LMFDB - Embedded newform 380.2.bh.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927188 + 0.432355i) q^{3} +(0.140904 - 2.23162i) q^{5} +(-0.231730 - 0.864827i) q^{7} +(-1.25562 + 1.49639i) q^{9} +O(q^{10})$	\(q+(-0.927188 + 0.432355i) q^{3} +(0.140904 - 2.23162i) q^{5} +(-0.231730 - 0.864827i) q^{7} +(-1.25562 + 1.49639i) q^{9} +(-3.29119 - 5.70051i) q^{11} +(-2.04641 + 4.38853i) q^{13} +(0.834209 + 2.13006i) q^{15} +(0.154168 - 1.76215i) q^{17} +(-3.61204 - 2.43990i) q^{19} +(0.588769 + 0.701667i) q^{21} +(5.10986 - 3.57796i) q^{23} +(-4.96029 - 0.628891i) q^{25} +(1.31157 - 4.89484i) q^{27} +(-3.21899 - 2.70106i) q^{29} +(-2.00481 - 1.15748i) q^{31} +(5.51619 + 3.86248i) q^{33} +(-1.96262 + 0.395276i) q^{35} +(-3.30447 - 3.30447i) q^{37} -4.95377i q^{39} +(-2.25386 + 6.19243i) q^{41} +(1.82673 - 2.60884i) q^{43} +(3.16245 + 3.01291i) q^{45} +(5.57863 - 0.488067i) q^{47} +(5.36795 - 3.09919i) q^{49} +(0.618932 + 1.70050i) q^{51} +(6.39127 + 9.12769i) q^{53} +(-13.1851 + 6.54147i) q^{55} +(4.40395 + 0.700564i) q^{57} +(1.36717 - 1.14719i) q^{59} +(1.13891 - 6.45906i) q^{61} +(1.58508 + 0.739134i) q^{63} +(9.50521 + 5.18517i) q^{65} +(0.953238 + 10.8956i) q^{67} +(-3.19085 + 5.52671i) q^{69} +(-10.2750 + 1.81176i) q^{71} +(3.06340 + 6.56949i) q^{73} +(4.87103 - 1.56151i) q^{75} +(-4.16729 + 4.16729i) q^{77} +(-1.84631 - 0.672002i) q^{79} +(-0.117372 - 0.665647i) q^{81} +(-15.1740 + 4.06586i) q^{83} +(-3.91074 - 0.592340i) q^{85} +(4.15243 + 1.11264i) q^{87} +(13.1850 - 4.79895i) q^{89} +(4.26953 + 0.752834i) q^{91} +(2.35928 + 0.206410i) q^{93} +(-5.95390 + 7.71693i) q^{95} +(12.2510 + 1.07182i) q^{97} +(12.6626 + 2.23276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−0.927188	+	0.432355i	−0.535312	+	0.249620i	−0.671424	−	0.741073i	$-0.734317\pi$
$3$	−0.927188	+	0.432355i	−0.535312	+	0.249620i	0.136112	+	0.990693i	$0.456539\pi$
$4$		0			0
$5$	0.140904	−	2.23162i	0.0630143	−	0.998013i
$5$	0.140904	−	2.23162i	0.0630143	−	0.998013i
$6$		0			0
$7$	−0.231730	−	0.864827i	−0.0875856	−	0.326874i	0.908206	−	0.418524i	$-0.137452\pi$
$7$	−0.231730	−	0.864827i	−0.0875856	−	0.326874i	−0.995791	+	0.0916503i	$0.970786\pi$
$8$		0			0
$9$	−1.25562	+	1.49639i	−0.418539	+	0.498795i
$10$		0			0
$11$	−3.29119	−	5.70051i	−0.992331	−	1.71877i	−0.603213	−	0.797580i	$-0.706113\pi$
$11$	−3.29119	−	5.70051i	−0.992331	−	1.71877i	−0.389118	−	0.921188i	$-0.627220\pi$
$12$		0			0
$13$	−2.04641	+	4.38853i	−0.567571	+	1.21716i	0.387798	+	0.921744i	$0.373236\pi$
$13$	−2.04641	+	4.38853i	−0.567571	+	1.21716i	−0.955369	+	0.295416i	$0.904542\pi$
$14$		0			0
$15$	0.834209	+	2.13006i	0.215392	+	0.549978i
$16$		0			0
$17$	0.154168	−	1.76215i	0.0373913	−	0.427384i	−0.954310	−	0.298819i	$-0.903407\pi$
$17$	0.154168	−	1.76215i	0.0373913	−	0.427384i	0.991701	−	0.128565i	$-0.0410372\pi$
$18$		0			0
$19$	−3.61204	−	2.43990i	−0.828660	−	0.559752i
$19$	−3.61204	−	2.43990i	−0.828660	−	0.559752i
$20$		0			0
$21$	0.588769	+	0.701667i	0.128480	+	0.153116i
$22$		0			0
$23$	5.10986	−	3.57796i	1.06548	−	0.746056i	0.0970331	−	0.995281i	$-0.469065\pi$
$23$	5.10986	−	3.57796i	1.06548	−	0.746056i	0.968446	+	0.249225i	$0.0801758\pi$
$24$		0			0
$25$	−4.96029	−	0.628891i	−0.992058	−	0.125778i
$26$		0			0
$27$	1.31157	−	4.89484i	0.252411	−	0.942012i
$28$		0			0
$29$	−3.21899	−	2.70106i	−0.597752	−	0.501574i	0.292970	−	0.956122i	$-0.405356\pi$
$29$	−3.21899	−	2.70106i	−0.597752	−	0.501574i	−0.890722	+	0.454548i	$0.849801\pi$
$30$		0			0
$31$	−2.00481	−	1.15748i	−0.360075	−	0.207889i	0.309039	−	0.951049i	$-0.399993\pi$
$31$	−2.00481	−	1.15748i	−0.360075	−	0.207889i	−0.669113	+	0.743160i	$0.733326\pi$
$32$		0			0
$33$	5.51619	+	3.86248i	0.960246	+	0.672372i
$34$		0			0
$35$	−1.96262	+	0.395276i	−0.331743	+	0.0668138i
$36$		0			0
$37$	−3.30447	−	3.30447i	−0.543251	−	0.543251i	0.381229	−	0.924481i	$-0.375501\pi$
$37$	−3.30447	−	3.30447i	−0.543251	−	0.543251i	−0.924481	+	0.381229i	$0.875501\pi$
$38$		0			0
$39$		−	4.95377i		−	0.793238i
$40$		0			0
$41$	−2.25386	+	6.19243i	−0.351994	+	0.967096i	0.629735	+	0.776810i	$0.283164\pi$
$41$	−2.25386	+	6.19243i	−0.351994	+	0.967096i	−0.981729	+	0.190285i	$0.939059\pi$
$42$		0			0
$43$	1.82673	−	2.60884i	0.278574	−	0.397845i	−0.655345	−	0.755330i	$-0.727477\pi$
$43$	1.82673	−	2.60884i	0.278574	−	0.397845i	0.933919	+	0.357485i	$0.116366\pi$
$44$		0			0
$45$	3.16245	+	3.01291i	0.471430	+	0.449138i
$46$		0			0
$47$	5.57863	−	0.488067i	0.813727	−	0.0711919i	0.327308	−	0.944918i	$-0.393858\pi$
$47$	5.57863	−	0.488067i	0.813727	−	0.0711919i	0.486419	+	0.873726i	$0.338303\pi$
$48$		0			0
$49$	5.36795	−	3.09919i	0.766850	−	0.442741i
$50$		0			0
$51$	0.618932	+	1.70050i	0.0866678	+	0.238118i
$52$		0			0
$53$	6.39127	+	9.12769i	0.877909	+	1.25378i	0.966227	+	0.257692i	$0.0829619\pi$
$53$	6.39127	+	9.12769i	0.877909	+	1.25378i	−0.0883182	+	0.996092i	$0.528149\pi$
$54$		0			0
$55$	−13.1851	+	6.54147i	−1.77788	+	0.882052i
$56$		0			0
$57$	4.40395	+	0.700564i	0.583317	+	0.0927920i
$58$		0			0
$59$	1.36717	−	1.14719i	0.177991	−	0.149352i	−0.549440	−	0.835533i	$-0.685159\pi$
$59$	1.36717	−	1.14719i	0.177991	−	0.149352i	0.727430	+	0.686181i	$0.240714\pi$
$60$		0			0
$61$	1.13891	−	6.45906i	0.145822	−	0.826998i	−0.820881	−	0.571099i	$-0.806517\pi$
$61$	1.13891	−	6.45906i	0.145822	−	0.826998i	0.966703	−	0.255900i	$-0.0823716\pi$
$62$		0			0
$63$	1.58508	+	0.739134i	0.199701	+	0.0931221i
$64$		0			0
$65$	9.50521	+	5.18517i	1.17898	+	0.643142i
$66$		0			0
$67$	0.953238	+	10.8956i	0.116457	+	1.33110i	0.799473	+	0.600702i	$0.205112\pi$
$67$	0.953238	+	10.8956i	0.116457	+	1.33110i	−0.683017	+	0.730403i	$0.739332\pi$
$68$		0			0
$69$	−3.19085	+	5.52671i	−0.384133	+	0.665338i
$70$		0			0
$71$	−10.2750	+	1.81176i	−1.21942	+	0.215016i	−0.746075	−	0.665862i	$-0.768064\pi$
$71$	−10.2750	+	1.81176i	−1.21942	+	0.215016i	−0.473343	+	0.880878i	$0.656953\pi$
$72$		0			0
$73$	3.06340	+	6.56949i	0.358544	+	0.768901i	0.999998	+	0.00173942i	$0.000553676\pi$
$73$	3.06340	+	6.56949i	0.358544	+	0.768901i	−0.641454	+	0.767161i	$0.721669\pi$
$74$		0			0
$75$	4.87103	−	1.56151i	0.562458	−	0.180307i
$76$		0			0
$77$	−4.16729	+	4.16729i	−0.474906	+	0.474906i
$78$		0			0
$79$	−1.84631	−	0.672002i	−0.207726	−	0.0756061i	0.236062	−	0.971738i	$-0.424143\pi$
$79$	−1.84631	−	0.672002i	−0.207726	−	0.0756061i	−0.443788	+	0.896132i	$0.646366\pi$
$80$		0			0
$81$	−0.117372	−	0.665647i	−0.0130413	−	0.0739608i
$82$		0			0
$83$	−15.1740	+	4.06586i	−1.66556	+	0.446287i	−0.963909	−	0.266231i	$-0.914222\pi$
$83$	−15.1740	+	4.06586i	−1.66556	+	0.446287i	−0.701655	+	0.712517i	$0.747555\pi$
$84$		0			0
$85$	−3.91074	−	0.592340i	−0.424179	−	0.0642483i
$86$		0			0
$87$	4.15243	+	1.11264i	0.445187	+	0.119287i
$88$		0			0
$89$	13.1850	−	4.79895i	1.39761	−	0.508688i	0.470140	−	0.882592i	$-0.344203\pi$
$89$	13.1850	−	4.79895i	1.39761	−	0.508688i	0.927467	+	0.373904i	$0.121981\pi$
$90$		0			0
$91$	4.26953	+	0.752834i	0.447569	+	0.0789184i
$92$		0			0
$93$	2.35928	+	0.206410i	0.244646	+	0.0214037i
$94$		0			0
$95$	−5.95390	+	7.71693i	−0.610857	+	0.791741i
$96$		0			0
$97$	12.2510	+	1.07182i	1.24390	+	0.108827i	0.690031	−	0.723779i	$-0.257597\pi$
$97$	12.2510	+	1.07182i	1.24390	+	0.108827i	0.553865	+	0.832606i	$0.313152\pi$
$98$		0			0
$99$	12.6626	+	2.23276i	1.27264	+	0.224401i
$100$		0			0
$101$	2.19784	−	0.799949i	0.218693	−	0.0795979i	−0.230350	−	0.973108i	$-0.573987\pi$
$101$	2.19784	−	0.799949i	0.218693	−	0.0795979i	0.449043	+	0.893510i	$0.351765\pi$
$102$		0			0
$103$	1.36414	+	0.365519i	0.134412	+	0.0360157i	0.325398	−	0.945577i	$-0.394502\pi$
$103$	1.36414	+	0.365519i	0.134412	+	0.0360157i	−0.190986	+	0.981593i	$0.561168\pi$
$104$		0			0
$105$	1.64882	−	1.21504i	0.160908	−	0.118576i
$106$		0			0
$107$	18.4313	−	4.93865i	1.78182	−	0.477437i	0.790906	−	0.611937i	$-0.209610\pi$
$107$	18.4313	−	4.93865i	1.78182	−	0.477437i	0.990914	+	0.134500i	$0.0429429\pi$
$108$		0			0
$109$	−3.00343	−	17.0333i	−0.287676	−	1.63149i	−0.695567	−	0.718461i	$-0.744847\pi$
$109$	−3.00343	−	17.0333i	−0.287676	−	1.63149i	0.407891	−	0.913030i	$-0.366264\pi$
$110$		0			0
$111$	4.49257	+	1.63516i	0.426415	+	0.155203i
$112$		0			0
$113$	4.01429	−	4.01429i	0.377632	−	0.377632i	−0.492615	−	0.870247i	$-0.663959\pi$
$113$	4.01429	−	4.01429i	0.377632	−	0.377632i	0.870247	+	0.492615i	$0.163959\pi$
$114$		0			0
$115$	−7.26466	−	11.9074i	−0.677433	−	1.11037i
$116$		0			0
$117$	−3.99743	−	8.57252i	−0.369563	−	0.792530i
$118$		0			0
$119$	−1.55968	+	0.275014i	−0.142976	+	0.0252105i
$120$		0			0
$121$	−16.1639	+	27.9966i	−1.46944	+	2.54515i
$122$		0			0
$123$	−0.587575	−	6.71602i	−0.0529799	−	0.605563i
$124$		0			0
$125$	−2.10237	+	10.9809i	−0.188042	+	0.982161i
$126$		0			0
$127$	−14.4882	−	6.75594i	−1.28562	−	0.599493i	−0.344885	−	0.938645i	$-0.612082\pi$
$127$	−14.4882	−	6.75594i	−1.28562	−	0.599493i	−0.940732	+	0.339152i	$0.889860\pi$
$128$		0			0
$129$	−0.565778	+	3.20869i	−0.0498140	+	0.282509i
$130$		0			0
$131$	5.36070	−	4.49816i	0.468366	−	0.393006i	−0.377832	−	0.925874i	$-0.623330\pi$
$131$	5.36070	−	4.49816i	0.468366	−	0.393006i	0.846198	+	0.532868i	$0.178886\pi$
$132$		0			0
$133$	−1.27308	+	3.68919i	−0.110390	+	0.319893i
$134$		0			0
$135$	−10.7386	−	3.61663i	−0.924235	−	0.311270i
$136$		0			0
$137$	−7.84956	−	11.2103i	−0.670633	−	0.957763i	−0.999908	−	0.0135290i	$-0.995693\pi$
$137$	−7.84956	−	11.2103i	−0.670633	−	0.957763i	0.329276	−	0.944234i	$-0.393195\pi$
$138$		0			0
$139$	−0.972536	−	2.67202i	−0.0824894	−	0.226638i	0.891590	−	0.452843i	$-0.149590\pi$
$139$	−0.972536	−	2.67202i	−0.0824894	−	0.226638i	−0.974080	+	0.226205i	$0.927368\pi$
$140$		0			0
$141$	−4.96142	+	2.86448i	−0.417827	+	0.241233i
$142$		0			0
$143$	31.7520	−	2.77794i	2.65523	−	0.232303i
$144$		0			0
$145$	−6.48131	+	6.80299i	−0.538244	+	0.564958i
$146$		0			0
$147$	−3.63715	+	5.19439i	−0.299987	+	0.428426i
$148$		0			0
$149$	−2.10420	+	5.78124i	−0.172383	+	0.473618i	−0.995556	−	0.0941727i	$-0.969979\pi$
$149$	−2.10420	+	5.78124i	−0.172383	+	0.473618i	0.823173	+	0.567791i	$0.192202\pi$
$150$		0			0
$151$			4.53944i			0.369415i	0.982794	+	0.184707i	$0.0591337\pi$
$151$			4.53944i			0.369415i	−0.982794	+	0.184707i	$0.940866\pi$
$152$		0			0
$153$	2.44328	+	2.44328i	0.197527	+	0.197527i
$154$		0			0
$155$	−2.86554	+	4.31089i	−0.230166	+	0.346259i
$156$		0			0
$157$	−5.61762	−	3.93350i	−0.448335	−	0.313927i	0.327514	−	0.944846i	$-0.393789\pi$
$157$	−5.61762	−	3.93350i	−0.448335	−	0.313927i	−0.775849	+	0.630919i	$0.782678\pi$
$158$		0			0
$159$	−9.87231	−	5.69978i	−0.782925	−	0.452022i
$160$		0			0
$161$	−4.27842	−	3.59002i	−0.337187	−	0.282933i
$162$		0			0
$163$	−0.880739	+	3.28696i	−0.0689848	+	0.257455i	−0.991802	−	0.127783i	$-0.959214\pi$
$163$	−0.880739	+	3.28696i	−0.0689848	+	0.257455i	0.922817	+	0.385238i	$0.125881\pi$
$164$		0			0
$165$	9.39686	−	11.7658i	0.731545	−	0.915969i
$166$		0			0
$167$	7.56611	−	5.29785i	0.585484	−	0.409960i	−0.242957	−	0.970037i	$-0.578117\pi$
$167$	7.56611	−	5.29785i	0.585484	−	0.409960i	0.828441	+	0.560077i	$0.189228\pi$
$168$		0			0
$169$	−6.71520	−	8.00287i	−0.516554	−	0.615605i
$170$		0			0
$171$	8.18638	−	2.34143i	0.626028	−	0.179053i
$172$		0			0
$173$	1.19177	−	13.6220i	0.0906085	−	1.03566i	−0.805728	−	0.592286i	$-0.798226\pi$
$173$	1.19177	−	13.6220i	0.0906085	−	1.03566i	0.896336	−	0.443374i	$-0.146219\pi$
$174$		0			0
$175$	0.605565	+	4.43553i	0.0457764	+	0.335294i
$176$		0			0
$177$	−0.771630	+	1.65477i	−0.0579993	+	0.124380i
$178$		0			0
$179$	−2.30145	−	3.98623i	−0.172019	−	0.297945i	0.767107	−	0.641519i	$-0.221696\pi$
$179$	−2.30145	−	3.98623i	−0.172019	−	0.297945i	−0.939126	+	0.343574i	$0.888362\pi$
$180$		0			0
$181$	12.1190	−	14.4429i	0.900801	−	1.07353i	−0.0961391	−	0.995368i	$-0.530649\pi$
$181$	12.1190	−	14.4429i	0.900801	−	1.07353i	0.996940	−	0.0781653i	$-0.0249062\pi$
$182$		0			0
$183$	1.73663	+	6.48118i	0.128375	+	0.479102i
$184$		0			0
$185$	−7.83994	+	6.90872i	−0.576404	+	0.507939i
$186$		0			0
$187$	−10.5526	+	4.92074i	−0.771679	+	0.359840i
$188$		0			0
$189$	−4.53712			−0.330027
$190$		0			0
$191$	3.67012			0.265560			0.132780	−	0.991146i	$-0.457610\pi$
$191$	3.67012			0.265560			0.132780	+	0.991146i	$0.457610\pi$
$192$		0			0
$193$	−12.7871	+	5.96272i	−0.920436	+	0.429206i	−0.824294	−	0.566161i	$-0.808428\pi$
$193$	−12.7871	+	5.96272i	−0.920436	+	0.429206i	−0.0961414	+	0.995368i	$0.530650\pi$
$194$		0			0
$195$	−11.0549	−	0.698007i	−0.791661	−	0.0499853i
$196$		0			0
$197$	−4.10619	−	15.3245i	−0.292554	−	1.09183i	−0.943141	−	0.332394i	$-0.892144\pi$
$197$	−4.10619	−	15.3245i	−0.292554	−	1.09183i	0.650587	−	0.759432i	$-0.274523\pi$
$198$		0			0
$199$	−6.47741	+	7.71948i	−0.459172	+	0.547219i	−0.945101	−	0.326779i	$-0.894037\pi$
$199$	−6.47741	+	7.71948i	−0.459172	+	0.547219i	0.485929	+	0.873998i	$0.338481\pi$
$200$		0			0
$201$	−5.59458	−	9.69009i	−0.394611	−	0.683486i
$202$		0			0
$203$	−1.59001	+	3.40979i	−0.111597	+	0.239320i
$204$		0			0
$205$	13.5016	+	5.90231i	0.942993	+	0.412235i
$206$		0			0
$207$	−1.06201	+	12.1389i	−0.0738150	+	0.843709i
$208$		0			0
$209$	−2.02077	+	28.6207i	−0.139779	+	1.97973i
$210$		0			0
$211$	−12.9235	−	15.4017i	−0.889693	−	1.06029i	−0.997809	−	0.0661562i	$-0.978926\pi$
$211$	−12.9235	−	15.4017i	−0.889693	−	1.06029i	0.108117	−	0.994138i	$-0.465518\pi$
$212$		0			0
$213$	8.74354	−	6.12229i	0.599097	−	0.419492i
$214$		0			0
$215$	−5.56457	−	4.44418i	−0.379500	−	0.303090i
$216$		0			0
$217$	−0.536444	+	2.00204i	−0.0364162	+	0.135907i
$218$		0			0
$219$	−5.68070	−	4.76668i	−0.383866	−	0.322102i
$220$		0			0
$221$	7.41777	+	4.28265i	0.498973	+	0.288082i
$222$		0			0
$223$	−7.29501	−	5.10802i	−0.488510	−	0.342058i	0.303229	−	0.952918i	$-0.401935\pi$
$223$	−7.29501	−	5.10802i	−0.488510	−	0.342058i	−0.791739	+	0.610859i	$0.790824\pi$
$224$		0			0
$225$	7.16928	−	6.63286i	0.477952	−	0.442191i
$226$		0			0
$227$	−2.08941	−	2.08941i	−0.138679	−	0.138679i	0.634359	−	0.773038i	$-0.281264\pi$
$227$	−2.08941	−	2.08941i	−0.138679	−	0.138679i	−0.773038	+	0.634359i	$0.781264\pi$
$228$		0			0
$229$		−	13.6171i		−	0.899842i	−0.893068	−	0.449921i	$-0.851452\pi$
$229$		−	13.6171i		−	0.899842i	0.893068	−	0.449921i	$-0.148548\pi$
$230$		0			0
$231$	2.06211	−	5.66560i	0.135677	−	0.372769i
$232$		0			0
$233$	−4.86394	+	6.94643i	−0.318647	+	0.455076i	−0.946240	−	0.323467i	$-0.895152\pi$
$233$	−4.86394	+	6.94643i	−0.318647	+	0.455076i	0.627592	+	0.778542i	$0.284041\pi$
$234$		0			0
$235$	−0.303129	−	12.5182i	−0.0197740	−	0.816596i
$236$		0			0
$237$	2.00242	−	0.175189i	0.130071	−	0.0113797i
$238$		0			0
$239$	6.83842	−	3.94816i	0.442340	−	0.255385i	−0.262249	−	0.965000i	$-0.584464\pi$
$239$	6.83842	−	3.94816i	0.442340	−	0.255385i	0.704590	+	0.709615i	$0.251131\pi$
$240$		0			0
$241$	2.16596	+	5.95092i	0.139522	+	0.383333i	0.989699	−	0.143164i	$-0.0457276\pi$
$241$	2.16596	+	5.95092i	0.139522	+	0.383333i	−0.850177	+	0.526496i	$0.823505\pi$
$242$		0			0
$243$	9.11644	+	13.0196i	0.584820	+	0.835209i
$244$		0			0
$245$	−6.15986	−	12.4159i	−0.393539	−	0.793225i
$246$		0			0
$247$	18.0993	−	10.8585i	1.15163	−	0.690913i
$248$		0			0
$249$	12.3113	−	10.3304i	0.780195	−	0.654661i
$250$		0			0
$251$	3.02348	−	17.1470i	0.190841	−	1.08231i	−0.727378	−	0.686237i	$-0.759261\pi$
$251$	3.02348	−	17.1470i	0.190841	−	1.08231i	0.918219	−	0.396074i	$-0.129628\pi$
$252$		0			0
$253$	−37.2137	−	17.3530i	−2.33961	−	1.09098i
$254$		0			0
$255$	3.88209	−	1.14161i	0.243106	−	0.0714907i
$256$		0			0
$257$	1.50409	+	17.1918i	0.0938225	+	1.07240i	0.886492	+	0.462744i	$0.153135\pi$
$257$	1.50409	+	17.1918i	0.0938225	+	1.07240i	−0.792669	+	0.609652i	$0.791309\pi$
$258$		0			0
$259$	−2.09205	+	3.62354i	−0.129994	+	0.225156i
$260$		0			0
$261$	8.08364	−	1.42536i	0.500365	−	0.0882278i
$262$		0			0
$263$	−3.34583	−	7.17515i	−0.206313	−	0.442439i	0.775738	−	0.631055i	$-0.217378\pi$
$263$	−3.34583	−	7.17515i	−0.206313	−	0.442439i	−0.982051	+	0.188616i	$0.939600\pi$
$264$		0			0
$265$	21.2701	−	12.9768i	1.30661	−	0.797158i
$266$		0			0
$267$	−10.1501	+	10.1501i	−0.621178	+	0.621178i
$268$		0			0
$269$	0.0678698	+	0.0247026i	0.00413810	+	0.00150614i	0.344088	−	0.938937i	$-0.388188\pi$
$269$	0.0678698	+	0.0247026i	0.00413810	+	0.00150614i	−0.339950	+	0.940443i	$0.610410\pi$
$270$		0			0
$271$	1.72211	+	9.76656i	0.104611	+	0.593276i	0.991375	+	0.131055i	$0.0418364\pi$
$271$	1.72211	+	9.76656i	0.104611	+	0.593276i	−0.886764	+	0.462222i	$0.847052\pi$
$272$		0			0
$273$	−4.28415	+	1.14793i	−0.259289	+	0.0694762i
$274$		0			0
$275$	12.7403	+	30.3460i	0.768267	+	1.82993i
$276$		0			0
$277$	−1.86145	−	0.498774i	−0.111844	−	0.0299684i	0.202463	−	0.979290i	$-0.435105\pi$
$277$	−1.86145	−	0.498774i	−0.111844	−	0.0299684i	−0.314307	+	0.949321i	$0.601772\pi$
$278$		0			0
$279$	4.24930	−	1.54662i	0.254399	−	0.0925937i
$280$		0			0
$281$	2.96336	+	0.522520i	0.176779	+	0.0311709i	0.261337	−	0.965248i	$-0.415837\pi$
$281$	2.96336	+	0.522520i	0.176779	+	0.0311709i	−0.0845578	+	0.996419i	$0.526948\pi$
$282$		0			0
$283$	8.07309	+	0.706303i	0.479895	+	0.0419854i	0.324537	−	0.945873i	$-0.394791\pi$
$283$	8.07309	+	0.706303i	0.479895	+	0.0419854i	0.155358	+	0.987858i	$0.450347\pi$
$284$		0			0
$285$	2.18393	−	9.72925i	0.129365	−	0.576311i
$286$		0			0
$287$	5.87767	+	0.514229i	0.346948	+	0.0303540i
$288$		0			0
$289$	13.6603	+	2.40868i	0.803548	+	0.141687i
$290$		0			0
$291$	−11.8224	+	4.30298i	−0.693039	+	0.252245i
$292$		0			0
$293$	−23.8889	−	6.40102i	−1.39561	−	0.373952i	−0.518842	−	0.854870i	$-0.673637\pi$
$293$	−23.8889	−	6.40102i	−1.39561	−	0.373952i	−0.876765	+	0.480918i	$0.840303\pi$
$294$		0			0
$295$	−2.36746	−	3.21266i	−0.137839	−	0.187048i
$296$		0			0
$297$	−32.2197	+	8.63324i	−1.86958	+	0.500952i
$298$		0			0
$299$	5.24515	+	29.7467i	0.303335	+	1.72030i
$300$		0			0
$301$	−2.67951	−	0.975260i	−0.154444	−	0.0562131i
$302$		0			0
$303$	−1.69195	+	1.69195i	−0.0972000	+	0.0972000i
$304$		0			0
$305$	−14.2537	−	3.45172i	−0.816166	−	0.197645i
$306$		0			0
$307$	−1.36436	−	2.92587i	−0.0778679	−	0.166988i	0.863520	−	0.504315i	$-0.168255\pi$
$307$	−1.36436	−	2.92587i	−0.0778679	−	0.166988i	−0.941388	+	0.337327i	$0.890477\pi$
$308$		0			0
$309$	−1.42285	+	0.250886i	−0.0809429	+	0.0142724i
$310$		0			0
$311$	5.82817	−	10.0947i	0.330485	−	0.572417i	−0.652122	−	0.758114i	$-0.726121\pi$
$311$	5.82817	−	10.0947i	0.330485	−	0.572417i	0.982607	+	0.185697i	$0.0594544\pi$
$312$		0			0
$313$	2.08773	+	23.8629i	0.118005	+	1.34881i	0.792203	+	0.610258i	$0.208934\pi$
$313$	2.08773	+	23.8629i	0.118005	+	1.34881i	−0.674198	+	0.738551i	$0.735510\pi$
$314$		0			0
$315$	1.87281	−	3.43315i	0.105521	−	0.193436i
$316$		0			0
$317$	−1.84495	−	0.860313i	−0.103623	−	0.0483200i	0.370116	−	0.928986i	$-0.379318\pi$
$317$	−1.84495	−	0.860313i	−0.103623	−	0.0483200i	−0.473738	+	0.880666i	$0.657096\pi$
$318$		0			0
$319$	−4.80308	+	27.2396i	−0.268921	+	1.52512i
$320$		0			0
$321$	−14.9540	+	12.5479i	−0.834652	+	0.700356i
$322$		0			0
$323$	−4.85634	+	5.98881i	−0.270214	+	0.333226i
$324$		0			0
$325$	12.9107	−	20.4814i	0.716156	−	1.13611i
$326$		0			0
$327$	10.1492	+	14.4945i	0.561250	+	0.801547i
$328$		0			0
$329$	−1.71483	−	4.71145i	−0.0945415	−	0.259751i
$330$		0			0
$331$	−10.2653	+	5.92669i	−0.564234	+	0.325760i	−0.754843	−	0.655906i	$-0.772287\pi$
$331$	−10.2653	+	5.92669i	−0.564234	+	0.325760i	0.190609	+	0.981666i	$0.438954\pi$
$332$		0			0
$333$	9.09390	−	0.795613i	0.498343	−	0.0435993i
$334$		0			0
$335$	24.4491	−	0.592038i	1.33580	−	0.0323465i
$336$		0			0
$337$	8.28126	−	11.8269i	0.451109	−	0.644250i	−0.527602	−	0.849491i	$-0.676909\pi$
$337$	8.28126	−	11.8269i	0.451109	−	0.644250i	0.978711	+	0.205241i	$0.0657978\pi$
$338$		0			0
$339$	−1.98640	+	5.45760i	−0.107887	+	0.296416i
$340$		0			0
$341$			15.2379i			0.825179i
$342$		0			0
$343$	−8.35585	−	8.35585i	−0.451174	−	0.451174i
$344$		0			0
$345$	11.8839	+	7.89951i	0.639810	+	0.425295i
$346$		0			0
$347$	21.4744	+	15.0365i	1.15280	+	0.807202i	0.983951	−	0.178439i	$-0.0571048\pi$
$347$	21.4744	+	15.0365i	1.15280	+	0.807202i	0.168853	+	0.985641i	$0.445994\pi$
$348$		0			0
$349$	20.7327	+	11.9700i	1.10980	+	0.640742i	0.938777	−	0.344526i	$-0.111960\pi$
$349$	20.7327	+	11.9700i	1.10980	+	0.640742i	0.171021	+	0.985267i	$0.445294\pi$
$350$		0			0
$351$	18.7972	+	15.7727i	1.00332	+	0.841884i
$352$		0			0
$353$	9.18455	−	34.2772i	0.488844	−	1.82439i	−0.0732429	−	0.997314i	$-0.523335\pi$
$353$	9.18455	−	34.2772i	0.488844	−	1.82439i	0.562087	−	0.827078i	$-0.309998\pi$
$354$		0			0
$355$	2.59538	+	23.1852i	0.137748	+	1.23054i
$356$		0			0
$357$	1.32721	−	0.929325i	0.0702436	−	0.0491851i
$358$		0			0
$359$	−6.20630	−	7.39638i	−0.327556	−	0.390366i	0.576983	−	0.816756i	$-0.304230\pi$
$359$	−6.20630	−	7.39638i	−0.327556	−	0.390366i	−0.904540	+	0.426390i	$0.859785\pi$
$360$		0			0
$361$	7.09374	+	17.6261i	0.373355	+	0.927689i
$362$		0			0
$363$	2.88246	−	32.9467i	0.151290	−	1.72925i
$364$		0			0
$365$	15.0923	−	5.91070i	0.789966	−	0.309380i
$366$		0			0
$367$	−3.70458	+	7.94451i	−0.193378	+	0.414700i	−0.978959	−	0.204059i	$-0.934587\pi$
$367$	−3.70458	+	7.94451i	−0.193378	+	0.414700i	0.785581	+	0.618759i	$0.212364\pi$
$368$		0			0
$369$	−6.43628	−	11.1480i	−0.335059	−	0.580340i
$370$		0			0
$371$	6.41282	−	7.64250i	0.332937	−	0.396779i
$372$		0			0
$373$	3.11876	+	11.6394i	0.161483	+	0.602663i	0.998463	+	0.0554291i	$0.0176527\pi$
$373$	3.11876	+	11.6394i	0.161483	+	0.602663i	−0.836979	+	0.547234i	$0.815681\pi$
$374$		0			0
$375$	−2.79835	−	11.0903i	−0.144506	−	0.572702i
$376$		0			0
$377$	18.4410	−	8.59920i	0.949762	−	0.442881i
$378$		0			0
$379$	−14.4409			−0.741780			−0.370890	−	0.928677i	$-0.620947\pi$
$379$	−14.4409			−0.741780			−0.370890	+	0.928677i	$0.620947\pi$
$380$		0			0
$381$	16.3542			0.837852
$382$		0			0
$383$	−0.612214	+	0.285480i	−0.0312827	+	0.0145873i	−0.438197	−	0.898879i	$-0.644383\pi$
$383$	−0.612214	+	0.285480i	−0.0312827	+	0.0145873i	0.406914	+	0.913466i	$0.366605\pi$
$384$		0			0
$385$	8.71263	+	9.88700i	0.444037	+	0.503888i
$386$		0			0
$387$	1.61016	+	6.00920i	0.0818491	+	0.305465i
$388$		0			0
$389$	−5.16497	+	6.15537i	−0.261874	+	0.312090i	−0.880920	−	0.473265i	$-0.843075\pi$
$389$	−5.16497	+	6.15537i	−0.261874	+	0.312090i	0.619046	+	0.785355i	$0.287520\pi$
$390$		0			0
$391$	−5.51713	−	9.55595i	−0.279013	−	0.483265i
$392$		0			0
$393$	−3.02557	+	6.48836i	−0.152620	+	0.327295i
$394$		0			0
$395$	−1.75981	+	4.02558i	−0.0885456	+	0.202549i
$396$		0			0
$397$	−0.564264	+	6.44956i	−0.0283196	+	0.323694i	0.968800	+	0.247845i	$0.0797224\pi$
$397$	−0.564264	+	6.44956i	−0.0283196	+	0.323694i	−0.997119	+	0.0758494i	$0.975833\pi$
$398$		0			0
$399$	−0.414659	−	3.97099i	−0.0207589	−	0.198798i
$400$		0			0
$401$	−22.3234	−	26.6040i	−1.11478	−	1.32854i	−0.938925	−	0.344121i	$-0.888177\pi$
$401$	−22.3234	−	26.6040i	−1.11478	−	1.32854i	−0.175851	−	0.984417i	$-0.556268\pi$
$402$		0			0
$403$	9.18229	−	6.42951i	0.457402	−	0.320276i
$404$		0			0
$405$	−1.50201	+	0.168137i	−0.0746356	+	0.00835478i
$406$		0			0
$407$	−7.96152	+	29.7128i	−0.394638	+	1.47281i
$408$		0			0
$409$	22.6213	+	18.9815i	1.11855	+	0.938574i	0.998530	−	0.0541972i	$-0.0172600\pi$
$409$	22.6213	+	18.9815i	1.11855	+	0.938574i	0.120019	+	0.992772i	$0.461704\pi$
$410$		0			0
$411$	12.1249	+	7.00029i	0.598075	+	0.345299i
$412$		0			0
$413$	−1.30894	−	0.916528i	−0.0644086	−	0.0450994i
$414$		0			0
$415$	6.93540	+	34.4356i	0.340445	+	1.69038i
$416$		0			0
$417$	2.05698	+	2.05698i	0.100731	+	0.100731i
$418$		0			0
$419$			11.1192i			0.543209i	0.962409	+	0.271604i	$0.0875542\pi$
$419$			11.1192i			0.543209i	−0.962409	+	0.271604i	$0.912446\pi$
$420$		0			0
$421$	−6.61915	+	18.1860i	−0.322598	+	0.886330i	0.667331	+	0.744761i	$0.267437\pi$
$421$	−6.61915	+	18.1860i	−0.322598	+	0.886330i	−0.989928	+	0.141568i	$0.954786\pi$
$422$		0			0
$423$	−6.27428	+	8.96061i	−0.305066	+	0.435680i
$424$		0			0
$425$	−1.87292	+	8.64383i	−0.0908499	+	0.419287i
$426$		0			0
$427$	−5.84989	+	0.511799i	−0.283096	+	0.0247677i
$428$		0			0
$429$	−28.2390	+	16.3038i	−1.36339	+	0.787155i
$430$		0			0
$431$	−9.01603	−	24.7713i	−0.434287	−	1.19319i	−0.943156	−	0.332350i	$-0.892159\pi$
$431$	−9.01603	−	24.7713i	−0.434287	−	1.19319i	0.508869	−	0.860844i	$-0.330064\pi$
$432$		0			0
$433$	−7.99195	−	11.4137i	−0.384069	−	0.548507i	0.579843	−	0.814728i	$-0.303114\pi$
$433$	−7.99195	−	11.4137i	−0.384069	−	0.548507i	−0.963912	+	0.266221i	$0.914225\pi$
$434$		0			0
$435$	3.06809	−	9.10988i	0.147104	−	0.436785i
$436$		0			0
$437$	−27.1869	+	0.456194i	−1.30053	+	0.0218227i
$438$		0			0
$439$	6.57153	−	5.51416i	0.313642	−	0.263177i	−0.472354	−	0.881409i	$-0.656595\pi$
$439$	6.57153	−	5.51416i	0.313642	−	0.263177i	0.785995	+	0.618232i	$0.212151\pi$
$440$		0			0
$441$	−2.10251	+	11.9239i	−0.100119	+	0.567805i
$442$		0			0
$443$	−8.91274	−	4.15608i	−0.423457	−	0.197461i	0.199195	−	0.979960i	$-0.436167\pi$
$443$	−8.91274	−	4.15608i	−0.423457	−	0.197461i	−0.622652	+	0.782499i	$0.713945\pi$
$444$		0			0
$445$	−8.85163	−	30.1002i	−0.419607	−	1.42688i
$446$		0			0
$447$	−0.548559	−	6.27006i	−0.0259460	−	0.296564i
$448$		0			0
$449$	10.2777	−	17.8015i	0.485034	−	0.840103i	−0.514818	−	0.857299i	$-0.672141\pi$
$449$	10.2777	−	17.8015i	0.485034	−	0.840103i	0.999852	+	0.0171960i	$0.00547393\pi$
$450$		0			0
$451$	42.7179	−	7.53232i	2.01151	−	0.354683i
$452$		0			0
$453$	−1.96265	−	4.20892i	−0.0922133	−	0.197752i
$454$		0			0
$455$	2.28164	−	9.42192i	0.106965	−	0.441706i
$456$		0			0
$457$	−6.81874	+	6.81874i	−0.318967	+	0.318967i	−0.848370	−	0.529403i	$-0.822416\pi$
$457$	−6.81874	+	6.81874i	−0.318967	+	0.318967i	0.529403	+	0.848370i	$0.322416\pi$
$458$		0			0
$459$	−8.42325	−	3.06581i	−0.393163	−	0.143100i
$460$		0			0
$461$	−0.297879	−	1.68936i	−0.0138736	−	0.0786812i	0.977085	−	0.212850i	$-0.0682746\pi$
$461$	−0.297879	−	1.68936i	−0.0138736	−	0.0786812i	−0.990958	+	0.134169i	$0.957164\pi$
$462$		0			0
$463$	−27.6599	+	7.41146i	−1.28547	+	0.344440i	−0.835937	−	0.548826i	$-0.815075\pi$
$463$	−27.6599	+	7.41146i	−1.28547	+	0.344440i	−0.449530	+	0.893265i	$0.648408\pi$
$464$		0			0
$465$	0.793062	−	5.23594i	0.0367774	−	0.242811i
$466$		0			0
$467$	32.9199	+	8.82087i	1.52335	+	0.408181i	0.920844	−	0.389931i	$-0.127501\pi$
$467$	32.9199	+	8.82087i	1.52335	+	0.408181i	0.602509	+	0.798112i	$0.294168\pi$
$468$		0			0
$469$	9.20188	−	3.34921i	0.424903	−	0.154652i
$470$		0			0
$471$	6.90925	+	1.21829i	0.318362	+	0.0561357i
$472$		0			0
$473$	−20.8839	−	1.82710i	−0.960241	−	0.0840102i
$474$		0			0
$475$	16.3824	+	14.3742i	0.751674	+	0.659534i
$476$		0			0
$477$	−21.6835	−	1.89706i	−0.992820	−	0.0868605i
$478$		0			0
$479$	10.5794	+	1.86544i	0.483386	+	0.0852340i	0.410030	−	0.912072i	$-0.365518\pi$
$479$	10.5794	+	1.86544i	0.483386	+	0.0852340i	0.0733556	+	0.997306i	$0.476629\pi$
$480$		0			0
$481$	21.2641	−	7.73948i	0.969557	−	0.352890i
$482$		0			0
$483$	5.51906	+	1.47883i	0.251126	+	0.0672890i
$484$		0			0
$485$	4.11811	−	27.1885i	0.186994	−	1.23457i
$486$		0			0
$487$	−32.1143	+	8.60500i	−1.45524	+	0.389930i	−0.897842	−	0.440317i	$-0.854866\pi$
$487$	−32.1143	+	8.60500i	−1.45524	+	0.389930i	−0.557396	+	0.830247i	$0.688199\pi$
$488$		0			0
$489$	−0.604523	−	3.42842i	−0.0273375	−	0.155039i
$490$		0			0
$491$	−28.2255	−	10.2732i	−1.27380	−	0.463625i	−0.385422	−	0.922741i	$-0.625944\pi$
$491$	−28.2255	−	10.2732i	−1.27380	−	0.463625i	−0.888376	+	0.459116i	$0.848166\pi$
$492$		0			0
$493$	−5.25594	+	5.25594i	−0.236715	+	0.236715i
$494$		0			0
$495$	6.76690	−	27.9436i	0.304150	−	1.25597i
$496$		0			0
$497$	3.94788	+	8.46626i	0.177087	+	0.379764i
$498$		0			0
$499$	−11.7726	+	2.07583i	−0.527015	+	0.0929269i	−0.430824	−	0.902436i	$-0.641777\pi$
$499$	−11.7726	+	2.07583i	−0.527015	+	0.0929269i	−0.0961908	+	0.995363i	$0.530666\pi$
$500$		0			0
$501$	−4.72466	+	8.18335i	−0.211082	+	0.365605i
$502$		0			0
$503$	−1.96665	−	22.4789i	−0.0876885	−	1.00228i	−0.904809	−	0.425817i	$-0.859987\pi$
$503$	−1.96665	−	22.4789i	−0.0876885	−	1.00228i	0.817121	−	0.576467i	$-0.195569\pi$
$504$		0			0
$505$	−1.47550	−	5.01747i	−0.0656589	−	0.223275i
$506$		0			0
$507$	9.68633	+	4.51681i	0.430185	+	0.200599i
$508$		0			0
$509$	−5.83807	+	33.1094i	−0.258768	+	1.46755i	0.527444	+	0.849590i	$0.323150\pi$
$509$	−5.83807	+	33.1094i	−0.258768	+	1.46755i	−0.786212	+	0.617957i	$0.787961\pi$
$510$		0			0
$511$	4.97159	−	4.17166i	0.219930	−	0.184543i
$512$		0			0
$513$	−16.6804	+	14.4803i	−0.736457	+	0.639320i
$514$		0			0
$515$	1.00791	−	2.99274i	0.0444140	−	0.131876i
$516$		0			0
$517$	−21.1426	−	30.1947i	−0.929849	−	1.32796i
$518$		0			0
$519$	4.78454	+	13.1454i	0.210018	+	0.577019i
$520$		0			0
$521$	27.9233	−	16.1215i	1.22334	−	0.706297i	0.257714	−	0.966221i	$-0.417031\pi$
$521$	27.9233	−	16.1215i	1.22334	−	0.706297i	0.965629	+	0.259924i	$0.0836975\pi$
$522$		0			0
$523$	27.8104	−	2.43310i	1.21607	−	0.106392i	0.538994	−	0.842309i	$-0.318804\pi$
$523$	27.8104	−	2.43310i	1.21607	−	0.106392i	0.677071	+	0.735917i	$0.263249\pi$
$524$		0			0
$525$	−2.47919	−	3.85075i	−0.108201	−	0.168060i
$526$		0			0
$527$	−2.34873	+	3.35433i	−0.102312	+	0.146117i
$528$		0			0
$529$	5.44237	−	14.9528i	0.236625	−	0.650122i
$530$		0			0
$531$			3.48625i			0.151290i
$532$		0			0
$533$	−22.5634	−	22.5634i	−0.977328	−	0.977328i
$534$		0			0
$535$	−8.42416	−	41.8276i	−0.364208	−	1.80836i
$536$		0			0
$537$	3.85735	+	2.70094i	0.166457	+	0.116554i
$538$		0			0
$539$	−35.3339	−	20.4000i	−1.52194	−	0.878692i
$540$		0			0
$541$	−21.8752	−	18.3554i	−0.940487	−	0.789162i	0.0371833	−	0.999308i	$-0.488161\pi$
$541$	−21.8752	−	18.3554i	−0.940487	−	0.789162i	−0.977670	+	0.210146i	$0.932606\pi$
$542$		0			0
$543$	−4.99217	+	18.6310i	−0.214234	+	0.799534i
$544$		0			0
$545$	−38.4350	+	4.30246i	−1.64638	+	0.184297i
$546$		0			0
$547$	−10.7325	+	7.51495i	−0.458887	+	0.321316i	−0.780060	−	0.625704i	$-0.784812\pi$
$547$	−10.7325	+	7.51495i	−0.458887	+	0.321316i	0.321173	+	0.947020i	$0.395923\pi$
$548$		0			0
$549$	8.23522	+	9.81435i	0.351470	+	0.418866i
$550$		0			0
$551$	5.03683	+	17.6104i	0.214576	+	0.750227i
$552$		0			0
$553$	−0.153320	+	1.75246i	−0.00651985	+	0.0745222i
$554$		0			0
$555$	4.28208	−	9.79532i	0.181764	−	0.415788i
$556$		0			0
$557$	18.8003	−	40.3174i	0.796594	−	1.70830i	0.0952779	−	0.995451i	$-0.469626\pi$
$557$	18.8003	−	40.3174i	0.796594	−	1.70830i	0.701316	−	0.712851i	$-0.252596\pi$
$558$		0			0
$559$	7.71076	+	13.3554i	0.326130	+	0.564875i
$560$		0			0
$561$	7.65670	−	9.12489i	0.323266	−	0.385253i
$562$		0			0
$563$	6.15348	+	22.9651i	0.259338	+	0.967864i	0.965625	+	0.259938i	$0.0837021\pi$
$563$	6.15348	+	22.9651i	0.259338	+	0.967864i	−0.706287	+	0.707926i	$0.749631\pi$
$564$		0			0
$565$	−8.39275	−	9.52401i	−0.353086	−	0.400678i
$566$		0			0
$567$	−0.548471	+	0.255756i	−0.0230336	+	0.0107407i
$568$		0			0
$569$	22.7013			0.951688			0.475844	−	0.879530i	$-0.342143\pi$
$569$	22.7013			0.951688			0.475844	+	0.879530i	$0.342143\pi$
$570$		0			0
$571$	−8.37020			−0.350282			−0.175141	−	0.984543i	$-0.556038\pi$
$571$	−8.37020			−0.350282			−0.175141	+	0.984543i	$0.556038\pi$
$572$		0			0
$573$	−3.40289	+	1.58679i	−0.142158	+	0.0662892i
$574$		0			0
$575$	−27.5965	+	14.5342i	−1.15085	+	0.606117i
$576$		0			0
$577$	0.961328	+	3.58773i	0.0400206	+	0.149359i	0.983045	−	0.183365i	$-0.0586990\pi$
$577$	0.961328	+	3.58773i	0.0400206	+	0.149359i	−0.943024	+	0.332724i	$0.892032\pi$
$578$		0			0
$579$	9.27803	−	11.0571i	0.385582	−	0.459519i
$580$		0			0
$581$	7.03253	+	12.1807i	0.291759	+	0.505341i
$582$		0			0
$583$	30.9975	−	66.4745i	1.28379	−	2.75309i
$584$		0			0
$585$	−19.6939	+	7.71286i	−0.814243	+	0.318888i
$586$		0			0
$587$	0.554411	−	6.33695i	0.0228830	−	0.261554i	−0.976132	−	0.217178i	$-0.930315\pi$
$587$	0.554411	−	6.33695i	0.0228830	−	0.261554i	0.999015	−	0.0443755i	$-0.0141298\pi$
$588$		0			0
$589$	4.41733	+	9.07241i	0.182013	+	0.373822i
$590$		0			0
$591$	10.4328	+	12.4334i	0.429150	+	0.511441i
$592$		0			0
$593$	−16.7122	+	11.7020i	−0.686289	+	0.480545i	−0.863970	−	0.503543i	$-0.832029\pi$
$593$	−16.7122	+	11.7020i	−0.686289	+	0.480545i	0.177681	+	0.984088i	$0.443141\pi$
$594$		0			0
$595$	0.393962	+	3.51937i	0.0161509	+	0.144280i
$596$		0			0
$597$	2.66822	−	9.95795i	0.109203	−	0.407552i
$598$		0			0
$599$	−6.47478	−	5.43298i	−0.264552	−	0.221986i	0.500856	−	0.865530i	$-0.333019\pi$
$599$	−6.47478	−	5.43298i	−0.264552	−	0.221986i	−0.765408	+	0.643545i	$0.777463\pi$
$600$		0			0
$601$	17.4777	+	10.0907i	0.712930	+	0.411610i	0.812145	−	0.583456i	$-0.198300\pi$
$601$	17.4777	+	10.0907i	0.712930	+	0.411610i	−0.0992153	+	0.995066i	$0.531633\pi$
$602$		0			0
$603$	−17.5008	−	12.2542i	−0.712690	−	0.499031i
$604$		0			0
$605$	60.2004	+	40.0165i	2.44749	+	1.62690i
$606$		0			0
$607$	−32.9685	−	32.9685i	−1.33815	−	1.33815i	−0.897851	−	0.440300i	$-0.854872\pi$
$607$	−32.9685	−	32.9685i	−1.33815	−	1.33815i	−0.440300	−	0.897851i	$-0.645128\pi$
$608$		0			0
$609$		−	3.84896i		−	0.155968i
$610$		0			0
$611$	−9.27425	+	25.4808i	−0.375196	+	1.03084i
$612$		0			0
$613$	14.4531	−	20.6411i	0.583754	−	0.833687i	−0.413284	−	0.910602i	$-0.635618\pi$
$613$	14.4531	−	20.6411i	0.583754	−	0.833687i	0.997038	+	0.0769155i	$0.0245072\pi$
$614$		0			0
$615$	−15.0704	+	0.364932i	−0.607698	+	0.0147155i
$616$		0			0
$617$	4.63257	−	0.405297i	0.186500	−	0.0163166i	0.00647698	−	0.999979i	$-0.497938\pi$
$617$	4.63257	−	0.405297i	0.186500	−	0.0163166i	0.180023	+	0.983662i	$0.442383\pi$
$618$		0			0
$619$	4.28588	−	2.47446i	0.172264	−	0.0994568i	−0.411389	−	0.911460i	$-0.634956\pi$
$619$	4.28588	−	2.47446i	0.172264	−	0.0994568i	0.583653	+	0.812003i	$0.301623\pi$
$620$		0			0
$621$	−10.8116	−	29.7047i	−0.433855	−	1.19201i
$622$		0			0
$623$	−7.20562	−	10.2907i	−0.288687	−	0.412288i
$624$		0			0
$625$	24.2090	+	6.23896i	0.968360	+	0.249558i
$626$		0			0
$627$	−10.5007	−	27.4104i	−0.419356	−	1.09467i
$628$		0			0
$629$	−6.33242	+	5.31353i	−0.252490	+	0.211864i
$630$		0			0
$631$	−1.17247	+	6.64940i	−0.0466753	+	0.264709i	−0.999211	−	0.0397185i	$-0.987354\pi$
$631$	−1.17247	+	6.64940i	−0.0466753	+	0.264709i	0.952536	+	0.304427i	$0.0984650\pi$
$632$		0			0
$633$	18.6415	+	8.69269i	0.740934	+	0.345503i
$634$		0			0
$635$	−17.1182	+	31.3802i	−0.679314	+	1.24529i
$636$		0			0
$637$	2.61588	+	29.8996i	0.103645	+	1.18467i
$638$		0			0
$639$	10.1904	−	17.6502i	0.403125	−	0.698233i
$640$		0			0
$641$	−24.2748	+	4.28031i	−0.958798	+	0.169062i	−0.631084	−	0.775715i	$-0.717390\pi$
$641$	−24.2748	+	4.28031i	−0.958798	+	0.169062i	−0.327715	+	0.944777i	$0.606278\pi$
$642$		0			0
$643$	13.5459	+	29.0493i	0.534199	+	1.14559i	0.969451	+	0.245285i	$0.0788815\pi$
$643$	13.5459	+	29.0493i	0.534199	+	1.14559i	−0.435252	+	0.900309i	$0.643341\pi$
$644$		0			0
$645$	7.08086	+	1.71472i	0.278809	+	0.0675171i
$646$		0			0
$647$	3.68079	−	3.68079i	0.144707	−	0.144707i	−0.631042	−	0.775749i	$-0.717372\pi$
$647$	3.68079	−	3.68079i	0.144707	−	0.144707i	0.775749	+	0.631042i	$0.217372\pi$
$648$		0			0
$649$	−11.0392	−	4.01794i	−0.433327	−	0.157718i
$650$		0			0
$651$	−0.368205	−	2.08820i	−0.0144311	−	0.0818429i
$652$		0			0
$653$	24.2323	−	6.49303i	0.948284	−	0.254092i	0.248650	−	0.968593i	$-0.420013\pi$
$653$	24.2323	−	6.49303i	0.948284	−	0.254092i	0.699634	+	0.714502i	$0.253346\pi$
$654$		0			0
$655$	−9.28286	−	12.5969i	−0.362711	−	0.492201i
$656$		0			0
$657$	−13.6769	−	3.66473i	−0.533589	−	0.142975i
$658$		0			0
$659$	−11.0580	+	4.02477i	−0.430757	+	0.156783i	−0.548294	−	0.836286i	$-0.684722\pi$
$659$	−11.0580	+	4.02477i	−0.430757	+	0.156783i	0.117537	+	0.993069i	$0.462500\pi$
$660$		0			0
$661$	15.3840	+	2.71261i	0.598368	+	0.105508i	0.464625	−	0.885508i	$-0.346189\pi$
$661$	15.3840	+	2.71261i	0.598368	+	0.105508i	0.133743	+	0.991016i	$0.457300\pi$
$662$		0			0
$663$	−8.72929	−	0.763714i	−0.339017	−	0.0296602i
$664$		0			0
$665$	8.05351	+	3.36085i	0.312302	+	0.130328i
$666$		0			0
$667$	−26.1129	−	2.28458i	−1.01109	−	0.0884593i
$668$		0			0
$669$	8.97232	+	1.58206i	0.346890	+	0.0611660i
$670$		0			0
$671$	−40.5683	+	14.7657i	−1.56612	+	0.570022i
$672$		0			0
$673$	48.3497	+	12.9553i	1.86374	+	0.499389i	0.999990	−	0.00452507i	$-0.00144038\pi$
$673$	48.3497	+	12.9553i	1.86374	+	0.499389i	0.863754	+	0.503914i	$0.168107\pi$
$674$		0			0
$675$	−9.58408	+	23.4550i	−0.368891	+	0.902784i
$676$		0			0
$677$	−37.9383	+	10.1655i	−1.45809	+	0.390694i	−0.898829	−	0.438299i	$-0.855581\pi$
$677$	−37.9383	+	10.1655i	−1.45809	+	0.390694i	−0.559260	+	0.828993i	$0.688915\pi$
$678$		0			0
$679$	−1.91197	−	10.8433i	−0.0733748	−	0.416129i
$680$		0			0
$681$	2.84064	+	1.03391i	0.108854	+	0.0396195i
$682$		0			0
$683$	−10.8810	+	10.8810i	−0.416350	+	0.416350i	−0.883943	−	0.467594i	$-0.845121\pi$
$683$	−10.8810	+	10.8810i	−0.416350	+	0.416350i	0.467594	+	0.883943i	$0.345121\pi$
$684$		0			0
$685$	−26.1233	+	15.9377i	−0.998119	+	0.608947i
$686$		0			0
$687$	5.88741	+	12.6256i	0.224619	+	0.481696i
$688$		0			0
$689$	−53.1363	+	9.36936i	−2.02433	+	0.356944i
$690$		0			0
$691$	16.6009	−	28.7535i	0.631526	−	1.09384i	−0.355713	−	0.934595i	$-0.615762\pi$
$691$	16.6009	−	28.7535i	0.631526	−	1.09384i	0.987240	−	0.159241i	$-0.0509046\pi$
$692$		0			0
$693$	−1.00335	−	11.4684i	−0.0381142	−	0.435648i
$694$		0			0
$695$	−6.09998	+	1.79384i	−0.231385	+	0.0680441i
$696$		0			0
$697$	10.5645	+	4.92632i	0.400160	+	0.186598i
$698$		0			0
$699$	1.50647	−	8.54359i	0.0569798	−	0.323148i
$700$		0			0
$701$	−10.3476	+	8.68267i	−0.390823	+	0.327940i	−0.816934	−	0.576731i	$-0.804328\pi$
$701$	−10.3476	+	8.68267i	−0.390823	+	0.327940i	0.426110	+	0.904671i	$0.359883\pi$
$702$		0			0
$703$	3.87330	+	19.9985i	0.146084	+	0.754257i
$704$		0			0
$705$	5.69335	+	11.4756i	0.214424	+	0.432198i
$706$		0			0
$707$	−1.20112	−	1.71538i	−0.0451729	−	0.0645135i
$708$		0			0
$709$	12.2990	+	33.7913i	0.461900	+	1.26906i	0.924055	+	0.382260i	$0.124854\pi$
$709$	12.2990	+	33.7913i	0.461900	+	1.26906i	−0.462155	+	0.886799i	$0.652924\pi$
$710$		0			0
$711$	3.32383	−	1.91901i	0.124653	−	0.0719686i
$712$		0			0
$713$	−14.3857	+	1.25859i	−0.538749	+	0.0471344i
$714$		0			0
$715$	−1.72533	−	71.2499i	−0.0645235	−	2.66460i
$716$		0			0
$717$	−4.63349	+	6.61731i	−0.173041	+	0.247128i
$718$		0			0
$719$	2.38786	−	6.56060i	0.0890523	−	0.244669i	−0.887169	−	0.461444i	$-0.847332\pi$
$719$	2.38786	−	6.56060i	0.0890523	−	0.244669i	0.976222	+	0.216775i	$0.0695538\pi$
$720$		0			0
$721$		−	1.26444i		−	0.0470904i
$722$		0			0
$723$	−4.58116	−	4.58116i	−0.170375	−	0.170375i
$724$		0			0
$725$	14.2685	+	15.4224i	0.529918	+	0.572775i
$726$		0			0
$727$	38.5095	+	26.9647i	1.42824	+	1.00006i	0.995114	+	0.0987304i	$0.0314781\pi$
$727$	38.5095	+	26.9647i	1.42824	+	1.00006i	0.433125	+	0.901334i	$0.357411\pi$
$728$		0			0
$729$	−12.3257	−	7.11623i	−0.456506	−	0.263564i
$730$		0			0
$731$	−4.31555	−	3.62118i	−0.159617	−	0.133934i
$732$		0			0
$733$	1.62880	−	6.07876i	0.0601611	−	0.224524i	−0.929299	−	0.369327i	$-0.879588\pi$
$733$	1.62880	−	6.07876i	0.0601611	−	0.224524i	0.989460	+	0.144803i	$0.0462549\pi$
$734$		0			0
$735$	11.0794	+	8.84866i	0.408671	+	0.326388i
$736$		0			0
$737$	58.9729	−	41.2933i	2.17230	−	1.52106i
$738$		0			0
$739$	−18.1059	−	21.5778i	−0.666036	−	0.793751i	0.322202	−	0.946671i	$-0.395577\pi$
$739$	−18.1059	−	21.5778i	−0.666036	−	0.793751i	−0.988239	+	0.152920i	$0.951132\pi$
$740$		0			0
$741$	−12.0867	+	17.8932i	−0.444017	+	0.657324i
$742$		0			0
$743$	−0.334538	+	3.82378i	−0.0122730	+	0.140281i	−0.999859	−	0.0167990i	$-0.994652\pi$
$743$	−0.334538	+	3.82378i	−0.0122730	+	0.140281i	0.987586	+	0.157080i	$0.0502080\pi$
$744$		0			0
$745$	12.6051	+	5.51038i	0.461814	+	0.201885i
$746$		0			0
$747$	12.9686	−	27.8113i	0.474497	−	1.01756i
$748$		0			0
$749$	−8.54215	−	14.7954i	−0.312123	−	0.540614i
$750$		0			0
$751$	25.1388	−	29.9593i	0.917330	−	1.09323i	−0.0780248	−	0.996951i	$-0.524861\pi$
$751$	25.1388	−	29.9593i	0.917330	−	1.09323i	0.995354	−	0.0962794i	$-0.0306942\pi$
$752$		0			0
$753$	4.61026	+	17.2057i	0.168007	+	0.627012i
$754$		0			0
$755$	10.1303	+	0.639627i	0.368680	+	0.0232784i
$756$		0			0
$757$	25.2913	−	11.7935i	0.919228	−	0.428643i	0.0953719	−	0.995442i	$-0.469596\pi$
$757$	25.2913	−	11.7935i	0.919228	−	0.428643i	0.823856	+	0.566798i	$0.191818\pi$
$758$		0			0
$759$	42.0068			1.52475
$760$		0			0
$761$	−7.16418			−0.259701			−0.129851	−	0.991534i	$-0.541450\pi$
$761$	−7.16418			−0.259701			−0.129851	+	0.991534i	$0.541450\pi$
$762$		0			0
$763$	−14.0348	+	6.54455i	−0.508095	+	0.236929i
$764$		0			0
$765$	5.79675	−	5.10821i	0.209582	−	0.184688i
$766$		0			0
$767$	2.23671	+	8.34750i	0.0807628	+	0.301411i
$768$		0			0
$769$	13.6400	−	16.2555i	0.491871	−	0.586189i	−0.461821	−	0.886973i	$-0.652804\pi$
$769$	13.6400	−	16.2555i	0.491871	−	0.586189i	0.953692	+	0.300784i	$0.0972482\pi$
$770$		0			0
$771$	−8.82754	−	15.2897i	−0.317916	−	0.550647i
$772$		0			0
$773$	−11.5447	+	24.7577i	−0.415235	+	0.890473i	0.581786	+	0.813342i	$0.302354\pi$
$773$	−11.5447	+	24.7577i	−0.415235	+	0.890473i	−0.997021	+	0.0771318i	$0.975424\pi$
$774$		0			0
$775$	9.21652	+	7.00223i	0.331067	+	0.251528i
$776$		0			0
$777$	0.373070	−	4.26421i	0.0133838	−	0.152978i
$778$		0			0
$779$	23.2500	−	16.8681i	0.833017	−	0.604364i
$780$		0			0
$781$	44.1449	+	52.6099i	1.57963	+	1.88253i
$782$		0			0
$783$	−17.4432	+	12.2138i	−0.623368	+	0.436487i
$784$		0			0
$785$	−9.56963	+	11.9822i	−0.341555	+	0.427662i
$786$		0			0
$787$	−9.53435	+	35.5827i	−0.339863	+	1.26839i	0.558637	+	0.829412i	$0.311324\pi$
$787$	−9.53435	+	35.5827i	−0.339863	+	1.26839i	−0.898500	+	0.438973i	$0.855342\pi$
$788$		0			0
$789$	6.20442	+	5.20613i	0.220883	+	0.185343i
$790$		0			0
$791$	−4.40189	−	2.54143i	−0.156513	−	0.0903630i
$792$		0			0
$793$	26.0151	+	18.2160i	0.923825	+	0.646869i
$794$		0			0
$795$	−14.1108	+	21.2282i	−0.500459	+	0.752885i
$796$		0			0
$797$	29.9209	+	29.9209i	1.05985	+	1.05985i	0.998091	+	0.0617610i	$0.0196717\pi$
$797$	29.9209	+	29.9209i	1.05985	+	1.05985i	0.0617610	+	0.998091i	$0.480328\pi$
$798$		0			0
$799$		−	9.90564i		−	0.350436i
$800$		0			0
$801$	−9.37423	+	25.7555i	−0.331222	+	0.910025i
$802$		0			0
$803$	27.3672	−	39.0844i	0.965767	−	1.37926i
$804$		0			0
$805$	−8.61443	+	9.04198i	−0.303619	+	0.318688i
$806$		0			0
$807$	−0.0736084	+	0.00643990i	−0.00259114	+	0.000226695i
$808$		0			0
$809$	7.02632	−	4.05665i	0.247032	−	0.142624i	−0.371372	−	0.928484i	$-0.621113\pi$
$809$	7.02632	−	4.05665i	0.247032	−	0.142624i	0.618405	+	0.785860i	$0.287779\pi$
$810$		0			0
$811$	8.33296	+	22.8946i	0.292610	+	0.803939i	0.995683	+	0.0928212i	$0.0295885\pi$
$811$	8.33296	+	22.8946i	0.292610	+	0.803939i	−0.703073	+	0.711118i	$0.748189\pi$
$812$		0			0
$813$	−5.81934	−	8.31088i	−0.204093	−	0.291475i
$814$		0			0
$815$	7.21116	+	2.42862i	0.252596	+	0.0850710i
$816$		0			0
$817$	−12.9636	+	4.96621i	−0.453538	+	0.173746i
$818$		0			0
$819$	−6.48742	+	5.44360i	−0.226689	+	0.190215i
$820$		0			0
$821$	4.19607	−	23.7971i	0.146444	−	0.830524i	−0.819753	−	0.572718i	$-0.805889\pi$
$821$	4.19607	−	23.7971i	0.146444	−	0.830524i	0.966197	−	0.257806i	$-0.0829997\pi$
$822$		0			0
$823$	−15.4684	−	7.21305i	−0.539196	−	0.251431i	0.133889	−	0.990996i	$-0.457253\pi$
$823$	−15.4684	−	7.21305i	−0.539196	−	0.251431i	−0.673085	+	0.739565i	$0.735031\pi$
$824$		0			0
$825$	−24.9329	−	22.6281i	−0.868051	−	0.787810i
$826$		0			0
$827$	0.958643	+	10.9573i	0.0333353	+	0.381024i	0.994476	+	0.104965i	$0.0334730\pi$
$827$	0.958643	+	10.9573i	0.0333353	+	0.381024i	−0.961141	+	0.276059i	$0.910971\pi$
$828$		0			0
$829$	8.23206	−	14.2583i	0.285911	−	0.495213i	−0.686918	−	0.726734i	$-0.741037\pi$
$829$	8.23206	−	14.2583i	0.285911	−	0.495213i	0.972830	+	0.231522i	$0.0743704\pi$
$830$		0			0
$831$	1.94156	−	0.342350i	0.0673520	−	0.0118760i
$832$		0			0
$833$	−4.63367	−	9.93694i	−0.160547	−	0.344294i
$834$		0			0
$835$	−10.7567	−	17.6312i	−0.372251	−	0.610153i
$836$		0			0
$837$	−8.29511	+	8.29511i	−0.286721	+	0.286721i
$838$		0			0
$839$	−33.9739	−	12.3655i	−1.17291	−	0.426904i	−0.319216	−	0.947682i	$-0.603420\pi$
$839$	−33.9739	−	12.3655i	−1.17291	−	0.426904i	−0.853692	+	0.520778i	$0.825642\pi$
$840$		0			0
$841$	−1.96958	−	11.1701i	−0.0679166	−	0.385174i
$842$		0			0
$843$	−2.97350	+	0.796748i	−0.102413	+	0.0274415i
$844$		0			0
$845$	−18.8056	+	13.8582i	−0.646932	+	0.476735i
$846$		0			0
$847$	27.9579	+	7.49129i	0.960644	+	0.257404i
$848$		0			0
$849$	−7.79064	+	2.83556i	−0.267374	+	0.0973162i
$850$		0			0
$851$	−28.7086	−	5.06210i	−0.984119	−	0.173527i
$852$		0			0
$853$	2.31270	+	0.202335i	0.0791854	+	0.00692782i	0.126680	−	0.991944i	$-0.459568\pi$
$853$	2.31270	+	0.202335i	0.0791854	+	0.00692782i	−0.0474942	+	0.998872i	$0.515124\pi$
$854$		0			0
$855$	−4.07169	−	18.5988i	−0.139249	−	0.636067i
$856$		0			0
$857$	31.2324	+	2.73248i	1.06688	+	0.0933398i	0.607047	−	0.794666i	$-0.292354\pi$
$857$	31.2324	+	2.73248i	1.06688	+	0.0933398i	0.459832	+	0.888006i	$0.347910\pi$
$858$		0			0
$859$	49.6986	+	8.76320i	1.69569	+	0.298997i	0.936187	−	0.351503i	$-0.114329\pi$
$859$	49.6986	+	8.76320i	1.69569	+	0.298997i	0.759507	+	0.650499i	$0.225440\pi$
$860$		0			0
$861$	−5.67203	+	2.06445i	−0.193302	+	0.0703563i
$862$		0			0
$863$	35.4924	+	9.51016i	1.20817	+	0.323729i	0.806046	−	0.591853i	$-0.201604\pi$
$863$	35.4924	+	9.51016i	1.20817	+	0.323729i	0.402129	+	0.915583i	$0.368270\pi$
$864$		0			0
$865$	−30.2312	−	4.57898i	−1.02789	−	0.155690i
$866$		0			0
$867$	−13.7071	+	3.67280i	−0.465517	+	0.124735i
$868$		0			0
$869$	2.24580	+	12.7366i	0.0761837	+	0.432059i
$870$		0			0
$871$	−49.7662	−	18.1134i	−1.68626	−	0.613750i
$872$		0			0
$873$	−16.9864	+	16.9864i	−0.574901	+	0.574901i
$874$		0			0
$875$	9.98375	−	0.726410i	0.337512	−	0.0245571i
$876$		0			0
$877$	12.9639	+	27.8012i	0.437760	+	0.938780i	0.994165	+	0.107868i	$0.0344025\pi$
$877$	12.9639	+	27.8012i	0.437760	+	0.938780i	−0.556405	+	0.830911i	$0.687820\pi$
$878$		0			0
$879$	24.9171	−	4.39355i	0.840431	−	0.148191i
$880$		0			0
$881$	1.08298	−	1.87578i	0.0364867	−	0.0631968i	−0.847205	−	0.531265i	$-0.821717\pi$
$881$	1.08298	−	1.87578i	0.0364867	−	0.0631968i	0.883692	+	0.468069i	$0.155050\pi$
$882$		0			0
$883$	2.55963	+	29.2568i	0.0861385	+	0.984568i	0.909130	+	0.416514i	$0.136748\pi$
$883$	2.55963	+	29.2568i	0.0861385	+	0.984568i	−0.822991	+	0.568054i	$0.807696\pi$
$884$		0			0
$885$	3.58409	+	1.95515i	0.120478	+	0.0657217i
$886$		0			0
$887$	19.3590	+	9.02726i	0.650012	+	0.303106i	0.719516	−	0.694476i	$-0.244364\pi$
$887$	19.3590	+	9.02726i	0.650012	+	0.303106i	−0.0695037	+	0.997582i	$0.522142\pi$
$888$		0			0
$889$	−2.48538	+	14.0953i	−0.0833571	+	0.472741i
$890$		0			0
$891$	−3.40823	+	2.85985i	−0.114180	+	0.0958085i
$892$		0			0
$893$	−21.3411	−	11.8484i	−0.714153	−	0.396492i
$894$		0			0
$895$	−9.22006	+	4.57430i	−0.308193	+	0.152902i
$896$		0			0
$897$	−17.7244	−	25.3130i	−0.591800	−	0.845178i
$898$		0			0
$899$	3.32706	+	9.14102i	0.110964	+	0.304870i
$900$		0			0
$901$	17.0697	−	9.85519i	0.568674	−	0.328324i
$902$		0			0
$903$	2.90606	−	0.254248i	0.0967078	−	0.00846083i
$904$		0			0
$905$	−30.5235	−	29.0802i	−1.01464	−	0.966659i
$906$		0			0
$907$	−2.37190	+	3.38743i	−0.0787578	+	0.112478i	−0.856598	−	0.515984i	$-0.827426\pi$
$907$	−2.37190	+	3.38743i	−0.0787578	+	0.112478i	0.777840	+	0.628462i	$0.216315\pi$
$908$		0			0
$909$	−1.56261	+	4.29325i	−0.0518286	+	0.142398i
$910$		0			0
$911$			46.0674i			1.52628i	0.646233	+	0.763140i	$0.276343\pi$
$911$			46.0674i			1.52628i	−0.646233	+	0.763140i	$0.723657\pi$
$912$		0			0
$913$	73.1180	+	73.1180i	2.41985	+	2.41985i
$914$		0			0
$915$	14.7083	−	2.96227i	0.486240	−	0.0979297i
$916$		0			0
$917$	−5.13236	−	3.59372i	−0.169486	−	0.118675i
$918$		0			0
$919$	39.0863	+	22.5665i	1.28934	+	0.744400i	0.978536	−	0.206074i	$-0.0660687\pi$
$919$	39.0863	+	22.5665i	1.28934	+	0.744400i	0.310803	+	0.950474i	$0.399402\pi$
$920$		0			0
$921$	2.53003	+	2.12294i	0.0833672	+	0.0699534i
$922$		0			0
$923$	13.0759	−	48.7998i	0.430397	−	1.60626i
$924$		0			0
$925$	14.3130	+	18.4693i	0.470608	+	0.607266i
$926$		0			0
$927$	−2.25979	+	1.58232i	−0.0742213	+	0.0519703i
$928$		0			0
$929$	14.6872	+	17.5035i	0.481871	+	0.574271i	0.951131	−	0.308789i	$-0.0999237\pi$
$929$	14.6872	+	17.5035i	0.481871	+	0.574271i	−0.469260	+	0.883060i	$0.655479\pi$
$930$		0			0
$931$	−26.9510	−	1.90288i	−0.883283	−	0.0623643i
$932$		0			0
$933$	−1.03932	+	11.8795i	−0.0340259	+	0.388917i
$934$		0			0
$935$	9.49433	+	24.2427i	0.310498	+	0.792821i
$936$		0			0
$937$	−2.00902	+	4.30836i	−0.0656319	+	0.140748i	−0.936387	−	0.350968i	$-0.885853\pi$
$937$	−2.00902	+	4.30836i	−0.0656319	+	0.140748i	0.870755	+	0.491716i	$0.163630\pi$
$938$		0			0
$939$	−12.2529	−	21.2227i	−0.399860	−	0.692577i
$940$		0			0
$941$	−15.5776	+	18.5646i	−0.507815	+	0.605190i	−0.957655	−	0.287919i	$-0.907037\pi$
$941$	−15.5776	+	18.5646i	−0.507815	+	0.605190i	0.449840	+	0.893109i	$0.351481\pi$
$942$		0			0
$943$	10.6394	+	39.7067i	0.346466	+	1.29303i
$944$		0			0
$945$	−0.639299	+	10.1251i	−0.0207964	+	0.329371i
$946$		0			0
$947$	33.9762	−	15.8434i	1.10408	−	0.514840i	0.216866	−	0.976201i	$-0.430416\pi$
$947$	33.9762	−	15.8434i	1.10408	−	0.514840i	0.887213	+	0.461361i	$0.152639\pi$
$948$		0			0
$949$	−35.0994			−1.13937
$950$		0			0
$951$	2.08257			0.0675321
$952$		0			0
$953$	5.13044	−	2.39236i	0.166191	−	0.0774962i	−0.337743	−	0.941239i	$-0.609663\pi$
$953$	5.13044	−	2.39236i	0.166191	−	0.0774962i	0.503934	+	0.863742i	$0.331886\pi$
$954$		0			0
$955$	0.517135	−	8.19032i	0.0167341	−	0.265033i
$956$		0			0
$957$	−7.32382	−	27.3329i	−0.236745	−	0.883546i
$958$		0			0
$959$	−7.87602	+	9.38627i	−0.254330	+	0.303098i
$960$		0			0
$961$	−12.8205	−	22.2057i	−0.413564	−	0.716314i
$962$		0			0
$963$	−15.7525	+	33.7813i	−0.507617	+	1.08859i
$964$		0			0
$965$	11.5048	+	29.3762i	0.370353	+	0.945653i
$966$		0			0
$967$	1.83478	−	20.9716i	0.0590024	−	0.674401i	−0.907889	−	0.419211i	$-0.862307\pi$
$967$	1.83478	−	20.9716i	0.0590024	−	0.674401i	0.966891	−	0.255189i	$-0.0821378\pi$
$968$		0			0
$969$	1.91345	−	7.65242i	0.0614688	−	0.245831i
$970$		0			0
$971$	−14.3991	−	17.1602i	−0.462090	−	0.550697i	0.483803	−	0.875177i	$-0.339255\pi$
$971$	−14.3991	−	17.1602i	−0.462090	−	0.550697i	−0.945893	+	0.324480i	$0.894811\pi$
$972$		0			0
$973$	−2.08547	+	1.46026i	−0.0668571	+	0.0468138i
$974$		0			0
$975$	−3.11538	+	24.5721i	−0.0997719	+	0.786938i
$976$		0			0
$977$	−0.290634	+	1.08466i	−0.00929821	+	0.0347014i	−0.970419	−	0.241427i	$-0.922385\pi$
$977$	−0.290634	+	1.08466i	−0.00929821	+	0.0347014i	0.961121	+	0.276128i	$0.0890514\pi$
$978$		0			0
$979$	−70.7508	−	59.3670i	−2.26121	−	1.89738i
$980$		0			0
$981$	29.2595	+	16.8930i	0.934183	+	0.539351i
$982$		0			0
$983$	4.31263	+	3.01973i	0.137551	+	0.0963145i	0.640327	−	0.768102i	$-0.278799\pi$
$983$	4.31263	+	3.01973i	0.137551	+	0.0963145i	−0.502776	+	0.864417i	$0.667688\pi$
$984$		0			0
$985$	−34.7771	+	7.00419i	−1.10809	+	0.223172i
$986$		0			0
$987$	3.62699	+	3.62699i	0.115448	+	0.115448i
$988$		0			0
$989$		−	19.8668i		−	0.631727i
$990$		0			0
$991$	5.10149	−	14.0162i	0.162054	−	0.445240i	−0.831915	−	0.554904i	$-0.812755\pi$
$991$	5.10149	−	14.0162i	0.162054	−	0.445240i	0.993969	+	0.109664i	$0.0349774\pi$
$992$		0			0
$993$	6.95546	−	9.93342i	0.220725	−	0.315228i
$994$		0			0
$995$	16.3143	+	15.5429i	0.517197	+	0.492742i
$996$		0			0
$997$	−6.46644	+	0.565740i	−0.204794	+	0.0179172i	−0.189091	−	0.981960i	$-0.560554\pi$
$997$	−6.46644	+	0.565740i	−0.204794	+	0.0179172i	−0.0157029	+	0.999877i	$0.504999\pi$
$998$		0			0
$999$	−20.5089	+	11.8408i	−0.648872	+	0.374627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.13.4	✓	120
5.2	odd	4	inner	380.2.bh.a.317.7	yes	120
19.3	odd	18	inner	380.2.bh.a.193.7	yes	120
95.22	even	36	inner	380.2.bh.a.117.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.4	✓	120	1.1	even	1	trivial
380.2.bh.a.117.4	yes	120	95.22	even	36	inner
380.2.bh.a.193.7	yes	120	19.3	odd	18	inner
380.2.bh.a.317.7	yes	120	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927188 + 0.432355i) q^{3} +(0.140904 - 2.23162i) q^{5} +(-0.231730 - 0.864827i) q^{7} +(-1.25562 + 1.49639i) q^{9} +O(q^{10})\)	\(q+(-0.927188 + 0.432355i) q^{3} +(0.140904 - 2.23162i) q^{5} +(-0.231730 - 0.864827i) q^{7} +(-1.25562 + 1.49639i) q^{9} +(-3.29119 - 5.70051i) q^{11} +(-2.04641 + 4.38853i) q^{13} +(0.834209 + 2.13006i) q^{15} +(0.154168 - 1.76215i) q^{17} +(-3.61204 - 2.43990i) q^{19} +(0.588769 + 0.701667i) q^{21} +(5.10986 - 3.57796i) q^{23} +(-4.96029 - 0.628891i) q^{25} +(1.31157 - 4.89484i) q^{27} +(-3.21899 - 2.70106i) q^{29} +(-2.00481 - 1.15748i) q^{31} +(5.51619 + 3.86248i) q^{33} +(-1.96262 + 0.395276i) q^{35} +(-3.30447 - 3.30447i) q^{37} -4.95377i q^{39} +(-2.25386 + 6.19243i) q^{41} +(1.82673 - 2.60884i) q^{43} +(3.16245 + 3.01291i) q^{45} +(5.57863 - 0.488067i) q^{47} +(5.36795 - 3.09919i) q^{49} +(0.618932 + 1.70050i) q^{51} +(6.39127 + 9.12769i) q^{53} +(-13.1851 + 6.54147i) q^{55} +(4.40395 + 0.700564i) q^{57} +(1.36717 - 1.14719i) q^{59} +(1.13891 - 6.45906i) q^{61} +(1.58508 + 0.739134i) q^{63} +(9.50521 + 5.18517i) q^{65} +(0.953238 + 10.8956i) q^{67} +(-3.19085 + 5.52671i) q^{69} +(-10.2750 + 1.81176i) q^{71} +(3.06340 + 6.56949i) q^{73} +(4.87103 - 1.56151i) q^{75} +(-4.16729 + 4.16729i) q^{77} +(-1.84631 - 0.672002i) q^{79} +(-0.117372 - 0.665647i) q^{81} +(-15.1740 + 4.06586i) q^{83} +(-3.91074 - 0.592340i) q^{85} +(4.15243 + 1.11264i) q^{87} +(13.1850 - 4.79895i) q^{89} +(4.26953 + 0.752834i) q^{91} +(2.35928 + 0.206410i) q^{93} +(-5.95390 + 7.71693i) q^{95} +(12.2510 + 1.07182i) q^{97} +(12.6626 + 2.23276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more