LMFDB - Embedded newform 882.2.l.c.227.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			227.21
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +(-1.25487 - 0.724499i) q^{10} +(1.21051 - 0.698887i) q^{11} +(-1.45331 + 0.942282i) q^{12} +(3.03494 - 1.75222i) q^{13} +(0.129520 + 2.50640i) q^{15} +1.00000 q^{16} +(3.95277 - 6.84639i) q^{17} +(2.73885 + 1.22421i) q^{18} +(-3.61019 + 2.08434i) q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 + 1.80925i) q^{23} +(-0.942282 - 1.45331i) q^{24} +(1.45020 + 2.51182i) q^{25} +(1.75222 + 3.03494i) q^{26} +(-0.801614 - 5.13395i) q^{27} +(4.06467 + 2.34674i) q^{29} +(-2.50640 + 0.129520i) q^{30} -0.917280i q^{31} +1.00000i q^{32} +(1.10069 - 2.15634i) q^{33} +(6.84639 + 3.95277i) q^{34} +(-1.22421 + 2.73885i) q^{36} +(2.14176 + 3.70963i) q^{37} +(-2.08434 - 3.61019i) q^{38} +(2.75961 - 5.40629i) q^{39} +(1.25487 + 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +(-1.21051 + 0.698887i) q^{44} +(2.54996 + 3.52052i) q^{45} +(-1.80925 + 3.13371i) q^{46} +8.31745 q^{47} +(1.45331 - 0.942282i) q^{48} +(-2.51182 + 1.45020i) q^{50} +(-0.706641 - 13.6745i) q^{51} +(-3.03494 + 1.75222i) q^{52} +(-5.16176 - 2.98014i) q^{53} +(5.13395 - 0.801614i) q^{54} +2.02537i q^{55} +(-3.28268 + 6.43101i) q^{57} +(-2.34674 + 4.06467i) q^{58} +9.44130 q^{59} +(-0.129520 - 2.50640i) q^{60} -9.85957i q^{61} +0.917280 q^{62} -1.00000 q^{64} +5.07794i q^{65} +(2.15634 + 1.10069i) q^{66} -2.97079 q^{67} +(-3.95277 + 6.84639i) q^{68} +(6.25907 - 0.323442i) q^{69} -12.9436i q^{71} +(-2.73885 - 1.22421i) q^{72} +(-9.79071 - 5.65267i) q^{73} +(-3.70963 + 2.14176i) q^{74} +(4.47443 + 2.28395i) q^{75} +(3.61019 - 2.08434i) q^{76} +(5.40629 + 2.75961i) q^{78} +15.6342 q^{79} +(-0.724499 + 1.25487i) q^{80} +(-6.00262 - 6.70586i) q^{81} +(-0.595352 + 0.343727i) q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 - 6.01497i) q^{86} +(8.11851 - 0.419530i) q^{87} +(-0.698887 - 1.21051i) q^{88} +(-0.533417 - 0.923906i) q^{89} +(-3.52052 + 2.54996i) q^{90} +(-3.13371 - 1.80925i) q^{92} +(-0.864336 - 1.33309i) q^{93} +8.31745i q^{94} -6.04043i q^{95} +(0.942282 + 1.45331i) q^{96} +(-10.9670 - 6.33179i) q^{97} +(-0.432231 - 4.17099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.45331	−	0.942282i	0.839068	−	0.544027i
$3$	1.45331	−	0.942282i	0.839068	−	0.544027i
$4$	−1.00000			−0.500000
$5$	−0.724499	+	1.25487i	−0.324006	+	0.561195i	−0.981311	−	0.192430i	$-0.938363\pi$
$5$	−0.724499	+	1.25487i	−0.324006	+	0.561195i	0.657305	+	0.753625i	$0.271696\pi$
$6$	0.942282	+	1.45331i	0.384685	+	0.593311i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.22421	−	2.73885i	0.408070	−	0.912951i
$10$	−1.25487	−	0.724499i	−0.396825	−	0.229107i
$11$	1.21051	−	0.698887i	0.364982	−	0.210722i	−0.306282	−	0.951941i	$-0.599085\pi$
$11$	1.21051	−	0.698887i	0.364982	−	0.210722i	0.671264	+	0.741218i	$0.265752\pi$
$12$	−1.45331	+	0.942282i	−0.419534	+	0.272013i
$13$	3.03494	−	1.75222i	0.841740	−	0.485979i	−0.0161150	−	0.999870i	$-0.505130\pi$
$13$	3.03494	−	1.75222i	0.841740	−	0.485979i	0.857855	+	0.513891i	$0.171796\pi$
$14$		0			0
$15$	0.129520	+	2.50640i	0.0334418	+	0.647148i
$16$	1.00000			0.250000
$17$	3.95277	−	6.84639i	0.958687	−	1.66049i	0.232990	−	0.972479i	$-0.425149\pi$
$17$	3.95277	−	6.84639i	0.958687	−	1.66049i	0.725697	−	0.688015i	$-0.241518\pi$
$18$	2.73885	+	1.22421i	0.645554	+	0.288549i
$19$	−3.61019	+	2.08434i	−0.828235	+	0.478181i	−0.853248	−	0.521506i	$-0.825371\pi$
$19$	−3.61019	+	2.08434i	−0.828235	+	0.478181i	0.0250133	+	0.999687i	$0.492037\pi$
$20$	0.724499	−	1.25487i	0.162003	−	0.280597i
$21$		0			0
$22$	0.698887	+	1.21051i	0.149003	+	0.258081i
$23$	3.13371	+	1.80925i	0.653424	+	0.377255i	0.789767	−	0.613407i	$-0.210202\pi$
$23$	3.13371	+	1.80925i	0.653424	+	0.377255i	−0.136343	+	0.990662i	$0.543535\pi$
$24$	−0.942282	−	1.45331i	−0.192342	−	0.296655i
$25$	1.45020	+	2.51182i	0.290040	+	0.502364i
$26$	1.75222	+	3.03494i	0.343639	+	0.595200i
$27$	−0.801614	−	5.13395i	−0.154271	−	0.988029i
$28$		0			0
$29$	4.06467	+	2.34674i	0.754791	+	0.435779i	0.827422	−	0.561580i	$-0.189806\pi$
$29$	4.06467	+	2.34674i	0.754791	+	0.435779i	−0.0726316	+	0.997359i	$0.523140\pi$
$30$	−2.50640	+	0.129520i	−0.457603	+	0.0236469i
$31$		−	0.917280i		−	0.164748i	−0.996601	−	0.0823741i	$-0.973750\pi$
$31$		−	0.917280i		−	0.164748i	0.996601	−	0.0823741i	$-0.0262502\pi$
$32$			1.00000i			0.176777i
$33$	1.10069	−	2.15634i	0.191606	−	0.375370i
$34$	6.84639	+	3.95277i	1.17415	+	0.677894i
$35$		0			0
$36$	−1.22421	+	2.73885i	−0.204035	+	0.456475i
$37$	2.14176	+	3.70963i	0.352103	+	0.609860i	0.986618	−	0.163051i	$-0.0521334\pi$
$37$	2.14176	+	3.70963i	0.352103	+	0.609860i	−0.634515	+	0.772911i	$0.718800\pi$
$38$	−2.08434	−	3.61019i	−0.338125	−	0.585650i
$39$	2.75961	−	5.40629i	0.441892	−	0.865699i
$40$	1.25487	+	0.724499i	0.198412	+	0.114553i
$41$	0.343727	+	0.595352i	0.0536811	+	0.0929784i	0.891617	−	0.452790i	$-0.149571\pi$
$41$	0.343727	+	0.595352i	0.0536811	+	0.0929784i	−0.837936	+	0.545768i	$0.816238\pi$
$42$		0			0
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.113739	+	0.993511i	$0.536283\pi$
$43$	−6.01497	+	10.4182i	−0.917275	+	1.58877i	−0.803536	+	0.595256i	$0.797051\pi$
$44$	−1.21051	+	0.698887i	−0.182491	+	0.105361i
$45$	2.54996	+	3.52052i	0.380126	+	0.524808i
$46$	−1.80925	+	3.13371i	−0.266759	+	0.462041i
$47$	8.31745			1.21322			0.606612	−	0.794998i	$-0.292528\pi$
$47$	8.31745			1.21322			0.606612	+	0.794998i	$0.292528\pi$
$48$	1.45331	−	0.942282i	0.209767	−	0.136007i
$49$		0			0
$50$	−2.51182	+	1.45020i	−0.355225	+	0.205089i
$51$	−0.706641	−	13.6745i	−0.0989495	−	1.91482i
$52$	−3.03494	+	1.75222i	−0.420870	+	0.242990i
$53$	−5.16176	−	2.98014i	−0.709022	−	0.409354i	0.101677	−	0.994818i	$-0.467579\pi$
$53$	−5.16176	−	2.98014i	−0.709022	−	0.409354i	−0.810699	+	0.585463i	$0.800913\pi$
$54$	5.13395	−	0.801614i	0.698642	−	0.109086i
$55$			2.02537i			0.273101i
$56$		0			0
$57$	−3.28268	+	6.43101i	−0.434802	+	0.851808i
$58$	−2.34674	+	4.06467i	−0.308142	+	0.533718i
$59$	9.44130			1.22915			0.614577	−	0.788857i	$-0.289327\pi$
$59$	9.44130			1.22915			0.614577	+	0.788857i	$0.289327\pi$
$60$	−0.129520	−	2.50640i	−0.0167209	−	0.323574i
$61$		−	9.85957i		−	1.26239i	−0.775625	−	0.631194i	$-0.782565\pi$
$61$		−	9.85957i		−	1.26239i	0.775625	−	0.631194i	$-0.217435\pi$
$62$	0.917280			0.116495
$63$		0			0
$64$	−1.00000			−0.125000
$65$			5.07794i			0.629840i
$66$	2.15634	+	1.10069i	0.265427	+	0.135486i
$67$	−2.97079			−0.362940			−0.181470	−	0.983396i	$-0.558086\pi$
$67$	−2.97079			−0.362940			−0.181470	+	0.983396i	$0.558086\pi$
$68$	−3.95277	+	6.84639i	−0.479343	+	0.830247i
$69$	6.25907	−	0.323442i	0.753504	−	0.0389378i
$70$		0			0
$71$		−	12.9436i		−	1.53612i	−0.640377	−	0.768061i	$-0.721222\pi$
$71$		−	12.9436i		−	1.53612i	0.640377	−	0.768061i	$-0.278778\pi$
$72$	−2.73885	−	1.22421i	−0.322777	−	0.144275i
$73$	−9.79071	−	5.65267i	−1.14592	−	0.661595i	−0.198027	−	0.980197i	$-0.563453\pi$
$73$	−9.79071	−	5.65267i	−1.14592	−	0.661595i	−0.947889	+	0.318602i	$0.896787\pi$
$74$	−3.70963	+	2.14176i	−0.431236	+	0.248974i
$75$	4.47443	+	2.28395i	0.516663	+	0.263728i
$76$	3.61019	−	2.08434i	0.414117	−	0.239091i
$77$		0			0
$78$	5.40629	+	2.75961i	0.612141	+	0.312465i
$79$	15.6342			1.75898			0.879491	−	0.475915i	$-0.157883\pi$
$79$	15.6342			1.75898			0.879491	+	0.475915i	$0.157883\pi$
$80$	−0.724499	+	1.25487i	−0.0810015	+	0.140299i
$81$	−6.00262	−	6.70586i	−0.666957	−	0.745096i
$82$	−0.595352	+	0.343727i	−0.0657457	+	0.0379583i
$83$	−4.11183	+	7.12189i	−0.451332	+	0.781729i	−0.998469	−	0.0553135i	$-0.982384\pi$
$83$	−4.11183	+	7.12189i	−0.451332	+	0.781729i	0.547137	+	0.837043i	$0.315718\pi$
$84$		0			0
$85$	5.72755	+	9.92041i	0.621240	+	1.07602i
$86$	−10.4182	−	6.01497i	−1.12343	−	0.648611i
$87$	8.11851	−	0.419530i	0.870396	−	0.0449783i
$88$	−0.698887	−	1.21051i	−0.0745016	−	0.129041i
$89$	−0.533417	−	0.923906i	−0.0565421	−	0.0979338i	0.836369	−	0.548167i	$-0.184674\pi$
$89$	−0.533417	−	0.923906i	−0.0565421	−	0.0979338i	−0.892911	+	0.450233i	$0.851341\pi$
$90$	−3.52052	+	2.54996i	−0.371096	+	0.268790i
$91$		0			0
$92$	−3.13371	−	1.80925i	−0.326712	−	0.188627i
$93$	−0.864336	−	1.33309i	−0.0896274	−	0.138235i
$94$			8.31745i			0.857879i
$95$		−	6.04043i		−	0.619735i
$96$	0.942282	+	1.45331i	0.0961712	+	0.148328i
$97$	−10.9670	−	6.33179i	−1.11353	−	0.642895i	−0.173787	−	0.984783i	$-0.555600\pi$
$97$	−10.9670	−	6.33179i	−1.11353	−	0.642895i	−0.939741	+	0.341888i	$0.888934\pi$
$98$		0			0
$99$	−0.432231	−	4.17099i	−0.0434409	−	0.419200i
$100$	−1.45020	−	2.51182i	−0.145020	−	0.251182i
$101$	−8.77726	−	15.2027i	−0.873370	−	1.51272i	−0.858489	−	0.512831i	$-0.828597\pi$
$101$	−8.77726	−	15.2027i	−0.873370	−	1.51272i	−0.0148801	−	0.999889i	$-0.504737\pi$
$102$	13.6745	−	0.706641i	1.35398	−	0.0699679i
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	0.678000	−	0.735062i	$-0.262847\pi$
$103$	3.86082	+	2.22905i	0.380418	+	0.219635i	−0.297582	+	0.954696i	$0.596180\pi$
$104$	−1.75222	−	3.03494i	−0.171820	−	0.297600i
$105$		0			0
$106$	2.98014	−	5.16176i	0.289457	−	0.501355i
$107$	−2.04566	+	1.18106i	−0.197762	+	0.114178i	−0.595611	−	0.803273i	$-0.703090\pi$
$107$	−2.04566	+	1.18106i	−0.197762	+	0.114178i	0.397849	+	0.917451i	$0.369757\pi$
$108$	0.801614	+	5.13395i	0.0771353	+	0.494014i
$109$	−6.49776	+	11.2545i	−0.622373	+	1.07798i	0.366670	+	0.930351i	$0.380498\pi$
$109$	−6.49776	+	11.2545i	−0.622373	+	1.07798i	−0.989043	+	0.147630i	$0.952836\pi$
$110$	−2.02537			−0.193112
$111$	6.60815	+	3.37310i	0.627218	+	0.320161i
$112$		0			0
$113$	2.90616	−	1.67787i	0.273388	−	0.157841i	−0.357038	−	0.934090i	$-0.616213\pi$
$113$	2.90616	−	1.67787i	0.273388	−	0.157841i	0.630426	+	0.776249i	$0.282880\pi$
$114$	−6.43101	−	3.28268i	−0.602319	−	0.307451i
$115$	−4.54074	+	2.62160i	−0.423427	+	0.244465i
$116$	−4.06467	−	2.34674i	−0.377395	−	0.217889i
$117$	−1.08367	−	10.4573i	−0.100186	−	0.966781i
$118$			9.44130i			0.869143i
$119$		0			0
$120$	2.50640	−	0.129520i	0.228802	−	0.0118235i
$121$	−4.52311	+	7.83426i	−0.411192	+	0.712206i
$122$	9.85957			0.892644
$123$	1.06053	+	0.541343i	0.0956248	+	0.0488113i
$124$			0.917280i			0.0823741i
$125$	−11.4477			−1.02391
$126$		0			0
$127$	−12.9075			−1.14535			−0.572677	−	0.819781i	$-0.694095\pi$
$127$	−12.9075			−1.14535			−0.572677	+	0.819781i	$0.694095\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.07530	+	20.8087i	0.0946753	+	1.83211i
$130$	−5.07794			−0.445364
$131$	−4.12856	+	7.15088i	−0.360714	+	0.624775i	−0.988079	−	0.153951i	$-0.950800\pi$
$131$	−4.12856	+	7.15088i	−0.360714	+	0.624775i	0.627364	+	0.778726i	$0.284134\pi$
$132$	−1.10069	+	2.15634i	−0.0958030	+	0.187685i
$133$		0			0
$134$		−	2.97079i		−	0.256637i
$135$	7.02320	+	2.71362i	0.604461	+	0.233551i
$136$	−6.84639	−	3.95277i	−0.587073	−	0.338947i
$137$	−11.3267	+	6.53946i	−0.967703	+	0.558703i	−0.898535	−	0.438902i	$-0.855368\pi$
$137$	−11.3267	+	6.53946i	−0.967703	+	0.558703i	−0.0691676	+	0.997605i	$0.522034\pi$
$138$	0.323442	+	6.25907i	0.0275332	+	0.532808i
$139$	−10.6722	+	6.16162i	−0.905207	+	0.522621i	−0.878886	−	0.477032i	$-0.841713\pi$
$139$	−10.6722	+	6.16162i	−0.905207	+	0.522621i	−0.0263210	+	0.999654i	$0.508379\pi$
$140$		0			0
$141$	12.0878	−	7.83738i	1.01798	−	0.660026i
$142$	12.9436			1.08620
$143$	2.44921	−	4.24216i	0.204813	−	0.354747i
$144$	1.22421	−	2.73885i	0.102018	−	0.228238i
$145$	−5.88971	+	3.40042i	−0.489113	+	0.282390i
$146$	5.65267	−	9.79071i	0.467818	−	0.810285i
$147$		0			0
$148$	−2.14176	−	3.70963i	−0.176051	−	0.304930i
$149$	0.538692	+	0.311014i	0.0441314	+	0.0254792i	0.521903	−	0.853005i	$-0.325222\pi$
$149$	0.538692	+	0.311014i	0.0441314	+	0.0254792i	−0.477772	+	0.878484i	$0.658555\pi$
$150$	−2.28395	+	4.47443i	−0.186484	+	0.365336i
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	0.870103	+	0.492870i	$0.164052\pi$
$151$	10.5911	+	18.3443i	0.861889	+	1.49284i	−0.00821353	+	0.999966i	$0.502614\pi$
$152$	2.08434	+	3.61019i	0.169063	+	0.292825i
$153$	−13.9122	−	19.2075i	−1.12474	−	1.55283i
$154$		0			0
$155$	1.15107	+	0.664569i	0.0924559	+	0.0533794i
$156$	−2.75961	+	5.40629i	−0.220946	+	0.432849i
$157$			15.0294i			1.19947i	0.800197	+	0.599737i	$0.204728\pi$
$157$			15.0294i			1.19947i	−0.800197	+	0.599737i	$0.795272\pi$
$158$			15.6342i			1.24379i
$159$	−10.3098	+	0.532764i	−0.817618	+	0.0422509i
$160$	−1.25487	−	0.724499i	−0.0992062	−	0.0572767i
$161$		0			0
$162$	6.70586	−	6.00262i	0.526862	−	0.471610i
$163$	1.51764	+	2.62863i	0.118871	+	0.205890i	0.919320	−	0.393510i	$-0.128739\pi$
$163$	1.51764	+	2.62863i	0.118871	+	0.205890i	−0.800450	+	0.599400i	$0.795406\pi$
$164$	−0.343727	−	0.595352i	−0.0268406	−	0.0464892i
$165$	1.90847	+	2.94349i	0.148574	+	0.229150i
$166$	−7.12189	−	4.11183i	−0.552766	−	0.319140i
$167$	3.05895	+	5.29826i	0.236709	+	0.409992i	0.959768	−	0.280794i	$-0.0905979\pi$
$167$	3.05895	+	5.29826i	0.236709	+	0.409992i	−0.723059	+	0.690786i	$0.757265\pi$
$168$		0			0
$169$	−0.359433	+	0.622557i	−0.0276487	+	0.0478890i
$170$	−9.92041	+	5.72755i	−0.760861	+	0.439283i
$171$	1.28908	+	12.4395i	0.0985782	+	0.951269i
$172$	6.01497	−	10.4182i	0.458637	−	0.794383i
$173$	−2.29515			−0.174497			−0.0872484	−	0.996187i	$-0.527807\pi$
$173$	−2.29515			−0.174497			−0.0872484	+	0.996187i	$0.527807\pi$
$174$	0.419530	+	8.11851i	0.0318045	+	0.615463i
$175$		0			0
$176$	1.21051	−	0.698887i	0.0912454	−	0.0526806i
$177$	13.7211	−	8.89637i	1.03134	−	0.668692i
$178$	0.923906	−	0.533417i	0.0692497	−	0.0399813i
$179$	−2.92364	−	1.68796i	−0.218523	−	0.126164i	0.386743	−	0.922187i	$-0.373600\pi$
$179$	−2.92364	−	1.68796i	−0.218523	−	0.126164i	−0.605266	+	0.796023i	$0.706933\pi$
$180$	−2.54996	−	3.52052i	−0.190063	−	0.262404i
$181$			1.68857i			0.125511i	0.998029	+	0.0627553i	$0.0199888\pi$
$181$			1.68857i			0.125511i	−0.998029	+	0.0627553i	$0.980011\pi$
$182$		0			0
$183$	−9.29049	−	14.3290i	−0.686773	−	1.05923i
$184$	1.80925	−	3.13371i	0.133380	−	0.231020i
$185$	−6.20681			−0.456334
$186$	1.33309	−	0.864336i	0.0977469	−	0.0633762i
$187$		−	11.0501i		−	0.808067i
$188$	−8.31745			−0.606612
$189$		0			0
$190$	6.04043			0.438219
$191$			8.94832i			0.647478i	0.946146	+	0.323739i	$0.104940\pi$
$191$			8.94832i			0.647478i	−0.946146	+	0.323739i	$0.895060\pi$
$192$	−1.45331	+	0.942282i	−0.104883	+	0.0680033i
$193$	25.6055			1.84313			0.921564	−	0.388227i	$-0.126912\pi$
$193$	25.6055			1.84313			0.921564	+	0.388227i	$0.126912\pi$
$194$	6.33179	−	10.9670i	0.454596	−	0.787383i
$195$	4.78485	+	7.37981i	0.342650	+	0.528479i
$196$		0			0
$197$		−	23.5602i		−	1.67860i	−0.543670	−	0.839299i	$-0.682966\pi$
$197$		−	23.5602i		−	1.67860i	0.543670	−	0.839299i	$-0.317034\pi$
$198$	4.17099	−	0.432231i	0.296419	−	0.0307173i
$199$	−11.7989	−	6.81212i	−0.836404	−	0.482898i	0.0196362	−	0.999807i	$-0.493749\pi$
$199$	−11.7989	−	6.81212i	−0.836404	−	0.482898i	−0.856040	+	0.516909i	$0.827083\pi$
$200$	2.51182	−	1.45020i	0.177613	−	0.102545i
$201$	−4.31748	+	2.79932i	−0.304531	+	0.197449i
$202$	15.2027	−	8.77726i	1.06965	−	0.617566i
$203$		0			0
$204$	0.706641	+	13.6745i	0.0494748	+	0.957409i
$205$	−0.996120			−0.0695720
$206$	−2.22905	+	3.86082i	−0.155305	+	0.268996i
$207$	8.79159	−	6.36787i	0.611058	−	0.442598i
$208$	3.03494	−	1.75222i	0.210435	−	0.121495i
$209$	−2.91344	+	5.04623i	−0.201527	+	0.349055i
$210$		0			0
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	−0.951015	−	0.309145i	$-0.899957\pi$
$211$	−10.7961	−	18.6994i	−0.743235	−	1.28732i	0.207780	−	0.978176i	$-0.433376\pi$
$212$	5.16176	+	2.98014i	0.354511	+	0.204677i
$213$	−12.1965	−	18.8110i	−0.835691	−	1.28891i
$214$	−1.18106	−	2.04566i	−0.0807359	−	0.139839i
$215$	−8.71569	−	15.0960i	−0.594405	−	1.02954i
$216$	−5.13395	+	0.801614i	−0.349321	+	0.0545429i
$217$		0			0
$218$	−11.2545	−	6.49776i	−0.762248	−	0.440084i
$219$	−19.5553	+	1.01053i	−1.32143	+	0.0682856i
$220$		−	2.02537i		−	0.136551i
$221$		−	27.7045i		−	1.86361i
$222$	−3.37310	+	6.60815i	−0.226388	+	0.443510i
$223$	−14.5710	−	8.41256i	−0.975745	−	0.563347i	−0.0747620	−	0.997201i	$-0.523820\pi$
$223$	−14.5710	−	8.41256i	−0.975745	−	0.563347i	−0.900983	+	0.433855i	$0.857153\pi$
$224$		0			0
$225$	8.65486	−	0.896887i	0.576991	−	0.0597924i
$226$	1.67787	+	2.90616i	0.111610	+	0.193315i
$227$	6.11065	+	10.5840i	0.405578	+	0.702482i	0.994389	−	0.105789i	$-0.0337369\pi$
$227$	6.11065	+	10.5840i	0.405578	+	0.702482i	−0.588810	+	0.808271i	$0.700404\pi$
$228$	3.28268	−	6.43101i	0.217401	−	0.425904i
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.939656	−	0.342120i	$-0.111145\pi$
$229$	16.8458	+	9.72591i	1.11320	+	0.642706i	0.173543	+	0.984826i	$0.444478\pi$
$230$	−2.62160	−	4.54074i	−0.172863	−	0.299408i
$231$		0			0
$232$	2.34674	−	4.06467i	0.154071	−	0.266859i
$233$	−24.7381	+	14.2825i	−1.62065	+	0.935681i	−0.633900	+	0.773415i	$0.718547\pi$
$233$	−24.7381	+	14.2825i	−1.62065	+	0.935681i	−0.986747	+	0.162265i	$0.948120\pi$
$234$	10.4573	−	1.08367i	0.683617	−	0.0708420i
$235$	−6.02598	+	10.4373i	−0.393092	+	0.680855i
$236$	−9.44130			−0.614577
$237$	22.7213	−	14.7318i	1.47591	−	0.956933i
$238$		0			0
$239$	−10.0020	+	5.77465i	−0.646975	+	0.373531i	−0.787296	−	0.616575i	$-0.788520\pi$
$239$	−10.0020	+	5.77465i	−0.646975	+	0.373531i	0.140322	+	0.990106i	$0.455186\pi$
$240$	0.129520	+	2.50640i	0.00836046	+	0.161787i
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	−0.499037	−	0.866581i	$-0.666313\pi$
$241$	0.0299000	−	0.0172628i	0.00192603	−	0.00111199i	0.500963	+	0.865469i	$0.332979\pi$
$242$	−7.83426	−	4.52311i	−0.503606	−	0.290757i
$243$	−15.0425	−	4.08953i	−0.964975	−	0.262344i
$244$			9.85957i			0.631194i
$245$		0			0
$246$	−0.541343	+	1.06053i	−0.0345148	+	0.0676170i
$247$	−7.30447	+	12.6517i	−0.464772	+	0.805009i
$248$	−0.917280			−0.0582473
$249$	0.735076	+	14.2248i	0.0465836	+	0.901460i
$250$		−	11.4477i		−	0.724014i
$251$	3.26317			0.205969			0.102985	−	0.994683i	$-0.467161\pi$
$251$	3.26317			0.205969			0.102985	+	0.994683i	$0.467161\pi$
$252$		0			0
$253$	5.05784			0.317984
$254$		−	12.9075i		−	0.809887i
$255$	17.6717	+	9.02045i	1.10665	+	0.564883i
$256$	1.00000			0.0625000
$257$	9.89851	−	17.1447i	0.617452	−	1.06946i	−0.372497	−	0.928034i	$-0.621498\pi$
$257$	9.89851	−	17.1447i	0.617452	−	1.06946i	0.989949	−	0.141425i	$-0.0451685\pi$
$258$	−20.8087	+	1.07530i	−1.29549	+	0.0669455i
$259$		0			0
$260$		−	5.07794i		−	0.314920i
$261$	11.4034	−	8.25963i	0.705852	−	0.511258i
$262$	−7.15088	−	4.12856i	−0.441783	−	0.255063i
$263$	15.2576	−	8.80897i	0.940823	−	0.543184i	0.0506045	−	0.998719i	$-0.483885\pi$
$263$	15.2576	−	8.80897i	0.940823	−	0.543184i	0.890218	+	0.455535i	$0.150552\pi$
$264$	−2.15634	−	1.10069i	−0.132713	−	0.0677429i
$265$	7.47939	−	4.31823i	0.459455	−	0.265266i
$266$		0			0
$267$	−1.64580	−	0.840091i	−0.100721	−	0.0514127i
$268$	2.97079			0.181470
$269$	−3.83672	+	6.64540i	−0.233929	+	0.405177i	−0.958961	−	0.283538i	$-0.908492\pi$
$269$	−3.83672	+	6.64540i	−0.233929	+	0.405177i	0.725032	+	0.688715i	$0.241825\pi$
$270$	−2.71362	+	7.02320i	−0.165146	+	0.427419i
$271$	−6.09146	+	3.51690i	−0.370030	+	0.213637i	−0.673471	−	0.739213i	$-0.735198\pi$
$271$	−6.09146	+	3.51690i	−0.370030	+	0.213637i	0.303442	+	0.952850i	$0.401864\pi$
$272$	3.95277	−	6.84639i	0.239672	−	0.415123i
$273$		0			0
$274$	−6.53946	−	11.3267i	−0.395063	−	0.684269i
$275$	3.51096	+	2.02705i	0.211719	+	0.122236i
$276$	−6.25907	+	0.323442i	−0.376752	+	0.0194689i
$277$	−8.65364	−	14.9885i	−0.519947	−	0.900575i	−0.999731	−	0.0231880i	$-0.992618\pi$
$277$	−8.65364	−	14.9885i	−0.519947	−	0.900575i	0.479784	−	0.877387i	$-0.340715\pi$
$278$	−6.16162	−	10.6722i	−0.369549	−	0.640078i
$279$	−2.51229	−	1.12294i	−0.150407	−	0.0672289i
$280$		0			0
$281$	14.3155	+	8.26508i	0.853994	+	0.493053i	0.861996	−	0.506915i	$-0.169214\pi$
$281$	14.3155	+	8.26508i	0.853994	+	0.493053i	−0.00800273	+	0.999968i	$0.502547\pi$
$282$	7.83738	+	12.0878i	0.466709	+	0.719819i
$283$			3.16284i			0.188011i	0.995572	+	0.0940057i	$0.0299672\pi$
$283$			3.16284i			0.188011i	−0.995572	+	0.0940057i	$0.970033\pi$
$284$			12.9436i			0.768061i
$285$	−5.69178	−	8.77860i	−0.337152	−	0.519999i
$286$	4.24216	+	2.44921i	0.250844	+	0.144825i
$287$		0			0
$288$	2.73885	+	1.22421i	0.161388	+	0.0721373i
$289$	−22.7487	−	39.4019i	−1.33816	−	2.31776i
$290$	−3.40042	−	5.88971i	−0.199680	−	0.345855i
$291$	−21.9047	+	1.13194i	−1.28408	+	0.0663556i
$292$	9.79071	+	5.65267i	0.572958	+	0.330797i
$293$	4.26045	+	7.37932i	0.248898	+	0.431104i	0.963220	−	0.268713i	$-0.0865982\pi$
$293$	4.26045	+	7.37932i	0.248898	+	0.431104i	−0.714322	+	0.699817i	$0.753265\pi$
$294$		0			0
$295$	−6.84022	+	11.8476i	−0.398253	+	0.689794i
$296$	3.70963	−	2.14176i	0.215618	−	0.124487i
$297$	−4.55841	−	5.65444i	−0.264506	−	0.328104i
$298$	−0.311014	+	0.538692i	−0.0180165	+	0.0312056i
$299$	12.6808			0.733351
$300$	−4.47443	−	2.28395i	−0.258332	−	0.131864i
$301$		0			0
$302$	−18.3443	+	10.5911i	−1.05559	+	0.609448i
$303$	−27.0812	−	13.8235i	−1.55578	−	0.794139i
$304$	−3.61019	+	2.08434i	−0.207059	+	0.119545i
$305$	12.3725	+	7.14325i	0.708446	+	0.409022i
$306$	19.2075	−	13.9122i	1.09802	−	0.795309i
$307$			25.0805i			1.43142i	0.698398	+	0.715710i	$0.253897\pi$
$307$			25.0805i			1.43142i	−0.698398	+	0.715710i	$0.746103\pi$
$308$		0			0
$309$	7.71136	−	0.398490i	0.438684	−	0.0226693i
$310$	−0.664569	+	1.15107i	−0.0377450	+	0.0653762i
$311$	−3.57355			−0.202638			−0.101319	−	0.994854i	$-0.532306\pi$
$311$	−3.57355			−0.202638			−0.101319	+	0.994854i	$0.532306\pi$
$312$	−5.40629	−	2.75961i	−0.306071	−	0.156232i
$313$			13.6293i			0.770372i	0.922839	+	0.385186i	$0.125863\pi$
$313$			13.6293i			0.770372i	−0.922839	+	0.385186i	$0.874137\pi$
$314$	−15.0294			−0.848157
$315$		0			0
$316$	−15.6342			−0.879491
$317$		−	4.28994i		−	0.240947i	−0.992717	−	0.120474i	$-0.961559\pi$
$317$		−	4.28994i		−	0.240947i	0.992717	−	0.120474i	$-0.0384413\pi$
$318$	−0.532764	−	10.3098i	−0.0298759	−	0.578143i
$319$	6.56042			0.367313
$320$	0.724499	−	1.25487i	0.0405007	−	0.0701494i
$321$	−1.86008	+	3.64404i	−0.103820	+	0.203391i
$322$		0			0
$323$			32.9557i			1.83370i
$324$	6.00262	+	6.70586i	0.333479	+	0.372548i
$325$	8.80254	+	5.08215i	0.488277	+	0.281907i
$326$	−2.62863	+	1.51764i	−0.145586	+	0.0840542i
$327$	1.16161	+	22.4789i	0.0642373	+	1.24309i
$328$	0.595352	−	0.343727i	0.0328728	−	0.0189791i
$329$		0			0
$330$	−2.94349	+	1.90847i	−0.162034	+	0.105058i
$331$	8.93923			0.491345			0.245672	−	0.969353i	$-0.420991\pi$
$331$	8.93923			0.491345			0.245672	+	0.969353i	$0.420991\pi$
$332$	4.11183	−	7.12189i	0.225666	−	0.390865i
$333$	12.7821	−	1.32458i	0.700454	−	0.0725867i
$334$	−5.29826	+	3.05895i	−0.289908	+	0.167379i
$335$	2.15234	−	3.72796i	0.117595	−	0.203680i
$336$		0			0
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	0.868006	−	0.496553i	$-0.165401\pi$
$337$	0.0729773	+	0.126400i	0.00397532	+	0.00688546i	−0.864031	+	0.503439i	$0.832068\pi$
$338$	−0.622557	−	0.359433i	−0.0338626	−	0.0195506i
$339$	2.64252	−	5.17688i	0.143522	−	0.281170i
$340$	−5.72755	−	9.92041i	−0.310620	−	0.538010i
$341$	−0.641075	−	1.11037i	−0.0347161	−	0.0601301i
$342$	−12.4395	+	1.28908i	−0.672649	+	0.0697053i
$343$		0			0
$344$	10.4182	+	6.01497i	0.561714	+	0.324306i
$345$	−4.12882	+	8.08865i	−0.222288	+	0.435479i
$346$		−	2.29515i		−	0.123388i
$347$		−	22.2844i		−	1.19629i	−0.801389	−	0.598144i	$-0.795905\pi$
$347$		−	22.2844i		−	1.19629i	0.801389	−	0.598144i	$-0.204095\pi$
$348$	−8.11851	+	0.419530i	−0.435198	+	0.0224891i
$349$	−2.79851	−	1.61572i	−0.149801	−	0.0864876i	0.423226	−	0.906024i	$-0.360898\pi$
$349$	−2.79851	−	1.61572i	−0.149801	−	0.0864876i	−0.573027	+	0.819537i	$0.694231\pi$
$350$		0			0
$351$	−11.4287	−	14.1766i	−0.610017	−	0.756691i
$352$	0.698887	+	1.21051i	0.0372508	+	0.0645203i
$353$	−3.13232	−	5.42533i	−0.166716	−	0.288761i	0.770547	−	0.637383i	$-0.219983\pi$
$353$	−3.13232	−	5.42533i	−0.166716	−	0.288761i	−0.937263	+	0.348622i	$0.886650\pi$
$354$	8.89637	+	13.7211i	0.472837	+	0.729270i
$355$	16.2425	+	9.37762i	0.862063	+	0.497712i
$356$	0.533417	+	0.923906i	0.0282711	+	0.0489669i
$357$		0			0
$358$	1.68796	−	2.92364i	0.0892116	−	0.154519i
$359$	10.4523	−	6.03463i	0.551651	−	0.318496i	−0.198137	−	0.980174i	$-0.563489\pi$
$359$	10.4523	−	6.03463i	0.551651	−	0.318496i	0.749787	+	0.661679i	$0.230156\pi$
$360$	3.52052	−	2.54996i	0.185548	−	0.134395i
$361$	−0.811015	+	1.40472i	−0.0426850	+	0.0739326i
$362$	−1.68857			−0.0887494
$363$	0.808603	+	15.6476i	0.0424406	+	0.821289i
$364$		0			0
$365$	14.1867	−	8.19071i	0.742567	−	0.428721i
$366$	14.3290	−	9.29049i	0.748989	−	0.485622i
$367$	14.7907	−	8.53940i	0.772067	−	0.445753i	−0.0615446	−	0.998104i	$-0.519603\pi$
$367$	14.7907	−	8.53940i	0.772067	−	0.445753i	0.833611	+	0.552351i	$0.186269\pi$
$368$	3.13371	+	1.80925i	0.163356	+	0.0943136i
$369$	2.05138	−	0.212580i	0.106790	−	0.0110665i
$370$		−	6.20681i		−	0.322677i
$371$		0			0
$372$	0.864336	+	1.33309i	0.0448137	+	0.0691175i
$373$	−1.93680	+	3.35463i	−0.100284	+	0.173696i	−0.911801	−	0.410631i	$-0.865308\pi$
$373$	−1.93680	+	3.35463i	−0.100284	+	0.173696i	0.811518	+	0.584328i	$0.198642\pi$
$374$	11.0501			0.571389
$375$	−16.6370	+	10.7869i	−0.859131	+	0.557035i
$376$		−	8.31745i		−	0.428939i
$377$	16.4480			0.847117
$378$		0			0
$379$	8.21884			0.422173			0.211087	−	0.977467i	$-0.432300\pi$
$379$	8.21884			0.422173			0.211087	+	0.977467i	$0.432300\pi$
$380$			6.04043i			0.309867i
$381$	−18.7586	+	12.1625i	−0.961030	+	0.623103i
$382$	−8.94832			−0.457836
$383$	−15.1513	+	26.2428i	−0.774195	+	1.34095i	0.161050	+	0.986946i	$0.448512\pi$
$383$	−15.1513	+	26.2428i	−0.774195	+	1.34095i	−0.935246	+	0.353999i	$0.884821\pi$
$384$	−0.942282	−	1.45331i	−0.0480856	−	0.0741638i
$385$		0			0
$386$			25.6055i			1.30329i
$387$	21.1704	+	29.2282i	1.07615	+	1.48575i
$388$	10.9670	+	6.33179i	0.556764	+	0.321448i
$389$	−18.2352	+	10.5281i	−0.924562	+	0.533796i	−0.885088	−	0.465424i	$-0.845902\pi$
$389$	−18.2352	+	10.5281i	−0.924562	+	0.533796i	−0.0394744	+	0.999221i	$0.512568\pi$
$390$	−7.37981	+	4.78485i	−0.373691	+	0.242290i
$391$	24.7737	−	14.3031i	1.25286	−	0.723338i
$392$		0			0
$393$	0.738068	+	14.2827i	0.0372306	+	0.720467i
$394$	23.5602			1.18695
$395$	−11.3269	+	19.6189i	−0.569921	+	0.987132i
$396$	0.432231	+	4.17099i	0.0217204	+	0.209600i
$397$	−0.516521	+	0.298214i	−0.0259235	+	0.0149669i	−0.512906	−	0.858445i	$-0.671431\pi$
$397$	−0.516521	+	0.298214i	−0.0259235	+	0.0149669i	0.486982	+	0.873412i	$0.338098\pi$
$398$	6.81212	−	11.7989i	0.341461	−	0.591427i
$399$		0			0
$400$	1.45020	+	2.51182i	0.0725101	+	0.125591i
$401$	2.02316	+	1.16807i	0.101032	+	0.0583309i	0.549665	−	0.835385i	$-0.314755\pi$
$401$	2.02316	+	1.16807i	0.101032	+	0.0583309i	−0.448633	+	0.893716i	$0.648089\pi$
$402$	−2.79932	−	4.31748i	−0.139618	−	0.215336i
$403$	−1.60728	−	2.78389i	−0.0800642	−	0.138675i
$404$	8.77726	+	15.2027i	0.436685	+	0.756360i
$405$	12.7639	−	2.67411i	0.634242	−	0.132878i
$406$		0			0
$407$	5.18523	+	2.99369i	0.257022	+	0.148392i
$408$	−13.6745	+	0.706641i	−0.676990	+	0.0349839i
$409$		−	9.64564i		−	0.476946i	−0.971149	−	0.238473i	$-0.923353\pi$
$409$		−	9.64564i		−	0.476946i	0.971149	−	0.238473i	$-0.0766469\pi$
$410$		−	0.996120i		−	0.0491948i
$411$	−10.2991	+	20.1768i	−0.508019	+	0.995246i
$412$	−3.86082	−	2.22905i	−0.190209	−	0.109817i
$413$		0			0
$414$	6.36787	+	8.79159i	0.312964	+	0.432083i
$415$	−5.95803	−	10.3196i	−0.292468	−	0.506570i
$416$	1.75222	+	3.03494i	0.0859098	+	0.148800i
$417$	−9.70407	+	19.0110i	−0.475210	+	0.930971i
$418$	−5.04623	−	2.91344i	−0.246819	−	0.142501i
$419$	14.4297	+	24.9930i	0.704939	+	1.22099i	0.966714	+	0.255861i	$0.0823590\pi$
$419$	14.4297	+	24.9930i	0.704939	+	1.22099i	−0.261775	+	0.965129i	$0.584308\pi$
$420$		0			0
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	−0.676466	−	0.736474i	$-0.736489\pi$
$421$	6.14672	−	10.6464i	0.299573	−	0.518875i	0.976038	+	0.217599i	$0.0698226\pi$
$422$	18.6994	−	10.7961i	0.910273	−	0.525546i
$423$	10.1823	−	22.7802i	0.495081	−	1.10761i
$424$	−2.98014	+	5.16176i	−0.144729	+	0.250677i
$425$	22.9292			1.11223
$426$	18.8110	−	12.1965i	0.911397	−	0.590923i
$427$		0			0
$428$	2.04566	−	1.18106i	0.0988808	−	0.0570889i
$429$	−0.437848	−	8.47301i	−0.0211395	−	0.409081i
$430$	15.0960	−	8.71569i	0.727995	−	0.420308i
$431$	24.0435	+	13.8815i	1.15814	+	0.668650i	0.950857	−	0.309631i	$-0.100206\pi$
$431$	24.0435	+	13.8815i	1.15814	+	0.668650i	0.207280	+	0.978282i	$0.433539\pi$
$432$	−0.801614	−	5.13395i	−0.0385677	−	0.247007i
$433$		−	21.3927i		−	1.02807i	−0.857769	−	0.514035i	$-0.828150\pi$
$433$		−	21.3927i		−	1.02807i	0.857769	−	0.514035i	$-0.171850\pi$
$434$		0			0
$435$	−5.35540	+	10.4916i	−0.256772	+	0.503035i
$436$	6.49776	−	11.2545i	0.311186	−	0.538990i
$437$	−15.0844			−0.721585
$438$	−1.01053	−	19.5553i	−0.0482852	−	0.934389i
$439$			2.63916i			0.125960i	0.998015	+	0.0629801i	$0.0200605\pi$
$439$			2.63916i			0.125960i	−0.998015	+	0.0629801i	$0.979940\pi$
$440$	2.02537			0.0965558
$441$		0			0
$442$	27.7045			1.31777
$443$		−	12.1750i		−	0.578452i	−0.957261	−	0.289226i	$-0.906602\pi$
$443$		−	12.1750i		−	0.578452i	0.957261	−	0.289226i	$-0.0933979\pi$
$444$	−6.60815	−	3.37310i	−0.313609	−	0.160080i
$445$	1.54584			0.0732799
$446$	8.41256	−	14.5710i	0.398346	−	0.689956i
$447$	1.07595	−	0.0556003i	0.0508906	−	0.00262981i
$448$		0			0
$449$			14.2454i			0.672283i	0.941811	+	0.336142i	$0.109122\pi$
$449$			14.2454i			0.672283i	−0.941811	+	0.336142i	$0.890878\pi$
$450$	0.896887	+	8.65486i	0.0422796	+	0.407994i
$451$	0.832168	+	0.480452i	0.0391853	+	0.0226236i
$452$	−2.90616	+	1.67787i	−0.136694	+	0.0789204i
$453$	32.6776	+	16.6801i	1.53533	+	0.783700i
$454$	−10.5840	+	6.11065i	−0.496730	+	0.286787i
$455$		0			0
$456$	6.43101	+	3.28268i	0.301160	+	0.153726i
$457$	−11.5631			−0.540900			−0.270450	−	0.962734i	$-0.587172\pi$
$457$	−11.5631			−0.540900			−0.270450	+	0.962734i	$0.587172\pi$
$458$	−9.72591	+	16.8458i	−0.454462	+	0.787151i
$459$	−38.3176	−	14.8051i	−1.78851	−	0.691044i
$460$	4.54074	−	2.62160i	0.211713	−	0.122233i
$461$	−11.0041	+	19.0597i	−0.512513	+	0.887698i	0.487382	+	0.873189i	$0.337952\pi$
$461$	−11.0041	+	19.0597i	−0.512513	+	0.887698i	−0.999895	+	0.0145095i	$0.995381\pi$
$462$		0			0
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	0.976382	−	0.216049i	$-0.0693171\pi$
$463$	6.47862	+	11.2213i	0.301087	+	0.521498i	−0.675295	+	0.737547i	$0.735984\pi$
$464$	4.06467	+	2.34674i	0.188698	+	0.108945i
$465$	2.29907	−	0.118806i	0.106617	−	0.00550949i
$466$	−14.2825	−	24.7381i	−0.661626	−	1.14597i
$467$	−1.42545	−	2.46895i	−0.0659619	−	0.114249i	0.831158	−	0.556036i	$-0.187678\pi$
$467$	−1.42545	−	2.46895i	−0.0659619	−	0.114249i	−0.897120	+	0.441786i	$0.854345\pi$
$468$	1.08367	+	10.4573i	0.0500928	+	0.483390i
$469$		0			0
$470$	−10.4373	−	6.02598i	−0.481437	−	0.277958i
$471$	14.1619	+	21.8423i	0.652546	+	1.00644i
$472$		−	9.44130i		−	0.434571i
$473$			16.8151i			0.773161i
$474$	14.7318	+	22.7213i	0.676654	+	1.04362i
$475$	−10.4710	−	6.04544i	−0.480443	−	0.277384i
$476$		0			0
$477$	−14.4813	+	10.4890i	−0.663051	+	0.480257i
$478$	−5.77465	−	10.0020i	−0.264126	−	0.457480i
$479$	16.6352	+	28.8130i	0.760081	+	1.31650i	0.942808	+	0.333336i	$0.108174\pi$
$479$	16.6352	+	28.8130i	0.760081	+	1.31650i	−0.182727	+	0.983164i	$0.558492\pi$
$480$	−2.50640	+	0.129520i	−0.114401	+	0.00591174i
$481$	13.0002	+	7.50567i	0.592758	+	0.342229i
$482$	0.0172628	+	0.0299000i	0.000786298	+	0.00136191i
$483$		0			0
$484$	4.52311	−	7.83426i	0.205596	−	0.356103i
$485$	15.8911	−	9.17475i	0.721579	−	0.416604i
$486$	4.08953	−	15.0425i	0.185505	−	0.682340i
$487$	5.22500	−	9.04997i	0.236767	−	0.410093i	−0.723017	−	0.690830i	$-0.757245\pi$
$487$	5.22500	−	9.04997i	0.236767	−	0.410093i	0.959785	+	0.280737i	$0.0905788\pi$
$488$	−9.85957			−0.446322
$489$	4.68250	+	2.39016i	0.211750	+	0.108087i
$490$		0			0
$491$	2.03404	−	1.17436i	0.0917952	−	0.0529980i	−0.453400	−	0.891307i	$-0.649789\pi$
$491$	2.03404	−	1.17436i	0.0917952	−	0.0529980i	0.545195	+	0.838309i	$0.316456\pi$
$492$	−1.06053	−	0.541343i	−0.0478124	−	0.0244056i
$493$	32.1334	−	18.5522i	1.44722	−	0.835550i
$494$	−12.6517	−	7.30447i	−0.569228	−	0.328644i
$495$	5.54719	+	2.47948i	0.249328	+	0.111444i
$496$		−	0.917280i		−	0.0411871i
$497$		0			0
$498$	−14.2248	+	0.735076i	−0.637429	+	0.0329396i
$499$	−17.3895	+	30.1195i	−0.778462	+	1.34834i	0.154366	+	0.988014i	$0.450667\pi$
$499$	−17.3895	+	30.1195i	−0.778462	+	1.34834i	−0.932828	+	0.360322i	$0.882667\pi$
$500$	11.4477			0.511956
$501$	9.43806	+	4.81762i	0.421661	+	0.215235i
$502$			3.26317i			0.145642i
$503$	17.8290			0.794956			0.397478	−	0.917612i	$-0.369886\pi$
$503$	17.8290			0.794956			0.397478	+	0.917612i	$0.369886\pi$
$504$		0			0
$505$	25.4365			1.13191
$506$			5.05784i			0.224849i
$507$	0.0642563	+	1.24345i	0.00285372	+	0.0552237i
$508$	12.9075			0.572677
$509$	−7.78061	+	13.4764i	−0.344869	+	0.597331i	−0.985330	−	0.170660i	$-0.945410\pi$
$509$	−7.78061	+	13.4764i	−0.344869	+	0.597331i	0.640461	+	0.767991i	$0.278743\pi$
$510$	−9.02045	+	17.6717i	−0.399432	+	0.782517i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	13.5949	+	16.8637i	0.600229	+	0.744550i
$514$	17.1447	+	9.89851i	0.756222	+	0.436605i
$515$	−5.59433	+	3.22989i	−0.246516	+	0.142326i
$516$	−1.07530	−	20.8087i	−0.0473376	−	0.916053i
$517$	10.0683	−	5.81295i	0.442805	−	0.255653i
$518$		0			0
$519$	−3.33556	+	2.16267i	−0.146415	+	0.0949309i
$520$	5.07794			0.222682
$521$	14.8188	−	25.6669i	0.649222	−	1.12449i	−0.334087	−	0.942542i	$-0.608428\pi$
$521$	14.8188	−	25.6669i	0.649222	−	1.12449i	0.983309	−	0.181944i	$-0.0582389\pi$
$522$	8.25963	+	11.4034i	0.361514	+	0.499113i
$523$	−19.2353	+	11.1055i	−0.841101	+	0.485610i	−0.857638	−	0.514253i	$-0.828069\pi$
$523$	−19.2353	+	11.1055i	−0.841101	+	0.485610i	0.0165371	+	0.999863i	$0.494736\pi$
$524$	4.12856	−	7.15088i	0.180357	−	0.312388i
$525$		0			0
$526$	8.80897	+	15.2576i	0.384089	+	0.665262i
$527$	−6.28006	−	3.62579i	−0.273564	−	0.157942i
$528$	1.10069	−	2.15634i	0.0479015	−	0.0938425i
$529$	−4.95323	−	8.57925i	−0.215358	−	0.373011i
$530$	4.31823	+	7.47939i	0.187572	+	0.324884i
$531$	11.5581	−	25.8583i	0.501581	−	1.12216i
$532$		0			0
$533$	2.08638	+	1.20457i	0.0903711	+	0.0521758i
$534$	0.840091	−	1.64580i	0.0363543	−	0.0712207i
$535$		−	3.42272i		−	0.147977i
$536$			2.97079i			0.128319i
$537$	−5.83948	+	0.301759i	−0.251992	+	0.0130219i
$538$	−6.64540	−	3.83672i	−0.286503	−	0.165413i
$539$		0			0
$540$	−7.02320	−	2.71362i	−0.302231	−	0.116776i
$541$	−11.0171	−	19.0822i	−0.473662	−	0.820406i	0.525884	−	0.850557i	$-0.323735\pi$
$541$	−11.0171	−	19.0822i	−0.473662	−	0.820406i	−0.999545	+	0.0301502i	$0.990401\pi$
$542$	−3.51690	−	6.09146i	−0.151064	−	0.261650i
$543$	1.59111	+	2.45402i	0.0682811	+	0.105312i
$544$	6.84639	+	3.95277i	0.293537	+	0.169473i
$545$	−9.41525	−	16.3077i	−0.403305	−	0.698545i
$546$		0			0
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	0.368215	+	0.929741i	$0.379969\pi$
$547$	−14.5256	+	25.1592i	−0.621072	+	1.07573i	−0.989286	+	0.145987i	$0.953364\pi$
$548$	11.3267	−	6.53946i	0.483851	−	0.279352i
$549$	−27.0039	−	12.0702i	−1.15250	−	0.515143i
$550$	−2.02705	+	3.51096i	−0.0864338	+	0.149708i
$551$	−19.5657			−0.833525
$552$	−0.323442	−	6.25907i	−0.0137666	−	0.266404i
$553$		0			0
$554$	14.9885	−	8.65364i	0.636802	−	0.367658i
$555$	−9.02040	+	5.84856i	−0.382895	+	0.248258i
$556$	10.6722	−	6.16162i	0.452603	−	0.261311i
$557$	14.9946	+	8.65716i	0.635344	+	0.366816i	0.782819	−	0.622250i	$-0.213781\pi$
$557$	14.9946	+	8.65716i	0.635344	+	0.366816i	−0.147475	+	0.989066i	$0.547115\pi$
$558$	1.12294	−	2.51229i	0.0475380	−	0.106354i
$559$			42.1583i			1.78311i
$560$		0			0
$561$	−10.4123	−	16.0593i	−0.439610	−	0.678023i
$562$	−8.26508	+	14.3155i	−0.348641	+	0.603865i
$563$	−20.7668			−0.875216			−0.437608	−	0.899166i	$-0.644174\pi$
$563$	−20.7668			−0.875216			−0.437608	+	0.899166i	$0.644174\pi$
$564$	−12.0878	+	7.83738i	−0.508989	+	0.330013i
$565$			4.86247i			0.204566i
$566$	−3.16284			−0.132944
$567$		0			0
$568$	−12.9436			−0.543101
$569$		−	14.7604i		−	0.618789i	−0.950934	−	0.309394i	$-0.899874\pi$
$569$		−	14.7604i		−	0.618789i	0.950934	−	0.309394i	$-0.100126\pi$
$570$	8.77860	−	5.69178i	0.367695	−	0.238403i
$571$	−22.2416			−0.930781			−0.465390	−	0.885106i	$-0.654086\pi$
$571$	−22.2416			−0.930781			−0.465390	+	0.885106i	$0.654086\pi$
$572$	−2.44921	+	4.24216i	−0.102407	+	0.177373i
$573$	8.43184	+	13.0047i	0.352245	+	0.543278i
$574$		0			0
$575$			10.4951i			0.437676i
$576$	−1.22421	+	2.73885i	−0.0510088	+	0.114119i
$577$	16.2104	+	9.35911i	0.674850	+	0.389625i	0.797912	−	0.602774i	$-0.205938\pi$
$577$	16.2104	+	9.35911i	0.674850	+	0.389625i	−0.123062	+	0.992399i	$0.539271\pi$
$578$	39.4019	−	22.7487i	1.63890	−	0.946222i
$579$	37.2128	−	24.1276i	1.54651	−	1.00271i
$580$	5.88971	−	3.40042i	0.244557	−	0.141195i
$581$		0			0
$582$	−1.13194	−	21.9047i	−0.0469205	−	0.907980i
$583$	−8.33113			−0.345040
$584$	−5.65267	+	9.79071i	−0.233909	+	0.405142i
$585$	13.9077	+	6.21646i	0.575013	+	0.257019i
$586$	−7.37932	+	4.26045i	−0.304837	+	0.175998i
$587$	10.7433	−	18.6079i	0.443423	−	0.768031i	−0.554518	−	0.832172i	$-0.687097\pi$
$587$	10.7433	−	18.6079i	0.443423	−	0.768031i	0.997941	+	0.0641405i	$0.0204306\pi$
$588$		0			0
$589$	1.91193	+	3.31155i	0.0787796	+	0.136450i
$590$	−11.8476	−	6.84022i	−0.487758	−	0.281607i
$591$	−22.2004	−	34.2403i	−0.913202	−	1.40846i
$592$	2.14176	+	3.70963i	0.0880257	+	0.152465i
$593$	7.04746	+	12.2066i	0.289404	+	0.501263i	0.973668	−	0.227972i	$-0.0732094\pi$
$593$	7.04746	+	12.2066i	0.289404	+	0.501263i	−0.684263	+	0.729235i	$0.739876\pi$
$594$	5.65444	−	4.55841i	0.232005	−	0.187034i
$595$		0			0
$596$	−0.538692	−	0.311014i	−0.0220657	−	0.0127396i
$597$	−23.5664	+	1.21781i	−0.964509	+	0.0498417i
$598$			12.6808i			0.518558i
$599$			19.1707i			0.783296i	0.920115	+	0.391648i	$0.128095\pi$
$599$			19.1707i			0.783296i	−0.920115	+	0.391648i	$0.871905\pi$
$600$	2.28395	−	4.47443i	0.0932420	−	0.182668i
$601$	−34.6795	−	20.0222i	−1.41460	−	0.816723i	−0.418787	−	0.908084i	$-0.637545\pi$
$601$	−34.6795	−	20.0222i	−1.41460	−	0.816723i	−0.995818	+	0.0913619i	$0.970878\pi$
$602$		0			0
$603$	−3.63688	+	8.13656i	−0.148105	+	0.331346i
$604$	−10.5911	−	18.3443i	−0.430945	−	0.746418i
$605$	−6.55399	−	11.3518i	−0.266457	−	0.461518i
$606$	13.8235	−	27.0812i	0.561541	−	1.10010i
$607$	−39.6529	−	22.8936i	−1.60946	−	0.929223i	−0.989490	−	0.144599i	$-0.953811\pi$
$607$	−39.6529	−	22.8936i	−1.60946	−	0.929223i	−0.619971	−	0.784625i	$-0.712856\pi$
$608$	−2.08434	−	3.61019i	−0.0845313	−	0.146413i
$609$		0			0
$610$	−7.14325	+	12.3725i	−0.289222	+	0.500947i
$611$	25.2429	−	14.5740i	1.02122	−	0.589601i
$612$	13.9122	+	19.2075i	0.562369	+	0.776416i
$613$	22.6481	−	39.2276i	0.914748	−	1.58439i	0.107477	−	0.994208i	$-0.465723\pi$
$613$	22.6481	−	39.2276i	0.914748	−	1.58439i	0.807270	−	0.590182i	$-0.200944\pi$
$614$	−25.0805			−1.01217
$615$	−1.44767	+	0.938625i	−0.0583756	+	0.0378490i
$616$		0			0
$617$	−28.6323	+	16.5308i	−1.15269	+	0.665506i	−0.949542	−	0.313641i	$-0.898451\pi$
$617$	−28.6323	+	16.5308i	−1.15269	+	0.665506i	−0.203149	+	0.979148i	$0.565118\pi$
$618$	0.398490	+	7.71136i	0.0160296	+	0.310196i
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	−0.300003	−	0.953938i	$-0.596988\pi$
$619$	9.35801	−	5.40285i	0.376130	−	0.217159i	0.676133	+	0.736779i	$0.263654\pi$
$620$	−1.15107	−	0.664569i	−0.0462279	−	0.0266897i
$621$	6.77656	−	17.5386i	0.271934	−	0.703801i
$622$		−	3.57355i		−	0.143286i
$623$		0			0
$624$	2.75961	−	5.40629i	0.110473	−	0.216425i
$625$	1.04283	−	1.80623i	0.0417131	−	0.0722491i
$626$	−13.6293			−0.544736
$627$	0.520840	+	10.0790i	0.0208003	+	0.402517i
$628$		−	15.0294i		−	0.599737i
$629$	33.8635			1.35022
$630$		0			0
$631$	−30.0554			−1.19648			−0.598242	−	0.801315i	$-0.704134\pi$
$631$	−30.0554			−1.19648			−0.598242	+	0.801315i	$0.704134\pi$
$632$		−	15.6342i		−	0.621894i
$633$	−33.3102	−	17.0030i	−1.32396	−	0.675810i
$634$	4.28994			0.170375
$635$	9.35146	−	16.1972i	0.371101	−	0.642767i
$636$	10.3098	−	0.532764i	0.408809	−	0.0211255i
$637$		0			0
$638$			6.56042i			0.259730i
$639$	−35.4506	−	15.8457i	−1.40240	−	0.626845i
$640$	1.25487	+	0.724499i	0.0496031	+	0.0286384i
$641$	9.66957	−	5.58273i	0.381925	−	0.220505i	−0.296730	−	0.954961i	$-0.595896\pi$
$641$	9.66957	−	5.58273i	0.381925	−	0.220505i	0.678655	+	0.734457i	$0.262563\pi$
$642$	−3.64404	−	1.86008i	−0.143819	−	0.0734117i
$643$	4.40588	−	2.54373i	0.173751	−	0.100315i	−0.410602	−	0.911814i	$-0.634682\pi$
$643$	4.40588	−	2.54373i	0.173751	−	0.100315i	0.584353	+	0.811499i	$0.301348\pi$
$644$		0			0
$645$	−26.8913	−	13.7265i	−1.05884	−	0.540482i
$646$	−32.9557			−1.29662
$647$	−6.45711	+	11.1840i	−0.253855	+	0.439690i	−0.964584	−	0.263776i	$-0.915032\pi$
$647$	−6.45711	+	11.1840i	−0.253855	+	0.439690i	0.710729	+	0.703466i	$0.248365\pi$
$648$	−6.70586	+	6.00262i	−0.263431	+	0.235805i
$649$	11.4288	−	6.59840i	0.448618	−	0.259010i
$650$	−5.08215	+	8.80254i	−0.199338	+	0.345264i
$651$		0			0
$652$	−1.51764	−	2.62863i	−0.0594353	−	0.102945i
$653$	31.5843	+	18.2352i	1.23599	+	0.713598i	0.968272	−	0.249900i	$-0.0803977\pi$
$653$	31.5843	+	18.2352i	1.23599	+	0.713598i	0.267716	+	0.963498i	$0.413731\pi$
$654$	−22.4789	+	1.16161i	−0.878995	+	0.0454227i
$655$	−5.98228	−	10.3616i	−0.233747	−	0.404862i
$656$	0.343727	+	0.595352i	0.0134203	+	0.0232446i
$657$	−27.4677	+	19.8952i	−1.07162	+	0.776187i
$658$		0			0
$659$	2.04111	+	1.17844i	0.0795104	+	0.0459054i	0.539228	−	0.842160i	$-0.318716\pi$
$659$	2.04111	+	1.17844i	0.0795104	+	0.0459054i	−0.459718	+	0.888065i	$0.652049\pi$
$660$	−1.90847	−	2.94349i	−0.0742871	−	0.114575i
$661$			7.76114i			0.301873i	0.988543	+	0.150937i	$0.0482290\pi$
$661$			7.76114i			0.301873i	−0.988543	+	0.150937i	$0.951771\pi$
$662$			8.93923i			0.347433i
$663$	−26.1054	−	40.2632i	−1.01385	−	1.56369i
$664$	7.12189	+	4.11183i	0.276383	+	0.159570i
$665$		0			0
$666$	1.32458	+	12.7821i	0.0513266	+	0.495296i
$667$	8.49167	+	14.7080i	0.328799	+	0.569497i
$668$	−3.05895	−	5.29826i	−0.118354	−	0.204996i
$669$	−29.1031	+	1.50392i	−1.12519	+	0.0581450i
$670$	3.72796	+	2.15234i	0.144024	+	0.0831520i
$671$	−6.89072	−	11.9351i	−0.266013	−	0.460749i
$672$		0			0
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	−0.298109	−	0.954532i	$-0.596356\pi$
$673$	17.5783	−	30.4465i	0.677594	−	1.17363i	0.975703	−	0.219096i	$-0.0703106\pi$
$674$	−0.126400	+	0.0729773i	−0.00486876	+	0.00281098i
$675$	11.7331	−	9.45877i	0.451606	−	0.364068i
$676$	0.359433	−	0.622557i	0.0138244	−	0.0239445i
$677$	14.0615			0.540427			0.270213	−	0.962800i	$-0.412906\pi$
$677$	14.0615			0.540427			0.270213	+	0.962800i	$0.412906\pi$
$678$	5.17688	+	2.64252i	0.198817	+	0.101485i
$679$		0			0
$680$	9.92041	−	5.72755i	0.380430	−	0.219642i
$681$	18.8537	+	9.62380i	0.722477	+	0.368785i
$682$	1.11037	−	0.641075i	0.0425184	−	0.0245480i
$683$	29.1299	+	16.8182i	1.11462	+	0.643529i	0.940023	−	0.341110i	$-0.110803\pi$
$683$	29.1299	+	16.8182i	1.11462	+	0.643529i	0.174601	+	0.984639i	$0.444136\pi$
$684$	−1.28908	−	12.4395i	−0.0492891	−	0.475634i
$685$		−	18.9513i		−	0.724093i
$686$		0			0
$687$	33.6466	−	1.73871i	1.28370	−	0.0663360i
$688$	−6.01497	+	10.4182i	−0.229319	+	0.397192i
$689$	−20.8875			−0.795751
$690$	−8.08865	−	4.12882i	−0.307930	−	0.157181i
$691$			4.40252i			0.167480i	0.996488	+	0.0837399i	$0.0266865\pi$
$691$			4.40252i			0.167480i	−0.996488	+	0.0837399i	$0.973314\pi$
$692$	2.29515			0.0872484
$693$		0			0
$694$	22.2844			0.845903
$695$		−	17.8563i		−	0.677330i
$696$	−0.419530	−	8.11851i	−0.0159022	−	0.307731i
$697$	5.43469			0.205853
$698$	1.61572	−	2.79851i	0.0611560	−	0.105925i
$699$	−22.4939	+	44.0672i	−0.850798	+	1.66677i
$700$		0			0
$701$		−	31.5424i		−	1.19134i	−0.803229	−	0.595670i	$-0.796887\pi$
$701$		−	31.5424i		−	1.19134i	0.803229	−	0.595670i	$-0.203113\pi$
$702$	14.1766	−	11.4287i	0.535062	−	0.431347i
$703$	−15.4643	−	8.92832i	−0.583247	−	0.336738i
$704$	−1.21051	+	0.698887i	−0.0456227	+	0.0263403i
$705$	1.07727	+	20.8468i	0.0405724	+	0.785136i
$706$	5.42533	−	3.13232i	0.204185	−	0.117886i
$707$		0			0
$708$	−13.7211	+	8.89637i	−0.515672	+	0.334346i
$709$	4.34537			0.163194			0.0815970	−	0.996665i	$-0.473998\pi$
$709$	4.34537			0.163194			0.0815970	+	0.996665i	$0.473998\pi$
$710$	−9.37762	+	16.2425i	−0.351936	+	0.609571i
$711$	19.1395	−	42.8197i	0.717788	−	1.60586i
$712$	−0.923906	+	0.533417i	−0.0346248	+	0.0199907i
$713$	1.65959	−	2.87449i	0.0621520	−	0.107651i
$714$		0			0
$715$	3.54890	+	6.14688i	0.132721	+	0.229880i
$716$	2.92364	+	1.68796i	0.109261	+	0.0630821i
$717$	−9.09462	+	17.8170i	−0.339645	+	0.665389i
$718$	6.03463	+	10.4523i	0.225210	+	0.390076i
$719$	−14.1500	−	24.5086i	−0.527707	−	0.914016i	−0.999478	−	0.0322946i	$-0.989719\pi$
$719$	−14.1500	−	24.5086i	−0.527707	−	0.914016i	0.471771	−	0.881721i	$-0.343615\pi$
$720$	2.54996	+	3.52052i	0.0950315	+	0.131202i
$721$		0			0
$722$	−1.40472	−	0.811015i	−0.0522782	−	0.0301829i
$723$	0.0271875	−	0.0532624i	0.00101112	−	0.00198085i
$724$		−	1.68857i		−	0.0627553i
$725$			13.6130i			0.505573i
$726$	−15.6476	+	0.808603i	−0.580739	+	0.0300101i
$727$	11.7770	+	6.79945i	0.436784	+	0.252178i	0.702233	−	0.711948i	$-0.252187\pi$
$727$	11.7770	+	6.79945i	0.436784	+	0.252178i	−0.265448	+	0.964125i	$0.585520\pi$
$728$		0			0
$729$	−25.7148	+	8.23089i	−0.952401	+	0.304848i
$730$	8.19071	+	14.1867i	0.303152	+	0.525074i
$731$	47.5516	+	82.3617i	1.75876	+	3.04626i
$732$	9.29049	+	14.3290i	0.343387	+	0.529615i
$733$	−41.0236	−	23.6850i	−1.51524	−	0.874825i	−0.999840	−	0.0178757i	$-0.994310\pi$
$733$	−41.0236	−	23.6850i	−1.51524	−	0.874825i	−0.515401	−	0.856949i	$-0.672357\pi$
$734$	8.53940	+	14.7907i	0.315195	+	0.545934i
$735$		0			0
$736$	−1.80925	+	3.13371i	−0.0666898	+	0.115510i
$737$	−3.59617	+	2.07625i	−0.132466	+	0.0764796i
$738$	0.212580	+	2.05138i	0.00782518	+	0.0755122i
$739$	−16.8601	+	29.2026i	−0.620210	+	1.07424i	0.369236	+	0.929336i	$0.379619\pi$
$739$	−16.8601	+	29.2026i	−0.620210	+	1.07424i	−0.989446	+	0.144900i	$0.953714\pi$
$740$	6.20681			0.228167
$741$	1.30583	+	25.2697i	0.0479708	+	0.928306i
$742$		0			0
$743$	6.86253	−	3.96208i	0.251762	−	0.145355i	−0.368809	−	0.929505i	$-0.620234\pi$
$743$	6.86253	−	3.96208i	0.251762	−	0.145355i	0.620571	+	0.784151i	$0.286901\pi$
$744$	−1.33309	+	0.864336i	−0.0488735	+	0.0316881i
$745$	−0.780564	+	0.450659i	−0.0285976	+	0.0165109i
$746$	−3.35463	−	1.93680i	−0.122822	−	0.0709112i
$747$	14.4721	+	19.9804i	0.529505	+	0.731044i
$748$			11.0501i			0.404033i
$749$		0			0
$750$	−10.7869	−	16.6370i	−0.393883	−	0.607497i
$751$	−2.06865	+	3.58301i	−0.0754861	+	0.130746i	−0.901298	−	0.433201i	$-0.857384\pi$
$751$	−2.06865	+	3.58301i	−0.0754861	+	0.130746i	0.825811	+	0.563946i	$0.190718\pi$
$752$	8.31745			0.303306
$753$	4.74239	−	3.07482i	0.172822	−	0.112053i
$754$			16.4480i			0.599002i
$755$	−30.6929			−1.11703
$756$		0			0
$757$	35.2411			1.28086			0.640430	−	0.768017i	$-0.278756\pi$
$757$	35.2411			1.28086			0.640430	+	0.768017i	$0.278756\pi$
$758$			8.21884i			0.298522i
$759$	7.35061	−	4.76591i	0.266810	−	0.172992i
$760$	−6.04043			−0.219109
$761$	−4.93597	+	8.54935i	−0.178929	+	0.309914i	−0.941514	−	0.336974i	$-0.890596\pi$
$761$	−4.93597	+	8.54935i	−0.178929	+	0.309914i	0.762585	+	0.646888i	$0.223930\pi$
$762$	−12.1625	−	18.7586i	−0.440600	−	0.679551i
$763$		0			0
$764$		−	8.94832i		−	0.323739i
$765$	34.1823	−	3.54224i	1.23586	−	0.128070i
$766$	−26.2428	−	15.1513i	−0.948192	−	0.547439i
$767$	28.6538	−	16.5433i	1.03463	−	0.597343i
$768$	1.45331	−	0.942282i	0.0524417	−	0.0340017i
$769$	−18.6213	+	10.7510i	−0.671503	+	0.387692i	−0.796646	−	0.604446i	$-0.793394\pi$
$769$	−18.6213	+	10.7510i	−0.671503	+	0.387692i	0.125143	+	0.992139i	$0.460061\pi$
$770$		0			0
$771$	−1.76957	−	34.2438i	−0.0637295	−	1.23326i
$772$	−25.6055			−0.921564
$773$	3.69775	−	6.40468i	0.132999	−	0.230360i	−0.791832	−	0.610738i	$-0.790873\pi$
$773$	3.69775	−	6.40468i	0.132999	−	0.230360i	0.924831	+	0.380378i	$0.124206\pi$
$774$	−29.2282	+	21.1704i	−1.05059	+	0.760955i
$775$	2.30404	−	1.33024i	0.0827637	−	0.0477836i
$776$	−6.33179	+	10.9670i	−0.227298	+	0.393691i
$777$		0			0
$778$	−10.5281	−	18.2352i	−0.377451	−	0.653764i
$779$	−2.48184	−	1.43289i	−0.0889211	−	0.0513386i
$780$	−4.78485	−	7.37981i	−0.171325	−	0.264239i
$781$	−9.04610	−	15.6683i	−0.323695	−	0.560656i
$782$	14.3031	+	24.7737i	0.511477	+	0.885904i
$783$	8.78974	−	22.7490i	0.314120	−	0.812983i
$784$		0			0
$785$	−18.8599	−	10.8888i	−0.673139	−	0.388637i
$786$	−14.2827	+	0.738068i	−0.509447	+	0.0263260i
$787$			17.8154i			0.635049i	0.948250	+	0.317524i	$0.102852\pi$
$787$			17.8154i			0.635049i	−0.948250	+	0.317524i	$0.897148\pi$
$788$			23.5602i			0.839299i
$789$	13.8734	−	27.1791i	0.493908	−	0.967601i
$790$	−19.6189	−	11.3269i	−0.698007	−	0.402995i
$791$		0			0
$792$	−4.17099	+	0.432231i	−0.148210	+	0.0153587i
$793$	−17.2762	−	29.9232i	−0.613495	−	1.06260i
$794$	−0.298214	−	0.516521i	−0.0105832	−	0.0183307i
$795$	6.80087	−	13.3234i	0.241202	−	0.472532i
$796$	11.7989	+	6.81212i	0.418202	+	0.241449i
$797$	−27.0403	−	46.8351i	−0.957815	−	1.65898i	−0.727790	−	0.685800i	$-0.759452\pi$
$797$	−27.0403	−	46.8351i	−0.957815	−	1.65898i	−0.230025	−	0.973185i	$-0.573881\pi$
$798$		0			0
$799$	32.8769	−	56.9445i	1.16310	−	2.01455i
$800$	−2.51182	+	1.45020i	−0.0888063	+	0.0512724i
$801$	−3.18346	+	0.329895i	−0.112482	+	0.0116563i
$802$	−1.16807	+	2.02316i	−0.0412462	+	0.0714404i
$803$	−15.8023			−0.557651
$804$	4.31748	−	2.79932i	0.152266	−	0.0987245i
$805$		0			0
$806$	2.78389	−	1.60728i	0.0980582	−	0.0566140i
$807$	0.685895	+	13.2731i	0.0241447	+	0.467235i
$808$	−15.2027	+	8.77726i	−0.534827	+	0.308783i
$809$	−36.0795	−	20.8305i	−1.26849	−	0.732363i	−0.293787	−	0.955871i	$-0.594916\pi$
$809$	−36.0795	−	20.8305i	−1.26849	−	0.732363i	−0.974702	+	0.223508i	$0.928249\pi$
$810$	2.67411	+	12.7639i	0.0939586	+	0.448477i
$811$		−	24.8645i		−	0.873111i	−0.899677	−	0.436556i	$-0.856198\pi$
$811$		−	24.8645i		−	0.873111i	0.899677	−	0.436556i	$-0.143802\pi$
$812$		0			0
$813$	−5.53885	+	10.8510i	−0.194256	+	0.380562i
$814$	−2.99369	+	5.18523i	−0.104929	+	0.181742i
$815$	−4.39811			−0.154059
$816$	−0.706641	−	13.6745i	−0.0247374	−	0.478705i
$817$		−	50.1491i		−	1.75450i
$818$	9.64564			0.337252
$819$		0			0
$820$	0.996120			0.0347860
$821$			34.5967i			1.20743i	0.797199	+	0.603716i	$0.206314\pi$
$821$			34.5967i			1.20743i	−0.797199	+	0.603716i	$0.793686\pi$
$822$	−20.1768	−	10.2991i	−0.703745	−	0.359224i
$823$	15.7623			0.549438			0.274719	−	0.961525i	$-0.411415\pi$
$823$	15.7623			0.549438			0.274719	+	0.961525i	$0.411415\pi$
$824$	2.22905	−	3.86082i	0.0776526	−	0.134498i
$825$	7.01256	−	0.362379i	0.244146	−	0.0126164i
$826$		0			0
$827$		−	17.6523i		−	0.613830i	−0.951737	−	0.306915i	$-0.900703\pi$
$827$		−	17.6523i		−	0.613830i	0.951737	−	0.306915i	$-0.0992967\pi$
$828$	−8.79159	+	6.36787i	−0.305529	+	0.221299i
$829$	32.6295	+	18.8387i	1.13327	+	0.654294i	0.944756	−	0.327776i	$-0.106299\pi$
$829$	32.6295	+	18.8387i	1.13327	+	0.654294i	0.188516	+	0.982070i	$0.439632\pi$
$830$	10.3196	−	5.95803i	0.358199	−	0.206806i
$831$	−26.6998	−	13.6288i	−0.926207	−	0.472778i
$832$	−3.03494	+	1.75222i	−0.105218	+	0.0607474i
$833$		0			0
$834$	−19.0110	−	9.70407i	−0.658296	−	0.336024i
$835$	−8.86484			−0.306781
$836$	2.91344	−	5.04623i	0.100763	−	0.174527i
$837$	−4.70927	+	0.735304i	−0.162776	+	0.0254158i
$838$	−24.9930	+	14.4297i	−0.863370	+	0.498467i
$839$	−10.5777	+	18.3211i	−0.365183	+	0.632516i	−0.988806	−	0.149210i	$-0.952327\pi$
$839$	−10.5777	+	18.3211i	−0.365183	+	0.632516i	0.623622	+	0.781726i	$0.285660\pi$
$840$		0			0
$841$	−3.48563	−	6.03728i	−0.120194	−	0.208182i
$842$	10.6464	+	6.14672i	0.366900	+	0.211830i
$843$	28.5929	−	1.47756i	0.984793	−	0.0508898i
$844$	10.7961	+	18.6994i	0.371617	+	0.643660i
$845$	−0.520818	−	0.902084i	−0.0179167	−	0.0310326i
$846$	22.7802	+	10.1823i	0.783201	+	0.350075i
$847$		0			0
$848$	−5.16176	−	2.98014i	−0.177256	−	0.102339i
$849$	2.98029	+	4.59658i	0.102283	+	0.157754i
$850$			22.9292i			0.786466i
$851$			15.4999i			0.531329i
$852$	12.1965	+	18.8110i	0.417845	+	0.644455i
$853$	34.7061	+	20.0376i	1.18831	+	0.686073i	0.957923	−	0.287026i	$-0.0926665\pi$
$853$	34.7061	+	20.0376i	1.18831	+	0.686073i	0.230390	+	0.973098i	$0.426000\pi$
$854$		0			0
$855$	−16.5438	−	7.39475i	−0.565787	−	0.252895i
$856$	1.18106	+	2.04566i	0.0403679	+	0.0699193i
$857$	−3.73018	−	6.46087i	−0.127421	−	0.220699i	0.795256	−	0.606274i	$-0.207336\pi$
$857$	−3.73018	−	6.46087i	−0.127421	−	0.220699i	−0.922677	+	0.385575i	$0.874003\pi$
$858$	8.47301	−	0.437848i	0.289264	−	0.0149479i
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.995213	−	0.0977257i	$-0.0311568\pi$
$859$	41.2721	+	23.8285i	1.40819	+	0.813017i	0.412974	+	0.910743i	$0.364490\pi$
$860$	8.71569	+	15.0960i	0.297203	+	0.514770i
$861$		0			0
$862$	−13.8815	+	24.0435i	−0.472807	+	0.818926i
$863$	37.1822	−	21.4671i	1.26570	−	0.730750i	0.291525	−	0.956563i	$-0.405837\pi$
$863$	37.1822	−	21.4671i	1.26570	−	0.730750i	0.974171	+	0.225813i	$0.0725039\pi$
$864$	5.13395	−	0.801614i	0.174660	−	0.0272715i
$865$	1.66283	−	2.88011i	0.0565380	−	0.0979267i
$866$	21.3927			0.726955
$867$	−70.1886	−	35.8275i	−2.38373	−	1.21676i
$868$		0			0
$869$	18.9253	−	10.9265i	0.641996	−	0.370657i
$870$	−10.4916	−	5.35540i	−0.355699	−	0.181565i
$871$	−9.01617	+	5.20549i	−0.305501	+	0.176381i
$872$	11.2545	+	6.49776i	0.381124	+	0.220042i
$873$	−30.7677	+	22.2855i	−1.04133	+	0.754249i
$874$		−	15.0844i		−	0.510237i
$875$		0			0
$876$	19.5553	−	1.01053i	0.660713	−	0.0341428i
$877$	−13.0702	+	22.6382i	−0.441349	+	0.764438i	−0.997790	−	0.0664486i	$-0.978833\pi$
$877$	−13.0702	+	22.6382i	−0.441349	+	0.764438i	0.556441	+	0.830887i	$0.312166\pi$
$878$	−2.63916			−0.0890674
$879$	13.1451	+	6.70988i	0.443375	+	0.226319i
$880$			2.02537i			0.0682753i
$881$	−11.2385			−0.378636			−0.189318	−	0.981916i	$-0.560628\pi$
$881$	−11.2385			−0.378636			−0.189318	+	0.981916i	$0.560628\pi$
$882$		0			0
$883$	−0.253239			−0.00852217			−0.00426108	−	0.999991i	$-0.501356\pi$
$883$	−0.253239			−0.00852217			−0.00426108	+	0.999991i	$0.501356\pi$
$884$			27.7045i			0.931803i
$885$	1.22283	+	23.6636i	0.0411051	+	0.795445i
$886$	12.1750			0.409027
$887$	−2.86053	+	4.95458i	−0.0960472	+	0.166359i	−0.910045	−	0.414509i	$-0.863953\pi$
$887$	−2.86053	+	4.95458i	−0.0960472	+	0.166359i	0.813998	+	0.580868i	$0.197287\pi$
$888$	3.37310	−	6.60815i	0.113194	−	0.221755i
$889$		0			0
$890$			1.54584i			0.0518167i
$891$	−11.9529	−	3.92235i	−0.400436	−	0.131404i
$892$	14.5710	+	8.41256i	0.487872	+	0.281673i
$893$	−30.0276	+	17.3364i	−1.00483	+	0.580141i
$894$	0.0556003	+	1.07595i	0.00185955	+	0.0359851i
$895$	4.23635	−	2.44586i	0.141605	−	0.0817559i
$896$		0			0
$897$	18.4292	−	11.9489i	0.615332	−	0.398963i
$898$	−14.2454			−0.475376
$899$	2.15262	−	3.72844i	0.0717938	−	0.124350i
$900$	−8.65486	+	0.896887i	−0.288495	+	0.0298962i
$901$	−40.8065	+	23.5596i	−1.35946	+	0.784885i
$902$	−0.480452	+	0.832168i	−0.0159973	+	0.0277082i
$903$		0			0
$904$	−1.67787	−	2.90616i	−0.0558052	−	0.0966574i
$905$	−2.11894	−	1.22337i	−0.0704359	−	0.0406662i
$906$	−16.6801	+	32.6776i	−0.554160	+	1.08564i
$907$	−11.8731	−	20.5648i	−0.394241	−	0.682845i	0.598763	−	0.800926i	$-0.295659\pi$
$907$	−11.8731	−	20.5648i	−0.394241	−	0.682845i	−0.993004	+	0.118081i	$0.962326\pi$
$908$	−6.11065	−	10.5840i	−0.202789	−	0.351241i
$909$	−52.3830	+	5.42835i	−1.73744	+	0.180047i
$910$		0			0
$911$	17.0673	+	9.85384i	0.565466	+	0.326472i	0.755337	−	0.655337i	$-0.227473\pi$
$911$	17.0673	+	9.85384i	0.565466	+	0.326472i	−0.189870	+	0.981809i	$0.560807\pi$
$912$	−3.28268	+	6.43101i	−0.108700	+	0.212952i
$913$			11.4948i			0.380423i
$914$		−	11.5631i		−	0.382474i
$915$	24.7120	−	1.27701i	0.816953	−	0.0422166i
$916$	−16.8458	−	9.72591i	−0.556600	−	0.321353i
$917$		0			0
$918$	14.8051	−	38.3176i	0.488642	−	1.26467i
$919$	27.3077	+	47.2983i	0.900797	+	1.56023i	0.826461	+	0.562994i	$0.190350\pi$
$919$	27.3077	+	47.2983i	0.900797	+	1.56023i	0.0743361	+	0.997233i	$0.476316\pi$
$920$	2.62160	+	4.54074i	0.0864316	+	0.149704i
$921$	23.6329	+	36.4497i	0.778731	+	1.20106i
$922$	−19.0597	−	11.0041i	−0.627698	−	0.362401i
$923$	−22.6800	−	39.2830i	−0.746523	−	1.29302i
$924$		0			0
$925$	−6.21196	+	10.7594i	−0.204248	+	0.353768i
$926$	−11.2213	+	6.47862i	−0.368755	+	0.212901i
$927$	10.8315	−	7.84540i	0.355753	−	0.257677i
$928$	−2.34674	+	4.06467i	−0.0770355	+	0.133429i
$929$	−22.7720			−0.747124			−0.373562	−	0.927605i	$-0.621864\pi$
$929$	−22.7720			−0.747124			−0.373562	+	0.927605i	$0.621864\pi$
$930$	0.118806	+	2.29907i	0.00389579	+	0.0753893i
$931$		0			0
$932$	24.7381	−	14.2825i	0.810323	−	0.467840i
$933$	−5.19347	+	3.36729i	−0.170027	+	0.110240i
$934$	2.46895	−	1.42545i	0.0807865	−	0.0466421i
$935$	13.8665	+	8.00582i	0.453483	+	0.261818i
$936$	−10.4573	+	1.08367i	−0.341809	+	0.0354210i
$937$			19.4429i			0.635173i	0.948229	+	0.317587i	$0.102872\pi$
$937$			19.4429i			0.635173i	−0.948229	+	0.317587i	$0.897128\pi$
$938$		0			0
$939$	12.8426	+	19.8075i	0.419103	+	0.646395i
$940$	6.02598	−	10.4373i	0.196546	−	0.340428i
$941$	19.4602			0.634383			0.317192	−	0.948361i	$-0.397260\pi$
$941$	19.4602			0.634383			0.317192	+	0.948361i	$0.397260\pi$
$942$	−21.8423	+	14.1619i	−0.711661	+	0.461420i
$943$			2.48755i			0.0810058i
$944$	9.44130			0.307288
$945$		0			0
$946$	−16.8151			−0.546707
$947$		−	30.2570i		−	0.983221i	−0.870815	−	0.491611i	$-0.836408\pi$
$947$		−	30.2570i		−	0.983221i	0.870815	−	0.491611i	$-0.163592\pi$
$948$	−22.7213	+	14.7318i	−0.737953	+	0.478466i
$949$	−39.6189			−1.28608
$950$	6.04544	−	10.4710i	0.196140	−	0.339724i
$951$	−4.04234	−	6.23461i	−0.131082	−	0.202171i
$952$		0			0
$953$			21.4885i			0.696082i	0.937479	+	0.348041i	$0.113153\pi$
$953$			21.4885i			0.696082i	−0.937479	+	0.348041i	$0.886847\pi$
$954$	−10.4890	−	14.4813i	−0.339593	−	0.468848i
$955$	−11.2290	−	6.48305i	−0.363361	−	0.209787i
$956$	10.0020	−	5.77465i	0.323487	−	0.186765i
$957$	9.53432	−	6.18176i	0.308201	−	0.199828i
$958$	−28.8130	+	16.6352i	−0.930906	+	0.537459i
$959$		0			0
$960$	−0.129520	−	2.50640i	−0.00418023	−	0.0808936i
$961$	30.1586			0.972858
$962$	−7.50567	+	13.0002i	−0.241992	+	0.419143i
$963$	0.730437	+	7.04864i	0.0235380	+	0.227139i
$964$	−0.0299000	+	0.0172628i	−0.000963015	+	0.000555997i
$965$	−18.5512	+	32.1316i	−0.597184	+	1.03435i
$966$		0			0
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	0.689951	−	0.723856i	$-0.257632\pi$
$967$	−8.76620	−	15.1835i	−0.281902	−	0.488268i	−0.971853	+	0.235587i	$0.924299\pi$
$968$	7.83426	+	4.52311i	0.251803	+	0.145378i
$969$	31.0536	+	47.8948i	0.997584	+	1.53860i
$970$	9.17475	+	15.8911i	0.294583	+	0.510234i
$971$	12.9458	+	22.4228i	0.415451	+	0.719582i	0.995476	−	0.0950171i	$-0.0302906\pi$
$971$	12.9458	+	22.4228i	0.415451	+	0.719582i	−0.580025	+	0.814599i	$0.696957\pi$
$972$	15.0425	+	4.08953i	0.482487	+	0.131172i
$973$		0			0
$974$	9.04997	+	5.22500i	0.289980	+	0.167420i
$975$	17.5816	−	0.908542i	0.563063	−	0.0290966i
$976$		−	9.85957i		−	0.315597i
$977$		−	54.4135i		−	1.74084i	−0.492308	−	0.870421i	$-0.663846\pi$
$977$		−	54.4135i		−	1.74084i	0.492308	−	0.870421i	$-0.336154\pi$
$978$	−2.39016	+	4.68250i	−0.0764289	+	0.149730i
$979$	−1.29141	−	0.745597i	−0.0412737	−	0.0238294i
$980$		0			0
$981$	22.8696	+	31.5742i	0.730172	+	1.00809i
$982$	1.17436	+	2.03404i	0.0374752	+	0.0649090i
$983$	−23.8665	−	41.3379i	−0.761222	−	1.31847i	−0.942221	−	0.334991i	$-0.891267\pi$
$983$	−23.8665	−	41.3379i	−0.761222	−	1.31847i	0.181000	−	0.983483i	$-0.442067\pi$
$984$	0.541343	−	1.06053i	0.0172574	−	0.0338085i
$985$	29.5650	+	17.0694i	0.942020	+	0.543876i
$986$	18.5522	+	32.1334i	0.590823	+	1.02334i
$987$		0			0
$988$	7.30447	−	12.6517i	0.232386	−	0.402505i
$989$	−37.6984	+	21.7652i	−1.19874	+	0.692092i
$990$	−2.47948	+	5.54719i	−0.0788031	+	0.176301i
$991$	−1.89016	+	3.27386i	−0.0600430	+	0.103997i	−0.894484	−	0.447099i	$-0.852457\pi$
$991$	−1.89016	+	3.27386i	−0.0600430	+	0.103997i	0.834441	+	0.551097i	$0.185790\pi$
$992$	0.917280			0.0291237
$993$	12.9915	−	8.42327i	0.412271	−	0.267304i
$994$		0			0
$995$	17.0966	−	9.87075i	0.542000	−	0.312924i
$996$	−0.735076	−	14.2248i	−0.0232918	−	0.450730i
$997$	2.58264	−	1.49109i	0.0817931	−	0.0472233i	−0.458546	−	0.888671i	$-0.651629\pi$
$997$	2.58264	−	1.49109i	0.0817931	−	0.0472233i	0.540339	+	0.841448i	$0.318296\pi$
$998$	−30.1195	−	17.3895i	−0.953417	−	0.550456i
$999$	17.3282	−	13.9694i	0.548240	−	0.441971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.21		48
3.2	odd	2		2646.2.l.c.521.10		48
7.2	even	3		882.2.t.c.803.19		48
7.3	odd	6		882.2.m.c.587.11	yes	48
7.4	even	3		882.2.m.c.587.2	yes	48
7.5	odd	6		882.2.t.c.803.18		48
7.6	odd	2	inner	882.2.l.c.227.16		48
9.4	even	3		2646.2.t.c.2285.2		48
9.5	odd	6		882.2.t.c.815.18		48
21.2	odd	6		2646.2.t.c.1979.1		48
21.5	even	6		2646.2.t.c.1979.2		48
21.11	odd	6		2646.2.m.c.1763.22		48
21.17	even	6		2646.2.m.c.1763.21		48
21.20	even	2		2646.2.l.c.521.9		48
63.4	even	3		2646.2.m.c.881.21		48
63.5	even	6	inner	882.2.l.c.509.9		48
63.13	odd	6		2646.2.t.c.2285.1		48
63.23	odd	6	inner	882.2.l.c.509.4		48
63.31	odd	6		2646.2.m.c.881.22		48
63.32	odd	6		882.2.m.c.293.11	yes	48
63.40	odd	6		2646.2.l.c.1097.10		48
63.41	even	6		882.2.t.c.815.19		48
63.58	even	3		2646.2.l.c.1097.9		48
63.59	even	6		882.2.m.c.293.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.16		48	7.6	odd	2	inner
882.2.l.c.227.21		48	1.1	even	1	trivial
882.2.l.c.509.4		48	63.23	odd	6	inner
882.2.l.c.509.9		48	63.5	even	6	inner
882.2.m.c.293.2	✓	48	63.59	even	6
882.2.m.c.293.11	yes	48	63.32	odd	6
882.2.m.c.587.2	yes	48	7.4	even	3
882.2.m.c.587.11	yes	48	7.3	odd	6
882.2.t.c.803.18		48	7.5	odd	6
882.2.t.c.803.19		48	7.2	even	3
882.2.t.c.815.18		48	9.5	odd	6
882.2.t.c.815.19		48	63.41	even	6
2646.2.l.c.521.9		48	21.20	even	2
2646.2.l.c.521.10		48	3.2	odd	2
2646.2.l.c.1097.9		48	63.58	even	3
2646.2.l.c.1097.10		48	63.40	odd	6
2646.2.m.c.881.21		48	63.4	even	3
2646.2.m.c.881.22		48	63.31	odd	6
2646.2.m.c.1763.21		48	21.17	even	6
2646.2.m.c.1763.22		48	21.11	odd	6
2646.2.t.c.1979.1		48	21.2	odd	6
2646.2.t.c.1979.2		48	21.5	even	6
2646.2.t.c.2285.1		48	63.13	odd	6
2646.2.t.c.2285.2		48	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.45331 - 0.942282i) q^{3} -1.00000 q^{4} +(-0.724499 + 1.25487i) q^{5} +(0.942282 + 1.45331i) q^{6} -1.00000i q^{8} +(1.22421 - 2.73885i) q^{9} +(-1.25487 - 0.724499i) q^{10} +(1.21051 - 0.698887i) q^{11} +(-1.45331 + 0.942282i) q^{12} +(3.03494 - 1.75222i) q^{13} +(0.129520 + 2.50640i) q^{15} +1.00000 q^{16} +(3.95277 - 6.84639i) q^{17} +(2.73885 + 1.22421i) q^{18} +(-3.61019 + 2.08434i) q^{19} +(0.724499 - 1.25487i) q^{20} +(0.698887 + 1.21051i) q^{22} +(3.13371 + 1.80925i) q^{23} +(-0.942282 - 1.45331i) q^{24} +(1.45020 + 2.51182i) q^{25} +(1.75222 + 3.03494i) q^{26} +(-0.801614 - 5.13395i) q^{27} +(4.06467 + 2.34674i) q^{29} +(-2.50640 + 0.129520i) q^{30} -0.917280i q^{31} +1.00000i q^{32} +(1.10069 - 2.15634i) q^{33} +(6.84639 + 3.95277i) q^{34} +(-1.22421 + 2.73885i) q^{36} +(2.14176 + 3.70963i) q^{37} +(-2.08434 - 3.61019i) q^{38} +(2.75961 - 5.40629i) q^{39} +(1.25487 + 0.724499i) q^{40} +(0.343727 + 0.595352i) q^{41} +(-6.01497 + 10.4182i) q^{43} +(-1.21051 + 0.698887i) q^{44} +(2.54996 + 3.52052i) q^{45} +(-1.80925 + 3.13371i) q^{46} +8.31745 q^{47} +(1.45331 - 0.942282i) q^{48} +(-2.51182 + 1.45020i) q^{50} +(-0.706641 - 13.6745i) q^{51} +(-3.03494 + 1.75222i) q^{52} +(-5.16176 - 2.98014i) q^{53} +(5.13395 - 0.801614i) q^{54} +2.02537i q^{55} +(-3.28268 + 6.43101i) q^{57} +(-2.34674 + 4.06467i) q^{58} +9.44130 q^{59} +(-0.129520 - 2.50640i) q^{60} -9.85957i q^{61} +0.917280 q^{62} -1.00000 q^{64} +5.07794i q^{65} +(2.15634 + 1.10069i) q^{66} -2.97079 q^{67} +(-3.95277 + 6.84639i) q^{68} +(6.25907 - 0.323442i) q^{69} -12.9436i q^{71} +(-2.73885 - 1.22421i) q^{72} +(-9.79071 - 5.65267i) q^{73} +(-3.70963 + 2.14176i) q^{74} +(4.47443 + 2.28395i) q^{75} +(3.61019 - 2.08434i) q^{76} +(5.40629 + 2.75961i) q^{78} +15.6342 q^{79} +(-0.724499 + 1.25487i) q^{80} +(-6.00262 - 6.70586i) q^{81} +(-0.595352 + 0.343727i) q^{82} +(-4.11183 + 7.12189i) q^{83} +(5.72755 + 9.92041i) q^{85} +(-10.4182 - 6.01497i) q^{86} +(8.11851 - 0.419530i) q^{87} +(-0.698887 - 1.21051i) q^{88} +(-0.533417 - 0.923906i) q^{89} +(-3.52052 + 2.54996i) q^{90} +(-3.13371 - 1.80925i) q^{92} +(-0.864336 - 1.33309i) q^{93} +8.31745i q^{94} -6.04043i q^{95} +(0.942282 + 1.45331i) q^{96} +(-10.9670 - 6.33179i) q^{97} +(-0.432231 - 4.17099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

L-functions

Modular forms

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