LMFDB - Embedded newform 1386.2.bk.c.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$-0.186243 - 0.0499037i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.c.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.90775 + 1.10144i) q^{5} +(-2.24014 + 1.40775i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.90775 + 1.10144i) q^{5} +(-2.24014 + 1.40775i) q^{7} -1.00000i q^{8} +(-1.10144 - 1.90775i) q^{10} +(1.82062 - 2.77225i) q^{11} -1.45937 q^{13} +(2.64390 - 0.0990746i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.80366 - 6.58813i) q^{17} +(0.0903227 - 0.156443i) q^{19} +2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +(1.14390 - 1.98129i) q^{23} +(-0.0736626 - 0.127587i) q^{25} +(1.26385 + 0.729686i) q^{26} +(-2.33922 - 1.23615i) q^{28} -4.45335i q^{29} +(7.40363 - 4.27449i) q^{31} +(0.866025 - 0.500000i) q^{32} +7.60732i q^{34} +(-5.82418 + 0.218249i) q^{35} +(-0.754735 + 1.30724i) q^{37} +(-0.156443 + 0.0903227i) q^{38} +(1.10144 - 1.90775i) q^{40} +7.10368 q^{41} +1.58174i q^{43} +(3.31114 + 0.190575i) q^{44} +(-1.98129 + 1.14390i) q^{46} +(0.472293 + 0.272679i) q^{47} +(3.03649 - 6.30712i) q^{49} +0.147325i q^{50} +(-0.729686 - 1.26385i) q^{52} +(2.41722 + 4.18675i) q^{53} +(6.52674 - 3.28346i) q^{55} +(1.40775 + 2.24014i) q^{56} +(-2.22668 + 3.85672i) q^{58} +(5.36041 - 3.09483i) q^{59} +(2.86310 - 4.95904i) q^{61} -8.54897 q^{62} -1.00000 q^{64} +(-2.78412 - 1.60741i) q^{65} +(1.49088 + 2.58228i) q^{67} +(3.80366 - 6.58813i) q^{68} +(5.15301 + 2.72308i) q^{70} +7.57488 q^{71} +(4.83822 + 8.38004i) q^{73} +(1.30724 - 0.754735i) q^{74} +0.180645 q^{76} +(-0.175810 + 8.77320i) q^{77} +(5.99185 + 3.45939i) q^{79} +(-1.90775 + 1.10144i) q^{80} +(-6.15197 - 3.55184i) q^{82} +5.84246 q^{83} -16.7580i q^{85} +(0.790869 - 1.36983i) q^{86} +(-2.77225 - 1.82062i) q^{88} +(-13.9527 - 8.05557i) q^{89} +(3.26920 - 2.05443i) q^{91} +2.28779 q^{92} +(-0.272679 - 0.472293i) q^{94} +(0.344626 - 0.198970i) q^{95} +11.3012i q^{97} +(-5.78323 + 3.94388i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5	$ 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.90775	+	1.10144i	0.853171	+	0.492579i	0.861720	−	0.507385i	$-0.169388\pi$
$5$	1.90775	+	1.10144i	0.853171	+	0.492579i	−0.00854833	+	0.999963i	$0.502721\pi$
$6$		0			0
$7$	−2.24014	+	1.40775i	−0.846695	+	0.532079i
$7$	−2.24014	+	1.40775i	−0.846695	+	0.532079i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.10144	−	1.90775i	−0.348306	−	0.603283i
$11$	1.82062	−	2.77225i	0.548936	−	0.835864i
$11$	1.82062	−	2.77225i	0.548936	−	0.835864i
$12$		0			0
$13$	−1.45937			−0.404757			−0.202378	−	0.979307i	$-0.564867\pi$
$13$	−1.45937			−0.404757			−0.202378	+	0.979307i	$0.564867\pi$
$14$	2.64390	−	0.0990746i	0.706611	−	0.0264788i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.80366	−	6.58813i	−0.922523	−	1.59786i	−0.795498	−	0.605957i	$-0.792790\pi$
$17$	−3.80366	−	6.58813i	−0.922523	−	1.59786i	−0.127025	−	0.991899i	$-0.540543\pi$
$18$		0			0
$19$	0.0903227	−	0.156443i	0.0207214	−	0.0358906i	−0.855479	−	0.517838i	$-0.826737\pi$
$19$	0.0903227	−	0.156443i	0.0207214	−	0.0358906i	0.876200	+	0.481947i	$0.160070\pi$
$20$			2.20288i			0.492579i
$21$		0			0
$22$	−2.96282	+	1.49053i	−0.631676	+	0.317782i
$23$	1.14390	−	1.98129i	0.238519	−	0.413127i	−0.721771	−	0.692132i	$-0.756671\pi$
$23$	1.14390	−	1.98129i	0.238519	−	0.413127i	0.960289	+	0.279006i	$0.0900048\pi$
$24$		0			0
$25$	−0.0736626	−	0.127587i	−0.0147325	−	0.0255175i
$26$	1.26385	+	0.729686i	0.247862	+	0.143103i
$27$		0			0
$28$	−2.33922	−	1.23615i	−0.442071	−	0.233610i
$29$		−	4.45335i		−	0.826967i	−0.910512	−	0.413483i	$-0.864312\pi$
$29$		−	4.45335i		−	0.826967i	0.910512	−	0.413483i	$-0.135688\pi$
$30$		0			0
$31$	7.40363	−	4.27449i	1.32973	−	0.767720i	0.344473	−	0.938796i	$-0.388058\pi$
$31$	7.40363	−	4.27449i	1.32973	−	0.767720i	0.985258	+	0.171076i	$0.0547243\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			7.60732i			1.30464i
$35$	−5.82418	+	0.218249i	−0.984466	+	0.0368909i
$36$		0			0
$37$	−0.754735	+	1.30724i	−0.124078	+	0.214909i	−0.921372	−	0.388682i	$-0.872931\pi$
$37$	−0.754735	+	1.30724i	−0.124078	+	0.214909i	0.797294	+	0.603591i	$0.206264\pi$
$38$	−0.156443	+	0.0903227i	−0.0253785	+	0.0146523i
$39$		0			0
$40$	1.10144	−	1.90775i	0.174153	−	0.301642i
$41$	7.10368			1.10941			0.554705	−	0.832047i	$-0.312831\pi$
$41$	7.10368			1.10941			0.554705	+	0.832047i	$0.312831\pi$
$42$		0			0
$43$			1.58174i			0.241213i	0.992700	+	0.120606i	$0.0384839\pi$
$43$			1.58174i			0.241213i	−0.992700	+	0.120606i	$0.961516\pi$
$44$	3.31114	+	0.190575i	0.499174	+	0.0287303i
$45$		0			0
$46$	−1.98129	+	1.14390i	−0.292125	+	0.168658i
$47$	0.472293	+	0.272679i	0.0688911	+	0.0397743i	0.534050	−	0.845453i	$-0.320669\pi$
$47$	0.472293	+	0.272679i	0.0688911	+	0.0397743i	−0.465159	+	0.885227i	$0.654003\pi$
$48$		0			0
$49$	3.03649	−	6.30712i	0.433784	−	0.901017i
$50$			0.147325i			0.0208349i
$51$		0			0
$52$	−0.729686	−	1.26385i	−0.101189	−	0.175265i
$53$	2.41722	+	4.18675i	0.332031	+	0.575094i	0.982910	−	0.184087i	$-0.0589329\pi$
$53$	2.41722	+	4.18675i	0.332031	+	0.575094i	−0.650879	+	0.759181i	$0.725600\pi$
$54$		0			0
$55$	6.52674	−	3.28346i	0.880065	−	0.442741i
$56$	1.40775	+	2.24014i	0.188118	+	0.299352i
$57$		0			0
$58$	−2.22668	+	3.85672i	−0.292377	+	0.506412i
$59$	5.36041	−	3.09483i	0.697866	−	0.402913i	−0.108686	−	0.994076i	$-0.534664\pi$
$59$	5.36041	−	3.09483i	0.697866	−	0.402913i	0.806552	+	0.591163i	$0.201331\pi$
$60$		0			0
$61$	2.86310	−	4.95904i	0.366583	−	0.634940i	−0.622446	−	0.782663i	$-0.713861\pi$
$61$	2.86310	−	4.95904i	0.366583	−	0.634940i	0.989029	+	0.147723i	$0.0471943\pi$
$62$	−8.54897			−1.08572
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.78412	−	1.60741i	−0.345327	−	0.199375i
$66$		0			0
$67$	1.49088	+	2.58228i	0.182140	+	0.315476i	0.942609	−	0.333898i	$-0.108364\pi$
$67$	1.49088	+	2.58228i	0.182140	+	0.315476i	−0.760469	+	0.649374i	$0.775031\pi$
$68$	3.80366	−	6.58813i	0.461261	−	0.798928i
$69$		0			0
$70$	5.15301	+	2.72308i	0.615903	+	0.325470i
$71$	7.57488			0.898973			0.449486	−	0.893287i	$-0.351607\pi$
$71$	7.57488			0.898973			0.449486	+	0.893287i	$0.351607\pi$
$72$		0			0
$73$	4.83822	+	8.38004i	0.566271	+	0.980810i	0.996930	+	0.0782953i	$0.0249477\pi$
$73$	4.83822	+	8.38004i	0.566271	+	0.980810i	−0.430659	+	0.902515i	$0.641719\pi$
$74$	1.30724	−	0.754735i	0.151964	−	0.0877362i
$75$		0			0
$76$	0.180645			0.0207214
$77$	−0.175810	+	8.77320i	−0.0200354	+	0.999799i
$78$		0			0
$79$	5.99185	+	3.45939i	0.674135	+	0.389212i	0.797642	−	0.603132i	$-0.206081\pi$
$79$	5.99185	+	3.45939i	0.674135	+	0.389212i	−0.123506	+	0.992344i	$0.539414\pi$
$80$	−1.90775	+	1.10144i	−0.213293	+	0.123145i
$81$		0			0
$82$	−6.15197	−	3.55184i	−0.679372	−	0.392235i
$83$	5.84246			0.641293			0.320647	−	0.947199i	$-0.396100\pi$
$83$	5.84246			0.641293			0.320647	+	0.947199i	$0.396100\pi$
$84$		0			0
$85$		−	16.7580i		−	1.81766i
$86$	0.790869	−	1.36983i	0.0852816	−	0.147712i
$87$		0			0
$88$	−2.77225	−	1.82062i	−0.295523	−	0.194078i
$89$	−13.9527	−	8.05557i	−1.47898	−	0.853889i	−0.479262	−	0.877672i	$-0.659096\pi$
$89$	−13.9527	−	8.05557i	−1.47898	−	0.853889i	−0.999717	+	0.0237828i	$0.992429\pi$
$90$		0			0
$91$	3.26920	−	2.05443i	0.342706	−	0.215363i
$92$	2.28779			0.238519
$93$		0			0
$94$	−0.272679	−	0.472293i	−0.0281247	−	0.0487133i
$95$	0.344626	−	0.198970i	0.0353579	−	0.0204139i
$96$		0			0
$97$			11.3012i			1.14746i	0.819045	+	0.573729i	$0.194504\pi$
$97$			11.3012i			1.14746i	−0.819045	+	0.573729i	$0.805496\pi$
$98$	−5.78323	+	3.94388i	−0.584195	+	0.398392i
$99$		0			0
$100$	0.0736626	−	0.127587i	0.00736626	−	0.0127587i
$101$	−0.258858	−	0.448355i	−0.0257573	−	0.0446130i	0.852859	−	0.522141i	$-0.174866\pi$
$101$	−0.258858	−	0.448355i	−0.0257573	−	0.0446130i	−0.878617	+	0.477528i	$0.841533\pi$
$102$		0			0
$103$	−2.50035	−	1.44358i	−0.246367	−	0.142240i	0.371733	−	0.928340i	$-0.378764\pi$
$103$	−2.50035	−	1.44358i	−0.246367	−	0.142240i	−0.618100	+	0.786100i	$0.712097\pi$
$104$			1.45937i			0.143103i
$105$		0			0
$106$		−	4.83444i		−	0.469562i
$107$	−4.52030	−	2.60980i	−0.436994	−	0.252299i	0.265328	−	0.964158i	$-0.414520\pi$
$107$	−4.52030	−	2.60980i	−0.436994	−	0.252299i	−0.702322	+	0.711860i	$0.747853\pi$
$108$		0			0
$109$	−8.70705	+	5.02702i	−0.833984	+	0.481501i	−0.855215	−	0.518274i	$-0.826575\pi$
$109$	−8.70705	+	5.02702i	−0.833984	+	0.481501i	0.0212309	+	0.999775i	$0.493241\pi$
$110$	−7.29405	−	0.419814i	−0.695460	−	0.0400276i
$111$		0			0
$112$	−0.0990746	−	2.64390i	−0.00936167	−	0.249825i
$113$	−7.83235			−0.736806			−0.368403	−	0.929666i	$-0.620095\pi$
$113$	−7.83235			−0.736806			−0.368403	+	0.929666i	$0.620095\pi$
$114$		0			0
$115$	4.36453	−	2.51986i	0.406995	−	0.234978i
$116$	3.85672	−	2.22668i	0.358087	−	0.206742i
$117$		0			0
$118$	−6.18967			−0.569805
$119$	17.7952	+	9.40376i	1.63128	+	0.862041i
$120$		0			0
$121$	−4.37072	−	10.0944i	−0.397338	−	0.917672i
$122$	−4.95904	+	2.86310i	−0.448971	+	0.259213i
$123$		0			0
$124$	7.40363	+	4.27449i	0.664865	+	0.383860i
$125$		−	11.3389i		−	1.01419i
$126$		0			0
$127$		−	13.4702i		−	1.19529i	−0.801762	−	0.597644i	$-0.796104\pi$
$127$		−	13.4702i		−	1.19529i	0.801762	−	0.597644i	$-0.203896\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.60741	+	2.78412i	0.140979	+	0.244183i
$131$	−1.31231	+	2.27298i	−0.114657	+	0.198592i	−0.917643	−	0.397407i	$-0.869910\pi$
$131$	−1.31231	+	2.27298i	−0.114657	+	0.198592i	0.802986	+	0.595998i	$0.203244\pi$
$132$		0			0
$133$	0.0178974	+	0.477607i	0.00155190	+	0.0414138i
$134$		−	2.98176i		−	0.257585i
$135$		0			0
$136$	−6.58813	+	3.80366i	−0.564928	+	0.326161i
$137$	−4.36145	−	7.55426i	−0.372624	−	0.645404i	0.617344	−	0.786693i	$-0.288209\pi$
$137$	−4.36145	−	7.55426i	−0.372624	−	0.645404i	−0.989968	+	0.141289i	$0.954875\pi$
$138$		0			0
$139$	4.09291			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$139$	4.09291			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$140$	−3.10110	−	4.93476i	−0.262091	−	0.417064i
$141$		0			0
$142$	−6.56004	−	3.78744i	−0.550506	−	0.317835i
$143$	−2.65696	+	4.04574i	−0.222186	+	0.338322i
$144$		0			0
$145$	4.90510	−	8.49588i	0.407346	−	0.705544i
$146$		−	9.67644i		−	0.800828i
$147$		0			0
$148$	−1.50947			−0.124078
$149$	−16.1009	−	9.29587i	−1.31904	−	0.761547i	−0.335464	−	0.942053i	$-0.608893\pi$
$149$	−16.1009	−	9.29587i	−1.31904	−	0.761547i	−0.983574	+	0.180506i	$0.942227\pi$
$150$		0			0
$151$	11.4354	−	6.60225i	0.930602	−	0.537283i	0.0435999	−	0.999049i	$-0.486117\pi$
$151$	11.4354	−	6.60225i	0.930602	−	0.537283i	0.887002	+	0.461766i	$0.152784\pi$
$152$	−0.156443	−	0.0903227i	−0.0126892	−	0.00732613i
$153$		0			0
$154$	4.53886	−	7.50991i	0.365752	−	0.605166i
$155$	18.8324			1.51265
$156$		0			0
$157$	4.98745	−	2.87951i	0.398042	−	0.229810i	−0.287597	−	0.957752i	$-0.592856\pi$
$157$	4.98745	−	2.87951i	0.398042	−	0.229810i	0.685639	+	0.727942i	$0.259523\pi$
$158$	−3.45939	−	5.99185i	−0.275215	−	0.476686i
$159$		0			0
$160$	2.20288			0.174153
$161$	0.226662	+	6.04868i	0.0178635	+	0.476703i
$162$		0			0
$163$	2.65644	−	4.60109i	0.208069	−	0.360386i	−0.743037	−	0.669250i	$-0.766616\pi$
$163$	2.65644	−	4.60109i	0.208069	−	0.360386i	0.951106	+	0.308864i	$0.0999489\pi$
$164$	3.55184	+	6.15197i	0.277352	+	0.480388i
$165$		0			0
$166$	−5.05972	−	2.92123i	−0.392710	−	0.226731i
$167$	16.0519			1.24213			0.621067	−	0.783757i	$-0.286699\pi$
$167$	16.0519			1.24213			0.621067	+	0.783757i	$0.286699\pi$
$168$		0			0
$169$	−10.8702			−0.836172
$170$	−8.37900	+	14.5129i	−0.642640	+	1.11308i
$171$		0			0
$172$	−1.36983	+	0.790869i	−0.104448	+	0.0603032i
$173$	−3.54738	+	6.14425i	−0.269703	+	0.467139i	−0.968785	−	0.247903i	$-0.920259\pi$
$173$	−3.54738	+	6.14425i	−0.269703	+	0.467139i	0.699082	+	0.715041i	$0.253592\pi$
$174$		0			0
$175$	0.344626	+	0.182116i	0.0260513	+	0.0137666i
$176$	1.49053	+	2.96282i	0.112353	+	0.223331i
$177$		0			0
$178$	8.05557	+	13.9527i	0.603791	+	1.04580i
$179$	−12.4864	−	21.6271i	−0.933278	−	1.61648i	−0.777676	−	0.628665i	$-0.783602\pi$
$179$	−12.4864	−	21.6271i	−0.933278	−	1.61648i	−0.155602	−	0.987820i	$-0.549732\pi$
$180$		0			0
$181$		−	19.3579i		−	1.43886i	−0.694566	−	0.719429i	$-0.744404\pi$
$181$		−	19.3579i		−	1.43886i	0.694566	−	0.719429i	$-0.255596\pi$
$182$	−3.85843	+	0.144587i	−0.286006	+	0.0107175i
$183$		0			0
$184$	−1.98129	−	1.14390i	−0.146062	−	0.0843291i
$185$	−2.87969	+	1.66259i	−0.211719	+	0.122236i
$186$		0			0
$187$	−25.1889	−	1.44976i	−1.84200	−	0.106017i
$188$			0.545357i			0.0397743i
$189$		0			0
$190$	−0.397940			−0.0288696
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	−14.3859	+	8.30569i	−1.03552	+	0.597857i	−0.918561	−	0.395280i	$-0.870647\pi$
$193$	−14.3859	+	8.30569i	−1.03552	+	0.597857i	−0.116957	+	0.993137i	$0.537314\pi$
$194$	5.65058	−	9.78709i	0.405688	−	0.702672i
$195$		0			0
$196$	6.98037	−	0.523886i	0.498598	−	0.0374204i
$197$		−	20.6396i		−	1.47051i	−0.677790	−	0.735256i	$-0.737062\pi$
$197$		−	20.6396i		−	1.47051i	0.677790	−	0.735256i	$-0.262938\pi$
$198$		0			0
$199$	0.628737	−	0.363001i	0.0445700	−	0.0257325i	−0.477549	−	0.878605i	$-0.658475\pi$
$199$	0.628737	−	0.363001i	0.0445700	−	0.0257325i	0.522119	+	0.852872i	$0.325142\pi$
$200$	−0.127587	+	0.0736626i	−0.00902179	+	0.00520873i
$201$		0			0
$202$			0.517716i			0.0364264i
$203$	6.26920	+	9.97615i	0.440012	+	0.700188i
$204$		0			0
$205$	13.5520	+	7.82428i	0.946516	+	0.546471i
$206$	1.44358	+	2.50035i	0.100579	+	0.174208i
$207$		0			0
$208$	0.729686	−	1.26385i	0.0505946	−	0.0876325i
$209$	−0.269257	−	0.535220i	−0.0186249	−	0.0370219i
$210$		0			0
$211$			10.2878i			0.708241i	0.935200	+	0.354120i	$0.115220\pi$
$211$			10.2878i			0.708241i	−0.935200	+	0.354120i	$0.884780\pi$
$212$	−2.41722	+	4.18675i	−0.166015	+	0.287547i
$213$		0			0
$214$	2.60980	+	4.52030i	0.178402	+	0.309001i
$215$	−1.74219	+	3.01756i	−0.118816	+	0.205796i
$216$		0			0
$217$	−10.5678	+	19.9979i	−0.717388	+	1.35755i
$218$	10.0540			0.680945
$219$		0			0
$220$	6.10693	+	4.01059i	0.411729	+	0.270394i
$221$	5.55095	+	9.61453i	0.373398	+	0.646744i
$222$		0			0
$223$			0.894768i			0.0599181i	0.999551	+	0.0299590i	$0.00953768\pi$
$223$			0.894768i			0.0599181i	−0.999551	+	0.0299590i	$0.990462\pi$
$224$	−1.23615	+	2.33922i	−0.0825935	+	0.156296i
$225$		0			0
$226$	6.78302	+	3.91618i	0.451200	+	0.260500i
$227$	6.74239	+	11.6782i	0.447508	+	0.775107i	0.998223	−	0.0595863i	$-0.0189781\pi$
$227$	6.74239	+	11.6782i	0.447508	+	0.775107i	−0.550715	+	0.834693i	$0.685645\pi$
$228$		0			0
$229$	−4.23097	−	2.44275i	−0.279590	−	0.161422i	0.353648	−	0.935379i	$-0.384941\pi$
$229$	−4.23097	−	2.44275i	−0.279590	−	0.161422i	−0.633238	+	0.773957i	$0.718275\pi$
$230$	−5.03973			−0.332310
$231$		0			0
$232$	−4.45335			−0.292377
$233$	19.6247	+	11.3303i	1.28566	+	0.742274i	0.977876	−	0.209184i	$-0.0670807\pi$
$233$	19.6247	+	11.3303i	1.28566	+	0.742274i	0.307780	+	0.951458i	$0.400414\pi$
$234$		0			0
$235$	0.600678	+	1.04041i	0.0391839	+	0.0678685i
$236$	5.36041	+	3.09483i	0.348933	+	0.201457i
$237$		0			0
$238$	−10.7092	−	17.0415i	−0.694174	−	1.10464i
$239$			25.2410i			1.63270i	0.577556	+	0.816351i	$0.304007\pi$
$239$			25.2410i			1.63270i	−0.577556	+	0.816351i	$0.695993\pi$
$240$		0			0
$241$	7.03345	+	12.1823i	0.453064	+	0.784730i	0.998575	−	0.0533739i	$-0.0169975\pi$
$241$	7.03345	+	12.1823i	0.453064	+	0.784730i	−0.545510	+	0.838104i	$0.683664\pi$
$242$	−1.26204	+	10.9274i	−0.0811272	+	0.702437i
$243$		0			0
$244$	5.72621			0.366583
$245$	12.7398	−	8.68790i	0.813914	−	0.555049i
$246$		0			0
$247$	−0.131814	+	0.228309i	−0.00838715	+	0.0145270i
$248$	−4.27449	−	7.40363i	−0.271430	−	0.470131i
$249$		0			0
$250$	−5.66947	+	9.81980i	−0.358569	+	0.621059i
$251$			3.03720i			0.191706i	0.995395	+	0.0958532i	$0.0305579\pi$
$251$			3.03720i			0.191706i	−0.995395	+	0.0958532i	$0.969442\pi$
$252$		0			0
$253$	−3.41002	−	6.77832i	−0.214386	−	0.426149i
$254$	−6.73510	+	11.6655i	−0.422598	+	0.731961i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−22.3160	−	12.8842i	−1.39204	−	0.803692i	−0.398496	−	0.917170i	$-0.630468\pi$
$257$	−22.3160	−	12.8842i	−1.39204	−	0.803692i	−0.993541	+	0.113478i	$0.963801\pi$
$258$		0			0
$259$	−0.149550	−	3.99088i	−0.00929260	−	0.247981i
$260$		−	3.21482i		−	0.199375i
$261$		0			0
$262$	2.27298	−	1.31231i	0.140425	−	0.0810747i
$263$	−5.55124	+	3.20501i	−0.342304	+	0.197629i	−0.661290	−	0.750130i	$-0.729991\pi$
$263$	−5.55124	+	3.20501i	−0.342304	+	0.197629i	0.318986	+	0.947759i	$0.396658\pi$
$264$		0			0
$265$			10.6497i			0.654205i
$266$	0.223304	−	0.422569i	0.0136917	−	0.0259094i
$267$		0			0
$268$	−1.49088	+	2.58228i	−0.0910701	+	0.157738i
$269$	−2.37423	+	1.37076i	−0.144759	+	0.0835767i	−0.570630	−	0.821207i	$-0.693301\pi$
$269$	−2.37423	+	1.37076i	−0.144759	+	0.0835767i	0.425871	+	0.904784i	$0.359968\pi$
$270$		0			0
$271$	−14.3001	+	24.7685i	−0.868670	+	1.50458i	−0.00531291	+	0.999986i	$0.501691\pi$
$271$	−14.3001	+	24.7685i	−0.868670	+	1.50458i	−0.863357	+	0.504594i	$0.831642\pi$
$272$	7.60732			0.461261
$273$		0			0
$274$			8.72291i			0.526970i
$275$	−0.487815	−	0.0280765i	−0.0294164	−	0.00169308i
$276$		0			0
$277$	9.32564	−	5.38416i	0.560324	−	0.323503i	−0.192952	−	0.981208i	$-0.561806\pi$
$277$	9.32564	−	5.38416i	0.560324	−	0.323503i	0.753275	+	0.657705i	$0.228473\pi$
$278$	−3.54456	−	2.04645i	−0.212589	−	0.122738i
$279$		0			0
$280$	0.218249	+	5.82418i	0.0130429	+	0.348061i
$281$			19.6289i			1.17096i	0.810686	+	0.585481i	$0.199094\pi$
$281$			19.6289i			1.17096i	−0.810686	+	0.585481i	$0.800906\pi$
$282$		0			0
$283$	−5.31163	−	9.20001i	−0.315744	−	0.546884i	0.663852	−	0.747864i	$-0.268921\pi$
$283$	−5.31163	−	9.20001i	−0.315744	−	0.546884i	−0.979595	+	0.200980i	$0.935587\pi$
$284$	3.78744	+	6.56004i	0.224743	+	0.389267i
$285$		0			0
$286$	4.32386	−	2.17524i	0.255675	−	0.128624i
$287$	−15.9133	+	10.0002i	−0.939331	+	0.590293i
$288$		0			0
$289$	−20.4356	+	35.3956i	−1.20210	+	2.08209i
$290$	−8.49588	+	4.90510i	−0.498895	+	0.288037i
$291$		0			0
$292$	−4.83822	+	8.38004i	−0.283135	+	0.490405i
$293$	−0.277651			−0.0162206			−0.00811028	−	0.999967i	$-0.502582\pi$
$293$	−0.277651			−0.0162206			−0.00811028	+	0.999967i	$0.502582\pi$
$294$		0			0
$295$	13.6351			0.793866
$296$	1.30724	+	0.754735i	0.0759818	+	0.0438681i
$297$		0			0
$298$	9.29587	+	16.1009i	0.538495	+	0.932701i
$299$	−1.66937	+	2.89143i	−0.0965421	+	0.167216i
$300$		0			0
$301$	−2.22669	−	3.54332i	−0.128344	−	0.204234i
$302$	−13.2045			−0.759833
$303$		0			0
$304$	0.0903227	+	0.156443i	0.00518036	+	0.00897265i
$305$	10.9242	−	6.30707i	0.625516	−	0.361142i
$306$		0			0
$307$	6.41443			0.366091			0.183045	−	0.983104i	$-0.441404\pi$
$307$	6.41443			0.366091			0.183045	+	0.983104i	$0.441404\pi$
$308$	−7.68572	+	4.23435i	−0.437935	+	0.241274i
$309$		0			0
$310$	−16.3093	−	9.41618i	−0.926306	−	0.534803i
$311$	9.78814	−	5.65119i	0.555035	−	0.320449i	−0.196115	−	0.980581i	$-0.562833\pi$
$311$	9.78814	−	5.65119i	0.555035	−	0.320449i	0.751150	+	0.660131i	$0.229499\pi$
$312$		0			0
$313$	−14.2432	−	8.22333i	−0.805075	−	0.464810i	0.0401677	−	0.999193i	$-0.487211\pi$
$313$	−14.2432	−	8.22333i	−0.805075	−	0.464810i	−0.845243	+	0.534383i	$0.820544\pi$
$314$	−5.75901			−0.325000
$315$		0			0
$316$			6.91879i			0.389212i
$317$	−14.0955	+	24.4141i	−0.791683	+	1.37124i	0.133241	+	0.991084i	$0.457461\pi$
$317$	−14.0955	+	24.4141i	−0.791683	+	1.37124i	−0.924924	+	0.380151i	$0.875872\pi$
$318$		0			0
$319$	−12.3458	−	8.10784i	−0.691232	−	0.453952i
$320$	−1.90775	−	1.10144i	−0.106646	−	0.0615723i
$321$		0			0
$322$	2.82805	−	5.35164i	0.157601	−	0.298235i
$323$	−1.37423			−0.0764640
$324$		0			0
$325$	0.107501	+	0.186198i	0.00596309	+	0.0103284i
$326$	−4.60109	+	2.65644i	−0.254831	+	0.147127i
$327$		0			0
$328$		−	7.10368i		−	0.392235i
$329$	−1.44187	+	0.0540311i	−0.0794928	+	0.00297883i
$330$		0			0
$331$	−9.55629	+	16.5520i	−0.525261	+	0.909779i	0.474306	+	0.880360i	$0.342699\pi$
$331$	−9.55629	+	16.5520i	−0.525261	+	0.909779i	−0.999567	+	0.0294190i	$0.990634\pi$
$332$	2.92123	+	5.05972i	0.160323	+	0.277688i
$333$		0			0
$334$	−13.9014	−	8.02596i	−0.760649	−	0.439161i
$335$			6.56846i			0.358874i
$336$		0			0
$337$		−	16.0358i		−	0.873525i	−0.899577	−	0.436763i	$-0.856125\pi$
$337$		−	16.0358i		−	0.873525i	0.899577	−	0.436763i	$-0.143875\pi$
$338$	9.41390	+	5.43512i	0.512049	+	0.295631i
$339$		0			0
$340$	14.5129	−	8.37900i	0.787070	−	0.454415i
$341$	1.62922	−	28.3069i	0.0882272	−	1.53290i
$342$		0			0
$343$	2.07668	+	18.4035i	0.112130	+	0.993694i
$344$	1.58174			0.0852816
$345$		0			0
$346$	6.14425	−	3.54738i	0.330317	−	0.190708i
$347$	−8.54848	+	4.93547i	−0.458907	+	0.264950i	−0.711584	−	0.702601i	$-0.752022\pi$
$347$	−8.54848	+	4.93547i	−0.458907	+	0.264950i	0.252678	+	0.967550i	$0.418689\pi$
$348$		0			0
$349$	31.1871			1.66940			0.834702	−	0.550701i	$-0.185640\pi$
$349$	31.1871			1.66940			0.834702	+	0.550701i	$0.185640\pi$
$350$	−0.207397	−	0.330030i	−0.0110858	−	0.0176408i
$351$		0			0
$352$	0.190575	−	3.31114i	0.0101577	−	0.176485i
$353$	22.4891	−	12.9841i	1.19698	−	0.691075i	0.237097	−	0.971486i	$-0.423804\pi$
$353$	22.4891	−	12.9841i	1.19698	−	0.691075i	0.959880	+	0.280411i	$0.0904709\pi$
$354$		0			0
$355$	14.4510	+	8.34327i	0.766978	+	0.442815i
$356$		−	16.1111i		−	0.853889i
$357$		0			0
$358$			24.9728i			1.31985i
$359$	−3.47334	−	2.00534i	−0.183316	−	0.105838i	0.405534	−	0.914080i	$-0.367086\pi$
$359$	−3.47334	−	2.00534i	−0.183316	−	0.105838i	−0.588850	+	0.808243i	$0.700419\pi$
$360$		0			0
$361$	9.48368	+	16.4262i	0.499141	+	0.864538i
$362$	−9.67893	+	16.7644i	−0.508713	+	0.881117i
$363$		0			0
$364$	3.41379	+	1.80400i	0.178931	+	0.0945552i
$365$			21.3160i			1.11573i
$366$		0			0
$367$	16.6148	−	9.59255i	0.867284	−	0.500727i	0.000839598	−	1.00000i	$-0.499733\pi$
$367$	16.6148	−	9.59255i	0.867284	−	0.500727i	0.866445	+	0.499273i	$0.166399\pi$
$368$	1.14390	+	1.98129i	0.0596297	+	0.103282i
$369$		0			0
$370$	3.32518			0.172868
$371$	−11.3088	−	5.97608i	−0.587124	−	0.310262i
$372$		0			0
$373$	−18.2116	−	10.5145i	−0.942961	−	0.544419i	−0.0520734	−	0.998643i	$-0.516583\pi$
$373$	−18.2116	−	10.5145i	−0.942961	−	0.544419i	−0.890887	+	0.454225i	$0.849916\pi$
$374$	21.0894	+	13.8500i	1.09051	+	0.716166i
$375$		0			0
$376$	0.272679	−	0.472293i	0.0140623	−	0.0243567i
$377$			6.49910i			0.334721i
$378$		0			0
$379$	20.7525			1.06599			0.532993	−	0.846120i	$-0.321067\pi$
$379$	20.7525			1.06599			0.532993	+	0.846120i	$0.321067\pi$
$380$	0.344626	+	0.198970i	0.0176789	+	0.0102069i
$381$		0			0
$382$	−5.19615	+	3.00000i	−0.265858	+	0.153493i
$383$	1.08778	+	0.628029i	0.0555829	+	0.0320908i	0.527534	−	0.849534i	$-0.323117\pi$
$383$	1.08778	+	0.628029i	0.0555829	+	0.0320908i	−0.471951	+	0.881625i	$0.656450\pi$
$384$		0			0
$385$	−9.99855	+	16.5434i	−0.509573	+	0.843131i
$386$	16.6114			0.845497
$387$		0			0
$388$	−9.78709	+	5.65058i	−0.496864	+	0.286865i
$389$	−8.32393	−	14.4175i	−0.422040	−	0.730994i	0.574099	−	0.818786i	$-0.305352\pi$
$389$	−8.32393	−	14.4175i	−0.422040	−	0.730994i	−0.996139	+	0.0877915i	$0.972019\pi$
$390$		0			0
$391$	−17.4040			−0.880156
$392$	−6.30712	−	3.03649i	−0.318558	−	0.153366i
$393$		0			0
$394$	−10.3198	+	17.8744i	−0.519904	+	0.900501i
$395$	7.62062	+	13.1993i	0.383435	+	0.664129i
$396$		0			0
$397$	12.2752	+	7.08712i	0.616077	+	0.355692i	0.775340	−	0.631544i	$-0.217579\pi$
$397$	12.2752	+	7.08712i	0.616077	+	0.355692i	−0.159263	+	0.987236i	$0.550912\pi$
$398$	−0.726003			−0.0363912
$399$		0			0
$400$	0.147325			0.00736626
$401$	−2.42635	+	4.20256i	−0.121166	+	0.209866i	−0.920228	−	0.391383i	$-0.871997\pi$
$401$	−2.42635	+	4.20256i	−0.121166	+	0.209866i	0.799062	+	0.601249i	$0.205330\pi$
$402$		0			0
$403$	−10.8046	+	6.23807i	−0.538218	+	0.310740i
$404$	0.258858	−	0.448355i	0.0128787	−	0.0223065i
$405$		0			0
$406$	−0.441214	−	11.7742i	−0.0218971	−	0.584344i
$407$	2.24991	+	4.47229i	0.111524	+	0.221683i
$408$		0			0
$409$	−5.31402	−	9.20415i	−0.262761	−	0.455116i	0.704213	−	0.709988i	$-0.251300\pi$
$409$	−5.31402	−	9.20415i	−0.262761	−	0.455116i	−0.966975	+	0.254872i	$0.917967\pi$
$410$	−7.82428	−	13.5520i	−0.386414	−	0.669288i
$411$		0			0
$412$		−	2.88716i		−	0.142240i
$413$	−7.65134	+	14.4790i	−0.376498	+	0.712464i
$414$		0			0
$415$	11.1459	+	6.43512i	0.547133	+	0.315887i
$416$	−1.26385	+	0.729686i	−0.0619655	+	0.0357758i
$417$		0			0
$418$	−0.0344265	+	0.598143i	−0.00168385	+	0.0292561i
$419$			11.3690i			0.555410i	0.960666	+	0.277705i	$0.0895739\pi$
$419$			11.3690i			0.555410i	−0.960666	+	0.277705i	$0.910426\pi$
$420$		0			0
$421$	27.2464			1.32791			0.663955	−	0.747772i	$-0.268877\pi$
$421$	27.2464			1.32791			0.663955	+	0.747772i	$0.268877\pi$
$422$	5.14390	−	8.90949i	0.250401	−	0.433707i
$423$		0			0
$424$	4.18675	−	2.41722i	0.203326	−	0.117391i
$425$	−0.560375	+	0.970598i	−0.0271822	+	0.0470809i
$426$		0			0
$427$	0.567322	+	15.1395i	0.0274546	+	0.732652i
$428$		−	5.21959i		−	0.252299i
$429$		0			0
$430$	3.01756	−	1.74219i	0.145520	−	0.0840158i
$431$	−13.1818	+	7.61049i	−0.634943	+	0.366584i	−0.782664	−	0.622445i	$-0.786140\pi$
$431$	−13.1818	+	7.61049i	−0.634943	+	0.366584i	0.147721	+	0.989029i	$0.452806\pi$
$432$		0			0
$433$		−	1.85534i		−	0.0891619i	−0.999006	−	0.0445810i	$-0.985805\pi$
$433$		−	1.85534i		−	0.0891619i	0.999006	−	0.0445810i	$-0.0141953\pi$
$434$	19.1509	−	12.0348i	0.919274	−	0.577689i
$435$		0			0
$436$	−8.70705	−	5.02702i	−0.416992	−	0.240750i
$437$	−0.206639	−	0.357910i	−0.00988490	−	0.0171212i
$438$		0			0
$439$	16.4702	−	28.5272i	0.786079	−	1.36153i	−0.142274	−	0.989827i	$-0.545441\pi$
$439$	16.4702	−	28.5272i	0.786079	−	1.36153i	0.928352	−	0.371701i	$-0.121225\pi$
$440$	−3.28346	−	6.52674i	−0.156533	−	0.311150i
$441$		0			0
$442$		−	11.1019i		−	0.528064i
$443$	−16.4306	+	28.4587i	−0.780643	+	1.35211i	0.150924	+	0.988545i	$0.451775\pi$
$443$	−16.4306	+	28.4587i	−0.780643	+	1.35211i	−0.931567	+	0.363569i	$0.881558\pi$
$444$		0			0
$445$	−17.7455	−	30.7360i	−0.841215	−	1.45703i
$446$	0.447384	−	0.774891i	0.0211842	−	0.0366922i
$447$		0			0
$448$	2.24014	−	1.40775i	0.105837	−	0.0665099i
$449$	−3.62716			−0.171176			−0.0855880	−	0.996331i	$-0.527277\pi$
$449$	−3.62716			−0.171176			−0.0855880	+	0.996331i	$0.527277\pi$
$450$		0			0
$451$	12.9331	−	19.6932i	0.608995	−	0.927315i
$452$	−3.91618	−	6.78302i	−0.184201	−	0.319046i
$453$		0			0
$454$		−	13.4848i		−	0.632872i
$455$	8.49965	−	0.318507i	0.398470	−	0.0149318i
$456$		0			0
$457$	−2.36916	−	1.36783i	−0.110825	−	0.0639846i	0.443563	−	0.896243i	$-0.353714\pi$
$457$	−2.36916	−	1.36783i	−0.110825	−	0.0639846i	−0.554388	+	0.832259i	$0.687048\pi$
$458$	2.44275	+	4.23097i	0.114142	+	0.197700i
$459$		0			0
$460$	4.36453	+	2.51986i	0.203497	+	0.117489i
$461$	20.4439			0.952169			0.476084	−	0.879400i	$-0.342056\pi$
$461$	20.4439			0.952169			0.476084	+	0.879400i	$0.342056\pi$
$462$		0			0
$463$	30.1701			1.40212			0.701062	−	0.713100i	$-0.252710\pi$
$463$	30.1701			1.40212			0.701062	+	0.713100i	$0.252710\pi$
$464$	3.85672	+	2.22668i	0.179044	+	0.103371i
$465$		0			0
$466$	−11.3303	−	19.6247i	−0.524867	−	0.909096i
$467$	−23.5318	−	13.5861i	−1.08892	−	0.628691i	−0.155634	−	0.987815i	$-0.549742\pi$
$467$	−23.5318	−	13.5861i	−1.08892	−	0.628691i	−0.933290	+	0.359124i	$0.883075\pi$
$468$		0			0
$469$	−6.97500	−	3.68590i	−0.322075	−	0.170199i
$470$		−	1.20136i		−	0.0554144i
$471$		0			0
$472$	−3.09483	−	5.36041i	−0.142451	−	0.246733i
$473$	4.38497	+	2.87974i	0.201621	+	0.132410i
$474$		0			0
$475$	−0.0266136			−0.00122112
$476$	0.753692	+	20.1130i	0.0345454	+	0.921876i
$477$		0			0
$478$	12.6205	−	21.8593i	0.577247	−	0.999822i
$479$	−10.8092	−	18.7221i	−0.493885	−	0.855434i	0.506090	−	0.862481i	$-0.331090\pi$
$479$	−10.8092	−	18.7221i	−0.493885	−	0.855434i	−0.999975	+	0.00704654i	$0.997757\pi$
$480$		0			0
$481$	1.10144	−	1.90775i	0.0502213	−	0.0869859i
$482$		−	14.0669i		−	0.640730i
$483$		0			0
$484$	6.55664	−	8.83235i	0.298029	−	0.401471i
$485$	−12.4475	+	21.5598i	−0.565214	+	0.978979i
$486$		0			0
$487$	−1.04287	−	1.80630i	−0.0472567	−	0.0818511i	0.841429	−	0.540367i	$-0.181715\pi$
$487$	−1.04287	−	1.80630i	−0.0472567	−	0.0818511i	−0.888686	+	0.458516i	$0.848381\pi$
$488$	−4.95904	−	2.86310i	−0.224485	−	0.129607i
$489$		0			0
$490$	−15.3769	+	1.15406i	−0.694658	+	0.0521350i
$491$		−	2.47983i		−	0.111913i	−0.998433	−	0.0559566i	$-0.982179\pi$
$491$		−	2.47983i		−	0.111913i	0.998433	−	0.0559566i	$-0.0178208\pi$
$492$		0			0
$493$	−29.3393	+	16.9390i	−1.32137	+	0.762896i
$494$	0.228309	−	0.131814i	0.0102721	−	0.00593061i
$495$		0			0
$496$			8.54897i			0.383860i
$497$	−16.9688	+	10.6635i	−0.761155	+	0.478325i
$498$		0			0
$499$	−7.69189	+	13.3227i	−0.344336	+	0.596408i	−0.985233	−	0.171219i	$-0.945229\pi$
$499$	−7.69189	+	13.3227i	−0.344336	+	0.596408i	0.640897	+	0.767627i	$0.278563\pi$
$500$	9.81980	−	5.66947i	0.439155	−	0.253546i
$501$		0			0
$502$	1.51860	−	2.63029i	0.0677784	−	0.117396i
$503$	15.5714			0.694295			0.347147	−	0.937811i	$-0.387150\pi$
$503$	15.5714			0.694295			0.347147	+	0.937811i	$0.387150\pi$
$504$		0			0
$505$		−	1.14047i		−	0.0507501i
$506$	−0.435996	+	7.57521i	−0.0193824	+	0.336759i
$507$		0			0
$508$	11.6655	−	6.73510i	0.517575	−	0.298822i
$509$	26.6346	+	15.3775i	1.18056	+	0.681595i	0.956144	−	0.292898i	$-0.0946198\pi$
$509$	26.6346	+	15.3775i	1.18056	+	0.681595i	0.224414	+	0.974494i	$0.427953\pi$
$510$		0			0
$511$	−22.6353	−	11.9615i	−1.00133	−	0.529146i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	12.8842	+	22.3160i	0.568296	+	0.984318i
$515$	−3.18003	−	5.50797i	−0.140129	−	0.242710i
$516$		0			0
$517$	1.61580	−	0.812872i	0.0710627	−	0.0357500i
$518$	−1.86593	+	3.53098i	−0.0819841	+	0.155142i
$519$		0			0
$520$	−1.60741	+	2.78412i	−0.0704896	+	0.122092i
$521$	3.19850	−	1.84666i	0.140129	−	0.0809035i	−0.428296	−	0.903638i	$-0.640886\pi$
$521$	3.19850	−	1.84666i	0.140129	−	0.0809035i	0.568425	+	0.822735i	$0.307553\pi$
$522$		0			0
$523$	14.6007	−	25.2891i	0.638444	−	1.10582i	−0.347331	−	0.937743i	$-0.612912\pi$
$523$	14.6007	−	25.2891i	0.638444	−	1.10582i	0.985774	−	0.168074i	$-0.0537548\pi$
$524$	−2.62462			−0.114657
$525$		0			0
$526$	6.41002			0.279490
$527$	−56.3218	−	32.5174i	−2.45341	−	1.41648i
$528$		0			0
$529$	8.88301	+	15.3858i	0.386218	+	0.668949i
$530$	5.32484	−	9.22289i	0.231296	−	0.400617i
$531$		0			0
$532$	−0.404671	+	0.254303i	−0.0175447	+	0.0110254i
$533$	−10.3669			−0.449041
$534$		0			0
$535$	−5.74906	−	9.95767i	−0.248554	−	0.430508i
$536$	2.58228	−	1.49088i	0.111538	−	0.0643963i
$537$		0			0
$538$	2.74152			0.118195
$539$	−11.9566	−	19.9007i	−0.515008	−	0.857185i
$540$		0			0
$541$	−14.0078	−	8.08743i	−0.602244	−	0.347706i	0.167680	−	0.985841i	$-0.446372\pi$
$541$	−14.0078	−	8.08743i	−0.602244	−	0.347706i	−0.769924	+	0.638136i	$0.779706\pi$
$542$	24.7685	−	14.3001i	1.06390	−	0.614242i
$543$		0			0
$544$	−6.58813	−	3.80366i	−0.282464	−	0.163081i
$545$	−22.1478			−0.948708
$546$		0			0
$547$			34.0719i			1.45681i	0.685146	+	0.728405i	$0.259738\pi$
$547$			34.0719i			1.45681i	−0.685146	+	0.728405i	$0.740262\pi$
$548$	4.36145	−	7.55426i	0.186312	−	0.322702i
$549$		0			0
$550$	0.408422	+	0.268223i	0.0174152	+	0.0114371i
$551$	−0.696698	−	0.402239i	−0.0296803	−	0.0171359i
$552$		0			0
$553$	−18.2926	+	0.685476i	−0.777878	+	0.0291494i
$554$	−10.7683			−0.457502
$555$		0			0
$556$	2.04645	+	3.54456i	0.0867889	+	0.150323i
$557$	−22.2451	+	12.8432i	−0.942555	+	0.544185i	−0.890760	−	0.454473i	$-0.849828\pi$
$557$	−22.2451	+	12.8432i	−0.942555	+	0.544185i	−0.0517949	+	0.998658i	$0.516494\pi$
$558$		0			0
$559$		−	2.30834i		−	0.0976325i
$560$	2.72308	−	5.15301i	0.115071	−	0.217755i
$561$		0			0
$562$	9.81445	−	16.9991i	0.413998	−	0.717065i
$563$	10.9683	+	18.9976i	0.462258	+	0.800654i	0.999073	−	0.0430456i	$-0.0137061\pi$
$563$	10.9683	+	18.9976i	0.462258	+	0.800654i	−0.536815	+	0.843700i	$0.680373\pi$
$564$		0			0
$565$	−14.9422	−	8.62686i	−0.628621	−	0.362935i
$566$			10.6233i			0.446529i
$567$		0			0
$568$		−	7.57488i		−	0.317835i
$569$	−2.22306	−	1.28348i	−0.0931956	−	0.0538065i	0.452678	−	0.891674i	$-0.350469\pi$
$569$	−2.22306	−	1.28348i	−0.0931956	−	0.0538065i	−0.545873	+	0.837868i	$0.683802\pi$
$570$		0			0
$571$	−29.7126	+	17.1546i	−1.24343	+	0.717897i	−0.969792	−	0.243934i	$-0.921562\pi$
$571$	−29.7126	+	17.1546i	−1.24343	+	0.717897i	−0.273643	+	0.961831i	$0.588229\pi$
$572$	−4.83219	−	0.278120i	−0.202044	−	0.0116288i
$573$		0			0
$574$	18.7814	−	0.703795i	0.783920	−	0.0293758i
$575$	−0.337049			−0.0140559
$576$		0			0
$577$	−17.9257	+	10.3494i	−0.746255	+	0.430851i	−0.824339	−	0.566096i	$-0.808453\pi$
$577$	−17.9257	+	10.3494i	−0.746255	+	0.430851i	0.0780842	+	0.996947i	$0.475120\pi$
$578$	35.3956	−	20.4356i	1.47226	−	0.850011i
$579$		0			0
$580$	9.81020			0.407346
$581$	−13.0880	+	8.22472i	−0.542980	+	0.341219i
$582$		0			0
$583$	16.0075	+	0.921323i	0.662964	+	0.0381573i
$584$	8.38004	−	4.83822i	0.346769	−	0.200207i
$585$		0			0
$586$	0.240453	+	0.138826i	0.00993303	+	0.00573484i
$587$		−	16.0435i		−	0.662184i	−0.943598	−	0.331092i	$-0.892583\pi$
$587$		−	16.0435i		−	0.662184i	0.943598	−	0.331092i	$-0.107417\pi$
$588$		0			0
$589$		−	1.54433i		−	0.0636331i
$590$	−11.8083	−	6.81755i	−0.486141	−	0.280674i
$591$		0			0
$592$	−0.754735	−	1.30724i	−0.0310194	−	0.0537272i
$593$	17.7436	−	30.7328i	0.728641	−	1.26204i	−0.228816	−	0.973470i	$-0.573485\pi$
$593$	17.7436	−	30.7328i	0.728641	−	1.26204i	0.957458	−	0.288574i	$-0.0931812\pi$
$594$		0			0
$595$	23.5911	+	37.5403i	0.967139	+	1.53900i
$596$		−	18.5917i		−	0.761547i
$597$		0			0
$598$	2.89143	−	1.66937i	0.118239	−	0.0682656i
$599$	0.374693	+	0.648987i	0.0153095	+	0.0265169i	0.873579	−	0.486683i	$-0.161793\pi$
$599$	0.374693	+	0.648987i	0.0153095	+	0.0265169i	−0.858269	+	0.513200i	$0.828460\pi$
$600$		0			0
$601$	18.5168			0.755317			0.377658	−	0.925945i	$-0.376729\pi$
$601$	18.5168			0.755317			0.377658	+	0.925945i	$0.376729\pi$
$602$	0.156710	+	4.18195i	0.00638702	+	0.170444i
$603$		0			0
$604$	11.4354	+	6.60225i	0.465301	+	0.268642i
$605$	2.78013	−	24.0717i	0.113028	−	0.978652i
$606$		0			0
$607$	−18.4955	+	32.0352i	−0.750710	+	1.30027i	0.196770	+	0.980450i	$0.436955\pi$
$607$	−18.4955	+	32.0352i	−0.750710	+	1.30027i	−0.947479	+	0.319817i	$0.896378\pi$
$608$		−	0.180645i		−	0.00732613i
$609$		0			0
$610$	−12.6141			−0.510732
$611$	−0.689252	−	0.397940i	−0.0278841	−	0.0160989i
$612$		0			0
$613$	2.79338	−	1.61276i	0.112824	−	0.0651387i	−0.442526	−	0.896756i	$-0.645918\pi$
$613$	2.79338	−	1.61276i	0.112824	−	0.0651387i	0.555350	+	0.831617i	$0.312584\pi$
$614$	−5.55506	−	3.20722i	−0.224184	−	0.129433i
$615$		0			0
$616$	8.77320	+	0.175810i	0.353482	+	0.00708358i
$617$	10.8351			0.436206			0.218103	−	0.975926i	$-0.430013\pi$
$617$	10.8351			0.436206			0.218103	+	0.975926i	$0.430013\pi$
$618$		0			0
$619$	4.44127	−	2.56417i	0.178510	−	0.103063i	−0.408083	−	0.912945i	$-0.633802\pi$
$619$	4.44127	−	2.56417i	0.178510	−	0.103063i	0.586592	+	0.809882i	$0.300469\pi$
$620$	9.41618	+	16.3093i	0.378163	+	0.654997i
$621$		0			0
$622$	−11.3024			−0.453184
$623$	42.5962	−	1.59621i	1.70658	−	0.0639506i
$624$		0			0
$625$	12.1208	−	20.9939i	0.484833	−	0.839756i
$626$	8.22333	+	14.2432i	0.328670	+	0.569274i
$627$		0			0
$628$	4.98745	+	2.87951i	0.199021	+	0.114905i
$629$	11.4830			0.457858
$630$		0			0
$631$	−29.9567			−1.19256			−0.596278	−	0.802778i	$-0.703354\pi$
$631$	−29.9567			−1.19256			−0.596278	+	0.802778i	$0.703354\pi$
$632$	3.45939	−	5.99185i	0.137607	−	0.238343i
$633$		0			0
$634$	24.4141	−	14.0955i	0.969610	−	0.559804i
$635$	14.8366	−	25.6978i	0.588773	−	1.01979i
$636$		0			0
$637$	−4.43136	+	9.20443i	−0.175577	+	0.364693i
$638$	6.63786	+	13.1945i	0.262795	+	0.522375i
$639$		0			0
$640$	1.10144	+	1.90775i	0.0435382	+	0.0754104i
$641$	4.61345	+	7.99073i	0.182220	+	0.315615i	0.942636	−	0.333821i	$-0.108338\pi$
$641$	4.61345	+	7.99073i	0.182220	+	0.315615i	−0.760416	+	0.649436i	$0.775005\pi$
$642$		0			0
$643$			1.79941i			0.0709616i	0.999370	+	0.0354808i	$0.0112963\pi$
$643$			1.79941i			0.0709616i	−0.999370	+	0.0354808i	$0.988704\pi$
$644$	−5.12498	+	3.22064i	−0.201953	+	0.126911i
$645$		0			0
$646$	1.19011	+	0.687113i	0.0468244	+	0.0270341i
$647$	35.2683	−	20.3622i	1.38654	−	0.800520i	0.393618	−	0.919274i	$-0.371223\pi$
$647$	35.2683	−	20.3622i	1.38654	−	0.800520i	0.992924	+	0.118754i	$0.0378899\pi$
$648$		0			0
$649$	1.17960	−	20.4949i	0.0463032	−	0.804495i
$650$		−	0.215002i		−	0.00843309i
$651$		0			0
$652$	5.31289			0.208069
$653$	−18.8692	+	32.6824i	−0.738408	+	1.27896i	0.214803	+	0.976657i	$0.431089\pi$
$653$	−18.8692	+	32.6824i	−0.738408	+	1.27896i	−0.953212	+	0.302304i	$0.902244\pi$
$654$		0			0
$655$	−5.00711	+	2.89086i	−0.195644	+	0.112955i
$656$	−3.55184	+	6.15197i	−0.138676	+	0.240194i
$657$		0			0
$658$	1.27571	+	0.674142i	0.0497324	+	0.0262808i
$659$		−	32.5997i		−	1.26991i	−0.772551	−	0.634953i	$-0.781019\pi$
$659$		−	32.5997i		−	1.26991i	0.772551	−	0.634953i	$-0.218981\pi$
$660$		0			0
$661$	10.9747	−	6.33624i	0.426866	−	0.246451i	−0.271145	−	0.962539i	$-0.587402\pi$
$661$	10.9747	−	6.33624i	0.426866	−	0.246451i	0.698011	+	0.716087i	$0.254069\pi$
$662$	16.5520	−	9.55629i	0.643311	−	0.371416i
$663$		0			0
$664$		−	5.84246i		−	0.226731i
$665$	−0.491912	+	0.930868i	−0.0190755	+	0.0360975i
$666$		0			0
$667$	−8.82336	−	5.09417i	−0.341642	−	0.197247i
$668$	8.02596	+	13.9014i	0.310534	+	0.537860i
$669$		0			0
$670$	3.28423	−	5.68846i	0.126881	−	0.219764i
$671$	−8.53508	−	16.9657i	−0.329493	−	0.654955i
$672$		0			0
$673$			1.20344i			0.0463893i	0.999731	+	0.0231947i	$0.00738375\pi$
$673$			1.20344i			0.0463893i	−0.999731	+	0.0231947i	$0.992616\pi$
$674$	−8.01790	+	13.8874i	−0.308838	+	0.534923i
$675$		0			0
$676$	−5.43512	−	9.41390i	−0.209043	−	0.362073i
$677$	−13.1579	+	22.7902i	−0.505701	+	0.875900i	0.494277	+	0.869304i	$0.335433\pi$
$677$	−13.1579	+	22.7902i	−0.505701	+	0.875900i	−0.999978	+	0.00659557i	$0.997901\pi$
$678$		0			0
$679$	−15.9092	−	25.3162i	−0.610539	−	0.971547i
$680$	−16.7580			−0.642640
$681$		0			0
$682$	−15.5644	+	23.6999i	−0.595991	+	0.907515i
$683$	16.4637	+	28.5160i	0.629966	+	1.09113i	0.987558	+	0.157255i	$0.0502645\pi$
$683$	16.4637	+	28.5160i	0.629966	+	1.09113i	−0.357592	+	0.933878i	$0.616402\pi$
$684$		0			0
$685$		−	19.2155i		−	0.734187i
$686$	7.40328	−	16.9762i	0.282658	−	0.648154i
$687$		0			0
$688$	−1.36983	−	0.790869i	−0.0522241	−	0.0301516i
$689$	−3.52762	−	6.11002i	−0.134392	−	0.232773i
$690$		0			0
$691$	24.4510	+	14.1168i	0.930159	+	0.537028i	0.886862	−	0.462034i	$-0.152880\pi$
$691$	24.4510	+	14.1168i	0.930159	+	0.537028i	0.0432974	+	0.999062i	$0.486214\pi$
$692$	−7.09477			−0.269703
$693$		0			0
$694$	9.87094			0.374696
$695$	7.80824	+	4.50809i	0.296183	+	0.171002i
$696$		0			0
$697$	−27.0200	−	46.8000i	−1.02346	−	1.77268i
$698$	−27.0088	−	15.5935i	−1.02230	−	0.590224i
$699$		0			0
$700$	0.0145962	+	0.389513i	0.000551684	+	0.0147222i
$701$		−	24.2464i		−	0.915775i	−0.889010	−	0.457888i	$-0.848606\pi$
$701$		−	24.2464i		−	0.915775i	0.889010	−	0.457888i	$-0.151394\pi$
$702$		0			0
$703$	0.136339	+	0.236147i	0.00514214	+	0.00890644i
$704$	−1.82062	+	2.77225i	−0.0686170	+	0.104483i
$705$		0			0
$706$	−25.9682			−0.977327
$707$	1.21105	+	0.639973i	0.0455463	+	0.0240687i
$708$		0			0
$709$	−21.6350	+	37.4729i	−0.812518	+	1.40732i	0.0985783	+	0.995129i	$0.468571\pi$
$709$	−21.6350	+	37.4729i	−0.812518	+	1.40732i	−0.911096	+	0.412193i	$0.864763\pi$
$710$	−8.34327	−	14.4510i	−0.313117	−	0.542335i
$711$		0			0
$712$	−8.05557	+	13.9527i	−0.301895	+	0.522898i
$713$		−	19.5583i		−	0.732463i
$714$		0			0
$715$	−9.52494	+	4.79178i	−0.356213	+	0.179203i
$716$	12.4864	−	21.6271i	0.466639	−	0.808242i
$717$		0			0
$718$	2.00534	+	3.47334i	0.0748385	+	0.129624i
$719$	−19.9268	−	11.5048i	−0.743145	−	0.429055i	0.0800668	−	0.996790i	$-0.474487\pi$
$719$	−19.9268	−	11.5048i	−0.743145	−	0.429055i	−0.823212	+	0.567735i	$0.807820\pi$
$720$		0			0
$721$	7.63334	−	0.286044i	0.284281	−	0.0106528i
$722$		−	18.9674i		−	0.705892i
$723$		0			0
$724$	16.7644	−	9.67893i	0.623044	−	0.359714i
$725$	−0.568192	+	0.328046i	−0.0211021	+	0.0121833i
$726$		0			0
$727$			39.3745i			1.46032i	0.683276	+	0.730160i	$0.260555\pi$
$727$			39.3745i			1.46032i	−0.683276	+	0.730160i	$0.739445\pi$
$728$	−2.05443	−	3.26920i	−0.0761422	−	0.121165i
$729$		0			0
$730$	10.6580	−	18.4602i	0.394471	−	0.683243i
$731$	10.4207	−	6.01639i	0.385423	−	0.222524i
$732$		0			0
$733$	4.09264	−	7.08867i	0.151165	−	0.261826i	−0.780491	−	0.625167i	$-0.785031\pi$
$733$	4.09264	−	7.08867i	0.151165	−	0.261826i	0.931656	+	0.363341i	$0.118364\pi$
$734$	−19.1851			−0.708135
$735$		0			0
$736$		−	2.28779i		−	0.0843291i
$737$	9.87305	+	0.568249i	0.363679	+	0.0209317i
$738$		0			0
$739$	33.0756	−	19.0962i	1.21671	−	0.702466i	0.252494	−	0.967598i	$-0.418749\pi$
$739$	33.0756	−	19.0962i	1.21671	−	0.702466i	0.964212	+	0.265133i	$0.0854157\pi$
$740$	−2.87969	−	1.66259i	−0.105860	−	0.0611180i
$741$		0			0
$742$	6.80568	+	10.8298i	0.249844	+	0.397576i
$743$		−	27.3005i		−	1.00156i	−0.865575	−	0.500779i	$-0.833047\pi$
$743$		−	27.3005i		−	1.00156i	0.865575	−	0.500779i	$-0.166953\pi$
$744$		0			0
$745$	−20.4777	−	35.4684i	−0.750244	−	1.29946i
$746$	10.5145	+	18.2116i	0.384962	+	0.666774i
$747$		0			0
$748$	−11.3389	−	22.5391i	−0.414592	−	0.824112i
$749$	13.8001	−	0.517129i	0.504243	−	0.0188955i
$750$		0			0
$751$	1.11584	−	1.93269i	0.0407175	−	0.0705247i	−0.844948	−	0.534848i	$-0.820369\pi$
$751$	1.11584	−	1.93269i	0.0407175	−	0.0705247i	0.885666	+	0.464323i	$0.153702\pi$
$752$	−0.472293	+	0.272679i	−0.0172228	+	0.00994357i
$753$		0			0
$754$	3.24955	−	5.62838i	0.118342	−	0.204974i
$755$	29.0879			1.05862
$756$		0			0
$757$	−16.6709			−0.605913			−0.302956	−	0.953004i	$-0.597974\pi$
$757$	−16.6709			−0.605913			−0.302956	+	0.953004i	$0.597974\pi$
$758$	−17.9722	−	10.3763i	−0.652780	−	0.376883i
$759$		0			0
$760$	−0.198970	−	0.344626i	−0.00721740	−	0.0125009i
$761$	22.8160	−	39.5185i	0.827081	−	1.43255i	−0.0732375	−	0.997315i	$-0.523333\pi$
$761$	22.8160	−	39.5185i	0.827081	−	1.43255i	0.900318	−	0.435232i	$-0.143334\pi$
$762$		0			0
$763$	12.4283	−	23.5186i	0.449933	−	0.851429i
$764$	6.00000			0.217072
$765$		0			0
$766$	−0.628029	−	1.08778i	−0.0226916	−	0.0393030i
$767$	−7.82283	+	4.51652i	−0.282466	+	0.163082i
$768$		0			0
$769$	−51.3570			−1.85198			−0.925991	−	0.377546i	$-0.876768\pi$
$769$	−51.3570			−1.85198			−0.925991	+	0.377546i	$0.876768\pi$
$770$	16.9307	−	9.32775i	0.610141	−	0.336149i
$771$		0			0
$772$	−14.3859	−	8.30569i	−0.517759	−	0.298928i
$773$	18.9208	−	10.9239i	0.680533	−	0.392906i	−0.119523	−	0.992831i	$-0.538137\pi$
$773$	18.9208	−	10.9239i	0.680533	−	0.392906i	0.800056	+	0.599926i	$0.204803\pi$
$774$		0			0
$775$	−1.09074	−	0.629740i	−0.0391806	−	0.0226209i
$776$	11.3012			0.405688
$777$		0			0
$778$			16.6479i			0.596854i
$779$	0.641624	−	1.11132i	0.0229886	−	0.0398173i
$780$		0			0
$781$	13.7909	−	20.9994i	0.493479	−	0.751419i
$782$	15.0723	+	8.70198i	0.538983	+	0.311182i
$783$		0			0
$784$	3.94388	+	5.78323i	0.140853	+	0.206544i
$785$	12.6864			0.452797
$786$		0			0
$787$	−10.2201	−	17.7017i	−0.364307	−	0.630998i	0.624358	−	0.781138i	$-0.285361\pi$
$787$	−10.2201	−	17.7017i	−0.364307	−	0.630998i	−0.988665	+	0.150141i	$0.952027\pi$
$788$	17.8744	−	10.3198i	0.636750	−	0.367628i
$789$		0			0
$790$		−	15.2412i		−	0.542259i
$791$	17.5456	−	11.0260i	0.623849	−	0.392039i
$792$		0			0
$793$	−4.17833	+	7.23709i	−0.148377	+	0.256996i
$794$	−7.08712	−	12.2752i	−0.251512	−	0.435632i
$795$		0			0
$796$	0.628737	+	0.363001i	0.0222850	+	0.0128662i
$797$		−	6.09214i		−	0.215795i	−0.994162	−	0.107897i	$-0.965588\pi$
$797$		−	6.09214i		−	0.215795i	0.994162	−	0.107897i	$-0.0344118\pi$
$798$		0			0
$799$		−	4.14871i		−	0.146771i
$800$	−0.127587	−	0.0736626i	−0.00451090	−	0.00260437i
$801$		0			0
$802$	4.20256	−	2.42635i	0.148398	−	0.0856774i
$803$	32.0401	+	1.84409i	1.13067	+	0.0650764i
$804$		0			0
$805$	−6.22984	+	11.7890i	−0.219573	+	0.415508i
$806$	12.4761			0.439453
$807$		0			0
$808$	−0.448355	+	0.258858i	−0.0157731	+	0.00910660i
$809$	30.1186	−	17.3890i	1.05891	−	0.611364i	0.133783	−	0.991011i	$-0.457288\pi$
$809$	30.1186	−	17.3890i	1.05891	−	0.611364i	0.925132	+	0.379646i	$0.123954\pi$
$810$		0			0
$811$	26.6602			0.936167			0.468083	−	0.883684i	$-0.344945\pi$
$811$	26.6602			0.936167			0.468083	+	0.883684i	$0.344945\pi$
$812$	−5.50500	+	10.4174i	−0.193188	+	0.365578i
$813$		0			0
$814$	0.287667	−	4.99807i	0.0100827	−	0.175182i
$815$	10.1357	−	5.85182i	0.355036	−	0.204980i
$816$		0			0
$817$	0.247452	+	0.142867i	0.00865727	+	0.00499827i
$818$			10.6280i			0.371601i
$819$		0			0
$820$			15.6486i			0.546471i
$821$	−11.0422	−	6.37522i	−0.385375	−	0.222497i	0.294779	−	0.955565i	$-0.404754\pi$
$821$	−11.0422	−	6.37522i	−0.385375	−	0.222497i	−0.680154	+	0.733069i	$0.738087\pi$
$822$		0			0
$823$	7.93819	+	13.7494i	0.276708	+	0.479272i	0.970565	−	0.240841i	$-0.0774232\pi$
$823$	7.93819	+	13.7494i	0.276708	+	0.479272i	−0.693857	+	0.720113i	$0.744090\pi$
$824$	−1.44358	+	2.50035i	−0.0502895	+	0.0871039i
$825$		0			0
$826$	13.8657	−	8.71350i	0.482451	−	0.303181i
$827$			35.9639i			1.25059i	0.780390	+	0.625293i	$0.215021\pi$
$827$			35.9639i			1.25059i	−0.780390	+	0.625293i	$0.784979\pi$
$828$		0			0
$829$	−31.0966	+	17.9536i	−1.08003	+	0.623555i	−0.930904	−	0.365264i	$-0.880979\pi$
$829$	−31.0966	+	17.9536i	−1.08003	+	0.623555i	−0.149124	+	0.988818i	$0.547645\pi$
$830$	−6.43512	−	11.1459i	−0.223366	−	0.386882i
$831$		0			0
$832$	1.45937			0.0505946
$833$	−53.1019	+	3.98537i	−1.83987	+	0.138085i
$834$		0			0
$835$	30.6230	+	17.6802i	1.05975	+	0.611849i
$836$	0.328886	−	0.500794i	0.0113747	−	0.0173203i
$837$		0			0
$838$	5.68448	−	9.84582i	0.196367	−	0.340118i
$839$			39.5137i			1.36416i	0.731276	+	0.682081i	$0.238925\pi$
$839$			39.5137i			1.36416i	−0.731276	+	0.682081i	$0.761075\pi$
$840$		0			0
$841$	9.16765			0.316126
$842$	−23.5961	−	13.6232i	−0.813176	−	0.469487i
$843$		0			0
$844$	−8.90949	+	5.14390i	−0.306677	+	0.177060i
$845$	−20.7377	−	11.9729i	−0.713398	−	0.411880i
$846$		0			0
$847$	24.0014	+	16.4600i	0.824698	+	0.565573i
$848$	−4.83444			−0.166015
$849$		0			0
$850$	0.970598	−	0.560375i	0.0332912	−	0.0192207i
$851$	1.72668	+	2.99069i	0.0591897	+	0.102520i
$852$		0			0
$853$	−8.92246			−0.305499			−0.152750	−	0.988265i	$-0.548813\pi$
$853$	−8.92246			−0.305499			−0.152750	+	0.988265i	$0.548813\pi$
$854$	7.07843	−	13.3948i	0.242219	−	0.458362i
$855$		0			0
$856$	−2.60980	+	4.52030i	−0.0892010	+	0.154501i
$857$	4.37047	+	7.56987i	0.149292	+	0.258582i	0.930966	−	0.365106i	$-0.118967\pi$
$857$	4.37047	+	7.56987i	0.149292	+	0.258582i	−0.781674	+	0.623687i	$0.785634\pi$
$858$		0			0
$859$	25.7825	+	14.8855i	0.879688	+	0.507888i	0.870556	−	0.492070i	$-0.163760\pi$
$859$	25.7825	+	14.8855i	0.879688	+	0.507888i	0.00913247	+	0.999958i	$0.497093\pi$
$860$	−3.48438			−0.118816
$861$		0			0
$862$	15.2210			0.518428
$863$	11.4864	−	19.8951i	0.391002	−	0.677236i	−0.601580	−	0.798813i	$-0.705462\pi$
$863$	11.4864	−	19.8951i	0.391002	−	0.677236i	0.992582	+	0.121577i	$0.0387951\pi$
$864$		0			0
$865$	−13.5350	+	7.81445i	−0.460205	+	0.265699i
$866$	−0.927669	+	1.60677i	−0.0315235	+	0.0546003i
$867$		0			0
$868$	−22.6026	+	0.846986i	−0.767182	+	0.0287486i
$869$	20.4991	−	10.3127i	0.695386	−	0.349833i
$870$		0			0
$871$	−2.17575	−	3.76851i	−0.0737225	−	0.127691i
$872$	5.02702	+	8.70705i	0.170236	+	0.294858i
$873$		0			0
$874$			0.413279i			0.0139794i
$875$	15.9624	+	25.4008i	0.539627	+	0.858705i
$876$		0			0
$877$	−28.7911	−	16.6225i	−0.972205	−	0.561303i	−0.0722974	−	0.997383i	$-0.523033\pi$
$877$	−28.7911	−	16.6225i	−0.972205	−	0.561303i	−0.899908	+	0.436080i	$0.856366\pi$
$878$	−28.5272	+	16.4702i	−0.962746	+	0.555842i
$879$		0			0
$880$	−0.419814	+	7.29405i	−0.0141519	+	0.245882i
$881$			2.73248i			0.0920594i	0.998940	+	0.0460297i	$0.0146569\pi$
$881$			2.73248i			0.0920594i	−0.998940	+	0.0460297i	$0.985343\pi$
$882$		0			0
$883$	−19.7473			−0.664550			−0.332275	−	0.943183i	$-0.607816\pi$
$883$	−19.7473			−0.664550			−0.332275	+	0.943183i	$0.607816\pi$
$884$	−5.55095	+	9.61453i	−0.186699	+	0.323372i
$885$		0			0
$886$	28.4587	−	16.4306i	0.956089	−	0.551998i
$887$	−12.2310	+	21.1847i	−0.410676	+	0.711312i	−0.994964	−	0.100235i	$-0.968041\pi$
$887$	−12.2310	+	21.1847i	−0.410676	+	0.711312i	0.584288	+	0.811547i	$0.301374\pi$
$888$		0			0
$889$	18.9627	+	30.1752i	0.635988	+	1.01204i
$890$			35.4909i			1.18966i
$891$		0			0
$892$	−0.774891	+	0.447384i	−0.0259453	+	0.0149795i
$893$	0.0853176	−	0.0492581i	0.00285504	−	0.00164836i
$894$		0			0
$895$		−	55.0121i		−	1.83885i
$896$	−2.64390	+	0.0990746i	−0.0883264	+	0.00330985i
$897$		0			0
$898$	3.14121	+	1.81358i	0.104824	+	0.0605199i
$899$	−19.0358	−	32.9710i	−0.634879	−	1.09964i
$900$		0			0
$901$	18.3886	−	31.8499i	0.612612	−	1.06107i
$902$	−21.0470	+	10.5883i	−0.700787	+	0.352550i
$903$		0			0
$904$			7.83235i			0.260500i
$905$	21.3215	−	36.9299i	0.708751	−	1.22759i
$906$		0			0
$907$	22.3109	+	38.6436i	0.740820	+	1.28314i	0.952122	+	0.305718i	$0.0988964\pi$
$907$	22.3109	+	38.6436i	0.740820	+	1.28314i	−0.211302	+	0.977421i	$0.567770\pi$
$908$	−6.74239	+	11.6782i	−0.223754	+	0.387554i
$909$		0			0
$910$	−7.52016	−	3.97399i	−0.249291	−	0.131736i
$911$	−37.0868			−1.22874			−0.614370	−	0.789018i	$-0.710590\pi$
$911$	−37.0868			−1.22874			−0.614370	+	0.789018i	$0.710590\pi$
$912$		0			0
$913$	10.6369	−	16.1968i	0.352029	−	0.536034i
$914$	1.36783	+	2.36916i	0.0452439	+	0.0783648i
$915$		0			0
$916$		−	4.88550i		−	0.161422i
$917$	−0.260033	−	6.93921i	−0.00858704	−	0.229153i
$918$		0			0
$919$	44.1563	+	25.4937i	1.45658	+	0.840958i	0.998841	−	0.0481269i	$-0.0153252\pi$
$919$	44.1563	+	25.4937i	1.45658	+	0.840958i	0.457741	+	0.889085i	$0.348659\pi$
$920$	−2.51986	−	4.36453i	−0.0830774	−	0.143894i
$921$		0			0
$922$	−17.7050	−	10.2220i	−0.583082	−	0.336642i
$923$	−11.0546			−0.363865
$924$		0			0
$925$	0.222383			0.00731191
$926$	−26.1281	−	15.0851i	−0.858622	−	0.495726i
$927$		0			0
$928$	−2.22668	−	3.85672i	−0.0730942	−	0.126603i
$929$	−10.5567	−	6.09489i	−0.346353	−	0.199967i	0.316725	−	0.948517i	$-0.397417\pi$
$929$	−10.5567	−	6.09489i	−0.346353	−	0.199967i	−0.663078	+	0.748551i	$0.730750\pi$
$930$		0			0
$931$	−0.712444	−	1.04471i	−0.0233494	−	0.0342391i
$932$			22.6606i			0.742274i
$933$		0			0
$934$	13.5861	+	23.5318i	0.444551	+	0.769986i
$935$	−46.4573	−	30.5099i	−1.51932	−	0.997779i
$936$		0			0
$937$	17.0188			0.555979			0.277990	−	0.960584i	$-0.410332\pi$
$937$	17.0188			0.555979			0.277990	+	0.960584i	$0.410332\pi$
$938$	4.19757	+	6.67958i	0.137056	+	0.218096i
$939$		0			0
$940$	−0.600678	+	1.04041i	−0.0195920	+	0.0339343i
$941$	6.79916	+	11.7765i	0.221646	+	0.383902i	0.955308	−	0.295612i	$-0.0955237\pi$
$941$	6.79916	+	11.7765i	0.221646	+	0.383902i	−0.733662	+	0.679515i	$0.762190\pi$
$942$		0			0
$943$	8.12587	−	14.0744i	0.264615	−	0.458326i
$944$			6.18967i			0.201457i
$945$		0			0
$946$	−2.35763	−	4.68641i	−0.0766531	−	0.152368i
$947$	−16.5425	+	28.6524i	−0.537558	+	0.931078i	0.461477	+	0.887152i	$0.347320\pi$
$947$	−16.5425	+	28.6524i	−0.537558	+	0.931078i	−0.999035	+	0.0439257i	$0.986014\pi$
$948$		0			0
$949$	−7.06076	−	12.2296i	−0.229202	−	0.396990i
$950$	0.0230481	+	0.0133068i	0.000747778	+	0.000431730i
$951$		0			0
$952$	9.40376	−	17.7952i	0.304778	−	0.576745i
$953$			0.427553i			0.0138498i	0.999976	+	0.00692490i	$0.00220428\pi$
$953$			0.427553i			0.0138498i	−0.999976	+	0.00692490i	$0.997796\pi$
$954$		0			0
$955$	11.4465	−	6.60864i	0.370400	−	0.213850i
$956$	−21.8593	+	12.6205i	−0.706981	+	0.408176i
$957$		0			0
$958$			21.6184i			0.698459i
$959$	20.4048	+	10.7828i	0.658905	+	0.348195i
$960$		0			0
$961$	21.0425	−	36.4466i	0.678790	−	1.17570i
$962$	−1.90775	+	1.10144i	−0.0615083	+	0.0355118i
$963$		0			0
$964$	−7.03345	+	12.1823i	−0.226532	+	0.392365i
$965$	−36.5928			−1.17797
$966$		0			0
$967$		−	6.75935i		−	0.217366i	−0.994076	−	0.108683i	$-0.965337\pi$
$967$		−	6.75935i		−	0.217366i	0.994076	−	0.108683i	$-0.0346634\pi$
$968$	−10.0944	+	4.37072i	−0.324446	+	0.140480i
$969$		0			0
$970$	21.5598	−	12.4475i	0.692242	−	0.399666i
$971$	−18.6089	−	10.7439i	−0.597189	−	0.344787i	0.170746	−	0.985315i	$-0.445382\pi$
$971$	−18.6089	−	10.7439i	−0.597189	−	0.344787i	−0.767935	+	0.640528i	$0.778716\pi$
$972$		0			0
$973$	−9.16870	+	5.76178i	−0.293935	+	0.184714i
$974$			2.08573i			0.0668311i
$975$		0			0
$976$	2.86310	+	4.95904i	0.0916457	+	0.158735i
$977$	21.6466	+	37.4931i	0.692537	+	1.19951i	0.971004	+	0.239064i	$0.0768405\pi$
$977$	21.6466	+	37.4931i	0.692537	+	1.19951i	−0.278467	+	0.960446i	$0.589826\pi$
$978$		0			0
$979$	−47.7345	+	24.0141i	−1.52560	+	0.767495i
$980$	13.8938	+	6.68901i	0.443822	+	0.213673i
$981$		0			0
$982$	−1.23992	+	2.14760i	−0.0395673	+	0.0685326i
$983$	−18.1526	+	10.4804i	−0.578977	+	0.334273i	−0.760727	−	0.649072i	$-0.775157\pi$
$983$	−18.1526	+	10.4804i	−0.578977	+	0.334273i	0.181750	+	0.983345i	$0.441824\pi$
$984$		0			0
$985$	22.7333	−	39.3752i	0.724342	−	1.25460i
$986$	33.8781			1.07890
$987$		0			0
$988$	−0.263629			−0.00838715
$989$	3.13387	+	1.80934i	0.0996514	+	0.0575338i
$990$		0			0
$991$	−19.2702	−	33.3770i	−0.612138	−	1.06025i	−0.990879	−	0.134751i	$-0.956976\pi$
$991$	−19.2702	−	33.3770i	−0.612138	−	1.06025i	0.378742	−	0.925502i	$-0.376357\pi$
$992$	4.27449	−	7.40363i	0.135715	−	0.235065i
$993$		0			0
$994$	20.0272	−	0.750478i	0.635224	−	0.0238037i
$995$	1.59930			0.0507011
$996$		0			0
$997$	9.72323	+	16.8411i	0.307938	+	0.533364i	0.977911	−	0.209021i	$-0.0670278\pi$
$997$	9.72323	+	16.8411i	0.307938	+	0.533364i	−0.669973	+	0.742385i	$0.733694\pi$
$998$	13.3227	−	7.69189i	0.421724	−	0.243482i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.c.901.3		16
3.2	odd	2		154.2.i.a.131.5	yes	16
7.3	odd	6	inner	1386.2.bk.c.703.7		16
11.10	odd	2	inner	1386.2.bk.c.901.7		16
12.11	even	2		1232.2.bn.b.593.8		16
21.2	odd	6		1078.2.c.b.1077.1		16
21.5	even	6		1078.2.c.b.1077.8		16
21.11	odd	6		1078.2.i.c.1011.4		16
21.17	even	6		154.2.i.a.87.1	✓	16
21.20	even	2		1078.2.i.c.901.8		16
33.32	even	2		154.2.i.a.131.1	yes	16
77.10	even	6	inner	1386.2.bk.c.703.3		16
84.59	odd	6		1232.2.bn.b.241.7		16
132.131	odd	2		1232.2.bn.b.593.7		16
231.32	even	6		1078.2.i.c.1011.8		16
231.65	even	6		1078.2.c.b.1077.9		16
231.131	odd	6		1078.2.c.b.1077.16		16
231.164	odd	6		154.2.i.a.87.5	yes	16
231.230	odd	2		1078.2.i.c.901.4		16
924.395	even	6		1232.2.bn.b.241.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.1	✓	16	21.17	even	6
154.2.i.a.87.5	yes	16	231.164	odd	6
154.2.i.a.131.1	yes	16	33.32	even	2
154.2.i.a.131.5	yes	16	3.2	odd	2
1078.2.c.b.1077.1		16	21.2	odd	6
1078.2.c.b.1077.8		16	21.5	even	6
1078.2.c.b.1077.9		16	231.65	even	6
1078.2.c.b.1077.16		16	231.131	odd	6
1078.2.i.c.901.4		16	231.230	odd	2
1078.2.i.c.901.8		16	21.20	even	2
1078.2.i.c.1011.4		16	21.11	odd	6
1078.2.i.c.1011.8		16	231.32	even	6
1232.2.bn.b.241.7		16	84.59	odd	6
1232.2.bn.b.241.8		16	924.395	even	6
1232.2.bn.b.593.7		16	132.131	odd	2
1232.2.bn.b.593.8		16	12.11	even	2
1386.2.bk.c.703.3		16	77.10	even	6	inner
1386.2.bk.c.703.7		16	7.3	odd	6	inner
1386.2.bk.c.901.3		16	1.1	even	1	trivial
1386.2.bk.c.901.7		16	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.90775 + 1.10144i) q^{5} +(-2.24014 + 1.40775i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.90775 + 1.10144i) q^{5} +(-2.24014 + 1.40775i) q^{7} -1.00000i q^{8} +(-1.10144 - 1.90775i) q^{10} +(1.82062 - 2.77225i) q^{11} -1.45937 q^{13} +(2.64390 - 0.0990746i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.80366 - 6.58813i) q^{17} +(0.0903227 - 0.156443i) q^{19} +2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +(1.14390 - 1.98129i) q^{23} +(-0.0736626 - 0.127587i) q^{25} +(1.26385 + 0.729686i) q^{26} +(-2.33922 - 1.23615i) q^{28} -4.45335i q^{29} +(7.40363 - 4.27449i) q^{31} +(0.866025 - 0.500000i) q^{32} +7.60732i q^{34} +(-5.82418 + 0.218249i) q^{35} +(-0.754735 + 1.30724i) q^{37} +(-0.156443 + 0.0903227i) q^{38} +(1.10144 - 1.90775i) q^{40} +7.10368 q^{41} +1.58174i q^{43} +(3.31114 + 0.190575i) q^{44} +(-1.98129 + 1.14390i) q^{46} +(0.472293 + 0.272679i) q^{47} +(3.03649 - 6.30712i) q^{49} +0.147325i q^{50} +(-0.729686 - 1.26385i) q^{52} +(2.41722 + 4.18675i) q^{53} +(6.52674 - 3.28346i) q^{55} +(1.40775 + 2.24014i) q^{56} +(-2.22668 + 3.85672i) q^{58} +(5.36041 - 3.09483i) q^{59} +(2.86310 - 4.95904i) q^{61} -8.54897 q^{62} -1.00000 q^{64} +(-2.78412 - 1.60741i) q^{65} +(1.49088 + 2.58228i) q^{67} +(3.80366 - 6.58813i) q^{68} +(5.15301 + 2.72308i) q^{70} +7.57488 q^{71} +(4.83822 + 8.38004i) q^{73} +(1.30724 - 0.754735i) q^{74} +0.180645 q^{76} +(-0.175810 + 8.77320i) q^{77} +(5.99185 + 3.45939i) q^{79} +(-1.90775 + 1.10144i) q^{80} +(-6.15197 - 3.55184i) q^{82} +5.84246 q^{83} -16.7580i q^{85} +(0.790869 - 1.36983i) q^{86} +(-2.77225 - 1.82062i) q^{88} +(-13.9527 - 8.05557i) q^{89} +(3.26920 - 2.05443i) q^{91} +2.28779 q^{92} +(-0.272679 - 0.472293i) q^{94} +(0.344626 - 0.198970i) q^{95} +11.3012i q^{97} +(-5.78323 + 3.94388i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5	\( 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

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