LMFDB - Embedded newform 560.2.ci.c.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.2
Root			$-1.45333 + 1.51725i$ of defining polynomial
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.c.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13459 + 0.304013i) q^{3} +(0.264946 + 2.22032i) q^{5} +(-0.698943 + 2.55176i) q^{7} +(-1.40320 + 0.810140i) q^{9} +O(q^{10})$	\(q+(-1.13459 + 0.304013i) q^{3} +(0.264946 + 2.22032i) q^{5} +(-0.698943 + 2.55176i) q^{7} +(-1.40320 + 0.810140i) q^{9} +(0.371536 - 0.643519i) q^{11} +(-2.05532 - 2.05532i) q^{13} +(-0.975610 - 2.43860i) q^{15} +(-1.69789 - 6.33660i) q^{17} +(0.946027 + 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(-5.11112 - 1.36952i) q^{23} +(-4.85961 + 1.17653i) q^{25} +(3.83750 - 3.83750i) q^{27} +9.69135i q^{29} +(-2.96403 - 1.71129i) q^{31} +(-0.225903 + 0.843083i) q^{33} +(-5.85090 - 0.875795i) q^{35} +(-0.691342 + 2.58012i) q^{37} +(2.95680 + 1.70711i) q^{39} +0.817699i q^{41} +(-1.59589 + 1.59589i) q^{43} +(-2.17054 - 2.90091i) q^{45} +(-4.54913 - 1.21894i) q^{47} +(-6.02296 - 3.56707i) q^{49} +(3.85282 + 6.67328i) q^{51} +(1.29040 + 4.81583i) q^{53} +(1.52725 + 0.654429i) q^{55} +(-1.57150 - 1.57150i) q^{57} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(-1.08652 - 4.14688i) q^{63} +(4.01892 - 5.10802i) q^{65} +(-13.2248 + 3.54358i) q^{67} +6.21538 q^{69} +16.0173 q^{71} +(-8.54906 + 2.29071i) q^{73} +(5.15599 - 2.81226i) q^{75} +(1.38242 + 1.39785i) q^{77} +(-5.70091 + 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-2.94629 - 10.9957i) q^{87} +(-3.01603 - 5.22392i) q^{89} +(6.68124 - 3.80814i) q^{91} +(3.88322 + 1.04051i) q^{93} +(-3.38749 + 2.53461i) q^{95} +(-3.16693 + 3.16693i) q^{97} +1.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.13459	+	0.304013i	−0.655056	+	0.175522i	−0.571014	−	0.820940i	$-0.693450\pi$
$3$	−1.13459	+	0.304013i	−0.655056	+	0.175522i	−0.0840425	+	0.996462i	$0.526783\pi$
$4$		0			0
$5$	0.264946	+	2.22032i	0.118487	+	0.992956i
$5$	0.264946	+	2.22032i	0.118487	+	0.992956i
$6$		0			0
$7$	−0.698943	+	2.55176i	−0.264175	+	0.964475i
$7$	−0.698943	+	2.55176i	−0.264175	+	0.964475i
$8$		0			0
$9$	−1.40320	+	0.810140i	−0.467734	+	0.270047i
$10$		0			0
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	−0.804563	−	0.593867i	$-0.797601\pi$
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	0.916586	+	0.399839i	$0.130934\pi$
$12$		0			0
$13$	−2.05532	−	2.05532i	−0.570044	−	0.570044i	0.362097	−	0.932141i	$-0.382061\pi$
$13$	−2.05532	−	2.05532i	−0.570044	−	0.570044i	−0.932141	+	0.362097i	$0.882061\pi$
$14$		0			0
$15$	−0.975610	−	2.43860i	−0.251901	−	0.629645i
$16$		0			0
$17$	−1.69789	−	6.33660i	−0.411798	−	1.53685i	−0.791163	−	0.611605i	$-0.790524\pi$
$17$	−1.69789	−	6.33660i	−0.411798	−	1.53685i	0.379365	−	0.925247i	$-0.376143\pi$
$18$		0			0
$19$	0.946027	+	1.63857i	0.217033	+	0.375913i	0.953900	−	0.300126i	$-0.0970286\pi$
$19$	0.946027	+	1.63857i	0.217033	+	0.375913i	−0.736866	+	0.676039i	$0.763695\pi$
$20$		0			0
$21$	0.0172465	−	3.10769i	0.00376349	−	0.678154i
$22$		0			0
$23$	−5.11112	−	1.36952i	−1.06574	−	0.285565i	−0.317000	−	0.948426i	$-0.602675\pi$
$23$	−5.11112	−	1.36952i	−1.06574	−	0.285565i	−0.748743	+	0.662861i	$0.769342\pi$
$24$		0			0
$25$	−4.85961	+	1.17653i	−0.971921	+	0.235306i
$26$		0			0
$27$	3.83750	−	3.83750i	0.738528	−	0.738528i
$28$		0			0
$29$			9.69135i			1.79964i	0.436263	+	0.899819i	$0.356302\pi$
$29$			9.69135i			1.79964i	−0.436263	+	0.899819i	$0.643698\pi$
$30$		0			0
$31$	−2.96403	−	1.71129i	−0.532356	−	0.307356i	0.209619	−	0.977783i	$-0.432778\pi$
$31$	−2.96403	−	1.71129i	−0.532356	−	0.307356i	−0.741975	+	0.670427i	$0.766111\pi$
$32$		0			0
$33$	−0.225903	+	0.843083i	−0.0393247	+	0.146762i
$34$		0			0
$35$	−5.85090	−	0.875795i	−0.988982	−	0.148036i
$36$		0			0
$37$	−0.691342	+	2.58012i	−0.113656	+	0.424170i	−0.999183	−	0.0404183i	$-0.987131\pi$
$37$	−0.691342	+	2.58012i	−0.113656	+	0.424170i	0.885527	+	0.464588i	$0.153798\pi$
$38$		0			0
$39$	2.95680	+	1.70711i	0.473466	+	0.273356i
$40$		0			0
$41$			0.817699i			0.127703i	0.997959	+	0.0638515i	$0.0203384\pi$
$41$			0.817699i			0.127703i	−0.997959	+	0.0638515i	$0.979662\pi$
$42$		0			0
$43$	−1.59589	+	1.59589i	−0.243371	+	0.243371i	−0.818243	−	0.574872i	$-0.805052\pi$
$43$	−1.59589	+	1.59589i	−0.243371	+	0.243371i	0.574872	+	0.818243i	$0.305052\pi$
$44$		0			0
$45$	−2.17054	−	2.90091i	−0.323565	−	0.432442i
$46$		0			0
$47$	−4.54913	−	1.21894i	−0.663560	−	0.177800i	−0.0887076	−	0.996058i	$-0.528274\pi$
$47$	−4.54913	−	1.21894i	−0.663560	−	0.177800i	−0.574852	+	0.818257i	$0.694940\pi$
$48$		0			0
$49$	−6.02296	−	3.56707i	−0.860423	−	0.509581i
$50$		0			0
$51$	3.85282	+	6.67328i	0.539502	+	0.934445i
$52$		0			0
$53$	1.29040	+	4.81583i	0.177250	+	0.661505i	0.996158	+	0.0875798i	$0.0279133\pi$
$53$	1.29040	+	4.81583i	0.177250	+	0.661505i	−0.818908	+	0.573925i	$0.805420\pi$
$54$		0			0
$55$	1.52725	+	0.654429i	0.205935	+	0.0882432i
$56$		0			0
$57$	−1.57150	−	1.57150i	−0.208150	−	0.208150i
$58$		0			0
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	−0.937001	−	0.349327i	$-0.886410\pi$
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	0.771026	+	0.636803i	$0.219744\pi$
$60$		0			0
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	−0.123927	−	0.992291i	$-0.539549\pi$
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	0.797386	+	0.603469i	$0.206215\pi$
$62$		0			0
$63$	−1.08652	−	4.14688i	−0.136889	−	0.522458i
$64$		0			0
$65$	4.01892	−	5.10802i	0.498485	−	0.633572i
$66$		0			0
$67$	−13.2248	+	3.54358i	−1.61567	+	0.432917i	−0.949725	−	0.313084i	$-0.898638\pi$
$67$	−13.2248	+	3.54358i	−1.61567	+	0.432917i	−0.665944	+	0.746002i	$0.731971\pi$
$68$		0			0
$69$	6.21538			0.748244
$70$		0			0
$71$	16.0173			1.90090			0.950450	−	0.310879i	$-0.100623\pi$
$71$	16.0173			1.90090			0.950450	+	0.310879i	$0.100623\pi$
$72$		0			0
$73$	−8.54906	+	2.29071i	−1.00059	+	0.268108i	−0.721693	−	0.692213i	$-0.756636\pi$
$73$	−8.54906	+	2.29071i	−1.00059	+	0.268108i	−0.278898	+	0.960321i	$0.589969\pi$
$74$		0			0
$75$	5.15599	−	2.81226i	0.595362	−	0.324732i
$76$		0			0
$77$	1.38242	+	1.39785i	0.157542	+	0.159300i
$78$		0			0
$79$	−5.70091	+	3.29142i	−0.641402	+	0.370314i	−0.785155	−	0.619300i	$-0.787417\pi$
$79$	−5.70091	+	3.29142i	−0.641402	+	0.370314i	0.143752	+	0.989614i	$0.454083\pi$
$80$		0			0
$81$	−0.756928	+	1.31104i	−0.0841031	+	0.145671i
$82$		0			0
$83$	9.23519	+	9.23519i	1.01369	+	1.01369i	0.999905	+	0.0137887i	$0.00438921\pi$
$83$	9.23519	+	9.23519i	1.01369	+	1.01369i	0.0137887	+	0.999905i	$0.495611\pi$
$84$		0			0
$85$	13.6194	−	5.44871i	1.47723	−	0.590995i
$86$		0			0
$87$	−2.94629	−	10.9957i	−0.315876	−	1.17886i
$88$		0			0
$89$	−3.01603	−	5.22392i	−0.319699	−	0.553735i	0.660726	−	0.750627i	$-0.270248\pi$
$89$	−3.01603	−	5.22392i	−0.319699	−	0.553735i	−0.980425	+	0.196892i	$0.936915\pi$
$90$		0			0
$91$	6.68124	−	3.80814i	0.700385	−	0.399201i
$92$		0			0
$93$	3.88322	+	1.04051i	0.402671	+	0.107895i
$94$		0			0
$95$	−3.38749	+	2.53461i	−0.347549	+	0.260046i
$96$		0			0
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	−0.849363	−	0.527810i	$-0.823013\pi$
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	0.527810	+	0.849363i	$0.323013\pi$
$98$		0			0
$99$			1.20398i			0.121005i
$100$		0			0
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.897265	−	0.441493i	$-0.145551\pi$
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.0662887	+	0.997800i	$0.478884\pi$
$102$		0			0
$103$	−0.627940	+	2.34351i	−0.0618728	+	0.230912i	−0.989937	−	0.141507i	$-0.954805\pi$
$103$	−0.627940	+	2.34351i	−0.0618728	+	0.230912i	0.928064	+	0.372420i	$0.121472\pi$
$104$		0			0
$105$	6.90463	−	0.785078i	0.673823	−	0.0766157i
$106$		0			0
$107$	1.71868	−	6.41422i	0.166151	−	0.620086i	−0.831739	−	0.555167i	$-0.812654\pi$
$107$	1.71868	−	6.41422i	0.166151	−	0.620086i	0.997891	−	0.0649189i	$-0.0206789\pi$
$108$		0			0
$109$	7.76000	+	4.48024i	0.743274	+	0.429129i	0.823258	−	0.567667i	$-0.192154\pi$
$109$	7.76000	+	4.48024i	0.743274	+	0.429129i	−0.0799848	+	0.996796i	$0.525487\pi$
$110$		0			0
$111$		−	3.13756i		−	0.297804i
$112$		0			0
$113$	0.307790	−	0.307790i	0.0289545	−	0.0289545i	−0.692481	−	0.721436i	$-0.743482\pi$
$113$	0.307790	−	0.307790i	0.0289545	−	0.0289545i	0.721436	+	0.692481i	$0.243482\pi$
$114$		0			0
$115$	1.68660	−	11.7112i	0.157276	−	1.09207i
$116$		0			0
$117$	4.54913	+	1.21894i	0.420568	+	0.112691i
$118$		0			0
$119$	17.3562	+	0.0963204i	1.59104	+	0.00882967i
$120$		0			0
$121$	5.22392	+	9.04810i	0.474902	+	0.822554i
$122$		0			0
$123$	−0.248591	−	0.927753i	−0.0224147	−	0.0836527i
$124$		0			0
$125$	−3.89980	−	10.4781i	−0.348808	−	0.937194i
$126$		0			0
$127$	11.1823	+	11.1823i	0.992267	+	0.992267i	0.999970	−	0.00770296i	$-0.00245195\pi$
$127$	11.1823	+	11.1823i	0.992267	+	0.992267i	−0.00770296	+	0.999970i	$0.502452\pi$
$128$		0			0
$129$	1.32551	−	2.29585i	0.116705	−	0.202139i
$130$		0			0
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	−0.0910579	−	0.995846i	$-0.529025\pi$
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	0.816899	+	0.576781i	$0.195692\pi$
$132$		0			0
$133$	−4.84245	+	1.26877i	−0.419893	+	0.110016i
$134$		0			0
$135$	9.53720	+	7.50374i	0.820832	+	0.645819i
$136$		0			0
$137$	−8.99233	+	2.40949i	−0.768267	+	0.205856i	−0.621606	−	0.783330i	$-0.713519\pi$
$137$	−8.99233	+	2.40949i	−0.768267	+	0.205856i	−0.146661	+	0.989187i	$0.546853\pi$
$138$		0			0
$139$	−22.1714			−1.88056			−0.940278	−	0.340408i	$-0.889435\pi$
$139$	−22.1714			−1.88056			−0.940278	+	0.340408i	$0.889435\pi$
$140$		0			0
$141$	5.53198			0.465877
$142$		0			0
$143$	−2.08627	+	0.559013i	−0.174462	+	0.0467470i
$144$		0			0
$145$	−21.5179	+	2.56768i	−1.78696	+	0.213235i
$146$		0			0
$147$	7.91803	+	2.21611i	0.653068	+	0.182781i
$148$		0			0
$149$	−3.41418	+	1.97118i	−0.279701	+	0.161485i	−0.633288	−	0.773916i	$-0.718295\pi$
$149$	−3.41418	+	1.97118i	−0.279701	+	0.161485i	0.353587	+	0.935402i	$0.384962\pi$
$150$		0			0
$151$	−9.97267	+	17.2732i	−0.811564	+	1.40567i	0.100205	+	0.994967i	$0.468050\pi$
$151$	−9.97267	+	17.2732i	−0.811564	+	1.40567i	−0.911769	+	0.410703i	$0.865283\pi$
$152$		0			0
$153$	7.51602	+	7.51602i	0.607634	+	0.607634i
$154$		0			0
$155$	3.01429	−	7.03449i	0.242113	−	0.565024i
$156$		0			0
$157$	−1.93165	−	7.20903i	−0.154163	−	0.575343i	−0.999176	−	0.0405972i	$-0.987074\pi$
$157$	−1.93165	−	7.20903i	−0.154163	−	0.575343i	0.845013	−	0.534746i	$-0.179593\pi$
$158$		0			0
$159$	−2.92815	−	5.07170i	−0.232217	−	0.402212i
$160$		0			0
$161$	7.06707	−	12.0851i	0.556963	−	0.952442i
$162$		0			0
$163$	11.7520	+	3.14893i	0.920486	+	0.246644i	0.687793	−	0.725907i	$-0.258580\pi$
$163$	11.7520	+	3.14893i	0.920486	+	0.246644i	0.232693	+	0.972550i	$0.425246\pi$
$164$		0			0
$165$	−1.93176	−	0.278205i	−0.150387	−	0.0216583i
$166$		0			0
$167$	1.45564	−	1.45564i	0.112641	−	0.112641i	−0.648540	−	0.761181i	$-0.724620\pi$
$167$	1.45564	−	1.45564i	0.112641	−	0.112641i	0.761181	+	0.648540i	$0.224620\pi$
$168$		0			0
$169$		−	4.55129i		−	0.350099i
$170$		0			0
$171$	−2.65494	−	1.53283i	−0.203028	−	0.117218i
$172$		0			0
$173$	2.43499	−	9.08750i	0.185129	−	0.690910i	−0.809474	−	0.587155i	$-0.800248\pi$
$173$	2.43499	−	9.08750i	0.185129	−	0.690910i	0.994603	−	0.103754i	$-0.0330856\pi$
$174$		0			0
$175$	0.394370	−	13.2229i	0.0298116	−	0.999556i
$176$		0			0
$177$	0.775156	−	2.89292i	0.0582643	−	0.217445i
$178$		0			0
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	0.638447	−	0.769665i	$-0.279577\pi$
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	−0.347326	+	0.937744i	$0.612910\pi$
$180$		0			0
$181$			17.8850i			1.32938i	0.747118	+	0.664691i	$0.231437\pi$
$181$			17.8850i			1.32938i	−0.747118	+	0.664691i	$0.768563\pi$
$182$		0			0
$183$	−5.04460	+	5.04460i	−0.372907	+	0.372907i
$184$		0			0
$185$	−5.91186	−	0.851405i	−0.434649	−	0.0625965i
$186$		0			0
$187$	−4.70855	−	1.26165i	−0.344323	−	0.0922612i
$188$		0			0
$189$	7.11019	+	12.4746i	0.517190	+	0.907392i
$190$		0			0
$191$	−1.38774	−	2.40364i	−0.100413	−	0.173921i	0.811442	−	0.584433i	$-0.198683\pi$
$191$	−1.38774	−	2.40364i	−0.100413	−	0.173921i	−0.911855	+	0.410512i	$0.865350\pi$
$192$		0			0
$193$	−1.33034	−	4.96491i	−0.0957602	−	0.357382i	0.901373	−	0.433043i	$-0.142560\pi$
$193$	−1.33034	−	4.96491i	−0.0957602	−	0.357382i	−0.997134	+	0.0756607i	$0.975893\pi$
$194$		0			0
$195$	−3.00693	+	7.01731i	−0.215330	+	0.502520i
$196$		0			0
$197$	1.34043	+	1.34043i	0.0955019	+	0.0955019i	0.753244	−	0.657742i	$-0.228488\pi$
$197$	1.34043	+	1.34043i	0.0955019	+	0.0955019i	−0.657742	+	0.753244i	$0.728488\pi$
$198$		0			0
$199$	−7.25148	+	12.5599i	−0.514043	+	0.890349i	0.485824	+	0.874057i	$0.338520\pi$
$199$	−7.25148	+	12.5599i	−0.514043	+	0.890349i	−0.999867	+	0.0162926i	$0.994814\pi$
$200$		0			0
$201$	13.9275	−	8.04103i	0.982368	−	0.567171i
$202$		0			0
$203$	−24.7300	−	6.77370i	−1.73571	−	0.475420i
$204$		0			0
$205$	−1.81555	+	0.216646i	−0.126803	+	0.0151312i
$206$		0			0
$207$	8.28144	−	2.21901i	0.575600	−	0.154232i
$208$		0			0
$209$	1.40593			0.0972504
$210$		0			0
$211$	−10.0324			−0.690660			−0.345330	−	0.938481i	$-0.612233\pi$
$211$	−10.0324			−0.690660			−0.345330	+	0.938481i	$0.612233\pi$
$212$		0			0
$213$	−18.1730	+	4.86945i	−1.24520	+	0.333649i
$214$		0			0
$215$	−3.96620	−	3.12055i	−0.270493	−	0.212820i
$216$		0			0
$217$	6.43848	−	6.36741i	0.437073	−	0.432248i
$218$		0			0
$219$	9.00328	−	5.19804i	0.608385	−	0.351251i
$220$		0			0
$221$	−9.53406	+	16.5135i	−0.641330	+	1.11082i
$222$		0			0
$223$	−3.13756	−	3.13756i	−0.210107	−	0.210107i	0.594206	−	0.804313i	$-0.297466\pi$
$223$	−3.13756	−	3.13756i	−0.210107	−	0.210107i	−0.804313	+	0.594206i	$0.797466\pi$
$224$		0			0
$225$	5.86586	−	5.58787i	0.391058	−	0.372525i
$226$		0			0
$227$	−0.173634	−	0.648012i	−0.0115245	−	0.0430101i	0.959924	−	0.280260i	$-0.0904207\pi$
$227$	−0.173634	−	0.648012i	−0.0115245	−	0.0430101i	−0.971449	+	0.237250i	$0.923754\pi$
$228$		0			0
$229$	6.60166	+	11.4344i	0.436250	+	0.755608i	0.997397	−	0.0721088i	$-0.0229729\pi$
$229$	6.60166	+	11.4344i	0.436250	+	0.755608i	−0.561146	+	0.827717i	$0.689640\pi$
$230$		0			0
$231$	−1.99345	−	1.16572i	−0.131159	−	0.0766986i
$232$		0			0
$233$	8.36389	+	2.24110i	0.547937	+	0.146819i	0.522158	−	0.852849i	$-0.325127\pi$
$233$	8.36389	+	2.24110i	0.547937	+	0.146819i	0.0257782	+	0.999668i	$0.491794\pi$
$234$		0			0
$235$	1.50115	−	10.4235i	0.0979243	−	0.679952i
$236$		0			0
$237$	5.46757	−	5.46757i	0.355157	−	0.355157i
$238$		0			0
$239$		−	4.00294i		−	0.258929i	−0.991584	−	0.129464i	$-0.958674\pi$
$239$		−	4.00294i		−	0.258929i	0.991584	−	0.129464i	$-0.0413258\pi$
$240$		0			0
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.0683274	−	0.997663i	$-0.521766\pi$
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.898165	+	0.439658i	$0.855100\pi$
$242$		0			0
$243$	−3.75364	+	14.0088i	−0.240796	+	0.898663i
$244$		0			0
$245$	6.32426	−	14.3180i	0.404042	−	0.914740i
$246$		0			0
$247$	1.42339	−	5.31218i	0.0905683	−	0.338006i
$248$		0			0
$249$	−13.2858	−	7.67055i	−0.841952	−	0.486101i
$250$		0			0
$251$			5.49938i			0.347118i	0.984824	+	0.173559i	$0.0555267\pi$
$251$			5.49938i			0.347118i	−0.984824	+	0.173559i	$0.944473\pi$
$252$		0			0
$253$	−2.78028	+	2.78028i	−0.174795	+	0.174795i
$254$		0			0
$255$	−13.7960	+	10.3225i	−0.863939	+	0.646422i
$256$		0			0
$257$	15.9473	+	4.27307i	0.994766	+	0.266547i	0.719251	−	0.694750i	$-0.244485\pi$
$257$	15.9473	+	4.27307i	0.994766	+	0.266547i	0.275515	+	0.961297i	$0.411152\pi$
$258$		0			0
$259$	−6.10065	−	3.56750i	−0.379076	−	0.221674i
$260$		0			0
$261$	−7.85135	−	13.5989i	−0.485986	−	0.841753i
$262$		0			0
$263$	2.55217	+	9.52484i	0.157374	+	0.587327i	0.998890	+	0.0470956i	$0.0149965\pi$
$263$	2.55217	+	9.52484i	0.157374	+	0.587327i	−0.841517	+	0.540231i	$0.818337\pi$
$264$		0			0
$265$	−10.3508	+	4.14102i	−0.635843	+	0.254381i
$266$		0			0
$267$	5.01010	+	5.01010i	0.306613	+	0.306613i
$268$		0			0
$269$	4.47922	−	7.75824i	0.273103	−	0.473028i	−0.696552	−	0.717506i	$-0.745283\pi$
$269$	4.47922	−	7.75824i	0.273103	−	0.473028i	0.969655	+	0.244478i	$0.0786167\pi$
$270$		0			0
$271$	19.7889	−	11.4251i	1.20209	−	0.694027i	0.241071	−	0.970507i	$-0.422501\pi$
$271$	19.7889	−	11.4251i	1.20209	−	0.694027i	0.961020	+	0.276480i	$0.0891680\pi$
$272$		0			0
$273$	−6.42276	+	6.35186i	−0.388723	+	0.384432i
$274$		0			0
$275$	−1.04840	+	3.56437i	−0.0632209	+	0.214940i
$276$		0			0
$277$	−20.7995	+	5.57320i	−1.24972	+	0.334861i	−0.822228	−	0.569158i	$-0.807269\pi$
$277$	−20.7995	+	5.57320i	−1.24972	+	0.334861i	−0.427491	+	0.904019i	$0.640603\pi$
$278$		0			0
$279$	5.54552			0.332002
$280$		0			0
$281$	−5.64885			−0.336982			−0.168491	−	0.985703i	$-0.553889\pi$
$281$	−5.64885			−0.336982			−0.168491	+	0.985703i	$0.553889\pi$
$282$		0			0
$283$	2.82870	−	0.757948i	0.168149	−	0.0450553i	−0.173762	−	0.984788i	$-0.555592\pi$
$283$	2.82870	−	0.757948i	0.168149	−	0.0450553i	0.341911	+	0.939732i	$0.388926\pi$
$284$		0			0
$285$	3.07286	−	3.90559i	0.182021	−	0.231347i
$286$		0			0
$287$	−2.08657	−	0.571524i	−0.123166	−	0.0337360i
$288$		0			0
$289$	−22.5473	+	13.0177i	−1.32631	+	0.765747i
$290$		0			0
$291$	2.63038	−	4.55596i	0.154196	−	0.267075i
$292$		0			0
$293$	−10.7875	−	10.7875i	−0.630212	−	0.630212i	0.317909	−	0.948121i	$-0.397019\pi$
$293$	−10.7875	−	10.7875i	−0.630212	−	0.630212i	−0.948121	+	0.317909i	$0.897019\pi$
$294$		0			0
$295$	−5.24056	−	2.24558i	−0.305117	−	0.130743i
$296$		0			0
$297$	−1.04374	−	3.89528i	−0.0605637	−	0.226027i
$298$		0			0
$299$	7.69020	+	13.3198i	0.444736	+	0.770305i
$300$		0			0
$301$	−2.95689	−	5.18776i	−0.170432	−	0.299018i
$302$		0			0
$303$	−12.6866	−	3.39936i	−0.728826	−	0.195288i
$304$		0			0
$305$	8.13624	+	10.8740i	0.465880	+	0.622645i
$306$		0			0
$307$	−6.89201	+	6.89201i	−0.393348	+	0.393348i	−0.875879	−	0.482531i	$-0.839718\pi$
$307$	−6.89201	+	6.89201i	−0.393348	+	0.393348i	0.482531	+	0.875879i	$0.339718\pi$
$308$		0			0
$309$		−	2.84982i		−	0.162121i
$310$		0			0
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	0.503091	−	0.864233i	$-0.332196\pi$
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	−0.496903	+	0.867806i	$0.665529\pi$
$312$		0			0
$313$	−3.02662	+	11.2955i	−0.171075	+	0.638459i	0.826112	+	0.563505i	$0.190548\pi$
$313$	−3.02662	+	11.2955i	−0.171075	+	0.638459i	−0.997187	+	0.0749536i	$0.976119\pi$
$314$		0			0
$315$	8.91951	−	3.51112i	0.502558	−	0.197829i
$316$		0			0
$317$	−2.83308	+	10.5732i	−0.159122	+	0.593851i	0.839595	+	0.543212i	$0.182792\pi$
$317$	−2.83308	+	10.5732i	−0.159122	+	0.593851i	−0.998717	+	0.0506382i	$0.983874\pi$
$318$		0			0
$319$	6.23657	+	3.60068i	0.349181	+	0.201600i
$320$		0			0
$321$			7.80001i			0.435354i
$322$		0			0
$323$	8.77670	−	8.77670i	0.488349	−	0.488349i
$324$		0			0
$325$	12.4062	+	7.56992i	0.688173	+	0.419904i
$326$		0			0
$327$	−10.1665	−	2.72410i	−0.562208	−	0.150643i
$328$		0			0
$329$	6.29002	−	10.7563i	0.346780	−	0.593016i
$330$		0			0
$331$	−2.73019	−	4.72883i	−0.150065	−	0.259920i	0.781186	−	0.624298i	$-0.214615\pi$
$331$	−2.73019	−	4.72883i	−0.150065	−	0.259920i	−0.931251	+	0.364378i	$0.881282\pi$
$332$		0			0
$333$	−1.12017	−	4.18052i	−0.0613848	−	0.229091i
$334$		0			0
$335$	−11.3717	−	28.4244i	−0.621304	−	1.55299i
$336$		0			0
$337$	20.4823	+	20.4823i	1.11574	+	1.11574i	0.992359	+	0.123385i	$0.0393751\pi$
$337$	20.4823	+	20.4823i	1.11574	+	1.11574i	0.123385	+	0.992359i	$0.460625\pi$
$338$		0			0
$339$	−0.255644	+	0.442788i	−0.0138847	+	0.0240490i
$340$		0			0
$341$	−2.20249	+	1.27161i	−0.119272	+	0.0688615i
$342$		0			0
$343$	13.3120	−	12.8760i	0.718781	−	0.695237i
$344$		0			0
$345$	1.64674	+	13.8001i	0.0886576	+	0.742973i
$346$		0			0
$347$	−20.8040	+	5.57442i	−1.11682	+	0.299250i	−0.769595	−	0.638532i	$-0.779542\pi$
$347$	−20.8040	+	5.57442i	−1.11682	+	0.299250i	−0.347223	+	0.937783i	$0.612875\pi$
$348$		0			0
$349$	−12.5744			−0.673093			−0.336546	−	0.941667i	$-0.609259\pi$
$349$	−12.5744			−0.673093			−0.336546	+	0.941667i	$0.609259\pi$
$350$		0			0
$351$	−15.7746			−0.841987
$352$		0			0
$353$	0.666012	−	0.178457i	0.0354482	−	0.00949832i	−0.241051	−	0.970512i	$-0.577492\pi$
$353$	0.666012	−	0.178457i	0.0354482	−	0.00949832i	0.276500	+	0.961014i	$0.410826\pi$
$354$		0			0
$355$	4.24371	+	35.5634i	0.225233	+	1.88751i
$356$		0			0
$357$	−19.7215	+	5.16723i	−1.04377	+	0.273479i
$358$		0			0
$359$	−19.1381	+	11.0494i	−1.01007	+	0.583165i	−0.911212	−	0.411937i	$-0.864852\pi$
$359$	−19.1381	+	11.0494i	−1.01007	+	0.583165i	−0.0988582	+	0.995102i	$0.531519\pi$
$360$		0			0
$361$	7.71007	−	13.3542i	0.405793	−	0.702854i
$362$		0			0
$363$	−8.67775	−	8.67775i	−0.455464	−	0.455464i
$364$		0			0
$365$	−7.35115	−	18.3747i	−0.384777	−	0.961775i
$366$		0			0
$367$	−3.47100	−	12.9539i	−0.181185	−	0.676191i	−0.995415	−	0.0956487i	$-0.969507\pi$
$367$	−3.47100	−	12.9539i	−0.181185	−	0.676191i	0.814230	−	0.580542i	$-0.197159\pi$
$368$		0			0
$369$	−0.662450	−	1.14740i	−0.0344858	−	0.0597311i
$370$		0			0
$371$	−13.1908	−	0.0732036i	−0.684830	−	0.00380054i
$372$		0			0
$373$	14.4564	+	3.87359i	0.748526	+	0.200567i	0.612864	−	0.790188i	$-0.290017\pi$
$373$	14.4564	+	3.87359i	0.748526	+	0.200567i	0.135662	+	0.990755i	$0.456684\pi$
$374$		0			0
$375$	7.61017	+	10.7028i	0.392987	+	0.552691i
$376$		0			0
$377$	19.9189	−	19.9189i	1.02587	−	1.02587i
$378$		0			0
$379$		−	1.71784i		−	0.0882395i	−0.999026	−	0.0441198i	$-0.985952\pi$
$379$		−	1.71784i		−	0.0882395i	0.999026	−	0.0441198i	$-0.0140483\pi$
$380$		0			0
$381$	−16.0869	−	9.28776i	−0.824156	−	0.475827i
$382$		0			0
$383$	2.70676	−	10.1017i	0.138309	−	0.516175i	−0.861654	−	0.507497i	$-0.830571\pi$
$383$	2.70676	−	10.1017i	0.138309	−	0.516175i	0.999962	−	0.00867837i	$-0.00276245\pi$
$384$		0			0
$385$	−2.73741	+	3.43977i	−0.139511	+	0.175307i
$386$		0			0
$387$	0.946464	−	3.53225i	0.0481114	−	0.179554i
$388$		0			0
$389$	18.8548	+	10.8858i	0.955978	+	0.551934i	0.894933	−	0.446201i	$-0.147223\pi$
$389$	18.8548	+	10.8858i	0.955978	+	0.551934i	0.0610449	+	0.998135i	$0.480557\pi$
$390$		0			0
$391$			34.7124i			1.75548i
$392$		0			0
$393$	−7.96759	+	7.96759i	−0.401912	+	0.401912i
$394$		0			0
$395$	−8.81843	−	11.7858i	−0.443703	−	0.593006i
$396$		0			0
$397$	−30.6188	−	8.20427i	−1.53671	−	0.411761i	−0.611510	−	0.791237i	$-0.709438\pi$
$397$	−30.6188	−	8.20427i	−1.53671	−	0.411761i	−0.925202	+	0.379476i	$0.876104\pi$
$398$		0			0
$399$	5.10848	−	2.91170i	0.255744	−	0.145767i
$400$		0			0
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$		0			0
$403$	2.57480	+	9.60930i	0.128260	+	0.478673i
$404$		0			0
$405$	−3.11146	−	1.33327i	−0.154610	−	0.0662505i
$406$		0			0
$407$	1.40350	+	1.40350i	0.0695690	+	0.0695690i
$408$		0			0
$409$	−9.36960	+	16.2286i	−0.463297	+	0.802454i	−0.999123	−	0.0418748i	$-0.986667\pi$
$409$	−9.36960	+	16.2286i	−0.463297	+	0.802454i	0.535826	+	0.844328i	$0.320000\pi$
$410$		0			0
$411$	9.47010	−	5.46757i	0.467126	−	0.269695i
$412$		0			0
$413$	−4.74360	−	4.79654i	−0.233417	−	0.236022i
$414$		0			0
$415$	−18.0582	+	22.9519i	−0.886443	+	1.12666i
$416$		0			0
$417$	25.1555	−	6.74040i	1.23187	−	0.330079i
$418$		0			0
$419$	31.5744			1.54251			0.771255	−	0.636526i	$-0.219629\pi$
$419$	31.5744			1.54251			0.771255	+	0.636526i	$0.219629\pi$
$420$		0			0
$421$	−13.5569			−0.660722			−0.330361	−	0.943855i	$-0.607171\pi$
$421$	−13.5569			−0.660722			−0.330361	+	0.943855i	$0.607171\pi$
$422$		0			0
$423$	7.37087	−	1.97502i	0.358384	−	0.0960287i
$424$		0			0
$425$	15.7063	+	28.7958i	0.761866	+	1.39680i
$426$		0			0
$427$	4.07282	+	15.5445i	0.197097	+	0.752252i
$428$		0			0
$429$	2.19711	−	1.26850i	0.106078	−	0.0612439i
$430$		0			0
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	−0.660800	−	0.750562i	$-0.729783\pi$
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	0.980406	+	0.196989i	$0.0631164\pi$
$432$		0			0
$433$	12.0535	+	12.0535i	0.579252	+	0.579252i	0.934697	−	0.355445i	$-0.115671\pi$
$433$	12.0535	+	12.0535i	0.579252	+	0.579252i	−0.355445	+	0.934697i	$0.615671\pi$
$434$		0			0
$435$	23.6334	−	9.45497i	1.13313	−	0.453331i
$436$		0			0
$437$	−2.59121	−	9.67052i	−0.123954	−	0.462604i
$438$		0			0
$439$	−17.5238	−	30.3521i	−0.836366	−	1.44863i	−0.892913	−	0.450228i	$-0.851343\pi$
$439$	−17.5238	−	30.3521i	−0.836366	−	1.44863i	0.0565475	−	0.998400i	$-0.481991\pi$
$440$		0			0
$441$	11.3413	+	0.125883i	0.540060	+	0.00599443i
$442$		0			0
$443$	−0.0609189	−	0.0163232i	−0.00289435	−	0.000775538i	0.257372	−	0.966313i	$-0.417144\pi$
$443$	−0.0609189	−	0.0163232i	−0.00289435	−	0.000775538i	−0.260266	+	0.965537i	$0.583810\pi$
$444$		0			0
$445$	10.7997	−	8.08060i	0.511954	−	0.383057i
$446$		0			0
$447$	3.27444	−	3.27444i	0.154876	−	0.154876i
$448$		0			0
$449$		−	24.5207i		−	1.15720i	−0.815611	−	0.578601i	$-0.803599\pi$
$449$		−	24.5207i		−	1.15720i	0.815611	−	0.578601i	$-0.196401\pi$
$450$		0			0
$451$	0.526205	+	0.303804i	0.0247780	+	0.0143056i
$452$		0			0
$453$	6.06364	−	22.6298i	0.284894	−	1.06324i
$454$		0			0
$455$	10.2254	+	13.8255i	0.479376	+	0.648151i
$456$		0			0
$457$	5.19531	−	19.3892i	0.243027	−	0.906987i	−0.731339	−	0.682015i	$-0.761104\pi$
$457$	5.19531	−	19.3892i	0.243027	−	0.906987i	0.974365	−	0.224973i	$-0.0722293\pi$
$458$		0			0
$459$	−30.8324	−	17.8011i	−1.43913	−	0.830884i
$460$		0			0
$461$			11.6940i			0.544642i	0.962207	+	0.272321i	$0.0877912\pi$
$461$			11.6940i			0.544642i	−0.962207	+	0.272321i	$0.912209\pi$
$462$		0			0
$463$	−2.77226	+	2.77226i	−0.128838	+	0.128838i	−0.768585	−	0.639747i	$-0.779039\pi$
$463$	−2.77226	+	2.77226i	−0.128838	+	0.128838i	0.639747	+	0.768585i	$0.279039\pi$
$464$		0			0
$465$	−1.28141	+	8.89765i	−0.0594239	+	0.412619i
$466$		0			0
$467$	20.2080	+	5.41472i	0.935116	+	0.250563i	0.694035	−	0.719942i	$-0.255831\pi$
$467$	20.2080	+	5.41472i	0.935116	+	0.250563i	0.241081	+	0.970505i	$0.422498\pi$
$468$		0			0
$469$	0.201026	−	36.2233i	0.00928250	−	1.67264i
$470$		0			0
$471$	4.38327	+	7.59205i	0.201971	+	0.349823i
$472$		0			0
$473$	0.434055	+	1.61992i	0.0199579	+	0.0744838i
$474$		0			0
$475$	−6.52514	−	6.84976i	−0.299394	−	0.314289i
$476$		0			0
$477$	−5.71218	−	5.71218i	−0.261543	−	0.261543i
$478$		0			0
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	−0.443145	−	0.896450i	$-0.646137\pi$
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	0.997921	−	0.0644496i	$-0.0205292\pi$
$480$		0			0
$481$	6.72392	−	3.88206i	0.306584	−	0.177007i
$482$		0			0
$483$	−4.34420	+	15.8602i	−0.197668	+	0.721663i
$484$		0			0
$485$	−7.87065	−	6.19252i	−0.357388	−	0.281188i
$486$		0			0
$487$	2.46890	−	0.661539i	0.111876	−	0.0299772i	−0.202446	−	0.979293i	$-0.564889\pi$
$487$	2.46890	−	0.661539i	0.111876	−	0.0299772i	0.314323	+	0.949316i	$0.398223\pi$
$488$		0			0
$489$	−14.2910			−0.646262
$490$		0			0
$491$	−14.5668			−0.657391			−0.328695	−	0.944436i	$-0.606609\pi$
$491$	−14.5668			−0.657391			−0.328695	+	0.944436i	$0.606609\pi$
$492$		0			0
$493$	61.4102	−	16.4548i	2.76578	−	0.741088i
$494$		0			0
$495$	−2.67323	+	0.318991i	−0.120153	+	0.0143376i
$496$		0			0
$497$	−11.1951	+	40.8722i	−0.502171	+	1.83337i
$498$		0			0
$499$	26.0565	−	15.0437i	1.16645	−	0.673450i	0.213608	−	0.976919i	$-0.431478\pi$
$499$	26.0565	−	15.0437i	1.16645	−	0.673450i	0.952841	+	0.303469i	$0.0981450\pi$
$500$		0			0
$501$	−1.20902	+	2.09409i	−0.0540152	+	0.0935572i
$502$		0			0
$503$	24.6819	+	24.6819i	1.10051	+	1.10051i	0.994349	+	0.106161i	$0.0338558\pi$
$503$	24.6819	+	24.6819i	1.10051	+	1.10051i	0.106161	+	0.994349i	$0.466144\pi$
$504$		0			0
$505$	−9.84777	+	22.9819i	−0.438220	+	1.02268i
$506$		0			0
$507$	1.38365	+	5.16386i	0.0614501	+	0.229335i
$508$		0			0
$509$	6.22521	+	10.7824i	0.275927	+	0.477920i	0.970369	−	0.241629i	$-0.0776817\pi$
$509$	6.22521	+	10.7824i	0.275927	+	0.477920i	−0.694441	+	0.719549i	$0.744348\pi$
$510$		0			0
$511$	0.129951	−	23.4162i	0.00574869	−	1.03587i
$512$		0			0
$513$	9.91839	+	2.65762i	0.437908	+	0.117337i
$514$		0			0
$515$	−5.36969	−	0.773324i	−0.236617	−	0.0340767i
$516$		0			0
$517$	−2.47458	+	2.47458i	−0.108832	+	0.108832i
$518$		0			0
$519$			11.0509i			0.485079i
$520$		0			0
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.986904	−	0.161308i	$-0.0515711\pi$
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.353756	+	0.935338i	$0.384904\pi$
$522$		0			0
$523$	4.25513	−	15.8804i	0.186064	−	0.694400i	−0.808336	−	0.588721i	$-0.799632\pi$
$523$	4.25513	−	15.8804i	0.186064	−	0.694400i	0.994400	−	0.105679i	$-0.0337016\pi$
$524$		0			0
$525$	3.57247	+	15.1225i	0.155916	+	0.659998i
$526$		0			0
$527$	−5.81115	+	21.6875i	−0.253137	+	0.944722i
$528$		0			0
$529$	4.32938	+	2.49957i	0.188234	+	0.108677i
$530$		0			0
$531$		−	4.13131i		−	0.179283i
$532$		0			0
$533$	1.68063	−	1.68063i	0.0727964	−	0.0727964i
$534$		0			0
$535$	14.6969	+	2.11660i	0.635404	+	0.0915086i
$536$		0			0
$537$	−5.10281	−	1.36729i	−0.220202	−	0.0590031i
$538$		0			0
$539$	−4.53322	+	2.55059i	−0.195260	+	0.109862i
$540$		0			0
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	0.996568	+	0.0827763i	$0.0263787\pi$
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	−0.426598	+	0.904441i	$0.640288\pi$
$542$		0			0
$543$	−5.43727	−	20.2922i	−0.233336	−	0.870820i
$544$		0			0
$545$	−7.89157	+	18.4167i	−0.338038	+	0.788884i
$546$		0			0
$547$	1.07403	+	1.07403i	0.0459223	+	0.0459223i	0.729695	−	0.683773i	$-0.239662\pi$
$547$	1.07403	+	1.07403i	0.0459223	+	0.0459223i	−0.683773	+	0.729695i	$0.739662\pi$
$548$		0			0
$549$	−4.92046	+	8.52249i	−0.210000	+	0.363731i
$550$		0			0
$551$	−15.8799	+	9.16828i	−0.676507	+	0.390582i
$552$		0			0
$553$	−4.41431	−	16.8479i	−0.187715	−	0.716444i
$554$		0			0
$555$	6.96638	−	0.831285i	0.295706	−	0.0352861i
$556$		0			0
$557$	−15.0145	+	4.02313i	−0.636186	+	0.170466i	−0.562475	−	0.826814i	$-0.690151\pi$
$557$	−15.0145	+	4.02313i	−0.636186	+	0.170466i	−0.0737108	+	0.997280i	$0.523484\pi$
$558$		0			0
$559$	6.56014			0.277464
$560$		0			0
$561$	5.72584			0.241745
$562$		0			0
$563$	26.5108	−	7.10355i	1.11730	−	0.299379i	0.347508	−	0.937677i	$-0.387028\pi$
$563$	26.5108	−	7.10355i	1.11730	−	0.299379i	0.769789	+	0.638298i	$0.220361\pi$
$564$		0			0
$565$	0.764940	+	0.601844i	0.0321813	+	0.0253198i
$566$		0			0
$567$	−2.81641	−	2.84784i	−0.118278	−	0.119598i
$568$		0			0
$569$	5.85207	−	3.37869i	0.245332	−	0.141642i	−0.372293	−	0.928115i	$-0.621428\pi$
$569$	5.85207	−	3.37869i	0.245332	−	0.141642i	0.617625	+	0.786473i	$0.288095\pi$
$570$		0			0
$571$	5.87721	−	10.1796i	0.245953	−	0.426004i	−0.716446	−	0.697643i	$-0.754232\pi$
$571$	5.87721	−	10.1796i	0.245953	−	0.426004i	0.962399	+	0.271639i	$0.0875656\pi$
$572$		0			0
$573$	2.30526	+	2.30526i	0.0963034	+	0.0963034i
$574$		0			0
$575$	26.4493	+	0.641957i	1.10301	+	0.0267715i
$576$		0			0
$577$	0.583767	+	2.17865i	0.0243025	+	0.0906983i	0.977012	−	0.213184i	$-0.0683835\pi$
$577$	0.583767	+	2.17865i	0.0243025	+	0.0906983i	−0.952709	+	0.303883i	$0.901717\pi$
$578$		0			0
$579$	3.01879	+	5.22870i	0.125457	+	0.217297i
$580$		0			0
$581$	−30.0209	+	17.1111i	−1.24547	+	0.709889i
$582$		0			0
$583$	3.57851	+	0.958858i	0.148207	+	0.0397118i
$584$		0			0
$585$	−1.50115	+	10.4235i	−0.0620649	+	0.430957i
$586$		0			0
$587$	12.8372	−	12.8372i	0.529847	−	0.529847i	−0.390680	−	0.920527i	$-0.627760\pi$
$587$	12.8372	−	12.8372i	0.529847	−	0.529847i	0.920527	+	0.390680i	$0.127760\pi$
$588$		0			0
$589$		−	6.47569i		−	0.266826i
$590$		0			0
$591$	−1.92835	−	1.11333i	−0.0793218	−	0.0457965i
$592$		0			0
$593$	9.40957	−	35.1170i	0.386405	−	1.44208i	−0.449535	−	0.893262i	$-0.648410\pi$
$593$	9.40957	−	35.1170i	0.386405	−	1.44208i	0.835940	−	0.548820i	$-0.184923\pi$
$594$		0			0
$595$	4.38460	+	38.5618i	0.179751	+	1.58088i
$596$		0			0
$597$	4.40908	−	16.4549i	0.180452	−	0.673455i
$598$		0			0
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.974186	−	0.225748i	$-0.0724826\pi$
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.291589	+	0.956544i	$0.405816\pi$
$600$		0			0
$601$		−	45.6631i		−	1.86264i	−0.364204	−	0.931319i	$-0.618659\pi$
$601$		−	45.6631i		−	1.86264i	0.364204	−	0.931319i	$-0.381341\pi$
$602$		0			0
$603$	15.6863	−	15.6863i	0.638796	−	0.638796i
$604$		0			0
$605$	−18.7056	+	13.9960i	−0.760490	+	0.569019i
$606$		0			0
$607$	1.13151	+	0.303188i	0.0459267	+	0.0123060i	0.281709	−	0.959500i	$-0.409099\pi$
$607$	1.13151	+	0.303188i	0.0459267	+	0.0123060i	−0.235783	+	0.971806i	$0.575765\pi$
$608$		0			0
$609$	30.1177	+	0.167142i	1.22043	+	0.00677293i
$610$		0			0
$611$	6.84463	+	11.8553i	0.276904	+	0.479612i
$612$		0			0
$613$	−3.60737	−	13.4629i	−0.145700	−	0.543760i	−0.999723	−	0.0235253i	$-0.992511\pi$
$613$	−3.60737	−	13.4629i	−0.145700	−	0.543760i	0.854023	−	0.520235i	$-0.174156\pi$
$614$		0			0
$615$	1.99404	−	0.797755i	0.0804076	−	0.0321686i
$616$		0			0
$617$	22.7725	+	22.7725i	0.916788	+	0.916788i	0.996794	−	0.0800065i	$-0.0254941\pi$
$617$	22.7725	+	22.7725i	0.916788	+	0.916788i	−0.0800065	+	0.996794i	$0.525494\pi$
$618$		0			0
$619$	−11.3386	+	19.6391i	−0.455738	+	0.789361i	−0.998730	−	0.0503763i	$-0.983958\pi$
$619$	−11.3386	+	19.6391i	−0.455738	+	0.789361i	0.542992	+	0.839738i	$0.317291\pi$
$620$		0			0
$621$	−24.8695	+	14.3584i	−0.997978	+	0.576183i
$622$		0			0
$623$	15.4382	−	4.04497i	0.618520	−	0.162058i
$624$		0			0
$625$	22.2316	−	11.4349i	0.889263	−	0.457397i
$626$		0			0
$627$	−1.59516	+	0.427421i	−0.0637045	+	0.0170696i
$628$		0			0
$629$	17.5231			0.698690
$630$		0			0
$631$	−32.4210			−1.29066			−0.645330	−	0.763904i	$-0.723280\pi$
$631$	−32.4210			−1.29066			−0.645330	+	0.763904i	$0.723280\pi$
$632$		0			0
$633$	11.3827	−	3.04998i	0.452421	−	0.121226i
$634$		0			0
$635$	−21.8655	+	27.7909i	−0.867706	+	1.10285i
$636$		0			0
$637$	5.04765	+	19.7106i	0.199995	+	0.780963i
$638$		0			0
$639$	−22.4755	+	12.9762i	−0.889116	+	0.513331i
$640$		0			0
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	−0.857448	−	0.514571i	$-0.827951\pi$
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	0.874355	+	0.485286i	$0.161285\pi$
$642$		0			0
$643$	−16.4254	−	16.4254i	−0.647754	−	0.647754i	0.304696	−	0.952450i	$-0.401445\pi$
$643$	−16.4254	−	16.4254i	−0.647754	−	0.647754i	−0.952450	+	0.304696i	$0.901445\pi$
$644$		0			0
$645$	5.44871	+	2.33478i	0.214543	+	0.0919317i
$646$		0			0
$647$	12.2805	+	45.8316i	0.482798	+	1.80183i	0.589779	+	0.807564i	$0.299215\pi$
$647$	12.2805	+	45.8316i	0.482798	+	1.80183i	−0.106982	+	0.994261i	$0.534119\pi$
$648$		0			0
$649$	0.947323	+	1.64081i	0.0371857	+	0.0644075i
$650$		0			0
$651$	−5.36927	+	9.18179i	−0.210438	+	0.359863i
$652$		0			0
$653$	−25.3781	−	6.80004i	−0.993121	−	0.266106i	−0.274560	−	0.961570i	$-0.588532\pi$
$653$	−25.3781	−	6.80004i	−0.993121	−	0.266106i	−0.718561	+	0.695464i	$0.755199\pi$
$654$		0			0
$655$	12.8506	+	17.1748i	0.502115	+	0.671074i
$656$		0			0
$657$	10.1403	−	10.1403i	0.395609	−	0.395609i
$658$		0			0
$659$		−	26.2355i		−	1.02199i	−0.859583	−	0.510996i	$-0.829277\pi$
$659$		−	26.2355i		−	1.02199i	0.859583	−	0.510996i	$-0.170723\pi$
$660$		0			0
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	0.234078	−	0.972218i	$-0.424793\pi$
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	−0.724926	+	0.688827i	$0.758126\pi$
$662$		0			0
$663$	5.79695	−	21.6345i	0.225135	−	0.840215i
$664$		0			0
$665$	−4.10006	−	10.4156i	−0.158993	−	0.403900i
$666$		0			0
$667$	13.2725	−	49.5336i	0.513913	−	1.91795i
$668$		0			0
$669$	4.51371	+	2.60599i	0.174510	+	0.100753i
$670$		0			0
$671$		−	4.51312i		−	0.174227i
$672$		0			0
$673$	−16.4201	+	16.4201i	−0.632950	+	0.632950i	−0.948807	−	0.315857i	$-0.897708\pi$
$673$	−16.4201	+	16.4201i	−0.632950	+	0.632950i	0.315857	+	0.948807i	$0.397708\pi$
$674$		0			0
$675$	−14.1338	+	23.1637i	−0.544011	+	0.891571i
$676$		0			0
$677$	−21.9882	−	5.89172i	−0.845075	−	0.226437i	−0.189796	−	0.981824i	$-0.560783\pi$
$677$	−21.9882	−	5.89172i	−0.845075	−	0.226437i	−0.655280	+	0.755386i	$0.727449\pi$
$678$		0			0
$679$	−5.86774	−	10.2947i	−0.225183	−	0.395076i
$680$		0			0
$681$	0.394008	+	0.682442i	0.0150984	+	0.0261512i
$682$		0			0
$683$	−7.93034	−	29.5964i	−0.303446	−	1.13248i	−0.934275	−	0.356554i	$-0.883952\pi$
$683$	−7.93034	−	29.5964i	−0.303446	−	1.13248i	0.630829	−	0.775922i	$-0.282715\pi$
$684$		0			0
$685$	−7.73231	−	19.3274i	−0.295436	−	0.738463i
$686$		0			0
$687$	−10.9664	−	10.9664i	−0.418394	−	0.418394i
$688$		0			0
$689$	7.24590	−	12.5503i	0.276047	−	0.478127i
$690$		0			0
$691$	−27.7284	+	16.0090i	−1.05484	+	0.609012i	−0.924000	−	0.382392i	$-0.875100\pi$
$691$	−27.7284	+	16.0090i	−1.05484	+	0.609012i	−0.130839	+	0.991404i	$0.541767\pi$
$692$		0			0
$693$	−3.07228	−	0.841516i	−0.116706	−	0.0319665i
$694$		0			0
$695$	−5.87423	−	49.2276i	−0.222822	−	1.86731i
$696$		0			0
$697$	5.18143	−	1.38836i	0.196261	−	0.0525879i
$698$		0			0
$699$	−10.1709			−0.384699
$700$		0			0
$701$	−18.5294			−0.699844			−0.349922	−	0.936779i	$-0.613792\pi$
$701$	−18.5294			−0.699844			−0.349922	+	0.936779i	$0.613792\pi$
$702$		0			0
$703$	−4.88174	+	1.30806i	−0.184118	+	0.0493343i
$704$		0			0
$705$	1.46568	+	12.2827i	0.0552006	+	0.462595i
$706$		0			0
$707$	−21.0347	+	20.8025i	−0.791092	+	0.782360i
$708$		0			0
$709$	23.1074	−	13.3411i	0.867818	−	0.501035i	0.00119522	−	0.999999i	$-0.499620\pi$
$709$	23.1074	−	13.3411i	0.867818	−	0.501035i	0.866622	+	0.498965i	$0.166286\pi$
$710$		0			0
$711$	5.33302	−	9.23706i	0.200004	−	0.346417i
$712$		0			0
$713$	12.8059	+	12.8059i	0.479585	+	0.479585i
$714$		0			0
$715$	−1.79393	−	4.48406i	−0.0670893	−	0.167694i
$716$		0			0
$717$	1.21695	+	4.54170i	0.0454477	+	0.169613i
$718$		0			0
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	−0.993364	−	0.115015i	$-0.963308\pi$
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	0.397076	−	0.917786i	$-0.370025\pi$
$720$		0			0
$721$	−5.54117	−	3.24033i	−0.206364	−	0.120676i
$722$		0			0
$723$	19.6569	+	5.26706i	0.731049	+	0.195884i
$724$		0			0
$725$	−11.4021	−	47.0961i	−0.423465	−	1.74911i
$726$		0			0
$727$	21.4539	−	21.4539i	0.795683	−	0.795683i	−0.186729	−	0.982412i	$-0.559789\pi$
$727$	21.4539	−	21.4539i	0.795683	−	0.795683i	0.982412	+	0.186729i	$0.0597885\pi$
$728$		0			0
$729$		−	21.5770i		−	0.799146i
$730$		0			0
$731$	12.8222	+	7.40288i	0.474245	+	0.273805i
$732$		0			0
$733$	−3.36789	+	12.5691i	−0.124396	+	0.464252i	−0.999817	−	0.0191085i	$-0.993917\pi$
$733$	−3.36789	+	12.5691i	−0.124396	+	0.464252i	0.875422	+	0.483360i	$0.160584\pi$
$734$		0			0
$735$	−2.82261	+	18.1677i	−0.104113	+	0.670125i
$736$		0			0
$737$	−2.63314	+	9.82700i	−0.0969928	+	0.361982i
$738$		0			0
$739$	−3.12136	−	1.80212i	−0.114821	−	0.0662920i	0.441490	−	0.897266i	$-0.354450\pi$
$739$	−3.12136	−	1.80212i	−0.114821	−	0.0662920i	−0.556311	+	0.830974i	$0.687784\pi$
$740$		0			0
$741$			6.45988i			0.237309i
$742$		0			0
$743$	−31.1070	+	31.1070i	−1.14121	+	1.14121i	−0.152977	+	0.988230i	$0.548886\pi$
$743$	−31.1070	+	31.1070i	−1.14121	+	1.14121i	−0.988230	+	0.152977i	$0.951114\pi$
$744$		0			0
$745$	−5.28121	−	7.05831i	−0.193489	−	0.258596i
$746$		0			0
$747$	−20.4406	−	5.47705i	−0.747884	−	0.200395i
$748$		0			0
$749$	15.1663	+	8.86884i	0.554164	+	0.324060i
$750$		0			0
$751$	−25.5141	−	44.1917i	−0.931023	−	1.61258i	−0.781576	−	0.623810i	$-0.785584\pi$
$751$	−25.5141	−	44.1917i	−0.931023	−	1.61258i	−0.149447	−	0.988770i	$-0.547749\pi$
$752$		0			0
$753$	−1.67188	−	6.23954i	−0.0609267	−	0.227382i
$754$		0			0
$755$	−40.9941	−	17.5660i	−1.49193	−	0.639293i
$756$		0			0
$757$	26.8141	+	26.8141i	0.974576	+	0.974576i	0.999685	−	0.0251083i	$-0.00799305\pi$
$757$	26.8141	+	26.8141i	0.974576	+	0.974576i	−0.0251083	+	0.999685i	$0.507993\pi$
$758$		0			0
$759$	2.30924	−	3.99972i	0.0838200	−	0.145181i
$760$		0			0
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.889326	−	0.457273i	$-0.848826\pi$
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.0486532	+	0.998816i	$0.515493\pi$
$762$		0			0
$763$	−16.8563	+	16.6702i	−0.610239	+	0.603503i
$764$		0			0
$765$	−14.6966	+	18.6793i	−0.531357	+	0.675351i
$766$		0			0
$767$	7.15874	−	1.91818i	0.258487	−	0.0692614i
$768$		0			0
$769$	−44.7341			−1.61315			−0.806576	−	0.591130i	$-0.798682\pi$
$769$	−44.7341			−1.61315			−0.806576	+	0.591130i	$0.798682\pi$
$770$		0			0
$771$	−19.3927			−0.698413
$772$		0			0
$773$	−23.3328	+	6.25202i	−0.839224	+	0.224869i	−0.652734	−	0.757587i	$-0.726378\pi$
$773$	−23.3328	+	6.25202i	−0.839224	+	0.224869i	−0.186490	+	0.982457i	$0.559711\pi$
$774$		0			0
$775$	16.4174	+	4.82891i	0.589731	+	0.173460i
$776$		0			0
$777$	8.00631	+	2.19298i	0.287225	+	0.0786726i
$778$		0			0
$779$	−1.33985	+	0.773565i	−0.0480052	+	0.0277158i
$780$		0			0
$781$	5.95099	−	10.3074i	0.212943	−	0.368828i
$782$		0			0
$783$	37.1906	+	37.1906i	1.32908	+	1.32908i
$784$		0			0
$785$	15.4945	−	6.19889i	0.553024	−	0.221248i
$786$		0			0
$787$	−3.28689	−	12.2669i	−0.117165	−	0.437266i	0.882275	−	0.470735i	$-0.156011\pi$
$787$	−3.28689	−	12.2669i	−0.117165	−	0.437266i	−0.999440	+	0.0334688i	$0.989345\pi$
$788$		0			0
$789$	−5.79134	−	10.0309i	−0.206177	−	0.357110i
$790$		0			0
$791$	0.570279	+	1.00054i	0.0202768	+	0.0355749i
$792$		0			0
$793$	−17.0524	−	4.56917i	−0.605547	−	0.162256i
$794$		0			0
$795$	10.4850	−	7.84514i	0.371864	−	0.278238i
$796$		0			0
$797$	8.99183	−	8.99183i	0.318507	−	0.318507i	−0.529687	−	0.848193i	$-0.677690\pi$
$797$	8.99183	−	8.99183i	0.318507	−	0.318507i	0.848193	+	0.529687i	$0.177690\pi$
$798$		0			0
$799$			30.8957i			1.09301i
$800$		0			0
$801$	8.46421	+	4.88682i	0.299068	+	0.172667i
$802$		0			0
$803$	−1.70216	+	6.35256i	−0.0600681	+	0.224177i
$804$		0			0
$805$	28.7052	+	12.4892i	1.01173	+	0.440187i
$806$		0			0
$807$	−2.72348	+	10.1642i	−0.0958710	+	0.357796i
$808$		0			0
$809$	−23.7782	−	13.7284i	−0.835997	−	0.482663i	0.0199044	−	0.999802i	$-0.493664\pi$
$809$	−23.7782	−	13.7284i	−0.835997	−	0.482663i	−0.855902	+	0.517139i	$0.826997\pi$
$810$		0			0
$811$			12.7335i			0.447132i	0.974689	+	0.223566i	$0.0717699\pi$
$811$			12.7335i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$812$		0			0
$813$	−18.9789	+	18.9789i	−0.665620	+	0.665620i
$814$		0			0
$815$	−3.87799	+	26.9274i	−0.135840	+	0.943226i
$816$		0			0
$817$	−4.12473	−	1.10522i	−0.144306	−	0.0386666i
$818$		0			0
$819$	−6.29002	+	10.7563i	−0.219791	+	0.375857i
$820$		0			0
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	−0.999410	−	0.0343601i	$-0.989061\pi$
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	0.469948	−	0.882694i	$-0.344273\pi$
$822$		0			0
$823$	−2.63314	−	9.82702i	−0.0917856	−	0.342549i	0.904727	−	0.425992i	$-0.140075\pi$
$823$	−2.63314	−	9.82702i	−0.0917856	−	0.342549i	−0.996513	+	0.0834435i	$0.973408\pi$
$824$		0			0
$825$	0.105891	−	4.36283i	0.00368666	−	0.151894i
$826$		0			0
$827$	15.9794	+	15.9794i	0.555660	+	0.555660i	0.928069	−	0.372409i	$-0.121468\pi$
$827$	15.9794	+	15.9794i	0.555660	+	0.555660i	−0.372409	+	0.928069i	$0.621468\pi$
$828$		0			0
$829$	−3.17447	+	5.49835i	−0.110254	+	0.190966i	−0.915873	−	0.401469i	$-0.868500\pi$
$829$	−3.17447	+	5.49835i	−0.110254	+	0.190966i	0.805619	+	0.592435i	$0.201833\pi$
$830$		0			0
$831$	21.9046	−	12.6466i	0.759861	−	0.438706i
$832$		0			0
$833$	−12.3768	+	44.2216i	−0.428830	+	1.53219i
$834$		0			0
$835$	3.61765	+	2.84632i	0.125194	+	0.0985009i
$836$		0			0
$837$	−17.9416	+	4.80743i	−0.620151	+	0.166169i
$838$		0			0
$839$	−39.7411			−1.37202			−0.686008	−	0.727594i	$-0.740638\pi$
$839$	−39.7411			−1.37202			−0.686008	+	0.727594i	$0.740638\pi$
$840$		0			0
$841$	−64.9222			−2.23870
$842$		0			0
$843$	6.40914	−	1.71732i	0.220742	−	0.0591478i
$844$		0			0
$845$	10.1053	−	1.20585i	0.347633	−	0.0414824i
$846$		0			0
$847$	−26.7398	+	7.00609i	−0.918790	+	0.240732i
$848$		0			0
$849$	−2.97899	+	1.71992i	−0.102239	+	0.0590276i
$850$		0			0
$851$	7.06707	−	12.2405i	0.242256	−	0.419600i
$852$		0			0
$853$	17.1451	+	17.1451i	0.587036	+	0.587036i	0.936828	−	0.349791i	$-0.113748\pi$
$853$	17.1451	+	17.1451i	0.587036	+	0.587036i	−0.349791	+	0.936828i	$0.613748\pi$
$854$		0			0
$855$	2.69995	−	6.30091i	0.0923363	−	0.215487i
$856$		0			0
$857$	4.35890	+	16.2677i	0.148897	+	0.555692i	0.999551	+	0.0299658i	$0.00953983\pi$
$857$	4.35890	+	16.2677i	0.148897	+	0.555692i	−0.850654	+	0.525727i	$0.823794\pi$
$858$		0			0
$859$	15.4345	+	26.7333i	0.526619	+	0.912130i	0.999519	+	0.0310142i	$0.00987370\pi$
$859$	15.4345	+	26.7333i	0.526619	+	0.912130i	−0.472900	+	0.881116i	$0.656793\pi$
$860$		0			0
$861$	2.54115	+	0.0141024i	0.0866023	+	0.000480610i
$862$		0			0
$863$	−1.24908	−	0.334691i	−0.0425193	−	0.0113930i	0.237497	−	0.971388i	$-0.423673\pi$
$863$	−1.24908	−	0.334691i	−0.0425193	−	0.0113930i	−0.280016	+	0.959995i	$0.590340\pi$
$864$		0			0
$865$	20.8223	+	2.99875i	0.707978	+	0.101960i
$866$		0			0
$867$	21.6244	−	21.6244i	0.734404	−	0.734404i
$868$		0			0
$869$			4.89152i			0.165934i
$870$		0			0
$871$	34.4645	+	19.8981i	1.16778	+	0.674221i
$872$		0			0
$873$	1.87819	−	7.00950i	0.0635671	−	0.237236i
$874$		0			0
$875$	29.4635	−	2.62772i	0.996047	−	0.0888332i
$876$		0			0
$877$	2.51177	−	9.37406i	0.0848165	−	0.316540i	−0.910463	−	0.413591i	$-0.864274\pi$
$877$	2.51177	−	9.37406i	0.0848165	−	0.316540i	0.995279	+	0.0970513i	$0.0309411\pi$
$878$		0			0
$879$	15.5189	+	8.95985i	0.523440	+	0.302208i
$880$		0			0
$881$			18.3500i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$881$			18.3500i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$882$		0			0
$883$	−23.7527	+	23.7527i	−0.799342	+	0.799342i	−0.982992	−	0.183650i	$-0.941209\pi$
$883$	−23.7527	+	23.7527i	−0.799342	+	0.799342i	0.183650	+	0.982992i	$0.441209\pi$
$884$		0			0
$885$	6.62858	+	0.954624i	0.222817	+	0.0320893i
$886$		0			0
$887$	−37.5247	−	10.0547i	−1.25996	−	0.337604i	−0.433781	−	0.901018i	$-0.642821\pi$
$887$	−37.5247	−	10.0547i	−1.25996	−	0.337604i	−0.826175	+	0.563414i	$0.809488\pi$
$888$		0			0
$889$	−36.3503	+	20.7187i	−1.21915	+	0.694884i
$890$		0			0
$891$	0.562452	+	0.974195i	0.0188429	+	0.0326368i
$892$		0			0
$893$	−2.30629	−	8.60721i	−0.0771772	−	0.288029i
$894$		0			0
$895$	−3.96097	+	9.24379i	−0.132401	+	0.308986i
$896$		0			0
$897$	−12.7746	−	12.7746i	−0.426532	−	0.426532i
$898$		0			0
$899$	16.5847	−	28.7255i	0.553130	−	0.958049i
$900$		0			0
$901$	28.3251	−	16.3535i	0.943644	−	0.544813i
$902$		0			0
$903$	4.93201	+	4.98705i	0.164127	+	0.165959i
$904$		0			0
$905$	−39.7104	+	4.73856i	−1.32002	+	0.157515i
$906$		0			0
$907$	33.5044	−	8.97748i	1.11250	−	0.298092i	0.344653	−	0.938730i	$-0.387997\pi$
$907$	33.5044	−	8.97748i	1.11250	−	0.298092i	0.767843	+	0.640638i	$0.221330\pi$
$908$		0			0
$909$	−18.1174			−0.600916
$910$		0			0
$911$	−48.1523			−1.59536			−0.797678	−	0.603083i	$-0.793939\pi$
$911$	−48.1523			−1.59536			−0.797678	+	0.603083i	$0.793939\pi$
$912$		0			0
$913$	9.37422	−	2.51182i	0.310242	−	0.0831290i
$914$		0			0
$915$	−12.5371	−	9.86405i	−0.414465	−	0.326095i
$916$		0			0
$917$	6.43273	+	24.5515i	0.212428	+	0.810761i
$918$		0			0
$919$	15.4242	−	8.90515i	0.508797	−	0.293754i	−0.223542	−	0.974694i	$-0.571762\pi$
$919$	15.4242	−	8.90515i	0.508797	−	0.293754i	0.732339	+	0.680940i	$0.238429\pi$
$920$		0			0
$921$	5.72435	−	9.91487i	0.188624	−	0.326706i
$922$		0			0
$923$	−32.9206	−	32.9206i	−1.08360	−	1.08360i
$924$		0			0
$925$	0.324064	−	13.3518i	0.0106552	−	0.439004i
$926$		0			0
$927$	−1.01744	−	3.79713i	−0.0334171	−	0.124714i
$928$		0			0
$929$	−16.1326	−	27.9424i	−0.529292	−	0.916761i	−0.999416	−	0.0341607i	$-0.989124\pi$
$929$	−16.1326	−	27.9424i	−0.529292	−	0.916761i	0.470124	−	0.882600i	$-0.344209\pi$
$930$		0			0
$931$	0.146998	−	13.2436i	0.00481766	−	0.434040i
$932$		0			0
$933$	−0.142980	−	0.0383114i	−0.00468096	−	0.00125426i
$934$		0			0
$935$	1.55376	−	10.7887i	0.0508133	−	0.352830i
$936$		0			0
$937$	28.9650	−	28.9650i	0.946244	−	0.946244i	−0.0523829	−	0.998627i	$-0.516682\pi$
$937$	28.9650	−	28.9650i	0.946244	−	0.946244i	0.998627	+	0.0523829i	$0.0166816\pi$
$938$		0			0
$939$		−	13.7359i		−	0.448254i
$940$		0			0
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.910048	−	0.414502i	$-0.136044\pi$
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.0960550	+	0.995376i	$0.469378\pi$
$942$		0			0
$943$	1.11985	−	4.17936i	0.0364675	−	0.136099i
$944$		0			0
$945$	−25.8137	+	19.0920i	−0.839720	+	0.621062i
$946$		0			0
$947$	−3.61149	+	13.4783i	−0.117358	+	0.437985i	−0.999452	−	0.0330871i	$-0.989466\pi$
$947$	−3.61149	+	13.4783i	−0.117358	+	0.437985i	0.882095	+	0.471072i	$0.156133\pi$
$948$		0			0
$949$	22.2792	+	12.8629i	0.723214	+	0.417548i
$950$		0			0
$951$		−	12.8576i		−	0.416935i
$952$		0			0
$953$	25.4475	−	25.4475i	0.824326	−	0.824326i	−0.162399	−	0.986725i	$-0.551923\pi$
$953$	25.4475	−	25.4475i	0.824326	−	0.824326i	0.986725	+	0.162399i	$0.0519232\pi$
$954$		0			0
$955$	4.96916	−	3.71806i	0.160798	−	0.120314i
$956$		0			0
$957$	−8.17061	−	2.18931i	−0.264118	−	0.0707703i
$958$		0			0
$959$	0.136689	−	24.6304i	0.00441392	−	0.795356i
$960$		0			0
$961$	−9.64300	−	16.7022i	−0.311064	−	0.538779i
$962$		0			0
$963$	2.78475	+	10.3928i	0.0897373	+	0.334904i
$964$		0			0
$965$	10.6712	−	4.26922i	0.343518	−	0.137431i
$966$		0			0
$967$	34.0735	+	34.0735i	1.09573	+	1.09573i	0.994904	+	0.100827i	$0.0321488\pi$
$967$	34.0735	+	34.0735i	1.09573	+	1.09573i	0.100827	+	0.994904i	$0.467851\pi$
$968$		0			0
$969$	−7.28974	+	12.6262i	−0.234180	+	0.405612i
$970$		0			0
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	−0.563966	−	0.825798i	$-0.690725\pi$
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	0.433179	+	0.901308i	$0.357392\pi$
$972$		0			0
$973$	15.4966	−	56.5762i	0.496797	−	1.81375i
$974$		0			0
$975$	−16.3773	−	4.81712i	−0.524494	−	0.154271i
$976$		0			0
$977$	26.5853	−	7.12351i	0.850540	−	0.227901i	0.192885	−	0.981221i	$-0.438215\pi$
$977$	26.5853	−	7.12351i	0.850540	−	0.227901i	0.657654	+	0.753320i	$0.271549\pi$
$978$		0			0
$979$	−4.48226			−0.143254
$980$		0			0
$981$	−14.5185			−0.463539
$982$		0			0
$983$	−43.3874	+	11.6256i	−1.38384	+	0.370799i	−0.872515	−	0.488587i	$-0.837513\pi$
$983$	−43.3874	+	11.6256i	−1.38384	+	0.370799i	−0.511327	+	0.859386i	$0.670846\pi$
$984$		0			0
$985$	−2.62104	+	3.33133i	−0.0835134	+	0.106145i
$986$		0			0
$987$	−3.86654	+	14.1163i	−0.123073	+	0.449326i
$988$		0			0
$989$	10.3424	−	5.97118i	0.328869	−	0.189872i
$990$		0			0
$991$	−3.08498	+	5.34334i	−0.0979975	+	0.169737i	−0.910856	−	0.412725i	$-0.864577\pi$
$991$	−3.08498	+	5.34334i	−0.0979975	+	0.169737i	0.812858	+	0.582462i	$0.197910\pi$
$992$		0			0
$993$	4.53527	+	4.53527i	0.143922	+	0.143922i
$994$		0			0
$995$	−29.8083	−	12.7729i	−0.944985	−	0.404927i
$996$		0			0
$997$	4.87184	+	18.1820i	0.154293	+	0.575829i	0.999165	+	0.0408602i	$0.0130098\pi$
$997$	4.87184	+	18.1820i	0.154293	+	0.575829i	−0.844872	+	0.534968i	$0.820324\pi$
$998$		0			0
$999$	7.24821	+	12.5543i	0.229323	+	0.397199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.17.2		16
4.3	odd	2		70.2.k.a.17.2	yes	16
5.3	odd	4	inner	560.2.ci.c.353.2		16
7.5	odd	6	inner	560.2.ci.c.257.2		16
12.11	even	2		630.2.bv.c.577.3		16
20.3	even	4		70.2.k.a.3.4	✓	16
20.7	even	4		350.2.o.c.143.1		16
20.19	odd	2		350.2.o.c.157.3		16
28.3	even	6		490.2.g.c.97.3		16
28.11	odd	6		490.2.g.c.97.2		16
28.19	even	6		70.2.k.a.47.4	yes	16
28.23	odd	6		490.2.l.c.117.3		16
28.27	even	2		490.2.l.c.227.1		16
35.33	even	12	inner	560.2.ci.c.33.2		16
60.23	odd	4		630.2.bv.c.73.2		16
84.47	odd	6		630.2.bv.c.397.2		16
140.3	odd	12		490.2.g.c.293.2		16
140.19	even	6		350.2.o.c.257.1		16
140.23	even	12		490.2.l.c.313.1		16
140.47	odd	12		350.2.o.c.243.3		16
140.83	odd	4		490.2.l.c.423.3		16
140.103	odd	12		70.2.k.a.33.2	yes	16
140.123	even	12		490.2.g.c.293.3		16
420.383	even	12		630.2.bv.c.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	20.3	even	4
70.2.k.a.17.2	yes	16	4.3	odd	2
70.2.k.a.33.2	yes	16	140.103	odd	12
70.2.k.a.47.4	yes	16	28.19	even	6
350.2.o.c.143.1		16	20.7	even	4
350.2.o.c.157.3		16	20.19	odd	2
350.2.o.c.243.3		16	140.47	odd	12
350.2.o.c.257.1		16	140.19	even	6
490.2.g.c.97.2		16	28.11	odd	6
490.2.g.c.97.3		16	28.3	even	6
490.2.g.c.293.2		16	140.3	odd	12
490.2.g.c.293.3		16	140.123	even	12
490.2.l.c.117.3		16	28.23	odd	6
490.2.l.c.227.1		16	28.27	even	2
490.2.l.c.313.1		16	140.23	even	12
490.2.l.c.423.3		16	140.83	odd	4
560.2.ci.c.17.2		16	1.1	even	1	trivial
560.2.ci.c.33.2		16	35.33	even	12	inner
560.2.ci.c.257.2		16	7.5	odd	6	inner
560.2.ci.c.353.2		16	5.3	odd	4	inner
630.2.bv.c.73.2		16	60.23	odd	4
630.2.bv.c.397.2		16	84.47	odd	6
630.2.bv.c.523.3		16	420.383	even	12
630.2.bv.c.577.3		16	12.11	even	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13459 + 0.304013i) q^{3} +(0.264946 + 2.22032i) q^{5} +(-0.698943 + 2.55176i) q^{7} +(-1.40320 + 0.810140i) q^{9} +O(q^{10})\)	\(q+(-1.13459 + 0.304013i) q^{3} +(0.264946 + 2.22032i) q^{5} +(-0.698943 + 2.55176i) q^{7} +(-1.40320 + 0.810140i) q^{9} +(0.371536 - 0.643519i) q^{11} +(-2.05532 - 2.05532i) q^{13} +(-0.975610 - 2.43860i) q^{15} +(-1.69789 - 6.33660i) q^{17} +(0.946027 + 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(-5.11112 - 1.36952i) q^{23} +(-4.85961 + 1.17653i) q^{25} +(3.83750 - 3.83750i) q^{27} +9.69135i q^{29} +(-2.96403 - 1.71129i) q^{31} +(-0.225903 + 0.843083i) q^{33} +(-5.85090 - 0.875795i) q^{35} +(-0.691342 + 2.58012i) q^{37} +(2.95680 + 1.70711i) q^{39} +0.817699i q^{41} +(-1.59589 + 1.59589i) q^{43} +(-2.17054 - 2.90091i) q^{45} +(-4.54913 - 1.21894i) q^{47} +(-6.02296 - 3.56707i) q^{49} +(3.85282 + 6.67328i) q^{51} +(1.29040 + 4.81583i) q^{53} +(1.52725 + 0.654429i) q^{55} +(-1.57150 - 1.57150i) q^{57} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(-1.08652 - 4.14688i) q^{63} +(4.01892 - 5.10802i) q^{65} +(-13.2248 + 3.54358i) q^{67} +6.21538 q^{69} +16.0173 q^{71} +(-8.54906 + 2.29071i) q^{73} +(5.15599 - 2.81226i) q^{75} +(1.38242 + 1.39785i) q^{77} +(-5.70091 + 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-2.94629 - 10.9957i) q^{87} +(-3.01603 - 5.22392i) q^{89} +(6.68124 - 3.80814i) q^{91} +(3.88322 + 1.04051i) q^{93} +(-3.38749 + 2.53461i) q^{95} +(-3.16693 + 3.16693i) q^{97} +1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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