LMFDB - Embedded newform 784.2.j.a.587.14

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			587.14
Character	$\chi$	$=$	784.587
Dual form			784.2.j.a.195.14

$q$-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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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	$-0.647963\pi$
$3$	0.771824	−	0.771824i	0.445613	−	0.445613i	0.893893	+	0.448280i	$0.147963\pi$
$4$	−1.99238	+	0.174459i	−0.996188	+	0.0872296i
$5$	−1.02430	+	1.02430i	−0.458080	+	0.458080i	−0.898025	−	0.439945i	$-0.854998\pi$
$5$	−1.02430	+	1.02430i	−0.458080	+	0.458080i	0.439945	+	0.898025i	$0.354998\pi$
$6$	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	0.189677	−	0.981847i	$-0.439256\pi$
$11$	3.88550	−	3.88550i	1.17152	−	1.17152i	0.981847	−	0.189677i	$-0.0607442\pi$
$12$	−1.40311	+	1.67242i	−0.405044	+	0.482785i
$13$	1.84531	+	1.84531i	0.511798	+	0.511798i	0.915077	−	0.403279i	$-0.132130\pi$
$13$	1.84531	+	1.84531i	0.511798	+	0.511798i	−0.403279	+	0.915077i	$0.632130\pi$
$14$		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	$-0.875903\pi$
$19$	−2.37516	+	2.37516i	−0.544900	+	0.544900i	0.380061	+	0.924961i	$0.375903\pi$
$20$	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	−0.887806	−	0.460219i	$-0.847771\pi$
$29$	−2.30263	+	2.30263i	−0.427587	+	0.427587i	0.460219	+	0.887806i	$0.347771\pi$
$30$	−2.23396	+	0.0976199i	−0.407864	+	0.0178229i
$31$	−7.59274			−1.36370			−0.681848	−	0.731494i	$-0.738824\pi$
$31$	−7.59274			−1.36370			−0.681848	+	0.731494i	$0.738824\pi$
$32$	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	0.906183	−	0.422886i	$-0.138983\pi$
$37$	2.93978	+	2.93978i	0.483297	+	0.483297i	−0.422886	+	0.906183i	$0.638983\pi$
$38$	−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	$-0.488733\pi$
$41$	0.453189			0.0707762			0.0353881	+	0.999374i	$0.488733\pi$
$42$		0			0
$43$	3.40842	−	3.40842i	0.519779	−	0.519779i	−0.397726	−	0.917504i	$-0.630200\pi$
$43$	3.40842	−	3.40842i	0.519779	−	0.519779i	0.917504	+	0.397726i	$0.130200\pi$
$44$	−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	$-0.580467\pi$
$47$	−3.42936			−0.500224			−0.250112	+	0.968217i	$0.580467\pi$
$48$	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	0.772727	−	0.634739i	$-0.218892\pi$
$53$	1.00457	+	1.00457i	0.137988	+	0.137988i	−0.634739	+	0.772727i	$0.718892\pi$
$54$	−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	$-0.103866\pi$
$59$	4.81367	+	4.81367i	0.626687	+	0.626687i	−0.320546	+	0.947233i	$0.603866\pi$
$60$	−0.275847	−	3.15026i	−0.0356118	−	0.406697i
$61$	−3.57478	−	3.57478i	−0.457704	−	0.457704i	0.440197	−	0.897901i	$-0.354908\pi$
$61$	−3.57478	−	3.57478i	−0.457704	−	0.457704i	−0.897901	+	0.440197i	$0.854908\pi$
$62$	−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	0.927687	−	0.373358i	$-0.121794\pi$
$67$	4.53739	+	4.53739i	0.554330	+	0.554330i	−0.373358	+	0.927687i	$0.621794\pi$
$68$	−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	$-0.163615\pi$
$73$	14.8799			1.74156			0.870780	+	0.491673i	$0.163615\pi$
$74$	−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	$-0.930434\pi$
$79$		−	3.85416i		−	0.433627i	0.976213	−	0.216813i	$-0.0695663\pi$
$80$	−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	$-0.810661\pi$
$83$	−2.44051	+	2.44051i	−0.267881	+	0.267881i	0.560365	+	0.828246i	$0.310661\pi$
$84$		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	$-0.367542\pi$
$89$	7.62687			0.808447			0.404223	+	0.914660i	$0.367542\pi$
$90$	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	−0.506270	+	0.862375i	$0.668976\pi$
$101$	−13.7547	+	13.7547i	−1.36865	+	1.36865i	−0.862375	+	0.506270i	$0.831024\pi$
$102$	−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	−0.166338	−	0.986069i	$-0.553194\pi$
$107$	8.47936	−	8.47936i	0.819730	−	0.819730i	0.986069	+	0.166338i	$0.0531944\pi$
$108$	−8.04194	−	6.74697i	−0.773836	−	0.649228i
$109$	7.33805	−	7.33805i	0.702858	−	0.702858i	−0.262165	−	0.965023i	$-0.584436\pi$
$109$	7.33805	−	7.33805i	0.702858	−	0.702858i	0.965023	+	0.262165i	$0.0844365\pi$
$110$	−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	$-0.791403\pi$
$127$		−	13.7356i		−	1.21884i	0.792849	−	0.609418i	$-0.208597\pi$
$128$	−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	$-0.709371\pi$
$131$	2.06043	−	2.06043i	0.180020	−	0.180020i	0.791365	+	0.611344i	$0.209371\pi$
$132$	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	$-0.900129\pi$
$137$		−	7.22491i		−	0.617266i	0.951181	−	0.308633i	$-0.0998714\pi$
$138$	0.583119	+	0.534290i	0.0496384	+	0.0454818i
$139$	−0.708981	−	0.708981i	−0.0601350	−	0.0601350i	0.676400	−	0.736535i	$-0.263539\pi$
$139$	−0.708981	−	0.708981i	−0.0601350	−	0.0601350i	−0.736535	+	0.676400i	$0.763539\pi$
$140$		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	0.926868	−	0.375387i	$-0.122490\pi$
$149$	6.73169	+	6.73169i	0.551482	+	0.551482i	−0.375387	+	0.926868i	$0.622490\pi$
$150$	−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	$-0.136107\pi$
$157$	6.20590	+	6.20590i	0.495285	+	0.495285i	−0.414682	+	0.909966i	$0.636107\pi$
$158$	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	0.261772	−	0.965130i	$-0.415693\pi$
$163$	−8.97988	−	8.97988i	−0.703358	−	0.703358i	−0.965130	+	0.261772i	$0.915693\pi$
$164$	−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	−0.996790	−	0.0800649i	$-0.974487\pi$
$173$	−14.1638	−	14.1638i	−1.07685	−	1.07685i	−0.0800649	−	0.996790i	$-0.525513\pi$
$174$	−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	0.863818	−	0.503804i	$-0.168067\pi$
$179$	4.81665	+	4.81665i	0.360013	+	0.360013i	−0.503804	+	0.863818i	$0.668067\pi$
$180$	4.01411	+	3.36773i	0.299194	+	0.251016i
$181$	6.32019	−	6.32019i	0.469776	−	0.469776i	−0.432066	−	0.901842i	$-0.642215\pi$
$181$	6.32019	−	6.32019i	0.469776	−	0.469776i	0.901842	+	0.432066i	$0.142215\pi$
$182$		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	$0.160083\pi$
$191$			13.3222i			0.963964i	−0.876181	+	0.481982i	$0.839917\pi$
$192$	−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	0.999998	+	0.00203129i	$0.000646580\pi$
$197$	14.0642	+	14.0642i	1.00203	+	1.00203i	0.00203129	+	0.999998i	$0.499353\pi$
$198$	−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	0.942085	−	0.335375i	$-0.108863\pi$
$211$	8.81296	+	8.81296i	0.606709	+	0.606709i	−0.335375	+	0.942085i	$0.608863\pi$
$212$	−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	$-0.441598\pi$
$223$	5.44902			0.364893			0.182447	+	0.983216i	$0.441598\pi$
$224$		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	$-0.765904\pi$
$227$	−1.06414	+	1.06414i	−0.0706293	+	0.0706293i	0.670910	+	0.741539i	$0.265904\pi$
$228$	−0.639640	−	7.30488i	−0.0423612	−	0.483778i
$229$	3.49849	−	3.49849i	0.231187	−	0.231187i	−0.582001	−	0.813188i	$-0.697730\pi$
$229$	3.49849	−	3.49849i	0.231187	−	0.231187i	0.813188	+	0.582001i	$0.197730\pi$
$230$	−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	$-0.866513\pi$
$233$		−	12.4306i		−	0.814354i	0.913349	−	0.407177i	$-0.133487\pi$
$234$	−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	$0.0762968\pi$
$239$			7.34038i			0.474810i	−0.971411	+	0.237405i	$0.923703\pi$
$240$	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	$-0.244293\pi$
$251$	0.401720	+	0.401720i	0.0253563	+	0.0253563i	−0.694315	+	0.719671i	$0.744293\pi$
$252$		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	$-0.344015\pi$
$269$	−6.75155	−	6.75155i	−0.411649	−	0.411649i	−0.882313	+	0.470664i	$0.844015\pi$
$270$	−0.469412	−	10.7422i	−0.0285675	−	0.653748i
$271$	7.28357			0.442445			0.221223	−	0.975223i	$-0.428995\pi$
$271$	7.28357			0.442445			0.221223	+	0.975223i	$0.428995\pi$
$272$	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	−0.852056	−	0.523450i	$-0.824645\pi$
$277$	−22.8930	−	22.8930i	−1.37551	−	1.37551i	−0.523450	−	0.852056i	$-0.675355\pi$
$278$	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	$0.0390132\pi$
$281$			4.09880i			0.244514i	−0.992498	+	0.122257i	$0.960987\pi$
$282$	−3.90308	−	3.57625i	−0.232425	−	0.212963i
$283$	9.65973	+	9.65973i	0.574211	+	0.574211i	0.933302	−	0.359091i	$-0.116913\pi$
$283$	9.65973	+	9.65973i	0.574211	+	0.574211i	−0.359091	+	0.933302i	$0.616913\pi$
$284$	−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	$-0.507774\pi$
$293$	16.6941	−	16.6941i	0.975280	−	0.975280i	0.999702	+	0.0244213i	$0.00777432\pi$
$294$		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	$-0.513566\pi$
$307$	16.7590	−	16.7590i	0.956484	−	0.956484i	0.999092	+	0.0426074i	$0.0135665\pi$
$308$		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	$-0.299422\pi$
$313$	20.8499			1.17851			0.589253	+	0.807949i	$0.299422\pi$
$314$	−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	−0.938169	−	0.346177i	$-0.887480\pi$
$317$	−10.5401	+	10.5401i	−0.591992	+	0.591992i	0.346177	+	0.938169i	$0.387480\pi$
$318$	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	−0.762855	−	0.646569i	$-0.776203\pi$
$331$	−2.11564	+	2.11564i	−0.116286	+	0.116286i	0.646569	+	0.762855i	$0.276203\pi$
$332$	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	−0.811629	−	0.584174i	$-0.801419\pi$
$347$	−4.23701	+	4.23701i	−0.227455	+	0.227455i	0.584174	+	0.811629i	$0.301419\pi$
$348$	−0.620106	−	7.08179i	−0.0332412	−	0.379624i
$349$	−3.15549	−	3.15549i	−0.168909	−	0.168909i	0.617590	−	0.786500i	$-0.288109\pi$
$349$	−3.15549	−	3.15549i	−0.168909	−	0.168909i	−0.786500	+	0.617590i	$0.788109\pi$
$350$		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	$-0.738297\pi$
$367$	−26.0782			−1.36127			−0.680637	+	0.732621i	$0.738297\pi$
$368$	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	0.896865	+	0.442305i	$0.145839\pi$
$373$	25.8637	+	25.8637i	1.33917	+	1.33917i	0.442305	+	0.896865i	$0.354161\pi$
$374$	−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	−0.713780	−	0.700370i	$-0.753018\pi$
$379$	−0.261074	+	0.261074i	−0.0134105	+	0.0134105i	0.700370	+	0.713780i	$0.253018\pi$
$380$	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	$-0.647881\pi$
$383$	−17.5370			−0.896097			−0.448048	+	0.894009i	$0.647881\pi$
$384$	−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	0.982897	−	0.184154i	$-0.0589544\pi$
$389$	15.7537	+	15.7537i	0.798744	+	0.798744i	−0.184154	+	0.982897i	$0.558954\pi$
$390$	−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	$-0.0475921\pi$
$397$	16.7346	+	16.7346i	0.839885	+	0.839885i	−0.148958	+	0.988843i	$0.547592\pi$
$398$	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	$-0.789621\pi$
$409$	−31.9303			−1.57885			−0.789425	+	0.613847i	$0.789621\pi$
$410$	−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	$-0.827339\pi$
$419$	−6.96449	+	6.96449i	−0.340238	+	0.340238i	0.516219	+	0.856457i	$0.327339\pi$
$420$		0			0
$421$	6.31935	+	6.31935i	0.307986	+	0.307986i	0.844128	−	0.536142i	$-0.180119\pi$
$421$	6.31935	+	6.31935i	0.307986	+	0.307986i	−0.536142	+	0.844128i	$0.680119\pi$
$422$	−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	$-0.950085\pi$
$431$		−	6.48444i		−	0.312344i	0.987730	−	0.156172i	$-0.0499155\pi$
$432$	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	−0.473521	−	0.880783i	$-0.657017\pi$
$443$	8.57187	−	8.57187i	0.407262	−	0.407262i	0.880783	+	0.473521i	$0.157017\pi$
$444$	−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	$-0.977552\pi$
$457$		−	3.01270i		−	0.140928i	0.997514	−	0.0704641i	$-0.0224480\pi$
$458$	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	$-0.0115721\pi$
$461$	20.6763	+	20.6763i	0.962993	+	0.962993i	−0.0363467	+	0.999339i	$0.511572\pi$
$462$		0			0
$463$			11.6775i			0.542697i	0.962481	+	0.271349i	$0.0874696\pi$
$463$			11.6775i			0.542697i	−0.962481	+	0.271349i	$0.912530\pi$
$464$	−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	$-0.674517\pi$
$467$	7.17951	−	7.17951i	0.332228	−	0.332228i	0.853432	+	0.521204i	$0.174517\pi$
$468$	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	$-0.415784\pi$
$479$	11.4462			0.522992			0.261496	+	0.965205i	$0.415784\pi$
$480$	−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	−0.916809	−	0.399326i	$-0.869244\pi$
$491$	−11.4667	+	11.4667i	−0.517483	+	0.517483i	0.399326	+	0.916809i	$0.369244\pi$
$492$	−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	0.941397	−	0.337302i	$-0.109514\pi$
$499$	13.4945	+	13.4945i	0.604095	+	0.604095i	−0.337302	+	0.941397i	$0.609514\pi$
$500$	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	$-0.141175\pi$
$509$	10.6969	+	10.6969i	0.474132	+	0.474132i	−0.429117	+	0.903249i	$0.641175\pi$
$510$	−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	$-0.449049\pi$
$521$	7.27601			0.318768			0.159384	+	0.987217i	$0.449049\pi$
$522$	5.62672	−	6.14095i	0.246275	−	0.268782i
$523$	−12.7559	−	12.7559i	−0.557776	−	0.557776i	0.370898	−	0.928674i	$-0.379050\pi$
$523$	−12.7559	−	12.7559i	−0.557776	−	0.557776i	−0.928674	+	0.370898i	$0.879050\pi$
$524$	−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	−0.664722	−	0.747091i	$-0.731450\pi$
$541$	1.91584	−	1.91584i	0.0823686	−	0.0823686i	0.747091	+	0.664722i	$0.231450\pi$
$542$	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	0.119078	−	0.992885i	$-0.462006\pi$
$547$	−20.4366	−	20.4366i	−0.873807	−	0.873807i	−0.992885	+	0.119078i	$0.962006\pi$
$548$	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	−0.632817	−	0.774301i	$-0.718101\pi$
$557$	3.33915	−	3.33915i	0.141484	−	0.141484i	0.774301	+	0.632817i	$0.218101\pi$
$558$	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	$-0.700575\pi$
$563$	5.18939	−	5.18939i	0.218707	−	0.218707i	0.807953	+	0.589247i	$0.200575\pi$
$564$	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	$0.0841896\pi$
$569$			12.4715i			0.522833i	−0.965226	+	0.261416i	$0.915810\pi$
$570$	5.07416	−	5.53789i	0.212533	−	0.231957i
$571$	27.1588	−	27.1588i	1.13656	−	1.13656i	0.147497	−	0.989063i	$-0.452878\pi$
$571$	27.1588	−	27.1588i	1.13656	−	1.13656i	0.989063	−	0.147497i	$-0.0471216\pi$
$572$	−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	$-0.320637\pi$
$587$	−7.54134	−	7.54134i	−0.311264	−	0.311264i	−0.845399	+	0.534135i	$0.820637\pi$
$588$		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	$-0.222932\pi$
$601$	37.4893			1.52922			0.764610	+	0.644493i	$0.222932\pi$
$602$		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	$-0.530272\pi$
$607$	−4.67915			−0.189921			−0.0949605	+	0.995481i	$0.530272\pi$
$608$	−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	0.775787	−	0.630995i	$-0.217353\pi$
$613$	3.58488	+	3.58488i	0.144792	+	0.144792i	−0.630995	+	0.775787i	$0.717353\pi$
$614$	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	$-0.892438\pi$
$617$		−	16.4696i		−	0.663041i	0.943448	−	0.331520i	$-0.107562\pi$
$618$	7.40599	−	8.08283i	0.297913	−	0.325139i
$619$	10.7503	+	10.7503i	0.432093	+	0.432093i	0.889340	−	0.457247i	$-0.151165\pi$
$619$	10.7503	+	10.7503i	0.432093	+	0.432093i	−0.457247	+	0.889340i	$0.651165\pi$
$620$	−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	$-0.615125\pi$
$643$	14.7445	−	14.7445i	0.581464	−	0.581464i	0.935306	+	0.353841i	$0.115125\pi$
$644$		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	−0.900413	−	0.435035i	$-0.856736\pi$
$653$	−11.8922	+	11.8922i	−0.465378	+	0.465378i	0.435035	+	0.900413i	$0.356736\pi$
$654$	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	0.946455	+	0.322834i	$0.104636\pi$
$659$	32.5839	+	32.5839i	1.26929	+	1.26929i	0.322834	+	0.946455i	$0.395364\pi$
$660$	−13.3122	−	11.1685i	−0.518175	−	0.434735i
$661$	−12.3984	+	12.3984i	−0.482241	+	0.482241i	−0.905847	−	0.423606i	$-0.860764\pi$
$661$	−12.3984	+	12.3984i	−0.482241	+	0.482241i	0.423606	+	0.905847i	$0.360764\pi$
$662$	−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	$-0.713848\pi$
$677$	4.17016	−	4.17016i	0.160272	−	0.160272i	0.782687	+	0.622415i	$0.213848\pi$
$678$	−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	−0.748887	−	0.662697i	$-0.769412\pi$
$683$	−2.25251	+	2.25251i	−0.0861899	+	0.0861899i	0.662697	+	0.748887i	$0.269412\pi$
$684$	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	$-0.881804\pi$
$691$	−14.9572	+	14.9572i	−0.568997	+	0.568997i	0.362850	+	0.931847i	$0.381804\pi$
$692$	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	−0.248435	−	0.968649i	$-0.579916\pi$
$701$	19.0687	−	19.0687i	0.720214	−	0.720214i	0.968649	+	0.248435i	$0.0799162\pi$
$702$	−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	0.0701596	−	0.997536i	$-0.477649\pi$
$709$	−24.6933	−	24.6933i	−0.927376	−	0.927376i	−0.997536	+	0.0701596i	$0.977649\pi$
$710$	−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	$-0.0897591\pi$
$719$	51.5103			1.92101			0.960505	+	0.278264i	$0.0897591\pi$
$720$	−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	$-0.371283\pi$
$733$	−14.2382	−	14.2382i	−0.525902	−	0.525902i	−0.919348	+	0.393446i	$0.871283\pi$
$734$	−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	0.187392	−	0.982285i	$-0.439997\pi$
$739$	−21.6088	−	21.6088i	−0.794893	−	0.794893i	−0.982285	+	0.187392i	$0.939997\pi$
$740$	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	$0.222968\pi$
$751$			35.3286i			1.28916i	−0.764537	+	0.644580i	$0.777032\pi$
$752$	−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	0.687577	−	0.726111i	$-0.258674\pi$
$757$	−1.06021	−	1.06021i	−0.0385339	−	0.0385339i	−0.726111	+	0.687577i	$0.758674\pi$
$758$	−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	$-0.685757\pi$
$761$	−30.4006			−1.10202			−0.551010	+	0.834498i	$0.685757\pi$
$762$	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	$-0.659733\pi$
$773$	11.0014	−	11.0014i	0.395694	−	0.395694i	0.876711	+	0.481017i	$0.159733\pi$
$774$	−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	$-0.846268\pi$
$787$	−11.8166	+	11.8166i	−0.421217	+	0.421217i	0.464406	+	0.885623i	$0.346268\pi$
$788$	−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	$-0.198267\pi$
$797$	6.46029	+	6.46029i	0.228835	+	0.228835i	−0.583371	+	0.812206i	$0.698267\pi$
$798$		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	$0.169083\pi$
$809$			28.8161i			1.01312i	−0.862205	+	0.506559i	$0.830917\pi$
$810$	−0.458170	−	0.419805i	−0.0160985	−	0.0147504i
$811$	32.3761	+	32.3761i	1.13688	+	1.13688i	0.989006	+	0.147873i	$0.0472427\pi$
$811$	32.3761	+	32.3761i	1.13688	+	1.13688i	0.147873	+	0.989006i	$0.452757\pi$
$812$		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	0.957145	−	0.289610i	$-0.0935257\pi$
$821$	19.1269	+	19.1269i	0.667534	+	0.667534i	−0.289610	+	0.957145i	$0.593526\pi$
$822$	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	−0.110466	+	0.993880i	$0.535234\pi$
$827$	−31.7583	+	31.7583i	−1.10435	+	1.10435i	−0.993880	+	0.110466i	$0.964766\pi$
$828$	−0.161656	−	1.84617i	−0.00561795	−	0.0641587i
$829$	29.0558	+	29.0558i	1.00915	+	1.00915i	0.999958	+	0.00919347i	$0.00292641\pi$
$829$	29.0558	+	29.0558i	1.00915	+	1.00915i	0.00919347	+	0.999958i	$0.497074\pi$
$830$	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	$-0.657411\pi$
$853$	11.8456	−	11.8456i	0.405585	−	0.405585i	0.880196	+	0.474611i	$0.157411\pi$
$854$		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	$-0.417007\pi$
$857$	15.0931			0.515571			0.257786	+	0.966202i	$0.417007\pi$
$858$	16.3208	+	14.9542i	0.557183	+	0.510526i
$859$	−32.2506	−	32.2506i	−1.10037	−	1.10037i	−0.994365	−	0.106010i	$-0.966193\pi$
$859$	−32.2506	−	32.2506i	−1.10037	−	1.10037i	−0.106010	−	0.994365i	$-0.533807\pi$
$860$	−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	$-0.847540\pi$
$863$		−	27.0774i		−	0.921724i	0.887472	−	0.460862i	$-0.152460\pi$
$864$	−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	−0.589865	−	0.807502i	$-0.700819\pi$
$877$	6.44516	−	6.44516i	0.217638	−	0.217638i	0.807502	+	0.589865i	$0.200819\pi$
$878$	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	0.252800	−	0.967518i	$-0.418648\pi$
$883$	−21.2381	−	21.2381i	−0.714718	−	0.714718i	−0.967518	+	0.252800i	$0.918648\pi$
$884$	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	−0.532245	−	0.846590i	$-0.678651\pi$
$907$	9.46697	−	9.46697i	0.314346	−	0.314346i	0.846590	+	0.532245i	$0.178651\pi$
$908$	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	$-0.806002\pi$
$911$		−	34.5549i		−	1.14485i	0.819955	−	0.572427i	$-0.193998\pi$
$912$	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	$-0.494920\pi$
$937$	0.977039			0.0319185			0.0159592	+	0.999873i	$0.494920\pi$
$938$		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	$-0.469026\pi$
$941$	−27.5503	−	27.5503i	−0.898115	−	0.898115i	−0.995269	+	0.0971546i	$0.969026\pi$
$942$	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	0.392858	−	0.919599i	$-0.371486\pi$
$947$	−16.2096	−	16.2096i	−0.526741	−	0.526741i	−0.919599	+	0.392858i	$0.871486\pi$
$948$	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	$0.187061\pi$
$953$			34.2308i			1.10884i	−0.832235	+	0.554422i	$0.812939\pi$
$954$	−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	$-0.409447\pi$
$971$	−21.1629	−	21.1629i	−0.679150	−	0.679150i	−0.959808	+	0.280658i	$0.909447\pi$
$972$	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	$0.127079\pi$
$991$			24.4732i			0.777416i	−0.921361	+	0.388708i	$0.872921\pi$
$992$	−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	$-0.511014\pi$
$997$	30.4640	−	30.4640i	0.964805	−	0.964805i	0.999401	+	0.0345959i	$0.0110144\pi$
$998$	−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.587.14		56
7.2	even	3		784.2.w.f.619.12		56
7.3	odd	6		784.2.w.f.411.3		56
7.4	even	3		112.2.v.a.75.3	yes	56
7.5	odd	6		112.2.v.a.59.12	yes	56
7.6	odd	2	inner	784.2.j.a.587.13		56
16.3	odd	4	inner	784.2.j.a.195.13		56
28.11	odd	6		448.2.z.a.271.10		56
28.19	even	6		448.2.z.a.143.10		56
56.5	odd	6		896.2.z.b.31.10		56
56.11	odd	6		896.2.z.a.159.5		56
56.19	even	6		896.2.z.a.31.5		56
56.53	even	6		896.2.z.b.159.10		56
112.3	even	12		784.2.w.f.19.12		56
112.5	odd	12		896.2.z.a.479.5		56
112.11	odd	12		896.2.z.b.607.10		56
112.19	even	12		112.2.v.a.3.3	✓	56
112.51	odd	12		784.2.w.f.227.3		56
112.53	even	12		896.2.z.a.607.5		56
112.61	odd	12		448.2.z.a.367.10		56
112.67	odd	12		112.2.v.a.19.12	yes	56
112.75	even	12		896.2.z.b.479.10		56
112.83	even	4	inner	784.2.j.a.195.14		56
112.109	even	12		448.2.z.a.47.10		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.3	✓	56	112.19	even	12
112.2.v.a.19.12	yes	56	112.67	odd	12
112.2.v.a.59.12	yes	56	7.5	odd	6
112.2.v.a.75.3	yes	56	7.4	even	3
448.2.z.a.47.10		56	112.109	even	12
448.2.z.a.143.10		56	28.19	even	6
448.2.z.a.271.10		56	28.11	odd	6
448.2.z.a.367.10		56	112.61	odd	12
784.2.j.a.195.13		56	16.3	odd	4	inner
784.2.j.a.195.14		56	112.83	even	4	inner
784.2.j.a.587.13		56	7.6	odd	2	inner
784.2.j.a.587.14		56	1.1	even	1	trivial
784.2.w.f.19.12		56	112.3	even	12
784.2.w.f.227.3		56	112.51	odd	12
784.2.w.f.411.3		56	7.3	odd	6
784.2.w.f.619.12		56	7.2	even	3
896.2.z.a.31.5		56	56.19	even	6
896.2.z.a.159.5		56	56.11	odd	6
896.2.z.a.479.5		56	112.5	odd	12
896.2.z.a.607.5		56	112.53	even	12
896.2.z.b.31.10		56	56.5	odd	6
896.2.z.b.159.10		56	56.53	even	6
896.2.z.b.479.10		56	112.75	even	12
896.2.z.b.607.10		56	112.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Fields

Representations

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Database

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