LMFDB - Embedded newform 966.2.l.d.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.896677 + 1.48188i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.18968 - 2.06059i) q^{5} +(1.51749 - 0.835007i) q^{6} +(1.24146 - 2.33640i) q^{7} -1.00000i q^{8} +(-1.39194 - 2.65754i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.896677 + 1.48188i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.18968 - 2.06059i) q^{5} +(1.51749 - 0.835007i) q^{6} +(1.24146 - 2.33640i) q^{7} -1.00000i q^{8} +(-1.39194 - 2.65754i) q^{9} +(-2.06059 + 1.18968i) q^{10} +(2.74069 - 1.58234i) q^{11} +(-1.73168 - 0.0356051i) q^{12} +2.15362i q^{13} +(-2.24334 + 1.40265i) q^{14} +(1.98679 + 3.61066i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69727 - 6.40386i) q^{17} +(-0.123314 + 2.99746i) q^{18} +(-7.34038 - 4.23797i) q^{19} +2.37937 q^{20} +(2.34908 + 3.93470i) q^{21} -3.16467 q^{22} +(-0.866025 - 0.500000i) q^{23} +(1.48188 + 0.896677i) q^{24} +(-0.330695 - 0.572780i) q^{25} +(1.07681 - 1.86509i) q^{26} +(5.18627 + 0.320266i) q^{27} +(2.64411 - 0.0930622i) q^{28} +7.43039i q^{29} +(0.0847177 - 4.12031i) q^{30} +(-6.86384 + 3.96284i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.112679 + 5.48022i) q^{33} +7.39454i q^{34} +(-3.33742 - 5.33773i) q^{35} +(1.60553 - 2.53422i) q^{36} +(-1.49395 + 2.58759i) q^{37} +(4.23797 + 7.34038i) q^{38} +(-3.19141 - 1.93110i) q^{39} +(-2.06059 - 1.18968i) q^{40} +5.77496 q^{41} +(-0.0670104 - 4.58209i) q^{42} -9.96100 q^{43} +(2.74069 + 1.58234i) q^{44} +(-7.13207 - 0.293409i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.93117 - 3.34488i) q^{47} +(-0.835007 - 1.51749i) q^{48} +(-3.91754 - 5.80111i) q^{49} +0.661389i q^{50} +(12.8050 + 0.263284i) q^{51} +(-1.86509 + 1.07681i) q^{52} +(-1.90180 + 1.09800i) q^{53} +(-4.33131 - 2.87049i) q^{54} -7.52992i q^{55} +(-2.33640 - 1.24146i) q^{56} +(12.8621 - 7.07748i) q^{57} +(3.71519 - 6.43491i) q^{58} +(-4.33833 - 7.51421i) q^{59} +(-2.13352 + 3.52594i) q^{60} +(-0.471560 - 0.272255i) q^{61} +7.92568 q^{62} +(-7.93711 - 0.0471049i) q^{63} -1.00000 q^{64} +(4.43773 + 2.56213i) q^{65} +(2.83769 - 4.68967i) q^{66} +(-2.25755 - 3.91019i) q^{67} +(3.69727 - 6.40386i) q^{68} +(1.51749 - 0.835007i) q^{69} +(0.221429 + 6.29132i) q^{70} -4.91507i q^{71} +(-2.65754 + 1.39194i) q^{72} +(7.56919 - 4.37008i) q^{73} +(2.58759 - 1.49395i) q^{74} +(1.14532 + 0.0235488i) q^{75} -8.47594i q^{76} +(-0.294512 - 8.36776i) q^{77} +(1.79829 + 3.26809i) q^{78} +(1.40410 - 2.43197i) q^{79} +(1.18968 + 2.06059i) q^{80} +(-5.12501 + 7.39826i) q^{81} +(-5.00126 - 2.88748i) q^{82} +10.7239 q^{83} +(-2.23301 + 4.00171i) q^{84} -17.5943 q^{85} +(8.62648 + 4.98050i) q^{86} +(-11.0109 - 6.66266i) q^{87} +(-1.58234 - 2.74069i) q^{88} +(5.03800 - 8.72608i) q^{89} +(6.02985 + 3.82013i) q^{90} +(5.03172 + 2.67364i) q^{91} -1.00000i q^{92} +(0.282195 - 13.7248i) q^{93} +(-3.34488 + 1.93117i) q^{94} +(-17.4655 + 10.0837i) q^{95} +(-0.0356051 + 1.73168i) q^{96} -5.10883i q^{97} +(0.492134 + 6.98268i) q^{98} +(-8.01999 - 5.08096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.896677	+	1.48188i	−0.517697	+	0.855564i
$3$	−0.896677	+	1.48188i	−0.517697	+	0.855564i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.18968	−	2.06059i	0.532043	−	0.921525i	−0.467258	−	0.884121i	$-0.654758\pi$
$5$	1.18968	−	2.06059i	0.532043	−	0.921525i	0.999300	−	0.0374038i	$-0.0119088\pi$
$6$	1.51749	−	0.835007i	0.619511	−	0.340890i
$7$	1.24146	−	2.33640i	0.469229	−	0.883077i
$7$	1.24146	−	2.33640i	0.469229	−	0.883077i
$8$		−	1.00000i		−	0.353553i
$9$	−1.39194	−	2.65754i	−0.463980	−	0.885846i
$10$	−2.06059	+	1.18968i	−0.651617	+	0.376211i
$11$	2.74069	−	1.58234i	0.826348	−	0.477092i	−0.0262523	−	0.999655i	$-0.508357\pi$
$11$	2.74069	−	1.58234i	0.826348	−	0.477092i	0.852601	+	0.522563i	$0.175024\pi$
$12$	−1.73168	−	0.0356051i	−0.499894	−	0.0102783i
$13$			2.15362i			0.597307i	0.954362	+	0.298653i	$0.0965374\pi$
$13$			2.15362i			0.597307i	−0.954362	+	0.298653i	$0.903463\pi$
$14$	−2.24334	+	1.40265i	−0.599558	+	0.374874i
$15$	1.98679	+	3.61066i	0.512987	+	0.932267i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.69727	−	6.40386i	−0.896720	−	1.55316i	−0.831662	−	0.555283i	$-0.812610\pi$
$17$	−3.69727	−	6.40386i	−0.896720	−	1.55316i	−0.0650579	−	0.997881i	$-0.520723\pi$
$18$	−0.123314	+	2.99746i	−0.0290653	+	0.706509i
$19$	−7.34038	−	4.23797i	−1.68400	−	0.972258i	−0.958956	−	0.283554i	$-0.908486\pi$
$19$	−7.34038	−	4.23797i	−1.68400	−	0.972258i	−0.725043	−	0.688703i	$-0.758180\pi$
$20$	2.37937			0.532043
$21$	2.34908	+	3.93470i	0.512610	+	0.858621i
$22$	−3.16467			−0.674711
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	1.48188	+	0.896677i	0.302488	+	0.183033i
$25$	−0.330695	−	0.572780i	−0.0661389	−	0.114556i
$26$	1.07681	−	1.86509i	0.211180	−	0.365774i
$27$	5.18627	+	0.320266i	0.998099	+	0.0616352i
$28$	2.64411	−	0.0930622i	0.499691	−	0.0175871i
$29$			7.43039i			1.37979i	0.723910	+	0.689894i	$0.242343\pi$
$29$			7.43039i			1.37979i	−0.723910	+	0.689894i	$0.757657\pi$
$30$	0.0847177	−	4.12031i	0.0154673	−	0.752263i
$31$	−6.86384	+	3.96284i	−1.23278	+	0.711747i	−0.967609	−	0.252454i	$-0.918762\pi$
$31$	−6.86384	+	3.96284i	−1.23278	+	0.711747i	−0.265173	+	0.964201i	$0.585429\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.112679	+	5.48022i	−0.0196148	+	0.953983i
$34$			7.39454i			1.26815i
$35$	−3.33742	−	5.33773i	−0.564127	−	0.902241i
$36$	1.60553	−	2.53422i	0.267588	−	0.422371i
$37$	−1.49395	+	2.58759i	−0.245603	+	0.425397i	−0.962301	−	0.271987i	$-0.912319\pi$
$37$	−1.49395	+	2.58759i	−0.245603	+	0.425397i	0.716698	+	0.697384i	$0.245653\pi$
$38$	4.23797	+	7.34038i	0.687490	+	1.19077i
$39$	−3.19141	−	1.93110i	−0.511034	−	0.309224i
$40$	−2.06059	−	1.18968i	−0.325808	−	0.188106i
$41$	5.77496			0.901897			0.450948	−	0.892550i	$-0.351086\pi$
$41$	5.77496			0.901897			0.450948	+	0.892550i	$0.351086\pi$
$42$	−0.0670104	−	4.58209i	−0.0103399	−	0.707031i
$43$	−9.96100			−1.51904			−0.759519	−	0.650485i	$-0.774566\pi$
$43$	−9.96100			−1.51904			−0.759519	+	0.650485i	$0.774566\pi$
$44$	2.74069	+	1.58234i	0.413174	+	0.238546i
$45$	−7.13207	−	0.293409i	−1.06319	−	0.0437388i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	1.93117	−	3.34488i	0.281690	−	0.487901i	−0.690111	−	0.723703i	$-0.742438\pi$
$47$	1.93117	−	3.34488i	0.281690	−	0.487901i	0.971801	+	0.235802i	$0.0757718\pi$
$48$	−0.835007	−	1.51749i	−0.120523	−	0.219030i
$49$	−3.91754	−	5.80111i	−0.559649	−	0.828730i
$50$			0.661389i			0.0935345i
$51$	12.8050	+	0.263284i	1.79306	+	0.0368671i
$52$	−1.86509	+	1.07681i	−0.258641	+	0.149327i
$53$	−1.90180	+	1.09800i	−0.261232	+	0.150822i	−0.624896	−	0.780708i	$-0.714859\pi$
$53$	−1.90180	+	1.09800i	−0.261232	+	0.150822i	0.363664	+	0.931530i	$0.381526\pi$
$54$	−4.33131	−	2.87049i	−0.589417	−	0.390625i
$55$		−	7.52992i		−	1.01533i
$56$	−2.33640	−	1.24146i	−0.312215	−	0.165897i
$57$	12.8621	−	7.07748i	1.70363	−	0.937435i
$58$	3.71519	−	6.43491i	0.487829	−	0.844945i
$59$	−4.33833	−	7.51421i	−0.564802	−	0.978267i	−0.997068	−	0.0765202i	$-0.975619\pi$
$59$	−4.33833	−	7.51421i	−0.564802	−	0.978267i	0.432266	−	0.901746i	$-0.357714\pi$
$60$	−2.13352	+	3.52594i	−0.275437	+	0.455197i
$61$	−0.471560	−	0.272255i	−0.0603771	−	0.0348587i	0.469508	−	0.882928i	$-0.344431\pi$
$61$	−0.471560	−	0.272255i	−0.0603771	−	0.0348587i	−0.529885	+	0.848070i	$0.677765\pi$
$62$	7.92568			1.00656
$63$	−7.93711	−	0.0471049i	−0.999982	−	0.00593466i
$64$	−1.00000			−0.125000
$65$	4.43773	+	2.56213i	0.550433	+	0.317793i
$66$	2.83769	−	4.68967i	0.349296	−	0.577258i
$67$	−2.25755	−	3.91019i	−0.275804	−	0.477706i	0.694534	−	0.719460i	$-0.255611\pi$
$67$	−2.25755	−	3.91019i	−0.275804	−	0.477706i	−0.970338	+	0.241754i	$0.922277\pi$
$68$	3.69727	−	6.40386i	0.448360	−	0.776582i
$69$	1.51749	−	0.835007i	0.182684	−	0.100523i
$70$	0.221429	+	6.29132i	0.0264659	+	0.751956i
$71$		−	4.91507i		−	0.583311i	−0.956523	−	0.291656i	$-0.905794\pi$
$71$		−	4.91507i		−	0.583311i	0.956523	−	0.291656i	$-0.0942061\pi$
$72$	−2.65754	+	1.39194i	−0.313194	+	0.164042i
$73$	7.56919	−	4.37008i	0.885907	−	0.511479i	0.0133056	−	0.999911i	$-0.495765\pi$
$73$	7.56919	−	4.37008i	0.885907	−	0.511479i	0.872602	+	0.488433i	$0.162431\pi$
$74$	2.58759	−	1.49395i	0.300801	−	0.173668i
$75$	1.14532	+	0.0235488i	0.132250	+	0.00271919i
$76$		−	8.47594i		−	0.972258i
$77$	−0.294512	−	8.36776i	−0.0335627	−	0.953595i
$78$	1.79829	+	3.26809i	0.203616	+	0.370038i
$79$	1.40410	−	2.43197i	0.157973	−	0.273618i	−0.776164	−	0.630531i	$-0.782837\pi$
$79$	1.40410	−	2.43197i	0.157973	−	0.273618i	0.934138	+	0.356913i	$0.116171\pi$
$80$	1.18968	+	2.06059i	0.133011	+	0.230381i
$81$	−5.12501	+	7.39826i	−0.569445	+	0.822029i
$82$	−5.00126	−	2.88748i	−0.552297	−	0.318869i
$83$	10.7239			1.17710			0.588548	−	0.808462i	$-0.299700\pi$
$83$	10.7239			1.17710			0.588548	+	0.808462i	$0.299700\pi$
$84$	−2.23301	+	4.00171i	−0.243641	+	0.436622i
$85$	−17.5943			−1.90837
$86$	8.62648	+	4.98050i	0.930217	+	0.537061i
$87$	−11.0109	−	6.66266i	−1.18050	−	0.714312i
$88$	−1.58234	−	2.74069i	−0.168678	−	0.292158i
$89$	5.03800	−	8.72608i	0.534027	−	0.924962i	−0.465182	−	0.885215i	$-0.654011\pi$
$89$	5.03800	−	8.72608i	0.534027	−	0.924962i	0.999210	−	0.0397476i	$-0.0126554\pi$
$90$	6.02985	+	3.82013i	0.635602	+	0.402677i
$91$	5.03172	+	2.67364i	0.527467	+	0.280273i
$92$		−	1.00000i		−	0.104257i
$93$	0.282195	−	13.7248i	0.0292622	−	1.42319i
$94$	−3.34488	+	1.93117i	−0.344998	+	0.199185i
$95$	−17.4655	+	10.0837i	−1.79192	+	1.03457i
$96$	−0.0356051	+	1.73168i	−0.00363393	+	0.176739i
$97$		−	5.10883i		−	0.518723i	−0.965780	−	0.259361i	$-0.916488\pi$
$97$		−	5.10883i		−	0.518723i	0.965780	−	0.259361i	$-0.0835121\pi$
$98$	0.492134	+	6.98268i	0.0497131	+	0.705357i
$99$	−8.01999	−	5.08096i	−0.806039	−	0.510656i
$100$	0.330695	−	0.572780i	0.0330695	−	0.0572780i
$101$	−3.98342	−	6.89948i	−0.396365	−	0.686524i	0.596910	−	0.802309i	$-0.296395\pi$
$101$	−3.98342	−	6.89948i	−0.396365	−	0.686524i	−0.993274	+	0.115785i	$0.963062\pi$
$102$	−10.9578	−	6.63052i	−1.08499	−	0.656519i
$103$	2.46427	+	1.42275i	0.242812	+	0.140187i	0.616468	−	0.787380i	$-0.288563\pi$
$103$	2.46427	+	1.42275i	0.242812	+	0.140187i	−0.373657	+	0.927567i	$0.621896\pi$
$104$	2.15362			0.211180
$105$	10.9025	−	0.159442i	1.06397	−	0.0155600i
$106$	2.19601			0.213295
$107$	−10.6647	−	6.15724i	−1.03099	−	0.595243i	−0.113723	−	0.993513i	$-0.536278\pi$
$107$	−10.6647	−	6.15724i	−1.03099	−	0.595243i	−0.917268	+	0.398270i	$0.869611\pi$
$108$	2.31578	+	4.65158i	0.222836	+	0.447598i
$109$	5.35294	+	9.27157i	0.512719	+	0.888056i	0.999891	+	0.0147496i	$0.00469511\pi$
$109$	5.35294	+	9.27157i	0.512719	+	0.888056i	−0.487172	+	0.873306i	$0.661972\pi$
$110$	−3.76496	+	6.52110i	−0.358975	+	0.621763i
$111$	−2.49491	−	4.53408i	−0.236807	−	0.430356i
$112$	1.40265	+	2.24334i	0.132538	+	0.211976i
$113$		−	5.80529i		−	0.546116i	−0.961998	−	0.273058i	$-0.911965\pi$
$113$		−	5.80529i		−	0.546116i	0.961998	−	0.273058i	$-0.0880351\pi$
$114$	−14.6777	−	0.301787i	−1.37469	−	0.0282650i
$115$	−2.06059	+	1.18968i	−0.192151	+	0.110939i
$116$	−6.43491	+	3.71519i	−0.597466	+	0.344947i
$117$	5.72332	−	2.99771i	0.529121	−	0.277138i
$118$			8.67666i			0.798751i
$119$	−19.5520	+	0.688152i	−1.79233	+	0.0630828i
$120$	3.61066	−	1.98679i	0.329606	−	0.181368i
$121$	−0.492421	+	0.852898i	−0.0447655	+	0.0775362i
$122$	0.272255	+	0.471560i	0.0246488	+	0.0426930i
$123$	−5.17827	+	8.55779i	−0.466909	+	0.771630i
$124$	−6.86384	−	3.96284i	−0.616391	−	0.355874i
$125$	10.3231			0.923331
$126$	6.85019	+	4.00935i	0.610263	+	0.357181i
$127$	13.4437			1.19294			0.596468	−	0.802637i	$-0.296570\pi$
$127$	13.4437			1.19294			0.596468	+	0.802637i	$0.296570\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.93180	−	14.7610i	0.786401	−	1.29963i
$130$	−2.56213	−	4.43773i	−0.224713	−	0.389215i
$131$	−5.20398	+	9.01356i	−0.454674	+	0.787519i	−0.998669	−	0.0515697i	$-0.983578\pi$
$131$	−5.20398	+	9.01356i	−0.454674	+	0.787519i	0.543995	+	0.839088i	$0.316911\pi$
$132$	−4.80235	+	2.64253i	−0.417991	+	0.230002i
$133$	−19.0144	+	11.8888i	−1.64876	+	1.03089i
$134$			4.51510i			0.390045i
$135$	6.82996	−	10.3058i	0.587830	−	0.886980i
$136$	−6.40386	+	3.69727i	−0.549126	+	0.317038i
$137$	8.00856	−	4.62375i	0.684218	−	0.395033i	−0.117225	−	0.993105i	$-0.537400\pi$
$137$	8.00856	−	4.62375i	0.684218	−	0.395033i	0.801442	+	0.598072i	$0.204066\pi$
$138$	−1.73168	−	0.0356051i	−0.147411	−	0.00303091i
$139$			15.4050i			1.30663i	0.757085	+	0.653317i	$0.226623\pi$
$139$			15.4050i			1.30663i	−0.757085	+	0.653317i	$0.773377\pi$
$140$	2.95390	−	5.55916i	0.249650	−	0.469834i
$141$	3.22508	+	5.86104i	0.271601	+	0.493588i
$142$	−2.45753	+	4.25657i	−0.206232	+	0.357204i
$143$	3.40775	+	5.90240i	0.284970	+	0.493583i
$144$	2.99746	+	0.123314i	0.249789	+	0.0102761i
$145$	15.3110	+	8.83981i	1.27151	+	0.734106i
$146$	−8.74015			−0.723340
$147$	12.1093	−	0.603602i	0.998760	−	0.0497843i
$148$	−2.98789			−0.245603
$149$	−0.236480	−	0.136532i	−0.0193732	−	0.0111851i	0.490282	−	0.871564i	$-0.336894\pi$
$149$	−0.236480	−	0.136532i	−0.0193732	−	0.0111851i	−0.509655	+	0.860379i	$0.670227\pi$
$150$	−0.980100	−	0.593053i	−0.0800248	−	0.0484225i
$151$	9.96279	+	17.2561i	0.810760	+	1.40428i	0.912333	+	0.409450i	$0.134279\pi$
$151$	9.96279	+	17.2561i	0.810760	+	1.40428i	−0.101572	+	0.994828i	$0.532387\pi$
$152$	−4.23797	+	7.34038i	−0.343745	+	0.595384i
$153$	−11.8721	+	18.7394i	−0.959804	+	1.51499i
$154$	−3.92882	+	7.39395i	−0.316594	+	0.595821i
$155$			18.8581i			1.51472i
$156$	0.0766799	−	3.72939i	0.00613931	−	0.298590i
$157$	13.3104	−	7.68478i	1.06229	−	0.613312i	0.136223	−	0.990678i	$-0.456504\pi$
$157$	13.3104	−	7.68478i	1.06229	−	0.613312i	0.926064	+	0.377366i	$0.123170\pi$
$158$	−2.43197	+	1.40410i	−0.193477	+	0.111704i
$159$	0.0781892	−	3.80279i	0.00620080	−	0.301581i
$160$		−	2.37937i		−	0.188106i
$161$	−2.24334	+	1.40265i	−0.176800	+	0.110544i
$162$	8.13752	−	3.84458i	0.639344	−	0.302059i
$163$	9.22292	−	15.9746i	0.722395	−	1.25122i	−0.237642	−	0.971353i	$-0.576375\pi$
$163$	9.22292	−	15.9746i	0.722395	−	1.25122i	0.960037	−	0.279872i	$-0.0902921\pi$
$164$	2.88748	+	5.00126i	0.225474	+	0.390533i
$165$	11.1584	+	6.75191i	0.868684	+	0.525635i
$166$	−9.28713	−	5.36193i	−0.720821	−	0.416166i
$167$	−7.53911			−0.583394			−0.291697	−	0.956511i	$-0.594220\pi$
$167$	−7.53911			−0.583394			−0.291697	+	0.956511i	$0.594220\pi$
$168$	3.93470	−	2.34908i	0.303568	−	0.181235i
$169$	8.36192			0.643225
$170$	15.2371	+	8.79716i	1.16863	+	0.674712i
$171$	−1.04520	+	25.4063i	−0.0799285	+	1.94287i
$172$	−4.98050	−	8.62648i	−0.379759	−	0.657763i
$173$	4.26112	−	7.38048i	0.323967	−	0.561127i	−0.657336	−	0.753598i	$-0.728317\pi$
$173$	4.26112	−	7.38048i	0.323967	−	0.561127i	0.981303	+	0.192471i	$0.0616500\pi$
$174$	6.20443	+	11.2755i	0.470357	+	0.854794i
$175$	−1.74879	+	0.0615503i	−0.132196	+	0.00465277i
$176$			3.16467i			0.238546i
$177$	15.0252	+	0.308934i	1.12937	+	0.0232209i
$178$	−8.72608	+	5.03800i	−0.654047	+	0.377614i
$179$	0.0883741	−	0.0510228i	0.00660539	−	0.00381362i	−0.496694	−	0.867926i	$-0.665453\pi$
$179$	0.0883741	−	0.0510228i	0.00660539	−	0.00381362i	0.503299	+	0.864112i	$0.332119\pi$
$180$	−3.31194	−	6.32326i	−0.246857	−	0.471308i
$181$		−	8.37882i		−	0.622793i	−0.950280	−	0.311396i	$-0.899203\pi$
$181$		−	8.37882i		−	0.622793i	0.950280	−	0.311396i	$-0.100797\pi$
$182$	−3.02078	−	4.83130i	−0.223915	−	0.358120i
$183$	0.826287	−	0.454671i	0.0610809	−	0.0336102i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	3.55465	+	6.15683i	0.261343	+	0.452659i
$186$	−7.10678	+	11.7449i	−0.521094	+	0.861179i
$187$	−20.2661	−	11.7007i	−1.48201	−	0.855636i
$188$	3.86233			0.281690
$189$	7.18683	−	11.7196i	0.522765	−	0.852477i
$190$	20.1674			1.46310
$191$	−8.85208	−	5.11075i	−0.640514	−	0.369801i	0.144299	−	0.989534i	$-0.453907\pi$
$191$	−8.85208	−	5.11075i	−0.640514	−	0.369801i	−0.784812	+	0.619733i	$0.787241\pi$
$192$	0.896677	−	1.48188i	0.0647121	−	0.106946i
$193$	−4.57900	−	7.93107i	−0.329604	−	0.570891i	0.652829	−	0.757505i	$-0.273582\pi$
$193$	−4.57900	−	7.93107i	−0.329604	−	0.570891i	−0.982433	+	0.186614i	$0.940249\pi$
$194$	−2.55441	+	4.42437i	−0.183396	+	0.317652i
$195$	−7.77598	+	4.27879i	−0.556849	+	0.306410i
$196$	3.06514	−	6.29324i	0.218938	−	0.449517i
$197$			11.1724i			0.795998i	0.917386	+	0.397999i	$0.130295\pi$
$197$			11.1724i			0.795998i	−0.917386	+	0.397999i	$0.869705\pi$
$198$	4.40503	+	8.41024i	0.313052	+	0.597690i
$199$	−12.7608	+	7.36743i	−0.904586	+	0.522263i	−0.878685	−	0.477401i	$-0.841579\pi$
$199$	−12.7608	+	7.36743i	−0.904586	+	0.522263i	−0.0259010	+	0.999665i	$0.508245\pi$
$200$	−0.572780	+	0.330695i	−0.0405016	+	0.0233836i
$201$	7.81873	+	0.160761i	0.551491	+	0.0113392i
$202$			7.96683i			0.560545i
$203$	17.3604	+	9.22455i	1.21846	+	0.647437i
$204$	6.17450	+	11.2211i	0.432301	+	0.785635i
$205$	6.87037	−	11.8998i	0.479848	−	0.831120i
$206$	−1.42275	−	2.46427i	−0.0991274	−	0.171694i
$207$	−0.123314	+	2.99746i	−0.00857090	+	0.208338i
$208$	−1.86509	−	1.07681i	−0.129321	−	0.0746633i
$209$	−26.8236			−1.85543
$210$	−9.52153	−	5.31315i	−0.657048	−	0.366642i
$211$	−8.68620			−0.597983			−0.298991	−	0.954256i	$-0.596650\pi$
$211$	−8.68620			−0.597983			−0.298991	+	0.954256i	$0.596650\pi$
$212$	−1.90180	−	1.09800i	−0.130616	−	0.0754112i
$213$	7.28354	+	4.40723i	0.499060	+	0.301978i
$214$	6.15724	+	10.6647i	0.420900	+	0.729021i
$215$	−11.8504	+	20.5256i	−0.808193	+	1.39983i
$216$	0.320266	−	5.18627i	0.0217913	−	0.352881i
$217$	0.737581	+	20.9564i	0.0500703	+	1.42261i
$218$		−	10.7059i		−	0.725094i
$219$	−0.311194	+	15.1352i	−0.0210286	+	1.02274i
$220$	6.52110	−	3.76496i	0.439653	−	0.253834i
$221$	13.7915	−	7.96251i	0.927715	−	0.535617i
$222$	−0.106384	+	5.17409i	−0.00714005	+	0.347262i
$223$		−	23.8764i		−	1.59888i	−0.600744	−	0.799442i	$-0.705129\pi$
$223$		−	23.8764i		−	1.59888i	0.600744	−	0.799442i	$-0.294871\pi$
$224$	−0.0930622	−	2.64411i	−0.00621798	−	0.176667i
$225$	−1.06188	+	1.67611i	−0.0707918	+	0.111741i
$226$	−2.90265	+	5.02753i	−0.193081	+	0.334426i
$227$	−2.25177	−	3.90017i	−0.149455	−	0.258864i	0.781571	−	0.623816i	$-0.214419\pi$
$227$	−2.25177	−	3.90017i	−0.149455	−	0.258864i	−0.931026	+	0.364952i	$0.881085\pi$
$228$	12.5603	+	7.60019i	0.831829	+	0.503335i
$229$	11.5357	+	6.66014i	0.762300	+	0.440114i	0.830121	−	0.557583i	$-0.188271\pi$
$229$	11.5357	+	6.66014i	0.762300	+	0.440114i	−0.0678208	+	0.997698i	$0.521605\pi$
$230$	2.37937			0.156891
$231$	12.6641	+	7.06675i	0.833237	+	0.464958i
$232$	7.43039			0.487829
$233$	−1.18764	−	0.685683i	−0.0778048	−	0.0449206i	0.460593	−	0.887612i	$-0.347637\pi$
$233$	−1.18764	−	0.685683i	−0.0778048	−	0.0449206i	−0.538398	+	0.842691i	$0.680970\pi$
$234$	−6.45540	−	0.265571i	−0.422003	−	0.0173609i
$235$	−4.59496	−	7.95870i	−0.299742	−	0.519168i
$236$	4.33833	−	7.51421i	0.282401	−	0.489133i
$237$	2.34487	+	4.26140i	0.152315	+	0.276808i
$238$	17.2766	+	9.18005i	1.11988	+	0.595054i
$239$			7.70669i			0.498504i	0.968439	+	0.249252i	$0.0801848\pi$
$239$			7.70669i			0.498504i	−0.968439	+	0.249252i	$0.919815\pi$
$240$	−4.12031	−	0.0847177i	−0.265965	−	0.00546850i
$241$	23.0099	−	13.2848i	1.48220	−	0.855746i	0.482400	−	0.875951i	$-0.339765\pi$
$241$	23.0099	−	13.2848i	1.48220	−	0.855746i	0.999796	+	0.0202045i	$0.00643172\pi$
$242$	0.852898	−	0.492421i	0.0548264	−	0.0316540i
$243$	−6.36786	−	14.2285i	−0.408498	−	0.912759i
$244$		−	0.544511i		−	0.0348587i
$245$	−16.6144	+	1.17097i	−1.06145	+	0.0748104i
$246$	8.76341	−	4.82213i	0.558735	−	0.307448i
$247$	9.12698	−	15.8084i	0.580736	−	1.00586i
$248$	3.96284	+	6.86384i	0.251641	+	0.435854i
$249$	−9.61584	+	15.8915i	−0.609379	+	1.00708i
$250$	−8.94011	−	5.16157i	−0.565422	−	0.326447i
$251$	−15.6268			−0.986354			−0.493177	−	0.869929i	$-0.664165\pi$
$251$	−15.6268			−0.986354			−0.493177	+	0.869929i	$0.664165\pi$
$252$	−3.92776	−	6.89729i	−0.247426	−	0.434489i
$253$	−3.16467			−0.198961
$254$	−11.6426	−	6.72186i	−0.730521	−	0.421767i
$255$	15.7764	−	26.0727i	0.987959	−	1.63274i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.301189	+	0.521674i	−0.0187876	+	0.0325411i	−0.875266	−	0.483641i	$-0.839314\pi$
$257$	−0.301189	+	0.521674i	−0.0187876	+	0.0325411i	0.856479	+	0.516182i	$0.172647\pi$
$258$	−15.1157	+	8.31751i	−0.941061	+	0.517825i
$259$	4.19097	+	6.70285i	0.260414	+	0.416495i
$260$			5.12425i			0.317793i
$261$	19.7465	−	10.3427i	1.22228	−	0.640194i
$262$	9.01356	−	5.20398i	0.556860	−	0.321503i
$263$	23.1327	−	13.3557i	1.42642	−	0.823545i	0.429586	−	0.903026i	$-0.358659\pi$
$263$	23.1327	−	13.3557i	1.42642	−	0.823545i	0.996836	+	0.0794805i	$0.0253261\pi$
$264$	5.48022	+	0.112679i	0.337284	+	0.00693489i
$265$			5.22511i			0.320976i
$266$	22.4114	−	0.788790i	1.37413	−	0.0483638i
$267$	8.41354	+	15.2902i	0.514900	+	0.935745i
$268$	2.25755	−	3.91019i	0.137902	−	0.238853i
$269$	−3.83960	−	6.65039i	−0.234105	−	0.405481i	0.724907	−	0.688846i	$-0.241883\pi$
$269$	−3.83960	−	6.65039i	−0.234105	−	0.405481i	−0.959012	+	0.283365i	$0.908549\pi$
$270$	−11.0678	+	5.51009i	−0.673566	+	0.335333i
$271$	−11.2087	−	6.47133i	−0.680878	−	0.393105i	0.119308	−	0.992857i	$-0.461932\pi$
$271$	−11.2087	−	6.47133i	−0.680878	−	0.393105i	−0.800186	+	0.599752i	$0.795266\pi$
$272$	7.39454			0.448360
$273$	−8.47384	+	5.05901i	−0.512860	+	0.306185i
$274$	−9.24749			−0.558661
$275$	−1.81266	−	1.04654i	−0.109308	−	0.0631087i
$276$	1.48188	+	0.896677i	0.0891987	+	0.0539736i
$277$	12.4936	+	21.6395i	0.750666	+	1.30019i	0.947500	+	0.319754i	$0.103600\pi$
$277$	12.4936	+	21.6395i	0.750666	+	1.30019i	−0.196835	+	0.980437i	$0.563066\pi$
$278$	7.70249	−	13.3411i	0.461965	−	0.800147i
$279$	20.0854	+	12.7249i	1.20248	+	0.761818i
$280$	−5.33773	+	3.33742i	−0.318990	+	0.199449i
$281$		−	1.18401i		−	0.0706320i	−0.999376	−	0.0353160i	$-0.988756\pi$
$281$		−	1.18401i		−	0.0706320i	0.999376	−	0.0353160i	$-0.0112438\pi$
$282$	0.137519	−	6.68835i	0.00818913	−	0.398285i
$283$	6.50760	−	3.75716i	0.386837	−	0.223340i	−0.293952	−	0.955820i	$-0.594971\pi$
$283$	6.50760	−	3.75716i	0.386837	−	0.223340i	0.680789	+	0.732480i	$0.261637\pi$
$284$	4.25657	−	2.45753i	0.252581	−	0.145828i
$285$	0.718063	−	34.9236i	0.0425344	−	2.06869i
$286$		−	6.81550i		−	0.403009i
$287$	7.16939	−	13.4926i	0.423196	−	0.796444i
$288$	−2.53422	−	1.60553i	−0.149331	−	0.0946065i
$289$	−18.8396	+	32.6312i	−1.10821	+	1.91948i
$290$	−8.83981	−	15.3110i	−0.519092	−	0.899093i
$291$	7.57067	+	4.58097i	0.443801	+	0.268541i
$292$	7.56919	+	4.37008i	0.442954	+	0.255739i
$293$	19.9214			1.16382			0.581911	−	0.813253i	$-0.302305\pi$
$293$	19.9214			1.16382			0.581911	+	0.813253i	$0.302305\pi$
$294$	−10.7888	−	5.53193i	−0.629214	−	0.322628i
$295$	−20.6450			−1.20200
$296$	2.58759	+	1.49395i	0.150401	+	0.0868338i
$297$	14.7207	−	7.32868i	0.854183	−	0.425253i
$298$	0.136532	+	0.236480i	0.00790906	+	0.0136989i
$299$	1.07681	−	1.86509i	0.0622735	−	0.107861i
$300$	0.552265	+	1.00365i	0.0318850	+	0.0579457i
$301$	−12.3662	+	23.2729i	−0.712776	+	1.34143i
$302$		−	19.9256i		−	1.14659i
$303$	13.7960	+	0.283660i	0.792562	+	0.0162959i
$304$	7.34038	−	4.23797i	0.421000	−	0.243064i
$305$	−1.12201	+	0.647796i	−0.0642464	+	0.0370927i
$306$	19.6513	−	10.2928i	1.12339	−	0.588397i
$307$			21.0638i			1.20217i	0.799184	+	0.601086i	$0.205265\pi$
$307$			21.0638i			1.20217i	−0.799184	+	0.601086i	$0.794735\pi$
$308$	7.09944	−	4.43893i	0.404528	−	0.252932i
$309$	−4.31799	+	2.37601i	−0.245642	+	0.135166i
$310$	9.42905	−	16.3316i	0.535534	−	0.927572i
$311$	−6.81985	−	11.8123i	−0.386718	−	0.669815i	0.605288	−	0.796007i	$-0.293058\pi$
$311$	−6.81985	−	11.8123i	−0.386718	−	0.669815i	−0.992006	+	0.126191i	$0.959725\pi$
$312$	−1.93110	+	3.19141i	−0.109327	+	0.180678i
$313$	−15.2224	−	8.78864i	−0.860419	−	0.496763i	0.00373350	−	0.999993i	$-0.498812\pi$
$313$	−15.2224	−	8.78864i	−0.860419	−	0.496763i	−0.864153	+	0.503230i	$0.832145\pi$
$314$	−15.3696			−0.867354
$315$	−9.53972	+	16.2991i	−0.537502	+	0.918351i
$316$	2.80820			0.157973
$317$	23.7882	+	13.7341i	1.33608	+	0.771386i	0.986224	−	0.165417i	$-0.0528971\pi$
$317$	23.7882	+	13.7341i	1.33608	+	0.771386i	0.349856	+	0.936803i	$0.386230\pi$
$318$	−1.96911	+	3.25422i	−0.110422	+	0.182488i
$319$	11.7574	+	20.3644i	0.658287	+	1.14019i
$320$	−1.18968	+	2.06059i	−0.0665053	+	0.115191i
$321$	18.6870	−	10.2827i	1.04301	−	0.573923i
$322$	2.64411	−	0.0930622i	0.147351	−	0.00518616i
$323$			62.6757i			3.48737i
$324$	−8.96959	−	0.739257i	−0.498310	−	0.0410698i
$325$	1.23355	−	0.712190i	0.0684250	−	0.0395052i
$326$	−15.9746	+	9.22292i	−0.884750	+	0.510810i
$327$	−18.5392	−	0.381185i	−1.02522	−	0.0210796i
$328$		−	5.77496i		−	0.318869i
$329$	−5.41751	−	8.66453i	−0.298677	−	0.477691i
$330$	−6.28754	−	11.4265i	−0.346118	−	0.629011i
$331$	−2.12473	+	3.68015i	−0.116786	+	0.202279i	−0.918492	−	0.395439i	$-0.870592\pi$
$331$	−2.12473	+	3.68015i	−0.116786	+	0.202279i	0.801706	+	0.597718i	$0.203926\pi$
$332$	5.36193	+	9.28713i	0.294274	+	0.509698i
$333$	8.95610	+	0.368448i	0.490791	+	0.0201908i
$334$	6.52906	+	3.76955i	0.357254	+	0.206261i
$335$	−10.7431			−0.586958
$336$	−4.58209	+	0.0670104i	−0.249973	+	0.00365572i
$337$	−34.5800			−1.88370			−0.941848	−	0.336040i	$-0.890912\pi$
$337$	−34.5800			−1.88370			−0.941848	+	0.336040i	$0.890912\pi$
$338$	−7.24164	−	4.18096i	−0.393893	−	0.227414i
$339$	8.60275	+	5.20547i	0.467237	+	0.282722i
$340$	−8.79716	−	15.2371i	−0.477093	−	0.826350i
$341$	−12.5411	+	21.7218i	−0.679138	+	1.17630i
$342$	13.6083	−	21.4799i	0.735855	−	1.16150i
$343$	−18.4172	+	1.95108i	−0.994435	+	0.105349i
$344$			9.96100i			0.537061i
$345$	0.0847177	−	4.12031i	0.00456105	−	0.221830i
$346$	−7.38048	+	4.26112i	−0.396777	+	0.229079i
$347$	3.59047	−	2.07296i	0.192746	−	0.111282i	−0.400521	−	0.916287i	$-0.631171\pi$
$347$	3.59047	−	2.07296i	0.192746	−	0.111282i	0.593268	+	0.805005i	$0.297838\pi$
$348$	0.264560	−	12.8671i	0.0141819	−	0.689749i
$349$		−	31.4937i		−	1.68582i	−0.538056	−	0.842909i	$-0.680841\pi$
$349$		−	31.4937i		−	1.68582i	0.538056	−	0.842909i	$-0.319159\pi$
$350$	1.54527	+	0.821090i	0.0825982	+	0.0438891i
$351$	−0.689730	+	11.1693i	−0.0368151	+	0.596171i
$352$	1.58234	−	2.74069i	0.0843388	−	0.146079i
$353$	−16.9764	−	29.4040i	−0.903563	−	1.56502i	−0.822835	−	0.568280i	$-0.807609\pi$
$353$	−16.9764	−	29.4040i	−0.903563	−	1.56502i	−0.0807276	−	0.996736i	$-0.525724\pi$
$354$	−12.8578	−	7.78016i	−0.683383	−	0.413511i
$355$	−10.1280	−	5.84738i	−0.537536	−	0.310347i
$356$	10.0760			0.534027
$357$	16.5121	−	29.5908i	0.873912	−	1.56611i
$358$	−0.102046			−0.00539328
$359$	−14.0407	−	8.10639i	−0.741039	−	0.427839i	0.0814082	−	0.996681i	$-0.474058\pi$
$359$	−14.0407	−	8.10639i	−0.741039	−	0.427839i	−0.822447	+	0.568842i	$0.807392\pi$
$360$	−0.293409	+	7.13207i	−0.0154640	+	0.375893i
$361$	26.4208	+	45.7622i	1.39057	+	2.40854i
$362$	−4.18941	+	7.25627i	−0.220190	+	0.381381i
$363$	−0.822350	−	1.49448i	−0.0431622	−	0.0784400i
$364$	0.200421	+	5.69442i	0.0105049	+	0.298468i
$365$		−	20.7960i		−	1.08851i
$366$	−0.942921	−	0.0193874i	−0.0492873	−	0.00101339i
$367$	8.33538	−	4.81244i	0.435104	−	0.251207i	−0.266415	−	0.963858i	$-0.585839\pi$
$367$	8.33538	−	4.81244i	0.435104	−	0.251207i	0.701518	+	0.712651i	$0.252506\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−8.03839	−	15.3472i	−0.418462	−	0.798941i
$370$		−	7.10929i		−	0.369595i
$371$	0.204365	+	5.80650i	0.0106101	+	0.301458i
$372$	12.0271	−	6.61800i	0.623576	−	0.343127i
$373$	−7.73610	+	13.3993i	−0.400560	+	0.693791i	−0.993794	−	0.111240i	$-0.964518\pi$
$373$	−7.73610	+	13.3993i	−0.400560	+	0.693791i	0.593233	+	0.805031i	$0.297851\pi$
$374$	11.7007	+	20.2661i	0.605026	+	1.04794i
$375$	−9.25653	+	15.2977i	−0.478005	+	0.789968i
$376$	−3.34488	−	1.93117i	−0.172499	−	0.0995923i
$377$	−16.0022			−0.824157
$378$	−12.0838	+	6.55607i	−0.621523	+	0.337208i
$379$	28.2401			1.45060			0.725298	−	0.688435i	$-0.241702\pi$
$379$	28.2401			1.45060			0.725298	+	0.688435i	$0.241702\pi$
$380$	−17.4655	−	10.0837i	−0.895960	−	0.517283i
$381$	−12.0547	+	19.9220i	−0.617580	+	1.02063i
$382$	5.11075	+	8.85208i	0.261489	+	0.452912i
$383$	13.6450	−	23.6339i	0.697229	−	1.20764i	−0.272194	−	0.962242i	$-0.587749\pi$
$383$	13.6450	−	23.6339i	0.697229	−	1.20764i	0.969423	−	0.245394i	$-0.0789175\pi$
$384$	−1.51749	+	0.835007i	−0.0774389	+	0.0426113i
$385$	−17.5929	−	9.34812i	−0.896618	−	0.476424i
$386$			9.15801i			0.466130i
$387$	13.8651	+	26.4717i	0.704803	+	1.34563i
$388$	4.42437	−	2.55441i	0.224614	−	0.129681i
$389$	12.4398	−	7.18213i	0.630724	−	0.364148i	−0.150309	−	0.988639i	$-0.548027\pi$
$389$	12.4398	−	7.18213i	0.630724	−	0.364148i	0.781032	+	0.624491i	$0.214693\pi$
$390$	8.87359	+	0.182450i	0.449332	+	0.00923870i
$391$			7.39454i			0.373958i
$392$	−5.80111	+	3.91754i	−0.293000	+	0.197866i
$393$	−8.69073	−	15.7939i	−0.438389	−	0.796699i
$394$	5.58618	−	9.67556i	0.281428	−	0.487447i
$395$	−3.34087	−	5.78655i	−0.168097	−	0.291153i
$396$	0.390248	−	9.48600i	0.0196107	−	0.476689i
$397$	−7.53542	−	4.35058i	−0.378192	−	0.218349i	0.298839	−	0.954303i	$-0.403401\pi$
$397$	−7.53542	−	4.35058i	−0.378192	−	0.218349i	−0.677031	+	0.735954i	$0.736734\pi$
$398$	14.7349			0.738592
$399$	−0.567977	−	38.8375i	−0.0284344	−	1.94431i
$400$	0.661389			0.0330695
$401$	16.0880	+	9.28840i	0.803396	+	0.463841i	0.844657	−	0.535308i	$-0.179804\pi$
$401$	16.0880	+	9.28840i	0.803396	+	0.463841i	−0.0412616	+	0.999148i	$0.513138\pi$
$402$	−6.69084	−	4.04859i	−0.333709	−	0.201925i
$403$	−8.53445	−	14.7821i	−0.425131	−	0.736349i
$404$	3.98342	−	6.89948i	0.198182	−	0.343262i
$405$	9.14766	+	19.3621i	0.454551	+	0.962113i
$406$	−10.4222	−	16.6689i	−0.517247	−	0.827263i
$407$			9.45570i			0.468702i
$408$	0.263284	−	12.8050i	0.0130345	−	0.633943i
$409$	−21.1380	+	12.2040i	−1.04520	+	0.603449i	−0.921303	−	0.388845i	$-0.872874\pi$
$409$	−21.1380	+	12.2040i	−1.04520	+	0.603449i	−0.123902	+	0.992295i	$0.539541\pi$
$410$	−11.8998	+	6.87037i	−0.587691	+	0.339303i
$411$	−0.329258	+	16.0137i	−0.0162411	+	0.789900i
$412$			2.84549i			0.140187i
$413$	−22.9421	+	0.807469i	−1.12891	+	0.0397330i
$414$	1.60553	−	2.53422i	0.0789073	−	0.124550i
$415$	12.7580	−	22.0975i	0.626265	−	1.08472i
$416$	1.07681	+	1.86509i	0.0527949	+	0.0914435i
$417$	−22.8283	−	13.8133i	−1.11791	−	0.676440i
$418$	23.2299	+	13.4118i	1.13621	+	0.655993i
$419$	−24.2366			−1.18403			−0.592017	−	0.805926i	$-0.701668\pi$
$419$	−24.2366			−1.18403			−0.592017	+	0.805926i	$0.701668\pi$
$420$	5.58931	+	9.36209i	0.272731	+	0.456823i
$421$	10.2721			0.500630			0.250315	−	0.968164i	$-0.419466\pi$
$421$	10.2721			0.500630			0.250315	+	0.968164i	$0.419466\pi$
$422$	7.52247	+	4.34310i	0.366188	+	0.211419i
$423$	−11.5772	−	0.476279i	−0.562903	−	0.0231575i
$424$	1.09800	+	1.90180i	0.0533238	+	0.0923595i
$425$	−2.44533	+	4.23544i	−0.118616	+	0.205449i
$426$	−4.10412	−	7.45855i	−0.198845	−	0.361368i
$427$	−1.22152	+	0.763759i	−0.0591136	+	0.0369609i
$428$		−	12.3145i		−	0.595243i
$429$	−11.8023	−	0.242667i	−0.569820	−	0.0117161i
$430$	20.5256	−	11.8504i	0.989830	−	0.571479i
$431$	−2.01532	+	1.16355i	−0.0970747	+	0.0560461i	−0.547751	−	0.836641i	$-0.684516\pi$
$431$	−2.01532	+	1.16355i	−0.0970747	+	0.0560461i	0.450677	+	0.892687i	$0.351183\pi$
$432$	−2.87049	+	4.33131i	−0.138107	+	0.208390i
$433$			6.88151i			0.330704i	0.986235	+	0.165352i	$0.0528760\pi$
$433$			6.88151i			0.330704i	−0.986235	+	0.165352i	$0.947124\pi$
$434$	9.83944	−	18.5176i	0.472308	−	0.888872i
$435$	−26.8286	+	14.7626i	−1.28633	+	0.707813i
$436$	−5.35294	+	9.27157i	−0.256360	+	0.444028i
$437$	4.23797	+	7.34038i	0.202730	+	0.351138i
$438$	7.83710	−	12.9519i	0.374471	−	0.618864i
$439$	30.2117	+	17.4427i	1.44192	+	0.832496i	0.997978	−	0.0635577i	$-0.0202447\pi$
$439$	30.2117	+	17.4427i	1.44192	+	0.832496i	0.443946	+	0.896053i	$0.353578\pi$
$440$	−7.52992			−0.358975
$441$	−9.96369	+	18.4858i	−0.474461	+	0.880276i
$442$	−15.9250			−0.757476
$443$	−7.48212	−	4.31980i	−0.355486	−	0.205240i	0.311613	−	0.950209i	$-0.399131\pi$
$443$	−7.48212	−	4.31980i	−0.355486	−	0.205240i	−0.667099	+	0.744969i	$0.732464\pi$
$444$	2.67917	−	4.42770i	0.127148	−	0.210129i
$445$	−11.9873	−	20.7625i	−0.568251	−	0.984239i
$446$	−11.9382	+	20.6776i	−0.565291	+	0.979112i
$447$	0.414369	−	0.228010i	0.0195990	−	0.0107845i
$448$	−1.24146	+	2.33640i	−0.0586536	+	0.110385i
$449$			11.9544i			0.564162i	0.959391	+	0.282081i	$0.0910247\pi$
$449$			11.9544i			0.564162i	−0.959391	+	0.282081i	$0.908975\pi$
$450$	1.75767	−	0.920613i	0.0828572	−	0.0433981i
$451$	15.8274	−	9.13793i	0.745281	−	0.430288i
$452$	5.02753	−	2.90265i	0.236475	−	0.136529i
$453$	−34.5048	−	0.709453i	−1.62118	−	0.0333330i
$454$			4.50353i			0.211361i
$455$	11.4954	−	7.18754i	0.538914	−	0.336957i
$456$	−7.07748	−	12.8621i	−0.331433	−	0.602324i
$457$	4.74729	−	8.22255i	0.222069	−	0.384634i	−0.733367	−	0.679833i	$-0.762052\pi$
$457$	4.74729	−	8.22255i	0.222069	−	0.384634i	0.955436	+	0.295198i	$0.0953857\pi$
$458$	−6.66014	−	11.5357i	−0.311208	−	0.539028i
$459$	−17.1241	−	34.3963i	−0.799285	−	1.60548i
$460$	−2.06059	−	1.18968i	−0.0960756	−	0.0554693i
$461$	−11.3596			−0.529072			−0.264536	−	0.964376i	$-0.585219\pi$
$461$	−11.3596			−0.529072			−0.264536	+	0.964376i	$0.585219\pi$
$462$	−7.43406	−	12.4520i	−0.345864	−	0.579321i
$463$	−0.505861			−0.0235094			−0.0117547	−	0.999931i	$-0.503742\pi$
$463$	−0.505861			−0.0235094			−0.0117547	+	0.999931i	$0.503742\pi$
$464$	−6.43491	−	3.71519i	−0.298733	−	0.172474i
$465$	−27.9455	−	16.9096i	−1.29594	−	0.784165i
$466$	0.685683	+	1.18764i	0.0317637	+	0.0550163i
$467$	5.68642	−	9.84917i	0.263136	−	0.455765i	−0.703937	−	0.710262i	$-0.748576\pi$
$467$	5.68642	−	9.84917i	0.263136	−	0.455765i	0.967074	+	0.254497i	$0.0819098\pi$
$468$	5.45775	+	3.45769i	0.252285	+	0.159832i
$469$	−11.9384	+	0.420186i	−0.551266	+	0.0194024i
$470$			9.18991i			0.423899i
$471$	−0.547235	+	26.6152i	−0.0252153	+	1.22636i
$472$	−7.51421	+	4.33833i	−0.345869	+	0.199688i
$473$	−27.3000	+	15.7617i	−1.25525	+	0.724722i
$474$	0.0999862	−	4.86291i	0.00459252	−	0.223361i
$475$			5.60590i			0.257216i
$476$	−10.3720	−	16.5885i	−0.475398	−	0.760331i
$477$	5.56517	+	3.52575i	0.254812	+	0.161433i
$478$	3.85335	−	6.67419i	0.176248	−	0.305270i
$479$	19.5610	+	33.8807i	0.893767	+	1.54805i	0.835324	+	0.549758i	$0.185280\pi$
$479$	19.5610	+	33.8807i	0.893767	+	1.54805i	0.0584429	+	0.998291i	$0.481386\pi$
$480$	3.52594	+	2.13352i	0.160936	+	0.0973816i
$481$	−5.57268	−	3.21739i	−0.254093	−	0.146700i
$482$	−26.5695			−1.21021
$483$	−0.0670104	−	4.58209i	−0.00304908	−	0.208492i
$484$	−0.984842			−0.0447655
$485$	−10.5272	−	6.07789i	−0.478016	−	0.275983i
$486$	−1.59952	+	15.5062i	−0.0725559	+	0.703374i
$487$	−12.9102	−	22.3612i	−0.585018	−	1.01328i	−0.994873	−	0.101130i	$-0.967754\pi$
$487$	−12.9102	−	22.3612i	−0.585018	−	1.01328i	0.409855	−	0.912151i	$-0.365579\pi$
$488$	−0.272255	+	0.471560i	−0.0123244	+	0.0213465i
$489$	15.4024	+	27.9913i	0.696521	+	1.26581i
$490$	14.9739	+	7.29309i	0.676454	+	0.329468i
$491$		−	27.9815i		−	1.26279i	−0.775462	−	0.631394i	$-0.782483\pi$
$491$		−	27.9815i		−	1.26279i	0.775462	−	0.631394i	$-0.217517\pi$
$492$	−10.0004	−	0.205618i	−0.450853	−	0.00926998i
$493$	47.5832	−	27.4722i	2.14304	−	1.23728i
$494$	−15.8084	+	9.12698i	−0.711253	+	0.410642i
$495$	−20.0110	+	10.4812i	−0.899430	+	0.471095i
$496$		−	7.92568i		−	0.355874i
$497$	−11.4836	−	6.10187i	−0.515109	−	0.273706i
$498$	16.2733	−	8.95450i	0.729224	−	0.401261i
$499$	0.270193	−	0.467987i	0.0120955	−	0.0209500i	−0.859914	−	0.510438i	$-0.829483\pi$
$499$	0.270193	−	0.467987i	0.0120955	−	0.0209500i	0.872010	+	0.489488i	$0.162816\pi$
$500$	5.16157	+	8.94011i	0.230833	+	0.399814i
$501$	6.76015	−	11.1721i	0.302021	−	0.499131i
$502$	13.5332	+	7.81340i	0.604016	+	0.348729i
$503$	−19.0928			−0.851304			−0.425652	−	0.904887i	$-0.639955\pi$
$503$	−19.0928			−0.851304			−0.425652	+	0.904887i	$0.639955\pi$
$504$	−0.0471049	+	7.93711i	−0.00209822	+	0.353547i
$505$	−18.9560			−0.843532
$506$	2.74069	+	1.58234i	0.121838	+	0.0703434i
$507$	−7.49795	+	12.3914i	−0.332996	+	0.550320i
$508$	6.72186	+	11.6426i	0.298234	+	0.516557i
$509$	8.43371	−	14.6076i	0.373818	−	0.647471i	−0.616332	−	0.787487i	$-0.711382\pi$
$509$	8.43371	−	14.6076i	0.373818	−	0.647471i	0.990149	+	0.140016i	$0.0447152\pi$
$510$	−26.6991	+	14.6914i	−1.18226	+	0.650546i
$511$	−0.813378	−	23.1100i	−0.0359817	−	1.02232i
$512$			1.00000i			0.0441942i
$513$	−36.7120	−	24.3302i	−1.62087	−	1.07420i
$514$	0.521674	−	0.301189i	0.0230101	−	0.0132849i
$515$	5.86340	−	3.38524i	0.258372	−	0.149171i
$516$	17.2493	+	0.354663i	0.759358	+	0.0156132i
$517$		−	12.2230i		−	0.537568i
$518$	−0.278060	−	7.90033i	−0.0122173	−	0.347120i
$519$	7.11613	+	12.9324i	0.312364	+	0.567668i
$520$	2.56213	−	4.43773i	0.112357	−	0.194607i
$521$	21.7825	+	37.7285i	0.954310	+	1.65291i	0.735939	+	0.677048i	$0.236741\pi$
$521$	21.7825	+	37.7285i	0.954310	+	1.65291i	0.218371	+	0.975866i	$0.429926\pi$
$522$	−22.2723	−	0.916269i	−0.974833	−	0.0401040i
$523$	13.8025	+	7.96886i	0.603540	+	0.348454i	0.770433	−	0.637521i	$-0.220040\pi$
$523$	13.8025	+	7.96886i	0.603540	+	0.348454i	−0.166893	+	0.985975i	$0.553374\pi$
$524$	−10.4080			−0.454674
$525$	1.47689	−	2.64669i	0.0644567	−	0.115511i
$526$	−26.7113			−1.16467
$527$	50.7549	+	29.3034i	2.21092	+	1.27648i
$528$	−4.68967	−	2.83769i	−0.204092	−	0.123495i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	2.61255	−	4.52508i	0.113482	−	0.196557i
$531$	−13.9306	+	21.9886i	−0.604536	+	0.954224i
$532$	−19.8032	−	10.5226i	−0.858578	−	0.456211i
$533$			12.4371i			0.538709i
$534$	0.358758	−	17.4485i	0.0155250	−	0.755069i
$535$	−25.3751	+	14.6503i	−1.09706	+	0.633389i
$536$	−3.91019	+	2.25755i	−0.168895	+	0.0975114i
$537$	−0.00363335	+	0.176711i	−0.000156790	+	0.00762563i
$538$			7.67921i			0.331074i
$539$	−19.9161	−	9.70016i	−0.857846	−	0.417816i
$540$	12.3400	+	0.762030i	0.531031	+	0.0327925i
$541$	1.28371	−	2.22346i	0.0551911	−	0.0955939i	−0.837110	−	0.547035i	$-0.815757\pi$
$541$	1.28371	−	2.22346i	0.0551911	−	0.0955939i	0.892301	+	0.451441i	$0.149090\pi$
$542$	6.47133	+	11.2087i	0.277967	+	0.481453i
$543$	12.4164	+	7.51309i	0.532839	+	0.322418i
$544$	−6.40386	−	3.69727i	−0.274563	−	0.158519i
$545$	25.4732			1.09115
$546$	9.86807	−	0.144315i	0.422314	−	0.00617611i
$547$	22.3183			0.954263			0.477132	−	0.878832i	$-0.341676\pi$
$547$	22.3183			0.954263			0.477132	+	0.878832i	$0.341676\pi$
$548$	8.00856	+	4.62375i	0.342109	+	0.197517i
$549$	−0.0671457	+	1.63215i	−0.00286571	+	0.0696585i
$550$	1.04654	+	1.81266i	0.0446246	+	0.0772921i
$551$	31.4898	−	54.5419i	1.34151	−	2.32356i
$552$	−0.835007	−	1.51749i	−0.0355403	−	0.0645885i
$553$	−3.93892	−	6.29974i	−0.167500	−	0.267892i
$554$		−	24.9871i		−	1.06160i
$555$	−12.3111	−	0.253127i	−0.522575	−	0.0107447i
$556$	−13.3411	+	7.70249i	−0.565789	+	0.326658i
$557$	38.0232	−	21.9527i	1.61110	−	0.930166i	0.621978	−	0.783034i	$-0.286329\pi$
$557$	38.0232	−	21.9527i	1.61110	−	0.930166i	0.989117	−	0.147132i	$-0.0470041\pi$
$558$	−11.0321	−	21.0628i	−0.467025	−	0.891659i
$559$		−	21.4522i		−	0.907331i
$560$	6.29132	−	0.221429i	0.265857	−	0.00935709i
$561$	35.5111	−	19.5403i	1.49928	−	0.824991i
$562$	−0.592004	+	1.02538i	−0.0249722	+	0.0432531i
$563$	20.3426	+	35.2344i	0.857339	+	1.48495i	0.874458	+	0.485101i	$0.161217\pi$
$563$	20.3426	+	35.2344i	0.857339	+	1.48495i	−0.0171193	+	0.999853i	$0.505450\pi$
$564$	−3.46327	+	5.72352i	−0.145830	+	0.241004i
$565$	−11.9623	−	6.90646i	−0.503259	−	0.290557i
$566$	−7.51433			−0.315851
$567$	10.9228	+	21.1587i	0.458714	+	0.888584i
$568$	−4.91507			−0.206232
$569$	1.64947	+	0.952322i	0.0691494	+	0.0399234i	0.534176	−	0.845373i	$-0.320622\pi$
$569$	1.64947	+	0.952322i	0.0691494	+	0.0399234i	−0.465027	+	0.885297i	$0.653955\pi$
$570$	−18.0836	+	29.8857i	−0.757440	+	1.25177i
$571$	9.96302	+	17.2565i	0.416939	+	0.722160i	0.995630	−	0.0933870i	$-0.0297694\pi$
$571$	9.96302	+	17.2565i	0.416939	+	0.722160i	−0.578690	+	0.815547i	$0.696436\pi$
$572$	−3.40775	+	5.90240i	−0.142485	+	0.246792i
$573$	15.5110	−	8.53503i	0.647980	−	0.356556i
$574$	−12.9552	+	8.10025i	−0.540739	+	0.338098i
$575$			0.661389i			0.0275818i
$576$	1.39194	+	2.65754i	0.0579975	+	0.110731i
$577$	33.6543	−	19.4303i	1.40105	−	0.808895i	0.406547	−	0.913630i	$-0.366733\pi$
$577$	33.6543	−	19.4303i	1.40105	−	0.808895i	0.994500	+	0.104735i	$0.0333996\pi$
$578$	32.6312	−	18.8396i	1.35728	−	0.783624i
$579$	15.8588	+	0.326072i	0.659069	+	0.0135511i
$580$			17.6796i			0.734106i
$581$	13.3133	−	25.0552i	0.552327	−	1.03947i
$582$	−4.26591	−	7.75257i	−0.176828	−	0.321354i
$583$	−3.47482	+	6.01857i	−0.143913	+	0.249264i
$584$	−4.37008	−	7.56919i	−0.180835	−	0.313215i
$585$	0.631891	−	15.3598i	0.0261255	−	0.635048i
$586$	−17.2524	−	9.96070i	−0.712692	−	0.411473i
$587$	−38.1409			−1.57425			−0.787123	−	0.616797i	$-0.788430\pi$
$587$	−38.1409			−1.57425			−0.787123	+	0.616797i	$0.788430\pi$
$588$	6.57740	+	10.1852i	0.271247	+	0.420030i
$589$	67.1776			2.76801
$590$	17.8791	+	10.3225i	0.736069	+	0.424970i
$591$	−16.5561	−	10.0180i	−0.681028	−	0.412086i
$592$	−1.49395	−	2.58759i	−0.0614008	−	0.106349i
$593$	−20.2256	+	35.0317i	−0.830565	+	1.43858i	0.0670256	+	0.997751i	$0.478649\pi$
$593$	−20.2256	+	35.0317i	−0.830565	+	1.43858i	−0.897591	+	0.440830i	$0.854684\pi$
$594$	−16.4129	−	1.01354i	−0.673428	−	0.0415859i
$595$	−21.8427	+	41.1074i	−0.895463	+	1.68524i
$596$		−	0.273063i		−	0.0111851i
$597$	0.524637	−	25.5161i	0.0214719	−	1.04431i
$598$	−1.86509	+	1.07681i	−0.0762692	+	0.0440340i
$599$	2.47759	−	1.43043i	0.101231	−	0.0584460i	−0.448530	−	0.893768i	$-0.648052\pi$
$599$	2.47759	−	1.43043i	0.101231	−	0.0584460i	0.549761	+	0.835322i	$0.314719\pi$
$600$	0.0235488	−	1.14532i	0.000961378	−	0.0467574i
$601$		−	22.3918i		−	0.913380i	−0.889626	−	0.456690i	$-0.849035\pi$
$601$		−	22.3918i		−	0.913380i	0.889626	−	0.456690i	$-0.150965\pi$
$602$	22.3459	−	13.9718i	0.910751	−	0.569448i
$603$	−7.24911	+	11.4423i	−0.295207	+	0.465966i
$604$	−9.96279	+	17.2561i	−0.405380	+	0.702139i
$605$	1.17165	+	2.02936i	0.0476344	+	0.0825051i
$606$	−11.8059	−	7.14368i	−0.479582	−	0.290192i
$607$	−22.0852	−	12.7509i	−0.896413	−	0.517544i	−0.0203780	−	0.999792i	$-0.506487\pi$
$607$	−22.0852	−	12.7509i	−0.896413	−	0.517544i	−0.876035	+	0.482248i	$0.839820\pi$
$608$	−8.47594			−0.343745
$609$	−29.2363	+	17.4545i	−1.18472	+	0.707294i
$610$	1.29559			0.0524569
$611$	7.20360	+	4.15900i	0.291426	+	0.168255i
$612$	−22.1649	−	0.911848i	−0.895962	−	0.0368593i
$613$	14.6707	+	25.4104i	0.592545	+	1.02632i	0.993888	+	0.110390i	$0.0352101\pi$
$613$	14.6707	+	25.4104i	0.592545	+	1.02632i	−0.401343	+	0.915928i	$0.631457\pi$
$614$	10.5319	−	18.2418i	0.425032	−	0.736177i
$615$	11.4736	+	20.8514i	0.462661	+	0.840809i
$616$	−8.36776	+	0.294512i	−0.337147	+	0.0118662i
$617$		−	13.9616i		−	0.562074i	−0.959697	−	0.281037i	$-0.909322\pi$
$617$		−	13.9616i		−	0.562074i	0.959697	−	0.281037i	$-0.0906784\pi$
$618$	4.92750	+	0.101314i	0.198213	+	0.00407545i
$619$	−19.9475	+	11.5167i	−0.801757	+	0.462894i	−0.844085	−	0.536209i	$-0.819856\pi$
$619$	−19.9475	+	11.5167i	−0.801757	+	0.462894i	0.0423285	+	0.999104i	$0.486522\pi$
$620$	−16.3316	+	9.42905i	−0.655893	+	0.378680i
$621$	−4.33131	−	2.87049i	−0.173810	−	0.115189i
$622$			13.6397i			0.546902i
$623$	−14.1331	−	22.6039i	−0.566232	−	0.905606i
$624$	3.26809	−	1.79829i	0.130828	−	0.0719891i
$625$	13.9348	−	24.1357i	0.557390	−	0.965428i
$626$	8.78864	+	15.2224i	0.351265	+	0.608408i
$627$	24.0521	−	39.7494i	0.960549	−	1.58744i
$628$	13.3104	+	7.68478i	0.531144	+	0.306656i
$629$	22.0941			0.880949
$630$	16.4112	−	9.34559i	0.653838	−	0.372337i
$631$	−27.1666			−1.08149			−0.540744	−	0.841187i	$-0.681857\pi$
$631$	−27.1666			−1.08149			−0.540744	+	0.841187i	$0.681857\pi$
$632$	−2.43197	−	1.40410i	−0.0967386	−	0.0558520i
$633$	7.78872	−	12.8719i	0.309574	−	0.511613i
$634$	−13.7341	−	23.7882i	−0.545452	−	0.944751i
$635$	15.9938	−	27.7020i	0.634693	−	1.09932i
$636$	3.33241	−	1.83368i	0.132139	−	0.0727103i
$637$	12.4934	−	8.43689i	0.495006	−	0.334282i
$638$		−	23.5148i		−	0.930958i
$639$	−13.0620	+	6.84148i	−0.516724	+	0.270645i
$640$	2.06059	−	1.18968i	0.0814521	−	0.0470264i
$641$	9.92364	−	5.72941i	0.391960	−	0.226298i	−0.291049	−	0.956708i	$-0.594004\pi$
$641$	9.92364	−	5.72941i	0.391960	−	0.226298i	0.683009	+	0.730410i	$0.260671\pi$
$642$	−21.3248	−	0.438459i	−0.841623	−	0.0173046i
$643$		−	7.46184i		−	0.294266i	−0.989117	−	0.147133i	$-0.952995\pi$
$643$		−	7.46184i		−	0.294266i	0.989117	−	0.147133i	$-0.0470045\pi$
$644$	−2.33640	−	1.24146i	−0.0920671	−	0.0489205i
$645$	−19.7904	−	35.9657i	−0.779246	−	1.41615i
$646$	31.3379	−	54.2788i	1.23297	−	2.13557i
$647$	−11.1984	−	19.3962i	−0.440255	−	0.762543i	0.557454	−	0.830208i	$-0.311778\pi$
$647$	−11.1984	−	19.3962i	−0.440255	−	0.762543i	−0.997708	+	0.0676648i	$0.978445\pi$
$648$	7.39826	+	5.12501i	0.290631	+	0.201329i
$649$	−23.7800	−	13.7294i	−0.933447	−	0.538926i
$650$	−1.42438			−0.0558688
$651$	−31.7163	−	17.6981i	−1.24306	−	0.693644i
$652$	18.4458			0.722395
$653$	−32.5247	−	18.7781i	−1.27279	−	0.734846i	−0.297278	−	0.954791i	$-0.596079\pi$
$653$	−32.5247	−	18.7781i	−1.27279	−	0.734846i	−0.975512	+	0.219945i	$0.929412\pi$
$654$	15.8648	+	9.59973i	0.620365	+	0.375379i
$655$	12.3822	+	21.4466i	0.483812	+	0.837987i
$656$	−2.88748	+	5.00126i	−0.112737	+	0.195266i
$657$	−22.1495	−	14.0325i	−0.864134	−	0.547461i
$658$	0.359437	+	10.2125i	0.0140123	+	0.398123i
$659$		−	29.2622i		−	1.13989i	−0.821682	−	0.569947i	$-0.806964\pi$
$659$		−	29.2622i		−	1.13989i	0.821682	−	0.569947i	$-0.193036\pi$
$660$	−0.268104	+	13.0394i	−0.0104359	+	0.507560i
$661$	−27.3483	+	15.7895i	−1.06372	+	0.614142i	−0.926460	−	0.376393i	$-0.877164\pi$
$661$	−27.3483	+	15.7895i	−1.06372	+	0.614142i	−0.137264	+	0.990534i	$0.543831\pi$
$662$	3.68015	−	2.12473i	0.143033	−	0.0825801i
$663$	−0.567013	+	27.5771i	−0.0220209	+	1.07101i
$664$		−	10.7239i		−	0.416166i
$665$	1.87682	+	53.3249i	0.0727800	+	2.06785i
$666$	−7.57199	−	4.79714i	−0.293408	−	0.185885i
$667$	3.71519	−	6.43491i	0.143853	−	0.249161i
$668$	−3.76955	−	6.52906i	−0.145848	−	0.252617i
$669$	35.3820	+	21.4094i	1.36795	+	0.827737i
$670$	9.30379	+	5.37154i	0.359437	+	0.207521i
$671$	−1.72320			−0.0665233
$672$	4.00171	+	2.23301i	0.154369	+	0.0861402i
$673$	11.0049			0.424208			0.212104	−	0.977247i	$-0.431968\pi$
$673$	11.0049			0.424208			0.212104	+	0.977247i	$0.431968\pi$
$674$	29.9472	+	17.2900i	1.15352	+	0.665987i
$675$	−1.53163	−	3.07650i	−0.0589525	−	0.118415i
$676$	4.18096	+	7.24164i	0.160806	+	0.278525i
$677$	−14.6665	+	25.4031i	−0.563679	+	0.976321i	0.433492	+	0.901157i	$0.357281\pi$
$677$	−14.6665	+	25.4031i	−0.563679	+	0.976321i	−0.997171	+	0.0751634i	$0.976052\pi$
$678$	−4.84746	−	8.80944i	−0.186166	−	0.338325i
$679$	−11.9363	−	6.34242i	−0.458072	−	0.243400i
$680$			17.5943i			0.674712i
$681$	7.79870	+	0.160349i	0.298847	+	0.00614458i
$682$	21.7218	−	12.5411i	0.831771	−	0.480223i
$683$	12.2442	−	7.06921i	0.468513	−	0.270496i	−0.247104	−	0.968989i	$-0.579479\pi$
$683$	12.2442	−	7.06921i	0.468513	−	0.270496i	0.715617	+	0.698493i	$0.246146\pi$
$684$	−22.5251	+	11.7980i	−0.861270	+	0.451108i
$685$		−	22.0032i		−	0.840698i
$686$	16.9253	+	7.51891i	0.646211	+	0.287073i
$687$	−20.2133	+	11.1225i	−0.771186	+	0.424351i
$688$	4.98050	−	8.62648i	0.189880	−	0.328881i
$689$	−2.36468	−	4.09575i	−0.0900872	−	0.156036i
$690$	−2.13352	+	3.52594i	−0.0812219	+	0.134230i
$691$	1.53052	+	0.883644i	0.0582236	+	0.0336154i	0.528829	−	0.848728i	$-0.322631\pi$
$691$	1.53052	+	0.883644i	0.0582236	+	0.0336154i	−0.470606	+	0.882344i	$0.655965\pi$
$692$	8.52224			0.323967
$693$	−21.8277	+	12.4301i	−0.829165	+	0.472180i
$694$	−4.14591			−0.157377
$695$	31.7434	+	18.3271i	1.20410	+	0.695185i
$696$	−6.66266	+	11.0109i	−0.252548	+	0.417369i
$697$	−21.3516	−	36.9820i	−0.808748	−	1.40079i
$698$	−15.7468	+	27.2743i	−0.596027	+	1.03235i
$699$	2.08103	−	1.14510i	0.0787117	−	0.0433117i
$700$	−0.927698	−	1.48372i	−0.0350637	−	0.0560793i
$701$			10.6445i			0.402035i	0.979588	+	0.201018i	$0.0644249\pi$
$701$			10.6445i			0.402035i	−0.979588	+	0.201018i	$0.935575\pi$
$702$	6.18195	−	9.32800i	0.233323	−	0.352063i
$703$	21.9323	−	12.6626i	0.827191	−	0.477579i
$704$	−2.74069	+	1.58234i	−0.103294	+	0.0596366i
$705$	15.9140	+	0.327208i	0.599357	+	0.0123234i
$706$			33.9528i			1.27783i
$707$	−21.0652	+	0.741412i	−0.792239	+	0.0278836i
$708$	7.24508	+	13.1667i	0.272287	+	0.494835i
$709$	−16.9546	+	29.3663i	−0.636745	+	1.10287i	0.349398	+	0.936974i	$0.386386\pi$
$709$	−16.9546	+	29.3663i	−0.636745	+	1.10287i	−0.986143	+	0.165900i	$0.946947\pi$
$710$	5.84738	+	10.1280i	0.219448	+	0.380095i
$711$	−8.41747	−	0.346289i	−0.315680	−	0.0129869i
$712$	−8.72608	−	5.03800i	−0.327024	−	0.188807i
$713$	7.92568			0.296819
$714$	−29.0953	+	17.3703i	−1.08886	+	0.650068i
$715$	16.2166			0.606466
$716$	0.0883741	+	0.0510228i	0.00330269	+	0.00190681i
$717$	−11.4204	−	6.91042i	−0.426502	−	0.258074i
$718$	8.10639	+	14.0407i	0.302528	+	0.523993i
$719$	−10.7366	+	18.5963i	−0.400407	+	0.693526i	−0.993775	−	0.111406i	$-0.964465\pi$
$719$	−10.7366	+	18.5963i	−0.400407	+	0.693526i	0.593368	+	0.804931i	$0.297798\pi$
$720$	3.82013	−	6.02985i	0.142368	−	0.224719i
$721$	6.38340	−	3.99123i	0.237730	−	0.148641i
$722$		−	52.8416i		−	1.96656i
$723$	−0.946011	+	46.0100i	−0.0351825	+	1.71113i
$724$	7.25627	−	4.18941i	0.269677	−	0.155698i
$725$	4.25598	−	2.45719i	0.158063	−	0.0912577i
$726$	−0.0350654	+	1.70544i	−0.00130140	+	0.0632946i
$727$		−	31.6065i		−	1.17222i	−0.810231	−	0.586110i	$-0.800659\pi$
$727$		−	31.6065i		−	1.17222i	0.810231	−	0.586110i	$-0.199341\pi$
$728$	2.67364	−	5.03172i	0.0990916	−	0.186488i
$729$	26.7949	+	3.32197i	0.992402	+	0.123036i
$730$	−10.3980	+	18.0099i	−0.384848	+	0.666576i
$731$	36.8285	+	63.7888i	1.36215	+	2.35932i
$732$	0.806900	+	0.488250i	0.0298239	+	0.0180463i
$733$	13.2006	+	7.62135i	0.487574	+	0.281501i	0.723567	−	0.690254i	$-0.242501\pi$
$733$	13.2006	+	7.62135i	0.487574	+	0.281501i	−0.235994	+	0.971755i	$0.575834\pi$
$734$	−9.62487			−0.355261
$735$	13.1625	−	25.6705i	0.485506	−	0.946870i
$736$	−1.00000			−0.0368605
$737$	−12.3745	−	7.14441i	−0.455820	−	0.263168i
$738$	−0.712131	+	17.3102i	−0.0262139	+	0.637198i
$739$	19.6677	+	34.0655i	0.723489	+	1.25312i	0.959593	+	0.281392i	$0.0907960\pi$
$739$	19.6677	+	34.0655i	0.723489	+	1.25312i	−0.236104	+	0.971728i	$0.575871\pi$
$740$	−3.55465	+	6.15683i	−0.130671	+	0.226329i
$741$	15.2422	+	27.7001i	0.559936	+	1.01759i
$742$	2.72626	−	5.13076i	0.100084	−	0.188356i
$743$		−	29.2465i		−	1.07295i	−0.843916	−	0.536475i	$-0.819755\pi$
$743$		−	29.2465i		−	1.07295i	0.843916	−	0.536475i	$-0.180245\pi$
$744$	−13.7248	−	0.282195i	−0.503175	−	0.0103458i
$745$	−0.562672	+	0.324859i	−0.0206147	+	0.0119019i
$746$	13.3993	−	7.73610i	0.490584	−	0.283239i
$747$	−14.9270	−	28.4990i	−0.546149	−	1.04273i
$748$		−	23.4013i		−	0.855636i
$749$	−27.6256	+	17.2729i	−1.00942	+	0.631139i
$750$	15.6652	−	8.61991i	0.572013	−	0.314754i
$751$	12.0682	−	20.9028i	0.440376	−	0.762753i	−0.557341	−	0.830283i	$-0.688179\pi$
$751$	12.0682	−	20.9028i	0.440376	−	0.762753i	0.997717	+	0.0675302i	$0.0215119\pi$
$752$	1.93117	+	3.34488i	0.0704224	+	0.121975i
$753$	14.0122	−	23.1570i	0.510633	−	0.843889i
$754$	13.8583	+	8.00111i	0.504691	+	0.291383i
$755$	47.4103			1.72544
$756$	13.7429	+	0.364173i	0.499825	+	0.0132448i
$757$	−20.7025			−0.752447			−0.376223	−	0.926529i	$-0.622777\pi$
$757$	−20.7025			−0.752447			−0.376223	+	0.926529i	$0.622777\pi$
$758$	−24.4566	−	14.1200i	−0.888305	−	0.512863i
$759$	2.83769	−	4.68967i	0.103002	−	0.170224i
$760$	10.0837	+	17.4655i	0.365774	+	0.633539i
$761$	−3.82228	+	6.62038i	−0.138558	+	0.239989i	−0.926951	−	0.375183i	$-0.877580\pi$
$761$	−3.82228	+	6.62038i	−0.138558	+	0.239989i	0.788393	+	0.615172i	$0.210913\pi$
$762$	20.4006	−	11.2256i	0.739037	−	0.406661i
$763$	28.3076	−	0.996314i	1.02480	−	0.0360690i
$764$		−	10.2215i		−	0.369801i
$765$	24.4902	+	46.7576i	0.885446	+	1.69052i
$766$	−23.6339	+	13.6450i	−0.853928	+	0.493016i
$767$	16.1827	−	9.34311i	0.584325	−	0.337360i
$768$	1.73168	+	0.0356051i	0.0624868	+	0.00128479i
$769$			22.7337i			0.819797i	0.912131	+	0.409898i	$0.134436\pi$
$769$			22.7337i			0.819797i	−0.912131	+	0.409898i	$0.865564\pi$
$770$	10.5619	+	16.8922i	0.380623	+	0.608751i
$771$	−0.502989	−	0.914099i	−0.0181147	−	0.0329205i
$772$	4.57900	−	7.93107i	0.164802	−	0.285445i
$773$	22.5941	+	39.1341i	0.812653	+	1.40756i	0.911001	+	0.412404i	$0.135311\pi$
$773$	22.5941	+	39.1341i	0.812653	+	1.40756i	−0.0983479	+	0.995152i	$0.531356\pi$
$774$	1.22833	−	29.8577i	0.0441513	−	1.07321i
$775$	4.53967	+	2.62098i	0.163070	+	0.0941483i
$776$	−5.10883			−0.183396
$777$	−13.6908	+	0.200220i	−0.491154	+	0.00718285i
$778$	−14.3643			−0.514984
$779$	−42.3904	−	24.4741i	−1.51879	−	0.876876i
$780$	−7.59353	−	4.59480i	−0.271892	−	0.164520i
$781$	−7.77729	−	13.4707i	−0.278293	−	0.482018i
$782$	3.69727	−	6.40386i	0.132214	−	0.229002i
$783$	−2.37970	+	38.5360i	−0.0850435	+	1.37717i
$784$	6.98268	−	0.492134i	0.249381	−	0.0175762i
$785$		−	36.5698i		−	1.30523i
$786$	−0.370577	+	18.0233i	−0.0132180	+	0.642870i
$787$	27.4744	−	15.8624i	0.979358	−	0.565433i	0.0772819	−	0.997009i	$-0.475376\pi$
$787$	27.4744	−	15.8624i	0.979358	−	0.565433i	0.902076	+	0.431577i	$0.142043\pi$
$788$	−9.67556	+	5.58618i	−0.344677	+	0.199000i
$789$	−0.951060	+	46.2556i	−0.0338586	+	1.64674i
$790$			6.68173i			0.237725i
$791$	−13.5635	−	7.20705i	−0.482262	−	0.256253i
$792$	−5.08096	+	8.01999i	−0.180544	+	0.284978i
$793$	0.586334	−	1.01556i	0.0208213	−	0.0360636i
$794$	4.35058	+	7.53542i	0.154396	+	0.267422i
$795$	−7.74299	−	4.68524i	−0.274615	−	0.166168i
$796$	−12.7608	−	7.36743i	−0.452293	−	0.261132i
$797$	18.6150			0.659376			0.329688	−	0.944090i	$-0.393056\pi$
$797$	18.6150			0.659376			0.329688	+	0.944090i	$0.393056\pi$
$798$	−18.9269	+	33.9183i	−0.670004	+	1.20069i
$799$	−28.5602			−1.01039
$800$	−0.572780	−	0.330695i	−0.0202508	−	0.0116918i
$801$	−30.2025	−	1.24251i	−1.06715	−	0.0439019i
$802$	−9.28840	−	16.0880i	−0.327985	−	0.568086i
$803$	13.8299	−	23.9540i	0.488045	−	0.845319i
$804$	3.77014	+	6.85160i	0.132963	+	0.241637i
$805$	0.221429	+	6.29132i	0.00780436	+	0.221740i
$806$			17.0689i			0.601226i
$807$	13.2980	+	0.273419i	0.468111	+	0.00962481i
$808$	−6.89948	+	3.98342i	−0.242723	+	0.140136i
$809$	15.0322	−	8.67884i	0.528503	−	0.305132i	−0.211903	−	0.977291i	$-0.567966\pi$
$809$	15.0322	−	8.67884i	0.528503	−	0.305132i	0.740407	+	0.672159i	$0.234633\pi$
$810$	1.75896	−	21.3419i	0.0618037	−	0.749879i
$811$			29.8532i			1.04829i	0.851629	+	0.524144i	$0.175615\pi$
$811$			29.8532i			1.04829i	−0.851629	+	0.524144i	$0.824385\pi$
$812$	0.691489	+	19.6468i	0.0242665	+	0.689467i
$813$	19.6403	−	10.8072i	0.688815	−	0.379025i
$814$	4.72785	−	8.18888i	0.165711	−	0.287020i
$815$	−21.9447	−	38.0094i	−0.768690	−	1.33141i
$816$	−6.63052	+	10.9578i	−0.232114	+	0.383601i
$817$	73.1175	+	42.2144i	2.55806	+	1.47690i
$818$	24.4080			0.853406
$819$	0.101446	−	17.0935i	0.00354481	−	0.597296i
$820$	13.7407			0.479848
$821$	−1.16651	−	0.673485i	−0.0407115	−	0.0235048i	0.479506	−	0.877539i	$-0.340816\pi$
$821$	−1.16651	−	0.673485i	−0.0407115	−	0.0235048i	−0.520218	+	0.854034i	$0.674149\pi$
$822$	8.29202	−	13.7037i	0.289217	−	0.477971i
$823$	8.69889	+	15.0669i	0.303224	+	0.525200i	0.976864	−	0.213860i	$-0.0686036\pi$
$823$	8.69889	+	15.0669i	0.303224	+	0.525200i	−0.673640	+	0.739059i	$0.735270\pi$
$824$	1.42275	−	2.46427i	0.0495637	−	0.0858469i
$825$	3.17622	−	1.74774i	0.110582	−	0.0608484i
$826$	20.2722	+	10.7717i	0.705359	+	0.374797i
$827$		−	24.6989i		−	0.858864i	−0.903099	−	0.429432i	$-0.858714\pi$
$827$		−	24.6989i		−	0.858864i	0.903099	−	0.429432i	$-0.141286\pi$
$828$	−2.65754	+	1.39194i	−0.0923558	+	0.0483732i
$829$	8.27090	−	4.77521i	0.287260	−	0.165850i	−0.349445	−	0.936957i	$-0.613630\pi$
$829$	8.27090	−	4.77521i	0.287260	−	0.165850i	0.636706	+	0.771107i	$0.280297\pi$
$830$	−22.0975	+	12.7580i	−0.767015	+	0.442836i
$831$	−43.2698	−	0.889670i	−1.50101	−	0.0308623i
$832$		−	2.15362i		−	0.0746633i
$833$	−22.6653	+	46.5356i	−0.785306	+	1.61236i
$834$	12.8633	+	23.3768i	0.445419	+	0.809474i
$835$	−8.96915	+	15.5350i	−0.310390	+	0.537612i
$836$	−13.4118	−	23.2299i	−0.463857	−	0.803423i
$837$	−36.8669	+	18.3541i	−1.27431	+	0.634411i
$838$	20.9895	+	12.1183i	0.725070	+	0.418619i
$839$	−40.5579			−1.40021			−0.700107	−	0.714038i	$-0.746865\pi$
$839$	−40.5579			−1.40021			−0.700107	+	0.714038i	$0.746865\pi$
$840$	−0.159442	−	10.9025i	−0.00550129	−	0.376171i
$841$	−26.2107			−0.903817
$842$	−8.89588	−	5.13604i	−0.306572	−	0.177000i
$843$	1.75456	+	1.06167i	0.0604302	+	0.0365659i
$844$	−4.34310	−	7.52247i	−0.149496	−	0.258934i
$845$	9.94804	−	17.2305i	0.342223	−	0.592748i
$846$	9.78802	+	6.20108i	0.336519	+	0.213197i
$847$	1.38139	+	2.20933i	0.0474651	+	0.0759136i
$848$		−	2.19601i		−	0.0754112i
$849$	−0.267549	+	13.0124i	−0.00918225	+	0.446586i
$850$	4.23544	−	2.44533i	0.145274	−	0.0838743i
$851$	2.58759	−	1.49395i	0.0887014	−	0.0512118i
$852$	−0.175002	+	8.51135i	−0.00599546	+	0.291594i
$853$		−	14.4898i		−	0.496121i	−0.968745	−	0.248061i	$-0.920207\pi$
$853$		−	14.4898i		−	0.496121i	0.968745	−	0.248061i	$-0.0797932\pi$
$854$	1.43975	−	0.0506734i	0.0492672	−	0.00173401i
$855$	51.1087	+	32.3792i	1.74788	+	1.10735i
$856$	−6.15724	+	10.6647i	−0.210450	+	0.364510i
$857$	0.0328422	+	0.0568844i	0.00112187	+	0.00194314i	0.866586	−	0.499028i	$-0.166310\pi$
$857$	0.0328422	+	0.0568844i	0.00112187	+	0.00194314i	−0.865464	+	0.500971i	$0.832976\pi$
$858$	10.0998	+	6.11131i	0.344800	+	0.208637i
$859$	42.4179	+	24.4900i	1.44728	+	0.835588i	0.998319	−	0.0579625i	$-0.0184604\pi$
$859$	42.4179	+	24.4900i	1.44728	+	0.835588i	0.448962	+	0.893551i	$0.351794\pi$
$860$	−23.7009			−0.808193
$861$	13.5658	+	22.7227i	0.462322	+	0.774388i
$862$	2.32710			0.0792612
$863$	13.9144	+	8.03349i	0.473652	+	0.273463i	0.717767	−	0.696283i	$-0.245164\pi$
$863$	13.9144	+	8.03349i	0.473652	+	0.273463i	−0.244115	+	0.969746i	$0.578498\pi$
$864$	4.65158	−	2.31578i	0.158250	−	0.0787844i
$865$	−10.1388	−	17.5609i	−0.344728	−	0.597087i
$866$	3.44075	−	5.95956i	0.116922	−	0.202514i
$867$	−31.4624	−	57.1777i	−1.06852	−	1.94186i
$868$	−17.7800	+	11.1170i	−0.603492	+	0.377334i
$869$		−	8.88703i		−	0.301472i
$870$	30.6155	+	0.629485i	1.03796	+	0.0213416i
$871$	8.42107	−	4.86191i	0.285337	−	0.164739i
$872$	9.27157	−	5.35294i	0.313975	−	0.181274i
$873$	−13.5769	+	7.11118i	−0.459508	+	0.240677i
$874$		−	8.47594i		−	0.286703i
$875$	12.8158	−	24.1190i	0.433253	−	0.815372i
$876$	−13.2631	+	7.29809i	−0.448117	+	0.246580i
$877$	3.06011	−	5.30026i	0.103332	−	0.178977i	−0.809723	−	0.586812i	$-0.800383\pi$
$877$	3.06011	−	5.30026i	0.103332	−	0.178977i	0.913056	+	0.407835i	$0.133716\pi$
$878$	−17.4427	−	30.2117i	−0.588663	−	1.01959i
$879$	−17.8631	+	29.5211i	−0.602507	+	0.995723i
$880$	6.52110	+	3.76496i	0.219826	+	0.126917i
$881$	38.0396			1.28159			0.640794	−	0.767713i	$-0.278605\pi$
$881$	38.0396			1.28159			0.640794	+	0.767713i	$0.278605\pi$
$882$	17.8717	−	11.0273i	0.601772	−	0.371310i
$883$	7.96245			0.267958			0.133979	−	0.990984i	$-0.457225\pi$
$883$	7.96245			0.267958			0.133979	+	0.990984i	$0.457225\pi$
$884$	13.7915	+	7.96251i	0.463858	+	0.267808i
$885$	18.5119	−	30.5934i	0.622270	−	1.02838i
$886$	4.31980	+	7.48212i	0.145127	+	0.251367i
$887$	6.78687	−	11.7552i	0.227881	−	0.394701i	−0.729299	−	0.684195i	$-0.760154\pi$
$887$	6.78687	−	11.7552i	0.227881	−	0.394701i	0.957180	+	0.289494i	$0.0934871\pi$
$888$	−4.53408	+	2.49491i	−0.152154	+	0.0837238i
$889$	16.6899	−	31.4099i	0.559760	−	1.05345i
$890$			23.9745i			0.803628i
$891$	−2.33951	+	28.3858i	−0.0783765	+	0.950961i
$892$	20.6776	−	11.9382i	0.692337	−	0.399721i
$893$	−28.3510	+	16.3685i	−0.948731	+	0.547750i
$894$	−0.472859	−	0.00972245i	−0.0158148	−	0.000325167i
$895$		−	0.242804i		−	0.00811604i
$896$	2.24334	−	1.40265i	0.0749447	−	0.0468593i
$897$	1.79829	+	3.26809i	0.0600431	+	0.109118i
$898$	5.97719	−	10.3528i	0.199462	−	0.345477i
$899$	−29.4454	−	51.0010i	−0.982060	−	1.70098i
$900$	−1.98249	−	0.0815584i	−0.0660830	−	0.00271861i
$901$	14.0629	+	8.11923i	0.468504	+	0.270491i
$902$	−18.2759			−0.608519
$903$	−23.3991	−	39.1935i	−0.778675	−	1.30428i
$904$	−5.80529			−0.193081
$905$	−17.2653	−	9.96814i	−0.573919	−	0.331352i
$906$	29.5273	+	17.8668i	0.980980	+	0.593585i
$907$	−6.67107	−	11.5546i	−0.221509	−	0.383665i	0.733757	−	0.679412i	$-0.237765\pi$
$907$	−6.67107	−	11.5546i	−0.221509	−	0.383665i	−0.955266	+	0.295746i	$0.904432\pi$
$908$	2.25177	−	3.90017i	0.0747275	−	0.129432i
$909$	−12.7910	+	20.1897i	−0.424249	+	0.669651i
$910$	−13.5491	+	0.476874i	−0.449148	+	0.0158082i
$911$			4.73653i			0.156928i	0.996917	+	0.0784641i	$0.0250016\pi$
$911$			4.73653i			0.156928i	−0.996917	+	0.0784641i	$0.974998\pi$
$912$	−0.301787	+	14.6777i	−0.00999317	+	0.486026i
$913$	29.3907	−	16.9687i	0.972691	−	0.561584i
$914$	−8.22255	+	4.74729i	−0.271978	+	0.157026i
$915$	0.0461297	−	2.24356i	0.00152500	−	0.0741697i
$916$			13.3203i			0.440114i
$917$	14.5987	+	23.3486i	0.482093	+	0.771038i
$918$	−2.36822	+	38.3501i	−0.0781628	+	1.26574i
$919$	−17.1010	+	29.6198i	−0.564110	+	0.977066i	0.433022	+	0.901383i	$0.357447\pi$
$919$	−17.1010	+	29.6198i	−0.564110	+	0.977066i	−0.997132	+	0.0756832i	$0.975886\pi$
$920$	1.18968	+	2.06059i	0.0392227	+	0.0679357i
$921$	−31.2140	−	18.8874i	−1.02854	−	0.622361i
$922$	9.83775	+	5.67982i	0.323989	+	0.187055i
$923$	10.5852			0.348416
$924$	0.212066	+	14.5008i	0.00697646	+	0.477041i
$925$	1.97616			0.0649757
$926$	0.438089	+	0.252931i	0.0143965	+	0.00831182i
$927$	0.350888	−	8.52926i	0.0115247	−	0.280138i
$928$	3.71519	+	6.43491i	0.121957	+	0.211236i
$929$	−3.46644	+	6.00405i	−0.113730	+	0.196986i	−0.917271	−	0.398263i	$-0.869613\pi$
$929$	−3.46644	+	6.00405i	−0.113730	+	0.196986i	0.803541	+	0.595249i	$0.202947\pi$
$930$	15.7467	+	28.6169i	0.516353	+	0.938385i
$931$	4.17130	+	59.1848i	0.136709	+	1.93970i
$932$		−	1.37137i		−	0.0449206i
$933$	23.6197	+	0.485643i	0.773273	+	0.0158992i
$934$	−9.84917	+	5.68642i	−0.322275	+	0.186065i
$935$	−48.2206	+	27.8401i	−1.57698	+	0.910470i
$936$	−2.99771	−	5.72332i	−0.0979831	−	0.187073i
$937$			21.1264i			0.690171i	0.938571	+	0.345085i	$0.112150\pi$
$937$			21.1264i			0.690171i	−0.938571	+	0.345085i	$0.887850\pi$
$938$	10.5491	+	5.60533i	0.344440	+	0.183021i
$939$	26.6733	−	14.6772i	0.870449	−	0.478971i
$940$	4.59496	−	7.95870i	0.149871	−	0.259584i
$941$	−3.47711	−	6.02253i	−0.113351	−	0.196329i	0.803769	−	0.594942i	$-0.202825\pi$
$941$	−3.47711	−	6.02253i	−0.113351	−	0.196329i	−0.917119	+	0.398613i	$0.869492\pi$
$942$	13.7815	−	22.7758i	0.449027	−	0.742077i
$943$	−5.00126	−	2.88748i	−0.162863	−	0.0940292i
$944$	8.67666			0.282401
$945$	−15.5993	−	28.7518i	−0.507445	−	0.935295i
$946$	31.5233			1.02491
$947$	2.71172	+	1.56561i	0.0881192	+	0.0508756i	0.543412	−	0.839466i	$-0.317132\pi$
$947$	2.71172	+	1.56561i	0.0881192	+	0.0508756i	−0.455293	+	0.890342i	$0.650465\pi$
$948$	−2.51805	+	4.16141i	−0.0817824	+	0.135156i
$949$	9.41148	+	16.3012i	0.305510	+	0.529158i
$950$	2.80295	−	4.85485i	0.0909397	−	0.157512i
$951$	−41.6827	+	22.9362i	−1.35165	+	0.743758i
$952$	0.688152	+	19.5520i	0.0223031	+	0.633684i
$953$			26.7066i			0.865112i	0.901607	+	0.432556i	$0.142388\pi$
$953$			26.7066i			0.865112i	−0.901607	+	0.432556i	$0.857612\pi$
$954$	−3.05671	−	5.83597i	−0.0989646	−	0.188947i
$955$	−21.0623	+	12.1603i	−0.681561	+	0.393500i
$956$	−6.67419	+	3.85335i	−0.215859	+	0.124626i
$957$	−40.7201	−	0.837246i	−1.31630	−	0.0270643i
$958$		−	39.1221i		−	1.26398i
$959$	−0.860592	−	24.4514i	−0.0277900	−	0.789578i
$960$	−1.98679	−	3.61066i	−0.0641234	−	0.116533i
$961$	15.9082	−	27.5538i	0.513168	−	0.888832i
$962$	3.21739	+	5.57268i	0.103733	+	0.179671i
$963$	−1.51854	+	36.9122i	−0.0489344	+	1.18948i
$964$	23.0099	+	13.2848i	0.741098	+	0.427873i
$965$	−21.7903			−0.701454
$966$	−2.23301	+	4.00171i	−0.0718459	+	0.128753i
$967$	24.6866			0.793869			0.396934	−	0.917847i	$-0.370074\pi$
$967$	24.6866			0.793869			0.396934	+	0.917847i	$0.370074\pi$
$968$	0.852898	+	0.492421i	0.0274132	+	0.0158270i
$969$	−92.8779	−	56.1999i	−2.98367	−	1.80540i
$970$	6.07789	+	10.5272i	0.195149	+	0.338008i
$971$	−3.44209	+	5.96188i	−0.110462	+	0.191326i	−0.915957	−	0.401277i	$-0.868566\pi$
$971$	−3.44209	+	5.96188i	−0.110462	+	0.191326i	0.805495	+	0.592603i	$0.201900\pi$
$972$	9.13832	−	12.6290i	0.293112	−	0.405075i
$973$	35.9922	+	19.1247i	1.15386	+	0.613110i
$974$			25.8205i			0.827341i
$975$	−0.0507153	+	2.46658i	−0.00162419	+	0.0789937i
$976$	0.471560	−	0.272255i	0.0150943	−	0.00871468i
$977$	−16.4048	+	9.47129i	−0.524835	+	0.303013i	−0.738911	−	0.673804i	$-0.764659\pi$
$977$	−16.4048	+	9.47129i	−0.524835	+	0.303013i	0.214076	+	0.976817i	$0.431326\pi$
$978$	0.656767	−	31.9424i	0.0210011	−	1.02141i
$979$		−	31.8873i		−	1.01912i
$980$	−9.32127	−	13.8030i	−0.297757	−	0.440920i
$981$	17.1886	−	27.1311i	0.548789	−	0.866230i
$982$	−13.9908	+	24.2327i	−0.446463	+	0.773296i
$983$	24.9900	+	43.2840i	0.797059	+	1.38055i	0.921524	+	0.388322i	$0.126945\pi$
$983$	24.9900	+	43.2840i	0.797059	+	1.38055i	−0.124465	+	0.992224i	$0.539721\pi$
$984$	8.55779	+	5.17827i	0.272813	+	0.165077i
$985$	23.0217	+	13.2916i	0.733532	+	0.423505i
$986$	−54.9443			−1.74978
$987$	17.6975	−	0.258817i	0.563319	−	0.00823822i
$988$	18.2540			0.580736
$989$	8.62648	+	4.98050i	0.274306	+	0.158371i
$990$	22.5707	+	0.928543i	0.717343	+	0.0295110i
$991$	−5.57437	−	9.65510i	−0.177076	−	0.306704i	0.763802	−	0.645451i	$-0.223330\pi$
$991$	−5.57437	−	9.65510i	−0.177076	−	0.306704i	−0.940878	+	0.338746i	$0.889997\pi$
$992$	−3.96284	+	6.86384i	−0.125820	+	0.217927i
$993$	−3.54834	−	6.44850i	−0.112603	−	0.204637i
$994$	6.89413	+	11.0262i	0.218668	+	0.349729i
$995$			35.0596i			1.11147i
$996$	−18.5703	−	0.381824i	−0.588424	−	0.0120986i
$997$	3.89342	−	2.24787i	0.123306	−	0.0711907i	−0.437078	−	0.899423i	$-0.643987\pi$
$997$	3.89342	−	2.24787i	0.123306	−	0.0711907i	0.560384	+	0.828233i	$0.310653\pi$
$998$	−0.467987	+	0.270193i	−0.0148139	+	0.00855280i
$999$	−8.57673	+	12.9415i	−0.271356	+	0.409451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.5	✓	56
3.2	odd	2	inner	966.2.l.d.47.15	yes	56
7.3	odd	6	inner	966.2.l.d.185.15	yes	56
21.17	even	6	inner	966.2.l.d.185.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.5	✓	56	1.1	even	1	trivial
966.2.l.d.47.15	yes	56	3.2	odd	2	inner
966.2.l.d.185.5	yes	56	21.17	even	6	inner
966.2.l.d.185.15	yes	56	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.896677 + 1.48188i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.18968 - 2.06059i) q^{5} +(1.51749 - 0.835007i) q^{6} +(1.24146 - 2.33640i) q^{7} -1.00000i q^{8} +(-1.39194 - 2.65754i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.896677 + 1.48188i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.18968 - 2.06059i) q^{5} +(1.51749 - 0.835007i) q^{6} +(1.24146 - 2.33640i) q^{7} -1.00000i q^{8} +(-1.39194 - 2.65754i) q^{9} +(-2.06059 + 1.18968i) q^{10} +(2.74069 - 1.58234i) q^{11} +(-1.73168 - 0.0356051i) q^{12} +2.15362i q^{13} +(-2.24334 + 1.40265i) q^{14} +(1.98679 + 3.61066i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.69727 - 6.40386i) q^{17} +(-0.123314 + 2.99746i) q^{18} +(-7.34038 - 4.23797i) q^{19} +2.37937 q^{20} +(2.34908 + 3.93470i) q^{21} -3.16467 q^{22} +(-0.866025 - 0.500000i) q^{23} +(1.48188 + 0.896677i) q^{24} +(-0.330695 - 0.572780i) q^{25} +(1.07681 - 1.86509i) q^{26} +(5.18627 + 0.320266i) q^{27} +(2.64411 - 0.0930622i) q^{28} +7.43039i q^{29} +(0.0847177 - 4.12031i) q^{30} +(-6.86384 + 3.96284i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.112679 + 5.48022i) q^{33} +7.39454i q^{34} +(-3.33742 - 5.33773i) q^{35} +(1.60553 - 2.53422i) q^{36} +(-1.49395 + 2.58759i) q^{37} +(4.23797 + 7.34038i) q^{38} +(-3.19141 - 1.93110i) q^{39} +(-2.06059 - 1.18968i) q^{40} +5.77496 q^{41} +(-0.0670104 - 4.58209i) q^{42} -9.96100 q^{43} +(2.74069 + 1.58234i) q^{44} +(-7.13207 - 0.293409i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.93117 - 3.34488i) q^{47} +(-0.835007 - 1.51749i) q^{48} +(-3.91754 - 5.80111i) q^{49} +0.661389i q^{50} +(12.8050 + 0.263284i) q^{51} +(-1.86509 + 1.07681i) q^{52} +(-1.90180 + 1.09800i) q^{53} +(-4.33131 - 2.87049i) q^{54} -7.52992i q^{55} +(-2.33640 - 1.24146i) q^{56} +(12.8621 - 7.07748i) q^{57} +(3.71519 - 6.43491i) q^{58} +(-4.33833 - 7.51421i) q^{59} +(-2.13352 + 3.52594i) q^{60} +(-0.471560 - 0.272255i) q^{61} +7.92568 q^{62} +(-7.93711 - 0.0471049i) q^{63} -1.00000 q^{64} +(4.43773 + 2.56213i) q^{65} +(2.83769 - 4.68967i) q^{66} +(-2.25755 - 3.91019i) q^{67} +(3.69727 - 6.40386i) q^{68} +(1.51749 - 0.835007i) q^{69} +(0.221429 + 6.29132i) q^{70} -4.91507i q^{71} +(-2.65754 + 1.39194i) q^{72} +(7.56919 - 4.37008i) q^{73} +(2.58759 - 1.49395i) q^{74} +(1.14532 + 0.0235488i) q^{75} -8.47594i q^{76} +(-0.294512 - 8.36776i) q^{77} +(1.79829 + 3.26809i) q^{78} +(1.40410 - 2.43197i) q^{79} +(1.18968 + 2.06059i) q^{80} +(-5.12501 + 7.39826i) q^{81} +(-5.00126 - 2.88748i) q^{82} +10.7239 q^{83} +(-2.23301 + 4.00171i) q^{84} -17.5943 q^{85} +(8.62648 + 4.98050i) q^{86} +(-11.0109 - 6.66266i) q^{87} +(-1.58234 - 2.74069i) q^{88} +(5.03800 - 8.72608i) q^{89} +(6.02985 + 3.82013i) q^{90} +(5.03172 + 2.67364i) q^{91} -1.00000i q^{92} +(0.282195 - 13.7248i) q^{93} +(-3.34488 + 1.93117i) q^{94} +(-17.4655 + 10.0837i) q^{95} +(-0.0356051 + 1.73168i) q^{96} -5.10883i q^{97} +(0.492134 + 6.98268i) q^{98} +(-8.01999 - 5.08096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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