LMFDB - Embedded newform 882.2.l.c.227.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.13
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.71914 - 0.211098i) q^{3} -1.00000 q^{4} +(0.584859 - 1.01301i) q^{5} +(0.211098 - 1.71914i) q^{6} -1.00000i q^{8} +(2.91088 + 0.725813i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.71914 - 0.211098i) q^{3} -1.00000 q^{4} +(0.584859 - 1.01301i) q^{5} +(0.211098 - 1.71914i) q^{6} -1.00000i q^{8} +(2.91088 + 0.725813i) q^{9} +(1.01301 + 0.584859i) q^{10} +(-4.99209 + 2.88218i) q^{11} +(1.71914 + 0.211098i) q^{12} +(-0.571028 + 0.329683i) q^{13} +(-1.21930 + 1.61804i) q^{15} +1.00000 q^{16} +(2.83946 - 4.91809i) q^{17} +(-0.725813 + 2.91088i) q^{18} +(3.16853 - 1.82935i) q^{19} +(-0.584859 + 1.01301i) q^{20} +(-2.88218 - 4.99209i) q^{22} +(-0.503113 - 0.290473i) q^{23} +(-0.211098 + 1.71914i) q^{24} +(1.81588 + 3.14519i) q^{25} +(-0.329683 - 0.571028i) q^{26} +(-4.85098 - 1.86225i) q^{27} +(6.53449 + 3.77269i) q^{29} +(-1.61804 - 1.21930i) q^{30} +3.17809i q^{31} +1.00000i q^{32} +(9.19051 - 3.90105i) q^{33} +(4.91809 + 2.83946i) q^{34} +(-2.91088 - 0.725813i) q^{36} +(5.29511 + 9.17140i) q^{37} +(1.82935 + 3.16853i) q^{38} +(1.05127 - 0.446228i) q^{39} +(-1.01301 - 0.584859i) q^{40} +(2.64145 + 4.57513i) q^{41} +(2.37970 - 4.12177i) q^{43} +(4.99209 - 2.88218i) q^{44} +(2.43771 - 2.52424i) q^{45} +(0.290473 - 0.503113i) q^{46} +5.34610 q^{47} +(-1.71914 - 0.211098i) q^{48} +(-3.14519 + 1.81588i) q^{50} +(-5.91962 + 7.85547i) q^{51} +(0.571028 - 0.329683i) q^{52} +(-4.14347 - 2.39223i) q^{53} +(1.86225 - 4.85098i) q^{54} +6.74269i q^{55} +(-5.83331 + 2.47604i) q^{57} +(-3.77269 + 6.53449i) q^{58} -1.02971 q^{59} +(1.21930 - 1.61804i) q^{60} +11.7011i q^{61} -3.17809 q^{62} -1.00000 q^{64} +0.771274i q^{65} +(3.90105 + 9.19051i) q^{66} +8.52200 q^{67} +(-2.83946 + 4.91809i) q^{68} +(0.803603 + 0.605569i) q^{69} +8.34154i q^{71} +(0.725813 - 2.91088i) q^{72} +(-0.899038 - 0.519060i) q^{73} +(-9.17140 + 5.29511i) q^{74} +(-2.45780 - 5.79035i) q^{75} +(-3.16853 + 1.82935i) q^{76} +(0.446228 + 1.05127i) q^{78} -1.26257 q^{79} +(0.584859 - 1.01301i) q^{80} +(7.94639 + 4.22550i) q^{81} +(-4.57513 + 2.64145i) q^{82} +(-6.21900 + 10.7716i) q^{83} +(-3.32137 - 5.75278i) q^{85} +(4.12177 + 2.37970i) q^{86} +(-10.4373 - 7.86519i) q^{87} +(2.88218 + 4.99209i) q^{88} +(-7.83957 - 13.5785i) q^{89} +(2.52424 + 2.43771i) q^{90} +(0.503113 + 0.290473i) q^{92} +(0.670889 - 5.46358i) q^{93} +5.34610i q^{94} -4.27965i q^{95} +(0.211098 - 1.71914i) q^{96} +(12.5887 + 7.26808i) q^{97} +(-16.6233 + 4.76635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.71914	−	0.211098i	−0.992545	−	0.121877i
$3$	−1.71914	−	0.211098i	−0.992545	−	0.121877i
$4$	−1.00000			−0.500000
$5$	0.584859	−	1.01301i	0.261557	−	0.453030i	−0.705099	−	0.709109i	$-0.749097\pi$
$5$	0.584859	−	1.01301i	0.261557	−	0.453030i	0.966656	+	0.256079i	$0.0824307\pi$
$6$	0.211098	−	1.71914i	0.0861804	−	0.701835i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.91088	+	0.725813i	0.970292	+	0.241938i
$10$	1.01301	+	0.584859i	0.320341	+	0.184949i
$11$	−4.99209	+	2.88218i	−1.50517	+	0.869010i	−0.505188	+	0.863009i	$0.668577\pi$
$11$	−4.99209	+	2.88218i	−1.50517	+	0.869010i	−0.999982	+	0.00600136i	$0.998090\pi$
$12$	1.71914	+	0.211098i	0.496273	+	0.0609387i
$13$	−0.571028	+	0.329683i	−0.158375	+	0.0914377i	−0.577093	−	0.816679i	$-0.695813\pi$
$13$	−0.571028	+	0.329683i	−0.158375	+	0.0914377i	0.418718	+	0.908116i	$0.362480\pi$
$14$		0			0
$15$	−1.21930	+	1.61804i	−0.314821	+	0.417775i
$16$	1.00000			0.250000
$17$	2.83946	−	4.91809i	0.688670	−	1.19281i	−0.283598	−	0.958943i	$-0.591528\pi$
$17$	2.83946	−	4.91809i	0.688670	−	1.19281i	0.972268	−	0.233868i	$-0.0751384\pi$
$18$	−0.725813	+	2.91088i	−0.171076	+	0.686100i
$19$	3.16853	−	1.82935i	0.726910	−	0.419682i	−0.0903806	−	0.995907i	$-0.528808\pi$
$19$	3.16853	−	1.82935i	0.726910	−	0.419682i	0.817291	+	0.576226i	$0.195475\pi$
$20$	−0.584859	+	1.01301i	−0.130779	+	0.226515i
$21$		0			0
$22$	−2.88218	−	4.99209i	−0.614483	−	1.06432i
$23$	−0.503113	−	0.290473i	−0.104906	−	0.0605677i	0.446629	−	0.894719i	$-0.352624\pi$
$23$	−0.503113	−	0.290473i	−0.104906	−	0.0605677i	−0.551535	+	0.834152i	$0.685958\pi$
$24$	−0.211098	+	1.71914i	−0.0430902	+	0.350918i
$25$	1.81588	+	3.14519i	0.363176	+	0.629039i
$26$	−0.329683	−	0.571028i	−0.0646562	−	0.111988i
$27$	−4.85098	−	1.86225i	−0.933572	−	0.358391i
$28$		0			0
$29$	6.53449	+	3.77269i	1.21342	+	0.700571i	0.963503	−	0.267696i	$-0.0862622\pi$
$29$	6.53449	+	3.77269i	1.21342	+	0.700571i	0.249920	+	0.968266i	$0.419596\pi$
$30$	−1.61804	−	1.21930i	−0.295412	−	0.222612i
$31$			3.17809i			0.570802i	0.958408	+	0.285401i	$0.0921268\pi$
$31$			3.17809i			0.570802i	−0.958408	+	0.285401i	$0.907873\pi$
$32$			1.00000i			0.176777i
$33$	9.19051	−	3.90105i	1.59986	−	0.679086i
$34$	4.91809	+	2.83946i	0.843445	+	0.486963i
$35$		0			0
$36$	−2.91088	−	0.725813i	−0.485146	−	0.120969i
$37$	5.29511	+	9.17140i	0.870511	+	1.50777i	0.861469	+	0.507811i	$0.169545\pi$
$37$	5.29511	+	9.17140i	0.870511	+	1.50777i	0.00904243	+	0.999959i	$0.497122\pi$
$38$	1.82935	+	3.16853i	0.296760	+	0.514003i
$39$	1.05127	−	0.446228i	0.168338	−	0.0714537i
$40$	−1.01301	−	0.584859i	−0.160170	−	0.0924744i
$41$	2.64145	+	4.57513i	0.412525	+	0.714514i	0.995165	−	0.0982159i	$-0.0313136\pi$
$41$	2.64145	+	4.57513i	0.412525	+	0.714514i	−0.582640	+	0.812730i	$0.697980\pi$
$42$		0			0
$43$	2.37970	−	4.12177i	0.362902	−	0.628564i	−0.625535	−	0.780196i	$-0.715119\pi$
$43$	2.37970	−	4.12177i	0.362902	−	0.628564i	0.988437	+	0.151632i	$0.0484528\pi$
$44$	4.99209	−	2.88218i	0.752585	−	0.434505i
$45$	2.43771	−	2.52424i	0.363392	−	0.376291i
$46$	0.290473	−	0.503113i	0.0428279	−	0.0741800i
$47$	5.34610			0.779808			0.389904	−	0.920855i	$-0.372508\pi$
$47$	5.34610			0.779808			0.389904	+	0.920855i	$0.372508\pi$
$48$	−1.71914	−	0.211098i	−0.248136	−	0.0304694i
$49$		0			0
$50$	−3.14519	+	1.81588i	−0.444798	+	0.256804i
$51$	−5.91962	+	7.85547i	−0.828913	+	1.09999i
$52$	0.571028	−	0.329683i	0.0791874	−	0.0457189i
$53$	−4.14347	−	2.39223i	−0.569150	−	0.328599i	0.187660	−	0.982234i	$-0.439910\pi$
$53$	−4.14347	−	2.39223i	−0.569150	−	0.328599i	−0.756810	+	0.653635i	$0.773243\pi$
$54$	1.86225	−	4.85098i	0.253421	−	0.660135i
$55$			6.74269i			0.909183i
$56$		0			0
$57$	−5.83331	+	2.47604i	−0.772641	+	0.327959i
$58$	−3.77269	+	6.53449i	−0.495378	+	0.858020i
$59$	−1.02971			−0.134057			−0.0670286	−	0.997751i	$-0.521352\pi$
$59$	−1.02971			−0.134057			−0.0670286	+	0.997751i	$0.521352\pi$
$60$	1.21930	−	1.61804i	0.157411	−	0.208888i
$61$			11.7011i			1.49817i	0.662474	+	0.749085i	$0.269507\pi$
$61$			11.7011i			1.49817i	−0.662474	+	0.749085i	$0.730493\pi$
$62$	−3.17809			−0.403618
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.771274i			0.0956647i
$66$	3.90105	+	9.19051i	0.480186	+	1.13127i
$67$	8.52200			1.04113			0.520564	−	0.853822i	$-0.325722\pi$
$67$	8.52200			1.04113			0.520564	+	0.853822i	$0.325722\pi$
$68$	−2.83946	+	4.91809i	−0.344335	+	0.596406i
$69$	0.803603	+	0.605569i	0.0967425	+	0.0729019i
$70$		0			0
$71$			8.34154i			0.989959i	0.868905	+	0.494979i	$0.164824\pi$
$71$			8.34154i			0.989959i	−0.868905	+	0.494979i	$0.835176\pi$
$72$	0.725813	−	2.91088i	0.0855379	−	0.343050i
$73$	−0.899038	−	0.519060i	−0.105224	−	0.0607514i	0.446464	−	0.894801i	$-0.352683\pi$
$73$	−0.899038	−	0.519060i	−0.105224	−	0.0607514i	−0.551689	+	0.834050i	$0.686016\pi$
$74$	−9.17140	+	5.29511i	−1.06615	+	0.615544i
$75$	−2.45780	−	5.79035i	−0.283803	−	0.668612i
$76$	−3.16853	+	1.82935i	−0.363455	+	0.209841i
$77$		0			0
$78$	0.446228	+	1.05127i	0.0505254	+	0.119033i
$79$	−1.26257			−0.142050			−0.0710249	−	0.997475i	$-0.522627\pi$
$79$	−1.26257			−0.142050			−0.0710249	+	0.997475i	$0.522627\pi$
$80$	0.584859	−	1.01301i	0.0653893	−	0.113258i
$81$	7.94639	+	4.22550i	0.882932	+	0.469501i
$82$	−4.57513	+	2.64145i	−0.505238	+	0.291699i
$83$	−6.21900	+	10.7716i	−0.682624	+	1.18234i	0.291553	+	0.956555i	$0.405828\pi$
$83$	−6.21900	+	10.7716i	−0.682624	+	1.18234i	−0.974177	+	0.225785i	$0.927505\pi$
$84$		0			0
$85$	−3.32137	−	5.75278i	−0.360253	−	0.623976i
$86$	4.12177	+	2.37970i	0.444462	+	0.256610i
$87$	−10.4373	−	7.86519i	−1.11899	−	0.843237i
$88$	2.88218	+	4.99209i	0.307242	+	0.532158i
$89$	−7.83957	−	13.5785i	−0.830993	−	1.43932i	−0.897252	−	0.441519i	$-0.854440\pi$
$89$	−7.83957	−	13.5785i	−0.830993	−	1.43932i	0.0662589	−	0.997802i	$-0.478894\pi$
$90$	2.52424	+	2.43771i	0.266078	+	0.256957i
$91$		0			0
$92$	0.503113	+	0.290473i	0.0524532	+	0.0302839i
$93$	0.670889	−	5.46358i	0.0695679	−	0.566547i
$94$			5.34610i			0.551408i
$95$		−	4.27965i		−	0.439083i
$96$	0.211098	−	1.71914i	0.0215451	−	0.175459i
$97$	12.5887	+	7.26808i	1.27819	+	0.737962i	0.976515	−	0.215450i	$-0.0691218\pi$
$97$	12.5887	+	7.26808i	1.27819	+	0.737962i	0.301672	+	0.953412i	$0.402455\pi$
$98$		0			0
$99$	−16.6233	+	4.76635i	−1.67070	+	0.479036i
$100$	−1.81588	−	3.14519i	−0.181588	−	0.314519i
$101$	−5.89265	−	10.2064i	−0.586340	−	1.01557i	−0.994707	−	0.102753i	$-0.967235\pi$
$101$	−5.89265	−	10.2064i	−0.586340	−	1.01557i	0.408366	−	0.912818i	$-0.366099\pi$
$102$	−7.85547	−	5.91962i	−0.777807	−	0.586130i
$103$	12.2817	+	7.09087i	1.21016	+	0.698684i	0.962793	−	0.270239i	$-0.0871026\pi$
$103$	12.2817	+	7.09087i	1.21016	+	0.698684i	0.247363	+	0.968923i	$0.420436\pi$
$104$	0.329683	+	0.571028i	0.0323281	+	0.0559939i
$105$		0			0
$106$	2.39223	−	4.14347i	0.232354	−	0.402450i
$107$	−7.42305	+	4.28570i	−0.717613	+	0.414314i	−0.813874	−	0.581042i	$-0.802645\pi$
$107$	−7.42305	+	4.28570i	−0.717613	+	0.414314i	0.0962602	+	0.995356i	$0.469312\pi$
$108$	4.85098	+	1.86225i	0.466786	+	0.179195i
$109$	5.51634	−	9.55458i	0.528369	−	0.915163i	−0.471084	−	0.882089i	$-0.656137\pi$
$109$	5.51634	−	9.55458i	0.528369	−	0.915163i	0.999453	−	0.0330740i	$-0.0105297\pi$
$110$	−6.74269			−0.642890
$111$	−7.16697	−	16.8847i	−0.680259	−	1.60263i
$112$		0			0
$113$	15.5623	−	8.98489i	1.46398	−	0.845227i	0.464785	−	0.885424i	$-0.346132\pi$
$113$	15.5623	−	8.98489i	1.46398	−	0.845227i	0.999192	+	0.0401964i	$0.0127983\pi$
$114$	−2.47604	−	5.83331i	−0.231902	−	0.546340i
$115$	−0.588501	+	0.339771i	−0.0548780	+	0.0316838i
$116$	−6.53449	−	3.77269i	−0.606712	−	0.350285i
$117$	−1.90148	+	0.545207i	−0.175792	+	0.0504044i
$118$		−	1.02971i		−	0.0947927i
$119$		0			0
$120$	1.61804	+	1.21930i	0.147706	+	0.111306i
$121$	11.1139	−	19.2499i	1.01036	−	1.74999i
$122$	−11.7011			−1.05937
$123$	−3.57522	−	8.42288i	−0.322367	−	0.759465i
$124$		−	3.17809i		−	0.285401i
$125$	10.0967			0.903079
$126$		0			0
$127$	21.6367			1.91994			0.959971	−	0.280099i	$-0.0903672\pi$
$127$	21.6367			1.91994			0.959971	+	0.280099i	$0.0903672\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.96114	+	6.58354i	−0.436804	+	0.579649i
$130$	−0.771274			−0.0676452
$131$	−4.97526	+	8.61741i	−0.434691	+	0.752906i	−0.997270	−	0.0738367i	$-0.976476\pi$
$131$	−4.97526	+	8.61741i	−0.434691	+	0.752906i	0.562580	+	0.826743i	$0.309809\pi$
$132$	−9.19051	+	3.90105i	−0.799931	+	0.339543i
$133$		0			0
$134$			8.52200i			0.736189i
$135$	−4.72362	+	3.82492i	−0.406544	+	0.329196i
$136$	−4.91809	−	2.83946i	−0.421722	−	0.243482i
$137$	−3.19357	+	1.84381i	−0.272845	+	0.157527i	−0.630180	−	0.776449i	$-0.717019\pi$
$137$	−3.19357	+	1.84381i	−0.272845	+	0.157527i	0.357335	+	0.933976i	$0.383686\pi$
$138$	−0.605569	+	0.803603i	−0.0515495	+	0.0684073i
$139$	7.66159	−	4.42342i	0.649848	−	0.375190i	−0.138550	−	0.990355i	$-0.544244\pi$
$139$	7.66159	−	4.42342i	0.649848	−	0.375190i	0.788398	+	0.615166i	$0.210911\pi$
$140$		0			0
$141$	−9.19068	−	1.12855i	−0.773995	−	0.0950411i
$142$	−8.34154			−0.700006
$143$	1.90041	−	3.29161i	0.158921	−	0.275259i
$144$	2.91088	+	0.725813i	0.242573	+	0.0604845i
$145$	7.64351	−	4.41298i	0.634759	−	0.366478i
$146$	0.519060	−	0.899038i	0.0429577	−	0.0744049i
$147$		0			0
$148$	−5.29511	−	9.17140i	−0.435256	−	0.753885i
$149$	−6.11064	−	3.52798i	−0.500603	−	0.289023i	0.228360	−	0.973577i	$-0.426664\pi$
$149$	−6.11064	−	3.52798i	−0.500603	−	0.289023i	−0.728962	+	0.684554i	$0.759997\pi$
$150$	5.79035	−	2.45780i	0.472780	−	0.200679i
$151$	8.10105	+	14.0314i	0.659254	+	1.14186i	0.980809	+	0.194970i	$0.0624611\pi$
$151$	8.10105	+	14.0314i	0.659254	+	1.14186i	−0.321555	+	0.946891i	$0.604206\pi$
$152$	−1.82935	−	3.16853i	−0.148380	−	0.257002i
$153$	11.8349	−	12.2550i	0.956797	−	0.990760i
$154$		0			0
$155$	3.21943	+	1.85874i	0.258590	+	0.149297i
$156$	−1.05127	+	0.446228i	−0.0841692	+	0.0357269i
$157$			12.8033i			1.02181i	0.859637	+	0.510905i	$0.170690\pi$
$157$			12.8033i			1.02181i	−0.859637	+	0.510905i	$0.829310\pi$
$158$		−	1.26257i		−	0.100444i
$159$	6.61821	+	4.98726i	0.524858	+	0.395516i
$160$	1.01301	+	0.584859i	0.0800852	+	0.0462372i
$161$		0			0
$162$	−4.22550	+	7.94639i	−0.331987	+	0.624327i
$163$	−6.42036	−	11.1204i	−0.502881	−	0.871016i	−0.999994	−	0.00333001i	$-0.998940\pi$
$163$	−6.42036	−	11.1204i	−0.502881	−	0.871016i	0.497113	−	0.867686i	$-0.334393\pi$
$164$	−2.64145	−	4.57513i	−0.206263	−	0.357257i
$165$	1.42337	−	11.5916i	0.110809	−	0.902406i
$166$	−10.7716	−	6.21900i	−0.836040	−	0.482688i
$167$	−12.3584	−	21.4054i	−0.956322	−	1.65640i	−0.731313	−	0.682042i	$-0.761092\pi$
$167$	−12.3584	−	21.4054i	−0.956322	−	1.65640i	−0.225009	−	0.974357i	$-0.572241\pi$
$168$		0			0
$169$	−6.28262	+	10.8818i	−0.483278	+	0.837063i
$170$	5.75278	−	3.32137i	0.441218	−	0.254737i
$171$	10.5510	−	3.02525i	0.806852	−	0.231347i
$172$	−2.37970	+	4.12177i	−0.181451	+	0.314282i
$173$	−12.7707			−0.970937			−0.485468	−	0.874254i	$-0.661351\pi$
$173$	−12.7707			−0.970937			−0.485468	+	0.874254i	$0.661351\pi$
$174$	7.86519	−	10.4373i	0.596259	−	0.791248i
$175$		0			0
$176$	−4.99209	+	2.88218i	−0.376293	+	0.217253i
$177$	1.77022	+	0.217370i	0.133058	+	0.0163385i
$178$	13.5785	−	7.83957i	1.01775	−	0.587601i
$179$	0.380000	+	0.219393i	0.0284025	+	0.0163982i	0.514134	−	0.857710i	$-0.328113\pi$
$179$	0.380000	+	0.219393i	0.0284025	+	0.0163982i	−0.485732	+	0.874108i	$0.661447\pi$
$180$	−2.43771	+	2.52424i	−0.181696	+	0.188145i
$181$		−	14.8740i		−	1.10557i	−0.833323	−	0.552787i	$-0.813564\pi$
$181$		−	14.8740i		−	1.10557i	0.833323	−	0.552787i	$-0.186436\pi$
$182$		0			0
$183$	2.47008	−	20.1158i	0.182593	−	1.48700i
$184$	−0.290473	+	0.503113i	−0.0214139	+	0.0370900i
$185$	12.3876			0.910754
$186$	5.46358	+	0.670889i	0.400609	+	0.0491919i
$187$			32.7353i			2.39385i
$188$	−5.34610			−0.389904
$189$		0			0
$190$	4.27965			0.310479
$191$		−	7.42503i		−	0.537256i	−0.963244	−	0.268628i	$-0.913430\pi$
$191$		−	7.42503i		−	0.537256i	0.963244	−	0.268628i	$-0.0865702\pi$
$192$	1.71914	+	0.211098i	0.124068	+	0.0152347i
$193$	−3.82307			−0.275191			−0.137595	−	0.990489i	$-0.543937\pi$
$193$	−3.82307			−0.275191			−0.137595	+	0.990489i	$0.543937\pi$
$194$	−7.26808	+	12.5887i	−0.521818	+	0.903815i
$195$	0.162814	−	1.32593i	0.0116594	−	0.0949516i
$196$		0			0
$197$			8.80043i			0.627005i	0.949587	+	0.313502i	$0.101502\pi$
$197$			8.80043i			0.627005i	−0.949587	+	0.313502i	$0.898498\pi$
$198$	−4.76635	−	16.6233i	−0.338730	−	1.18136i
$199$	−14.5174	−	8.38165i	−1.02911	−	0.594159i	−0.112383	−	0.993665i	$-0.535848\pi$
$199$	−14.5174	−	8.38165i	−1.02911	−	0.594159i	−0.916731	+	0.399506i	$0.869182\pi$
$200$	3.14519	−	1.81588i	0.222399	−	0.128402i
$201$	−14.6505	−	1.79898i	−1.03337	−	0.126890i
$202$	10.2064	−	5.89265i	0.718117	−	0.414605i
$203$		0			0
$204$	5.91962	−	7.85547i	0.414456	−	0.549993i
$205$	6.17951			0.431596
$206$	−7.09087	+	12.2817i	−0.494044	+	0.855710i
$207$	−1.25367	−	1.21070i	−0.0871362	−	0.0841492i
$208$	−0.571028	+	0.329683i	−0.0395937	+	0.0228594i
$209$	−10.5450	+	18.2645i	−0.729416	+	1.26338i
$210$		0			0
$211$	−7.61019	−	13.1812i	−0.523907	−	0.907434i	−0.999613	−	0.0278293i	$-0.991141\pi$
$211$	−7.61019	−	13.1812i	−0.523907	−	0.907434i	0.475705	−	0.879605i	$-0.342193\pi$
$212$	4.14347	+	2.39223i	0.284575	+	0.164299i
$213$	1.76088	−	14.3403i	0.120654	−	0.982579i
$214$	−4.28570	−	7.42305i	−0.292964	−	0.507429i
$215$	−2.78359	−	4.82131i	−0.189839	−	0.328811i
$216$	−1.86225	+	4.85098i	−0.126710	+	0.330067i
$217$		0			0
$218$	9.55458	+	5.51634i	0.647118	+	0.373614i
$219$	1.43600	+	1.08212i	0.0970358	+	0.0731230i
$220$		−	6.74269i		−	0.454592i
$221$			3.74449i			0.251882i
$222$	16.8847	−	7.16697i	1.13323	−	0.481015i
$223$	−13.2581	−	7.65455i	−0.887825	−	0.512586i	−0.0145948	−	0.999893i	$-0.504646\pi$
$223$	−13.2581	−	7.65455i	−0.887825	−	0.512586i	−0.873231	+	0.487307i	$0.837979\pi$
$224$		0			0
$225$	3.00297	+	10.4733i	0.200198	+	0.698217i
$226$	8.98489	+	15.5623i	0.597666	+	1.03519i
$227$	2.74286	+	4.75077i	0.182050	+	0.315320i	0.942578	−	0.333985i	$-0.108393\pi$
$227$	2.74286	+	4.75077i	0.182050	+	0.315320i	−0.760528	+	0.649305i	$0.775060\pi$
$228$	5.83331	−	2.47604i	0.386320	−	0.163980i
$229$	−16.6739	−	9.62669i	−1.10184	−	0.636150i	−0.165139	−	0.986270i	$-0.552807\pi$
$229$	−16.6739	−	9.62669i	−1.10184	−	0.636150i	−0.936705	+	0.350121i	$0.886141\pi$
$230$	−0.339771	−	0.588501i	−0.0224039	−	0.0388046i
$231$		0			0
$232$	3.77269	−	6.53449i	0.247689	−	0.429010i
$233$	2.52528	−	1.45797i	0.165436	−	0.0955147i	−0.414996	−	0.909823i	$-0.636217\pi$
$233$	2.52528	−	1.45797i	0.165436	−	0.0955147i	0.580432	+	0.814309i	$0.302884\pi$
$234$	−0.545207	−	1.90148i	−0.0356413	−	0.124304i
$235$	3.12672	−	5.41563i	0.203964	−	0.353277i
$236$	1.02971			0.0670286
$237$	2.17053	+	0.266525i	0.140991	+	0.0173127i
$238$		0			0
$239$	7.39276	−	4.26821i	0.478198	−	0.276088i	−0.241467	−	0.970409i	$-0.577629\pi$
$239$	7.39276	−	4.26821i	0.478198	−	0.276088i	0.719665	+	0.694321i	$0.244295\pi$
$240$	−1.21930	+	1.61804i	−0.0787054	+	0.104444i
$241$	−1.36977	+	0.790838i	−0.0882347	+	0.0509424i	−0.543468	−	0.839430i	$-0.682889\pi$
$241$	−1.36977	+	0.790838i	−0.0882347	+	0.0509424i	0.455233	+	0.890372i	$0.349556\pi$
$242$	19.2499	+	11.1139i	1.23743	+	0.714431i
$243$	−12.7689	−	8.94170i	−0.819129	−	0.573610i
$244$		−	11.7011i		−	0.749085i
$245$		0			0
$246$	8.42288	−	3.57522i	0.537023	−	0.227948i
$247$	−1.20621	+	2.08922i	−0.0767495	+	0.132934i
$248$	3.17809			0.201809
$249$	12.9652	−	17.2051i	0.821635	−	1.09033i
$250$			10.0967i			0.638573i
$251$	0.524263			0.0330912			0.0165456	−	0.999863i	$-0.494733\pi$
$251$	0.524263			0.0330912			0.0165456	+	0.999863i	$0.494733\pi$
$252$		0			0
$253$	3.34878			0.210536
$254$			21.6367i			1.35760i
$255$	4.49549	+	10.5910i	0.281519	+	0.663232i
$256$	1.00000			0.0625000
$257$	1.17787	−	2.04013i	0.0734737	−	0.127260i	−0.826948	−	0.562279i	$-0.809925\pi$
$257$	1.17787	−	2.04013i	0.0734737	−	0.127260i	0.900422	+	0.435019i	$0.143258\pi$
$258$	−6.58354	−	4.96114i	−0.409873	−	0.308867i
$259$		0			0
$260$		−	0.771274i		−	0.0478324i
$261$	16.2828	+	15.7246i	1.00788	+	0.973331i
$262$	−8.61741	−	4.97526i	−0.532385	−	0.307373i
$263$	3.85949	−	2.22828i	0.237987	−	0.137402i	−0.376264	−	0.926512i	$-0.622792\pi$
$263$	3.85949	−	2.22828i	0.237987	−	0.137402i	0.614251	+	0.789111i	$0.289458\pi$
$264$	−3.90105	−	9.19051i	−0.240093	−	0.565637i
$265$	−4.84670	+	2.79824i	−0.297730	+	0.171895i
$266$		0			0
$267$	10.6109	+	24.9983i	0.649377	+	1.52987i
$268$	−8.52200			−0.520564
$269$	−4.76668	+	8.25613i	−0.290630	+	0.503385i	−0.973959	−	0.226725i	$-0.927198\pi$
$269$	−4.76668	+	8.25613i	−0.290630	+	0.503385i	0.683329	+	0.730110i	$0.260531\pi$
$270$	−3.82492	−	4.72362i	−0.232777	−	0.287470i
$271$	−10.6509	+	6.14930i	−0.646996	+	0.373543i	−0.787304	−	0.616564i	$-0.788524\pi$
$271$	−10.6509	+	6.14930i	−0.646996	+	0.373543i	0.140308	+	0.990108i	$0.455191\pi$
$272$	2.83946	−	4.91809i	0.172167	−	0.298203i
$273$		0			0
$274$	−1.84381	−	3.19357i	−0.111389	−	0.192931i
$275$	−18.1300	−	10.4674i	−1.09328	−	0.631207i
$276$	−0.803603	−	0.605569i	−0.0483712	−	0.0364510i
$277$	8.52259	+	14.7616i	0.512073	+	0.886936i	0.999902	+	0.0139972i	$0.00445561\pi$
$277$	8.52259	+	14.7616i	0.512073	+	0.886936i	−0.487829	+	0.872939i	$0.662211\pi$
$278$	4.42342	+	7.66159i	0.265299	+	0.459512i
$279$	−2.30670	+	9.25102i	−0.138099	+	0.553844i
$280$		0			0
$281$	8.31719	+	4.80193i	0.496162	+	0.286459i	0.727127	−	0.686503i	$-0.240855\pi$
$281$	8.31719	+	4.80193i	0.496162	+	0.286459i	−0.230965	+	0.972962i	$0.574188\pi$
$282$	1.12855	−	9.19068i	0.0672042	−	0.547297i
$283$			27.8681i			1.65658i	0.560296	+	0.828292i	$0.310687\pi$
$283$			27.8681i			1.65658i	−0.560296	+	0.828292i	$0.689313\pi$
$284$		−	8.34154i		−	0.494979i
$285$	−0.903426	+	7.35731i	−0.0535143	+	0.435810i
$286$	3.29161	+	1.90041i	0.194637	+	0.112374i
$287$		0			0
$288$	−0.725813	+	2.91088i	−0.0427690	+	0.171525i
$289$	−7.62505	−	13.2070i	−0.448532	−	0.776881i
$290$	4.41298	+	7.64351i	0.259139	+	0.448843i
$291$	−20.1074	−	15.1523i	−1.17872	−	0.888243i
$292$	0.899038	+	0.519060i	0.0526122	+	0.0303757i
$293$	−0.271017	−	0.469416i	−0.0158330	−	0.0274236i	0.858000	−	0.513649i	$-0.171707\pi$
$293$	−0.271017	−	0.469416i	−0.0158330	−	0.0274236i	−0.873833	+	0.486226i	$0.838373\pi$
$294$		0			0
$295$	−0.602237	+	1.04311i	−0.0350636	+	0.0607319i
$296$	9.17140	−	5.29511i	0.533077	−	0.307772i
$297$	29.5839	−	4.68488i	1.71663	−	0.271844i
$298$	3.52798	−	6.11064i	0.204370	−	0.353980i
$299$	0.383056			0.0221527
$300$	2.45780	+	5.79035i	0.141901	+	0.334306i
$301$		0			0
$302$	−14.0314	+	8.10105i	−0.807418	+	0.466163i
$303$	7.97574	+	18.7901i	0.458194	+	1.07946i
$304$	3.16853	−	1.82935i	0.181728	−	0.104920i
$305$	11.8533	+	6.84349i	0.678717	+	0.391857i
$306$	12.2550	+	11.8349i	0.700573	+	0.676558i
$307$			13.6813i			0.780832i	0.920639	+	0.390416i	$0.127669\pi$
$307$			13.6813i			0.780832i	−0.920639	+	0.390416i	$0.872331\pi$
$308$		0			0
$309$	−19.6172	−	14.7828i	−1.11598	−	0.840967i
$310$	−1.85874	+	3.21943i	−0.105569	+	0.182851i
$311$	21.0614			1.19428			0.597140	−	0.802137i	$-0.296304\pi$
$311$	21.0614			1.19428			0.597140	+	0.802137i	$0.296304\pi$
$312$	−0.446228	−	1.05127i	−0.0252627	−	0.0595166i
$313$		−	33.2171i		−	1.87754i	−0.344541	−	0.938771i	$-0.611965\pi$
$313$		−	33.2171i		−	1.87754i	0.344541	−	0.938771i	$-0.388035\pi$
$314$	−12.8033			−0.722529
$315$		0			0
$316$	1.26257			0.0710249
$317$			7.10600i			0.399113i	0.979886	+	0.199556i	$0.0639501\pi$
$317$			7.10600i			0.399113i	−0.979886	+	0.199556i	$0.936050\pi$
$318$	−4.98726	+	6.61821i	−0.279672	+	0.371131i
$319$	−43.4943			−2.43521
$320$	−0.584859	+	1.01301i	−0.0326946	+	0.0566288i
$321$	13.6660	−	5.80072i	0.762759	−	0.323765i
$322$		0			0
$323$		−	20.7775i		−	1.15609i
$324$	−7.94639	−	4.22550i	−0.441466	−	0.234750i
$325$	−2.07384	−	1.19733i	−0.115036	−	0.0664159i
$326$	11.1204	−	6.42036i	0.615901	−	0.355591i
$327$	−11.5003	+	15.2612i	−0.635968	+	0.843944i
$328$	4.57513	−	2.64145i	0.252619	−	0.145850i
$329$		0			0
$330$	11.5916	+	1.42337i	0.638097	+	0.0783538i
$331$	6.97225			0.383229			0.191615	−	0.981470i	$-0.438628\pi$
$331$	6.97225			0.383229			0.191615	+	0.981470i	$0.438628\pi$
$332$	6.21900	−	10.7716i	0.341312	−	0.591170i
$333$	8.75668	+	30.5401i	0.479863	+	1.67359i
$334$	21.4054	−	12.3584i	1.17125	−	0.676222i
$335$	4.98418	−	8.63284i	0.272315	−	0.471663i
$336$		0			0
$337$	3.96019	+	6.85926i	0.215726	+	0.373648i	0.953497	−	0.301403i	$-0.0974550\pi$
$337$	3.96019	+	6.85926i	0.215726	+	0.373648i	−0.737771	+	0.675051i	$0.764122\pi$
$338$	−10.8818	−	6.28262i	−0.591893	−	0.341729i
$339$	−28.6504	+	12.1611i	−1.55608	+	0.660500i
$340$	3.32137	+	5.75278i	0.180126	+	0.311988i
$341$	−9.15983	−	15.8653i	−0.496033	−	0.859154i
$342$	3.02525	+	10.5510i	0.163587	+	0.570530i
$343$		0			0
$344$	−4.12177	−	2.37970i	−0.222231	−	0.128305i
$345$	1.08344	−	0.459883i	0.0583305	−	0.0247592i
$346$		−	12.7707i		−	0.686556i
$347$		−	8.94074i		−	0.479964i	−0.970777	−	0.239982i	$-0.922858\pi$
$347$		−	8.94074i		−	0.479964i	0.970777	−	0.239982i	$-0.0771415\pi$
$348$	10.4373	+	7.86519i	0.559497	+	0.421618i
$349$	−1.32673	−	0.765989i	−0.0710183	−	0.0410025i	0.464070	−	0.885798i	$-0.346388\pi$
$349$	−1.32673	−	0.765989i	−0.0710183	−	0.0410025i	−0.535089	+	0.844796i	$0.679722\pi$
$350$		0			0
$351$	3.38400	−	0.535888i	0.180625	−	0.0286036i
$352$	−2.88218	−	4.99209i	−0.153621	−	0.266079i
$353$	2.98494	+	5.17007i	0.158872	+	0.275175i	0.934462	−	0.356062i	$-0.115881\pi$
$353$	2.98494	+	5.17007i	0.158872	+	0.275175i	−0.775590	+	0.631237i	$0.782548\pi$
$354$	−0.217370	+	1.77022i	−0.0115531	+	0.0940860i
$355$	8.45003	+	4.87863i	0.448481	+	0.258931i
$356$	7.83957	+	13.5785i	0.415496	+	0.719661i
$357$		0			0
$358$	−0.219393	+	0.380000i	−0.0115953	+	0.0200836i
$359$	−23.7156	+	13.6922i	−1.25166	+	0.722646i	−0.971439	−	0.237289i	$-0.923741\pi$
$359$	−23.7156	+	13.6922i	−1.25166	+	0.722646i	−0.280221	+	0.959935i	$0.590408\pi$
$360$	−2.52424	−	2.43771i	−0.133039	−	0.128478i
$361$	−2.80696	+	4.86179i	−0.147735	+	0.255884i
$362$	14.8740			0.781759
$363$	−23.1700	+	30.7471i	−1.21611	+	1.61381i
$364$		0			0
$365$	−1.05162	+	0.607154i	−0.0550444	+	0.0317799i
$366$	20.1158	+	2.47008i	1.05147	+	0.129113i
$367$	13.6569	−	7.88479i	0.712882	−	0.411583i	−0.0992452	−	0.995063i	$-0.531643\pi$
$367$	13.6569	−	7.88479i	0.712882	−	0.411583i	0.812127	+	0.583480i	$0.198309\pi$
$368$	−0.503113	−	0.290473i	−0.0262266	−	0.0151419i
$369$	4.36824	+	15.2348i	0.227402	+	0.793093i
$370$			12.3876i			0.644000i
$371$		0			0
$372$	−0.670889	+	5.46358i	−0.0347839	+	0.283273i
$373$	8.21122	−	14.2222i	0.425161	−	0.736400i	−0.571275	−	0.820759i	$-0.693551\pi$
$373$	8.21122	−	14.2222i	0.425161	−	0.736400i	0.996435	+	0.0843589i	$0.0268842\pi$
$374$	−32.7353			−1.69270
$375$	−17.3577	−	2.13140i	−0.896347	−	0.110065i
$376$		−	5.34610i		−	0.275704i
$377$	−4.97517			−0.256234
$378$		0			0
$379$	−9.75267			−0.500961			−0.250480	−	0.968122i	$-0.580589\pi$
$379$	−9.75267			−0.500961			−0.250480	+	0.968122i	$0.580589\pi$
$380$			4.27965i			0.219541i
$381$	−37.1964	−	4.56745i	−1.90563	−	0.233998i
$382$	7.42503			0.379897
$383$	14.1233	−	24.4623i	0.721667	−	1.24996i	−0.238664	−	0.971102i	$-0.576709\pi$
$383$	14.1233	−	24.4623i	0.721667	−	1.24996i	0.960331	−	0.278862i	$-0.0899572\pi$
$384$	−0.211098	+	1.71914i	−0.0107725	+	0.0877294i
$385$		0			0
$386$		−	3.82307i		−	0.194589i
$387$	9.91866	−	10.2707i	0.504194	−	0.522091i
$388$	−12.5887	−	7.26808i	−0.639094	−	0.368981i
$389$	−5.35592	+	3.09224i	−0.271556	+	0.156783i	−0.629595	−	0.776924i	$-0.716779\pi$
$389$	−5.35592	+	3.09224i	−0.271556	+	0.156783i	0.358039	+	0.933707i	$0.383446\pi$
$390$	1.32593	+	0.162814i	0.0671409	+	0.00824443i
$391$	−2.85714	+	1.64957i	−0.144492	+	0.0834223i
$392$		0			0
$393$	10.3723	−	13.7643i	0.523213	−	0.694315i
$394$	−8.80043			−0.443359
$395$	−0.738424	+	1.27899i	−0.0371541	+	0.0643529i
$396$	16.6233	−	4.76635i	0.835350	−	0.239518i
$397$	19.4575	−	11.2338i	0.976545	−	0.563808i	0.0753197	−	0.997159i	$-0.476002\pi$
$397$	19.4575	−	11.2338i	0.976545	−	0.563808i	0.901225	+	0.433351i	$0.142669\pi$
$398$	8.38165	−	14.5174i	0.420134	−	0.727693i
$399$		0			0
$400$	1.81588	+	3.14519i	0.0907939	+	0.157260i
$401$	−0.546925	−	0.315767i	−0.0273121	−	0.0157687i	0.486282	−	0.873802i	$-0.338353\pi$
$401$	−0.546925	−	0.315767i	−0.0273121	−	0.0157687i	−0.513594	+	0.858033i	$0.671686\pi$
$402$	1.79898	−	14.6505i	0.0897249	−	0.730701i
$403$	−1.04776	−	1.81478i	−0.0521928	−	0.0904006i
$404$	5.89265	+	10.2064i	0.293170	+	0.507786i
$405$	8.92798	−	5.57842i	0.443635	−	0.277194i
$406$		0			0
$407$	−52.8673	−	30.5230i	−2.62054	−	1.51297i
$408$	7.85547	+	5.91962i	0.388904	+	0.293065i
$409$			8.03570i			0.397340i	0.980066	+	0.198670i	$0.0636622\pi$
$409$			8.03570i			0.397340i	−0.980066	+	0.198670i	$0.936338\pi$
$410$			6.17951i			0.305184i
$411$	5.87942	−	2.49561i	0.290010	−	0.123099i
$412$	−12.2817	−	7.09087i	−0.605078	−	0.349342i
$413$		0			0
$414$	1.21070	−	1.25367i	0.0595025	−	0.0616146i
$415$	7.27448	+	12.5998i	0.357090	+	0.618498i
$416$	−0.329683	−	0.571028i	−0.0161641	−	0.0279970i
$417$	−14.1051	+	5.98713i	−0.690730	+	0.293191i
$418$	−18.2645	−	10.5450i	−0.893348	−	0.515775i
$419$	14.0455	+	24.3275i	0.686168	+	1.18848i	0.973068	+	0.230518i	$0.0740420\pi$
$419$	14.0455	+	24.3275i	0.686168	+	1.18848i	−0.286900	+	0.957961i	$0.592625\pi$
$420$		0			0
$421$	−20.4254	+	35.3779i	−0.995474	+	1.72421i	−0.415439	+	0.909621i	$0.636372\pi$
$421$	−20.4254	+	35.3779i	−0.995474	+	1.72421i	−0.580035	+	0.814591i	$0.696961\pi$
$422$	13.1812	−	7.61019i	0.641653	−	0.370458i
$423$	15.5618	+	3.88027i	0.756642	+	0.188665i
$424$	−2.39223	+	4.14347i	−0.116177	+	0.201225i
$425$	20.6245			1.00043
$426$	14.3403	+	1.76088i	0.694788	+	0.0853150i
$427$		0			0
$428$	7.42305	−	4.28570i	0.358807	−	0.207157i
$429$	−3.96193	+	5.25757i	−0.191284	+	0.253838i
$430$	4.82131	−	2.78359i	0.232504	−	0.134236i
$431$	−2.90971	−	1.67992i	−0.140156	−	0.0809191i	0.428282	−	0.903645i	$-0.359119\pi$
$431$	−2.90971	−	1.67992i	−0.140156	−	0.0809191i	−0.568438	+	0.822726i	$0.692452\pi$
$432$	−4.85098	−	1.86225i	−0.233393	−	0.0895977i
$433$		−	12.7148i		−	0.611033i	−0.952187	−	0.305517i	$-0.901171\pi$
$433$		−	12.7148i		−	0.611033i	0.952187	−	0.305517i	$-0.0988292\pi$
$434$		0			0
$435$	−14.0718	+	5.97300i	−0.674693	+	0.286384i
$436$	−5.51634	+	9.55458i	−0.264185	+	0.457581i
$437$	−2.12550			−0.101677
$438$	−1.08212	+	1.43600i	−0.0517058	+	0.0686147i
$439$			17.0606i			0.814256i	0.913371	+	0.407128i	$0.133470\pi$
$439$			17.0606i			0.814256i	−0.913371	+	0.407128i	$0.866530\pi$
$440$	6.74269			0.321445
$441$		0			0
$442$	−3.74449			−0.178107
$443$			4.91728i			0.233627i	0.993154	+	0.116814i	$0.0372680\pi$
$443$			4.91728i			0.233627i	−0.993154	+	0.116814i	$0.962732\pi$
$444$	7.16697	+	16.8847i	0.340129	+	0.801313i
$445$	−18.3402			−0.869408
$446$	7.65455	−	13.2581i	0.362453	−	0.627787i
$447$	9.76028	+	7.35502i	0.461645	+	0.347881i
$448$		0			0
$449$			4.88329i			0.230457i	0.993339	+	0.115228i	$0.0367600\pi$
$449$			4.88329i			0.230457i	−0.993339	+	0.115228i	$0.963240\pi$
$450$	−10.4733	+	3.00297i	−0.493714	+	0.141561i
$451$	−26.3727	−	15.2263i	−1.24184	−	0.716977i
$452$	−15.5623	+	8.98489i	−0.731988	+	0.422614i
$453$	−10.9648	−	25.8321i	−0.515172	−	1.21370i
$454$	−4.75077	+	2.74286i	−0.222965	+	0.128729i
$455$		0			0
$456$	2.47604	+	5.83331i	0.115951	+	0.273170i
$457$	−12.1305			−0.567439			−0.283719	−	0.958907i	$-0.591568\pi$
$457$	−12.1305			−0.567439			−0.283719	+	0.958907i	$0.591568\pi$
$458$	9.62669	−	16.6739i	0.449826	−	0.779121i
$459$	−22.9329	+	18.5697i	−1.07042	+	0.866762i
$460$	0.588501	−	0.339771i	0.0274390	−	0.0158419i
$461$	−3.32024	+	5.75083i	−0.154639	+	0.267843i	−0.932928	−	0.360064i	$-0.882755\pi$
$461$	−3.32024	+	5.75083i	−0.154639	+	0.267843i	0.778288	+	0.627907i	$0.216088\pi$
$462$		0			0
$463$	3.64017	+	6.30496i	0.169173	+	0.293016i	0.938129	−	0.346285i	$-0.112557\pi$
$463$	3.64017	+	6.30496i	0.169173	+	0.293016i	−0.768956	+	0.639301i	$0.779224\pi$
$464$	6.53449	+	3.77269i	0.303356	+	0.175143i
$465$	−5.14226	−	3.87504i	−0.238467	−	0.179701i
$466$	1.45797	+	2.52528i	0.0675391	+	0.116981i
$467$	17.1931	+	29.7794i	0.795604	+	1.37803i	0.922455	+	0.386104i	$0.126180\pi$
$467$	17.1931	+	29.7794i	0.795604	+	1.37803i	−0.126851	+	0.991922i	$0.540487\pi$
$468$	1.90148	−	0.545207i	0.0878960	−	0.0252022i
$469$		0			0
$470$	5.41563	+	3.12672i	0.249804	+	0.144225i
$471$	2.70274	−	22.0106i	0.124536	−	1.01419i
$472$			1.02971i			0.0473964i
$473$			27.4350i			1.26146i
$474$	−0.266525	+	2.17053i	−0.0122419	+	0.0996956i
$475$	11.5073	+	6.64376i	0.527992	+	0.304836i
$476$		0			0
$477$	−10.3248	−	9.97088i	−0.472741	−	0.456535i
$478$	4.26821	+	7.39276i	0.195223	+	0.338137i
$479$	10.6903	+	18.5161i	0.488452	+	0.846023i	0.999912	−	0.0132839i	$-0.00422852\pi$
$479$	10.6903	+	18.5161i	0.488452	+	0.846023i	−0.511460	+	0.859307i	$0.670895\pi$
$480$	−1.61804	−	1.21930i	−0.0738529	−	0.0556531i
$481$	−6.04732	−	3.49142i	−0.275734	−	0.159195i
$482$	−0.790838	−	1.36977i	−0.0360217	−	0.0623914i
$483$		0			0
$484$	−11.1139	+	19.2499i	−0.505179	+	0.874996i
$485$	14.7252	−	8.50161i	0.668638	−	0.386038i
$486$	8.94170	−	12.7689i	0.405604	−	0.579211i
$487$	1.42429	−	2.46694i	0.0645408	−	0.111788i	−0.831949	−	0.554851i	$-0.812775\pi$
$487$	1.42429	−	2.46694i	0.0645408	−	0.111788i	0.896490	+	0.443064i	$0.146108\pi$
$488$	11.7011			0.529683
$489$	8.68999	+	20.4728i	0.392975	+	0.925812i
$490$		0			0
$491$	−0.159838	+	0.0922824i	−0.00721338	+	0.00416464i	−0.503602	−	0.863936i	$-0.667992\pi$
$491$	−0.159838	+	0.0922824i	−0.00721338	+	0.00416464i	0.496389	+	0.868100i	$0.334659\pi$
$492$	3.57522	+	8.42288i	0.161183	+	0.379733i
$493$	37.1088	−	21.4248i	1.67130	−	0.964924i
$494$	−2.08922	−	1.20621i	−0.0939985	−	0.0542701i
$495$	−4.89393	+	19.6271i	−0.219966	+	0.882173i
$496$			3.17809i			0.142700i
$497$		0			0
$498$	17.2051	+	12.9652i	0.770979	+	0.580984i
$499$	−5.41653	+	9.38170i	−0.242477	+	0.419983i	−0.961419	−	0.275087i	$-0.911293\pi$
$499$	−5.41653	+	9.38170i	−0.242477	+	0.419983i	0.718942	+	0.695070i	$0.244627\pi$
$500$	−10.0967			−0.451540
$501$	16.7272	+	39.4077i	0.747315	+	1.76060i
$502$			0.524263i			0.0233990i
$503$	17.6633			0.787570			0.393785	−	0.919203i	$-0.371166\pi$
$503$	17.6633			0.787570			0.393785	+	0.919203i	$0.371166\pi$
$504$		0			0
$505$	−13.7855			−0.613446
$506$			3.34878i			0.148871i
$507$	13.0978	−	17.3811i	0.581695	−	0.771922i
$508$	−21.6367			−0.959971
$509$	−3.55628	+	6.15966i	−0.157629	+	0.273022i	−0.934013	−	0.357238i	$-0.883718\pi$
$509$	−3.55628	+	6.15966i	−0.157629	+	0.273022i	0.776384	+	0.630260i	$0.217052\pi$
$510$	−10.5910	+	4.49549i	−0.468976	+	0.199064i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−18.7772	+	2.97354i	−0.829033	+	0.131285i
$514$	2.04013	+	1.17787i	0.0899865	+	0.0519537i
$515$	14.3662	−	8.29433i	0.633050	−	0.365492i
$516$	4.96114	−	6.58354i	0.218402	−	0.289824i
$517$	−26.6882	+	15.4084i	−1.17374	+	0.677662i
$518$		0			0
$519$	21.9546	+	2.69586i	0.963699	+	0.118335i
$520$	0.771274			0.0338226
$521$	−19.2668	+	33.3711i	−0.844095	+	1.46202i	0.0423090	+	0.999105i	$0.486529\pi$
$521$	−19.2668	+	33.3711i	−0.844095	+	1.46202i	−0.886404	+	0.462912i	$0.846805\pi$
$522$	−15.7246	+	16.2828i	−0.688249	+	0.712679i
$523$	19.6786	−	11.3615i	0.860486	−	0.496802i	−0.00368891	−	0.999993i	$-0.501174\pi$
$523$	19.6786	−	11.3615i	0.860486	−	0.496802i	0.864175	+	0.503191i	$0.167841\pi$
$524$	4.97526	−	8.61741i	0.217345	−	0.376453i
$525$		0			0
$526$	2.22828	+	3.85949i	0.0971576	+	0.168282i
$527$	15.6301	+	9.02406i	0.680859	+	0.393094i
$528$	9.19051	−	3.90105i	0.399966	−	0.169771i
$529$	−11.3313	−	19.6263i	−0.492663	−	0.853318i
$530$	−2.79824	−	4.84670i	−0.121548	−	0.210527i
$531$	−2.99736	−	0.747379i	−0.130075	−	0.0324335i
$532$		0			0
$533$	−3.01669	−	1.74168i	−0.130667	−	0.0754407i
$534$	−24.9983	+	10.6109i	−1.08178	+	0.459179i
$535$			10.0261i			0.433467i
$536$		−	8.52200i		−	0.368095i
$537$	−0.606959	−	0.457384i	−0.0261922	−	0.0197376i
$538$	−8.25613	−	4.76668i	−0.355947	−	0.205506i
$539$		0			0
$540$	4.72362	−	3.82492i	0.203272	−	0.164598i
$541$	10.6657	+	18.4735i	0.458553	+	0.794237i	0.998885	−	0.0472149i	$-0.0150346\pi$
$541$	10.6657	+	18.4735i	0.458553	+	0.794237i	−0.540332	+	0.841452i	$0.681701\pi$
$542$	−6.14930	−	10.6509i	−0.264135	−	0.457495i
$543$	−3.13987	+	25.5704i	−0.134745	+	1.09733i
$544$	4.91809	+	2.83946i	0.210861	+	0.121741i
$545$	−6.45257	−	11.1762i	−0.276398	−	0.478735i
$546$		0			0
$547$	−4.51312	+	7.81695i	−0.192967	+	0.334229i	−0.946232	−	0.323488i	$-0.895144\pi$
$547$	−4.51312	+	7.81695i	−0.192967	+	0.334229i	0.753265	+	0.657717i	$0.228478\pi$
$548$	3.19357	−	1.84381i	0.136423	−	0.0787637i
$549$	−8.49281	+	34.0604i	−0.362464	+	1.45366i
$550$	10.4674	−	18.1300i	0.446331	−	0.773068i
$551$	27.6063			1.17607
$552$	0.605569	−	0.803603i	0.0257747	−	0.0342036i
$553$		0			0
$554$	−14.7616	+	8.52259i	−0.627159	+	0.362090i
$555$	−21.2960	−	2.61500i	−0.903964	−	0.111000i
$556$	−7.66159	+	4.42342i	−0.324924	+	0.187595i
$557$	2.10247	+	1.21386i	0.0890843	+	0.0514329i	0.543880	−	0.839163i	$-0.316955\pi$
$557$	2.10247	+	1.21386i	0.0890843	+	0.0514329i	−0.454796	+	0.890596i	$0.650288\pi$
$558$	−9.25102	−	2.30670i	−0.391627	−	0.0976504i
$559$			3.13820i			0.132732i
$560$		0			0
$561$	6.91037	−	56.2766i	0.291756	−	2.37600i
$562$	−4.80193	+	8.31719i	−0.202557	+	0.350840i
$563$	6.13147			0.258410			0.129205	−	0.991618i	$-0.458757\pi$
$563$	6.13147			0.258410			0.129205	+	0.991618i	$0.458757\pi$
$564$	9.19068	+	1.12855i	0.386998	+	0.0475205i
$565$		−	21.0196i		−	0.884301i
$566$	−27.8681			−1.17138
$567$		0			0
$568$	8.34154			0.350003
$569$		−	32.1341i		−	1.34713i	−0.739127	−	0.673566i	$-0.764762\pi$
$569$		−	32.1341i		−	1.34713i	0.739127	−	0.673566i	$-0.235238\pi$
$570$	−7.35731	−	0.903426i	−0.308164	−	0.0378403i
$571$	3.91046			0.163648			0.0818239	−	0.996647i	$-0.473926\pi$
$571$	3.91046			0.163648			0.0818239	+	0.996647i	$0.473926\pi$
$572$	−1.90041	+	3.29161i	−0.0794603	+	0.137629i
$573$	−1.56741	+	12.7646i	−0.0654794	+	0.533251i
$574$		0			0
$575$		−	2.10985i		−	0.0879869i
$576$	−2.91088	−	0.725813i	−0.121286	−	0.0302422i
$577$	13.2404	+	7.64437i	0.551207	+	0.318239i	0.749609	−	0.661881i	$-0.230242\pi$
$577$	13.2404	+	7.64437i	0.551207	+	0.318239i	−0.198402	+	0.980121i	$0.563575\pi$
$578$	13.2070	−	7.62505i	0.549338	−	0.317160i
$579$	6.57239	+	0.807043i	0.273139	+	0.0335396i
$580$	−7.64351	+	4.41298i	−0.317380	+	0.183239i
$581$		0			0
$582$	15.1523	−	20.1074i	0.628082	−	0.833479i
$583$	27.5794			1.14222
$584$	−0.519060	+	0.899038i	−0.0214789	+	0.0372025i
$585$	−0.559801	+	2.24508i	−0.0231449	+	0.0928227i
$586$	0.469416	−	0.271017i	0.0193914	−	0.0111956i
$587$	11.6794	−	20.2293i	0.482061	−	0.834955i	−0.517727	−	0.855546i	$-0.673222\pi$
$587$	11.6794	−	20.2293i	0.482061	−	0.834955i	0.999788	+	0.0205915i	$0.00655493\pi$
$588$		0			0
$589$	5.81384	+	10.0699i	0.239555	+	0.414922i
$590$	−1.04311	−	0.602237i	−0.0429440	−	0.0247937i
$591$	1.85775	−	15.1292i	0.0764177	−	0.622330i
$592$	5.29511	+	9.17140i	0.217628	+	0.376942i
$593$	5.26150	+	9.11319i	0.216064	+	0.374234i	0.953601	−	0.301073i	$-0.0973447\pi$
$593$	5.26150	+	9.11319i	0.216064	+	0.374234i	−0.737537	+	0.675306i	$0.764011\pi$
$594$	4.68488	+	29.5839i	0.192223	+	1.21384i
$595$		0			0
$596$	6.11064	+	3.52798i	0.250301	+	0.144512i
$597$	23.1881	+	17.4738i	0.949027	+	0.715156i
$598$			0.383056i			0.0156643i
$599$		−	34.0337i		−	1.39058i	−0.718730	−	0.695290i	$-0.755276\pi$
$599$		−	34.0337i		−	1.39058i	0.718730	−	0.695290i	$-0.244724\pi$
$600$	−5.79035	+	2.45780i	−0.236390	+	0.100339i
$601$	−35.2808	−	20.3694i	−1.43913	−	0.830885i	−0.441345	−	0.897338i	$-0.645498\pi$
$601$	−35.2808	−	20.3694i	−1.43913	−	0.830885i	−0.997790	+	0.0664531i	$0.978832\pi$
$602$		0			0
$603$	24.8065	+	6.18539i	1.01020	+	0.251888i
$604$	−8.10105	−	14.0314i	−0.329627	−	0.570931i
$605$	−13.0002	−	22.5170i	−0.528533	−	0.915446i
$606$	−18.7901	+	7.97574i	−0.763295	+	0.323992i
$607$	−35.2279	−	20.3388i	−1.42986	−	0.825528i	−0.432747	−	0.901515i	$-0.642456\pi$
$607$	−35.2279	−	20.3388i	−1.42986	−	0.825528i	−0.997109	+	0.0759877i	$0.975789\pi$
$608$	1.82935	+	3.16853i	0.0741899	+	0.128501i
$609$		0			0
$610$	−6.84349	+	11.8533i	−0.277085	+	0.479925i
$611$	−3.05277	+	1.76252i	−0.123502	+	0.0713039i
$612$	−11.8349	+	12.2550i	−0.478398	+	0.495380i
$613$	14.0710	−	24.3717i	0.568323	−	0.984365i	−0.428409	−	0.903585i	$-0.640926\pi$
$613$	14.0710	−	24.3717i	0.568323	−	0.984365i	0.996732	−	0.0807797i	$-0.0257410\pi$
$614$	−13.6813			−0.552131
$615$	−10.6234	−	1.30448i	−0.428378	−	0.0526018i
$616$		0			0
$617$	3.75514	−	2.16803i	0.151176	−	0.0872817i	−0.422504	−	0.906361i	$-0.638849\pi$
$617$	3.75514	−	2.16803i	0.151176	−	0.0872817i	0.573680	+	0.819080i	$0.305515\pi$
$618$	14.7828	−	19.6172i	0.594653	−	0.789118i
$619$	3.76114	−	2.17149i	0.151173	−	0.0872797i	−0.422506	−	0.906360i	$-0.638849\pi$
$619$	3.76114	−	2.17149i	0.151173	−	0.0872797i	0.573678	+	0.819081i	$0.305516\pi$
$620$	−3.21943	−	1.85874i	−0.129295	−	0.0746486i
$621$	1.89966	+	2.34600i	0.0762307	+	0.0941418i
$622$			21.0614i			0.844484i
$623$		0			0
$624$	1.05127	−	0.446228i	0.0420846	−	0.0178634i
$625$	−3.17423	+	5.49792i	−0.126969	+	0.219917i
$626$	33.2171			1.32762
$627$	21.9840	−	29.1732i	0.877956	−	1.16507i
$628$		−	12.8033i		−	0.510905i
$629$	60.1410			2.39798
$630$		0			0
$631$	34.8449			1.38715			0.693577	−	0.720383i	$-0.256034\pi$
$631$	34.8449			1.38715			0.693577	+	0.720383i	$0.256034\pi$
$632$			1.26257i			0.0502222i
$633$	10.3004	+	24.2669i	0.409406	+	0.964522i
$634$	−7.10600			−0.282215
$635$	12.6544	−	21.9181i	0.502175	−	0.869792i
$636$	−6.61821	−	4.98726i	−0.262429	−	0.197758i
$637$		0			0
$638$		−	43.4943i		−	1.72196i
$639$	−6.05440	+	24.2812i	−0.239508	+	0.960549i
$640$	−1.01301	−	0.584859i	−0.0400426	−	0.0231186i
$641$	19.6777	−	11.3609i	0.777222	−	0.448729i	−0.0582231	−	0.998304i	$-0.518543\pi$
$641$	19.6777	−	11.3609i	0.777222	−	0.448729i	0.835445	+	0.549575i	$0.185210\pi$
$642$	5.80072	+	13.6660i	0.228936	+	0.539352i
$643$	−6.64900	+	3.83880i	−0.262211	+	0.151387i	−0.625343	−	0.780350i	$-0.715041\pi$
$643$	−6.64900	+	3.83880i	−0.262211	+	0.151387i	0.363132	+	0.931738i	$0.381707\pi$
$644$		0			0
$645$	3.76760	+	8.87611i	0.148349	+	0.349497i
$646$	20.7775			0.817478
$647$	7.51498	−	13.0163i	0.295444	−	0.511724i	−0.679644	−	0.733542i	$-0.737866\pi$
$647$	7.51498	−	13.0163i	0.295444	−	0.511724i	0.975088	+	0.221818i	$0.0711990\pi$
$648$	4.22550	−	7.94639i	0.165994	−	0.312164i
$649$	5.14041	−	2.96782i	0.201779	−	0.116497i
$650$	1.19733	−	2.07384i	0.0469632	−	0.0813426i
$651$		0			0
$652$	6.42036	+	11.1204i	0.251441	+	0.435508i
$653$	41.7040	+	24.0778i	1.63200	+	0.942238i	0.983474	+	0.181049i	$0.0579492\pi$
$653$	41.7040	+	24.0778i	1.63200	+	0.942238i	0.648530	+	0.761189i	$0.275384\pi$
$654$	−15.2612	−	11.5003i	−0.596758	−	0.449697i
$655$	5.81966	+	10.0799i	0.227393	+	0.393856i
$656$	2.64145	+	4.57513i	0.103131	+	0.178629i
$657$	−2.24025	−	2.16345i	−0.0874004	−	0.0844043i
$658$		0			0
$659$	−38.5699	−	22.2684i	−1.50247	−	0.867452i	−0.999996	−	0.00286104i	$-0.999089\pi$
$659$	−38.5699	−	22.2684i	−1.50247	−	0.867452i	−0.502476	−	0.864591i	$-0.667577\pi$
$660$	−1.42337	+	11.5916i	−0.0554045	+	0.451203i
$661$			29.2550i			1.13789i	0.822376	+	0.568944i	$0.192648\pi$
$661$			29.2550i			1.13789i	−0.822376	+	0.568944i	$0.807352\pi$
$662$			6.97225i			0.270984i
$663$	0.790454	−	6.43730i	0.0306987	−	0.250004i
$664$	10.7716	+	6.21900i	0.418020	+	0.241344i
$665$		0			0
$666$	−30.5401	+	8.75668i	−1.18340	+	0.339315i
$667$	−2.19173	−	3.79618i	−0.0848639	−	0.146989i
$668$	12.3584	+	21.4054i	0.478161	+	0.828199i
$669$	21.1766	+	15.9580i	0.818734	+	0.616971i
$670$	8.63284	+	4.98418i	0.333516	+	0.192555i
$671$	−33.7247	−	58.4128i	−1.30193	−	2.25500i
$672$		0			0
$673$	−7.96391	+	13.7939i	−0.306986	+	0.531716i	−0.977702	−	0.209999i	$-0.932654\pi$
$673$	−7.96391	+	13.7939i	−0.306986	+	0.531716i	0.670715	+	0.741715i	$0.265987\pi$
$674$	−6.85926	+	3.96019i	−0.264209	+	0.152541i
$675$	−2.95164	−	18.6389i	−0.113609	−	0.717412i
$676$	6.28262	−	10.8818i	0.241639	−	0.418531i
$677$	−32.5318			−1.25030			−0.625150	−	0.780505i	$-0.714962\pi$
$677$	−32.5318			−1.25030			−0.625150	+	0.780505i	$0.714962\pi$
$678$	−12.1611	−	28.6504i	−0.467044	−	1.10031i
$679$		0			0
$680$	−5.75278	+	3.32137i	−0.220609	+	0.127369i
$681$	−3.71248	−	8.74625i	−0.142262	−	0.335157i
$682$	15.8653	−	9.15983i	0.607514	−	0.350748i
$683$	−15.2586	−	8.80957i	−0.583855	−	0.337089i	0.178809	−	0.983884i	$-0.442776\pi$
$683$	−15.2586	−	8.80957i	−0.583855	−	0.337089i	−0.762664	+	0.646795i	$0.776109\pi$
$684$	−10.5510	+	3.02525i	−0.403426	+	0.115673i
$685$			4.31348i			0.164810i
$686$		0			0
$687$	26.6326	+	20.0694i	1.01610	+	0.765697i
$688$	2.37970	−	4.12177i	0.0907254	−	0.157141i
$689$	3.15472			0.120185
$690$	0.459883	+	1.08344i	0.0175074	+	0.0412459i
$691$			18.3766i			0.699080i	0.936921	+	0.349540i	$0.113662\pi$
$691$			18.3766i			0.699080i	−0.936921	+	0.349540i	$0.886338\pi$
$692$	12.7707			0.485468
$693$		0			0
$694$	8.94074			0.339386
$695$		−	10.3483i		−	0.392534i
$696$	−7.86519	+	10.4373i	−0.298129	+	0.395624i
$697$	30.0011			1.13637
$698$	0.765989	−	1.32673i	0.0289931	−	0.0502176i
$699$	−4.64907	+	1.97337i	−0.175844	+	0.0746397i
$700$		0			0
$701$		−	28.1696i		−	1.06395i	−0.846760	−	0.531975i	$-0.821450\pi$
$701$		−	28.1696i		−	1.06395i	0.846760	−	0.531975i	$-0.178550\pi$
$702$	0.535888	+	3.38400i	0.0202258	+	0.127721i
$703$	33.5554	+	19.3732i	1.26557	+	0.730675i
$704$	4.99209	−	2.88218i	0.188146	−	0.108626i
$705$	−6.51849	+	8.65018i	−0.245500	+	0.325784i
$706$	−5.17007	+	2.98494i	−0.194578	+	0.112340i
$707$		0			0
$708$	−1.77022	−	0.217370i	−0.0665289	−	0.00816927i
$709$	−33.1625			−1.24544			−0.622722	−	0.782443i	$-0.713973\pi$
$709$	−33.1625			−1.24544			−0.622722	+	0.782443i	$0.713973\pi$
$710$	−4.87863	+	8.45003i	−0.183092	+	0.317124i
$711$	−3.67517	−	0.916388i	−0.137830	−	0.0343672i
$712$	−13.5785	+	7.83957i	−0.508877	+	0.293800i
$713$	0.923148	−	1.59894i	0.0345722	−	0.0598808i
$714$		0			0
$715$	−2.22295	−	3.85026i	−0.0831337	−	0.143992i
$716$	−0.380000	−	0.219393i	−0.0142013	−	0.00819911i
$717$	−13.6102	+	5.77705i	−0.508282	+	0.215748i
$718$	−13.6922	−	23.7156i	−0.510988	−	0.885057i
$719$	17.8533	+	30.9227i	0.665814	+	1.15322i	0.979064	+	0.203553i	$0.0652489\pi$
$719$	17.8533	+	30.9227i	0.665814	+	1.15322i	−0.313250	+	0.949671i	$0.601418\pi$
$720$	2.43771	−	2.52424i	0.0908480	−	0.0940727i
$721$		0			0
$722$	−4.86179	−	2.80696i	−0.180937	−	0.104464i
$723$	2.52177	−	1.07040i	0.0937857	−	0.0398088i
$724$			14.8740i			0.552787i
$725$			27.4030i			1.01772i
$726$	−30.7471	−	23.1700i	−1.14113	−	0.859920i
$727$	−10.0523	−	5.80367i	−0.372817	−	0.215246i	0.301871	−	0.953349i	$-0.402389\pi$
$727$	−10.0523	−	5.80367i	−0.372817	−	0.215246i	−0.674689	+	0.738103i	$0.735722\pi$
$728$		0			0
$729$	20.0640	+	18.0675i	0.743112	+	0.669167i
$730$	−0.607154	−	1.05162i	−0.0224718	−	0.0389223i
$731$	−13.5141	−	23.4072i	−0.499839	−	0.865746i
$732$	−2.47008	+	20.1158i	−0.0912966	+	0.743501i
$733$	−3.25764	−	1.88080i	−0.120324	−	0.0694689i	0.438630	−	0.898668i	$-0.355464\pi$
$733$	−3.25764	−	1.88080i	−0.120324	−	0.0694689i	−0.558954	+	0.829199i	$0.688797\pi$
$734$	7.88479	+	13.6569i	0.291033	+	0.504084i
$735$		0			0
$736$	0.290473	−	0.503113i	0.0107070	−	0.0185450i
$737$	−42.5426	+	24.5620i	−1.56708	+	0.904752i
$738$	−15.2348	+	4.36824i	−0.560801	+	0.160797i
$739$	3.44781	−	5.97178i	0.126830	−	0.219675i	−0.795617	−	0.605800i	$-0.792853\pi$
$739$	3.44781	−	5.97178i	0.126830	−	0.219675i	0.922447	+	0.386125i	$0.126187\pi$
$740$	−12.3876			−0.455377
$741$	2.51468	−	3.33703i	0.0923790	−	0.122589i
$742$		0			0
$743$	−12.9943	+	7.50227i	−0.476715	+	0.275232i	−0.719047	−	0.694962i	$-0.755421\pi$
$743$	−12.9943	+	7.50227i	−0.476715	+	0.275232i	0.242331	+	0.970194i	$0.422088\pi$
$744$	−5.46358	−	0.670889i	−0.200304	−	0.0245960i
$745$	−7.14773	+	4.12674i	−0.261872	+	0.151192i
$746$	14.2222	+	8.21122i	0.520713	+	0.300634i
$747$	−25.9209	+	26.8410i	−0.948397	+	0.982061i
$748$		−	32.7353i		−	1.19692i
$749$		0			0
$750$	2.13140	−	17.3577i	0.0778277	−	0.633813i
$751$	1.28336	−	2.22285i	0.0468305	−	0.0811129i	−0.841660	−	0.540008i	$-0.818421\pi$
$751$	1.28336	−	2.22285i	0.0468305	−	0.0811129i	0.888491	+	0.458895i	$0.151755\pi$
$752$	5.34610			0.194952
$753$	−0.901280	−	0.110671i	−0.0328445	−	0.00403307i
$754$		−	4.97517i		−	0.181185i
$755$	18.9519			0.689730
$756$		0			0
$757$	−8.74001			−0.317661			−0.158831	−	0.987306i	$-0.550772\pi$
$757$	−8.74001			−0.317661			−0.158831	+	0.987306i	$0.550772\pi$
$758$		−	9.75267i		−	0.354233i
$759$	−5.75702	−	0.706921i	−0.208966	−	0.0256596i
$760$	−4.27965			−0.155239
$761$	−11.1340	+	19.2847i	−0.403608	+	0.699069i	−0.994158	−	0.107932i	$-0.965577\pi$
$761$	−11.1340	+	19.2847i	−0.403608	+	0.699069i	0.590551	+	0.807001i	$0.298911\pi$
$762$	4.56745	−	37.1964i	0.165461	−	1.34748i
$763$		0			0
$764$			7.42503i			0.268628i
$765$	−5.49264	−	19.1563i	−0.198587	−	0.692598i
$766$	24.4623	+	14.1233i	0.883858	+	0.510296i
$767$	0.587995	−	0.339479i	0.0212313	−	0.0122579i
$768$	−1.71914	−	0.211098i	−0.0620341	−	0.00761734i
$769$	19.3368	−	11.1641i	0.697304	−	0.402589i	−0.109039	−	0.994038i	$-0.534777\pi$
$769$	19.3368	−	11.1641i	0.697304	−	0.402589i	0.806342	+	0.591449i	$0.201444\pi$
$770$		0			0
$771$	−2.45559	+	3.25863i	−0.0884361	+	0.117357i
$772$	3.82307			0.137595
$773$	13.2482	−	22.9465i	0.476504	−	0.825329i	−0.523134	−	0.852251i	$-0.675237\pi$
$773$	13.2482	−	22.9465i	0.476504	−	0.825329i	0.999638	+	0.0269220i	$0.00857057\pi$
$774$	10.2707	+	9.91866i	0.369174	+	0.356519i
$775$	−9.99571	+	5.77103i	−0.359057	+	0.207301i
$776$	7.26808	−	12.5887i	0.260909	−	0.451907i
$777$		0			0
$778$	−3.09224	−	5.35592i	−0.110862	−	0.192019i
$779$	16.7390	+	9.66427i	0.599737	+	0.346259i
$780$	−0.162814	+	1.32593i	−0.00582969	+	0.0474758i
$781$	−24.0418	−	41.6417i	−0.860284	−	1.49006i
$782$	−1.64957	−	2.85714i	−0.0589885	−	0.102171i
$783$	−24.6730	−	30.4701i	−0.881740	−	1.08891i
$784$		0			0
$785$	12.9698	+	7.48810i	0.462911	+	0.267262i
$786$	13.7643	+	10.3723i	0.490955	+	0.369967i
$787$		−	24.7069i		−	0.880704i	−0.897825	−	0.440352i	$-0.854854\pi$
$787$		−	24.7069i		−	0.880704i	0.897825	−	0.440352i	$-0.145146\pi$
$788$		−	8.80043i		−	0.313502i
$789$	−7.10539	+	3.01599i	−0.252959	+	0.107372i
$790$	−1.27899	−	0.738424i	−0.0455043	−	0.0262719i
$791$		0			0
$792$	4.76635	+	16.6233i	0.169365	+	0.590682i
$793$	−3.85765	−	6.68165i	−0.136989	−	0.237272i
$794$	11.2338	+	19.4575i	0.398673	+	0.690522i
$795$	8.92285	−	3.78744i	0.316461	−	0.134327i
$796$	14.5174	+	8.38165i	0.514557	+	0.297080i
$797$	5.22781	+	9.05484i	0.185179	+	0.320739i	0.943637	−	0.330983i	$-0.107380\pi$
$797$	5.22781	+	9.05484i	0.185179	+	0.320739i	−0.758458	+	0.651722i	$0.774047\pi$
$798$		0			0
$799$	15.1800	−	26.2926i	0.537031	−	0.930164i
$800$	−3.14519	+	1.81588i	−0.111199	+	0.0642010i
$801$	−12.9645	−	45.2155i	−0.458079	−	1.59761i
$802$	0.315767	−	0.546925i	0.0111501	−	0.0193126i
$803$	5.98410			0.211174
$804$	14.6505	+	1.79898i	0.516684	+	0.0634451i
$805$		0			0
$806$	1.81478	−	1.04776i	0.0639229	−	0.0369059i
$807$	9.93744	−	13.1872i	0.349814	−	0.464211i
$808$	−10.2064	+	5.89265i	−0.359059	+	0.207303i
$809$	−27.1354	−	15.6666i	−0.954031	−	0.550810i	−0.0597000	−	0.998216i	$-0.519014\pi$
$809$	−27.1354	−	15.6666i	−0.954031	−	0.550810i	−0.894331	+	0.447406i	$0.852348\pi$
$810$	5.57842	+	8.92798i	0.196006	+	0.313697i
$811$			12.4653i			0.437717i	0.975757	+	0.218858i	$0.0702333\pi$
$811$			12.4653i			0.437717i	−0.975757	+	0.218858i	$0.929767\pi$
$812$		0			0
$813$	19.6085	−	8.32312i	0.687699	−	0.291904i
$814$	30.5230	−	52.8673i	1.06983	−	1.85300i
$815$	−15.0200			−0.526129
$816$	−5.91962	+	7.85547i	−0.207228	+	0.274996i
$817$		−	17.4133i		−	0.609213i
$818$	−8.03570			−0.280962
$819$		0			0
$820$	−6.17951			−0.215798
$821$		−	36.8844i		−	1.28727i	−0.765331	−	0.643637i	$-0.777425\pi$
$821$		−	36.8844i		−	1.28727i	0.765331	−	0.643637i	$-0.222575\pi$
$822$	2.49561	+	5.87942i	0.0870444	+	0.205068i
$823$	14.7112			0.512800			0.256400	−	0.966571i	$-0.417464\pi$
$823$	14.7112			0.512800			0.256400	+	0.966571i	$0.417464\pi$
$824$	7.09087	−	12.2817i	0.247022	−	0.427855i
$825$	28.9584	+	21.8221i	1.00820	+	0.759748i
$826$		0			0
$827$			44.3837i			1.54337i	0.636004	+	0.771686i	$0.280586\pi$
$827$			44.3837i			1.54337i	−0.636004	+	0.771686i	$0.719414\pi$
$828$	1.25367	+	1.21070i	0.0435681	+	0.0420746i
$829$	−47.7610	−	27.5748i	−1.65881	−	0.957712i	−0.973267	−	0.229677i	$-0.926233\pi$
$829$	−47.7610	−	27.5748i	−1.65881	−	0.957712i	−0.685540	−	0.728035i	$-0.740434\pi$
$830$	−12.5998	+	7.27448i	−0.437344	+	0.252501i
$831$	−11.5354	−	27.1763i	−0.400158	−	0.942735i
$832$	0.571028	−	0.329683i	0.0197968	−	0.0114297i
$833$		0			0
$834$	−5.98713	−	14.1051i	−0.207317	−	0.488420i
$835$	−28.9117			−1.00053
$836$	10.5450	−	18.2645i	0.364708	−	0.631692i
$837$	5.91841	−	15.4169i	0.204570	−	0.532884i
$838$	−24.3275	+	14.0455i	−0.840381	+	0.485194i
$839$	3.89752	−	6.75071i	0.134557	−	0.233060i	−0.790871	−	0.611983i	$-0.790372\pi$
$839$	3.89752	−	6.75071i	0.134557	−	0.233060i	0.925428	+	0.378923i	$0.123705\pi$
$840$		0			0
$841$	13.9664	+	24.1904i	0.481598	+	0.834153i
$842$	−35.3779	−	20.4254i	−1.21920	−	0.703907i
$843$	−13.2847	−	10.0109i	−0.457550	−	0.344795i
$844$	7.61019	+	13.1812i	0.261954	+	0.453717i
$845$	7.34890	+	12.7287i	0.252810	+	0.437879i
$846$	−3.88027	+	15.5618i	−0.133406	+	0.535026i
$847$		0			0
$848$	−4.14347	−	2.39223i	−0.142287	−	0.0821497i
$849$	5.88289	−	47.9091i	0.201900	−	1.64424i
$850$			20.6245i			0.707413i
$851$		−	6.15234i		−	0.210900i
$852$	−1.76088	+	14.3403i	−0.0603268	+	0.491289i
$853$	−21.3756	−	12.3412i	−0.731887	−	0.422555i	0.0872249	−	0.996189i	$-0.472200\pi$
$853$	−21.3756	−	12.3412i	−0.731887	−	0.422555i	−0.819112	+	0.573633i	$0.805533\pi$
$854$		0			0
$855$	3.10623	−	12.4575i	0.106231	−	0.426039i
$856$	4.28570	+	7.42305i	0.146482	+	0.253715i
$857$	−15.0201	−	26.0156i	−0.513077	−	0.888676i	−0.999885	−	0.0151669i	$-0.995172\pi$
$857$	−15.0201	−	26.0156i	−0.513077	−	0.888676i	0.486808	−	0.873509i	$-0.338161\pi$
$858$	−5.25757	−	3.96193i	−0.179490	−	0.135258i
$859$	−41.5656	−	23.9979i	−1.41820	−	0.818799i	−0.422060	−	0.906568i	$-0.638693\pi$
$859$	−41.5656	−	23.9979i	−1.41820	−	0.818799i	−0.996141	+	0.0877689i	$0.972026\pi$
$860$	2.78359	+	4.82131i	0.0949195	+	0.164405i
$861$		0			0
$862$	1.67992	−	2.90971i	0.0572184	−	0.0991052i
$863$	36.8446	−	21.2722i	1.25420	−	0.724115i	0.282263	−	0.959337i	$-0.408915\pi$
$863$	36.8446	−	21.2722i	1.25420	−	0.724115i	0.971942	+	0.235222i	$0.0755817\pi$
$864$	1.86225	−	4.85098i	0.0633552	−	0.165034i
$865$	−7.46905	+	12.9368i	−0.253955	+	0.439864i
$866$	12.7148			0.432066
$867$	10.3206	+	24.3143i	0.350504	+	0.825755i
$868$		0			0
$869$	6.30284	−	3.63895i	0.213809	−	0.123443i
$870$	−5.97300	−	14.0718i	−0.202504	−	0.477080i
$871$	−4.86631	+	2.80956i	−0.164888	+	0.0951984i
$872$	−9.55458	−	5.51634i	−0.323559	−	0.186807i
$873$	31.3688	+	30.2935i	1.06167	+	1.02528i
$874$		−	2.12550i		−	0.0718963i
$875$		0			0
$876$	−1.43600	−	1.08212i	−0.0485179	−	0.0365615i
$877$	−16.8006	+	29.0995i	−0.567317	+	0.982621i	0.429513	+	0.903061i	$0.358685\pi$
$877$	−16.8006	+	29.0995i	−0.567317	+	0.982621i	−0.996830	+	0.0795608i	$0.974648\pi$
$878$	−17.0606			−0.575766
$879$	0.366824	+	0.864202i	0.0123727	+	0.0291488i
$880$			6.74269i			0.227296i
$881$	−36.1880			−1.21921			−0.609603	−	0.792707i	$-0.708671\pi$
$881$	−36.1880			−1.21921			−0.609603	+	0.792707i	$0.708671\pi$
$882$		0			0
$883$	2.99025			0.100630			0.0503149	−	0.998733i	$-0.483977\pi$
$883$	2.99025			0.100630			0.0503149	+	0.998733i	$0.483977\pi$
$884$		−	3.74449i		−	0.125941i
$885$	1.25553	−	1.66611i	0.0422041	−	0.0560057i
$886$	−4.91728			−0.165199
$887$	−2.93491	+	5.08341i	−0.0985445	+	0.170684i	−0.911082	−	0.412224i	$-0.864752\pi$
$887$	−2.93491	+	5.08341i	−0.0985445	+	0.170684i	0.812538	+	0.582908i	$0.198085\pi$
$888$	−16.8847	+	7.16697i	−0.566614	+	0.240508i
$889$		0			0
$890$		−	18.3402i		−	0.614765i
$891$	−51.8477	+	1.80886i	−1.73696	+	0.0605991i
$892$	13.2581	+	7.65455i	0.443913	+	0.256293i
$893$	16.9393	−	9.77988i	0.566851	−	0.327271i
$894$	−7.35502	+	9.76028i	−0.245989	+	0.326433i
$895$	0.444493	−	0.256628i	0.0148578	−	0.00857814i
$896$		0			0
$897$	−0.658526	−	0.0808624i	−0.0219876	−	0.00269992i
$898$	−4.88329			−0.162958
$899$	−11.9899	+	20.7672i	−0.399887	+	0.692625i
$900$	−3.00297	−	10.4733i	−0.100099	−	0.349109i
$901$	−23.5304	+	13.5853i	−0.783912	+	0.452592i
$902$	15.2263	−	26.3727i	0.506980	−	0.878114i
$903$		0			0
$904$	−8.98489	−	15.5623i	−0.298833	−	0.517594i
$905$	−15.0674	−	8.69918i	−0.500858	−	0.289171i
$906$	25.8321	−	10.9648i	0.858213	−	0.364282i
$907$	−7.12662	−	12.3437i	−0.236636	−	0.409865i	0.723111	−	0.690732i	$-0.242711\pi$
$907$	−7.12662	−	12.3437i	−0.236636	−	0.409865i	−0.959747	+	0.280867i	$0.909378\pi$
$908$	−2.74286	−	4.75077i	−0.0910250	−	0.157660i
$909$	−9.74485	−	33.9864i	−0.323216	−	1.12726i
$910$		0			0
$911$	24.3461	+	14.0562i	0.806623	+	0.465704i	0.845782	−	0.533529i	$-0.179135\pi$
$911$	24.3461	+	14.0562i	0.806623	+	0.465704i	−0.0391589	+	0.999233i	$0.512468\pi$
$912$	−5.83331	+	2.47604i	−0.193160	+	0.0819898i
$913$		−	71.6971i		−	2.37283i
$914$		−	12.1305i		−	0.401240i
$915$	−18.9328	−	14.2671i	−0.625898	−	0.471656i
$916$	16.6739	+	9.62669i	0.550922	+	0.318075i
$917$		0			0
$918$	−18.5697	−	22.9329i	−0.612893	−	0.756898i
$919$	1.20114	+	2.08044i	0.0396220	+	0.0686273i	0.885156	−	0.465294i	$-0.154051\pi$
$919$	1.20114	+	2.08044i	0.0396220	+	0.0686273i	−0.845534	+	0.533921i	$0.820718\pi$
$920$	0.339771	+	0.588501i	0.0112019	+	0.0194023i
$921$	2.88809	−	23.5200i	0.0951658	−	0.775011i
$922$	−5.75083	−	3.32024i	−0.189393	−	0.109346i
$923$	−2.75007	−	4.76326i	−0.0905195	−	0.156784i
$924$		0			0
$925$	−19.2306	+	33.3083i	−0.632297	+	1.09517i
$926$	−6.30496	+	3.64017i	−0.207194	+	0.119623i
$927$	30.6040	+	29.5549i	1.00517	+	0.970710i
$928$	−3.77269	+	6.53449i	−0.123845	+	0.214505i
$929$	−22.3572			−0.733516			−0.366758	−	0.930316i	$-0.619532\pi$
$929$	−22.3572			−0.733516			−0.366758	+	0.930316i	$0.619532\pi$
$930$	3.87504	−	5.14226i	0.127068	−	0.168621i
$931$		0			0
$932$	−2.52528	+	1.45797i	−0.0827182	+	0.0477574i
$933$	−36.2074	−	4.44601i	−1.18538	−	0.145556i
$934$	−29.7794	+	17.1931i	−0.974412	+	0.562577i
$935$	33.1611	+	19.1456i	1.08448	+	0.626127i
$936$	0.545207	+	1.90148i	0.0178207	+	0.0621518i
$937$		−	15.6773i		−	0.512156i	−0.966656	−	0.256078i	$-0.917570\pi$
$937$		−	15.6773i		−	0.512156i	0.966656	−	0.256078i	$-0.0824305\pi$
$938$		0			0
$939$	−7.01207	+	57.1048i	−0.228830	+	1.86355i
$940$	−3.12672	+	5.41563i	−0.101982	+	0.176638i
$941$	38.2897			1.24821			0.624105	−	0.781341i	$-0.285464\pi$
$941$	38.2897			1.24821			0.624105	+	0.781341i	$0.285464\pi$
$942$	22.0106	+	2.70274i	0.717143	+	0.0880600i
$943$		−	3.06908i		−	0.0999428i
$944$	−1.02971			−0.0335143
$945$		0			0
$946$	−27.4350			−0.891988
$947$		−	53.6544i		−	1.74353i	−0.489922	−	0.871766i	$-0.662975\pi$
$947$		−	53.6544i		−	1.74353i	0.489922	−	0.871766i	$-0.337025\pi$
$948$	−2.17053	−	0.266525i	−0.0704954	−	0.00865634i
$949$	0.684502			0.0222199
$950$	−6.64376	+	11.5073i	−0.215552	+	0.373347i
$951$	1.50006	−	12.2162i	0.0486429	−	0.396138i
$952$		0			0
$953$			18.0861i			0.585866i	0.956133	+	0.292933i	$0.0946313\pi$
$953$			18.0861i			0.585866i	−0.956133	+	0.292933i	$0.905369\pi$
$954$	9.97088	−	10.3248i	0.322819	−	0.334278i
$955$	−7.52160	−	4.34260i	−0.243393	−	0.140523i
$956$	−7.39276	+	4.26821i	−0.239099	+	0.138044i
$957$	74.7727	+	9.18156i	2.41706	+	0.296798i
$958$	−18.5161	+	10.6903i	−0.598229	+	0.345388i
$959$		0			0
$960$	1.21930	−	1.61804i	0.0393527	−	0.0522219i
$961$	20.8997			0.674185
$962$	3.49142	−	6.04732i	0.112568	−	0.194973i
$963$	−24.7182	+	7.08739i	−0.796533	+	0.228388i
$964$	1.36977	−	0.790838i	0.0441174	−	0.0254712i
$965$	−2.23596	+	3.87280i	−0.0719781	+	0.124670i
$966$		0			0
$967$	−13.8281	−	23.9509i	−0.444681	−	0.770209i	0.553349	−	0.832949i	$-0.313349\pi$
$967$	−13.8281	−	23.9509i	−0.444681	−	0.770209i	−0.998030	+	0.0627399i	$0.980016\pi$
$968$	−19.2499	−	11.1139i	−0.618716	−	0.357216i
$969$	−4.38608	+	35.7193i	−0.140901	+	1.14747i
$970$	8.50161	+	14.7252i	0.272970	+	0.472798i
$971$	−3.83935	−	6.64995i	−0.123211	−	0.213407i	0.797821	−	0.602894i	$-0.205986\pi$
$971$	−3.83935	−	6.64995i	−0.123211	−	0.213407i	−0.921032	+	0.389487i	$0.872652\pi$
$972$	12.7689	+	8.94170i	0.409564	+	0.286805i
$973$		0			0
$974$	2.46694	+	1.42429i	0.0790460	+	0.0456372i
$975$	3.31246	+	2.49616i	0.106084	+	0.0799411i
$976$			11.7011i			0.374543i
$977$			29.4635i			0.942622i	0.881967	+	0.471311i	$0.156219\pi$
$977$			29.4635i			0.942622i	−0.881967	+	0.471311i	$0.843781\pi$
$978$	−20.4728	+	8.68999i	−0.654648	+	0.277875i
$979$	78.2716	+	45.1901i	2.50157	+	1.44428i
$980$		0			0
$981$	22.9922	−	23.8084i	0.734085	−	0.760142i
$982$	−0.0922824	−	0.159838i	−0.00294485	−	0.00510063i
$983$	16.4573	+	28.5050i	0.524908	+	0.909167i	0.999579	+	0.0290038i	$0.00923350\pi$
$983$	16.4573	+	28.5050i	0.524908	+	0.909167i	−0.474672	+	0.880163i	$0.657433\pi$
$984$	−8.42288	+	3.57522i	−0.268512	+	0.113974i
$985$	8.91489	+	5.14701i	0.284052	+	0.163998i
$986$	21.4248	+	37.1088i	0.682304	+	1.18179i
$987$		0			0
$988$	1.20621	−	2.08922i	0.0383747	−	0.0664670i
$989$	−2.39452	+	1.38248i	−0.0761414	+	0.0439602i
$990$	−19.6271	−	4.89393i	−0.623791	−	0.155539i
$991$	−7.31686	+	12.6732i	−0.232428	+	0.402577i	−0.958522	−	0.285019i	$-0.908000\pi$
$991$	−7.31686	+	12.6732i	−0.232428	+	0.402577i	0.726094	+	0.687595i	$0.241334\pi$
$992$	−3.17809			−0.100904
$993$	−11.9863	−	1.47183i	−0.380373	−	0.0467070i
$994$		0			0
$995$	−16.9813	+	9.80417i	−0.538344	+	0.310813i
$996$	−12.9652	+	17.2051i	−0.410818	+	0.545164i
$997$	12.9041	−	7.45020i	0.408678	−	0.235950i	−0.281544	−	0.959548i	$-0.590846\pi$
$997$	12.9041	−	7.45020i	0.408678	−	0.235950i	0.690221	+	0.723598i	$0.257513\pi$
$998$	−9.38170	−	5.41653i	−0.296972	−	0.171457i
$999$	−8.60700	−	54.3511i	−0.272314	−	1.71959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.13		48
3.2	odd	2		2646.2.l.c.521.7		48
7.2	even	3		882.2.t.c.803.21		48
7.3	odd	6		882.2.m.c.587.4	yes	48
7.4	even	3		882.2.m.c.587.9	yes	48
7.5	odd	6		882.2.t.c.803.16		48
7.6	odd	2	inner	882.2.l.c.227.24		48
9.4	even	3		2646.2.t.c.2285.5		48
9.5	odd	6		882.2.t.c.815.16		48
21.2	odd	6		2646.2.t.c.1979.6		48
21.5	even	6		2646.2.t.c.1979.5		48
21.11	odd	6		2646.2.m.c.1763.17		48
21.17	even	6		2646.2.m.c.1763.18		48
21.20	even	2		2646.2.l.c.521.8		48
63.4	even	3		2646.2.m.c.881.18		48
63.5	even	6	inner	882.2.l.c.509.1		48
63.13	odd	6		2646.2.t.c.2285.6		48
63.23	odd	6	inner	882.2.l.c.509.12		48
63.31	odd	6		2646.2.m.c.881.17		48
63.32	odd	6		882.2.m.c.293.4	✓	48
63.40	odd	6		2646.2.l.c.1097.7		48
63.41	even	6		882.2.t.c.815.21		48
63.58	even	3		2646.2.l.c.1097.8		48
63.59	even	6		882.2.m.c.293.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.13		48	1.1	even	1	trivial
882.2.l.c.227.24		48	7.6	odd	2	inner
882.2.l.c.509.1		48	63.5	even	6	inner
882.2.l.c.509.12		48	63.23	odd	6	inner
882.2.m.c.293.4	✓	48	63.32	odd	6
882.2.m.c.293.9	yes	48	63.59	even	6
882.2.m.c.587.4	yes	48	7.3	odd	6
882.2.m.c.587.9	yes	48	7.4	even	3
882.2.t.c.803.16		48	7.5	odd	6
882.2.t.c.803.21		48	7.2	even	3
882.2.t.c.815.16		48	9.5	odd	6
882.2.t.c.815.21		48	63.41	even	6
2646.2.l.c.521.7		48	3.2	odd	2
2646.2.l.c.521.8		48	21.20	even	2
2646.2.l.c.1097.7		48	63.40	odd	6
2646.2.l.c.1097.8		48	63.58	even	3
2646.2.m.c.881.17		48	63.31	odd	6
2646.2.m.c.881.18		48	63.4	even	3
2646.2.m.c.1763.17		48	21.11	odd	6
2646.2.m.c.1763.18		48	21.17	even	6
2646.2.t.c.1979.5		48	21.5	even	6
2646.2.t.c.1979.6		48	21.2	odd	6
2646.2.t.c.2285.5		48	9.4	even	3
2646.2.t.c.2285.6		48	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.71914 - 0.211098i) q^{3} -1.00000 q^{4} +(0.584859 - 1.01301i) q^{5} +(0.211098 - 1.71914i) q^{6} -1.00000i q^{8} +(2.91088 + 0.725813i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.71914 - 0.211098i) q^{3} -1.00000 q^{4} +(0.584859 - 1.01301i) q^{5} +(0.211098 - 1.71914i) q^{6} -1.00000i q^{8} +(2.91088 + 0.725813i) q^{9} +(1.01301 + 0.584859i) q^{10} +(-4.99209 + 2.88218i) q^{11} +(1.71914 + 0.211098i) q^{12} +(-0.571028 + 0.329683i) q^{13} +(-1.21930 + 1.61804i) q^{15} +1.00000 q^{16} +(2.83946 - 4.91809i) q^{17} +(-0.725813 + 2.91088i) q^{18} +(3.16853 - 1.82935i) q^{19} +(-0.584859 + 1.01301i) q^{20} +(-2.88218 - 4.99209i) q^{22} +(-0.503113 - 0.290473i) q^{23} +(-0.211098 + 1.71914i) q^{24} +(1.81588 + 3.14519i) q^{25} +(-0.329683 - 0.571028i) q^{26} +(-4.85098 - 1.86225i) q^{27} +(6.53449 + 3.77269i) q^{29} +(-1.61804 - 1.21930i) q^{30} +3.17809i q^{31} +1.00000i q^{32} +(9.19051 - 3.90105i) q^{33} +(4.91809 + 2.83946i) q^{34} +(-2.91088 - 0.725813i) q^{36} +(5.29511 + 9.17140i) q^{37} +(1.82935 + 3.16853i) q^{38} +(1.05127 - 0.446228i) q^{39} +(-1.01301 - 0.584859i) q^{40} +(2.64145 + 4.57513i) q^{41} +(2.37970 - 4.12177i) q^{43} +(4.99209 - 2.88218i) q^{44} +(2.43771 - 2.52424i) q^{45} +(0.290473 - 0.503113i) q^{46} +5.34610 q^{47} +(-1.71914 - 0.211098i) q^{48} +(-3.14519 + 1.81588i) q^{50} +(-5.91962 + 7.85547i) q^{51} +(0.571028 - 0.329683i) q^{52} +(-4.14347 - 2.39223i) q^{53} +(1.86225 - 4.85098i) q^{54} +6.74269i q^{55} +(-5.83331 + 2.47604i) q^{57} +(-3.77269 + 6.53449i) q^{58} -1.02971 q^{59} +(1.21930 - 1.61804i) q^{60} +11.7011i q^{61} -3.17809 q^{62} -1.00000 q^{64} +0.771274i q^{65} +(3.90105 + 9.19051i) q^{66} +8.52200 q^{67} +(-2.83946 + 4.91809i) q^{68} +(0.803603 + 0.605569i) q^{69} +8.34154i q^{71} +(0.725813 - 2.91088i) q^{72} +(-0.899038 - 0.519060i) q^{73} +(-9.17140 + 5.29511i) q^{74} +(-2.45780 - 5.79035i) q^{75} +(-3.16853 + 1.82935i) q^{76} +(0.446228 + 1.05127i) q^{78} -1.26257 q^{79} +(0.584859 - 1.01301i) q^{80} +(7.94639 + 4.22550i) q^{81} +(-4.57513 + 2.64145i) q^{82} +(-6.21900 + 10.7716i) q^{83} +(-3.32137 - 5.75278i) q^{85} +(4.12177 + 2.37970i) q^{86} +(-10.4373 - 7.86519i) q^{87} +(2.88218 + 4.99209i) q^{88} +(-7.83957 - 13.5785i) q^{89} +(2.52424 + 2.43771i) q^{90} +(0.503113 + 0.290473i) q^{92} +(0.670889 - 5.46358i) q^{93} +5.34610i q^{94} -4.27965i q^{95} +(0.211098 - 1.71914i) q^{96} +(12.5887 + 7.26808i) q^{97} +(-16.6233 + 4.76635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

L-functions

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