LMFDB - Embedded newform 306.2.n.c.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [306,2,Mod(13,306)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(306, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("306.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 306 = 2 \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	306.n (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.44342230185$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	306.115
Dual form			306.2.n.c.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.732051 - 2.73205i) q^{5} +(0.866025 + 1.50000i) q^{6} +(-0.267949 - 1.00000i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.732051 - 2.73205i) q^{5} +(0.866025 + 1.50000i) q^{6} +(-0.267949 - 1.00000i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(2.00000 - 2.00000i) q^{10} +(0.598076 + 2.23205i) q^{11} +1.73205i q^{12} +(-1.73205 - 3.00000i) q^{13} +(0.267949 - 1.00000i) q^{14} +(3.46410 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 + 2.96410i) q^{17} +3.00000i q^{18} -1.00000i q^{19} +(2.73205 - 0.732051i) q^{20} +(0.464102 - 1.73205i) q^{21} +(-0.598076 + 2.23205i) q^{22} +(-1.73205 - 0.464102i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(-2.59808 - 1.50000i) q^{25} -3.46410i q^{26} +5.19615i q^{27} +(0.732051 - 0.732051i) q^{28} +(-8.46410 + 2.26795i) q^{29} +(4.73205 - 1.26795i) q^{30} +(-0.866025 + 0.500000i) q^{32} +(-1.03590 + 3.86603i) q^{33} +(-3.96410 + 1.13397i) q^{34} -2.92820 q^{35} +(-1.50000 + 2.59808i) q^{36} +(3.46410 + 3.46410i) q^{37} +(0.500000 - 0.866025i) q^{38} -6.00000i q^{39} +(2.73205 + 0.732051i) q^{40} +(-9.96410 - 2.66987i) q^{41} +(1.26795 - 1.26795i) q^{42} +(4.50000 + 2.59808i) q^{43} +(-1.63397 + 1.63397i) q^{44} +(8.19615 - 2.19615i) q^{45} +(-1.26795 - 1.26795i) q^{46} +(5.00000 - 8.66025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(5.13397 - 2.96410i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(-6.86603 + 1.96410i) q^{51} +(1.73205 - 3.00000i) q^{52} -2.53590i q^{53} +(-2.59808 + 4.50000i) q^{54} +6.53590 q^{55} +(1.00000 - 0.267949i) q^{56} +(0.866025 - 1.50000i) q^{57} +(-8.46410 - 2.26795i) q^{58} +(-1.50000 + 0.866025i) q^{59} +(4.73205 + 1.26795i) q^{60} +(-2.73205 - 10.1962i) q^{61} +(2.19615 - 2.19615i) q^{63} -1.00000 q^{64} +(-9.46410 + 2.53590i) q^{65} +(-2.83013 + 2.83013i) q^{66} +(2.33013 + 4.03590i) q^{67} +(-4.00000 - 1.00000i) q^{68} +(-2.19615 - 2.19615i) q^{69} +(-2.53590 - 1.46410i) q^{70} +(5.46410 + 5.46410i) q^{71} +(-2.59808 + 1.50000i) q^{72} +(3.90192 + 3.90192i) q^{73} +(1.26795 + 4.73205i) q^{74} +(-2.59808 - 4.50000i) q^{75} +(0.866025 - 0.500000i) q^{76} +(2.07180 - 1.19615i) q^{77} +(3.00000 - 5.19615i) q^{78} +(-3.26795 - 12.1962i) q^{79} +(2.00000 + 2.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.29423 - 7.29423i) q^{82} +(-3.92820 - 2.26795i) q^{83} +(1.73205 - 0.464102i) q^{84} +(6.00000 + 10.0000i) q^{85} +(2.59808 + 4.50000i) q^{86} +(-14.6603 - 3.92820i) q^{87} +(-2.23205 + 0.598076i) q^{88} +6.92820 q^{89} +(8.19615 + 2.19615i) q^{90} +(-2.53590 + 2.53590i) q^{91} +(-0.464102 - 1.73205i) q^{92} +(8.66025 - 5.00000i) q^{94} +(-2.73205 - 0.732051i) q^{95} -1.73205 q^{96} +(2.50000 - 0.669873i) q^{97} +5.92820 q^{98} +(-4.90192 + 4.90192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 2 * q^4 - 4 * q^5 - 8 * q^7 + 6 * q^9	$ 4 q + 6 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{7} + 6 q^{9} + 8 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{16} - 8 q^{17} + 4 q^{20} - 12 q^{21} + 8 q^{22} - 4 q^{28} - 20 q^{29} + 12 q^{30} - 18 q^{33} - 2 q^{34} + 16 q^{35} - 6 q^{36} + 2 q^{38} + 4 q^{40} - 26 q^{41} + 12 q^{42} + 18 q^{43} - 10 q^{44} + 12 q^{45} - 12 q^{46} + 20 q^{47} - 6 q^{48} + 24 q^{49} - 6 q^{50} - 24 q^{51} + 40 q^{55} + 4 q^{56} - 20 q^{58} - 6 q^{59} + 12 q^{60} - 4 q^{61} - 12 q^{63} - 4 q^{64} - 24 q^{65} + 6 q^{66} - 8 q^{67} - 16 q^{68} + 12 q^{69} - 24 q^{70} + 8 q^{71} + 26 q^{73} + 12 q^{74} + 36 q^{77} + 12 q^{78} - 20 q^{79} + 8 q^{80} - 18 q^{81} + 2 q^{82} + 12 q^{83} + 24 q^{85} - 24 q^{87} - 2 q^{88} + 12 q^{90} - 24 q^{91} + 12 q^{92} - 4 q^{95} + 10 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^4 - 4 * q^5 - 8 * q^7 + 6 * q^9 + 8 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^16 - 8 * q^17 + 4 * q^20 - 12 * q^21 + 8 * q^22 - 4 * q^28 - 20 * q^29 + 12 * q^30 - 18 * q^33 - 2 * q^34 + 16 * q^35 - 6 * q^36 + 2 * q^38 + 4 * q^40 - 26 * q^41 + 12 * q^42 + 18 * q^43 - 10 * q^44 + 12 * q^45 - 12 * q^46 + 20 * q^47 - 6 * q^48 + 24 * q^49 - 6 * q^50 - 24 * q^51 + 40 * q^55 + 4 * q^56 - 20 * q^58 - 6 * q^59 + 12 * q^60 - 4 * q^61 - 12 * q^63 - 4 * q^64 - 24 * q^65 + 6 * q^66 - 8 * q^67 - 16 * q^68 + 12 * q^69 - 24 * q^70 + 8 * q^71 + 26 * q^73 + 12 * q^74 + 36 * q^77 + 12 * q^78 - 20 * q^79 + 8 * q^80 - 18 * q^81 + 2 * q^82 + 12 * q^83 + 24 * q^85 - 24 * q^87 - 2 * q^88 + 12 * q^90 - 24 * q^91 + 12 * q^92 - 4 * q^95 + 10 * q^97 - 4 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/306\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.732051	−	2.73205i	0.327383	−	1.22181i	−0.584511	−	0.811386i	$-0.698714\pi$
$5$	0.732051	−	2.73205i	0.327383	−	1.22181i	0.911894	−	0.410425i	$-0.134620\pi$
$6$	0.866025	+	1.50000i	0.353553	+	0.612372i
$7$	−0.267949	−	1.00000i	−0.101275	−	0.377964i	0.896621	−	0.442799i	$-0.146015\pi$
$7$	−0.267949	−	1.00000i	−0.101275	−	0.377964i	−0.997896	+	0.0648349i	$0.979348\pi$
$8$			1.00000i			0.353553i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$	0.598076	+	2.23205i	0.180327	+	0.672989i	0.995583	+	0.0938879i	$0.0299295\pi$
$11$	0.598076	+	2.23205i	0.180327	+	0.672989i	−0.815256	+	0.579101i	$0.803404\pi$
$12$			1.73205i			0.500000i
$13$	−1.73205	−	3.00000i	−0.480384	−	0.832050i	0.519362	−	0.854554i	$-0.326170\pi$
$13$	−1.73205	−	3.00000i	−0.480384	−	0.832050i	−0.999747	+	0.0225039i	$0.992836\pi$
$14$	0.267949	−	1.00000i	0.0716124	−	0.267261i
$15$	3.46410	−	3.46410i	0.894427	−	0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.86603	+	2.96410i	−0.695113	+	0.718900i
$17$	−2.86603	+	2.96410i	−0.695113	+	0.718900i
$18$			3.00000i			0.707107i
$19$		−	1.00000i		−	0.229416i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$		−	1.00000i		−	0.229416i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$	2.73205	−	0.732051i	0.610905	−	0.163692i
$21$	0.464102	−	1.73205i	0.101275	−	0.377964i
$22$	−0.598076	+	2.23205i	−0.127510	+	0.475875i
$23$	−1.73205	−	0.464102i	−0.361158	−	0.0967719i	0.0736772	−	0.997282i	$-0.476527\pi$
$23$	−1.73205	−	0.464102i	−0.361158	−	0.0967719i	−0.434835	+	0.900510i	$0.643193\pi$
$24$	−0.866025	+	1.50000i	−0.176777	+	0.306186i
$25$	−2.59808	−	1.50000i	−0.519615	−	0.300000i
$26$		−	3.46410i		−	0.679366i
$27$			5.19615i			1.00000i
$28$	0.732051	−	0.732051i	0.138345	−	0.138345i
$29$	−8.46410	+	2.26795i	−1.57174	+	0.421148i	−0.936358	−	0.351047i	$-0.885826\pi$
$29$	−8.46410	+	2.26795i	−1.57174	+	0.421148i	−0.635386	+	0.772194i	$0.719159\pi$
$30$	4.73205	−	1.26795i	0.863950	−	0.231495i
$31$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$31$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.03590	+	3.86603i	−0.180327	+	0.672989i
$34$	−3.96410	+	1.13397i	−0.679838	+	0.194475i
$35$	−2.92820			−0.494957
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	0.931987	−	0.362492i	$-0.118074\pi$
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	−0.362492	+	0.931987i	$0.618074\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$		−	6.00000i		−	0.960769i
$40$	2.73205	+	0.732051i	0.431975	+	0.115747i
$41$	−9.96410	−	2.66987i	−1.55613	−	0.416964i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−9.96410	−	2.66987i	−1.55613	−	0.416964i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	1.26795	−	1.26795i	0.195649	−	0.195649i
$43$	4.50000	+	2.59808i	0.686244	+	0.396203i	0.802203	−	0.597051i	$-0.203661\pi$
$43$	4.50000	+	2.59808i	0.686244	+	0.396203i	−0.115960	+	0.993254i	$0.536994\pi$
$44$	−1.63397	+	1.63397i	−0.246331	+	0.246331i
$45$	8.19615	−	2.19615i	1.22181	−	0.327383i
$46$	−1.26795	−	1.26795i	−0.186949	−	0.186949i
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	−0.227844	−	0.973698i	$-0.573168\pi$
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	0.957169	−	0.289530i	$-0.0934991\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	5.13397	−	2.96410i	0.733425	−	0.423443i
$50$	−1.50000	−	2.59808i	−0.212132	−	0.367423i
$51$	−6.86603	+	1.96410i	−0.961436	+	0.275029i
$52$	1.73205	−	3.00000i	0.240192	−	0.416025i
$53$		−	2.53590i		−	0.348332i	−0.984716	−	0.174166i	$-0.944277\pi$
$53$		−	2.53590i		−	0.348332i	0.984716	−	0.174166i	$-0.0557230\pi$
$54$	−2.59808	+	4.50000i	−0.353553	+	0.612372i
$55$	6.53590			0.881300
$56$	1.00000	−	0.267949i	0.133631	−	0.0358062i
$57$	0.866025	−	1.50000i	0.114708	−	0.198680i
$58$	−8.46410	−	2.26795i	−1.11139	−	0.297796i
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	−0.594454	−	0.804130i	$-0.702632\pi$
$59$	−1.50000	+	0.866025i	−0.195283	+	0.112747i	0.399170	+	0.916877i	$0.369298\pi$
$60$	4.73205	+	1.26795i	0.610905	+	0.163692i
$61$	−2.73205	−	10.1962i	−0.349803	−	1.30548i	−0.886899	−	0.461963i	$-0.847145\pi$
$61$	−2.73205	−	10.1962i	−0.349803	−	1.30548i	0.537096	−	0.843521i	$-0.319521\pi$
$62$		0			0
$63$	2.19615	−	2.19615i	0.276689	−	0.276689i
$64$	−1.00000			−0.125000
$65$	−9.46410	+	2.53590i	−1.17388	+	0.314539i
$66$	−2.83013	+	2.83013i	−0.348365	+	0.348365i
$67$	2.33013	+	4.03590i	0.284670	+	0.493063i	0.972529	−	0.232781i	$-0.0747825\pi$
$67$	2.33013	+	4.03590i	0.284670	+	0.493063i	−0.687859	+	0.725844i	$0.741449\pi$
$68$	−4.00000	−	1.00000i	−0.485071	−	0.121268i
$69$	−2.19615	−	2.19615i	−0.264386	−	0.264386i
$70$	−2.53590	−	1.46410i	−0.303098	−	0.174994i
$71$	5.46410	+	5.46410i	0.648470	+	0.648470i	0.952623	−	0.304153i	$-0.0983736\pi$
$71$	5.46410	+	5.46410i	0.648470	+	0.648470i	−0.304153	+	0.952623i	$0.598374\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	3.90192	+	3.90192i	0.456686	+	0.456686i	0.897566	−	0.440880i	$-0.145334\pi$
$73$	3.90192	+	3.90192i	0.456686	+	0.456686i	−0.440880	+	0.897566i	$0.645334\pi$
$74$	1.26795	+	4.73205i	0.147396	+	0.550090i
$75$	−2.59808	−	4.50000i	−0.300000	−	0.519615i
$76$	0.866025	−	0.500000i	0.0993399	−	0.0573539i
$77$	2.07180	−	1.19615i	0.236103	−	0.136314i
$78$	3.00000	−	5.19615i	0.339683	−	0.588348i
$79$	−3.26795	−	12.1962i	−0.367673	−	1.37217i	−0.863761	−	0.503902i	$-0.831897\pi$
$79$	−3.26795	−	12.1962i	−0.367673	−	1.37217i	0.496088	−	0.868272i	$-0.334769\pi$
$80$	2.00000	+	2.00000i	0.223607	+	0.223607i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−7.29423	−	7.29423i	−0.805513	−	0.805513i
$83$	−3.92820	−	2.26795i	−0.431176	−	0.248940i	0.268671	−	0.963232i	$-0.413415\pi$
$83$	−3.92820	−	2.26795i	−0.431176	−	0.248940i	−0.699848	+	0.714292i	$0.746749\pi$
$84$	1.73205	−	0.464102i	0.188982	−	0.0506376i
$85$	6.00000	+	10.0000i	0.650791	+	1.08465i
$86$	2.59808	+	4.50000i	0.280158	+	0.485247i
$87$	−14.6603	−	3.92820i	−1.57174	−	0.421148i
$88$	−2.23205	+	0.598076i	−0.237937	+	0.0637551i
$89$	6.92820			0.734388			0.367194	−	0.930144i	$-0.380318\pi$
$89$	6.92820			0.734388			0.367194	+	0.930144i	$0.380318\pi$
$90$	8.19615	+	2.19615i	0.863950	+	0.231495i
$91$	−2.53590	+	2.53590i	−0.265834	+	0.265834i
$92$	−0.464102	−	1.73205i	−0.0483859	−	0.180579i
$93$		0			0
$94$	8.66025	−	5.00000i	0.893237	−	0.515711i
$95$	−2.73205	−	0.732051i	−0.280302	−	0.0751068i
$96$	−1.73205			−0.176777
$97$	2.50000	−	0.669873i	0.253837	−	0.0680153i	−0.129657	−	0.991559i	$-0.541388\pi$
$97$	2.50000	−	0.669873i	0.253837	−	0.0680153i	0.383493	+	0.923544i	$0.374721\pi$
$98$	5.92820			0.598839
$99$	−4.90192	+	4.90192i	−0.492662	+	0.492662i
$100$		−	3.00000i		−	0.300000i
$101$	−8.73205	+	15.1244i	−0.868872	+	1.50493i	−0.00572059	+	0.999984i	$0.501821\pi$
$101$	−8.73205	+	15.1244i	−0.868872	+	1.50493i	−0.863151	+	0.504946i	$0.831512\pi$
$102$	−6.92820	−	1.73205i	−0.685994	−	0.171499i
$103$	−3.73205	−	6.46410i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$103$	−3.73205	−	6.46410i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$104$	3.00000	−	1.73205i	0.294174	−	0.169842i
$105$	−4.39230	−	2.53590i	−0.428645	−	0.247478i
$106$	1.26795	−	2.19615i	0.123154	−	0.213309i
$107$	13.2942	+	13.2942i	1.28520	+	1.28520i	0.937667	+	0.347534i	$0.112981\pi$
$107$	13.2942	+	13.2942i	1.28520	+	1.28520i	0.347534	+	0.937667i	$0.387019\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−4.92820	+	4.92820i	−0.472036	+	0.472036i	−0.902573	−	0.430537i	$-0.858324\pi$
$109$	−4.92820	+	4.92820i	−0.472036	+	0.472036i	0.430537	+	0.902573i	$0.358324\pi$
$110$	5.66025	+	3.26795i	0.539684	+	0.311587i
$111$	2.19615	+	8.19615i	0.208450	+	0.777944i
$112$	1.00000	+	0.267949i	0.0944911	+	0.0253188i
$113$	−6.09808	−	1.63397i	−0.573659	−	0.153711i	−0.0396847	−	0.999212i	$-0.512635\pi$
$113$	−6.09808	−	1.63397i	−0.573659	−	0.153711i	−0.533974	+	0.845501i	$0.679302\pi$
$114$	1.50000	−	0.866025i	0.140488	−	0.0811107i
$115$	−2.53590	+	4.39230i	−0.236474	+	0.409585i
$116$	−6.19615	−	6.19615i	−0.575298	−	0.575298i
$117$	5.19615	−	9.00000i	0.480384	−	0.832050i
$118$	−1.73205			−0.159448
$119$	3.73205	+	2.07180i	0.342117	+	0.189921i
$120$	3.46410	+	3.46410i	0.316228	+	0.316228i
$121$	4.90192	−	2.83013i	0.445629	−	0.257284i
$122$	2.73205	−	10.1962i	0.247348	−	0.923116i
$123$	−12.6340	−	12.6340i	−1.13917	−	1.13917i
$124$		0			0
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	3.00000	−	0.803848i	0.267261	−	0.0716124i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.50000	+	7.79423i	0.396203	+	0.686244i
$130$	−9.46410	−	2.53590i	−0.830057	−	0.222413i
$131$	4.63397	−	17.2942i	0.404872	−	1.51100i	−0.399419	−	0.916768i	$-0.630788\pi$
$131$	4.63397	−	17.2942i	0.404872	−	1.51100i	0.804291	−	0.594235i	$-0.202545\pi$
$132$	−3.86603	+	1.03590i	−0.336494	+	0.0901634i
$133$	−1.00000	+	0.267949i	−0.0867110	+	0.0232341i
$134$			4.66025i			0.402585i
$135$	14.1962	+	3.80385i	1.22181	+	0.327383i
$136$	−2.96410	−	2.86603i	−0.254170	−	0.245760i
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.165200	+	0.986260i	$0.552827\pi$
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.771526	+	0.636198i	$0.780506\pi$
$138$	−0.803848	−	3.00000i	−0.0684280	−	0.255377i
$139$	5.69615	−	21.2583i	0.483141	−	1.80311i	−0.105147	−	0.994457i	$-0.533531\pi$
$139$	5.69615	−	21.2583i	0.483141	−	1.80311i	0.588288	−	0.808651i	$-0.299802\pi$
$140$	−1.46410	−	2.53590i	−0.123739	−	0.214323i
$141$	15.0000	−	8.66025i	1.26323	−	0.729325i
$142$	2.00000	+	7.46410i	0.167836	+	0.626373i
$143$	5.66025	−	5.66025i	0.473334	−	0.473334i
$144$	−3.00000			−0.250000
$145$			24.7846i			2.05825i
$146$	1.42820	+	5.33013i	0.118199	+	0.441124i
$147$	10.2679			0.846886
$148$	−1.26795	+	4.73205i	−0.104225	+	0.388972i
$149$	5.73205	+	9.92820i	0.469588	+	0.813350i	0.999395	−	0.0347678i	$-0.0110692\pi$
$149$	5.73205	+	9.92820i	0.469588	+	0.813350i	−0.529808	+	0.848118i	$0.677736\pi$
$150$		−	5.19615i		−	0.424264i
$151$	18.1244	+	10.4641i	1.47494	+	0.851557i	0.999601	−	0.0282467i	$-0.00899239\pi$
$151$	18.1244	+	10.4641i	1.47494	+	0.851557i	0.475338	+	0.879803i	$0.342326\pi$
$152$	1.00000			0.0811107
$153$	−12.0000	−	3.00000i	−0.970143	−	0.242536i
$154$	2.39230			0.192777
$155$		0			0
$156$	5.19615	−	3.00000i	0.416025	−	0.240192i
$157$	10.1962	+	17.6603i	0.813742	+	1.40944i	0.910228	+	0.414107i	$0.135906\pi$
$157$	10.1962	+	17.6603i	0.813742	+	1.40944i	−0.0964865	+	0.995334i	$0.530760\pi$
$158$	3.26795	−	12.1962i	0.259984	−	0.970274i
$159$	2.19615	−	3.80385i	0.174166	−	0.301665i
$160$	0.732051	+	2.73205i	0.0578737	+	0.215988i
$161$			1.85641i			0.146305i
$162$	−7.79423	+	4.50000i	−0.612372	+	0.353553i
$163$	−4.26795	+	4.26795i	−0.334292	+	0.334292i	−0.854214	−	0.519922i	$-0.825961\pi$
$163$	−4.26795	+	4.26795i	−0.334292	+	0.334292i	0.519922	+	0.854214i	$0.325961\pi$
$164$	−2.66987	−	9.96410i	−0.208482	−	0.778066i
$165$	9.80385	+	5.66025i	0.763228	+	0.440650i
$166$	−2.26795	−	3.92820i	−0.176027	−	0.304888i
$167$	−6.19615	+	23.1244i	−0.479473	+	1.78942i	0.124283	+	0.992247i	$0.460337\pi$
$167$	−6.19615	+	23.1244i	−0.479473	+	1.78942i	−0.603756	+	0.797170i	$0.706330\pi$
$168$	1.73205	+	0.464102i	0.133631	+	0.0358062i
$169$	0.500000	−	0.866025i	0.0384615	−	0.0666173i
$170$	0.196152	+	11.6603i	0.0150442	+	0.894301i
$171$	2.59808	−	1.50000i	0.198680	−	0.114708i
$172$			5.19615i			0.396203i
$173$	3.73205	−	1.00000i	0.283743	−	0.0760286i	−0.114141	−	0.993465i	$-0.536412\pi$
$173$	3.73205	−	1.00000i	0.283743	−	0.0760286i	0.397883	+	0.917436i	$0.369745\pi$
$174$	−10.7321	−	10.7321i	−0.813595	−	0.813595i
$175$	−0.803848	+	3.00000i	−0.0607652	+	0.226779i
$176$	−2.23205	−	0.598076i	−0.168247	−	0.0450817i
$177$	−3.00000			−0.225494
$178$	6.00000	+	3.46410i	0.449719	+	0.259645i
$179$		−	9.07180i		−	0.678058i	−0.940776	−	0.339029i	$-0.889902\pi$
$179$		−	9.07180i		−	0.678058i	0.940776	−	0.339029i	$-0.110098\pi$
$180$	6.00000	+	6.00000i	0.447214	+	0.447214i
$181$	−11.2679	+	11.2679i	−0.837540	+	0.837540i	−0.988535	−	0.150995i	$-0.951752\pi$
$181$	−11.2679	+	11.2679i	−0.837540	+	0.837540i	0.150995	+	0.988535i	$0.451752\pi$
$182$	−3.46410	+	0.928203i	−0.256776	+	0.0688030i
$183$	4.73205	−	17.6603i	0.349803	−	1.30548i
$184$	0.464102	−	1.73205i	0.0342140	−	0.127688i
$185$	12.0000	−	6.92820i	0.882258	−	0.509372i
$186$		0			0
$187$	−8.33013	−	4.62436i	−0.609159	−	0.338166i
$188$	10.0000			0.729325
$189$	5.19615	−	1.39230i	0.377964	−	0.101275i
$190$	−2.00000	−	2.00000i	−0.145095	−	0.145095i
$191$	3.92820	−	6.80385i	0.284235	−	0.492309i	−0.688189	−	0.725532i	$-0.741594\pi$
$191$	3.92820	−	6.80385i	0.284235	−	0.492309i	0.972423	+	0.233223i	$0.0749271\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−5.59808	−	1.50000i	−0.402958	−	0.107972i	0.0516469	−	0.998665i	$-0.483553\pi$
$193$	−5.59808	−	1.50000i	−0.402958	−	0.107972i	−0.454605	+	0.890693i	$0.650220\pi$
$194$	2.50000	+	0.669873i	0.179490	+	0.0480941i
$195$	−16.3923	−	4.39230i	−1.17388	−	0.314539i
$196$	5.13397	+	2.96410i	0.366712	+	0.211722i
$197$	9.46410	−	9.46410i	0.674289	−	0.674289i	−0.284413	−	0.958702i	$-0.591799\pi$
$197$	9.46410	−	9.46410i	0.674289	−	0.674289i	0.958702	+	0.284413i	$0.0917986\pi$
$198$	−6.69615	+	1.79423i	−0.475875	+	0.127510i
$199$	−3.66025	−	3.66025i	−0.259469	−	0.259469i	0.565369	−	0.824838i	$-0.308734\pi$
$199$	−3.66025	−	3.66025i	−0.259469	−	0.259469i	−0.824838	+	0.565369i	$0.808734\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$			8.07180i			0.569341i
$202$	−15.1244	+	8.73205i	−1.06415	+	0.614385i
$203$	4.53590	+	7.85641i	0.318358	+	0.551412i
$204$	−5.13397	−	4.96410i	−0.359450	−	0.347557i
$205$	−14.5885	+	25.2679i	−1.01890	+	1.76479i
$206$		−	7.46410i		−	0.520049i
$207$	−1.39230	−	5.19615i	−0.0967719	−	0.361158i
$208$	3.46410			0.240192
$209$	2.23205	−	0.598076i	0.154394	−	0.0413698i
$210$	−2.53590	−	4.39230i	−0.174994	−	0.303098i
$211$	15.2942	+	4.09808i	1.05290	+	0.282123i	0.743449	−	0.668793i	$-0.233189\pi$
$211$	15.2942	+	4.09808i	1.05290	+	0.282123i	0.309449	+	0.950916i	$0.399855\pi$
$212$	2.19615	−	1.26795i	0.150832	−	0.0870831i
$213$	3.46410	+	12.9282i	0.237356	+	0.885826i
$214$	4.86603	+	18.1603i	0.332635	+	1.24141i
$215$	10.3923	−	10.3923i	0.708749	−	0.708749i
$216$	−5.19615			−0.353553
$217$		0			0
$218$	−6.73205	+	1.80385i	−0.455952	+	0.122172i
$219$	2.47372	+	9.23205i	0.167159	+	0.623844i
$220$	3.26795	+	5.66025i	0.220325	+	0.381614i
$221$	13.8564	+	3.46410i	0.932083	+	0.233021i
$222$	−2.19615	+	8.19615i	−0.147396	+	0.550090i
$223$	−2.07180	−	1.19615i	−0.138738	−	0.0801003i	0.429025	−	0.903293i	$-0.358857\pi$
$223$	−2.07180	−	1.19615i	−0.138738	−	0.0801003i	−0.567762	+	0.823193i	$0.692191\pi$
$224$	0.732051	+	0.732051i	0.0489122	+	0.0489122i
$225$		−	9.00000i		−	0.600000i
$226$	−4.46410	−	4.46410i	−0.296948	−	0.296948i
$227$	1.69615	+	6.33013i	0.112578	+	0.420145i	0.999094	−	0.0425513i	$-0.0135486\pi$
$227$	1.69615	+	6.33013i	0.112578	+	0.420145i	−0.886517	+	0.462697i	$0.846882\pi$
$228$	1.73205			0.114708
$229$	−11.5359	+	6.66025i	−0.762314	+	0.440122i	−0.830126	−	0.557576i	$-0.811731\pi$
$229$	−11.5359	+	6.66025i	−0.762314	+	0.440122i	0.0678122	+	0.997698i	$0.478398\pi$
$230$	−4.39230	+	2.53590i	−0.289620	+	0.167212i
$231$	4.14359			0.272628
$232$	−2.26795	−	8.46410i	−0.148898	−	0.555695i
$233$	−9.75833	−	9.75833i	−0.639289	−	0.639289i	0.311091	−	0.950380i	$-0.399306\pi$
$233$	−9.75833	−	9.75833i	−0.639289	−	0.639289i	−0.950380	+	0.311091i	$0.899306\pi$
$234$	9.00000	−	5.19615i	0.588348	−	0.339683i
$235$	−20.0000	−	20.0000i	−1.30466	−	1.30466i
$236$	−1.50000	−	0.866025i	−0.0976417	−	0.0563735i
$237$	5.66025	−	21.1244i	0.367673	−	1.37217i
$238$	2.19615	+	3.66025i	0.142355	+	0.237259i
$239$	−8.46410	−	14.6603i	−0.547497	−	0.948293i	−0.998445	−	0.0557428i	$-0.982247\pi$
$239$	−8.46410	−	14.6603i	−0.547497	−	0.948293i	0.450948	−	0.892550i	$-0.351086\pi$
$240$	1.26795	+	4.73205i	0.0818458	+	0.305453i
$241$	11.5981	−	3.10770i	0.747098	−	0.200184i	0.134867	−	0.990864i	$-0.456939\pi$
$241$	11.5981	−	3.10770i	0.747098	−	0.200184i	0.612230	+	0.790679i	$0.290272\pi$
$242$	5.66025			0.363855
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	7.46410	−	7.46410i	0.477840	−	0.477840i
$245$	−4.33975	−	16.1962i	−0.277256	−	1.03473i
$246$	−4.62436	−	17.2583i	−0.294838	−	1.10035i
$247$	−3.00000	+	1.73205i	−0.190885	+	0.110208i
$248$		0			0
$249$	−3.92820	−	6.80385i	−0.248940	−	0.431176i
$250$	5.46410	−	1.46410i	0.345580	−	0.0925979i
$251$	−6.80385			−0.429455			−0.214728	−	0.976674i	$-0.568886\pi$
$251$	−6.80385			−0.429455			−0.214728	+	0.976674i	$0.568886\pi$
$252$	3.00000	+	0.803848i	0.188982	+	0.0506376i
$253$		−	4.14359i		−	0.260505i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$	0.339746	+	20.1962i	0.0212757	+	1.26473i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.0359	−	5.79423i	0.626022	−	0.361434i	−0.153188	−	0.988197i	$-0.548954\pi$
$257$	10.0359	−	5.79423i	0.626022	−	0.361434i	0.779210	+	0.626763i	$0.215621\pi$
$258$			9.00000i			0.560316i
$259$	2.53590	−	4.39230i	0.157573	−	0.272925i
$260$	−6.92820	−	6.92820i	−0.429669	−	0.429669i
$261$	−18.5885	−	18.5885i	−1.15060	−	1.15060i
$262$	12.6603	−	12.6603i	0.782153	−	0.782153i
$263$	26.6603	+	15.3923i	1.64394	+	0.949130i	0.979413	+	0.201868i	$0.0647011\pi$
$263$	26.6603	+	15.3923i	1.64394	+	0.949130i	0.664529	+	0.747263i	$0.268632\pi$
$264$	−3.86603	−	1.03590i	−0.237937	−	0.0637551i
$265$	−6.92820	−	1.85641i	−0.425596	−	0.114038i
$266$	−1.00000	−	0.267949i	−0.0613139	−	0.0164290i
$267$	10.3923	+	6.00000i	0.635999	+	0.367194i
$268$	−2.33013	+	4.03590i	−0.142335	+	0.246532i
$269$	1.46410	+	1.46410i	0.0892679	+	0.0892679i	0.750331	−	0.661063i	$-0.229894\pi$
$269$	1.46410	+	1.46410i	0.0892679	+	0.0892679i	−0.661063	+	0.750331i	$0.729894\pi$
$270$	10.3923	+	10.3923i	0.632456	+	0.632456i
$271$	17.4641			1.06087			0.530434	−	0.847726i	$-0.322029\pi$
$271$	17.4641			1.06087			0.530434	+	0.847726i	$0.322029\pi$
$272$	−1.13397	−	3.96410i	−0.0687573	−	0.240359i
$273$	−6.00000	+	1.60770i	−0.363137	+	0.0973021i
$274$	−18.9904	+	10.9641i	−1.14725	+	0.662366i
$275$	1.79423	−	6.69615i	0.108196	−	0.403793i
$276$	0.803848	−	3.00000i	0.0483859	−	0.180579i
$277$	−28.3205	+	7.58846i	−1.70161	+	0.455946i	−0.973345	−	0.229345i	$-0.926342\pi$
$277$	−28.3205	+	7.58846i	−1.70161	+	0.455946i	−0.728269	+	0.685291i	$0.759675\pi$
$278$	15.5622	−	15.5622i	0.933357	−	0.933357i
$279$		0			0
$280$		−	2.92820i		−	0.174994i
$281$	−4.26795	−	2.46410i	−0.254605	−	0.146996i	0.367266	−	0.930116i	$-0.380294\pi$
$281$	−4.26795	−	2.46410i	−0.254605	−	0.146996i	−0.621871	+	0.783120i	$0.713627\pi$
$282$	17.3205			1.03142
$283$	−28.7583	−	7.70577i	−1.70951	−	0.458061i	−0.734202	−	0.678931i	$-0.762444\pi$
$283$	−28.7583	−	7.70577i	−1.70951	−	0.458061i	−0.975303	+	0.220870i	$0.929110\pi$
$284$	−2.00000	+	7.46410i	−0.118678	+	0.442913i
$285$	−3.46410	−	3.46410i	−0.205196	−	0.205196i
$286$	7.73205	−	2.07180i	0.457206	−	0.122508i
$287$			10.6795i			0.630390i
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	−0.571797	−	16.9904i	−0.0336351	−	0.999434i
$290$	−12.3923	+	21.4641i	−0.727701	+	1.26042i
$291$	4.33013	+	1.16025i	0.253837	+	0.0680153i
$292$	−1.42820	+	5.33013i	−0.0835793	+	0.311922i
$293$	−7.73205	−	13.3923i	−0.451711	−	0.782387i	0.546781	−	0.837276i	$-0.315853\pi$
$293$	−7.73205	−	13.3923i	−0.451711	−	0.782387i	−0.998492	+	0.0548887i	$0.982520\pi$
$294$	8.89230	+	5.13397i	0.518610	+	0.299419i
$295$	1.26795	+	4.73205i	0.0738229	+	0.275511i
$296$	−3.46410	+	3.46410i	−0.201347	+	0.201347i
$297$	−11.5981	+	3.10770i	−0.672989	+	0.180327i
$298$			11.4641i			0.664098i
$299$	1.60770	+	6.00000i	0.0929754	+	0.346989i
$300$	2.59808	−	4.50000i	0.150000	−	0.259808i
$301$	1.39230	−	5.19615i	0.0802511	−	0.299501i
$302$	10.4641	+	18.1244i	0.602141	+	1.04294i
$303$	−26.1962	+	15.1244i	−1.50493	+	0.868872i
$304$	0.866025	+	0.500000i	0.0496700	+	0.0286770i
$305$	−29.8564			−1.70957
$306$	−8.89230	−	8.59808i	−0.508339	−	0.491519i
$307$	6.07180			0.346536			0.173268	−	0.984875i	$-0.444567\pi$
$307$	6.07180			0.346536			0.173268	+	0.984875i	$0.444567\pi$
$308$	2.07180	+	1.19615i	0.118052	+	0.0681571i
$309$		−	12.9282i		−	0.735460i
$310$		0			0
$311$	−4.60770	+	17.1962i	−0.261278	+	0.975104i	0.703211	+	0.710982i	$0.251749\pi$
$311$	−4.60770	+	17.1962i	−0.261278	+	0.975104i	−0.964489	+	0.264123i	$0.914918\pi$
$312$	6.00000			0.339683
$313$	−2.52628	−	9.42820i	−0.142794	−	0.532914i	−0.999844	−	0.0176802i	$-0.994372\pi$
$313$	−2.52628	−	9.42820i	−0.142794	−	0.532914i	0.857050	−	0.515233i	$-0.172295\pi$
$314$			20.3923i			1.15080i
$315$	−4.39230	−	7.60770i	−0.247478	−	0.428645i
$316$	8.92820	−	8.92820i	0.502251	−	0.502251i
$317$	−6.66025	−	24.8564i	−0.374077	−	1.39607i	−0.854689	−	0.519141i	$-0.826252\pi$
$317$	−6.66025	−	24.8564i	−0.374077	−	1.39607i	0.480611	−	0.876934i	$-0.340415\pi$
$318$	3.80385	−	2.19615i	0.213309	−	0.123154i
$319$	−10.1244	−	17.5359i	−0.566855	−	0.981822i
$320$	−0.732051	+	2.73205i	−0.0409229	+	0.152726i
$321$	8.42820	+	31.4545i	0.470416	+	1.75562i
$322$	−0.928203	+	1.60770i	−0.0517267	+	0.0895933i
$323$	2.96410	+	2.86603i	0.164927	+	0.159470i
$324$	−9.00000			−0.500000
$325$			10.3923i			0.576461i
$326$	−5.83013	+	1.56218i	−0.322901	+	0.0865210i
$327$	−11.6603	+	3.12436i	−0.644814	+	0.172777i
$328$	2.66987	−	9.96410i	0.147419	−	0.550175i
$329$	−10.0000	−	2.67949i	−0.551318	−	0.147725i
$330$	5.66025	+	9.80385i	0.311587	+	0.539684i
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	0.580176	−	0.814491i	$-0.302984\pi$
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	−0.415282	+	0.909693i	$0.636317\pi$
$332$		−	4.53590i		−	0.248940i
$333$	−3.80385	+	14.1962i	−0.208450	+	0.777944i
$334$	−16.9282	+	16.9282i	−0.926270	+	0.926270i
$335$	12.7321	−	3.41154i	0.695626	−	0.186392i
$336$	1.26795	+	1.26795i	0.0691723	+	0.0691723i
$337$	−0.964102	+	3.59808i	−0.0525180	+	0.196000i	−0.987201	−	0.159484i	$-0.949017\pi$
$337$	−0.964102	+	3.59808i	−0.0525180	+	0.196000i	0.934683	+	0.355483i	$0.115684\pi$
$338$	0.866025	−	0.500000i	0.0471056	−	0.0271964i
$339$	−7.73205	−	7.73205i	−0.419947	−	0.419947i
$340$	−5.66025	+	10.1962i	−0.306970	+	0.552964i
$341$		0			0
$342$	3.00000			0.162221
$343$	−9.46410	−	9.46410i	−0.511013	−	0.511013i
$344$	−2.59808	+	4.50000i	−0.140079	+	0.242624i
$345$	−7.60770	+	4.39230i	−0.409585	+	0.236474i
$346$	3.73205	+	1.00000i	0.200636	+	0.0537603i
$347$	−9.79423	−	2.62436i	−0.525782	−	0.140883i	−0.0138421	−	0.999904i	$-0.504406\pi$
$347$	−9.79423	−	2.62436i	−0.525782	−	0.140883i	−0.511940	+	0.859021i	$0.671073\pi$
$348$	−3.92820	−	14.6603i	−0.210574	−	0.785872i
$349$	−17.0718	−	9.85641i	−0.913832	−	0.527601i	−0.0321701	−	0.999482i	$-0.510242\pi$
$349$	−17.0718	−	9.85641i	−0.913832	−	0.527601i	−0.881662	+	0.471881i	$0.843575\pi$
$350$	−2.19615	+	2.19615i	−0.117389	+	0.117389i
$351$	15.5885	−	9.00000i	0.832050	−	0.480384i
$352$	−1.63397	−	1.63397i	−0.0870911	−	0.0870911i
$353$	10.8660	−	18.8205i	0.578340	−	1.00171i	−0.417330	−	0.908755i	$-0.637034\pi$
$353$	10.8660	−	18.8205i	0.578340	−	1.00171i	0.995670	−	0.0929594i	$-0.0296327\pi$
$354$	−2.59808	−	1.50000i	−0.138086	−	0.0797241i
$355$	18.9282	−	10.9282i	1.00460	−	0.580009i
$356$	3.46410	+	6.00000i	0.183597	+	0.317999i
$357$	3.80385	+	6.33975i	0.201321	+	0.335535i
$358$	4.53590	−	7.85641i	0.239730	−	0.415224i
$359$		−	18.3923i		−	0.970709i	−0.874318	−	0.485354i	$-0.838691\pi$
$359$		−	18.3923i		−	0.970709i	0.874318	−	0.485354i	$-0.161309\pi$
$360$	2.19615	+	8.19615i	0.115747	+	0.431975i
$361$	18.0000			0.947368
$362$	−15.3923	+	4.12436i	−0.809002	+	0.216771i
$363$	9.80385			0.514569
$364$	−3.46410	−	0.928203i	−0.181568	−	0.0486511i
$365$	13.5167	−	7.80385i	0.707494	−	0.408472i
$366$	12.9282	−	12.9282i	0.675768	−	0.675768i
$367$	2.19615	+	8.19615i	0.114638	+	0.427836i	0.999260	−	0.0384744i	$-0.0122498\pi$
$367$	2.19615	+	8.19615i	0.114638	+	0.427836i	−0.884621	+	0.466310i	$0.845583\pi$
$368$	1.26795	−	1.26795i	0.0660964	−	0.0660964i
$369$	−8.00962	−	29.8923i	−0.416964	−	1.55613i
$370$	13.8564			0.720360
$371$	−2.53590	+	0.679492i	−0.131657	+	0.0352775i
$372$		0			0
$373$	1.19615	+	2.07180i	0.0619344	+	0.107274i	0.895330	−	0.445403i	$-0.146940\pi$
$373$	1.19615	+	2.07180i	0.0619344	+	0.107274i	−0.833396	+	0.552677i	$0.813606\pi$
$374$	−4.90192	−	8.16987i	−0.253472	−	0.422454i
$375$	9.46410	−	2.53590i	0.488724	−	0.130953i
$376$	8.66025	+	5.00000i	0.446619	+	0.257855i
$377$	21.4641	+	21.4641i	1.10546	+	1.10546i
$378$	5.19615	+	1.39230i	0.267261	+	0.0716124i
$379$	−3.16987	−	3.16987i	−0.162825	−	0.162825i	0.620992	−	0.783817i	$-0.286730\pi$
$379$	−3.16987	−	3.16987i	−0.162825	−	0.162825i	−0.783817	+	0.620992i	$0.786730\pi$
$380$	−0.732051	−	2.73205i	−0.0375534	−	0.140151i
$381$	1.73205	−	3.00000i	0.0887357	−	0.153695i
$382$	6.80385	−	3.92820i	0.348115	−	0.200984i
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	−0.467255	−	0.884122i	$-0.654757\pi$
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	0.532045	+	0.846716i	$0.321424\pi$
$384$	−0.866025	−	1.50000i	−0.0441942	−	0.0765466i
$385$	−1.75129	−	6.53590i	−0.0892539	−	0.333100i
$386$	−4.09808	−	4.09808i	−0.208587	−	0.208587i
$387$			15.5885i			0.792406i
$388$	1.83013	+	1.83013i	0.0929106	+	0.0929106i
$389$	−9.58846	−	5.53590i	−0.486154	−	0.280681i	0.236823	−	0.971553i	$-0.423894\pi$
$389$	−9.58846	−	5.53590i	−0.486154	−	0.280681i	−0.722978	+	0.690872i	$0.757227\pi$
$390$	−12.0000	−	12.0000i	−0.607644	−	0.607644i
$391$	6.33975	−	3.80385i	0.320615	−	0.192369i
$392$	2.96410	+	5.13397i	0.149710	+	0.259305i
$393$	21.9282	−	21.9282i	1.10613	−	1.10613i
$394$	12.9282	−	3.46410i	0.651313	−	0.174519i
$395$	−35.7128			−1.79691
$396$	−6.69615	−	1.79423i	−0.336494	−	0.0901634i
$397$	5.07180	−	5.07180i	0.254546	−	0.254546i	−0.568285	−	0.822832i	$-0.692393\pi$
$397$	5.07180	−	5.07180i	0.254546	−	0.254546i	0.822832	+	0.568285i	$0.192393\pi$
$398$	−1.33975	−	5.00000i	−0.0671554	−	0.250627i
$399$	−1.73205	−	0.464102i	−0.0867110	−	0.0232341i
$400$	2.59808	−	1.50000i	0.129904	−	0.0750000i
$401$	−19.3564	−	5.18653i	−0.966613	−	0.259003i	−0.259216	−	0.965819i	$-0.583464\pi$
$401$	−19.3564	−	5.18653i	−0.966613	−	0.259003i	−0.707397	+	0.706816i	$0.750131\pi$
$402$	−4.03590	+	6.99038i	−0.201292	+	0.348649i
$403$		0			0
$404$	−17.4641			−0.868872
$405$	18.0000	+	18.0000i	0.894427	+	0.894427i
$406$			9.07180i			0.450226i
$407$	−5.66025	+	9.80385i	−0.280568	+	0.485959i
$408$	−1.96410	−	6.86603i	−0.0972375	−	0.339919i
$409$	15.5263	+	26.8923i	0.767725	+	1.32974i	0.938794	+	0.344480i	$0.111945\pi$
$409$	15.5263	+	26.8923i	0.767725	+	1.32974i	−0.171069	+	0.985259i	$0.554722\pi$
$410$	−25.2679	+	14.5885i	−1.24790	+	0.720473i
$411$	−32.8923	+	18.9904i	−1.62246	+	0.936726i
$412$	3.73205	−	6.46410i	0.183865	−	0.318463i
$413$	1.26795	+	1.26795i	0.0623917	+	0.0623917i
$414$	1.39230	−	5.19615i	0.0684280	−	0.255377i
$415$	−9.07180	+	9.07180i	−0.445317	+	0.445317i
$416$	3.00000	+	1.73205i	0.147087	+	0.0849208i
$417$	26.9545	−	26.9545i	1.31997	−	1.31997i
$418$	2.23205	+	0.598076i	0.109173	+	0.0292529i
$419$	7.63397	+	2.04552i	0.372944	+	0.0999301i	0.440422	−	0.897791i	$-0.354829\pi$
$419$	7.63397	+	2.04552i	0.372944	+	0.0999301i	−0.0674783	+	0.997721i	$0.521495\pi$
$420$		−	5.07180i		−	0.247478i
$421$	8.39230	−	14.5359i	0.409016	−	0.708436i	−0.585764	−	0.810482i	$-0.699205\pi$
$421$	8.39230	−	14.5359i	0.409016	−	0.708436i	0.994780	+	0.102045i	$0.0325387\pi$
$422$	11.1962	+	11.1962i	0.545020	+	0.545020i
$423$	30.0000			1.45865
$424$	2.53590			0.123154
$425$	11.8923	−	3.40192i	0.576862	−	0.165018i
$426$	−3.46410	+	12.9282i	−0.167836	+	0.626373i
$427$	−9.46410	+	5.46410i	−0.458000	+	0.264426i
$428$	−4.86603	+	18.1603i	−0.235208	+	0.877809i
$429$	13.3923	−	3.58846i	0.646587	−	0.173252i
$430$	14.1962	−	3.80385i	0.684599	−	0.183438i
$431$	−20.5885	+	20.5885i	−0.991711	+	0.991711i	−0.999966	−	0.00825484i	$-0.997372\pi$
$431$	−20.5885	+	20.5885i	−0.991711	+	0.991711i	0.00825484	+	0.999966i	$0.497372\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$			4.07180i			0.195678i	0.995202	+	0.0978390i	$0.0311930\pi$
$433$			4.07180i			0.195678i	−0.995202	+	0.0978390i	$0.968807\pi$
$434$		0			0
$435$	−21.4641	+	37.1769i	−1.02912	+	1.78250i
$436$	−6.73205	−	1.80385i	−0.322407	−	0.0863886i
$437$	−0.464102	+	1.73205i	−0.0222010	+	0.0828552i
$438$	−2.47372	+	9.23205i	−0.118199	+	0.441124i
$439$	6.73205	−	1.80385i	0.321303	−	0.0860929i	−0.0945626	−	0.995519i	$-0.530145\pi$
$439$	6.73205	−	1.80385i	0.321303	−	0.0860929i	0.415866	+	0.909426i	$0.363479\pi$
$440$			6.53590i			0.311587i
$441$	15.4019	+	8.89230i	0.733425	+	0.423443i
$442$	10.2679	+	9.92820i	0.488397	+	0.472236i
$443$	6.06218	−	10.5000i	0.288023	−	0.498870i	−0.685315	−	0.728247i	$-0.740335\pi$
$443$	6.06218	−	10.5000i	0.288023	−	0.498870i	0.973338	+	0.229377i	$0.0736688\pi$
$444$	−6.00000	+	6.00000i	−0.284747	+	0.284747i
$445$	5.07180	−	18.9282i	0.240426	−	0.897283i
$446$	−1.19615	−	2.07180i	−0.0566395	−	0.0981024i
$447$			19.8564i			0.939176i
$448$	0.267949	+	1.00000i	0.0126594	+	0.0472456i
$449$	−8.36603	+	8.36603i	−0.394817	+	0.394817i	−0.876400	−	0.481583i	$-0.840062\pi$
$449$	−8.36603	+	8.36603i	−0.394817	+	0.394817i	0.481583	+	0.876400i	$0.340062\pi$
$450$	4.50000	−	7.79423i	0.212132	−	0.367423i
$451$		−	23.8372i		−	1.12245i
$452$	−1.63397	−	6.09808i	−0.0768557	−	0.286829i
$453$	18.1244	+	31.3923i	0.851557	+	1.47494i
$454$	−1.69615	+	6.33013i	−0.0796044	+	0.297088i
$455$	5.07180	+	8.78461i	0.237769	+	0.411829i
$456$	1.50000	+	0.866025i	0.0702439	+	0.0405554i
$457$	23.1340	+	13.3564i	1.08216	+	0.624786i	0.931479	−	0.363796i	$-0.118519\pi$
$457$	23.1340	+	13.3564i	1.08216	+	0.624786i	0.150683	+	0.988582i	$0.451853\pi$
$458$	−13.3205			−0.622426
$459$	−15.4019	−	14.8923i	−0.718900	−	0.695113i
$460$	−5.07180			−0.236474
$461$	15.5885	+	9.00000i	0.726027	+	0.419172i	0.816967	−	0.576685i	$-0.195654\pi$
$461$	15.5885	+	9.00000i	0.726027	+	0.419172i	−0.0909401	+	0.995856i	$0.528987\pi$
$462$	3.58846	+	2.07180i	0.166950	+	0.0963887i
$463$	13.8564	+	24.0000i	0.643962	+	1.11537i	0.984540	+	0.175158i	$0.0560438\pi$
$463$	13.8564	+	24.0000i	0.643962	+	1.11537i	−0.340578	+	0.940216i	$0.610623\pi$
$464$	2.26795	−	8.46410i	0.105287	−	0.392936i
$465$		0			0
$466$	−3.57180	−	13.3301i	−0.165460	−	0.617506i
$467$			36.8564i			1.70551i	0.522310	+	0.852756i	$0.325070\pi$
$467$			36.8564i			1.70551i	−0.522310	+	0.852756i	$0.674930\pi$
$468$	10.3923			0.480384
$469$	3.41154	−	3.41154i	0.157530	−	0.157530i
$470$	−7.32051	−	27.3205i	−0.337670	−	1.26020i
$471$			35.3205i			1.62748i
$472$	−0.866025	−	1.50000i	−0.0398621	−	0.0690431i
$473$	−3.10770	+	11.5981i	−0.142892	+	0.533280i
$474$	15.4641	−	15.4641i	0.710290	−	0.710290i
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$	0.0717968	+	4.26795i	0.00329080	+	0.195621i
$477$	6.58846	−	3.80385i	0.301665	−	0.174166i
$478$		−	16.9282i		−	0.774278i
$479$	29.5885	−	7.92820i	1.35193	−	0.362249i	0.491084	−	0.871112i	$-0.336601\pi$
$479$	29.5885	−	7.92820i	1.35193	−	0.362249i	0.860847	+	0.508863i	$0.169934\pi$
$480$	−1.26795	+	4.73205i	−0.0578737	+	0.215988i
$481$	4.39230	−	16.3923i	0.200272	−	0.747425i
$482$	11.5981	+	3.10770i	0.528278	+	0.141552i
$483$	−1.60770	+	2.78461i	−0.0731527	+	0.126704i
$484$	4.90192	+	2.83013i	0.222815	+	0.128642i
$485$		−	7.32051i		−	0.332407i
$486$	−15.5885			−0.707107
$487$	12.5885	−	12.5885i	0.570437	−	0.570437i	−0.361813	−	0.932251i	$-0.617842\pi$
$487$	12.5885	−	12.5885i	0.570437	−	0.570437i	0.932251	+	0.361813i	$0.117842\pi$
$488$	10.1962	−	2.73205i	0.461558	−	0.123674i
$489$	−10.0981	+	2.70577i	−0.456651	+	0.122359i
$490$	4.33975	−	16.1962i	0.196050	−	0.731668i
$491$	10.3301	−	5.96410i	0.466192	−	0.269156i	−0.248452	−	0.968644i	$-0.579922\pi$
$491$	10.3301	−	5.96410i	0.466192	−	0.269156i	0.714644	+	0.699488i	$0.246589\pi$
$492$	4.62436	−	17.2583i	0.208482	−	0.778066i
$493$	17.5359	−	31.5885i	0.789777	−	1.42267i
$494$	−3.46410			−0.155857
$495$	9.80385	+	16.9808i	0.440650	+	0.763228i
$496$		0			0
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$		−	7.85641i		−	0.352054i
$499$	−29.2583	−	7.83975i	−1.30978	−	0.350955i	−0.464642	−	0.885499i	$-0.653817\pi$
$499$	−29.2583	−	7.83975i	−1.30978	−	0.350955i	−0.845141	+	0.534544i	$0.820484\pi$
$500$	5.46410	+	1.46410i	0.244362	+	0.0654766i
$501$	−29.3205	+	29.3205i	−1.30994	+	1.30994i
$502$	−5.89230	−	3.40192i	−0.262986	−	0.151835i
$503$	16.3923	−	16.3923i	0.730897	−	0.730897i	−0.239901	−	0.970797i	$-0.577115\pi$
$503$	16.3923	−	16.3923i	0.730897	−	0.730897i	0.970797	+	0.239901i	$0.0771149\pi$
$504$	2.19615	+	2.19615i	0.0978244	+	0.0978244i
$505$	34.9282	+	34.9282i	1.55428	+	1.55428i
$506$	2.07180	−	3.58846i	0.0921026	−	0.159526i
$507$	1.50000	−	0.866025i	0.0666173	−	0.0384615i
$508$	1.73205	−	1.00000i	0.0768473	−	0.0443678i
$509$	−5.85641	−	10.1436i	−0.259581	−	0.449607i	0.706549	−	0.707664i	$-0.250251\pi$
$509$	−5.85641	−	10.1436i	−0.259581	−	0.449607i	−0.966130	+	0.258057i	$0.916918\pi$
$510$	−9.80385	+	17.6603i	−0.434122	+	0.782009i
$511$	2.85641	−	4.94744i	0.126360	−	0.218862i
$512$		−	1.00000i		−	0.0441942i
$513$	5.19615			0.229416
$514$	11.5885			0.511145
$515$	−20.3923	+	5.46410i	−0.898592	+	0.240777i
$516$	−4.50000	+	7.79423i	−0.198101	+	0.343122i
$517$	22.3205	+	5.98076i	0.981655	+	0.263034i
$518$	4.39230	−	2.53590i	0.192987	−	0.111421i
$519$	6.46410	+	1.73205i	0.283743	+	0.0760286i
$520$	−2.53590	−	9.46410i	−0.111207	−	0.415028i
$521$	25.7583	−	25.7583i	1.12849	−	1.12849i	0.138071	−	0.990422i	$-0.455910\pi$
$521$	25.7583	−	25.7583i	1.12849	−	1.12849i	0.990422	−	0.138071i	$-0.0440901\pi$
$522$	−6.80385	−	25.3923i	−0.297796	−	1.11139i
$523$	−43.1769			−1.88799			−0.943997	−	0.329953i	$-0.892967\pi$
$523$	−43.1769			−1.88799			−0.943997	+	0.329953i	$0.892967\pi$
$524$	17.2942	−	4.63397i	0.755502	−	0.202436i
$525$	−3.80385	+	3.80385i	−0.166014	+	0.166014i
$526$	15.3923	+	26.6603i	0.671136	+	1.16244i
$527$		0			0
$528$	−2.83013	−	2.83013i	−0.123165	−	0.123165i
$529$	−17.1340	−	9.89230i	−0.744955	−	0.430100i
$530$	−5.07180	−	5.07180i	−0.220305	−	0.220305i
$531$	−4.50000	−	2.59808i	−0.195283	−	0.112747i
$532$	−0.732051	−	0.732051i	−0.0317384	−	0.0317384i
$533$	9.24871	+	34.5167i	0.400606	+	1.49508i
$534$	6.00000	+	10.3923i	0.259645	+	0.449719i
$535$	46.0526	−	26.5885i	1.99103	−	1.14952i
$536$	−4.03590	+	2.33013i	−0.174324	+	0.100646i
$537$	7.85641	−	13.6077i	0.339029	−	0.587215i
$538$	0.535898	+	2.00000i	0.0231042	+	0.0862261i
$539$	9.68653	+	9.68653i	0.417229	+	0.417229i
$540$	3.80385	+	14.1962i	0.163692	+	0.610905i
$541$	−18.9282	−	18.9282i	−0.813787	−	0.813787i	0.171412	−	0.985199i	$-0.445167\pi$
$541$	−18.9282	−	18.9282i	−0.813787	−	0.813787i	−0.985199	+	0.171412i	$0.945167\pi$
$542$	15.1244	+	8.73205i	0.649647	+	0.375074i
$543$	−26.6603	+	7.14359i	−1.14410	+	0.306561i
$544$	1.00000	−	4.00000i	0.0428746	−	0.171499i
$545$	9.85641	+	17.0718i	0.422202	+	0.731275i
$546$	−6.00000	−	1.60770i	−0.256776	−	0.0688030i
$547$	−31.5526	+	8.45448i	−1.34909	+	0.361488i	−0.859799	−	0.510633i	$-0.829411\pi$
$547$	−31.5526	+	8.45448i	−1.34909	+	0.361488i	−0.489291	+	0.872120i	$0.662744\pi$
$548$	−21.9282			−0.936726
$549$	22.3923	−	22.3923i	0.955680	−	0.955680i
$550$	4.90192	−	4.90192i	0.209019	−	0.209019i
$551$	2.26795	+	8.46410i	0.0966179	+	0.360583i
$552$	2.19615	−	2.19615i	0.0934745	−	0.0934745i
$553$	−11.3205	+	6.53590i	−0.481397	+	0.277935i
$554$	−28.3205	−	7.58846i	−1.20322	−	0.322403i
$555$	24.0000			1.01874
$556$	21.2583	−	5.69615i	0.901554	−	0.241571i
$557$	−38.7846			−1.64336			−0.821678	−	0.569952i	$-0.806962\pi$
$557$	−38.7846			−1.64336			−0.821678	+	0.569952i	$0.806962\pi$
$558$		0			0
$559$		−	18.0000i		−	0.761319i
$560$	1.46410	−	2.53590i	0.0618696	−	0.107161i
$561$	−8.49038	−	14.1506i	−0.358464	−	0.597440i
$562$	−2.46410	−	4.26795i	−0.103942	−	0.180033i
$563$	−8.89230	+	5.13397i	−0.374766	+	0.216371i	−0.675539	−	0.737325i	$-0.736089\pi$
$563$	−8.89230	+	5.13397i	−0.374766	+	0.216371i	0.300773	+	0.953696i	$0.402755\pi$
$564$	15.0000	+	8.66025i	0.631614	+	0.364662i
$565$	−8.92820	+	15.4641i	−0.375612	+	0.650580i
$566$	−21.0526	−	21.0526i	−0.884905	−	0.884905i
$567$	9.00000	+	2.41154i	0.377964	+	0.101275i
$568$	−5.46410	+	5.46410i	−0.229269	+	0.229269i
$569$	−15.8205	−	9.13397i	−0.663230	−	0.382916i	0.130276	−	0.991478i	$-0.458414\pi$
$569$	−15.8205	−	9.13397i	−0.663230	−	0.382916i	−0.793507	+	0.608562i	$0.791747\pi$
$570$	−1.26795	−	4.73205i	−0.0531085	−	0.198204i
$571$	14.1603	+	3.79423i	0.592588	+	0.158784i	0.542636	−	0.839968i	$-0.317426\pi$
$571$	14.1603	+	3.79423i	0.592588	+	0.158784i	0.0499524	+	0.998752i	$0.484093\pi$
$572$	7.73205	+	2.07180i	0.323293	+	0.0866262i
$573$	11.7846	−	6.80385i	0.492309	−	0.284235i
$574$	−5.33975	+	9.24871i	−0.222877	+	0.386034i
$575$	3.80385	+	3.80385i	0.158631	+	0.158631i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	5.14359			0.214131			0.107065	−	0.994252i	$-0.465855\pi$
$577$	5.14359			0.214131			0.107065	+	0.994252i	$0.465855\pi$
$578$	8.00000	−	15.0000i	0.332756	−	0.623918i
$579$	−7.09808	−	7.09808i	−0.294986	−	0.294986i
$580$	−21.4641	+	12.3923i	−0.891248	+	0.514562i
$581$	−1.21539	+	4.53590i	−0.0504229	+	0.188181i
$582$	3.16987	+	3.16987i	0.131395	+	0.131395i
$583$	5.66025	−	1.51666i	0.234424	−	0.0628137i
$584$	−3.90192	+	3.90192i	−0.161463	+	0.161463i
$585$	−20.7846	−	20.7846i	−0.859338	−	0.859338i
$586$		−	15.4641i		−	0.638816i
$587$	8.47372	+	4.89230i	0.349748	+	0.201927i	0.664574	−	0.747222i	$-0.268613\pi$
$587$	8.47372	+	4.89230i	0.349748	+	0.201927i	−0.314826	+	0.949149i	$0.601946\pi$
$588$	5.13397	+	8.89230i	0.211722	+	0.366712i
$589$		0			0
$590$	−1.26795	+	4.73205i	−0.0522006	+	0.194815i
$591$	22.3923	−	6.00000i	0.921096	−	0.246807i
$592$	−4.73205	+	1.26795i	−0.194486	+	0.0521124i
$593$		−	6.92820i		−	0.284507i	−0.989830	−	0.142254i	$-0.954565\pi$
$593$		−	6.92820i		−	0.284507i	0.989830	−	0.142254i	$-0.0454349\pi$
$594$	−11.5981	−	3.10770i	−0.475875	−	0.127510i
$595$	8.39230	−	8.67949i	0.344051	−	0.355824i
$596$	−5.73205	+	9.92820i	−0.234794	+	0.406675i
$597$	−2.32051	−	8.66025i	−0.0949721	−	0.354441i
$598$	−1.60770	+	6.00000i	−0.0657435	+	0.245358i
$599$	4.73205	+	8.19615i	0.193346	+	0.334886i	0.946357	−	0.323122i	$-0.104733\pi$
$599$	4.73205	+	8.19615i	0.193346	+	0.334886i	−0.753011	+	0.658008i	$0.771399\pi$
$600$	4.50000	−	2.59808i	0.183712	−	0.106066i
$601$	−10.1340	−	37.8205i	−0.413373	−	1.54273i	−0.788071	−	0.615584i	$-0.788920\pi$
$601$	−10.1340	−	37.8205i	−0.413373	−	1.54273i	0.374698	−	0.927147i	$-0.377746\pi$
$602$	3.80385	−	3.80385i	0.155033	−	0.155033i
$603$	−6.99038	+	12.1077i	−0.284670	+	0.493063i
$604$			20.9282i			0.851557i
$605$	−4.14359	−	15.4641i	−0.168461	−	0.628705i
$606$	−30.2487			−1.22877
$607$	−12.5885	+	46.9808i	−0.510950	+	1.90689i	−0.100701	+	0.994917i	$0.532108\pi$
$607$	−12.5885	+	46.9808i	−0.510950	+	1.90689i	−0.410249	+	0.911974i	$0.634558\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$			15.7128i			0.636715i
$610$	−25.8564	−	14.9282i	−1.04690	−	0.604425i
$611$	−34.6410			−1.40143
$612$	−3.40192	−	11.8923i	−0.137515	−	0.480718i
$613$	−25.8564			−1.04433			−0.522165	−	0.852844i	$-0.674876\pi$
$613$	−25.8564			−1.04433			−0.522165	+	0.852844i	$0.674876\pi$
$614$	5.25833	+	3.03590i	0.212209	+	0.122519i
$615$	−43.7654	+	25.2679i	−1.76479	+	1.01890i
$616$	1.19615	+	2.07180i	0.0481944	+	0.0834751i
$617$	−0.428203	+	1.59808i	−0.0172388	+	0.0643361i	−0.974009	−	0.226507i	$-0.927269\pi$
$617$	−0.428203	+	1.59808i	−0.0172388	+	0.0643361i	0.956771	+	0.290844i	$0.0939359\pi$
$618$	6.46410	−	11.1962i	0.260024	−	0.450375i
$619$	−5.38269	−	20.0885i	−0.216348	−	0.807423i	−0.985688	−	0.168583i	$-0.946081\pi$
$619$	−5.38269	−	20.0885i	−0.216348	−	0.807423i	0.769339	−	0.638841i	$-0.220586\pi$
$620$		0			0
$621$	2.41154	−	9.00000i	0.0967719	−	0.361158i
$622$	−12.5885	+	12.5885i	−0.504751	+	0.504751i
$623$	−1.85641	−	6.92820i	−0.0743754	−	0.277573i
$624$	5.19615	+	3.00000i	0.208013	+	0.120096i
$625$	−15.5000	−	26.8468i	−0.620000	−	1.07387i
$626$	2.52628	−	9.42820i	0.100970	−	0.376827i
$627$	3.86603	+	1.03590i	0.154394	+	0.0413698i
$628$	−10.1962	+	17.6603i	−0.406871	+	0.704721i
$629$	−20.1962	+	0.339746i	−0.805273	+	0.0135466i
$630$		−	8.78461i		−	0.349987i
$631$			21.4641i			0.854472i	0.904140	+	0.427236i	$0.140513\pi$
$631$			21.4641i			0.854472i	−0.904140	+	0.427236i	$0.859487\pi$
$632$	12.1962	−	3.26795i	0.485137	−	0.129992i
$633$	19.3923	+	19.3923i	0.770775	+	0.770775i
$634$	6.66025	−	24.8564i	0.264512	−	0.987174i
$635$	−5.46410	−	1.46410i	−0.216836	−	0.0581011i
$636$	4.39230			0.174166
$637$	−17.7846	−	10.2679i	−0.704652	−	0.406831i
$638$		−	20.2487i		−	0.801654i
$639$	−6.00000	+	22.3923i	−0.237356	+	0.885826i
$640$	−2.00000	+	2.00000i	−0.0790569	+	0.0790569i
$641$	−44.9186	+	12.0359i	−1.77418	+	0.475389i	−0.989502	−	0.144518i	$-0.953837\pi$
$641$	−44.9186	+	12.0359i	−1.77418	+	0.475389i	−0.784675	+	0.619907i	$0.787170\pi$
$642$	−8.42820	+	31.4545i	−0.332635	+	1.24141i
$643$	−6.16025	+	22.9904i	−0.242937	+	0.906652i	0.731473	+	0.681871i	$0.238833\pi$
$643$	−6.16025	+	22.9904i	−0.242937	+	0.906652i	−0.974409	+	0.224781i	$0.927833\pi$
$644$	−1.60770	+	0.928203i	−0.0633521	+	0.0365763i
$645$	24.5885	−	6.58846i	0.968170	−	0.259420i
$646$	1.13397	+	3.96410i	0.0446156	+	0.155965i
$647$	15.4641			0.607957			0.303978	−	0.952679i	$-0.401685\pi$
$647$	15.4641			0.607957			0.303978	+	0.952679i	$0.401685\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	−2.83013	−	2.83013i	−0.111092	−	0.111092i
$650$	−5.19615	+	9.00000i	−0.203810	+	0.353009i
$651$		0			0
$652$	−5.83013	−	1.56218i	−0.228325	−	0.0611796i
$653$	−23.3923	−	6.26795i	−0.915412	−	0.245284i	−0.229789	−	0.973241i	$-0.573803\pi$
$653$	−23.3923	−	6.26795i	−0.915412	−	0.245284i	−0.685623	+	0.727957i	$0.740470\pi$
$654$	−11.6603	−	3.12436i	−0.455952	−	0.122172i
$655$	−43.8564	−	25.3205i	−1.71361	−	0.989354i
$656$	7.29423	−	7.29423i	0.284792	−	0.284792i
$657$	−4.28461	+	15.9904i	−0.167159	+	0.623844i
$658$	−7.32051	−	7.32051i	−0.285383	−	0.285383i
$659$	16.9282	−	29.3205i	0.659429	−	1.14216i	−0.321334	−	0.946966i	$-0.604131\pi$
$659$	16.9282	−	29.3205i	0.659429	−	1.14216i	0.980764	−	0.195199i	$-0.0625353\pi$
$660$			11.3205i			0.440650i
$661$	−30.2487	+	17.4641i	−1.17654	+	0.679275i	−0.955211	−	0.295925i	$-0.904372\pi$
$661$	−30.2487	+	17.4641i	−1.17654	+	0.679275i	−0.221327	+	0.975200i	$0.571039\pi$
$662$	1.73205	+	3.00000i	0.0673181	+	0.116598i
$663$	17.7846	+	17.1962i	0.690697	+	0.667843i
$664$	2.26795	−	3.92820i	0.0880135	−	0.152444i
$665$			2.92820i			0.113551i
$666$	−10.3923	+	10.3923i	−0.402694	+	0.402694i
$667$	15.7128			0.608403
$668$	−23.1244	+	6.19615i	−0.894708	+	0.239736i
$669$	−2.07180	−	3.58846i	−0.0801003	−	0.138738i
$670$	12.7321	+	3.41154i	0.491882	+	0.131799i
$671$	21.1244	−	12.1962i	0.815497	−	0.470827i
$672$	0.464102	+	1.73205i	0.0179031	+	0.0668153i
$673$	6.75833	+	25.2224i	0.260514	+	0.972253i	0.964939	+	0.262474i	$0.0845385\pi$
$673$	6.75833	+	25.2224i	0.260514	+	0.972253i	−0.704424	+	0.709779i	$0.748795\pi$
$674$	−2.63397	+	2.63397i	−0.101457	+	0.101457i
$675$	7.79423	−	13.5000i	0.300000	−	0.519615i
$676$	1.00000			0.0384615
$677$	40.0526	−	10.7321i	1.53934	−	0.412466i	0.613291	−	0.789857i	$-0.289845\pi$
$677$	40.0526	−	10.7321i	1.53934	−	0.412466i	0.926054	+	0.377391i	$0.123179\pi$
$678$	−2.83013	−	10.5622i	−0.108690	−	0.405638i
$679$	−1.33975	−	2.32051i	−0.0514147	−	0.0890529i
$680$	−10.0000	+	6.00000i	−0.383482	+	0.230089i
$681$	−2.93782	+	10.9641i	−0.112578	+	0.420145i
$682$		0			0
$683$	14.8827	+	14.8827i	0.569470	+	0.569470i	0.931980	−	0.362510i	$-0.118080\pi$
$683$	14.8827	+	14.8827i	0.569470	+	0.569470i	−0.362510	+	0.931980i	$0.618080\pi$
$684$	2.59808	+	1.50000i	0.0993399	+	0.0573539i
$685$	43.8564	+	43.8564i	1.67567	+	1.67567i
$686$	−3.46410	−	12.9282i	−0.132260	−	0.493601i
$687$	−23.0718			−0.880244
$688$	−4.50000	+	2.59808i	−0.171561	+	0.0990507i
$689$	−7.60770	+	4.39230i	−0.289830	+	0.167333i
$690$	−8.78461			−0.334424
$691$	12.2417	+	45.6865i	0.465695	+	1.73800i	0.654575	+	0.755997i	$0.272848\pi$
$691$	12.2417	+	45.6865i	0.465695	+	1.73800i	−0.188880	+	0.982000i	$0.560486\pi$
$692$	2.73205	+	2.73205i	0.103857	+	0.103857i
$693$	6.21539	+	3.58846i	0.236103	+	0.136314i
$694$	−7.16987	−	7.16987i	−0.272165	−	0.272165i
$695$	−53.9090	−	31.1244i	−2.04488	−	1.18061i
$696$	3.92820	−	14.6603i	0.148898	−	0.555695i
$697$	36.4711	−	21.8827i	1.38144	−	0.828866i
$698$	−9.85641	−	17.0718i	−0.373070	−	0.646177i
$699$	−6.18653	−	23.0885i	−0.233996	−	0.873286i
$700$	−3.00000	+	0.803848i	−0.113389	+	0.0303826i
$701$	−38.7846			−1.46487			−0.732437	−	0.680835i	$-0.761617\pi$
$701$	−38.7846			−1.46487			−0.732437	+	0.680835i	$0.761617\pi$
$702$	18.0000			0.679366
$703$	3.46410	−	3.46410i	0.130651	−	0.130651i
$704$	−0.598076	−	2.23205i	−0.0225408	−	0.0841236i
$705$	−12.6795	−	47.3205i	−0.477537	−	1.78219i
$706$	18.8205	−	10.8660i	0.708319	−	0.408948i
$707$	17.4641	+	4.67949i	0.656805	+	0.175990i
$708$	−1.50000	−	2.59808i	−0.0563735	−	0.0976417i
$709$	−16.9282	+	4.53590i	−0.635752	+	0.170349i	−0.562279	−	0.826948i	$-0.690075\pi$
$709$	−16.9282	+	4.53590i	−0.635752	+	0.170349i	−0.0734735	+	0.997297i	$0.523408\pi$
$710$	21.8564			0.820256
$711$	26.7846	−	26.7846i	1.00450	−	1.00450i
$712$			6.92820i			0.259645i
$713$		0			0
$714$	0.124356	+	7.39230i	0.00465389	+	0.276650i
$715$	−11.3205	−	19.6077i	−0.423363	−	0.733286i
$716$	7.85641	−	4.53590i	0.293608	−	0.169514i
$717$		−	29.3205i		−	1.09499i
$718$	9.19615	−	15.9282i	0.343197	−	0.594435i
$719$	−3.85641	−	3.85641i	−0.143820	−	0.143820i	0.631531	−	0.775351i	$-0.282427\pi$
$719$	−3.85641	−	3.85641i	−0.143820	−	0.143820i	−0.775351	+	0.631531i	$0.782427\pi$
$720$	−2.19615	+	8.19615i	−0.0818458	+	0.305453i
$721$	−5.46410	+	5.46410i	−0.203494	+	0.203494i
$722$	15.5885	+	9.00000i	0.580142	+	0.334945i
$723$	20.0885	+	5.38269i	0.747098	+	0.200184i
$724$	−15.3923	−	4.12436i	−0.572051	−	0.153280i
$725$	25.3923	+	6.80385i	0.943047	+	0.252689i
$726$	8.49038	+	4.90192i	0.315108	+	0.181927i
$727$	3.53590	−	6.12436i	0.131139	−	0.227140i	−0.792977	−	0.609252i	$-0.791470\pi$
$727$	3.53590	−	6.12436i	0.131139	−	0.227140i	0.924116	+	0.382112i	$0.124803\pi$
$728$	−2.53590	−	2.53590i	−0.0939866	−	0.0939866i
$729$	−27.0000			−1.00000
$730$	15.6077			0.577667
$731$	−20.5981	+	5.89230i	−0.761847	+	0.217935i
$732$	17.6603	−	4.73205i	0.652742	−	0.174902i
$733$	−10.8564	+	6.26795i	−0.400991	+	0.231512i	−0.686911	−	0.726741i	$-0.741034\pi$
$733$	−10.8564	+	6.26795i	−0.400991	+	0.231512i	0.285921	+	0.958253i	$0.407701\pi$
$734$	−2.19615	+	8.19615i	−0.0810615	+	0.302526i
$735$	7.51666	−	28.0526i	0.277256	−	1.03473i
$736$	1.73205	−	0.464102i	0.0638442	−	0.0171070i
$737$	−7.61474	+	7.61474i	−0.280492	+	0.280492i
$738$	8.00962	−	29.8923i	0.294838	−	1.10035i
$739$		−	0.215390i		−	0.00792326i	−0.999992	−	0.00396163i	$-0.998739\pi$
$739$		−	0.215390i		−	0.00792326i	0.999992	−	0.00396163i	$-0.00126103\pi$
$740$	12.0000	+	6.92820i	0.441129	+	0.254686i
$741$	−6.00000			−0.220416
$742$	−2.53590	−	0.679492i	−0.0930958	−	0.0249449i
$743$	−4.85641	+	18.1244i	−0.178164	+	0.664918i	0.817827	+	0.575465i	$0.195179\pi$
$743$	−4.85641	+	18.1244i	−0.178164	+	0.664918i	−0.995991	+	0.0894536i	$0.971488\pi$
$744$		0			0
$745$	31.3205	−	8.39230i	1.14749	−	0.307470i
$746$			2.39230i			0.0875885i
$747$		−	13.6077i		−	0.497880i
$748$	−0.160254	−	9.52628i	−0.00585947	−	0.348315i
$749$	9.73205	−	16.8564i	0.355601	−	0.615920i
$750$	9.46410	+	2.53590i	0.345580	+	0.0925979i
$751$	4.73205	−	17.6603i	0.172675	−	0.644432i	−0.824261	−	0.566210i	$-0.808409\pi$
$751$	4.73205	−	17.6603i	0.172675	−	0.644432i	0.996936	−	0.0782218i	$-0.0249242\pi$
$752$	5.00000	+	8.66025i	0.182331	+	0.315807i
$753$	−10.2058	−	5.89230i	−0.371919	−	0.214728i
$754$	7.85641	+	29.3205i	0.286113	+	1.06779i
$755$	41.8564	−	41.8564i	1.52331	−	1.52331i
$756$	3.80385	+	3.80385i	0.138345	+	0.138345i
$757$			35.8564i			1.30322i	0.758553	+	0.651612i	$0.225907\pi$
$757$			35.8564i			1.30322i	−0.758553	+	0.651612i	$0.774093\pi$
$758$	−1.16025	−	4.33013i	−0.0421423	−	0.157277i
$759$	3.58846	−	6.21539i	0.130253	−	0.225604i
$760$	0.732051	−	2.73205i	0.0265543	−	0.0991019i
$761$	1.92820	+	3.33975i	0.0698973	+	0.121066i	0.898856	−	0.438244i	$-0.144400\pi$
$761$	1.92820	+	3.33975i	0.0698973	+	0.121066i	−0.828959	+	0.559310i	$0.811066\pi$
$762$	3.00000	−	1.73205i	0.108679	−	0.0627456i
$763$	6.24871	+	3.60770i	0.226219	+	0.130607i
$764$	7.85641			0.284235
$765$	−16.9808	+	30.5885i	−0.613941	+	1.10593i
$766$	1.46410			0.0529001
$767$	5.19615	+	3.00000i	0.187622	+	0.108324i
$768$		−	1.73205i		−	0.0625000i
$769$	1.53590	+	2.66025i	0.0553859	+	0.0959312i	0.892389	−	0.451267i	$-0.149028\pi$
$769$	1.53590	+	2.66025i	0.0553859	+	0.0959312i	−0.837003	+	0.547198i	$0.815694\pi$
$770$	1.75129	−	6.53590i	0.0631121	−	0.235537i
$771$	20.0718			0.722868
$772$	−1.50000	−	5.59808i	−0.0539862	−	0.201479i
$773$		−	23.1769i		−	0.833616i	−0.908995	−	0.416808i	$-0.863149\pi$
$773$		−	23.1769i		−	0.833616i	0.908995	−	0.416808i	$-0.136851\pi$
$774$	−7.79423	+	13.5000i	−0.280158	+	0.485247i
$775$		0			0
$776$	0.669873	+	2.50000i	0.0240470	+	0.0897448i
$777$	7.60770	−	4.39230i	0.272925	−	0.157573i
$778$	−5.53590	−	9.58846i	−0.198472	−	0.343763i
$779$	−2.66987	+	9.96410i	−0.0956581	+	0.357001i
$780$	−4.39230	−	16.3923i	−0.157270	−	0.586939i
$781$	−8.92820	+	15.4641i	−0.319476	+	0.553349i
$782$	7.39230	−	0.124356i	0.264348	−	0.00444695i
$783$	−11.7846	−	43.9808i	−0.421148	−	1.57174i
$784$			5.92820i			0.211722i
$785$	55.7128	−	14.9282i	1.98848	−	0.532810i
$786$	29.9545	−	8.02628i	1.06844	−	0.286288i
$787$	−11.0263	+	41.1506i	−0.393044	+	1.46686i	0.432041	+	0.901854i	$0.357794\pi$
$787$	−11.0263	+	41.1506i	−0.393044	+	1.46686i	−0.825086	+	0.565008i	$0.808873\pi$
$788$	12.9282	+	3.46410i	0.460548	+	0.123404i
$789$	26.6603	+	46.1769i	0.949130	+	1.64394i
$790$	−30.9282	−	17.8564i	−1.10038	−	0.635302i
$791$			6.53590i			0.232390i
$792$	−4.90192	−	4.90192i	−0.174182	−	0.174182i
$793$	−25.8564	+	25.8564i	−0.918188	+	0.918188i
$794$	6.92820	−	1.85641i	0.245873	−	0.0658814i
$795$	−8.78461	−	8.78461i	−0.311558	−	0.311558i
$796$	1.33975	−	5.00000i	0.0474860	−	0.177220i
$797$	19.1769	−	11.0718i	0.679281	−	0.392183i	−0.120303	−	0.992737i	$-0.538387\pi$
$797$	19.1769	−	11.0718i	0.679281	−	0.392183i	0.799584	+	0.600554i	$0.205053\pi$
$798$	−1.26795	−	1.26795i	−0.0448849	−	0.0448849i
$799$	11.3397	+	39.6410i	0.401171	+	1.40240i
$800$	3.00000			0.106066
$801$	10.3923	+	18.0000i	0.367194	+	0.635999i
$802$	−14.1699	−	14.1699i	−0.500356	−	0.500356i
$803$	−6.37564	+	11.0429i	−0.224992	+	0.389697i
$804$	−6.99038	+	4.03590i	−0.246532	+	0.142335i
$805$	5.07180	+	1.35898i	0.178757	+	0.0478979i
$806$		0			0
$807$	0.928203	+	3.46410i	0.0326743	+	0.121942i
$808$	−15.1244	−	8.73205i	−0.532073	−	0.307192i
$809$	22.1506	−	22.1506i	0.778775	−	0.778775i	−0.200848	−	0.979622i	$-0.564370\pi$
$809$	22.1506	−	22.1506i	0.778775	−	0.778775i	0.979622	+	0.200848i	$0.0643696\pi$
$810$	6.58846	+	24.5885i	0.231495	+	0.863950i
$811$	−13.9737	−	13.9737i	−0.490684	−	0.490684i	0.417838	−	0.908522i	$-0.362788\pi$
$811$	−13.9737	−	13.9737i	−0.490684	−	0.490684i	−0.908522	+	0.417838i	$0.862788\pi$
$812$	−4.53590	+	7.85641i	−0.159179	+	0.275706i
$813$	26.1962	+	15.1244i	0.918739	+	0.530434i
$814$	−9.80385	+	5.66025i	−0.343625	+	0.198392i
$815$	8.53590	+	14.7846i	0.298999	+	0.517882i
$816$	1.73205	−	6.92820i	0.0606339	−	0.242536i
$817$	2.59808	−	4.50000i	0.0908952	−	0.157435i
$818$			31.0526i			1.08573i
$819$	−10.3923	−	2.78461i	−0.363137	−	0.0973021i
$820$	−29.1769			−1.01890
$821$	−29.0526	+	7.78461i	−1.01394	+	0.271685i	−0.727275	−	0.686346i	$-0.759214\pi$
$821$	−29.0526	+	7.78461i	−1.01394	+	0.271685i	−0.286666	+	0.958031i	$0.592547\pi$
$822$	−37.9808			−1.32473
$823$	6.92820	+	1.85641i	0.241502	+	0.0647103i	0.377540	−	0.925993i	$-0.376770\pi$
$823$	6.92820	+	1.85641i	0.241502	+	0.0647103i	−0.136038	+	0.990704i	$0.543437\pi$
$824$	6.46410	−	3.73205i	0.225188	−	0.130012i
$825$	8.49038	−	8.49038i	0.295597	−	0.295597i
$826$	0.464102	+	1.73205i	0.0161482	+	0.0602658i
$827$	−13.3397	+	13.3397i	−0.463868	+	0.463868i	−0.899921	−	0.436053i	$-0.856376\pi$
$827$	−13.3397	+	13.3397i	−0.463868	+	0.463868i	0.436053	+	0.899921i	$0.356376\pi$
$828$	3.80385	−	3.80385i	0.132193	−	0.132193i
$829$	−22.0000			−0.764092			−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000			−0.764092			−0.382046	+	0.924143i	$0.624780\pi$
$830$	−12.3923	+	3.32051i	−0.430143	+	0.115257i
$831$	−49.0526	−	13.1436i	−1.70161	−	0.455946i
$832$	1.73205	+	3.00000i	0.0600481	+	0.104006i
$833$	−5.92820	+	23.7128i	−0.205400	+	0.821600i
$834$	36.8205	−	9.86603i	1.27499	−	0.341633i
$835$	58.6410	+	33.8564i	2.02936	+	1.17165i
$836$	1.63397	+	1.63397i	0.0565122	+	0.0565122i
$837$		0			0
$838$	5.58846	+	5.58846i	0.193050	+	0.193050i
$839$	5.85641	+	21.8564i	0.202186	+	0.754567i	0.990289	+	0.139024i	$0.0443965\pi$
$839$	5.85641	+	21.8564i	0.202186	+	0.754567i	−0.788103	+	0.615543i	$0.788937\pi$
$840$	2.53590	−	4.39230i	0.0874968	−	0.151549i
$841$	41.3827	−	23.8923i	1.42699	−	0.823873i
$842$	14.5359	−	8.39230i	0.500940	−	0.289218i
$843$	−4.26795	−	7.39230i	−0.146996	−	0.254605i
$844$	4.09808	+	15.2942i	0.141062	+	0.526449i
$845$	−2.00000	−	2.00000i	−0.0688021	−	0.0688021i
$846$	25.9808	+	15.0000i	0.893237	+	0.515711i
$847$	−4.14359	−	4.14359i	−0.142376	−	0.142376i
$848$	2.19615	+	1.26795i	0.0754162	+	0.0435416i
$849$	−36.4641	−	36.4641i	−1.25144	−	1.25144i
$850$	12.0000	+	3.00000i	0.411597	+	0.102899i
$851$	−4.39230	−	7.60770i	−0.150566	−	0.260788i
$852$	−9.46410	+	9.46410i	−0.324235	+	0.324235i
$853$	−2.46410	+	0.660254i	−0.0843692	+	0.0226067i	−0.300757	−	0.953701i	$-0.597239\pi$
$853$	−2.46410	+	0.660254i	−0.0843692	+	0.0226067i	0.216387	+	0.976308i	$0.430573\pi$
$854$	−10.9282			−0.373955
$855$	−2.19615	−	8.19615i	−0.0751068	−	0.280302i
$856$	−13.2942	+	13.2942i	−0.454387	+	0.454387i
$857$	6.50962	+	24.2942i	0.222364	+	0.829875i	0.983443	+	0.181216i	$0.0580033\pi$
$857$	6.50962	+	24.2942i	0.222364	+	0.829875i	−0.761079	+	0.648659i	$0.775330\pi$
$858$	13.3923	+	3.58846i	0.457206	+	0.122508i
$859$	−29.8923	+	17.2583i	−1.01991	+	0.588847i	−0.914079	−	0.405537i	$-0.867084\pi$
$859$	−29.8923	+	17.2583i	−1.01991	+	0.588847i	−0.105834	+	0.994384i	$0.533751\pi$
$860$	14.1962	+	3.80385i	0.484085	+	0.129710i
$861$	−9.24871	+	16.0192i	−0.315195	+	0.545934i
$862$	−28.1244	+	7.53590i	−0.957919	+	0.256674i
$863$	33.8564			1.15249			0.576243	−	0.817279i	$-0.304518\pi$
$863$	33.8564			1.15249			0.576243	+	0.817279i	$0.304518\pi$
$864$	−2.59808	−	4.50000i	−0.0883883	−	0.153093i
$865$		−	10.9282i		−	0.371570i
$866$	−2.03590	+	3.52628i	−0.0691826	+	0.119828i
$867$	13.8564	−	25.9808i	0.470588	−	0.882353i
$868$		0			0
$869$	25.2679	−	14.5885i	0.857156	−	0.494880i
$870$	−37.1769	+	21.4641i	−1.26042	+	0.727701i
$871$	8.07180	−	13.9808i	0.273502	−	0.473720i
$872$	−4.92820	−	4.92820i	−0.166890	−	0.166890i
$873$	5.49038	+	5.49038i	0.185821	+	0.185821i
$874$	−1.26795	+	1.26795i	−0.0428890	+	0.0428890i
$875$	−5.07180	−	2.92820i	−0.171458	−	0.0989913i
$876$	−6.75833	+	6.75833i	−0.228343	+	0.228343i
$877$	−9.26795	−	2.48334i	−0.312956	−	0.0838564i	0.0989221	−	0.995095i	$-0.468461\pi$
$877$	−9.26795	−	2.48334i	−0.312956	−	0.0838564i	−0.411879	+	0.911239i	$0.635127\pi$
$878$	6.73205	+	1.80385i	0.227196	+	0.0608769i
$879$		−	26.7846i		−	0.903422i
$880$	−3.26795	+	5.66025i	−0.110163	+	0.190807i
$881$	4.32051	+	4.32051i	0.145562	+	0.145562i	0.776132	−	0.630570i	$-0.217179\pi$
$881$	4.32051	+	4.32051i	0.145562	+	0.145562i	−0.630570	+	0.776132i	$0.717179\pi$
$882$	8.89230	+	15.4019i	0.299419	+	0.518610i
$883$	48.3731			1.62788			0.813942	−	0.580947i	$-0.197318\pi$
$883$	48.3731			1.62788			0.813942	+	0.580947i	$0.197318\pi$
$884$	3.92820	+	13.7321i	0.132120	+	0.461859i
$885$	−2.19615	+	8.19615i	−0.0738229	+	0.275511i
$886$	10.5000	−	6.06218i	0.352754	−	0.203663i
$887$	5.71281	−	21.3205i	0.191817	−	0.715873i	−0.801250	−	0.598329i	$-0.795831\pi$
$887$	5.71281	−	21.3205i	0.191817	−	0.715873i	0.993068	−	0.117543i	$-0.0375019\pi$
$888$	−8.19615	+	2.19615i	−0.275045	+	0.0736980i
$889$	−2.00000	+	0.535898i	−0.0670778	+	0.0179735i
$890$	13.8564	−	13.8564i	0.464468	−	0.464468i
$891$	−20.0885	−	5.38269i	−0.672989	−	0.180327i
$892$		−	2.39230i		−	0.0801003i
$893$	−8.66025	−	5.00000i	−0.289804	−	0.167319i
$894$	−9.92820	+	17.1962i	−0.332049	+	0.575125i
$895$	−24.7846	−	6.64102i	−0.828458	−	0.221985i
$896$	−0.267949	+	1.00000i	−0.00895155	+	0.0334077i
$897$	−2.78461	+	10.3923i	−0.0929754	+	0.346989i
$898$	−11.4282	+	3.06218i	−0.381364	+	0.102186i
$899$		0			0
$900$	7.79423	−	4.50000i	0.259808	−	0.150000i
$901$	7.51666	+	7.26795i	0.250416	+	0.242130i
$902$	11.9186	−	20.6436i	0.396845	−	0.687356i
$903$	6.58846	−	6.58846i	0.219250	−	0.219250i
$904$	1.63397	−	6.09808i	0.0543452	−	0.202819i
$905$	22.5359	+	39.0333i	0.749119	+	1.29751i
$906$			36.2487i			1.20428i
$907$	9.91858	+	37.0167i	0.329341	+	1.22912i	0.909875	+	0.414882i	$0.136177\pi$
$907$	9.91858	+	37.0167i	0.329341	+	1.22912i	−0.580534	+	0.814236i	$0.697156\pi$
$908$	−4.63397	+	4.63397i	−0.153784	+	0.153784i
$909$	−52.3923			−1.73774
$910$			10.1436i			0.336257i
$911$	−9.66025	−	36.0526i	−0.320058	−	1.19447i	−0.919187	−	0.393822i	$-0.871153\pi$
$911$	−9.66025	−	36.0526i	−0.320058	−	1.19447i	0.599128	−	0.800653i	$-0.295514\pi$
$912$	0.866025	+	1.50000i	0.0286770	+	0.0496700i
$913$	2.71281	−	10.1244i	0.0897810	−	0.335067i
$914$	13.3564	+	23.1340i	0.441791	+	0.765204i
$915$	−44.7846	−	25.8564i	−1.48053	−	0.854786i
$916$	−11.5359	−	6.66025i	−0.381157	−	0.220061i
$917$	−18.5359			−0.612109
$918$	−5.89230	−	20.5981i	−0.194475	−	0.679838i
$919$	8.92820			0.294514			0.147257	−	0.989098i	$-0.452956\pi$
$919$	8.92820			0.294514			0.147257	+	0.989098i	$0.452956\pi$
$920$	−4.39230	−	2.53590i	−0.144810	−	0.0836061i
$921$	9.10770	+	5.25833i	0.300109	+	0.173268i
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	6.92820	−	25.8564i	0.228045	−	0.851074i
$924$	2.07180	+	3.58846i	0.0681571	+	0.118052i
$925$	−3.80385	−	14.1962i	−0.125070	−	0.466767i
$926$			27.7128i			0.910700i
$927$	11.1962	−	19.3923i	0.367730	−	0.636927i
$928$	6.19615	−	6.19615i	0.203399	−	0.203399i
$929$	7.04552	+	26.2942i	0.231156	+	0.862686i	0.979844	+	0.199763i	$0.0640174\pi$
$929$	7.04552	+	26.2942i	0.231156	+	0.862686i	−0.748688	+	0.662922i	$0.769316\pi$
$930$		0			0
$931$	−2.96410	−	5.13397i	−0.0971445	−	0.168259i
$932$	3.57180	−	13.3301i	0.116998	−	0.436643i
$933$	−21.8038	+	21.8038i	−0.713826	+	0.713826i
$934$	−18.4282	+	31.9186i	−0.602989	+	1.04441i
$935$	−18.7321	+	19.3731i	−0.612604	+	0.633567i
$936$	9.00000	+	5.19615i	0.294174	+	0.169842i
$937$		−	41.7128i		−	1.36270i	−0.731959	−	0.681349i	$-0.761394\pi$
$937$		−	41.7128i		−	1.36270i	0.731959	−	0.681349i	$-0.238606\pi$
$938$	4.66025	−	1.24871i	0.152163	−	0.0407719i
$939$	4.37564	−	16.3301i	0.142794	−	0.532914i
$940$	7.32051	−	27.3205i	0.238769	−	0.891097i
$941$	−4.73205	−	1.26795i	−0.154260	−	0.0413340i	0.180862	−	0.983508i	$-0.442111\pi$
$941$	−4.73205	−	1.26795i	−0.154260	−	0.0413340i	−0.335123	+	0.942174i	$0.608778\pi$
$942$	−17.6603	+	30.5885i	−0.575402	+	0.996626i
$943$	16.0192	+	9.24871i	0.521658	+	0.301179i
$944$		−	1.73205i		−	0.0563735i
$945$		−	15.2154i		−	0.494957i
$946$	−8.49038	+	8.49038i	−0.276046	+	0.276046i
$947$	15.6962	−	4.20577i	0.510056	−	0.136669i	0.00539312	−	0.999985i	$-0.498283\pi$
$947$	15.6962	−	4.20577i	0.510056	−	0.136669i	0.504663	+	0.863316i	$0.331617\pi$
$948$	21.1244	−	5.66025i	0.686087	−	0.183837i
$949$	4.94744	−	18.4641i	0.160601	−	0.599370i
$950$	−2.59808	+	1.50000i	−0.0842927	+	0.0486664i
$951$	11.5359	−	43.0526i	0.374077	−	1.39607i
$952$	−2.07180	+	3.73205i	−0.0671473	+	0.120956i
$953$	4.66025			0.150960			0.0754802	−	0.997147i	$-0.475951\pi$
$953$	4.66025			0.150960			0.0754802	+	0.997147i	$0.475951\pi$
$954$	7.60770			0.246308
$955$	−15.7128	−	15.7128i	−0.508455	−	0.508455i
$956$	8.46410	−	14.6603i	0.273749	−	0.474147i
$957$		−	35.0718i		−	1.13371i
$958$	29.5885	+	7.92820i	0.955960	+	0.256149i
$959$	21.9282	+	5.87564i	0.708099	+	0.189734i
$960$	−3.46410	+	3.46410i	−0.111803	+	0.111803i
$961$	26.8468	+	15.5000i	0.866025	+	0.500000i
$962$	12.0000	−	12.0000i	0.386896	−	0.386896i
$963$	−14.5981	+	54.4808i	−0.470416	+	1.75562i
$964$	8.49038	+	8.49038i	0.273457	+	0.273457i
$965$	−8.19615	+	14.1962i	−0.263843	+	0.456990i
$966$	−2.78461	+	1.60770i	−0.0895933	+	0.0517267i
$967$	−19.1436	+	11.0526i	−0.615616	+	0.355426i	−0.775160	−	0.631764i	$-0.782331\pi$
$967$	−19.1436	+	11.0526i	−0.615616	+	0.355426i	0.159544	+	0.987191i	$0.448998\pi$
$968$	2.83013	+	4.90192i	0.0909637	+	0.157554i
$969$	1.96410	+	6.86603i	0.0630960	+	0.220569i
$970$	3.66025	−	6.33975i	0.117524	−	0.203557i
$971$		−	22.3923i		−	0.718603i	−0.933221	−	0.359302i	$-0.883015\pi$
$971$		−	22.3923i		−	0.718603i	0.933221	−	0.359302i	$-0.116985\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	−22.7846			−0.730441
$974$	17.1962	−	4.60770i	0.551000	−	0.147640i
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$	10.1962	+	2.73205i	0.326371	+	0.0874508i
$977$	−38.4282	+	22.1865i	−1.22943	+	0.709810i	−0.966910	−	0.255117i	$-0.917886\pi$
$977$	−38.4282	+	22.1865i	−1.22943	+	0.709810i	−0.262517	+	0.964927i	$0.584553\pi$
$978$	−10.0981	−	2.70577i	−0.322901	−	0.0865210i
$979$	4.14359	+	15.4641i	0.132430	+	0.494235i
$980$	11.8564	−	11.8564i	0.378739	−	0.378739i
$981$	−20.1962	−	5.41154i	−0.644814	−	0.172777i
$982$	11.9282			0.380644
$983$	25.6603	−	6.87564i	0.818435	−	0.219299i	0.174773	−	0.984609i	$-0.444081\pi$
$983$	25.6603	−	6.87564i	0.818435	−	0.219299i	0.643662	+	0.765310i	$0.277414\pi$
$984$	12.6340	−	12.6340i	0.402756	−	0.402756i
$985$	−18.9282	−	32.7846i	−0.603103	−	1.04460i
$986$	30.9808	−	18.5885i	0.986628	−	0.591977i
$987$	−12.6795	−	12.6795i	−0.403593	−	0.403593i
$988$	−3.00000	−	1.73205i	−0.0954427	−	0.0551039i
$989$	−6.58846	−	6.58846i	−0.209501	−	0.209501i
$990$			19.6077i			0.623173i
$991$	2.14359	+	2.14359i	0.0680935	+	0.0680935i	0.740333	−	0.672240i	$-0.234668\pi$
$991$	2.14359	+	2.14359i	0.0680935	+	0.0680935i	−0.672240	+	0.740333i	$0.734668\pi$
$992$		0			0
$993$	3.00000	+	5.19615i	0.0952021	+	0.164895i
$994$	6.92820	−	4.00000i	0.219749	−	0.126872i
$995$	−12.6795	+	7.32051i	−0.401967	+	0.232076i
$996$	3.92820	−	6.80385i	0.124470	−	0.215588i
$997$	4.39230	+	16.3923i	0.139106	+	0.519150i	0.999947	+	0.0102763i	$0.00327112\pi$
$997$	4.39230	+	16.3923i	0.139106	+	0.519150i	−0.860842	+	0.508873i	$0.830062\pi$
$998$	−21.4186	−	21.4186i	−0.677993	−	0.677993i
$999$	−18.0000	+	18.0000i	−0.569495	+	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	306.2.n.c.115.1	yes	4
3.2	odd	2		918.2.o.b.829.1		4
9.4	even	3		306.2.n.b.13.1	✓	4
9.5	odd	6		918.2.o.c.523.1		4
17.4	even	4		306.2.n.b.259.1	yes	4
51.38	odd	4		918.2.o.c.667.1		4
153.4	even	12	inner	306.2.n.c.157.1	yes	4
153.140	odd	12		918.2.o.b.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
306.2.n.b.13.1	✓	4	9.4	even	3
306.2.n.b.259.1	yes	4	17.4	even	4
306.2.n.c.115.1	yes	4	1.1	even	1	trivial
306.2.n.c.157.1	yes	4	153.4	even	12	inner
918.2.o.b.361.1		4	153.140	odd	12
918.2.o.b.829.1		4	3.2	odd	2
918.2.o.c.523.1		4	9.5	odd	6
918.2.o.c.667.1		4	51.38	odd	4

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:	\( N \)	\(=\)	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	306.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.732051 - 2.73205i) q^{5} +(0.866025 + 1.50000i) q^{6} +(-0.267949 - 1.00000i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.732051 - 2.73205i) q^{5} +(0.866025 + 1.50000i) q^{6} +(-0.267949 - 1.00000i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(2.00000 - 2.00000i) q^{10} +(0.598076 + 2.23205i) q^{11} +1.73205i q^{12} +(-1.73205 - 3.00000i) q^{13} +(0.267949 - 1.00000i) q^{14} +(3.46410 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 + 2.96410i) q^{17} +3.00000i q^{18} -1.00000i q^{19} +(2.73205 - 0.732051i) q^{20} +(0.464102 - 1.73205i) q^{21} +(-0.598076 + 2.23205i) q^{22} +(-1.73205 - 0.464102i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(-2.59808 - 1.50000i) q^{25} -3.46410i q^{26} +5.19615i q^{27} +(0.732051 - 0.732051i) q^{28} +(-8.46410 + 2.26795i) q^{29} +(4.73205 - 1.26795i) q^{30} +(-0.866025 + 0.500000i) q^{32} +(-1.03590 + 3.86603i) q^{33} +(-3.96410 + 1.13397i) q^{34} -2.92820 q^{35} +(-1.50000 + 2.59808i) q^{36} +(3.46410 + 3.46410i) q^{37} +(0.500000 - 0.866025i) q^{38} -6.00000i q^{39} +(2.73205 + 0.732051i) q^{40} +(-9.96410 - 2.66987i) q^{41} +(1.26795 - 1.26795i) q^{42} +(4.50000 + 2.59808i) q^{43} +(-1.63397 + 1.63397i) q^{44} +(8.19615 - 2.19615i) q^{45} +(-1.26795 - 1.26795i) q^{46} +(5.00000 - 8.66025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(5.13397 - 2.96410i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(-6.86603 + 1.96410i) q^{51} +(1.73205 - 3.00000i) q^{52} -2.53590i q^{53} +(-2.59808 + 4.50000i) q^{54} +6.53590 q^{55} +(1.00000 - 0.267949i) q^{56} +(0.866025 - 1.50000i) q^{57} +(-8.46410 - 2.26795i) q^{58} +(-1.50000 + 0.866025i) q^{59} +(4.73205 + 1.26795i) q^{60} +(-2.73205 - 10.1962i) q^{61} +(2.19615 - 2.19615i) q^{63} -1.00000 q^{64} +(-9.46410 + 2.53590i) q^{65} +(-2.83013 + 2.83013i) q^{66} +(2.33013 + 4.03590i) q^{67} +(-4.00000 - 1.00000i) q^{68} +(-2.19615 - 2.19615i) q^{69} +(-2.53590 - 1.46410i) q^{70} +(5.46410 + 5.46410i) q^{71} +(-2.59808 + 1.50000i) q^{72} +(3.90192 + 3.90192i) q^{73} +(1.26795 + 4.73205i) q^{74} +(-2.59808 - 4.50000i) q^{75} +(0.866025 - 0.500000i) q^{76} +(2.07180 - 1.19615i) q^{77} +(3.00000 - 5.19615i) q^{78} +(-3.26795 - 12.1962i) q^{79} +(2.00000 + 2.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.29423 - 7.29423i) q^{82} +(-3.92820 - 2.26795i) q^{83} +(1.73205 - 0.464102i) q^{84} +(6.00000 + 10.0000i) q^{85} +(2.59808 + 4.50000i) q^{86} +(-14.6603 - 3.92820i) q^{87} +(-2.23205 + 0.598076i) q^{88} +6.92820 q^{89} +(8.19615 + 2.19615i) q^{90} +(-2.53590 + 2.53590i) q^{91} +(-0.464102 - 1.73205i) q^{92} +(8.66025 - 5.00000i) q^{94} +(-2.73205 - 0.732051i) q^{95} -1.73205 q^{96} +(2.50000 - 0.669873i) q^{97} +5.92820 q^{98} +(-4.90192 + 4.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 2 * q^4 - 4 * q^5 - 8 * q^7 + 6 * q^9	\( 4 q + 6 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{7} + 6 q^{9} + 8 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{16} - 8 q^{17} + 4 q^{20} - 12 q^{21} + 8 q^{22} - 4 q^{28} - 20 q^{29} + 12 q^{30} - 18 q^{33} - 2 q^{34} + 16 q^{35} - 6 q^{36} + 2 q^{38} + 4 q^{40} - 26 q^{41} + 12 q^{42} + 18 q^{43} - 10 q^{44} + 12 q^{45} - 12 q^{46} + 20 q^{47} - 6 q^{48} + 24 q^{49} - 6 q^{50} - 24 q^{51} + 40 q^{55} + 4 q^{56} - 20 q^{58} - 6 q^{59} + 12 q^{60} - 4 q^{61} - 12 q^{63} - 4 q^{64} - 24 q^{65} + 6 q^{66} - 8 q^{67} - 16 q^{68} + 12 q^{69} - 24 q^{70} + 8 q^{71} + 26 q^{73} + 12 q^{74} + 36 q^{77} + 12 q^{78} - 20 q^{79} + 8 q^{80} - 18 q^{81} + 2 q^{82} + 12 q^{83} + 24 q^{85} - 24 q^{87} - 2 q^{88} + 12 q^{90} - 24 q^{91} + 12 q^{92} - 4 q^{95} + 10 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^4 - 4 * q^5 - 8 * q^7 + 6 * q^9 + 8 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^16 - 8 * q^17 + 4 * q^20 - 12 * q^21 + 8 * q^22 - 4 * q^28 - 20 * q^29 + 12 * q^30 - 18 * q^33 - 2 * q^34 + 16 * q^35 - 6 * q^36 + 2 * q^38 + 4 * q^40 - 26 * q^41 + 12 * q^42 + 18 * q^43 - 10 * q^44 + 12 * q^45 - 12 * q^46 + 20 * q^47 - 6 * q^48 + 24 * q^49 - 6 * q^50 - 24 * q^51 + 40 * q^55 + 4 * q^56 - 20 * q^58 - 6 * q^59 + 12 * q^60 - 4 * q^61 - 12 * q^63 - 4 * q^64 - 24 * q^65 + 6 * q^66 - 8 * q^67 - 16 * q^68 + 12 * q^69 - 24 * q^70 + 8 * q^71 + 26 * q^73 + 12 * q^74 + 36 * q^77 + 12 * q^78 - 20 * q^79 + 8 * q^80 - 18 * q^81 + 2 * q^82 + 12 * q^83 + 24 * q^85 - 24 * q^87 - 2 * q^88 + 12 * q^90 - 24 * q^91 + 12 * q^92 - 4 * q^95 + 10 * q^97 - 4 * q^98 - 30 * q^99

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