LMFDB - Embedded newform 847.2.f.u.372.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(148,847)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("847.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,1,-8,-1,12,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.3
Root			$2.52809 + 1.83676i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.u.148.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.656626 - 2.02089i) q^{2} +(2.52809 - 1.83676i) q^{3} +(-2.03479 - 1.47836i) q^{4} +(0.149831 + 0.461131i) q^{5} +(-2.05188 - 6.31504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.885558 + 0.643395i) q^{8} +(2.09047 - 6.43381i) q^{9} +1.03028 q^{10} -7.85952 q^{12} +(-1.73351 + 5.33519i) q^{13} +(1.71907 - 1.24898i) q^{14} +(1.22577 + 0.890576i) q^{15} +(-0.835692 - 2.57200i) q^{16} +(-1.73351 - 5.33519i) q^{17} +(-11.6293 - 8.44921i) q^{18} +(-4.27165 + 3.10353i) q^{19} +(0.376845 - 1.15981i) q^{20} +3.12489 q^{21} +2.48486 q^{23} +(-1.05700 + 3.25312i) q^{24} +(3.85489 - 2.80074i) q^{25} +(9.64354 + 7.00644i) q^{26} +(-3.63556 - 11.1891i) q^{27} +(-0.777220 - 2.39204i) q^{28} +(4.27165 + 3.10353i) q^{29} +(2.60463 - 1.89237i) q^{30} +(-2.20171 + 6.77617i) q^{31} -7.93567 q^{32} -11.9201 q^{34} +(-0.149831 + 0.461131i) q^{35} +(-13.7652 + 10.0010i) q^{36} +(0.190193 + 0.138183i) q^{37} +(3.46701 + 10.6704i) q^{38} +(5.41701 + 16.6718i) q^{39} +(-0.429373 - 0.311958i) q^{40} +(1.93375 - 1.40496i) q^{41} +(2.05188 - 6.31504i) q^{42} -1.03028 q^{43} +3.28005 q^{45} +(1.63162 - 5.02162i) q^{46} +(1.30231 - 0.946186i) q^{47} +(-6.83684 - 4.96726i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-3.12876 - 9.62934i) q^{50} +(-14.1819 - 10.3038i) q^{51} +(11.4147 - 8.29323i) q^{52} +(-0.936407 + 2.88196i) q^{53} -24.9991 q^{54} -1.09461 q^{56} +(-5.09864 + 15.6920i) q^{57} +(9.07676 - 6.59465i) q^{58} +(-2.52809 - 1.83676i) q^{59} +(-1.17760 - 3.62427i) q^{60} +(0.738629 + 2.27327i) q^{61} +(12.2482 + 8.89881i) q^{62} +(5.47293 - 3.97631i) q^{63} +(-3.53938 + 10.8931i) q^{64} -2.71995 q^{65} +10.0147 q^{67} +(-4.36001 + 13.4187i) q^{68} +(6.28194 - 4.56410i) q^{69} +(0.833511 + 0.605581i) q^{70} +(3.73145 + 11.4842i) q^{71} +(2.28825 + 7.04251i) q^{72} +(1.93375 + 1.40496i) q^{73} +(0.404138 - 0.293623i) q^{74} +(4.60120 - 14.1610i) q^{75} +13.2800 q^{76} +37.2489 q^{78} +(-2.79051 + 8.58830i) q^{79} +(1.06082 - 0.770727i) q^{80} +(-13.3239 - 9.68039i) q^{81} +(-1.56950 - 4.83043i) q^{82} +(0.994879 + 3.06192i) q^{83} +(-6.35848 - 4.61971i) q^{84} +(2.20049 - 1.59875i) q^{85} +(-0.676506 + 2.08207i) q^{86} +16.4995 q^{87} -1.26537 q^{89} +(2.15376 - 6.62860i) q^{90} +(-4.53838 + 3.29733i) q^{91} +(-5.05617 - 3.67352i) q^{92} +(6.88009 + 21.1748i) q^{93} +(-1.05700 - 3.25312i) q^{94} +(-2.07116 - 1.50479i) q^{95} +(-20.0620 + 14.5759i) q^{96} +(-2.71786 + 8.36472i) q^{97} +2.12489 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23}+ \cdots - 8 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.656626	−	2.02089i	0.464304	−	1.42898i	−0.395551	−	0.918444i	$-0.629446\pi$
$2$	0.656626	−	2.02089i	0.464304	−	1.42898i	0.859855	−	0.510538i	$-0.170554\pi$
$3$	2.52809	−	1.83676i	1.45959	−	1.06045i	0.476122	−	0.879379i	$-0.342042\pi$
$3$	2.52809	−	1.83676i	1.45959	−	1.06045i	0.983469	−	0.181075i	$-0.0579578\pi$
$4$	−2.03479	−	1.47836i	−1.01739	−	0.739181i
$5$	0.149831	+	0.461131i	0.0670063	+	0.206224i	0.978954	−	0.204083i	$-0.0654214\pi$
$5$	0.149831	+	0.461131i	0.0670063	+	0.206224i	−0.911947	+	0.410307i	$0.865421\pi$
$6$	−2.05188	−	6.31504i	−0.837677	−	2.57810i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−0.885558	+	0.643395i	−0.313092	+	0.227475i
$9$	2.09047	−	6.43381i	0.696824	−	2.14460i
$10$	1.03028			0.325802
$11$		0			0
$11$		0			0
$12$	−7.85952			−2.26885
$13$	−1.73351	+	5.33519i	−0.480788	+	1.47971i	0.357201	+	0.934028i	$0.383731\pi$
$13$	−1.73351	+	5.33519i	−0.480788	+	1.47971i	−0.837989	+	0.545687i	$0.816269\pi$
$14$	1.71907	−	1.24898i	0.459440	−	0.333803i
$15$	1.22577	+	0.890576i	0.316493	+	0.229946i
$16$	−0.835692	−	2.57200i	−0.208923	−	0.642999i
$17$	−1.73351	−	5.33519i	−0.420437	−	1.29397i	−0.907296	−	0.420492i	$-0.861857\pi$
$17$	−1.73351	−	5.33519i	−0.420437	−	1.29397i	0.486859	−	0.873481i	$-0.338143\pi$
$18$	−11.6293	−	8.44921i	−2.74106	−	1.99150i
$19$	−4.27165	+	3.10353i	−0.979983	+	0.711999i	−0.957705	−	0.287752i	$-0.907092\pi$
$19$	−4.27165	+	3.10353i	−0.979983	+	0.711999i	−0.0222783	+	0.999752i	$0.507092\pi$
$20$	0.376845	−	1.15981i	0.0842650	−	0.259341i
$21$	3.12489			0.681906
$22$		0			0
$23$	2.48486			0.518130			0.259065	−	0.965860i	$-0.416586\pi$
$23$	2.48486			0.518130			0.259065	+	0.965860i	$0.416586\pi$
$24$	−1.05700	+	3.25312i	−0.215760	+	0.664040i
$25$	3.85489	−	2.80074i	0.770978	−	0.560149i
$26$	9.64354	+	7.00644i	1.89125	+	1.37408i
$27$	−3.63556	−	11.1891i	−0.699663	−	2.15334i
$28$	−0.777220	−	2.39204i	−0.146881	−	0.452053i
$29$	4.27165	+	3.10353i	0.793225	+	0.576312i	0.908919	−	0.416973i	$-0.136909\pi$
$29$	4.27165	+	3.10353i	0.793225	+	0.576312i	−0.115694	+	0.993285i	$0.536909\pi$
$30$	2.60463	−	1.89237i	0.475537	−	0.345498i
$31$	−2.20171	+	6.77617i	−0.395439	+	1.21704i	0.533180	+	0.846002i	$0.320997\pi$
$31$	−2.20171	+	6.77617i	−0.395439	+	1.21704i	−0.928619	+	0.371034i	$0.879003\pi$
$32$	−7.93567			−1.40284
$33$		0			0
$34$	−11.9201			−2.04428
$35$	−0.149831	+	0.461131i	−0.0253260	+	0.0779454i
$36$	−13.7652	+	10.0010i	−2.29419	+	1.66683i
$37$	0.190193	+	0.138183i	0.0312675	+	0.0227172i	0.603309	−	0.797507i	$-0.293848\pi$
$37$	0.190193	+	0.138183i	0.0312675	+	0.0227172i	−0.572042	+	0.820225i	$0.693848\pi$
$38$	3.46701	+	10.6704i	0.562424	+	1.73096i
$39$	5.41701	+	16.6718i	0.867416	+	2.66963i
$40$	−0.429373	−	0.311958i	−0.0678899	−	0.0493249i
$41$	1.93375	−	1.40496i	0.302002	−	0.219417i	−0.426455	−	0.904509i	$-0.640238\pi$
$41$	1.93375	−	1.40496i	0.302002	−	0.219417i	0.728457	+	0.685092i	$0.240238\pi$
$42$	2.05188	−	6.31504i	0.316612	−	0.974431i
$43$	−1.03028			−0.157116			−0.0785578	−	0.996910i	$-0.525032\pi$
$43$	−1.03028			−0.157116			−0.0785578	+	0.996910i	$0.525032\pi$
$44$		0			0
$45$	3.28005			0.488961
$46$	1.63162	−	5.02162i	0.240570	−	0.740398i
$47$	1.30231	−	0.946186i	0.189962	−	0.138015i	−0.488739	−	0.872430i	$-0.662543\pi$
$47$	1.30231	−	0.946186i	0.189962	−	0.138015i	0.678701	+	0.734414i	$0.262543\pi$
$48$	−6.83684	−	4.96726i	−0.986814	−	0.716962i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−3.12876	−	9.62934i	−0.442474	−	1.36179i
$51$	−14.1819	−	10.3038i	−1.98587	−	1.44282i
$52$	11.4147	−	8.29323i	1.58293	−	1.15006i
$53$	−0.936407	+	2.88196i	−0.128625	+	0.395868i	−0.994544	−	0.104316i	$-0.966735\pi$
$53$	−0.936407	+	2.88196i	−0.128625	+	0.395868i	0.865919	+	0.500185i	$0.166735\pi$
$54$	−24.9991			−3.40194
$55$		0			0
$56$	−1.09461			−0.146273
$57$	−5.09864	+	15.6920i	−0.675331	+	2.07846i
$58$	9.07676	−	6.59465i	1.19184	−	0.865920i
$59$	−2.52809	−	1.83676i	−0.329129	−	0.239126i	0.410932	−	0.911666i	$-0.365203\pi$
$59$	−2.52809	−	1.83676i	−0.329129	−	0.239126i	−0.740061	+	0.672540i	$0.765203\pi$
$60$	−1.17760	−	3.62427i	−0.152027	−	0.467891i
$61$	0.738629	+	2.27327i	0.0945717	+	0.291062i	0.987142	−	0.159847i	$-0.0511000\pi$
$61$	0.738629	+	2.27327i	0.0945717	+	0.291062i	−0.892570	+	0.450909i	$0.851100\pi$
$62$	12.2482	+	8.89881i	1.55552	+	1.13015i
$63$	5.47293	−	3.97631i	0.689524	−	0.500968i
$64$	−3.53938	+	10.8931i	−0.442422	+	1.36164i
$65$	−2.71995			−0.337369
$66$		0			0
$67$	10.0147			1.22349			0.611744	−	0.791056i	$-0.290468\pi$
$67$	10.0147			1.22349			0.611744	+	0.791056i	$0.290468\pi$
$68$	−4.36001	+	13.4187i	−0.528729	+	1.62726i
$69$	6.28194	−	4.56410i	0.756257	−	0.549453i
$70$	0.833511	+	0.605581i	0.0996236	+	0.0723808i
$71$	3.73145	+	11.4842i	0.442842	+	1.36293i	0.884833	+	0.465908i	$0.154272\pi$
$71$	3.73145	+	11.4842i	0.442842	+	1.36293i	−0.441991	+	0.897019i	$0.645728\pi$
$72$	2.28825	+	7.04251i	0.269673	+	0.829968i
$73$	1.93375	+	1.40496i	0.226329	+	0.164438i	0.695171	−	0.718844i	$-0.255329\pi$
$73$	1.93375	+	1.40496i	0.226329	+	0.164438i	−0.468842	+	0.883282i	$0.655329\pi$
$74$	0.404138	−	0.293623i	0.0469801	−	0.0341330i
$75$	4.60120	−	14.1610i	0.531301	−	1.63518i
$76$	13.2800			1.52333
$77$		0			0
$78$	37.2489			4.21760
$79$	−2.79051	+	8.58830i	−0.313957	+	0.966260i	0.662225	+	0.749305i	$0.269612\pi$
$79$	−2.79051	+	8.58830i	−0.313957	+	0.966260i	−0.976182	+	0.216954i	$0.930388\pi$
$80$	1.06082	−	0.770727i	0.118603	−	0.0861699i
$81$	−13.3239	−	9.68039i	−1.48044	−	1.07560i
$82$	−1.56950	−	4.83043i	−0.173322	−	0.533432i
$83$	0.994879	+	3.06192i	0.109202	+	0.336090i	0.990694	−	0.136110i	$-0.0434601\pi$
$83$	0.994879	+	3.06192i	0.109202	+	0.336090i	−0.881492	+	0.472200i	$0.843460\pi$
$84$	−6.35848	−	4.61971i	−0.693767	−	0.504052i
$85$	2.20049	−	1.59875i	0.238676	−	0.173409i
$86$	−0.676506	+	2.08207i	−0.0729495	+	0.224515i
$87$	16.4995			1.76894
$88$		0			0
$89$	−1.26537			−0.134129			−0.0670643	−	0.997749i	$-0.521363\pi$
$89$	−1.26537			−0.134129			−0.0670643	+	0.997749i	$0.521363\pi$
$90$	2.15376	−	6.62860i	0.227027	−	0.698716i
$91$	−4.53838	+	3.29733i	−0.475752	+	0.345654i
$92$	−5.05617	−	3.67352i	−0.527142	−	0.382991i
$93$	6.88009	+	21.1748i	0.713432	+	2.19572i
$94$	−1.05700	−	3.25312i	−0.109021	−	0.335533i
$95$	−2.07116	−	1.50479i	−0.212496	−	0.154388i
$96$	−20.0620	+	14.5759i	−2.04757	+	1.48765i
$97$	−2.71786	+	8.36472i	−0.275957	+	0.849308i	0.713008	+	0.701156i	$0.247333\pi$
$97$	−2.71786	+	8.36472i	−0.275957	+	0.849308i	−0.988965	+	0.148152i	$0.952667\pi$
$98$	2.12489			0.214646
$99$		0			0
$100$	−11.9844			−1.19844
$101$	4.00188	−	12.3165i	0.398202	−	1.22554i	−0.528238	−	0.849096i	$-0.677147\pi$
$101$	4.00188	−	12.3165i	0.398202	−	1.22554i	0.926440	−	0.376443i	$-0.122853\pi$
$102$	−30.1350	+	21.8943i	−2.98381	+	2.16786i
$103$	−9.84561	−	7.15325i	−0.970117	−	0.704831i	−0.0146385	−	0.999893i	$-0.504660\pi$
$103$	−9.84561	−	7.15325i	−0.970117	−	0.704831i	−0.955478	+	0.295062i	$0.904660\pi$
$104$	−1.89751	−	5.83995i	−0.186066	−	0.572654i
$105$	0.468203	+	1.44098i	0.0456920	+	0.140625i
$106$	5.20925	+	3.78474i	0.505967	+	0.367607i
$107$	8.54330	−	6.20707i	0.825912	−	0.600060i	−0.0924881	−	0.995714i	$-0.529482\pi$
$107$	8.54330	−	6.20707i	0.825912	−	0.600060i	0.918400	+	0.395654i	$0.129482\pi$
$108$	−9.14393	+	28.1421i	−0.879875	+	2.70798i
$109$	7.34060			0.703102			0.351551	−	0.936169i	$-0.385654\pi$
$109$	7.34060			0.703102			0.351551	+	0.936169i	$0.385654\pi$
$110$		0			0
$111$	0.734633			0.0697283
$112$	0.835692	−	2.57200i	0.0789655	−	0.243031i
$113$	−11.1360	+	8.09081i	−1.04759	+	0.761119i	−0.971753	−	0.236001i	$-0.924163\pi$
$113$	−11.1360	+	8.09081i	−1.04759	+	0.761119i	−0.0758381	+	0.997120i	$0.524163\pi$
$114$	28.3638	+	20.6075i	2.65652	+	1.93007i
$115$	0.372308	+	1.14585i	0.0347179	+	0.106851i
$116$	−4.10376	−	12.6301i	−0.381025	−	1.17267i
$117$	30.7017	+	22.3061i	2.83838	+	2.06220i
$118$	−5.37189	+	3.90291i	−0.494523	+	0.359292i
$119$	1.73351	−	5.33519i	0.158910	−	0.489076i
$120$	−1.65848			−0.151398
$121$		0			0
$122$	5.07901			0.459832
$123$	2.30813	−	7.10369i	0.208117	−	0.640518i
$124$	14.4976	−	10.5332i	1.30193	−	0.945905i
$125$	3.83040	+	2.78295i	0.342601	+	0.248914i
$126$	−4.44201	−	13.6711i	−0.395726	−	1.21792i
$127$	−0.791113	−	2.43479i	−0.0701999	−	0.216053i	0.909802	−	0.415044i	$-0.136234\pi$
$127$	−0.791113	−	2.43479i	−0.0701999	−	0.216053i	−0.980001	+	0.198991i	$0.936234\pi$
$128$	6.84946	+	4.97643i	0.605413	+	0.439858i
$129$	−2.60463	+	1.89237i	−0.229325	+	0.166614i
$130$	−1.78599	+	5.49672i	−0.156642	+	0.482094i
$131$	2.71995			0.237643			0.118822	−	0.992916i	$-0.462088\pi$
$131$	2.71995			0.237643			0.118822	+	0.992916i	$0.462088\pi$
$132$		0			0
$133$	−5.28005			−0.457838
$134$	6.57590	−	20.2385i	0.568071	−	1.74834i
$135$	4.61492	−	3.35294i	0.397189	−	0.288575i
$136$	4.96775	+	3.60928i	0.425981	+	0.309494i
$137$	−2.99881	−	9.22939i	−0.256206	−	0.788520i	−0.993590	−	0.113046i	$-0.963939\pi$
$137$	−2.99881	−	9.22939i	−0.256206	−	0.788520i	0.737384	−	0.675474i	$-0.236061\pi$
$138$	−5.09864	−	15.6920i	−0.434025	−	1.33579i
$139$	−15.9530	−	11.5906i	−1.35312	−	0.983098i	−0.998850	−	0.0479549i	$-0.984730\pi$
$139$	−15.9530	−	11.5906i	−1.35312	−	0.983098i	−0.354269	−	0.935143i	$-0.615270\pi$
$140$	0.986592	−	0.716801i	0.0833822	−	0.0605807i
$141$	1.55444	−	4.78408i	0.130908	−	0.402892i
$142$	25.6585			2.15321
$143$		0			0
$144$	−18.2947			−1.52456
$145$	−0.791113	+	2.43479i	−0.0656983	+	0.202199i
$146$	4.10901	−	2.98537i	0.340064	−	0.247071i
$147$	2.52809	+	1.83676i	0.208513	+	0.151494i
$148$	−0.182718	−	0.562347i	−0.0150193	−	0.0462246i
$149$	−3.26325	−	10.0432i	−0.267336	−	0.822775i	−0.991146	−	0.132776i	$-0.957611\pi$
$149$	−3.26325	−	10.0432i	−0.267336	−	0.822775i	0.723810	−	0.689999i	$-0.242389\pi$
$150$	−25.5966	−	18.5970i	−2.08995	−	1.51844i
$151$	12.5149	−	9.09261i	1.01845	−	0.739946i	0.0524839	−	0.998622i	$-0.483286\pi$
$151$	12.5149	−	9.09261i	1.01845	−	0.739946i	0.965964	+	0.258676i	$0.0832862\pi$
$152$	1.78599	−	5.49672i	0.144863	−	0.445842i
$153$	−37.9494			−3.06803
$154$		0			0
$155$	−3.45459			−0.277479
$156$	13.6245	−	41.9320i	1.09084	−	3.35725i
$157$	−7.36651	+	5.35208i	−0.587912	+	0.427143i	−0.841568	−	0.540152i	$-0.818367\pi$
$157$	−7.36651	+	5.35208i	−0.587912	+	0.427143i	0.253656	+	0.967294i	$0.418367\pi$
$158$	15.5237	+	11.2786i	1.23500	+	0.897277i
$159$	2.92616	+	9.00581i	0.232060	+	0.714207i
$160$	−1.18901	−	3.65938i	−0.0939991	−	0.289300i
$161$	2.01030	+	1.46057i	0.158433	+	0.115109i
$162$	−28.3118	+	20.5697i	−2.22438	+	1.61611i
$163$	−4.10376	+	12.6301i	−0.321431	+	0.989264i	0.651594	+	0.758567i	$0.274100\pi$
$163$	−4.10376	+	12.6301i	−0.321431	+	0.989264i	−0.973026	+	0.230696i	$0.925900\pi$
$164$	−6.01182			−0.469444
$165$		0			0
$166$	6.84106			0.530969
$167$	−3.10888	+	9.56815i	−0.240572	+	0.740406i	0.755761	+	0.654848i	$0.227267\pi$
$167$	−3.10888	+	9.56815i	−0.240572	+	0.740406i	−0.996333	+	0.0855581i	$0.972733\pi$
$168$	−2.76727	+	2.01054i	−0.213499	+	0.155116i
$169$	−14.9419	−	10.8560i	−1.14938	−	0.835074i
$170$	−1.78599	−	5.49672i	−0.136979	−	0.421579i
$171$	11.0378	+	33.9708i	0.844081	+	2.59781i
$172$	2.09639	+	1.52312i	0.159849	+	0.116137i
$173$	−6.60954	+	4.80211i	−0.502514	+	0.365098i	−0.809976	−	0.586462i	$-0.800520\pi$
$173$	−6.60954	+	4.80211i	−0.502514	+	0.365098i	0.307462	+	0.951560i	$0.400520\pi$
$174$	10.8340	−	33.3437i	0.821325	−	2.52778i
$175$	4.76491			0.360193
$176$		0			0
$177$	−9.76491			−0.733975
$178$	−0.830873	+	2.55716i	−0.0622765	+	0.191667i
$179$	9.92215	−	7.20886i	0.741616	−	0.538816i	−0.151601	−	0.988442i	$-0.548443\pi$
$179$	9.92215	−	7.20886i	0.741616	−	0.538816i	0.893217	+	0.449626i	$0.148443\pi$
$180$	−6.67420	−	4.84909i	−0.497466	−	0.361430i
$181$	−2.17701	−	6.70015i	−0.161816	−	0.498018i	0.836972	−	0.547246i	$-0.184324\pi$
$181$	−2.17701	−	6.70015i	−0.161816	−	0.498018i	−0.998788	+	0.0492280i	$0.984324\pi$
$182$	3.68350	+	11.3367i	0.273040	+	0.840329i
$183$	6.04276	+	4.39032i	0.446694	+	0.324542i
$184$	−2.20049	+	1.59875i	−0.162222	+	0.117861i
$185$	−0.0352238	+	0.108408i	−0.00258971	+	0.00797030i
$186$	47.3094			3.46889
$187$		0			0
$188$	−4.04874			−0.295284
$189$	3.63556	−	11.1891i	0.264448	−	0.813887i
$190$	−4.40098	+	3.19750i	−0.319280	+	0.231971i
$191$	−15.2056	−	11.0475i	−1.10024	−	0.799371i	−0.119141	−	0.992877i	$-0.538014\pi$
$191$	−15.2056	−	11.0475i	−1.10024	−	0.799371i	−0.981099	+	0.193506i	$0.938014\pi$
$192$	11.0602	+	34.0396i	0.798198	+	2.45660i
$193$	−5.09864	−	15.6920i	−0.367008	−	1.12953i	−0.948714	−	0.316136i	$-0.897615\pi$
$193$	−5.09864	−	15.6920i	−0.367008	−	1.12953i	0.581706	−	0.813399i	$-0.302385\pi$
$194$	15.1195	+	10.9850i	1.08552	+	0.788675i
$195$	−6.87627	+	4.99591i	−0.492420	+	0.357764i
$196$	0.777220	−	2.39204i	0.0555157	−	0.170860i
$197$	−24.4995			−1.74552			−0.872760	−	0.488149i	$-0.837672\pi$
$197$	−24.4995			−1.74552			−0.872760	+	0.488149i	$0.837672\pi$
$198$		0			0
$199$	−15.3893			−1.09092			−0.545461	−	0.838136i	$-0.683645\pi$
$199$	−15.3893			−1.09092			−0.545461	+	0.838136i	$0.683645\pi$
$200$	−1.61174	+	4.96044i	−0.113968	+	0.350756i
$201$	25.3180	−	18.3946i	1.78579	−	1.29745i
$202$	−22.2625	−	16.1747i	−1.56639	−	1.13805i
$203$	1.63162	+	5.02162i	0.114518	+	0.352449i
$204$	13.6245	+	41.9320i	0.953908	+	2.93583i
$205$	0.937604	+	0.681209i	0.0654851	+	0.0475777i
$206$	−20.9208	+	15.1998i	−1.45762	+	1.05902i
$207$	5.19453	−	15.9871i	0.361045	−	1.11118i
$208$	15.1708			1.05190
$209$		0			0
$210$	3.21949			0.222166
$211$	4.46189	−	13.7323i	0.307169	−	0.945370i	−0.671689	−	0.740833i	$-0.734431\pi$
$211$	4.46189	−	13.7323i	0.307169	−	0.945370i	0.978859	−	0.204537i	$-0.0655690\pi$
$212$	6.16597	−	4.47984i	0.423481	−	0.307677i
$213$	30.5272	+	22.1793i	2.09169	+	1.51970i
$214$	−6.93403	−	21.3407i	−0.474000	−	1.45882i
$215$	−0.154367	−	0.475092i	−0.0105277	−	0.0324010i
$216$	10.4185	+	7.56949i	0.708889	+	0.515038i
$217$	−5.76415	+	4.18790i	−0.391296	+	0.284293i
$218$	4.82003	−	14.8345i	0.326453	−	1.00472i
$219$	7.46927			0.504726
$220$		0			0
$221$	31.4693			2.11685
$222$	0.482379	−	1.48461i	0.0323751	−	0.0996404i
$223$	−13.9584	+	10.1414i	−0.934725	+	0.679117i	−0.947145	−	0.320806i	$-0.896046\pi$
$223$	−13.9584	+	10.1414i	−0.934725	+	0.679117i	0.0124203	+	0.999923i	$0.496046\pi$
$224$	−6.42009	−	4.66447i	−0.428960	−	0.311658i
$225$	−9.96091	−	30.6565i	−0.664061	−	2.04377i
$226$	9.03839	+	27.8173i	0.601225	+	1.85038i
$227$	8.67262	+	6.30103i	0.575622	+	0.418214i	0.837143	−	0.546984i	$-0.184224\pi$
$227$	8.67262	+	6.30103i	0.575622	+	0.418214i	−0.261521	+	0.965198i	$0.584224\pi$
$228$	33.5731	−	24.3923i	2.22343	−	1.61542i
$229$	1.68556	−	5.18762i	0.111385	−	0.342808i	−0.879791	−	0.475361i	$-0.842318\pi$
$229$	1.68556	−	5.18762i	0.111385	−	0.342808i	0.991176	+	0.132553i	$0.0423175\pi$
$230$	2.56009			0.168808
$231$		0			0
$232$	−5.77959			−0.379449
$233$	−9.20240	+	28.3221i	−0.602869	+	1.85544i	−0.0920461	+	0.995755i	$0.529341\pi$
$233$	−9.20240	+	28.3221i	−0.602869	+	1.85544i	−0.510823	+	0.859686i	$0.670659\pi$
$234$	65.2377	−	47.3979i	4.26472	−	3.09850i
$235$	0.631442	+	0.458769i	0.0411907	+	0.0299268i
$236$	2.42872	+	7.47485i	0.158097	+	0.486571i
$237$	8.72002	+	26.8375i	0.566426	+	1.74328i
$238$	−9.64354	−	7.00644i	−0.625098	−	0.454160i
$239$	2.07116	−	1.50479i	0.133972	−	0.0973365i	−0.518781	−	0.854907i	$-0.673614\pi$
$239$	2.07116	−	1.50479i	0.133972	−	0.0973365i	0.652753	+	0.757571i	$0.273614\pi$
$240$	1.26619	−	3.89693i	0.0817321	−	0.251546i
$241$	−27.3893			−1.76430			−0.882151	−	0.470966i	$-0.843905\pi$
$241$	−27.3893			−1.76430			−0.882151	+	0.470966i	$0.843905\pi$
$242$		0			0
$243$	−16.1698			−1.03730
$244$	1.85775	−	5.71758i	0.118930	−	0.366030i
$245$	−0.392262	+	0.284995i	−0.0250607	+	0.0182076i
$246$	−12.8402	−	9.32894i	−0.818660	−	0.594791i
$247$	−9.15300	−	28.1700i	−0.582391	−	1.79242i
$248$	−2.41001	−	7.41726i	−0.153036	−	0.470996i
$249$	8.13916	+	5.91344i	0.515798	+	0.374749i
$250$	8.13916	−	5.91344i	0.514766	−	0.373999i
$251$	3.04222	−	9.36300i	0.192023	−	0.590987i	−0.807975	−	0.589217i	$-0.799436\pi$
$251$	3.04222	−	9.36300i	0.192023	−	0.590987i	0.999998	−	0.00177049i	$-0.000563565\pi$
$252$	−17.0147			−1.07182
$253$		0			0
$254$	−5.43991			−0.341330
$255$	2.62650	−	8.08354i	0.164478	−	0.506211i
$256$	−3.97810	+	2.89026i	−0.248631	+	0.180641i
$257$	18.2025	+	13.2249i	1.13544	+	0.824947i	0.986478	−	0.163896i	$-0.0524062\pi$
$257$	18.2025	+	13.2249i	1.13544	+	0.824947i	0.148964	+	0.988843i	$0.452406\pi$
$258$	2.11400	+	6.50623i	0.131612	+	0.405060i
$259$	0.0726471	+	0.223585i	0.00451407	+	0.0138929i
$260$	5.53453	+	4.02107i	0.343237	+	0.249376i
$261$	28.8973	−	20.9951i	1.78870	−	1.29957i
$262$	1.78599	−	5.49672i	0.110339	−	0.339588i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	−1.46927			−0.0902563
$266$	−3.46701	+	10.6704i	−0.212576	+	0.654243i
$267$	−3.19896	+	2.32418i	−0.195773	+	0.142237i
$268$	−20.3778	−	14.8053i	−1.24477	−	0.904378i
$269$	2.84898	+	8.76826i	0.173705	+	0.534610i	0.999572	−	0.0292553i	$-0.00931359\pi$
$269$	2.84898	+	8.76826i	0.173705	+	0.534610i	−0.825867	+	0.563866i	$0.809314\pi$
$270$	−3.74563	−	11.5279i	−0.227952	−	0.701563i
$271$	8.54330	+	6.20707i	0.518968	+	0.377052i	0.816215	−	0.577748i	$-0.196068\pi$
$271$	8.54330	+	6.20707i	0.518968	+	0.377052i	−0.297247	+	0.954801i	$0.596068\pi$
$272$	−12.2734	+	8.91715i	−0.744184	+	0.540682i
$273$	−5.41701	+	16.6718i	−0.327852	+	1.00903i
$274$	−20.6206			−1.24574
$275$		0			0
$276$	−19.5298			−1.17556
$277$	5.73538	−	17.6517i	0.344606	−	1.06059i	−0.617189	−	0.786815i	$-0.711728\pi$
$277$	5.73538	−	17.6517i	0.344606	−	1.06059i	0.961794	−	0.273773i	$-0.0882715\pi$
$278$	−33.8984	+	24.6286i	−2.03309	+	1.47713i
$279$	38.9940	+	28.3308i	2.33451	+	1.69612i
$280$	−0.164006	−	0.504758i	−0.00980123	−	0.0301651i
$281$	−7.92891	−	24.4027i	−0.472999	−	1.45574i	−0.848637	−	0.528975i	$-0.822577\pi$
$281$	−7.92891	−	24.4027i	−0.472999	−	1.45574i	0.375638	−	0.926766i	$-0.377423\pi$
$282$	−8.64739	−	6.28270i	−0.514945	−	0.374129i
$283$	24.4963	−	17.7976i	1.45616	−	1.05796i	0.471812	−	0.881699i	$-0.343600\pi$
$283$	24.4963	−	17.7976i	1.45616	−	1.05796i	0.984344	−	0.176260i	$-0.0563999\pi$
$284$	9.38512	−	28.8844i	0.556904	−	1.71397i
$285$	−8.00000			−0.473879
$286$		0			0
$287$	2.39025			0.141092
$288$	−16.5893	+	51.0566i	−0.977533	+	3.00854i
$289$	−11.7059	+	8.50482i	−0.688581	+	0.500284i
$290$	4.40098	+	3.19750i	0.258434	+	0.187763i
$291$	8.49301	+	26.1388i	0.497869	+	1.53228i
$292$	−1.85775	−	5.71758i	−0.108717	−	0.334596i
$293$	2.46722	+	1.79254i	0.144137	+	0.104721i	0.657517	−	0.753440i	$-0.271607\pi$
$293$	2.46722	+	1.79254i	0.144137	+	0.104721i	−0.513380	+	0.858161i	$0.671607\pi$
$294$	5.37189	−	3.90291i	0.313295	−	0.227622i
$295$	0.468203	−	1.44098i	0.0272599	−	0.0838972i
$296$	−0.257333			−0.0149572
$297$		0			0
$298$	−22.4390			−1.29986
$299$	−4.30753	+	13.2572i	−0.249111	+	0.766684i
$300$	−30.2976	+	22.0125i	−1.74923	+	1.27089i
$301$	−0.833511	−	0.605581i	−0.0480428	−	0.0349051i
$302$	−10.1575	−	31.2616i	−0.584499	−	1.79890i
$303$	−12.5054	−	38.4877i	−0.718417	−	2.21106i
$304$	11.5521	+	8.39306i	0.662556	+	0.481375i
$305$	−0.937604	+	0.681209i	−0.0536871	+	0.0390059i
$306$	−24.9186	+	76.6915i	−1.42450	+	4.38416i
$307$	−3.71904			−0.212257			−0.106128	−	0.994352i	$-0.533845\pi$
$307$	−3.71904			−0.212257			−0.106128	+	0.994352i	$0.533845\pi$
$308$		0			0
$309$	−38.0294			−2.16341
$310$	−2.26837	+	6.98132i	−0.128835	+	0.396513i
$311$	−3.37347	+	2.45097i	−0.191292	+	0.138982i	−0.679309	−	0.733852i	$-0.737720\pi$
$311$	−3.37347	+	2.45097i	−0.191292	+	0.138982i	0.488017	+	0.872834i	$0.337720\pi$
$312$	−15.5237	−	11.2786i	−0.878854	−	0.638525i
$313$	−3.61685	−	11.1315i	−0.204436	−	0.629190i	−0.999736	−	0.0229737i	$-0.992687\pi$
$313$	−3.61685	−	11.1315i	−0.204436	−	0.629190i	0.795300	−	0.606216i	$-0.207313\pi$
$314$	5.97891	+	18.4012i	0.337409	+	1.03844i
$315$	2.65361	+	1.92796i	0.149514	+	0.108628i
$316$	18.3747	−	13.3500i	1.03366	−	0.750997i
$317$	−0.690681	+	2.12570i	−0.0387925	+	0.119391i	−0.968577	−	0.248712i	$-0.919993\pi$
$317$	−0.690681	+	2.12570i	−0.0387925	+	0.119391i	0.929785	+	0.368103i	$0.119993\pi$
$318$	20.1211			1.12834
$319$		0			0
$320$	−5.55345			−0.310447
$321$	10.1973	−	31.3840i	0.569157	−	1.75168i
$322$	4.27165	−	3.10353i	0.238050	−	0.172953i
$323$	23.9629	+	17.4100i	1.33333	+	0.968721i
$324$	12.8002	+	39.3951i	0.711125	+	2.18862i
$325$	8.26000	+	25.4217i	0.458183	+	1.41014i
$326$	22.8293	+	16.5865i	1.26440	+	0.918639i
$327$	18.5577	−	13.4829i	1.02624	−	0.745608i
$328$	−0.808510	+	2.48834i	−0.0446425	+	0.137395i
$329$	1.60975			0.0887482
$330$		0			0
$331$	22.3250			1.22709			0.613547	−	0.789659i	$-0.289742\pi$
$331$	22.3250			1.22709			0.613547	+	0.789659i	$0.289742\pi$
$332$	2.50226	−	7.70116i	0.137329	−	0.422656i
$333$	1.28664	−	0.934796i	0.0705072	−	0.0512265i
$334$	17.2948	+	12.5654i	0.946328	+	0.687548i
$335$	1.50051	+	4.61808i	0.0819814	+	0.252313i
$336$	−2.61144	−	8.03719i	−0.142466	−	0.438465i
$337$	−10.7438	−	7.80582i	−0.585251	−	0.425210i	0.255362	−	0.966845i	$-0.417805\pi$
$337$	−10.7438	−	7.80582i	−0.585251	−	0.425210i	−0.840613	+	0.541636i	$0.817805\pi$
$338$	−31.7499	+	23.0677i	−1.72697	+	1.25472i
$339$	−13.2920	+	40.9085i	−0.721921	+	2.22185i
$340$	−6.84106			−0.371008
$341$		0			0
$342$	75.8989			4.10414
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	0.912369	−	0.662875i	0.0491916	−	0.0357398i
$345$	3.04588	+	2.21296i	0.163984	+	0.119142i
$346$	5.36453	+	16.5103i	0.288399	+	0.887600i
$347$	5.57138	+	17.1469i	0.299087	+	0.920496i	0.981818	+	0.189826i	$0.0607923\pi$
$347$	5.57138	+	17.1469i	0.299087	+	0.920496i	−0.682731	+	0.730670i	$0.739208\pi$
$348$	−33.5731	−	24.3923i	−1.79971	−	1.30756i
$349$	−17.7575	+	12.9016i	−0.950535	+	0.690604i	−0.950933	−	0.309396i	$-0.899873\pi$
$349$	−17.7575	+	12.9016i	−0.950535	+	0.690604i	0.000398242		1.00000i	$0.499873\pi$
$350$	3.12876	−	9.62934i	0.167239	−	0.514710i
$351$	65.9982			3.52272
$352$		0			0
$353$	18.8557			1.00359			0.501795	−	0.864987i	$-0.332673\pi$
$353$	18.8557			1.00359			0.501795	+	0.864987i	$0.332673\pi$
$354$	−6.41189	+	19.7338i	−0.340788	+	1.04884i
$355$	−4.73665	+	3.44138i	−0.251395	+	0.182649i
$356$	2.57476	+	1.87067i	0.136462	+	0.0991453i
$357$	−5.41701	−	16.6718i	−0.286699	−	0.882368i
$358$	−8.05315	−	24.7851i	−0.425622	−	1.30993i
$359$	1.23765	+	0.899204i	0.0653206	+	0.0474582i	0.619966	−	0.784628i	$-0.287146\pi$
$359$	1.23765	+	0.899204i	0.0653206	+	0.0474582i	−0.554646	+	0.832087i	$0.687146\pi$
$360$	−2.90467	+	2.11037i	−0.153090	+	0.111226i
$361$	2.74373	−	8.44433i	0.144407	−	0.444439i
$362$	−14.9697			−0.786791
$363$		0			0
$364$	14.1093			0.739528
$365$	−0.358133	+	1.10222i	−0.0187455	+	0.0576928i
$366$	12.8402	−	9.32894i	0.671167	−	0.487631i
$367$	−11.8559	−	8.61382i	−0.618873	−	0.449638i	0.233655	−	0.972320i	$-0.424932\pi$
$367$	−11.8559	−	8.61382i	−0.618873	−	0.449638i	−0.852528	+	0.522682i	$0.824932\pi$
$368$	−2.07658	−	6.39106i	−0.108249	−	0.333157i
$369$	−4.99676	−	15.3784i	−0.260121	−	0.800569i
$370$	0.195951	+	0.142367i	0.0101870	+	0.00740129i
$371$	−2.45154	+	1.78115i	−0.127278	+	0.0924728i
$372$	17.3044	−	53.2574i	0.897191	−	2.76127i
$373$	−10.0606			−0.520916			−0.260458	−	0.965485i	$-0.583873\pi$
$373$	−10.0606			−0.520916			−0.260458	+	0.965485i	$0.583873\pi$
$374$		0			0
$375$	14.7952			0.764020
$376$	−0.544502	+	1.67580i	−0.0280805	+	0.0864230i
$377$	−23.9629	+	17.4100i	−1.23415	+	0.896663i
$378$	−20.2247	−	14.6941i	−1.04025	−	0.755783i
$379$	−5.52942	−	17.0178i	−0.284027	−	0.874146i	−0.986689	−	0.162621i	$-0.948005\pi$
$379$	−5.52942	−	17.0178i	−0.284027	−	0.874146i	0.702661	−	0.711524i	$-0.251995\pi$
$380$	1.98976	+	6.12384i	0.102072	+	0.314147i
$381$	−6.47214	−	4.70228i	−0.331578	−	0.240905i
$382$	−32.3102	+	23.4747i	−1.65313	+	1.20107i
$383$	−5.86052	+	18.0368i	−0.299458	+	0.921638i	0.682229	+	0.731139i	$0.261011\pi$
$383$	−5.86052	+	18.0368i	−0.299458	+	0.921638i	−0.981687	+	0.190499i	$0.938989\pi$
$384$	26.4565			1.35010
$385$		0			0
$386$	−35.0596			−1.78449
$387$	−2.15376	+	6.62860i	−0.109482	+	0.336951i
$388$	17.8963	−	13.0025i	0.908549	−	0.660100i
$389$	−27.7205	−	20.1401i	−1.40549	−	1.02115i	−0.993959	−	0.109748i	$-0.964996\pi$
$389$	−27.7205	−	20.1401i	−1.40549	−	1.02115i	−0.411527	−	0.911398i	$-0.635004\pi$
$390$	5.58102	+	17.1766i	0.282606	+	0.869771i
$391$	−4.30753	−	13.2572i	−0.217841	−	0.670446i
$392$	−0.885558	−	0.643395i	−0.0447274	−	0.0324964i
$393$	6.87627	−	4.99591i	0.346862	−	0.252010i
$394$	−16.0870	+	49.5108i	−0.810453	+	2.49432i
$395$	−4.37844			−0.220303
$396$		0			0
$397$	16.2791			0.817026			0.408513	−	0.912752i	$-0.366047\pi$
$397$	16.2791			0.817026			0.408513	+	0.912752i	$0.366047\pi$
$398$	−10.1050	+	31.1001i	−0.506520	+	1.55891i
$399$	−13.3484	+	9.69819i	−0.668256	+	0.485517i
$400$	−10.4250	−	7.57421i	−0.521250	−	0.378710i
$401$	8.94250	+	27.5222i	0.446567	+	1.37439i	0.880756	+	0.473570i	$0.157035\pi$
$401$	8.94250	+	27.5222i	0.446567	+	1.37439i	−0.434189	+	0.900822i	$0.642965\pi$
$402$	−20.5489	−	63.2431i	−1.02489	−	3.15428i
$403$	−32.3354	−	23.4931i	−1.61074	−	1.17027i
$404$	−26.3512	+	19.1453i	−1.31102	+	0.952514i
$405$	2.46760	−	7.59449i	0.122616	−	0.377373i
$406$	11.2195			0.556814
$407$		0			0
$408$	19.1883			0.949963
$409$	−4.79299	+	14.7513i	−0.236998	+	0.729405i	0.759852	+	0.650096i	$0.225271\pi$
$409$	−4.79299	+	14.7513i	−0.236998	+	0.729405i	−0.996850	+	0.0793090i	$0.974729\pi$
$410$	1.99230	−	1.44749i	0.0983928	−	0.0714865i
$411$	−24.5334	−	17.8246i	−1.21015	−	0.879222i
$412$	9.45865	+	29.1107i	0.465994	+	1.43418i
$413$	−0.965643	−	2.97194i	−0.0475162	−	0.146240i
$414$	−28.8973	−	20.9951i	−1.42023	−	1.03185i
$415$	−1.26288	+	0.917539i	−0.0619925	+	0.0450402i
$416$	13.7565	−	42.3383i	0.674470	−	2.07580i
$417$	−61.6197			−3.01753
$418$		0			0
$419$	−12.9503			−0.632666			−0.316333	−	0.948648i	$-0.602452\pi$
$419$	−12.9503			−0.632666			−0.316333	+	0.948648i	$0.602452\pi$
$420$	1.17760	−	3.62427i	0.0574608	−	0.176846i
$421$	13.8268	−	10.0457i	0.673876	−	0.489599i	−0.197445	−	0.980314i	$-0.563264\pi$
$421$	13.8268	−	10.0457i	0.673876	−	0.489599i	0.871320	+	0.490715i	$0.163264\pi$
$422$	−24.8216	−	18.0340i	−1.20830	−	0.877879i
$423$	−3.36513	−	10.3568i	−0.163618	−	0.503565i
$424$	−1.02500	−	3.15462i	−0.0497784	−	0.153202i
$425$	−21.6250	−	15.7115i	−1.04897	−	0.762118i
$426$	64.8668	−	47.1285i	3.14281	−	2.28338i
$427$	−0.738629	+	2.27327i	−0.0357447	+	0.110011i
$428$	−26.5601			−1.28383
$429$		0			0
$430$	−1.06147			−0.0511886
$431$	−5.97891	+	18.4012i	−0.287994	+	0.886354i	0.697491	+	0.716593i	$0.254300\pi$
$431$	−5.97891	+	18.4012i	−0.287994	+	0.886354i	−0.985485	+	0.169761i	$0.945700\pi$
$432$	−25.7401	+	18.7013i	−1.23842	+	0.899766i
$433$	−12.8031	−	9.30197i	−0.615276	−	0.447024i	0.235992	−	0.971755i	$-0.424166\pi$
$433$	−12.8031	−	9.30197i	−0.615276	−	0.447024i	−0.851268	+	0.524731i	$0.824166\pi$
$434$	4.67838	+	14.3986i	0.224570	+	0.691154i
$435$	2.47214	+	7.60845i	0.118530	+	0.364797i
$436$	−14.9366	−	10.8521i	−0.715332	−	0.519719i
$437$	−10.6145	+	7.71185i	−0.507758	+	0.368908i
$438$	4.90451	−	15.0945i	0.234347	−	0.721245i
$439$	11.0596			0.527848			0.263924	−	0.964544i	$-0.414983\pi$
$439$	11.0596			0.527848			0.263924	+	0.964544i	$0.414983\pi$
$440$		0			0
$441$	6.76491			0.322139
$442$	20.6635	−	63.5958i	0.982864	−	3.02494i
$443$	28.0757	−	20.3982i	1.33392	−	0.969146i	0.334271	−	0.942477i	$-0.391510\pi$
$443$	28.0757	−	20.3982i	1.33392	−	0.969146i	0.999644	−	0.0266694i	$-0.00849013\pi$
$444$	−1.49482	−	1.08605i	−0.0709412	−	0.0515418i
$445$	−0.189591	−	0.583500i	−0.00898746	−	0.0276606i
$446$	11.3291	+	34.8675i	0.536450	+	1.65102i
$447$	−26.6968	−	19.3964i	−1.26272	−	0.917417i
$448$	−9.26621	+	6.73230i	−0.437787	+	0.318071i
$449$	−11.2154	+	34.5175i	−0.529288	+	1.62898i	0.226390	+	0.974037i	$0.427307\pi$
$449$	−11.2154	+	34.5175i	−0.529288	+	1.62898i	−0.755678	+	0.654943i	$0.772693\pi$
$450$	−68.4939			−3.22883
$451$		0			0
$452$	34.6206			1.62842
$453$	14.9378	−	45.9738i	0.701838	−	2.16004i
$454$	18.4283	−	13.3890i	0.864885	−	0.628375i
$455$	−2.20049	−	1.59875i	−0.103160	−	0.0749505i
$456$	−5.58102	−	17.1766i	−0.261355	−	0.804368i
$457$	0.636746	+	1.95970i	0.0297857	+	0.0916710i	0.964844	−	0.262822i	$-0.0846533\pi$
$457$	0.636746	+	1.95970i	0.0297857	+	0.0916710i	−0.935059	+	0.354493i	$0.884653\pi$
$458$	−9.37681	−	6.81265i	−0.438149	−	0.318334i
$459$	−53.3936	+	38.7927i	−2.49220	+	1.81069i
$460$	0.936407	−	2.88196i	0.0436602	−	0.134372i
$461$	7.17076			0.333975			0.166988	−	0.985959i	$-0.446596\pi$
$461$	7.17076			0.333975			0.166988	+	0.985959i	$0.446596\pi$
$462$		0			0
$463$	3.45459			0.160548			0.0802741	−	0.996773i	$-0.474420\pi$
$463$	3.45459			0.160548			0.0802741	+	0.996773i	$0.474420\pi$
$464$	4.41249	−	13.5803i	0.204845	−	0.630448i
$465$	−8.73349	+	6.34525i	−0.405006	+	0.294254i
$466$	51.1932	+	37.1940i	2.37148	+	1.72298i
$467$	−4.17042	−	12.8352i	−0.192984	−	0.593944i	−0.999994	−	0.00340617i	$-0.998916\pi$
$467$	−4.17042	−	12.8352i	−0.192984	−	0.593944i	0.807010	−	0.590537i	$-0.201084\pi$
$468$	−29.4951	−	90.7765i	−1.36341	−	4.19614i
$469$	8.10205	+	5.88648i	0.374118	+	0.271812i
$470$	1.34174	−	0.974833i	0.0618899	−	0.0449657i
$471$	−8.79267	+	27.0610i	−0.405145	+	1.24691i
$472$	3.42053			0.157443
$473$		0			0
$474$	59.9612			2.75411
$475$	−7.77454	+	23.9276i	−0.356720	+	1.09787i
$476$	−11.4147	+	8.29323i	−0.523190	+	0.380120i
$477$	16.5845	+	12.0493i	0.759351	+	0.551701i
$478$	−1.68102	−	5.17366i	−0.0768882	−	0.236638i
$479$	−10.8340	−	33.3437i	−0.495019	−	1.52351i	−0.816927	−	0.576741i	$-0.804324\pi$
$479$	−10.8340	−	33.3437i	−0.495019	−	1.52351i	0.321908	−	0.946771i	$-0.395676\pi$
$480$	−9.72732	−	7.06731i	−0.443989	−	0.322577i
$481$	−1.06693	+	0.775172i	−0.0486480	+	0.0353448i
$482$	−17.9845	+	55.3507i	−0.819173	+	2.52116i
$483$	7.76491			0.353316
$484$		0			0
$485$	−4.26445			−0.193639
$486$	−10.6175	+	32.6774i	−0.481621	+	1.48228i
$487$	−24.0000	+	17.4370i	−1.08754	+	0.790146i	−0.978983	−	0.203944i	$-0.934624\pi$
$487$	−24.0000	+	17.4370i	−1.08754	+	0.790146i	−0.108560	+	0.994090i	$0.534624\pi$
$488$	−2.11671	−	1.53788i	−0.0958188	−	0.0696164i
$489$	12.8238	+	39.4675i	0.579911	+	1.78478i
$490$	0.318373	+	0.979851i	0.0143826	+	0.0442651i
$491$	20.6541	+	15.0061i	0.932105	+	0.677214i	0.946507	−	0.322683i	$-0.104585\pi$
$491$	20.6541	+	15.0061i	0.932105	+	0.677214i	−0.0144027	+	0.999896i	$0.504585\pi$
$492$	−15.1984	+	11.0423i	−0.685196	+	0.497824i
$493$	9.15300	−	28.1700i	0.412230	−	1.26871i
$494$	−62.9385			−2.83174
$495$		0			0
$496$	19.2682			0.865169
$497$	−3.73145	+	11.4842i	−0.167378	+	0.515138i
$498$	17.2948	−	12.5654i	0.774998	−	0.563069i
$499$	20.7581	+	15.0817i	0.929262	+	0.675149i	0.945812	−	0.324714i	$-0.105268\pi$
$499$	20.7581	+	15.0817i	0.929262	+	0.675149i	−0.0165497	+	0.999863i	$0.505268\pi$
$500$	−3.67985	−	11.3254i	−0.164568	−	0.506488i
$501$	9.71490	+	29.8994i	0.434030	+	1.33581i
$502$	−16.9240	−	12.2960i	−0.755353	−	0.548796i
$503$	2.07116	−	1.50479i	0.0923484	−	0.0670951i	−0.540653	−	0.841246i	$-0.681823\pi$
$503$	2.07116	−	1.50479i	0.0923484	−	0.0670951i	0.633001	+	0.774151i	$0.281823\pi$
$504$	−2.28825	+	7.04251i	−0.101927	+	0.313698i
$505$	6.27913			0.279418
$506$		0			0
$507$	−57.7143			−2.56318
$508$	−1.98976	+	6.12384i	−0.0882812	+	0.271702i
$509$	−10.8850	+	7.90841i	−0.482469	+	0.350534i	−0.802281	−	0.596947i	$-0.796380\pi$
$509$	−10.8850	+	7.90841i	−0.482469	+	0.350534i	0.319812	+	0.947481i	$0.396380\pi$
$510$	−14.6113	−	10.6157i	−0.646999	−	0.470072i
$511$	0.738629	+	2.27327i	0.0326750	+	0.100563i
$512$	8.46129	+	26.0412i	0.373940	+	1.15087i
$513$	50.2555	+	36.5128i	2.21884	+	1.61208i
$514$	38.6783	−	28.1014i	1.70602	−	1.23950i
$515$	1.82341	−	5.61189i	0.0803492	−	0.247290i
$516$	8.09747			0.356471
$517$		0			0
$518$	0.499542			0.0219486
$519$	−7.88915	+	24.2803i	−0.346295	+	1.06579i
$520$	2.40867	−	1.75000i	0.105627	−	0.0767428i
$521$	26.0773	+	18.9462i	1.14247	+	0.830050i	0.987461	−	0.157864i	$-0.0504608\pi$
$521$	26.0773	+	18.9462i	1.14247	+	0.830050i	0.155004	+	0.987914i	$0.450461\pi$
$522$	−23.4540	−	72.1841i	−1.02656	−	3.15941i
$523$	9.99351	+	30.7569i	0.436986	+	1.34490i	0.891038	+	0.453929i	$0.149978\pi$
$523$	9.99351	+	30.7569i	0.436986	+	1.34490i	−0.454052	+	0.890975i	$0.650022\pi$
$524$	−5.53453	−	4.02107i	−0.241777	−	0.175661i
$525$	12.0461	−	8.75200i	0.525735	−	0.381969i
$526$	10.5060	−	32.3342i	0.458084	−	1.40984i
$527$	39.9688			1.74107
$528$		0			0
$529$	−16.8255			−0.731542
$530$	−0.964758	+	2.96922i	−0.0419064	+	0.128975i
$531$	−17.1023	+	12.4255i	−0.742175	+	0.539222i
$532$	10.7438	+	7.80582i	0.465802	+	0.338425i
$533$	4.14352	+	12.7524i	0.179476	+	0.552370i
$534$	2.59638	+	7.99084i	0.112356	+	0.345798i
$535$	4.14232	+	3.00957i	0.179088	+	0.130115i
$536$	−8.86858	+	6.44340i	−0.383064	+	0.278312i
$537$	11.8431	−	36.4492i	0.511067	−	1.57290i
$538$	19.5904			0.844601
$539$		0			0
$540$	−14.3472			−0.617407
$541$	7.26204	−	22.3503i	0.312220	−	0.960913i	−0.664664	−	0.747142i	$-0.731425\pi$
$541$	7.26204	−	22.3503i	0.312220	−	0.960913i	0.976884	−	0.213771i	$-0.0685746\pi$
$542$	18.1535	−	13.1893i	0.779761	−	0.566529i
$543$	−17.8103	−	12.9399i	−0.764311	−	0.555304i
$544$	13.7565	+	42.3383i	0.589807	+	1.81524i
$545$	1.09985	+	3.38498i	0.0471122	+	0.144997i
$546$	30.1350	+	21.8943i	1.28966	+	0.936991i
$547$	−3.33404	+	2.42232i	−0.142553	+	0.103571i	−0.656776	−	0.754085i	$-0.728080\pi$
$547$	−3.33404	+	2.42232i	−0.142553	+	0.103571i	0.514223	+	0.857657i	$0.328080\pi$
$548$	−7.54242	+	23.2132i	−0.322196	+	0.991619i
$549$	16.1698			0.690112
$550$		0			0
$551$	−27.8789			−1.18768
$552$	−2.62650	+	8.08354i	−0.111791	+	0.344059i
$553$	−7.30565	+	5.30786i	−0.310668	+	0.225713i
$554$	−31.9061	−	23.1811i	−1.35556	−	0.984871i
$555$	0.110070	+	0.338762i	0.00467223	+	0.0143796i
$556$	15.3260	+	47.1687i	0.649969	+	2.00040i
$557$	−11.2773	−	8.19340i	−0.477832	−	0.347166i	0.322653	−	0.946517i	$-0.395425\pi$
$557$	−11.2773	−	8.19340i	−0.477832	−	0.347166i	−0.800486	+	0.599352i	$0.795425\pi$
$558$	82.8577	−	60.1997i	3.50765	−	2.54845i
$559$	1.78599	−	5.49672i	0.0755394	−	0.232486i
$560$	1.31124			0.0554100
$561$		0			0
$562$	−54.5213			−2.29984
$563$	−0.840512	+	2.58683i	−0.0354233	+	0.109022i	−0.967205	−	0.253998i	$-0.918254\pi$
$563$	−0.840512	+	2.58683i	−0.0354233	+	0.109022i	0.931781	+	0.363020i	$0.118254\pi$
$564$	−10.2356	+	7.43656i	−0.430995	+	0.313136i
$565$	−5.39944	−	3.92293i	−0.227156	−	0.165039i
$566$	−19.8821	−	61.1907i	−0.835705	−	2.57204i
$567$	−5.08928	−	15.6632i	−0.213730	−	0.657793i
$568$	−10.6933	−	7.76915i	−0.448681	−	0.325986i
$569$	−22.4252	+	16.2928i	−0.940112	+	0.683031i	−0.948448	−	0.316934i	$-0.897347\pi$
$569$	−22.4252	+	16.2928i	−0.940112	+	0.683031i	0.00833555	+	0.999965i	$0.497347\pi$
$570$	−5.25301	+	16.1671i	−0.220024	+	0.677165i
$571$	−38.1193			−1.59524			−0.797621	−	0.603159i	$-0.793908\pi$
$571$	−38.1193			−1.59524			−0.797621	+	0.603159i	$0.793908\pi$
$572$		0			0
$573$	−58.7328			−2.45360
$574$	1.56950	−	4.83043i	0.0655097	−	0.201618i
$575$	9.57888	−	6.95946i	0.399467	−	0.290230i
$576$	62.6851	+	45.5434i	2.61188	+	1.89764i
$577$	7.17068	+	22.0691i	0.298519	+	0.918748i	0.982017	+	0.188795i	$0.0604582\pi$
$577$	7.17068	+	22.0691i	0.298519	+	0.918748i	−0.683497	+	0.729953i	$0.739542\pi$
$578$	9.50089	+	29.2407i	0.395185	+	1.21625i
$579$	−41.7123	−	30.3057i	−1.73350	−	1.25946i
$580$	5.20925	−	3.78474i	0.216302	−	0.157153i
$581$	−0.994879	+	3.06192i	−0.0412745	+	0.127030i
$582$	58.4002			2.42077
$583$		0			0
$584$	−2.61639			−0.108267
$585$	−5.68599	+	17.4997i	−0.235087	+	0.723522i
$586$	5.24256	−	3.80894i	0.216568	−	0.157346i
$587$	8.93936	+	6.49482i	0.368967	+	0.268070i	0.756782	−	0.653667i	$-0.226770\pi$
$587$	8.93936	+	6.49482i	0.368967	+	0.268070i	−0.387816	+	0.921737i	$0.626770\pi$
$588$	−2.42872	−	7.47485i	−0.100159	−	0.308257i
$589$	−11.6251	−	35.7785i	−0.479005	−	1.47423i
$590$	−2.60463	−	1.89237i	−0.107231	−	0.0779077i
$591$	−61.9369	+	44.9998i	−2.54775	+	1.85105i
$592$	0.196464	−	0.604653i	0.00807461	−	0.0248511i
$593$	36.3884			1.49429			0.747147	−	0.664659i	$-0.231423\pi$
$593$	36.3884			1.49429			0.747147	+	0.664659i	$0.231423\pi$
$594$		0			0
$595$	2.71995			0.111507
$596$	−8.20752	+	25.2602i	−0.336193	+	1.03470i
$597$	−38.9056	+	28.2665i	−1.59230	+	1.15687i
$598$	23.9629	+	17.4100i	0.979914	+	0.711949i
$599$	9.16498	+	28.2069i	0.374471	+	1.15250i	0.943835	+	0.330417i	$0.107189\pi$
$599$	9.16498	+	28.2069i	0.374471	+	1.15250i	−0.569364	+	0.822085i	$0.692811\pi$
$600$	5.03652	+	15.5008i	0.205615	+	0.632818i
$601$	1.12548	+	0.817709i	0.0459093	+	0.0333550i	0.610503	−	0.792014i	$-0.290967\pi$
$601$	1.12548	+	0.817709i	0.0459093	+	0.0333550i	−0.564594	+	0.825369i	$0.690967\pi$
$602$	−1.77112	+	1.28679i	−0.0721853	+	0.0524457i
$603$	20.9354	−	64.4326i	0.852556	−	2.62390i
$604$	−38.9073			−1.58312
$605$		0			0
$606$	−85.9906			−3.49313
$607$	−9.56053	+	29.4243i	−0.388050	+	1.19430i	0.546193	+	0.837659i	$0.316076\pi$
$607$	−9.56053	+	29.4243i	−0.388050	+	1.19430i	−0.934243	+	0.356636i	$0.883924\pi$
$608$	33.8984	−	24.6286i	1.37476	−	0.998822i
$609$	13.3484	+	9.69819i	0.540905	+	0.392990i
$610$	0.760991	+	2.34209i	0.0308116	+	0.0948285i
$611$	2.79051	+	8.58830i	0.112892	+	0.347446i
$612$	77.2191	+	56.1030i	3.12140	+	2.26783i
$613$	6.60146	−	4.79624i	0.266631	−	0.193719i	−0.446434	−	0.894816i	$-0.647306\pi$
$613$	6.60146	−	4.79624i	0.266631	−	0.193719i	0.713065	+	0.701098i	$0.247306\pi$
$614$	−2.44201	+	7.51575i	−0.0985517	+	0.303311i
$615$	3.62156			0.146036
$616$		0			0
$617$	−27.5298			−1.10831			−0.554154	−	0.832414i	$-0.686958\pi$
$617$	−27.5298			−1.10831			−0.554154	+	0.832414i	$0.686958\pi$
$618$	−24.9711	+	76.8530i	−1.00448	+	3.09148i
$619$	−16.1589	+	11.7401i	−0.649481	+	0.471876i	−0.863094	−	0.505043i	$-0.831477\pi$
$619$	−16.1589	+	11.7401i	−0.649481	+	0.471876i	0.213613	+	0.976918i	$0.431477\pi$
$620$	7.02935	+	5.10713i	0.282306	+	0.205107i
$621$	−9.03386	−	27.8034i	−0.362516	−	1.11571i
$622$	2.73802	+	8.42677i	0.109785	+	0.337883i
$623$	−1.02370	−	0.743764i	−0.0410138	−	0.0297983i
$624$	38.3530	−	27.8651i	1.53535	−	1.11550i
$625$	6.65280	−	20.4752i	0.266112	−	0.819008i
$626$	−24.8704			−0.994022
$627$		0			0
$628$	22.9016			0.913874
$629$	0.407532	−	1.25426i	0.0162494	−	0.0500104i
$630$	5.63863	−	4.09670i	0.224648	−	0.163216i
$631$	13.9427	+	10.1300i	0.555052	+	0.403269i	0.829645	−	0.558292i	$-0.188543\pi$
$631$	13.9427	+	10.1300i	0.555052	+	0.403269i	−0.274593	+	0.961561i	$0.588543\pi$
$632$	−3.05452	−	9.40084i	−0.121502	−	0.373945i
$633$	−13.9429	−	42.9118i	−0.554181	−	1.70559i
$634$	3.84227	+	2.79158i	0.152596	+	0.110868i
$635$	1.00423	−	0.729613i	0.0398515	−	0.0289538i
$636$	7.35971	−	22.6508i	0.291831	−	0.898165i
$637$	−5.60975			−0.222266
$638$		0			0
$639$	81.6878			3.23152
$640$	−1.26853	+	3.90412i	−0.0501429	+	0.154324i
$641$	35.9324	−	26.1064i	1.41925	−	1.03114i	0.427350	−	0.904086i	$-0.359447\pi$
$641$	35.9324	−	26.1064i	1.41925	−	1.03114i	0.991896	−	0.127056i	$-0.0405527\pi$
$642$	−56.7277	−	41.2151i	−2.23886	−	1.62663i
$643$	−6.96326	−	21.4307i	−0.274604	−	0.845145i	−0.989324	−	0.145734i	$-0.953446\pi$
$643$	−6.96326	−	21.4307i	−0.274604	−	0.845145i	0.714719	−	0.699411i	$-0.246554\pi$
$644$	−1.93129	−	5.94389i	−0.0761033	−	0.234222i
$645$	−1.26288	−	0.917539i	−0.0497260	−	0.0361281i
$646$	50.9183	−	36.9943i	2.00336	−	1.45552i
$647$	−5.80204	+	17.8569i	−0.228102	+	0.702025i	0.769860	+	0.638213i	$0.220326\pi$
$647$	−5.80204	+	17.8569i	−0.228102	+	0.702025i	−0.997962	+	0.0638126i	$0.979674\pi$
$648$	18.0274			0.708184
$649$		0			0
$650$	56.7980			2.22780
$651$	−6.88009	+	21.1748i	−0.269652	+	0.829904i
$652$	27.0221	−	19.6327i	1.05827	−	0.768876i
$653$	−25.5751	−	18.5814i	−1.00083	−	0.727147i	−0.0385660	−	0.999256i	$-0.512279\pi$
$653$	−25.5751	−	18.5814i	−1.00083	−	0.727147i	−0.962267	+	0.272109i	$0.912279\pi$
$654$	−15.0620	−	46.3562i	−0.588972	−	1.81267i
$655$	0.407532	+	1.25426i	0.0159236	+	0.0490078i
$656$	−5.22956	−	3.79950i	−0.204180	−	0.148346i
$657$	13.0817	−	9.50439i	0.510365	−	0.370802i
$658$	1.05700	−	3.25312i	0.0412062	−	0.126820i
$659$	−19.8477			−0.773157			−0.386578	−	0.922257i	$-0.626343\pi$
$659$	−19.8477			−0.773157			−0.386578	+	0.922257i	$0.626343\pi$
$660$		0			0
$661$	31.4234			1.22223			0.611114	−	0.791542i	$-0.290722\pi$
$661$	31.4234			1.22223			0.611114	+	0.791542i	$0.290722\pi$
$662$	14.6592	−	45.1163i	0.569745	−	1.75349i
$663$	79.5570	−	57.8015i	3.08974	−	2.24483i
$664$	−2.85105	−	2.07141i	−0.110642	−	0.0803862i
$665$	−0.791113	−	2.43479i	−0.0306780	−	0.0944173i
$666$	−1.04428	−	3.21396i	−0.0404649	−	0.124538i
$667$	10.6145	+	7.71185i	0.410993	+	0.298604i
$668$	20.4711	−	14.8731i	0.792051	−	0.575459i
$669$	−16.6608	+	51.2766i	−0.644142	+	1.98247i
$670$	10.3179			0.398615
$671$		0			0
$672$	−24.7980			−0.956606
$673$	5.93915	−	18.2788i	0.228937	−	0.704597i	−0.768931	−	0.639332i	$-0.779211\pi$
$673$	5.93915	−	18.2788i	0.228937	−	0.704597i	0.997868	−	0.0652647i	$-0.0207892\pi$
$674$	−22.8293	+	16.5865i	−0.879352	+	0.638887i
$675$	−45.3525	−	32.9505i	−1.74562	−	1.26826i
$676$	14.3547	+	44.1792i	0.552103	+	1.69920i
$677$	−7.95127	−	24.4715i	−0.305592	−	0.940516i	−0.979456	−	0.201660i	$-0.935366\pi$
$677$	−7.95127	−	24.4715i	−0.305592	−	0.940516i	0.673863	−	0.738856i	$-0.264634\pi$
$678$	73.9436	+	53.7232i	2.83979	+	2.06323i
$679$	−7.11545	+	5.16968i	−0.273066	+	0.198394i
$680$	−0.920032	+	2.83157i	−0.0352816	+	0.108586i
$681$	33.4986			1.28367
$682$		0			0
$683$	−11.0596			−0.423185			−0.211593	−	0.977358i	$-0.567865\pi$
$683$	−11.0596			−0.423185			−0.211593	+	0.977358i	$0.567865\pi$
$684$	27.7616	−	85.4413i	1.06149	−	3.26693i
$685$	3.80665	−	2.76569i	0.145444	−	0.105672i
$686$	1.71907	+	1.24898i	0.0656343	+	0.0476861i
$687$	−5.26718	−	16.2107i	−0.200955	−	0.618477i
$688$	0.860994	+	2.64987i	0.0328251	+	0.101025i
$689$	−13.7525	−	9.99181i	−0.523930	−	0.380658i
$690$	6.47214	−	4.70228i	0.246390	−	0.179013i
$691$	13.9137	−	42.8219i	0.529301	−	1.62902i	−0.226350	−	0.974046i	$-0.572679\pi$
$691$	13.9137	−	42.8219i	0.529301	−	1.62902i	0.755651	−	0.654975i	$-0.227321\pi$
$692$	20.5483			0.781128
$693$		0			0
$694$	38.3103			1.45424
$695$	2.95451	−	9.09306i	0.112071	−	0.344919i
$696$	−14.6113	+	10.6157i	−0.553840	+	0.402388i
$697$	−10.8479	−	7.88144i	−0.410893	−	0.298531i
$698$	14.4126	+	44.3573i	0.545523	+	1.67895i
$699$	28.7564	+	88.5032i	1.08767	+	3.34750i
$700$	−9.69559	−	7.04426i	−0.366459	−	0.266248i
$701$	37.8447	−	27.4958i	1.42938	−	1.03850i	0.439244	−	0.898368i	$-0.355246\pi$
$701$	37.8447	−	27.4958i	1.42938	−	1.03850i	0.990132	−	0.140135i	$-0.0447535\pi$
$702$	43.3361	−	133.375i	1.63562	−	5.03391i
$703$	−1.24129			−0.0468162
$704$		0			0
$705$	2.43899			0.0918577
$706$	12.3812	−	38.1053i	0.465971	−	1.43411i
$707$	10.4771	−	7.61202i	0.394030	−	0.286280i
$708$	19.8695	+	14.4361i	0.746743	+	0.542540i
$709$	−2.82573	−	8.69671i	−0.106123	−	0.326612i	0.883870	−	0.467733i	$-0.154929\pi$
$709$	−2.82573	−	8.69671i	−0.106123	−	0.326612i	−0.989992	+	0.141121i	$0.954929\pi$
$710$	3.84443	+	11.8319i	0.144279	+	0.444044i
$711$	49.4220	+	35.9072i	1.85347	+	1.34663i
$712$	1.12056	−	0.814131i	0.0419946	−	0.0305109i
$713$	−5.47095	+	16.8378i	−0.204889	+	0.630582i
$714$	−37.2489			−1.39400
$715$		0			0
$716$	−30.8468			−1.15280
$717$	2.47214	−	7.60845i	0.0923236	−	0.284143i
$718$	2.62986	−	1.91071i	0.0981456	−	0.0713069i
$719$	24.6471	+	17.9072i	0.919182	+	0.667824i	0.943320	−	0.331884i	$-0.107684\pi$
$719$	24.6471	+	17.9072i	0.919182	+	0.667824i	−0.0241386	+	0.999709i	$0.507684\pi$
$720$	−2.74111	−	8.43627i	−0.102155	−	0.314401i
$721$	−3.76069	−	11.5742i	−0.140055	−	0.431046i
$722$	−15.2634	−	11.0895i	−0.568046	−	0.412710i
$723$	−69.2426	+	50.3077i	−2.57516	+	1.87096i
$724$	−5.47548	+	16.8518i	−0.203495	+	0.626292i
$725$	25.1589			0.934380
$726$		0			0
$727$	−6.12580			−0.227193			−0.113597	−	0.993527i	$-0.536237\pi$
$727$	−6.12580			−0.227193			−0.113597	+	0.993527i	$0.536237\pi$
$728$	1.89751	−	5.83995i	0.0703265	−	0.216443i
$729$	−0.906992	+	0.658969i	−0.0335923	+	0.0244062i
$730$	1.99230	+	1.44749i	0.0737384	+	0.0535741i
$731$	1.78599	+	5.49672i	0.0660573	+	0.203303i
$732$	−5.80527	−	17.8668i	−0.214569	−	0.660375i
$733$	−34.0358	−	24.7284i	−1.25714	−	0.913366i	−0.258526	−	0.966004i	$-0.583237\pi$
$733$	−34.0358	−	24.7284i	−1.25714	−	0.913366i	−0.998614	+	0.0526384i	$0.983237\pi$
$734$	−25.1924	+	18.3034i	−0.929870	+	0.675590i
$735$	−0.468203	+	1.44098i	−0.0172699	+	0.0531514i
$736$	−19.7190			−0.726853
$737$		0			0
$738$	−34.3591			−1.26477
$739$	8.92379	−	27.4646i	0.328267	−	1.01030i	−0.641678	−	0.766974i	$-0.721761\pi$
$739$	8.92379	−	27.4646i	0.328267	−	1.01030i	0.969944	−	0.243327i	$-0.0782387\pi$
$740$	0.231939	−	0.168514i	0.00852625	−	0.00619468i
$741$	−74.8812	−	54.4044i	−2.75083	−	1.99859i
$742$	1.98976	+	6.12384i	0.0730463	+	0.224813i
$743$	4.53674	+	13.9626i	0.166437	+	0.512240i	0.999139	−	0.0414808i	$-0.0132075\pi$
$743$	4.53674	+	13.9626i	0.166437	+	0.512240i	−0.832702	+	0.553721i	$0.813208\pi$
$744$	−19.7165	−	14.3248i	−0.722840	−	0.525174i
$745$	4.14232	−	3.00957i	0.151763	−	0.110262i
$746$	−6.60602	+	20.3312i	−0.241863	+	0.744379i
$747$	21.7796			0.796873
$748$		0			0
$749$	10.5601			0.385857
$750$	9.71490	−	29.8994i	0.354738	−	1.09177i
$751$	5.34434	−	3.88289i	0.195018	−	0.141689i	−0.485991	−	0.873964i	$-0.661541\pi$
$751$	5.34434	−	3.88289i	0.195018	−	0.141689i	0.681009	+	0.732275i	$0.261541\pi$
$752$	−3.52192	−	2.55882i	−0.128431	−	0.0933107i
$753$	−9.50660	−	29.2583i	−0.346440	−	1.06623i
$754$	19.4491	+	59.8581i	0.708294	+	2.17990i
$755$	6.06800	+	4.40866i	0.220837	+	0.160448i
$756$	−23.9391	+	17.3928i	−0.870657	+	0.632569i
$757$	0.772401	−	2.37721i	0.0280734	−	0.0864010i	−0.936038	−	0.351899i	$-0.885536\pi$
$757$	0.772401	−	2.37721i	0.0280734	−	0.0864010i	0.964112	+	0.265498i	$0.0855362\pi$
$758$	−38.0218			−1.38101
$759$		0			0
$760$	2.80230			0.101650
$761$	3.72326	−	11.4590i	0.134968	−	0.415390i	−0.860617	−	0.509253i	$-0.829922\pi$
$761$	3.72326	−	11.4590i	0.134968	−	0.415390i	0.995585	+	0.0938635i	$0.0299217\pi$
$762$	−13.7525	+	9.99181i	−0.498202	+	0.361965i
$763$	5.93867	+	4.31470i	0.214994	+	0.156202i
$764$	14.6080	+	44.9588i	0.528499	+	1.62655i
$765$	−5.68599	−	17.4997i	−0.205577	−	0.632702i
$766$	32.6022	+	23.6869i	1.17796	+	0.855841i
$767$	14.1819	−	10.3038i	0.512079	−	0.372048i
$768$	−4.74826	+	14.6137i	−0.171338	+	0.527325i
$769$	−0.489560			−0.0176540			−0.00882699	−	0.999961i	$-0.502810\pi$
$769$	−0.489560			−0.0176540			−0.00882699	+	0.999961i	$0.502810\pi$
$770$		0			0
$771$	70.3085			2.53210
$772$	−12.8238	+	39.4675i	−0.461538	+	1.42047i
$773$	37.7958	−	27.4602i	1.35942	−	0.987676i	0.360937	−	0.932590i	$-0.382457\pi$
$773$	37.7958	−	27.4602i	1.35942	−	0.987676i	0.998482	−	0.0550854i	$-0.0175431\pi$
$774$	11.9814	+	8.70502i	0.430664	+	0.312895i
$775$	10.4910	+	32.2878i	0.376846	+	1.15981i
$776$	−2.97500	−	9.15610i	−0.106796	−	0.328685i
$777$	0.594330	+	0.431806i	0.0213215	+	0.0154910i
$778$	−58.9029	+	42.7955i	−2.11177	+	1.53429i
$779$	−3.89999	+	12.0029i	−0.139732	+	0.430050i
$780$	21.3775			0.765438
$781$		0			0
$782$	−29.6197			−1.05920
$783$	19.1959	−	59.0789i	0.686006	−	2.11131i
$784$	2.18787	−	1.58958i	0.0781382	−	0.0567707i
$785$	−3.57174	−	2.59502i	−0.127481	−	0.0926203i
$786$	−5.58102	−	17.1766i	−0.199068	−	0.612669i
$787$	2.57710	+	7.93151i	0.0918638	+	0.282728i	0.986424	−	0.164220i	$-0.0525108\pi$
$787$	2.57710	+	7.93151i	0.0918638	+	0.282728i	−0.894560	+	0.446948i	$0.852511\pi$
$788$	49.8514	+	36.2192i	1.77588	+	1.29025i
$789$	40.4494	−	29.3882i	1.44004	−	1.04625i
$790$	−2.87499	+	8.84832i	−0.102288	+	0.314809i
$791$	−13.7649			−0.489424
$792$		0			0
$793$	−13.4087			−0.476157
$794$	10.6893	−	32.8983i	0.379349	−	1.16752i
$795$	−3.71443	+	2.69869i	−0.131737	+	0.0957127i
$796$	31.3141	+	22.7510i	1.10990	+	0.806388i
$797$	−9.73871	−	29.9727i	−0.344963	−	1.06169i	−0.961604	−	0.274442i	$-0.911507\pi$
$797$	−9.73871	−	29.9727i	−0.344963	−	1.06169i	0.616641	−	0.787245i	$-0.288493\pi$
$798$	10.8340	+	33.3437i	0.383520	+	1.18035i
$799$	−7.30565	−	5.30786i	−0.258455	−	0.187779i
$800$	−30.5911	+	22.2258i	−1.08156	+	0.785799i
$801$	−2.64521	+	8.14113i	−0.0934641	+	0.287653i
$802$	61.4911			2.17132
$803$		0			0
$804$	−78.7106			−2.77591
$805$	−0.372308	+	1.14585i	−0.0131221	+	0.0403858i
$806$	−68.7091	+	49.9201i	−2.42018	+	1.75836i
$807$	23.3077	+	16.9340i	0.820469	+	0.596106i
$808$	4.38049	+	13.4818i	0.154105	+	0.474287i
$809$	−4.78991	−	14.7418i	−0.168404	−	0.518295i	0.830867	−	0.556471i	$-0.187845\pi$
$809$	−4.78991	−	14.7418i	−0.168404	−	0.518295i	−0.999271	+	0.0381767i	$0.987845\pi$
$810$	−13.7273	−	9.97348i	−0.482329	−	0.350432i
$811$	−39.1076	+	28.4134i	−1.37325	+	0.997728i	−0.375779	+	0.926709i	$0.622625\pi$
$811$	−39.1076	+	28.4134i	−1.37325	+	0.997728i	−0.997475	+	0.0710186i	$0.977375\pi$
$812$	4.10376	−	12.6301i	0.144014	−	0.443229i
$813$	32.9991			1.15733
$814$		0			0
$815$	−6.43899			−0.225548
$816$	−14.6495	+	45.0866i	−0.512836	+	1.57835i
$817$	4.40098	−	3.19750i	0.153971	−	0.111866i
$818$	26.6635	+	19.3722i	0.932268	+	0.677332i
$819$	11.7270	+	36.0921i	0.409775	+	1.26116i
$820$	−0.900754	−	2.77224i	−0.0314557	−	0.0968107i
$821$	−8.54330	−	6.20707i	−0.298163	−	0.216628i	0.428638	−	0.903476i	$-0.358994\pi$
$821$	−8.54330	−	6.20707i	−0.298163	−	0.216628i	−0.726801	+	0.686848i	$0.758994\pi$
$822$	−52.1308	+	37.8752i	−1.81827	+	1.32105i
$823$	5.97147	−	18.3783i	0.208152	−	0.640627i	−0.791417	−	0.611277i	$-0.790656\pi$
$823$	5.97147	−	18.3783i	0.208152	−	0.640627i	0.999569	−	0.0293503i	$-0.00934383\pi$
$824$	13.3212			0.464067
$825$		0			0
$826$	−6.64002			−0.231036
$827$	0.164006	−	0.504758i	0.00570305	−	0.0175522i	−0.948165	−	0.317780i	$-0.897063\pi$
$827$	0.164006	−	0.504758i	0.00570305	−	0.0175522i	0.953868	+	0.300228i	$0.0970627\pi$
$828$	−34.2045	+	24.8510i	−1.18869	+	0.863634i
$829$	38.1819	+	27.7408i	1.32611	+	0.963477i	0.999834	+	0.0182029i	$0.00579448\pi$
$829$	38.1819	+	27.7408i	1.32611	+	0.963477i	0.326278	+	0.945274i	$0.394206\pi$
$830$	1.02500	+	3.15462i	0.0355783	+	0.109499i
$831$	−17.9224	−	55.1595i	−0.621722	−	1.91346i
$832$	−51.9811	−	37.7665i	−1.80212	−	1.30932i
$833$	4.53838	−	3.29733i	0.157246	−	0.114246i
$834$	−40.4611	+	124.526i	−1.40105	+	4.31200i
$835$	−4.87798			−0.168809
$836$		0			0
$837$	83.8236			2.89737
$838$	−8.50353	+	26.1712i	−0.293750	+	0.904068i
$839$	30.6646	−	22.2792i	1.05866	−	0.769162i	0.0848203	−	0.996396i	$-0.472968\pi$
$839$	30.6646	−	22.2792i	1.05866	−	0.769162i	0.973840	+	0.227235i	$0.0729684\pi$
$840$	−1.34174	−	0.974833i	−0.0462945	−	0.0336349i
$841$	−0.346440	−	1.06623i	−0.0119462	−	0.0367667i
$842$	−11.2223	−	34.5386i	−0.386745	−	1.19028i
$843$	−64.8668	−	47.1285i	−2.23413	−	1.62319i
$844$	−29.3803	+	21.3460i	−1.01131	+	0.734761i
$845$	2.76726	−	8.51675i	0.0951967	−	0.292985i
$846$	−23.1396			−0.795555
$847$		0			0
$848$	8.19495			0.281416
$849$	29.2388	−	89.9878i	1.00347	−	3.08837i
$850$	−45.9506	+	33.3851i	−1.57609	+	1.14510i
$851$	0.472603	+	0.343366i	0.0162006	+	0.0117704i
$852$	−29.3274	−	90.2605i	−1.00474	−	3.09227i
$853$	1.93727	+	5.96231i	0.0663310	+	0.204146i	0.978729	−	0.205159i	$-0.0657712\pi$
$853$	1.93727	+	5.96231i	0.0663310	+	0.204146i	−0.912398	+	0.409305i	$0.865771\pi$
$854$	4.10901	+	2.98537i	0.140607	+	0.102157i
$855$	−14.0112	+	10.1797i	−0.479173	+	0.348140i
$856$	−3.57198	+	10.9934i	−0.122088	+	0.375748i
$857$	−36.9503			−1.26220			−0.631100	−	0.775702i	$-0.717396\pi$
$857$	−36.9503			−1.26220			−0.631100	+	0.775702i	$0.717396\pi$
$858$		0			0
$859$	8.90447			0.303817			0.151908	−	0.988395i	$-0.451458\pi$
$859$	8.90447			0.303817			0.151908	+	0.988395i	$0.451458\pi$
$860$	−0.388254	+	1.19492i	−0.0132394	+	0.0407465i
$861$	6.04276	−	4.39032i	0.205937	−	0.149622i
$862$	33.2608	+	24.1654i	1.13287	+	0.823077i
$863$	−13.0156	−	40.0578i	−0.443055	−	1.36358i	−0.884603	−	0.466346i	$-0.845570\pi$
$863$	−13.0156	−	40.0578i	−0.443055	−	1.36358i	0.441547	−	0.897238i	$-0.354430\pi$
$864$	28.8506	+	88.7929i	0.981516	+	3.02080i
$865$	−3.20471	−	2.32836i	−0.108964	−	0.0791667i
$866$	−27.2051	+	19.7656i	−0.924465	+	0.671663i
$867$	−13.9721	+	43.0018i	−0.474519	+	1.46042i
$868$	17.9201			0.608247
$869$		0			0
$870$	16.9991			0.576323
$871$	−17.3605	+	53.4302i	−0.588239	+	1.81041i
$872$	−6.50052	+	4.72291i	−0.220135	+	0.159938i
$873$	48.1354	+	34.9724i	1.62914	+	1.18364i
$874$	8.61505	+	26.5144i	0.291408	+	0.896863i
$875$	1.46308	+	4.50290i	0.0494612	+	0.152226i
$876$	−15.1984	−	11.0423i	−0.513506	−	0.373084i
$877$	19.6912	−	14.3065i	0.664925	−	0.483096i	−0.203397	−	0.979096i	$-0.565198\pi$
$877$	19.6912	−	14.3065i	0.664925	−	0.483096i	0.868323	+	0.496000i	$0.165198\pi$
$878$	7.26204	−	22.3503i	0.245082	−	0.754285i
$879$	9.52982			0.321433
$880$		0			0
$881$	5.64380			0.190145			0.0950723	−	0.995470i	$-0.469692\pi$
$881$	5.64380			0.190145			0.0950723	+	0.995470i	$0.469692\pi$
$882$	4.44201	−	13.6711i	0.149570	−	0.460330i
$883$	−12.2815	+	8.92302i	−0.413305	+	0.300283i	−0.774938	−	0.632037i	$-0.782219\pi$
$883$	−12.2815	+	8.92302i	−0.413305	+	0.300283i	0.361634	+	0.932320i	$0.382219\pi$
$884$	−64.0333	−	46.5229i	−2.15367	−	1.56474i
$885$	−1.46308	−	4.50290i	−0.0491810	−	0.151363i
$886$	−22.7872	−	70.1317i	−0.765550	−	2.35612i
$887$	21.6958	+	15.7629i	0.728472	+	0.529266i	0.889080	−	0.457752i	$-0.151345\pi$
$887$	21.6958	+	15.7629i	0.728472	+	0.529266i	−0.160608	+	0.987018i	$0.551345\pi$
$888$	−0.650560	+	0.472659i	−0.0218314	+	0.0158614i
$889$	0.791113	−	2.43479i	0.0265331	−	0.0816604i
$890$	−1.30368			−0.0436994
$891$		0			0
$892$	43.3951			1.45297
$893$	−2.62650	+	8.08354i	−0.0878926	+	0.270506i
$894$	−56.7277	+	41.2151i	−1.89726	+	1.37844i
$895$	4.81087	+	3.49530i	0.160810	+	0.116835i
$896$	2.61626	+	8.05203i	0.0874032	+	0.268999i
$897$	13.4605	+	41.4272i	0.449434	+	1.38322i
$898$	62.3915	+	45.3301i	2.08203	+	1.51269i
$899$	−30.4350	+	22.1123i	−1.01506	+	0.737487i
$900$	−25.0531	+	77.1054i	−0.835102	+	2.57018i
$901$	16.9991			0.566322
$902$		0			0
$903$	−3.21949			−0.107138
$904$	4.65602	−	14.3298i	0.154857	−	0.476601i
$905$	2.76347	−	2.00778i	0.0918607	−	0.0667407i
$906$	−83.0992	−	60.3751i	−2.76079	−	2.00583i
$907$	9.91866	+	30.5265i	0.329344	+	1.01362i	0.969441	+	0.245323i	$0.0788939\pi$
$907$	9.91866	+	30.5265i	0.329344	+	1.01362i	−0.640098	+	0.768294i	$0.721106\pi$
$908$	−8.33177	−	25.6425i	−0.276499	−	0.850978i
$909$	−70.8763	−	51.4946i	−2.35082	−	1.70797i
$910$	−4.67579	+	3.39716i	−0.155001	+	0.112615i
$911$	3.75760	−	11.5647i	0.124495	−	0.383156i	−0.869314	−	0.494261i	$-0.835439\pi$
$911$	3.75760	−	11.5647i	0.124495	−	0.383156i	0.993809	+	0.111105i	$0.0354389\pi$
$912$	44.6206			1.47754
$913$		0			0
$914$	4.37844			0.144826
$915$	−1.11912	+	3.44431i	−0.0369971	+	0.113865i
$916$	−11.0989	+	8.06385i	−0.366719	+	0.266437i
$917$	2.20049	+	1.59875i	0.0726665	+	0.0527953i
$918$	43.3361	+	133.375i	1.43030	+	4.40202i
$919$	12.3607	+	38.0423i	0.407741	+	1.25490i	0.918585	+	0.395225i	$0.129333\pi$
$919$	12.3607	+	38.0423i	0.407741	+	1.25490i	−0.510843	+	0.859674i	$0.670667\pi$
$920$	−1.06693	−	0.775172i	−0.0351757	−	0.0255567i
$921$	−9.40204	+	6.83098i	−0.309808	+	0.225089i
$922$	4.70850	−	14.4913i	0.155066	−	0.477245i
$923$	−67.7390			−2.22966
$924$		0			0
$925$	1.12019			0.0368315
$926$	2.26837	−	6.98132i	0.0745433	−	0.229421i
$927$	−66.6046	+	48.3911i	−2.18758	+	1.58937i
$928$	−33.8984	−	24.6286i	−1.11277	−	0.808474i
$929$	−6.60658	−	20.3330i	−0.216755	−	0.667103i	−0.999024	−	0.0441629i	$-0.985938\pi$
$929$	−6.60658	−	20.3330i	−0.216755	−	0.667103i	0.782269	−	0.622940i	$-0.214062\pi$
$930$	7.08840	+	21.8158i	0.232438	+	0.715370i
$931$	−4.27165	−	3.10353i	−0.139998	−	0.101714i
$932$	60.5952	−	44.0250i	1.98486	−	1.44209i
$933$	−4.02658	+	12.3925i	−0.131824	+	0.405713i
$934$	−28.6769			−0.938338
$935$		0			0
$936$	−41.5398			−1.35777
$937$	9.73726	−	29.9682i	0.318102	−	0.979019i	−0.656356	−	0.754451i	$-0.727903\pi$
$937$	9.73726	−	29.9682i	0.318102	−	0.979019i	0.974459	−	0.224567i	$-0.0720969\pi$
$938$	17.2159	−	12.5081i	0.562120	−	0.408404i
$939$	−29.5896	−	21.4981i	−0.965621	−	0.701564i
$940$	−0.606625	−	1.86700i	−0.0197859	−	0.0608948i
$941$	−13.2043	−	40.6386i	−0.430447	−	1.32478i	−0.897681	−	0.440646i	$-0.854749\pi$
$941$	−13.2043	−	40.6386i	−0.430447	−	1.32478i	0.467234	−	0.884134i	$-0.345251\pi$
$942$	48.9138	+	35.5380i	1.59370	+	1.15789i
$943$	4.80511	−	3.49112i	0.156476	−	0.113687i
$944$	−2.61144	+	8.03719i	−0.0849952	+	0.261588i
$945$	5.70436			0.185563
$946$		0			0
$947$	3.29473			0.107064			0.0535321	−	0.998566i	$-0.482952\pi$
$947$	3.29473			0.107064			0.0535321	+	0.998566i	$0.482952\pi$
$948$	21.9321	−	67.4999i	0.712320	−	2.19230i
$949$	−10.8479	+	7.88144i	−0.352137	+	0.255842i
$950$	43.2499	+	31.4229i	1.40321	+	1.01949i
$951$	2.15830	+	6.64256i	0.0699877	+	0.215400i
$952$	1.89751	+	5.83995i	0.0614988	+	0.189274i
$953$	31.2937	+	22.7362i	1.01370	+	0.736499i	0.964983	−	0.262313i	$-0.0844854\pi$
$953$	31.2937	+	22.7362i	1.01370	+	0.736499i	0.0487212	+	0.998812i	$0.484485\pi$
$954$	35.2401	−	25.6034i	1.14094	−	0.828942i
$955$	2.81609	−	8.66704i	0.0911266	−	0.280459i
$956$	−6.43899			−0.208252
$957$		0			0
$958$	−74.4977			−2.40691
$959$	2.99881	−	9.22939i	0.0968367	−	0.298033i
$960$	−14.0396	+	10.2004i	−0.453126	+	0.329215i
$961$	−15.9894	−	11.6170i	−0.515787	−	0.374741i
$962$	0.865959	+	2.66515i	0.0279196	+	0.0859278i
$963$	−22.0756	−	67.9416i	−0.711376	−	2.18939i
$964$	55.7315	+	40.4913i	1.79499	+	1.30414i
$965$	6.47214	−	4.70228i	0.208345	−	0.151372i
$966$	5.09864	−	15.6920i	0.164046	−	0.504882i
$967$	3.34816			0.107670			0.0538348	−	0.998550i	$-0.482856\pi$
$967$	3.34816			0.107670			0.0538348	+	0.998550i	$0.482856\pi$
$968$		0			0
$969$	92.5583			2.97340
$970$	−2.80015	+	8.61797i	−0.0899073	+	0.276706i
$971$	−47.5002	+	34.5109i	−1.52435	+	1.10751i	−0.565076	+	0.825039i	$0.691153\pi$
$971$	−47.5002	+	34.5109i	−1.52435	+	1.10751i	−0.959277	+	0.282468i	$0.908847\pi$
$972$	32.9022	+	23.9049i	1.05534	+	0.766749i
$973$	−6.09352	−	18.7539i	−0.195349	−	0.601223i
$974$	19.4792	+	59.9508i	0.624154	+	1.92095i
$975$	67.5756	+	49.0965i	2.16415	+	1.57235i
$976$	5.22956	−	3.79950i	0.167394	−	0.121619i
$977$	4.25359	−	13.0912i	0.136084	−	0.418825i	−0.859673	−	0.510845i	$-0.829333\pi$
$977$	4.25359	−	13.0912i	0.136084	−	0.418825i	0.995757	+	0.0920204i	$0.0293325\pi$
$978$	88.1798			2.81968
$979$		0			0
$980$	1.21949			0.0389553
$981$	15.3453	−	47.2280i	0.489938	−	1.50787i
$982$	43.8875	−	31.8861i	1.40051	−	1.01753i
$983$	−40.6239	−	29.5150i	−1.29570	−	0.941382i	−0.295797	−	0.955251i	$-0.595585\pi$
$983$	−40.6239	−	29.5150i	−1.29570	−	0.941382i	−0.999904	+	0.0138693i	$0.995585\pi$
$984$	2.52650	+	7.77577i	0.0805419	+	0.247882i
$985$	−3.67078	−	11.2975i	−0.116961	−	0.359968i
$986$	−50.9183	−	36.9943i	−1.62157	−	1.17814i
$987$	4.06958	−	2.95672i	0.129536	−	0.0941135i
$988$	−23.0211	+	70.8515i	−0.732397	+	2.25409i
$989$	−2.56009			−0.0814062
$990$		0			0
$991$	−4.65940			−0.148011			−0.0740054	−	0.997258i	$-0.523578\pi$
$991$	−4.65940			−0.148011			−0.0740054	+	0.997258i	$0.523578\pi$
$992$	17.4720	−	53.7734i	0.554738	−	1.70731i
$993$	56.4395	−	41.0057i	1.79105	−	1.30128i
$994$	20.7581	+	15.0817i	0.658409	+	0.478362i
$995$	−2.30579	−	7.09650i	−0.0730986	−	0.224974i
$996$	−7.81927	−	24.0652i	−0.247763	−	0.762536i
$997$	2.74203	+	1.99220i	0.0868410	+	0.0630937i	0.630359	−	0.776304i	$-0.282908\pi$
$997$	2.74203	+	1.99220i	0.0868410	+	0.0630937i	−0.543518	+	0.839398i	$0.682908\pi$
$998$	44.1087	−	32.0468i	1.39624	−	1.01442i
$999$	0.854687	−	2.63046i	0.0270411	−	0.0832240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.u.372.3		12
11.2	odd	10		847.2.f.t.729.3		12
11.3	even	5	inner	847.2.f.u.323.1		12
11.4	even	5		847.2.a.i.1.3	✓	3
11.5	even	5	inner	847.2.f.u.148.3		12
11.6	odd	10		847.2.f.t.148.1		12
11.7	odd	10		847.2.a.j.1.1	yes	3
11.8	odd	10		847.2.f.t.323.3		12
11.9	even	5	inner	847.2.f.u.729.1		12
11.10	odd	2		847.2.f.t.372.1		12
33.26	odd	10		7623.2.a.ce.1.1		3
33.29	even	10		7623.2.a.bz.1.3		3
77.48	odd	10		5929.2.a.t.1.3		3
77.62	even	10		5929.2.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.3	✓	3	11.4	even	5
847.2.a.j.1.1	yes	3	11.7	odd	10
847.2.f.t.148.1		12	11.6	odd	10
847.2.f.t.323.3		12	11.8	odd	10
847.2.f.t.372.1		12	11.10	odd	2
847.2.f.t.729.3		12	11.2	odd	10
847.2.f.u.148.3		12	11.5	even	5	inner
847.2.f.u.323.1		12	11.3	even	5	inner
847.2.f.u.372.3		12	1.1	even	1	trivial
847.2.f.u.729.1		12	11.9	even	5	inner
5929.2.a.t.1.3		3	77.48	odd	10
5929.2.a.y.1.1		3	77.62	even	10
7623.2.a.bz.1.3		3	33.29	even	10
7623.2.a.ce.1.1		3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.656626 - 2.02089i) q^{2} +(2.52809 - 1.83676i) q^{3} +(-2.03479 - 1.47836i) q^{4} +(0.149831 + 0.461131i) q^{5} +(-2.05188 - 6.31504i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.885558 + 0.643395i) q^{8} +(2.09047 - 6.43381i) q^{9} +1.03028 q^{10} -7.85952 q^{12} +(-1.73351 + 5.33519i) q^{13} +(1.71907 - 1.24898i) q^{14} +(1.22577 + 0.890576i) q^{15} +(-0.835692 - 2.57200i) q^{16} +(-1.73351 - 5.33519i) q^{17} +(-11.6293 - 8.44921i) q^{18} +(-4.27165 + 3.10353i) q^{19} +(0.376845 - 1.15981i) q^{20} +3.12489 q^{21} +2.48486 q^{23} +(-1.05700 + 3.25312i) q^{24} +(3.85489 - 2.80074i) q^{25} +(9.64354 + 7.00644i) q^{26} +(-3.63556 - 11.1891i) q^{27} +(-0.777220 - 2.39204i) q^{28} +(4.27165 + 3.10353i) q^{29} +(2.60463 - 1.89237i) q^{30} +(-2.20171 + 6.77617i) q^{31} -7.93567 q^{32} -11.9201 q^{34} +(-0.149831 + 0.461131i) q^{35} +(-13.7652 + 10.0010i) q^{36} +(0.190193 + 0.138183i) q^{37} +(3.46701 + 10.6704i) q^{38} +(5.41701 + 16.6718i) q^{39} +(-0.429373 - 0.311958i) q^{40} +(1.93375 - 1.40496i) q^{41} +(2.05188 - 6.31504i) q^{42} -1.03028 q^{43} +3.28005 q^{45} +(1.63162 - 5.02162i) q^{46} +(1.30231 - 0.946186i) q^{47} +(-6.83684 - 4.96726i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-3.12876 - 9.62934i) q^{50} +(-14.1819 - 10.3038i) q^{51} +(11.4147 - 8.29323i) q^{52} +(-0.936407 + 2.88196i) q^{53} -24.9991 q^{54} -1.09461 q^{56} +(-5.09864 + 15.6920i) q^{57} +(9.07676 - 6.59465i) q^{58} +(-2.52809 - 1.83676i) q^{59} +(-1.17760 - 3.62427i) q^{60} +(0.738629 + 2.27327i) q^{61} +(12.2482 + 8.89881i) q^{62} +(5.47293 - 3.97631i) q^{63} +(-3.53938 + 10.8931i) q^{64} -2.71995 q^{65} +10.0147 q^{67} +(-4.36001 + 13.4187i) q^{68} +(6.28194 - 4.56410i) q^{69} +(0.833511 + 0.605581i) q^{70} +(3.73145 + 11.4842i) q^{71} +(2.28825 + 7.04251i) q^{72} +(1.93375 + 1.40496i) q^{73} +(0.404138 - 0.293623i) q^{74} +(4.60120 - 14.1610i) q^{75} +13.2800 q^{76} +37.2489 q^{78} +(-2.79051 + 8.58830i) q^{79} +(1.06082 - 0.770727i) q^{80} +(-13.3239 - 9.68039i) q^{81} +(-1.56950 - 4.83043i) q^{82} +(0.994879 + 3.06192i) q^{83} +(-6.35848 - 4.61971i) q^{84} +(2.20049 - 1.59875i) q^{85} +(-0.676506 + 2.08207i) q^{86} +16.4995 q^{87} -1.26537 q^{89} +(2.15376 - 6.62860i) q^{90} +(-4.53838 + 3.29733i) q^{91} +(-5.05617 - 3.67352i) q^{92} +(6.88009 + 21.1748i) q^{93} +(-1.05700 - 3.25312i) q^{94} +(-2.07116 - 1.50479i) q^{95} +(-20.0620 + 14.5759i) q^{96} +(-2.71786 + 8.36472i) q^{97} +2.12489 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23}+ \cdots - 8 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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