LMFDB - Embedded newform 637.2.r.d.324.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(116,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.116"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,0,0,0,0,2,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			324.3
Root			$1.98293 - 0.531325i$ of defining polynomial
Character	$\chi$	$=$	637.324
Dual form			637.2.r.d.116.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.596598 - 0.344446i) q^{2} +(-1.10716 - 1.91766i) q^{3} +(-0.762714 - 1.32106i) q^{4} +(2.78368 + 1.60716i) q^{5} +1.52543i q^{6} +2.42864i q^{8} +(-0.951606 + 1.64823i) q^{9} +(-1.10716 - 1.91766i) q^{10} +(-2.32865 + 1.34445i) q^{11} +(-1.68889 + 2.92525i) q^{12} +(-3.59210 - 0.311108i) q^{13} -7.11753i q^{15} +(-0.688892 + 1.19320i) q^{16} +(-1.79605 - 3.11085i) q^{17} +(1.13545 - 0.655554i) q^{18} +(-7.40120 - 4.27309i) q^{19} -4.90321i q^{20} +1.85236 q^{22} +(-1.64050 + 2.84143i) q^{23} +(4.65730 - 2.68889i) q^{24} +(2.66593 + 4.61752i) q^{25} +(2.03588 + 1.42289i) q^{26} -2.42864 q^{27} +2.05086 q^{29} +(-2.45161 + 4.24631i) q^{30} +(-5.05459 + 2.91827i) q^{31} +(5.02851 - 2.90321i) q^{32} +(5.15637 + 2.97703i) q^{33} +2.47457i q^{34} +2.90321 q^{36} +(3.40636 + 1.96666i) q^{37} +(2.94370 + 5.09863i) q^{38} +(3.38044 + 7.23287i) q^{39} +(-3.90321 + 6.76056i) q^{40} -0.755569i q^{41} -8.80642 q^{43} +(3.55219 + 2.05086i) q^{44} +(-5.29794 + 3.05877i) q^{45} +(1.95744 - 1.13013i) q^{46} +(-1.63027 - 0.941234i) q^{47} +3.05086 q^{48} -3.67307i q^{50} +(-3.97703 + 6.88842i) q^{51} +(2.32876 + 4.98267i) q^{52} +(-1.26271 - 2.18708i) q^{53} +(1.44892 + 0.836535i) q^{54} -8.64296 q^{55} +18.9240i q^{57} +(-1.22354 - 0.706409i) q^{58} +(6.34957 - 3.66593i) q^{59} +(-9.40268 + 5.42864i) q^{60} +(4.52543 - 7.83827i) q^{61} +4.02074 q^{62} -1.24443 q^{64} +(-9.49928 - 6.63911i) q^{65} +(-2.05086 - 3.55219i) q^{66} +(0.371213 - 0.214320i) q^{67} +(-2.73975 + 4.74538i) q^{68} +7.26517 q^{69} +8.98418i q^{71} +(-4.00296 - 2.31111i) q^{72} +(5.01481 - 2.89530i) q^{73} +(-1.35482 - 2.34661i) q^{74} +(5.90321 - 10.2247i) q^{75} +13.0366i q^{76} +(0.474572 - 5.47949i) q^{78} +(2.23975 - 3.87936i) q^{79} +(-3.83531 + 2.21432i) q^{80} +(5.54371 + 9.60199i) q^{81} +(-0.260253 + 0.450771i) q^{82} +10.8272i q^{83} -11.5462i q^{85} +(5.25390 + 3.03334i) q^{86} +(-2.27062 - 3.93284i) q^{87} +(-3.26517 - 5.65545i) q^{88} +(-4.64360 - 2.68098i) q^{89} +4.21432 q^{90} +5.00492 q^{92} +(11.1925 + 6.46198i) q^{93} +(0.648409 + 1.12308i) q^{94} +(-13.7351 - 23.7898i) q^{95} +(-11.1347 - 6.42864i) q^{96} -9.62867i q^{97} -5.11753i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 2 q^{9} - 20 q^{12} - 16 q^{13} - 8 q^{16} - 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} - 4 q^{38} + 8 q^{39} - 20 q^{40} - 52 q^{43}+ \cdots - 58 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 2 * q^9 - 20 * q^12 - 16 * q^13 - 8 * q^16 - 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 - 4 * q^38 + 8 * q^39 - 20 * q^40 - 52 * q^43 - 16 * q^48 - 8 * q^51 - 20 * q^52 - 2 * q^53 - 24 * q^55 + 28 * q^61 - 32 * q^62 - 16 * q^64 + 6 * q^65 + 28 * q^66 + 20 * q^68 + 8 * q^69 + 24 * q^74 + 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 - 56 * q^82 - 40 * q^87 + 40 * q^88 + 24 * q^90 - 72 * q^92 + 20 * q^94 - 58 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.596598	−	0.344446i	−0.421859	−	0.243560i	0.274014	−	0.961726i	$-0.411649\pi$
$2$	−0.596598	−	0.344446i	−0.421859	−	0.243560i	−0.695872	+	0.718166i	$0.744982\pi$
$3$	−1.10716	−	1.91766i	−0.639219	−	1.10716i	−0.985604	−	0.169068i	$-0.945924\pi$
$3$	−1.10716	−	1.91766i	−0.639219	−	1.10716i	0.346385	−	0.938092i	$-0.387409\pi$
$4$	−0.762714	−	1.32106i	−0.381357	−	0.660530i
$5$	2.78368	+	1.60716i	1.24490	+	0.718744i	0.970088	−	0.242754i	$-0.0780508\pi$
$5$	2.78368	+	1.60716i	1.24490	+	0.718744i	0.274813	+	0.961498i	$0.411384\pi$
$6$			1.52543i			0.622753i
$7$		0			0
$7$		0			0
$8$			2.42864i			0.858654i
$9$	−0.951606	+	1.64823i	−0.317202	+	0.549410i
$10$	−1.10716	−	1.91766i	−0.350115	−	0.606416i
$11$	−2.32865	+	1.34445i	−0.702114	+	0.405366i	−0.808134	−	0.588998i	$-0.799522\pi$
$11$	−2.32865	+	1.34445i	−0.702114	+	0.405366i	0.106020	+	0.994364i	$0.466189\pi$
$12$	−1.68889	+	2.92525i	−0.487541	+	0.844446i
$13$	−3.59210	−	0.311108i	−0.996270	−	0.0862858i
$13$	−3.59210	−	0.311108i	−0.996270	−	0.0862858i
$14$		0			0
$15$		−	7.11753i		−	1.83774i
$16$	−0.688892	+	1.19320i	−0.172223	+	0.298299i
$17$	−1.79605	−	3.11085i	−0.435607	−	0.754493i	0.561738	−	0.827315i	$-0.310133\pi$
$17$	−1.79605	−	3.11085i	−0.435607	−	0.754493i	−0.997345	+	0.0728222i	$0.976799\pi$
$18$	1.13545	−	0.655554i	0.267629	−	0.154516i
$19$	−7.40120	−	4.27309i	−1.69795	−	0.980313i	−0.947701	−	0.319160i	$-0.896599\pi$
$19$	−7.40120	−	4.27309i	−1.69795	−	0.980313i	−0.750251	−	0.661153i	$-0.770067\pi$
$20$		−	4.90321i		−	1.09639i
$21$		0			0
$22$	1.85236			0.394924
$23$	−1.64050	+	2.84143i	−0.342068	+	0.592478i	−0.984817	−	0.173599i	$-0.944460\pi$
$23$	−1.64050	+	2.84143i	−0.342068	+	0.592478i	0.642749	+	0.766077i	$0.277794\pi$
$24$	4.65730	−	2.68889i	0.950667	−	0.548868i
$25$	2.66593	+	4.61752i	0.533185	+	0.923504i
$26$	2.03588	+	1.42289i	0.399269	+	0.279052i
$27$	−2.42864			−0.467392
$28$		0			0
$29$	2.05086			0.380834			0.190417	−	0.981703i	$-0.439016\pi$
$29$	2.05086			0.380834			0.190417	+	0.981703i	$0.439016\pi$
$30$	−2.45161	+	4.24631i	−0.447600	+	0.775266i
$31$	−5.05459	+	2.91827i	−0.907831	+	0.524136i	−0.879733	−	0.475469i	$-0.842278\pi$
$31$	−5.05459	+	2.91827i	−0.907831	+	0.524136i	−0.0280982	+	0.999605i	$0.508945\pi$
$32$	5.02851	−	2.90321i	0.888923	−	0.513220i
$33$	5.15637	+	2.97703i	0.897609	+	0.518235i
$34$			2.47457i			0.424386i
$35$		0			0
$36$	2.90321			0.483869
$37$	3.40636	+	1.96666i	0.560002	+	0.323317i	0.753146	−	0.657853i	$-0.228535\pi$
$37$	3.40636	+	1.96666i	0.560002	+	0.323317i	−0.193144	+	0.981170i	$0.561869\pi$
$38$	2.94370	+	5.09863i	0.477530	+	0.827107i
$39$	3.38044	+	7.23287i	0.541303	+	1.15819i
$40$	−3.90321	+	6.76056i	−0.617152	+	1.06894i
$41$		−	0.755569i		−	0.118000i	−0.998258	−	0.0590000i	$-0.981209\pi$
$41$		−	0.755569i		−	0.118000i	0.998258	−	0.0590000i	$-0.0187912\pi$
$42$		0			0
$43$	−8.80642			−1.34297			−0.671484	−	0.741019i	$-0.734343\pi$
$43$	−8.80642			−1.34297			−0.671484	+	0.741019i	$0.734343\pi$
$44$	3.55219	+	2.05086i	0.535512	+	0.309178i
$45$	−5.29794	+	3.05877i	−0.789770	+	0.455974i
$46$	1.95744	−	1.13013i	0.288608	−	0.166628i
$47$	−1.63027	−	0.941234i	−0.237799	−	0.137293i	0.376366	−	0.926471i	$-0.377174\pi$
$47$	−1.63027	−	0.941234i	−0.237799	−	0.137293i	−0.614165	+	0.789178i	$0.710507\pi$
$48$	3.05086			0.440353
$49$		0			0
$50$		−	3.67307i		−	0.519451i
$51$	−3.97703	+	6.88842i	−0.556896	+	0.964572i
$52$	2.32876	+	4.98267i	0.322940	+	0.690972i
$53$	−1.26271	−	2.18708i	−0.173447	−	0.300419i	0.766176	−	0.642631i	$-0.222157\pi$
$53$	−1.26271	−	2.18708i	−0.173447	−	0.300419i	−0.939623	+	0.342212i	$0.888824\pi$
$54$	1.44892	+	0.836535i	0.197173	+	0.113838i
$55$	−8.64296			−1.16542
$56$		0			0
$57$			18.9240i			2.50654i
$58$	−1.22354	−	0.706409i	−0.160658	−	0.0927560i
$59$	6.34957	−	3.66593i	0.826644	−	0.477263i	−0.0260585	−	0.999660i	$-0.508296\pi$
$59$	6.34957	−	3.66593i	0.826644	−	0.477263i	0.852702	+	0.522398i	$0.174962\pi$
$60$	−9.40268	+	5.42864i	−1.21388	+	0.700834i
$61$	4.52543	−	7.83827i	0.579422	−	1.00359i	−0.416124	−	0.909308i	$-0.636612\pi$
$61$	4.52543	−	7.83827i	0.579422	−	1.00359i	0.995546	−	0.0942799i	$-0.0300549\pi$
$62$	4.02074			0.510635
$63$		0			0
$64$	−1.24443			−0.155554
$65$	−9.49928	−	6.63911i	−1.17824	−	0.823480i
$66$	−2.05086	−	3.55219i	−0.252443	−	0.437244i
$67$	0.371213	−	0.214320i	0.0453508	−	0.0261833i	−0.477153	−	0.878820i	$-0.658331\pi$
$67$	0.371213	−	0.214320i	0.0453508	−	0.0261833i	0.522504	+	0.852637i	$0.324998\pi$
$68$	−2.73975	+	4.74538i	−0.332243	+	0.575462i
$69$	7.26517			0.874624
$70$		0			0
$71$			8.98418i			1.06623i	0.846044	+	0.533113i	$0.178978\pi$
$71$			8.98418i			1.06623i	−0.846044	+	0.533113i	$0.821022\pi$
$72$	−4.00296	−	2.31111i	−0.471753	−	0.272367i
$73$	5.01481	−	2.89530i	0.586939	−	0.338869i	−0.176947	−	0.984220i	$-0.556622\pi$
$73$	5.01481	−	2.89530i	0.586939	−	0.338869i	0.763886	+	0.645351i	$0.223289\pi$
$74$	−1.35482	−	2.34661i	−0.157494	−	0.272788i
$75$	5.90321	−	10.2247i	0.681644	−	1.18064i
$76$			13.0366i			1.49540i
$77$		0			0
$78$	0.474572	−	5.47949i	0.0537347	−	0.620431i
$79$	2.23975	−	3.87936i	0.251991	−	0.436462i	−0.712083	−	0.702096i	$-0.752248\pi$
$79$	2.23975	−	3.87936i	0.251991	−	0.436462i	0.964074	+	0.265634i	$0.0855812\pi$
$80$	−3.83531	+	2.21432i	−0.428801	+	0.247568i
$81$	5.54371	+	9.60199i	0.615968	+	1.06689i
$82$	−0.260253	+	0.450771i	−0.0287401	+	0.0497793i
$83$			10.8272i			1.18844i	0.804304	+	0.594218i	$0.202538\pi$
$83$			10.8272i			1.18844i	−0.804304	+	0.594218i	$0.797462\pi$
$84$		0			0
$85$		−	11.5462i		−	1.25236i
$86$	5.25390	+	3.03334i	0.566542	+	0.327093i
$87$	−2.27062	−	3.93284i	−0.243436	−	0.421644i
$88$	−3.26517	−	5.65545i	−0.348069	−	0.602873i
$89$	−4.64360	−	2.68098i	−0.492220	−	0.284183i	0.233275	−	0.972411i	$-0.425056\pi$
$89$	−4.64360	−	2.68098i	−0.492220	−	0.284183i	−0.725495	+	0.688227i	$0.758389\pi$
$90$	4.21432			0.444228
$91$		0			0
$92$	5.00492			0.521799
$93$	11.1925	+	6.46198i	1.16061	+	0.670076i
$94$	0.648409	+	1.12308i	0.0668783	+	0.115837i
$95$	−13.7351	−	23.7898i	−1.40919	−	2.44078i
$96$	−11.1347	−	6.42864i	−1.13643	−	0.656120i
$97$		−	9.62867i		−	0.977643i	−0.872384	−	0.488822i	$-0.837427\pi$
$97$		−	9.62867i		−	0.977643i	0.872384	−	0.488822i	$-0.162573\pi$
$98$		0			0
$99$		−	5.11753i		−	0.514331i
$100$	4.06668	−	7.04369i	0.406668	−	0.704369i
$101$	−6.84691	−	11.8592i	−0.681293	−	1.18003i	−0.974587	−	0.224011i	$-0.928085\pi$
$101$	−6.84691	−	11.8592i	−0.681293	−	1.18003i	0.293294	−	0.956022i	$-0.405249\pi$
$102$	4.74538	−	2.73975i	0.469863	−	0.271275i
$103$	−6.14764	+	10.6480i	−0.605745	+	1.04918i	0.386188	+	0.922420i	$0.373792\pi$
$103$	−6.14764	+	10.6480i	−0.605745	+	1.04918i	−0.991933	+	0.126761i	$0.959542\pi$
$104$	0.755569	−	8.72393i	0.0740896	−	0.855451i
$105$		0			0
$106$			1.73975i			0.168979i
$107$	9.09457	−	15.7522i	0.879205	−	1.52283i	0.0269898	−	0.999636i	$-0.491408\pi$
$107$	9.09457	−	15.7522i	0.879205	−	1.52283i	0.852215	−	0.523192i	$-0.175259\pi$
$108$	1.85236	+	3.20838i	0.178243	+	0.308726i
$109$	7.24167	−	4.18098i	0.693626	−	0.400465i	−0.111343	−	0.993782i	$-0.535515\pi$
$109$	7.24167	−	4.18098i	0.693626	−	0.400465i	0.804969	+	0.593317i	$0.202182\pi$
$110$	5.15637	+	2.97703i	0.491641	+	0.283849i
$111$		−	8.70964i		−	0.826682i
$112$		0			0
$113$	−8.46520			−0.796339			−0.398170	−	0.917312i	$-0.630354\pi$
$113$	−8.46520			−0.796339			−0.398170	+	0.917312i	$0.630354\pi$
$114$	6.51828	−	11.2900i	0.610493	−	1.05741i
$115$	−9.13325	+	5.27309i	−0.851680	+	0.491718i
$116$	−1.56422	−	2.70930i	−0.145234	−	0.251552i
$117$	3.93104	−	5.62456i	0.363425	−	0.519991i
$118$	−5.05086			−0.464969
$119$		0			0
$120$	17.2859			1.57798
$121$	−1.88493	+	3.26479i	−0.171357	+	0.296799i
$122$	−5.39972	+	3.11753i	−0.488868	+	0.282248i
$123$	−1.44892	+	0.836535i	−0.130645	+	0.0754279i
$124$	7.71041	+	4.45161i	0.692415	+	0.399766i
$125$			1.06668i			0.0954065i
$126$		0			0
$127$	−4.08742			−0.362700			−0.181350	−	0.983419i	$-0.558047\pi$
$127$	−4.08742			−0.362700			−0.181350	+	0.983419i	$0.558047\pi$
$128$	−9.31460	−	5.37778i	−0.823302	−	0.475333i
$129$	9.75012	+	16.8877i	0.858450	+	1.48688i
$130$	3.38044	+	7.23287i	0.296484	+	0.634365i
$131$	2.96989	−	5.14400i	0.259480	−	0.449433i	−0.706622	−	0.707591i	$-0.749782\pi$
$131$	2.96989	−	5.14400i	0.259480	−	0.449433i	0.966103	+	0.258158i	$0.0831154\pi$
$132$		−	9.08250i		−	0.790530i
$133$		0			0
$134$	−0.295286			−0.0255089
$135$	−6.76056	−	3.90321i	−0.581856	−	0.335935i
$136$	7.55514	−	4.36196i	0.647848	−	0.374035i
$137$	−14.1699	+	8.18098i	−1.21061	+	0.698948i	−0.962893	−	0.269883i	$-0.913015\pi$
$137$	−14.1699	+	8.18098i	−1.21061	+	0.698948i	−0.247721	+	0.968831i	$0.579682\pi$
$138$	−4.33439	−	2.50246i	−0.368968	−	0.213024i
$139$	−3.03011			−0.257011			−0.128505	−	0.991709i	$-0.541018\pi$
$139$	−3.03011			−0.257011			−0.128505	+	0.991709i	$0.541018\pi$
$140$		0			0
$141$			4.16839i			0.351041i
$142$	3.09457	−	5.35994i	0.259690	−	0.449797i
$143$	8.78302	−	4.10493i	0.734473	−	0.343271i
$144$	−1.31111	−	2.27091i	−0.109259	−	0.189242i
$145$	5.70893	+	3.29605i	0.474101	+	0.273722i
$146$	−3.98910			−0.330140
$147$		0			0
$148$		−	6.00000i		−	0.493197i
$149$	12.5892	+	7.26840i	1.03135	+	0.595451i	0.917371	−	0.398032i	$-0.130307\pi$
$149$	12.5892	+	7.26840i	1.03135	+	0.595451i	0.113979	+	0.993483i	$0.463640\pi$
$150$	−7.04369	+	4.06668i	−0.575115	+	0.332043i
$151$	17.2987	−	9.98741i	1.40775	−	0.812764i	0.412577	−	0.910923i	$-0.364629\pi$
$151$	17.2987	−	9.98741i	1.40775	−	0.812764i	0.995171	+	0.0981592i	$0.0312954\pi$
$152$	10.3778	−	17.9748i	0.841749	−	1.45795i
$153$	6.83654			0.552701
$154$		0			0
$155$	−18.7605			−1.50688
$156$	6.97674	−	9.98236i	0.558587	−	0.799229i
$157$	3.69926	+	6.40731i	0.295233	+	0.511359i	0.975039	−	0.222033i	$-0.0712693\pi$
$157$	3.69926	+	6.40731i	0.295233	+	0.511359i	−0.679806	+	0.733392i	$0.737936\pi$
$158$	−2.67246	+	1.54294i	−0.212609	+	0.122750i
$159$	−2.79605	+	4.84290i	−0.221741	+	0.384067i
$160$	18.6637			1.47550
$161$		0			0
$162$		−	7.63804i		−	0.600101i
$163$	2.01518	+	1.16346i	0.157841	+	0.0911296i	0.576840	−	0.816857i	$-0.304286\pi$
$163$	2.01518	+	1.16346i	0.157841	+	0.0911296i	−0.418999	+	0.907987i	$0.637619\pi$
$164$	−0.998151	+	0.576283i	−0.0779425	+	0.0450001i
$165$	9.56914	+	16.5742i	0.744956	+	1.29030i
$166$	3.72938	−	6.45947i	0.289456	−	0.501352i
$167$		−	3.42219i		−	0.264817i	−0.991195	−	0.132408i	$-0.957729\pi$
$167$		−	3.42219i		−	0.264817i	0.991195	−	0.132408i	$-0.0422710\pi$
$168$		0			0
$169$	12.8064	+	2.23506i	0.985110	+	0.171928i
$170$	−3.97703	+	6.88842i	−0.305025	+	0.528318i
$171$	14.0861	−	8.13259i	1.07719	−	0.621915i
$172$	6.71678	+	11.6338i	0.512150	+	0.887069i
$173$	−4.13727	+	7.16596i	−0.314551	+	0.544818i	−0.979342	−	0.202211i	$-0.935187\pi$
$173$	−4.13727	+	7.16596i	−0.314551	+	0.544818i	0.664791	+	0.747029i	$0.268521\pi$
$174$			3.12843i			0.237166i
$175$		0			0
$176$		−	3.70471i		−	0.279253i
$177$	−14.0600	−	8.11753i	−1.05681	−	0.610151i
$178$	1.84691	+	3.19894i	0.138432	+	0.239770i
$179$	−8.11285	−	14.0519i	−0.606383	−	1.05029i	−0.991831	−	0.127556i	$-0.959287\pi$
$179$	−8.11285	−	14.0519i	−0.606383	−	1.05029i	0.385449	−	0.922729i	$-0.374047\pi$
$180$	8.08162	+	4.66593i	0.602368	+	0.347778i
$181$	−9.20495			−0.684199			−0.342099	−	0.939664i	$-0.611138\pi$
$181$	−9.20495			−0.684199			−0.342099	+	0.939664i	$0.611138\pi$
$182$		0			0
$183$	−20.0415			−1.48151
$184$	−6.90080	−	3.98418i	−0.508734	−	0.293718i
$185$	6.32148	+	10.9491i	0.464764	+	0.804996i
$186$	−4.45161	−	7.71041i	−0.326408	−	0.565355i
$187$	8.36475	+	4.82939i	0.611691	+	0.353160i
$188$			2.87157i			0.209431i
$189$		0			0
$190$			18.9240i			1.37289i
$191$	3.33407	−	5.77479i	0.241245	−	0.417849i	−0.719824	−	0.694157i	$-0.755778\pi$
$191$	3.33407	−	5.77479i	0.241245	−	0.417849i	0.961069	+	0.276308i	$0.0891109\pi$
$192$	1.37778	+	2.38639i	0.0994330	+	0.172223i
$193$	−17.8431	+	10.3017i	−1.28438	+	0.741535i	−0.977645	−	0.210261i	$-0.932569\pi$
$193$	−17.8431	+	10.3017i	−1.28438	+	0.741535i	−0.306732	+	0.951796i	$0.599235\pi$
$194$	−3.31656	+	5.74445i	−0.238115	+	0.412427i
$195$	−2.21432	+	25.5669i	−0.158571	+	1.83088i
$196$		0			0
$197$		−	8.36842i		−	0.596225i	−0.954531	−	0.298112i	$-0.903643\pi$
$197$		−	8.36842i		−	0.596225i	0.954531	−	0.298112i	$-0.0963571\pi$
$198$	−1.76271	+	3.05311i	−0.125271	+	0.216975i
$199$	0.300736	+	0.520890i	0.0213186	+	0.0369249i	0.876488	−	0.481424i	$-0.159880\pi$
$199$	0.300736	+	0.520890i	0.0213186	+	0.0369249i	−0.855169	+	0.518349i	$0.826547\pi$
$200$	−11.2143	+	6.47457i	−0.792970	+	0.457821i
$201$	−0.821984	−	0.474572i	−0.0579783	−	0.0334738i
$202$			9.43356i			0.663743i
$203$		0			0
$204$	12.1334			0.849505
$205$	1.21432	−	2.10326i	0.0848118	−	0.146898i
$206$	7.33534	−	4.23506i	0.511078	−	0.295071i
$207$	−3.12222	−	5.40784i	−0.217009	−	0.375871i
$208$	2.84579	−	4.07177i	0.197320	−	0.282326i
$209$	22.9797			1.58954
$210$		0			0
$211$	−1.90321			−0.131023			−0.0655113	−	0.997852i	$-0.520868\pi$
$211$	−1.90321			−0.131023			−0.0655113	+	0.997852i	$0.520868\pi$
$212$	−1.92618	+	3.33624i	−0.132290	+	0.229134i
$213$	17.2286	−	9.94692i	1.18048	−	0.681552i
$214$	−10.8516	+	6.26517i	−0.741800	+	0.428279i
$215$	−24.5143	−	14.1533i	−1.67186	−	0.965249i
$216$		−	5.89829i		−	0.401328i
$217$		0			0
$218$	−5.76049			−0.390150
$219$	−11.1044	−	6.41112i	−0.750365	−	0.433224i
$220$	6.59210	+	11.4179i	0.444440	+	0.769792i
$221$	5.48380	+	11.7333i	0.368880	+	0.789265i
$222$	−3.00000	+	5.19615i	−0.201347	+	0.348743i
$223$		−	10.6336i		−	0.712078i	−0.934471	−	0.356039i	$-0.884127\pi$
$223$		−	10.6336i		−	0.712078i	0.934471	−	0.356039i	$-0.115873\pi$
$224$		0			0
$225$	−10.1476			−0.676510
$226$	5.05033	+	2.91581i	0.335943	+	0.193957i
$227$	−13.0344	+	7.52543i	−0.865125	+	0.499480i	−0.865725	−	0.500520i	$-0.833142\pi$
$227$	−13.0344	+	7.52543i	−0.865125	+	0.499480i	0.000600144		1.00000i	$0.499809\pi$
$228$	24.9997	−	14.4336i	1.65564	−	0.955886i
$229$	5.65930	+	3.26740i	0.373977	+	0.215916i	0.675195	−	0.737640i	$-0.264060\pi$
$229$	5.65930	+	3.26740i	0.373977	+	0.215916i	−0.301218	+	0.953555i	$0.597393\pi$
$230$	7.26517			0.479051
$231$		0			0
$232$			4.98079i			0.327005i
$233$	−13.9795	+	24.2132i	−0.915827	+	1.58626i	−0.110141	+	0.993916i	$0.535130\pi$
$233$	−13.9795	+	24.2132i	−0.915827	+	1.58626i	−0.805686	+	0.592343i	$0.798203\pi$
$234$	−4.28261	+	2.00157i	−0.279963	+	0.130847i
$235$	−3.02543	−	5.24019i	−0.197357	−	0.341833i
$236$	−9.68581	−	5.59210i	−0.630492	−	0.364015i
$237$	−9.91903			−0.644310
$238$		0			0
$239$		−	19.5812i		−	1.26660i	−0.773905	−	0.633301i	$-0.781699\pi$
$239$		−	19.5812i		−	1.26660i	0.773905	−	0.633301i	$-0.218301\pi$
$240$	8.49261	+	4.90321i	0.548196	+	0.316501i
$241$	−11.5679	+	6.67876i	−0.745157	+	0.430217i	−0.823941	−	0.566675i	$-0.808230\pi$
$241$	−11.5679	+	6.67876i	−0.745157	+	0.430217i	0.0787843	+	0.996892i	$0.474896\pi$
$242$	2.24909	−	1.29851i	0.144577	−	0.0834716i
$243$	8.63259	−	14.9521i	0.553781	−	0.959176i
$244$	−13.8064			−0.883866
$245$		0			0
$246$	1.15257			0.0734849
$247$	25.2565	+	17.6519i	1.60703	+	1.12317i
$248$	−7.08742	−	12.2758i	−0.450052	−	0.779512i
$249$	20.7628	−	11.9874i	1.31579	−	0.759671i
$250$	0.367413	−	0.636377i	0.0232372	−	0.0402480i
$251$	3.29682			0.208093			0.104047	−	0.994572i	$-0.466821\pi$
$251$	3.29682			0.208093			0.104047	+	0.994572i	$0.466821\pi$
$252$		0			0
$253$		−	8.82225i		−	0.554650i
$254$	2.43855	+	1.40790i	0.153008	+	0.0883392i
$255$	−22.1416	+	12.7835i	−1.38656	+	0.800531i
$256$	4.94914	+	8.57217i	0.309322	+	0.535761i
$257$	11.8469	−	20.5194i	0.738990	−	1.27997i	−0.213961	−	0.976842i	$-0.568636\pi$
$257$	11.8469	−	20.5194i	0.738990	−	1.27997i	0.952951	−	0.303126i	$-0.0980302\pi$
$258$		−	13.4336i		−	0.836337i
$259$		0			0
$260$	−1.52543	+	17.6128i	−0.0946030	+	1.09230i
$261$	−1.95161	+	3.38028i	−0.120801	+	0.209234i
$262$	−3.54366	+	2.04593i	−0.218928	+	0.126398i
$263$	−4.99532	−	8.65214i	−0.308024	−	0.533514i	0.669906	−	0.742446i	$-0.266335\pi$
$263$	−4.99532	−	8.65214i	−0.308024	−	0.533514i	−0.977930	+	0.208932i	$0.933001\pi$
$264$	−7.23014	+	12.5230i	−0.444984	+	0.770736i
$265$		−	8.11753i		−	0.498656i
$266$		0			0
$267$			11.8731i			0.726622i
$268$	−0.566258	−	0.326929i	−0.0345897	−	0.0199704i
$269$	−9.10171	−	15.7646i	−0.554941	−	0.961186i	−0.997908	−	0.0646482i	$-0.979407\pi$
$269$	−9.10171	−	15.7646i	−0.554941	−	0.961186i	0.442967	−	0.896538i	$-0.353926\pi$
$270$	2.68889	+	4.65730i	0.163641	+	0.283434i
$271$	20.9360	+	12.0874i	1.27177	+	0.734258i	0.975322	−	0.220789i	$-0.0708634\pi$
$271$	20.9360	+	12.0874i	1.27177	+	0.734258i	0.296451	+	0.955048i	$0.404197\pi$
$272$	4.94914			0.300086
$273$		0			0
$274$	11.2716			0.680944
$275$	−12.4160	−	7.16839i	−0.748714	−	0.432270i
$276$	−5.54125	−	9.59772i	−0.333544	−	0.577715i
$277$	0.847673	+	1.46821i	0.0509317	+	0.0882163i	0.890367	−	0.455243i	$-0.150448\pi$
$277$	0.847673	+	1.46821i	0.0509317	+	0.0882163i	−0.839436	+	0.543459i	$0.817114\pi$
$278$	1.80776	+	1.04371i	0.108422	+	0.0625976i
$279$		−	11.1082i		−	0.665028i
$280$		0			0
$281$		−	11.6479i		−	0.694854i	−0.937707	−	0.347427i	$-0.887055\pi$
$281$		−	11.6479i		−	0.694854i	0.937707	−	0.347427i	$-0.112945\pi$
$282$	1.43578	−	2.48685i	0.0854997	−	0.148090i
$283$	−6.06668	−	10.5078i	−0.360626	−	0.624623i	0.627438	−	0.778667i	$-0.284104\pi$
$283$	−6.06668	−	10.5078i	−0.360626	−	0.624623i	−0.988064	+	0.154043i	$0.950770\pi$
$284$	11.8686	−	6.85236i	0.704274	−	0.406613i
$285$	−30.4138	+	52.6783i	−1.80156	+	3.12039i
$286$	−6.65386	−	0.576283i	−0.393451	−	0.0340763i
$287$		0			0
$288$			11.0509i			0.651178i
$289$	2.04839	−	3.54792i	0.120494	−	0.208701i
$290$	−2.27062	−	3.93284i	−0.133336	−	0.230944i
$291$	−18.4645	+	10.6605i	−1.08241	+	0.624928i
$292$	−7.64973	−	4.41657i	−0.447666	−	0.258460i
$293$			11.4538i			0.669140i	0.942371	+	0.334570i	$0.108591\pi$
$293$			11.4538i			0.669140i	−0.942371	+	0.334570i	$0.891409\pi$
$294$		0			0
$295$	23.5669			1.37212
$296$	−4.77631	+	8.27282i	−0.277618	+	0.480848i
$297$	5.65545	−	3.26517i	0.328162	−	0.189465i
$298$	−5.00715	−	8.67263i	−0.290056	−	0.502392i
$299$	6.77683	−	9.69633i	0.391914	−	0.560753i
$300$	−18.0098			−1.03980
$301$		0			0
$302$	−13.7605			−0.791827
$303$	−15.1612	+	26.2600i	−0.870991	+	1.50860i
$304$	10.1973	−	5.88739i	0.584853	−	0.337665i
$305$	25.1947	−	14.5462i	1.44264	−	0.832911i
$306$	−4.07866	−	2.35482i	−0.233162	−	0.134616i
$307$			3.96989i			0.226574i	0.993562	+	0.113287i	$0.0361379\pi$
$307$			3.96989i			0.226574i	−0.993562	+	0.113287i	$0.963862\pi$
$308$		0			0
$309$	27.2257			1.54882
$310$	11.1925	+	6.46198i	0.635690	+	0.367016i
$311$	−13.6741	−	23.6842i	−0.775386	−	1.34301i	−0.934577	−	0.355760i	$-0.884222\pi$
$311$	−13.6741	−	23.6842i	−0.775386	−	1.34301i	0.159192	−	0.987248i	$-0.449111\pi$
$312$	−17.5660	+	8.20986i	−0.994481	+	0.464792i
$313$	−9.55162	+	16.5439i	−0.539890	+	0.935116i	0.459020	+	0.888426i	$0.348201\pi$
$313$	−9.55162	+	16.5439i	−0.539890	+	0.935116i	−0.998909	+	0.0466901i	$0.985133\pi$
$314$		−	5.09679i		−	0.287628i
$315$		0			0
$316$	−6.83314			−0.384394
$317$	−8.58070	−	4.95407i	−0.481940	−	0.278248i	0.239285	−	0.970949i	$-0.423087\pi$
$317$	−8.58070	−	4.95407i	−0.481940	−	0.278248i	−0.721225	+	0.692701i	$0.756420\pi$
$318$	3.33624	−	1.92618i	0.187087	−	0.108015i
$319$	−4.77572	+	2.75726i	−0.267389	+	0.154377i
$320$	−3.46410	−	2.00000i	−0.193649	−	0.111803i
$321$	−40.2766			−2.24802
$322$		0			0
$323$			30.6987i			1.70812i
$324$	8.45653	−	14.6471i	0.469807	−	0.813730i
$325$	−8.13974	−	17.4160i	−0.451511	−	0.966066i
$326$	−0.801502	−	1.38824i	−0.0443911	−	0.0768876i
$327$	−16.0354	−	9.25803i	−0.886758	−	0.511970i
$328$	1.83500			0.101321
$329$		0			0
$330$		−	13.1842i		−	0.725767i
$331$	−20.2817	−	11.7096i	−1.11478	−	0.643620i	−0.174718	−	0.984618i	$-0.555902\pi$
$331$	−20.2817	−	11.7096i	−1.11478	−	0.643620i	−0.940064	+	0.340999i	$0.889235\pi$
$332$	14.3033	−	8.25803i	0.784997	−	0.453218i
$333$	−6.48302	+	3.74297i	−0.355267	+	0.205114i
$334$	−1.17876	+	2.04167i	−0.0644988	+	0.111715i
$335$	1.37778			0.0752764
$336$		0			0
$337$	7.51606			0.409426			0.204713	−	0.978822i	$-0.434374\pi$
$337$	7.51606			0.409426			0.204713	+	0.978822i	$0.434374\pi$
$338$	−6.87043	−	5.74456i	−0.373702	−	0.312463i
$339$	9.37233	+	16.2334i	0.509035	+	0.881675i
$340$	−15.2532	+	8.80642i	−0.827219	+	0.477595i
$341$	7.84691	−	13.5912i	0.424934	−	0.736007i
$342$	−11.2050			−0.605894
$343$		0			0
$344$		−	21.3876i		−	1.15314i
$345$	20.2239	+	11.6763i	1.08882	+	0.628631i
$346$	4.93658	−	2.85013i	0.265392	−	0.153224i
$347$	−2.82225	−	4.88827i	−0.151506	−	0.262416i	0.780275	−	0.625436i	$-0.215079\pi$
$347$	−2.82225	−	4.88827i	−0.151506	−	0.262416i	−0.931781	+	0.363020i	$0.881746\pi$
$348$	−3.46367	+	5.99926i	−0.185672	+	0.321594i
$349$			24.1590i			1.29320i	0.762828	+	0.646601i	$0.223810\pi$
$349$			24.1590i			1.29320i	−0.762828	+	0.646601i	$0.776190\pi$
$350$		0			0
$351$	8.72393	+	0.755569i	0.465649	+	0.0403293i
$352$	−7.80642	+	13.5211i	−0.416084	+	0.720678i
$353$	−31.2886	+	18.0645i	−1.66532	+	0.961474i	−0.695213	+	0.718804i	$0.744690\pi$
$353$	−31.2886	+	18.0645i	−1.66532	+	0.961474i	−0.970109	+	0.242670i	$0.921977\pi$
$354$	5.59210	+	9.68581i	0.297217	+	0.514795i
$355$	−14.4390	+	25.0091i	−0.766343	+	1.32735i
$356$			8.17929i			0.433501i
$357$		0			0
$358$			11.1778i			0.590763i
$359$	15.0799	+	8.70641i	0.795889	+	0.459507i	0.842032	−	0.539428i	$-0.181360\pi$
$359$	15.0799	+	8.70641i	0.795889	+	0.459507i	−0.0461427	+	0.998935i	$0.514693\pi$
$360$	−7.42864	−	12.8668i	−0.391524	−	0.678139i
$361$	27.0185	+	46.7975i	1.42203	+	2.46302i
$362$	5.49166	+	3.17061i	0.288635	+	0.166644i
$363$	8.34767			0.438139
$364$		0			0
$365$	18.6128			0.974241
$366$	11.9567	+	6.90321i	0.624987	+	0.360837i
$367$	1.46912	+	2.54460i	0.0766876	+	0.132827i	0.901819	−	0.432114i	$-0.142232\pi$
$367$	1.46912	+	2.54460i	0.0766876	+	0.132827i	−0.825131	+	0.564941i	$0.808899\pi$
$368$	−2.26025	−	3.91487i	−0.117824	−	0.204077i
$369$	1.24535	+	0.719004i	0.0648304	+	0.0374298i
$370$		−	8.70964i		−	0.452792i
$371$		0			0
$372$		−	19.7146i		−	1.02215i
$373$	9.38493	−	16.2552i	0.485933	−	0.841661i	−0.513936	−	0.857828i	$-0.671813\pi$
$373$	9.38493	−	16.2552i	0.485933	−	0.841661i	0.999869	+	0.0161675i	$0.00514648\pi$
$374$	−3.32693	−	5.76241i	−0.172031	−	0.297967i
$375$	2.04552	−	1.18098i	0.105630	−	0.0609856i
$376$	2.28592	−	3.95933i	0.117887	−	0.204187i
$377$	−7.36689	−	0.638037i	−0.379414	−	0.0328606i
$378$		0			0
$379$			23.6894i			1.21684i	0.793615	+	0.608421i	$0.208197\pi$
$379$			23.6894i			1.21684i	−0.793615	+	0.608421i	$0.791803\pi$
$380$	−20.9518	+	36.2897i	−1.07481	+	1.86162i
$381$	4.52543	+	7.83827i	0.231845	+	0.401567i
$382$	−3.97820	+	2.29682i	−0.203543	+	0.117515i
$383$	27.3775	+	15.8064i	1.39893	+	0.807671i	0.994280	−	0.106803i	$-0.0340614\pi$
$383$	27.3775	+	15.8064i	1.39893	+	0.807671i	0.404646	+	0.914473i	$0.367395\pi$
$384$			23.8163i			1.21537i
$385$		0			0
$386$	14.1936			0.722434
$387$	8.38025	−	14.5150i	0.425992	−	0.737839i
$388$	−12.7200	+	7.34392i	−0.645762	+	0.372831i
$389$	−10.0279	−	17.3688i	−0.508434	−	0.880634i	−0.999952	−	0.00976644i	$-0.996891\pi$
$389$	−10.0279	−	17.3688i	−0.508434	−	0.880634i	0.491518	−	0.870867i	$-0.336442\pi$
$390$	10.1275	−	14.4905i	0.512825	−	0.733753i
$391$	11.7857			0.596027
$392$		0			0
$393$	−13.1526			−0.663459
$394$	−2.88247	+	4.99258i	−0.145217	+	0.251523i
$395$	12.4695	−	7.19926i	0.627408	−	0.362234i
$396$	−6.76056	+	3.90321i	−0.339731	+	0.196144i
$397$	−19.8087	−	11.4366i	−0.994169	−	0.573984i	−0.0876515	−	0.996151i	$-0.527936\pi$
$397$	−19.8087	−	11.4366i	−0.994169	−	0.573984i	−0.906518	+	0.422167i	$0.861270\pi$
$398$		−	0.414349i		−	0.0207695i
$399$		0			0
$400$	−7.34614			−0.367307
$401$	−4.86087	−	2.80642i	−0.242740	−	0.140146i	0.373695	−	0.927552i	$-0.378091\pi$
$401$	−4.86087	−	2.80642i	−0.242740	−	0.140146i	−0.616436	+	0.787405i	$0.711424\pi$
$402$	0.326929	+	0.566258i	0.0163057	+	0.0282424i
$403$	19.0645	−	8.91020i	0.949670	−	0.443849i
$404$	−10.4445	+	18.0903i	−0.519631	+	0.900028i
$405$			35.6385i			1.77089i
$406$		0			0
$407$	−10.5763			−0.524247
$408$	−16.7295	−	9.65878i	−0.828234	−	0.478181i
$409$	22.6184	−	13.0588i	1.11841	−	0.645714i	0.177416	−	0.984136i	$-0.443226\pi$
$409$	22.6184	−	13.0588i	1.11841	−	0.645714i	0.940995	+	0.338422i	$0.109893\pi$
$410$	−1.44892	+	0.836535i	−0.0715571	+	0.0413135i
$411$	31.3766	+	18.1153i	1.54770	+	0.893562i
$412$	18.7556			0.924021
$413$		0			0
$414$			4.30174i			0.211419i
$415$	−17.4010	+	30.1394i	−0.854181	+	1.47948i
$416$	−18.9661	+	8.86423i	−0.929892	+	0.434605i
$417$	3.35482	+	5.81072i	0.164286	+	0.284552i
$418$	−13.7097	−	7.91528i	−0.670562	−	0.387149i
$419$	25.2464			1.23337			0.616685	−	0.787210i	$-0.288475\pi$
$419$	25.2464			1.23337			0.616685	+	0.787210i	$0.288475\pi$
$420$		0			0
$421$		−	8.22861i		−	0.401038i	−0.979690	−	0.200519i	$-0.935737\pi$
$421$		−	8.22861i		−	0.401038i	0.979690	−	0.200519i	$-0.0642628\pi$
$422$	1.13545	+	0.655554i	0.0552730	+	0.0319119i
$423$	3.10274	−	1.79137i	0.150860	−	0.0870993i
$424$	5.31164	−	3.06668i	0.257956	−	0.148931i
$425$	9.57628	−	16.5866i	0.464518	−	0.804569i
$426$	−13.7047			−0.663996
$427$		0			0
$428$	−27.7462			−1.34116
$429$	−17.5961	−	12.2980i	−0.849545	−	0.593753i
$430$	9.75012	+	16.8877i	0.470192	+	0.814397i
$431$	−1.24535	+	0.719004i	−0.0599864	+	0.0346332i	−0.529693	−	0.848189i	$-0.677693\pi$
$431$	−1.24535	+	0.719004i	−0.0599864	+	0.0346332i	0.469707	+	0.882822i	$0.344360\pi$
$432$	1.67307	−	2.89784i	0.0804957	−	0.139423i
$433$	−16.5018			−0.793024			−0.396512	−	0.918029i	$-0.629780\pi$
$433$	−16.5018			−0.793024			−0.396512	+	0.918029i	$0.629780\pi$
$434$		0			0
$435$		−	14.5970i		−	0.699874i
$436$	−11.0466	−	6.37778i	−0.529038	−	0.305440i
$437$	24.2833	−	14.0200i	1.16163	−	0.670666i
$438$	4.41657	+	7.64973i	0.211032	+	0.365518i
$439$	5.08097	−	8.80049i	0.242501	−	0.420025i	−0.718925	−	0.695088i	$-0.755365\pi$
$439$	5.08097	−	8.80049i	0.242501	−	0.420025i	0.961426	+	0.275063i	$0.0886988\pi$
$440$		−	20.9906i		−	1.00069i
$441$		0			0
$442$	0.769859	−	8.88892i	0.0366185	−	0.422803i
$443$	−1.60393	+	2.77809i	−0.0762052	+	0.131991i	−0.901610	−	0.432550i	$-0.857614\pi$
$443$	−1.60393	+	2.77809i	−0.0762052	+	0.131991i	0.825405	+	0.564542i	$0.190947\pi$
$444$	−11.5059	+	6.64296i	−0.546048	+	0.315261i
$445$	−8.61753	−	14.9260i	−0.408510	−	0.707560i
$446$	−3.66270	+	6.34398i	−0.173434	+	0.300396i
$447$		−	32.1891i		−	1.52249i
$448$		0			0
$449$			18.4099i			0.868817i	0.900716	+	0.434409i	$0.143043\pi$
$449$			18.4099i			0.868817i	−0.900716	+	0.434409i	$0.856957\pi$
$450$	6.05406	+	3.49532i	0.285391	+	0.164771i
$451$	1.01582	+	1.75945i	0.0478332	+	0.0828495i
$452$	6.45653	+	11.1830i	0.303690	+	0.526006i
$453$	−38.3048	−	22.1153i	−1.79972	−	1.03907i
$454$	10.3684			0.486614
$455$		0			0
$456$	−45.9595			−2.15225
$457$	−2.94706	−	1.70149i	−0.137858	−	0.0795922i	0.429485	−	0.903074i	$-0.358695\pi$
$457$	−2.94706	−	1.70149i	−0.137858	−	0.0795922i	−0.567343	+	0.823482i	$0.692028\pi$
$458$	−2.25088	−	3.89865i	−0.105177	−	0.182172i
$459$	4.36196	+	7.55514i	0.203599	+	0.352644i
$460$	13.9321	+	8.04371i	0.649588	+	0.375040i
$461$		−	17.5714i		−	0.818380i	−0.912449	−	0.409190i	$-0.865811\pi$
$461$		−	17.5714i		−	0.818380i	0.912449	−	0.409190i	$-0.134189\pi$
$462$		0			0
$463$		−	15.7714i		−	0.732959i	−0.930426	−	0.366479i	$-0.880563\pi$
$463$		−	15.7714i		−	0.732959i	0.930426	−	0.366479i	$-0.119437\pi$
$464$	−1.41282	+	2.44707i	−0.0655884	+	0.113602i
$465$	20.7709	+	35.9762i	0.963226	+	1.66836i
$466$	16.6803	−	9.63036i	0.772699	−	0.446118i
$467$	1.88347	−	3.26227i	0.0871567	−	0.150960i	−0.819151	−	0.573577i	$-0.805555\pi$
$467$	1.88347	−	3.26227i	0.0871567	−	0.150960i	0.906308	+	0.422617i	$0.138889\pi$
$468$	−10.4286	−	0.903212i	−0.482064	−	0.0417510i
$469$		0			0
$470$			4.16839i			0.192273i
$471$	8.19135	−	14.1878i	0.377438	−	0.653741i
$472$	8.90321	+	15.4208i	0.409804	+	0.709801i
$473$	20.5071	−	11.8398i	0.942916	−	0.544393i
$474$	5.91768	+	3.41657i	0.271808	+	0.156928i
$475$		−	45.5669i		−	2.09075i
$476$		0			0
$477$	4.80642			0.220071
$478$	−6.74467	+	11.6821i	−0.308494	+	0.534327i
$479$	−10.4817	+	6.05162i	−0.478922	+	0.276506i	−0.719967	−	0.694008i	$-0.755843\pi$
$479$	−10.4817	+	6.05162i	−0.478922	+	0.276506i	0.241045	+	0.970514i	$0.422510\pi$
$480$	−20.6637	−	35.7906i	−0.943165	−	1.63361i
$481$	−11.6241	−	8.12420i	−0.530016	−	0.370432i
$482$	9.20189			0.419135
$483$		0			0
$484$	5.75065			0.261393
$485$	15.4748	−	26.8032i	0.702675	−	1.21707i
$486$	−10.3004	+	5.94692i	−0.467234	+	0.269758i
$487$	−15.0496	+	8.68889i	−0.681963	+	0.393731i	−0.800594	−	0.599207i	$-0.795483\pi$
$487$	−15.0496	+	8.68889i	−0.681963	+	0.393731i	0.118631	+	0.992938i	$0.462149\pi$
$488$	19.0363	+	10.9906i	0.861734	+	0.497523i
$489$		−	5.15257i		−	0.233007i
$490$		0			0
$491$	19.3921			0.875152			0.437576	−	0.899181i	$-0.355837\pi$
$491$	19.3921			0.875152			0.437576	+	0.899181i	$0.355837\pi$
$492$	2.21023	+	1.27607i	0.0996446	+	0.0575299i
$493$	−3.68344	−	6.37991i	−0.165894	−	0.287337i
$494$	−8.98784	−	19.2306i	−0.404382	−	0.865226i
$495$	8.22469	−	14.2456i	0.369672	−	0.640291i
$496$		−	8.04149i		−	0.361073i
$497$		0			0
$498$	−16.5161			−0.740102
$499$	9.24063	+	5.33508i	0.413667	+	0.238831i	0.692364	−	0.721548i	$-0.256569\pi$
$499$	9.24063	+	5.33508i	0.413667	+	0.238831i	−0.278697	+	0.960379i	$0.589903\pi$
$500$	1.40914	−	0.813569i	0.0630188	−	0.0363839i
$501$	−6.56258	+	3.78891i	−0.293194	+	0.169276i
$502$	−1.96688	−	1.13558i	−0.0877859	−	0.0506832i
$503$	4.27655			0.190682			0.0953410	−	0.995445i	$-0.469606\pi$
$503$	4.27655			0.190682			0.0953410	+	0.995445i	$0.469606\pi$
$504$		0			0
$505$		−	44.0163i		−	1.95870i
$506$	−3.03879	+	5.26334i	−0.135091	+	0.233984i
$507$	−9.89267	−	27.0329i	−0.439349	−	1.20057i
$508$	3.11753	+	5.39972i	0.138318	+	0.239574i
$509$	28.6451	+	16.5383i	1.26967	+	0.733046i	0.974926	−	0.222530i	$-0.0714316\pi$
$509$	28.6451	+	16.5383i	1.26967	+	0.733046i	0.294746	+	0.955576i	$0.404765\pi$
$510$	17.6128			0.779910
$511$		0			0
$512$			14.6923i			0.649313i
$513$	17.9748	+	10.3778i	0.793609	+	0.458190i
$514$	−14.1357	+	8.16124i	−0.623498	+	0.359977i
$515$	−34.2262	+	19.7605i	−1.50819	+	0.870751i
$516$	14.8731	−	25.7610i	0.654752	−	1.13406i
$517$	5.06175			0.222616
$518$		0			0
$519$	18.3225			0.804268
$520$	16.1240	−	23.0703i	0.707084	−	1.01170i
$521$	12.1891	+	21.1122i	0.534015	+	0.924942i	0.999210	+	0.0397336i	$0.0126509\pi$
$521$	12.1891	+	21.1122i	0.534015	+	0.924942i	−0.465195	+	0.885208i	$0.654016\pi$
$522$	2.32865	−	1.34445i	0.101922	−	0.0588448i
$523$	17.4701	−	30.2591i	0.763915	−	1.32314i	−0.176903	−	0.984228i	$-0.556608\pi$
$523$	17.4701	−	30.2591i	0.763915	−	1.32314i	0.940818	−	0.338912i	$-0.110059\pi$
$524$	−9.06070			−0.395818
$525$		0			0
$526$			6.88247i			0.300090i
$527$	18.1566	+	10.4827i	0.790914	+	0.456635i
$528$	−7.10437	+	4.10171i	−0.309178	+	0.178504i
$529$	6.11753	+	10.5959i	0.265980	+	0.460690i
$530$	−2.79605	+	4.84290i	−0.121453	+	0.210362i
$531$			13.9541i			0.605555i
$532$		0			0
$533$	−0.235063	+	2.71408i	−0.0101817	+	0.117560i
$534$	4.08964	−	7.08347i	0.176976	−	0.306532i
$535$	50.6328	−	29.2328i	2.18905	−	1.26385i
$536$	0.520505	+	0.901542i	0.0224824	+	0.0389407i
$537$	−17.9644	+	31.1153i	−0.775223	+	1.34273i
$538$			12.5402i			0.540646i
$539$		0			0
$540$			11.9081i			0.512445i
$541$	−26.4097	−	15.2477i	−1.13544	−	0.655548i	−0.190144	−	0.981756i	$-0.560896\pi$
$541$	−26.4097	−	15.2477i	−1.13544	−	0.655548i	−0.945298	+	0.326208i	$0.894229\pi$
$542$	−8.32693	−	14.4227i	−0.357672	−	0.619506i
$543$	10.1914	+	17.6519i	0.437353	+	0.757517i
$544$	−18.0629	−	10.4286i	−0.774442	−	0.447124i
$545$	26.8780			1.15133
$546$		0			0
$547$	−10.0049			−0.427780			−0.213890	−	0.976858i	$-0.568613\pi$
$547$	−10.0049			−0.427780			−0.213890	+	0.976858i	$0.568613\pi$
$548$	21.6151	+	12.4795i	0.923352	+	0.533098i
$549$	8.61285	+	14.9179i	0.367587	+	0.636680i
$550$	4.93825	+	8.55329i	0.210568	+	0.364714i
$551$	−15.1788	−	8.76348i	−0.646638	−	0.373337i
$552$			17.6445i			0.750999i
$553$		0			0
$554$		−	1.16791i		−	0.0496198i
$555$	13.9978	−	24.2449i	0.594173	−	1.02914i
$556$	2.31111	+	4.00296i	0.0980128	+	0.169763i
$557$	−12.2920	+	7.09679i	−0.520829	+	0.300701i	−0.737274	−	0.675594i	$-0.763887\pi$
$557$	−12.2920	+	7.09679i	−0.520829	+	0.300701i	0.216445	+	0.976295i	$0.430554\pi$
$558$	−3.82616	+	6.62711i	−0.161974	+	0.280548i
$559$	31.6336	+	2.73975i	1.33796	+	0.115879i
$560$		0			0
$561$		−	21.3876i		−	0.902986i
$562$	−4.01207	+	6.94910i	−0.169239	+	0.293130i
$563$	10.6795	+	18.4975i	0.450088	+	0.779576i	0.998391	−	0.0567041i	$-0.0180592\pi$
$563$	10.6795	+	18.4975i	0.450088	+	0.779576i	−0.548303	+	0.836280i	$0.684726\pi$
$564$	5.50668	−	3.17929i	0.231873	−	0.133872i
$565$	−23.5644	−	13.6049i	−0.991364	−	0.572364i
$566$			8.35857i			0.351337i
$567$		0			0
$568$	−21.8193			−0.915519
$569$	17.1336	−	29.6763i	0.718278	−	1.24409i	−0.243404	−	0.969925i	$-0.578264\pi$
$569$	17.1336	−	29.6763i	0.718278	−	1.24409i	0.961682	−	0.274168i	$-0.0884025\pi$
$570$	36.2897	−	20.9518i	1.52001	−	0.877576i
$571$	−18.8247	−	32.6053i	−0.787789	−	1.36449i	−0.927318	−	0.374273i	$-0.877892\pi$
$571$	−18.8247	−	32.6053i	−0.787789	−	1.36449i	0.139529	−	0.990218i	$-0.455441\pi$
$572$	−12.1218	−	8.47200i	−0.506837	−	0.354232i
$573$	−14.7654			−0.616834
$574$		0			0
$575$	−17.4938			−0.729541
$576$	1.18421	−	2.05111i	0.0493420	−	0.0854629i
$577$	−24.5925	+	14.1985i	−1.02380	+	0.591091i	−0.915202	−	0.402995i	$-0.867969\pi$
$577$	−24.5925	+	14.1985i	−1.02380	+	0.591091i	−0.108598	+	0.994086i	$0.534636\pi$
$578$	−2.44414	+	1.41112i	−0.101663	+	0.0586950i
$579$	39.5104	+	22.8113i	1.64200	+	0.948007i
$580$		−	10.0558i		−	0.417543i
$581$		0			0
$582$	14.6878			0.608830
$583$	5.88083	+	3.39530i	0.243559	+	0.140619i
$584$	7.03164	+	12.1792i	0.290971	+	0.503977i
$585$	19.9824	−	9.33918i	0.826169	−	0.386127i
$586$	3.94523	−	6.83333i	0.162976	−	0.282282i
$587$			6.23659i			0.257412i	0.991683	+	0.128706i	$0.0410823\pi$
$587$			6.23659i			0.257412i	−0.991683	+	0.128706i	$0.958918\pi$
$588$		0			0
$589$	49.8800			2.05527
$590$	−14.0600	−	8.11753i	−0.578840	−	0.334193i
$591$	−16.0478	+	9.26517i	−0.660116	+	0.381118i
$592$	−4.69323	+	2.70964i	−0.192890	+	0.111365i
$593$	−15.2159	−	8.78491i	−0.624843	−	0.360753i	0.153909	−	0.988085i	$-0.450814\pi$
$593$	−15.2159	−	8.78491i	−0.624843	−	0.360753i	−0.778752	+	0.627332i	$0.784147\pi$
$594$	−4.49871			−0.184584
$595$		0			0
$596$		−	22.1748i		−	0.908317i
$597$	0.665926	−	1.15342i	0.0272545	−	0.0472062i
$598$	−7.38291	+	3.45056i	−0.301909	+	0.141104i
$599$	−8.49063	−	14.7062i	−0.346918	−	0.600879i	0.638782	−	0.769387i	$-0.279438\pi$
$599$	−8.49063	−	14.7062i	−0.346918	−	0.600879i	−0.985700	+	0.168508i	$0.946105\pi$
$600$	24.8320	+	14.3368i	1.01376	+	0.585296i
$601$	18.7052			0.763001			0.381500	−	0.924369i	$-0.375408\pi$
$601$	18.7052			0.763001			0.381500	+	0.924369i	$0.375408\pi$
$602$		0			0
$603$			0.815792i			0.0332216i
$604$	−26.3879	−	15.2351i	−1.07371	−	0.619906i
$605$	−10.4941	+	6.05877i	−0.426645	+	0.246324i
$606$	18.0903	−	10.4445i	0.734870	−	0.424277i
$607$	−5.17876	+	8.96987i	−0.210199	+	0.364076i	−0.951777	−	0.306791i	$-0.900745\pi$
$607$	−5.17876	+	8.96987i	−0.210199	+	0.364076i	0.741577	+	0.670867i	$0.234078\pi$
$608$	−49.6227			−2.01247
$609$		0			0
$610$	−20.0415			−0.811456
$611$	5.56326	+	3.88820i	0.225065	+	0.157300i
$612$	−5.21432	−	9.03147i	−0.210776	−	0.365075i
$613$	−6.08147	+	3.51114i	−0.245628	+	0.141814i	−0.617761	−	0.786366i	$-0.711960\pi$
$613$	−6.08147	+	3.51114i	−0.245628	+	0.141814i	0.372133	+	0.928180i	$0.378627\pi$
$614$	1.36741	−	2.36843i	0.0551843	−	0.0955820i
$615$	−5.37778			−0.216853
$616$		0			0
$617$			29.9813i			1.20700i	0.797363	+	0.603500i	$0.206228\pi$
$617$			29.9813i			1.20700i	−0.797363	+	0.603500i	$0.793772\pi$
$618$	−16.2428	−	9.37778i	−0.653381	−	0.377230i
$619$	0.0247512	−	0.0142901i	0.000994834	−	0.000574368i	−0.499503	−	0.866312i	$-0.666484\pi$
$619$	0.0247512	−	0.0142901i	0.000994834	−	0.000574368i	0.500497	+	0.865738i	$0.333151\pi$
$620$	14.3089	+	24.7837i	0.574659	+	0.995338i
$621$	3.98418	−	6.90080i	0.159880	−	0.276920i
$622$			18.8399i			0.755412i
$623$		0			0
$624$	−10.9590	−	0.949145i	−0.438711	−	0.0379962i
$625$	11.6153	−	20.1183i	0.464612	−	0.804732i
$626$	11.3970	−	6.58004i	0.455514	−	0.262991i
$627$	−25.4422	−	44.0672i	−1.01607	−	1.75988i
$628$	5.64296	−	9.77389i	0.225179	−	0.390021i
$629$		−	14.1289i		−	0.563356i
$630$		0			0
$631$			12.1936i			0.485419i	0.970099	+	0.242709i	$0.0780361\pi$
$631$			12.1936i			0.485419i	−0.970099	+	0.242709i	$0.921964\pi$
$632$	9.42156	+	5.43954i	0.374769	+	0.216373i
$633$	2.10716	+	3.64971i	0.0837521	+	0.145063i
$634$	3.41282	+	5.91117i	0.135540	+	0.234763i
$635$	−11.3781	−	6.56914i	−0.451525	−	0.260688i
$636$	8.53035			0.338250
$637$		0			0
$638$	3.79892			0.150401
$639$	−14.8080	−	8.54940i	−0.585795	−	0.338209i
$640$	−17.2859	−	29.9401i	−0.683286	−	1.18349i
$641$	−1.41258	−	2.44666i	−0.0557935	−	0.0966373i	0.836780	−	0.547540i	$-0.184436\pi$
$641$	−1.41258	−	2.44666i	−0.0557935	−	0.0966373i	−0.892573	+	0.450903i	$0.851102\pi$
$642$	24.0289	+	13.8731i	0.948346	+	0.547528i
$643$			37.7275i			1.48783i	0.668276	+	0.743913i	$0.267032\pi$
$643$			37.7275i			1.48783i	−0.668276	+	0.743913i	$0.732968\pi$
$644$		0			0
$645$			62.6800i			2.46802i
$646$	10.5741	−	18.3148i	0.416031	−	0.720587i
$647$	−6.18320	−	10.7096i	−0.243087	−	0.421039i	0.718505	−	0.695522i	$-0.244827\pi$
$647$	−6.18320	−	10.7096i	−0.243087	−	0.421039i	−0.961592	+	0.274483i	$0.911493\pi$
$648$	−23.3198	+	13.4637i	−0.916087	+	0.528903i
$649$	−9.85728	+	17.0733i	−0.386932	+	0.670186i
$650$	−1.14272	+	13.1941i	−0.0448212	+	0.517513i
$651$		0			0
$652$		−	3.54956i		−	0.139012i
$653$	16.5002	−	28.5793i	0.645704	−	1.11839i	−0.338434	−	0.940990i	$-0.609897\pi$
$653$	16.5002	−	28.5793i	0.645704	−	1.11839i	0.984138	−	0.177402i	$-0.0567694\pi$
$654$	6.37778	+	11.0466i	0.249391	+	0.431958i
$655$	16.5345	−	9.54617i	0.646055	−	0.373000i
$656$	0.901542	+	0.520505i	0.0351993	+	0.0203223i
$657$			11.0207i			0.429960i
$658$		0			0
$659$	32.8118			1.27817			0.639084	−	0.769137i	$-0.279314\pi$
$659$	32.8118			1.27817			0.639084	+	0.769137i	$0.279314\pi$
$660$	14.5970	−	25.2828i	0.568188	−	0.984131i
$661$	−12.7364	+	7.35336i	−0.495388	+	0.286013i	−0.726807	−	0.686842i	$-0.758997\pi$
$661$	−12.7364	+	7.35336i	−0.495388	+	0.286013i	0.231419	+	0.972854i	$0.425663\pi$
$662$	8.06668	+	13.9719i	0.313520	+	0.543033i
$663$	16.4290	−	23.5067i	0.638048	−	0.912923i
$664$	−26.2953			−1.02046
$665$		0			0
$666$	5.15701			0.199830
$667$	−3.36442	+	5.82735i	−0.130271	+	0.225636i
$668$	−4.52091	+	2.61015i	−0.174919	+	0.100990i
$669$	−20.3916	+	11.7731i	−0.788384	+	0.455174i
$670$	−0.821984	−	0.474572i	−0.0317560	−	0.0183343i
$671$			24.3368i			0.939511i
$672$		0			0
$673$	−21.2908			−0.820702			−0.410351	−	0.911928i	$-0.634594\pi$
$673$	−21.2908			−0.820702			−0.410351	+	0.911928i	$0.634594\pi$
$674$	−4.48407	−	2.58888i	−0.172720	−	0.0997198i
$675$	−6.47457	−	11.2143i	−0.249206	−	0.431638i
$676$	−6.81499	−	18.6228i	−0.262115	−	0.716260i
$677$	−1.53580	+	2.66008i	−0.0590256	+	0.102235i	−0.894028	−	0.448011i	$-0.852133\pi$
$677$	−1.53580	+	2.66008i	−0.0590256	+	0.102235i	0.835003	+	0.550246i	$0.185466\pi$
$678$		−	12.9131i		−	0.495923i
$679$		0			0
$680$	28.0415			1.07534
$681$	28.8624	+	16.6637i	1.10601	+	0.638554i
$682$	−9.36290	+	5.40567i	−0.358524	+	0.206994i
$683$	21.4749	−	12.3985i	0.821713	−	0.474416i	−0.0292935	−	0.999571i	$-0.509326\pi$
$683$	21.4749	−	12.3985i	0.821713	−	0.474416i	0.851007	+	0.525154i	$0.175992\pi$
$684$	−21.4873	−	12.4057i	−0.821586	−	0.474343i
$685$	−52.5926			−2.00946
$686$		0			0
$687$		−	14.4701i		−	0.552070i
$688$	6.06668	−	10.5078i	0.231290	−	0.400606i
$689$	3.85538	+	8.24908i	0.146878	+	0.314265i
$690$	−8.04371	−	13.9321i	−0.306219	−	0.530387i
$691$	−23.4652	−	13.5476i	−0.892658	−	0.515376i	−0.0178467	−	0.999841i	$-0.505681\pi$
$691$	−23.4652	−	13.5476i	−0.892658	−	0.515376i	−0.874811	+	0.484465i	$0.839014\pi$
$692$	12.6222			0.479825
$693$		0			0
$694$			3.88845i			0.147603i
$695$	−8.43487	−	4.86987i	−0.319953	−	0.184725i
$696$	9.55144	−	5.51453i	0.362047	−	0.209028i
$697$	−2.35046	+	1.35704i	−0.0890302	+	0.0514016i
$698$	8.32148	−	14.4132i	0.314973	−	0.545549i
$699$	61.9101			2.34166
$700$		0			0
$701$	−13.5205			−0.510662			−0.255331	−	0.966854i	$-0.582185\pi$
$701$	−13.5205			−0.510662			−0.255331	+	0.966854i	$0.582185\pi$
$702$	−4.94443	−	3.45569i	−0.186615	−	0.130427i
$703$	−16.8074	−	29.1113i	−0.633904	−	1.09795i
$704$	2.89784	−	1.67307i	0.109217	−	0.0630562i
$705$	−6.69926	+	11.6035i	−0.252309	+	0.437012i
$706$	24.8889			0.936707
$707$		0			0
$708$			24.7654i			0.930741i
$709$	−44.1459	−	25.4876i	−1.65793	−	0.957209i	−0.973666	−	0.227977i	$-0.926789\pi$
$709$	−44.1459	−	25.4876i	−1.65793	−	0.957209i	−0.684267	−	0.729231i	$-0.739878\pi$
$710$	17.2286	−	9.94692i	0.646577	−	0.373301i
$711$	4.26271	+	7.38324i	0.159864	+	0.276893i
$712$	6.51114	−	11.2776i	0.244015	−	0.422647i
$713$		−	19.1497i		−	0.717160i
$714$		0			0
$715$	31.0464	+	2.68889i	1.16107	+	0.100559i
$716$	−12.3756	+	21.4351i	−0.462496	+	0.801067i
$717$	−37.5500	+	21.6795i	−1.40233	+	0.809637i
$718$	−5.99778	−	10.3885i	−0.223835	−	0.387694i
$719$	−20.7709	+	35.9762i	−0.774622	+	1.34169i	0.160384	+	0.987055i	$0.448727\pi$
$719$	−20.7709	+	35.9762i	−0.774622	+	1.34169i	−0.935006	+	0.354631i	$0.884607\pi$
$720$		−	8.42864i		−	0.314117i
$721$		0			0
$722$		−	37.2257i		−	1.38540i
$723$	25.6151	+	14.7889i	0.952637	+	0.550005i
$724$	7.02074	+	12.1603i	0.260924	+	0.451933i
$725$	5.46743	+	9.46986i	0.203055	+	0.351702i
$726$	−4.98021	−	2.87532i	−0.184833	−	0.106713i
$727$	−20.8988			−0.775092			−0.387546	−	0.921850i	$-0.626677\pi$
$727$	−20.8988			−0.775092			−0.387546	+	0.921850i	$0.626677\pi$
$728$		0			0
$729$	−4.96836			−0.184013
$730$	−11.1044	−	6.41112i	−0.410992	−	0.237286i
$731$	15.8168	+	27.3955i	0.585005	+	1.01326i
$732$	15.2859	+	26.4760i	0.564984	+	0.978581i
$733$	16.7641	+	9.67876i	0.619196	+	0.357493i	0.776556	−	0.630048i	$-0.216965\pi$
$733$	16.7641	+	9.67876i	0.619196	+	0.357493i	−0.157360	+	0.987541i	$0.550298\pi$
$734$		−	2.02413i		−	0.0747122i
$735$		0			0
$736$			19.0509i			0.702224i
$737$	−0.576283	+	0.998151i	−0.0212276	+	0.0367674i
$738$	−0.495316	−	0.857913i	−0.0182328	−	0.0315802i
$739$	1.13545	−	0.655554i	0.0417683	−	0.0241149i	−0.478970	−	0.877831i	$-0.658990\pi$
$739$	1.13545	−	0.655554i	0.0417683	−	0.0241149i	0.520739	+	0.853716i	$0.325657\pi$
$740$	9.64296	−	16.7021i	0.354482	−	0.613981i
$741$	5.88739	−	67.9768i	0.216279	−	2.49719i
$742$		0			0
$743$		−	21.5210i		−	0.789528i	−0.918783	−	0.394764i	$-0.870826\pi$
$743$		−	21.5210i		−	0.789528i	0.918783	−	0.394764i	$-0.129174\pi$
$744$	−15.6938	+	27.1825i	−0.575363	+	0.996558i
$745$	23.3630	+	40.4658i	0.855953	+	1.48255i
$746$	−11.1981	+	6.46520i	−0.409990	+	0.236708i
$747$	−17.8457	−	10.3032i	−0.652939	−	0.376974i
$748$		−	14.7338i		−	0.538720i
$749$		0			0
$750$	−1.62714			−0.0594147
$751$	−8.15878	+	14.1314i	−0.297718	+	0.515663i	−0.975614	−	0.219495i	$-0.929559\pi$
$751$	−8.15878	+	14.1314i	−0.297718	+	0.515663i	0.677895	+	0.735158i	$0.262892\pi$
$752$	2.24615	−	1.29682i	0.0819088	−	0.0472901i
$753$	−3.65010	−	6.32217i	−0.133017	−	0.230393i
$754$	4.17530	+	2.91815i	0.152055	+	0.106273i
$755$	64.2054			2.33667
$756$		0			0
$757$	−18.7462			−0.681342			−0.340671	−	0.940183i	$-0.610654\pi$
$757$	−18.7462			−0.681342			−0.340671	+	0.940183i	$0.610654\pi$
$758$	8.15971	−	14.1330i	0.296374	−	0.513335i
$759$	−16.9180	+	9.76764i	−0.614086	+	0.354543i
$760$	57.7769	−	33.3575i	2.09579	−	1.21000i
$761$	8.91731	+	5.14841i	0.323252	+	0.186630i	0.652841	−	0.757495i	$-0.273577\pi$
$761$	8.91731	+	5.14841i	0.323252	+	0.186630i	−0.329589	+	0.944124i	$0.606910\pi$
$762$		−	6.23506i		−	0.225873i
$763$		0			0
$764$	−10.1718			−0.368002
$765$	19.0307	+	10.9874i	0.688058	+	0.397250i
$766$	−10.8889	−	18.8602i	−0.393433	−	0.681445i
$767$	−23.9488	+	11.1930i	−0.864742	+	0.404155i
$768$	10.9590	−	18.9815i	0.395448	−	0.684937i
$769$		−	9.36641i		−	0.337761i	−0.985637	−	0.168881i	$-0.945985\pi$
$769$		−	9.36641i		−	0.337761i	0.985637	−	0.168881i	$-0.0540153\pi$
$770$		0			0
$771$	−52.4657			−1.88951
$772$	27.2184	+	15.7146i	0.979612	+	0.565579i
$773$	3.21690	−	1.85728i	0.115704	−	0.0668017i	−0.441031	−	0.897492i	$-0.645387\pi$
$773$	3.21690	−	1.85728i	0.115704	−	0.0668017i	0.556735	+	0.830690i	$0.312054\pi$
$774$	−9.99928	+	5.77309i	−0.359417	+	0.207509i
$775$	−26.9503	−	15.5598i	−0.968084	−	0.558923i
$776$	23.3846			0.839457
$777$		0			0
$778$			13.8163i			0.495337i
$779$	−3.22861	+	5.59212i	−0.115677	+	0.200358i
$780$	35.4643	−	16.5750i	1.26983	−	0.593480i
$781$	−12.0787	−	20.9210i	−0.432211	−	0.748612i
$782$	−7.03131	−	4.05953i	−0.251439	−	0.145169i
$783$	−4.98079			−0.177999
$784$		0			0
$785$			23.7812i			0.848789i
$786$	7.84680	+	4.53035i	0.279886	+	0.161592i
$787$	5.40105	−	3.11830i	0.192527	−	0.111155i	−0.400638	−	0.916236i	$-0.631212\pi$
$787$	5.40105	−	3.11830i	0.192527	−	0.111155i	0.593165	+	0.805081i	$0.297878\pi$
$788$	−11.0552	+	6.38271i	−0.393824	+	0.227375i
$789$	−11.0612	+	19.1586i	−0.393790	+	0.682064i
$790$	−9.91903			−0.352903
$791$		0			0
$792$	12.4286			0.441632
$793$	−18.6944	+	26.7480i	−0.663856	+	0.949849i
$794$	7.87855	+	13.6460i	0.279599	+	0.484280i
$795$	−15.5666	+	8.98741i	−0.552092	+	0.318750i
$796$	0.458751	−	0.794580i	0.0162600	−	0.0281631i
$797$	−40.0701			−1.41935			−0.709677	−	0.704527i	$-0.751159\pi$
$797$	−40.0701			−1.41935			−0.709677	+	0.704527i	$0.751159\pi$
$798$		0			0
$799$			6.76202i			0.239223i
$800$	26.8113	+	15.4795i	0.947922	+	0.547283i
$801$	8.83775	−	5.10248i	0.312266	−	0.180287i
$802$	1.93332	+	3.34861i	0.0682680	+	0.118244i
$803$	−7.78515	+	13.4843i	−0.274732	+	0.475850i
$804$			1.44785i			0.0510618i
$805$		0			0
$806$	−14.4429	−	1.25088i	−0.508730	−	0.0440605i
$807$	−20.1541	+	34.9079i	−0.709458	+	1.22882i
$808$	28.8017	−	16.6287i	1.01324	−	0.584995i
$809$	1.28568	+	2.22686i	0.0452021	+	0.0782924i	0.887741	−	0.460343i	$-0.152273\pi$
$809$	1.28568	+	2.22686i	0.0452021	+	0.0782924i	−0.842539	+	0.538635i	$0.818940\pi$
$810$	12.2755	−	21.2619i	0.431319	−	0.747066i
$811$			28.3654i			0.996042i	0.867165	+	0.498021i	$0.165940\pi$
$811$			28.3654i			0.996042i	−0.867165	+	0.498021i	$0.834060\pi$
$812$		0			0
$813$		−	53.5308i		−	1.87741i
$814$	6.30979	+	3.64296i	0.221158	+	0.127686i
$815$	3.73975	+	6.47743i	0.130998	+	0.226895i
$816$	−5.47949	−	9.49076i	−0.191821	−	0.332243i
$817$	65.1781	+	37.6306i	2.28029	+	1.31653i
$818$	−17.9922			−0.629081
$819$		0			0
$820$	−3.70471			−0.129374
$821$	27.5263	+	15.8923i	0.960674	+	0.554646i	0.896380	−	0.443285i	$-0.146187\pi$
$821$	27.5263	+	15.8923i	0.960674	+	0.554646i	0.0642938	+	0.997931i	$0.479521\pi$
$822$	−12.4795	−	21.6151i	−0.435272	−	0.753914i
$823$	15.4565	+	26.7715i	0.538781	+	0.933196i	0.998970	+	0.0453747i	$0.0144482\pi$
$823$	15.4565	+	26.7715i	0.538781	+	0.933196i	−0.460189	+	0.887821i	$0.652218\pi$
$824$	−25.8602	−	14.9304i	−0.900884	−	0.520125i
$825$			31.7462i			1.10526i
$826$		0			0
$827$		−	49.7560i		−	1.73019i	−0.501610	−	0.865094i	$-0.667259\pi$
$827$		−	49.7560i		−	1.73019i	0.501610	−	0.865094i	$-0.332741\pi$
$828$	−4.76271	+	8.24926i	−0.165516	+	0.286682i
$829$	9.95952	+	17.2504i	0.345908	+	0.599131i	0.985518	−	0.169569i	$-0.0542375\pi$
$829$	9.95952	+	17.2504i	0.345908	+	0.599131i	−0.639610	+	0.768700i	$0.720904\pi$
$830$	20.7628	−	11.9874i	0.720687	−	0.416089i
$831$	1.87702	−	3.25109i	0.0651131	−	0.112779i
$832$	4.47013	+	0.387152i	0.154974	+	0.0134221i
$833$		0			0
$834$		−	4.62222i		−	0.160054i
$835$	5.50000	−	9.52628i	0.190335	−	0.329670i
$836$	−17.5270	−	30.3576i	−0.606183	−	1.04994i
$837$	12.2758	−	7.08742i	0.424313	−	0.244977i
$838$	−15.0620	−	8.69604i	−0.520307	−	0.300400i
$839$			11.5625i			0.399181i	0.979879	+	0.199590i	$0.0639611\pi$
$839$			11.5625i			0.399181i	−0.979879	+	0.199590i	$0.936039\pi$
$840$		0			0
$841$	−24.7940			−0.854965
$842$	−2.83431	+	4.90917i	−0.0976769	+	0.169181i
$843$	−22.3366	+	12.8961i	−0.769315	+	0.444164i
$844$	1.45161	+	2.51426i	0.0499663	+	0.0865442i
$845$	32.0569	+	26.8037i	1.10279	+	0.922075i
$846$	−2.46812			−0.0848557
$847$		0			0
$848$	3.47949			0.119486
$849$	−13.4336	+	23.2676i	−0.461039	+	0.798542i
$850$	−11.4264	+	6.59703i	−0.391922	+	0.226276i
$851$	−11.1762	+	6.45261i	−0.383117	+	0.221193i
$852$	−26.2809	−	15.1733i	−0.900370	−	0.519829i
$853$			1.74467i			0.0597363i	0.999554	+	0.0298682i	$0.00950875\pi$
$853$			1.74467i			0.0597363i	−0.999554	+	0.0298682i	$0.990491\pi$
$854$		0			0
$855$	52.2815			1.78799
$856$	38.2565	+	22.0874i	1.30758	+	0.754932i
$857$	21.1684	+	36.6647i	0.723098	+	1.25244i	0.959752	+	0.280849i	$0.0906160\pi$
$857$	21.1684	+	36.6647i	0.723098	+	1.25244i	−0.236654	+	0.971594i	$0.576051\pi$
$858$	6.26177	+	13.3979i	0.213773	+	0.457395i
$859$	−2.68889	+	4.65730i	−0.0917438	+	0.158905i	−0.908245	−	0.418439i	$-0.862577\pi$
$859$	−2.68889	+	4.65730i	−0.0917438	+	0.158905i	0.816501	+	0.577344i	$0.195911\pi$
$860$			43.1798i			1.47242i
$861$		0			0
$862$	0.990632			0.0337411
$863$	−13.3620	−	7.71456i	−0.454848	−	0.262607i	0.255027	−	0.966934i	$-0.417915\pi$
$863$	−13.3620	−	7.71456i	−0.454848	−	0.262607i	−0.709875	+	0.704327i	$0.751249\pi$
$864$	−12.2124	+	7.05086i	−0.415476	+	0.239875i
$865$	−23.0337	+	13.2985i	−0.783169	+	0.452163i
$866$	9.84492	+	5.68397i	0.334544	+	0.193149i
$867$	−9.07160			−0.308088
$868$		0			0
$869$			12.0449i			0.408595i
$870$	−5.02789	+	8.70856i	−0.170461	+	0.295248i
$871$	−1.40011	+	0.654372i	−0.0474410	+	0.0221725i
$872$	10.1541	+	17.5874i	0.343861	+	0.595585i
$873$	15.8703	+	9.16270i	0.537127	+	0.310110i
$874$	−19.3165			−0.653391
$875$		0			0
$876$			19.5594i			0.660851i
$877$	−33.3576	−	19.2590i	−1.12641	−	0.650331i	−0.183378	−	0.983042i	$-0.558703\pi$
$877$	−33.3576	−	19.2590i	−1.12641	−	0.650331i	−0.943029	+	0.332711i	$0.892037\pi$
$878$	−6.06259	+	3.50024i	−0.204603	+	0.118127i
$879$	21.9645	−	12.6812i	0.740845	−	0.427727i
$880$	5.95407	−	10.3127i	0.200712	−	0.347643i
$881$	−41.7373			−1.40617			−0.703083	−	0.711108i	$-0.748194\pi$
$881$	−41.7373			−1.40617			−0.703083	+	0.711108i	$0.748194\pi$
$882$		0			0
$883$	−52.8439			−1.77834			−0.889170	−	0.457577i	$-0.848717\pi$
$883$	−52.8439			−1.77834			−0.889170	+	0.457577i	$0.848717\pi$
$884$	11.3178	−	16.1935i	0.380658	−	0.544648i
$885$	−26.0923	−	45.1933i	−0.877084	−	1.51915i
$886$	1.91381	−	1.10494i	0.0642956	−	0.0371211i
$887$	4.49532	−	7.78612i	0.150938	−	0.261432i	−0.780635	−	0.624988i	$-0.785104\pi$
$887$	4.49532	−	7.78612i	0.150938	−	0.261432i	0.931573	+	0.363556i	$0.118437\pi$
$888$	21.1526			0.709834
$889$		0			0
$890$			11.8731i			0.397987i
$891$	−25.8187	−	14.9064i	−0.864959	−	0.499384i
$892$	−14.0476	+	8.11039i	−0.470348	+	0.271556i
$893$	8.04395	+	13.9325i	0.269180	+	0.466234i
$894$	−11.0874	+	19.2040i	−0.370819	+	0.642277i
$895$		−	52.1546i		−	1.74334i
$896$		0			0
$897$	−26.0973	−	2.26025i	−0.871362	−	0.0754676i
$898$	6.34122	−	10.9833i	0.211609	−	0.366518i
$899$	−10.3662	+	5.98494i	−0.345733	+	0.199609i
$900$	7.73975	+	13.4056i	0.257992	+	0.446855i
$901$	−4.53580	+	7.85623i	−0.151109	+	0.261729i
$902$		−	1.39958i		−	0.0466010i
$903$		0			0
$904$		−	20.5589i		−	0.683780i
$905$	−25.6237	−	14.7938i	−0.851759	−	0.491764i
$906$	15.2351	+	26.3879i	0.506151	+	0.876679i
$907$	−10.3501	−	17.9270i	−0.343671	−	0.595255i	0.641441	−	0.767173i	$-0.278337\pi$
$907$	−10.3501	−	17.9270i	−0.343671	−	0.595255i	−0.985111	+	0.171918i	$0.945004\pi$
$908$	19.8831	+	11.4795i	0.659843	+	0.380960i
$909$	26.0622			0.864430
$910$		0			0
$911$	29.8988			0.990590			0.495295	−	0.868725i	$-0.335060\pi$
$911$	29.8988			0.990590			0.495295	+	0.868725i	$0.335060\pi$
$912$	−22.5800	−	13.0366i	−0.747698	−	0.431684i
$913$	−14.5565	−	25.2127i	−0.481751	−	0.834418i
$914$	1.17214	+	2.03021i	0.0387710	+	0.0671533i
$915$	−55.7891	−	32.2099i	−1.84433	−	1.06483i
$916$		−	9.96836i		−	0.329364i
$917$		0			0
$918$		−	6.00984i		−	0.198354i
$919$	−19.2924	+	33.4154i	−0.636397	+	1.10227i	0.349821	+	0.936817i	$0.386242\pi$
$919$	−19.2924	+	33.4154i	−0.636397	+	1.10227i	−0.986217	+	0.165455i	$0.947091\pi$
$920$	−12.8064	−	22.1814i	−0.422215	−	0.731298i
$921$	7.61289	−	4.39530i	0.250853	−	0.144830i
$922$	−6.05239	+	10.4830i	−0.199325	+	0.345241i
$923$	2.79505	−	32.2721i	0.0920001	−	1.06225i
$924$		0			0
$925$			20.9719i			0.689552i
$926$	−5.43239	+	9.40918i	−0.178520	+	0.309205i
$927$	−11.7003	−	20.2655i	−0.384287	−	0.665605i
$928$	10.3127	−	5.95407i	0.338532	−	0.195452i
$929$	2.81961	+	1.62790i	0.0925085	+	0.0534098i	0.545541	−	0.838084i	$-0.316324\pi$
$929$	2.81961	+	1.62790i	0.0925085	+	0.0534098i	−0.453032	+	0.891494i	$0.649658\pi$
$930$		−	28.6178i		−	0.938414i
$931$		0			0
$932$	42.6494			1.39703
$933$	−30.2788	+	52.4444i	−0.991283	+	1.71695i
$934$	−2.24735	+	1.29751i	−0.0735356	+	0.0424558i
$935$	15.5232	+	26.8870i	0.507663	+	0.879298i
$936$	13.6600	+	9.54709i	0.446492	+	0.312056i
$937$	11.6840			0.381699			0.190849	−	0.981619i	$-0.438876\pi$
$937$	11.6840			0.381699			0.190849	+	0.981619i	$0.438876\pi$
$938$		0			0
$939$	42.3007			1.38043
$940$	−4.61507	+	7.99354i	−0.150527	+	0.260720i
$941$	36.3470	−	20.9849i	1.18488	−	0.684090i	0.227740	−	0.973722i	$-0.426866\pi$
$941$	36.3470	−	20.9849i	1.18488	−	0.684090i	0.957138	+	0.289632i	$0.0935330\pi$
$942$	−9.77389	+	5.64296i	−0.318451	+	0.183858i
$943$	2.14689	+	1.23951i	0.0699124	+	0.0403640i
$944$			10.1017i			0.328783i
$945$		0			0
$946$	−16.3126			−0.530370
$947$	−17.6284	−	10.1778i	−0.572846	−	0.330733i	0.185439	−	0.982656i	$-0.440629\pi$
$947$	−17.6284	−	10.1778i	−0.572846	−	0.330733i	−0.758285	+	0.651923i	$0.773962\pi$
$948$	7.56538	+	13.1036i	0.245712	+	0.425586i
$949$	−18.9145	+	8.84008i	−0.613990	+	0.286961i
$950$	−15.6953	+	27.1851i	−0.509224	+	0.882002i
$951$			21.9398i			0.711446i
$952$		0			0
$953$	30.5496			0.989597			0.494799	−	0.869008i	$-0.335242\pi$
$953$	30.5496			0.989597			0.494799	+	0.869008i	$0.335242\pi$
$954$	−2.86750	−	1.65555i	−0.0928389	−	0.0536005i
$955$	18.5620	−	10.7168i	0.600653	−	0.346787i
$956$	−25.8679	+	14.9349i	−0.836629	+	0.483028i
$957$	10.5750	+	6.10546i	0.341840	+	0.197362i
$958$	8.33783			0.269383
$959$		0			0
$960$			8.85728i			0.285867i
$961$	1.53257	−	2.65449i	0.0494378	−	0.0856288i
$962$	4.13660	+	8.85077i	0.133369	+	0.285360i
$963$	17.3089	+	29.9799i	0.557771	+	0.966088i
$964$	17.6461	+	10.1880i	0.568342	+	0.328132i
$965$	−66.2262			−2.13190
$966$		0			0
$967$			54.4548i			1.75115i	0.483084	+	0.875574i	$0.339516\pi$
$967$			54.4548i			1.75115i	−0.483084	+	0.875574i	$0.660484\pi$
$968$	−7.92901	−	4.57781i	−0.254848	−	0.147137i
$969$	58.8697	−	33.9884i	1.89117	−	1.09187i
$970$	−18.4645	+	10.6605i	−0.592859	+	0.342287i
$971$	−27.3017	+	47.2880i	−0.876155	+	1.51754i	−0.0206267	+	0.999787i	$0.506566\pi$
$971$	−27.3017	+	47.2880i	−0.876155	+	1.51754i	−0.855528	+	0.517757i	$0.826767\pi$
$972$	−26.3368			−0.844752
$973$		0			0
$974$	11.9714			0.383589
$975$	−24.3859	+	34.8915i	−0.780975	+	1.11742i
$976$	6.23506	+	10.7994i	0.199580	+	0.345682i
$977$	28.2735	−	16.3237i	0.904549	−	0.522242i	0.0258756	−	0.999665i	$-0.491763\pi$
$977$	28.2735	−	16.3237i	0.904549	−	0.522242i	0.878673	+	0.477424i	$0.158429\pi$
$978$	−1.77478	+	3.07401i	−0.0567512	+	0.0982960i
$979$	14.4177			0.460793
$980$		0			0
$981$			15.9146i			0.508114i
$982$	−11.5693	−	6.67952i	−0.369190	−	0.213152i
$983$	−23.8202	+	13.7526i	−0.759745	+	0.438639i	−0.829204	−	0.558946i	$-0.811206\pi$
$983$	−23.8202	+	13.7526i	−0.759745	+	0.438639i	0.0694590	+	0.997585i	$0.477873\pi$
$984$	−2.03164	−	3.51891i	−0.0647664	−	0.112179i
$985$	13.4494	−	23.2950i	0.428533	−	0.742241i
$986$			5.07499i			0.161621i
$987$		0			0
$988$	4.05578	−	46.8287i	0.129031	−	1.48982i
$989$	14.4469	−	25.0228i	0.459385	−	0.795679i
$990$	−9.81367	+	5.66593i	−0.311899	+	0.180075i
$991$	3.14695	+	5.45068i	0.0999662	+	0.173147i	0.911670	−	0.410922i	$-0.134793\pi$
$991$	3.14695	+	5.45068i	0.0999662	+	0.173147i	−0.811704	+	0.584069i	$0.801460\pi$
$992$	−16.9447	+	29.3491i	−0.537995	+	0.931834i
$993$			51.8578i			1.64566i
$994$		0			0
$995$			1.93332i			0.0612905i
$996$	−31.6721	−	18.2859i	−1.00357	−	0.579411i
$997$	−10.4351	−	18.0741i	−0.330483	−	0.572413i	0.652124	−	0.758112i	$-0.273878\pi$
$997$	−10.4351	−	18.0741i	−0.330483	−	0.572413i	−0.982607	+	0.185700i	$0.940545\pi$
$998$	−3.67529	−	6.36580i	−0.116339	−	0.201506i
$999$	−8.27282	−	4.77631i	−0.261740	−	0.151116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.d.324.3		12
7.2	even	3		637.2.c.d.246.4		6
7.3	odd	6		637.2.r.e.116.4		12
7.4	even	3	inner	637.2.r.d.116.4		12
7.5	odd	6		91.2.c.a.64.4	yes	6
7.6	odd	2		637.2.r.e.324.3		12
13.12	even	2	inner	637.2.r.d.324.4		12
21.5	even	6		819.2.c.b.64.3		6
28.19	even	6		1456.2.k.c.337.6		6
91.5	even	12		1183.2.a.j.1.2		3
91.12	odd	6		91.2.c.a.64.3	✓	6
91.25	even	6	inner	637.2.r.d.116.3		12
91.38	odd	6		637.2.r.e.116.3		12
91.44	odd	12		8281.2.a.bi.1.2		3
91.47	even	12		1183.2.a.h.1.2		3
91.51	even	6		637.2.c.d.246.3		6
91.86	odd	12		8281.2.a.be.1.2		3
91.90	odd	2		637.2.r.e.324.4		12
273.194	even	6		819.2.c.b.64.4		6
364.103	even	6		1456.2.k.c.337.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.3	✓	6	91.12	odd	6
91.2.c.a.64.4	yes	6	7.5	odd	6
637.2.c.d.246.3		6	91.51	even	6
637.2.c.d.246.4		6	7.2	even	3
637.2.r.d.116.3		12	91.25	even	6	inner
637.2.r.d.116.4		12	7.4	even	3	inner
637.2.r.d.324.3		12	1.1	even	1	trivial
637.2.r.d.324.4		12	13.12	even	2	inner
637.2.r.e.116.3		12	91.38	odd	6
637.2.r.e.116.4		12	7.3	odd	6
637.2.r.e.324.3		12	7.6	odd	2
637.2.r.e.324.4		12	91.90	odd	2
819.2.c.b.64.3		6	21.5	even	6
819.2.c.b.64.4		6	273.194	even	6
1183.2.a.h.1.2		3	91.47	even	12
1183.2.a.j.1.2		3	91.5	even	12
1456.2.k.c.337.5		6	364.103	even	6
1456.2.k.c.337.6		6	28.19	even	6
8281.2.a.be.1.2		3	91.86	odd	12
8281.2.a.bi.1.2		3	91.44	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.596598 - 0.344446i) q^{2} +(-1.10716 - 1.91766i) q^{3} +(-0.762714 - 1.32106i) q^{4} +(2.78368 + 1.60716i) q^{5} +1.52543i q^{6} +2.42864i q^{8} +(-0.951606 + 1.64823i) q^{9} +(-1.10716 - 1.91766i) q^{10} +(-2.32865 + 1.34445i) q^{11} +(-1.68889 + 2.92525i) q^{12} +(-3.59210 - 0.311108i) q^{13} -7.11753i q^{15} +(-0.688892 + 1.19320i) q^{16} +(-1.79605 - 3.11085i) q^{17} +(1.13545 - 0.655554i) q^{18} +(-7.40120 - 4.27309i) q^{19} -4.90321i q^{20} +1.85236 q^{22} +(-1.64050 + 2.84143i) q^{23} +(4.65730 - 2.68889i) q^{24} +(2.66593 + 4.61752i) q^{25} +(2.03588 + 1.42289i) q^{26} -2.42864 q^{27} +2.05086 q^{29} +(-2.45161 + 4.24631i) q^{30} +(-5.05459 + 2.91827i) q^{31} +(5.02851 - 2.90321i) q^{32} +(5.15637 + 2.97703i) q^{33} +2.47457i q^{34} +2.90321 q^{36} +(3.40636 + 1.96666i) q^{37} +(2.94370 + 5.09863i) q^{38} +(3.38044 + 7.23287i) q^{39} +(-3.90321 + 6.76056i) q^{40} -0.755569i q^{41} -8.80642 q^{43} +(3.55219 + 2.05086i) q^{44} +(-5.29794 + 3.05877i) q^{45} +(1.95744 - 1.13013i) q^{46} +(-1.63027 - 0.941234i) q^{47} +3.05086 q^{48} -3.67307i q^{50} +(-3.97703 + 6.88842i) q^{51} +(2.32876 + 4.98267i) q^{52} +(-1.26271 - 2.18708i) q^{53} +(1.44892 + 0.836535i) q^{54} -8.64296 q^{55} +18.9240i q^{57} +(-1.22354 - 0.706409i) q^{58} +(6.34957 - 3.66593i) q^{59} +(-9.40268 + 5.42864i) q^{60} +(4.52543 - 7.83827i) q^{61} +4.02074 q^{62} -1.24443 q^{64} +(-9.49928 - 6.63911i) q^{65} +(-2.05086 - 3.55219i) q^{66} +(0.371213 - 0.214320i) q^{67} +(-2.73975 + 4.74538i) q^{68} +7.26517 q^{69} +8.98418i q^{71} +(-4.00296 - 2.31111i) q^{72} +(5.01481 - 2.89530i) q^{73} +(-1.35482 - 2.34661i) q^{74} +(5.90321 - 10.2247i) q^{75} +13.0366i q^{76} +(0.474572 - 5.47949i) q^{78} +(2.23975 - 3.87936i) q^{79} +(-3.83531 + 2.21432i) q^{80} +(5.54371 + 9.60199i) q^{81} +(-0.260253 + 0.450771i) q^{82} +10.8272i q^{83} -11.5462i q^{85} +(5.25390 + 3.03334i) q^{86} +(-2.27062 - 3.93284i) q^{87} +(-3.26517 - 5.65545i) q^{88} +(-4.64360 - 2.68098i) q^{89} +4.21432 q^{90} +5.00492 q^{92} +(11.1925 + 6.46198i) q^{93} +(0.648409 + 1.12308i) q^{94} +(-13.7351 - 23.7898i) q^{95} +(-11.1347 - 6.42864i) q^{96} -9.62867i q^{97} -5.11753i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 2 q^{9} - 20 q^{12} - 16 q^{13} - 8 q^{16} - 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} - 4 q^{38} + 8 q^{39} - 20 q^{40} - 52 q^{43}+ \cdots - 58 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 2 * q^9 - 20 * q^12 - 16 * q^13 - 8 * q^16 - 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 - 4 * q^38 + 8 * q^39 - 20 * q^40 - 52 * q^43 - 16 * q^48 - 8 * q^51 - 20 * q^52 - 2 * q^53 - 24 * q^55 + 28 * q^61 - 32 * q^62 - 16 * q^64 + 6 * q^65 + 28 * q^66 + 20 * q^68 + 8 * q^69 + 24 * q^74 + 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 - 56 * q^82 - 40 * q^87 + 40 * q^88 + 24 * q^90 - 72 * q^92 + 20 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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