LMFDB - Embedded newform 420.2.l.h.239.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 9 x^{14} - 16 x^{13} + 18 x^{12} - 4 x^{11} - 36 x^{10} + 102 x^{9} - 170 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 9x^14 - 16x^13 + 18x^12 - 4x^11 - 36x^10 + 102x^9 - 170x^8 + 204x^7 - 144x^6 - 32x^5 + 288x^4 - 512x^3 + 576x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.14
Root			$-0.167106 - 1.40431i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25945 + 0.643263i) q^{2} +(1.48716 + 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(-2.05223 - 0.887900i) q^{5} +(1.30184 + 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 + 2.79488i) q^{8} +(1.42327 + 2.64089i) q^{9} +O(q^{10})$	\(q+(1.25945 + 0.643263i) q^{2} +(1.48716 + 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(-2.05223 - 0.887900i) q^{5} +(1.30184 + 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 + 2.79488i) q^{8} +(1.42327 + 2.64089i) q^{9} +(-2.01352 - 2.43839i) q^{10} +2.75993 q^{11} +(0.304900 + 3.45066i) q^{12} -1.90761i q^{13} +(1.25945 + 0.643263i) q^{14} +(-2.26361 - 3.14262i) q^{15} +(-1.25084 + 3.79939i) q^{16} -5.03780 q^{17} +(0.0937425 + 4.24160i) q^{18} +1.90761i q^{19} +(-0.967402 - 4.36625i) q^{20} +(1.48716 + 0.887900i) q^{21} +(3.47600 + 1.77536i) q^{22} -2.05073i q^{23} +(-1.83568 + 4.54206i) q^{24} +(3.42327 + 3.64434i) q^{25} +(1.22710 - 2.40254i) q^{26} +(-0.228229 + 5.19114i) q^{27} +(1.17242 + 1.62032i) q^{28} -4.94433i q^{29} +(-0.829376 - 5.41407i) q^{30} -6.92361i q^{31} +(-4.01938 + 3.98052i) q^{32} +(4.10445 + 2.45055i) q^{33} +(-6.34485 - 3.24063i) q^{34} +(-2.05223 - 0.887900i) q^{35} +(-2.61041 + 5.40239i) q^{36} -6.48126i q^{37} +(-1.22710 + 2.40254i) q^{38} +(1.69377 - 2.83692i) q^{39} +(1.59025 - 6.12136i) q^{40} -11.1795i q^{41} +(1.30184 + 2.07490i) q^{42} -9.36439 q^{43} +(3.23581 + 4.47196i) q^{44} +(-0.576017 - 6.68343i) q^{45} +(1.31916 - 2.58279i) q^{46} +7.51739i q^{47} +(-5.23368 + 4.53967i) q^{48} +1.00000 q^{49} +(1.96716 + 6.79193i) q^{50} +(-7.49199 - 4.47306i) q^{51} +(3.09093 - 2.23653i) q^{52} +6.14747 q^{53} +(-3.62671 + 6.39116i) q^{54} +(-5.66401 - 2.45055i) q^{55} +(0.434319 + 2.79488i) q^{56} +(-1.69377 + 2.83692i) q^{57} +(3.18051 - 6.22714i) q^{58} +0.716916 q^{59} +(2.43812 - 7.35225i) q^{60} +5.13115 q^{61} +(4.45370 - 8.71993i) q^{62} +(1.42327 + 2.64089i) q^{63} +(-7.62273 + 2.42774i) q^{64} +(-1.69377 + 3.91485i) q^{65} +(3.59300 + 5.72658i) q^{66} +3.58761 q^{67} +(-5.90644 - 8.16282i) q^{68} +(1.82085 - 3.04976i) q^{69} +(-2.01352 - 2.43839i) q^{70} +4.49721 q^{71} +(-6.76283 + 5.12485i) q^{72} -6.11618i q^{73} +(4.16916 - 8.16282i) q^{74} +(1.85512 + 8.45923i) q^{75} +(-3.09093 + 2.23653i) q^{76} +2.75993 q^{77} +(3.95810 - 2.48341i) q^{78} +14.6546i q^{79} +(5.94049 - 6.68659i) q^{80} +(-4.94862 + 7.51739i) q^{81} +(7.19138 - 14.0800i) q^{82} -7.71558i q^{83} +(0.304900 + 3.45066i) q^{84} +(10.3387 + 4.47306i) q^{85} +(-11.7940 - 6.02377i) q^{86} +(4.39007 - 7.35300i) q^{87} +(1.19869 + 7.71369i) q^{88} +13.5677i q^{89} +(3.57374 - 8.78797i) q^{90} -1.90761i q^{91} +(3.32283 - 2.40433i) q^{92} +(6.14747 - 10.2965i) q^{93} +(-4.83566 + 9.46777i) q^{94} +(1.69377 - 3.91485i) q^{95} +(-9.51176 + 2.35085i) q^{96} +16.6772i q^{97} +(1.25945 + 0.643263i) q^{98} +(3.92812 + 7.28869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	1.25945	+	0.643263i	0.890565	+	0.454856i
$2$	1.25945	+	0.643263i	0.890565	+	0.454856i
$3$	1.48716	+	0.887900i	0.858610	+	0.512629i
$3$	1.48716	+	0.887900i	0.858610	+	0.512629i
$4$	1.17242	+	1.62032i	0.586212	+	0.810158i
$5$	−2.05223	−	0.887900i	−0.917784	−	0.397081i
$5$	−2.05223	−	0.887900i	−0.917784	−	0.397081i
$6$	1.30184	+	2.07490i	0.531476	+	0.847074i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.434319	+	2.79488i	0.153555	+	0.988140i
$9$	1.42327	+	2.64089i	0.474422	+	0.880297i
$10$	−2.01352	−	2.43839i	−0.636731	−	0.771086i
$11$	2.75993			0.832151			0.416076	−	0.909330i	$-0.363405\pi$
$11$	2.75993			0.832151			0.416076	+	0.909330i	$0.363405\pi$
$12$	0.304900	+	3.45066i	0.0880170	+	0.996119i
$13$		−	1.90761i		−	0.529076i	−0.964375	−	0.264538i	$-0.914781\pi$
$13$		−	1.90761i		−	0.529076i	0.964375	−	0.264538i	$-0.0852195\pi$
$14$	1.25945	+	0.643263i	0.336602	+	0.171919i
$15$	−2.26361	−	3.14262i	−0.584463	−	0.811421i
$16$	−1.25084	+	3.79939i	−0.312711	+	0.949848i
$17$	−5.03780			−1.22185			−0.610923	−	0.791690i	$-0.709201\pi$
$17$	−5.03780			−1.22185			−0.610923	+	0.791690i	$0.709201\pi$
$18$	0.0937425	+	4.24160i	0.0220953	+	0.999756i
$19$			1.90761i			0.437636i	0.975766	+	0.218818i	$0.0702201\pi$
$19$			1.90761i			0.437636i	−0.975766	+	0.218818i	$0.929780\pi$
$20$	−0.967402	−	4.36625i	−0.216318	−	0.976323i
$21$	1.48716	+	0.887900i	0.324524	+	0.193756i
$22$	3.47600	+	1.77536i	0.741085	+	0.378509i
$23$		−	2.05073i		−	0.427607i	−0.976877	−	0.213804i	$-0.931415\pi$
$23$		−	2.05073i		−	0.427607i	0.976877	−	0.213804i	$-0.0685853\pi$
$24$	−1.83568	+	4.54206i	−0.374706	+	0.927144i
$25$	3.42327	+	3.64434i	0.684653	+	0.728869i
$26$	1.22710	−	2.40254i	0.240653	−	0.471177i
$27$	−0.228229	+	5.19114i	−0.0439227	+	0.999035i
$28$	1.17242	+	1.62032i	0.221567	+	0.306211i
$29$		−	4.94433i		−	0.918140i	−0.888400	−	0.459070i	$-0.848183\pi$
$29$		−	4.94433i		−	0.918140i	0.888400	−	0.459070i	$-0.151817\pi$
$30$	−0.829376	−	5.41407i	−0.151423	−	0.988469i
$31$		−	6.92361i		−	1.24352i	−0.783209	−	0.621758i	$-0.786419\pi$
$31$		−	6.92361i		−	1.24352i	0.783209	−	0.621758i	$-0.213581\pi$
$32$	−4.01938	+	3.98052i	−0.710533	+	0.703664i
$33$	4.10445	+	2.45055i	0.714494	+	0.426585i
$34$	−6.34485	−	3.24063i	−1.08813	−	0.555764i
$35$	−2.05223	−	0.887900i	−0.346890	−	0.150083i
$36$	−2.61041	+	5.40239i	−0.435068	+	0.900398i
$37$		−	6.48126i		−	1.06551i	−0.846269	−	0.532756i	$-0.821156\pi$
$37$		−	6.48126i		−	1.06551i	0.846269	−	0.532756i	$-0.178844\pi$
$38$	−1.22710	+	2.40254i	−0.199061	+	0.389743i
$39$	1.69377	−	2.83692i	0.271220	−	0.454270i
$40$	1.59025	−	6.12136i	0.251441	−	0.967873i
$41$		−	11.1795i		−	1.74595i	−0.487766	−	0.872975i	$-0.662188\pi$
$41$		−	11.1795i		−	1.74595i	0.487766	−	0.872975i	$-0.337812\pi$
$42$	1.30184	+	2.07490i	0.200879	+	0.320164i
$43$	−9.36439			−1.42806			−0.714028	−	0.700117i	$-0.753131\pi$
$43$	−9.36439			−1.42806			−0.714028	+	0.700117i	$0.753131\pi$
$44$	3.23581	+	4.47196i	0.487817	+	0.674174i
$45$	−0.576017	−	6.68343i	−0.0858675	−	0.996307i
$46$	1.31916	−	2.58279i	0.194500	−	0.380812i
$47$			7.51739i			1.09652i	0.836307	+	0.548262i	$0.184710\pi$
$47$			7.51739i			1.09652i	−0.836307	+	0.548262i	$0.815290\pi$
$48$	−5.23368	+	4.53967i	−0.755417	+	0.655245i
$49$	1.00000			0.142857
$50$	1.96716	+	6.79193i	0.278198	+	0.960524i
$51$	−7.49199	−	4.47306i	−1.04909	−	0.626354i
$52$	3.09093	−	2.23653i	0.428635	−	0.310151i
$53$	6.14747			0.844420			0.422210	−	0.906498i	$-0.361254\pi$
$53$	6.14747			0.844420			0.422210	+	0.906498i	$0.361254\pi$
$54$	−3.62671	+	6.39116i	−0.493533	+	0.869727i
$55$	−5.66401	−	2.45055i	−0.763735	−	0.330432i
$56$	0.434319	+	2.79488i	0.0580384	+	0.373482i
$57$	−1.69377	+	2.83692i	−0.224345	+	0.375759i
$58$	3.18051	−	6.22714i	0.417621	−	0.817663i
$59$	0.716916			0.0933345			0.0466672	−	0.998910i	$-0.485140\pi$
$59$	0.716916			0.0933345			0.0466672	+	0.998910i	$0.485140\pi$
$60$	2.43812	−	7.35225i	0.314759	−	0.949172i
$61$	5.13115			0.656976			0.328488	−	0.944508i	$-0.393461\pi$
$61$	5.13115			0.656976			0.328488	+	0.944508i	$0.393461\pi$
$62$	4.45370	−	8.71993i	0.565621	−	1.10743i
$63$	1.42327	+	2.64089i	0.179315	+	0.332721i
$64$	−7.62273	+	2.42774i	−0.952842	+	0.303468i
$65$	−1.69377	+	3.91485i	−0.210086	+	0.485577i
$66$	3.59300	+	5.72658i	0.442268	+	0.704894i
$67$	3.58761			0.438296			0.219148	−	0.975692i	$-0.429672\pi$
$67$	3.58761			0.438296			0.219148	+	0.975692i	$0.429672\pi$
$68$	−5.90644	−	8.16282i	−0.716261	−	0.989887i
$69$	1.82085	−	3.04976i	0.219204	−	0.367148i
$70$	−2.01352	−	2.43839i	−0.240662	−	0.291443i
$71$	4.49721			0.533721			0.266860	−	0.963735i	$-0.414014\pi$
$71$	4.49721			0.533721			0.266860	+	0.963735i	$0.414014\pi$
$72$	−6.76283	+	5.12485i	−0.797007	+	0.603970i
$73$		−	6.11618i		−	0.715845i	−0.933751	−	0.357922i	$-0.883485\pi$
$73$		−	6.11618i		−	0.715845i	0.933751	−	0.357922i	$-0.116515\pi$
$74$	4.16916	−	8.16282i	0.484655	−	0.948908i
$75$	1.85512	+	8.45923i	0.214211	+	0.976788i
$76$	−3.09093	+	2.23653i	−0.354554	+	0.256548i
$77$	2.75993			0.314524
$78$	3.95810	−	2.48341i	0.448167	−	0.281191i
$79$			14.6546i			1.64878i	0.566025	+	0.824388i	$0.308480\pi$
$79$			14.6546i			1.64878i	−0.566025	+	0.824388i	$0.691520\pi$
$80$	5.94049	−	6.68659i	0.664167	−	0.747584i
$81$	−4.94862	+	7.51739i	−0.549847	+	0.835265i
$82$	7.19138	−	14.0800i	0.794155	−	1.55488i
$83$		−	7.71558i		−	0.846895i	−0.905921	−	0.423448i	$-0.860820\pi$
$83$		−	7.71558i		−	0.846895i	0.905921	−	0.423448i	$-0.139180\pi$
$84$	0.304900	+	3.45066i	0.0332673	+	0.376498i
$85$	10.3387	+	4.47306i	1.12139	+	0.485172i
$86$	−11.7940	−	6.02377i	−1.27178	−	0.649560i
$87$	4.39007	−	7.35300i	0.470665	−	0.788324i
$88$	1.19869	+	7.71369i	0.127781	+	0.822282i
$89$			13.5677i			1.43817i	0.694920	+	0.719087i	$0.255440\pi$
$89$			13.5677i			1.43817i	−0.694920	+	0.719087i	$0.744560\pi$
$90$	3.57374	−	8.78797i	0.376705	−	0.926333i
$91$		−	1.90761i		−	0.199972i
$92$	3.32283	−	2.40433i	0.346429	−	0.250669i
$93$	6.14747	−	10.2965i	0.637463	−	1.06770i
$94$	−4.83566	+	9.46777i	−0.498760	+	0.976526i
$95$	1.69377	−	3.91485i	0.173777	−	0.401655i
$96$	−9.51176	+	2.35085i	−0.970790	+	0.239932i
$97$			16.6772i			1.69331i	0.532143	+	0.846654i	$0.321387\pi$
$97$			16.6772i			1.69331i	−0.532143	+	0.846654i	$0.678613\pi$
$98$	1.25945	+	0.643263i	0.127224	+	0.0649794i
$99$	3.92812	+	7.28869i	0.394791	+	0.732541i
$100$	−1.89147	+	9.81949i	−0.189147	+	0.981949i
$101$		−	7.71558i		−	0.767729i	−0.923389	−	0.383865i	$-0.874593\pi$
$101$		−	7.71558i		−	0.767729i	0.923389	−	0.383865i	$-0.125407\pi$
$102$	−6.55842	−	10.4529i	−0.649381	−	1.03499i
$103$	−20.2109			−1.99144			−0.995721	−	0.0924150i	$-0.970541\pi$
$103$	−20.2109			−1.99144			−0.995721	+	0.0924150i	$0.970541\pi$
$104$	5.33155	−	0.828513i	0.522801	−	0.0812424i
$105$	−2.26361	−	3.14262i	−0.220906	−	0.306688i
$106$	7.74243	+	3.95444i	0.752011	+	0.384089i
$107$		−	1.27396i		−	0.123158i	−0.998102	−	0.0615791i	$-0.980386\pi$
$107$		−	1.27396i		−	0.123158i	0.998102	−	0.0615791i	$-0.0196136\pi$
$108$	−8.67886	+	5.71641i	−0.835124	+	0.550062i
$109$	−14.6383			−1.40210			−0.701048	−	0.713114i	$-0.747284\pi$
$109$	−14.6383			−1.40210			−0.701048	+	0.713114i	$0.747284\pi$
$110$	−5.55719	−	6.72979i	−0.529857	−	0.641660i
$111$	5.75471	−	9.63865i	0.546213	−	0.914860i
$112$	−1.25084	+	3.79939i	−0.118193	+	0.359009i
$113$	8.83651			0.831269			0.415634	−	0.909532i	$-0.363560\pi$
$113$	8.83651			0.831269			0.415634	+	0.909532i	$0.363560\pi$
$114$	−3.95810	+	2.48341i	−0.370710	+	0.232593i
$115$	−1.82085	+	4.20857i	−0.169795	+	0.392451i
$116$	8.01138	−	5.79686i	0.743838	−	0.538225i
$117$	5.03780	−	2.71504i	0.465744	−	0.251006i
$118$	0.902919	+	0.461166i	0.0831204	+	0.0424537i
$119$	−5.03780			−0.461814
$120$	7.80012	−	7.69144i	0.712050	−	0.702129i
$121$	−3.38276			−0.307524
$122$	6.46242	+	3.30068i	0.585080	+	0.298830i
$123$	9.92631	−	16.6257i	0.895025	−	1.49909i
$124$	11.2184	−	8.11740i	1.00744	−	0.728964i
$125$	−3.78950	−	10.5185i	−0.338944	−	0.940807i
$126$	0.0937425	+	4.24160i	0.00835125	+	0.377872i
$127$	−2.15684			−0.191388			−0.0956941	−	0.995411i	$-0.530507\pi$
$127$	−2.15684			−0.191388			−0.0956941	+	0.995411i	$0.530507\pi$
$128$	−11.1621	−	1.84581i	−0.986602	−	0.163148i
$129$	−13.9263	−	8.31464i	−1.22614	−	0.732063i
$130$	−4.65150	+	3.84102i	−0.407963	+	0.336879i
$131$	−2.93626			−0.256543			−0.128271	−	0.991739i	$-0.540943\pi$
$131$	−2.93626			−0.256543			−0.128271	+	0.991739i	$0.540943\pi$
$132$	0.841504	+	9.52359i	0.0732435	+	0.828922i
$133$			1.90761i			0.165411i
$134$	4.51841	+	2.30778i	0.390331	+	0.199361i
$135$	5.07759	−	10.4507i	0.437009	−	0.899457i
$136$	−2.18801	−	14.0800i	−0.187621	−	1.20735i
$137$	−16.4887			−1.40873			−0.704363	−	0.709840i	$-0.748767\pi$
$137$	−16.4887			−1.40873			−0.704363	+	0.709840i	$0.748767\pi$
$138$	4.25506	−	2.66973i	0.362215	−	0.227263i
$139$			10.8537i			0.920602i	0.887763	+	0.460301i	$0.152258\pi$
$139$			10.8537i			0.920602i	−0.887763	+	0.460301i	$0.847742\pi$
$140$	−0.967402	−	4.36625i	−0.0817604	−	0.369015i
$141$	−6.67469	+	11.1795i	−0.562110	+	0.941486i
$142$	5.66401	+	2.89289i	0.475313	+	0.242766i
$143$		−	5.26488i		−	0.440272i
$144$	−11.8141	+	2.10421i	−0.984506	+	0.175351i
$145$	−4.39007	+	10.1469i	−0.364576	+	0.842654i
$146$	3.93431	−	7.70302i	0.325606	−	0.637506i
$147$	1.48716	+	0.887900i	0.122659	+	0.0732328i
$148$	10.5017	−	7.59879i	0.863233	−	0.624617i
$149$			13.6420i			1.11760i	0.829303	+	0.558800i	$0.188738\pi$
$149$			13.6420i			1.11760i	−0.829303	+	0.558800i	$0.811262\pi$
$150$	−3.10509	+	11.8473i	−0.253529	+	0.967328i
$151$		−	1.35036i		−	0.109891i	−0.998489	−	0.0549455i	$-0.982501\pi$
$151$		−	1.35036i		−	0.109891i	0.998489	−	0.0549455i	$-0.0174985\pi$
$152$	−5.33155	+	0.828513i	−0.432446	+	0.0672013i
$153$	−7.17013	−	13.3043i	−0.579670	−	1.07559i
$154$	3.47600	+	1.77536i	0.280104	+	0.143063i
$155$	−6.14747	+	14.2088i	−0.493777	+	1.14128i
$156$	6.58251	−	0.581631i	0.527023	−	0.0465677i
$157$			1.90761i			0.152244i	0.997099	+	0.0761220i	$0.0242538\pi$
$157$			1.90761i			0.152244i	−0.997099	+	0.0761220i	$0.975746\pi$
$158$	−9.42679	+	18.4568i	−0.749955	+	1.46834i
$159$	9.14225	+	5.45834i	0.725028	+	0.432875i
$160$	11.7830	−	4.60012i	0.931527	−	0.363672i
$161$		−	2.05073i		−	0.161620i
$162$	−11.0682	+	6.28450i	−0.869600	+	0.493757i
$163$	24.4368			1.91404			0.957021	−	0.290019i	$-0.0936617\pi$
$163$	24.4368			1.91404			0.957021	+	0.290019i	$0.0936617\pi$
$164$	18.1144	−	13.1072i	1.41449	−	1.02350i
$165$	−6.24743	−	8.67342i	−0.486361	−	0.675225i
$166$	4.96315	−	9.71739i	0.385215	−	0.754215i
$167$		−	3.53470i		−	0.273523i	−0.990604	−	0.136762i	$-0.956331\pi$
$167$		−	3.53470i		−	0.273523i	0.990604	−	0.136762i	$-0.0436694\pi$
$168$	−1.83568	+	4.54206i	−0.141625	+	0.350427i
$169$	9.36102			0.720078
$170$	10.1437	+	12.2841i	0.777987	+	0.942147i
$171$	−5.03780	+	2.71504i	−0.385250	+	0.207624i
$172$	−10.9790	−	15.1733i	−0.837144	−	1.15695i
$173$	16.8691			1.28253			0.641266	−	0.767318i	$-0.278409\pi$
$173$	16.8691			1.28253			0.641266	+	0.767318i	$0.278409\pi$
$174$	10.2590	−	6.43675i	0.777732	−	0.487969i
$175$	3.42327	+	3.64434i	0.258775	+	0.275487i
$176$	−3.45224	+	10.4861i	−0.260223	+	0.790418i
$177$	1.06617	+	0.636550i	0.0801379	+	0.0478460i
$178$	−8.72761	+	17.0878i	−0.654162	+	1.28079i
$179$	4.19377			0.313457			0.156728	−	0.987642i	$-0.449905\pi$
$179$	4.19377			0.313457			0.156728	+	0.987642i	$0.449905\pi$
$180$	10.1539	−	8.76914i	0.756829	−	0.653613i
$181$	−9.70038			−0.721023			−0.360512	−	0.932755i	$-0.617398\pi$
$181$	−9.70038			−0.721023			−0.360512	+	0.932755i	$0.617398\pi$
$182$	1.22710	−	2.40254i	0.0909585	−	0.178088i
$183$	7.63082	+	4.55595i	0.564086	+	0.336785i
$184$	5.73155	−	0.890673i	0.422536	−	0.0656613i
$185$	−5.75471	+	13.3010i	−0.423095	+	0.977910i
$186$	14.3658	−	9.01345i	1.05335	−	0.660899i
$187$	−13.9040			−1.01676
$188$	−12.1805	+	8.81357i	−0.888357	+	0.642796i
$189$	−0.228229	+	5.19114i	−0.0166012	+	0.377600i
$190$	4.65150	−	3.84102i	0.337455	−	0.278657i
$191$	−7.79773			−0.564224			−0.282112	−	0.959381i	$-0.591035\pi$
$191$	−7.79773			−0.564224			−0.282112	+	0.959381i	$0.591035\pi$
$192$	−13.4918	−	3.15779i	−0.973686	−	0.227894i
$193$			2.15779i			0.155321i	0.996980	+	0.0776606i	$0.0247451\pi$
$193$			2.15779i			0.155321i	−0.996980	+	0.0776606i	$0.975255\pi$
$194$	−10.7278	+	21.0040i	−0.770211	+	1.50800i
$195$	−5.99489	+	4.31810i	−0.429303	+	0.309225i
$196$	1.17242	+	1.62032i	0.0837446	+	0.115737i
$197$	14.9679			1.06642			0.533208	−	0.845984i	$-0.320986\pi$
$197$	14.9679			1.06642			0.533208	+	0.845984i	$0.320986\pi$
$198$	0.258723	+	11.7066i	0.0183867	+	0.831948i
$199$		−	10.7388i		−	0.761255i	−0.924728	−	0.380628i	$-0.875708\pi$
$199$		−	10.7388i		−	0.761255i	0.924728	−	0.380628i	$-0.124292\pi$
$200$	−8.69872	+	11.1504i	−0.615093	+	0.788455i
$201$	5.33533	+	3.18544i	0.376325	+	0.224683i
$202$	4.96315	−	9.71739i	0.349206	−	0.683713i
$203$		−	4.94433i		−	0.347024i
$204$	−1.53602	−	17.3837i	−0.107543	−	1.21710i
$205$	−9.92631	+	22.9429i	−0.693283	+	1.60240i
$206$	−25.4546	−	13.0009i	−1.77351	−	0.905819i
$207$	5.41576	−	2.91874i	0.376422	−	0.202866i
$208$	7.24777	+	2.38612i	0.502542	+	0.165448i
$209$			5.26488i			0.364180i
$210$	−0.829376	−	5.41407i	−0.0572324	−	0.373606i
$211$			13.5827i			0.935073i	0.883974	+	0.467536i	$0.154858\pi$
$211$			13.5827i			0.935073i	−0.883974	+	0.467536i	$0.845142\pi$
$212$	7.20745	+	9.96084i	0.495009	+	0.684113i
$213$	6.68806	+	3.99308i	0.458258	+	0.273601i
$214$	0.819491	−	1.60449i	0.0560192	−	0.109680i
$215$	19.2178	+	8.31464i	1.31065	+	0.567054i
$216$	−14.6077	+	1.61674i	−0.993931	+	0.110005i
$217$		−	6.92361i		−	0.470005i
$218$	−18.4362	−	9.41630i	−1.24866	−	0.637752i
$219$	5.43056	−	9.09571i	0.366963	−	0.614631i
$220$	−2.66997	−	12.0506i	−0.180009	−	0.812449i
$221$			9.61016i			0.646449i
$222$	13.4480	−	8.43759i	0.902568	−	0.566294i
$223$	−11.6417			−0.779585			−0.389793	−	0.920903i	$-0.627453\pi$
$223$	−11.6417			−0.779585			−0.389793	+	0.920903i	$0.627453\pi$
$224$	−4.01938	+	3.98052i	−0.268556	+	0.265960i
$225$	−4.75210	+	14.2274i	−0.316807	+	0.948490i
$226$	11.1291	+	5.68420i	0.740299	+	0.378108i
$227$			3.16030i			0.209756i	0.994485	+	0.104878i	$0.0334453\pi$
$227$			3.16030i			0.209756i	−0.994485	+	0.104878i	$0.966555\pi$
$228$	−6.58251	+	0.581631i	−0.435938	+	0.0385194i
$229$	−3.43808			−0.227195			−0.113597	−	0.993527i	$-0.536237\pi$
$229$	−3.43808			−0.227195			−0.113597	+	0.993527i	$0.536237\pi$
$230$	−5.00048	+	4.12919i	−0.329722	+	0.272271i
$231$	4.10445	+	2.45055i	0.270053	+	0.161234i
$232$	13.8188	−	2.14742i	0.907251	−	0.140985i
$233$	−17.5699			−1.15104			−0.575520	−	0.817787i	$-0.695200\pi$
$233$	−17.5699			−1.15104			−0.575520	+	0.817787i	$0.695200\pi$
$234$	8.09133	−	0.178824i	0.528947	−	0.0116901i
$235$	6.67469	−	15.4274i	0.435409	−	1.00637i
$236$	0.840529	+	1.16163i	0.0547138	+	0.0756156i
$237$	−13.0119	+	21.7937i	−0.845211	+	1.41566i
$238$	−6.34485	−	3.24063i	−0.411275	−	0.210059i
$239$	−17.5275			−1.13376			−0.566879	−	0.823801i	$-0.691849\pi$
$239$	−17.5275			−1.13376			−0.566879	+	0.823801i	$0.691849\pi$
$240$	14.7715	−	4.66944i	0.953494	−	0.301411i
$241$	6.21092			0.400081			0.200040	−	0.979788i	$-0.435893\pi$
$241$	6.21092			0.400081			0.200040	+	0.979788i	$0.435893\pi$
$242$	−4.26042	−	2.17601i	−0.273870	−	0.139879i
$243$	−14.0341	+	6.78564i	−0.900286	+	0.435299i
$244$	6.01588	+	8.31408i	0.385127	+	0.532254i
$245$	−2.05223	−	0.887900i	−0.131112	−	0.0567259i
$246$	23.1964	−	14.5540i	1.47895	−	0.927929i
$247$	3.63898			0.231543
$248$	19.3507	−	3.00706i	1.22877	−	0.190948i
$249$	6.85067	−	11.4743i	0.434143	−	0.727153i
$250$	1.99350	−	15.6852i	0.126080	−	0.992020i
$251$	22.4760			1.41867			0.709335	−	0.704871i	$-0.248995\pi$
$251$	22.4760			1.41867			0.709335	+	0.704871i	$0.248995\pi$
$252$	−2.61041	+	5.40239i	−0.164440	+	0.340318i
$253$		−	5.65989i		−	0.355834i
$254$	−2.71642	−	1.38741i	−0.170444	−	0.0870541i
$255$	11.4036	+	15.8319i	0.714123	+	0.991430i
$256$	−12.8708	−	9.50488i	−0.804424	−	0.594055i
$257$	−7.25715			−0.452688			−0.226344	−	0.974047i	$-0.572677\pi$
$257$	−7.25715			−0.452688			−0.226344	+	0.974047i	$0.572677\pi$
$258$	−12.1910	−	19.4302i	−0.758977	−	1.20967i
$259$		−	6.48126i		−	0.402726i
$260$	−8.32911	+	1.84543i	−0.516549	+	0.114449i
$261$	13.0575	−	7.03711i	0.808236	−	0.435586i
$262$	−3.69808	−	1.88879i	−0.228468	−	0.116690i
$263$			16.3928i			1.01082i	0.862878	+	0.505412i	$0.168659\pi$
$263$			16.3928i			1.01082i	−0.862878	+	0.505412i	$0.831341\pi$
$264$	−5.06634	+	12.5358i	−0.311812	+	0.771524i
$265$	−12.6160	−	5.45834i	−0.774995	−	0.335303i
$266$	−1.22710	+	2.40254i	−0.0752381	+	0.147309i
$267$	−12.0468	+	20.1773i	−0.737251	+	1.23483i
$268$	4.20620	+	5.81305i	0.256934	+	0.355089i
$269$			4.53372i			0.276426i	0.990403	+	0.138213i	$0.0441359\pi$
$269$			4.53372i			0.276426i	−0.990403	+	0.138213i	$0.955864\pi$
$270$	13.1175	−	9.89595i	0.798309	−	0.602249i
$271$			27.5166i			1.67151i	0.549100	+	0.835756i	$0.314970\pi$
$271$			27.5166i			1.67151i	−0.549100	+	0.835756i	$0.685030\pi$
$272$	6.30149	−	19.1406i	0.382084	−	1.16057i
$273$	1.69377	−	2.83692i	0.102512	−	0.171698i
$274$	−20.7667	−	10.6066i	−1.25456	−	0.640767i
$275$	9.44799	+	10.0582i	0.569735	+	0.606529i
$276$	7.07637	−	0.625268i	0.425948	−	0.0376367i
$277$		−	24.3449i		−	1.46274i	−0.681980	−	0.731371i	$-0.738881\pi$
$277$		−	24.3449i		−	1.46274i	0.681980	−	0.731371i	$-0.261119\pi$
$278$	−6.98181	+	13.6697i	−0.418741	+	0.819856i
$279$	18.2845	−	9.85414i	1.09466	−	0.589952i
$280$	1.59025	−	6.12136i	0.0950359	−	0.365821i
$281$			10.5636i			0.630170i	0.949064	+	0.315085i	$0.102033\pi$
$281$			10.5636i			0.630170i	−0.949064	+	0.315085i	$0.897967\pi$
$282$	−15.5978	+	9.78646i	−0.928836	+	0.582775i
$283$	−5.53680			−0.329129			−0.164564	−	0.986366i	$-0.552622\pi$
$283$	−5.53680			−0.329129			−0.164564	+	0.986366i	$0.552622\pi$
$284$	5.27264	+	7.28690i	0.312874	+	0.432398i
$285$	5.99489	−	4.31810i	0.355107	−	0.255782i
$286$	3.38671	−	6.63085i	0.200260	−	0.392090i
$287$		−	11.1795i		−	0.659907i
$288$	−16.2328	−	4.94941i	−0.956526	−	0.291647i
$289$	8.37939			0.492906
$290$	−12.0562	+	9.95552i	−0.707965	+	0.584608i
$291$	−14.8076	+	24.8015i	−0.868040	+	1.45389i
$292$	9.91014	−	7.17076i	0.579947	−	0.419637i
$293$	25.2198			1.47336			0.736678	−	0.676244i	$-0.236393\pi$
$293$	25.2198			1.47336			0.736678	+	0.676244i	$0.236393\pi$
$294$	1.30184	+	2.07490i	0.0759251	+	0.121011i
$295$	−1.47127	−	0.636550i	−0.0856608	−	0.0370613i
$296$	18.1144	−	2.81494i	1.05288	−	0.163615i
$297$	−0.629897	+	14.3272i	−0.0365504	+	0.831348i
$298$	−8.77543	+	17.1815i	−0.508347	+	0.995295i
$299$	−3.91200			−0.226237
$300$	−11.5316	+	12.9237i	−0.665779	+	0.746149i
$301$	−9.36439			−0.539754
$302$	0.868639	−	1.70071i	0.0499846	−	0.0978650i
$303$	6.85067	−	11.4743i	0.393561	−	0.659180i
$304$	−7.24777	−	2.38612i	−0.415688	−	0.136853i
$305$	−10.5303	−	4.55595i	−0.602962	−	0.260873i
$306$	−0.472256	−	21.3683i	−0.0269971	−	1.22155i
$307$	19.0825			1.08909			0.544547	−	0.838730i	$-0.316701\pi$
$307$	19.0825			1.08909			0.544547	+	0.838730i	$0.316701\pi$
$308$	3.23581	+	4.47196i	0.184378	+	0.254814i
$309$	−30.0568	−	17.9453i	−1.70987	−	1.02087i
$310$	−16.8824	+	13.9408i	−0.958858	+	0.791786i
$311$	−6.95370			−0.394308			−0.197154	−	0.980373i	$-0.563170\pi$
$311$	−6.95370			−0.394308			−0.197154	+	0.980373i	$0.563170\pi$
$312$	8.66448	+	3.50176i	0.490530	+	0.198248i
$313$			34.5408i			1.95236i	0.216963	+	0.976180i	$0.430385\pi$
$313$			34.5408i			1.95236i	−0.216963	+	0.976180i	$0.569615\pi$
$314$	−1.22710	+	2.40254i	−0.0692491	+	0.135583i
$315$	−0.576017	−	6.68343i	−0.0324549	−	0.376568i
$316$	−23.7451	+	17.1815i	−1.33577	+	0.966533i
$317$	8.19278			0.460153			0.230076	−	0.973173i	$-0.426102\pi$
$317$	8.19278			0.460153			0.230076	+	0.973173i	$0.426102\pi$
$318$	8.00305	+	12.7554i	0.448789	+	0.715286i
$319$		−	13.6460i		−	0.764031i
$320$	17.7992	+	1.78595i	0.995004	+	0.0998375i
$321$	1.13115	−	1.89458i	0.0631345	−	0.105745i
$322$	1.31916	−	2.58279i	0.0735140	−	0.143933i
$323$		−	9.61016i		−	0.534724i
$324$	−17.9824	+	0.795237i	−0.999024	+	0.0441799i
$325$	6.95199	−	6.53026i	0.385627	−	0.362234i
$326$	30.7770	+	15.7193i	1.70458	+	0.870613i
$327$	−21.7695	−	12.9974i	−1.20385	−	0.718756i
$328$	31.2455	−	4.85549i	1.72524	−	0.268099i
$329$			7.51739i			0.414447i
$330$	−2.28902	−	14.9425i	−0.126007	−	0.822556i
$331$		−	4.63660i		−	0.254850i	−0.991848	−	0.127425i	$-0.959329\pi$
$331$		−	4.63660i		−	0.254850i	0.991848	−	0.127425i	$-0.0406713\pi$
$332$	12.5017	−	9.04594i	0.686119	−	0.496460i
$333$	17.1163	−	9.22456i	0.937968	−	0.505503i
$334$	2.27374	−	4.45177i	0.124414	−	0.243590i
$335$	−7.36258	−	3.18544i	−0.402261	−	0.174039i
$336$	−5.23368	+	4.53967i	−0.285521	+	0.247659i
$337$		−	18.4352i		−	1.00423i	−0.864801	−	0.502114i	$-0.832556\pi$
$337$		−	18.4352i		−	1.00423i	0.864801	−	0.502114i	$-0.167444\pi$
$338$	11.7897	+	6.02160i	0.641277	+	0.327532i
$339$	13.1413	+	7.84594i	0.713736	+	0.426133i
$340$	4.87358	+	21.9963i	0.264307	+	1.19292i
$341$		−	19.1087i		−	1.03479i
$342$	−8.09133	+	0.178824i	−0.437529	+	0.00966971i
$343$	1.00000			0.0539949
$344$	−4.06714	−	26.1724i	−0.219285	−	1.41112i
$345$	−6.44467	+	4.64207i	−0.346969	+	0.249920i
$346$	21.2458	+	10.8513i	1.14218	+	0.583368i
$347$		−	2.86847i		−	0.153987i	−0.997032	−	0.0769936i	$-0.975468\pi$
$347$		−	2.86847i		−	0.153987i	0.997032	−	0.0769936i	$-0.0245321\pi$
$348$	17.0612	−	1.50753i	0.914576	−	0.0808119i
$349$	−2.76610			−0.148066			−0.0740330	−	0.997256i	$-0.523587\pi$
$349$	−2.76610			−0.148066			−0.0740330	+	0.997256i	$0.523587\pi$
$350$	1.96716	+	6.79193i	0.105149	+	0.363044i
$351$	9.90267	+	0.435373i	0.528566	+	0.0232385i
$352$	−11.0932	+	10.9860i	−0.591271	+	0.585555i
$353$	23.6750			1.26009			0.630045	−	0.776558i	$-0.283036\pi$
$353$	23.6750			1.26009			0.630045	+	0.776558i	$0.283036\pi$
$354$	0.933312	+	1.48753i	0.0496050	+	0.0790612i
$355$	−9.22930	−	3.99308i	−0.489840	−	0.211930i
$356$	−21.9840	+	15.9071i	−1.16515	+	0.843075i
$357$	−7.49199	−	4.47306i	−0.396518	−	0.236739i
$358$	5.28183	+	2.69770i	0.279154	+	0.142578i
$359$	−15.7410			−0.830778			−0.415389	−	0.909644i	$-0.636355\pi$
$359$	−15.7410			−0.830778			−0.415389	+	0.909644i	$0.636355\pi$
$360$	18.4292	−	4.51264i	0.971305	−	0.237837i
$361$	15.3610			0.808475
$362$	−12.2171	−	6.23990i	−0.642118	−	0.327962i
$363$	−5.03070	−	3.00356i	−0.264043	−	0.157646i
$364$	3.09093	−	2.23653i	0.162009	−	0.117226i
$365$	−5.43056	+	12.5518i	−0.284248	+	0.656990i
$366$	6.67995	+	10.6466i	0.349167	+	0.556507i
$367$	19.3280			1.00891			0.504457	−	0.863437i	$-0.331693\pi$
$367$	19.3280			1.00891			0.504457	+	0.863437i	$0.331693\pi$
$368$	7.79154	+	2.56514i	0.406162	+	0.133717i
$369$	29.5239	−	15.9114i	1.53695	−	0.828317i
$370$	−15.8038	+	13.0502i	−0.821602	+	0.678445i
$371$	6.14747			0.319161
$372$	23.8910	−	2.11101i	1.23869	−	0.109451i
$373$		−	34.4749i		−	1.78504i	−0.451007	−	0.892520i	$-0.648935\pi$
$373$		−	34.4749i		−	1.78504i	0.451007	−	0.892520i	$-0.351065\pi$
$374$	−17.5114	−	8.94393i	−0.905491	−	0.462479i
$375$	3.70383	−	19.0074i	0.191265	−	0.981538i
$376$	−21.0102	+	3.26495i	−1.08352	+	0.168377i
$377$	−9.43187			−0.485766
$378$	−3.62671	+	6.39116i	−0.186538	+	0.328726i
$379$		−	16.3121i		−	0.837895i	−0.908010	−	0.418947i	$-0.862399\pi$
$379$		−	16.3121i		−	0.837895i	0.908010	−	0.418947i	$-0.137601\pi$
$380$	8.32911	−	1.84543i	0.427274	−	0.0946684i
$381$	−3.20755	−	1.91505i	−0.164328	−	0.0981112i
$382$	−9.82085	−	5.01599i	−0.502478	−	0.256641i
$383$			20.4691i			1.04592i	0.852356	+	0.522962i	$0.175173\pi$
$383$			20.4691i			1.04592i	−0.852356	+	0.522962i	$0.824827\pi$
$384$	−14.9609	−	12.6559i	−0.763472	−	0.645841i
$385$	−5.66401	−	2.45055i	−0.288665	−	0.124891i
$386$	−1.38803	+	2.71763i	−0.0706488	+	0.138324i
$387$	−13.3280	−	24.7303i	−0.677501	−	1.25711i
$388$	−27.0222	+	19.5527i	−1.37185	+	0.992638i
$389$		−	12.5062i		−	0.634088i	−0.948411	−	0.317044i	$-0.897310\pi$
$389$		−	12.5062i		−	0.634088i	0.948411	−	0.317044i	$-0.102690\pi$
$390$	−10.3279	+	1.58213i	−0.522976	+	0.0801141i
$391$			10.3312i			0.522470i
$392$	0.434319	+	2.79488i	0.0219364	+	0.141163i
$393$	−4.36668	−	2.60711i	−0.220270	−	0.131511i
$394$	18.8513	+	9.62828i	0.949713	+	0.485066i
$395$	13.0119	−	30.0746i	0.654698	−	1.51322i
$396$	−7.20455	+	14.9102i	−0.362042	+	0.749267i
$397$		−	7.33769i		−	0.368268i	−0.982901	−	0.184134i	$-0.941052\pi$
$397$		−	7.33769i		−	0.368268i	0.982901	−	0.184134i	$-0.0589481\pi$
$398$	6.90790	−	13.5250i	0.346262	−	0.677947i
$399$	−1.69377	+	2.83692i	−0.0847945	+	0.142023i
$400$	−18.1283	+	8.44784i	−0.906413	+	0.422392i
$401$			11.3403i			0.566310i	0.959074	+	0.283155i	$0.0913810\pi$
$401$			11.3403i			0.566310i	−0.959074	+	0.283155i	$0.908619\pi$
$402$	4.67050	+	7.44392i	0.232944	+	0.371269i
$403$	−13.2076			−0.657915
$404$	12.5017	−	9.04594i	0.621982	−	0.450052i
$405$	16.8304	−	11.0335i	0.836309	−	0.548259i
$406$	3.18051	−	6.22714i	0.157846	−	0.309048i
$407$		−	17.8879i		−	0.886668i
$408$	9.24776	−	22.8820i	0.457832	−	1.13283i
$409$	10.5692			0.522615			0.261307	−	0.965256i	$-0.415846\pi$
$409$	10.5692			0.522615			0.261307	+	0.965256i	$0.415846\pi$
$410$	−27.2600	+	22.5102i	−1.34628	+	1.11170i
$411$	−24.5213	−	14.6403i	−1.20955	−	0.722154i
$412$	−23.6958	−	32.7481i	−1.16741	−	1.61338i
$413$	0.716916			0.0352771
$414$	8.69840	−	0.192241i	0.427503	−	0.00944812i
$415$	−6.85067	+	15.8341i	−0.336286	+	0.777267i
$416$	7.59329	+	7.66742i	0.372292	+	0.375926i
$417$	−9.63703	+	16.1412i	−0.471927	+	0.790438i
$418$	−3.38671	+	6.63085i	−0.165649	+	0.324326i
$419$	−39.1526			−1.91273			−0.956365	−	0.292175i	$-0.905621\pi$
$419$	−39.1526			−1.91273			−0.956365	+	0.292175i	$0.905621\pi$
$420$	2.43812	−	7.35225i	0.118968	−	0.358753i
$421$	28.0122			1.36523			0.682614	−	0.730779i	$-0.260843\pi$
$421$	28.0122			1.36523			0.682614	+	0.730779i	$0.260843\pi$
$422$	−8.73727	+	17.1067i	−0.425323	+	0.832743i
$423$	−19.8526	+	10.6992i	−0.965267	+	0.520215i
$424$	2.66997	+	17.1815i	0.129665	+	0.834405i
$425$	−17.2457	−	18.3595i	−0.836540	−	0.890565i
$426$	5.85467	+	9.33126i	0.283660	+	0.452101i
$427$	5.13115			0.248314
$428$	2.06421	−	1.49362i	0.0997776	−	0.0721968i
$429$	4.67469	−	7.82970i	0.225696	−	0.378022i
$430$	18.8554	+	22.8340i	0.909288	+	1.10115i
$431$	−37.8527			−1.82330			−0.911650	−	0.410967i	$-0.865191\pi$
$431$	−37.8527			−1.82330			−0.911650	+	0.410967i	$0.865191\pi$
$432$	−19.4377	−	7.36043i	−0.935197	−	0.354129i
$433$		−	18.2920i		−	0.879058i	−0.898228	−	0.439529i	$-0.855145\pi$
$433$		−	18.2920i		−	0.879058i	0.898228	−	0.439529i	$-0.144855\pi$
$434$	4.45370	−	8.71993i	0.213785	−	0.418570i
$435$	−15.5382	+	11.1921i	−0.744997	+	0.536618i
$436$	−17.1623	−	23.7187i	−0.821926	−	1.13592i
$437$	3.91200			0.187136
$438$	12.6904	−	7.96231i	0.606373	−	0.380454i
$439$		−	12.5549i		−	0.599211i	−0.954063	−	0.299605i	$-0.903145\pi$
$439$		−	12.5549i		−	0.599211i	0.954063	−	0.299605i	$-0.0968550\pi$
$440$	4.38900	−	16.8946i	0.209237	−	0.805417i
$441$	1.42327	+	2.64089i	0.0677746	+	0.125757i
$442$	−6.18186	+	12.1035i	−0.294041	+	0.575705i
$443$		−	29.7757i		−	1.41468i	−0.706872	−	0.707342i	$-0.749894\pi$
$443$		−	29.7757i		−	1.41468i	0.706872	−	0.707342i	$-0.250106\pi$
$444$	22.3646	−	1.97614i	1.06138	−	0.0937833i
$445$	12.0468	−	27.8440i	0.571072	−	1.31993i
$446$	−14.6621	−	7.48867i	−0.694271	−	0.354599i
$447$	−12.1128	+	20.2878i	−0.572914	+	0.959582i
$448$	−7.62273	+	2.42774i	−0.360140	+	0.114700i
$449$		−	23.7253i		−	1.11967i	−0.828605	−	0.559834i	$-0.810865\pi$
$449$		−	23.7253i		−	1.11967i	0.828605	−	0.559834i	$-0.189135\pi$
$450$	−15.1370	+	14.8618i	−0.713563	+	0.700591i
$451$		−	30.8548i		−	1.45289i
$452$	10.3601	+	14.3179i	0.487300	+	0.673459i
$453$	1.19899	−	2.00820i	0.0563333	−	0.0943535i
$454$	−2.03290	+	3.98024i	−0.0954090	+	0.186802i
$455$	−1.69377	+	3.91485i	−0.0794051	+	0.183531i
$456$	−8.66448	−	3.50176i	−0.405752	−	0.163985i
$457$		−	5.67383i		−	0.265411i	−0.991156	−	0.132705i	$-0.957634\pi$
$457$		−	5.67383i		−	0.265411i	0.991156	−	0.132705i	$-0.0423664\pi$
$458$	−4.33009	−	2.21159i	−0.202332	−	0.103341i
$459$	1.14977	−	26.1519i	0.0536668	−	1.22067i
$460$	−8.95401	+	1.98388i	−0.417483	+	0.0924990i
$461$			12.2891i			0.572360i	0.958176	+	0.286180i	$0.0923856\pi$
$461$			12.2891i			0.572360i	−0.958176	+	0.286180i	$0.907614\pi$
$462$	3.59300	+	5.72658i	0.167162	+	0.266425i
$463$	0.893880			0.0415421			0.0207711	−	0.999784i	$-0.493388\pi$
$463$	0.893880			0.0415421			0.0207711	+	0.999784i	$0.493388\pi$
$464$	18.7855	+	6.18458i	0.872094	+	0.287112i
$465$	−21.7583	+	15.6724i	−1.00901	+	0.726789i
$466$	−22.1284	−	11.3021i	−1.02508	−	0.523558i
$467$			29.0874i			1.34601i	0.739640	+	0.673003i	$0.234996\pi$
$467$			29.0874i			1.34601i	−0.739640	+	0.673003i	$0.765004\pi$
$468$	10.3057	+	4.97964i	0.476379	+	0.230184i
$469$	3.58761			0.165660
$470$	18.3303	−	15.1364i	0.845514	−	0.698191i
$471$	−1.69377	+	2.83692i	−0.0780447	+	0.130718i
$472$	0.311370	+	2.00369i	0.0143320	+	0.0922275i
$473$	−25.8451			−1.18836
$474$	−30.4069	+	19.0781i	−1.39663	+	0.876284i
$475$	−6.95199	+	6.53026i	−0.318979	+	0.299629i
$476$	−5.90644	−	8.16282i	−0.270721	−	0.374142i
$477$	8.74949	+	16.2348i	0.400612	+	0.743341i
$478$	−22.0750	−	11.2748i	−1.00969	−	0.515697i
$479$	−24.2741			−1.10911			−0.554555	−	0.832147i	$-0.687111\pi$
$479$	−24.2741			−1.10911			−0.554555	+	0.832147i	$0.687111\pi$
$480$	21.6076	+	3.62102i	0.986247	+	0.165276i
$481$	−12.3637			−0.563737
$482$	7.82234	+	3.99526i	0.356298	+	0.181979i
$483$	1.82085	−	3.04976i	0.0828513	−	0.138769i
$484$	−3.96603	−	5.48114i	−0.180274	−	0.249143i
$485$	14.8076	−	34.2253i	0.672381	−	1.55409i
$486$	−22.0402	−	0.481428i	−0.999762	−	0.0218380i
$487$	38.1623			1.72930			0.864648	−	0.502378i	$-0.167541\pi$
$487$	38.1623			1.72930			0.864648	+	0.502378i	$0.167541\pi$
$488$	2.22856	+	14.3410i	0.100882	+	0.649184i
$489$	36.3414	+	21.6975i	1.64342	+	0.981194i
$490$	−2.01352	−	2.43839i	−0.0909616	−	0.110155i
$491$	26.4225			1.19243			0.596216	−	0.802824i	$-0.296670\pi$
$491$	26.4225			1.19243			0.596216	+	0.802824i	$0.296670\pi$
$492$	38.5767	−	3.40864i	1.73917	−	0.153673i
$493$			24.9085i			1.12182i
$494$	4.58311	+	2.34082i	0.206204	+	0.105319i
$495$	−1.58977	−	18.4458i	−0.0714547	−	0.829078i
$496$	26.3055	+	8.66034i	1.18115	+	0.388861i
$497$	4.49721			0.201728
$498$	16.0091	−	10.0445i	0.717383	−	0.450104i
$499$		−	34.9059i		−	1.56260i	−0.624155	−	0.781300i	$-0.714557\pi$
$499$		−	34.9059i		−	1.56260i	0.624155	−	0.781300i	$-0.285443\pi$
$500$	12.6004	−	18.4724i	0.563509	−	0.826110i
$501$	3.13846	−	5.25665i	0.140216	−	0.234850i
$502$	28.3073	+	14.4580i	1.26342	+	0.645291i
$503$			8.03971i			0.358473i	0.983806	+	0.179236i	$0.0573627\pi$
$503$			8.03971i			0.358473i	−0.983806	+	0.179236i	$0.942637\pi$
$504$	−6.76283	+	5.12485i	−0.301240	+	0.228279i
$505$	−6.85067	+	15.8341i	−0.304851	+	0.704609i
$506$	3.64080	−	7.12834i	0.161853	−	0.316893i
$507$	13.9213	+	8.31165i	0.618266	+	0.369133i
$508$	−2.52873	−	3.49475i	−0.112194	−	0.155055i
$509$			5.53741i			0.245441i	0.992441	+	0.122721i	$0.0391619\pi$
$509$			5.53741i			0.245441i	−0.992441	+	0.122721i	$0.960838\pi$
$510$	4.17823	+	27.2750i	0.185015	+	1.20776i
$511$		−	6.11618i		−	0.270564i
$512$	−10.0960	−	20.2502i	−0.446183	−	0.894942i
$513$	−9.90267	−	0.435373i	−0.437214	−	0.0192222i
$514$	−9.14001	−	4.66826i	−0.403148	−	0.205908i
$515$	41.4774	+	17.9453i	1.82771	+	0.790763i
$516$	−2.85520	−	32.3133i	−0.125693	−	1.42251i
$517$			20.7475i			0.912474i
$518$	4.16916	−	8.16282i	0.183182	−	0.358654i
$519$	25.0870	+	14.9781i	1.10120	+	0.657464i
$520$	−11.6772	−	3.03359i	−0.512078	−	0.133032i
$521$		−	12.7331i		−	0.557846i	−0.960313	−	0.278923i	$-0.910023\pi$
$521$		−	12.7331i		−	0.557846i	0.960313	−	0.278923i	$-0.0899775\pi$
$522$	20.9719	−	0.463494i	0.917916	−	0.0202866i
$523$	22.8415			0.998791			0.499396	−	0.866374i	$-0.333555\pi$
$523$	22.8415			0.998791			0.499396	+	0.866374i	$0.333555\pi$
$524$	−3.44255	−	4.75767i	−0.150388	−	0.207840i
$525$	1.85512	+	8.45923i	0.0809640	+	0.369191i
$526$	−10.5449	+	20.6459i	−0.459779	+	0.900205i
$527$			34.8797i			1.51938i
$528$	−14.4446	+	12.5292i	−0.628621	+	0.545263i
$529$	18.7945			0.817152
$530$	−12.3781	−	14.9899i	−0.537669	−	0.651120i
$531$	1.02036	+	1.89330i	0.0442799	+	0.0821621i
$532$	−3.09093	+	2.23653i	−0.134009	+	0.0969659i
$533$	−21.3262			−0.923740
$534$	−28.1516	+	17.6630i	−1.21824	+	0.764355i
$535$	−1.13115	+	2.61445i	−0.0489038	+	0.113033i
$536$	1.55817	+	10.0269i	0.0673026	+	0.433098i
$537$	6.23678	+	3.72364i	0.269137	+	0.160687i
$538$	−2.91638	+	5.71000i	−0.125734	+	0.246175i
$539$	2.75993			0.118879
$540$	22.8866	−	4.02541i	0.984882	−	0.173226i
$541$	−16.5179			−0.710158			−0.355079	−	0.934836i	$-0.615546\pi$
$541$	−16.5179			−0.710158			−0.355079	+	0.934836i	$0.615546\pi$
$542$	−17.7004	+	34.6557i	−0.760297	+	1.48859i
$543$	−14.4260	−	8.61297i	−0.619078	−	0.369618i
$544$	20.2488	−	20.0531i	0.868162	−	0.859768i
$545$	30.0412	+	12.9974i	1.28682	+	0.556746i
$546$	3.95810	−	2.48341i	0.169391	−	0.106280i
$547$	−22.5719			−0.965106			−0.482553	−	0.875867i	$-0.660290\pi$
$547$	−22.5719			−0.965106			−0.482553	+	0.875867i	$0.660290\pi$
$548$	−19.3318	−	26.7169i	−0.825812	−	1.14129i
$549$	7.30299	+	13.5508i	0.311684	+	0.578334i
$550$	5.42922	+	18.7453i	0.231503	+	0.799301i
$551$	9.43187			0.401811
$552$	9.31455	+	3.76448i	0.396453	+	0.160227i
$553$			14.6546i			0.623179i
$554$	15.6602	−	30.6611i	0.665337	−	1.30267i
$555$	−20.3681	+	14.6711i	−0.864579	+	0.622752i
$556$	−17.5865	+	12.7252i	−0.745832	+	0.539668i
$557$	−9.27395			−0.392950			−0.196475	−	0.980509i	$-0.562949\pi$
$557$	−9.27395			−0.392950			−0.196475	+	0.980509i	$0.562949\pi$
$558$	29.3672	−	0.649036i	1.24321	−	0.0274759i
$559$			17.8636i			0.755550i
$560$	5.94049	−	6.68659i	0.251032	−	0.282560i
$561$	−20.6774	−	12.3454i	−0.873000	−	0.521221i
$562$	−6.79516	+	13.3043i	−0.286636	+	0.561207i
$563$		−	13.5713i		−	0.571962i	−0.958235	−	0.285981i	$-0.907681\pi$
$563$		−	13.5713i		−	0.571962i	0.958235	−	0.285981i	$-0.0923194\pi$
$564$	−25.9399	+	2.29205i	−1.09227	+	0.0965128i
$565$	−18.1345	−	7.84594i	−0.762925	−	0.330081i
$566$	−6.97332	−	3.56162i	−0.293111	−	0.149706i
$567$	−4.94862	+	7.51739i	−0.207823	+	0.315701i
$568$	1.95323	+	12.5692i	0.0819556	+	0.527391i
$569$		−	16.4865i		−	0.691148i	−0.938392	−	0.345574i	$-0.887684\pi$
$569$		−	16.4865i		−	0.691148i	0.938392	−	0.345574i	$-0.112316\pi$
$570$	10.3279	−	1.58213i	0.432590	−	0.0662680i
$571$		−	7.86631i		−	0.329195i	−0.986361	−	0.164597i	$-0.947368\pi$
$571$		−	7.86631i		−	0.329195i	0.986361	−	0.164597i	$-0.0526325\pi$
$572$	8.53077	−	6.17268i	0.356689	−	0.258093i
$573$	−11.5964	−	6.92361i	−0.484448	−	0.289238i
$574$	7.19138	−	14.0800i	0.300162	−	0.587690i
$575$	7.47357	−	7.02020i	0.311670	−	0.292763i
$576$	−17.2606	−	16.6755i	−0.719191	−	0.694812i
$577$		−	31.2545i		−	1.30114i	−0.759445	−	0.650572i	$-0.774529\pi$
$577$		−	31.2545i		−	1.30114i	0.759445	−	0.650572i	$-0.225471\pi$
$578$	10.5534	+	5.39016i	0.438964	+	0.224201i
$579$	−1.91590	+	3.20897i	−0.0796222	+	0.133360i
$580$	−21.5882	+	4.78316i	−0.896401	+	0.198610i
$581$		−	7.71558i		−	0.320096i
$582$	−34.6034	+	21.7111i	−1.43436	+	0.899952i
$583$	16.9666			0.702685
$584$	17.0940	−	2.65638i	0.707355	−	0.109922i
$585$	−12.7494	+	1.09882i	−0.527122	+	0.0454304i
$586$	31.7630	+	16.2230i	1.31212	+	0.670164i
$587$		−	2.10458i		−	0.0868654i	−0.999056	−	0.0434327i	$-0.986171\pi$
$587$		−	2.10458i		−	0.0868654i	0.999056	−	0.0434327i	$-0.0138294\pi$
$588$	0.304900	+	3.45066i	0.0125739	+	0.142303i
$589$	13.2076			0.544208
$590$	−1.44352	−	1.74812i	−0.0594290	−	0.0719689i
$591$	22.2595	+	13.2900i	0.915635	+	0.546676i
$592$	24.6249	+	8.10703i	1.01208	+	0.333197i
$593$	−3.52377			−0.144704			−0.0723520	−	0.997379i	$-0.523050\pi$
$593$	−3.52377			−0.144704			−0.0723520	+	0.997379i	$0.523050\pi$
$594$	−10.0095	+	17.6392i	−0.410694	+	0.723745i
$595$	10.3387	+	4.47306i	0.423845	+	0.183378i
$596$	−22.1044	+	15.9943i	−0.905432	+	0.655151i
$597$	9.53501	−	15.9703i	0.390242	−	0.653622i
$598$	−4.92697	−	2.51645i	−0.201479	−	0.102905i
$599$	−13.1436			−0.537031			−0.268516	−	0.963275i	$-0.586533\pi$
$599$	−13.1436			−0.537031			−0.268516	+	0.963275i	$0.586533\pi$
$600$	−22.8368	+	8.85884i	−0.932310	+	0.361661i
$601$	−15.5022			−0.632347			−0.316174	−	0.948701i	$-0.602398\pi$
$601$	−15.5022			−0.632347			−0.316174	+	0.948701i	$0.602398\pi$
$602$	−11.7940	−	6.02377i	−0.480686	−	0.245510i
$603$	5.10612	+	9.47448i	0.207937	+	0.385831i
$604$	2.18801	−	1.58320i	0.0890290	−	0.0644194i
$605$	6.94220	+	3.00356i	0.282240	+	0.122112i
$606$	16.0091	−	10.0445i	0.650323	−	0.408029i
$607$	8.78015			0.356375			0.178188	−	0.983997i	$-0.442977\pi$
$607$	8.78015			0.356375			0.178188	+	0.983997i	$0.442977\pi$
$608$	−7.59329	−	7.66742i	−0.307949	−	0.310955i
$609$	4.39007	−	7.35300i	0.177895	−	0.297958i
$610$	−10.3317	−	12.5117i	−0.418317	−	0.506585i
$611$	14.3403			0.580145
$612$	13.1507	−	27.2161i	0.531585	−	1.10015i
$613$		−	7.21143i		−	0.291267i	−0.989339	−	0.145633i	$-0.953478\pi$
$613$		−	7.21143i		−	0.291267i	0.989339	−	0.145633i	$-0.0465220\pi$
$614$	24.0334	+	12.2751i	0.969910	+	0.495381i
$615$	−35.1330	+	25.3061i	−1.41670	+	1.02044i
$616$	1.19869	+	7.71369i	0.0482967	+	0.310793i
$617$	−4.53960			−0.182758			−0.0913788	−	0.995816i	$-0.529127\pi$
$617$	−4.53960			−0.182758			−0.0913788	+	0.995816i	$0.529127\pi$
$618$	−26.3115	−	41.9356i	−1.05840	−	1.68690i
$619$			18.1564i			0.729766i	0.931053	+	0.364883i	$0.118891\pi$
$619$			18.1564i			0.729766i	−0.931053	+	0.364883i	$0.881109\pi$
$620$	−30.2302	+	6.69791i	−1.21407	+	0.268995i
$621$	10.6456	+	0.468037i	0.427195	+	0.0187817i
$622$	−8.75783	−	4.47306i	−0.351157	−	0.179353i
$623$			13.5677i			0.543579i
$624$	8.65992	+	9.98383i	0.346674	+	0.399673i
$625$	−1.56249	+	24.9511i	−0.0624997	+	0.998045i
$626$	−22.2188	+	43.5023i	−0.888042	+	1.73870i
$627$	−4.67469	+	7.82970i	−0.186689	+	0.312688i
$628$	−3.09093	+	2.23653i	−0.123342	+	0.0892473i
$629$			32.6513i			1.30189i
$630$	3.57374	−	8.78797i	0.142381	−	0.350121i
$631$		−	46.0384i		−	1.83276i	−0.400310	−	0.916380i	$-0.631098\pi$
$631$		−	46.0384i		−	1.83276i	0.400310	−	0.916380i	$-0.368902\pi$
$632$	−40.9580	+	6.36480i	−1.62922	+	0.253178i
$633$	−12.0601	+	20.1996i	−0.479346	+	0.802863i
$634$	10.3184	+	5.27012i	0.409796	+	0.209303i
$635$	4.42632	+	1.91505i	0.175653	+	0.0759966i
$636$	1.87436	+	21.2128i	0.0743234	+	0.841143i
$637$		−	1.90761i		−	0.0755823i
$638$	8.77800	−	17.1865i	0.347524	−	0.680420i
$639$	6.40073	+	11.8767i	0.253209	+	0.469833i
$640$	21.2683	+	13.6989i	0.840704	+	0.541495i
$641$			28.5533i			1.12779i	0.825847	+	0.563894i	$0.190697\pi$
$641$			28.5533i			1.12779i	−0.825847	+	0.563894i	$0.809303\pi$
$642$	2.64333	−	1.65849i	0.104324	−	0.0654556i
$643$	28.9229			1.14061			0.570305	−	0.821433i	$-0.306825\pi$
$643$	28.9229			1.14061			0.570305	+	0.821433i	$0.306825\pi$
$644$	3.32283	−	2.40433i	0.130938	−	0.0947438i
$645$	21.1974	+	29.4287i	0.834645	+	1.15875i
$646$	6.18186	−	12.1035i	0.243222	−	0.476206i
$647$			5.44152i			0.213928i	0.994263	+	0.106964i	$0.0341130\pi$
$647$			5.44152i			0.213928i	−0.994263	+	0.106964i	$0.965887\pi$
$648$	−23.1595	−	10.5659i	−0.909791	−	0.415067i
$649$	1.97864			0.0776684
$650$	12.9564	−	3.75257i	0.508190	−	0.147188i
$651$	6.14747	−	10.2965i	0.240938	−	0.403551i
$652$	28.6504	+	39.5954i	1.12203	+	1.55068i
$653$	−36.5529			−1.43042			−0.715212	−	0.698907i	$-0.753670\pi$
$653$	−36.5529			−1.43042			−0.715212	+	0.698907i	$0.753670\pi$
$654$	−19.0568	−	30.3730i	−0.745180	−	1.18768i
$655$	6.02588	+	2.60711i	0.235451	+	0.101868i
$656$	42.4754	+	13.9838i	1.65839	+	0.545977i
$657$	16.1522	−	8.70495i	0.630156	−	0.339613i
$658$	−4.83566	+	9.46777i	−0.188514	+	0.369092i
$659$	9.10215			0.354570			0.177285	−	0.984160i	$-0.443269\pi$
$659$	9.10215			0.354570			0.177285	+	0.984160i	$0.443269\pi$
$660$	6.72904	−	20.2917i	0.261927	−	0.789854i
$661$	−1.54757			−0.0601935			−0.0300968	−	0.999547i	$-0.509582\pi$
$661$	−1.54757			−0.0601935			−0.0300968	+	0.999547i	$0.509582\pi$
$662$	2.98255	−	5.83956i	0.115920	−	0.226961i
$663$	−8.53286	+	14.2918i	−0.331389	+	0.555048i
$664$	21.5641	−	3.35103i	0.836851	−	0.130045i
$665$	1.69377	−	3.91485i	0.0656815	−	0.151811i
$666$	27.4909	−	0.607570i	1.06525	−	0.0235428i
$667$	−10.1395			−0.392603
$668$	5.72732	−	4.14417i	0.221597	−	0.160343i
$669$	−17.3130	−	10.3367i	−0.669360	−	0.399638i
$670$	−7.22372	−	8.74797i	−0.279077	−	0.337964i
$671$	14.1616			0.546704
$672$	−9.51176	+	2.35085i	−0.366924	+	0.0906859i
$673$			3.16034i			0.121822i	0.998143	+	0.0609110i	$0.0194006\pi$
$673$			3.16034i			0.121822i	−0.998143	+	0.0609110i	$0.980599\pi$
$674$	11.8587	−	23.2182i	0.456779	−	0.894330i
$675$	−19.6996	+	16.9389i	−0.758237	+	0.651979i
$676$	10.9751	+	15.1678i	0.422119	+	0.583377i
$677$	11.8437			0.455189			0.227595	−	0.973756i	$-0.426914\pi$
$677$	11.8437			0.455189			0.227595	+	0.973756i	$0.426914\pi$
$678$	11.5038	+	18.3349i	0.441799	+	0.704146i
$679$			16.6772i			0.640010i
$680$	−8.01138	+	30.8382i	−0.307222	+	1.18259i
$681$	−2.80603	+	4.69986i	−0.107527	+	0.180099i
$682$	12.2919	−	24.0664i	0.470682	−	0.921551i
$683$			4.05943i			0.155330i	0.996980	+	0.0776648i	$0.0247464\pi$
$683$			4.05943i			0.155330i	−0.996980	+	0.0776648i	$0.975254\pi$
$684$	−10.3057	−	4.97964i	−0.394047	−	0.190401i
$685$	33.8386	+	14.6403i	1.29291	+	0.559378i
$686$	1.25945	+	0.643263i	0.0480860	+	0.0245599i
$687$	−5.11296	−	3.05267i	−0.195072	−	0.116467i
$688$	11.7134	−	35.5790i	0.446568	−	1.35644i
$689$		−	11.7270i		−	0.446763i
$690$	−11.1028	+	1.70083i	−0.422677	+	0.0647494i
$691$			40.8932i			1.55565i	0.628481	+	0.777825i	$0.283677\pi$
$691$			40.8932i			1.55565i	−0.628481	+	0.777825i	$0.716323\pi$
$692$	19.7777	+	27.3332i	0.751836	+	1.03905i
$693$	3.92812	+	7.28869i	0.149217	+	0.276874i
$694$	1.84518	−	3.61269i	0.0700420	−	0.137136i
$695$	9.63703	−	22.2743i	0.365553	−	0.844913i
$696$	22.4575	+	9.07619i	0.851248	+	0.344032i
$697$			56.3202i			2.13328i
$698$	−3.48376	−	1.77933i	−0.131862	−	0.0673487i
$699$	−26.1292	−	15.6003i	−0.988295	−	0.590057i
$700$	−1.89147	+	9.81949i	−0.0714907	+	0.371142i
$701$		−	34.0369i		−	1.28555i	−0.766053	−	0.642777i	$-0.777782\pi$
$701$		−	34.0369i		−	1.28555i	0.766053	−	0.642777i	$-0.222218\pi$
$702$	12.1919	+	6.91836i	0.460152	+	0.261117i
$703$	12.3637			0.466307
$704$	−21.0382	+	6.70041i	−0.792909	+	0.252531i
$705$	23.6243	−	17.0165i	0.889742	−	0.640877i
$706$	29.8174	+	15.2292i	1.12219	+	0.573160i
$707$		−	7.71558i		−	0.290174i
$708$	0.218588	+	2.47383i	0.00821502	+	0.0929722i
$709$	−38.5746			−1.44870			−0.724351	−	0.689432i	$-0.757860\pi$
$709$	−38.5746			−1.44870			−0.724351	+	0.689432i	$0.757860\pi$
$710$	−9.05523	−	10.9659i	−0.339837	−	0.411545i
$711$	−38.7013	+	20.8575i	−1.45141	+	0.782216i
$712$	−37.9202	+	5.89272i	−1.42112	+	0.220839i
$713$	−14.1985			−0.531737
$714$	−6.55842	−	10.4529i	−0.245443	−	0.391191i
$715$	−4.67469	+	10.8047i	−0.174823	+	0.404074i
$716$	4.91687	+	6.79522i	0.183752	+	0.253949i
$717$	−26.0661	−	15.5627i	−0.973457	−	0.581198i
$718$	−19.8250	−	10.1256i	−0.739862	−	0.377884i
$719$	10.8657			0.405222			0.202611	−	0.979259i	$-0.435057\pi$
$719$	10.8657			0.405222			0.202611	+	0.979259i	$0.435057\pi$
$720$	26.1135	+	6.17140i	0.973192	+	0.229994i
$721$	−20.2109			−0.752694
$722$	19.3464	+	9.88118i	0.719999	+	0.367739i
$723$	9.23661	+	5.51468i	0.343513	+	0.205093i
$724$	−11.3730	−	15.7177i	−0.422673	−	0.584143i
$725$	18.0189	−	16.9258i	0.669203	−	0.628607i
$726$	−4.40383	−	7.01889i	−0.163441	−	0.260495i
$727$	4.65736			0.172732			0.0863659	−	0.996263i	$-0.472475\pi$
$727$	4.65736			0.172732			0.0863659	+	0.996263i	$0.472475\pi$
$728$	5.33155	−	0.828513i	0.197600	−	0.0307067i
$729$	−26.8958	−	2.36954i	−0.996142	−	0.0877607i
$730$	−14.9136	+	12.3151i	−0.551978	+	0.455801i
$731$	47.1759			1.74486
$732$	1.56449	+	17.7058i	0.0578251	+	0.654426i
$733$			7.36632i			0.272081i	0.990703	+	0.136041i	$0.0434378\pi$
$733$			7.36632i			0.272081i	−0.990703	+	0.136041i	$0.956562\pi$
$734$	24.3427	+	12.4330i	0.898504	+	0.458911i
$735$	−2.26361	−	3.14262i	−0.0834947	−	0.115917i
$736$	8.16299	+	8.24268i	0.300892	+	0.303829i
$737$	9.90156			0.364729
$738$	47.4191	−	1.04800i	1.74552	−	0.0385773i
$739$			33.9459i			1.24872i	0.781137	+	0.624360i	$0.214640\pi$
$739$			33.9459i			1.24872i	−0.781137	+	0.624360i	$0.785360\pi$
$740$	−28.2988	+	6.26999i	−1.04028	+	0.230489i
$741$	5.41173	+	3.23105i	0.198805	+	0.118696i
$742$	7.74243	+	3.95444i	0.284233	+	0.145172i
$743$			5.51110i			0.202183i	0.994877	+	0.101091i	$0.0322334\pi$
$743$			5.51110i			0.202183i	−0.994877	+	0.101091i	$0.967767\pi$
$744$	31.4474	+	12.7095i	1.15292	+	0.465953i
$745$	12.1128	−	27.9966i	0.443778	−	1.02571i
$746$	22.1764	−	43.4193i	0.811936	−	1.58970i
$747$	20.3760	−	10.9813i	0.745520	−	0.401786i
$748$	−16.3014	−	22.5288i	−0.596037	−	0.823736i
$749$		−	1.27396i		−	0.0465494i
$750$	16.8916	−	21.5563i	0.616792	−	0.787126i
$751$			19.4438i			0.709514i	0.934959	+	0.354757i	$0.115436\pi$
$751$			19.4438i			0.709514i	−0.934959	+	0.354757i	$0.884564\pi$
$752$	−28.5615	−	9.40307i	−1.04153	−	0.342895i
$753$	33.4253	+	19.9564i	1.21808	+	0.727252i
$754$	−11.8790	−	6.06718i	−0.432606	−	0.220954i
$755$	−1.19899	+	2.77125i	−0.0436356	+	0.100856i
$756$	−8.67886	+	5.71641i	−0.315647	+	0.207904i
$757$		−	26.8731i		−	0.976718i	−0.872643	−	0.488359i	$-0.837596\pi$
$757$		−	26.8731i		−	0.976718i	0.872643	−	0.488359i	$-0.162404\pi$
$758$	10.4930	−	20.5442i	0.381121	−	0.746200i
$759$	5.02541	−	8.41713i	0.182411	−	0.305523i
$760$	11.6772	+	3.03359i	0.423576	+	0.110040i
$761$			43.9086i			1.59169i	0.605503	+	0.795843i	$0.292972\pi$
$761$			43.9086i			1.59169i	−0.605503	+	0.795843i	$0.707028\pi$
$762$	−2.80786	−	4.47521i	−0.101718	−	0.162120i
$763$	−14.6383			−0.529943
$764$	−9.14225	−	12.6348i	−0.330755	−	0.457110i
$765$	2.90185	+	33.6697i	0.104917	+	1.21733i
$766$	−13.1670	+	25.7798i	−0.475745	+	0.931464i
$767$		−	1.36760i		−	0.0493811i
$768$	−10.7015	−	25.5632i	−0.386156	−	0.922433i
$769$	−24.2477			−0.874393			−0.437197	−	0.899366i	$-0.644029\pi$
$769$	−24.2477			−0.874393			−0.437197	+	0.899366i	$0.644029\pi$
$770$	−5.55719	−	6.72979i	−0.200267	−	0.242525i
$771$	−10.7925	−	6.44362i	−0.388683	−	0.232061i
$772$	−3.49630	+	2.52985i	−0.125835	+	0.0910512i
$773$	−17.0431			−0.612998			−0.306499	−	0.951871i	$-0.599158\pi$
$773$	−17.0431			−0.612998			−0.306499	+	0.951871i	$0.599158\pi$
$774$	−0.877841	−	39.7200i	−0.0315533	−	1.42771i
$775$	25.2320	−	23.7014i	0.906360	−	0.851378i
$776$	−46.6107	+	7.24321i	−1.67323	+	0.260016i
$777$	5.75471	−	9.63865i	0.206449	−	0.345785i
$778$	8.04476	−	15.7509i	0.288419	−	0.564696i
$779$	21.3262			0.764090
$780$	−14.0252	−	4.65098i	−0.502184	−	0.166532i
$781$	12.4120			0.444137
$782$	−6.64566	+	13.0116i	−0.237648	+	0.465293i
$783$	25.6667	+	1.12844i	0.917254	+	0.0403272i
$784$	−1.25084	+	3.79939i	−0.0446729	+	0.135693i
$785$	1.69377	−	3.91485i	0.0604532	−	0.139727i
$786$	−3.82256	−	6.09245i	−0.136346	−	0.217311i
$787$	−11.5435			−0.411483			−0.205741	−	0.978606i	$-0.565961\pi$
$787$	−11.5435			−0.411483			−0.205741	+	0.978606i	$0.565961\pi$
$788$	17.5487	+	24.2526i	0.625146	+	0.863965i
$789$	−14.5552	+	24.3787i	−0.518178	+	0.867904i
$790$	35.7337	−	29.5074i	1.27135	−	1.04983i
$791$	8.83651			0.314190
$792$	−18.6650	+	14.1443i	−0.663231	+	0.502594i
$793$		−	9.78824i		−	0.347590i
$794$	4.72007	−	9.24145i	0.167509	−	0.327967i
$795$	−13.9155	−	19.3192i	−0.493532	−	0.685180i
$796$	17.4003	−	12.5905i	0.616737	−	0.446257i
$797$	8.66018			0.306759			0.153380	−	0.988167i	$-0.450984\pi$
$797$	8.66018			0.306759			0.153380	+	0.988167i	$0.450984\pi$
$798$	−3.95810	+	2.48341i	−0.140115	+	0.0879118i
$799$		−	37.8711i		−	1.33978i
$800$	−28.2658	−	1.02163i	−0.999347	−	0.0361200i
$801$	−35.8309	+	19.3105i	−1.26602	+	0.682302i
$802$	−7.29483	+	14.2826i	−0.257589	+	0.504336i
$803$		−	16.8802i		−	0.595691i
$804$	1.09386	+	12.3796i	0.0385775	+	0.436595i
$805$	−1.82085	+	4.20857i	−0.0641764	+	0.148332i
$806$	−16.6342	−	8.49593i	−0.585916	−	0.299257i
$807$	−4.02550	+	6.74236i	−0.141704	+	0.237342i
$808$	21.5641	−	3.35103i	0.758624	−	0.117889i
$809$			29.1441i			1.02465i	0.858791	+	0.512326i	$0.171216\pi$
$809$			29.1441i			1.02465i	−0.858791	+	0.512326i	$0.828784\pi$
$810$	28.2945	−	3.06976i	0.994166	−	0.107860i
$811$		−	37.4623i		−	1.31548i	−0.753246	−	0.657739i	$-0.771513\pi$
$811$		−	37.4623i		−	1.31548i	0.753246	−	0.657739i	$-0.228487\pi$
$812$	8.01138	−	5.79686i	0.281144	−	0.203430i
$813$	−24.4320	+	40.9214i	−0.856867	+	1.43518i
$814$	11.5066	−	22.5288i	0.403306	−	0.789635i
$815$	−50.1499	−	21.6975i	−1.75668	−	0.760030i
$816$	26.3662	−	22.8699i	0.923002	−	0.800608i
$817$		−	17.8636i		−	0.624969i
$818$	13.3114	+	6.79880i	0.465422	+	0.237714i
$819$	5.03780	−	2.71504i	0.176035	−	0.0948712i
$820$	−48.8126	+	10.8151i	−1.70461	+	0.377680i
$821$		−	22.2823i		−	0.777658i	−0.921310	−	0.388829i	$-0.872880\pi$
$821$		−	22.2823i		−	0.777658i	0.921310	−	0.388829i	$-0.127120\pi$
$822$	−21.4657	−	34.2124i	−0.748703	−	1.19329i
$823$	−12.5937			−0.438988			−0.219494	−	0.975614i	$-0.570441\pi$
$823$	−12.5937			−0.438988			−0.219494	+	0.975614i	$0.570441\pi$
$824$	−8.77800	−	56.4871i	−0.305796	−	1.96782i
$825$	5.12000	+	23.3469i	0.178256	+	0.812835i
$826$	0.902919	+	0.461166i	0.0314166	+	0.0160460i
$827$		−	32.6595i		−	1.13568i	−0.823138	−	0.567841i	$-0.807779\pi$
$827$		−	32.6595i		−	1.13568i	0.823138	−	0.567841i	$-0.192221\pi$
$828$	11.0788	+	5.35324i	0.385017	+	0.186038i
$829$	−19.9927			−0.694375			−0.347187	−	0.937796i	$-0.612863\pi$
$829$	−19.9927			−0.694375			−0.347187	+	0.937796i	$0.612863\pi$
$830$	−18.8136	+	15.5355i	−0.653029	+	0.539245i
$831$	21.6158	−	36.2046i	0.749844	−	1.25592i
$832$	4.63119	+	14.5412i	0.160558	+	0.504126i
$833$	−5.03780			−0.174549
$834$	−22.5204	+	14.1299i	−0.779817	+	0.489277i
$835$	−3.13846	+	7.25400i	−0.108611	+	0.251035i
$836$	−8.53077	+	6.17268i	−0.295043	+	0.213486i
$837$	35.9414	+	1.58017i	1.24232	+	0.0546186i
$838$	−49.3107	−	25.1854i	−1.70341	−	0.870016i
$839$	−7.38656			−0.255012			−0.127506	−	0.991838i	$-0.540697\pi$
$839$	−7.38656			−0.255012			−0.127506	+	0.991838i	$0.540697\pi$
$840$	7.80012	−	7.69144i	0.269130	−	0.265380i
$841$	4.55356			0.157019
$842$	35.2799	+	18.0192i	1.21583	+	0.620982i
$843$	−9.37939	+	15.7097i	−0.323044	+	0.541070i
$844$	−22.0083	+	15.9247i	−0.757556	+	0.548151i
$845$	−19.2109	−	8.31165i	−0.660876	−	0.285929i
$846$	−31.8858	+	0.704699i	−1.09626	+	0.0242280i
$847$	−3.38276			−0.116233
$848$	−7.68952	+	23.3567i	−0.264059	+	0.802071i
$849$	−8.23409	−	4.91613i	−0.282593	−	0.168721i
$850$	−9.91014	−	34.2164i	−0.339915	−	1.17361i
$851$	−13.2913			−0.455621
$852$	1.37120	+	15.5183i	0.0469765	+	0.531649i
$853$		−	0.362131i		−	0.0123991i	−0.999981	−	0.00619956i	$-0.998027\pi$
$853$		−	0.362131i		−	0.0123991i	0.999981	−	0.00619956i	$-0.00197339\pi$
$854$	6.46242	+	3.30068i	0.221139	+	0.112947i
$855$	12.7494	−	1.09882i	0.436020	−	0.0375787i
$856$	3.56056	−	0.553305i	0.121698	−	0.0189116i
$857$	−4.56811			−0.156044			−0.0780218	−	0.996952i	$-0.524860\pi$
$857$	−4.56811			−0.156044			−0.0780218	+	0.996952i	$0.524860\pi$
$858$	10.9241	−	6.85405i	0.372942	−	0.233994i
$859$			16.7842i			0.572669i	0.958130	+	0.286334i	$0.0924368\pi$
$859$			16.7842i			0.572669i	−0.958130	+	0.286334i	$0.907563\pi$
$860$	9.05913	+	40.8872i	0.308914	+	1.39424i
$861$	9.92631	−	16.6257i	0.338288	−	0.566602i
$862$	−47.6736	−	24.3493i	−1.62377	−	0.829339i
$863$			26.2477i			0.893481i	0.894664	+	0.446741i	$0.147415\pi$
$863$			26.2477i			0.893481i	−0.894664	+	0.446741i	$0.852585\pi$
$864$	−19.7461	−	21.7736i	−0.671776	−	0.740754i
$865$	−34.6192	−	14.9781i	−1.17709	−	0.509269i
$866$	11.7666	−	23.0379i	0.399845	−	0.782858i
$867$	12.4615	+	7.44007i	0.423214	+	0.252678i
$868$	11.2184	−	8.11740i	0.380778	−	0.275523i
$869$			40.4458i			1.37203i
$870$	−26.7690	+	4.10071i	−0.907553	+	0.139027i
$871$		−	6.84376i		−	0.231892i
$872$	−6.35771	−	40.9124i	−0.215299	−	1.38547i
$873$	−44.0426	+	23.7360i	−1.49062	+	0.803343i
$874$	4.92697	+	2.51645i	0.166657	+	0.0851201i
$875$	−3.78950	−	10.5185i	−0.128109	−	0.355592i
$876$	21.1048	−	1.86482i	0.713066	−	0.0630065i
$877$			30.5051i			1.03008i	0.857165	+	0.515042i	$0.172224\pi$
$877$			30.5051i			1.03008i	−0.857165	+	0.515042i	$0.827776\pi$
$878$	8.07608	−	15.8122i	0.272555	−	0.533636i
$879$	37.5058	+	22.3926i	1.26504	+	0.755285i
$880$	16.3954	−	18.4546i	0.552688	−	0.622103i
$881$		−	21.4921i		−	0.724088i	−0.932161	−	0.362044i	$-0.882079\pi$
$881$		−	21.4921i		−	0.724088i	0.932161	−	0.362044i	$-0.117921\pi$
$882$	0.0937425	+	4.24160i	0.00315647	+	0.142822i
$883$	26.3164			0.885617			0.442808	−	0.896616i	$-0.353982\pi$
$883$	26.3164			0.885617			0.442808	+	0.896616i	$0.353982\pi$
$884$	−15.5715	+	11.2672i	−0.523726	+	0.378956i
$885$	−1.62282	−	2.25299i	−0.0545505	−	0.0757335i
$886$	19.1536	−	37.5009i	0.643477	−	1.25987i
$887$		−	58.2531i		−	1.95595i	−0.208727	−	0.977974i	$-0.566932\pi$
$887$		−	58.2531i		−	1.95595i	0.208727	−	0.977974i	$-0.433068\pi$
$888$	29.4383	+	11.8975i	0.987883	+	0.399254i
$889$	−2.15684			−0.0723379
$890$	33.0833	−	27.3189i	1.10896	−	0.915731i
$891$	−13.6579	+	20.7475i	−0.457556	+	0.695067i
$892$	−13.6490	−	18.8632i	−0.457002	−	0.631587i
$893$	−14.3403			−0.479878
$894$	−28.3058	+	17.7598i	−0.946689	+	0.593977i
$895$	−8.60656	−	3.72364i	−0.287685	−	0.124468i
$896$	−11.1621	−	1.84581i	−0.372900	−	0.0616641i
$897$	−5.81776	−	3.47347i	−0.194249	−	0.115976i
$898$	15.2616	−	29.8808i	0.509287	−	0.997137i
$899$	−34.2326			−1.14172
$900$	−28.6243	+	8.98059i	−0.954142	+	0.299353i
$901$	−30.9697			−1.03175
$902$	19.8477	−	38.8600i	0.660857	−	1.29390i
$903$	−13.9263	−	8.31464i	−0.463438	−	0.276694i
$904$	3.83787	+	24.6970i	0.127646	+	0.821410i
$905$	19.9074	+	8.61297i	0.661743	+	0.286305i
$906$	2.80187	−	1.75796i	0.0930857	−	0.0584044i
$907$	−28.7261			−0.953833			−0.476917	−	0.878949i	$-0.658246\pi$
$907$	−28.7261			−0.953833			−0.476917	+	0.878949i	$0.658246\pi$
$908$	−5.12068	+	3.70521i	−0.169936	+	0.122962i
$909$	20.3760	−	10.9813i	0.675830	−	0.364228i
$910$	−4.65150	+	3.84102i	−0.154196	+	0.127328i
$911$	−1.93202			−0.0640108			−0.0320054	−	0.999488i	$-0.510189\pi$
$911$	−1.93202			−0.0640108			−0.0320054	+	0.999488i	$0.510189\pi$
$912$	−8.65992	−	9.98383i	−0.286759	−	0.330598i
$913$		−	21.2945i		−	0.704745i
$914$	3.64977	−	7.14590i	0.120724	−	0.236365i
$915$	−11.6149	−	16.1252i	−0.383978	−	0.533084i
$916$	−4.03089	−	5.57078i	−0.133184	−	0.184064i
$917$	−2.93626			−0.0969640
$918$	18.2706	−	32.1974i	0.603021	−	1.06267i
$919$		−	39.8495i		−	1.31451i	−0.753666	−	0.657257i	$-0.771717\pi$
$919$		−	39.8495i		−	1.31451i	0.753666	−	0.657257i	$-0.228283\pi$
$920$	−12.5533	−	3.26119i	−0.413869	−	0.107518i
$921$	28.3786	+	16.9433i	0.935108	+	0.558302i
$922$	−7.90513	+	15.4775i	−0.260341	+	0.509724i
$923$		−	8.57893i		−	0.282379i
$924$	0.841504	+	9.52359i	0.0276834	+	0.313303i
$925$	23.6199	−	22.1871i	0.776619	−	0.729507i
$926$	1.12580	+	0.575000i	0.0369960	+	0.0188957i
$927$	−28.7655	−	53.3749i	−0.944784	−	1.75306i
$928$	19.6810	+	19.8732i	0.646062	+	0.652369i
$929$		−	33.7414i		−	1.10702i	−0.832842	−	0.553510i	$-0.813288\pi$
$929$		−	33.7414i		−	1.10702i	0.832842	−	0.553510i	$-0.186712\pi$
$930$	−37.4849	+	5.74227i	−1.22918	+	0.188297i
$931$			1.90761i			0.0625194i
$932$	−20.5994	−	28.4687i	−0.674754	−	0.932525i
$933$	−10.3412	−	6.17419i	−0.338557	−	0.202134i
$934$	−18.7109	+	36.6341i	−0.612239	+	1.19871i
$935$	28.5341	+	12.3454i	0.933166	+	0.403736i
$936$	9.77623	+	12.9009i	0.319546	+	0.421678i
$937$		−	2.95584i		−	0.0965631i	−0.998834	−	0.0482816i	$-0.984626\pi$
$937$		−	2.95584i		−	0.0965631i	0.998834	−	0.0482816i	$-0.0153745\pi$
$938$	4.51841	+	2.30778i	0.147531	+	0.0753516i
$939$	−30.6688	+	51.3675i	−1.00084	+	1.67632i
$940$	32.8228	−	7.27234i	1.07056	−	0.237197i
$941$			10.7787i			0.351375i	0.984446	+	0.175687i	$0.0562148\pi$
$941$			10.7787i			0.351375i	−0.984446	+	0.175687i	$0.943785\pi$
$942$	−3.95810	+	2.48341i	−0.128962	+	0.0809139i
$943$	−22.9262			−0.746580
$944$	−0.896748	+	2.72384i	−0.0291867	+	0.0886536i
$945$	5.07759	−	10.4507i	0.165174	−	0.339963i
$946$	−32.5506	−	16.6252i	−1.05831	−	0.540532i
$947$		−	34.5592i		−	1.12302i	−0.827469	−	0.561511i	$-0.810220\pi$
$947$		−	34.5592i		−	1.12302i	0.827469	−	0.561511i	$-0.189780\pi$
$948$	−50.5681	+	4.46820i	−1.64238	+	0.145120i
$949$	−11.6673			−0.378736
$950$	−12.9564	+	3.75257i	−0.420360	+	0.121749i
$951$	12.1839	+	7.27437i	0.395092	+	0.235888i
$952$	−2.18801	−	14.0800i	−0.0709139	−	0.456337i
$953$	32.9065			1.06595			0.532973	−	0.846132i	$-0.321075\pi$
$953$	32.9065			1.06595			0.532973	+	0.846132i	$0.321075\pi$
$954$	0.576279	+	26.0751i	0.0186577	+	0.844214i
$955$	16.0027	+	6.92361i	0.517836	+	0.224043i
$956$	−20.5497	−	28.4001i	−0.664623	−	0.918523i
$957$	12.1163	−	20.2938i	0.391665	−	0.656005i
$958$	−30.5719	−	15.6146i	−0.987735	−	0.504485i
$959$	−16.4887			−0.532448
$960$	24.8844	+	18.4599i	0.803141	+	0.595790i
$961$	−16.9363			−0.546333
$962$	−15.5715	−	7.95313i	−0.502045	−	0.256419i
$963$	3.36439	−	1.81318i	0.108416	−	0.0584290i
$964$	7.28183	+	10.0636i	0.234532	+	0.324128i
$965$	1.91590	−	4.42828i	0.0616751	−	0.142551i
$966$	4.25506	−	2.66973i	0.136904	−	0.0858972i
$967$	0.335417			0.0107863			0.00539314	−	0.999985i	$-0.498283\pi$
$967$	0.335417			0.0107863			0.00539314	+	0.999985i	$0.498283\pi$
$968$	−1.46920	−	9.45443i	−0.0472219	−	0.303877i
$969$	8.53286	−	14.2918i	0.274115	−	0.459119i
$970$	40.6654	−	33.5798i	1.30569	−	1.07818i
$971$	−56.6148			−1.81685			−0.908427	−	0.418044i	$-0.862716\pi$
$971$	−56.6148			−1.81685			−0.908427	+	0.418044i	$0.862716\pi$
$972$	−27.4488	−	14.7840i	−0.880420	−	0.474196i
$973$			10.8537i			0.347955i
$974$	48.0634	+	24.5484i	1.54005	+	0.786581i
$975$	16.1369	−	3.53884i	0.516795	−	0.113334i
$976$	−6.41826	+	19.4953i	−0.205443	+	0.624028i
$977$	59.0104			1.88791			0.943955	−	0.330073i	$-0.107073\pi$
$977$	59.0104			1.88791			0.943955	+	0.330073i	$0.107073\pi$
$978$	31.8130	+	50.7040i	1.01727	+	1.62133i
$979$			37.4460i			1.19678i
$980$	−0.967402	−	4.36625i	−0.0309025	−	0.139475i
$981$	−20.8342	−	38.6582i	−0.665186	−	1.23426i
$982$	33.2778	+	16.9966i	1.06194	+	0.542384i
$983$			37.6136i			1.19969i	0.800117	+	0.599844i	$0.204771\pi$
$983$			37.6136i			1.19969i	−0.800117	+	0.599844i	$0.795229\pi$
$984$	50.7781	+	20.5220i	1.61875	+	0.654217i
$985$	−30.7174	−	13.2900i	−0.978739	−	0.423453i
$986$	−16.0228	+	31.3711i	−0.510269	+	0.999058i
$987$	−6.67469	+	11.1795i	−0.212458	+	0.355848i
$988$	4.26643	+	5.89630i	0.135733	+	0.187586i
$989$			19.2038i			0.610647i
$990$	9.86329	−	24.2542i	0.313476	−	0.770849i
$991$			45.8372i			1.45607i	0.685541	+	0.728034i	$0.259566\pi$
$991$			45.8372i			1.45607i	−0.685541	+	0.728034i	$0.740434\pi$
$992$	27.5596	+	27.8286i	0.875017	+	0.883560i
$993$	4.11684	−	6.89535i	0.130644	−	0.218817i
$994$	5.66401	+	2.89289i	0.179651	+	0.0917570i
$995$	−9.53501	+	22.0385i	−0.302280	+	0.698668i
$996$	26.6238	−	2.35248i	0.843609	−	0.0745412i
$997$			13.7556i			0.435645i	0.975988	+	0.217823i	$0.0698954\pi$
$997$			13.7556i			0.435645i	−0.975988	+	0.217823i	$0.930105\pi$
$998$	22.4537	−	43.9621i	0.710758	−	1.39160i
$999$	33.6451	+	1.47921i	1.06448	+	0.0468002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.h.239.14	yes	16
3.2	odd	2	inner	420.2.l.h.239.3	yes	16
4.3	odd	2		420.2.l.g.239.13	yes	16
5.4	even	2		420.2.l.g.239.3	✓	16
12.11	even	2		420.2.l.g.239.4	yes	16
15.14	odd	2		420.2.l.g.239.14	yes	16
20.19	odd	2	inner	420.2.l.h.239.4	yes	16
60.59	even	2	inner	420.2.l.h.239.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.g.239.3	✓	16	5.4	even	2
420.2.l.g.239.4	yes	16	12.11	even	2
420.2.l.g.239.13	yes	16	4.3	odd	2
420.2.l.g.239.14	yes	16	15.14	odd	2
420.2.l.h.239.3	yes	16	3.2	odd	2	inner
420.2.l.h.239.4	yes	16	20.19	odd	2	inner
420.2.l.h.239.13	yes	16	60.59	even	2	inner
420.2.l.h.239.14	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25945 + 0.643263i) q^{2} +(1.48716 + 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(-2.05223 - 0.887900i) q^{5} +(1.30184 + 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 + 2.79488i) q^{8} +(1.42327 + 2.64089i) q^{9} +O(q^{10})\)	\(q+(1.25945 + 0.643263i) q^{2} +(1.48716 + 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(-2.05223 - 0.887900i) q^{5} +(1.30184 + 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 + 2.79488i) q^{8} +(1.42327 + 2.64089i) q^{9} +(-2.01352 - 2.43839i) q^{10} +2.75993 q^{11} +(0.304900 + 3.45066i) q^{12} -1.90761i q^{13} +(1.25945 + 0.643263i) q^{14} +(-2.26361 - 3.14262i) q^{15} +(-1.25084 + 3.79939i) q^{16} -5.03780 q^{17} +(0.0937425 + 4.24160i) q^{18} +1.90761i q^{19} +(-0.967402 - 4.36625i) q^{20} +(1.48716 + 0.887900i) q^{21} +(3.47600 + 1.77536i) q^{22} -2.05073i q^{23} +(-1.83568 + 4.54206i) q^{24} +(3.42327 + 3.64434i) q^{25} +(1.22710 - 2.40254i) q^{26} +(-0.228229 + 5.19114i) q^{27} +(1.17242 + 1.62032i) q^{28} -4.94433i q^{29} +(-0.829376 - 5.41407i) q^{30} -6.92361i q^{31} +(-4.01938 + 3.98052i) q^{32} +(4.10445 + 2.45055i) q^{33} +(-6.34485 - 3.24063i) q^{34} +(-2.05223 - 0.887900i) q^{35} +(-2.61041 + 5.40239i) q^{36} -6.48126i q^{37} +(-1.22710 + 2.40254i) q^{38} +(1.69377 - 2.83692i) q^{39} +(1.59025 - 6.12136i) q^{40} -11.1795i q^{41} +(1.30184 + 2.07490i) q^{42} -9.36439 q^{43} +(3.23581 + 4.47196i) q^{44} +(-0.576017 - 6.68343i) q^{45} +(1.31916 - 2.58279i) q^{46} +7.51739i q^{47} +(-5.23368 + 4.53967i) q^{48} +1.00000 q^{49} +(1.96716 + 6.79193i) q^{50} +(-7.49199 - 4.47306i) q^{51} +(3.09093 - 2.23653i) q^{52} +6.14747 q^{53} +(-3.62671 + 6.39116i) q^{54} +(-5.66401 - 2.45055i) q^{55} +(0.434319 + 2.79488i) q^{56} +(-1.69377 + 2.83692i) q^{57} +(3.18051 - 6.22714i) q^{58} +0.716916 q^{59} +(2.43812 - 7.35225i) q^{60} +5.13115 q^{61} +(4.45370 - 8.71993i) q^{62} +(1.42327 + 2.64089i) q^{63} +(-7.62273 + 2.42774i) q^{64} +(-1.69377 + 3.91485i) q^{65} +(3.59300 + 5.72658i) q^{66} +3.58761 q^{67} +(-5.90644 - 8.16282i) q^{68} +(1.82085 - 3.04976i) q^{69} +(-2.01352 - 2.43839i) q^{70} +4.49721 q^{71} +(-6.76283 + 5.12485i) q^{72} -6.11618i q^{73} +(4.16916 - 8.16282i) q^{74} +(1.85512 + 8.45923i) q^{75} +(-3.09093 + 2.23653i) q^{76} +2.75993 q^{77} +(3.95810 - 2.48341i) q^{78} +14.6546i q^{79} +(5.94049 - 6.68659i) q^{80} +(-4.94862 + 7.51739i) q^{81} +(7.19138 - 14.0800i) q^{82} -7.71558i q^{83} +(0.304900 + 3.45066i) q^{84} +(10.3387 + 4.47306i) q^{85} +(-11.7940 - 6.02377i) q^{86} +(4.39007 - 7.35300i) q^{87} +(1.19869 + 7.71369i) q^{88} +13.5677i q^{89} +(3.57374 - 8.78797i) q^{90} -1.90761i q^{91} +(3.32283 - 2.40433i) q^{92} +(6.14747 - 10.2965i) q^{93} +(-4.83566 + 9.46777i) q^{94} +(1.69377 - 3.91485i) q^{95} +(-9.51176 + 2.35085i) q^{96} +16.6772i q^{97} +(1.25945 + 0.643263i) q^{98} +(3.92812 + 7.28869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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