LMFDB - Embedded newform 770.2.n.g.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 10 x^{10} - 9 x^{9} + 27 x^{8} - 26 x^{7} + 47 x^{6} + 46 x^{5} + 137 x^{4} + \cdots + 1 $ x^12 - 2x^11 + 10x^10 - 9x^9 + 27x^8 - 26x^7 + 47x^6 + 46x^5 + 137x^4 - 57x^3 + 113x^2 - 17*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.2
Root			$0.248272 - 0.764103i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.g.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.248272 + 0.764103i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.649985 - 0.472241i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.90484 + 1.38395i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.248272 + 0.764103i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.649985 - 0.472241i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.90484 + 1.38395i) q^{9} +1.00000 q^{10} +(-3.22166 + 0.787978i) q^{11} -0.803425 q^{12} +(2.13834 + 1.55360i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.248272 - 0.764103i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.29806 + 0.943099i) q^{17} +(-0.727583 - 2.23927i) q^{18} +(0.590037 - 1.81595i) q^{19} +(-0.809017 - 0.587785i) q^{20} +0.803425 q^{21} +(3.06954 + 1.25616i) q^{22} -4.22916 q^{23} +(0.649985 + 0.472241i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.816775 - 2.51377i) q^{26} +(-3.48035 + 2.52862i) q^{27} +(0.809017 - 0.587785i) q^{28} +(2.77477 + 8.53988i) q^{29} +(-0.248272 + 0.764103i) q^{30} +(-2.00312 - 1.45536i) q^{31} +1.00000 q^{32} +(0.197752 - 2.65731i) q^{33} +1.60450 q^{34} +(0.809017 + 0.587785i) q^{35} +(-0.727583 + 2.23927i) q^{36} +(-1.73320 - 5.33426i) q^{37} +(-1.54474 + 1.12232i) q^{38} +(-1.71800 + 1.24820i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-2.99616 + 9.22125i) q^{41} +(-0.649985 - 0.472241i) q^{42} -4.00169 q^{43} +(-1.74496 - 2.82048i) q^{44} -2.35451 q^{45} +(3.42146 + 2.48584i) q^{46} +(-2.02252 + 6.22469i) q^{47} +(-0.248272 - 0.764103i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.398351 - 1.22600i) q^{51} +(-0.816775 + 2.51377i) q^{52} +(-8.12885 - 5.90596i) q^{53} +4.30195 q^{54} +(2.14322 - 2.53113i) q^{55} -1.00000 q^{56} +(1.24108 + 0.901698i) q^{57} +(2.77477 - 8.53988i) q^{58} +(1.28756 + 3.96270i) q^{59} +(0.649985 - 0.472241i) q^{60} +(-10.7299 + 7.79571i) q^{61} +(0.765125 + 2.35481i) q^{62} +(0.727583 - 2.23927i) q^{63} +(-0.809017 - 0.587785i) q^{64} -2.64314 q^{65} +(-1.72191 + 2.03357i) q^{66} -10.5029 q^{67} +(-1.29806 - 0.943099i) q^{68} +(1.04998 - 3.23151i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-3.70925 + 2.69493i) q^{71} +(1.90484 - 1.38395i) q^{72} +(1.14118 + 3.51218i) q^{73} +(-1.73320 + 5.33426i) q^{74} +(0.649985 + 0.472241i) q^{75} +1.90940 q^{76} +(1.74496 + 2.82048i) q^{77} +2.12356 q^{78} +(11.2839 + 8.19826i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.11470 + 3.43068i) q^{81} +(7.84406 - 5.69904i) q^{82} +(10.9705 - 7.97052i) q^{83} +(0.248272 + 0.764103i) q^{84} +(0.495817 - 1.52597i) q^{85} +(3.23744 + 2.35214i) q^{86} -7.21424 q^{87} +(-0.246136 + 3.30748i) q^{88} -3.41009 q^{89} +(1.90484 + 1.38395i) q^{90} +(0.816775 - 2.51377i) q^{91} +(-1.30688 - 4.02217i) q^{92} +(1.60936 - 1.16927i) q^{93} +(5.29503 - 3.84707i) q^{94} +(0.590037 + 1.81595i) q^{95} +(-0.248272 + 0.764103i) q^{96} +(14.1345 + 10.2693i) q^{97} +1.00000 q^{98} +(-7.22725 - 2.95763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.248272	+	0.764103i	−0.143340	+	0.441155i	−0.996794	−	0.0800135i	$-0.974504\pi$
$3$	−0.248272	+	0.764103i	−0.143340	+	0.441155i	0.853454	+	0.521168i	$0.174504\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	0.649985	−	0.472241i	0.265355	−	0.192792i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	1.90484	+	1.38395i	0.634946	+	0.461315i
$10$	1.00000			0.316228
$11$	−3.22166	+	0.787978i	−0.971367	+	0.237584i
$11$	−3.22166	+	0.787978i	−0.971367	+	0.237584i
$12$	−0.803425			−0.231929
$13$	2.13834	+	1.55360i	0.593070	+	0.430890i	0.843412	−	0.537267i	$-0.180543\pi$
$13$	2.13834	+	1.55360i	0.593070	+	0.430890i	−0.250343	+	0.968157i	$0.580543\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−0.248272	−	0.764103i	−0.0641036	−	0.197290i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.29806	+	0.943099i	−0.314827	+	0.228735i	−0.733965	−	0.679187i	$-0.762332\pi$
$17$	−1.29806	+	0.943099i	−0.314827	+	0.228735i	0.419138	+	0.907923i	$0.362332\pi$
$18$	−0.727583	−	2.23927i	−0.171493	−	0.527801i
$19$	0.590037	−	1.81595i	0.135364	−	0.416607i	−0.860283	−	0.509817i	$-0.829713\pi$
$19$	0.590037	−	1.81595i	0.135364	−	0.416607i	0.995646	+	0.0932105i	$0.0297130\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	0.803425			0.175322
$22$	3.06954	+	1.25616i	0.654428	+	0.267813i
$23$	−4.22916			−0.881840			−0.440920	−	0.897546i	$-0.645348\pi$
$23$	−4.22916			−0.881840			−0.440920	+	0.897546i	$0.645348\pi$
$24$	0.649985	+	0.472241i	0.132678	+	0.0963959i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.816775	−	2.51377i	−0.160183	−	0.492992i
$27$	−3.48035	+	2.52862i	−0.669793	+	0.486633i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	2.77477	+	8.53988i	0.515263	+	1.58582i	0.782804	+	0.622269i	$0.213789\pi$
$29$	2.77477	+	8.53988i	0.515263	+	1.58582i	−0.267541	+	0.963546i	$0.586211\pi$
$30$	−0.248272	+	0.764103i	−0.0453281	+	0.139505i
$31$	−2.00312	−	1.45536i	−0.359772	−	0.261389i	0.393185	−	0.919459i	$-0.371373\pi$
$31$	−2.00312	−	1.45536i	−0.359772	−	0.261389i	−0.752957	+	0.658070i	$0.771373\pi$
$32$	1.00000			0.176777
$33$	0.197752	−	2.65731i	0.0344242	−	0.462579i
$34$	1.60450			0.275169
$35$	0.809017	+	0.587785i	0.136749	+	0.0993538i
$36$	−0.727583	+	2.23927i	−0.121264	+	0.373212i
$37$	−1.73320	−	5.33426i	−0.284937	−	0.876946i	−0.986418	−	0.164257i	$-0.947477\pi$
$37$	−1.73320	−	5.33426i	−0.284937	−	0.876946i	0.701480	−	0.712689i	$-0.252523\pi$
$38$	−1.54474	+	1.12232i	−0.250589	+	0.182064i
$39$	−1.71800	+	1.24820i	−0.275100	+	0.199872i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	−2.99616	+	9.22125i	−0.467922	+	1.44012i	0.387348	+	0.921934i	$0.373391\pi$
$41$	−2.99616	+	9.22125i	−0.467922	+	1.44012i	−0.855270	+	0.518183i	$0.826609\pi$
$42$	−0.649985	−	0.472241i	−0.100295	−	0.0728684i
$43$	−4.00169			−0.610252			−0.305126	−	0.952312i	$-0.598699\pi$
$43$	−4.00169			−0.610252			−0.305126	+	0.952312i	$0.598699\pi$
$44$	−1.74496	−	2.82048i	−0.263062	−	0.425204i
$45$	−2.35451			−0.350989
$46$	3.42146	+	2.48584i	0.504467	+	0.366516i
$47$	−2.02252	+	6.22469i	−0.295015	+	0.907964i	0.688201	+	0.725520i	$0.258401\pi$
$47$	−2.02252	+	6.22469i	−0.295015	+	0.907964i	−0.983216	+	0.182444i	$0.941599\pi$
$48$	−0.248272	−	0.764103i	−0.0358350	−	0.110289i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	−0.398351	−	1.22600i	−0.0557804	−	0.171674i
$52$	−0.816775	+	2.51377i	−0.113266	+	0.348598i
$53$	−8.12885	−	5.90596i	−1.11658	−	0.811246i	−0.132896	−	0.991130i	$-0.542428\pi$
$53$	−8.12885	−	5.90596i	−1.11658	−	0.811246i	−0.983688	+	0.179884i	$0.942428\pi$
$54$	4.30195			0.585421
$55$	2.14322	−	2.53113i	0.288991	−	0.341298i
$56$	−1.00000			−0.133631
$57$	1.24108	+	0.901698i	0.164385	+	0.119433i
$58$	2.77477	−	8.53988i	0.364346	−	1.12134i
$59$	1.28756	+	3.96270i	0.167626	+	0.515900i	0.999220	−	0.0394838i	$-0.0125714\pi$
$59$	1.28756	+	3.96270i	0.167626	+	0.515900i	−0.831594	+	0.555384i	$0.812571\pi$
$60$	0.649985	−	0.472241i	0.0839126	−	0.0609661i
$61$	−10.7299	+	7.79571i	−1.37382	+	0.998139i	−0.376392	+	0.926460i	$0.622836\pi$
$61$	−10.7299	+	7.79571i	−1.37382	+	0.998139i	−0.997428	+	0.0716784i	$0.977164\pi$
$62$	0.765125	+	2.35481i	0.0971710	+	0.299062i
$63$	0.727583	−	2.23927i	0.0916668	−	0.282122i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.64314			−0.327841
$66$	−1.72191	+	2.03357i	−0.211953	+	0.250316i
$67$	−10.5029			−1.28314			−0.641570	−	0.767065i	$-0.721716\pi$
$67$	−10.5029			−1.28314			−0.641570	+	0.767065i	$0.721716\pi$
$68$	−1.29806	−	0.943099i	−0.157413	−	0.114368i
$69$	1.04998	−	3.23151i	0.126403	−	0.389028i
$70$	−0.309017	−	0.951057i	−0.0369346	−	0.113673i
$71$	−3.70925	+	2.69493i	−0.440207	+	0.319829i	−0.785717	−	0.618586i	$-0.787706\pi$
$71$	−3.70925	+	2.69493i	−0.440207	+	0.319829i	0.345510	+	0.938415i	$0.387706\pi$
$72$	1.90484	−	1.38395i	0.224487	−	0.163099i
$73$	1.14118	+	3.51218i	0.133565	+	0.411070i	0.995364	−	0.0961797i	$-0.0306623\pi$
$73$	1.14118	+	3.51218i	0.133565	+	0.411070i	−0.861799	+	0.507249i	$0.830662\pi$
$74$	−1.73320	+	5.33426i	−0.201481	+	0.620095i
$75$	0.649985	+	0.472241i	0.0750538	+	0.0545297i
$76$	1.90940			0.219023
$77$	1.74496	+	2.82048i	0.198857	+	0.321424i
$78$	2.12356			0.240446
$79$	11.2839	+	8.19826i	1.26954	+	0.922376i	0.999184	−	0.0403841i	$-0.0128582\pi$
$79$	11.2839	+	8.19826i	1.26954	+	0.922376i	0.270357	+	0.962760i	$0.412858\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	1.11470	+	3.43068i	0.123855	+	0.381187i
$82$	7.84406	−	5.69904i	0.866232	−	0.629354i
$83$	10.9705	−	7.97052i	1.20417	−	0.874878i	0.209478	−	0.977813i	$-0.432824\pi$
$83$	10.9705	−	7.97052i	1.20417	−	0.874878i	0.994688	+	0.102936i	$0.0328236\pi$
$84$	0.248272	+	0.764103i	0.0270887	+	0.0833704i
$85$	0.495817	−	1.52597i	0.0537789	−	0.165514i
$86$	3.23744	+	2.35214i	0.349102	+	0.253637i
$87$	−7.21424			−0.773448
$88$	−0.246136	+	3.30748i	−0.0262382	+	0.352578i
$89$	−3.41009			−0.361469			−0.180735	−	0.983532i	$-0.557847\pi$
$89$	−3.41009			−0.361469			−0.180735	+	0.983532i	$0.557847\pi$
$90$	1.90484	+	1.38395i	0.200787	+	0.145881i
$91$	0.816775	−	2.51377i	0.0856212	−	0.263515i
$92$	−1.30688	−	4.02217i	−0.136252	−	0.419340i
$93$	1.60936	−	1.16927i	0.166883	−	0.121248i
$94$	5.29503	−	3.84707i	0.546141	−	0.396795i
$95$	0.590037	+	1.81595i	0.0605365	+	0.186312i
$96$	−0.248272	+	0.764103i	−0.0253392	+	0.0779859i
$97$	14.1345	+	10.2693i	1.43515	+	1.04269i	0.989029	+	0.147719i	$0.0471930\pi$
$97$	14.1345	+	10.2693i	1.43515	+	1.04269i	0.446116	+	0.894975i	$0.352807\pi$
$98$	1.00000			0.101015
$99$	−7.22725	−	2.95763i	−0.726366	−	0.297253i
$100$	1.00000			0.100000
$101$	8.61553	+	6.25955i	0.857278	+	0.622849i	0.927143	−	0.374708i	$-0.122257\pi$
$101$	8.61553	+	6.25955i	0.857278	+	0.622849i	−0.0698652	+	0.997556i	$0.522257\pi$
$102$	−0.398351	+	1.22600i	−0.0394427	+	0.121392i
$103$	−2.12192	−	6.53058i	−0.209079	−	0.643478i	−0.999521	−	0.0309416i	$-0.990149\pi$
$103$	−2.12192	−	6.53058i	−0.209079	−	0.643478i	0.790443	−	0.612536i	$-0.209851\pi$
$104$	2.13834	−	1.55360i	0.209682	−	0.152343i
$105$	−0.649985	+	0.472241i	−0.0634320	+	0.0460860i
$106$	3.10495	+	9.55604i	0.301579	+	0.928165i
$107$	−0.890804	+	2.74161i	−0.0861172	+	0.265042i	−0.984837	−	0.173482i	$-0.944498\pi$
$107$	−0.890804	+	2.74161i	−0.0861172	+	0.265042i	0.898720	+	0.438523i	$0.144498\pi$
$108$	−3.48035	−	2.52862i	−0.334897	−	0.243317i
$109$	−18.4938			−1.77139			−0.885693	−	0.464271i	$-0.846316\pi$
$109$	−18.4938			−1.77139			−0.885693	+	0.464271i	$0.846316\pi$
$110$	−3.22166	+	0.787978i	−0.307173	+	0.0751307i
$111$	4.50623			0.427712
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	3.69479	−	11.3714i	0.347577	−	1.06973i	−0.612613	−	0.790383i	$-0.709882\pi$
$113$	3.69479	−	11.3714i	0.347577	−	1.06973i	0.960190	−	0.279348i	$-0.0901184\pi$
$114$	−0.474051	−	1.45898i	−0.0443989	−	0.136646i
$115$	3.42146	−	2.48584i	0.319053	−	0.231805i
$116$	−7.26445	+	5.27793i	−0.674487	+	0.490044i
$117$	1.92310	+	5.91870i	0.177791	+	0.547184i
$118$	1.28756	−	3.96270i	0.118530	−	0.364796i
$119$	1.29806	+	0.943099i	0.118993	+	0.0864538i
$120$	−0.803425			−0.0733423
$121$	9.75818	−	5.07719i	0.887107	−	0.461563i
$122$	13.2629			1.20076
$123$	−6.30212	−	4.57875i	−0.568243	−	0.412852i
$124$	0.765125	−	2.35481i	0.0687103	−	0.211469i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−1.90484	+	1.38395i	−0.169696	+	0.123292i
$127$	10.8477	−	7.88134i	0.962581	−	0.699356i	0.00883223	−	0.999961i	$-0.497189\pi$
$127$	10.8477	−	7.88134i	0.962581	−	0.699356i	0.953749	+	0.300605i	$0.0971886\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.993508	−	3.05770i	0.0874735	−	0.269216i
$130$	2.13834	+	1.55360i	0.187545	+	0.136260i
$131$	−8.49928			−0.742585			−0.371293	−	0.928516i	$-0.621085\pi$
$131$	−8.49928			−0.742585			−0.371293	+	0.928516i	$0.621085\pi$
$132$	2.58836	−	0.633081i	0.225288	−	0.0551026i
$133$	−1.90940			−0.165566
$134$	8.49706	+	6.17348i	0.734035	+	0.533307i
$135$	1.32937	−	4.09139i	0.114414	−	0.352131i
$136$	0.495817	+	1.52597i	0.0425159	+	0.130851i
$137$	−8.15058	+	5.92174i	−0.696351	+	0.505929i	−0.878742	−	0.477298i	$-0.841616\pi$
$137$	−8.15058	+	5.92174i	−0.696351	+	0.505929i	0.182391	+	0.983226i	$0.441616\pi$
$138$	−2.74889	+	1.99718i	−0.234001	+	0.170011i
$139$	4.27063	+	13.1436i	0.362230	+	1.11483i	0.951697	+	0.307037i	$0.0993376\pi$
$139$	4.27063	+	13.1436i	0.362230	+	1.11483i	−0.589467	+	0.807792i	$0.700662\pi$
$140$	−0.309017	+	0.951057i	−0.0261167	+	0.0803789i
$141$	−4.25416	−	3.09083i	−0.358265	−	0.260295i
$142$	4.58489			0.384755
$143$	−8.11322	−	3.32019i	−0.678461	−	0.277649i
$144$	−2.35451			−0.196209
$145$	−7.26445	−	5.27793i	−0.603280	−	0.438309i
$146$	1.14118	−	3.51218i	0.0944444	−	0.290670i
$147$	−0.248272	−	0.764103i	−0.0204771	−	0.0630221i
$148$	4.53759	−	3.29675i	0.372987	−	0.270991i
$149$	14.8566	−	10.7940i	1.21710	−	0.884278i	0.221247	−	0.975218i	$-0.428987\pi$
$149$	14.8566	−	10.7940i	1.21710	−	0.884278i	0.995856	+	0.0909401i	$0.0289872\pi$
$150$	−0.248272	−	0.764103i	−0.0202713	−	0.0623887i
$151$	6.35704	−	19.5650i	0.517329	−	1.59217i	−0.261676	−	0.965156i	$-0.584275\pi$
$151$	6.35704	−	19.5650i	0.517329	−	1.59217i	0.779005	−	0.627018i	$-0.215725\pi$
$152$	−1.54474	−	1.12232i	−0.125295	−	0.0910319i
$153$	−3.77780			−0.305417
$154$	0.246136	−	3.30748i	0.0198342	−	0.266524i
$155$	2.47600			0.198877
$156$	−1.71800	−	1.24820i	−0.137550	−	0.0999359i
$157$	−1.43658	+	4.42133i	−0.114651	+	0.352860i	−0.991874	−	0.127223i	$-0.959394\pi$
$157$	−1.43658	+	4.42133i	−0.114651	+	0.352860i	0.877223	+	0.480083i	$0.159394\pi$
$158$	−4.31008	−	13.2651i	−0.342891	−	1.05531i
$159$	6.53093	−	4.74499i	0.517936	−	0.376303i
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	1.30688	+	4.02217i	0.102997	+	0.316991i
$162$	1.11470	−	3.43068i	0.0875788	−	0.269540i
$163$	−4.04023	−	2.93540i	−0.316455	−	0.229918i	0.418206	−	0.908352i	$-0.362659\pi$
$163$	−4.04023	−	2.93540i	−0.316455	−	0.229918i	−0.734661	+	0.678434i	$0.762659\pi$
$164$	−9.69579			−0.757114
$165$	1.40194	+	2.26605i	0.109141	+	0.176411i
$166$	−13.5603			−1.05248
$167$	1.51162	+	1.09826i	0.116973	+	0.0849857i	0.644734	−	0.764407i	$-0.276968\pi$
$167$	1.51162	+	1.09826i	0.116973	+	0.0849857i	−0.527761	+	0.849393i	$0.676968\pi$
$168$	0.248272	−	0.764103i	0.0191546	−	0.0589518i
$169$	−1.85837	−	5.71949i	−0.142952	−	0.439960i
$170$	−1.29806	+	0.943099i	−0.0995570	+	0.0723324i
$171$	3.63710	−	2.64250i	0.278136	−	0.202077i
$172$	−1.23659	−	3.80583i	−0.0942891	−	0.290192i
$173$	−3.64020	+	11.2034i	−0.276760	+	0.851779i	0.711989	+	0.702191i	$0.247795\pi$
$173$	−3.64020	+	11.2034i	−0.276760	+	0.851779i	−0.988748	+	0.149588i	$0.952205\pi$
$174$	5.83644	+	4.24042i	0.442460	+	0.321466i
$175$	−1.00000			−0.0755929
$176$	2.14322	−	2.53113i	0.161551	−	0.190791i
$177$	−3.34758			−0.251619
$178$	2.75882	+	2.00440i	0.206782	+	0.150236i
$179$	−3.20466	+	9.86294i	−0.239528	+	0.737191i	0.756961	+	0.653460i	$0.226683\pi$
$179$	−3.20466	+	9.86294i	−0.239528	+	0.737191i	−0.996488	+	0.0837303i	$0.973317\pi$
$180$	−0.727583	−	2.23927i	−0.0542308	−	0.166905i
$181$	18.3435	−	13.3273i	1.36346	−	0.990611i	0.365242	−	0.930912i	$-0.380986\pi$
$181$	18.3435	−	13.3273i	1.36346	−	0.990611i	0.998216	−	0.0596985i	$-0.0190139\pi$
$182$	−2.13834	+	1.55360i	−0.158505	+	0.115160i
$183$	−3.29280	−	10.1342i	−0.243411	−	0.749141i
$184$	−1.30688	+	4.02217i	−0.0963446	+	0.296518i
$185$	4.53759	+	3.29675i	0.333610	+	0.242382i
$186$	−1.98928			−0.145861
$187$	3.43878	−	4.06119i	0.251469	−	0.296984i
$188$	−6.54502			−0.477345
$189$	3.48035	+	2.52862i	0.253158	+	0.183930i
$190$	0.590037	−	1.81595i	0.0428058	−	0.131743i
$191$	−2.62245	−	8.07107i	−0.189754	−	0.584002i	0.810244	−	0.586093i	$-0.199335\pi$
$191$	−2.62245	−	8.07107i	−0.189754	−	0.584002i	−0.999998	+	0.00209040i	$0.999335\pi$
$192$	0.649985	−	0.472241i	0.0469086	−	0.0340811i
$193$	20.3531	−	14.7874i	1.46505	−	1.06442i	0.483038	−	0.875599i	$-0.339533\pi$
$193$	20.3531	−	14.7874i	1.46505	−	1.06442i	0.982011	−	0.188822i	$-0.0604668\pi$
$194$	−5.39891	−	16.6161i	−0.387619	−	1.19297i
$195$	0.656217	−	2.01963i	0.0469927	−	0.144629i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−13.2603			−0.944757			−0.472379	−	0.881396i	$-0.656604\pi$
$197$	−13.2603			−0.944757			−0.472379	+	0.881396i	$0.656604\pi$
$198$	4.10852	+	6.64085i	0.291980	+	0.471944i
$199$	3.59813			0.255065			0.127532	−	0.991834i	$-0.459294\pi$
$199$	3.59813			0.255065			0.127532	+	0.991834i	$0.459294\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	2.60759	−	8.02533i	0.183925	−	0.566063i
$202$	−3.29084	−	10.1282i	−0.231543	−	0.712615i
$203$	7.26445	−	5.27793i	0.509865	−	0.370438i
$204$	1.04290	−	0.757710i	0.0730174	−	0.0530503i
$205$	−2.99616	−	9.22125i	−0.209261	−	0.644040i
$206$	−2.12192	+	6.53058i	−0.147841	+	0.455007i
$207$	−8.05585	−	5.85292i	−0.559920	−	0.406806i
$208$	−2.64314			−0.183269
$209$	−0.469972	+	6.31530i	−0.0325087	+	0.436838i
$210$	0.803425			0.0554416
$211$	8.09486	+	5.88126i	0.557273	+	0.404883i	0.830460	−	0.557078i	$-0.188078\pi$
$211$	8.09486	+	5.88126i	0.557273	+	0.404883i	−0.273187	+	0.961961i	$0.588078\pi$
$212$	3.10495	−	9.55604i	0.213249	−	0.656312i
$213$	−1.13830	−	3.50332i	−0.0779950	−	0.240044i
$214$	2.33215	−	1.69441i	0.159423	−	0.115827i
$215$	3.23744	−	2.35214i	0.220791	−	0.160414i
$216$	1.32937	+	4.09139i	0.0904525	+	0.278384i
$217$	−0.765125	+	2.35481i	−0.0519401	+	0.159855i
$218$	14.9618	+	10.8704i	1.01334	+	0.736236i
$219$	−2.96699			−0.200491
$220$	3.06954	+	1.25616i	0.206948	+	0.0846901i
$221$	−4.24090			−0.285274
$222$	−3.64561	−	2.64869i	−0.244678	−	0.177769i
$223$	7.73769	−	23.8142i	0.518154	−	1.59471i	−0.259315	−	0.965793i	$-0.583497\pi$
$223$	7.73769	−	23.8142i	0.518154	−	1.59471i	0.777469	−	0.628922i	$-0.216503\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	1.90484	−	1.38395i	0.126989	−	0.0922630i
$226$	−9.67309	+	7.02791i	−0.643444	+	0.467490i
$227$	−0.0565265	−	0.173971i	−0.00375180	−	0.0115468i	0.949163	−	0.314785i	$-0.101932\pi$
$227$	−0.0565265	−	0.173971i	−0.00375180	−	0.0115468i	−0.952915	+	0.303238i	$0.901932\pi$
$228$	−0.474051	+	1.45898i	−0.0313948	+	0.0966232i
$229$	0.108709	+	0.0789815i	0.00718367	+	0.00521924i	0.591371	−	0.806399i	$-0.298587\pi$
$229$	0.108709	+	0.0789815i	0.00718367	+	0.00521924i	−0.584188	+	0.811619i	$0.698587\pi$
$230$	−4.22916			−0.278862
$231$	−2.58836	+	0.633081i	−0.170302	+	0.0416537i
$232$	8.97936			0.589524
$233$	2.37050	+	1.72227i	0.155296	+	0.112830i	0.662720	−	0.748867i	$-0.269402\pi$
$233$	2.37050	+	1.72227i	0.155296	+	0.112830i	−0.507423	+	0.861697i	$0.669402\pi$
$234$	1.92310	−	5.91870i	0.125717	−	0.386918i
$235$	−2.02252	−	6.22469i	−0.131935	−	0.406054i
$236$	−3.37088	+	2.44909i	−0.219425	+	0.159422i
$237$	−9.06579	+	6.58669i	−0.588887	+	0.427851i
$238$	−0.495817	−	1.52597i	−0.0321390	−	0.0989137i
$239$	2.55684	−	7.86914i	0.165388	−	0.509012i	−0.833677	−	0.552253i	$-0.813768\pi$
$239$	2.55684	−	7.86914i	0.165388	−	0.509012i	0.999065	+	0.0432406i	$0.0137682\pi$
$240$	0.649985	+	0.472241i	0.0419563	+	0.0304831i
$241$	16.5842			1.06828			0.534142	−	0.845395i	$-0.320635\pi$
$241$	16.5842			1.06828			0.534142	+	0.845395i	$0.320635\pi$
$242$	−10.8788	−	1.62818i	−0.699318	−	0.104663i
$243$	−15.8040			−1.01383
$244$	−10.7299	−	7.79571i	−0.686910	−	0.499069i
$245$	0.309017	−	0.951057i	0.0197424	−	0.0607608i
$246$	2.40719	+	7.40858i	0.153477	+	0.472354i
$247$	4.08295	−	2.96644i	0.259792	−	0.188750i
$248$	−2.00312	+	1.45536i	−0.127199	+	0.0924151i
$249$	3.36663	+	10.3614i	0.213352	+	0.656629i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	10.9610	+	7.96366i	0.691855	+	0.502662i	0.877269	−	0.479998i	$-0.159363\pi$
$251$	10.9610	+	7.96366i	0.691855	+	0.502662i	−0.185415	+	0.982660i	$0.559363\pi$
$252$	2.35451			0.148320
$253$	13.6249	−	3.33248i	0.856590	−	0.209511i
$254$	−13.4085			−0.841327
$255$	1.04290	+	0.757710i	0.0653088	+	0.0474496i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.69288	+	17.5209i	0.355112	+	1.09292i	0.955944	+	0.293548i	$0.0948360\pi$
$257$	5.69288	+	17.5209i	0.355112	+	1.09292i	−0.600832	+	0.799375i	$0.705164\pi$
$258$	−2.60104	+	1.88976i	−0.161934	+	0.117652i
$259$	−4.53759	+	3.29675i	−0.281952	+	0.204850i
$260$	−0.816775	−	2.51377i	−0.0506542	−	0.155898i
$261$	−6.53323	+	20.1072i	−0.404397	+	1.24460i
$262$	6.87606	+	4.99575i	0.424804	+	0.308638i
$263$	−19.1658			−1.18181			−0.590907	−	0.806740i	$-0.701230\pi$
$263$	−19.1658			−1.18181			−0.590907	+	0.806740i	$0.701230\pi$
$264$	−2.46614	−	1.00923i	−0.151781	−	0.0621137i
$265$	10.0478			0.617232
$266$	1.54474	+	1.12232i	0.0947139	+	0.0688137i
$267$	0.846630	−	2.60566i	0.0518129	−	0.159464i
$268$	−3.24559	−	9.98890i	−0.198256	−	0.610169i
$269$	−7.35126	+	5.34100i	−0.448214	+	0.325647i	−0.788890	−	0.614534i	$-0.789344\pi$
$269$	−7.35126	+	5.34100i	−0.448214	+	0.325647i	0.340676	+	0.940181i	$0.389344\pi$
$270$	−3.48035	+	2.52862i	−0.211807	+	0.153887i
$271$	5.92506	+	18.2355i	0.359922	+	1.10773i	0.953100	+	0.302655i	$0.0978729\pi$
$271$	5.92506	+	18.2355i	0.359922	+	1.10773i	−0.593178	+	0.805071i	$0.702127\pi$
$272$	0.495817	−	1.52597i	0.0300633	−	0.0925253i
$273$	1.71800	+	1.24820i	0.103978	+	0.0755445i
$274$	10.0747			0.608633
$275$	−0.246136	+	3.30748i	−0.0148426	+	0.199448i
$276$	3.39781			0.204524
$277$	16.7217	+	12.1490i	1.00471	+	0.729964i	0.963093	−	0.269170i	$-0.0867493\pi$
$277$	16.7217	+	12.1490i	1.00471	+	0.729964i	0.0416161	+	0.999134i	$0.486749\pi$
$278$	4.27063	−	13.1436i	0.256135	−	0.788303i
$279$	−1.80149	−	5.54443i	−0.107853	−	0.331936i
$280$	0.809017	−	0.587785i	0.0483480	−	0.0351269i
$281$	1.10959	−	0.806163i	0.0661925	−	0.0480916i	−0.554197	−	0.832386i	$-0.686975\pi$
$281$	1.10959	−	0.806163i	0.0661925	−	0.0480916i	0.620389	+	0.784294i	$0.286975\pi$
$282$	1.62495	+	5.00107i	0.0967641	+	0.297809i
$283$	−1.98856	+	6.12017i	−0.118208	+	0.363806i	−0.992603	−	0.121409i	$-0.961259\pi$
$283$	−1.98856	+	6.12017i	−0.118208	+	0.363806i	0.874395	+	0.485215i	$0.161259\pi$
$284$	−3.70925	−	2.69493i	−0.220104	−	0.159915i
$285$	−1.53406			−0.0908699
$286$	4.61217	+	7.45492i	0.272723	+	0.440819i
$287$	9.69579			0.572324
$288$	1.90484	+	1.38395i	0.112244	+	0.0815497i
$289$	−4.45775	+	13.7196i	−0.262221	+	0.807033i
$290$	2.77477	+	8.53988i	0.162940	+	0.501479i
$291$	−11.3560	+	8.25065i	−0.665703	+	0.483662i
$292$	−2.98764	+	2.17065i	−0.174838	+	0.127028i
$293$	1.42065	+	4.37230i	0.0829951	+	0.255433i	0.983940	−	0.178502i	$-0.0571250\pi$
$293$	1.42065	+	4.37230i	0.0829951	+	0.255433i	−0.900945	+	0.433934i	$0.857125\pi$
$294$	−0.248272	+	0.764103i	−0.0144795	+	0.0445634i
$295$	−3.37088	−	2.44909i	−0.196260	−	0.142591i
$296$	−5.60877			−0.326003
$297$	9.22000	−	10.8888i	0.534999	−	0.631832i
$298$	−18.3638			−1.06379
$299$	−9.04339	−	6.57041i	−0.522993	−	0.379976i
$300$	−0.248272	+	0.764103i	−0.0143340	+	0.0441155i
$301$	1.23659	+	3.80583i	0.0712759	+	0.219365i
$302$	−16.6429	+	12.0918i	−0.957694	+	0.695805i
$303$	−6.92194	+	5.02908i	−0.397655	+	0.288913i
$304$	0.590037	+	1.81595i	0.0338409	+	0.104152i
$305$	4.09845	−	12.6137i	0.234676	−	0.722260i
$306$	3.05630	+	2.22053i	0.174717	+	0.126940i
$307$	−24.8042			−1.41565			−0.707825	−	0.706388i	$-0.750323\pi$
$307$	−24.8042			−1.41565			−0.707825	+	0.706388i	$0.750323\pi$
$308$	−2.14322	+	2.53113i	−0.122121	+	0.144225i
$309$	5.51685			0.313843
$310$	−2.00312	−	1.45536i	−0.113770	−	0.0826586i
$311$	7.97333	−	24.5394i	0.452126	−	1.39150i	−0.422350	−	0.906433i	$-0.638795\pi$
$311$	7.97333	−	24.5394i	0.452126	−	1.39150i	0.874476	−	0.485069i	$-0.161205\pi$
$312$	0.656217	+	2.01963i	0.0371510	+	0.114339i
$313$	−13.3553	+	9.70322i	−0.754888	+	0.548458i	−0.897338	−	0.441344i	$-0.854502\pi$
$313$	−13.3553	+	9.70322i	−0.754888	+	0.548458i	0.142450	+	0.989802i	$0.454502\pi$
$314$	3.76101	−	2.73253i	0.212246	−	0.154206i
$315$	0.727583	+	2.23927i	0.0409947	+	0.126169i
$316$	−4.31008	+	13.2651i	−0.242461	+	0.746218i
$317$	−1.88569	−	1.37004i	−0.105911	−	0.0769489i	0.533569	−	0.845756i	$-0.320850\pi$
$317$	−1.88569	−	1.37004i	−0.105911	−	0.0769489i	−0.639480	+	0.768808i	$0.720850\pi$
$318$	−8.07267			−0.452693
$319$	−15.6686	−	25.3261i	−0.877274	−	1.41799i
$320$	1.00000			0.0559017
$321$	−1.87371	−	1.36133i	−0.104580	−	0.0759821i
$322$	1.30688	−	4.02217i	0.0728296	−	0.224147i
$323$	0.946712	+	2.91368i	0.0526765	+	0.162122i
$324$	−2.91831	+	2.12028i	−0.162128	+	0.117793i
$325$	2.13834	−	1.55360i	0.118614	−	0.0861781i
$326$	1.54323	+	4.74958i	0.0854716	+	0.263055i
$327$	4.59150	−	14.1312i	0.253910	−	0.781456i
$328$	7.84406	+	5.69904i	0.433116	+	0.314677i
$329$	6.54502			0.360839
$330$	0.197752	−	2.65731i	0.0108859	−	0.146280i
$331$	6.54411			0.359697			0.179848	−	0.983694i	$-0.442439\pi$
$331$	6.54411			0.359697			0.179848	+	0.983694i	$0.442439\pi$
$332$	10.9705	+	7.97052i	0.602083	+	0.437439i
$333$	4.08084	−	12.5595i	0.223629	−	0.688259i
$334$	−0.577388	−	1.77702i	−0.0315933	−	0.0972341i
$335$	8.49706	−	6.17348i	0.464244	−	0.337293i
$336$	−0.649985	+	0.472241i	−0.0354596	+	0.0257629i
$337$	5.15321	+	15.8600i	0.280713	+	0.863947i	0.987651	+	0.156671i	$0.0500761\pi$
$337$	5.15321	+	15.8600i	0.280713	+	0.863947i	−0.706938	+	0.707276i	$0.749924\pi$
$338$	−1.85837	+	5.71949i	−0.101082	+	0.311099i
$339$	7.77160	+	5.64640i	0.422096	+	0.306670i
$340$	1.60450			0.0870160
$341$	7.60017	+	3.11024i	0.411572	+	0.168429i
$342$	−4.49570			−0.243099
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−1.23659	+	3.80583i	−0.0666725	+	0.205197i
$345$	1.04998	+	3.23151i	0.0565291	+	0.173979i
$346$	9.53018	−	6.92408i	0.512346	−	0.372241i
$347$	−23.6893	+	17.2113i	−1.27171	+	0.923950i	−0.999269	−	0.0382231i	$-0.987830\pi$
$347$	−23.6893	+	17.2113i	−1.27171	+	0.923950i	−0.272439	+	0.962173i	$0.587830\pi$
$348$	−2.22932	−	6.86115i	−0.119504	−	0.367796i
$349$	−5.18642	+	15.9622i	−0.277623	+	0.854435i	0.710891	+	0.703302i	$0.248292\pi$
$349$	−5.18642	+	15.9622i	−0.277623	+	0.854435i	−0.988514	+	0.151132i	$0.951708\pi$
$350$	0.809017	+	0.587785i	0.0432438	+	0.0314184i
$351$	−11.3706			−0.606920
$352$	−3.22166	+	0.787978i	−0.171715	+	0.0419994i
$353$	22.9110			1.21943			0.609715	−	0.792621i	$-0.291284\pi$
$353$	22.9110			1.21943			0.609715	+	0.792621i	$0.291284\pi$
$354$	2.70825	+	1.96766i	0.143942	+	0.104580i
$355$	1.41681	−	4.36049i	0.0751963	−	0.231431i
$356$	−1.05378	−	3.24319i	−0.0558500	−	0.171889i
$357$	−1.04290	+	0.757710i	−0.0551960	+	0.0401022i
$358$	8.38992	−	6.09563i	0.443421	−	0.322164i
$359$	2.58498	+	7.95576i	0.136430	+	0.419889i	0.995810	−	0.0914492i	$-0.0291499\pi$
$359$	2.58498	+	7.95576i	0.136430	+	0.419889i	−0.859380	+	0.511338i	$0.829150\pi$
$360$	−0.727583	+	2.23927i	−0.0383470	+	0.118020i
$361$	12.4218	+	9.02497i	0.653779	+	0.474998i
$362$	−22.6738			−1.19171
$363$	1.45681	+	8.71678i	0.0764629	+	0.457512i
$364$	2.64314			0.138538
$365$	−2.98764	−	2.17065i	−0.156380	−	0.113617i
$366$	−3.29280	+	10.1342i	−0.172117	+	0.529722i
$367$	−0.557226	−	1.71496i	−0.0290869	−	0.0895204i	0.935459	−	0.353435i	$-0.114986\pi$
$367$	−0.557226	−	1.71496i	−0.0290869	−	0.0895204i	−0.964546	+	0.263914i	$0.914986\pi$
$368$	3.42146	−	2.48584i	0.178356	−	0.129583i
$369$	−18.4689	+	13.4184i	−0.961453	+	0.698536i
$370$	−1.73320	−	5.33426i	−0.0901050	−	0.277315i
$371$	−3.10495	+	9.55604i	−0.161201	+	0.496125i
$372$	1.60936	+	1.16927i	0.0834415	+	0.0606238i
$373$	9.60451			0.497303			0.248651	−	0.968593i	$-0.420013\pi$
$373$	9.60451			0.497303			0.248651	+	0.968593i	$0.420013\pi$
$374$	−5.16914	+	1.26431i	−0.267290	+	0.0653758i
$375$	−0.803425			−0.0414887
$376$	5.29503	+	3.84707i	0.273071	+	0.198397i
$377$	−7.33411	+	22.5721i	−0.377726	+	1.16252i
$378$	−1.32937	−	4.09139i	−0.0683756	−	0.210439i
$379$	4.80593	−	3.49171i	0.246864	−	0.179357i	−0.457472	−	0.889224i	$-0.651245\pi$
$379$	4.80593	−	3.49171i	0.246864	−	0.179357i	0.704336	+	0.709867i	$0.251245\pi$
$380$	−1.54474	+	1.12232i	−0.0792433	+	0.0575737i
$381$	3.32897	+	10.2455i	0.170548	+	0.524893i
$382$	−2.62245	+	8.07107i	−0.134176	+	0.412952i
$383$	23.8060	+	17.2960i	1.21643	+	0.883786i	0.995799	−	0.0915714i	$-0.0291890\pi$
$383$	23.8060	+	17.2960i	1.21643	+	0.883786i	0.220629	+	0.975358i	$0.429189\pi$
$384$	−0.803425			−0.0409996
$385$	−3.06954	−	1.25616i	−0.156438	−	0.0640197i
$386$	−25.1578			−1.28050
$387$	−7.62257	−	5.53812i	−0.387477	−	0.281519i
$388$	−5.39891	+	16.6161i	−0.274088	+	0.843557i
$389$	−5.82858	−	17.9385i	−0.295520	−	0.909519i	−0.983046	−	0.183358i	$-0.941303\pi$
$389$	−5.82858	−	17.9385i	−0.295520	−	0.909519i	0.687526	−	0.726160i	$-0.258697\pi$
$390$	−1.71800	+	1.24820i	−0.0869943	+	0.0632050i
$391$	5.48972	−	3.98851i	0.277627	−	0.201708i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	2.11013	−	6.49432i	0.106442	−	0.327595i
$394$	10.7278	+	7.79421i	0.540459	+	0.392667i
$395$	−13.9477			−0.701785
$396$	0.579529	−	7.78749i	0.0291225	−	0.391336i
$397$	25.4542			1.27751			0.638756	−	0.769409i	$-0.279449\pi$
$397$	25.4542			1.27751			0.638756	+	0.769409i	$0.279449\pi$
$398$	−2.91095	−	2.11493i	−0.145913	−	0.106012i
$399$	0.474051	−	1.45898i	0.0237322	−	0.0730402i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−12.1245	+	8.80895i	−0.605467	+	0.439898i	−0.847815	−	0.530292i	$-0.822082\pi$
$401$	−12.1245	+	8.80895i	−0.605467	+	0.439898i	0.242348	+	0.970189i	$0.422082\pi$
$402$	−6.82675	+	4.95993i	−0.340488	+	0.247379i
$403$	−2.02233	−	6.22410i	−0.100740	−	0.310044i
$404$	−3.29084	+	10.1282i	−0.163725	+	0.503895i
$405$	−2.91831	−	2.12028i	−0.145012	−	0.105357i
$406$	−8.97936			−0.445638
$407$	9.78707	+	15.8194i	0.485127	+	0.784140i
$408$	−1.28909			−0.0638196
$409$	−3.93000	−	2.85531i	−0.194326	−	0.141186i	0.486368	−	0.873754i	$-0.338322\pi$
$409$	−3.93000	−	2.85531i	−0.194326	−	0.141186i	−0.680694	+	0.732568i	$0.738322\pi$
$410$	−2.99616	+	9.22125i	−0.147970	+	0.455405i
$411$	−2.50126	−	7.69808i	−0.123378	−	0.379718i
$412$	5.55525	−	4.03612i	0.273687	−	0.198846i
$413$	3.37088	−	2.44909i	0.165870	−	0.120512i
$414$	3.07706	+	9.47022i	0.151229	+	0.465436i
$415$	−4.19035	+	12.8966i	−0.205696	+	0.633068i
$416$	2.13834	+	1.55360i	0.104841	+	0.0761714i
$417$	−11.1034			−0.543734
$418$	4.09226	−	4.83294i	0.200159	−	0.236387i
$419$	−1.77493			−0.0867109			−0.0433554	−	0.999060i	$-0.513805\pi$
$419$	−1.77493			−0.0867109			−0.0433554	+	0.999060i	$0.513805\pi$
$420$	−0.649985	−	0.472241i	−0.0317160	−	0.0230430i
$421$	−5.22997	+	16.0962i	−0.254893	+	0.784480i	0.738958	+	0.673752i	$0.235318\pi$
$421$	−5.22997	+	16.0962i	−0.254893	+	0.784480i	−0.993851	+	0.110728i	$0.964682\pi$
$422$	−3.09196	−	9.51608i	−0.150514	−	0.463236i
$423$	−12.4672	+	9.05795i	−0.606176	+	0.440413i
$424$	−8.12885	+	5.90596i	−0.394772	+	0.286819i
$425$	0.495817	+	1.52597i	0.0240506	+	0.0740202i
$426$	−1.13830	+	3.50332i	−0.0551508	+	0.169737i
$427$	10.7299	+	7.79571i	0.519255	+	0.377261i
$428$	−2.88270			−0.139341
$429$	4.55125	−	5.37502i	0.219737	−	0.259508i
$430$	−4.00169			−0.192979
$431$	−3.36245	−	2.44296i	−0.161963	−	0.117673i	0.503851	−	0.863790i	$-0.331916\pi$
$431$	−3.36245	−	2.44296i	−0.161963	−	0.117673i	−0.665815	+	0.746117i	$0.731916\pi$
$432$	1.32937	−	4.09139i	0.0639596	−	0.196847i
$433$	6.87285	+	21.1525i	0.330288	+	1.01652i	0.968997	+	0.247073i	$0.0794689\pi$
$433$	6.87285	+	21.1525i	0.330288	+	1.01652i	−0.638709	+	0.769449i	$0.720531\pi$
$434$	2.00312	−	1.45536i	0.0961531	−	0.0698593i
$435$	5.83644	−	4.24042i	0.279836	−	0.203313i
$436$	−5.71490	−	17.5887i	−0.273694	−	0.842344i
$437$	−2.49536	+	7.67992i	−0.119369	+	0.367381i
$438$	2.40034	+	1.74395i	0.114693	+	0.0833293i
$439$	−21.6172			−1.03173			−0.515866	−	0.856669i	$-0.672530\pi$
$439$	−21.6172			−1.03173			−0.515866	+	0.856669i	$0.672530\pi$
$440$	−1.74496	−	2.82048i	−0.0831877	−	0.134461i
$441$	−2.35451			−0.112119
$442$	3.43096	+	2.49274i	0.163194	+	0.118568i
$443$	−4.00059	+	12.3126i	−0.190074	+	0.584987i	−0.999999	−	0.00154626i	$-0.999508\pi$
$443$	−4.00059	+	12.3126i	−0.190074	+	0.584987i	0.809925	+	0.586534i	$0.199508\pi$
$444$	1.39250	+	4.28567i	0.0660851	+	0.203389i
$445$	2.75882	−	2.00440i	0.130781	−	0.0950178i
$446$	−20.2575	+	14.7180i	−0.959222	+	0.696916i
$447$	4.55922	+	14.0318i	0.215644	+	0.663684i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−11.2098	−	8.14441i	−0.529024	−	0.384359i	0.290968	−	0.956733i	$-0.406023\pi$
$449$	−11.2098	−	8.14441i	−0.529024	−	0.384359i	−0.819993	+	0.572374i	$0.806023\pi$
$450$	−2.35451			−0.110993
$451$	2.38648	−	32.0686i	0.112375	−	1.51005i
$452$	11.9566			0.562391
$453$	13.3714	+	9.71486i	0.628241	+	0.456444i
$454$	−0.0565265	+	0.173971i	−0.00265292	+	0.00816485i
$455$	0.816775	+	2.51377i	0.0382910	+	0.117848i
$456$	1.24108	−	0.901698i	0.0581189	−	0.0422259i
$457$	8.08043	−	5.87077i	0.377986	−	0.274623i	−0.382528	−	0.923944i	$-0.624947\pi$
$457$	8.08043	−	5.87077i	0.377986	−	0.274623i	0.760515	+	0.649321i	$0.224947\pi$
$458$	−0.0415230	−	0.127795i	−0.00194024	−	0.00597145i
$459$	2.13298	−	6.56463i	0.0995588	−	0.306410i
$460$	3.42146	+	2.48584i	0.159526	+	0.115903i
$461$	27.8198			1.29570			0.647850	−	0.761768i	$-0.275668\pi$
$461$	27.8198			1.29570			0.647850	+	0.761768i	$0.275668\pi$
$462$	2.46614	+	1.00923i	0.114735	+	0.0469535i
$463$	−10.2727			−0.477413			−0.238707	−	0.971092i	$-0.576723\pi$
$463$	−10.2727			−0.477413			−0.238707	+	0.971092i	$0.576723\pi$
$464$	−7.26445	−	5.27793i	−0.337244	−	0.245022i
$465$	−0.614721	+	1.89192i	−0.0285070	+	0.0877355i
$466$	−0.905450	−	2.78669i	−0.0419441	−	0.129091i
$467$	−7.31181	+	5.31234i	−0.338350	+	0.245826i	−0.743965	−	0.668218i	$-0.767057\pi$
$467$	−7.31181	+	5.31234i	−0.338350	+	0.245826i	0.405615	+	0.914044i	$0.367057\pi$
$468$	−5.03475	+	3.65796i	−0.232731	+	0.169089i
$469$	3.24559	+	9.98890i	0.149867	+	0.461244i
$470$	−2.02252	+	6.22469i	−0.0932920	+	0.287123i
$471$	−3.02169	−	2.19538i	−0.139232	−	0.101158i
$472$	4.16663			0.191785
$473$	12.8921	−	3.15324i	0.592779	−	0.144986i
$474$	11.2059			0.514706
$475$	−1.54474	−	1.12232i	−0.0708774	−	0.0514954i
$476$	−0.495817	+	1.52597i	−0.0227257	+	0.0699426i
$477$	−7.31062	−	22.4998i	−0.334730	−	1.03019i
$478$	−6.69389	+	4.86340i	−0.306171	+	0.222447i
$479$	31.8995	−	23.1764i	1.45753	−	1.05895i	0.473528	−	0.880779i	$-0.342980\pi$
$479$	31.8995	−	23.1764i	1.45753	−	1.05895i	0.983999	−	0.178176i	$-0.0570196\pi$
$480$	−0.248272	−	0.764103i	−0.0113320	−	0.0348764i
$481$	4.58110	−	14.0992i	0.208880	−	0.642867i
$482$	−13.4169	−	9.74797i	−0.611124	−	0.444008i
$483$	−3.39781			−0.154606
$484$	7.84414	+	7.71164i	0.356552	+	0.350529i
$485$	−17.4713			−0.793329
$486$	12.7857	+	9.28935i	0.579971	+	0.421373i
$487$	−5.84616	+	17.9926i	−0.264915	+	0.815323i	0.726798	+	0.686851i	$0.241007\pi$
$487$	−5.84616	+	17.9926i	−0.264915	+	0.815323i	−0.991713	+	0.128473i	$0.958993\pi$
$488$	4.09845	+	12.6137i	0.185528	+	0.570997i
$489$	3.24602	−	2.35837i	0.146790	−	0.106649i
$490$	−0.809017	+	0.587785i	−0.0365477	+	0.0265534i
$491$	−0.469465	−	1.44487i	−0.0211867	−	0.0652059i	0.939904	−	0.341438i	$-0.110914\pi$
$491$	−0.469465	−	1.44487i	−0.0211867	−	0.0652059i	−0.961091	+	0.276232i	$0.910914\pi$
$492$	2.40719	−	7.40858i	0.108525	−	0.334005i
$493$	−11.6558	−	8.46842i	−0.524950	−	0.381399i
$494$	−5.04681			−0.227067
$495$	7.58542	−	1.85530i	0.340939	−	0.0833895i
$496$	2.47600			0.111176
$497$	3.70925	+	2.69493i	0.166383	+	0.120884i
$498$	3.36663	−	10.3614i	0.150862	−	0.464307i
$499$	3.65173	+	11.2389i	0.163474	+	0.503120i	0.998921	−	0.0464508i	$-0.0147911\pi$
$499$	3.65173	+	11.2389i	0.163474	+	0.503120i	−0.835447	+	0.549571i	$0.814791\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	−1.21448	+	0.882368i	−0.0542588	+	0.0394213i
$502$	−4.18675	−	12.8855i	−0.186864	−	0.575107i
$503$	−4.95943	+	15.2636i	−0.221130	+	0.680568i	0.777531	+	0.628844i	$0.216472\pi$
$503$	−4.95943	+	15.2636i	−0.221130	+	0.680568i	−0.998661	+	0.0517242i	$0.983528\pi$
$504$	−1.90484	−	1.38395i	−0.0848482	−	0.0616458i
$505$	−10.6494			−0.473891
$506$	−12.9816	−	5.31248i	−0.577101	−	0.236169i
$507$	4.83166			0.214581
$508$	10.8477	+	7.88134i	0.481290	+	0.349678i
$509$	12.4461	−	38.3052i	0.551665	−	1.69785i	−0.152929	−	0.988237i	$-0.548870\pi$
$509$	12.4461	−	38.3052i	0.551665	−	1.69785i	0.704593	−	0.709612i	$-0.251130\pi$
$510$	−0.398351	−	1.22600i	−0.0176393	−	0.0542882i
$511$	2.98764	−	2.17065i	0.132165	−	0.0960238i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	2.53831	+	7.81211i	0.112069	+	0.344913i
$514$	5.69288	−	17.5209i	0.251102	−	0.772813i
$515$	5.55525	+	4.03612i	0.244793	+	0.177853i
$516$	3.21506			0.141535
$517$	1.61097	−	21.6475i	0.0708502	−	0.952057i
$518$	5.60877			0.246435
$519$	−7.65679	−	5.56298i	−0.336096	−	0.244188i
$520$	−0.816775	+	2.51377i	−0.0358179	+	0.110236i
$521$	−8.49492	−	26.1447i	−0.372169	−	1.14542i	−0.945369	−	0.326003i	$-0.894298\pi$
$521$	−8.49492	−	26.1447i	−0.372169	−	1.14542i	0.573200	−	0.819416i	$-0.305702\pi$
$522$	17.1042	−	12.4269i	0.748631	−	0.543912i
$523$	−16.3716	+	11.8946i	−0.715879	+	0.520117i	−0.885065	−	0.465468i	$-0.845886\pi$
$523$	−16.3716	+	11.8946i	−0.715879	+	0.520117i	0.169186	+	0.985584i	$0.445886\pi$
$524$	−2.62642	−	8.08329i	−0.114736	−	0.353120i
$525$	0.248272	−	0.764103i	0.0108355	−	0.0333482i
$526$	15.5055	+	11.2654i	0.676070	+	0.491193i
$527$	3.97273			0.173055
$528$	1.40194	+	2.26605i	0.0610118	+	0.0986170i
$529$	−5.11424			−0.222358
$530$	−8.12885	−	5.90596i	−0.353095	−	0.256538i
$531$	−3.03157	+	9.33022i	−0.131559	+	0.404897i
$532$	−0.590037	−	1.81595i	−0.0255814	−	0.0787313i
$533$	−20.7329	+	15.0634i	−0.898043	+	0.652466i
$534$	−2.21651	+	1.61039i	−0.0959177	+	0.0696883i
$535$	−0.890804	−	2.74161i	−0.0385128	−	0.118530i
$536$	−3.24559	+	9.98890i	−0.140188	+	0.431455i
$537$	−6.74067	−	4.89738i	−0.290881	−	0.211338i
$538$	9.08666			0.391754
$539$	2.14322	−	2.53113i	0.0923148	−	0.109024i
$540$	4.30195			0.185126
$541$	−21.4595	−	15.5913i	−0.922617	−	0.670320i	0.0215570	−	0.999768i	$-0.493138\pi$
$541$	−21.4595	−	15.5913i	−0.922617	−	0.670320i	−0.944174	+	0.329447i	$0.893138\pi$
$542$	5.92506	−	18.2355i	0.254503	−	0.783281i
$543$	5.62926	+	17.3251i	0.241575	+	0.743491i
$544$	−1.29806	+	0.943099i	−0.0556541	+	0.0404350i
$545$	14.9618	−	10.8704i	0.640894	−	0.465637i
$546$	−0.656217	−	2.01963i	−0.0280835	−	0.0864321i
$547$	0.981371	−	3.02035i	0.0419604	−	0.129141i	−0.927882	−	0.372874i	$-0.878372\pi$
$547$	0.981371	−	3.02035i	0.0419604	−	0.129141i	0.969842	+	0.243734i	$0.0783722\pi$
$548$	−8.15058	−	5.92174i	−0.348175	−	0.252964i
$549$	−31.2275			−1.33276
$550$	2.14322	−	2.53113i	0.0913870	−	0.107928i
$551$	17.1452			0.730409
$552$	−2.74889	−	1.99718i	−0.117000	−	0.0850057i
$553$	4.31008	−	13.2651i	0.183283	−	0.564088i
$554$	−6.38712	−	19.6575i	−0.271363	−	0.835168i
$555$	−3.64561	+	2.64869i	−0.154748	+	0.112431i
$556$	−11.1807	+	8.12322i	−0.474165	+	0.344501i
$557$	−9.03031	−	27.7924i	−0.382626	−	1.17760i	−0.938188	−	0.346127i	$-0.887497\pi$
$557$	−9.03031	−	27.7924i	−0.382626	−	1.17760i	0.555561	−	0.831476i	$-0.312503\pi$
$558$	−1.80149	+	5.54443i	−0.0762633	+	0.234714i
$559$	−8.55699	−	6.21702i	−0.361922	−	0.262952i
$560$	−1.00000			−0.0422577
$561$	2.24941	+	3.63586i	0.0949703	+	0.153506i
$562$	−1.37153			−0.0578543
$563$	4.97934	+	3.61770i	0.209854	+	0.152468i	0.687748	−	0.725950i	$-0.258600\pi$
$563$	4.97934	+	3.61770i	0.209854	+	0.152468i	−0.477894	+	0.878418i	$0.658600\pi$
$564$	1.62495	−	5.00107i	0.0684226	−	0.210583i
$565$	3.69479	+	11.3714i	0.155441	+	0.478398i
$566$	5.20613	−	3.78247i	0.218830	−	0.158989i
$567$	2.91831	−	2.12028i	0.122558	−	0.0890433i
$568$	1.41681	+	4.36049i	0.0594479	+	0.182962i
$569$	−1.10952	+	3.41474i	−0.0465133	+	0.143153i	−0.971616	−	0.236564i	$-0.923979\pi$
$569$	−1.10952	+	3.41474i	−0.0465133	+	0.143153i	0.925103	+	0.379717i	$0.123979\pi$
$570$	1.24108	+	0.901698i	0.0519831	+	0.0377680i
$571$	−28.1128			−1.17649			−0.588243	−	0.808684i	$-0.700180\pi$
$571$	−28.1128			−1.17649			−0.588243	+	0.808684i	$0.700180\pi$
$572$	0.650572	−	8.74212i	0.0272018	−	0.365527i
$573$	6.81821			0.284835
$574$	−7.84406	−	5.69904i	−0.327405	−	0.237873i
$575$	−1.30688	+	4.02217i	−0.0545007	+	0.167736i
$576$	−0.727583	−	2.23927i	−0.0303160	−	0.0933029i
$577$	−23.0876	+	16.7741i	−0.961149	+	0.698315i	−0.953417	−	0.301655i	$-0.902461\pi$
$577$	−23.0876	+	16.7741i	−0.961149	+	0.698315i	−0.00773133	+	0.999970i	$0.502461\pi$
$578$	11.6705	−	8.47915i	0.485431	−	0.352686i
$579$	6.24599	+	19.2232i	0.259574	+	0.798888i
$580$	2.77477	−	8.53988i	0.115216	−	0.354599i
$581$	−10.9705	−	7.97052i	−0.455132	−	0.330673i
$582$	14.0368			0.581846
$583$	30.8422	+	12.6216i	1.27735	+	0.522734i
$584$	3.69293			0.152814
$585$	−5.03475	−	3.65796i	−0.208161	−	0.151238i
$586$	1.42065	−	4.37230i	0.0586864	−	0.180618i
$587$	−6.02913	−	18.5557i	−0.248849	−	0.765878i	−0.994980	−	0.100078i	$-0.968091\pi$
$587$	−6.02913	−	18.5557i	−0.248849	−	0.765878i	0.746131	−	0.665799i	$-0.231909\pi$
$588$	0.649985	−	0.472241i	0.0268049	−	0.0194749i
$589$	−3.82477	+	2.77886i	−0.157597	+	0.114501i
$590$	1.28756	+	3.96270i	0.0530080	+	0.163142i
$591$	3.29216	−	10.1322i	0.135421	−	0.416784i
$592$	4.53759	+	3.29675i	0.186494	+	0.135496i
$593$	4.84298			0.198877			0.0994386	−	0.995044i	$-0.468295\pi$
$593$	4.84298			0.198877			0.0994386	+	0.995044i	$0.468295\pi$
$594$	−13.8594	+	3.38984i	−0.568658	+	0.139087i
$595$	−1.60450			−0.0657779
$596$	14.8566	+	10.7940i	0.608552	+	0.442139i
$597$	−0.893315	+	2.74934i	−0.0365610	+	0.112523i
$598$	3.45427	+	10.6311i	0.141255	+	0.434740i
$599$	2.97029	−	2.15805i	0.121363	−	0.0881753i	−0.525448	−	0.850826i	$-0.676102\pi$
$599$	2.97029	−	2.15805i	0.121363	−	0.0881753i	0.646811	+	0.762650i	$0.276102\pi$
$600$	0.649985	−	0.472241i	0.0265355	−	0.0192792i
$601$	−0.535752	−	1.64887i	−0.0218538	−	0.0672590i	0.939535	−	0.342453i	$-0.111258\pi$
$601$	−0.535752	−	1.64887i	−0.0218538	−	0.0672590i	−0.961389	+	0.275194i	$0.911258\pi$
$602$	1.23659	−	3.80583i	0.0503997	−	0.155114i
$603$	−20.0064	−	14.5355i	−0.814724	−	0.591932i
$604$	20.5718			0.837055
$605$	−4.91024	+	9.84325i	−0.199629	+	0.400185i
$606$	8.55598			0.347563
$607$	23.0237	+	16.7277i	0.934504	+	0.678957i	0.947092	−	0.320964i	$-0.104007\pi$
$607$	23.0237	+	16.7277i	0.934504	+	0.678957i	−0.0125871	+	0.999921i	$0.504007\pi$
$608$	0.590037	−	1.81595i	0.0239292	−	0.0736464i
$609$	2.22932	+	6.86115i	0.0903367	+	0.278028i
$610$	−10.7299	+	7.79571i	−0.434440	+	0.315639i
$611$	−13.9955	+	10.1683i	−0.566198	+	0.411367i
$612$	−1.16740	−	3.59290i	−0.0471895	−	0.145234i
$613$	−2.49656	+	7.68362i	−0.100835	+	0.310339i	−0.988730	−	0.149707i	$-0.952167\pi$
$613$	−2.49656	+	7.68362i	−0.100835	+	0.310339i	0.887895	+	0.460046i	$0.152167\pi$
$614$	20.0670	+	14.5795i	0.809839	+	0.588382i
$615$	7.78984			0.314117
$616$	3.22166	−	0.787978i	0.129804	−	0.0317485i
$617$	2.53152			0.101915			0.0509577	−	0.998701i	$-0.483773\pi$
$617$	2.53152			0.101915			0.0509577	+	0.998701i	$0.483773\pi$
$618$	−4.46323	−	3.24272i	−0.179537	−	0.130441i
$619$	−8.53828	+	26.2781i	−0.343183	+	1.05621i	0.619367	+	0.785102i	$0.287389\pi$
$619$	−8.53828	+	26.2781i	−0.343183	+	1.05621i	−0.962550	+	0.271106i	$0.912611\pi$
$620$	0.765125	+	2.35481i	0.0307282	+	0.0945716i
$621$	14.7189	−	10.6939i	0.590650	−	0.429133i
$622$	−20.8745	+	15.1662i	−0.836990	+	0.608109i
$623$	1.05378	+	3.24319i	0.0422187	+	0.129936i
$624$	0.656217	−	2.01963i	0.0262697	−	0.0808499i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	16.5081			0.659797
$627$	−4.70886	−	1.92702i	−0.188054	−	0.0769577i
$628$	−4.64886			−0.185510
$629$	7.28054	+	5.28962i	0.290294	+	0.210911i
$630$	0.727583	−	2.23927i	0.0289876	−	0.0892147i
$631$	−9.98071	−	30.7175i	−0.397326	−	1.22284i	−0.927135	−	0.374727i	$-0.877737\pi$
$631$	−9.98071	−	30.7175i	−0.397326	−	1.22284i	0.529809	−	0.848117i	$-0.322263\pi$
$632$	11.2839	−	8.19826i	0.448851	−	0.326109i
$633$	−6.50362	+	4.72515i	−0.258496	+	0.187808i
$634$	0.720270	+	2.21676i	0.0286056	+	0.0880389i
$635$	−4.14347	+	12.7523i	−0.164428	+	0.506059i
$636$	6.53093	+	4.74499i	0.258968	+	0.188151i
$637$	−2.64314			−0.104725
$638$	−2.21014	+	29.6990i	−0.0875004	+	1.17580i
$639$	−10.7952			−0.427050
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	9.70231	−	29.8606i	0.383218	−	1.17942i	−0.554546	−	0.832153i	$-0.687108\pi$
$641$	9.70231	−	29.8606i	0.383218	−	1.17942i	0.937765	−	0.347272i	$-0.112892\pi$
$642$	0.715694	+	2.20268i	0.0282462	+	0.0869328i
$643$	−3.33755	+	2.42487i	−0.131620	+	0.0956275i	−0.651647	−	0.758522i	$-0.725922\pi$
$643$	−3.33755	+	2.42487i	−0.131620	+	0.0956275i	0.520027	+	0.854150i	$0.325922\pi$
$644$	−3.42146	+	2.48584i	−0.134824	+	0.0979556i
$645$	0.993508	+	3.05770i	0.0391193	+	0.120397i
$646$	0.946712	−	2.91368i	0.0372479	−	0.114637i
$647$	−16.9317	−	12.3016i	−0.665655	−	0.483626i	0.202913	−	0.979197i	$-0.434959\pi$
$647$	−16.9317	−	12.3016i	−0.665655	−	0.483626i	−0.868568	+	0.495570i	$0.834959\pi$
$648$	3.60723			0.141705
$649$	−7.27060	−	11.7519i	−0.285396	−	0.461303i
$650$	−2.64314			−0.103672
$651$	−1.60936	−	1.16927i	−0.0630758	−	0.0458273i
$652$	1.54323	−	4.74958i	0.0604376	−	0.186008i
$653$	−0.620662	−	1.91020i	−0.0242884	−	0.0747519i	0.938178	−	0.346154i	$-0.112513\pi$
$653$	−0.620662	−	1.91020i	−0.0242884	−	0.0747519i	−0.962466	+	0.271402i	$0.912513\pi$
$654$	−12.0207	+	8.73355i	−0.470046	+	0.341509i
$655$	6.87606	−	4.99575i	0.268670	−	0.195200i
$656$	−2.99616	−	9.22125i	−0.116981	−	0.360029i
$657$	−2.68691	+	8.26946i	−0.104826	+	0.322622i
$658$	−5.29503	−	3.84707i	−0.206422	−	0.149974i
$659$	11.7132			0.456282			0.228141	−	0.973628i	$-0.426735\pi$
$659$	11.7132			0.456282			0.228141	+	0.973628i	$0.426735\pi$
$660$	−1.72191	+	2.03357i	−0.0670254	+	0.0791568i
$661$	35.8654			1.39500			0.697502	−	0.716583i	$-0.254295\pi$
$661$	35.8654			1.39500			0.697502	+	0.716583i	$0.254295\pi$
$662$	−5.29429	−	3.84653i	−0.205769	−	0.149500i
$663$	1.05290	−	3.24049i	0.0408912	−	0.125850i
$664$	−4.19035	−	12.8966i	−0.162617	−	0.500484i
$665$	1.54474	−	1.12232i	0.0599023	−	0.0435216i
$666$	−10.6838	+	7.76223i	−0.413988	+	0.300780i
$667$	−11.7350	−	36.1165i	−0.454379	−	1.39844i
$668$	−0.577388	+	1.77702i	−0.0223398	+	0.0687549i
$669$	16.2754	+	11.8248i	0.629244	+	0.457172i
$670$	−10.5029			−0.405764
$671$	28.4252	−	33.5700i	1.09734	−	1.29596i
$672$	0.803425			0.0309928
$673$	26.9902	+	19.6095i	1.04039	+	0.755891i	0.970362	−	0.241654i	$-0.0776900\pi$
$673$	26.9902	+	19.6095i	1.04039	+	0.755891i	0.0700317	+	0.997545i	$0.477690\pi$
$674$	5.15321	−	15.8600i	0.198494	−	0.610902i
$675$	1.32937	+	4.09139i	0.0511676	+	0.157478i
$676$	4.86528	−	3.53484i	0.187126	−	0.135955i
$677$	10.7383	−	7.80184i	0.412707	−	0.299849i	−0.361990	−	0.932182i	$-0.617903\pi$
$677$	10.7383	−	7.80184i	0.412707	−	0.299849i	0.774697	+	0.632333i	$0.217903\pi$
$678$	−2.96849	−	9.13607i	−0.114004	−	0.350869i
$679$	5.39891	−	16.6161i	0.207191	−	0.637669i
$680$	−1.29806	−	0.943099i	−0.0497785	−	0.0361662i
$681$	0.146965			0.00563173
$682$	−4.32052	−	6.98351i	−0.165441	−	0.267412i
$683$	−15.3702			−0.588123			−0.294061	−	0.955787i	$-0.595007\pi$
$683$	−15.3702			−0.588123			−0.294061	+	0.955787i	$0.595007\pi$
$684$	3.63710	+	2.64250i	0.139068	+	0.101039i
$685$	3.11324	−	9.58158i	0.118951	−	0.366093i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−0.0873393	+	0.0634557i	−0.00333220	+	0.00242099i
$688$	3.23744	−	2.35214i	0.123426	−	0.0896743i
$689$	−8.20680	−	25.2579i	−0.312654	−	0.962251i
$690$	1.04998	−	3.23151i	0.0399721	−	0.123021i
$691$	−16.8112	−	12.2141i	−0.639529	−	0.464645i	0.220159	−	0.975464i	$-0.429342\pi$
$691$	−16.8112	−	12.2141i	−0.639529	−	0.464645i	−0.859688	+	0.510819i	$0.829342\pi$
$692$	−11.7799			−0.447806
$693$	−0.579529	+	7.78749i	−0.0220145	+	0.295822i
$694$	29.2816			1.11151
$695$	−11.1807	−	8.12322i	−0.424106	−	0.308131i
$696$	−2.22932	+	6.86115i	−0.0845023	+	0.260071i
$697$	−4.80733	−	14.7955i	−0.182091	−	0.560418i
$698$	13.5782	−	9.86516i	0.513943	−	0.373402i
$699$	−1.90452	+	1.38371i	−0.0720355	+	0.0523368i
$700$	−0.309017	−	0.951057i	−0.0116797	−	0.0359466i
$701$	−1.29353	+	3.98108i	−0.0488560	+	0.150363i	−0.972508	−	0.232868i	$-0.925189\pi$
$701$	−1.29353	+	3.98108i	−0.0488560	+	0.150363i	0.923652	+	0.383232i	$0.125189\pi$
$702$	9.19904	+	6.68349i	0.347195	+	0.252252i
$703$	−10.7094			−0.403912
$704$	3.06954	+	1.25616i	0.115688	+	0.0473432i
$705$	5.25844			0.198044
$706$	−18.5354	−	13.4667i	−0.697588	−	0.506828i
$707$	3.29084	−	10.1282i	0.123765	−	0.380909i
$708$	−1.03446	−	3.18374i	−0.0388773	−	0.119652i
$709$	−4.43769	+	3.22417i	−0.166661	+	0.121086i	−0.667989	−	0.744171i	$-0.732845\pi$
$709$	−4.43769	+	3.22417i	−0.166661	+	0.121086i	0.501328	+	0.865257i	$0.332845\pi$
$710$	−3.70925	+	2.69493i	−0.139206	+	0.101139i
$711$	10.1481	+	31.2327i	0.380584	+	1.17132i
$712$	−1.05378	+	3.24319i	−0.0394919	+	0.121544i
$713$	8.47153	+	6.15492i	0.317261	+	0.230504i
$714$	1.28909			0.0482431
$715$	8.51529	−	2.08273i	0.318454	−	0.0778898i
$716$	−10.3705			−0.387564
$717$	5.37804	+	3.90738i	0.200847	+	0.145924i
$718$	2.58498	−	7.95576i	0.0964707	−	0.296906i
$719$	−5.13007	−	15.7887i	−0.191319	−	0.588820i	−1.00000		0.000572186i	$-0.999818\pi$
$719$	−5.13007	−	15.7887i	−0.191319	−	0.588820i	0.808681	−	0.588248i	$-0.200182\pi$
$720$	1.90484	−	1.38395i	0.0709891	−	0.0515766i
$721$	−5.55525	+	4.03612i	−0.206888	+	0.150313i
$722$	−4.74471	−	14.6027i	−0.176580	−	0.543456i
$723$	−4.11740	+	12.6721i	−0.153128	+	0.471279i
$724$	18.3435	+	13.3273i	0.681729	+	0.495305i
$725$	8.97936			0.333485
$726$	3.94501	−	7.90831i	0.146413	−	0.293505i
$727$	−22.9499			−0.851164			−0.425582	−	0.904920i	$-0.639931\pi$
$727$	−22.9499			−0.851164			−0.425582	+	0.904920i	$0.639931\pi$
$728$	−2.13834	−	1.55360i	−0.0792523	−	0.0575802i
$729$	0.579598	−	1.78382i	0.0214666	−	0.0660673i
$730$	1.14118	+	3.51218i	0.0422368	+	0.129992i
$731$	5.19445	−	3.77399i	0.192124	−	0.139586i
$732$	8.62065	−	6.26327i	0.318629	−	0.231497i
$733$	−4.92826	−	15.1676i	−0.182029	−	0.560229i	0.817855	−	0.575424i	$-0.195163\pi$
$733$	−4.92826	−	15.1676i	−0.182029	−	0.560229i	−0.999885	+	0.0151952i	$0.995163\pi$
$734$	−0.557226	+	1.71496i	−0.0205676	+	0.0633005i
$735$	0.649985	+	0.472241i	0.0239750	+	0.0174189i
$736$	−4.22916			−0.155889
$737$	33.8369	−	8.27609i	1.24640	−	0.304854i
$738$	22.8288			0.840340
$739$	33.7005	+	24.4848i	1.23969	+	0.900688i	0.997578	−	0.0695594i	$-0.0221594\pi$
$739$	33.7005	+	24.4848i	1.23969	+	0.900688i	0.242114	+	0.970248i	$0.422159\pi$
$740$	−1.73320	+	5.33426i	−0.0637139	+	0.196091i
$741$	1.25298	+	3.85628i	0.0460294	+	0.141664i
$742$	8.12885	−	5.90596i	0.298420	−	0.216815i
$743$	33.9657	−	24.6775i	1.24608	−	0.905330i	0.248092	−	0.968736i	$-0.420196\pi$
$743$	33.9657	−	24.6775i	1.24608	−	0.905330i	0.997988	+	0.0634061i	$0.0201963\pi$
$744$	−0.614721	−	1.89192i	−0.0225368	−	0.0693610i
$745$	−5.67473	+	17.4650i	−0.207906	+	0.639869i
$746$	−7.77021	−	5.64539i	−0.284488	−	0.206692i
$747$	31.9277			1.16817
$748$	4.92506	+	2.01550i	0.180078	+	0.0736939i
$749$	2.88270			0.105332
$750$	0.649985	+	0.472241i	0.0237341	+	0.0172438i
$751$	9.56603	−	29.4412i	0.349070	−	1.07433i	−0.610299	−	0.792171i	$-0.708951\pi$
$751$	9.56603	−	29.4412i	0.349070	−	1.07433i	0.959369	−	0.282155i	$-0.0910492\pi$
$752$	−2.02252	−	6.22469i	−0.0737538	−	0.226991i
$753$	−8.80638	+	6.39821i	−0.320922	+	0.233164i
$754$	19.2009	−	13.9503i	0.699257	−	0.508040i
$755$	6.35704	+	19.5650i	0.231356	+	0.712042i
$756$	−1.32937	+	4.09139i	−0.0483489	+	0.148803i
$757$	−16.1658	−	11.7452i	−0.587557	−	0.426885i	0.253883	−	0.967235i	$-0.418292\pi$
$757$	−16.1658	−	11.7452i	−0.587557	−	0.426885i	−0.841441	+	0.540349i	$0.818292\pi$
$758$	−5.94046			−0.215767
$759$	−0.836324	+	11.2382i	−0.0303566	+	0.407920i
$760$	1.90940			0.0692612
$761$	−6.73485	−	4.89316i	−0.244138	−	0.177377i	0.458987	−	0.888443i	$-0.348213\pi$
$761$	−6.73485	−	4.89316i	−0.244138	−	0.177377i	−0.703125	+	0.711066i	$0.748213\pi$
$762$	3.32897	−	10.2455i	0.120596	−	0.371155i
$763$	5.71490	+	17.5887i	0.206893	+	0.636753i
$764$	6.86567	−	4.98820i	0.248391	−	0.180467i
$765$	3.05630	−	2.22053i	0.110501	−	0.0802836i
$766$	−9.09307	−	27.9856i	−0.328546	−	1.01116i
$767$	−3.40320	+	10.4740i	−0.122882	+	0.378193i
$768$	0.649985	+	0.472241i	0.0234543	+	0.0170405i
$769$	−38.3934			−1.38450			−0.692251	−	0.721657i	$-0.743381\pi$
$769$	−38.3934			−1.38450			−0.692251	+	0.721657i	$0.743381\pi$
$770$	1.74496	+	2.82048i	0.0628840	+	0.101643i
$771$	−14.8011			−0.533050
$772$	20.3531	+	14.7874i	0.732525	+	0.532210i
$773$	8.68995	−	26.7449i	0.312556	−	0.961948i	−0.664193	−	0.747561i	$-0.731225\pi$
$773$	8.68995	−	26.7449i	0.312556	−	0.961948i	0.976749	−	0.214387i	$-0.0687753\pi$
$774$	2.91156	+	8.96087i	0.104654	+	0.322092i
$775$	−2.00312	+	1.45536i	−0.0719544	+	0.0522779i
$776$	14.1345	−	10.2693i	0.507400	−	0.368648i
$777$	−1.39250	−	4.28567i	−0.0499557	−	0.153748i
$778$	−5.82858	+	17.9385i	−0.208965	+	0.643127i
$779$	14.9774	+	10.8818i	0.536623	+	0.389879i
$780$	2.12356			0.0760358
$781$	9.82640	−	11.6049i	0.351616	−	0.415258i
$782$	−6.78566			−0.242655
$783$	−31.2513	−	22.7054i	−1.11683	−	0.811424i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−1.43658	−	4.42133i	−0.0512736	−	0.157804i
$786$	−5.52440	+	4.01371i	−0.197049	+	0.143164i
$787$	24.4296	−	17.7491i	0.870821	−	0.632688i	−0.0599865	−	0.998199i	$-0.519106\pi$
$787$	24.4296	−	17.7491i	0.870821	−	0.632688i	0.930807	+	0.365511i	$0.119106\pi$
$788$	−4.09766	−	12.6113i	−0.145973	−	0.449259i
$789$	4.75833	−	14.6446i	0.169401	−	0.521363i
$790$	11.2839	+	8.19826i	0.401464	+	0.291681i
$791$	−11.9566			−0.425128
$792$	−5.04622	+	5.95957i	−0.179310	+	0.211764i
$793$	−35.0556			−1.24486
$794$	−20.5929	−	14.9616i	−0.730815	−	0.530968i
$795$	−2.49459	+	7.67756i	−0.0884740	+	0.272295i
$796$	1.11188	+	3.42203i	0.0394097	+	0.121290i
$797$	−37.5565	+	27.2864i	−1.33032	+	0.966533i	−0.330578	+	0.943779i	$0.607244\pi$
$797$	−37.5565	+	27.2864i	−1.33032	+	0.966533i	−0.999741	+	0.0227544i	$0.992756\pi$
$798$	−1.24108	+	0.901698i	−0.0439338	+	0.0319198i
$799$	−3.24513	−	9.98748i	−0.114804	−	0.353332i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	−6.49567	−	4.71938i	−0.229513	−	0.166751i
$802$	14.9867			0.529198
$803$	−6.44400	−	10.4158i	−0.227404	−	0.367567i
$804$	8.43833			0.297597
$805$	−3.42146	−	2.48584i	−0.120591	−	0.0876142i
$806$	−2.02233	+	6.22410i	−0.0712336	+	0.219235i
$807$	−2.25596	−	6.94314i	−0.0794136	−	0.244410i
$808$	8.61553	−	6.25955i	0.303093	−	0.220210i
$809$	9.76308	−	7.09329i	0.343251	−	0.249387i	−0.402781	−	0.915296i	$-0.631956\pi$
$809$	9.76308	−	7.09329i	0.343251	−	0.249387i	0.746032	+	0.665910i	$0.231956\pi$
$810$	1.11470	+	3.43068i	0.0391664	+	0.120542i
$811$	4.62097	−	14.2219i	0.162264	−	0.499398i	−0.836560	−	0.547875i	$-0.815437\pi$
$811$	4.62097	−	14.2219i	0.162264	−	0.499398i	0.998824	+	0.0484772i	$0.0154368\pi$
$812$	7.26445	+	5.27793i	0.254932	+	0.185219i
$813$	−15.4048			−0.540270
$814$	1.38052	−	18.5509i	0.0483872	−	0.650208i
$815$	4.99400			0.174932
$816$	1.04290	+	0.757710i	0.0365087	+	0.0265251i
$817$	−2.36115	+	7.26686i	−0.0826060	+	0.254235i
$818$	1.50113	+	4.61999i	0.0524857	+	0.161534i
$819$	5.03475	−	3.65796i	0.175928	−	0.127819i
$820$	7.84406	−	5.69904i	0.273926	−	0.199019i
$821$	7.37291	+	22.6915i	0.257316	+	0.791938i	0.993364	+	0.115009i	$0.0366897\pi$
$821$	7.37291	+	22.6915i	0.257316	+	0.791938i	−0.736048	+	0.676929i	$0.763310\pi$
$822$	−2.50126	+	7.69808i	−0.0872414	+	0.268501i
$823$	34.2941	+	24.9162i	1.19542	+	0.868523i	0.993826	−	0.110947i	$-0.0353884\pi$
$823$	34.2941	+	24.9162i	1.19542	+	0.868523i	0.201592	+	0.979470i	$0.435388\pi$
$824$	−6.86666			−0.239212
$825$	−2.46614	−	1.00923i	−0.0858601	−	0.0351368i
$826$	−4.16663			−0.144976
$827$	42.8451	+	31.1288i	1.48987	+	1.08245i	0.974205	+	0.225664i	$0.0724550\pi$
$827$	42.8451	+	31.1288i	1.48987	+	1.08245i	0.515665	+	0.856790i	$0.327545\pi$
$828$	3.07706	−	9.47022i	0.106935	−	0.329113i
$829$	13.8461	+	42.6138i	0.480894	+	1.48004i	0.837841	+	0.545914i	$0.183818\pi$
$829$	13.8461	+	42.6138i	0.480894	+	1.48004i	−0.356947	+	0.934125i	$0.616182\pi$
$830$	10.9705	−	7.97052i	0.380791	−	0.276661i
$831$	−13.4346	+	9.76083i	−0.466042	+	0.338599i
$832$	−0.816775	−	2.51377i	−0.0283166	−	0.0871494i
$833$	0.495817	−	1.52597i	0.0171790	−	0.0528716i
$834$	8.98282	+	6.52640i	0.311049	+	0.225991i
$835$	−1.86847			−0.0646610
$836$	−6.15144	+	1.50456i	−0.212752	+	0.0520365i
$837$	10.6516			0.368174
$838$	1.43595	+	1.04328i	0.0496039	+	0.0360394i
$839$	−12.5495	+	38.6233i	−0.433255	+	1.33342i	0.461609	+	0.887084i	$0.347272\pi$
$839$	−12.5495	+	38.6233i	−0.433255	+	1.33342i	−0.894864	+	0.446339i	$0.852728\pi$
$840$	0.248272	+	0.764103i	0.00856620	+	0.0263640i
$841$	−41.7686	+	30.3467i	−1.44030	+	1.04644i
$842$	13.6922	−	9.94799i	0.471866	−	0.342830i
$843$	0.340511	+	1.04799i	0.0117278	+	0.0360946i
$844$	−3.09196	+	9.51608i	−0.106430	+	0.327557i
$845$	4.86528	+	3.53484i	0.167371	+	0.121602i
$846$	15.4103			0.529817
$847$	−7.84414	−	7.71164i	−0.269528	−	0.264975i
$848$	10.0478			0.345043
$849$	−4.18273	−	3.03893i	−0.143551	−	0.104296i
$850$	0.495817	−	1.52597i	0.0170064	−	0.0523402i
$851$	7.32999	+	22.5594i	0.251269	+	0.773326i
$852$	2.98011	−	2.16517i	0.102097	−	0.0741776i
$853$	0.0945276	−	0.0686783i	0.00323656	−	0.00235150i	−0.586166	−	0.810191i	$-0.699363\pi$
$853$	0.0945276	−	0.0686783i	0.00323656	−	0.00235150i	0.589402	+	0.807840i	$0.299363\pi$
$854$	−4.09845	−	12.6137i	−0.140246	−	0.431633i
$855$	−1.38925	+	4.27566i	−0.0475112	+	0.146225i
$856$	2.33215	+	1.69441i	0.0797114	+	0.0579137i
$857$	22.2623			0.760465			0.380233	−	0.924891i	$-0.375844\pi$
$857$	22.2623			0.760465			0.380233	+	0.924891i	$0.375844\pi$
$858$	−6.84140	+	1.67332i	−0.233561	+	0.0571262i
$859$	37.0142			1.26291			0.631454	−	0.775413i	$-0.282458\pi$
$859$	37.0142			1.26291			0.631454	+	0.775413i	$0.282458\pi$
$860$	3.23744	+	2.35214i	0.110396	+	0.0802071i
$861$	−2.40719	+	7.40858i	−0.0820369	+	0.252484i
$862$	1.28434	+	3.95279i	0.0437448	+	0.134633i
$863$	−35.6176	+	25.8777i	−1.21244	+	0.880886i	−0.995450	−	0.0952888i	$-0.969623\pi$
$863$	−35.6176	+	25.8777i	−1.21244	+	0.880886i	−0.216986	+	0.976175i	$0.569623\pi$
$864$	−3.48035	+	2.52862i	−0.118404	+	0.0860254i
$865$	−3.64020	−	11.2034i	−0.123771	−	0.380927i
$866$	6.87285	−	21.1525i	0.233549	−	0.718790i
$867$	−9.37641	−	6.81236i	−0.318440	−	0.231360i
$868$	−2.47600			−0.0840408
$869$	−42.8130	−	17.5205i	−1.45233	−	0.594342i
$870$	−7.21424			−0.244586
$871$	−22.4589	−	16.3174i	−0.760991	−	0.552892i
$872$	−5.71490	+	17.5887i	−0.193531	+	0.595627i
$873$	12.7118	+	39.1229i	0.430229	+	1.32411i
$874$	6.53293	−	4.74645i	0.220980	−	0.160551i
$875$	0.809017	−	0.587785i	0.0273498	−	0.0198708i
$876$	−0.916850	−	2.82177i	−0.0309775	−	0.0953389i
$877$	−9.08815	+	27.9704i	−0.306885	+	0.944495i	0.672082	+	0.740477i	$0.265400\pi$
$877$	−9.08815	+	27.9704i	−0.306885	+	0.944495i	−0.978967	+	0.204018i	$0.934600\pi$
$878$	17.4887	+	12.7063i	0.590214	+	0.428816i
$879$	−3.69359			−0.124582
$880$	−0.246136	+	3.30748i	−0.00829725	+	0.111495i
$881$	34.0756			1.14804			0.574019	−	0.818842i	$-0.305384\pi$
$881$	34.0756			1.14804			0.574019	+	0.818842i	$0.305384\pi$
$882$	1.90484	+	1.38395i	0.0641392	+	0.0465999i
$883$	−5.69682	+	17.5330i	−0.191713	+	0.590033i	0.808286	+	0.588790i	$0.200396\pi$
$883$	−5.69682	+	17.5330i	−0.191713	+	0.590033i	−0.999999	+	0.00124270i	$0.999604\pi$
$884$	−1.31051	−	4.03334i	−0.0440773	−	0.135656i
$885$	2.70825	−	1.96766i	0.0910367	−	0.0661421i
$886$	10.4737	−	7.60958i	0.351870	−	0.255649i
$887$	0.678672	+	2.08874i	0.0227876	+	0.0701329i	0.961804	−	0.273740i	$-0.0882609\pi$
$887$	0.678672	+	2.08874i	0.0227876	+	0.0701329i	−0.939016	+	0.343873i	$0.888261\pi$
$888$	1.39250	−	4.28567i	0.0467292	−	0.143818i
$889$	−10.8477	−	7.88134i	−0.363821	−	0.264332i
$890$	−3.41009			−0.114307
$891$	−6.29447	−	10.1741i	−0.210873	−	0.340846i
$892$	25.0397			0.838391
$893$	10.1103	+	7.34559i	0.338330	+	0.245811i
$894$	4.55922	−	14.0318i	0.152483	−	0.469295i
$895$	−3.20466	−	9.86294i	−0.107120	−	0.329682i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	7.26569	−	5.27883i	0.242594	−	0.176255i
$898$	4.28177	+	13.1779i	0.142885	+	0.439753i
$899$	6.87033	−	21.1447i	0.229138	−	0.705216i
$900$	1.90484	+	1.38395i	0.0634946	+	0.0461315i
$901$	16.1217			0.537091
$902$	−20.7802	+	24.5413i	−0.691904	+	0.817137i
$903$	−3.21506			−0.106990
$904$	−9.67309	−	7.02791i	−0.321722	−	0.233745i
$905$	−7.00658	+	21.5640i	−0.232907	+	0.716813i
$906$	−5.10741	−	15.7190i	−0.169682	−	0.522228i
$907$	−3.92055	+	2.84844i	−0.130180	+	0.0945810i	−0.650970	−	0.759104i	$-0.725637\pi$
$907$	−3.92055	+	2.84844i	−0.130180	+	0.0945810i	0.520790	+	0.853685i	$0.325637\pi$
$908$	0.147988	−	0.107520i	0.00491117	−	0.00356817i
$909$	7.74831	+	23.8469i	0.256995	+	0.790950i
$910$	0.816775	−	2.51377i	0.0270758	−	0.0833308i
$911$	−48.2638	−	35.0657i	−1.59905	−	1.16178i	−0.889301	−	0.457323i	$-0.848808\pi$
$911$	−48.2638	−	35.0657i	−1.59905	−	1.16178i	−0.709749	−	0.704455i	$-0.751192\pi$
$912$	−1.53406			−0.0507978
$913$	−29.0625	+	34.3228i	−0.961830	+	1.13592i
$914$	−9.98796			−0.330372
$915$	8.62065	+	6.26327i	0.284990	+	0.207057i
$916$	−0.0415230	+	0.127795i	−0.00137196	+	0.00422246i
$917$	2.62642	+	8.08329i	0.0867321	+	0.266934i
$918$	−5.58420	+	4.05716i	−0.184306	+	0.133906i
$919$	13.6856	−	9.94317i	0.451446	−	0.327995i	−0.338720	−	0.940887i	$-0.609994\pi$
$919$	13.6856	−	9.94317i	0.451446	−	0.327995i	0.790167	+	0.612892i	$0.209994\pi$
$920$	−1.30688	−	4.02217i	−0.0430866	−	0.132607i
$921$	6.15819	−	18.9530i	0.202919	−	0.624521i
$922$	−22.5067	−	16.3521i	−0.741220	−	0.538528i
$923$	−12.1185			−0.398885
$924$	−1.40194	−	2.26605i	−0.0461206	−	0.0745474i
$925$	−5.60877			−0.184415
$926$	8.31079	+	6.03815i	0.273110	+	0.198426i
$927$	4.99607	−	15.3763i	0.164092	−	0.505024i
$928$	2.77477	+	8.53988i	0.0910864	+	0.280335i
$929$	−19.4102	+	14.1024i	−0.636829	+	0.462683i	−0.858759	−	0.512379i	$-0.828764\pi$
$929$	−19.4102	+	14.1024i	−0.636829	+	0.462683i	0.221931	+	0.975062i	$0.428764\pi$
$930$	1.60936	−	1.16927i	0.0527730	−	0.0383418i
$931$	0.590037	+	1.81595i	0.0193377	+	0.0595153i
$932$	−0.905450	+	2.78669i	−0.0296590	+	0.0912810i
$933$	16.7711	+	12.1849i	0.549060	+	0.398915i
$934$	9.03790			0.295729
$935$	−0.394924	+	5.30684i	−0.0129154	+	0.173552i
$936$	6.22329			0.203415
$937$	−24.6885	−	17.9373i	−0.806539	−	0.585985i	0.106286	−	0.994336i	$-0.466104\pi$
$937$	−24.6885	−	17.9373i	−0.806539	−	0.585985i	−0.912825	+	0.408351i	$0.866104\pi$
$938$	3.24559	−	9.98890i	0.105972	−	0.326149i
$939$	−4.09850	−	12.6139i	−0.133750	−	0.411639i
$940$	5.29503	−	3.84707i	0.172705	−	0.125478i
$941$	−14.2918	+	10.3836i	−0.465898	+	0.338495i	−0.795841	−	0.605506i	$-0.792971\pi$
$941$	−14.2918	+	10.3836i	−0.465898	+	0.338495i	0.329942	+	0.944001i	$0.392971\pi$
$942$	1.15418	+	3.55221i	0.0376053	+	0.115737i
$943$	12.6712	−	38.9981i	0.412633	−	1.26995i
$944$	−3.37088	−	2.44909i	−0.109713	−	0.0797109i
$945$	−4.30195			−0.139942
$946$	−12.2833	−	5.02675i	−0.399366	−	0.163434i
$947$	4.02455			0.130780			0.0653902	−	0.997860i	$-0.479171\pi$
$947$	4.02455			0.130780			0.0653902	+	0.997860i	$0.479171\pi$
$948$	−9.06579	−	6.58669i	−0.294443	−	0.213926i
$949$	−3.01629	+	9.28318i	−0.0979128	+	0.301345i
$950$	0.590037	+	1.81595i	0.0191433	+	0.0589171i
$951$	1.51501	−	1.10072i	0.0491276	−	0.0356933i
$952$	1.29806	−	0.943099i	0.0420705	−	0.0305660i
$953$	−15.9308	−	49.0300i	−0.516049	−	1.58824i	−0.781365	−	0.624075i	$-0.785476\pi$
$953$	−15.9308	−	49.0300i	−0.516049	−	1.58824i	0.265316	−	0.964162i	$-0.414524\pi$
$954$	−7.31062	+	22.4998i	−0.236690	+	0.728457i
$955$	6.86567	+	4.98820i	0.222168	+	0.161414i
$956$	8.27410			0.267604
$957$	23.2418	−	5.68466i	0.751302	−	0.183759i
$958$	−39.4300			−1.27392
$959$	8.15058	+	5.92174i	0.263196	+	0.191223i
$960$	−0.248272	+	0.764103i	−0.00801294	+	0.0246613i
$961$	−7.68508	−	23.6522i	−0.247906	−	0.762975i
$962$	−11.9935	+	8.71377i	−0.386685	+	0.280943i
$963$	−5.49108	+	3.98950i	−0.176947	+	0.128560i
$964$	5.12481	+	15.7725i	0.165059	+	0.508000i
$965$	−7.77420	+	23.9265i	−0.250260	+	0.770222i
$966$	2.74889	+	1.99718i	0.0884440	+	0.0642583i
$967$	25.3238			0.814359			0.407179	−	0.913348i	$-0.366512\pi$
$967$	25.3238			0.814359			0.407179	+	0.913348i	$0.366512\pi$
$968$	−1.81325	−	10.8495i	−0.0582802	−	0.348717i
$969$	−2.46139			−0.0790713
$970$	14.1345	+	10.2693i	0.453833	+	0.329729i
$971$	−12.7509	+	39.2431i	−0.409195	+	1.25937i	0.508146	+	0.861271i	$0.330331\pi$
$971$	−12.7509	+	39.2431i	−0.409195	+	1.25937i	−0.917341	+	0.398102i	$0.869669\pi$
$972$	−4.88370	−	15.0305i	−0.156645	−	0.482103i
$973$	11.1807	−	8.12322i	0.358435	−	0.260418i
$974$	15.3054	−	11.1201i	0.490418	−	0.356309i
$975$	0.656217	+	2.01963i	0.0210158	+	0.0646799i
$976$	4.09845	−	12.6137i	0.131188	−	0.403756i
$977$	−11.3840	−	8.27097i	−0.364207	−	0.264612i	0.390598	−	0.920561i	$-0.372268\pi$
$977$	−11.3840	−	8.27097i	−0.364207	−	0.264612i	−0.754805	+	0.655950i	$0.772268\pi$
$978$	−4.01230			−0.128299
$979$	10.9862	−	2.68708i	0.351119	−	0.0858794i
$980$	1.00000			0.0319438
$981$	−35.2277	−	25.5944i	−1.12473	−	0.817167i
$982$	−0.469465	+	1.44487i	−0.0149812	+	0.0461075i
$983$	15.8842	+	48.8867i	0.506629	+	1.55924i	0.798015	+	0.602637i	$0.205883\pi$
$983$	15.8842	+	48.8867i	0.506629	+	1.55924i	−0.291386	+	0.956605i	$0.594117\pi$
$984$	−6.30212	+	4.57875i	−0.200904	+	0.145965i
$985$	10.7278	−	7.79421i	0.341816	−	0.248344i
$986$	4.45211	+	13.7022i	0.141784	+	0.436367i
$987$	−1.62495	+	5.00107i	−0.0517226	+	0.159186i
$988$	4.08295	+	2.96644i	0.129896	+	0.0943750i
$989$	16.9238			0.538145
$990$	−7.22725	−	2.95763i	−0.229697	−	0.0939997i
$991$	45.9460			1.45952			0.729761	−	0.683702i	$-0.239631\pi$
$991$	45.9460			1.45952			0.729761	+	0.683702i	$0.239631\pi$
$992$	−2.00312	−	1.45536i	−0.0635993	−	0.0462076i
$993$	−1.62472	+	5.00037i	−0.0515589	+	0.158682i
$994$	−1.41681	−	4.36049i	−0.0449384	−	0.138306i
$995$	−2.91095	+	2.11493i	−0.0922833	+	0.0670477i
$996$	−8.81395	+	6.40371i	−0.279281	+	0.202909i
$997$	3.77275	+	11.6113i	0.119484	+	0.367734i	0.992856	−	0.119320i	$-0.0380714\pi$
$997$	3.77275	+	11.6113i	0.119484	+	0.367734i	−0.873372	+	0.487054i	$0.838071\pi$
$998$	3.65173	−	11.2389i	0.115593	−	0.355760i
$999$	19.5205	+	14.1824i	0.617600	+	0.448713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.g.631.2	yes	12
11.3	even	5	inner	770.2.n.g.421.2	✓	12
11.5	even	5		8470.2.a.db.1.3		6
11.6	odd	10		8470.2.a.cv.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.421.2	✓	12	11.3	even	5	inner
770.2.n.g.631.2	yes	12	1.1	even	1	trivial
8470.2.a.cv.1.3		6	11.6	odd	10
8470.2.a.db.1.3		6	11.5	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.248272 + 0.764103i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.649985 - 0.472241i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.90484 + 1.38395i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.248272 + 0.764103i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.649985 - 0.472241i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(1.90484 + 1.38395i) q^{9} +1.00000 q^{10} +(-3.22166 + 0.787978i) q^{11} -0.803425 q^{12} +(2.13834 + 1.55360i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.248272 - 0.764103i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.29806 + 0.943099i) q^{17} +(-0.727583 - 2.23927i) q^{18} +(0.590037 - 1.81595i) q^{19} +(-0.809017 - 0.587785i) q^{20} +0.803425 q^{21} +(3.06954 + 1.25616i) q^{22} -4.22916 q^{23} +(0.649985 + 0.472241i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.816775 - 2.51377i) q^{26} +(-3.48035 + 2.52862i) q^{27} +(0.809017 - 0.587785i) q^{28} +(2.77477 + 8.53988i) q^{29} +(-0.248272 + 0.764103i) q^{30} +(-2.00312 - 1.45536i) q^{31} +1.00000 q^{32} +(0.197752 - 2.65731i) q^{33} +1.60450 q^{34} +(0.809017 + 0.587785i) q^{35} +(-0.727583 + 2.23927i) q^{36} +(-1.73320 - 5.33426i) q^{37} +(-1.54474 + 1.12232i) q^{38} +(-1.71800 + 1.24820i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-2.99616 + 9.22125i) q^{41} +(-0.649985 - 0.472241i) q^{42} -4.00169 q^{43} +(-1.74496 - 2.82048i) q^{44} -2.35451 q^{45} +(3.42146 + 2.48584i) q^{46} +(-2.02252 + 6.22469i) q^{47} +(-0.248272 - 0.764103i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.398351 - 1.22600i) q^{51} +(-0.816775 + 2.51377i) q^{52} +(-8.12885 - 5.90596i) q^{53} +4.30195 q^{54} +(2.14322 - 2.53113i) q^{55} -1.00000 q^{56} +(1.24108 + 0.901698i) q^{57} +(2.77477 - 8.53988i) q^{58} +(1.28756 + 3.96270i) q^{59} +(0.649985 - 0.472241i) q^{60} +(-10.7299 + 7.79571i) q^{61} +(0.765125 + 2.35481i) q^{62} +(0.727583 - 2.23927i) q^{63} +(-0.809017 - 0.587785i) q^{64} -2.64314 q^{65} +(-1.72191 + 2.03357i) q^{66} -10.5029 q^{67} +(-1.29806 - 0.943099i) q^{68} +(1.04998 - 3.23151i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-3.70925 + 2.69493i) q^{71} +(1.90484 - 1.38395i) q^{72} +(1.14118 + 3.51218i) q^{73} +(-1.73320 + 5.33426i) q^{74} +(0.649985 + 0.472241i) q^{75} +1.90940 q^{76} +(1.74496 + 2.82048i) q^{77} +2.12356 q^{78} +(11.2839 + 8.19826i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.11470 + 3.43068i) q^{81} +(7.84406 - 5.69904i) q^{82} +(10.9705 - 7.97052i) q^{83} +(0.248272 + 0.764103i) q^{84} +(0.495817 - 1.52597i) q^{85} +(3.23744 + 2.35214i) q^{86} -7.21424 q^{87} +(-0.246136 + 3.30748i) q^{88} -3.41009 q^{89} +(1.90484 + 1.38395i) q^{90} +(0.816775 - 2.51377i) q^{91} +(-1.30688 - 4.02217i) q^{92} +(1.60936 - 1.16927i) q^{93} +(5.29503 - 3.84707i) q^{94} +(0.590037 + 1.81595i) q^{95} +(-0.248272 + 0.764103i) q^{96} +(14.1345 + 10.2693i) q^{97} +1.00000 q^{98} +(-7.22725 - 2.95763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9	\( 12 q - 3 q^{2} - 2 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} - 7 q^{9} + 12 q^{10} + 7 q^{11} - 2 q^{12} + 8 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} - 20 q^{23} + 3 q^{24} - 3 q^{25} - 2 q^{26} + 7 q^{27} + 3 q^{28} + 20 q^{29} - 2 q^{30} + 2 q^{31} + 12 q^{32} + 33 q^{33} - 42 q^{34} + 3 q^{35} + 8 q^{36} - 4 q^{37} - 14 q^{38} + 18 q^{39} - 3 q^{40} - 14 q^{41} - 3 q^{42} - 38 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 10 q^{47} - 2 q^{48} - 3 q^{49} - 3 q^{50} + 13 q^{51} - 2 q^{52} + 8 q^{53} - 8 q^{54} - 3 q^{55} - 12 q^{56} + 33 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} - 34 q^{61} + 2 q^{62} - 8 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} - 54 q^{67} + 8 q^{68} + 38 q^{69} + 3 q^{70} + 18 q^{71} - 7 q^{72} + 24 q^{73} - 4 q^{74} + 3 q^{75} + 6 q^{76} - 2 q^{77} - 52 q^{78} + 2 q^{79} - 3 q^{80} + 2 q^{81} + 21 q^{82} + 33 q^{83} + 2 q^{84} + 13 q^{85} + 7 q^{86} - 16 q^{87} - 3 q^{88} + 2 q^{89} - 7 q^{90} + 2 q^{91} - 10 q^{92} - 32 q^{93} + 11 q^{95} - 2 q^{96} - q^{97} + 12 q^{98} - 47 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 2 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 - 7 * q^9 + 12 * q^10 + 7 * q^11 - 2 * q^12 + 8 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 - 20 * q^23 + 3 * q^24 - 3 * q^25 - 2 * q^26 + 7 * q^27 + 3 * q^28 + 20 * q^29 - 2 * q^30 + 2 * q^31 + 12 * q^32 + 33 * q^33 - 42 * q^34 + 3 * q^35 + 8 * q^36 - 4 * q^37 - 14 * q^38 + 18 * q^39 - 3 * q^40 - 14 * q^41 - 3 * q^42 - 38 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 10 * q^47 - 2 * q^48 - 3 * q^49 - 3 * q^50 + 13 * q^51 - 2 * q^52 + 8 * q^53 - 8 * q^54 - 3 * q^55 - 12 * q^56 + 33 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 - 34 * q^61 + 2 * q^62 - 8 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 - 54 * q^67 + 8 * q^68 + 38 * q^69 + 3 * q^70 + 18 * q^71 - 7 * q^72 + 24 * q^73 - 4 * q^74 + 3 * q^75 + 6 * q^76 - 2 * q^77 - 52 * q^78 + 2 * q^79 - 3 * q^80 + 2 * q^81 + 21 * q^82 + 33 * q^83 + 2 * q^84 + 13 * q^85 + 7 * q^86 - 16 * q^87 - 3 * q^88 + 2 * q^89 - 7 * q^90 + 2 * q^91 - 10 * q^92 - 32 * q^93 + 11 * q^95 - 2 * q^96 - q^97 + 12 * q^98 - 47 * q^99

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