LMFDB - Embedded newform 784.2.j.a.195.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(195,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.195"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			195.13
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0617395 - 1.41287i) q^{2} +(-0.771824 - 0.771824i) q^{3} +(-1.99238 - 0.174459i) q^{4} +(1.02430 + 1.02430i) q^{5} +(-1.13814 + 1.04283i) q^{6} +(-0.369496 + 2.80419i) q^{8} -1.80857i q^{9} +(1.51044 - 1.38396i) q^{10} +(3.88550 + 3.88550i) q^{11} +(1.40311 + 1.67242i) q^{12} +(-1.84531 + 1.84531i) q^{13} -1.58116i q^{15} +(3.93913 + 0.695177i) q^{16} +6.57514i q^{17} +(-2.55527 - 0.111660i) q^{18} +(2.37516 + 2.37516i) q^{19} +(-1.86209 - 2.21949i) q^{20} +(5.72958 - 5.24981i) q^{22} +0.512345 q^{23} +(2.44953 - 1.87916i) q^{24} -2.90162i q^{25} +(2.49325 + 2.72111i) q^{26} +(-3.71137 + 3.71137i) q^{27} +(-2.30263 - 2.30263i) q^{29} +(-2.23396 - 0.0976199i) q^{30} +7.59274 q^{31} +(1.22539 - 5.52254i) q^{32} -5.99785i q^{33} +(9.28979 + 0.405946i) q^{34} +(-0.315522 + 3.60336i) q^{36} +(2.93978 - 2.93978i) q^{37} +(3.50243 - 3.20914i) q^{38} +2.84852 q^{39} +(-3.25080 + 2.49385i) q^{40} -0.453189 q^{41} +(3.40842 + 3.40842i) q^{43} +(-7.06353 - 8.41925i) q^{44} +(1.85252 - 1.85252i) q^{45} +(0.0316320 - 0.723875i) q^{46} +3.42936 q^{47} +(-2.50376 - 3.57687i) q^{48} +(-4.09960 - 0.179145i) q^{50} +(5.07485 - 5.07485i) q^{51} +(3.99849 - 3.35463i) q^{52} +(1.00457 - 1.00457i) q^{53} +(5.01453 + 5.47281i) q^{54} +7.95984i q^{55} -3.66642i q^{57} +(-3.39546 + 3.11114i) q^{58} +(-4.81367 + 4.81367i) q^{59} +(-0.275847 + 3.15026i) q^{60} +(3.57478 - 3.57478i) q^{61} +(0.468772 - 10.7275i) q^{62} +(-7.72695 - 2.07227i) q^{64} -3.78031 q^{65} +(-8.47416 - 0.370305i) q^{66} +(4.53739 - 4.53739i) q^{67} +(1.14709 - 13.1002i) q^{68} +(-0.395441 - 0.395441i) q^{69} +6.44865 q^{71} +(5.07158 + 0.668260i) q^{72} -14.8799 q^{73} +(-3.97201 - 4.33502i) q^{74} +(-2.23954 + 2.23954i) q^{75} +(-4.31785 - 5.14659i) q^{76} +(0.175866 - 4.02457i) q^{78} +3.85416i q^{79} +(3.32278 + 4.74691i) q^{80} +0.303337 q^{81} +(-0.0279796 + 0.640295i) q^{82} +(2.44051 + 2.44051i) q^{83} +(-6.73491 + 6.73491i) q^{85} +(5.02607 - 4.60520i) q^{86} +3.55445i q^{87} +(-12.3314 + 9.46001i) q^{88} -7.62687 q^{89} +(-2.50299 - 2.73174i) q^{90} +(-1.02079 - 0.0893834i) q^{92} +(-5.86026 - 5.86026i) q^{93} +(0.211727 - 4.84523i) q^{94} +4.86575i q^{95} +(-5.20822 + 3.31664i) q^{96} -11.2152i q^{97} +(7.02722 - 7.02722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.0617395	−	1.41287i	0.0436564	−	0.999047i
$2$	0.0617395	−	1.41287i	0.0436564	−	0.999047i
$3$	−0.771824	−	0.771824i	−0.445613	−	0.445613i	0.448280	−	0.893893i	$-0.352037\pi$
$3$	−0.771824	−	0.771824i	−0.445613	−	0.445613i	−0.893893	+	0.448280i	$0.852037\pi$
$4$	−1.99238	−	0.174459i	−0.996188	−	0.0872296i
$5$	1.02430	+	1.02430i	0.458080	+	0.458080i	0.898025	−	0.439945i	$-0.145002\pi$
$5$	1.02430	+	1.02430i	0.458080	+	0.458080i	−0.439945	+	0.898025i	$0.645002\pi$
$6$	−1.13814	+	1.04283i	−0.464642	+	0.425734i
$7$		0			0
$7$		0			0
$8$	−0.369496	+	2.80419i	−0.130636	+	0.991430i
$9$		−	1.80857i		−	0.602858i
$10$	1.51044	−	1.38396i	0.477642	−	0.437646i
$11$	3.88550	+	3.88550i	1.17152	+	1.17152i	0.981847	+	0.189677i	$0.0607442\pi$
$11$	3.88550	+	3.88550i	1.17152	+	1.17152i	0.189677	+	0.981847i	$0.439256\pi$
$12$	1.40311	+	1.67242i	0.405044	+	0.482785i
$13$	−1.84531	+	1.84531i	−0.511798	+	0.511798i	−0.915077	−	0.403279i	$-0.867870\pi$
$13$	−1.84531	+	1.84531i	−0.511798	+	0.511798i	0.403279	+	0.915077i	$0.367870\pi$
$14$		0			0
$15$		−	1.58116i		−	0.408253i
$16$	3.93913	+	0.695177i	0.984782	+	0.173794i
$17$			6.57514i			1.59471i	0.603513	+	0.797353i	$0.293767\pi$
$17$			6.57514i			1.59471i	−0.603513	+	0.797353i	$0.706233\pi$
$18$	−2.55527	−	0.111660i	−0.602283	−	0.0263186i
$19$	2.37516	+	2.37516i	0.544900	+	0.544900i	0.924961	−	0.380061i	$-0.124097\pi$
$19$	2.37516	+	2.37516i	0.544900	+	0.544900i	−0.380061	+	0.924961i	$0.624097\pi$
$20$	−1.86209	−	2.21949i	−0.416376	−	0.496292i
$21$		0			0
$22$	5.72958	−	5.24981i	1.22155	−	1.11926i
$23$	0.512345			0.106831			0.0534157	−	0.998572i	$-0.482989\pi$
$23$	0.512345			0.106831			0.0534157	+	0.998572i	$0.482989\pi$
$24$	2.44953	−	1.87916i	0.500008	−	0.383581i
$25$		−	2.90162i		−	0.580325i
$26$	2.49325	+	2.72111i	0.488967	+	0.533653i
$27$	−3.71137	+	3.71137i	−0.714254	+	0.714254i
$28$		0			0
$29$	−2.30263	−	2.30263i	−0.427587	−	0.427587i	0.460219	−	0.887806i	$-0.347771\pi$
$29$	−2.30263	−	2.30263i	−0.427587	−	0.427587i	−0.887806	+	0.460219i	$0.847771\pi$
$30$	−2.23396	−	0.0976199i	−0.407864	−	0.0178229i
$31$	7.59274			1.36370			0.681848	−	0.731494i	$-0.261176\pi$
$31$	7.59274			1.36370			0.681848	+	0.731494i	$0.261176\pi$
$32$	1.22539	−	5.52254i	0.216621	−	0.976256i
$33$		−	5.99785i		−	1.04409i
$34$	9.28979	+	0.405946i	1.59319	+	0.0696191i
$35$		0			0
$36$	−0.315522	+	3.60336i	−0.0525871	+	0.600560i
$37$	2.93978	−	2.93978i	0.483297	−	0.483297i	−0.422886	−	0.906183i	$-0.638983\pi$
$37$	2.93978	−	2.93978i	0.483297	−	0.483297i	0.906183	+	0.422886i	$0.138983\pi$
$38$	3.50243	−	3.20914i	0.568169	−	0.520592i
$39$	2.84852			0.456128
$40$	−3.25080	+	2.49385i	−0.513997	+	0.394313i
$41$	−0.453189			−0.0707762			−0.0353881	−	0.999374i	$-0.511267\pi$
$41$	−0.453189			−0.0707762			−0.0353881	+	0.999374i	$0.511267\pi$
$42$		0			0
$43$	3.40842	+	3.40842i	0.519779	+	0.519779i	0.917504	−	0.397726i	$-0.130200\pi$
$43$	3.40842	+	3.40842i	0.519779	+	0.519779i	−0.397726	+	0.917504i	$0.630200\pi$
$44$	−7.06353	−	8.41925i	−1.06487	−	1.26925i
$45$	1.85252	−	1.85252i	0.276157	−	0.276157i
$46$	0.0316320	−	0.723875i	0.00466388	−	0.106730i
$47$	3.42936			0.500224			0.250112	−	0.968217i	$-0.419533\pi$
$47$	3.42936			0.500224			0.250112	+	0.968217i	$0.419533\pi$
$48$	−2.50376	−	3.57687i	−0.361387	−	0.516277i
$49$		0			0
$50$	−4.09960	−	0.179145i	−0.579771	−	0.0253349i
$51$	5.07485	−	5.07485i	0.710622	−	0.710622i
$52$	3.99849	−	3.35463i	0.554491	−	0.465203i
$53$	1.00457	−	1.00457i	0.137988	−	0.137988i	−0.634739	−	0.772727i	$-0.718892\pi$
$53$	1.00457	−	1.00457i	0.137988	−	0.137988i	0.772727	+	0.634739i	$0.218892\pi$
$54$	5.01453	+	5.47281i	0.682392	+	0.744755i
$55$			7.95984i			1.07330i
$56$		0			0
$57$		−	3.66642i		−	0.485629i
$58$	−3.39546	+	3.11114i	−0.445846	+	0.408512i
$59$	−4.81367	+	4.81367i	−0.626687	+	0.626687i	−0.947233	−	0.320546i	$-0.896134\pi$
$59$	−4.81367	+	4.81367i	−0.626687	+	0.626687i	0.320546	+	0.947233i	$0.396134\pi$
$60$	−0.275847	+	3.15026i	−0.0356118	+	0.406697i
$61$	3.57478	−	3.57478i	0.457704	−	0.457704i	−0.440197	−	0.897901i	$-0.645092\pi$
$61$	3.57478	−	3.57478i	0.457704	−	0.457704i	0.897901	+	0.440197i	$0.145092\pi$
$62$	0.468772	−	10.7275i	0.0595341	−	1.36240i
$63$		0			0
$64$	−7.72695	−	2.07227i	−0.965868	−	0.259034i
$65$	−3.78031			−0.468889
$66$	−8.47416	−	0.370305i	−1.04310	−	0.0455813i
$67$	4.53739	−	4.53739i	0.554330	−	0.554330i	−0.373358	−	0.927687i	$-0.621794\pi$
$67$	4.53739	−	4.53739i	0.554330	−	0.554330i	0.927687	+	0.373358i	$0.121794\pi$
$68$	1.14709	−	13.1002i	0.139106	−	1.58863i
$69$	−0.395441	−	0.395441i	−0.0476055	−	0.0476055i
$70$		0			0
$71$	6.44865			0.765314			0.382657	−	0.923890i	$-0.375009\pi$
$71$	6.44865			0.765314			0.382657	+	0.923890i	$0.375009\pi$
$72$	5.07158	+	0.668260i	0.597692	+	0.0787552i
$73$	−14.8799			−1.74156			−0.870780	−	0.491673i	$-0.836385\pi$
$73$	−14.8799			−1.74156			−0.870780	+	0.491673i	$0.836385\pi$
$74$	−3.97201	−	4.33502i	−0.461737	−	0.503935i
$75$	−2.23954	+	2.23954i	−0.258600	+	0.258600i
$76$	−4.31785	−	5.14659i	−0.495291	−	0.590354i
$77$		0			0
$78$	0.175866	−	4.02457i	0.0199129	−	0.455693i
$79$			3.85416i			0.433627i	0.976213	+	0.216813i	$0.0695663\pi$
$79$			3.85416i			0.433627i	−0.976213	+	0.216813i	$0.930434\pi$
$80$	3.32278	+	4.74691i	0.371498	+	0.530721i
$81$	0.303337			0.0337041
$82$	−0.0279796	+	0.640295i	−0.00308983	+	0.0707087i
$83$	2.44051	+	2.44051i	0.267881	+	0.267881i	0.828246	−	0.560365i	$-0.189339\pi$
$83$	2.44051	+	2.44051i	0.267881	+	0.267881i	−0.560365	+	0.828246i	$0.689339\pi$
$84$		0			0
$85$	−6.73491	+	6.73491i	−0.730503	+	0.730503i
$86$	5.02607	−	4.60520i	0.541975	−	0.496592i
$87$			3.55445i			0.381077i
$88$	−12.3314	+	9.46001i	−1.31453	+	1.00844i
$89$	−7.62687			−0.808447			−0.404223	−	0.914660i	$-0.632458\pi$
$89$	−7.62687			−0.808447			−0.404223	+	0.914660i	$0.632458\pi$
$90$	−2.50299	−	2.73174i	−0.263838	−	0.287950i
$91$		0			0
$92$	−1.02079	−	0.0893834i	−0.106424	−	0.00931886i
$93$	−5.86026	−	5.86026i	−0.607681	−	0.607681i
$94$	0.211727	−	4.84523i	0.0218380	−	0.499747i
$95$			4.86575i			0.499216i
$96$	−5.20822	+	3.31664i	−0.531561	+	0.338503i
$97$		−	11.2152i		−	1.13873i	−0.822085	−	0.569365i	$-0.807189\pi$
$97$		−	11.2152i		−	1.13873i	0.822085	−	0.569365i	$-0.192811\pi$
$98$		0			0
$99$	7.02722	−	7.02722i	0.706263	−	0.706263i
$100$	−0.506215	+	5.78113i	−0.0506215	+	0.578113i
$101$	13.7547	+	13.7547i	1.36865	+	1.36865i	0.862375	+	0.506270i	$0.168976\pi$
$101$	13.7547	+	13.7547i	1.36865	+	1.36865i	0.506270	+	0.862375i	$0.331024\pi$
$102$	−6.85677	−	7.48340i	−0.678921	−	0.740967i
$103$		−	7.10181i		−	0.699762i	−0.936794	−	0.349881i	$-0.886222\pi$
$103$		−	7.10181i		−	0.699762i	0.936794	−	0.349881i	$-0.113778\pi$
$104$	−4.49277	−	5.85644i	−0.440553	−	0.574271i
$105$		0			0
$106$	−1.35729	−	1.48134i	−0.131832	−	0.143880i
$107$	8.47936	+	8.47936i	0.819730	+	0.819730i	0.986069	−	0.166338i	$-0.0531944\pi$
$107$	8.47936	+	8.47936i	0.819730	+	0.819730i	−0.166338	+	0.986069i	$0.553194\pi$
$108$	8.04194	−	6.74697i	0.773836	−	0.649228i
$109$	7.33805	+	7.33805i	0.702858	+	0.702858i	0.965023	−	0.262165i	$-0.0844365\pi$
$109$	7.33805	+	7.33805i	0.702858	+	0.702858i	−0.262165	+	0.965023i	$0.584436\pi$
$110$	11.2462	+	0.491436i	1.07228	+	0.0468566i
$111$	−4.53799			−0.430727
$112$		0			0
$113$	−13.4601			−1.26622			−0.633109	−	0.774062i	$-0.718222\pi$
$113$	−13.4601			−1.26622			−0.633109	+	0.774062i	$0.718222\pi$
$114$	−5.18015	−	0.226363i	−0.485166	−	0.0212008i
$115$	0.524795	+	0.524795i	0.0489374	+	0.0489374i
$116$	4.18598	+	4.98941i	0.388659	+	0.463255i
$117$	3.33739	+	3.33739i	0.308542	+	0.308542i
$118$	6.50388	+	7.09826i	0.598730	+	0.653448i
$119$		0			0
$120$	4.43386	+	0.584231i	0.404755	+	0.0533327i
$121$			19.1943i			1.74494i
$122$	−4.82998	−	5.27139i	−0.437286	−	0.477249i
$123$	0.349782	+	0.349782i	0.0315388	+	0.0315388i
$124$	−15.1276	−	1.32462i	−1.35850	−	0.118955i
$125$	8.09362	−	8.09362i	0.723916	−	0.723916i
$126$		0			0
$127$			13.7356i			1.21884i	0.792849	+	0.609418i	$0.208597\pi$
$127$			13.7356i			1.21884i	−0.792849	+	0.609418i	$0.791403\pi$
$128$	−3.40490	+	10.7892i	−0.300953	+	0.953639i
$129$		−	5.26140i		−	0.463240i
$130$	−0.233394	+	5.34106i	−0.0204700	+	0.468442i
$131$	−2.06043	−	2.06043i	−0.180020	−	0.180020i	0.611344	−	0.791365i	$-0.290629\pi$
$131$	−2.06043	−	2.06043i	−0.180020	−	0.180020i	−0.791365	+	0.611344i	$0.790629\pi$
$132$	−1.04638	+	11.9500i	−0.0910758	+	1.04011i
$133$		0			0
$134$	−6.13058	−	6.69085i	−0.529601	−	0.578001i
$135$	−7.60311			−0.654372
$136$	−18.4379	−	2.42949i	−1.58104	−	0.208327i
$137$			7.22491i			0.617266i	0.951181	+	0.308633i	$0.0998714\pi$
$137$			7.22491i			0.617266i	−0.951181	+	0.308633i	$0.900129\pi$
$138$	−0.583119	+	0.534290i	−0.0496384	+	0.0454818i
$139$	0.708981	−	0.708981i	0.0601350	−	0.0601350i	−0.676400	−	0.736535i	$-0.736461\pi$
$139$	0.708981	−	0.708981i	0.0601350	−	0.0601350i	0.736535	+	0.676400i	$0.236461\pi$
$140$		0			0
$141$	−2.64687	−	2.64687i	−0.222906	−	0.222906i
$142$	0.398137	−	9.11108i	0.0334109	−	0.764585i
$143$	−14.3399			−1.19917
$144$	1.25728	−	7.12421i	0.104773	−	0.593684i
$145$		−	4.71715i		−	0.391738i
$146$	−0.918677	+	21.0233i	−0.0760303	+	1.73990i
$147$		0			0
$148$	−6.37002	+	5.34428i	−0.523613	+	0.439297i
$149$	6.73169	−	6.73169i	0.551482	−	0.551482i	−0.375387	−	0.926868i	$-0.622490\pi$
$149$	6.73169	−	6.73169i	0.551482	−	0.551482i	0.926868	+	0.375387i	$0.122490\pi$
$150$	3.02591	+	3.30244i	0.247064	+	0.269643i
$151$	−7.10145			−0.577908			−0.288954	−	0.957343i	$-0.593307\pi$
$151$	−7.10145			−0.577908			−0.288954	+	0.957343i	$0.593307\pi$
$152$	−7.53802	+	5.78279i	−0.611414	+	0.469046i
$153$	11.8916			0.961381
$154$		0			0
$155$	7.77723	+	7.77723i	0.624683	+	0.624683i
$156$	−5.67532	−	0.496950i	−0.454389	−	0.0397878i
$157$	−6.20590	+	6.20590i	−0.495285	+	0.495285i	−0.909966	−	0.414682i	$-0.863893\pi$
$157$	−6.20590	+	6.20590i	−0.495285	+	0.495285i	0.414682	+	0.909966i	$0.363893\pi$
$158$	5.44541	+	0.237954i	0.433214	+	0.0189306i
$159$	−1.55070			−0.122978
$160$	6.91190	−	4.40156i	0.546433	−	0.347974i
$161$		0			0
$162$	0.0187278	−	0.428574i	0.00147140	−	0.0336719i
$163$	−8.97988	+	8.97988i	−0.703358	+	0.703358i	−0.965130	−	0.261772i	$-0.915693\pi$
$163$	−8.97988	+	8.97988i	−0.703358	+	0.703358i	0.261772	+	0.965130i	$0.415693\pi$
$164$	0.902922	+	0.0790629i	0.0705064	+	0.00617378i
$165$	6.14360	−	6.14360i	0.478278	−	0.478278i
$166$	3.59879	−	3.29744i	0.279320	−	0.255931i
$167$			21.5280i			1.66588i	0.553361	+	0.832942i	$0.313345\pi$
$167$			21.5280i			1.66588i	−0.553361	+	0.832942i	$0.686655\pi$
$168$		0			0
$169$			6.18963i			0.476126i
$170$	9.09971	+	9.93133i	0.697916	+	0.761698i
$171$	4.29566	−	4.29566i	0.328497	−	0.328497i
$172$	−6.19622	−	7.38548i	−0.472458	−	0.563138i
$173$	14.1638	−	14.1638i	1.07685	−	1.07685i	0.0800649	−	0.996790i	$-0.474487\pi$
$173$	14.1638	−	14.1638i	1.07685	−	1.07685i	0.996790	−	0.0800649i	$-0.0255127\pi$
$174$	5.02195	+	0.219450i	0.380713	+	0.0166364i
$175$		0			0
$176$	12.6044	+	18.0066i	0.950091	+	1.35730i
$177$	7.43062			0.558520
$178$	−0.470879	+	10.7757i	−0.0352939	+	0.807676i
$179$	4.81665	−	4.81665i	0.360013	−	0.360013i	−0.503804	−	0.863818i	$-0.668067\pi$
$179$	4.81665	−	4.81665i	0.360013	−	0.360013i	0.863818	+	0.503804i	$0.168067\pi$
$180$	−4.01411	+	3.36773i	−0.299194	+	0.251016i
$181$	−6.32019	−	6.32019i	−0.469776	−	0.469776i	0.432066	−	0.901842i	$-0.357785\pi$
$181$	−6.32019	−	6.32019i	−0.469776	−	0.469776i	−0.901842	+	0.432066i	$0.857785\pi$
$182$		0			0
$183$	−5.51821			−0.407917
$184$	−0.189309	+	1.43671i	−0.0139561	+	0.105916i
$185$	6.02243			0.442778
$186$	−8.64157	+	7.91795i	−0.633631	+	0.580572i
$187$	−25.5477	+	25.5477i	−1.86824	+	1.86824i
$188$	−6.83259	−	0.598284i	−0.498318	−	0.0436344i
$189$		0			0
$190$	6.87465	+	0.300409i	0.498740	+	0.0217940i
$191$		−	13.3222i		−	0.963964i	−0.876181	−	0.481982i	$-0.839917\pi$
$191$		−	13.3222i		−	0.963964i	0.876181	−	0.481982i	$-0.160083\pi$
$192$	4.36442	+	7.56327i	0.314975	+	0.545832i
$193$	−10.5154			−0.756918			−0.378459	−	0.925618i	$-0.623546\pi$
$193$	−10.5154			−0.756918			−0.378459	+	0.925618i	$0.623546\pi$
$194$	−15.8456	−	0.692421i	−1.13765	−	0.0497129i
$195$	2.91773	+	2.91773i	0.208943	+	0.208943i
$196$		0			0
$197$	14.0642	−	14.0642i	1.00203	−	1.00203i	0.00203129	−	0.999998i	$-0.499353\pi$
$197$	14.0642	−	14.0642i	1.00203	−	1.00203i	0.999998	−	0.00203129i	$-0.000646580\pi$
$198$	−9.49466	−	10.3624i	−0.674756	−	0.736422i
$199$		−	24.1913i		−	1.71488i	−0.514585	−	0.857439i	$-0.672054\pi$
$199$		−	24.1913i		−	1.71488i	0.514585	−	0.857439i	$-0.327946\pi$
$200$	8.13670	+	1.07214i	0.575352	+	0.0758116i
$201$	−7.00413			−0.494033
$202$	20.2828	−	18.5843i	1.42709	−	1.30759i
$203$		0			0
$204$	−10.9964	+	9.22566i	−0.769900	+	0.645926i
$205$	−0.464201	−	0.464201i	−0.0324212	−	0.0324212i
$206$	−10.0339	−	0.438462i	−0.699095	−	0.0305491i
$207$		−	0.926615i		−	0.0644042i
$208$	−8.55175	+	5.98611i	−0.592957	+	0.415062i
$209$			18.4574i			1.27673i
$210$		0			0
$211$	8.81296	−	8.81296i	0.606709	−	0.606709i	−0.335375	−	0.942085i	$-0.608863\pi$
$211$	8.81296	−	8.81296i	0.606709	−	0.606709i	0.942085	+	0.335375i	$0.108863\pi$
$212$	−2.17673	+	1.82622i	−0.149498	+	0.125425i
$213$	−4.97723	−	4.97723i	−0.341034	−	0.341034i
$214$	12.5037	−	11.4567i	0.854735	−	0.783162i
$215$			6.98248i			0.476201i
$216$	−9.03606	−	11.7787i	−0.614826	−	0.801441i
$217$		0			0
$218$	10.8207	−	9.91463i	0.732872	−	0.671504i
$219$	11.4847	+	11.4847i	0.776062	+	0.776062i
$220$	1.38867	−	15.8590i	0.0936239	−	1.06921i
$221$	−12.1332	−	12.1332i	−0.816167	−	0.816167i
$222$	−0.280173	+	6.41157i	−0.0188040	+	0.430316i
$223$	−5.44902			−0.364893			−0.182447	−	0.983216i	$-0.558402\pi$
$223$	−5.44902			−0.364893			−0.182447	+	0.983216i	$0.558402\pi$
$224$		0			0
$225$	−5.24780			−0.349853
$226$	−0.831019	+	19.0173i	−0.0552786	+	1.26501i
$227$	1.06414	+	1.06414i	0.0706293	+	0.0706293i	0.741539	−	0.670910i	$-0.234096\pi$
$227$	1.06414	+	1.06414i	0.0706293	+	0.0706293i	−0.670910	+	0.741539i	$0.734096\pi$
$228$	−0.639640	+	7.30488i	−0.0423612	+	0.483778i
$229$	−3.49849	−	3.49849i	−0.231187	−	0.231187i	0.582001	−	0.813188i	$-0.302270\pi$
$229$	−3.49849	−	3.49849i	−0.231187	−	0.231187i	−0.813188	+	0.582001i	$0.802270\pi$
$230$	0.773865	−	0.709064i	0.0510271	−	0.0467543i
$231$		0			0
$232$	7.30781	−	5.60619i	0.479781	−	0.368064i
$233$			12.4306i			0.814354i	0.913349	+	0.407177i	$0.133487\pi$
$233$			12.4306i			0.814354i	−0.913349	+	0.407177i	$0.866513\pi$
$234$	4.92133	−	4.50923i	0.321717	−	0.294778i
$235$	3.51269	+	3.51269i	0.229143	+	0.229143i
$236$	10.4304	−	8.75086i	0.678964	−	0.569632i
$237$	2.97474	−	2.97474i	0.193230	−	0.193230i
$238$		0			0
$239$		−	7.34038i		−	0.474810i	−0.971411	−	0.237405i	$-0.923703\pi$
$239$		−	7.34038i		−	0.474810i	0.971411	−	0.237405i	$-0.0762968\pi$
$240$	1.09918	−	6.22838i	0.0709520	−	0.402040i
$241$		−	10.3739i		−	0.668241i	−0.942530	−	0.334120i	$-0.891561\pi$
$241$		−	10.3739i		−	0.668241i	0.942530	−	0.334120i	$-0.108439\pi$
$242$	27.1189	+	1.18505i	1.74327	+	0.0761776i
$243$	10.9000	+	10.9000i	0.699235	+	0.699235i
$244$	−7.74596	+	6.49865i	−0.495884	+	0.416034i
$245$		0			0
$246$	0.515790	−	0.472600i	0.0328856	−	0.0301318i
$247$	−8.76584			−0.557757
$248$	−2.80548	+	21.2915i	−0.178148	+	1.35201i
$249$		−	3.76729i		−	0.238743i
$250$	−10.9355	−	11.9349i	−0.691622	−	0.754829i
$251$	−0.401720	+	0.401720i	−0.0253563	+	0.0253563i	−0.719671	−	0.694315i	$-0.755707\pi$
$251$	−0.401720	+	0.401720i	−0.0253563	+	0.0253563i	0.694315	+	0.719671i	$0.255707\pi$
$252$		0			0
$253$	1.99072	+	1.99072i	0.125156	+	0.125156i
$254$	19.4065	+	0.848029i	1.21767	+	0.0532100i
$255$	10.3963			0.651044
$256$	15.0335	+	5.47678i	0.939591	+	0.342299i
$257$		−	9.14767i		−	0.570616i	−0.958436	−	0.285308i	$-0.907904\pi$
$257$		−	9.14767i		−	0.570616i	0.958436	−	0.285308i	$-0.0920958\pi$
$258$	−7.43365	−	0.324836i	−0.462799	−	0.0202234i
$259$		0			0
$260$	7.53179	+	0.659509i	0.467102	+	0.0409010i
$261$	−4.16447	+	4.16447i	−0.257774	+	0.257774i
$262$	−3.03832	+	2.78390i	−0.187708	+	0.171990i
$263$	4.58232			0.282558			0.141279	−	0.989970i	$-0.454879\pi$
$263$	4.58232			0.282558			0.141279	+	0.989970i	$0.454879\pi$
$264$	16.8191	+	2.21618i	1.03514	+	0.136397i
$265$	2.05795			0.126419
$266$		0			0
$267$	5.88661	+	5.88661i	0.360254	+	0.360254i
$268$	−9.83177	+	8.24859i	−0.600571	+	0.503863i
$269$	6.75155	−	6.75155i	0.411649	−	0.411649i	−0.470664	−	0.882313i	$-0.655985\pi$
$269$	6.75155	−	6.75155i	0.411649	−	0.411649i	0.882313	+	0.470664i	$0.155985\pi$
$270$	−0.469412	+	10.7422i	−0.0285675	+	0.653748i
$271$	−7.28357			−0.442445			−0.221223	−	0.975223i	$-0.571005\pi$
$271$	−7.28357			−0.442445			−0.221223	+	0.975223i	$0.571005\pi$
$272$	−4.57088	+	25.9003i	−0.277151	+	1.57044i
$273$		0			0
$274$	10.2078	+	0.446062i	0.616677	+	0.0269476i
$275$	11.2743	−	11.2743i	0.679864	−	0.679864i
$276$	0.718878	+	0.856855i	0.0432714	+	0.0515766i
$277$	−22.8930	+	22.8930i	−1.37551	+	1.37551i	−0.523450	+	0.852056i	$0.675355\pi$
$277$	−22.8930	+	22.8930i	−1.37551	+	1.37551i	−0.852056	+	0.523450i	$0.824645\pi$
$278$	−0.957922	−	1.04547i	−0.0574523	−	0.0627029i
$279$		−	13.7320i		−	0.822115i
$280$		0			0
$281$		−	4.09880i		−	0.244514i	−0.992498	−	0.122257i	$-0.960987\pi$
$281$		−	4.09880i		−	0.244514i	0.992498	−	0.122257i	$-0.0390132\pi$
$282$	−3.90308	+	3.57625i	−0.232425	+	0.212963i
$283$	−9.65973	+	9.65973i	−0.574211	+	0.574211i	−0.933302	−	0.359091i	$-0.883087\pi$
$283$	−9.65973	+	9.65973i	−0.574211	+	0.574211i	0.359091	+	0.933302i	$0.383087\pi$
$284$	−12.8481	−	1.12503i	−0.762397	−	0.0667581i
$285$	3.75551	−	3.75551i	0.222457	−	0.222457i
$286$	−0.885341	+	20.2604i	−0.0523513	+	1.19802i
$287$		0			0
$288$	−9.98792	−	2.21621i	−0.588544	−	0.130591i
$289$	−26.2325			−1.54309
$290$	−6.66470	−	0.291235i	−0.391365	−	0.0171019i
$291$	−8.65616	+	8.65616i	−0.507433	+	0.507433i
$292$	29.6463	+	2.59593i	1.73492	+	0.151916i
$293$	−16.6941	−	16.6941i	−0.975280	−	0.975280i	0.0244213	−	0.999702i	$-0.492226\pi$
$293$	−16.6941	−	16.6941i	−0.975280	−	0.975280i	−0.999702	+	0.0244213i	$0.992226\pi$
$294$		0			0
$295$	−9.86128			−0.574146
$296$	7.15746	+	9.32994i	0.416019	+	0.542292i
$297$	−28.8411			−1.67353
$298$	−9.09536	−	9.92658i	−0.526880	−	0.575032i
$299$	−0.945438	+	0.945438i	−0.0546761	+	0.0546761i
$300$	4.85272	−	4.07131i	0.280172	−	0.235057i
$301$		0			0
$302$	−0.438440	+	10.0334i	−0.0252294	+	0.577357i
$303$		−	21.2324i		−	1.21977i
$304$	7.70491	+	11.0072i	0.441907	+	0.631308i
$305$	7.32329			0.419330
$306$	0.734183	−	16.8013i	0.0419705	−	0.960465i
$307$	−16.7590	−	16.7590i	−0.956484	−	0.956484i	0.0426074	−	0.999092i	$-0.486434\pi$
$307$	−16.7590	−	16.7590i	−0.956484	−	0.956484i	−0.999092	+	0.0426074i	$0.986434\pi$
$308$		0			0
$309$	−5.48135	+	5.48135i	−0.311823	+	0.311823i
$310$	11.4683	−	10.5080i	0.651358	−	0.596816i
$311$		−	21.4836i		−	1.21822i	−0.793085	−	0.609111i	$-0.791526\pi$
$311$		−	21.4836i		−	1.21822i	0.793085	−	0.609111i	$-0.208474\pi$
$312$	−1.05251	+	7.98778i	−0.0595869	+	0.452219i
$313$	−20.8499			−1.17851			−0.589253	−	0.807949i	$-0.700578\pi$
$313$	−20.8499			−1.17851			−0.589253	+	0.807949i	$0.700578\pi$
$314$	8.38495	+	9.15125i	0.473190	+	0.516435i
$315$		0			0
$316$	0.672394	−	7.67894i	0.0378251	−	0.431974i
$317$	−10.5401	−	10.5401i	−0.591992	−	0.591992i	0.346177	−	0.938169i	$-0.387480\pi$
$317$	−10.5401	−	10.5401i	−0.591992	−	0.591992i	−0.938169	+	0.346177i	$0.887480\pi$
$318$	−0.0957392	+	2.19092i	−0.00536879	+	0.122861i
$319$		−	17.8937i		−	1.00186i
$320$	−5.79208	−	10.0373i	−0.323787	−	0.561104i
$321$		−	13.0891i		−	0.730565i
$322$		0			0
$323$	−15.6170	+	15.6170i	−0.868955	+	0.868955i
$324$	−0.604361	−	0.0529198i	−0.0335756	−	0.00293999i
$325$	5.35441	+	5.35441i	0.297009	+	0.297009i
$326$	12.1329	+	13.2418i	0.671982	+	0.733394i
$327$		−	11.3274i		−	0.626405i
$328$	0.167451	−	1.27083i	0.00924595	−	0.0701697i
$329$		0			0
$330$	−8.30077	−	9.05938i	−0.456942	−	0.498702i
$331$	−2.11564	−	2.11564i	−0.116286	−	0.116286i	0.646569	−	0.762855i	$-0.276203\pi$
$331$	−2.11564	−	2.11564i	−0.116286	−	0.116286i	−0.762855	+	0.646569i	$0.776203\pi$
$332$	−4.43665	−	5.28819i	−0.243493	−	0.290227i
$333$	−5.31681	−	5.31681i	−0.291360	−	0.291360i
$334$	30.4161	+	1.32913i	1.66430	+	0.0727265i
$335$	9.29528			0.507855
$336$		0			0
$337$	−20.5605			−1.12000			−0.560000	−	0.828493i	$-0.689199\pi$
$337$	−20.5605			−1.12000			−0.560000	+	0.828493i	$0.689199\pi$
$338$	8.74512	+	0.382145i	0.475672	+	0.0207859i
$339$	10.3888	+	10.3888i	0.564243	+	0.564243i
$340$	14.5934	−	12.2435i	0.791440	−	0.663997i
$341$	29.5016	+	29.5016i	1.59760	+	1.59760i
$342$	−5.80397	−	6.33440i	−0.313843	−	0.342525i
$343$		0			0
$344$	−10.8172	+	8.29845i	−0.583227	+	0.447422i
$345$		−	0.810099i		−	0.0436143i
$346$	−19.1371	−	20.8860i	−1.02882	−	1.12284i
$347$	−4.23701	−	4.23701i	−0.227455	−	0.227455i	0.584174	−	0.811629i	$-0.301419\pi$
$347$	−4.23701	−	4.23701i	−0.227455	−	0.227455i	−0.811629	+	0.584174i	$0.801419\pi$
$348$	0.620106	−	7.08179i	0.0332412	−	0.379624i
$349$	3.15549	−	3.15549i	0.168909	−	0.168909i	−0.617590	−	0.786500i	$-0.711891\pi$
$349$	3.15549	−	3.15549i	0.168909	−	0.168909i	0.786500	+	0.617590i	$0.211891\pi$
$350$		0			0
$351$		−	13.6973i		−	0.731108i
$352$	26.2191	−	16.6966i	1.39748	−	0.889931i
$353$			6.96846i			0.370894i	0.982654	+	0.185447i	$0.0593732\pi$
$353$			6.96846i			0.370894i	−0.982654	+	0.185447i	$0.940627\pi$
$354$	0.458763	−	10.4985i	0.0243830	−	0.557987i
$355$	6.60535	+	6.60535i	0.350575	+	0.350575i
$356$	15.1956	+	1.33058i	0.805365	+	0.0705205i
$357$		0			0
$358$	−6.50790	−	7.10265i	−0.343953	−	0.375387i
$359$	−37.2374			−1.96531			−0.982656	−	0.185437i	$-0.940630\pi$
$359$	−37.2374			−1.96531			−0.982656	+	0.185437i	$0.940630\pi$
$360$	4.51032	+	5.87932i	0.237715	+	0.309867i
$361$		−	7.71720i		−	0.406169i
$362$	−9.31978	+	8.53937i	−0.489837	+	0.448819i
$363$	14.8146	−	14.8146i	0.777566	−	0.777566i
$364$		0			0
$365$	−15.2415	−	15.2415i	−0.797774	−	0.797774i
$366$	−0.340691	+	7.79648i	−0.0178082	+	0.407529i
$367$	26.0782			1.36127			0.680637	−	0.732621i	$-0.261703\pi$
$367$	26.0782			1.36127			0.680637	+	0.732621i	$0.261703\pi$
$368$	2.01819	+	0.356171i	0.105206	+	0.0185667i
$369$			0.819625i			0.0426680i
$370$	0.371822	−	8.50888i	0.0193301	−	0.442356i
$371$		0			0
$372$	10.6535	+	12.6982i	0.552357	+	0.658372i
$373$	25.8637	−	25.8637i	1.33917	−	1.33917i	0.442305	−	0.896865i	$-0.354161\pi$
$373$	25.8637	−	25.8637i	1.33917	−	1.33917i	0.896865	−	0.442305i	$-0.145839\pi$
$374$	34.5182	+	37.6728i	1.78489	+	1.94801i
$375$	−12.4937			−0.645173
$376$	−1.26714	+	9.61658i	−0.0653475	+	0.495937i
$377$	8.49813			0.437676
$378$		0			0
$379$	−0.261074	−	0.261074i	−0.0134105	−	0.0134105i	0.700370	−	0.713780i	$-0.253018\pi$
$379$	−0.261074	−	0.261074i	−0.0134105	−	0.0134105i	−0.713780	+	0.700370i	$0.753018\pi$
$380$	0.848875	−	9.69441i	0.0435464	−	0.497313i
$381$	10.6015	−	10.6015i	0.543129	−	0.543129i
$382$	−18.8225	−	0.822509i	−0.963045	−	0.0420832i
$383$	17.5370			0.896097			0.448048	−	0.894009i	$-0.352119\pi$
$383$	17.5370			0.896097			0.448048	+	0.894009i	$0.352119\pi$
$384$	10.9553	−	5.69938i	0.559063	−	0.290845i
$385$		0			0
$386$	−0.649218	+	14.8569i	−0.0330443	+	0.756197i
$387$	6.16438	−	6.16438i	0.313353	−	0.313353i
$388$	−1.95659	+	22.3449i	−0.0993310	+	1.13439i
$389$	15.7537	−	15.7537i	0.798744	−	0.798744i	−0.184154	−	0.982897i	$-0.558954\pi$
$389$	15.7537	−	15.7537i	0.798744	−	0.798744i	0.982897	+	0.184154i	$0.0589544\pi$
$390$	4.30250	−	3.94222i	0.217866	−	0.199622i
$391$			3.36874i			0.170365i
$392$		0			0
$393$			3.18058i			0.160439i
$394$	−19.0024	−	20.7391i	−0.957329	−	1.04482i
$395$	−3.94781	+	3.94781i	−0.198636	+	0.198636i
$396$	−15.2268	+	12.7749i	−0.765177	+	0.641963i
$397$	−16.7346	+	16.7346i	−0.839885	+	0.839885i	−0.988843	−	0.148958i	$-0.952408\pi$
$397$	−16.7346	+	16.7346i	−0.839885	+	0.839885i	0.148958	+	0.988843i	$0.452408\pi$
$398$	−34.1791	−	1.49356i	−1.71324	−	0.0748655i
$399$		0			0
$400$	2.01714	−	11.4299i	0.100857	−	0.571493i
$401$	7.74461			0.386747			0.193374	−	0.981125i	$-0.438057\pi$
$401$	7.74461			0.386747			0.193374	+	0.981125i	$0.438057\pi$
$402$	−0.432431	+	9.89589i	−0.0215677	+	0.493562i
$403$	−14.0110	+	14.0110i	−0.697937	+	0.697937i
$404$	−25.0049	−	29.8042i	−1.24404	−	1.48281i
$405$	0.310707	+	0.310707i	0.0154392	+	0.0154392i
$406$		0			0
$407$	22.8451			1.13239
$408$	12.3557	+	16.1060i	0.611699	+	0.797365i
$409$	31.9303			1.57885			0.789425	−	0.613847i	$-0.210379\pi$
$409$	31.9303			1.57885			0.789425	+	0.613847i	$0.210379\pi$
$410$	−0.684512	+	0.627193i	−0.0338057	+	0.0309749i
$411$	5.57636	−	5.57636i	0.275062	−	0.275062i
$412$	−1.23898	+	14.1495i	−0.0610400	+	0.697095i
$413$		0			0
$414$	−1.30918	−	0.0572087i	−0.0643428	−	0.00281166i
$415$			4.99963i			0.245422i
$416$	7.92958	+	12.4520i	0.388780	+	0.610512i
$417$	−1.09442			−0.0535938
$418$	26.0778	+	1.13955i	1.27551	+	0.0557373i
$419$	6.96449	+	6.96449i	0.340238	+	0.340238i	0.856457	−	0.516219i	$-0.172661\pi$
$419$	6.96449	+	6.96449i	0.340238	+	0.340238i	−0.516219	+	0.856457i	$0.672661\pi$
$420$		0			0
$421$	6.31935	−	6.31935i	0.307986	−	0.307986i	−0.536142	−	0.844128i	$-0.680119\pi$
$421$	6.31935	−	6.31935i	0.307986	−	0.307986i	0.844128	+	0.536142i	$0.180119\pi$
$422$	−11.9074	−	12.9956i	−0.579644	−	0.632617i
$423$		−	6.20226i		−	0.301564i
$424$	2.44581	+	3.18817i	0.118779	+	0.154831i
$425$	19.0786			0.925447
$426$	−7.33944	+	6.72486i	−0.355597	+	0.325821i
$427$		0			0
$428$	−15.4148	−	18.3734i	−0.745101	−	0.888110i
$429$	11.0679	+	11.0679i	0.534364	+	0.534364i
$430$	9.86530	+	0.431095i	0.475747	+	0.0207892i
$431$			6.48444i			0.312344i	0.987730	+	0.156172i	$0.0499155\pi$
$431$			6.48444i			0.312344i	−0.987730	+	0.156172i	$0.950085\pi$
$432$	−17.1996	+	12.0395i	−0.827518	+	0.579252i
$433$		−	17.1718i		−	0.825223i	−0.910907	−	0.412612i	$-0.864617\pi$
$433$		−	17.1718i		−	0.825223i	0.910907	−	0.412612i	$-0.135383\pi$
$434$		0			0
$435$	−3.64081	+	3.64081i	−0.174564	+	0.174564i
$436$	−13.3400	−	15.9004i	−0.638869	−	0.761489i
$437$	1.21690	+	1.21690i	0.0582124	+	0.0582124i
$438$	16.9353	−	15.5172i	0.809202	−	0.741442i
$439$		−	31.2986i		−	1.49380i	−0.664937	−	0.746900i	$-0.731542\pi$
$439$		−	31.2986i		−	1.49380i	0.664937	−	0.746900i	$-0.268458\pi$
$440$	−22.3209	−	2.94112i	−1.06411	−	0.140213i
$441$		0			0
$442$	−17.8917	+	16.3935i	−0.851020	+	0.779758i
$443$	8.57187	+	8.57187i	0.407262	+	0.407262i	0.880783	−	0.473521i	$-0.157017\pi$
$443$	8.57187	+	8.57187i	0.407262	+	0.407262i	−0.473521	+	0.880783i	$0.657017\pi$
$444$	9.04138	+	0.791694i	0.429085	+	0.0375721i
$445$	−7.81220	−	7.81220i	−0.370334	−	0.370334i
$446$	−0.336420	+	7.69873i	−0.0159299	+	0.364545i
$447$	−10.3914			−0.491495
$448$		0			0
$449$	33.4968			1.58081			0.790406	−	0.612583i	$-0.209869\pi$
$449$	33.4968			1.58081			0.790406	+	0.612583i	$0.209869\pi$
$450$	−0.323997	+	7.41444i	−0.0152733	+	0.349520i
$451$	−1.76087	−	1.76087i	−0.0829160	−	0.0829160i
$452$	26.8176	+	2.34824i	1.26139	+	0.110452i
$453$	5.48108	+	5.48108i	0.257523	+	0.257523i
$454$	1.56918	−	1.43778i	0.0736454	−	0.0674786i
$455$		0			0
$456$	10.2813	+	1.35473i	0.481467	+	0.0634408i
$457$			3.01270i			0.140928i	0.997514	+	0.0704641i	$0.0224480\pi$
$457$			3.01270i			0.140928i	−0.997514	+	0.0704641i	$0.977552\pi$
$458$	−5.15889	+	4.72690i	−0.241059	+	0.220873i
$459$	−24.4028	−	24.4028i	−1.13903	−	1.13903i
$460$	−0.954034	−	1.13714i	−0.0444820	−	0.0530196i
$461$	−20.6763	+	20.6763i	−0.962993	+	0.962993i	−0.999339	−	0.0363467i	$-0.988428\pi$
$461$	−20.6763	+	20.6763i	−0.962993	+	0.962993i	0.0363467	+	0.999339i	$0.488428\pi$
$462$		0			0
$463$		−	11.6775i		−	0.542697i	−0.962481	−	0.271349i	$-0.912530\pi$
$463$		−	11.6775i		−	0.542697i	0.962481	−	0.271349i	$-0.0874696\pi$
$464$	−7.46961	−	10.6711i	−0.346768	−	0.495392i
$465$		−	12.0053i		−	0.556733i
$466$	17.5627	+	0.767457i	0.813577	+	0.0355518i
$467$	−7.17951	−	7.17951i	−0.332228	−	0.332228i	0.521204	−	0.853432i	$-0.325483\pi$
$467$	−7.17951	−	7.17951i	−0.332228	−	0.332228i	−0.853432	+	0.521204i	$0.825483\pi$
$468$	−6.06709	−	7.23157i	−0.280451	−	0.334279i
$469$		0			0
$470$	5.17984	−	4.74609i	0.238928	−	0.218921i
$471$	9.57973			0.441411
$472$	−11.7198	−	15.2771i	−0.539448	−	0.703184i
$473$			26.4868i			1.21787i
$474$	−4.01924	−	4.38656i	−0.184610	−	0.201481i
$475$	6.89183	−	6.89183i	0.316219	−	0.316219i
$476$		0			0
$477$	−1.81683	−	1.81683i	−0.0831870	−	0.0831870i
$478$	−10.3710	−	0.453192i	−0.474357	−	0.0207285i
$479$	−11.4462			−0.522992			−0.261496	−	0.965205i	$-0.584216\pi$
$479$	−11.4462			−0.522992			−0.261496	+	0.965205i	$0.584216\pi$
$480$	−8.73200	−	1.93754i	−0.398560	−	0.0884360i
$481$			10.8496i			0.494701i
$482$	−14.6569	−	0.640478i	−0.667604	−	0.0291730i
$483$		0			0
$484$	3.34862	−	38.2423i	0.152210	−	1.73828i
$485$	11.4877	−	11.4877i	0.521630	−	0.521630i
$486$	16.0732	−	14.7273i	0.729095	−	0.668043i
$487$	−9.70073			−0.439582			−0.219791	−	0.975547i	$-0.570538\pi$
$487$	−9.70073			−0.439582			−0.219791	+	0.975547i	$0.570538\pi$
$488$	8.70349	+	11.3452i	0.393989	+	0.513574i
$489$	13.8618			0.626851
$490$		0			0
$491$	−11.4667	−	11.4667i	−0.517483	−	0.517483i	0.399326	−	0.916809i	$-0.369244\pi$
$491$	−11.4667	−	11.4667i	−0.517483	−	0.517483i	−0.916809	+	0.399326i	$0.869244\pi$
$492$	−0.635875	−	0.757920i	−0.0286675	−	0.0341697i
$493$	15.1401	−	15.1401i	0.681875	−	0.681875i
$494$	−0.541199	+	12.3850i	−0.0243497	+	0.557225i
$495$	14.3960			0.647050
$496$	29.9088	+	5.27830i	1.34294	+	0.237002i
$497$		0			0
$498$	−5.32268	−	0.232591i	−0.238515	−	0.0104226i
$499$	13.4945	−	13.4945i	0.604095	−	0.604095i	−0.337302	−	0.941397i	$-0.609514\pi$
$499$	13.4945	−	13.4945i	0.604095	−	0.604095i	0.941397	+	0.337302i	$0.109514\pi$
$500$	−17.5376	+	14.7135i	−0.784303	+	0.658009i
$501$	16.6158	−	16.6158i	0.742339	−	0.742339i
$502$	0.542774	+	0.592378i	0.0242252	+	0.0264391i
$503$		−	22.4043i		−	0.998960i	−0.866325	−	0.499480i	$-0.833524\pi$
$503$		−	22.4043i		−	0.998960i	0.866325	−	0.499480i	$-0.166476\pi$
$504$		0			0
$505$			28.1779i			1.25390i
$506$	2.93553	−	2.68971i	0.130500	−	0.119572i
$507$	4.77731	−	4.77731i	0.212168	−	0.212168i
$508$	2.39630	−	27.3665i	0.106319	−	1.21419i
$509$	−10.6969	+	10.6969i	−0.474132	+	0.474132i	−0.903249	−	0.429117i	$-0.858825\pi$
$509$	−10.6969	+	10.6969i	−0.474132	+	0.474132i	0.429117	+	0.903249i	$0.358825\pi$
$510$	0.641864	−	14.6886i	0.0284222	−	0.650423i
$511$		0			0
$512$	8.66611	−	20.9021i	0.382992	−	0.923752i
$513$	−17.6302			−0.778394
$514$	−12.9244	−	0.564772i	−0.570072	−	0.0249110i
$515$	7.27438	−	7.27438i	0.320547	−	0.320547i
$516$	−0.917900	+	10.4827i	−0.0404083	+	0.461475i
$517$	13.3248	+	13.3248i	0.586025	+	0.586025i
$518$		0			0
$519$	−21.8639			−0.959721
$520$	1.39681	−	10.6007i	0.0612540	−	0.464871i
$521$	−7.27601			−0.318768			−0.159384	−	0.987217i	$-0.550951\pi$
$521$	−7.27601			−0.318768			−0.159384	+	0.987217i	$0.550951\pi$
$522$	5.62672	+	6.14095i	0.246275	+	0.268782i
$523$	12.7559	−	12.7559i	0.557776	−	0.557776i	−0.370898	−	0.928674i	$-0.620950\pi$
$523$	12.7559	−	12.7559i	0.557776	−	0.557776i	0.928674	+	0.370898i	$0.120950\pi$
$524$	3.74569	+	4.46461i	0.163631	+	0.195037i
$525$		0			0
$526$	0.282910	−	6.47421i	0.0123355	−	0.282289i
$527$			49.9233i			2.17469i
$528$	4.16957	−	23.6263i	0.181457	−	1.02820i
$529$	−22.7375			−0.988587
$530$	0.127057	−	2.90761i	0.00551900	−	0.126298i
$531$	8.70588	+	8.70588i	0.377803	+	0.377803i
$532$		0			0
$533$	0.836275	−	0.836275i	0.0362231	−	0.0362231i
$534$	8.68042	−	7.95354i	0.375638	−	0.344184i
$535$			17.3708i			0.751005i
$536$	11.0471	+	14.4002i	0.477164	+	0.621995i
$537$	−7.43522			−0.320853
$538$	−9.12219	−	9.95586i	−0.393286	−	0.429228i
$539$		0			0
$540$	15.1483	+	1.32643i	0.651878	+	0.0570806i
$541$	1.91584	+	1.91584i	0.0823686	+	0.0823686i	0.747091	−	0.664722i	$-0.231450\pi$
$541$	1.91584	+	1.91584i	0.0823686	+	0.0823686i	−0.664722	+	0.747091i	$0.731450\pi$
$542$	−0.449684	+	10.2907i	−0.0193156	+	0.442023i
$543$			9.75615i			0.418677i
$544$	36.3115	+	8.05712i	1.55684	+	0.345446i
$545$			15.0327i			0.643931i
$546$		0			0
$547$	−20.4366	+	20.4366i	−0.873807	+	0.873807i	−0.992885	−	0.119078i	$-0.962006\pi$
$547$	−20.4366	+	20.4366i	−0.873807	+	0.873807i	0.119078	+	0.992885i	$0.462006\pi$
$548$	1.26045	−	14.3947i	0.0538438	−	0.614913i
$549$	−6.46526	−	6.46526i	−0.275930	−	0.275930i
$550$	−15.2330	−	16.6251i	−0.649536	−	0.708896i
$551$		−	10.9382i		−	0.465984i
$552$	1.25500	−	0.962777i	0.0534165	−	0.0409785i
$553$		0			0
$554$	30.9313	+	33.7581i	1.31415	+	1.43424i
$555$	−4.64826	−	4.64826i	−0.197308	−	0.197308i
$556$	−1.53624	+	1.28887i	−0.0651513	+	0.0546602i
$557$	3.33915	+	3.33915i	0.141484	+	0.141484i	0.774301	−	0.632817i	$-0.218101\pi$
$557$	3.33915	+	3.33915i	0.141484	+	0.141484i	−0.632817	+	0.774301i	$0.718101\pi$
$558$	−19.4015	−	0.847809i	−0.821332	−	0.0358906i
$559$	−12.5792			−0.532044
$560$		0			0
$561$	39.4367			1.66502
$562$	−5.79105	−	0.253058i	−0.244281	−	0.0106746i
$563$	−5.18939	−	5.18939i	−0.218707	−	0.218707i	0.589247	−	0.807953i	$-0.299425\pi$
$563$	−5.18939	−	5.18939i	−0.218707	−	0.218707i	−0.807953	+	0.589247i	$0.799425\pi$
$564$	4.81179	+	5.73533i	0.202613	+	0.241501i
$565$	−13.7872	−	13.7872i	−0.580030	−	0.580030i
$566$	13.0515	+	14.2443i	0.548596	+	0.598732i
$567$		0			0
$568$	−2.38275	+	18.0832i	−0.0999779	+	0.758756i
$569$		−	12.4715i		−	0.522833i	−0.965226	−	0.261416i	$-0.915810\pi$
$569$		−	12.4715i		−	0.522833i	0.965226	−	0.261416i	$-0.0841896\pi$
$570$	−5.07416	−	5.53789i	−0.212533	−	0.231957i
$571$	27.1588	+	27.1588i	1.13656	+	1.13656i	0.989063	+	0.147497i	$0.0471216\pi$
$571$	27.1588	+	27.1588i	1.13656	+	1.13656i	0.147497	+	0.989063i	$0.452878\pi$
$572$	28.5706	+	2.50174i	1.19460	+	0.104603i
$573$	−10.2824	+	10.2824i	−0.429555	+	0.429555i
$574$		0			0
$575$		−	1.48663i		−	0.0619969i
$576$	−3.74786	+	13.9748i	−0.156161	+	0.582281i
$577$		−	18.9417i		−	0.788552i	−0.918992	−	0.394276i	$-0.870995\pi$
$577$		−	18.9417i		−	0.788552i	0.918992	−	0.394276i	$-0.129005\pi$
$578$	−1.61958	+	37.0629i	−0.0673656	+	1.54162i
$579$	8.11608	+	8.11608i	0.337293	+	0.337293i
$580$	−0.822951	+	9.39835i	−0.0341712	+	0.390245i
$581$		0			0
$582$	11.6956	+	12.7644i	0.484797	+	0.529102i
$583$	7.80649			0.323312
$584$	5.49806	−	41.7260i	0.227511	−	1.72663i
$585$			6.83696i			0.282674i
$586$	−24.6172	+	22.5558i	−1.01693	+	0.931773i
$587$	7.54134	−	7.54134i	0.311264	−	0.311264i	−0.534135	−	0.845399i	$-0.679363\pi$
$587$	7.54134	−	7.54134i	0.311264	−	0.311264i	0.845399	+	0.534135i	$0.179363\pi$
$588$		0			0
$589$	18.0340	+	18.0340i	0.743078	+	0.743078i
$590$	−0.608830	+	13.9327i	−0.0250651	+	0.573598i
$591$	−21.7101			−0.893035
$592$	13.6238	−	9.53651i	0.559936	−	0.391948i
$593$			11.8708i			0.487475i	0.969841	+	0.243737i	$0.0783735\pi$
$593$			11.8708i			0.487475i	−0.969841	+	0.243737i	$0.921627\pi$
$594$	−1.78064	+	40.7486i	−0.0730604	+	1.67194i
$595$		0			0
$596$	−14.5865	+	12.2377i	−0.597485	+	0.501274i
$597$	−18.6715	+	18.6715i	−0.764172	+	0.764172i
$598$	1.27741	+	1.39415i	0.0522370	+	0.0570109i
$599$	21.8341			0.892116			0.446058	−	0.895004i	$-0.352827\pi$
$599$	21.8341			0.892116			0.446058	+	0.895004i	$0.352827\pi$
$600$	−5.45260	−	7.10760i	−0.222602	−	0.290167i
$601$	−37.4893			−1.52922			−0.764610	−	0.644493i	$-0.777068\pi$
$601$	−37.4893			−1.52922			−0.764610	+	0.644493i	$0.777068\pi$
$602$		0			0
$603$	−8.20620	−	8.20620i	−0.334182	−	0.334182i
$604$	14.1488	+	1.23891i	0.575705	+	0.0504107i
$605$	−19.6607	+	19.6607i	−0.799321	+	0.799321i
$606$	−29.9986	−	1.31088i	−1.21861	−	0.0532509i
$607$	4.67915			0.189921			0.0949605	−	0.995481i	$-0.469728\pi$
$607$	4.67915			0.189921			0.0949605	+	0.995481i	$0.469728\pi$
$608$	16.0274	−	10.2064i	0.649998	−	0.413925i
$609$		0			0
$610$	0.452136	−	10.3468i	0.0183065	−	0.418930i
$611$	−6.32825	+	6.32825i	−0.256014	+	0.256014i
$612$	−23.6926	−	2.07460i	−0.957717	−	0.0838609i
$613$	3.58488	−	3.58488i	0.144792	−	0.144792i	−0.630995	−	0.775787i	$-0.717353\pi$
$613$	3.58488	−	3.58488i	0.144792	−	0.144792i	0.775787	+	0.630995i	$0.217353\pi$
$614$	−24.7128	+	22.6435i	−0.997329	+	0.913816i
$615$			0.716563i			0.0288946i
$616$		0			0
$617$			16.4696i			0.663041i	0.943448	+	0.331520i	$0.107562\pi$
$617$			16.4696i			0.663041i	−0.943448	+	0.331520i	$0.892438\pi$
$618$	7.40599	+	8.08283i	0.297913	+	0.325139i
$619$	−10.7503	+	10.7503i	−0.432093	+	0.432093i	−0.889340	−	0.457247i	$-0.848835\pi$
$619$	−10.7503	+	10.7503i	−0.432093	+	0.432093i	0.457247	+	0.889340i	$0.348835\pi$
$620$	−14.1384	−	16.8520i	−0.567811	−	0.676792i
$621$	−1.90151	+	1.90151i	−0.0763048	+	0.0763048i
$622$	−30.3534	−	1.32638i	−1.21706	−	0.0531832i
$623$		0			0
$624$	11.2207	+	1.98022i	0.449186	+	0.0792723i
$625$	2.07246			0.0828985
$626$	−1.28726	+	29.4581i	−0.0514493	+	1.17738i
$627$	14.2459	−	14.2459i	0.568926	−	0.568926i
$628$	13.4472	−	11.2818i	0.536600	−	0.450193i
$629$	19.3295	+	19.3295i	0.770717	+	0.770717i
$630$		0			0
$631$	−6.82302			−0.271620			−0.135810	−	0.990735i	$-0.543364\pi$
$631$	−6.82302			−0.271620			−0.135810	+	0.990735i	$0.543364\pi$
$632$	−10.8078	−	1.42410i	−0.429911	−	0.0566475i
$633$	−13.6041			−0.540715
$634$	−15.5425	+	14.2410i	−0.617272	+	0.565584i
$635$	−14.0694	+	14.0694i	−0.558325	+	0.558325i
$636$	3.08957	+	0.270533i	0.122509	+	0.0107273i
$637$		0			0
$638$	−25.2814	−	1.10475i	−1.00090	−	0.0437375i
$639$		−	11.6629i		−	0.461376i
$640$	−14.5390	+	7.56373i	−0.574704	+	0.298982i
$641$	33.0759			1.30642			0.653210	−	0.757177i	$-0.273422\pi$
$641$	33.0759			1.30642			0.653210	+	0.757177i	$0.273422\pi$
$642$	−18.4932	−	0.808117i	−0.729868	−	0.0318939i
$643$	−14.7445	−	14.7445i	−0.581464	−	0.581464i	0.353841	−	0.935306i	$-0.384875\pi$
$643$	−14.7445	−	14.7445i	−0.581464	−	0.581464i	−0.935306	+	0.353841i	$0.884875\pi$
$644$		0			0
$645$	5.38925	−	5.38925i	0.212201	−	0.212201i
$646$	21.1006	+	23.0289i	0.830191	+	0.906062i
$647$			11.1144i			0.436951i	0.975842	+	0.218476i	$0.0701084\pi$
$647$			11.1144i			0.436951i	−0.975842	+	0.218476i	$0.929892\pi$
$648$	−0.112082	+	0.850613i	−0.00440298	+	0.0334152i
$649$	−37.4071			−1.46836
$650$	7.89563	−	7.23448i	0.309692	−	0.283759i
$651$		0			0
$652$	19.4579	−	16.3247i	0.762031	−	0.639324i
$653$	−11.8922	−	11.8922i	−0.465378	−	0.465378i	0.435035	−	0.900413i	$-0.356736\pi$
$653$	−11.8922	−	11.8922i	−0.465378	−	0.465378i	−0.900413	+	0.435035i	$0.856736\pi$
$654$	−16.0041	−	0.699347i	−0.625808	−	0.0273466i
$655$		−	4.22099i		−	0.164928i
$656$	−1.78517	−	0.315046i	−0.0696991	−	0.0123005i
$657$			26.9114i			1.04991i
$658$		0			0
$659$	32.5839	−	32.5839i	1.26929	−	1.26929i	0.322834	−	0.946455i	$-0.395364\pi$
$659$	32.5839	−	32.5839i	1.26929	−	1.26929i	0.946455	−	0.322834i	$-0.104636\pi$
$660$	−13.3122	+	11.1685i	−0.518175	+	0.434735i
$661$	12.3984	+	12.3984i	0.482241	+	0.482241i	0.905847	−	0.423606i	$-0.139236\pi$
$661$	12.3984	+	12.3984i	0.482241	+	0.482241i	−0.423606	+	0.905847i	$0.639236\pi$
$662$	−3.11973	+	2.85850i	−0.121252	+	0.111099i
$663$			18.7294i			0.727389i
$664$	−7.74542	+	5.94190i	−0.300580	+	0.230590i
$665$		0			0
$666$	−7.84020	+	7.18368i	−0.303801	+	0.278362i
$667$	−1.17974	−	1.17974i	−0.0456797	−	0.0456797i
$668$	3.75575	−	42.8918i	0.145314	−	1.65953i
$669$	4.20569	+	4.20569i	0.162601	+	0.162601i
$670$	0.573886	−	13.1330i	0.0221711	−	0.507371i
$671$	27.7796			1.07242
$672$		0			0
$673$	11.0728			0.426827			0.213413	−	0.976962i	$-0.431542\pi$
$673$	11.0728			0.426827			0.213413	+	0.976962i	$0.431542\pi$
$674$	−1.26939	+	29.0492i	−0.0488952	+	1.11893i
$675$	10.7690	+	10.7690i	0.414499	+	0.414499i
$676$	1.07984	−	12.3321i	0.0415323	−	0.474311i
$677$	−4.17016	−	4.17016i	−0.160272	−	0.160272i	0.622415	−	0.782687i	$-0.286152\pi$
$677$	−4.17016	−	4.17016i	−0.160272	−	0.160272i	−0.782687	+	0.622415i	$0.786152\pi$
$678$	15.3194	−	14.0366i	0.588338	−	0.539073i
$679$		0			0
$680$	−16.3974	−	21.3745i	−0.628813	−	0.819674i
$681$		−	1.64266i		−	0.0629467i
$682$	43.5032	−	39.8604i	1.66582	−	1.52633i
$683$	−2.25251	−	2.25251i	−0.0861899	−	0.0861899i	0.662697	−	0.748887i	$-0.269412\pi$
$683$	−2.25251	−	2.25251i	−0.0861899	−	0.0861899i	−0.748887	+	0.662697i	$0.769412\pi$
$684$	−9.30799	+	7.80915i	−0.355900	+	0.298590i
$685$	−7.40047	+	7.40047i	−0.282757	+	0.282757i
$686$		0			0
$687$			5.40044i			0.206040i
$688$	11.0567	+	15.7956i	0.421534	+	0.602203i
$689$			3.70748i			0.141244i
$690$	−1.14456	−	0.0500151i	−0.0435727	−	0.00190404i
$691$	14.9572	+	14.9572i	0.568997	+	0.568997i	0.931847	−	0.362850i	$-0.118196\pi$
$691$	14.9572	+	14.9572i	0.568997	+	0.568997i	−0.362850	+	0.931847i	$0.618196\pi$
$692$	−30.6906	+	25.7486i	−1.16668	+	0.978816i
$693$		0			0
$694$	−6.24792	+	5.72474i	−0.237168	+	0.217308i
$695$	1.45242			0.0550933
$696$	−9.96734	−	1.31335i	−0.377811	−	0.0497825i
$697$		−	2.97978i		−	0.112867i
$698$	−4.26346	−	4.65310i	−0.161374	−	0.176122i
$699$	9.59422	−	9.59422i	0.362887	−	0.362887i
$700$		0			0
$701$	19.0687	+	19.0687i	0.720214	+	0.720214i	0.968649	−	0.248435i	$-0.0799162\pi$
$701$	19.0687	+	19.0687i	0.720214	+	0.720214i	−0.248435	+	0.968649i	$0.579916\pi$
$702$	−19.3524	−	0.845665i	−0.730411	−	0.0319176i
$703$	13.9649			0.526697
$704$	−21.9713	−	38.0749i	−0.828073	−	1.43500i
$705$		−	5.42237i		−	0.204218i
$706$	9.84549	+	0.430229i	0.370540	+	0.0161919i
$707$		0			0
$708$	−14.8046	−	1.29634i	−0.556391	−	0.0487194i
$709$	−24.6933	+	24.6933i	−0.927376	+	0.927376i	−0.997536	−	0.0701596i	$-0.977649\pi$
$709$	−24.6933	+	24.6933i	−0.927376	+	0.927376i	0.0701596	+	0.997536i	$0.477649\pi$
$710$	9.74028	−	8.92466i	0.365546	−	0.334936i
$711$	6.97054			0.261416
$712$	2.81810	−	21.3872i	0.105613	−	0.801519i
$713$	3.89011			0.145686
$714$		0			0
$715$	−14.6884	−	14.6884i	−0.549315	−	0.549315i
$716$	−10.4369	+	8.75627i	−0.390045	+	0.327237i
$717$	−5.66549	+	5.66549i	−0.211582	+	0.211582i
$718$	−2.29902	+	52.6114i	−0.0857985	+	1.96344i
$719$	−51.5103			−1.92101			−0.960505	−	0.278264i	$-0.910241\pi$
$719$	−51.5103			−1.92101			−0.960505	+	0.278264i	$0.910241\pi$
$720$	8.58514	−	6.00949i	0.319949	−	0.223960i
$721$		0			0
$722$	−10.9034	−	0.476456i	−0.405781	−	0.0177319i
$723$	−8.00682	+	8.00682i	−0.297777	+	0.297777i
$724$	11.4896	+	13.6948i	0.427007	+	0.508964i
$725$	−6.68135	+	6.68135i	−0.248139	+	0.248139i
$726$	−20.0164	−	21.8457i	−0.742879	−	0.810770i
$727$		−	10.3415i		−	0.383546i	−0.981439	−	0.191773i	$-0.938576\pi$
$727$		−	10.3415i		−	0.383546i	0.981439	−	0.191773i	$-0.0614237\pi$
$728$		0			0
$729$		−	17.7358i		−	0.656881i
$730$	−22.4751	+	20.5931i	−0.831842	+	0.762186i
$731$	−22.4108	+	22.4108i	−0.828894	+	0.828894i
$732$	10.9943	+	0.962702i	0.406363	+	0.0355825i
$733$	14.2382	−	14.2382i	0.525902	−	0.525902i	−0.393446	−	0.919348i	$-0.628717\pi$
$733$	14.2382	−	14.2382i	0.525902	−	0.525902i	0.919348	+	0.393446i	$0.128717\pi$
$734$	1.61006	−	36.8450i	0.0594283	−	1.35998i
$735$		0			0
$736$	0.627823	−	2.82945i	0.0231419	−	0.104295i
$737$	35.2601			1.29882
$738$	1.15802	+	0.0506033i	0.0426273	+	0.00186273i
$739$	−21.6088	+	21.6088i	−0.794893	+	0.794893i	−0.982285	−	0.187392i	$-0.939997\pi$
$739$	−21.6088	+	21.6088i	−0.794893	+	0.794893i	0.187392	+	0.982285i	$0.439997\pi$
$740$	−11.9989	−	1.05067i	−0.441090	−	0.0386233i
$741$	6.76569	+	6.76569i	0.248544	+	0.248544i
$742$		0			0
$743$	−36.5659			−1.34147			−0.670735	−	0.741697i	$-0.734021\pi$
$743$	−36.5659			−1.34147			−0.670735	+	0.741697i	$0.734021\pi$
$744$	18.5986	−	14.2679i	0.681858	−	0.523088i
$745$	13.7905			0.505246
$746$	−34.9451	−	38.1387i	−1.27943	−	1.39636i
$747$	4.41385	−	4.41385i	0.161494	−	0.161494i
$748$	55.3577	−	46.4437i	2.02408	−	1.69815i
$749$		0			0
$750$	−0.771356	+	17.6519i	−0.0281659	+	0.644557i
$751$		−	35.3286i		−	1.28916i	−0.764537	−	0.644580i	$-0.777032\pi$
$751$		−	35.3286i		−	1.28916i	0.764537	−	0.644580i	$-0.222968\pi$
$752$	13.5087	+	2.38401i	0.492612	+	0.0869361i
$753$	0.620114			0.0225982
$754$	0.524671	−	12.0067i	0.0191074	−	0.437259i
$755$	−7.27401	−	7.27401i	−0.264728	−	0.264728i
$756$		0			0
$757$	−1.06021	+	1.06021i	−0.0385339	+	0.0385339i	−0.726111	−	0.687577i	$-0.758674\pi$
$757$	−1.06021	+	1.06021i	−0.0385339	+	0.0385339i	0.687577	+	0.726111i	$0.258674\pi$
$758$	−0.384981	+	0.352744i	−0.0139831	+	0.0128122i
$759$		−	3.07297i		−	0.111542i
$760$	−13.6445	−	1.79787i	−0.494938	−	0.0652158i
$761$	30.4006			1.10202			0.551010	−	0.834498i	$-0.314243\pi$
$761$	30.4006			1.10202			0.551010	+	0.834498i	$0.314243\pi$
$762$	−14.3239	−	15.6330i	−0.518901	−	0.566323i
$763$		0			0
$764$	−2.32419	+	26.5429i	−0.0840862	+	0.960289i
$765$	12.1806	+	12.1806i	0.440390	+	0.440390i
$766$	1.08272	−	24.7774i	0.0391204	−	0.895242i
$767$		−	17.7655i		−	0.641474i
$768$	−7.37608	−	15.8303i	−0.266161	−	0.571227i
$769$			38.0523i			1.37220i	0.727507	+	0.686101i	$0.240679\pi$
$769$			38.0523i			1.37220i	−0.727507	+	0.686101i	$0.759321\pi$
$770$		0			0
$771$	−7.06039	+	7.06039i	−0.254274	+	0.254274i
$772$	20.9507	+	1.83452i	0.754033	+	0.0660257i
$773$	−11.0014	−	11.0014i	−0.395694	−	0.395694i	0.481017	−	0.876711i	$-0.340267\pi$
$773$	−11.0014	−	11.0014i	−0.395694	−	0.395694i	−0.876711	+	0.481017i	$0.840267\pi$
$774$	−8.32885	−	9.09002i	−0.299374	−	0.326734i
$775$		−	22.0313i		−	0.791387i
$776$	31.4495	+	4.14397i	1.12897	+	0.148760i
$777$		0			0
$778$	−21.2852	−	23.2305i	−0.763112	−	0.832853i
$779$	−1.07640	−	1.07640i	−0.0385659	−	0.0385659i
$780$	−5.30420	−	6.32225i	−0.189921	−	0.226373i
$781$	25.0563	+	25.0563i	0.896584	+	0.896584i
$782$	4.75958	+	0.207985i	0.170202	+	0.00743751i
$783$	17.0918			0.610812
$784$		0			0
$785$	−12.7134			−0.453760
$786$	4.49372	+	0.196367i	0.160286	+	0.00700418i
$787$	11.8166	+	11.8166i	0.421217	+	0.421217i	0.885623	−	0.464406i	$-0.153732\pi$
$787$	11.8166	+	11.8166i	0.421217	+	0.421217i	−0.464406	+	0.885623i	$0.653732\pi$
$788$	−30.4747	+	25.5675i	−1.08562	+	0.910803i
$789$	−3.53675	−	3.53675i	−0.125912	−	0.125912i
$790$	5.33399	+	5.82146i	0.189775	+	0.207118i
$791$		0			0
$792$	17.1091	+	22.3022i	0.607946	+	0.792474i
$793$			13.1932i			0.468504i
$794$	22.6105	+	24.6769i	0.802418	+	0.875751i
$795$	−1.58838	−	1.58838i	−0.0563339	−	0.0563339i
$796$	−4.22040	+	48.1983i	−0.149588	+	1.70834i
$797$	−6.46029	+	6.46029i	−0.228835	+	0.228835i	−0.812206	−	0.583371i	$-0.801733\pi$
$797$	−6.46029	+	6.46029i	−0.228835	+	0.228835i	0.583371	+	0.812206i	$0.301733\pi$
$798$		0			0
$799$			22.5486i			0.797710i
$800$	−16.0243	−	3.55562i	−0.566545	−	0.125710i
$801$			13.7938i			0.487379i
$802$	0.478148	−	10.9421i	0.0168840	−	0.386379i
$803$	−57.8159	−	57.8159i	−2.04028	−	2.04028i
$804$	13.9549	+	1.22193i	0.492150	+	0.0430943i
$805$		0			0
$806$	18.9306	+	20.6607i	0.666802	+	0.727741i
$807$	−10.4220			−0.366872
$808$	−43.6531	+	33.4885i	−1.53571	+	1.17812i
$809$		−	28.8161i		−	1.01312i	−0.862205	−	0.506559i	$-0.830917\pi$
$809$		−	28.8161i		−	1.01312i	0.862205	−	0.506559i	$-0.169083\pi$
$810$	0.458170	−	0.419805i	0.0160985	−	0.0147504i
$811$	−32.3761	+	32.3761i	−1.13688	+	1.13688i	−0.147873	+	0.989006i	$0.547243\pi$
$811$	−32.3761	+	32.3761i	−1.13688	+	1.13688i	−0.989006	+	0.147873i	$0.952757\pi$
$812$		0			0
$813$	5.62163	+	5.62163i	0.197159	+	0.197159i
$814$	1.41044	−	32.2770i	0.0494360	−	1.13131i
$815$	−18.3962			−0.644389
$816$	23.5184	−	16.4626i	0.823309	−	0.576305i
$817$			16.1911i			0.566455i
$818$	1.97136	−	45.1132i	0.0689270	−	1.57735i
$819$		0			0
$820$	0.843878	+	1.00585i	0.0294695	+	0.0351257i
$821$	19.1269	−	19.1269i	0.667534	−	0.667534i	−0.289610	−	0.957145i	$-0.593526\pi$
$821$	19.1269	−	19.1269i	0.667534	−	0.667534i	0.957145	+	0.289610i	$0.0935257\pi$
$822$	−7.53436	−	8.22293i	−0.262791	−	0.286808i
$823$	24.3399			0.848435			0.424218	−	0.905560i	$-0.360549\pi$
$823$	24.3399			0.848435			0.424218	+	0.905560i	$0.360549\pi$
$824$	19.9148	+	2.62409i	0.693765	+	0.0914144i
$825$	−17.4035			−0.605913
$826$		0			0
$827$	−31.7583	−	31.7583i	−1.10435	−	1.10435i	−0.993880	−	0.110466i	$-0.964766\pi$
$827$	−31.7583	−	31.7583i	−1.10435	−	1.10435i	−0.110466	−	0.993880i	$-0.535234\pi$
$828$	−0.161656	+	1.84617i	−0.00561795	+	0.0641587i
$829$	−29.0558	+	29.0558i	−1.00915	+	1.00915i	−0.00919347	+	0.999958i	$0.502926\pi$
$829$	−29.0558	+	29.0558i	−1.00915	+	1.00915i	−0.999958	+	0.00919347i	$0.997074\pi$
$830$	7.06380	+	0.308675i	0.245188	+	0.0107143i
$831$	35.3387			1.22589
$832$	18.0826	−	10.4346i	0.626902	−	0.361756i
$833$		0			0
$834$	−0.0675688	+	1.54626i	−0.00233971	+	0.0535427i
$835$	−22.0511	+	22.0511i	−0.763109	+	0.763109i
$836$	3.22007	−	36.7741i	0.111368	−	1.27186i
$837$	−28.1795	+	28.1795i	−0.974026	+	0.974026i
$838$	10.2699	−	9.40991i	0.354767	−	0.325060i
$839$		−	12.4384i		−	0.429423i	−0.976678	−	0.214711i	$-0.931119\pi$
$839$		−	12.4384i		−	0.429423i	0.976678	−	0.214711i	$-0.0688811\pi$
$840$		0			0
$841$		−	18.3958i		−	0.634339i
$842$	−8.53824	−	9.31855i	−0.294247	−	0.321138i
$843$	−3.16355	+	3.16355i	−0.108959	+	0.108959i
$844$	−19.0962	+	16.0212i	−0.657319	+	0.551473i
$845$	−6.34004	+	6.34004i	−0.218104	+	0.218104i
$846$	−8.76296	−	0.382924i	−0.301277	−	0.0131652i
$847$		0			0
$848$	4.65546	−	3.25876i	0.159869	−	0.111906i
$849$	14.9112			0.511752
$850$	1.17790	−	26.9555i	0.0404017	−	0.924565i
$851$	1.50618	−	1.50618i	0.0516313	−	0.0516313i
$852$	9.04819	+	10.7848i	0.309986	+	0.369482i
$853$	−11.8456	−	11.8456i	−0.405585	−	0.405585i	0.474611	−	0.880196i	$-0.342589\pi$
$853$	−11.8456	−	11.8456i	−0.405585	−	0.405585i	−0.880196	+	0.474611i	$0.842589\pi$
$854$		0			0
$855$	8.80008			0.300956
$856$	−26.9108	+	20.6446i	−0.919792	+	0.705619i
$857$	−15.0931			−0.515571			−0.257786	−	0.966202i	$-0.582993\pi$
$857$	−15.0931			−0.515571			−0.257786	+	0.966202i	$0.582993\pi$
$858$	16.3208	−	14.9542i	0.557183	−	0.510526i
$859$	32.2506	−	32.2506i	1.10037	−	1.10037i	0.106010	−	0.994365i	$-0.466193\pi$
$859$	32.2506	−	32.2506i	1.10037	−	1.10037i	0.994365	−	0.106010i	$-0.0338075\pi$
$860$	1.21816	−	13.9117i	0.0415388	−	0.474386i
$861$		0			0
$862$	9.16164	+	0.400346i	0.312047	+	0.0136358i
$863$			27.0774i			0.921724i	0.887472	+	0.460862i	$0.152460\pi$
$863$			27.0774i			0.921724i	−0.887472	+	0.460862i	$0.847540\pi$
$864$	15.9483	+	25.0441i	0.542573	+	0.852017i
$865$	29.0159			0.986572
$866$	−24.2614	−	1.06018i	−0.824437	−	0.0360263i
$867$	20.2469	+	20.2469i	0.687619	+	0.687619i
$868$		0			0
$869$	−14.9754	+	14.9754i	−0.508004	+	0.508004i
$870$	4.91920	+	5.36876i	0.166776	+	0.182018i
$871$			16.7458i			0.567410i
$872$	−23.2887	+	17.8659i	−0.788654	+	0.605016i
$873$	−20.2835			−0.686493
$874$	1.79445	−	1.64419i	0.0606983	−	0.0556156i
$875$		0			0
$876$	−20.8782	−	24.8854i	−0.705408	−	0.840799i
$877$	6.44516	+	6.44516i	0.217638	+	0.217638i	0.807502	−	0.589865i	$-0.200819\pi$
$877$	6.44516	+	6.44516i	0.217638	+	0.217638i	−0.589865	+	0.807502i	$0.700819\pi$
$878$	−44.2207	−	1.93236i	−1.49237	−	0.0652139i
$879$			25.7698i			0.869195i
$880$	−5.53349	+	31.3548i	−0.186534	+	1.05697i
$881$		−	0.723819i		−	0.0243861i	−0.999926	−	0.0121930i	$-0.996119\pi$
$881$		−	0.723819i		−	0.0243861i	0.999926	−	0.0121930i	$-0.00388126\pi$
$882$		0			0
$883$	−21.2381	+	21.2381i	−0.714718	+	0.714718i	−0.967518	−	0.252800i	$-0.918648\pi$
$883$	−21.2381	+	21.2381i	−0.714718	+	0.714718i	0.252800	+	0.967518i	$0.418648\pi$
$884$	22.0571	+	26.2906i	0.741862	+	0.884250i
$885$	7.61117	+	7.61117i	0.255847	+	0.255847i
$886$	12.6401	−	11.5817i	0.424653	−	0.389094i
$887$		−	20.2358i		−	0.679452i	−0.940524	−	0.339726i	$-0.889666\pi$
$887$		−	20.2358i		−	0.679452i	0.940524	−	0.339726i	$-0.110334\pi$
$888$	1.67677	−	12.7254i	0.0562686	−	0.427036i
$889$		0			0
$890$	−11.5199	+	10.5553i	−0.386148	+	0.353813i
$891$	1.17862	+	1.17862i	0.0394851	+	0.0394851i
$892$	10.8565	+	0.950631i	0.363502	+	0.0318295i
$893$	8.14530	+	8.14530i	0.272572	+	0.272572i
$894$	−0.641558	+	14.6816i	−0.0214569	+	0.491026i
$895$	9.86738			0.329830
$896$		0			0
$897$	1.45942			0.0487288
$898$	2.06808	−	47.3265i	0.0690126	−	1.57931i
$899$	−17.4832	−	17.4832i	−0.583099	−	0.583099i
$900$	10.4556	+	0.915527i	0.348520	+	0.0305176i
$901$	6.60516	+	6.60516i	0.220050	+	0.220050i
$902$	−2.59658	+	2.37915i	−0.0864567	+	0.0792171i
$903$		0			0
$904$	4.97344	−	37.7446i	0.165414	−	1.25537i
$905$		−	12.9475i		−	0.430390i
$906$	8.08242	−	7.40562i	0.268520	−	0.246035i
$907$	9.46697	+	9.46697i	0.314346	+	0.314346i	0.846590	−	0.532245i	$-0.178651\pi$
$907$	9.46697	+	9.46697i	0.314346	+	0.314346i	−0.532245	+	0.846590i	$0.678651\pi$
$908$	−1.93452	−	2.30581i	−0.0641992	−	0.0765211i
$909$	24.8764	−	24.8764i	0.825099	−	0.825099i
$910$		0			0
$911$			34.5549i			1.14485i	0.819955	+	0.572427i	$0.193998\pi$
$911$			34.5549i			1.14485i	−0.819955	+	0.572427i	$0.806002\pi$
$912$	2.54881	−	14.4425i	0.0843995	−	0.478239i
$913$			18.9652i			0.627658i
$914$	4.25654	+	0.186003i	0.140794	+	0.00615242i
$915$	−5.65229	−	5.65229i	−0.186859	−	0.186859i
$916$	6.35996	+	7.58065i	0.210139	+	0.250472i
$917$		0			0
$918$	−35.9845	+	32.9713i	−1.18767	+	1.08821i
$919$	53.5178			1.76539			0.882695	−	0.469946i	$-0.155727\pi$
$919$	53.5178			1.76539			0.882695	+	0.469946i	$0.155727\pi$
$920$	−1.66553	+	1.27771i	−0.0549110	+	0.0421250i
$921$			25.8700i			0.852444i
$922$	27.9363	+	30.4894i	0.920034	+	1.00412i
$923$	−11.8998	+	11.8998i	−0.391686	+	0.391686i
$924$		0			0
$925$	−8.53014	−	8.53014i	−0.280469	−	0.280469i
$926$	−16.4987	−	0.720960i	−0.542180	−	0.0236922i
$927$	−12.8442			−0.421857
$928$	−15.5380	+	9.89472i	−0.510058	+	0.324810i
$929$			0.0493449i			0.00161895i	1.00000		0.000809477i	$0.000257665\pi$
$929$			0.0493449i			0.00161895i	−1.00000		0.000809477i	$0.999742\pi$
$930$	−16.9619	−	0.741202i	−0.556203	−	0.0243050i
$931$		0			0
$932$	2.16863	−	24.7664i	0.0710357	−	0.811250i
$933$	−16.5815	+	16.5815i	−0.542855	+	0.542855i
$934$	−10.5869	+	9.70042i	−0.346415	+	0.317407i
$935$	−52.3370			−1.71160
$936$	−10.5918	+	8.12551i	−0.346204	+	0.265591i
$937$	−0.977039			−0.0319185			−0.0159592	−	0.999873i	$-0.505080\pi$
$937$	−0.977039			−0.0319185			−0.0159592	+	0.999873i	$0.505080\pi$
$938$		0			0
$939$	16.0925	+	16.0925i	0.525157	+	0.525157i
$940$	−6.38579	−	7.61143i	−0.208281	−	0.248258i
$941$	27.5503	−	27.5503i	0.898115	−	0.898115i	−0.0971546	−	0.995269i	$-0.530974\pi$
$941$	27.5503	−	27.5503i	0.898115	−	0.898115i	0.995269	+	0.0971546i	$0.0309741\pi$
$942$	0.591448	−	13.5349i	0.0192704	−	0.440990i
$943$	−0.232189			−0.00756112
$944$	−22.3080	+	15.6153i	−0.726064	+	0.508235i
$945$		0			0
$946$	37.4223	+	1.63528i	1.21671	+	0.0531677i
$947$	−16.2096	+	16.2096i	−0.526741	+	0.526741i	−0.919599	−	0.392858i	$-0.871486\pi$
$947$	−16.2096	+	16.2096i	−0.526741	+	0.526741i	0.392858	+	0.919599i	$0.371486\pi$
$948$	−6.44576	+	5.40782i	−0.209349	+	0.175638i
$949$	27.4581	−	27.4581i	0.891327	−	0.891327i
$950$	−9.31173	−	10.1627i	−0.302112	−	0.329722i
$951$			16.2702i			0.527599i
$952$		0			0
$953$		−	34.2308i		−	1.10884i	−0.832235	−	0.554422i	$-0.812939\pi$
$953$		−	34.2308i		−	1.10884i	0.832235	−	0.554422i	$-0.187061\pi$
$954$	−2.67911	+	2.45477i	−0.0867393	+	0.0794760i
$955$	13.6460	−	13.6460i	0.441573	−	0.441573i
$956$	−1.28060	+	14.6248i	−0.0414175	+	0.473000i
$957$	−13.8108	+	13.8108i	−0.446440	+	0.446440i
$958$	−0.706685	+	16.1720i	−0.0228320	+	0.522493i
$959$		0			0
$960$	−3.27659	+	12.2175i	−0.105751	+	0.394319i
$961$	26.6497			0.859667
$962$	15.3291	+	0.669851i	0.494229	+	0.0215969i
$963$	15.3355	−	15.3355i	0.494181	−	0.494181i
$964$	−1.80982	+	20.6687i	−0.0582904	+	0.665693i
$965$	−10.7710	−	10.7710i	−0.346729	−	0.346729i
$966$		0			0
$967$	21.2761			0.684193			0.342096	−	0.939665i	$-0.388863\pi$
$967$	21.2761			0.684193			0.342096	+	0.939665i	$0.388863\pi$
$968$	−53.8244	−	7.09221i	−1.72998	−	0.227952i
$969$	24.1072			0.774435
$970$	−15.5213	−	16.9398i	−0.498360	−	0.543905i
$971$	21.1629	−	21.1629i	0.679150	−	0.679150i	−0.280658	−	0.959808i	$-0.590553\pi$
$971$	21.1629	−	21.1629i	0.679150	−	0.679150i	0.959808	+	0.280658i	$0.0905527\pi$
$972$	−19.8153	−	23.6185i	−0.635576	−	0.757564i
$973$		0			0
$974$	−0.598918	+	13.7058i	−0.0191906	+	0.439163i
$975$		−	8.26532i		−	0.264702i
$976$	16.5666	−	11.5964i	0.530285	−	0.371192i
$977$	−3.01443			−0.0964403			−0.0482201	−	0.998837i	$-0.515355\pi$
$977$	−3.01443			−0.0964403			−0.0482201	+	0.998837i	$0.515355\pi$
$978$	0.855819	−	19.5848i	0.0273661	−	0.626254i
$979$	−29.6342	−	29.6342i	−0.947115	−	0.947115i
$980$		0			0
$981$	13.2714	−	13.2714i	0.423724	−	0.423724i
$982$	−16.9088	+	15.4929i	−0.539581	+	0.494398i
$983$			40.7478i			1.29965i	0.760083	+	0.649826i	$0.225158\pi$
$983$			40.7478i			1.29965i	−0.760083	+	0.649826i	$0.774842\pi$
$984$	−1.11010	+	0.851612i	−0.0353886	+	0.0271484i
$985$	28.8118			0.918020
$986$	−20.4562	−	22.3256i	−0.651457	−	0.710993i
$987$		0			0
$988$	17.4649	+	1.52928i	0.555631	+	0.0486529i
$989$	1.74629	+	1.74629i	0.0555287	+	0.0555287i
$990$	0.888799	−	20.3395i	0.0282479	−	0.646433i
$991$		−	24.4732i		−	0.777416i	−0.921361	−	0.388708i	$-0.872921\pi$
$991$		−	24.4732i		−	0.777416i	0.921361	−	0.388708i	$-0.127079\pi$
$992$	9.30407	−	41.9312i	0.295405	−	1.33132i
$993$			3.26581i			0.103637i
$994$		0			0
$995$	24.7792	−	24.7792i	0.785552	−	0.785552i
$996$	−0.657239	+	7.50587i	−0.0208254	+	0.237833i
$997$	−30.4640	−	30.4640i	−0.964805	−	0.964805i	0.0345959	−	0.999401i	$-0.488986\pi$
$997$	−30.4640	−	30.4640i	−0.964805	−	0.964805i	−0.999401	+	0.0345959i	$0.988986\pi$
$998$	−18.2327	−	19.8990i	−0.577146	−	0.629892i
$999$			21.8213i			0.690394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.13		56
7.2	even	3		784.2.w.f.227.3		56
7.3	odd	6		784.2.w.f.19.12		56
7.4	even	3		112.2.v.a.19.12	yes	56
7.5	odd	6		112.2.v.a.3.3	✓	56
7.6	odd	2	inner	784.2.j.a.195.14		56
16.11	odd	4	inner	784.2.j.a.587.14		56
28.11	odd	6		448.2.z.a.47.10		56
28.19	even	6		448.2.z.a.367.10		56
56.5	odd	6		896.2.z.b.479.10		56
56.11	odd	6		896.2.z.a.607.5		56
56.19	even	6		896.2.z.a.479.5		56
56.53	even	6		896.2.z.b.607.10		56
112.5	odd	12		448.2.z.a.143.10		56
112.11	odd	12		112.2.v.a.75.3	yes	56
112.19	even	12		896.2.z.b.31.10		56
112.27	even	4	inner	784.2.j.a.587.13		56
112.53	even	12		448.2.z.a.271.10		56
112.59	even	12		784.2.w.f.411.3		56
112.61	odd	12		896.2.z.a.31.5		56
112.67	odd	12		896.2.z.b.159.10		56
112.75	even	12		112.2.v.a.59.12	yes	56
112.107	odd	12		784.2.w.f.619.12		56
112.109	even	12		896.2.z.a.159.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.3	✓	56	7.5	odd	6
112.2.v.a.19.12	yes	56	7.4	even	3
112.2.v.a.59.12	yes	56	112.75	even	12
112.2.v.a.75.3	yes	56	112.11	odd	12
448.2.z.a.47.10		56	28.11	odd	6
448.2.z.a.143.10		56	112.5	odd	12
448.2.z.a.271.10		56	112.53	even	12
448.2.z.a.367.10		56	28.19	even	6
784.2.j.a.195.13		56	1.1	even	1	trivial
784.2.j.a.195.14		56	7.6	odd	2	inner
784.2.j.a.587.13		56	112.27	even	4	inner
784.2.j.a.587.14		56	16.11	odd	4	inner
784.2.w.f.19.12		56	7.3	odd	6
784.2.w.f.227.3		56	7.2	even	3
784.2.w.f.411.3		56	112.59	even	12
784.2.w.f.619.12		56	112.107	odd	12
896.2.z.a.31.5		56	112.61	odd	12
896.2.z.a.159.5		56	112.109	even	12
896.2.z.a.479.5		56	56.19	even	6
896.2.z.a.607.5		56	56.11	odd	6
896.2.z.b.31.10		56	112.19	even	12
896.2.z.b.159.10		56	112.67	odd	12
896.2.z.b.479.10		56	56.5	odd	6
896.2.z.b.607.10		56	56.53	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0617395 - 1.41287i) q^{2} +(-0.771824 - 0.771824i) q^{3} +(-1.99238 - 0.174459i) q^{4} +(1.02430 + 1.02430i) q^{5} +(-1.13814 + 1.04283i) q^{6} +(-0.369496 + 2.80419i) q^{8} -1.80857i q^{9} +(1.51044 - 1.38396i) q^{10} +(3.88550 + 3.88550i) q^{11} +(1.40311 + 1.67242i) q^{12} +(-1.84531 + 1.84531i) q^{13} -1.58116i q^{15} +(3.93913 + 0.695177i) q^{16} +6.57514i q^{17} +(-2.55527 - 0.111660i) q^{18} +(2.37516 + 2.37516i) q^{19} +(-1.86209 - 2.21949i) q^{20} +(5.72958 - 5.24981i) q^{22} +0.512345 q^{23} +(2.44953 - 1.87916i) q^{24} -2.90162i q^{25} +(2.49325 + 2.72111i) q^{26} +(-3.71137 + 3.71137i) q^{27} +(-2.30263 - 2.30263i) q^{29} +(-2.23396 - 0.0976199i) q^{30} +7.59274 q^{31} +(1.22539 - 5.52254i) q^{32} -5.99785i q^{33} +(9.28979 + 0.405946i) q^{34} +(-0.315522 + 3.60336i) q^{36} +(2.93978 - 2.93978i) q^{37} +(3.50243 - 3.20914i) q^{38} +2.84852 q^{39} +(-3.25080 + 2.49385i) q^{40} -0.453189 q^{41} +(3.40842 + 3.40842i) q^{43} +(-7.06353 - 8.41925i) q^{44} +(1.85252 - 1.85252i) q^{45} +(0.0316320 - 0.723875i) q^{46} +3.42936 q^{47} +(-2.50376 - 3.57687i) q^{48} +(-4.09960 - 0.179145i) q^{50} +(5.07485 - 5.07485i) q^{51} +(3.99849 - 3.35463i) q^{52} +(1.00457 - 1.00457i) q^{53} +(5.01453 + 5.47281i) q^{54} +7.95984i q^{55} -3.66642i q^{57} +(-3.39546 + 3.11114i) q^{58} +(-4.81367 + 4.81367i) q^{59} +(-0.275847 + 3.15026i) q^{60} +(3.57478 - 3.57478i) q^{61} +(0.468772 - 10.7275i) q^{62} +(-7.72695 - 2.07227i) q^{64} -3.78031 q^{65} +(-8.47416 - 0.370305i) q^{66} +(4.53739 - 4.53739i) q^{67} +(1.14709 - 13.1002i) q^{68} +(-0.395441 - 0.395441i) q^{69} +6.44865 q^{71} +(5.07158 + 0.668260i) q^{72} -14.8799 q^{73} +(-3.97201 - 4.33502i) q^{74} +(-2.23954 + 2.23954i) q^{75} +(-4.31785 - 5.14659i) q^{76} +(0.175866 - 4.02457i) q^{78} +3.85416i q^{79} +(3.32278 + 4.74691i) q^{80} +0.303337 q^{81} +(-0.0279796 + 0.640295i) q^{82} +(2.44051 + 2.44051i) q^{83} +(-6.73491 + 6.73491i) q^{85} +(5.02607 - 4.60520i) q^{86} +3.55445i q^{87} +(-12.3314 + 9.46001i) q^{88} -7.62687 q^{89} +(-2.50299 - 2.73174i) q^{90} +(-1.02079 - 0.0893834i) q^{92} +(-5.86026 - 5.86026i) q^{93} +(0.211727 - 4.84523i) q^{94} +4.86575i q^{95} +(-5.20822 + 3.31664i) q^{96} -11.2152i q^{97} +(7.02722 - 7.02722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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