LMFDB - Embedded newform 245.2.l.a.178.1

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			178.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.178
Dual form			245.2.l.a.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86603 - 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -3.73205i q^{6} +(0.366025 + 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(-1.86603 - 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -3.73205i q^{6} +(0.366025 + 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(0.866025 - 4.23205i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-0.866025 + 3.23205i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-4.09808 + 1.36603i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(1.36603 - 0.366025i) q^{18} +(-1.36603 - 2.36603i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-1.86603 + 6.96410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(4.73205 - 2.73205i) q^{26} +(3.09808 + 3.09808i) q^{27} +3.00000i q^{29} +(8.33013 - 0.500000i) q^{30} +(-0.464102 - 0.267949i) q^{31} +(1.96410 + 7.33013i) q^{32} +(-1.36603 - 0.366025i) q^{33} +2.00000 q^{34} -1.26795 q^{36} +(4.73205 + 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(-4.73205 - 2.73205i) q^{39} +(-0.767949 + 0.866025i) q^{40} -0.464102i q^{41} +(-5.83013 - 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(-0.901924 - 1.36603i) q^{45} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(6.09808 - 6.09808i) q^{48} +(9.56218 + 1.36603i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-4.73205 + 1.26795i) q^{52} +(6.83013 - 1.83013i) q^{53} +(-4.23205 - 7.33013i) q^{54} +(-1.46410 - 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(1.50000 - 5.59808i) q^{58} +(1.09808 - 1.90192i) q^{59} +(-7.33013 - 1.50000i) q^{60} +(7.33013 - 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} -5.73205i q^{64} +(-4.73205 - 4.19615i) q^{65} +(2.36603 + 1.36603i) q^{66} +(-0.303848 - 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} -13.9282 q^{69} +4.73205 q^{71} +(-0.366025 - 0.0980762i) q^{72} +(-0.928203 - 3.46410i) q^{73} +(-8.19615 - 4.73205i) q^{74} +(-3.59808 - 8.96410i) q^{75} -4.73205i q^{76} +(7.46410 + 7.46410i) q^{78} +(5.83013 - 3.36603i) q^{79} +(8.33013 - 5.50000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.232051 + 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(7.96410 + 13.7942i) q^{86} +(-5.59808 + 1.50000i) q^{87} +(-0.366025 + 0.0980762i) q^{88} +(8.33013 + 14.4282i) q^{89} +(1.00000 + 3.00000i) q^{90} +(-8.83013 + 8.83013i) q^{92} +(0.267949 - 1.00000i) q^{93} +(0.633975 - 1.09808i) q^{94} +(5.09808 - 3.36603i) 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 - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} - 6 q^{15} - 2 q^{16} - 4 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} + 12 q^{26} + 2 q^{27} + 16 q^{30} + 12 q^{31} - 6 q^{32} - 2 q^{33} + 8 q^{34} - 12 q^{36} + 12 q^{37} + 2 q^{38} - 12 q^{39} - 10 q^{40} - 6 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} - 18 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} + 6 q^{58} - 6 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{62} - 12 q^{65} + 6 q^{66} - 22 q^{67} - 28 q^{69} + 12 q^{71} + 2 q^{72} + 24 q^{73} - 12 q^{74} - 4 q^{75} + 16 q^{78} + 6 q^{79} + 16 q^{80} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 4 q^{85} + 18 q^{86} - 12 q^{87} + 2 q^{88} + 16 q^{89} + 4 q^{90} - 18 q^{92} + 8 q^{93} + 6 q^{94} + 10 q^{95} - 30 q^{96} + 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 - 6 * q^15 - 2 * q^16 - 4 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 + 12 * q^26 + 2 * q^27 + 16 * q^30 + 12 * q^31 - 6 * q^32 - 2 * q^33 + 8 * q^34 - 12 * q^36 + 12 * q^37 + 2 * q^38 - 12 * q^39 - 10 * q^40 - 6 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 - 18 * 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 + 6 * q^58 - 6 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^62 - 12 * q^65 + 6 * q^66 - 22 * q^67 - 28 * q^69 + 12 * q^71 + 2 * q^72 + 24 * q^73 - 12 * q^74 - 4 * q^75 + 16 * q^78 + 6 * q^79 + 16 * q^80 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 4 * q^85 + 18 * q^86 - 12 * q^87 + 2 * q^88 + 16 * q^89 + 4 * q^90 - 18 * q^92 + 8 * q^93 + 6 * q^94 + 10 * q^95 - 30 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.86603	−	0.500000i	−1.31948	−	0.353553i	−0.470696	−	0.882295i	$-0.655997\pi$
$2$	−1.86603	−	0.500000i	−1.31948	−	0.353553i	−0.848783	+	0.528742i	$0.822664\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	0.946112	+	0.323840i	$0.104974\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	−0.657437	+	0.753510i	$0.728359\pi$
$4$	1.50000	+	0.866025i	0.750000	+	0.433013i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		−	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
$10$	0.866025	−	4.23205i	0.273861	−	1.33829i
$11$	−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	$0.201867\pi$
$12$	−0.866025	+	3.23205i	−0.250000	+	0.933013i
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$		0			0
$15$	−4.09808	+	1.36603i	−1.05812	+	0.352706i
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	−0.378039	−	0.925790i	$-0.623401\pi$
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	0.135503	+	0.990777i	$0.456735\pi$
$18$	1.36603	−	0.366025i	0.321975	−	0.0862730i
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	0.665706	−	0.746214i	$-0.268131\pi$
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	−0.979093	+	0.203411i	$0.934797\pi$
$20$	−1.73205	+	3.46410i	−0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	0.442519	+	0.896759i	$0.354085\pi$
$23$	−1.86603	+	6.96410i	−0.389093	+	1.45212i	−0.831612	+	0.555357i	$0.812582\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	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	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$	8.33013	−	0.500000i	1.52087	−	0.0912871i
$31$	−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	$0.681991\pi$
$32$	1.96410	+	7.33013i	0.347207	+	1.29580i
$33$	−1.36603	−	0.366025i	−0.237795	−	0.0637168i
$34$	2.00000			0.342997
$35$		0			0
$36$	−1.26795			−0.211325
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.625878	−	0.779921i	$-0.284741\pi$
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.152066	+	0.988370i	$0.451407\pi$
$38$	1.36603	+	5.09808i	0.221599	+	0.827017i
$39$	−4.73205	−	2.73205i	−0.757735	−	0.437478i
$40$	−0.767949	+	0.866025i	−0.121423	+	0.136931i
$41$		−	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	0.105349	−	0.994435i	$-0.466404\pi$
$43$	−5.83013	−	5.83013i	−0.889086	−	0.889086i	−0.994435	+	0.105349i	$0.966404\pi$
$44$	−1.09808	+	0.633975i	−0.165541	+	0.0955753i
$45$	−0.901924	−	1.36603i	−0.134451	−	0.203635i
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	−0.977208	−	0.212285i	$-0.931909\pi$
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	0.952429	+	0.304760i	$0.0985762\pi$
$48$	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
$52$	−4.73205	+	1.26795i	−0.656217	+	0.175833i
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.695344	+	0.718677i	$0.255252\pi$
$54$	−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
$58$	1.50000	−	5.59808i	0.196960	−	0.735063i
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	−0.785652	−	0.618669i	$-0.787672\pi$
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	0.928609	+	0.371060i	$0.121005\pi$
$60$	−7.33013	−	1.50000i	−0.946315	−	0.193649i
$61$	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
$65$	−4.73205	−	4.19615i	−0.586939	−	0.520469i
$66$	2.36603	+	1.36603i	0.291238	+	0.168146i
$67$	−0.303848	−	1.13397i	−0.0371209	−	0.138537i	0.944878	−	0.327421i	$-0.106180\pi$
$67$	−0.303848	−	1.13397i	−0.0371209	−	0.138537i	−0.981999	+	0.188884i	$0.939513\pi$
$68$	−1.73205	−	0.464102i	−0.210042	−	0.0562806i
$69$	−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	$0.409402\pi$
$72$	−0.366025	−	0.0980762i	−0.0431365	−	0.0115584i
$73$	−0.928203	−	3.46410i	−0.108638	−	0.405442i	0.890094	−	0.455776i	$-0.150638\pi$
$73$	−0.928203	−	3.46410i	−0.108638	−	0.405442i	−0.998732	+	0.0503336i	$0.983972\pi$
$74$	−8.19615	−	4.73205i	−0.952783	−	0.550090i
$75$	−3.59808	−	8.96410i	−0.415470	−	1.03509i
$76$		−	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	−0.134788	−	0.990874i	$-0.543035\pi$
$79$	5.83013	−	3.36603i	0.655941	−	0.378707i	0.790728	+	0.612167i	$0.209702\pi$
$80$	8.33013	−	5.50000i	0.931337	−	0.614919i
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−0.232051	+	0.866025i	−0.0256257	+	0.0956365i
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	−0.516331	−	0.856389i	$-0.672703\pi$
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	0.856389	+	0.516331i	$0.172703\pi$
$84$		0			0
$85$	−0.732051	−	2.19615i	−0.0794021	−	0.238206i
$86$	7.96410	+	13.7942i	0.858791	+	1.48747i
$87$	−5.59808	+	1.50000i	−0.600177	+	0.160817i
$88$	−0.366025	+	0.0980762i	−0.0390184	+	0.0104550i
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.847998	+	0.529999i	$0.177808\pi$
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.0349934	+	0.999388i	$0.488859\pi$
$90$	1.00000	+	3.00000i	0.105409	+	0.316228i
$91$		0			0
$92$	−8.83013	+	8.83013i	−0.920604	+	0.920604i
$93$	0.267949	−	1.00000i	0.0277850	−	0.103695i
$94$	0.633975	−	1.09808i	0.0653895	−	0.113258i
$95$	5.09808	−	3.36603i	0.523052	−	0.345347i
$96$	−12.6962	+	7.33013i	−1.29580	+	0.748128i
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	0.983870	−	0.178883i	$-0.0572484\pi$
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	−0.178883	+	0.983870i	$0.557248\pi$
$98$		0			0
$99$		−	0.535898i		−	0.0538598i
$100$	−7.96410	−	3.40192i	−0.796410	−	0.340192i
$101$	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	$0.468274\pi$
$102$	1.00000	+	3.73205i	0.0990148	+	0.369528i
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	0.367102	−	0.930181i	$-0.380350\pi$
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	−0.147171	+	0.989111i	$0.547017\pi$
$104$	−1.46410			−0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	−8.59808	−	2.30385i	−0.831207	−	0.222721i	−0.181967	−	0.983305i	$-0.558246\pi$
$107$	−8.59808	−	2.30385i	−0.831207	−	0.222721i	−0.649240	+	0.760583i	$0.724913\pi$
$108$	1.96410	+	7.33013i	0.188996	+	0.705342i
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.954061	−	0.299614i	$-0.0968578\pi$
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.217557	+	0.976048i	$0.430191\pi$
$110$	2.36603	+	2.09808i	0.225592	+	0.200044i
$111$			9.46410i			0.898293i
$112$		0			0
$113$	−4.26795	−	4.26795i	−0.401495	−	0.401495i	0.477265	−	0.878760i	$-0.341628\pi$
$113$	−4.26795	−	4.26795i	−0.401495	−	0.401495i	−0.878760	+	0.477265i	$0.841628\pi$
$114$	−8.83013	+	5.09808i	−0.827017	+	0.477479i
$115$	−15.7942	−	3.23205i	−1.47282	−	0.301390i
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$	0.535898	−	2.00000i	0.0495438	−	0.184900i
$118$	−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
$122$	−15.7942	+	4.23205i	−1.42994	+	0.383152i
$123$	0.866025	−	0.232051i	0.0780869	−	0.0209233i
$124$	−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	−0.933132	−	0.359535i	$-0.882935\pi$
$127$	−6.46410	+	6.46410i	−0.573596	+	0.573596i	0.359535	+	0.933132i	$0.382935\pi$
$128$	1.06218	−	3.96410i	0.0938841	−	0.350380i
$129$	7.96410	−	13.7942i	0.701200	−	1.21451i
$130$	6.73205	+	10.1962i	0.590440	+	0.894262i
$131$	−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
$135$	−6.50000	+	7.33013i	−0.559431	+	0.630877i
$136$	−0.464102	−	0.267949i	−0.0397964	−	0.0229765i
$137$	2.80385	+	10.4641i	0.239549	+	0.894009i	0.976045	+	0.217567i	$0.0698121\pi$
$137$	2.80385	+	10.4641i	0.239549	+	0.894009i	−0.736496	+	0.676441i	$0.763521\pi$
$138$	25.9904	+	6.96410i	2.21245	+	0.592824i
$139$	11.6603			0.989010			0.494505	−	0.869175i	$-0.335349\pi$
$139$	11.6603			0.989010			0.494505	+	0.869175i	$0.335349\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$	−8.83013	−	2.36603i	−0.741008	−	0.198552i
$143$	−0.535898	−	2.00000i	−0.0448141	−	0.167248i
$144$	2.83013	+	1.63397i	0.235844	+	0.136165i
$145$	−6.69615	+	0.401924i	−0.556085	+	0.0333780i
$146$			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	−0.0471484	−	0.998888i	$-0.515013\pi$
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	0.841488	+	0.540276i	$0.181680\pi$
$150$	2.23205	+	18.5263i	0.182246	+	1.51266i
$151$	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	$-0.0239980\pi$
$152$	0.366025	−	1.36603i	0.0296886	−	0.110799i
$153$	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
$157$	23.7583	−	6.36603i	1.89612	−	0.508064i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	23.7583	−	6.36603i	1.89612	−	0.508064i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	−12.5622	+	3.36603i	−0.999393	+	0.267787i
$159$	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
$163$	1.43782	−	5.36603i	0.112619	−	0.420300i	−0.886479	−	0.462769i	$-0.846856\pi$
$163$	1.43782	−	5.36603i	0.112619	−	0.420300i	0.999098	+	0.0424696i	$0.0135226\pi$
$164$	0.401924	−	0.696152i	0.0313850	−	0.0543604i
$165$	0.633975	−	3.09808i	0.0493549	−	0.241185i
$166$	−7.33013	+	4.23205i	−0.568928	+	0.328471i
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	0.155354	−	0.987859i	$-0.450348\pi$
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	−0.987859	+	0.155354i	$0.950348\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	0.267949	+	4.46410i	0.0205508	+	0.342381i
$171$	1.73205	+	1.00000i	0.132453	+	0.0764719i
$172$	−3.69615	−	13.7942i	−0.281829	−	1.05180i
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.744317	−	0.667827i	$-0.767225\pi$
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.978511	+	0.206197i	$0.933891\pi$
$174$	11.1962			0.848778
$175$		0			0
$176$	3.26795			0.246331
$177$	4.09808	+	1.09808i	0.308030	+	0.0825365i
$178$	−8.33013	−	31.0885i	−0.624369	−	2.33018i
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.307488	−	0.951552i	$-0.599489\pi$
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.977812	+	0.209483i	$0.932822\pi$
$180$	−0.169873	−	2.83013i	−0.0126616	−	0.210945i
$181$		−	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
$185$	−2.19615	+	10.7321i	−0.161464	+	0.789036i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	0.196152	−	0.732051i	0.0143441	−	0.0535329i
$188$	−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	$-0.373631\pi$
$192$	10.6962	−	2.86603i	0.771928	−	0.206838i
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	−0.368591	−	0.929592i	$-0.620160\pi$
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	0.145587	+	0.989346i	$0.453493\pi$
$194$	−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	0.00633876	−	0.999980i	$-0.497982\pi$
$197$	14.1244	−	14.1244i	1.00632	−	1.00632i	0.999980	−	0.00633876i	$-0.00201770\pi$
$198$	−0.267949	+	1.00000i	−0.0190423	+	0.0710669i
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.0361978	+	0.999345i	$0.511525\pi$
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.847359	+	0.531021i	$0.821809\pi$
$200$	−2.03590	−	1.59808i	−0.143960	−	0.113001i
$201$	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
$205$	1.03590	−	0.0621778i	0.0723503	−	0.00434269i
$206$	−3.86603	−	2.23205i	−0.269359	−	0.155514i
$207$	−1.36603	−	5.09808i	−0.0949453	−	0.354341i
$208$	12.1962	+	3.26795i	0.845651	+	0.226592i
$209$	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	$0.385853\pi$
$212$	11.8301	+	3.16987i	0.812496	+	0.217708i
$213$	2.36603	+	8.83013i	0.162117	+	0.605030i
$214$	14.8923	+	8.59808i	1.01802	+	0.587752i
$215$	12.2321	−	13.7942i	0.834219	−	0.940759i
$216$			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
$220$	−1.56218	−	2.36603i	−0.105322	−	0.159517i
$221$	1.46410	−	2.53590i	0.0984861	−	0.170583i
$222$	4.73205	−	17.6603i	0.317594	−	1.18528i
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	−0.881779	−	0.471662i	$-0.843654\pi$
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	0.471662	+	0.881779i	$0.343654\pi$
$224$		0			0
$225$	2.92820	−	2.19615i	0.195214	−	0.146410i
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	−0.262072	−	0.965048i	$-0.584406\pi$
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	0.255563	+	0.966792i	$0.417739\pi$
$228$	8.83013	−	2.36603i	0.584789	−	0.156694i
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	0.902838	−	0.429981i	$-0.141480\pi$
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	−0.823794	+	0.566890i	$0.808147\pi$
$230$	27.8564	+	13.9282i	1.83680	+	0.918399i
$231$		0			0
$232$	−1.09808	+	1.09808i	−0.0720922	+	0.0720922i
$233$	−0.464102	+	1.73205i	−0.0304043	+	0.113470i	−0.979460	−	0.201637i	$-0.935374\pi$
$233$	−0.464102	+	1.73205i	−0.0304043	+	0.113470i	0.949056	+	0.315107i	$0.102041\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	−1.43782	−	0.294229i	−0.0937932	−	0.0191934i
$236$	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	$0.202788\pi$
$239$			18.3923i			1.18970i	−0.803837	+	0.594850i	$0.797212\pi$
$240$	14.4282	+	12.7942i	0.931337	+	0.825864i
$241$	−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	$0.848468\pi$
$242$	−5.23205	−	19.5263i	−0.336329	−	1.25520i
$243$	−7.19615	−	1.92820i	−0.461633	−	0.123694i
$244$	14.6603			0.938527
$245$		0			0
$246$	−1.73205			−0.110432
$247$	7.46410	+	2.00000i	0.474929	+	0.127257i
$248$	−0.0717968	−	0.267949i	−0.00455910	−	0.0170148i
$249$	7.33013	+	4.23205i	0.464528	+	0.268195i
$250$	−1.76795	+	21.5263i	−0.111815	+	1.36144i
$251$			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
$255$	3.73205	−	2.46410i	0.233710	−	0.154308i
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	−0.984992	−	0.172600i	$-0.944783\pi$
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	0.939328	+	0.343020i	$0.111450\pi$
$258$	−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
$262$	15.9282	−	4.26795i	0.984048	−	0.263675i
$263$	−8.06218	+	2.16025i	−0.497135	+	0.133207i	−0.498670	−	0.866792i	$-0.666178\pi$
$263$	−8.06218	+	2.16025i	−0.497135	+	0.133207i	0.00153494	+	0.999999i	$0.499511\pi$
$264$	−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
$268$	0.526279	−	1.96410i	0.0321476	−	0.119977i
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	−0.930507	−	0.366275i	$-0.880633\pi$
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	0.782457	+	0.622705i	$0.213966\pi$
$270$	15.7942	−	10.4282i	0.961206	−	0.634640i
$271$	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
$275$	1.43782	−	3.36603i	0.0867039	−	0.202979i
$276$	−20.8923	−	12.0622i	−1.25757	−	0.726058i
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	−0.926562	−	0.376141i	$-0.877251\pi$
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	0.614356	−	0.789029i	$-0.289416\pi$
$278$	−21.7583	−	5.83013i	−1.30498	−	0.349668i
$279$	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	$0.373989\pi$
$282$	2.36603	+	0.633975i	0.140895	+	0.0377526i
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	0.770523	+	0.637413i	$0.219995\pi$
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	−0.348586	+	0.937277i	$0.613338\pi$
$284$	7.09808	+	4.09808i	0.421193	+	0.243176i
$285$	8.83013	+	7.83013i	0.523052	+	0.463817i
$286$			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
$290$	12.6962	+	2.59808i	0.745544	+	0.152564i
$291$	−10.8301	+	18.7583i	−0.634873	+	1.09963i
$292$	1.60770	−	6.00000i	0.0940832	−	0.351123i
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.0774974	−	0.996993i	$-0.475307\pi$
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.996993	−	0.0774974i	$-0.0246929\pi$
$294$		0			0
$295$	4.39230	+	2.19615i	0.255730	+	0.127865i
$296$	1.26795	+	2.19615i	0.0736980	+	0.127649i
$297$	−3.09808	+	0.830127i	−0.179769	+	0.0481689i
$298$	−20.8923	+	5.59808i	−1.21026	+	0.324288i
$299$	−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
$303$	−5.86603	+	21.8923i	−0.336994	+	1.25768i
$304$	−6.09808	+	10.5622i	−0.349749	+	0.605782i
$305$	10.4282	+	15.7942i	0.597117	+	0.904375i
$306$	−1.26795	+	0.732051i	−0.0724838	+	0.0418486i
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	0.390257	−	0.920706i	$-0.372386\pi$
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	−0.920706	+	0.390257i	$0.872386\pi$
$308$		0			0
$309$			4.46410i			0.253954i
$310$	−1.53590	+	1.73205i	−0.0872332	+	0.0983739i
$311$	−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	$0.844887\pi$
$312$	−0.732051	−	2.73205i	−0.0414442	−	0.154672i
$313$	−19.3923	−	5.19615i	−1.09612	−	0.293704i	−0.334935	−	0.942241i	$-0.608714\pi$
$313$	−19.3923	−	5.19615i	−1.09612	−	0.293704i	−0.761183	+	0.648537i	$0.775381\pi$
$314$	−47.5167			−2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	4.46410	+	1.19615i	0.250729	+	0.0671826i	0.381994	−	0.924165i	$-0.375237\pi$
$317$	4.46410	+	1.19615i	0.250729	+	0.0671826i	−0.131265	+	0.991347i	$0.541904\pi$
$318$	−6.83013	−	25.4904i	−0.383015	−	1.42943i
$319$	−1.90192	−	1.09808i	−0.106487	−	0.0614805i
$320$	12.7942	−	0.767949i	0.715219	−	0.0429297i
$321$		−	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
$325$	8.73205	−	11.1244i	0.484367	−	0.617068i
$326$	−5.36603	+	9.29423i	−0.297197	+	0.514760i
$327$	−7.06218	+	26.3564i	−0.390539	+	1.45751i
$328$	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	$-0.418242\pi$
$332$	7.33013	−	1.96410i	0.402293	−	0.107794i
$333$	−3.46410	+	0.928203i	−0.189832	+	0.0508652i
$334$	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	−0.0983001	−	0.995157i	$-0.531340\pi$
$337$	16.4641	−	16.4641i	0.896857	−	0.896857i	0.995157	+	0.0983001i	$0.0313405\pi$
$338$	2.50000	−	9.33013i	0.135982	−	0.507492i
$339$	5.83013	−	10.0981i	0.316649	−	0.548452i
$340$	0.803848	−	3.92820i	0.0435948	−	0.213037i
$341$	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
$345$	−1.86603	−	31.0885i	−0.100463	−	1.67375i
$346$	39.2487	+	22.6603i	2.11002	+	1.21822i
$347$	−2.08846	−	7.79423i	−0.112114	−	0.418416i	0.886941	−	0.461884i	$-0.152826\pi$
$347$	−2.08846	−	7.79423i	−0.112114	−	0.418416i	−0.999055	+	0.0434674i	$0.986160\pi$
$348$	−9.69615	−	2.59808i	−0.519768	−	0.139272i
$349$	9.73205			0.520945			0.260472	−	0.965481i	$-0.416122\pi$
$349$	9.73205			0.520945			0.260472	+	0.965481i	$0.416122\pi$
$350$		0			0
$351$	−12.3923			−0.661452
$352$	−5.36603	−	1.43782i	−0.286010	−	0.0766362i
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	0.917048	−	0.398777i	$-0.130565\pi$
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	−0.993575	+	0.113173i	$0.963899\pi$
$354$	−7.09808	−	4.09808i	−0.377258	−	0.217810i
$355$	0.633975	+	10.5622i	0.0336479	+	0.560582i
$356$			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	−0.788941	−	0.614468i	$-0.789371\pi$
$359$	−12.3397	+	7.12436i	−0.651267	+	0.376009i	0.137675	+	0.990478i	$0.456037\pi$
$360$	0.169873	−	0.830127i	0.00895309	−	0.0437515i
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−4.59808	+	17.1603i	−0.241670	+	0.901923i
$363$	−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
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	−0.307193	−	0.951647i	$-0.599390\pi$
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	0.209787	+	0.977747i	$0.432723\pi$
$368$	31.0885	−	8.33013i	1.62060	−	0.434238i
$369$	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
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	0.762987	+	0.646414i	$0.223732\pi$
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	−0.983973	+	0.178317i	$0.942935\pi$
$374$	−0.732051	+	1.26795i	−0.0378534	+	0.0655641i
$375$	19.5263	−	9.23205i	1.00833	−	0.476741i
$376$	−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	$-0.831515\pi$
$379$		−	19.6603i		−	1.00988i	0.863155	−	0.504940i	$-0.168485\pi$
$380$	10.5622	−	0.633975i	0.541828	−	0.0325222i
$381$	−15.2942	−	8.83013i	−0.783547	−	0.452381i
$382$	8.36603	+	31.2224i	0.428043	+	1.59748i
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.892626	−	0.450797i	$-0.148860\pi$
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.547638	+	0.836715i	$0.315527\pi$
$384$	7.92820			0.404584
$385$		0			0
$386$	6.19615			0.315376
$387$	5.83013	+	1.56218i	0.296362	+	0.0794100i
$388$	5.02628	+	18.7583i	0.255171	+	0.952310i
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	0.683040	−	0.730381i	$-0.260658\pi$
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	−0.291009	+	0.956720i	$0.593991\pi$
$390$	−15.6603	+	17.6603i	−0.792988	+	0.894262i
$391$		−	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
$395$	8.29423	+	12.5622i	0.417328	+	0.632072i
$396$	0.464102	−	0.803848i	0.0233220	−	0.0403949i
$397$	5.36603	−	20.0263i	0.269313	−	1.00509i	−0.690244	−	0.723577i	$-0.742497\pi$
$397$	5.36603	−	20.0263i	0.269313	−	1.00509i	0.959557	−	0.281514i	$-0.0908365\pi$
$398$	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	$0.921898\pi$
$402$	−4.23205	+	1.13397i	−0.211076	+	0.0565575i
$403$	1.46410	−	0.392305i	0.0729321	−	0.0195421i
$404$	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
$408$	0.267949	−	1.00000i	0.0132655	−	0.0495074i
$409$	3.42820	−	5.93782i	0.169514	−	0.293606i	−0.768735	−	0.639567i	$-0.779114\pi$
$409$	3.42820	−	5.93782i	0.169514	−	0.293606i	0.938249	+	0.345961i	$0.112447\pi$
$410$	−1.96410	−	0.401924i	−0.0970001	−	0.0198496i
$411$	−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
$415$	7.33013	+	6.50000i	0.359822	+	0.319072i
$416$	−18.5885	−	10.7321i	−0.911374	−	0.526182i
$417$	5.83013	+	21.7583i	0.285503	+	1.06551i
$418$	−3.73205	−	1.00000i	−0.182541	−	0.0489116i
$419$	−3.85641			−0.188398			−0.0941989	−	0.995553i	$-0.530029\pi$
$419$	−3.85641			−0.188398			−0.0941989	+	0.995553i	$0.530029\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	−19.0263	−	5.09808i	−0.926185	−	0.248170i
$423$	−0.124356	−	0.464102i	−0.00604638	−	0.0225654i
$424$	3.16987	+	1.83013i	0.153943	+	0.0888788i
$425$	4.80385	−	1.92820i	0.233021	−	0.0935316i
$426$		−	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
$430$	−29.7224	+	19.6244i	−1.43334	+	0.946370i
$431$	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	$0.134443\pi$
$432$	5.06218	−	18.8923i	0.243554	−	0.908956i
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.194833	+	0.980836i	$0.562417\pi$
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.980836	+	0.194833i	$0.937583\pi$
$434$		0			0
$435$	−4.09808	−	12.2942i	−0.196488	−	0.589463i
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	19.0263	−	5.09808i	0.910150	−	0.243874i
$438$	−12.9282	+	3.46410i	−0.617733	+	0.165521i
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	−0.949054	−	0.315113i	$-0.897957\pi$
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	0.201631	−	0.979462i	$-0.435376\pi$
$440$	−0.267949	−	0.803848i	−0.0127740	−	0.0383219i
$441$		0			0
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	0.937822	−	3.50000i	0.0445573	−	0.166290i	−0.940062	−	0.341003i	$-0.889233\pi$
$443$	0.937822	−	3.50000i	0.0445573	−	0.166290i	0.984619	+	0.174713i	$0.0558999\pi$
$444$	−8.19615	+	14.1962i	−0.388972	+	0.673720i
$445$	−31.0885	+	20.5263i	−1.47373	+	0.973039i
$446$	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	$-0.961960\pi$
$449$		−	5.05256i		−	0.238445i	0.992868	−	0.119222i	$-0.0380402\pi$
$450$	−6.56218	+	2.63397i	−0.309344	+	0.124167i
$451$	0.294229	+	0.169873i	0.0138547	+	0.00799901i
$452$	−2.70577	−	10.0981i	−0.127269	−	0.474974i
$453$	25.8564	+	6.92820i	1.21484	+	0.325515i
$454$	0.196152			0.00920589
$455$		0			0
$456$	2.73205			0.127940
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.893724	−	0.448618i	$-0.148084\pi$
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.549678	+	0.835376i	$0.314750\pi$
$458$	−1.19615	−	4.46410i	−0.0558925	−	0.208594i
$459$	−3.92820	−	2.26795i	−0.183353	−	0.105859i
$460$	−20.8923	−	18.5263i	−0.974109	−	0.863792i
$461$			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	0.986862	−	0.161563i	$-0.0516534\pi$
$463$	17.7583	+	17.7583i	0.825300	+	0.825300i	−0.161563	+	0.986862i	$0.551653\pi$
$464$	11.5981	−	6.69615i	0.538427	−	0.310861i
$465$	2.26795	+	0.464102i	0.105174	+	0.0215222i
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	0.443303	+	0.896372i	$0.353807\pi$
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	−0.832097	+	0.554629i	$0.812860\pi$
$468$	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
$472$	1.09808	−	0.294229i	0.0505431	−	0.0135430i
$473$	5.83013	−	1.56218i	0.268070	−	0.0718290i
$474$	−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
$478$	9.19615	−	34.3205i	0.420622	−	1.56978i
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	−0.375161	−	0.926960i	$-0.622412\pi$
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	0.990351	−	0.138581i	$-0.0442542\pi$
$480$	−18.0622	−	27.3564i	−0.824422	−	1.24864i
$481$	−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
$485$	−16.6340	+	18.7583i	−0.755310	+	0.851772i
$486$	12.4641	+	7.19615i	0.565383	+	0.326424i
$487$	2.22243	+	8.29423i	0.100708	+	0.375847i	0.997823	−	0.0659498i	$-0.0210077\pi$
$487$	2.22243	+	8.29423i	0.100708	+	0.375847i	−0.897115	+	0.441797i	$0.854341\pi$
$488$	4.23205	+	1.13397i	0.191576	+	0.0513326i
$489$	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	$0.630880\pi$
$492$	1.50000	+	0.401924i	0.0676252	+	0.0181201i
$493$	−0.803848	−	3.00000i	−0.0362035	−	0.135113i
$494$	−12.9282	−	7.46410i	−0.581667	−	0.335826i
$495$	1.19615	−	0.0717968i	0.0537631	−	0.00322702i
$496$			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	0.319095	−	0.947723i	$-0.396621\pi$
$499$	29.0263	−	16.7583i	1.29939	−	0.750206i	0.980300	+	0.197517i	$0.0632877\pi$
$500$	6.52628	−	18.2321i	0.291864	−	0.815362i
$501$	14.6962	−	25.4545i	0.656576	−	1.13722i
$502$	2.92820	−	10.9282i	0.130692	−	0.487750i
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	−0.991741	−	0.128253i	$-0.959063\pi$
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	0.128253	+	0.991741i	$0.459063\pi$
$504$		0			0
$505$	−11.7321	+	23.4641i	−0.522069	+	1.04414i
$506$	5.09808	+	8.83013i	0.226637	+	0.392547i
$507$	−9.33013	+	2.50000i	−0.414365	+	0.111029i
$508$	−15.2942	+	4.09808i	−0.678572	+	0.181823i
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	0.993353	+	0.115104i	$0.0367200\pi$
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	−0.396994	+	0.917821i	$0.629947\pi$
$510$	−8.19615	+	2.73205i	−0.362932	+	0.120977i
$511$		0			0
$512$	20.6865	−	20.6865i	0.914224	−	0.914224i
$513$	3.09808	−	11.5622i	0.136783	−	0.510483i
$514$	2.73205	−	4.73205i	0.120506	−	0.208722i
$515$	−1.03590	+	5.06218i	−0.0456471	+	0.223066i
$516$	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
$520$	−0.196152	−	3.26795i	−0.00860185	−	0.143309i
$521$	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	$0.639745\pi$
$522$	1.09808	+	4.09808i	0.0480615	+	0.179368i
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.0723082	−	0.997382i	$-0.523037\pi$
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.561312	+	0.827604i	$0.689703\pi$
$524$	−14.7846			−0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	0.535898	+	0.143594i	0.0233441	+	0.00625503i
$528$	1.63397	+	6.09808i	0.0711096	+	0.265385i
$529$	−25.0981	−	14.4904i	−1.09122	−	0.630017i
$530$	−1.83013	−	30.4904i	−0.0794956	−	1.32442i
$531$			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
$535$	3.99038	−	19.5000i	0.172519	−	0.843059i
$536$	0.303848	−	0.526279i	0.0131242	−	0.0227318i
$537$	9.92820	−	37.0526i	0.428434	−	1.59894i
$538$	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	$0.701557\pi$
$542$	−46.1506	+	12.3660i	−1.98234	+	0.531166i
$543$	17.1603	−	4.59808i	0.736417	−	0.197322i
$544$	−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	−0.573204	−	0.819413i	$-0.694300\pi$
$547$	5.75833	−	5.75833i	0.246208	−	0.246208i	0.819413	+	0.573204i	$0.194300\pi$
$548$	−4.85641	+	18.1244i	−0.207455	+	0.774234i
$549$	−3.09808	+	5.36603i	−0.132223	+	0.229016i
$550$	−4.36603	+	5.56218i	−0.186168	+	0.237172i
$551$	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
$555$	−21.1244	+	1.26795i	−0.896679	+	0.0538214i
$556$	17.4904	+	10.0981i	0.741757	+	0.428254i
$557$	−1.77757	−	6.63397i	−0.0753180	−	0.281091i	0.917987	−	0.396610i	$-0.129813\pi$
$557$	−1.77757	−	6.63397i	−0.0753180	−	0.281091i	−0.993305	+	0.115519i	$0.963147\pi$
$558$	−0.732051	−	0.196152i	−0.0309902	−	0.00830379i
$559$	23.3205			0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$	−24.1244	−	6.46410i	−1.01762	−	0.272672i
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	−0.975269	−	0.221021i	$-0.929061\pi$
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	0.734097	−	0.679044i	$-0.237606\pi$
$564$	−1.90192	−	1.09808i	−0.0800854	−	0.0462373i
$565$	8.95448	−	10.0981i	0.376718	−	0.424829i
$566$		−	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	−0.747989	−	0.663712i	$-0.768980\pi$
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	0.200797	+	0.979633i	$0.435647\pi$
$570$	−12.5622	−	19.0263i	−0.526172	−	0.796923i
$571$	−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	$0.304492\pi$
$572$	0.928203	−	3.46410i	0.0388101	−	0.144841i
$573$	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
$577$	−27.4904	+	7.36603i	−1.14444	+	0.306652i	−0.780735	−	0.624863i	$-0.785155\pi$
$577$	−27.4904	+	7.36603i	−1.14444	+	0.306652i	−0.363705	+	0.931514i	$0.618488\pi$
$578$	29.7224	−	7.96410i	1.23629	−	0.331263i
$579$	−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
$583$	−1.33975	+	5.00000i	−0.0554866	+	0.207079i
$584$	0.928203	−	1.60770i	0.0384093	−	0.0665269i
$585$	4.53590	+	0.928203i	0.187536	+	0.0383765i
$586$	−43.5167	+	25.1244i	−1.79766	+	1.03788i
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.997789	−	0.0664553i	$-0.978831\pi$
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.0664553	−	0.997789i	$-0.521169\pi$
$588$		0			0
$589$			1.46410i			0.0603273i
$590$	−7.09808	−	6.29423i	−0.292223	−	0.259129i
$591$	33.4186	+	19.2942i	1.37466	+	0.793659i
$592$	−5.66025	−	21.1244i	−0.232635	−	0.868206i
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	0.391027	−	0.920379i	$-0.372120\pi$
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	−0.121550	+	0.992585i	$0.538787\pi$
$594$	6.19615			0.254231
$595$		0			0
$596$	19.3923			0.794340
$597$	−46.5167	−	12.4641i	−1.90380	−	0.510122i
$598$	10.1962	+	38.0526i	0.416952	+	1.55608i
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.985980	−	0.166864i	$-0.0533640\pi$
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.348482	+	0.937316i	$0.386697\pi$
$600$	1.96410	−	4.59808i	0.0801841	−	0.187716i
$601$		−	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
$605$	−19.5263	+	12.8923i	−0.793856	+	0.524147i
$606$	21.8923	−	37.9186i	0.889314	−	1.54034i
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	−0.996789	−	0.0800683i	$-0.974486\pi$
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	0.903279	+	0.429053i	$0.141153\pi$
$608$	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
$612$	1.26795	−	0.339746i	0.0512538	−	0.0137334i
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.520258	−	0.854009i	$-0.674164\pi$
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.0235520	+	0.999723i	$0.507498\pi$
$614$	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	−0.346590	+	0.938017i	$0.612660\pi$
$617$	−31.9090	+	31.9090i	−1.28461	+	1.28461i	−0.938017	+	0.346590i	$0.887340\pi$
$618$	2.23205	−	8.33013i	0.0897863	−	0.335087i
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	−0.867990	−	0.496582i	$-0.834588\pi$
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	0.864048	+	0.503410i	$0.167921\pi$
$620$	1.73205	−	1.14359i	0.0695608	−	0.0459278i
$621$	−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
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	33.5885	+	19.3923i	1.34246	+	0.775072i
$627$	1.00000	+	3.73205i	0.0399362	+	0.149044i
$628$	41.1506	+	11.0263i	1.64209	+	0.439996i
$629$	−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	$0.322479\pi$
$632$	3.36603	+	0.901924i	0.133893	+	0.0358766i
$633$	5.09808	+	19.0263i	0.202630	+	0.756227i
$634$	−7.73205	−	4.46410i	−0.307079	−	0.177292i
$635$	−15.2942	−	13.5622i	−0.606933	−	0.538199i
$636$			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
$640$	8.99038	+	1.83975i	0.355376	+	0.0727223i
$641$	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	$0.124677\pi$
$642$	−8.59808	+	32.0885i	−0.339339	+	1.26643i
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	−0.0346302	−	0.999400i	$-0.511025\pi$
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	0.999400	+	0.0346302i	$0.0110253\pi$
$644$		0			0
$645$	31.8564	+	15.9282i	1.25434	+	0.627172i
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	−0.363436	−	0.931619i	$-0.618397\pi$
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	0.151065	+	0.988524i	$0.451730\pi$
$648$	−5.33013	+	1.42820i	−0.209387	+	0.0561051i
$649$	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
$653$	2.33975	−	8.73205i	0.0915613	−	0.341712i	−0.904914	−	0.425594i	$-0.860065\pi$
$653$	2.33975	−	8.73205i	0.0915613	−	0.341712i	0.996476	+	0.0838822i	$0.0267319\pi$
$654$	26.3564	−	45.6506i	1.03062	−	1.78508i
$655$	−10.5167	−	15.9282i	−0.410920	−	0.622366i
$656$	−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	$0.0645457\pi$
$659$			10.3397i			0.402779i	−0.979511	+	0.201390i	$0.935454\pi$
$660$	3.63397	−	4.09808i	0.141452	−	0.159517i
$661$	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	$0.577754\pi$
$662$	12.9282	+	48.2487i	0.502469	+	1.87524i
$663$	5.46410	+	1.46410i	0.212208	+	0.0568610i
$664$	2.26795			0.0880135
$665$		0			0
$666$	6.92820			0.268462
$667$	−20.8923	−	5.59808i	−0.808953	−	0.216758i
$668$	−6.82051	−	25.4545i	−0.263893	−	0.984864i
$669$	−14.4904	−	8.36603i	−0.560230	−	0.323449i
$670$	−5.06218	+	0.303848i	−0.195569	+	0.0117387i
$671$			6.19615i			0.239200i
$672$		0			0
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	0.316662	−	0.948539i	$-0.397438\pi$
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	−0.948539	+	0.316662i	$0.897438\pi$
$674$	−38.9545	+	22.4904i	−1.50047	+	0.866297i
$675$	−17.2321	−	13.5263i	−0.663262	−	0.520627i
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	−0.992380	−	0.123213i	$-0.960680\pi$
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	0.921033	+	0.389485i	$0.127347\pi$
$678$	−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
$682$	−0.732051	+	0.196152i	−0.0280317	+	0.00751106i
$683$	−18.4282	+	4.93782i	−0.705136	+	0.188941i	−0.593530	−	0.804812i	$-0.702266\pi$
$683$	−18.4282	+	4.93782i	−0.705136	+	0.188941i	−0.111606	+	0.993753i	$0.535599\pi$
$684$	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
$688$	−9.52628	+	35.5526i	−0.363186	+	1.35543i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$	−12.0622	+	58.9449i	−0.459199	+	2.24399i
$691$	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
$695$	1.56218	+	26.0263i	0.0592568	+	0.987233i
$696$	−2.59808	−	1.50000i	−0.0984798	−	0.0568574i
$697$	0.124356	+	0.464102i	0.00471031	+	0.0175791i
$698$	−18.1603	−	4.86603i	−0.687376	−	0.184182i
$699$	−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	$0.647925\pi$
$702$	23.1244	+	6.19615i	0.872773	+	0.233859i
$703$	−3.46410	−	12.9282i	−0.130651	−	0.487596i
$704$	3.63397	+	2.09808i	0.136961	+	0.0790742i
$705$	−0.169873	−	2.83013i	−0.00639779	−	0.106589i
$706$			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	−0.362959	−	0.931805i	$-0.618233\pi$
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	0.625488	+	0.780234i	$0.284900\pi$
$710$	4.09808	−	20.0263i	0.153798	−	0.751573i
$711$	−2.46410	+	4.26795i	−0.0924110	+	0.160061i
$712$	−2.23205	+	8.33013i	−0.0836496	+	0.312185i
$713$	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
$717$	−34.3205	+	9.19615i	−1.28172	+	0.343437i
$718$	26.5885	−	7.12436i	0.992272	−	0.265879i
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	0.926816	−	0.375516i	$-0.122534\pi$
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	−0.788614	+	0.614888i	$0.789201\pi$
$720$	−3.26795	+	6.53590i	−0.121789	+	0.243579i
$721$		0			0
$722$	−15.7583	+	15.7583i	−0.586464	+	0.586464i
$723$	8.39230	−	31.3205i	0.312113	−	1.16482i
$724$	7.96410	−	13.7942i	0.295984	−	0.512658i
$725$	−1.79423	−	14.8923i	−0.0666360	−	0.553086i
$726$	33.8205	−	19.5263i	1.25520	−	0.724688i
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	0.610338	−	0.792141i	$-0.291033\pi$
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	−0.792141	+	0.610338i	$0.791033\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$	−15.4641	+	0.928203i	−0.572352	+	0.0343543i
$731$	7.39230	+	4.26795i	0.273414	+	0.157856i
$732$	7.33013	+	27.3564i	0.270929	+	1.01112i
$733$	9.83013	+	2.63397i	0.363084	+	0.0972881i	0.435749	−	0.900068i	$-0.356484\pi$
$733$	9.83013	+	2.63397i	0.363084	+	0.0972881i	−0.0726647	+	0.997356i	$0.523150\pi$
$734$	3.73205			0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	0.830127	+	0.222432i	0.0305781	+	0.00819338i
$738$	−0.169873	−	0.633975i	−0.00625311	−	0.0233369i
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	0.630525	−	0.776169i	$-0.282840\pi$
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	−0.356920	+	0.934135i	$0.616173\pi$
$740$	−12.5885	+	14.1962i	−0.462761	+	0.521861i
$741$			14.9282i			0.548401i
$742$		0			0
$743$	−14.8301	−	14.8301i	−0.544065	−	0.544065i	0.380653	−	0.924718i	$-0.375699\pi$
$743$	−14.8301	−	14.8301i	−0.544065	−	0.544065i	−0.924718	+	0.380653i	$0.875699\pi$
$744$	0.464102	−	0.267949i	0.0170148	−	0.00982349i
$745$	13.7942	+	20.8923i	0.505381	+	0.765435i
$746$	15.9282	−	27.5885i	0.583173	−	1.01009i
$747$	−0.830127	+	3.09808i	−0.0303728	+	0.113353i
$748$	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	$0.917910\pi$
$752$	2.83013	−	0.758330i	0.103204	−	0.0276535i
$753$	−10.9282	+	2.92820i	−0.398246	+	0.106710i
$754$	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	−0.518331	−	0.855180i	$-0.673446\pi$
$757$	9.26795	−	9.26795i	0.336849	−	0.336849i	0.855180	+	0.518331i	$0.173446\pi$
$758$	−9.83013	+	36.6865i	−0.357046	+	1.33251i
$759$	5.09808	−	8.83013i	0.185048	−	0.320513i
$760$	3.09808	+	0.633975i	0.112379	+	0.0229967i
$761$	−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
$765$	1.26795	+	1.12436i	0.0458428	+	0.0406512i
$766$	−48.8205	−	28.1865i	−1.76396	−	1.01842i
$767$	1.60770	+	6.00000i	0.0580505	+	0.216647i
$768$	−36.1865	−	9.69615i	−1.30577	−	0.349880i
$769$	−47.1769			−1.70124			−0.850622	−	0.525778i	$-0.823774\pi$
$769$	−47.1769			−1.70124			−0.850622	+	0.525778i	$0.823774\pi$
$770$		0			0
$771$	−5.46410			−0.196785
$772$	−5.36603	−	1.43782i	−0.193127	−	0.0517484i
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	−0.996919	−	0.0784412i	$-0.975006\pi$
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	0.824136	−	0.566391i	$-0.191661\pi$
$774$	−10.0981	−	5.83013i	−0.362968	−	0.209560i
$775$	2.46410	+	1.05256i	0.0885131	+	0.0378090i
$776$			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
$780$	17.6603	−	11.6603i	0.632339	−	0.417504i
$781$	−1.73205	+	3.00000i	−0.0619777	+	0.107348i
$782$	−3.73205	+	13.9282i	−0.133458	+	0.498072i
$783$	−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
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.103243	−	0.994656i	$-0.467078\pi$
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.586739	+	0.809776i	$0.300412\pi$
$788$	33.4186	−	8.95448i	1.19049	−	0.318990i
$789$	−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
$793$	−6.19615	+	23.1244i	−0.220032	+	0.821170i
$794$	−20.0263	+	34.6865i	−0.710706	+	1.23098i
$795$	−25.4904	+	16.8301i	−0.904051	+	0.596903i
$796$	−37.3923	+	21.5885i	−1.32534	+	0.765183i
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.999002	+	0.0446702i	$0.0142237\pi$
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.0446702	+	0.999002i	$0.485776\pi$
$798$		0			0
$799$		−	0.679492i		−	0.0240387i
$800$	−14.1340	−	35.2128i	−0.499711	−	1.24496i
$801$	−10.5622	−	6.09808i	−0.373196	−	0.215465i
$802$	5.50000	+	20.5263i	0.194212	+	0.724808i
$803$	2.53590	+	0.679492i	0.0894899	+	0.0239787i
$804$	3.92820			0.138537
$805$		0			0
$806$	−2.92820			−0.103142
$807$	−9.06218	−	2.42820i	−0.319004	−	0.0854768i
$808$	1.57180	+	5.86603i	0.0552956	+	0.206366i
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	0.0608532	−	0.998147i	$-0.480618\pi$
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	−0.833994	+	0.551774i	$0.813951\pi$
$810$	34.4545	+	30.5526i	1.21061	+	1.07351i
$811$		−	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
$815$	12.1699	+	2.49038i	0.426292	+	0.0872342i
$816$	−4.46410	+	7.73205i	−0.156275	+	0.270676i
$817$	−5.83013	+	21.7583i	−0.203970	+	0.761228i
$818$	−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	$0.750876\pi$
$822$	39.0526	−	10.4641i	1.36211	−	0.364977i
$823$	24.6962	−	6.61731i	0.860854	−	0.230665i	0.198725	−	0.980055i	$-0.436320\pi$
$823$	24.6962	−	6.61731i	0.860854	−	0.230665i	0.662129	+	0.749390i	$0.269653\pi$
$824$	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	−0.769729	−	0.638370i	$-0.779609\pi$
$827$	−3.77757	+	3.77757i	−0.131359	+	0.131359i	0.638370	+	0.769729i	$0.279609\pi$
$828$	2.36603	−	8.83013i	0.0822251	−	0.306868i
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	−0.989986	−	0.141166i	$-0.954915\pi$
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	0.617246	+	0.786770i	$0.288248\pi$
$830$	−10.4282	−	15.7942i	−0.361968	−	0.548226i
$831$	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
$835$	22.5718	−	25.4545i	0.781129	−	0.880889i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$	−0.607695	−	2.26795i	−0.0210050	−	0.0783918i
$838$	7.19615	+	1.92820i	0.248587	+	0.0666087i
$839$	31.1244			1.07453			0.537266	−	0.843413i	$-0.319457\pi$
$839$	31.1244			1.07453			0.537266	+	0.843413i	$0.319457\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	64.6769	+	17.3301i	2.22891	+	0.597236i
$843$	6.46410	+	24.1244i	0.222635	+	0.830887i
$844$	15.2942	+	8.83013i	0.526449	+	0.303946i
$845$	−11.1603	+	0.669873i	−0.383924	+	0.0230443i
$846$			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
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	−17.6603	+	30.5885i	−0.605386	+	1.04856i
$852$	−4.09808	+	15.2942i	−0.140398	+	0.523972i
$853$	6.12436	−	6.12436i	0.209694	−	0.209694i	−0.594443	−	0.804137i	$-0.702628\pi$
$853$	6.12436	−	6.12436i	0.209694	−	0.209694i	0.804137	+	0.594443i	$0.202628\pi$
$854$		0			0
$855$	−2.00000	+	4.00000i	−0.0683986	+	0.136797i
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.137820	−	0.990457i	$-0.455991\pi$
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.614584	+	0.788851i	$0.289324\pi$
$858$	−7.46410	+	2.00000i	−0.254820	+	0.0682789i
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	0.628394	−	0.777895i	$-0.283713\pi$
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	−0.987874	+	0.155257i	$0.950379\pi$
$860$	30.2942	−	10.0981i	1.03302	−	0.344342i
$861$		0			0
$862$	−5.73205	+	5.73205i	−0.195234	+	0.195234i
$863$	8.94486	−	33.3827i	0.304487	−	1.13636i	−0.628900	−	0.777487i	$-0.716494\pi$
$863$	8.94486	−	33.3827i	0.304487	−	1.13636i	0.933386	−	0.358873i	$-0.116839\pi$
$864$	−16.6244	+	28.7942i	−0.565572	+	0.979600i
$865$	10.5167	−	51.3923i	0.357577	−	1.74739i
$866$	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
$870$	1.50000	+	24.9904i	0.0508548	+	0.847253i
$871$	2.87564	+	1.66025i	0.0974375	+	0.0562556i
$872$	1.89230	+	7.06218i	0.0640815	+	0.239156i
$873$	−7.92820	−	2.12436i	−0.268329	−	0.0718985i
$874$	−38.0526			−1.28715
$875$		0			0
$876$	12.0000			0.405442
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.0123853	−	0.999923i	$-0.503942\pi$
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.510688	+	0.859766i	$0.670609\pi$
$878$	15.6603	+	58.4449i	0.528508	+	1.97242i
$879$	43.5167	+	25.1244i	1.46778	+	0.847423i
$880$	0.437822	+	7.29423i	0.0147590	+	0.245888i
$881$		−	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	0.972180	−	0.234237i	$-0.0752591\pi$
$883$	21.9282	+	21.9282i	0.737943	+	0.737943i	−0.234237	+	0.972180i	$0.575259\pi$
$884$	4.39230	−	2.53590i	0.147729	−	0.0852915i
$885$	−1.90192	+	9.29423i	−0.0639325	+	0.312422i
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	−0.574774	−	0.818312i	$-0.694910\pi$
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	0.906925	−	0.421292i	$-0.138423\pi$
$888$	−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
$892$	−14.4904	+	3.88269i	−0.485174	+	0.130002i
$893$	1.73205	−	0.464102i	0.0579609	−	0.0155306i
$894$	−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
$898$	−2.52628	+	9.42820i	−0.0843030	+	0.314623i
$899$	0.803848	−	1.39230i	0.0268098	−	0.0464360i
$900$	6.29423	−	0.758330i	0.209808	−	0.0252777i
$901$	−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
$905$	20.5263	−	1.23205i	0.682317	−	0.0409548i
$906$	−44.7846	−	25.8564i	−1.48787	−	0.859022i
$907$	−0.454483	−	1.69615i	−0.0150908	−	0.0563198i	0.957970	−	0.286869i	$-0.0926144\pi$
$907$	−0.454483	−	1.69615i	−0.0150908	−	0.0563198i	−0.973061	+	0.230549i	$0.925948\pi$
$908$	−0.169873	−	0.0455173i	−0.00563743	−	0.00151055i
$909$	−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	$0.286527\pi$
$912$	−22.7583	−	6.09808i	−0.753604	−	0.201927i
$913$	0.830127	+	3.09808i	0.0274732	+	0.102531i
$914$	−53.4449	−	30.8564i	−1.76780	−	1.02064i
$915$	−24.2583	+	27.3564i	−0.801956	+	0.904375i
$916$			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	−0.981846	−	0.189678i	$-0.939256\pi$
$919$	−39.6673	+	22.9019i	−1.30850	+	0.755465i	−0.326657	+	0.945143i	$0.605922\pi$
$920$	−4.59808	−	6.96410i	−0.151594	−	0.229600i
$921$	12.6962	−	21.9904i	0.418352	−	0.724608i
$922$	13.1962	−	49.2487i	0.434592	−	1.62192i
$923$	−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
$927$	−1.63397	+	0.437822i	−0.0536668	+	0.0143800i
$928$	−21.9904	+	5.89230i	−0.721870	+	0.193424i
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	0.851921	−	0.523670i	$-0.175438\pi$
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	−0.879472	+	0.475950i	$0.842104\pi$
$930$	−4.00000	−	2.00000i	−0.131165	−	0.0655826i
$931$		0			0
$932$	−2.19615	+	2.19615i	−0.0719374	+	0.0719374i
$933$	9.36603	−	34.9545i	0.306630	−	1.14436i
$934$	31.3564	−	54.3109i	1.02601	−	1.77711i
$935$	1.66025	+	0.339746i	0.0542961	+	0.0111109i
$936$	0.928203	−	0.535898i	0.0303393	−	0.0175164i
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.999946	+	0.0104348i	$0.00332156\pi$
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.0104348	+	0.999946i	$0.496678\pi$
$938$		0			0
$939$		−	38.7846i		−	1.26569i
$940$	−1.90192	−	1.68653i	−0.0620339	−	0.0550087i
$941$	−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	$0.821273\pi$
$942$	−23.7583	−	88.6673i	−0.774088	−	2.88894i
$943$	3.23205	+	0.866025i	0.105250	+	0.0282017i
$944$	−9.80385			−0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	43.6506	+	11.6962i	1.41846	+	0.380074i	0.884935	−	0.465714i	$-0.154202\pi$
$947$	43.6506	+	11.6962i	1.41846	+	0.380074i	0.533520	+	0.845788i	$0.320869\pi$
$948$	5.83013	+	21.7583i	0.189354	+	0.706678i
$949$	8.78461	+	5.07180i	0.285160	+	0.164637i
$950$	−9.83013	−	24.4904i	−0.318931	−	0.794573i
$951$			8.92820i			0.289517i
$952$		0			0
$953$	−10.1436	−	10.1436i	−0.328583	−	0.328583i	0.523464	−	0.852048i	$-0.324639\pi$
$953$	−10.1436	−	10.1436i	−0.328583	−	0.328583i	−0.852048	+	0.523464i	$0.824639\pi$
$954$	8.66025	−	5.00000i	0.280386	−	0.161881i
$955$	31.2224	−	20.6147i	1.01033	−	0.667077i
$956$	−15.9282	+	27.5885i	−0.515155	+	0.892274i
$957$	1.09808	−	4.09808i	0.0354958	−	0.132472i
$958$	−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
$962$	25.8564	−	6.92820i	0.833644	−	0.223374i
$963$	6.29423	−	1.68653i	0.202829	−	0.0543478i
$964$	−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	−0.729847	−	0.683610i	$-0.760409\pi$
$967$	−1.43782	+	1.43782i	−0.0462372	+	0.0462372i	0.683610	+	0.729847i	$0.260409\pi$
$968$	−1.40192	+	5.23205i	−0.0450595	+	0.168164i
$969$	−2.73205	+	4.73205i	−0.0877661	+	0.152015i
$970$	40.4186	−	26.6865i	1.29776	−	0.856853i
$971$	−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
$975$	25.1244	+	10.7321i	0.804623	+	0.343701i
$976$	−32.7224	−	18.8923i	−1.04742	−	0.604728i
$977$	−11.5622	−	43.1506i	−0.369907	−	1.38051i	−0.860646	−	0.509204i	$-0.829940\pi$
$977$	−11.5622	−	43.1506i	−0.369907	−	1.38051i	0.490739	−	0.871307i	$-0.336727\pi$
$978$	−20.0263	−	5.36603i	−0.640370	−	0.171587i
$979$	−12.1962			−0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$	33.0526	+	8.85641i	1.05475	+	0.282619i
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	0.875878	−	0.482532i	$-0.160283\pi$
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	−0.999799	+	0.0200540i	$0.993616\pi$
$984$	0.401924	+	0.232051i	0.0128129	+	0.00739751i
$985$	33.4186	+	29.6340i	1.06480	+	0.944217i
$986$			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
$990$	−2.26795	−	0.464102i	−0.0720802	−	0.0147501i
$991$	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	$0.0437491\pi$
$992$	1.05256	−	3.92820i	0.0334188	−	0.124721i
$993$	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
$997$	−25.6865	+	6.88269i	−0.813501	+	0.217977i	−0.641503	−	0.767121i	$-0.721689\pi$
$997$	−25.6865	+	6.88269i	−0.813501	+	0.217977i	−0.171998	+	0.985097i	$0.555022\pi$
$998$	−62.5429	+	16.7583i	−1.97976	+	0.530476i
$999$	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.a.178.1		4
5.2	odd	4		245.2.l.b.227.1		4
7.2	even	3		35.2.k.b.33.1	yes	4
7.3	odd	6		245.2.f.a.48.2		4
7.4	even	3		245.2.f.b.48.2		4
7.5	odd	6		245.2.l.b.68.1		4
7.6	odd	2		35.2.k.a.3.1	✓	4
21.2	odd	6		315.2.bz.a.208.1		4
21.20	even	2		315.2.bz.b.73.1		4
28.23	odd	6		560.2.ci.b.33.1		4
28.27	even	2		560.2.ci.a.353.1		4
35.2	odd	12		35.2.k.a.12.1	yes	4
35.9	even	6		175.2.o.a.68.1		4
35.12	even	12	inner	245.2.l.a.117.1		4
35.13	even	4		175.2.o.a.157.1		4
35.17	even	12		245.2.f.b.97.2		4
35.23	odd	12		175.2.o.b.82.1		4
35.27	even	4		35.2.k.b.17.1	yes	4
35.32	odd	12		245.2.f.a.97.2		4
35.34	odd	2		175.2.o.b.143.1		4
105.2	even	12		315.2.bz.b.82.1		4
105.62	odd	4		315.2.bz.a.262.1		4
140.27	odd	4		560.2.ci.b.17.1		4
140.107	even	12		560.2.ci.a.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	7.6	odd	2
35.2.k.a.12.1	yes	4	35.2	odd	12
35.2.k.b.17.1	yes	4	35.27	even	4
35.2.k.b.33.1	yes	4	7.2	even	3
175.2.o.a.68.1		4	35.9	even	6
175.2.o.a.157.1		4	35.13	even	4
175.2.o.b.82.1		4	35.23	odd	12
175.2.o.b.143.1		4	35.34	odd	2
245.2.f.a.48.2		4	7.3	odd	6
245.2.f.a.97.2		4	35.32	odd	12
245.2.f.b.48.2		4	7.4	even	3
245.2.f.b.97.2		4	35.17	even	12
245.2.l.a.117.1		4	35.12	even	12	inner
245.2.l.a.178.1		4	1.1	even	1	trivial
245.2.l.b.68.1		4	7.5	odd	6
245.2.l.b.227.1		4	5.2	odd	4
315.2.bz.a.208.1		4	21.2	odd	6
315.2.bz.a.262.1		4	105.62	odd	4
315.2.bz.b.73.1		4	21.20	even	2
315.2.bz.b.82.1		4	105.2	even	12
560.2.ci.a.257.1		4	140.107	even	12
560.2.ci.a.353.1		4	28.27	even	2
560.2.ci.b.17.1		4	140.27	odd	4
560.2.ci.b.33.1		4	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86603 - 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -3.73205i q^{6} +(0.366025 + 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(-1.86603 - 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -3.73205i q^{6} +(0.366025 + 0.366025i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(0.866025 - 4.23205i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-0.866025 + 3.23205i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-4.09808 + 1.36603i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(1.36603 - 0.366025i) q^{18} +(-1.36603 - 2.36603i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-1.86603 + 6.96410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(4.73205 - 2.73205i) q^{26} +(3.09808 + 3.09808i) q^{27} +3.00000i q^{29} +(8.33013 - 0.500000i) q^{30} +(-0.464102 - 0.267949i) q^{31} +(1.96410 + 7.33013i) q^{32} +(-1.36603 - 0.366025i) q^{33} +2.00000 q^{34} -1.26795 q^{36} +(4.73205 + 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(-4.73205 - 2.73205i) q^{39} +(-0.767949 + 0.866025i) q^{40} -0.464102i q^{41} +(-5.83013 - 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(-0.901924 - 1.36603i) q^{45} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(6.09808 - 6.09808i) q^{48} +(9.56218 + 1.36603i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(-4.73205 + 1.26795i) q^{52} +(6.83013 - 1.83013i) q^{53} +(-4.23205 - 7.33013i) q^{54} +(-1.46410 - 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(1.50000 - 5.59808i) q^{58} +(1.09808 - 1.90192i) q^{59} +(-7.33013 - 1.50000i) q^{60} +(7.33013 - 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} -5.73205i q^{64} +(-4.73205 - 4.19615i) q^{65} +(2.36603 + 1.36603i) q^{66} +(-0.303848 - 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} -13.9282 q^{69} +4.73205 q^{71} +(-0.366025 - 0.0980762i) q^{72} +(-0.928203 - 3.46410i) q^{73} +(-8.19615 - 4.73205i) q^{74} +(-3.59808 - 8.96410i) q^{75} -4.73205i q^{76} +(7.46410 + 7.46410i) q^{78} +(5.83013 - 3.36603i) q^{79} +(8.33013 - 5.50000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.232051 + 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(7.96410 + 13.7942i) q^{86} +(-5.59808 + 1.50000i) q^{87} +(-0.366025 + 0.0980762i) q^{88} +(8.33013 + 14.4282i) q^{89} +(1.00000 + 3.00000i) q^{90} +(-8.83013 + 8.83013i) q^{92} +(0.267949 - 1.00000i) q^{93} +(0.633975 - 1.09808i) q^{94} +(5.09808 - 3.36603i) q^{95} +(-12.6962 + 7.33013i) q^{96} +(7.92820 + 7.92820i) q^{97} -0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} + 2 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 8 q^{13} - 6 q^{15} - 2 q^{16} - 4 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} + 12 q^{26} + 2 q^{27} + 16 q^{30} + 12 q^{31} - 6 q^{32} - 2 q^{33} + 8 q^{34} - 12 q^{36} + 12 q^{37} + 2 q^{38} - 12 q^{39} - 10 q^{40} - 6 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} - 18 q^{47} + 14 q^{48} + 14 q^{50} - 4 q^{51} - 12 q^{52} + 10 q^{53} - 10 q^{54} + 8 q^{55} + 8 q^{57} + 6 q^{58} - 6 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{62} - 12 q^{65} + 6 q^{66} - 22 q^{67} - 28 q^{69} + 12 q^{71} + 2 q^{72} + 24 q^{73} - 12 q^{74} - 4 q^{75} + 16 q^{78} + 6 q^{79} + 16 q^{80} - 4 q^{81} + 6 q^{82} + 2 q^{83} + 4 q^{85} + 18 q^{86} - 12 q^{87} + 2 q^{88} + 16 q^{89} + 4 q^{90} - 18 q^{92} + 8 q^{93} + 6 q^{94} + 10 q^{95} - 30 q^{96} + 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 8 * q^13 - 6 * q^15 - 2 * q^16 - 4 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 + 12 * q^26 + 2 * q^27 + 16 * q^30 + 12 * q^31 - 6 * q^32 - 2 * q^33 + 8 * q^34 - 12 * q^36 + 12 * q^37 + 2 * q^38 - 12 * q^39 - 10 * q^40 - 6 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 - 18 * 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 + 6 * q^58 - 6 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^62 - 12 * q^65 + 6 * q^66 - 22 * q^67 - 28 * q^69 + 12 * q^71 + 2 * q^72 + 24 * q^73 - 12 * q^74 - 4 * q^75 + 16 * q^78 + 6 * q^79 + 16 * q^80 - 4 * q^81 + 6 * q^82 + 2 * q^83 + 4 * q^85 + 18 * q^86 - 12 * q^87 + 2 * q^88 + 16 * q^89 + 4 * q^90 - 18 * q^92 + 8 * q^93 + 6 * q^94 + 10 * q^95 - 30 * q^96 + 4 * q^97

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