LMFDB - Embedded newform 630.2.j.g.421.2

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			421.2
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.g.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.68614 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.68614 - 0.396143i) 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} +(2.68614 - 1.33591i) q^{9} +1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.18614 - 1.26217i) q^{12} +(-1.18614 - 2.05446i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.18614 + 1.26217i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +(0.186141 - 2.99422i) q^{18} -1.37228 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} +(-1.68614 + 0.396143i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.37228 q^{26} +(4.00000 - 3.31662i) q^{27} -1.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(1.68614 - 0.396143i) 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} -0.744563 q^{37} +(-0.686141 + 1.18843i) q^{38} +(-2.81386 - 2.99422i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(0.313859 + 0.543620i) q^{41} +(-1.18614 - 1.26217i) q^{42} +(-4.68614 + 8.11663i) q^{43} -1.00000 q^{44} +(2.50000 + 1.65831i) q^{45} +2.00000 q^{46} +(3.18614 - 5.51856i) q^{47} +(-0.500000 + 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.05842 - 1.18843i) q^{51} +(-1.18614 + 2.05446i) q^{52} -10.7446 q^{53} +(-0.872281 - 5.12241i) q^{54} +1.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.31386 + 0.543620i) q^{57} +(-1.00000 - 1.73205i) q^{58} +(3.05842 + 5.29734i) q^{59} +(0.500000 - 1.65831i) q^{60} +(-5.74456 + 9.94987i) q^{61} +2.00000 q^{62} +(0.186141 - 2.99422i) q^{63} +1.00000 q^{64} +(1.18614 - 2.05446i) q^{65} +(-1.18614 - 1.26217i) q^{66} +(0.686141 + 1.18843i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(2.37228 + 2.52434i) q^{69} +(0.500000 - 0.866025i) q^{70} +1.11684 q^{71} +(-2.68614 + 1.33591i) q^{72} -8.48913 q^{73} +(-0.372281 + 0.644810i) q^{74} +(-0.500000 + 1.65831i) q^{75} +(0.686141 + 1.18843i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-4.00000 + 0.939764i) q^{78} +(-8.55842 + 14.8236i) q^{79} -1.00000 q^{80} +(5.43070 - 7.17687i) q^{81} +0.627719 q^{82} +(-3.18614 + 5.51856i) q^{83} +(-1.68614 + 0.396143i) q^{84} +(1.50000 + 2.59808i) q^{85} +(4.68614 + 8.11663i) q^{86} +(1.00000 - 3.31662i) q^{87} +(-0.500000 + 0.866025i) q^{88} +7.48913 q^{89} +(2.68614 - 1.33591i) q^{90} -2.37228 q^{91} +(1.00000 - 1.73205i) q^{92} +(2.37228 + 2.52434i) q^{93} +(-3.18614 - 5.51856i) q^{94} +(-0.686141 - 1.18843i) q^{95} +(1.18614 + 1.26217i) q^{96} +(3.24456 - 5.61975i) q^{97} -1.00000 q^{98} +(0.186141 - 2.99422i) 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
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$4$	−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
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$	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	$0.118496\pi$
$12$	−1.18614	−	1.26217i	−0.342409	−	0.364357i
$13$	−1.18614	−	2.05446i	−0.328976	−	0.569804i	0.653333	−	0.757071i	$-0.273370\pi$
$13$	−1.18614	−	2.05446i	−0.328976	−	0.569804i	−0.982309	+	0.187267i	$0.940037\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.18614	+	1.26217i	0.306260	+	0.325891i
$16$	−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	$0.381478\pi$
$18$	0.186141	−	2.99422i	0.0438738	−	0.705744i
$19$	−1.37228			−0.314823			−0.157411	−	0.987533i	$-0.550315\pi$
$19$	−1.37228			−0.314823			−0.157411	+	0.987533i	$0.550315\pi$
$20$	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	$0.766471\pi$
$24$	−1.68614	+	0.396143i	−0.344182	+	0.0808625i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.37228			−0.465243
$27$	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	$0.107213\pi$
$30$	1.68614	−	0.396143i	0.307846	−	0.0723256i
$31$	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
$37$	−0.744563			−0.122405			−0.0612027	−	0.998125i	$-0.519494\pi$
$37$	−0.744563			−0.122405			−0.0612027	+	0.998125i	$0.519494\pi$
$38$	−0.686141	+	1.18843i	−0.111307	+	0.192789i
$39$	−2.81386	−	2.99422i	−0.450578	−	0.479459i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	0.313859	+	0.543620i	0.0490166	+	0.0848992i	0.889493	−	0.456949i	$-0.151058\pi$
$41$	0.313859	+	0.543620i	0.0490166	+	0.0848992i	−0.840476	+	0.541849i	$0.817725\pi$
$42$	−1.18614	−	1.26217i	−0.183025	−	0.194757i
$43$	−4.68614	+	8.11663i	−0.714630	+	1.23778i	0.248472	+	0.968639i	$0.420071\pi$
$43$	−4.68614	+	8.11663i	−0.714630	+	1.23778i	−0.963102	+	0.269136i	$0.913262\pi$
$44$	−1.00000			−0.150756
$45$	2.50000	+	1.65831i	0.372678	+	0.247207i
$46$	2.00000			0.294884
$47$	3.18614	−	5.51856i	0.464746	−	0.804964i	−0.534444	−	0.845204i	$-0.679479\pi$
$47$	3.18614	−	5.51856i	0.464746	−	0.804964i	0.999190	+	0.0402398i	$0.0128122\pi$
$48$	−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
$51$	5.05842	−	1.18843i	0.708321	−	0.166414i
$52$	−1.18614	+	2.05446i	−0.164488	+	0.284902i
$53$	−10.7446			−1.47588			−0.737940	−	0.674867i	$-0.764201\pi$
$53$	−10.7446			−1.47588			−0.737940	+	0.674867i	$0.764201\pi$
$54$	−0.872281	−	5.12241i	−0.118702	−	0.697072i
$55$	1.00000			0.134840
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−2.31386	+	0.543620i	−0.306478	+	0.0720043i
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	3.05842	+	5.29734i	0.398173	+	0.689655i	0.993501	−	0.113828i	$-0.0363112\pi$
$59$	3.05842	+	5.29734i	0.398173	+	0.689655i	−0.595328	+	0.803483i	$0.702978\pi$
$60$	0.500000	−	1.65831i	0.0645497	−	0.214087i
$61$	−5.74456	+	9.94987i	−0.735516	+	1.27395i	0.218981	+	0.975729i	$0.429727\pi$
$61$	−5.74456	+	9.94987i	−0.735516	+	1.27395i	−0.954497	+	0.298222i	$0.903607\pi$
$62$	2.00000			0.254000
$63$	0.186141	−	2.99422i	0.0234515	−	0.377236i
$64$	1.00000			0.125000
$65$	1.18614	−	2.05446i	0.147123	−	0.254824i
$66$	−1.18614	−	1.26217i	−0.146004	−	0.155362i
$67$	0.686141	+	1.18843i	0.0838254	+	0.145190i	0.904890	−	0.425645i	$-0.139953\pi$
$67$	0.686141	+	1.18843i	0.0838254	+	0.145190i	−0.821065	+	0.570835i	$0.806620\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	2.37228	+	2.52434i	0.285589	+	0.303895i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	1.11684			0.132545			0.0662725	−	0.997802i	$-0.478889\pi$
$71$	1.11684			0.132545			0.0662725	+	0.997802i	$0.478889\pi$
$72$	−2.68614	+	1.33591i	−0.316565	+	0.157438i
$73$	−8.48913			−0.993577			−0.496788	−	0.867872i	$-0.665488\pi$
$73$	−8.48913			−0.993577			−0.496788	+	0.867872i	$0.665488\pi$
$74$	−0.372281	+	0.644810i	−0.0432768	+	0.0749577i
$75$	−0.500000	+	1.65831i	−0.0577350	+	0.191485i
$76$	0.686141	+	1.18843i	0.0787057	+	0.136322i
$77$	−0.500000	−	0.866025i	−0.0569803	−	0.0986928i
$78$	−4.00000	+	0.939764i	−0.452911	+	0.106407i
$79$	−8.55842	+	14.8236i	−0.962898	+	1.66779i	−0.247737	+	0.968827i	$0.579687\pi$
$79$	−8.55842	+	14.8236i	−0.962898	+	1.66779i	−0.715160	+	0.698961i	$0.753646\pi$
$80$	−1.00000			−0.111803
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$	0.627719			0.0693199
$83$	−3.18614	+	5.51856i	−0.349724	+	0.605740i	−0.986200	−	0.165556i	$-0.947058\pi$
$83$	−3.18614	+	5.51856i	−0.349724	+	0.605740i	0.636476	+	0.771297i	$0.280391\pi$
$84$	−1.68614	+	0.396143i	−0.183973	+	0.0432228i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	4.68614	+	8.11663i	0.505320	+	0.875239i
$87$	1.00000	−	3.31662i	0.107211	−	0.355580i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	7.48913			0.793846			0.396923	−	0.917852i	$-0.370078\pi$
$89$	7.48913			0.793846			0.396923	+	0.917852i	$0.370078\pi$
$90$	2.68614	−	1.33591i	0.283144	−	0.140817i
$91$	−2.37228			−0.248683
$92$	1.00000	−	1.73205i	0.104257	−	0.180579i
$93$	2.37228	+	2.52434i	0.245994	+	0.261762i
$94$	−3.18614	−	5.51856i	−0.328625	−	0.569196i
$95$	−0.686141	−	1.18843i	−0.0703965	−	0.121930i
$96$	1.18614	+	1.26217i	0.121060	+	0.128820i
$97$	3.24456	−	5.61975i	0.329435	−	0.570599i	−0.652965	−	0.757389i	$-0.726475\pi$
$97$	3.24456	−	5.61975i	0.329435	−	0.570599i	0.982400	+	0.186790i	$0.0598083\pi$
$98$	−1.00000			−0.101015
$99$	0.186141	−	2.99422i	0.0187078	−	0.300930i
$100$	1.00000			0.100000
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	−0.562242	−	0.826973i	$-0.690061\pi$
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	0.997300	+	0.0734297i	$0.0233944\pi$
$102$	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	$0.962288\pi$
$104$	1.18614	+	2.05446i	0.116311	+	0.201456i
$105$	1.68614	−	0.396143i	0.164550	−	0.0386596i
$106$	−5.37228	+	9.30506i	−0.521802	+	0.903788i
$107$	14.8614			1.43671			0.718353	−	0.695679i	$-0.244896\pi$
$107$	14.8614			1.43671			0.718353	+	0.695679i	$0.244896\pi$
$108$	−4.87228	−	1.80579i	−0.468835	−	0.173762i
$109$	−19.1168			−1.83106			−0.915531	−	0.402248i	$-0.868229\pi$
$109$	−19.1168			−1.83106			−0.915531	+	0.402248i	$0.868229\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−1.25544	+	0.294954i	−0.119161	+	0.0279958i
$112$	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	$0.742264\pi$
$114$	−0.686141	+	2.27567i	−0.0642630	+	0.213136i
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$	−2.00000			−0.185695
$117$	−5.93070	−	3.93398i	−0.548294	−	0.363697i
$118$	6.11684			0.563101
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	−1.18614	−	1.26217i	−0.108279	−	0.115220i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	5.74456	+	9.94987i	0.520088	+	0.900819i
$123$	0.744563	+	0.792287i	0.0671350	+	0.0714381i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$	−2.50000	−	1.65831i	−0.222718	−	0.147734i
$127$	6.74456			0.598483			0.299242	−	0.954177i	$-0.403266\pi$
$127$	6.74456			0.598483			0.299242	+	0.954177i	$0.403266\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.68614	+	15.5422i	−0.412592	+	1.36841i
$130$	−1.18614	−	2.05446i	−0.104031	−	0.180188i
$131$	−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	$0.889242\pi$
$132$	−1.68614	+	0.396143i	−0.146760	+	0.0344799i
$133$	−0.686141	+	1.18843i	−0.0594959	+	0.103050i
$134$	1.37228			0.118547
$135$	4.87228	+	1.80579i	0.419339	+	0.155418i
$136$	−3.00000			−0.257248
$137$	−0.686141	+	1.18843i	−0.0586210	+	0.101534i	−0.893847	−	0.448373i	$-0.852004\pi$
$137$	−0.686141	+	1.18843i	−0.0586210	+	0.101534i	0.835226	+	0.549907i	$0.185337\pi$
$138$	3.37228	−	0.792287i	0.287068	−	0.0674439i
$139$	1.31386	+	2.27567i	0.111440	+	0.193020i	0.916351	−	0.400376i	$-0.131120\pi$
$139$	1.31386	+	2.27567i	0.111440	+	0.193020i	−0.804911	+	0.593396i	$0.797787\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	3.18614	−	10.5672i	0.268321	−	0.889922i
$142$	0.558422	−	0.967215i	0.0468617	−	0.0811669i
$143$	−2.37228			−0.198380
$144$	−0.186141	+	2.99422i	−0.0155117	+	0.249518i
$145$	2.00000			0.166091
$146$	−4.24456	+	7.35180i	−0.351283	+	0.608439i
$147$	−1.18614	−	1.26217i	−0.0978312	−	0.104102i
$148$	0.372281	+	0.644810i	0.0306013	+	0.0530031i
$149$	7.93070	+	13.7364i	0.649709	+	1.12533i	0.983192	+	0.182572i	$0.0584424\pi$
$149$	7.93070	+	13.7364i	0.649709	+	1.12533i	−0.333484	+	0.942756i	$0.608224\pi$
$150$	1.18614	+	1.26217i	0.0968480	+	0.103056i
$151$	−4.93070	+	8.54023i	−0.401255	+	0.694994i	−0.993878	−	0.110486i	$-0.964759\pi$
$151$	−4.93070	+	8.54023i	−0.401255	+	0.694994i	0.592623	+	0.805480i	$0.298093\pi$
$152$	1.37228			0.111307
$153$	8.05842	−	4.00772i	0.651485	−	0.324005i
$154$	−1.00000			−0.0805823
$155$	−1.00000	+	1.73205i	−0.0803219	+	0.139122i
$156$	−1.18614	+	3.93398i	−0.0949673	+	0.314971i
$157$	−5.93070	−	10.2723i	−0.473322	−	0.819817i	0.526212	−	0.850353i	$-0.323612\pi$
$157$	−5.93070	−	10.2723i	−0.473322	−	0.819817i	−0.999534	+	0.0305363i	$0.990278\pi$
$158$	8.55842	+	14.8236i	0.680871	+	1.17930i
$159$	−18.1168	+	4.25639i	−1.43676	+	0.337554i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.00000			0.157622
$162$	−3.50000	−	8.29156i	−0.274986	−	0.651447i
$163$	12.7446			0.998231			0.499116	−	0.866535i	$-0.333658\pi$
$163$	12.7446			0.998231			0.499116	+	0.866535i	$0.333658\pi$
$164$	0.313859	−	0.543620i	0.0245083	−	0.0424496i
$165$	1.68614	−	0.396143i	0.131266	−	0.0308397i
$166$	3.18614	+	5.51856i	0.247292	+	0.428323i
$167$	8.18614	+	14.1788i	0.633463	+	1.09719i	0.986839	+	0.161708i	$0.0517003\pi$
$167$	8.18614	+	14.1788i	0.633463	+	1.09719i	−0.353376	+	0.935481i	$0.614966\pi$
$168$	−0.500000	+	1.65831i	−0.0385758	+	0.127942i
$169$	3.68614	−	6.38458i	0.283549	−	0.491122i
$170$	3.00000			0.230089
$171$	−3.68614	+	1.83324i	−0.281886	+	0.140191i
$172$	9.37228			0.714630
$173$	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	$-0.0732068\pi$
$174$	−2.37228	−	2.52434i	−0.179842	−	0.191370i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	7.25544	+	7.72049i	0.545352	+	0.580308i
$178$	3.74456	−	6.48577i	0.280667	−	0.486129i
$179$	−23.1168			−1.72783			−0.863917	−	0.503634i	$-0.831996\pi$
$179$	−23.1168			−1.72783			−0.863917	+	0.503634i	$0.831996\pi$
$180$	0.186141	−	2.99422i	0.0138741	−	0.223176i
$181$	−8.74456			−0.649978			−0.324989	−	0.945718i	$-0.605361\pi$
$181$	−8.74456			−0.649978			−0.324989	+	0.945718i	$0.605361\pi$
$182$	−1.18614	+	2.05446i	−0.0879226	+	0.152286i
$183$	−5.74456	+	19.0526i	−0.424650	+	1.40841i
$184$	−1.00000	−	1.73205i	−0.0737210	−	0.127688i
$185$	−0.372281	−	0.644810i	−0.0273707	−	0.0474074i
$186$	3.37228	−	0.792287i	0.247268	−	0.0580933i
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$	−6.37228			−0.464746
$189$	−0.872281	−	5.12241i	−0.0634491	−	0.372601i
$190$	−1.37228			−0.0995558
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	−0.749482	−	0.662025i	$-0.769697\pi$
$191$	2.74456	−	4.75372i	0.198590	−	0.343967i	0.948071	+	0.318058i	$0.103031\pi$
$192$	1.68614	−	0.396143i	0.121687	−	0.0285892i
$193$	−2.68614	−	4.65253i	−0.193353	−	0.334897i	0.753007	−	0.658013i	$-0.228603\pi$
$193$	−2.68614	−	4.65253i	−0.193353	−	0.334897i	−0.946359	+	0.323116i	$0.895269\pi$
$194$	−3.24456	−	5.61975i	−0.232946	−	0.403474i
$195$	1.18614	−	3.93398i	0.0849413	−	0.281718i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	4.74456			0.338036			0.169018	−	0.985613i	$-0.445940\pi$
$197$	4.74456			0.338036			0.169018	+	0.985613i	$0.445940\pi$
$198$	−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
$201$	1.62772	+	1.73205i	0.114810	+	0.122169i
$202$	−4.37228	−	7.57301i	−0.307633	−	0.532835i
$203$	−1.00000	−	1.73205i	−0.0701862	−	0.121566i
$204$	−3.55842	−	3.78651i	−0.249139	−	0.265108i
$205$	−0.313859	+	0.543620i	−0.0219209	+	0.0379681i
$206$	−8.00000			−0.557386
$207$	5.00000	+	3.31662i	0.347524	+	0.230521i
$208$	2.37228			0.164488
$209$	−0.686141	+	1.18843i	−0.0474613	+	0.0822055i
$210$	0.500000	−	1.65831i	0.0345033	−	0.114434i
$211$	12.6753	+	21.9542i	0.872601	+	1.51139i	0.859296	+	0.511478i	$0.170902\pi$
$211$	12.6753	+	21.9542i	0.872601	+	1.51139i	0.0133051	+	0.999911i	$0.495765\pi$
$212$	5.37228	+	9.30506i	0.368970	+	0.639074i
$213$	1.88316	−	0.442430i	0.129032	−	0.0303148i
$214$	7.43070	−	12.8704i	0.507952	−	0.879799i
$215$	−9.37228			−0.639184
$216$	−4.00000	+	3.31662i	−0.272166	+	0.225668i
$217$	2.00000			0.135769
$218$	−9.55842	+	16.5557i	−0.647378	+	1.12129i
$219$	−14.3139	+	3.36291i	−0.967241	+	0.227245i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	−3.55842	−	6.16337i	−0.239365	−	0.414593i
$222$	−0.372281	+	1.23472i	−0.0249859	+	0.0828688i
$223$	4.93070	−	8.54023i	0.330184	−	0.571896i	−0.652363	−	0.757906i	$-0.726222\pi$
$223$	4.93070	−	8.54023i	0.330184	−	0.571896i	0.982548	+	0.186010i	$0.0595558\pi$
$224$	1.00000			0.0668153
$225$	−0.186141	+	2.99422i	−0.0124094	+	0.199615i
$226$	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	$0.0920405\pi$
$228$	1.62772	+	1.73205i	0.107798	+	0.114708i
$229$	−2.37228	−	4.10891i	−0.156765	−	0.271525i	0.776935	−	0.629580i	$-0.216773\pi$
$229$	−2.37228	−	4.10891i	−0.156765	−	0.271525i	−0.933700	+	0.358056i	$0.883440\pi$
$230$	1.00000	+	1.73205i	0.0659380	+	0.114208i
$231$	−1.18614	−	1.26217i	−0.0780423	−	0.0830446i
$232$	−1.00000	+	1.73205i	−0.0656532	+	0.113715i
$233$	7.37228			0.482974			0.241487	−	0.970404i	$-0.422365\pi$
$233$	7.37228			0.482974			0.241487	+	0.970404i	$0.422365\pi$
$234$	−6.37228	+	3.16915i	−0.416569	+	0.207174i
$235$	6.37228			0.415682
$236$	3.05842	−	5.29734i	0.199086	−	0.344828i
$237$	−8.55842	+	28.3851i	−0.555929	+	1.84381i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	0.999649	−	0.0265017i	$-0.00843674\pi$
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	−0.522776	+	0.852470i	$0.675103\pi$
$240$	−1.68614	+	0.396143i	−0.108840	+	0.0255710i
$241$	6.31386	−	10.9359i	0.406711	−	0.704445i	−0.587808	−	0.809001i	$-0.700009\pi$
$241$	6.31386	−	10.9359i	0.406711	−	0.704445i	0.994519	+	0.104556i	$0.0333421\pi$
$242$	10.0000			0.642824
$243$	6.31386	−	14.2525i	0.405034	−	0.914302i
$244$	11.4891			0.735516
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	1.05842	−	0.248667i	0.0674825	−	0.0158544i
$247$	1.62772	+	2.81929i	0.103569	+	0.179387i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−3.18614	+	10.5672i	−0.201913	+	0.669671i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−17.6060			−1.11128			−0.555639	−	0.831423i	$-0.687527\pi$
$251$	−17.6060			−1.11128			−0.555639	+	0.831423i	$0.687527\pi$
$252$	−2.68614	+	1.33591i	−0.169211	+	0.0841543i
$253$	2.00000			0.125739
$254$	3.37228	−	5.84096i	0.211596	−	0.366495i
$255$	3.55842	+	3.78651i	0.222837	+	0.237120i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.12772	−	3.68532i	−0.132723	−	0.229884i	0.792002	−	0.610518i	$-0.209039\pi$
$257$	−2.12772	−	3.68532i	−0.132723	−	0.229884i	−0.924725	+	0.380635i	$0.875706\pi$
$258$	11.1168	+	11.8294i	0.692104	+	0.736466i
$259$	−0.372281	+	0.644810i	−0.0231324	+	0.0400666i
$260$	−2.37228			−0.147123
$261$	0.372281	−	5.98844i	0.0230436	−	0.370675i
$262$	−4.00000			−0.247121
$263$	−11.4891	+	19.8997i	−0.708450	+	1.22707i	0.256982	+	0.966416i	$0.417272\pi$
$263$	−11.4891	+	19.8997i	−0.708450	+	1.22707i	−0.965432	+	0.260655i	$0.916062\pi$
$264$	−0.500000	+	1.65831i	−0.0307729	+	0.102062i
$265$	−5.37228	−	9.30506i	−0.330017	−	0.571606i
$266$	0.686141	+	1.18843i	0.0420700	+	0.0728673i
$267$	12.6277	−	2.96677i	0.772804	−	0.181563i
$268$	0.686141	−	1.18843i	0.0419127	−	0.0725949i
$269$	−4.51087			−0.275033			−0.137516	−	0.990499i	$-0.543912\pi$
$269$	−4.51087			−0.275033			−0.137516	+	0.990499i	$0.543912\pi$
$270$	4.00000	−	3.31662i	0.243432	−	0.201843i
$271$	−9.48913			−0.576423			−0.288212	−	0.957567i	$-0.593061\pi$
$271$	−9.48913			−0.576423			−0.288212	+	0.957567i	$0.593061\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−4.00000	+	0.939764i	−0.242091	+	0.0568771i
$274$	0.686141	+	1.18843i	0.0414513	+	0.0717957i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	1.00000	−	3.31662i	0.0601929	−	0.199637i
$277$	7.74456	−	13.4140i	0.465326	−	0.805968i	−0.533890	−	0.845554i	$-0.679271\pi$
$277$	7.74456	−	13.4140i	0.465326	−	0.805968i	0.999216	+	0.0395859i	$0.0126039\pi$
$278$	2.62772			0.157600
$279$	5.00000	+	3.31662i	0.299342	+	0.198561i
$280$	−1.00000			−0.0597614
$281$	12.9307	−	22.3966i	0.771381	−	1.33607i	−0.165425	−	0.986222i	$-0.552900\pi$
$281$	12.9307	−	22.3966i	0.771381	−	1.33607i	0.936806	−	0.349849i	$-0.113767\pi$
$282$	−7.55842	−	8.04290i	−0.450097	−	0.478947i
$283$	−14.3030	−	24.7735i	−0.850224	−	1.47263i	−0.881006	−	0.473105i	$-0.843133\pi$
$283$	−14.3030	−	24.7735i	−0.850224	−	1.47263i	0.0307817	−	0.999526i	$-0.490200\pi$
$284$	−0.558422	−	0.967215i	−0.0331362	−	0.0573937i
$285$	−1.62772	−	1.73205i	−0.0964177	−	0.102598i
$286$	−1.18614	+	2.05446i	−0.0701380	+	0.121483i
$287$	0.627719			0.0370531
$288$	2.50000	+	1.65831i	0.147314	+	0.0977170i
$289$	−8.00000			−0.470588
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	3.24456	−	10.7610i	0.190200	−	0.630821i
$292$	4.24456	+	7.35180i	0.248394	+	0.430231i
$293$	−11.7446	−	20.3422i	−0.686125	−	1.18840i	−0.973082	−	0.230459i	$-0.925977\pi$
$293$	−11.7446	−	20.3422i	−0.686125	−	1.18840i	0.286957	−	0.957943i	$-0.407356\pi$
$294$	−1.68614	+	0.396143i	−0.0983377	+	0.0231036i
$295$	−3.05842	+	5.29734i	−0.178068	+	0.308423i
$296$	0.744563			0.0432768
$297$	−0.872281	−	5.12241i	−0.0506149	−	0.297233i
$298$	15.8614			0.918827
$299$	2.37228	−	4.10891i	0.137193	−	0.237625i
$300$	1.68614	−	0.396143i	0.0973494	−	0.0228714i
$301$	4.68614	+	8.11663i	0.270105	+	0.467835i
$302$	4.93070	+	8.54023i	0.283730	+	0.491435i
$303$	4.37228	−	14.5012i	0.251181	−	0.833073i
$304$	0.686141	−	1.18843i	0.0393529	−	0.0681612i
$305$	−11.4891			−0.657865
$306$	0.558422	−	8.98266i	0.0319229	−	0.513504i
$307$	19.2337			1.09772			0.548862	−	0.835913i	$-0.315061\pi$
$307$	19.2337			1.09772			0.548862	+	0.835913i	$0.315061\pi$
$308$	−0.500000	+	0.866025i	−0.0284901	+	0.0493464i
$309$	−9.48913	−	10.0974i	−0.539817	−	0.574418i
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	−16.1168	−	27.9152i	−0.913902	−	1.58293i	−0.808500	−	0.588496i	$-0.799720\pi$
$311$	−16.1168	−	27.9152i	−0.913902	−	1.58293i	−0.105402	−	0.994430i	$-0.533613\pi$
$312$	2.81386	+	2.99422i	0.159303	+	0.169514i
$313$	8.05842	−	13.9576i	0.455489	−	0.788930i	−0.543227	−	0.839586i	$-0.682798\pi$
$313$	8.05842	−	13.9576i	0.455489	−	0.788930i	0.998716	+	0.0506557i	$0.0161311\pi$
$314$	−11.8614			−0.669378
$315$	2.68614	−	1.33591i	0.151347	−	0.0752698i
$316$	17.1168			0.962898
$317$	13.1168	−	22.7190i	0.736715	−	1.27603i	−0.217251	−	0.976116i	$-0.569709\pi$
$317$	13.1168	−	22.7190i	0.736715	−	1.27603i	0.953967	−	0.299913i	$-0.0969576\pi$
$318$	−5.37228	+	17.8178i	−0.301263	+	0.999175i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	25.0584	−	5.88725i	1.39862	−	0.328594i
$322$	1.00000	−	1.73205i	0.0557278	−	0.0965234i
$323$	−4.11684			−0.229067
$324$	−8.93070	−	1.11469i	−0.496150	−	0.0619273i
$325$	2.37228			0.131590
$326$	6.37228	−	11.0371i	0.352928	−	0.611289i
$327$	−32.2337	+	7.57301i	−1.78253	+	0.418789i
$328$	−0.313859	−	0.543620i	−0.0173300	−	0.0300164i
$329$	−3.18614	−	5.51856i	−0.175658	−	0.304248i
$330$	0.500000	−	1.65831i	0.0275241	−	0.0912871i
$331$	−10.3030	+	17.8453i	−0.566303	+	0.980866i	0.430624	+	0.902531i	$0.358294\pi$
$331$	−10.3030	+	17.8453i	−0.566303	+	0.980866i	−0.996927	+	0.0783345i	$0.975040\pi$
$332$	6.37228			0.349724
$333$	−2.00000	+	0.994667i	−0.109599	+	0.0545074i
$334$	16.3723			0.895851
$335$	−0.686141	+	1.18843i	−0.0374879	+	0.0649309i
$336$	1.18614	+	1.26217i	0.0647093	+	0.0688570i
$337$	−8.05842	−	13.9576i	−0.438970	−	0.760319i	0.558640	−	0.829410i	$-0.311323\pi$
$337$	−8.05842	−	13.9576i	−0.438970	−	0.760319i	−0.997610	+	0.0690914i	$0.977990\pi$
$338$	−3.68614	−	6.38458i	−0.200500	−	0.347276i
$339$	7.11684	+	7.57301i	0.386534	+	0.411310i
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	2.00000			0.108306
$342$	−0.255437	+	4.10891i	−0.0138125	+	0.222185i
$343$	−1.00000			−0.0539949
$344$	4.68614	−	8.11663i	0.252660	−	0.437620i
$345$	−1.00000	+	3.31662i	−0.0538382	+	0.178561i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	1.56930	+	2.71810i	0.0842443	+	0.145915i	0.905069	−	0.425265i	$-0.139819\pi$
$347$	1.56930	+	2.71810i	0.0842443	+	0.145915i	−0.820825	+	0.571180i	$0.806486\pi$
$348$	−3.37228	+	0.792287i	−0.180773	+	0.0424710i
$349$	8.74456	−	15.1460i	0.468086	−	0.810748i	−0.531249	−	0.847216i	$-0.678277\pi$
$349$	8.74456	−	15.1460i	0.468086	−	0.810748i	0.999335	+	0.0364674i	$0.0116105\pi$
$350$	1.00000			0.0534522
$351$	−11.5584	−	4.28384i	−0.616943	−	0.228654i
$352$	1.00000			0.0533002
$353$	9.43070	−	16.3345i	0.501946	−	0.869395i	−0.498052	−	0.867147i	$-0.665951\pi$
$353$	9.43070	−	16.3345i	0.501946	−	0.869395i	0.999997	−	0.00224815i	$-0.000715608\pi$
$354$	10.3139	−	2.42315i	0.548175	−	0.128789i
$355$	0.558422	+	0.967215i	0.0296380	+	0.0513345i
$356$	−3.74456	−	6.48577i	−0.198461	−	0.343745i
$357$	1.50000	−	4.97494i	0.0793884	−	0.263302i
$358$	−11.5584	+	20.0198i	−0.610882	+	1.05808i
$359$	−2.51087			−0.132519			−0.0662594	−	0.997802i	$-0.521107\pi$
$359$	−2.51087			−0.132519			−0.0662594	+	0.997802i	$0.521107\pi$
$360$	−2.50000	−	1.65831i	−0.131762	−	0.0874007i
$361$	−17.1168			−0.900887
$362$	−4.37228	+	7.57301i	−0.229802	+	0.398029i
$363$	11.8614	+	12.6217i	0.622562	+	0.662467i
$364$	1.18614	+	2.05446i	0.0621707	+	0.107683i
$365$	−4.24456	−	7.35180i	−0.222171	−	0.384811i
$366$	13.6277	+	14.5012i	0.712332	+	0.757991i
$367$	16.3030	−	28.2376i	0.851009	−	1.47399i	−0.0292899	−	0.999571i	$-0.509325\pi$
$367$	16.3030	−	28.2376i	0.851009	−	1.47399i	0.880299	−	0.474420i	$-0.157342\pi$
$368$	−2.00000			−0.104257
$369$	1.56930	+	1.04095i	0.0816943	+	0.0541899i
$370$	−0.744563			−0.0387080
$371$	−5.37228	+	9.30506i	−0.278915	+	0.483095i
$372$	1.00000	−	3.31662i	0.0518476	−	0.171959i
$373$	−4.62772	−	8.01544i	−0.239614	−	0.415024i	0.720989	−	0.692946i	$-0.243688\pi$
$373$	−4.62772	−	8.01544i	−0.239614	−	0.415024i	−0.960604	+	0.277922i	$0.910354\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$	−1.68614	+	0.396143i	−0.0870719	+	0.0204568i
$376$	−3.18614	+	5.51856i	−0.164313	+	0.284598i
$377$	−4.74456			−0.244357
$378$	−4.87228	−	1.80579i	−0.250603	−	0.0928798i
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$	−0.686141	+	1.18843i	−0.0351983	+	0.0609652i
$381$	11.3723	−	2.67181i	0.582620	−	0.136881i
$382$	−2.74456	−	4.75372i	−0.140424	−	0.243222i
$383$	5.55842	+	9.62747i	0.284022	+	0.491941i	0.972372	−	0.233439i	$-0.0749978\pi$
$383$	5.55842	+	9.62747i	0.284022	+	0.491941i	−0.688349	+	0.725379i	$0.741664\pi$
$384$	0.500000	−	1.65831i	0.0255155	−	0.0846254i
$385$	0.500000	−	0.866025i	0.0254824	−	0.0441367i
$386$	−5.37228			−0.273442
$387$	−1.74456	+	28.0627i	−0.0886811	+	1.42651i
$388$	−6.48913			−0.329435
$389$	10.8139	−	18.7302i	0.548284	−	0.949656i	−0.450108	−	0.892974i	$-0.648614\pi$
$389$	10.8139	−	18.7302i	0.548284	−	0.949656i	0.998392	−	0.0566823i	$-0.0180522\pi$
$390$	−2.81386	−	2.99422i	−0.142485	−	0.151618i
$391$	3.00000	+	5.19615i	0.151717	+	0.262781i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−4.74456	−	5.04868i	−0.239332	−	0.254672i
$394$	2.37228	−	4.10891i	0.119514	−	0.207004i
$395$	−17.1168			−0.861242
$396$	−2.68614	+	1.33591i	−0.134984	+	0.0671319i
$397$	−19.2554			−0.966403			−0.483201	−	0.875509i	$-0.660526\pi$
$397$	−19.2554			−0.966403			−0.483201	+	0.875509i	$0.660526\pi$
$398$	−12.0000	+	20.7846i	−0.601506	+	1.04184i
$399$	−0.686141	+	2.27567i	−0.0343500	+	0.113926i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−12.8030	−	22.1754i	−0.639351	−	1.10739i	−0.985576	−	0.169236i	$-0.945870\pi$
$401$	−12.8030	−	22.1754i	−0.639351	−	1.10739i	0.346225	−	0.938152i	$-0.387463\pi$
$402$	2.31386	−	0.543620i	0.115405	−	0.0271133i
$403$	2.37228	−	4.10891i	0.118172	−	0.204679i
$404$	−8.74456			−0.435058
$405$	8.93070	+	1.11469i	0.443770	+	0.0553895i
$406$	−2.00000			−0.0992583
$407$	−0.372281	+	0.644810i	−0.0184533	+	0.0319621i
$408$	−5.05842	+	1.18843i	−0.250429	+	0.0588361i
$409$	10.3139	+	17.8641i	0.509988	+	0.883324i	0.999933	+	0.0115713i	$0.00368333\pi$
$409$	10.3139	+	17.8641i	0.509988	+	0.883324i	−0.489946	+	0.871753i	$0.662983\pi$
$410$	0.313859	+	0.543620i	0.0155004	+	0.0268475i
$411$	−0.686141	+	2.27567i	−0.0338448	+	0.112251i
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	6.11684			0.300990
$414$	5.37228	−	2.67181i	0.264033	−	0.131313i
$415$	−6.37228			−0.312803
$416$	1.18614	−	2.05446i	0.0581553	−	0.100728i
$417$	3.11684	+	3.31662i	0.152633	+	0.162416i
$418$	0.686141	+	1.18843i	0.0335602	+	0.0581280i
$419$	7.25544	+	12.5668i	0.354451	+	0.613928i	0.987024	−	0.160573i	$-0.0513343\pi$
$419$	7.25544	+	12.5668i	0.354451	+	0.613928i	−0.632573	+	0.774501i	$0.718001\pi$
$420$	−1.18614	−	1.26217i	−0.0578777	−	0.0615875i
$421$	9.44158	−	16.3533i	0.460154	−	0.797011i	−0.538814	−	0.842425i	$-0.681127\pi$
$421$	9.44158	−	16.3533i	0.460154	−	0.797011i	0.998968	+	0.0454141i	$0.0144607\pi$
$422$	25.3505			1.23404
$423$	1.18614	−	19.0800i	0.0576721	−	0.927702i
$424$	10.7446			0.521802
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	0.558422	−	1.85208i	0.0270556	−	0.0897334i
$427$	5.74456	+	9.94987i	0.277999	+	0.481508i
$428$	−7.43070	−	12.8704i	−0.359177	−	0.622112i
$429$	−4.00000	+	0.939764i	−0.193122	+	0.0453722i
$430$	−4.68614	+	8.11663i	−0.225986	+	0.391419i
$431$	−36.6060			−1.76325			−0.881624	−	0.471953i	$-0.843549\pi$
$431$	−36.6060			−1.76325			−0.881624	+	0.471953i	$0.843549\pi$
$432$	0.872281	+	5.12241i	0.0419677	+	0.246452i
$433$	5.37228			0.258175			0.129088	−	0.991633i	$-0.458795\pi$
$433$	5.37228			0.258175			0.129088	+	0.991633i	$0.458795\pi$
$434$	1.00000	−	1.73205i	0.0480015	−	0.0831411i
$435$	3.37228	−	0.792287i	0.161689	−	0.0379873i
$436$	9.55842	+	16.5557i	0.457765	+	0.792873i
$437$	−1.37228	−	2.37686i	−0.0656451	−	0.113701i
$438$	−4.24456	+	14.0776i	−0.202813	+	0.672655i
$439$	−2.62772	+	4.55134i	−0.125414	+	0.217224i	−0.921895	−	0.387440i	$-0.873359\pi$
$439$	−2.62772	+	4.55134i	−0.125414	+	0.217224i	0.796481	+	0.604664i	$0.206693\pi$
$440$	−1.00000			−0.0476731
$441$	−2.50000	−	1.65831i	−0.119048	−	0.0789673i
$442$	−7.11684			−0.338514
$443$	0.0584220	−	0.101190i	0.00277571	−	0.00480767i	−0.864634	−	0.502402i	$-0.832450\pi$
$443$	0.0584220	−	0.101190i	0.00277571	−	0.00480767i	0.867410	+	0.497594i	$0.165783\pi$
$444$	0.883156	+	0.939764i	0.0419127	+	0.0445992i
$445$	3.74456	+	6.48577i	0.177509	+	0.307455i
$446$	−4.93070	−	8.54023i	−0.233476	−	0.404392i
$447$	18.8139	+	20.0198i	0.889865	+	0.946903i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	6.62772			0.312781			0.156391	−	0.987695i	$-0.450014\pi$
$449$	6.62772			0.312781			0.156391	+	0.987695i	$0.450014\pi$
$450$	2.50000	+	1.65831i	0.117851	+	0.0781736i
$451$	0.627719			0.0295581
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	−4.93070	+	16.3533i	−0.231665	+	0.768345i
$454$	−3.50000	−	6.06218i	−0.164263	−	0.284512i
$455$	−1.18614	−	2.05446i	−0.0556071	−	0.0963144i
$456$	2.31386	−	0.543620i	0.108356	−	0.0254574i
$457$	−0.686141	+	1.18843i	−0.0320963	+	0.0555924i	−0.881627	−	0.471946i	$-0.843552\pi$
$457$	−0.686141	+	1.18843i	−0.0320963	+	0.0555924i	0.849531	+	0.527539i	$0.176885\pi$
$458$	−4.74456			−0.221699
$459$	12.0000	−	9.94987i	0.560112	−	0.464420i
$460$	2.00000			0.0932505
$461$	−16.3723	+	28.3576i	−0.762533	+	1.32075i	0.179008	+	0.983848i	$0.442711\pi$
$461$	−16.3723	+	28.3576i	−0.762533	+	1.32075i	−0.941541	+	0.336899i	$0.890622\pi$
$462$	−1.68614	+	0.396143i	−0.0784464	+	0.0184303i
$463$	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
$466$	3.68614	−	6.38458i	0.170757	−	0.295760i
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$	−0.441578	+	7.10313i	−0.0204120	+	0.328342i
$469$	1.37228			0.0633661
$470$	3.18614	−	5.51856i	0.146966	−	0.254552i
$471$	−14.0693	−	14.9711i	−0.648279	−	0.689832i
$472$	−3.05842	−	5.29734i	−0.140775	−	0.243830i
$473$	4.68614	+	8.11663i	0.215469	+	0.373203i
$474$	20.3030	+	21.6043i	0.932547	+	0.992321i
$475$	0.686141	−	1.18843i	0.0314823	−	0.0545289i
$476$	−3.00000			−0.137505
$477$	−28.8614	+	14.3537i	−1.32147	+	0.657213i
$478$	14.7446			0.674401
$479$	−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
$481$	0.883156	+	1.52967i	0.0402684	+	0.0697470i
$482$	−6.31386	−	10.9359i	−0.287588	−	0.498118i
$483$	3.37228	−	0.792287i	0.153444	−	0.0360503i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	6.48913			0.294656
$486$	−9.18614	−	12.5942i	−0.416692	−	0.571286i
$487$	12.9783			0.588101			0.294050	−	0.955790i	$-0.404997\pi$
$487$	12.9783			0.588101			0.294050	+	0.955790i	$0.404997\pi$
$488$	5.74456	−	9.94987i	0.260044	−	0.450410i
$489$	21.4891	−	5.04868i	0.971772	−	0.228309i
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	−10.9891	−	19.0337i	−0.495932	−	0.858980i	0.504057	−	0.863671i	$-0.331840\pi$
$491$	−10.9891	−	19.0337i	−0.495932	−	0.858980i	−0.999989	+	0.00469064i	$0.998507\pi$
$492$	0.313859	−	1.04095i	0.0141499	−	0.0469298i
$493$	3.00000	−	5.19615i	0.135113	−	0.234023i
$494$	3.25544			0.146469
$495$	2.68614	−	1.33591i	0.120733	−	0.0600446i
$496$	−2.00000			−0.0898027
$497$	0.558422	−	0.967215i	0.0250486	−	0.0433855i
$498$	7.55842	+	8.04290i	0.338701	+	0.360411i
$499$	19.7337	+	34.1798i	0.883401	+	1.53010i	0.847535	+	0.530739i	$0.178086\pi$
$499$	19.7337	+	34.1798i	0.883401	+	1.53010i	0.0358660	+	0.999357i	$0.488581\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	19.4198	+	20.6646i	0.867614	+	0.923226i
$502$	−8.80298	+	15.2472i	−0.392896	+	0.680517i
$503$	3.76631			0.167932			0.0839658	−	0.996469i	$-0.473241\pi$
$503$	3.76631			0.167932			0.0839658	+	0.996469i	$0.473241\pi$
$504$	−0.186141	+	2.99422i	−0.00829136	+	0.133373i
$505$	8.74456			0.389128
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	3.68614	−	12.2255i	0.163707	−	0.542956i
$508$	−3.37228	−	5.84096i	−0.149621	−	0.259151i
$509$	17.8614	+	30.9369i	0.791693	+	1.37125i	0.924918	+	0.380167i	$0.124133\pi$
$509$	17.8614	+	30.9369i	0.791693	+	1.37125i	−0.133225	+	0.991086i	$0.542533\pi$
$510$	5.05842	−	1.18843i	0.223991	−	0.0526246i
$511$	−4.24456	+	7.35180i	−0.187768	+	0.325224i
$512$	−1.00000			−0.0441942
$513$	−5.48913	+	4.55134i	−0.242351	+	0.200947i
$514$	−4.25544			−0.187699
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$	15.8030	−	3.71277i	0.695688	−	0.163446i
$517$	−3.18614	−	5.51856i	−0.140126	−	0.242706i
$518$	0.372281	+	0.644810i	0.0163571	+	0.0283313i
$519$	9.00000	−	29.8496i	0.395056	−	1.31025i
$520$	−1.18614	+	2.05446i	−0.0520157	+	0.0900939i
$521$	34.6277			1.51707			0.758534	−	0.651634i	$-0.225916\pi$
$521$	34.6277			1.51707			0.758534	+	0.651634i	$0.225916\pi$
$522$	−5.00000	−	3.31662i	−0.218844	−	0.145165i
$523$	3.11684			0.136290			0.0681450	−	0.997675i	$-0.478292\pi$
$523$	3.11684			0.136290			0.0681450	+	0.997675i	$0.478292\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$	1.18614	+	1.26217i	0.0517674	+	0.0550856i
$526$	11.4891	+	19.8997i	0.500950	+	0.867670i
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	1.18614	+	1.26217i	0.0516201	+	0.0549289i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	−10.7446			−0.466714
$531$	15.2921	+	10.1436i	0.663621	+	0.440196i
$532$	1.37228			0.0594959
$533$	0.744563	−	1.28962i	0.0322506	−	0.0558597i
$534$	3.74456	−	12.4193i	0.162043	−	0.537436i
$535$	7.43070	+	12.8704i	0.321257	+	0.556434i
$536$	−0.686141	−	1.18843i	−0.0296368	−	0.0513324i
$537$	−38.9783	+	9.15759i	−1.68204	+	0.395179i
$538$	−2.25544	+	3.90653i	−0.0972388	+	0.168423i
$539$	−1.00000			−0.0430730
$540$	−0.872281	−	5.12241i	−0.0375370	−	0.220434i
$541$	−19.8614			−0.853909			−0.426954	−	0.904273i	$-0.640413\pi$
$541$	−19.8614			−0.853909			−0.426954	+	0.904273i	$0.640413\pi$
$542$	−4.74456	+	8.21782i	−0.203796	+	0.352986i
$543$	−14.7446	+	3.46410i	−0.632750	+	0.148659i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−9.55842	−	16.5557i	−0.409438	−	0.709167i
$546$	−1.18614	+	3.93398i	−0.0507621	+	0.168359i
$547$	−2.68614	+	4.65253i	−0.114851	+	0.198928i	−0.917720	−	0.397227i	$-0.869972\pi$
$547$	−2.68614	+	4.65253i	−0.114851	+	0.198928i	0.802869	+	0.596155i	$0.203306\pi$
$548$	1.37228			0.0586210
$549$	−2.13859	+	34.4010i	−0.0912729	+	1.46820i
$550$	1.00000			0.0426401
$551$	−1.37228	+	2.37686i	−0.0584611	+	0.101258i
$552$	−2.37228	−	2.52434i	−0.100971	−	0.107443i
$553$	8.55842	+	14.8236i	0.363941	+	0.630365i
$554$	−7.74456	−	13.4140i	−0.329035	−	0.569905i
$555$	−0.883156	−	0.939764i	−0.0374879	−	0.0398908i
$556$	1.31386	−	2.27567i	0.0557200	−	0.0965100i
$557$	−44.7446			−1.89589			−0.947944	−	0.318437i	$-0.896842\pi$
$557$	−44.7446			−1.89589			−0.947944	+	0.318437i	$0.896842\pi$
$558$	5.37228	−	2.67181i	0.227427	−	0.113107i
$559$	22.2337			0.940385
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	1.50000	−	4.97494i	0.0633300	−	0.210042i
$562$	−12.9307	−	22.3966i	−0.545449	−	0.944745i
$563$	−7.61684	−	13.1928i	−0.321012	−	0.556009i	0.659685	−	0.751542i	$-0.270690\pi$
$563$	−7.61684	−	13.1928i	−0.321012	−	0.556009i	−0.980697	+	0.195533i	$0.937356\pi$
$564$	−10.7446	+	2.52434i	−0.452428	+	0.106294i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	−28.6060			−1.20240
$567$	−3.50000	−	8.29156i	−0.146986	−	0.348213i
$568$	−1.11684			−0.0468617
$569$	−9.98913	+	17.3017i	−0.418766	+	0.725324i	−0.995816	−	0.0913852i	$-0.970871\pi$
$569$	−9.98913	+	17.3017i	−0.418766	+	0.725324i	0.577050	+	0.816709i	$0.304204\pi$
$570$	−2.31386	+	0.543620i	−0.0969169	+	0.0227697i
$571$	16.9891	+	29.4260i	0.710973	+	1.23144i	0.964492	+	0.264111i	$0.0850784\pi$
$571$	16.9891	+	29.4260i	0.710973	+	1.23144i	−0.253520	+	0.967330i	$0.581588\pi$
$572$	1.18614	+	2.05446i	0.0495950	+	0.0859011i
$573$	2.74456	−	9.10268i	0.114656	−	0.380270i
$574$	0.313859	−	0.543620i	0.0131002	−	0.0226903i
$575$	−2.00000			−0.0834058
$576$	2.68614	−	1.33591i	0.111923	−	0.0556628i
$577$	11.9783			0.498661			0.249331	−	0.968418i	$-0.419789\pi$
$577$	11.9783			0.498661			0.249331	+	0.968418i	$0.419789\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−6.37228	−	6.78073i	−0.264823	−	0.281797i
$580$	−1.00000	−	1.73205i	−0.0415227	−	0.0719195i
$581$	3.18614	+	5.51856i	0.132183	+	0.228948i
$582$	−7.69702	−	8.19037i	−0.319052	−	0.339502i
$583$	−5.37228	+	9.30506i	−0.222497	+	0.385376i
$584$	8.48913			0.351283
$585$	0.441578	−	7.10313i	0.0182570	−	0.293678i
$586$	−23.4891			−0.970327
$587$	−13.8030	+	23.9075i	−0.569710	+	0.986767i	0.426884	+	0.904306i	$0.359611\pi$
$587$	−13.8030	+	23.9075i	−0.569710	+	0.986767i	−0.996594	+	0.0824606i	$0.973722\pi$
$588$	−0.500000	+	1.65831i	−0.0206197	+	0.0683877i
$589$	−1.37228	−	2.37686i	−0.0565439	−	0.0979369i
$590$	3.05842	+	5.29734i	0.125913	+	0.218088i
$591$	8.00000	−	1.87953i	0.329076	−	0.0773134i
$592$	0.372281	−	0.644810i	0.0153007	−	0.0265015i
$593$	26.4674			1.08688			0.543442	−	0.839446i	$-0.317121\pi$
$593$	26.4674			1.08688			0.543442	+	0.839446i	$0.317121\pi$
$594$	−4.87228	−	1.80579i	−0.199912	−	0.0740924i
$595$	3.00000			0.122988
$596$	7.93070	−	13.7364i	0.324854	−	0.562664i
$597$	−40.4674	+	9.50744i	−1.65622	+	0.389114i
$598$	−2.37228	−	4.10891i	−0.0970098	−	0.168026i
$599$	11.5584	+	20.0198i	0.472264	+	0.817986i	0.999496	−	0.0317356i	$-0.0101034\pi$
$599$	11.5584	+	20.0198i	0.472264	+	0.817986i	−0.527232	+	0.849721i	$0.676770\pi$
$600$	0.500000	−	1.65831i	0.0204124	−	0.0677003i
$601$	7.17527	−	12.4279i	0.292685	−	0.506946i	−0.681759	−	0.731577i	$-0.738785\pi$
$601$	7.17527	−	12.4279i	0.292685	−	0.506946i	0.974444	+	0.224632i	$0.0721179\pi$
$602$	9.37228			0.381986
$603$	3.43070	+	2.27567i	0.139709	+	0.0926725i
$604$	9.86141			0.401255
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	−10.3723	−	11.0371i	−0.421345	−	0.448352i
$607$	1.48913	+	2.57924i	0.0604417	+	0.104688i	0.894663	−	0.446742i	$-0.147416\pi$
$607$	1.48913	+	2.57924i	0.0604417	+	0.104688i	−0.834221	+	0.551430i	$0.814082\pi$
$608$	−0.686141	−	1.18843i	−0.0278267	−	0.0481972i
$609$	−2.37228	−	2.52434i	−0.0961297	−	0.102291i
$610$	−5.74456	+	9.94987i	−0.232591	+	0.402859i
$611$	−15.1168			−0.611562
$612$	−7.50000	−	4.97494i	−0.303170	−	0.201100i
$613$	−8.51087			−0.343751			−0.171875	−	0.985119i	$-0.554983\pi$
$613$	−8.51087			−0.343751			−0.171875	+	0.985119i	$0.554983\pi$
$614$	9.61684	−	16.6569i	0.388104	−	0.672216i
$615$	−0.313859	+	1.04095i	−0.0126560	+	0.0419753i
$616$	0.500000	+	0.866025i	0.0201456	+	0.0348932i
$617$	8.54755	+	14.8048i	0.344111	+	0.596018i	0.985192	−	0.171455i	$-0.0548469\pi$
$617$	8.54755	+	14.8048i	0.344111	+	0.596018i	−0.641081	+	0.767474i	$0.721514\pi$
$618$	−13.4891	+	3.16915i	−0.542612	+	0.127482i
$619$	5.43070	−	9.40625i	0.218278	−	0.378069i	−0.736003	−	0.676978i	$-0.763289\pi$
$619$	5.43070	−	9.40625i	0.218278	−	0.378069i	0.954282	+	0.298909i	$0.0966226\pi$
$620$	2.00000			0.0803219
$621$	9.74456	+	3.61158i	0.391036	+	0.144928i
$622$	−32.2337			−1.29245
$623$	3.74456	−	6.48577i	0.150023	−	0.259847i
$624$	4.00000	−	0.939764i	0.160128	−	0.0376207i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.05842	−	13.9576i	−0.322079	−	0.557858i
$627$	−0.686141	+	2.27567i	−0.0274018	+	0.0908816i
$628$	−5.93070	+	10.2723i	−0.236661	+	0.409909i
$629$	−2.23369			−0.0890630
$630$	0.186141	−	2.99422i	0.00741602	−	0.119293i
$631$	−10.1386			−0.403611			−0.201806	−	0.979426i	$-0.564681\pi$
$631$	−10.1386			−0.403611			−0.201806	+	0.979426i	$0.564681\pi$
$632$	8.55842	−	14.8236i	0.340436	−	0.589652i
$633$	30.0693	+	31.9967i	1.19515	+	1.27175i
$634$	−13.1168	−	22.7190i	−0.520936	−	0.902288i
$635$	3.37228	+	5.84096i	0.133825	+	0.231792i
$636$	12.7446	+	13.5615i	0.505355	+	0.537747i
$637$	−1.18614	+	2.05446i	−0.0469966	+	0.0814005i
$638$	−2.00000			−0.0791808
$639$	3.00000	−	1.49200i	0.118678	−	0.0590226i
$640$	1.00000			0.0395285
$641$	−2.56930	+	4.45015i	−0.101481	+	0.175770i	−0.912295	−	0.409534i	$-0.865691\pi$
$641$	−2.56930	+	4.45015i	−0.101481	+	0.175770i	0.810814	+	0.585304i	$0.199025\pi$
$642$	7.43070	−	24.6449i	0.293266	−	0.972655i
$643$	−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
$645$	−15.8030	+	3.71277i	−0.622242	+	0.146190i
$646$	−2.05842	+	3.56529i	−0.0809875	+	0.140275i
$647$	−16.2337			−0.638212			−0.319106	−	0.947719i	$-0.603383\pi$
$647$	−16.2337			−0.638212			−0.319106	+	0.947719i	$0.603383\pi$
$648$	−5.43070	+	7.17687i	−0.213338	+	0.281934i
$649$	6.11684			0.240107
$650$	1.18614	−	2.05446i	0.0465243	−	0.0805824i
$651$	3.37228	−	0.792287i	0.132170	−	0.0310522i
$652$	−6.37228	−	11.0371i	−0.249558	−	0.432247i
$653$	−6.62772	−	11.4795i	−0.259363	−	0.449229i	0.706709	−	0.707505i	$-0.250179\pi$
$653$	−6.62772	−	11.4795i	−0.259363	−	0.449229i	−0.966071	+	0.258275i	$0.916846\pi$
$654$	−9.55842	+	31.7017i	−0.373764	+	1.23963i
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	−0.627719			−0.0245083
$657$	−22.8030	+	11.3407i	−0.889629	+	0.442442i
$658$	−6.37228			−0.248417
$659$	14.4416	−	25.0135i	0.562564	−	0.974389i	−0.434708	−	0.900572i	$-0.643148\pi$
$659$	14.4416	−	25.0135i	0.562564	−	0.974389i	0.997272	−	0.0738179i	$-0.0235183\pi$
$660$	−1.18614	−	1.26217i	−0.0461705	−	0.0491299i
$661$	22.3723	+	38.7499i	0.870181	+	1.50720i	0.861809	+	0.507233i	$0.169331\pi$
$661$	22.3723	+	38.7499i	0.870181	+	1.50720i	0.00837167	+	0.999965i	$0.497335\pi$
$662$	10.3030	+	17.8453i	0.400437	+	0.693577i
$663$	−8.44158	−	8.98266i	−0.327844	−	0.348858i
$664$	3.18614	−	5.51856i	0.123646	−	0.214162i
$665$	−1.37228			−0.0532148
$666$	−0.138593	+	2.22938i	−0.00537038	+	0.0863869i
$667$	4.00000			0.154881
$668$	8.18614	−	14.1788i	0.316731	−	0.548595i
$669$	4.93070	−	16.3533i	0.190632	−	0.632255i
$670$	0.686141	+	1.18843i	0.0265079	+	0.0459131i
$671$	5.74456	+	9.94987i	0.221766	+	0.384111i
$672$	1.68614	−	0.396143i	0.0650443	−	0.0152816i
$673$	−0.627719	+	1.08724i	−0.0241968	+	0.0419100i	−0.877870	−	0.478899i	$-0.841036\pi$
$673$	−0.627719	+	1.08724i	−0.0241968	+	0.0419100i	0.853673	+	0.520809i	$0.174369\pi$
$674$	−16.1168			−0.620798
$675$	0.872281	+	5.12241i	0.0335741	+	0.197162i
$676$	−7.37228			−0.283549
$677$	−11.9307	+	20.6646i	−0.458534	+	0.794204i	−0.998884	−	0.0472361i	$-0.984959\pi$
$677$	−11.9307	+	20.6646i	−0.458534	+	0.794204i	0.540350	+	0.841441i	$0.318292\pi$
$678$	10.1168	−	2.37686i	0.388535	−	0.0912828i
$679$	−3.24456	−	5.61975i	−0.124515	−	0.215666i
$680$	−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
$683$	−20.8614			−0.798240			−0.399120	−	0.916899i	$-0.630684\pi$
$683$	−20.8614			−0.798240			−0.399120	+	0.916899i	$0.630684\pi$
$684$	3.43070	+	2.27567i	0.131176	+	0.0870125i
$685$	−1.37228			−0.0524322
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−5.62772	−	5.98844i	−0.214711	−	0.228473i
$688$	−4.68614	−	8.11663i	−0.178657	−	0.309444i
$689$	12.7446	+	22.0742i	0.485529	+	0.840961i
$690$	2.37228	+	2.52434i	0.0903112	+	0.0960999i
$691$	10.3723	−	17.9653i	0.394580	−	0.683433i	−0.598467	−	0.801147i	$-0.704223\pi$
$691$	10.3723	−	17.9653i	0.394580	−	0.683433i	0.993048	+	0.117714i	$0.0375567\pi$
$692$	−18.0000			−0.684257
$693$	−2.50000	−	1.65831i	−0.0949671	−	0.0629941i
$694$	3.13859			0.119139
$695$	−1.31386	+	2.27567i	−0.0498375	+	0.0863211i
$696$	−1.00000	+	3.31662i	−0.0379049	+	0.125716i
$697$	0.941578	+	1.63086i	0.0356648	+	0.0617733i
$698$	−8.74456	−	15.1460i	−0.330987	−	0.573286i
$699$	12.4307	−	2.92048i	0.470172	−	0.110463i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−2.13859			−0.0807736			−0.0403868	−	0.999184i	$-0.512859\pi$
$701$	−2.13859			−0.0807736			−0.0403868	+	0.999184i	$0.512859\pi$
$702$	−9.48913	+	7.86797i	−0.358144	+	0.296957i
$703$	1.02175			0.0385360
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	10.7446	−	2.52434i	0.404664	−	0.0950721i
$706$	−9.43070	−	16.3345i	−0.354929	−	0.614755i
$707$	−4.37228	−	7.57301i	−0.164437	−	0.284812i
$708$	3.05842	−	10.1436i	0.114943	−	0.381221i
$709$	−15.2337	+	26.3855i	−0.572113	+	0.990929i	0.424236	+	0.905552i	$0.360543\pi$
$709$	−15.2337	+	26.3855i	−0.572113	+	0.990929i	−0.996349	+	0.0853772i	$0.972790\pi$
$710$	1.11684			0.0419144
$711$	−3.18614	+	51.2516i	−0.119490	+	1.92208i
$712$	−7.48913			−0.280667
$713$	−2.00000	+	3.46410i	−0.0749006	+	0.129732i
$714$	−3.55842	−	3.78651i	−0.133171	−	0.141706i
$715$	−1.18614	−	2.05446i	−0.0443591	−	0.0768323i
$716$	11.5584	+	20.0198i	0.431959	+	0.748174i
$717$	17.4891	+	18.6101i	0.653143	+	0.695008i
$718$	−1.25544	+	2.17448i	−0.0468525	+	0.0811509i
$719$	39.7228			1.48141			0.740705	−	0.671830i	$-0.234491\pi$
$719$	39.7228			1.48141			0.740705	+	0.671830i	$0.234491\pi$
$720$	−2.68614	+	1.33591i	−0.100107	+	0.0497863i
$721$	−8.00000			−0.297936
$722$	−8.55842	+	14.8236i	−0.318511	+	0.551678i
$723$	6.31386	−	20.9407i	0.234815	−	0.778793i
$724$	4.37228	+	7.57301i	0.162495	+	0.281449i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	16.8614	−	3.96143i	0.625785	−	0.147023i
$727$	25.7921	−	44.6732i	0.956576	−	1.65684i	0.225858	−	0.974160i	$-0.427482\pi$
$727$	25.7921	−	44.6732i	0.956576	−	1.65684i	0.730719	−	0.682679i	$-0.239185\pi$
$728$	2.37228			0.0879226
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−8.48913			−0.314197
$731$	−14.0584	+	24.3499i	−0.519970	+	0.900614i
$732$	19.3723	−	4.55134i	0.716020	−	0.168222i
$733$	−1.86141	−	3.22405i	−0.0687526	−	0.119083i	0.829600	−	0.558358i	$-0.188569\pi$
$733$	−1.86141	−	3.22405i	−0.0687526	−	0.119083i	−0.898352	+	0.439275i	$0.855235\pi$
$734$	−16.3030	−	28.2376i	−0.601754	−	1.04227i
$735$	0.500000	−	1.65831i	0.0184428	−	0.0611678i
$736$	−1.00000	+	1.73205i	−0.0368605	+	0.0638442i
$737$	1.37228			0.0505486
$738$	1.68614	−	0.838574i	0.0620677	−	0.0308683i
$739$	−14.1168			−0.519296			−0.259648	−	0.965703i	$-0.583607\pi$
$739$	−14.1168			−0.519296			−0.259648	+	0.965703i	$0.583607\pi$
$740$	−0.372281	+	0.644810i	−0.0136853	+	0.0237037i
$741$	3.86141	+	4.10891i	0.141852	+	0.150945i
$742$	5.37228	+	9.30506i	0.197223	+	0.341600i
$743$	19.6060	+	33.9585i	0.719273	+	1.24582i	0.961288	+	0.275545i	$0.0888584\pi$
$743$	19.6060	+	33.9585i	0.719273	+	1.24582i	−0.242015	+	0.970273i	$0.577808\pi$
$744$	−2.37228	−	2.52434i	−0.0869721	−	0.0925467i
$745$	−7.93070	+	13.7364i	−0.290558	+	0.503262i
$746$	−9.25544			−0.338866
$747$	−1.18614	+	19.0800i	−0.0433986	+	0.698101i
$748$	−3.00000			−0.109691
$749$	7.43070	−	12.8704i	0.271512	−	0.470273i
$750$	−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	$0.952232\pi$
$752$	3.18614	+	5.51856i	0.116187	+	0.201241i
$753$	−29.6861	+	6.97449i	−1.08182	+	0.254165i
$754$	−2.37228	+	4.10891i	−0.0863934	+	0.149638i
$755$	−9.86141			−0.358893
$756$	−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
$759$	3.37228	−	0.792287i	0.122406	−	0.0287582i
$760$	0.686141	+	1.18843i	0.0248889	+	0.0431089i
$761$	20.4891	+	35.4882i	0.742730	+	1.28645i	0.951248	+	0.308428i	$0.0998028\pi$
$761$	20.4891	+	35.4882i	0.742730	+	1.28645i	−0.208518	+	0.978019i	$0.566864\pi$
$762$	3.37228	−	11.1846i	0.122165	−	0.405175i
$763$	−9.55842	+	16.5557i	−0.346038	+	0.599356i
$764$	−5.48913			−0.198590
$765$	7.50000	+	4.97494i	0.271163	+	0.179869i
$766$	11.1168			0.401668
$767$	7.25544	−	12.5668i	0.261979	−	0.453760i
$768$	−1.18614	−	1.26217i	−0.0428012	−	0.0455446i
$769$	−19.2337	−	33.3137i	−0.693585	−	1.20132i	−0.970656	−	0.240474i	$-0.922697\pi$
$769$	−19.2337	−	33.3137i	−0.693585	−	1.20132i	0.277071	−	0.960849i	$-0.410636\pi$
$770$	−0.500000	−	0.866025i	−0.0180187	−	0.0312094i
$771$	−5.04755	−	5.37108i	−0.181783	−	0.193435i
$772$	−2.68614	+	4.65253i	−0.0966763	+	0.167448i
$773$	42.6060			1.53243			0.766215	−	0.642584i	$-0.222138\pi$
$773$	42.6060			1.53243			0.766215	+	0.642584i	$0.222138\pi$
$774$	23.4307	+	15.5422i	0.842199	+	0.558652i
$775$	−2.00000			−0.0718421
$776$	−3.24456	+	5.61975i	−0.116473	+	0.201737i
$777$	−0.372281	+	1.23472i	−0.0133555	+	0.0442952i
$778$	−10.8139	−	18.7302i	−0.387696	−	0.671509i
$779$	−0.430703	−	0.746000i	−0.0154315	−	0.0267282i
$780$	−4.00000	+	0.939764i	−0.143223	+	0.0336489i
$781$	0.558422	−	0.967215i	0.0199819	−	0.0346097i
$782$	6.00000			0.214560
$783$	−1.74456	−	10.2448i	−0.0623456	−	0.366120i
$784$	1.00000			0.0357143
$785$	5.93070	−	10.2723i	0.211676	−	0.366633i
$786$	−6.74456	+	1.58457i	−0.240571	+	0.0565199i
$787$	20.6753	+	35.8106i	0.736994	+	1.27651i	0.953843	+	0.300305i	$0.0970886\pi$
$787$	20.6753	+	35.8106i	0.736994	+	1.27651i	−0.216849	+	0.976205i	$0.569578\pi$
$788$	−2.37228	−	4.10891i	−0.0845090	−	0.146374i
$789$	−11.4891	+	38.1051i	−0.409024	+	1.35658i
$790$	−8.55842	+	14.8236i	−0.304495	+	0.527401i
$791$	6.00000			0.213335
$792$	−0.186141	+	2.99422i	−0.00661422	+	0.106395i
$793$	27.2554			0.967869
$794$	−9.62772	+	16.6757i	−0.341675	+	0.591798i
$795$	−12.7446	−	13.5615i	−0.452003	−	0.480975i
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	−6.81386	−	11.8020i	−0.241359	−	0.418047i	0.719742	−	0.694241i	$-0.244260\pi$
$797$	−6.81386	−	11.8020i	−0.241359	−	0.418047i	−0.961102	+	0.276195i	$0.910927\pi$
$798$	1.62772	+	1.73205i	0.0576206	+	0.0613139i
$799$	9.55842	−	16.5557i	0.338153	−	0.585698i
$800$	−1.00000			−0.0353553
$801$	20.1168	−	10.0048i	0.710794	−	0.353501i
$802$	−25.6060			−0.904178
$803$	−4.24456	+	7.35180i	−0.149787	+	0.259439i
$804$	0.686141	−	2.27567i	0.0241983	−	0.0802567i
$805$	1.00000	+	1.73205i	0.0352454	+	0.0610468i
$806$	−2.37228	−	4.10891i	−0.0835600	−	0.144730i
$807$	−7.60597	+	1.78695i	−0.267743	+	0.0629037i
$808$	−4.37228	+	7.57301i	−0.153816	+	0.266418i
$809$	19.9783			0.702398			0.351199	−	0.936301i	$-0.385774\pi$
$809$	19.9783			0.702398			0.351199	+	0.936301i	$0.385774\pi$
$810$	5.43070	−	7.17687i	0.190815	−	0.252170i
$811$	33.0951			1.16213			0.581063	−	0.813859i	$-0.302637\pi$
$811$	33.0951			1.16213			0.581063	+	0.813859i	$0.302637\pi$
$812$	−1.00000	+	1.73205i	−0.0350931	+	0.0607831i
$813$	−16.0000	+	3.75906i	−0.561144	+	0.131836i
$814$	0.372281	+	0.644810i	0.0130485	+	0.0226006i
$815$	6.37228	+	11.0371i	0.223211	+	0.386613i
$816$	−1.50000	+	4.97494i	−0.0525105	+	0.174158i
$817$	6.43070	−	11.1383i	0.224982	−	0.389680i
$818$	20.6277			0.721231
$819$	−6.37228	+	3.16915i	−0.222666	+	0.110739i
$820$	0.627719			0.0219209
$821$	4.06930	−	7.04823i	0.142019	−	0.245985i	−0.786238	−	0.617924i	$-0.787974\pi$
$821$	4.06930	−	7.04823i	0.142019	−	0.245985i	0.928257	+	0.371939i	$0.121307\pi$
$822$	1.62772	+	1.73205i	0.0567732	+	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
$825$	1.18614	+	1.26217i	0.0412961	+	0.0439431i
$826$	3.05842	−	5.29734i	0.106416	−	0.184318i
$827$	16.7446			0.582265			0.291133	−	0.956683i	$-0.405968\pi$
$827$	16.7446			0.582265			0.291133	+	0.956683i	$0.405968\pi$
$828$	0.372281	−	5.98844i	0.0129377	−	0.208113i
$829$	−32.0000			−1.11141			−0.555703	−	0.831381i	$-0.687551\pi$
$829$	−32.0000			−1.11141			−0.555703	+	0.831381i	$0.687551\pi$
$830$	−3.18614	+	5.51856i	−0.110593	+	0.191552i
$831$	7.74456	−	25.6858i	0.268656	−	0.891031i
$832$	−1.18614	−	2.05446i	−0.0411220	−	0.0712254i
$833$	−1.50000	−	2.59808i	−0.0519719	−	0.0900180i
$834$	4.43070	−	1.04095i	0.153423	−	0.0360453i
$835$	−8.18614	+	14.1788i	−0.283293	+	0.490678i
$836$	1.37228			0.0474613
$837$	9.74456	+	3.61158i	0.336821	+	0.124834i
$838$	14.5109			0.501270
$839$	−19.6060	+	33.9585i	−0.676873	+	1.17238i	0.299044	+	0.954239i	$0.403332\pi$
$839$	−19.6060	+	33.9585i	−0.676873	+	1.17238i	−0.975918	+	0.218140i	$0.930001\pi$
$840$	−1.68614	+	0.396143i	−0.0581774	+	0.0136682i
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−9.44158	−	16.3533i	−0.325378	−	0.563572i
$843$	12.9307	−	42.8863i	0.445357	−	1.47708i
$844$	12.6753	−	21.9542i	0.436301	−	0.755695i
$845$	7.37228			0.253614
$846$	−15.9307	−	10.5672i	−0.547709	−	0.363309i
$847$	10.0000			0.343604
$848$	5.37228	−	9.30506i	0.184485	−	0.319537i
$849$	−33.9307	−	36.1056i	−1.16450	−	1.23914i
$850$	1.50000	+	2.59808i	0.0514496	+	0.0891133i
$851$	−0.744563	−	1.28962i	−0.0255233	−	0.0442076i
$852$	−1.32473	−	1.40965i	−0.0453846	−	0.0482937i
$853$	−11.8614	+	20.5446i	−0.406127	+	0.703432i	−0.994452	−	0.105192i	$-0.966454\pi$
$853$	−11.8614	+	20.5446i	−0.406127	+	0.703432i	0.588325	+	0.808625i	$0.299788\pi$
$854$	11.4891			0.393150
$855$	−3.43070	−	2.27567i	−0.117328	−	0.0778263i
$856$	−14.8614			−0.507952
$857$	−21.6753	+	37.5427i	−0.740413	+	1.28243i	0.211894	+	0.977293i	$0.432037\pi$
$857$	−21.6753	+	37.5427i	−0.740413	+	1.28243i	−0.952307	+	0.305140i	$0.901297\pi$
$858$	−1.18614	+	3.93398i	−0.0404942	+	0.134304i
$859$	−4.80298	−	8.31901i	−0.163876	−	0.283841i	0.772380	−	0.635161i	$-0.219066\pi$
$859$	−4.80298	−	8.31901i	−0.163876	−	0.283841i	−0.936255	+	0.351320i	$0.885733\pi$
$860$	4.68614	+	8.11663i	0.159796	+	0.276775i
$861$	1.05842	−	0.248667i	0.0360709	−	0.00847454i
$862$	−18.3030	+	31.7017i	−0.623402	+	1.07976i
$863$	4.51087			0.153552			0.0767760	−	0.997048i	$-0.475537\pi$
$863$	4.51087			0.153552			0.0767760	+	0.997048i	$0.475537\pi$
$864$	4.87228	+	1.80579i	0.165758	+	0.0614342i
$865$	18.0000			0.612018
$866$	2.68614	−	4.65253i	0.0912788	−	0.158099i
$867$	−13.4891	+	3.16915i	−0.458115	+	0.107630i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	8.55842	+	14.8236i	0.290325	+	0.502857i
$870$	1.00000	−	3.31662i	0.0339032	−	0.112444i
$871$	1.62772	−	2.81929i	0.0551531	−	0.0955280i
$872$	19.1168			0.647378
$873$	1.20789	−	19.4299i	0.0408809	−	0.657601i
$874$	−2.74456			−0.0928362
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	10.0693	+	10.7147i	0.340210	+	0.362016i
$877$	−15.7446	−	27.2704i	−0.531656	−	0.920855i	−0.999317	−	0.0369475i	$-0.988237\pi$
$877$	−15.7446	−	27.2704i	−0.531656	−	0.920855i	0.467661	−	0.883908i	$-0.345097\pi$
$878$	2.62772	+	4.55134i	0.0886812	+	0.153600i
$879$	−27.8614	−	29.6472i	−0.939742	−	0.999977i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	25.2554			0.850877			0.425439	−	0.904987i	$-0.360120\pi$
$881$	25.2554			0.850877			0.425439	+	0.904987i	$0.360120\pi$
$882$	−2.68614	+	1.33591i	−0.0904471	+	0.0449823i
$883$	−24.3505			−0.819461			−0.409730	−	0.912207i	$-0.634377\pi$
$883$	−24.3505			−0.819461			−0.409730	+	0.912207i	$0.634377\pi$
$884$	−3.55842	+	6.16337i	−0.119683	+	0.207296i
$885$	−3.05842	+	10.1436i	−0.102808	+	0.340975i
$886$	−0.0584220	−	0.101190i	−0.00196272	−	0.00339954i
$887$	−11.3723	−	19.6974i	−0.381844	−	0.661373i	0.609482	−	0.792800i	$-0.291377\pi$
$887$	−11.3723	−	19.6974i	−0.381844	−	0.661373i	−0.991326	+	0.131427i	$0.958044\pi$
$888$	1.25544	−	0.294954i	0.0421297	−	0.00989800i
$889$	3.37228	−	5.84096i	0.113103	−	0.195900i
$890$	7.48913			0.251036
$891$	−3.50000	−	8.29156i	−0.117254	−	0.277778i
$892$	−9.86141			−0.330184
$893$	−4.37228	+	7.57301i	−0.146313	+	0.253421i
$894$	26.7446	−	6.28339i	0.894472	−	0.210148i
$895$	−11.5584	−	20.0198i	−0.386355	−	0.669187i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	2.37228	−	7.86797i	0.0792082	−	0.262704i
$898$	3.31386	−	5.73977i	0.110585	−	0.191539i
$899$	4.00000			0.133407
$900$	2.68614	−	1.33591i	0.0895380	−	0.0445302i
$901$	−32.2337			−1.07386
$902$	0.313859	−	0.543620i	0.0104504	−	0.0181006i
$903$	11.1168	+	11.8294i	0.369945	+	0.393658i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	−4.37228	−	7.57301i	−0.145340	−	0.251735i
$906$	11.6970	+	12.4468i	0.388607	+	0.413516i
$907$	11.9416	−	20.6834i	0.396514	−	0.686782i	−0.596780	−	0.802405i	$-0.703553\pi$
$907$	11.9416	−	20.6834i	0.396514	−	0.686782i	0.993293	+	0.115624i	$0.0368866\pi$
$908$	−7.00000			−0.232303
$909$	1.62772	−	26.1831i	0.0539880	−	0.868440i
$910$	−2.37228			−0.0786404
$911$	−7.44158	+	12.8892i	−0.246550	+	0.427038i	−0.962566	−	0.271046i	$-0.912630\pi$
$911$	−7.44158	+	12.8892i	−0.246550	+	0.427038i	0.716016	+	0.698084i	$0.245964\pi$
$912$	0.686141	−	2.27567i	0.0227204	−	0.0753550i
$913$	3.18614	+	5.51856i	0.105446	+	0.182638i
$914$	0.686141	+	1.18843i	0.0226955	+	0.0393098i
$915$	−19.3723	+	4.55134i	−0.640428	+	0.150463i
$916$	−2.37228	+	4.10891i	−0.0783824	+	0.135762i
$917$	−4.00000			−0.132092
$918$	−2.61684	−	15.3672i	−0.0863687	−	0.507195i
$919$	33.2554			1.09700			0.548498	−	0.836152i	$-0.315200\pi$
$919$	33.2554			1.09700			0.548498	+	0.836152i	$0.315200\pi$
$920$	1.00000	−	1.73205i	0.0329690	−	0.0571040i
$921$	32.4307	−	7.61930i	1.06863	−	0.251064i
$922$	16.3723	+	28.3576i	0.539192	+	0.933909i
$923$	−1.32473	−	2.29451i	−0.0436042	−	0.0755246i
$924$	−0.500000	+	1.65831i	−0.0164488	+	0.0545545i
$925$	0.372281	−	0.644810i	0.0122405	−	0.0212012i
$926$	28.0000			0.920137
$927$	−20.0000	−	13.2665i	−0.656886	−	0.435729i
$928$	2.00000			0.0656532
$929$	26.4891	−	45.8805i	0.869080	−	1.50529i	0.00614188	−	0.999981i	$-0.498045\pi$
$929$	26.4891	−	45.8805i	0.869080	−	1.50529i	0.862938	−	0.505310i	$-0.168622\pi$
$930$	2.37228	+	2.52434i	0.0777902	+	0.0827763i
$931$	0.686141	+	1.18843i	0.0224874	+	0.0389492i
$932$	−3.68614	−	6.38458i	−0.120744	−	0.209134i
$933$	−38.2337	−	40.6844i	−1.25171	−	1.33195i
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$	3.00000			0.0981105
$936$	5.93070	+	3.93398i	0.193851	+	0.128586i
$937$	−45.8614			−1.49823			−0.749113	−	0.662442i	$-0.769520\pi$
$937$	−45.8614			−1.49823			−0.749113	+	0.662442i	$0.769520\pi$
$938$	0.686141	−	1.18843i	0.0224033	−	0.0388036i
$939$	8.05842	−	26.7268i	0.262977	−	0.872195i
$940$	−3.18614	−	5.51856i	−0.103920	−	0.179995i
$941$	−3.25544	−	5.63858i	−0.106124	−	0.183813i	0.808073	−	0.589083i	$-0.200511\pi$
$941$	−3.25544	−	5.63858i	−0.106124	−	0.183813i	−0.914197	+	0.405270i	$0.867177\pi$
$942$	−20.0000	+	4.69882i	−0.651635	+	0.153096i
$943$	−0.627719	+	1.08724i	−0.0204413	+	0.0354054i
$944$	−6.11684			−0.199086
$945$	4.00000	−	3.31662i	0.130120	−	0.107890i
$946$	9.37228			0.304719
$947$	27.9198	−	48.3586i	0.907273	−	1.57144i	0.0894352	−	0.995993i	$-0.471494\pi$
$947$	27.9198	−	48.3586i	0.907273	−	1.57144i	0.817837	−	0.575449i	$-0.195173\pi$
$948$	28.8614	−	6.78073i	0.937375	−	0.220228i
$949$	10.0693	+	17.4405i	0.326863	+	0.566144i
$950$	−0.686141	−	1.18843i	−0.0222613	−	0.0385578i
$951$	13.1168	−	43.5036i	0.425343	−	1.41070i
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	51.3288			1.66270			0.831351	−	0.555747i	$-0.187568\pi$
$953$	51.3288			1.66270			0.831351	+	0.555747i	$0.187568\pi$
$954$	−2.00000	+	32.1716i	−0.0647524	+	1.04159i
$955$	5.48913			0.177624
$956$	7.37228	−	12.7692i	0.238437	−	0.412984i
$957$	−2.37228	−	2.52434i	−0.0766850	−	0.0816003i
$958$	5.00000	+	8.66025i	0.161543	+	0.279800i
$959$	0.686141	+	1.18843i	0.0221566	+	0.0383764i
$960$	1.18614	+	1.26217i	0.0382825	+	0.0407363i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	1.76631			0.0569482
$963$	39.9198	−	19.8535i	1.28640	−	0.639769i
$964$	−12.6277			−0.406711
$965$	2.68614	−	4.65253i	0.0864699	−	0.149770i
$966$	1.00000	−	3.31662i	0.0321745	−	0.106711i
$967$	−27.9783	−	48.4598i	−0.899720	−	1.55836i	−0.827852	−	0.560946i	$-0.810437\pi$
$967$	−27.9783	−	48.4598i	−0.899720	−	1.55836i	−0.0718677	−	0.997414i	$-0.522896\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	−6.94158	+	1.63086i	−0.222996	+	0.0523908i
$970$	3.24456	−	5.61975i	0.104177	−	0.180439i
$971$	15.2554			0.489570			0.244785	−	0.969577i	$-0.421283\pi$
$971$	15.2554			0.489570			0.244785	+	0.969577i	$0.421283\pi$
$972$	−15.5000	+	1.65831i	−0.497163	+	0.0531904i
$973$	2.62772			0.0842408
$974$	6.48913	−	11.2395i	0.207925	−	0.360137i
$975$	4.00000	−	0.939764i	0.128103	−	0.0300965i
$976$	−5.74456	−	9.94987i	−0.183879	−	0.318488i
$977$	21.6861	+	37.5615i	0.693801	+	1.20170i	0.970583	+	0.240766i	$0.0773987\pi$
$977$	21.6861	+	37.5615i	0.693801	+	1.20170i	−0.276782	+	0.960933i	$0.589268\pi$
$978$	6.37228	−	21.1345i	0.203763	−	0.675806i
$979$	3.74456	−	6.48577i	0.119677	−	0.207286i
$980$	−1.00000			−0.0319438
$981$	−51.3505	+	25.5383i	−1.63950	+	0.815376i
$982$	−21.9783			−0.701354
$983$	8.06930	−	13.9764i	0.257371	−	0.445779i	−0.708166	−	0.706046i	$-0.750477\pi$
$983$	8.06930	−	13.9764i	0.257371	−	0.445779i	0.965537	+	0.260267i	$0.0838106\pi$
$984$	−0.744563	−	0.792287i	−0.0237358	−	0.0252572i
$985$	2.37228	+	4.10891i	0.0755872	+	0.130921i
$986$	−3.00000	−	5.19615i	−0.0955395	−	0.165479i
$987$	−7.55842	−	8.04290i	−0.240587	−	0.256008i
$988$	1.62772	−	2.81929i	0.0517846	−	0.0896936i
$989$	−18.7446			−0.596042
$990$	0.186141	−	2.99422i	0.00591594	−	0.0951625i
$991$	4.60597			0.146313			0.0731567	−	0.997320i	$-0.476693\pi$
$991$	4.60597			0.146313			0.0731567	+	0.997320i	$0.476693\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	−10.3030	+	34.1711i	−0.326955	+	1.08439i
$994$	−0.558422	−	0.967215i	−0.0177121	−	0.0306782i
$995$	−12.0000	−	20.7846i	−0.380426	−	0.658916i
$996$	10.7446	−	2.52434i	0.340454	−	0.0799867i
$997$	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	$-0.0143026\pi$
$998$	39.4674			1.24932
$999$	−2.97825	+	2.46943i	−0.0942277	+	0.0781295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.g.421.2	yes	4
3.2	odd	2		1890.2.j.f.1261.1		4
9.2	odd	6		5670.2.a.bk.1.2		2
9.4	even	3	inner	630.2.j.g.211.2	✓	4
9.5	odd	6		1890.2.j.f.631.1		4
9.7	even	3		5670.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.g.211.2	✓	4	9.4	even	3	inner
630.2.j.g.421.2	yes	4	1.1	even	1	trivial
1890.2.j.f.631.1		4	9.5	odd	6
1890.2.j.f.1261.1		4	3.2	odd	2
5670.2.a.s.1.2		2	9.7	even	3
5670.2.a.bk.1.2		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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.68614 - 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.68614 - 0.396143i) 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} +(2.68614 - 1.33591i) q^{9} +1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.18614 - 1.26217i) q^{12} +(-1.18614 - 2.05446i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.18614 + 1.26217i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +(0.186141 - 2.99422i) q^{18} -1.37228 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} +(-1.68614 + 0.396143i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.37228 q^{26} +(4.00000 - 3.31662i) q^{27} -1.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(1.68614 - 0.396143i) 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} -0.744563 q^{37} +(-0.686141 + 1.18843i) q^{38} +(-2.81386 - 2.99422i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(0.313859 + 0.543620i) q^{41} +(-1.18614 - 1.26217i) q^{42} +(-4.68614 + 8.11663i) q^{43} -1.00000 q^{44} +(2.50000 + 1.65831i) q^{45} +2.00000 q^{46} +(3.18614 - 5.51856i) q^{47} +(-0.500000 + 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.05842 - 1.18843i) q^{51} +(-1.18614 + 2.05446i) q^{52} -10.7446 q^{53} +(-0.872281 - 5.12241i) q^{54} +1.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.31386 + 0.543620i) q^{57} +(-1.00000 - 1.73205i) q^{58} +(3.05842 + 5.29734i) q^{59} +(0.500000 - 1.65831i) q^{60} +(-5.74456 + 9.94987i) q^{61} +2.00000 q^{62} +(0.186141 - 2.99422i) q^{63} +1.00000 q^{64} +(1.18614 - 2.05446i) q^{65} +(-1.18614 - 1.26217i) q^{66} +(0.686141 + 1.18843i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(2.37228 + 2.52434i) q^{69} +(0.500000 - 0.866025i) q^{70} +1.11684 q^{71} +(-2.68614 + 1.33591i) q^{72} -8.48913 q^{73} +(-0.372281 + 0.644810i) q^{74} +(-0.500000 + 1.65831i) q^{75} +(0.686141 + 1.18843i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-4.00000 + 0.939764i) q^{78} +(-8.55842 + 14.8236i) q^{79} -1.00000 q^{80} +(5.43070 - 7.17687i) q^{81} +0.627719 q^{82} +(-3.18614 + 5.51856i) q^{83} +(-1.68614 + 0.396143i) q^{84} +(1.50000 + 2.59808i) q^{85} +(4.68614 + 8.11663i) q^{86} +(1.00000 - 3.31662i) q^{87} +(-0.500000 + 0.866025i) q^{88} +7.48913 q^{89} +(2.68614 - 1.33591i) q^{90} -2.37228 q^{91} +(1.00000 - 1.73205i) q^{92} +(2.37228 + 2.52434i) q^{93} +(-3.18614 - 5.51856i) q^{94} +(-0.686141 - 1.18843i) q^{95} +(1.18614 + 1.26217i) q^{96} +(3.24456 - 5.61975i) q^{97} -1.00000 q^{98} +(0.186141 - 2.99422i) 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

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