LMFDB - Embedded newform 170.2.g.e.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(89,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("170.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	170.89
Dual form			170.2.g.e.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.292893 - 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.292893 + 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} -2.82843i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.292893 - 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.292893 + 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} -2.82843i q^{9} +(2.12132 + 0.707107i) q^{10} +(-1.58579 - 1.58579i) q^{11} +(-0.292893 - 0.292893i) q^{12} -3.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(0.414214 + 0.828427i) q^{15} +1.00000 q^{16} +(-2.12132 + 3.53553i) q^{17} +2.82843i q^{18} -7.24264i q^{19} +(-2.12132 - 0.707107i) q^{20} -0.585786 q^{21} +(1.58579 + 1.58579i) q^{22} +(2.82843 - 2.82843i) q^{23} +(0.292893 + 0.292893i) q^{24} +(4.00000 + 3.00000i) q^{25} +3.00000i q^{26} +(-1.70711 + 1.70711i) q^{27} +(1.00000 - 1.00000i) q^{28} +(0.707107 - 0.707107i) q^{29} +(-0.414214 - 0.828427i) q^{30} +(-5.36396 + 5.36396i) q^{31} -1.00000 q^{32} +0.928932i q^{33} +(2.12132 - 3.53553i) q^{34} +(-2.82843 + 1.41421i) q^{35} -2.82843i q^{36} +(5.24264 + 5.24264i) q^{37} +7.24264i q^{38} +(-0.878680 + 0.878680i) q^{39} +(2.12132 + 0.707107i) q^{40} +(4.41421 + 4.41421i) q^{41} +0.585786 q^{42} +3.75736 q^{43} +(-1.58579 - 1.58579i) q^{44} +(-2.00000 + 6.00000i) q^{45} +(-2.82843 + 2.82843i) q^{46} +1.58579i q^{47} +(-0.292893 - 0.292893i) q^{48} +5.00000i q^{49} +(-4.00000 - 3.00000i) q^{50} +(1.65685 - 0.414214i) q^{51} -3.00000i q^{52} -3.00000 q^{53} +(1.70711 - 1.70711i) q^{54} +(2.24264 + 4.48528i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(-2.12132 + 2.12132i) q^{57} +(-0.707107 + 0.707107i) q^{58} -12.8995i q^{59} +(0.414214 + 0.828427i) q^{60} +(6.12132 + 6.12132i) q^{61} +(5.36396 - 5.36396i) q^{62} +(-2.82843 - 2.82843i) q^{63} +1.00000 q^{64} +(-2.12132 + 6.36396i) q^{65} -0.928932i q^{66} -14.4853i q^{67} +(-2.12132 + 3.53553i) q^{68} -1.65685 q^{69} +(2.82843 - 1.41421i) q^{70} +(3.70711 - 3.70711i) q^{71} +2.82843i q^{72} +(-8.36396 - 8.36396i) q^{73} +(-5.24264 - 5.24264i) q^{74} +(-0.292893 - 2.05025i) q^{75} -7.24264i q^{76} -3.17157 q^{77} +(0.878680 - 0.878680i) q^{78} +(-0.242641 - 0.242641i) q^{79} +(-2.12132 - 0.707107i) q^{80} -7.48528 q^{81} +(-4.41421 - 4.41421i) q^{82} +4.24264 q^{83} -0.585786 q^{84} +(7.00000 - 6.00000i) q^{85} -3.75736 q^{86} -0.414214 q^{87} +(1.58579 + 1.58579i) q^{88} +11.4853 q^{89} +(2.00000 - 6.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(2.82843 - 2.82843i) q^{92} +3.14214 q^{93} -1.58579i q^{94} +(-5.12132 + 15.3640i) q^{95} +(0.292893 + 0.292893i) q^{96} +(0.121320 + 0.121320i) q^{97} -5.00000i q^{98} +(-4.48528 + 4.48528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 16 q^{25} - 4 q^{27} + 4 q^{28} + 4 q^{30} + 4 q^{31} - 4 q^{32} + 4 q^{37} - 12 q^{39} + 12 q^{41} + 8 q^{42} + 32 q^{43} - 12 q^{44} - 8 q^{45} - 4 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{69} + 12 q^{71} - 8 q^{73} - 4 q^{74} - 4 q^{75} - 24 q^{77} + 12 q^{78} + 16 q^{79} + 4 q^{81} - 12 q^{82} - 8 q^{84} + 28 q^{85} - 32 q^{86} + 4 q^{87} + 12 q^{88} + 12 q^{89} + 8 q^{90} - 12 q^{91} - 44 q^{93} - 12 q^{95} + 4 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^21 + 12 * q^22 + 4 * q^24 + 16 * q^25 - 4 * q^27 + 4 * q^28 + 4 * q^30 + 4 * q^31 - 4 * q^32 + 4 * q^37 - 12 * q^39 + 12 * q^41 + 8 * q^42 + 32 * q^43 - 12 * q^44 - 8 * q^45 - 4 * q^48 - 16 * q^50 - 16 * q^51 - 12 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^69 + 12 * q^71 - 8 * q^73 - 4 * q^74 - 4 * q^75 - 24 * q^77 + 12 * q^78 + 16 * q^79 + 4 * q^81 - 12 * q^82 - 8 * q^84 + 28 * q^85 - 32 * q^86 + 4 * q^87 + 12 * q^88 + 12 * q^89 + 8 * q^90 - 12 * q^91 - 44 * q^93 - 12 * q^95 + 4 * q^96 - 8 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.292893	−	0.292893i	−0.169102	−	0.169102i	0.617483	−	0.786585i	$-0.288153\pi$
$3$	−0.292893	−	0.292893i	−0.169102	−	0.169102i	−0.786585	+	0.617483i	$0.788153\pi$
$4$	1.00000			0.500000
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$6$	0.292893	+	0.292893i	0.119573	+	0.119573i
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$	−1.00000			−0.353553
$9$		−	2.82843i		−	0.942809i
$10$	2.12132	+	0.707107i	0.670820	+	0.223607i
$11$	−1.58579	−	1.58579i	−0.478133	−	0.478133i	0.426401	−	0.904534i	$-0.359781\pi$
$11$	−1.58579	−	1.58579i	−0.478133	−	0.478133i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	−0.292893	−	0.292893i	−0.0845510	−	0.0845510i
$13$		−	3.00000i		−	0.832050i	−0.909353	−	0.416025i	$-0.863423\pi$
$13$		−	3.00000i		−	0.832050i	0.909353	−	0.416025i	$-0.136577\pi$
$14$	−1.00000	+	1.00000i	−0.267261	+	0.267261i
$15$	0.414214	+	0.828427i	0.106949	+	0.213899i
$16$	1.00000			0.250000
$17$	−2.12132	+	3.53553i	−0.514496	+	0.857493i
$17$	−2.12132	+	3.53553i	−0.514496	+	0.857493i
$18$			2.82843i			0.666667i
$19$		−	7.24264i		−	1.66158i	−0.556589	−	0.830788i	$-0.687890\pi$
$19$		−	7.24264i		−	1.66158i	0.556589	−	0.830788i	$-0.312110\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$	−0.585786			−0.127829
$22$	1.58579	+	1.58579i	0.338091	+	0.338091i
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	−0.347801	−	0.937568i	$-0.613071\pi$
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	0.937568	+	0.347801i	$0.113071\pi$
$24$	0.292893	+	0.292893i	0.0597866	+	0.0597866i
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$			3.00000i			0.588348i
$27$	−1.70711	+	1.70711i	−0.328533	+	0.328533i
$28$	1.00000	−	1.00000i	0.188982	−	0.188982i
$29$	0.707107	−	0.707107i	0.131306	−	0.131306i	−0.638399	−	0.769706i	$-0.720403\pi$
$29$	0.707107	−	0.707107i	0.131306	−	0.131306i	0.769706	+	0.638399i	$0.220403\pi$
$30$	−0.414214	−	0.828427i	−0.0756247	−	0.151249i
$31$	−5.36396	+	5.36396i	−0.963396	+	0.963396i	−0.999353	−	0.0359575i	$-0.988552\pi$
$31$	−5.36396	+	5.36396i	−0.963396	+	0.963396i	0.0359575	+	0.999353i	$0.488552\pi$
$32$	−1.00000			−0.176777
$33$			0.928932i			0.161706i
$34$	2.12132	−	3.53553i	0.363803	−	0.606339i
$35$	−2.82843	+	1.41421i	−0.478091	+	0.239046i
$36$		−	2.82843i		−	0.471405i
$37$	5.24264	+	5.24264i	0.861885	+	0.861885i	0.991557	−	0.129672i	$-0.0413925\pi$
$37$	5.24264	+	5.24264i	0.861885	+	0.861885i	−0.129672	+	0.991557i	$0.541392\pi$
$38$			7.24264i			1.17491i
$39$	−0.878680	+	0.878680i	−0.140701	+	0.140701i
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$	4.41421	+	4.41421i	0.689384	+	0.689384i	0.962096	−	0.272712i	$-0.0879205\pi$
$41$	4.41421	+	4.41421i	0.689384	+	0.689384i	−0.272712	+	0.962096i	$0.587920\pi$
$42$	0.585786			0.0903888
$43$	3.75736			0.572992			0.286496	−	0.958081i	$-0.407509\pi$
$43$	3.75736			0.572992			0.286496	+	0.958081i	$0.407509\pi$
$44$	−1.58579	−	1.58579i	−0.239066	−	0.239066i
$45$	−2.00000	+	6.00000i	−0.298142	+	0.894427i
$46$	−2.82843	+	2.82843i	−0.417029	+	0.417029i
$47$			1.58579i			0.231311i	0.993289	+	0.115655i	$0.0368968\pi$
$47$			1.58579i			0.231311i	−0.993289	+	0.115655i	$0.963103\pi$
$48$	−0.292893	−	0.292893i	−0.0422755	−	0.0422755i
$49$			5.00000i			0.714286i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	1.65685	−	0.414214i	0.232006	−	0.0580015i
$52$		−	3.00000i		−	0.416025i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	1.70711	−	1.70711i	0.232308	−	0.232308i
$55$	2.24264	+	4.48528i	0.302398	+	0.604795i
$56$	−1.00000	+	1.00000i	−0.133631	+	0.133631i
$57$	−2.12132	+	2.12132i	−0.280976	+	0.280976i
$58$	−0.707107	+	0.707107i	−0.0928477	+	0.0928477i
$59$		−	12.8995i		−	1.67937i	−0.543073	−	0.839686i	$-0.682739\pi$
$59$		−	12.8995i		−	1.67937i	0.543073	−	0.839686i	$-0.317261\pi$
$60$	0.414214	+	0.828427i	0.0534747	+	0.106949i
$61$	6.12132	+	6.12132i	0.783755	+	0.783755i	0.980462	−	0.196707i	$-0.0630249\pi$
$61$	6.12132	+	6.12132i	0.783755	+	0.783755i	−0.196707	+	0.980462i	$0.563025\pi$
$62$	5.36396	−	5.36396i	0.681224	−	0.681224i
$63$	−2.82843	−	2.82843i	−0.356348	−	0.356348i
$64$	1.00000			0.125000
$65$	−2.12132	+	6.36396i	−0.263117	+	0.789352i
$66$		−	0.928932i		−	0.114344i
$67$		−	14.4853i		−	1.76966i	−0.465915	−	0.884829i	$-0.654275\pi$
$67$		−	14.4853i		−	1.76966i	0.465915	−	0.884829i	$-0.345725\pi$
$68$	−2.12132	+	3.53553i	−0.257248	+	0.428746i
$69$	−1.65685			−0.199462
$70$	2.82843	−	1.41421i	0.338062	−	0.169031i
$71$	3.70711	−	3.70711i	0.439953	−	0.439953i	−0.452043	−	0.891996i	$-0.649305\pi$
$71$	3.70711	−	3.70711i	0.439953	−	0.439953i	0.891996	+	0.452043i	$0.149305\pi$
$72$			2.82843i			0.333333i
$73$	−8.36396	−	8.36396i	−0.978928	−	0.978928i	0.0208549	−	0.999783i	$-0.493361\pi$
$73$	−8.36396	−	8.36396i	−0.978928	−	0.978928i	−0.999783	+	0.0208549i	$0.993361\pi$
$74$	−5.24264	−	5.24264i	−0.609445	−	0.609445i
$75$	−0.292893	−	2.05025i	−0.0338204	−	0.236743i
$76$		−	7.24264i		−	0.830788i
$77$	−3.17157			−0.361434
$78$	0.878680	−	0.878680i	0.0994909	−	0.0994909i
$79$	−0.242641	−	0.242641i	−0.0272992	−	0.0272992i	0.693325	−	0.720625i	$-0.256145\pi$
$79$	−0.242641	−	0.242641i	−0.0272992	−	0.0272992i	−0.720625	+	0.693325i	$0.756145\pi$
$80$	−2.12132	−	0.707107i	−0.237171	−	0.0790569i
$81$	−7.48528			−0.831698
$82$	−4.41421	−	4.41421i	−0.487468	−	0.487468i
$83$	4.24264			0.465690			0.232845	−	0.972514i	$-0.425196\pi$
$83$	4.24264			0.465690			0.232845	+	0.972514i	$0.425196\pi$
$84$	−0.585786			−0.0639145
$85$	7.00000	−	6.00000i	0.759257	−	0.650791i
$86$	−3.75736			−0.405166
$87$	−0.414214			−0.0444084
$88$	1.58579	+	1.58579i	0.169045	+	0.169045i
$89$	11.4853			1.21744			0.608719	−	0.793386i	$-0.291684\pi$
$89$	11.4853			1.21744			0.608719	+	0.793386i	$0.291684\pi$
$90$	2.00000	−	6.00000i	0.210819	−	0.632456i
$91$	−3.00000	−	3.00000i	−0.314485	−	0.314485i
$92$	2.82843	−	2.82843i	0.294884	−	0.294884i
$93$	3.14214			0.325824
$94$		−	1.58579i		−	0.163561i
$95$	−5.12132	+	15.3640i	−0.525436	+	1.57631i
$96$	0.292893	+	0.292893i	0.0298933	+	0.0298933i
$97$	0.121320	+	0.121320i	0.0123182	+	0.0123182i	0.713239	−	0.700921i	$-0.247227\pi$
$97$	0.121320	+	0.121320i	0.0123182	+	0.0123182i	−0.700921	+	0.713239i	$0.747227\pi$
$98$		−	5.00000i		−	0.505076i
$99$	−4.48528	+	4.48528i	−0.450788	+	0.450788i
$100$	4.00000	+	3.00000i	0.400000	+	0.300000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	−1.65685	+	0.414214i	−0.164053	+	0.0410133i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$			3.00000i			0.294174i
$105$	1.24264	+	0.414214i	0.121269	+	0.0404231i
$106$	3.00000			0.291386
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$	−1.70711	+	1.70711i	−0.164266	+	0.164266i
$109$	8.60660	+	8.60660i	0.824363	+	0.824363i	0.986730	−	0.162367i	$-0.0519130\pi$
$109$	8.60660	+	8.60660i	0.824363	+	0.824363i	−0.162367	+	0.986730i	$0.551913\pi$
$110$	−2.24264	−	4.48528i	−0.213827	−	0.427655i
$111$		−	3.07107i		−	0.291493i
$112$	1.00000	−	1.00000i	0.0944911	−	0.0944911i
$113$	2.46447	−	2.46447i	0.231837	−	0.231837i	−0.581622	−	0.813459i	$-0.697582\pi$
$113$	2.46447	−	2.46447i	0.231837	−	0.231837i	0.813459	+	0.581622i	$0.197582\pi$
$114$	2.12132	−	2.12132i	0.198680	−	0.198680i
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$	0.707107	−	0.707107i	0.0656532	−	0.0656532i
$117$	−8.48528			−0.784465
$118$			12.8995i			1.18749i
$119$	1.41421	+	5.65685i	0.129641	+	0.518563i
$120$	−0.414214	−	0.828427i	−0.0378124	−	0.0756247i
$121$		−	5.97056i		−	0.542778i
$122$	−6.12132	−	6.12132i	−0.554198	−	0.554198i
$123$		−	2.58579i		−	0.233153i
$124$	−5.36396	+	5.36396i	−0.481698	+	0.481698i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$	2.82843	+	2.82843i	0.251976	+	0.251976i
$127$	17.7279			1.57310			0.786549	−	0.617527i	$-0.211866\pi$
$127$	17.7279			1.57310			0.786549	+	0.617527i	$0.211866\pi$
$128$	−1.00000			−0.0883883
$129$	−1.10051	−	1.10051i	−0.0968941	−	0.0968941i
$130$	2.12132	−	6.36396i	0.186052	−	0.558156i
$131$	7.58579	−	7.58579i	0.662773	−	0.662773i	−0.293260	−	0.956033i	$-0.594740\pi$
$131$	7.58579	−	7.58579i	0.662773	−	0.662773i	0.956033	+	0.293260i	$0.0947400\pi$
$132$			0.928932i			0.0808532i
$133$	−7.24264	−	7.24264i	−0.628017	−	0.628017i
$134$			14.4853i			1.25134i
$135$	4.82843	−	2.41421i	0.415565	−	0.207782i
$136$	2.12132	−	3.53553i	0.181902	−	0.303170i
$137$			4.58579i			0.391790i	0.980625	+	0.195895i	$0.0627612\pi$
$137$			4.58579i			0.391790i	−0.980625	+	0.195895i	$0.937239\pi$
$138$	1.65685			0.141041
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	−0.997893	−	0.0648849i	$-0.979332\pi$
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	0.0648849	+	0.997893i	$0.479332\pi$
$140$	−2.82843	+	1.41421i	−0.239046	+	0.119523i
$141$	0.464466	−	0.464466i	0.0391151	−	0.0391151i
$142$	−3.70711	+	3.70711i	−0.311093	+	0.311093i
$143$	−4.75736	+	4.75736i	−0.397830	+	0.397830i
$144$		−	2.82843i		−	0.235702i
$145$	−2.00000	+	1.00000i	−0.166091	+	0.0830455i
$146$	8.36396	+	8.36396i	0.692206	+	0.692206i
$147$	1.46447	−	1.46447i	0.120787	−	0.120787i
$148$	5.24264	+	5.24264i	0.430942	+	0.430942i
$149$	−12.7279			−1.04271			−0.521356	−	0.853339i	$-0.674574\pi$
$149$	−12.7279			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$150$	0.292893	+	2.05025i	0.0239146	+	0.167402i
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$			7.24264i			0.587456i
$153$	10.0000	+	6.00000i	0.808452	+	0.485071i
$154$	3.17157			0.255573
$155$	15.1716	−	7.58579i	1.21861	−	0.609305i
$156$	−0.878680	+	0.878680i	−0.0703507	+	0.0703507i
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0.242641	+	0.242641i	0.0193035	+	0.0193035i
$159$	0.878680	+	0.878680i	0.0696838	+	0.0696838i
$160$	2.12132	+	0.707107i	0.167705	+	0.0559017i
$161$		−	5.65685i		−	0.445823i
$162$	7.48528			0.588099
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	−0.860598	−	0.509284i	$-0.829910\pi$
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	0.509284	+	0.860598i	$0.329910\pi$
$164$	4.41421	+	4.41421i	0.344692	+	0.344692i
$165$	0.656854	−	1.97056i	0.0511360	−	0.153408i
$166$	−4.24264			−0.329293
$167$	−1.07107	−	1.07107i	−0.0828817	−	0.0828817i	0.664451	−	0.747332i	$-0.268666\pi$
$167$	−1.07107	−	1.07107i	−0.0828817	−	0.0828817i	−0.747332	+	0.664451i	$0.768666\pi$
$168$	0.585786			0.0451944
$169$	4.00000			0.307692
$170$	−7.00000	+	6.00000i	−0.536875	+	0.460179i
$171$	−20.4853			−1.56655
$172$	3.75736			0.286496
$173$	17.6569	+	17.6569i	1.34243	+	1.34243i	0.893639	+	0.448787i	$0.148144\pi$
$173$	17.6569	+	17.6569i	1.34243	+	1.34243i	0.448787	+	0.893639i	$0.351856\pi$
$174$	0.414214			0.0314014
$175$	7.00000	−	1.00000i	0.529150	−	0.0755929i
$176$	−1.58579	−	1.58579i	−0.119533	−	0.119533i
$177$	−3.77817	+	3.77817i	−0.283985	+	0.283985i
$178$	−11.4853			−0.860858
$179$		−	0.686292i		−	0.0512958i	−0.999671	−	0.0256479i	$-0.991835\pi$
$179$		−	0.686292i		−	0.0512958i	0.999671	−	0.0256479i	$-0.00816488\pi$
$180$	−2.00000	+	6.00000i	−0.149071	+	0.447214i
$181$	−14.0000	−	14.0000i	−1.04061	−	1.04061i	−0.999140	−	0.0414721i	$-0.986795\pi$
$181$	−14.0000	−	14.0000i	−1.04061	−	1.04061i	−0.0414721	−	0.999140i	$-0.513205\pi$
$182$	3.00000	+	3.00000i	0.222375	+	0.222375i
$183$		−	3.58579i		−	0.265069i
$184$	−2.82843	+	2.82843i	−0.208514	+	0.208514i
$185$	−7.41421	−	14.8284i	−0.545104	−	1.09021i
$186$	−3.14214			−0.230393
$187$	8.97056	−	2.24264i	0.655993	−	0.163998i
$188$			1.58579i			0.115655i
$189$			3.41421i			0.248347i
$190$	5.12132	−	15.3640i	0.371540	−	1.11462i
$191$	21.2132			1.53493			0.767467	−	0.641089i	$-0.221517\pi$
$191$	21.2132			1.53493			0.767467	+	0.641089i	$0.221517\pi$
$192$	−0.292893	−	0.292893i	−0.0211377	−	0.0211377i
$193$	18.4853	−	18.4853i	1.33060	−	1.33060i	0.425767	−	0.904833i	$-0.360004\pi$
$193$	18.4853	−	18.4853i	1.33060	−	1.33060i	0.904833	−	0.425767i	$-0.139996\pi$
$194$	−0.121320	−	0.121320i	−0.00871029	−	0.00871029i
$195$	2.48528	−	1.24264i	0.177975	−	0.0889873i
$196$			5.00000i			0.357143i
$197$	3.34315	−	3.34315i	0.238189	−	0.238189i	−0.577911	−	0.816100i	$-0.696132\pi$
$197$	3.34315	−	3.34315i	0.238189	−	0.238189i	0.816100	+	0.577911i	$0.196132\pi$
$198$	4.48528	−	4.48528i	0.318755	−	0.318755i
$199$	−7.12132	+	7.12132i	−0.504817	+	0.504817i	−0.912931	−	0.408114i	$-0.866187\pi$
$199$	−7.12132	+	7.12132i	−0.504817	+	0.504817i	0.408114	+	0.912931i	$0.366187\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	−4.24264	+	4.24264i	−0.299253	+	0.299253i
$202$		0			0
$203$		−	1.41421i		−	0.0992583i
$204$	1.65685	−	0.414214i	0.116003	−	0.0290008i
$205$	−6.24264	−	12.4853i	−0.436005	−	0.872010i
$206$		0			0
$207$	−8.00000	−	8.00000i	−0.556038	−	0.556038i
$208$		−	3.00000i		−	0.208013i
$209$	−11.4853	+	11.4853i	−0.794454	+	0.794454i
$210$	−1.24264	−	0.414214i	−0.0857504	−	0.0285835i
$211$	−8.00000	−	8.00000i	−0.550743	−	0.550743i	0.375912	−	0.926655i	$-0.377329\pi$
$211$	−8.00000	−	8.00000i	−0.550743	−	0.550743i	−0.926655	+	0.375912i	$0.877329\pi$
$212$	−3.00000			−0.206041
$213$	−2.17157			−0.148794
$214$	2.82843	+	2.82843i	0.193347	+	0.193347i
$215$	−7.97056	−	2.65685i	−0.543588	−	0.181196i
$216$	1.70711	−	1.70711i	0.116154	−	0.116154i
$217$			10.7279i			0.728259i
$218$	−8.60660	−	8.60660i	−0.582913	−	0.582913i
$219$			4.89949i			0.331077i
$220$	2.24264	+	4.48528i	0.151199	+	0.302398i
$221$	10.6066	+	6.36396i	0.713477	+	0.428086i
$222$			3.07107i			0.206117i
$223$	−23.2426			−1.55644			−0.778221	−	0.627990i	$-0.783878\pi$
$223$	−23.2426			−1.55644			−0.778221	+	0.627990i	$0.783878\pi$
$224$	−1.00000	+	1.00000i	−0.0668153	+	0.0668153i
$225$	8.48528	−	11.3137i	0.565685	−	0.754247i
$226$	−2.46447	+	2.46447i	−0.163934	+	0.163934i
$227$	−4.05025	+	4.05025i	−0.268825	+	0.268825i	−0.828627	−	0.559802i	$-0.810877\pi$
$227$	−4.05025	+	4.05025i	−0.268825	+	0.268825i	0.559802	+	0.828627i	$0.310877\pi$
$228$	−2.12132	+	2.12132i	−0.140488	+	0.140488i
$229$		−	7.75736i		−	0.512621i	−0.966595	−	0.256310i	$-0.917493\pi$
$229$		−	7.75736i		−	0.512621i	0.966595	−	0.256310i	$-0.0825069\pi$
$230$	8.00000	−	4.00000i	0.527504	−	0.263752i
$231$	0.928932	+	0.928932i	0.0611193	+	0.0611193i
$232$	−0.707107	+	0.707107i	−0.0464238	+	0.0464238i
$233$	−10.9497	−	10.9497i	−0.717342	−	0.717342i	0.250718	−	0.968060i	$-0.419333\pi$
$233$	−10.9497	−	10.9497i	−0.717342	−	0.717342i	−0.968060	+	0.250718i	$0.919333\pi$
$234$	8.48528			0.554700
$235$	1.12132	−	3.36396i	0.0731469	−	0.219441i
$236$		−	12.8995i		−	0.839686i
$237$			0.142136i			0.00923270i
$238$	−1.41421	−	5.65685i	−0.0916698	−	0.366679i
$239$	22.2426			1.43876			0.719378	−	0.694618i	$-0.244427\pi$
$239$	22.2426			1.43876			0.719378	+	0.694618i	$0.244427\pi$
$240$	0.414214	+	0.828427i	0.0267374	+	0.0534747i
$241$	2.75736	−	2.75736i	0.177617	−	0.177617i	−0.612699	−	0.790316i	$-0.709916\pi$
$241$	2.75736	−	2.75736i	0.177617	−	0.177617i	0.790316	+	0.612699i	$0.209916\pi$
$242$			5.97056i			0.383802i
$243$	7.31371	+	7.31371i	0.469175	+	0.469175i
$244$	6.12132	+	6.12132i	0.391877	+	0.391877i
$245$	3.53553	−	10.6066i	0.225877	−	0.677631i
$246$			2.58579i			0.164864i
$247$	−21.7279			−1.38251
$248$	5.36396	−	5.36396i	0.340612	−	0.340612i
$249$	−1.24264	−	1.24264i	−0.0787492	−	0.0787492i
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$	20.4853			1.29302			0.646510	−	0.762906i	$-0.276228\pi$
$251$	20.4853			1.29302			0.646510	+	0.762906i	$0.276228\pi$
$252$	−2.82843	−	2.82843i	−0.178174	−	0.178174i
$253$	−8.97056			−0.563974
$254$	−17.7279			−1.11235
$255$	−3.80761	−	0.292893i	−0.238442	−	0.0183417i
$256$	1.00000			0.0625000
$257$	6.72792			0.419676			0.209838	−	0.977736i	$-0.432706\pi$
$257$	6.72792			0.419676			0.209838	+	0.977736i	$0.432706\pi$
$258$	1.10051	+	1.10051i	0.0685145	+	0.0685145i
$259$	10.4853			0.651524
$260$	−2.12132	+	6.36396i	−0.131559	+	0.394676i
$261$	−2.00000	−	2.00000i	−0.123797	−	0.123797i
$262$	−7.58579	+	7.58579i	−0.468651	+	0.468651i
$263$	4.75736			0.293351			0.146676	−	0.989185i	$-0.453143\pi$
$263$	4.75736			0.293351			0.146676	+	0.989185i	$0.453143\pi$
$264$		−	0.928932i		−	0.0571718i
$265$	6.36396	+	2.12132i	0.390935	+	0.130312i
$266$	7.24264	+	7.24264i	0.444075	+	0.444075i
$267$	−3.36396	−	3.36396i	−0.205871	−	0.205871i
$268$		−	14.4853i		−	0.884829i
$269$	−11.2929	+	11.2929i	−0.688540	+	0.688540i	−0.961909	−	0.273369i	$-0.911862\pi$
$269$	−11.2929	+	11.2929i	−0.688540	+	0.688540i	0.273369	+	0.961909i	$0.411862\pi$
$270$	−4.82843	+	2.41421i	−0.293849	+	0.146924i
$271$	−6.48528			−0.393953			−0.196976	−	0.980408i	$-0.563112\pi$
$271$	−6.48528			−0.393953			−0.196976	+	0.980408i	$0.563112\pi$
$272$	−2.12132	+	3.53553i	−0.128624	+	0.214373i
$273$			1.75736i			0.106360i
$274$		−	4.58579i		−	0.277037i
$275$	−1.58579	−	11.1005i	−0.0956265	−	0.669386i
$276$	−1.65685			−0.0997309
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	0.909956	−	0.414704i	$-0.136115\pi$
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	−0.414704	+	0.909956i	$0.636115\pi$
$278$	11.0000	−	11.0000i	0.659736	−	0.659736i
$279$	15.1716	+	15.1716i	0.908298	+	0.908298i
$280$	2.82843	−	1.41421i	0.169031	−	0.0845154i
$281$			3.34315i			0.199435i	0.995016	+	0.0997177i	$0.0317940\pi$
$281$			3.34315i			0.199435i	−0.995016	+	0.0997177i	$0.968206\pi$
$282$	−0.464466	+	0.464466i	−0.0276586	+	0.0276586i
$283$	−19.1213	+	19.1213i	−1.13664	+	1.13664i	−0.147597	+	0.989048i	$0.547154\pi$
$283$	−19.1213	+	19.1213i	−1.13664	+	1.13664i	−0.989048	+	0.147597i	$0.952846\pi$
$284$	3.70711	−	3.70711i	0.219976	−	0.219976i
$285$	6.00000	−	3.00000i	0.355409	−	0.177705i
$286$	4.75736	−	4.75736i	0.281309	−	0.281309i
$287$	8.82843			0.521126
$288$			2.82843i			0.166667i
$289$	−8.00000	−	15.0000i	−0.470588	−	0.882353i
$290$	2.00000	−	1.00000i	0.117444	−	0.0587220i
$291$		−	0.0710678i		−	0.00416607i
$292$	−8.36396	−	8.36396i	−0.489464	−	0.489464i
$293$		−	20.6569i		−	1.20679i	−0.797444	−	0.603393i	$-0.793815\pi$
$293$		−	20.6569i		−	1.20679i	0.797444	−	0.603393i	$-0.206185\pi$
$294$	−1.46447	+	1.46447i	−0.0854094	+	0.0854094i
$295$	−9.12132	+	27.3640i	−0.531064	+	1.59319i
$296$	−5.24264	−	5.24264i	−0.304722	−	0.304722i
$297$	5.41421			0.314165
$298$	12.7279			0.737309
$299$	−8.48528	−	8.48528i	−0.490716	−	0.490716i
$300$	−0.292893	−	2.05025i	−0.0169102	−	0.118371i
$301$	3.75736	−	3.75736i	0.216571	−	0.216571i
$302$		−	12.0000i		−	0.690522i
$303$		0			0
$304$		−	7.24264i		−	0.415394i
$305$	−8.65685	−	17.3137i	−0.495690	−	0.991380i
$306$	−10.0000	−	6.00000i	−0.571662	−	0.342997i
$307$		−	33.2132i		−	1.89558i	−0.318899	−	0.947789i	$-0.603313\pi$
$307$		−	33.2132i		−	1.89558i	0.318899	−	0.947789i	$-0.396687\pi$
$308$	−3.17157			−0.180717
$309$		0			0
$310$	−15.1716	+	7.58579i	−0.861687	+	0.430844i
$311$	−1.41421	+	1.41421i	−0.0801927	+	0.0801927i	−0.746065	−	0.665873i	$-0.768059\pi$
$311$	−1.41421	+	1.41421i	−0.0801927	+	0.0801927i	0.665873	+	0.746065i	$0.268059\pi$
$312$	0.878680	−	0.878680i	0.0497454	−	0.0497454i
$313$	−22.4853	+	22.4853i	−1.27094	+	1.27094i	−0.325349	+	0.945594i	$0.605482\pi$
$313$	−22.4853	+	22.4853i	−1.27094	+	1.27094i	−0.945594	+	0.325349i	$0.894518\pi$
$314$		−	12.0000i		−	0.677199i
$315$	4.00000	+	8.00000i	0.225374	+	0.450749i
$316$	−0.242641	−	0.242641i	−0.0136496	−	0.0136496i
$317$	−14.1421	+	14.1421i	−0.794301	+	0.794301i	−0.982190	−	0.187889i	$-0.939836\pi$
$317$	−14.1421	+	14.1421i	−0.794301	+	0.794301i	0.187889	+	0.982190i	$0.439836\pi$
$318$	−0.878680	−	0.878680i	−0.0492739	−	0.0492739i
$319$	−2.24264			−0.125564
$320$	−2.12132	−	0.707107i	−0.118585	−	0.0395285i
$321$			1.65685i			0.0924766i
$322$			5.65685i			0.315244i
$323$	25.6066	+	15.3640i	1.42479	+	0.854874i
$324$	−7.48528			−0.415849
$325$	9.00000	−	12.0000i	0.499230	−	0.665640i
$326$	4.48528	−	4.48528i	0.248417	−	0.248417i
$327$		−	5.04163i		−	0.278803i
$328$	−4.41421	−	4.41421i	−0.243734	−	0.243734i
$329$	1.58579	+	1.58579i	0.0874272	+	0.0874272i
$330$	−0.656854	+	1.97056i	−0.0361586	+	0.108476i
$331$			15.7279i			0.864485i	0.901757	+	0.432242i	$0.142278\pi$
$331$			15.7279i			0.864485i	−0.901757	+	0.432242i	$0.857722\pi$
$332$	4.24264			0.232845
$333$	14.8284	−	14.8284i	0.812593	−	0.812593i
$334$	1.07107	+	1.07107i	0.0586062	+	0.0586062i
$335$	−10.2426	+	30.7279i	−0.559615	+	1.67885i
$336$	−0.585786			−0.0319573
$337$	12.8492	+	12.8492i	0.699943	+	0.699943i	0.964398	−	0.264455i	$-0.0851921\pi$
$337$	12.8492	+	12.8492i	0.699943	+	0.699943i	−0.264455	+	0.964398i	$0.585192\pi$
$338$	−4.00000			−0.217571
$339$	−1.44365			−0.0784083
$340$	7.00000	−	6.00000i	0.379628	−	0.325396i
$341$	17.0122			0.921262
$342$	20.4853			1.10772
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−3.75736			−0.202583
$345$	3.51472	+	1.17157i	0.189226	+	0.0630754i
$346$	−17.6569	−	17.6569i	−0.949238	−	0.949238i
$347$	15.7071	−	15.7071i	0.843202	−	0.843202i	−0.146072	−	0.989274i	$-0.546663\pi$
$347$	15.7071	−	15.7071i	0.843202	−	0.843202i	0.989274	+	0.146072i	$0.0466632\pi$
$348$	−0.414214			−0.0222042
$349$		−	10.9706i		−	0.587241i	−0.955922	−	0.293620i	$-0.905140\pi$
$349$		−	10.9706i		−	0.587241i	0.955922	−	0.293620i	$-0.0948602\pi$
$350$	−7.00000	+	1.00000i	−0.374166	+	0.0534522i
$351$	5.12132	+	5.12132i	0.273356	+	0.273356i
$352$	1.58579	+	1.58579i	0.0845227	+	0.0845227i
$353$			11.3137i			0.602168i	0.953598	+	0.301084i	$0.0973484\pi$
$353$			11.3137i			0.602168i	−0.953598	+	0.301084i	$0.902652\pi$
$354$	3.77817	−	3.77817i	0.200808	−	0.200808i
$355$	−10.4853	+	5.24264i	−0.556501	+	0.278250i
$356$	11.4853			0.608719
$357$	1.24264	−	2.07107i	0.0657675	−	0.109613i
$358$			0.686292i			0.0362716i
$359$			7.07107i			0.373197i	0.982436	+	0.186598i	$0.0597463\pi$
$359$			7.07107i			0.373197i	−0.982436	+	0.186598i	$0.940254\pi$
$360$	2.00000	−	6.00000i	0.105409	−	0.316228i
$361$	−33.4558			−1.76083
$362$	14.0000	+	14.0000i	0.735824	+	0.735824i
$363$	−1.74874	+	1.74874i	−0.0917849	+	0.0917849i
$364$	−3.00000	−	3.00000i	−0.157243	−	0.157243i
$365$	11.8284	+	23.6569i	0.619128	+	1.23826i
$366$			3.58579i			0.187432i
$367$	−18.2426	+	18.2426i	−0.952258	+	0.952258i	−0.998911	−	0.0466531i	$-0.985144\pi$
$367$	−18.2426	+	18.2426i	−0.952258	+	0.952258i	0.0466531	+	0.998911i	$0.485144\pi$
$368$	2.82843	−	2.82843i	0.147442	−	0.147442i
$369$	12.4853	−	12.4853i	0.649958	−	0.649958i
$370$	7.41421	+	14.8284i	0.385447	+	0.770893i
$371$	−3.00000	+	3.00000i	−0.155752	+	0.155752i
$372$	3.14214			0.162912
$373$			32.4853i			1.68202i	0.541016	+	0.841012i	$0.318040\pi$
$373$			32.4853i			1.68202i	−0.541016	+	0.841012i	$0.681960\pi$
$374$	−8.97056	+	2.24264i	−0.463857	+	0.115964i
$375$	−0.828427	+	4.55635i	−0.0427798	+	0.235289i
$376$		−	1.58579i		−	0.0817807i
$377$	−2.12132	−	2.12132i	−0.109254	−	0.109254i
$378$		−	3.41421i		−	0.175608i
$379$	0.485281	−	0.485281i	0.0249272	−	0.0249272i	−0.694533	−	0.719461i	$-0.744389\pi$
$379$	0.485281	−	0.485281i	0.0249272	−	0.0249272i	0.719461	+	0.694533i	$0.244389\pi$
$380$	−5.12132	+	15.3640i	−0.262718	+	0.788155i
$381$	−5.19239	−	5.19239i	−0.266014	−	0.266014i
$382$	−21.2132			−1.08536
$383$	−13.2426			−0.676667			−0.338334	−	0.941026i	$-0.609863\pi$
$383$	−13.2426			−0.676667			−0.338334	+	0.941026i	$0.609863\pi$
$384$	0.292893	+	0.292893i	0.0149466	+	0.0149466i
$385$	6.72792	+	2.24264i	0.342887	+	0.114296i
$386$	−18.4853	+	18.4853i	−0.940876	+	0.940876i
$387$		−	10.6274i		−	0.540222i
$388$	0.121320	+	0.121320i	0.00615911	+	0.00615911i
$389$		−	16.6274i		−	0.843044i	−0.906818	−	0.421522i	$-0.861496\pi$
$389$		−	16.6274i		−	0.843044i	0.906818	−	0.421522i	$-0.138504\pi$
$390$	−2.48528	+	1.24264i	−0.125847	+	0.0629236i
$391$	4.00000	+	16.0000i	0.202289	+	0.809155i
$392$		−	5.00000i		−	0.252538i
$393$	−4.44365			−0.224153
$394$	−3.34315	+	3.34315i	−0.168425	+	0.168425i
$395$	0.343146	+	0.686292i	0.0172655	+	0.0345311i
$396$	−4.48528	+	4.48528i	−0.225394	+	0.225394i
$397$	4.72792	−	4.72792i	0.237288	−	0.237288i	−0.578438	−	0.815726i	$-0.696338\pi$
$397$	4.72792	−	4.72792i	0.237288	−	0.237288i	0.815726	+	0.578438i	$0.196338\pi$
$398$	7.12132	−	7.12132i	0.356960	−	0.356960i
$399$			4.24264i			0.212398i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$	−2.10051	−	2.10051i	−0.104894	−	0.104894i	0.652712	−	0.757606i	$-0.273631\pi$
$401$	−2.10051	−	2.10051i	−0.104894	−	0.104894i	−0.757606	+	0.652712i	$0.773631\pi$
$402$	4.24264	−	4.24264i	0.211604	−	0.211604i
$403$	16.0919	+	16.0919i	0.801594	+	0.801594i
$404$		0			0
$405$	15.8787	+	5.29289i	0.789018	+	0.263006i
$406$			1.41421i			0.0701862i
$407$		−	16.6274i		−	0.824190i
$408$	−1.65685	+	0.414214i	−0.0820265	+	0.0205066i
$409$	25.4853			1.26017			0.630083	−	0.776528i	$-0.283021\pi$
$409$	25.4853			1.26017			0.630083	+	0.776528i	$0.283021\pi$
$410$	6.24264	+	12.4853i	0.308302	+	0.616604i
$411$	1.34315	−	1.34315i	0.0662525	−	0.0662525i
$412$		0			0
$413$	−12.8995	−	12.8995i	−0.634743	−	0.634743i
$414$	8.00000	+	8.00000i	0.393179	+	0.393179i
$415$	−9.00000	−	3.00000i	−0.441793	−	0.147264i
$416$			3.00000i			0.147087i
$417$	6.44365			0.315547
$418$	11.4853	−	11.4853i	0.561763	−	0.561763i
$419$	−11.3137	−	11.3137i	−0.552711	−	0.552711i	0.374511	−	0.927222i	$-0.377810\pi$
$419$	−11.3137	−	11.3137i	−0.552711	−	0.552711i	−0.927222	+	0.374511i	$0.877810\pi$
$420$	1.24264	+	0.414214i	0.0606347	+	0.0202116i
$421$	−19.2132			−0.936394			−0.468197	−	0.883624i	$-0.655096\pi$
$421$	−19.2132			−0.936394			−0.468197	+	0.883624i	$0.655096\pi$
$422$	8.00000	+	8.00000i	0.389434	+	0.389434i
$423$	4.48528			0.218082
$424$	3.00000			0.145693
$425$	−19.0919	+	7.77817i	−0.926092	+	0.377297i
$426$	2.17157			0.105213
$427$	12.2426			0.592463
$428$	−2.82843	−	2.82843i	−0.136717	−	0.136717i
$429$	2.78680			0.134548
$430$	7.97056	+	2.65685i	0.384375	+	0.128125i
$431$	17.6569	+	17.6569i	0.850501	+	0.850501i	0.990195	−	0.139694i	$-0.0446119\pi$
$431$	17.6569	+	17.6569i	0.850501	+	0.850501i	−0.139694	+	0.990195i	$0.544612\pi$
$432$	−1.70711	+	1.70711i	−0.0821332	+	0.0821332i
$433$	−5.75736			−0.276681			−0.138341	−	0.990385i	$-0.544177\pi$
$433$	−5.75736			−0.276681			−0.138341	+	0.990385i	$0.544177\pi$
$434$		−	10.7279i		−	0.514957i
$435$	0.878680	+	0.292893i	0.0421295	+	0.0140432i
$436$	8.60660	+	8.60660i	0.412181	+	0.412181i
$437$	−20.4853	−	20.4853i	−0.979944	−	0.979944i
$438$		−	4.89949i		−	0.234107i
$439$	20.9706	−	20.9706i	1.00087	−	1.00087i	0.000870732	−	1.00000i	$-0.499723\pi$
$439$	20.9706	−	20.9706i	1.00087	−	1.00087i	1.00000		0.000870732i	$-0.000277162\pi$
$440$	−2.24264	−	4.48528i	−0.106914	−	0.213827i
$441$	14.1421			0.673435
$442$	−10.6066	−	6.36396i	−0.504505	−	0.302703i
$443$			37.7990i			1.79588i	0.440114	+	0.897942i	$0.354938\pi$
$443$			37.7990i			1.79588i	−0.440114	+	0.897942i	$0.645062\pi$
$444$		−	3.07107i		−	0.145746i
$445$	−24.3640	−	8.12132i	−1.15496	−	0.384988i
$446$	23.2426			1.10057
$447$	3.72792	+	3.72792i	0.176325	+	0.176325i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	−28.7990	−	28.7990i	−1.35911	−	1.35911i	−0.875018	−	0.484090i	$-0.839151\pi$
$449$	−28.7990	−	28.7990i	−1.35911	−	1.35911i	−0.484090	−	0.875018i	$-0.660849\pi$
$450$	−8.48528	+	11.3137i	−0.400000	+	0.533333i
$451$		−	14.0000i		−	0.659234i
$452$	2.46447	−	2.46447i	0.115919	−	0.115919i
$453$	3.51472	−	3.51472i	0.165136	−	0.165136i
$454$	4.05025	−	4.05025i	0.190088	−	0.190088i
$455$	4.24264	+	8.48528i	0.198898	+	0.397796i
$456$	2.12132	−	2.12132i	0.0993399	−	0.0993399i
$457$	−2.24264			−0.104906			−0.0524532	−	0.998623i	$-0.516704\pi$
$457$	−2.24264			−0.104906			−0.0524532	+	0.998623i	$0.516704\pi$
$458$			7.75736i			0.362478i
$459$	−2.41421	−	9.65685i	−0.112686	−	0.450743i
$460$	−8.00000	+	4.00000i	−0.373002	+	0.186501i
$461$			40.2843i			1.87623i	0.346330	+	0.938113i	$0.387428\pi$
$461$			40.2843i			1.87623i	−0.346330	+	0.938113i	$0.612572\pi$
$462$	−0.928932	−	0.928932i	−0.0432178	−	0.0432178i
$463$		−	25.2426i		−	1.17312i	−0.809904	−	0.586562i	$-0.800481\pi$
$463$		−	25.2426i		−	1.17312i	0.809904	−	0.586562i	$-0.199519\pi$
$464$	0.707107	−	0.707107i	0.0328266	−	0.0328266i
$465$	−6.66548	−	2.22183i	−0.309104	−	0.103035i
$466$	10.9497	+	10.9497i	0.507237	+	0.507237i
$467$	−18.7279			−0.866625			−0.433312	−	0.901244i	$-0.642655\pi$
$467$	−18.7279			−0.866625			−0.433312	+	0.901244i	$0.642655\pi$
$468$	−8.48528			−0.392232
$469$	−14.4853	−	14.4853i	−0.668868	−	0.668868i
$470$	−1.12132	+	3.36396i	−0.0517227	+	0.155168i
$471$	3.51472	−	3.51472i	0.161950	−	0.161950i
$472$			12.8995i			0.593747i
$473$	−5.95837	−	5.95837i	−0.273966	−	0.273966i
$474$		−	0.142136i		−	0.00652851i
$475$	21.7279	−	28.9706i	0.996945	−	1.32926i
$476$	1.41421	+	5.65685i	0.0648204	+	0.259281i
$477$			8.48528i			0.388514i
$478$	−22.2426			−1.01735
$479$	−10.0503	+	10.0503i	−0.459208	+	0.459208i	−0.898395	−	0.439188i	$-0.855266\pi$
$479$	−10.0503	+	10.0503i	−0.459208	+	0.459208i	0.439188	+	0.898395i	$0.355266\pi$
$480$	−0.414214	−	0.828427i	−0.0189062	−	0.0378124i
$481$	15.7279	−	15.7279i	0.717132	−	0.717132i
$482$	−2.75736	+	2.75736i	−0.125594	+	0.125594i
$483$	−1.65685	+	1.65685i	−0.0753895	+	0.0753895i
$484$		−	5.97056i		−	0.271389i
$485$	−0.171573	−	0.343146i	−0.00779072	−	0.0155814i
$486$	−7.31371	−	7.31371i	−0.331757	−	0.331757i
$487$	11.2426	−	11.2426i	0.509453	−	0.509453i	−0.404906	−	0.914358i	$-0.632696\pi$
$487$	11.2426	−	11.2426i	0.509453	−	0.509453i	0.914358	+	0.404906i	$0.132696\pi$
$488$	−6.12132	−	6.12132i	−0.277099	−	0.277099i
$489$	2.62742			0.118816
$490$	−3.53553	+	10.6066i	−0.159719	+	0.479157i
$491$		−	6.89949i		−	0.311370i	−0.987807	−	0.155685i	$-0.950242\pi$
$491$		−	6.89949i		−	0.311370i	0.987807	−	0.155685i	$-0.0497585\pi$
$492$		−	2.58579i		−	0.116576i
$493$	1.00000	+	4.00000i	0.0450377	+	0.180151i
$494$	21.7279			0.977585
$495$	12.6863	−	6.34315i	0.570206	−	0.285103i
$496$	−5.36396	+	5.36396i	−0.240849	+	0.240849i
$497$		−	7.41421i		−	0.332573i
$498$	1.24264	+	1.24264i	0.0556841	+	0.0556841i
$499$	−8.51472	−	8.51472i	−0.381171	−	0.381171i	0.490353	−	0.871524i	$-0.336868\pi$
$499$	−8.51472	−	8.51472i	−0.381171	−	0.381171i	−0.871524	+	0.490353i	$0.836868\pi$
$500$	−6.36396	−	9.19239i	−0.284605	−	0.411096i
$501$			0.627417i			0.0280309i
$502$	−20.4853			−0.914303
$503$	13.0711	−	13.0711i	0.582810	−	0.582810i	−0.352864	−	0.935674i	$-0.614792\pi$
$503$	13.0711	−	13.0711i	0.582810	−	0.582810i	0.935674	+	0.352864i	$0.114792\pi$
$504$	2.82843	+	2.82843i	0.125988	+	0.125988i
$505$		0			0
$506$	8.97056			0.398790
$507$	−1.17157	−	1.17157i	−0.0520314	−	0.0520314i
$508$	17.7279			0.786549
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$	3.80761	+	0.292893i	0.168604	+	0.0129695i
$511$	−16.7279			−0.740000
$512$	−1.00000			−0.0441942
$513$	12.3640	+	12.3640i	0.545882	+	0.545882i
$514$	−6.72792			−0.296756
$515$		0			0
$516$	−1.10051	−	1.10051i	−0.0484470	−	0.0484470i
$517$	2.51472	−	2.51472i	0.110597	−	0.110597i
$518$	−10.4853			−0.460697
$519$		−	10.3431i		−	0.454014i
$520$	2.12132	−	6.36396i	0.0930261	−	0.279078i
$521$	−11.3137	−	11.3137i	−0.495663	−	0.495663i	0.414422	−	0.910085i	$-0.363984\pi$
$521$	−11.3137	−	11.3137i	−0.495663	−	0.495663i	−0.910085	+	0.414422i	$0.863984\pi$
$522$	2.00000	+	2.00000i	0.0875376	+	0.0875376i
$523$		−	26.4853i		−	1.15812i	−0.815285	−	0.579060i	$-0.803420\pi$
$523$		−	26.4853i		−	1.15812i	0.815285	−	0.579060i	$-0.196580\pi$
$524$	7.58579	−	7.58579i	0.331387	−	0.331387i
$525$	−2.34315	−	1.75736i	−0.102263	−	0.0766974i
$526$	−4.75736			−0.207431
$527$	−7.58579	−	30.3431i	−0.330442	−	1.32177i
$528$			0.928932i			0.0404266i
$529$			7.00000i			0.304348i
$530$	−6.36396	−	2.12132i	−0.276433	−	0.0921443i
$531$	−36.4853			−1.58333
$532$	−7.24264	−	7.24264i	−0.314008	−	0.314008i
$533$	13.2426	−	13.2426i	0.573602	−	0.573602i
$534$	3.36396	+	3.36396i	0.145573	+	0.145573i
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$			14.4853i			0.625669i
$537$	−0.201010	+	0.201010i	−0.00867423	+	0.00867423i
$538$	11.2929	−	11.2929i	0.486871	−	0.486871i
$539$	7.92893	−	7.92893i	0.341523	−	0.341523i
$540$	4.82843	−	2.41421i	0.207782	−	0.103891i
$541$	20.9706	−	20.9706i	0.901595	−	0.901595i	−0.0939792	−	0.995574i	$-0.529959\pi$
$541$	20.9706	−	20.9706i	0.901595	−	0.901595i	0.995574	+	0.0939792i	$0.0299587\pi$
$542$	6.48528			0.278567
$543$			8.20101i			0.351939i
$544$	2.12132	−	3.53553i	0.0909509	−	0.151585i
$545$	−12.1716	−	24.3431i	−0.521373	−	1.04275i
$546$		−	1.75736i		−	0.0752080i
$547$	2.39340	+	2.39340i	0.102334	+	0.102334i	0.756420	−	0.654086i	$-0.226947\pi$
$547$	2.39340	+	2.39340i	0.102334	+	0.102334i	−0.654086	+	0.756420i	$0.726947\pi$
$548$			4.58579i			0.195895i
$549$	17.3137	−	17.3137i	0.738931	−	0.738931i
$550$	1.58579	+	11.1005i	0.0676182	+	0.473327i
$551$	−5.12132	−	5.12132i	−0.218176	−	0.218176i
$552$	1.65685			0.0705204
$553$	−0.485281			−0.0206363
$554$	−8.24264	−	8.24264i	−0.350196	−	0.350196i
$555$	−2.17157	+	6.51472i	−0.0921781	+	0.276534i
$556$	−11.0000	+	11.0000i	−0.466504	+	0.466504i
$557$			34.7990i			1.47448i	0.675631	+	0.737240i	$0.263871\pi$
$557$			34.7990i			1.47448i	−0.675631	+	0.737240i	$0.736129\pi$
$558$	−15.1716	−	15.1716i	−0.642264	−	0.642264i
$559$		−	11.2721i		−	0.476758i
$560$	−2.82843	+	1.41421i	−0.119523	+	0.0597614i
$561$	−3.28427	−	1.97056i	−0.138662	−	0.0831972i
$562$		−	3.34315i		−	0.141022i
$563$	−45.9411			−1.93619			−0.968094	−	0.250588i	$-0.919376\pi$
$563$	−45.9411			−1.93619			−0.968094	+	0.250588i	$0.919376\pi$
$564$	0.464466	−	0.464466i	0.0195576	−	0.0195576i
$565$	−6.97056	+	3.48528i	−0.293254	+	0.146627i
$566$	19.1213	−	19.1213i	0.803729	−	0.803729i
$567$	−7.48528	+	7.48528i	−0.314352	+	0.314352i
$568$	−3.70711	+	3.70711i	−0.155547	+	0.155547i
$569$			20.3137i			0.851595i	0.904818	+	0.425797i	$0.140006\pi$
$569$			20.3137i			0.851595i	−0.904818	+	0.425797i	$0.859994\pi$
$570$	−6.00000	+	3.00000i	−0.251312	+	0.125656i
$571$	−20.2132	−	20.2132i	−0.845896	−	0.845896i	0.143722	−	0.989618i	$-0.454093\pi$
$571$	−20.2132	−	20.2132i	−0.845896	−	0.845896i	−0.989618	+	0.143722i	$0.954093\pi$
$572$	−4.75736	+	4.75736i	−0.198915	+	0.198915i
$573$	−6.21320	−	6.21320i	−0.259560	−	0.259560i
$574$	−8.82843			−0.368491
$575$	19.7990	−	2.82843i	0.825675	−	0.117954i
$576$		−	2.82843i		−	0.117851i
$577$			4.97056i			0.206927i	0.994633	+	0.103464i	$0.0329925\pi$
$577$			4.97056i			0.206927i	−0.994633	+	0.103464i	$0.967007\pi$
$578$	8.00000	+	15.0000i	0.332756	+	0.623918i
$579$	−10.8284			−0.450014
$580$	−2.00000	+	1.00000i	−0.0830455	+	0.0415227i
$581$	4.24264	−	4.24264i	0.176014	−	0.176014i
$582$			0.0710678i			0.00294586i
$583$	4.75736	+	4.75736i	0.197030	+	0.197030i
$584$	8.36396	+	8.36396i	0.346103	+	0.346103i
$585$	18.0000	+	6.00000i	0.744208	+	0.248069i
$586$			20.6569i			0.853327i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$	1.46447	−	1.46447i	0.0603936	−	0.0603936i
$589$	38.8492	+	38.8492i	1.60076	+	1.60076i
$590$	9.12132	−	27.3640i	0.375519	−	1.12656i
$591$	−1.95837			−0.0805566
$592$	5.24264	+	5.24264i	0.215471	+	0.215471i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	−5.41421			−0.222148
$595$	1.00000	−	13.0000i	0.0409960	−	0.532948i
$596$	−12.7279			−0.521356
$597$	4.17157			0.170731
$598$	8.48528	+	8.48528i	0.346989	+	0.346989i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	0.292893	+	2.05025i	0.0119573	+	0.0837012i
$601$	28.7279	+	28.7279i	1.17184	+	1.17184i	0.981772	+	0.190065i	$0.0608698\pi$
$601$	28.7279	+	28.7279i	1.17184	+	1.17184i	0.190065	+	0.981772i	$0.439130\pi$
$602$	−3.75736	+	3.75736i	−0.153139	+	0.153139i
$603$	−40.9706			−1.66845
$604$			12.0000i			0.488273i
$605$	−4.22183	+	12.6655i	−0.171642	+	0.514925i
$606$		0			0
$607$	26.4558	+	26.4558i	1.07381	+	1.07381i	0.997050	+	0.0767600i	$0.0244575\pi$
$607$	26.4558	+	26.4558i	1.07381	+	1.07381i	0.0767600	+	0.997050i	$0.475542\pi$
$608$			7.24264i			0.293728i
$609$	−0.414214	+	0.414214i	−0.0167848	+	0.0167848i
$610$	8.65685	+	17.3137i	0.350506	+	0.701012i
$611$	4.75736			0.192462
$612$	10.0000	+	6.00000i	0.404226	+	0.242536i
$613$			4.02944i			0.162747i	0.996684	+	0.0813737i	$0.0259307\pi$
$613$			4.02944i			0.162747i	−0.996684	+	0.0813737i	$0.974069\pi$
$614$			33.2132i			1.34038i
$615$	−1.82843	+	5.48528i	−0.0737293	+	0.221188i
$616$	3.17157			0.127786
$617$	−19.4350	−	19.4350i	−0.782425	−	0.782425i	0.197815	−	0.980239i	$-0.436616\pi$
$617$	−19.4350	−	19.4350i	−0.782425	−	0.782425i	−0.980239	+	0.197815i	$0.936616\pi$
$618$		0			0
$619$	5.75736	+	5.75736i	0.231408	+	0.231408i	0.813280	−	0.581872i	$-0.197680\pi$
$619$	5.75736	+	5.75736i	0.231408	+	0.231408i	−0.581872	+	0.813280i	$0.697680\pi$
$620$	15.1716	−	7.58579i	0.609305	−	0.304653i
$621$			9.65685i			0.387516i
$622$	1.41421	−	1.41421i	0.0567048	−	0.0567048i
$623$	11.4853	−	11.4853i	0.460148	−	0.460148i
$624$	−0.878680	+	0.878680i	−0.0351753	+	0.0351753i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	22.4853	−	22.4853i	0.898693	−	0.898693i
$627$	6.72792			0.268687
$628$			12.0000i			0.478852i
$629$	−29.6569	+	7.41421i	−1.18250	+	0.295624i
$630$	−4.00000	−	8.00000i	−0.159364	−	0.318728i
$631$			2.48528i			0.0989375i	0.998776	+	0.0494687i	$0.0157528\pi$
$631$			2.48528i			0.0989375i	−0.998776	+	0.0494687i	$0.984247\pi$
$632$	0.242641	+	0.242641i	0.00965173	+	0.00965173i
$633$			4.68629i			0.186263i
$634$	14.1421	−	14.1421i	0.561656	−	0.561656i
$635$	−37.6066	−	12.5355i	−1.49237	−	0.497457i
$636$	0.878680	+	0.878680i	0.0348419	+	0.0348419i
$637$	15.0000			0.594322
$638$	2.24264			0.0887870
$639$	−10.4853	−	10.4853i	−0.414791	−	0.414791i
$640$	2.12132	+	0.707107i	0.0838525	+	0.0279508i
$641$	3.55635	−	3.55635i	0.140467	−	0.140467i	−0.633376	−	0.773844i	$-0.718332\pi$
$641$	3.55635	−	3.55635i	0.140467	−	0.140467i	0.773844	+	0.633376i	$0.218332\pi$
$642$		−	1.65685i		−	0.0653908i
$643$	−3.75736	−	3.75736i	−0.148176	−	0.148176i	0.629127	−	0.777303i	$-0.283413\pi$
$643$	−3.75736	−	3.75736i	−0.148176	−	0.148176i	−0.777303	+	0.629127i	$0.783413\pi$
$644$		−	5.65685i		−	0.222911i
$645$	1.55635	+	3.11270i	0.0612812	+	0.122562i
$646$	−25.6066	−	15.3640i	−1.00748	−	0.604487i
$647$			47.5269i			1.86848i	0.356651	+	0.934238i	$0.383919\pi$
$647$			47.5269i			1.86848i	−0.356651	+	0.934238i	$0.616081\pi$
$648$	7.48528			0.294050
$649$	−20.4558	+	20.4558i	−0.802962	+	0.802962i
$650$	−9.00000	+	12.0000i	−0.353009	+	0.470679i
$651$	3.14214	−	3.14214i	0.123150	−	0.123150i
$652$	−4.48528	+	4.48528i	−0.175657	+	0.175657i
$653$	4.79899	−	4.79899i	0.187799	−	0.187799i	−0.606945	−	0.794744i	$-0.707605\pi$
$653$	4.79899	−	4.79899i	0.187799	−	0.187799i	0.794744	+	0.606945i	$0.207605\pi$
$654$			5.04163i			0.197143i
$655$	−21.4558	+	10.7279i	−0.838349	+	0.419175i
$656$	4.41421	+	4.41421i	0.172346	+	0.172346i
$657$	−23.6569	+	23.6569i	−0.922942	+	0.922942i
$658$	−1.58579	−	1.58579i	−0.0618204	−	0.0618204i
$659$	30.2132			1.17694			0.588470	−	0.808519i	$-0.299731\pi$
$659$	30.2132			1.17694			0.588470	+	0.808519i	$0.299731\pi$
$660$	0.656854	−	1.97056i	0.0255680	−	0.0767041i
$661$			12.0000i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$661$			12.0000i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$662$		−	15.7279i		−	0.611283i
$663$	−1.24264	−	4.97056i	−0.0482602	−	0.193041i
$664$	−4.24264			−0.164646
$665$	10.2426	+	20.4853i	0.397193	+	0.794385i
$666$	−14.8284	+	14.8284i	−0.574590	+	0.574590i
$667$		−	4.00000i		−	0.154881i
$668$	−1.07107	−	1.07107i	−0.0414409	−	0.0414409i
$669$	6.80761	+	6.80761i	0.263197	+	0.263197i
$670$	10.2426	−	30.7279i	0.395708	−	1.18712i
$671$		−	19.4142i		−	0.749477i
$672$	0.585786			0.0225972
$673$	25.8787	−	25.8787i	0.997550	−	0.997550i	−0.00244721	−	0.999997i	$-0.500779\pi$
$673$	25.8787	−	25.8787i	0.997550	−	0.997550i	0.999997	+	0.00244721i	$0.000778973\pi$
$674$	−12.8492	−	12.8492i	−0.494934	−	0.494934i
$675$	−11.9497	+	1.70711i	−0.459946	+	0.0657066i
$676$	4.00000			0.153846
$677$	22.4142	+	22.4142i	0.861448	+	0.861448i	0.991506	−	0.130058i	$-0.0415164\pi$
$677$	22.4142	+	22.4142i	0.861448	+	0.861448i	−0.130058	+	0.991506i	$0.541516\pi$
$678$	1.44365			0.0554431
$679$	0.242641			0.00931169
$680$	−7.00000	+	6.00000i	−0.268438	+	0.230089i
$681$	2.37258			0.0909176
$682$	−17.0122			−0.651431
$683$	24.5355	+	24.5355i	0.938826	+	0.938826i	0.998234	−	0.0594077i	$-0.0189212\pi$
$683$	24.5355	+	24.5355i	0.938826	+	0.938826i	−0.0594077	+	0.998234i	$0.518921\pi$
$684$	−20.4853			−0.783274
$685$	3.24264	−	9.72792i	0.123895	−	0.371685i
$686$	−12.0000	−	12.0000i	−0.458162	−	0.458162i
$687$	−2.27208	+	2.27208i	−0.0866852	+	0.0866852i
$688$	3.75736			0.143248
$689$			9.00000i			0.342873i
$690$	−3.51472	−	1.17157i	−0.133803	−	0.0446010i
$691$	9.48528	+	9.48528i	0.360837	+	0.360837i	0.864121	−	0.503284i	$-0.167875\pi$
$691$	9.48528	+	9.48528i	0.360837	+	0.360837i	−0.503284	+	0.864121i	$0.667875\pi$
$692$	17.6569	+	17.6569i	0.671213	+	0.671213i
$693$			8.97056i			0.340764i
$694$	−15.7071	+	15.7071i	−0.596234	+	0.596234i
$695$	31.1127	−	15.5563i	1.18017	−	0.590086i
$696$	0.414214			0.0157007
$697$	−24.9706	+	6.24264i	−0.945828	+	0.236457i
$698$			10.9706i			0.415242i
$699$			6.41421i			0.242608i
$700$	7.00000	−	1.00000i	0.264575	−	0.0377964i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	−5.12132	−	5.12132i	−0.193292	−	0.193292i
$703$	37.9706	−	37.9706i	1.43209	−	1.43209i
$704$	−1.58579	−	1.58579i	−0.0597666	−	0.0597666i
$705$	−1.31371	+	0.656854i	−0.0494771	+	0.0247386i
$706$		−	11.3137i		−	0.425797i
$707$		0			0
$708$	−3.77817	+	3.77817i	−0.141992	+	0.141992i
$709$	2.60660	−	2.60660i	0.0978930	−	0.0978930i	−0.656464	−	0.754357i	$-0.727949\pi$
$709$	2.60660	−	2.60660i	0.0978930	−	0.0978930i	0.754357	+	0.656464i	$0.227949\pi$
$710$	10.4853	−	5.24264i	0.393506	−	0.196753i
$711$	−0.686292	+	0.686292i	−0.0257379	+	0.0257379i
$712$	−11.4853			−0.430429
$713$			30.3431i			1.13636i
$714$	−1.24264	+	2.07107i	−0.0465047	+	0.0775078i
$715$	13.4558	−	6.72792i	0.503220	−	0.251610i
$716$		−	0.686292i		−	0.0256479i
$717$	−6.51472	−	6.51472i	−0.243297	−	0.243297i
$718$		−	7.07107i		−	0.263890i
$719$	−27.7487	+	27.7487i	−1.03485	+	1.03485i	−0.0354830	+	0.999370i	$0.511297\pi$
$719$	−27.7487	+	27.7487i	−1.03485	+	1.03485i	−0.999370	+	0.0354830i	$0.988703\pi$
$720$	−2.00000	+	6.00000i	−0.0745356	+	0.223607i
$721$		0			0
$722$	33.4558			1.24510
$723$	−1.61522			−0.0600708
$724$	−14.0000	−	14.0000i	−0.520306	−	0.520306i
$725$	4.94975	−	0.707107i	0.183829	−	0.0262613i
$726$	1.74874	−	1.74874i	0.0649017	−	0.0649017i
$727$		−	16.7574i		−	0.621496i	−0.950492	−	0.310748i	$-0.899420\pi$
$727$		−	16.7574i		−	0.621496i	0.950492	−	0.310748i	$-0.100580\pi$
$728$	3.00000	+	3.00000i	0.111187	+	0.111187i
$729$			18.1716i			0.673021i
$730$	−11.8284	−	23.6569i	−0.437790	−	0.875579i
$731$	−7.97056	+	13.2843i	−0.294802	+	0.491337i
$732$		−	3.58579i		−	0.132534i
$733$	−32.9706			−1.21780			−0.608898	−	0.793249i	$-0.708388\pi$
$733$	−32.9706			−1.21780			−0.608898	+	0.793249i	$0.708388\pi$
$734$	18.2426	−	18.2426i	0.673348	−	0.673348i
$735$	−4.14214	+	2.07107i	−0.152785	+	0.0763925i
$736$	−2.82843	+	2.82843i	−0.104257	+	0.104257i
$737$	−22.9706	+	22.9706i	−0.846132	+	0.846132i
$738$	−12.4853	+	12.4853i	−0.459590	+	0.459590i
$739$			35.1838i			1.29426i	0.762381	+	0.647128i	$0.224030\pi$
$739$			35.1838i			1.29426i	−0.762381	+	0.647128i	$0.775970\pi$
$740$	−7.41421	−	14.8284i	−0.272552	−	0.545104i
$741$	6.36396	+	6.36396i	0.233786	+	0.233786i
$742$	3.00000	−	3.00000i	0.110133	−	0.110133i
$743$	−17.8284	−	17.8284i	−0.654062	−	0.654062i	0.299907	−	0.953968i	$-0.403044\pi$
$743$	−17.8284	−	17.8284i	−0.654062	−	0.654062i	−0.953968	+	0.299907i	$0.903044\pi$
$744$	−3.14214			−0.115196
$745$	27.0000	+	9.00000i	0.989203	+	0.329734i
$746$		−	32.4853i		−	1.18937i
$747$		−	12.0000i		−	0.439057i
$748$	8.97056	−	2.24264i	0.327996	−	0.0819991i
$749$	−5.65685			−0.206697
$750$	0.828427	−	4.55635i	0.0302499	−	0.166374i
$751$	19.3640	−	19.3640i	0.706601	−	0.706601i	−0.259218	−	0.965819i	$-0.583465\pi$
$751$	19.3640	−	19.3640i	0.706601	−	0.706601i	0.965819	+	0.259218i	$0.0834648\pi$
$752$			1.58579i			0.0578277i
$753$	−6.00000	−	6.00000i	−0.218652	−	0.218652i
$754$	2.12132	+	2.12132i	0.0772539	+	0.0772539i
$755$	8.48528	−	25.4558i	0.308811	−	0.926433i
$756$			3.41421i			0.124174i
$757$	32.9411			1.19727			0.598633	−	0.801024i	$-0.295711\pi$
$757$	32.9411			1.19727			0.598633	+	0.801024i	$0.295711\pi$
$758$	−0.485281	+	0.485281i	−0.0176262	+	0.0176262i
$759$	2.62742	+	2.62742i	0.0953692	+	0.0953692i
$760$	5.12132	−	15.3640i	0.185770	−	0.557309i
$761$	20.4853			0.742591			0.371295	−	0.928515i	$-0.378914\pi$
$761$	20.4853			0.742591			0.371295	+	0.928515i	$0.378914\pi$
$762$	5.19239	+	5.19239i	0.188100	+	0.188100i
$763$	17.2132			0.623160
$764$	21.2132			0.767467
$765$	−16.9706	−	19.7990i	−0.613572	−	0.715834i
$766$	13.2426			0.478476
$767$	−38.6985			−1.39732
$768$	−0.292893	−	0.292893i	−0.0105689	−	0.0105689i
$769$	−14.4558			−0.521291			−0.260646	−	0.965435i	$-0.583935\pi$
$769$	−14.4558			−0.521291			−0.260646	+	0.965435i	$0.583935\pi$
$770$	−6.72792	−	2.24264i	−0.242457	−	0.0808192i
$771$	−1.97056	−	1.97056i	−0.0709681	−	0.0709681i
$772$	18.4853	−	18.4853i	0.665300	−	0.665300i
$773$	−32.4853			−1.16841			−0.584207	−	0.811605i	$-0.698594\pi$
$773$	−32.4853			−1.16841			−0.584207	+	0.811605i	$0.698594\pi$
$774$			10.6274i			0.381995i
$775$	−37.5477	+	5.36396i	−1.34875	+	0.192679i
$776$	−0.121320	−	0.121320i	−0.00435515	−	0.00435515i
$777$	−3.07107	−	3.07107i	−0.110174	−	0.110174i
$778$			16.6274i			0.596122i
$779$	31.9706	−	31.9706i	1.14546	−	1.14546i
$780$	2.48528	−	1.24264i	0.0889873	−	0.0444937i
$781$	−11.7574			−0.420711
$782$	−4.00000	−	16.0000i	−0.143040	−	0.572159i
$783$			2.41421i			0.0862770i
$784$			5.00000i			0.178571i
$785$	8.48528	−	25.4558i	0.302853	−	0.908558i
$786$	4.44365			0.158500
$787$	1.36396	+	1.36396i	0.0486200	+	0.0486200i	0.730999	−	0.682379i	$-0.239055\pi$
$787$	1.36396	+	1.36396i	0.0486200	+	0.0486200i	−0.682379	+	0.730999i	$0.739055\pi$
$788$	3.34315	−	3.34315i	0.119095	−	0.119095i
$789$	−1.39340	−	1.39340i	−0.0496063	−	0.0496063i
$790$	−0.343146	−	0.686292i	−0.0122086	−	0.0244172i
$791$		−	4.92893i		−	0.175253i
$792$	4.48528	−	4.48528i	0.159378	−	0.159378i
$793$	18.3640	−	18.3640i	0.652123	−	0.652123i
$794$	−4.72792	+	4.72792i	−0.167788	+	0.167788i
$795$	−1.24264	−	2.48528i	−0.0440719	−	0.0881438i
$796$	−7.12132	+	7.12132i	−0.252409	+	0.252409i
$797$	−28.9706			−1.02619			−0.513095	−	0.858332i	$-0.671501\pi$
$797$	−28.9706			−1.02619			−0.513095	+	0.858332i	$0.671501\pi$
$798$		−	4.24264i		−	0.150188i
$799$	−5.60660	−	3.36396i	−0.198347	−	0.119008i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		−	32.4853i		−	1.14781i
$802$	2.10051	+	2.10051i	0.0741714	+	0.0741714i
$803$			26.5269i			0.936114i
$804$	−4.24264	+	4.24264i	−0.149626	+	0.149626i
$805$	−4.00000	+	12.0000i	−0.140981	+	0.422944i
$806$	−16.0919	−	16.0919i	−0.566812	−	0.566812i
$807$	6.61522			0.232867
$808$		0			0
$809$	35.1421	+	35.1421i	1.23553	+	1.23553i	0.961809	+	0.273723i	$0.0882552\pi$
$809$	35.1421	+	35.1421i	1.23553	+	1.23553i	0.273723	+	0.961809i	$0.411745\pi$
$810$	−15.8787	−	5.29289i	−0.557920	−	0.185973i
$811$	9.48528	−	9.48528i	0.333073	−	0.333073i	−0.520679	−	0.853752i	$-0.674321\pi$
$811$	9.48528	−	9.48528i	0.333073	−	0.333073i	0.853752	+	0.520679i	$0.174321\pi$
$812$		−	1.41421i		−	0.0496292i
$813$	1.89949	+	1.89949i	0.0666182	+	0.0666182i
$814$			16.6274i			0.582791i
$815$	12.6863	−	6.34315i	0.444381	−	0.222191i
$816$	1.65685	−	0.414214i	0.0580015	−	0.0145004i
$817$		−	27.2132i		−	0.952069i
$818$	−25.4853			−0.891072
$819$	−8.48528	+	8.48528i	−0.296500	+	0.296500i
$820$	−6.24264	−	12.4853i	−0.218002	−	0.436005i
$821$	−18.0208	+	18.0208i	−0.628931	+	0.628931i	−0.947799	−	0.318868i	$-0.896697\pi$
$821$	−18.0208	+	18.0208i	−0.628931	+	0.628931i	0.318868	+	0.947799i	$0.396697\pi$
$822$	−1.34315	+	1.34315i	−0.0468476	+	0.0468476i
$823$	10.7279	−	10.7279i	0.373952	−	0.373952i	−0.494962	−	0.868914i	$-0.664818\pi$
$823$	10.7279	−	10.7279i	0.373952	−	0.373952i	0.868914	+	0.494962i	$0.164818\pi$
$824$		0			0
$825$	−2.78680	+	3.71573i	−0.0970238	+	0.129365i
$826$	12.8995	+	12.8995i	0.448831	+	0.448831i
$827$	5.31371	−	5.31371i	0.184776	−	0.184776i	−0.608657	−	0.793433i	$-0.708292\pi$
$827$	5.31371	−	5.31371i	0.184776	−	0.184776i	0.793433	+	0.608657i	$0.208292\pi$
$828$	−8.00000	−	8.00000i	−0.278019	−	0.278019i
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	9.00000	+	3.00000i	0.312395	+	0.104132i
$831$		−	4.82843i		−	0.167496i
$832$		−	3.00000i		−	0.104006i
$833$	−17.6777	−	10.6066i	−0.612495	−	0.367497i
$834$	−6.44365			−0.223125
$835$	1.51472	+	3.02944i	0.0524190	+	0.104838i
$836$	−11.4853	+	11.4853i	−0.397227	+	0.397227i
$837$		−	18.3137i		−	0.633014i
$838$	11.3137	+	11.3137i	0.390826	+	0.390826i
$839$	−2.97918	−	2.97918i	−0.102853	−	0.102853i	0.653808	−	0.756661i	$-0.273170\pi$
$839$	−2.97918	−	2.97918i	−0.102853	−	0.102853i	−0.756661	+	0.653808i	$0.773170\pi$
$840$	−1.24264	−	0.414214i	−0.0428752	−	0.0142917i
$841$			28.0000i			0.965517i
$842$	19.2132			0.662131
$843$	0.979185	−	0.979185i	0.0337249	−	0.0337249i
$844$	−8.00000	−	8.00000i	−0.275371	−	0.275371i
$845$	−8.48528	−	2.82843i	−0.291903	−	0.0973009i
$846$	−4.48528			−0.154207
$847$	−5.97056	−	5.97056i	−0.205151	−	0.205151i
$848$	−3.00000			−0.103020
$849$	11.2010			0.384418
$850$	19.0919	−	7.77817i	0.654846	−	0.266789i
$851$	29.6569			1.01662
$852$	−2.17157			−0.0743969
$853$	−8.51472	−	8.51472i	−0.291538	−	0.291538i	0.546149	−	0.837688i	$-0.316093\pi$
$853$	−8.51472	−	8.51472i	−0.291538	−	0.291538i	−0.837688	+	0.546149i	$0.816093\pi$
$854$	−12.2426			−0.418935
$855$	43.4558	+	14.4853i	1.48616	+	0.495386i
$856$	2.82843	+	2.82843i	0.0966736	+	0.0966736i
$857$	25.4350	−	25.4350i	0.868844	−	0.868844i	−0.123500	−	0.992345i	$-0.539412\pi$
$857$	25.4350	−	25.4350i	0.868844	−	0.868844i	0.992345	+	0.123500i	$0.0394120\pi$
$858$	−2.78680			−0.0951397
$859$			45.7279i			1.56022i	0.625645	+	0.780108i	$0.284836\pi$
$859$			45.7279i			1.56022i	−0.625645	+	0.780108i	$0.715164\pi$
$860$	−7.97056	−	2.65685i	−0.271794	−	0.0905980i
$861$	−2.58579	−	2.58579i	−0.0881234	−	0.0881234i
$862$	−17.6569	−	17.6569i	−0.601395	−	0.601395i
$863$		−	55.1127i		−	1.87606i	−0.346557	−	0.938029i	$-0.612649\pi$
$863$		−	55.1127i		−	1.87606i	0.346557	−	0.938029i	$-0.387351\pi$
$864$	1.70711	−	1.70711i	0.0580770	−	0.0580770i
$865$	−24.9706	−	49.9411i	−0.849025	−	1.69805i
$866$	5.75736			0.195643
$867$	−2.05025	+	6.73654i	−0.0696302	+	0.228785i
$868$			10.7279i			0.364129i
$869$			0.769553i			0.0261053i
$870$	−0.878680	−	0.292893i	−0.0297900	−	0.00993001i
$871$	−43.4558			−1.47245
$872$	−8.60660	−	8.60660i	−0.291456	−	0.291456i
$873$	0.343146	−	0.343146i	0.0116137	−	0.0116137i
$874$	20.4853	+	20.4853i	0.692925	+	0.692925i
$875$	−15.5563	−	2.82843i	−0.525901	−	0.0956183i
$876$			4.89949i			0.165539i
$877$	−8.51472	+	8.51472i	−0.287522	+	0.287522i	−0.836099	−	0.548578i	$-0.815169\pi$
$877$	−8.51472	+	8.51472i	−0.287522	+	0.287522i	0.548578	+	0.836099i	$0.315169\pi$
$878$	−20.9706	+	20.9706i	−0.707722	+	0.707722i
$879$	−6.05025	+	6.05025i	−0.204070	+	0.204070i
$880$	2.24264	+	4.48528i	0.0755994	+	0.151199i
$881$	−8.44365	+	8.44365i	−0.284474	+	0.284474i	−0.834890	−	0.550416i	$-0.814469\pi$
$881$	−8.44365	+	8.44365i	−0.284474	+	0.284474i	0.550416	+	0.834890i	$0.314469\pi$
$882$	−14.1421			−0.476190
$883$			18.7279i			0.630245i	0.949051	+	0.315122i	$0.102046\pi$
$883$			18.7279i			0.630245i	−0.949051	+	0.315122i	$0.897954\pi$
$884$	10.6066	+	6.36396i	0.356739	+	0.214043i
$885$	10.6863	−	5.34315i	0.359216	−	0.179608i
$886$		−	37.7990i		−	1.26988i
$887$	−19.5858	−	19.5858i	−0.657626	−	0.657626i	0.297192	−	0.954818i	$-0.403950\pi$
$887$	−19.5858	−	19.5858i	−0.657626	−	0.657626i	−0.954818	+	0.297192i	$0.903950\pi$
$888$			3.07107i			0.103058i
$889$	17.7279	−	17.7279i	0.594575	−	0.594575i
$890$	24.3640	+	8.12132i	0.816682	+	0.272227i
$891$	11.8701	+	11.8701i	0.397662	+	0.397662i
$892$	−23.2426			−0.778221
$893$	11.4853			0.384340
$894$	−3.72792	−	3.72792i	−0.124680	−	0.124680i
$895$	−0.485281	+	1.45584i	−0.0162212	+	0.0486635i
$896$	−1.00000	+	1.00000i	−0.0334077	+	0.0334077i
$897$			4.97056i			0.165962i
$898$	28.7990	+	28.7990i	0.961035	+	0.961035i
$899$			7.58579i			0.253000i
$900$	8.48528	−	11.3137i	0.282843	−	0.377124i
$901$	6.36396	−	10.6066i	0.212014	−	0.353357i
$902$			14.0000i			0.466149i
$903$	−2.20101			−0.0732450
$904$	−2.46447	+	2.46447i	−0.0819669	+	0.0819669i
$905$	19.7990	+	39.5980i	0.658141	+	1.31628i
$906$	−3.51472	+	3.51472i	−0.116769	+	0.116769i
$907$	−7.84924	+	7.84924i	−0.260630	+	0.260630i	−0.825310	−	0.564680i	$-0.809000\pi$
$907$	−7.84924	+	7.84924i	−0.260630	+	0.260630i	0.564680	+	0.825310i	$0.309000\pi$
$908$	−4.05025	+	4.05025i	−0.134412	+	0.134412i
$909$		0			0
$910$	−4.24264	−	8.48528i	−0.140642	−	0.281284i
$911$	−35.3137	−	35.3137i	−1.17000	−	1.17000i	−0.982210	−	0.187785i	$-0.939869\pi$
$911$	−35.3137	−	35.3137i	−1.17000	−	1.17000i	−0.187785	−	0.982210i	$-0.560131\pi$
$912$	−2.12132	+	2.12132i	−0.0702439	+	0.0702439i
$913$	−6.72792	−	6.72792i	−0.222662	−	0.222662i
$914$	2.24264			0.0741800
$915$	−2.53553	+	7.60660i	−0.0838222	+	0.251466i
$916$		−	7.75736i		−	0.256310i
$917$		−	15.1716i		−	0.501009i
$918$	2.41421	+	9.65685i	0.0796809	+	0.318724i
$919$	−31.2132			−1.02963			−0.514814	−	0.857302i	$-0.672139\pi$
$919$	−31.2132			−1.02963			−0.514814	+	0.857302i	$0.672139\pi$
$920$	8.00000	−	4.00000i	0.263752	−	0.131876i
$921$	−9.72792	+	9.72792i	−0.320546	+	0.320546i
$922$		−	40.2843i		−	1.32669i
$923$	−11.1213	−	11.1213i	−0.366063	−	0.366063i
$924$	0.928932	+	0.928932i	0.0305596	+	0.0305596i
$925$	5.24264	+	36.6985i	0.172377	+	1.20664i
$926$			25.2426i			0.829525i
$927$		0			0
$928$	−0.707107	+	0.707107i	−0.0232119	+	0.0232119i
$929$	−15.3431	−	15.3431i	−0.503392	−	0.503392i	0.409098	−	0.912490i	$-0.365843\pi$
$929$	−15.3431	−	15.3431i	−0.503392	−	0.503392i	−0.912490	+	0.409098i	$0.865843\pi$
$930$	6.66548	+	2.22183i	0.218570	+	0.0728565i
$931$	36.2132			1.18684
$932$	−10.9497	−	10.9497i	−0.358671	−	0.358671i
$933$	0.828427			0.0271215
$934$	18.7279			0.612796
$935$	−20.6152	−	1.58579i	−0.674190	−	0.0518608i
$936$	8.48528			0.277350
$937$	47.2132			1.54239			0.771194	−	0.636600i	$-0.219660\pi$
$937$	47.2132			1.54239			0.771194	+	0.636600i	$0.219660\pi$
$938$	14.4853	+	14.4853i	0.472961	+	0.472961i
$939$	13.1716			0.429838
$940$	1.12132	−	3.36396i	0.0365734	−	0.109720i
$941$	14.8076	+	14.8076i	0.482714	+	0.482714i	0.905997	−	0.423283i	$-0.139122\pi$
$941$	14.8076	+	14.8076i	0.482714	+	0.482714i	−0.423283	+	0.905997i	$0.639122\pi$
$942$	−3.51472	+	3.51472i	−0.114516	+	0.114516i
$943$	24.9706			0.813153
$944$		−	12.8995i		−	0.419843i
$945$	2.41421	−	7.24264i	0.0785344	−	0.235603i
$946$	5.95837	+	5.95837i	0.193723	+	0.193723i
$947$	26.2929	+	26.2929i	0.854404	+	0.854404i	0.990672	−	0.136268i	$-0.0435108\pi$
$947$	26.2929	+	26.2929i	0.854404	+	0.854404i	−0.136268	+	0.990672i	$0.543511\pi$
$948$			0.142136i			0.00461635i
$949$	−25.0919	+	25.0919i	−0.814517	+	0.814517i
$950$	−21.7279	+	28.9706i	−0.704947	+	0.939929i
$951$	8.28427			0.268636
$952$	−1.41421	−	5.65685i	−0.0458349	−	0.183340i
$953$			4.58579i			0.148548i	0.997238	+	0.0742741i	$0.0236640\pi$
$953$			4.58579i			0.148548i	−0.997238	+	0.0742741i	$0.976336\pi$
$954$		−	8.48528i		−	0.274721i
$955$	−45.0000	−	15.0000i	−1.45617	−	0.485389i
$956$	22.2426			0.719378
$957$	0.656854	+	0.656854i	0.0212331	+	0.0212331i
$958$	10.0503	−	10.0503i	0.324709	−	0.324709i
$959$	4.58579	+	4.58579i	0.148083	+	0.148083i
$960$	0.414214	+	0.828427i	0.0133687	+	0.0267374i
$961$		−	26.5442i		−	0.856263i
$962$	−15.7279	+	15.7279i	−0.507089	+	0.507089i
$963$	−8.00000	+	8.00000i	−0.257796	+	0.257796i
$964$	2.75736	−	2.75736i	0.0888086	−	0.0888086i
$965$	−52.2843	+	26.1421i	−1.68309	+	0.841545i
$966$	1.65685	−	1.65685i	0.0533084	−	0.0533084i
$967$	30.9706			0.995946			0.497973	−	0.867192i	$-0.334078\pi$
$967$	30.9706			0.995946			0.497973	+	0.867192i	$0.334078\pi$
$968$			5.97056i			0.191901i
$969$	−3.00000	−	12.0000i	−0.0963739	−	0.385496i
$970$	0.171573	+	0.343146i	0.00550887	+	0.0110177i
$971$			30.5563i			0.980600i	0.871554	+	0.490300i	$0.163113\pi$
$971$			30.5563i			0.980600i	−0.871554	+	0.490300i	$0.836887\pi$
$972$	7.31371	+	7.31371i	0.234587	+	0.234587i
$973$			22.0000i			0.705288i
$974$	−11.2426	+	11.2426i	−0.360237	+	0.360237i
$975$	−6.15076	+	0.878680i	−0.196982	+	0.0281403i
$976$	6.12132	+	6.12132i	0.195939	+	0.195939i
$977$	0.727922			0.0232883			0.0116441	−	0.999932i	$-0.496293\pi$
$977$	0.727922			0.0232883			0.0116441	+	0.999932i	$0.496293\pi$
$978$	−2.62742			−0.0840155
$979$	−18.2132	−	18.2132i	−0.582097	−	0.582097i
$980$	3.53553	−	10.6066i	0.112938	−	0.338815i
$981$	24.3431	−	24.3431i	0.777217	−	0.777217i
$982$			6.89949i			0.220172i
$983$	−44.0122	−	44.0122i	−1.40377	−	1.40377i	−0.787657	−	0.616114i	$-0.788706\pi$
$983$	−44.0122	−	44.0122i	−1.40377	−	1.40377i	−0.616114	−	0.787657i	$-0.711294\pi$
$984$			2.58579i			0.0824319i
$985$	−9.45584	+	4.72792i	−0.301288	+	0.150644i
$986$	−1.00000	−	4.00000i	−0.0318465	−	0.127386i
$987$		−	0.928932i		−	0.0295682i
$988$	−21.7279			−0.691257
$989$	10.6274	−	10.6274i	0.337932	−	0.337932i
$990$	−12.6863	+	6.34315i	−0.403197	+	0.201598i
$991$	21.1213	−	21.1213i	0.670941	−	0.670941i	−0.286992	−	0.957933i	$-0.592655\pi$
$991$	21.1213	−	21.1213i	0.670941	−	0.670941i	0.957933	+	0.286992i	$0.0926553\pi$
$992$	5.36396	−	5.36396i	0.170306	−	0.170306i
$993$	4.60660	−	4.60660i	0.146186	−	0.146186i
$994$			7.41421i			0.235165i
$995$	20.1421	−	10.0711i	0.638549	−	0.319274i
$996$	−1.24264	−	1.24264i	−0.0393746	−	0.0393746i
$997$	30.6985	−	30.6985i	0.972231	−	0.972231i	−0.0273939	−	0.999625i	$-0.508721\pi$
$997$	30.6985	−	30.6985i	0.972231	−	0.972231i	0.999625	+	0.0273939i	$0.00872086\pi$
$998$	8.51472	+	8.51472i	0.269529	+	0.269529i
$999$	−17.8995			−0.566315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.g.e.89.2	✓	4
3.2	odd	2		1530.2.n.o.1279.2		4
5.2	odd	4		850.2.h.h.701.2		4
5.3	odd	4		850.2.h.k.701.1		4
5.4	even	2		170.2.g.f.89.1	yes	4
15.14	odd	2		1530.2.n.j.1279.1		4
17.13	even	4		170.2.g.f.149.1	yes	4
51.47	odd	4		1530.2.n.j.829.1		4
85.13	odd	4		850.2.h.k.251.1		4
85.47	odd	4		850.2.h.h.251.2		4
85.64	even	4	inner	170.2.g.e.149.2	yes	4
255.149	odd	4		1530.2.n.o.829.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.e.89.2	✓	4	1.1	even	1	trivial
170.2.g.e.149.2	yes	4	85.64	even	4	inner
170.2.g.f.89.1	yes	4	5.4	even	2
170.2.g.f.149.1	yes	4	17.13	even	4
850.2.h.h.251.2		4	85.47	odd	4
850.2.h.h.701.2		4	5.2	odd	4
850.2.h.k.251.1		4	85.13	odd	4
850.2.h.k.701.1		4	5.3	odd	4
1530.2.n.j.829.1		4	51.47	odd	4
1530.2.n.j.1279.1		4	15.14	odd	2
1530.2.n.o.829.2		4	255.149	odd	4
1530.2.n.o.1279.2		4	3.2	odd	2

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.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.292893 - 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.292893 + 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} -2.82843i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.292893 - 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(0.292893 + 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} -2.82843i q^{9} +(2.12132 + 0.707107i) q^{10} +(-1.58579 - 1.58579i) q^{11} +(-0.292893 - 0.292893i) q^{12} -3.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(0.414214 + 0.828427i) q^{15} +1.00000 q^{16} +(-2.12132 + 3.53553i) q^{17} +2.82843i q^{18} -7.24264i q^{19} +(-2.12132 - 0.707107i) q^{20} -0.585786 q^{21} +(1.58579 + 1.58579i) q^{22} +(2.82843 - 2.82843i) q^{23} +(0.292893 + 0.292893i) q^{24} +(4.00000 + 3.00000i) q^{25} +3.00000i q^{26} +(-1.70711 + 1.70711i) q^{27} +(1.00000 - 1.00000i) q^{28} +(0.707107 - 0.707107i) q^{29} +(-0.414214 - 0.828427i) q^{30} +(-5.36396 + 5.36396i) q^{31} -1.00000 q^{32} +0.928932i q^{33} +(2.12132 - 3.53553i) q^{34} +(-2.82843 + 1.41421i) q^{35} -2.82843i q^{36} +(5.24264 + 5.24264i) q^{37} +7.24264i q^{38} +(-0.878680 + 0.878680i) q^{39} +(2.12132 + 0.707107i) q^{40} +(4.41421 + 4.41421i) q^{41} +0.585786 q^{42} +3.75736 q^{43} +(-1.58579 - 1.58579i) q^{44} +(-2.00000 + 6.00000i) q^{45} +(-2.82843 + 2.82843i) q^{46} +1.58579i q^{47} +(-0.292893 - 0.292893i) q^{48} +5.00000i q^{49} +(-4.00000 - 3.00000i) q^{50} +(1.65685 - 0.414214i) q^{51} -3.00000i q^{52} -3.00000 q^{53} +(1.70711 - 1.70711i) q^{54} +(2.24264 + 4.48528i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(-2.12132 + 2.12132i) q^{57} +(-0.707107 + 0.707107i) q^{58} -12.8995i q^{59} +(0.414214 + 0.828427i) q^{60} +(6.12132 + 6.12132i) q^{61} +(5.36396 - 5.36396i) q^{62} +(-2.82843 - 2.82843i) q^{63} +1.00000 q^{64} +(-2.12132 + 6.36396i) q^{65} -0.928932i q^{66} -14.4853i q^{67} +(-2.12132 + 3.53553i) q^{68} -1.65685 q^{69} +(2.82843 - 1.41421i) q^{70} +(3.70711 - 3.70711i) q^{71} +2.82843i q^{72} +(-8.36396 - 8.36396i) q^{73} +(-5.24264 - 5.24264i) q^{74} +(-0.292893 - 2.05025i) q^{75} -7.24264i q^{76} -3.17157 q^{77} +(0.878680 - 0.878680i) q^{78} +(-0.242641 - 0.242641i) q^{79} +(-2.12132 - 0.707107i) q^{80} -7.48528 q^{81} +(-4.41421 - 4.41421i) q^{82} +4.24264 q^{83} -0.585786 q^{84} +(7.00000 - 6.00000i) q^{85} -3.75736 q^{86} -0.414214 q^{87} +(1.58579 + 1.58579i) q^{88} +11.4853 q^{89} +(2.00000 - 6.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(2.82843 - 2.82843i) q^{92} +3.14214 q^{93} -1.58579i q^{94} +(-5.12132 + 15.3640i) q^{95} +(0.292893 + 0.292893i) q^{96} +(0.121320 + 0.121320i) q^{97} -5.00000i q^{98} +(-4.48528 + 4.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 16 q^{25} - 4 q^{27} + 4 q^{28} + 4 q^{30} + 4 q^{31} - 4 q^{32} + 4 q^{37} - 12 q^{39} + 12 q^{41} + 8 q^{42} + 32 q^{43} - 12 q^{44} - 8 q^{45} - 4 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{69} + 12 q^{71} - 8 q^{73} - 4 q^{74} - 4 q^{75} - 24 q^{77} + 12 q^{78} + 16 q^{79} + 4 q^{81} - 12 q^{82} - 8 q^{84} + 28 q^{85} - 32 q^{86} + 4 q^{87} + 12 q^{88} + 12 q^{89} + 8 q^{90} - 12 q^{91} - 44 q^{93} - 12 q^{95} + 4 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^21 + 12 * q^22 + 4 * q^24 + 16 * q^25 - 4 * q^27 + 4 * q^28 + 4 * q^30 + 4 * q^31 - 4 * q^32 + 4 * q^37 - 12 * q^39 + 12 * q^41 + 8 * q^42 + 32 * q^43 - 12 * q^44 - 8 * q^45 - 4 * q^48 - 16 * q^50 - 16 * q^51 - 12 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^69 + 12 * q^71 - 8 * q^73 - 4 * q^74 - 4 * q^75 - 24 * q^77 + 12 * q^78 + 16 * q^79 + 4 * q^81 - 12 * q^82 - 8 * q^84 + 28 * q^85 - 32 * q^86 + 4 * q^87 + 12 * q^88 + 12 * q^89 + 8 * q^90 - 12 * q^91 - 44 * q^93 - 12 * q^95 + 4 * q^96 - 8 * q^97 + 16 * q^99

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