LMFDB - Embedded newform 784.2.j.a.195.6

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)

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")

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);

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			195.6
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10953 + 0.876896i) q^{2} +(1.81900 + 1.81900i) q^{3} +(0.462106 - 1.94588i) q^{4} +(-2.28693 - 2.28693i) q^{5} +(-3.61331 - 0.423158i) q^{6} +(1.19362 + 2.56423i) q^{8} +3.61753i q^{9} +(4.54282 + 0.532014i) q^{10} +(1.02778 + 1.02778i) q^{11} +(4.38013 - 2.69899i) q^{12} +(3.11315 - 3.11315i) q^{13} -8.31987i q^{15} +(-3.57292 - 1.79841i) q^{16} -2.33761i q^{17} +(-3.17220 - 4.01375i) q^{18} +(3.22573 + 3.22573i) q^{19} +(-5.50691 + 3.39330i) q^{20} +(-2.04161 - 0.239095i) q^{22} +2.30899 q^{23} +(-2.49315 + 6.83553i) q^{24} +5.46013i q^{25} +(-0.724218 + 6.18404i) q^{26} +(-1.12329 + 1.12329i) q^{27} +(-1.55163 - 1.55163i) q^{29} +(7.29566 + 9.23113i) q^{30} +7.77905 q^{31} +(5.54127 - 1.13769i) q^{32} +3.73908i q^{33} +(2.04984 + 2.59365i) q^{34} +(7.03929 + 1.67168i) q^{36} +(0.744267 - 0.744267i) q^{37} +(-6.40767 - 0.750408i) q^{38} +11.3256 q^{39} +(3.13450 - 8.59395i) q^{40} +2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(2.47489 - 1.52500i) q^{44} +(8.27305 - 8.27305i) q^{45} +(-2.56189 + 2.02475i) q^{46} +2.85031 q^{47} +(-3.22783 - 9.77044i) q^{48} +(-4.78797 - 6.05817i) q^{50} +(4.25212 - 4.25212i) q^{51} +(-4.61922 - 7.49643i) q^{52} +(-8.12024 + 8.12024i) q^{53} +(0.261313 - 2.23133i) q^{54} -4.70094i q^{55} +11.7352i q^{57} +(3.08219 + 0.360958i) q^{58} +(2.76264 - 2.76264i) q^{59} +(-16.1895 - 3.84466i) q^{60} +(10.1788 - 10.1788i) q^{61} +(-8.63107 + 6.82142i) q^{62} +(-5.15056 + 6.12142i) q^{64} -14.2391 q^{65} +(-3.27878 - 4.14861i) q^{66} +(-1.90049 + 1.90049i) q^{67} +(-4.54872 - 1.08023i) q^{68} +(4.20006 + 4.20006i) q^{69} -7.48345 q^{71} +(-9.27618 + 4.31795i) q^{72} -11.3042 q^{73} +(-0.173140 + 1.47843i) q^{74} +(-9.93198 + 9.93198i) q^{75} +(7.76752 - 4.78626i) q^{76} +(-12.5661 + 9.93142i) q^{78} +0.816047i q^{79} +(4.05818 + 12.2839i) q^{80} +6.76606 q^{81} +(-3.07572 + 2.43084i) q^{82} +(-2.65285 - 2.65285i) q^{83} +(-5.34597 + 5.34597i) q^{85} +(-14.1462 - 1.65667i) q^{86} -5.64483i q^{87} +(-1.40869 + 3.86225i) q^{88} -4.81889 q^{89} +(-1.92458 + 16.4338i) q^{90} +(1.06700 - 4.49303i) q^{92} +(14.1501 + 14.1501i) q^{93} +(-3.16250 + 2.49943i) q^{94} -14.7541i q^{95} +(12.1490 + 8.01011i) q^{96} -5.86541i q^{97} +(-3.71804 + 3.71804i) 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 $

$2$	−1.10953	+	0.876896i	−0.784555	+	0.620059i
$2$	−1.10953	+	0.876896i	−0.784555	+	0.620059i
$3$	1.81900	+	1.81900i	1.05020	+	1.05020i	0.998671	+	0.0515294i	$0.0164096\pi$
$3$	1.81900	+	1.81900i	1.05020	+	1.05020i	0.0515294	+	0.998671i	$0.483590\pi$
$4$	0.462106	−	1.94588i	0.231053	−	0.972941i
$5$	−2.28693	−	2.28693i	−1.02275	−	1.02275i	−0.999735	−	0.0230125i	$-0.992674\pi$
$5$	−2.28693	−	2.28693i	−1.02275	−	1.02275i	−0.0230125	−	0.999735i	$-0.507326\pi$
$6$	−3.61331	−	0.423158i	−1.47513	−	0.172753i
$7$		0			0
$7$		0			0
$8$	1.19362	+	2.56423i	0.422007	+	0.906592i
$9$			3.61753i			1.20584i
$10$	4.54282	+	0.532014i	1.43657	+	0.168238i
$11$	1.02778	+	1.02778i	0.309888	+	0.309888i	0.844866	−	0.534978i	$-0.179680\pi$
$11$	1.02778	+	1.02778i	0.309888	+	0.309888i	−0.534978	+	0.844866i	$0.679680\pi$
$12$	4.38013	−	2.69899i	1.26444	−	0.779132i
$13$	3.11315	−	3.11315i	0.863433	−	0.863433i	−0.128303	−	0.991735i	$-0.540953\pi$
$13$	3.11315	−	3.11315i	0.863433	−	0.863433i	0.991735	+	0.128303i	$0.0409528\pi$
$14$		0			0
$15$		−	8.31987i		−	2.14818i
$16$	−3.57292	−	1.79841i	−0.893229	−	0.449602i
$17$		−	2.33761i		−	0.566955i	−0.958979	−	0.283477i	$-0.908512\pi$
$17$		−	2.33761i		−	0.566955i	0.958979	−	0.283477i	$-0.0914881\pi$
$18$	−3.17220	−	4.01375i	−0.747695	−	0.946051i
$19$	3.22573	+	3.22573i	0.740033	+	0.740033i	0.972584	−	0.232551i	$-0.0747073\pi$
$19$	3.22573	+	3.22573i	0.740033	+	0.740033i	−0.232551	+	0.972584i	$0.574707\pi$
$20$	−5.50691	+	3.39330i	−1.23138	+	0.758764i
$21$		0			0
$22$	−2.04161	−	0.239095i	−0.435274	−	0.0509753i
$23$	2.30899			0.481458			0.240729	−	0.970592i	$-0.422613\pi$
$23$	2.30899			0.481458			0.240729	+	0.970592i	$0.422613\pi$
$24$	−2.49315	+	6.83553i	−0.508911	+	1.39530i
$25$			5.46013i			1.09203i
$26$	−0.724218	+	6.18404i	−0.142031	+	1.21279i
$27$	−1.12329	+	1.12329i	−0.216177	+	0.216177i
$28$		0			0
$29$	−1.55163	−	1.55163i	−0.288130	−	0.288130i	0.548210	−	0.836341i	$-0.315309\pi$
$29$	−1.55163	−	1.55163i	−0.288130	−	0.288130i	−0.836341	+	0.548210i	$0.815309\pi$
$30$	7.29566	+	9.23113i	1.33200	+	1.68537i
$31$	7.77905			1.39716			0.698579	−	0.715533i	$-0.253816\pi$
$31$	7.77905			1.39716			0.698579	+	0.715533i	$0.253816\pi$
$32$	5.54127	−	1.13769i	0.979567	−	0.201118i
$33$			3.73908i			0.650890i
$34$	2.04984	+	2.59365i	0.351545	+	0.444807i
$35$		0			0
$36$	7.03929	+	1.67168i	1.17322	+	0.278614i
$37$	0.744267	−	0.744267i	0.122357	−	0.122357i	−0.643277	−	0.765634i	$-0.722426\pi$
$37$	0.744267	−	0.744267i	0.122357	−	0.122357i	0.765634	+	0.643277i	$0.222426\pi$
$38$	−6.40767	−	0.750408i	−1.03946	−	0.121732i
$39$	11.3256			1.81356
$40$	3.13450	−	8.59395i	0.495608	−	1.35882i
$41$	2.77210			0.432929			0.216464	−	0.976290i	$-0.430547\pi$
$41$	2.77210			0.432929			0.216464	+	0.976290i	$0.430547\pi$
$42$		0			0
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.995935	+	0.0900717i	$0.0287096\pi$
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.0900717	+	0.995935i	$0.471290\pi$
$44$	2.47489	−	1.52500i	0.373104	−	0.229902i
$45$	8.27305	−	8.27305i	1.23327	−	1.23327i
$46$	−2.56189	+	2.02475i	−0.377730	+	0.298533i
$47$	2.85031			0.415761			0.207880	−	0.978154i	$-0.433344\pi$
$47$	2.85031			0.415761			0.207880	+	0.978154i	$0.433344\pi$
$48$	−3.22783	−	9.77044i	−0.465898	−	1.41024i
$49$		0			0
$50$	−4.78797	−	6.05817i	−0.677121	−	0.856754i
$51$	4.25212	−	4.25212i	0.595416	−	0.595416i
$52$	−4.61922	−	7.49643i	−0.640570	−	1.03957i
$53$	−8.12024	+	8.12024i	−1.11540	+	1.11540i	−0.122993	+	0.992408i	$0.539249\pi$
$53$	−8.12024	+	8.12024i	−1.11540	+	1.11540i	−0.992408	+	0.122993i	$0.960751\pi$
$54$	0.261313	−	2.23133i	0.0355602	−	0.303646i
$55$		−	4.70094i		−	0.633875i
$56$		0			0
$57$			11.7352i			1.55437i
$58$	3.08219	+	0.360958i	0.404712	+	0.0473962i
$59$	2.76264	−	2.76264i	0.359665	−	0.359665i	−0.504025	−	0.863689i	$-0.668148\pi$
$59$	2.76264	−	2.76264i	0.359665	−	0.359665i	0.863689	+	0.504025i	$0.168148\pi$
$60$	−16.1895	−	3.84466i	−2.09005	−	0.496344i
$61$	10.1788	−	10.1788i	1.30326	−	1.30326i	0.377086	−	0.926178i	$-0.376926\pi$
$61$	10.1788	−	10.1788i	1.30326	−	1.30326i	0.926178	−	0.377086i	$-0.123074\pi$
$62$	−8.63107	+	6.82142i	−1.09615	+	0.866321i
$63$		0			0
$64$	−5.15056	+	6.12142i	−0.643819	+	0.765177i
$65$	−14.2391			−1.76615
$66$	−3.27878	−	4.14861i	−0.403590	−	0.510659i
$67$	−1.90049	+	1.90049i	−0.232182	+	0.232182i	−0.813603	−	0.581421i	$-0.802497\pi$
$67$	−1.90049	+	1.90049i	−0.232182	+	0.232182i	0.581421	+	0.813603i	$0.302497\pi$
$68$	−4.54872	−	1.08023i	−0.551614	−	0.130997i
$69$	4.20006	+	4.20006i	0.505628	+	0.505628i
$70$		0			0
$71$	−7.48345			−0.888122			−0.444061	−	0.895997i	$-0.646463\pi$
$71$	−7.48345			−0.888122			−0.444061	+	0.895997i	$0.646463\pi$
$72$	−9.27618	+	4.31795i	−1.09321	+	0.508875i
$73$	−11.3042			−1.32306			−0.661529	−	0.749920i	$-0.730092\pi$
$73$	−11.3042			−1.32306			−0.661529	+	0.749920i	$0.730092\pi$
$74$	−0.173140	+	1.47843i	−0.0201272	+	0.171864i
$75$	−9.93198	+	9.93198i	−1.14685	+	1.14685i
$76$	7.76752	−	4.78626i	0.890995	−	0.549022i
$77$		0			0
$78$	−12.5661	+	9.93142i	−1.42283	+	1.12451i
$79$			0.816047i			0.0918125i	0.998946	+	0.0459062i	$0.0146175\pi$
$79$			0.816047i			0.0918125i	−0.998946	+	0.0459062i	$0.985382\pi$
$80$	4.05818	+	12.2839i	0.453719	+	1.37338i
$81$	6.76606			0.751785
$82$	−3.07572	+	2.43084i	−0.339657	+	0.268442i
$83$	−2.65285	−	2.65285i	−0.291188	−	0.291188i	0.546361	−	0.837550i	$-0.316013\pi$
$83$	−2.65285	−	2.65285i	−0.291188	−	0.291188i	−0.837550	+	0.546361i	$0.816013\pi$
$84$		0			0
$85$	−5.34597	+	5.34597i	−0.579852	+	0.579852i
$86$	−14.1462	−	1.65667i	−1.52542	−	0.178643i
$87$		−	5.64483i		−	0.605189i
$88$	−1.40869	+	3.86225i	−0.150167	+	0.411718i
$89$	−4.81889			−0.510801			−0.255400	−	0.966835i	$-0.582207\pi$
$89$	−4.81889			−0.510801			−0.255400	+	0.966835i	$0.582207\pi$
$90$	−1.92458	+	16.4338i	−0.202868	+	1.73227i
$91$		0			0
$92$	1.06700	−	4.49303i	0.111242	−	0.468430i
$93$	14.1501	+	14.1501i	1.46730	+	1.46730i
$94$	−3.16250	+	2.49943i	−0.326187	+	0.257796i
$95$		−	14.7541i		−	1.51373i
$96$	12.1490	+	8.01011i	1.23996	+	0.817528i
$97$		−	5.86541i		−	0.595542i	−0.954637	−	0.297771i	$-0.903757\pi$
$97$		−	5.86541i		−	0.595542i	0.954637	−	0.297771i	$-0.0962432\pi$
$98$		0			0
$99$	−3.71804	+	3.71804i	−0.373677	+	0.373677i
$100$	10.6248	+	2.52316i	1.06248	+	0.252316i
$101$	−1.02078	−	1.02078i	−0.101572	−	0.101572i	0.654495	−	0.756066i	$-0.272881\pi$
$101$	−1.02078	−	1.02078i	−0.101572	−	0.101572i	−0.756066	+	0.654495i	$0.772881\pi$
$102$	−0.989180	+	8.44652i	−0.0979434	+	0.836330i
$103$		−	2.42642i		−	0.239082i	−0.992829	−	0.119541i	$-0.961858\pi$
$103$		−	2.42642i		−	0.239082i	0.992829	−	0.119541i	$-0.0381423\pi$
$104$	11.6987	+	4.26692i	1.14716	+	0.418406i
$105$		0			0
$106$	1.88903	−	16.1302i	0.183479	−	1.56671i
$107$	3.18265	+	3.18265i	0.307678	+	0.307678i	0.844008	−	0.536330i	$-0.180190\pi$
$107$	3.18265	+	3.18265i	0.307678	+	0.307678i	−0.536330	+	0.844008i	$0.680190\pi$
$108$	1.66671	+	2.70487i	0.160379	+	0.260276i
$109$	2.30243	+	2.30243i	0.220533	+	0.220533i	0.808723	−	0.588190i	$-0.200159\pi$
$109$	2.30243	+	2.30243i	0.220533	+	0.220533i	−0.588190	+	0.808723i	$0.700159\pi$
$110$	4.12224	+	5.21583i	0.393040	+	0.497310i
$111$	2.70765			0.256998
$112$		0			0
$113$	11.5397			1.08556			0.542781	−	0.839875i	$-0.317372\pi$
$113$	11.5397			1.08556			0.542781	+	0.839875i	$0.317372\pi$
$114$	−10.2906	−	13.0205i	−0.963799	−	1.21949i
$115$	−5.28051	−	5.28051i	−0.492410	−	0.492410i
$116$	−3.73630	+	2.30227i	−0.346907	+	0.213760i
$117$	11.2619	+	11.2619i	1.04116	+	1.04116i
$118$	−0.642678	+	5.48777i	−0.0591633	+	0.505190i
$119$		0			0
$120$	21.3341	−	9.93074i	1.94752	−	0.906548i
$121$		−	8.88732i		−	0.807938i
$122$	−2.36792	+	20.2195i	−0.214381	+	1.83058i
$123$	5.04245	+	5.04245i	0.454662	+	0.454662i
$124$	3.59474	−	15.1371i	0.322817	−	1.35935i
$125$	1.05228	−	1.05228i	0.0941192	−	0.0941192i
$126$		0			0
$127$		−	4.49210i		−	0.398610i	−0.979938	−	0.199305i	$-0.936132\pi$
$127$		−	4.49210i		−	0.398610i	0.979938	−	0.199305i	$-0.0638684\pi$
$128$	0.346836	−	11.3084i	0.0306563	−	0.999530i
$129$			25.9078i			2.28105i
$130$	15.7987	−	12.4862i	1.38564	−	1.09512i
$131$	−9.78107	−	9.78107i	−0.854576	−	0.854576i	0.136117	−	0.990693i	$-0.456538\pi$
$131$	−9.78107	−	9.78107i	−0.854576	−	0.854576i	−0.990693	+	0.136117i	$0.956538\pi$
$132$	7.27581	+	1.72785i	0.633278	+	0.150390i
$133$		0			0
$134$	0.442115	−	3.77518i	0.0381929	−	0.326126i
$135$	5.13778			0.442190
$136$	5.99418	−	2.79022i	0.513997	−	0.239259i
$137$		−	2.52213i		−	0.215480i	−0.994179	−	0.107740i	$-0.965639\pi$
$137$		−	2.52213i		−	0.215480i	0.994179	−	0.107740i	$-0.0343614\pi$
$138$	−8.34310	−	0.977068i	−0.710212	−	0.0831736i
$139$	−6.00381	+	6.00381i	−0.509237	+	0.509237i	−0.914292	−	0.405055i	$-0.867252\pi$
$139$	−6.00381	+	6.00381i	−0.509237	+	0.509237i	0.405055	+	0.914292i	$0.367252\pi$
$140$		0			0
$141$	5.18472	+	5.18472i	0.436632	+	0.436632i
$142$	8.30310	−	6.56221i	0.696780	−	0.550688i
$143$	6.39929			0.535135
$144$	6.50580	−	12.9251i	0.542150	−	1.07709i
$145$			7.09694i			0.589369i
$146$	12.5423	−	9.91262i	1.03801	−	0.820374i
$147$		0			0
$148$	−1.10433	−	1.79219i	−0.0907750	−	0.147317i
$149$	−6.00918	+	6.00918i	−0.492291	+	0.492291i	−0.909028	−	0.416736i	$-0.863174\pi$
$149$	−6.00918	+	6.00918i	−0.492291	+	0.492291i	0.416736	+	0.909028i	$0.363174\pi$
$150$	2.31050	−	19.7291i	0.188651	−	1.61088i
$151$	−10.2385			−0.833200			−0.416600	−	0.909090i	$-0.636778\pi$
$151$	−10.2385			−0.833200			−0.416600	+	0.909090i	$0.636778\pi$
$152$	−4.42123	+	12.1218i	−0.358609	+	0.983208i
$153$	8.45639			0.683659
$154$		0			0
$155$	−17.7902	−	17.7902i	−1.42894	−	1.42894i
$156$	5.23365	−	22.0384i	0.419027	−	1.76448i
$157$	10.3817	−	10.3817i	0.828554	−	0.828554i	−0.158763	−	0.987317i	$-0.550751\pi$
$157$	10.3817	−	10.3817i	0.828554	−	0.828554i	0.987317	+	0.158763i	$0.0507505\pi$
$158$	−0.715589	−	0.905427i	−0.0569292	−	0.0720319i
$159$	−29.5415			−2.34279
$160$	−15.2743	−	10.0707i	−1.20754	−	0.796157i
$161$		0			0
$162$	−7.50714	+	5.93313i	−0.589816	+	0.466151i
$163$	−16.2550	+	16.2550i	−1.27319	+	1.27319i	−0.328783	+	0.944406i	$0.606638\pi$
$163$	−16.2550	+	16.2550i	−1.27319	+	1.27319i	−0.944406	+	0.328783i	$0.893362\pi$
$164$	1.28100	−	5.39418i	0.100030	−	0.421214i
$165$	8.55102	−	8.55102i	0.665696	−	0.665696i
$166$	5.26969	+	0.617138i	0.409007	+	0.0478992i
$167$			3.82099i			0.295677i	0.989011	+	0.147839i	$0.0472316\pi$
$167$			3.82099i			0.295677i	−0.989011	+	0.147839i	$0.952768\pi$
$168$		0			0
$169$		−	6.38341i		−	0.491032i
$170$	1.24364	−	10.6194i	0.0953831	−	0.814468i
$171$	−11.6692	+	11.6692i	−0.892364	+	0.892364i
$172$	17.1483	−	10.5666i	1.30755	−	0.805696i
$173$	−5.87834	+	5.87834i	−0.446922	+	0.446922i	−0.894330	−	0.447408i	$-0.852347\pi$
$173$	−5.87834	+	5.87834i	−0.446922	+	0.446922i	0.447408	+	0.894330i	$0.352347\pi$
$174$	4.94993	+	6.26310i	0.375253	+	0.474804i
$175$		0			0
$176$	−1.82381	−	5.52056i	−0.137475	−	0.416128i
$177$	10.0505			0.755440
$178$	5.34669	−	4.22566i	0.400751	−	0.316727i
$179$	−13.6633	+	13.6633i	−1.02124	+	1.02124i	−0.0214740	+	0.999769i	$0.506836\pi$
$179$	−13.6633	+	13.6633i	−1.02124	+	1.02124i	−0.999769	+	0.0214740i	$0.993164\pi$
$180$	−12.2754	−	19.9214i	−0.914951	−	1.48485i
$181$	6.07189	+	6.07189i	0.451320	+	0.451320i	0.895793	−	0.444472i	$-0.146609\pi$
$181$	6.07189	+	6.07189i	0.451320	+	0.451320i	−0.444472	+	0.895793i	$0.646609\pi$
$182$		0			0
$183$	37.0306			2.73738
$184$	2.75605	+	5.92079i	0.203179	+	0.436486i
$185$	−3.40418			−0.250280
$186$	−28.1081	−	3.29176i	−2.06099	−	0.241364i
$187$	2.40256	−	2.40256i	0.175693	−	0.175693i
$188$	1.31715	−	5.54637i	0.0960627	−	0.404511i
$189$		0			0
$190$	12.9378	+	16.3700i	0.938605	+	1.18761i
$191$		−	15.2082i		−	1.10043i	−0.835024	−	0.550213i	$-0.814546\pi$
$191$		−	15.2082i		−	1.10043i	0.835024	−	0.550213i	$-0.185454\pi$
$192$	−20.5037	+	1.76600i	−1.47973	+	0.127450i
$193$	22.4794			1.61811			0.809053	−	0.587736i	$-0.199981\pi$
$193$	22.4794			1.61811			0.809053	+	0.587736i	$0.199981\pi$
$194$	5.14336	+	6.50784i	0.369271	+	0.467236i
$195$	−25.9010	−	25.9010i	−1.85481	−	1.85481i
$196$		0			0
$197$	−8.31581	+	8.31581i	−0.592477	+	0.592477i	−0.938300	−	0.345823i	$-0.887600\pi$
$197$	−8.31581	+	8.31581i	−0.592477	+	0.592477i	0.345823	+	0.938300i	$0.387600\pi$
$198$	0.864935	−	7.38560i	0.0614682	−	0.524872i
$199$		−	10.2201i		−	0.724484i	−0.932084	−	0.362242i	$-0.882011\pi$
$199$		−	10.2201i		−	0.724484i	0.932084	−	0.362242i	$-0.117989\pi$
$200$	−14.0010	+	6.51730i	−0.990022	+	0.460843i
$201$	−6.91399			−0.487675
$202$	2.02771	+	0.237467i	0.142669	+	0.0167081i
$203$		0			0
$204$	−6.30920	−	10.2391i	−0.441732	−	0.716878i
$205$	−6.33960	−	6.33960i	−0.442777	−	0.442777i
$206$	2.12771	+	2.69218i	0.148245	+	0.187573i
$207$			8.35285i			0.580563i
$208$	−16.7217	+	5.52431i	−1.15944	+	0.383042i
$209$			6.63070i			0.458655i
$210$		0			0
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	−0.481467	−	0.876464i	$-0.659896\pi$
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	0.876464	+	0.481467i	$0.159896\pi$
$212$	12.0486	+	19.5534i	0.827503	+	1.34294i
$213$	−13.6124	−	13.6124i	−0.932706	−	0.932706i
$214$	−6.32210	−	0.740386i	−0.432170	−	0.0506118i
$215$		−	32.5724i		−	2.22142i
$216$	−4.22115	−	1.53960i	−0.287213	−	0.104756i
$217$		0			0
$218$	−4.57361	−	0.535620i	−0.309764	−	0.0362768i
$219$	−20.5624	−	20.5624i	−1.38948	−	1.38948i
$220$	−9.14748	−	2.17233i	−0.616723	−	0.146459i
$221$	−7.27734	−	7.27734i	−0.489527	−	0.489527i
$222$	−3.00421	+	2.37432i	−0.201629	+	0.159354i
$223$	−17.4929			−1.17141			−0.585705	−	0.810524i	$-0.699182\pi$
$223$	−17.4929			−1.17141			−0.585705	+	0.810524i	$0.699182\pi$
$224$		0			0
$225$	−19.7522			−1.31681
$226$	−12.8036	+	10.1191i	−0.851682	+	0.673112i
$227$	12.3930	+	12.3930i	0.822550	+	0.822550i	0.986473	−	0.163923i	$-0.0524148\pi$
$227$	12.3930	+	12.3930i	0.822550	+	0.822550i	−0.163923	+	0.986473i	$0.552415\pi$
$228$	22.8353	+	5.42291i	1.51231	+	0.359141i
$229$	4.94300	+	4.94300i	0.326643	+	0.326643i	0.851308	−	0.524666i	$-0.175810\pi$
$229$	4.94300	+	4.94300i	0.326643	+	0.326643i	−0.524666	+	0.851308i	$0.675810\pi$
$230$	10.4893	+	1.22842i	0.691646	+	0.0809993i
$231$		0			0
$232$	2.12668	−	5.83078i	0.139624	−	0.382810i
$233$		−	28.9752i		−	1.89823i	−0.314927	−	0.949116i	$-0.601980\pi$
$233$		−	28.9752i		−	1.89823i	0.314927	−	0.949116i	$-0.398020\pi$
$234$	−22.3710	−	2.61988i	−1.46243	−	0.171267i
$235$	−6.51847	−	6.51847i	−0.425218	−	0.425218i
$236$	−4.09914	−	6.65240i	−0.266831	−	0.433034i
$237$	−1.48439	+	1.48439i	−0.0964215	+	0.0964215i
$238$		0			0
$239$		−	13.3587i		−	0.864105i	−0.901848	−	0.432053i	$-0.857789\pi$
$239$		−	13.3587i		−	0.864105i	0.901848	−	0.432053i	$-0.142211\pi$
$240$	−14.9625	+	29.7262i	−0.965826	+	1.91882i
$241$		−	12.1833i		−	0.784794i	−0.919796	−	0.392397i	$-0.871646\pi$
$241$		−	12.1833i		−	0.784794i	0.919796	−	0.392397i	$-0.128354\pi$
$242$	7.79326	+	9.86074i	0.500970	+	0.633872i
$243$	15.6773	+	15.6773i	1.00570	+	1.00570i
$244$	−15.1031	−	24.5105i	−0.966877	−	1.56912i
$245$		0			0
$246$	−10.0164	−	1.17304i	−0.638625	−	0.0747900i
$247$	20.0844			1.27794
$248$	9.28520	+	19.9473i	0.589611	+	1.26665i
$249$		−	9.65108i		−	0.611612i
$250$	−0.244795	+	2.09028i	−0.0154822	+	0.132201i
$251$	6.68926	−	6.68926i	0.422223	−	0.422223i	−0.463746	−	0.885968i	$-0.653495\pi$
$251$	6.68926	−	6.68926i	0.422223	−	0.422223i	0.885968	+	0.463746i	$0.153495\pi$
$252$		0			0
$253$	2.37314	+	2.37314i	0.149198	+	0.149198i
$254$	3.93911	+	4.98412i	0.247162	+	0.312731i
$255$	−19.4486			−1.21792
$256$	9.53146	+	12.8511i	0.595716	+	0.803195i
$257$			3.84327i			0.239736i	0.992790	+	0.119868i	$0.0382472\pi$
$257$			3.84327i			0.239736i	−0.992790	+	0.119868i	$0.961753\pi$
$258$	−22.7184	−	28.7454i	−1.41439	−	1.78961i
$259$		0			0
$260$	−6.57999	+	27.7077i	−0.408074	+	1.71836i
$261$	5.61306	−	5.61306i	0.347440	−	0.347440i
$262$	19.4293	+	2.27539i	1.20035	+	0.140574i
$263$	−6.31567			−0.389441			−0.194720	−	0.980859i	$-0.562380\pi$
$263$	−6.31567			−0.389441			−0.194720	+	0.980859i	$0.562380\pi$
$264$	−9.58786	+	4.46303i	−0.590092	+	0.274680i
$265$	37.1409			2.28155
$266$		0			0
$267$	−8.76556	−	8.76556i	−0.536444	−	0.536444i
$268$	2.81990	+	4.57636i	0.172253	+	0.279545i
$269$	−17.0505	+	17.0505i	−1.03958	+	1.03958i	−0.0404010	+	0.999184i	$0.512864\pi$
$269$	−17.0505	+	17.0505i	−1.03958	+	1.03958i	−0.999184	+	0.0404010i	$0.987136\pi$
$270$	−5.70051	+	4.50530i	−0.346922	+	0.274184i
$271$	−9.46629			−0.575036			−0.287518	−	0.957775i	$-0.592830\pi$
$271$	−9.46629			−0.575036			−0.287518	+	0.957775i	$0.592830\pi$
$272$	−4.20398	+	8.35210i	−0.254904	+	0.506420i
$273$		0			0
$274$	2.21165	+	2.79837i	0.133610	+	0.169056i
$275$	−5.61183	+	5.61183i	−0.338406	+	0.338406i
$276$	10.1137	−	6.23195i	0.608773	−	0.375119i
$277$	−8.29249	+	8.29249i	−0.498247	+	0.498247i	−0.910892	−	0.412645i	$-0.864605\pi$
$277$	−8.29249	+	8.29249i	−0.498247	+	0.498247i	0.412645	+	0.910892i	$0.364605\pi$
$278$	1.39668	−	11.9261i	0.0837672	−	0.715281i
$279$			28.1409i			1.68475i
$280$		0			0
$281$			5.59517i			0.333780i	0.985976	+	0.166890i	$0.0533724\pi$
$281$			5.59517i			0.333780i	−0.985976	+	0.166890i	$0.946628\pi$
$282$	−10.2991	−	1.20613i	−0.613300	−	0.0718241i
$283$	2.71268	−	2.71268i	0.161252	−	0.161252i	−0.621869	−	0.783121i	$-0.713626\pi$
$283$	2.71268	−	2.71268i	0.161252	−	0.161252i	0.783121	+	0.621869i	$0.213626\pi$
$284$	−3.45815	+	14.5619i	−0.205203	+	0.864090i
$285$	26.8376	−	26.8376i	1.58972	−	1.58972i
$286$	−7.10019	+	5.61151i	−0.419843	+	0.331816i
$287$		0			0
$288$	4.11564	+	20.0457i	0.242516	+	1.18120i
$289$	11.5356			0.678562
$290$	−6.22328	−	7.87426i	−0.365444	−	0.462392i
$291$	10.6692	−	10.6692i	0.625439	−	0.625439i
$292$	−5.22374	+	21.9967i	−0.305696	+	1.28726i
$293$	−9.74731	−	9.74731i	−0.569444	−	0.569444i	0.362529	−	0.931973i	$-0.381913\pi$
$293$	−9.74731	−	9.74731i	−0.569444	−	0.569444i	−0.931973	+	0.362529i	$0.881913\pi$
$294$		0			0
$295$	−12.6359			−0.735692
$296$	2.79684	+	1.02010i	0.162563	+	0.0592922i
$297$	−2.30900			−0.133982
$298$	1.39793	−	11.9368i	0.0809798	−	0.691480i
$299$	7.18824	−	7.18824i	0.415707	−	0.415707i
$300$	14.7368	+	23.9161i	0.850832	+	1.38080i
$301$		0			0
$302$	11.3599	−	8.97813i	0.653691	−	0.516633i
$303$		−	3.71361i		−	0.213341i
$304$	−5.72408	−	17.3264i	−0.328299	−	0.993739i
$305$	−46.5566			−2.66582
$306$	−9.38260	+	7.41538i	−0.536368	+	0.423909i
$307$	20.5735	+	20.5735i	1.17419	+	1.17419i	0.981201	+	0.192988i	$0.0618178\pi$
$307$	20.5735	+	20.5735i	1.17419	+	1.17419i	0.192988	+	0.981201i	$0.438182\pi$
$308$		0			0
$309$	4.41365	−	4.41365i	0.251084	−	0.251084i
$310$	35.3388	+	4.13856i	2.00711	+	0.235054i
$311$		−	0.571890i		−	0.0324289i	−0.999869	−	0.0162145i	$-0.994839\pi$
$311$		−	0.571890i		−	0.0324289i	0.999869	−	0.0162145i	$-0.00516145\pi$
$312$	13.5185	+	29.0416i	0.765334	+	1.64416i
$313$	1.41457			0.0799564			0.0399782	−	0.999201i	$-0.487271\pi$
$313$	1.41457			0.0799564			0.0399782	+	0.999201i	$0.487271\pi$
$314$	−2.41513	+	20.6226i	−0.136294	+	1.16380i
$315$		0			0
$316$	1.58793	+	0.377100i	0.0893281	+	0.0212135i
$317$	18.5146	+	18.5146i	1.03988	+	1.03988i	0.999171	+	0.0407118i	$0.0129626\pi$
$317$	18.5146	+	18.5146i	1.03988	+	1.03988i	0.0407118	+	0.999171i	$0.487037\pi$
$318$	32.7771	−	25.9048i	1.83805	−	1.45267i
$319$		−	3.18948i		−	0.178576i
$320$	25.7783	−	2.22030i	1.44105	−	0.124119i
$321$			11.5785i			0.646248i
$322$		0			0
$323$	7.54051	−	7.54051i	0.419565	−	0.419565i
$324$	3.12664	−	13.1660i	0.173702	−	0.731442i
$325$	16.9982	+	16.9982i	0.942891	+	0.942891i
$326$	3.78143	−	32.2893i	0.209434	−	1.78834i
$327$			8.37626i			0.463208i
$328$	3.30882	+	7.10830i	0.182699	+	0.392490i
$329$		0			0
$330$	−1.98924	+	16.9860i	−0.109504	+	0.935046i
$331$	−1.98663	−	1.98663i	−0.109195	−	0.109195i	0.650398	−	0.759593i	$-0.274602\pi$
$331$	−1.98663	−	1.98663i	−0.109195	−	0.109195i	−0.759593	+	0.650398i	$0.774602\pi$
$332$	−6.38803	+	3.93624i	−0.350589	+	0.216029i
$333$	2.69241	+	2.69241i	0.147543	+	0.147543i
$334$	−3.35062	−	4.23950i	−0.183337	−	0.231975i
$335$	8.69259			0.474927
$336$		0			0
$337$	−23.9205			−1.30303			−0.651517	−	0.758634i	$-0.725867\pi$
$337$	−23.9205			−1.30303			−0.651517	+	0.758634i	$0.725867\pi$
$338$	5.59759	+	7.08257i	0.304469	+	0.385241i
$339$	20.9907	+	20.9907i	1.14006	+	1.14006i
$340$	7.93222	+	12.8730i	0.430185	+	0.698138i
$341$	7.99517	+	7.99517i	0.432963	+	0.432963i
$342$	2.71462	−	23.1799i	0.146790	−	1.25343i
$343$		0			0
$344$	−9.76072	+	26.7612i	−0.526263	+	1.44287i
$345$		−	19.2105i		−	1.03426i
$346$	1.36749	−	11.6769i	0.0735167	−	0.627753i
$347$	−8.84419	−	8.84419i	−0.474781	−	0.474781i	0.428677	−	0.903458i	$-0.358980\pi$
$347$	−8.84419	−	8.84419i	−0.474781	−	0.474781i	−0.903458	+	0.428677i	$0.858980\pi$
$348$	−10.9842	−	2.60851i	−0.588813	−	0.139831i
$349$	−21.9157	+	21.9157i	−1.17312	+	1.17312i	−0.191662	+	0.981461i	$0.561388\pi$
$349$	−21.9157	+	21.9157i	−1.17312	+	1.17312i	−0.981461	+	0.191662i	$0.938612\pi$
$350$		0			0
$351$			6.99394i			0.373309i
$352$	6.86452	+	4.52592i	0.365880	+	0.241232i
$353$			21.0137i			1.11845i	0.829017	+	0.559224i	$0.188901\pi$
$353$			21.0137i			1.11845i	−0.829017	+	0.559224i	$0.811099\pi$
$354$	−11.1513	+	8.81323i	−0.592684	+	0.468418i
$355$	17.1141	+	17.1141i	0.908325	+	0.908325i
$356$	−2.22684	+	9.37699i	−0.118022	+	0.496979i
$357$		0			0
$358$	3.17852	−	27.1411i	0.167990	−	1.43445i
$359$	−9.56621			−0.504885			−0.252443	−	0.967612i	$-0.581234\pi$
$359$	−9.56621			−0.504885			−0.252443	+	0.967612i	$0.581234\pi$
$360$	31.0889	+	11.3392i	1.63853	+	0.597626i
$361$			1.81066i			0.0952976i
$362$	−12.0614	−	1.41252i	−0.633931	−	0.0742402i
$363$	16.1661	−	16.1661i	0.848498	−	0.848498i
$364$		0			0
$365$	25.8520	+	25.8520i	1.35315	+	1.35315i
$366$	−41.0865	+	32.4720i	−2.14762	+	1.69734i
$367$	−6.12610			−0.319780			−0.159890	−	0.987135i	$-0.551114\pi$
$367$	−6.12610			−0.319780			−0.159890	+	0.987135i	$0.551114\pi$
$368$	−8.24983	−	4.15251i	−0.430052	−	0.216464i
$369$			10.0282i			0.522045i
$370$	3.77703	−	2.98511i	0.196359	−	0.155189i
$371$		0			0
$372$	34.0733	−	20.9956i	1.76662	−	1.08857i
$373$	−11.6156	+	11.6156i	−0.601435	+	0.601435i	−0.940693	−	0.339258i	$-0.889824\pi$
$373$	−11.6156	+	11.6156i	−0.601435	+	0.601435i	0.339258	+	0.940693i	$0.389824\pi$
$374$	−0.558912	+	4.77250i	−0.0289007	+	0.246780i
$375$	3.82821			0.197688
$376$	3.40218	+	7.30886i	0.175454	+	0.376925i
$377$	−9.66091			−0.497562
$378$		0			0
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	0.845257	−	0.534360i	$-0.179447\pi$
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	−0.534360	+	0.845257i	$0.679447\pi$
$380$	−28.7097	−	6.81794i	−1.47277	−	0.349753i
$381$	8.17114	−	8.17114i	0.418620	−	0.418620i
$382$	13.3360	+	16.8739i	0.682330	+	0.863345i
$383$	19.2806			0.985193			0.492596	−	0.870258i	$-0.336048\pi$
$383$	19.2806			0.985193			0.492596	+	0.870258i	$0.336048\pi$
$384$	21.2009	−	19.9391i	1.08190	−	1.01751i
$385$		0			0
$386$	−24.9416	+	19.7121i	−1.26949	+	1.00332i
$387$	−25.7620	+	25.7620i	−1.30955	+	1.30955i
$388$	−11.4134	−	2.71044i	−0.579428	−	0.137602i
$389$	20.2394	−	20.2394i	1.02618	−	1.02618i	0.0265310	−	0.999648i	$-0.491554\pi$
$389$	20.2394	−	20.2394i	1.02618	−	1.02618i	0.999648	−	0.0265310i	$-0.00844607\pi$
$390$	51.4504	+	6.02540i	2.60529	+	0.305108i
$391$		−	5.39753i		−	0.272965i
$392$		0			0
$393$		−	35.5835i		−	1.79495i
$394$	1.93452	−	16.5187i	0.0974599	−	0.832202i
$395$	1.86625	−	1.86625i	0.0939010	−	0.0939010i
$396$	5.51674	+	8.95299i	0.277226	+	0.449905i
$397$	6.55770	−	6.55770i	0.329122	−	0.329122i	−0.523131	−	0.852252i	$-0.675236\pi$
$397$	6.55770	−	6.55770i	0.329122	−	0.329122i	0.852252	+	0.523131i	$0.175236\pi$
$398$	8.96198	+	11.3395i	0.449223	+	0.568398i
$399$		0			0
$400$	9.81954	−	19.5086i	0.490977	−	0.975429i
$401$	−35.0562			−1.75062			−0.875312	−	0.483558i	$-0.839344\pi$
$401$	−35.0562			−1.75062			−0.875312	+	0.483558i	$0.839344\pi$
$402$	7.67126	−	6.06285i	0.382608	−	0.302387i
$403$	24.2173	−	24.2173i	1.20635	−	1.20635i
$404$	−2.45803	+	1.51461i	−0.122292	+	0.0753548i
$405$	−15.4735	−	15.4735i	−0.768886	−	0.768886i
$406$		0			0
$407$	1.52989			0.0758338
$408$	15.9788	+	5.82801i	0.791070	+	0.288530i
$409$	−34.8784			−1.72463			−0.862314	−	0.506374i	$-0.830985\pi$
$409$	−34.8784			−1.72463			−0.862314	+	0.506374i	$0.830985\pi$
$410$	12.5931	+	1.47479i	0.621931	+	0.0728349i
$411$	4.58776	−	4.58776i	0.226297	−	0.226297i
$412$	−4.72152	−	1.12126i	−0.232613	−	0.0552406i
$413$		0			0
$414$	−7.32458	−	9.26772i	−0.359984	−	0.455484i
$415$			12.1338i			0.595624i
$416$	13.7090	−	20.7926i	0.672139	−	1.01944i
$417$	−21.8419			−1.06960
$418$	−5.81444	−	7.35695i	−0.284393	−	0.359840i
$419$	−8.57828	−	8.57828i	−0.419076	−	0.419076i	0.465809	−	0.884885i	$-0.345763\pi$
$419$	−8.57828	−	8.57828i	−0.419076	−	0.419076i	−0.884885	+	0.465809i	$0.845763\pi$
$420$		0			0
$421$	−7.41183	+	7.41183i	−0.361230	+	0.361230i	−0.864266	−	0.503035i	$-0.832217\pi$
$421$	−7.41183	+	7.41183i	−0.361230	+	0.361230i	0.503035	+	0.864266i	$0.332217\pi$
$422$	−1.33476	+	11.3974i	−0.0649753	+	0.554819i
$423$			10.3111i			0.501342i
$424$	−30.5146	−	11.1297i	−1.48192	−	0.540506i
$425$	12.7637			0.619129
$426$	27.0400	+	3.16668i	1.31009	+	0.153426i
$427$		0			0
$428$	7.66379	−	4.72234i	0.370443	−	0.228263i
$429$	11.6403	+	11.6403i	0.562000	+	0.562000i
$430$	28.5627	+	36.1400i	1.37741	+	1.74283i
$431$		−	1.61239i		−	0.0776661i	−0.999246	−	0.0388331i	$-0.987636\pi$
$431$		−	1.61239i		−	0.0776661i	0.999246	−	0.0388331i	$-0.0123641\pi$
$432$	6.03355	−	1.99329i	0.290290	−	0.0959021i
$433$		−	13.0869i		−	0.628917i	−0.949271	−	0.314458i	$-0.898177\pi$
$433$		−	13.0869i		−	0.628917i	0.949271	−	0.314458i	$-0.101823\pi$
$434$		0			0
$435$	−12.9093	+	12.9093i	−0.618956	+	0.618956i
$436$	5.54424	−	3.41630i	0.265521	−	0.163611i
$437$	7.44818	+	7.44818i	0.356295	+	0.356295i
$438$	40.8456	+	4.78346i	1.95168	+	0.228563i
$439$			1.97867i			0.0944367i	0.998885	+	0.0472184i	$0.0150357\pi$
$439$			1.97867i			0.0944367i	−0.998885	+	0.0472184i	$0.984964\pi$
$440$	12.0543	−	5.61113i	0.574666	−	0.267500i
$441$		0			0
$442$	14.4559	+	1.69294i	0.687597	+	0.0805251i
$443$	24.5351	+	24.5351i	1.16570	+	1.16570i	0.983208	+	0.182491i	$0.0584161\pi$
$443$	24.5351	+	24.5351i	1.16570	+	1.16570i	0.182491	+	0.983208i	$0.441584\pi$
$444$	1.25122	−	5.26876i	0.0593802	−	0.250044i
$445$	11.0205	+	11.0205i	0.522420	+	0.522420i
$446$	19.4089	−	15.3394i	0.919036	−	0.726344i
$447$	−21.8614			−1.03401
$448$		0			0
$449$	20.0460			0.946031			0.473015	−	0.881054i	$-0.343166\pi$
$449$	20.0460			0.946031			0.473015	+	0.881054i	$0.343166\pi$
$450$	21.9156	−	17.3206i	1.03311	−	0.816502i
$451$	2.84912	+	2.84912i	0.134160	+	0.134160i
$452$	5.33255	−	22.4548i	0.250822	−	1.05619i
$453$	−18.6239	−	18.6239i	−0.875027	−	0.875027i
$454$	−24.6177	−	2.88300i	−1.15537	−	0.135306i
$455$		0			0
$456$	−30.0918	+	14.0074i	−1.40918	+	0.655954i
$457$			30.0060i			1.40362i	0.712364	+	0.701810i	$0.247625\pi$
$457$			30.0060i			1.40362i	−0.712364	+	0.701810i	$0.752375\pi$
$458$	−9.81890	−	1.14990i	−0.458807	−	0.0537313i
$459$	2.62582	+	2.62582i	0.122563	+	0.122563i
$460$	−12.7154	+	7.83510i	−0.592859	+	0.365313i
$461$	−18.2334	+	18.2334i	−0.849213	+	0.849213i	−0.990035	−	0.140822i	$-0.955026\pi$
$461$	−18.2334	+	18.2334i	−0.849213	+	0.849213i	0.140822	+	0.990035i	$0.455026\pi$
$462$		0			0
$463$			31.3804i			1.45837i	0.684316	+	0.729186i	$0.260101\pi$
$463$			31.3804i			1.45837i	−0.684316	+	0.729186i	$0.739899\pi$
$464$	2.75338	+	8.33430i	0.127822	+	0.386910i
$465$		−	64.7206i		−	3.00135i
$466$	25.4083	+	32.1489i	1.17702	+	1.48927i
$467$	−16.8599	−	16.8599i	−0.780183	−	0.780183i	0.199679	−	0.979861i	$-0.436010\pi$
$467$	−16.8599	−	16.8599i	−0.780183	−	0.780183i	−0.979861	+	0.199679i	$0.936010\pi$
$468$	27.1186	−	16.7102i	1.25356	−	0.772428i
$469$		0			0
$470$	12.9485	+	1.51641i	0.597268	+	0.0699466i
$471$	37.7688			1.74030
$472$	10.3816	+	3.78651i	0.477850	+	0.174288i
$473$			14.6386i			0.673082i
$474$	0.345317	−	2.94863i	0.0158609	−	0.135435i
$475$	−17.6129	+	17.6129i	−0.808135	+	0.808135i
$476$		0			0
$477$	−29.3752	−	29.3752i	−1.34500	−	1.34500i
$478$	11.7142	+	14.8219i	0.535796	+	0.677938i
$479$	−35.3568			−1.61549			−0.807747	−	0.589530i	$-0.799313\pi$
$479$	−35.3568			−1.61549			−0.807747	+	0.589530i	$0.799313\pi$
$480$	−9.46546	−	46.1026i	−0.432037	−	2.10429i
$481$		−	4.63403i		−	0.211294i
$482$	10.6835	+	13.5177i	0.486619	+	0.615714i
$483$		0			0
$484$	−17.2937	−	4.10688i	−0.786077	−	0.186677i
$485$	−13.4138	+	13.4138i	−0.609089	+	0.609089i
$486$	−31.1419	−	3.64705i	−1.41262	−	0.165434i
$487$	−10.6231			−0.481377			−0.240688	−	0.970602i	$-0.577373\pi$
$487$	−10.6231			−0.481377			−0.240688	+	0.970602i	$0.577373\pi$
$488$	38.2505	+	13.9512i	1.73152	+	0.631542i
$489$	−59.1357			−2.67421
$490$		0			0
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.969572	+	0.244806i	$0.0787243\pi$
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.244806	+	0.969572i	$0.421276\pi$
$492$	12.1422	−	7.48187i	0.547411	−	0.337309i
$493$	−3.62711	+	3.62711i	−0.163357	+	0.163357i
$494$	−22.2842	+	17.6119i	−1.00261	+	0.792397i
$495$	17.0058			0.764354
$496$	−27.7939	−	13.9899i	−1.24798	−	0.628165i
$497$		0			0
$498$	8.46299	+	10.7081i	0.379236	+	0.479843i
$499$	8.96334	−	8.96334i	0.401254	−	0.401254i	−0.477421	−	0.878675i	$-0.658428\pi$
$499$	8.96334	−	8.96334i	0.401254	−	0.401254i	0.878675	+	0.477421i	$0.158428\pi$
$500$	−1.56135	−	2.53389i	−0.0698259	−	0.113319i
$501$	−6.95039	+	6.95039i	−0.310521	+	0.310521i
$502$	−1.55614	+	13.2877i	−0.0694538	+	0.593060i
$503$			13.7074i			0.611183i	0.952163	+	0.305591i	$0.0988542\pi$
$503$			13.7074i			0.611183i	−0.952163	+	0.305591i	$0.901146\pi$
$504$		0			0
$505$			4.66892i			0.207764i
$506$	−4.71407	−	0.552069i	−0.209566	−	0.0245425i
$507$	11.6114	−	11.6114i	0.515682	−	0.515682i
$508$	−8.74111	−	2.07583i	−0.387824	−	0.0921000i
$509$	−16.8495	+	16.8495i	−0.746841	+	0.746841i	−0.973885	−	0.227044i	$-0.927094\pi$
$509$	−16.8495	+	16.8495i	−0.746841	+	0.746841i	0.227044	+	0.973885i	$0.427094\pi$
$510$	21.5788	−	17.0544i	0.955526	−	0.755183i
$511$		0			0
$512$	−21.8445	−	5.90058i	−0.965401	−	0.260771i
$513$	−7.24686			−0.319957
$514$	−3.37015	−	4.26421i	−0.148651	−	0.188086i
$515$	−5.54905	+	5.54905i	−0.244520	+	0.244520i
$516$	50.4135	+	11.9721i	2.21933	+	0.527044i
$517$	2.92950	+	2.92950i	0.128839	+	0.128839i
$518$		0			0
$519$	−21.3854			−0.938715
$520$	−16.9961	−	36.5124i	−0.745327	−	1.60118i
$521$	23.7178			1.03910			0.519548	−	0.854441i	$-0.326100\pi$
$521$	23.7178			1.03910			0.519548	+	0.854441i	$0.326100\pi$
$522$	−1.30578	+	11.1499i	−0.0571524	+	0.488019i
$523$	−13.2772	+	13.2772i	−0.580570	+	0.580570i	−0.935060	−	0.354490i	$-0.884654\pi$
$523$	−13.2772	+	13.2772i	−0.580570	+	0.580570i	0.354490	+	0.935060i	$0.384654\pi$
$524$	−23.5527	+	14.5129i	−1.02890	+	0.634000i
$525$		0			0
$526$	7.00742	−	5.53819i	0.305538	−	0.241476i
$527$		−	18.1844i		−	0.792125i
$528$	6.72439	−	13.3594i	0.292641	−	0.581394i
$529$	−17.6686			−0.768198
$530$	−41.2089	+	32.5687i	−1.79000	+	1.41469i
$531$	9.99392	+	9.99392i	0.433699	+	0.433699i
$532$		0			0
$533$	8.62996	−	8.62996i	0.373805	−	0.373805i
$534$	17.4121	+	2.03915i	0.753496	+	0.0882426i
$535$		−	14.5570i		−	0.629355i
$536$	−7.14175	−	2.60484i	−0.308477	−	0.112512i
$537$	−49.7071			−2.14502
$538$	3.96648	−	33.8694i	0.171007	−	1.46022i
$539$		0			0
$540$	2.37420	−	9.99751i	0.102169	−	0.430224i
$541$	−18.4840	−	18.4840i	−0.794689	−	0.794689i	0.187564	−	0.982252i	$-0.439941\pi$
$541$	−18.4840	−	18.4840i	−0.794689	−	0.794689i	−0.982252	+	0.187564i	$0.939941\pi$
$542$	10.5031	−	8.30096i	0.451148	−	0.356557i
$543$			22.0896i			0.947953i
$544$	−2.65949	−	12.9533i	−0.114025	−	0.555370i
$545$		−	10.5310i		−	0.451100i
$546$		0			0
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.0200929	+	0.999798i	$0.506396\pi$
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.999798	+	0.0200929i	$0.993604\pi$
$548$	−4.90777	−	1.16549i	−0.209649	−	0.0497873i
$549$	36.8222	+	36.8222i	1.57153	+	1.57153i
$550$	1.30549	−	11.1475i	0.0556663	−	0.475330i
$551$		−	10.0103i		−	0.426452i
$552$	−5.75665	+	15.7832i	−0.245020	+	0.671777i
$553$		0			0
$554$	1.92910	−	16.4724i	0.0819595	−	0.699845i
$555$	−6.19220	−	6.19220i	−0.262844	−	0.262844i
$556$	8.90832	+	14.4571i	0.377797	+	0.613118i
$557$	30.4684	+	30.4684i	1.29099	+	1.29099i	0.934178	+	0.356809i	$0.116135\pi$
$557$	30.4684	+	30.4684i	1.29099	+	1.29099i	0.356809	+	0.934178i	$0.383865\pi$
$558$	−24.6767	−	31.2232i	−1.04465	−	1.32178i
$559$	44.3401			1.87539
$560$		0			0
$561$	8.74052			0.369025
$562$	−4.90638	−	6.20800i	−0.206963	−	0.261869i
$563$	6.30834	+	6.30834i	0.265865	+	0.265865i	0.827431	−	0.561567i	$-0.189801\pi$
$563$	6.30834	+	6.30834i	0.265865	+	0.265865i	−0.561567	+	0.827431i	$0.689801\pi$
$564$	12.4847	−	7.69297i	0.525703	−	0.323932i
$565$	−26.3905	−	26.3905i	−1.11026	−	1.11026i
$566$	−0.631056	+	5.38854i	−0.0265253	+	0.226497i
$567$		0			0
$568$	−8.93237	−	19.1893i	−0.374794	−	0.805164i
$569$			6.34568i			0.266025i	0.991114	+	0.133012i	$0.0424650\pi$
$569$			6.34568i			0.266025i	−0.991114	+	0.133012i	$0.957535\pi$
$570$	−6.24329	+	53.3110i	−0.261503	+	2.23295i
$571$	−26.5416	−	26.5416i	−1.11073	−	1.11073i	−0.993052	−	0.117680i	$-0.962454\pi$
$571$	−26.5416	−	26.5416i	−1.11073	−	1.11073i	−0.117680	−	0.993052i	$-0.537546\pi$
$572$	2.95715	−	12.4523i	0.123645	−	0.520655i
$573$	27.6637	−	27.6637i	1.15567	−	1.15567i
$574$		0			0
$575$			12.6074i			0.525765i
$576$	−22.1444	−	18.6323i	−0.922684	−	0.776346i
$577$			1.89263i			0.0787913i	0.999224	+	0.0393957i	$0.0125433\pi$
$577$			1.89263i			0.0787913i	−0.999224	+	0.0393957i	$0.987457\pi$
$578$	−12.7990	+	10.1155i	−0.532370	+	0.420749i
$579$	40.8901	+	40.8901i	1.69934	+	1.69934i
$580$	13.8098	+	3.27954i	0.573421	+	0.136175i
$581$		0			0
$582$	−2.48199	+	21.1935i	−0.102882	+	0.878500i
$583$	−16.6917			−0.691299
$584$	−13.4929	−	28.9866i	−0.558340	−	1.19947i
$585$		−	51.5105i		−	2.12970i
$586$	19.3623	+	2.26754i	0.799849	+	0.0936711i
$587$	−26.8519	+	26.8519i	−1.10830	+	1.10830i	−0.114923	+	0.993374i	$0.536662\pi$
$587$	−26.8519	+	26.8519i	−1.10830	+	1.10830i	−0.993374	+	0.114923i	$0.963338\pi$
$588$		0			0
$589$	25.0931	+	25.0931i	1.03394	+	1.03394i
$590$	14.0199	−	11.0804i	0.577191	−	0.456173i
$591$	−30.2529			−1.24444
$592$	−3.99770	+	1.32071i	−0.164304	+	0.0542808i
$593$		−	27.5841i		−	1.13274i	−0.824150	−	0.566372i	$-0.808347\pi$
$593$		−	27.5841i		−	1.13274i	0.824150	−	0.566372i	$-0.191653\pi$
$594$	2.56190	−	2.02475i	0.105116	−	0.0830765i
$595$		0			0
$596$	8.91628	+	14.4700i	0.365225	+	0.592716i
$597$	18.5904	−	18.5904i	0.760854	−	0.760854i
$598$	−1.67221	+	14.2789i	−0.0683819	+	0.583907i
$599$	23.6202			0.965095			0.482548	−	0.875870i	$-0.339712\pi$
$599$	23.6202			0.965095			0.482548	+	0.875870i	$0.339712\pi$
$600$	−37.3229	−	13.6129i	−1.52370	−	0.555744i
$601$	−5.61717			−0.229129			−0.114565	−	0.993416i	$-0.536547\pi$
$601$	−5.61717			−0.229129			−0.114565	+	0.993416i	$0.536547\pi$
$602$		0			0
$603$	−6.87508	−	6.87508i	−0.279975	−	0.279975i
$604$	−4.73129	+	19.9230i	−0.192513	+	0.810655i
$605$	−20.3247	+	20.3247i	−0.826317	+	0.826317i
$606$	3.25645	+	4.12036i	0.132284	+	0.167378i
$607$	−4.86562			−0.197489			−0.0987446	−	0.995113i	$-0.531483\pi$
$607$	−4.86562			−0.197489			−0.0987446	+	0.995113i	$0.531483\pi$
$608$	21.5445	+	14.2047i	0.873746	+	0.576078i
$609$		0			0
$610$	51.6558	−	40.8253i	2.09148	−	1.65297i
$611$	8.87345	−	8.87345i	0.358981	−	0.358981i
$612$	3.90775	−	16.4551i	0.157961	−	0.665160i
$613$	−2.92168	+	2.92168i	−0.118006	+	0.118006i	−0.763644	−	0.645638i	$-0.776592\pi$
$613$	−2.92168	+	2.92168i	−0.118006	+	0.118006i	0.645638	+	0.763644i	$0.276592\pi$
$614$	−40.8676	−	4.78604i	−1.64928	−	0.193149i
$615$		−	23.0635i		−	0.930010i
$616$		0			0
$617$		−	25.3025i		−	1.01864i	−0.860578	−	0.509319i	$-0.829897\pi$
$617$		−	25.3025i		−	1.01864i	0.860578	−	0.509319i	$-0.170103\pi$
$618$	−1.02676	+	8.76739i	−0.0413022	+	0.352676i
$619$	−12.9870	+	12.9870i	−0.521990	+	0.521990i	−0.918172	−	0.396182i	$-0.870335\pi$
$619$	−12.9870	+	12.9870i	−0.521990	+	0.521990i	0.396182	+	0.918172i	$0.370335\pi$
$620$	−42.8385	+	26.3966i	−1.72044	+	1.06011i
$621$	−2.59367	+	2.59367i	−0.104080	+	0.104080i
$622$	0.501488	+	0.634528i	0.0201078	+	0.0254423i
$623$		0			0
$624$	−40.4656	−	20.3681i	−1.61992	−	0.815378i
$625$	22.4876			0.899505
$626$	−1.56951	+	1.24043i	−0.0627302	+	0.0495777i
$627$	−12.0613	+	12.0613i	−0.481680	+	0.481680i
$628$	−15.4042	−	24.9991i	−0.614694	−	0.997574i
$629$	−1.73981	−	1.73981i	−0.0693707	−	0.0693707i
$630$		0			0
$631$	−41.4293			−1.64928			−0.824638	−	0.565661i	$-0.808621\pi$
$631$	−41.4293			−1.64928			−0.824638	+	0.565661i	$0.808621\pi$
$632$	−2.09253	+	0.974048i	−0.0832365	+	0.0387455i
$633$	20.8736			0.829653
$634$	−36.7778	−	4.30709i	−1.46063	−	0.171056i
$635$	−10.2731	+	10.2731i	−0.407677	+	0.407677i
$636$	−13.6513	+	57.4842i	−0.541308	+	2.27940i
$637$		0			0
$638$	2.79684	+	3.53881i	0.110728	+	0.140103i
$639$		−	27.0716i		−	1.07094i
$640$	−26.6547	+	25.0683i	−1.05362	+	0.990913i
$641$	34.1867			1.35029			0.675146	−	0.737684i	$-0.264080\pi$
$641$	34.1867			1.35029			0.675146	+	0.737684i	$0.264080\pi$
$642$	−10.1531	−	12.8467i	−0.400712	−	0.507017i
$643$	3.46526	+	3.46526i	0.136657	+	0.136657i	0.772126	−	0.635469i	$-0.219193\pi$
$643$	3.46526	+	3.46526i	0.136657	+	0.136657i	−0.635469	+	0.772126i	$0.719193\pi$
$644$		0			0
$645$	59.2493	−	59.2493i	2.33294	−	2.33294i
$646$	−1.75416	+	14.9787i	−0.0690166	+	0.589327i
$647$		−	31.5107i		−	1.23881i	−0.785071	−	0.619406i	$-0.787373\pi$
$647$		−	31.5107i		−	1.23881i	0.785071	−	0.619406i	$-0.212627\pi$
$648$	8.07609	+	17.3497i	0.317259	+	0.681562i
$649$	5.67878			0.222912
$650$	−33.7656	−	3.95433i	−1.32440	−	0.155101i
$651$		0			0
$652$	24.1188	+	39.1418i	0.944563	+	1.53291i
$653$	−14.1761	−	14.1761i	−0.554752	−	0.554752i	0.373057	−	0.927809i	$-0.378310\pi$
$653$	−14.1761	−	14.1761i	−0.554752	−	0.554752i	−0.927809	+	0.373057i	$0.878310\pi$
$654$	−7.34511	−	9.29370i	−0.287217	−	0.363412i
$655$			44.7373i			1.74803i
$656$	−9.90447	−	4.98536i	−0.386705	−	0.194646i
$657$		−	40.8933i		−	1.59540i
$658$		0			0
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.157643	−	0.987496i	$-0.449610\pi$
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.987496	−	0.157643i	$-0.0503896\pi$
$660$	−12.6878	−	20.5908i	−0.493872	−	0.801494i
$661$	−34.2922	−	34.2922i	−1.33381	−	1.33381i	−0.901932	−	0.431878i	$-0.857851\pi$
$661$	−34.2922	−	34.2922i	−1.33381	−	1.33381i	−0.431878	−	0.901932i	$-0.642149\pi$
$662$	3.94629	+	0.462153i	0.153377	+	0.0179621i
$663$		−	26.4750i		−	1.02820i
$664$	3.63603	−	9.96901i	0.141105	−	0.386873i
$665$		0			0
$666$	−5.34827	−	0.626340i	−0.207241	−	0.0242702i
$667$	−3.58270	−	3.58270i	−0.138723	−	0.138723i
$668$	7.43520	+	1.76570i	0.287677	+	0.0683171i
$669$	−31.8196	−	31.8196i	−1.23022	−	1.23022i
$670$	−9.64467	+	7.62250i	−0.372606	+	0.294483i
$671$	20.9232			0.807733
$672$		0			0
$673$	11.6457			0.448909			0.224454	−	0.974485i	$-0.427940\pi$
$673$	11.6457			0.448909			0.224454	+	0.974485i	$0.427940\pi$
$674$	26.5405	−	20.9758i	1.02230	−	0.807959i
$675$	−6.13331	−	6.13331i	−0.236071	−	0.236071i
$676$	−12.4214	−	2.94981i	−0.477745	−	0.113454i
$677$	23.8819	+	23.8819i	0.917856	+	0.917856i	0.996873	−	0.0790174i	$-0.0251783\pi$
$677$	23.8819	+	23.8819i	0.917856	+	0.917856i	−0.0790174	+	0.996873i	$0.525178\pi$
$678$	−41.6964	−	4.88310i	−1.60134	−	0.187534i
$679$		0			0
$680$	−20.0893	−	7.32725i	−0.770391	−	0.280987i
$681$			45.0857i			1.72769i
$682$	−15.8818	−	1.85993i	−0.608146	−	0.0712205i
$683$	4.81294	+	4.81294i	0.184162	+	0.184162i	0.793167	−	0.609005i	$-0.208431\pi$
$683$	4.81294	+	4.81294i	0.184162	+	0.184162i	−0.609005	+	0.793167i	$0.708431\pi$
$684$	17.3144	+	28.0992i	0.662034	+	1.07440i
$685$	−5.76794	+	5.76794i	−0.220382	+	0.220382i
$686$		0			0
$687$			17.9827i			0.686081i
$688$	−12.6370	−	38.2515i	−0.481782	−	1.45832i
$689$			50.5591i			1.92615i
$690$	16.8456	+	21.3146i	0.641302	+	0.811433i
$691$	21.7818	+	21.7818i	0.828617	+	0.828617i	0.987325	−	0.158709i	$-0.0507330\pi$
$691$	21.7818	+	21.7818i	0.828617	+	0.828617i	−0.158709	+	0.987325i	$0.550733\pi$
$692$	8.72214	+	14.1550i	0.331566	+	0.538091i
$693$		0			0
$694$	17.5683	+	2.05744i	0.666884	+	0.0780994i
$695$	27.4606			1.04164
$696$	14.4746	−	6.73777i	0.548660	−	0.255394i
$697$		−	6.48009i		−	0.245451i
$698$	5.09830	−	43.5340i	0.192974	−	1.64779i
$699$	52.7060	−	52.7060i	1.99352	−	1.99352i
$700$		0			0
$701$	−28.2191	−	28.2191i	−1.06582	−	1.06582i	−0.997675	−	0.0681440i	$-0.978292\pi$
$701$	−28.2191	−	28.2191i	−1.06582	−	1.06582i	−0.0681440	−	0.997675i	$-0.521708\pi$
$702$	−6.13296	−	7.75998i	−0.231474	−	0.292881i
$703$	4.80161			0.181096
$704$	−11.5851	+	0.997839i	−0.436632	+	0.0376075i
$705$		−	23.7142i		−	0.893129i
$706$	−18.4269	−	23.3153i	−0.693504	−	0.877484i
$707$		0			0
$708$	4.64439	−	19.5571i	0.174547	−	0.734999i
$709$	−13.6018	+	13.6018i	−0.510828	+	0.510828i	−0.914780	−	0.403952i	$-0.867636\pi$
$709$	−13.6018	+	13.6018i	−0.510828	+	0.510828i	0.403952	+	0.914780i	$0.367636\pi$
$710$	−33.9960	−	3.98130i	−1.27585	−	0.149415i
$711$	−2.95208			−0.110711
$712$	−5.75191	−	12.3567i	−0.215562	−	0.463088i
$713$	17.9618			0.672673
$714$		0			0
$715$	−14.6347	−	14.6347i	−0.547308	−	0.547308i
$716$	20.2733	+	32.9011i	0.757648	+	1.22957i
$717$	24.2996	−	24.2996i	0.907484	−	0.907484i
$718$	10.6140	−	8.38857i	0.396110	−	0.313059i
$719$	23.8578			0.889746			0.444873	−	0.895594i	$-0.353249\pi$
$719$	23.8578			0.889746			0.444873	+	0.895594i	$0.353249\pi$
$720$	−44.4372	+	14.6806i	−1.65608	+	0.547114i
$721$		0			0
$722$	−1.58776	−	2.00897i	−0.0590902	−	0.0747662i
$723$	22.1614	−	22.1614i	0.824191	−	0.824191i
$724$	14.6210	−	9.00933i	0.543387	−	0.334829i
$725$	8.47209	−	8.47209i	0.314646	−	0.314646i
$726$	−3.76074	+	32.1126i	−0.139574	+	1.19181i
$727$		−	28.5645i		−	1.05940i	−0.848185	−	0.529700i	$-0.822305\pi$
$727$		−	28.5645i		−	1.05940i	0.848185	−	0.529700i	$-0.177695\pi$
$728$		0			0
$729$			36.7360i			1.36059i
$730$	−51.3530	−	6.01399i	−1.90066	−	0.222588i
$731$	16.6471	−	16.6471i	0.615717	−	0.615717i
$732$	17.1120	−	72.0571i	0.632480	−	2.66331i
$733$	−16.5137	+	16.5137i	−0.609949	+	0.609949i	−0.942933	−	0.332984i	$-0.891945\pi$
$733$	−16.5137	+	16.5137i	−0.609949	+	0.609949i	0.332984	+	0.942933i	$0.391945\pi$
$734$	6.79708	−	5.37196i	0.250885	−	0.198283i
$735$		0			0
$736$	12.7947	−	2.62692i	0.471620	−	0.0968297i
$737$	−3.90658			−0.143901
$738$	−8.79365	−	11.1265i	−0.323699	−	0.409573i
$739$	−1.25933	+	1.25933i	−0.0463252	+	0.0463252i	−0.729890	−	0.683565i	$-0.760429\pi$
$739$	−1.25933	+	1.25933i	−0.0463252	+	0.0463252i	0.683565	+	0.729890i	$0.260429\pi$
$740$	−1.57309	+	6.62413i	−0.0578280	+	0.243508i
$741$	36.5335	+	36.5335i	1.34209	+	1.34209i
$742$		0			0
$743$	16.7041			0.612815			0.306407	−	0.951900i	$-0.400873\pi$
$743$	16.7041			0.612815			0.306407	+	0.951900i	$0.400873\pi$
$744$	−19.3943	+	53.1739i	−0.711030	+	1.94945i
$745$	27.4852			1.00698
$746$	2.70217	−	23.0736i	0.0989334	−	0.844784i
$747$	9.59677	−	9.59677i	0.351127	−	0.351127i
$748$	−3.56486	−	5.78534i	−0.130344	−	0.211533i
$749$		0			0
$750$	−4.24751	+	3.35695i	−0.155097	+	0.122578i
$751$		−	1.74951i		−	0.0638404i	−0.999490	−	0.0319202i	$-0.989838\pi$
$751$		−	1.74951i		−	0.0638404i	0.999490	−	0.0319202i	$-0.0101622\pi$
$752$	−10.1839	−	5.12602i	−0.371370	−	0.186927i
$753$	24.3356			0.886837
$754$	10.7190	−	8.47161i	0.390365	−	0.308518i
$755$	23.4148	+	23.4148i	0.852153	+	0.852153i
$756$		0			0
$757$	−15.6771	+	15.6771i	−0.569792	+	0.569792i	−0.932070	−	0.362278i	$-0.881999\pi$
$757$	−15.6771	+	15.6771i	−0.569792	+	0.569792i	0.362278	+	0.932070i	$0.381999\pi$
$758$	−12.0229	−	1.40801i	−0.436691	−	0.0511413i
$759$			8.63350i			0.313376i
$760$	37.8328	−	17.6107i	1.37234	−	0.638807i
$761$	−51.9629			−1.88365			−0.941826	−	0.336100i	$-0.890892\pi$
$761$	−51.9629			−1.88365			−0.941826	+	0.336100i	$0.890892\pi$
$762$	−1.90087	+	16.2314i	−0.0688612	+	0.588000i
$763$		0			0
$764$	−29.5934	−	7.02780i	−1.07065	−	0.254257i
$765$	−19.3392	−	19.3392i	−0.699210	−	0.699210i
$766$	−21.3924	+	16.9071i	−0.772938	+	0.610878i
$767$		−	17.2010i		−	0.621092i
$768$	−6.03846	+	40.7139i	−0.217894	+	1.46914i
$769$			34.9699i			1.26105i	0.776170	+	0.630524i	$0.217160\pi$
$769$			34.9699i			1.26105i	−0.776170	+	0.630524i	$0.782840\pi$
$770$		0			0
$771$	−6.99090	+	6.99090i	−0.251771	+	0.251771i
$772$	10.3879	−	43.7423i	0.373868	−	1.57432i
$773$	9.72110	+	9.72110i	0.349644	+	0.349644i	0.859977	−	0.510333i	$-0.170478\pi$
$773$	9.72110	+	9.72110i	0.349644	+	0.349644i	−0.510333	+	0.859977i	$0.670478\pi$
$774$	5.99306	−	51.1742i	0.215416	−	1.83942i
$775$			42.4746i			1.52573i
$776$	15.0403	−	7.00106i	0.539914	−	0.251323i
$777$		0			0
$778$	−4.70834	+	40.2041i	−0.168802	+	1.44139i
$779$	8.94204	+	8.94204i	0.320382	+	0.320382i
$780$	−62.3693	+	38.4313i	−2.23318	+	1.37606i
$781$	−7.69136	−	7.69136i	−0.275219	−	0.275219i
$782$	4.73307	+	5.98871i	0.169254	+	0.214156i
$783$	3.48586			0.124574
$784$		0			0
$785$	−47.4847			−1.69480
$786$	31.2031	+	39.4809i	1.11298	+	1.40824i
$787$	−17.5555	−	17.5555i	−0.625785	−	0.625785i	0.321220	−	0.947005i	$-0.395907\pi$
$787$	−17.5555	−	17.5555i	−0.625785	−	0.625785i	−0.947005	+	0.321220i	$0.895907\pi$
$788$	12.3388	+	20.0244i	0.439552	+	0.713339i
$789$	−11.4882	−	11.4882i	−0.408991	−	0.408991i
$790$	−0.434148	+	3.70716i	−0.0154463	+	0.131895i
$791$		0			0
$792$	−13.9718	−	5.09599i	−0.496467	−	0.181078i
$793$		−	63.3764i		−	2.25056i
$794$	−1.52553	+	13.0264i	−0.0541391	+	0.462289i
$795$	67.5593	+	67.5593i	2.39608	+	2.39608i
$796$	−19.8871	−	4.72277i	−0.704881	−	0.167394i
$797$	13.3302	−	13.3302i	0.472179	−	0.472179i	−0.430440	−	0.902619i	$-0.641642\pi$
$797$	13.3302	−	13.3302i	0.472179	−	0.472179i	0.902619	+	0.430440i	$0.141642\pi$
$798$		0			0
$799$		−	6.66293i		−	0.235717i
$800$	6.21195	+	30.2560i	0.219626	+	1.06971i
$801$		−	17.4325i		−	0.615946i
$802$	38.8959	−	30.7407i	1.37346	−	1.08549i
$803$	−11.6183	−	11.6183i	−0.410000	−	0.410000i
$804$	−3.19499	+	13.4538i	−0.112679	+	0.474479i
$805$		0			0
$806$	−5.63373	+	48.1059i	−0.198440	+	1.69446i
$807$	−62.0296			−2.18355
$808$	1.39910	−	3.83595i	0.0492201	−	0.134948i
$809$			21.6623i			0.761605i	0.924656	+	0.380803i	$0.124352\pi$
$809$			21.6623i			0.761605i	−0.924656	+	0.380803i	$0.875648\pi$
$810$	30.7370	+	3.59964i	1.07999	+	0.126478i
$811$	1.51326	−	1.51326i	0.0531379	−	0.0531379i	−0.680039	−	0.733176i	$-0.738037\pi$
$811$	1.51326	−	1.51326i	0.0531379	−	0.0531379i	0.733176	+	0.680039i	$0.238037\pi$
$812$		0			0
$813$	−17.2192	−	17.2192i	−0.603904	−	0.603904i
$814$	−1.69746	+	1.34156i	−0.0594958	+	0.0470215i
$815$	74.3481			2.60430
$816$	−22.8395	+	7.54543i	−0.799543	+	0.264143i
$817$			45.9436i			1.60736i
$818$	38.6986	−	30.5848i	1.35307	−	1.06937i
$819$		0			0
$820$	−15.2657	+	9.40655i	−0.533101	+	0.328491i
$821$	33.9360	−	33.9360i	1.18437	−	1.18437i	0.205774	−	0.978599i	$-0.434029\pi$
$821$	33.9360	−	33.9360i	1.18437	−	1.18437i	0.978599	−	0.205774i	$-0.0659713\pi$
$822$	−1.06726	+	9.11323i	−0.0372249	+	0.317860i
$823$	30.0816			1.04858			0.524290	−	0.851540i	$-0.324331\pi$
$823$	30.0816			1.04858			0.524290	+	0.851540i	$0.324331\pi$
$824$	6.22189	−	2.89621i	0.216750	−	0.100894i
$825$	−20.4158			−0.710789
$826$		0			0
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	0.980739	−	0.195325i	$-0.0625760\pi$
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	−0.195325	+	0.980739i	$0.562576\pi$
$828$	16.2537	+	3.85990i	0.564854	+	0.134141i
$829$	23.4068	−	23.4068i	0.812951	−	0.812951i	−0.172125	−	0.985075i	$-0.555063\pi$
$829$	23.4068	−	23.4068i	0.812951	−	0.812951i	0.985075	+	0.172125i	$0.0550632\pi$
$830$	−10.6401	−	13.4628i	−0.369322	−	0.467300i
$831$	−30.1681			−1.04652
$832$	3.02245	+	35.0914i	0.104785	+	1.21657i
$833$		0			0
$834$	24.2342	−	19.1531i	0.839161	−	0.663216i
$835$	8.73836	−	8.73836i	0.302403	−	0.302403i
$836$	12.9026	+	3.06409i	0.446244	+	0.105974i
$837$	−8.73812	+	8.73812i	−0.302034	+	0.302034i
$838$	17.0401	+	1.99558i	0.588640	+	0.0689362i
$839$		−	35.7894i		−	1.23559i	−0.786340	−	0.617794i	$-0.788027\pi$
$839$		−	35.7894i		−	1.23559i	0.786340	−	0.617794i	$-0.211973\pi$
$840$		0			0
$841$		−	24.1849i		−	0.833962i
$842$	1.72423	−	14.7230i	0.0594208	−	0.507389i
$843$	−10.1776	+	10.1776i	−0.350536	+	0.350536i
$844$	−8.51341	−	13.8162i	−0.293044	−	0.475574i
$845$	−14.5984	+	14.5984i	−0.502201	+	0.502201i
$846$	−9.04176	−	11.4404i	−0.310862	−	0.393331i
$847$		0			0
$848$	43.6164	−	14.4094i	1.49779	−	0.494822i
$849$	9.86874			0.338694
$850$	−14.1617	+	11.1924i	−0.485741	+	0.383897i
$851$	1.71851	−	1.71851i	0.0589096	−	0.0589096i
$852$	−32.7785	+	20.1978i	−1.12297	+	0.691964i
$853$	−1.27195	−	1.27195i	−0.0435507	−	0.0435507i	0.684996	−	0.728547i	$-0.259804\pi$
$853$	−1.27195	−	1.27195i	−0.0435507	−	0.0435507i	−0.728547	+	0.684996i	$0.759804\pi$
$854$		0			0
$855$	53.3733			1.82533
$856$	−4.36218	+	11.9599i	−0.149096	+	0.408782i
$857$	−34.2754			−1.17082			−0.585412	−	0.810736i	$-0.699067\pi$
$857$	−34.2754			−1.17082			−0.585412	+	0.810736i	$0.699067\pi$
$858$	−23.1226	−	2.70791i	−0.789393	−	0.0924465i
$859$	31.6036	−	31.6036i	1.07830	−	1.07830i	0.0816404	−	0.996662i	$-0.473984\pi$
$859$	31.6036	−	31.6036i	1.07830	−	1.07830i	0.996662	−	0.0816404i	$-0.0260159\pi$
$860$	−63.3821	−	15.0519i	−2.16131	−	0.513266i
$861$		0			0
$862$	1.41390	+	1.78899i	0.0481576	+	0.0609333i
$863$			37.6268i			1.28083i	0.768028	+	0.640416i	$0.221238\pi$
$863$			37.6268i			1.28083i	−0.768028	+	0.640416i	$0.778762\pi$
$864$	−4.94649	+	7.50241i	−0.168283	+	0.255237i
$865$	26.8867			0.914176
$866$	11.4759	+	14.5203i	0.389966	+	0.493420i
$867$	20.9832	+	20.9832i	0.712627	+	0.712627i
$868$		0			0
$869$	−0.838719	+	0.838719i	−0.0284516	+	0.0284516i
$870$	3.00313	−	25.6434i	0.101816	−	0.869394i
$871$			11.8330i			0.400947i
$872$	−3.15575	+	8.65220i	−0.106867	+	0.293000i
$873$	21.2183			0.718131
$874$	−14.7952	−	1.73269i	−0.500457	−	0.0586090i
$875$		0			0
$876$	−49.5139	+	30.5100i	−1.67292	+	1.03084i
$877$	15.0158	+	15.0158i	0.507047	+	0.507047i	0.913619	−	0.406572i	$-0.133276\pi$
$877$	15.0158	+	15.0158i	0.507047	+	0.507047i	−0.406572	+	0.913619i	$0.633276\pi$
$878$	−1.73509	−	2.19539i	−0.0585564	−	0.0740908i
$879$		−	35.4607i		−	1.19606i
$880$	−8.45421	+	16.7961i	−0.284991	+	0.566196i
$881$			3.13017i			0.105458i	0.998609	+	0.0527291i	$0.0167920\pi$
$881$			3.13017i			0.105458i	−0.998609	+	0.0527291i	$0.983208\pi$
$882$		0			0
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	−0.600702	−	0.799473i	$-0.705112\pi$
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	0.799473	+	0.600702i	$0.205112\pi$
$884$	−17.5238	+	10.7980i	−0.589388	+	0.363174i
$885$	−22.9848	−	22.9848i	−0.772625	−	0.772625i
$886$	−48.7372	−	5.70765i	−1.63736	−	0.191752i
$887$			48.4630i			1.62723i	0.581405	+	0.813615i	$0.302503\pi$
$887$			48.4630i			1.62723i	−0.581405	+	0.813615i	$0.697497\pi$
$888$	3.23189	+	6.94303i	0.108455	+	0.232993i
$889$		0			0
$890$	−21.8913	−	2.56371i	−0.733799	−	0.0859359i
$891$	6.95404	+	6.95404i	0.232969	+	0.232969i
$892$	−8.08357	+	34.0391i	−0.270658	+	1.13971i
$893$	9.19433	+	9.19433i	0.307677	+	0.307677i
$894$	24.2559	−	19.1702i	0.811238	−	0.641147i
$895$	62.4941			2.08895
$896$		0			0
$897$	26.1508			0.873151
$898$	−22.2416	+	17.5783i	−0.742213	+	0.586595i
$899$	−12.0702	−	12.0702i	−0.402563	−	0.402563i
$900$	−9.12760	+	38.4354i	−0.304253	+	1.28118i
$901$	18.9820	+	18.9820i	0.632382	+	0.632382i
$902$	−5.65955	−	0.662796i	−0.188443	−	0.0220687i
$903$		0			0
$904$	13.7740	+	29.5904i	0.458115	+	0.984161i
$905$		−	27.7720i		−	0.923173i
$906$	36.9950	+	4.33252i	1.22908	+	0.143938i
$907$	−26.5002	−	26.5002i	−0.879924	−	0.879924i	0.113602	−	0.993526i	$-0.463761\pi$
$907$	−26.5002	−	26.5002i	−0.879924	−	0.879924i	−0.993526	+	0.113602i	$0.963761\pi$
$908$	29.8421	−	18.3884i	0.990346	−	0.610240i
$909$	3.69271	−	3.69271i	0.122480	−	0.122480i
$910$		0			0
$911$		−	12.0871i		−	0.400463i	−0.979749	−	0.200231i	$-0.935831\pi$
$911$		−	12.0871i		−	0.400463i	0.979749	−	0.200231i	$-0.0641694\pi$
$912$	21.1047	−	41.9289i	0.698846	−	1.38841i
$913$		−	5.45311i		−	0.180472i
$914$	−26.3121	−	33.2925i	−0.870328	−	1.10122i
$915$	−84.6865	−	84.6865i	−2.79965	−	2.79965i
$916$	11.9027	−	7.33431i	0.393276	−	0.242332i
$917$		0			0
$918$	−5.21599	−	0.610849i	−0.172153	−	0.0201610i
$919$	−55.2615			−1.82291			−0.911455	−	0.411400i	$-0.865040\pi$
$919$	−55.2615			−1.82291			−0.911455	+	0.411400i	$0.865040\pi$
$920$	7.23754	−	19.8434i	0.238614	−	0.654216i
$921$			74.8463i			2.46627i
$922$	4.24167	−	36.2192i	0.139692	−	1.19282i
$923$	−23.2971	+	23.2971i	−0.766833	+	0.766833i
$924$		0			0
$925$	4.06379	+	4.06379i	0.133617	+	0.133617i
$926$	−27.5174	−	34.8174i	−0.904277	−	1.14417i
$927$	8.77763			0.288295
$928$	−10.3633	−	6.83271i	−0.340191	−	0.224295i
$929$			9.98464i			0.327585i	0.986495	+	0.163793i	$0.0523728\pi$
$929$			9.98464i			0.327585i	−0.986495	+	0.163793i	$0.947627\pi$
$930$	56.7533	+	71.8094i	1.86101	+	2.35472i
$931$		0			0
$932$	−56.3824	−	13.3896i	−1.84687	−	0.438592i
$933$	1.04027	−	1.04027i	0.0340569	−	0.0340569i
$934$	33.4909	+	3.92215i	1.09586	+	0.128337i
$935$	−10.9890			−0.359378
$936$	−15.4357	+	42.3206i	−0.504533	+	1.38329i
$937$	7.92416			0.258871			0.129436	−	0.991588i	$-0.458683\pi$
$937$	7.92416			0.258871			0.129436	+	0.991588i	$0.458683\pi$
$938$		0			0
$939$	2.57311	+	2.57311i	0.0839703	+	0.0839703i
$940$	−15.6964	+	9.67196i	−0.511960	+	0.315464i
$941$	4.47065	−	4.47065i	0.145739	−	0.145739i	−0.630473	−	0.776212i	$-0.717139\pi$
$941$	4.47065	−	4.47065i	0.145739	−	0.145739i	0.776212	+	0.630473i	$0.217139\pi$
$942$	−41.9056	+	33.1193i	−1.36536	+	1.07909i
$943$	6.40075			0.208437
$944$	−14.8390	+	4.90232i	−0.482969	+	0.159557i
$945$		0			0
$946$	−12.8365	−	16.2419i	−0.417351	−	0.528070i
$947$	−8.04460	+	8.04460i	−0.261414	+	0.261414i	−0.825628	−	0.564214i	$-0.809179\pi$
$947$	−8.04460	+	8.04460i	−0.261414	+	0.261414i	0.564214	+	0.825628i	$0.309179\pi$
$948$	2.20250	+	3.57439i	0.0715340	+	0.116091i
$949$	−35.1917	+	35.1917i	−1.14237	+	1.14237i
$950$	4.09732	−	34.9867i	0.132935	−	1.13512i
$951$			67.3561i			2.18417i
$952$		0			0
$953$		−	12.7329i		−	0.412460i	−0.978504	−	0.206230i	$-0.933880\pi$
$953$		−	12.7329i		−	0.412460i	0.978504	−	0.206230i	$-0.0661195\pi$
$954$	58.3517	+	6.83362i	1.88920	+	0.221246i
$955$	−34.7801	+	34.7801i	−1.12546	+	1.12546i
$956$	−25.9945	−	6.17315i	−0.840723	−	0.199654i
$957$	5.80166	−	5.80166i	0.187541	−	0.187541i
$958$	39.2294	−	31.0042i	1.26744	−	1.00170i
$959$		0			0
$960$	50.9294	+	42.8519i	1.64374	+	1.38304i
$961$	29.5136			0.952050
$962$	4.06356	+	5.14159i	0.131015	+	0.165771i
$963$	−11.5133	+	11.5133i	−0.371012	+	0.371012i
$964$	−23.7072	−	5.62996i	−0.763558	−	0.181329i
$965$	−51.4090	−	51.4090i	−1.65491	−	1.65491i
$966$		0			0
$967$	−10.6644			−0.342944			−0.171472	−	0.985189i	$-0.554852\pi$
$967$	−10.6644			−0.342944			−0.171472	+	0.985189i	$0.554852\pi$
$968$	22.7891	−	10.6081i	0.732471	−	0.340956i
$969$	27.4324			0.881255
$970$	3.12048	−	26.6455i	0.100193	−	0.855536i
$971$	−1.62971	+	1.62971i	−0.0523000	+	0.0523000i	−0.732773	−	0.680473i	$-0.761774\pi$
$971$	−1.62971	+	1.62971i	−0.0523000	+	0.0523000i	0.680473	+	0.732773i	$0.261774\pi$
$972$	37.7509	−	23.2617i	1.21086	−	0.746119i
$973$		0			0
$974$	11.7866	−	9.31532i	0.377666	−	0.298482i
$975$			61.8395i			1.98045i
$976$	−54.6737	+	18.0624i	−1.75006	+	0.578164i
$977$	−15.3255			−0.490305			−0.245153	−	0.969484i	$-0.578838\pi$
$977$	−15.3255			−0.490305			−0.245153	+	0.969484i	$0.578838\pi$
$978$	65.6127	−	51.8558i	2.09806	−	1.65817i
$979$	−4.95277	−	4.95277i	−0.158291	−	0.158291i
$980$		0			0
$981$	−8.32913	+	8.32913i	−0.265929	+	0.265929i
$982$	−53.4523	−	6.25985i	−1.70573	−	0.199760i
$983$		−	18.6119i		−	0.593628i	−0.954935	−	0.296814i	$-0.904076\pi$
$983$		−	18.6119i		−	0.593628i	0.954935	−	0.296814i	$-0.0959241\pi$
$984$	−6.91125	+	18.9488i	−0.220323	+	0.604064i
$985$	38.0354			1.21191
$986$	0.843782	−	7.20498i	0.0268715	−	0.229453i
$987$		0			0
$988$	9.28110	−	39.0818i	0.295271	−	1.24336i
$989$	16.4433	+	16.4433i	0.522867	+	0.522867i
$990$	−18.8684	+	14.9123i	−0.599678	+	0.473945i
$991$			27.4305i			0.871359i	0.900102	+	0.435680i	$0.143492\pi$
$991$			27.4305i			0.871359i	−0.900102	+	0.435680i	$0.856508\pi$
$992$	43.1058	−	8.85017i	1.36861	−	0.280993i
$993$		−	7.22736i		−	0.229353i
$994$		0			0
$995$	−23.3727	+	23.3727i	−0.740965	+	0.740965i
$996$	−18.7799	−	4.45982i	−0.595063	−	0.141315i
$997$	−13.7329	−	13.7329i	−0.434926	−	0.434926i	0.455374	−	0.890300i	$-0.349505\pi$
$997$	−13.7329	−	13.7329i	−0.434926	−	0.434926i	−0.890300	+	0.455374i	$0.849505\pi$
$998$	−2.08516	+	17.8050i	−0.0660046	+	0.563607i
$999$			1.67206i			0.0529015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.6		56
7.2	even	3		112.2.v.a.3.13	✓	56
7.3	odd	6		112.2.v.a.19.7	yes	56
7.4	even	3		784.2.w.f.19.7		56
7.5	odd	6		784.2.w.f.227.13		56
7.6	odd	2	inner	784.2.j.a.195.5		56
16.11	odd	4	inner	784.2.j.a.587.5		56
28.3	even	6		448.2.z.a.47.12		56
28.23	odd	6		448.2.z.a.367.12		56
56.3	even	6		896.2.z.a.607.3		56
56.37	even	6		896.2.z.b.479.12		56
56.45	odd	6		896.2.z.b.607.12		56
56.51	odd	6		896.2.z.a.479.3		56
112.3	even	12		896.2.z.b.159.12		56
112.11	odd	12		784.2.w.f.411.13		56
112.27	even	4	inner	784.2.j.a.587.6		56
112.37	even	12		448.2.z.a.143.12		56
112.45	odd	12		896.2.z.a.159.3		56
112.51	odd	12		896.2.z.b.31.12		56
112.59	even	12		112.2.v.a.75.13	yes	56
112.75	even	12		784.2.w.f.619.7		56
112.93	even	12		896.2.z.a.31.3		56
112.101	odd	12		448.2.z.a.271.12		56
112.107	odd	12		112.2.v.a.59.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	7.2	even	3
112.2.v.a.19.7	yes	56	7.3	odd	6
112.2.v.a.59.7	yes	56	112.107	odd	12
112.2.v.a.75.13	yes	56	112.59	even	12
448.2.z.a.47.12		56	28.3	even	6
448.2.z.a.143.12		56	112.37	even	12
448.2.z.a.271.12		56	112.101	odd	12
448.2.z.a.367.12		56	28.23	odd	6
784.2.j.a.195.5		56	7.6	odd	2	inner
784.2.j.a.195.6		56	1.1	even	1	trivial
784.2.j.a.587.5		56	16.11	odd	4	inner
784.2.j.a.587.6		56	112.27	even	4	inner
784.2.w.f.19.7		56	7.4	even	3
784.2.w.f.227.13		56	7.5	odd	6
784.2.w.f.411.13		56	112.11	odd	12
784.2.w.f.619.7		56	112.75	even	12
896.2.z.a.31.3		56	112.93	even	12
896.2.z.a.159.3		56	112.45	odd	12
896.2.z.a.479.3		56	56.51	odd	6
896.2.z.a.607.3		56	56.3	even	6
896.2.z.b.31.12		56	112.51	odd	12
896.2.z.b.159.12		56	112.3	even	12
896.2.z.b.479.12		56	56.37	even	6
896.2.z.b.607.12		56	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-1.10953 + 0.876896i) q^{2} +(1.81900 + 1.81900i) q^{3} +(0.462106 - 1.94588i) q^{4} +(-2.28693 - 2.28693i) q^{5} +(-3.61331 - 0.423158i) q^{6} +(1.19362 + 2.56423i) q^{8} +3.61753i q^{9} +(4.54282 + 0.532014i) q^{10} +(1.02778 + 1.02778i) q^{11} +(4.38013 - 2.69899i) q^{12} +(3.11315 - 3.11315i) q^{13} -8.31987i q^{15} +(-3.57292 - 1.79841i) q^{16} -2.33761i q^{17} +(-3.17220 - 4.01375i) q^{18} +(3.22573 + 3.22573i) q^{19} +(-5.50691 + 3.39330i) q^{20} +(-2.04161 - 0.239095i) q^{22} +2.30899 q^{23} +(-2.49315 + 6.83553i) q^{24} +5.46013i q^{25} +(-0.724218 + 6.18404i) q^{26} +(-1.12329 + 1.12329i) q^{27} +(-1.55163 - 1.55163i) q^{29} +(7.29566 + 9.23113i) q^{30} +7.77905 q^{31} +(5.54127 - 1.13769i) q^{32} +3.73908i q^{33} +(2.04984 + 2.59365i) q^{34} +(7.03929 + 1.67168i) q^{36} +(0.744267 - 0.744267i) q^{37} +(-6.40767 - 0.750408i) q^{38} +11.3256 q^{39} +(3.13450 - 8.59395i) q^{40} +2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(2.47489 - 1.52500i) q^{44} +(8.27305 - 8.27305i) q^{45} +(-2.56189 + 2.02475i) q^{46} +2.85031 q^{47} +(-3.22783 - 9.77044i) q^{48} +(-4.78797 - 6.05817i) q^{50} +(4.25212 - 4.25212i) q^{51} +(-4.61922 - 7.49643i) q^{52} +(-8.12024 + 8.12024i) q^{53} +(0.261313 - 2.23133i) q^{54} -4.70094i q^{55} +11.7352i q^{57} +(3.08219 + 0.360958i) q^{58} +(2.76264 - 2.76264i) q^{59} +(-16.1895 - 3.84466i) q^{60} +(10.1788 - 10.1788i) q^{61} +(-8.63107 + 6.82142i) q^{62} +(-5.15056 + 6.12142i) q^{64} -14.2391 q^{65} +(-3.27878 - 4.14861i) q^{66} +(-1.90049 + 1.90049i) q^{67} +(-4.54872 - 1.08023i) q^{68} +(4.20006 + 4.20006i) q^{69} -7.48345 q^{71} +(-9.27618 + 4.31795i) q^{72} -11.3042 q^{73} +(-0.173140 + 1.47843i) q^{74} +(-9.93198 + 9.93198i) q^{75} +(7.76752 - 4.78626i) q^{76} +(-12.5661 + 9.93142i) q^{78} +0.816047i q^{79} +(4.05818 + 12.2839i) q^{80} +6.76606 q^{81} +(-3.07572 + 2.43084i) q^{82} +(-2.65285 - 2.65285i) q^{83} +(-5.34597 + 5.34597i) q^{85} +(-14.1462 - 1.65667i) q^{86} -5.64483i q^{87} +(-1.40869 + 3.86225i) q^{88} -4.81889 q^{89} +(-1.92458 + 16.4338i) q^{90} +(1.06700 - 4.49303i) q^{92} +(14.1501 + 14.1501i) q^{93} +(-3.16250 + 2.49943i) q^{94} -14.7541i q^{95} +(12.1490 + 8.01011i) q^{96} -5.86541i q^{97} +(-3.71804 + 3.71804i) 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

Groups

Database

Properties

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