LMFDB - Embedded newform 80.2.j.b.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.3
Root			$-0.635486 - 1.26339i$ of defining polynomial
Character	$\chi$	$=$	80.67
Dual form			80.2.j.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14628 + 0.828280i) q^{2} -0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(2.22257 + 0.245325i) q^{5} +(0.573759 + 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(0.853049 + 2.69672i) q^{8} +2.52015 q^{9} +O(q^{10})$	\(q+(-1.14628 + 0.828280i) q^{2} -0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(2.22257 + 0.245325i) q^{5} +(0.573759 + 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(0.853049 + 2.69672i) q^{8} +2.52015 q^{9} +(-2.75088 + 1.55970i) q^{10} +(0.843672 + 0.843672i) q^{11} +(-1.31538 - 0.434957i) q^{12} -3.68390 q^{13} +(0.678995 + 0.109350i) q^{14} +(0.169939 - 1.53960i) q^{15} +(-3.21147 - 2.38463i) q^{16} +(0.412137 + 0.412137i) q^{17} +(-2.88879 + 2.08739i) q^{18} +(-5.37721 - 5.37721i) q^{19} +(1.86140 - 4.06635i) q^{20} +(-0.238204 + 0.238204i) q^{21} +(-1.66588 - 0.268286i) q^{22} +(-3.08788 + 3.08788i) q^{23} +(1.86805 - 0.590917i) q^{24} +(4.87963 + 1.09050i) q^{25} +(4.22278 - 3.05130i) q^{26} -3.82387i q^{27} +(-0.868890 + 0.437052i) q^{28} +(-4.22969 + 4.22969i) q^{29} +(1.08042 + 1.90557i) q^{30} +8.75966i q^{31} +(5.65638 + 0.0734474i) q^{32} +(0.584422 - 0.584422i) q^{33} +(-0.813788 - 0.131059i) q^{34} +(-0.679919 - 0.848640i) q^{35} +(1.58241 - 4.78546i) q^{36} -5.41752 q^{37} +(10.6176 + 1.70994i) q^{38} +2.55188i q^{39} +(1.23439 + 6.20293i) q^{40} +2.54777i q^{41} +(0.0757484 - 0.470348i) q^{42} +4.30732 q^{43} +(2.13178 - 1.07228i) q^{44} +(5.60121 + 0.618255i) q^{45} +(0.981939 - 6.09720i) q^{46} +(4.56972 - 4.56972i) q^{47} +(-1.65186 + 2.22462i) q^{48} -6.76350i q^{49} +(-6.49665 + 2.79168i) q^{50} +(0.285492 - 0.285492i) q^{51} +(-2.31314 + 6.99528i) q^{52} -6.07536i q^{53} +(3.16724 + 4.38322i) q^{54} +(1.66815 + 2.08209i) q^{55} +(0.633987 - 1.22067i) q^{56} +(-3.72486 + 3.72486i) q^{57} +(1.34503 - 8.35177i) q^{58} +(-7.33694 + 7.33694i) q^{59} +(-2.81681 - 1.28942i) q^{60} +(-4.81576 - 4.81576i) q^{61} +(-7.25545 - 10.0410i) q^{62} +(-0.866609 - 0.866609i) q^{63} +(-6.54461 + 4.60087i) q^{64} +(-8.18773 - 0.903753i) q^{65} +(-0.185845 + 1.15397i) q^{66} +14.3626 q^{67} +(1.04138 - 0.523815i) q^{68} +(2.13901 + 2.13901i) q^{69} +(1.48229 + 0.409613i) q^{70} -2.97605 q^{71} +(2.14981 + 6.79614i) q^{72} +(-6.87152 - 6.87152i) q^{73} +(6.20998 - 4.48722i) q^{74} +(0.755404 - 3.38018i) q^{75} +(-13.5870 + 6.83429i) q^{76} -0.580231i q^{77} +(-2.11367 - 2.92517i) q^{78} +10.1654 q^{79} +(-6.55271 - 6.08785i) q^{80} +4.91161 q^{81} +(-2.11027 - 2.92046i) q^{82} +7.15276i q^{83} +(0.302751 + 0.601890i) q^{84} +(0.814896 + 1.01711i) q^{85} +(-4.93739 + 3.56767i) q^{86} +(2.92996 + 2.92996i) q^{87} +(-1.55545 + 2.99484i) q^{88} +1.10953 q^{89} +(-6.93263 + 3.93068i) q^{90} +(1.26679 + 1.26679i) q^{91} +(3.92461 + 7.80240i) q^{92} +6.06792 q^{93} +(-1.45316 + 9.02318i) q^{94} +(-10.6321 - 13.2704i) q^{95} +(0.0508779 - 3.91824i) q^{96} +(7.15920 + 7.15920i) q^{97} +(5.60207 + 7.75285i) q^{98} +(2.12618 + 2.12618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.14628	+	0.828280i	−0.810541	+	0.585682i
$2$	−1.14628	+	0.828280i	−0.810541	+	0.585682i
$3$		−	0.692712i		−	0.399937i	−0.979802	−	0.199969i	$-0.935916\pi$
$3$		−	0.692712i		−	0.399937i	0.979802	−	0.199969i	$-0.0640841\pi$
$4$	0.627905	−	1.89888i	0.313952	−	0.949439i
$5$	2.22257	+	0.245325i	0.993963	+	0.109713i
$5$	2.22257	+	0.245325i	0.993963	+	0.109713i
$6$	0.573759	+	0.794040i	0.234236	+	0.324166i
$7$	−0.343872	−	0.343872i	−0.129971	−	0.129971i	0.639129	−	0.769100i	$-0.279295\pi$
$7$	−0.343872	−	0.343872i	−0.129971	−	0.129971i	−0.769100	+	0.639129i	$0.779295\pi$
$8$	0.853049	+	2.69672i	0.301598	+	0.953435i
$9$	2.52015			0.840050
$10$	−2.75088	+	1.55970i	−0.869904	+	0.493220i
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	0.822762	−	0.568386i	$-0.192432\pi$
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	−0.568386	+	0.822762i	$0.692432\pi$
$12$	−1.31538	−	0.434957i	−0.379716	−	0.125561i
$13$	−3.68390			−1.02173			−0.510865	−	0.859661i	$-0.670675\pi$
$13$	−3.68390			−1.02173			−0.510865	+	0.859661i	$0.670675\pi$
$14$	0.678995	+	0.109350i	0.181469	+	0.0292251i
$15$	0.169939	−	1.53960i	0.0438782	−	0.397523i
$16$	−3.21147	−	2.38463i	−0.802868	−	0.596157i
$17$	0.412137	+	0.412137i	0.0999579	+	0.0999579i	0.755317	−	0.655359i	$-0.227483\pi$
$17$	0.412137	+	0.412137i	0.0999579	+	0.0999579i	−0.655359	+	0.755317i	$0.727483\pi$
$18$	−2.88879	+	2.08739i	−0.680895	+	0.492003i
$19$	−5.37721	−	5.37721i	−1.23362	−	1.23362i	−0.962565	−	0.271052i	$-0.912629\pi$
$19$	−5.37721	−	5.37721i	−1.23362	−	1.23362i	−0.271052	−	0.962565i	$-0.587371\pi$
$20$	1.86140	−	4.06635i	0.416222	−	0.909263i
$21$	−0.238204	+	0.238204i	−0.0519804	+	0.0519804i
$22$	−1.66588	−	0.268286i	−0.355167	−	0.0571987i
$23$	−3.08788	+	3.08788i	−0.643868	+	0.643868i	−0.951504	−	0.307636i	$-0.900462\pi$
$23$	−3.08788	+	3.08788i	−0.643868	+	0.643868i	0.307636	+	0.951504i	$0.400462\pi$
$24$	1.86805	−	0.590917i	0.381314	−	0.120621i
$25$	4.87963	+	1.09050i	0.975926	+	0.218101i
$26$	4.22278	−	3.05130i	0.828154	−	0.598410i
$27$		−	3.82387i		−	0.735905i
$28$	−0.868890	+	0.437052i	−0.164205	+	0.0825951i
$29$	−4.22969	+	4.22969i	−0.785434	+	0.785434i	−0.980742	−	0.195308i	$-0.937429\pi$
$29$	−4.22969	+	4.22969i	−0.785434	+	0.785434i	0.195308	+	0.980742i	$0.437429\pi$
$30$	1.08042	+	1.90557i	0.197257	+	0.347907i
$31$			8.75966i			1.57328i	0.617411	+	0.786641i	$0.288182\pi$
$31$			8.75966i			1.57328i	−0.617411	+	0.786641i	$0.711818\pi$
$32$	5.65638	+	0.0734474i	0.999916	+	0.0129838i
$33$	0.584422	−	0.584422i	0.101735	−	0.101735i
$34$	−0.813788	−	0.131059i	−0.139564	−	0.0224764i
$35$	−0.679919	−	0.848640i	−0.114927	−	0.143446i
$36$	1.58241	−	4.78546i	0.263736	−	0.797576i
$37$	−5.41752			−0.890634			−0.445317	−	0.895373i	$-0.646909\pi$
$37$	−5.41752			−0.890634			−0.445317	+	0.895373i	$0.646909\pi$
$38$	10.6176	+	1.70994i	1.72240	+	0.277389i
$39$			2.55188i			0.408628i
$40$	1.23439	+	6.20293i	0.195174	+	0.980769i
$41$			2.54777i			0.397895i	0.980010	+	0.198948i	$0.0637524\pi$
$41$			2.54777i			0.397895i	−0.980010	+	0.198948i	$0.936248\pi$
$42$	0.0757484	−	0.470348i	0.0116882	−	0.0725763i
$43$	4.30732			0.656861			0.328430	−	0.944528i	$-0.393480\pi$
$43$	4.30732			0.656861			0.328430	+	0.944528i	$0.393480\pi$
$44$	2.13178	−	1.07228i	0.321377	−	0.161653i
$45$	5.60121	+	0.618255i	0.834979	+	0.0921641i
$46$	0.981939	−	6.09720i	0.144779	−	0.898983i
$47$	4.56972	−	4.56972i	0.666562	−	0.666562i	−0.290356	−	0.956919i	$-0.593774\pi$
$47$	4.56972	−	4.56972i	0.666562	−	0.666562i	0.956919	+	0.290356i	$0.0937738\pi$
$48$	−1.65186	+	2.22462i	−0.238425	+	0.321097i
$49$		−	6.76350i		−	0.966215i
$50$	−6.49665	+	2.79168i	−0.918766	+	0.394803i
$51$	0.285492	−	0.285492i	0.0399769	−	0.0399769i
$52$	−2.31314	+	6.99528i	−0.320775	+	0.970071i
$53$		−	6.07536i		−	0.834515i	−0.908788	−	0.417257i	$-0.862991\pi$
$53$		−	6.07536i		−	0.834515i	0.908788	−	0.417257i	$-0.137009\pi$
$54$	3.16724	+	4.38322i	0.431007	+	0.596481i
$55$	1.66815	+	2.08209i	0.224933	+	0.280749i
$56$	0.633987	−	1.22067i	0.0847201	−	0.163118i
$57$	−3.72486	+	3.72486i	−0.493369	+	0.493369i
$58$	1.34503	−	8.35177i	0.176611	−	1.09664i
$59$	−7.33694	+	7.33694i	−0.955189	+	0.955189i	−0.999038	−	0.0438495i	$-0.986038\pi$
$59$	−7.33694	+	7.33694i	−0.955189	+	0.955189i	0.0438495	+	0.999038i	$0.486038\pi$
$60$	−2.81681	−	1.28942i	−0.363648	−	0.166463i
$61$	−4.81576	−	4.81576i	−0.616595	−	0.616595i	0.328062	−	0.944656i	$-0.393605\pi$
$61$	−4.81576	−	4.81576i	−0.616595	−	0.616595i	−0.944656	+	0.328062i	$0.893605\pi$
$62$	−7.25545	−	10.0410i	−0.921444	−	1.27521i
$63$	−0.866609	−	0.866609i	−0.109183	−	0.109183i
$64$	−6.54461	+	4.60087i	−0.818077	+	0.575109i
$65$	−8.18773	−	0.903753i	−1.01556	−	0.112097i
$66$	−0.185845	+	1.15397i	−0.0228759	+	0.142044i
$67$	14.3626			1.75467			0.877334	−	0.479880i	$-0.159320\pi$
$67$	14.3626			1.75467			0.877334	+	0.479880i	$0.159320\pi$
$68$	1.04138	−	0.523815i	0.126286	−	0.0635219i
$69$	2.13901	+	2.13901i	0.257507	+	0.257507i
$70$	1.48229	+	0.409613i	0.177167	+	0.0489582i
$71$	−2.97605			−0.353193			−0.176596	−	0.984283i	$-0.556509\pi$
$71$	−2.97605			−0.353193			−0.176596	+	0.984283i	$0.556509\pi$
$72$	2.14981	+	6.79614i	0.253358	+	0.800933i
$73$	−6.87152	−	6.87152i	−0.804250	−	0.804250i	0.179507	−	0.983757i	$-0.442550\pi$
$73$	−6.87152	−	6.87152i	−0.804250	−	0.804250i	−0.983757	+	0.179507i	$0.942550\pi$
$74$	6.20998	−	4.48722i	0.721895	−	0.521629i
$75$	0.755404	−	3.38018i	0.0872266	−	0.390309i
$76$	−13.5870	+	6.83429i	−1.55854	+	0.783947i
$77$		−	0.580231i		−	0.0661234i
$78$	−2.11367	−	2.92517i	−0.239326	−	0.331210i
$79$	10.1654			1.14369			0.571847	−	0.820360i	$-0.306227\pi$
$79$	10.1654			1.14369			0.571847	+	0.820360i	$0.306227\pi$
$80$	−6.55271	−	6.08785i	−0.732615	−	0.680643i
$81$	4.91161			0.545734
$82$	−2.11027	−	2.92046i	−0.233040	−	0.322510i
$83$			7.15276i			0.785118i	0.919727	+	0.392559i	$0.128410\pi$
$83$			7.15276i			0.785118i	−0.919727	+	0.392559i	$0.871590\pi$
$84$	0.302751	+	0.601890i	0.0330329	+	0.0656716i
$85$	0.814896	+	1.01711i	0.0883878	+	0.110321i
$86$	−4.93739	+	3.56767i	−0.532412	+	0.384712i
$87$	2.92996	+	2.92996i	0.314124	+	0.314124i
$88$	−1.55545	+	2.99484i	−0.165812	+	0.319251i
$89$	1.10953			0.117610			0.0588050	−	0.998269i	$-0.481271\pi$
$89$	1.10953			0.117610			0.0588050	+	0.998269i	$0.481271\pi$
$90$	−6.93263	+	3.93068i	−0.730763	+	0.414330i
$91$	1.26679	+	1.26679i	0.132796	+	0.132796i
$92$	3.92461	+	7.80240i	0.409169	+	0.813457i
$93$	6.06792			0.629214
$94$	−1.45316	+	9.02318i	−0.149882	+	0.930670i
$95$	−10.6321	−	13.2704i	−1.09083	−	1.36151i
$96$	0.0508779	−	3.91824i	0.00519270	−	0.399904i
$97$	7.15920	+	7.15920i	0.726906	+	0.726906i	0.970002	−	0.243096i	$-0.0781630\pi$
$97$	7.15920	+	7.15920i	0.726906	+	0.726906i	−0.243096	+	0.970002i	$0.578163\pi$
$98$	5.60207	+	7.75285i	0.565895	+	0.783156i
$99$	2.12618	+	2.12618i	0.213689	+	0.213689i
$100$	5.13467	−	8.58109i	0.513467	−	0.858109i
$101$	0.953394	−	0.953394i	0.0948663	−	0.0948663i	−0.658081	−	0.752947i	$-0.728632\pi$
$101$	0.953394	−	0.953394i	0.0948663	−	0.0948663i	0.752947	+	0.658081i	$0.228632\pi$
$102$	−0.0907858	+	0.563721i	−0.00898914	+	0.0558167i
$103$	9.59425	−	9.59425i	0.945350	−	0.945350i	−0.0532322	−	0.998582i	$-0.516952\pi$
$103$	9.59425	−	9.59425i	0.945350	−	0.945350i	0.998582	+	0.0532322i	$0.0169524\pi$
$104$	−3.14255	−	9.93446i	−0.308152	−	0.974154i
$105$	−0.587863	+	0.470988i	−0.0573696	+	0.0459637i
$106$	5.03210	+	6.96405i	0.488761	+	0.676408i
$107$		−	5.28201i		−	0.510631i	−0.966858	−	0.255316i	$-0.917821\pi$
$107$		−	5.28201i		−	0.510631i	0.966858	−	0.255316i	$-0.0821794\pi$
$108$	−7.26107	−	2.40103i	−0.698697	−	0.231039i
$109$	1.53980	−	1.53980i	0.147486	−	0.147486i	−0.629508	−	0.776994i	$-0.716744\pi$
$109$	1.53980	−	1.53980i	0.147486	−	0.147486i	0.776994	+	0.629508i	$0.216744\pi$
$110$	−3.63672	−	1.00497i	−0.346747	−	0.0958197i
$111$			3.75278i			0.356198i
$112$	0.284329	+	1.92434i	0.0268665	+	0.181833i
$113$	−2.99656	+	2.99656i	−0.281893	+	0.281893i	−0.833863	−	0.551971i	$-0.813876\pi$
$113$	−2.99656	+	2.99656i	−0.281893	+	0.281893i	0.551971	+	0.833863i	$0.313876\pi$
$114$	1.18450	−	7.35494i	0.110938	−	0.688854i
$115$	−7.62056	+	6.10550i	−0.710621	+	0.569340i
$116$	5.37582	+	10.6875i	0.499133	+	0.992310i
$117$	−9.28399			−0.858305
$118$	2.33313	−	14.4872i	0.214782	−	1.33366i
$119$		−	0.283445i		−	0.0259833i
$120$	4.29684	−	0.855076i	0.392246	−	0.0780574i
$121$		−	9.57643i		−	0.870585i
$122$	9.50899	+	1.53140i	0.860904	+	0.138646i
$123$	1.76487			0.159133
$124$	16.6335	+	5.50023i	1.49373	+	0.493935i
$125$	10.5778	+	3.62081i	0.946107	+	0.323855i
$126$	1.71117	+	0.275580i	0.152443	+	0.0245506i
$127$	−10.5522	+	10.5522i	−0.936360	+	0.936360i	−0.998093	−	0.0617330i	$-0.980337\pi$
$127$	−10.5522	+	10.5522i	−0.936360	+	0.936360i	0.0617330	+	0.998093i	$0.480337\pi$
$128$	3.69113	−	10.6947i	0.326253	−	0.945282i
$129$		−	2.98373i		−	0.262703i
$130$	10.1340	−	5.74578i	0.888808	−	0.503938i
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	−0.743285	−	0.668975i	$-0.766733\pi$
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	0.668975	+	0.743285i	$0.266733\pi$
$132$	−0.742784	−	1.47671i	−0.0646511	−	0.128531i
$133$			3.69814i			0.320670i
$134$	−16.4635	+	11.8962i	−1.42223	+	1.02768i
$135$	0.938091	−	8.49883i	0.0807380	−	0.731463i
$136$	−0.759845	+	1.46299i	−0.0651562	+	0.125451i
$137$	−5.50145	+	5.50145i	−0.470021	+	0.470021i	−0.901921	−	0.431901i	$-0.857843\pi$
$137$	−5.50145	+	5.50145i	−0.470021	+	0.470021i	0.431901	+	0.901921i	$0.357843\pi$
$138$	−4.22360	−	0.680201i	−0.359537	−	0.0579025i
$139$	3.03517	−	3.03517i	0.257440	−	0.257440i	−0.566572	−	0.824012i	$-0.691731\pi$
$139$	3.03517	−	3.03517i	0.257440	−	0.257440i	0.824012	+	0.566572i	$0.191731\pi$
$140$	−2.03839	+	0.758219i	−0.172275	+	0.0640812i
$141$	−3.16550	−	3.16550i	−0.266583	−	0.266583i
$142$	3.41138	−	2.46501i	0.286277	−	0.206859i
$143$	−3.10801	−	3.10801i	−0.259905	−	0.259905i
$144$	−8.09339	−	6.00962i	−0.674449	−	0.500802i
$145$	−10.4384	+	8.36313i	−0.866864	+	0.694520i
$146$	13.5682	+	2.18513i	1.12291	+	0.180842i
$147$	−4.68516			−0.386425
$148$	−3.40168	+	10.2872i	−0.279617	+	0.845603i
$149$	11.1571	+	11.1571i	0.914023	+	0.914023i	0.996586	−	0.0825625i	$-0.0263104\pi$
$149$	11.1571	+	11.1571i	0.914023	+	0.914023i	−0.0825625	+	0.996586i	$0.526310\pi$
$150$	1.93383	+	4.50031i	0.157897	+	0.367449i
$151$	3.18265			0.259000			0.129500	−	0.991579i	$-0.458663\pi$
$151$	3.18265			0.259000			0.129500	+	0.991579i	$0.458663\pi$
$152$	9.91381	−	19.0879i	0.804116	−	1.54823i
$153$	1.03865	+	1.03865i	0.0839696	+	0.0839696i
$154$	0.480593	+	0.665105i	0.0387273	+	0.0535957i
$155$	−2.14896	+	19.4690i	−0.172609	+	1.56378i
$156$	4.84571	+	1.60234i	0.387968	+	0.128290i
$157$		−	7.05454i		−	0.563014i	−0.959559	−	0.281507i	$-0.909166\pi$
$157$		−	7.05454i		−	0.563014i	0.959559	−	0.281507i	$-0.0908342\pi$
$158$	−11.6523	+	8.41978i	−0.927011	+	0.669842i
$159$	−4.20847			−0.333754
$160$	12.5537	+	1.55089i	0.992455	+	0.122609i
$161$	2.12367			0.167369
$162$	−5.63007	+	4.06819i	−0.442340	+	0.319627i
$163$			16.0208i			1.25484i	0.778680	+	0.627422i	$0.215890\pi$
$163$			16.0208i			1.25484i	−0.778680	+	0.627422i	$0.784110\pi$
$164$	4.83791	+	1.59976i	0.377777	+	0.124920i
$165$	1.44229	−	1.15554i	0.112282	−	0.0899591i
$166$	−5.92449	−	8.19905i	−0.459830	−	0.636370i
$167$	−16.6023	−	16.6023i	−1.28473	−	1.28473i	−0.937946	−	0.346780i	$-0.887275\pi$
$167$	−16.6023	−	16.6023i	−1.28473	−	1.28473i	−0.346780	−	0.937946i	$-0.612725\pi$
$168$	−0.845571	−	0.439171i	−0.0652372	−	0.0338827i
$169$	0.571141			0.0439339
$170$	−1.77655	−	0.490929i	−0.136255	−	0.0376525i
$171$	−13.5514	−	13.5514i	−1.03630	−	1.03630i
$172$	2.70459	−	8.17908i	0.206223	−	0.623649i
$173$	14.9958			1.14011			0.570054	−	0.821607i	$-0.306922\pi$
$173$	14.9958			1.14011			0.570054	+	0.821607i	$0.306922\pi$
$174$	−5.78537	−	0.931719i	−0.438588	−	0.0706335i
$175$	−1.30298	−	2.05296i	−0.0984957	−	0.155189i
$176$	−0.697585	−	4.72127i	−0.0525825	−	0.355879i
$177$	5.08239	+	5.08239i	0.382016	+	0.382016i
$178$	−1.27183	+	0.919002i	−0.0953277	+	0.0688821i
$179$	−9.91310	−	9.91310i	−0.740940	−	0.740940i	0.231819	−	0.972759i	$-0.425532\pi$
$179$	−9.91310	−	9.91310i	−0.740940	−	0.740940i	−0.972759	+	0.231819i	$0.925532\pi$
$180$	4.69102	−	10.2478i	0.349648	−	0.763826i
$181$	1.04015	−	1.04015i	0.0773139	−	0.0773139i	−0.667392	−	0.744706i	$-0.732590\pi$
$181$	1.04015	−	1.04015i	0.0773139	−	0.0773139i	0.744706	+	0.667392i	$0.232590\pi$
$182$	−2.50135	−	0.402837i	−0.185413	−	0.0298602i
$183$	−3.33593	+	3.33593i	−0.246599	+	0.246599i
$184$	−10.9613	−	5.69304i	−0.808075	−	0.419696i
$185$	−12.0408	−	1.32905i	−0.885258	−	0.0977138i
$186$	−6.95552	+	5.02594i	−0.510004	+	0.368520i
$187$			0.695417i			0.0508539i
$188$	−5.80799	−	11.5467i	−0.423591	−	0.842129i
$189$	−1.31492	+	1.31492i	−0.0956466	+	0.0956466i
$190$	23.1789	+	6.40522i	1.68157	+	0.464684i
$191$		−	3.08419i		−	0.223164i	−0.993755	−	0.111582i	$-0.964408\pi$
$191$		−	3.08419i		−	0.223164i	0.993755	−	0.111582i	$-0.0355918\pi$
$192$	3.18708	+	4.53353i	0.230008	+	0.327179i
$193$	−12.0915	+	12.0915i	−0.870368	+	0.870368i	−0.992512	−	0.122144i	$-0.961023\pi$
$193$	−12.0915	+	12.0915i	−0.870368	+	0.870368i	0.122144	+	0.992512i	$0.461023\pi$
$194$	−14.1362	−	2.27661i	−1.01492	−	0.163451i
$195$	−0.626040	+	5.67174i	−0.0448317	+	0.406162i
$196$	−12.8431	−	4.24683i	−0.917362	−	0.303345i
$197$	13.0186			0.927540			0.463770	−	0.885956i	$-0.346496\pi$
$197$	13.0186			0.927540			0.463770	+	0.885956i	$0.346496\pi$
$198$	−4.19827	−	0.676120i	−0.298358	−	0.0480498i
$199$		−	10.6279i		−	0.753395i	−0.926336	−	0.376697i	$-0.877060\pi$
$199$		−	10.6279i		−	0.753395i	0.926336	−	0.376697i	$-0.122940\pi$
$200$	1.22178	+	14.0893i	0.0863932	+	0.996261i
$201$		−	9.94913i		−	0.701758i
$202$	−0.303177	+	1.88253i	−0.0213315	+	0.132455i
$203$	2.90894			0.204168
$204$	−0.362853	−	0.721377i	−0.0254048	−	0.0505065i
$205$	−0.625032	+	5.66260i	−0.0436541	+	0.395493i
$206$	−3.05095	+	18.9444i	−0.212570	+	1.31992i
$207$	−7.78192	+	7.78192i	−0.540881	+	0.540881i
$208$	11.8308	+	8.78474i	0.820315	+	0.609112i
$209$		−	9.07320i		−	0.627607i
$210$	0.283744	−	1.02680i	0.0195802	−	0.0708558i
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	−0.191225	−	0.981546i	$-0.561246\pi$
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	0.981546	+	0.191225i	$0.0612460\pi$
$212$	−11.5364	−	3.81475i	−0.792321	−	0.261998i
$213$			2.06155i			0.141255i
$214$	4.37499	+	6.05465i	0.299068	+	0.413888i
$215$	9.57332	+	1.05669i	0.652895	+	0.0720659i
$216$	10.3119	−	3.26195i	0.701638	−	0.221948i
$217$	3.01220	−	3.01220i	0.204482	−	0.204482i
$218$	−0.489652	+	3.04042i	−0.0331634	+	0.205923i
$219$	−4.75998	+	4.75998i	−0.321650	+	0.321650i
$220$	5.00108	−	1.86025i	0.337173	−	0.125418i
$221$	−1.51827	−	1.51827i	−0.102130	−	0.102130i
$222$	−3.10835	−	4.30173i	−0.208619	−	0.288713i
$223$	2.17863	+	2.17863i	0.145892	+	0.145892i	0.776280	−	0.630388i	$-0.217104\pi$
$223$	2.17863	+	2.17863i	0.145892	+	0.145892i	−0.630388	+	0.776280i	$0.717104\pi$
$224$	−1.91981	−	1.97033i	−0.128273	−	0.131648i
$225$	12.2974	+	2.74823i	0.819827	+	0.183215i
$226$	0.952898	−	5.91688i	0.0633859	−	0.393585i
$227$	9.32318			0.618801			0.309401	−	0.950932i	$-0.399872\pi$
$227$	9.32318			0.618801			0.309401	+	0.950932i	$0.399872\pi$
$228$	4.73419	+	9.41190i	0.313530	+	0.623318i
$229$	−2.72259	−	2.72259i	−0.179914	−	0.179914i	0.611404	−	0.791318i	$-0.290605\pi$
$229$	−2.72259	−	2.72259i	−0.179914	−	0.179914i	−0.791318	+	0.611404i	$0.790605\pi$
$230$	3.67822	−	13.3106i	0.242535	−	0.877672i
$231$	−0.401933			−0.0264452
$232$	−15.0144	−	7.79816i	−0.985746	−	0.511974i
$233$	12.3897	+	12.3897i	0.811679	+	0.811679i	0.984886	−	0.173206i	$-0.0554127\pi$
$233$	12.3897	+	12.3897i	0.811679	+	0.811679i	−0.173206	+	0.984886i	$0.555413\pi$
$234$	10.6420	−	7.68974i	0.695691	−	0.502694i
$235$	11.2776	−	9.03546i	0.735669	−	0.589408i
$236$	9.32506	+	18.5389i	0.607010	+	1.20678i
$237$		−	7.04168i		−	0.457406i
$238$	0.234772	+	0.324906i	0.0152180	+	0.0210606i
$239$	25.2180			1.63122			0.815609	−	0.578604i	$-0.196402\pi$
$239$	25.2180			1.63122			0.815609	+	0.578604i	$0.196402\pi$
$240$	−4.21713	+	4.53914i	−0.272215	+	0.293000i
$241$	12.0218			0.774391			0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218			0.774391			0.387195	+	0.921998i	$0.373444\pi$
$242$	7.93197	+	10.9773i	0.509886	+	0.705645i
$243$		−	14.8740i		−	0.954164i
$244$	−12.1684	+	6.12070i	−0.779000	+	0.391838i
$245$	1.65926	−	15.0324i	0.106006	−	0.960382i
$246$	−2.02303	+	1.46181i	−0.128984	+	0.0932015i
$247$	19.8091	+	19.8091i	1.26042	+	1.26042i
$248$	−23.6224	+	7.47242i	−1.50002	+	0.474499i
$249$	4.95480			0.313998
$250$	−15.1241	+	4.61092i	−0.956534	+	0.291620i
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	0.902790	−	0.430081i	$-0.141515\pi$
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	−0.430081	+	0.902790i	$0.641515\pi$
$252$	−2.18973	+	1.10144i	−0.137940	+	0.0693840i
$253$	−5.21032			−0.327570
$254$	3.35559	−	20.8360i	0.210548	−	1.30737i
$255$	0.704565	−	0.564488i	0.0441215	−	0.0353496i
$256$	4.62710	+	15.3163i	0.289194	+	0.957271i
$257$	−10.0809	−	10.0809i	−0.628832	−	0.628832i	0.318942	−	0.947774i	$-0.396672\pi$
$257$	−10.0809	−	10.0809i	−0.628832	−	0.628832i	−0.947774	+	0.318942i	$0.896672\pi$
$258$	2.47137	+	3.42019i	0.153861	+	0.212932i
$259$	1.86293	+	1.86293i	0.115757	+	0.115757i
$260$	−6.85723	+	14.9800i	−0.425267	+	0.929022i
$261$	−10.6595	+	10.6595i	−0.659804	+	0.659804i
$262$	0.270461	−	1.67939i	0.0167091	−	0.103753i
$263$	−3.83599	+	3.83599i	−0.236537	+	0.236537i	−0.815415	−	0.578877i	$-0.803491\pi$
$263$	−3.83599	+	3.83599i	−0.236537	+	0.236537i	0.578877	+	0.815415i	$0.303491\pi$
$264$	2.07456	+	1.07748i	0.127681	+	0.0663144i
$265$	1.49044	−	13.5029i	0.0915568	−	0.829477i
$266$	−3.06310	−	4.23910i	−0.187811	−	0.259916i
$267$		−	0.768585i		−	0.0470367i
$268$	9.01833	−	27.2728i	0.550882	−	1.66595i
$269$	−13.4250	+	13.4250i	−0.818539	+	0.818539i	−0.985896	−	0.167357i	$-0.946477\pi$
$269$	−13.4250	+	13.4250i	−0.818539	+	0.818539i	0.167357	+	0.985896i	$0.446477\pi$
$270$	5.96409	+	10.5190i	0.362963	+	0.640167i
$271$		−	12.3519i		−	0.750326i	−0.926959	−	0.375163i	$-0.877587\pi$
$271$		−	12.3519i		−	0.750326i	0.926959	−	0.375163i	$-0.122413\pi$
$272$	−0.340773	−	2.30636i	−0.0206624	−	0.139844i
$273$	0.877522	−	0.877522i	0.0531100	−	0.0531100i
$274$	1.74945	−	10.8629i	0.105688	−	0.656253i
$275$	3.19678	+	5.03684i	0.192773	+	0.303733i
$276$	5.40482	−	2.71863i	0.325332	−	0.163642i
$277$	−6.78804			−0.407854			−0.203927	−	0.978986i	$-0.565370\pi$
$277$	−6.78804			−0.407854			−0.203927	+	0.978986i	$0.565370\pi$
$278$	−0.965177	+	5.99312i	−0.0578875	+	0.359443i
$279$			22.0757i			1.32164i
$280$	1.70854	−	2.55748i	0.102105	−	0.152839i
$281$			21.5509i			1.28562i	0.766026	+	0.642810i	$0.222232\pi$
$281$			21.5509i			1.28562i	−0.766026	+	0.642810i	$0.777768\pi$
$282$	6.25046	+	1.00662i	0.372210	+	0.0599434i
$283$	−9.86809			−0.586597			−0.293299	−	0.956021i	$-0.594753\pi$
$283$	−9.86809			−0.586597			−0.293299	+	0.956021i	$0.594753\pi$
$284$	−1.86868	+	5.65116i	−0.110886	+	0.335335i
$285$	−9.19255	+	7.36495i	−0.544520	+	0.436262i
$286$	6.13694	+	0.988339i	0.362885	+	0.0584417i
$287$	0.876108	−	0.876108i	0.0517150	−	0.0517150i
$288$	14.2549	+	0.185099i	0.839979	+	0.0109070i
$289$		−	16.6603i		−	0.980017i
$290$	5.03832	−	18.2324i	0.295860	−	1.07064i
$291$	4.95926	−	4.95926i	0.290717	−	0.290717i
$292$	−17.3628	+	8.73351i	−1.01608	+	0.511090i
$293$		−	14.1972i		−	0.829410i	−0.909956	−	0.414705i	$-0.863885\pi$
$293$		−	14.1972i		−	0.829410i	0.909956	−	0.414705i	$-0.136115\pi$
$294$	5.37049	−	3.88062i	0.313214	−	0.226323i
$295$	−18.1068	+	14.5069i	−1.05422	+	0.844626i
$296$	−4.62141	−	14.6095i	−0.268614	−	0.849162i
$297$	3.22610	−	3.22610i	0.187197	−	0.187197i
$298$	−22.0303	−	3.54792i	−1.27618	−	0.205526i
$299$	11.3755	−	11.3755i	0.657859	−	0.657859i
$300$	−5.94422	−	3.55685i	−0.343190	−	0.205355i
$301$	−1.48117	−	1.48117i	−0.0853731	−	0.0853731i
$302$	−3.64820	+	2.63612i	−0.209930	+	0.151692i
$303$	−0.660428	−	0.660428i	−0.0379406	−	0.0379406i
$304$	4.44611	+	30.0914i	0.255002	+	1.72586i
$305$	−9.52194	−	11.8848i	−0.545224	−	0.680521i
$306$	−2.05087	−	0.330287i	−0.117240	−	0.0188813i
$307$	−20.4161			−1.16521			−0.582604	−	0.812756i	$-0.697966\pi$
$307$	−20.4161			−1.16521			−0.582604	+	0.812756i	$0.697966\pi$
$308$	−1.10179	−	0.364329i	−0.0627801	−	0.0207596i
$309$	−6.64605	−	6.64605i	−0.378081	−	0.378081i
$310$	−13.6624	−	24.0968i	−0.775975	−	1.36860i
$311$	−6.81074			−0.386202			−0.193101	−	0.981179i	$-0.561854\pi$
$311$	−6.81074			−0.386202			−0.193101	+	0.981179i	$0.561854\pi$
$312$	−6.88172	+	2.17688i	−0.389601	+	0.123242i
$313$	−1.20933	−	1.20933i	−0.0683555	−	0.0683555i	0.672103	−	0.740458i	$-0.265391\pi$
$313$	−1.20933	−	1.20933i	−0.0683555	−	0.0683555i	−0.740458	+	0.672103i	$0.765391\pi$
$314$	5.84314	+	8.08646i	0.329747	+	0.456345i
$315$	−1.71350	−	2.13870i	−0.0965447	−	0.120502i
$316$	6.38289	−	19.3028i	0.359065	−	1.08587i
$317$		−	3.44178i		−	0.193310i	−0.995318	−	0.0966548i	$-0.969186\pi$
$317$		−	3.44178i		−	0.193310i	0.995318	−	0.0966548i	$-0.0308143\pi$
$318$	4.82408	−	3.48580i	0.270521	−	0.195474i
$319$	−7.13694			−0.399592
$320$	−15.6746	+	8.62020i	−0.876235	+	0.481884i
$321$	−3.65891			−0.204221
$322$	−2.43432	+	1.75899i	−0.135659	+	0.0980249i
$323$		−	4.43229i		−	0.246619i
$324$	3.08402	−	9.32654i	0.171334	−	0.518141i
$325$	−17.9761	−	4.01731i	−0.997134	−	0.222840i
$326$	−13.2697	−	18.3643i	−0.734940	−	1.01710i
$327$	−1.06664	−	1.06664i	−0.0589852	−	0.0589852i
$328$	−6.87063	+	2.17338i	−0.379367	+	0.120005i
$329$	−3.14280			−0.173268
$330$	−0.696151	+	2.51920i	−0.0383219	+	0.138677i
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	0.665128	−	0.746730i	$-0.268377\pi$
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	−0.746730	+	0.665128i	$0.768377\pi$
$332$	13.5822	+	4.49125i	0.745421	+	0.246489i
$333$	−13.6530			−0.748177
$334$	32.7822	+	5.27950i	1.79376	+	0.288881i
$335$	31.9218	+	3.52350i	1.74408	+	0.192509i
$336$	1.33301	−	0.196958i	0.0727219	−	0.0107449i
$337$	6.21211	+	6.21211i	0.338395	+	0.338395i	0.855763	−	0.517368i	$-0.173088\pi$
$337$	6.21211	+	6.21211i	0.338395	+	0.338395i	−0.517368	+	0.855763i	$0.673088\pi$
$338$	−0.654686	+	0.473065i	−0.0356102	+	0.0257313i
$339$	2.07575	+	2.07575i	0.112739	+	0.112739i
$340$	2.44304	−	0.908739i	0.132493	−	0.0492833i
$341$	−7.39028	+	7.39028i	−0.400206	+	0.400206i
$342$	26.7580	+	4.30930i	1.44691	+	0.233020i
$343$	−4.73288	+	4.73288i	−0.255552	+	0.255552i
$344$	3.67436	+	11.6156i	0.198108	+	0.626274i
$345$	4.22935	+	5.27886i	0.227701	+	0.284204i
$346$	−17.1893	+	12.4207i	−0.924104	+	0.667741i
$347$			10.1502i			0.544889i	0.962171	+	0.272445i	$0.0878321\pi$
$347$			10.1502i			0.544889i	−0.962171	+	0.272445i	$0.912168\pi$
$348$	7.40336	−	3.72390i	0.396862	−	0.199622i
$349$	−3.99595	+	3.99595i	−0.213898	+	0.213898i	−0.805921	−	0.592023i	$-0.798329\pi$
$349$	−3.99595	+	3.99595i	−0.213898	+	0.213898i	0.592023	+	0.805921i	$0.298329\pi$
$350$	3.19400	+	1.27404i	0.170726	+	0.0681001i
$351$			14.0868i			0.751897i
$352$	4.71016	+	4.83409i	0.251053	+	0.257658i
$353$	22.6637	−	22.6637i	1.20627	−	1.20627i	0.234043	−	0.972226i	$-0.424804\pi$
$353$	22.6637	−	22.6637i	1.20627	−	1.20627i	0.972226	−	0.234043i	$-0.0751957\pi$
$354$	−10.0355	−	1.61619i	−0.533379	−	0.0858994i
$355$	−6.61449	−	0.730100i	−0.351061	−	0.0387497i
$356$	0.696680	−	2.10686i	0.0369239	−	0.111664i
$357$	−0.196346			−0.0103917
$358$	19.5740	+	3.15234i	1.03452	+	0.166606i
$359$			4.31874i			0.227934i	0.993485	+	0.113967i	$0.0363559\pi$
$359$			4.31874i			0.227934i	−0.993485	+	0.113967i	$0.963644\pi$
$360$	3.11085	+	15.6323i	0.163956	+	0.823895i
$361$			38.8288i			2.04362i
$362$	−0.330766	+	2.05384i	−0.0173847	+	0.107947i
$363$	−6.63371			−0.348180
$364$	3.20091	−	1.61006i	0.167773	−	0.0843899i
$365$	−13.5867	−	16.9582i	−0.711159	−	0.887632i
$366$	1.06082	−	6.58699i	0.0554499	−	0.344308i
$367$	−6.46940	+	6.46940i	−0.337700	+	0.337700i	−0.855501	−	0.517801i	$-0.826751\pi$
$367$	−6.46940	+	6.46940i	−0.337700	+	0.337700i	0.517801	+	0.855501i	$0.326751\pi$
$368$	17.2801	−	2.55320i	0.900787	−	0.133095i
$369$			6.42077i			0.334252i
$370$	14.9029	−	8.44970i	0.774767	−	0.439279i
$371$	−2.08915	+	2.08915i	−0.108463	+	0.108463i
$372$	3.81008	−	11.5222i	0.197543	−	0.597400i
$373$			16.7831i			0.868995i	0.900673	+	0.434497i	$0.143074\pi$
$373$			16.7831i			0.868995i	−0.900673	+	0.434497i	$0.856926\pi$
$374$	−0.576000	−	0.797141i	−0.0297842	−	0.0412192i
$375$	2.50818	−	7.32736i	0.129522	−	0.378383i
$376$	16.2215	+	8.42507i	0.836558	+	0.434490i
$377$	15.5818	−	15.5818i	0.802502	−	0.802502i
$378$	0.418142	−	2.59639i	0.0215069	−	0.133544i
$379$	−7.31046	+	7.31046i	−0.375513	+	0.375513i	−0.869480	−	0.493967i	$-0.835546\pi$
$379$	−7.31046	+	7.31046i	−0.375513	+	0.375513i	0.493967	+	0.869480i	$0.335546\pi$
$380$	−31.8748	+	11.8564i	−1.63514	+	0.608223i
$381$	7.30966	+	7.30966i	0.374485	+	0.374485i
$382$	2.55457	+	3.53533i	0.130703	+	0.180883i
$383$	−5.31492	−	5.31492i	−0.271580	−	0.271580i	0.558156	−	0.829736i	$-0.311509\pi$
$383$	−5.31492	−	5.31492i	−0.271580	−	0.271580i	−0.829736	+	0.558156i	$0.811509\pi$
$384$	−7.40831	−	2.55689i	−0.378054	−	0.130481i
$385$	0.142345	−	1.28960i	0.00725457	−	0.0657242i
$386$	3.84508	−	23.8754i	0.195710	−	1.21523i
$387$	10.8551			0.551796
$388$	18.0897	−	9.09915i	0.918367	−	0.461939i
$389$	−1.28845	−	1.28845i	−0.0653271	−	0.0653271i	0.673688	−	0.739016i	$-0.264709\pi$
$389$	−1.28845	−	1.28845i	−0.0653271	−	0.0653271i	−0.739016	+	0.673688i	$0.764709\pi$
$390$	−3.98017	−	7.01992i	−0.201544	−	0.355468i
$391$	−2.54526			−0.128719
$392$	18.2393	−	5.76960i	0.921223	−	0.291409i
$393$	0.589160	+	0.589160i	0.0297192	+	0.0297192i
$394$	−14.9230	+	10.7831i	−0.751809	+	0.543244i
$395$	22.5933	+	2.49382i	1.13679	+	0.125478i
$396$	5.37239	−	2.70232i	0.269973	−	0.135797i
$397$			9.53832i			0.478715i	0.970932	+	0.239357i	$0.0769367\pi$
$397$			9.53832i			0.478715i	−0.970932	+	0.239357i	$0.923063\pi$
$398$	8.80291	+	12.1826i	0.441250	+	0.610657i
$399$	2.56175			0.128248
$400$	−13.0704	−	15.1382i	−0.653518	−	0.756911i
$401$	−24.6103			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$401$	−24.6103			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$402$	8.24067	+	11.4045i	0.411007	+	0.568803i
$403$		−	32.2697i		−	1.60747i
$404$	−1.21174	−	2.40902i	−0.0602862	−	0.119853i
$405$	10.9164	+	1.20494i	0.542440	+	0.0598739i
$406$	−3.33446	+	2.40942i	−0.165486	+	0.119578i
$407$	−4.57061	−	4.57061i	−0.226557	−	0.226557i
$408$	1.01343	+	0.526354i	0.0501724	+	0.0260584i
$409$	−16.9457			−0.837911			−0.418955	−	0.908007i	$-0.637604\pi$
$409$	−16.9457			−0.837911			−0.418955	+	0.908007i	$0.637604\pi$
$410$	−3.97376	−	7.00862i	−0.196250	−	0.346131i
$411$	3.81092	+	3.81092i	0.187979	+	0.187979i
$412$	−12.1940	−	24.2426i	−0.600757	−	1.19435i
$413$	5.04594			0.248294
$414$	2.47463	−	15.3659i	0.121622	−	0.755190i
$415$	−1.75475	+	15.8975i	−0.0861373	+	0.780378i
$416$	−20.8375	−	0.270573i	−1.02164	−	0.0132659i
$417$	−2.10250	−	2.10250i	−0.102960	−	0.102960i
$418$	7.51515	+	10.4004i	0.367578	+	0.508701i
$419$	−6.56956	−	6.56956i	−0.320944	−	0.320944i	0.528185	−	0.849129i	$-0.322873\pi$
$419$	−6.56956	−	6.56956i	−0.320944	−	0.320944i	−0.849129	+	0.528185i	$0.822873\pi$
$420$	0.525227	+	1.41202i	0.0256285	+	0.0688993i
$421$	13.8805	−	13.8805i	0.676493	−	0.676493i	−0.282712	−	0.959205i	$-0.591234\pi$
$421$	13.8805	−	13.8805i	0.676493	−	0.676493i	0.959205	+	0.282712i	$0.0912341\pi$
$422$	−3.65064	+	22.6681i	−0.177710	+	1.10346i
$423$	11.5164	−	11.5164i	0.559946	−	0.559946i
$424$	16.3836	−	5.18258i	0.795656	−	0.251688i
$425$	1.56164	+	2.46051i	0.0757507	+	0.119352i
$426$	−1.70754	−	2.36311i	−0.0827305	−	0.114493i
$427$			3.31201i			0.160279i
$428$	−10.0299	−	3.31660i	−0.484813	−	0.160314i
$429$	−2.15295	+	2.15295i	−0.103946	+	0.103946i
$430$	−11.8489	+	6.71813i	−0.571406	+	0.323977i
$431$		−	12.3740i		−	0.596035i	−0.954560	−	0.298017i	$-0.903675\pi$
$431$		−	12.3740i		−	0.596035i	0.954560	−	0.298017i	$-0.0963254\pi$
$432$	−9.11852	+	12.2803i	−0.438715	+	0.590834i
$433$	−0.145326	+	0.145326i	−0.00698392	+	0.00698392i	−0.710590	−	0.703606i	$-0.751572\pi$
$433$	−0.145326	+	0.145326i	−0.00698392	+	0.00698392i	0.703606	+	0.710590i	$0.251572\pi$
$434$	−0.957873	+	5.94777i	−0.0459794	+	0.285502i
$435$	5.79324	+	7.23082i	0.277765	+	0.346691i
$436$	−1.95704	−	3.89074i	−0.0937253	−	0.186332i
$437$	33.2084			1.58857
$438$	1.51366	−	9.39886i	0.0723256	−	0.449095i
$439$		−	3.65842i		−	0.174607i	−0.996182	−	0.0873035i	$-0.972175\pi$
$439$		−	3.65842i		−	0.174607i	0.996182	−	0.0873035i	$-0.0278250\pi$
$440$	−4.19182	+	6.27465i	−0.199837	+	0.299132i
$441$		−	17.0450i		−	0.811669i
$442$	2.99792	+	0.482807i	0.142596	+	0.0229648i
$443$	3.94027			0.187208			0.0936039	−	0.995610i	$-0.470161\pi$
$443$	3.94027			0.187208			0.0936039	+	0.995610i	$0.470161\pi$
$444$	7.12607	+	2.35639i	0.338188	+	0.111829i
$445$	2.46601	+	0.272195i	0.116900	+	0.0129033i
$446$	−4.30184	−	0.692800i	−0.203698	−	0.0328050i
$447$	7.72864	−	7.72864i	0.365552	−	0.365552i
$448$	3.83262	+	0.668398i	0.181074	+	0.0315788i
$449$			38.0014i			1.79340i	0.442642	+	0.896698i	$0.354041\pi$
$449$			38.0014i			1.79340i	−0.442642	+	0.896698i	$0.645959\pi$
$450$	−16.3725	+	7.03546i	−0.771809	+	0.331655i
$451$	−2.14949	+	2.14949i	−0.101215	+	0.101215i
$452$	3.80855	+	7.57165i	0.179139	+	0.356140i
$453$		−	2.20466i		−	0.103584i
$454$	−10.6870	+	7.72221i	−0.501564	+	0.362421i
$455$	2.50476	+	3.12631i	0.117425	+	0.146564i
$456$	−13.2224	−	6.86742i	−0.619195	−	0.321596i
$457$	18.1142	−	18.1142i	0.847348	−	0.847348i	−0.142454	−	0.989801i	$-0.545499\pi$
$457$	18.1142	−	18.1142i	0.847348	−	0.847348i	0.989801	+	0.142454i	$0.0454993\pi$
$458$	5.37592	+	0.865778i	0.251200	+	0.0404551i
$459$	1.57596	−	1.57596i	0.0735595	−	0.0735595i
$460$	6.80860	+	18.3042i	0.317453	+	0.853437i
$461$	12.4144	+	12.4144i	0.578197	+	0.578197i	0.934406	−	0.356209i	$-0.115931\pi$
$461$	12.4144	+	12.4144i	0.578197	+	0.578197i	−0.356209	+	0.934406i	$0.615931\pi$
$462$	0.460726	−	0.332913i	0.0214349	−	0.0154885i
$463$	−8.56578	−	8.56578i	−0.398085	−	0.398085i	0.479472	−	0.877557i	$-0.340828\pi$
$463$	−8.56578	−	8.56578i	−0.398085	−	0.398085i	−0.877557	+	0.479472i	$0.840828\pi$
$464$	23.6698	−	3.49729i	1.09884	−	0.162358i
$465$	13.4864	+	1.48861i	0.625416	+	0.0690327i
$466$	−24.4643	−	3.93991i	−1.13329	−	0.182513i
$467$	−34.3465			−1.58937			−0.794684	−	0.607023i	$-0.792364\pi$
$467$	−34.3465			−1.58937			−0.794684	+	0.607023i	$0.792364\pi$
$468$	−5.82946	+	17.6292i	−0.269467	+	0.814908i
$469$	−4.93889	−	4.93889i	−0.228057	−	0.228057i
$470$	−5.44336	+	19.6981i	−0.251083	+	0.908608i
$471$	−4.88677			−0.225170
$472$	−26.0445	−	13.5269i	−1.19879	−	0.622627i
$473$	3.63397	+	3.63397i	0.167090	+	0.167090i
$474$	5.83248	+	8.07172i	0.267895	+	0.370746i
$475$	−20.3749	−	32.1027i	−0.934866	−	1.47297i
$476$	−0.538227	−	0.177976i	−0.0246696	−	0.00815753i
$477$		−	15.3108i		−	0.701034i
$478$	−28.9068	+	20.8876i	−1.32217	+	0.955375i
$479$	−23.4504			−1.07148			−0.535738	−	0.844384i	$-0.679966\pi$
$479$	−23.4504			−1.07148			−0.535738	+	0.844384i	$0.679966\pi$
$480$	1.07432	−	8.69608i	0.0490358	−	0.396920i
$481$	19.9576			0.909988
$482$	−13.7803	+	9.95740i	−0.627675	+	0.453547i
$483$		−	1.47109i		−	0.0669370i
$484$	−18.1845	−	6.01309i	−0.826567	−	0.273322i
$485$	14.1555	+	17.6681i	0.642767	+	0.802269i
$486$	12.3198	+	17.0497i	0.558837	+	0.773389i
$487$	−5.31215	−	5.31215i	−0.240716	−	0.240716i	0.576430	−	0.817146i	$-0.304445\pi$
$487$	−5.31215	−	5.31215i	−0.240716	−	0.240716i	−0.817146	+	0.576430i	$0.804445\pi$
$488$	8.87868	−	17.0948i	0.401919	−	0.773847i
$489$	11.0978			0.501859
$490$	10.5490	+	18.6056i	0.476557	+	0.840515i
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	0.618171	−	0.786044i	$-0.287874\pi$
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	−0.786044	+	0.618171i	$0.787874\pi$
$492$	1.10817	−	3.35128i	0.0499602	−	0.151087i
$493$	−3.48642			−0.157021
$494$	−39.1142	−	6.29925i	−1.75983	−	0.283417i
$495$	4.20398	+	5.24719i	0.188955	+	0.235844i
$496$	20.8885	−	28.1314i	0.937923	−	1.26314i
$497$	1.02338	+	1.02338i	0.0459050	+	0.0459050i
$498$	−5.67958	+	4.10396i	−0.254508	+	0.183903i
$499$	13.6065	+	13.6065i	0.609111	+	0.609111i	0.942714	−	0.333603i	$-0.108264\pi$
$499$	13.6065	+	13.6065i	0.609111	+	0.609111i	−0.333603	+	0.942714i	$0.608264\pi$
$500$	13.5173	−	17.8124i	0.604513	−	0.796595i
$501$	−11.5006	+	11.5006i	−0.513810	+	0.513810i
$502$	−14.7877	−	2.38152i	−0.660007	−	0.106292i
$503$	−9.31208	+	9.31208i	−0.415205	+	0.415205i	−0.883547	−	0.468342i	$-0.844852\pi$
$503$	−9.31208	+	9.31208i	−0.415205	+	0.415205i	0.468342	+	0.883547i	$0.344852\pi$
$504$	1.59774	−	3.07626i	0.0711691	−	0.137028i
$505$	2.35288	−	1.88509i	0.104702	−	0.0838856i
$506$	5.97247	−	4.31560i	0.265509	−	0.191852i
$507$		−	0.395636i		−	0.0175708i
$508$	13.4116	+	26.6632i	0.595044	+	1.18299i
$509$	7.94836	−	7.94836i	0.352305	−	0.352305i	−0.508662	−	0.860966i	$-0.669860\pi$
$509$	7.94836	−	7.94836i	0.352305	−	0.352305i	0.860966	+	0.508662i	$0.169860\pi$
$510$	−0.340073	+	1.23064i	−0.0150587	+	0.0544935i
$511$			4.72585i			0.209059i
$512$	−17.9902	−	13.7242i	−0.795060	−	0.606531i
$513$	−20.5618	+	20.5618i	−0.907824	+	0.907824i
$514$	19.9054	+	3.20571i	0.877989	+	0.141398i
$515$	23.6776	−	18.9702i	1.04336	−	0.835926i
$516$	−5.66575	−	1.87350i	−0.249421	−	0.0824762i
$517$	7.71069			0.339116
$518$	−3.67847	−	0.592408i	−0.161623	−	0.0260289i
$519$		−	10.3878i		−	0.455972i
$520$	−4.54737	−	22.8510i	−0.199415	−	1.00208i
$521$		−	29.3979i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$521$		−	29.3979i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$522$	3.38968	−	21.0477i	0.148362	−	0.921233i
$523$	−19.5121			−0.853205			−0.426602	−	0.904439i	$-0.640290\pi$
$523$	−19.5121			−0.853205			−0.426602	+	0.904439i	$0.640290\pi$
$524$	1.08098	+	2.14906i	0.0472228	+	0.0938821i
$525$	−1.42211	+	0.902587i	−0.0620660	+	0.0393921i
$526$	1.21984	−	7.57438i	0.0531874	−	0.330259i
$527$	−3.61018	+	3.61018i	−0.157262	+	0.157262i
$528$	−3.27048	+	0.483226i	−0.142329	+	0.0210297i
$529$			3.92999i			0.170869i
$530$	9.47574	+	16.7126i	0.411600	+	0.725948i
$531$	−18.4902	+	18.4902i	−0.802406	+	0.802406i
$532$	7.02232	+	2.32208i	0.304456	+	0.100675i
$533$		−	9.38575i		−	0.406542i
$534$	0.636604	+	0.881012i	0.0275485	+	0.0381251i
$535$	1.29581	−	11.7396i	0.0560227	−	0.507549i
$536$	12.2520	+	38.7319i	0.529205	+	1.67296i
$537$	−6.86692	+	6.86692i	−0.296329	+	0.296329i
$538$	4.26913	−	26.5085i	0.184055	−	1.14286i
$539$	5.70618	−	5.70618i	0.245783	−	0.245783i
$540$	−15.5492	−	7.11777i	−0.669131	−	0.306300i
$541$	8.47183	+	8.47183i	0.364232	+	0.364232i	0.865369	−	0.501136i	$-0.167084\pi$
$541$	8.47183	+	8.47183i	0.364232	+	0.364232i	−0.501136	+	0.865369i	$0.667084\pi$
$542$	10.2309	+	14.1587i	0.439453	+	0.608170i
$543$	−0.720526	−	0.720526i	−0.0309207	−	0.0309207i
$544$	2.30093	+	2.36147i	0.0986516	+	0.101247i
$545$	3.80006	−	3.04456i	0.162777	−	0.130415i
$546$	−0.279050	+	1.73272i	−0.0119422	+	0.0741534i
$547$	9.97988			0.426709			0.213355	−	0.976975i	$-0.431561\pi$
$547$	9.97988			0.426709			0.213355	+	0.976975i	$0.431561\pi$
$548$	6.99219	+	13.9010i	0.298692	+	0.593820i
$549$	−12.1364	−	12.1364i	−0.517971	−	0.517971i
$550$	−7.83631	−	3.12578i	−0.334141	−	0.133284i
$551$	45.4879			1.93785
$552$	−3.94364	+	7.59300i	−0.167852	+	0.323180i
$553$	−3.49559	−	3.49559i	−0.148648	−	0.148648i
$554$	7.78098	−	5.62240i	0.330582	−	0.238873i
$555$	−0.920650	+	8.34081i	−0.0390794	+	0.354048i
$556$	−3.85762	−	7.66922i	−0.163600	−	0.325247i
$557$			13.4866i			0.571445i	0.958312	+	0.285722i	$0.0922335\pi$
$557$			13.4866i			0.571445i	−0.958312	+	0.285722i	$0.907766\pi$
$558$	−18.2848	−	25.3048i	−0.774059	−	1.07124i
$559$	−15.8678			−0.671135
$560$	0.159851	+	4.34674i	0.00675495	+	0.183683i
$561$	0.481724			0.0203384
$562$	−17.8502	−	24.7033i	−0.752965	−	1.04205i
$563$			20.3451i			0.857445i	0.903436	+	0.428723i	$0.141036\pi$
$563$			20.3451i			0.857445i	−0.903436	+	0.428723i	$0.858964\pi$
$564$	−7.99853	+	4.02327i	−0.336799	+	0.169410i
$565$	−7.39519	+	5.92493i	−0.311118	+	0.249264i
$566$	11.3116	−	8.17354i	0.475461	−	0.343560i
$567$	−1.68896	−	1.68896i	−0.0709298	−	0.0709298i
$568$	−2.53872	−	8.02559i	−0.106522	−	0.336746i
$569$	−17.1460			−0.718797			−0.359399	−	0.933184i	$-0.617018\pi$
$569$	−17.1460			−0.718797			−0.359399	+	0.933184i	$0.617018\pi$
$570$	4.43697	−	16.0563i	0.185844	−	0.672524i
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	0.825571	−	0.564298i	$-0.190853\pi$
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	−0.564298	+	0.825571i	$0.690853\pi$
$572$	−7.85325	+	3.95019i	−0.328361	+	0.165166i
$573$	−2.13645			−0.0892516
$574$	−0.278600	+	1.72993i	−0.0116285	+	0.0722057i
$575$	−18.4351	+	11.7004i	−0.768795	+	0.487939i
$576$	−16.4934	+	11.5949i	−0.687225	+	0.483120i
$577$	−10.0373	−	10.0373i	−0.417859	−	0.417859i	0.466606	−	0.884465i	$-0.345477\pi$
$577$	−10.0373	−	10.0373i	−0.417859	−	0.417859i	−0.884465	+	0.466606i	$0.845477\pi$
$578$	13.7994	+	19.0973i	0.573979	+	0.794343i
$579$	8.37596	+	8.37596i	0.348093	+	0.348093i
$580$	9.32623	+	25.0725i	0.387251	+	1.04108i
$581$	2.45963	−	2.45963i	0.102043	−	0.102043i
$582$	−1.57703	+	9.79235i	−0.0653701	+	0.405906i
$583$	5.12561	−	5.12561i	0.212281	−	0.212281i
$584$	12.6688	−	24.3923i	0.524240	−	1.00936i
$585$	−20.6343	−	2.27759i	−0.853124	−	0.0941669i
$586$	11.7593	+	16.2739i	0.485771	+	0.672270i
$587$			30.6857i			1.26654i	0.773933	+	0.633268i	$0.218287\pi$
$587$			30.6857i			1.26654i	−0.773933	+	0.633268i	$0.781713\pi$
$588$	−2.94183	+	8.89655i	−0.121319	+	0.366887i
$589$	47.1025	−	47.1025i	1.94083	−	1.94083i
$590$	8.73962	−	31.6265i	0.359804	−	1.30204i
$591$		−	9.01817i		−	0.370958i
$592$	17.3982	+	12.9188i	0.715062	+	0.530958i
$593$	−2.10671	+	2.10671i	−0.0865123	+	0.0865123i	−0.749039	−	0.662526i	$-0.769484\pi$
$593$	−2.10671	+	2.10671i	−0.0865123	+	0.0865123i	0.662526	+	0.749039i	$0.269484\pi$
$594$	−1.02589	+	6.37011i	−0.0420928	+	0.261369i
$595$	0.0695360	−	0.629976i	0.00285070	−	0.0258265i
$596$	28.1915	−	14.1803i	1.15477	−	0.580850i
$597$	−7.36210			−0.301311
$598$	−3.61737	+	22.4615i	−0.147925	+	0.918518i
$599$		−	32.1322i		−	1.31289i	−0.754375	−	0.656444i	$-0.772060\pi$
$599$		−	32.1322i		−	1.31289i	0.754375	−	0.656444i	$-0.227940\pi$
$600$	9.75980	−	0.846344i	0.398442	−	0.0345519i
$601$			14.9811i			0.611091i	0.952177	+	0.305546i	$0.0988388\pi$
$601$			14.9811i			0.611091i	−0.952177	+	0.305546i	$0.901161\pi$
$602$	2.92465	+	0.471008i	0.119200	+	0.0191968i
$603$	36.1959			1.47401
$604$	1.99840	−	6.04345i	0.0813136	−	0.245905i
$605$	2.34934	−	21.2843i	0.0955141	−	0.865330i
$606$	1.30405	+	0.210014i	0.0529735	+	0.00853125i
$607$	27.3357	−	27.3357i	1.10952	−	1.10952i	0.116310	−	0.993213i	$-0.462893\pi$
$607$	27.3357	−	27.3357i	1.10952	−	1.10952i	0.993213	−	0.116310i	$-0.0371067\pi$
$608$	−30.0206	−	30.8105i	−1.21750	−	1.24953i
$609$		−	2.01506i		−	0.0816544i
$610$	20.7587	+	5.73644i	0.840496	+	0.232261i
$611$	−16.8344	+	16.8344i	−0.681047	+	0.681047i
$612$	2.62443	−	1.32009i	0.106086	−	0.0533616i
$613$			48.3829i			1.95417i	0.212859	+	0.977083i	$0.431723\pi$
$613$			48.3829i			1.95417i	−0.212859	+	0.977083i	$0.568277\pi$
$614$	23.4025	−	16.9103i	0.944449	−	0.682442i
$615$	3.92255	+	0.432967i	0.158173	+	0.0174589i
$616$	1.56472	−	0.494965i	0.0630444	−	0.0199427i
$617$	−31.1565	+	31.1565i	−1.25432	+	1.25432i	−0.300549	+	0.953766i	$0.597170\pi$
$617$	−31.1565	+	31.1565i	−1.25432	+	1.25432i	−0.953766	+	0.300549i	$0.902830\pi$
$618$	13.1230	+	2.11343i	0.527885	+	0.0850146i
$619$	0.198272	−	0.198272i	0.00796922	−	0.00796922i	−0.703111	−	0.711080i	$-0.748206\pi$
$619$	0.198272	−	0.198272i	0.00796922	−	0.00796922i	0.711080	+	0.703111i	$0.248206\pi$
$620$	35.6198	+	16.3053i	1.43053	+	0.654835i
$621$	11.8077	+	11.8077i	0.473825	+	0.473825i
$622$	7.80700	−	5.64120i	0.313032	−	0.226191i
$623$	−0.381537	−	0.381537i	−0.0152859	−	0.0152859i
$624$	6.08529	−	8.19530i	0.243607	−	0.328075i
$625$	22.6216	+	10.6425i	0.904864	+	0.425700i
$626$	2.38790	+	0.384565i	0.0954395	+	0.0153703i
$627$	−6.28512			−0.251003
$628$	−13.3957	−	4.42958i	−0.534547	−	0.176759i
$629$	−2.23276	−	2.23276i	−0.0890259	−	0.0890259i
$630$	3.73559	+	1.03229i	0.148829	+	0.0411273i
$631$	−32.3314			−1.28709			−0.643547	−	0.765407i	$-0.722538\pi$
$631$	−32.3314			−1.28709			−0.643547	+	0.765407i	$0.722538\pi$
$632$	8.67157	+	27.4132i	0.344936	+	1.09044i
$633$	−7.95239	−	7.95239i	−0.316079	−	0.316079i
$634$	2.85076	+	3.94523i	0.113218	+	0.156685i
$635$	−26.0418	+	20.8644i	−1.03344	+	0.827977i
$636$	−2.64252	+	7.99138i	−0.104783	+	0.316879i
$637$			24.9161i			0.987212i
$638$	8.18092	−	5.91139i	0.323886	−	0.234034i
$639$	−7.50010			−0.296700
$640$	10.8275	−	22.8641i	0.427993	−	0.903782i
$641$	−46.5662			−1.83926			−0.919628	−	0.392790i	$-0.871510\pi$
$641$	−46.5662			−1.83926			−0.919628	+	0.392790i	$0.871510\pi$
$642$	4.19413	−	3.03060i	0.165529	−	0.119608i
$643$			40.2247i			1.58631i	0.609021	+	0.793154i	$0.291563\pi$
$643$			40.2247i			1.58631i	−0.609021	+	0.793154i	$0.708437\pi$
$644$	1.33346	−	4.03259i	0.0525458	−	0.158906i
$645$	0.731984	−	6.63156i	0.0288218	−	0.261117i
$646$	3.67118	+	5.08064i	0.144441	+	0.199895i
$647$	−10.7938	−	10.7938i	−0.424349	−	0.424349i	0.462349	−	0.886698i	$-0.347007\pi$
$647$	−10.7938	−	10.7938i	−0.424349	−	0.424349i	−0.886698	+	0.462349i	$0.847007\pi$
$648$	4.18984	+	13.2452i	0.164593	+	0.520322i
$649$	−12.3799			−0.485956
$650$	23.9330	−	10.2843i	0.938731	−	0.403383i
$651$	−2.08659	−	2.08659i	−0.0817799	−	0.0817799i
$652$	30.4215	+	10.0595i	1.19140	+	0.393961i
$653$	−3.92443			−0.153575			−0.0767875	−	0.997047i	$-0.524466\pi$
$653$	−3.92443			−0.153575			−0.0767875	+	0.997047i	$0.524466\pi$
$654$	2.10614	+	0.339188i	0.0823564	+	0.0132633i
$655$	−2.09898	+	1.68167i	−0.0820138	+	0.0657084i
$656$	6.07549	−	8.18210i	0.237208	−	0.319457i
$657$	−17.3173	−	17.3173i	−0.675610	−	0.675610i
$658$	3.60252	−	2.60312i	0.140441	−	0.101480i
$659$	34.6142	+	34.6142i	1.34838	+	1.34838i	0.887425	+	0.460952i	$0.152492\pi$
$659$	34.6142	+	34.6142i	1.34838	+	1.34838i	0.460952	+	0.887425i	$0.347508\pi$
$660$	−1.28862	−	3.46431i	−0.0501594	−	0.134848i
$661$	21.7641	−	21.7641i	0.846525	−	0.846525i	−0.143173	−	0.989698i	$-0.545730\pi$
$661$	21.7641	−	21.7641i	0.846525	−	0.846525i	0.989698	+	0.143173i	$0.0457304\pi$
$662$	2.93146	+	0.472104i	0.113934	+	0.0183489i
$663$	−1.05173	+	1.05173i	−0.0408456	+	0.0408456i
$664$	−19.2890	+	6.10166i	−0.748559	+	0.236790i
$665$	−0.907246	+	8.21938i	−0.0351815	+	0.318734i
$666$	15.6501	−	11.3085i	0.606428	−	0.438194i
$667$		−	26.1216i		−	1.01143i
$668$	−41.9505	+	21.1011i	−1.62311	+	0.816426i
$669$	1.50917	−	1.50917i	0.0583477	−	0.0583477i
$670$	−39.5097	+	22.4013i	−1.52639	+	0.865438i
$671$		−	8.12584i		−	0.313695i
$672$	−1.36487	+	1.32988i	−0.0526510	+	0.0513012i
$673$	29.4450	−	29.4450i	1.13502	−	1.13502i	0.145691	−	0.989330i	$-0.453459\pi$
$673$	29.4450	−	29.4450i	1.13502	−	1.13502i	0.989330	−	0.145691i	$-0.0465405\pi$
$674$	−12.2662	−	1.97544i	−0.472475	−	0.0760910i
$675$	4.16995	−	18.6591i	0.160501	−	0.718189i
$676$	0.358622	−	1.08453i	0.0137932	−	0.0417126i
$677$	−34.7351			−1.33498			−0.667490	−	0.744619i	$-0.732631\pi$
$677$	−34.7351			−1.33498			−0.667490	+	0.744619i	$0.732631\pi$
$678$	−4.09869	−	0.660084i	−0.157409	−	0.0253504i
$679$		−	4.92370i		−	0.188954i
$680$	−2.04772	+	3.06519i	−0.0785264	+	0.117545i
$681$		−	6.45828i		−	0.247482i
$682$	2.35009	−	14.5925i	0.0899897	−	0.558777i
$683$	−22.2693			−0.852110			−0.426055	−	0.904697i	$-0.640097\pi$
$683$	−22.2693			−0.852110			−0.426055	+	0.904697i	$0.640097\pi$
$684$	−34.2414	+	17.2234i	−1.30925	+	0.658554i
$685$	−13.5770	+	10.8777i	−0.518750	+	0.415616i
$686$	1.50505	−	9.34535i	0.0574629	−	0.356807i
$687$	−1.88597	+	1.88597i	−0.0719543	+	0.0719543i
$688$	−13.8328	−	10.2714i	−0.527372	−	0.391592i
$689$			22.3810i			0.852650i
$690$	−9.22038	−	2.54795i	−0.351014	−	0.0969987i
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	−0.342205	−	0.939625i	$-0.611174\pi$
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	0.939625	+	0.342205i	$0.111174\pi$
$692$	9.41591	−	28.4751i	0.357939	−	1.08246i
$693$		−	1.46227i		−	0.0555470i
$694$	−8.40717	−	11.6349i	−0.319132	−	0.441655i
$695$	7.49048	−	6.00128i	0.284130	−	0.227641i
$696$	−5.40188	+	10.4007i	−0.204758	+	0.394237i
$697$	−1.05003	+	1.05003i	−0.0397728	+	0.0397728i
$698$	1.27070	−	7.89023i	0.0480968	−	0.298650i
$699$	8.58253	−	8.58253i	0.324621	−	0.324621i
$700$	−4.71647	+	1.18513i	−0.178266	+	0.0447936i
$701$	−21.5588	−	21.5588i	−0.814266	−	0.814266i	0.171004	−	0.985270i	$-0.445299\pi$
$701$	−21.5588	−	21.5588i	−0.814266	−	0.814266i	−0.985270	+	0.171004i	$0.945299\pi$
$702$	−11.6678	−	16.1474i	−0.440373	−	0.609443i
$703$	29.1311	+	29.1311i	1.09870	+	1.09870i
$704$	−9.40314	−	1.63988i	−0.354394	−	0.0618053i
$705$	−6.25897	−	7.81212i	−0.235726	−	0.294221i
$706$	−7.20702	+	44.7509i	−0.271240	+	1.68422i
$707$	−0.655691			−0.0246598
$708$	12.8421	−	6.45958i	0.482635	−	0.242766i
$709$	−2.96687	−	2.96687i	−0.111423	−	0.111423i	0.649197	−	0.760620i	$-0.275105\pi$
$709$	−2.96687	−	2.96687i	−0.111423	−	0.111423i	−0.760620	+	0.649197i	$0.775105\pi$
$710$	8.18677	−	4.64175i	0.307244	−	0.174202i
$711$	25.6183			0.960760
$712$	0.946485	+	2.99210i	0.0354710	+	0.112134i
$713$	−27.0488	−	27.0488i	−1.01299	−	1.01299i
$714$	0.225067	−	0.162629i	0.00842290	−	0.00608624i
$715$	−6.14529	−	7.67023i	−0.229821	−	0.286850i
$716$	−25.0482	+	12.5993i	−0.936096	+	0.470857i
$717$		−	17.4688i		−	0.652385i
$718$	−3.57712	−	4.95047i	−0.133497	−	0.184750i
$719$	−25.8357			−0.963509			−0.481755	−	0.876306i	$-0.660000\pi$
$719$	−25.8357			−0.963509			−0.481755	+	0.876306i	$0.660000\pi$
$720$	−16.5138	−	15.3423i	−0.615434	−	0.571774i
$721$	−6.59839			−0.245737
$722$	−32.1611	−	44.5085i	−1.19691	−	1.65644i
$723$		−	8.32763i		−	0.309708i
$724$	−1.32201	−	2.62824i	−0.0491320	−	0.0976777i
$725$	−25.2518	+	16.0268i	−0.937829	+	0.595222i
$726$	7.60407	−	5.49457i	0.282214	−	0.203923i
$727$	28.9620	+	28.9620i	1.07414	+	1.07414i	0.997022	+	0.0771198i	$0.0245724\pi$
$727$	28.9620	+	28.9620i	1.07414	+	1.07414i	0.0771198	+	0.997022i	$0.475428\pi$
$728$	−2.33555	+	4.49682i	−0.0865612	+	0.166663i
$729$	4.43146			0.164128
$730$	29.6202	+	8.18521i	1.09629	+	0.302948i
$731$	1.77521	+	1.77521i	0.0656584	+	0.0656584i
$732$	4.23988	+	8.42918i	0.156711	+	0.311551i
$733$	21.1673			0.781832			0.390916	−	0.920426i	$-0.372158\pi$
$733$	21.1673			0.781832			0.390916	+	0.920426i	$0.372158\pi$
$734$	2.05725	−	12.7742i	0.0759346	−	0.471504i
$735$	−10.4131	−	1.14939i	−0.384093	−	0.0423957i
$736$	−17.6930	+	17.2394i	−0.652173	+	0.635453i
$737$	12.1173	+	12.1173i	0.446347	+	0.446347i
$738$	−5.31820	−	7.35999i	−0.195765	−	0.270925i
$739$	2.23302	+	2.23302i	0.0821431	+	0.0821431i	0.746985	−	0.664841i	$-0.231501\pi$
$739$	2.23302	+	2.23302i	0.0821431	+	0.0821431i	−0.664841	+	0.746985i	$0.731501\pi$
$740$	−10.0842	+	22.0295i	−0.370702	+	0.809821i
$741$	13.7220	−	13.7220i	0.504091	−	0.504091i
$742$	0.664344	−	4.12514i	0.0243888	−	0.151439i
$743$	−18.4514	+	18.4514i	−0.676915	+	0.676915i	−0.959301	−	0.282386i	$-0.908874\pi$
$743$	−18.4514	+	18.4514i	−0.676915	+	0.676915i	0.282386	+	0.959301i	$0.408874\pi$
$744$	5.17624	+	16.3635i	0.189770	+	0.599915i
$745$	22.0603	+	27.5345i	0.808226	+	1.00879i
$746$	−13.9011	−	19.2381i	−0.508955	−	0.704356i
$747$			18.0260i			0.659538i
$748$	1.32051	+	0.436655i	0.0482827	+	0.0159657i
$749$	−1.81634	+	1.81634i	−0.0663675	+	0.0663675i
$750$	3.19404	+	10.4767i	0.116630	+	0.382554i
$751$		−	42.4243i		−	1.54808i	−0.633134	−	0.774042i	$-0.718232\pi$
$751$		−	42.4243i		−	1.54808i	0.633134	−	0.774042i	$-0.281768\pi$
$752$	−25.5726	+	3.77845i	−0.932537	+	0.137786i
$753$	5.18780	−	5.18780i	0.189054	−	0.189054i
$754$	−4.95496	+	30.7671i	−0.180449	+	1.12047i
$755$	7.07365	+	0.780782i	0.257437	+	0.0284156i
$756$	1.67123	+	3.32253i	0.0607821	+	0.120839i
$757$	−19.7595			−0.718170			−0.359085	−	0.933305i	$-0.616911\pi$
$757$	−19.7595			−0.718170			−0.359085	+	0.933305i	$0.616911\pi$
$758$	2.32471	−	14.4349i	0.0844372	−	0.524300i
$759$			3.60925i			0.131007i
$760$	26.7169	−	39.9920i	0.969122	−	1.45066i
$761$		−	48.0351i		−	1.74127i	−0.491928	−	0.870636i	$-0.663708\pi$
$761$		−	48.0351i		−	1.74127i	0.491928	−	0.870636i	$-0.336292\pi$
$762$	−14.4333	−	2.32445i	−0.522865	−	0.0842061i
$763$	−1.05899			−0.0383379
$764$	−5.85649	−	1.93657i	−0.211880	−	0.0700628i
$765$	2.05366	+	2.56327i	0.0742502	+	0.0926753i
$766$	10.4946	+	1.69013i	0.379186	+	0.0610669i
$767$	27.0286	−	27.0286i	0.975946	−	0.975946i
$768$	10.6098	−	3.20525i	0.382848	−	0.115659i
$769$			24.0184i			0.866127i	0.901363	+	0.433064i	$0.142567\pi$
$769$			24.0184i			0.866127i	−0.901363	+	0.433064i	$0.857433\pi$
$770$	0.904985	+	1.59614i	0.0326134	+	0.0575210i
$771$	−6.98319	+	6.98319i	−0.251493	+	0.251493i
$772$	15.3680	+	30.5527i	0.553107	+	1.09962i
$773$		−	22.4630i		−	0.807937i	−0.914773	−	0.403969i	$-0.867630\pi$
$773$		−	22.4630i		−	0.807937i	0.914773	−	0.403969i	$-0.132370\pi$
$774$	−12.4430	+	8.99106i	−0.447253	+	0.323177i
$775$	−9.55244	+	42.7439i	−0.343134	+	1.53541i
$776$	−13.1992	+	25.4135i	−0.473824	+	0.912292i
$777$	1.29048	−	1.29048i	0.0462956	−	0.0462956i
$778$	2.54412	+	0.409725i	0.0912113	+	0.0146893i
$779$	13.6999	−	13.6999i	0.490850	−	0.490850i
$780$	10.3768	+	4.75008i	0.371551	+	0.170080i
$781$	−2.51081	−	2.51081i	−0.0898440	−	0.0898440i
$782$	2.91757	−	2.10819i	0.104332	−	0.0753886i
$783$	16.1738	+	16.1738i	0.578005	+	0.578005i
$784$	−16.1284	+	21.7208i	−0.576016	+	0.775743i
$785$	1.73065	−	15.6792i	0.0617697	−	0.559615i
$786$	−1.16333	−	0.187352i	−0.0414946	−	0.00668261i
$787$	26.1054			0.930556			0.465278	−	0.885165i	$-0.345954\pi$
$787$	26.1054			0.930556			0.465278	+	0.885165i	$0.345954\pi$
$788$	8.17446	−	24.7208i	0.291203	−	0.880642i
$789$	2.65724	+	2.65724i	0.0946001	+	0.0946001i
$790$	−27.9637	+	15.8549i	−0.994905	+	0.564093i
$791$	2.06087			0.0732759
$792$	−3.91998	+	7.54745i	−0.139290	+	0.268187i
$793$	17.7408	+	17.7408i	0.629994	+	0.629994i
$794$	−7.90040	−	10.9336i	−0.280375	−	0.388018i
$795$	−9.35363	−	1.03244i	−0.331739	−	0.0366170i
$796$	−20.1812	−	6.67333i	−0.715302	−	0.236530i
$797$			43.4888i			1.54045i	0.637770	+	0.770227i	$0.279857\pi$
$797$			43.4888i			1.54045i	−0.637770	+	0.770227i	$0.720143\pi$
$798$	−2.93647	+	2.12185i	−0.103950	+	0.0751125i
$799$	3.76670			0.133256
$800$	27.5209	+	6.52669i	0.973012	+	0.230753i
$801$	2.79618			0.0987983
$802$	28.2103	−	20.3842i	0.996139	−	0.719793i
$803$		−	11.5946i		−	0.409165i
$804$	−18.8922	−	6.24710i	−0.666276	−	0.220318i
$805$	4.72001	+	0.520989i	0.166358	+	0.0183625i
$806$	26.7284	+	36.9901i	0.941467	+	1.30292i
$807$	9.29969	+	9.29969i	0.327364	+	0.327364i
$808$	3.38433	+	1.75775i	0.119060	+	0.0618373i
$809$	36.6271			1.28774			0.643870	−	0.765135i	$-0.277328\pi$
$809$	36.6271			1.28774			0.643870	+	0.765135i	$0.277328\pi$
$810$	−13.5112	+	7.66063i	−0.474737	+	0.269167i
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	0.955338	−	0.295516i	$-0.0954917\pi$
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	−0.295516	+	0.955338i	$0.595492\pi$
$812$	1.82654	−	5.52373i	0.0640990	−	0.193845i
$813$	−8.55633			−0.300084
$814$	9.02493	+	1.45344i	0.316324	+	0.0509431i
$815$	−3.93029	+	35.6073i	−0.137672	+	1.24727i
$816$	−1.59764	+	0.236058i	−0.0559287	+	0.00826367i
$817$	−23.1614	−	23.1614i	−0.810314	−	0.810314i
$818$	19.4245	−	14.0358i	0.679161	−	0.490750i
$819$	3.19250	+	3.19250i	0.111555	+	0.111555i
$820$	10.3601	+	4.74243i	0.361791	+	0.165613i
$821$	3.91048	−	3.91048i	0.136477	−	0.136477i	−0.635568	−	0.772045i	$-0.719234\pi$
$821$	3.91048	−	3.91048i	0.136477	−	0.136477i	0.772045	+	0.635568i	$0.219234\pi$
$822$	−7.52488	−	1.21186i	−0.262460	−	0.0422686i
$823$	35.4412	−	35.4412i	1.23540	−	1.23540i	0.273542	−	0.961860i	$-0.411805\pi$
$823$	35.4412	−	35.4412i	1.23540	−	1.23540i	0.961860	−	0.273542i	$-0.0881952\pi$
$824$	34.0574	+	17.6887i	1.18645	+	0.616214i
$825$	3.48908	−	2.21445i	0.121474	−	0.0770972i
$826$	−5.78405	+	4.17945i	−0.201253	+	0.145422i
$827$		−	44.0700i		−	1.53246i	−0.642565	−	0.766232i	$-0.722130\pi$
$827$		−	44.0700i		−	1.53246i	0.642565	−	0.766232i	$-0.277870\pi$
$828$	9.89061	+	19.6632i	0.343723	+	0.683344i
$829$	15.1609	−	15.1609i	0.526561	−	0.526561i	−0.392984	−	0.919545i	$-0.628557\pi$
$829$	15.1609	−	15.1609i	0.526561	−	0.526561i	0.919545	+	0.392984i	$0.128557\pi$
$830$	−11.1562	−	19.6764i	−0.387236	−	0.682977i
$831$			4.70216i			0.163116i
$832$	24.1097	−	16.9492i	0.835854	−	0.587607i
$833$	2.78749	−	2.78749i	0.0965808	−	0.0965808i
$834$	4.15151	+	0.668590i	0.143755	+	0.0231514i
$835$	−32.8269	−	40.9728i	−1.13602	−	1.41792i
$836$	−17.2289	−	5.69711i	−0.595874	−	0.197039i
$837$	33.4958			1.15779
$838$	12.9720	+	2.08910i	0.448109	+	0.0721669i
$839$			40.3143i			1.39180i	0.718137	+	0.695901i	$0.244995\pi$
$839$			40.3143i			1.39180i	−0.718137	+	0.695901i	$0.755005\pi$
$840$	−1.77160	−	1.18353i	−0.0611260	−	0.0408356i
$841$		−	6.78056i		−	0.233812i
$842$	−4.41396	+	27.4078i	−0.152115	+	0.944535i
$843$	14.9286			0.514168
$844$	−14.5909	−	29.0077i	−0.502238	−	0.998485i
$845$	1.26940	+	0.140115i	0.0436687	+	0.00482011i
$846$	−3.66218	+	22.7398i	−0.125908	+	0.781809i
$847$	−3.29307	+	3.29307i	−0.113151	+	0.113151i
$848$	−14.4875	+	19.5108i	−0.497502	+	0.670005i
$849$			6.83575i			0.234602i
$850$	−3.82807	−	1.52696i	−0.131302	−	0.0523741i
$851$	16.7286	−	16.7286i	0.573450	−	0.573450i
$852$	3.91463	+	1.29446i	0.134113	+	0.0443473i
$853$		−	28.6203i		−	0.979941i	−0.871739	−	0.489971i	$-0.837008\pi$
$853$		−	28.6203i		−	0.979941i	0.871739	−	0.489971i	$-0.162992\pi$
$854$	−2.74327	−	3.79648i	−0.0938728	−	0.129913i
$855$	−26.7944	−	33.4434i	−0.916349	−	1.14374i
$856$	14.2441	−	4.50582i	0.486854	−	0.154006i
$857$	−7.19794	+	7.19794i	−0.245877	+	0.245877i	−0.819276	−	0.573399i	$-0.805624\pi$
$857$	−7.19794	+	7.19794i	−0.245877	+	0.245877i	0.573399	+	0.819276i	$0.305624\pi$
$858$	0.684634	−	4.25113i	0.0233730	−	0.145131i
$859$	−18.8135	+	18.8135i	−0.641910	+	0.641910i	−0.951025	−	0.309115i	$-0.899967\pi$
$859$	−18.8135	+	18.8135i	−0.641910	+	0.641910i	0.309115	+	0.951025i	$0.399967\pi$
$860$	8.01766	−	17.5151i	0.273400	−	0.597259i
$861$	−0.606890	−	0.606890i	−0.0206828	−	0.0206828i
$862$	10.2491	+	14.1840i	0.349087	+	0.483110i
$863$	19.2328	+	19.2328i	0.654691	+	0.654691i	0.954119	−	0.299428i	$-0.0967958\pi$
$863$	19.2328	+	19.2328i	0.654691	+	0.654691i	−0.299428	+	0.954119i	$0.596796\pi$
$864$	0.280854	−	21.6293i	0.00955484	−	0.735843i
$865$	33.3292	+	3.67883i	1.13323	+	0.125084i
$866$	0.0462133	−	0.286955i	0.00157039	−	0.00975112i
$867$	−11.5408			−0.391945
$868$	−3.82843	−	7.61118i	−0.129945	−	0.258340i
$869$	8.57624	+	8.57624i	0.290929	+	0.290929i
$870$	−12.6298	−	3.49011i	−0.428191	−	0.118326i
$871$	−52.9103			−1.79280
$872$	5.46593	+	2.83888i	0.185100	+	0.0961367i
$873$	18.0423	+	18.0423i	0.610638	+	0.610638i
$874$	−38.0660	+	27.5058i	−1.28760	+	0.930398i
$875$	−2.39231	−	4.88250i	−0.0808749	−	0.165059i
$876$	6.04981	+	12.0274i	0.204404	+	0.406369i
$877$			35.4397i			1.19671i	0.801229	+	0.598357i	$0.204180\pi$
$877$			35.4397i			1.19671i	−0.801229	+	0.598357i	$0.795820\pi$
$878$	3.03020	+	4.19357i	0.102264	+	0.141526i
$879$	−9.83458			−0.331712
$880$	−0.392187	−	10.6645i	−0.0132206	−	0.359500i
$881$	30.2010			1.01750			0.508748	−	0.860915i	$-0.330108\pi$
$881$	30.2010			1.01750			0.508748	+	0.860915i	$0.330108\pi$
$882$	14.1181	+	19.5384i	0.475380	+	0.657891i
$883$		−	28.9931i		−	0.975696i	−0.872928	−	0.487848i	$-0.837782\pi$
$883$		−	28.9931i		−	0.975696i	0.872928	−	0.487848i	$-0.162218\pi$
$884$	−3.83634	+	1.92968i	−0.129030	+	0.0649023i
$885$	10.0491	+	12.5428i	0.337798	+	0.421622i
$886$	−4.51664	+	3.26364i	−0.151740	+	0.109644i
$887$	5.33418	+	5.33418i	0.179104	+	0.179104i	0.790965	−	0.611861i	$-0.209579\pi$
$887$	5.33418	+	5.33418i	0.179104	+	0.179104i	−0.611861	+	0.790965i	$0.709579\pi$
$888$	−10.1202	+	3.20131i	−0.339612	+	0.107429i
$889$	7.25724			0.243400
$890$	−3.05219	+	1.73054i	−0.102310	+	0.0580077i
$891$	4.14379	+	4.14379i	0.138822	+	0.138822i
$892$	5.50493	−	2.76898i	0.184319	−	0.0927125i
$893$	−49.1447			−1.64456
$894$	−2.45769	+	15.2606i	−0.0821974	+	0.510392i
$895$	−19.6006	−	24.4645i	−0.655176	−	0.817757i
$896$	−4.94687	+	2.40831i	−0.165263	+	0.0804561i
$897$	−7.87991	−	7.87991i	−0.263103	−	0.263103i
$898$	−31.4758	−	43.5602i	−1.05036	−	1.45362i
$899$	−37.0507	−	37.0507i	−1.23571	−	1.23571i
$900$	12.9401	−	21.6256i	0.431338	−	0.720855i
$901$	2.50388	−	2.50388i	0.0834163	−	0.0834163i
$902$	0.683531	−	4.24428i	0.0227591	−	0.141319i
$903$	−1.02602	+	1.02602i	−0.0341439	+	0.0341439i
$904$	−10.6371	−	5.52467i	−0.353785	−	0.183748i
$905$	2.56699	−	2.05664i	0.0853295	−	0.0683649i
$906$	1.82607	+	2.52715i	0.0606672	+	0.0839589i
$907$			26.2683i			0.872226i	0.899892	+	0.436113i	$0.143645\pi$
$907$			26.2683i			0.872226i	−0.899892	+	0.436113i	$0.856355\pi$
$908$	5.85407	−	17.7036i	0.194274	−	0.587514i
$909$	2.40270	−	2.40270i	0.0796924	−	0.0796924i
$910$	−5.46060	−	1.50898i	−0.181017	−	0.0500221i
$911$			33.5196i			1.11055i	0.831665	+	0.555277i	$0.187388\pi$
$911$			33.5196i			1.11055i	−0.831665	+	0.555277i	$0.812612\pi$
$912$	20.8447	−	3.07988i	0.690236	−	0.101985i
$913$	−6.03459	+	6.03459i	−0.199716	+	0.199716i
$914$	−5.76028	+	35.7676i	−0.190533	+	1.18309i
$915$	−8.23273	+	6.59596i	−0.272166	+	0.218056i
$916$	−6.87940	+	3.46034i	−0.227302	+	0.114333i
$917$	0.584935			0.0193163
$918$	−0.501151	+	3.11182i	−0.0165405	+	0.102705i
$919$		−	25.7545i		−	0.849564i	−0.905296	−	0.424782i	$-0.860351\pi$
$919$		−	25.7545i		−	0.849564i	0.905296	−	0.424782i	$-0.139649\pi$
$920$	−22.9655	−	15.3422i	−0.757151	−	0.505819i
$921$			14.1425i			0.466011i
$922$	−24.5130	−	3.94775i	−0.807292	−	0.130012i
$923$	10.9635			0.360868
$924$	−0.252375	+	0.763221i	−0.00830254	+	0.0251081i
$925$	−26.4355	−	5.90782i	−0.869193	−	0.194248i
$926$	16.9136	+	2.72390i	0.555816	+	0.0895128i
$927$	24.1790	−	24.1790i	0.794141	−	0.794141i
$928$	−24.2354	+	23.6141i	−0.795565	+	0.775170i
$929$			9.06425i			0.297388i	0.988883	+	0.148694i	$0.0475070\pi$
$929$			9.06425i			0.297388i	−0.988883	+	0.148694i	$0.952493\pi$
$930$	−16.6921	+	9.46414i	−0.547356	+	0.310341i
$931$	−36.3688	+	36.3688i	−1.19194	+	1.19194i
$932$	31.3062	−	15.7470i	1.02547	−	0.515811i
$933$			4.71788i			0.154456i
$934$	39.3707	−	28.4486i	1.28825	−	0.930865i
$935$	−0.170603	+	1.54561i	−0.00557931	+	0.0505469i
$936$	−7.91970	−	25.0363i	−0.258864	−	0.818338i
$937$	−3.38621	+	3.38621i	−0.110623	+	0.110623i	−0.760251	−	0.649629i	$-0.774924\pi$
$937$	−3.38621	+	3.38621i	−0.110623	+	0.110623i	0.649629	+	0.760251i	$0.274924\pi$
$938$	9.75212	+	1.57055i	0.318418	+	0.0512804i
$939$	−0.837719	+	0.837719i	−0.0273379	+	0.0273379i
$940$	−10.0760	−	27.0882i	−0.328642	−	0.883519i
$941$	−16.9347	−	16.9347i	−0.552054	−	0.552054i	0.374979	−	0.927033i	$-0.377650\pi$
$941$	−16.9347	−	16.9347i	−0.552054	−	0.552054i	−0.927033	+	0.374979i	$0.877650\pi$
$942$	5.60159	−	4.04761i	0.182510	−	0.131878i
$943$	−7.86722	−	7.86722i	−0.256192	−	0.256192i
$944$	41.0583	−	6.06651i	1.33633	−	0.197448i
$945$	−3.24509	+	2.59993i	−0.105563	+	0.0845756i
$946$	−7.17548	−	1.15559i	−0.233295	−	0.0375716i
$947$	−1.08633			−0.0353011			−0.0176505	−	0.999844i	$-0.505619\pi$
$947$	−1.08633			−0.0353011			−0.0176505	+	0.999844i	$0.505619\pi$
$948$	−13.3713	−	4.42150i	−0.434279	−	0.143604i
$949$	25.3140	+	25.3140i	0.821727	+	0.821727i
$950$	49.9453	+	19.9224i	1.62044	+	0.646368i
$951$	−2.38416			−0.0773117
$952$	0.764372	−	0.241792i	0.0247734	−	0.00783654i
$953$	10.7914	+	10.7914i	0.349567	+	0.349567i	0.859948	−	0.510381i	$-0.170496\pi$
$953$	10.7914	+	10.7914i	0.349567	+	0.349567i	−0.510381	+	0.859948i	$0.670496\pi$
$954$	12.6816	+	17.5504i	0.410583	+	0.568217i
$955$	0.756627	−	6.85482i	0.0244839	−	0.221817i
$956$	15.8345	−	47.8859i	0.512124	−	1.54874i
$957$			4.94385i			0.159812i
$958$	26.8807	−	19.4235i	0.868475	−	0.627544i
$959$	3.78359			0.122178
$960$	5.97132	+	10.8580i	0.192723	+	0.350439i
$961$	−45.7317			−1.47522
$962$	−22.8770	+	16.5305i	−0.737583	+	0.532964i
$963$		−	13.3115i		−	0.428956i
$964$	7.54853	−	22.8279i	0.243122	−	0.735237i
$965$	−29.8407	+	23.9079i	−0.960605	+	0.769624i
$966$	1.21848	+	1.68628i	0.0392038	+	0.0542552i
$967$	−31.4724	−	31.4724i	−1.01208	−	1.01208i	−0.999926	−	0.0121587i	$-0.996130\pi$
$967$	−31.4724	−	31.4724i	−1.01208	−	1.01208i	−0.0121587	−	0.999926i	$-0.503870\pi$
$968$	25.8250	−	8.16917i	0.830046	−	0.262567i
$969$	−3.07030			−0.0986323
$970$	−30.8603	−	8.52789i	−0.990864	−	0.273814i
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	0.230909	−	0.972975i	$-0.425830\pi$
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	−0.972975	+	0.230909i	$0.925830\pi$
$972$	−28.2438	−	9.33942i	−0.905921	−	0.299562i
$973$	−2.08742			−0.0669196
$974$	10.4891	+	1.68925i	0.336094	+	0.0541271i
$975$	−2.78284	+	12.4523i	−0.0891221	+	0.398791i
$976$	3.98188	+	26.9495i	0.127457	+	0.862632i
$977$	15.3820	+	15.3820i	0.492114	+	0.492114i	0.908972	−	0.416858i	$-0.136869\pi$
$977$	15.3820	+	15.3820i	0.492114	+	0.492114i	−0.416858	+	0.908972i	$0.636869\pi$
$978$	−12.7211	+	9.19207i	−0.406777	+	0.293930i
$979$	0.936080	+	0.936080i	0.0299173	+	0.0299173i
$980$	−27.5028	−	12.5896i	−0.878543	−	0.402160i
$981$	3.88052	−	3.88052i	0.123896	−	0.123896i
$982$	7.34496	+	1.18289i	0.234387	+	0.0377475i
$983$	−38.5198	+	38.5198i	−1.22859	+	1.22859i	−0.264093	+	0.964497i	$0.585073\pi$
$983$	−38.5198	+	38.5198i	−1.22859	+	1.22859i	−0.964497	+	0.264093i	$0.914927\pi$
$984$	1.50552	+	4.75937i	0.0479943	+	0.151723i
$985$	28.9348	+	3.19380i	0.921941	+	0.101763i
$986$	3.99641	−	2.88773i	0.127272	−	0.0919642i
$987$			2.17705i			0.0692964i
$988$	50.0533	−	25.1769i	1.59241	−	0.800982i
$989$	−13.3005	+	13.3005i	−0.422931	+	0.422931i
$990$	−9.16507	−	2.53266i	−0.291285	−	0.0804933i
$991$			22.0556i			0.700619i	0.936634	+	0.350310i	$0.113924\pi$
$991$			22.0556i			0.700619i	−0.936634	+	0.350310i	$0.886076\pi$
$992$	−0.643375	+	49.5480i	−0.0204272	+	1.57315i
$993$	−1.02841	+	1.02841i	−0.0326356	+	0.0326356i
$994$	−2.02073	−	0.325433i	−0.0640936	−	0.0103221i
$995$	2.60730	−	23.6213i	0.0826569	−	0.748847i
$996$	3.11114	−	9.40856i	0.0985804	−	0.298122i
$997$	0.840040			0.0266043			0.0133022	−	0.999912i	$-0.495766\pi$
$997$	0.840040			0.0266043			0.0133022	+	0.999912i	$0.495766\pi$
$998$	−26.8668	−	4.32684i	−0.850455	−	0.136964i
$999$			20.7159i			0.655422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.j.b.67.3	yes	18
3.2	odd	2		720.2.bd.g.307.7		18
4.3	odd	2		320.2.j.b.47.6		18
5.2	odd	4		400.2.s.d.243.3		18
5.3	odd	4		80.2.s.b.3.7	yes	18
5.4	even	2		400.2.j.d.307.7		18
8.3	odd	2		640.2.j.c.607.4		18
8.5	even	2		640.2.j.d.607.6		18
15.8	even	4		720.2.z.g.163.3		18
16.3	odd	4		640.2.s.d.287.4		18
16.5	even	4		320.2.s.b.207.4		18
16.11	odd	4		80.2.s.b.27.7	yes	18
16.13	even	4		640.2.s.c.287.6		18
20.3	even	4		320.2.s.b.303.4		18
20.7	even	4		1600.2.s.d.943.6		18
20.19	odd	2		1600.2.j.d.1007.4		18
40.3	even	4		640.2.s.c.223.6		18
40.13	odd	4		640.2.s.d.223.4		18
48.11	even	4		720.2.z.g.667.3		18
80.3	even	4		640.2.j.d.543.4		18
80.13	odd	4		640.2.j.c.543.6		18
80.27	even	4		400.2.j.d.43.7		18
80.37	odd	4		1600.2.j.d.143.6		18
80.43	even	4	inner	80.2.j.b.43.3	✓	18
80.53	odd	4		320.2.j.b.143.4		18
80.59	odd	4		400.2.s.d.107.3		18
80.69	even	4		1600.2.s.d.207.6		18
240.203	odd	4		720.2.bd.g.523.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.3	✓	18	80.43	even	4	inner
80.2.j.b.67.3	yes	18	1.1	even	1	trivial
80.2.s.b.3.7	yes	18	5.3	odd	4
80.2.s.b.27.7	yes	18	16.11	odd	4
320.2.j.b.47.6		18	4.3	odd	2
320.2.j.b.143.4		18	80.53	odd	4
320.2.s.b.207.4		18	16.5	even	4
320.2.s.b.303.4		18	20.3	even	4
400.2.j.d.43.7		18	80.27	even	4
400.2.j.d.307.7		18	5.4	even	2
400.2.s.d.107.3		18	80.59	odd	4
400.2.s.d.243.3		18	5.2	odd	4
640.2.j.c.543.6		18	80.13	odd	4
640.2.j.c.607.4		18	8.3	odd	2
640.2.j.d.543.4		18	80.3	even	4
640.2.j.d.607.6		18	8.5	even	2
640.2.s.c.223.6		18	40.3	even	4
640.2.s.c.287.6		18	16.13	even	4
640.2.s.d.223.4		18	40.13	odd	4
640.2.s.d.287.4		18	16.3	odd	4
720.2.z.g.163.3		18	15.8	even	4
720.2.z.g.667.3		18	48.11	even	4
720.2.bd.g.307.7		18	3.2	odd	2
720.2.bd.g.523.7		18	240.203	odd	4
1600.2.j.d.143.6		18	80.37	odd	4
1600.2.j.d.1007.4		18	20.19	odd	2
1600.2.s.d.207.6		18	80.69	even	4
1600.2.s.d.943.6		18	20.7	even	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14628 + 0.828280i) q^{2} -0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(2.22257 + 0.245325i) q^{5} +(0.573759 + 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(0.853049 + 2.69672i) q^{8} +2.52015 q^{9} +O(q^{10})\)	\(q+(-1.14628 + 0.828280i) q^{2} -0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(2.22257 + 0.245325i) q^{5} +(0.573759 + 0.794040i) q^{6} +(-0.343872 - 0.343872i) q^{7} +(0.853049 + 2.69672i) q^{8} +2.52015 q^{9} +(-2.75088 + 1.55970i) q^{10} +(0.843672 + 0.843672i) q^{11} +(-1.31538 - 0.434957i) q^{12} -3.68390 q^{13} +(0.678995 + 0.109350i) q^{14} +(0.169939 - 1.53960i) q^{15} +(-3.21147 - 2.38463i) q^{16} +(0.412137 + 0.412137i) q^{17} +(-2.88879 + 2.08739i) q^{18} +(-5.37721 - 5.37721i) q^{19} +(1.86140 - 4.06635i) q^{20} +(-0.238204 + 0.238204i) q^{21} +(-1.66588 - 0.268286i) q^{22} +(-3.08788 + 3.08788i) q^{23} +(1.86805 - 0.590917i) q^{24} +(4.87963 + 1.09050i) q^{25} +(4.22278 - 3.05130i) q^{26} -3.82387i q^{27} +(-0.868890 + 0.437052i) q^{28} +(-4.22969 + 4.22969i) q^{29} +(1.08042 + 1.90557i) q^{30} +8.75966i q^{31} +(5.65638 + 0.0734474i) q^{32} +(0.584422 - 0.584422i) q^{33} +(-0.813788 - 0.131059i) q^{34} +(-0.679919 - 0.848640i) q^{35} +(1.58241 - 4.78546i) q^{36} -5.41752 q^{37} +(10.6176 + 1.70994i) q^{38} +2.55188i q^{39} +(1.23439 + 6.20293i) q^{40} +2.54777i q^{41} +(0.0757484 - 0.470348i) q^{42} +4.30732 q^{43} +(2.13178 - 1.07228i) q^{44} +(5.60121 + 0.618255i) q^{45} +(0.981939 - 6.09720i) q^{46} +(4.56972 - 4.56972i) q^{47} +(-1.65186 + 2.22462i) q^{48} -6.76350i q^{49} +(-6.49665 + 2.79168i) q^{50} +(0.285492 - 0.285492i) q^{51} +(-2.31314 + 6.99528i) q^{52} -6.07536i q^{53} +(3.16724 + 4.38322i) q^{54} +(1.66815 + 2.08209i) q^{55} +(0.633987 - 1.22067i) q^{56} +(-3.72486 + 3.72486i) q^{57} +(1.34503 - 8.35177i) q^{58} +(-7.33694 + 7.33694i) q^{59} +(-2.81681 - 1.28942i) q^{60} +(-4.81576 - 4.81576i) q^{61} +(-7.25545 - 10.0410i) q^{62} +(-0.866609 - 0.866609i) q^{63} +(-6.54461 + 4.60087i) q^{64} +(-8.18773 - 0.903753i) q^{65} +(-0.185845 + 1.15397i) q^{66} +14.3626 q^{67} +(1.04138 - 0.523815i) q^{68} +(2.13901 + 2.13901i) q^{69} +(1.48229 + 0.409613i) q^{70} -2.97605 q^{71} +(2.14981 + 6.79614i) q^{72} +(-6.87152 - 6.87152i) q^{73} +(6.20998 - 4.48722i) q^{74} +(0.755404 - 3.38018i) q^{75} +(-13.5870 + 6.83429i) q^{76} -0.580231i q^{77} +(-2.11367 - 2.92517i) q^{78} +10.1654 q^{79} +(-6.55271 - 6.08785i) q^{80} +4.91161 q^{81} +(-2.11027 - 2.92046i) q^{82} +7.15276i q^{83} +(0.302751 + 0.601890i) q^{84} +(0.814896 + 1.01711i) q^{85} +(-4.93739 + 3.56767i) q^{86} +(2.92996 + 2.92996i) q^{87} +(-1.55545 + 2.99484i) q^{88} +1.10953 q^{89} +(-6.93263 + 3.93068i) q^{90} +(1.26679 + 1.26679i) q^{91} +(3.92461 + 7.80240i) q^{92} +6.06792 q^{93} +(-1.45316 + 9.02318i) q^{94} +(-10.6321 - 13.2704i) q^{95} +(0.0508779 - 3.91824i) q^{96} +(7.15920 + 7.15920i) q^{97} +(5.60207 + 7.75285i) q^{98} +(2.12618 + 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

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