LMFDB - Embedded newform 273.2.by.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (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:	$2.17991597518$
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			97.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	273.97
Dual form			273.2.by.b.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 1.86603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.366025 - 0.366025i) q^{5} +(-0.500000 + 1.86603i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.366025 + 0.366025i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 1.86603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.366025 - 0.366025i) q^{5} +(-0.500000 + 1.86603i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.366025 + 0.366025i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 0.267949i) q^{11} -1.73205 q^{12} +(-0.232051 - 3.59808i) q^{13} +(-5.09808 - 0.366025i) q^{14} +(-0.133975 - 0.500000i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(2.59808 + 4.50000i) q^{17} +(-1.36603 + 1.36603i) q^{18} +(0.732051 - 2.73205i) q^{19} +(0.866025 + 0.232051i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.63397 + 2.09808i) q^{23} +(0.133975 + 0.500000i) q^{24} -4.73205i q^{25} +(6.59808 - 2.23205i) q^{26} +1.00000i q^{27} +(-0.866025 - 4.50000i) q^{28} +(3.50000 - 6.06218i) q^{29} +(0.866025 - 0.500000i) q^{30} +(-6.73205 - 6.73205i) q^{31} +(-7.33013 - 1.96410i) q^{32} +(-1.00000 - 0.267949i) q^{33} +(-7.09808 + 7.09808i) q^{34} +(1.23205 - 0.598076i) q^{35} +(-1.50000 - 0.866025i) q^{36} +(2.50000 - 0.669873i) q^{37} +5.46410 q^{38} +(1.59808 - 3.23205i) q^{39} -0.267949i q^{40} +(7.59808 - 2.03590i) q^{41} +(-4.23205 - 2.86603i) q^{42} +(6.92820 - 4.00000i) q^{43} +(1.26795 - 1.26795i) q^{44} +(0.133975 - 0.500000i) q^{45} +(-2.09808 + 7.83013i) q^{46} +(-9.46410 + 9.46410i) q^{47} +(-3.86603 + 2.23205i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(8.83013 - 2.36603i) q^{50} +5.19615i q^{51} +(3.46410 + 5.19615i) q^{52} +4.26795 q^{53} +(-1.86603 + 0.500000i) q^{54} +(0.464102 + 0.267949i) q^{55} +(-1.23205 + 0.598076i) q^{56} +(2.00000 - 2.00000i) q^{57} +(13.0622 + 3.50000i) q^{58} +(5.09808 + 1.36603i) q^{59} +(0.633975 + 0.633975i) q^{60} +(0.401924 - 0.232051i) q^{61} +(9.19615 - 15.9282i) q^{62} +(-2.59808 + 0.500000i) q^{63} -5.73205i q^{64} +(-1.23205 + 1.40192i) q^{65} -2.00000i q^{66} +(1.56218 + 5.83013i) q^{67} +(-7.79423 - 4.50000i) q^{68} +(2.09808 + 3.63397i) q^{69} +(1.73205 + 2.00000i) q^{70} +(-5.46410 - 1.46410i) q^{71} +(-0.133975 + 0.500000i) q^{72} +(-7.29423 + 7.29423i) q^{73} +(2.50000 + 4.33013i) q^{74} +(2.36603 - 4.09808i) q^{75} +(1.26795 + 4.73205i) q^{76} +(0.196152 - 2.73205i) q^{77} +(6.83013 + 1.36603i) q^{78} -1.66025 q^{79} +(2.23205 - 0.598076i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.59808 + 13.1603i) q^{82} +(-6.92820 - 6.92820i) q^{83} +(1.50000 - 4.33013i) q^{84} +(0.696152 - 2.59808i) q^{85} +(10.9282 + 10.9282i) q^{86} +(6.06218 - 3.50000i) q^{87} +(-0.464102 - 0.267949i) q^{88} +(-1.16987 - 4.36603i) q^{89} +1.00000 q^{90} +(9.19615 + 2.53590i) q^{91} -7.26795 q^{92} +(-2.46410 - 9.19615i) q^{93} +(-22.3923 - 12.9282i) q^{94} +(-1.26795 + 0.732051i) q^{95} +(-5.36603 - 5.36603i) q^{96} +(0.0980762 - 0.366025i) q^{97} +(5.33013 - 12.4282i) q^{98} +(-0.732051 - 0.732051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 6 q^{13} - 10 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{19} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 4 q^{24} + 16 q^{26} + 14 q^{29} - 20 q^{31} - 12 q^{32} - 4 q^{33} - 18 q^{34} - 2 q^{35} - 6 q^{36} + 10 q^{37} + 8 q^{38} - 4 q^{39} + 20 q^{41} - 10 q^{42} + 12 q^{44} + 4 q^{45} + 2 q^{46} - 24 q^{47} - 12 q^{48} - 22 q^{49} + 18 q^{50} + 24 q^{53} - 4 q^{54} - 12 q^{55} + 2 q^{56} + 8 q^{57} + 28 q^{58} + 10 q^{59} + 6 q^{60} + 12 q^{61} + 16 q^{62} + 2 q^{65} - 18 q^{67} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 2 q^{73} + 10 q^{74} + 6 q^{75} + 12 q^{76} - 20 q^{77} + 10 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} + 20 q^{82} + 6 q^{84} - 18 q^{85} + 16 q^{86} + 12 q^{88} - 22 q^{89} + 4 q^{90} + 16 q^{91} - 36 q^{92} + 4 q^{93} - 48 q^{94} - 12 q^{95} - 18 q^{96} - 10 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 6 * q^13 - 10 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^19 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 4 * q^24 + 16 * q^26 + 14 * q^29 - 20 * q^31 - 12 * q^32 - 4 * q^33 - 18 * q^34 - 2 * q^35 - 6 * q^36 + 10 * q^37 + 8 * q^38 - 4 * q^39 + 20 * q^41 - 10 * q^42 + 12 * q^44 + 4 * q^45 + 2 * q^46 - 24 * q^47 - 12 * q^48 - 22 * q^49 + 18 * q^50 + 24 * q^53 - 4 * q^54 - 12 * q^55 + 2 * q^56 + 8 * q^57 + 28 * q^58 + 10 * q^59 + 6 * q^60 + 12 * q^61 + 16 * q^62 + 2 * q^65 - 18 * q^67 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 2 * q^73 + 10 * q^74 + 6 * q^75 + 12 * q^76 - 20 * q^77 + 10 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 + 20 * q^82 + 6 * q^84 - 18 * q^85 + 16 * q^86 + 12 * q^88 - 22 * q^89 + 4 * q^90 + 16 * q^91 - 36 * q^92 + 4 * q^93 - 48 * q^94 - 12 * q^95 - 18 * q^96 - 10 * q^97 + 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

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	+	1.86603i	0.353553	+	1.31948i	0.882295	+	0.470696i	$0.155997\pi$
$2$	0.500000	+	1.86603i	0.353553	+	1.31948i	−0.528742	+	0.848783i	$0.677336\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.50000	+	0.866025i	−0.750000	+	0.433013i
$5$	−0.366025	−	0.366025i	−0.163692	−	0.163692i	0.620508	−	0.784200i	$-0.286926\pi$
$5$	−0.366025	−	0.366025i	−0.163692	−	0.163692i	−0.784200	+	0.620508i	$0.786926\pi$
$6$	−0.500000	+	1.86603i	−0.204124	+	0.761802i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$	0.366025	+	0.366025i	0.129410	+	0.129410i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000	+	0.267949i	−0.301511	+	0.0807897i	−0.406403	−	0.913694i	$-0.633217\pi$
$11$	−1.00000	+	0.267949i	−0.301511	+	0.0807897i	0.104892	+	0.994484i	$0.466550\pi$
$12$	−1.73205			−0.500000
$13$	−0.232051	−	3.59808i	−0.0643593	−	0.997927i
$13$	−0.232051	−	3.59808i	−0.0643593	−	0.997927i
$14$	−5.09808	−	0.366025i	−1.36252	−	0.0978244i
$15$	−0.133975	−	0.500000i	−0.0345921	−	0.129099i
$16$	−2.23205	+	3.86603i	−0.558013	+	0.966506i
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	0.987526	+	0.157459i	$0.0503301\pi$
$17$	2.59808	+	4.50000i	0.630126	+	1.09141i	−0.357400	+	0.933952i	$0.616337\pi$
$18$	−1.36603	+	1.36603i	−0.321975	+	0.321975i
$19$	0.732051	−	2.73205i	0.167944	−	0.626775i	−0.829702	−	0.558206i	$-0.811490\pi$
$19$	0.732051	−	2.73205i	0.167944	−	0.626775i	0.997646	−	0.0685694i	$-0.0218435\pi$
$20$	0.866025	+	0.232051i	0.193649	+	0.0518881i
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	3.63397	+	2.09808i	0.757736	+	0.437479i	0.828482	−	0.560015i	$-0.189205\pi$
$23$	3.63397	+	2.09808i	0.757736	+	0.437479i	−0.0707462	+	0.997494i	$0.522538\pi$
$24$	0.133975	+	0.500000i	0.0273474	+	0.102062i
$25$		−	4.73205i		−	0.946410i
$26$	6.59808	−	2.23205i	1.29399	−	0.437741i
$27$			1.00000i			0.192450i
$28$	−0.866025	−	4.50000i	−0.163663	−	0.850420i
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$	0.866025	−	0.500000i	0.158114	−	0.0912871i
$31$	−6.73205	−	6.73205i	−1.20911	−	1.20911i	−0.971315	−	0.237797i	$-0.923575\pi$
$31$	−6.73205	−	6.73205i	−1.20911	−	1.20911i	−0.237797	−	0.971315i	$-0.576425\pi$
$32$	−7.33013	−	1.96410i	−1.29580	−	0.347207i
$33$	−1.00000	−	0.267949i	−0.174078	−	0.0466440i
$34$	−7.09808	+	7.09808i	−1.21731	+	1.21731i
$35$	1.23205	−	0.598076i	0.208255	−	0.101093i
$36$	−1.50000	−	0.866025i	−0.250000	−	0.144338i
$37$	2.50000	−	0.669873i	0.410997	−	0.110126i	−0.0473952	−	0.998876i	$-0.515092\pi$
$37$	2.50000	−	0.669873i	0.410997	−	0.110126i	0.458393	+	0.888750i	$0.348425\pi$
$38$	5.46410			0.886394
$39$	1.59808	−	3.23205i	0.255897	−	0.517542i
$40$		−	0.267949i		−	0.0423665i
$41$	7.59808	−	2.03590i	1.18662	−	0.317954i	0.389071	−	0.921208i	$-0.372796\pi$
$41$	7.59808	−	2.03590i	1.18662	−	0.317954i	0.797549	+	0.603254i	$0.206129\pi$
$42$	−4.23205	−	2.86603i	−0.653020	−	0.442237i
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.132068	−	0.991241i	$-0.457838\pi$
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.924473	+	0.381246i	$0.124505\pi$
$44$	1.26795	−	1.26795i	0.191151	−	0.191151i
$45$	0.133975	−	0.500000i	0.0199718	−	0.0745356i
$46$	−2.09808	+	7.83013i	−0.309344	+	1.15449i
$47$	−9.46410	+	9.46410i	−1.38048	+	1.38048i	−0.536722	+	0.843759i	$0.680338\pi$
$47$	−9.46410	+	9.46410i	−1.38048	+	1.38048i	−0.843759	+	0.536722i	$0.819662\pi$
$48$	−3.86603	+	2.23205i	−0.558013	+	0.322169i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	8.83013	−	2.36603i	1.24877	−	0.334607i
$51$			5.19615i			0.727607i
$52$	3.46410	+	5.19615i	0.480384	+	0.720577i
$53$	4.26795			0.586248			0.293124	−	0.956074i	$-0.405305\pi$
$53$	4.26795			0.586248			0.293124	+	0.956074i	$0.405305\pi$
$54$	−1.86603	+	0.500000i	−0.253934	+	0.0680414i
$55$	0.464102	+	0.267949i	0.0625794	+	0.0361303i
$56$	−1.23205	+	0.598076i	−0.164640	+	0.0799213i
$57$	2.00000	−	2.00000i	0.264906	−	0.264906i
$58$	13.0622	+	3.50000i	1.71515	+	0.459573i
$59$	5.09808	+	1.36603i	0.663713	+	0.177841i	0.574921	−	0.818209i	$-0.305033\pi$
$59$	5.09808	+	1.36603i	0.663713	+	0.177841i	0.0887919	+	0.996050i	$0.471699\pi$
$60$	0.633975	+	0.633975i	0.0818458	+	0.0818458i
$61$	0.401924	−	0.232051i	0.0514611	−	0.0297111i	−0.474049	−	0.880499i	$-0.657208\pi$
$61$	0.401924	−	0.232051i	0.0514611	−	0.0297111i	0.525510	+	0.850788i	$0.323875\pi$
$62$	9.19615	−	15.9282i	1.16791	−	2.02288i
$63$	−2.59808	+	0.500000i	−0.327327	+	0.0629941i
$64$		−	5.73205i		−	0.716506i
$65$	−1.23205	+	1.40192i	−0.152817	+	0.173887i
$66$		−	2.00000i		−	0.246183i
$67$	1.56218	+	5.83013i	0.190850	+	0.712263i	0.993302	+	0.115546i	$0.0368619\pi$
$67$	1.56218	+	5.83013i	0.190850	+	0.712263i	−0.802452	+	0.596717i	$0.796471\pi$
$68$	−7.79423	−	4.50000i	−0.945189	−	0.545705i
$69$	2.09808	+	3.63397i	0.252579	+	0.437479i
$70$	1.73205	+	2.00000i	0.207020	+	0.239046i
$71$	−5.46410	−	1.46410i	−0.648470	−	0.173757i	−0.0804327	−	0.996760i	$-0.525630\pi$
$71$	−5.46410	−	1.46410i	−0.648470	−	0.173757i	−0.568037	+	0.823003i	$0.692297\pi$
$72$	−0.133975	+	0.500000i	−0.0157891	+	0.0589256i
$73$	−7.29423	+	7.29423i	−0.853725	+	0.853725i	−0.990590	−	0.136865i	$-0.956297\pi$
$73$	−7.29423	+	7.29423i	−0.853725	+	0.853725i	0.136865	+	0.990590i	$0.456297\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$	2.36603	−	4.09808i	0.273205	−	0.473205i
$76$	1.26795	+	4.73205i	0.145444	+	0.542803i
$77$	0.196152	−	2.73205i	0.0223536	−	0.311346i
$78$	6.83013	+	1.36603i	0.773360	+	0.154672i
$79$	−1.66025			−0.186793			−0.0933966	−	0.995629i	$-0.529772\pi$
$79$	−1.66025			−0.186793			−0.0933966	+	0.995629i	$0.529772\pi$
$80$	2.23205	−	0.598076i	0.249551	−	0.0668670i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.59808	+	13.1603i	0.839067	+	1.45331i
$83$	−6.92820	−	6.92820i	−0.760469	−	0.760469i	0.215938	−	0.976407i	$-0.430719\pi$
$83$	−6.92820	−	6.92820i	−0.760469	−	0.760469i	−0.976407	+	0.215938i	$0.930719\pi$
$84$	1.50000	−	4.33013i	0.163663	−	0.472456i
$85$	0.696152	−	2.59808i	0.0755083	−	0.281801i
$86$	10.9282	+	10.9282i	1.17842	+	1.17842i
$87$	6.06218	−	3.50000i	0.649934	−	0.375239i
$88$	−0.464102	−	0.267949i	−0.0494734	−	0.0285635i
$89$	−1.16987	−	4.36603i	−0.124006	−	0.462798i	0.875796	−	0.482681i	$-0.160337\pi$
$89$	−1.16987	−	4.36603i	−0.124006	−	0.462798i	−0.999802	+	0.0198836i	$0.993670\pi$
$90$	1.00000			0.105409
$91$	9.19615	+	2.53590i	0.964019	+	0.265834i
$92$	−7.26795			−0.757736
$93$	−2.46410	−	9.19615i	−0.255515	−	0.953597i
$94$	−22.3923	−	12.9282i	−2.30959	−	1.33344i
$95$	−1.26795	+	0.732051i	−0.130089	+	0.0751068i
$96$	−5.36603	−	5.36603i	−0.547668	−	0.547668i
$97$	0.0980762	−	0.366025i	0.00995813	−	0.0371642i	−0.960768	−	0.277353i	$-0.910543\pi$
$97$	0.0980762	−	0.366025i	0.00995813	−	0.0371642i	0.970726	+	0.240189i	$0.0772094\pi$
$98$	5.33013	−	12.4282i	0.538424	−	1.25544i
$99$	−0.732051	−	0.732051i	−0.0735739	−	0.0735739i
$100$	4.09808	+	7.09808i	0.409808	+	0.709808i
$101$	−4.96410	+	8.59808i	−0.493947	+	0.855541i	−0.999976	−	0.00697585i	$-0.997780\pi$
$101$	−4.96410	+	8.59808i	−0.493947	+	0.855541i	0.506029	+	0.862516i	$0.331113\pi$
$102$	−9.69615	+	2.59808i	−0.960062	+	0.257248i
$103$	6.92820			0.682656			0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820			0.682656			0.341328	+	0.939944i	$0.389123\pi$
$104$	1.23205	−	1.40192i	0.120813	−	0.137470i
$105$	1.36603	+	0.0980762i	0.133310	+	0.00957126i
$106$	2.13397	+	7.96410i	0.207270	+	0.773542i
$107$	0.267949	−	0.464102i	0.0259036	−	0.0448664i	−0.852783	−	0.522265i	$-0.825087\pi$
$107$	0.267949	−	0.464102i	0.0259036	−	0.0448664i	0.878687	+	0.477399i	$0.158420\pi$
$108$	−0.866025	−	1.50000i	−0.0833333	−	0.144338i
$109$	4.26795	−	4.26795i	0.408795	−	0.408795i	−0.472523	−	0.881318i	$-0.656657\pi$
$109$	4.26795	−	4.26795i	0.408795	−	0.408795i	0.881318	+	0.472523i	$0.156657\pi$
$110$	−0.267949	+	1.00000i	−0.0255480	+	0.0953463i
$111$	2.50000	+	0.669873i	0.237289	+	0.0635815i
$112$	−7.73205	−	8.92820i	−0.730610	−	0.843636i
$113$	−4.23205	−	7.33013i	−0.398118	−	0.689560i	0.595376	−	0.803447i	$-0.297003\pi$
$113$	−4.23205	−	7.33013i	−0.398118	−	0.689560i	−0.993494	+	0.113887i	$0.963670\pi$
$114$	4.73205	+	2.73205i	0.443197	+	0.255880i
$115$	−0.562178	−	2.09808i	−0.0524234	−	0.195647i
$116$			12.1244i			1.12572i
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$			10.1962i			0.938632i
$119$	−13.5000	+	2.59808i	−1.23754	+	0.238165i
$120$	0.133975	−	0.232051i	0.0122302	−	0.0211832i
$121$	−8.59808	+	4.96410i	−0.781643	+	0.451282i
$122$	0.633975	+	0.633975i	0.0573974	+	0.0573974i
$123$	7.59808	+	2.03590i	0.685095	+	0.183571i
$124$	15.9282	+	4.26795i	1.43039	+	0.383273i
$125$	−3.56218	+	3.56218i	−0.318611	+	0.318611i
$126$	−2.23205	−	4.59808i	−0.198847	−	0.409629i
$127$	−12.7583	−	7.36603i	−1.13212	−	0.653629i	−0.187652	−	0.982236i	$-0.560088\pi$
$127$	−12.7583	−	7.36603i	−1.13212	−	0.653629i	−0.944467	+	0.328607i	$0.893421\pi$
$128$	−3.96410	+	1.06218i	−0.350380	+	0.0938841i
$129$	8.00000			0.704361
$130$	−3.23205	−	1.59808i	−0.283470	−	0.140161i
$131$			3.80385i			0.332344i	0.986097	+	0.166172i	$0.0531406\pi$
$131$			3.80385i			0.332344i	−0.986097	+	0.166172i	$0.946859\pi$
$132$	1.73205	−	0.464102i	0.150756	−	0.0403949i
$133$	6.19615	+	4.19615i	0.537275	+	0.363853i
$134$	−10.0981	+	5.83013i	−0.872341	+	0.503646i
$135$	0.366025	−	0.366025i	0.0315025	−	0.0315025i
$136$	−0.696152	+	2.59808i	−0.0596946	+	0.222783i
$137$	1.06218	−	3.96410i	0.0907480	−	0.338676i	−0.905593	−	0.424149i	$-0.860573\pi$
$137$	1.06218	−	3.96410i	0.0907480	−	0.338676i	0.996341	+	0.0854727i	$0.0272400\pi$
$138$	−5.73205	+	5.73205i	−0.487945	+	0.487945i
$139$	−1.90192	+	1.09808i	−0.161319	+	0.0931376i	−0.578486	−	0.815692i	$-0.696356\pi$
$139$	−1.90192	+	1.09808i	−0.161319	+	0.0931376i	0.417167	+	0.908830i	$0.363023\pi$
$140$	−1.33013	+	1.96410i	−0.112416	+	0.165997i
$141$	−12.9282	+	3.46410i	−1.08875	+	0.291730i
$142$		−	10.9282i		−	0.917074i
$143$	1.19615	+	3.53590i	0.100027	+	0.295687i
$144$	−4.46410			−0.372008
$145$	−3.50000	+	0.937822i	−0.290659	+	0.0778819i
$146$	−17.2583	−	9.96410i	−1.42831	−	0.824635i
$147$	−2.59808	−	6.50000i	−0.214286	−	0.536111i
$148$	−3.16987	+	3.16987i	−0.260562	+	0.260562i
$149$	−18.5263	−	4.96410i	−1.51773	−	0.406675i	−0.598737	−	0.800945i	$-0.704331\pi$
$149$	−18.5263	−	4.96410i	−1.51773	−	0.406675i	−0.918995	+	0.394270i	$0.870997\pi$
$150$	8.83013	+	2.36603i	0.720977	+	0.193185i
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$	1.26795	−	0.732051i	0.102844	−	0.0593772i
$153$	−2.59808	+	4.50000i	−0.210042	+	0.363803i
$154$	5.19615	−	1.00000i	0.418718	−	0.0805823i
$155$			4.92820i			0.395843i
$156$	0.401924	+	6.23205i	0.0321797	+	0.498963i
$157$		−	18.6603i		−	1.48925i	−0.667483	−	0.744625i	$-0.732628\pi$
$157$		−	18.6603i		−	1.48925i	0.667483	−	0.744625i	$-0.267372\pi$
$158$	−0.830127	−	3.09808i	−0.0660414	−	0.246470i
$159$	3.69615	+	2.13397i	0.293124	+	0.169235i
$160$	1.96410	+	3.40192i	0.155276	+	0.268946i
$161$	−8.39230	+	7.26795i	−0.661406	+	0.572795i
$162$	−1.86603	−	0.500000i	−0.146609	−	0.0392837i
$163$	−3.36603	+	12.5622i	−0.263647	+	0.983946i	0.699426	+	0.714705i	$0.253439\pi$
$163$	−3.36603	+	12.5622i	−0.263647	+	0.983946i	−0.963073	+	0.269240i	$0.913227\pi$
$164$	−9.63397	+	9.63397i	−0.752287	+	0.752287i
$165$	0.267949	+	0.464102i	0.0208598	+	0.0361303i
$166$	9.46410	−	16.3923i	0.734557	−	1.27229i
$167$	2.36603	+	8.83013i	0.183089	+	0.683296i	0.995032	+	0.0995592i	$0.0317433\pi$
$167$	2.36603	+	8.83013i	0.183089	+	0.683296i	−0.811943	+	0.583737i	$0.801590\pi$
$168$	−1.36603	−	0.0980762i	−0.105391	−	0.00756674i
$169$	−12.8923	+	1.66987i	−0.991716	+	0.128452i
$170$	5.19615			0.398527
$171$	2.73205	−	0.732051i	0.208925	−	0.0559813i
$172$	−6.92820	+	12.0000i	−0.528271	+	0.914991i
$173$	−5.66025	−	9.80385i	−0.430341	−	0.745373i	0.566561	−	0.824020i	$-0.308273\pi$
$173$	−5.66025	−	9.80385i	−0.430341	−	0.745373i	−0.996903	+	0.0786468i	$0.974940\pi$
$174$	9.56218	+	9.56218i	0.724907	+	0.724907i
$175$	11.8301	+	4.09808i	0.894274	+	0.309785i
$176$	1.19615	−	4.46410i	0.0901634	−	0.336494i
$177$	3.73205	+	3.73205i	0.280518	+	0.280518i
$178$	7.56218	−	4.36603i	0.566809	−	0.327247i
$179$	11.3660	+	6.56218i	0.849537	+	0.490480i	0.860494	−	0.509460i	$-0.170155\pi$
$179$	11.3660	+	6.56218i	0.849537	+	0.490480i	−0.0109579	+	0.999940i	$0.503488\pi$
$180$	0.232051	+	0.866025i	0.0172960	+	0.0645497i
$181$	−5.92820			−0.440640			−0.220320	−	0.975428i	$-0.570710\pi$
$181$	−5.92820			−0.440640			−0.220320	+	0.975428i	$0.570710\pi$
$182$	−0.133975	+	18.4282i	−0.00993086	+	1.36599i
$183$	0.464102			0.0343074
$184$	0.562178	+	2.09808i	0.0414443	+	0.154672i
$185$	−1.16025	−	0.669873i	−0.0853036	−	0.0492500i
$186$	15.9282	−	9.19615i	1.16791	−	0.674295i
$187$	−3.80385	−	3.80385i	−0.278165	−	0.278165i
$188$	6.00000	−	22.3923i	0.437595	−	1.63313i
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$	−2.00000	−	2.00000i	−0.145095	−	0.145095i
$191$	9.73205	+	16.8564i	0.704186	+	1.21969i	0.966984	+	0.254836i	$0.0820214\pi$
$191$	9.73205	+	16.8564i	0.704186	+	1.21969i	−0.262798	+	0.964851i	$0.584645\pi$
$192$	2.86603	−	4.96410i	0.206838	−	0.358253i
$193$	20.2583	−	5.42820i	1.45823	−	0.390731i	0.559350	−	0.828932i	$-0.311051\pi$
$193$	20.2583	−	5.42820i	1.45823	−	0.390731i	0.898877	+	0.438201i	$0.144384\pi$
$194$	0.732051			0.0525582
$195$	−1.76795	+	0.598076i	−0.126605	+	0.0428291i
$196$	12.0000	+	1.73205i	0.857143	+	0.123718i
$197$	−1.16987	−	4.36603i	−0.0833500	−	0.311066i	0.911647	−	0.410975i	$-0.134812\pi$
$197$	−1.16987	−	4.36603i	−0.0833500	−	0.311066i	−0.994997	+	0.0999085i	$0.968145\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	−12.7321	−	22.0526i	−0.902551	−	1.56326i	−0.824171	−	0.566341i	$-0.808359\pi$
$199$	−12.7321	−	22.0526i	−0.902551	−	1.56326i	−0.0783801	−	0.996924i	$-0.524975\pi$
$200$	1.73205	−	1.73205i	0.122474	−	0.122474i
$201$	−1.56218	+	5.83013i	−0.110188	+	0.411225i
$202$	−18.5263	−	4.96410i	−1.30350	−	0.349273i
$203$	12.1244	+	14.0000i	0.850963	+	0.982607i
$204$	−4.50000	−	7.79423i	−0.315063	−	0.545705i
$205$	−3.52628	−	2.03590i	−0.246286	−	0.142193i
$206$	3.46410	+	12.9282i	0.241355	+	0.900751i
$207$			4.19615i			0.291653i
$208$	14.4282	+	7.13397i	1.00042	+	0.494652i
$209$			2.92820i			0.202548i
$210$	0.500000	+	2.59808i	0.0345033	+	0.179284i
$211$	−6.19615	+	10.7321i	−0.426561	+	0.738825i	−0.996565	−	0.0828170i	$-0.973608\pi$
$211$	−6.19615	+	10.7321i	−0.426561	+	0.738825i	0.570004	+	0.821642i	$0.306942\pi$
$212$	−6.40192	+	3.69615i	−0.439686	+	0.253853i
$213$	−4.00000	−	4.00000i	−0.274075	−	0.274075i
$214$	1.00000	+	0.267949i	0.0683586	+	0.0183166i
$215$	−4.00000	−	1.07180i	−0.272798	−	0.0730959i
$216$	−0.366025	+	0.366025i	−0.0249049	+	0.0249049i
$217$	22.6603	−	11.0000i	1.53828	−	0.746729i
$218$	10.0981	+	5.83013i	0.683928	+	0.394866i
$219$	−9.96410	+	2.66987i	−0.673312	+	0.180413i
$220$	−0.928203			−0.0625794
$221$	15.5885	−	10.3923i	1.04859	−	0.699062i
$222$			5.00000i			0.335578i
$223$	28.4904	−	7.63397i	1.90786	−	0.511209i	0.913263	−	0.407371i	$-0.133554\pi$
$223$	28.4904	−	7.63397i	1.90786	−	0.511209i	0.994594	−	0.103838i	$-0.0331123\pi$
$224$	11.2583	−	16.6244i	0.752229	−	1.11076i
$225$	4.09808	−	2.36603i	0.273205	−	0.157735i
$226$	11.5622	−	11.5622i	0.769105	−	0.769105i
$227$	−7.63397	+	28.4904i	−0.506685	+	1.89097i	−0.0556861	+	0.998448i	$0.517735\pi$
$227$	−7.63397	+	28.4904i	−0.506685	+	1.89097i	−0.450999	+	0.892525i	$0.648932\pi$
$228$	−1.26795	+	4.73205i	−0.0839720	+	0.313388i
$229$	−12.1244	+	12.1244i	−0.801200	+	0.801200i	−0.983283	−	0.182083i	$-0.941716\pi$
$229$	−12.1244	+	12.1244i	−0.801200	+	0.801200i	0.182083	+	0.983283i	$0.441716\pi$
$230$	3.63397	−	2.09808i	0.239617	−	0.138343i
$231$	1.53590	−	2.26795i	0.101055	−	0.149220i
$232$	3.50000	−	0.937822i	0.229786	−	0.0615710i
$233$			2.00000i			0.131024i	0.997852	+	0.0655122i	$0.0208681\pi$
$233$			2.00000i			0.131024i	−0.997852	+	0.0655122i	$0.979132\pi$
$234$	5.23205	+	4.59808i	0.342030	+	0.300586i
$235$	6.92820			0.451946
$236$	−8.83013	+	2.36603i	−0.574792	+	0.154015i
$237$	−1.43782	−	0.830127i	−0.0933966	−	0.0539225i
$238$	−11.5981	−	23.8923i	−0.751792	−	1.54871i
$239$	−17.6603	+	17.6603i	−1.14235	+	1.14235i	−0.154327	+	0.988020i	$0.549321\pi$
$239$	−17.6603	+	17.6603i	−1.14235	+	1.14235i	−0.988020	+	0.154327i	$0.950679\pi$
$240$	2.23205	+	0.598076i	0.144078	+	0.0386057i
$241$	12.5263	+	3.35641i	0.806889	+	0.216205i	0.638606	−	0.769534i	$-0.279511\pi$
$241$	12.5263	+	3.35641i	0.806889	+	0.216205i	0.168282	+	0.985739i	$0.446178\pi$
$242$	−13.5622	−	13.5622i	−0.871810	−	0.871810i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−0.401924	+	0.696152i	−0.0257305	+	0.0445666i
$245$	0.428203	+	3.59808i	0.0273569	+	0.229873i
$246$			15.1962i			0.968871i
$247$	−10.0000	−	2.00000i	−0.636285	−	0.127257i
$248$		−	4.92820i		−	0.312941i
$249$	−2.53590	−	9.46410i	−0.160706	−	0.599763i
$250$	−8.42820	−	4.86603i	−0.533046	−	0.307754i
$251$	1.43782	+	2.49038i	0.0907545	+	0.157191i	0.907829	−	0.419341i	$-0.137739\pi$
$251$	1.43782	+	2.49038i	0.0907545	+	0.157191i	−0.817074	+	0.576532i	$0.804405\pi$
$252$	3.46410	−	3.00000i	0.218218	−	0.188982i
$253$	−4.19615	−	1.12436i	−0.263810	−	0.0706876i
$254$	7.36603	−	27.4904i	0.462186	−	1.72490i
$255$	1.90192	−	1.90192i	0.119103	−	0.119103i
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	5.69615	−	9.86603i	0.355316	−	0.615426i	−0.631856	−	0.775086i	$-0.717707\pi$
$257$	5.69615	−	9.86603i	0.355316	−	0.615426i	0.987172	+	0.159660i	$0.0510399\pi$
$258$	4.00000	+	14.9282i	0.249029	+	0.929389i
$259$	−0.490381	+	6.83013i	−0.0304708	+	0.424403i
$260$	0.633975	−	3.16987i	0.0393174	−	0.196587i
$261$	7.00000			0.433289
$262$	−7.09808	+	1.90192i	−0.438521	+	0.117501i
$263$	5.66025	−	9.80385i	0.349026	−	0.604531i	−0.637051	−	0.770822i	$-0.719846\pi$
$263$	5.66025	−	9.80385i	0.349026	−	0.604531i	0.986077	+	0.166291i	$0.0531791\pi$
$264$	−0.267949	−	0.464102i	−0.0164911	−	0.0285635i
$265$	−1.56218	−	1.56218i	−0.0959638	−	0.0959638i
$266$	−4.73205	+	13.6603i	−0.290141	+	0.837564i
$267$	1.16987	−	4.36603i	0.0715951	−	0.267196i
$268$	−7.39230	−	7.39230i	−0.451557	−	0.451557i
$269$	12.9282	−	7.46410i	0.788246	−	0.455094i	−0.0510984	−	0.998694i	$-0.516272\pi$
$269$	12.9282	−	7.46410i	0.788246	−	0.455094i	0.839345	+	0.543599i	$0.182939\pi$
$270$	0.866025	+	0.500000i	0.0527046	+	0.0304290i
$271$	1.09808	+	4.09808i	0.0667034	+	0.248940i	0.991224	−	0.132191i	$-0.0422012\pi$
$271$	1.09808	+	4.09808i	0.0667034	+	0.248940i	−0.924521	+	0.381131i	$0.875535\pi$
$272$	−23.1962			−1.40647
$273$	6.69615	+	6.79423i	0.405270	+	0.411205i
$274$	7.92820			0.478960
$275$	1.26795	+	4.73205i	0.0764602	+	0.285353i
$276$	−6.29423	−	3.63397i	−0.378868	−	0.218740i
$277$	11.7679	−	6.79423i	0.707068	−	0.408226i	−0.102907	−	0.994691i	$-0.532814\pi$
$277$	11.7679	−	6.79423i	0.707068	−	0.408226i	0.809974	+	0.586465i	$0.199481\pi$
$278$	−3.00000	−	3.00000i	−0.179928	−	0.179928i
$279$	2.46410	−	9.19615i	0.147522	−	0.550559i
$280$	0.669873	+	0.232051i	0.0400326	+	0.0138677i
$281$	−8.02628	−	8.02628i	−0.478808	−	0.478808i	0.425943	−	0.904750i	$-0.359943\pi$
$281$	−8.02628	−	8.02628i	−0.478808	−	0.478808i	−0.904750	+	0.425943i	$0.859943\pi$
$282$	−12.9282	−	22.3923i	−0.769863	−	1.33344i
$283$	−9.73205	+	16.8564i	−0.578510	+	1.00201i	0.417140	+	0.908842i	$0.363032\pi$
$283$	−9.73205	+	16.8564i	−0.578510	+	1.00201i	−0.995650	+	0.0931672i	$0.970301\pi$
$284$	9.46410	−	2.53590i	0.561591	−	0.150478i
$285$	−1.46410			−0.0867259
$286$	−6.00000	+	4.00000i	−0.354787	+	0.236525i
$287$	−1.49038	+	20.7583i	−0.0879744	+	1.22533i
$288$	−1.96410	−	7.33013i	−0.115736	−	0.431932i
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	−3.50000	−	6.06218i	−0.205527	−	0.355983i
$291$	0.267949	−	0.267949i	0.0157075	−	0.0157075i
$292$	4.62436	−	17.2583i	0.270620	−	1.00997i
$293$	−22.2583	−	5.96410i	−1.30035	−	0.348427i	−0.458765	−	0.888558i	$-0.651708\pi$
$293$	−22.2583	−	5.96410i	−1.30035	−	0.348427i	−0.841581	+	0.540131i	$0.818375\pi$
$294$	10.8301	−	8.09808i	0.631626	−	0.472289i
$295$	−1.36603	−	2.36603i	−0.0795331	−	0.137755i
$296$	1.16025	+	0.669873i	0.0674384	+	0.0389356i
$297$	−0.267949	−	1.00000i	−0.0155480	−	0.0580259i
$298$		−	37.0526i		−	2.14640i
$299$	6.70577	−	13.5622i	0.387805	−	0.784321i
$300$			8.19615i			0.473205i
$301$	4.00000	+	20.7846i	0.230556	+	1.19800i
$302$		0			0
$303$	−8.59808	+	4.96410i	−0.493947	+	0.285180i
$304$	8.92820	+	8.92820i	0.512068	+	0.512068i
$305$	−0.232051	−	0.0621778i	−0.0132872	−	0.00356029i
$306$	−9.69615	−	2.59808i	−0.554292	−	0.148522i
$307$	9.92820	−	9.92820i	0.566632	−	0.566632i	−0.364551	−	0.931183i	$-0.618778\pi$
$307$	9.92820	−	9.92820i	0.566632	−	0.566632i	0.931183	+	0.364551i	$0.118778\pi$
$308$	2.07180	+	4.26795i	0.118052	+	0.243189i
$309$	6.00000	+	3.46410i	0.341328	+	0.197066i
$310$	−9.19615	+	2.46410i	−0.522306	+	0.139952i
$311$	3.66025			0.207554			0.103777	−	0.994601i	$-0.466907\pi$
$311$	3.66025			0.207554			0.103777	+	0.994601i	$0.466907\pi$
$312$	1.76795	−	0.598076i	0.100090	−	0.0338594i
$313$			30.3923i			1.71787i	0.512081	+	0.858937i	$0.328875\pi$
$313$			30.3923i			1.71787i	−0.512081	+	0.858937i	$0.671125\pi$
$314$	34.8205	−	9.33013i	1.96503	−	0.526530i
$315$	1.13397	+	0.767949i	0.0638922	+	0.0432690i
$316$	2.49038	−	1.43782i	0.140095	−	0.0808838i
$317$	−0.241670	+	0.241670i	−0.0135735	+	0.0135735i	−0.713861	−	0.700287i	$-0.753055\pi$
$317$	−0.241670	+	0.241670i	−0.0135735	+	0.0135735i	0.700287	+	0.713861i	$0.253055\pi$
$318$	−2.13397	+	7.96410i	−0.119667	+	0.446605i
$319$	−1.87564	+	7.00000i	−0.105016	+	0.391925i
$320$	−2.09808	+	2.09808i	−0.117286	+	0.117286i
$321$	0.464102	−	0.267949i	0.0259036	−	0.0149555i
$322$	−17.7583	−	12.0263i	−0.989633	−	0.670198i
$323$	14.1962	−	3.80385i	0.789895	−	0.211652i
$324$		−	1.73205i		−	0.0962250i
$325$	−17.0263	+	1.09808i	−0.944448	+	0.0609103i
$326$	−25.1244			−1.39151
$327$	5.83013	−	1.56218i	0.322407	−	0.0863886i
$328$	3.52628	+	2.03590i	0.194706	+	0.112414i
$329$	−15.4641	−	31.8564i	−0.852564	−	1.75630i
$330$	−0.732051	+	0.732051i	−0.0402981	+	0.0402981i
$331$	20.7583	+	5.56218i	1.14098	+	0.305725i	0.779345	−	0.626595i	$-0.215552\pi$
$331$	20.7583	+	5.56218i	1.14098	+	0.305725i	0.361636	+	0.932320i	$0.382218\pi$
$332$	16.3923	+	4.39230i	0.899645	+	0.241059i
$333$	1.83013	+	1.83013i	0.100290	+	0.100290i
$334$	−15.2942	+	8.83013i	−0.836863	+	0.483163i
$335$	1.56218	−	2.70577i	0.0853509	−	0.147832i
$336$	−2.23205	−	11.5981i	−0.121768	−	0.632727i
$337$		−	17.5359i		−	0.955241i	−0.878566	−	0.477621i	$-0.841499\pi$
$337$		−	17.5359i		−	0.955241i	0.878566	−	0.477621i	$-0.158501\pi$
$338$	−9.56218	−	23.2224i	−0.520114	−	1.26313i
$339$		−	8.46410i		−	0.459707i
$340$	1.20577	+	4.50000i	0.0653921	+	0.244047i
$341$	8.53590	+	4.92820i	0.462245	+	0.266877i
$342$	2.73205	+	4.73205i	0.147732	+	0.255880i
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	4.00000	+	1.07180i	0.215666	+	0.0577874i
$345$	0.562178	−	2.09808i	0.0302666	−	0.112957i
$346$	15.4641	−	15.4641i	0.831355	−	0.831355i
$347$	5.83013	+	10.0981i	0.312978	+	0.542093i	0.979006	−	0.203834i	$-0.0653402\pi$
$347$	5.83013	+	10.0981i	0.312978	+	0.542093i	−0.666028	+	0.745927i	$0.732007\pi$
$348$	−6.06218	+	10.5000i	−0.324967	+	0.562859i
$349$	7.56218	+	28.2224i	0.404794	+	1.51071i	0.804435	+	0.594040i	$0.202468\pi$
$349$	7.56218	+	28.2224i	0.404794	+	1.51071i	−0.399641	+	0.916672i	$0.630865\pi$
$350$	−1.73205	+	24.1244i	−0.0925820	+	1.28950i
$351$	3.59808	−	0.232051i	0.192051	−	0.0123860i
$352$	7.85641			0.418748
$353$	7.69615	−	2.06218i	0.409625	−	0.109759i	−0.0481215	−	0.998841i	$-0.515323\pi$
$353$	7.69615	−	2.06218i	0.409625	−	0.109759i	0.457746	+	0.889083i	$0.348657\pi$
$354$	−5.09808	+	8.83013i	−0.270960	+	0.469316i
$355$	1.46410	+	2.53590i	0.0777064	+	0.134592i
$356$	5.53590	+	5.53590i	0.293402	+	0.293402i
$357$	−12.9904	−	4.50000i	−0.687524	−	0.238165i
$358$	−6.56218	+	24.4904i	−0.346822	+	1.29436i
$359$	−19.1962	−	19.1962i	−1.01313	−	1.01313i	−0.999913	−	0.0132216i	$-0.995791\pi$
$359$	−19.1962	−	19.1962i	−1.01313	−	1.01313i	−0.0132216	−	0.999913i	$-0.504209\pi$
$360$	0.232051	−	0.133975i	0.0122302	−	0.00706108i
$361$	9.52628	+	5.50000i	0.501383	+	0.289474i
$362$	−2.96410	−	11.0622i	−0.155790	−	0.581415i
$363$	−9.92820			−0.521096
$364$	−15.9904	+	4.16025i	−0.838124	+	0.218057i
$365$	5.33975			0.279495
$366$	0.232051	+	0.866025i	0.0121295	+	0.0452679i
$367$	19.2224	+	11.0981i	1.00340	+	0.579315i	0.909253	−	0.416243i	$-0.136654\pi$
$367$	19.2224	+	11.0981i	1.00340	+	0.579315i	0.0941495	+	0.995558i	$0.469987\pi$
$368$	−16.2224	+	9.36603i	−0.845653	+	0.488238i
$369$	5.56218	+	5.56218i	0.289555	+	0.289555i
$370$	0.669873	−	2.50000i	0.0348250	−	0.129969i
$371$	−3.69615	+	10.6699i	−0.191895	+	0.553952i
$372$	11.6603	+	11.6603i	0.604556	+	0.604556i
$373$	−13.8660	−	24.0167i	−0.717956	−	1.24354i	−0.961808	−	0.273723i	$-0.911745\pi$
$373$	−13.8660	−	24.0167i	−0.717956	−	1.24354i	0.243853	−	0.969812i	$-0.421589\pi$
$374$	5.19615	−	9.00000i	0.268687	−	0.465379i
$375$	−4.86603	+	1.30385i	−0.251280	+	0.0673304i
$376$	−6.92820			−0.357295
$377$	−22.6244	−	11.1865i	−1.16521	−	0.576136i
$378$	0.366025	−	5.09808i	0.0188263	−	0.262217i
$379$	2.87564	+	10.7321i	0.147712	+	0.551268i	0.999620	+	0.0275766i	$0.00877901\pi$
$379$	2.87564	+	10.7321i	0.147712	+	0.551268i	−0.851908	+	0.523692i	$0.824554\pi$
$380$	1.26795	−	2.19615i	0.0650444	−	0.112660i
$381$	−7.36603	−	12.7583i	−0.377373	−	0.653629i
$382$	−26.5885	+	26.5885i	−1.36038	+	1.36038i
$383$	5.75833	−	21.4904i	0.294237	−	1.09811i	−0.647585	−	0.761994i	$-0.724221\pi$
$383$	5.75833	−	21.4904i	0.294237	−	1.09811i	0.941821	−	0.336114i	$-0.109113\pi$
$384$	−3.96410	−	1.06218i	−0.202292	−	0.0542040i
$385$	−1.07180	+	0.928203i	−0.0546238	+	0.0473056i
$386$	20.2583	+	35.0885i	1.03112	+	1.78596i
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$	0.169873	+	0.633975i	0.00862399	+	0.0321852i
$389$			29.7321i			1.50747i	0.657176	+	0.753737i	$0.271751\pi$
$389$			29.7321i			1.50747i	−0.657176	+	0.753737i	$0.728249\pi$
$390$	−2.00000	−	3.00000i	−0.101274	−	0.151911i
$391$			21.8038i			1.10267i
$392$	−0.428203	−	3.59808i	−0.0216275	−	0.181730i
$393$	−1.90192	+	3.29423i	−0.0959394	+	0.166172i
$394$	7.56218	−	4.36603i	0.380977	−	0.219957i
$395$	0.607695	+	0.607695i	0.0305765	+	0.0305765i
$396$	1.73205	+	0.464102i	0.0870388	+	0.0233220i
$397$	−24.2224	−	6.49038i	−1.21569	−	0.325743i	−0.406697	−	0.913563i	$-0.633320\pi$
$397$	−24.2224	−	6.49038i	−1.21569	−	0.325743i	−0.808992	+	0.587820i	$0.799986\pi$
$398$	34.7846	−	34.7846i	1.74359	−	1.74359i
$399$	3.26795	+	6.73205i	0.163602	+	0.337024i
$400$	18.2942	+	10.5622i	0.914711	+	0.528109i
$401$	6.33013	−	1.69615i	0.316111	−	0.0847018i	−0.0972748	−	0.995258i	$-0.531013\pi$
$401$	6.33013	−	1.69615i	0.316111	−	0.0847018i	0.413386	+	0.910556i	$0.364346\pi$
$402$	−11.6603			−0.581561
$403$	−22.6603	+	25.7846i	−1.12879	+	1.28442i
$404$		−	17.1962i		−	0.855541i
$405$	0.500000	−	0.133975i	0.0248452	−	0.00665725i
$406$	−20.0622	+	29.6244i	−0.995669	+	1.47023i
$407$	−2.32051	+	1.33975i	−0.115023	+	0.0664087i
$408$	−1.90192	+	1.90192i	−0.0941593	+	0.0941593i
$409$	−3.23205	+	12.0622i	−0.159815	+	0.596436i	0.838830	+	0.544393i	$0.183240\pi$
$409$	−3.23205	+	12.0622i	−0.159815	+	0.596436i	−0.998645	+	0.0520432i	$0.983427\pi$
$410$	2.03590	−	7.59808i	0.100546	−	0.375242i
$411$	2.90192	−	2.90192i	0.143141	−	0.143141i
$412$	−10.3923	+	6.00000i	−0.511992	+	0.295599i
$413$	−7.83013	+	11.5622i	−0.385295	+	0.568938i
$414$	−7.83013	+	2.09808i	−0.384830	+	0.103115i
$415$			5.07180i			0.248965i
$416$	−5.36603	+	26.8301i	−0.263091	+	1.31546i
$417$	−2.19615			−0.107546
$418$	−5.46410	+	1.46410i	−0.267258	+	0.0716116i
$419$	26.6603	+	15.3923i	1.30244	+	0.751963i	0.980822	−	0.194907i	$-0.0624404\pi$
$419$	26.6603	+	15.3923i	1.30244	+	0.751963i	0.321617	+	0.946870i	$0.395774\pi$
$420$	−2.13397	+	1.03590i	−0.104127	+	0.0505467i
$421$	5.24167	−	5.24167i	0.255463	−	0.255463i	−0.567743	−	0.823206i	$-0.692183\pi$
$421$	5.24167	−	5.24167i	0.255463	−	0.255463i	0.823206	+	0.567743i	$0.192183\pi$
$422$	−23.1244	−	6.19615i	−1.12568	−	0.301624i
$423$	−12.9282	−	3.46410i	−0.628591	−	0.168430i
$424$	1.56218	+	1.56218i	0.0758661	+	0.0758661i
$425$	21.2942	−	12.2942i	1.03292	−	0.596358i
$426$	5.46410	−	9.46410i	0.264737	−	0.458537i
$427$	0.232051	+	1.20577i	0.0112297	+	0.0583514i
$428$			0.928203i			0.0448664i
$429$	−0.732051	+	3.66025i	−0.0353437	+	0.176719i
$430$		−	8.00000i		−	0.385794i
$431$	−4.36603	−	16.2942i	−0.210304	−	0.784865i	−0.987767	−	0.155937i	$-0.950160\pi$
$431$	−4.36603	−	16.2942i	−0.210304	−	0.784865i	0.777463	−	0.628929i	$-0.216506\pi$
$432$	−3.86603	−	2.23205i	−0.186004	−	0.107390i
$433$	7.06218	+	12.2321i	0.339387	+	0.587835i	0.984317	−	0.176406i	$-0.0564472\pi$
$433$	7.06218	+	12.2321i	0.339387	+	0.587835i	−0.644931	+	0.764241i	$0.723114\pi$
$434$	31.8564	+	36.7846i	1.52916	+	1.76572i
$435$	−3.50000	−	0.937822i	−0.167812	−	0.0449651i
$436$	−2.70577	+	10.0981i	−0.129583	+	0.483610i
$437$	8.39230	−	8.39230i	0.401458	−	0.401458i
$438$	−9.96410	−	17.2583i	−0.476103	−	0.824635i
$439$	−4.12436	+	7.14359i	−0.196845	+	0.340945i	−0.947504	−	0.319745i	$-0.896403\pi$
$439$	−4.12436	+	7.14359i	−0.196845	+	0.340945i	0.750659	+	0.660690i	$0.229736\pi$
$440$	0.0717968	+	0.267949i	0.00342278	+	0.0127740i
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	27.1865	+	23.8923i	1.29313	+	1.13644i
$443$	−10.3923			−0.493753			−0.246877	−	0.969047i	$-0.579404\pi$
$443$	−10.3923			−0.493753			−0.246877	+	0.969047i	$0.579404\pi$
$444$	−4.33013	+	1.16025i	−0.205499	+	0.0550632i
$445$	−1.16987	+	2.02628i	−0.0554573	+	0.0960549i
$446$	28.4904	+	49.3468i	1.34906	+	2.33664i
$447$	−13.5622	−	13.5622i	−0.641469	−	0.641469i
$448$	14.3301	+	4.96410i	0.677035	+	0.234532i
$449$	−2.83013	+	10.5622i	−0.133562	+	0.498460i	−1.00000		0.000825198i	$-0.999737\pi$
$449$	−2.83013	+	10.5622i	−0.133562	+	0.498460i	0.866438	+	0.499285i	$0.166404\pi$
$450$	6.46410	+	6.46410i	0.304721	+	0.304721i
$451$	−7.05256	+	4.07180i	−0.332092	+	0.191733i
$452$	12.6962	+	7.33013i	0.597177	+	0.344780i
$453$		0			0
$454$	−56.9808			−2.67424
$455$	−2.43782	−	4.29423i	−0.114287	−	0.201317i
$456$	1.46410			0.0685628
$457$	−8.47372	−	31.6244i	−0.396384	−	1.47932i	−0.819410	−	0.573208i	$-0.805699\pi$
$457$	−8.47372	−	31.6244i	−0.396384	−	1.47932i	0.423026	−	0.906117i	$-0.360968\pi$
$458$	−28.6865	−	16.5622i	−1.34043	−	0.773900i
$459$	−4.50000	+	2.59808i	−0.210042	+	0.121268i
$460$	2.66025	+	2.66025i	0.124035	+	0.124035i
$461$	8.96410	−	33.4545i	0.417500	−	1.55813i	−0.362275	−	0.932071i	$-0.618000\pi$
$461$	8.96410	−	33.4545i	0.417500	−	1.55813i	0.779775	−	0.626060i	$-0.215333\pi$
$462$	5.00000	+	1.73205i	0.232621	+	0.0805823i
$463$	2.19615	+	2.19615i	0.102064	+	0.102064i	0.756295	−	0.654231i	$-0.227008\pi$
$463$	2.19615	+	2.19615i	0.102064	+	0.102064i	−0.654231	+	0.756295i	$0.727008\pi$
$464$	15.6244	+	27.0622i	0.725343	+	1.25633i
$465$	−2.46410	+	4.26795i	−0.114270	+	0.197921i
$466$	−3.73205	+	1.00000i	−0.172884	+	0.0463241i
$467$	10.7846			0.499052			0.249526	−	0.968368i	$-0.419725\pi$
$467$	10.7846			0.499052			0.249526	+	0.968368i	$0.419725\pi$
$468$	−2.76795	+	5.59808i	−0.127948	+	0.258771i
$469$	−15.9282	−	1.14359i	−0.735496	−	0.0528062i
$470$	3.46410	+	12.9282i	0.159787	+	0.596334i
$471$	9.33013	−	16.1603i	0.429910	−	0.744625i
$472$	1.36603	+	2.36603i	0.0628764	+	0.108905i
$473$	−5.85641	+	5.85641i	−0.269278	+	0.269278i
$474$	0.830127	−	3.09808i	0.0381290	−	0.142299i
$475$	−12.9282	−	3.46410i	−0.593187	−	0.158944i
$476$	18.0000	−	15.5885i	0.825029	−	0.714496i
$477$	2.13397	+	3.69615i	0.0977080	+	0.169235i
$478$	−41.7846	−	24.1244i	−1.91118	−	1.10342i
$479$	4.80385	+	17.9282i	0.219493	+	0.819161i	0.984536	+	0.175181i	$0.0560511\pi$
$479$	4.80385	+	17.9282i	0.219493	+	0.819161i	−0.765043	+	0.643979i	$0.777282\pi$
$480$			3.92820i			0.179297i
$481$	−2.99038	−	8.83975i	−0.136350	−	0.403058i
$482$			25.0526i			1.14111i
$483$	−10.9019	+	2.09808i	−0.496055	+	0.0954658i
$484$	8.59808	−	14.8923i	0.390822	−	0.676923i
$485$	−0.169873	+	0.0980762i	−0.00771353	+	0.00445341i
$486$	−1.36603	−	1.36603i	−0.0619642	−	0.0619642i
$487$	−31.9545	−	8.56218i	−1.44800	−	0.387989i	−0.552670	−	0.833400i	$-0.686391\pi$
$487$	−31.9545	−	8.56218i	−1.44800	−	0.387989i	−0.895326	+	0.445411i	$0.853058\pi$
$488$	0.232051	+	0.0621778i	0.0105044	+	0.00281466i
$489$	−9.19615	+	9.19615i	−0.415864	+	0.415864i
$490$	−6.50000	+	2.59808i	−0.293640	+	0.117369i
$491$	−16.0981	−	9.29423i	−0.726496	−	0.419443i	0.0906429	−	0.995883i	$-0.471108\pi$
$491$	−16.0981	−	9.29423i	−0.726496	−	0.419443i	−0.817139	+	0.576441i	$0.804441\pi$
$492$	−13.1603	+	3.52628i	−0.593310	+	0.158977i
$493$	36.3731			1.63816
$494$	−1.26795	−	19.6603i	−0.0570477	−	0.884557i
$495$			0.535898i			0.0240868i
$496$	41.0526	−	11.0000i	1.84331	−	0.493915i
$497$	8.39230	−	12.3923i	0.376446	−	0.555871i
$498$	16.3923	−	9.46410i	0.734557	−	0.424097i
$499$	18.3923	−	18.3923i	0.823353	−	0.823353i	−0.163235	−	0.986587i	$-0.552193\pi$
$499$	18.3923	−	18.3923i	0.823353	−	0.823353i	0.986587	+	0.163235i	$0.0521928\pi$
$500$	2.25833	−	8.42820i	0.100996	−	0.376921i
$501$	−2.36603	+	8.83013i	−0.105706	+	0.394501i
$502$	−3.92820	+	3.92820i	−0.175324	+	0.175324i
$503$	−33.4641	+	19.3205i	−1.49209	+	0.861459i	−0.999959	−	0.00906194i	$-0.997115\pi$
$503$	−33.4641	+	19.3205i	−1.49209	+	0.861459i	−0.492132	+	0.870521i	$0.663782\pi$
$504$	−1.13397	−	0.767949i	−0.0505112	−	0.0342072i
$505$	4.96410	−	1.33013i	0.220900	−	0.0591899i
$506$		−	8.39230i		−	0.373083i
$507$	−12.0000	−	5.00000i	−0.532939	−	0.222058i
$508$	25.5167			1.13212
$509$	6.79423	−	1.82051i	0.301149	−	0.0806926i	−0.105081	−	0.994464i	$-0.533510\pi$
$509$	6.79423	−	1.82051i	0.301149	−	0.0806926i	0.406229	+	0.913771i	$0.366843\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$	−11.9186	−	24.5526i	−0.527247	−	1.08614i
$512$	20.6865	−	20.6865i	0.914224	−	0.914224i
$513$	2.73205	+	0.732051i	0.120623	+	0.0323208i
$514$	21.2583	+	5.69615i	0.937665	+	0.251247i
$515$	−2.53590	−	2.53590i	−0.111745	−	0.111745i
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	6.92820	−	12.0000i	0.304702	−	0.527759i
$518$	−12.9904	+	2.50000i	−0.570765	+	0.109844i
$519$		−	11.3205i		−	0.496915i
$520$	−0.964102	+	0.0621778i	−0.0422787	+	0.00272668i
$521$		−	6.60770i		−	0.289488i	−0.989469	−	0.144744i	$-0.953764\pi$
$521$		−	6.60770i		−	0.289488i	0.989469	−	0.144744i	$-0.0462359\pi$
$522$	3.50000	+	13.0622i	0.153191	+	0.571716i
$523$	−0.758330	−	0.437822i	−0.0331595	−	0.0191446i	0.483329	−	0.875439i	$-0.339428\pi$
$523$	−0.758330	−	0.437822i	−0.0331595	−	0.0191446i	−0.516488	+	0.856294i	$0.672761\pi$
$524$	−3.29423	−	5.70577i	−0.143909	−	0.249258i
$525$	8.19615	+	9.46410i	0.357709	+	0.413047i
$526$	21.1244	+	5.66025i	0.921066	+	0.246799i
$527$	12.8038	−	47.7846i	0.557744	−	2.08153i
$528$	3.26795	−	3.26795i	0.142219	−	0.142219i
$529$	−2.69615	−	4.66987i	−0.117224	−	0.203038i
$530$	2.13397	−	3.69615i	0.0926939	−	0.160551i
$531$	1.36603	+	5.09808i	0.0592805	+	0.221238i
$532$	−12.9282	−	0.928203i	−0.560509	−	0.0402427i
$533$	−9.08846	−	26.8660i	−0.393665	−	1.16370i
$534$	8.73205			0.377873
$535$	−0.267949	+	0.0717968i	−0.0115845	+	0.00310405i
$536$	−1.56218	+	2.70577i	−0.0674758	+	0.116872i
$537$	6.56218	+	11.3660i	0.283179	+	0.490480i
$538$	20.3923	+	20.3923i	0.879175	+	0.879175i
$539$	6.66025	+	2.85641i	0.286877	+	0.123034i
$540$	−0.232051	+	0.866025i	−0.00998588	+	0.0372678i
$541$	7.56218	+	7.56218i	0.325123	+	0.325123i	0.850729	−	0.525605i	$-0.176161\pi$
$541$	7.56218	+	7.56218i	0.325123	+	0.325123i	−0.525605	+	0.850729i	$0.676161\pi$
$542$	−7.09808	+	4.09808i	−0.304888	+	0.176027i
$543$	−5.13397	−	2.96410i	−0.220320	−	0.127202i
$544$	−10.2058	−	38.0885i	−0.437569	−	1.63303i
$545$	−3.12436			−0.133833
$546$	−9.33013	+	15.8923i	−0.399293	+	0.680128i
$547$	12.7321			0.544383			0.272192	−	0.962243i	$-0.412252\pi$
$547$	12.7321			0.544383			0.272192	+	0.962243i	$0.412252\pi$
$548$	1.83975	+	6.86603i	0.0785901	+	0.293302i
$549$	0.401924	+	0.232051i	0.0171537	+	0.00990369i
$550$	−8.19615	+	4.73205i	−0.349485	+	0.201775i
$551$	−14.0000	−	14.0000i	−0.596420	−	0.596420i
$552$	−0.562178	+	2.09808i	−0.0239279	+	0.0893001i
$553$	1.43782	−	4.15064i	0.0611424	−	0.176503i
$554$	18.5622	+	18.5622i	0.788631	+	0.788631i
$555$	−0.669873	−	1.16025i	−0.0284345	−	0.0492500i
$556$	1.90192	−	3.29423i	0.0806595	−	0.139706i
$557$	4.42820	−	1.18653i	0.187629	−	0.0502750i	−0.163781	−	0.986497i	$-0.552369\pi$
$557$	4.42820	−	1.18653i	0.187629	−	0.0502750i	0.351410	+	0.936222i	$0.385702\pi$
$558$	18.3923			0.778608
$559$	−16.0000	−	24.0000i	−0.676728	−	1.01509i
$560$	−0.437822	+	6.09808i	−0.0185014	+	0.257691i
$561$	−1.39230	−	5.19615i	−0.0587832	−	0.219382i
$562$	10.9641	−	18.9904i	0.462493	−	0.801061i
$563$	−10.9545	−	18.9737i	−0.461676	−	0.799647i	0.537368	−	0.843348i	$-0.319419\pi$
$563$	−10.9545	−	18.9737i	−0.461676	−	0.799647i	−0.999045	+	0.0437007i	$0.986085\pi$
$564$	16.3923	−	16.3923i	0.690241	−	0.690241i
$565$	−1.13397	+	4.23205i	−0.0477067	+	0.178044i
$566$	−36.3205	−	9.73205i	−1.52666	−	0.409069i
$567$	−1.73205	−	2.00000i	−0.0727393	−	0.0839921i
$568$	−1.46410	−	2.53590i	−0.0614323	−	0.106404i
$569$	−18.0000	−	10.3923i	−0.754599	−	0.435668i	0.0727541	−	0.997350i	$-0.476821\pi$
$569$	−18.0000	−	10.3923i	−0.754599	−	0.435668i	−0.827353	+	0.561682i	$0.810155\pi$
$570$	−0.732051	−	2.73205i	−0.0306622	−	0.114433i
$571$		−	36.5885i		−	1.53118i	−0.643329	−	0.765590i	$-0.722447\pi$
$571$		−	36.5885i		−	1.53118i	0.643329	−	0.765590i	$-0.277553\pi$
$572$	−4.85641	−	4.26795i	−0.203057	−	0.178452i
$573$			19.4641i			0.813125i
$574$	−39.4808	+	7.59808i	−1.64790	+	0.317138i
$575$	9.92820	−	17.1962i	0.414035	−	0.717129i
$576$	4.96410	−	2.86603i	0.206838	−	0.119418i
$577$	−8.83013	−	8.83013i	−0.367603	−	0.367603i	0.498999	−	0.866602i	$-0.333701\pi$
$577$	−8.83013	−	8.83013i	−0.367603	−	0.367603i	−0.866602	+	0.498999i	$0.833701\pi$
$578$	−18.6603	−	5.00000i	−0.776164	−	0.207973i
$579$	20.2583	+	5.42820i	0.841907	+	0.225588i
$580$	4.43782	−	4.43782i	0.184271	−	0.184271i
$581$	23.3205	−	11.3205i	0.967498	−	0.469654i
$582$	0.633975	+	0.366025i	0.0262791	+	0.0151722i
$583$	−4.26795	+	1.14359i	−0.176760	+	0.0473628i
$584$	−5.33975			−0.220960
$585$	−1.83013	−	0.366025i	−0.0756664	−	0.0151333i
$586$		−	44.5167i		−	1.83897i
$587$	21.9282	−	5.87564i	0.905074	−	0.242514i	0.223880	−	0.974617i	$-0.428128\pi$
$587$	21.9282	−	5.87564i	0.905074	−	0.242514i	0.681194	+	0.732103i	$0.261461\pi$
$588$	9.52628	+	7.50000i	0.392857	+	0.309295i
$589$	−23.3205	+	13.4641i	−0.960905	+	0.554779i
$590$	3.73205	−	3.73205i	0.153646	−	0.153646i
$591$	1.16987	−	4.36603i	0.0481221	−	0.179594i
$592$	−2.99038	+	11.1603i	−0.122904	+	0.458684i
$593$	−11.9019	+	11.9019i	−0.488753	+	0.488753i	−0.907913	−	0.419159i	$-0.862325\pi$
$593$	−11.9019	+	11.9019i	−0.488753	+	0.488753i	0.419159	+	0.907913i	$0.362325\pi$
$594$	1.73205	−	1.00000i	0.0710669	−	0.0410305i
$595$	5.89230	+	3.99038i	0.241561	+	0.163590i
$596$	32.0885	−	8.59808i	1.31439	−	0.352191i
$597$		−	25.4641i		−	1.04218i
$598$	28.6603	+	5.73205i	1.17200	+	0.234401i
$599$	−36.1962			−1.47893			−0.739467	−	0.673192i	$-0.764923\pi$
$599$	−36.1962			−1.47893			−0.739467	+	0.673192i	$0.764923\pi$
$600$	2.36603	−	0.633975i	0.0965926	−	0.0258819i
$601$	12.8205	+	7.40192i	0.522959	+	0.301931i	0.738145	−	0.674642i	$-0.235702\pi$
$601$	12.8205	+	7.40192i	0.522959	+	0.301931i	−0.215185	+	0.976573i	$0.569036\pi$
$602$	−36.7846	+	17.8564i	−1.49923	+	0.727773i
$603$	−4.26795	+	4.26795i	−0.173804	+	0.173804i
$604$		0			0
$605$	4.96410	+	1.33013i	0.201819	+	0.0540774i
$606$	−13.5622	−	13.5622i	−0.550926	−	0.550926i
$607$	−3.04552	+	1.75833i	−0.123614	+	0.0713684i	−0.560532	−	0.828133i	$-0.689403\pi$
$607$	−3.04552	+	1.75833i	−0.123614	+	0.0713684i	0.436918	+	0.899501i	$0.356070\pi$
$608$	−10.7321	+	18.5885i	−0.435242	+	0.753861i
$609$	3.50000	+	18.1865i	0.141827	+	0.736956i
$610$		−	0.464102i		−	0.0187909i
$611$	36.2487	+	31.8564i	1.46647	+	1.28877i
$612$		−	9.00000i		−	0.363803i
$613$	2.76795	+	10.3301i	0.111796	+	0.417230i	0.999027	−	0.0440957i	$-0.0140407\pi$
$613$	2.76795	+	10.3301i	0.111796	+	0.417230i	−0.887231	+	0.461326i	$0.847374\pi$
$614$	23.4904	+	13.5622i	0.947995	+	0.547325i
$615$	−2.03590	−	3.52628i	−0.0820953	−	0.142193i
$616$	1.07180	−	0.928203i	0.0431839	−	0.0373984i
$617$	34.6506	+	9.28461i	1.39498	+	0.373784i	0.876540	−	0.481329i	$-0.159846\pi$
$617$	34.6506	+	9.28461i	1.39498	+	0.373784i	0.518442	+	0.855113i	$0.326512\pi$
$618$	−3.46410	+	12.9282i	−0.139347	+	0.520049i
$619$	12.8564	−	12.8564i	0.516743	−	0.516743i	−0.399842	−	0.916584i	$-0.630935\pi$
$619$	12.8564	−	12.8564i	0.516743	−	0.516743i	0.916584	+	0.399842i	$0.130935\pi$
$620$	−4.26795	−	7.39230i	−0.171405	−	0.296882i
$621$	−2.09808	+	3.63397i	−0.0841929	+	0.145826i
$622$	1.83013	+	6.83013i	0.0733814	+	0.273863i
$623$	11.9282	+	0.856406i	0.477893	+	0.0343112i
$624$	8.92820	+	13.3923i	0.357414	+	0.536121i
$625$	−21.0526			−0.842102
$626$	−56.7128	+	15.1962i	−2.26670	+	0.607360i
$627$	−1.46410	+	2.53590i	−0.0584706	+	0.101274i
$628$	16.1603	+	27.9904i	0.644864	+	1.11694i
$629$	9.50962	+	9.50962i	0.379173	+	0.379173i
$630$	−0.866025	+	2.50000i	−0.0345033	+	0.0996024i
$631$	9.80385	−	36.5885i	0.390285	−	1.45656i	−0.439380	−	0.898301i	$-0.644802\pi$
$631$	9.80385	−	36.5885i	0.390285	−	1.45656i	0.829665	−	0.558262i	$-0.188532\pi$
$632$	−0.607695	−	0.607695i	−0.0241728	−	0.0241728i
$633$	−10.7321	+	6.19615i	−0.426561	+	0.246275i
$634$	−0.571797	−	0.330127i	−0.0227090	−	0.0131110i
$635$	1.97372	+	7.36603i	0.0783247	+	0.292312i
$636$	−7.39230			−0.293124
$637$	−14.3038	+	20.7942i	−0.566739	+	0.823897i
$638$	−14.0000			−0.554265
$639$	−1.46410	−	5.46410i	−0.0579190	−	0.216157i
$640$	1.83975	+	1.06218i	0.0727223	+	0.0419863i
$641$	28.7487	−	16.5981i	1.13551	−	0.655585i	0.190192	−	0.981747i	$-0.439089\pi$
$641$	28.7487	−	16.5981i	1.13551	−	0.655585i	0.945314	+	0.326162i	$0.105756\pi$
$642$	0.732051	+	0.732051i	0.0288917	+	0.0288917i
$643$	8.07180	−	30.1244i	0.318321	−	1.18799i	−0.602537	−	0.798091i	$-0.705844\pi$
$643$	8.07180	−	30.1244i	0.318321	−	1.18799i	0.920858	−	0.389898i	$-0.127490\pi$
$644$	6.29423	−	18.1699i	0.248027	−	0.715993i
$645$	−2.92820	−	2.92820i	−0.115298	−	0.115298i
$646$	14.1962	+	24.5885i	0.558540	+	0.967420i
$647$	−21.2224	+	36.7583i	−0.834340	+	1.44512i	0.0602269	+	0.998185i	$0.480818\pi$
$647$	−21.2224	+	36.7583i	−0.834340	+	1.44512i	−0.894567	+	0.446934i	$0.852516\pi$
$648$	−0.500000	+	0.133975i	−0.0196419	+	0.00526302i
$649$	−5.46410			−0.214485
$650$	−10.5622	−	31.2224i	−0.414283	−	1.22464i
$651$	25.1244	+	1.80385i	0.984701	+	0.0706984i
$652$	−5.83013	−	21.7583i	−0.228325	−	0.852122i
$653$	−13.2679	+	22.9808i	−0.519215	+	0.899307i	0.480536	+	0.876975i	$0.340442\pi$
$653$	−13.2679	+	22.9808i	−0.519215	+	0.899307i	−0.999751	+	0.0223315i	$0.992891\pi$
$654$	5.83013	+	10.0981i	0.227976	+	0.394866i
$655$	1.39230	−	1.39230i	0.0544019	−	0.0544019i
$656$	−9.08846	+	33.9186i	−0.354845	+	1.32430i
$657$	−9.96410	−	2.66987i	−0.388737	−	0.104162i
$658$	51.7128	−	44.7846i	2.01598	−	1.74589i
$659$	−4.39230	−	7.60770i	−0.171100	−	0.296354i	0.767705	−	0.640804i	$-0.221399\pi$
$659$	−4.39230	−	7.60770i	−0.171100	−	0.296354i	−0.938805	+	0.344450i	$0.888065\pi$
$660$	−0.803848	−	0.464102i	−0.0312897	−	0.0180651i
$661$	−6.79423	−	25.3564i	−0.264265	−	0.986250i	−0.962699	−	0.270575i	$-0.912786\pi$
$661$	−6.79423	−	25.3564i	−0.264265	−	0.986250i	0.698434	−	0.715675i	$-0.253881\pi$
$662$			41.5167i			1.61359i
$663$	18.6962	−	1.20577i	0.726098	−	0.0468283i
$664$		−	5.07180i		−	0.196824i
$665$	−0.732051	−	3.80385i	−0.0283877	−	0.147507i
$666$	−2.50000	+	4.33013i	−0.0968730	+	0.167789i
$667$	25.4378	−	14.6865i	0.984956	−	0.568665i
$668$	−11.1962	−	11.1962i	−0.433192	−	0.433192i
$669$	28.4904	+	7.63397i	1.10150	+	0.295147i
$670$	5.83013	+	1.56218i	0.225237	+	0.0603522i
$671$	−0.339746	+	0.339746i	−0.0131157	+	0.0131157i
$672$	18.0622	−	8.76795i	0.696764	−	0.338231i
$673$	32.0429	+	18.5000i	1.23516	+	0.713123i	0.968102	−	0.250557i	$-0.0806136\pi$
$673$	32.0429	+	18.5000i	1.23516	+	0.713123i	0.267063	+	0.963679i	$0.413947\pi$
$674$	32.7224	−	8.76795i	1.26042	−	0.337729i
$675$	4.73205			0.182137
$676$	17.8923	−	13.6699i	0.688166	−	0.525764i
$677$			1.60770i			0.0617887i	0.999523	+	0.0308944i	$0.00983555\pi$
$677$			1.60770i			0.0617887i	−0.999523	+	0.0308944i	$0.990164\pi$
$678$	15.7942	−	4.23205i	0.606574	−	0.162531i
$679$	0.830127	+	0.562178i	0.0318574	+	0.0215744i
$680$	1.20577	−	0.696152i	0.0462392	−	0.0266962i
$681$	−20.8564	+	20.8564i	−0.799219	+	0.799219i
$682$	−4.92820	+	18.3923i	−0.188711	+	0.704278i
$683$	−4.75833	+	17.7583i	−0.182072	+	0.679504i	0.813166	+	0.582032i	$0.197742\pi$
$683$	−4.75833	+	17.7583i	−0.182072	+	0.679504i	−0.995238	+	0.0974716i	$0.968924\pi$
$684$	−3.46410	+	3.46410i	−0.132453	+	0.132453i
$685$	−1.83975	+	1.06218i	−0.0702931	+	0.0405837i
$686$	26.4545	+	24.0885i	1.01004	+	0.919702i
$687$	−16.5622	+	4.43782i	−0.631886	+	0.169313i
$688$			35.7128i			1.36154i
$689$	−0.990381	−	15.3564i	−0.0377305	−	0.585032i
$690$	4.19615			0.159745
$691$	−23.4904	+	6.29423i	−0.893616	+	0.239444i	−0.676273	−	0.736651i	$-0.736406\pi$
$691$	−23.4904	+	6.29423i	−0.893616	+	0.239444i	−0.217344	+	0.976095i	$0.569739\pi$
$692$	16.9808	+	9.80385i	0.645512	+	0.372686i
$693$	2.46410	−	1.19615i	0.0936035	−	0.0454381i
$694$	−15.9282	+	15.9282i	−0.604626	+	0.604626i
$695$	1.09808	+	0.294229i	0.0416524	+	0.0111607i
$696$	3.50000	+	0.937822i	0.132667	+	0.0355481i
$697$	28.9019	+	28.9019i	1.09474	+	1.09474i
$698$	−48.8827	+	28.2224i	−1.85024	+	1.06823i
$699$	−1.00000	+	1.73205i	−0.0378235	+	0.0655122i
$700$	−21.2942	+	4.09808i	−0.804846	+	0.154893i
$701$			21.0718i			0.795871i	0.917413	+	0.397935i	$0.130273\pi$
$701$			21.0718i			0.795871i	−0.917413	+	0.397935i	$0.869727\pi$
$702$	2.23205	+	6.59808i	0.0842433	+	0.249028i
$703$		−	7.32051i		−	0.276098i
$704$	1.53590	+	5.73205i	0.0578863	+	0.216035i
$705$	6.00000	+	3.46410i	0.225973	+	0.130466i
$706$	7.69615	+	13.3301i	0.289649	+	0.501686i
$707$	−17.1962	−	19.8564i	−0.646728	−	0.746777i
$708$	−8.83013	−	2.36603i	−0.331856	−	0.0889207i
$709$	−4.69615	+	17.5263i	−0.176368	+	0.658213i	0.819947	+	0.572440i	$0.194003\pi$
$709$	−4.69615	+	17.5263i	−0.176368	+	0.658213i	−0.996315	+	0.0857737i	$0.972664\pi$
$710$	−4.00000	+	4.00000i	−0.150117	+	0.150117i
$711$	−0.830127	−	1.43782i	−0.0311322	−	0.0539225i
$712$	1.16987	−	2.02628i	0.0438428	−	0.0759380i
$713$	−10.3397	−	38.5885i	−0.387227	−	1.44515i
$714$	1.90192	−	26.4904i	0.0711777	−	0.991378i
$715$	0.856406	−	1.73205i	0.0320278	−	0.0647750i
$716$	−22.7321			−0.849537
$717$	−24.1244	+	6.46410i	−0.900941	+	0.241406i
$718$	26.2224	−	45.4186i	0.978612	−	1.69501i
$719$	9.29423	+	16.0981i	0.346616	+	0.600357i	0.985646	−	0.168825i	$-0.0539973\pi$
$719$	9.29423	+	16.0981i	0.346616	+	0.600357i	−0.639030	+	0.769182i	$0.720664\pi$
$720$	1.63397	+	1.63397i	0.0608946	+	0.0608946i
$721$	−6.00000	+	17.3205i	−0.223452	+	0.645049i
$722$	−5.50000	+	20.5263i	−0.204689	+	0.763909i
$723$	9.16987	+	9.16987i	0.341031	+	0.341031i
$724$	8.89230	−	5.13397i	0.330480	−	0.190803i
$725$	−28.6865	−	16.5622i	−1.06539	−	0.615104i
$726$	−4.96410	−	18.5263i	−0.184235	−	0.687575i
$727$	16.8756			0.625883			0.312942	−	0.949772i	$-0.398686\pi$
$727$	16.8756			0.625883			0.312942	+	0.949772i	$0.398686\pi$
$728$	2.43782	+	4.29423i	0.0903517	+	0.159155i
$729$	−1.00000			−0.0370370
$730$	2.66987	+	9.96410i	0.0988164	+	0.368788i
$731$	36.0000	+	20.7846i	1.33151	+	0.768747i
$732$	−0.696152	+	0.401924i	−0.0257305	+	0.0148555i
$733$	−23.3660	−	23.3660i	−0.863044	−	0.863044i	0.128647	−	0.991690i	$-0.458937\pi$
$733$	−23.3660	−	23.3660i	−0.863044	−	0.863044i	−0.991690	+	0.128647i	$0.958937\pi$
$734$	−11.0981	+	41.4186i	−0.409637	+	1.52879i
$735$	−1.42820	+	3.33013i	−0.0526801	+	0.122834i
$736$	−22.5167	−	22.5167i	−0.829975	−	0.829975i
$737$	−3.12436	−	5.41154i	−0.115087	−	0.199337i
$738$	−7.59808	+	13.1603i	−0.279689	+	0.484436i
$739$	−9.92820	+	2.66025i	−0.365215	+	0.0978590i	−0.436759	−	0.899578i	$-0.643874\pi$
$739$	−9.92820	+	2.66025i	−0.365215	+	0.0978590i	0.0715445	+	0.997437i	$0.477207\pi$
$740$	2.32051			0.0853036
$741$	−7.66025	−	6.73205i	−0.281406	−	0.247308i
$742$	−21.7583	−	1.56218i	−0.798773	−	0.0573494i
$743$	5.05256	+	18.8564i	0.185360	+	0.691774i	0.994553	+	0.104231i	$0.0332382\pi$
$743$	5.05256	+	18.8564i	0.185360	+	0.691774i	−0.809193	+	0.587543i	$0.800095\pi$
$744$	2.46410	−	4.26795i	0.0903383	−	0.156471i
$745$	4.96410	+	8.59808i	0.181871	+	0.315009i
$746$	37.8827	−	37.8827i	1.38698	−	1.38698i
$747$	2.53590	−	9.46410i	0.0927837	−	0.346273i
$748$	9.00000	+	2.41154i	0.329073	+	0.0881747i
$749$	0.928203	+	1.07180i	0.0339158	+	0.0391626i
$750$	−4.86603	−	8.42820i	−0.177682	−	0.307754i
$751$	18.1244	+	10.4641i	0.661367	+	0.381840i	0.792798	−	0.609485i	$-0.208624\pi$
$751$	18.1244	+	10.4641i	0.661367	+	0.381840i	−0.131431	+	0.991325i	$0.541957\pi$
$752$	−15.4641	−	57.7128i	−0.563918	−	2.10457i
$753$			2.87564i			0.104794i
$754$	9.56218	−	47.8109i	0.348234	−	1.74117i
$755$		0			0
$756$	4.50000	−	0.866025i	0.163663	−	0.0314970i
$757$	−8.00000	+	13.8564i	−0.290765	+	0.503620i	−0.973991	−	0.226587i	$-0.927243\pi$
$757$	−8.00000	+	13.8564i	−0.290765	+	0.503620i	0.683226	+	0.730207i	$0.260576\pi$
$758$	−18.5885	+	10.7321i	−0.675163	+	0.389806i
$759$	−3.07180	−	3.07180i	−0.111499	−	0.111499i
$760$	−0.732051	−	0.196152i	−0.0265543	−	0.00711520i
$761$	25.9545	+	6.95448i	0.940849	+	0.252100i	0.696475	−	0.717581i	$-0.254751\pi$
$761$	25.9545	+	6.95448i	0.940849	+	0.252100i	0.244374	+	0.969681i	$0.421417\pi$
$762$	20.1244	−	20.1244i	0.729028	−	0.729028i
$763$	6.97372	+	14.3660i	0.252466	+	0.520085i
$764$	−29.1962	−	16.8564i	−1.05628	−	0.609843i
$765$	2.59808	−	0.696152i	0.0939336	−	0.0251694i
$766$	42.9808			1.55296
$767$	3.73205	−	18.6603i	0.134757	−	0.673783i
$768$		−	19.3923i		−	0.699760i
$769$	−19.5622	+	5.24167i	−0.705430	+	0.189019i	−0.593662	−	0.804715i	$-0.702318\pi$
$769$	−19.5622	+	5.24167i	−0.705430	+	0.189019i	−0.111769	+	0.993734i	$0.535652\pi$
$770$	−2.26795	−	1.53590i	−0.0817312	−	0.0553499i
$771$	9.86603	−	5.69615i	0.355316	−	0.205142i
$772$	−25.6865	+	25.6865i	−0.924479	+	0.924479i
$773$	−7.36603	+	27.4904i	−0.264938	+	0.988760i	0.697351	+	0.716730i	$0.254362\pi$
$773$	−7.36603	+	27.4904i	−0.264938	+	0.988760i	−0.962289	+	0.272031i	$0.912305\pi$
$774$	−4.00000	+	14.9282i	−0.143777	+	0.536583i
$775$	−31.8564	+	31.8564i	−1.14432	+	1.14432i
$776$	0.169873	−	0.0980762i	0.00609808	−	0.00352073i
$777$	−3.83975	+	5.66987i	−0.137750	+	0.203406i
$778$	−55.4808	+	14.8660i	−1.98908	+	0.532973i
$779$		−	22.2487i		−	0.797143i
$780$	2.13397	−	2.42820i	0.0764085	−	0.0869436i
$781$	5.85641			0.209559
$782$	−40.6865	+	10.9019i	−1.45495	+	0.389852i
$783$	6.06218	+	3.50000i	0.216645	+	0.125080i
$784$	29.0167	−	11.5981i	1.03631	−	0.414217i
$785$	−6.83013	+	6.83013i	−0.243778	+	0.243778i
$786$	−7.09808	−	1.90192i	−0.253180	−	0.0678394i
$787$	3.46410	+	0.928203i	0.123482	+	0.0330869i	0.320031	−	0.947407i	$-0.396307\pi$
$787$	3.46410	+	0.928203i	0.123482	+	0.0330869i	−0.196549	+	0.980494i	$0.562973\pi$
$788$	5.53590	+	5.53590i	0.197208	+	0.197208i
$789$	9.80385	−	5.66025i	0.349026	−	0.201510i
$790$	−0.830127	+	1.43782i	−0.0295346	+	0.0511554i
$791$	21.9904	−	4.23205i	0.781888	−	0.150474i
$792$		−	0.535898i		−	0.0190423i
$793$	−0.928203	−	1.39230i	−0.0329615	−	0.0494422i
$794$		−	48.4449i		−	1.71924i
$795$	−0.571797	−	2.13397i	−0.0202795	−	0.0756843i
$796$	38.1962	+	22.0526i	1.35383	+	0.781632i
$797$	18.6603	+	32.3205i	0.660980	+	1.14485i	0.980358	+	0.197224i	$0.0631926\pi$
$797$	18.6603	+	32.3205i	0.660980	+	1.14485i	−0.319378	+	0.947627i	$0.603474\pi$
$798$	−10.9282	+	9.46410i	−0.386854	+	0.335026i
$799$	−67.1769	−	18.0000i	−2.37655	−	0.636794i
$800$	−9.29423	+	34.6865i	−0.328601	+	1.22635i
$801$	3.19615	−	3.19615i	0.112930	−	0.112930i
$802$	6.33013	+	10.9641i	0.223525	+	0.387156i
$803$	5.33975	−	9.24871i	0.188436	−	0.326380i
$804$	−2.70577	−	10.0981i	−0.0954252	−	0.356132i
$805$	5.73205	+	0.411543i	0.202028	+	0.0145050i
$806$	−59.4449	−	29.3923i	−2.09386	−	1.03530i
$807$	14.9282			0.525498
$808$	−4.96410	+	1.33013i	−0.174636	+	0.0467937i
$809$	−3.23205	+	5.59808i	−0.113633	+	0.196818i	−0.917232	−	0.398352i	$-0.869582\pi$
$809$	−3.23205	+	5.59808i	−0.113633	+	0.196818i	0.803600	+	0.595170i	$0.202915\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−0.928203	−	0.928203i	−0.0325936	−	0.0325936i	0.690622	−	0.723216i	$-0.257337\pi$
$811$	−0.928203	−	0.928203i	−0.0325936	−	0.0325936i	−0.723216	+	0.690622i	$0.757337\pi$
$812$	−30.3109	−	10.5000i	−1.06370	−	0.368478i
$813$	−1.09808	+	4.09808i	−0.0385112	+	0.143726i
$814$	−3.66025	−	3.66025i	−0.128292	−	0.128292i
$815$	5.83013	−	3.36603i	0.204220	−	0.117907i
$816$	−20.0885	−	11.5981i	−0.703237	−	0.406014i
$817$	−5.85641	−	21.8564i	−0.204890	−	0.764659i
$818$	−24.1244			−0.843488
$819$	2.40192	+	9.23205i	0.0839300	+	0.322594i
$820$	7.05256			0.246286
$821$	5.56218	+	20.7583i	0.194121	+	0.724471i	0.992493	+	0.122305i	$0.0390286\pi$
$821$	5.56218	+	20.7583i	0.194121	+	0.724471i	−0.798371	+	0.602166i	$0.794305\pi$
$822$	6.86603	+	3.96410i	0.239480	+	0.138264i
$823$	−41.7846	+	24.1244i	−1.45652	+	0.840922i	−0.998838	−	0.0481938i	$-0.984653\pi$
$823$	−41.7846	+	24.1244i	−1.45652	+	0.840922i	−0.457682	+	0.889116i	$0.651320\pi$
$824$	2.53590	+	2.53590i	0.0883422	+	0.0883422i
$825$	−1.26795	+	4.73205i	−0.0441443	+	0.164749i
$826$	−25.4904	−	8.83013i	−0.886924	−	0.307239i
$827$	−24.0718	−	24.0718i	−0.837058	−	0.837058i	0.151412	−	0.988471i	$-0.451618\pi$
$827$	−24.0718	−	24.0718i	−0.837058	−	0.837058i	−0.988471	+	0.151412i	$0.951618\pi$
$828$	−3.63397	−	6.29423i	−0.126289	−	0.218740i
$829$	−18.9904	+	32.8923i	−0.659563	+	1.14240i	0.321166	+	0.947023i	$0.395925\pi$
$829$	−18.9904	+	32.8923i	−0.659563	+	1.14240i	−0.980729	+	0.195374i	$0.937408\pi$
$830$	−9.46410	+	2.53590i	−0.328504	+	0.0880223i
$831$	13.5885			0.471378
$832$	−20.6244	+	1.33013i	−0.715021	+	0.0461139i
$833$	5.19615	−	36.0000i	0.180036	−	1.24733i
$834$	−1.09808	−	4.09808i	−0.0380233	−	0.141905i
$835$	2.36603	−	4.09808i	0.0818797	−	0.141820i
$836$	−2.53590	−	4.39230i	−0.0877059	−	0.151911i
$837$	6.73205	−	6.73205i	0.232694	−	0.232694i
$838$	−15.3923	+	57.4449i	−0.531718	+	1.98440i
$839$	18.5622	+	4.97372i	0.640838	+	0.171712i	0.564583	−	0.825376i	$-0.309037\pi$
$839$	18.5622	+	4.97372i	0.640838	+	0.171712i	0.0762548	+	0.997088i	$0.475704\pi$
$840$	0.464102	+	0.535898i	0.0160130	+	0.0184903i
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	12.4019	+	7.16025i	0.427399	+	0.246759i
$843$	−2.93782	−	10.9641i	−0.101184	−	0.377624i
$844$		−	21.4641i		−	0.738825i
$845$	5.33013	+	4.10770i	0.183362	+	0.141309i
$846$		−	25.8564i		−	0.888962i
$847$	−4.96410	−	25.7942i	−0.170569	−	0.886300i
$848$	−9.52628	+	16.5000i	−0.327134	+	0.566612i
$849$	−16.8564	+	9.73205i	−0.578510	+	0.334003i
$850$	33.5885	+	33.5885i	1.15207	+	1.15207i
$851$	10.4904	+	2.81089i	0.359606	+	0.0963560i
$852$	9.46410	+	2.53590i	0.324235	+	0.0868784i
$853$	14.5622	−	14.5622i	0.498599	−	0.498599i	−0.412402	−	0.911002i	$-0.635310\pi$
$853$	14.5622	−	14.5622i	0.498599	−	0.498599i	0.911002	+	0.412402i	$0.135310\pi$
$854$	−2.13397	+	1.03590i	−0.0730231	+	0.0354477i
$855$	−1.26795	−	0.732051i	−0.0433629	−	0.0250356i
$856$	0.267949	−	0.0717968i	0.00915831	−	0.00245396i
$857$	56.3205			1.92387			0.961936	−	0.273275i	$-0.0881069\pi$
$857$	56.3205			1.92387			0.961936	+	0.273275i	$0.0881069\pi$
$858$	−7.19615	+	0.464102i	−0.245673	+	0.0158442i
$859$		−	41.5167i		−	1.41653i	−0.705947	−	0.708265i	$-0.749478\pi$
$859$		−	41.5167i		−	1.41653i	0.705947	−	0.708265i	$-0.250522\pi$
$860$	6.92820	−	1.85641i	0.236250	−	0.0633029i
$861$	−11.6699	+	17.2321i	−0.397708	+	0.587267i
$862$	28.2224	−	16.2942i	0.961260	−	0.554984i
$863$	−11.8564	+	11.8564i	−0.403597	+	0.403597i	−0.879498	−	0.475902i	$-0.842122\pi$
$863$	−11.8564	+	11.8564i	−0.403597	+	0.403597i	0.475902	+	0.879498i	$0.342122\pi$
$864$	1.96410	−	7.33013i	0.0668201	−	0.249376i
$865$	−1.51666	+	5.66025i	−0.0515680	+	0.192454i
$866$	−19.2942	+	19.2942i	−0.655645	+	0.655645i
$867$	−8.66025	+	5.00000i	−0.294118	+	0.169809i
$868$	−24.4641	+	36.1244i	−0.830366	+	1.22614i
$869$	1.66025	−	0.444864i	0.0563203	−	0.0150910i
$870$		−	7.00000i		−	0.237322i
$871$	20.6147	−	6.97372i	0.698504	−	0.236296i
$872$	3.12436			0.105804
$873$	0.366025	−	0.0980762i	0.0123881	−	0.00331938i
$874$	19.8564	+	11.4641i	0.671653	+	0.387779i
$875$	−5.82051	−	11.9904i	−0.196769	−	0.405349i
$876$	12.6340	−	12.6340i	0.426862	−	0.426862i
$877$	39.8468	+	10.6769i	1.34553	+	0.360534i	0.858483	−	0.512842i	$-0.171407\pi$
$877$	39.8468	+	10.6769i	1.34553	+	0.360534i	0.487047	+	0.873376i	$0.338074\pi$
$878$	−15.3923	−	4.12436i	−0.519465	−	0.139190i
$879$	−16.2942	−	16.2942i	−0.549591	−	0.549591i
$880$	−2.07180	+	1.19615i	−0.0698403	+	0.0403223i
$881$	4.62436	−	8.00962i	0.155799	−	0.269851i	−0.777551	−	0.628820i	$-0.783538\pi$
$881$	4.62436	−	8.00962i	0.155799	−	0.269851i	0.933349	+	0.358969i	$0.116872\pi$
$882$	13.4282	−	1.59808i	0.452151	−	0.0538100i
$883$			40.9282i			1.37734i	0.725073	+	0.688672i	$0.241806\pi$
$883$			40.9282i			1.37734i	−0.725073	+	0.688672i	$0.758194\pi$
$884$	−14.3827	+	29.0885i	−0.483742	+	0.978351i
$885$		−	2.73205i		−	0.0918369i
$886$	−5.19615	−	19.3923i	−0.174568	−	0.651497i
$887$	−35.1051	−	20.2679i	−1.17871	−	0.680531i	−0.222998	−	0.974819i	$-0.571584\pi$
$887$	−35.1051	−	20.2679i	−1.17871	−	0.680531i	−0.955717	+	0.294288i	$0.904918\pi$
$888$	0.669873	+	1.16025i	0.0224795	+	0.0389356i
$889$	29.4641	−	25.5167i	0.988194	−	0.855801i
$890$	−4.36603	−	1.16987i	−0.146350	−	0.0392142i
$891$	0.267949	−	1.00000i	0.00897664	−	0.0335013i
$892$	−36.1244	+	36.1244i	−1.20953	+	1.20953i
$893$	18.9282	+	32.7846i	0.633408	+	1.09710i
$894$	18.5263	−	32.0885i	0.619611	−	1.07320i
$895$	−1.75833	−	6.56218i	−0.0587745	−	0.219349i
$896$	0.777568	−	10.8301i	0.0259767	−	0.361809i
$897$	12.5885	−	8.39230i	0.420316	−	0.280211i
$898$	−21.1244			−0.704929
$899$	−64.3731	+	17.2487i	−2.14696	+	0.575277i
$900$	−4.09808	+	7.09808i	−0.136603	+	0.236603i
$901$	11.0885	+	19.2058i	0.369410	+	0.639837i
$902$	−11.1244	−	11.1244i	−0.370401	−	0.370401i
$903$	−6.92820	+	20.0000i	−0.230556	+	0.665558i
$904$	1.13397	−	4.23205i	0.0377154	−	0.140756i
$905$	2.16987	+	2.16987i	0.0721290	+	0.0721290i
$906$		0			0
$907$	36.0788	+	20.8301i	1.19798	+	0.691653i	0.960104	−	0.279643i	$-0.0902161\pi$
$907$	36.0788	+	20.8301i	1.19798	+	0.691653i	0.237874	+	0.971296i	$0.423549\pi$
$908$	−13.2224	−	49.3468i	−0.438802	−	1.63763i
$909$	−9.92820			−0.329298
$910$	6.79423	−	6.69615i	0.225226	−	0.221975i
$911$	−18.9282			−0.627119			−0.313560	−	0.949568i	$-0.601522\pi$
$911$	−18.9282			−0.627119			−0.313560	+	0.949568i	$0.601522\pi$
$912$	3.26795	+	12.1962i	0.108213	+	0.403855i
$913$	8.78461	+	5.07180i	0.290728	+	0.167852i
$914$	54.7750	−	31.6244i	1.81180	−	1.04604i
$915$	−0.169873	−	0.169873i	−0.00561583	−	0.00561583i
$916$	7.68653	−	28.6865i	0.253970	−	0.947830i
$917$	−9.50962	−	3.29423i	−0.314035	−	0.108785i
$918$	−7.09808	−	7.09808i	−0.234271	−	0.234271i
$919$	−22.2224	−	38.4904i	−0.733050	−	1.26968i	−0.955573	−	0.294753i	$-0.904763\pi$
$919$	−22.2224	−	38.4904i	−0.733050	−	1.26968i	0.222523	−	0.974927i	$-0.428571\pi$
$920$	0.562178	−	0.973721i	0.0185345	−	0.0321026i
$921$	13.5622	−	3.63397i	0.446889	−	0.119744i
$922$	66.9090			2.20353
$923$	−4.00000	+	20.0000i	−0.131662	+	0.658308i
$924$	−0.339746	+	4.73205i	−0.0111768	+	0.155673i
$925$	−3.16987	−	11.8301i	−0.104225	−	0.388972i
$926$	−3.00000	+	5.19615i	−0.0985861	+	0.170756i
$927$	3.46410	+	6.00000i	0.113776	+	0.197066i
$928$	−37.5622	+	37.5622i	−1.23304	+	1.23304i
$929$	8.04294	−	30.0167i	0.263880	−	0.984815i	−0.699052	−	0.715071i	$-0.746394\pi$
$929$	8.04294	−	30.0167i	0.263880	−	0.984815i	0.962932	−	0.269744i	$-0.0869390\pi$
$930$	−9.19615	−	2.46410i	−0.301554	−	0.0808011i
$931$	−15.8564	+	11.8564i	−0.519673	+	0.388578i
$932$	−1.73205	−	3.00000i	−0.0567352	−	0.0982683i
$933$	3.16987	+	1.83013i	0.103777	+	0.0599157i
$934$	5.39230	+	20.1244i	0.176442	+	0.658489i
$935$			2.78461i			0.0910665i
$936$	1.83013	+	0.366025i	0.0598196	+	0.0119639i
$937$			29.1051i			0.950823i	0.879764	+	0.475411i	$0.157701\pi$
$937$			29.1051i			0.950823i	−0.879764	+	0.475411i	$0.842299\pi$
$938$	−5.83013	−	30.2942i	−0.190360	−	0.989142i
$939$	−15.1962	+	26.3205i	−0.495908	+	0.858937i
$940$	−10.3923	+	6.00000i	−0.338960	+	0.195698i
$941$	−3.67949	−	3.67949i	−0.119948	−	0.119948i	0.644585	−	0.764533i	$-0.277030\pi$
$941$	−3.67949	−	3.67949i	−0.119948	−	0.119948i	−0.764533	+	0.644585i	$0.777030\pi$
$942$	34.8205	+	9.33013i	1.13451	+	0.303992i
$943$	31.8827	+	8.54294i	1.03824	+	0.278196i
$944$	−16.6603	+	16.6603i	−0.542245	+	0.542245i
$945$	0.598076	+	1.23205i	0.0194554	+	0.0400786i
$946$	−13.8564	−	8.00000i	−0.450511	−	0.260102i
$947$	26.3923	−	7.07180i	0.857635	−	0.229803i	0.196901	−	0.980423i	$-0.436912\pi$
$947$	26.3923	−	7.07180i	0.857635	−	0.229803i	0.660733	+	0.750621i	$0.270245\pi$
$948$	2.87564			0.0933966
$949$	27.9378	+	24.5526i	0.906900	+	0.797010i
$950$		−	25.8564i		−	0.838893i
$951$	−0.330127	+	0.0884573i	−0.0107051	+	0.00286842i
$952$	−5.89230	−	3.99038i	−0.190971	−	0.129329i
$953$	−41.9090	+	24.1962i	−1.35756	+	0.783790i	−0.989295	−	0.145929i	$-0.953383\pi$
$953$	−41.9090	+	24.1962i	−1.35756	+	0.783790i	−0.368269	+	0.929719i	$0.620050\pi$
$954$	−5.83013	+	5.83013i	−0.188757	+	0.188757i
$955$	2.60770	−	9.73205i	0.0843830	−	0.314922i
$956$	11.1962	−	41.7846i	0.362109	−	1.35141i
$957$	−5.12436	+	5.12436i	−0.165647	+	0.165647i
$958$	−31.0526	+	17.9282i	−1.00326	+	0.579234i
$959$	8.99038	+	6.08846i	0.290315	+	0.196607i
$960$	−2.86603	+	0.767949i	−0.0925006	+	0.0247855i
$961$			59.6410i			1.92390i
$962$	15.0000	−	10.0000i	0.483619	−	0.322413i
$963$	0.535898			0.0172691
$964$	−21.6962	+	5.81347i	−0.698786	+	0.187239i
$965$	−9.40192	−	5.42820i	−0.302659	−	0.174740i
$966$	−9.36603	−	19.2942i	−0.301347	−	0.620782i
$967$	18.8564	−	18.8564i	0.606381	−	0.606381i	−0.335617	−	0.941998i	$-0.608945\pi$
$967$	18.8564	−	18.8564i	0.606381	−	0.606381i	0.941998	+	0.335617i	$0.108945\pi$
$968$	−4.96410	−	1.33013i	−0.159552	−	0.0427519i
$969$	14.1962	+	3.80385i	0.456046	+	0.122197i
$970$	−0.267949	−	0.267949i	−0.00860333	−	0.00860333i
$971$	−24.8827	+	14.3660i	−0.798523	+	0.461028i	−0.842955	−	0.537985i	$-0.819186\pi$
$971$	−24.8827	+	14.3660i	−0.798523	+	0.461028i	0.0444312	+	0.999012i	$0.485852\pi$
$972$	0.866025	−	1.50000i	0.0277778	−	0.0481125i
$973$	−1.09808	−	5.70577i	−0.0352027	−	0.182919i
$974$		−	63.9090i		−	2.04778i
$975$	−15.2942	−	7.56218i	−0.489807	−	0.242184i
$976$			2.07180i			0.0663166i
$977$	15.1795	+	56.6506i	0.485635	+	1.81241i	0.577184	+	0.816614i	$0.304151\pi$
$977$	15.1795	+	56.6506i	0.485635	+	1.81241i	−0.0915494	+	0.995801i	$0.529182\pi$
$978$	−21.7583	−	12.5622i	−0.695755	−	0.401694i
$979$	2.33975	+	4.05256i	0.0747786	+	0.129520i
$980$	−3.75833	−	5.02628i	−0.120055	−	0.160559i
$981$	5.83013	+	1.56218i	0.186142	+	0.0498765i
$982$	9.29423	−	34.6865i	0.296591	−	1.10689i
$983$	11.8756	−	11.8756i	0.378774	−	0.378774i	−0.491886	−	0.870660i	$-0.663692\pi$
$983$	11.8756	−	11.8756i	0.378774	−	0.378774i	0.870660	+	0.491886i	$0.163692\pi$
$984$	2.03590	+	3.52628i	0.0649021	+	0.112414i
$985$	−1.16987	+	2.02628i	−0.0372753	+	0.0645626i
$986$	18.1865	+	67.8731i	0.579177	+	2.16152i
$987$	2.53590	−	35.3205i	0.0807185	−	1.12426i
$988$	16.7321	−	5.66025i	0.532317	−	0.180077i
$989$	33.5692			1.06744
$990$	−1.00000	+	0.267949i	−0.0317821	+	0.00851598i
$991$	6.63397	−	11.4904i	0.210735	−	0.365004i	−0.741210	−	0.671274i	$-0.765748\pi$
$991$	6.63397	−	11.4904i	0.210735	−	0.365004i	0.951945	+	0.306270i	$0.0990809\pi$
$992$	36.1244	+	62.5692i	1.14695	+	1.98657i
$993$	15.1962	+	15.1962i	0.482235	+	0.482235i
$994$	27.3205	+	9.46410i	0.866554	+	0.300183i
$995$	−3.41154	+	12.7321i	−0.108153	+	0.403633i
$996$	12.0000	+	12.0000i	0.380235	+	0.380235i
$997$	26.1340	−	15.0885i	0.827671	−	0.477856i	−0.0253834	−	0.999678i	$-0.508081\pi$
$997$	26.1340	−	15.0885i	0.827671	−	0.477856i	0.853055	+	0.521822i	$0.174747\pi$
$998$	43.5167	+	25.1244i	1.37750	+	0.795298i
$999$	0.669873	+	2.50000i	0.0211938	+	0.0790965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.b.97.1	yes	4
3.2	odd	2		819.2.fm.a.370.1		4
7.6	odd	2		273.2.by.a.97.1	yes	4
13.11	odd	12		273.2.by.a.76.1	✓	4
21.20	even	2		819.2.fm.b.370.1		4
39.11	even	12		819.2.fm.b.622.1		4
91.76	even	12	inner	273.2.by.b.76.1	yes	4
273.167	odd	12		819.2.fm.a.622.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.a.76.1	✓	4	13.11	odd	12
273.2.by.a.97.1	yes	4	7.6	odd	2
273.2.by.b.76.1	yes	4	91.76	even	12	inner
273.2.by.b.97.1	yes	4	1.1	even	1	trivial
819.2.fm.a.370.1		4	3.2	odd	2
819.2.fm.a.622.1		4	273.167	odd	12
819.2.fm.b.370.1		4	21.20	even	2
819.2.fm.b.622.1		4	39.11	even	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.86603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.366025 - 0.366025i) q^{5} +(-0.500000 + 1.86603i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.366025 + 0.366025i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 1.86603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(-0.366025 - 0.366025i) q^{5} +(-0.500000 + 1.86603i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.366025 + 0.366025i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 0.267949i) q^{11} -1.73205 q^{12} +(-0.232051 - 3.59808i) q^{13} +(-5.09808 - 0.366025i) q^{14} +(-0.133975 - 0.500000i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(2.59808 + 4.50000i) q^{17} +(-1.36603 + 1.36603i) q^{18} +(0.732051 - 2.73205i) q^{19} +(0.866025 + 0.232051i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.63397 + 2.09808i) q^{23} +(0.133975 + 0.500000i) q^{24} -4.73205i q^{25} +(6.59808 - 2.23205i) q^{26} +1.00000i q^{27} +(-0.866025 - 4.50000i) q^{28} +(3.50000 - 6.06218i) q^{29} +(0.866025 - 0.500000i) q^{30} +(-6.73205 - 6.73205i) q^{31} +(-7.33013 - 1.96410i) q^{32} +(-1.00000 - 0.267949i) q^{33} +(-7.09808 + 7.09808i) q^{34} +(1.23205 - 0.598076i) q^{35} +(-1.50000 - 0.866025i) q^{36} +(2.50000 - 0.669873i) q^{37} +5.46410 q^{38} +(1.59808 - 3.23205i) q^{39} -0.267949i q^{40} +(7.59808 - 2.03590i) q^{41} +(-4.23205 - 2.86603i) q^{42} +(6.92820 - 4.00000i) q^{43} +(1.26795 - 1.26795i) q^{44} +(0.133975 - 0.500000i) q^{45} +(-2.09808 + 7.83013i) q^{46} +(-9.46410 + 9.46410i) q^{47} +(-3.86603 + 2.23205i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(8.83013 - 2.36603i) q^{50} +5.19615i q^{51} +(3.46410 + 5.19615i) q^{52} +4.26795 q^{53} +(-1.86603 + 0.500000i) q^{54} +(0.464102 + 0.267949i) q^{55} +(-1.23205 + 0.598076i) q^{56} +(2.00000 - 2.00000i) q^{57} +(13.0622 + 3.50000i) q^{58} +(5.09808 + 1.36603i) q^{59} +(0.633975 + 0.633975i) q^{60} +(0.401924 - 0.232051i) q^{61} +(9.19615 - 15.9282i) q^{62} +(-2.59808 + 0.500000i) q^{63} -5.73205i q^{64} +(-1.23205 + 1.40192i) q^{65} -2.00000i q^{66} +(1.56218 + 5.83013i) q^{67} +(-7.79423 - 4.50000i) q^{68} +(2.09808 + 3.63397i) q^{69} +(1.73205 + 2.00000i) q^{70} +(-5.46410 - 1.46410i) q^{71} +(-0.133975 + 0.500000i) q^{72} +(-7.29423 + 7.29423i) q^{73} +(2.50000 + 4.33013i) q^{74} +(2.36603 - 4.09808i) q^{75} +(1.26795 + 4.73205i) q^{76} +(0.196152 - 2.73205i) q^{77} +(6.83013 + 1.36603i) q^{78} -1.66025 q^{79} +(2.23205 - 0.598076i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.59808 + 13.1603i) q^{82} +(-6.92820 - 6.92820i) q^{83} +(1.50000 - 4.33013i) q^{84} +(0.696152 - 2.59808i) q^{85} +(10.9282 + 10.9282i) q^{86} +(6.06218 - 3.50000i) q^{87} +(-0.464102 - 0.267949i) q^{88} +(-1.16987 - 4.36603i) q^{89} +1.00000 q^{90} +(9.19615 + 2.53590i) q^{91} -7.26795 q^{92} +(-2.46410 - 9.19615i) q^{93} +(-22.3923 - 12.9282i) q^{94} +(-1.26795 + 0.732051i) q^{95} +(-5.36603 - 5.36603i) q^{96} +(0.0980762 - 0.366025i) q^{97} +(5.33013 - 12.4282i) q^{98} +(-0.732051 - 0.732051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 6 q^{13} - 10 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{19} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 4 q^{24} + 16 q^{26} + 14 q^{29} - 20 q^{31} - 12 q^{32} - 4 q^{33} - 18 q^{34} - 2 q^{35} - 6 q^{36} + 10 q^{37} + 8 q^{38} - 4 q^{39} + 20 q^{41} - 10 q^{42} + 12 q^{44} + 4 q^{45} + 2 q^{46} - 24 q^{47} - 12 q^{48} - 22 q^{49} + 18 q^{50} + 24 q^{53} - 4 q^{54} - 12 q^{55} + 2 q^{56} + 8 q^{57} + 28 q^{58} + 10 q^{59} + 6 q^{60} + 12 q^{61} + 16 q^{62} + 2 q^{65} - 18 q^{67} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 2 q^{73} + 10 q^{74} + 6 q^{75} + 12 q^{76} - 20 q^{77} + 10 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} + 20 q^{82} + 6 q^{84} - 18 q^{85} + 16 q^{86} + 12 q^{88} - 22 q^{89} + 4 q^{90} + 16 q^{91} - 36 q^{92} + 4 q^{93} - 48 q^{94} - 12 q^{95} - 18 q^{96} - 10 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 6 * q^13 - 10 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^19 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 4 * q^24 + 16 * q^26 + 14 * q^29 - 20 * q^31 - 12 * q^32 - 4 * q^33 - 18 * q^34 - 2 * q^35 - 6 * q^36 + 10 * q^37 + 8 * q^38 - 4 * q^39 + 20 * q^41 - 10 * q^42 + 12 * q^44 + 4 * q^45 + 2 * q^46 - 24 * q^47 - 12 * q^48 - 22 * q^49 + 18 * q^50 + 24 * q^53 - 4 * q^54 - 12 * q^55 + 2 * q^56 + 8 * q^57 + 28 * q^58 + 10 * q^59 + 6 * q^60 + 12 * q^61 + 16 * q^62 + 2 * q^65 - 18 * q^67 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 2 * q^73 + 10 * q^74 + 6 * q^75 + 12 * q^76 - 20 * q^77 + 10 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 + 20 * q^82 + 6 * q^84 - 18 * q^85 + 16 * q^86 + 12 * q^88 - 22 * q^89 + 4 * q^90 + 16 * q^91 - 36 * q^92 + 4 * q^93 - 48 * q^94 - 12 * q^95 - 18 * q^96 - 10 * q^97 + 4 * q^98 + 4 * q^99

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