LMFDB - Embedded newform 882.2.m.b.587.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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([5, 3]))

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

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

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (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:	$7.04280545828$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			587.1
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	882.587
Dual form			882.2.m.b.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.59238 - 0.681407i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.714925 + 1.23829i) q^{5} +(1.03834 + 1.38631i) q^{6} -1.00000i q^{8} +(2.07137 + 2.17012i) q^{9} -1.42985i q^{10} +(-2.96133 - 1.70972i) q^{11} +(-0.206076 - 1.71975i) q^{12} +(-5.48813 + 3.16857i) q^{13} +(-0.294657 - 2.45898i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.28402 q^{17} +(-0.708796 - 2.91507i) q^{18} -2.16707i q^{19} +(-0.714925 + 1.23829i) q^{20} +(1.70972 + 2.96133i) q^{22} +(6.97507 - 4.02706i) q^{23} +(-0.681407 + 1.59238i) q^{24} +(1.47776 - 2.55956i) q^{25} +6.33715 q^{26} +(-1.81967 - 4.86711i) q^{27} +(-0.298879 - 0.172558i) q^{29} +(-0.974311 + 2.27687i) q^{30} +(-3.76052 + 2.17114i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.55055 + 4.74040i) q^{33} +(-1.97802 - 1.14201i) q^{34} +(-0.843698 + 2.87892i) q^{36} -2.15571 q^{37} +(-1.08353 + 1.87673i) q^{38} +(10.8983 - 1.30593i) q^{39} +(1.23829 - 0.714925i) q^{40} +(0.202180 + 0.350186i) q^{41} +(2.90883 - 5.03824i) q^{43} -3.41945i q^{44} +(-1.20636 + 4.11642i) q^{45} -8.05411 q^{46} +(2.75915 - 4.77898i) q^{47} +(1.38631 - 1.03834i) q^{48} +(-2.55956 + 1.47776i) q^{50} +(-3.63703 - 1.55635i) q^{51} +(-5.48813 - 3.16857i) q^{52} -9.88782i q^{53} +(-0.857672 + 5.12488i) q^{54} -4.88930i q^{55} +(-1.47666 + 3.45080i) q^{57} +(0.172558 + 0.298879i) q^{58} +(-5.51480 - 9.55191i) q^{59} +(1.98221 - 1.48467i) q^{60} +(-9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(-7.84721 - 4.53059i) q^{65} +(-0.704664 - 5.88058i) q^{66} +(-2.12683 - 3.68377i) q^{67} +(1.14201 + 1.97802i) q^{68} +(-13.8510 + 1.65976i) q^{69} -3.55393i q^{71} +(2.17012 - 2.07137i) q^{72} +0.232161i q^{73} +(1.86690 + 1.07786i) q^{74} +(-4.09727 + 3.06884i) q^{75} +(1.87673 - 1.08353i) q^{76} +(-10.0912 - 4.31818i) q^{78} +(-7.28100 + 12.6111i) q^{79} -1.42985 q^{80} +(-0.418868 + 8.99025i) q^{81} -0.404360i q^{82} +(0.811624 - 1.40577i) q^{83} +(1.63290 + 2.82827i) q^{85} +(-5.03824 + 2.90883i) q^{86} +(0.358347 + 0.478436i) q^{87} +(-1.70972 + 2.96133i) q^{88} +4.05949 q^{89} +(3.10295 - 2.96175i) q^{90} +(6.97507 + 4.02706i) q^{92} +(7.46763 - 0.894838i) q^{93} +(-4.77898 + 2.75915i) q^{94} +(2.68345 - 1.54929i) q^{95} +(-1.71975 + 0.206076i) q^{96} +(-9.18719 - 5.30423i) q^{97} +(-2.42369 - 9.96791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Character values

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

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

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.59238	−	0.681407i	−0.919363	−	0.393411i
$3$	−1.59238	−	0.681407i	−0.919363	−	0.393411i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	0.980430	−	0.196866i	$-0.0630764\pi$
$5$	0.714925	+	1.23829i	0.319724	+	0.553779i	−0.660706	+	0.750645i	$0.729743\pi$
$6$	1.03834	+	1.38631i	0.423901	+	0.565958i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.07137	+	2.17012i	0.690456	+	0.723374i
$10$		−	1.42985i		−	0.452158i
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.0179923	−	0.999838i	$-0.505727\pi$
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.874881	+	0.484337i	$0.839061\pi$
$12$	−0.206076	−	1.71975i	−0.0594889	−	0.496448i
$13$	−5.48813	+	3.16857i	−1.52213	+	0.878804i	−0.522476	+	0.852654i	$0.674991\pi$
$13$	−5.48813	+	3.16857i	−1.52213	+	0.878804i	−0.999658	+	0.0261501i	$0.991675\pi$
$14$		0			0
$15$	−0.294657	−	2.45898i	−0.0760802	−	0.634907i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.28402			0.553955			0.276978	−	0.960876i	$-0.410667\pi$
$17$	2.28402			0.553955			0.276978	+	0.960876i	$0.410667\pi$
$18$	−0.708796	−	2.91507i	−0.167065	−	0.687088i
$19$		−	2.16707i		−	0.497159i	−0.968611	−	0.248580i	$-0.920036\pi$
$19$		−	2.16707i		−	0.497159i	0.968611	−	0.248580i	$-0.0799638\pi$
$20$	−0.714925	+	1.23829i	−0.159862	+	0.276889i
$21$		0			0
$22$	1.70972	+	2.96133i	0.364514	+	0.631357i
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.455675	−	0.890146i	$-0.349398\pi$
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.998727	+	0.0504469i	$0.0160646\pi$
$24$	−0.681407	+	1.59238i	−0.139092	+	0.325044i
$25$	1.47776	−	2.55956i	0.295553	−	0.511912i
$26$	6.33715			1.24282
$27$	−1.81967	−	4.86711i	−0.350196	−	0.936676i
$28$		0			0
$29$	−0.298879	−	0.172558i	−0.0555003	−	0.0320431i	0.471993	−	0.881602i	$-0.343535\pi$
$29$	−0.298879	−	0.172558i	−0.0555003	−	0.0320431i	−0.527493	+	0.849559i	$0.676868\pi$
$30$	−0.974311	+	2.27687i	−0.177884	+	0.415698i
$31$	−3.76052	+	2.17114i	−0.675410	+	0.389948i	−0.798123	−	0.602494i	$-0.794174\pi$
$31$	−3.76052	+	2.17114i	−0.675410	+	0.389948i	0.122713	+	0.992442i	$0.460840\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.55055	+	4.74040i	0.618071	+	0.825198i
$34$	−1.97802	−	1.14201i	−0.339227	−	0.195853i
$35$		0			0
$36$	−0.843698	+	2.87892i	−0.140616	+	0.479820i
$37$	−2.15571			−0.354397			−0.177199	−	0.984175i	$-0.556703\pi$
$37$	−2.15571			−0.354397			−0.177199	+	0.984175i	$0.556703\pi$
$38$	−1.08353	+	1.87673i	−0.175772	+	0.304447i
$39$	10.8983	−	1.30593i	1.74512	−	0.209116i
$40$	1.23829	−	0.714925i	0.195790	−	0.113040i
$41$	0.202180	+	0.350186i	0.0315752	+	0.0546898i	0.881381	−	0.472406i	$-0.156614\pi$
$41$	0.202180	+	0.350186i	0.0315752	+	0.0546898i	−0.849806	+	0.527096i	$0.823281\pi$
$42$		0			0
$43$	2.90883	−	5.03824i	0.443592	−	0.768325i	−0.554361	−	0.832277i	$-0.687037\pi$
$43$	2.90883	−	5.03824i	0.443592	−	0.768325i	0.997953	+	0.0639521i	$0.0203705\pi$
$44$		−	3.41945i		−	0.515501i
$45$	−1.20636	+	4.11642i	−0.179834	+	0.613640i
$46$	−8.05411			−1.18751
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	−0.591560	−	0.806261i	$-0.701488\pi$
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	0.994023	+	0.109175i	$0.0348209\pi$
$48$	1.38631	−	1.03834i	0.200096	−	0.149872i
$49$		0			0
$50$	−2.55956	+	1.47776i	−0.361977	+	0.208987i
$51$	−3.63703	−	1.55635i	−0.509286	−	0.217932i
$52$	−5.48813	−	3.16857i	−0.761067	−	0.439402i
$53$		−	9.88782i		−	1.35820i	−0.734047	−	0.679098i	$-0.762371\pi$
$53$		−	9.88782i		−	1.35820i	0.734047	−	0.679098i	$-0.237629\pi$
$54$	−0.857672	+	5.12488i	−0.116714	+	0.697408i
$55$		−	4.88930i		−	0.659273i
$56$		0			0
$57$	−1.47666	+	3.45080i	−0.195588	+	0.457070i
$58$	0.172558	+	0.298879i	0.0226579	+	0.0392447i
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	−0.961805	−	0.273737i	$-0.911740\pi$
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	0.243839	−	0.969816i	$-0.421593\pi$
$60$	1.98221	−	1.48467i	0.255903	−	0.191670i
$61$	−9.94175	−	5.73987i	−1.27291	−	0.734915i	−0.297376	−	0.954760i	$-0.596112\pi$
$61$	−9.94175	−	5.73987i	−1.27291	−	0.734915i	−0.975535	+	0.219845i	$0.929445\pi$
$62$	4.34228			0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.84721	−	4.53059i	−0.973326	−	0.561950i
$66$	−0.704664	−	5.88058i	−0.0867382	−	0.723850i
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	0.706364	−	0.707849i	$-0.250334\pi$
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	−0.966197	+	0.257804i	$0.917001\pi$
$68$	1.14201	+	1.97802i	0.138489	+	0.239870i
$69$	−13.8510	+	1.65976i	−1.66747	+	0.199811i
$70$		0			0
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$	2.17012	−	2.07137i	0.255751	−	0.244113i
$73$			0.232161i			0.0271724i	0.999908	+	0.0135862i	$0.00432475\pi$
$73$			0.232161i			0.0271724i	−0.999908	+	0.0135862i	$0.995675\pi$
$74$	1.86690	+	1.07786i	0.217023	+	0.125298i
$75$	−4.09727	+	3.06884i	−0.473112	+	0.354360i
$76$	1.87673	−	1.08353i	0.215276	−	0.124290i
$77$		0			0
$78$	−10.0912	−	4.31818i	−1.14260	−	0.488937i
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	0.0871130	+	0.996198i	$0.472236\pi$
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	−0.906290	+	0.422657i	$0.861097\pi$
$80$	−1.42985			−0.159862
$81$	−0.418868	+	8.99025i	−0.0465409	+	0.998916i
$82$		−	0.404360i		−	0.0446541i
$83$	0.811624	−	1.40577i	0.0890873	−	0.154304i	−0.818038	−	0.575164i	$-0.804938\pi$
$83$	0.811624	−	1.40577i	0.0890873	−	0.154304i	0.907126	+	0.420860i	$0.138272\pi$
$84$		0			0
$85$	1.63290	+	2.82827i	0.177113	+	0.306769i
$86$	−5.03824	+	2.90883i	−0.543287	+	0.313667i
$87$	0.358347	+	0.478436i	0.0384188	+	0.0512937i
$88$	−1.70972	+	2.96133i	−0.182257	+	0.315679i
$89$	4.05949			0.430305			0.215152	−	0.976580i	$-0.430975\pi$
$89$	4.05949			0.430305			0.215152	+	0.976580i	$0.430975\pi$
$90$	3.10295	−	2.96175i	0.327080	−	0.312196i
$91$		0			0
$92$	6.97507	+	4.02706i	0.727201	+	0.419850i
$93$	7.46763	−	0.894838i	0.774357	−	0.0927903i
$94$	−4.77898	+	2.75915i	−0.492914	+	0.284584i
$95$	2.68345	−	1.54929i	0.275316	−	0.158954i
$96$	−1.71975	+	0.206076i	−0.175521	+	0.0210325i
$97$	−9.18719	−	5.30423i	−0.932818	−	0.538563i	−0.0451164	−	0.998982i	$-0.514366\pi$
$97$	−9.18719	−	5.30423i	−0.932818	−	0.538563i	−0.887702	+	0.460419i	$0.847699\pi$
$98$		0			0
$99$	−2.42369	−	9.96791i	−0.243590	−	1.00181i
$100$	2.95553			0.295553
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	−0.993780	−	0.111364i	$-0.964478\pi$
$101$	−4.02443	+	6.97052i	−0.400446	+	0.693593i	0.593334	+	0.804957i	$0.297811\pi$
$102$	2.37159	+	3.16635i	0.234822	+	0.313515i
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	−0.375114	−	0.926979i	$-0.622396\pi$
$103$	2.43692	−	1.40695i	0.240117	−	0.138631i	0.615230	+	0.788347i	$0.289063\pi$
$104$	3.16857	+	5.48813i	0.310704	+	0.538156i
$105$		0			0
$106$	−4.94391	+	8.56310i	−0.480195	+	0.831722i
$107$		−	15.8216i		−	1.52953i	−0.644310	−	0.764764i	$-0.722855\pi$
$107$		−	15.8216i		−	1.52953i	0.644310	−	0.764764i	$-0.277145\pi$
$108$	3.30521	−	4.00944i	0.318044	−	0.385809i
$109$	−10.2135			−0.978275			−0.489138	−	0.872207i	$-0.662688\pi$
$109$	−10.2135			−0.978275			−0.489138	+	0.872207i	$0.662688\pi$
$110$	−2.44465	+	4.23425i	−0.233088	+	0.403720i
$111$	3.43272	+	1.46892i	0.325819	+	0.139424i
$112$		0			0
$113$	7.28808	−	4.20778i	0.685605	−	0.395834i	−0.116359	−	0.993207i	$-0.537122\pi$
$113$	7.28808	−	4.20778i	0.685605	−	0.395834i	0.801963	+	0.597373i	$0.203789\pi$
$114$	3.00422	−	2.25015i	0.281371	−	0.210746i
$115$	9.97330	+	5.75809i	0.930015	+	0.536945i
$116$		−	0.345115i		−	0.0320431i
$117$	−18.2441	−	5.34664i	−1.68667	−	0.494297i
$118$			11.0296i			1.01536i
$119$		0			0
$120$	−2.45898	+	0.294657i	−0.224473	+	0.0268984i
$121$	0.346305	+	0.599818i	0.0314823	+	0.0545289i
$122$	5.73987	+	9.94175i	0.519664	+	0.900084i
$123$	−0.0833287	−	0.695397i	−0.00751349	−	0.0627018i
$124$	−3.76052	−	2.17114i	−0.337705	−	0.194974i
$125$	11.3752			1.01743
$126$		0			0
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−8.06507	+	6.04071i	−0.710089	+	0.531855i
$130$	4.53059	+	7.84721i	0.397359	+	0.688246i
$131$	2.22833	+	3.85959i	0.194690	+	0.337214i	0.946799	−	0.321825i	$-0.104296\pi$
$131$	2.22833	+	3.85959i	0.194690	+	0.337214i	−0.752109	+	0.659039i	$0.770963\pi$
$132$	−2.33004	+	5.44507i	−0.202804	+	0.473932i
$133$		0			0
$134$			4.25366i			0.367460i
$135$	4.72595	−	5.73290i	0.406745	−	0.493410i
$136$		−	2.28402i		−	0.195853i
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	0.0982292	−	0.995164i	$-0.468682\pi$
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	−0.812723	+	0.582651i	$0.802016\pi$
$138$	12.8252	+	5.48813i	1.09176	+	0.467181i
$139$	16.0680	−	9.27686i	1.36287	−	0.786853i	0.372864	−	0.927886i	$-0.378376\pi$
$139$	16.0680	−	9.27686i	1.36287	−	0.786853i	0.990005	+	0.141033i	$0.0450423\pi$
$140$		0			0
$141$	−7.65005	+	5.72987i	−0.644251	+	0.482542i
$142$	−1.77696	+	3.07779i	−0.149119	+	0.258282i
$143$	21.6695			1.81210
$144$	−2.91507	+	0.708796i	−0.242922	+	0.0590663i
$145$		−	0.493463i		−	0.0409799i
$146$	0.116080	−	0.201057i	0.00960689	−	0.0166396i
$147$		0			0
$148$	−1.07786	−	1.86690i	−0.0885993	−	0.153458i
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	−0.251087	−	0.967965i	$-0.580788\pi$
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	0.712738	+	0.701430i	$0.247455\pi$
$150$	5.08276	−	0.609062i	0.415006	−	0.0497297i
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	−0.959078	−	0.283142i	$-0.908623\pi$
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	0.724747	+	0.689015i	$0.241956\pi$
$152$	−2.16707			−0.175772
$153$	4.73104	+	4.95660i	0.382482	+	0.400717i
$154$		0			0
$155$	−5.37699	−	3.10441i	−0.431890	−	0.249352i
$156$	6.58012	+	8.78524i	0.526831	+	0.703382i
$157$	6.89669	−	3.98180i	0.550415	−	0.317783i	−0.198874	−	0.980025i	$-0.563728\pi$
$157$	6.89669	−	3.98180i	0.550415	−	0.317783i	0.749290	+	0.662243i	$0.230395\pi$
$158$	12.6111	−	7.28100i	1.00328	−	0.579245i
$159$	−6.73763	+	15.7452i	−0.534329	+	1.24868i
$160$	1.23829	+	0.714925i	0.0978952	+	0.0565198i
$161$		0			0
$162$	4.85787	−	7.57635i	0.381671	−	0.595254i
$163$	−11.3851			−0.891751			−0.445876	−	0.895095i	$-0.647108\pi$
$163$	−11.3851			−0.891751			−0.445876	+	0.895095i	$0.647108\pi$
$164$	−0.202180	+	0.350186i	−0.0157876	+	0.0273449i
$165$	−3.33160	+	7.78563i	−0.259365	+	0.606111i
$166$	−1.40577	+	0.811624i	−0.109109	+	0.0629942i
$167$	−5.66418	−	9.81065i	−0.438308	−	0.759171i	0.559252	−	0.828998i	$-0.311089\pi$
$167$	−5.66418	−	9.81065i	−0.438308	−	0.759171i	−0.997559	+	0.0698271i	$0.977755\pi$
$168$		0			0
$169$	13.5797	−	23.5208i	1.04459	−	1.80929i
$170$		−	3.26580i		−	0.250476i
$171$	4.70280	−	4.48879i	0.359632	−	0.343267i
$172$	5.81766			0.443592
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	−0.0776528	−	0.996980i	$-0.524743\pi$
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	0.902237	−	0.431241i	$-0.141924\pi$
$174$	−0.0711198	−	0.593511i	−0.00539158	−	0.0449940i
$175$		0			0
$176$	2.96133	−	1.70972i	0.223218	−	0.128875i
$177$	2.27293	+	18.9681i	0.170844	+	1.42573i
$178$	−3.51562	−	2.02974i	−0.263507	−	0.152136i
$179$			20.7912i			1.55400i	0.629498	+	0.777002i	$0.283261\pi$
$179$			20.7912i			1.55400i	−0.629498	+	0.777002i	$0.716739\pi$
$180$	−4.16811	+	1.01347i	−0.310672	+	0.0755398i
$181$			21.5301i			1.60032i	0.599788	+	0.800159i	$0.295252\pi$
$181$			21.5301i			1.60032i	−0.599788	+	0.800159i	$0.704748\pi$
$182$		0			0
$183$	11.9199	+	15.9145i	0.881143	+	1.17643i
$184$	−4.02706	−	6.97507i	−0.296879	−	0.514209i
$185$	−1.54117	−	2.66939i	−0.113309	−	0.196258i
$186$	−6.91457	−	2.95886i	−0.507001	−	0.216954i
$187$	−6.76372	−	3.90503i	−0.494612	−	0.285564i
$188$	5.51829			0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$	6.38207	+	3.68469i	0.461791	+	0.266615i	0.712797	−	0.701371i	$-0.247428\pi$
$191$	6.38207	+	3.68469i	0.461791	+	0.266615i	−0.251006	+	0.967985i	$0.580761\pi$
$192$	1.59238	+	0.681407i	0.114920	+	0.0491763i
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	0.912383	−	0.409337i	$-0.134240\pi$
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	−0.810688	+	0.585478i	$0.800907\pi$
$194$	5.30423	+	9.18719i	0.380821	+	0.659602i
$195$	9.40859	+	12.5616i	0.673763	+	0.899553i
$196$		0			0
$197$			26.0883i			1.85871i	0.369183	+	0.929357i	$0.379637\pi$
$197$			26.0883i			1.85871i	−0.369183	+	0.929357i	$0.620363\pi$
$198$	−2.88498	+	9.84431i	−0.205026	+	0.699604i
$199$		−	15.4165i		−	1.09285i	−0.837509	−	0.546424i	$-0.815989\pi$
$199$		−	15.4165i		−	1.09285i	0.837509	−	0.546424i	$-0.184011\pi$
$200$	−2.55956	−	1.47776i	−0.180988	−	0.104494i
$201$	0.876575	+	7.31522i	0.0618288	+	0.515976i
$202$	6.97052	−	4.02443i	0.490444	−	0.283158i
$203$		0			0
$204$	−0.470680	−	3.92793i	−0.0329542	−	0.275010i
$205$	−0.289087	+	0.500713i	−0.0201907	+	0.0349713i
$206$	−2.81391			−0.196054
$207$	23.1871	+	6.79524i	1.61162	+	0.472301i
$208$		−	6.33715i		−	0.439402i
$209$	−3.70508	+	6.41739i	−0.256286	+	0.443900i
$210$		0			0
$211$	4.42465	+	7.66371i	0.304605	+	0.527592i	0.977173	−	0.212443i	$-0.0681421\pi$
$211$	4.42465	+	7.66371i	0.304605	+	0.527592i	−0.672568	+	0.740035i	$0.734809\pi$
$212$	8.56310	−	4.94391i	0.588116	−	0.339549i
$213$	−2.42167	+	5.65921i	−0.165930	+	0.387763i
$214$	−7.91078	+	13.7019i	−0.540770	+	0.936641i
$215$	8.31838			0.567309
$216$	−4.86711	+	1.81967i	−0.331165	+	0.123813i
$217$		0			0
$218$	8.84514	+	5.10675i	0.599069	+	0.345873i
$219$	0.158196	−	0.369689i	0.0106899	−	0.0249813i
$220$	4.23425	−	2.44465i	0.285473	−	0.164818i
$221$	−12.5350	+	7.23707i	−0.843194	+	0.486818i
$222$	−2.23836	−	2.98848i	−0.150229	−	0.200574i
$223$	−6.88961	−	3.97772i	−0.461363	−	0.266368i	0.251254	−	0.967921i	$-0.419157\pi$
$223$	−6.88961	−	3.97772i	−0.461363	−	0.266368i	−0.712617	+	0.701553i	$0.752490\pi$
$224$		0			0
$225$	8.61556	−	2.09487i	0.574370	−	0.139658i
$226$	−8.41555			−0.559794
$227$	4.61984	−	8.00180i	0.306630	−	0.531098i	−0.670993	−	0.741464i	$-0.734132\pi$
$227$	4.61984	−	8.00180i	0.306630	−	0.531098i	0.977623	+	0.210365i	$0.0674654\pi$
$228$	−3.72681	+	0.446579i	−0.246814	+	0.0295754i
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	−0.238509	−	0.971140i	$-0.576659\pi$
$229$	7.31319	−	4.22227i	0.483269	−	0.279016i	0.721778	+	0.692125i	$0.243325\pi$
$230$	−5.75809	−	9.97330i	−0.379677	−	0.657620i
$231$		0			0
$232$	−0.172558	+	0.298879i	−0.0113290	+	0.0196223i
$233$			16.6480i			1.09065i	0.838226	+	0.545323i	$0.183593\pi$
$233$			16.6480i			1.09065i	−0.838226	+	0.545323i	$0.816407\pi$
$234$	13.1266	+	13.7524i	0.858111	+	0.899022i
$235$	7.89034			0.514709
$236$	5.51480	−	9.55191i	0.358983	−	0.621776i
$237$	20.1874	−	15.1203i	1.31131	−	0.982170i
$238$		0			0
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.529242	+	0.848471i	$0.677524\pi$
$239$	−23.6325	+	13.6442i	−1.52866	+	0.882572i	−0.999418	+	0.0341012i	$0.989143\pi$
$240$	2.27687	+	0.974311i	0.146971	+	0.0628915i
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.995466	−	0.0951223i	$-0.0303242\pi$
$241$	21.9018	+	12.6450i	1.41082	+	0.814537i	0.415354	+	0.909660i	$0.363658\pi$
$242$		−	0.692610i		−	0.0445227i
$243$	6.79302	−	14.0305i	0.435772	−	0.900057i
$244$		−	11.4797i		−	0.734915i
$245$		0			0
$246$	−0.275534	+	0.643896i	−0.0175674	+	0.0410533i
$247$	6.86651	+	11.8931i	0.436906	+	0.756743i
$248$	2.17114	+	3.76052i	0.137868	+	0.238794i
$249$	−2.25032	+	1.68548i	−0.142608	+	0.106813i
$250$	−9.85123	−	5.68761i	−0.623046	−	0.359716i
$251$	−8.19337			−0.517161			−0.258581	−	0.965990i	$-0.583255\pi$
$251$	−8.19337			−0.517161			−0.258581	+	0.965990i	$0.583255\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$	−5.00366	−	2.88886i	−0.313958	−	0.181264i
$255$	−0.673002	−	5.61636i	−0.0421450	−	0.351710i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	0.743821	−	0.668379i	$-0.233012\pi$
$257$	−3.31723	−	5.74560i	−0.206923	−	0.358401i	−0.950744	+	0.309978i	$0.899678\pi$
$258$	10.0049	−	1.19888i	0.622878	−	0.0746388i
$259$		0			0
$260$		−	9.06117i		−	0.561950i
$261$	−0.244616	−	1.00603i	−0.0151414	−	0.0622719i
$262$		−	4.45667i		−	0.275334i
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	0.329807	−	0.944048i	$-0.393016\pi$
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	−0.652666	+	0.757645i	$0.726350\pi$
$264$	4.74040	−	3.55055i	0.291752	−	0.218521i
$265$	12.2440	−	7.06905i	0.752140	−	0.434248i
$266$		0			0
$267$	−6.46426	−	2.76616i	−0.395606	−	0.169286i
$268$	2.12683	−	3.68377i	0.129917	−	0.225022i
$269$	−6.82139			−0.415907			−0.207954	−	0.978139i	$-0.566680\pi$
$269$	−6.82139			−0.415907			−0.207954	+	0.978139i	$0.566680\pi$
$270$	−6.95924	+	2.60186i	−0.423526	+	0.158344i
$271$		−	5.07815i		−	0.308475i	−0.988034	−	0.154238i	$-0.950708\pi$
$271$		−	5.07815i		−	0.308475i	0.988034	−	0.154238i	$-0.0492922\pi$
$272$	−1.14201	+	1.97802i	−0.0692444	+	0.119935i
$273$		0			0
$274$	4.82834	+	8.36293i	0.291691	+	0.505223i
$275$	−8.75228	+	5.05313i	−0.527783	+	0.304715i
$276$	−8.36291	−	11.1655i	−0.503388	−	0.672083i
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	−0.834765	−	0.550607i	$-0.814396\pi$
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	0.894222	+	0.447624i	$0.147730\pi$
$278$	−18.5537			−1.11278
$279$	−12.5011	−	3.66357i	−0.748420	−	0.219332i
$280$		0			0
$281$	−15.2703	−	8.81631i	−0.910950	−	0.525937i	−0.0302131	−	0.999543i	$-0.509619\pi$
$281$	−15.2703	−	8.81631i	−0.910950	−	0.525937i	−0.880737	+	0.473606i	$0.842952\pi$
$282$	9.49008	−	1.13719i	0.565126	−	0.0677184i
$283$	4.46337	−	2.57693i	0.265320	−	0.153182i	−0.361439	−	0.932396i	$-0.617714\pi$
$283$	4.46337	−	2.57693i	0.265320	−	0.153182i	0.626759	+	0.779213i	$0.284381\pi$
$284$	3.07779	−	1.77696i	0.182633	−	0.105443i
$285$	−5.32878	+	0.638542i	−0.315650	+	0.0378240i
$286$	−18.7664	−	10.8348i	−1.10968	−	0.640673i
$287$		0			0
$288$	2.87892	+	0.843698i	0.169642	+	0.0497154i
$289$	−11.7833			−0.693134
$290$	−0.246732	+	0.427352i	−0.0144886	+	0.0250949i
$291$	11.0152	+	14.7066i	0.645722	+	0.862115i
$292$	−0.201057	+	0.116080i	−0.0117660	+	0.00679310i
$293$	1.03248	+	1.78831i	0.0603183	+	0.104474i	0.894608	−	0.446852i	$-0.147455\pi$
$293$	1.03248	+	1.78831i	0.0603183	+	0.104474i	−0.834289	+	0.551327i	$0.814122\pi$
$294$		0			0
$295$	7.88534	−	13.6578i	0.459102	−	0.795188i
$296$			2.15571i			0.125298i
$297$	−2.93276	+	17.5243i	−0.170176	+	1.01686i
$298$	−6.50694			−0.376937
$299$	−25.5201	+	44.2020i	−1.47586	+	2.55627i
$300$	−4.70633	−	2.01392i	−0.271720	−	0.116274i
$301$		0			0
$302$	4.98745	−	2.87950i	0.286995	−	0.165697i
$303$	11.1582	−	8.35746i	0.641022	−	0.480124i
$304$	1.87673	+	1.08353i	0.107638	+	0.0621449i
$305$		−	16.4143i		−	0.939881i
$306$	−1.61890	−	6.65806i	−0.0925464	−	0.380616i
$307$		−	1.09119i		−	0.0622772i	−0.999515	−	0.0311386i	$-0.990087\pi$
$307$		−	1.09119i		−	0.0622772i	0.999515	−	0.0311386i	$-0.00991333\pi$
$308$		0			0
$309$	−4.83921	+	0.579878i	−0.275293	+	0.0329881i
$310$	3.10441	+	5.37699i	0.176318	+	0.305392i
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	0.565429	−	0.824797i	$-0.308711\pi$
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	−0.997010	+	0.0772777i	$0.975377\pi$
$312$	−1.30593	−	10.8983i	−0.0739338	−	0.616995i
$313$	10.0202	+	5.78518i	0.566377	+	0.326998i	0.755701	−	0.654917i	$-0.227296\pi$
$313$	10.0202	+	5.78518i	0.566377	+	0.326998i	−0.189324	+	0.981915i	$0.560630\pi$
$314$	−7.96361			−0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$	−14.8613	−	8.58020i	−0.834696	−	0.481912i	0.0207618	−	0.999784i	$-0.493391\pi$
$317$	−14.8613	−	8.58020i	−0.834696	−	0.481912i	−0.855458	+	0.517872i	$0.826724\pi$
$318$	13.7076	−	10.2669i	0.768682	−	0.575740i
$319$	0.590051	+	1.02200i	0.0330365	+	0.0572210i
$320$	−0.714925	−	1.23829i	−0.0399655	−	0.0692223i
$321$	−10.7809	+	25.1940i	−0.601733	+	1.40619i
$322$		0			0
$323$		−	4.94962i		−	0.275404i
$324$	−7.99522	+	4.13237i	−0.444179	+	0.229576i
$325$			18.7296i			1.03893i
$326$	9.85980	+	5.69256i	0.546084	+	0.315282i
$327$	16.2638	+	6.95955i	0.899390	+	0.384864i
$328$	0.350186	−	0.202180i	0.0193358	−	0.0111635i
$329$		0			0
$330$	6.77807	−	5.07676i	0.373120	−	0.279466i
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	−0.229591	−	0.973287i	$-0.573739\pi$
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	0.957687	−	0.287812i	$-0.0929280\pi$
$332$	1.62325			0.0890873
$333$	−4.46528	−	4.67816i	−0.244696	−	0.256362i
$334$			11.3284i			0.619860i
$335$	3.04105	−	5.26725i	0.166150	−	0.287780i
$336$		0			0
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	0.955236	−	0.295846i	$-0.0956015\pi$
$337$	4.06451	+	7.03993i	0.221408	+	0.383490i	−0.733828	+	0.679335i	$0.762268\pi$
$338$	−23.5208	+	13.5797i	−1.27936	+	0.738640i
$339$	−14.4726	+	1.73424i	−0.786045	+	0.0941909i
$340$	−1.63290	+	2.82827i	−0.0885565	+	0.153384i
$341$	14.8482			0.804075
$342$	−6.31714	+	1.53601i	−0.341592	+	0.0830578i
$343$		0			0
$344$	−5.03824	−	2.90883i	−0.271644	−	0.156834i
$345$	−11.9577	−	15.9650i	−0.643782	−	0.859525i
$346$	−18.7853	+	10.8457i	−1.00991	+	0.583069i
$347$	22.1851	−	12.8086i	1.19096	−	0.687599i	0.232433	−	0.972612i	$-0.425331\pi$
$347$	22.1851	−	12.8086i	1.19096	−	0.687599i	0.958524	+	0.285013i	$0.0919979\pi$
$348$	−0.235164	+	0.549556i	−0.0126061	+	0.0294593i
$349$	9.11932	+	5.26504i	0.488146	+	0.281831i	0.723805	−	0.690005i	$-0.242391\pi$
$349$	9.11932	+	5.26504i	0.488146	+	0.281831i	−0.235659	+	0.971836i	$0.575725\pi$
$350$		0			0
$351$	25.4084	+	20.9456i	1.35620	+	1.11799i
$352$	−3.41945			−0.182257
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	−0.642966	−	0.765895i	$-0.722296\pi$
$353$	6.42186	−	11.1230i	0.341801	−	0.592017i	0.984767	+	0.173878i	$0.0556297\pi$
$354$	7.51565	−	17.5633i	0.399452	−	0.933481i
$355$	4.40078	−	2.54079i	0.233569	−	0.134851i
$356$	2.02974	+	3.51562i	0.107576	+	0.186327i
$357$		0			0
$358$	10.3956	−	18.0057i	0.549424	−	0.951630i
$359$			29.6621i			1.56551i	0.622333	+	0.782753i	$0.286185\pi$
$359$			29.6621i			1.56551i	−0.622333	+	0.782753i	$0.713815\pi$
$360$	4.11642	+	1.20636i	0.216955	+	0.0635808i
$361$	14.3038			0.752833
$362$	10.7650	−	18.6456i	0.565798	−	0.979991i
$363$	−0.142730	−	1.19112i	−0.00749139	−	0.0625173i
$364$		0			0
$365$	−0.287482	+	0.165978i	−0.0150475	+	0.00868767i
$366$	−2.36570	−	19.7423i	−0.123657	−	1.03195i
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.152651	−	0.988280i	$-0.548781\pi$
$367$	−20.7828	−	11.9989i	−1.08485	−	0.626340i	−0.932201	+	0.361940i	$0.882115\pi$
$368$			8.05411i			0.419850i
$369$	−0.341157	+	1.16412i	−0.0177599	+	0.0606016i
$370$			3.08235i			0.160244i
$371$		0			0
$372$	4.50877	+	6.01974i	0.233769	+	0.312109i
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	0.977594	−	0.210500i	$-0.0675091\pi$
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	−0.671095	+	0.741371i	$0.734176\pi$
$374$	3.90503	+	6.76372i	0.201925	+	0.349744i
$375$	−18.1137	−	7.75115i	−0.935387	−	0.400268i
$376$	−4.77898	−	2.75915i	−0.246457	−	0.142292i
$377$	2.18705			0.112639
$378$		0			0
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$	2.68345	+	1.54929i	0.137658	+	0.0794769i
$381$	−9.20036	−	3.93699i	−0.471349	−	0.201698i
$382$	−3.68469	−	6.38207i	−0.188525	−	0.326535i
$383$	−8.77603	−	15.2005i	−0.448434	−	0.776711i	0.549850	−	0.835263i	$-0.314685\pi$
$383$	−8.77603	−	15.2005i	−0.448434	−	0.776711i	−0.998284	+	0.0585527i	$0.981351\pi$
$384$	−1.03834	−	1.38631i	−0.0529876	−	0.0707447i
$385$		0			0
$386$		−	2.82559i		−	0.143819i
$387$	16.9589	−	4.12353i	0.862067	−	0.209611i
$388$		−	10.6085i		−	0.538563i
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.0631489	−	0.998004i	$-0.520114\pi$
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.895871	+	0.444313i	$0.853448\pi$
$390$	−1.86729	−	15.5829i	−0.0945537	−	0.789073i
$391$	15.9312	−	9.19786i	0.805674	−	0.465156i
$392$		0			0
$393$	−0.918411	−	7.66435i	−0.0463277	−	0.386615i
$394$	13.0441	−	22.5931i	0.657154	−	1.13822i
$395$	−20.8215			−1.04764
$396$	7.42062	−	7.08293i	0.372900	−	0.355931i
$397$			38.9869i			1.95670i	0.206965	+	0.978348i	$0.433641\pi$
$397$			38.9869i			1.95670i	−0.206965	+	0.978348i	$0.566359\pi$
$398$	−7.70826	+	13.3511i	−0.386380	+	0.669230i
$399$		0			0
$400$	1.47776	+	2.55956i	0.0738882	+	0.127978i
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.0940373	−	0.995569i	$-0.470023\pi$
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.909206	+	0.416346i	$0.136689\pi$
$402$	2.89847	−	6.77345i	0.144563	−	0.337829i
$403$	13.7588	−	23.8310i	0.685376	−	1.18711i
$404$	−8.04886			−0.400446
$405$	−11.4320	+	5.90868i	−0.568059	+	0.293605i
$406$		0			0
$407$	6.38377	+	3.68567i	0.316432	+	0.182692i
$408$	−1.55635	+	3.63703i	−0.0770506	+	0.180060i
$409$	−21.3205	+	12.3094i	−1.05423	+	0.608659i	−0.923830	−	0.382803i	$-0.874959\pi$
$409$	−21.3205	+	12.3094i	−1.05423	+	0.608659i	−0.130398	+	0.991462i	$0.541626\pi$
$410$	0.500713	−	0.289087i	0.0247285	−	0.0142770i
$411$	10.0269	+	13.3871i	0.494592	+	0.660338i
$412$	2.43692	+	1.40695i	0.120058	+	0.0693157i
$413$		0			0
$414$	−16.6830	−	17.4784i	−0.819926	−	0.859017i
$415$	2.32100			0.113933
$416$	−3.16857	+	5.48813i	−0.155352	+	0.269078i
$417$	−31.9077	+	3.82347i	−1.56253	+	0.187236i
$418$	6.41739	−	3.70508i	0.313885	−	0.181222i
$419$	8.53996	+	14.7916i	0.417204	+	0.722619i	0.995657	−	0.0930969i	$-0.0296766\pi$
$419$	8.53996	+	14.7916i	0.417204	+	0.722619i	−0.578453	+	0.815716i	$0.696343\pi$
$420$		0			0
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	−0.987716	−	0.156258i	$-0.950057\pi$
$421$	−7.35652	+	12.7419i	−0.358535	+	0.621000i	0.629182	+	0.777258i	$0.283390\pi$
$422$		−	8.84930i		−	0.430777i
$423$	16.0862	−	3.91134i	0.782137	−	0.190176i
$424$	−9.88782			−0.480195
$425$	3.37524	−	5.84608i	0.163723	−	0.283577i
$426$	4.92684	−	3.69019i	0.238706	−	0.178790i
$427$		0			0
$428$	13.7019	−	7.91078i	0.662305	−	0.382382i
$429$	−34.5062	−	14.7658i	−1.66598	−	0.712899i
$430$	−7.20393	−	4.15919i	−0.347404	−	0.200574i
$431$			9.61042i			0.462917i	0.972845	+	0.231459i	$0.0743498\pi$
$431$			9.61042i			0.462917i	−0.972845	+	0.231459i	$0.925650\pi$
$432$	5.12488	+	0.857672i	0.246571	+	0.0412648i
$433$			9.04314i			0.434585i	0.976106	+	0.217293i	$0.0697226\pi$
$433$			9.04314i			0.434585i	−0.976106	+	0.217293i	$0.930277\pi$
$434$		0			0
$435$	−0.336249	+	0.785782i	−0.0161219	+	0.0376754i
$436$	−5.10675	−	8.84514i	−0.244569	−	0.423606i
$437$	−8.72690	−	15.1154i	−0.417464	−	0.723069i
$438$	−0.321846	+	0.241062i	−0.0153784	+	0.0115184i
$439$	0.791370	+	0.456897i	0.0377700	+	0.0218065i	0.518766	−	0.854916i	$-0.326392\pi$
$439$	0.791370	+	0.456897i	0.0377700	+	0.0218065i	−0.480996	+	0.876723i	$0.659725\pi$
$440$	−4.88930			−0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$	25.4279	+	14.6808i	1.20812	+	0.697507i	0.962348	−	0.271821i	$-0.0876259\pi$
$443$	25.4279	+	14.6808i	1.20812	+	0.697507i	0.245770	+	0.969328i	$0.420959\pi$
$444$	0.444240	+	3.70728i	0.0210827	+	0.175940i
$445$	2.90223	+	5.02681i	0.137579	+	0.238294i
$446$	3.97772	+	6.88961i	0.188351	+	0.326233i
$447$	−11.1903	+	1.34092i	−0.529283	+	0.0634234i
$448$		0			0
$449$			3.36736i			0.158915i	0.996838	+	0.0794577i	$0.0253189\pi$
$449$			3.36736i			0.158915i	−0.996838	+	0.0794577i	$0.974681\pi$
$450$	−8.50872	−	2.49357i	−0.401105	−	0.117548i
$451$		−	1.38269i		−	0.0651082i
$452$	7.28808	+	4.20778i	0.342802	+	0.197917i
$453$	7.98375	−	5.97981i	0.375109	−	0.280956i
$454$	−8.00180	+	4.61984i	−0.375543	+	0.216820i
$455$		0			0
$456$	3.45080	+	1.47666i	0.161599	+	0.0691507i
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	−0.633362	−	0.773856i	$-0.718325\pi$
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	0.986860	+	0.161579i	$0.0516588\pi$
$458$	−8.44454			−0.394588
$459$	−4.15617	−	11.1166i	−0.193993	−	0.518877i
$460$			11.5162i			0.536945i
$461$	5.19445	−	8.99706i	0.241930	−	0.419035i	−0.719334	−	0.694664i	$-0.755553\pi$
$461$	5.19445	−	8.99706i	0.241930	−	0.419035i	0.961264	+	0.275629i	$0.0888863\pi$
$462$		0			0
$463$	−2.65722	−	4.60244i	−0.123492	−	0.213894i	0.797651	−	0.603120i	$-0.206076\pi$
$463$	−2.65722	−	4.60244i	−0.123492	−	0.213894i	−0.921142	+	0.389226i	$0.872743\pi$
$464$	0.298879	−	0.172558i	0.0138751	−	0.00801078i
$465$	6.44686	+	8.60732i	0.298966	+	0.399155i
$466$	8.32399	−	14.4176i	0.385601	−	0.667881i
$467$	−19.4999			−0.902346			−0.451173	−	0.892436i	$-0.648994\pi$
$467$	−19.4999			−0.902346			−0.451173	+	0.892436i	$0.648994\pi$
$468$	−4.49174	−	18.4732i	−0.207631	−	0.853924i
$469$		0			0
$470$	−6.83323	−	3.94517i	−0.315193	−	0.181977i
$471$	−13.6954	+	1.64110i	−0.631051	+	0.0756181i
$472$	−9.55191	+	5.51480i	−0.439662	+	0.253839i
$473$	−17.2280	+	9.94659i	−0.792144	+	0.457345i
$474$	−25.0430	+	3.00087i	−1.15026	+	0.137835i
$475$	−5.54674	−	3.20241i	−0.254502	−	0.146937i
$476$		0			0
$477$	21.4578	−	20.4813i	0.982484	−	0.937775i
$478$	27.2885			1.24815
$479$	−13.9012	+	24.0776i	−0.635163	+	1.10013i	0.351318	+	0.936256i	$0.385734\pi$
$479$	−13.9012	+	24.0776i	−0.635163	+	1.10013i	−0.986481	+	0.163878i	$0.947600\pi$
$480$	−1.48467	−	1.98221i	−0.0677657	−	0.0904752i
$481$	11.8308	−	6.83054i	0.539440	−	0.311446i
$482$	−12.6450	−	21.9018i	−0.575965	−	0.997600i
$483$		0			0
$484$	−0.346305	+	0.599818i	−0.0157411	+	0.0272645i
$485$		−	15.1685i		−	0.688767i
$486$	−12.8982	+	8.75426i	−0.585073	+	0.397101i
$487$	−7.47675			−0.338804			−0.169402	−	0.985547i	$-0.554184\pi$
$487$	−7.47675			−0.338804			−0.169402	+	0.985547i	$0.554184\pi$
$488$	−5.73987	+	9.94175i	−0.259832	+	0.450042i
$489$	18.1295	+	7.75790i	0.819843	+	0.350824i
$490$		0			0
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	−0.00130103	−	0.999999i	$-0.500414\pi$
$491$	19.1466	−	11.0543i	0.864073	−	0.498873i	0.865374	+	0.501126i	$0.167081\pi$
$492$	0.560567	−	0.419863i	0.0252723	−	0.0189289i
$493$	−0.682643	−	0.394124i	−0.0307447	−	0.0177505i
$494$		−	13.7330i		−	0.617878i
$495$	10.6104	−	10.1275i	0.476901	−	0.455199i
$496$		−	4.34228i		−	0.194974i
$497$		0			0
$498$	2.79158	−	0.334512i	0.125094	−	0.0149898i
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	−0.954063	−	0.299606i	$-0.903145\pi$
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	0.217565	−	0.976046i	$-0.430189\pi$
$500$	5.68761	+	9.85123i	0.254358	+	0.440560i
$501$	2.33450	+	19.4819i	0.104298	+	0.870388i
$502$	7.09567	+	4.09669i	0.316695	+	0.182844i
$503$	−25.6142			−1.14208			−0.571039	−	0.820923i	$-0.693460\pi$
$503$	−25.6142			−1.14208			−0.571039	+	0.820923i	$0.693460\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$	23.8509	+	13.7703i	1.06030	+	0.612165i
$507$	−37.6513	+	28.2008i	−1.67215	+	1.25244i
$508$	2.88886	+	5.00366i	0.128173	+	0.222002i
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	0.523760	−	0.851866i	$-0.324529\pi$
$509$	−10.7358	−	18.5950i	−0.475857	−	0.824209i	−0.999617	+	0.0276567i	$0.991195\pi$
$510$	−2.22534	+	5.20041i	−0.0985398	+	0.230278i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−10.5474	+	3.94336i	−0.465677	+	0.174103i
$514$			6.63445i			0.292633i
$515$	3.48443	+	2.01173i	0.153542	+	0.0886476i
$516$	−9.26394	−	3.96420i	−0.407822	−	0.174514i
$517$	−16.3415	+	9.43475i	−0.718697	+	0.414940i
$518$		0			0
$519$	−30.0710	+	22.5231i	−1.31997	+	0.988654i
$520$	−4.53059	+	7.84721i	−0.198679	+	0.344123i
$521$	6.46175			0.283094			0.141547	−	0.989932i	$-0.454792\pi$
$521$	6.46175			0.283094			0.141547	+	0.989932i	$0.454792\pi$
$522$	−0.291173	+	0.993559i	−0.0127443	+	0.0434869i
$523$			13.6058i			0.594941i	0.954731	+	0.297470i	$0.0961429\pi$
$523$			13.6058i			0.594941i	−0.954731	+	0.297470i	$0.903857\pi$
$524$	−2.22833	+	3.85959i	−0.0973452	+	0.168607i
$525$		0			0
$526$	3.02295	+	5.23590i	0.131807	+	0.228296i
$527$	−8.58910	+	4.95892i	−0.374147	+	0.216014i
$528$	−5.88058	+	0.704664i	−0.255920	+	0.0306666i
$529$	20.9344	−	36.2594i	0.910190	−	1.57649i
$530$	−14.1381			−0.614120
$531$	9.30564	−	31.7533i	0.403830	−	1.37798i
$532$		0			0
$533$	−2.21918	−	1.28124i	−0.0961233	−	0.0554968i
$534$	4.21513	+	5.62770i	0.182406	+	0.243534i
$535$	19.5916	−	11.3112i	0.847020	−	0.489027i
$536$	−3.68377	+	2.12683i	−0.159115	+	0.0918650i
$537$	14.1673	−	33.1075i	0.611362	−	1.42869i
$538$	5.90750	+	3.41069i	0.254690	+	0.147045i
$539$		0			0
$540$	7.32781	+	1.22634i	0.315339	+	0.0527734i
$541$	29.8575			1.28368			0.641838	−	0.766840i	$-0.278172\pi$
$541$	29.8575			1.28368			0.641838	+	0.766840i	$0.278172\pi$
$542$	−2.53907	+	4.39780i	−0.109063	+	0.188902i
$543$	14.6708	−	34.2841i	0.629582	−	1.47127i
$544$	1.97802	−	1.14201i	0.0848067	−	0.0489632i
$545$	−7.30188	−	12.6472i	−0.312778	−	0.541748i
$546$		0			0
$547$	−9.07207	+	15.7133i	−0.387894	+	0.671852i	−0.992166	−	0.124926i	$-0.960131\pi$
$547$	−9.07207	+	15.7133i	−0.387894	+	0.671852i	0.604272	+	0.796778i	$0.293464\pi$
$548$		−	9.65668i		−	0.412513i
$549$	−8.13680	−	33.4642i	−0.347270	−	1.42822i
$550$	10.1063			0.430933
$551$	−0.373944	+	0.647690i	−0.0159305	+	0.0275925i
$552$	1.65976	+	13.8510i	0.0706439	+	0.589540i
$553$		0			0
$554$	−1.71398	+	0.989567i	−0.0728201	+	0.0420427i
$555$	0.635196	+	5.30086i	0.0269626	+	0.225009i
$556$	16.0680	+	9.27686i	0.681435	+	0.393426i
$557$			37.5369i			1.59049i	0.606289	+	0.795245i	$0.292658\pi$
$557$			37.5369i			1.59049i	−0.606289	+	0.795245i	$0.707342\pi$
$558$	8.99446	+	9.42328i	0.380766	+	0.398919i
$559$			36.8674i			1.55932i
$560$		0			0
$561$	8.10951	+	10.8272i	0.342384	+	0.457123i
$562$	8.81631	+	15.2703i	0.371894	+	0.644139i
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	0.781380	−	0.624056i	$-0.214516\pi$
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	−0.931138	+	0.364667i	$0.881183\pi$
$564$	−8.78724	−	3.76021i	−0.370010	−	0.158333i
$565$	10.4209	+	6.01649i	0.438409	+	0.253116i
$566$	−5.15385			−0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$	−35.6499	−	20.5825i	−1.49452	−	0.862862i	−0.494541	−	0.869154i	$-0.664664\pi$
$569$	−35.6499	−	20.5825i	−1.49452	−	0.862862i	−0.999980	+	0.00629202i	$0.997997\pi$
$570$	4.93413	+	2.11140i	0.206668	+	0.0884367i
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	0.816000	−	0.578052i	$-0.196187\pi$
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	−0.908608	+	0.417650i	$0.862854\pi$
$572$	10.8348	+	18.7664i	0.453024	+	0.784661i
$573$	−7.65193	−	10.2162i	−0.319664	−	0.426789i
$574$		0			0
$575$		−	23.8042i		−	0.992702i
$576$	−2.07137	−	2.17012i	−0.0863070	−	0.0904218i
$577$		−	2.74290i		−	0.114188i	−0.998369	−	0.0570941i	$-0.981816\pi$
$577$		−	2.74290i		−	0.114188i	0.998369	−	0.0570941i	$-0.0181835\pi$
$578$	10.2046	+	5.89164i	0.424456	+	0.245060i
$579$	−0.582285	−	4.85930i	−0.0241989	−	0.201946i
$580$	0.427352	−	0.246732i	0.0177448	−	0.0102450i
$581$		0			0
$582$	−2.18614	−	18.2439i	−0.0906186	−	0.756233i
$583$	−16.9054	+	29.2811i	−0.700151	+	1.21270i
$584$	0.232161			0.00960689
$585$	−6.42252	−	26.4139i	−0.265539	−	1.09208i
$586$		−	2.06497i		−	0.0853029i
$587$	9.90248	−	17.1516i	0.408719	−	0.707922i	−0.586027	−	0.810291i	$-0.699309\pi$
$587$	9.90248	−	17.1516i	0.408719	−	0.707922i	0.994747	+	0.102369i	$0.0326422\pi$
$588$		0			0
$589$	4.70501	+	8.14931i	0.193866	+	0.335786i
$590$	−13.6578	+	7.88534i	−0.562283	+	0.324634i
$591$	17.7767	−	41.5425i	0.731238	−	1.70883i
$592$	1.07786	−	1.86690i	0.0442996	−	0.0767292i
$593$	−0.869700			−0.0357143			−0.0178572	−	0.999841i	$-0.505684\pi$
$593$	−0.869700			−0.0357143			−0.0178572	+	0.999841i	$0.505684\pi$
$594$	11.3020	−	13.7101i	0.463726	−	0.562531i
$595$		0			0
$596$	5.63517	+	3.25347i	0.230826	+	0.133267i
$597$	−10.5049	+	24.5490i	−0.429938	+	1.00472i
$598$	44.2020	−	25.5201i	1.80756	−	1.04359i
$599$	−2.33277	+	1.34682i	−0.0953143	+	0.0550297i	−0.546899	−	0.837198i	$-0.684192\pi$
$599$	−2.33277	+	1.34682i	−0.0953143	+	0.0550297i	0.451585	+	0.892228i	$0.350859\pi$
$600$	3.06884	+	4.09727i	0.125285	+	0.167270i
$601$	0.115325	+	0.0665827i	0.00470419	+	0.00271596i	0.502350	−	0.864664i	$-0.332469\pi$
$601$	0.115325	+	0.0665827i	0.00470419	+	0.00271596i	−0.497646	+	0.867380i	$0.665802\pi$
$602$		0			0
$603$	3.58880	−	12.2459i	0.146147	−	0.498693i
$604$	−5.75901			−0.234331
$605$	−0.495165	+	0.857650i	−0.0201313	+	0.0348684i
$606$	−13.8420	+	1.65867i	−0.562294	+	0.0673790i
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.560594	−	0.828091i	$-0.310573\pi$
$607$	38.3860	−	22.1622i	1.55804	−	0.899534i	0.997445	−	0.0714432i	$-0.0227605\pi$
$608$	−1.08353	−	1.87673i	−0.0439431	−	0.0761117i
$609$		0			0
$610$	−8.20716	+	14.2152i	−0.332298	+	0.575557i
$611$			34.9702i			1.41474i
$612$	−1.92702	+	6.57550i	−0.0778951	+	0.265799i
$613$	−6.59802			−0.266492			−0.133246	−	0.991083i	$-0.542540\pi$
$613$	−6.59802			−0.266492			−0.133246	+	0.991083i	$0.542540\pi$
$614$	−0.545593	+	0.944994i	−0.0220183	+	0.0381369i
$615$	0.801527	−	0.600342i	0.0323207	−	0.0242081i
$616$		0			0
$617$	−7.99450	+	4.61563i	−0.321846	+	0.185818i	−0.652215	−	0.758034i	$-0.726160\pi$
$617$	−7.99450	+	4.61563i	−0.321846	+	0.185818i	0.330369	+	0.943852i	$0.392827\pi$
$618$	4.48082	+	1.91742i	0.180245	+	0.0771299i
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	0.609469	−	0.792810i	$-0.291383\pi$
$619$	5.66289	+	3.26947i	0.227611	+	0.131411i	−0.381859	+	0.924221i	$0.624716\pi$
$620$		−	6.20881i		−	0.249352i
$621$	−32.2925	−	26.6205i	−1.29585	−	1.06824i
$622$			15.2220i			0.610347i
$623$		0			0
$624$	−4.31818	+	10.0912i	−0.172866	+	0.403970i
$625$	0.743610	+	1.28797i	0.0297444	+	0.0515188i
$626$	−5.78518	−	10.0202i	−0.231222	−	0.400489i
$627$	10.2728	−	7.69428i	0.410255	−	0.307280i
$628$	6.89669	+	3.98180i	0.275208	+	0.158891i
$629$	−4.92368			−0.196320
$630$		0			0
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$	12.6111	+	7.28100i	0.501641	+	0.289623i
$633$	−1.82362	−	15.2186i	−0.0724825	−	0.604883i
$634$	8.58020	+	14.8613i	0.340763	+	0.590219i
$635$	4.13064	+	7.15449i	0.163920	+	0.283917i
$636$	−17.0046	+	2.03764i	−0.674274	+	0.0807976i
$637$		0			0
$638$		−	1.18010i		−	0.0467207i
$639$	7.71246	−	7.36149i	0.305100	−	0.291216i
$640$			1.42985i			0.0565198i
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	0.737398	−	0.675459i	$-0.236054\pi$
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	−0.216265	+	0.976335i	$0.569388\pi$
$642$	21.9336	−	16.4282i	0.865648	−	0.648368i
$643$	−16.5813	+	9.57324i	−0.653904	+	0.377532i	−0.789950	−	0.613171i	$-0.789894\pi$
$643$	−16.5813	+	9.57324i	−0.653904	+	0.377532i	0.136046	+	0.990702i	$0.456560\pi$
$644$		0			0
$645$	−13.2461	−	5.66821i	−0.521563	−	0.223185i
$646$	−2.47481	+	4.28649i	−0.0973700	+	0.168650i
$647$	−1.58798			−0.0624300			−0.0312150	−	0.999513i	$-0.509938\pi$
$647$	−1.58798			−0.0624300			−0.0312150	+	0.999513i	$0.509938\pi$
$648$	8.99025	+	0.418868i	0.353170	+	0.0164547i
$649$			37.7151i			1.48045i
$650$	9.36481	−	16.2203i	0.367318	−	0.636213i
$651$		0			0
$652$	−5.69256	−	9.85980i	−0.222938	−	0.386140i
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	−0.163695	−	0.986511i	$-0.552341\pi$
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	0.772496	+	0.635019i	$0.219008\pi$
$654$	−10.6051	−	14.1590i	−0.414692	−	0.553662i
$655$	−3.18619	+	5.51863i	−0.124495	+	0.215631i
$656$	−0.404360			−0.0157876
$657$	−0.503818	+	0.480891i	−0.0196558	+	0.0187613i
$658$		0			0
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	0.683574	−	0.729881i	$-0.260424\pi$
$659$	10.0955	+	5.82866i	0.393266	+	0.227052i	−0.290308	+	0.956933i	$0.593758\pi$
$660$	−8.40836	+	1.00756i	−0.327295	+	0.0392194i
$661$	−15.7786	+	9.10975i	−0.613715	+	0.354328i	−0.774418	−	0.632674i	$-0.781957\pi$
$661$	−15.7786	+	9.10975i	−0.613715	+	0.354328i	0.160703	+	0.987003i	$0.448624\pi$
$662$	−22.9437	+	13.2466i	−0.891732	+	0.514842i
$663$	24.8919	−	2.98277i	0.966721	−	0.115841i
$664$	−1.40577	−	0.811624i	−0.0545546	−	0.0314971i
$665$		0			0
$666$	1.52796	+	6.28404i	0.0592073	+	0.243502i
$667$	−2.77960			−0.107626
$668$	5.66418	−	9.81065i	0.219154	−	0.379585i
$669$	8.26046	+	11.0287i	0.319368	+	0.426394i
$670$	−5.26725	+	3.04105i	−0.203491	+	0.117486i
$671$	19.6272	+	33.9953i	0.757699	+	1.31237i
$672$		0			0
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	−0.815807	−	0.578324i	$-0.803707\pi$
$673$	2.41106	−	4.17608i	0.0929395	−	0.160976i	0.908747	+	0.417348i	$0.137040\pi$
$674$		−	8.12902i		−	0.313118i
$675$	−15.1467	−	2.53487i	−0.582998	−	0.0975674i
$676$	27.1594			1.04459
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	−0.998014	−	0.0629856i	$-0.979938\pi$
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	0.553554	+	0.832813i	$0.313271\pi$
$678$	13.4008	+	5.73442i	0.514654	+	0.220229i
$679$		0			0
$680$	2.82827	−	1.63290i	0.108459	−	0.0626189i
$681$	−12.8090	+	9.59394i	−0.490844	+	0.367641i
$682$	−12.8589	−	7.42410i	−0.492393	−	0.284283i
$683$			7.85243i			0.300465i	0.988651	+	0.150233i	$0.0480022\pi$
$683$			7.85243i			0.300465i	−0.988651	+	0.150233i	$0.951998\pi$
$684$	6.23881	+	1.82835i	0.238547	+	0.0699087i
$685$		−	13.8076i		−	0.527562i
$686$		0			0
$687$	−14.5225	+	1.74021i	−0.554067	+	0.0663933i
$688$	2.90883	+	5.03824i	0.110898	+	0.192081i
$689$	31.3303	+	54.2656i	1.19359	+	2.06736i
$690$	2.37320	+	19.8049i	0.0903463	+	0.753960i
$691$	−14.8676	−	8.58379i	−0.565589	−	0.326543i	0.189797	−	0.981823i	$-0.439217\pi$
$691$	−14.8676	−	8.58379i	−0.565589	−	0.326543i	−0.755386	+	0.655281i	$0.772550\pi$
$692$	21.6914			0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$	22.9748	+	13.2645i	0.871485	+	0.503152i
$696$	0.478436	−	0.358347i	0.0181351	−	0.0135831i
$697$	0.461782	+	0.799830i	0.0174912	+	0.0302957i
$698$	−5.26504	−	9.11932i	−0.199285	−	0.345171i
$699$	11.3441	−	26.5100i	0.429071	−	1.00270i
$700$		0			0
$701$		−	34.9404i		−	1.31968i	−0.751406	−	0.659840i	$-0.770624\pi$
$701$		−	34.9404i		−	1.31968i	0.751406	−	0.659840i	$-0.229376\pi$
$702$	−11.5315	−	30.8436i	−0.435230	−	1.16412i
$703$			4.67157i			0.176192i
$704$	2.96133	+	1.70972i	0.111609	+	0.0644376i
$705$	−12.5644	−	5.37653i	−0.473204	−	0.202492i
$706$	−11.1230	+	6.42186i	−0.418619	+	0.241690i
$707$		0			0
$708$	−15.2904	+	11.4525i	−0.574649	+	0.430410i
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	−0.541864	−	0.840466i	$-0.682281\pi$
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	0.998797	+	0.0490345i	$0.0156144\pi$
$710$	−5.08158			−0.190708
$711$	−42.4492	+	10.3215i	−1.59197	+	0.387086i
$712$		−	4.05949i		−	0.152136i
$713$	−17.4866	+	30.2877i	−0.654879	+	1.13428i
$714$		0			0
$715$	15.4921	+	26.8331i	0.579372	+	1.00350i
$716$	−18.0057	+	10.3956i	−0.672904	+	0.388501i
$717$	46.9293	−	5.62349i	1.75261	−	0.210013i
$718$	14.8311	−	25.6881i	0.553490	−	0.958673i
$719$	−17.5377			−0.654047			−0.327024	−	0.945016i	$-0.606046\pi$
$719$	−17.5377			−0.654047			−0.327024	+	0.945016i	$0.606046\pi$
$720$	−2.96175	−	3.10295i	−0.110378	−	0.115640i
$721$		0			0
$722$	−12.3875	−	7.15191i	−0.461014	−	0.266167i
$723$	−26.2597	−	35.0598i	−0.976608	−	1.30389i
$724$	−18.6456	+	10.7650i	−0.692958	+	0.400079i
$725$	−0.883344	+	0.509999i	−0.0328066	+	0.0189409i
$726$	−0.471950	+	1.10290i	−0.0175157	+	0.0409325i
$727$	−33.8627	−	19.5507i	−1.25590	−	0.725094i	−0.283625	−	0.958935i	$-0.591537\pi$
$727$	−33.8627	−	19.5507i	−1.25590	−	0.725094i	−0.972275	+	0.233841i	$0.924870\pi$
$728$		0			0
$729$	−20.3776	+	17.7131i	−0.754725	+	0.656041i
$730$	0.331955			0.0122862
$731$	6.64381	−	11.5074i	0.245730	−	0.425617i
$732$	−7.82238	+	18.2802i	−0.289124	+	0.675654i
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	−0.825719	−	0.564082i	$-0.809230\pi$
$733$	−20.3073	+	11.7245i	−0.750069	+	0.433053i	0.0756499	+	0.997134i	$0.475897\pi$
$734$	11.9989	+	20.7828i	0.442889	+	0.767107i
$735$		0			0
$736$	4.02706	−	6.97507i	0.148439	−	0.257104i
$737$			14.5451i			0.535777i
$738$	0.877510	−	0.837578i	0.0323016	−	0.0308317i
$739$	−26.7323			−0.983364			−0.491682	−	0.870775i	$-0.663618\pi$
$739$	−26.7323			−0.983364			−0.491682	+	0.870775i	$0.663618\pi$
$740$	1.54117	−	2.66939i	0.0566547	−	0.0981288i
$741$	−2.83004	−	23.6173i	−0.103964	−	0.867605i
$742$		0			0
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	−0.689458	−	0.724326i	$-0.742151\pi$
$743$	−11.0914	+	6.40360i	−0.406903	+	0.234925i	0.282555	+	0.959251i	$0.408818\pi$
$744$	−0.894838	−	7.46763i	−0.0328063	−	0.273776i
$745$	8.05745	+	4.65197i	0.295202	+	0.170435i
$746$		−	11.8390i		−	0.433455i
$747$	4.73187	−	1.15055i	0.173130	−	0.0420965i
$748$		−	7.81007i		−	0.285564i
$749$		0			0
$750$	11.8113	+	15.7695i	0.431289	+	0.575822i
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	0.944243	−	0.329249i	$-0.106796\pi$
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	−0.757260	+	0.653114i	$0.773462\pi$
$752$	2.75915	+	4.77898i	0.100616	+	0.174272i
$753$	13.0470	+	5.58302i	0.475459	+	0.203457i
$754$	−1.89404	−	1.09352i	−0.0689768	−	0.0398238i
$755$	−8.23452			−0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$	11.3778	+	6.56897i	0.413260	+	0.238596i
$759$	43.8552	+	18.7664i	1.59184	+	0.681176i
$760$	−1.54929	−	2.68345i	−0.0561987	−	0.0973390i
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	0.679651	−	0.733536i	$-0.262131\pi$
$761$	−8.14993	−	14.1161i	−0.295435	−	0.511708i	−0.975086	+	0.221827i	$0.928798\pi$
$762$	5.99925	+	8.00971i	0.217330	+	0.290161i
$763$		0			0
$764$			7.36938i			0.266615i
$765$	−2.75535	+	9.40198i	−0.0996198	+	0.339929i
$766$			17.5521i			0.634181i
$767$	60.5319	+	34.9481i	2.18568	+	1.26190i
$768$	0.206076	+	1.71975i	0.00743611	+	0.0620561i
$769$	41.4043	−	23.9048i	1.49308	−	0.862029i	0.493110	−	0.869967i	$-0.335860\pi$
$769$	41.4043	−	23.9048i	1.49308	−	0.862029i	0.999968	+	0.00793771i	$0.00252668\pi$
$770$		0			0
$771$	1.36720	+	11.4096i	0.0492384	+	0.410906i
$772$	−1.41279	+	2.44703i	−0.0508476	+	0.0880706i
$773$	12.5088			0.449911			0.224956	−	0.974369i	$-0.427776\pi$
$773$	12.5088			0.449911			0.224956	+	0.974369i	$0.427776\pi$
$774$	−16.7486	−	4.90834i	−0.602015	−	0.176427i
$775$			12.8337i			0.461001i
$776$	−5.30423	+	9.18719i	−0.190411	+	0.329801i
$777$		0			0
$778$	10.9205	+	18.9148i	0.391518	+	0.678130i
$779$	0.758876	−	0.438137i	0.0271896	−	0.0156979i
$780$	−6.17435	+	14.4289i	−0.221077	+	0.516636i
$781$	−6.07623	+	10.5243i	−0.217425	+	0.376590i
$782$	−18.3957			−0.657830
$783$	−0.295996	+	1.76867i	−0.0105780	+	0.0632073i
$784$		0			0
$785$	9.86123	+	5.69338i	0.351962	+	0.203206i
$786$	−3.03681	+	7.09672i	−0.108319	+	0.253132i
$787$	0.226048	−	0.130509i	0.00805773	−	0.00465213i	−0.495966	−	0.868342i	$-0.665186\pi$
$787$	0.226048	−	0.130509i	0.00805773	−	0.00465213i	0.504023	+	0.863690i	$0.331853\pi$
$788$	−22.5931	+	13.0441i	−0.804846	+	0.464678i
$789$	6.27770	+	8.38148i	0.223492	+	0.298388i
$790$	18.0319	+	10.4107i	0.641548	+	0.370398i
$791$		0			0
$792$	−9.96791	+	2.42369i	−0.354194	+	0.0861221i
$793$	72.7489			2.58339
$794$	19.4935	−	33.7636i	0.691797	−	1.19823i
$795$	−24.3140	+	2.91352i	−0.862328	+	0.103332i
$796$	13.3511	−	7.70826i	0.473217	−	0.273212i
$797$	1.85220	+	3.20810i	0.0656083	+	0.113637i	0.896964	−	0.442104i	$-0.145768\pi$
$797$	1.85220	+	3.20810i	0.0656083	+	0.113637i	−0.831355	+	0.555741i	$0.812435\pi$
$798$		0			0
$799$	6.30194	−	10.9153i	0.222946	−	0.386155i
$800$		−	2.95553i		−	0.104494i
$801$	8.40869	+	8.80958i	0.297106	+	0.311271i
$802$	−23.1979			−0.819145
$803$	0.396931	−	0.687504i	0.0140074	−	0.0242615i
$804$	−5.89688	+	4.41674i	−0.207967	+	0.155767i
$805$		0			0
$806$	−23.8310	+	13.7588i	−0.839411	+	0.484634i
$807$	10.8623	+	4.64814i	0.382370	+	0.163622i
$808$	6.97052	+	4.02443i	0.245222	+	0.141579i
$809$		−	6.86211i		−	0.241259i	−0.992698	−	0.120629i	$-0.961509\pi$
$809$		−	6.86211i		−	0.241259i	0.992698	−	0.120629i	$-0.0384913\pi$
$810$	12.8547	+	0.598918i	0.451668	+	0.0210438i
$811$		−	23.1945i		−	0.814470i	−0.913323	−	0.407235i	$-0.866493\pi$
$811$		−	23.1945i		−	0.814470i	0.913323	−	0.407235i	$-0.133507\pi$
$812$		0			0
$813$	−3.46029	+	8.08635i	−0.121358	+	0.283601i
$814$	−3.68567	−	6.38377i	−0.129183	−	0.223751i
$815$	−8.13951	−	14.0980i	−0.285114	−	0.493833i
$816$	3.16635	−	2.37159i	0.110844	−	0.0830221i
$817$	−10.9182	−	6.30363i	−0.381980	−	0.220536i
$818$	24.6187			0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$	3.28550	+	1.89688i	0.114665	+	0.0662017i	0.556236	−	0.831025i	$-0.312245\pi$
$821$	3.28550	+	1.89688i	0.114665	+	0.0662017i	−0.441571	+	0.897226i	$0.645579\pi$
$822$	−1.99001	−	16.6071i	−0.0694094	−	0.579238i
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	0.966196	−	0.257810i	$-0.0830007\pi$
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	−0.706368	+	0.707845i	$0.749667\pi$
$824$	−1.40695	−	2.43692i	−0.0490136	−	0.0848940i
$825$	17.3802	−	2.08265i	0.605102	−	0.0725087i
$826$		0			0
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$	5.70872	+	23.4783i	0.198392	+	0.815926i
$829$		−	14.1343i		−	0.490903i	−0.969409	−	0.245452i	$-0.921064\pi$
$829$		−	14.1343i		−	0.490903i	0.969409	−	0.245452i	$-0.0789363\pi$
$830$	−2.01005	−	1.16050i	−0.0697697	−	0.0402816i
$831$	−2.74369	+	2.05502i	−0.0951775	+	0.0712877i
$832$	5.48813	−	3.16857i	0.190267	−	0.109851i
$833$		0			0
$834$	29.5446	+	12.6426i	1.02305	+	0.437779i
$835$	8.09893	−	14.0278i	0.280275	−	0.485451i
$836$	−7.41017			−0.256286
$837$	17.4101	+	14.3521i	0.601782	+	0.496082i
$838$		−	17.0799i		−	0.590016i
$839$	8.92488	−	15.4583i	0.308121	−	0.533681i	−0.669830	−	0.742514i	$-0.733633\pi$
$839$	8.92488	−	15.4583i	0.308121	−	0.533681i	0.977951	+	0.208833i	$0.0669665\pi$
$840$		0			0
$841$	−14.4404	−	25.0116i	−0.497946	−	0.862469i
$842$	12.7419	−	7.35652i	0.439114	−	0.253522i
$843$	18.3087	+	24.4442i	0.630584	+	0.841904i
$844$	−4.42465	+	7.66371i	−0.152303	+	0.263796i
$845$	38.8339			1.33593
$846$	−15.8867	−	4.65577i	−0.546197	−	0.160069i
$847$		0			0
$848$	8.56310	+	4.94391i	0.294058	+	0.169775i
$849$	−8.86332	+	1.06208i	−0.304189	+	0.0364506i
$850$	−5.84608	+	3.37524i	−0.200519	+	0.115770i
$851$	−15.0362	+	8.68118i	−0.515436	+	0.297587i
$852$	−6.11186	+	0.732377i	−0.209389	+	0.0250908i
$853$	35.2392	+	20.3454i	1.20657	+	0.696612i	0.962008	−	0.273022i	$-0.0880233\pi$
$853$	35.2392	+	20.3454i	1.20657	+	0.696612i	0.244559	+	0.969634i	$0.421357\pi$
$854$		0			0
$855$	8.92057	+	2.61427i	0.305077	+	0.0894060i
$856$	−15.8216			−0.540770
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	−0.815645	−	0.578553i	$-0.803618\pi$
$857$	2.72896	−	4.72669i	0.0932194	−	0.161461i	0.908864	+	0.417092i	$0.136951\pi$
$858$	22.5004	+	30.0406i	0.768150	+	1.02557i
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.984779	−	0.173810i	$-0.944392\pi$
$859$	−38.8822	+	22.4487i	−1.32664	+	0.765938i	−0.341865	+	0.939749i	$0.611059\pi$
$860$	4.15919	+	7.20393i	0.141827	+	0.245652i
$861$		0			0
$862$	4.80521	−	8.32286i	0.163666	−	0.283478i
$863$			22.7117i			0.773117i	0.922265	+	0.386558i	$0.126336\pi$
$863$			22.7117i			0.773117i	−0.922265	+	0.386558i	$0.873664\pi$
$864$	−4.00944	−	3.30521i	−0.136404	−	0.112445i
$865$	31.0155			1.05456
$866$	4.52157	−	7.83159i	0.153649	−	0.266128i
$867$	18.7635	+	8.02921i	0.637241	+	0.272686i
$868$		0			0
$869$	43.1229	−	24.8970i	1.46284	−	0.844573i
$870$	0.684092	−	0.512383i	0.0231929	−	0.0173714i
$871$	23.3446	+	13.4780i	0.791002	+	0.456685i
$872$			10.2135i			0.345873i
$873$	−7.51923	−	30.9244i	−0.254487	−	1.04663i
$874$			17.4538i			0.590384i
$875$		0			0
$876$	0.399258	−	0.0478427i	0.0134897	−	0.00161645i
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	0.999853	+	0.0171413i	$0.00545653\pi$
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	−0.485082	+	0.874469i	$0.661210\pi$
$878$	−0.456897	−	0.791370i	−0.0154195	−	0.0267074i
$879$	−0.425539	−	3.55122i	−0.0143531	−	0.119780i
$880$	4.23425	+	2.44465i	0.142737	+	0.0824091i
$881$	29.3810			0.989871			0.494935	−	0.868930i	$-0.335192\pi$
$881$	29.3810			0.989871			0.494935	+	0.868930i	$0.335192\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$	−12.5350	−	7.23707i	−0.421597	−	0.243409i
$885$	−21.8630	+	16.3753i	−0.734917	+	0.550451i
$886$	−14.6808	−	25.4279i	−0.493212	−	0.854268i
$887$	−16.3537	−	28.3254i	−0.549103	−	0.951074i	−0.998336	−	0.0576593i	$-0.981636\pi$
$887$	−16.3537	−	28.3254i	−0.549103	−	0.951074i	0.449234	−	0.893414i	$-0.351697\pi$
$888$	1.46892	−	3.43272i	0.0492937	−	0.115195i
$889$		0			0
$890$		−	5.80446i		−	0.194566i
$891$	16.6112	−	25.9069i	0.556497	−	0.867914i
$892$		−	7.95544i		−	0.266368i
$893$	−10.3564	−	5.97926i	−0.346563	−	0.200088i
$894$	10.3615	+	4.43387i	0.346542	+	0.148291i
$895$	−25.7454	+	14.8641i	−0.860575	+	0.496853i
$896$		0			0
$897$	70.7573	−	52.9970i	2.36252	−	1.76952i
$898$	1.68368	−	2.91622i	0.0561851	−	0.0973154i
$899$	1.49859			0.0499807
$900$	6.12199	+	6.41386i	0.204066	+	0.213795i
$901$		−	22.5839i		−	0.752380i
$902$	−0.691343	+	1.19744i	−0.0230192	+	0.0398704i
$903$		0			0
$904$	−4.20778	−	7.28808i	−0.139949	−	0.242398i
$905$	−26.6604	+	15.3924i	−0.886222	+	0.511661i
$906$	−9.90404	+	1.18679i	−0.329040	+	0.0394285i
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.178123	+	0.984008i	$0.557002\pi$
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.763115	+	0.646263i	$0.776331\pi$
$908$	9.23968			0.306630
$909$	−23.4630	+	5.70500i	−0.778218	+	0.189223i
$910$		0			0
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	0.510265	−	0.860017i	$-0.329547\pi$
$911$	0.621795	+	0.358994i	0.0206010	+	0.0118940i	−0.489664	+	0.871911i	$0.662881\pi$
$912$	−2.25015	−	3.00422i	−0.0745100	−	0.0994797i
$913$	−4.80697	+	2.77530i	−0.159087	+	0.0918492i
$914$	−13.0890	+	7.55693i	−0.432945	+	0.249961i
$915$	−11.1848	+	26.1379i	−0.369759	+	0.864092i
$916$	7.31319	+	4.22227i	0.241635	+	0.139508i
$917$		0			0
$918$	−1.95894	+	11.7053i	−0.0646546	+	0.386333i
$919$	−37.9441			−1.25166			−0.625829	−	0.779960i	$-0.715239\pi$
$919$	−37.9441			−1.25166			−0.625829	+	0.779960i	$0.715239\pi$
$920$	5.75809	−	9.97330i	0.189839	−	0.328810i
$921$	−0.743542	+	1.73758i	−0.0245005	+	0.0572554i
$922$	−8.99706	+	5.19445i	−0.296302	+	0.171070i
$923$	11.2609	+	19.5044i	0.370656	+	0.641996i
$924$		0			0
$925$	−3.18563	+	5.51768i	−0.104743	+	0.181420i
$926$			5.31444i			0.174643i
$927$	8.10102	+	2.37409i	0.266072	+	0.0779753i
$928$	−0.345115			−0.0113290
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	0.264057	+	0.964507i	$0.414939\pi$
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	−0.967316	+	0.253574i	$0.918394\pi$
$930$	−1.27948	−	10.6776i	−0.0419559	−	0.350132i
$931$		0			0
$932$	−14.4176	+	8.32399i	−0.472263	+	0.272661i
$933$	3.13688	+	26.1780i	0.102697	+	0.857030i
$934$	16.8874	+	9.74994i	0.552572	+	0.319028i
$935$		−	11.1672i		−	0.365208i
$936$	−5.34664	+	18.2441i	−0.174760	+	0.596328i
$937$			8.64637i			0.282464i	0.989976	+	0.141232i	$0.0451064\pi$
$937$			8.64637i			0.282464i	−0.989976	+	0.141232i	$0.954894\pi$
$938$		0			0
$939$	−12.0140	−	16.0401i	−0.392061	−	0.523448i
$940$	3.94517	+	6.83323i	0.128677	+	0.222875i
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	0.771980	−	0.635646i	$-0.219266\pi$
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	−0.936476	+	0.350731i	$0.885933\pi$
$942$	12.6811	+	5.42646i	0.413173	+	0.176804i
$943$	2.82044	+	1.62838i	0.0918460	+	0.0530273i
$944$	11.0296			0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$	−50.4627	−	29.1346i	−1.63982	−	0.946749i	−0.980895	−	0.194537i	$-0.937680\pi$
$947$	−50.4627	−	29.1346i	−1.63982	−	0.946749i	−0.658922	−	0.752212i	$-0.728987\pi$
$948$	23.1883	+	9.92265i	0.753121	+	0.322273i
$949$	−0.735619	−	1.27413i	−0.0238792	−	0.0413600i
$950$	3.20241	+	5.54674i	0.103900	+	0.179960i
$951$	17.8183	+	23.7896i	0.577799	+	0.771430i
$952$		0			0
$953$			46.9356i			1.52039i	0.649694	+	0.760196i	$0.274897\pi$
$953$			46.9356i			1.52039i	−0.649694	+	0.760196i	$0.725103\pi$
$954$	−28.8236	+	7.00845i	−0.933200	+	0.226907i
$955$			10.5371i			0.340973i
$956$	−23.6325	−	13.6442i	−0.764330	−	0.441286i
$957$	−0.243190	−	2.02948i	−0.00786123	−	0.0656037i
$958$	24.0776	−	13.9012i	0.777912	−	0.449128i
$959$		0			0
$960$	0.294657	+	2.45898i	0.00951002	+	0.0793633i
$961$	−6.07230	+	10.5175i	−0.195881	+	0.339275i
$962$	−13.6611			−0.440451
$963$	34.3347	−	32.7723i	1.10642	−	1.05607i
$964$			25.2900i			0.814537i
$965$	−2.02008	+	3.49889i	−0.0650288	+	0.112633i
$966$		0			0
$967$	6.43145	+	11.1396i	0.206822	+	0.358226i	0.950712	−	0.310077i	$-0.100355\pi$
$967$	6.43145	+	11.1396i	0.206822	+	0.358226i	−0.743890	+	0.668302i	$0.767021\pi$
$968$	0.599818	−	0.346305i	0.0192789	−	0.0111307i
$969$	−3.37270	+	7.88168i	−0.108347	+	0.253196i
$970$	−7.58425	+	13.1363i	−0.243516	+	0.421782i
$971$	−34.7484			−1.11513			−0.557565	−	0.830133i	$-0.688264\pi$
$971$	−34.7484			−1.11513			−0.557565	+	0.830133i	$0.688264\pi$
$972$	15.5473	−	1.13232i	0.498679	−	0.0363193i
$973$		0			0
$974$	6.47506	+	3.73838i	0.207474	+	0.119785i
$975$	12.7625	−	29.8247i	0.408727	−	0.955156i
$976$	9.94175	−	5.73987i	0.318228	−	0.183729i
$977$	17.6381	−	10.1834i	0.564293	−	0.325795i	−0.190574	−	0.981673i	$-0.561035\pi$
$977$	17.6381	−	10.1834i	0.564293	−	0.325795i	0.754867	+	0.655878i	$0.227701\pi$
$978$	−11.8216	−	15.7833i	−0.378014	−	0.504693i
$979$	−12.0215	−	6.94060i	−0.384208	−	0.221822i
$980$		0			0
$981$	−21.1559	−	22.1645i	−0.675456	−	0.707659i
$982$	−22.1086			−0.705513
$983$	−14.6682	+	25.4061i	−0.467843	+	0.810328i	−0.999325	−	0.0367416i	$-0.988302\pi$
$983$	−14.6682	+	25.4061i	−0.467843	+	0.810328i	0.531482	+	0.847070i	$0.321635\pi$
$984$	−0.695397	+	0.0833287i	−0.0221684	+	0.00265642i
$985$	−32.3048	+	18.6512i	−1.02932	+	0.594276i
$986$	0.394124	+	0.682643i	0.0125515	+	0.0217398i
$987$		0			0
$988$	−6.86651	+	11.8931i	−0.218453	+	0.378371i
$989$		−	46.8561i		−	1.48994i
$990$	−14.2526	+	3.46551i	−0.452978	+	0.110141i
$991$	29.6227			0.940996			0.470498	−	0.882401i	$-0.344074\pi$
$991$	29.6227			0.940996			0.470498	+	0.882401i	$0.344074\pi$
$992$	−2.17114	+	3.76052i	−0.0689338	+	0.119397i
$993$	−36.7276	+	27.5089i	−1.16551	+	0.872967i
$994$		0			0
$995$	19.0901	−	11.0217i	0.605196	−	0.349410i
$996$	−2.58483	−	1.10609i	−0.0819035	−	0.0350479i
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	0.0813562	−	0.996685i	$-0.474075\pi$
$997$	−23.4011	−	13.5106i	−0.741120	−	0.427886i	−0.822477	+	0.568799i	$0.807408\pi$
$998$			32.9042i			1.04157i
$999$	3.92270	+	10.4921i	0.124109	+	0.331955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.b.587.1		16
3.2	odd	2		2646.2.m.b.1763.6		16
7.2	even	3		126.2.l.a.101.7	yes	16
7.3	odd	6		126.2.t.a.47.6	yes	16
7.4	even	3		882.2.t.a.803.7		16
7.5	odd	6		882.2.l.b.227.6		16
7.6	odd	2		882.2.m.a.587.4		16
9.4	even	3		2646.2.m.a.881.7		16
9.5	odd	6		882.2.m.a.293.4		16
21.2	odd	6		378.2.l.a.143.2		16
21.5	even	6		2646.2.l.a.521.3		16
21.11	odd	6		2646.2.t.b.1979.3		16
21.17	even	6		378.2.t.a.89.2		16
21.20	even	2		2646.2.m.a.1763.7		16
28.3	even	6		1008.2.df.c.929.6		16
28.23	odd	6		1008.2.ca.c.353.3		16
63.2	odd	6		1134.2.k.b.647.2		16
63.4	even	3		2646.2.l.a.1097.7		16
63.5	even	6		882.2.t.a.815.7		16
63.13	odd	6		2646.2.m.b.881.6		16
63.16	even	3		1134.2.k.a.647.7		16
63.23	odd	6		126.2.t.a.59.6	yes	16
63.31	odd	6		378.2.l.a.341.6		16
63.32	odd	6		882.2.l.b.509.2		16
63.38	even	6		1134.2.k.a.971.7		16
63.40	odd	6		2646.2.t.b.2285.3		16
63.41	even	6	inner	882.2.m.b.293.1		16
63.52	odd	6		1134.2.k.b.971.2		16
63.58	even	3		378.2.t.a.17.2		16
63.59	even	6		126.2.l.a.5.3	✓	16
84.23	even	6		3024.2.ca.c.2033.3		16
84.59	odd	6		3024.2.df.c.1601.3		16
252.23	even	6		1008.2.df.c.689.6		16
252.31	even	6		3024.2.ca.c.2609.3		16
252.59	odd	6		1008.2.ca.c.257.3		16
252.247	odd	6		3024.2.df.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	63.59	even	6
126.2.l.a.101.7	yes	16	7.2	even	3
126.2.t.a.47.6	yes	16	7.3	odd	6
126.2.t.a.59.6	yes	16	63.23	odd	6
378.2.l.a.143.2		16	21.2	odd	6
378.2.l.a.341.6		16	63.31	odd	6
378.2.t.a.17.2		16	63.58	even	3
378.2.t.a.89.2		16	21.17	even	6
882.2.l.b.227.6		16	7.5	odd	6
882.2.l.b.509.2		16	63.32	odd	6
882.2.m.a.293.4		16	9.5	odd	6
882.2.m.a.587.4		16	7.6	odd	2
882.2.m.b.293.1		16	63.41	even	6	inner
882.2.m.b.587.1		16	1.1	even	1	trivial
882.2.t.a.803.7		16	7.4	even	3
882.2.t.a.815.7		16	63.5	even	6
1008.2.ca.c.257.3		16	252.59	odd	6
1008.2.ca.c.353.3		16	28.23	odd	6
1008.2.df.c.689.6		16	252.23	even	6
1008.2.df.c.929.6		16	28.3	even	6
1134.2.k.a.647.7		16	63.16	even	3
1134.2.k.a.971.7		16	63.38	even	6
1134.2.k.b.647.2		16	63.2	odd	6
1134.2.k.b.971.2		16	63.52	odd	6
2646.2.l.a.521.3		16	21.5	even	6
2646.2.l.a.1097.7		16	63.4	even	3
2646.2.m.a.881.7		16	9.4	even	3
2646.2.m.a.1763.7		16	21.20	even	2
2646.2.m.b.881.6		16	63.13	odd	6
2646.2.m.b.1763.6		16	3.2	odd	2
2646.2.t.b.1979.3		16	21.11	odd	6
2646.2.t.b.2285.3		16	63.40	odd	6
3024.2.ca.c.2033.3		16	84.23	even	6
3024.2.ca.c.2609.3		16	252.31	even	6
3024.2.df.c.17.3		16	252.247	odd	6
3024.2.df.c.1601.3		16	84.59	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.59238 - 0.681407i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.714925 + 1.23829i) q^{5} +(1.03834 + 1.38631i) q^{6} -1.00000i q^{8} +(2.07137 + 2.17012i) q^{9} -1.42985i q^{10} +(-2.96133 - 1.70972i) q^{11} +(-0.206076 - 1.71975i) q^{12} +(-5.48813 + 3.16857i) q^{13} +(-0.294657 - 2.45898i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.28402 q^{17} +(-0.708796 - 2.91507i) q^{18} -2.16707i q^{19} +(-0.714925 + 1.23829i) q^{20} +(1.70972 + 2.96133i) q^{22} +(6.97507 - 4.02706i) q^{23} +(-0.681407 + 1.59238i) q^{24} +(1.47776 - 2.55956i) q^{25} +6.33715 q^{26} +(-1.81967 - 4.86711i) q^{27} +(-0.298879 - 0.172558i) q^{29} +(-0.974311 + 2.27687i) q^{30} +(-3.76052 + 2.17114i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.55055 + 4.74040i) q^{33} +(-1.97802 - 1.14201i) q^{34} +(-0.843698 + 2.87892i) q^{36} -2.15571 q^{37} +(-1.08353 + 1.87673i) q^{38} +(10.8983 - 1.30593i) q^{39} +(1.23829 - 0.714925i) q^{40} +(0.202180 + 0.350186i) q^{41} +(2.90883 - 5.03824i) q^{43} -3.41945i q^{44} +(-1.20636 + 4.11642i) q^{45} -8.05411 q^{46} +(2.75915 - 4.77898i) q^{47} +(1.38631 - 1.03834i) q^{48} +(-2.55956 + 1.47776i) q^{50} +(-3.63703 - 1.55635i) q^{51} +(-5.48813 - 3.16857i) q^{52} -9.88782i q^{53} +(-0.857672 + 5.12488i) q^{54} -4.88930i q^{55} +(-1.47666 + 3.45080i) q^{57} +(0.172558 + 0.298879i) q^{58} +(-5.51480 - 9.55191i) q^{59} +(1.98221 - 1.48467i) q^{60} +(-9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(-7.84721 - 4.53059i) q^{65} +(-0.704664 - 5.88058i) q^{66} +(-2.12683 - 3.68377i) q^{67} +(1.14201 + 1.97802i) q^{68} +(-13.8510 + 1.65976i) q^{69} -3.55393i q^{71} +(2.17012 - 2.07137i) q^{72} +0.232161i q^{73} +(1.86690 + 1.07786i) q^{74} +(-4.09727 + 3.06884i) q^{75} +(1.87673 - 1.08353i) q^{76} +(-10.0912 - 4.31818i) q^{78} +(-7.28100 + 12.6111i) q^{79} -1.42985 q^{80} +(-0.418868 + 8.99025i) q^{81} -0.404360i q^{82} +(0.811624 - 1.40577i) q^{83} +(1.63290 + 2.82827i) q^{85} +(-5.03824 + 2.90883i) q^{86} +(0.358347 + 0.478436i) q^{87} +(-1.70972 + 2.96133i) q^{88} +4.05949 q^{89} +(3.10295 - 2.96175i) q^{90} +(6.97507 + 4.02706i) q^{92} +(7.46763 - 0.894838i) q^{93} +(-4.77898 + 2.75915i) q^{94} +(2.68345 - 1.54929i) q^{95} +(-1.71975 + 0.206076i) q^{96} +(-9.18719 - 5.30423i) q^{97} +(-2.42369 - 9.96791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

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