LMFDB - Embedded newform 170.2.n.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, degree $4$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			59.2
Root			$-0.826884 - 1.99627i$ of defining polynomial
Character	$\chi$	$=$	170.59
Dual form			170.2.n.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.99627 - 0.826884i) q^{3} +1.00000i q^{4} +(-1.27343 + 1.83804i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(1.32795 + 3.20595i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.99627 - 0.826884i) q^{3} +1.00000i q^{4} +(-1.27343 + 1.83804i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(1.32795 + 3.20595i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +(-2.20014 + 0.399242i) q^{10} +(1.63382 + 3.94439i) q^{11} +(0.826884 - 1.99627i) q^{12} -5.21229 q^{13} +(-1.32795 + 3.20595i) q^{14} +(4.06195 - 2.61625i) q^{15} -1.00000 q^{16} +(2.46922 - 3.30196i) q^{17} +1.66885i q^{18} +(-0.305686 + 0.305686i) q^{19} +(-1.83804 - 1.27343i) q^{20} -7.49802i q^{21} +(-1.63382 + 3.94439i) q^{22} +(6.86651 - 2.84420i) q^{23} +(1.99627 - 0.826884i) q^{24} +(-1.75677 - 4.68121i) q^{25} +(-3.68564 - 3.68564i) q^{26} +(1.10071 + 2.65734i) q^{27} +(-3.20595 + 1.32795i) q^{28} +(3.46752 + 1.43630i) q^{29} +(4.72221 + 1.02226i) q^{30} +(-0.648377 + 1.56532i) q^{31} +(-0.707107 - 0.707107i) q^{32} -9.22506i q^{33} +(4.08084 - 0.588835i) q^{34} +(-7.58371 - 1.64172i) q^{35} +(-1.18005 + 1.18005i) q^{36} +(-4.56523 - 1.89098i) q^{37} -0.432305 q^{38} +(10.4052 + 4.30996i) q^{39} +(-0.399242 - 2.20014i) q^{40} +(-4.20525 + 1.74187i) q^{41} +(5.30190 - 5.30190i) q^{42} +(2.38395 - 2.38395i) q^{43} +(-3.94439 + 1.63382i) q^{44} +(-3.67170 + 0.666274i) q^{45} +(6.86651 + 2.84420i) q^{46} +3.47098 q^{47} +(1.99627 + 0.826884i) q^{48} +(-3.56493 + 3.56493i) q^{49} +(2.06789 - 4.55234i) q^{50} +(-7.65958 + 4.54986i) q^{51} -5.21229i q^{52} +(9.73490 + 9.73490i) q^{53} +(-1.10071 + 2.65734i) q^{54} +(-9.33048 - 2.01986i) q^{55} +(-3.20595 - 1.32795i) q^{56} +(0.863000 - 0.357466i) q^{57} +(1.43630 + 3.46752i) q^{58} +(6.37226 + 6.37226i) q^{59} +(2.61625 + 4.06195i) q^{60} +(5.75032 - 2.38186i) q^{61} +(-1.56532 + 0.648377i) q^{62} +(-2.21615 + 5.35025i) q^{63} -1.00000i q^{64} +(6.63746 - 9.58039i) q^{65} +(6.52310 - 6.52310i) q^{66} -0.409276i q^{67} +(3.30196 + 2.46922i) q^{68} -16.0593 q^{69} +(-4.20162 - 6.52336i) q^{70} +(-3.84587 + 9.28474i) q^{71} -1.66885 q^{72} +(0.401916 - 0.970312i) q^{73} +(-1.89098 - 4.56523i) q^{74} +(-0.363817 + 10.7976i) q^{75} +(-0.305686 - 0.305686i) q^{76} +(-10.4759 + 10.4759i) q^{77} +(4.30996 + 10.4052i) q^{78} +(0.218700 + 0.527989i) q^{79} +(1.27343 - 1.83804i) q^{80} -11.2215i q^{81} +(-4.20525 - 1.74187i) q^{82} +(-10.6949 - 10.6949i) q^{83} +7.49802 q^{84} +(2.92476 + 8.74333i) q^{85} +3.37141 q^{86} +(-5.73448 - 5.73448i) q^{87} +(-3.94439 - 1.63382i) q^{88} -14.5683i q^{89} +(-3.06741 - 2.12515i) q^{90} +(-6.92165 - 16.7103i) q^{91} +(2.84420 + 6.86651i) q^{92} +(2.58868 - 2.58868i) q^{93} +(2.45435 + 2.45435i) q^{94} +(-0.172594 - 0.951131i) q^{95} +(0.826884 + 1.99627i) q^{96} +(-3.70749 + 8.95068i) q^{97} -5.04157 q^{98} +(-2.72660 + 6.58259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.99627	−	0.826884i	−1.15255	−	0.477402i	−0.277162	−	0.960823i	$-0.589394\pi$
$3$	−1.99627	−	0.826884i	−1.15255	−	0.477402i	−0.875388	+	0.483422i	$0.839394\pi$
$4$			1.00000i			0.500000i
$5$	−1.27343	+	1.83804i	−0.569493	+	0.821996i
$5$	−1.27343	+	1.83804i	−0.569493	+	0.821996i
$6$	−0.826884	−	1.99627i	−0.337574	−	0.814976i
$7$	1.32795	+	3.20595i	0.501917	+	1.21174i	0.948438	+	0.316962i	$0.102663\pi$
$7$	1.32795	+	3.20595i	0.501917	+	1.21174i	−0.446521	+	0.894773i	$0.647337\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.18005	+	1.18005i	0.393351	+	0.393351i
$10$	−2.20014	+	0.399242i	−0.695745	+	0.126251i
$11$	1.63382	+	3.94439i	0.492615	+	1.18928i	0.953385	+	0.301758i	$0.0975734\pi$
$11$	1.63382	+	3.94439i	0.492615	+	1.18928i	−0.460770	+	0.887520i	$0.652427\pi$
$12$	0.826884	−	1.99627i	0.238701	−	0.576275i
$13$	−5.21229			−1.44563			−0.722814	−	0.691042i	$-0.757152\pi$
$13$	−5.21229			−1.44563			−0.722814	+	0.691042i	$0.757152\pi$
$14$	−1.32795	+	3.20595i	−0.354909	+	0.856827i
$15$	4.06195	−	2.61625i	1.04879	−	0.675514i
$16$	−1.00000			−0.250000
$17$	2.46922	−	3.30196i	0.598874	−	0.800843i
$17$	2.46922	−	3.30196i	0.598874	−	0.800843i
$18$			1.66885i			0.393351i
$19$	−0.305686	+	0.305686i	−0.0701292	+	0.0701292i	−0.741301	−	0.671172i	$-0.765791\pi$
$19$	−0.305686	+	0.305686i	−0.0701292	+	0.0701292i	0.671172	+	0.741301i	$0.265791\pi$
$20$	−1.83804	−	1.27343i	−0.410998	−	0.284747i
$21$		−	7.49802i		−	1.63620i
$22$	−1.63382	+	3.94439i	−0.348331	+	0.840946i
$23$	6.86651	−	2.84420i	1.43177	−	0.593057i	0.473980	−	0.880536i	$-0.342817\pi$
$23$	6.86651	−	2.84420i	1.43177	−	0.593057i	0.957787	+	0.287479i	$0.0928170\pi$
$24$	1.99627	−	0.826884i	0.407488	−	0.168787i
$25$	−1.75677	−	4.68121i	−0.351355	−	0.936242i
$26$	−3.68564	−	3.68564i	−0.722814	−	0.722814i
$27$	1.10071	+	2.65734i	0.211831	+	0.511406i
$28$	−3.20595	+	1.32795i	−0.605868	+	0.250959i
$29$	3.46752	+	1.43630i	0.643903	+	0.266713i	0.680647	−	0.732611i	$-0.261699\pi$
$29$	3.46752	+	1.43630i	0.643903	+	0.266713i	−0.0367441	+	0.999325i	$0.511699\pi$
$30$	4.72221	+	1.02226i	0.862153	+	0.186639i
$31$	−0.648377	+	1.56532i	−0.116452	+	0.281140i	−0.971349	−	0.237658i	$-0.923620\pi$
$31$	−0.648377	+	1.56532i	−0.116452	+	0.281140i	0.854897	+	0.518798i	$0.173620\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		−	9.22506i		−	1.60588i
$34$	4.08084	−	0.588835i	0.699859	−	0.100984i
$35$	−7.58371	−	1.64172i	−1.28188	−	0.277501i
$36$	−1.18005	+	1.18005i	−0.196676	+	0.196676i
$37$	−4.56523	−	1.89098i	−0.750519	−	0.310875i	−0.0255657	−	0.999673i	$-0.508139\pi$
$37$	−4.56523	−	1.89098i	−0.750519	−	0.310875i	−0.724953	+	0.688798i	$0.758139\pi$
$38$	−0.432305			−0.0701292
$39$	10.4052	+	4.30996i	1.66616	+	0.690146i
$40$	−0.399242	−	2.20014i	−0.0631257	−	0.347872i
$41$	−4.20525	+	1.74187i	−0.656750	+	0.272035i	−0.686070	−	0.727535i	$-0.740666\pi$
$41$	−4.20525	+	1.74187i	−0.656750	+	0.272035i	0.0293201	+	0.999570i	$0.490666\pi$
$42$	5.30190	−	5.30190i	0.818101	−	0.818101i
$43$	2.38395	−	2.38395i	0.363549	−	0.363549i	−0.501569	−	0.865118i	$-0.667244\pi$
$43$	2.38395	−	2.38395i	0.363549	−	0.363549i	0.865118	+	0.501569i	$0.167244\pi$
$44$	−3.94439	+	1.63382i	−0.594639	+	0.246307i
$45$	−3.67170	+	0.666274i	−0.547344	+	0.0993223i
$46$	6.86651	+	2.84420i	1.01241	+	0.419355i
$47$	3.47098			0.506294			0.253147	−	0.967428i	$-0.418534\pi$
$47$	3.47098			0.506294			0.253147	+	0.967428i	$0.418534\pi$
$48$	1.99627	+	0.826884i	0.288137	+	0.119350i
$49$	−3.56493	+	3.56493i	−0.509276	+	0.509276i
$50$	2.06789	−	4.55234i	0.292444	−	0.643799i
$51$	−7.65958	+	4.54986i	−1.07256	+	0.637108i
$52$		−	5.21229i		−	0.722814i
$53$	9.73490	+	9.73490i	1.33719	+	1.33719i	0.898769	+	0.438422i	$0.144463\pi$
$53$	9.73490	+	9.73490i	1.33719	+	1.33719i	0.438422	+	0.898769i	$0.355537\pi$
$54$	−1.10071	+	2.65734i	−0.149787	+	0.361619i
$55$	−9.33048	−	2.01986i	−1.25812	−	0.272358i
$56$	−3.20595	−	1.32795i	−0.428413	−	0.177455i
$57$	0.863000	−	0.357466i	0.114307	−	0.0473476i
$58$	1.43630	+	3.46752i	0.188595	+	0.455308i
$59$	6.37226	+	6.37226i	0.829598	+	0.829598i	0.987461	−	0.157863i	$-0.0504605\pi$
$59$	6.37226	+	6.37226i	0.829598	+	0.829598i	−0.157863	+	0.987461i	$0.550461\pi$
$60$	2.61625	+	4.06195i	0.337757	+	0.524396i
$61$	5.75032	−	2.38186i	0.736253	−	0.304966i	0.0171342	−	0.999853i	$-0.494546\pi$
$61$	5.75032	−	2.38186i	0.736253	−	0.304966i	0.719119	+	0.694887i	$0.244546\pi$
$62$	−1.56532	+	0.648377i	−0.198796	+	0.0823439i
$63$	−2.21615	+	5.35025i	−0.279208	+	0.674068i
$64$		−	1.00000i		−	0.125000i
$65$	6.63746	−	9.58039i	0.823276	−	1.18830i
$66$	6.52310	−	6.52310i	0.802938	−	0.802938i
$67$		−	0.409276i		−	0.0500010i	−0.999687	−	0.0250005i	$-0.992041\pi$
$67$		−	0.409276i		−	0.0500010i	0.999687	−	0.0250005i	$-0.00795873\pi$
$68$	3.30196	+	2.46922i	0.400422	+	0.299437i
$69$	−16.0593			−1.93331
$70$	−4.20162	−	6.52336i	−0.502190	−	0.779691i
$71$	−3.84587	+	9.28474i	−0.456420	+	1.10190i	0.513416	+	0.858140i	$0.328380\pi$
$71$	−3.84587	+	9.28474i	−0.456420	+	1.10190i	−0.969836	+	0.243757i	$0.921620\pi$
$72$	−1.66885			−0.196676
$73$	0.401916	−	0.970312i	0.0470407	−	0.113566i	−0.898613	−	0.438743i	$-0.855424\pi$
$73$	0.401916	−	0.970312i	0.0470407	−	0.113566i	0.945653	+	0.325177i	$0.105424\pi$
$74$	−1.89098	−	4.56523i	−0.219822	−	0.530697i
$75$	−0.363817	+	10.7976i	−0.0420099	+	1.24680i
$76$	−0.305686	−	0.305686i	−0.0350646	−	0.0350646i
$77$	−10.4759	+	10.4759i	−1.19384	+	1.19384i
$78$	4.30996	+	10.4052i	0.488007	+	1.17815i
$79$	0.218700	+	0.527989i	0.0246057	+	0.0594034i	0.935705	−	0.352784i	$-0.114765\pi$
$79$	0.218700	+	0.527989i	0.0246057	+	0.0594034i	−0.911099	+	0.412187i	$0.864765\pi$
$80$	1.27343	−	1.83804i	0.142373	−	0.205499i
$81$		−	11.2215i		−	1.24683i
$82$	−4.20525	−	1.74187i	−0.464393	−	0.192358i
$83$	−10.6949	−	10.6949i	−1.17391	−	1.17391i	−0.981269	−	0.192644i	$-0.938294\pi$
$83$	−10.6949	−	10.6949i	−1.17391	−	1.17391i	−0.192644	−	0.981269i	$-0.561706\pi$
$84$	7.49802			0.818101
$85$	2.92476	+	8.74333i	0.317235	+	0.948347i
$86$	3.37141			0.363549
$87$	−5.73448	−	5.73448i	−0.614801	−	0.614801i
$88$	−3.94439	−	1.63382i	−0.420473	−	0.174166i
$89$		−	14.5683i		−	1.54424i	−0.635478	−	0.772119i	$-0.719197\pi$
$89$		−	14.5683i		−	1.54424i	0.635478	−	0.772119i	$-0.280803\pi$
$90$	−3.06741	−	2.12515i	−0.323333	−	0.224011i
$91$	−6.92165	−	16.7103i	−0.725586	−	1.75172i
$92$	2.84420	+	6.86651i	0.296529	+	0.715883i
$93$	2.58868	−	2.58868i	0.268433	−	0.268433i
$94$	2.45435	+	2.45435i	0.253147	+	0.253147i
$95$	−0.172594	−	0.951131i	−0.0177078	−	0.0975840i
$96$	0.826884	+	1.99627i	0.0843935	+	0.203744i
$97$	−3.70749	+	8.95068i	−0.376439	+	0.908804i	0.616188	+	0.787599i	$0.288676\pi$
$97$	−3.70749	+	8.95068i	−0.376439	+	0.908804i	−0.992627	+	0.121205i	$0.961324\pi$
$98$	−5.04157			−0.509276
$99$	−2.72660	+	6.58259i	−0.274033	+	0.661575i
$100$	4.68121	−	1.75677i	0.468121	−	0.175677i
$101$	11.0547			1.09999			0.549993	−	0.835170i	$-0.314631\pi$
$101$	11.0547			1.09999			0.549993	+	0.835170i	$0.314631\pi$
$102$	−8.63338	−	2.19891i	−0.854832	−	0.217724i
$103$			6.34442i			0.625135i	0.949896	+	0.312567i	$0.101189\pi$
$103$			6.34442i			0.625135i	−0.949896	+	0.312567i	$0.898811\pi$
$104$	3.68564	−	3.68564i	0.361407	−	0.361407i
$105$	13.7816	+	9.54817i	1.34495	+	0.931806i
$106$			13.7672i			1.33719i
$107$	0.619790	−	1.49630i	0.0599173	−	0.144653i	−0.891085	−	0.453836i	$-0.850055\pi$
$107$	0.619790	−	1.49630i	0.0599173	−	0.144653i	0.951003	+	0.309182i	$0.100055\pi$
$108$	−2.65734	+	1.10071i	−0.255703	+	0.105916i
$109$	−7.65614	+	3.17128i	−0.733325	+	0.303753i	−0.717918	−	0.696128i	$-0.754905\pi$
$109$	−7.65614	+	3.17128i	−0.733325	+	0.303753i	−0.0154075	+	0.999881i	$0.504905\pi$
$110$	−5.16939	−	8.02591i	−0.492882	−	0.765240i
$111$	7.54983	+	7.54983i	0.716598	+	0.716598i
$112$	−1.32795	−	3.20595i	−0.125479	−	0.302934i
$113$	6.24358	−	2.58618i	0.587347	−	0.243287i	−0.0691619	−	0.997605i	$-0.522033\pi$
$113$	6.24358	−	2.58618i	0.587347	−	0.243287i	0.656509	+	0.754318i	$0.272033\pi$
$114$	0.863000	+	0.357466i	0.0808274	+	0.0334798i
$115$	−3.51624	+	16.2428i	−0.327891	+	1.51465i
$116$	−1.43630	+	3.46752i	−0.133357	+	0.321952i
$117$	−6.15078	−	6.15078i	−0.568640	−	0.568640i
$118$			9.01174i			0.829598i
$119$	13.8649	+	3.53137i	1.27100	+	0.323720i
$120$	−1.02226	+	4.72221i	−0.0933194	+	0.431076i
$121$	−5.11065	+	5.11065i	−0.464605	+	0.464605i
$122$	5.75032	+	2.38186i	0.520609	+	0.215643i
$123$	9.83517			0.886807
$124$	−1.56532	−	0.648377i	−0.140570	−	0.0582260i
$125$	10.8414	+	2.73216i	0.969682	+	0.244372i
$126$	−5.35025	+	2.21615i	−0.476638	+	0.197430i
$127$	1.28241	−	1.28241i	0.113796	−	0.113796i	−0.647916	−	0.761712i	$-0.724359\pi$
$127$	1.28241	−	1.28241i	0.113796	−	0.113796i	0.761712	+	0.647916i	$0.224359\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−6.73026	+	2.78777i	−0.592567	+	0.245449i
$130$	11.4678	−	2.08096i	1.00579	−	0.182513i
$131$	−3.98341	−	1.64998i	−0.348032	−	0.144160i	0.201818	−	0.979423i	$-0.435315\pi$
$131$	−3.98341	−	1.64998i	−0.348032	−	0.144160i	−0.549850	+	0.835263i	$0.685315\pi$
$132$	9.22506			0.802938
$133$	−1.38595	−	0.574079i	−0.120177	−	0.0497790i
$134$	0.289402	−	0.289402i	0.0250005	−	0.0250005i
$135$	−6.28597	−	1.36079i	−0.541010	−	0.117118i
$136$	0.588835	+	4.08084i	0.0504922	+	0.349929i
$137$			4.41897i			0.377538i	0.982022	+	0.188769i	$0.0604497\pi$
$137$			4.41897i			0.377538i	−0.982022	+	0.188769i	$0.939550\pi$
$138$	−11.3556	−	11.3556i	−0.966654	−	0.966654i
$139$	2.07037	−	4.99833i	0.175607	−	0.423952i	−0.811429	−	0.584451i	$-0.801310\pi$
$139$	2.07037	−	4.99833i	0.175607	−	0.423952i	0.987036	+	0.160498i	$0.0513101\pi$
$140$	1.64172	−	7.58371i	0.138751	−	0.640940i
$141$	−6.92902	−	2.87009i	−0.583529	−	0.241706i
$142$	−9.28474	+	3.84587i	−0.779158	+	0.322738i
$143$	−8.51593	−	20.5593i	−0.712138	−	1.71925i
$144$	−1.18005	−	1.18005i	−0.0983379	−	0.0983379i
$145$	−7.05560	+	4.54443i	−0.585936	+	0.377394i
$146$	0.970312	−	0.401916i	0.0803036	−	0.0332628i
$147$	10.0644	−	4.16879i	0.830094	−	0.343836i
$148$	1.89098	−	4.56523i	0.155438	−	0.375260i
$149$		−	10.4546i		−	0.856472i	−0.903667	−	0.428236i	$-0.859135\pi$
$149$		−	10.4546i		−	0.856472i	0.903667	−	0.428236i	$-0.140865\pi$
$150$	−7.89234	+	7.37782i	−0.644407	+	0.602397i
$151$	12.2681	−	12.2681i	0.998364	−	0.998364i	−0.00163493	−	0.999999i	$-0.500520\pi$
$151$	12.2681	−	12.2681i	0.998364	−	0.998364i	0.999999	+	0.00163493i	$0.000520415\pi$
$152$		−	0.432305i		−	0.0350646i
$153$	6.81031	−	0.982677i	0.550581	−	0.0794447i
$154$	−14.8151			−1.19384
$155$	−2.05146	−	3.18506i	−0.164777	−	0.255830i
$156$	−4.30996	+	10.4052i	−0.345073	+	0.833079i
$157$	−2.90181			−0.231589			−0.115795	−	0.993273i	$-0.536941\pi$
$157$	−2.90181			−0.231589			−0.115795	+	0.993273i	$0.536941\pi$
$158$	−0.218700	+	0.527989i	−0.0173989	+	0.0420046i
$159$	−11.3839	−	27.4832i	−0.902802	−	2.17956i
$160$	2.20014	−	0.399242i	0.173936	−	0.0315628i
$161$	18.2367	+	18.2367i	1.43726	+	1.43726i
$162$	7.93479	−	7.93479i	0.623416	−	0.623416i
$163$	−1.43563	−	3.46591i	−0.112447	−	0.271471i	0.857631	−	0.514266i	$-0.171936\pi$
$163$	−1.43563	−	3.46591i	−0.112447	−	0.271471i	−0.970078	+	0.242795i	$0.921936\pi$
$164$	−1.74187	−	4.20525i	−0.136017	−	0.328375i
$165$	16.9560	+	11.7474i	1.32002	+	0.914536i
$166$		−	15.1248i		−	1.17391i
$167$	21.8009	+	9.03022i	1.68700	+	0.698779i	0.999621	−	0.0275182i	$-0.00876043\pi$
$167$	21.8009	+	9.03022i	1.68700	+	0.698779i	0.687381	+	0.726297i	$0.258760\pi$
$168$	5.30190	+	5.30190i	0.409050	+	0.409050i
$169$	14.1680			1.08984
$170$	−4.11435	+	8.25058i	−0.315556	+	0.632791i
$171$	−0.721452			−0.0551708
$172$	2.38395	+	2.38395i	0.181774	+	0.181774i
$173$	−13.9467	−	5.77690i	−1.06035	−	0.439209i	−0.216771	−	0.976222i	$-0.569553\pi$
$173$	−13.9467	−	5.77690i	−1.06035	−	0.439209i	−0.843574	+	0.537013i	$0.819553\pi$
$174$		−	8.10978i		−	0.614801i
$175$	12.6748	−	11.8485i	0.958127	−	0.895665i
$176$	−1.63382	−	3.94439i	−0.123154	−	0.297319i
$177$	−7.45166	−	17.9899i	−0.560101	−	1.35220i
$178$	10.3013	−	10.3013i	0.772119	−	0.772119i
$179$	−8.99629	−	8.99629i	−0.672415	−	0.672415i	0.285858	−	0.958272i	$-0.407722\pi$
$179$	−8.99629	−	8.99629i	−0.672415	−	0.672415i	−0.958272	+	0.285858i	$0.907722\pi$
$180$	−0.666274	−	3.67170i	−0.0496611	−	0.273672i
$181$	−5.92939	−	14.3148i	−0.440728	−	1.06401i	−0.975694	−	0.219138i	$-0.929676\pi$
$181$	−5.92939	−	14.3148i	−0.440728	−	1.06401i	0.534966	−	0.844873i	$-0.320324\pi$
$182$	6.92165	−	16.7103i	0.513067	−	1.23865i
$183$	−13.4487			−0.994159
$184$	−2.84420	+	6.86651i	−0.209677	+	0.506206i
$185$	9.28917	−	5.98305i	0.682954	−	0.439882i
$186$	3.66094			0.268433
$187$	17.0585	+	4.34476i	1.24744	+	0.317721i
$188$			3.47098i			0.253147i
$189$	−7.05763	+	7.05763i	−0.513367	+	0.513367i
$190$	0.550509	−	0.794594i	0.0399381	−	0.0576459i
$191$			8.44496i			0.611056i	0.952183	+	0.305528i	$0.0988329\pi$
$191$			8.44496i			0.611056i	−0.952183	+	0.305528i	$0.901167\pi$
$192$	−0.826884	+	1.99627i	−0.0596752	+	0.144069i
$193$	−19.7167	+	8.16694i	−1.41924	+	0.587870i	−0.954670	−	0.297666i	$-0.903792\pi$
$193$	−19.7167	+	8.16694i	−1.41924	+	0.587870i	−0.464572	+	0.885535i	$0.653792\pi$
$194$	−8.95068	+	3.70749i	−0.642622	+	0.266183i
$195$	−21.1721	+	13.6367i	−1.51616	+	0.976543i
$196$	−3.56493	−	3.56493i	−0.254638	−	0.254638i
$197$	0.345500	+	0.834111i	0.0246159	+	0.0594280i	0.935710	−	0.352771i	$-0.114761\pi$
$197$	0.345500	+	0.834111i	0.0246159	+	0.0594280i	−0.911094	+	0.412199i	$0.864761\pi$
$198$	−6.58259	+	2.72660i	−0.467804	+	0.193771i
$199$	−0.329021	−	0.136285i	−0.0233237	−	0.00966099i	0.370991	−	0.928636i	$-0.379018\pi$
$199$	−0.329021	−	0.136285i	−0.0233237	−	0.00966099i	−0.394315	+	0.918975i	$0.629018\pi$
$200$	4.55234	+	2.06789i	0.321899	+	0.146222i
$201$	−0.338423	+	0.817026i	−0.0238705	+	0.0576286i
$202$	7.81686	+	7.81686i	0.549993	+	0.549993i
$203$			13.0240i			0.914109i
$204$	−4.54986	−	7.65958i	−0.318554	−	0.536278i
$205$	2.15345	−	9.94757i	0.150403	−	0.694768i
$206$	−4.48618	+	4.48618i	−0.312567	+	0.312567i
$207$	11.4592	+	4.74654i	0.796467	+	0.329908i
$208$	5.21229			0.361407
$209$	−1.70518	−	0.706309i	−0.117950	−	0.0488564i
$210$	2.99352	+	16.4967i	0.206573	+	1.13838i
$211$	−10.4640	+	4.33435i	−0.720374	+	0.298389i	−0.712590	−	0.701581i	$-0.752478\pi$
$211$	−10.4640	+	4.33435i	−0.720374	+	0.298389i	−0.00778455	+	0.999970i	$0.502478\pi$
$212$	−9.73490	+	9.73490i	−0.668596	+	0.668596i
$213$	15.3548	−	15.3548i	1.05209	−	1.05209i
$214$	1.49630	−	0.619790i	0.102285	−	0.0423680i
$215$	1.34601	+	7.41757i	0.0917970	+	0.505874i
$216$	−2.65734	−	1.10071i	−0.180809	−	0.0748937i
$217$	−5.87935			−0.399116
$218$	−7.65614	−	3.17128i	−0.518539	−	0.214786i
$219$	−1.60467	+	1.60467i	−0.108434	+	0.108434i
$220$	2.01986	−	9.33048i	0.136179	−	0.629061i
$221$	−12.8703	+	17.2108i	−0.865750	+	1.15772i
$222$			10.6771i			0.716598i
$223$	12.2971	+	12.2971i	0.823478	+	0.823478i	0.986605	−	0.163127i	$-0.0521581\pi$
$223$	12.2971	+	12.2971i	0.823478	+	0.823478i	−0.163127	+	0.986605i	$0.552158\pi$
$224$	1.32795	−	3.20595i	0.0887273	−	0.214207i
$225$	3.45100	−	7.59717i	0.230066	−	0.506478i
$226$	6.24358	+	2.58618i	0.415317	+	0.172030i
$227$	−11.0487	+	4.57652i	−0.733328	+	0.303755i	−0.717919	−	0.696127i	$-0.754905\pi$
$227$	−11.0487	+	4.57652i	−0.733328	+	0.303755i	−0.0154095	+	0.999881i	$0.504905\pi$
$228$	0.357466	+	0.863000i	0.0236738	+	0.0571536i
$229$	−8.31862	−	8.31862i	−0.549710	−	0.549710i	0.376647	−	0.926357i	$-0.377077\pi$
$229$	−8.31862	−	8.31862i	−0.549710	−	0.549710i	−0.926357	+	0.376647i	$0.877077\pi$
$230$	−13.9717	+	8.99904i	−0.921270	+	0.593379i
$231$	29.5751	−	12.2504i	1.94590	−	0.806017i
$232$	−3.46752	+	1.43630i	−0.227654	+	0.0942974i
$233$	8.94925	−	21.6054i	0.586285	−	1.41542i	−0.300744	−	0.953705i	$-0.597235\pi$
$233$	8.94925	−	21.6054i	0.586285	−	1.41542i	0.887030	−	0.461713i	$-0.152765\pi$
$234$		−	8.69852i		−	0.568640i
$235$	−4.42003	+	6.37979i	−0.288331	+	0.416172i
$236$	−6.37226	+	6.37226i	−0.414799	+	0.414799i
$237$		−	1.23485i		−	0.0802122i
$238$	7.30692	+	12.3010i	0.473638	+	0.797358i
$239$	13.2057			0.854206			0.427103	−	0.904203i	$-0.359534\pi$
$239$	13.2057			0.854206			0.427103	+	0.904203i	$0.359534\pi$
$240$	−4.06195	+	2.61625i	−0.262198	+	0.168879i
$241$	−8.66402	+	20.9168i	−0.558098	+	1.34737i	0.353171	+	0.935559i	$0.385103\pi$
$241$	−8.66402	+	20.9168i	−0.558098	+	1.34737i	−0.911270	+	0.411810i	$0.864897\pi$
$242$	−7.22756			−0.464605
$243$	−5.97675	+	14.4291i	−0.383409	+	0.925630i
$244$	2.38186	+	5.75032i	0.152483	+	0.368126i
$245$	−2.01281	−	11.0921i	−0.128593	−	0.708651i
$246$	6.95451	+	6.95451i	0.443404	+	0.443404i
$247$	1.59332	−	1.59332i	0.101381	−	0.101381i
$248$	−0.648377	−	1.56532i	−0.0411720	−	0.0993979i
$249$	12.5065	+	30.1933i	0.792565	+	1.91342i
$250$	5.73408	+	9.59793i	0.362655	+	0.607027i
$251$			3.13046i			0.197593i	0.995108	+	0.0987965i	$0.0314993\pi$
$251$			3.13046i			0.197593i	−0.995108	+	0.0987965i	$0.968501\pi$
$252$	−5.35025	−	2.21615i	−0.337034	−	0.139604i
$253$	22.4373	+	22.4373i	1.41062	+	1.41062i
$254$	1.81360			0.113796
$255$	1.39109	−	19.8725i	0.0871135	−	1.24447i
$256$	1.00000			0.0625000
$257$	−5.80608	−	5.80608i	−0.362173	−	0.362173i	0.502439	−	0.864613i	$-0.332436\pi$
$257$	−5.80608	−	5.80608i	−0.362173	−	0.362173i	−0.864613	+	0.502439i	$0.832436\pi$
$258$	−6.73026	−	2.78777i	−0.419008	−	0.173559i
$259$		−	17.1470i		−	1.06546i
$260$	9.58039	+	6.63746i	0.594150	+	0.411638i
$261$	2.39696	+	5.78677i	0.148368	+	0.358192i
$262$	−1.64998	−	3.98341i	−0.101936	−	0.246096i
$263$	−17.8286	+	17.8286i	−1.09936	+	1.09936i	−0.104871	+	0.994486i	$0.533443\pi$
$263$	−17.8286	+	17.8286i	−1.09936	+	1.09936i	−0.994486	+	0.104871i	$0.966557\pi$
$264$	6.52310	+	6.52310i	0.401469	+	0.401469i
$265$	−30.2898	+	5.49645i	−1.86069	+	0.337644i
$266$	−0.574079	−	1.38595i	−0.0351991	−	0.0849780i
$267$	−12.0463	+	29.0823i	−0.737222	+	1.77981i
$268$	0.409276			0.0250005
$269$	5.72583	−	13.8234i	0.349110	−	0.842827i	−0.647615	−	0.761968i	$-0.724234\pi$
$269$	5.72583	−	13.8234i	0.349110	−	0.842827i	0.996726	−	0.0808593i	$-0.0257664\pi$
$270$	−3.48263	−	5.40707i	−0.211946	−	0.329064i
$271$	−1.77027			−0.107536			−0.0537681	−	0.998553i	$-0.517123\pi$
$271$	−1.77027			−0.107536			−0.0537681	+	0.998553i	$0.517123\pi$
$272$	−2.46922	+	3.30196i	−0.149719	+	0.200211i
$273$			39.0818i			2.36534i
$274$	−3.12468	+	3.12468i	−0.188769	+	0.188769i
$275$	15.5943	−	14.5776i	0.940369	−	0.879065i
$276$		−	16.0593i		−	0.966654i
$277$	6.08957	−	14.7015i	0.365887	−	0.883329i	−0.628528	−	0.777787i	$-0.716342\pi$
$277$	6.08957	−	14.7015i	0.365887	−	0.883329i	0.994415	−	0.105542i	$-0.0336578\pi$
$278$	4.99833	−	2.07037i	0.299780	−	0.124173i
$279$	−2.61228	+	1.08204i	−0.156393	+	0.0647802i
$280$	6.52336	−	4.20162i	0.389845	−	0.251095i
$281$	−1.76322	−	1.76322i	−0.105185	−	0.105185i	0.652556	−	0.757741i	$-0.273697\pi$
$281$	−1.76322	−	1.76322i	−0.105185	−	0.105185i	−0.757741	+	0.652556i	$0.773697\pi$
$282$	−2.87009	−	6.92902i	−0.170912	−	0.412617i
$283$	16.6129	−	6.88128i	0.987534	−	0.409050i	0.170323	−	0.985388i	$-0.445519\pi$
$283$	16.6129	−	6.88128i	0.987534	−	0.409050i	0.817211	+	0.576339i	$0.195519\pi$
$284$	−9.28474	−	3.84587i	−0.550948	−	0.228210i
$285$	−0.441930	+	2.04143i	−0.0261776	+	0.120924i
$286$	8.51593	−	20.5593i	0.503558	−	1.21570i
$287$	−11.1687	−	11.1687i	−0.659269	−	0.659269i
$288$		−	1.66885i		−	0.0983379i
$289$	−4.80589	−	16.3065i	−0.282699	−	0.959209i
$290$	−8.20246	−	1.77567i	−0.481665	−	0.104271i
$291$	14.8024	−	14.8024i	0.867729	−	0.867729i
$292$	0.970312	+	0.401916i	0.0567832	+	0.0235204i
$293$	6.71505			0.392297			0.196149	−	0.980574i	$-0.437157\pi$
$293$	6.71505			0.392297			0.196149	+	0.980574i	$0.437157\pi$
$294$	10.0644	+	4.16879i	0.586965	+	0.243129i
$295$	−19.8271	+	3.59786i	−1.15438	+	0.209476i
$296$	4.56523	−	1.89098i	0.265349	−	0.109911i
$297$	−8.68323	+	8.68323i	−0.503852	+	0.503852i
$298$	7.39250	−	7.39250i	0.428236	−	0.428236i
$299$	−35.7902	+	14.8248i	−2.06980	+	0.857341i
$300$	−10.7976	−	0.363817i	−0.623402	−	0.0210050i
$301$	10.8086	+	4.47706i	0.622996	+	0.258054i
$302$	17.3497			0.998364
$303$	−22.0682	−	9.14097i	−1.26779	−	0.525135i
$304$	0.305686	−	0.305686i	0.0175323	−	0.0175323i
$305$	−2.94465	+	13.6024i	−0.168610	+	0.778873i
$306$	5.51047	+	4.12076i	0.315013	+	0.235568i
$307$		−	33.9861i		−	1.93969i	−0.243726	−	0.969844i	$-0.578370\pi$
$307$		−	33.9861i		−	1.93969i	0.243726	−	0.969844i	$-0.421630\pi$
$308$	−10.4759	−	10.4759i	−0.596919	−	0.596919i
$309$	5.24610	−	12.6652i	0.298440	−	0.720499i
$310$	0.801577	−	3.70278i	0.0455265	−	0.210304i
$311$	−24.0661	−	9.96849i	−1.36466	−	0.565261i	−0.424325	−	0.905510i	$-0.639489\pi$
$311$	−24.0661	−	9.96849i	−1.36466	−	0.565261i	−0.940335	+	0.340249i	$0.889489\pi$
$312$	−10.4052	+	4.30996i	−0.589076	+	0.244003i
$313$	0.809278	+	1.95377i	0.0457431	+	0.110434i	0.945100	−	0.326783i	$-0.105964\pi$
$313$	0.809278	+	1.95377i	0.0457431	+	0.110434i	−0.899356	+	0.437216i	$0.855964\pi$
$314$	−2.05189	−	2.05189i	−0.115795	−	0.115795i
$315$	−7.01187	−	10.8865i	−0.395074	−	0.613385i
$316$	−0.527989	+	0.218700i	−0.0297017	+	0.0123029i
$317$	−7.50100	+	3.10702i	−0.421298	+	0.174507i	−0.583253	−	0.812291i	$-0.698220\pi$
$317$	−7.50100	+	3.10702i	−0.421298	+	0.174507i	0.161954	+	0.986798i	$0.448220\pi$
$318$	11.3839	−	27.4832i	0.638377	−	1.54118i
$319$			16.0239i			0.897167i
$320$	1.83804	+	1.27343i	0.102749	+	0.0711867i
$321$	−2.47454	+	2.47454i	−0.138115	+	0.138115i
$322$			25.7907i			1.43726i
$323$	0.254557	+	1.76417i	0.0141639	+	0.0981610i
$324$	11.2215			0.623416
$325$	9.15681	+	24.3998i	0.507929	+	1.35346i
$326$	1.43563	−	3.46591i	0.0795120	−	0.191959i
$327$	17.9060			0.990206
$328$	1.74187	−	4.20525i	0.0961789	−	0.232196i
$329$	4.60928	+	11.1278i	0.254118	+	0.613494i
$330$	3.68303	+	20.2964i	0.202744	+	1.11728i
$331$	0.185865	+	0.185865i	0.0102161	+	0.0102161i	0.712196	−	0.701980i	$-0.247701\pi$
$331$	0.185865	+	0.185865i	0.0102161	+	0.0102161i	−0.701980	+	0.712196i	$0.747701\pi$
$332$	10.6949	−	10.6949i	0.586956	−	0.586956i
$333$	−3.15576	−	7.61868i	−0.172935	−	0.417501i
$334$	9.03022	+	21.8009i	0.494111	+	1.19289i
$335$	0.752264	+	0.521182i	0.0411006	+	0.0284752i
$336$			7.49802i			0.409050i
$337$	19.4419	+	8.05310i	1.05907	+	0.438680i	0.843120	−	0.537725i	$-0.180716\pi$
$337$	19.4419	+	8.05310i	1.05907	+	0.438680i	0.215947	+	0.976405i	$0.430716\pi$
$338$	10.0183	+	10.0183i	0.544921	+	0.544921i
$339$	−14.6024			−0.793092
$340$	−8.74333	+	2.92476i	−0.474174	+	0.158617i
$341$	−7.23356			−0.391719
$342$	−0.510144	−	0.510144i	−0.0275854	−	0.0275854i
$343$	6.27863	+	2.60069i	0.339014	+	0.140424i
$344$			3.37141i			0.181774i
$345$	20.4503	−	29.5176i	1.10101	−	1.58917i
$346$	−5.77690	−	13.9467i	−0.310568	−	0.749777i
$347$	13.4154	+	32.3876i	0.720176	+	1.73866i	0.672850	+	0.739779i	$0.265070\pi$
$347$	13.4154	+	32.3876i	0.720176	+	1.73866i	0.0473262	+	0.998879i	$0.484930\pi$
$348$	5.73448	−	5.73448i	0.307400	−	0.307400i
$349$	24.8197	+	24.8197i	1.32857	+	1.32857i	0.906619	+	0.421950i	$0.138654\pi$
$349$	24.8197	+	24.8197i	1.32857	+	1.32857i	0.421950	+	0.906619i	$0.361346\pi$
$350$	17.3406	+	0.584277i	0.926896	+	0.0312309i
$351$	−5.73721	−	13.8508i	−0.306229	−	0.739303i
$352$	1.63382	−	3.94439i	0.0870828	−	0.210237i
$353$	−16.7906			−0.893676			−0.446838	−	0.894615i	$-0.647450\pi$
$353$	−16.7906			−0.893676			−0.446838	+	0.894615i	$0.647450\pi$
$354$	7.45166	−	17.9899i	0.396051	−	0.956152i
$355$	−12.1683	−	18.8923i	−0.645826	−	1.00270i
$356$	14.5683			0.772119
$357$	−24.7582	−	18.5143i	−1.31034	−	0.979879i
$358$		−	12.7227i		−	0.672415i
$359$	17.1981	−	17.1981i	0.907681	−	0.907681i	−0.0884041	−	0.996085i	$-0.528177\pi$
$359$	17.1981	−	17.1981i	0.907681	−	0.907681i	0.996085	+	0.0884041i	$0.0281767\pi$
$360$	2.12515	−	3.06741i	0.112005	−	0.161667i
$361$			18.8131i			0.990164i
$362$	5.92939	−	14.3148i	0.311642	−	0.752369i
$363$	14.4282	−	5.97635i	0.757283	−	0.313677i
$364$	16.7103	−	6.92165i	0.875860	−	0.362793i
$365$	1.27166	+	1.97436i	0.0665617	+	0.103343i
$366$	−9.50969	−	9.50969i	−0.497080	−	0.497080i
$367$	−7.31730	−	17.6655i	−0.381960	−	0.922133i	−0.991587	−	0.129444i	$-0.958681\pi$
$367$	−7.31730	−	17.6655i	−0.381960	−	0.922133i	0.609627	−	0.792689i	$-0.291319\pi$
$368$	−6.86651	+	2.84420i	−0.357942	+	0.148264i
$369$	−7.01793	−	2.90692i	−0.365339	−	0.151328i
$370$	10.7991	+	2.33779i	0.561418	+	0.121536i
$371$	−18.2822	+	44.1371i	−0.949163	+	2.29148i
$372$	2.58868	+	2.58868i	0.134217	+	0.134217i
$373$		−	6.43835i		−	0.333365i	−0.986011	−	0.166683i	$-0.946694\pi$
$373$		−	6.43835i		−	0.333365i	0.986011	−	0.166683i	$-0.0533055\pi$
$374$	8.98995	+	15.1344i	0.464859	+	0.782580i
$375$	−19.3832	−	14.4187i	−1.00094	−	0.744578i
$376$	−2.45435	+	2.45435i	−0.126573	+	0.126573i
$377$	−18.0737	−	7.48639i	−0.930845	−	0.385569i
$378$	−9.98100			−0.513367
$379$	−15.4328	−	6.39249i	−0.792732	−	0.328360i	−0.0506903	−	0.998714i	$-0.516142\pi$
$379$	−15.4328	−	6.39249i	−0.792732	−	0.328360i	−0.742041	+	0.670354i	$0.766142\pi$
$380$	0.951131	−	0.172594i	0.0487920	−	0.00885390i
$381$	−3.62045	+	1.49964i	−0.185481	+	0.0768289i
$382$	−5.97149	+	5.97149i	−0.305528	+	0.305528i
$383$	−0.704366	+	0.704366i	−0.0359914	+	0.0359914i	−0.724873	−	0.688882i	$-0.758102\pi$
$383$	−0.704366	+	0.704366i	−0.0359914	+	0.0359914i	0.688882	+	0.724873i	$0.258102\pi$
$384$	−1.99627	+	0.826884i	−0.101872	+	0.0421967i
$385$	−5.91482	−	32.5954i	−0.301447	−	1.66121i
$386$	−19.7167	−	8.16694i	−1.00356	−	0.415687i
$387$	5.62638			0.286005
$388$	−8.95068	−	3.70749i	−0.454402	−	0.188220i
$389$	−7.00072	+	7.00072i	−0.354950	+	0.354950i	−0.861948	−	0.506997i	$-0.830755\pi$
$389$	−7.00072	+	7.00072i	−0.354950	+	0.354950i	0.506997	+	0.861948i	$0.330755\pi$
$390$	−24.6135	−	5.32833i	−1.24635	−	0.269810i
$391$	7.56350	−	29.6959i	0.382503	−	1.50179i
$392$		−	5.04157i		−	0.254638i
$393$	6.58764	+	6.58764i	0.332302	+	0.332302i
$394$	−0.345500	+	0.834111i	−0.0174060	+	0.0420219i
$395$	−1.24896	−	0.270375i	−0.0628422	−	0.0136041i
$396$	−6.58259	−	2.72660i	−0.330787	−	0.137017i
$397$	34.3102	−	14.2118i	1.72198	−	0.713268i	0.722214	−	0.691670i	$-0.243125\pi$
$397$	34.3102	−	14.2118i	1.72198	−	0.713268i	0.999767	−	0.0215980i	$-0.00687540\pi$
$398$	−0.136285	−	0.329021i	−0.00683135	−	0.0164923i
$399$	2.29204	+	2.29204i	0.114745	+	0.114745i
$400$	1.75677	+	4.68121i	0.0878387	+	0.234061i
$401$	11.9320	−	4.94241i	0.595858	−	0.246812i	−0.0643108	−	0.997930i	$-0.520485\pi$
$401$	11.9320	−	4.94241i	0.595858	−	0.246812i	0.660168	+	0.751118i	$0.270485\pi$
$402$	−0.817026	+	0.338423i	−0.0407496	+	0.0168790i
$403$	3.37953	−	8.15890i	0.168346	−	0.406424i
$404$			11.0547i			0.549993i
$405$	20.6255	+	14.2897i	1.02489	+	0.710063i
$406$	−9.20939	+	9.20939i	−0.457054	+	0.457054i
$407$		−	21.0966i		−	1.04572i
$408$	2.19891	−	8.63338i	0.108862	−	0.427416i
$409$	10.7462			0.531366			0.265683	−	0.964060i	$-0.414403\pi$
$409$	10.7462			0.531366			0.265683	+	0.964060i	$0.414403\pi$
$410$	8.55671	−	5.51127i	0.422586	−	0.272182i
$411$	3.65397	−	8.82147i	0.180237	−	0.435131i
$412$	−6.34442			−0.312567
$413$	−11.9671	+	28.8912i	−0.588864	+	1.42164i
$414$	4.74654	+	11.4592i	0.233280	+	0.563188i
$415$	33.2767	−	6.03845i	1.63349	−	0.296416i
$416$	3.68564	+	3.68564i	0.180704	+	0.180704i
$417$	−8.26607	+	8.26607i	−0.404791	+	0.404791i
$418$	−0.706309	−	1.70518i	−0.0345467	−	0.0834031i
$419$	0.821783	+	1.98396i	0.0401467	+	0.0969228i	0.942681	−	0.333695i	$-0.108296\pi$
$419$	0.821783	+	1.98396i	0.0401467	+	0.0969228i	−0.902534	+	0.430618i	$0.858296\pi$
$420$	−9.54817	+	13.7816i	−0.465903	+	0.672476i
$421$		−	27.9741i		−	1.36337i	−0.731644	−	0.681687i	$-0.761246\pi$
$421$		−	27.9741i		−	1.36337i	0.731644	−	0.681687i	$-0.238754\pi$
$422$	−10.4640	−	4.33435i	−0.509382	−	0.210993i
$423$	4.09594	+	4.09594i	0.199151	+	0.199151i
$424$	−13.7672			−0.668596
$425$	−19.7950	−	5.75815i	−0.960201	−	0.279311i
$426$	21.7150			1.05209
$427$	15.2723	+	15.2723i	0.739076	+	0.739076i
$428$	1.49630	+	0.619790i	0.0723266	+	0.0299587i
$429$			48.0837i			2.32150i
$430$	−4.29324	+	6.19679i	−0.207039	+	0.298836i
$431$	6.62107	+	15.9847i	0.318926	+	0.769955i	0.999312	+	0.0371008i	$0.0118123\pi$
$431$	6.62107	+	15.9847i	0.318926	+	0.769955i	−0.680386	+	0.732854i	$0.738188\pi$
$432$	−1.10071	−	2.65734i	−0.0529578	−	0.127851i
$433$	3.89798	−	3.89798i	0.187325	−	0.187325i	−0.607214	−	0.794539i	$-0.707713\pi$
$433$	3.89798	−	3.89798i	0.187325	−	0.187325i	0.794539	+	0.607214i	$0.207713\pi$
$434$	−4.15733	−	4.15733i	−0.199558	−	0.199558i
$435$	17.8426	−	3.23776i	0.855489	−	0.155239i
$436$	−3.17128	−	7.65614i	−0.151877	−	0.366663i
$437$	−1.22956	+	2.96843i	−0.0588180	+	0.141999i
$438$	−2.26935			−0.108434
$439$	2.10538	−	5.08283i	0.100484	−	0.242590i	−0.865640	−	0.500666i	$-0.833088\pi$
$439$	2.10538	−	5.08283i	0.100484	−	0.242590i	0.966125	+	0.258076i	$0.0830884\pi$
$440$	8.02591	−	5.16939i	0.382620	−	0.246441i
$441$	−8.41362			−0.400649
$442$	−21.2705	+	3.06918i	−1.01174	+	0.145986i
$443$		−	15.0462i		−	0.714865i	−0.933939	−	0.357433i	$-0.883652\pi$
$443$		−	15.0462i		−	0.714865i	0.933939	−	0.357433i	$-0.116348\pi$
$444$	−7.54983	+	7.54983i	−0.358299	+	0.358299i
$445$	26.7771	+	18.5517i	1.26936	+	0.879433i
$446$			17.3908i			0.823478i
$447$	−8.64472	+	20.8702i	−0.408881	+	0.987127i
$448$	3.20595	−	1.32795i	0.151467	−	0.0627397i
$449$	10.3001	−	4.26643i	0.486091	−	0.201345i	−0.126159	−	0.992010i	$-0.540265\pi$
$449$	10.3001	−	4.26643i	0.486091	−	0.201345i	0.612249	+	0.790665i	$0.290265\pi$
$450$	7.81223	−	2.93179i	0.368272	−	0.138206i
$451$	−13.7412	−	13.7412i	−0.647050	−	0.647050i
$452$	2.58618	+	6.24358i	0.121644	+	0.293673i
$453$	−34.6348	+	14.3462i	−1.62728	+	0.674043i
$454$	−11.0487	−	4.57652i	−0.518542	−	0.214787i
$455$	39.5285	+	8.55712i	1.85312	+	0.401164i
$456$	−0.357466	+	0.863000i	−0.0167399	+	0.0404137i
$457$	−15.4608	−	15.4608i	−0.723225	−	0.723225i	0.246036	−	0.969261i	$-0.420872\pi$
$457$	−15.4608	−	15.4608i	−0.723225	−	0.723225i	−0.969261	+	0.246036i	$0.920872\pi$
$458$		−	11.7643i		−	0.549710i
$459$	11.4923	+	2.92708i	0.536416	+	0.136624i
$460$	−16.2428	−	3.51624i	−0.757324	−	0.163945i
$461$	6.63452	−	6.63452i	0.309000	−	0.309000i	−0.535521	−	0.844522i	$-0.679885\pi$
$461$	6.63452	−	6.63452i	0.309000	−	0.309000i	0.844522	+	0.535521i	$0.179885\pi$
$462$	29.5751	+	12.2504i	1.37596	+	0.569940i
$463$	−19.1390			−0.889464			−0.444732	−	0.895664i	$-0.646701\pi$
$463$	−19.1390			−0.889464			−0.444732	+	0.895664i	$0.646701\pi$
$464$	−3.46752	−	1.43630i	−0.160976	−	0.0666784i
$465$	1.46160	+	8.05457i	0.0677801	+	0.373522i
$466$	21.6054	−	8.94925i	1.00085	−	0.414566i
$467$	14.0361	−	14.0361i	0.649512	−	0.649512i	−0.303363	−	0.952875i	$-0.598109\pi$
$467$	14.0361	−	14.0361i	0.649512	−	0.649512i	0.952875	+	0.303363i	$0.0981095\pi$
$468$	6.15078	−	6.15078i	0.284320	−	0.284320i
$469$	1.31212	−	0.543497i	0.0605880	−	0.0250964i
$470$	−7.63663	+	1.38576i	−0.352251	+	0.0639203i
$471$	5.79280	+	2.39946i	0.266918	+	0.110561i
$472$	−9.01174			−0.414799
$473$	13.2982	+	5.50828i	0.611450	+	0.253271i
$474$	0.873172	−	0.873172i	0.0401061	−	0.0401061i
$475$	1.96800	+	0.893960i	0.0902981	+	0.0410177i
$476$	−3.53137	+	13.8649i	−0.161860	+	0.635498i
$477$			22.9754i			1.05197i
$478$	9.33784	+	9.33784i	0.427103	+	0.427103i
$479$	−3.80402	+	9.18371i	−0.173810	+	0.419614i	−0.986646	−	0.162878i	$-0.947922\pi$
$479$	−3.80402	+	9.18371i	−0.173810	+	0.419614i	0.812836	+	0.582492i	$0.197922\pi$
$480$	−4.72221	−	1.02226i	−0.215538	−	0.0466597i
$481$	23.7953	+	9.85633i	1.08497	+	0.449410i
$482$	−20.9168	+	8.66402i	−0.952733	+	0.394635i
$483$	−21.3259	−	51.4852i	−0.970361	−	2.34266i
$484$	−5.11065	−	5.11065i	−0.232302	−	0.232302i
$485$	−11.7305	−	18.2125i	−0.532654	−	0.826989i
$486$	−14.4291	+	5.97675i	−0.654519	+	0.271111i
$487$	−8.06967	+	3.34257i	−0.365672	+	0.151466i	−0.557951	−	0.829874i	$-0.688412\pi$
$487$	−8.06967	+	3.34257i	−0.365672	+	0.151466i	0.192279	+	0.981340i	$0.438412\pi$
$488$	−2.38186	+	5.75032i	−0.107822	+	0.260305i
$489$			8.10601i			0.366566i
$490$	6.42007	−	9.26660i	0.290029	−	0.418622i
$491$	−1.63435	+	1.63435i	−0.0737571	+	0.0737571i	−0.743023	−	0.669266i	$-0.766609\pi$
$491$	−1.63435	+	1.63435i	−0.0737571	+	0.0737571i	0.669266	+	0.743023i	$0.266609\pi$
$492$			9.83517i			0.443404i
$493$	13.3047	−	7.90310i	0.599213	−	0.355938i
$494$	2.25330			0.101381
$495$	−8.62693	−	13.3940i	−0.387752	−	0.602017i
$496$	0.648377	−	1.56532i	0.0291130	−	0.0702849i
$497$	−34.8736			−1.56429
$498$	−12.5065	+	30.1933i	−0.560428	+	1.35299i
$499$	11.1408	+	26.8962i	0.498730	+	1.20404i	0.950168	+	0.311738i	$0.100911\pi$
$499$	11.1408	+	26.8962i	0.498730	+	1.20404i	−0.451438	+	0.892303i	$0.649089\pi$
$500$	−2.73216	+	10.8414i	−0.122186	+	0.484841i
$501$	−36.0536	−	36.0536i	−1.61076	−	1.61076i
$502$	−2.21357	+	2.21357i	−0.0987965	+	0.0987965i
$503$	11.5670	+	27.9252i	0.515747	+	1.24512i	0.940494	+	0.339811i	$0.110363\pi$
$503$	11.5670	+	27.9252i	0.515747	+	1.24512i	−0.424747	+	0.905312i	$0.639637\pi$
$504$	−2.21615	−	5.35025i	−0.0987150	−	0.238319i
$505$	−14.0774	+	20.3190i	−0.626434	+	0.904183i
$506$			31.7311i			1.41062i
$507$	−28.2831	−	11.7153i	−1.25610	−	0.520293i
$508$	1.28241	+	1.28241i	0.0568978	+	0.0568978i
$509$	37.2373			1.65052			0.825258	−	0.564756i	$-0.191030\pi$
$509$	37.2373			1.65052			0.825258	+	0.564756i	$0.191030\pi$
$510$	15.0356	−	13.0683i	0.665789	−	0.578676i
$511$	3.64450			0.161223
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.14878	−	0.475842i	−0.0507200	−	0.0210089i
$514$		−	8.21104i		−	0.362173i
$515$	−11.6613	−	8.07915i	−0.513858	−	0.356010i
$516$	−2.78777	−	6.73026i	−0.122725	−	0.296283i
$517$	5.67095	+	13.6909i	0.249408	+	0.602124i
$518$	12.1248	−	12.1248i	0.532732	−	0.532732i
$519$	23.0645	+	23.0645i	1.01242	+	1.01242i
$520$	2.08096	+	11.4678i	0.0912563	+	0.502894i
$521$	3.27311	+	7.90198i	0.143398	+	0.346192i	0.979218	−	0.202811i	$-0.0650076\pi$
$521$	3.27311	+	7.90198i	0.143398	+	0.346192i	−0.835820	+	0.549003i	$0.815008\pi$
$522$	−2.39696	+	5.78677i	−0.104912	+	0.253280i
$523$	−39.2933			−1.71818			−0.859088	−	0.511828i	$-0.828969\pi$
$523$	−39.2933			−1.71818			−0.859088	+	0.511828i	$0.828969\pi$
$524$	1.64998	−	3.98341i	0.0720798	−	0.174016i
$525$	−35.0998	+	13.1723i	−1.53188	+	0.574887i
$526$	−25.2134			−1.09936
$527$	3.56764	+	6.00604i	0.155409	+	0.261627i
$528$			9.22506i			0.401469i
$529$	22.7960	−	22.7960i	0.991133	−	0.991133i
$530$	−25.3047	−	17.5315i	−1.09917	−	0.761522i
$531$			15.0392i			0.652647i
$532$	0.574079	−	1.38595i	0.0248895	−	0.0600886i
$533$	21.9190	−	9.07915i	0.949417	−	0.393261i
$534$	−29.0823	+	12.0463i	−1.25852	+	0.521294i
$535$	1.96101	+	3.04463i	0.0847819	+	0.131631i
$536$	0.289402	+	0.289402i	0.0125002	+	0.0125002i
$537$	10.5202	+	25.3980i	0.453979	+	1.09600i
$538$	13.8234	−	5.72583i	0.595969	−	0.246858i
$539$	−19.8859	−	8.23701i	−0.856547	−	0.354793i
$540$	1.36079	−	6.28597i	0.0585589	−	0.270505i
$541$	11.7894	−	28.4621i	0.506866	−	1.22368i	−0.438813	−	0.898579i	$-0.644601\pi$
$541$	11.7894	−	28.4621i	0.506866	−	1.22368i	0.945678	−	0.325104i	$-0.105399\pi$
$542$	−1.25177	−	1.25177i	−0.0537681	−	0.0537681i
$543$			33.4792i			1.43673i
$544$	−4.08084	+	0.588835i	−0.174965	+	0.0252461i
$545$	3.92059	−	18.1107i	0.167940	−	0.775776i
$546$	−27.6350	+	27.6350i	−1.18267	+	1.18267i
$547$	5.07321	+	2.10139i	0.216915	+	0.0898491i	0.488495	−	0.872567i	$-0.337546\pi$
$547$	5.07321	+	2.10139i	0.216915	+	0.0898491i	−0.271580	+	0.962416i	$0.587546\pi$
$548$	−4.41897			−0.188769
$549$	9.59641	+	3.97496i	0.409565	+	0.169647i
$550$	21.3348	+	0.718856i	0.909717	+	0.0306521i
$551$	−1.49903	+	0.620918i	−0.0638608	+	0.0264520i
$552$	11.3556	−	11.3556i	0.483327	−	0.483327i
$553$	−1.40228	+	1.40228i	−0.0596312	+	0.0596312i
$554$	14.7015	−	6.08957i	0.624608	−	0.258721i
$555$	−23.4910	+	4.26273i	−0.997139	+	0.180943i
$556$	4.99833	+	2.07037i	0.211976	+	0.0878034i
$557$	−9.65747			−0.409200			−0.204600	−	0.978846i	$-0.565589\pi$
$557$	−9.65747			−0.409200			−0.204600	+	0.978846i	$0.565589\pi$
$558$	−2.61228	−	1.08204i	−0.110587	−	0.0458065i
$559$	−12.4258	+	12.4258i	−0.525556	+	0.525556i
$560$	7.58371	+	1.64172i	0.320470	+	0.0693753i
$561$	−30.4608	−	22.7787i	−1.28606	−	0.961718i
$562$		−	2.49357i		−	0.105185i
$563$	13.5365	+	13.5365i	0.570496	+	0.570496i	0.932267	−	0.361771i	$-0.117828\pi$
$563$	13.5365	+	13.5365i	0.570496	+	0.570496i	−0.361771	+	0.932267i	$0.617828\pi$
$564$	2.87009	−	6.92902i	0.120853	−	0.291764i
$565$	−3.19725	+	14.7693i	−0.134509	+	0.621347i
$566$	16.6129	+	6.88128i	0.698292	+	0.289242i
$567$	35.9756	−	14.9016i	1.51083	−	0.625807i
$568$	−3.84587	−	9.28474i	−0.161369	−	0.389579i
$569$	−16.9921	−	16.9921i	−0.712348	−	0.712348i	0.254678	−	0.967026i	$-0.418030\pi$
$569$	−16.9921	−	16.9921i	−0.712348	−	0.712348i	−0.967026	+	0.254678i	$0.918030\pi$
$570$	−1.75600	+	1.13102i	−0.0735509	+	0.0473733i
$571$	12.8892	−	5.33889i	0.539397	−	0.223426i	−0.0963163	−	0.995351i	$-0.530706\pi$
$571$	12.8892	−	5.33889i	0.539397	−	0.223426i	0.635713	+	0.771925i	$0.280706\pi$
$572$	20.5593	−	8.51593i	0.859627	−	0.356069i
$573$	6.98300	−	16.8585i	0.291719	−	0.704272i
$574$		−	15.7950i		−	0.659269i
$575$	−25.3772	−	27.1470i	−1.05830	−	1.13211i
$576$	1.18005	−	1.18005i	0.0491689	−	0.0491689i
$577$		−	14.4087i		−	0.599842i	−0.953964	−	0.299921i	$-0.903040\pi$
$577$		−	14.4087i		−	0.599842i	0.953964	−	0.299921i	$-0.0969603\pi$
$578$	8.13219	−	14.9287i	0.338255	−	0.620954i
$579$	46.1132			1.91640
$580$	−4.54443	−	7.05560i	−0.188697	−	0.292968i
$581$	20.0850	−	48.4894i	0.833265	−	2.01168i
$582$	20.9337			0.867729
$583$	−22.4932	+	54.3033i	−0.931571	+	2.24901i
$584$	0.401916	+	0.970312i	0.0166314	+	0.0401518i
$585$	19.1379	−	3.47281i	0.791257	−	0.143583i
$586$	4.74825	+	4.74825i	0.196149	+	0.196149i
$587$	−9.34651	+	9.34651i	−0.385772	+	0.385772i	−0.873176	−	0.487405i	$-0.837944\pi$
$587$	−9.34651	+	9.34651i	−0.385772	+	0.385772i	0.487405	+	0.873176i	$0.337944\pi$
$588$	4.16879	+	10.0644i	0.171918	+	0.415047i
$589$	−0.280297	−	0.676696i	−0.0115494	−	0.0278828i
$590$	−16.5639	−	11.4758i	−0.681926	−	0.472450i
$591$		−	1.95080i		−	0.0802453i
$592$	4.56523	+	1.89098i	0.187630	+	0.0777188i
$593$	23.3715	+	23.3715i	0.959754	+	0.959754i	0.999221	−	0.0394671i	$-0.0125660\pi$
$593$	23.3715	+	23.3715i	0.959754	+	0.959754i	−0.0394671	+	0.999221i	$0.512566\pi$
$594$	−12.2799			−0.503852
$595$	−24.1467	+	20.9873i	−0.989920	+	0.860397i
$596$	10.4546			0.428236
$597$	0.544125	+	0.544125i	0.0222695	+	0.0222695i
$598$	−35.7902	−	14.8248i	−1.46357	−	0.606231i
$599$			14.3939i			0.588118i	0.955787	+	0.294059i	$0.0950062\pi$
$599$			14.3939i			0.588118i	−0.955787	+	0.294059i	$0.904994\pi$
$600$	−7.37782	−	7.89234i	−0.301198	−	0.322203i
$601$	14.6516	+	35.3721i	0.597652	+	1.44286i	0.875968	+	0.482370i	$0.160224\pi$
$601$	14.6516	+	35.3721i	0.597652	+	1.44286i	−0.278316	+	0.960490i	$0.589776\pi$
$602$	4.47706	+	10.8086i	0.182471	+	0.440525i
$603$	0.482967	−	0.482967i	0.0196680	−	0.0196680i
$604$	12.2681	+	12.2681i	0.499182	+	0.499182i
$605$	−2.88554	−	15.9016i	−0.117314	−	0.646493i
$606$	−9.14097	−	22.0682i	−0.371326	−	0.896461i
$607$	6.37537	−	15.3915i	0.258768	−	0.624722i	−0.740089	−	0.672509i	$-0.765217\pi$
$607$	6.37537	−	15.3915i	0.258768	−	0.624722i	0.998858	+	0.0477868i	$0.0152168\pi$
$608$	0.432305			0.0175323
$609$	10.7694	−	25.9996i	0.436397	−	1.05356i
$610$	−11.7006	+	7.53619i	−0.473742	+	0.305131i
$611$	−18.0917			−0.731913
$612$	0.982677	+	6.81031i	0.0397224	+	0.275290i
$613$		−	0.270516i		−	0.0109261i	−0.999985	−	0.00546303i	$-0.998261\pi$
$613$		−	0.270516i		−	0.0109261i	0.999985	−	0.00546303i	$-0.00173894\pi$
$614$	24.0318	−	24.0318i	0.969844	−	0.969844i
$615$	−12.5244	+	18.0774i	−0.505031	+	0.728952i
$616$		−	14.8151i		−	0.596919i
$617$	13.8689	−	33.4825i	0.558340	−	1.34795i	−0.352739	−	0.935722i	$-0.614750\pi$
$617$	13.8689	−	33.4825i	0.558340	−	1.34795i	0.911079	−	0.412231i	$-0.135250\pi$
$618$	12.6652	−	5.24610i	0.509469	−	0.211029i
$619$	−2.78040	+	1.15168i	−0.111754	+	0.0462899i	−0.437860	−	0.899043i	$-0.644263\pi$
$619$	−2.78040	+	1.15168i	−0.111754	+	0.0462899i	0.326106	+	0.945333i	$0.394263\pi$
$620$	3.18506	−	2.05146i	0.127915	−	0.0823886i
$621$	15.1160	+	15.1160i	0.606586	+	0.606586i
$622$	−9.96849	−	24.0661i	−0.399700	−	0.964961i
$623$	46.7053	−	19.3460i	1.87121	−	0.775080i
$624$	−10.4052	−	4.30996i	−0.416540	−	0.172536i
$625$	−18.8275	+	16.4477i	−0.753100	+	0.657906i
$626$	−0.809278	+	1.95377i	−0.0323453	+	0.0780884i
$627$	2.81997	+	2.81997i	0.112619	+	0.112619i
$628$		−	2.90181i		−	0.115795i
$629$	−17.5165	+	10.4050i	−0.698429	+	0.414873i
$630$	2.73978	−	12.6561i	0.109156	−	0.504229i
$631$	−14.7927	+	14.7927i	−0.588890	+	0.588890i	−0.937331	−	0.348441i	$-0.886711\pi$
$631$	−14.7927	+	14.7927i	−0.588890	+	0.588890i	0.348441	+	0.937331i	$0.386711\pi$
$632$	−0.527989	−	0.218700i	−0.0210023	−	0.00869943i
$633$	24.4731			0.972719
$634$	−7.50100	−	3.10702i	−0.297903	−	0.123395i
$635$	0.724067	+	3.99018i	0.0287337	+	0.158345i
$636$	27.4832	−	11.3839i	1.08978	−	0.451401i
$637$	18.5814	−	18.5814i	0.736223	−	0.736223i
$638$	−11.3306	+	11.3306i	−0.448583	+	0.448583i
$639$	−15.4948	+	6.41817i	−0.612966	+	0.253899i
$640$	0.399242	+	2.20014i	0.0157814	+	0.0869681i
$641$	−22.3306	−	9.24965i	−0.882007	−	0.365339i	−0.104732	−	0.994500i	$-0.533399\pi$
$641$	−22.3306	−	9.24965i	−0.882007	−	0.365339i	−0.777275	+	0.629161i	$0.783399\pi$
$642$	−3.49953			−0.138115
$643$	11.6947	+	4.84409i	0.461193	+	0.191032i	0.601168	−	0.799123i	$-0.294702\pi$
$643$	11.6947	+	4.84409i	0.461193	+	0.191032i	−0.139975	+	0.990155i	$0.544702\pi$
$644$	−18.2367	+	18.2367i	−0.718629	+	0.718629i
$645$	3.44647	−	15.9205i	0.135705	−	0.626869i
$646$	−1.06746	+	1.42746i	−0.0419986	+	0.0561625i
$647$		−	11.1531i		−	0.438472i	−0.975672	−	0.219236i	$-0.929643\pi$
$647$		−	11.1531i		−	0.438472i	0.975672	−	0.219236i	$-0.0703565\pi$
$648$	7.93479	+	7.93479i	0.311708	+	0.311708i
$649$	−14.7235	+	35.5458i	−0.577950	+	1.39529i
$650$	−10.7784	+	23.7281i	−0.422765	+	0.930694i
$651$	11.7368	+	4.86154i	0.460001	+	0.190539i
$652$	3.46591	−	1.43563i	0.135736	−	0.0562235i
$653$	−11.3392	−	27.3752i	−0.443736	−	1.07127i	−0.974627	−	0.223834i	$-0.928143\pi$
$653$	−11.3392	−	27.3752i	−0.443736	−	1.07127i	0.530891	−	0.847440i	$-0.321857\pi$
$654$	12.6615	+	12.6615i	0.495103	+	0.495103i
$655$	8.10531	−	5.22053i	0.316701	−	0.203983i
$656$	4.20525	−	1.74187i	0.164188	−	0.0680087i
$657$	1.61930	−	0.670737i	0.0631750	−	0.0261680i
$658$	−4.60928	+	11.1278i	−0.179688	+	0.433806i
$659$		−	30.0437i		−	1.17034i	−0.810912	−	0.585169i	$-0.801028\pi$
$659$		−	30.0437i		−	1.17034i	0.810912	−	0.585169i	$-0.198972\pi$
$660$	−11.7474	+	16.9560i	−0.457268	+	0.660012i
$661$	−20.9920	+	20.9920i	−0.816494	+	0.816494i	−0.985598	−	0.169104i	$-0.945913\pi$
$661$	−20.9920	+	20.9920i	−0.816494	+	0.816494i	0.169104	+	0.985598i	$0.445913\pi$
$662$			0.262853i			0.0102161i
$663$	39.9240	−	23.7152i	1.55052	−	0.921021i
$664$	15.1248			0.586956
$665$	2.82008	−	1.81638i	0.109358	−	0.0704363i
$666$	3.15576	−	7.61868i	0.122283	−	0.295218i
$667$	27.8949			1.08010
$668$	−9.03022	+	21.8009i	−0.349390	+	0.843501i
$669$	−14.3802	−	34.7168i	−0.555969	−	1.34223i
$670$	0.163400	+	0.900463i	0.00631269	+	0.0347879i
$671$	18.7900	+	18.7900i	0.725378	+	0.725378i
$672$	−5.30190	+	5.30190i	−0.204525	+	0.204525i
$673$	−14.4888	−	34.9790i	−0.558502	−	1.34834i	−0.910952	−	0.412513i	$-0.864651\pi$
$673$	−14.4888	−	34.9790i	−0.558502	−	1.34834i	0.352450	−	0.935831i	$-0.385349\pi$
$674$	8.05310	+	19.4419i	0.310194	+	0.748874i
$675$	10.5059	−	9.82100i	0.404372	−	0.378010i
$676$			14.1680i			0.544921i
$677$	−0.664177	−	0.275111i	−0.0255264	−	0.0105734i	0.369884	−	0.929078i	$-0.379398\pi$
$677$	−0.664177	−	0.275111i	−0.0255264	−	0.0105734i	−0.395410	+	0.918505i	$0.629398\pi$
$678$	−10.3254	−	10.3254i	−0.396546	−	0.396546i
$679$	−33.6188			−1.29017
$680$	−8.25058	−	4.11435i	−0.316395	−	0.157778i
$681$	25.8405			0.990210
$682$	−5.11490	−	5.11490i	−0.195860	−	0.195860i
$683$	−34.0830	−	14.1176i	−1.30415	−	0.540197i	−0.380979	−	0.924584i	$-0.624413\pi$
$683$	−34.0830	−	14.1176i	−1.30415	−	0.540197i	−0.923172	+	0.384387i	$0.874413\pi$
$684$		−	0.721452i		−	0.0275854i
$685$	−8.12223	−	5.62723i	−0.310335	−	0.215005i
$686$	2.60069	+	6.27863i	0.0992949	+	0.239719i
$687$	9.72771	+	23.4848i	0.371135	+	0.896000i
$688$	−2.38395	+	2.38395i	−0.0908872	+	0.0908872i
$689$	−50.7411	−	50.7411i	−1.93308	−	1.93308i
$690$	35.3326	−	6.41153i	1.34509	−	0.244083i
$691$	14.8476	+	35.8452i	0.564828	+	1.36362i	0.905866	+	0.423565i	$0.139222\pi$
$691$	14.8476	+	35.8452i	0.564828	+	1.36362i	−0.341038	+	0.940050i	$0.610778\pi$
$692$	5.77690	−	13.9467i	0.219605	−	0.530173i
$693$	−24.7242			−0.939196
$694$	−13.4154	+	32.3876i	−0.509241	+	1.22942i
$695$	6.55065	+	10.1704i	0.248480	+	0.385786i
$696$	8.10978			0.307400
$697$	−4.63211	+	18.1867i	−0.175454	+	0.688869i
$698$			35.1004i			1.32857i
$699$	−35.7303	+	35.7303i	−1.35145	+	1.35145i
$700$	11.8485	+	12.6748i	0.447833	+	0.479064i
$701$		−	20.7195i		−	0.782566i	−0.920270	−	0.391283i	$-0.872031\pi$
$701$		−	20.7195i		−	0.782566i	0.920270	−	0.391283i	$-0.127969\pi$
$702$	5.73721	−	13.8508i	0.216537	−	0.522766i
$703$	1.97357	−	0.817481i	0.0744347	−	0.0308319i
$704$	3.94439	−	1.63382i	0.148660	−	0.0615769i
$705$	14.0989	−	9.08096i	0.530997	−	0.342009i
$706$	−11.8728	−	11.8728i	−0.446838	−	0.446838i
$707$	14.6801	+	35.4409i	0.552102	+	1.33289i
$708$	17.9899	−	7.45166i	0.676102	−	0.280051i
$709$	−11.7625	−	4.87221i	−0.441752	−	0.182980i	0.150710	−	0.988578i	$-0.451844\pi$
$709$	−11.7625	−	4.87221i	−0.441752	−	0.182980i	−0.592462	+	0.805598i	$0.701844\pi$
$710$	4.75458	−	21.9631i	0.178436	−	0.824262i
$711$	−0.364978	+	0.881134i	−0.0136877	+	0.0330451i
$712$	10.3013	+	10.3013i	0.386059	+	0.386059i
$713$			12.5924i			0.471589i
$714$	−4.41510	−	30.5982i	−0.165231	−	1.14511i
$715$	48.6332	+	10.5281i	1.81878	+	0.393729i
$716$	8.99629	−	8.99629i	0.336207	−	0.336207i
$717$	−26.3622	−	10.9196i	−0.984515	−	0.407799i
$718$	24.3218			0.907681
$719$	−20.3836	−	8.44316i	−0.760179	−	0.314877i	−0.0312920	−	0.999510i	$-0.509962\pi$
$719$	−20.3836	−	8.44316i	−0.760179	−	0.314877i	−0.728887	+	0.684634i	$0.759962\pi$
$720$	3.67170	−	0.666274i	0.136836	−	0.0248306i
$721$	−20.3399	+	8.42507i	−0.757498	+	0.313766i
$722$	−13.3029	+	13.3029i	−0.495082	+	0.495082i
$723$	34.5915	−	34.5915i	1.28647	−	1.28647i
$724$	14.3148	−	5.92939i	0.532006	−	0.220364i
$725$	0.631949	−	18.7555i	0.0234700	−	0.696560i
$726$	14.4282	+	5.97635i	0.535480	+	0.221803i
$727$	23.3953			0.867682			0.433841	−	0.900989i	$-0.357158\pi$
$727$	23.3953			0.867682			0.433841	+	0.900989i	$0.357158\pi$
$728$	16.7103	+	6.92165i	0.619327	+	0.256533i
$729$	0.0580801	−	0.0580801i	0.00215111	−	0.00215111i
$730$	−0.496882	+	2.29528i	−0.0183904	+	0.0849522i
$731$	−1.98521	−	13.7582i	−0.0734255	−	0.508865i
$732$		−	13.4487i		−	0.497080i
$733$	−21.9647	−	21.9647i	−0.811283	−	0.811283i	0.173543	−	0.984826i	$-0.444478\pi$
$733$	−21.9647	−	21.9647i	−0.811283	−	0.811283i	−0.984826	+	0.173543i	$0.944478\pi$
$734$	7.31730	−	17.6655i	0.270086	−	0.652046i
$735$	−5.15381	+	23.8073i	−0.190101	+	0.878147i
$736$	−6.86651	−	2.84420i	−0.253103	−	0.104839i
$737$	1.61434	−	0.668682i	0.0594650	−	0.0246312i
$738$	−2.90692	−	7.01793i	−0.107005	−	0.258334i
$739$	5.46858	+	5.46858i	0.201165	+	0.201165i	0.800499	−	0.599334i	$-0.204568\pi$
$739$	5.46858	+	5.46858i	0.201165	+	0.201165i	−0.599334	+	0.800499i	$0.704568\pi$
$740$	5.98305	+	9.28917i	0.219941	+	0.341477i
$741$	−4.49821	+	1.86322i	−0.165246	+	0.0684470i
$742$	−44.1371	+	18.2822i	−1.62032	+	0.671160i
$743$	−12.6211	+	30.4700i	−0.463023	+	1.11784i	0.504127	+	0.863629i	$0.331814\pi$
$743$	−12.6211	+	30.4700i	−0.463023	+	1.11784i	−0.967150	+	0.254206i	$0.918186\pi$
$744$			3.66094i			0.134217i
$745$	19.2159	+	13.3131i	0.704017	+	0.487755i
$746$	4.55260	−	4.55260i	0.166683	−	0.166683i
$747$		−	25.2410i		−	0.923520i
$748$	−4.34476	+	17.0585i	−0.158860	+	0.623720i
$749$	5.62013			0.205355
$750$	−3.51042	−	23.9015i	−0.128182	−	0.872760i
$751$	13.6564	−	32.9695i	0.498329	−	1.20307i	−0.452054	−	0.891991i	$-0.649308\pi$
$751$	13.6564	−	32.9695i	0.498329	−	1.20307i	0.950383	−	0.311083i	$-0.100692\pi$
$752$	−3.47098			−0.126573
$753$	2.58853	−	6.24926i	0.0943312	−	0.227736i
$754$	−7.48639	−	18.0737i	−0.272638	−	0.658207i
$755$	6.92673	+	38.1718i	0.252090	+	1.38921i
$756$	−7.05763	−	7.05763i	−0.256684	−	0.256684i
$757$	−36.8619	+	36.8619i	−1.33977	+	1.33977i	−0.443491	+	0.896279i	$0.646260\pi$
$757$	−36.8619	+	36.8619i	−1.33977	+	1.33977i	−0.896279	+	0.443491i	$0.853740\pi$
$758$	−6.39249	−	15.4328i	−0.232186	−	0.560546i
$759$	−26.2379	−	63.3440i	−0.952377	−	2.29924i
$760$	0.794594	+	0.550509i	0.0288230	+	0.0199691i
$761$			30.3827i			1.10137i	0.834713	+	0.550686i	$0.185634\pi$
$761$			30.3827i			1.10137i	−0.834713	+	0.550686i	$0.814366\pi$
$762$	−3.62045	−	1.49964i	−0.131155	−	0.0543262i
$763$	−20.3339	−	20.3339i	−0.736137	−	0.736137i
$764$	−8.44496			−0.305528
$765$	−6.86622	+	13.7690i	−0.248249	+	0.497818i
$766$	−0.996123			−0.0359914
$767$	−33.2141	−	33.2141i	−1.19929	−	1.19929i
$768$	−1.99627	−	0.826884i	−0.0720343	−	0.0298376i
$769$		−	16.6957i		−	0.602063i	−0.953614	−	0.301031i	$-0.902669\pi$
$769$		−	16.6957i		−	0.602063i	0.953614	−	0.301031i	$-0.0973309\pi$
$770$	18.8660	−	27.2308i	0.679883	−	0.981330i
$771$	6.78958	+	16.3915i	0.244521	+	0.590325i
$772$	−8.16694	−	19.7167i	−0.293935	−	0.709621i
$773$	16.1621	−	16.1621i	0.581312	−	0.581312i	−0.353952	−	0.935264i	$-0.615162\pi$
$773$	16.1621	−	16.1621i	0.581312	−	0.581312i	0.935264	+	0.353952i	$0.115162\pi$
$774$	3.97845	+	3.97845i	0.143002	+	0.143002i
$775$	8.46665	+	0.285276i	0.304131	+	0.0102474i
$776$	−3.70749	−	8.95068i	−0.133091	−	0.321311i
$777$	−14.1786	+	34.2302i	−0.508654	+	1.22800i
$778$	−9.90051			−0.354950
$779$	0.753021	−	1.81795i	0.0269798	−	0.0651350i
$780$	−13.6367	−	21.1721i	−0.488271	−	0.758082i
$781$	−42.9061			−1.53530
$782$	26.3464	−	15.6500i	0.942145	−	0.559642i
$783$			10.7953i			0.385794i
$784$	3.56493	−	3.56493i	0.127319	−	0.127319i
$785$	3.69524	−	5.33363i	0.131889	−	0.190366i
$786$			9.31633i			0.332302i
$787$	−0.207485	+	0.500913i	−0.00739604	+	0.0178556i	−0.927534	−	0.373738i	$-0.878076\pi$
$787$	−0.207485	+	0.500913i	−0.00739604	+	0.0178556i	0.920138	+	0.391593i	$0.128076\pi$
$788$	−0.834111	+	0.345500i	−0.0297140	+	0.0123079i
$789$	50.3329	−	20.8486i	1.79190	−	0.742229i
$790$	−0.691966	−	1.07433i	−0.0246190	−	0.0382231i
$791$	16.5823	+	16.5823i	0.589599	+	0.589599i
$792$	−2.72660	−	6.58259i	−0.0968854	−	0.233902i
$793$	−29.9723	+	12.4149i	−1.06435	+	0.440867i
$794$	34.3102	+	14.2118i	1.21762	+	0.504356i
$795$	65.0117	+	14.0737i	2.30573	+	0.499143i
$796$	0.136285	−	0.329021i	0.00483049	−	0.0116618i
$797$	30.3202	+	30.3202i	1.07400	+	1.07400i	0.997034	+	0.0769632i	$0.0245224\pi$
$797$	30.3202	+	30.3202i	1.07400	+	1.07400i	0.0769632	+	0.997034i	$0.475478\pi$
$798$			3.24143i			0.114745i
$799$	8.57061	−	11.4610i	0.303206	−	0.405462i
$800$	−2.06789	+	4.55234i	−0.0731110	+	0.160950i
$801$	17.1914	−	17.1914i	0.607428	−	0.607428i
$802$	11.9320	+	4.94241i	0.421335	+	0.174523i
$803$	4.48394			0.158235
$804$	−0.817026	−	0.338423i	−0.0288143	−	0.0119353i
$805$	−56.7430	+	10.2967i	−1.99993	+	0.362911i
$806$	8.15890	−	3.37953i	0.287385	−	0.119039i
$807$	−22.8607	+	22.8607i	−0.804734	+	0.804734i
$808$	−7.81686	+	7.81686i	−0.274996	+	0.274996i
$809$	20.9224	−	8.66632i	0.735591	−	0.304692i	0.0167436	−	0.999860i	$-0.494670\pi$
$809$	20.9224	−	8.66632i	0.735591	−	0.304692i	0.718847	+	0.695168i	$0.244670\pi$
$810$	4.48009	+	24.6888i	0.157414	+	0.867477i
$811$	17.2005	+	7.12470i	0.603993	+	0.250182i	0.663658	−	0.748036i	$-0.269003\pi$
$811$	17.2005	+	7.12470i	0.603993	+	0.250182i	−0.0596648	+	0.998218i	$0.519003\pi$
$812$	−13.0240			−0.457054
$813$	3.53394	+	1.46381i	0.123941	+	0.0513380i
$814$	14.9175	−	14.9175i	0.522859	−	0.522859i
$815$	8.19864	+	1.77484i	0.287186	+	0.0621700i
$816$	7.65958	−	4.54986i	0.268139	−	0.159277i
$817$			1.45748i			0.0509907i
$818$	7.59872	+	7.59872i	0.265683	+	0.265683i
$819$	11.5512	−	27.8870i	0.403631	−	0.974452i
$820$	9.94757	+	2.15345i	0.347384	+	0.0752017i
$821$	−8.29260	−	3.43491i	−0.289414	−	0.119879i	0.233253	−	0.972416i	$-0.425063\pi$
$821$	−8.29260	−	3.43491i	−0.289414	−	0.119879i	−0.522667	+	0.852537i	$0.675063\pi$
$822$	8.82147	−	3.65397i	0.307684	−	0.127447i
$823$	4.41319	+	10.6544i	0.153834	+	0.371389i	0.981943	−	0.189179i	$-0.0605828\pi$
$823$	4.41319	+	10.6544i	0.153834	+	0.371389i	−0.828108	+	0.560568i	$0.810583\pi$
$824$	−4.48618	−	4.48618i	−0.156284	−	0.156284i
$825$	−43.1845	+	16.2063i	−1.50349	+	0.564232i
$826$	−28.8912	+	11.9671i	−1.00525	+	0.416389i
$827$	7.64533	−	3.16680i	0.265854	−	0.110120i	−0.245775	−	0.969327i	$-0.579042\pi$
$827$	7.64533	−	3.16680i	0.265854	−	0.110120i	0.511629	+	0.859207i	$0.329042\pi$
$828$	−4.74654	+	11.4592i	−0.164954	+	0.398234i
$829$			11.0240i			0.382880i	0.981504	+	0.191440i	$0.0613157\pi$
$829$			11.0240i			0.382880i	−0.981504	+	0.191440i	$0.938684\pi$
$830$	27.8000	+	19.2603i	0.964951	+	0.668535i
$831$	−24.3129	+	24.3129i	−0.843406	+	0.843406i
$832$			5.21229i			0.180704i
$833$	2.96865	+	20.5739i	0.102858	+	0.712842i
$834$	−11.6900			−0.404791
$835$	−44.3597	+	28.5715i	−1.53513	+	0.988759i
$836$	0.706309	−	1.70518i	0.0244282	−	0.0589749i
$837$	−4.87327			−0.168445
$838$	−0.821783	+	1.98396i	−0.0283880	+	0.0685348i
$839$	14.9538	+	36.1016i	0.516262	+	1.24637i	0.940184	+	0.340667i	$0.110653\pi$
$839$	14.9538	+	36.1016i	0.516262	+	1.24637i	−0.423922	+	0.905699i	$0.639347\pi$
$840$	−16.4967	+	2.99352i	−0.569189	+	0.103286i
$841$	−10.5453	−	10.5453i	−0.363632	−	0.363632i
$842$	19.7807	−	19.7807i	0.681687	−	0.681687i
$843$	2.06189	+	4.97785i	0.0710153	+	0.171446i
$844$	−4.33435	−	10.4640i	−0.149194	−	0.360187i
$845$	−18.0418	+	26.0412i	−0.620658	+	0.895846i
$846$			5.79253i			0.199151i
$847$	−23.1712	−	9.59782i	−0.796172	−	0.329785i
$848$	−9.73490	−	9.73490i	−0.334298	−	0.334298i
$849$	−38.8539			−1.33346
$850$	−9.92558	−	18.0688i	−0.340445	−	0.619756i
$851$	−36.7255			−1.25894
$852$	15.3548	+	15.3548i	0.526047	+	0.526047i
$853$	−34.8497	−	14.4352i	−1.19323	−	0.494252i	−0.304424	−	0.952536i	$-0.598464\pi$
$853$	−34.8497	−	14.4352i	−1.19323	−	0.494252i	−0.888806	+	0.458284i	$0.848464\pi$
$854$			21.5982i			0.739076i
$855$	0.918716	−	1.32606i	0.0314194	−	0.0453502i
$856$	0.619790	+	1.49630i	0.0211840	+	0.0511426i
$857$	−12.4506	−	30.0585i	−0.425305	−	1.02678i	−0.980758	−	0.195230i	$-0.937455\pi$
$857$	−12.4506	−	30.0585i	−0.425305	−	1.02678i	0.555452	−	0.831548i	$-0.312545\pi$
$858$	−34.0003	+	34.0003i	−1.16075	+	1.16075i
$859$	2.67780	+	2.67780i	0.0913655	+	0.0913655i	0.751312	−	0.659947i	$-0.229421\pi$
$859$	2.67780	+	2.67780i	0.0913655	+	0.0913655i	−0.659947	+	0.751312i	$0.729421\pi$
$860$	−7.41757	+	1.34601i	−0.252937	+	0.0458985i
$861$	13.0606	+	31.5311i	0.445104	+	1.07458i
$862$	−6.62107	+	15.9847i	−0.225515	+	0.544440i
$863$	−27.0902			−0.922163			−0.461081	−	0.887358i	$-0.652538\pi$
$863$	−27.0902			−0.922163			−0.461081	+	0.887358i	$0.652538\pi$
$864$	1.10071	−	2.65734i	0.0374468	−	0.0904047i
$865$	28.3782	−	18.2781i	0.964888	−	0.621473i
$866$	5.51258			0.187325
$867$	−3.88975	+	36.5263i	−0.132103	+	1.24050i
$868$		−	5.87935i		−	0.199558i
$869$	−1.72528	+	1.72528i	−0.0585260	+	0.0585260i
$870$	14.9061	+	10.3272i	0.505364	+	0.350125i
$871$			2.13326i			0.0722828i
$872$	3.17128	−	7.65614i	0.107393	−	0.259270i
$873$	−14.9373	+	6.18725i	−0.505552	+	0.209407i
$874$	−2.96843	+	1.22956i	−0.100409	+	0.0415906i
$875$	5.63762	+	38.3851i	0.190586	+	1.29765i
$876$	−1.60467	−	1.60467i	−0.0542168	−	0.0542168i
$877$	2.17663	+	5.25485i	0.0734995	+	0.177444i	0.956359	−	0.292193i	$-0.0943850\pi$
$877$	2.17663	+	5.25485i	0.0734995	+	0.177444i	−0.882860	+	0.469637i	$0.844385\pi$
$878$	5.08283	−	2.10538i	0.171537	−	0.0710531i
$879$	−13.4051	−	5.55256i	−0.452142	−	0.187283i
$880$	9.33048	+	2.01986i	0.314531	+	0.0680895i
$881$	−5.52498	+	13.3385i	−0.186141	+	0.449385i	−0.989211	−	0.146501i	$-0.953199\pi$
$881$	−5.52498	+	13.3385i	−0.186141	+	0.449385i	0.803069	+	0.595886i	$0.203199\pi$
$882$	−5.94933	−	5.94933i	−0.200324	−	0.200324i
$883$		−	29.8519i		−	1.00460i	−0.864694	−	0.502299i	$-0.832488\pi$
$883$		−	29.8519i		−	1.00460i	0.864694	−	0.502299i	$-0.167512\pi$
$884$	−17.2108	−	12.8703i	−0.578861	−	0.432875i
$885$	42.5553	+	9.21236i	1.43048	+	0.309670i
$886$	10.6393	−	10.6393i	0.357433	−	0.357433i
$887$	12.6831	+	5.25350i	0.425856	+	0.176395i	0.585309	−	0.810810i	$-0.300973\pi$
$887$	12.6831	+	5.25350i	0.425856	+	0.176395i	−0.159453	+	0.987206i	$0.550973\pi$
$888$	−10.6771			−0.358299
$889$	5.81433	+	2.40837i	0.195006	+	0.0807743i
$890$	5.81628	+	32.0523i	0.194962	+	1.07439i
$891$	44.2619	−	18.3339i	1.48283	−	0.614208i
$892$	−12.2971	+	12.2971i	−0.411739	+	0.411739i
$893$	−1.06103	+	1.06103i	−0.0355060	+	0.0355060i
$894$	−20.8702	+	8.64472i	−0.698004	+	0.289123i
$895$	27.9917	−	5.07943i	0.935658	−	0.169786i
$896$	3.20595	+	1.32795i	0.107103	+	0.0443636i
$897$	83.7055			2.79485
$898$	10.3001	+	4.26643i	0.343718	+	0.142373i
$899$	−4.49653	+	4.49653i	−0.149968	+	0.149968i
$900$	7.59717	+	3.45100i	0.253239	+	0.115033i
$901$	56.1819	−	8.10663i	1.87169	−	0.270071i
$902$		−	19.4331i		−	0.647050i
$903$	−17.8749	−	17.8749i	−0.594839	−	0.594839i
$904$	−2.58618	+	6.24358i	−0.0860149	+	0.207658i
$905$	33.8618	+	7.33040i	1.12560	+	0.243671i
$906$	−34.6348	−	14.3462i	−1.15066	−	0.476621i
$907$	−49.3266	+	20.4318i	−1.63786	+	0.678425i	−0.996080	−	0.0884604i	$-0.971805\pi$
$907$	−49.3266	+	20.4318i	−1.63786	+	0.678425i	−0.641784	+	0.766886i	$0.721805\pi$
$908$	−4.57652	−	11.0487i	−0.151877	−	0.366664i
$909$	13.0452	+	13.0452i	0.432681	+	0.432681i
$910$	21.9001	+	34.0016i	0.725980	+	1.12714i
$911$	−45.5839	+	18.8815i	−1.51026	+	0.625571i	−0.975612	−	0.219502i	$-0.929557\pi$
$911$	−45.5839	+	18.8815i	−1.51026	+	0.625571i	−0.534650	+	0.845073i	$0.679557\pi$
$912$	−0.863000	+	0.357466i	−0.0285768	+	0.0118369i
$913$	24.7112	−	59.6581i	0.817821	−	1.97439i
$914$		−	21.8649i		−	0.723225i
$915$	17.1260	−	24.7193i	0.566167	−	0.817195i
$916$	8.31862	−	8.31862i	0.274855	−	0.274855i
$917$		−	14.9617i		−	0.494079i
$918$	6.05655	+	10.1961i	0.199896	+	0.336520i
$919$	−22.4050			−0.739074			−0.369537	−	0.929216i	$-0.620484\pi$
$919$	−22.4050			−0.739074			−0.369537	+	0.929216i	$0.620484\pi$
$920$	−8.99904	−	13.9717i	−0.296689	−	0.460635i
$921$	−28.1025	+	67.8456i	−0.926010	+	2.23559i
$922$	9.38263			0.309000
$923$	20.0458	−	48.3948i	0.659815	−	1.59293i
$924$	12.2504	+	29.5751i	0.403009	+	0.972949i
$925$	−0.832003	+	24.6928i	−0.0273561	+	0.811895i
$926$	−13.5333	−	13.5333i	−0.444732	−	0.444732i
$927$	−7.48676	+	7.48676i	−0.245898	+	0.245898i
$928$	−1.43630	−	3.46752i	−0.0471487	−	0.113827i
$929$	2.78146	+	6.71505i	0.0912569	+	0.220314i	0.962917	−	0.269797i	$-0.0869565\pi$
$929$	2.78146	+	6.71505i	0.0912569	+	0.220314i	−0.871660	+	0.490110i	$0.836956\pi$
$930$	−4.66194	+	6.72895i	−0.152871	+	0.220651i
$931$		−	2.17950i		−	0.0714302i
$932$	21.6054	+	8.94925i	0.707709	+	0.293143i
$933$	39.7997	+	39.7997i	1.30298	+	1.30298i
$934$	19.8500			0.649512
$935$	−29.7085	+	25.8214i	−0.971573	+	0.844450i
$936$	8.69852			0.284320
$937$	−15.8604	−	15.8604i	−0.518135	−	0.518135i	0.398872	−	0.917007i	$-0.369402\pi$
$937$	−15.8604	−	15.8604i	−0.518135	−	0.518135i	−0.917007	+	0.398872i	$0.869402\pi$
$938$	1.31212	+	0.543497i	0.0428422	+	0.0177458i
$939$		−	4.56944i		−	0.149118i
$940$	−6.37979	−	4.42003i	−0.208086	−	0.144166i
$941$	18.5277	+	44.7297i	0.603984	+	1.45815i	0.869447	+	0.494026i	$0.164475\pi$
$941$	18.5277	+	44.7297i	0.603984	+	1.45815i	−0.265463	+	0.964121i	$0.585525\pi$
$942$	2.39946	+	5.79280i	0.0781786	+	0.188740i
$943$	−23.9212	+	23.9212i	−0.778981	+	0.778981i
$944$	−6.37226	−	6.37226i	−0.207399	−	0.207399i
$945$	−3.98483	−	21.9596i	−0.129627	−	0.714345i
$946$	5.50828	+	13.2982i	0.179089	+	0.432360i
$947$	−11.0613	+	26.7043i	−0.359444	+	0.867773i	0.635935	+	0.771743i	$0.280615\pi$
$947$	−11.0613	+	26.7043i	−0.359444	+	0.867773i	−0.995378	+	0.0960307i	$0.969385\pi$
$948$	1.23485			0.0401061
$949$	−2.09490	+	5.05754i	−0.0680034	+	0.164175i
$950$	0.759463	+	2.02371i	0.0246402	+	0.0656579i
$951$	17.5432			0.568877
$952$	−12.3010	+	7.30692i	−0.398679	+	0.236819i
$953$			8.42766i			0.272999i	0.990640	+	0.136499i	$0.0435851\pi$
$953$			8.42766i			0.272999i	−0.990640	+	0.136499i	$0.956415\pi$
$954$	−16.2461	+	16.2461i	−0.525986	+	0.525986i
$955$	−15.5222	−	10.7540i	−0.502285	−	0.347992i
$956$			13.2057i			0.427103i
$957$	13.2499	−	31.9881i	0.428309	−	1.03403i
$958$	−9.18371	+	3.80402i	−0.296712	+	0.122902i
$959$	−14.1670	+	5.86816i	−0.457476	+	0.189493i
$960$	−2.61625	−	4.06195i	−0.0844393	−	0.131099i
$961$	19.8905	+	19.8905i	0.641628	+	0.641628i
$962$	9.85633	+	23.7953i	0.317781	+	0.767191i
$963$	2.49711	−	1.03434i	0.0804681	−	0.0333310i
$964$	−20.9168	−	8.66402i	−0.673684	−	0.279049i
$965$	10.0967	−	46.6401i	0.325023	−	1.50140i
$966$	21.3259	−	51.4852i	0.686149	−	1.65651i
$967$	−23.4943	−	23.4943i	−0.755527	−	0.755527i	0.219978	−	0.975505i	$-0.429401\pi$
$967$	−23.4943	−	23.4943i	−0.755527	−	0.755527i	−0.975505	+	0.219978i	$0.929401\pi$
$968$		−	7.22756i		−	0.232302i
$969$	0.950599	−	3.73226i	0.0305376	−	0.119897i
$970$	4.58351	−	21.1729i	0.147168	−	0.679822i
$971$	28.5627	−	28.5627i	0.916621	−	0.916621i	−0.0801605	−	0.996782i	$-0.525543\pi$
$971$	28.5627	−	28.5627i	0.916621	−	0.916621i	0.996782	+	0.0801605i	$0.0255433\pi$
$972$	−14.4291	−	5.97675i	−0.462815	−	0.191704i
$973$	18.7737			0.601858
$974$	−8.06967	−	3.34257i	−0.258569	−	0.107103i
$975$	1.89632	−	56.2804i	0.0607307	−	1.80241i
$976$	−5.75032	+	2.38186i	−0.184063	+	0.0762415i
$977$	−0.211408	+	0.211408i	−0.00676354	+	0.00676354i	−0.710480	−	0.703717i	$-0.751522\pi$
$977$	−0.211408	+	0.211408i	−0.00676354	+	0.00676354i	0.703717	+	0.710480i	$0.251522\pi$
$978$	−5.73181	+	5.73181i	−0.183283	+	0.183283i
$979$	57.4630	−	23.8020i	1.83653	−	0.760714i
$980$	11.0921	−	2.01281i	0.354326	−	0.0642967i
$981$	−12.7769	−	5.29238i	−0.407936	−	0.168973i
$982$	−2.31132			−0.0737571
$983$	−20.7949	−	8.61355i	−0.663256	−	0.274730i	0.0255520	−	0.999673i	$-0.491866\pi$
$983$	−20.7949	−	8.61355i	−0.663256	−	0.274730i	−0.688808	+	0.724944i	$0.741866\pi$
$984$	−6.95451	+	6.95451i	−0.221702	+	0.221702i
$985$	−1.97310	−	0.427136i	−0.0628681	−	0.0136097i
$986$	14.9962	+	3.81950i	0.477575	+	0.121638i
$987$		−	26.0254i		−	0.828399i
$988$	1.59332	+	1.59332i	0.0506904	+	0.0506904i
$989$	9.58898	−	23.1498i	0.304912	−	0.736122i
$990$	3.37084	−	15.5712i	0.107132	−	0.494884i
$991$	8.04403	+	3.33195i	0.255527	+	0.105843i	0.506770	−	0.862081i	$-0.330839\pi$
$991$	8.04403	+	3.33195i	0.255527	+	0.105843i	−0.251243	+	0.967924i	$0.580839\pi$
$992$	1.56532	−	0.648377i	0.0496990	−	0.0205860i
$993$	−0.217349	−	0.524726i	−0.00689735	−	0.0166517i
$994$	−24.6593	−	24.6593i	−0.782146	−	0.782146i
$995$	0.669481	−	0.431205i	0.0212240	−	0.0136701i
$996$	−30.1933	+	12.5065i	−0.956710	+	0.396282i
$997$	2.88867	−	1.19653i	0.0914852	−	0.0378944i	−0.336471	−	0.941694i	$-0.609234\pi$
$997$	2.88867	−	1.19653i	0.0914852	−	0.0378944i	0.427957	+	0.903799i	$0.359234\pi$
$998$	−11.1408	+	26.8962i	−0.352655	+	0.851385i
$999$		−	14.2128i		−	0.449673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.59.2	yes	20
5.2	odd	4		850.2.l.i.501.2		20
5.3	odd	4		850.2.l.h.501.4		20
5.4	even	2		170.2.n.b.59.4	yes	20
17.15	even	8		170.2.n.b.49.4	yes	20
85.32	odd	8		850.2.l.i.151.2		20
85.49	even	8	inner	170.2.n.a.49.2	✓	20
85.83	odd	8		850.2.l.h.151.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.2	✓	20	85.49	even	8	inner
170.2.n.a.59.2	yes	20	1.1	even	1	trivial
170.2.n.b.49.4	yes	20	17.15	even	8
170.2.n.b.59.4	yes	20	5.4	even	2
850.2.l.h.151.4		20	85.83	odd	8
850.2.l.h.501.4		20	5.3	odd	4
850.2.l.i.151.2		20	85.32	odd	8
850.2.l.i.501.2		20	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.99627 - 0.826884i) q^{3} +1.00000i q^{4} +(-1.27343 + 1.83804i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(1.32795 + 3.20595i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.99627 - 0.826884i) q^{3} +1.00000i q^{4} +(-1.27343 + 1.83804i) q^{5} +(-0.826884 - 1.99627i) q^{6} +(1.32795 + 3.20595i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.18005 + 1.18005i) q^{9} +(-2.20014 + 0.399242i) q^{10} +(1.63382 + 3.94439i) q^{11} +(0.826884 - 1.99627i) q^{12} -5.21229 q^{13} +(-1.32795 + 3.20595i) q^{14} +(4.06195 - 2.61625i) q^{15} -1.00000 q^{16} +(2.46922 - 3.30196i) q^{17} +1.66885i q^{18} +(-0.305686 + 0.305686i) q^{19} +(-1.83804 - 1.27343i) q^{20} -7.49802i q^{21} +(-1.63382 + 3.94439i) q^{22} +(6.86651 - 2.84420i) q^{23} +(1.99627 - 0.826884i) q^{24} +(-1.75677 - 4.68121i) q^{25} +(-3.68564 - 3.68564i) q^{26} +(1.10071 + 2.65734i) q^{27} +(-3.20595 + 1.32795i) q^{28} +(3.46752 + 1.43630i) q^{29} +(4.72221 + 1.02226i) q^{30} +(-0.648377 + 1.56532i) q^{31} +(-0.707107 - 0.707107i) q^{32} -9.22506i q^{33} +(4.08084 - 0.588835i) q^{34} +(-7.58371 - 1.64172i) q^{35} +(-1.18005 + 1.18005i) q^{36} +(-4.56523 - 1.89098i) q^{37} -0.432305 q^{38} +(10.4052 + 4.30996i) q^{39} +(-0.399242 - 2.20014i) q^{40} +(-4.20525 + 1.74187i) q^{41} +(5.30190 - 5.30190i) q^{42} +(2.38395 - 2.38395i) q^{43} +(-3.94439 + 1.63382i) q^{44} +(-3.67170 + 0.666274i) q^{45} +(6.86651 + 2.84420i) q^{46} +3.47098 q^{47} +(1.99627 + 0.826884i) q^{48} +(-3.56493 + 3.56493i) q^{49} +(2.06789 - 4.55234i) q^{50} +(-7.65958 + 4.54986i) q^{51} -5.21229i q^{52} +(9.73490 + 9.73490i) q^{53} +(-1.10071 + 2.65734i) q^{54} +(-9.33048 - 2.01986i) q^{55} +(-3.20595 - 1.32795i) q^{56} +(0.863000 - 0.357466i) q^{57} +(1.43630 + 3.46752i) q^{58} +(6.37226 + 6.37226i) q^{59} +(2.61625 + 4.06195i) q^{60} +(5.75032 - 2.38186i) q^{61} +(-1.56532 + 0.648377i) q^{62} +(-2.21615 + 5.35025i) q^{63} -1.00000i q^{64} +(6.63746 - 9.58039i) q^{65} +(6.52310 - 6.52310i) q^{66} -0.409276i q^{67} +(3.30196 + 2.46922i) q^{68} -16.0593 q^{69} +(-4.20162 - 6.52336i) q^{70} +(-3.84587 + 9.28474i) q^{71} -1.66885 q^{72} +(0.401916 - 0.970312i) q^{73} +(-1.89098 - 4.56523i) q^{74} +(-0.363817 + 10.7976i) q^{75} +(-0.305686 - 0.305686i) q^{76} +(-10.4759 + 10.4759i) q^{77} +(4.30996 + 10.4052i) q^{78} +(0.218700 + 0.527989i) q^{79} +(1.27343 - 1.83804i) q^{80} -11.2215i q^{81} +(-4.20525 - 1.74187i) q^{82} +(-10.6949 - 10.6949i) q^{83} +7.49802 q^{84} +(2.92476 + 8.74333i) q^{85} +3.37141 q^{86} +(-5.73448 - 5.73448i) q^{87} +(-3.94439 - 1.63382i) q^{88} -14.5683i q^{89} +(-3.06741 - 2.12515i) q^{90} +(-6.92165 - 16.7103i) q^{91} +(2.84420 + 6.86651i) q^{92} +(2.58868 - 2.58868i) q^{93} +(2.45435 + 2.45435i) q^{94} +(-0.172594 - 0.951131i) q^{95} +(0.826884 + 1.99627i) q^{96} +(-3.70749 + 8.95068i) q^{97} -5.04157 q^{98} +(-2.72660 + 6.58259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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