LMFDB - Embedded newform 630.2.j.g.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.g.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(1.68614 + 0.396143i) q^{12} +(1.68614 + 2.92048i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-1.68614 - 0.396143i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +(-2.68614 - 1.33591i) q^{18} +4.37228 q^{19} +(0.500000 - 0.866025i) q^{20} +(0.500000 + 1.65831i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(1.00000 + 1.73205i) q^{23} +(1.18614 - 1.26217i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.37228 q^{26} +(4.00000 + 3.31662i) q^{27} -1.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(-1.18614 + 1.26217i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 + 1.65831i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{35} +(-2.50000 + 1.65831i) q^{36} +10.7446 q^{37} +(2.18614 - 3.78651i) q^{38} +(-5.68614 - 1.33591i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.18614 + 5.51856i) q^{41} +(1.68614 + 0.396143i) q^{42} +(-1.81386 + 3.14170i) q^{43} -1.00000 q^{44} +(2.50000 - 1.65831i) q^{45} +2.00000 q^{46} +(0.313859 - 0.543620i) q^{47} +(-0.500000 - 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.55842 + 3.78651i) q^{51} +(1.68614 - 2.92048i) q^{52} +0.744563 q^{53} +(4.87228 - 1.80579i) q^{54} +1.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-5.18614 + 5.51856i) q^{57} +(-1.00000 - 1.73205i) q^{58} +(-5.55842 - 9.62747i) q^{59} +(0.500000 + 1.65831i) q^{60} +(5.74456 - 9.94987i) q^{61} +2.00000 q^{62} +(-2.68614 - 1.33591i) q^{63} +1.00000 q^{64} +(-1.68614 + 2.92048i) q^{65} +(1.68614 + 0.396143i) q^{66} +(-2.18614 - 3.78651i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-3.37228 - 0.792287i) q^{69} +(0.500000 - 0.866025i) q^{70} -16.1168 q^{71} +(0.186141 + 2.99422i) q^{72} +14.4891 q^{73} +(5.37228 - 9.30506i) q^{74} +(-0.500000 - 1.65831i) q^{75} +(-2.18614 - 3.78651i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-4.00000 + 4.25639i) q^{78} +(0.0584220 - 0.101190i) q^{79} -1.00000 q^{80} +(-8.93070 + 1.11469i) q^{81} +6.37228 q^{82} +(-0.313859 + 0.543620i) q^{83} +(1.18614 - 1.26217i) q^{84} +(1.50000 + 2.59808i) q^{85} +(1.81386 + 3.14170i) q^{86} +(1.00000 + 3.31662i) q^{87} +(-0.500000 + 0.866025i) q^{88} -15.4891 q^{89} +(-0.186141 - 2.99422i) q^{90} +3.37228 q^{91} +(1.00000 - 1.73205i) q^{92} +(-3.37228 - 0.792287i) q^{93} +(-0.313859 - 0.543620i) q^{94} +(2.18614 + 3.78651i) q^{95} +(-1.68614 - 0.396143i) q^{96} +(-8.24456 + 14.2800i) q^{97} -1.00000 q^{98} +(-2.68614 - 1.33591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 4 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} + q^{12} + q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 12 q^{17} - 5 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21} - 2 q^{22} + 4 q^{23} - q^{24} - 2 q^{25} + 2 q^{26} + 16 q^{27} - 4 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} + 2 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} - 10 q^{36} + 20 q^{37} + 3 q^{38} - 17 q^{39} - 2 q^{40} + 7 q^{41} + q^{42} - 13 q^{43} - 4 q^{44} + 10 q^{45} + 8 q^{46} + 7 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + 3 q^{51} + q^{52} - 20 q^{53} + 8 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 4 q^{58} - 5 q^{59} + 2 q^{60} + 8 q^{62} - 5 q^{63} + 4 q^{64} - q^{65} + q^{66} - 3 q^{67} - 6 q^{68} - 2 q^{69} + 2 q^{70} - 30 q^{71} - 5 q^{72} + 12 q^{73} + 10 q^{74} - 2 q^{75} - 3 q^{76} - 2 q^{77} - 16 q^{78} - 17 q^{79} - 4 q^{80} - 7 q^{81} + 14 q^{82} - 7 q^{83} - q^{84} + 6 q^{85} + 13 q^{86} + 4 q^{87} - 2 q^{88} - 16 q^{89} + 5 q^{90} + 2 q^{91} + 4 q^{92} - 2 q^{93} - 7 q^{94} + 3 q^{95} - q^{96} - 10 q^{97} - 4 q^{98} - 5 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 4 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 + q^12 + q^13 - 2 * q^14 - q^15 - 2 * q^16 + 12 * q^17 - 5 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 - 2 * q^22 + 4 * q^23 - q^24 - 2 * q^25 + 2 * q^26 + 16 * q^27 - 4 * q^28 + 4 * q^29 + q^30 + 4 * q^31 + 2 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 - 10 * q^36 + 20 * q^37 + 3 * q^38 - 17 * q^39 - 2 * q^40 + 7 * q^41 + q^42 - 13 * q^43 - 4 * q^44 + 10 * q^45 + 8 * q^46 + 7 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + 3 * q^51 + q^52 - 20 * q^53 + 8 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 4 * q^58 - 5 * q^59 + 2 * q^60 + 8 * q^62 - 5 * q^63 + 4 * q^64 - q^65 + q^66 - 3 * q^67 - 6 * q^68 - 2 * q^69 + 2 * q^70 - 30 * q^71 - 5 * q^72 + 12 * q^73 + 10 * q^74 - 2 * q^75 - 3 * q^76 - 2 * q^77 - 16 * q^78 - 17 * q^79 - 4 * q^80 - 7 * q^81 + 14 * q^82 - 7 * q^83 - q^84 + 6 * q^85 + 13 * q^86 + 4 * q^87 - 2 * q^88 - 16 * q^89 + 5 * q^90 + 2 * q^91 + 4 * q^92 - 2 * q^93 - 7 * q^94 + 3 * q^95 - q^96 - 10 * q^97 - 4 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	+	1.65831i	0.204124	+	0.677003i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$	1.00000			0.316228
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	1.68614	+	0.396143i	0.486747	+	0.114357i
$13$	1.68614	+	2.92048i	0.467651	+	0.809996i	0.999317	−	0.0369586i	$-0.0117670\pi$
$13$	1.68614	+	2.92048i	0.467651	+	0.809996i	−0.531666	+	0.846954i	$0.678434\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−1.68614	−	0.396143i	−0.435360	−	0.102284i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	−2.68614	−	1.33591i	−0.633129	−	0.314876i
$19$	4.37228			1.00307			0.501535	−	0.865137i	$-0.332769\pi$
$19$	4.37228			1.00307			0.501535	+	0.865137i	$0.332769\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	0.500000	+	1.65831i	0.109109	+	0.361873i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$	1.18614	−	1.26217i	0.242120	−	0.257639i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.37228			0.661359
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$	−1.00000			−0.188982
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$	−1.18614	+	1.26217i	−0.216559	+	0.230439i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.500000	+	1.65831i	0.0870388	+	0.288675i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	1.00000			0.169031
$36$	−2.50000	+	1.65831i	−0.416667	+	0.276385i
$37$	10.7446			1.76640			0.883198	−	0.469001i	$-0.155386\pi$
$37$	10.7446			1.76640			0.883198	+	0.469001i	$0.155386\pi$
$38$	2.18614	−	3.78651i	0.354639	−	0.614252i
$39$	−5.68614	−	1.33591i	−0.910511	−	0.213916i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	3.18614	+	5.51856i	0.497592	+	0.861854i	0.999996	−	0.00277878i	$-0.000884515\pi$
$41$	3.18614	+	5.51856i	0.497592	+	0.861854i	−0.502405	+	0.864633i	$0.667551\pi$
$42$	1.68614	+	0.396143i	0.260177	+	0.0611263i
$43$	−1.81386	+	3.14170i	−0.276611	+	0.479104i	−0.970540	−	0.240939i	$-0.922545\pi$
$43$	−1.81386	+	3.14170i	−0.276611	+	0.479104i	0.693929	+	0.720043i	$0.255878\pi$
$44$	−1.00000			−0.150756
$45$	2.50000	−	1.65831i	0.372678	−	0.247207i
$46$	2.00000			0.294884
$47$	0.313859	−	0.543620i	0.0457811	−	0.0792952i	−0.842227	−	0.539123i	$-0.818756\pi$
$47$	0.313859	−	0.543620i	0.0457811	−	0.0792952i	0.888008	+	0.459828i	$0.152089\pi$
$48$	−0.500000	−	1.65831i	−0.0721688	−	0.239357i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−3.55842	+	3.78651i	−0.498279	+	0.530217i
$52$	1.68614	−	2.92048i	0.233826	−	0.404998i
$53$	0.744563			0.102274			0.0511368	−	0.998692i	$-0.483716\pi$
$53$	0.744563			0.102274			0.0511368	+	0.998692i	$0.483716\pi$
$54$	4.87228	−	1.80579i	0.663034	−	0.245737i
$55$	1.00000			0.134840
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−5.18614	+	5.51856i	−0.686921	+	0.730951i
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	−5.55842	−	9.62747i	−0.723645	−	1.25339i	−0.959529	−	0.281609i	$-0.909132\pi$
$59$	−5.55842	−	9.62747i	−0.723645	−	1.25339i	0.235884	−	0.971781i	$-0.424201\pi$
$60$	0.500000	+	1.65831i	0.0645497	+	0.214087i
$61$	5.74456	−	9.94987i	0.735516	−	1.27395i	−0.218981	−	0.975729i	$-0.570273\pi$
$61$	5.74456	−	9.94987i	0.735516	−	1.27395i	0.954497	−	0.298222i	$-0.0963935\pi$
$62$	2.00000			0.254000
$63$	−2.68614	−	1.33591i	−0.338422	−	0.168309i
$64$	1.00000			0.125000
$65$	−1.68614	+	2.92048i	−0.209140	+	0.362241i
$66$	1.68614	+	0.396143i	0.207550	+	0.0487619i
$67$	−2.18614	−	3.78651i	−0.267080	−	0.462595i	0.701027	−	0.713135i	$-0.252725\pi$
$67$	−2.18614	−	3.78651i	−0.267080	−	0.462595i	−0.968106	+	0.250540i	$0.919392\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	−3.37228	−	0.792287i	−0.405975	−	0.0953801i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−16.1168			−1.91272			−0.956359	−	0.292195i	$-0.905614\pi$
$71$	−16.1168			−1.91272			−0.956359	+	0.292195i	$0.905614\pi$
$72$	0.186141	+	2.99422i	0.0219369	+	0.352872i
$73$	14.4891			1.69582			0.847912	−	0.530137i	$-0.177860\pi$
$73$	14.4891			1.69582			0.847912	+	0.530137i	$0.177860\pi$
$74$	5.37228	−	9.30506i	0.624515	−	1.08169i
$75$	−0.500000	−	1.65831i	−0.0577350	−	0.191485i
$76$	−2.18614	−	3.78651i	−0.250768	−	0.434342i
$77$	−0.500000	−	0.866025i	−0.0569803	−	0.0986928i
$78$	−4.00000	+	4.25639i	−0.452911	+	0.481941i
$79$	0.0584220	−	0.101190i	0.00657299	−	0.0113847i	−0.862720	−	0.505682i	$-0.831241\pi$
$79$	0.0584220	−	0.101190i	0.00657299	−	0.0113847i	0.869293	+	0.494297i	$0.164574\pi$
$80$	−1.00000			−0.111803
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$	6.37228			0.703701
$83$	−0.313859	+	0.543620i	−0.0344505	+	0.0596701i	−0.882737	−	0.469868i	$-0.844301\pi$
$83$	−0.313859	+	0.543620i	−0.0344505	+	0.0596701i	0.848286	+	0.529538i	$0.177635\pi$
$84$	1.18614	−	1.26217i	0.129419	−	0.137714i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	1.81386	+	3.14170i	0.195593	+	0.338778i
$87$	1.00000	+	3.31662i	0.107211	+	0.355580i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−15.4891			−1.64184			−0.820922	−	0.571040i	$-0.806540\pi$
$89$	−15.4891			−1.64184			−0.820922	+	0.571040i	$0.806540\pi$
$90$	−0.186141	−	2.99422i	−0.0196209	−	0.315618i
$91$	3.37228			0.353511
$92$	1.00000	−	1.73205i	0.104257	−	0.180579i
$93$	−3.37228	−	0.792287i	−0.349689	−	0.0821563i
$94$	−0.313859	−	0.543620i	−0.0323721	−	0.0560702i
$95$	2.18614	+	3.78651i	0.224293	+	0.388487i
$96$	−1.68614	−	0.396143i	−0.172091	−	0.0404312i
$97$	−8.24456	+	14.2800i	−0.837109	+	1.44991i	0.0551936	+	0.998476i	$0.482422\pi$
$97$	−8.24456	+	14.2800i	−0.837109	+	1.44991i	−0.892302	+	0.451439i	$0.850911\pi$
$98$	−1.00000			−0.101015
$99$	−2.68614	−	1.33591i	−0.269967	−	0.134264i
$100$	1.00000			0.100000
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	−0.926187	−	0.377064i	$-0.876934\pi$
$101$	−1.37228	+	2.37686i	−0.136547	+	0.236507i	0.789640	+	0.613570i	$0.210267\pi$
$102$	1.50000	+	4.97494i	0.148522	+	0.492592i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−1.68614	−	2.92048i	−0.165340	−	0.286377i
$105$	−1.18614	+	1.26217i	−0.115755	+	0.123175i
$106$	0.372281	−	0.644810i	0.0361592	−	0.0626295i
$107$	−13.8614			−1.34003			−0.670016	−	0.742346i	$-0.733713\pi$
$107$	−13.8614			−1.34003			−0.670016	+	0.742346i	$0.733713\pi$
$108$	0.872281	−	5.12241i	0.0839353	−	0.492905i
$109$	−1.88316			−0.180374			−0.0901868	−	0.995925i	$-0.528746\pi$
$109$	−1.88316			−0.180374			−0.0901868	+	0.995925i	$0.528746\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−12.7446	+	13.5615i	−1.20966	+	1.28720i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	2.18614	+	7.25061i	0.204751	+	0.679082i
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$	−2.00000			−0.185695
$117$	8.43070	−	5.59230i	0.779419	−	0.517008i
$118$	−11.1168			−1.02339
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	1.68614	+	0.396143i	0.153923	+	0.0361628i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−5.74456	−	9.94987i	−0.520088	−	0.900819i
$123$	−10.7446	−	2.52434i	−0.968805	−	0.227612i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$	−2.50000	+	1.65831i	−0.222718	+	0.147734i
$127$	−4.74456			−0.421012			−0.210506	−	0.977593i	$-0.567511\pi$
$127$	−4.74456			−0.421012			−0.210506	+	0.977593i	$0.567511\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.81386	−	6.01589i	−0.159701	−	0.529670i
$130$	1.68614	+	2.92048i	0.147884	+	0.256143i
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	1.18614	−	1.26217i	0.103240	−	0.109858i
$133$	2.18614	−	3.78651i	0.189562	−	0.328332i
$134$	−4.37228			−0.377708
$135$	−0.872281	+	5.12241i	−0.0750740	+	0.440867i
$136$	−3.00000			−0.257248
$137$	2.18614	−	3.78651i	0.186775	−	0.323503i	−0.757398	−	0.652953i	$-0.773530\pi$
$137$	2.18614	−	3.78651i	0.186775	−	0.323503i	0.944173	+	0.329450i	$0.106863\pi$
$138$	−2.37228	+	2.52434i	−0.201942	+	0.214886i
$139$	4.18614	+	7.25061i	0.355064	+	0.614989i	0.987129	−	0.159927i	$-0.0511258\pi$
$139$	4.18614	+	7.25061i	0.355064	+	0.614989i	−0.632065	+	0.774915i	$0.717792\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	0.313859	+	1.04095i	0.0264317	+	0.0876641i
$142$	−8.05842	+	13.9576i	−0.676248	+	1.17130i
$143$	3.37228			0.282004
$144$	2.68614	+	1.33591i	0.223845	+	0.111326i
$145$	2.00000			0.166091
$146$	7.24456	−	12.5480i	0.599564	−	1.03848i
$147$	1.68614	+	0.396143i	0.139071	+	0.0326734i
$148$	−5.37228	−	9.30506i	−0.441599	−	0.764872i
$149$	−6.43070	−	11.1383i	−0.526824	−	0.912485i	−0.999511	−	0.0312555i	$-0.990049\pi$
$149$	−6.43070	−	11.1383i	−0.526824	−	0.912485i	0.472688	−	0.881230i	$-0.343284\pi$
$150$	−1.68614	−	0.396143i	−0.137673	−	0.0323450i
$151$	9.43070	−	16.3345i	0.767460	−	1.32928i	−0.171477	−	0.985188i	$-0.554854\pi$
$151$	9.43070	−	16.3345i	0.767460	−	1.32928i	0.938936	−	0.344091i	$-0.111813\pi$
$152$	−4.37228			−0.354639
$153$	−0.558422	−	8.98266i	−0.0451457	−	0.726205i
$154$	−1.00000			−0.0805823
$155$	−1.00000	+	1.73205i	−0.0803219	+	0.139122i
$156$	1.68614	+	5.59230i	0.134999	+	0.447742i
$157$	8.43070	+	14.6024i	0.672843	+	1.16540i	0.977094	+	0.212807i	$0.0682605\pi$
$157$	8.43070	+	14.6024i	0.672843	+	1.16540i	−0.304251	+	0.952592i	$0.598406\pi$
$158$	−0.0584220	−	0.101190i	−0.00464780	−	0.00805023i
$159$	−0.883156	+	0.939764i	−0.0700388	+	0.0745281i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.00000			0.157622
$162$	−3.50000	+	8.29156i	−0.274986	+	0.651447i
$163$	1.25544			0.0983334			0.0491667	−	0.998791i	$-0.484343\pi$
$163$	1.25544			0.0983334			0.0491667	+	0.998791i	$0.484343\pi$
$164$	3.18614	−	5.51856i	0.248796	−	0.430927i
$165$	−1.18614	+	1.26217i	−0.0923409	+	0.0982597i
$166$	0.313859	+	0.543620i	0.0243602	+	0.0421931i
$167$	5.31386	+	9.20387i	0.411199	+	0.712217i	0.995021	−	0.0996643i	$-0.0317769\pi$
$167$	5.31386	+	9.20387i	0.411199	+	0.712217i	−0.583822	+	0.811881i	$0.698444\pi$
$168$	−0.500000	−	1.65831i	−0.0385758	−	0.127942i
$169$	0.813859	−	1.40965i	0.0626046	−	0.108434i
$170$	3.00000			0.230089
$171$	−0.813859	−	13.0916i	−0.0622374	−	1.00114i
$172$	3.62772			0.276611
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$	3.37228	+	0.792287i	0.255652	+	0.0600631i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	18.7446	+	4.40387i	1.40893	+	0.331015i
$178$	−7.74456	+	13.4140i	−0.580480	+	1.00542i
$179$	−5.88316			−0.439728			−0.219864	−	0.975531i	$-0.570561\pi$
$179$	−5.88316			−0.439728			−0.219864	+	0.975531i	$0.570561\pi$
$180$	−2.68614	−	1.33591i	−0.200213	−	0.0995727i
$181$	2.74456			0.204002			0.102001	−	0.994784i	$-0.467476\pi$
$181$	2.74456			0.204002			0.102001	+	0.994784i	$0.467476\pi$
$182$	1.68614	−	2.92048i	0.124985	−	0.216480i
$183$	5.74456	+	19.0526i	0.424650	+	1.40841i
$184$	−1.00000	−	1.73205i	−0.0737210	−	0.127688i
$185$	5.37228	+	9.30506i	0.394978	+	0.684122i
$186$	−2.37228	+	2.52434i	−0.173944	+	0.185093i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	−0.627719			−0.0457811
$189$	4.87228	−	1.80579i	0.354406	−	0.131352i
$190$	4.37228			0.317199
$191$	−8.74456	+	15.1460i	−0.632734	+	1.09593i	0.354256	+	0.935148i	$0.384734\pi$
$191$	−8.74456	+	15.1460i	−0.632734	+	1.09593i	−0.986990	+	0.160780i	$0.948599\pi$
$192$	−1.18614	+	1.26217i	−0.0856023	+	0.0910892i
$193$	0.186141	+	0.322405i	0.0133987	+	0.0232072i	0.872647	−	0.488352i	$-0.162402\pi$
$193$	0.186141	+	0.322405i	0.0133987	+	0.0232072i	−0.859248	+	0.511559i	$0.829068\pi$
$194$	8.24456	+	14.2800i	0.591925	+	1.02524i
$195$	−1.68614	−	5.59230i	−0.120747	−	0.400473i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−6.74456			−0.480530			−0.240265	−	0.970707i	$-0.577234\pi$
$197$	−6.74456			−0.480530			−0.240265	+	0.970707i	$0.577234\pi$
$198$	−2.50000	+	1.65831i	−0.177667	+	0.117851i
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	7.37228	+	1.73205i	0.520001	+	0.122169i
$202$	1.37228	+	2.37686i	0.0965534	+	0.167235i
$203$	−1.00000	−	1.73205i	−0.0701862	−	0.121566i
$204$	5.05842	+	1.18843i	0.354160	+	0.0832068i
$205$	−3.18614	+	5.51856i	−0.222530	+	0.385433i
$206$	−8.00000			−0.557386
$207$	5.00000	−	3.31662i	0.347524	−	0.230521i
$208$	−3.37228			−0.233826
$209$	2.18614	−	3.78651i	0.151219	−	0.261918i
$210$	0.500000	+	1.65831i	0.0345033	+	0.114434i
$211$	−13.1753	−	22.8202i	−0.907023	−	1.57101i	−0.818179	−	0.574964i	$-0.805016\pi$
$211$	−13.1753	−	22.8202i	−0.907023	−	1.57101i	−0.0888439	−	0.996046i	$-0.528317\pi$
$212$	−0.372281	−	0.644810i	−0.0255684	−	0.0442857i
$213$	19.1168	−	20.3422i	1.30986	−	1.39382i
$214$	−6.93070	+	12.0043i	−0.473773	+	0.820599i
$215$	−3.62772			−0.247408
$216$	−4.00000	−	3.31662i	−0.272166	−	0.225668i
$217$	2.00000			0.135769
$218$	−0.941578	+	1.63086i	−0.0637717	+	0.110456i
$219$	−17.1861	+	18.2877i	−1.16133	+	1.23577i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	5.05842	+	8.76144i	0.340266	+	0.589358i
$222$	5.37228	+	17.8178i	0.360564	+	1.19586i
$223$	−9.43070	+	16.3345i	−0.631527	+	1.09384i	0.355713	+	0.934595i	$0.384238\pi$
$223$	−9.43070	+	16.3345i	−0.631527	+	1.09384i	−0.987240	+	0.159241i	$0.949095\pi$
$224$	1.00000			0.0668153
$225$	2.68614	+	1.33591i	0.179076	+	0.0890605i
$226$	6.00000			0.399114
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	−0.726182	−	0.687502i	$-0.758707\pi$
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	0.958485	+	0.285141i	$0.0920405\pi$
$228$	7.37228	+	1.73205i	0.488241	+	0.114708i
$229$	3.37228	+	5.84096i	0.222847	+	0.385982i	0.955671	−	0.294436i	$-0.0951318\pi$
$229$	3.37228	+	5.84096i	0.222847	+	0.385982i	−0.732825	+	0.680418i	$0.761798\pi$
$230$	1.00000	+	1.73205i	0.0659380	+	0.114208i
$231$	1.68614	+	0.396143i	0.110940	+	0.0260643i
$232$	−1.00000	+	1.73205i	−0.0656532	+	0.113715i
$233$	1.62772			0.106635			0.0533177	−	0.998578i	$-0.483020\pi$
$233$	1.62772			0.106635			0.0533177	+	0.998578i	$0.483020\pi$
$234$	−0.627719	−	10.0974i	−0.0410353	−	0.660084i
$235$	0.627719			0.0409479
$236$	−5.55842	+	9.62747i	−0.361822	+	0.626695i
$237$	0.0584220	+	0.193764i	0.00379492	+	0.0125863i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	1.62772	+	2.81929i	0.105288	+	0.182365i	0.913856	−	0.406038i	$-0.133090\pi$
$239$	1.62772	+	2.81929i	0.105288	+	0.182365i	−0.808568	+	0.588403i	$0.799757\pi$
$240$	1.18614	−	1.26217i	0.0765651	−	0.0814727i
$241$	9.18614	−	15.9109i	0.591731	−	1.02491i	−0.402268	−	0.915522i	$-0.631778\pi$
$241$	9.18614	−	15.9109i	0.591731	−	1.02491i	0.993999	−	0.109387i	$-0.0348887\pi$
$242$	10.0000			0.642824
$243$	9.18614	−	12.5942i	0.589291	−	0.807921i
$244$	−11.4891			−0.735516
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	−7.55842	+	8.04290i	−0.481907	+	0.512796i
$247$	7.37228	+	12.7692i	0.469087	+	0.812483i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−0.313859	−	1.04095i	−0.0198900	−	0.0659678i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	22.6060			1.42688			0.713438	−	0.700718i	$-0.247137\pi$
$251$	22.6060			1.42688			0.713438	+	0.700718i	$0.247137\pi$
$252$	0.186141	+	2.99422i	0.0117258	+	0.188618i
$253$	2.00000			0.125739
$254$	−2.37228	+	4.10891i	−0.148850	+	0.257816i
$255$	−5.05842	−	1.18843i	−0.316771	−	0.0744224i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.87228	−	13.6352i	−0.491059	−	0.850540i	0.508888	−	0.860833i	$-0.330057\pi$
$257$	−7.87228	−	13.6352i	−0.491059	−	0.850540i	−0.999947	+	0.0102931i	$0.996724\pi$
$258$	−6.11684	−	1.43710i	−0.380818	−	0.0894698i
$259$	5.37228	−	9.30506i	0.333817	−	0.578189i
$260$	3.37228			0.209140
$261$	−5.37228	−	2.67181i	−0.332536	−	0.165381i
$262$	−4.00000			−0.247121
$263$	11.4891	−	19.8997i	0.708450	−	1.22707i	−0.256982	−	0.966416i	$-0.582728\pi$
$263$	11.4891	−	19.8997i	0.708450	−	1.22707i	0.965432	−	0.260655i	$-0.0839385\pi$
$264$	−0.500000	−	1.65831i	−0.0307729	−	0.102062i
$265$	0.372281	+	0.644810i	0.0228691	+	0.0396104i
$266$	−2.18614	−	3.78651i	−0.134041	−	0.232166i
$267$	18.3723	−	19.5499i	1.12437	−	1.19643i
$268$	−2.18614	+	3.78651i	−0.133540	+	0.231298i
$269$	−27.4891			−1.67604			−0.838021	−	0.545638i	$-0.816287\pi$
$269$	−27.4891			−1.67604			−0.838021	+	0.545638i	$0.816287\pi$
$270$	4.00000	+	3.31662i	0.243432	+	0.201843i
$271$	13.4891			0.819406			0.409703	−	0.912219i	$-0.365632\pi$
$271$	13.4891			0.819406			0.409703	+	0.912219i	$0.365632\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−4.00000	+	4.25639i	−0.242091	+	0.257608i
$274$	−2.18614	−	3.78651i	−0.132070	−	0.228751i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	1.00000	+	3.31662i	0.0601929	+	0.199637i
$277$	−3.74456	+	6.48577i	−0.224989	+	0.389692i	−0.956316	−	0.292334i	$-0.905568\pi$
$277$	−3.74456	+	6.48577i	−0.224989	+	0.389692i	0.731327	+	0.682027i	$0.238901\pi$
$278$	8.37228			0.502136
$279$	5.00000	−	3.31662i	0.299342	−	0.198561i
$280$	−1.00000			−0.0597614
$281$	−1.43070	+	2.47805i	−0.0853486	+	0.147828i	−0.905540	−	0.424262i	$-0.860534\pi$
$281$	−1.43070	+	2.47805i	−0.0853486	+	0.147828i	0.820191	+	0.572090i	$0.193867\pi$
$282$	1.05842	+	0.248667i	0.0630281	+	0.0148079i
$283$	5.80298	+	10.0511i	0.344952	+	0.597474i	0.985345	−	0.170573i	$-0.0545620\pi$
$283$	5.80298	+	10.0511i	0.344952	+	0.597474i	−0.640393	+	0.768047i	$0.721229\pi$
$284$	8.05842	+	13.9576i	0.478179	+	0.828231i
$285$	−7.37228	−	1.73205i	−0.436696	−	0.102598i
$286$	1.68614	−	2.92048i	0.0997036	−	0.172692i
$287$	6.37228			0.376144
$288$	2.50000	−	1.65831i	0.147314	−	0.0977170i
$289$	−8.00000			−0.470588
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	−8.24456	−	27.3441i	−0.483305	−	1.60294i
$292$	−7.24456	−	12.5480i	−0.423956	−	0.734313i
$293$	−0.255437	−	0.442430i	−0.0149228	−	0.0258471i	0.858468	−	0.512868i	$-0.171417\pi$
$293$	−0.255437	−	0.442430i	−0.0149228	−	0.0258471i	−0.873390	+	0.487021i	$0.838084\pi$
$294$	1.18614	−	1.26217i	0.0691771	−	0.0736112i
$295$	5.55842	−	9.62747i	0.323624	−	0.560533i
$296$	−10.7446			−0.624515
$297$	4.87228	−	1.80579i	0.282718	−	0.104783i
$298$	−12.8614			−0.745041
$299$	−3.37228	+	5.84096i	−0.195024	+	0.337792i
$300$	−1.18614	+	1.26217i	−0.0684819	+	0.0728714i
$301$	1.81386	+	3.14170i	0.104549	+	0.181084i
$302$	−9.43070	−	16.3345i	−0.542676	−	0.939942i
$303$	−1.37228	−	4.55134i	−0.0788355	−	0.261468i
$304$	−2.18614	+	3.78651i	−0.125384	+	0.217171i
$305$	11.4891			0.657865
$306$	−8.05842	−	4.00772i	−0.460669	−	0.229106i
$307$	−15.2337			−0.869432			−0.434716	−	0.900567i	$-0.643151\pi$
$307$	−15.2337			−0.869432			−0.434716	+	0.900567i	$0.643151\pi$
$308$	−0.500000	+	0.866025i	−0.0284901	+	0.0493464i
$309$	13.4891	+	3.16915i	0.767370	+	0.180287i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	1.11684	+	1.93443i	0.0633304	+	0.109691i	0.895952	−	0.444151i	$-0.146494\pi$
$311$	1.11684	+	1.93443i	0.0633304	+	0.109691i	−0.832622	+	0.553842i	$0.813161\pi$
$312$	5.68614	+	1.33591i	0.321914	+	0.0756309i
$313$	−0.558422	+	0.967215i	−0.0315639	+	0.0546702i	−0.881376	−	0.472416i	$-0.843382\pi$
$313$	−0.558422	+	0.967215i	−0.0315639	+	0.0546702i	0.849812	+	0.527086i	$0.176715\pi$
$314$	16.8614			0.951544
$315$	−0.186141	−	2.99422i	−0.0104878	−	0.168705i
$316$	−0.116844			−0.00657299
$317$	−4.11684	+	7.13058i	−0.231225	+	0.400493i	−0.958169	−	0.286203i	$-0.907607\pi$
$317$	−4.11684	+	7.13058i	−0.231225	+	0.400493i	0.726944	+	0.686697i	$0.240940\pi$
$318$	0.372281	+	1.23472i	0.0208765	+	0.0692395i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	16.4416	−	17.4954i	0.917679	−	0.976500i
$322$	1.00000	−	1.73205i	0.0557278	−	0.0965234i
$323$	13.1168			0.729841
$324$	5.43070	+	7.17687i	0.301706	+	0.398715i
$325$	−3.37228			−0.187061
$326$	0.627719	−	1.08724i	0.0347661	−	0.0602167i
$327$	2.23369	−	2.37686i	0.123523	−	0.131441i
$328$	−3.18614	−	5.51856i	−0.175925	−	0.304711i
$329$	−0.313859	−	0.543620i	−0.0173036	−	0.0299708i
$330$	0.500000	+	1.65831i	0.0275241	+	0.0912871i
$331$	9.80298	−	16.9793i	0.538821	−	0.933265i	−0.460147	−	0.887843i	$-0.652203\pi$
$331$	9.80298	−	16.9793i	0.538821	−	0.933265i	0.998968	−	0.0454223i	$-0.0144633\pi$
$332$	0.627719			0.0344505
$333$	−2.00000	−	32.1716i	−0.109599	−	1.76299i
$334$	10.6277			0.581523
$335$	2.18614	−	3.78651i	0.119442	−	0.206879i
$336$	−1.68614	−	0.396143i	−0.0919865	−	0.0216114i
$337$	0.558422	+	0.967215i	0.0304192	+	0.0526876i	0.880834	−	0.473425i	$-0.156982\pi$
$337$	0.558422	+	0.967215i	0.0304192	+	0.0526876i	−0.850415	+	0.526112i	$0.823649\pi$
$338$	−0.813859	−	1.40965i	−0.0442681	−	0.0766746i
$339$	−10.1168	−	2.37686i	−0.549472	−	0.129093i
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	2.00000			0.108306
$342$	−11.7446	−	5.84096i	−0.635073	−	0.315843i
$343$	−1.00000			−0.0539949
$344$	1.81386	−	3.14170i	0.0977967	−	0.169389i
$345$	−1.00000	−	3.31662i	−0.0538382	−	0.178561i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	15.9307	+	27.5928i	0.855205	+	1.48126i	0.876455	+	0.481484i	$0.159902\pi$
$347$	15.9307	+	27.5928i	0.855205	+	1.48126i	−0.0212498	+	0.999774i	$0.506765\pi$
$348$	2.37228	−	2.52434i	0.127168	−	0.135319i
$349$	−2.74456	+	4.75372i	−0.146913	+	0.254461i	−0.930085	−	0.367344i	$-0.880267\pi$
$349$	−2.74456	+	4.75372i	−0.146913	+	0.254461i	0.783172	+	0.621805i	$0.213600\pi$
$350$	1.00000			0.0534522
$351$	−2.94158	+	17.2742i	−0.157010	+	0.922030i
$352$	1.00000			0.0533002
$353$	−4.93070	+	8.54023i	−0.262435	+	0.454551i	−0.966888	−	0.255200i	$-0.917859\pi$
$353$	−4.93070	+	8.54023i	−0.262435	+	0.454551i	0.704454	+	0.709750i	$0.251192\pi$
$354$	13.1861	−	14.0313i	0.700835	−	0.745757i
$355$	−8.05842	−	13.9576i	−0.427697	−	0.740792i
$356$	7.74456	+	13.4140i	0.410461	+	0.710939i
$357$	1.50000	+	4.97494i	0.0793884	+	0.263302i
$358$	−2.94158	+	5.09496i	−0.155467	+	0.269277i
$359$	−25.4891			−1.34526			−0.672632	−	0.739977i	$-0.734836\pi$
$359$	−25.4891			−1.34526			−0.672632	+	0.739977i	$0.734836\pi$
$360$	−2.50000	+	1.65831i	−0.131762	+	0.0874007i
$361$	0.116844			0.00614968
$362$	1.37228	−	2.37686i	0.0721255	−	0.124925i
$363$	−16.8614	−	3.96143i	−0.884994	−	0.207921i
$364$	−1.68614	−	2.92048i	−0.0883778	−	0.153075i
$365$	7.24456	+	12.5480i	0.379198	+	0.656790i
$366$	19.3723	+	4.55134i	1.01261	+	0.237902i
$367$	−3.80298	+	6.58696i	−0.198514	+	0.343837i	−0.948047	−	0.318131i	$-0.896945\pi$
$367$	−3.80298	+	6.58696i	−0.198514	+	0.343837i	0.749533	+	0.661967i	$0.230278\pi$
$368$	−2.00000			−0.104257
$369$	15.9307	−	10.5672i	0.829319	−	0.550108i
$370$	10.7446			0.558583
$371$	0.372281	−	0.644810i	0.0193279	−	0.0334769i
$372$	1.00000	+	3.31662i	0.0518476	+	0.171959i
$373$	−10.3723	−	17.9653i	−0.537056	−	0.930209i	−0.999061	−	0.0433313i	$-0.986203\pi$
$373$	−10.3723	−	17.9653i	−0.537056	−	0.930209i	0.462004	−	0.886878i	$-0.347130\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$	1.18614	−	1.26217i	0.0612520	−	0.0651781i
$376$	−0.313859	+	0.543620i	−0.0161861	+	0.0280351i
$377$	6.74456			0.347363
$378$	0.872281	−	5.12241i	0.0448653	−	0.263469i
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$	2.18614	−	3.78651i	0.112147	−	0.194244i
$381$	5.62772	−	5.98844i	0.288317	−	0.306797i
$382$	8.74456	+	15.1460i	0.447411	+	0.774938i
$383$	−3.05842	−	5.29734i	−0.156278	−	0.270682i	0.777246	−	0.629197i	$-0.216616\pi$
$383$	−3.05842	−	5.29734i	−0.156278	−	0.270682i	−0.933524	+	0.358516i	$0.883283\pi$
$384$	0.500000	+	1.65831i	0.0255155	+	0.0846254i
$385$	0.500000	−	0.866025i	0.0254824	−	0.0441367i
$386$	0.372281			0.0189486
$387$	9.74456	+	4.84630i	0.495344	+	0.246351i
$388$	16.4891			0.837109
$389$	13.6861	−	23.7051i	0.693915	−	1.20190i	−0.276630	−	0.960976i	$-0.589218\pi$
$389$	13.6861	−	23.7051i	0.693915	−	1.20190i	0.970545	−	0.240919i	$-0.0774489\pi$
$390$	−5.68614	−	1.33591i	−0.287929	−	0.0676463i
$391$	3.00000	+	5.19615i	0.151717	+	0.262781i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	6.74456	+	1.58457i	0.340218	+	0.0799312i
$394$	−3.37228	+	5.84096i	−0.169893	+	0.294263i
$395$	0.116844			0.00587906
$396$	0.186141	+	2.99422i	0.00935392	+	0.150465i
$397$	−30.7446			−1.54303			−0.771513	−	0.636214i	$-0.780500\pi$
$397$	−30.7446			−1.54303			−0.771513	+	0.636214i	$0.780500\pi$
$398$	−12.0000	+	20.7846i	−0.601506	+	1.04184i
$399$	2.18614	+	7.25061i	0.109444	+	0.362984i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	7.30298	+	12.6491i	0.364694	+	0.631668i	0.988727	−	0.149730i	$-0.0478404\pi$
$401$	7.30298	+	12.6491i	0.364694	+	0.631668i	−0.624033	+	0.781398i	$0.714507\pi$
$402$	5.18614	−	5.51856i	0.258661	−	0.275241i
$403$	−3.37228	+	5.84096i	−0.167985	+	0.290959i
$404$	2.74456			0.136547
$405$	−5.43070	−	7.17687i	−0.269854	−	0.356622i
$406$	−2.00000			−0.0992583
$407$	5.37228	−	9.30506i	0.266294	−	0.461235i
$408$	3.55842	−	3.78651i	0.176168	−	0.187460i
$409$	13.1861	+	22.8391i	0.652013	+	1.12932i	0.982634	+	0.185556i	$0.0594085\pi$
$409$	13.1861	+	22.8391i	0.652013	+	1.12932i	−0.330621	+	0.943764i	$0.607258\pi$
$410$	3.18614	+	5.51856i	0.157352	+	0.272542i
$411$	2.18614	+	7.25061i	0.107834	+	0.357646i
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	−11.1168			−0.547024
$414$	−0.372281	−	5.98844i	−0.0182966	−	0.294316i
$415$	−0.627719			−0.0308135
$416$	−1.68614	+	2.92048i	−0.0826698	+	0.143188i
$417$	−14.1168	−	3.31662i	−0.691305	−	0.162416i
$418$	−2.18614	−	3.78651i	−0.106928	−	0.185204i
$419$	18.7446	+	32.4665i	0.915732	+	1.58609i	0.805826	+	0.592152i	$0.201721\pi$
$419$	18.7446	+	32.4665i	0.915732	+	1.58609i	0.109906	+	0.993942i	$0.464945\pi$
$420$	1.68614	+	0.396143i	0.0822752	+	0.0193298i
$421$	18.0584	−	31.2781i	0.880114	−	1.52440i	0.0288999	−	0.999582i	$-0.490800\pi$
$421$	18.0584	−	31.2781i	0.880114	−	1.52440i	0.851214	−	0.524819i	$-0.175867\pi$
$422$	−26.3505			−1.28272
$423$	−1.68614	−	0.838574i	−0.0819830	−	0.0407729i
$424$	−0.744563			−0.0361592
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	−8.05842	−	26.7268i	−0.390432	−	1.29492i
$427$	−5.74456	−	9.94987i	−0.277999	−	0.481508i
$428$	6.93070	+	12.0043i	0.335008	+	0.580251i
$429$	−4.00000	+	4.25639i	−0.193122	+	0.205500i
$430$	−1.81386	+	3.14170i	−0.0874721	+	0.151506i
$431$	3.60597			0.173693			0.0868467	−	0.996222i	$-0.472321\pi$
$431$	3.60597			0.173693			0.0868467	+	0.996222i	$0.472321\pi$
$432$	−4.87228	+	1.80579i	−0.234418	+	0.0868811i
$433$	−0.372281			−0.0178907			−0.00894535	−	0.999960i	$-0.502847\pi$
$433$	−0.372281			−0.0178907			−0.00894535	+	0.999960i	$0.502847\pi$
$434$	1.00000	−	1.73205i	0.0480015	−	0.0831411i
$435$	−2.37228	+	2.52434i	−0.113742	+	0.121033i
$436$	0.941578	+	1.63086i	0.0450934	+	0.0781041i
$437$	4.37228	+	7.57301i	0.209155	+	0.362266i
$438$	7.24456	+	24.0275i	0.346159	+	1.14808i
$439$	−8.37228	+	14.5012i	−0.399587	+	0.692105i	−0.993675	−	0.112295i	$-0.964180\pi$
$439$	−8.37228	+	14.5012i	−0.399587	+	0.692105i	0.594088	+	0.804400i	$0.297513\pi$
$440$	−1.00000			−0.0476731
$441$	−2.50000	+	1.65831i	−0.119048	+	0.0789673i
$442$	10.1168			0.481209
$443$	−8.55842	+	14.8236i	−0.406623	+	0.704292i	−0.994509	−	0.104652i	$-0.966627\pi$
$443$	−8.55842	+	14.8236i	−0.406623	+	0.704292i	0.587886	+	0.808944i	$0.299960\pi$
$444$	18.1168	+	4.25639i	0.859787	+	0.201999i
$445$	−7.74456	−	13.4140i	−0.367127	−	0.635883i
$446$	9.43070	+	16.3345i	0.446557	+	0.773459i
$447$	21.6861	+	5.09496i	1.02572	+	0.240983i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	12.3723			0.583884			0.291942	−	0.956436i	$-0.405699\pi$
$449$	12.3723			0.583884			0.291942	+	0.956436i	$0.405699\pi$
$450$	2.50000	−	1.65831i	0.117851	−	0.0781736i
$451$	6.37228			0.300059
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	9.43070	+	31.2781i	0.443093	+	1.46957i
$454$	−3.50000	−	6.06218i	−0.164263	−	0.284512i
$455$	1.68614	+	2.92048i	0.0790475	+	0.136914i
$456$	5.18614	−	5.51856i	0.242863	−	0.258430i
$457$	2.18614	−	3.78651i	0.102263	−	0.177125i	−0.810353	−	0.585941i	$-0.800725\pi$
$457$	2.18614	−	3.78651i	0.102263	−	0.177125i	0.912617	+	0.408816i	$0.134058\pi$
$458$	6.74456			0.315153
$459$	12.0000	+	9.94987i	0.560112	+	0.464420i
$460$	2.00000			0.0932505
$461$	−10.6277	+	18.4077i	−0.494982	+	0.857334i	−0.999983	−	0.00578439i	$-0.998159\pi$
$461$	−10.6277	+	18.4077i	−0.494982	+	0.857334i	0.505001	+	0.863119i	$0.331492\pi$
$462$	1.18614	−	1.26217i	0.0551843	−	0.0587214i
$463$	14.0000	+	24.2487i	0.650635	+	1.12693i	0.982969	+	0.183771i	$0.0588306\pi$
$463$	14.0000	+	24.2487i	0.650635	+	1.12693i	−0.332334	+	0.943162i	$0.607836\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$	−1.00000	−	3.31662i	−0.0463739	−	0.153805i
$466$	0.813859	−	1.40965i	0.0377013	−	0.0653006i
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$	−9.05842	−	4.50506i	−0.418726	−	0.208246i
$469$	−4.37228			−0.201893
$470$	0.313859	−	0.543620i	0.0144773	−	0.0250753i
$471$	−28.4307	−	6.67954i	−1.31002	−	0.307777i
$472$	5.55842	+	9.62747i	0.255847	+	0.443140i
$473$	1.81386	+	3.14170i	0.0834013	+	0.144455i
$474$	0.197015	+	0.0462870i	0.00904922	+	0.00212603i
$475$	−2.18614	+	3.78651i	−0.100307	+	0.173737i
$476$	−3.00000			−0.137505
$477$	−0.138593	−	2.22938i	−0.00634576	−	0.102076i
$478$	3.25544			0.148900
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$	−0.500000	−	1.65831i	−0.0228218	−	0.0756913i
$481$	18.1168	+	31.3793i	0.826057	+	1.43077i
$482$	−9.18614	−	15.9109i	−0.418417	−	0.724720i
$483$	−2.37228	+	2.52434i	−0.107943	+	0.114861i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−16.4891			−0.748733
$486$	−6.31386	−	14.2525i	−0.286402	−	0.646509i
$487$	−32.9783			−1.49439			−0.747194	−	0.664606i	$-0.768599\pi$
$487$	−32.9783			−1.49439			−0.747194	+	0.664606i	$0.768599\pi$
$488$	−5.74456	+	9.94987i	−0.260044	+	0.450410i
$489$	−1.48913	+	1.58457i	−0.0673406	+	0.0716569i
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	11.9891	+	20.7658i	0.541062	+	0.937146i	0.998843	+	0.0480817i	$0.0153108\pi$
$491$	11.9891	+	20.7658i	0.541062	+	0.937146i	−0.457782	+	0.889065i	$0.651356\pi$
$492$	3.18614	+	10.5672i	0.143642	+	0.476408i
$493$	3.00000	−	5.19615i	0.135113	−	0.234023i
$494$	14.7446			0.663389
$495$	−0.186141	−	2.99422i	−0.00836640	−	0.134580i
$496$	−2.00000			−0.0898027
$497$	−8.05842	+	13.9576i	−0.361470	+	0.626084i
$498$	−1.05842	−	0.248667i	−0.0474290	−	0.0111430i
$499$	−14.7337	−	25.5195i	−0.659570	−	1.14241i	−0.980727	−	0.195383i	$-0.937405\pi$
$499$	−14.7337	−	25.5195i	−0.659570	−	1.14241i	0.321156	−	0.947026i	$-0.395928\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−17.9198	−	4.21010i	−0.800599	−	0.188093i
$502$	11.3030	−	19.5773i	0.504477	−	0.873780i
$503$	38.2337			1.70476			0.852378	−	0.522926i	$-0.175160\pi$
$503$	38.2337			1.70476			0.852378	+	0.522926i	$0.175160\pi$
$504$	2.68614	+	1.33591i	0.119650	+	0.0595060i
$505$	−2.74456			−0.122131
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	0.813859	+	2.69927i	0.0361448	+	0.119879i
$508$	2.37228	+	4.10891i	0.105253	+	0.182303i
$509$	−10.8614	−	18.8125i	−0.481423	−	0.833850i	0.518349	−	0.855169i	$-0.326547\pi$
$509$	−10.8614	−	18.8125i	−0.481423	−	0.833850i	−0.999773	+	0.0213192i	$0.993213\pi$
$510$	−3.55842	+	3.78651i	−0.157570	+	0.167669i
$511$	7.24456	−	12.5480i	0.320481	−	0.555089i
$512$	−1.00000			−0.0441942
$513$	17.4891	+	14.5012i	0.772164	+	0.640244i
$514$	−15.7446			−0.694463
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$	−4.30298	+	4.57879i	−0.189428	+	0.201570i
$517$	−0.313859	−	0.543620i	−0.0138035	−	0.0239084i
$518$	−5.37228	−	9.30506i	−0.236044	−	0.408841i
$519$	9.00000	+	29.8496i	0.395056	+	1.31025i
$520$	1.68614	−	2.92048i	0.0739422	−	0.128072i
$521$	40.3723			1.76874			0.884371	−	0.466785i	$-0.154588\pi$
$521$	40.3723			1.76874			0.884371	+	0.466785i	$0.154588\pi$
$522$	−5.00000	+	3.31662i	−0.218844	+	0.145165i
$523$	−14.1168			−0.617286			−0.308643	−	0.951178i	$-0.599875\pi$
$523$	−14.1168			−0.617286			−0.308643	+	0.951178i	$0.599875\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$	−1.68614	−	0.396143i	−0.0735892	−	0.0172891i
$526$	−11.4891	−	19.8997i	−0.500950	−	0.867670i
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	−1.68614	−	0.396143i	−0.0733799	−	0.0172399i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	0.744563			0.0323417
$531$	−27.7921	+	18.4352i	−1.20607	+	0.800020i
$532$	−4.37228			−0.189562
$533$	−10.7446	+	18.6101i	−0.465399	+	0.806094i
$534$	−7.74456	−	25.6858i	−0.335140	−	1.11153i
$535$	−6.93070	−	12.0043i	−0.299640	−	0.518992i
$536$	2.18614	+	3.78651i	0.0944269	+	0.163552i
$537$	6.97825	−	7.42554i	0.301134	−	0.320436i
$538$	−13.7446	+	23.8063i	−0.592570	+	1.02636i
$539$	−1.00000			−0.0430730
$540$	4.87228	−	1.80579i	0.209670	−	0.0777088i
$541$	8.86141			0.380982			0.190491	−	0.981689i	$-0.438992\pi$
$541$	8.86141			0.380982			0.190491	+	0.981689i	$0.438992\pi$
$542$	6.74456	−	11.6819i	0.289704	−	0.501782i
$543$	−3.25544	+	3.46410i	−0.139704	+	0.148659i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−0.941578	−	1.63086i	−0.0403328	−	0.0698584i
$546$	1.68614	+	5.59230i	0.0721602	+	0.239328i
$547$	0.186141	−	0.322405i	0.00795880	−	0.0137850i	−0.862019	−	0.506877i	$-0.830800\pi$
$547$	0.186141	−	0.322405i	0.00795880	−	0.0137850i	0.869977	+	0.493092i	$0.164133\pi$
$548$	−4.37228			−0.186775
$549$	−30.8614	−	15.3484i	−1.31713	−	0.655054i
$550$	1.00000			0.0426401
$551$	4.37228	−	7.57301i	0.186265	−	0.322621i
$552$	3.37228	+	0.792287i	0.143534	+	0.0337220i
$553$	−0.0584220	−	0.101190i	−0.00248436	−	0.00430303i
$554$	3.74456	+	6.48577i	0.159091	+	0.275554i
$555$	−18.1168	−	4.25639i	−0.769017	−	0.180674i
$556$	4.18614	−	7.25061i	0.177532	−	0.307494i
$557$	−33.2554			−1.40908			−0.704539	−	0.709665i	$-0.748846\pi$
$557$	−33.2554			−1.40908			−0.704539	+	0.709665i	$0.748846\pi$
$558$	−0.372281	−	5.98844i	−0.0157599	−	0.253511i
$559$	−12.2337			−0.517430
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	1.50000	+	4.97494i	0.0633300	+	0.210042i
$562$	1.43070	+	2.47805i	0.0603506	+	0.104530i
$563$	9.61684	+	16.6569i	0.405302	+	0.702003i	0.994357	−	0.106090i	$-0.0338332\pi$
$563$	9.61684	+	16.6569i	0.405302	+	0.702003i	−0.589055	+	0.808093i	$0.700500\pi$
$564$	0.744563	−	0.792287i	0.0313517	−	0.0333613i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	11.6060			0.487835
$567$	−3.50000	+	8.29156i	−0.146986	+	0.348213i
$568$	16.1168			0.676248
$569$	12.9891	−	22.4978i	0.544532	−	0.943158i	−0.454104	−	0.890949i	$-0.650040\pi$
$569$	12.9891	−	22.4978i	0.544532	−	0.943158i	0.998636	−	0.0522091i	$-0.0166262\pi$
$570$	−5.18614	+	5.51856i	−0.217224	+	0.231147i
$571$	−5.98913	−	10.3735i	−0.250637	−	0.434116i	0.713064	−	0.701099i	$-0.247307\pi$
$571$	−5.98913	−	10.3735i	−0.250637	−	0.434116i	−0.963701	+	0.266982i	$0.913973\pi$
$572$	−1.68614	−	2.92048i	−0.0705011	−	0.122111i
$573$	−8.74456	−	29.0024i	−0.365309	−	1.21159i
$574$	3.18614	−	5.51856i	0.132987	−	0.230340i
$575$	−2.00000			−0.0834058
$576$	−0.186141	−	2.99422i	−0.00775586	−	0.124759i
$577$	−33.9783			−1.41453			−0.707267	−	0.706947i	$-0.750072\pi$
$577$	−33.9783			−1.41453			−0.707267	+	0.706947i	$0.750072\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−0.627719	−	0.147477i	−0.0260871	−	0.00612893i
$580$	−1.00000	−	1.73205i	−0.0415227	−	0.0719195i
$581$	0.313859	+	0.543620i	0.0130211	+	0.0225532i
$582$	−27.8030	−	6.53206i	−1.15247	−	0.270763i
$583$	0.372281	−	0.644810i	0.0154183	−	0.0267053i
$584$	−14.4891			−0.599564
$585$	9.05842	+	4.50506i	0.374520	+	0.186261i
$586$	−0.510875			−0.0211040
$587$	6.30298	−	10.9171i	0.260152	−	0.450597i	−0.706130	−	0.708082i	$-0.749561\pi$
$587$	6.30298	−	10.9171i	0.260152	−	0.450597i	0.966282	+	0.257486i	$0.0828940\pi$
$588$	−0.500000	−	1.65831i	−0.0206197	−	0.0683877i
$589$	4.37228	+	7.57301i	0.180157	+	0.312041i
$590$	−5.55842	−	9.62747i	−0.228837	−	0.396357i
$591$	8.00000	−	8.51278i	0.329076	−	0.350169i
$592$	−5.37228	+	9.30506i	−0.220799	+	0.382436i
$593$	−42.4674			−1.74393			−0.871963	−	0.489572i	$-0.837153\pi$
$593$	−42.4674			−1.74393			−0.871963	+	0.489572i	$0.837153\pi$
$594$	0.872281	−	5.12241i	0.0357901	−	0.210175i
$595$	3.00000			0.122988
$596$	−6.43070	+	11.1383i	−0.263412	+	0.456243i
$597$	28.4674	−	30.2921i	1.16509	−	1.23977i
$598$	3.37228	+	5.84096i	0.137903	+	0.238855i
$599$	2.94158	+	5.09496i	0.120190	+	0.208175i	0.919842	−	0.392288i	$-0.128316\pi$
$599$	2.94158	+	5.09496i	0.120190	+	0.208175i	−0.799653	+	0.600463i	$0.794983\pi$
$600$	0.500000	+	1.65831i	0.0204124	+	0.0677003i
$601$	−18.6753	+	32.3465i	−0.761780	+	1.31944i	0.180152	+	0.983639i	$0.442341\pi$
$601$	−18.6753	+	32.3465i	−0.761780	+	1.31944i	−0.941932	+	0.335803i	$0.890992\pi$
$602$	3.62772			0.147855
$603$	−10.9307	+	7.25061i	−0.445133	+	0.295268i
$604$	−18.8614			−0.767460
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	−4.62772	−	1.08724i	−0.187988	−	0.0441661i
$607$	−21.4891	−	37.2203i	−0.872217	−	1.51072i	−0.859698	−	0.510802i	$-0.829349\pi$
$607$	−21.4891	−	37.2203i	−0.872217	−	1.51072i	−0.0125183	−	0.999922i	$-0.503985\pi$
$608$	2.18614	+	3.78651i	0.0886597	+	0.153563i
$609$	3.37228	+	0.792287i	0.136652	+	0.0321051i
$610$	5.74456	−	9.94987i	0.232591	−	0.402859i
$611$	2.11684			0.0856383
$612$	−7.50000	+	4.97494i	−0.303170	+	0.201100i
$613$	−31.4891			−1.27183			−0.635917	−	0.771758i	$-0.719378\pi$
$613$	−31.4891			−1.27183			−0.635917	+	0.771758i	$0.719378\pi$
$614$	−7.61684	+	13.1928i	−0.307391	+	0.532416i
$615$	−3.18614	−	10.5672i	−0.128478	−	0.426112i
$616$	0.500000	+	0.866025i	0.0201456	+	0.0348932i
$617$	−23.0475	−	39.9195i	−0.927859	−	1.60710i	−0.786897	−	0.617085i	$-0.788314\pi$
$617$	−23.0475	−	39.9195i	−0.927859	−	1.60710i	−0.140962	−	0.990015i	$-0.545020\pi$
$618$	9.48913	−	10.0974i	0.381709	−	0.406175i
$619$	−8.93070	+	15.4684i	−0.358955	+	0.621729i	−0.987787	−	0.155813i	$-0.950200\pi$
$619$	−8.93070	+	15.4684i	−0.358955	+	0.621729i	0.628831	+	0.777542i	$0.283534\pi$
$620$	2.00000			0.0803219
$621$	−1.74456	+	10.2448i	−0.0700069	+	0.411111i
$622$	2.23369			0.0895627
$623$	−7.74456	+	13.4140i	−0.310279	+	0.537420i
$624$	4.00000	−	4.25639i	0.160128	−	0.170392i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.558422	+	0.967215i	0.0223190	+	0.0386577i
$627$	2.18614	+	7.25061i	0.0873060	+	0.289561i
$628$	8.43070	−	14.6024i	0.336422	−	0.582699i
$629$	32.2337			1.28524
$630$	−2.68614	−	1.33591i	−0.107018	−	0.0532238i
$631$	−38.8614			−1.54705			−0.773524	−	0.633767i	$-0.781508\pi$
$631$	−38.8614			−1.54705			−0.773524	+	0.633767i	$0.781508\pi$
$632$	−0.0584220	+	0.101190i	−0.00232390	+	0.00402512i
$633$	44.4307	+	10.4386i	1.76596	+	0.414897i
$634$	4.11684	+	7.13058i	0.163501	+	0.283192i
$635$	−2.37228	−	4.10891i	−0.0941411	−	0.163057i
$636$	1.25544	+	0.294954i	0.0497813	+	0.0116957i
$637$	1.68614	−	2.92048i	0.0668073	−	0.115714i
$638$	−2.00000			−0.0791808
$639$	3.00000	+	48.2574i	0.118678	+	1.90903i
$640$	1.00000			0.0395285
$641$	−16.9307	+	29.3248i	−0.668723	+	1.15826i	0.309539	+	0.950887i	$0.399825\pi$
$641$	−16.9307	+	29.3248i	−0.668723	+	1.15826i	−0.978262	+	0.207375i	$0.933508\pi$
$642$	−6.93070	−	22.9865i	−0.273533	−	0.907206i
$643$	−17.5000	−	30.3109i	−0.690133	−	1.19534i	−0.971794	−	0.235831i	$-0.924219\pi$
$643$	−17.5000	−	30.3109i	−0.690133	−	1.19534i	0.281661	−	0.959514i	$-0.409114\pi$
$644$	−1.00000	−	1.73205i	−0.0394055	−	0.0682524i
$645$	4.30298	−	4.57879i	0.169430	−	0.180290i
$646$	6.55842	−	11.3595i	0.258038	−	0.446934i
$647$	18.2337			0.716840			0.358420	−	0.933560i	$-0.383316\pi$
$647$	18.2337			0.716840			0.358420	+	0.933560i	$0.383316\pi$
$648$	8.93070	−	1.11469i	0.350831	−	0.0437892i
$649$	−11.1168			−0.436374
$650$	−1.68614	+	2.92048i	−0.0661359	+	0.114551i
$651$	−2.37228	+	2.52434i	−0.0929770	+	0.0989366i
$652$	−0.627719	−	1.08724i	−0.0245834	−	0.0425796i
$653$	−12.3723	−	21.4294i	−0.484165	−	0.838598i	0.515670	−	0.856787i	$-0.327543\pi$
$653$	−12.3723	−	21.4294i	−0.484165	−	0.838598i	−0.999835	+	0.0181894i	$0.994210\pi$
$654$	−0.941578	−	3.12286i	−0.0368186	−	0.122114i
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	−6.37228			−0.248796
$657$	−2.69702	−	43.3836i	−0.105221	−	1.69256i
$658$	−0.627719			−0.0244710
$659$	23.0584	−	39.9384i	0.898229	−	1.55578i	0.0684714	−	0.997653i	$-0.478188\pi$
$659$	23.0584	−	39.9384i	0.898229	−	1.55578i	0.829757	−	0.558124i	$-0.188479\pi$
$660$	1.68614	+	0.396143i	0.0656329	+	0.0154199i
$661$	16.6277	+	28.8001i	0.646743	+	1.12019i	0.983896	+	0.178742i	$0.0572028\pi$
$661$	16.6277	+	28.8001i	0.646743	+	1.12019i	−0.337153	+	0.941450i	$0.609464\pi$
$662$	−9.80298	−	16.9793i	−0.381004	−	0.659918i
$663$	−17.0584	−	4.00772i	−0.662494	−	0.155647i
$664$	0.313859	−	0.543620i	0.0121801	−	0.0210966i
$665$	4.37228			0.169550
$666$	−28.8614	−	14.3537i	−1.11836	−	0.556196i
$667$	4.00000			0.154881
$668$	5.31386	−	9.20387i	0.205599	−	0.356109i
$669$	−9.43070	−	31.2781i	−0.364612	−	1.20928i
$670$	−2.18614	−	3.78651i	−0.0844580	−	0.146286i
$671$	−5.74456	−	9.94987i	−0.221766	−	0.384111i
$672$	−1.18614	+	1.26217i	−0.0457564	+	0.0486892i
$673$	−6.37228	+	11.0371i	−0.245633	+	0.425450i	−0.962310	−	0.271957i	$-0.912329\pi$
$673$	−6.37228	+	11.0371i	−0.245633	+	0.425450i	0.716676	+	0.697406i	$0.245663\pi$
$674$	1.11684			0.0430192
$675$	−4.87228	+	1.80579i	−0.187534	+	0.0695049i
$676$	−1.62772			−0.0626046
$677$	2.43070	−	4.21010i	0.0934195	−	0.161807i	−0.815528	−	0.578717i	$-0.803554\pi$
$677$	2.43070	−	4.21010i	0.0934195	−	0.161807i	0.908948	+	0.416910i	$0.136887\pi$
$678$	−7.11684	+	7.57301i	−0.273321	+	0.290840i
$679$	8.24456	+	14.2800i	0.316397	+	0.548016i
$680$	−1.50000	−	2.59808i	−0.0575224	−	0.0996317i
$681$	3.50000	+	11.6082i	0.134120	+	0.444827i
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	7.86141			0.300808			0.150404	−	0.988625i	$-0.451942\pi$
$683$	7.86141			0.300808			0.150404	+	0.988625i	$0.451942\pi$
$684$	−10.9307	+	7.25061i	−0.417946	+	0.277234i
$685$	4.37228			0.167056
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−11.3723	−	2.67181i	−0.433880	−	0.101936i
$688$	−1.81386	−	3.14170i	−0.0691527	−	0.119776i
$689$	1.25544	+	2.17448i	0.0478284	+	0.0828411i
$690$	−3.37228	−	0.792287i	−0.128381	−	0.0301619i
$691$	4.62772	−	8.01544i	0.176047	−	0.304922i	−0.764476	−	0.644652i	$-0.777002\pi$
$691$	4.62772	−	8.01544i	0.176047	−	0.304922i	0.940523	+	0.339730i	$0.110336\pi$
$692$	−18.0000			−0.684257
$693$	−2.50000	+	1.65831i	−0.0949671	+	0.0629941i
$694$	31.8614			1.20944
$695$	−4.18614	+	7.25061i	−0.158789	+	0.275031i
$696$	−1.00000	−	3.31662i	−0.0379049	−	0.125716i
$697$	9.55842	+	16.5557i	0.362051	+	0.627091i
$698$	2.74456	+	4.75372i	0.103883	+	0.179931i
$699$	−1.93070	+	2.05446i	−0.0730259	+	0.0777067i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−30.8614			−1.16562			−0.582810	−	0.812609i	$-0.698047\pi$
$701$	−30.8614			−1.16562			−0.582810	+	0.812609i	$0.698047\pi$
$702$	13.4891	+	11.1846i	0.509114	+	0.422135i
$703$	46.9783			1.77182
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−0.744563	+	0.792287i	−0.0280419	+	0.0298393i
$706$	4.93070	+	8.54023i	0.185569	+	0.321416i
$707$	1.37228	+	2.37686i	0.0516100	+	0.0893911i
$708$	−5.55842	−	18.4352i	−0.208898	−	0.692837i
$709$	19.2337	−	33.3137i	0.722336	−	1.25112i	−0.237725	−	0.971333i	$-0.576402\pi$
$709$	19.2337	−	33.3137i	0.722336	−	1.25112i	0.960061	−	0.279791i	$-0.0902651\pi$
$710$	−16.1168			−0.604854
$711$	−0.313859	−	0.156093i	−0.0117706	−	0.00585393i
$712$	15.4891			0.580480
$713$	−2.00000	+	3.46410i	−0.0749006	+	0.129732i
$714$	5.05842	+	1.18843i	0.189307	+	0.0444759i
$715$	1.68614	+	2.92048i	0.0630581	+	0.109220i
$716$	2.94158	+	5.09496i	0.109932	+	0.190408i
$717$	−5.48913	−	1.28962i	−0.204995	−	0.0481618i
$718$	−12.7446	+	22.0742i	−0.475623	+	0.823803i
$719$	−17.7228			−0.660949			−0.330475	−	0.943815i	$-0.607209\pi$
$719$	−17.7228			−0.660949			−0.330475	+	0.943815i	$0.607209\pi$
$720$	0.186141	+	2.99422i	0.00693705	+	0.111588i
$721$	−8.00000			−0.297936
$722$	0.0584220	−	0.101190i	0.00217424	−	0.00376590i
$723$	9.18614	+	30.4670i	0.341636	+	1.13308i
$724$	−1.37228	−	2.37686i	−0.0510004	−	0.0883353i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	−11.8614	+	12.6217i	−0.440218	+	0.468435i
$727$	−17.2921	+	29.9508i	−0.641329	+	1.11081i	0.343808	+	0.939040i	$0.388283\pi$
$727$	−17.2921	+	29.9508i	−0.641329	+	1.11081i	−0.985136	+	0.171774i	$0.945050\pi$
$728$	−3.37228			−0.124985
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	14.4891			0.536267
$731$	−5.44158	+	9.42509i	−0.201264	+	0.348600i
$732$	13.6277	−	14.5012i	0.503695	−	0.535980i
$733$	26.8614	+	46.5253i	0.992149	+	1.71845i	0.604383	+	0.796694i	$0.293420\pi$
$733$	26.8614	+	46.5253i	0.992149	+	1.71845i	0.387766	+	0.921758i	$0.373247\pi$
$734$	3.80298	+	6.58696i	0.140371	+	0.243129i
$735$	0.500000	+	1.65831i	0.0184428	+	0.0611678i
$736$	−1.00000	+	1.73205i	−0.0368605	+	0.0638442i
$737$	−4.37228			−0.161055
$738$	−1.18614	−	19.0800i	−0.0436624	−	0.702345i
$739$	3.11684			0.114655			0.0573275	−	0.998355i	$-0.481742\pi$
$739$	3.11684			0.114655			0.0573275	+	0.998355i	$0.481742\pi$
$740$	5.37228	−	9.30506i	0.197489	−	0.342061i
$741$	−24.8614	−	5.84096i	−0.913307	−	0.214573i
$742$	−0.372281	−	0.644810i	−0.0136669	−	0.0236717i
$743$	−20.6060	−	35.6906i	−0.755960	−	1.30936i	−0.944896	−	0.327371i	$-0.893837\pi$
$743$	−20.6060	−	35.6906i	−0.755960	−	1.30936i	0.188936	−	0.981989i	$-0.439496\pi$
$744$	3.37228	+	0.792287i	0.123634	+	0.0290467i
$745$	6.43070	−	11.1383i	0.235603	−	0.408076i
$746$	−20.7446			−0.759512
$747$	1.68614	+	0.838574i	0.0616927	+	0.0306818i
$748$	−3.00000			−0.109691
$749$	−6.93070	+	12.0043i	−0.253242	+	0.438629i
$750$	−0.500000	−	1.65831i	−0.0182574	−	0.0605530i
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	0.623856	−	0.781540i	$-0.285565\pi$
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	−0.988761	+	0.149505i	$0.952232\pi$
$752$	0.313859	+	0.543620i	0.0114453	+	0.0198238i
$753$	−26.8139	+	28.5326i	−0.977151	+	1.03978i
$754$	3.37228	−	5.84096i	0.122811	−	0.212715i
$755$	18.8614			0.686437
$756$	−4.00000	−	3.31662i	−0.145479	−	0.120624i
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	8.50000	−	14.7224i	0.308734	−	0.534743i
$759$	−2.37228	+	2.52434i	−0.0861084	+	0.0916277i
$760$	−2.18614	−	3.78651i	−0.0792997	−	0.137351i
$761$	−2.48913	−	4.31129i	−0.0902307	−	0.156284i	0.817377	−	0.576103i	$-0.195427\pi$
$761$	−2.48913	−	4.31129i	−0.0902307	−	0.156284i	−0.907608	+	0.419818i	$0.862094\pi$
$762$	−2.37228	−	7.86797i	−0.0859387	−	0.285026i
$763$	−0.941578	+	1.63086i	−0.0340874	+	0.0590411i
$764$	17.4891			0.632734
$765$	7.50000	−	4.97494i	0.271163	−	0.179869i
$766$	−6.11684			−0.221011
$767$	18.7446	−	32.4665i	0.676827	−	1.17230i
$768$	1.68614	+	0.396143i	0.0608434	+	0.0142946i
$769$	15.2337	+	26.3855i	0.549341	+	0.951486i	0.998320	+	0.0579439i	$0.0184545\pi$
$769$	15.2337	+	26.3855i	0.549341	+	0.951486i	−0.448979	+	0.893542i	$0.648212\pi$
$770$	−0.500000	−	0.866025i	−0.0180187	−	0.0312094i
$771$	26.5475	+	6.23711i	0.956087	+	0.224624i
$772$	0.186141	−	0.322405i	0.00669935	−	0.0116036i
$773$	2.39403			0.0861073			0.0430537	−	0.999073i	$-0.486291\pi$
$773$	2.39403			0.0861073			0.0430537	+	0.999073i	$0.486291\pi$
$774$	9.06930	−	6.01589i	0.325989	−	0.216237i
$775$	−2.00000			−0.0718421
$776$	8.24456	−	14.2800i	0.295963	−	0.512622i
$777$	5.37228	+	17.8178i	0.192730	+	0.639212i
$778$	−13.6861	−	23.7051i	−0.490672	−	0.849869i
$779$	13.9307	+	24.1287i	0.499119	+	0.864500i
$780$	−4.00000	+	4.25639i	−0.143223	+	0.152403i
$781$	−8.05842	+	13.9576i	−0.288353	+	0.499442i
$782$	6.00000			0.214560
$783$	9.74456	−	3.61158i	0.348242	−	0.129067i
$784$	1.00000			0.0357143
$785$	−8.43070	+	14.6024i	−0.300905	+	0.521182i
$786$	4.74456	−	5.04868i	0.169233	−	0.180080i
$787$	−5.17527	−	8.96382i	−0.184478	−	0.319526i	0.758922	−	0.651181i	$-0.225726\pi$
$787$	−5.17527	−	8.96382i	−0.184478	−	0.319526i	−0.943401	+	0.331655i	$0.892393\pi$
$788$	3.37228	+	5.84096i	0.120133	+	0.208076i
$789$	11.4891	+	38.1051i	0.409024	+	1.35658i
$790$	0.0584220	−	0.101190i	0.00207856	−	0.00360017i
$791$	6.00000			0.213335
$792$	2.68614	+	1.33591i	0.0954479	+	0.0474694i
$793$	38.7446			1.37586
$794$	−15.3723	+	26.6256i	−0.545542	+	0.944906i
$795$	−1.25544	−	0.294954i	−0.0445258	−	0.0104609i
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	−9.68614	−	16.7769i	−0.343101	−	0.594268i	0.641906	−	0.766783i	$-0.278144\pi$
$797$	−9.68614	−	16.7769i	−0.343101	−	0.594268i	−0.985007	+	0.172515i	$0.944811\pi$
$798$	7.37228	+	1.73205i	0.260976	+	0.0613139i
$799$	0.941578	−	1.63086i	0.0333106	−	0.0576957i
$800$	−1.00000			−0.0353553
$801$	2.88316	+	46.3778i	0.101871	+	1.63868i
$802$	14.6060			0.515755
$803$	7.24456	−	12.5480i	0.255655	−	0.442808i
$804$	−2.18614	−	7.25061i	−0.0770992	−	0.255709i
$805$	1.00000	+	1.73205i	0.0352454	+	0.0610468i
$806$	3.37228	+	5.84096i	0.118784	+	0.205739i
$807$	32.6060	−	34.6959i	1.14778	−	1.22135i
$808$	1.37228	−	2.37686i	0.0482767	−	0.0836177i
$809$	−25.9783			−0.913347			−0.456673	−	0.889634i	$-0.650959\pi$
$809$	−25.9783			−0.913347			−0.456673	+	0.889634i	$0.650959\pi$
$810$	−8.93070	+	1.11469i	−0.313793	+	0.0391663i
$811$	−30.0951			−1.05678			−0.528391	−	0.849001i	$-0.677204\pi$
$811$	−30.0951			−1.05678			−0.528391	+	0.849001i	$0.677204\pi$
$812$	−1.00000	+	1.73205i	−0.0350931	+	0.0607831i
$813$	−16.0000	+	17.0256i	−0.561144	+	0.597112i
$814$	−5.37228	−	9.30506i	−0.188298	−	0.326142i
$815$	0.627719	+	1.08724i	0.0219880	+	0.0380844i
$816$	−1.50000	−	4.97494i	−0.0525105	−	0.174158i
$817$	−7.93070	+	13.7364i	−0.277460	+	0.480575i
$818$	26.3723			0.922085
$819$	−0.627719	−	10.0974i	−0.0219343	−	0.352830i
$820$	6.37228			0.222530
$821$	18.4307	−	31.9229i	0.643236	−	1.11412i	−0.341470	−	0.939893i	$-0.610925\pi$
$821$	18.4307	−	31.9229i	0.643236	−	1.11412i	0.984706	−	0.174225i	$-0.0557419\pi$
$822$	7.37228	+	1.73205i	0.257138	+	0.0604122i
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	0.742299	−	0.670069i	$-0.233735\pi$
$823$	−6.00000	−	10.3923i	−0.209147	−	0.362253i	−0.951446	+	0.307816i	$0.900402\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$	−1.68614	−	0.396143i	−0.0587039	−	0.0137919i
$826$	−5.55842	+	9.62747i	−0.193402	+	0.334982i
$827$	5.25544			0.182749			0.0913747	−	0.995817i	$-0.470874\pi$
$827$	5.25544			0.182749			0.0913747	+	0.995817i	$0.470874\pi$
$828$	−5.37228	−	2.67181i	−0.186700	−	0.0928520i
$829$	−32.0000			−1.11141			−0.555703	−	0.831381i	$-0.687551\pi$
$829$	−32.0000			−1.11141			−0.555703	+	0.831381i	$0.687551\pi$
$830$	−0.313859	+	0.543620i	−0.0108942	+	0.0188693i
$831$	−3.74456	−	12.4193i	−0.129897	−	0.430821i
$832$	1.68614	+	2.92048i	0.0584564	+	0.101249i
$833$	−1.50000	−	2.59808i	−0.0519719	−	0.0900180i
$834$	−9.93070	+	10.5672i	−0.343872	+	0.365913i
$835$	−5.31386	+	9.20387i	−0.183894	+	0.318513i
$836$	−4.37228			−0.151219
$837$	−1.74456	+	10.2448i	−0.0603009	+	0.354113i
$838$	37.4891			1.29504
$839$	20.6060	−	35.6906i	0.711397	−	1.23218i	−0.252936	−	0.967483i	$-0.581396\pi$
$839$	20.6060	−	35.6906i	0.711397	−	1.23218i	0.964333	−	0.264693i	$-0.0852705\pi$
$840$	1.18614	−	1.26217i	0.0409257	−	0.0435490i
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−18.0584	−	31.2781i	−0.622334	−	1.07791i
$843$	−1.43070	−	4.74511i	−0.0492760	−	0.163430i
$844$	−13.1753	+	22.8202i	−0.453511	+	0.785505i
$845$	1.62772			0.0559952
$846$	−1.56930	+	1.04095i	−0.0539535	+	0.0357887i
$847$	10.0000			0.343604
$848$	−0.372281	+	0.644810i	−0.0127842	+	0.0221429i
$849$	−19.5693	−	4.59763i	−0.671617	−	0.157790i
$850$	1.50000	+	2.59808i	0.0514496	+	0.0891133i
$851$	10.7446	+	18.6101i	0.368319	+	0.637947i
$852$	−27.1753	−	6.38458i	−0.931009	−	0.218732i
$853$	16.8614	−	29.2048i	0.577324	−	0.999954i	−0.418461	−	0.908235i	$-0.637430\pi$
$853$	16.8614	−	29.2048i	0.577324	−	0.999954i	0.995785	−	0.0917191i	$-0.0292362\pi$
$854$	−11.4891			−0.393150
$855$	10.9307	−	7.25061i	0.373822	−	0.247966i
$856$	13.8614			0.473773
$857$	4.17527	−	7.23177i	0.142624	−	0.247033i	−0.785860	−	0.618405i	$-0.787779\pi$
$857$	4.17527	−	7.23177i	0.142624	−	0.247033i	0.928484	+	0.371372i	$0.121113\pi$
$858$	1.68614	+	5.59230i	0.0575639	+	0.190918i
$859$	15.3030	+	26.5055i	0.522131	+	0.904358i	0.999669	+	0.0257462i	$0.00819617\pi$
$859$	15.3030	+	26.5055i	0.522131	+	0.904358i	−0.477537	+	0.878611i	$0.658470\pi$
$860$	1.81386	+	3.14170i	0.0618521	+	0.107131i
$861$	−7.55842	+	8.04290i	−0.257590	+	0.274101i
$862$	1.80298	−	3.12286i	0.0614099	−	0.106365i
$863$	27.4891			0.935741			0.467870	−	0.883797i	$-0.345021\pi$
$863$	27.4891			0.935741			0.467870	+	0.883797i	$0.345021\pi$
$864$	−0.872281	+	5.12241i	−0.0296756	+	0.174268i
$865$	18.0000			0.612018
$866$	−0.186141	+	0.322405i	−0.00632532	+	0.0109558i
$867$	9.48913	−	10.0974i	0.322268	−	0.342924i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	−0.0584220	−	0.101190i	−0.00198183	−	0.00343263i
$870$	1.00000	+	3.31662i	0.0339032	+	0.112444i
$871$	7.37228	−	12.7692i	0.249800	−	0.432667i
$872$	1.88316			0.0637717
$873$	44.2921	+	22.0279i	1.49906	+	0.745533i
$874$	8.74456			0.295789
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	24.4307	+	5.73977i	0.825437	+	0.193929i
$877$	−4.25544	−	7.37063i	−0.143696	−	0.248889i	0.785190	−	0.619255i	$-0.212565\pi$
$877$	−4.25544	−	7.37063i	−0.143696	−	0.248889i	−0.928886	+	0.370367i	$0.879232\pi$
$878$	8.37228	+	14.5012i	0.282551	+	0.489392i
$879$	0.861407	+	0.202380i	0.0290545	+	0.00682610i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	36.7446			1.23796			0.618978	−	0.785408i	$-0.287547\pi$
$881$	36.7446			1.23796			0.618978	+	0.785408i	$0.287547\pi$
$882$	0.186141	+	2.99422i	0.00626768	+	0.100821i
$883$	27.3505			0.920419			0.460209	−	0.887810i	$-0.347774\pi$
$883$	27.3505			0.920419			0.460209	+	0.887810i	$0.347774\pi$
$884$	5.05842	−	8.76144i	0.170133	−	0.294679i
$885$	5.55842	+	18.4352i	0.186844	+	0.619692i
$886$	8.55842	+	14.8236i	0.287526	+	0.498009i
$887$	−5.62772	−	9.74749i	−0.188960	−	0.327289i	0.755944	−	0.654637i	$-0.227178\pi$
$887$	−5.62772	−	9.74749i	−0.188960	−	0.327289i	−0.944904	+	0.327348i	$0.893845\pi$
$888$	12.7446	−	13.5615i	0.427680	−	0.455093i
$889$	−2.37228	+	4.10891i	−0.0795638	+	0.137808i
$890$	−15.4891			−0.519197
$891$	−3.50000	+	8.29156i	−0.117254	+	0.277778i
$892$	18.8614			0.631527
$893$	1.37228	−	2.37686i	0.0459216	−	0.0795386i
$894$	15.2554	−	16.2333i	0.510218	−	0.542922i
$895$	−2.94158	−	5.09496i	−0.0983261	−	0.170306i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−3.37228	−	11.1846i	−0.112597	−	0.373443i
$898$	6.18614	−	10.7147i	0.206434	−	0.357555i
$899$	4.00000			0.133407
$900$	−0.186141	−	2.99422i	−0.00620469	−	0.0998073i
$901$	2.23369			0.0744149
$902$	3.18614	−	5.51856i	0.106087	−	0.183748i
$903$	−6.11684	−	1.43710i	−0.203556	−	0.0478236i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	1.37228	+	2.37686i	0.0456162	+	0.0790095i
$906$	31.8030	+	7.47182i	1.05658	+	0.248235i
$907$	20.5584	−	35.6082i	0.682631	−	1.18235i	−0.291544	−	0.956557i	$-0.594169\pi$
$907$	20.5584	−	35.6082i	0.682631	−	1.18235i	0.974175	−	0.225794i	$-0.0724978\pi$
$908$	−7.00000			−0.232303
$909$	7.37228	+	3.66648i	0.244523	+	0.121610i
$910$	3.37228			0.111790
$911$	−16.0584	+	27.8140i	−0.532039	+	0.921519i	0.467261	+	0.884119i	$0.345241\pi$
$911$	−16.0584	+	27.8140i	−0.532039	+	0.921519i	−0.999300	+	0.0373997i	$0.988093\pi$
$912$	−2.18614	−	7.25061i	−0.0723904	−	0.240092i
$913$	0.313859	+	0.543620i	0.0103872	+	0.0179912i
$914$	−2.18614	−	3.78651i	−0.0723111	−	0.125247i
$915$	−13.6277	+	14.5012i	−0.450518	+	0.479395i
$916$	3.37228	−	5.84096i	0.111423	−	0.192991i
$917$	−4.00000			−0.132092
$918$	14.6168	−	5.41737i	0.482428	−	0.178800i
$919$	44.7446			1.47599			0.737993	−	0.674808i	$-0.235774\pi$
$919$	44.7446			1.47599			0.737993	+	0.674808i	$0.235774\pi$
$920$	1.00000	−	1.73205i	0.0329690	−	0.0571040i
$921$	18.0693	−	19.2275i	0.595404	−	0.633567i
$922$	10.6277	+	18.4077i	0.350005	+	0.606227i
$923$	−27.1753	−	47.0689i	−0.894485	−	1.54929i
$924$	−0.500000	−	1.65831i	−0.0164488	−	0.0545545i
$925$	−5.37228	+	9.30506i	−0.176640	+	0.305949i
$926$	28.0000			0.920137
$927$	−20.0000	+	13.2665i	−0.656886	+	0.435729i
$928$	2.00000			0.0656532
$929$	3.51087	−	6.08101i	0.115188	−	0.199512i	−0.802667	−	0.596428i	$-0.796586\pi$
$929$	3.51087	−	6.08101i	0.115188	−	0.199512i	0.917855	+	0.396916i	$0.129920\pi$
$930$	−3.37228	−	0.792287i	−0.110581	−	0.0259801i
$931$	−2.18614	−	3.78651i	−0.0716479	−	0.124098i
$932$	−0.813859	−	1.40965i	−0.0266588	−	0.0461745i
$933$	−3.76631	−	0.884861i	−0.123304	−	0.0289690i
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$	3.00000			0.0981105
$936$	−8.43070	+	5.59230i	−0.275566	+	0.182790i
$937$	−17.1386			−0.559893			−0.279947	−	0.960016i	$-0.590317\pi$
$937$	−17.1386			−0.559893			−0.279947	+	0.960016i	$0.590317\pi$
$938$	−2.18614	+	3.78651i	−0.0713800	+	0.123634i
$939$	−0.558422	−	1.85208i	−0.0182234	−	0.0604402i
$940$	−0.313859	−	0.543620i	−0.0102370	−	0.0177309i
$941$	−14.7446	−	25.5383i	−0.480659	−	0.832526i	0.519095	−	0.854717i	$-0.326269\pi$
$941$	−14.7446	−	25.5383i	−0.480659	−	0.832526i	−0.999754	+	0.0221909i	$0.992936\pi$
$942$	−20.0000	+	21.2819i	−0.651635	+	0.693403i
$943$	−6.37228	+	11.0371i	−0.207510	+	0.359418i
$944$	11.1168			0.361822
$945$	4.00000	+	3.31662i	0.130120	+	0.107890i
$946$	3.62772			0.117947
$947$	−9.41983	+	16.3156i	−0.306103	+	0.530186i	−0.977506	−	0.210906i	$-0.932359\pi$
$947$	−9.41983	+	16.3156i	−0.306103	+	0.530186i	0.671403	+	0.741092i	$0.265692\pi$
$948$	0.138593	−	0.147477i	0.00450130	−	0.00478982i
$949$	24.4307	+	42.3152i	0.793054	+	1.37361i
$950$	2.18614	+	3.78651i	0.0709278	+	0.122850i
$951$	−4.11684	−	13.6540i	−0.133498	−	0.442762i
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	−46.3288			−1.50074			−0.750368	−	0.661020i	$-0.770124\pi$
$953$	−46.3288			−1.50074			−0.750368	+	0.661020i	$0.770124\pi$
$954$	−2.00000	−	0.994667i	−0.0647524	−	0.0322035i
$955$	−17.4891			−0.565935
$956$	1.62772	−	2.81929i	0.0526442	−	0.0911824i
$957$	3.37228	+	0.792287i	0.109010	+	0.0256110i
$958$	5.00000	+	8.66025i	0.161543	+	0.279800i
$959$	−2.18614	−	3.78651i	−0.0705942	−	0.122273i
$960$	−1.68614	−	0.396143i	−0.0544200	−	0.0127855i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	36.2337			1.16822
$963$	2.58017	+	41.5041i	0.0831449	+	1.33745i
$964$	−18.3723			−0.591731
$965$	−0.186141	+	0.322405i	−0.00599208	+	0.0103786i
$966$	1.00000	+	3.31662i	0.0321745	+	0.106711i
$967$	17.9783	+	31.1392i	0.578142	+	1.00137i	0.995692	+	0.0927170i	$0.0295552\pi$
$967$	17.9783	+	31.1392i	0.578142	+	1.00137i	−0.417551	+	0.908654i	$0.637111\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	−15.5584	+	16.5557i	−0.499809	+	0.531845i
$970$	−8.24456	+	14.2800i	−0.264717	+	0.458503i
$971$	26.7446			0.858274			0.429137	−	0.903239i	$-0.358818\pi$
$971$	26.7446			0.858274			0.429137	+	0.903239i	$0.358818\pi$
$972$	−15.5000	−	1.65831i	−0.497163	−	0.0531904i
$973$	8.37228			0.268403
$974$	−16.4891	+	28.5600i	−0.528346	+	0.915122i
$975$	4.00000	−	4.25639i	0.128103	−	0.136314i
$976$	5.74456	+	9.94987i	0.183879	+	0.318488i
$977$	18.8139	+	32.5866i	0.601909	+	1.04254i	0.992532	+	0.121986i	$0.0389262\pi$
$977$	18.8139	+	32.5866i	0.601909	+	1.04254i	−0.390623	+	0.920551i	$0.627740\pi$
$978$	0.627719	+	2.08191i	0.0200722	+	0.0665721i
$979$	−7.74456	+	13.4140i	−0.247517	+	0.428713i
$980$	−1.00000			−0.0319438
$981$	0.350532	+	5.63858i	0.0111916	+	0.180026i
$982$	23.9783			0.765177
$983$	22.4307	−	38.8511i	0.715428	−	1.23916i	−0.247366	−	0.968922i	$-0.579565\pi$
$983$	22.4307	−	38.8511i	0.715428	−	1.23916i	0.962794	−	0.270236i	$-0.0871017\pi$
$984$	10.7446	+	2.52434i	0.342524	+	0.0804729i
$985$	−3.37228	−	5.84096i	−0.107450	−	0.186109i
$986$	−3.00000	−	5.19615i	−0.0955395	−	0.165479i
$987$	1.05842	+	0.248667i	0.0336899	+	0.00791515i
$988$	7.37228	−	12.7692i	0.234544	−	0.406241i
$989$	−7.25544			−0.230709
$990$	−2.68614	−	1.33591i	−0.0853712	−	0.0424579i
$991$	−35.6060			−1.13106			−0.565530	−	0.824727i	$-0.691329\pi$
$991$	−35.6060			−1.13106			−0.565530	+	0.824727i	$0.691329\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	9.80298	+	32.5128i	0.311088	+	1.03176i
$994$	8.05842	+	13.9576i	0.255598	+	0.442708i
$995$	−12.0000	−	20.7846i	−0.380426	−	0.658916i
$996$	−0.744563	+	0.792287i	−0.0235924	+	0.0251046i
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	−0.460595	−	0.887610i	$-0.652364\pi$
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	0.998991	−	0.0449179i	$-0.0143026\pi$
$998$	−29.4674			−0.932773
$999$	42.9783	+	35.6357i	1.35977	+	1.12746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.g.421.1	yes	4
3.2	odd	2		1890.2.j.f.1261.2		4
9.2	odd	6		5670.2.a.bk.1.1		2
9.4	even	3	inner	630.2.j.g.211.1	✓	4
9.5	odd	6		1890.2.j.f.631.2		4
9.7	even	3		5670.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.g.211.1	✓	4	9.4	even	3	inner
630.2.j.g.421.1	yes	4	1.1	even	1	trivial
1890.2.j.f.631.2		4	9.5	odd	6
1890.2.j.f.1261.2		4	3.2	odd	2
5670.2.a.s.1.1		2	9.7	even	3
5670.2.a.bk.1.1		2	9.2	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(1.68614 + 0.396143i) q^{12} +(1.68614 + 2.92048i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-1.68614 - 0.396143i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +(-2.68614 - 1.33591i) q^{18} +4.37228 q^{19} +(0.500000 - 0.866025i) q^{20} +(0.500000 + 1.65831i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(1.00000 + 1.73205i) q^{23} +(1.18614 - 1.26217i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.37228 q^{26} +(4.00000 + 3.31662i) q^{27} -1.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(-1.18614 + 1.26217i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 + 1.65831i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{35} +(-2.50000 + 1.65831i) q^{36} +10.7446 q^{37} +(2.18614 - 3.78651i) q^{38} +(-5.68614 - 1.33591i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.18614 + 5.51856i) q^{41} +(1.68614 + 0.396143i) q^{42} +(-1.81386 + 3.14170i) q^{43} -1.00000 q^{44} +(2.50000 - 1.65831i) q^{45} +2.00000 q^{46} +(0.313859 - 0.543620i) q^{47} +(-0.500000 - 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.55842 + 3.78651i) q^{51} +(1.68614 - 2.92048i) q^{52} +0.744563 q^{53} +(4.87228 - 1.80579i) q^{54} +1.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-5.18614 + 5.51856i) q^{57} +(-1.00000 - 1.73205i) q^{58} +(-5.55842 - 9.62747i) q^{59} +(0.500000 + 1.65831i) q^{60} +(5.74456 - 9.94987i) q^{61} +2.00000 q^{62} +(-2.68614 - 1.33591i) q^{63} +1.00000 q^{64} +(-1.68614 + 2.92048i) q^{65} +(1.68614 + 0.396143i) q^{66} +(-2.18614 - 3.78651i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-3.37228 - 0.792287i) q^{69} +(0.500000 - 0.866025i) q^{70} -16.1168 q^{71} +(0.186141 + 2.99422i) q^{72} +14.4891 q^{73} +(5.37228 - 9.30506i) q^{74} +(-0.500000 - 1.65831i) q^{75} +(-2.18614 - 3.78651i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-4.00000 + 4.25639i) q^{78} +(0.0584220 - 0.101190i) q^{79} -1.00000 q^{80} +(-8.93070 + 1.11469i) q^{81} +6.37228 q^{82} +(-0.313859 + 0.543620i) q^{83} +(1.18614 - 1.26217i) q^{84} +(1.50000 + 2.59808i) q^{85} +(1.81386 + 3.14170i) q^{86} +(1.00000 + 3.31662i) q^{87} +(-0.500000 + 0.866025i) q^{88} -15.4891 q^{89} +(-0.186141 - 2.99422i) q^{90} +3.37228 q^{91} +(1.00000 - 1.73205i) q^{92} +(-3.37228 - 0.792287i) q^{93} +(-0.313859 - 0.543620i) q^{94} +(2.18614 + 3.78651i) q^{95} +(-1.68614 - 0.396143i) q^{96} +(-8.24456 + 14.2800i) q^{97} -1.00000 q^{98} +(-2.68614 - 1.33591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 4 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} + q^{12} + q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 12 q^{17} - 5 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21} - 2 q^{22} + 4 q^{23} - q^{24} - 2 q^{25} + 2 q^{26} + 16 q^{27} - 4 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} + 2 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} - 10 q^{36} + 20 q^{37} + 3 q^{38} - 17 q^{39} - 2 q^{40} + 7 q^{41} + q^{42} - 13 q^{43} - 4 q^{44} + 10 q^{45} + 8 q^{46} + 7 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + 3 q^{51} + q^{52} - 20 q^{53} + 8 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 4 q^{58} - 5 q^{59} + 2 q^{60} + 8 q^{62} - 5 q^{63} + 4 q^{64} - q^{65} + q^{66} - 3 q^{67} - 6 q^{68} - 2 q^{69} + 2 q^{70} - 30 q^{71} - 5 q^{72} + 12 q^{73} + 10 q^{74} - 2 q^{75} - 3 q^{76} - 2 q^{77} - 16 q^{78} - 17 q^{79} - 4 q^{80} - 7 q^{81} + 14 q^{82} - 7 q^{83} - q^{84} + 6 q^{85} + 13 q^{86} + 4 q^{87} - 2 q^{88} - 16 q^{89} + 5 q^{90} + 2 q^{91} + 4 q^{92} - 2 q^{93} - 7 q^{94} + 3 q^{95} - q^{96} - 10 q^{97} - 4 q^{98} - 5 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 4 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 + q^12 + q^13 - 2 * q^14 - q^15 - 2 * q^16 + 12 * q^17 - 5 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 - 2 * q^22 + 4 * q^23 - q^24 - 2 * q^25 + 2 * q^26 + 16 * q^27 - 4 * q^28 + 4 * q^29 + q^30 + 4 * q^31 + 2 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 - 10 * q^36 + 20 * q^37 + 3 * q^38 - 17 * q^39 - 2 * q^40 + 7 * q^41 + q^42 - 13 * q^43 - 4 * q^44 + 10 * q^45 + 8 * q^46 + 7 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + 3 * q^51 + q^52 - 20 * q^53 + 8 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 4 * q^58 - 5 * q^59 + 2 * q^60 + 8 * q^62 - 5 * q^63 + 4 * q^64 - q^65 + q^66 - 3 * q^67 - 6 * q^68 - 2 * q^69 + 2 * q^70 - 30 * q^71 - 5 * q^72 + 12 * q^73 + 10 * q^74 - 2 * q^75 - 3 * q^76 - 2 * q^77 - 16 * q^78 - 17 * q^79 - 4 * q^80 - 7 * q^81 + 14 * q^82 - 7 * q^83 - q^84 + 6 * q^85 + 13 * q^86 + 4 * q^87 - 2 * q^88 - 16 * q^89 + 5 * q^90 + 2 * q^91 + 4 * q^92 - 2 * q^93 - 7 * q^94 + 3 * q^95 - q^96 - 10 * q^97 - 4 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more