LMFDB - Embedded newform 770.2.n.g.421.1

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			421.1
Root			$0.846504 + 2.60527i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.g.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.846504 - 2.60527i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.21618 + 1.61015i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.64382 + 2.64739i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.846504 - 2.60527i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.21618 + 1.61015i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.64382 + 2.64739i) q^{9} +1.00000 q^{10} +(2.28197 + 2.40679i) q^{11} -2.73934 q^{12} +(-2.14548 + 1.55878i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.846504 + 2.60527i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.40203 + 3.92480i) q^{17} +(1.39181 - 4.28356i) q^{18} +(1.82981 + 5.63159i) q^{19} +(-0.809017 + 0.587785i) q^{20} +2.73934 q^{21} +(-3.26082 - 0.605824i) q^{22} -6.62208 q^{23} +(2.21618 - 1.61015i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.819499 - 2.52216i) q^{26} +(3.33314 + 2.42167i) q^{27} +(0.809017 + 0.587785i) q^{28} +(0.341304 - 1.05043i) q^{29} +(-0.846504 - 2.60527i) q^{30} +(4.51349 - 3.27924i) q^{31} +1.00000 q^{32} +(4.33864 - 7.98250i) q^{33} -6.67727 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.39181 + 4.28356i) q^{36} +(1.28301 - 3.94870i) q^{37} +(-4.79052 - 3.48051i) q^{38} +(5.87720 + 4.27003i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.80882 + 8.64466i) q^{41} +(-2.21618 + 1.61015i) q^{42} -5.51500 q^{43} +(2.99416 - 1.42654i) q^{44} +4.50401 q^{45} +(5.35738 - 3.89236i) q^{46} +(0.280352 + 0.862836i) q^{47} +(-0.846504 + 2.60527i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(5.65234 - 17.3961i) q^{51} +(0.819499 + 2.52216i) q^{52} +(7.47629 - 5.43185i) q^{53} -4.11999 q^{54} +(-0.431477 - 3.28844i) q^{55} -1.00000 q^{56} +(13.1229 - 9.53432i) q^{57} +(0.341304 + 1.05043i) q^{58} +(0.533678 - 1.64249i) q^{59} +(2.21618 + 1.61015i) q^{60} +(7.22871 + 5.25197i) q^{61} +(-1.72400 + 5.30592i) q^{62} +(-1.39181 - 4.28356i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.65196 q^{65} +(1.18196 + 9.00816i) q^{66} -4.10699 q^{67} +(5.40203 - 3.92480i) q^{68} +(5.60562 + 17.2523i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(5.68064 + 4.12723i) q^{71} +(-3.64382 - 2.64739i) q^{72} +(0.298955 - 0.920088i) q^{73} +(1.28301 + 3.94870i) q^{74} +(2.21618 - 1.61015i) q^{75} +5.92140 q^{76} +(-2.99416 + 1.42654i) q^{77} -7.26462 q^{78} +(-8.69338 + 6.31611i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-0.687858 + 2.11701i) q^{81} +(-7.35359 - 5.34269i) q^{82} +(12.8659 + 9.34759i) q^{83} +(0.846504 - 2.60527i) q^{84} +(-2.06339 - 6.35046i) q^{85} +(4.46173 - 3.24163i) q^{86} -3.02556 q^{87} +(-1.58382 + 2.91402i) q^{88} +12.5040 q^{89} +(-3.64382 + 2.64739i) q^{90} +(-0.819499 - 2.52216i) q^{91} +(-2.04634 + 6.29798i) q^{92} +(-12.3640 - 8.98297i) q^{93} +(-0.733972 - 0.533262i) q^{94} +(1.82981 - 5.63159i) q^{95} +(-0.846504 - 2.60527i) q^{96} +(-9.25206 + 6.72201i) q^{97} +1.00000 q^{98} +(-14.6868 - 2.72863i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$3$	−0.846504	−	2.60527i	−0.488729	−	1.50415i	−0.826506	−	0.562928i	$-0.809675\pi$
$3$	−0.846504	−	2.60527i	−0.488729	−	1.50415i	0.337777	−	0.941226i	$-0.390325\pi$
$4$	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
$6$	2.21618	+	1.61015i	0.904750	+	0.657339i
$7$	−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
$9$	−3.64382	+	2.64739i	−1.21461	+	0.882463i
$10$	1.00000			0.316228
$11$	2.28197	+	2.40679i	0.688039	+	0.725673i
$11$	2.28197	+	2.40679i	0.688039	+	0.725673i
$12$	−2.73934			−0.790780
$13$	−2.14548	+	1.55878i	−0.595048	+	0.432328i	−0.844118	−	0.536158i	$-0.819875\pi$
$13$	−2.14548	+	1.55878i	−0.595048	+	0.432328i	0.249070	+	0.968486i	$0.419875\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.846504	+	2.60527i	−0.218566	+	0.672678i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.40203	+	3.92480i	1.31018	+	0.951904i	0.999999	+	0.00122803i	$0.000390895\pi$
$17$	5.40203	+	3.92480i	1.31018	+	0.951904i	0.310185	+	0.950676i	$0.399609\pi$
$18$	1.39181	−	4.28356i	0.328054	−	1.00965i
$19$	1.82981	+	5.63159i	0.419788	+	1.29198i	0.907897	+	0.419192i	$0.137687\pi$
$19$	1.82981	+	5.63159i	0.419788	+	1.29198i	−0.488109	+	0.872783i	$0.662313\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	2.73934			0.597774
$22$	−3.26082	−	0.605824i	−0.695210	−	0.129162i
$23$	−6.62208			−1.38080			−0.690400	−	0.723428i	$-0.742565\pi$
$23$	−6.62208			−1.38080			−0.690400	+	0.723428i	$0.742565\pi$
$24$	2.21618	−	1.61015i	0.452375	−	0.328670i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.819499	−	2.52216i	0.160717	−	0.494636i
$27$	3.33314	+	2.42167i	0.641463	+	0.466050i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	0.341304	−	1.05043i	0.0633786	−	0.195059i	−0.914353	−	0.404917i	$-0.867300\pi$
$29$	0.341304	−	1.05043i	0.0633786	−	0.195059i	0.977732	+	0.209858i	$0.0673003\pi$
$30$	−0.846504	−	2.60527i	−0.154550	−	0.475655i
$31$	4.51349	−	3.27924i	0.810646	−	0.588969i	−0.103372	−	0.994643i	$-0.532963\pi$
$31$	4.51349	−	3.27924i	0.810646	−	0.588969i	0.914018	+	0.405674i	$0.132963\pi$
$32$	1.00000			0.176777
$33$	4.33864	−	7.98250i	0.755260	−	1.38957i
$34$	−6.67727			−1.14514
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	1.39181	+	4.28356i	0.231969	+	0.713927i
$37$	1.28301	−	3.94870i	0.210926	−	0.649163i	−0.788492	−	0.615045i	$-0.789138\pi$
$37$	1.28301	−	3.94870i	0.210926	−	0.649163i	0.999418	−	0.0341177i	$-0.0108621\pi$
$38$	−4.79052	−	3.48051i	−0.777124	−	0.564614i
$39$	5.87720	+	4.27003i	0.941105	+	0.683753i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	2.80882	+	8.64466i	0.438664	+	1.35007i	0.889285	+	0.457354i	$0.151203\pi$
$41$	2.80882	+	8.64466i	0.438664	+	1.35007i	−0.450621	+	0.892716i	$0.648797\pi$
$42$	−2.21618	+	1.61015i	−0.341963	+	0.248451i
$43$	−5.51500			−0.841029			−0.420515	−	0.907286i	$-0.638150\pi$
$43$	−5.51500			−0.841029			−0.420515	+	0.907286i	$0.638150\pi$
$44$	2.99416	−	1.42654i	0.451386	−	0.215059i
$45$	4.50401			0.671417
$46$	5.35738	−	3.89236i	0.789902	−	0.573898i
$47$	0.280352	+	0.862836i	0.0408936	+	0.125858i	0.969419	−	0.245411i	$-0.0789229\pi$
$47$	0.280352	+	0.862836i	0.0408936	+	0.125858i	−0.928526	+	0.371269i	$0.878923\pi$
$48$	−0.846504	+	2.60527i	−0.122182	+	0.376038i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	5.65234	−	17.3961i	0.791485	−	2.43594i
$52$	0.819499	+	2.52216i	0.113644	+	0.349761i
$53$	7.47629	−	5.43185i	1.02695	−	0.746121i	0.0592525	−	0.998243i	$-0.481128\pi$
$53$	7.47629	−	5.43185i	1.02695	−	0.746121i	0.967696	+	0.252122i	$0.0811283\pi$
$54$	−4.11999			−0.560659
$55$	−0.431477	−	3.28844i	−0.0581804	−	0.443413i
$56$	−1.00000			−0.133631
$57$	13.1229	−	9.53432i	1.73817	−	1.26285i
$58$	0.341304	+	1.05043i	0.0448154	+	0.137928i
$59$	0.533678	−	1.64249i	0.0694789	−	0.213834i	−0.910288	−	0.413975i	$-0.864140\pi$
$59$	0.533678	−	1.64249i	0.0694789	−	0.213834i	0.979767	+	0.200141i	$0.0641400\pi$
$60$	2.21618	+	1.61015i	0.286107	+	0.207869i
$61$	7.22871	+	5.25197i	0.925542	+	0.672446i	0.944897	−	0.327367i	$-0.106161\pi$
$61$	7.22871	+	5.25197i	0.925542	+	0.672446i	−0.0193553	+	0.999813i	$0.506161\pi$
$62$	−1.72400	+	5.30592i	−0.218948	+	0.673853i
$63$	−1.39181	−	4.28356i	−0.175352	−	0.539678i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.65196			0.328935
$66$	1.18196	+	9.00816i	0.145490	+	1.10883i
$67$	−4.10699			−0.501748			−0.250874	−	0.968020i	$-0.580718\pi$
$67$	−4.10699			−0.501748			−0.250874	+	0.968020i	$0.580718\pi$
$68$	5.40203	−	3.92480i	0.655092	−	0.475952i
$69$	5.60562	+	17.2523i	0.674837	+	2.07694i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	5.68064	+	4.12723i	0.674168	+	0.489812i	0.871418	−	0.490541i	$-0.163201\pi$
$71$	5.68064	+	4.12723i	0.674168	+	0.489812i	−0.197250	+	0.980353i	$0.563201\pi$
$72$	−3.64382	−	2.64739i	−0.429428	−	0.311998i
$73$	0.298955	−	0.920088i	0.0349900	−	0.107688i	−0.932036	−	0.362365i	$-0.881969\pi$
$73$	0.298955	−	0.920088i	0.0349900	−	0.107688i	0.967026	+	0.254677i	$0.0819692\pi$
$74$	1.28301	+	3.94870i	0.149147	+	0.459027i
$75$	2.21618	−	1.61015i	0.255902	−	0.185924i
$76$	5.92140			0.679231
$77$	−2.99416	+	1.42654i	−0.341216	+	0.162570i
$78$	−7.26462			−0.822556
$79$	−8.69338	+	6.31611i	−0.978081	+	0.710618i	−0.957279	−	0.289166i	$-0.906622\pi$
$79$	−8.69338	+	6.31611i	−0.978081	+	0.710618i	−0.0208022	+	0.999784i	$0.506622\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	−0.687858	+	2.11701i	−0.0764286	+	0.235223i
$82$	−7.35359	−	5.34269i	−0.812068	−	0.590002i
$83$	12.8659	+	9.34759i	1.41221	+	1.02603i	0.992997	+	0.118144i	$0.0376943\pi$
$83$	12.8659	+	9.34759i	1.41221	+	1.02603i	0.419214	+	0.907887i	$0.362306\pi$
$84$	0.846504	−	2.60527i	0.0923611	−	0.284258i
$85$	−2.06339	−	6.35046i	−0.223806	−	0.688804i
$86$	4.46173	−	3.24163i	0.481120	−	0.349554i
$87$	−3.02556			−0.324374
$88$	−1.58382	+	2.91402i	−0.168836	+	0.310635i
$89$	12.5040			1.32543			0.662713	−	0.748874i	$-0.269405\pi$
$89$	12.5040			1.32543			0.662713	+	0.748874i	$0.269405\pi$
$90$	−3.64382	+	2.64739i	−0.384092	+	0.279059i
$91$	−0.819499	−	2.52216i	−0.0859069	−	0.264394i
$92$	−2.04634	+	6.29798i	−0.213345	+	0.656609i
$93$	−12.3640	−	8.98297i	−1.28209	−	0.931491i
$94$	−0.733972	−	0.533262i	−0.0757034	−	0.0550017i
$95$	1.82981	−	5.63159i	0.187735	−	0.577789i
$96$	−0.846504	−	2.60527i	−0.0863959	−	0.265899i
$97$	−9.25206	+	6.72201i	−0.939404	+	0.682517i	−0.948277	−	0.317444i	$-0.897176\pi$
$97$	−9.25206	+	6.72201i	−0.939404	+	0.682517i	0.00887322	+	0.999961i	$0.497176\pi$
$98$	1.00000			0.101015
$99$	−14.6868	−	2.72863i	−1.47608	−	0.274238i
$100$	1.00000			0.100000
$101$	−6.21239	+	4.51356i	−0.618156	+	0.449116i	−0.852277	−	0.523091i	$-0.824779\pi$
$101$	−6.21239	+	4.51356i	−0.618156	+	0.449116i	0.234121	+	0.972207i	$0.424779\pi$
$102$	5.65234	+	17.3961i	0.559665	+	1.72247i
$103$	−0.400074	+	1.23130i	−0.0394204	+	0.121324i	−0.968830	−	0.247726i	$-0.920317\pi$
$103$	−0.400074	+	1.23130i	−0.0394204	+	0.121324i	0.929410	+	0.369050i	$0.120317\pi$
$104$	−2.14548	−	1.55878i	−0.210381	−	0.152851i
$105$	−2.21618	−	1.61015i	−0.216277	−	0.157134i
$106$	−2.85569	+	8.78891i	−0.277369	+	0.853655i
$107$	−4.33832	−	13.3520i	−0.419401	−	1.29078i	−0.908255	−	0.418418i	$-0.862585\pi$
$107$	−4.33832	−	13.3520i	−0.419401	−	1.29078i	0.488854	−	0.872366i	$-0.337415\pi$
$108$	3.33314	−	2.42167i	0.320732	−	0.233025i
$109$	−13.6269			−1.30522			−0.652609	−	0.757695i	$-0.726326\pi$
$109$	−13.6269			−1.30522			−0.652609	+	0.757695i	$0.726326\pi$
$110$	2.28197	+	2.40679i	0.217577	+	0.229478i
$111$	−11.3735			−1.07953
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	3.82644	+	11.7766i	0.359962	+	1.10785i	0.953076	+	0.302730i	$0.0978980\pi$
$113$	3.82644	+	11.7766i	0.359962	+	1.10785i	−0.593115	+	0.805118i	$0.702102\pi$
$114$	−5.01249	+	15.4269i	−0.469463	+	1.44486i
$115$	5.35738	+	3.89236i	0.499578	+	0.362965i
$116$	−0.893546	−	0.649199i	−0.0829636	−	0.0602766i
$117$	3.69103	−	11.3598i	0.341236	−	1.05022i
$118$	0.533678	+	1.64249i	0.0491290	+	0.151204i
$119$	−5.40203	+	3.92480i	−0.495203	+	0.359786i
$120$	−2.73934			−0.250067
$121$	−0.585243	+	10.9844i	−0.0532039	+	0.998584i
$122$	−8.93518			−0.808953
$123$	20.1440	−	14.6355i	1.81632	−	1.31964i
$124$	−1.72400	−	5.30592i	−0.154820	−	0.476486i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	3.64382	+	2.64739i	0.324617	+	0.235848i
$127$	−6.99020	−	5.07868i	−0.620280	−	0.450660i	0.232739	−	0.972539i	$-0.425231\pi$
$127$	−6.99020	−	5.07868i	−0.620280	−	0.450660i	−0.853019	+	0.521879i	$0.825231\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.66847	+	14.3681i	0.411036	+	1.26504i
$130$	−2.14548	+	1.55878i	−0.188171	+	0.136714i
$131$	6.27193			0.547981			0.273991	−	0.961732i	$-0.411656\pi$
$131$	6.27193			0.547981			0.273991	+	0.961732i	$0.411656\pi$
$132$	−6.25110	−	6.59302i	−0.544088	−	0.573848i
$133$	−5.92140			−0.513451
$134$	3.32262	−	2.41403i	0.287031	−	0.208540i
$135$	−1.27315	−	3.91834i	−0.109575	−	0.337237i
$136$	−2.06339	+	6.35046i	−0.176934	+	0.544548i
$137$	8.83280	+	6.41740i	0.754637	+	0.548276i	0.897261	−	0.441501i	$-0.145554\pi$
$137$	8.83280	+	6.41740i	0.754637	+	0.548276i	−0.142624	+	0.989777i	$0.545554\pi$
$138$	−14.6757	−	10.6625i	−1.24928	−	0.907654i
$139$	3.88370	−	11.9528i	0.329411	−	1.01382i	−0.639998	−	0.768376i	$-0.721065\pi$
$139$	3.88370	−	11.9528i	0.329411	−	1.01382i	0.969410	−	0.245448i	$-0.0789350\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	2.01060	−	1.46079i	0.169323	−	0.123020i
$142$	−7.02166			−0.589245
$143$	−8.64756	−	1.60662i	−0.723145	−	0.134352i
$144$	4.50401			0.375334
$145$	−0.893546	+	0.649199i	−0.0742049	+	0.0539130i
$146$	0.298955	+	0.920088i	0.0247417	+	0.0761470i
$147$	−0.846504	+	2.60527i	−0.0698185	+	0.214879i
$148$	−3.35897	−	2.44043i	−0.276105	−	0.200602i
$149$	15.3192	+	11.1300i	1.25500	+	0.911809i	0.998501	−	0.0547362i	$-0.0174318\pi$
$149$	15.3192	+	11.1300i	1.25500	+	0.911809i	0.256496	+	0.966545i	$0.417432\pi$
$150$	−0.846504	+	2.60527i	−0.0691167	+	0.212719i
$151$	−2.80541	−	8.63415i	−0.228301	−	0.702638i	−0.997940	−	0.0641582i	$-0.979564\pi$
$151$	−2.80541	−	8.63415i	−0.228301	−	0.702638i	0.769639	−	0.638479i	$-0.220436\pi$
$152$	−4.79052	+	3.48051i	−0.388562	+	0.282307i
$153$	−30.0745			−2.43138
$154$	1.58382	−	2.91402i	0.127628	−	0.234818i
$155$	−5.57898			−0.448114
$156$	5.87720	−	4.27003i	0.470552	−	0.341876i
$157$	4.02651	+	12.3923i	0.321350	+	0.989015i	0.973061	+	0.230547i	$0.0740516\pi$
$157$	4.02651	+	12.3923i	0.321350	+	0.989015i	−0.651711	+	0.758468i	$0.725948\pi$
$158$	3.32057	−	10.2197i	0.264171	−	0.813034i
$159$	−20.4801	−	14.8797i	−1.62418	−	1.18004i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	2.04634	−	6.29798i	0.161274	−	0.496350i
$162$	−0.687858	−	2.11701i	−0.0540432	−	0.166328i
$163$	−6.80737	+	4.94584i	−0.533194	+	0.387388i	−0.821551	−	0.570135i	$-0.806891\pi$
$163$	−6.80737	+	4.94584i	−0.533194	+	0.387388i	0.288357	+	0.957523i	$0.406891\pi$
$164$	9.08954			0.709773
$165$	−8.20203	+	3.90779i	−0.638527	+	0.304221i
$166$	−15.9031			−1.23432
$167$	9.08902	−	6.60356i	0.703329	−	0.510999i	−0.177686	−	0.984087i	$-0.556861\pi$
$167$	9.08902	−	6.60356i	0.703329	−	0.510999i	0.881015	+	0.473089i	$0.156861\pi$
$168$	0.846504	+	2.60527i	0.0653092	+	0.201001i
$169$	−1.84395	+	5.67508i	−0.141842	+	0.436545i
$170$	5.40203	+	3.92480i	0.414317	+	0.301019i
$171$	−21.5765	−	15.6762i	−1.65000	−	1.19879i
$172$	−1.70423	+	5.24507i	−0.129946	+	0.399933i
$173$	−0.00921279	−	0.0283540i	−0.000700435	−	0.00215572i	0.950706	−	0.310095i	$-0.100361\pi$
$173$	−0.00921279	−	0.0283540i	−0.000700435	−	0.00215572i	−0.951406	+	0.307939i	$0.900361\pi$
$174$	2.44773	−	1.77838i	0.185562	−	0.134819i
$175$	−1.00000			−0.0755929
$176$	−0.431477	−	3.28844i	−0.0325238	−	0.247875i
$177$	−4.73089			−0.355596
$178$	−10.1160	+	7.34969i	−0.758225	+	0.550883i
$179$	−7.32220	−	22.5354i	−0.547287	−	1.68438i	−0.715489	−	0.698624i	$-0.753796\pi$
$179$	−7.32220	−	22.5354i	−0.547287	−	1.68438i	0.168202	−	0.985753i	$-0.446204\pi$
$180$	1.39181	−	4.28356i	0.103740	−	0.319278i
$181$	4.35402	+	3.16338i	0.323631	+	0.235132i	0.737723	−	0.675103i	$-0.235901\pi$
$181$	4.35402	+	3.16338i	0.323631	+	0.235132i	−0.414092	+	0.910235i	$0.635901\pi$
$182$	2.14548	+	1.55878i	0.159033	+	0.115544i
$183$	7.56366	−	23.2786i	0.559122	−	1.72080i
$184$	−2.04634	−	6.29798i	−0.150858	−	0.464293i
$185$	−3.35897	+	2.44043i	−0.246956	+	0.179424i
$186$	15.2827			1.12058
$187$	2.88109	+	21.9578i	0.210686	+	1.60571i
$188$	0.907239			0.0661672
$189$	−3.33314	+	2.42167i	−0.242450	+	0.176150i
$190$	1.82981	+	5.63159i	0.132749	+	0.408558i
$191$	−3.81786	+	11.7502i	−0.276250	+	0.850211i	0.712635	+	0.701534i	$0.247501\pi$
$191$	−3.81786	+	11.7502i	−0.276250	+	0.850211i	−0.988886	+	0.148677i	$0.952499\pi$
$192$	2.21618	+	1.61015i	0.159939	+	0.116202i
$193$	−9.54732	−	6.93653i	−0.687231	−	0.499302i	0.188518	−	0.982070i	$-0.439632\pi$
$193$	−9.54732	−	6.93653i	−0.687231	−	0.499302i	−0.875749	+	0.482767i	$0.839632\pi$
$194$	3.53397	−	10.8764i	0.253724	−	0.780883i
$195$	−2.24489	−	6.90906i	−0.160760	−	0.494768i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	19.4626			1.38665			0.693325	−	0.720625i	$-0.256145\pi$
$197$	19.4626			1.38665			0.693325	+	0.720625i	$0.256145\pi$
$198$	13.4857	−	6.42516i	0.958387	−	0.456616i
$199$	15.5751			1.10409			0.552043	−	0.833815i	$-0.313848\pi$
$199$	15.5751			1.10409			0.552043	+	0.833815i	$0.313848\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	3.47658	+	10.6998i	0.245219	+	0.754706i
$202$	2.37292	−	7.30310i	0.166958	−	0.513844i
$203$	0.893546	+	0.649199i	0.0627146	+	0.0455648i
$204$	−14.7980	−	10.7514i	−1.03607	−	0.752747i
$205$	2.80882	−	8.64466i	0.196177	−	0.603769i
$206$	−0.400074	−	1.23130i	−0.0278745	−	0.0857887i
$207$	24.1297	−	17.5312i	1.67713	−	1.21850i
$208$	2.65196			0.183880
$209$	−9.37845	+	17.2551i	−0.648721	+	1.19356i
$210$	2.73934			0.189033
$211$	−11.1781	+	8.12134i	−0.769530	+	0.559096i	−0.901819	−	0.432115i	$-0.857767\pi$
$211$	−11.1781	+	8.12134i	−0.769530	+	0.559096i	0.132288	+	0.991211i	$0.457767\pi$
$212$	−2.85569	−	8.78891i	−0.196130	−	0.603625i
$213$	5.94386	−	18.2933i	0.407267	−	1.25344i
$214$	11.3579	+	8.25197i	0.776407	+	0.564093i
$215$	4.46173	+	3.24163i	0.304287	+	0.221078i
$216$	−1.27315	+	3.91834i	−0.0866266	+	0.266609i
$217$	1.72400	+	5.30592i	0.117033	+	0.360190i
$218$	11.0244	−	8.00968i	0.746665	−	0.542484i
$219$	−2.65015			−0.179080
$220$	−3.26082	−	0.605824i	−0.219845	−	0.0408446i
$221$	−17.7078			−1.19116
$222$	9.20136	−	6.68518i	0.617555	−	0.448680i
$223$	−2.77516	−	8.54106i	−0.185838	−	0.571951i	0.814124	−	0.580692i	$-0.197218\pi$
$223$	−2.77516	−	8.54106i	−0.185838	−	0.571951i	−0.999962	+	0.00874035i	$0.997218\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	−3.64382	−	2.64739i	−0.242921	−	0.176493i
$226$	−10.0178	−	7.27833i	−0.666372	−	0.484147i
$227$	−5.72792	+	17.6287i	−0.380175	+	1.17006i	0.559745	+	0.828665i	$0.310899\pi$
$227$	−5.72792	+	17.6287i	−0.380175	+	1.17006i	−0.939920	+	0.341394i	$0.889101\pi$
$228$	−5.01249	−	15.4269i	−0.331960	−	1.02167i
$229$	21.3398	−	15.5043i	1.41018	−	1.02455i	0.416880	−	0.908962i	$-0.363124\pi$
$229$	21.3398	−	15.5043i	1.41018	−	1.02455i	0.993297	−	0.115592i	$-0.0368765\pi$
$230$	−6.62208			−0.436647
$231$	6.25110	+	6.59302i	0.411292	+	0.433789i
$232$	1.10448			0.0725129
$233$	−10.4387	+	7.58416i	−0.683862	+	0.496855i	−0.874637	−	0.484779i	$-0.838900\pi$
$233$	−10.4387	+	7.58416i	−0.683862	+	0.496855i	0.190774	+	0.981634i	$0.438900\pi$
$234$	3.69103	+	11.3598i	0.241290	+	0.742614i
$235$	0.280352	−	0.862836i	0.0182882	−	0.0562852i
$236$	−1.39719	−	1.01512i	−0.0909491	−	0.0660784i
$237$	23.8141	+	17.3020i	1.54689	+	1.12388i
$238$	2.06339	−	6.35046i	0.133750	−	0.411639i
$239$	2.29842	+	7.07381i	0.148673	+	0.457567i	0.997465	−	0.0711592i	$-0.0226698\pi$
$239$	2.29842	+	7.07381i	0.148673	+	0.457567i	−0.848792	+	0.528726i	$0.822670\pi$
$240$	2.21618	−	1.61015i	0.143054	−	0.103934i
$241$	−29.9278			−1.92782			−0.963908	−	0.266234i	$-0.914221\pi$
$241$	−29.9278			−1.92782			−0.963908	+	0.266234i	$0.914221\pi$
$242$	−5.98301	−	9.23058i	−0.384602	−	0.593364i
$243$	18.4576			1.18406
$244$	7.22871	−	5.25197i	0.462771	−	0.336223i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−7.69433	+	23.6807i	−0.490572	+	1.50983i
$247$	−12.7042	−	9.23016i	−0.808351	−	0.587301i
$248$	4.51349	+	3.27924i	0.286607	+	0.208232i
$249$	13.4620	−	41.4318i	0.853120	−	2.62563i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−2.07764	+	1.50950i	−0.131140	+	0.0952786i	−0.651421	−	0.758716i	$-0.725827\pi$
$251$	−2.07764	+	1.50950i	−0.131140	+	0.0952786i	0.520282	+	0.853995i	$0.325827\pi$
$252$	−4.50401			−0.283726
$253$	−15.1114	−	15.9379i	−0.950045	−	1.00201i
$254$	8.64037			0.542145
$255$	−14.7980	+	10.7514i	−0.926687	+	0.673278i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−8.58183	+	26.4122i	−0.535320	+	1.64755i	0.207636	+	0.978206i	$0.433423\pi$
$257$	−8.58183	+	26.4122i	−0.535320	+	1.64755i	−0.742957	+	0.669340i	$0.766577\pi$
$258$	−12.2222	−	8.87995i	−0.760921	−	0.552842i
$259$	3.35897	+	2.44043i	0.208716	+	0.151641i
$260$	0.819499	−	2.52216i	0.0508232	−	0.156418i
$261$	1.53724	+	4.73112i	0.0951525	+	0.292849i
$262$	−5.07410	+	3.68655i	−0.313479	+	0.227756i
$263$	−14.1621			−0.873273			−0.436637	−	0.899638i	$-0.643830\pi$
$263$	−14.1621			−0.873273			−0.436637	+	0.899638i	$0.643830\pi$
$264$	8.93252	+	1.65956i	0.549759	+	0.102139i
$265$	−9.24121			−0.567683
$266$	4.79052	−	3.48051i	0.293725	−	0.213404i
$267$	−10.5847	−	32.5764i	−0.647774	−	1.99364i
$268$	−1.26913	+	3.90598i	−0.0775244	+	0.238595i
$269$	−19.8763	−	14.4410i	−1.21188	−	0.880482i	−0.216480	−	0.976287i	$-0.569457\pi$
$269$	−19.8763	−	14.4410i	−1.21188	−	0.880482i	−0.995400	+	0.0958049i	$0.969457\pi$
$270$	3.33314	+	2.42167i	0.202848	+	0.147378i
$271$	3.24012	−	9.97206i	0.196823	−	0.605759i	−0.803127	−	0.595807i	$-0.796832\pi$
$271$	3.24012	−	9.97206i	0.196823	−	0.605759i	0.999950	−	0.00995200i	$-0.00316787\pi$
$272$	−2.06339	−	6.35046i	−0.125111	−	0.385053i
$273$	−5.87720	+	4.27003i	−0.355704	+	0.258434i
$274$	−10.9179			−0.659577
$275$	−1.58382	+	2.91402i	−0.0955081	+	0.175722i
$276$	18.1402			1.09191
$277$	24.9519	−	18.1286i	1.49922	−	1.08924i	0.528522	−	0.848919i	$-0.322746\pi$
$277$	24.9519	−	18.1286i	1.49922	−	1.08924i	0.970693	−	0.240324i	$-0.0772537\pi$
$278$	3.88370	+	11.9528i	0.232929	+	0.716882i
$279$	−7.76490	+	23.8979i	−0.464872	+	1.43073i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	3.59594	+	2.61260i	0.214516	+	0.155855i	0.689855	−	0.723948i	$-0.257674\pi$
$281$	3.59594	+	2.61260i	0.214516	+	0.155855i	−0.475339	+	0.879803i	$0.657674\pi$
$282$	−0.767981	+	2.36360i	−0.0457326	+	0.140751i
$283$	−1.79617	−	5.52804i	−0.106771	−	0.328608i	0.883371	−	0.468674i	$-0.155268\pi$
$283$	−1.79617	−	5.52804i	−0.106771	−	0.328608i	−0.990142	+	0.140067i	$0.955268\pi$
$284$	5.68064	−	4.12723i	0.337084	−	0.244906i
$285$	−16.2208			−0.960835
$286$	7.94037	−	3.78313i	0.469524	−	0.223701i
$287$	−9.08954			−0.536538
$288$	−3.64382	+	2.64739i	−0.214714	+	0.155999i
$289$	8.52453	+	26.2358i	0.501443	+	1.54328i
$290$	0.341304	−	1.05043i	0.0200421	−	0.0616831i
$291$	25.3446	+	18.4139i	1.48572	+	1.07944i
$292$	−0.782674	−	0.568646i	−0.0458025	−	0.0332775i
$293$	2.52197	−	7.76183i	0.147335	−	0.453451i	−0.849969	−	0.526833i	$-0.823379\pi$
$293$	2.52197	−	7.76183i	0.147335	−	0.453451i	0.997304	+	0.0733822i	$0.0233793\pi$
$294$	−0.846504	−	2.60527i	−0.0493691	−	0.151942i
$295$	−1.39719	+	1.01512i	−0.0813473	+	0.0591023i
$296$	4.15191			0.241325
$297$	1.77768	+	13.5483i	0.103152	+	0.786153i
$298$	−18.9356			−1.09691
$299$	14.2075	−	10.3224i	0.821642	−	0.596958i
$300$	−0.846504	−	2.60527i	−0.0488729	−	0.150415i
$301$	1.70423	−	5.24507i	0.0982301	−	0.302321i
$302$	7.34465	+	5.33620i	0.422637	+	0.307064i
$303$	17.0179	+	12.3642i	0.977651	+	0.710305i
$304$	1.82981	−	5.63159i	0.104947	−	0.322994i
$305$	−2.76112	−	8.49786i	−0.158101	−	0.486586i
$306$	24.3308	−	17.6773i	1.39090	−	1.01055i
$307$	−15.7830			−0.900782			−0.450391	−	0.892832i	$-0.648715\pi$
$307$	−15.7830			−0.900782			−0.450391	+	0.892832i	$0.648715\pi$
$308$	0.431477	+	3.28844i	0.0245857	+	0.187376i
$309$	3.54653			0.201755
$310$	4.51349	−	3.27924i	0.256349	−	0.186248i
$311$	−2.01414	−	6.19887i	−0.114211	−	0.351506i	0.877570	−	0.479448i	$-0.159163\pi$
$311$	−2.01414	−	6.19887i	−0.114211	−	0.351506i	−0.991782	+	0.127942i	$0.959163\pi$
$312$	−2.24489	+	6.90906i	−0.127092	+	0.391149i
$313$	7.72561	+	5.61299i	0.436677	+	0.317265i	0.784313	−	0.620365i	$-0.213015\pi$
$313$	7.72561	+	5.61299i	0.436677	+	0.317265i	−0.347636	+	0.937630i	$0.613015\pi$
$314$	−10.5415	−	7.65887i	−0.594893	−	0.432215i
$315$	−1.39181	+	4.28356i	−0.0784198	+	0.241351i
$316$	3.32057	+	10.2197i	0.186797	+	0.574902i
$317$	5.27695	−	3.83393i	0.296383	−	0.215335i	−0.429649	−	0.902996i	$-0.641363\pi$
$317$	5.27695	−	3.83393i	0.296383	−	0.215335i	0.726032	+	0.687661i	$0.241363\pi$
$318$	25.3148			1.41959
$319$	3.30700	−	1.57559i	0.185156	−	0.0882162i
$320$	1.00000			0.0559017
$321$	−31.1131	+	22.6050i	−1.73656	+	1.26169i
$322$	2.04634	+	6.29798i	0.114038	+	0.350972i
$323$	−12.2182	+	37.6037i	−0.679837	+	2.09232i
$324$	1.80083	+	1.30838i	0.100046	+	0.0726879i
$325$	−2.14548	−	1.55878i	−0.119010	−	0.0864656i
$326$	2.60018	−	8.00254i	0.144011	−	0.443220i
$327$	11.5352	+	35.5017i	0.637898	+	1.96325i
$328$	−7.35359	+	5.34269i	−0.406034	+	0.295001i
$329$	−0.907239			−0.0500177
$330$	4.33864	−	7.98250i	0.238834	−	0.439422i
$331$	−20.3519			−1.11864			−0.559319	−	0.828952i	$-0.688937\pi$
$331$	−20.3519			−1.11864			−0.559319	+	0.828952i	$0.688937\pi$
$332$	12.8659	−	9.34759i	0.706105	−	0.513016i
$333$	5.77869	+	17.7850i	0.316670	+	0.974611i
$334$	−3.47170	+	10.6848i	−0.189963	+	0.584645i
$335$	3.32262	+	2.41403i	0.181534	+	0.131892i
$336$	−2.21618	−	1.61015i	−0.120902	−	0.0878407i
$337$	−6.30254	+	19.3972i	−0.343321	+	1.05663i	0.619155	+	0.785269i	$0.287475\pi$
$337$	−6.30254	+	19.3972i	−0.343321	+	1.05663i	−0.962476	+	0.271366i	$0.912525\pi$
$338$	−1.84395	−	5.67508i	−0.100297	−	0.308684i
$339$	27.4421	−	19.9378i	1.49045	−	1.08288i
$340$	−6.67727			−0.362126
$341$	18.1921	+	3.37988i	0.985156	+	0.183031i
$342$	26.6700			1.44215
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−1.70423	−	5.24507i	−0.0918858	−	0.282795i
$345$	5.60562	−	17.2523i	0.301796	−	0.928834i
$346$	0.0241194	+	0.0175238i	0.00129667	+	0.000942083i
$347$	20.3401	+	14.7780i	1.09192	+	0.793324i	0.979722	−	0.200363i	$-0.0642120\pi$
$347$	20.3401	+	14.7780i	1.09192	+	0.793324i	0.112195	+	0.993686i	$0.464212\pi$
$348$	−0.934949	+	2.87748i	−0.0501185	+	0.154249i
$349$	2.00465	+	6.16969i	0.107307	+	0.330256i	0.990265	−	0.139196i	$-0.0444517\pi$
$349$	2.00465	+	6.16969i	0.107307	+	0.330256i	−0.882958	+	0.469452i	$0.844452\pi$
$350$	0.809017	−	0.587785i	0.0432438	−	0.0314184i
$351$	−10.9260			−0.583188
$352$	2.28197	+	2.40679i	0.121629	+	0.128282i
$353$	−0.671105			−0.0357193			−0.0178597	−	0.999841i	$-0.505685\pi$
$353$	−0.671105			−0.0357193			−0.0178597	+	0.999841i	$0.505685\pi$
$354$	3.82737	−	2.78075i	0.203423	−	0.147795i
$355$	−2.16981	−	6.67800i	−0.115162	−	0.354431i
$356$	3.86396	−	11.8920i	0.204790	−	0.630277i
$357$	14.7980	+	10.7514i	0.783194	+	0.569024i
$358$	19.1698	+	13.9277i	1.01315	+	0.736100i
$359$	−10.3981	+	32.0022i	−0.548792	+	1.68901i	0.163006	+	0.986625i	$0.447881\pi$
$359$	−10.3981	+	32.0022i	−0.548792	+	1.68901i	−0.711798	+	0.702384i	$0.752119\pi$
$360$	1.39181	+	4.28356i	0.0733550	+	0.225764i
$361$	−12.9952	+	9.44160i	−0.683960	+	0.496926i
$362$	−5.38186			−0.282864
$363$	29.1128	−	7.77364i	1.52803	−	0.408010i
$364$	−2.65196			−0.139000
$365$	−0.782674	+	0.568646i	−0.0409670	+	0.0297643i
$366$	7.56366	+	23.2786i	0.395359	+	1.21679i
$367$	−1.65878	+	5.10520i	−0.0865876	+	0.266489i	−0.984970	−	0.172725i	$-0.944743\pi$
$367$	−1.65878	+	5.10520i	−0.0865876	+	0.266489i	0.898383	+	0.439214i	$0.144743\pi$
$368$	5.35738	+	3.89236i	0.279273	+	0.202903i
$369$	−33.1206	−	24.0635i	−1.72419	−	1.25270i
$370$	1.28301	−	3.94870i	0.0667006	−	0.205283i
$371$	2.85569	+	8.78891i	0.148260	+	0.456298i
$372$	−12.3640	+	8.98297i	−0.641043	+	0.465745i
$373$	16.1242			0.834878			0.417439	−	0.908705i	$-0.362928\pi$
$373$	16.1242			0.834878			0.417439	+	0.908705i	$0.362928\pi$
$374$	−15.2373	−	16.0708i	−0.787903	−	0.831000i
$375$	−2.73934			−0.141459
$376$	−0.733972	+	0.533262i	−0.0378517	+	0.0275009i
$377$	0.905123	+	2.78568i	0.0466162	+	0.143470i
$378$	1.27315	−	3.91834i	0.0654836	−	0.201538i
$379$	22.1319	+	16.0798i	1.13684	+	0.825964i	0.986676	−	0.162697i	$-0.0520194\pi$
$379$	22.1319	+	16.0798i	1.13684	+	0.825964i	0.150165	+	0.988661i	$0.452019\pi$
$380$	−4.79052	−	3.48051i	−0.245748	−	0.178547i
$381$	−7.31410	+	22.5105i	−0.374713	+	1.15325i
$382$	−3.81786	−	11.7502i	−0.195339	−	0.601190i
$383$	−0.107075	+	0.0777943i	−0.00547126	+	0.00397510i	−0.590518	−	0.807025i	$-0.701076\pi$
$383$	−0.107075	+	0.0777943i	−0.00547126	+	0.00397510i	0.585046	+	0.811000i	$0.301076\pi$
$384$	−2.73934			−0.139792
$385$	3.26082	+	0.605824i	0.166187	+	0.0308757i
$386$	11.8011			0.600662
$387$	20.0956	−	14.6003i	1.02152	−	0.742177i
$388$	3.53397	+	10.8764i	0.179410	+	0.552168i
$389$	5.05743	−	15.5652i	0.256422	−	0.789185i	−0.737125	−	0.675757i	$-0.763817\pi$
$389$	5.05743	−	15.5652i	0.256422	−	0.789185i	0.993546	−	0.113428i	$-0.0361831\pi$
$390$	5.87720	+	4.27003i	0.297604	+	0.216222i
$391$	−35.7727	−	25.9904i	−1.80910	−	1.31439i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−5.30921	−	16.3401i	−0.267814	−	0.824248i
$394$	−15.7455	+	11.4398i	−0.793249	+	0.576329i
$395$	10.7456			0.540670
$396$	−7.13355	+	13.1248i	−0.358474	+	0.659544i
$397$	34.8294			1.74804			0.874018	−	0.485893i	$-0.161505\pi$
$397$	34.8294			1.74804			0.874018	+	0.485893i	$0.161505\pi$
$398$	−12.6005	+	9.15479i	−0.631605	+	0.458888i
$399$	5.01249	+	15.4269i	0.250938	+	0.772309i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	9.59533	+	6.97141i	0.479168	+	0.348136i	0.801003	−	0.598660i	$-0.204300\pi$
$401$	9.59533	+	6.97141i	0.479168	+	0.348136i	−0.321836	+	0.946796i	$0.604300\pi$
$402$	−9.10180	−	6.61285i	−0.453957	−	0.329819i
$403$	−4.57197	+	14.0711i	−0.227746	+	0.700930i
$404$	2.37292	+	7.30310i	0.118057	+	0.363343i
$405$	1.80083	−	1.30838i	0.0894842	−	0.0650141i
$406$	−1.10448			−0.0548146
$407$	12.4315	−	5.92288i	0.616205	−	0.293586i
$408$	18.2913			0.905557
$409$	6.30003	−	4.57724i	0.311516	−	0.226330i	−0.421031	−	0.907046i	$-0.638331\pi$
$409$	6.30003	−	4.57724i	0.311516	−	0.226330i	0.732547	+	0.680717i	$0.238331\pi$
$410$	2.80882	+	8.64466i	0.138718	+	0.426929i
$411$	9.24208	−	28.4442i	0.455878	−	1.40305i
$412$	1.04741	+	0.760985i	0.0516020	+	0.0374911i
$413$	1.39719	+	1.01512i	0.0687510	+	0.0499506i
$414$	−9.21671	+	28.3661i	−0.452977	+	1.39412i
$415$	−4.91432	−	15.1247i	−0.241234	−	0.742443i
$416$	−2.14548	+	1.55878i	−0.105191	+	0.0764255i
$417$	−34.4279			−1.68594
$418$	−2.55495	−	19.4722i	−0.124967	−	0.952415i
$419$	−9.59415			−0.468705			−0.234352	−	0.972152i	$-0.575297\pi$
$419$	−9.59415			−0.468705			−0.234352	+	0.972152i	$0.575297\pi$
$420$	−2.21618	+	1.61015i	−0.108138	+	0.0785671i
$421$	6.09413	+	18.7558i	0.297010	+	0.914102i	0.982539	+	0.186057i	$0.0595709\pi$
$421$	6.09413	+	18.7558i	0.297010	+	0.914102i	−0.685529	+	0.728045i	$0.740429\pi$
$422$	4.26964	−	13.1406i	0.207843	−	0.639675i
$423$	−3.30581	−	2.40181i	−0.160734	−	0.116780i
$424$	7.47629	+	5.43185i	0.363081	+	0.263794i
$425$	−2.06339	+	6.35046i	−0.100089	+	0.308043i
$426$	5.94386	+	18.2933i	0.287981	+	0.886315i
$427$	−7.22871	+	5.25197i	−0.349822	+	0.254161i
$428$	−14.0391			−0.678605
$429$	3.13452	+	23.8892i	0.151336	+	1.15338i
$430$	−5.51500			−0.265957
$431$	15.0160	−	10.9098i	0.723294	−	0.525504i	−0.164141	−	0.986437i	$-0.552485\pi$
$431$	15.0160	−	10.9098i	0.723294	−	0.525504i	0.887435	+	0.460933i	$0.152485\pi$
$432$	−1.27315	−	3.91834i	−0.0612543	−	0.188521i
$433$	−4.84775	+	14.9198i	−0.232968	+	0.717001i	0.764417	+	0.644723i	$0.223027\pi$
$433$	−4.84775	+	14.9198i	−0.232968	+	0.717001i	−0.997384	+	0.0722788i	$0.976973\pi$
$434$	−4.51349	−	3.27924i	−0.216654	−	0.157409i
$435$	2.44773	+	1.77838i	0.117360	+	0.0852668i
$436$	−4.21094	+	12.9599i	−0.201667	+	0.620668i
$437$	−12.1172	−	37.2928i	−0.579643	−	1.78396i
$438$	2.14401	−	1.55772i	0.102445	−	0.0744306i
$439$	−6.85571			−0.327205			−0.163602	−	0.986526i	$-0.552311\pi$
$439$	−6.85571			−0.327205			−0.163602	+	0.986526i	$0.552311\pi$
$440$	2.99416	−	1.42654i	0.142741	−	0.0680078i
$441$	4.50401			0.214476
$442$	14.3259	−	10.4084i	0.681415	−	0.495077i
$443$	4.22381	+	12.9995i	0.200679	+	0.617627i	0.999863	+	0.0165405i	$0.00526526\pi$
$443$	4.22381	+	12.9995i	0.200679	+	0.617627i	−0.799184	+	0.601086i	$0.794735\pi$
$444$	−3.51461	+	10.8169i	−0.166796	+	0.513345i
$445$	−10.1160	−	7.34969i	−0.479544	−	0.348409i
$446$	7.26546	+	5.27866i	0.344029	+	0.249952i
$447$	16.0290	−	49.3323i	0.758147	−	2.33334i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	29.9013	−	21.7246i	1.41113	−	1.02525i	0.417973	−	0.908459i	$-0.362741\pi$
$449$	29.9013	−	21.7246i	1.41113	−	1.02525i	0.993157	−	0.116787i	$-0.0372595\pi$
$450$	4.50401			0.212321
$451$	−14.3962	+	26.4871i	−0.677891	+	1.24723i
$452$	12.3826			0.582430
$453$	−20.1195	+	14.6177i	−0.945298	+	0.686799i
$454$	−5.72792	−	17.6287i	−0.268824	−	0.827357i
$455$	−0.819499	+	2.52216i	−0.0384187	+	0.118241i
$456$	13.1229	+	9.53432i	0.614535	+	0.446486i
$457$	−5.84065	−	4.24348i	−0.273214	−	0.198502i	0.442738	−	0.896651i	$-0.354007\pi$
$457$	−5.84065	−	4.24348i	−0.273214	−	0.198502i	−0.715952	+	0.698149i	$0.754007\pi$
$458$	−8.15110	+	25.0865i	−0.380876	+	1.17221i
$459$	8.50114	+	26.1638i	0.396799	+	1.22122i
$460$	5.35738	−	3.89236i	0.249789	−	0.181482i
$461$	−35.7004			−1.66273			−0.831367	−	0.555724i	$-0.812441\pi$
$461$	−35.7004			−1.66273			−0.831367	+	0.555724i	$0.812441\pi$
$462$	−8.93252	−	1.65956i	−0.415578	−	0.0772097i
$463$	−19.9145			−0.925504			−0.462752	−	0.886488i	$-0.653138\pi$
$463$	−19.9145			−0.925504			−0.462752	+	0.886488i	$0.653138\pi$
$464$	−0.893546	+	0.649199i	−0.0414818	+	0.0301383i
$465$	4.72263	+	14.5348i	0.219007	+	0.674033i
$466$	3.98723	−	12.2714i	0.184705	−	0.568463i
$467$	−10.3741	−	7.53723i	−0.480057	−	0.348782i	0.321291	−	0.946981i	$-0.395883\pi$
$467$	−10.3741	−	7.53723i	−0.480057	−	0.348782i	−0.801348	+	0.598199i	$0.795883\pi$
$468$	−9.66324	−	7.02075i	−0.446683	−	0.324534i
$469$	1.26913	−	3.90598i	0.0586029	−	0.180361i
$470$	0.280352	+	0.862836i	0.0129317	+	0.0397996i
$471$	28.8769	−	20.9803i	1.33058	−	0.966721i
$472$	1.72702			0.0794924
$473$	−12.5851	−	13.2734i	−0.578661	−	0.610313i
$474$	−29.4359			−1.35204
$475$	−4.79052	+	3.48051i	−0.219804	+	0.159697i
$476$	2.06339	+	6.35046i	0.0945754	+	0.291073i
$477$	−12.8620	+	39.5853i	−0.588913	+	1.81249i
$478$	−6.01735	−	4.37186i	−0.275227	−	0.199964i
$479$	3.17183	+	2.30447i	0.144925	+	0.105294i	0.657885	−	0.753118i	$-0.271451\pi$
$479$	3.17183	+	2.30447i	0.144925	+	0.105294i	−0.512960	+	0.858412i	$0.671451\pi$
$480$	−0.846504	+	2.60527i	−0.0386374	+	0.118914i
$481$	3.40249	+	10.4718i	0.155140	+	0.477472i
$482$	24.2121	−	17.5911i	1.10283	−	0.801253i
$483$	−18.1402			−0.825406
$484$	10.2660	+	3.95097i	0.466634	+	0.179590i
$485$	11.4362			0.519290
$486$	−14.9325	+	10.8491i	−0.677353	+	0.492126i
$487$	−12.6824	−	39.0324i	−0.574694	−	1.76873i	−0.637220	−	0.770682i	$-0.719916\pi$
$487$	−12.6824	−	39.0324i	−0.574694	−	1.76873i	0.0625263	−	0.998043i	$-0.480084\pi$
$488$	−2.76112	+	8.49786i	−0.124990	+	0.384680i
$489$	18.6477	+	13.5484i	0.843279	+	0.612678i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	3.17281	−	9.76490i	0.143187	−	0.440684i	−0.853586	−	0.520951i	$-0.825577\pi$
$491$	3.17281	−	9.76490i	0.143187	−	0.440684i	0.996773	+	0.0802672i	$0.0255774\pi$
$492$	−7.69433	−	23.6807i	−0.346887	−	1.06761i
$493$	5.96645	−	4.33488i	0.268715	−	0.195233i
$494$	15.7033			0.706525
$495$	10.2780	+	10.8402i	0.461962	+	0.487230i
$496$	−5.57898			−0.250504
$497$	−5.68064	+	4.12723i	−0.254812	+	0.185131i
$498$	13.4620	+	41.4318i	0.603247	+	1.85660i
$499$	10.3342	−	31.8055i	0.462624	−	1.42381i	−0.399321	−	0.916811i	$-0.630754\pi$
$499$	10.3342	−	31.8055i	0.462624	−	1.42381i	0.861946	−	0.507001i	$-0.169246\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−24.8979	−	18.0894i	−1.11236	−	0.808175i
$502$	0.793590	−	2.44242i	0.0354196	−	0.109010i
$503$	−6.45748	−	19.8741i	−0.287925	−	0.886142i	−0.985507	−	0.169637i	$-0.945741\pi$
$503$	−6.45748	−	19.8741i	−0.287925	−	0.886142i	0.697582	−	0.716505i	$-0.254259\pi$
$504$	3.64382	−	2.64739i	0.162308	−	0.117924i
$505$	7.67893			0.341708
$506$	21.5935	+	4.01182i	0.959946	+	0.178347i
$507$	16.3460			0.725953
$508$	−6.99020	+	5.07868i	−0.310140	+	0.225330i
$509$	−13.6698	−	42.0713i	−0.605903	−	1.86478i	−0.490461	−	0.871463i	$-0.663172\pi$
$509$	−13.6698	−	42.0713i	−0.605903	−	1.86478i	−0.115442	−	0.993314i	$-0.536828\pi$
$510$	5.65234	−	17.3961i	0.250290	−	0.770312i
$511$	0.782674	+	0.568646i	0.0346234	+	0.0251554i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−7.53881	+	23.2021i	−0.332847	+	1.02440i
$514$	−8.58183	−	26.4122i	−0.378528	−	1.16499i
$515$	1.04741	−	0.760985i	0.0461542	−	0.0335330i
$516$	15.1075			0.665070
$517$	−1.43691	+	2.64371i	−0.0631951	+	0.116270i
$518$	−4.15191			−0.182424
$519$	−0.0660713	+	0.0480036i	−0.00290021	+	0.00210712i
$520$	0.819499	+	2.52216i	0.0359374	+	0.110604i
$521$	9.03172	−	27.7968i	0.395687	−	1.21780i	−0.532738	−	0.846280i	$-0.678837\pi$
$521$	9.03172	−	27.7968i	0.395687	−	1.21780i	0.928425	−	0.371519i	$-0.121163\pi$
$522$	−4.02453	−	2.92400i	−0.176149	−	0.127980i
$523$	19.1253	+	13.8954i	0.836291	+	0.607601i	0.921332	−	0.388776i	$-0.127102\pi$
$523$	19.1253	+	13.8954i	0.836291	+	0.607601i	−0.0850408	+	0.996377i	$0.527102\pi$
$524$	1.93813	−	5.96496i	0.0846678	−	0.260581i
$525$	0.846504	+	2.60527i	0.0369445	+	0.113703i
$526$	11.4574	−	8.32428i	0.499566	−	0.362956i
$527$	37.2524			1.62274
$528$	−8.20203	+	3.90779i	−0.356947	+	0.170065i
$529$	20.8520			0.906608
$530$	7.47629	−	5.43185i	0.324749	−	0.235944i
$531$	2.40369	+	7.39779i	0.104311	+	0.321037i
$532$	−1.82981	+	5.63159i	−0.0793325	+	0.244160i
$533$	−19.5014	−	14.1686i	−0.844699	−	0.613710i
$534$	27.7112	+	20.1333i	1.19918	+	0.871254i
$535$	−4.33832	+	13.3520i	−0.187562	+	0.577256i
$536$	−1.26913	−	3.90598i	−0.0548180	−	0.168712i
$537$	−52.5126	+	38.1526i	−2.26609	+	1.64641i
$538$	24.5685			1.05922
$539$	−0.431477	−	3.28844i	−0.0185850	−	0.141643i
$540$	−4.11999			−0.177296
$541$	0.0516636	−	0.0375358i	0.00222119	−	0.00161379i	−0.586674	−	0.809823i	$-0.699563\pi$
$541$	0.0516636	−	0.0375358i	0.00222119	−	0.00161379i	0.588895	+	0.808209i	$0.299563\pi$
$542$	3.24012	+	9.97206i	0.139175	+	0.428337i
$543$	4.55577	−	14.0212i	0.195507	−	0.601707i
$544$	5.40203	+	3.92480i	0.231610	+	0.168275i
$545$	11.0244	+	8.00968i	0.472232	+	0.343097i
$546$	2.24489	−	6.90906i	0.0960724	−	0.295681i
$547$	5.47650	+	16.8549i	0.234158	+	0.720664i	0.997232	+	0.0743532i	$0.0236892\pi$
$547$	5.47650	+	16.8549i	0.234158	+	0.720664i	−0.763074	+	0.646311i	$0.776311\pi$
$548$	8.83280	−	6.41740i	0.377318	−	0.274138i
$549$	−40.2441			−1.71758
$550$	−0.431477	−	3.28844i	−0.0183983	−	0.140219i
$551$	6.54009			0.278617
$552$	−14.6757	+	10.6625i	−0.624639	+	0.453827i
$553$	−3.32057	−	10.2197i	−0.141205	−	0.434585i
$554$	−9.53078	+	29.3327i	−0.404924	+	1.24623i
$555$	9.20136	+	6.68518i	0.390576	+	0.283770i
$556$	−10.1677	−	7.38724i	−0.431205	−	0.313289i
$557$	−11.6696	+	35.9153i	−0.494456	+	1.52178i	0.323346	+	0.946281i	$0.395192\pi$
$557$	−11.6696	+	35.9153i	−0.494456	+	1.52178i	−0.817802	+	0.575500i	$0.804808\pi$
$558$	−7.76490	−	23.8979i	−0.328714	−	1.01168i
$559$	11.8323	−	8.59667i	0.500453	−	0.363600i
$560$	−1.00000			−0.0422577
$561$	54.7672	−	26.0934i	2.31227	−	1.10166i
$562$	−4.44483			−0.187494
$563$	32.7020	−	23.7594i	1.37823	−	1.00134i	0.381183	−	0.924500i	$-0.375517\pi$
$563$	32.7020	−	23.7594i	1.37823	−	1.00134i	0.997043	−	0.0768404i	$-0.0244832\pi$
$564$	−0.767981	−	2.36360i	−0.0323378	−	0.0995257i
$565$	3.82644	−	11.7766i	0.160980	−	0.495445i
$566$	4.70243	+	3.41651i	0.197658	+	0.143607i
$567$	−1.80083	−	1.30838i	−0.0756279	−	0.0549469i
$568$	−2.16981	+	6.67800i	−0.0910433	+	0.280202i
$569$	−10.4310	−	32.1034i	−0.437292	−	1.34585i	−0.890720	−	0.454553i	$-0.849799\pi$
$569$	−10.4310	−	32.1034i	−0.437292	−	1.34585i	0.453428	−	0.891293i	$-0.350201\pi$
$570$	13.1229	−	9.53432i	0.549656	−	0.399349i
$571$	−9.90555			−0.414534			−0.207267	−	0.978284i	$-0.566457\pi$
$571$	−9.90555			−0.414534			−0.207267	+	0.978284i	$0.566457\pi$
$572$	−4.20023	+	7.72785i	−0.175620	+	0.323117i
$573$	33.8442			1.41386
$574$	7.35359	−	5.34269i	0.306933	−	0.223000i
$575$	−2.04634	−	6.29798i	−0.0853381	−	0.262644i
$576$	1.39181	−	4.28356i	0.0579923	−	0.178482i
$577$	−20.8710	−	15.1637i	−0.868871	−	0.631272i	0.0614124	−	0.998112i	$-0.480440\pi$
$577$	−20.8710	−	15.1637i	−0.868871	−	0.631272i	−0.930284	+	0.366840i	$0.880440\pi$
$578$	−22.3175	−	16.2146i	−0.928286	−	0.674439i
$579$	−9.98970	+	30.7451i	−0.415158	+	1.27772i
$580$	0.341304	+	1.05043i	0.0141719	+	0.0436166i
$581$	−12.8659	+	9.34759i	−0.533765	+	0.387803i
$582$	−31.3276			−1.29857
$583$	30.1340	+	5.59855i	1.24802	+	0.231868i
$584$	0.967438			0.0400329
$585$	−9.66324	+	7.02075i	−0.399526	+	0.290272i
$586$	2.52197	+	7.76183i	0.104182	+	0.320638i
$587$	0.235214	−	0.723914i	0.00970832	−	0.0298791i	−0.946085	−	0.323918i	$-0.895000\pi$
$587$	0.235214	−	0.723914i	0.00970832	−	0.0298791i	0.955793	+	0.294039i	$0.0949997\pi$
$588$	2.21618	+	1.61015i	0.0913935	+	0.0664013i
$589$	26.7262	+	19.4177i	1.10123	+	0.800093i
$590$	0.533678	−	1.64249i	0.0219712	−	0.0676203i
$591$	−16.4751	−	50.7052i	−0.677696	−	2.08573i
$592$	−3.35897	+	2.44043i	−0.138053	+	0.100301i
$593$	−23.5344			−0.966442			−0.483221	−	0.875498i	$-0.660533\pi$
$593$	−23.5344			−0.966442			−0.483221	+	0.875498i	$0.660533\pi$
$594$	−9.40168	−	9.91593i	−0.385756	−	0.406856i
$595$	6.67727			0.273741
$596$	15.3192	−	11.1300i	0.627499	−	0.455904i
$597$	−13.1843	−	40.5772i	−0.539599	−	1.66072i
$598$	−5.42679	+	16.7019i	−0.221918	+	0.682993i
$599$	−9.91274	−	7.20203i	−0.405024	−	0.294267i	0.366560	−	0.930394i	$-0.380535\pi$
$599$	−9.91274	−	7.20203i	−0.405024	−	0.294267i	−0.771584	+	0.636127i	$0.780535\pi$
$600$	2.21618	+	1.61015i	0.0904750	+	0.0657339i
$601$	9.17884	−	28.2496i	0.374413	−	1.15232i	−0.569461	−	0.822018i	$-0.692848\pi$
$601$	9.17884	−	28.2496i	0.374413	−	1.15232i	0.943874	−	0.330306i	$-0.107152\pi$
$602$	1.70423	+	5.24507i	0.0694592	+	0.213773i
$603$	14.9651	−	10.8728i	0.609426	−	0.442774i
$604$	−9.07849			−0.369398
$605$	6.92995	−	8.54259i	0.281743	−	0.347305i
$606$	−21.0352			−0.854498
$607$	−31.1479	+	22.6302i	−1.26425	+	0.918533i	−0.998958	−	0.0456342i	$-0.985469\pi$
$607$	−31.1479	+	22.6302i	−1.26425	+	0.918533i	−0.265294	+	0.964167i	$0.585469\pi$
$608$	1.82981	+	5.63159i	0.0742088	+	0.228391i
$609$	0.934949	−	2.87748i	0.0378861	−	0.116601i
$610$	7.22871	+	5.25197i	0.292682	+	0.212646i
$611$	−1.94646	−	1.41419i	−0.0787454	−	0.0572118i
$612$	−9.29352	+	28.6025i	−0.375668	+	1.15619i
$613$	3.40842	+	10.4900i	0.137665	+	0.423689i	0.995995	−	0.0894090i	$-0.0284978\pi$
$613$	3.40842	+	10.4900i	0.137665	+	0.423689i	−0.858330	+	0.513098i	$0.828498\pi$
$614$	12.7687	−	9.27700i	0.515302	−	0.374389i
$615$	−24.8994			−1.00404
$616$	−2.28197	−	2.40679i	−0.0919431	−	0.0969722i
$617$	−21.3964			−0.861388			−0.430694	−	0.902498i	$-0.641731\pi$
$617$	−21.3964			−0.861388			−0.430694	+	0.902498i	$0.641731\pi$
$618$	−2.86921	+	2.08460i	−0.115416	+	0.0838549i
$619$	−15.1480	−	46.6206i	−0.608848	−	1.87384i	−0.467793	−	0.883838i	$-0.654951\pi$
$619$	−15.1480	−	46.6206i	−0.608848	−	1.87384i	−0.141055	−	0.990002i	$-0.545049\pi$
$620$	−1.72400	+	5.30592i	−0.0692375	+	0.213091i
$621$	−22.0723	−	16.0365i	−0.885732	−	0.643522i
$622$	5.27308	+	3.83112i	0.211431	+	0.153614i
$623$	−3.86396	+	11.8920i	−0.154806	+	0.476445i
$624$	−2.24489	−	6.90906i	−0.0898675	−	0.276584i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−9.54938			−0.381670
$627$	52.8930	+	9.82692i	2.11234	+	0.392450i
$628$	13.0301			0.519956
$629$	22.4287	−	16.2954i	0.894292	−	0.649741i
$630$	−1.39181	−	4.28356i	−0.0554512	−	0.170661i
$631$	5.12729	−	15.7802i	0.204114	−	0.628199i	−0.795634	−	0.605777i	$-0.792862\pi$
$631$	5.12729	−	15.7802i	0.204114	−	0.628199i	0.999749	−	0.0224217i	$-0.00713765\pi$
$632$	−8.69338	−	6.31611i	−0.345804	−	0.251241i
$633$	30.6206	+	22.2472i	1.21706	+	0.884245i
$634$	−2.01562	+	6.20343i	−0.0800503	+	0.246370i
$635$	2.67002	+	8.21748i	0.105957	+	0.326101i
$636$	−20.4801	+	14.8797i	−0.812090	+	0.590018i
$637$	2.65196			0.105074
$638$	−1.74931	+	3.21848i	−0.0692557	+	0.127421i
$639$	−31.6256			−1.25109
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	3.34546	+	10.2963i	0.132138	+	0.406678i	0.995134	−	0.0985325i	$-0.0314149\pi$
$641$	3.34546	+	10.2963i	0.132138	+	0.406678i	−0.862996	+	0.505210i	$0.831415\pi$
$642$	11.8841	−	36.5756i	0.469030	−	1.44352i
$643$	0.359045	+	0.260861i	0.0141593	+	0.0102874i	0.594842	−	0.803842i	$-0.297214\pi$
$643$	0.359045	+	0.260861i	0.0141593	+	0.0102874i	−0.580683	+	0.814130i	$0.697214\pi$
$644$	−5.35738	−	3.89236i	−0.211110	−	0.153381i
$645$	4.66847	−	14.3681i	0.183821	−	0.565742i
$646$	−12.2182	−	37.6037i	−0.480717	−	1.47950i
$647$	−25.7829	+	18.7324i	−1.01363	+	0.736446i	−0.964968	−	0.262369i	$-0.915496\pi$
$647$	−25.7829	+	18.7324i	−1.01363	+	0.736446i	−0.0486634	+	0.998815i	$0.515496\pi$
$648$	−2.22595			−0.0874437
$649$	5.17096	−	2.46366i	0.202978	−	0.0967073i
$650$	2.65196			0.104018
$651$	12.3640	−	8.98297i	0.484583	−	0.352070i
$652$	2.60018	+	8.00254i	0.101831	+	0.313404i
$653$	7.28629	−	22.4249i	0.285135	−	0.877554i	−0.701224	−	0.712941i	$-0.747363\pi$
$653$	7.28629	−	22.4249i	0.285135	−	0.877554i	0.986358	−	0.164613i	$-0.0526374\pi$
$654$	−30.1996	−	21.9413i	−1.18090	−	0.857971i
$655$	−5.07410	−	3.68655i	−0.198261	−	0.144045i
$656$	2.80882	−	8.64466i	0.109666	−	0.337517i
$657$	1.34649	+	4.14408i	0.0525317	+	0.161676i
$658$	0.733972	−	0.533262i	0.0286132	−	0.0207887i
$659$	−18.1283			−0.706178			−0.353089	−	0.935590i	$-0.614869\pi$
$659$	−18.1283			−0.706178			−0.353089	+	0.935590i	$0.614869\pi$
$660$	1.18196	+	9.00816i	0.0460079	+	0.350642i
$661$	35.1392			1.36676			0.683378	−	0.730065i	$-0.260510\pi$
$661$	35.1392			1.36676			0.683378	+	0.730065i	$0.260510\pi$
$662$	16.4650	−	11.9625i	0.639930	−	0.464936i
$663$	14.9897	+	46.1337i	0.582153	+	1.79168i
$664$	−4.91432	+	15.1247i	−0.190713	+	0.586953i
$665$	4.79052	+	3.48051i	0.185768	+	0.134969i
$666$	−15.1288	−	10.9917i	−0.586229	−	0.425920i
$667$	−2.26014	+	6.95601i	−0.0875131	+	0.269338i
$668$	−3.47170	−	10.6848i	−0.134324	−	0.413407i
$669$	−19.9026	+	14.4601i	−0.769478	+	0.559059i
$670$	−4.10699			−0.158667
$671$	3.85533	+	29.3828i	0.148833	+	1.13431i
$672$	2.73934			0.105672
$673$	9.35904	−	6.79974i	0.360764	−	0.262111i	−0.392606	−	0.919707i	$-0.628427\pi$
$673$	9.35904	−	6.79974i	0.360764	−	0.262111i	0.753371	+	0.657596i	$0.228427\pi$
$674$	−6.30254	−	19.3972i	−0.242765	−	0.747153i
$675$	−1.27315	+	3.91834i	−0.0490034	+	0.150817i
$676$	4.82751	+	3.50739i	0.185674	+	0.134900i
$677$	3.25553	+	2.36528i	0.125120	+	0.0909052i	0.648585	−	0.761142i	$-0.275361\pi$
$677$	3.25553	+	2.36528i	0.125120	+	0.0909052i	−0.523465	+	0.852047i	$0.675361\pi$
$678$	−10.4819	+	32.2601i	−0.402557	+	1.23894i
$679$	−3.53397	−	10.8764i	−0.135621	−	0.417400i
$680$	5.40203	−	3.92480i	0.207158	−	0.150509i
$681$	50.7763			1.94575
$682$	−16.7043	+	7.95865i	−0.639642	+	0.304753i
$683$	−2.85171			−0.109118			−0.0545588	−	0.998511i	$-0.517375\pi$
$683$	−2.85171			−0.109118			−0.0545588	+	0.998511i	$0.517375\pi$
$684$	−21.5765	+	15.6762i	−0.824998	+	0.599396i
$685$	−3.37383	−	10.3836i	−0.128907	−	0.396736i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−58.4572	−	42.4716i	−2.23028	−	1.62039i
$688$	4.46173	+	3.24163i	0.170102	+	0.123586i
$689$	−7.57316	+	23.3078i	−0.288515	+	0.887956i
$690$	5.60562	+	17.2523i	0.213402	+	0.656785i
$691$	−7.37973	+	5.36169i	−0.280738	+	0.203968i	−0.719239	−	0.694762i	$-0.755510\pi$
$691$	−7.37973	+	5.36169i	−0.280738	+	0.203968i	0.438501	+	0.898731i	$0.355510\pi$
$692$	−0.0298132			−0.00113333
$693$	7.13355	−	13.1248i	0.270981	−	0.498568i
$694$	−25.1418			−0.954370
$695$	−10.1677	+	7.38724i	−0.385682	+	0.280214i
$696$	−0.934949	−	2.87748i	−0.0354392	−	0.109071i
$697$	−18.7553	+	57.7228i	−0.710406	+	2.18641i
$698$	−5.24825	−	3.81308i	−0.198649	−	0.144327i
$699$	28.5952	+	20.7756i	1.08157	+	0.785807i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	−15.9303	−	49.0286i	−0.601681	−	1.85178i	−0.518172	−	0.855276i	$-0.673387\pi$
$701$	−15.9303	−	49.0286i	−0.601681	−	1.85178i	−0.0835084	−	0.996507i	$-0.526613\pi$
$702$	8.83934	−	6.42215i	0.333619	−	0.242389i
$703$	24.5851			0.927246
$704$	−3.26082	−	0.605824i	−0.122897	−	0.0228329i
$705$	−2.48524			−0.0935995
$706$	0.542935	−	0.394465i	0.0204336	−	0.0148459i
$707$	−2.37292	−	7.30310i	−0.0892429	−	0.274661i
$708$	−1.46193	+	4.49935i	−0.0549426	+	0.169096i
$709$	−24.6308	−	17.8953i	−0.925029	−	0.672073i	0.0197420	−	0.999805i	$-0.493716\pi$
$709$	−24.6308	−	17.8953i	−0.925029	−	0.672073i	−0.944771	+	0.327733i	$0.893716\pi$
$710$	5.68064	+	4.12723i	0.213191	+	0.154892i
$711$	14.9559	−	46.0295i	0.560889	−	1.72624i
$712$	3.86396	+	11.8920i	0.144808	+	0.445673i
$713$	−29.8887	+	21.7154i	−1.11934	+	0.813248i
$714$	−18.2913			−0.684536
$715$	6.05168	+	6.38269i	0.226320	+	0.238699i
$716$	−23.6951			−0.885529
$717$	16.4836	−	11.9760i	0.615591	−	0.447253i
$718$	−10.3981	−	32.0022i	−0.388055	−	1.19431i
$719$	12.7699	−	39.3016i	0.476236	−	1.46570i	−0.368048	−	0.929807i	$-0.619974\pi$
$719$	12.7699	−	39.3016i	0.476236	−	1.46570i	0.844284	−	0.535896i	$-0.180026\pi$
$720$	−3.64382	−	2.64739i	−0.135797	−	0.0986623i
$721$	−1.04741	−	0.760985i	−0.0390075	−	0.0283406i
$722$	4.96374	−	15.2768i	0.184731	−	0.568545i
$723$	25.3340	+	77.9699i	0.942180	+	2.89973i
$724$	4.35402	−	3.16338i	0.161816	−	0.117566i
$725$	1.10448			0.0410195
$726$	−18.9835	+	23.4011i	−0.704545	+	0.868496i
$727$	−2.01006			−0.0745492			−0.0372746	−	0.999305i	$-0.511868\pi$
$727$	−2.01006			−0.0745492			−0.0372746	+	0.999305i	$0.511868\pi$
$728$	2.14548	−	1.55878i	0.0795167	−	0.0577722i
$729$	−13.5609	−	41.7361i	−0.502254	−	1.54578i
$730$	0.298955	−	0.920088i	0.0110648	−	0.0340540i
$731$	−29.7922	−	21.6453i	−1.10190	−	0.800579i
$732$	−19.8019	−	14.3869i	−0.731900	−	0.531757i
$733$	−7.40993	+	22.8054i	−0.273692	+	0.842338i	0.715870	+	0.698233i	$0.246030\pi$
$733$	−7.40993	+	22.8054i	−0.273692	+	0.842338i	−0.989562	+	0.144104i	$0.953970\pi$
$734$	−1.65878	−	5.10520i	−0.0612267	−	0.188436i
$735$	2.21618	−	1.61015i	0.0817449	−	0.0593911i
$736$	−6.62208			−0.244093
$737$	−9.37201	−	9.88464i	−0.345222	−	0.364105i
$738$	40.9393			1.50700
$739$	10.4367	−	7.58269i	0.383919	−	0.278934i	−0.379040	−	0.925380i	$-0.623746\pi$
$739$	10.4367	−	7.58269i	0.383919	−	0.278934i	0.762959	+	0.646447i	$0.223746\pi$
$740$	1.28301	+	3.94870i	0.0471644	+	0.145157i
$741$	−13.2929	+	40.9113i	−0.488327	+	1.50292i
$742$	−7.47629	−	5.43185i	−0.274463	−	0.199409i
$743$	10.2331	+	7.43477i	0.375415	+	0.272755i	0.759453	−	0.650562i	$-0.225467\pi$
$743$	10.2331	+	7.43477i	0.375415	+	0.272755i	−0.384038	+	0.923317i	$0.625467\pi$
$744$	4.72263	−	14.5348i	0.173140	−	0.532870i
$745$	−5.85141	−	18.0088i	−0.214379	−	0.659791i
$746$	−13.0447	+	9.47755i	−0.477602	+	0.346998i
$747$	−71.6275			−2.62071
$748$	21.7734	+	4.04525i	0.796115	+	0.147909i
$749$	14.0391			0.512977
$750$	2.21618	−	1.61015i	0.0809233	−	0.0587942i
$751$	−2.34064	−	7.20374i	−0.0854111	−	0.262868i	0.899225	−	0.437486i	$-0.144131\pi$
$751$	−2.34064	−	7.20374i	−0.0854111	−	0.262868i	−0.984636	+	0.174618i	$0.944131\pi$
$752$	0.280352	−	0.862836i	0.0102234	−	0.0314644i
$753$	5.69138	+	4.13503i	0.207406	+	0.150689i
$754$	−2.36964	−	1.72165i	−0.0862973	−	0.0626987i
$755$	−2.80541	+	8.63415i	−0.102099	+	0.314229i
$756$	1.27315	+	3.91834i	0.0463039	+	0.142509i
$757$	−20.3418	+	14.7792i	−0.739335	+	0.537159i	−0.892503	−	0.451042i	$-0.851053\pi$
$757$	−20.3418	+	14.7792i	−0.739335	+	0.537159i	0.153168	+	0.988200i	$0.451053\pi$
$758$	−27.3566			−0.993636
$759$	−28.7308	+	52.8608i	−1.04286	+	1.91872i
$760$	5.92140			0.214792
$761$	−27.4802	+	19.9655i	−0.996156	+	0.723749i	−0.961261	−	0.275642i	$-0.911110\pi$
$761$	−27.4802	+	19.9655i	−0.996156	+	0.723749i	−0.0348952	+	0.999391i	$0.511110\pi$
$762$	−7.31410	−	22.5105i	−0.264962	−	0.815469i
$763$	4.21094	−	12.9599i	0.152446	−	0.469181i
$764$	9.99528	+	7.26199i	0.361616	+	0.262730i
$765$	24.3308	+	17.6773i	0.879680	+	0.639125i
$766$	0.0408989	−	0.125874i	0.00147774	−	0.00454800i
$767$	1.41529	+	4.35581i	0.0511031	+	0.157279i
$768$	2.21618	−	1.61015i	0.0799694	−	0.0581011i
$769$	22.3766			0.806919			0.403460	−	0.914997i	$-0.367808\pi$
$769$	22.3766			0.806919			0.403460	+	0.914997i	$0.367808\pi$
$770$	−2.99416	+	1.42654i	−0.107902	+	0.0514090i
$771$	76.0754			2.73979
$772$	−9.54732	+	6.93653i	−0.343615	+	0.249651i
$773$	15.6126	+	48.0507i	0.561547	+	1.72826i	0.677994	+	0.735068i	$0.262850\pi$
$773$	15.6126	+	48.0507i	0.561547	+	1.72826i	−0.116446	+	0.993197i	$0.537150\pi$
$774$	−7.67585	+	23.6238i	−0.275903	+	0.849142i
$775$	4.51349	+	3.27924i	0.162129	+	0.117794i
$776$	−9.25206	−	6.72201i	−0.332129	−	0.241306i
$777$	3.51461	−	10.8169i	0.126086	−	0.388052i
$778$	5.05743	+	15.5652i	0.181318	+	0.558038i
$779$	−43.5436	+	31.6362i	−1.56011	+	1.13349i
$780$	−7.26462			−0.260115
$781$	3.02969	+	23.0903i	0.108411	+	0.826236i
$782$	44.2175			1.58121
$783$	3.68140	−	2.67469i	0.131562	−	0.0955857i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	4.02651	−	12.3923i	0.143712	−	0.442301i
$786$	13.8997	+	10.0987i	0.495786	+	0.360210i
$787$	20.9780	+	15.2414i	0.747786	+	0.543299i	0.895140	−	0.445785i	$-0.147076\pi$
$787$	20.9780	+	15.2414i	0.747786	+	0.543299i	−0.147354	+	0.989084i	$0.547076\pi$
$788$	6.01426	−	18.5100i	0.214249	−	0.659391i
$789$	11.9883	+	36.8961i	0.426794	+	1.31354i
$790$	−8.69338	+	6.31611i	−0.309296	+	0.224717i
$791$	−12.3826			−0.440276
$792$	−1.94338	−	14.8111i	−0.0690549	−	0.526291i
$793$	−23.6957			−0.841459
$794$	−28.1776	+	20.4722i	−0.999984	+	0.726531i
$795$	7.82272	+	24.0759i	0.277443	+	0.853882i
$796$	4.81296	−	14.8128i	0.170591	−	0.525024i
$797$	−9.35560	−	6.79724i	−0.331392	−	0.240771i	0.409629	−	0.912252i	$-0.365658\pi$
$797$	−9.35560	−	6.79724i	−0.331392	−	0.240771i	−0.741021	+	0.671482i	$0.765658\pi$
$798$	−13.1229	−	9.53432i	−0.464545	−	0.337511i
$799$	−1.87199	+	5.76139i	−0.0662262	+	0.203823i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	−45.5624	+	33.1030i	−1.60987	+	1.16964i
$802$	−11.8605			−0.418808
$803$	2.89666	−	1.38009i	0.102221	−	0.0487024i
$804$	11.2504			0.396773
$805$	−5.35738	+	3.89236i	−0.188823	+	0.137188i
$806$	−4.57197	−	14.0711i	−0.161041	−	0.495632i
$807$	−20.7973	+	64.0075i	−0.732100	+	2.25317i
$808$	−6.21239	−	4.51356i	−0.218551	−	0.158787i
$809$	−5.23284	−	3.80188i	−0.183977	−	0.133667i	0.491985	−	0.870604i	$-0.336272\pi$
$809$	−5.23284	−	3.80188i	−0.183977	−	0.133667i	−0.675962	+	0.736937i	$0.736272\pi$
$810$	−0.687858	+	2.11701i	−0.0241688	+	0.0743841i
$811$	−10.9228	−	33.6169i	−0.383551	−	1.18045i	−0.937526	−	0.347915i	$-0.886890\pi$
$811$	−10.9228	−	33.6169i	−0.383551	−	1.18045i	0.553976	−	0.832533i	$-0.313110\pi$
$812$	0.893546	−	0.649199i	0.0313573	−	0.0227824i
$813$	−28.7227			−1.00735
$814$	−6.57589	+	12.0987i	−0.230485	+	0.424061i
$815$	8.41437			0.294743
$816$	−14.7980	+	10.7514i	−0.518034	+	0.376374i
$817$	−10.0914	−	31.0582i	−0.353054	−	1.08659i
$818$	−2.40640	+	7.40613i	−0.0841377	+	0.258949i
$819$	9.66324	+	7.02075i	0.337661	+	0.245325i
$820$	−7.35359	−	5.34269i	−0.256798	−	0.186575i
$821$	9.48588	−	29.1945i	0.331059	−	1.01890i	−0.637571	−	0.770391i	$-0.720061\pi$
$821$	9.48588	−	29.1945i	0.331059	−	1.01890i	0.968631	−	0.248505i	$-0.0799392\pi$
$822$	9.24208	+	28.4442i	0.322354	+	0.992105i
$823$	−15.8888	+	11.5439i	−0.553848	+	0.402394i	−0.829202	−	0.558949i	$-0.811205\pi$
$823$	−15.8888	+	11.5439i	−0.553848	+	0.402394i	0.275354	+	0.961343i	$0.411205\pi$
$824$	−1.29467			−0.0451018
$825$	8.93252	+	1.65956i	0.310990	+	0.0577785i
$826$	−1.72702			−0.0600906
$827$	22.9662	−	16.6859i	0.798612	−	0.580225i	−0.111895	−	0.993720i	$-0.535692\pi$
$827$	22.9662	−	16.6859i	0.798612	−	0.580225i	0.910506	+	0.413495i	$0.135692\pi$
$828$	−9.21671	−	28.3661i	−0.320303	−	0.985791i
$829$	10.0361	−	30.8879i	0.348567	−	1.07278i	−0.611079	−	0.791570i	$-0.709264\pi$
$829$	10.0361	−	30.8879i	0.348567	−	1.07278i	0.959646	−	0.281210i	$-0.0907359\pi$
$830$	12.8659	+	9.34759i	0.446580	+	0.324459i
$831$	−68.3519	−	49.6605i	−2.37110	−	1.72270i
$832$	0.819499	−	2.52216i	0.0284110	−	0.0874401i
$833$	−2.06339	−	6.35046i	−0.0714922	−	0.220031i
$834$	27.8527	−	20.2362i	0.964461	−	0.700722i
$835$	−11.2346			−0.388791
$836$	13.5125	+	14.2516i	0.467338	+	0.492900i
$837$	22.9853			0.794489
$838$	7.76183	−	5.63930i	0.268128	−	0.194806i
$839$	8.16010	+	25.1142i	0.281718	+	0.867039i	0.987363	+	0.158474i	$0.0506573\pi$
$839$	8.16010	+	25.1142i	0.281718	+	0.867039i	−0.705645	+	0.708565i	$0.749343\pi$
$840$	0.846504	−	2.60527i	0.0292072	−	0.0898904i
$841$	22.4746	+	16.3287i	0.774986	+	0.563060i
$842$	−15.9546	−	11.5917i	−0.549833	−	0.399477i
$843$	3.76256	−	11.5800i	0.129590	−	0.398836i
$844$	4.26964	+	13.1406i	0.146967	+	0.452318i
$845$	4.82751	−	3.50739i	0.166072	−	0.120658i
$846$	4.08621			0.140487
$847$	−10.2660	−	3.95097i	−0.352742	−	0.135757i
$848$	−9.24121			−0.317344
$849$	−12.8816	+	9.35901i	−0.442094	+	0.321200i
$850$	−2.06339	−	6.35046i	−0.0707737	−	0.217819i
$851$	−8.49621	+	26.1486i	−0.291246	+	0.896364i
$852$	−15.5612	−	11.3059i	−0.533119	−	0.387334i
$853$	−22.6911	−	16.4861i	−0.776930	−	0.564473i	0.127126	−	0.991887i	$-0.459425\pi$
$853$	−22.6911	−	16.4861i	−0.776930	−	0.564473i	−0.904056	+	0.427414i	$0.859425\pi$
$854$	2.76112	−	8.49786i	0.0944837	−	0.290791i
$855$	8.24149	+	25.3647i	0.281853	+	0.867455i
$856$	11.3579	−	8.25197i	0.388204	−	0.282047i
$857$	47.9742			1.63877			0.819383	−	0.573246i	$-0.194316\pi$
$857$	47.9742			1.63877			0.819383	+	0.573246i	$0.194316\pi$
$858$	−16.5776	−	17.4844i	−0.565951	−	0.596907i
$859$	−28.1815			−0.961541			−0.480770	−	0.876847i	$-0.659643\pi$
$859$	−28.1815			−0.961541			−0.480770	+	0.876847i	$0.659643\pi$
$860$	4.46173	−	3.24163i	0.152144	−	0.110539i
$861$	7.69433	+	23.6807i	0.262222	+	0.807036i
$862$	−5.73560	+	17.6523i	−0.195355	+	0.601241i
$863$	−5.70782	−	4.14698i	−0.194297	−	0.141165i	0.486384	−	0.873745i	$-0.338316\pi$
$863$	−5.70782	−	4.14698i	−0.194297	−	0.141165i	−0.680680	+	0.732581i	$0.738316\pi$
$864$	3.33314	+	2.42167i	0.113396	+	0.0823868i
$865$	−0.00921279	+	0.0283540i	−0.000313244	+	0.000964066i
$866$	−4.84775	−	14.9198i	−0.164733	−	0.506997i
$867$	61.1353	−	44.4174i	2.07627	−	1.50850i
$868$	5.57898			0.189363
$869$	−35.0395	−	6.50994i	−1.18863	−	0.220835i
$870$	−3.02556			−0.102576
$871$	8.81144	−	6.40189i	0.298564	−	0.216920i
$872$	−4.21094	−	12.9599i	−0.142600	−	0.438879i
$873$	15.9170	−	48.9876i	0.538710	−	1.65798i
$874$	31.7232	+	23.0482i	1.07305	+	0.779619i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−0.818940	+	2.52044i	−0.0276694	+	0.0851577i
$877$	−13.6177	−	41.9109i	−0.459836	−	1.41523i	−0.865362	−	0.501146i	$-0.832912\pi$
$877$	−13.6177	−	41.9109i	−0.459836	−	1.41523i	0.405526	−	0.914083i	$-0.367088\pi$
$878$	5.54638	−	4.02968i	0.187181	−	0.135995i
$879$	−22.3565			−0.754067
$880$	−1.58382	+	2.91402i	−0.0533907	+	0.0982315i
$881$	2.79232			0.0940757			0.0470379	−	0.998893i	$-0.485022\pi$
$881$	2.79232			0.0940757			0.0470379	+	0.998893i	$0.485022\pi$
$882$	−3.64382	+	2.64739i	−0.122694	+	0.0891422i
$883$	−4.47322	−	13.7671i	−0.150536	−	0.463301i	0.847146	−	0.531361i	$-0.178319\pi$
$883$	−4.47322	−	13.7671i	−0.150536	−	0.463301i	−0.997681	+	0.0680597i	$0.978319\pi$
$884$	−5.47202	+	16.8411i	−0.184044	+	0.566429i
$885$	3.82737	+	2.78075i	0.128656	+	0.0934739i
$886$	−11.0581	−	8.03416i	−0.371503	−	0.269913i
$887$	−8.59588	+	26.4554i	−0.288621	+	0.888286i	0.696668	+	0.717393i	$0.254665\pi$
$887$	−8.59588	+	26.4554i	−0.288621	+	0.888286i	−0.985290	+	0.170892i	$0.945335\pi$
$888$	−3.51461	−	10.8169i	−0.117943	−	0.362990i
$889$	6.99020	−	5.07868i	0.234444	−	0.170333i
$890$	12.5040			0.419136
$891$	−6.66485	+	3.17542i	−0.223281	+	0.106381i
$892$	−8.98060			−0.300693
$893$	−4.34614	+	3.15766i	−0.145438	+	0.105667i
$894$	16.0290	+	49.3323i	0.536091	+	1.64992i
$895$	−7.32220	+	22.5354i	−0.244754	+	0.753276i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	−38.9193	−	28.2765i	−1.29948	−	0.944126i
$898$	−11.4213	+	35.1511i	−0.381133	+	1.17301i
$899$	−1.90413	−	5.86030i	−0.0635062	−	0.195452i
$900$	−3.64382	+	2.64739i	−0.121461	+	0.0882463i
$901$	61.7061			2.05573
$902$	−3.92193	−	29.8904i	−0.130586	−	0.995241i
$903$	−15.1075			−0.502745
$904$	−10.0178	+	7.27833i	−0.333186	+	0.242074i
$905$	−1.66309	−	5.11845i	−0.0552829	−	0.170143i
$906$	7.68497	−	23.6519i	0.255316	−	0.785782i
$907$	23.9124	+	17.3734i	0.793998	+	0.576873i	0.909147	−	0.416475i	$-0.136735\pi$
$907$	23.9124	+	17.3734i	0.793998	+	0.576873i	−0.115149	+	0.993348i	$0.536735\pi$
$908$	14.9959	+	10.8951i	0.497656	+	0.361568i
$909$	10.6876	−	32.8932i	0.354487	−	1.09100i
$910$	−0.819499	−	2.52216i	−0.0271661	−	0.0836088i
$911$	−39.3910	+	28.6192i	−1.30508	+	0.948198i	−0.999991	−	0.00412537i	$-0.998687\pi$
$911$	−39.3910	+	28.6192i	−1.30508	+	0.948198i	−0.305091	+	0.952323i	$0.598687\pi$
$912$	−16.2208			−0.537123
$913$	6.86181	+	52.2963i	0.227093	+	1.73075i
$914$	7.21944			0.238798
$915$	−19.8019	+	14.3869i	−0.654632	+	0.475618i
$916$	−8.15110	−	25.0865i	−0.269320	−	0.828881i
$917$	−1.93813	+	5.96496i	−0.0640028	+	0.196980i
$918$	−22.2563	−	16.1701i	−0.734567	−	0.533694i
$919$	33.8086	+	24.5634i	1.11524	+	0.810272i	0.983481	−	0.181010i	$-0.0579366\pi$
$919$	33.8086	+	24.5634i	1.11524	+	0.810272i	0.131762	+	0.991281i	$0.457937\pi$
$920$	−2.04634	+	6.29798i	−0.0674657	+	0.207638i
$921$	13.3603	+	41.1189i	0.440238	+	1.35491i
$922$	28.8822	−	20.9842i	0.951186	−	0.691077i
$923$	−18.6211			−0.612922
$924$	8.20203	−	3.90779i	0.269827	−	0.128557i
$925$	4.15191			0.136514
$926$	16.1112	−	11.7054i	0.529445	−	0.384665i
$927$	−1.80193	−	5.54578i	−0.0591833	−	0.182147i
$928$	0.341304	−	1.05043i	0.0112039	−	0.0344819i
$929$	−8.29017	−	6.02316i	−0.271992	−	0.197614i	0.443425	−	0.896311i	$-0.353763\pi$
$929$	−8.29017	−	6.02316i	−0.271992	−	0.197614i	−0.715417	+	0.698698i	$0.753763\pi$
$930$	−12.3640	−	8.98297i	−0.405431	−	0.294563i
$931$	1.82981	−	5.63159i	0.0599697	−	0.184568i
$932$	3.98723	+	12.2714i	0.130606	+	0.401964i
$933$	−14.4448	+	10.4947i	−0.472901	+	0.343582i
$934$	12.8231			0.419585
$935$	10.5756	−	19.4577i	0.345860	−	0.636335i
$936$	11.9444			0.390416
$937$	26.9822	−	19.6037i	0.881470	−	0.640426i	−0.0521697	−	0.998638i	$-0.516614\pi$
$937$	26.9822	−	19.6037i	0.881470	−	0.640426i	0.933640	+	0.358212i	$0.116614\pi$
$938$	1.26913	+	3.90598i	0.0414385	+	0.127535i
$939$	8.08359	−	24.8787i	0.263798	−	0.811886i
$940$	−0.733972	−	0.533262i	−0.0239395	−	0.0173931i
$941$	3.86158	+	2.80560i	0.125884	+	0.0914600i	0.648946	−	0.760835i	$-0.275210\pi$
$941$	3.86158	+	2.80560i	0.125884	+	0.0914600i	−0.523062	+	0.852295i	$0.675210\pi$
$942$	−11.0300	+	33.9468i	−0.359377	+	1.10605i
$943$	−18.6002	−	57.2457i	−0.605707	−	1.86418i
$944$	−1.39719	+	1.01512i	−0.0454745	+	0.0330392i
$945$	4.11999			0.134023
$946$	17.9834	+	3.34112i	0.584692	+	0.108629i
$947$	9.18216			0.298380			0.149190	−	0.988809i	$-0.452333\pi$
$947$	9.18216			0.298380			0.149190	+	0.988809i	$0.452333\pi$
$948$	23.8141	−	17.3020i	0.773447	−	0.561942i
$949$	0.792815	+	2.44003i	0.0257359	+	0.0792068i
$950$	1.82981	−	5.63159i	0.0593670	−	0.182713i
$951$	−14.4554	−	10.5024i	−0.468748	−	0.340565i
$952$	−5.40203	−	3.92480i	−0.175081	−	0.127204i
$953$	15.4475	−	47.5426i	0.500395	−	1.54006i	−0.307982	−	0.951392i	$-0.599654\pi$
$953$	15.4475	−	47.5426i	0.500395	−	1.54006i	0.808377	−	0.588665i	$-0.200346\pi$
$954$	−12.8620	−	39.5853i	−0.416424	−	1.28162i
$955$	9.99528	−	7.26199i	0.323440	−	0.234993i
$956$	7.43785			0.240557
$957$	−6.90423	−	7.28188i	−0.223182	−	0.235390i
$958$	−3.92060			−0.126669
$959$	−8.83280	+	6.41740i	−0.285226	+	0.207229i
$960$	−0.846504	−	2.60527i	−0.0273208	−	0.0840848i
$961$	0.0386282	−	0.118885i	0.00124607	−	0.00383501i
$962$	−8.90783	−	6.47192i	−0.287200	−	0.208663i
$963$	51.1559	+	37.1669i	1.64847	+	1.19769i
$964$	−9.24819	+	28.4630i	−0.297864	+	0.916731i
$965$	3.64675	+	11.2235i	0.117393	+	0.361299i
$966$	14.6757	−	10.6625i	0.472183	−	0.343061i
$967$	4.16857			0.134052			0.0670261	−	0.997751i	$-0.478649\pi$
$967$	4.16857			0.134052			0.0670261	+	0.997751i	$0.478649\pi$
$968$	−10.6277	+	2.83777i	−0.341586	+	0.0912095i
$969$	108.310			3.47943
$970$	−9.25206	+	6.72201i	−0.297066	+	0.215831i
$971$	13.4510	+	41.3980i	0.431664	+	1.32853i	0.896467	+	0.443111i	$0.146125\pi$
$971$	13.4510	+	41.3980i	0.431664	+	1.32853i	−0.464802	+	0.885414i	$0.653875\pi$
$972$	5.70372	−	17.5542i	0.182947	−	0.563052i
$973$	10.1677	+	7.38724i	0.325960	+	0.236824i
$974$	33.2029	+	24.1233i	1.06389	+	0.772961i
$975$	−2.24489	+	6.90906i	−0.0718940	+	0.221267i
$976$	−2.76112	−	8.49786i	−0.0883814	−	0.272010i
$977$	19.9273	−	14.4781i	0.637532	−	0.463194i	−0.221469	−	0.975167i	$-0.571085\pi$
$977$	19.9273	−	14.4781i	0.637532	−	0.463194i	0.859001	+	0.511973i	$0.171085\pi$
$978$	−23.0499			−0.737053
$979$	28.5338	+	30.0946i	0.911945	+	0.961826i
$980$	1.00000			0.0319438
$981$	49.6539	−	36.0756i	1.58533	−	1.15181i
$982$	3.17281	+	9.76490i	0.101248	+	0.311611i
$983$	11.6898	−	35.9776i	0.372847	−	1.14751i	−0.572072	−	0.820203i	$-0.693860\pi$
$983$	11.6898	−	35.9776i	0.372847	−	1.14751i	0.944919	−	0.327303i	$-0.106140\pi$
$984$	20.1440	+	14.6355i	0.642168	+	0.466562i
$985$	−15.7455	−	11.4398i	−0.501695	−	0.364502i
$986$	−2.27898	+	7.01398i	−0.0725775	+	0.223371i
$987$	0.767981	+	2.36360i	0.0244451	+	0.0752343i
$988$	−12.7042	+	9.23016i	−0.404175	+	0.293651i
$989$	36.5208			1.16129
$990$	−14.6868	−	2.72863i	−0.466776	−	0.0867217i
$991$	−26.2409			−0.833570			−0.416785	−	0.909005i	$-0.636843\pi$
$991$	−26.2409			−0.833570			−0.416785	+	0.909005i	$0.636843\pi$
$992$	4.51349	−	3.27924i	0.143303	−	0.104116i
$993$	17.2279	+	53.0221i	0.546712	+	1.68261i
$994$	2.16981	−	6.67800i	0.0688223	−	0.211813i
$995$	−12.6005	−	9.15479i	−0.399462	−	0.290226i
$996$	−35.2440	−	25.6063i	−1.11675	−	0.811365i
$997$	−1.93970	+	5.96977i	−0.0614308	+	0.189065i	−0.977062	−	0.212954i	$-0.931691\pi$
$997$	−1.93970	+	5.96977i	−0.0614308	+	0.189065i	0.915631	+	0.402019i	$0.131691\pi$
$998$	10.3342	+	31.8055i	0.327125	+	1.00679i
$999$	13.8389	−	10.0545i	0.437843	−	0.318112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.g.421.1	✓	12
11.2	odd	10		8470.2.a.cv.1.1		6
11.4	even	5	inner	770.2.n.g.631.1	yes	12
11.9	even	5		8470.2.a.db.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.421.1	✓	12	1.1	even	1	trivial
770.2.n.g.631.1	yes	12	11.4	even	5	inner
8470.2.a.cv.1.1		6	11.2	odd	10
8470.2.a.db.1.1		6	11.9	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.846504 - 2.60527i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.21618 + 1.61015i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.64382 + 2.64739i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.846504 - 2.60527i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.21618 + 1.61015i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.64382 + 2.64739i) q^{9} +1.00000 q^{10} +(2.28197 + 2.40679i) q^{11} -2.73934 q^{12} +(-2.14548 + 1.55878i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.846504 + 2.60527i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.40203 + 3.92480i) q^{17} +(1.39181 - 4.28356i) q^{18} +(1.82981 + 5.63159i) q^{19} +(-0.809017 + 0.587785i) q^{20} +2.73934 q^{21} +(-3.26082 - 0.605824i) q^{22} -6.62208 q^{23} +(2.21618 - 1.61015i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.819499 - 2.52216i) q^{26} +(3.33314 + 2.42167i) q^{27} +(0.809017 + 0.587785i) q^{28} +(0.341304 - 1.05043i) q^{29} +(-0.846504 - 2.60527i) q^{30} +(4.51349 - 3.27924i) q^{31} +1.00000 q^{32} +(4.33864 - 7.98250i) q^{33} -6.67727 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.39181 + 4.28356i) q^{36} +(1.28301 - 3.94870i) q^{37} +(-4.79052 - 3.48051i) q^{38} +(5.87720 + 4.27003i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.80882 + 8.64466i) q^{41} +(-2.21618 + 1.61015i) q^{42} -5.51500 q^{43} +(2.99416 - 1.42654i) q^{44} +4.50401 q^{45} +(5.35738 - 3.89236i) q^{46} +(0.280352 + 0.862836i) q^{47} +(-0.846504 + 2.60527i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(5.65234 - 17.3961i) q^{51} +(0.819499 + 2.52216i) q^{52} +(7.47629 - 5.43185i) q^{53} -4.11999 q^{54} +(-0.431477 - 3.28844i) q^{55} -1.00000 q^{56} +(13.1229 - 9.53432i) q^{57} +(0.341304 + 1.05043i) q^{58} +(0.533678 - 1.64249i) q^{59} +(2.21618 + 1.61015i) q^{60} +(7.22871 + 5.25197i) q^{61} +(-1.72400 + 5.30592i) q^{62} +(-1.39181 - 4.28356i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.65196 q^{65} +(1.18196 + 9.00816i) q^{66} -4.10699 q^{67} +(5.40203 - 3.92480i) q^{68} +(5.60562 + 17.2523i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(5.68064 + 4.12723i) q^{71} +(-3.64382 - 2.64739i) q^{72} +(0.298955 - 0.920088i) q^{73} +(1.28301 + 3.94870i) q^{74} +(2.21618 - 1.61015i) q^{75} +5.92140 q^{76} +(-2.99416 + 1.42654i) q^{77} -7.26462 q^{78} +(-8.69338 + 6.31611i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-0.687858 + 2.11701i) q^{81} +(-7.35359 - 5.34269i) q^{82} +(12.8659 + 9.34759i) q^{83} +(0.846504 - 2.60527i) q^{84} +(-2.06339 - 6.35046i) q^{85} +(4.46173 - 3.24163i) q^{86} -3.02556 q^{87} +(-1.58382 + 2.91402i) q^{88} +12.5040 q^{89} +(-3.64382 + 2.64739i) q^{90} +(-0.819499 - 2.52216i) q^{91} +(-2.04634 + 6.29798i) q^{92} +(-12.3640 - 8.98297i) q^{93} +(-0.733972 - 0.533262i) q^{94} +(1.82981 - 5.63159i) q^{95} +(-0.846504 - 2.60527i) q^{96} +(-9.25206 + 6.72201i) q^{97} +1.00000 q^{98} +(-14.6868 - 2.72863i) 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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