LMFDB - Embedded newform 245.2.l.b.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(68,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("245.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.l (of order $12$, degree $4$, not 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:	$1.95633484952$
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:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.227
Dual form			245.2.l.b.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.86603i) q^{2} +(1.86603 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -3.73205i q^{6} +(0.366025 - 0.366025i) q^{8} +(0.633975 - 0.366025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.86603i) q^{2} +(1.86603 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -3.73205i q^{6} +(0.366025 - 0.366025i) q^{8} +(0.633975 - 0.366025i) q^{9} +(-3.23205 + 2.86603i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-3.23205 - 0.866025i) q^{12} +(2.00000 + 2.00000i) q^{13} +(-4.09808 - 1.36603i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-0.267949 - 1.00000i) q^{17} +(-0.366025 - 1.36603i) q^{18} +(1.36603 + 2.36603i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(6.96410 + 1.86603i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(4.73205 - 2.73205i) q^{26} +(-3.09808 + 3.09808i) q^{27} -3.00000i q^{29} +(-4.59808 + 6.96410i) q^{30} +(-0.464102 - 0.267949i) q^{31} +(-7.33013 + 1.96410i) q^{32} +(-0.366025 + 1.36603i) q^{33} -2.00000 q^{34} -1.26795 q^{36} +(-1.26795 + 4.73205i) q^{37} +(5.09808 - 1.36603i) q^{38} +(4.73205 + 2.73205i) q^{39} +(-1.13397 + 0.232051i) q^{40} -0.464102i q^{41} +(-5.83013 + 5.83013i) q^{43} +(1.09808 - 0.633975i) q^{44} +(-1.63397 - 0.0980762i) q^{45} +(6.96410 - 12.0622i) q^{46} +(-0.633975 - 0.169873i) q^{47} +(-6.09808 - 6.09808i) q^{48} +(9.56218 - 1.36603i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.26795 - 4.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(4.23205 + 7.33013i) q^{54} +(1.46410 - 0.732051i) q^{55} +(3.73205 + 3.73205i) q^{57} +(-5.59808 - 1.50000i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(4.96410 + 5.59808i) q^{60} +(7.33013 - 4.23205i) q^{61} +(-0.732051 + 0.732051i) q^{62} +5.73205i q^{64} +(-1.26795 - 6.19615i) q^{65} +(2.36603 + 1.36603i) q^{66} +(1.13397 - 0.303848i) q^{67} +(-0.464102 + 1.73205i) q^{68} +13.9282 q^{69} +4.73205 q^{71} +(0.0980762 - 0.366025i) q^{72} +(-3.46410 + 0.928203i) q^{73} +(8.19615 + 4.73205i) q^{74} +(5.96410 + 7.59808i) q^{75} -4.73205i q^{76} +(7.46410 - 7.46410i) q^{78} +(-5.83013 + 3.36603i) q^{79} +(-0.598076 + 9.96410i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.866025 - 0.232051i) q^{82} +(-3.09808 - 3.09808i) q^{83} +(-0.732051 + 2.19615i) q^{85} +(7.96410 + 13.7942i) q^{86} +(-1.50000 - 5.59808i) q^{87} +(0.0980762 + 0.366025i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(-1.00000 + 3.00000i) q^{90} +(-8.83013 - 8.83013i) q^{92} +(-1.00000 - 0.267949i) q^{93} +(-0.633975 + 1.09808i) q^{94} +(0.366025 - 6.09808i) q^{95} +(-12.6962 + 7.33013i) q^{96} +(-7.92820 + 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 4 * q^5 - 2 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 6 q^{12} + 8 q^{13} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{22} + 14 q^{23} + 2 q^{24} - 6 q^{25} + 12 q^{26} - 2 q^{27} - 8 q^{30} + 12 q^{31} - 12 q^{32} + 2 q^{33} - 8 q^{34} - 12 q^{36} - 12 q^{37} + 10 q^{38} + 12 q^{39} - 8 q^{40} - 6 q^{43} - 6 q^{44} - 10 q^{45} + 14 q^{46} - 6 q^{47} - 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} + 10 q^{54} - 8 q^{55} + 8 q^{57} - 12 q^{58} + 6 q^{59} + 6 q^{60} + 12 q^{61} + 4 q^{62} - 12 q^{65} + 6 q^{66} + 8 q^{67} + 12 q^{68} + 28 q^{69} + 12 q^{71} - 10 q^{72} + 12 q^{74} + 10 q^{75} + 16 q^{78} - 6 q^{79} + 8 q^{80} - 4 q^{81} - 2 q^{83} + 4 q^{85} + 18 q^{86} - 6 q^{87} - 10 q^{88} - 16 q^{89} - 4 q^{90} - 18 q^{92} - 4 q^{93} - 6 q^{94} - 2 q^{95} - 30 q^{96} - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 4 * q^5 - 2 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^11 - 6 * q^12 + 8 * q^13 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^22 + 14 * q^23 + 2 * q^24 - 6 * q^25 + 12 * q^26 - 2 * q^27 - 8 * q^30 + 12 * q^31 - 12 * q^32 + 2 * q^33 - 8 * q^34 - 12 * q^36 - 12 * q^37 + 10 * q^38 + 12 * q^39 - 8 * q^40 - 6 * q^43 - 6 * q^44 - 10 * q^45 + 14 * q^46 - 6 * q^47 - 14 * q^48 + 14 * q^50 - 4 * q^51 - 12 * q^52 + 10 * q^53 + 10 * q^54 - 8 * q^55 + 8 * q^57 - 12 * q^58 + 6 * q^59 + 6 * q^60 + 12 * q^61 + 4 * q^62 - 12 * q^65 + 6 * q^66 + 8 * q^67 + 12 * q^68 + 28 * q^69 + 12 * q^71 - 10 * q^72 + 12 * q^74 + 10 * q^75 + 16 * q^78 - 6 * q^79 + 8 * q^80 - 4 * q^81 - 2 * q^83 + 4 * q^85 + 18 * q^86 - 6 * q^87 - 10 * q^88 - 16 * q^89 - 4 * q^90 - 18 * q^92 - 4 * q^93 - 6 * q^94 - 2 * q^95 - 30 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.500000	−	1.86603i	0.353553	−	1.31948i	−0.528742	−	0.848783i	$-0.677336\pi$
$2$	0.500000	−	1.86603i	0.353553	−	1.31948i	0.882295	−	0.470696i	$-0.155997\pi$
$3$	1.86603	−	0.500000i	1.07735	−	0.288675i	0.323840	−	0.946112i	$-0.395026\pi$
$3$	1.86603	−	0.500000i	1.07735	−	0.288675i	0.753510	+	0.657437i	$0.228359\pi$
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$		−	3.73205i		−	1.52360i
$7$		0			0
$7$		0			0
$8$	0.366025	−	0.366025i	0.129410	−	0.129410i
$9$	0.633975	−	0.366025i	0.211325	−	0.122008i
$10$	−3.23205	+	2.86603i	−1.02206	+	0.906317i
$11$	−0.366025	+	0.633975i	−0.110361	+	0.191151i	−0.915916	−	0.401371i	$-0.868534\pi$
$11$	−0.366025	+	0.633975i	−0.110361	+	0.191151i	0.805555	+	0.592521i	$0.201867\pi$
$12$	−3.23205	−	0.866025i	−0.933013	−	0.250000i
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$		0			0
$15$	−4.09808	−	1.36603i	−1.05812	−	0.352706i
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	0.925790	−	0.378039i	$-0.123401\pi$
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	−0.990777	+	0.135503i	$0.956735\pi$
$18$	−0.366025	−	1.36603i	−0.0862730	−	0.321975i
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	0.979093	−	0.203411i	$-0.0652027\pi$
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	−0.665706	+	0.746214i	$0.731869\pi$
$20$	1.73205	+	3.46410i	0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	6.96410	+	1.86603i	1.45212	+	0.389093i	0.896759	−	0.442519i	$-0.145915\pi$
$23$	6.96410	+	1.86603i	1.45212	+	0.389093i	0.555357	+	0.831612i	$0.312582\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	4.73205	−	2.73205i	0.928032	−	0.535799i
$27$	−3.09808	+	3.09808i	−0.596225	+	0.596225i
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−4.59808	+	6.96410i	−0.839490	+	1.27147i
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	0.457743	−	0.889085i	$-0.348658\pi$
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	−0.541098	+	0.840959i	$0.681991\pi$
$32$	−7.33013	+	1.96410i	−1.29580	+	0.347207i
$33$	−0.366025	+	1.36603i	−0.0637168	+	0.237795i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−1.26795			−0.211325
$37$	−1.26795	+	4.73205i	−0.208450	+	0.777944i	0.779921	+	0.625878i	$0.215259\pi$
$37$	−1.26795	+	4.73205i	−0.208450	+	0.777944i	−0.988370	+	0.152066i	$0.951407\pi$
$38$	5.09808	−	1.36603i	0.827017	−	0.221599i
$39$	4.73205	+	2.73205i	0.757735	+	0.437478i
$40$	−1.13397	+	0.232051i	−0.179297	+	0.0366905i
$41$		−	0.464102i		−	0.0724805i	−0.999343	−	0.0362402i	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$		0			0
$43$	−5.83013	+	5.83013i	−0.889086	+	0.889086i	−0.994435	−	0.105349i	$-0.966404\pi$
$43$	−5.83013	+	5.83013i	−0.889086	+	0.889086i	0.105349	+	0.994435i	$0.466404\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$	−1.63397	−	0.0980762i	−0.243579	−	0.0146203i
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	0.212285	−	0.977208i	$-0.431909\pi$
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	−0.304760	+	0.952429i	$0.598576\pi$
$48$	−6.09808	−	6.09808i	−0.880181	−	0.880181i
$49$		0			0
$50$	9.56218	−	1.36603i	1.35230	−	0.193185i
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−1.26795	−	4.73205i	−0.175833	−	0.656217i
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	0.718677	−	0.695344i	$-0.244748\pi$
$54$	4.23205	+	7.33013i	0.575909	+	0.997504i
$55$	1.46410	−	0.732051i	0.197419	−	0.0987097i
$56$		0			0
$57$	3.73205	+	3.73205i	0.494322	+	0.494322i
$58$	−5.59808	−	1.50000i	−0.735063	−	0.196960i
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	−0.928609	−	0.371060i	$-0.878995\pi$
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	0.785652	+	0.618669i	$0.212328\pi$
$60$	4.96410	+	5.59808i	0.640863	+	0.722709i
$61$	7.33013	−	4.23205i	0.938527	−	0.541859i	0.0490285	−	0.998797i	$-0.484387\pi$
$61$	7.33013	−	4.23205i	0.938527	−	0.541859i	0.889498	+	0.456939i	$0.151054\pi$
$62$	−0.732051	+	0.732051i	−0.0929705	+	0.0929705i
$63$		0			0
$64$			5.73205i			0.716506i
$65$	−1.26795	−	6.19615i	−0.157270	−	0.768538i
$66$	2.36603	+	1.36603i	0.291238	+	0.168146i
$67$	1.13397	−	0.303848i	0.138537	−	0.0371209i	−0.188884	−	0.981999i	$-0.560487\pi$
$67$	1.13397	−	0.303848i	0.138537	−	0.0371209i	0.327421	+	0.944878i	$0.393820\pi$
$68$	−0.464102	+	1.73205i	−0.0562806	+	0.210042i
$69$	13.9282			1.67676
$70$		0			0
$71$	4.73205			0.561591			0.280796	−	0.959768i	$-0.409402\pi$
$71$	4.73205			0.561591			0.280796	+	0.959768i	$0.409402\pi$
$72$	0.0980762	−	0.366025i	0.0115584	−	0.0431365i
$73$	−3.46410	+	0.928203i	−0.405442	+	0.108638i	−0.455776	−	0.890094i	$-0.650638\pi$
$73$	−3.46410	+	0.928203i	−0.405442	+	0.108638i	0.0503336	+	0.998732i	$0.483972\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$	5.96410	+	7.59808i	0.688675	+	0.877350i
$76$		−	4.73205i		−	0.542803i
$77$		0			0
$78$	7.46410	−	7.46410i	0.845143	−	0.845143i
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	−0.790728	−	0.612167i	$-0.790298\pi$
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	0.134788	+	0.990874i	$0.456965\pi$
$80$	−0.598076	+	9.96410i	−0.0668670	+	1.11402i
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−0.866025	−	0.232051i	−0.0956365	−	0.0256257i
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	0.516331	−	0.856389i	$-0.327297\pi$
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	−0.856389	+	0.516331i	$0.827297\pi$
$84$		0			0
$85$	−0.732051	+	2.19615i	−0.0794021	+	0.238206i
$86$	7.96410	+	13.7942i	0.858791	+	1.48747i
$87$	−1.50000	−	5.59808i	−0.160817	−	0.600177i
$88$	0.0980762	+	0.366025i	0.0104550	+	0.0390184i
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.0349934	−	0.999388i	$-0.511141\pi$
$90$	−1.00000	+	3.00000i	−0.105409	+	0.316228i
$91$		0			0
$92$	−8.83013	−	8.83013i	−0.920604	−	0.920604i
$93$	−1.00000	−	0.267949i	−0.103695	−	0.0277850i
$94$	−0.633975	+	1.09808i	−0.0653895	+	0.113258i
$95$	0.366025	−	6.09808i	0.0375534	−	0.625649i
$96$	−12.6962	+	7.33013i	−1.29580	+	0.748128i
$97$	−7.92820	+	7.92820i	−0.804987	+	0.804987i	−0.983870	−	0.178883i	$-0.942752\pi$
$97$	−7.92820	+	7.92820i	−0.804987	+	0.804987i	0.178883	+	0.983870i	$0.442752\pi$
$98$		0			0
$99$			0.535898i			0.0538598i
$100$	1.03590	−	8.59808i	0.103590	−	0.859808i
$101$	10.1603	+	5.86603i	1.01098	+	0.583691i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	10.1603	+	5.86603i	1.01098	+	0.583691i	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−3.73205	+	1.00000i	−0.369528	+	0.0990148i
$103$	0.598076	−	2.23205i	0.0589302	−	0.219931i	−0.930181	−	0.367102i	$-0.880350\pi$
$103$	0.598076	−	2.23205i	0.0589302	−	0.219931i	0.989111	+	0.147171i	$0.0470168\pi$
$104$	1.46410			0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	2.30385	−	8.59808i	0.222721	−	0.831207i	−0.760583	−	0.649240i	$-0.775087\pi$
$107$	2.30385	−	8.59808i	0.222721	−	0.831207i	0.983305	−	0.181967i	$-0.0582464\pi$
$108$	7.33013	−	1.96410i	0.705342	−	0.188996i
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.217557	−	0.976048i	$-0.569809\pi$
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.954061	+	0.299614i	$0.903142\pi$
$110$	−0.633975	−	3.09808i	−0.0604471	−	0.295390i
$111$			9.46410i			0.898293i
$112$		0			0
$113$	−4.26795	+	4.26795i	−0.401495	+	0.401495i	−0.878760	−	0.477265i	$-0.841628\pi$
$113$	−4.26795	+	4.26795i	−0.401495	+	0.401495i	0.477265	+	0.878760i	$0.341628\pi$
$114$	8.83013	−	5.09808i	0.827017	−	0.477479i
$115$	−10.6962	−	12.0622i	−0.997421	−	1.12480i
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$	2.00000	+	0.535898i	0.184900	+	0.0495438i
$118$	3.00000	+	3.00000i	0.276172	+	0.276172i
$119$		0			0
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	5.23205	+	9.06218i	0.475641	+	0.823834i
$122$	−4.23205	−	15.7942i	−0.383152	−	1.42994i
$123$	−0.232051	−	0.866025i	−0.0209233	−	0.0780869i
$124$	0.464102	+	0.803848i	0.0416776	+	0.0721876i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$	−6.46410	−	6.46410i	−0.573596	−	0.573596i	0.359535	−	0.933132i	$-0.382935\pi$
$127$	−6.46410	−	6.46410i	−0.573596	−	0.573596i	−0.933132	+	0.359535i	$0.882935\pi$
$128$	−3.96410	−	1.06218i	−0.350380	−	0.0938841i
$129$	−7.96410	+	13.7942i	−0.701200	+	1.21451i
$130$	−12.1962	−	0.732051i	−1.06967	−	0.0642051i
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	−0.786872	−	0.617117i	$-0.788301\pi$
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	0.141003	+	0.990009i	$0.454967\pi$
$132$	1.73205	−	1.73205i	0.150756	−	0.150756i
$133$		0			0
$134$		−	2.26795i		−	0.195921i
$135$	9.59808	−	1.96410i	0.826071	−	0.169043i
$136$	−0.464102	−	0.267949i	−0.0397964	−	0.0229765i
$137$	−10.4641	+	2.80385i	−0.894009	+	0.239549i	−0.676441	−	0.736496i	$-0.736479\pi$
$137$	−10.4641	+	2.80385i	−0.894009	+	0.239549i	−0.217567	+	0.976045i	$0.569812\pi$
$138$	6.96410	−	25.9904i	0.592824	−	2.21245i
$139$	−11.6603			−0.989010			−0.494505	−	0.869175i	$-0.664651\pi$
$139$	−11.6603			−0.989010			−0.494505	+	0.869175i	$0.664651\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$	2.36603	−	8.83013i	0.198552	−	0.741008i
$143$	−2.00000	+	0.535898i	−0.167248	+	0.0448141i
$144$	−2.83013	−	1.63397i	−0.235844	−	0.136165i
$145$	−3.69615	+	5.59808i	−0.306949	+	0.464895i
$146$			6.92820i			0.573382i
$147$		0			0
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	−0.841488	−	0.540276i	$-0.818320\pi$
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	0.0471484	+	0.998888i	$0.484987\pi$
$150$	17.1603	−	7.33013i	1.40113	−	0.598502i
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	−0.433350	−	0.901226i	$-0.642669\pi$
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	0.997159	−	0.0753205i	$-0.0239980\pi$
$152$	1.36603	+	0.366025i	0.110799	+	0.0296886i
$153$	−0.535898	−	0.535898i	−0.0433248	−	0.0433248i
$154$		0			0
$155$	0.535898	+	1.07180i	0.0430444	+	0.0860888i
$156$	−4.73205	−	8.19615i	−0.378867	−	0.656217i
$157$	6.36603	+	23.7583i	0.508064	+	1.89612i	0.438948	+	0.898513i	$0.355351\pi$
$157$	6.36603	+	23.7583i	0.508064	+	1.89612i	0.0691164	+	0.997609i	$0.477982\pi$
$158$	3.36603	+	12.5622i	0.267787	+	0.999393i
$159$	−6.83013	−	11.8301i	−0.541664	−	0.938190i
$160$	16.0981	+	5.36603i	1.27266	+	0.424222i
$161$		0			0
$162$	14.5622	+	14.5622i	1.14411	+	1.14411i
$163$	−5.36603	−	1.43782i	−0.420300	−	0.112619i	0.0424696	−	0.999098i	$-0.486477\pi$
$163$	−5.36603	−	1.43782i	−0.420300	−	0.112619i	−0.462769	+	0.886479i	$0.653144\pi$
$164$	−0.401924	+	0.696152i	−0.0313850	+	0.0543604i
$165$	2.36603	−	2.09808i	0.184195	−	0.163335i
$166$	−7.33013	+	4.23205i	−0.568928	+	0.328471i
$167$	10.7583	−	10.7583i	0.832505	−	0.832505i	−0.155354	−	0.987859i	$-0.549652\pi$
$167$	10.7583	−	10.7583i	0.832505	−	0.832505i	0.987859	+	0.155354i	$0.0496519\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	3.73205	+	2.46410i	0.286235	+	0.188988i
$171$	1.73205	+	1.00000i	0.132453	+	0.0764719i
$172$	13.7942	−	3.69615i	1.05180	−	0.281829i
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	0.206197	+	0.978511i	$0.433891\pi$
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	−0.667827	+	0.744317i	$0.732775\pi$
$174$	−11.1962			−0.848778
$175$		0			0
$176$	3.26795			0.246331
$177$	−1.09808	+	4.09808i	−0.0825365	+	0.308030i
$178$	−31.0885	+	8.33013i	−2.33018	+	0.624369i
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.977812	−	0.209483i	$-0.0671781\pi$
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.307488	+	0.951552i	$0.400511\pi$
$180$	2.36603	+	1.56218i	0.176353	+	0.116438i
$181$		−	9.19615i		−	0.683545i	−0.939783	−	0.341772i	$-0.888973\pi$
$181$		−	9.19615i		−	0.683545i	0.939783	−	0.341772i	$-0.111027\pi$
$182$		0			0
$183$	11.5622	−	11.5622i	0.854701	−	0.854701i
$184$	3.23205	−	1.86603i	0.238270	−	0.137565i
$185$	8.19615	−	7.26795i	0.602593	−	0.534350i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	0.732051	+	0.196152i	0.0535329	+	0.0143441i
$188$	0.803848	+	0.803848i	0.0586266	+	0.0586266i
$189$		0			0
$190$	−11.1962	−	3.73205i	−0.812254	−	0.270751i
$191$	−8.36603	−	14.4904i	−0.605344	−	1.04849i	−0.991997	−	0.126262i	$-0.959702\pi$
$191$	−8.36603	−	14.4904i	−0.605344	−	1.04849i	0.386653	−	0.922225i	$-0.373631\pi$
$192$	2.86603	+	10.6962i	0.206838	+	0.771928i
$193$	0.830127	+	3.09808i	0.0597539	+	0.223004i	0.989346	−	0.145587i	$-0.0465070\pi$
$193$	0.830127	+	3.09808i	0.0597539	+	0.223004i	−0.929592	+	0.368591i	$0.879840\pi$
$194$	10.8301	+	18.7583i	0.777558	+	1.34677i
$195$	−5.46410	−	10.9282i	−0.391292	−	0.782585i
$196$		0			0
$197$	14.1244	+	14.1244i	1.00632	+	1.00632i	0.999980	+	0.00633876i	$0.00201770\pi$
$197$	14.1244	+	14.1244i	1.00632	+	1.00632i	0.00633876	+	0.999980i	$0.497982\pi$
$198$	1.00000	+	0.267949i	0.0710669	+	0.0190423i
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.0361978	−	0.999345i	$-0.488475\pi$
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.847359	−	0.531021i	$-0.178191\pi$
$200$	2.40192	+	0.964102i	0.169842	+	0.0681723i
$201$	1.96410	−	1.13397i	0.138537	−	0.0799844i
$202$	16.0263	−	16.0263i	1.12761	−	1.12761i
$203$		0			0
$204$			3.46410i			0.242536i
$205$	−0.571797	+	0.866025i	−0.0399360	+	0.0604858i
$206$	−3.86603	−	2.23205i	−0.269359	−	0.155514i
$207$	5.09808	−	1.36603i	0.354341	−	0.0949453i
$208$	3.26795	−	12.1962i	0.226592	−	0.845651i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	10.1962			0.701932			0.350966	−	0.936388i	$-0.385853\pi$
$211$	10.1962			0.701932			0.350966	+	0.936388i	$0.385853\pi$
$212$	−3.16987	+	11.8301i	−0.217708	+	0.812496i
$213$	8.83013	−	2.36603i	0.605030	−	0.162117i
$214$	−14.8923	−	8.59808i	−1.01802	−	0.587752i
$215$	18.0622	−	3.69615i	1.23183	−	0.252076i
$216$			2.26795i			0.154314i
$217$		0			0
$218$	−19.2942	+	19.2942i	−1.30677	+	1.30677i
$219$	−6.00000	+	3.46410i	−0.405442	+	0.234082i
$220$	−2.83013	−	0.169873i	−0.190807	−	0.0114528i
$221$	1.46410	−	2.53590i	0.0984861	−	0.170583i
$222$	17.6603	+	4.73205i	1.18528	+	0.317594i
$223$	6.12436	+	6.12436i	0.410117	+	0.410117i	0.881779	−	0.471662i	$-0.156346\pi$
$223$	6.12436	+	6.12436i	0.410117	+	0.410117i	−0.471662	+	0.881779i	$0.656346\pi$
$224$		0			0
$225$	2.92820	+	2.19615i	0.195214	+	0.146410i
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	0.965048	−	0.262072i	$-0.0844059\pi$
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	−0.966792	+	0.255563i	$0.917739\pi$
$228$	−2.36603	−	8.83013i	−0.156694	−	0.584789i
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	0.823794	−	0.566890i	$-0.191853\pi$
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	−0.902838	+	0.429981i	$0.858520\pi$
$230$	−27.8564	+	13.9282i	−1.83680	+	0.918399i
$231$		0			0
$232$	−1.09808	−	1.09808i	−0.0720922	−	0.0720922i
$233$	1.73205	+	0.464102i	0.113470	+	0.0304043i	0.315107	−	0.949056i	$-0.397959\pi$
$233$	1.73205	+	0.464102i	0.113470	+	0.0304043i	−0.201637	+	0.979460i	$0.564626\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$	0.973721	+	1.09808i	0.0635185	+	0.0716306i
$236$	3.29423	−	1.90192i	0.214436	−	0.123805i
$237$	−9.19615	+	9.19615i	−0.597354	+	0.597354i
$238$		0			0
$239$		−	18.3923i		−	1.18970i	−0.803837	−	0.594850i	$-0.797212\pi$
$239$		−	18.3923i		−	1.18970i	0.803837	−	0.594850i	$-0.202788\pi$
$240$	3.86603	+	18.8923i	0.249551	+	1.21949i
$241$	−14.5359	−	8.39230i	−0.936340	−	0.540596i	−0.0475286	−	0.998870i	$-0.515135\pi$
$241$	−14.5359	−	8.39230i	−0.936340	−	0.540596i	−0.888811	+	0.458274i	$0.848468\pi$
$242$	19.5263	−	5.23205i	1.25520	−	0.336329i
$243$	−1.92820	+	7.19615i	−0.123694	+	0.461633i
$244$	−14.6603			−0.938527
$245$		0			0
$246$	−1.73205			−0.110432
$247$	−2.00000	+	7.46410i	−0.127257	+	0.474929i
$248$	−0.267949	+	0.0717968i	−0.0170148	+	0.00455910i
$249$	−7.33013	−	4.23205i	−0.464528	−	0.268195i
$250$	−19.5263	−	9.23205i	−1.23495	−	0.583886i
$251$			5.85641i			0.369653i	0.982771	+	0.184827i	$0.0591723\pi$
$251$			5.85641i			0.369653i	−0.982771	+	0.184827i	$0.940828\pi$
$252$		0			0
$253$	−3.73205	+	3.73205i	−0.234632	+	0.234632i
$254$	−15.2942	+	8.83013i	−0.959645	+	0.554051i
$255$	−0.267949	+	4.46410i	−0.0167796	+	0.279553i
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	0.172600	−	0.984992i	$-0.444783\pi$
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	−0.343020	+	0.939328i	$0.611450\pi$
$258$	21.7583	+	21.7583i	1.35461	+	1.35461i
$259$		0			0
$260$	−3.46410	+	10.3923i	−0.214834	+	0.644503i
$261$	−1.09808	−	1.90192i	−0.0679692	−	0.117726i
$262$	4.26795	+	15.9282i	0.263675	+	0.984048i
$263$	2.16025	+	8.06218i	0.133207	+	0.497135i	0.999999	−	0.00153494i	$-0.000488585\pi$
$263$	2.16025	+	8.06218i	0.133207	+	0.497135i	−0.866792	+	0.498670i	$0.833822\pi$
$264$	0.366025	+	0.633975i	0.0225273	+	0.0390184i
$265$	−5.00000	+	15.0000i	−0.307148	+	0.921443i
$266$		0			0
$267$	−22.7583	−	22.7583i	−1.39279	−	1.39279i
$268$	−1.96410	−	0.526279i	−0.119977	−	0.0321476i
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	−0.782457	−	0.622705i	$-0.786034\pi$
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	0.930507	+	0.366275i	$0.119367\pi$
$270$	1.13397	−	18.8923i	0.0690115	−	1.14975i
$271$	21.4186	−	12.3660i	1.30109	−	0.751183i	0.320496	−	0.947250i	$-0.396150\pi$
$271$	21.4186	−	12.3660i	1.30109	−	0.751183i	0.980590	+	0.196067i	$0.0628171\pi$
$272$	−3.26795	+	3.26795i	−0.198149	+	0.198149i
$273$		0			0
$274$			20.9282i			1.26432i
$275$	−3.63397	−	0.437822i	−0.219137	−	0.0264017i
$276$	−20.8923	−	12.0622i	−1.25757	−	0.726058i
$277$	19.3923	−	5.19615i	1.16517	−	0.312207i	0.376141	−	0.926562i	$-0.377251\pi$
$277$	19.3923	−	5.19615i	1.16517	−	0.312207i	0.789029	+	0.614356i	$0.210584\pi$
$278$	−5.83013	+	21.7583i	−0.349668	+	1.30498i
$279$	−0.392305			−0.0234867
$280$		0			0
$281$	12.9282			0.771232			0.385616	−	0.922659i	$-0.373989\pi$
$281$	12.9282			0.771232			0.385616	+	0.922659i	$0.373989\pi$
$282$	−0.633975	+	2.36603i	−0.0377526	+	0.140895i
$283$	26.4904	−	7.09808i	1.57469	−	0.421937i	0.637413	−	0.770523i	$-0.280005\pi$
$283$	26.4904	−	7.09808i	1.57469	−	0.421937i	0.937277	+	0.348586i	$0.113338\pi$
$284$	−7.09808	−	4.09808i	−0.421193	−	0.243176i
$285$	−2.36603	−	11.5622i	−0.140151	−	0.684884i
$286$			4.00000i			0.236525i
$287$		0			0
$288$	−3.92820	+	3.92820i	−0.231472	+	0.231472i
$289$	13.7942	−	7.96410i	0.811425	−	0.468477i
$290$	8.59808	+	9.69615i	0.504896	+	0.569378i
$291$	−10.8301	+	18.7583i	−0.634873	+	1.09963i
$292$	6.00000	+	1.60770i	0.351123	+	0.0940832i
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.996993	−	0.0774974i	$-0.975307\pi$
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.0774974	−	0.996993i	$-0.524693\pi$
$294$		0			0
$295$	4.39230	−	2.19615i	0.255730	−	0.127865i
$296$	1.26795	+	2.19615i	0.0736980	+	0.127649i
$297$	−0.830127	−	3.09808i	−0.0481689	−	0.179769i
$298$	5.59808	+	20.8923i	0.324288	+	1.21026i
$299$	10.1962	+	17.6603i	0.589659	+	1.02132i
$300$	−2.36603	−	16.5622i	−0.136603	−	0.956218i
$301$		0			0
$302$	−18.9282	−	18.9282i	−1.08920	−	1.08920i
$303$	21.8923	+	5.86603i	1.25768	+	0.336994i
$304$	6.09808	−	10.5622i	0.349749	−	0.605782i
$305$	−18.8923	−	1.13397i	−1.08177	−	0.0649312i
$306$	−1.26795	+	0.732051i	−0.0724838	+	0.0418486i
$307$	9.29423	−	9.29423i	0.530450	−	0.530450i	−0.390257	−	0.920706i	$-0.627614\pi$
$307$	9.29423	−	9.29423i	0.530450	−	0.530450i	0.920706	+	0.390257i	$0.127614\pi$
$308$		0			0
$309$		−	4.46410i		−	0.253954i
$310$	2.26795	−	0.464102i	0.128811	−	0.0263592i
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.0362898	−	0.999341i	$-0.511554\pi$
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.883600	+	0.468243i	$0.844887\pi$
$312$	2.73205	−	0.732051i	0.154672	−	0.0414442i
$313$	−5.19615	+	19.3923i	−0.293704	+	1.09612i	0.648537	+	0.761183i	$0.275381\pi$
$313$	−5.19615	+	19.3923i	−0.293704	+	1.09612i	−0.942241	+	0.334935i	$0.891286\pi$
$314$	47.5167			2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	−1.19615	+	4.46410i	−0.0671826	+	0.250729i	−0.991347	−	0.131265i	$-0.958096\pi$
$317$	−1.19615	+	4.46410i	−0.0671826	+	0.250729i	0.924165	+	0.381994i	$0.124763\pi$
$318$	−25.4904	+	6.83013i	−1.42943	+	0.383015i
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$	7.06218	−	10.6962i	0.394788	−	0.597933i
$321$		−	17.1962i		−	0.959796i
$322$		0			0
$323$	2.00000	−	2.00000i	0.111283	−	0.111283i
$324$	15.9904	−	9.23205i	0.888355	−	0.512892i
$325$	−5.26795	+	13.1244i	−0.292213	+	0.728008i
$326$	−5.36603	+	9.29423i	−0.297197	+	0.514760i
$327$	−26.3564	−	7.06218i	−1.45751	−	0.390539i
$328$	−0.169873	−	0.169873i	−0.00937967	−	0.00937967i
$329$		0			0
$330$	−2.73205	−	5.46410i	−0.150394	−	0.300789i
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	−0.964633	−	0.263597i	$-0.915091\pi$
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	0.254035	−	0.967195i	$-0.418242\pi$
$332$	1.96410	+	7.33013i	0.107794	+	0.402293i
$333$	0.928203	+	3.46410i	0.0508652	+	0.189832i
$334$	−14.6962	−	25.4545i	−0.804138	−	1.39281i
$335$	−2.49038	−	0.830127i	−0.136064	−	0.0453547i
$336$		0			0
$337$	16.4641	+	16.4641i	0.896857	+	0.896857i	0.995157	−	0.0983001i	$-0.0313405\pi$
$337$	16.4641	+	16.4641i	0.896857	+	0.896857i	−0.0983001	+	0.995157i	$0.531340\pi$
$338$	−9.33013	−	2.50000i	−0.507492	−	0.135982i
$339$	−5.83013	+	10.0981i	−0.316649	+	0.548452i
$340$	3.00000	−	2.66025i	0.162698	−	0.144273i
$341$	0.339746	−	0.196152i	0.0183983	−	0.0106222i
$342$	2.73205	−	2.73205i	0.147732	−	0.147732i
$343$		0			0
$344$			4.26795i			0.230112i
$345$	−25.9904	−	17.1603i	−1.39928	−	0.923877i
$346$	39.2487	+	22.6603i	2.11002	+	1.21822i
$347$	7.79423	−	2.08846i	0.418416	−	0.112114i	−0.0434674	−	0.999055i	$-0.513840\pi$
$347$	7.79423	−	2.08846i	0.418416	−	0.112114i	0.461884	+	0.886941i	$0.347174\pi$
$348$	−2.59808	+	9.69615i	−0.139272	+	0.519768i
$349$	−9.73205			−0.520945			−0.260472	−	0.965481i	$-0.583878\pi$
$349$	−9.73205			−0.520945			−0.260472	+	0.965481i	$0.583878\pi$
$350$		0			0
$351$	−12.3923			−0.661452
$352$	1.43782	−	5.36603i	0.0766362	−	0.286010i
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	−0.398777	−	0.917048i	$-0.630565\pi$
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	0.113173	+	0.993575i	$0.463899\pi$
$354$	7.09808	+	4.09808i	0.377258	+	0.217810i
$355$	−8.83013	−	5.83013i	−0.468654	−	0.309431i
$356$			28.8564i			1.52939i
$357$		0			0
$358$	27.1244	−	27.1244i	1.43357	−	1.43357i
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	−0.137675	−	0.990478i	$-0.543963\pi$
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	0.788941	+	0.614468i	$0.210629\pi$
$360$	−0.633975	+	0.562178i	−0.0334134	+	0.0296294i
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−17.1603	−	4.59808i	−0.901923	−	0.241670i
$363$	14.2942	+	14.2942i	0.750252	+	0.750252i
$364$		0			0
$365$	7.60770	+	2.53590i	0.398205	+	0.132735i
$366$	−15.7942	−	27.3564i	−0.825578	−	1.42994i
$367$	−0.500000	−	1.86603i	−0.0260998	−	0.0974057i	0.951647	−	0.307193i	$-0.0993896\pi$
$367$	−0.500000	−	1.86603i	−0.0260998	−	0.0974057i	−0.977747	+	0.209787i	$0.932723\pi$
$368$	−8.33013	−	31.0885i	−0.434238	−	1.62060i
$369$	−0.169873	−	0.294229i	−0.00884323	−	0.0153169i
$370$	−9.46410	−	18.9282i	−0.492015	−	0.984030i
$371$		0			0
$372$	1.26795	+	1.26795i	0.0657401	+	0.0657401i
$373$	15.9282	+	4.26795i	0.824731	+	0.220986i	0.646414	−	0.762987i	$-0.276268\pi$
$373$	15.9282	+	4.26795i	0.824731	+	0.220986i	0.178317	+	0.983973i	$0.442935\pi$
$374$	0.732051	−	1.26795i	0.0378534	−	0.0655641i
$375$	−1.76795	−	21.5263i	−0.0912965	−	1.11161i
$376$	−0.294229	+	0.169873i	−0.0151737	+	0.00876053i
$377$	6.00000	−	6.00000i	0.309016	−	0.309016i
$378$		0			0
$379$			19.6603i			1.00988i	0.863155	+	0.504940i	$0.168485\pi$
$379$			19.6603i			1.00988i	−0.863155	+	0.504940i	$0.831515\pi$
$380$	−5.83013	+	8.83013i	−0.299079	+	0.452976i
$381$	−15.2942	−	8.83013i	−0.783547	−	0.452381i
$382$	−31.2224	+	8.36603i	−1.59748	+	0.428043i
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	−0.450797	−	0.892626i	$-0.648860\pi$
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	0.836715	−	0.547638i	$-0.184473\pi$
$384$	−7.92820			−0.404584
$385$		0			0
$386$	6.19615			0.315376
$387$	−1.56218	+	5.83013i	−0.0794100	+	0.296362i
$388$	18.7583	−	5.02628i	0.952310	−	0.255171i
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	0.291009	−	0.956720i	$-0.406009\pi$
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	−0.683040	+	0.730381i	$0.739342\pi$
$390$	−23.1244	+	4.73205i	−1.17095	+	0.239617i
$391$		−	7.46410i		−	0.377476i
$392$		0			0
$393$	−11.6603	+	11.6603i	−0.588182	+	0.588182i
$394$	33.4186	−	19.2942i	1.68360	−	0.972029i
$395$	15.0263	+	0.901924i	0.756054	+	0.0453807i
$396$	0.464102	−	0.803848i	0.0233220	−	0.0403949i
$397$	20.0263	+	5.36603i	1.00509	+	0.269313i	0.723577	−	0.690244i	$-0.242497\pi$
$397$	20.0263	+	5.36603i	1.00509	+	0.269313i	0.281514	+	0.959557i	$0.409164\pi$
$398$	−34.0526	−	34.0526i	−1.70690	−	1.70690i
$399$		0			0
$400$	13.3923	−	17.8564i	0.669615	−	0.892820i
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	0.695392	−	0.718631i	$-0.255231\pi$
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	−0.970049	+	0.242911i	$0.921898\pi$
$402$	−1.13397	−	4.23205i	−0.0565575	−	0.211076i
$403$	−0.392305	−	1.46410i	−0.0195421	−	0.0729321i
$404$	−10.1603	−	17.5981i	−0.505492	−	0.875537i
$405$	21.3205	−	10.6603i	1.05942	−	0.529712i
$406$		0			0
$407$	−2.53590	−	2.53590i	−0.125700	−	0.125700i
$408$	−1.00000	−	0.267949i	−0.0495074	−	0.0132655i
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	−0.938249	−	0.345961i	$-0.887553\pi$
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	0.768735	+	0.639567i	$0.220886\pi$
$410$	1.33013	+	1.50000i	0.0656903	+	0.0740797i
$411$	−18.1244	+	10.4641i	−0.894009	+	0.516156i
$412$	−2.83013	+	2.83013i	−0.139430	+	0.139430i
$413$		0			0
$414$		−	10.1962i		−	0.501114i
$415$	1.96410	+	9.59808i	0.0964140	+	0.471151i
$416$	−18.5885	−	10.7321i	−0.911374	−	0.526182i
$417$	−21.7583	+	5.83013i	−1.06551	+	0.285503i
$418$	−1.00000	+	3.73205i	−0.0489116	+	0.182541i
$419$	3.85641			0.188398			0.0941989	−	0.995553i	$-0.469971\pi$
$419$	3.85641			0.188398			0.0941989	+	0.995553i	$0.469971\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	5.09808	−	19.0263i	0.248170	−	0.926185i
$423$	−0.464102	+	0.124356i	−0.0225654	+	0.00604638i
$424$	−3.16987	−	1.83013i	−0.153943	−	0.0888788i
$425$	4.07180	−	3.19615i	0.197511	−	0.155036i
$426$		−	17.6603i		−	0.855642i
$427$		0			0
$428$	−10.9019	+	10.9019i	−0.526964	+	0.526964i
$429$	−3.46410	+	2.00000i	−0.167248	+	0.0965609i
$430$	2.13397	−	35.5526i	0.102909	−	1.71450i
$431$	2.09808	−	3.63397i	0.101061	−	0.175042i	−0.811061	−	0.584961i	$-0.801110\pi$
$431$	2.09808	−	3.63397i	0.101061	−	0.175042i	0.912122	+	0.409919i	$0.134443\pi$
$432$	18.8923	+	5.06218i	0.908956	+	0.243554i
$433$	24.4641	+	24.4641i	1.17567	+	1.17567i	0.980836	+	0.194833i	$0.0624166\pi$
$433$	24.4641	+	24.4641i	1.17567	+	1.17567i	0.194833	+	0.980836i	$0.437583\pi$
$434$		0			0
$435$	−4.09808	+	12.2942i	−0.196488	+	0.589463i
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	5.09808	+	19.0263i	0.243874	+	0.910150i
$438$	3.46410	+	12.9282i	0.165521	+	0.617733i
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	0.949054	+	0.315113i	$0.102043\pi$
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	−0.201631	+	0.979462i	$0.564624\pi$
$440$	0.267949	−	0.803848i	0.0127740	−	0.0383219i
$441$		0			0
$442$	−4.00000	−	4.00000i	−0.190261	−	0.190261i
$443$	−3.50000	−	0.937822i	−0.166290	−	0.0445573i	0.174713	−	0.984619i	$-0.444100\pi$
$443$	−3.50000	−	0.937822i	−0.166290	−	0.0445573i	−0.341003	+	0.940062i	$0.610767\pi$
$444$	8.19615	−	14.1962i	0.388972	−	0.673720i
$445$	−2.23205	+	37.1865i	−0.105809	+	1.76281i
$446$	14.4904	−	8.36603i	0.686139	−	0.396143i
$447$	−15.2942	+	15.2942i	−0.723392	+	0.723392i
$448$		0			0
$449$			5.05256i			0.238445i	0.992868	+	0.119222i	$0.0380402\pi$
$449$			5.05256i			0.238445i	−0.992868	+	0.119222i	$0.961960\pi$
$450$	5.56218	−	4.36603i	0.262204	−	0.205816i
$451$	0.294229	+	0.169873i	0.0138547	+	0.00799901i
$452$	10.0981	−	2.70577i	0.474974	−	0.127269i
$453$	6.92820	−	25.8564i	0.325515	−	1.21484i
$454$	−0.196152			−0.00920589
$455$		0			0
$456$	2.73205			0.127940
$457$	−8.26795	+	30.8564i	−0.386758	+	1.44340i	0.448618	+	0.893724i	$0.351916\pi$
$457$	−8.26795	+	30.8564i	−0.386758	+	1.44340i	−0.835376	+	0.549678i	$0.814750\pi$
$458$	−4.46410	+	1.19615i	−0.208594	+	0.0558925i
$459$	3.92820	+	2.26795i	0.183353	+	0.105859i
$460$	5.59808	+	27.3564i	0.261012	+	1.27550i
$461$			26.3923i			1.22921i	0.788834	+	0.614606i	$0.210685\pi$
$461$			26.3923i			1.22921i	−0.788834	+	0.614606i	$0.789315\pi$
$462$		0			0
$463$	17.7583	−	17.7583i	0.825300	−	0.825300i	−0.161563	−	0.986862i	$-0.551653\pi$
$463$	17.7583	−	17.7583i	0.825300	−	0.825300i	0.986862	+	0.161563i	$0.0516534\pi$
$464$	−11.5981	+	6.69615i	−0.538427	+	0.310861i
$465$	1.53590	+	1.73205i	0.0712256	+	0.0803219i
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.554629	−	0.832097i	$-0.687140\pi$
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.896372	+	0.443303i	$0.853807\pi$
$468$	−2.53590	−	2.53590i	−0.117222	−	0.117222i
$469$		0			0
$470$	2.53590	−	1.26795i	0.116972	−	0.0584861i
$471$	23.7583	+	41.1506i	1.09473	+	1.89612i
$472$	0.294229	+	1.09808i	0.0135430	+	0.0505431i
$473$	−1.56218	−	5.83013i	−0.0718290	−	0.268070i
$474$	12.5622	+	21.7583i	0.577000	+	0.999393i
$475$	−8.19615	+	10.9282i	−0.376065	+	0.501420i
$476$		0			0
$477$	−3.66025	−	3.66025i	−0.167592	−	0.167592i
$478$	−34.3205	−	9.19615i	−1.56978	−	0.420622i
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	0.375161	+	0.926960i	$0.377588\pi$
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	−0.990351	+	0.138581i	$0.955746\pi$
$480$	32.7224	+	1.96410i	1.49357	+	0.0896486i
$481$	−12.0000	+	6.92820i	−0.547153	+	0.315899i
$482$	−22.9282	+	22.9282i	−1.04435	+	1.04435i
$483$		0			0
$484$		−	18.1244i		−	0.823834i
$485$	24.5622	−	5.02628i	1.11531	−	0.228232i
$486$	12.4641	+	7.19615i	0.565383	+	0.326424i
$487$	−8.29423	+	2.22243i	−0.375847	+	0.100708i	−0.441797	−	0.897115i	$-0.645659\pi$
$487$	−8.29423	+	2.22243i	−0.375847	+	0.100708i	0.0659498	+	0.997823i	$0.478992\pi$
$488$	1.13397	−	4.23205i	0.0513326	−	0.191576i
$489$	−10.7321			−0.485320
$490$		0			0
$491$	−17.7128			−0.799368			−0.399684	−	0.916653i	$-0.630880\pi$
$491$	−17.7128			−0.799368			−0.399684	+	0.916653i	$0.630880\pi$
$492$	−0.401924	+	1.50000i	−0.0181201	+	0.0676252i
$493$	−3.00000	+	0.803848i	−0.135113	+	0.0362035i
$494$	12.9282	+	7.46410i	0.581667	+	0.335826i
$495$	0.660254	−	1.00000i	0.0296762	−	0.0449467i
$496$			2.39230i			0.107418i
$497$		0			0
$498$	−11.5622	+	11.5622i	−0.518114	+	0.518114i
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.980300	−	0.197517i	$-0.936712\pi$
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.319095	+	0.947723i	$0.603379\pi$
$500$	−12.5263	+	14.7679i	−0.560192	+	0.660443i
$501$	14.6962	−	25.4545i	0.656576	−	1.13722i
$502$	10.9282	+	2.92820i	0.487750	+	0.130692i
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	0.991741	−	0.128253i	$-0.0409370\pi$
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	−0.128253	+	0.991741i	$0.540937\pi$
$504$		0			0
$505$	−11.7321	−	23.4641i	−0.522069	−	1.04414i
$506$	5.09808	+	8.83013i	0.226637	+	0.392547i
$507$	−2.50000	−	9.33013i	−0.111029	−	0.414365i
$508$	4.09808	+	15.2942i	0.181823	+	0.678572i
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	−0.993353	−	0.115104i	$-0.963280\pi$
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	0.396994	−	0.917821i	$-0.370053\pi$
$510$	8.19615	+	2.73205i	0.362932	+	0.120977i
$511$		0			0
$512$	20.6865	+	20.6865i	0.914224	+	0.914224i
$513$	−11.5622	−	3.09808i	−0.510483	−	0.136783i
$514$	−2.73205	+	4.73205i	−0.120506	+	0.208722i
$515$	−3.86603	+	3.42820i	−0.170357	+	0.151065i
$516$	23.8923	−	13.7942i	1.05180	−	0.607257i
$517$	0.339746	−	0.339746i	0.0149420	−	0.0149420i
$518$		0			0
$519$			45.3205i			1.98935i
$520$	−2.73205	−	1.80385i	−0.119808	−	0.0791039i
$521$	3.33975	+	1.92820i	0.146317	+	0.0844761i	0.571371	−	0.820692i	$-0.306412\pi$
$521$	3.33975	+	1.92820i	0.146317	+	0.0844761i	−0.425054	+	0.905168i	$0.639745\pi$
$522$	−4.09808	+	1.09808i	−0.179368	+	0.0480615i
$523$	−3.88269	+	14.4904i	−0.169778	+	0.633620i	0.827604	+	0.561312i	$0.189703\pi$
$523$	−3.88269	+	14.4904i	−0.169778	+	0.633620i	−0.997382	+	0.0723082i	$0.976963\pi$
$524$	14.7846			0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	−0.143594	+	0.535898i	−0.00625503	+	0.0233441i
$528$	6.09808	−	1.63397i	0.265385	−	0.0711096i
$529$	25.0981	+	14.4904i	1.09122	+	0.630017i
$530$	25.4904	+	16.8301i	1.10723	+	0.731054i
$531$			1.60770i			0.0697680i
$532$		0			0
$533$	0.928203	−	0.928203i	0.0402049	−	0.0402049i
$534$	−53.8468	+	31.0885i	−2.33018	+	1.34533i
$535$	−14.8923	+	13.2058i	−0.643850	+	0.570935i
$536$	0.303848	−	0.526279i	0.0131242	−	0.0227318i
$537$	37.0526	+	9.92820i	1.59894	+	0.428434i
$538$	−6.63397	−	6.63397i	−0.286011	−	0.286011i
$539$		0			0
$540$	−16.0981	−	5.36603i	−0.692751	−	0.230917i
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	0.993999	−	0.109392i	$-0.0348903\pi$
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	−0.591735	+	0.806132i	$0.701557\pi$
$542$	−12.3660	−	46.1506i	−0.531166	−	1.98234i
$543$	−4.59808	−	17.1603i	−0.197322	−	0.736417i
$544$	3.92820	+	6.80385i	0.168420	+	0.291713i
$545$	14.1244	+	28.2487i	0.605021	+	1.21004i
$546$		0			0
$547$	5.75833	+	5.75833i	0.246208	+	0.246208i	0.819413	−	0.573204i	$-0.194300\pi$
$547$	5.75833	+	5.75833i	0.246208	+	0.246208i	−0.573204	+	0.819413i	$0.694300\pi$
$548$	18.1244	+	4.85641i	0.774234	+	0.207455i
$549$	3.09808	−	5.36603i	0.132223	−	0.229016i
$550$	−2.63397	+	6.56218i	−0.112313	+	0.279812i
$551$	7.09808	−	4.09808i	0.302388	−	0.174584i
$552$	5.09808	−	5.09808i	0.216989	−	0.216989i
$553$		0			0
$554$		−	38.7846i		−	1.64780i
$555$	11.6603	−	17.6603i	0.494950	−	0.749636i
$556$	17.4904	+	10.0981i	0.741757	+	0.428254i
$557$	6.63397	−	1.77757i	0.281091	−	0.0753180i	−0.115519	−	0.993305i	$-0.536853\pi$
$557$	6.63397	−	1.77757i	0.281091	−	0.0753180i	0.396610	+	0.917987i	$0.370187\pi$
$558$	−0.196152	+	0.732051i	−0.00830379	+	0.0309902i
$559$	−23.3205			−0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$	6.46410	−	24.1244i	0.272672	−	1.01762i
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.679044	−	0.734097i	$-0.737606\pi$
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.221021	+	0.975269i	$0.570939\pi$
$564$	1.90192	+	1.09808i	0.0800854	+	0.0462373i
$565$	13.2224	−	2.70577i	0.556272	−	0.113833i
$566$		−	52.9808i		−	2.22695i
$567$		0			0
$568$	1.73205	−	1.73205i	0.0726752	−	0.0726752i
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	−0.200797	−	0.979633i	$-0.564353\pi$
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	0.747989	+	0.663712i	$0.231020\pi$
$570$	−22.7583	−	1.36603i	−0.953242	−	0.0572165i
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	−0.995898	−	0.0904849i	$-0.971158\pi$
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	0.576311	+	0.817230i	$0.304492\pi$
$572$	3.46410	+	0.928203i	0.144841	+	0.0388101i
$573$	−22.8564	−	22.8564i	−0.954840	−	0.954840i
$574$		0			0
$575$	5.09808	+	35.6865i	0.212604	+	1.48823i
$576$	2.09808	+	3.63397i	0.0874198	+	0.151416i
$577$	−7.36603	−	27.4904i	−0.306652	−	1.14444i	−0.931514	−	0.363705i	$-0.881512\pi$
$577$	−7.36603	−	27.4904i	−0.306652	−	1.14444i	0.624863	−	0.780735i	$-0.285155\pi$
$578$	−7.96410	−	29.7224i	−0.331263	−	1.23629i
$579$	3.09808	+	5.36603i	0.128752	+	0.223004i
$580$	10.3923	−	5.19615i	0.431517	−	0.215758i
$581$		0			0
$582$	29.5885	+	29.5885i	1.22648	+	1.22648i
$583$	5.00000	+	1.33975i	0.207079	+	0.0554866i
$584$	−0.928203	+	1.60770i	−0.0384093	+	0.0665269i
$585$	−3.07180	−	3.46410i	−0.127003	−	0.143223i
$586$	−43.5167	+	25.1244i	−1.79766	+	1.03788i
$587$	25.7846	−	25.7846i	1.06424	−	1.06424i	0.0664553	−	0.997789i	$-0.478831\pi$
$587$	25.7846	−	25.7846i	1.06424	−	1.06424i	0.997789	−	0.0664553i	$-0.0211690\pi$
$588$		0			0
$589$		−	1.46410i		−	0.0603273i
$590$	−1.90192	−	9.29423i	−0.0783010	−	0.382637i
$591$	33.4186	+	19.2942i	1.37466	+	0.793659i
$592$	21.1244	−	5.66025i	0.868206	−	0.232635i
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	−0.920379	−	0.391027i	$-0.872120\pi$
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	0.992585	+	0.121550i	$0.0387866\pi$
$594$	−6.19615			−0.254231
$595$		0			0
$596$	19.3923			0.794340
$597$	12.4641	−	46.5167i	0.510122	−	1.90380i
$598$	38.0526	−	10.1962i	1.55608	−	0.416952i
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.348482	−	0.937316i	$-0.613303\pi$
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.985980	+	0.166864i	$0.946636\pi$
$600$	4.96410	+	0.598076i	0.202659	+	0.0244164i
$601$		−	21.1769i		−	0.863824i	−0.901916	−	0.431912i	$-0.857839\pi$
$601$		−	21.1769i		−	0.863824i	0.901916	−	0.431912i	$-0.142161\pi$
$602$		0			0
$603$	0.607695	−	0.607695i	0.0247473	−	0.0247473i
$604$	−20.7846	+	12.0000i	−0.845714	+	0.488273i
$605$	1.40192	−	23.3564i	0.0569963	−	0.949573i
$606$	21.8923	−	37.9186i	0.889314	−	1.54034i
$607$	−8.59808	−	2.30385i	−0.348985	−	0.0935103i	0.0800683	−	0.996789i	$-0.474486\pi$
$607$	−8.59808	−	2.30385i	−0.348985	−	0.0935103i	−0.429053	+	0.903279i	$0.641153\pi$
$608$	−14.6603	−	14.6603i	−0.594552	−	0.594552i
$609$		0			0
$610$	−11.5622	+	34.6865i	−0.468139	+	1.40442i
$611$	−0.928203	−	1.60770i	−0.0375511	−	0.0650404i
$612$	0.339746	+	1.26795i	0.0137334	+	0.0512538i
$613$	3.60770	+	13.4641i	0.145713	+	0.543810i	0.999723	+	0.0235520i	$0.00749753\pi$
$613$	3.60770	+	13.4641i	0.145713	+	0.543810i	−0.854009	+	0.520258i	$0.825836\pi$
$614$	−12.6962	−	21.9904i	−0.512375	−	0.887460i
$615$	−0.633975	+	1.90192i	−0.0255643	+	0.0766930i
$616$		0			0
$617$	−31.9090	−	31.9090i	−1.28461	−	1.28461i	−0.938017	−	0.346590i	$-0.887340\pi$
$617$	−31.9090	−	31.9090i	−1.28461	−	1.28461i	−0.346590	−	0.938017i	$-0.612660\pi$
$618$	−8.33013	−	2.23205i	−0.335087	−	0.0897863i
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	−0.864048	−	0.503410i	$-0.832079\pi$
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	0.867990	+	0.496582i	$0.165412\pi$
$620$	0.124356	−	2.07180i	0.00499424	−	0.0832054i
$621$	−27.3564	+	15.7942i	−1.09777	+	0.633801i
$622$	−25.5885	+	25.5885i	−1.02600	+	1.02600i
$623$		0			0
$624$		−	24.3923i		−	0.976474i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	33.5885	+	19.3923i	1.34246	+	0.775072i
$627$	−3.73205	+	1.00000i	−0.149044	+	0.0399362i
$628$	11.0263	−	41.1506i	0.439996	−	1.64209i
$629$	5.07180			0.202226
$630$		0			0
$631$	26.5885			1.05847			0.529235	−	0.848475i	$-0.322479\pi$
$631$	26.5885			1.05847			0.529235	+	0.848475i	$0.322479\pi$
$632$	−0.901924	+	3.36603i	−0.0358766	+	0.133893i
$633$	19.0263	−	5.09808i	0.756227	−	0.202630i
$634$	7.73205	+	4.46410i	0.307079	+	0.177292i
$635$	4.09808	+	20.0263i	0.162627	+	0.794719i
$636$			23.6603i			0.938190i
$637$		0			0
$638$	3.00000	−	3.00000i	0.118771	−	0.118771i
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$	6.08846	+	6.86603i	0.240667	+	0.271403i
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	−0.792735	−	0.609566i	$-0.791344\pi$
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	0.924267	+	0.381746i	$0.124677\pi$
$642$	−32.0885	−	8.59808i	−1.26643	−	0.339339i
$643$	−24.4641	−	24.4641i	−0.964770	−	0.964770i	0.0346302	−	0.999400i	$-0.488975\pi$
$643$	−24.4641	−	24.4641i	−0.964770	−	0.964770i	−0.999400	+	0.0346302i	$0.988975\pi$
$644$		0			0
$645$	31.8564	−	15.9282i	1.25434	−	0.627172i
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	0.931619	−	0.363436i	$-0.118397\pi$
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	−0.988524	+	0.151065i	$0.951730\pi$
$648$	1.42820	+	5.33013i	0.0561051	+	0.209387i
$649$	−0.803848	−	1.39230i	−0.0315538	−	0.0546527i
$650$	21.8564	+	16.3923i	0.857279	+	0.642959i
$651$		0			0
$652$	6.80385	+	6.80385i	0.266459	+	0.266459i
$653$	−8.73205	−	2.33975i	−0.341712	−	0.0915613i	0.0838822	−	0.996476i	$-0.473268\pi$
$653$	−8.73205	−	2.33975i	−0.341712	−	0.0915613i	−0.425594	+	0.904914i	$0.639935\pi$
$654$	−26.3564	+	45.6506i	−1.03062	+	1.78508i
$655$	19.0526	+	1.14359i	0.744445	+	0.0446839i
$656$	−1.79423	+	1.03590i	−0.0700529	+	0.0404450i
$657$	−1.85641	+	1.85641i	−0.0724253	+	0.0724253i
$658$		0			0
$659$		−	10.3397i		−	0.402779i	−0.979511	−	0.201390i	$-0.935454\pi$
$659$		−	10.3397i		−	0.402779i	0.979511	−	0.201390i	$-0.0645457\pi$
$660$	−5.36603	+	1.09808i	−0.208872	+	0.0427426i
$661$	12.2776	+	7.08846i	0.477542	+	0.275709i	0.719392	−	0.694605i	$-0.244421\pi$
$661$	12.2776	+	7.08846i	0.477542	+	0.275709i	−0.241850	+	0.970314i	$0.577754\pi$
$662$	−48.2487	+	12.9282i	−1.87524	+	0.502469i
$663$	1.46410	−	5.46410i	0.0568610	−	0.212208i
$664$	−2.26795			−0.0880135
$665$		0			0
$666$	6.92820			0.268462
$667$	5.59808	−	20.8923i	0.216758	−	0.808953i
$668$	−25.4545	+	6.82051i	−0.984864	+	0.263893i
$669$	14.4904	+	8.36603i	0.560230	+	0.323449i
$670$	−2.79423	+	4.23205i	−0.107950	+	0.163498i
$671$			6.19615i			0.239200i
$672$		0			0
$673$	−16.3923	+	16.3923i	−0.631877	+	0.631877i	−0.948539	−	0.316662i	$-0.897438\pi$
$673$	−16.3923	+	16.3923i	−0.631877	+	0.631877i	0.316662	+	0.948539i	$0.397438\pi$
$674$	38.9545	−	22.4904i	1.50047	−	0.866297i
$675$	−20.3301	−	8.16025i	−0.782507	−	0.314088i
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	0.123213	−	0.992380i	$-0.460680\pi$
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	−0.389485	+	0.921033i	$0.627347\pi$
$678$	15.9282	+	15.9282i	0.611719	+	0.611719i
$679$		0			0
$680$	0.535898	+	1.07180i	0.0205508	+	0.0411015i
$681$	−0.0980762	−	0.169873i	−0.00375829	−	0.00650955i
$682$	−0.196152	−	0.732051i	−0.00751106	−	0.0280317i
$683$	4.93782	+	18.4282i	0.188941	+	0.705136i	0.993753	+	0.111606i	$0.0355994\pi$
$683$	4.93782	+	18.4282i	0.188941	+	0.705136i	−0.804812	+	0.593530i	$0.797734\pi$
$684$	−1.73205	−	3.00000i	−0.0662266	−	0.114708i
$685$	22.9808	+	7.66025i	0.878050	+	0.292683i
$686$		0			0
$687$	−3.26795	−	3.26795i	−0.124680	−	0.124680i
$688$	35.5526	+	9.52628i	1.35543	+	0.363186i
$689$	10.0000	−	17.3205i	0.380970	−	0.659859i
$690$	−45.0167	+	39.9186i	−1.71375	+	1.51967i
$691$	24.9737	−	14.4186i	0.950045	−	0.548509i	0.0569502	−	0.998377i	$-0.481862\pi$
$691$	24.9737	−	14.4186i	0.950045	−	0.548509i	0.893095	+	0.449868i	$0.148529\pi$
$692$	28.7321	−	28.7321i	1.09223	−	1.09223i
$693$		0			0
$694$		−	15.5885i		−	0.591730i
$695$	21.7583	+	14.3660i	0.825341	+	0.544934i
$696$	−2.59808	−	1.50000i	−0.0984798	−	0.0568574i
$697$	−0.464102	+	0.124356i	−0.0175791	+	0.00471031i
$698$	−4.86603	+	18.1603i	−0.184182	+	0.687376i
$699$	3.46410			0.131024
$700$		0			0
$701$	−23.7321			−0.896347			−0.448174	−	0.893947i	$-0.647925\pi$
$701$	−23.7321			−0.896347			−0.448174	+	0.893947i	$0.647925\pi$
$702$	−6.19615	+	23.1244i	−0.233859	+	0.872773i
$703$	−12.9282	+	3.46410i	−0.487596	+	0.130651i
$704$	−3.63397	−	2.09808i	−0.136961	−	0.0790742i
$705$	2.36603	+	1.56218i	0.0891097	+	0.0588350i
$706$			10.7321i			0.403906i
$707$		0			0
$708$	5.19615	−	5.19615i	0.195283	−	0.195283i
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	−0.625488	−	0.780234i	$-0.715100\pi$
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	0.362959	+	0.931805i	$0.381767\pi$
$710$	−15.2942	+	13.5622i	−0.573982	+	0.508979i
$711$	−2.46410	+	4.26795i	−0.0924110	+	0.160061i
$712$	−8.33013	−	2.23205i	−0.312185	−	0.0836496i
$713$	−2.73205	−	2.73205i	−0.102316	−	0.102316i
$714$		0			0
$715$	4.39230	+	1.46410i	0.164263	+	0.0547543i
$716$	−17.1962	−	29.7846i	−0.642650	−	1.11310i
$717$	−9.19615	−	34.3205i	−0.343437	−	1.28172i
$718$	−7.12436	−	26.5885i	−0.265879	−	0.992272i
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	0.788614	−	0.614888i	$-0.210799\pi$
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	−0.926816	+	0.375516i	$0.877466\pi$
$720$	3.26795	+	6.53590i	0.121789	+	0.243579i
$721$		0			0
$722$	−15.7583	−	15.7583i	−0.586464	−	0.586464i
$723$	−31.3205	−	8.39230i	−1.16482	−	0.312113i
$724$	−7.96410	+	13.7942i	−0.295984	+	0.512658i
$725$	13.7942	−	5.89230i	0.512305	−	0.218835i
$726$	33.8205	−	19.5263i	1.25520	−	0.724688i
$727$	4.90192	−	4.90192i	0.181802	−	0.181802i	−0.610338	−	0.792141i	$-0.708967\pi$
$727$	4.90192	−	4.90192i	0.181802	−	0.181802i	0.792141	+	0.610338i	$0.208967\pi$
$728$		0			0
$729$		−	17.5885i		−	0.651424i
$730$	8.53590	−	12.9282i	0.315928	−	0.478494i
$731$	7.39230	+	4.26795i	0.273414	+	0.157856i
$732$	−27.3564	+	7.33013i	−1.01112	+	0.270929i
$733$	2.63397	−	9.83013i	0.0972881	−	0.363084i	−0.900068	−	0.435749i	$-0.856484\pi$
$733$	2.63397	−	9.83013i	0.0972881	−	0.363084i	0.997356	+	0.0726647i	$0.0231503\pi$
$734$	−3.73205			−0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	−0.222432	+	0.830127i	−0.00819338	+	0.0305781i
$738$	−0.633975	+	0.169873i	−0.0233369	+	0.00625311i
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	0.356920	−	0.934135i	$-0.383827\pi$
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	−0.630525	+	0.776169i	$0.717160\pi$
$740$	−18.5885	+	3.80385i	−0.683325	+	0.139832i
$741$			14.9282i			0.548401i
$742$		0			0
$743$	−14.8301	+	14.8301i	−0.544065	+	0.544065i	−0.924718	−	0.380653i	$-0.875699\pi$
$743$	−14.8301	+	14.8301i	−0.544065	+	0.544065i	0.380653	+	0.924718i	$0.375699\pi$
$744$	−0.464102	+	0.267949i	−0.0170148	+	0.00982349i
$745$	24.9904	+	1.50000i	0.915577	+	0.0549557i
$746$	15.9282	−	27.5885i	0.583173	−	1.01009i
$747$	−3.09808	−	0.830127i	−0.113353	−	0.0303728i
$748$	−0.928203	−	0.928203i	−0.0339385	−	0.0339385i
$749$		0			0
$750$	−41.0526	−	7.46410i	−1.49903	−	0.272550i
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	0.704338	−	0.709864i	$-0.251244\pi$
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	−0.966930	+	0.255043i	$0.917910\pi$
$752$	0.758330	+	2.83013i	0.0276535	+	0.103204i
$753$	2.92820	+	10.9282i	0.106710	+	0.398246i
$754$	−8.19615	−	14.1962i	−0.298486	−	0.516993i
$755$	−27.7128	+	13.8564i	−1.00857	+	0.504286i
$756$		0			0
$757$	9.26795	+	9.26795i	0.336849	+	0.336849i	0.855180	−	0.518331i	$-0.173446\pi$
$757$	9.26795	+	9.26795i	0.336849	+	0.336849i	−0.518331	+	0.855180i	$0.673446\pi$
$758$	36.6865	+	9.83013i	1.33251	+	0.357046i
$759$	−5.09808	+	8.83013i	−0.185048	+	0.320513i
$760$	−2.09808	−	2.36603i	−0.0761052	−	0.0858248i
$761$	−11.0718	+	6.39230i	−0.401352	+	0.231721i	−0.687067	−	0.726594i	$-0.741102\pi$
$761$	−11.0718	+	6.39230i	−0.401352	+	0.231721i	0.285715	+	0.958315i	$0.407769\pi$
$762$	−24.1244	+	24.1244i	−0.873933	+	0.873933i
$763$		0			0
$764$			28.9808i			1.04849i
$765$	0.339746	+	1.66025i	0.0122835	+	0.0600266i
$766$	−48.8205	−	28.1865i	−1.76396	−	1.01842i
$767$	−6.00000	+	1.60770i	−0.216647	+	0.0580505i
$768$	−9.69615	+	36.1865i	−0.349880	+	1.30577i
$769$	47.1769			1.70124			0.850622	−	0.525778i	$-0.176226\pi$
$769$	47.1769			1.70124			0.850622	+	0.525778i	$0.176226\pi$
$770$		0			0
$771$	−5.46410			−0.196785
$772$	1.43782	−	5.36603i	0.0517484	−	0.193127i
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.566391	−	0.824136i	$-0.691661\pi$
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.0784412	+	0.996919i	$0.524994\pi$
$774$	10.0981	+	5.83013i	0.362968	+	0.209560i
$775$	0.320508	−	2.66025i	0.0115130	−	0.0955591i
$776$			5.80385i			0.208346i
$777$		0			0
$778$	−12.1962	+	12.1962i	−0.437253	+	0.437253i
$779$	1.09808	−	0.633975i	0.0393427	−	0.0227145i
$780$	−1.26795	+	21.1244i	−0.0453999	+	0.756373i
$781$	−1.73205	+	3.00000i	−0.0619777	+	0.107348i
$782$	−13.9282	−	3.73205i	−0.498072	−	0.133458i
$783$	9.29423	+	9.29423i	0.332149	+	0.332149i
$784$		0			0
$785$	17.3923	−	52.1769i	0.620758	−	1.86227i
$786$	15.9282	+	27.5885i	0.568140	+	0.984048i
$787$	5.18653	+	19.3564i	0.184880	+	0.689981i	0.994656	+	0.103243i	$0.0329218\pi$
$787$	5.18653	+	19.3564i	0.184880	+	0.689981i	−0.809776	+	0.586739i	$0.800412\pi$
$788$	−8.95448	−	33.4186i	−0.318990	−	1.19049i
$789$	8.06218	+	13.9641i	0.287021	+	0.497135i
$790$	9.19615	−	27.5885i	0.327184	−	0.981553i
$791$		0			0
$792$	0.196152	+	0.196152i	0.00696997	+	0.00696997i
$793$	23.1244	+	6.19615i	0.821170	+	0.220032i
$794$	20.0263	−	34.6865i	0.710706	−	1.23098i
$795$	−1.83013	+	30.4904i	−0.0649079	+	1.08138i
$796$	−37.3923	+	21.5885i	−1.32534	+	0.765183i
$797$	−29.4641	+	29.4641i	−1.04367	+	1.04367i	−0.0446702	+	0.999002i	$0.514224\pi$
$797$	−29.4641	+	29.4641i	−1.04367	+	1.04367i	−0.999002	+	0.0446702i	$0.985776\pi$
$798$		0			0
$799$			0.679492i			0.0240387i
$800$	−23.4282	−	29.8468i	−0.828312	−	1.05524i
$801$	−10.5622	−	6.09808i	−0.373196	−	0.215465i
$802$	−20.5263	+	5.50000i	−0.724808	+	0.194212i
$803$	0.679492	−	2.53590i	0.0239787	−	0.0894899i
$804$	−3.92820			−0.138537
$805$		0			0
$806$	−2.92820			−0.103142
$807$	2.42820	−	9.06218i	0.0854768	−	0.319004i
$808$	5.86603	−	1.57180i	0.206366	−	0.0552956i
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	0.833994	−	0.551774i	$-0.186049\pi$
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	−0.0608532	+	0.998147i	$0.519382\pi$
$810$	−9.23205	−	45.1147i	−0.324381	−	1.58517i
$811$		−	29.0718i		−	1.02085i	−0.859923	−	0.510424i	$-0.829488\pi$
$811$		−	29.0718i		−	1.02085i	0.859923	−	0.510424i	$-0.170512\pi$
$812$		0			0
$813$	33.7846	−	33.7846i	1.18488	−	1.18488i
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	8.24167	+	9.29423i	0.288693	+	0.325563i
$816$	−4.46410	+	7.73205i	−0.156275	+	0.270676i
$817$	−21.7583	−	5.83013i	−0.761228	−	0.203970i
$818$	9.36603	+	9.36603i	0.327475	+	0.327475i
$819$		0			0
$820$	1.60770	−	0.803848i	0.0561432	−	0.0280716i
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	0.965210	−	0.261477i	$-0.0842096\pi$
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	−0.709051	+	0.705157i	$0.750876\pi$
$822$	10.4641	+	39.0526i	0.364977	+	1.36211i
$823$	−6.61731	−	24.6962i	−0.230665	−	0.860854i	−0.980055	−	0.198725i	$-0.936320\pi$
$823$	−6.61731	−	24.6962i	−0.230665	−	0.860854i	0.749390	−	0.662129i	$-0.230347\pi$
$824$	−0.598076	−	1.03590i	−0.0208350	−	0.0360872i
$825$	−7.00000	+	1.00000i	−0.243709	+	0.0348155i
$826$		0			0
$827$	−3.77757	−	3.77757i	−0.131359	−	0.131359i	0.638370	−	0.769729i	$-0.279609\pi$
$827$	−3.77757	−	3.77757i	−0.131359	−	0.131359i	−0.769729	+	0.638370i	$0.779609\pi$
$828$	−8.83013	−	2.36603i	−0.306868	−	0.0822251i
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	−0.617246	−	0.786770i	$-0.711752\pi$
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	0.989986	+	0.141166i	$0.0450852\pi$
$830$	18.8923	+	1.13397i	0.655761	+	0.0393608i
$831$	33.5885	−	19.3923i	1.16517	−	0.672712i
$832$	−11.4641	+	11.4641i	−0.397446	+	0.397446i
$833$		0			0
$834$			43.5167i			1.50686i
$835$	−33.3301	+	6.82051i	−1.15344	+	0.236033i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$	2.26795	−	0.607695i	0.0783918	−	0.0210050i
$838$	1.92820	−	7.19615i	0.0666087	−	0.248587i
$839$	−31.1244			−1.07453			−0.537266	−	0.843413i	$-0.680543\pi$
$839$	−31.1244			−1.07453			−0.537266	+	0.843413i	$0.680543\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−17.3301	+	64.6769i	−0.597236	+	2.22891i
$843$	24.1244	−	6.46410i	0.830887	−	0.222635i
$844$	−15.2942	−	8.83013i	−0.526449	−	0.303946i
$845$	−6.16025	+	9.33013i	−0.211919	+	0.320966i
$846$			0.928203i			0.0319123i
$847$		0			0
$848$	−22.3205	+	22.3205i	−0.766489	+	0.766489i
$849$	45.8827	−	26.4904i	1.57469	−	0.909148i
$850$	−3.92820	−	9.19615i	−0.134736	−	0.315425i
$851$	−17.6603	+	30.5885i	−0.605386	+	1.04856i
$852$	−15.2942	−	4.09808i	−0.523972	−	0.140398i
$853$	−6.12436	−	6.12436i	−0.209694	−	0.209694i	0.594443	−	0.804137i	$-0.297372\pi$
$853$	−6.12436	−	6.12436i	−0.209694	−	0.209694i	−0.804137	+	0.594443i	$0.797372\pi$
$854$		0			0
$855$	−2.00000	−	4.00000i	−0.0683986	−	0.136797i
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	0.990457	+	0.137820i	$0.0440094\pi$
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	−0.788851	+	0.614584i	$0.789324\pi$
$858$	2.00000	+	7.46410i	0.0682789	+	0.254820i
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	0.987874	−	0.155257i	$-0.0496207\pi$
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	−0.628394	+	0.777895i	$0.716287\pi$
$860$	−30.2942	−	10.0981i	−1.03302	−	0.344342i
$861$		0			0
$862$	−5.73205	−	5.73205i	−0.195234	−	0.195234i
$863$	−33.3827	−	8.94486i	−1.13636	−	0.304487i	−0.358873	−	0.933386i	$-0.616839\pi$
$863$	−33.3827	−	8.94486i	−1.13636	−	0.304487i	−0.777487	+	0.628900i	$0.783506\pi$
$864$	16.6244	−	28.7942i	0.565572	−	0.979600i
$865$	39.2487	−	34.8038i	1.33450	−	1.18337i
$866$	57.8827	−	33.4186i	1.96693	−	1.13561i
$867$	21.7583	−	21.7583i	0.738952	−	0.738952i
$868$		0			0
$869$		−	4.92820i		−	0.167178i
$870$	20.8923	+	13.7942i	0.708315	+	0.467668i
$871$	2.87564	+	1.66025i	0.0974375	+	0.0562556i
$872$	−7.06218	+	1.89230i	−0.239156	+	0.0640815i
$873$	−2.12436	+	7.92820i	−0.0718985	+	0.268329i
$874$	38.0526			1.28715
$875$		0			0
$876$	12.0000			0.405442
$877$	4.15064	−	15.4904i	0.140157	−	0.523073i	−0.859766	−	0.510688i	$-0.829391\pi$
$877$	4.15064	−	15.4904i	0.140157	−	0.523073i	0.999923	−	0.0123853i	$-0.00394248\pi$
$878$	58.4449	−	15.6603i	1.97242	−	0.528508i
$879$	−43.5167	−	25.1244i	−1.46778	−	0.847423i
$880$	−6.09808	−	4.02628i	−0.205566	−	0.135726i
$881$		−	52.8564i		−	1.78078i	−0.455201	−	0.890389i	$-0.650433\pi$
$881$		−	52.8564i		−	1.78078i	0.455201	−	0.890389i	$-0.349567\pi$
$882$		0			0
$883$	21.9282	−	21.9282i	0.737943	−	0.737943i	−0.234237	−	0.972180i	$-0.575259\pi$
$883$	21.9282	−	21.9282i	0.737943	−	0.737943i	0.972180	+	0.234237i	$0.0752591\pi$
$884$	−4.39230	+	2.53590i	−0.147729	+	0.0852915i
$885$	7.09808	−	6.29423i	0.238599	−	0.211578i
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.818312	−	0.574774i	$-0.194910\pi$
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.421292	+	0.906925i	$0.361577\pi$
$888$	3.46410	+	3.46410i	0.116248	+	0.116248i
$889$		0			0
$890$	68.2750	+	22.7583i	2.28858	+	0.762861i
$891$	−3.90192	−	6.75833i	−0.130719	−	0.226413i
$892$	−3.88269	−	14.4904i	−0.130002	−	0.485174i
$893$	−0.464102	−	1.73205i	−0.0155306	−	0.0579609i
$894$	20.8923	+	36.1865i	0.698743	+	1.21026i
$895$	−19.8564	−	39.7128i	−0.663726	−	1.32745i
$896$		0			0
$897$	27.8564	+	27.8564i	0.930098	+	0.930098i
$898$	9.42820	+	2.52628i	0.314623	+	0.0843030i
$899$	−0.803848	+	1.39230i	−0.0268098	+	0.0464360i
$900$	−2.49038	−	5.83013i	−0.0830127	−	0.194338i
$901$	−6.33975	+	3.66025i	−0.211208	+	0.121941i
$902$	0.464102	−	0.464102i	0.0154529	−	0.0154529i
$903$		0			0
$904$			3.12436i			0.103915i
$905$	−11.3301	+	17.1603i	−0.376626	+	0.570426i
$906$	−44.7846	−	25.8564i	−1.48787	−	0.859022i
$907$	1.69615	−	0.454483i	0.0563198	−	0.0150908i	−0.230549	−	0.973061i	$-0.574052\pi$
$907$	1.69615	−	0.454483i	0.0563198	−	0.0150908i	0.286869	+	0.957970i	$0.407386\pi$
$908$	−0.0455173	+	0.169873i	−0.00151055	+	0.00563743i
$909$	8.58846			0.284861
$910$		0			0
$911$	37.5167			1.24298			0.621491	−	0.783421i	$-0.286527\pi$
$911$	37.5167			1.24298			0.621491	+	0.783421i	$0.286527\pi$
$912$	6.09808	−	22.7583i	0.201927	−	0.753604i
$913$	3.09808	−	0.830127i	0.102531	−	0.0274732i
$914$	53.4449	+	30.8564i	1.76780	+	1.02064i
$915$	−35.8205	+	7.33013i	−1.18419	+	0.242327i
$916$			4.14359i			0.136908i
$917$		0			0
$918$	6.19615	−	6.19615i	0.204504	−	0.204504i
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.326657	−	0.945143i	$-0.394078\pi$
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.981846	+	0.189678i	$0.0607445\pi$
$920$	−8.33013	−	0.500000i	−0.274636	−	0.0164845i
$921$	12.6962	−	21.9904i	0.418352	−	0.724608i
$922$	49.2487	+	13.1962i	1.62192	+	0.434592i
$923$	9.46410	+	9.46410i	0.311515	+	0.311515i
$924$		0			0
$925$	−24.2487	+	3.46410i	−0.797293	+	0.113899i
$926$	−24.2583	−	42.0167i	−0.797178	−	1.38075i
$927$	−0.437822	−	1.63397i	−0.0143800	−	0.0536668i
$928$	5.89230	+	21.9904i	0.193424	+	0.721870i
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	0.879472	−	0.475950i	$-0.157896\pi$
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	−0.851921	+	0.523670i	$0.824562\pi$
$930$	4.00000	−	2.00000i	0.131165	−	0.0655826i
$931$		0			0
$932$	−2.19615	−	2.19615i	−0.0719374	−	0.0719374i
$933$	−34.9545	−	9.36603i	−1.14436	−	0.306630i
$934$	−31.3564	+	54.3109i	−1.02601	+	1.77711i
$935$	−1.12436	−	1.26795i	−0.0367704	−	0.0414664i
$936$	0.928203	−	0.535898i	0.0303393	−	0.0175164i
$937$	−30.9282	+	30.9282i	−1.01038	+	1.01038i	−0.0104348	+	0.999946i	$0.503322\pi$
$937$	−30.9282	+	30.9282i	−1.01038	+	1.01038i	−0.999946	+	0.0104348i	$0.996678\pi$
$938$		0			0
$939$			38.7846i			1.26569i
$940$	−0.509619	−	2.49038i	−0.0166219	−	0.0812273i
$941$	−24.8038	−	14.3205i	−0.808582	−	0.466835i	0.0378810	−	0.999282i	$-0.487939\pi$
$941$	−24.8038	−	14.3205i	−0.808582	−	0.466835i	−0.846463	+	0.532447i	$0.821273\pi$
$942$	88.6673	−	23.7583i	2.88894	−	0.774088i
$943$	0.866025	−	3.23205i	0.0282017	−	0.105250i
$944$	9.80385			0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	−11.6962	+	43.6506i	−0.380074	+	1.41846i	0.465714	+	0.884935i	$0.345798\pi$
$947$	−11.6962	+	43.6506i	−0.380074	+	1.41846i	−0.845788	+	0.533520i	$0.820869\pi$
$948$	21.7583	−	5.83013i	0.706678	−	0.189354i
$949$	−8.78461	−	5.07180i	−0.285160	−	0.164637i
$950$	16.2942	+	20.7583i	0.528655	+	0.673489i
$951$			8.92820i			0.289517i
$952$		0			0
$953$	−10.1436	+	10.1436i	−0.328583	+	0.328583i	−0.852048	−	0.523464i	$-0.824639\pi$
$953$	−10.1436	+	10.1436i	−0.328583	+	0.328583i	0.523464	+	0.852048i	$0.324639\pi$
$954$	−8.66025	+	5.00000i	−0.280386	+	0.161881i
$955$	−2.24167	+	37.3468i	−0.0725387	+	1.20851i
$956$	−15.9282	+	27.5885i	−0.515155	+	0.892274i
$957$	4.09808	+	1.09808i	0.132472	+	0.0354958i
$958$	36.7846	+	36.7846i	1.18846	+	1.18846i
$959$		0			0
$960$	7.83013	−	23.4904i	0.252716	−	0.758149i
$961$	−15.3564	−	26.5981i	−0.495368	−	0.858002i
$962$	6.92820	+	25.8564i	0.223374	+	0.833644i
$963$	−1.68653	−	6.29423i	−0.0543478	−	0.202829i
$964$	14.5359	+	25.1769i	0.468170	+	0.810894i
$965$	2.26795	−	6.80385i	0.0730079	−	0.219024i
$966$		0			0
$967$	−1.43782	−	1.43782i	−0.0462372	−	0.0462372i	0.683610	−	0.729847i	$-0.260409\pi$
$967$	−1.43782	−	1.43782i	−0.0462372	−	0.0462372i	−0.729847	+	0.683610i	$0.760409\pi$
$968$	5.23205	+	1.40192i	0.168164	+	0.0450595i
$969$	2.73205	−	4.73205i	0.0877661	−	0.152015i
$970$	2.90192	−	48.3468i	0.0931752	−	1.55232i
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.991874	−	0.127224i	$-0.959393\pi$
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.385758	+	0.922600i	$0.626060\pi$
$972$	9.12436	−	9.12436i	0.292664	−	0.292664i
$973$		0			0
$974$			16.5885i			0.531528i
$975$	−3.26795	+	27.1244i	−0.104658	+	0.868675i
$976$	−32.7224	−	18.8923i	−1.04742	−	0.604728i
$977$	43.1506	−	11.5622i	1.38051	−	0.369907i	0.509204	−	0.860646i	$-0.329940\pi$
$977$	43.1506	−	11.5622i	1.38051	−	0.369907i	0.871307	+	0.490739i	$0.163273\pi$
$978$	−5.36603	+	20.0263i	−0.171587	+	0.640370i
$979$	12.1962			0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$	−8.85641	+	33.0526i	−0.282619	+	1.05475i
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	−0.482532	−	0.875878i	$-0.660283\pi$
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	0.0200540	+	0.999799i	$0.493616\pi$
$984$	−0.401924	−	0.232051i	−0.0128129	−	0.00739751i
$985$	−8.95448	−	43.7583i	−0.285314	−	1.39426i
$986$			6.00000i			0.191079i
$987$		0			0
$988$	9.46410	−	9.46410i	0.301093	−	0.301093i
$989$	−51.4808	+	29.7224i	−1.63699	+	0.945118i
$990$	−1.53590	−	1.73205i	−0.0488141	−	0.0550482i
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	−0.613939	−	0.789354i	$-0.710416\pi$
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	0.990570	+	0.137009i	$0.0437491\pi$
$992$	3.92820	+	1.05256i	0.124721	+	0.0334188i
$993$	−35.3205	−	35.3205i	−1.12086	−	1.12086i
$994$		0			0
$995$	−49.8564	+	24.9282i	−1.58055	+	0.790277i
$996$	7.33013	+	12.6962i	0.232264	+	0.402293i
$997$	−6.88269	−	25.6865i	−0.217977	−	0.813501i	−0.985097	−	0.171998i	$-0.944978\pi$
$997$	−6.88269	−	25.6865i	−0.217977	−	0.813501i	0.767121	−	0.641503i	$-0.221689\pi$
$998$	16.7583	+	62.5429i	0.530476	+	1.97976i
$999$	−10.7321	−	18.5885i	−0.339547	−	0.588113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.l.b.227.1		4
5.3	odd	4		245.2.l.a.178.1		4
7.2	even	3		35.2.k.a.12.1	yes	4
7.3	odd	6		245.2.f.b.97.2		4
7.4	even	3		245.2.f.a.97.2		4
7.5	odd	6		245.2.l.a.117.1		4
7.6	odd	2		35.2.k.b.17.1	yes	4
21.2	odd	6		315.2.bz.b.82.1		4
21.20	even	2		315.2.bz.a.262.1		4
28.23	odd	6		560.2.ci.a.257.1		4
28.27	even	2		560.2.ci.b.17.1		4
35.2	odd	12		175.2.o.a.68.1		4
35.3	even	12		245.2.f.a.48.2		4
35.9	even	6		175.2.o.b.82.1		4
35.13	even	4		35.2.k.a.3.1	✓	4
35.18	odd	12		245.2.f.b.48.2		4
35.23	odd	12		35.2.k.b.33.1	yes	4
35.27	even	4		175.2.o.b.143.1		4
35.33	even	12	inner	245.2.l.b.68.1		4
35.34	odd	2		175.2.o.a.157.1		4
105.23	even	12		315.2.bz.a.208.1		4
105.83	odd	4		315.2.bz.b.73.1		4
140.23	even	12		560.2.ci.b.33.1		4
140.83	odd	4		560.2.ci.a.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	35.13	even	4
35.2.k.a.12.1	yes	4	7.2	even	3
35.2.k.b.17.1	yes	4	7.6	odd	2
35.2.k.b.33.1	yes	4	35.23	odd	12
175.2.o.a.68.1		4	35.2	odd	12
175.2.o.a.157.1		4	35.34	odd	2
175.2.o.b.82.1		4	35.9	even	6
175.2.o.b.143.1		4	35.27	even	4
245.2.f.a.48.2		4	35.3	even	12
245.2.f.a.97.2		4	7.4	even	3
245.2.f.b.48.2		4	35.18	odd	12
245.2.f.b.97.2		4	7.3	odd	6
245.2.l.a.117.1		4	7.5	odd	6
245.2.l.a.178.1		4	5.3	odd	4
245.2.l.b.68.1		4	35.33	even	12	inner
245.2.l.b.227.1		4	1.1	even	1	trivial
315.2.bz.a.208.1		4	105.23	even	12
315.2.bz.a.262.1		4	21.20	even	2
315.2.bz.b.73.1		4	105.83	odd	4
315.2.bz.b.82.1		4	21.2	odd	6
560.2.ci.a.257.1		4	28.23	odd	6
560.2.ci.a.353.1		4	140.83	odd	4
560.2.ci.b.17.1		4	28.27	even	2
560.2.ci.b.33.1		4	140.23	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.86603i) q^{2} +(1.86603 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -3.73205i q^{6} +(0.366025 - 0.366025i) q^{8} +(0.633975 - 0.366025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 1.86603i) q^{2} +(1.86603 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -3.73205i q^{6} +(0.366025 - 0.366025i) q^{8} +(0.633975 - 0.366025i) q^{9} +(-3.23205 + 2.86603i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-3.23205 - 0.866025i) q^{12} +(2.00000 + 2.00000i) q^{13} +(-4.09808 - 1.36603i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-0.267949 - 1.00000i) q^{17} +(-0.366025 - 1.36603i) q^{18} +(1.36603 + 2.36603i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(6.96410 + 1.86603i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(4.73205 - 2.73205i) q^{26} +(-3.09808 + 3.09808i) q^{27} -3.00000i q^{29} +(-4.59808 + 6.96410i) q^{30} +(-0.464102 - 0.267949i) q^{31} +(-7.33013 + 1.96410i) q^{32} +(-0.366025 + 1.36603i) q^{33} -2.00000 q^{34} -1.26795 q^{36} +(-1.26795 + 4.73205i) q^{37} +(5.09808 - 1.36603i) q^{38} +(4.73205 + 2.73205i) q^{39} +(-1.13397 + 0.232051i) q^{40} -0.464102i q^{41} +(-5.83013 + 5.83013i) q^{43} +(1.09808 - 0.633975i) q^{44} +(-1.63397 - 0.0980762i) q^{45} +(6.96410 - 12.0622i) q^{46} +(-0.633975 - 0.169873i) q^{47} +(-6.09808 - 6.09808i) q^{48} +(9.56218 - 1.36603i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.26795 - 4.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(4.23205 + 7.33013i) q^{54} +(1.46410 - 0.732051i) q^{55} +(3.73205 + 3.73205i) q^{57} +(-5.59808 - 1.50000i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(4.96410 + 5.59808i) q^{60} +(7.33013 - 4.23205i) q^{61} +(-0.732051 + 0.732051i) q^{62} +5.73205i q^{64} +(-1.26795 - 6.19615i) q^{65} +(2.36603 + 1.36603i) q^{66} +(1.13397 - 0.303848i) q^{67} +(-0.464102 + 1.73205i) q^{68} +13.9282 q^{69} +4.73205 q^{71} +(0.0980762 - 0.366025i) q^{72} +(-3.46410 + 0.928203i) q^{73} +(8.19615 + 4.73205i) q^{74} +(5.96410 + 7.59808i) q^{75} -4.73205i q^{76} +(7.46410 - 7.46410i) q^{78} +(-5.83013 + 3.36603i) q^{79} +(-0.598076 + 9.96410i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.866025 - 0.232051i) q^{82} +(-3.09808 - 3.09808i) q^{83} +(-0.732051 + 2.19615i) q^{85} +(7.96410 + 13.7942i) q^{86} +(-1.50000 - 5.59808i) q^{87} +(0.0980762 + 0.366025i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(-1.00000 + 3.00000i) q^{90} +(-8.83013 - 8.83013i) q^{92} +(-1.00000 - 0.267949i) q^{93} +(-0.633975 + 1.09808i) q^{94} +(0.366025 - 6.09808i) q^{95} +(-12.6962 + 7.33013i) q^{96} +(-7.92820 + 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 4 * q^5 - 2 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} - 6 q^{4} - 4 q^{5} - 2 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 6 q^{12} + 8 q^{13} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{22} + 14 q^{23} + 2 q^{24} - 6 q^{25} + 12 q^{26} - 2 q^{27} - 8 q^{30} + 12 q^{31} - 12 q^{32} + 2 q^{33} - 8 q^{34} - 12 q^{36} - 12 q^{37} + 10 q^{38} + 12 q^{39} - 8 q^{40} - 6 q^{43} - 6 q^{44} - 10 q^{45} + 14 q^{46} - 6 q^{47} - 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} + 10 q^{54} - 8 q^{55} + 8 q^{57} - 12 q^{58} + 6 q^{59} + 6 q^{60} + 12 q^{61} + 4 q^{62} - 12 q^{65} + 6 q^{66} + 8 q^{67} + 12 q^{68} + 28 q^{69} + 12 q^{71} - 10 q^{72} + 12 q^{74} + 10 q^{75} + 16 q^{78} - 6 q^{79} + 8 q^{80} - 4 q^{81} - 2 q^{83} + 4 q^{85} + 18 q^{86} - 6 q^{87} - 10 q^{88} - 16 q^{89} - 4 q^{90} - 18 q^{92} - 4 q^{93} - 6 q^{94} - 2 q^{95} - 30 q^{96} - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 - 4 * q^5 - 2 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^11 - 6 * q^12 + 8 * q^13 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^22 + 14 * q^23 + 2 * q^24 - 6 * q^25 + 12 * q^26 - 2 * q^27 - 8 * q^30 + 12 * q^31 - 12 * q^32 + 2 * q^33 - 8 * q^34 - 12 * q^36 - 12 * q^37 + 10 * q^38 + 12 * q^39 - 8 * q^40 - 6 * q^43 - 6 * q^44 - 10 * q^45 + 14 * q^46 - 6 * q^47 - 14 * q^48 + 14 * q^50 - 4 * q^51 - 12 * q^52 + 10 * q^53 + 10 * q^54 - 8 * q^55 + 8 * q^57 - 12 * q^58 + 6 * q^59 + 6 * q^60 + 12 * q^61 + 4 * q^62 - 12 * q^65 + 6 * q^66 + 8 * q^67 + 12 * q^68 + 28 * q^69 + 12 * q^71 - 10 * q^72 + 12 * q^74 + 10 * q^75 + 16 * q^78 - 6 * q^79 + 8 * q^80 - 4 * q^81 - 2 * q^83 + 4 * q^85 + 18 * q^86 - 6 * q^87 - 10 * q^88 - 16 * q^89 - 4 * q^90 - 18 * q^92 - 4 * q^93 - 6 * q^94 - 2 * q^95 - 30 * q^96 - 4 * q^97

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