LMFDB - Embedded newform 210.2.j.a.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(113,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("210.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.j (of order $4$, degree $2$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-0.678294i$ of defining polynomial
Character	$\chi$	$=$	210.197
Dual form			210.2.j.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.67762 + 0.430811i) q^{3} -1.00000i q^{4} +(-2.22680 - 0.203331i) q^{5} +(0.881625 - 1.49088i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.62880 - 1.44547i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.67762 + 0.430811i) q^{3} -1.00000i q^{4} +(-2.22680 - 0.203331i) q^{5} +(0.881625 - 1.49088i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.62880 - 1.44547i) q^{9} +(1.71837 - 1.43081i) q^{10} -5.11849i q^{11} +(0.430811 + 1.67762i) q^{12} +(2.66102 - 2.66102i) q^{13} -1.00000 q^{14} +(3.82332 - 0.618221i) q^{15} -1.00000 q^{16} +(-0.660063 + 0.660063i) q^{17} +(-0.836740 + 2.88095i) q^{18} -4.57375i q^{19} +(-0.203331 + 2.22680i) q^{20} +(-1.49088 - 0.881625i) q^{21} +(3.61932 + 3.61932i) q^{22} +(-0.915044 - 0.915044i) q^{23} +(-1.49088 - 0.881625i) q^{24} +(4.91731 + 0.905557i) q^{25} +3.76325i q^{26} +(-3.78740 + 3.55747i) q^{27} +(0.707107 - 0.707107i) q^{28} +8.71047 q^{29} +(-2.26635 + 3.14065i) q^{30} -9.86542 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.20510 + 8.58686i) q^{33} -0.933471i q^{34} +(-1.43081 - 1.71837i) q^{35} +(-1.44547 - 2.62880i) q^{36} +(-8.30181 - 8.30181i) q^{37} +(3.23413 + 3.23413i) q^{38} +(-3.31778 + 5.61057i) q^{39} +(-1.43081 - 1.71837i) q^{40} -2.55167i q^{41} +(1.67762 - 0.430811i) q^{42} +(1.01688 - 1.01688i) q^{43} -5.11849 q^{44} +(-6.14774 + 2.68427i) q^{45} +1.29407 q^{46} +(-2.54338 + 2.54338i) q^{47} +(1.67762 - 0.430811i) q^{48} +1.00000i q^{49} +(-4.11739 + 2.83674i) q^{50} +(0.822971 - 1.39170i) q^{51} +(-2.66102 - 2.66102i) q^{52} +(0.551238 + 0.551238i) q^{53} +(0.162584 - 5.19361i) q^{54} +(-1.04075 + 11.3979i) q^{55} +1.00000i q^{56} +(1.97043 + 7.67301i) q^{57} +(-6.15923 + 6.15923i) q^{58} -1.36204 q^{59} +(-0.618221 - 3.82332i) q^{60} +8.09345 q^{61} +(6.97590 - 6.97590i) q^{62} +(2.88095 + 0.836740i) q^{63} +1.00000i q^{64} +(-6.46664 + 5.38450i) q^{65} +(-7.63107 - 4.51259i) q^{66} +(-1.67348 - 1.67348i) q^{67} +(0.660063 + 0.660063i) q^{68} +(1.92931 + 1.14088i) q^{69} +(2.22680 + 0.203331i) q^{70} -3.62916i q^{71} +(2.88095 + 0.836740i) q^{72} +(5.95286 - 5.95286i) q^{73} +11.7405 q^{74} +(-8.63950 + 0.599256i) q^{75} -4.57375 q^{76} +(3.61932 - 3.61932i) q^{77} +(-1.62125 - 6.31330i) q^{78} +7.87966i q^{79} +(2.22680 + 0.203331i) q^{80} +(4.82121 - 7.59973i) q^{81} +(1.80431 + 1.80431i) q^{82} +(-3.65347 - 3.65347i) q^{83} +(-0.881625 + 1.49088i) q^{84} +(1.60404 - 1.33562i) q^{85} +1.43808i q^{86} +(-14.6128 + 3.75257i) q^{87} +(3.61932 - 3.61932i) q^{88} +5.65138 q^{89} +(2.44904 - 6.24517i) q^{90} +3.76325 q^{91} +(-0.915044 + 0.915044i) q^{92} +(16.5504 - 4.25014i) q^{93} -3.59688i q^{94} +(-0.929986 + 10.1849i) q^{95} +(-0.881625 + 1.49088i) q^{96} +(3.76976 + 3.76976i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-7.39864 - 13.4555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^3 - 4 * q^5	$ 12 q + 4 q^{3} - 4 q^{5} - 4 q^{12} - 12 q^{14} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{33} - 8 q^{35} + 4 q^{36} - 20 q^{37} - 4 q^{38} - 40 q^{39} - 8 q^{40} - 4 q^{42} + 8 q^{43} + 8 q^{44} + 8 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 16 q^{50} + 8 q^{51} - 24 q^{53} - 4 q^{54} - 16 q^{55} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 q^{93} + 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 4 * q^5 - 4 * q^12 - 12 * q^14 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * q^33 - 8 * q^35 + 4 * q^36 - 20 * q^37 - 4 * q^38 - 40 * q^39 - 8 * q^40 - 4 * q^42 + 8 * q^43 + 8 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 16 * q^50 + 8 * q^51 - 24 * q^53 - 4 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.67762	+	0.430811i	−0.968573	+	0.248729i
$3$	−1.67762	+	0.430811i	−0.968573	+	0.248729i
$4$		−	1.00000i		−	0.500000i
$5$	−2.22680	−	0.203331i	−0.995857	−	0.0909324i
$5$	−2.22680	−	0.203331i	−0.995857	−	0.0909324i
$6$	0.881625	−	1.49088i	0.359922	−	0.608651i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.62880	−	1.44547i	0.876268	−	0.481825i
$10$	1.71837	−	1.43081i	0.543395	−	0.452462i
$11$		−	5.11849i		−	1.54328i	−0.636059	−	0.771641i	$-0.719436\pi$
$11$		−	5.11849i		−	1.54328i	0.636059	−	0.771641i	$-0.280564\pi$
$12$	0.430811	+	1.67762i	0.124365	+	0.484287i
$13$	2.66102	−	2.66102i	0.738034	−	0.738034i	−0.234163	−	0.972197i	$-0.575235\pi$
$13$	2.66102	−	2.66102i	0.738034	−	0.738034i	0.972197	+	0.234163i	$0.0752350\pi$
$14$	−1.00000			−0.267261
$15$	3.82332	−	0.618221i	0.987178	−	0.159624i
$16$	−1.00000			−0.250000
$17$	−0.660063	+	0.660063i	−0.160089	+	0.160089i	−0.782606	−	0.622517i	$-0.786110\pi$
$17$	−0.660063	+	0.660063i	−0.160089	+	0.160089i	0.622517	+	0.782606i	$0.286110\pi$
$18$	−0.836740	+	2.88095i	−0.197221	+	0.679046i
$19$		−	4.57375i		−	1.04929i	−0.851321	−	0.524646i	$-0.824198\pi$
$19$		−	4.57375i		−	1.04929i	0.851321	−	0.524646i	$-0.175802\pi$
$20$	−0.203331	+	2.22680i	−0.0454662	+	0.497929i
$21$	−1.49088	−	0.881625i	−0.325338	−	0.192386i
$22$	3.61932	+	3.61932i	0.771641	+	0.771641i
$23$	−0.915044	−	0.915044i	−0.190800	−	0.190800i	0.605242	−	0.796042i	$-0.293076\pi$
$23$	−0.915044	−	0.915044i	−0.190800	−	0.190800i	−0.796042	+	0.605242i	$0.793076\pi$
$24$	−1.49088	−	0.881625i	−0.304326	−	0.179961i
$25$	4.91731	+	0.905557i	0.983463	+	0.181111i
$26$			3.76325i			0.738034i
$27$	−3.78740	+	3.55747i	−0.728885	+	0.684636i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	8.71047			1.61749			0.808747	−	0.588157i	$-0.200146\pi$
$29$	8.71047			1.61749			0.808747	+	0.588157i	$0.200146\pi$
$30$	−2.26635	+	3.14065i	−0.413777	+	0.573401i
$31$	−9.86542			−1.77188			−0.885941	−	0.463798i	$-0.846486\pi$
$31$	−9.86542			−1.77188			−0.885941	+	0.463798i	$0.846486\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.20510	+	8.58686i	0.383859	+	1.49478i
$34$		−	0.933471i		−	0.160089i
$35$	−1.43081	−	1.71837i	−0.241851	−	0.290457i
$36$	−1.44547	−	2.62880i	−0.240912	−	0.438134i
$37$	−8.30181	−	8.30181i	−1.36481	−	1.36481i	−0.867671	−	0.497139i	$-0.834384\pi$
$37$	−8.30181	−	8.30181i	−1.36481	−	1.36481i	−0.497139	−	0.867671i	$-0.665616\pi$
$38$	3.23413	+	3.23413i	0.524646	+	0.524646i
$39$	−3.31778	+	5.61057i	−0.531269	+	0.898411i
$40$	−1.43081	−	1.71837i	−0.226231	−	0.271697i
$41$		−	2.55167i		−	0.398504i	−0.979948	−	0.199252i	$-0.936149\pi$
$41$		−	2.55167i		−	0.398504i	0.979948	−	0.199252i	$-0.0638513\pi$
$42$	1.67762	−	0.430811i	0.258862	−	0.0664757i
$43$	1.01688	−	1.01688i	0.155072	−	0.155072i	−0.625307	−	0.780379i	$-0.715026\pi$
$43$	1.01688	−	1.01688i	0.155072	−	0.155072i	0.780379	+	0.625307i	$0.215026\pi$
$44$	−5.11849			−0.771641
$45$	−6.14774	+	2.68427i	−0.916451	+	0.400147i
$46$	1.29407			0.190800
$47$	−2.54338	+	2.54338i	−0.370990	+	0.370990i	−0.867838	−	0.496848i	$-0.834491\pi$
$47$	−2.54338	+	2.54338i	−0.370990	+	0.370990i	0.496848	+	0.867838i	$0.334491\pi$
$48$	1.67762	−	0.430811i	0.242143	−	0.0621823i
$49$			1.00000i			0.142857i
$50$	−4.11739	+	2.83674i	−0.582287	+	0.401176i
$51$	0.822971	−	1.39170i	0.115239	−	0.194877i
$52$	−2.66102	−	2.66102i	−0.369017	−	0.369017i
$53$	0.551238	+	0.551238i	0.0757184	+	0.0757184i	0.743952	−	0.668233i	$-0.232949\pi$
$53$	0.551238	+	0.551238i	0.0757184	+	0.0757184i	−0.668233	+	0.743952i	$0.732949\pi$
$54$	0.162584	−	5.19361i	0.0221249	−	0.706761i
$55$	−1.04075	+	11.3979i	−0.140334	+	1.53689i
$56$			1.00000i			0.133631i
$57$	1.97043	+	7.67301i	0.260989	+	1.01632i
$58$	−6.15923	+	6.15923i	−0.808747	+	0.808747i
$59$	−1.36204			−0.177323			−0.0886615	−	0.996062i	$-0.528259\pi$
$59$	−1.36204			−0.177323			−0.0886615	+	0.996062i	$0.528259\pi$
$60$	−0.618221	−	3.82332i	−0.0798120	−	0.493589i
$61$	8.09345			1.03626			0.518130	−	0.855302i	$-0.326628\pi$
$61$	8.09345			1.03626			0.518130	+	0.855302i	$0.326628\pi$
$62$	6.97590	−	6.97590i	0.885941	−	0.885941i
$63$	2.88095	+	0.836740i	0.362965	+	0.105419i
$64$			1.00000i			0.125000i
$65$	−6.46664	+	5.38450i	−0.802088	+	0.667865i
$66$	−7.63107	−	4.51259i	−0.939320	−	0.555461i
$67$	−1.67348	−	1.67348i	−0.204448	−	0.204448i	0.597455	−	0.801903i	$-0.296179\pi$
$67$	−1.67348	−	1.67348i	−0.204448	−	0.204448i	−0.801903	+	0.597455i	$0.796179\pi$
$68$	0.660063	+	0.660063i	0.0800444	+	0.0800444i
$69$	1.92931	+	1.14088i	0.232261	+	0.137346i
$70$	2.22680	+	0.203331i	0.266154	+	0.0243027i
$71$		−	3.62916i		−	0.430702i	−0.976537	−	0.215351i	$-0.930910\pi$
$71$		−	3.62916i		−	0.430702i	0.976537	−	0.215351i	$-0.0690896\pi$
$72$	2.88095	+	0.836740i	0.339523	+	0.0986107i
$73$	5.95286	−	5.95286i	0.696729	−	0.696729i	−0.266974	−	0.963704i	$-0.586024\pi$
$73$	5.95286	−	5.95286i	0.696729	−	0.696729i	0.963704	+	0.266974i	$0.0860239\pi$
$74$	11.7405			1.36481
$75$	−8.63950	+	0.599256i	−0.997603	+	0.0691962i
$76$	−4.57375			−0.524646
$77$	3.61932	−	3.61932i	0.412459	−	0.412459i
$78$	−1.62125	−	6.31330i	−0.183571	−	0.714840i
$79$			7.87966i			0.886531i	0.896390	+	0.443265i	$0.146180\pi$
$79$			7.87966i			0.886531i	−0.896390	+	0.443265i	$0.853820\pi$
$80$	2.22680	+	0.203331i	0.248964	+	0.0227331i
$81$	4.82121	−	7.59973i	0.535690	−	0.844415i
$82$	1.80431	+	1.80431i	0.199252	+	0.199252i
$83$	−3.65347	−	3.65347i	−0.401020	−	0.401020i	0.477572	−	0.878592i	$-0.341517\pi$
$83$	−3.65347	−	3.65347i	−0.401020	−	0.401020i	−0.878592	+	0.477572i	$0.841517\pi$
$84$	−0.881625	+	1.49088i	−0.0961932	+	0.162669i
$85$	1.60404	−	1.33562i	0.173983	−	0.144868i
$86$			1.43808i			0.155072i
$87$	−14.6128	+	3.75257i	−1.56666	+	0.402318i
$88$	3.61932	−	3.61932i	0.385820	−	0.385820i
$89$	5.65138			0.599045			0.299523	−	0.954089i	$-0.403173\pi$
$89$	5.65138			0.599045			0.299523	+	0.954089i	$0.403173\pi$
$90$	2.44904	−	6.24517i	0.258152	−	0.658299i
$91$	3.76325			0.394496
$92$	−0.915044	+	0.915044i	−0.0953999	+	0.0953999i
$93$	16.5504	−	4.25014i	1.71620	−	0.440719i
$94$		−	3.59688i		−	0.370990i
$95$	−0.929986	+	10.1849i	−0.0954146	+	1.04494i
$96$	−0.881625	+	1.49088i	−0.0899805	+	0.152163i
$97$	3.76976	+	3.76976i	0.382761	+	0.382761i	0.872096	−	0.489335i	$-0.162760\pi$
$97$	3.76976	+	3.76976i	0.382761	+	0.382761i	−0.489335	+	0.872096i	$0.662760\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−7.39864	−	13.4555i	−0.743591	−	1.35233i
$100$	0.905557	−	4.91731i	0.0905557	−	0.491731i
$101$			9.35180i			0.930539i	0.885169	+	0.465269i	$0.154043\pi$
$101$			9.35180i			0.930539i	−0.885169	+	0.465269i	$0.845957\pi$
$102$	0.402150	+	1.56601i	0.0398188	+	0.155058i
$103$	4.21956	−	4.21956i	0.415766	−	0.415766i	−0.467975	−	0.883741i	$-0.655016\pi$
$103$	4.21956	−	4.21956i	0.415766	−	0.415766i	0.883741	+	0.467975i	$0.155016\pi$
$104$	3.76325			0.369017
$105$	3.14065	+	2.26635i	0.306496	+	0.221173i
$106$	−0.779568			−0.0757184
$107$	9.84339	−	9.84339i	0.951597	−	0.951597i	−0.0472848	−	0.998881i	$-0.515057\pi$
$107$	9.84339	−	9.84339i	0.951597	−	0.951597i	0.998881	+	0.0472848i	$0.0150568\pi$
$108$	3.55747	+	3.78740i	0.342318	+	0.364443i
$109$			11.0771i			1.06100i	0.847686	+	0.530498i	$0.177995\pi$
$109$			11.0771i			1.06100i	−0.847686	+	0.530498i	$0.822005\pi$
$110$	−7.32359	−	8.79543i	−0.698277	−	0.838611i
$111$	17.5038	+	10.3508i	1.66139	+	0.982450i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−6.81822	−	6.81822i	−0.641404	−	0.641404i	0.309496	−	0.950901i	$-0.399840\pi$
$113$	−6.81822	−	6.81822i	−0.641404	−	0.641404i	−0.950901	+	0.309496i	$0.899840\pi$
$114$	−6.81894	−	4.03234i	−0.638652	−	0.377663i
$115$	1.85157	+	2.22368i	0.172659	+	0.207359i
$116$		−	8.71047i		−	0.808747i
$117$	3.14886	−	10.8417i	0.291112	−	1.00232i
$118$	0.963111	−	0.963111i	0.0886615	−	0.0886615i
$119$	−0.933471			−0.0855711
$120$	3.14065	+	2.26635i	0.286700	+	0.206888i
$121$	−15.1989			−1.38172
$122$	−5.72293	+	5.72293i	−0.518130	+	0.518130i
$123$	1.09929	+	4.28073i	0.0991196	+	0.385981i
$124$			9.86542i			0.885941i
$125$	−10.7658	−	3.01634i	−0.962919	−	0.269790i
$126$	−2.62880	+	1.44547i	−0.234192	+	0.128773i
$127$	2.49131	+	2.49131i	0.221068	+	0.221068i	0.808948	−	0.587880i	$-0.200037\pi$
$127$	2.49131	+	2.49131i	0.221068	+	0.221068i	−0.587880	+	0.808948i	$0.700037\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.26785	+	2.14402i	−0.111628	+	0.188770i
$130$	0.765186	−	8.38002i	0.0671112	−	0.734976i
$131$		−	2.05511i		−	0.179556i	−0.995962	−	0.0897778i	$-0.971384\pi$
$131$		−	2.05511i		−	0.179556i	0.995962	−	0.0897778i	$-0.0286157\pi$
$132$	8.58686	−	2.20510i	0.747391	−	0.191930i
$133$	3.23413	−	3.23413i	0.280435	−	0.280435i
$134$	2.36666			0.204448
$135$	9.15714	−	7.15170i	0.788121	−	0.615520i
$136$	−0.933471			−0.0800444
$137$	−8.74776	+	8.74776i	−0.747371	+	0.747371i	−0.973985	−	0.226613i	$-0.927235\pi$
$137$	−8.74776	+	8.74776i	−0.747371	+	0.747371i	0.226613	+	0.973985i	$0.427235\pi$
$138$	−2.17095	+	0.557499i	−0.184804	+	0.0474575i
$139$		−	0.0502116i		−	0.00425889i	−0.999998	−	0.00212945i	$-0.999322\pi$
$139$		−	0.0502116i		−	0.00425889i	0.999998	−	0.00212945i	$-0.000677824\pi$
$140$	−1.71837	+	1.43081i	−0.145228	+	0.120926i
$141$	3.17110	−	5.36253i	0.267055	−	0.451607i
$142$	2.56620	+	2.56620i	0.215351	+	0.215351i
$143$	−13.6204	−	13.6204i	−1.13899	−	1.13899i
$144$	−2.62880	+	1.44547i	−0.219067	+	0.120456i
$145$	−19.3965	−	1.77111i	−1.61079	−	0.147083i
$146$			8.41861i			0.696729i
$147$	−0.430811	−	1.67762i	−0.0355327	−	0.138368i
$148$	−8.30181	+	8.30181i	−0.682405	+	0.682405i
$149$	11.7819			0.965211			0.482605	−	0.875838i	$-0.339691\pi$
$149$	11.7819			0.965211			0.482605	+	0.875838i	$0.339691\pi$
$150$	5.68531	−	6.53278i	0.464203	−	0.533400i
$151$	13.0407			1.06123			0.530617	−	0.847612i	$-0.321960\pi$
$151$	13.0407			1.06123			0.530617	+	0.847612i	$0.321960\pi$
$152$	3.23413	−	3.23413i	0.262323	−	0.262323i
$153$	−0.781072	+	2.68928i	−0.0631459	+	0.217415i
$154$			5.11849i			0.412459i
$155$	21.9684	+	2.00595i	1.76454	+	0.161121i
$156$	5.61057	+	3.31778i	0.449205	+	0.265635i
$157$	8.84559	+	8.84559i	0.705955	+	0.705955i	0.965682	−	0.259727i	$-0.0836326\pi$
$157$	8.84559	+	8.84559i	0.705955	+	0.705955i	−0.259727	+	0.965682i	$0.583633\pi$
$158$	−5.57176	−	5.57176i	−0.443265	−	0.443265i
$159$	−1.16225	−	0.687287i	−0.0921721	−	0.0545054i
$160$	−1.71837	+	1.43081i	−0.135849	+	0.113116i
$161$		−	1.29407i		−	0.101987i
$162$	1.96471	+	8.78293i	0.154362	+	0.690052i
$163$	−9.97183	+	9.97183i	−0.781054	+	0.781054i	−0.980009	−	0.198955i	$-0.936245\pi$
$163$	−9.97183	+	9.97183i	−0.781054	+	0.781054i	0.198955	+	0.980009i	$0.436245\pi$
$164$	−2.55167			−0.199252
$165$	−3.16436	−	19.5696i	−0.246345	−	1.52349i
$166$	5.16678			0.401020
$167$	1.53541	−	1.53541i	0.118814	−	0.118814i	−0.645200	−	0.764014i	$-0.723226\pi$
$167$	1.53541	−	1.53541i	0.118814	−	0.118814i	0.764014	+	0.645200i	$0.223226\pi$
$168$	−0.430811	−	1.67762i	−0.0332378	−	0.129431i
$169$		−	1.16205i		−	0.0893887i
$170$	−0.189804	+	2.07866i	−0.0145573	+	0.159426i
$171$	−6.61124	−	12.0235i	−0.505574	−	0.919460i
$172$	−1.01688	−	1.01688i	−0.0775362	−	0.0775362i
$173$	−6.82152	−	6.82152i	−0.518631	−	0.518631i	0.398526	−	0.917157i	$-0.369522\pi$
$173$	−6.82152	−	6.82152i	−0.518631	−	0.518631i	−0.917157	+	0.398526i	$0.869522\pi$
$174$	7.67937	−	12.9863i	0.582172	−	0.984489i
$175$	2.83674	+	4.11739i	0.214437	+	0.311245i
$176$			5.11849i			0.385820i
$177$	2.28499	−	0.586784i	0.171750	−	0.0441054i
$178$	−3.99613	+	3.99613i	−0.299523	+	0.299523i
$179$	−9.67016			−0.722782			−0.361391	−	0.932414i	$-0.617698\pi$
$179$	−9.67016			−0.722782			−0.361391	+	0.932414i	$0.617698\pi$
$180$	2.68427	+	6.14774i	0.200074	+	0.458225i
$181$	−20.0487			−1.49020			−0.745102	−	0.666950i	$-0.767599\pi$
$181$	−20.0487			−1.49020			−0.745102	+	0.666950i	$0.767599\pi$
$182$	−2.66102	+	2.66102i	−0.197248	+	0.197248i
$183$	−13.5777	+	3.48675i	−1.00369	+	0.257748i
$184$		−	1.29407i		−	0.0953999i
$185$	16.7985	+	20.1745i	1.23505	+	1.48326i
$186$	−8.69760	+	14.7082i	−0.637739	+	1.07846i
$187$	3.37853	+	3.37853i	0.247062	+	0.247062i
$188$	2.54338	+	2.54338i	0.185495	+	0.185495i
$189$	−5.19361	−	0.162584i	−0.377779	−	0.0118262i
$190$	−6.54418	−	7.85938i	−0.474765	−	0.570179i
$191$			20.5852i			1.48950i	0.667346	+	0.744748i	$0.267430\pi$
$191$			20.5852i			1.48950i	−0.667346	+	0.744748i	$0.732570\pi$
$192$	−0.430811	−	1.67762i	−0.0310911	−	0.121072i
$193$	−3.33427	+	3.33427i	−0.240006	+	0.240006i	−0.816852	−	0.576847i	$-0.804283\pi$
$193$	−3.33427	+	3.33427i	−0.240006	+	0.240006i	0.576847	+	0.816852i	$0.304283\pi$
$194$	−5.33124			−0.382761
$195$	8.52884	−	11.8190i	0.610763	−	0.846379i
$196$	1.00000			0.0714286
$197$	−12.0863	+	12.0863i	−0.861114	+	0.861114i	−0.991468	−	0.130354i	$-0.958389\pi$
$197$	−12.0863	+	12.0863i	−0.861114	+	0.861114i	0.130354	+	0.991468i	$0.458389\pi$
$198$	14.7461	+	4.28284i	1.04796	+	0.304368i
$199$		−	13.4749i		−	0.955210i	−0.878575	−	0.477605i	$-0.841505\pi$
$199$		−	13.4749i		−	0.955210i	0.878575	−	0.477605i	$-0.158495\pi$
$200$	2.83674	+	4.11739i	0.200588	+	0.291143i
$201$	3.52841	+	2.08651i	0.248875	+	0.147171i
$202$	−6.61272	−	6.61272i	−0.465269	−	0.465269i
$203$	6.15923	+	6.15923i	0.432293	+	0.432293i
$204$	−1.39170	−	0.822971i	−0.0974383	−	0.0576195i
$205$	−0.518834	+	5.68208i	−0.0362370	+	0.396853i
$206$			5.96736i			0.415766i
$207$	−3.72814	−	1.08280i	−0.259124	−	0.0752596i
$208$	−2.66102	+	2.66102i	−0.184509	+	0.184509i
$209$	−23.4107			−1.61935
$210$	−3.82332	+	0.618221i	−0.263834	+	0.0426613i
$211$	−20.9033			−1.43904			−0.719521	−	0.694471i	$-0.755638\pi$
$211$	−20.9033			−1.43904			−0.719521	+	0.694471i	$0.755638\pi$
$212$	0.551238	−	0.551238i	0.0378592	−	0.0378592i
$213$	1.56348	+	6.08834i	0.107128	+	0.417166i
$214$			13.9207i			0.951597i
$215$	−2.47115	+	2.05763i	−0.168531	+	0.140329i
$216$	−5.19361	−	0.162584i	−0.353380	−	0.0110624i
$217$	−6.97590	−	6.97590i	−0.473555	−	0.473555i
$218$	−7.83271	−	7.83271i	−0.530498	−	0.530498i
$219$	−7.42206	+	12.5512i	−0.501537	+	0.848130i
$220$	11.3979	+	1.04075i	0.768444	+	0.0701672i
$221$			3.51288i			0.236302i
$222$	−19.6961	+	5.05796i	−1.32192	+	0.339468i
$223$	−3.30682	+	3.30682i	−0.221441	+	0.221441i	−0.809105	−	0.587664i	$-0.800048\pi$
$223$	−3.30682	+	3.30682i	−0.221441	+	0.221441i	0.587664	+	0.809105i	$0.300048\pi$
$224$	1.00000			0.0668153
$225$	14.2356	−	4.72732i	0.949040	−	0.315154i
$226$	9.64242			0.641404
$227$	19.6412	−	19.6412i	1.30363	−	1.30363i	0.377706	−	0.925926i	$-0.376713\pi$
$227$	19.6412	−	19.6412i	1.30363	−	1.30363i	0.925926	−	0.377706i	$-0.123287\pi$
$228$	7.67301	−	1.97043i	0.508158	−	0.130495i
$229$		−	1.41048i		−	0.0932069i	−0.998913	−	0.0466034i	$-0.985160\pi$
$229$		−	1.41048i		−	0.0932069i	0.998913	−	0.0466034i	$-0.0148397\pi$
$230$	−2.88163	−	0.263124i	−0.190009	−	0.0173499i
$231$	−4.51259	+	7.63107i	−0.296906	+	0.502088i
$232$	6.15923	+	6.15923i	0.404373	+	0.404373i
$233$	−9.42431	−	9.42431i	−0.617407	−	0.617407i	0.327459	−	0.944866i	$-0.393808\pi$
$233$	−9.42431	−	9.42431i	−0.617407	−	0.617407i	−0.944866	+	0.327459i	$0.893808\pi$
$234$	5.43968	+	9.89284i	0.355603	+	0.646715i
$235$	6.18075	−	5.14646i	0.403188	−	0.335718i
$236$			1.36204i			0.0886615i
$237$	−3.39465	−	13.2191i	−0.220506	−	0.858670i
$238$	0.660063	−	0.660063i	0.0427856	−	0.0427856i
$239$	23.5817			1.52538			0.762688	−	0.646767i	$-0.223879\pi$
$239$	23.5817			1.52538			0.762688	+	0.646767i	$0.223879\pi$
$240$	−3.82332	+	0.618221i	−0.246794	+	0.0399060i
$241$	24.3495			1.56849			0.784245	−	0.620451i	$-0.213050\pi$
$241$	24.3495			1.56849			0.784245	+	0.620451i	$0.213050\pi$
$242$	10.7472	−	10.7472i	0.690859	−	0.690859i
$243$	−4.81409	+	14.8265i	−0.308824	+	0.951119i
$244$		−	8.09345i		−	0.518130i
$245$	0.203331	−	2.22680i	0.0129903	−	0.142265i
$246$	−3.80425	−	2.24962i	−0.242550	−	0.143430i
$247$	−12.1709	−	12.1709i	−0.774413	−	0.774413i
$248$	−6.97590	−	6.97590i	−0.442970	−	0.442970i
$249$	7.70308	+	4.55517i	0.488163	+	0.288672i
$250$	9.74542	−	5.47967i	0.616354	−	0.346565i
$251$			16.0687i			1.01425i	0.861873	+	0.507123i	$0.169291\pi$
$251$			16.0687i			1.01425i	−0.861873	+	0.507123i	$0.830709\pi$
$252$	0.836740	−	2.88095i	0.0527097	−	0.181483i
$253$	−4.68364	+	4.68364i	−0.294458	+	0.294458i
$254$	−3.52325			−0.221068
$255$	−2.11557	+	2.93170i	−0.132482	+	0.183590i
$256$	1.00000			0.0625000
$257$	13.3686	−	13.3686i	0.833912	−	0.833912i	−0.154138	−	0.988049i	$-0.549260\pi$
$257$	13.3686	−	13.3686i	0.833912	−	0.833912i	0.988049	+	0.154138i	$0.0492599\pi$
$258$	−0.619543	−	2.41255i	−0.0385710	−	0.150199i
$259$		−	11.7405i		−	0.729522i
$260$	5.38450	+	6.46664i	0.333933	+	0.401044i
$261$	22.8981	−	12.5908i	1.41736	−	0.779348i
$262$	1.45318	+	1.45318i	0.0897778	+	0.0897778i
$263$	16.6109	+	16.6109i	1.02427	+	1.02427i	0.999698	+	0.0245723i	$0.00782239\pi$
$263$	16.6109	+	16.6109i	1.02427	+	1.02427i	0.0245723	+	0.999698i	$0.492178\pi$
$264$	−4.51259	+	7.63107i	−0.277730	+	0.469660i
$265$	−1.11542	−	1.33958i	−0.0685194	−	0.0822899i
$266$			4.57375i			0.280435i
$267$	−9.48086	+	2.43468i	−0.580219	+	0.149000i
$268$	−1.67348	+	1.67348i	−0.102224	+	0.102224i
$269$	1.05024			0.0640340			0.0320170	−	0.999487i	$-0.489807\pi$
$269$	1.05024			0.0640340			0.0320170	+	0.999487i	$0.489807\pi$
$270$	−1.41806	+	11.5321i	−0.0863006	+	0.701821i
$271$	25.6890			1.56050			0.780249	−	0.625469i	$-0.215093\pi$
$271$	25.6890			1.56050			0.780249	+	0.625469i	$0.215093\pi$
$272$	0.660063	−	0.660063i	0.0400222	−	0.0400222i
$273$	−6.31330	+	1.62125i	−0.382098	+	0.0981226i
$274$		−	12.3712i		−	0.747371i
$275$	4.63508	−	25.1692i	0.279506	−	1.51776i
$276$	1.14088	−	1.92931i	0.0686730	−	0.116131i
$277$	1.71978	+	1.71978i	0.103332	+	0.103332i	0.756883	−	0.653551i	$-0.226721\pi$
$277$	1.71978	+	1.71978i	0.103332	+	0.103332i	−0.653551	+	0.756883i	$0.726721\pi$
$278$	0.0355050	+	0.0355050i	0.00212945	+	0.00212945i
$279$	−25.9342	+	14.2602i	−1.55264	+	0.853736i
$280$	0.203331	−	2.22680i	0.0121514	−	0.133077i
$281$		−	29.3325i		−	1.74983i	−0.484275	−	0.874916i	$-0.660917\pi$
$281$		−	29.3325i		−	1.74983i	0.484275	−	0.874916i	$-0.339083\pi$
$282$	1.54958	+	6.03419i	0.0922760	+	0.359331i
$283$	−0.440015	+	0.440015i	−0.0261562	+	0.0261562i	−0.720064	−	0.693908i	$-0.755888\pi$
$283$	−0.440015	+	0.440015i	−0.0261562	+	0.0261562i	0.693908	+	0.720064i	$0.255888\pi$
$284$	−3.62916			−0.215351
$285$	−2.82759	−	17.4869i	−0.167492	−	1.03584i
$286$	19.2621			1.13899
$287$	1.80431	−	1.80431i	0.106505	−	0.106505i
$288$	0.836740	−	2.88095i	0.0493054	−	0.169762i
$289$			16.1286i			0.948743i
$290$	14.9678	−	12.4630i	0.878938	−	0.731855i
$291$	−7.94827	−	4.70016i	−0.465936	−	0.275528i
$292$	−5.95286	−	5.95286i	−0.348365	−	0.348365i
$293$	6.16657	+	6.16657i	0.360255	+	0.360255i	0.863907	−	0.503652i	$-0.168011\pi$
$293$	6.16657	+	6.16657i	0.360255	+	0.360255i	−0.503652	+	0.863907i	$0.668011\pi$
$294$	1.49088	+	0.881625i	0.0869502	+	0.0514174i
$295$	3.03301	+	0.276946i	0.176588	+	0.0161244i
$296$		−	11.7405i		−	0.682405i
$297$	18.2089	+	19.3858i	1.05659	+	1.12488i
$298$	−8.33106	+	8.33106i	−0.482605	+	0.482605i
$299$	−4.86990			−0.281634
$300$	0.599256	+	8.63950i	0.0345981	+	0.498802i
$301$	1.43808			0.0828897
$302$	−9.22114	+	9.22114i	−0.530617	+	0.530617i
$303$	−4.02886	−	15.6887i	−0.231452	−	0.901295i
$304$			4.57375i			0.262323i
$305$	−18.0225	−	1.64565i	−1.03197	−	0.0942296i
$306$	−1.34931	−	2.45391i	−0.0771348	−	0.140281i
$307$	−11.9319	−	11.9319i	−0.680991	−	0.680991i	0.279232	−	0.960224i	$-0.409920\pi$
$307$	−11.9319	−	11.9319i	−0.680991	−	0.680991i	−0.960224	+	0.279232i	$0.909920\pi$
$308$	−3.61932	−	3.61932i	−0.206230	−	0.206230i
$309$	−5.26098	+	8.89665i	−0.299287	+	0.506113i
$310$	−16.9524	+	14.1156i	−0.962831	+	0.801710i
$311$		−	11.6450i		−	0.660328i	−0.943924	−	0.330164i	$-0.892896\pi$
$311$		−	11.6450i		−	0.660328i	0.943924	−	0.330164i	$-0.107104\pi$
$312$	−6.31330	+	1.62125i	−0.357420	+	0.0917853i
$313$	21.4297	−	21.4297i	1.21128	−	1.21128i	0.240672	−	0.970606i	$-0.422632\pi$
$313$	21.4297	−	21.4297i	1.21128	−	1.21128i	0.970606	−	0.240672i	$-0.0773679\pi$
$314$	−12.5096			−0.705955
$315$	−6.24517	−	2.44904i	−0.351876	−	0.137988i
$316$	7.87966			0.443265
$317$	−10.2198	+	10.2198i	−0.574002	+	0.574002i	−0.933244	−	0.359242i	$-0.883035\pi$
$317$	−10.2198	+	10.2198i	−0.574002	+	0.574002i	0.359242	+	0.933244i	$0.383035\pi$
$318$	1.30782	−	0.335847i	0.0733388	−	0.0188334i
$319$		−	44.5844i		−	2.49625i
$320$	0.203331	−	2.22680i	0.0113666	−	0.124482i
$321$	−12.2728	+	20.7541i	−0.685001	+	1.15838i
$322$	0.915044	+	0.915044i	0.0509934	+	0.0509934i
$323$	3.01897	+	3.01897i	0.167980	+	0.167980i
$324$	−7.59973	−	4.82121i	−0.422207	−	0.267845i
$325$	15.4948	−	10.6754i	0.859495	−	0.592163i
$326$		−	14.1023i		−	0.781054i
$327$	−4.77215	−	18.5832i	−0.263901	−	1.02765i
$328$	1.80431	−	1.80431i	0.0996261	−	0.0996261i
$329$	−3.59688			−0.198302
$330$	16.0754	+	11.6003i	0.884919	+	0.638574i
$331$	8.10042			0.445240			0.222620	−	0.974905i	$-0.428539\pi$
$331$	8.10042			0.445240			0.222620	+	0.974905i	$0.428539\pi$
$332$	−3.65347	+	3.65347i	−0.200510	+	0.200510i
$333$	−33.8239	−	9.82378i	−1.85354	−	0.538340i
$334$			2.17140i			0.118814i
$335$	3.38624	+	4.06678i	0.185010	+	0.222192i
$336$	1.49088	+	0.881625i	0.0813344	+	0.0480966i
$337$	0.775056	+	0.775056i	0.0422200	+	0.0422200i	0.727902	−	0.685682i	$-0.240496\pi$
$337$	0.775056	+	0.775056i	0.0422200	+	0.0422200i	−0.685682	+	0.727902i	$0.740496\pi$
$338$	0.821696	+	0.821696i	0.0446944	+	0.0446944i
$339$	14.3757	+	8.50100i	0.780783	+	0.461711i
$340$	−1.33562	−	1.60404i	−0.0724342	−	0.0869915i
$341$			50.4960i			2.73451i
$342$	13.1768	+	3.82704i	0.712517	+	0.206943i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	1.43808			0.0775362
$345$	−4.06421	−	2.93281i	−0.218810	−	0.157897i
$346$	9.64709			0.518631
$347$	−6.04424	+	6.04424i	−0.324472	+	0.324472i	−0.850480	−	0.526008i	$-0.823688\pi$
$347$	−6.04424	+	6.04424i	−0.324472	+	0.324472i	0.526008	+	0.850480i	$0.323688\pi$
$348$	3.75257	+	14.6128i	0.201159	+	0.783331i
$349$			11.2187i			0.600525i	0.953857	+	0.300263i	$0.0970744\pi$
$349$			11.2187i			0.600525i	−0.953857	+	0.300263i	$0.902926\pi$
$350$	−4.91731	−	0.905557i	−0.262841	−	0.0484041i
$351$	−0.611844	+	19.5448i	−0.0326578	+	1.04323i
$352$	−3.61932	−	3.61932i	−0.192910	−	0.192910i
$353$	−13.1367	−	13.1367i	−0.699198	−	0.699198i	0.265040	−	0.964238i	$-0.414615\pi$
$353$	−13.1367	−	13.1367i	−0.699198	−	0.699198i	−0.964238	+	0.265040i	$0.914615\pi$
$354$	−1.20081	+	2.03065i	−0.0638225	+	0.107928i
$355$	−0.737921	+	8.08143i	−0.0391648	+	0.428918i
$356$		−	5.65138i		−	0.299523i
$357$	1.56601	−	0.402150i	0.0828819	−	0.0212840i
$358$	6.83784	−	6.83784i	0.361391	−	0.361391i
$359$	−4.10021			−0.216401			−0.108200	−	0.994129i	$-0.534509\pi$
$359$	−4.10021			−0.216401			−0.108200	+	0.994129i	$0.534509\pi$
$360$	−6.24517	−	2.44904i	−0.329150	−	0.129076i
$361$	−1.91923			−0.101012
$362$	14.1765	−	14.1765i	0.745102	−	0.745102i
$363$	25.4979	−	6.54786i	1.33829	−	0.343674i
$364$		−	3.76325i		−	0.197248i
$365$	−14.4663	+	12.0455i	−0.757198	+	0.630488i
$366$	7.13539	−	12.0664i	0.372973	−	0.630721i
$367$	22.3293	+	22.3293i	1.16558	+	1.16558i	0.983234	+	0.182348i	$0.0583698\pi$
$367$	22.3293	+	22.3293i	1.16558	+	1.16558i	0.182348	+	0.983234i	$0.441630\pi$
$368$	0.915044	+	0.915044i	0.0477000	+	0.0477000i
$369$	−3.68838	−	6.70785i	−0.192009	−	0.349196i
$370$	−26.1439	−	2.38722i	−1.35916	−	0.124105i
$371$			0.779568i			0.0404732i
$372$	−4.25014	−	16.5504i	−0.220359	−	0.858098i
$373$	16.1487	−	16.1487i	0.836148	−	0.836148i	−0.152202	−	0.988349i	$-0.548636\pi$
$373$	16.1487	−	16.1487i	0.836148	−	0.836148i	0.988349	+	0.152202i	$0.0486363\pi$
$374$	−4.77796			−0.247062
$375$	19.3603	+	0.422251i	0.999762	+	0.0218050i
$376$	−3.59688			−0.185495
$377$	23.1787	−	23.1787i	1.19377	−	1.19377i
$378$	3.78740	−	3.55747i	0.194803	−	0.182977i
$379$		−	17.9824i		−	0.923694i	−0.886960	−	0.461847i	$-0.847187\pi$
$379$		−	17.9824i		−	0.923694i	0.886960	−	0.461847i	$-0.152813\pi$
$380$	10.1849	+	0.929986i	0.522472	+	0.0477073i
$381$	−5.25275	−	3.10618i	−0.269107	−	0.159135i
$382$	−14.5560	−	14.5560i	−0.744748	−	0.744748i
$383$	12.8721	+	12.8721i	0.657733	+	0.657733i	0.954843	−	0.297110i	$-0.0960229\pi$
$383$	12.8721	+	12.8721i	0.657733	+	0.657733i	−0.297110	+	0.954843i	$0.596023\pi$
$384$	1.49088	+	0.881625i	0.0760814	+	0.0449902i
$385$	−8.79543	+	7.32359i	−0.448256	+	0.373245i
$386$		−	4.71537i		−	0.240006i
$387$	1.20330	−	4.14304i	0.0611672	−	0.210603i
$388$	3.76976	−	3.76976i	0.191380	−	0.191380i
$389$	7.82278			0.396631			0.198315	−	0.980138i	$-0.436453\pi$
$389$	7.82278			0.396631			0.198315	+	0.980138i	$0.436453\pi$
$390$	2.32652	+	14.3881i	0.117808	+	0.728571i
$391$	1.20797			0.0610899
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	0.885364	+	3.44768i	0.0446607	+	0.173913i
$394$		−	17.0926i		−	0.861114i
$395$	1.60218	−	17.5465i	0.0806144	−	0.882858i
$396$	−13.4555	+	7.39864i	−0.676164	+	0.371796i
$397$	15.1217	+	15.1217i	0.758937	+	0.758937i	0.976129	−	0.217192i	$-0.0696897\pi$
$397$	15.1217	+	15.1217i	0.758937	+	0.758937i	−0.217192	+	0.976129i	$0.569690\pi$
$398$	9.52819	+	9.52819i	0.477605	+	0.477605i
$399$	−4.03234	+	6.81894i	−0.201869	+	0.341374i
$400$	−4.91731	−	0.905557i	−0.245866	−	0.0452778i
$401$			17.0712i			0.852493i	0.904607	+	0.426246i	$0.140164\pi$
$401$			17.0712i			0.852493i	−0.904607	+	0.426246i	$0.859836\pi$
$402$	−3.97035	+	1.01958i	−0.198023	+	0.0508522i
$403$	−26.2521	+	26.2521i	−1.30771	+	1.30771i
$404$	9.35180			0.465269
$405$	−12.2812	+	15.9428i	−0.610255	+	0.792205i
$406$	−8.71047			−0.432293
$407$	−42.4927	+	42.4927i	−2.10629	+	2.10629i
$408$	1.56601	−	0.402150i	0.0775289	−	0.0199094i
$409$		−	1.08737i		−	0.0537671i	−0.999639	−	0.0268836i	$-0.991442\pi$
$409$		−	1.08737i		−	0.0537671i	0.999639	−	0.0268836i	$-0.00855834\pi$
$410$	−3.65096	−	4.38471i	−0.180308	−	0.216545i
$411$	10.9068	−	18.4440i	0.537991	−	0.909777i
$412$	−4.21956	−	4.21956i	−0.207883	−	0.207883i
$413$	−0.963111	−	0.963111i	−0.0473916	−	0.0473916i
$414$	3.40185	−	1.87054i	0.167192	−	0.0919321i
$415$	7.39269	+	8.87842i	0.362893	+	0.435825i
$416$		−	3.76325i		−	0.184509i
$417$	0.0216317	+	0.0842359i	0.00105931	+	0.00412505i
$418$	16.5539	−	16.5539i	0.809676	−	0.809676i
$419$	35.7634			1.74715			0.873577	−	0.486685i	$-0.161794\pi$
$419$	35.7634			1.74715			0.873577	+	0.486685i	$0.161794\pi$
$420$	2.26635	−	3.14065i	0.110587	−	0.153248i
$421$	−36.8504			−1.79598			−0.897989	−	0.440018i	$-0.854972\pi$
$421$	−36.8504			−1.79598			−0.897989	+	0.440018i	$0.854972\pi$
$422$	14.7809	−	14.7809i	0.719521	−	0.719521i
$423$	−3.00965	+	10.3624i	−0.146334	+	0.503839i
$424$			0.779568i			0.0378592i
$425$	−3.84346	+	2.64801i	−0.186435	+	0.128448i
$426$	−5.41066	−	3.19956i	−0.262147	−	0.155019i
$427$	5.72293	+	5.72293i	0.276952	+	0.276952i
$428$	−9.84339	−	9.84339i	−0.475798	−	0.475798i
$429$	28.7176	+	16.9820i	1.38650	+	0.819898i
$430$	0.292407	−	3.20233i	0.0141011	−	0.154430i
$431$			8.14190i			0.392181i	0.980586	+	0.196091i	$0.0628247\pi$
$431$			8.14190i			0.392181i	−0.980586	+	0.196091i	$0.937175\pi$
$432$	3.78740	−	3.55747i	0.182221	−	0.171159i
$433$	3.87199	−	3.87199i	0.186076	−	0.186076i	−0.607921	−	0.793997i	$-0.707996\pi$
$433$	3.87199	−	3.87199i	0.186076	−	0.186076i	0.793997	+	0.607921i	$0.207996\pi$
$434$	9.86542			0.473555
$435$	33.3029	−	5.38500i	1.59675	−	0.258191i
$436$	11.0771			0.530498
$437$	−4.18519	+	4.18519i	−0.200205	+	0.200205i
$438$	−3.62684	−	14.1232i	−0.173297	−	0.674833i
$439$			24.4939i			1.16903i	0.811383	+	0.584515i	$0.198715\pi$
$439$			24.4939i			1.16903i	−0.811383	+	0.584515i	$0.801285\pi$
$440$	−8.79543	+	7.32359i	−0.419306	+	0.349138i
$441$	1.44547	+	2.62880i	0.0688321	+	0.125181i
$442$	−2.48398	−	2.48398i	−0.118151	−	0.118151i
$443$	16.7488	+	16.7488i	0.795760	+	0.795760i	0.982424	−	0.186664i	$-0.0597675\pi$
$443$	16.7488	+	16.7488i	0.795760	+	0.795760i	−0.186664	+	0.982424i	$0.559768\pi$
$444$	10.3508	−	17.5038i	0.491225	−	0.830693i
$445$	−12.5845	−	1.14910i	−0.596563	−	0.0544726i
$446$		−	4.67655i		−	0.221441i
$447$	−19.7655	+	5.07578i	−0.934877	+	0.240076i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−14.5848			−0.688297			−0.344149	−	0.938915i	$-0.611832\pi$
$449$	−14.5848			−0.688297			−0.344149	+	0.938915i	$0.611832\pi$
$450$	−6.72338	+	13.4088i	−0.316943	+	0.632097i
$451$	−13.0607			−0.615004
$452$	−6.81822	+	6.81822i	−0.320702	+	0.320702i
$453$	−21.8773	+	5.61807i	−1.02788	+	0.263960i
$454$			27.7768i			1.30363i
$455$	−8.38002	−	0.765186i	−0.392861	−	0.0358725i
$456$	−4.03234	+	6.81894i	−0.188831	+	0.319326i
$457$	8.72594	+	8.72594i	0.408182	+	0.408182i	0.881104	−	0.472922i	$-0.156801\pi$
$457$	8.72594	+	8.72594i	0.408182	+	0.408182i	−0.472922	+	0.881104i	$0.656801\pi$
$458$	0.997357	+	0.997357i	0.0466034	+	0.0466034i
$459$	0.151767	−	4.84808i	0.00708389	−	0.226289i
$460$	2.22368	−	1.85157i	0.103680	−	0.0863297i
$461$		−	19.9418i		−	0.928784i	−0.885630	−	0.464392i	$-0.846273\pi$
$461$		−	19.9418i		−	0.928784i	0.885630	−	0.464392i	$-0.153727\pi$
$462$	−2.20510	−	8.58686i	−0.102591	−	0.399497i
$463$	9.70556	−	9.70556i	0.451055	−	0.451055i	−0.444649	−	0.895705i	$-0.646672\pi$
$463$	9.70556	−	9.70556i	0.451055	−	0.451055i	0.895705	+	0.444649i	$0.146672\pi$
$464$	−8.71047			−0.404373
$465$	−37.7187	+	6.09901i	−1.74916	+	0.282835i
$466$	13.3280			0.617407
$467$	5.73494	−	5.73494i	0.265382	−	0.265382i	−0.561854	−	0.827236i	$-0.689912\pi$
$467$	5.73494	−	5.73494i	0.265382	−	0.265382i	0.827236	+	0.561854i	$0.189912\pi$
$468$	−10.8417	−	3.14886i	−0.501159	−	0.145556i
$469$		−	2.36666i		−	0.109282i
$470$	−0.731358	+	8.00955i	−0.0337350	+	0.369453i
$471$	−18.6503	−	11.0287i	−0.859360	−	0.508177i
$472$	−0.963111	−	0.963111i	−0.0443308	−	0.0443308i
$473$	−5.20488	−	5.20488i	−0.239320	−	0.239320i
$474$	11.7477	+	6.94691i	0.539588	+	0.319082i
$475$	4.14180	−	22.4906i	0.190039	−	1.03194i
$476$			0.933471i			0.0427856i
$477$	2.24590	+	0.652296i	0.102833	+	0.0298666i
$478$	−16.6748	+	16.6748i	−0.762688	+	0.762688i
$479$	−9.59046			−0.438199			−0.219100	−	0.975702i	$-0.570312\pi$
$479$	−9.59046			−0.438199			−0.219100	+	0.975702i	$0.570312\pi$
$480$	2.26635	−	3.14065i	0.103444	−	0.143350i
$481$	−44.1826			−2.01455
$482$	−17.2177	+	17.2177i	−0.784245	+	0.784245i
$483$	0.557499	+	2.17095i	0.0253671	+	0.0987817i
$484$			15.1989i			0.690859i
$485$	−7.62800	−	9.16102i	−0.346370	−	0.415980i
$486$	−7.07983	−	13.8880i	−0.321147	−	0.629972i
$487$	14.2720	+	14.2720i	0.646725	+	0.646725i	0.952200	−	0.305475i	$-0.0988151\pi$
$487$	14.2720	+	14.2720i	0.646725	+	0.646725i	−0.305475	+	0.952200i	$0.598815\pi$
$488$	5.72293	+	5.72293i	0.259065	+	0.259065i
$489$	12.4329	−	21.0249i	0.562237	−	0.950779i
$490$	1.43081	+	1.71837i	0.0646375	+	0.0776278i
$491$		−	28.6728i		−	1.29398i	−0.762497	−	0.646992i	$-0.776027\pi$
$491$		−	28.6728i		−	1.29398i	0.762497	−	0.646992i	$-0.223973\pi$
$492$	4.28073	−	1.09929i	0.192990	−	0.0495598i
$493$	−5.74946	+	5.74946i	−0.258943	+	0.258943i
$494$	17.2122			0.774413
$495$	13.7394	+	31.4671i	0.617540	+	1.41434i
$496$	9.86542			0.442970
$497$	2.56620	−	2.56620i	0.115110	−	0.115110i
$498$	−8.66789	+	2.22591i	−0.388417	+	0.0997454i
$499$		−	14.3520i		−	0.642483i	−0.946997	−	0.321242i	$-0.895900\pi$
$499$		−	14.3520i		−	0.642483i	0.946997	−	0.321242i	$-0.104100\pi$
$500$	−3.01634	+	10.7658i	−0.134895	+	0.481460i
$501$	−1.91436	+	3.23730i	−0.0855273	+	0.144632i
$502$	−11.3623	−	11.3623i	−0.507123	−	0.507123i
$503$	23.0425	+	23.0425i	1.02741	+	1.02741i	0.999614	+	0.0277992i	$0.00884991\pi$
$503$	23.0425	+	23.0425i	1.02741	+	1.02741i	0.0277992	+	0.999614i	$0.491150\pi$
$504$	1.44547	+	2.62880i	0.0643865	+	0.117096i
$505$	1.90151	−	20.8246i	0.0846162	−	0.926684i
$506$		−	6.62367i		−	0.294458i
$507$	0.500626	+	1.94948i	0.0222336	+	0.0865795i
$508$	2.49131	−	2.49131i	0.110534	−	0.110534i
$509$	−36.0312			−1.59706			−0.798528	−	0.601957i	$-0.794388\pi$
$509$	−36.0312			−1.59706			−0.798528	+	0.601957i	$0.794388\pi$
$510$	−0.577091	−	3.56896i	−0.0255540	−	0.158036i
$511$	8.41861			0.372418
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	16.2710	+	17.3226i	0.718382	+	0.764813i
$514$			18.9061i			0.833912i
$515$	−10.2541	+	8.53817i	−0.451850	+	0.376237i
$516$	2.14402	+	1.26785i	0.0943850	+	0.0558140i
$517$	13.0182	+	13.0182i	0.572542	+	0.572542i
$518$	8.30181	+	8.30181i	0.364761	+	0.364761i
$519$	14.3827	+	8.50512i	0.631331	+	0.373333i
$520$	−8.38002	−	0.765186i	−0.367488	−	0.0335556i
$521$			6.46917i			0.283420i	0.989908	+	0.141710i	$0.0452600\pi$
$521$			6.46917i			0.283420i	−0.989908	+	0.141710i	$0.954740\pi$
$522$	−7.28840	+	25.0944i	−0.319005	+	1.09835i
$523$	−7.55711	+	7.55711i	−0.330449	+	0.330449i	−0.852757	−	0.522308i	$-0.825071\pi$
$523$	−7.55711	+	7.55711i	−0.330449	+	0.330449i	0.522308	+	0.852757i	$0.325071\pi$
$524$	−2.05511			−0.0897778
$525$	−6.53278	−	5.68531i	−0.285114	−	0.248127i
$526$	−23.4913			−1.02427
$527$	6.51180	−	6.51180i	0.283659	−	0.283659i
$528$	−2.20510	−	8.58686i	−0.0959648	−	0.373695i
$529$		−	21.3254i		−	0.927191i
$530$	1.73595	+	0.158510i	0.0754047	+	0.00688525i
$531$	−3.58055	+	1.96880i	−0.155382	+	0.0854386i
$532$	−3.23413	−	3.23413i	−0.140217	−	0.140217i
$533$	−6.79005	−	6.79005i	−0.294110	−	0.294110i
$534$	4.98240	−	8.42556i	0.215609	−	0.364609i
$535$	−23.9208	+	19.9178i	−1.03419	+	0.861123i
$536$		−	2.36666i		−	0.102224i
$537$	16.2228	−	4.16602i	0.700067	−	0.179777i
$538$	−0.742629	+	0.742629i	−0.0320170	+	0.0320170i
$539$	5.11849			0.220469
$540$	−7.15170	−	9.15714i	−0.307760	−	0.394061i
$541$	−23.7219			−1.01988			−0.509942	−	0.860209i	$-0.670333\pi$
$541$	−23.7219			−1.01988			−0.509942	+	0.860209i	$0.670333\pi$
$542$	−18.1649	+	18.1649i	−0.780249	+	0.780249i
$543$	33.6340	−	8.63719i	1.44337	−	0.370657i
$544$			0.933471i			0.0400222i
$545$	2.25232	−	24.6666i	0.0964790	−	1.05660i
$546$	3.31778	−	5.61057i	0.141988	−	0.240110i
$547$	17.2270	+	17.2270i	0.736574	+	0.736574i	0.971913	−	0.235339i	$-0.0756201\pi$
$547$	17.2270	+	17.2270i	0.736574	+	0.736574i	−0.235339	+	0.971913i	$0.575620\pi$
$548$	8.74776	+	8.74776i	0.373686	+	0.373686i
$549$	21.2761	−	11.6989i	0.908041	−	0.499295i
$550$	14.5198	+	21.0748i	0.619127	+	0.898633i
$551$		−	39.8396i		−	1.69722i
$552$	0.557499	+	2.17095i	0.0237287	+	0.0924018i
$553$	−5.57176	+	5.57176i	−0.236935	+	0.236935i
$554$	−2.43214			−0.103332
$555$	−36.8729	−	26.6082i	−1.56517	−	1.12945i
$556$	−0.0502116			−0.00212945
$557$	−7.02290	+	7.02290i	−0.297570	+	0.297570i	−0.840061	−	0.542491i	$-0.817481\pi$
$557$	−7.02290	+	7.02290i	−0.297570	+	0.297570i	0.542491	+	0.840061i	$0.317481\pi$
$558$	8.25479	−	28.4218i	0.349453	−	1.20319i
$559$		−	5.41187i		−	0.228898i
$560$	1.43081	+	1.71837i	0.0604628	+	0.0726142i
$561$	−7.12338	−	4.21237i	−0.300749	−	0.177846i
$562$	20.7412	+	20.7412i	0.874916	+	0.874916i
$563$	−16.2207	−	16.2207i	−0.683621	−	0.683621i	0.277194	−	0.960814i	$-0.410596\pi$
$563$	−16.2207	−	16.2207i	−0.683621	−	0.683621i	−0.960814	+	0.277194i	$0.910596\pi$
$564$	−5.36253	−	3.17110i	−0.225803	−	0.133527i
$565$	13.7965	+	16.5692i	0.580422	+	0.697071i
$566$		−	0.622275i		−	0.0261562i
$567$	8.78293	−	1.96471i	0.368848	−	0.0825102i
$568$	2.56620	−	2.56620i	0.107675	−	0.107675i
$569$	−15.0582			−0.631272			−0.315636	−	0.948880i	$-0.602218\pi$
$569$	−15.0582			−0.631272			−0.315636	+	0.948880i	$0.602218\pi$
$570$	14.3645	+	10.3657i	0.601665	+	0.434173i
$571$	−11.1090			−0.464896			−0.232448	−	0.972609i	$-0.574674\pi$
$571$	−11.1090			−0.464896			−0.232448	+	0.972609i	$0.574674\pi$
$572$	−13.6204	+	13.6204i	−0.569497	+	0.569497i
$573$	−8.86836	−	34.5342i	−0.370481	−	1.44269i
$574$			2.55167i			0.106505i
$575$	−3.67093	−	5.32818i	−0.153088	−	0.222200i
$576$	1.44547	+	2.62880i	0.0602281	+	0.109533i
$577$	−12.2383	−	12.2383i	−0.509487	−	0.509487i	0.404882	−	0.914369i	$-0.367313\pi$
$577$	−12.2383	−	12.2383i	−0.509487	−	0.509487i	−0.914369	+	0.404882i	$0.867313\pi$
$578$	−11.4047	−	11.4047i	−0.474372	−	0.474372i
$579$	4.15719	−	7.03007i	0.172767	−	0.292160i
$580$	−1.77111	+	19.3965i	−0.0735413	+	0.805396i
$581$		−	5.16678i		−	0.214354i
$582$	8.94379	−	2.29676i	0.370732	−	0.0952038i
$583$	2.82150	−	2.82150i	0.116855	−	0.116855i
$584$	8.41861			0.348365
$585$	−9.21636	+	23.5022i	−0.381050	+	0.971694i
$586$	−8.72085			−0.360255
$587$	1.80620	−	1.80620i	0.0745497	−	0.0745497i	−0.668849	−	0.743398i	$-0.733213\pi$
$587$	1.80620	−	1.80620i	0.0745497	−	0.0745497i	0.743398	+	0.668849i	$0.233213\pi$
$588$	−1.67762	+	0.430811i	−0.0691838	+	0.0177664i
$589$			45.1220i			1.85922i
$590$	−2.34049	+	1.94883i	−0.0963564	+	0.0802320i
$591$	15.0693	−	25.4831i	0.619868	−	1.04824i
$592$	8.30181	+	8.30181i	0.341202	+	0.341202i
$593$	28.3207	+	28.3207i	1.16299	+	1.16299i	0.983817	+	0.179175i	$0.0573428\pi$
$593$	28.3207	+	28.3207i	1.16299	+	1.16299i	0.179175	+	0.983817i	$0.442657\pi$
$594$	−26.5834	−	0.832183i	−1.09073	−	0.0341449i
$595$	2.07866	+	0.189804i	0.0852166	+	0.00778119i
$596$		−	11.7819i		−	0.482605i
$597$	5.80514	+	22.6057i	0.237589	+	0.925191i
$598$	3.44354	−	3.44354i	0.140817	−	0.140817i
$599$	8.99206			0.367405			0.183703	−	0.982982i	$-0.441192\pi$
$599$	8.99206			0.367405			0.183703	+	0.982982i	$0.441192\pi$
$600$	−6.53278	−	5.68531i	−0.266700	−	0.232102i
$601$	1.77419			0.0723709			0.0361855	−	0.999345i	$-0.488479\pi$
$601$	1.77419			0.0723709			0.0361855	+	0.999345i	$0.488479\pi$
$602$	−1.01688	+	1.01688i	−0.0414449	+	0.0414449i
$603$	−6.81822	−	1.98028i	−0.277659	−	0.0806431i
$604$		−	13.0407i		−	0.530617i
$605$	33.8450	+	3.09041i	1.37599	+	0.125643i
$606$	13.9425	+	8.24478i	0.566374	+	0.334921i
$607$	−22.9565	−	22.9565i	−0.931777	−	0.931777i	0.0660402	−	0.997817i	$-0.478963\pi$
$607$	−22.9565	−	22.9565i	−0.931777	−	0.931777i	−0.997817	+	0.0660402i	$0.978963\pi$
$608$	−3.23413	−	3.23413i	−0.131161	−	0.131161i
$609$	−12.9863	−	7.67937i	−0.526232	−	0.311184i
$610$	13.9075	−	11.5802i	0.563098	−	0.468868i
$611$			13.5360i			0.547606i
$612$	2.68928	+	0.781072i	0.108708	+	0.0315730i
$613$	17.8179	−	17.8179i	0.719657	−	0.719657i	−0.248878	−	0.968535i	$-0.580062\pi$
$613$	17.8179	−	17.8179i	0.719657	−	0.719657i	0.968535	+	0.248878i	$0.0800618\pi$
$614$	16.8743			0.680991
$615$	−1.57750	−	9.75587i	−0.0636109	−	0.393395i
$616$	5.11849			0.206230
$617$	22.3285	−	22.3285i	0.898910	−	0.898910i	−0.0964302	−	0.995340i	$-0.530742\pi$
$617$	22.3285	−	22.3285i	0.898910	−	0.898910i	0.995340	+	0.0964302i	$0.0307424\pi$
$618$	−2.57081	−	10.0110i	−0.103413	−	0.402700i
$619$		−	44.8213i		−	1.80152i	−0.434319	−	0.900759i	$-0.643011\pi$
$619$		−	44.8213i		−	1.80152i	0.434319	−	0.900759i	$-0.356989\pi$
$620$	2.00595	−	21.9684i	0.0805607	−	0.882270i
$621$	6.72088	+	0.210394i	0.269700	+	0.00844284i
$622$	8.23427	+	8.23427i	0.330164	+	0.330164i
$623$	3.99613	+	3.99613i	0.160102	+	0.160102i
$624$	3.31778	−	5.61057i	0.132817	−	0.224603i
$625$	23.3599	+	8.90581i	0.934397	+	0.356233i
$626$			30.3062i			1.21128i
$627$	39.2742	−	10.0856i	1.56846	−	0.402780i
$628$	8.84559	−	8.84559i	0.352977	−	0.352977i
$629$	10.9594			0.436982
$630$	6.14774	−	2.68427i	0.244932	−	0.106944i
$631$	30.1896			1.20183			0.600914	−	0.799314i	$-0.294804\pi$
$631$	30.1896			1.20183			0.600914	+	0.799314i	$0.294804\pi$
$632$	−5.57176	+	5.57176i	−0.221633	+	0.221633i
$633$	35.0677	−	9.00537i	1.39382	−	0.357931i
$634$		−	14.4530i		−	0.574002i
$635$	−5.04110	−	6.05422i	−0.200050	−	0.240254i
$636$	−0.687287	+	1.16225i	−0.0272527	+	0.0460861i
$637$	2.66102	+	2.66102i	0.105433	+	0.105433i
$638$	31.5259	+	31.5259i	1.24812	+	1.24812i
$639$	−5.24586	−	9.54034i	−0.207523	−	0.377410i
$640$	1.43081	+	1.71837i	0.0565578	+	0.0679243i
$641$		−	45.9893i		−	1.81647i	−0.418462	−	0.908234i	$-0.637431\pi$
$641$		−	45.9893i		−	1.81647i	0.418462	−	0.908234i	$-0.362569\pi$
$642$	−5.99718	−	23.3535i	−0.236690	−	0.921691i
$643$	−6.36667	+	6.36667i	−0.251077	+	0.251077i	−0.821412	−	0.570335i	$-0.806813\pi$
$643$	−6.36667	+	6.36667i	−0.251077	+	0.251077i	0.570335	+	0.821412i	$0.306813\pi$
$644$	−1.29407			−0.0509934
$645$	3.25920	−	4.51651i	0.128331	−	0.177837i
$646$	−4.26947			−0.167980
$647$	−8.36361	+	8.36361i	−0.328808	+	0.328808i	−0.852133	−	0.523325i	$-0.824691\pi$
$647$	−8.36361	+	8.36361i	−0.328808	+	0.328808i	0.523325	+	0.852133i	$0.324691\pi$
$648$	8.78293	−	1.96471i	0.345026	−	0.0771812i
$649$			6.97160i			0.273659i
$650$	−3.40784	+	18.5051i	−0.133666	+	0.725829i
$651$	14.7082	+	8.69760i	0.576460	+	0.340886i
$652$	9.97183	+	9.97183i	0.390527	+	0.390527i
$653$	−12.5810	−	12.5810i	−0.492334	−	0.492334i	0.416707	−	0.909041i	$-0.363184\pi$
$653$	−12.5810	−	12.5810i	−0.492334	−	0.492334i	−0.909041	+	0.416707i	$0.863184\pi$
$654$	16.5147	+	9.76588i	0.645777	+	0.381876i
$655$	−0.417867	+	4.57632i	−0.0163274	+	0.178812i
$656$			2.55167i			0.0996261i
$657$	7.04419	−	24.2536i	0.274820	−	0.946223i
$658$	2.54338	−	2.54338i	0.0991512	−	0.0991512i
$659$	−9.08235			−0.353798			−0.176899	−	0.984229i	$-0.556607\pi$
$659$	−9.08235			−0.353798			−0.176899	+	0.984229i	$0.556607\pi$
$660$	−19.5696	+	3.16436i	−0.761747	+	0.123172i
$661$	4.47568			0.174084			0.0870420	−	0.996205i	$-0.472259\pi$
$661$	4.47568			0.174084			0.0870420	+	0.996205i	$0.472259\pi$
$662$	−5.72786	+	5.72786i	−0.222620	+	0.222620i
$663$	−1.51339	−	5.89328i	−0.0587752	−	0.228876i
$664$		−	5.16678i		−	0.200510i
$665$	−7.85938	+	6.54418i	−0.304774	+	0.253772i
$666$	30.8636	−	16.9706i	1.19594	−	0.657599i
$667$	−7.97046	−	7.97046i	−0.308618	−	0.308618i
$668$	−1.53541	−	1.53541i	−0.0594068	−	0.0594068i
$669$	4.12297	−	6.97220i	0.159403	−	0.269561i
$670$	−5.27008	−	0.481215i	−0.203601	−	0.0185910i
$671$		−	41.4262i		−	1.59924i
$672$	−1.67762	+	0.430811i	−0.0647155	+	0.0166189i
$673$	−11.5712	+	11.5712i	−0.446035	+	0.446035i	−0.894034	−	0.447999i	$-0.852137\pi$
$673$	−11.5712	+	11.5712i	−0.446035	+	0.446035i	0.447999	+	0.894034i	$0.352137\pi$
$674$	−1.09609			−0.0422200
$675$	−21.8453	+	14.0635i	−0.840827	+	0.541304i
$676$	−1.16205			−0.0446944
$677$	12.8813	−	12.8813i	0.495067	−	0.495067i	−0.414831	−	0.909898i	$-0.636159\pi$
$677$	12.8813	−	12.8813i	0.495067	−	0.495067i	0.909898	+	0.414831i	$0.136159\pi$
$678$	−16.1763	+	4.15406i	−0.621247	+	0.159536i
$679$			5.33124i			0.204594i
$680$	2.07866	+	0.189804i	0.0797128	+	0.00727864i
$681$	−24.4888	+	41.4121i	−0.938411	+	1.58691i
$682$	−35.7061	−	35.7061i	−1.36726	−	1.36726i
$683$	4.66122	+	4.66122i	0.178357	+	0.178357i	0.790639	−	0.612282i	$-0.209748\pi$
$683$	4.66122	+	4.66122i	0.178357	+	0.178357i	−0.612282	+	0.790639i	$0.709748\pi$
$684$	−12.0235	+	6.61124i	−0.459730	+	0.252787i
$685$	21.2582	−	17.7008i	0.812235	−	0.676315i
$686$		−	1.00000i		−	0.0381802i
$687$	0.607649	+	2.36624i	0.0231833	+	0.0902777i
$688$	−1.01688	+	1.01688i	−0.0387681	+	0.0387681i
$689$	2.93371			0.111765
$690$	4.94764	−	0.800020i	0.188353	−	0.0304562i
$691$	−15.2567			−0.580393			−0.290197	−	0.956967i	$-0.593721\pi$
$691$	−15.2567			−0.580393			−0.290197	+	0.956967i	$0.593721\pi$
$692$	−6.82152	+	6.82152i	−0.259315	+	0.259315i
$693$	4.28284	−	14.7461i	0.162692	−	0.560158i
$694$		−	8.54785i		−	0.324472i
$695$	−0.0102096	+	0.111811i	−0.000387271	+	0.00424125i
$696$	−12.9863	−	7.67937i	−0.492245	−	0.291086i
$697$	1.68427	+	1.68427i	0.0637961	+	0.0637961i
$698$	−7.93285	−	7.93285i	−0.300263	−	0.300263i
$699$	19.8705	+	11.7503i	0.751571	+	0.444437i
$700$	4.11739	−	2.83674i	0.155623	−	0.107219i
$701$		−	22.5053i		−	0.850012i	−0.905190	−	0.425006i	$-0.860272\pi$
$701$		−	22.5053i		−	0.850012i	0.905190	−	0.425006i	$-0.139728\pi$
$702$	−13.3877	−	14.2529i	−0.505285	−	0.537942i
$703$	−37.9705	+	37.9705i	−1.43208	+	1.43208i
$704$	5.11849			0.192910
$705$	−8.15179	+	11.2965i	−0.307014	+	0.425452i
$706$	18.5782			0.699198
$707$	−6.61272	+	6.61272i	−0.248697	+	0.248697i
$708$	−0.586784	−	2.28499i	−0.0220527	−	0.0858752i
$709$		−	2.18889i		−	0.0822055i	−0.999155	−	0.0411028i	$-0.986913\pi$
$709$		−	2.18889i		−	0.0822055i	0.999155	−	0.0411028i	$-0.0130871\pi$
$710$	−5.19264	−	6.23622i	−0.194876	−	0.234041i
$711$	11.3898	+	20.7141i	0.427152	+	0.776838i
$712$	3.99613	+	3.99613i	0.149761	+	0.149761i
$713$	9.02729	+	9.02729i	0.338075	+	0.338075i
$714$	−0.822971	+	1.39170i	−0.0307989	+	0.0520830i
$715$	27.5605	+	33.0994i	1.03070	+	1.23785i
$716$			9.67016i			0.361391i
$717$	−39.5611	+	10.1593i	−1.47744	+	0.379405i
$718$	2.89929	−	2.89929i	0.108200	−	0.108200i
$719$	−36.4233			−1.35836			−0.679179	−	0.733972i	$-0.737664\pi$
$719$	−36.4233			−1.35836			−0.679179	+	0.733972i	$0.737664\pi$
$720$	6.14774	−	2.68427i	0.229113	−	0.100037i
$721$	5.96736			0.222236
$722$	1.35710	−	1.35710i	0.0505061	−	0.0505061i
$723$	−40.8492	+	10.4901i	−1.51920	+	0.390129i
$724$			20.0487i			0.745102i
$725$	42.8321	+	7.88783i	1.59074	+	0.292947i
$726$	−13.3997	+	22.6598i	−0.497311	+	0.840984i
$727$	−18.7018	−	18.7018i	−0.693611	−	0.693611i	0.269414	−	0.963025i	$-0.413170\pi$
$727$	−18.7018	−	18.7018i	−0.693611	−	0.693611i	−0.963025	+	0.269414i	$0.913170\pi$
$728$	2.66102	+	2.66102i	0.0986240	+	0.0986240i
$729$	1.68879	−	26.9471i	0.0625479	−	0.998042i
$730$	1.71177	−	18.7466i	0.0633553	−	0.693843i
$731$			1.34241i			0.0496508i
$732$	3.48675	+	13.5777i	0.128874	+	0.501847i
$733$	16.9813	−	16.9813i	0.627217	−	0.627217i	−0.320150	−	0.947367i	$-0.603733\pi$
$733$	16.9813	−	16.9813i	0.627217	−	0.627217i	0.947367	+	0.320150i	$0.103733\pi$
$734$	−31.5785			−1.16558
$735$	0.618221	+	3.82332i	0.0228034	+	0.141025i
$736$	−1.29407			−0.0477000
$737$	−8.56568	+	8.56568i	−0.315521	+	0.315521i
$738$	7.35124	+	2.13509i	0.270603	+	0.0785936i
$739$			38.3267i			1.40987i	0.709272	+	0.704935i	$0.249024\pi$
$739$			38.3267i			1.40987i	−0.709272	+	0.704935i	$0.750976\pi$
$740$	20.1745	−	16.7985i	0.741631	−	0.617525i
$741$	25.6614	+	15.1747i	0.942694	+	0.557456i
$742$	−0.551238	−	0.551238i	−0.0202366	−	0.0202366i
$743$	4.74090	+	4.74090i	0.173927	+	0.173927i	0.788702	−	0.614775i	$-0.210753\pi$
$743$	4.74090	+	4.74090i	0.173927	+	0.173927i	−0.614775	+	0.788702i	$0.710753\pi$
$744$	14.7082	+	8.69760i	0.539229	+	0.318870i
$745$	−26.2360	−	2.39563i	−0.961212	−	0.0877689i
$746$			22.8377i			0.836148i
$747$	−14.8852	−	4.32325i	−0.544623	−	0.158180i
$748$	3.37853	−	3.37853i	0.123531	−	0.123531i
$749$	13.9207			0.508650
$750$	−13.9884	+	13.3912i	−0.510784	+	0.488979i
$751$	11.1768			0.407846			0.203923	−	0.978987i	$-0.434631\pi$
$751$	11.1768			0.407846			0.203923	+	0.978987i	$0.434631\pi$
$752$	2.54338	−	2.54338i	0.0927475	−	0.0927475i
$753$	−6.92258	−	26.9571i	−0.252273	−	0.982372i
$754$			32.7797i			1.19377i
$755$	−29.0390	−	2.65157i	−1.05684	−	0.0965006i
$756$	−0.162584	+	5.19361i	−0.00591312	+	0.188890i
$757$	3.45116	+	3.45116i	0.125435	+	0.125435i	0.767037	−	0.641603i	$-0.221730\pi$
$757$	3.45116	+	3.45116i	0.125435	+	0.125435i	−0.641603	+	0.767037i	$0.721730\pi$
$758$	12.7155	+	12.7155i	0.461847	+	0.461847i
$759$	5.83959	−	9.87512i	0.211964	−	0.358444i
$760$	−7.85938	+	6.54418i	−0.285090	+	0.237382i
$761$			10.4354i			0.378283i	0.981950	+	0.189141i	$0.0605704\pi$
$761$			10.4354i			0.378283i	−0.981950	+	0.189141i	$0.939430\pi$
$762$	5.91066	−	1.51785i	0.214121	−	0.0549861i
$763$	−7.83271	+	7.83271i	−0.283563	+	0.283563i
$764$	20.5852			0.744748
$765$	2.28611	−	5.82969i	0.0826544	−	0.210773i
$766$	−18.2039			−0.657733
$767$	−3.62443	+	3.62443i	−0.130870	+	0.130870i
$768$	−1.67762	+	0.430811i	−0.0605358	+	0.0155456i
$769$			32.5260i			1.17292i	0.809978	+	0.586460i	$0.199479\pi$
$769$			32.5260i			1.17292i	−0.809978	+	0.586460i	$0.800521\pi$
$770$	1.04075	−	11.3979i	0.0375059	−	0.410751i
$771$	−16.6681	+	28.1868i	−0.600286	+	1.01512i
$772$	3.33427	+	3.33427i	0.120003	+	0.120003i
$773$	37.7224	+	37.7224i	1.35678	+	1.35678i	0.877858	+	0.478920i	$0.158972\pi$
$773$	37.7224	+	37.7224i	1.35678	+	1.35678i	0.478920	+	0.877858i	$0.341028\pi$
$774$	2.07871	+	3.78044i	0.0747177	+	0.135885i
$775$	−48.5114	−	8.93370i	−1.74258	−	0.320908i
$776$			5.33124i			0.191380i
$777$	5.05796	+	19.6961i	0.181453	+	0.706595i
$778$	−5.53154	+	5.53154i	−0.198315	+	0.198315i
$779$	−11.6707			−0.418147
$780$	−11.8190	−	8.52884i	−0.423189	−	0.305382i
$781$	−18.5758			−0.664694
$782$	−0.854166	+	0.854166i	−0.0305449	+	0.0305449i
$783$	−32.9900	+	30.9873i	−1.17897	+	1.10739i
$784$		−	1.00000i		−	0.0357143i
$785$	−17.8988	−	21.4960i	−0.638836	−	0.767224i
$786$	−3.06393	−	1.81183i	−0.109287	−	0.0646260i
$787$	−4.83658	−	4.83658i	−0.172406	−	0.172406i	0.615630	−	0.788035i	$-0.288902\pi$
$787$	−4.83658	−	4.83658i	−0.172406	−	0.172406i	−0.788035	+	0.615630i	$0.788902\pi$
$788$	12.0863	+	12.0863i	0.430557	+	0.430557i
$789$	−35.0229	−	20.7105i	−1.24685	−	0.737315i
$790$	11.2743	+	13.5401i	0.401122	+	0.481736i
$791$		−	9.64242i		−	0.342845i
$792$	4.28284	−	14.7461i	0.152184	−	0.523980i
$793$	21.5368	−	21.5368i	0.764795	−	0.764795i
$794$	−21.3853			−0.758937
$795$	2.44835	+	1.76677i	0.0868339	+	0.0626610i
$796$	−13.4749			−0.477605
$797$	−21.5354	+	21.5354i	−0.762822	+	0.762822i	−0.976832	−	0.214009i	$-0.931348\pi$
$797$	−21.5354	+	21.5354i	−0.762822	+	0.762822i	0.214009	+	0.976832i	$0.431348\pi$
$798$	−1.97043	−	7.67301i	−0.0697523	−	0.271622i
$799$		−	3.35758i		−	0.118783i
$800$	4.11739	−	2.83674i	0.145572	−	0.100294i
$801$	14.8564	−	8.16892i	0.524924	−	0.288635i
$802$	−12.0711	−	12.0711i	−0.426246	−	0.426246i
$803$	−30.4696	−	30.4696i	−1.07525	−	1.07525i
$804$	2.08651	−	3.52841i	0.0735854	−	0.124438i
$805$	−0.263124	+	2.88163i	−0.00927391	+	0.101564i
$806$		−	37.1260i		−	1.30771i
$807$	−1.76190	+	0.452454i	−0.0620217	+	0.0159271i
$808$	−6.61272	+	6.61272i	−0.232635	+	0.232635i
$809$	−8.89737			−0.312815			−0.156407	−	0.987693i	$-0.549991\pi$
$809$	−8.89737			−0.312815			−0.156407	+	0.987693i	$0.549991\pi$
$810$	−2.58919	−	19.9574i	−0.0909748	−	0.701230i
$811$	16.6237			0.583738			0.291869	−	0.956458i	$-0.405723\pi$
$811$	16.6237			0.583738			0.291869	+	0.956458i	$0.405723\pi$
$812$	6.15923	−	6.15923i	0.216147	−	0.216147i
$813$	−43.0964	+	11.0671i	−1.51146	+	0.388141i
$814$		−	60.0938i		−	2.10629i
$815$	24.2329	−	20.1777i	0.848842	−	0.706795i
$816$	−0.822971	+	1.39170i	−0.0288098	+	0.0487191i
$817$	−4.65095	−	4.65095i	−0.162716	−	0.162716i
$818$	0.768889	+	0.768889i	0.0268836	+	0.0268836i
$819$	9.89284	−	5.43968i	0.345684	−	0.190078i
$820$	5.68208	+	0.518834i	0.198427	+	0.0181185i
$821$			28.2027i			0.984281i	0.870516	+	0.492140i	$0.163785\pi$
$821$			28.2027i			0.984281i	−0.870516	+	0.492140i	$0.836215\pi$
$822$	5.32965	+	20.7541i	0.185893	+	0.723884i
$823$	15.1141	−	15.1141i	0.526846	−	0.526846i	−0.392785	−	0.919630i	$-0.628488\pi$
$823$	15.1141	−	15.1141i	0.526846	−	0.526846i	0.919630	+	0.392785i	$0.128488\pi$
$824$	5.96736			0.207883
$825$	3.06729	+	44.2211i	0.106789	+	1.53958i
$826$	1.36204			0.0473916
$827$	17.4527	−	17.4527i	0.606889	−	0.606889i	−0.335243	−	0.942132i	$-0.608818\pi$
$827$	17.4527	−	17.4527i	0.606889	−	0.606889i	0.942132	+	0.335243i	$0.108818\pi$
$828$	−1.08280	+	3.72814i	−0.0376298	+	0.129562i
$829$		−	9.48644i		−	0.329478i	−0.986337	−	0.164739i	$-0.947322\pi$
$829$		−	9.48644i		−	0.329478i	0.986337	−	0.164739i	$-0.0526782\pi$
$830$	−11.5054	−	1.05057i	−0.399359	−	0.0364657i
$831$	−3.62604	−	2.14424i	−0.125786	−	0.0743828i
$832$	2.66102	+	2.66102i	0.0922543	+	0.0922543i
$833$	−0.660063	−	0.660063i	−0.0228698	−	0.0228698i
$834$	−0.0748597	−	0.0442678i	−0.00259218	−	0.00153287i
$835$	−3.73125	+	3.10686i	−0.129125	+	0.107517i
$836$			23.4107i			0.809676i
$837$	37.3643	−	35.0959i	1.29150	−	1.21309i
$838$	−25.2885	+	25.2885i	−0.873577	+	0.873577i
$839$	15.0379			0.519165			0.259582	−	0.965721i	$-0.416415\pi$
$839$	15.0379			0.519165			0.259582	+	0.965721i	$0.416415\pi$
$840$	0.618221	+	3.82332i	0.0213306	+	0.131917i
$841$	46.8723			1.61629
$842$	26.0572	−	26.0572i	0.897989	−	0.897989i
$843$	12.6368	+	49.2088i	0.435234	+	1.69484i
$844$			20.9033i			0.719521i
$845$	−0.236282	+	2.58767i	−0.00812833	+	0.0890184i
$846$	−5.19920	−	9.45549i	−0.178752	−	0.325086i
$847$	−10.7472	−	10.7472i	−0.369280	−	0.369280i
$848$	−0.551238	−	0.551238i	−0.0189296	−	0.0189296i
$849$	0.548614	−	0.927741i	0.0188284	−	0.0318400i
$850$	0.845311	−	4.59017i	0.0289939	−	0.157441i
$851$			15.1930i			0.520811i
$852$	6.08834	−	1.56348i	0.208583	−	0.0535641i
$853$	10.4909	−	10.4909i	0.359202	−	0.359202i	−0.504317	−	0.863519i	$-0.668256\pi$
$853$	10.4909	−	10.4909i	0.359202	−	0.359202i	0.863519	+	0.504317i	$0.168256\pi$
$854$	−8.09345			−0.276952
$855$	12.2772	+	28.1182i	0.419871	+	0.961624i
$856$	13.9207			0.475798
$857$	−4.66985	+	4.66985i	−0.159519	+	0.159519i	−0.782354	−	0.622834i	$-0.785981\pi$
$857$	−4.66985	+	4.66985i	−0.159519	+	0.159519i	0.622834	+	0.782354i	$0.285981\pi$
$858$	−32.3145	+	8.29835i	−1.10320	+	0.283301i
$859$		−	12.9895i		−	0.443195i	−0.975138	−	0.221598i	$-0.928873\pi$
$859$		−	12.9895i		−	0.443195i	0.975138	−	0.221598i	$-0.0711271\pi$
$860$	2.05763	+	2.47115i	0.0701644	+	0.0842656i
$861$	−2.24962	+	3.80425i	−0.0766668	+	0.129649i
$862$	−5.75719	−	5.75719i	−0.196091	−	0.196091i
$863$	1.91455	+	1.91455i	0.0651719	+	0.0651719i	0.738941	−	0.673770i	$-0.235326\pi$
$863$	1.91455	+	1.91455i	0.0651719	+	0.0651719i	−0.673770	+	0.738941i	$0.735326\pi$
$864$	−0.162584	+	5.19361i	−0.00553121	+	0.176690i
$865$	13.8032	+	16.5772i	0.469322	+	0.563643i
$866$			5.47583i			0.186076i
$867$	−6.94840	−	27.0577i	−0.235980	−	0.918927i
$868$	−6.97590	+	6.97590i	−0.236778	+	0.236778i
$869$	40.3319			1.36817
$870$	−19.7410	+	27.3565i	−0.669282	+	0.927472i
$871$	−8.90633			−0.301779
$872$	−7.83271	+	7.83271i	−0.265249	+	0.265249i
$873$	15.3590	+	4.46086i	0.519825	+	0.150977i
$874$		−	5.91875i		−	0.200205i
$875$	−5.47967	−	9.74542i	−0.185247	−	0.329455i
$876$	12.5512	+	7.42206i	0.424065	+	0.250768i
$877$	−34.9916	−	34.9916i	−1.18158	−	1.18158i	−0.979334	−	0.202248i	$-0.935175\pi$
$877$	−34.9916	−	34.9916i	−1.18158	−	1.18158i	−0.202248	−	0.979334i	$-0.564825\pi$
$878$	−17.3198	−	17.3198i	−0.584515	−	0.584515i
$879$	−13.0018	−	7.68852i	−0.438539	−	0.259327i
$880$	1.04075	−	11.3979i	0.0350836	−	0.384222i
$881$			2.67655i			0.0901753i	0.998983	+	0.0450877i	$0.0143567\pi$
$881$			2.67655i			0.0901753i	−0.998983	+	0.0450877i	$0.985643\pi$
$882$	−2.88095	−	0.836740i	−0.0970066	−	0.0281745i
$883$	23.3569	−	23.3569i	0.786024	−	0.786024i	−0.194816	−	0.980840i	$-0.562411\pi$
$883$	23.3569	−	23.3569i	0.786024	−	0.786024i	0.980840	+	0.194816i	$0.0624110\pi$
$884$	3.51288			0.118151
$885$	−5.20754	+	0.842044i	−0.175049	+	0.0283050i
$886$	−23.6864			−0.795760
$887$	−27.7866	+	27.7866i	−0.932983	+	0.932983i	−0.997891	−	0.0649087i	$-0.979324\pi$
$887$	−27.7866	+	27.7866i	−0.932983	+	0.932983i	0.0649087	+	0.997891i	$0.479324\pi$
$888$	5.05796	+	19.6961i	0.169734	+	0.660959i
$889$			3.52325i			0.118166i
$890$	9.71113	−	8.08606i	0.325518	−	0.271045i
$891$	−38.8991	−	24.6773i	−1.30317	−	0.826720i
$892$	3.30682	+	3.30682i	0.110721	+	0.110721i
$893$	11.6328	+	11.6328i	0.389276	+	0.389276i
$894$	10.3872	−	17.5654i	0.347400	−	0.587476i
$895$	21.5335	+	1.96624i	0.719787	+	0.0657243i
$896$		−	1.00000i		−	0.0334077i
$897$	8.16983	−	2.09801i	0.272783	−	0.0700505i
$898$	10.3130	−	10.3130i	0.344149	−	0.344149i
$899$	−85.9324			−2.86601
$900$	−4.72732	−	14.2356i	−0.157577	−	0.474520i
$901$	−0.727704			−0.0242433
$902$	9.23531	−	9.23531i	0.307502	−	0.307502i
$903$	−2.41255	+	0.619543i	−0.0802847	+	0.0206171i
$904$		−	9.64242i		−	0.320702i
$905$	44.6444	+	4.07651i	1.48403	+	0.135508i
$906$	11.4970	−	19.4421i	0.381962	−	0.645922i
$907$	25.5557	+	25.5557i	0.848564	+	0.848564i	0.989954	−	0.141390i	$-0.0451570\pi$
$907$	25.5557	+	25.5557i	0.848564	+	0.848564i	−0.141390	+	0.989954i	$0.545157\pi$
$908$	−19.6412	−	19.6412i	−0.651816	−	0.651816i
$909$	13.5178	+	24.5840i	0.448357	+	0.815401i
$910$	6.46664	−	5.38450i	0.214367	−	0.178494i
$911$			40.2447i			1.33337i	0.745341	+	0.666683i	$0.232287\pi$
$911$			40.2447i			1.33337i	−0.745341	+	0.666683i	$0.767713\pi$
$912$	−1.97043	−	7.67301i	−0.0652473	−	0.254079i
$913$	−18.7002	+	18.7002i	−0.618887	+	0.618887i
$914$	−12.3403			−0.408182
$915$	30.9439	−	5.00354i	1.02297	−	0.165412i
$916$	−1.41048			−0.0466034
$917$	1.45318	−	1.45318i	0.0479882	−	0.0479882i
$918$	3.32080	+	3.53543i	0.109603	+	0.116686i
$919$			56.3005i			1.85718i	0.371107	+	0.928590i	$0.378978\pi$
$919$			56.3005i			1.85718i	−0.371107	+	0.928590i	$0.621022\pi$
$920$	−0.263124	+	2.88163i	−0.00867494	+	0.0950047i
$921$	25.1576	+	14.8768i	0.828972	+	0.490207i
$922$	14.1010	+	14.1010i	0.464392	+	0.464392i
$923$	−9.65726	−	9.65726i	−0.317873	−	0.317873i
$924$	7.63107	+	4.51259i	0.251044	+	0.148453i
$925$	−33.3049	−	48.3404i	−1.09506	−	1.58942i
$926$			13.7257i			0.451055i
$927$	4.99313	−	17.1917i	0.163996	−	0.564649i
$928$	6.15923	−	6.15923i	0.202187	−	0.202187i
$929$	23.0895			0.757541			0.378770	−	0.925491i	$-0.376347\pi$
$929$	23.0895			0.757541			0.378770	+	0.925491i	$0.376347\pi$
$930$	22.3585	−	30.9838i	0.733164	−	1.01600i
$931$	4.57375			0.149899
$932$	−9.42431	+	9.42431i	−0.308704	+	0.308704i
$933$	5.01680	+	19.5359i	0.164243	+	0.639576i
$934$			8.11044i			0.265382i
$935$	−6.83635	−	8.21027i	−0.223573	−	0.268505i
$936$	9.89284	−	5.43968i	0.323358	−	0.177802i
$937$	−9.64496	−	9.64496i	−0.315087	−	0.315087i	0.531790	−	0.846877i	$-0.321520\pi$
$937$	−9.64496	−	9.64496i	−0.315087	−	0.315087i	−0.846877	+	0.531790i	$0.821520\pi$
$938$	1.67348	+	1.67348i	0.0546411	+	0.0546411i
$939$	−26.7187	+	45.1830i	−0.871932	+	1.47449i
$940$	−5.14646	−	6.18075i	−0.167859	−	0.201594i
$941$			51.3926i			1.67535i	0.546167	+	0.837676i	$0.316086\pi$
$941$			51.3926i			1.67535i	−0.546167	+	0.837676i	$0.683914\pi$
$942$	20.9862	−	5.38926i	0.683769	−	0.175592i
$943$	−2.33489	+	2.33489i	−0.0760346	+	0.0760346i
$944$	1.36204			0.0443308
$945$	11.5321	+	1.41806i	0.375139	+	0.0461296i
$946$	7.36081			0.239320
$947$	−36.6347	+	36.6347i	−1.19047	+	1.19047i	−0.213531	+	0.976936i	$0.568497\pi$
$947$	−36.6347	+	36.6347i	−1.19047	+	1.19047i	−0.976936	+	0.213531i	$0.931503\pi$
$948$	−13.2191	+	3.39465i	−0.429335	+	0.110253i
$949$		−	31.6814i		−	1.02842i
$950$	12.9746	+	18.8319i	0.420950	+	0.610989i
$951$	12.7421	−	21.5478i	0.413192	−	0.698734i
$952$	−0.660063	−	0.660063i	−0.0213928	−	0.0213928i
$953$	6.87447	+	6.87447i	0.222686	+	0.222686i	0.809629	−	0.586943i	$-0.199669\pi$
$953$	6.87447	+	6.87447i	0.222686	+	0.222686i	−0.586943	+	0.809629i	$0.699669\pi$
$954$	−2.04933	+	1.12685i	−0.0663495	+	0.0364830i
$955$	4.18562	−	45.8393i	0.135443	−	1.48332i
$956$		−	23.5817i		−	0.762688i
$957$	19.2075	+	74.7956i	0.620890	+	2.41780i
$958$	6.78148	−	6.78148i	0.219100	−	0.219100i
$959$	−12.3712			−0.399487
$960$	0.618221	+	3.82332i	0.0199530	+	0.123397i
$961$	66.3265			2.13956
$962$	31.2418	−	31.2418i	1.00728	−	1.00728i
$963$	11.6480	−	40.1047i	0.375351	−	1.29236i
$964$		−	24.3495i		−	0.784245i
$965$	8.10272	−	6.74680i	0.260836	−	0.217187i
$966$	−1.92931	−	1.14088i	−0.0620744	−	0.0367073i
$967$	−11.2771	−	11.2771i	−0.362647	−	0.362647i	0.502140	−	0.864787i	$-0.332546\pi$
$967$	−11.2771	−	11.2771i	−0.362647	−	0.362647i	−0.864787	+	0.502140i	$0.832546\pi$
$968$	−10.7472	−	10.7472i	−0.345430	−	0.345430i
$969$	−6.36528	−	3.76407i	−0.204482	−	0.120919i
$970$	11.8716	+	1.08401i	0.381175	+	0.0348054i
$971$			22.4417i			0.720189i	0.932916	+	0.360094i	$0.117256\pi$
$971$			22.4417i			0.720189i	−0.932916	+	0.360094i	$0.882744\pi$
$972$	14.8265	+	4.81409i	0.475560	+	0.154412i
$973$	0.0355050	−	0.0355050i	0.00113824	−	0.00113824i
$974$	−20.1836			−0.646725
$975$	−21.3952	+	24.5845i	−0.685196	+	0.787334i
$976$	−8.09345			−0.259065
$977$	−12.4873	+	12.4873i	−0.399505	+	0.399505i	−0.878058	−	0.478553i	$-0.841161\pi$
$977$	−12.4873	+	12.4873i	−0.399505	+	0.399505i	0.478553	+	0.878058i	$0.341161\pi$
$978$	6.07543	+	23.6583i	0.194271	+	0.756508i
$979$		−	28.9265i		−	0.924495i
$980$	−2.22680	−	0.203331i	−0.0711326	−	0.00649517i
$981$	16.0117	+	29.1196i	0.511214	+	0.929717i
$982$	20.2747	+	20.2747i	0.646992	+	0.646992i
$983$	−26.0926	−	26.0926i	−0.832224	−	0.832224i	0.155597	−	0.987821i	$-0.450270\pi$
$983$	−26.0926	−	26.0926i	−0.832224	−	0.832224i	−0.987821	+	0.155597i	$0.950270\pi$
$984$	−2.24962	+	3.80425i	−0.0717152	+	0.121275i
$985$	29.3714	−	24.4563i	0.935850	−	0.779243i
$986$		−	8.13097i		−	0.258943i
$987$	6.03419	−	1.54958i	0.192070	−	0.0493236i
$988$	−12.1709	+	12.1709i	−0.387206	+	0.387206i
$989$	−1.86098			−0.0591756
$990$	−31.9658	−	12.5354i	−1.01594	−	0.398401i
$991$	3.54343			0.112561			0.0562804	−	0.998415i	$-0.482076\pi$
$991$	3.54343			0.112561			0.0562804	+	0.998415i	$0.482076\pi$
$992$	−6.97590	+	6.97590i	−0.221485	+	0.221485i
$993$	−13.5894	+	3.48976i	−0.431247	+	0.110744i
$994$			3.62916i			0.115110i
$995$	−2.73987	+	30.0060i	−0.0868596	+	0.951253i
$996$	4.55517	−	7.70308i	0.144336	−	0.244081i
$997$	−33.4928	−	33.4928i	−1.06073	−	1.06073i	−0.998033	−	0.0626944i	$-0.980031\pi$
$997$	−33.4928	−	33.4928i	−1.06073	−	1.06073i	−0.0626944	−	0.998033i	$-0.519969\pi$
$998$	10.1484	+	10.1484i	0.321242	+	0.321242i
$999$	60.9758	+	1.90882i	1.92919	+	0.0603924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.j.a.197.1	yes	12
3.2	odd	2		210.2.j.b.197.5	yes	12
5.2	odd	4		1050.2.j.d.743.2		12
5.3	odd	4		210.2.j.b.113.5	yes	12
5.4	even	2		1050.2.j.c.407.6		12
15.2	even	4		1050.2.j.c.743.6		12
15.8	even	4	inner	210.2.j.a.113.1	✓	12
15.14	odd	2		1050.2.j.d.407.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.1	✓	12	15.8	even	4	inner
210.2.j.a.197.1	yes	12	1.1	even	1	trivial
210.2.j.b.113.5	yes	12	5.3	odd	4
210.2.j.b.197.5	yes	12	3.2	odd	2
1050.2.j.c.407.6		12	5.4	even	2
1050.2.j.c.743.6		12	15.2	even	4
1050.2.j.d.407.2		12	15.14	odd	2
1050.2.j.d.743.2		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.67762 + 0.430811i) q^{3} -1.00000i q^{4} +(-2.22680 - 0.203331i) q^{5} +(0.881625 - 1.49088i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.62880 - 1.44547i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.67762 + 0.430811i) q^{3} -1.00000i q^{4} +(-2.22680 - 0.203331i) q^{5} +(0.881625 - 1.49088i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.62880 - 1.44547i) q^{9} +(1.71837 - 1.43081i) q^{10} -5.11849i q^{11} +(0.430811 + 1.67762i) q^{12} +(2.66102 - 2.66102i) q^{13} -1.00000 q^{14} +(3.82332 - 0.618221i) q^{15} -1.00000 q^{16} +(-0.660063 + 0.660063i) q^{17} +(-0.836740 + 2.88095i) q^{18} -4.57375i q^{19} +(-0.203331 + 2.22680i) q^{20} +(-1.49088 - 0.881625i) q^{21} +(3.61932 + 3.61932i) q^{22} +(-0.915044 - 0.915044i) q^{23} +(-1.49088 - 0.881625i) q^{24} +(4.91731 + 0.905557i) q^{25} +3.76325i q^{26} +(-3.78740 + 3.55747i) q^{27} +(0.707107 - 0.707107i) q^{28} +8.71047 q^{29} +(-2.26635 + 3.14065i) q^{30} -9.86542 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.20510 + 8.58686i) q^{33} -0.933471i q^{34} +(-1.43081 - 1.71837i) q^{35} +(-1.44547 - 2.62880i) q^{36} +(-8.30181 - 8.30181i) q^{37} +(3.23413 + 3.23413i) q^{38} +(-3.31778 + 5.61057i) q^{39} +(-1.43081 - 1.71837i) q^{40} -2.55167i q^{41} +(1.67762 - 0.430811i) q^{42} +(1.01688 - 1.01688i) q^{43} -5.11849 q^{44} +(-6.14774 + 2.68427i) q^{45} +1.29407 q^{46} +(-2.54338 + 2.54338i) q^{47} +(1.67762 - 0.430811i) q^{48} +1.00000i q^{49} +(-4.11739 + 2.83674i) q^{50} +(0.822971 - 1.39170i) q^{51} +(-2.66102 - 2.66102i) q^{52} +(0.551238 + 0.551238i) q^{53} +(0.162584 - 5.19361i) q^{54} +(-1.04075 + 11.3979i) q^{55} +1.00000i q^{56} +(1.97043 + 7.67301i) q^{57} +(-6.15923 + 6.15923i) q^{58} -1.36204 q^{59} +(-0.618221 - 3.82332i) q^{60} +8.09345 q^{61} +(6.97590 - 6.97590i) q^{62} +(2.88095 + 0.836740i) q^{63} +1.00000i q^{64} +(-6.46664 + 5.38450i) q^{65} +(-7.63107 - 4.51259i) q^{66} +(-1.67348 - 1.67348i) q^{67} +(0.660063 + 0.660063i) q^{68} +(1.92931 + 1.14088i) q^{69} +(2.22680 + 0.203331i) q^{70} -3.62916i q^{71} +(2.88095 + 0.836740i) q^{72} +(5.95286 - 5.95286i) q^{73} +11.7405 q^{74} +(-8.63950 + 0.599256i) q^{75} -4.57375 q^{76} +(3.61932 - 3.61932i) q^{77} +(-1.62125 - 6.31330i) q^{78} +7.87966i q^{79} +(2.22680 + 0.203331i) q^{80} +(4.82121 - 7.59973i) q^{81} +(1.80431 + 1.80431i) q^{82} +(-3.65347 - 3.65347i) q^{83} +(-0.881625 + 1.49088i) q^{84} +(1.60404 - 1.33562i) q^{85} +1.43808i q^{86} +(-14.6128 + 3.75257i) q^{87} +(3.61932 - 3.61932i) q^{88} +5.65138 q^{89} +(2.44904 - 6.24517i) q^{90} +3.76325 q^{91} +(-0.915044 + 0.915044i) q^{92} +(16.5504 - 4.25014i) q^{93} -3.59688i q^{94} +(-0.929986 + 10.1849i) q^{95} +(-0.881625 + 1.49088i) q^{96} +(3.76976 + 3.76976i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-7.39864 - 13.4555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^3 - 4 * q^5	\( 12 q + 4 q^{3} - 4 q^{5} - 4 q^{12} - 12 q^{14} + 20 q^{15} - 12 q^{16} + 28 q^{17} - 4 q^{21} + 4 q^{22} - 24 q^{23} - 4 q^{24} + 20 q^{25} - 20 q^{27} + 8 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{33} - 8 q^{35} + 4 q^{36} - 20 q^{37} - 4 q^{38} - 40 q^{39} - 8 q^{40} - 4 q^{42} + 8 q^{43} + 8 q^{44} + 8 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 16 q^{50} + 8 q^{51} - 24 q^{53} - 4 q^{54} - 16 q^{55} - 12 q^{57} - 8 q^{58} + 32 q^{59} - 4 q^{60} + 28 q^{62} + 8 q^{63} - 8 q^{66} - 28 q^{68} - 32 q^{69} + 4 q^{70} + 8 q^{72} - 24 q^{73} + 8 q^{74} + 36 q^{75} + 4 q^{77} + 4 q^{80} - 36 q^{81} + 32 q^{82} - 24 q^{83} - 36 q^{85} - 64 q^{87} + 4 q^{88} + 48 q^{89} + 48 q^{90} + 24 q^{91} - 24 q^{92} + 76 q^{93} + 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 4 * q^5 - 4 * q^12 - 12 * q^14 + 20 * q^15 - 12 * q^16 + 28 * q^17 - 4 * q^21 + 4 * q^22 - 24 * q^23 - 4 * q^24 + 20 * q^25 - 20 * q^27 + 8 * q^29 + 16 * q^30 - 8 * q^31 + 4 * q^33 - 8 * q^35 + 4 * q^36 - 20 * q^37 - 4 * q^38 - 40 * q^39 - 8 * q^40 - 4 * q^42 + 8 * q^43 + 8 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 16 * q^50 + 8 * q^51 - 24 * q^53 - 4 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^58 + 32 * q^59 - 4 * q^60 + 28 * q^62 + 8 * q^63 - 8 * q^66 - 28 * q^68 - 32 * q^69 + 4 * q^70 + 8 * q^72 - 24 * q^73 + 8 * q^74 + 36 * q^75 + 4 * q^77 + 4 * q^80 - 36 * q^81 + 32 * q^82 - 24 * q^83 - 36 * q^85 - 64 * q^87 + 4 * q^88 + 48 * q^89 + 48 * q^90 + 24 * q^91 - 24 * q^92 + 76 * q^93 + 8 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more