96 * q^65 + 16 * q^67 + 12 * q^68 - 8 * q^70 - 6 * q^72 - 16 * q^74 + 6 * q^75 - 48 * q^78 + 14 * q^81 - 12 * q^82 + 32 * q^83 + 4 * q^84 - 16 * q^87 + 16 * q^90 - 12 * q^91 + 4 * q^93 - 24 * q^95 - 10 * q^96 + 4 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

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