LMFDB - Embedded newform 510.2.l.d.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.4030726144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 4x^{6} - 16x^{5} + 18x^{4} - 8x^{3} + 172x^{2} + 184x + 274 $ x^8 - 4x^7 + 4x^6 - 16x^5 + 18x^4 - 8x^3 + 172x^2 + 184*x + 274
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.4
Root			$3.21154 - 0.330265i$ of defining polynomial
Character	$\chi$	$=$	510.137
Dual form			510.2.l.d.443.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(1.79733 + 1.33026i) q^{5} +(0.292893 + 1.70711i) q^{6} +(2.88128 + 2.88128i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(1.79733 + 1.33026i) q^{5} +(0.292893 + 1.70711i) q^{6} +(2.88128 + 2.88128i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(2.21154 - 0.330265i) q^{10} -1.41421i q^{11} +(1.41421 + 1.00000i) q^{12} +(-4.42309 + 4.42309i) q^{13} +4.07474 q^{14} +(-3.67861 + 1.21154i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.70711 - 1.29289i) q^{18} -2.48008i q^{19} +(1.33026 - 1.79733i) q^{20} +(-6.95602 + 1.19346i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(3.89015 + 3.89015i) q^{23} +(1.70711 - 0.292893i) q^{24} +(1.46079 + 4.78185i) q^{25} +6.25519i q^{26} +(5.00000 + 1.41421i) q^{27} +(2.88128 - 2.88128i) q^{28} +9.25151 q^{29} +(-1.74448 + 3.45786i) q^{30} -3.14061 q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.00000 + 1.41421i) q^{33} +1.00000i q^{34} +(1.34574 + 9.01147i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-4.06173 - 4.06173i) q^{37} +(-1.75368 - 1.75368i) q^{38} +(-1.83210 - 10.6783i) q^{39} +(-0.330265 - 2.21154i) q^{40} +4.69669i q^{41} +(-4.07474 + 5.76256i) q^{42} +(3.18045 - 3.18045i) q^{43} -1.41421 q^{44} +(1.96523 - 6.41388i) q^{45} +5.50151 q^{46} +(6.00000 - 6.00000i) q^{47} +(1.00000 - 1.41421i) q^{48} +9.60353i q^{49} +(4.41421 + 2.34834i) q^{50} +(-0.292893 - 1.70711i) q^{51} +(4.42309 + 4.42309i) q^{52} +(-2.66053 - 2.66053i) q^{53} +(4.53553 - 2.53553i) q^{54} +(1.88128 - 2.54181i) q^{55} -4.07474i q^{56} +(3.50737 + 2.48008i) q^{57} +(6.54181 - 6.54181i) q^{58} +1.18932 q^{59} +(1.21154 + 3.67861i) q^{60} -8.86458 q^{61} +(-2.22075 + 2.22075i) q^{62} +(5.26821 - 11.0308i) q^{63} +1.00000i q^{64} +(-13.8336 + 2.06587i) q^{65} +(2.41421 - 0.414214i) q^{66} +(-4.84098 - 4.84098i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-9.39166 + 1.61135i) q^{69} +(7.32366 + 5.42049i) q^{70} -10.9209i q^{71} +(-1.29289 + 2.70711i) q^{72} +(-5.32106 + 5.32106i) q^{73} -5.74415 q^{74} +(-8.22335 - 2.71598i) q^{75} -2.48008 q^{76} +(4.07474 - 4.07474i) q^{77} +(-8.84617 - 6.25519i) q^{78} -7.94300i q^{79} +(-1.79733 - 1.33026i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(3.32106 + 3.32106i) q^{82} +(0.819553 + 0.819553i) q^{83} +(1.19346 + 6.95602i) q^{84} +(-2.21154 + 0.330265i) q^{85} -4.49783i q^{86} +(-9.25151 + 13.0836i) q^{87} +(-1.00000 + 1.00000i) q^{88} +3.90685 q^{89} +(-3.14567 - 5.92492i) q^{90} -25.4883 q^{91} +(3.89015 - 3.89015i) q^{92} +(3.14061 - 4.44150i) q^{93} -8.48528i q^{94} +(3.29917 - 4.45753i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(11.9246 + 11.9246i) q^{97} +(6.79072 + 6.79072i) q^{98} +(-4.00000 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9	$ 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 16 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{22} - 16 q^{23} + 8 q^{24} + 8 q^{25} + 40 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 24 q^{35} - 8 q^{37} - 16 q^{38} - 24 q^{39} + 4 q^{40} - 8 q^{42} + 16 q^{43} - 4 q^{45} + 8 q^{46} + 48 q^{47} + 8 q^{48} + 24 q^{50} - 8 q^{51} - 8 q^{52} - 8 q^{53} + 8 q^{54} + 32 q^{57} + 24 q^{58} - 32 q^{59} - 12 q^{60} - 24 q^{61} - 16 q^{62} + 8 q^{63} - 24 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{69} - 16 q^{72} - 16 q^{73} + 24 q^{74} - 32 q^{75} - 16 q^{76} + 8 q^{77} + 16 q^{78} - 4 q^{80} - 56 q^{81} + 16 q^{83} + 4 q^{85} - 8 q^{87} - 8 q^{88} + 16 q^{89} + 4 q^{90} - 64 q^{91} - 16 q^{92} + 8 q^{93} + 32 q^{95} - 8 q^{96} + 16 q^{97} - 8 q^{98} - 32 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 16 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^22 - 16 * q^23 + 8 * q^24 + 8 * q^25 + 40 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 24 * q^35 - 8 * q^37 - 16 * q^38 - 24 * q^39 + 4 * q^40 - 8 * q^42 + 16 * q^43 - 4 * q^45 + 8 * q^46 + 48 * q^47 + 8 * q^48 + 24 * q^50 - 8 * q^51 - 8 * q^52 - 8 * q^53 + 8 * q^54 + 32 * q^57 + 24 * q^58 - 32 * q^59 - 12 * q^60 - 24 * q^61 - 16 * q^62 + 8 * q^63 - 24 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^69 - 16 * q^72 - 16 * q^73 + 24 * q^74 - 32 * q^75 - 16 * q^76 + 8 * q^77 + 16 * q^78 - 4 * q^80 - 56 * q^81 + 16 * q^83 + 4 * q^85 - 8 * q^87 - 8 * q^88 + 16 * q^89 + 4 * q^90 - 64 * q^91 - 16 * q^92 + 8 * q^93 + 32 * q^95 - 8 * q^96 + 16 * q^97 - 8 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$		−	1.00000i		−	0.500000i
$5$	1.79733	+	1.33026i	0.803790	+	0.594913i
$5$	1.79733	+	1.33026i	0.803790	+	0.594913i
$6$	0.292893	+	1.70711i	0.119573	+	0.696923i
$7$	2.88128	+	2.88128i	1.08902	+	1.08902i	0.995629	+	0.0933915i	$0.0297708\pi$
$7$	2.88128	+	2.88128i	1.08902	+	1.08902i	0.0933915	+	0.995629i	$0.470229\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	2.21154	−	0.330265i	0.699351	−	0.104439i
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$	1.41421	+	1.00000i	0.408248	+	0.288675i
$13$	−4.42309	+	4.42309i	−1.22674	+	1.22674i	−0.261555	+	0.965189i	$0.584235\pi$
$13$	−4.42309	+	4.42309i	−1.22674	+	1.22674i	−0.965189	+	0.261555i	$0.915765\pi$
$14$	4.07474			1.08902
$15$	−3.67861	+	1.21154i	−0.949813	+	0.312819i
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$		−	2.48008i		−	0.568970i	−0.958680	−	0.284485i	$-0.908177\pi$
$19$		−	2.48008i		−	0.568970i	0.958680	−	0.284485i	$-0.0918226\pi$
$20$	1.33026	−	1.79733i	0.297456	−	0.401895i
$21$	−6.95602	+	1.19346i	−1.51793	+	0.260435i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	3.89015	+	3.89015i	0.811153	+	0.811153i	0.984807	−	0.173654i	$-0.0555574\pi$
$23$	3.89015	+	3.89015i	0.811153	+	0.811153i	−0.173654	+	0.984807i	$0.555557\pi$
$24$	1.70711	−	0.292893i	0.348462	−	0.0597866i
$25$	1.46079	+	4.78185i	0.292158	+	0.956370i
$26$			6.25519i			1.22674i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	2.88128	−	2.88128i	0.544510	−	0.544510i
$29$	9.25151			1.71796			0.858982	−	0.512007i	$-0.171098\pi$
$29$	9.25151			1.71796			0.858982	+	0.512007i	$0.171098\pi$
$30$	−1.74448	+	3.45786i	−0.318497	+	0.631316i
$31$	−3.14061			−0.564071			−0.282035	−	0.959404i	$-0.591010\pi$
$31$	−3.14061			−0.564071			−0.282035	+	0.959404i	$0.591010\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.00000	+	1.41421i	0.348155	+	0.246183i
$34$			1.00000i			0.171499i
$35$	1.34574	+	9.01147i	0.227472	+	1.52322i
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	−4.06173	−	4.06173i	−0.667744	−	0.667744i	0.289450	−	0.957193i	$-0.406528\pi$
$37$	−4.06173	−	4.06173i	−0.667744	−	0.667744i	−0.957193	+	0.289450i	$0.906528\pi$
$38$	−1.75368	−	1.75368i	−0.284485	−	0.284485i
$39$	−1.83210	−	10.6783i	−0.293371	−	1.70989i
$40$	−0.330265	−	2.21154i	−0.0522195	−	0.349676i
$41$			4.69669i			0.733499i	0.930320	+	0.366750i	$0.119529\pi$
$41$			4.69669i			0.733499i	−0.930320	+	0.366750i	$0.880471\pi$
$42$	−4.07474	+	5.76256i	−0.628747	+	0.889182i
$43$	3.18045	−	3.18045i	0.485014	−	0.485014i	−0.421715	−	0.906728i	$-0.638572\pi$
$43$	3.18045	−	3.18045i	0.485014	−	0.485014i	0.906728	+	0.421715i	$0.138572\pi$
$44$	−1.41421			−0.213201
$45$	1.96523	−	6.41388i	0.292959	−	0.956125i
$46$	5.50151			0.811153
$47$	6.00000	−	6.00000i	0.875190	−	0.875190i	−0.117842	−	0.993032i	$-0.537598\pi$
$47$	6.00000	−	6.00000i	0.875190	−	0.875190i	0.993032	+	0.117842i	$0.0375978\pi$
$48$	1.00000	−	1.41421i	0.144338	−	0.204124i
$49$			9.60353i			1.37193i
$50$	4.41421	+	2.34834i	0.624264	+	0.332106i
$51$	−0.292893	−	1.70711i	−0.0410133	−	0.239043i
$52$	4.42309	+	4.42309i	0.613372	+	0.613372i
$53$	−2.66053	−	2.66053i	−0.365452	−	0.365452i	0.500364	−	0.865815i	$-0.333200\pi$
$53$	−2.66053	−	2.66053i	−0.365452	−	0.365452i	−0.865815	+	0.500364i	$0.833200\pi$
$54$	4.53553	−	2.53553i	0.617208	−	0.345042i
$55$	1.88128	−	2.54181i	0.253672	−	0.342737i
$56$		−	4.07474i		−	0.544510i
$57$	3.50737	+	2.48008i	0.464562	+	0.328495i
$58$	6.54181	−	6.54181i	0.858982	−	0.858982i
$59$	1.18932			0.154836			0.0774181	−	0.996999i	$-0.475332\pi$
$59$	1.18932			0.154836			0.0774181	+	0.996999i	$0.475332\pi$
$60$	1.21154	+	3.67861i	0.156410	+	0.474906i
$61$	−8.86458			−1.13499			−0.567497	−	0.823376i	$-0.692088\pi$
$61$	−8.86458			−1.13499			−0.567497	+	0.823376i	$0.692088\pi$
$62$	−2.22075	+	2.22075i	−0.282035	+	0.282035i
$63$	5.26821	−	11.0308i	0.663732	−	1.38975i
$64$			1.00000i			0.125000i
$65$	−13.8336	+	2.06587i	−1.71585	+	0.256240i
$66$	2.41421	−	0.414214i	0.297169	−	0.0509862i
$67$	−4.84098	−	4.84098i	−0.591419	−	0.591419i	0.346595	−	0.938015i	$-0.387338\pi$
$67$	−4.84098	−	4.84098i	−0.591419	−	0.591419i	−0.938015	+	0.346595i	$0.887338\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$	−9.39166	+	1.61135i	−1.13062	+	0.193984i
$70$	7.32366	+	5.42049i	0.875345	+	0.647872i
$71$		−	10.9209i		−	1.29607i	−0.761609	−	0.648037i	$-0.775590\pi$
$71$		−	10.9209i		−	1.29607i	0.761609	−	0.648037i	$-0.224410\pi$
$72$	−1.29289	+	2.70711i	−0.152369	+	0.319036i
$73$	−5.32106	+	5.32106i	−0.622783	+	0.622783i	−0.946242	−	0.323459i	$-0.895154\pi$
$73$	−5.32106	+	5.32106i	−0.622783	+	0.622783i	0.323459	+	0.946242i	$0.395154\pi$
$74$	−5.74415			−0.667744
$75$	−8.22335	−	2.71598i	−0.949550	−	0.313614i
$76$	−2.48008			−0.284485
$77$	4.07474	−	4.07474i	0.464360	−	0.464360i
$78$	−8.84617	−	6.25519i	−1.00163	−	0.708261i
$79$		−	7.94300i		−	0.893658i	−0.894619	−	0.446829i	$-0.852553\pi$
$79$		−	7.94300i		−	0.893658i	0.894619	−	0.446829i	$-0.147447\pi$
$80$	−1.79733	−	1.33026i	−0.200948	−	0.148728i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	3.32106	+	3.32106i	0.366750	+	0.366750i
$83$	0.819553	+	0.819553i	0.0899577	+	0.0899577i	0.750654	−	0.660696i	$-0.229739\pi$
$83$	0.819553	+	0.819553i	0.0899577	+	0.0899577i	−0.660696	+	0.750654i	$0.729739\pi$
$84$	1.19346	+	6.95602i	0.130218	+	0.758964i
$85$	−2.21154	+	0.330265i	−0.239876	+	0.0358223i
$86$		−	4.49783i		−	0.485014i
$87$	−9.25151	+	13.0836i	−0.991866	+	1.40271i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	3.90685			0.414125			0.207062	−	0.978328i	$-0.433610\pi$
$89$	3.90685			0.414125			0.207062	+	0.978328i	$0.433610\pi$
$90$	−3.14567	−	5.92492i	−0.331583	−	0.624542i
$91$	−25.4883			−2.67190
$92$	3.89015	−	3.89015i	0.405576	−	0.405576i
$93$	3.14061	−	4.44150i	0.325666	−	0.460562i
$94$		−	8.48528i		−	0.875190i
$95$	3.29917	−	4.45753i	0.338487	−	0.457333i
$96$	−0.292893	−	1.70711i	−0.0298933	−	0.174231i
$97$	11.9246	+	11.9246i	1.21076	+	1.21076i	0.970777	+	0.239982i	$0.0771414\pi$
$97$	11.9246	+	11.9246i	1.21076	+	1.21076i	0.239982	+	0.970777i	$0.422859\pi$
$98$	6.79072	+	6.79072i	0.685967	+	0.685967i
$99$	−4.00000	+	1.41421i	−0.402015	+	0.142134i
$100$	4.78185	−	1.46079i	0.478185	−	0.146079i
$101$		−	16.3535i		−	1.62724i	−0.581398	−	0.813619i	$-0.697494\pi$
$101$		−	16.3535i		−	1.62724i	0.581398	−	0.813619i	$-0.302506\pi$
$102$	−1.41421	−	1.00000i	−0.140028	−	0.0990148i
$103$	4.72272	−	4.72272i	0.465344	−	0.465344i	−0.435058	−	0.900402i	$-0.643272\pi$
$103$	4.72272	−	4.72272i	0.465344	−	0.465344i	0.900402	+	0.435058i	$0.143272\pi$
$104$	6.25519			0.613372
$105$	−14.0899	−	7.10830i	−1.37503	−	0.693699i
$106$	−3.76256			−0.365452
$107$	12.0836	−	12.0836i	1.16817	−	1.16817i	0.185528	−	0.982639i	$-0.440600\pi$
$107$	12.0836	−	12.0836i	1.16817	−	1.16817i	0.982639	−	0.185528i	$-0.0593997\pi$
$108$	1.41421	−	5.00000i	0.136083	−	0.481125i
$109$		−	2.66053i		−	0.254833i	−0.991849	−	0.127416i	$-0.959332\pi$
$109$		−	2.66053i		−	0.254833i	0.991849	−	0.127416i	$-0.0406684\pi$
$110$	−0.467065	−	3.12759i	−0.0445329	−	0.298204i
$111$	9.80587	−	1.68242i	0.930732	−	0.159688i
$112$	−2.88128	−	2.88128i	−0.272255	−	0.272255i
$113$	−4.84098	−	4.84098i	−0.455401	−	0.455401i	0.441742	−	0.897142i	$-0.354361\pi$
$113$	−4.84098	−	4.84098i	−0.455401	−	0.455401i	−0.897142	+	0.441742i	$0.854361\pi$
$114$	4.23377	−	0.726400i	0.396529	−	0.0680336i
$115$	1.81695	+	12.1668i	0.169432	+	1.13456i
$116$		−	9.25151i		−	0.858982i
$117$	16.9335	+	8.08729i	1.56550	+	0.747670i
$118$	0.840976	−	0.840976i	0.0774181	−	0.0774181i
$119$	−4.07474			−0.373531
$120$	3.45786	+	1.74448i	0.315658	+	0.159248i
$121$	9.00000			0.818182
$122$	−6.26821	+	6.26821i	−0.567497	+	0.567497i
$123$	−6.64212	−	4.69669i	−0.598900	−	0.423486i
$124$			3.14061i			0.282035i
$125$	−3.73560	+	10.5378i	−0.334123	+	0.942530i
$126$	−4.07474	−	11.5251i	−0.363007	−	1.02674i
$127$	−8.48528	−	8.48528i	−0.752947	−	0.752947i	0.222081	−	0.975028i	$-0.428715\pi$
$127$	−8.48528	−	8.48528i	−0.752947	−	0.752947i	−0.975028	+	0.222081i	$0.928715\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	1.31738	+	7.67828i	0.115989	+	0.676035i
$130$	−8.32106	+	11.2426i	−0.729805	+	0.986045i
$131$		−	1.07107i		−	0.0935796i	−0.998905	−	0.0467898i	$-0.985101\pi$
$131$		−	1.07107i		−	0.0935796i	0.998905	−	0.0467898i	$-0.0148991\pi$
$132$	1.41421	−	2.00000i	0.123091	−	0.174078i
$133$	7.14581	−	7.14581i	0.619620	−	0.619620i
$134$	−6.84617			−0.591419
$135$	7.10537	+	9.19313i	0.611533	+	0.791219i
$136$	1.00000			0.0857493
$137$	−0.171573	+	0.171573i	−0.0146585	+	0.0146585i	−0.714398	−	0.699740i	$-0.753299\pi$
$137$	−0.171573	+	0.171573i	−0.0146585	+	0.0146585i	0.699740	+	0.714398i	$0.253299\pi$
$138$	−5.50151	+	7.78030i	−0.468319	+	0.662304i
$139$		−	5.28247i		−	0.448054i	−0.974583	−	0.224027i	$-0.928080\pi$
$139$		−	5.28247i		−	0.448054i	0.974583	−	0.224027i	$-0.0719203\pi$
$140$	9.01147	−	1.34574i	0.761608	−	0.113736i
$141$	2.48528	+	14.4853i	0.209298	+	1.21988i
$142$	−7.72226	−	7.72226i	−0.648037	−	0.648037i
$143$	6.25519	+	6.25519i	0.523085	+	0.523085i
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	16.6280	+	12.3070i	1.38088	+	1.02204i
$146$			7.52511i			0.622783i
$147$	−13.5814	−	9.60353i	−1.12018	−	0.792086i
$148$	−4.06173	+	4.06173i	−0.333872	+	0.333872i
$149$	−11.5762			−0.948363			−0.474182	−	0.880427i	$-0.657256\pi$
$149$	−11.5762			−0.948363			−0.474182	+	0.880427i	$0.657256\pi$
$150$	−7.73527	+	3.89430i	−0.631582	+	0.317968i
$151$	11.7257			0.954227			0.477113	−	0.878842i	$-0.341683\pi$
$151$	11.7257			0.954227			0.477113	+	0.878842i	$0.341683\pi$
$152$	−1.75368	+	1.75368i	−0.142243	+	0.142243i
$153$	2.70711	+	1.29289i	0.218857	+	0.104524i
$154$		−	5.76256i		−	0.464360i
$155$	−5.64472	−	4.17785i	−0.453395	−	0.335573i
$156$	−10.6783	+	1.83210i	−0.854946	+	0.146686i
$157$	0.921581	+	0.921581i	0.0735502	+	0.0735502i	0.742925	−	0.669375i	$-0.233438\pi$
$157$	0.921581	+	0.921581i	0.0735502	+	0.0735502i	−0.669375	+	0.742925i	$0.733438\pi$
$158$	−5.61655	−	5.61655i	−0.446829	−	0.446829i
$159$	6.42309	−	1.10203i	0.509384	−	0.0873965i
$160$	−2.21154	+	0.330265i	−0.174838	+	0.0261097i
$161$			22.4172i			1.76672i
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	8.08882	−	8.08882i	0.633565	−	0.633565i	−0.315395	−	0.948960i	$-0.602137\pi$
$163$	8.08882	−	8.08882i	0.633565	−	0.633565i	0.948960	+	0.315395i	$0.102137\pi$
$164$	4.69669			0.366750
$165$	1.71338	+	5.20234i	0.133387	+	0.405001i
$166$	1.15902			0.0899577
$167$	−1.99586	+	1.99586i	−0.154444	+	0.154444i	−0.780099	−	0.625656i	$-0.784832\pi$
$167$	−1.99586	+	1.99586i	−0.154444	+	0.154444i	0.625656	+	0.780099i	$0.284832\pi$
$168$	5.76256	+	4.07474i	0.444591	+	0.314373i
$169$		−	26.1274i		−	2.00980i
$170$	−1.33026	+	1.79733i	−0.102027	+	0.137849i
$171$	−7.01473	+	2.48008i	−0.536430	+	0.189657i
$172$	−3.18045	−	3.18045i	−0.242507	−	0.242507i
$173$	−10.1490	−	10.1490i	−0.771616	−	0.771616i	0.206773	−	0.978389i	$-0.433704\pi$
$173$	−10.1490	−	10.1490i	−0.771616	−	0.771616i	−0.978389	+	0.206773i	$0.933704\pi$
$174$	2.70971	+	15.7933i	0.205422	+	1.19729i
$175$	−9.56890	+	17.9868i	−0.723341	+	1.35967i
$176$			1.41421i			0.106600i
$177$	−1.18932	+	1.68195i	−0.0893948	+	0.126423i
$178$	2.76256	−	2.76256i	0.207062	−	0.207062i
$179$	−23.3986			−1.74889			−0.874446	−	0.485123i	$-0.838775\pi$
$179$	−23.3986			−1.74889			−0.874446	+	0.485123i	$0.838775\pi$
$180$	−6.41388	−	1.96523i	−0.478063	−	0.146479i
$181$	−1.46292			−0.108738			−0.0543690	−	0.998521i	$-0.517315\pi$
$181$	−1.46292			−0.108738			−0.0543690	+	0.998521i	$0.517315\pi$
$182$	−18.0229	+	18.0229i	−1.33595	+	1.33595i
$183$	8.86458	−	12.5364i	0.655289	−	0.926719i
$184$		−	5.50151i		−	0.405576i
$185$	−1.89709	−	12.7034i	−0.139477	−	0.933975i
$186$	−0.919864	−	5.36136i	−0.0674477	−	0.393114i
$187$	1.00000	+	1.00000i	0.0731272	+	0.0731272i
$188$	−6.00000	−	6.00000i	−0.437595	−	0.437595i
$189$	10.3317	+	18.4811i	0.751517	+	1.34430i
$190$	−0.819085	−	5.48481i	−0.0594226	−	0.397910i
$191$			20.4592i			1.48038i	0.672398	+	0.740190i	$0.265264\pi$
$191$			20.4592i			1.48038i	−0.672398	+	0.740190i	$0.734736\pi$
$192$	−1.41421	−	1.00000i	−0.102062	−	0.0721688i
$193$	−15.9298	+	15.9298i	−1.14665	+	1.14665i	−0.159445	+	0.987207i	$0.550970\pi$
$193$	−15.9298	+	15.9298i	−1.14665	+	1.14665i	−0.987207	+	0.159445i	$0.949030\pi$
$194$	16.8639			1.21076
$195$	10.9120	−	21.6296i	0.781428	−	1.54893i
$196$	9.60353			0.685967
$197$	9.04030	−	9.04030i	0.644095	−	0.644095i	−0.307465	−	0.951560i	$-0.599481\pi$
$197$	9.04030	−	9.04030i	0.644095	−	0.644095i	0.951560	+	0.307465i	$0.0994806\pi$
$198$	−1.82843	+	3.82843i	−0.129941	+	0.272074i
$199$			10.1102i			0.716696i	0.933588	+	0.358348i	$0.116660\pi$
$199$			10.1102i			0.716696i	−0.933588	+	0.358348i	$0.883340\pi$
$200$	2.34834	−	4.41421i	0.166053	−	0.312132i
$201$	11.6872	−	2.00520i	0.824348	−	0.141436i
$202$	−11.5637	−	11.5637i	−0.813619	−	0.813619i
$203$	26.6562	+	26.6562i	1.87090	+	1.87090i
$204$	−1.70711	+	0.292893i	−0.119521	+	0.0205066i
$205$	−6.24784	+	8.44150i	−0.436368	+	0.589580i
$206$		−	6.67894i		−	0.465344i
$207$	7.11286	−	14.8932i	0.494378	−	1.03515i
$208$	4.42309	−	4.42309i	0.306686	−	0.306686i
$209$	−3.50737			−0.242610
$210$	−14.9894	+	4.93673i	−1.03437	+	0.340667i
$211$	9.28247			0.639032			0.319516	−	0.947581i	$-0.396480\pi$
$211$	9.28247			0.639032			0.319516	+	0.947581i	$0.396480\pi$
$212$	−2.66053	+	2.66053i	−0.182726	+	0.182726i
$213$	15.4445	+	10.9209i	1.05824	+	0.748289i
$214$		−	17.0888i		−	1.16817i
$215$	9.94715	−	1.48548i	0.678390	−	0.101309i
$216$	−2.53553	−	4.53553i	−0.172521	−	0.308604i
$217$	−9.04898	−	9.04898i	−0.614285	−	0.614285i
$218$	−1.88128	−	1.88128i	−0.127416	−	0.127416i
$219$	−2.20406	−	12.8462i	−0.148936	−	0.868064i
$220$	−2.54181	−	1.88128i	−0.171369	−	0.126836i
$221$		−	6.25519i		−	0.420770i
$222$	5.74415	−	8.12345i	0.385522	−	0.545210i
$223$	−11.1020	+	11.1020i	−0.743447	+	0.743447i	−0.973240	−	0.229793i	$-0.926195\pi$
$223$	−11.1020	+	11.1020i	−0.743447	+	0.743447i	0.229793	+	0.973240i	$0.426195\pi$
$224$	−4.07474			−0.272255
$225$	12.0643	−	8.91359i	0.804288	−	0.594239i
$226$	−6.84617			−0.455401
$227$	14.2071	−	14.2071i	0.942956	−	0.942956i	−0.0555024	−	0.998459i	$-0.517676\pi$
$227$	14.2071	−	14.2071i	0.942956	−	0.942956i	0.998459	+	0.0555024i	$0.0176760\pi$
$228$	2.48008	−	3.50737i	0.164248	−	0.232281i
$229$			8.24784i			0.545033i	0.962151	+	0.272516i	$0.0878559\pi$
$229$			8.24784i			0.545033i	−0.962151	+	0.272516i	$0.912144\pi$
$230$	9.88802	+	7.31846i	0.651997	+	0.482565i
$231$	1.68781	+	9.83730i	0.111050	+	0.647247i
$232$	−6.54181	−	6.54181i	−0.429491	−	0.429491i
$233$	12.9905	+	12.9905i	0.851034	+	0.851034i	0.990260	−	0.139227i	$-0.0444618\pi$
$233$	12.9905	+	12.9905i	0.851034	+	0.851034i	−0.139227	+	0.990260i	$0.544462\pi$
$234$	17.6923	−	6.25519i	1.15659	−	0.408915i
$235$	18.7656	−	2.80239i	1.22413	−	0.182808i
$236$		−	1.18932i		−	0.0774181i
$237$	11.2331	+	7.94300i	0.729669	+	0.515954i
$238$	−2.88128	+	2.88128i	−0.186766	+	0.186766i
$239$	−19.4372			−1.25729			−0.628643	−	0.777694i	$-0.716389\pi$
$239$	−19.4372			−1.25729			−0.628643	+	0.777694i	$0.716389\pi$
$240$	3.67861	−	1.21154i	0.237453	−	0.0782048i
$241$	−18.6421			−1.20084			−0.600422	−	0.799683i	$-0.705001\pi$
$241$	−18.6421			−1.20084			−0.600422	+	0.799683i	$0.705001\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$			8.86458i			0.567497i
$245$	−12.7752	+	17.2607i	−0.816180	+	1.10275i
$246$	−8.01775	+	1.37563i	−0.511193	+	0.0877068i
$247$	10.9696	+	10.9696i	0.697981	+	0.697981i
$248$	2.22075	+	2.22075i	0.141018	+	0.141018i
$249$	−1.97858	+	0.339470i	−0.125387	+	0.0215130i
$250$	4.80988	+	10.0928i	0.304203	+	0.638326i
$251$			18.0303i			1.13806i	0.822316	+	0.569031i	$0.192682\pi$
$251$			18.0303i			1.13806i	−0.822316	+	0.569031i	$0.807318\pi$
$252$	−11.0308	−	5.26821i	−0.694873	−	0.331866i
$253$	5.50151	−	5.50151i	0.345877	−	0.345877i
$254$	−12.0000			−0.752947
$255$	1.74448	−	3.45786i	0.109243	−	0.216540i
$256$	1.00000			0.0625000
$257$	0.171573	−	0.171573i	0.0107024	−	0.0107024i	−0.701735	−	0.712438i	$-0.747591\pi$
$257$	0.171573	−	0.171573i	0.0107024	−	0.0107024i	0.712438	+	0.701735i	$0.247591\pi$
$258$	6.36089	+	4.49783i	0.396012	+	0.280023i
$259$		−	23.4059i		−	1.45437i
$260$	2.06587	+	13.8336i	0.128120	+	0.857925i
$261$	−9.25151	−	26.1672i	−0.572654	−	1.61971i
$262$	−0.757359	−	0.757359i	−0.0467898	−	0.0467898i
$263$	9.58731	+	9.58731i	0.591179	+	0.591179i	0.937950	−	0.346771i	$-0.112722\pi$
$263$	9.58731	+	9.58731i	0.591179	+	0.591179i	−0.346771	+	0.937950i	$0.612722\pi$
$264$	−0.414214	−	2.41421i	−0.0254931	−	0.148585i
$265$	−1.24264	−	8.32106i	−0.0763348	−	0.511159i
$266$		−	10.1057i		−	0.619620i
$267$	−3.90685	+	5.52511i	−0.239095	+	0.338132i
$268$	−4.84098	+	4.84098i	−0.295710	+	0.295710i
$269$	30.2732			1.84579			0.922895	−	0.385051i	$-0.125816\pi$
$269$	30.2732			1.84579			0.922895	+	0.385051i	$0.125816\pi$
$270$	11.5248	+	1.47627i	0.701376	+	0.0898430i
$271$	14.5649			0.884758			0.442379	−	0.896828i	$-0.354135\pi$
$271$	14.5649			0.884758			0.442379	+	0.896828i	$0.354135\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$	25.4883	−	36.0459i	1.54262	−	2.18160i
$274$			0.242641i			0.0146585i
$275$	6.76256	−	2.06587i	0.407798	−	0.124577i
$276$	1.61135	+	9.39166i	0.0969921	+	0.565311i
$277$	−12.0433	−	12.0433i	−0.723613	−	0.723613i	0.245727	−	0.969339i	$-0.420973\pi$
$277$	−12.0433	−	12.0433i	−0.723613	−	0.723613i	−0.969339	+	0.245727i	$0.920973\pi$
$278$	−3.73527	−	3.73527i	−0.224027	−	0.224027i
$279$	3.14061	+	8.88300i	0.188024	+	0.531811i
$280$	5.42049	−	7.32366i	0.323936	−	0.437672i
$281$		−	15.2751i		−	0.911237i	−0.890175	−	0.455619i	$-0.849418\pi$
$281$		−	15.2751i		−	0.911237i	0.890175	−	0.455619i	$-0.150582\pi$
$282$	12.0000	+	8.48528i	0.714590	+	0.505291i
$283$	−17.4047	+	17.4047i	−1.03460	+	1.03460i	−0.0352211	+	0.999380i	$0.511214\pi$
$283$	−17.4047	+	17.4047i	−1.03460	+	1.03460i	−0.999380	+	0.0352211i	$0.988786\pi$
$284$	−10.9209			−0.648037
$285$	3.00473	+	9.12326i	0.177985	+	0.540415i
$286$	8.84617			0.523085
$287$	−13.5325	+	13.5325i	−0.798796	+	0.798796i
$288$	2.70711	+	1.29289i	0.159518	+	0.0761845i
$289$		−	1.00000i		−	0.0588235i
$290$	20.4601	−	3.05545i	1.20146	−	0.179422i
$291$	−28.7885	+	4.93933i	−1.68761	+	0.289549i
$292$	5.32106	+	5.32106i	0.311391	+	0.311391i
$293$	−11.1458	−	11.1458i	−0.651145	−	0.651145i	0.302124	−	0.953269i	$-0.402304\pi$
$293$	−11.1458	−	11.1458i	−0.651145	−	0.651145i	−0.953269	+	0.302124i	$0.902304\pi$
$294$	−16.3943	+	2.81281i	−0.956133	+	0.164046i
$295$	2.13760	+	1.58211i	0.124456	+	0.0921141i
$296$			5.74415i			0.333872i
$297$	2.00000	−	7.07107i	0.116052	−	0.410305i
$298$	−8.18564	+	8.18564i	−0.474182	+	0.474182i
$299$	−34.4130			−1.99015
$300$	−2.71598	+	8.22335i	−0.156807	+	0.474775i
$301$	18.3275			1.05638
$302$	8.29135	−	8.29135i	0.477113	−	0.477113i
$303$	23.1274	+	16.3535i	1.32863	+	0.939486i
$304$			2.48008i			0.142243i
$305$	−15.9326	−	11.7922i	−0.912297	−	0.675222i
$306$	2.82843	−	1.00000i	0.161690	−	0.0571662i
$307$	9.66573	+	9.66573i	0.551652	+	0.551652i	0.926917	−	0.375265i	$-0.122448\pi$
$307$	9.66573	+	9.66573i	0.551652	+	0.551652i	−0.375265	+	0.926917i	$0.622448\pi$
$308$	−4.07474	−	4.07474i	−0.232180	−	0.232180i
$309$	1.95622	+	11.4017i	0.111285	+	0.648618i
$310$	−6.94560	+	1.03723i	−0.394484	+	0.0589110i
$311$		−	21.7056i		−	1.23081i	−0.788211	−	0.615405i	$-0.788993\pi$
$311$		−	21.7056i		−	1.23081i	0.788211	−	0.615405i	$-0.211007\pi$
$312$	−6.25519	+	8.84617i	−0.354130	+	0.500816i
$313$	−5.40166	+	5.40166i	−0.305320	+	0.305320i	−0.843091	−	0.537771i	$-0.819267\pi$
$313$	−5.40166	+	5.40166i	−0.305320	+	0.305320i	0.537771	+	0.843091i	$0.319267\pi$
$314$	1.30331			0.0735502
$315$	24.1425	−	12.8178i	1.36028	−	0.722202i
$316$	−7.94300			−0.446829
$317$	−14.8978	+	14.8978i	−0.836743	+	0.836743i	−0.988429	−	0.151686i	$-0.951530\pi$
$317$	−14.8978	+	14.8978i	−0.836743	+	0.836743i	0.151686	+	0.988429i	$0.451530\pi$
$318$	3.76256	−	5.32106i	0.210994	−	0.298390i
$319$		−	13.0836i		−	0.732542i
$320$	−1.33026	+	1.79733i	−0.0743641	+	0.100474i
$321$	5.00520	+	29.1724i	0.279363	+	1.62825i
$322$	15.8514	+	15.8514i	0.883362	+	0.883362i
$323$	1.75368	+	1.75368i	0.0975776	+	0.0975776i
$324$	5.65685	+	7.00000i	0.314270	+	0.388889i
$325$	−27.6117	−	14.6893i	−1.53162	−	0.814818i
$326$		−	11.4393i		−	0.633565i
$327$	3.76256	+	2.66053i	0.208070	+	0.147128i
$328$	3.32106	−	3.32106i	0.183375	−	0.183375i
$329$	34.5753			1.90620
$330$	4.89015	+	2.46707i	0.269194	+	0.135807i
$331$	26.4485			1.45374			0.726869	−	0.686776i	$-0.240975\pi$
$331$	26.4485			1.45374			0.726869	+	0.686776i	$0.240975\pi$
$332$	0.819553	−	0.819553i	0.0449788	−	0.0449788i
$333$	−7.42657	+	15.5500i	−0.406973	+	0.852136i
$334$			2.82257i			0.154444i
$335$	−2.26105	−	15.1406i	−0.123534	−	0.827220i
$336$	6.95602	−	1.19346i	0.379482	−	0.0651088i
$337$	0.156838	+	0.156838i	0.00854351	+	0.00854351i	0.711366	−	0.702822i	$-0.248077\pi$
$337$	0.156838	+	0.156838i	0.00854351	+	0.00854351i	−0.702822	+	0.711366i	$0.748077\pi$
$338$	−18.4749	−	18.4749i	−1.00490	−	1.00490i
$339$	11.6872	−	2.00520i	0.634759	−	0.108907i
$340$	0.330265	+	2.21154i	0.0179111	+	0.119938i
$341$			4.44150i			0.240521i
$342$	−3.20648	+	6.71385i	−0.173387	+	0.363043i
$343$	−7.50151	+	7.50151i	−0.405043	+	0.405043i
$344$	−4.49783			−0.242507
$345$	−19.0234	−	9.59726i	−1.02419	−	0.516699i
$346$	−14.3529			−0.771616
$347$	−8.76776	+	8.76776i	−0.470678	+	0.470678i	−0.902134	−	0.431456i	$-0.858000\pi$
$347$	−8.76776	+	8.76776i	−0.470678	+	0.470678i	0.431456	+	0.902134i	$0.358000\pi$
$348$	13.0836	+	9.25151i	0.701355	+	0.495933i
$349$			7.68195i			0.411205i	0.978636	+	0.205603i	$0.0659155\pi$
$349$			7.68195i			0.411205i	−0.978636	+	0.205603i	$0.934085\pi$
$350$	5.95235	+	19.4848i	0.318166	+	1.04151i
$351$	−28.3706	+	15.8602i	−1.51431	+	0.846557i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	20.8774	+	20.8774i	1.11119	+	1.11119i	0.992989	+	0.118203i	$0.0377133\pi$
$353$	20.8774	+	20.8774i	1.11119	+	1.11119i	0.118203	+	0.992989i	$0.462287\pi$
$354$	0.348344	+	2.03030i	0.0185143	+	0.107909i
$355$	14.5277	−	19.6285i	0.771051	−	1.04177i
$356$		−	3.90685i		−	0.207062i
$357$	4.07474	−	5.76256i	0.215658	−	0.304987i
$358$	−16.5453	+	16.5453i	−0.874446	+	0.874446i
$359$	13.2699			0.700360			0.350180	−	0.936682i	$-0.386120\pi$
$359$	13.2699			0.700360			0.350180	+	0.936682i	$0.386120\pi$
$360$	−5.92492	+	3.14567i	−0.312271	+	0.165792i
$361$	12.8492			0.676273
$362$	−1.03444	+	1.03444i	−0.0543690	+	0.0543690i
$363$	−9.00000	+	12.7279i	−0.472377	+	0.668043i
$364$			25.4883i			1.33595i
$365$	−16.6421	+	2.48528i	−0.871088	+	0.130086i
$366$	−2.59638	−	15.1328i	−0.135715	−	0.791004i
$367$	14.7446	+	14.7446i	0.769663	+	0.769663i	0.978047	−	0.208384i	$-0.0668205\pi$
$367$	14.7446	+	14.7446i	0.769663	+	0.769663i	−0.208384	+	0.978047i	$0.566820\pi$
$368$	−3.89015	−	3.89015i	−0.202788	−	0.202788i
$369$	13.2842	−	4.69669i	0.691550	−	0.244500i
$370$	−10.3241	−	7.64124i	−0.536726	−	0.397249i
$371$		−	15.3315i		−	0.795970i
$372$	−4.44150	−	3.14061i	−0.230281	−	0.162833i
$373$	−19.9482	+	19.9482i	−1.03288	+	1.03288i	−0.0334379	+	0.999441i	$0.510646\pi$
$373$	−19.9482	+	19.9482i	−1.03288	+	1.03288i	−0.999441	+	0.0334379i	$0.989354\pi$
$374$	1.41421			0.0731272
$375$	−11.1671	−	15.8207i	−0.576666	−	0.816980i
$376$	−8.48528			−0.437595
$377$	−40.9203	+	40.9203i	−2.10750	+	2.10750i
$378$	20.3737	+	5.76256i	1.04791	+	0.296394i
$379$			25.2560i			1.29732i	0.761080	+	0.648658i	$0.224669\pi$
$379$			25.2560i			1.29732i	−0.761080	+	0.648658i	$0.775331\pi$
$380$	−4.45753	−	3.29917i	−0.228666	−	0.169244i
$381$	20.4853	−	3.51472i	1.04949	−	0.180064i
$382$	14.4669	+	14.4669i	0.740190	+	0.740190i
$383$	−16.7506	−	16.7506i	−0.855915	−	0.855915i	0.134939	−	0.990854i	$-0.456916\pi$
$383$	−16.7506	−	16.7506i	−0.855915	−	0.855915i	−0.990854	+	0.134939i	$0.956916\pi$
$384$	−1.70711	+	0.292893i	−0.0871154	+	0.0149466i
$385$	12.7441	−	1.90317i	0.649502	−	0.0969946i
$386$			22.5281i			1.14665i
$387$	−12.1761	−	5.81521i	−0.618946	−	0.295604i
$388$	11.9246	−	11.9246i	0.605380	−	0.605380i
$389$	21.8505			1.10786			0.553932	−	0.832562i	$-0.313127\pi$
$389$	21.8505			1.10786			0.553932	+	0.832562i	$0.313127\pi$
$390$	−7.57844	−	23.0104i	−0.383749	−	1.16518i
$391$	−5.50151			−0.278223
$392$	6.79072	−	6.79072i	0.342983	−	0.342983i
$393$	1.51472	+	1.07107i	0.0764074	+	0.0540282i
$394$		−	12.7849i		−	0.644095i
$395$	10.5663	−	14.2762i	0.531648	−	0.718314i
$396$	1.41421	+	4.00000i	0.0710669	+	0.201008i
$397$	−1.98112	−	1.98112i	−0.0994296	−	0.0994296i	0.655642	−	0.755072i	$-0.272398\pi$
$397$	−1.98112	−	1.98112i	−0.0994296	−	0.0994296i	−0.755072	+	0.655642i	$0.772398\pi$
$398$	7.14902	+	7.14902i	0.358348	+	0.358348i
$399$	2.95989	+	17.2515i	0.148180	+	0.863656i
$400$	−1.46079	−	4.78185i	−0.0730395	−	0.239093i
$401$			0.273875i			0.0136767i	0.999977	+	0.00683834i	$0.00217673\pi$
$401$			0.273875i			0.0136767i	−0.999977	+	0.00683834i	$0.997823\pi$
$402$	6.84617	−	9.68195i	0.341456	−	0.482892i
$403$	13.8912	−	13.8912i	0.691970	−	0.691970i
$404$	−16.3535			−0.813619
$405$	−20.1064	+	0.855380i	−0.999096	+	0.0425042i
$406$	37.6975			1.87090
$407$	−5.74415	+	5.74415i	−0.284727	+	0.284727i
$408$	−1.00000	+	1.41421i	−0.0495074	+	0.0700140i
$409$			8.61393i			0.425931i	0.977060	+	0.212966i	$0.0683123\pi$
$409$			8.61393i			0.425931i	−0.977060	+	0.212966i	$0.931688\pi$
$410$	1.55115	+	10.3869i	0.0766059	+	0.512974i
$411$	−0.0710678	−	0.414214i	−0.00350552	−	0.0204316i
$412$	−4.72272	−	4.72272i	−0.232672	−	0.232672i
$413$	3.42676	+	3.42676i	0.168620	+	0.168620i
$414$	−5.50151	−	15.5606i	−0.270384	−	0.764762i
$415$	0.382785	+	2.56323i	0.0187902	+	0.125824i
$416$		−	6.25519i		−	0.306686i
$417$	7.47055	+	5.28247i	0.365834	+	0.258684i
$418$	−2.48008	+	2.48008i	−0.121305	+	0.121305i
$419$	−36.1096			−1.76407			−0.882034	−	0.471186i	$-0.843826\pi$
$419$	−36.1096			−1.76407			−0.882034	+	0.471186i	$0.843826\pi$
$420$	−7.10830	+	14.0899i	−0.346850	+	0.687516i
$421$	−35.9726			−1.75320			−0.876600	−	0.481221i	$-0.840194\pi$
$421$	−35.9726			−1.75320			−0.876600	+	0.481221i	$0.840194\pi$
$422$	6.56370	−	6.56370i	0.319516	−	0.319516i
$423$	−22.9706	−	10.9706i	−1.11687	−	0.533407i
$424$			3.76256i			0.182726i
$425$	−4.41421	−	2.34834i	−0.214121	−	0.113911i
$426$	18.6432	−	3.19866i	0.903265	−	0.154976i
$427$	−25.5413	−	25.5413i	−1.23603	−	1.23603i
$428$	−12.0836	−	12.0836i	−0.584084	−	0.584084i
$429$	−15.1014	+	2.59098i	−0.729101	+	0.125094i
$430$	5.98331	−	8.08409i	0.288541	−	0.389849i
$431$			0.903171i			0.0435042i	0.999763	+	0.0217521i	$0.00692445\pi$
$431$			0.903171i			0.0435042i	−0.999763	+	0.0217521i	$0.993076\pi$
$432$	−5.00000	−	1.41421i	−0.240563	−	0.0680414i
$433$	5.48829	−	5.48829i	0.263751	−	0.263751i	−0.562825	−	0.826576i	$-0.690286\pi$
$433$	5.48829	−	5.48829i	0.263751	−	0.263751i	0.826576	+	0.562825i	$0.190286\pi$
$434$	−12.7972			−0.614285
$435$	−34.0327	+	11.2086i	−1.63174	+	0.537412i
$436$	−2.66053			−0.127416
$437$	9.64790	−	9.64790i	0.461522	−	0.461522i
$438$	−10.6421	−	7.52511i	−0.508500	−	0.359564i
$439$		−	12.1008i		−	0.577539i	−0.957399	−	0.288769i	$-0.906754\pi$
$439$		−	12.1008i		−	0.577539i	0.957399	−	0.288769i	$-0.0932461\pi$
$440$	−3.12759	+	0.467065i	−0.149102	+	0.0222665i
$441$	27.1629	−	9.60353i	1.29347	−	0.457311i
$442$	−4.42309	−	4.42309i	−0.210385	−	0.210385i
$443$	−5.83144	−	5.83144i	−0.277060	−	0.277060i	0.554874	−	0.831934i	$-0.312766\pi$
$443$	−5.83144	−	5.83144i	−0.277060	−	0.277060i	−0.831934	+	0.554874i	$0.812766\pi$
$444$	−1.68242	−	9.80587i	−0.0798442	−	0.465366i
$445$	7.02189	+	5.19714i	0.332870	+	0.246368i
$446$			15.7006i			0.743447i
$447$	11.5762	−	16.3713i	0.547538	−	0.774335i
$448$	−2.88128	+	2.88128i	−0.136128	+	0.136128i
$449$	−10.8713			−0.513047			−0.256524	−	0.966538i	$-0.582577\pi$
$449$	−10.8713			−0.513047			−0.256524	+	0.966538i	$0.582577\pi$
$450$	2.22791	−	14.8336i	0.105024	−	0.699264i
$451$	6.64212			0.312765
$452$	−4.84098	+	4.84098i	−0.227700	+	0.227700i
$453$	−11.7257	+	16.5827i	−0.550923	+	0.779123i
$454$		−	20.0918i		−	0.942956i
$455$	−45.8109	−	33.9062i	−2.14765	−	1.58955i
$456$	−0.726400	−	4.23377i	−0.0340168	−	0.198264i
$457$	2.83578	+	2.83578i	0.132652	+	0.132652i	0.770315	−	0.637663i	$-0.220099\pi$
$457$	2.83578	+	2.83578i	0.132652	+	0.132652i	−0.637663	+	0.770315i	$0.720099\pi$
$458$	5.83210	+	5.83210i	0.272516	+	0.272516i
$459$	−4.53553	+	2.53553i	−0.211701	+	0.118349i
$460$	12.1668	−	1.81695i	0.567281	−	0.0847159i
$461$		−	16.9592i		−	0.789870i	−0.918709	−	0.394935i	$-0.870767\pi$
$461$		−	16.9592i		−	0.789870i	0.918709	−	0.394935i	$-0.129233\pi$
$462$	8.14949	+	5.76256i	0.379148	+	0.268098i
$463$	−12.0000	+	12.0000i	−0.557687	+	0.557687i	−0.928648	−	0.370961i	$-0.879028\pi$
$463$	−12.0000	+	12.0000i	−0.557687	+	0.557687i	0.370961	+	0.928648i	$0.379028\pi$
$464$	−9.25151			−0.429491
$465$	11.5531	−	3.80499i	0.535762	−	0.176452i
$466$	18.3713			0.851034
$467$	8.28642	−	8.28642i	0.383450	−	0.383450i	−0.488893	−	0.872343i	$-0.662599\pi$
$467$	8.28642	−	8.28642i	0.383450	−	0.383450i	0.872343	+	0.488893i	$0.162599\pi$
$468$	8.08729	−	16.9335i	0.373835	−	0.782750i
$469$		−	27.8964i		−	1.28814i
$470$	11.2877	−	15.2509i	0.520661	−	0.703469i
$471$	−2.22489	+	0.381731i	−0.102518	+	0.0175893i
$472$	−0.840976	−	0.840976i	−0.0387091	−	0.0387091i
$473$	−4.49783	−	4.49783i	−0.206810	−	0.206810i
$474$	13.5596	−	2.32645i	0.622811	−	0.106857i
$475$	11.8594	−	3.62288i	0.544146	−	0.166229i
$476$			4.07474i			0.186766i
$477$	−4.86458	+	10.1856i	−0.222734	+	0.466369i
$478$	−13.7441	+	13.7441i	−0.628643	+	0.628643i
$479$	11.3520			0.518687			0.259344	−	0.965785i	$-0.416494\pi$
$479$	11.3520			0.518687			0.259344	+	0.965785i	$0.416494\pi$
$480$	1.74448	−	3.45786i	0.0796242	−	0.157829i
$481$	35.9307			1.63830
$482$	−13.1820	+	13.1820i	−0.600422	+	0.600422i
$483$	−31.7027	−	22.4172i	−1.44252	−	1.02002i
$484$		−	9.00000i		−	0.409091i
$485$	5.56956	+	37.2953i	0.252901	+	1.69349i
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	6.24612	+	6.24612i	0.283039	+	0.283039i	0.834320	−	0.551281i	$-0.185861\pi$
$487$	6.24612	+	6.24612i	0.283039	+	0.283039i	−0.551281	+	0.834320i	$0.685861\pi$
$488$	6.26821	+	6.26821i	0.283748	+	0.283748i
$489$	3.35050	+	19.5281i	0.151515	+	0.883092i
$490$	3.17171	+	21.2386i	0.143283	+	0.959464i
$491$			19.1517i			0.864303i	0.901801	+	0.432151i	$0.142245\pi$
$491$			19.1517i			0.864303i	−0.901801	+	0.432151i	$0.857755\pi$
$492$	−4.69669	+	6.64212i	−0.211743	+	0.299450i
$493$	−6.54181	+	6.54181i	−0.294628	+	0.294628i
$494$	15.5134			0.697981
$495$	−9.07060	−	2.77925i	−0.407693	−	0.124918i
$496$	3.14061			0.141018
$497$	31.4662	−	31.4662i	1.41145	−	1.41145i
$498$	−1.15902	+	1.63911i	−0.0519371	+	0.0734501i
$499$			1.60052i			0.0716492i	0.999358	+	0.0358246i	$0.0114058\pi$
$499$			1.60052i			0.0716492i	−0.999358	+	0.0358246i	$0.988594\pi$
$500$	10.5378	+	3.73560i	0.471265	+	0.167061i
$501$	−0.826710	−	4.81842i	−0.0369347	−	0.215271i
$502$	12.7493	+	12.7493i	0.569031	+	0.569031i
$503$	−1.00473	−	1.00473i	−0.0447987	−	0.0447987i	0.684353	−	0.729151i	$-0.260085\pi$
$503$	−1.00473	−	1.00473i	−0.0447987	−	0.0447987i	−0.729151	+	0.684353i	$0.760085\pi$
$504$	−11.5251	+	4.07474i	−0.513369	+	0.181503i
$505$	21.7545	−	29.3927i	0.968064	−	1.30796i
$506$		−	7.78030i		−	0.345877i
$507$	36.9497	+	26.1274i	1.64099	+	1.16036i
$508$	−8.48528	+	8.48528i	−0.376473	+	0.376473i
$509$	−38.9623			−1.72697			−0.863486	−	0.504372i	$-0.831724\pi$
$509$	−38.9623			−1.72697			−0.863486	+	0.504372i	$0.831724\pi$
$510$	−1.21154	−	3.67861i	−0.0536481	−	0.162892i
$511$	−30.6629			−1.35645
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.50737	−	12.4004i	0.154854	−	0.547492i
$514$		−	0.242641i		−	0.0107024i
$515$	14.7708	−	2.20582i	0.650878	−	0.0972000i
$516$	7.67828	−	1.31738i	0.338017	−	0.0579946i
$517$	−8.48528	−	8.48528i	−0.373182	−	0.373182i
$518$	−16.5505	−	16.5505i	−0.727187	−	0.727187i
$519$	24.5019	−	4.20386i	1.07551	−	0.184529i
$520$	11.2426	+	8.32106i	0.493022	+	0.364903i
$521$		−	17.2591i		−	0.756137i	−0.925778	−	0.378068i	$-0.876588\pi$
$521$		−	17.2591i		−	0.756137i	0.925778	−	0.378068i	$-0.123412\pi$
$522$	−25.0448	−	11.9612i	−1.09618	−	0.523528i
$523$	−17.3211	+	17.3211i	−0.757397	+	0.757397i	−0.975848	−	0.218451i	$-0.929900\pi$
$523$	−17.3211	+	17.3211i	−0.757397	+	0.757397i	0.218451	+	0.975848i	$0.429900\pi$
$524$	−1.07107			−0.0467898
$525$	−15.8683	−	31.5193i	−0.692548	−	1.37561i
$526$	13.5585			0.591179
$527$	2.22075	−	2.22075i	0.0967373	−	0.0967373i
$528$	−2.00000	−	1.41421i	−0.0870388	−	0.0615457i
$529$			7.26657i			0.315938i
$530$	−6.76256	−	5.00520i	−0.293747	−	0.217412i
$531$	−1.18932	−	3.36391i	−0.0516121	−	0.145981i
$532$	−7.14581	−	7.14581i	−0.309810	−	0.309810i
$533$	−20.7739	−	20.7739i	−0.899816	−	0.899816i
$534$	1.14429	+	6.66940i	0.0495182	+	0.288613i
$535$	37.7927	−	5.64384i	1.63392	−	0.244004i
$536$			6.84617i			0.295710i
$537$	23.3986	−	33.0906i	1.00972	−	1.42796i
$538$	21.4064	−	21.4064i	0.922895	−	0.922895i
$539$	13.5814			0.584994
$540$	9.19313	−	7.10537i	0.395609	−	0.305767i
$541$	6.14882			0.264359			0.132179	−	0.991226i	$-0.457803\pi$
$541$	6.14882			0.264359			0.132179	+	0.991226i	$0.457803\pi$
$542$	10.2990	−	10.2990i	0.442379	−	0.442379i
$543$	1.46292	−	2.06888i	0.0627799	−	0.0887842i
$544$		−	1.00000i		−	0.0428746i
$545$	3.53921	−	4.78185i	0.151603	−	0.204832i
$546$	−7.46535	−	43.5112i	−0.319487	−	1.86211i
$547$	−15.0438	−	15.0438i	−0.643226	−	0.643226i	0.308121	−	0.951347i	$-0.400300\pi$
$547$	−15.0438	−	15.0438i	−0.643226	−	0.643226i	−0.951347	+	0.308121i	$0.900300\pi$
$548$	0.171573	+	0.171573i	0.00732923	+	0.00732923i
$549$	8.86458	+	25.0728i	0.378331	+	1.07008i
$550$	3.32106	−	6.24264i	0.141610	−	0.266187i
$551$		−	22.9445i		−	0.977470i
$552$	7.78030	+	5.50151i	0.331152	+	0.234160i
$553$	22.8860	−	22.8860i	0.973212	−	0.973212i
$554$	−17.0318			−0.723613
$555$	19.8625	+	10.0205i	0.843114	+	0.425348i
$556$	−5.28247			−0.224027
$557$	−1.58145	+	1.58145i	−0.0670081	+	0.0670081i	−0.739817	−	0.672809i	$-0.765088\pi$
$557$	−1.58145	+	1.58145i	−0.0670081	+	0.0670081i	0.672809	+	0.739817i	$0.265088\pi$
$558$	8.50198	+	4.06048i	0.359917	+	0.171894i
$559$			28.1348i			1.18997i
$560$	−1.34574	−	9.01147i	−0.0568681	−	0.380804i
$561$	−2.41421	+	0.414214i	−0.101928	+	0.0174881i
$562$	−10.8011	−	10.8011i	−0.455619	−	0.455619i
$563$	−7.77972	−	7.77972i	−0.327876	−	0.327876i	0.523902	−	0.851778i	$-0.324476\pi$
$563$	−7.77972	−	7.77972i	−0.327876	−	0.327876i	−0.851778	+	0.523902i	$0.824476\pi$
$564$	14.4853	−	2.48528i	0.609940	−	0.104649i
$565$	−2.26105	−	15.1406i	−0.0951231	−	0.636970i
$566$			24.6139i			1.03460i
$567$	−36.4679	−	3.86998i	−1.53151	−	0.162524i
$568$	−7.72226	+	7.72226i	−0.324019	+	0.324019i
$569$	9.56679			0.401061			0.200530	−	0.979687i	$-0.435733\pi$
$569$	9.56679			0.401061			0.200530	+	0.979687i	$0.435733\pi$
$570$	8.57578	+	4.32645i	0.359200	+	0.181215i
$571$	16.5343			0.691937			0.345969	−	0.938246i	$-0.387550\pi$
$571$	16.5343			0.691937			0.345969	+	0.938246i	$0.387550\pi$
$572$	6.25519	−	6.25519i	0.261543	−	0.261543i
$573$	−28.9337	−	20.4592i	−1.20872	−	0.854697i
$574$			19.1378i			0.798796i
$575$	−12.9194	+	24.2848i	−0.538777	+	1.01275i
$576$	2.82843	−	1.00000i	0.117851	−	0.0416667i
$577$	13.7604	+	13.7604i	0.572852	+	0.572852i	0.932924	−	0.360073i	$-0.117248\pi$
$577$	13.7604	+	13.7604i	0.572852	+	0.572852i	−0.360073	+	0.932924i	$0.617248\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$	−6.59834	−	38.4579i	−0.274217	−	1.59826i
$580$	12.3070	−	16.6280i	0.511019	−	0.690441i
$581$			4.72272i			0.195932i
$582$	−16.8639	+	23.8492i	−0.699032	+	0.988581i
$583$	−3.76256	+	3.76256i	−0.155829	+	0.155829i
$584$	7.52511			0.311391
$585$	19.6768	+	37.0615i	0.813535	+	1.53231i
$586$	−15.7626			−0.651145
$587$	−0.343146	+	0.343146i	−0.0141631	+	0.0141631i	−0.714153	−	0.699990i	$-0.753188\pi$
$587$	−0.343146	+	0.343146i	−0.0141631	+	0.0141631i	0.699990	+	0.714153i	$0.253188\pi$
$588$	−9.60353	+	13.5814i	−0.396043	+	0.560089i
$589$			7.78898i			0.320939i
$590$	2.63023	−	0.392791i	0.108285	−	0.0161709i
$591$	3.74462	+	21.8252i	0.154033	+	0.897770i
$592$	4.06173	+	4.06173i	0.166936	+	0.166936i
$593$	4.58880	+	4.58880i	0.188439	+	0.188439i	0.795021	−	0.606582i	$-0.207460\pi$
$593$	4.58880	+	4.58880i	0.188439	+	0.188439i	−0.606582	+	0.795021i	$0.707460\pi$
$594$	−3.58579	−	6.41421i	−0.147127	−	0.263178i
$595$	−7.32366	−	5.42049i	−0.300241	−	0.222218i
$596$			11.5762i			0.474182i
$597$	−14.2980	−	10.1102i	−0.585180	−	0.413784i
$598$	−24.3336	+	24.3336i	−0.995077	+	0.995077i
$599$	16.0251			0.654768			0.327384	−	0.944891i	$-0.393833\pi$
$599$	16.0251			0.654768			0.327384	+	0.944891i	$0.393833\pi$
$600$	3.89430	+	7.73527i	0.158984	+	0.315791i
$601$	−30.5385			−1.24569			−0.622846	−	0.782344i	$-0.714024\pi$
$601$	−30.5385			−1.24569			−0.622846	+	0.782344i	$0.714024\pi$
$602$	12.9595	−	12.9595i	0.528190	−	0.528190i
$603$	−8.85137	+	18.5333i	−0.360456	+	0.754735i
$604$		−	11.7257i		−	0.477113i
$605$	16.1760	+	11.9724i	0.657647	+	0.486747i
$606$	27.9172	−	4.78984i	1.13406	−	0.194574i
$607$	−30.3828	−	30.3828i	−1.23320	−	1.23320i	−0.962728	−	0.270471i	$-0.912821\pi$
$607$	−30.3828	−	30.3828i	−1.23320	−	1.23320i	−0.270471	−	0.962728i	$-0.587179\pi$
$608$	1.75368	+	1.75368i	0.0711213	+	0.0711213i
$609$	−64.3537	+	11.0414i	−2.60775	+	0.447418i
$610$	−19.6044	+	2.92766i	−0.793760	+	0.118538i
$611$			53.0770i			2.14727i
$612$	1.29289	−	2.70711i	0.0522621	−	0.109428i
$613$	−20.8514	+	20.8514i	−0.842179	+	0.842179i	−0.989142	−	0.146963i	$-0.953050\pi$
$613$	−20.8514	+	20.8514i	−0.842179	+	0.842179i	0.146963	+	0.989142i	$0.453050\pi$
$614$	13.6694			0.551652
$615$	−5.69024	−	17.2773i	−0.229453	−	0.696687i
$616$	−5.76256			−0.232180
$617$	−6.84617	+	6.84617i	−0.275617	+	0.275617i	−0.831356	−	0.555740i	$-0.812435\pi$
$617$	−6.84617	+	6.84617i	−0.275617	+	0.275617i	0.555740	+	0.831356i	$0.312435\pi$
$618$	9.44545	+	6.67894i	0.379952	+	0.268666i
$619$		−	41.9025i		−	1.68421i	−0.539317	−	0.842103i	$-0.681318\pi$
$619$		−	41.9025i		−	1.68421i	0.539317	−	0.842103i	$-0.318682\pi$
$620$	−4.17785	+	5.64472i	−0.167786	+	0.226697i
$621$	13.9493	+	24.9523i	0.559764	+	1.00130i
$622$	−15.3481	−	15.3481i	−0.615405	−	0.615405i
$623$	11.2567	+	11.2567i	0.450991	+	0.450991i
$624$	1.83210	+	10.6783i	0.0733428	+	0.427473i
$625$	−20.7322	+	13.9706i	−0.829287	+	0.558823i
$626$			7.63911i			0.305320i
$627$	3.50737	−	4.96017i	0.140071	−	0.198090i
$628$	0.921581	−	0.921581i	0.0367751	−	0.0367751i
$629$	5.74415			0.229034
$630$	8.00780	−	26.1349i	0.319038	−	1.04124i
$631$	20.0472			0.798067			0.399034	−	0.916936i	$-0.369346\pi$
$631$	20.0472			0.798067			0.399034	+	0.916936i	$0.369346\pi$
$632$	−5.61655	+	5.61655i	−0.223414	+	0.223414i
$633$	−9.28247	+	13.1274i	−0.368945	+	0.521767i
$634$			21.0686i			0.836743i
$635$	−3.96318	−	26.5385i	−0.157274	−	1.05315i
$636$	−1.10203	−	6.42309i	−0.0436982	−	0.254692i
$637$	−42.4773	−	42.4773i	−1.68301	−	1.68301i
$638$	−9.25151	−	9.25151i	−0.366271	−	0.366271i
$639$	−30.8890	+	10.9209i	−1.22195	+	0.432025i
$640$	0.330265	+	2.21154i	0.0130549	+	0.0874189i
$641$		−	49.1187i		−	1.94007i	−0.242959	−	0.970036i	$-0.578118\pi$
$641$		−	49.1187i		−	1.94007i	0.242959	−	0.970036i	$-0.421882\pi$
$642$	24.1672	+	17.0888i	0.953805	+	0.674442i
$643$	18.0888	−	18.0888i	0.713353	−	0.713353i	−0.253882	−	0.967235i	$-0.581707\pi$
$643$	18.0888	−	18.0888i	0.713353	−	0.713353i	0.967235	+	0.253882i	$0.0817075\pi$
$644$	22.4172			0.883362
$645$	−7.84637	+	15.5529i	−0.308950	+	0.612394i
$646$	2.48008			0.0975776
$647$	−34.7760	+	34.7760i	−1.36718	+	1.36718i	−0.502756	+	0.864428i	$0.667681\pi$
$647$	−34.7760	+	34.7760i	−1.36718	+	1.36718i	−0.864428	+	0.502756i	$0.832319\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$		−	1.68195i		−	0.0660224i
$650$	−29.9114	+	9.13752i	−1.17322	+	0.358403i
$651$	21.8462	−	3.74821i	0.856219	−	0.146904i
$652$	−8.08882	−	8.08882i	−0.316782	−	0.316782i
$653$	−8.97838	−	8.97838i	−0.351351	−	0.351351i	0.509261	−	0.860612i	$-0.329919\pi$
$653$	−8.97838	−	8.97838i	−0.351351	−	0.351351i	−0.860612	+	0.509261i	$0.829919\pi$
$654$	4.54181	−	0.779251i	0.177599	−	0.0304711i
$655$	1.42480	−	1.92506i	0.0556717	−	0.0752184i
$656$		−	4.69669i		−	0.183375i
$657$	20.3713	+	9.72917i	0.794760	+	0.379571i
$658$	24.4485	−	24.4485i	0.953100	−	0.953100i
$659$	−0.569804			−0.0221964			−0.0110982	−	0.999938i	$-0.503533\pi$
$659$	−0.569804			−0.0221964			−0.0110982	+	0.999938i	$0.503533\pi$
$660$	5.20234	−	1.71338i	0.202501	−	0.0666933i
$661$	−36.5017			−1.41975			−0.709876	−	0.704327i	$-0.751249\pi$
$661$	−36.5017			−1.41975			−0.709876	+	0.704327i	$0.751249\pi$
$662$	18.7019	−	18.7019i	0.726869	−	0.726869i
$663$	8.84617	+	6.25519i	0.343557	+	0.242931i
$664$		−	1.15902i		−	0.0449788i
$665$	22.3492	−	3.33756i	0.866665	−	0.129425i
$666$	5.74415	+	16.2469i	0.222581	+	0.629555i
$667$	35.9898	+	35.9898i	1.39353	+	1.39353i
$668$	1.99586	+	1.99586i	0.0772220	+	0.0772220i
$669$	−4.59861	−	26.8027i	−0.177793	−	1.03625i
$670$	−12.3048	−	9.10723i	−0.475377	−	0.351843i
$671$			12.5364i			0.483963i
$672$	4.07474	−	5.76256i	0.157187	−	0.222295i
$673$	−28.7279	+	28.7279i	−1.10738	+	1.10738i	−0.113886	+	0.993494i	$0.536330\pi$
$673$	−28.7279	+	28.7279i	−1.10738	+	1.10738i	−0.993494	+	0.113886i	$0.963670\pi$
$674$	0.221802			0.00854351
$675$	0.541395	+	25.9751i	0.0208383	+	0.999783i
$676$	−26.1274			−1.00490
$677$	12.8975	−	12.8975i	0.495691	−	0.495691i	−0.414402	−	0.910094i	$-0.636009\pi$
$677$	12.8975	−	12.8975i	0.495691	−	0.495691i	0.910094	+	0.414402i	$0.136009\pi$
$678$	6.84617	−	9.68195i	0.262926	−	0.371833i
$679$			68.7162i			2.63708i
$680$	1.79733	+	1.33026i	0.0689245	+	0.0510133i
$681$	5.88476	+	34.2989i	0.225504	+	1.31434i
$682$	3.14061	+	3.14061i	0.120260	+	0.120260i
$683$	25.9203	+	25.9203i	0.991811	+	0.991811i	0.999967	−	0.00815577i	$-0.00259609\pi$
$683$	25.9203	+	25.9203i	0.991811	+	0.991811i	−0.00815577	+	0.999967i	$0.502596\pi$
$684$	2.48008	+	7.01473i	0.0948284	+	0.268215i
$685$	−0.536610	+	0.0801357i	−0.0205028	+	0.00306183i
$686$			10.6087i			0.405043i
$687$	−11.6642	−	8.24784i	−0.445017	−	0.314675i
$688$	−3.18045	+	3.18045i	−0.121253	+	0.121253i
$689$	23.5355			0.896632
$690$	−20.2379	+	6.66531i	−0.770443	+	0.253744i
$691$	3.12126			0.118739			0.0593693	−	0.998236i	$-0.481091\pi$
$691$	3.12126			0.118739			0.0593693	+	0.998236i	$0.481091\pi$
$692$	−10.1490	+	10.1490i	−0.385808	+	0.385808i
$693$	−15.5999	−	7.45037i	−0.592590	−	0.283016i
$694$			12.3995i			0.470678i
$695$	7.02709	−	9.49435i	0.266553	−	0.360141i
$696$	15.7933	−	2.70971i	0.598644	−	0.102711i
$697$	−3.32106	−	3.32106i	−0.125794	−	0.125794i
$698$	5.43196	+	5.43196i	0.205603	+	0.205603i
$699$	−31.3618	+	5.38083i	−1.18621	+	0.203522i
$700$	17.9868	+	9.56890i	0.679837	+	0.361670i
$701$			21.6746i			0.818638i	0.912391	+	0.409319i	$0.134234\pi$
$701$			21.6746i			0.818638i	−0.912391	+	0.409319i	$0.865766\pi$
$702$	−8.84617	+	31.2759i	−0.333877	+	1.18043i
$703$	−10.0734	+	10.0734i	−0.379926	+	0.379926i
$704$	1.41421			0.0533002
$705$	−14.8024	+	29.3409i	−0.557490	+	1.10504i
$706$	29.5251			1.11119
$707$	47.1191	−	47.1191i	1.77210	−	1.77210i
$708$	1.68195	+	1.18932i	0.0632117	+	0.0446974i
$709$		−	12.1050i		−	0.454614i	−0.973823	−	0.227307i	$-0.927008\pi$
$709$		−	12.1050i		−	0.454614i	0.973823	−	0.227307i	$-0.0729921\pi$
$710$	−3.60680	−	24.1521i	−0.135361	−	0.906412i
$711$	−22.4662	+	7.94300i	−0.842549	+	0.297886i
$712$	−2.76256	−	2.76256i	−0.103531	−	0.103531i
$713$	−12.2175	−	12.2175i	−0.457548	−	0.457548i
$714$	−1.19346	−	6.95602i	−0.0446643	−	0.260323i
$715$	2.92158	+	19.5637i	0.109261	+	0.731641i
$716$			23.3986i			0.874446i
$717$	19.4372	−	27.4883i	0.725894	−	1.02657i
$718$	9.38325	−	9.38325i	0.350180	−	0.350180i
$719$	32.8247			1.22415			0.612077	−	0.790798i	$-0.290334\pi$
$719$	32.8247			1.22415			0.612077	+	0.790798i	$0.290334\pi$
$720$	−1.96523	+	6.41388i	−0.0732397	+	0.239031i
$721$	27.2150			1.01354
$722$	9.08575	−	9.08575i	0.338136	−	0.338136i
$723$	18.6421	−	26.3639i	0.693308	−	0.980485i
$724$			1.46292i			0.0543690i
$725$	13.5145	+	44.2394i	0.501917	+	1.64301i
$726$	2.63604	+	15.3640i	0.0978326	+	0.570210i
$727$	−1.94820	−	1.94820i	−0.0722548	−	0.0722548i	0.670056	−	0.742311i	$-0.266270\pi$
$727$	−1.94820	−	1.94820i	−0.0722548	−	0.0722548i	−0.742311	+	0.670056i	$0.766270\pi$
$728$	18.0229	+	18.0229i	0.667975	+	0.667975i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−10.0104	+	13.5251i	−0.370501	+	0.500587i
$731$			4.49783i			0.166358i
$732$	−12.5364	−	8.86458i	−0.463359	−	0.327644i
$733$	11.6434	−	11.6434i	0.430058	−	0.430058i	−0.458590	−	0.888648i	$-0.651645\pi$
$733$	11.6434	−	11.6434i	0.430058	−	0.430058i	0.888648	+	0.458590i	$0.151645\pi$
$734$	20.8520			0.769663
$735$	−11.6351	−	35.3276i	−0.429167	−	1.30308i
$736$	−5.50151			−0.202788
$737$	−6.84617	+	6.84617i	−0.252182	+	0.252182i
$738$	6.07232	−	12.7144i	0.223525	−	0.468025i
$739$		−	8.57015i		−	0.315258i	−0.987498	−	0.157629i	$-0.949615\pi$
$739$		−	8.57015i		−	0.315258i	0.987498	−	0.157629i	$-0.0503850\pi$
$740$	−12.7034	+	1.89709i	−0.466987	+	0.0697384i
$741$	−26.4830	+	4.54377i	−0.972878	+	0.166919i
$742$	−10.8410	−	10.8410i	−0.397985	−	0.397985i
$743$	11.9517	+	11.9517i	0.438465	+	0.438465i	0.891495	−	0.453030i	$-0.149657\pi$
$743$	11.9517	+	11.9517i	0.438465	+	0.438465i	−0.453030	+	0.891495i	$0.649657\pi$
$744$	−5.36136	+	0.919864i	−0.196557	+	0.0337239i
$745$	−20.8063	−	15.3995i	−0.762285	−	0.564193i
$746$			28.2110i			1.03288i
$747$	1.49849	−	3.13760i	0.0548270	−	0.114799i
$748$	1.00000	−	1.00000i	0.0365636	−	0.0365636i
$749$	69.6325			2.54432
$750$	−19.0833	−	3.29063i	−0.696823	−	0.120157i
$751$	41.1835			1.50281			0.751403	−	0.659844i	$-0.229378\pi$
$751$	41.1835			1.50281			0.751403	+	0.659844i	$0.229378\pi$
$752$	−6.00000	+	6.00000i	−0.218797	+	0.218797i
$753$	−25.4987	−	18.0303i	−0.929224	−	0.657061i
$754$			57.8700i			2.10750i
$755$	21.0750	+	15.5983i	0.766998	+	0.567682i
$756$	18.4811	−	10.3317i	0.672152	−	0.375758i
$757$	−12.4659	−	12.4659i	−0.453082	−	0.453082i	0.443294	−	0.896376i	$-0.353810\pi$
$757$	−12.4659	−	12.4659i	−0.453082	−	0.453082i	−0.896376	+	0.443294i	$0.853810\pi$
$758$	17.8587	+	17.8587i	0.648658	+	0.648658i
$759$	2.27880	+	13.2818i	0.0827151	+	0.482099i
$760$	−5.48481	+	0.819085i	−0.198955	+	0.0297113i
$761$			17.6569i			0.640060i	0.947407	+	0.320030i	$0.103693\pi$
$761$			17.6569i			0.640060i	−0.947407	+	0.320030i	$0.896307\pi$
$762$	12.0000	−	16.9706i	0.434714	−	0.614779i
$763$	7.66573	−	7.66573i	0.277518	−	0.277518i
$764$	20.4592			0.740190
$765$	3.14567	+	5.92492i	0.113732	+	0.214216i
$766$	−23.6889			−0.855915
$767$	−5.26047	+	5.26047i	−0.189944	+	0.189944i
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$			41.3743i			1.49200i	0.665948	+	0.745998i	$0.268027\pi$
$769$			41.3743i			1.49200i	−0.665948	+	0.745998i	$0.731973\pi$
$770$	7.66573	−	10.3572i	0.276254	−	0.373248i
$771$	0.0710678	+	0.414214i	0.00255944	+	0.0149175i
$772$	15.9298	+	15.9298i	0.573326	+	0.573326i
$773$	−19.9978	−	19.9978i	−0.719273	−	0.719273i	0.249184	−	0.968456i	$-0.419838\pi$
$773$	−19.9978	−	19.9978i	−0.719273	−	0.719273i	−0.968456	+	0.249184i	$0.919838\pi$
$774$	−12.7218	+	4.49783i	−0.457275	+	0.161671i
$775$	−4.58778	−	15.0179i	−0.164798	−	0.539460i
$776$		−	16.8639i		−	0.605380i
$777$	33.1010	+	23.4059i	1.18749	+	0.839683i
$778$	15.4506	−	15.4506i	0.553932	−	0.553932i
$779$	11.6482			0.417339
$780$	−21.6296	−	10.9120i	−0.774463	−	0.390714i
$781$	−15.4445			−0.552648
$782$	−3.89015	+	3.89015i	−0.139112	+	0.139112i
$783$	46.2576	+	13.0836i	1.65311	+	0.467570i
$784$		−	9.60353i		−	0.342983i
$785$	0.430438	+	2.88233i	0.0153630	+	0.102875i
$786$	1.82843	−	0.313708i	0.0652178	−	0.0111896i
$787$	−7.55549	−	7.55549i	−0.269324	−	0.269324i	0.559504	−	0.828828i	$-0.310992\pi$
$787$	−7.55549	−	7.55549i	−0.269324	−	0.269324i	−0.828828	+	0.559504i	$0.810992\pi$
$788$	−9.04030	−	9.04030i	−0.322047	−	0.322047i
$789$	−23.1458	+	3.97119i	−0.824013	+	0.141378i
$790$	−2.62330	−	17.5663i	−0.0933327	−	0.624981i
$791$		−	27.8964i		−	0.991882i
$792$	3.82843	+	1.82843i	0.136037	+	0.0649703i
$793$	39.2088	−	39.2088i	1.39235	−	1.39235i
$794$	−2.80173			−0.0994296
$795$	13.0104	+	6.56370i	0.461431	+	0.232790i
$796$	10.1102			0.358348
$797$	−16.9846	+	16.9846i	−0.601625	+	0.601625i	−0.940744	−	0.339118i	$-0.889871\pi$
$797$	−16.9846	+	16.9846i	−0.601625	+	0.601625i	0.339118	+	0.940744i	$0.389871\pi$
$798$	14.2916	+	10.1057i	0.505918	+	0.357738i
$799$			8.48528i			0.300188i
$800$	−4.41421	−	2.34834i	−0.156066	−	0.0830265i
$801$	−3.90685	−	11.0502i	−0.138042	−	0.390441i
$802$	0.193659	+	0.193659i	0.00683834	+	0.00683834i
$803$	7.52511	+	7.52511i	0.265556	+	0.265556i
$804$	−2.00520	−	11.6872i	−0.0707179	−	0.412174i
$805$	−29.8208	+	40.2912i	−1.05105	+	1.42008i
$806$		−	19.6451i		−	0.691970i
$807$	−30.2732	+	42.8128i	−1.06567	+	1.50708i
$808$	−11.5637	+	11.5637i	−0.406810	+	0.406810i
$809$	−14.7084			−0.517120			−0.258560	−	0.965995i	$-0.583248\pi$
$809$	−14.7084			−0.517120			−0.258560	+	0.965995i	$0.583248\pi$
$810$	−13.6125	+	14.8222i	−0.478296	+	0.520800i
$811$	0.603534			0.0211929			0.0105965	−	0.999944i	$-0.496627\pi$
$811$	0.603534			0.0211929			0.0105965	+	0.999944i	$0.496627\pi$
$812$	26.6562	−	26.6562i	0.935449	−	0.935449i
$813$	−14.5649	+	20.5979i	−0.510815	+	0.722402i
$814$			8.12345i			0.284727i
$815$	25.2985	−	3.77800i	0.886169	−	0.132338i
$816$	0.292893	+	1.70711i	0.0102533	+	0.0597607i
$817$	−7.88777	−	7.88777i	−0.275958	−	0.275958i
$818$	6.09097	+	6.09097i	0.212966	+	0.212966i
$819$	25.4883	+	72.0918i	0.890633	+	2.51909i
$820$	8.44150	+	6.24784i	0.294790	+	0.218184i
$821$		−	21.0557i		−	0.734851i	−0.930053	−	0.367425i	$-0.880239\pi$
$821$		−	21.0557i		−	0.734851i	0.930053	−	0.367425i	$-0.119761\pi$
$822$	−0.343146	−	0.242641i	−0.0119686	−	0.00846307i
$823$	−3.62761	+	3.62761i	−0.126451	+	0.126451i	−0.767500	−	0.641049i	$-0.778499\pi$
$823$	−3.62761	+	3.62761i	−0.126451	+	0.126451i	0.641049	+	0.767500i	$0.278499\pi$
$824$	−6.67894			−0.232672
$825$	−3.84098	+	11.6296i	−0.133726	+	0.404890i
$826$	4.84617			0.168620
$827$	−30.5866	+	30.5866i	−1.06360	+	1.06360i	−0.0657669	+	0.997835i	$0.520949\pi$
$827$	−30.5866	+	30.5866i	−1.06360	+	1.06360i	−0.997835	+	0.0657669i	$0.979051\pi$
$828$	−14.8932	−	7.11286i	−0.517573	−	0.247189i
$829$		−	39.6555i		−	1.37729i	−0.725097	−	0.688647i	$-0.758205\pi$
$829$		−	39.6555i		−	1.37729i	0.725097	−	0.688647i	$-0.241795\pi$
$830$	2.08315	+	1.54181i	0.0723071	+	0.0535170i
$831$	29.0751	−	4.98850i	1.00861	−	0.173049i
$832$	−4.42309	−	4.42309i	−0.153343	−	0.153343i
$833$	−6.79072	−	6.79072i	−0.235285	−	0.235285i
$834$	9.01775	−	1.54720i	0.312259	−	0.0535752i
$835$	−6.24223	+	0.932194i	−0.216021	+	0.0322599i
$836$			3.50737i			0.121305i
$837$	−15.7031	−	4.44150i	−0.542777	−	0.153521i
$838$	−25.5333	+	25.5333i	−0.882034	+	0.882034i
$839$	11.8339			0.408550			0.204275	−	0.978913i	$-0.434516\pi$
$839$	11.8339			0.408550			0.204275	+	0.978913i	$0.434516\pi$
$840$	4.93673	+	14.9894i	0.170333	+	0.517183i
$841$	56.5905			1.95140
$842$	−25.4365	+	25.4365i	−0.876600	+	0.876600i
$843$	21.6023	+	15.2751i	0.744022	+	0.526103i
$844$		−	9.28247i		−	0.319516i
$845$	34.7564	−	46.9596i	1.19566	−	1.61546i
$846$	−24.0000	+	8.48528i	−0.825137	+	0.291730i
$847$	25.9315	+	25.9315i	0.891017	+	0.891017i
$848$	2.66053	+	2.66053i	0.0913630	+	0.0913630i
$849$	−7.20925	−	42.0186i	−0.247421	−	1.44207i
$850$	−4.78185	+	1.46079i	−0.164016	+	0.0501047i
$851$		−	31.6015i		−	1.08328i
$852$	10.9209	−	15.4445i	0.374144	−	0.529120i
$853$	37.7550	−	37.7550i	1.29271	−	1.29271i	0.359601	−	0.933106i	$-0.382913\pi$
$853$	37.7550	−	37.7550i	1.29271	−	1.29271i	0.933106	−	0.359601i	$-0.117087\pi$
$854$	−36.1209			−1.23603
$855$	−15.9070	−	4.87393i	−0.544007	−	0.166685i
$856$	−17.0888			−0.584084
$857$	3.96877	−	3.96877i	0.135570	−	0.135570i	−0.636065	−	0.771635i	$-0.719439\pi$
$857$	3.96877	−	3.96877i	0.135570	−	0.135570i	0.771635	+	0.636065i	$0.219439\pi$
$858$	−8.84617	+	12.5104i	−0.302003	+	0.427097i
$859$			20.8197i			0.710361i	0.934798	+	0.355180i	$0.115581\pi$
$859$			20.8197i			0.710361i	−0.934798	+	0.355180i	$0.884419\pi$
$860$	−1.48548	−	9.94715i	−0.0506543	−	0.339195i
$861$	−5.60533	−	32.6703i	−0.191029	−	1.11340i
$862$	0.638638	+	0.638638i	0.0217521	+	0.0217521i
$863$	0.960830	+	0.960830i	0.0327070	+	0.0327070i	0.723271	−	0.690564i	$-0.242638\pi$
$863$	0.960830	+	0.960830i	0.0327070	+	0.0327070i	−0.690564	+	0.723271i	$0.742638\pi$
$864$	−4.53553	+	2.53553i	−0.154302	+	0.0862606i
$865$	−4.74025	−	31.7420i	−0.161173	−	1.07926i
$866$		−	7.76162i		−	0.263751i
$867$	1.41421	+	1.00000i	0.0480292	+	0.0339618i
$868$	−9.04898	+	9.04898i	−0.307142	+	0.307142i
$869$	−11.2331			−0.381057
$870$	−16.1391	+	31.9904i	−0.547166	+	1.08458i
$871$	42.8241			1.45104
$872$	−1.88128	+	1.88128i	−0.0637081	+	0.0637081i
$873$	21.8032	−	45.6524i	0.737928	−	1.54510i
$874$		−	13.6442i		−	0.461522i
$875$	−41.1257	+	19.5990i	−1.39030	+	0.662568i
$876$	−12.8462	+	2.20406i	−0.434032	+	0.0744681i
$877$	−5.66744	−	5.66744i	−0.191376	−	0.191376i	0.604914	−	0.796290i	$-0.293207\pi$
$877$	−5.66744	−	5.66744i	−0.191376	−	0.191376i	−0.796290	+	0.604914i	$0.793207\pi$
$878$	−8.55654	−	8.55654i	−0.288769	−	0.288769i
$879$	26.9084	−	4.61675i	0.907597	−	0.155719i
$880$	−1.88128	+	2.54181i	−0.0634179	+	0.0856843i
$881$			39.9038i			1.34439i	0.740373	+	0.672196i	$0.234649\pi$
$881$			39.9038i			1.34439i	−0.740373	+	0.672196i	$0.765351\pi$
$882$	12.4163	−	25.9978i	0.418080	−	0.875391i
$883$	−4.68414	+	4.68414i	−0.157634	+	0.157634i	−0.781517	−	0.623884i	$-0.785554\pi$
$883$	−4.68414	+	4.68414i	−0.157634	+	0.157634i	0.623884	+	0.781517i	$0.285554\pi$
$884$	−6.25519			−0.210385
$885$	−4.37504	+	1.44091i	−0.147065	+	0.0484358i
$886$	−8.24690			−0.277060
$887$	16.3622	−	16.3622i	0.549390	−	0.549390i	−0.376875	−	0.926264i	$-0.623001\pi$
$887$	16.3622	−	16.3622i	0.549390	−	0.549390i	0.926264	+	0.376875i	$0.123001\pi$
$888$	−8.12345	−	5.74415i	−0.272605	−	0.192761i
$889$		−	48.8969i		−	1.63995i
$890$	8.64016	−	1.29029i	0.289619	−	0.0432508i
$891$	8.00000	+	9.89949i	0.268010	+	0.331646i
$892$	11.1020	+	11.1020i	0.371723	+	0.371723i
$893$	−14.8805	−	14.8805i	−0.497957	−	0.497957i
$894$	−3.39060	−	19.7619i	−0.113399	−	0.660937i
$895$	−42.0550	−	31.1263i	−1.40574	−	1.04044i
$896$			4.07474i			0.136128i
$897$	34.4130	−	48.6673i	1.14902	−	1.62495i
$898$	−7.68715	+	7.68715i	−0.256524	+	0.256524i
$899$	−29.0554			−0.969053
$900$	−8.91359	−	12.0643i	−0.297120	−	0.402144i
$901$	3.76256			0.125349
$902$	4.69669	−	4.69669i	0.156383	−	0.156383i
$903$	−18.3275	+	25.9190i	−0.609901	+	0.862531i
$904$			6.84617i			0.227700i
$905$	−2.62935	−	1.94607i	−0.0874026	−	0.0646896i
$906$	3.43439	+	20.0171i	0.114100	+	0.665023i
$907$	21.9696	+	21.9696i	0.729489	+	0.729489i	0.970518	−	0.241029i	$-0.0774848\pi$
$907$	21.9696	+	21.9696i	0.729489	+	0.729489i	−0.241029	+	0.970518i	$0.577485\pi$
$908$	−14.2071	−	14.2071i	−0.471478	−	0.471478i
$909$	−46.2548	+	16.3535i	−1.53417	+	0.542413i
$910$	−56.3685	+	8.41789i	−1.86860	+	0.279050i
$911$		−	57.2446i		−	1.89660i	−0.317378	−	0.948299i	$-0.602802\pi$
$911$		−	57.2446i		−	1.89660i	0.317378	−	0.948299i	$-0.397198\pi$
$912$	−3.50737	−	2.48008i	−0.116141	−	0.0821238i
$913$	1.15902	−	1.15902i	0.0383581	−	0.0383581i
$914$	4.01040			0.132652
$915$	32.6093	−	10.7398i	1.07803	−	0.355048i
$916$	8.24784			0.272516
$917$	3.08604	−	3.08604i	0.101910	−	0.101910i
$918$	−1.41421	+	5.00000i	−0.0466760	+	0.165025i
$919$			9.12990i			0.301167i	0.988597	+	0.150584i	$0.0481153\pi$
$919$			9.12990i			0.301167i	−0.988597	+	0.150584i	$0.951885\pi$
$920$	7.31846	−	9.88802i	0.241283	−	0.325998i
$921$	−23.3351	+	4.00368i	−0.768919	+	0.131926i
$922$	−11.9920	−	11.9920i	−0.394935	−	0.394935i
$923$	48.3042	+	48.3042i	1.58995	+	1.58995i
$924$	9.83730	−	1.68781i	0.323623	−	0.0555250i
$925$	13.4892	−	25.3559i	0.443523	−	0.833697i
$926$			16.9706i			0.557687i
$927$	−18.0806	−	8.63516i	−0.593845	−	0.283616i
$928$	−6.54181	+	6.54181i	−0.214745	+	0.214745i
$929$	8.25613			0.270875			0.135437	−	0.990786i	$-0.456756\pi$
$929$	8.25613			0.270875			0.135437	+	0.990786i	$0.456756\pi$
$930$	5.47873	−	10.8598i	0.179655	−	0.356107i
$931$	23.8176			0.780589
$932$	12.9905	−	12.9905i	0.425517	−	0.425517i
$933$	30.6963	+	21.7056i	1.00495	+	0.710608i
$934$		−	11.7188i		−	0.383450i
$935$	0.467065	+	3.12759i	0.0152747	+	0.102283i
$936$	−6.25519	−	17.6923i	−0.204457	−	0.578293i
$937$	−16.5607	−	16.5607i	−0.541014	−	0.541014i	0.382812	−	0.923826i	$-0.374956\pi$
$937$	−16.5607	−	16.5607i	−0.541014	−	0.541014i	−0.923826	+	0.382812i	$0.874956\pi$
$938$	−19.7257	−	19.7257i	−0.644068	−	0.644068i
$939$	−2.23744	−	13.0408i	−0.0730162	−	0.425569i
$940$	−2.80239	−	18.7656i	−0.0914039	−	0.612065i
$941$			44.9010i			1.46373i	0.681449	+	0.731866i	$0.261350\pi$
$941$			44.9010i			1.46373i	−0.681449	+	0.731866i	$0.738650\pi$
$942$	−1.30331	+	1.84316i	−0.0424642	+	0.0600535i
$943$	−18.2708	+	18.2708i	−0.594980	+	0.594980i
$944$	−1.18932			−0.0387091
$945$	−6.01542	+	46.9605i	−0.195682	+	1.52763i
$946$	−6.36089			−0.206810
$947$	−41.1577	+	41.1577i	−1.33745	+	1.33745i	−0.438921	+	0.898526i	$0.644639\pi$
$947$	−41.1577	+	41.1577i	−1.33745	+	1.33745i	−0.898526	+	0.438921i	$0.855361\pi$
$948$	7.94300	−	11.2331i	0.257977	−	0.364834i
$949$		−	47.0710i		−	1.52799i
$950$	5.82409	−	10.9476i	0.188958	−	0.355188i
$951$	−6.17086	−	35.9664i	−0.200104	−	1.16629i
$952$	2.88128	+	2.88128i	0.0933828	+	0.0933828i
$953$	10.5281	+	10.5281i	0.341039	+	0.341039i	0.856758	−	0.515719i	$-0.172475\pi$
$953$	10.5281	+	10.5281i	0.341039	+	0.341039i	−0.515719	+	0.856758i	$0.672475\pi$
$954$	3.76256	+	10.6421i	0.121817	+	0.344551i
$955$	−27.2162	+	36.7720i	−0.880696	+	1.18991i
$956$			19.4372i			0.628643i
$957$	18.5030	+	13.0836i	0.598118	+	0.422933i
$958$	8.02709	−	8.02709i	0.259344	−	0.259344i
$959$	−0.988699			−0.0319267
$960$	−1.21154	−	3.67861i	−0.0391024	−	0.118727i
$961$	−21.1365			−0.681824
$962$	25.4069	−	25.4069i	0.819150	−	0.819150i
$963$	−46.2612	−	22.0940i	−1.49075	−	0.711970i
$964$			18.6421i			0.600422i
$965$	−49.8219	+	7.44025i	−1.60382	+	0.239510i
$966$	−38.2686	+	6.56585i	−1.23127	+	0.211253i
$967$	−8.70431	−	8.70431i	−0.279912	−	0.279912i	0.553162	−	0.833074i	$-0.313421\pi$
$967$	−8.70431	−	8.70431i	−0.279912	−	0.279912i	−0.833074	+	0.553162i	$0.813421\pi$
$968$	−6.36396	−	6.36396i	−0.204545	−	0.204545i
$969$	−4.23377	+	0.726400i	−0.136008	+	0.0233353i
$970$	30.3100	+	22.4335i	0.973197	+	0.720296i
$971$		−	21.3934i		−	0.686546i	−0.939236	−	0.343273i	$-0.888464\pi$
$971$		−	21.3934i		−	0.686546i	0.939236	−	0.343273i	$-0.111536\pi$
$972$	−15.5563	+	1.00000i	−0.498970	+	0.0320750i
$973$	15.2203	−	15.2203i	0.487940	−	0.487940i
$974$	8.83335			0.283039
$975$	48.3856	−	24.3596i	1.54958	−	0.780130i
$976$	8.86458			0.283748
$977$	22.5269	−	22.5269i	0.720699	−	0.720699i	−0.248049	−	0.968748i	$-0.579789\pi$
$977$	22.5269	−	22.5269i	0.720699	−	0.720699i	0.968748	+	0.248049i	$0.0797893\pi$
$978$	16.1776	+	11.4393i	0.517304	+	0.365789i
$979$		−	5.52511i		−	0.176583i
$980$	17.2607	+	12.7752i	0.551373	+	0.408090i
$981$	−7.52511	+	2.66053i	−0.240258	+	0.0849442i
$982$	13.5423	+	13.5423i	0.432151	+	0.432151i
$983$	12.0632	+	12.0632i	0.384758	+	0.384758i	0.872813	−	0.488055i	$-0.162293\pi$
$983$	12.0632	+	12.0632i	0.384758	+	0.384758i	−0.488055	+	0.872813i	$0.662293\pi$
$984$	1.37563	+	8.01775i	0.0438534	+	0.255596i
$985$	28.2744	−	4.22241i	0.900897	−	0.134537i
$986$			9.25151i			0.294628i
$987$	−34.5753	+	48.8969i	−1.10055	+	1.55641i
$988$	10.9696	−	10.9696i	0.348990	−	0.348990i
$989$	24.7448			0.786840
$990$	−8.37911	+	4.44865i	−0.266306	+	0.141388i
$991$	−11.9396			−0.379273			−0.189636	−	0.981854i	$-0.560731\pi$
$991$	−11.9396			−0.379273			−0.189636	+	0.981854i	$0.560731\pi$
$992$	2.22075	−	2.22075i	0.0705088	−	0.0705088i
$993$	−26.4485	+	37.4038i	−0.839317	+	1.18697i
$994$		−	44.4999i		−	1.41145i
$995$	−13.4493	+	18.1714i	−0.426371	+	0.576073i
$996$	0.339470	+	1.97858i	0.0107565	+	0.0626936i
$997$	4.90884	+	4.90884i	0.155464	+	0.155464i	0.780553	−	0.625089i	$-0.214937\pi$
$997$	4.90884	+	4.90884i	0.155464	+	0.155464i	−0.625089	+	0.780553i	$0.714937\pi$
$998$	1.13174	+	1.13174i	0.0358246	+	0.0358246i
$999$	−14.5645	−	26.0528i	−0.460800	−	0.824273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.d.137.4	✓	8
3.2	odd	2		510.2.l.e.137.1	yes	8
5.3	odd	4		510.2.l.e.443.1	yes	8
15.8	even	4	inner	510.2.l.d.443.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.d.137.4	✓	8	1.1	even	1	trivial
510.2.l.d.443.4	yes	8	15.8	even	4	inner
510.2.l.e.137.1	yes	8	3.2	odd	2
510.2.l.e.443.1	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(1.79733 + 1.33026i) q^{5} +(0.292893 + 1.70711i) q^{6} +(2.88128 + 2.88128i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(1.79733 + 1.33026i) q^{5} +(0.292893 + 1.70711i) q^{6} +(2.88128 + 2.88128i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(2.21154 - 0.330265i) q^{10} -1.41421i q^{11} +(1.41421 + 1.00000i) q^{12} +(-4.42309 + 4.42309i) q^{13} +4.07474 q^{14} +(-3.67861 + 1.21154i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.70711 - 1.29289i) q^{18} -2.48008i q^{19} +(1.33026 - 1.79733i) q^{20} +(-6.95602 + 1.19346i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(3.89015 + 3.89015i) q^{23} +(1.70711 - 0.292893i) q^{24} +(1.46079 + 4.78185i) q^{25} +6.25519i q^{26} +(5.00000 + 1.41421i) q^{27} +(2.88128 - 2.88128i) q^{28} +9.25151 q^{29} +(-1.74448 + 3.45786i) q^{30} -3.14061 q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.00000 + 1.41421i) q^{33} +1.00000i q^{34} +(1.34574 + 9.01147i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-4.06173 - 4.06173i) q^{37} +(-1.75368 - 1.75368i) q^{38} +(-1.83210 - 10.6783i) q^{39} +(-0.330265 - 2.21154i) q^{40} +4.69669i q^{41} +(-4.07474 + 5.76256i) q^{42} +(3.18045 - 3.18045i) q^{43} -1.41421 q^{44} +(1.96523 - 6.41388i) q^{45} +5.50151 q^{46} +(6.00000 - 6.00000i) q^{47} +(1.00000 - 1.41421i) q^{48} +9.60353i q^{49} +(4.41421 + 2.34834i) q^{50} +(-0.292893 - 1.70711i) q^{51} +(4.42309 + 4.42309i) q^{52} +(-2.66053 - 2.66053i) q^{53} +(4.53553 - 2.53553i) q^{54} +(1.88128 - 2.54181i) q^{55} -4.07474i q^{56} +(3.50737 + 2.48008i) q^{57} +(6.54181 - 6.54181i) q^{58} +1.18932 q^{59} +(1.21154 + 3.67861i) q^{60} -8.86458 q^{61} +(-2.22075 + 2.22075i) q^{62} +(5.26821 - 11.0308i) q^{63} +1.00000i q^{64} +(-13.8336 + 2.06587i) q^{65} +(2.41421 - 0.414214i) q^{66} +(-4.84098 - 4.84098i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-9.39166 + 1.61135i) q^{69} +(7.32366 + 5.42049i) q^{70} -10.9209i q^{71} +(-1.29289 + 2.70711i) q^{72} +(-5.32106 + 5.32106i) q^{73} -5.74415 q^{74} +(-8.22335 - 2.71598i) q^{75} -2.48008 q^{76} +(4.07474 - 4.07474i) q^{77} +(-8.84617 - 6.25519i) q^{78} -7.94300i q^{79} +(-1.79733 - 1.33026i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(3.32106 + 3.32106i) q^{82} +(0.819553 + 0.819553i) q^{83} +(1.19346 + 6.95602i) q^{84} +(-2.21154 + 0.330265i) q^{85} -4.49783i q^{86} +(-9.25151 + 13.0836i) q^{87} +(-1.00000 + 1.00000i) q^{88} +3.90685 q^{89} +(-3.14567 - 5.92492i) q^{90} -25.4883 q^{91} +(3.89015 - 3.89015i) q^{92} +(3.14061 - 4.44150i) q^{93} -8.48528i q^{94} +(3.29917 - 4.45753i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(11.9246 + 11.9246i) q^{97} +(6.79072 + 6.79072i) q^{98} +(-4.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9	\( 8 q - 8 q^{3} + 4 q^{5} + 8 q^{6} + 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 16 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{22} - 16 q^{23} + 8 q^{24} + 8 q^{25} + 40 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 24 q^{35} - 8 q^{37} - 16 q^{38} - 24 q^{39} + 4 q^{40} - 8 q^{42} + 16 q^{43} - 4 q^{45} + 8 q^{46} + 48 q^{47} + 8 q^{48} + 24 q^{50} - 8 q^{51} - 8 q^{52} - 8 q^{53} + 8 q^{54} + 32 q^{57} + 24 q^{58} - 32 q^{59} - 12 q^{60} - 24 q^{61} - 16 q^{62} + 8 q^{63} - 24 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{69} - 16 q^{72} - 16 q^{73} + 24 q^{74} - 32 q^{75} - 16 q^{76} + 8 q^{77} + 16 q^{78} - 4 q^{80} - 56 q^{81} + 16 q^{83} + 4 q^{85} - 8 q^{87} - 8 q^{88} + 16 q^{89} + 4 q^{90} - 64 q^{91} - 16 q^{92} + 8 q^{93} + 32 q^{95} - 8 q^{96} + 16 q^{97} - 8 q^{98} - 32 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 4 * q^5 + 8 * q^6 + 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 16 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^22 - 16 * q^23 + 8 * q^24 + 8 * q^25 + 40 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 24 * q^35 - 8 * q^37 - 16 * q^38 - 24 * q^39 + 4 * q^40 - 8 * q^42 + 16 * q^43 - 4 * q^45 + 8 * q^46 + 48 * q^47 + 8 * q^48 + 24 * q^50 - 8 * q^51 - 8 * q^52 - 8 * q^53 + 8 * q^54 + 32 * q^57 + 24 * q^58 - 32 * q^59 - 12 * q^60 - 24 * q^61 - 16 * q^62 + 8 * q^63 - 24 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^69 - 16 * q^72 - 16 * q^73 + 24 * q^74 - 32 * q^75 - 16 * q^76 + 8 * q^77 + 16 * q^78 - 4 * q^80 - 56 * q^81 + 16 * q^83 + 4 * q^85 - 8 * q^87 - 8 * q^88 + 16 * q^89 + 4 * q^90 - 64 * q^91 - 16 * q^92 + 8 * q^93 + 32 * q^95 - 8 * q^96 + 16 * q^97 - 8 * q^98 - 32 * q^99

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