LMFDB - Embedded newform 440.2.y.b.81.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(81,440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("440.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1,0,3,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.3
Root			$0.945349 + 2.90948i$ of defining polynomial
Character	$\chi$	$=$	440.81
Dual form			440.2.y.b.201.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.584258 - 1.79816i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.846938 - 2.60661i) q^{7} +(-0.464972 - 0.337822i) q^{9} +(-2.57134 - 2.09480i) q^{11} +(-0.159232 - 0.115689i) q^{13} +(-0.584258 - 1.79816i) q^{15} +(1.18771 - 0.862919i) q^{17} +(-0.828640 + 2.55029i) q^{19} -5.18193 q^{21} +1.81736 q^{23} +(0.309017 - 0.951057i) q^{25} +(3.70970 - 2.69525i) q^{27} +(0.426278 + 1.31195i) q^{29} +(-4.77653 - 3.47035i) q^{31} +(-5.26912 + 3.39978i) q^{33} +(-2.21731 - 1.61097i) q^{35} +(1.41413 + 4.35226i) q^{37} +(-0.301059 + 0.218732i) q^{39} +(0.381414 - 1.17387i) q^{41} +2.96514 q^{43} -0.574737 q^{45} +(2.87419 - 8.84584i) q^{47} +(-0.413981 + 0.300774i) q^{49} +(-0.857741 - 2.63985i) q^{51} +(-2.17939 - 1.58342i) q^{53} +(-3.31155 - 0.183336i) q^{55} +(4.10170 + 2.98006i) q^{57} +(4.39089 + 13.5138i) q^{59} +(-6.10021 + 4.43206i) q^{61} +(-0.486767 + 1.49811i) q^{63} -0.196821 q^{65} +10.6500 q^{67} +(1.06181 - 3.26790i) q^{69} +(5.56338 - 4.04203i) q^{71} +(3.22348 + 9.92086i) q^{73} +(-1.52961 - 1.11132i) q^{75} +(-3.28257 + 8.47665i) q^{77} +(-1.51552 - 1.10109i) q^{79} +(-3.21189 - 9.88518i) q^{81} +(4.68742 - 3.40561i) q^{83} +(0.453664 - 1.39623i) q^{85} +2.60815 q^{87} +17.3060 q^{89} +(-0.166695 + 0.513036i) q^{91} +(-9.03097 + 6.56138i) q^{93} +(0.828640 + 2.55029i) q^{95} +(14.8203 + 10.7675i) q^{97} +(0.487931 + 1.84268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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			0
$2$		0			0
$3$	0.584258	−	1.79816i	0.337321	−	1.03817i	−0.628246	−	0.778015i	$-0.716227\pi$
$3$	0.584258	−	1.79816i	0.337321	−	1.03817i	0.965567	−	0.260153i	$-0.0837732\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−0.846938	−	2.60661i	−0.320113	−	0.985205i	−0.973599	−	0.228267i	$-0.926694\pi$
$7$	−0.846938	−	2.60661i	−0.320113	−	0.985205i	0.653486	−	0.756939i	$-0.273306\pi$
$8$		0			0
$9$	−0.464972	−	0.337822i	−0.154991	−	0.112607i
$10$		0			0
$11$	−2.57134	−	2.09480i	−0.775288	−	0.631607i
$11$	−2.57134	−	2.09480i	−0.775288	−	0.631607i
$12$		0			0
$13$	−0.159232	−	0.115689i	−0.0441629	−	0.0320862i	0.565485	−	0.824759i	$-0.308689\pi$
$13$	−0.159232	−	0.115689i	−0.0441629	−	0.0320862i	−0.609648	+	0.792672i	$0.708689\pi$
$14$		0			0
$15$	−0.584258	−	1.79816i	−0.150855	−	0.464283i
$16$		0			0
$17$	1.18771	−	0.862919i	0.288061	−	0.209289i	−0.434365	−	0.900737i	$-0.643027\pi$
$17$	1.18771	−	0.862919i	0.288061	−	0.209289i	0.722426	+	0.691448i	$0.243027\pi$
$18$		0			0
$19$	−0.828640	+	2.55029i	−0.190103	+	0.585077i	−0.999999	−	0.00149654i	$-0.999524\pi$
$19$	−0.828640	+	2.55029i	−0.190103	+	0.585077i	0.809896	+	0.586574i	$0.199524\pi$
$20$		0			0
$21$	−5.18193			−1.13079
$22$		0			0
$23$	1.81736			0.378945			0.189473	−	0.981886i	$-0.439322\pi$
$23$	1.81736			0.378945			0.189473	+	0.981886i	$0.439322\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	3.70970	−	2.69525i	0.713932	−	0.518702i
$28$		0			0
$29$	0.426278	+	1.31195i	0.0791577	+	0.243622i	0.982802	−	0.184661i	$-0.0591186\pi$
$29$	0.426278	+	1.31195i	0.0791577	+	0.243622i	−0.903645	+	0.428283i	$0.859119\pi$
$30$		0			0
$31$	−4.77653	−	3.47035i	−0.857889	−	0.623293i	0.0694206	−	0.997587i	$-0.477885\pi$
$31$	−4.77653	−	3.47035i	−0.857889	−	0.623293i	−0.927310	+	0.374294i	$0.877885\pi$
$32$		0			0
$33$	−5.26912	+	3.39978i	−0.917236	+	0.591825i
$34$		0			0
$35$	−2.21731	−	1.61097i	−0.374794	−	0.272304i
$36$		0			0
$37$	1.41413	+	4.35226i	0.232482	+	0.715507i	0.997445	+	0.0714327i	$0.0227571\pi$
$37$	1.41413	+	4.35226i	0.232482	+	0.715507i	−0.764963	+	0.644074i	$0.777243\pi$
$38$		0			0
$39$	−0.301059	+	0.218732i	−0.0482080	+	0.0350252i
$40$		0			0
$41$	0.381414	−	1.17387i	0.0595668	−	0.183328i	−0.916845	−	0.399242i	$-0.869273\pi$
$41$	0.381414	−	1.17387i	0.0595668	−	0.183328i	0.976412	+	0.215914i	$0.0692732\pi$
$42$		0			0
$43$	2.96514			0.452180			0.226090	−	0.974106i	$-0.427406\pi$
$43$	2.96514			0.452180			0.226090	+	0.974106i	$0.427406\pi$
$44$		0			0
$45$	−0.574737			−0.0856768
$46$		0			0
$47$	2.87419	−	8.84584i	0.419243	−	1.29030i	−0.489156	−	0.872196i	$-0.662695\pi$
$47$	2.87419	−	8.84584i	0.419243	−	1.29030i	0.908400	−	0.418102i	$-0.137305\pi$
$48$		0			0
$49$	−0.413981	+	0.300774i	−0.0591401	+	0.0429678i
$50$		0			0
$51$	−0.857741	−	2.63985i	−0.120108	−	0.369653i
$52$		0			0
$53$	−2.17939	−	1.58342i	−0.299362	−	0.217500i	0.427956	−	0.903799i	$-0.359234\pi$
$53$	−2.17939	−	1.58342i	−0.299362	−	0.217500i	−0.727319	+	0.686300i	$0.759234\pi$
$54$		0			0
$55$	−3.31155	−	0.183336i	−0.446530	−	0.0247211i
$56$		0			0
$57$	4.10170	+	2.98006i	0.543283	+	0.394718i
$58$		0			0
$59$	4.39089	+	13.5138i	0.571646	+	1.75934i	0.647327	+	0.762212i	$0.275887\pi$
$59$	4.39089	+	13.5138i	0.571646	+	1.75934i	−0.0756817	+	0.997132i	$0.524113\pi$
$60$		0			0
$61$	−6.10021	+	4.43206i	−0.781052	+	0.567467i	−0.905294	−	0.424785i	$-0.860350\pi$
$61$	−6.10021	+	4.43206i	−0.781052	+	0.567467i	0.124243	+	0.992252i	$0.460350\pi$
$62$		0			0
$63$	−0.486767	+	1.49811i	−0.0613269	+	0.188745i
$64$		0			0
$65$	−0.196821			−0.0244127
$66$		0			0
$67$	10.6500			1.30111			0.650553	−	0.759461i	$-0.274537\pi$
$67$	10.6500			1.30111			0.650553	+	0.759461i	$0.274537\pi$
$68$		0			0
$69$	1.06181	−	3.26790i	0.127826	−	0.393409i
$70$		0			0
$71$	5.56338	−	4.04203i	0.660252	−	0.479701i	−0.206496	−	0.978447i	$-0.566206\pi$
$71$	5.56338	−	4.04203i	0.660252	−	0.479701i	0.866748	+	0.498746i	$0.166206\pi$
$72$		0			0
$73$	3.22348	+	9.92086i	0.377280	+	1.16115i	0.941927	+	0.335817i	$0.109012\pi$
$73$	3.22348	+	9.92086i	0.377280	+	1.16115i	−0.564647	+	0.825332i	$0.690988\pi$
$74$		0			0
$75$	−1.52961	−	1.11132i	−0.176624	−	0.128325i
$76$		0			0
$77$	−3.28257	+	8.47665i	−0.374083	+	0.966004i
$78$		0			0
$79$	−1.51552	−	1.10109i	−0.170509	−	0.123882i	0.499258	−	0.866453i	$-0.333606\pi$
$79$	−1.51552	−	1.10109i	−0.170509	−	0.123882i	−0.669767	+	0.742571i	$0.733606\pi$
$80$		0			0
$81$	−3.21189	−	9.88518i	−0.356876	−	1.09835i
$82$		0			0
$83$	4.68742	−	3.40561i	0.514512	−	0.373815i	−0.300021	−	0.953933i	$-0.596994\pi$
$83$	4.68742	−	3.40561i	0.514512	−	0.373815i	0.814532	+	0.580118i	$0.196994\pi$
$84$		0			0
$85$	0.453664	−	1.39623i	0.0492067	−	0.151443i
$86$		0			0
$87$	2.60815			0.279623
$88$		0			0
$89$	17.3060			1.83443			0.917214	−	0.398396i	$-0.130433\pi$
$89$	17.3060			1.83443			0.917214	+	0.398396i	$0.130433\pi$
$90$		0			0
$91$	−0.166695	+	0.513036i	−0.0174744	+	0.0537807i
$92$		0			0
$93$	−9.03097	+	6.56138i	−0.936468	+	0.680383i
$94$		0			0
$95$	0.828640	+	2.55029i	0.0850167	+	0.261655i
$96$		0			0
$97$	14.8203	+	10.7675i	1.50477	+	1.09328i	0.968433	+	0.249274i	$0.0801919\pi$
$97$	14.8203	+	10.7675i	1.50477	+	1.09328i	0.536336	+	0.844005i	$0.319808\pi$
$98$		0			0
$99$	0.487931	+	1.84268i	0.0490389	+	0.185196i
$100$		0			0
$101$	−4.04540	−	2.93916i	−0.402533	−	0.292457i	0.368039	−	0.929810i	$-0.380029\pi$
$101$	−4.04540	−	2.93916i	−0.402533	−	0.292457i	−0.770572	+	0.637353i	$0.780029\pi$
$102$		0			0
$103$	2.83633	+	8.72933i	0.279472	+	0.860127i	0.988001	+	0.154445i	$0.0493590\pi$
$103$	2.83633	+	8.72933i	0.279472	+	0.860127i	−0.708529	+	0.705681i	$0.750641\pi$
$104$		0			0
$105$	−4.19227	+	3.04586i	−0.409123	+	0.297246i
$106$		0			0
$107$	−5.19508	+	15.9888i	−0.502228	+	1.54570i	0.303155	+	0.952941i	$0.401960\pi$
$107$	−5.19508	+	15.9888i	−0.502228	+	1.54570i	−0.805382	+	0.592756i	$0.798040\pi$
$108$		0			0
$109$	−9.91076			−0.949279			−0.474639	−	0.880180i	$-0.657422\pi$
$109$	−9.91076			−0.949279			−0.474639	+	0.880180i	$0.657422\pi$
$110$		0			0
$111$	8.65227			0.821238
$112$		0			0
$113$	3.91566	−	12.0511i	0.368354	−	1.13368i	−0.579500	−	0.814972i	$-0.696752\pi$
$113$	3.91566	−	12.0511i	0.368354	−	1.13368i	0.947854	−	0.318705i	$-0.103248\pi$
$114$		0			0
$115$	1.47027	−	1.06822i	0.137104	−	0.0996117i
$116$		0			0
$117$	0.0349561	+	0.107584i	0.00323170	+	0.00994614i
$118$		0			0
$119$	−3.25521	−	2.36505i	−0.298404	−	0.216803i
$120$		0			0
$121$	2.22359	+	10.7729i	0.202144	+	0.979356i
$122$		0			0
$123$	−1.88796	−	1.37169i	−0.170232	−	0.123681i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−8.44647	+	6.13672i	−0.749503	+	0.544546i	−0.895673	−	0.444714i	$-0.853305\pi$
$127$	−8.44647	+	6.13672i	−0.749503	+	0.544546i	0.146170	+	0.989260i	$0.453305\pi$
$128$		0			0
$129$	1.73241	−	5.33180i	0.152530	−	0.469439i
$130$		0			0
$131$	−20.9537			−1.83073			−0.915367	−	0.402621i	$-0.868099\pi$
$131$	−20.9537			−1.83073			−0.915367	+	0.402621i	$0.868099\pi$
$132$		0			0
$133$	7.34942			0.637276
$134$		0			0
$135$	1.41698	−	4.36101i	0.121954	−	0.375336i
$136$		0			0
$137$	−2.39537	+	1.74033i	−0.204650	+	0.148687i	−0.685390	−	0.728176i	$-0.740368\pi$
$137$	−2.39537	+	1.74033i	−0.204650	+	0.148687i	0.480740	+	0.876863i	$0.340368\pi$
$138$		0			0
$139$	5.07571	+	15.6214i	0.430516	+	1.32499i	0.897613	+	0.440785i	$0.145300\pi$
$139$	5.07571	+	15.6214i	0.430516	+	1.32499i	−0.467097	+	0.884206i	$0.654700\pi$
$140$		0			0
$141$	−14.2270	−	10.3365i	−1.19813	−	0.870490i
$142$		0			0
$143$	0.167094	+	0.631034i	0.0139731	+	0.0527697i
$144$		0			0
$145$	1.11601	+	0.810828i	0.0926795	+	0.0673356i
$146$		0			0
$147$	0.298969	+	0.920133i	0.0246586	+	0.0758913i
$148$		0			0
$149$	15.5198	−	11.2758i	1.27143	−	0.923751i	0.272176	−	0.962248i	$-0.412257\pi$
$149$	15.5198	−	11.2758i	1.27143	−	0.923751i	0.999259	+	0.0384962i	$0.0122568\pi$
$150$		0			0
$151$	−2.79658	+	8.60698i	−0.227582	+	0.700426i	0.770437	+	0.637516i	$0.220038\pi$
$151$	−2.79658	+	8.60698i	−0.227582	+	0.700426i	−0.998019	+	0.0629100i	$0.979962\pi$
$152$		0			0
$153$	−0.843764			−0.0682142
$154$		0			0
$155$	−5.90411			−0.474230
$156$		0			0
$157$	−5.62084	+	17.2992i	−0.448592	+	1.38062i	0.429904	+	0.902874i	$0.358547\pi$
$157$	−5.62084	+	17.2992i	−0.448592	+	1.38062i	−0.878496	+	0.477749i	$0.841453\pi$
$158$		0			0
$159$	−4.12057	+	2.99377i	−0.326783	+	0.237421i
$160$		0			0
$161$	−1.53919	−	4.73714i	−0.121305	−	0.373339i
$162$		0			0
$163$	−5.13464	−	3.73054i	−0.402176	−	0.292198i	0.368251	−	0.929727i	$-0.379957\pi$
$163$	−5.13464	−	3.73054i	−0.402176	−	0.292198i	−0.770427	+	0.637528i	$0.779957\pi$
$164$		0			0
$165$	−2.26447	+	5.84759i	−0.176289	+	0.455234i
$166$		0			0
$167$	−11.2664	−	8.18555i	−0.871824	−	0.633417i	0.0592518	−	0.998243i	$-0.481129\pi$
$167$	−11.2664	−	8.18555i	−0.871824	−	0.633417i	−0.931076	+	0.364826i	$0.881129\pi$
$168$		0			0
$169$	−4.00525	−	12.3269i	−0.308096	−	0.948222i
$170$		0			0
$171$	1.24684	−	0.905882i	0.0953482	−	0.0692745i
$172$		0			0
$173$	7.48352	−	23.0319i	0.568961	−	1.75108i	−0.0869170	−	0.996216i	$-0.527701\pi$
$173$	7.48352	−	23.0319i	0.568961	−	1.75108i	0.655878	−	0.754867i	$-0.272299\pi$
$174$		0			0
$175$	−2.74075			−0.207181
$176$		0			0
$177$	26.8654			2.01932
$178$		0			0
$179$	0.438716	−	1.35023i	0.0327912	−	0.100921i	−0.933321	−	0.359042i	$-0.883103\pi$
$179$	0.438716	−	1.35023i	0.0327912	−	0.100921i	0.966113	+	0.258121i	$0.0831034\pi$
$180$		0			0
$181$	−4.55387	+	3.30858i	−0.338487	+	0.245925i	−0.744023	−	0.668154i	$-0.767085\pi$
$181$	−4.55387	+	3.30858i	−0.338487	+	0.245925i	0.405536	+	0.914079i	$0.367085\pi$
$182$		0			0
$183$	4.40546	+	13.5586i	0.325661	+	1.00228i
$184$		0			0
$185$	3.70225	+	2.68984i	0.272195	+	0.197761i
$186$		0			0
$187$	−4.86165	−	0.269153i	−0.355519	−	0.0196825i
$188$		0			0
$189$	−10.1674	−	7.38701i	−0.739566	−	0.537326i
$190$		0			0
$191$	−0.692998	−	2.13283i	−0.0501436	−	0.154326i	0.922849	−	0.385161i	$-0.125854\pi$
$191$	−0.692998	−	2.13283i	−0.0501436	−	0.154326i	−0.972993	+	0.230835i	$0.925854\pi$
$192$		0			0
$193$	7.52951	−	5.47051i	0.541986	−	0.393776i	−0.282836	−	0.959168i	$-0.591275\pi$
$193$	7.52951	−	5.47051i	0.541986	−	0.393776i	0.824822	+	0.565392i	$0.191275\pi$
$194$		0			0
$195$	−0.114994	+	0.353916i	−0.00823491	+	0.0253445i
$196$		0			0
$197$	14.3935			1.02549			0.512747	−	0.858540i	$-0.328628\pi$
$197$	14.3935			1.02549			0.512747	+	0.858540i	$0.328628\pi$
$198$		0			0
$199$	3.00915			0.213313			0.106657	−	0.994296i	$-0.465985\pi$
$199$	3.00915			0.213313			0.106657	+	0.994296i	$0.465985\pi$
$200$		0			0
$201$	6.22235	−	19.1504i	0.438891	−	1.35077i
$202$		0			0
$203$	3.05870	−	2.22228i	0.214679	−	0.155973i
$204$		0			0
$205$	−0.381414	−	1.17387i	−0.0266391	−	0.0819867i
$206$		0			0
$207$	−0.845021	−	0.613944i	−0.0587330	−	0.0426720i
$208$		0			0
$209$	7.47308	−	4.82183i	0.516924	−	0.333533i
$210$		0			0
$211$	−12.6553	−	9.19461i	−0.871226	−	0.632983i	0.0596896	−	0.998217i	$-0.480989\pi$
$211$	−12.6553	−	9.19461i	−0.871226	−	0.632983i	−0.930916	+	0.365234i	$0.880989\pi$
$212$		0			0
$213$	−4.01778	−	12.3654i	−0.275293	−	0.847266i
$214$		0			0
$215$	2.39885	−	1.74287i	0.163600	−	0.118862i
$216$		0			0
$217$	−5.00042	+	15.3897i	−0.339450	+	1.04472i
$218$		0			0
$219$	19.7226			1.33273
$220$		0			0
$221$	−0.288950			−0.0194369
$222$		0			0
$223$	1.61039	−	4.95627i	0.107840	−	0.331897i	−0.882547	−	0.470225i	$-0.844173\pi$
$223$	1.61039	−	4.95627i	0.107840	−	0.331897i	0.990386	+	0.138328i	$0.0441728\pi$
$224$		0			0
$225$	−0.464972	+	0.337822i	−0.0309981	+	0.0225215i
$226$		0			0
$227$	−4.25942	−	13.1091i	−0.282708	−	0.870084i	−0.987076	−	0.160250i	$-0.948770\pi$
$227$	−4.25942	−	13.1091i	−0.282708	−	0.870084i	0.704369	−	0.709834i	$-0.251230\pi$
$228$		0			0
$229$	−19.8857	−	14.4478i	−1.31408	−	0.954736i	−0.999986	−	0.00534478i	$-0.998299\pi$
$229$	−19.8857	−	14.4478i	−1.31408	−	0.954736i	−0.314096	−	0.949391i	$-0.601701\pi$
$230$		0			0
$231$	13.3245	+	10.8551i	0.876688	+	0.714215i
$232$		0			0
$233$	−6.49548	−	4.71924i	−0.425533	−	0.309168i	0.354327	−	0.935122i	$-0.384710\pi$
$233$	−6.49548	−	4.71924i	−0.425533	−	0.309168i	−0.779860	+	0.625954i	$0.784710\pi$
$234$		0			0
$235$	−2.87419	−	8.84584i	−0.187491	−	0.577039i
$236$		0			0
$237$	−2.86539	+	2.08183i	−0.186127	+	0.135229i
$238$		0			0
$239$	−0.420928	+	1.29548i	−0.0272276	+	0.0837978i	−0.963747	−	0.266818i	$-0.914028\pi$
$239$	−0.420928	+	1.29548i	−0.0272276	+	0.0837978i	0.936519	+	0.350616i	$0.114028\pi$
$240$		0			0
$241$	−2.94349			−0.189607			−0.0948035	−	0.995496i	$-0.530222\pi$
$241$	−2.94349			−0.189607			−0.0948035	+	0.995496i	$0.530222\pi$
$242$		0			0
$243$	−5.89538			−0.378189
$244$		0			0
$245$	−0.158127	+	0.486663i	−0.0101023	+	0.0310918i
$246$		0			0
$247$	0.426986	−	0.310223i	0.0271684	−	0.0197390i
$248$		0			0
$249$	−3.38517	−	10.4185i	−0.214527	−	0.660245i
$250$		0			0
$251$	−12.7102	−	9.23452i	−0.802263	−	0.582878i	0.109314	−	0.994007i	$-0.465134\pi$
$251$	−12.7102	−	9.23452i	−0.802263	−	0.582878i	−0.911577	+	0.411129i	$0.865134\pi$
$252$		0			0
$253$	−4.67305	−	3.80701i	−0.293792	−	0.239345i
$254$		0			0
$255$	−2.24559	−	1.63152i	−0.140625	−	0.102170i
$256$		0			0
$257$	−2.75170	−	8.46888i	−0.171647	−	0.528274i	0.827818	−	0.560997i	$-0.189582\pi$
$257$	−2.75170	−	8.46888i	−0.171647	−	0.528274i	−0.999464	+	0.0327230i	$0.989582\pi$
$258$		0			0
$259$	10.1469	−	7.37219i	0.630500	−	0.458085i
$260$		0			0
$261$	0.244998	−	0.754025i	0.0151650	−	0.0466730i
$262$		0			0
$263$	0.671733			0.0414208			0.0207104	−	0.999786i	$-0.493407\pi$
$263$	0.671733			0.0414208			0.0207104	+	0.999786i	$0.493407\pi$
$264$		0			0
$265$	−2.69388			−0.165484
$266$		0			0
$267$	10.1111	−	31.1189i	0.618791	−	1.90444i
$268$		0			0
$269$	−21.6092	+	15.7000i	−1.31754	+	0.957247i	−0.317579	+	0.948232i	$0.602870\pi$
$269$	−21.6092	+	15.7000i	−1.31754	+	0.957247i	−0.999959	+	0.00901560i	$0.997130\pi$
$270$		0			0
$271$	6.89382	+	21.2170i	0.418770	+	1.28884i	0.908835	+	0.417155i	$0.136973\pi$
$271$	6.89382	+	21.2170i	0.418770	+	1.28884i	−0.490065	+	0.871686i	$0.663027\pi$
$272$		0			0
$273$	0.825127	+	0.599490i	0.0499390	+	0.0362828i
$274$		0			0
$275$	−2.78687	+	1.79816i	−0.168054	+	0.108433i
$276$		0			0
$277$	−18.5266	−	13.4604i	−1.11315	−	0.808754i	−0.129997	−	0.991514i	$-0.541497\pi$
$277$	−18.5266	−	13.4604i	−1.11315	−	0.808754i	−0.983158	+	0.182760i	$0.941497\pi$
$278$		0			0
$279$	1.04859	+	3.22723i	0.0627775	+	0.193209i
$280$		0			0
$281$	22.9302	−	16.6598i	1.36790	−	0.993840i	0.370006	−	0.929030i	$-0.379356\pi$
$281$	22.9302	−	16.6598i	1.36790	−	0.993840i	0.997898	−	0.0648103i	$-0.0206442\pi$
$282$		0			0
$283$	−9.59685	+	29.5361i	−0.570474	+	1.75574i	0.0806255	+	0.996744i	$0.474308\pi$
$283$	−9.59685	+	29.5361i	−0.570474	+	1.75574i	−0.651099	+	0.758993i	$0.725692\pi$
$284$		0			0
$285$	5.06997			0.300319
$286$		0			0
$287$	−3.38286			−0.199684
$288$		0			0
$289$	−4.58727	+	14.1182i	−0.269840	+	0.830481i
$290$		0			0
$291$	28.0206	−	20.3582i	1.64260	−	1.19342i
$292$		0			0
$293$	2.42573	+	7.46562i	0.141712	+	0.436146i	0.996574	−	0.0827109i	$-0.0263578\pi$
$293$	2.42573	+	7.46562i	0.141712	+	0.436146i	−0.854861	+	0.518857i	$0.826358\pi$
$294$		0			0
$295$	11.4955	+	8.35197i	0.669294	+	0.486271i
$296$		0			0
$297$	−15.1849	−	0.840677i	−0.881119	−	0.0487810i
$298$		0			0
$299$	−0.289381	−	0.210248i	−0.0167353	−	0.0121589i
$300$		0			0
$301$	−2.51129	−	7.72896i	−0.144748	−	0.445490i
$302$		0			0
$303$	−7.64863	+	5.55706i	−0.439402	+	0.319245i
$304$		0			0
$305$	−2.33007	+	7.17122i	−0.133420	+	0.410623i
$306$		0			0
$307$	10.0601			0.574160			0.287080	−	0.957907i	$-0.407315\pi$
$307$	10.0601			0.574160			0.287080	+	0.957907i	$0.407315\pi$
$308$		0			0
$309$	17.3539			0.987228
$310$		0			0
$311$	−6.91116	+	21.2704i	−0.391896	+	1.20613i	0.539456	+	0.842014i	$0.318630\pi$
$311$	−6.91116	+	21.2704i	−0.391896	+	1.20613i	−0.931353	+	0.364119i	$0.881370\pi$
$312$		0			0
$313$	−14.6825	+	10.6675i	−0.829906	+	0.602962i	−0.919533	−	0.393013i	$-0.871433\pi$
$313$	−14.6825	+	10.6675i	−0.829906	+	0.602962i	0.0896265	+	0.995975i	$0.471433\pi$
$314$		0			0
$315$	0.486767	+	1.49811i	0.0274262	+	0.0844092i
$316$		0			0
$317$	2.03597	+	1.47922i	0.114352	+	0.0830814i	0.643491	−	0.765453i	$-0.277485\pi$
$317$	2.03597	+	1.47922i	0.114352	+	0.0830814i	−0.529140	+	0.848535i	$0.677485\pi$
$318$		0			0
$319$	1.65217	−	4.26643i	0.0925037	−	0.238874i
$320$		0			0
$321$	25.7152	+	18.6832i	1.43528	+	1.04279i
$322$		0			0
$323$	1.21652	+	3.74405i	0.0676887	+	0.208324i
$324$		0			0
$325$	−0.159232	+	0.115689i	−0.00883258	+	0.00641725i
$326$		0			0
$327$	−5.79044	+	17.8211i	−0.320212	+	0.985511i
$328$		0			0
$329$	−25.4919			−1.40541
$330$		0			0
$331$	−7.54546			−0.414736			−0.207368	−	0.978263i	$-0.566490\pi$
$331$	−7.54546			−0.414736			−0.207368	+	0.978263i	$0.566490\pi$
$332$		0			0
$333$	0.812756	−	2.50140i	0.0445387	−	0.137076i
$334$		0			0
$335$	8.61604	−	6.25992i	0.470745	−	0.342016i
$336$		0			0
$337$	−7.10791	−	21.8759i	−0.387193	−	1.19166i	−0.934877	−	0.354972i	$-0.884490\pi$
$337$	−7.10791	−	21.8759i	−0.387193	−	1.19166i	0.547684	−	0.836685i	$-0.315510\pi$
$338$		0			0
$339$	−19.3821	−	14.0820i	−1.05269	−	0.764827i
$340$		0			0
$341$	5.01237	+	18.9293i	0.271435	+	1.02508i
$342$		0			0
$343$	−14.3866	−	10.4525i	−0.776802	−	0.564380i
$344$		0			0
$345$	−1.06181	−	3.26790i	−0.0571657	−	0.175938i
$346$		0			0
$347$	−3.29647	+	2.39502i	−0.176964	+	0.128572i	−0.672741	−	0.739878i	$-0.734883\pi$
$347$	−3.29647	+	2.39502i	−0.176964	+	0.128572i	0.495777	+	0.868450i	$0.334883\pi$
$348$		0			0
$349$	−7.35692	+	22.6423i	−0.393807	+	1.21201i	0.536080	+	0.844167i	$0.319905\pi$
$349$	−7.35692	+	22.6423i	−0.393807	+	1.21201i	−0.929887	+	0.367846i	$0.880095\pi$
$350$		0			0
$351$	−0.902511			−0.0481725
$352$		0			0
$353$	−7.00060			−0.372605			−0.186302	−	0.982492i	$-0.559650\pi$
$353$	−7.00060			−0.372605			−0.186302	+	0.982492i	$0.559650\pi$
$354$		0			0
$355$	2.12502	−	6.54015i	0.112785	−	0.347115i
$356$		0			0
$357$	−6.15461	+	4.47159i	−0.325737	+	0.236661i
$358$		0			0
$359$	11.2699	+	34.6851i	0.594801	+	1.83061i	0.555716	+	0.831372i	$0.312444\pi$
$359$	11.2699	+	34.6851i	0.594801	+	1.83061i	0.0390849	+	0.999236i	$0.487556\pi$
$360$		0			0
$361$	9.55397	+	6.94137i	0.502841	+	0.365335i
$362$		0			0
$363$	20.6706	+	2.29579i	1.08492	+	0.120498i
$364$		0			0
$365$	8.43919	+	6.13143i	0.441727	+	0.320934i
$366$		0			0
$367$	−9.01878	−	27.7569i	−0.470776	−	1.44890i	−0.851570	−	0.524241i	$-0.824349\pi$
$367$	−9.01878	−	27.7569i	−0.470776	−	1.44890i	0.380794	−	0.924660i	$-0.375651\pi$
$368$		0			0
$369$	−0.573906	+	0.416967i	−0.0298764	+	0.0217065i
$370$		0			0
$371$	−2.28155	+	7.02188i	−0.118452	+	0.364558i
$372$		0			0
$373$	20.0215			1.03667			0.518337	−	0.855176i	$-0.326551\pi$
$373$	20.0215			1.03667			0.518337	+	0.855176i	$0.326551\pi$
$374$		0			0
$375$	−1.89070			−0.0976352
$376$		0			0
$377$	0.0839004	−	0.258219i	0.00432109	−	0.0132990i
$378$		0			0
$379$	−6.62561	+	4.81379i	−0.340335	+	0.247268i	−0.744803	−	0.667284i	$-0.767457\pi$
$379$	−6.62561	+	4.81379i	−0.340335	+	0.247268i	0.404468	+	0.914552i	$0.367457\pi$
$380$		0			0
$381$	6.09989	+	18.7735i	0.312507	+	0.961797i
$382$		0			0
$383$	−16.4111	−	11.9234i	−0.838567	−	0.609255i	0.0834027	−	0.996516i	$-0.473421\pi$
$383$	−16.4111	−	11.9234i	−0.838567	−	0.609255i	−0.921970	+	0.387261i	$0.873421\pi$
$384$		0			0
$385$	2.32680	+	8.78720i	0.118584	+	0.447837i
$386$		0			0
$387$	−1.37871	−	1.00169i	−0.0700837	−	0.0509188i
$388$		0			0
$389$	4.02524	+	12.3884i	0.204088	+	0.628118i	0.999750	+	0.0223769i	$0.00712338\pi$
$389$	4.02524	+	12.3884i	0.204088	+	0.628118i	−0.795662	+	0.605741i	$0.792877\pi$
$390$		0			0
$391$	2.15849	−	1.56823i	0.109159	−	0.0793090i
$392$		0			0
$393$	−12.2424	+	37.6781i	−0.617545	+	1.90061i
$394$		0			0
$395$	−1.87328			−0.0942552
$396$		0			0
$397$	−0.593277			−0.0297757			−0.0148878	−	0.999889i	$-0.504739\pi$
$397$	−0.593277			−0.0297757			−0.0148878	+	0.999889i	$0.504739\pi$
$398$		0			0
$399$	4.29396	−	13.2154i	0.214967	−	0.661599i
$400$		0			0
$401$	7.31889	−	5.31748i	0.365488	−	0.265542i	−0.389850	−	0.920879i	$-0.627473\pi$
$401$	7.31889	−	5.31748i	0.365488	−	0.265542i	0.755337	+	0.655336i	$0.227473\pi$
$402$		0			0
$403$	0.359094	+	1.10518i	0.0178878	+	0.0550529i
$404$		0			0
$405$	−8.40883	−	6.10937i	−0.417838	−	0.303577i
$406$		0			0
$407$	5.48091	−	14.1535i	0.271679	−	0.701562i
$408$		0			0
$409$	14.3654	+	10.4371i	0.710323	+	0.516080i	0.883278	−	0.468850i	$-0.155331\pi$
$409$	14.3654	+	10.4371i	0.710323	+	0.516080i	−0.172955	+	0.984930i	$0.555331\pi$
$410$		0			0
$411$	1.72989	+	5.32405i	0.0853292	+	0.262616i
$412$		0			0
$413$	31.5063	−	22.8907i	1.55032	−	1.12638i
$414$		0			0
$415$	1.79044	−	5.51040i	0.0878891	−	0.270495i
$416$		0			0
$417$	31.0553			1.52079
$418$		0			0
$419$	−9.43701			−0.461028			−0.230514	−	0.973069i	$-0.574041\pi$
$419$	−9.43701			−0.461028			−0.230514	+	0.973069i	$0.574041\pi$
$420$		0			0
$421$	−7.49246	+	23.0594i	−0.365160	+	1.12385i	0.584720	+	0.811235i	$0.301204\pi$
$421$	−7.49246	+	23.0594i	−0.365160	+	1.12385i	−0.949881	+	0.312613i	$0.898796\pi$
$422$		0			0
$423$	−4.32474	+	3.14211i	−0.210276	+	0.152774i
$424$		0			0
$425$	−0.453664	−	1.39623i	−0.0220059	−	0.0677272i
$426$		0			0
$427$	16.7191	+	12.1472i	0.809096	+	0.587843i
$428$		0			0
$429$	1.23233	+	0.0682248i	0.0594973	+	0.00329393i
$430$		0			0
$431$	−7.77858	−	5.65147i	−0.374681	−	0.272222i	0.384468	−	0.923138i	$-0.374385\pi$
$431$	−7.77858	−	5.65147i	−0.374681	−	0.272222i	−0.759149	+	0.650917i	$0.774385\pi$
$432$		0			0
$433$	−2.91798	−	8.98061i	−0.140229	−	0.431581i	0.856138	−	0.516748i	$-0.172858\pi$
$433$	−2.91798	−	8.98061i	−0.140229	−	0.431581i	−0.996367	+	0.0851672i	$0.972858\pi$
$434$		0			0
$435$	2.11004	−	1.53303i	0.101168	−	0.0735032i
$436$		0			0
$437$	−1.50594	+	4.63480i	−0.0720387	+	0.221712i
$438$		0			0
$439$	17.8211			0.850555			0.425278	−	0.905063i	$-0.360176\pi$
$439$	17.8211			0.850555			0.425278	+	0.905063i	$0.360176\pi$
$440$		0			0
$441$	0.294098			0.0140047
$442$		0			0
$443$	−5.44386	+	16.7545i	−0.258646	+	0.796029i	0.734444	+	0.678670i	$0.237443\pi$
$443$	−5.44386	+	16.7545i	−0.258646	+	0.796029i	−0.993089	+	0.117360i	$0.962557\pi$
$444$		0			0
$445$	14.0008	−	10.1722i	0.663702	−	0.482208i
$446$		0			0
$447$	−11.2082	−	34.4951i	−0.530127	−	1.63156i
$448$		0			0
$449$	6.48121	+	4.70887i	0.305867	+	0.222226i	0.730121	−	0.683318i	$-0.239464\pi$
$449$	6.48121	+	4.70887i	0.305867	+	0.222226i	−0.424254	+	0.905543i	$0.639464\pi$
$450$		0			0
$451$	−3.43978	+	2.21944i	−0.161973	+	0.104509i
$452$		0			0
$453$	13.8428	+	10.0574i	0.650392	+	0.472537i
$454$		0			0
$455$	0.166695	+	0.513036i	0.00781480	+	0.0240515i
$456$		0			0
$457$	−6.64671	+	4.82912i	−0.310920	+	0.225896i	−0.732291	−	0.680992i	$-0.761549\pi$
$457$	−6.64671	+	4.82912i	−0.310920	+	0.225896i	0.421371	+	0.906888i	$0.361549\pi$
$458$		0			0
$459$	2.08025	−	6.40234i	0.0970976	−	0.298836i
$460$		0			0
$461$	5.47559			0.255024			0.127512	−	0.991837i	$-0.459301\pi$
$461$	5.47559			0.255024			0.127512	+	0.991837i	$0.459301\pi$
$462$		0			0
$463$	27.1843			1.26336			0.631681	−	0.775228i	$-0.282365\pi$
$463$	27.1843			1.26336			0.631681	+	0.775228i	$0.282365\pi$
$464$		0			0
$465$	−3.44952	+	10.6165i	−0.159968	+	0.492330i
$466$		0			0
$467$	−5.70662	+	4.14610i	−0.264071	+	0.191859i	−0.711940	−	0.702241i	$-0.752183\pi$
$467$	−5.70662	+	4.14610i	−0.264071	+	0.191859i	0.447869	+	0.894099i	$0.352183\pi$
$468$		0			0
$469$	−9.01990	−	27.7604i	−0.416500	−	1.28186i
$470$		0			0
$471$	27.8227	+	20.2143i	1.28200	+	0.931428i
$472$		0			0
$473$	−7.62439	−	6.21139i	−0.350570	−	0.285600i
$474$		0			0
$475$	2.16941	+	1.57617i	0.0995393	+	0.0723195i
$476$		0			0
$477$	0.478442	+	1.47249i	0.0219064	+	0.0674208i
$478$		0			0
$479$	4.29627	−	3.12142i	0.196302	−	0.142622i	−0.485293	−	0.874352i	$-0.661287\pi$
$479$	4.29627	−	3.12142i	0.196302	−	0.142622i	0.681594	+	0.731730i	$0.261287\pi$
$480$		0			0
$481$	0.278332	−	0.856616i	0.0126908	−	0.0390583i
$482$		0			0
$483$	−9.41742			−0.428507
$484$		0			0
$485$	18.3188			0.831816
$486$		0			0
$487$	3.66123	−	11.2681i	0.165906	−	0.510607i	−0.833196	−	0.552978i	$-0.813491\pi$
$487$	3.66123	−	11.2681i	0.165906	−	0.510607i	0.999102	+	0.0423714i	$0.0134913\pi$
$488$		0			0
$489$	−9.70806	+	7.05332i	−0.439014	+	0.318962i
$490$		0			0
$491$	11.8597	+	36.5003i	0.535220	+	1.64724i	0.743174	+	0.669098i	$0.233319\pi$
$491$	11.8597	+	36.5003i	0.535220	+	1.64724i	−0.207955	+	0.978138i	$0.566681\pi$
$492$		0			0
$493$	1.63840	+	1.19037i	0.0737897	+	0.0536114i
$494$		0			0
$495$	1.47785	+	1.20396i	0.0664242	+	0.0541141i
$496$		0			0
$497$	−15.2478	−	11.0782i	−0.683959	−	0.496925i
$498$		0			0
$499$	3.30243	+	10.1638i	0.147837	+	0.454996i	0.997365	−	0.0725480i	$-0.0231131\pi$
$499$	3.30243	+	10.1638i	0.147837	+	0.454996i	−0.849528	+	0.527544i	$0.823113\pi$
$500$		0			0
$501$	−21.3014	+	15.4764i	−0.951678	+	0.691435i
$502$		0			0
$503$	10.9725	−	33.7699i	0.489239	−	1.50572i	−0.336506	−	0.941681i	$-0.609245\pi$
$503$	10.9725	−	33.7699i	0.489239	−	1.50572i	0.825746	−	0.564042i	$-0.190755\pi$
$504$		0			0
$505$	−5.00039			−0.222515
$506$		0			0
$507$	−24.5058			−1.08834
$508$		0			0
$509$	−6.61223	+	20.3503i	−0.293082	+	0.902013i	0.690777	+	0.723068i	$0.257269\pi$
$509$	−6.61223	+	20.3503i	−0.293082	+	0.902013i	−0.983859	+	0.178946i	$0.942731\pi$
$510$		0			0
$511$	23.1297	−	16.8047i	1.02320	−	0.743397i
$512$		0			0
$513$	3.79968	+	11.6942i	0.167760	+	0.516312i
$514$		0			0
$515$	7.42561	+	5.39502i	0.327212	+	0.237733i
$516$		0			0
$517$	−25.9208	+	16.7248i	−1.14000	+	0.735556i
$518$		0			0
$519$	−37.0427	−	26.9131i	−1.62600	−	1.18135i
$520$		0			0
$521$	−5.98604	−	18.4231i	−0.262253	−	0.807132i	−0.992314	−	0.123749i	$-0.960508\pi$
$521$	−5.98604	−	18.4231i	−0.262253	−	0.807132i	0.730060	−	0.683383i	$-0.239492\pi$
$522$		0			0
$523$	−0.723508	+	0.525659i	−0.0316368	+	0.0229855i	−0.603491	−	0.797370i	$-0.706224\pi$
$523$	−0.723508	+	0.525659i	−0.0316368	+	0.0229855i	0.571854	+	0.820355i	$0.306224\pi$
$524$		0			0
$525$	−1.60130	+	4.92831i	−0.0698866	+	0.215089i
$526$		0			0
$527$	−8.66774			−0.377573
$528$		0			0
$529$	−19.6972			−0.856400
$530$		0			0
$531$	2.52361	−	7.76687i	0.109515	−	0.337054i
$532$		0			0
$533$	−0.196537	+	0.142792i	−0.00851295	+	0.00618502i
$534$		0			0
$535$	5.19508	+	15.9888i	0.224603	+	0.691257i
$536$		0			0
$537$	−2.17161	−	1.57776i	−0.0937117	−	0.0680856i
$538$		0			0
$539$	1.69455	+	0.0938147i	0.0729894	+	0.00404088i
$540$		0			0
$541$	32.4842	+	23.6012i	1.39661	+	1.01469i	0.995104	+	0.0988357i	$0.0315118\pi$
$541$	32.4842	+	23.6012i	1.39661	+	1.01469i	0.401502	+	0.915858i	$0.368488\pi$
$542$		0			0
$543$	3.28872	+	10.1217i	0.141133	+	0.434362i
$544$		0			0
$545$	−8.01797	+	5.82540i	−0.343452	+	0.249533i
$546$		0			0
$547$	−1.38974	+	4.27718i	−0.0594209	+	0.182879i	−0.976361	−	0.216146i	$-0.930651\pi$
$547$	−1.38974	+	4.27718i	−0.0594209	+	0.182879i	0.916940	+	0.399025i	$0.130651\pi$
$548$		0			0
$549$	4.33367			0.184957
$550$		0			0
$551$	−3.69908			−0.157586
$552$		0			0
$553$	−1.58656	+	4.88292i	−0.0674672	+	0.207643i
$554$		0			0
$555$	6.99984	−	5.08568i	0.297127	−	0.215875i
$556$		0			0
$557$	−7.40826	−	22.8003i	−0.313898	−	0.966079i	−0.976206	−	0.216847i	$-0.930423\pi$
$557$	−7.40826	−	22.8003i	−0.313898	−	0.966079i	0.662308	−	0.749232i	$-0.269577\pi$
$558$		0			0
$559$	−0.472144	−	0.343033i	−0.0199696	−	0.0145087i
$560$		0			0
$561$	−3.32443	+	8.58476i	−0.140358	+	0.362449i
$562$		0			0
$563$	−14.8408	−	10.7825i	−0.625464	−	0.454426i	0.229362	−	0.973341i	$-0.426336\pi$
$563$	−14.8408	−	10.7825i	−0.625464	−	0.454426i	−0.854826	+	0.518915i	$0.826336\pi$
$564$		0			0
$565$	−3.91566	−	12.0511i	−0.164733	−	0.506996i
$566$		0			0
$567$	−23.0465	+	16.7443i	−0.967862	+	0.703193i
$568$		0			0
$569$	−0.835924	+	2.57271i	−0.0350437	+	0.107854i	−0.967048	−	0.254593i	$-0.918058\pi$
$569$	−0.835924	+	2.57271i	−0.0350437	+	0.107854i	0.932005	+	0.362447i	$0.118058\pi$
$570$		0			0
$571$	13.6593			0.571626			0.285813	−	0.958285i	$-0.407736\pi$
$571$	13.6593			0.571626			0.285813	+	0.958285i	$0.407736\pi$
$572$		0			0
$573$	−4.24006			−0.177131
$574$		0			0
$575$	0.561595	−	1.72841i	0.0234201	−	0.0720797i
$576$		0			0
$577$	−6.66339	+	4.84124i	−0.277401	+	0.201543i	−0.717783	−	0.696267i	$-0.754843\pi$
$577$	−6.66339	+	4.84124i	−0.277401	+	0.201543i	0.440382	+	0.897810i	$0.354843\pi$
$578$		0			0
$579$	−5.43768	−	16.7355i	−0.225982	−	0.695502i
$580$		0			0
$581$	−12.8471	−	9.33393i	−0.532986	−	0.387237i
$582$		0			0
$583$	2.28700	+	8.63691i	0.0947179	+	0.357704i
$584$		0			0
$585$	0.0915164	+	0.0664905i	0.00378374	+	0.00274905i
$586$		0			0
$587$	6.91475	+	21.2814i	0.285402	+	0.878378i	0.986278	+	0.165094i	$0.0527928\pi$
$587$	6.91475	+	21.2814i	0.285402	+	0.878378i	−0.700875	+	0.713284i	$0.747207\pi$
$588$		0			0
$589$	12.8084	−	9.30587i	0.527762	−	0.383442i
$590$		0			0
$591$	8.40951	−	25.8818i	0.345921	−	1.06464i
$592$		0			0
$593$	−44.5253			−1.82844			−0.914218	−	0.405223i	$-0.867194\pi$
$593$	−44.5253			−1.82844			−0.914218	+	0.405223i	$0.867194\pi$
$594$		0			0
$595$	−4.02366			−0.164954
$596$		0			0
$597$	1.75812	−	5.41094i	0.0719551	−	0.221455i
$598$		0			0
$599$	−32.3034	+	23.4698i	−1.31988	+	0.958950i	−0.319948	+	0.947435i	$0.603666\pi$
$599$	−32.3034	+	23.4698i	−1.31988	+	0.958950i	−0.999934	+	0.0115153i	$0.996334\pi$
$600$		0			0
$601$	9.57420	+	29.4664i	0.390540	+	1.20196i	0.932381	+	0.361477i	$0.117727\pi$
$601$	9.57420	+	29.4664i	0.390540	+	1.20196i	−0.541841	+	0.840481i	$0.682273\pi$
$602$		0			0
$603$	−4.95196	−	3.59781i	−0.201659	−	0.146514i
$604$		0			0
$605$	8.13108	+	7.40848i	0.330575	+	0.301197i
$606$		0			0
$607$	−21.4902	−	15.6136i	−0.872261	−	0.633735i	0.0589318	−	0.998262i	$-0.481231\pi$
$607$	−21.4902	−	15.6136i	−0.872261	−	0.633735i	−0.931193	+	0.364527i	$0.881231\pi$
$608$		0			0
$609$	−2.20894	−	6.79842i	−0.0895107	−	0.275486i
$610$		0			0
$611$	−1.48102	+	1.07603i	−0.0599158	+	0.0435314i
$612$		0			0
$613$	8.73428	−	26.8813i	0.352774	−	1.08573i	−0.604515	−	0.796594i	$-0.706633\pi$
$613$	8.73428	−	26.8813i	0.352774	−	1.08573i	0.957289	−	0.289133i	$-0.0933671\pi$
$614$		0			0
$615$	−2.33365			−0.0941020
$616$		0			0
$617$	−3.98722			−0.160520			−0.0802598	−	0.996774i	$-0.525575\pi$
$617$	−3.98722			−0.160520			−0.0802598	+	0.996774i	$0.525575\pi$
$618$		0			0
$619$	9.15264	−	28.1689i	0.367876	−	1.13221i	−0.580285	−	0.814414i	$-0.697059\pi$
$619$	9.15264	−	28.1689i	0.367876	−	1.13221i	0.948161	−	0.317792i	$-0.102941\pi$
$620$		0			0
$621$	6.74185	−	4.89824i	0.270541	−	0.196560i
$622$		0			0
$623$	−14.6571	−	45.1098i	−0.587223	−	1.80729i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−4.30422	−	16.2550i	−0.171894	−	0.649162i
$628$		0			0
$629$	5.43522	+	3.94892i	0.216717	+	0.157454i
$630$		0			0
$631$	−10.7460	−	33.0729i	−0.427793	−	1.31661i	−0.900295	−	0.435281i	$-0.856649\pi$
$631$	−10.7460	−	33.0729i	−0.427793	−	1.31661i	0.472502	−	0.881330i	$-0.343351\pi$
$632$		0			0
$633$	−23.9273	+	17.3842i	−0.951026	+	0.690961i
$634$		0			0
$635$	−3.22626	+	9.92942i	−0.128030	+	0.394037i
$636$		0			0
$637$	0.100715			0.00399047
$638$		0			0
$639$	−3.95231			−0.156351
$640$		0			0
$641$	8.35332	−	25.7089i	0.329936	−	1.01544i	−0.639226	−	0.769019i	$-0.720745\pi$
$641$	8.35332	−	25.7089i	0.329936	−	1.01544i	0.969163	−	0.246421i	$-0.0792547\pi$
$642$		0			0
$643$	25.3914	−	18.4479i	1.00134	−	0.727515i	0.0389639	−	0.999241i	$-0.487594\pi$
$643$	25.3914	−	18.4479i	1.00134	−	0.727515i	0.962375	+	0.271725i	$0.0875943\pi$
$644$		0			0
$645$	−1.73241	−	5.33180i	−0.0682134	−	0.209939i
$646$		0			0
$647$	34.9191	+	25.3702i	1.37281	+	0.997406i	0.997512	+	0.0705030i	$0.0224604\pi$
$647$	34.9191	+	25.3702i	1.37281	+	0.997406i	0.375300	+	0.926903i	$0.377540\pi$
$648$		0			0
$649$	17.0182	−	43.9466i	0.668025	−	1.72505i
$650$		0			0
$651$	24.7516	+	17.9831i	0.970092	+	0.704813i
$652$		0			0
$653$	3.05688	+	9.40812i	0.119625	+	0.368168i	0.992884	−	0.119089i	$-0.0379974\pi$
$653$	3.05688	+	9.40812i	0.119625	+	0.368168i	−0.873259	+	0.487257i	$0.837997\pi$
$654$		0			0
$655$	−16.9519	+	12.3163i	−0.662366	+	0.481237i
$656$		0			0
$657$	1.85266	−	5.70189i	0.0722790	−	0.222452i
$658$		0			0
$659$	12.3139			0.479683			0.239842	−	0.970812i	$-0.422904\pi$
$659$	12.3139			0.479683			0.239842	+	0.970812i	$0.422904\pi$
$660$		0			0
$661$	−26.4390			−1.02836			−0.514179	−	0.857683i	$-0.671903\pi$
$661$	−26.4390			−1.02836			−0.514179	+	0.857683i	$0.671903\pi$
$662$		0			0
$663$	−0.168821	+	0.519579i	−0.00655648	+	0.0201788i
$664$		0			0
$665$	5.94581	−	4.31988i	0.230568	−	0.167518i
$666$		0			0
$667$	0.774699	+	2.38428i	0.0299965	+	0.0923196i
$668$		0			0
$669$	−7.97129	−	5.79148i	−0.308188	−	0.223912i
$670$		0			0
$671$	24.9700	+	1.38241i	0.963957	+	0.0533672i
$672$		0			0
$673$	11.8293	+	8.59452i	0.455988	+	0.331294i	0.791955	−	0.610579i	$-0.209063\pi$
$673$	11.8293	+	8.59452i	0.455988	+	0.331294i	−0.335968	+	0.941874i	$0.609063\pi$
$674$		0			0
$675$	−1.41698	−	4.36101i	−0.0545395	−	0.167855i
$676$		0			0
$677$	23.5945	−	17.1424i	0.906812	−	0.658838i	−0.0333944	−	0.999442i	$-0.510632\pi$
$677$	23.5945	−	17.1424i	0.906812	−	0.658838i	0.940207	+	0.340605i	$0.110632\pi$
$678$		0			0
$679$	15.5149	−	47.7500i	0.595408	−	1.83248i
$680$		0			0
$681$	−26.0609			−0.998657
$682$		0			0
$683$	25.7011			0.983427			0.491713	−	0.870757i	$-0.336371\pi$
$683$	25.7011			0.983427			0.491713	+	0.870757i	$0.336371\pi$
$684$		0			0
$685$	−0.914948	+	2.81592i	−0.0349584	+	0.107591i
$686$		0			0
$687$	−37.5978	+	27.3164i	−1.43444	+	1.04218i
$688$		0			0
$689$	0.163844	+	0.504261i	0.00624198	+	0.0192108i
$690$		0			0
$691$	−1.51873	−	1.10342i	−0.0577751	−	0.0419760i	0.558523	−	0.829489i	$-0.311368\pi$
$691$	−1.51873	−	1.10342i	−0.0577751	−	0.0419760i	−0.616298	+	0.787513i	$0.711368\pi$
$692$		0			0
$693$	4.38990	−	2.83248i	0.166759	−	0.107597i
$694$		0			0
$695$	13.2884	+	9.65457i	0.504057	+	0.366219i
$696$		0			0
$697$	−0.559948	−	1.72334i	−0.0212096	−	0.0652763i
$698$		0			0
$699$	−12.2810	+	8.92266i	−0.464510	+	0.337486i
$700$		0			0
$701$	12.1980	−	37.5416i	0.460712	−	1.41792i	−0.403585	−	0.914942i	$-0.632236\pi$
$701$	12.1980	−	37.5416i	0.460712	−	1.41792i	0.864297	−	0.502983i	$-0.167764\pi$
$702$		0			0
$703$	−12.2713			−0.462822
$704$		0			0
$705$	−17.5855			−0.662308
$706$		0			0
$707$	−4.23502	+	13.0341i	−0.159274	+	0.490196i
$708$		0			0
$709$	28.1044	−	20.4191i	1.05548	−	0.766854i	0.0822367	−	0.996613i	$-0.473794\pi$
$709$	28.1044	−	20.4191i	1.05548	−	0.766854i	0.973248	+	0.229759i	$0.0737936\pi$
$710$		0			0
$711$	0.332702	+	1.02395i	0.0124773	+	0.0384012i
$712$		0			0
$713$	−8.68066	−	6.30687i	−0.325093	−	0.236194i
$714$		0			0
$715$	0.506094	+	0.412302i	0.0189269	+	0.0154192i
$716$		0			0
$717$	2.08355	+	1.51379i	0.0778118	+	0.0565336i
$718$		0			0
$719$	6.73570	+	20.7303i	0.251199	+	0.773111i	0.994555	+	0.104215i	$0.0332330\pi$
$719$	6.73570	+	20.7303i	0.251199	+	0.773111i	−0.743356	+	0.668896i	$0.766767\pi$
$720$		0			0
$721$	20.3517	−	14.7864i	0.757939	−	0.550675i
$722$		0			0
$723$	−1.71976	+	5.29287i	−0.0639585	+	0.196844i
$724$		0			0
$725$	1.37946			0.0512320
$726$		0			0
$727$	33.0916			1.22730			0.613650	−	0.789578i	$-0.289701\pi$
$727$	33.0916			1.22730			0.613650	+	0.789578i	$0.289701\pi$
$728$		0			0
$729$	6.19124	−	19.0547i	0.229305	−	0.705729i
$730$		0			0
$731$	3.52172	−	2.55868i	0.130255	−	0.0946361i
$732$		0			0
$733$	−11.6813	−	35.9515i	−0.431460	−	1.32790i	−0.896671	−	0.442698i	$-0.854021\pi$
$733$	−11.6813	−	35.9515i	−0.431460	−	1.32790i	0.465210	−	0.885200i	$-0.345979\pi$
$734$		0			0
$735$	0.782712	+	0.568674i	0.0288708	+	0.0209758i
$736$		0			0
$737$	−27.3848	−	22.3097i	−1.00873	−	0.821788i
$738$		0			0
$739$	−22.4999	−	16.3471i	−0.827671	−	0.601338i	0.0912283	−	0.995830i	$-0.470921\pi$
$739$	−22.4999	−	16.3471i	−0.827671	−	0.601338i	−0.918900	+	0.394492i	$0.870921\pi$
$740$		0			0
$741$	−0.308361	−	0.949039i	−0.0113279	−	0.0348638i
$742$		0			0
$743$	−18.3458	+	13.3290i	−0.673042	+	0.488993i	−0.871042	−	0.491208i	$-0.836555\pi$
$743$	−18.3458	+	13.3290i	−0.673042	+	0.488993i	0.198000	+	0.980202i	$0.436555\pi$
$744$		0			0
$745$	5.92805	−	18.2447i	0.217187	−	0.668433i
$746$		0			0
$747$	−3.33001			−0.121839
$748$		0			0
$749$	46.0765			1.68360
$750$		0			0
$751$	0.527015	−	1.62199i	0.0192311	−	0.0591871i	−0.940980	−	0.338461i	$-0.890094\pi$
$751$	0.527015	−	1.62199i	0.0192311	−	0.0591871i	0.960212	+	0.279274i	$0.0900937\pi$
$752$		0			0
$753$	−24.0312	+	17.4597i	−0.875746	+	0.636266i
$754$		0			0
$755$	2.79658	+	8.60698i	0.101778	+	0.313240i
$756$		0			0
$757$	6.69710	+	4.86573i	0.243410	+	0.176848i	0.702801	−	0.711386i	$-0.251932\pi$
$757$	6.69710	+	4.86573i	0.243410	+	0.176848i	−0.459391	+	0.888234i	$0.651932\pi$
$758$		0			0
$759$	−9.57588	+	6.17861i	−0.347582	+	0.224269i
$760$		0			0
$761$	11.4932	+	8.35033i	0.416630	+	0.302699i	0.776280	−	0.630388i	$-0.217104\pi$
$761$	11.4932	+	8.35033i	0.416630	+	0.302699i	−0.359651	+	0.933087i	$0.617104\pi$
$762$		0			0
$763$	8.39380	+	25.8335i	0.303876	+	0.935234i
$764$		0			0
$765$	−0.682619	+	0.495952i	−0.0246801	+	0.0179312i
$766$		0			0
$767$	0.864221	−	2.65980i	0.0312052	−	0.0960397i
$768$		0			0
$769$	−31.0174			−1.11852			−0.559258	−	0.828993i	$-0.688914\pi$
$769$	−31.0174			−1.11852			−0.559258	+	0.828993i	$0.688914\pi$
$770$		0			0
$771$	−16.8361			−0.606337
$772$		0			0
$773$	−3.77691	+	11.6241i	−0.135846	+	0.418091i	−0.995721	−	0.0924144i	$-0.970542\pi$
$773$	−3.77691	+	11.6241i	−0.135846	+	0.418091i	0.859875	+	0.510505i	$0.170542\pi$
$774$		0			0
$775$	−4.77653	+	3.47035i	−0.171578	+	0.124659i
$776$		0			0
$777$	−7.32794	−	22.5531i	−0.262888	−	0.809087i
$778$		0			0
$779$	2.67766	+	1.94543i	0.0959371	+	0.0697024i
$780$		0			0
$781$	−22.7726	−	1.26075i	−0.814869	−	0.0451133i
$782$		0			0
$783$	5.11739	+	3.71800i	0.182881	+	0.132871i
$784$		0			0
$785$	5.62084	+	17.2992i	0.200616	+	0.617434i
$786$		0			0
$787$	−6.21365	+	4.51448i	−0.221493	+	0.160924i	−0.692998	−	0.720939i	$-0.743711\pi$
$787$	−6.21365	+	4.51448i	−0.221493	+	0.160924i	0.471506	+	0.881863i	$0.343711\pi$
$788$		0			0
$789$	0.392465	−	1.20788i	0.0139721	−	0.0430018i
$790$		0			0
$791$	−34.7289			−1.23482
$792$		0			0
$793$	1.48408			0.0527014
$794$		0			0
$795$	−1.57392	+	4.84402i	−0.0558211	+	0.171800i
$796$		0			0
$797$	0.928405	−	0.674526i	0.0328858	−	0.0238929i	−0.571221	−	0.820796i	$-0.693530\pi$
$797$	0.928405	−	0.674526i	0.0328858	−	0.0238929i	0.604107	+	0.796903i	$0.293530\pi$
$798$		0			0
$799$	−4.21956	−	12.9865i	−0.149277	−	0.459428i
$800$		0			0
$801$	−8.04679	−	5.84633i	−0.284319	−	0.206570i
$802$		0			0
$803$	12.4936	−	32.2625i	0.440889	−	1.13852i
$804$		0			0
$805$	−4.02965	−	2.92771i	−0.142027	−	0.103188i
$806$		0			0
$807$	15.6058	+	48.0297i	0.549350	+	1.69073i
$808$		0			0
$809$	−0.400346	+	0.290868i	−0.0140754	+	0.0102264i	−0.594801	−	0.803873i	$-0.702769\pi$
$809$	−0.400346	+	0.290868i	−0.0140754	+	0.0102264i	0.580725	+	0.814100i	$0.302769\pi$
$810$		0			0
$811$	7.34897	−	22.6178i	0.258057	−	0.794219i	−0.735155	−	0.677900i	$-0.762890\pi$
$811$	7.34897	−	22.6178i	0.258057	−	0.794219i	0.993212	−	0.116319i	$-0.0371096\pi$
$812$		0			0
$813$	42.1793			1.47929
$814$		0			0
$815$	−6.34677			−0.222318
$816$		0			0
$817$	−2.45704	+	7.56198i	−0.0859608	+	0.264560i
$818$		0			0
$819$	0.250823	−	0.182234i	0.00876448	−	0.00636777i
$820$		0			0
$821$	12.9113	+	39.7368i	0.450606	+	1.38682i	0.876217	+	0.481917i	$0.160059\pi$
$821$	12.9113	+	39.7368i	0.450606	+	1.38682i	−0.425611	+	0.904906i	$0.639941\pi$
$822$		0			0
$823$	18.8927	+	13.7264i	0.658558	+	0.478471i	0.866176	−	0.499739i	$-0.166571\pi$
$823$	18.8927	+	13.7264i	0.658558	+	0.478471i	−0.207617	+	0.978210i	$0.566571\pi$
$824$		0			0
$825$	1.60513	+	6.06182i	0.0558835	+	0.211045i
$826$		0			0
$827$	15.5711	+	11.3130i	0.541459	+	0.393393i	0.824627	−	0.565677i	$-0.191385\pi$
$827$	15.5711	+	11.3130i	0.541459	+	0.393393i	−0.283167	+	0.959070i	$0.591385\pi$
$828$		0			0
$829$	5.44902	+	16.7704i	0.189252	+	0.582459i	0.999996	−	0.00294280i	$-0.000936725\pi$
$829$	5.44902	+	16.7704i	0.189252	+	0.582459i	−0.810743	+	0.585402i	$0.800937\pi$
$830$		0			0
$831$	−35.0282	+	25.4495i	−1.21511	+	0.882832i
$832$		0			0
$833$	−0.232143	+	0.714464i	−0.00804329	+	0.0247547i
$834$		0			0
$835$	−13.9261			−0.481932
$836$		0			0
$837$	−27.0729			−0.935778
$838$		0			0
$839$	−9.23509	+	28.4227i	−0.318831	+	0.981260i	0.655318	+	0.755353i	$0.272535\pi$
$839$	−9.23509	+	28.4227i	−0.318831	+	0.981260i	−0.974149	+	0.225907i	$0.927465\pi$
$840$		0			0
$841$	21.9220	−	15.9273i	0.755931	−	0.549216i
$842$		0			0
$843$	−16.5598	−	50.9658i	−0.570350	−	1.75536i
$844$		0			0
$845$	−10.4859	−	7.61844i	−0.360725	−	0.262082i
$846$		0			0
$847$	26.1975	−	14.9200i	0.900157	−	0.512658i
$848$		0			0
$849$	47.5036	+	34.5134i	1.63032	+	1.18450i
$850$		0			0
$851$	2.56999	+	7.90961i	0.0880981	+	0.271138i
$852$		0			0
$853$	7.10427	−	5.16155i	0.243245	−	0.176728i	−0.459483	−	0.888187i	$-0.651965\pi$
$853$	7.10427	−	5.16155i	0.243245	−	0.176728i	0.702728	+	0.711459i	$0.251965\pi$
$854$		0			0
$855$	0.476250	−	1.46575i	0.0162874	−	0.0501275i
$856$		0			0
$857$	25.6711			0.876909			0.438454	−	0.898753i	$-0.355526\pi$
$857$	25.6711			0.876909			0.438454	+	0.898753i	$0.355526\pi$
$858$		0			0
$859$	−41.5338			−1.41711			−0.708557	−	0.705654i	$-0.750654\pi$
$859$	−41.5338			−1.41711			−0.708557	+	0.705654i	$0.750654\pi$
$860$		0			0
$861$	−1.97646	+	6.08292i	−0.0673576	+	0.207305i
$862$		0			0
$863$	2.29192	−	1.66518i	0.0780178	−	0.0566833i	−0.548093	−	0.836418i	$-0.684646\pi$
$863$	2.29192	−	1.66518i	0.0780178	−	0.0566833i	0.626110	+	0.779734i	$0.284646\pi$
$864$		0			0
$865$	−7.48352	−	23.0319i	−0.254447	−	0.783108i
$866$		0			0
$867$	22.7066	+	16.4973i	0.771156	+	0.560278i
$868$		0			0
$869$	1.59035	+	6.00599i	0.0539489	+	0.203739i
$870$		0			0
$871$	−1.69582	−	1.23209i	−0.0574607	−	0.0417476i
$872$		0			0
$873$	−3.25349	−	10.0132i	−0.110114	−	0.338896i
$874$		0			0
$875$	−2.21731	+	1.61097i	−0.0749589	+	0.0544608i
$876$		0			0
$877$	8.04430	−	24.7578i	0.271637	−	0.836012i	−0.718453	−	0.695576i	$-0.755149\pi$
$877$	8.04430	−	24.7578i	0.271637	−	0.836012i	0.990090	−	0.140437i	$-0.0448506\pi$
$878$		0			0
$879$	14.8416			0.500595
$880$		0			0
$881$	−37.6862			−1.26968			−0.634841	−	0.772643i	$-0.718934\pi$
$881$	−37.6862			−1.26968			−0.634841	+	0.772643i	$0.718934\pi$
$882$		0			0
$883$	−14.6888	+	45.2076i	−0.494319	+	1.52136i	0.323696	+	0.946161i	$0.395074\pi$
$883$	−14.6888	+	45.2076i	−0.494319	+	1.52136i	−0.818015	+	0.575196i	$0.804926\pi$
$884$		0			0
$885$	21.7345	−	15.7911i	0.730598	−	0.530811i
$886$		0			0
$887$	14.7497	+	45.3949i	0.495246	+	1.52421i	0.816572	+	0.577243i	$0.195872\pi$
$887$	14.7497	+	45.3949i	0.495246	+	1.52421i	−0.321326	+	0.946969i	$0.604128\pi$
$888$		0			0
$889$	23.1497	+	16.8192i	0.776415	+	0.564098i
$890$		0			0
$891$	−12.4487	+	32.1464i	−0.417046	+	1.07695i
$892$		0			0
$893$	20.1778	+	14.6600i	0.675225	+	0.490580i
$894$		0			0
$895$	−0.438716	−	1.35023i	−0.0146647	−	0.0451332i
$896$		0			0
$897$	−0.547132	+	0.397515i	−0.0182682	+	0.0132726i
$898$		0			0
$899$	2.51679	−	7.74588i	0.0839396	−	0.258340i
$900$		0			0
$901$	−3.95484			−0.131755
$902$		0			0
$903$	−15.3651			−0.511320
$904$		0			0
$905$	−1.73942	+	5.35340i	−0.0578204	+	0.177953i
$906$		0			0
$907$	−27.2746	+	19.8161i	−0.905637	+	0.657984i	−0.939908	−	0.341429i	$-0.889089\pi$
$907$	−27.2746	+	19.8161i	−0.905637	+	0.657984i	0.0342706	+	0.999413i	$0.489089\pi$
$908$		0			0
$909$	0.888088	+	2.73325i	0.0294560	+	0.0906563i
$910$		0			0
$911$	−31.5226	−	22.9025i	−1.04439	−	0.758793i	−0.0732513	−	0.997314i	$-0.523338\pi$
$911$	−31.5226	−	22.9025i	−1.04439	−	0.758793i	−0.971137	+	0.238521i	$0.923338\pi$
$912$		0			0
$913$	−19.1871	−	1.06225i	−0.634999	−	0.0351552i
$914$		0			0
$915$	11.5336	+	8.37969i	0.381291	+	0.277024i
$916$		0			0
$917$	17.7465	+	54.6181i	0.586041	+	1.80365i
$918$		0			0
$919$	−10.1459	+	7.37146i	−0.334684	+	0.243162i	−0.742415	−	0.669940i	$-0.766320\pi$
$919$	−10.1459	+	7.37146i	−0.334684	+	0.243162i	0.407732	+	0.913102i	$0.366320\pi$
$920$		0			0
$921$	5.87769	−	18.0897i	0.193676	−	0.596075i
$922$		0			0
$923$	−1.35348			−0.0445505
$924$		0			0
$925$	4.57623			0.150466
$926$		0			0
$927$	1.63015	−	5.01707i	0.0535410	−	0.164782i
$928$		0			0
$929$	−21.4840	+	15.6090i	−0.704867	+	0.512115i	−0.881514	−	0.472159i	$-0.843475\pi$
$929$	−21.4840	+	15.6090i	−0.704867	+	0.512115i	0.176647	+	0.984274i	$0.443475\pi$
$930$		0			0
$931$	−0.424022	−	1.30501i	−0.0138968	−	0.0427698i
$932$		0			0
$933$	34.2096	+	24.8548i	1.11997	+	0.813708i
$934$		0			0
$935$	−4.09136	+	2.63985i	−0.133802	+	0.0863325i
$936$		0			0
$937$	−0.458446	−	0.333080i	−0.0149768	−	0.0108813i	0.580272	−	0.814423i	$-0.302946\pi$
$937$	−0.458446	−	0.333080i	−0.0149768	−	0.0108813i	−0.595248	+	0.803542i	$0.702946\pi$
$938$		0			0
$939$	10.6035	+	32.6341i	0.346031	+	1.06497i
$940$		0			0
$941$	−9.26957	+	6.73474i	−0.302179	+	0.219546i	−0.728533	−	0.685010i	$-0.759798\pi$
$941$	−9.26957	+	6.73474i	−0.302179	+	0.219546i	0.426354	+	0.904556i	$0.359798\pi$
$942$		0			0
$943$	0.693166	−	2.13334i	0.0225726	−	0.0694713i
$944$		0			0
$945$	−12.5675			−0.408822
$946$		0			0
$947$	30.2412			0.982707			0.491354	−	0.870960i	$-0.336502\pi$
$947$	30.2412			0.982707			0.491354	+	0.870960i	$0.336502\pi$
$948$		0			0
$949$	0.634450	−	1.95264i	0.0205951	−	0.0633852i
$950$		0			0
$951$	3.84941	−	2.79676i	0.124826	−	0.0906912i
$952$		0			0
$953$	12.9093	+	39.7307i	0.418173	+	1.28700i	0.909382	+	0.415962i	$0.136555\pi$
$953$	12.9093	+	39.7307i	0.418173	+	1.28700i	−0.491209	+	0.871042i	$0.663445\pi$
$954$		0			0
$955$	−1.81429	−	1.31816i	−0.0587092	−	0.0426547i
$956$		0			0
$957$	−6.70644	−	5.46356i	−0.216788	−	0.176612i
$958$		0			0
$959$	6.56510	+	4.76982i	0.211998	+	0.154026i
$960$		0			0
$961$	1.19235	+	3.66967i	0.0384629	+	0.118377i
$962$		0			0
$963$	7.81694	−	5.67934i	0.251898	−	0.183014i
$964$		0			0
$965$	2.87602	−	8.85147i	0.0925823	−	0.284939i
$966$		0			0
$967$	13.9026			0.447078			0.223539	−	0.974695i	$-0.428239\pi$
$967$	13.9026			0.447078			0.223539	+	0.974695i	$0.428239\pi$
$968$		0			0
$969$	7.44316			0.239109
$970$		0			0
$971$	−1.62233	+	4.99302i	−0.0520631	+	0.160234i	−0.973708	−	0.227802i	$-0.926846\pi$
$971$	−1.62233	+	4.99302i	−0.0520631	+	0.160234i	0.921644	+	0.388035i	$0.126846\pi$
$972$		0			0
$973$	36.4201	−	26.4608i	1.16757	−	0.848293i
$974$		0			0
$975$	0.114994	+	0.353916i	0.00368276	+	0.0113344i
$976$		0			0
$977$	−42.9202	−	31.1833i	−1.37314	−	0.997643i	−0.997485	−	0.0708833i	$-0.977418\pi$
$977$	−42.9202	−	31.1833i	−1.37314	−	0.997643i	−0.375654	−	0.926760i	$-0.622582\pi$
$978$		0			0
$979$	−44.4995	−	36.2526i	−1.42221	−	1.15864i
$980$		0			0
$981$	4.60823	+	3.34807i	0.147129	+	0.106896i
$982$		0			0
$983$	0.444147	+	1.36694i	0.0141661	+	0.0435988i	0.957890	−	0.287136i	$-0.0927033\pi$
$983$	0.444147	+	1.36694i	0.0141661	+	0.0435988i	−0.943724	+	0.330735i	$0.892703\pi$
$984$		0			0
$985$	11.6446	−	8.46029i	0.371027	−	0.269567i
$986$		0			0
$987$	−14.8938	+	45.8385i	−0.474076	+	1.45906i
$988$		0			0
$989$	5.38872			0.171351
$990$		0			0
$991$	−22.6101			−0.718234			−0.359117	−	0.933292i	$-0.616922\pi$
$991$	−22.6101			−0.718234			−0.359117	+	0.933292i	$0.616922\pi$
$992$		0			0
$993$	−4.40849	+	13.5679i	−0.139899	+	0.430566i
$994$		0			0
$995$	2.43445	−	1.76873i	0.0771774	−	0.0560727i
$996$		0			0
$997$	−18.2495	−	56.1662i	−0.577968	−	1.77880i	−0.625843	−	0.779949i	$-0.715245\pi$
$997$	−18.2495	−	56.1662i	−0.577968	−	1.77880i	0.0478747	−	0.998853i	$-0.484755\pi$
$998$		0			0
$999$	16.9764	+	12.3341i	0.537111	+	0.390234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.b.81.3	✓	12
4.3	odd	2		880.2.bo.j.81.1		12
11.3	even	5	inner	440.2.y.b.201.3	yes	12
11.5	even	5		4840.2.a.bf.1.5		6
11.6	odd	10		4840.2.a.be.1.5		6
44.3	odd	10		880.2.bo.j.641.1		12
44.27	odd	10		9680.2.a.cx.1.2		6
44.39	even	10		9680.2.a.cy.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.81.3	✓	12	1.1	even	1	trivial
440.2.y.b.201.3	yes	12	11.3	even	5	inner
880.2.bo.j.81.1		12	4.3	odd	2
880.2.bo.j.641.1		12	44.3	odd	10
4840.2.a.be.1.5		6	11.6	odd	10
4840.2.a.bf.1.5		6	11.5	even	5
9680.2.a.cx.1.2		6	44.27	odd	10
9680.2.a.cy.1.2		6	44.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.584258 - 1.79816i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.846938 - 2.60661i) q^{7} +(-0.464972 - 0.337822i) q^{9} +(-2.57134 - 2.09480i) q^{11} +(-0.159232 - 0.115689i) q^{13} +(-0.584258 - 1.79816i) q^{15} +(1.18771 - 0.862919i) q^{17} +(-0.828640 + 2.55029i) q^{19} -5.18193 q^{21} +1.81736 q^{23} +(0.309017 - 0.951057i) q^{25} +(3.70970 - 2.69525i) q^{27} +(0.426278 + 1.31195i) q^{29} +(-4.77653 - 3.47035i) q^{31} +(-5.26912 + 3.39978i) q^{33} +(-2.21731 - 1.61097i) q^{35} +(1.41413 + 4.35226i) q^{37} +(-0.301059 + 0.218732i) q^{39} +(0.381414 - 1.17387i) q^{41} +2.96514 q^{43} -0.574737 q^{45} +(2.87419 - 8.84584i) q^{47} +(-0.413981 + 0.300774i) q^{49} +(-0.857741 - 2.63985i) q^{51} +(-2.17939 - 1.58342i) q^{53} +(-3.31155 - 0.183336i) q^{55} +(4.10170 + 2.98006i) q^{57} +(4.39089 + 13.5138i) q^{59} +(-6.10021 + 4.43206i) q^{61} +(-0.486767 + 1.49811i) q^{63} -0.196821 q^{65} +10.6500 q^{67} +(1.06181 - 3.26790i) q^{69} +(5.56338 - 4.04203i) q^{71} +(3.22348 + 9.92086i) q^{73} +(-1.52961 - 1.11132i) q^{75} +(-3.28257 + 8.47665i) q^{77} +(-1.51552 - 1.10109i) q^{79} +(-3.21189 - 9.88518i) q^{81} +(4.68742 - 3.40561i) q^{83} +(0.453664 - 1.39623i) q^{85} +2.60815 q^{87} +17.3060 q^{89} +(-0.166695 + 0.513036i) q^{91} +(-9.03097 + 6.56138i) q^{93} +(0.828640 + 2.55029i) q^{95} +(14.8203 + 10.7675i) q^{97} +(0.487931 + 1.84268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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