LMFDB - Embedded newform 637.2.r.d.116.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			116.3
Root			$1.98293 + 0.531325i$ of defining polynomial
Character	$\chi$	$=$	637.116
Dual form			637.2.r.d.324.3

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.695872	−	0.718166i	$-0.744982\pi$
$2$	−0.596598	+	0.344446i	−0.421859	+	0.243560i	0.274014	+	0.961726i	$0.411649\pi$
$3$	−1.10716	+	1.91766i	−0.639219	+	1.10716i	0.346385	+	0.938092i	$0.387409\pi$
$3$	−1.10716	+	1.91766i	−0.639219	+	1.10716i	−0.985604	+	0.169068i	$0.945924\pi$
$4$	−0.762714	+	1.32106i	−0.381357	+	0.660530i
$5$	2.78368	−	1.60716i	1.24490	−	0.718744i	0.274813	−	0.961498i	$-0.411384\pi$
$5$	2.78368	−	1.60716i	1.24490	−	0.718744i	0.970088	+	0.242754i	$0.0780508\pi$
$6$		−	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	0.106020	−	0.994364i	$-0.466189\pi$
$11$	−2.32865	−	1.34445i	−0.702114	−	0.405366i	−0.808134	+	0.588998i	$0.799522\pi$
$12$	−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	−0.997345	−	0.0728222i	$-0.976799\pi$
$17$	−1.79605	+	3.11085i	−0.435607	+	0.754493i	0.561738	+	0.827315i	$0.310133\pi$
$18$	1.13545	+	0.655554i	0.267629	+	0.154516i
$19$	−7.40120	+	4.27309i	−1.69795	+	0.980313i	−0.750251	+	0.661153i	$0.770067\pi$
$19$	−7.40120	+	4.27309i	−1.69795	+	0.980313i	−0.947701	+	0.319160i	$0.896599\pi$
$20$			4.90321i			1.09639i
$21$		0			0
$22$	1.85236			0.394924
$23$	−1.64050	−	2.84143i	−0.342068	−	0.592478i	0.642749	−	0.766077i	$-0.277794\pi$
$23$	−1.64050	−	2.84143i	−0.342068	−	0.592478i	−0.984817	+	0.173599i	$0.944460\pi$
$24$	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	−0.0280982	−	0.999605i	$-0.508945\pi$
$31$	−5.05459	−	2.91827i	−0.907831	−	0.524136i	−0.879733	+	0.475469i	$0.842278\pi$
$32$	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	−0.193144	−	0.981170i	$-0.561869\pi$
$37$	3.40636	−	1.96666i	0.560002	−	0.323317i	0.753146	+	0.657853i	$0.228535\pi$
$38$	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	$0.0187912\pi$
$41$			0.755569i			0.118000i	−0.998258	+	0.0590000i	$0.981209\pi$
$42$		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	−0.614165	−	0.789178i	$-0.710507\pi$
$47$	−1.63027	+	0.941234i	−0.237799	+	0.137293i	0.376366	+	0.926471i	$0.377174\pi$
$48$	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	−0.939623	−	0.342212i	$-0.888824\pi$
$53$	−1.26271	+	2.18708i	−0.173447	+	0.300419i	0.766176	+	0.642631i	$0.222157\pi$
$54$	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	0.852702	−	0.522398i	$-0.174962\pi$
$59$	6.34957	+	3.66593i	0.826644	+	0.477263i	−0.0260585	+	0.999660i	$0.508296\pi$
$60$	−9.40268	−	5.42864i	−1.21388	−	0.700834i
$61$	4.52543	+	7.83827i	0.579422	+	1.00359i	0.995546	+	0.0942799i	$0.0300549\pi$
$61$	4.52543	+	7.83827i	0.579422	+	1.00359i	−0.416124	+	0.909308i	$0.636612\pi$
$62$	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	0.522504	−	0.852637i	$-0.324998\pi$
$67$	0.371213	+	0.214320i	0.0453508	+	0.0261833i	−0.477153	+	0.878820i	$0.658331\pi$
$68$	−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	$-0.821022\pi$
$71$		−	8.98418i		−	1.06623i	0.846044	−	0.533113i	$-0.178978\pi$
$72$	−4.00296	+	2.31111i	−0.471753	+	0.272367i
$73$	5.01481	+	2.89530i	0.586939	+	0.338869i	0.763886	−	0.645351i	$-0.223289\pi$
$73$	5.01481	+	2.89530i	0.586939	+	0.338869i	−0.176947	+	0.984220i	$0.556622\pi$
$74$	−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	0.964074	−	0.265634i	$-0.0855812\pi$
$79$	2.23975	+	3.87936i	0.251991	+	0.436462i	−0.712083	+	0.702096i	$0.752248\pi$
$80$	−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	$-0.797462\pi$
$83$		−	10.8272i		−	1.18844i	0.804304	−	0.594218i	$-0.202538\pi$
$84$		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	−0.725495	−	0.688227i	$-0.758389\pi$
$89$	−4.64360	+	2.68098i	−0.492220	+	0.284183i	0.233275	+	0.972411i	$0.425056\pi$
$90$	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	$0.162573\pi$
$97$			9.62867i			0.977643i	−0.872384	+	0.488822i	$0.837427\pi$
$98$		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	0.293294	+	0.956022i	$0.405249\pi$
$101$	−6.84691	+	11.8592i	−0.681293	+	1.18003i	−0.974587	+	0.224011i	$0.928085\pi$
$102$	4.74538	+	2.73975i	0.469863	+	0.271275i
$103$	−6.14764	−	10.6480i	−0.605745	−	1.04918i	−0.991933	−	0.126761i	$-0.959542\pi$
$103$	−6.14764	−	10.6480i	−0.605745	−	1.04918i	0.386188	−	0.922420i	$-0.373792\pi$
$104$	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	0.852215	+	0.523192i	$0.175259\pi$
$107$	9.09457	+	15.7522i	0.879205	+	1.52283i	0.0269898	+	0.999636i	$0.491408\pi$
$108$	1.85236	−	3.20838i	0.178243	−	0.308726i
$109$	7.24167	+	4.18098i	0.693626	+	0.400465i	0.804969	−	0.593317i	$-0.202182\pi$
$109$	7.24167	+	4.18098i	0.693626	+	0.400465i	−0.111343	+	0.993782i	$0.535515\pi$
$110$	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	0.966103	−	0.258158i	$-0.0831154\pi$
$131$	2.96989	+	5.14400i	0.259480	+	0.449433i	−0.706622	+	0.707591i	$0.749782\pi$
$132$			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	−0.247721	−	0.968831i	$-0.579682\pi$
$137$	−14.1699	−	8.18098i	−1.21061	−	0.698948i	−0.962893	+	0.269883i	$0.913015\pi$
$138$	−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	0.113979	−	0.993483i	$-0.463640\pi$
$149$	12.5892	−	7.26840i	1.03135	−	0.595451i	0.917371	+	0.398032i	$0.130307\pi$
$150$	−7.04369	−	4.06668i	−0.575115	−	0.332043i
$151$	17.2987	+	9.98741i	1.40775	+	0.812764i	0.995171	−	0.0981592i	$-0.0312954\pi$
$151$	17.2987	+	9.98741i	1.40775	+	0.812764i	0.412577	+	0.910923i	$0.364629\pi$
$152$	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	−0.679806	−	0.733392i	$-0.737936\pi$
$157$	3.69926	−	6.40731i	0.295233	−	0.511359i	0.975039	+	0.222033i	$0.0712693\pi$
$158$	−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	−0.418999	−	0.907987i	$-0.637619\pi$
$163$	2.01518	−	1.16346i	0.157841	−	0.0911296i	0.576840	+	0.816857i	$0.304286\pi$
$164$	−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	$0.0422710\pi$
$167$			3.42219i			0.264817i	−0.991195	+	0.132408i	$0.957729\pi$
$168$		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	0.664791	−	0.747029i	$-0.268521\pi$
$173$	−4.13727	−	7.16596i	−0.314551	−	0.544818i	−0.979342	+	0.202211i	$0.935187\pi$
$174$		−	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	0.385449	+	0.922729i	$0.374047\pi$
$179$	−8.11285	+	14.0519i	−0.606383	+	1.05029i	−0.991831	+	0.127556i	$0.959287\pi$
$180$	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	0.961069	−	0.276308i	$-0.0891109\pi$
$191$	3.33407	+	5.77479i	0.241245	+	0.417849i	−0.719824	+	0.694157i	$0.755778\pi$
$192$	1.37778	−	2.38639i	0.0994330	−	0.172223i
$193$	−17.8431	−	10.3017i	−1.28438	−	0.741535i	−0.306732	−	0.951796i	$-0.599235\pi$
$193$	−17.8431	−	10.3017i	−1.28438	−	0.741535i	−0.977645	+	0.210261i	$0.932569\pi$
$194$	−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	$0.0963571\pi$
$197$			8.36842i			0.596225i	−0.954531	+	0.298112i	$0.903643\pi$
$198$	−1.76271	−	3.05311i	−0.125271	−	0.216975i
$199$	0.300736	−	0.520890i	0.0213186	−	0.0369249i	−0.855169	−	0.518349i	$-0.826547\pi$
$199$	0.300736	−	0.520890i	0.0213186	−	0.0369249i	0.876488	+	0.481424i	$0.159880\pi$
$200$	−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	$0.115873\pi$
$223$			10.6336i			0.712078i	−0.934471	+	0.356039i	$0.884127\pi$
$224$		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	0.000600144	−	1.00000i	$-0.499809\pi$
$227$	−13.0344	−	7.52543i	−0.865125	−	0.499480i	−0.865725	+	0.500520i	$0.833142\pi$
$228$	24.9997	+	14.4336i	1.65564	+	0.955886i
$229$	5.65930	−	3.26740i	0.373977	−	0.215916i	−0.301218	−	0.953555i	$-0.597393\pi$
$229$	5.65930	−	3.26740i	0.373977	−	0.215916i	0.675195	+	0.737640i	$0.264060\pi$
$230$	7.26517			0.479051
$231$		0			0
$232$		−	4.98079i		−	0.327005i
$233$	−13.9795	−	24.2132i	−0.915827	−	1.58626i	−0.805686	−	0.592343i	$-0.798203\pi$
$233$	−13.9795	−	24.2132i	−0.915827	−	1.58626i	−0.110141	−	0.993916i	$-0.535130\pi$
$234$	−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	$0.218301\pi$
$239$			19.5812i			1.26660i	−0.773905	+	0.633301i	$0.781699\pi$
$240$	8.49261	−	4.90321i	0.548196	−	0.316501i
$241$	−11.5679	−	6.67876i	−0.745157	−	0.430217i	0.0787843	−	0.996892i	$-0.474896\pi$
$241$	−11.5679	−	6.67876i	−0.745157	−	0.430217i	−0.823941	+	0.566675i	$0.808230\pi$
$242$	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	0.952951	+	0.303126i	$0.0980302\pi$
$257$	11.8469	+	20.5194i	0.738990	+	1.27997i	−0.213961	+	0.976842i	$0.568636\pi$
$258$			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	−0.977930	−	0.208932i	$-0.933001\pi$
$263$	−4.99532	+	8.65214i	−0.308024	+	0.533514i	0.669906	+	0.742446i	$0.266335\pi$
$264$	−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	0.442967	+	0.896538i	$0.353926\pi$
$269$	−9.10171	+	15.7646i	−0.554941	+	0.961186i	−0.997908	+	0.0646482i	$0.979407\pi$
$270$	2.68889	−	4.65730i	0.163641	−	0.283434i
$271$	20.9360	−	12.0874i	1.27177	−	0.734258i	0.296451	−	0.955048i	$-0.404197\pi$
$271$	20.9360	−	12.0874i	1.27177	−	0.734258i	0.975322	+	0.220789i	$0.0708634\pi$
$272$	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	−0.839436	−	0.543459i	$-0.817114\pi$
$277$	0.847673	−	1.46821i	0.0509317	−	0.0882163i	0.890367	+	0.455243i	$0.150448\pi$
$278$	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	$0.112945\pi$
$281$			11.6479i			0.694854i	−0.937707	+	0.347427i	$0.887055\pi$
$282$	1.43578	+	2.48685i	0.0854997	+	0.148090i
$283$	−6.06668	+	10.5078i	−0.360626	+	0.624623i	−0.988064	−	0.154043i	$-0.950770\pi$
$283$	−6.06668	+	10.5078i	−0.360626	+	0.624623i	0.627438	+	0.778667i	$0.284104\pi$
$284$	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	$-0.891409\pi$
$293$		−	11.4538i		−	0.669140i	0.942371	−	0.334570i	$-0.108591\pi$
$294$		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	$-0.963862\pi$
$307$		−	3.96989i		−	0.226574i	0.993562	−	0.113287i	$-0.0361379\pi$
$308$		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	0.159192	+	0.987248i	$0.449111\pi$
$311$	−13.6741	+	23.6842i	−0.775386	+	1.34301i	−0.934577	+	0.355760i	$0.884222\pi$
$312$	−17.5660	−	8.20986i	−0.994481	−	0.464792i
$313$	−9.55162	−	16.5439i	−0.539890	−	0.935116i	−0.998909	−	0.0466901i	$-0.985133\pi$
$313$	−9.55162	−	16.5439i	−0.539890	−	0.935116i	0.459020	−	0.888426i	$-0.348201\pi$
$314$			5.09679i			0.287628i
$315$		0			0
$316$	−6.83314			−0.384394
$317$	−8.58070	+	4.95407i	−0.481940	+	0.278248i	−0.721225	−	0.692701i	$-0.756420\pi$
$317$	−8.58070	+	4.95407i	−0.481940	+	0.278248i	0.239285	+	0.970949i	$0.423087\pi$
$318$	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	−0.940064	−	0.340999i	$-0.889235\pi$
$331$	−20.2817	+	11.7096i	−1.11478	+	0.643620i	−0.174718	+	0.984618i	$0.555902\pi$
$332$	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	−0.931781	−	0.363020i	$-0.881746\pi$
$347$	−2.82225	+	4.88827i	−0.151506	+	0.262416i	0.780275	+	0.625436i	$0.215079\pi$
$348$	−3.46367	−	5.99926i	−0.185672	−	0.321594i
$349$		−	24.1590i		−	1.29320i	−0.762828	−	0.646601i	$-0.776190\pi$
$349$		−	24.1590i		−	1.29320i	0.762828	−	0.646601i	$-0.223810\pi$
$350$		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	−0.970109	−	0.242670i	$-0.921977\pi$
$353$	−31.2886	−	18.0645i	−1.66532	−	0.961474i	−0.695213	−	0.718804i	$-0.744690\pi$
$354$	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	−0.0461427	−	0.998935i	$-0.514693\pi$
$359$	15.0799	−	8.70641i	0.795889	−	0.459507i	0.842032	+	0.539428i	$0.181360\pi$
$360$	−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	−0.825131	−	0.564941i	$-0.808899\pi$
$367$	1.46912	−	2.54460i	0.0766876	−	0.132827i	0.901819	+	0.432114i	$0.142232\pi$
$368$	−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	0.999869	−	0.0161675i	$-0.00514648\pi$
$373$	9.38493	+	16.2552i	0.485933	+	0.841661i	−0.513936	+	0.857828i	$0.671813\pi$
$374$	−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	$-0.791803\pi$
$379$		−	23.6894i		−	1.21684i	0.793615	−	0.608421i	$-0.208197\pi$
$380$	−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	0.404646	−	0.914473i	$-0.367395\pi$
$383$	27.3775	−	15.8064i	1.39893	−	0.807671i	0.994280	+	0.106803i	$0.0340614\pi$
$384$		−	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	0.491518	+	0.870867i	$0.336442\pi$
$389$	−10.0279	+	17.3688i	−0.508434	+	0.880634i	−0.999952	+	0.00976644i	$0.996891\pi$
$390$	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	−0.906518	−	0.422167i	$-0.861270\pi$
$397$	−19.8087	+	11.4366i	−0.994169	+	0.573984i	−0.0876515	+	0.996151i	$0.527936\pi$
$398$			0.414349i			0.0207695i
$399$		0			0
$400$	−7.34614			−0.367307
$401$	−4.86087	+	2.80642i	−0.242740	+	0.140146i	−0.616436	−	0.787405i	$-0.711424\pi$
$401$	−4.86087	+	2.80642i	−0.242740	+	0.140146i	0.373695	+	0.927552i	$0.378091\pi$
$402$	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	0.940995	−	0.338422i	$-0.109893\pi$
$409$	22.6184	+	13.0588i	1.11841	+	0.645714i	0.177416	+	0.984136i	$0.443226\pi$
$410$	−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	$0.0642628\pi$
$421$			8.22861i			0.401038i	−0.979690	+	0.200519i	$0.935737\pi$
$422$	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	0.469707	−	0.882822i	$-0.344360\pi$
$431$	−1.24535	−	0.719004i	−0.0599864	−	0.0346332i	−0.529693	+	0.848189i	$0.677693\pi$
$432$	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	0.961426	−	0.275063i	$-0.0886988\pi$
$439$	5.08097	+	8.80049i	0.242501	+	0.420025i	−0.718925	+	0.695088i	$0.755365\pi$
$440$			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	0.825405	−	0.564542i	$-0.190947\pi$
$443$	−1.60393	−	2.77809i	−0.0762052	−	0.131991i	−0.901610	+	0.432550i	$0.857614\pi$
$444$	−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	$-0.856957\pi$
$449$		−	18.4099i		−	0.868817i	0.900716	−	0.434409i	$-0.143043\pi$
$450$	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	−0.567343	−	0.823482i	$-0.692028\pi$
$457$	−2.94706	+	1.70149i	−0.137858	+	0.0795922i	0.429485	+	0.903074i	$0.358695\pi$
$458$	−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	$0.134189\pi$
$461$			17.5714i			0.818380i	−0.912449	+	0.409190i	$0.865811\pi$
$462$		0			0
$463$			15.7714i			0.732959i	0.930426	+	0.366479i	$0.119437\pi$
$463$			15.7714i			0.732959i	−0.930426	+	0.366479i	$0.880563\pi$
$464$	−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	0.906308	−	0.422617i	$-0.138889\pi$
$467$	1.88347	+	3.26227i	0.0871567	+	0.150960i	−0.819151	+	0.573577i	$0.805555\pi$
$468$	−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	0.241045	−	0.970514i	$-0.422510\pi$
$479$	−10.4817	−	6.05162i	−0.478922	−	0.276506i	−0.719967	+	0.694008i	$0.755843\pi$
$480$	−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	0.118631	−	0.992938i	$-0.462149\pi$
$487$	−15.0496	−	8.68889i	−0.681963	−	0.393731i	−0.800594	+	0.599207i	$0.795483\pi$
$488$	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	−0.278697	−	0.960379i	$-0.589903\pi$
$499$	9.24063	−	5.33508i	0.413667	−	0.238831i	0.692364	+	0.721548i	$0.256569\pi$
$500$	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	0.294746	−	0.955576i	$-0.404765\pi$
$509$	28.6451	−	16.5383i	1.26967	−	0.733046i	0.974926	+	0.222530i	$0.0714316\pi$
$510$	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	−0.465195	−	0.885208i	$-0.654016\pi$
$521$	12.1891	−	21.1122i	0.534015	−	0.924942i	0.999210	−	0.0397336i	$-0.0126509\pi$
$522$	2.32865	+	1.34445i	0.101922	+	0.0588448i
$523$	17.4701	+	30.2591i	0.763915	+	1.32314i	0.940818	+	0.338912i	$0.110059\pi$
$523$	17.4701	+	30.2591i	0.763915	+	1.32314i	−0.176903	+	0.984228i	$0.556608\pi$
$524$	−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	−0.945298	−	0.326208i	$-0.894229\pi$
$541$	−26.4097	+	15.2477i	−1.13544	+	0.655548i	−0.190144	+	0.981756i	$0.560896\pi$
$542$	−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	0.216445	−	0.976295i	$-0.430554\pi$
$557$	−12.2920	−	7.09679i	−0.520829	−	0.300701i	−0.737274	+	0.675594i	$0.763887\pi$
$558$	−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	−0.548303	−	0.836280i	$-0.684726\pi$
$563$	10.6795	−	18.4975i	0.450088	−	0.779576i	0.998391	+	0.0567041i	$0.0180592\pi$
$564$	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	0.961682	+	0.274168i	$0.0884025\pi$
$569$	17.1336	+	29.6763i	0.718278	+	1.24409i	−0.243404	+	0.969925i	$0.578264\pi$
$570$	36.2897	+	20.9518i	1.52001	+	0.877576i
$571$	−18.8247	+	32.6053i	−0.787789	+	1.36449i	0.139529	+	0.990218i	$0.455441\pi$
$571$	−18.8247	+	32.6053i	−0.787789	+	1.36449i	−0.927318	+	0.374273i	$0.877892\pi$
$572$	−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	−0.108598	−	0.994086i	$-0.534636\pi$
$577$	−24.5925	−	14.1985i	−1.02380	−	0.591091i	−0.915202	+	0.402995i	$0.867969\pi$
$578$	−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	$-0.958918\pi$
$587$		−	6.23659i		−	0.257412i	0.991683	−	0.128706i	$-0.0410823\pi$
$588$		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	−0.778752	−	0.627332i	$-0.784147\pi$
$593$	−15.2159	+	8.78491i	−0.624843	+	0.360753i	0.153909	+	0.988085i	$0.450814\pi$
$594$	−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	−0.985700	−	0.168508i	$-0.946105\pi$
$599$	−8.49063	+	14.7062i	−0.346918	+	0.600879i	0.638782	+	0.769387i	$0.279438\pi$
$600$	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	0.741577	−	0.670867i	$-0.234078\pi$
$607$	−5.17876	−	8.96987i	−0.210199	−	0.364076i	−0.951777	+	0.306791i	$0.900745\pi$
$608$	−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	0.372133	−	0.928180i	$-0.378627\pi$
$613$	−6.08147	−	3.51114i	−0.245628	−	0.141814i	−0.617761	+	0.786366i	$0.711960\pi$
$614$	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	$-0.793772\pi$
$617$		−	29.9813i		−	1.20700i	0.797363	−	0.603500i	$-0.206228\pi$
$618$	−16.2428	+	9.37778i	−0.653381	+	0.377230i
$619$	0.0247512	+	0.0142901i	0.000994834	+	0.000574368i	0.500497	−	0.865738i	$-0.333151\pi$
$619$	0.0247512	+	0.0142901i	0.000994834	+	0.000574368i	−0.499503	+	0.866312i	$0.666484\pi$
$620$	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	$-0.921964\pi$
$631$		−	12.1936i		−	0.485419i	0.970099	−	0.242709i	$-0.0780361\pi$
$632$	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	−0.892573	−	0.450903i	$-0.851102\pi$
$641$	−1.41258	+	2.44666i	−0.0557935	+	0.0966373i	0.836780	+	0.547540i	$0.184436\pi$
$642$	24.0289	−	13.8731i	0.948346	−	0.547528i
$643$		−	37.7275i		−	1.48783i	−0.668276	−	0.743913i	$-0.732968\pi$
$643$		−	37.7275i		−	1.48783i	0.668276	−	0.743913i	$-0.267032\pi$
$644$		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	−0.961592	−	0.274483i	$-0.911493\pi$
$647$	−6.18320	+	10.7096i	−0.243087	+	0.421039i	0.718505	+	0.695522i	$0.244827\pi$
$648$	−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	0.984138	+	0.177402i	$0.0567694\pi$
$653$	16.5002	+	28.5793i	0.645704	+	1.11839i	−0.338434	+	0.940990i	$0.609897\pi$
$654$	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	0.231419	−	0.972854i	$-0.425663\pi$
$661$	−12.7364	−	7.35336i	−0.495388	−	0.286013i	−0.726807	+	0.686842i	$0.758997\pi$
$662$	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	0.835003	−	0.550246i	$-0.185466\pi$
$677$	−1.53580	−	2.66008i	−0.0590256	−	0.102235i	−0.894028	+	0.448011i	$0.852133\pi$
$678$			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	0.851007	−	0.525154i	$-0.175992\pi$
$683$	21.4749	+	12.3985i	0.821713	+	0.474416i	−0.0292935	+	0.999571i	$0.509326\pi$
$684$	−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	−0.874811	−	0.484465i	$-0.839014\pi$
$691$	−23.4652	+	13.5476i	−0.892658	+	0.515376i	−0.0178467	+	0.999841i	$0.505681\pi$
$692$	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	−0.684267	+	0.729231i	$0.739878\pi$
$709$	−44.1459	+	25.4876i	−1.65793	+	0.957209i	−0.973666	+	0.227977i	$0.926789\pi$
$710$	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	−0.935006	−	0.354631i	$-0.884607\pi$
$719$	−20.7709	−	35.9762i	−0.774622	−	1.34169i	0.160384	−	0.987055i	$-0.448727\pi$
$720$			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	−0.157360	−	0.987541i	$-0.550298\pi$
$733$	16.7641	−	9.67876i	0.619196	−	0.357493i	0.776556	+	0.630048i	$0.216965\pi$
$734$			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	0.520739	−	0.853716i	$-0.325657\pi$
$739$	1.13545	+	0.655554i	0.0417683	+	0.0241149i	−0.478970	+	0.877831i	$0.658990\pi$
$740$	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	$0.129174\pi$
$743$			21.5210i			0.789528i	−0.918783	+	0.394764i	$0.870826\pi$
$744$	−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	0.677895	−	0.735158i	$-0.262892\pi$
$751$	−8.15878	−	14.1314i	−0.297718	−	0.515663i	−0.975614	+	0.219495i	$0.929559\pi$
$752$	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	−0.329589	−	0.944124i	$-0.606910\pi$
$761$	8.91731	−	5.14841i	0.323252	−	0.186630i	0.652841	+	0.757495i	$0.273577\pi$
$762$			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	$0.0540153\pi$
$769$			9.36641i			0.337761i	−0.985637	+	0.168881i	$0.945985\pi$
$770$		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	0.556735	−	0.830690i	$-0.312054\pi$
$773$	3.21690	+	1.85728i	0.115704	+	0.0668017i	−0.441031	+	0.897492i	$0.645387\pi$
$774$	−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	0.593165	−	0.805081i	$-0.297878\pi$
$787$	5.40105	+	3.11830i	0.192527	+	0.111155i	−0.400638	+	0.916236i	$0.631212\pi$
$788$	−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	−0.842539	−	0.538635i	$-0.818940\pi$
$809$	1.28568	−	2.22686i	0.0452021	−	0.0782924i	0.887741	+	0.460343i	$0.152273\pi$
$810$	12.2755	+	21.2619i	0.431319	+	0.747066i
$811$		−	28.3654i		−	0.996042i	−0.867165	−	0.498021i	$-0.834060\pi$
$811$		−	28.3654i		−	0.996042i	0.867165	−	0.498021i	$-0.165940\pi$
$812$		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	0.0642938	−	0.997931i	$-0.479521\pi$
$821$	27.5263	−	15.8923i	0.960674	−	0.554646i	0.896380	+	0.443285i	$0.146187\pi$
$822$	−12.4795	+	21.6151i	−0.435272	+	0.753914i
$823$	15.4565	−	26.7715i	0.538781	−	0.933196i	−0.460189	−	0.887821i	$-0.652218\pi$
$823$	15.4565	−	26.7715i	0.538781	−	0.933196i	0.998970	−	0.0453747i	$-0.0144482\pi$
$824$	−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	$0.332741\pi$
$827$			49.7560i			1.73019i	−0.501610	+	0.865094i	$0.667259\pi$
$828$	−4.76271	−	8.24926i	−0.165516	−	0.286682i
$829$	9.95952	−	17.2504i	0.345908	−	0.599131i	−0.639610	−	0.768700i	$-0.720904\pi$
$829$	9.95952	−	17.2504i	0.345908	−	0.599131i	0.985518	+	0.169569i	$0.0542375\pi$
$830$	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	$-0.936039\pi$
$839$		−	11.5625i		−	0.399181i	0.979879	−	0.199590i	$-0.0639611\pi$
$840$		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	$-0.990491\pi$
$853$		−	1.74467i		−	0.0597363i	0.999554	−	0.0298682i	$-0.00950875\pi$
$854$		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	−0.236654	−	0.971594i	$-0.576051\pi$
$857$	21.1684	−	36.6647i	0.723098	−	1.25244i	0.959752	−	0.280849i	$-0.0906160\pi$
$858$	6.26177	−	13.3979i	0.213773	−	0.457395i
$859$	−2.68889	−	4.65730i	−0.0917438	−	0.158905i	0.816501	−	0.577344i	$-0.195911\pi$
$859$	−2.68889	−	4.65730i	−0.0917438	−	0.158905i	−0.908245	+	0.418439i	$0.862577\pi$
$860$		−	43.1798i		−	1.47242i
$861$		0			0
$862$	0.990632			0.0337411
$863$	−13.3620	+	7.71456i	−0.454848	+	0.262607i	−0.709875	−	0.704327i	$-0.751249\pi$
$863$	−13.3620	+	7.71456i	−0.454848	+	0.262607i	0.255027	+	0.966934i	$0.417915\pi$
$864$	−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	−0.943029	−	0.332711i	$-0.892037\pi$
$877$	−33.3576	+	19.2590i	−1.12641	+	0.650331i	−0.183378	+	0.983042i	$0.558703\pi$
$878$	−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	0.931573	−	0.363556i	$-0.118437\pi$
$887$	4.49532	+	7.78612i	0.150938	+	0.261432i	−0.780635	+	0.624988i	$0.785104\pi$
$888$	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	−0.985111	−	0.171918i	$-0.945004\pi$
$907$	−10.3501	+	17.9270i	−0.343671	+	0.595255i	0.641441	+	0.767173i	$0.278337\pi$
$908$	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	−0.986217	−	0.165455i	$-0.947091\pi$
$919$	−19.2924	−	33.4154i	−0.636397	−	1.10227i	0.349821	−	0.936817i	$-0.386242\pi$
$920$	−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	−0.453032	−	0.891494i	$-0.649658\pi$
$929$	2.81961	−	1.62790i	0.0925085	−	0.0534098i	0.545541	+	0.838084i	$0.316324\pi$
$930$			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	0.957138	−	0.289632i	$-0.0935330\pi$
$941$	36.3470	+	20.9849i	1.18488	+	0.684090i	0.227740	+	0.973722i	$0.426866\pi$
$942$	−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	−0.758285	−	0.651923i	$-0.773962\pi$
$947$	−17.6284	+	10.1778i	−0.572846	+	0.330733i	0.185439	+	0.982656i	$0.440629\pi$
$948$	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	$-0.660484\pi$
$967$		−	54.4548i		−	1.75115i	0.483084	−	0.875574i	$-0.339516\pi$
$968$	−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	−0.855528	−	0.517757i	$-0.826767\pi$
$971$	−27.3017	−	47.2880i	−0.876155	−	1.51754i	−0.0206267	−	0.999787i	$-0.506566\pi$
$972$	−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	0.878673	−	0.477424i	$-0.158429\pi$
$977$	28.2735	+	16.3237i	0.904549	+	0.522242i	0.0258756	+	0.999665i	$0.491763\pi$
$978$	−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	0.0694590	−	0.997585i	$-0.477873\pi$
$983$	−23.8202	−	13.7526i	−0.759745	−	0.438639i	−0.829204	+	0.558946i	$0.811206\pi$
$984$	−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	−0.811704	−	0.584069i	$-0.801460\pi$
$991$	3.14695	−	5.45068i	0.0999662	−	0.173147i	0.911670	+	0.410922i	$0.134793\pi$
$992$	−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	−0.982607	−	0.185700i	$-0.940545\pi$
$997$	−10.4351	+	18.0741i	−0.330483	+	0.572413i	0.652124	+	0.758112i	$0.273878\pi$
$998$	−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.116.3		12
7.2	even	3	inner	637.2.r.d.324.4		12
7.3	odd	6		91.2.c.a.64.3	✓	6
7.4	even	3		637.2.c.d.246.3		6
7.5	odd	6		637.2.r.e.324.4		12
7.6	odd	2		637.2.r.e.116.3		12
13.12	even	2	inner	637.2.r.d.116.4		12
21.17	even	6		819.2.c.b.64.4		6
28.3	even	6		1456.2.k.c.337.5		6
91.12	odd	6		637.2.r.e.324.3		12
91.18	odd	12		8281.2.a.be.1.2		3
91.25	even	6		637.2.c.d.246.4		6
91.31	even	12		1183.2.a.h.1.2		3
91.38	odd	6		91.2.c.a.64.4	yes	6
91.51	even	6	inner	637.2.r.d.324.3		12
91.60	odd	12		8281.2.a.bi.1.2		3
91.73	even	12		1183.2.a.j.1.2		3
91.90	odd	2		637.2.r.e.116.4		12
273.38	even	6		819.2.c.b.64.3		6
364.311	even	6		1456.2.k.c.337.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.3	✓	6	7.3	odd	6
91.2.c.a.64.4	yes	6	91.38	odd	6
637.2.c.d.246.3		6	7.4	even	3
637.2.c.d.246.4		6	91.25	even	6
637.2.r.d.116.3		12	1.1	even	1	trivial
637.2.r.d.116.4		12	13.12	even	2	inner
637.2.r.d.324.3		12	91.51	even	6	inner
637.2.r.d.324.4		12	7.2	even	3	inner
637.2.r.e.116.3		12	7.6	odd	2
637.2.r.e.116.4		12	91.90	odd	2
637.2.r.e.324.3		12	91.12	odd	6
637.2.r.e.324.4		12	7.5	odd	6
819.2.c.b.64.3		6	273.38	even	6
819.2.c.b.64.4		6	21.17	even	6
1183.2.a.h.1.2		3	91.31	even	12
1183.2.a.j.1.2		3	91.73	even	12
1456.2.k.c.337.5		6	28.3	even	6
1456.2.k.c.337.6		6	364.311	even	6
8281.2.a.be.1.2		3	91.18	odd	12
8281.2.a.bi.1.2		3	91.60	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 $\F_{q}$

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

Properties

Related objects

Downloads

Learn more