LMFDB - Embedded newform 441.2.s.d.362.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (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:	$3.52140272914$
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			362.19
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28562 - 0.742253i) q^{2} +(-1.72526 + 0.153190i) q^{3} +(0.101880 - 0.176462i) q^{4} -0.308431 q^{5} +(-2.10433 + 1.47753i) q^{6} +2.66653i q^{8} +(2.95307 - 0.528586i) q^{9} +O(q^{10})$	\(q+(1.28562 - 0.742253i) q^{2} +(-1.72526 + 0.153190i) q^{3} +(0.101880 - 0.176462i) q^{4} -0.308431 q^{5} +(-2.10433 + 1.47753i) q^{6} +2.66653i q^{8} +(2.95307 - 0.528586i) q^{9} +(-0.396525 + 0.228934i) q^{10} +3.16248i q^{11} +(-0.148738 + 0.320050i) q^{12} +(-3.00394 + 1.73432i) q^{13} +(0.532124 - 0.0472485i) q^{15} +(2.18300 + 3.78107i) q^{16} +(2.44124 + 4.22836i) q^{17} +(3.40418 - 2.87148i) q^{18} +(4.62558 + 2.67058i) q^{19} +(-0.0314230 + 0.0544262i) q^{20} +(2.34736 + 4.06575i) q^{22} -5.97291i q^{23} +(-0.408486 - 4.60047i) q^{24} -4.90487 q^{25} +(-2.57462 + 4.45937i) q^{26} +(-5.01384 + 1.36433i) q^{27} +(2.70372 + 1.56099i) q^{29} +(0.649039 - 0.455715i) q^{30} +(6.51414 + 3.76094i) q^{31} +(0.994457 + 0.574150i) q^{32} +(-0.484460 - 5.45611i) q^{33} +(6.27702 + 3.62404i) q^{34} +(0.207584 - 0.574955i) q^{36} +(-5.92568 + 10.2636i) q^{37} +7.92899 q^{38} +(4.91690 - 3.45234i) q^{39} -0.822440i q^{40} +(-2.58920 - 4.48462i) q^{41} +(2.75159 - 4.76589i) q^{43} +(0.558056 + 0.322194i) q^{44} +(-0.910816 + 0.163032i) q^{45} +(-4.43341 - 7.67889i) q^{46} +(-4.23198 - 7.33000i) q^{47} +(-4.34547 - 6.18892i) q^{48} +(-6.30580 + 3.64066i) q^{50} +(-4.85953 - 6.92105i) q^{51} +0.706773i q^{52} +(-0.0740521 + 0.0427540i) q^{53} +(-5.43322 + 5.47555i) q^{54} -0.975406i q^{55} +(-8.38945 - 3.89886i) q^{57} +4.63461 q^{58} +(1.04433 - 1.80884i) q^{59} +(0.0458754 - 0.0987132i) q^{60} +(4.69964 - 2.71334i) q^{61} +11.1663 q^{62} -7.02734 q^{64} +(0.926507 - 0.534919i) q^{65} +(-4.67265 - 6.65489i) q^{66} +(0.0554134 - 0.0959787i) q^{67} +0.994857 q^{68} +(0.914990 + 10.3048i) q^{69} -7.78899i q^{71} +(1.40949 + 7.87444i) q^{72} +(-8.32679 + 4.80748i) q^{73} +17.5934i q^{74} +(8.46219 - 0.751378i) q^{75} +(0.942510 - 0.544159i) q^{76} +(3.75876 - 8.08799i) q^{78} +(-2.56825 - 4.44834i) q^{79} +(-0.673305 - 1.16620i) q^{80} +(8.44119 - 3.12190i) q^{81} +(-6.65745 - 3.84368i) q^{82} +(4.42464 - 7.66370i) q^{83} +(-0.752954 - 1.30416i) q^{85} -8.16950i q^{86} +(-4.90376 - 2.27894i) q^{87} -8.43284 q^{88} +(0.936885 - 1.62273i) q^{89} +(-1.04995 + 0.885654i) q^{90} +(-1.05399 - 0.608521i) q^{92} +(-11.8147 - 5.49071i) q^{93} +(-10.8814 - 6.28240i) q^{94} +(-1.42667 - 0.823689i) q^{95} +(-1.80365 - 0.838219i) q^{96} +(10.9813 + 6.34007i) q^{97} +(1.67164 + 9.33900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.28562	−	0.742253i	0.909071	−	0.524852i	0.0289389	−	0.999581i	$-0.490787\pi$
$2$	1.28562	−	0.742253i	0.909071	−	0.524852i	0.880132	+	0.474729i	$0.157454\pi$
$3$	−1.72526	+	0.153190i	−0.996081	+	0.0884443i
$3$	−1.72526	+	0.153190i	−0.996081	+	0.0884443i
$4$	0.101880	−	0.176462i	0.0509401	−	0.0882308i
$5$	−0.308431			−0.137934			−0.0689672	−	0.997619i	$-0.521970\pi$
$5$	−0.308431			−0.137934			−0.0689672	+	0.997619i	$0.521970\pi$
$6$	−2.10433	+	1.47753i	−0.859088	+	0.603198i
$7$		0			0
$7$		0			0
$8$			2.66653i			0.942761i
$9$	2.95307	−	0.528586i	0.984355	−	0.176195i
$10$	−0.396525	+	0.228934i	−0.125392	+	0.0723952i
$11$			3.16248i			0.953523i	0.879033	+	0.476761i	$0.158189\pi$
$11$			3.16248i			0.953523i	−0.879033	+	0.476761i	$0.841811\pi$
$12$	−0.148738	+	0.320050i	−0.0429370	+	0.0923904i
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	−0.854927	−	0.518748i	$-0.826398\pi$
$13$	−3.00394	+	1.73432i	−0.833143	+	0.481015i	0.0217849	+	0.999763i	$0.493065\pi$
$14$		0			0
$15$	0.532124	−	0.0472485i	0.137394	−	0.0121995i
$16$	2.18300	+	3.78107i	0.545750	+	0.945267i
$17$	2.44124	+	4.22836i	0.592088	+	1.02553i	0.993951	+	0.109827i	$0.0350297\pi$
$17$	2.44124	+	4.22836i	0.592088	+	1.02553i	−0.401862	+	0.915700i	$0.631637\pi$
$18$	3.40418	−	2.87148i	0.802372	−	0.676815i
$19$	4.62558	+	2.67058i	1.06118	+	0.612673i	0.925759	−	0.378115i	$-0.123428\pi$
$19$	4.62558	+	2.67058i	1.06118	+	0.612673i	0.135422	+	0.990788i	$0.456761\pi$
$20$	−0.0314230	+	0.0544262i	−0.00702639	+	0.0121701i
$21$		0			0
$22$	2.34736	+	4.06575i	0.500459	+	0.866820i
$23$		−	5.97291i		−	1.24544i	−0.782446	−	0.622719i	$-0.786028\pi$
$23$		−	5.97291i		−	1.24544i	0.782446	−	0.622719i	$-0.213972\pi$
$24$	−0.408486	−	4.60047i	−0.0833818	−	0.939066i
$25$	−4.90487			−0.980974
$26$	−2.57462	+	4.45937i	−0.504924	+	0.874554i
$27$	−5.01384	+	1.36433i	−0.964914	+	0.262566i
$28$		0			0
$29$	2.70372	+	1.56099i	0.502069	+	0.289869i	0.729567	−	0.683909i	$-0.239721\pi$
$29$	2.70372	+	1.56099i	0.502069	+	0.289869i	−0.227499	+	0.973778i	$0.573055\pi$
$30$	0.649039	−	0.455715i	0.118498	−	0.0832017i
$31$	6.51414	+	3.76094i	1.16997	+	0.675485i	0.953674	−	0.300842i	$-0.0972678\pi$
$31$	6.51414	+	3.76094i	1.16997	+	0.675485i	0.216300	+	0.976327i	$0.430601\pi$
$32$	0.994457	+	0.574150i	0.175797	+	0.101496i
$33$	−0.484460	−	5.45611i	−0.0843337	−	0.949786i
$34$	6.27702	+	3.62404i	1.07650	+	0.621518i
$35$		0			0
$36$	0.207584	−	0.574955i	0.0345973	−	0.0958259i
$37$	−5.92568	+	10.2636i	−0.974176	+	1.68732i	−0.291550	+	0.956556i	$0.594171\pi$
$37$	−5.92568	+	10.2636i	−0.974176	+	1.68732i	−0.682626	+	0.730768i	$0.739162\pi$
$38$	7.92899			1.28625
$39$	4.91690	−	3.45234i	0.787335	−	0.552817i
$40$		−	0.822440i		−	0.130039i
$41$	−2.58920	−	4.48462i	−0.404365	−	0.700380i	0.589883	−	0.807489i	$-0.299174\pi$
$41$	−2.58920	−	4.48462i	−0.404365	−	0.700380i	−0.994247	+	0.107109i	$0.965841\pi$
$42$		0			0
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	−0.576287	−	0.817247i	$-0.695499\pi$
$43$	2.75159	−	4.76589i	0.419613	−	0.726792i	0.995900	+	0.0904557i	$0.0288323\pi$
$44$	0.558056	+	0.322194i	0.0841301	+	0.0485726i
$45$	−0.910816	+	0.163032i	−0.135776	+	0.0243034i
$46$	−4.43341	−	7.67889i	−0.653671	−	1.13219i
$47$	−4.23198	−	7.33000i	−0.617298	−	1.06919i	−0.989977	−	0.141231i	$-0.954894\pi$
$47$	−4.23198	−	7.33000i	−0.617298	−	1.06919i	0.372679	−	0.927960i	$-0.378439\pi$
$48$	−4.34547	−	6.18892i	−0.627215	−	0.893294i
$49$		0			0
$50$	−6.30580	+	3.64066i	−0.891775	+	0.514867i
$51$	−4.85953	−	6.92105i	−0.680470	−	0.969141i
$52$			0.706773i			0.0980118i
$53$	−0.0740521	+	0.0427540i	−0.0101718	+	0.00587272i	−0.505077	−	0.863074i	$-0.668536\pi$
$53$	−0.0740521	+	0.0427540i	−0.0101718	+	0.00587272i	0.494905	+	0.868947i	$0.335203\pi$
$54$	−5.43322	+	5.47555i	−0.739367	+	0.745128i
$55$		−	0.975406i		−	0.131524i
$56$		0			0
$57$	−8.38945	−	3.89886i	−1.11121	−	0.516417i
$58$	4.63461			0.608555
$59$	1.04433	−	1.80884i	0.135960	−	0.235490i	−0.790004	−	0.613102i	$-0.789921\pi$
$59$	1.04433	−	1.80884i	0.135960	−	0.235490i	0.925964	+	0.377612i	$0.123255\pi$
$60$	0.0458754	−	0.0987132i	0.00592248	−	0.0127438i
$61$	4.69964	−	2.71334i	0.601727	−	0.347407i	−0.167994	−	0.985788i	$-0.553729\pi$
$61$	4.69964	−	2.71334i	0.601727	−	0.347407i	0.769721	+	0.638381i	$0.220396\pi$
$62$	11.1663			1.41812
$63$		0			0
$64$	−7.02734			−0.878418
$65$	0.926507	−	0.534919i	0.114919	−	0.0663485i
$66$	−4.67265	−	6.65489i	−0.575163	−	0.819160i
$67$	0.0554134	−	0.0959787i	0.00676982	−	0.0117257i	−0.862621	−	0.505851i	$-0.831178\pi$
$67$	0.0554134	−	0.0959787i	0.00676982	−	0.0117257i	0.869390	+	0.494126i	$0.164512\pi$
$68$	0.994857			0.120644
$69$	0.914990	+	10.3048i	0.110152	+	1.24056i
$70$		0			0
$71$		−	7.78899i		−	0.924384i	−0.886780	−	0.462192i	$-0.847063\pi$
$71$		−	7.78899i		−	0.924384i	0.886780	−	0.462192i	$-0.152937\pi$
$72$	1.40949	+	7.87444i	0.166110	+	0.928011i
$73$	−8.32679	+	4.80748i	−0.974577	+	0.562672i	−0.900629	−	0.434590i	$-0.856893\pi$
$73$	−8.32679	+	4.80748i	−0.974577	+	0.562672i	−0.0739487	+	0.997262i	$0.523560\pi$
$74$			17.5934i			2.04520i
$75$	8.46219	−	0.751378i	0.977130	−	0.0867616i
$76$	0.942510	−	0.544159i	0.108113	−	0.0624193i
$77$		0			0
$78$	3.75876	−	8.08799i	0.425596	−	0.915784i
$79$	−2.56825	−	4.44834i	−0.288951	−	0.500477i	0.684609	−	0.728911i	$-0.259973\pi$
$79$	−2.56825	−	4.44834i	−0.288951	−	0.500477i	−0.973560	+	0.228433i	$0.926640\pi$
$80$	−0.673305	−	1.16620i	−0.0752778	−	0.130385i
$81$	8.44119	−	3.12190i	0.937910	−	0.346878i
$82$	−6.65745	−	3.84368i	−0.735193	−	0.424464i
$83$	4.42464	−	7.66370i	0.485667	−	0.841201i	−0.514197	−	0.857672i	$-0.671910\pi$
$83$	4.42464	−	7.66370i	0.485667	−	0.841201i	0.999864	+	0.0164715i	$0.00524328\pi$
$84$		0			0
$85$	−0.752954	−	1.30416i	−0.0816694	−	0.141455i
$86$		−	8.16950i		−	0.880940i
$87$	−4.90376	−	2.27894i	−0.525738	−	0.244328i
$88$	−8.43284			−0.898944
$89$	0.936885	−	1.62273i	0.0993096	−	0.172009i	−0.812089	−	0.583533i	$-0.801670\pi$
$89$	0.936885	−	1.62273i	0.0993096	−	0.172009i	0.911399	+	0.411524i	$0.135003\pi$
$90$	−1.04995	+	0.885654i	−0.110675	+	0.0933562i
$91$		0			0
$92$	−1.05399	−	0.608521i	−0.109886	−	0.0634427i
$93$	−11.8147	−	5.49071i	−1.22513	−	0.569360i
$94$	−10.8814	−	6.28240i	−1.12233	−	0.647980i
$95$	−1.42667	−	0.823689i	−0.146373	−	0.0845087i
$96$	−1.80365	−	0.838219i	−0.184085	−	0.0855504i
$97$	10.9813	+	6.34007i	1.11498	+	0.643736i	0.940116	−	0.340855i	$-0.110717\pi$
$97$	10.9813	+	6.34007i	1.11498	+	0.643736i	0.174868	+	0.984592i	$0.444050\pi$
$98$		0			0
$99$	1.67164	+	9.33900i	0.168006	+	0.938605i
$100$	−0.499709	+	0.865522i	−0.0499709	+	0.0865522i
$101$	−7.36643			−0.732988			−0.366494	−	0.930421i	$-0.619442\pi$
$101$	−7.36643			−0.732988			−0.366494	+	0.930421i	$0.619442\pi$
$102$	−11.3847	−	5.29085i	−1.12725	−	0.523872i
$103$			7.98037i			0.786329i	0.919468	+	0.393165i	$0.128620\pi$
$103$			7.98037i			0.786329i	−0.919468	+	0.393165i	$0.871380\pi$
$104$	−4.62463	−	8.01009i	−0.453482	−	0.785454i
$105$		0			0
$106$	−0.0634686	+	0.109931i	−0.00616462	+	0.0106774i
$107$	14.5228	+	8.38472i	1.40397	+	0.810582i	0.994797	−	0.101876i	$-0.0324844\pi$
$107$	14.5228	+	8.38472i	1.40397	+	0.810582i	0.409172	+	0.912457i	$0.365818\pi$
$108$	−0.270059	+	1.02375i	−0.0259864	+	0.0985103i
$109$	4.43255	+	7.67740i	0.424561	+	0.735361i	0.996379	−	0.0850190i	$-0.0270951\pi$
$109$	4.43255	+	7.67740i	0.424561	+	0.735361i	−0.571818	+	0.820380i	$0.693762\pi$
$110$	−0.723998	−	1.25400i	−0.0690305	−	0.119564i
$111$	8.65108	−	18.6151i	0.821125	−	1.76687i
$112$		0			0
$113$	13.5621	−	7.83007i	1.27581	−	0.736591i	0.299738	−	0.954022i	$-0.403101\pi$
$113$	13.5621	−	7.83007i	1.27581	−	0.736591i	0.976076	+	0.217430i	$0.0697674\pi$
$114$	−13.6796	+	1.21464i	−1.28121	+	0.113762i
$115$			1.84223i			0.171789i
$116$	0.550911	−	0.318069i	0.0511508	−	0.0295320i
$117$	−7.95409	+	6.70942i	−0.735356	+	0.620286i
$118$		−	3.10063i		−	0.285437i
$119$		0			0
$120$	0.125990	+	1.41893i	0.0115012	+	0.129530i
$121$	0.998733			0.0907939
$122$	4.02797	−	6.97664i	0.364675	−	0.631635i
$123$	5.15405	+	7.34051i	0.464725	+	0.661872i
$124$	1.32732	−	0.766330i	0.119197	−	0.0688185i
$125$	3.05497			0.273245
$126$		0			0
$127$	−6.78064			−0.601685			−0.300842	−	0.953674i	$-0.597268\pi$
$127$	−6.78064			−0.601685			−0.300842	+	0.953674i	$0.597268\pi$
$128$	−11.0234	+	6.36437i	−0.974341	+	0.562536i
$129$	−4.01713	+	8.64393i	−0.353688	+	0.761056i
$130$	0.794091	−	1.37541i	0.0696464	−	0.120631i
$131$	19.5421			1.70740			0.853701	−	0.520764i	$-0.174353\pi$
$131$	19.5421			1.70740			0.853701	+	0.520764i	$0.174353\pi$
$132$	−1.01215	−	0.470381i	−0.0880964	−	0.0409414i
$133$		0			0
$134$		−	0.164523i		−	0.0142126i
$135$	1.54642	−	0.420802i	0.133095	−	0.0362168i
$136$	−11.2750	+	6.50965i	−0.966826	+	0.558198i
$137$			1.58852i			0.135717i	0.997695	+	0.0678584i	$0.0216166\pi$
$137$			1.58852i			0.135717i	−0.997695	+	0.0678584i	$0.978383\pi$
$138$	8.82513	+	12.5690i	0.751245	+	1.06994i
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	−0.658928	−	0.752206i	$-0.728990\pi$
$139$	−3.97274	+	2.29366i	−0.336963	+	0.194546i	0.321965	+	0.946752i	$0.395657\pi$
$140$		0			0
$141$	8.42416	+	11.9979i	0.709442	+	1.01040i
$142$	−5.78141	−	10.0137i	−0.485165	−	0.840330i
$143$	−5.48476	−	9.49989i	−0.458659	−	0.794421i
$144$	8.44517	+	10.0118i	0.703764	+	0.834320i
$145$	−0.833911	−	0.481459i	−0.0692525	−	0.0399830i
$146$	−7.13673	+	12.3612i	−0.590640	+	1.02302i
$147$		0			0
$148$	1.20742	+	2.09131i	0.0992493	+	0.171905i
$149$			9.73373i			0.797418i	0.917077	+	0.398709i	$0.130542\pi$
$149$			9.73373i			0.797418i	−0.917077	+	0.398709i	$0.869458\pi$
$150$	10.3215	−	7.24708i	0.842743	−	0.591721i
$151$	−6.01833			−0.489765			−0.244882	−	0.969553i	$-0.578749\pi$
$151$	−6.01833			−0.489765			−0.244882	+	0.969553i	$0.578749\pi$
$152$	−7.12118	+	12.3343i	−0.577604	+	1.00044i
$153$	9.44420	+	11.1962i	0.763518	+	0.905160i
$154$		0			0
$155$	−2.00916	−	1.15999i	−0.161380	−	0.0931726i
$156$	−0.108271	−	1.21937i	−0.00866859	−	0.0976277i
$157$	14.1600	+	8.17531i	1.13009	+	0.652461i	0.943959	−	0.330063i	$-0.107070\pi$
$157$	14.1600	+	8.17531i	1.13009	+	0.652461i	0.186136	+	0.982524i	$0.440403\pi$
$158$	−6.60359	−	3.81258i	−0.525353	−	0.303313i
$159$	0.121210	−	0.0851060i	0.00961257	−	0.00674934i
$160$	−0.306721	−	0.177086i	−0.0242484	−	0.0139998i
$161$		0			0
$162$	8.53493	−	10.2791i	0.670567	−	0.807601i
$163$	3.23235	−	5.59860i	0.253177	−	0.438516i	−0.711221	−	0.702968i	$-0.751858\pi$
$163$	3.23235	−	5.59860i	0.253177	−	0.438516i	0.964399	+	0.264452i	$0.0851910\pi$
$164$	−1.05515			−0.0823935
$165$	0.149422	+	1.68283i	0.0116325	+	0.131008i
$166$		−	13.1368i		−	1.01961i
$167$	−1.33556	−	2.31325i	−0.103348	−	0.179005i	0.809714	−	0.586825i	$-0.199622\pi$
$167$	−1.33556	−	2.31325i	−0.103348	−	0.179005i	−0.913062	+	0.407820i	$0.866289\pi$
$168$		0			0
$169$	−0.484236	+	0.838722i	−0.0372489	+	0.0645171i
$170$	−1.93603	−	1.11777i	−0.148487	−	0.0857287i
$171$	15.0713	+	5.44138i	1.15253	+	0.416113i
$172$	−0.560665	−	0.971100i	−0.0427503	−	0.0740457i
$173$	−10.0983	−	17.4908i	−0.767760	−	1.32980i	−0.938775	−	0.344531i	$-0.888038\pi$
$173$	−10.0983	−	17.4908i	−0.767760	−	1.32980i	0.171015	−	0.985268i	$-0.445295\pi$
$174$	−7.99593	+	0.709977i	−0.606170	+	0.0538232i
$175$		0			0
$176$	−11.9575	+	6.90369i	−0.901334	+	0.520385i
$177$	−1.52465	+	3.28070i	−0.114600	+	0.246592i
$178$		−	2.78163i		−	0.208492i
$179$	19.0198	−	10.9811i	1.42161	−	0.820765i	0.425170	−	0.905113i	$-0.360214\pi$
$179$	19.0198	−	10.9811i	1.42161	−	0.820765i	0.996436	+	0.0843484i	$0.0268809\pi$
$180$	−0.0640252	+	0.177334i	−0.00477216	+	0.0132177i
$181$		−	2.50569i		−	0.186246i	−0.995655	−	0.0931232i	$-0.970315\pi$
$181$		−	2.50569i		−	0.186246i	0.995655	−	0.0931232i	$-0.0296850\pi$
$182$		0			0
$183$	−7.69245	+	5.40116i	−0.568642	+	0.399265i
$184$	15.9269			1.17415
$185$	1.82766	−	3.16561i	0.134372	−	0.232740i
$186$	−19.2648	+	1.71056i	−1.41256	+	0.125425i
$187$	−13.3721	+	7.72038i	−0.977864	+	0.564570i
$188$	−1.72462			−0.125781
$189$		0			0
$190$	−2.44554			−0.177418
$191$	1.82276	−	1.05237i	0.131891	−	0.0761470i	−0.432603	−	0.901584i	$-0.642405\pi$
$191$	1.82276	−	1.05237i	0.131891	−	0.0761470i	0.564494	+	0.825437i	$0.309071\pi$
$192$	12.1240	−	1.07652i	0.874976	−	0.0776911i
$193$	2.97730	−	5.15683i	0.214311	−	0.371197i	−0.738748	−	0.673981i	$-0.764583\pi$
$193$	2.97730	−	5.15683i	0.214311	−	0.371197i	0.953059	+	0.302784i	$0.0979162\pi$
$194$	18.8237			1.35147
$195$	−1.51652	+	1.06481i	−0.108601	+	0.0762525i
$196$		0			0
$197$		−	7.64511i		−	0.544692i	−0.962199	−	0.272346i	$-0.912200\pi$
$197$		−	7.64511i		−	0.544692i	0.962199	−	0.272346i	$-0.0877995\pi$
$198$	9.08101	+	10.7656i	0.645359	+	0.765080i
$199$	5.93394	−	3.42596i	0.420646	−	0.242860i	−0.274708	−	0.961528i	$-0.588581\pi$
$199$	5.93394	−	3.42596i	0.420646	−	0.242860i	0.695354	+	0.718668i	$0.255248\pi$
$200$		−	13.0790i		−	0.924824i
$201$	−0.0808996	+	0.174077i	−0.00570622	+	0.0122785i
$202$	−9.47044	+	5.46776i	−0.666338	+	0.384710i
$203$		0			0
$204$	−1.71639	+	0.152402i	−0.120171	+	0.0106703i
$205$	0.798588	+	1.38320i	0.0557758	+	0.0966066i
$206$	5.92346	+	10.2597i	0.412707	+	0.714829i
$207$	−3.15720	−	17.6384i	−0.219440	−	1.22595i
$208$	−13.1152	−	7.57207i	−0.909376	−	0.525028i
$209$	−8.44565	+	14.6283i	−0.584198	+	1.01186i
$210$		0			0
$211$	−2.74784	−	4.75940i	−0.189169	−	0.327651i	0.755804	−	0.654798i	$-0.227246\pi$
$211$	−2.74784	−	4.75940i	−0.189169	−	0.327651i	−0.944974	+	0.327147i	$0.893913\pi$
$212$			0.0174231i			0.00119663i
$213$	1.19320	+	13.4381i	0.0817565	+	0.920761i
$214$	24.8944			1.70174
$215$	−0.848675	+	1.46995i	−0.0578791	+	0.100250i
$216$	−3.63803	−	13.3696i	−0.247537	−	0.909683i
$217$		0			0
$218$	11.3971	+	6.58015i	0.771912	+	0.445664i
$219$	13.6294	−	9.56974i	0.920993	−	0.646663i
$220$	−0.172122	−	0.0993745i	−0.0116044	−	0.00669983i
$221$	−14.6667	−	8.46781i	−0.986588	−	0.569607i
$222$	−2.69514	−	30.3533i	−0.180886	−	2.03718i
$223$	−17.6080	−	10.1660i	−1.17912	−	0.680764i	−0.223307	−	0.974748i	$-0.571685\pi$
$223$	−17.6080	−	10.1660i	−1.17912	−	0.680764i	−0.955810	+	0.293985i	$0.905019\pi$
$224$		0			0
$225$	−14.4844	+	2.59265i	−0.965627	+	0.172843i
$226$	11.6238	−	20.1330i	0.773204	−	1.33923i
$227$	0.322470			0.0214031			0.0107016	−	0.999943i	$-0.496594\pi$
$227$	0.322470			0.0214031			0.0107016	+	0.999943i	$0.496594\pi$
$228$	−1.54272	+	1.08320i	−0.102169	+	0.0717367i
$229$			2.65779i			0.175631i	0.996137	+	0.0878157i	$0.0279887\pi$
$229$			2.65779i			0.175631i	−0.996137	+	0.0878157i	$0.972011\pi$
$230$	1.36740	+	2.36841i	0.0901637	+	0.156168i
$231$		0			0
$232$	−4.16244	+	7.20956i	−0.273278	+	0.473331i
$233$	20.1415	+	11.6287i	1.31952	+	0.761823i	0.983651	−	0.180087i	$-0.0576378\pi$
$233$	20.1415	+	11.6287i	1.31952	+	0.761823i	0.335866	+	0.941910i	$0.390971\pi$
$234$	−5.24585	+	14.5297i	−0.342932	+	0.949837i
$235$	1.30527	+	2.26080i	0.0851466	+	0.147478i
$236$	−0.212793	−	0.368569i	−0.0138517	−	0.0239918i
$237$	5.11235	+	7.28112i	0.332083	+	0.472960i
$238$		0			0
$239$	−0.291265	+	0.168162i	−0.0188404	+	0.0108775i	−0.509391	−	0.860535i	$-0.670129\pi$
$239$	−0.291265	+	0.168162i	−0.0188404	+	0.0108775i	0.490550	+	0.871413i	$0.336796\pi$
$240$	1.34028	+	1.90885i	0.0865146	+	0.123216i
$241$		−	22.1525i		−	1.42697i	−0.700673	−	0.713483i	$-0.747117\pi$
$241$		−	22.1525i		−	1.42697i	0.700673	−	0.713483i	$-0.252883\pi$
$242$	1.28399	−	0.741313i	0.0825381	−	0.0476534i
$243$	−14.0850	+	6.67921i	−0.903555	+	0.428471i
$244$		−	1.10574i		−	0.0707878i
$245$		0			0
$246$	12.0747	+	5.61151i	0.769853	+	0.357777i
$247$	−18.5266			−1.17882
$248$	−10.0287	+	17.3701i	−0.636820	+	1.10301i
$249$	−6.45967	+	13.8997i	−0.409365	+	0.880859i
$250$	3.92753	−	2.26756i	0.248399	−	0.143413i
$251$	−13.9800			−0.882409			−0.441205	−	0.897407i	$-0.645449\pi$
$251$	−13.9800			−0.882409			−0.441205	+	0.897407i	$0.645449\pi$
$252$		0			0
$253$	18.8892			1.18755
$254$	−8.71734	+	5.03296i	−0.546974	+	0.315796i
$255$	1.49883	+	2.13467i	0.0938602	+	0.133678i
$256$	−2.42061	+	4.19261i	−0.151288	+	0.262038i
$257$	−19.3813			−1.20897			−0.604486	−	0.796616i	$-0.706621\pi$
$257$	−19.3813			−1.20897			−0.604486	+	0.796616i	$0.706621\pi$
$258$	1.25149	+	14.0945i	0.0779142	+	0.877488i
$259$		0			0
$260$		−	0.217991i		−	0.0135192i
$261$	8.80939	+	3.18057i	0.545288	+	0.196872i
$262$	25.1237	−	14.5052i	1.55215	−	0.896134i
$263$		−	5.08964i		−	0.313841i	−0.987611	−	0.156920i	$-0.949843\pi$
$263$		−	5.08964i		−	0.313841i	0.987611	−	0.156920i	$-0.0501566\pi$
$264$	14.5489	−	1.29183i	0.895421	−	0.0795065i
$265$	0.0228400	−	0.0131867i	0.00140305	−	0.000810050i
$266$		0			0
$267$	−1.36779	+	2.94316i	−0.0837072	+	0.180119i
$268$	−0.0112910	−	0.0195567i	−0.000689710	−	0.00119461i
$269$	−2.52800	−	4.37863i	−0.154135	−	0.266970i	0.778609	−	0.627510i	$-0.215926\pi$
$269$	−2.52800	−	4.37863i	−0.154135	−	0.266970i	−0.932744	+	0.360540i	$0.882592\pi$
$270$	1.67577	−	1.68883i	0.101984	−	0.102779i
$271$	27.1767	+	15.6905i	1.65087	+	0.953128i	0.976717	+	0.214533i	$0.0688231\pi$
$271$	27.1767	+	15.6905i	1.65087	+	0.953128i	0.674150	+	0.738595i	$0.264510\pi$
$272$	−10.6585	+	18.4610i	−0.646265	+	1.11936i
$273$		0			0
$274$	1.17909	+	2.04224i	0.0712313	+	0.123376i
$275$		−	15.5115i		−	0.935381i
$276$	1.91163	+	0.888398i	0.115066	+	0.0534753i
$277$	26.0558			1.56554			0.782771	−	0.622310i	$-0.213806\pi$
$277$	26.0558			1.56554			0.782771	+	0.622310i	$0.213806\pi$
$278$	−3.40496	+	5.89756i	−0.204216	+	0.353712i
$279$	21.2247	+	7.66301i	1.27069	+	0.458773i
$280$		0			0
$281$	−4.14335	−	2.39217i	−0.247172	−	0.142705i	0.371297	−	0.928514i	$-0.378913\pi$
$281$	−4.14335	−	2.39217i	−0.247172	−	0.142705i	−0.618469	+	0.785810i	$0.712247\pi$
$282$	19.7357	+	9.17187i	1.17525	+	0.546177i
$283$	0.927241	+	0.535343i	0.0551188	+	0.0318228i	0.527306	−	0.849675i	$-0.323202\pi$
$283$	0.927241	+	0.535343i	0.0551188	+	0.0318228i	−0.472187	+	0.881498i	$0.656535\pi$
$284$	−1.37446	−	0.793544i	−0.0815591	−	0.0470882i
$285$	2.58757	+	1.20253i	0.153274	+	0.0712317i
$286$	−14.1026	−	8.14217i	−0.833907	−	0.481457i
$287$		0			0
$288$	3.24019	+	1.16985i	0.190930	+	0.0689339i
$289$	−3.41933	+	5.92245i	−0.201137	+	0.348380i
$290$	−1.42946			−0.0839406
$291$	−19.9169	−	9.25606i	−1.16755	−	0.542600i
$292$			1.95915i			0.114650i
$293$	1.36267	+	2.36021i	0.0796079	+	0.137885i	0.903081	−	0.429471i	$-0.141300\pi$
$293$	1.36267	+	2.36021i	0.0796079	+	0.137885i	−0.823473	+	0.567356i	$0.807967\pi$
$294$		0			0
$295$	−0.322104	+	0.557900i	−0.0187536	+	0.0324822i
$296$	−27.3682	−	15.8010i	−1.59074	−	0.918415i
$297$	−4.31467	−	15.8562i	−0.250362	−	0.920068i
$298$	7.22489	+	12.5139i	0.418527	+	0.724910i
$299$	10.3590	+	17.9422i	0.599074	+	1.03763i
$300$	0.729540	−	1.56980i	0.0421200	−	0.0906326i
$301$		0			0
$302$	−7.73729	+	4.46713i	−0.445231	+	0.257054i
$303$	12.7090	−	1.12846i	0.730115	−	0.0648286i
$304$			23.3195i			1.33747i
$305$	−1.44951	+	0.836876i	−0.0829988	+	0.0479194i
$306$	20.4521	+	7.38408i	1.16917	+	0.422120i
$307$		−	8.31294i		−	0.474444i	−0.971455	−	0.237222i	$-0.923763\pi$
$307$		−	8.31294i		−	0.474444i	0.971455	−	0.237222i	$-0.0762369\pi$
$308$		0			0
$309$	−1.22251	−	13.7682i	−0.0695464	−	0.783248i
$310$	−3.44402			−0.195607
$311$	−3.00023	+	5.19656i	−0.170128	+	0.294670i	−0.938464	−	0.345376i	$-0.887751\pi$
$311$	−3.00023	+	5.19656i	−0.170128	+	0.294670i	0.768337	+	0.640046i	$0.221085\pi$
$312$	9.20577	+	13.1111i	0.521174	+	0.742268i
$313$	−10.2410	+	5.91263i	−0.578854	+	0.334201i	−0.760678	−	0.649130i	$-0.775133\pi$
$313$	−10.2410	+	5.91263i	−0.578854	+	0.334201i	0.181824	+	0.983331i	$0.441800\pi$
$314$	24.2726			1.36978
$315$		0			0
$316$	−1.04662			−0.0588767
$317$	−25.6726	+	14.8221i	−1.44192	+	0.832491i	−0.997978	−	0.0635652i	$-0.979753\pi$
$317$	−25.6726	+	14.8221i	−1.44192	+	0.832491i	−0.443940	+	0.896057i	$0.646420\pi$
$318$	0.0926597	−	0.199382i	0.00519610	−	0.0111808i
$319$	−4.93661	+	8.55046i	−0.276397	+	0.478734i
$320$	2.16745			0.121164
$321$	−26.3400	−	12.2411i	−1.47016	−	0.683232i
$322$		0			0
$323$			26.0781i			1.45103i
$324$	0.309095	−	1.80761i	0.0171719	−	0.100423i
$325$	14.7339	−	8.50664i	0.817291	−	0.471863i
$326$		−	9.59690i		−	0.531523i
$327$	−8.82341	−	12.5665i	−0.487936	−	0.694929i
$328$	11.9584	−	6.90417i	0.660291	−	0.381219i
$329$		0			0
$330$	1.44119	+	2.05257i	0.0793348	+	0.112990i
$331$	8.52504	+	14.7658i	0.468579	+	0.811602i	0.999355	−	0.0359097i	$-0.0114329\pi$
$331$	8.52504	+	14.7658i	0.468579	+	0.811602i	−0.530776	+	0.847512i	$0.678100\pi$
$332$	−0.901567	−	1.56156i	−0.0494799	−	0.0857017i
$333$	−12.0737	+	33.4413i	−0.661637	+	1.83257i
$334$	−3.43404	−	1.98264i	−0.187902	−	0.108485i
$335$	−0.0170912	+	0.0296028i	−0.000933791	+	0.00161737i
$336$		0			0
$337$	10.1065	+	17.5050i	0.550536	+	0.953556i	0.998236	+	0.0593723i	$0.0189099\pi$
$337$	10.1065	+	17.5050i	0.550536	+	0.953556i	−0.447700	+	0.894184i	$0.647757\pi$
$338$			1.43770i			0.0782008i
$339$	−22.1987	+	15.5865i	−1.20567	+	0.846543i
$340$	−0.306845			−0.0166410
$341$	−11.8939	+	20.6008i	−0.644090	+	1.11560i
$342$	23.4148	−	4.19116i	1.26613	−	0.226632i
$343$		0			0
$344$	12.7084	+	7.33719i	0.685191	+	0.395595i
$345$	−0.282211	−	3.17833i	−0.0151937	−	0.171115i
$346$	−25.9652	−	14.9910i	−1.39590	−	0.805921i
$347$	−15.3128	−	8.84086i	−0.822036	−	0.474602i	0.0290824	−	0.999577i	$-0.490741\pi$
$347$	−15.3128	−	8.84086i	−0.822036	−	0.474602i	−0.851118	+	0.524975i	$0.824075\pi$
$348$	−0.901742	+	0.633147i	−0.0483385	+	0.0339402i
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	0.399795	−	0.916605i	$-0.369081\pi$
$349$	−3.62628	−	2.09363i	−0.194110	−	0.112070i	−0.593905	+	0.804535i	$0.702415\pi$
$350$		0			0
$351$	12.6951	−	12.7940i	0.677613	−	0.682893i
$352$	−1.81574	+	3.14495i	−0.0967791	+	0.167626i
$353$	−30.4953			−1.62310			−0.811551	−	0.584281i	$-0.801377\pi$
$353$	−30.4953			−1.62310			−0.811551	+	0.584281i	$0.801377\pi$
$354$	0.474986	+	5.34941i	0.0252452	+	0.284318i
$355$			2.40237i			0.127504i
$356$	−0.190900	−	0.330649i	−0.0101177	−	0.0175243i
$357$		0			0
$358$	16.3015	−	28.2350i	0.861561	−	1.49227i
$359$	−4.66901	−	2.69565i	−0.246421	−	0.142271i	0.371703	−	0.928352i	$-0.378774\pi$
$359$	−4.66901	−	2.69565i	−0.246421	−	0.142271i	−0.618124	+	0.786080i	$0.712107\pi$
$360$	−0.434731	−	2.42872i	−0.0229123	−	0.128005i
$361$	4.76400	+	8.25150i	0.250737	+	0.434289i
$362$	−1.85986	−	3.22137i	−0.0977519	−	0.169311i
$363$	−1.72308	+	0.152996i	−0.0904381	+	0.00803021i
$364$		0			0
$365$	2.56824	−	1.48277i	0.134428	−	0.0776119i
$366$	−5.88055	+	12.6536i	−0.307381	+	0.661414i
$367$		−	20.0014i		−	1.04407i	−0.852925	−	0.522033i	$-0.825174\pi$
$367$		−	20.0014i		−	1.04407i	0.852925	−	0.522033i	$-0.174826\pi$
$368$	22.5840	−	13.0389i	1.17727	−	0.679698i
$369$	−10.0166	−	11.8748i	−0.521442	−	0.618176i
$370$		−	5.42636i		−	0.282103i
$371$		0			0
$372$	−2.17259	+	1.52545i	−0.112643	+	0.0790911i
$373$	−26.0949			−1.35114			−0.675571	−	0.737295i	$-0.736103\pi$
$373$	−26.0949			−1.35114			−0.675571	+	0.737295i	$0.736103\pi$
$374$	−11.4609	+	19.8509i	−0.592632	+	1.02647i
$375$	−5.27062	+	0.467991i	−0.272174	+	0.0241669i
$376$	19.5457	−	11.2847i	1.00799	−	0.581964i
$377$	−10.8291			−0.557726
$378$		0			0
$379$	30.5222			1.56782			0.783910	−	0.620875i	$-0.213222\pi$
$379$	30.5222			1.56782			0.783910	+	0.620875i	$0.213222\pi$
$380$	−0.290699	+	0.167835i	−0.0149126	+	0.00860977i
$381$	11.6984	−	1.03873i	0.599327	−	0.0532156i
$382$	1.56225	−	2.70590i	0.0799319	−	0.138446i
$383$	22.7086			1.16035			0.580177	−	0.814490i	$-0.302983\pi$
$383$	22.7086			1.16035			0.580177	+	0.814490i	$0.302983\pi$
$384$	18.0433	−	12.6689i	0.920770	−	0.646507i
$385$		0			0
$386$		−	8.83964i		−	0.449926i
$387$	5.60644	−	15.5284i	0.284991	−	0.789355i
$388$	2.23756	−	1.29185i	0.113595	−	0.0655840i
$389$			4.49318i			0.227813i	0.993491	+	0.113907i	$0.0363365\pi$
$389$			4.49318i			0.227813i	−0.993491	+	0.113907i	$0.963664\pi$
$390$	−1.15932	+	2.49458i	−0.0587043	+	0.126318i
$391$	25.2556	−	14.5813i	1.27723	−	0.737409i
$392$		0			0
$393$	−33.7153	+	2.99366i	−1.70071	+	0.151010i
$394$	−5.67461	−	9.82872i	−0.285883	−	0.495164i
$395$	0.792127	+	1.37200i	0.0398562	+	0.0690330i
$396$	1.81828	+	0.656479i	0.0913722	+	0.0329893i
$397$	−8.35854	−	4.82581i	−0.419503	−	0.242200i	0.275362	−	0.961341i	$-0.411202\pi$
$397$	−8.35854	−	4.82581i	−0.419503	−	0.242200i	−0.694865	+	0.719140i	$0.744536\pi$
$398$	5.08587	−	8.80898i	0.254931	−	0.441554i
$399$		0			0
$400$	−10.7073	−	18.5457i	−0.535367	−	0.927283i
$401$		−	19.9020i		−	0.993856i	−0.867792	−	0.496928i	$-0.834461\pi$
$401$		−	19.9020i		−	0.993856i	0.867792	−	0.496928i	$-0.165539\pi$
$402$	0.0252033	+	0.283845i	0.00125703	+	0.0141569i
$403$	−26.0908			−1.29967
$404$	−0.750494	+	1.29989i	−0.0373385	+	0.0646721i
$405$	−2.60352	+	0.962890i	−0.129370	+	0.0478464i
$406$		0			0
$407$	−32.4584	−	18.7398i	−1.60890	−	0.928900i
$408$	18.4552	−	12.9581i	0.913668	−	0.641520i
$409$	−2.10072	−	1.21285i	−0.103874	−	0.0599718i	0.447163	−	0.894453i	$-0.352434\pi$
$409$	−2.10072	−	1.21285i	−0.103874	−	0.0599718i	−0.551037	+	0.834481i	$0.685768\pi$
$410$	2.05336	+	1.18551i	0.101408	+	0.0585482i
$411$	−0.243346	−	2.74062i	−0.0120034	−	0.135185i
$412$	1.40823	+	0.813042i	0.0693785	+	0.0400557i
$413$		0			0
$414$	−17.1511	−	20.3328i	−0.842931	−	0.999304i
$415$	−1.36470	+	2.36372i	−0.0669903	+	0.116031i
$416$	−3.98305			−0.195285
$417$	6.50265	−	4.56575i	0.318436	−	0.223586i
$418$			25.0753i			1.22647i
$419$	14.6878	+	25.4399i	0.717544	+	1.24282i	0.961970	+	0.273155i	$0.0880671\pi$
$419$	14.6878	+	25.4399i	0.717544	+	1.24282i	−0.244426	+	0.969668i	$0.578600\pi$
$420$		0			0
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.0444443	+	0.999012i	$0.514152\pi$
$421$	−18.2078	+	31.5368i	−0.887392	+	1.53701i	−0.842948	+	0.537996i	$0.819182\pi$
$422$	−7.06537	−	4.07919i	−0.343937	−	0.198572i
$423$	−16.3719	−	19.4090i	−0.796027	−	0.943699i
$424$	−0.114005	−	0.197462i	−0.00553656	−	0.00958961i
$425$	−11.9740	−	20.7395i	−0.580823	−	1.00602i
$426$	11.5084	+	16.3906i	0.557586	+	0.794127i
$427$		0			0
$428$	2.95916	−	1.70847i	0.143037	−	0.0825822i
$429$	10.9179	+	15.5496i	0.527124	+	0.750742i
$430$			2.51973i			0.121512i
$431$	−16.8459	+	9.72598i	−0.811438	+	0.468484i	−0.847455	−	0.530867i	$-0.821866\pi$
$431$	−16.8459	+	9.72598i	−0.811438	+	0.468484i	0.0360172	+	0.999351i	$0.488533\pi$
$432$	−16.1039	−	15.9793i	−0.774797	−	0.768806i
$433$			9.94623i			0.477985i	0.971021	+	0.238993i	$0.0768172\pi$
$433$			9.94623i			0.477985i	−0.971021	+	0.238993i	$0.923183\pi$
$434$		0			0
$435$	1.51247	+	0.702896i	0.0725174	+	0.0337013i
$436$	1.80636			0.0865087
$437$	15.9511	−	27.6282i	0.763046	−	1.32163i
$438$	10.4191	−	22.4196i	0.497845	−	1.07125i
$439$	6.38746	−	3.68780i	0.304857	−	0.176009i	−0.339766	−	0.940510i	$-0.610348\pi$
$439$	6.38746	−	3.68780i	0.304857	−	0.176009i	0.644623	+	0.764501i	$0.277014\pi$
$440$	2.60095			0.123995
$441$		0			0
$442$	−25.1411			−1.19584
$443$	−0.744629	+	0.429911i	−0.0353784	+	0.0204257i	−0.517585	−	0.855632i	$-0.673169\pi$
$443$	−0.744629	+	0.429911i	−0.0353784	+	0.0204257i	0.482207	+	0.876058i	$0.339835\pi$
$444$	−2.40349	−	3.42310i	−0.114064	−	0.162453i
$445$	−0.288964	+	0.500501i	−0.0136982	+	0.0237260i
$446$	−30.1829			−1.42920
$447$	−1.49111	−	16.7932i	−0.0705271	−	0.794293i
$448$		0			0
$449$		−	15.6497i		−	0.738556i	−0.929319	−	0.369278i	$-0.879605\pi$
$449$		−	15.6497i		−	0.738556i	0.929319	−	0.369278i	$-0.120395\pi$
$450$	−16.6970	+	14.0843i	−0.787106	+	0.663938i
$451$	14.1825	−	8.18828i	0.667829	−	0.385571i
$452$		−	3.19092i		−	0.150088i
$453$	10.3832	−	0.921948i	0.487845	−	0.0433169i
$454$	0.414575	−	0.239355i	0.0194570	−	0.0112335i
$455$		0			0
$456$	10.3964	−	22.3707i	0.486857	−	1.04761i
$457$	2.81559	+	4.87675i	0.131708	+	0.228125i	0.924335	−	0.381582i	$-0.124621\pi$
$457$	2.81559	+	4.87675i	0.131708	+	0.228125i	−0.792627	+	0.609707i	$0.791287\pi$
$458$	1.97275	+	3.41690i	0.0921806	+	0.159661i
$459$	−18.0089	−	17.8696i	−0.840582	−	0.834083i
$460$	0.325083	+	0.187687i	0.0151571	+	0.00875093i
$461$	11.3342	−	19.6314i	0.527886	−	0.914326i	−0.471585	−	0.881821i	$-0.656318\pi$
$461$	11.3342	−	19.6314i	0.527886	−	0.914326i	0.999472	−	0.0325056i	$-0.0103487\pi$
$462$		0			0
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.675937	−	0.736960i	$-0.736261\pi$
$463$	−21.0052	−	36.3821i	−0.976194	−	1.69082i	−0.300257	−	0.953858i	$-0.597073\pi$
$464$			13.6306i			0.632785i
$465$	3.64403	+	1.69350i	0.168988	+	0.0785343i
$466$	34.5258			1.59938
$467$	12.4016	−	21.4802i	0.573879	−	0.993987i	−0.422284	−	0.906464i	$-0.638771\pi$
$467$	12.4016	−	21.4802i	0.573879	−	0.993987i	0.996162	−	0.0875236i	$-0.0278953\pi$
$468$	0.373591	+	2.08715i	0.0172692	+	0.0964785i
$469$		0			0
$470$	3.35617	+	1.93769i	0.154809	+	0.0893788i
$471$	−25.6822	−	11.9354i	−1.18337	−	0.549953i
$472$	4.82331	+	2.78474i	0.222011	+	0.128178i
$473$	15.0720	+	8.70184i	0.693013	+	0.400111i
$474$	11.9770	+	5.56611i	0.550121	+	0.255660i
$475$	−22.6879	−	13.0989i	−1.04099	−	0.601017i
$476$		0			0
$477$	−0.196082	+	0.165398i	−0.00897796	+	0.00757307i
$478$	−0.249637	+	0.432385i	−0.0114181	+	0.0197768i
$479$	3.29294			0.150458			0.0752291	−	0.997166i	$-0.476031\pi$
$479$	3.29294			0.150458			0.0752291	+	0.997166i	$0.476031\pi$
$480$	0.556303	+	0.258533i	0.0253916	+	0.0118003i
$481$		−	41.1082i		−	1.87437i
$482$	−16.4427	−	28.4797i	−0.748946	−	1.29721i
$483$		0			0
$484$	0.101751	−	0.176238i	0.00462505	−	0.00801082i
$485$	−3.38698	−	1.95547i	−0.153795	−	0.0887934i
$486$	−13.1503	+	19.0416i	−0.596512	+	0.863744i
$487$	−5.22240	−	9.04546i	−0.236650	−	0.409889i	0.723101	−	0.690742i	$-0.242716\pi$
$487$	−5.22240	−	9.04546i	−0.236650	−	0.409889i	−0.959751	+	0.280853i	$0.909383\pi$
$488$	7.23519	+	12.5317i	0.327522	+	0.567284i
$489$	−4.71901	+	10.1542i	−0.213401	+	0.459190i
$490$		0			0
$491$	−26.2797	+	15.1726i	−1.18599	+	0.684731i	−0.957392	−	0.288791i	$-0.906747\pi$
$491$	−26.2797	+	15.1726i	−1.18599	+	0.684731i	−0.228596	+	0.973521i	$0.573413\pi$
$492$	1.82041	−	0.161639i	0.0820706	−	0.00728724i
$493$			15.2431i			0.686513i
$494$	−23.8182	+	13.7514i	−1.07163	+	0.618707i
$495$	−0.515586	−	2.88044i	−0.0231739	−	0.129466i
$496$			32.8405i			1.47458i
$497$		0			0
$498$	2.01243	+	22.6645i	0.0901792	+	1.01562i
$499$	1.96951			0.0881676			0.0440838	−	0.999028i	$-0.485963\pi$
$499$	1.96951			0.0881676			0.0440838	+	0.999028i	$0.485963\pi$
$500$	0.311241	−	0.539085i	0.0139191	−	0.0241086i
$501$	2.65855	+	3.78637i	0.118775	+	0.169163i
$502$	−17.9730	+	10.3767i	−0.802173	+	0.463135i
$503$	17.3024			0.771477			0.385739	−	0.922608i	$-0.373947\pi$
$503$	17.3024			0.771477			0.385739	+	0.922608i	$0.373947\pi$
$504$		0			0
$505$	2.27203			0.101104
$506$	24.2843	−	14.0206i	1.07957	−	0.623290i
$507$	0.706951	−	1.52120i	0.0313968	−	0.0675587i
$508$	−0.690813	+	1.19652i	−0.0306499	+	0.0530872i
$509$	−0.481784			−0.0213547			−0.0106774	−	0.999943i	$-0.503399\pi$
$509$	−0.481784			−0.0213547			−0.0106774	+	0.999943i	$0.503399\pi$
$510$	3.51139	+	1.63186i	0.155487	+	0.0722600i
$511$		0			0
$512$		−	18.2707i		−	0.807457i
$513$	−26.8355	−	7.07904i	−1.18482	−	0.312547i
$514$	−24.9170	+	14.3858i	−1.09904	+	0.634532i
$515$		−	2.46139i		−	0.108462i
$516$	1.11606	+	1.58951i	0.0491317	+	0.0699745i
$517$	23.1810	−	13.3835i	1.01950	−	0.588607i
$518$		0			0
$519$	20.1017	+	28.6292i	0.882365	+	1.25668i
$520$	1.42638	+	2.47056i	0.0625508	+	0.108341i
$521$	7.20770	+	12.4841i	0.315775	+	0.546939i	0.979602	−	0.200948i	$-0.0644021\pi$
$521$	7.20770	+	12.4841i	0.315775	+	0.546939i	−0.663827	+	0.747886i	$0.731069\pi$
$522$	13.6863	−	2.44979i	0.599034	−	0.107225i
$523$	−5.90591	−	3.40978i	−0.258247	−	0.149099i	0.365287	−	0.930895i	$-0.380971\pi$
$523$	−5.90591	−	3.40978i	−0.258247	−	0.149099i	−0.623535	+	0.781796i	$0.714304\pi$
$524$	1.99095	−	3.44843i	0.0869752	−	0.150645i
$525$		0			0
$526$	−3.77780	−	6.54334i	−0.164720	−	0.285303i
$527$			36.7255i			1.59979i
$528$	19.5723	−	13.7425i	0.851777	−	0.598064i
$529$	−12.6756			−0.551114
$530$	0.0195757	−	0.0339061i	0.000850313	−	0.00147279i
$531$	2.12785	−	5.89363i	0.0923410	−	0.255762i
$532$		0			0
$533$	15.5556	+	8.98102i	0.673787	+	0.389011i
$534$	0.426117	+	4.79904i	0.0184399	+	0.207675i
$535$	−4.47927	−	2.58611i	−0.193656	−	0.111807i
$536$	0.255930	+	0.147761i	0.0110545	+	0.00638232i
$537$	−31.1320	+	21.8589i	−1.34344	+	0.943282i
$538$	−6.50011	−	3.75284i	−0.280240	−	0.161796i
$539$		0			0
$540$	0.0832945	−	0.315756i	0.00358442	−	0.0135880i
$541$	8.91128	−	15.4348i	0.383126	−	0.663594i	−0.608381	−	0.793645i	$-0.708181\pi$
$541$	8.91128	−	15.4348i	0.383126	−	0.663594i	0.991507	+	0.130051i	$0.0415142\pi$
$542$	46.5852			2.00101
$543$	0.383847	+	4.32297i	0.0164724	+	0.185517i
$544$			5.60656i			0.240379i
$545$	−1.36713	−	2.36795i	−0.0585616	−	0.101432i
$546$		0			0
$547$	−6.79325	+	11.7663i	−0.290458	+	0.503089i	−0.973918	−	0.226900i	$-0.927141\pi$
$547$	−6.79325	+	11.7663i	−0.290458	+	0.503089i	0.683460	+	0.729988i	$0.260474\pi$
$548$	0.280314	+	0.161839i	0.0119744	+	0.00691342i
$549$	12.4441	−	10.4968i	0.531101	−	0.447993i
$550$	−11.5135	−	19.9420i	−0.490937	−	0.850328i
$551$	8.33752	+	14.4410i	0.355191	+	0.615208i
$552$	−27.4782	+	2.43985i	−1.16955	+	0.103847i
$553$		0			0
$554$	33.4979	−	19.3400i	1.42319	−	0.821678i
$555$	−2.66826	+	5.74148i	−0.113261	+	0.243712i
$556$			0.934715i			0.0396407i
$557$	6.24761	−	3.60706i	0.264720	−	0.152836i	−0.361766	−	0.932269i	$-0.617826\pi$
$557$	6.24761	−	3.60706i	0.264720	−	0.152836i	0.626486	+	0.779433i	$0.284493\pi$
$558$	32.9748	−	5.90234i	1.39593	−	0.249866i
$559$			19.0886i			0.807361i
$560$		0			0
$561$	21.8877	−	15.3681i	0.924098	−	0.648844i
$562$	−7.10238			−0.299596
$563$	11.5472	−	20.0004i	0.486657	−	0.842915i	−0.513225	−	0.858254i	$-0.671549\pi$
$563$	11.5472	−	20.0004i	0.486657	−	0.842915i	0.999882	+	0.0153392i	$0.00488280\pi$
$564$	2.97542	−	0.264195i	0.125288	−	0.0111246i
$565$	−4.18296	+	2.41504i	−0.175979	+	0.101601i
$566$	1.58944			0.0668092
$567$		0			0
$568$	20.7696			0.871473
$569$	22.6039	−	13.0504i	0.947605	−	0.547100i	0.0552688	−	0.998472i	$-0.482398\pi$
$569$	22.6039	−	13.0504i	0.947605	−	0.547100i	0.892336	+	0.451372i	$0.149065\pi$
$570$	4.21921	−	0.374633i	0.176723	−	0.0156917i
$571$	12.3318	−	21.3594i	0.516071	−	0.893862i	−0.483754	−	0.875204i	$-0.660727\pi$
$571$	12.3318	−	21.3594i	0.516071	−	0.893862i	0.999826	−	0.0186582i	$-0.00593945\pi$
$572$	−2.23516			−0.0934565
$573$	−2.98353	+	2.09485i	−0.124639	+	0.0875136i
$574$		0			0
$575$			29.2963i			1.22174i
$576$	−20.7522	+	3.71456i	−0.864675	+	0.154773i
$577$	−16.7403	+	9.66501i	−0.696907	+	0.402360i	−0.806194	−	0.591651i	$-0.798477\pi$
$577$	−16.7403	+	9.66501i	−0.696907	+	0.402360i	0.109287	+	0.994010i	$0.465143\pi$
$578$			10.1520i			0.422269i
$579$	−4.34665	+	9.35299i	−0.180641	+	0.388697i
$580$	−0.169918	+	0.0981022i	−0.00705546	+	0.00407347i
$581$		0			0
$582$	−32.4759	+	2.88361i	−1.34617	+	0.119530i
$583$	−0.135209	−	0.234188i	−0.00559977	−	0.00969908i
$584$	−12.8193	−	22.2036i	−0.530465	−	0.918793i
$585$	2.45329	−	2.06939i	0.101431	−	0.0855588i
$586$	3.50375	+	2.02289i	0.144738	+	0.0835648i
$587$	−7.65692	+	13.2622i	−0.316035	+	0.547389i	−0.979657	−	0.200679i	$-0.935685\pi$
$587$	−7.65692	+	13.2622i	−0.316035	+	0.547389i	0.663622	+	0.748068i	$0.269018\pi$
$588$		0			0
$589$	20.0878	+	34.7931i	0.827703	+	1.43362i
$590$			0.956331i			0.0393715i
$591$	1.17116	+	13.1898i	0.0481749	+	0.542557i
$592$	−51.7431			−2.12663
$593$	19.6195	−	33.9820i	0.805678	−	1.39547i	−0.110155	−	0.993914i	$-0.535135\pi$
$593$	19.6195	−	33.9820i	0.805678	−	1.39547i	0.915833	−	0.401560i	$-0.131532\pi$
$594$	−17.3163	−	17.1824i	−0.710497	−	0.705004i
$595$		0			0
$596$	1.71763	+	0.991674i	0.0703569	+	0.0406206i
$597$	−9.71279	+	6.81971i	−0.397518	+	0.279112i
$598$	26.6354	+	15.3779i	1.08920	+	0.628851i
$599$	29.7113	+	17.1538i	1.21397	+	0.700887i	0.963622	−	0.267269i	$-0.0861211\pi$
$599$	29.7113	+	17.1538i	1.21397	+	0.700887i	0.250350	+	0.968155i	$0.419454\pi$
$600$	2.00357	+	22.5647i	0.0817954	+	0.921200i
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.902133	−	0.431458i	$-0.142001\pi$
$601$	24.0139	+	13.8644i	0.979547	+	0.565541i	0.0774133	+	0.996999i	$0.475334\pi$
$602$		0			0
$603$	0.112906	−	0.312722i	0.00459790	−	0.0127350i
$604$	−0.613149	+	1.06200i	−0.0249487	+	0.0432123i
$605$	−0.308040			−0.0125236
$606$	15.5014	−	10.8841i	0.629701	−	0.442136i
$607$			15.0718i			0.611747i	0.952072	+	0.305873i	$0.0989485\pi$
$607$			15.0718i			0.611747i	−0.952072	+	0.305873i	$0.901052\pi$
$608$	3.06663	+	5.31156i	0.124368	+	0.215412i
$609$		0			0
$610$	−1.24235	+	2.15181i	−0.0503012	+	0.0871243i
$611$	25.4252	+	14.6793i	1.02859	+	0.593859i
$612$	2.93788	−	0.525868i	0.118757	−	0.0212570i
$613$	−4.82944	−	8.36484i	−0.195059	−	0.337853i	0.751861	−	0.659322i	$-0.229157\pi$
$613$	−4.82944	−	8.36484i	−0.195059	−	0.337853i	−0.946920	+	0.321469i	$0.895823\pi$
$614$	−6.17031	−	10.6873i	−0.249013	−	0.431304i
$615$	−1.58967	−	2.26404i	−0.0641016	−	0.0912949i
$616$		0			0
$617$	15.9761	−	9.22381i	0.643174	−	0.371337i	−0.142662	−	0.989771i	$-0.545566\pi$
$617$	15.9761	−	9.22381i	0.643174	−	0.371337i	0.785836	+	0.618435i	$0.212233\pi$
$618$	−11.7912	−	16.7933i	−0.474312	−	0.675526i
$619$			33.8927i			1.36226i	0.732162	+	0.681130i	$0.238511\pi$
$619$			33.8927i			1.36226i	−0.732162	+	0.681130i	$0.761489\pi$
$620$	−0.409387	+	0.236360i	−0.0164414	+	0.00949244i
$621$	8.14902	+	29.9472i	0.327009	+	1.20174i
$622$			8.90774i			0.357168i
$623$		0			0
$624$	23.7871	+	11.0547i	0.952248	+	0.442542i
$625$	23.5821			0.943284
$626$	−8.77733	+	15.2028i	−0.350813	+	0.607626i
$627$	12.3301	−	26.5315i	0.492415	−	1.05956i
$628$	2.88526	−	1.66580i	0.115134	−	0.0664728i
$629$	−57.8641			−2.30719
$630$		0			0
$631$	−10.0134			−0.398629			−0.199314	−	0.979936i	$-0.563871\pi$
$631$	−10.0134			−0.398629			−0.199314	+	0.979936i	$0.563871\pi$
$632$	11.8616	−	6.84831i	0.471830	−	0.272411i
$633$	5.46985	+	7.79028i	0.217407	+	0.309636i
$634$	−22.0035	+	38.1112i	−0.873870	+	1.51359i
$635$	2.09136			0.0829931
$636$	−0.00266905	−	0.0300595i	−0.000105835	−	0.00119194i
$637$		0			0
$638$			14.6569i			0.580271i
$639$	−4.11716	−	23.0014i	−0.162872	−	0.909922i
$640$	3.39996	−	1.96297i	0.134395	−	0.0775931i
$641$			40.1458i			1.58567i	0.609439	+	0.792833i	$0.291395\pi$
$641$			40.1458i			1.58567i	−0.609439	+	0.792833i	$0.708605\pi$
$642$	−42.9493	+	3.81357i	−1.69507	+	0.150510i
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.957226	−	0.289342i	$-0.906564\pi$
$643$	−30.0552	+	17.3524i	−1.18526	+	0.684311i	−0.228036	+	0.973653i	$0.573230\pi$
$644$		0			0
$645$	1.23901	−	2.66605i	0.0487858	−	0.104976i
$646$	19.3566	+	33.5266i	0.761575	+	1.31909i
$647$	−7.18466	−	12.4442i	−0.282458	−	0.489232i	0.689532	−	0.724256i	$-0.257816\pi$
$647$	−7.18466	−	12.4442i	−0.282458	−	0.489232i	−0.971990	+	0.235024i	$0.924483\pi$
$648$	8.32464	+	22.5087i	0.327023	+	0.884225i
$649$	5.72040	+	3.30268i	0.224545	+	0.129641i
$650$	12.6282	−	21.8726i	0.495317	−	0.857915i
$651$		0			0
$652$	−0.658626	−	1.14077i	−0.0257938	−	0.0446761i
$653$		−	1.12174i		−	0.0438971i	−0.999759	−	0.0219485i	$-0.993013\pi$
$653$		−	1.12174i		−	0.0438971i	0.999759	−	0.0219485i	$-0.00698700\pi$
$654$	−20.6711	−	9.60655i	−0.808304	−	0.375646i
$655$	−6.02738			−0.235509
$656$	11.3044	−	19.5799i	0.441364	−	0.764466i
$657$	−22.0484	+	18.5982i	−0.860190	+	0.725586i
$658$		0			0
$659$	−5.45240	−	3.14795i	−0.212395	−	0.122627i	0.390029	−	0.920803i	$-0.372465\pi$
$659$	−5.45240	−	3.14795i	−0.212395	−	0.122627i	−0.602424	+	0.798176i	$0.705798\pi$
$660$	0.312178	+	0.145080i	0.0121515	+	0.00564723i
$661$	−37.6913	−	21.7611i	−1.46602	−	0.846409i	−0.466745	−	0.884392i	$-0.654573\pi$
$661$	−37.6913	−	21.7611i	−1.46602	−	0.846409i	−0.999278	+	0.0379828i	$0.987907\pi$
$662$	21.9199	+	12.6555i	0.851943	+	0.491869i
$663$	26.6011	+	12.3624i	1.03310	+	0.480116i
$664$	20.4355	+	11.7984i	0.793051	+	0.457868i
$665$		0			0
$666$	9.29965	+	51.9546i	0.360354	+	2.01320i
$667$	9.32368	−	16.1491i	0.361014	−	0.625295i
$668$	−0.544267			−0.0210583
$669$	31.9357	+	14.8416i	1.23471	+	0.573809i
$670$			0.0507440i			0.00196041i
$671$	8.58086	+	14.8625i	0.331261	+	0.573760i
$672$		0			0
$673$	−11.6052	+	20.1008i	−0.447347	+	0.774827i	−0.998212	−	0.0597668i	$-0.980964\pi$
$673$	−11.6052	+	20.1008i	−0.447347	+	0.774827i	0.550866	+	0.834594i	$0.314298\pi$
$674$	25.9862	+	15.0032i	1.00095	+	0.577900i
$675$	24.5922	−	6.69187i	0.946556	−	0.257570i
$676$	0.0986682	+	0.170898i	0.00379493	+	0.00657301i
$677$	22.8213	+	39.5276i	0.877093	+	1.51917i	0.854517	+	0.519424i	$0.173853\pi$
$677$	22.8213	+	39.5276i	0.877093	+	1.51917i	0.0225758	+	0.999745i	$0.492813\pi$
$678$	−16.9699	+	36.5154i	−0.651726	+	1.40237i
$679$		0			0
$680$	3.47757	−	2.00778i	0.133359	−	0.0769947i
$681$	−0.556346	+	0.0493993i	−0.0213192	+	0.00189298i
$682$			35.3131i			1.35221i
$683$	−3.81262	+	2.20122i	−0.145886	+	0.0842272i	−0.571166	−	0.820834i	$-0.693509\pi$
$683$	−3.81262	+	2.20122i	−0.145886	+	0.0842272i	0.425280	+	0.905062i	$0.360175\pi$
$684$	2.49566	−	2.10513i	0.0954240	−	0.0804918i
$685$		−	0.489950i		−	0.0187200i
$686$		0			0
$687$	−0.407146	−	4.58538i	−0.0155336	−	0.174943i
$688$	24.0269			0.916016
$689$	0.148299	−	0.256861i	0.00564973	−	0.00978562i
$690$	−2.72194	−	3.87665i	−0.103623	−	0.147582i
$691$	8.08070	−	4.66539i	0.307404	−	0.177480i	−0.338360	−	0.941017i	$-0.609872\pi$
$691$	8.08070	−	4.66539i	0.307404	−	0.177480i	0.645764	+	0.763537i	$0.276539\pi$
$692$	−4.11527			−0.156439
$693$		0			0
$694$	−26.2486			−0.996385
$695$	1.22531	−	0.707436i	0.0464788	−	0.0268346i
$696$	6.07687	−	13.0760i	0.230343	−	0.495645i
$697$	12.6417	−	21.8961i	0.478839	−	0.829374i
$698$	−6.21603			−0.235280
$699$	−36.5309	−	16.9771i	−1.38172	−	0.642134i
$700$		0			0
$701$		−	22.9051i		−	0.865116i	−0.901606	−	0.432558i	$-0.857611\pi$
$701$		−	22.9051i		−	0.865116i	0.901606	−	0.432558i	$-0.142389\pi$
$702$	6.82467	−	25.8712i	0.257580	−	0.976445i
$703$	−54.8195	+	31.6500i	−2.06756	+	1.19370i
$704$		−	22.2238i		−	0.837592i
$705$	−2.59827	−	3.70052i	−0.0978565	−	0.139370i
$706$	−39.2054	+	22.6353i	−1.47552	+	0.851889i
$707$		0			0
$708$	0.423586	+	0.603281i	0.0159193	+	0.0226727i
$709$	−2.78180	−	4.81822i	−0.104473	−	0.180952i	0.809050	−	0.587740i	$-0.199982\pi$
$709$	−2.78180	−	4.81822i	−0.104473	−	0.180952i	−0.913523	+	0.406788i	$0.866649\pi$
$710$	1.78316	+	3.08853i	0.0669210	+	0.115910i
$711$	−9.93554	−	11.7787i	−0.372612	−	0.441736i
$712$	4.32707	+	2.49823i	0.162164	+	0.0936252i
$713$	22.4637	−	38.9083i	0.841274	−	1.45713i
$714$		0			0
$715$	1.69167	+	2.93006i	0.0632649	+	0.109578i
$716$		−	4.47502i		−	0.167239i
$717$	0.476748	−	0.334742i	0.0178045	−	0.0125012i
$718$	−8.00344			−0.298686
$719$	−9.99888	+	17.3186i	−0.372895	+	0.645873i	−0.990010	−	0.141000i	$-0.954968\pi$
$719$	−9.99888	+	17.3186i	−0.372895	+	0.645873i	0.617114	+	0.786873i	$0.288302\pi$
$720$	−2.60475	−	3.08796i	−0.0970733	−	0.115081i
$721$		0			0
$722$	12.2494	+	7.07220i	0.455876	+	0.263200i
$723$	3.39354	+	38.2188i	0.126207	+	1.42137i
$724$	−0.442158	−	0.255280i	−0.0164327	−	0.00948741i
$725$	−13.2614	−	7.65648i	−0.492516	−	0.284354i
$726$	−2.10166	+	1.47565i	−0.0780000	+	0.0547667i
$727$	25.0380	+	14.4557i	0.928610	+	0.536133i	0.886372	−	0.462975i	$-0.153218\pi$
$727$	25.0380	+	14.4557i	0.928610	+	0.536133i	0.0422381	+	0.999108i	$0.486551\pi$
$728$		0			0
$729$	23.2772	−	13.6811i	0.862119	−	0.506707i
$730$	2.20119	−	3.81257i	0.0814696	−	0.141109i
$731$	26.8692			0.993793
$732$	0.169389	+	1.90769i	0.00626078	+	0.0705104i
$733$		−	31.8117i		−	1.17499i	−0.809227	−	0.587496i	$-0.800114\pi$
$733$		−	31.8117i		−	1.17499i	0.809227	−	0.587496i	$-0.199886\pi$
$734$	−14.8461	−	25.7143i	−0.547981	−	0.949131i
$735$		0			0
$736$	3.42935	−	5.93980i	0.126407	−	0.218944i
$737$	0.303531	+	0.175244i	0.0111807	+	0.00645518i
$738$	−21.6916	−	7.83161i	−0.798479	−	0.288285i
$739$	−11.3935	−	19.7342i	−0.419118	−	0.725934i	0.576733	−	0.816933i	$-0.304327\pi$
$739$	−11.3935	−	19.7342i	−0.419118	−	0.725934i	−0.995851	+	0.0909988i	$0.970994\pi$
$740$	−0.372405	−	0.645025i	−0.0136899	−	0.0237116i
$741$	31.9633	−	2.83809i	1.17420	−	0.104260i
$742$		0			0
$743$	11.8554	−	6.84471i	0.434932	−	0.251108i	−0.266513	−	0.963831i	$-0.585872\pi$
$743$	11.8554	−	6.84471i	0.434932	−	0.251108i	0.701446	+	0.712723i	$0.252538\pi$
$744$	14.6411	−	31.5044i	0.536770	−	1.15501i
$745$		−	3.00218i		−	0.109991i
$746$	−33.5481	+	19.3690i	−1.22828	+	0.709150i
$747$	9.01533	−	24.9702i	0.329854	−	0.913613i
$748$			3.14621i			0.115037i
$749$		0			0
$750$	−6.42865	+	4.51380i	−0.234741	+	0.164820i
$751$	20.4060			0.744625			0.372312	−	0.928107i	$-0.378565\pi$
$751$	20.4060			0.744625			0.372312	+	0.928107i	$0.378565\pi$
$752$	18.4768	−	32.0028i	0.673781	−	1.16702i
$753$	24.1192	−	2.14160i	0.878951	−	0.0780441i
$754$	−13.9221	+	8.03793i	−0.507013	+	0.292724i
$755$	1.85624			0.0675554
$756$		0			0
$757$	−4.02306			−0.146221			−0.0731104	−	0.997324i	$-0.523293\pi$
$757$	−4.02306			−0.146221			−0.0731104	+	0.997324i	$0.523293\pi$
$758$	39.2400	−	22.6552i	1.42526	−	0.822874i
$759$	−32.5888	+	2.89364i	−1.18290	+	0.105032i
$760$	2.19639	−	3.80426i	0.0796715	−	0.137995i
$761$	−45.9190			−1.66456			−0.832280	−	0.554355i	$-0.812965\pi$
$761$	−45.9190			−1.66456			−0.832280	+	0.554355i	$0.812965\pi$
$762$	14.2687	−	10.0186i	0.516900	−	0.362935i
$763$		0			0
$764$		−	0.428864i		−	0.0155157i
$765$	−2.91288	−	3.45325i	−0.105315	−	0.124853i
$766$	29.1946	−	16.8555i	1.05485	−	0.609015i
$767$			7.24484i			0.261596i
$768$	3.53392	−	7.60418i	0.127519	−	0.274392i
$769$	5.22983	−	3.01944i	0.188592	−	0.108884i	−0.402731	−	0.915318i	$-0.631939\pi$
$769$	5.22983	−	3.01944i	0.188592	−	0.108884i	0.591323	+	0.806434i	$0.298606\pi$
$770$		0			0
$771$	33.4378	−	2.96902i	1.20423	−	0.106927i
$772$	−0.606656	−	1.05076i	−0.0218340	−	0.0378176i
$773$	19.1157	+	33.1094i	0.687545	+	1.19086i	0.972630	+	0.232360i	$0.0746448\pi$
$773$	19.1157	+	33.1094i	0.687545	+	1.19086i	−0.285085	+	0.958502i	$0.592022\pi$
$774$	−4.31829	−	24.1251i	−0.155218	−	0.867158i
$775$	−31.9510	−	18.4469i	−1.14771	−	0.662633i
$776$	−16.9060	+	29.2820i	−0.606889	+	1.05116i
$777$		0			0
$778$	3.33508	+	5.77653i	0.119568	+	0.207098i
$779$		−	27.6587i		−	0.990974i
$780$	0.0333940	+	0.376091i	0.00119570	+	0.0134662i
$781$	24.6325			0.881421
$782$	21.6461	−	37.4921i	0.774061	−	1.34071i
$783$	−15.6857	−	4.13781i	−0.560563	−	0.147873i
$784$		0			0
$785$	−4.36739	−	2.52152i	−0.155879	−	0.0899968i
$786$	−41.1230	+	28.8740i	−1.46681	+	1.02990i
$787$	41.7875	+	24.1260i	1.48957	+	0.860001i	0.999929	−	0.0119261i	$-0.00379628\pi$
$787$	41.7875	+	24.1260i	1.48957	+	0.860001i	0.489636	+	0.871927i	$0.337130\pi$
$788$	−1.34907	−	0.778886i	−0.0480586	−	0.0277467i
$789$	0.779682	+	8.78096i	0.0277574	+	0.312611i
$790$	2.03675	+	1.17592i	0.0724643	+	0.0418373i
$791$		0			0
$792$	−24.9027	+	4.45749i	−0.884880	+	0.158390i
$793$	−9.41161	+	16.3014i	−0.334216	+	0.578879i
$794$	−14.3279			−0.508478
$795$	−0.0373849	+	0.0262493i	−0.00132590	+	0.000930967i
$796$		−	1.39615i		−	0.0494853i
$797$	12.6517	+	21.9133i	0.448145	+	0.776209i	0.998265	−	0.0588759i	$-0.0187516\pi$
$797$	12.6517	+	21.9133i	0.448145	+	0.776209i	−0.550121	+	0.835085i	$0.685418\pi$
$798$		0			0
$799$	20.6626	−	35.7886i	0.730989	−	1.26611i
$800$	−4.87769	−	2.81613i	−0.172452	−	0.0995653i
$801$	1.90893	−	5.28726i	0.0674487	−	0.186816i
$802$	−14.7723	−	25.5864i	−0.521628	−	0.903486i
$803$	−15.2035	−	26.3333i	−0.536521	−	0.929282i
$804$	0.0224759	+	0.0320107i	0.000792664	+	0.00112893i
$805$		0			0
$806$	−33.5428	+	19.3660i	−1.18150	+	0.682137i
$807$	5.03223	+	7.16703i	0.177143	+	0.252291i
$808$		−	19.6428i		−	0.691032i
$809$	−9.65975	+	5.57706i	−0.339619	+	0.196079i	−0.660103	−	0.751175i	$-0.729488\pi$
$809$	−9.65975	+	5.57706i	−0.339619	+	0.196079i	0.320485	+	0.947254i	$0.396154\pi$
$810$	−2.63244	+	3.17039i	−0.0924943	+	0.111396i
$811$			1.90097i			0.0667520i	0.999443	+	0.0333760i	$0.0106259\pi$
$811$			1.90097i			0.0667520i	−0.999443	+	0.0333760i	$0.989374\pi$
$812$		0			0
$813$	−49.2906	−	22.9070i	−1.72870	−	0.803383i
$814$	−55.6389			−1.95014
$815$	−0.996957	+	1.72678i	−0.0349219	+	0.0604865i
$816$	15.5606	−	33.4829i	0.544731	−	1.17214i
$817$	25.4554	−	14.6967i	0.890572	−	0.514172i
$818$	−3.60098			−0.125905
$819$		0			0
$820$	0.325441			0.0113649
$821$	8.79955	−	5.08042i	0.307106	−	0.177308i	−0.338524	−	0.940958i	$-0.609928\pi$
$821$	8.79955	−	5.08042i	0.307106	−	0.177308i	0.645631	+	0.763650i	$0.276594\pi$
$822$	−2.34709	−	3.34278i	−0.0818640	−	0.116593i
$823$	−15.9763	+	27.6717i	−0.556898	+	0.964576i	0.440855	+	0.897578i	$0.354675\pi$
$823$	−15.9763	+	27.6717i	−0.556898	+	0.964576i	−0.997753	+	0.0669975i	$0.978658\pi$
$824$	−21.2799			−0.741320
$825$	2.37621	+	26.7615i	0.0827292	+	0.931716i
$826$		0			0
$827$			13.7400i			0.477787i	0.971046	+	0.238894i	$0.0767847\pi$
$827$			13.7400i			0.477787i	−0.971046	+	0.238894i	$0.923215\pi$
$828$	−3.43416	−	1.23988i	−0.119345	−	0.0430887i
$829$	15.5086	−	8.95388i	0.538635	−	0.310981i	−0.205891	−	0.978575i	$-0.566009\pi$
$829$	15.5086	−	8.95388i	0.538635	−	0.310981i	0.744526	+	0.667594i	$0.232676\pi$
$830$			4.05180i			0.140640i
$831$	−44.9531	+	3.99149i	−1.55941	+	0.138463i
$832$	21.1097	−	12.1877i	0.731848	−	0.422532i
$833$		0			0
$834$	4.97100	−	10.6964i	0.172132	−	0.370388i
$835$	0.411927	+	0.713478i	0.0142553	+	0.0246909i
$836$	1.72089	+	2.98067i	0.0595182	+	0.103089i
$837$	−37.7920	−	9.96931i	−1.30628	−	0.344590i
$838$	37.7658	+	21.8041i	1.30460	+	0.753209i
$839$	27.5601	−	47.7356i	0.951482	−	1.64802i	0.209261	−	0.977860i	$-0.432894\pi$
$839$	27.5601	−	47.7356i	0.951482	−	1.64802i	0.742221	−	0.670155i	$-0.233773\pi$
$840$		0			0
$841$	−9.62659	−	16.6737i	−0.331951	−	0.574957i
$842$			54.0591i			1.86300i
$843$	7.51483	+	3.49240i	0.258825	+	0.120285i
$844$	−1.11980			−0.0385452
$845$	0.149353	−	0.258688i	0.00513791	−	0.00889912i
$846$	−35.4544	−	12.8006i	−1.21895	−	0.440092i
$847$		0			0
$848$	−0.323312	−	0.186664i	−0.0111026	−	0.00641007i
$849$	−1.68174	−	0.781563i	−0.0577173	−	0.0268232i
$850$	−30.7880	−	17.7755i	−1.05602	−	0.609693i
$851$	61.3034	+	35.3936i	2.10145	+	1.21328i
$852$	2.49287	+	1.15852i	0.0854042	+	0.0396902i
$853$	2.07425	+	1.19757i	0.0710209	+	0.0410039i	0.535090	−	0.844795i	$-0.320278\pi$
$853$	2.07425	+	1.19757i	0.0710209	+	0.0410039i	−0.464069	+	0.885799i	$0.653611\pi$
$854$		0			0
$855$	−4.64845	−	1.67829i	−0.158974	−	0.0573963i
$856$	−22.3581	+	38.7254i	−0.764185	+	1.32361i
$857$	30.4922			1.04159			0.520796	−	0.853681i	$-0.325635\pi$
$857$	30.4922			1.04159			0.520796	+	0.853681i	$0.325635\pi$
$858$	25.5781	+	11.8870i	0.873221	+	0.405815i
$859$			44.9683i			1.53430i	0.641469	+	0.767149i	$0.278325\pi$
$859$			44.9683i			1.53430i	−0.641469	+	0.767149i	$0.721675\pi$
$860$	0.172926	+	0.299517i	0.00589674	+	0.0102134i
$861$		0			0
$862$	−14.4383	+	25.0078i	−0.491770	+	0.851770i
$863$	−45.4835	−	26.2599i	−1.54828	−	0.893897i	−0.998274	−	0.0587340i	$-0.981294\pi$
$863$	−45.4835	−	26.2599i	−1.54828	−	0.893897i	−0.550002	−	0.835163i	$-0.685373\pi$
$864$	−5.76938	−	1.52193i	−0.196278	−	0.0517771i
$865$	3.11463	+	5.39470i	0.105901	+	0.183425i
$866$	7.38262	+	12.7871i	0.250872	+	0.434523i
$867$	4.99198	−	10.7416i	0.169537	−	0.364804i
$868$		0			0
$869$	14.0678	−	8.12203i	0.477217	−	0.275521i
$870$	2.46619	−	0.218979i	0.0836117	−	0.00742408i
$871$			0.384419i			0.0130255i
$872$	−20.4720	+	11.8195i	−0.693270	+	0.400259i
$873$	35.7798	+	12.9181i	1.21096	+	0.437210i
$874$		−	47.3591i		−	1.60195i
$875$		0			0
$876$	−0.300122	−	3.38004i	−0.0101402	−	0.114201i
$877$	1.36775			0.0461857			0.0230929	−	0.999733i	$-0.492649\pi$
$877$	1.36775			0.0461857			0.0230929	+	0.999733i	$0.492649\pi$
$878$	5.47457	−	9.48224i	0.184758	−	0.320010i
$879$	−2.71252	−	3.86323i	−0.0914910	−	0.130304i
$880$	3.68808	−	2.12931i	0.124325	−	0.0717791i
$881$	20.7141			0.697876			0.348938	−	0.937146i	$-0.386542\pi$
$881$	20.7141			0.697876			0.348938	+	0.937146i	$0.386542\pi$
$882$		0			0
$883$	−14.3561			−0.483120			−0.241560	−	0.970386i	$-0.577659\pi$
$883$	−14.3561			−0.483120			−0.241560	+	0.970386i	$0.577659\pi$
$884$	−2.98849	+	1.72541i	−0.100514	+	0.0580317i
$885$	0.470249	−	1.01187i	0.0158073	−	0.0340136i
$886$	−0.638206	+	1.10541i	−0.0214410	+	0.0371368i
$887$	44.1826			1.48351			0.741754	−	0.670672i	$-0.233994\pi$
$887$	44.1826			1.48351			0.741754	+	0.670672i	$0.233994\pi$
$888$	49.6378	+	23.0684i	1.66574	+	0.774124i
$889$		0			0
$890$			0.857939i			0.0287582i
$891$	9.87294	+	26.6951i	0.330756	+	0.894319i
$892$	−3.58781	+	2.07142i	−0.120129	+	0.0693563i
$893$		−	45.2074i		−	1.51281i
$894$	−14.3818	−	20.4830i	−0.481001	−	0.685053i
$895$	−5.86629	+	3.38691i	−0.196089	+	0.113212i
$896$		0			0
$897$	−20.6205	−	29.3682i	−0.688499	−	0.980576i
$898$	−11.6161	−	20.1196i	−0.387633	−	0.671400i
$899$	11.7416	+	20.3371i	0.391605	+	0.678279i
$900$	−1.01817	+	2.82008i	−0.0339390	+	0.0940027i
$901$	−0.361558	−	0.208746i	−0.0120453	−	0.00695433i
$902$	12.1556	−	21.0540i	0.404736	−	0.701023i
$903$		0			0
$904$	20.8791	+	36.1637i	0.694429	+	1.20279i
$905$			0.772832i			0.0256898i
$906$	12.6645	−	8.89224i	0.420751	−	0.295425i
$907$	−14.3615			−0.476866			−0.238433	−	0.971159i	$-0.576634\pi$
$907$	−14.3615			−0.476866			−0.238433	+	0.971159i	$0.576634\pi$
$908$	0.0328534	−	0.0569037i	0.00109028	−	0.00188841i
$909$	−21.7536	+	3.89380i	−0.721520	+	0.129149i
$910$		0			0
$911$	−41.6920	−	24.0709i	−1.38132	−	0.797505i	−0.389003	−	0.921237i	$-0.627180\pi$
$911$	−41.6920	−	24.0709i	−1.38132	−	0.797505i	−0.992316	+	0.123732i	$0.960514\pi$
$912$	−3.57232	−	40.2323i	−0.118291	−	1.33223i
$913$	24.2363	+	13.9928i	0.802104	+	0.463095i
$914$	7.23957	+	4.17977i	0.239464	+	0.138254i
$915$	2.37259	−	1.66588i	0.0784354	−	0.0550724i
$916$	0.468997	+	0.270776i	0.0154961	+	0.00894668i
$917$		0			0
$918$	−36.4164	−	9.60643i	−1.20192	−	0.317059i
$919$	−11.5321	+	19.9741i	−0.380408	+	0.658886i	−0.991121	−	0.132966i	$-0.957550\pi$
$919$	−11.5321	+	19.9741i	−0.380408	+	0.658886i	0.610713	+	0.791852i	$0.290883\pi$
$920$	−4.91236			−0.161956
$921$	1.27346	+	14.3420i	0.0419619	+	0.472585i
$922$		−	33.6514i		−	1.10825i
$923$	13.5086	+	23.3977i	0.444642	+	0.770143i
$924$		0			0
$925$	29.0647	−	50.3416i	0.955642	−	1.65522i
$926$	−54.0094	−	31.1824i	−1.77486	−	1.02472i
$927$	4.21832	+	23.5666i	0.138548	+	0.774027i
$928$	1.79249	+	3.10469i	0.0588414	+	0.101916i
$929$	18.7804	+	32.5286i	0.616165	+	1.06723i	0.990179	+	0.139806i	$0.0446479\pi$
$929$	18.7804	+	32.5286i	0.616165	+	1.06723i	−0.374014	+	0.927423i	$0.622019\pi$
$930$	5.94185	−	0.527590i	0.194841	−	0.0173004i
$931$		0			0
$932$	4.10405	−	2.36947i	0.134433	−	0.0776147i
$933$	4.38013	−	9.42504i	0.143399	−	0.308562i
$934$		−	36.8206i		−	1.20481i
$935$	4.12436	−	2.38120i	0.134881	−	0.0778736i
$936$	−17.8909	−	21.2098i	−0.584781	−	0.693264i
$937$		−	18.9436i		−	0.618859i	−0.950922	−	0.309430i	$-0.899862\pi$
$937$		−	18.9436i		−	0.618859i	0.950922	−	0.309430i	$-0.100138\pi$
$938$		0			0
$939$	16.7626	−	11.7697i	0.547027	−	0.384088i
$940$	0.531926			0.0173495
$941$	−27.7551	+	48.0733i	−0.904792	+	1.56714i	−0.0835947	+	0.996500i	$0.526640\pi$
$941$	−27.7551	+	48.0733i	−0.904792	+	1.56714i	−0.821197	+	0.570645i	$0.806693\pi$
$942$	−41.8766	+	3.71832i	−1.36441	+	0.121149i
$943$	−26.7862	+	15.4650i	−0.872280	+	0.503611i
$944$	9.11911			0.296802
$945$		0			0
$946$	25.8359			0.839997
$947$	−16.3036	+	9.41290i	−0.529797	+	0.305878i	−0.740934	−	0.671578i	$-0.765617\pi$
$947$	−16.3036	+	9.41290i	−0.529797	+	0.305878i	0.211137	+	0.977456i	$0.432283\pi$
$948$	1.80569	−	0.160331i	0.0586460	−	0.00520731i
$949$	16.6754	−	28.8827i	0.541308	−	0.937573i
$950$	−38.8907			−1.26178
$951$	42.0214	−	29.5048i	1.36264	−	0.956758i
$952$		0			0
$953$			35.0089i			1.13405i	0.823701	+	0.567024i	$0.191905\pi$
$953$			35.0089i			1.13405i	−0.823701	+	0.567024i	$0.808095\pi$
$954$	−0.129319	+	0.358182i	−0.00418686	+	0.0115966i
$955$	−0.562196	+	0.324584i	−0.0181922	+	0.0105033i
$956$			0.0685294i			0.00221640i
$957$	7.20711	−	15.5080i	0.232973	−	0.501304i
$958$	4.23347	−	2.44420i	0.136777	−	0.0789684i
$959$		0			0
$960$	−3.73942	+	0.332032i	−0.120689	+	0.0107163i
$961$	12.7893	+	22.1518i	0.412559	+	0.714573i
$962$	−30.5127	−	52.8496i	−0.983770	−	1.70394i
$963$	47.3187	+	17.0841i	1.52482	+	0.550527i
$964$	−3.90906	−	2.25690i	−0.125902	−	0.0726898i
$965$	−0.918291	+	1.59053i	−0.0295608	+	0.0512008i
$966$		0			0
$967$	−7.47001	−	12.9384i	−0.240219	−	0.416072i	0.720557	−	0.693395i	$-0.243886\pi$
$967$	−7.47001	−	12.9384i	−0.240219	−	0.416072i	−0.960777	+	0.277323i	$0.910553\pi$
$968$			2.66315i			0.0855969i
$969$	−3.99491	−	44.9917i	−0.128335	−	1.44534i
$970$	−5.80582			−0.186414
$971$	−15.1782	+	26.2894i	−0.487091	+	0.843666i	−0.999890	−	0.0148426i	$-0.995275\pi$
$971$	−15.1782	+	26.2894i	−0.487091	+	0.843666i	0.512799	+	0.858509i	$0.328609\pi$
$972$	−0.256362	+	3.16595i	−0.00822281	+	0.101548i
$973$		0			0
$974$	−13.4280	−	7.75269i	−0.430262	−	0.248412i
$975$	−24.1168	+	16.9333i	−0.772355	+	0.542299i
$976$	20.5186	+	11.8464i	0.656785	+	0.379195i
$977$	−47.1306	−	27.2109i	−1.50784	−	0.870554i	−0.999958	−	0.00912839i	$-0.997094\pi$
$977$	−47.1306	−	27.2109i	−1.50784	−	0.870554i	−0.507885	−	0.861425i	$-0.669572\pi$
$978$	1.47015	+	16.5572i	0.0470102	+	0.529440i
$979$	5.13186	+	2.96288i	0.164015	+	0.0946940i
$980$		0			0
$981$	17.1478	+	20.3289i	0.547486	+	0.649051i
$982$	−22.5239	+	39.0125i	−0.718765	+	1.24494i
$983$	−26.2686			−0.837839			−0.418920	−	0.908023i	$-0.637591\pi$
$983$	−26.2686			−0.837839			−0.418920	+	0.908023i	$0.637591\pi$
$984$	−19.5737	+	13.7434i	−0.623987	+	0.438124i
$985$			2.35799i			0.0751318i
$986$	11.3142	+	19.5968i	0.360318	+	0.624089i
$987$		0			0
$988$	−1.88750	+	3.26924i	−0.0600492	+	0.104008i
$989$	−28.4662	−	16.4350i	−0.905173	−	0.522602i
$990$	−2.80086	−	3.32045i	−0.0890172	−	0.105531i
$991$	16.2471	+	28.1408i	0.516106	+	0.893921i	0.999825	+	0.0186981i	$0.00595214\pi$
$991$	16.2471	+	28.1408i	0.516106	+	0.893921i	−0.483720	+	0.875223i	$0.660715\pi$
$992$	4.31869	+	7.48019i	0.137118	+	0.237496i
$993$	−16.9699	−	24.1690i	−0.538524	−	0.766979i
$994$		0			0
$995$	−1.83021	+	1.05667i	−0.0580216	+	0.0334988i
$996$	1.79465	+	2.55599i	0.0568658	+	0.0809896i
$997$		−	36.7993i		−	1.16545i	−0.812671	−	0.582723i	$-0.801987\pi$
$997$		−	36.7993i		−	1.16545i	0.812671	−	0.582723i	$-0.198013\pi$
$998$	2.53205	−	1.46188i	0.0801506	−	0.0462750i
$999$	15.7075	−	59.5446i	0.496964	−	1.88391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.362.19		48
3.2	odd	2		1323.2.s.d.656.5		48
7.2	even	3		441.2.o.e.146.6	yes	48
7.3	odd	6		441.2.i.d.227.19		48
7.4	even	3		441.2.i.d.227.20		48
7.5	odd	6		441.2.o.e.146.5	✓	48
7.6	odd	2	inner	441.2.s.d.362.20		48
9.4	even	3		1323.2.i.d.1097.5		48
9.5	odd	6		441.2.i.d.68.5		48
21.2	odd	6		1323.2.o.e.440.19		48
21.5	even	6		1323.2.o.e.440.20		48
21.11	odd	6		1323.2.i.d.521.13		48
21.17	even	6		1323.2.i.d.521.5		48
21.20	even	2		1323.2.s.d.656.6		48
63.4	even	3		1323.2.s.d.962.6		48
63.5	even	6		441.2.o.e.293.6	yes	48
63.13	odd	6		1323.2.i.d.1097.13		48
63.23	odd	6		441.2.o.e.293.5	yes	48
63.31	odd	6		1323.2.s.d.962.5		48
63.32	odd	6	inner	441.2.s.d.374.20		48
63.40	odd	6		1323.2.o.e.881.19		48
63.41	even	6		441.2.i.d.68.6		48
63.58	even	3		1323.2.o.e.881.20		48
63.59	even	6	inner	441.2.s.d.374.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.5		48	9.5	odd	6
441.2.i.d.68.6		48	63.41	even	6
441.2.i.d.227.19		48	7.3	odd	6
441.2.i.d.227.20		48	7.4	even	3
441.2.o.e.146.5	✓	48	7.5	odd	6
441.2.o.e.146.6	yes	48	7.2	even	3
441.2.o.e.293.5	yes	48	63.23	odd	6
441.2.o.e.293.6	yes	48	63.5	even	6
441.2.s.d.362.19		48	1.1	even	1	trivial
441.2.s.d.362.20		48	7.6	odd	2	inner
441.2.s.d.374.19		48	63.59	even	6	inner
441.2.s.d.374.20		48	63.32	odd	6	inner
1323.2.i.d.521.5		48	21.17	even	6
1323.2.i.d.521.13		48	21.11	odd	6
1323.2.i.d.1097.5		48	9.4	even	3
1323.2.i.d.1097.13		48	63.13	odd	6
1323.2.o.e.440.19		48	21.2	odd	6
1323.2.o.e.440.20		48	21.5	even	6
1323.2.o.e.881.19		48	63.40	odd	6
1323.2.o.e.881.20		48	63.58	even	3
1323.2.s.d.656.5		48	3.2	odd	2
1323.2.s.d.656.6		48	21.20	even	2
1323.2.s.d.962.5		48	63.31	odd	6
1323.2.s.d.962.6		48	63.4	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28562 - 0.742253i) q^{2} +(-1.72526 + 0.153190i) q^{3} +(0.101880 - 0.176462i) q^{4} -0.308431 q^{5} +(-2.10433 + 1.47753i) q^{6} +2.66653i q^{8} +(2.95307 - 0.528586i) q^{9} +O(q^{10})\)	\(q+(1.28562 - 0.742253i) q^{2} +(-1.72526 + 0.153190i) q^{3} +(0.101880 - 0.176462i) q^{4} -0.308431 q^{5} +(-2.10433 + 1.47753i) q^{6} +2.66653i q^{8} +(2.95307 - 0.528586i) q^{9} +(-0.396525 + 0.228934i) q^{10} +3.16248i q^{11} +(-0.148738 + 0.320050i) q^{12} +(-3.00394 + 1.73432i) q^{13} +(0.532124 - 0.0472485i) q^{15} +(2.18300 + 3.78107i) q^{16} +(2.44124 + 4.22836i) q^{17} +(3.40418 - 2.87148i) q^{18} +(4.62558 + 2.67058i) q^{19} +(-0.0314230 + 0.0544262i) q^{20} +(2.34736 + 4.06575i) q^{22} -5.97291i q^{23} +(-0.408486 - 4.60047i) q^{24} -4.90487 q^{25} +(-2.57462 + 4.45937i) q^{26} +(-5.01384 + 1.36433i) q^{27} +(2.70372 + 1.56099i) q^{29} +(0.649039 - 0.455715i) q^{30} +(6.51414 + 3.76094i) q^{31} +(0.994457 + 0.574150i) q^{32} +(-0.484460 - 5.45611i) q^{33} +(6.27702 + 3.62404i) q^{34} +(0.207584 - 0.574955i) q^{36} +(-5.92568 + 10.2636i) q^{37} +7.92899 q^{38} +(4.91690 - 3.45234i) q^{39} -0.822440i q^{40} +(-2.58920 - 4.48462i) q^{41} +(2.75159 - 4.76589i) q^{43} +(0.558056 + 0.322194i) q^{44} +(-0.910816 + 0.163032i) q^{45} +(-4.43341 - 7.67889i) q^{46} +(-4.23198 - 7.33000i) q^{47} +(-4.34547 - 6.18892i) q^{48} +(-6.30580 + 3.64066i) q^{50} +(-4.85953 - 6.92105i) q^{51} +0.706773i q^{52} +(-0.0740521 + 0.0427540i) q^{53} +(-5.43322 + 5.47555i) q^{54} -0.975406i q^{55} +(-8.38945 - 3.89886i) q^{57} +4.63461 q^{58} +(1.04433 - 1.80884i) q^{59} +(0.0458754 - 0.0987132i) q^{60} +(4.69964 - 2.71334i) q^{61} +11.1663 q^{62} -7.02734 q^{64} +(0.926507 - 0.534919i) q^{65} +(-4.67265 - 6.65489i) q^{66} +(0.0554134 - 0.0959787i) q^{67} +0.994857 q^{68} +(0.914990 + 10.3048i) q^{69} -7.78899i q^{71} +(1.40949 + 7.87444i) q^{72} +(-8.32679 + 4.80748i) q^{73} +17.5934i q^{74} +(8.46219 - 0.751378i) q^{75} +(0.942510 - 0.544159i) q^{76} +(3.75876 - 8.08799i) q^{78} +(-2.56825 - 4.44834i) q^{79} +(-0.673305 - 1.16620i) q^{80} +(8.44119 - 3.12190i) q^{81} +(-6.65745 - 3.84368i) q^{82} +(4.42464 - 7.66370i) q^{83} +(-0.752954 - 1.30416i) q^{85} -8.16950i q^{86} +(-4.90376 - 2.27894i) q^{87} -8.43284 q^{88} +(0.936885 - 1.62273i) q^{89} +(-1.04995 + 0.885654i) q^{90} +(-1.05399 - 0.608521i) q^{92} +(-11.8147 - 5.49071i) q^{93} +(-10.8814 - 6.28240i) q^{94} +(-1.42667 - 0.823689i) q^{95} +(-1.80365 - 0.838219i) q^{96} +(10.9813 + 6.34007i) q^{97} +(1.67164 + 9.33900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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