LMFDB - Embedded newform 420.2.l.h.239.3

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			239.3
Root			$1.37874 + 0.314767i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25945 - 0.643263i) q^{2} +(1.48716 - 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(2.05223 + 0.887900i) q^{5} +(-2.44415 + 0.161632i) q^{6} +1.00000 q^{7} +(-0.434319 - 2.79488i) q^{8} +(1.42327 - 2.64089i) q^{9} +O(q^{10})$	\(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} +(-2.44415 + 0.161632i) 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} +(3.18226 + 1.36867i) q^{12} -1.90761i q^{13} +(-1.25945 - 0.643263i) q^{14} +(3.84035 - 0.501726i) q^{15} +(-1.25084 + 3.79939i) q^{16} +5.03780 q^{17} +(-3.49132 + 2.41053i) 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} +(-3.12748 - 3.77079i) 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} +(-5.15946 - 1.83846i) 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} +(5.94775 - 0.790106i) 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} +(-2.44415 + 0.161632i) q^{42} -9.36439 q^{43} +(-3.23581 - 4.47196i) q^{44} +(5.26571 - 4.15599i) q^{45} +(1.31916 - 2.58279i) q^{46} -7.51739i q^{47} +(1.51328 + 6.76091i) 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} +(-3.05183 + 6.68479i) 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} +(5.31547 + 5.63434i) 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} +(6.74570 - 0.446094i) 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} +(-7.99914 - 2.83087i) q^{72} -6.11618i q^{73} +(-4.16916 + 8.16282i) q^{74} +(8.32675 + 2.38019i) q^{75} +(-3.09093 + 2.23653i) q^{76} -2.75993 q^{77} +(0.308331 + 4.66249i) 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} +(3.18226 + 1.36867i) 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} +(-9.30530 + 1.84702i) 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} +(2.44314 - 9.48847i) 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
$6$	−2.44415	+	0.161632i	−0.997821	+	0.0659860i
$7$	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	$-0.636595\pi$
$11$	−2.75993			−0.832151			−0.416076	+	0.909330i	$0.636595\pi$
$12$	3.18226	+	1.36867i	0.918638	+	0.395100i
$13$		−	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
$15$	3.84035	−	0.501726i	0.991574	−	0.129545i
$16$	−1.25084	+	3.79939i	−0.312711	+	0.949848i
$17$	5.03780			1.22185			0.610923	−	0.791690i	$-0.290799\pi$
$17$	5.03780			1.22185			0.610923	+	0.791690i	$0.290799\pi$
$18$	−3.49132	+	2.41053i	−0.822912	+	0.568168i
$19$			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	$0.0685853\pi$
$23$			2.05073i			0.427607i	−0.976877	+	0.213804i	$0.931415\pi$
$24$	−3.12748	−	3.77079i	−0.638394	−	0.769710i
$25$	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	$0.151817\pi$
$29$			4.94433i			0.918140i	−0.888400	+	0.459070i	$0.848183\pi$
$30$	−5.15946	−	1.83846i	−0.941985	−	0.335655i
$31$		−	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
$36$	5.94775	−	0.790106i	0.991292	−	0.131684i
$37$		−	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	$0.337812\pi$
$41$			11.1795i			1.74595i	−0.487766	+	0.872975i	$0.662188\pi$
$42$	−2.44415	+	0.161632i	−0.377141	+	0.0249404i
$43$	−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
$45$	5.26571	−	4.15599i	0.784966	−	0.619538i
$46$	1.31916	−	2.58279i	0.194500	−	0.380812i
$47$		−	7.51739i		−	1.09652i	−0.836307	−	0.548262i	$-0.815290\pi$
$47$		−	7.51739i		−	1.09652i	0.836307	−	0.548262i	$-0.184710\pi$
$48$	1.51328	+	6.76091i	0.218424	+	0.975854i
$49$	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	$-0.638746\pi$
$53$	−6.14747			−0.844420			−0.422210	+	0.906498i	$0.638746\pi$
$54$	−3.05183	+	6.68479i	−0.415301	+	0.909684i
$55$	−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	$-0.514860\pi$
$59$	−0.716916			−0.0933345			−0.0466672	+	0.998910i	$0.514860\pi$
$60$	5.31547	+	5.63434i	0.686224	+	0.727390i
$61$	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
$66$	6.74570	−	0.446094i	0.830338	−	0.0549103i
$67$	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	$-0.585986\pi$
$71$	−4.49721			−0.533721			−0.266860	+	0.963735i	$0.585986\pi$
$72$	−7.99914	−	2.83087i	−0.942707	−	0.333621i
$73$		−	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
$75$	8.32675	+	2.38019i	0.961490	+	0.274841i
$76$	−3.09093	+	2.23653i	−0.354554	+	0.256548i
$77$	−2.75993			−0.314524
$78$	0.308331	+	4.66249i	0.0349116	+	0.527923i
$79$			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	$0.139180\pi$
$83$			7.71558i			0.846895i	−0.905921	+	0.423448i	$0.860820\pi$
$84$	3.18226	+	1.36867i	0.347213	+	0.149334i
$85$	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	$-0.744560\pi$
$89$		−	13.5677i		−	1.43817i	0.694920	−	0.719087i	$-0.255440\pi$
$90$	−9.30530	+	1.84702i	−0.980864	+	0.194693i
$91$		−	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
$96$	2.44314	−	9.48847i	0.249352	−	0.968413i
$97$			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	$0.125407\pi$
$101$			7.71558i			0.767729i	−0.923389	+	0.383865i	$0.874593\pi$
$102$	−12.3131	+	0.814269i	−1.21918	+	0.0806247i
$103$	−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
$105$	3.84035	−	0.501726i	0.374780	−	0.0489634i
$106$	7.74243	+	3.95444i	0.752011	+	0.384089i
$107$			1.27396i			0.123158i	0.998102	+	0.0615791i	$0.0196136\pi$
$107$			1.27396i			0.123158i	−0.998102	+	0.0615791i	$0.980386\pi$
$108$	8.14370	−	6.45602i	0.783628	−	0.621231i
$109$	−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	$-0.636440\pi$
$113$	−8.83651			−0.831269			−0.415634	+	0.909532i	$0.636440\pi$
$114$	−0.308331	−	4.66249i	−0.0288779	−	0.436682i
$115$	−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
$120$	−3.07020	−	10.5154i	−0.280270	−	0.959921i
$121$	−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
$126$	−3.49132	+	2.41053i	−0.311032	+	0.214747i
$127$	−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	$-0.459057\pi$
$131$	2.93626			0.256543			0.128271	+	0.991739i	$0.459057\pi$
$132$	−8.78282	−	3.77743i	−0.764446	−	0.328783i
$133$			1.90761i			0.165411i
$134$	−4.51841	−	2.30778i	−0.390331	−	0.199361i
$135$	4.14083	−	10.8560i	0.356386	−	0.934339i
$136$	−2.18801	−	14.0800i	−0.187621	−	1.20735i
$137$	16.4887			1.40873			0.704363	−	0.709840i	$-0.251233\pi$
$137$	16.4887			1.40873			0.704363	+	0.709840i	$0.251233\pi$
$138$	−0.331464	−	5.01230i	−0.0282161	−	0.426675i
$139$			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
$144$	8.25351	+	8.71089i	0.687792	+	0.725907i
$145$	−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	$-0.811262\pi$
$149$		−	13.6420i		−	1.11760i	0.829303	−	0.558800i	$-0.188738\pi$
$150$	−8.95602	−	8.35402i	−0.731256	−	0.682103i
$151$		−	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
$156$	2.61088	−	6.07051i	0.209038	−	0.486030i
$157$			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
$162$	1.39688	+	12.6510i	0.109749	+	0.993959i
$163$	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
$165$	−10.5991	+	1.38473i	−0.825139	+	0.107801i
$166$	4.96315	−	9.71739i	0.385215	−	0.754215i
$167$			3.53470i			0.273523i	0.990604	+	0.136762i	$0.0436694\pi$
$167$			3.53470i			0.273523i	−0.990604	+	0.136762i	$0.956331\pi$
$168$	−3.12748	−	3.77079i	−0.241290	−	0.290923i
$169$	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	$-0.721591\pi$
$173$	−16.8691			−1.28253			−0.641266	+	0.767318i	$0.721591\pi$
$174$	−0.799163	−	12.0847i	−0.0605844	−	0.916139i
$175$	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	$-0.550095\pi$
$179$	−4.19377			−0.313457			−0.156728	+	0.987642i	$0.550095\pi$
$180$	12.9077	+	3.65953i	0.962081	+	0.272765i
$181$	−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
$186$	1.11908	+	16.9223i	0.0820547	+	1.24081i
$187$	−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	$-0.408965\pi$
$191$	7.79773			0.564224			0.282112	+	0.959381i	$0.408965\pi$
$192$	−9.18060	+	10.3787i	−0.662553	+	0.749015i
$193$			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
$195$	−0.957098	−	7.32589i	−0.0685392	−	0.524618i
$196$	1.17242	+	1.62032i	0.0837446	+	0.115737i
$197$	−14.9679			−1.06642			−0.533208	−	0.845984i	$-0.679014\pi$
$197$	−14.9679			−1.06642			−0.533208	+	0.845984i	$0.679014\pi$
$198$	9.63582	−	6.65292i	0.684788	−	0.472802i
$199$		−	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
$204$	16.0316	+	6.89506i	1.12243	+	0.482751i
$205$	−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
$210$	−5.15946	−	1.83846i	−0.356037	−	0.126866i
$211$			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
$216$	−14.4095	+	2.89249i	−0.980442	+	0.196809i
$217$		−	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
$222$	1.04758	+	15.8412i	0.0703089	+	1.06319i
$223$	−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
$225$	14.4965	−	3.85360i	0.966436	−	0.256907i
$226$	11.1291	+	5.68420i	0.740299	+	0.378108i
$227$		−	3.16030i		−	0.209756i	−0.994485	−	0.104878i	$-0.966555\pi$
$227$		−	3.16030i		−	0.209756i	0.994485	−	0.104878i	$-0.0334453\pi$
$228$	−2.61088	+	6.07051i	−0.172910	+	0.402029i
$229$	−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	$-0.304800\pi$
$233$	17.5699			1.15104			0.575520	+	0.817787i	$0.304800\pi$
$234$	4.59836	+	6.66008i	0.300604	+	0.435383i
$235$	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	$-0.308151\pi$
$239$	17.5275			1.13376			0.566879	+	0.823801i	$0.308151\pi$
$240$	−2.89741	+	15.2186i	−0.187027	+	0.982355i
$241$	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
$246$	−1.80697	−	27.3245i	−0.115208	−	1.74214i
$247$	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	$-0.751005\pi$
$251$	−22.4760			−1.41867			−0.709335	+	0.704871i	$0.751005\pi$
$252$	5.94775	−	0.790106i	0.374673	−	0.0497720i
$253$		−	5.65989i		−	0.355834i
$254$	2.71642	+	1.38741i	0.170444	+	0.0870541i
$255$	19.3469	−	2.52759i	1.21155	−	0.158284i
$256$	−12.8708	−	9.50488i	−0.804424	−	0.594055i
$257$	7.25715			0.452688			0.226344	−	0.974047i	$-0.427323\pi$
$257$	7.25715			0.452688			0.226344	+	0.974047i	$0.427323\pi$
$258$	22.8880	−	1.51358i	1.42494	−	0.0942317i
$259$		−	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	$-0.831341\pi$
$263$		−	16.3928i		−	1.01082i	0.862878	−	0.505412i	$-0.168659\pi$
$264$	8.63163	+	10.4071i	0.531240	+	0.640515i
$265$	−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	$-0.955864\pi$
$269$		−	4.53372i		−	0.276426i	0.990403	−	0.138213i	$-0.0441359\pi$
$270$	−12.1985	+	11.0090i	−0.742375	+	0.669985i
$271$			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
$276$	−2.80677	+	6.52595i	−0.168948	+	0.392816i
$277$		−	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	$-0.897967\pi$
$281$		−	10.5636i		−	0.630170i	0.949064	−	0.315085i	$-0.102033\pi$
$282$	1.21505	+	18.3736i	0.0723552	+	1.09413i
$283$	−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
$285$	0.957098	+	7.32589i	0.0566936	+	0.433948i
$286$	3.38671	−	6.63085i	0.200260	−	0.392090i
$287$			11.1795i			0.659907i
$288$	−4.79148	−	16.2801i	−0.282340	−	0.959314i
$289$	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	$-0.763607\pi$
$293$	−25.2198			−1.47336			−0.736678	+	0.676244i	$0.763607\pi$
$294$	−2.44415	+	0.161632i	−0.142546	+	0.00942657i
$295$	−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
$300$	5.90582	+	16.2825i	0.340973	+	0.940073i
$301$	−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
$306$	−17.5886	+	12.1438i	−1.00547	+	0.694214i
$307$	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	$-0.436830\pi$
$311$	6.95370			0.394308			0.197154	+	0.980373i	$0.436830\pi$
$312$	−7.19321	+	5.96601i	−0.407235	+	0.337759i
$313$			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
$315$	5.26571	−	4.15599i	0.296689	−	0.234164i
$316$	−23.7451	+	17.1815i	−1.33577	+	0.966533i
$317$	−8.19278			−0.460153			−0.230076	−	0.973173i	$-0.573898\pi$
$317$	−8.19278			−0.460153			−0.230076	+	0.973173i	$0.573898\pi$
$318$	15.0253	−	0.993628i	0.842580	−	0.0557199i
$319$		−	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
$324$	6.37865	−	16.8319i	0.354369	−	0.935106i
$325$	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
$330$	14.2398	+	5.07402i	0.783874	+	0.279316i
$331$		−	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
$336$	1.51328	+	6.76091i	0.0825565	+	0.368838i
$337$		−	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
$342$	−4.59836	−	6.66008i	−0.248651	−	0.360136i
$343$	1.00000			0.0539949
$344$	4.06714	+	26.1724i	0.219285	+	1.41112i
$345$	1.02891	+	7.87552i	0.0553944	+	0.424004i
$346$	21.2458	+	10.8513i	1.14218	+	0.583368i
$347$			2.86847i			0.153987i	0.997032	+	0.0769936i	$0.0245321\pi$
$347$			2.86847i			0.153987i	−0.997032	+	0.0769936i	$0.975468\pi$
$348$	−6.76714	+	15.7341i	−0.362757	+	0.843438i
$349$	−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	$-0.716964\pi$
$353$	−23.6750			−1.26009			−0.630045	+	0.776558i	$0.716964\pi$
$354$	1.75225	−	0.115877i	0.0931311	−	0.00615877i
$355$	−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	$-0.363645\pi$
$359$	15.7410			0.830778			0.415389	+	0.909644i	$0.363645\pi$
$360$	−13.9025	−	12.9120i	−0.732726	−	0.680523i
$361$	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
$366$	−12.5413	+	0.829358i	−0.655544	+	0.0433512i
$367$	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
$372$	9.47610	−	22.0327i	0.491313	−	1.14234i
$373$		−	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
$375$	14.9750	+	12.2780i	0.773306	+	0.634034i
$376$	−21.0102	+	3.26495i	−1.08352	+	0.168377i
$377$	9.43187			0.485766
$378$	−3.05183	+	6.68479i	−0.156969	+	0.343828i
$379$		−	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	$-0.824827\pi$
$383$		−	20.4691i		−	1.04592i	0.852356	−	0.522962i	$-0.175173\pi$
$384$	18.2387	−	7.16585i	0.930740	−	0.365681i
$385$	−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	$0.102690\pi$
$389$			12.5062i			0.634088i	−0.948411	+	0.317044i	$0.897310\pi$
$390$	−3.50706	+	9.84225i	−0.177587	+	0.498382i
$391$			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
$396$	−16.4154	+	2.18064i	−0.824905	+	0.109581i
$397$		−	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	$-0.908619\pi$
$401$		−	11.3403i		−	0.566310i	0.959074	−	0.283155i	$-0.0913810\pi$
$402$	−8.76865	+	0.579872i	−0.437341	+	0.0289214i
$403$	−13.2076			−0.657915
$404$	−12.5017	+	9.04594i	−0.621982	+	0.450052i
$405$	−3.48101	−	19.8213i	−0.172973	−	0.984927i
$406$	3.18051	−	6.22714i	0.157846	−	0.309048i
$407$			17.8879i			0.886668i
$408$	−15.7556	−	18.9965i	−0.780018	−	0.940467i
$409$	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
$414$	−4.94336	−	7.15976i	−0.242953	−	0.351883i
$415$	−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	$-0.0943790\pi$
$419$	39.1526			1.91273			0.956365	+	0.292175i	$0.0943790\pi$
$420$	5.31547	+	5.63434i	0.259368	+	0.274928i
$421$	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
$426$	10.9919	−	0.726893i	0.532558	−	0.0352181i
$427$	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	$-0.134809\pi$
$431$	37.8527			1.82330			0.911650	+	0.410967i	$0.134809\pi$
$432$	20.0087	+	5.62616i	0.962667	+	0.270689i
$433$		−	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
$435$	2.48070	+	18.9880i	0.118941	+	0.910403i
$436$	−17.1623	−	23.7187i	−0.821926	−	1.13592i
$437$	−3.91200			−0.187136
$438$	0.988570	+	14.9489i	0.0472357	+	0.714284i
$439$		−	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	$0.250106\pi$
$443$			29.7757i			1.41468i	−0.706872	+	0.707342i	$0.749894\pi$
$444$	8.87068	−	20.6250i	0.420984	−	0.978821i
$445$	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	$0.189135\pi$
$449$			23.7253i			1.11967i	−0.828605	+	0.559834i	$0.810865\pi$
$450$	−20.7365	−	4.47168i	−0.977530	−	0.210797i
$451$		−	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
$456$	7.19321	−	5.96601i	0.336853	−	0.279384i
$457$		−	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	$-0.907614\pi$
$461$		−	12.2891i		−	0.572360i	0.958176	−	0.286180i	$-0.0923856\pi$
$462$	6.74570	−	0.446094i	0.313838	−	0.0207542i
$463$	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
$465$	−3.47375	−	26.5891i	−0.161091	−	1.23304i
$466$	−22.1284	−	11.3021i	−1.02508	−	0.523558i
$467$		−	29.0874i		−	1.34601i	−0.739640	−	0.673003i	$-0.765004\pi$
$467$		−	29.0874i		−	1.34601i	0.739640	−	0.673003i	$-0.234996\pi$
$468$	−1.50722	−	11.3460i	−0.0696711	−	0.524469i
$469$	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
$474$	−2.36866	−	35.8182i	−0.108796	−	1.64518i
$475$	−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	$-0.312889\pi$
$479$	24.2741			1.10911			0.554555	+	0.832147i	$0.312889\pi$
$480$	13.4387	−	17.3032i	0.613390	−	0.789780i
$481$	−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
$486$	13.3102	+	17.5738i	0.603765	+	0.797163i
$487$	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	$-0.703330\pi$
$491$	−26.4225			−1.19243			−0.596216	+	0.802824i	$0.703330\pi$
$492$	−15.3010	+	35.5761i	−0.689824	+	1.60390i
$493$			24.9085i			1.12182i
$494$	−4.58311	−	2.34082i	−0.206204	−	0.105319i
$495$	−14.5330	+	11.4703i	−0.653211	+	0.515550i
$496$	26.3055	+	8.66034i	1.18115	+	0.388861i
$497$	−4.49721			−0.201728
$498$	−1.24709	−	18.8581i	−0.0558832	−	0.845050i
$499$		−	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	$-0.942637\pi$
$503$		−	8.03971i		−	0.358473i	0.983806	−	0.179236i	$-0.0573627\pi$
$504$	−7.99914	−	2.83087i	−0.356310	−	0.126097i
$505$	−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	$-0.960838\pi$
$509$		−	5.53741i		−	0.245441i	0.992441	−	0.122721i	$-0.0391619\pi$
$510$	−25.9923	−	9.26177i	−1.15096	−	0.410118i
$511$		−	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
$516$	−29.7999	−	12.8167i	−1.31187	−	0.564224i
$517$			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	$0.0899775\pi$
$521$			12.7331i			0.557846i	−0.960313	+	0.278923i	$0.910023\pi$
$522$	−11.9185	−	17.2623i	−0.521658	−	0.755549i
$523$	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
$525$	8.32675	+	2.38019i	0.363409	+	0.103880i
$526$	−10.5449	+	20.6459i	−0.459779	+	0.900205i
$527$		−	34.8797i		−	1.51938i
$528$	−4.17657	−	18.6597i	−0.181762	−	0.812058i
$529$	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
$534$	2.19298	+	33.1615i	0.0948994	+	1.43504i
$535$	−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
$540$	22.4450	−	6.01842i	0.965880	−	0.258992i
$541$	−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
$546$	0.308331	+	4.66249i	0.0131954	+	0.199536i
$547$	−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
$552$	7.73289	−	6.41362i	0.329134	−	0.272982i
$553$			14.6546i			0.623179i
$554$	−15.6602	+	30.6611i	−0.665337	+	1.30267i
$555$	−3.25182	−	24.8903i	−0.138032	−	1.05653i
$556$	−17.5865	+	12.7252i	−0.745832	+	0.539668i
$557$	9.27395			0.392950			0.196475	−	0.980509i	$-0.437051\pi$
$557$	9.27395			0.392950			0.196475	+	0.980509i	$0.437051\pi$
$558$	16.6896	+	24.1725i	0.706527	+	1.02330i
$559$			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	$0.0923194\pi$
$563$			13.5713i			0.571962i	−0.958235	+	0.285981i	$0.907681\pi$
$564$	10.2888	−	23.9223i	0.433236	−	1.00731i
$565$	−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	$0.112316\pi$
$569$			16.4865i			0.691148i	−0.938392	+	0.345574i	$0.887684\pi$
$570$	3.50706	−	9.84225i	0.146895	−	0.412247i
$571$		−	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
$576$	−4.43777	+	23.5861i	−0.184907	+	0.982756i
$577$		−	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
$582$	−2.69556	−	40.7615i	−0.111735	−	1.68962i
$583$	16.9666			0.702685
$584$	−17.0940	+	2.65638i	−0.707355	+	0.109922i
$585$	−7.92802	−	10.0449i	−0.327783	−	0.415307i
$586$	31.7630	+	16.2230i	1.31212	+	0.670164i
$587$			2.10458i			0.0868654i	0.999056	+	0.0434327i	$0.0138294\pi$
$587$			2.10458i			0.0868654i	−0.999056	+	0.0434327i	$0.986171\pi$
$588$	3.18226	+	1.36867i	0.131234	+	0.0564428i
$589$	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	$-0.476950\pi$
$593$	3.52377			0.144704			0.0723520	+	0.997379i	$0.476950\pi$
$594$	8.42284	−	18.4496i	0.345593	−	0.756995i
$595$	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	$-0.413467\pi$
$599$	13.1436			0.537031			0.268516	+	0.963275i	$0.413467\pi$
$600$	3.03588	−	24.3060i	0.123939	−	0.992290i
$601$	−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
$606$	−1.24709	−	18.8581i	−0.0506594	−	0.766056i
$607$	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
$612$	29.9636	−	3.98039i	1.21120	−	0.160898i
$613$		−	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
$615$	5.60906	+	42.9333i	0.226179	+	1.73124i
$616$	1.19869	+	7.71369i	0.0482967	+	0.310793i
$617$	4.53960			0.182758			0.0913788	−	0.995816i	$-0.470873\pi$
$617$	4.53960			0.182758			0.0913788	+	0.995816i	$0.470873\pi$
$618$	49.3985	−	3.26673i	1.98710	−	0.131407i
$619$			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
$624$	12.8972	−	2.88676i	0.516301	−	0.115563i
$625$	−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
$630$	−9.30530	+	1.84702i	−0.370732	+	0.0735869i
$631$		−	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
$636$	−19.5628	−	8.41383i	−0.775717	−	0.333630i
$637$		−	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	$-0.809303\pi$
$641$		−	28.5533i		−	1.12779i	0.825847	−	0.563894i	$-0.190697\pi$
$642$	−0.205912	−	3.11375i	−0.00812672	−	0.122890i
$643$	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
$645$	−35.9625	+	4.69836i	−1.41602	+	0.184998i
$646$	6.18186	−	12.1035i	0.243222	−	0.476206i
$647$		−	5.44152i		−	0.213928i	−0.994263	−	0.106964i	$-0.965887\pi$
$647$		−	5.44152i		−	0.213928i	0.994263	−	0.106964i	$-0.0341130\pi$
$648$	−18.8609	+	17.0958i	−0.740927	+	0.671585i
$649$	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	$-0.246330\pi$
$653$	36.5529			1.43042			0.715212	+	0.698907i	$0.246330\pi$
$654$	35.7783	−	2.36602i	1.39904	−	0.0925188i
$655$	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	$-0.556731\pi$
$659$	−9.10215			−0.354570			−0.177285	+	0.984160i	$0.556731\pi$
$660$	−14.6704	−	15.5504i	−0.571043	−	0.605299i
$661$	−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
$666$	15.6233	+	22.6282i	0.605391	+	0.876824i
$667$	−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
$672$	2.44314	−	9.48847i	0.0942463	−	0.366026i
$673$			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
$675$	18.1370	−	18.6024i	0.698094	−	0.716006i
$676$	10.9751	+	15.1678i	0.422119	+	0.583377i
$677$	−11.8437			−0.455189			−0.227595	−	0.973756i	$-0.573086\pi$
$677$	−11.8437			−0.455189			−0.227595	+	0.973756i	$0.573086\pi$
$678$	21.5978	−	1.42826i	0.829457	−	0.0548521i
$679$			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	$-0.975254\pi$
$683$		−	4.05943i		−	0.155330i	0.996980	−	0.0776648i	$-0.0247464\pi$
$684$	1.50722	+	11.3460i	0.0576298	+	0.433825i
$685$	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
$690$	3.77018	−	10.5807i	0.143528	−	0.402800i
$691$			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
$696$	18.6441	−	15.4633i	0.706701	−	0.586135i
$697$			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	$0.222218\pi$
$701$			34.0369i			1.28555i	−0.766053	+	0.642777i	$0.777782\pi$
$702$	12.7520	+	5.82170i	0.481292	+	0.219726i
$703$	12.3637			0.466307
$704$	21.0382	−	6.70041i	0.792909	−	0.252531i
$705$	−3.77167	−	28.8694i	−0.142049	−	1.08728i
$706$	29.8174	+	15.2292i	1.12219	+	0.573160i
$707$			7.71558i			0.290174i
$708$	−2.28141	−	0.981218i	−0.0857406	−	0.0368764i
$709$	−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
$714$	−12.3131	+	0.814269i	−0.460808	+	0.0304733i
$715$	−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	$-0.564943\pi$
$719$	−10.8657			−0.405222			−0.202611	+	0.979259i	$0.564943\pi$
$720$	9.20367	+	25.2050i	0.343000	+	0.939335i
$721$	−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
$726$	8.26799	−	0.546763i	0.306854	−	0.0202923i
$727$	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
$732$	16.3286	+	7.02283i	0.603523	+	0.259571i
$733$			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
$735$	3.84035	−	0.501726i	0.141653	−	0.0185064i
$736$	8.16299	+	8.24268i	0.300892	+	0.303829i
$737$	−9.90156			−0.364729
$738$	−26.9486	−	39.0313i	−0.991993	−	1.43676i
$739$			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	$-0.967767\pi$
$743$		−	5.51110i		−	0.202183i	0.994877	−	0.101091i	$-0.0322334\pi$
$744$	−26.1075	+	21.6534i	−0.957147	+	0.793853i
$745$	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
$750$	−10.9623	−	25.0964i	−0.400285	−	0.916391i
$751$			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
$756$	8.14370	−	6.45602i	0.296183	−	0.234803i
$757$		−	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	$-0.707028\pi$
$761$		−	43.9086i		−	1.59169i	0.605503	−	0.795843i	$-0.292972\pi$
$762$	5.27163	−	0.348614i	0.190971	−	0.0126289i
$763$	−14.6383			−0.529943
$764$	9.14225	+	12.6348i	0.330755	+	0.457110i
$765$	26.5276	−	20.9370i	0.959107	−	0.756980i
$766$	−13.1670	+	25.7798i	−0.475745	+	0.931464i
$767$			1.36760i			0.0493811i
$768$	−27.5803	−	2.70727i	−0.995217	−	0.0976903i
$769$	−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	$-0.400842\pi$
$773$	17.0431			0.612998			0.306499	+	0.951871i	$0.400842\pi$
$774$	32.6941	−	22.5732i	1.17516	−	0.811376i
$775$	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
$780$	10.7481	−	10.1399i	0.384845	−	0.363065i
$781$	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
$786$	−7.17668	+	0.474594i	−0.255984	+	0.0169282i
$787$	−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
$792$	22.0771	+	7.81302i	0.784475	+	0.277624i
$793$		−	9.78824i		−	0.347590i
$794$	−4.72007	+	9.24145i	−0.167509	+	0.327967i
$795$	−23.6084	+	3.08435i	−0.837305	+	0.109390i
$796$	17.4003	−	12.5905i	0.616737	−	0.446257i
$797$	−8.66018			−0.306759			−0.153380	−	0.988167i	$-0.549016\pi$
$797$	−8.66018			−0.306759			−0.153380	+	0.988167i	$0.549016\pi$
$798$	−0.308331	−	4.66249i	−0.0109148	−	0.165050i
$799$		−	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
$804$	11.4167	+	4.91023i	0.402635	+	0.173171i
$805$	−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	$-0.828784\pi$
$809$		−	29.1441i		−	1.02465i	0.858791	−	0.512326i	$-0.171216\pi$
$810$	−8.36614	+	27.2031i	−0.293956	+	0.955819i
$811$		−	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
$816$	7.62362	+	34.0601i	0.266880	+	1.19234i
$817$		−	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	$0.127120\pi$
$821$			22.2823i			0.777658i	−0.921310	+	0.388829i	$0.872880\pi$
$822$	−40.3009	+	2.66510i	−1.40566	+	0.0929561i
$823$	−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
$825$	−22.9813	−	6.56917i	−0.800105	−	0.228709i
$826$	0.902919	+	0.461166i	0.0314166	+	0.0160460i
$827$			32.6595i			1.13568i	0.823138	+	0.567841i	$0.192221\pi$
$827$			32.6595i			1.13568i	−0.823138	+	0.567841i	$0.807779\pi$
$828$	1.62030	+	12.1972i	0.0563092	+	0.423883i
$829$	−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
$834$	−1.75431	−	26.5282i	−0.0607468	−	0.918595i
$835$	−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	$-0.459303\pi$
$839$	7.38656			0.255012			0.127506	+	0.991838i	$0.459303\pi$
$840$	−3.07020	−	10.5154i	−0.105932	−	0.362816i
$841$	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
$846$	18.1209	+	26.2456i	0.623010	+	0.902343i
$847$	−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
$852$	−14.3113	−	6.15518i	−0.490296	−	0.210873i
$853$		−	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
$855$	7.92802	+	10.0449i	0.271132	+	0.343530i
$856$	3.56056	−	0.553305i	0.121698	−	0.0189116i
$857$	4.56811			0.156044			0.0780218	−	0.996952i	$-0.475140\pi$
$857$	4.56811			0.156044			0.0780218	+	0.996952i	$0.475140\pi$
$858$	−0.850973	−	12.8682i	−0.0290518	−	0.439312i
$859$			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	$-0.852585\pi$
$863$		−	26.2477i		−	0.893481i	0.894664	−	0.446741i	$-0.147415\pi$
$864$	−21.5808	−	19.9567i	−0.734193	−	0.678941i
$865$	−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
$870$	9.08994	−	25.5101i	0.308178	−	0.864874i
$871$		−	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
$876$	8.37100	−	19.4632i	0.282830	−	0.657602i
$877$			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	$0.117921\pi$
$881$			21.4921i			0.724088i	−0.932161	+	0.362044i	$0.882079\pi$
$882$	−3.49132	+	2.41053i	−0.117559	+	0.0811669i
$883$	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
$885$	−2.75321	+	0.359695i	−0.0925480	+	0.0120910i
$886$	19.1536	−	37.5009i	0.643477	−	1.25987i
$887$			58.2531i			1.95595i	0.208727	+	0.977974i	$0.433068\pi$
$887$			58.2531i			1.95595i	−0.208727	+	0.977974i	$0.566932\pi$
$888$	−24.4395	+	20.2700i	−0.820136	+	0.680216i
$889$	−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
$894$	2.20499	+	33.3432i	0.0737459	+	1.11516i
$895$	−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
$900$	23.2402	+	18.9709i	0.774672	+	0.632364i
$901$	−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
$906$	0.218262	+	3.30049i	0.00725126	+	0.109651i
$907$	−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	$-0.489811\pi$
$911$	1.93202			0.0640108			0.0320054	+	0.999488i	$0.489811\pi$
$912$	−12.8972	+	2.88676i	−0.427069	+	0.0955902i
$913$		−	21.2945i		−	0.704745i
$914$	−3.64977	+	7.14590i	−0.120724	+	0.236365i
$915$	19.7054	−	2.57443i	0.651440	−	0.0851080i
$916$	−4.03089	−	5.57078i	−0.133184	−	0.184064i
$917$	2.93626			0.0969640
$918$	−15.3745	+	33.6766i	−0.507433	+	1.11149i
$919$		−	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
$924$	−8.78282	−	3.77743i	−0.288933	−	0.124268i
$925$	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	$0.186712\pi$
$929$			33.7414i			1.10702i	−0.832842	+	0.553510i	$0.813288\pi$
$930$	−12.7288	+	35.7221i	−0.417392	+	1.17137i
$931$			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
$936$	−5.40020	+	15.2592i	−0.176511	+	0.498764i
$937$		−	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	$-0.943785\pi$
$941$		−	10.7787i		−	0.351375i	0.984446	−	0.175687i	$-0.0562148\pi$
$942$	−0.308331	−	4.66249i	−0.0100460	−	0.151912i
$943$	−22.9262			−0.746580
$944$	0.896748	−	2.72384i	0.0291867	−	0.0886536i
$945$	4.14083	−	10.8560i	0.134701	−	0.353147i
$946$	−32.5506	−	16.6252i	−1.05831	−	0.540532i
$947$			34.5592i			1.12302i	0.827469	+	0.561511i	$0.189780\pi$
$947$			34.5592i			1.12302i	−0.827469	+	0.561511i	$0.810220\pi$
$948$	−20.0573	+	46.6348i	−0.651431	+	1.51463i
$949$	−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	$-0.678925\pi$
$953$	−32.9065			−1.06595			−0.532973	+	0.846132i	$0.678925\pi$
$954$	21.4628	−	14.8187i	0.694884	−	0.479773i
$955$	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
$960$	−28.0559	+	13.1479i	−0.905500	+	0.424347i
$961$	−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
$966$	−0.331464	−	5.01230i	−0.0106647	−	0.161268i
$967$	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	$-0.137284\pi$
$971$	56.6148			1.81685			0.908427	+	0.418044i	$0.137284\pi$
$972$	−5.45900	−	30.6953i	−0.175097	−	0.984551i
$973$			10.8537i			0.347955i
$974$	−48.0634	−	24.5484i	−1.54005	−	0.786581i
$975$	4.54048	−	15.8842i	0.145412	−	0.508701i
$976$	−6.41826	+	19.4953i	−0.205443	+	0.624028i
$977$	−59.0104			−1.88791			−0.943955	−	0.330073i	$-0.892927\pi$
$977$	−59.0104			−1.88791			−0.943955	+	0.330073i	$0.892927\pi$
$978$	−59.7274	+	3.94978i	−1.90987	+	0.126300i
$979$			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	$-0.795229\pi$
$983$		−	37.6136i		−	1.19969i	0.800117	−	0.599844i	$-0.204771\pi$
$984$	42.1557	−	34.9637i	1.34387	−	1.11460i
$985$	−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
$990$	25.6820	−	5.09765i	0.816228	−	0.162014i
$991$			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
$996$	−10.5601	+	24.5530i	−0.334608	+	0.777990i
$997$			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.239.3	yes	16
3.2	odd	2	inner	420.2.l.h.239.14	yes	16
4.3	odd	2		420.2.l.g.239.4	yes	16
5.4	even	2		420.2.l.g.239.14	yes	16
12.11	even	2		420.2.l.g.239.13	yes	16
15.14	odd	2		420.2.l.g.239.3	✓	16
20.19	odd	2	inner	420.2.l.h.239.13	yes	16
60.59	even	2	inner	420.2.l.h.239.4	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.25945 - 0.643263i) q^{2} +(1.48716 - 0.887900i) q^{3} +(1.17242 + 1.62032i) q^{4} +(2.05223 + 0.887900i) q^{5} +(-2.44415 + 0.161632i) q^{6} +1.00000 q^{7} +(-0.434319 - 2.79488i) q^{8} +(1.42327 - 2.64089i) q^{9} +O(q^{10})\)	\(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} +(-2.44415 + 0.161632i) 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} +(3.18226 + 1.36867i) q^{12} -1.90761i q^{13} +(-1.25945 - 0.643263i) q^{14} +(3.84035 - 0.501726i) q^{15} +(-1.25084 + 3.79939i) q^{16} +5.03780 q^{17} +(-3.49132 + 2.41053i) 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} +(-3.12748 - 3.77079i) 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} +(-5.15946 - 1.83846i) 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} +(5.94775 - 0.790106i) 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} +(-2.44415 + 0.161632i) q^{42} -9.36439 q^{43} +(-3.23581 - 4.47196i) q^{44} +(5.26571 - 4.15599i) q^{45} +(1.31916 - 2.58279i) q^{46} -7.51739i q^{47} +(1.51328 + 6.76091i) 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} +(-3.05183 + 6.68479i) 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} +(5.31547 + 5.63434i) 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} +(6.74570 - 0.446094i) 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} +(-7.99914 - 2.83087i) q^{72} -6.11618i q^{73} +(-4.16916 + 8.16282i) q^{74} +(8.32675 + 2.38019i) q^{75} +(-3.09093 + 2.23653i) q^{76} -2.75993 q^{77} +(0.308331 + 4.66249i) 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} +(3.18226 + 1.36867i) 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} +(-9.30530 + 1.84702i) 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} +(2.44314 - 9.48847i) 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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