LMFDB - Embedded newform 693.2.be.a.89.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(89,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("693.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.15
Character	$\chi$	$=$	693.89
Dual form			693.2.be.a.584.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.130783 + 0.0755078i) q^{2} +(-0.988597 - 1.71230i) q^{4} +(-0.0122719 + 0.0212556i) q^{5} +(-2.58612 + 0.558556i) q^{7} -0.600618i q^{8} +O(q^{10})$	\(q+(0.130783 + 0.0755078i) q^{2} +(-0.988597 - 1.71230i) q^{4} +(-0.0122719 + 0.0212556i) q^{5} +(-2.58612 + 0.558556i) q^{7} -0.600618i q^{8} +(-0.00320993 + 0.00185325i) q^{10} +(0.866025 - 0.500000i) q^{11} +2.81699i q^{13} +(-0.380397 - 0.122222i) q^{14} +(-1.93184 + 3.34605i) q^{16} +(-1.69429 - 2.93460i) q^{17} +(-3.85918 - 2.22810i) q^{19} +0.0485279 q^{20} +0.151016 q^{22} +(-6.52887 - 3.76945i) q^{23} +(2.49970 + 4.32961i) q^{25} +(-0.212704 + 0.368415i) q^{26} +(3.51305 + 3.87603i) q^{28} +5.93410i q^{29} +(-4.63428 + 2.67560i) q^{31} +(-1.54561 + 0.892357i) q^{32} -0.511729i q^{34} +(0.0198642 - 0.0618240i) q^{35} +(-5.59426 + 9.68954i) q^{37} +(-0.336478 - 0.582796i) q^{38} +(0.0127665 + 0.00737074i) q^{40} -10.3430 q^{41} -0.950427 q^{43} +(-1.71230 - 0.988597i) q^{44} +(-0.569245 - 0.985962i) q^{46} +(6.24322 - 10.8136i) q^{47} +(6.37603 - 2.88898i) q^{49} +0.754987i q^{50} +(4.82353 - 2.78486i) q^{52} +(2.51756 - 1.45352i) q^{53} +0.0245438i q^{55} +(0.335479 + 1.55327i) q^{56} +(-0.448071 + 0.776081i) q^{58} +(5.64685 + 9.78064i) q^{59} +(-9.14023 - 5.27712i) q^{61} -0.808115 q^{62} +7.45785 q^{64} +(-0.0598767 - 0.0345698i) q^{65} +(0.0160709 + 0.0278356i) q^{67} +(-3.34994 + 5.80227i) q^{68} +(0.00726611 - 0.00658565i) q^{70} -11.6031i q^{71} +(-3.59324 + 2.07456i) q^{73} +(-1.46327 + 0.844820i) q^{74} +8.81077i q^{76} +(-1.96037 + 1.77678i) q^{77} +(1.29044 - 2.23511i) q^{79} +(-0.0474148 - 0.0821249i) q^{80} +(-1.35270 - 0.780980i) q^{82} +4.32112 q^{83} +0.0831688 q^{85} +(-0.124300 - 0.0717647i) q^{86} +(-0.300309 - 0.520151i) q^{88} +(8.66763 - 15.0128i) q^{89} +(-1.57344 - 7.28506i) q^{91} +14.9059i q^{92} +(1.63302 - 0.942823i) q^{94} +(0.0947191 - 0.0546861i) q^{95} +4.42939i q^{97} +(1.05202 + 0.103609i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 32 q^{4} - 4 q^{7}+O(q^{10}) $ 56 * q + 32 * q^4 - 4 * q^7	$ 56 q + 32 q^{4} - 4 q^{7} - 40 q^{16} - 12 q^{19} - 36 q^{25} + 48 q^{28} + 12 q^{31} - 12 q^{37} - 120 q^{40} - 8 q^{43} - 56 q^{46} + 20 q^{49} + 72 q^{52} + 32 q^{58} + 24 q^{61} - 64 q^{64} + 44 q^{67} + 40 q^{70} + 12 q^{73} - 20 q^{79} + 168 q^{82} - 16 q^{85} + 24 q^{88} - 92 q^{91} - 96 q^{94}+O(q^{100}) $ 56 * q + 32 * q^4 - 4 * q^7 - 40 * q^16 - 12 * q^19 - 36 * q^25 + 48 * q^28 + 12 * q^31 - 12 * q^37 - 120 * q^40 - 8 * q^43 - 56 * q^46 + 20 * q^49 + 72 * q^52 + 32 * q^58 + 24 * q^61 - 64 * q^64 + 44 * q^67 + 40 * q^70 + 12 * q^73 - 20 * q^79 + 168 * q^82 - 16 * q^85 + 24 * q^88 - 92 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.130783	+	0.0755078i	0.0924778	+	0.0533921i	0.545526	−	0.838094i	$-0.316330\pi$
$2$	0.130783	+	0.0755078i	0.0924778	+	0.0533921i	−0.453048	+	0.891486i	$0.649663\pi$
$3$		0			0
$3$		0			0
$4$	−0.988597	−	1.71230i	−0.494299	−	0.856150i
$5$	−0.0122719	+	0.0212556i	−0.00548817	+	0.00950579i	−0.868756	−	0.495240i	$-0.835080\pi$
$5$	−0.0122719	+	0.0212556i	−0.00548817	+	0.00950579i	0.863268	+	0.504745i	$0.168414\pi$
$6$		0			0
$7$	−2.58612	+	0.558556i	−0.977461	+	0.211114i
$7$	−2.58612	+	0.558556i	−0.977461	+	0.211114i
$8$		−	0.600618i		−	0.212351i
$9$		0			0
$10$	−0.00320993	+	0.00185325i	−0.00101507	+	0.000586049i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$			2.81699i			0.781291i	0.920541	+	0.390646i	$0.127748\pi$
$13$			2.81699i			0.781291i	−0.920541	+	0.390646i	$0.872252\pi$
$14$	−0.380397	−	0.122222i	−0.101665	−	0.0326653i
$15$		0			0
$16$	−1.93184	+	3.34605i	−0.482961	+	0.836513i
$17$	−1.69429	−	2.93460i	−0.410926	−	0.711745i	0.584065	−	0.811707i	$-0.301461\pi$
$17$	−1.69429	−	2.93460i	−0.410926	−	0.711745i	−0.994991	+	0.0999620i	$0.968128\pi$
$18$		0			0
$19$	−3.85918	−	2.22810i	−0.885356	−	0.511161i	−0.0129357	−	0.999916i	$-0.504118\pi$
$19$	−3.85918	−	2.22810i	−0.885356	−	0.511161i	−0.872421	+	0.488756i	$0.837451\pi$
$20$	0.0485279			0.0108512
$21$		0			0
$22$	0.151016			0.0321966
$23$	−6.52887	−	3.76945i	−1.36136	−	0.785984i	−0.371559	−	0.928410i	$-0.621176\pi$
$23$	−6.52887	−	3.76945i	−1.36136	−	0.785984i	−0.989806	+	0.142426i	$0.954510\pi$
$24$		0			0
$25$	2.49970	+	4.32961i	0.499940	+	0.865921i
$26$	−0.212704	+	0.368415i	−0.0417148	+	0.0722521i
$27$		0			0
$28$	3.51305	+	3.87603i	0.663903	+	0.732500i
$29$			5.93410i			1.10193i	0.834527	+	0.550967i	$0.185741\pi$
$29$			5.93410i			1.10193i	−0.834527	+	0.550967i	$0.814259\pi$
$30$		0			0
$31$	−4.63428	+	2.67560i	−0.832340	+	0.480552i	−0.854653	−	0.519199i	$-0.826230\pi$
$31$	−4.63428	+	2.67560i	−0.832340	+	0.480552i	0.0223129	+	0.999751i	$0.492897\pi$
$32$	−1.54561	+	0.892357i	−0.273227	+	0.157748i
$33$		0			0
$34$		−	0.511729i		−	0.0877608i
$35$	0.0198642	−	0.0618240i	0.00335767	−	0.0104502i
$36$		0			0
$37$	−5.59426	+	9.68954i	−0.919690	+	1.59295i	−0.119805	+	0.992797i	$0.538227\pi$
$37$	−5.59426	+	9.68954i	−0.919690	+	1.59295i	−0.799885	+	0.600153i	$0.795106\pi$
$38$	−0.336478	−	0.582796i	−0.0545839	−	0.0945420i
$39$		0			0
$40$	0.0127665	+	0.00737074i	0.00201856	+	0.00116542i
$41$	−10.3430			−1.61531			−0.807655	−	0.589655i	$-0.799264\pi$
$41$	−10.3430			−1.61531			−0.807655	+	0.589655i	$0.799264\pi$
$42$		0			0
$43$	−0.950427			−0.144939			−0.0724694	−	0.997371i	$-0.523088\pi$
$43$	−0.950427			−0.144939			−0.0724694	+	0.997371i	$0.523088\pi$
$44$	−1.71230	−	0.988597i	−0.258139	−	0.149037i
$45$		0			0
$46$	−0.569245	−	0.985962i	−0.0839306	−	0.145372i
$47$	6.24322	−	10.8136i	0.910667	−	1.57732i	0.0975418	−	0.995231i	$-0.468902\pi$
$47$	6.24322	−	10.8136i	0.910667	−	1.57732i	0.813125	−	0.582089i	$-0.197765\pi$
$48$		0			0
$49$	6.37603	−	2.88898i	0.910862	−	0.412712i
$50$			0.754987i			0.106771i
$51$		0			0
$52$	4.82353	−	2.78486i	0.668903	−	0.386191i
$53$	2.51756	−	1.45352i	0.345814	−	0.199656i	−0.317026	−	0.948417i	$-0.602684\pi$
$53$	2.51756	−	1.45352i	0.345814	−	0.199656i	0.662840	+	0.748761i	$0.269351\pi$
$54$		0			0
$55$			0.0245438i			0.00330949i
$56$	0.335479	+	1.55327i	0.0448302	+	0.207565i
$57$		0			0
$58$	−0.448071	+	0.776081i	−0.0588346	+	0.101904i
$59$	5.64685	+	9.78064i	0.735158	+	1.27333i	0.954654	+	0.297717i	$0.0962252\pi$
$59$	5.64685	+	9.78064i	0.735158	+	1.27333i	−0.219497	+	0.975613i	$0.570441\pi$
$60$		0			0
$61$	−9.14023	−	5.27712i	−1.17029	−	0.675665i	−0.216539	−	0.976274i	$-0.569477\pi$
$61$	−9.14023	−	5.27712i	−1.17029	−	0.675665i	−0.953748	+	0.300609i	$0.902810\pi$
$62$	−0.808115			−0.102631
$63$		0			0
$64$	7.45785			0.932232
$65$	−0.0598767	−	0.0345698i	−0.00742679	−	0.00428786i
$66$		0			0
$67$	0.0160709	+	0.0278356i	0.00196337	+	0.00340066i	0.867005	−	0.498299i	$-0.166042\pi$
$67$	0.0160709	+	0.0278356i	0.00196337	+	0.00340066i	−0.865042	+	0.501699i	$0.832708\pi$
$68$	−3.34994	+	5.80227i	−0.406240	+	0.703629i
$69$		0			0
$70$	0.00726611	−	0.00658565i	0.000868466	−	0.000787136i
$71$		−	11.6031i		−	1.37704i	−0.725219	−	0.688518i	$-0.758261\pi$
$71$		−	11.6031i		−	1.37704i	0.725219	−	0.688518i	$-0.241739\pi$
$72$		0			0
$73$	−3.59324	+	2.07456i	−0.420557	+	0.242809i	−0.695315	−	0.718705i	$-0.744735\pi$
$73$	−3.59324	+	2.07456i	−0.420557	+	0.242809i	0.274759	+	0.961513i	$0.411402\pi$
$74$	−1.46327	+	0.844820i	−0.170102	+	0.0982084i
$75$		0			0
$76$			8.81077i			1.01066i
$77$	−1.96037	+	1.77678i	−0.223405	+	0.202483i
$78$		0			0
$79$	1.29044	−	2.23511i	0.145186	−	0.251469i	−0.784256	−	0.620437i	$-0.786955\pi$
$79$	1.29044	−	2.23511i	0.145186	−	0.251469i	0.929442	+	0.368967i	$0.120289\pi$
$80$	−0.0474148	−	0.0821249i	−0.00530114	−	0.00918184i
$81$		0			0
$82$	−1.35270	−	0.780980i	−0.149380	−	0.0862448i
$83$	4.32112			0.474304			0.237152	−	0.971472i	$-0.423786\pi$
$83$	4.32112			0.474304			0.237152	+	0.971472i	$0.423786\pi$
$84$		0			0
$85$	0.0831688			0.00902092
$86$	−0.124300	−	0.0717647i	−0.0134036	−	0.00773858i
$87$		0			0
$88$	−0.300309	−	0.520151i	−0.0320131	−	0.0554483i
$89$	8.66763	−	15.0128i	0.918766	−	1.59135i	0.117475	−	0.993076i	$-0.462520\pi$
$89$	8.66763	−	15.0128i	0.918766	−	1.59135i	0.801291	−	0.598274i	$-0.204147\pi$
$90$		0			0
$91$	−1.57344	−	7.28506i	−0.164942	−	0.763682i
$92$			14.9059i			1.55404i
$93$		0			0
$94$	1.63302	−	0.942823i	0.168433	−	0.0972448i
$95$	0.0947191	−	0.0546861i	0.00971797	−	0.00561067i
$96$		0			0
$97$			4.42939i			0.449737i	0.974389	+	0.224868i	$0.0721952\pi$
$97$			4.42939i			0.449737i	−0.974389	+	0.224868i	$0.927805\pi$
$98$	1.05202	+	0.103609i	0.106270	+	0.0104661i
$99$		0			0
$100$	4.94239	−	8.56047i	0.494239	−	0.856047i
$101$	−7.39318	−	12.8054i	−0.735649	−	1.27418i	−0.954438	−	0.298409i	$-0.903544\pi$
$101$	−7.39318	−	12.8054i	−0.735649	−	1.27418i	0.218789	−	0.975772i	$-0.429789\pi$
$102$		0			0
$103$	−12.4476	−	7.18662i	−1.22650	−	0.708118i	−0.260202	−	0.965554i	$-0.583789\pi$
$103$	−12.4476	−	7.18662i	−1.22650	−	0.708118i	−0.966295	+	0.257436i	$0.917122\pi$
$104$	1.69193			0.165908
$105$		0			0
$106$	0.439007			0.0426401
$107$	6.46695	+	3.73369i	0.625183	+	0.360950i	0.778884	−	0.627168i	$-0.215786\pi$
$107$	6.46695	+	3.73369i	0.625183	+	0.360950i	−0.153701	+	0.988117i	$0.549119\pi$
$108$		0			0
$109$	−6.45445	−	11.1794i	−0.618224	−	1.07080i	−0.989810	−	0.142397i	$-0.954519\pi$
$109$	−6.45445	−	11.1794i	−0.618224	−	1.07080i	0.371585	−	0.928399i	$-0.378814\pi$
$110$	−0.00185325	+	0.00320993i	−0.000176701	+	0.000306054i
$111$		0			0
$112$	3.12702	−	9.73233i	0.295476	−	0.919619i
$113$			10.6796i			1.00465i	0.864679	+	0.502326i	$0.167522\pi$
$113$			10.6796i			1.00465i	−0.864679	+	0.502326i	$0.832478\pi$
$114$		0			0
$115$	0.160244	−	0.0925167i	0.0149428	−	0.00862722i
$116$	10.1610	−	5.86643i	0.943421	−	0.544685i
$117$		0			0
$118$			1.70553i			0.157006i
$119$	6.02078	+	6.64287i	0.551924	+	0.608951i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−0.796927	−	1.38032i	−0.0721504	−	0.124968i
$123$		0			0
$124$	9.16286	+	5.29018i	0.822849	+	0.475072i
$125$	−0.245424			−0.0219514
$126$		0			0
$127$	14.8995			1.32211			0.661057	−	0.750336i	$-0.270108\pi$
$127$	14.8995			1.32211			0.661057	+	0.750336i	$0.270108\pi$
$128$	4.06658	+	2.34784i	0.359438	+	0.207522i
$129$		0			0
$130$	−0.00522058	−	0.00904231i	−0.000457875	−	0.000793063i
$131$	−4.77364	+	8.26819i	−0.417075	+	0.722395i	−0.995644	−	0.0932385i	$-0.970278\pi$
$131$	−4.77364	+	8.26819i	−0.417075	+	0.722395i	0.578569	+	0.815634i	$0.303611\pi$
$132$		0			0
$133$	11.2248	+	3.60656i	0.973315	+	0.312729i
$134$			0.00485391i			0.000419314i
$135$		0			0
$136$	−1.76257	+	1.01762i	−0.151139	+	0.0872604i
$137$	−3.78876	+	2.18744i	−0.323696	+	0.186886i	−0.653039	−	0.757324i	$-0.726506\pi$
$137$	−3.78876	+	2.18744i	−0.323696	+	0.186886i	0.329343	+	0.944210i	$0.393173\pi$
$138$		0			0
$139$		−	1.78966i		−	0.151797i	−0.997116	−	0.0758984i	$-0.975818\pi$
$139$		−	1.78966i		−	0.151797i	0.997116	−	0.0758984i	$-0.0241825\pi$
$140$	−0.125499	+	0.0271056i	−0.0106066	+	0.00229084i
$141$		0			0
$142$	0.876126	−	1.51749i	0.0735229	−	0.127345i
$143$	1.40849	+	2.43958i	0.117784	+	0.204008i
$144$		0			0
$145$	−0.126133	−	0.0728228i	−0.0104748	−	0.00604760i
$146$	−0.626581			−0.0518562
$147$		0			0
$148$	22.1219			1.81841
$149$	−9.88801	−	5.70884i	−0.810057	−	0.467687i	0.0369186	−	0.999318i	$-0.488246\pi$
$149$	−9.88801	−	5.70884i	−0.810057	−	0.467687i	−0.846976	+	0.531632i	$0.821579\pi$
$150$		0			0
$151$	−6.55660	−	11.3564i	−0.533568	−	0.924167i	−0.999231	−	0.0392052i	$-0.987517\pi$
$151$	−6.55660	−	11.3564i	−0.533568	−	0.924167i	0.465663	−	0.884962i	$-0.345816\pi$
$152$	−1.33824	+	2.31789i	−0.108545	+	0.188006i
$153$		0			0
$154$	−0.390544	+	0.0843506i	−0.0314710	+	0.00679717i
$155$		−	0.131339i		−	0.0105494i
$156$		0			0
$157$	−0.147251	+	0.0850155i	−0.0117519	+	0.00678498i	−0.505864	−	0.862613i	$-0.668826\pi$
$157$	−0.147251	+	0.0850155i	−0.0117519	+	0.00678498i	0.494113	+	0.869398i	$0.335493\pi$
$158$	0.337536	−	0.194877i	0.0268530	−	0.0155036i
$159$		0			0
$160$		−	0.0438037i		−	0.00346299i
$161$	18.9899	+	6.10150i	1.49661	+	0.480866i
$162$		0			0
$163$	1.93855	−	3.35768i	0.151839	−	0.262993i	−0.780064	−	0.625699i	$-0.784814\pi$
$163$	1.93855	−	3.35768i	0.151839	−	0.262993i	0.931904	+	0.362706i	$0.118147\pi$
$164$	10.2251	+	17.7104i	0.798446	+	1.38295i
$165$		0			0
$166$	0.565130	+	0.326278i	0.0438626	+	0.0253241i
$167$	−2.11725			−0.163837			−0.0819187	−	0.996639i	$-0.526105\pi$
$167$	−2.11725			−0.163837			−0.0819187	+	0.996639i	$0.526105\pi$
$168$		0			0
$169$	5.06459			0.389584
$170$	0.0108771	+	0.00627989i	0.000834235	+	0.000481646i
$171$		0			0
$172$	0.939590	+	1.62742i	0.0716430	+	0.124089i
$173$	−0.491331	+	0.851009i	−0.0373552	+	0.0647010i	−0.884099	−	0.467301i	$-0.845227\pi$
$173$	−0.491331	+	0.851009i	−0.0373552	+	0.0647010i	0.846743	+	0.532002i	$0.178560\pi$
$174$		0			0
$175$	−8.88285	−	9.80066i	−0.671480	−	0.740860i
$176$			3.86369i			0.291236i
$177$		0			0
$178$	2.26716	−	1.30895i	0.169931	−	0.0981097i
$179$	11.0742	−	6.39371i	0.827727	−	0.477888i	−0.0253469	−	0.999679i	$-0.508069\pi$
$179$	11.0742	−	6.39371i	0.827727	−	0.477888i	0.853074	+	0.521790i	$0.174736\pi$
$180$		0			0
$181$			8.04483i			0.597968i	0.954258	+	0.298984i	$0.0966477\pi$
$181$			8.04483i			0.597968i	−0.954258	+	0.298984i	$0.903352\pi$
$182$	0.344299	−	1.07157i	0.0255211	−	0.0794302i
$183$		0			0
$184$	−2.26400	+	3.92136i	−0.166904	+	0.289087i
$185$	−0.137305	−	0.237818i	−0.0100948	−	0.0174848i
$186$		0			0
$187$	−2.93460	−	1.69429i	−0.214599	−	0.123899i
$188$	−24.6881			−1.80056
$189$		0			0
$190$	0.0165169			0.00119826
$191$	3.77467	+	2.17931i	0.273125	+	0.157689i	0.630307	−	0.776346i	$-0.282929\pi$
$191$	3.77467	+	2.17931i	0.273125	+	0.157689i	−0.357182	+	0.934035i	$0.616262\pi$
$192$		0			0
$193$	7.33009	+	12.6961i	0.527632	+	0.913885i	0.999481	+	0.0322058i	$0.0102532\pi$
$193$	7.33009	+	12.6961i	0.527632	+	0.913885i	−0.471850	+	0.881679i	$0.656413\pi$
$194$	−0.334454	+	0.579291i	−0.0240124	+	0.0415907i
$195$		0			0
$196$	−11.2501	−	8.06164i	−0.803581	−	0.575831i
$197$			21.0209i			1.49768i	0.662754	+	0.748838i	$0.269388\pi$
$197$			21.0209i			1.49768i	−0.662754	+	0.748838i	$0.730612\pi$
$198$		0			0
$199$	3.95684	−	2.28448i	0.280493	−	0.161942i	−0.353154	−	0.935565i	$-0.614891\pi$
$199$	3.95684	−	2.28448i	0.280493	−	0.161942i	0.633646	+	0.773623i	$0.281557\pi$
$200$	2.60044	−	1.50137i	0.183879	−	0.106163i
$201$		0			0
$202$		−	2.23297i		−	0.157111i
$203$	−3.31452	−	15.3463i	−0.232634	−	1.07710i
$204$		0			0
$205$	0.126929	−	0.219847i	0.00886510	−	0.0153548i
$206$	−1.08529	−	1.87978i	−0.0756158	−	0.130970i
$207$		0			0
$208$	−9.42577	−	5.44197i	−0.653560	−	0.377333i
$209$	−4.45620			−0.308242
$210$		0			0
$211$	5.48069			0.377306			0.188653	−	0.982044i	$-0.439588\pi$
$211$	5.48069			0.377306			0.188653	+	0.982044i	$0.439588\pi$
$212$	−4.97771	−	2.87388i	−0.341871	−	0.197379i
$213$		0			0
$214$	0.563846	+	0.976610i	0.0385437	+	0.0667597i
$215$	0.0116636	−	0.0202019i	0.000795448	−	0.00137776i
$216$		0			0
$217$	10.4903	−	9.50792i	0.712129	−	0.645440i
$218$		−	1.94945i		−	0.132033i
$219$		0			0
$220$	0.0420264	−	0.0242640i	0.00283342	−	0.00163588i
$221$	8.26672	−	4.77279i	0.556080	−	0.321053i
$222$		0			0
$223$			5.94809i			0.398314i	0.979968	+	0.199157i	$0.0638203\pi$
$223$			5.94809i			0.398314i	−0.979968	+	0.199157i	$0.936180\pi$
$224$	3.49869	−	3.17105i	0.233766	−	0.211875i
$225$		0			0
$226$	−0.806392	+	1.39671i	−0.0536404	+	0.0929079i
$227$	−10.2421	−	17.7398i	−0.679792	−	1.17743i	−0.975043	−	0.222014i	$-0.928737\pi$
$227$	−10.2421	−	17.7398i	−0.679792	−	1.17743i	0.295252	−	0.955420i	$-0.404597\pi$
$228$		0			0
$229$	−4.57093	−	2.63903i	−0.302055	−	0.174392i	0.341310	−	0.939951i	$-0.389129\pi$
$229$	−4.57093	−	2.63903i	−0.302055	−	0.174392i	−0.643366	+	0.765559i	$0.722463\pi$
$230$	0.0279429			0.00184250
$231$		0			0
$232$	3.56413			0.233996
$233$	15.8792	+	9.16788i	1.04028	+	0.600608i	0.919914	−	0.392121i	$-0.128259\pi$
$233$	15.8792	+	9.16788i	1.04028	+	0.600608i	0.120370	+	0.992729i	$0.461592\pi$
$234$		0			0
$235$	0.153232	+	0.265406i	0.00999578	+	0.0173132i
$236$	11.1649	−	19.3382i	0.726775	−	1.25881i
$237$		0			0
$238$	0.285829	+	1.32339i	0.0185275	+	0.0857828i
$239$			7.39387i			0.478270i	0.970986	+	0.239135i	$0.0768638\pi$
$239$			7.39387i			0.478270i	−0.970986	+	0.239135i	$0.923136\pi$
$240$		0			0
$241$	−26.3422	+	15.2087i	−1.69685	+	0.979676i	−0.748131	+	0.663551i	$0.769049\pi$
$241$	−26.3422	+	15.2087i	−1.69685	+	0.979676i	−0.948717	+	0.316125i	$0.897618\pi$
$242$	0.130783	−	0.0755078i	0.00840707	−	0.00485383i
$243$		0			0
$244$			20.8678i			1.33592i
$245$	−0.0168391	+	0.170980i	−0.00107581	+	0.0109235i
$246$		0			0
$247$	6.27652	−	10.8713i	0.399365	−	0.691721i
$248$	1.60701	+	2.78343i	0.102046	+	0.176748i
$249$		0			0
$250$	−0.0320973	−	0.0185314i	−0.00203001	−	0.00117203i
$251$	7.48450			0.472417			0.236209	−	0.971702i	$-0.424095\pi$
$251$	7.48450			0.472417			0.236209	+	0.971702i	$0.424095\pi$
$252$		0			0
$253$	−7.53889			−0.473966
$254$	1.94860	+	1.12503i	0.122266	+	0.0705904i
$255$		0			0
$256$	−7.10329	−	12.3033i	−0.443956	−	0.768954i
$257$	−9.41623	+	16.3094i	−0.587368	+	1.01735i	0.407207	+	0.913336i	$0.366503\pi$
$257$	−9.41623	+	16.3094i	−0.587368	+	1.01735i	−0.994576	+	0.104016i	$0.966831\pi$
$258$		0			0
$259$	9.05527	−	28.1830i	0.562667	−	1.75121i
$260$			0.136702i			0.00847793i
$261$		0			0
$262$	−1.24863	+	0.720894i	−0.0771404	+	0.0445370i
$263$	−22.7656	+	13.1437i	−1.40379	+	0.810477i	−0.994779	−	0.102053i	$-0.967459\pi$
$263$	−22.7656	+	13.1437i	−1.40379	+	0.810477i	−0.409009	+	0.912531i	$0.634125\pi$
$264$		0			0
$265$			0.0713497i			0.00438298i
$266$	1.19570	+	1.31924i	0.0733128	+	0.0808878i
$267$		0			0
$268$	0.0317753	−	0.0550364i	0.00194098	−	0.00336188i
$269$	−4.31934	−	7.48131i	−0.263355	−	0.456143i	0.703777	−	0.710421i	$-0.251496\pi$
$269$	−4.31934	−	7.48131i	−0.263355	−	0.456143i	−0.967131	+	0.254278i	$0.918162\pi$
$270$		0			0
$271$	−2.75077	−	1.58816i	−0.167098	−	0.0964739i	0.414119	−	0.910223i	$-0.364090\pi$
$271$	−2.75077	−	1.58816i	−0.167098	−	0.0964739i	−0.581217	+	0.813749i	$0.697423\pi$
$272$	13.0924			0.793844
$273$		0			0
$274$	−0.660676			−0.0399129
$275$	4.32961	+	2.49970i	0.261085	+	0.150738i
$276$		0			0
$277$	4.45392	+	7.71442i	0.267610	+	0.463515i	0.968244	−	0.250006i	$-0.0804327\pi$
$277$	4.45392	+	7.71442i	0.267610	+	0.463515i	−0.700634	+	0.713521i	$0.747099\pi$
$278$	0.135133	−	0.234058i	0.00810475	−	0.0140378i
$279$		0			0
$280$	−0.0371327	−	0.0119308i	−0.00221910	−	0.000713003i
$281$		−	26.9821i		−	1.60961i	−0.593536	−	0.804807i	$-0.702269\pi$
$281$		−	26.9821i		−	1.60961i	0.593536	−	0.804807i	$-0.297731\pi$
$282$		0			0
$283$	−20.5583	+	11.8694i	−1.22207	+	0.705560i	−0.965358	−	0.260929i	$-0.915971\pi$
$283$	−20.5583	+	11.8694i	−1.22207	+	0.705560i	−0.256707	+	0.966489i	$0.582638\pi$
$284$	−19.8680	+	11.4708i	−1.17895	+	0.680667i
$285$		0			0
$286$			0.425409i			0.0251549i
$287$	26.7483	−	5.77716i	1.57890	−	0.341015i
$288$		0			0
$289$	2.75875	−	4.77830i	0.162280	−	0.281077i
$290$	−0.0109974	−	0.0190480i	−0.000645788	−	0.00111854i
$291$		0			0
$292$	7.10453	+	4.10180i	0.415761	+	0.240040i
$293$	−23.2562			−1.35864			−0.679322	−	0.733840i	$-0.737726\pi$
$293$	−23.2562			−1.35864			−0.679322	+	0.733840i	$0.737726\pi$
$294$		0			0
$295$	−0.277191			−0.0161387
$296$	5.81972	+	3.36001i	0.338264	+	0.195297i
$297$		0			0
$298$	−0.862124	−	1.49324i	−0.0499415	−	0.0865013i
$299$	10.6185	−	18.3917i	0.614082	−	1.06362i
$300$		0			0
$301$	2.45792	−	0.530867i	0.141672	−	0.0305986i
$302$		−	1.98030i		−	0.113953i
$303$		0			0
$304$	14.9107	−	8.60867i	0.855185	−	0.493741i
$305$	0.224336	−	0.129521i	0.0128455	−	0.00741633i
$306$		0			0
$307$			4.53854i			0.259028i	0.991578	+	0.129514i	$0.0413417\pi$
$307$			4.53854i			0.259028i	−0.991578	+	0.129514i	$0.958658\pi$
$308$	4.98040	+	1.60022i	0.283785	+	0.0911807i
$309$		0			0
$310$	0.00991712	−	0.0171770i	0.000563254	−	0.000975585i
$311$	−14.2081	−	24.6091i	−0.805666	−	1.39546i	−0.915840	−	0.401543i	$-0.868474\pi$
$311$	−14.2081	−	24.6091i	−0.805666	−	1.39546i	0.110174	−	0.993912i	$-0.464859\pi$
$312$		0			0
$313$	8.28008	+	4.78050i	0.468018	+	0.270210i	0.715409	−	0.698705i	$-0.246240\pi$
$313$	8.28008	+	4.78050i	0.468018	+	0.270210i	−0.247392	+	0.968915i	$0.579574\pi$
$314$	−0.0256773			−0.00144906
$315$		0			0
$316$	−5.10290			−0.287061
$317$	−11.1647	−	6.44596i	−0.627073	−	0.362041i	0.152544	−	0.988297i	$-0.451253\pi$
$317$	−11.1647	−	6.44596i	−0.627073	−	0.362041i	−0.779618	+	0.626256i	$0.784587\pi$
$318$		0			0
$319$	2.96705	+	5.13908i	0.166123	+	0.287733i
$320$	−0.0915221	+	0.158521i	−0.00511624	+	0.00886159i
$321$		0			0
$322$	2.02285	+	2.23186i	0.112729	+	0.124377i
$323$			15.1002i			0.840197i
$324$		0			0
$325$	−12.1964	+	7.04161i	−0.676536	+	0.390599i
$326$	0.507061	−	0.292752i	0.0280835	−	0.0162140i
$327$		0			0
$328$			6.21222i			0.343012i
$329$	−10.1057	+	31.4524i	−0.557147	+	1.73402i
$330$		0			0
$331$	−6.86191	+	11.8852i	−0.377165	+	0.653268i	−0.990648	−	0.136439i	$-0.956434\pi$
$331$	−6.86191	+	11.8852i	−0.377165	+	0.653268i	0.613484	+	0.789707i	$0.289768\pi$
$332$	−4.27185	−	7.39905i	−0.234448	−	0.406076i
$333$		0			0
$334$	−0.276901	−	0.159869i	−0.0151513	−	0.00874762i
$335$	−0.000788883	0		−4.31013e−5	0
$336$		0			0
$337$	0.315540			0.0171886			0.00859429	−	0.999963i	$-0.497264\pi$
$337$	0.315540			0.0171886			0.00859429	+	0.999963i	$0.497264\pi$
$338$	0.662365	+	0.382416i	0.0360279	+	0.0208007i
$339$		0			0
$340$	−0.0822205	−	0.142410i	−0.00445903	−	0.00772327i
$341$	−2.67560	+	4.63428i	−0.144892	+	0.250960i
$342$		0			0
$343$	−14.8755	+	11.0326i	−0.803203	+	0.595706i
$344$			0.570844i			0.0307778i
$345$		0			0
$346$	−0.128516	+	0.0741986i	−0.00690905	+	0.00398894i
$347$	3.81495	−	2.20256i	0.204797	−	0.118240i	−0.394094	−	0.919070i	$-0.628942\pi$
$347$	3.81495	−	2.20256i	0.204797	−	0.118240i	0.598891	+	0.800830i	$0.295608\pi$
$348$		0			0
$349$			26.0716i			1.39558i	0.716303	+	0.697789i	$0.245833\pi$
$349$			26.0716i			1.39558i	−0.716303	+	0.697789i	$0.754167\pi$
$350$	−0.421702	−	1.95249i	−0.0225409	−	0.104365i
$351$		0			0
$352$	−0.892357	+	1.54561i	−0.0475628	+	0.0823811i
$353$	−5.89034	−	10.2024i	−0.313511	−	0.543017i	0.665609	−	0.746301i	$-0.268172\pi$
$353$	−5.89034	−	10.2024i	−0.313511	−	0.543017i	−0.979120	+	0.203284i	$0.934839\pi$
$354$		0			0
$355$	0.246631	+	0.142393i	0.0130898	+	0.00755741i
$356$	−34.2752			−1.81658
$357$		0			0
$358$	1.93110			0.102062
$359$	−4.38266	−	2.53033i	−0.231308	−	0.133546i	0.379867	−	0.925041i	$-0.375970\pi$
$359$	−4.38266	−	2.53033i	−0.231308	−	0.133546i	−0.611175	+	0.791495i	$0.709303\pi$
$360$		0			0
$361$	0.428844	+	0.742779i	0.0225707	+	0.0390936i
$362$	−0.607448	+	1.05213i	−0.0319267	+	0.0552987i
$363$		0			0
$364$	−10.9187	+	9.89620i	−0.572296	+	0.518702i
$365$		−	0.101835i		−	0.00533030i
$366$		0			0
$367$	−31.0035	+	17.8999i	−1.61837	+	0.934367i	−0.631030	+	0.775759i	$0.717367\pi$
$367$	−31.0035	+	17.8999i	−1.61837	+	0.934367i	−0.987342	+	0.158608i	$0.949299\pi$
$368$	25.2255	−	14.5640i	1.31497	−	0.759199i
$369$		0			0
$370$		−	0.0414703i		−	0.00215594i
$371$	−5.69885	+	5.16516i	−0.295870	+	0.268162i
$372$		0			0
$373$	−6.29989	+	10.9117i	−0.326196	+	0.564988i	−0.981754	−	0.190157i	$-0.939100\pi$
$373$	−6.29989	+	10.9117i	−0.326196	+	0.564988i	0.655558	+	0.755145i	$0.272434\pi$
$374$	−0.255864	−	0.443170i	−0.0132304	−	0.0229158i
$375$		0			0
$376$	−6.49483	−	3.74979i	−0.334945	−	0.193381i
$377$	−16.7163			−0.860931
$378$		0			0
$379$	8.98376			0.461465			0.230732	−	0.973017i	$-0.425888\pi$
$379$	8.98376			0.461465			0.230732	+	0.973017i	$0.425888\pi$
$380$	−0.187278	−	0.108125i	−0.00960716	−	0.00554670i
$381$		0			0
$382$	0.329109	+	0.570034i	0.0168387	+	0.0291655i
$383$	9.83486	−	17.0345i	0.502538	−	0.870421i	−0.497458	−	0.867488i	$-0.665733\pi$
$383$	9.83486	−	17.0345i	0.502538	−	0.870421i	0.999996	−	0.00293288i	$-0.000933567\pi$
$384$		0			0
$385$	−0.0137091	−	0.0634733i	−0.000698680	−	0.00323490i
$386$			2.21392i			0.112685i
$387$		0			0
$388$	7.58445	−	4.37889i	0.385042	−	0.222304i
$389$	3.82123	−	2.20619i	0.193744	−	0.111858i	−0.399990	−	0.916520i	$-0.630986\pi$
$389$	3.82123	−	2.20619i	0.193744	−	0.111858i	0.593734	+	0.804661i	$0.297653\pi$
$390$		0			0
$391$			25.5462i			1.29192i
$392$	−1.73518	−	3.82956i	−0.0876397	−	0.193422i
$393$		0			0
$394$	−1.58724	+	2.74918i	−0.0799640	+	0.138502i
$395$	0.0316724	+	0.0548582i	0.00159361	+	0.00276021i
$396$		0			0
$397$	18.0003	+	10.3925i	0.903409	+	0.521584i	0.878305	−	0.478101i	$-0.158675\pi$
$397$	18.0003	+	10.3925i	0.903409	+	0.521584i	0.0251047	+	0.999685i	$0.492008\pi$
$398$	0.689984			0.0345858
$399$		0			0
$400$	−19.3161			−0.965805
$401$	−19.6486	−	11.3441i	−0.981206	−	0.566499i	−0.0785718	−	0.996908i	$-0.525036\pi$
$401$	−19.6486	−	11.3441i	−0.981206	−	0.566499i	−0.902634	+	0.430409i	$0.858369\pi$
$402$		0			0
$403$	−7.53713	−	13.0547i	−0.375451	−	0.650300i
$404$	−14.6178	+	25.3187i	−0.727260	+	1.25965i
$405$		0			0
$406$	0.725280	−	2.25731i	0.0359950	−	0.112028i
$407$			11.1885i			0.554594i
$408$		0			0
$409$	16.3569	−	9.44364i	0.808795	−	0.466958i	−0.0377422	−	0.999288i	$-0.512017\pi$
$409$	16.3569	−	9.44364i	0.808795	−	0.466958i	0.846537	+	0.532329i	$0.178683\pi$
$410$	0.0332004	−	0.0191682i	0.00163965	−	0.000946652i
$411$		0			0
$412$			28.4187i			1.40009i
$413$	−20.0665	−	22.1398i	−0.987406	−	1.08943i
$414$		0			0
$415$	−0.0530284	+	0.0918479i	−0.00260306	+	0.00450864i
$416$	−2.51376	−	4.35395i	−0.123247	−	0.213470i
$417$		0			0
$418$	−0.582796	−	0.336478i	−0.0285055	−	0.0164577i
$419$	−4.98807			−0.243683			−0.121842	−	0.992550i	$-0.538880\pi$
$419$	−4.98807			−0.243683			−0.121842	+	0.992550i	$0.538880\pi$
$420$		0			0
$421$	22.5594			1.09948			0.549739	−	0.835336i	$-0.314727\pi$
$421$	22.5594			1.09948			0.549739	+	0.835336i	$0.314727\pi$
$422$	0.716782	+	0.413835i	0.0348924	+	0.0201451i
$423$		0			0
$424$	−0.873008	−	1.51209i	−0.0423970	−	0.0734338i
$425$	8.47044	−	14.6712i	0.410876	−	0.711659i
$426$		0			0
$427$	26.5853	+	8.54192i	1.28655	+	0.413373i
$428$		−	14.7645i		−	0.713668i
$429$		0			0
$430$	0.00305080	−	0.00176138i	0.000147123	−	8.49413e-5i
$431$	−13.0763	+	7.54959i	−0.629862	+	0.363651i	−0.780699	−	0.624908i	$-0.785137\pi$
$431$	−13.0763	+	7.54959i	−0.629862	+	0.363651i	0.150837	+	0.988559i	$0.451803\pi$
$432$		0			0
$433$		−	14.1933i		−	0.682085i	−0.940048	−	0.341043i	$-0.889220\pi$
$433$		−	14.1933i		−	0.682085i	0.940048	−	0.341043i	$-0.110780\pi$
$434$	2.08988	−	0.451377i	0.100318	−	0.0216668i
$435$		0			0
$436$	−12.7617	+	22.1039i	−0.611175	+	1.05859i
$437$	16.7974	+	29.0939i	0.803528	+	1.39175i
$438$		0			0
$439$	−24.5301	−	14.1624i	−1.17076	−	0.675936i	−0.216898	−	0.976194i	$-0.569594\pi$
$439$	−24.5301	−	14.1624i	−1.17076	−	0.675936i	−0.953858	+	0.300258i	$0.902927\pi$
$440$	0.0147415			0.000702772
$441$		0			0
$442$	1.44153			0.0685667
$443$	−4.06354	−	2.34608i	−0.193065	−	0.111466i	0.400352	−	0.916361i	$-0.368888\pi$
$443$	−4.06354	−	2.34608i	−0.193065	−	0.111466i	−0.593416	+	0.804896i	$0.702221\pi$
$444$		0			0
$445$	0.212737	+	0.368471i	0.0100847	+	0.0174672i
$446$	−0.449127	+	0.777911i	−0.0212668	+	0.0368352i
$447$		0			0
$448$	−19.2869	+	4.16563i	−0.911220	+	0.196807i
$449$			4.99512i			0.235735i	0.993029	+	0.117867i	$0.0376057\pi$
$449$			4.99512i			0.235735i	−0.993029	+	0.117867i	$0.962394\pi$
$450$		0			0
$451$	−8.95733	+	5.17152i	−0.421784	+	0.243517i
$452$	18.2867	−	10.5578i	0.860132	−	0.496598i
$453$		0			0
$454$		−	3.09343i		−	0.145182i
$455$	0.174157	+	0.0559572i	0.00816463	+	0.00262331i
$456$		0			0
$457$	10.2337	−	17.7253i	0.478713	−	0.829155i	−0.520989	−	0.853563i	$-0.674437\pi$
$457$	10.2337	−	17.7253i	0.478713	−	0.829155i	0.999702	+	0.0244084i	$0.00777020\pi$
$458$	−0.398534	−	0.690282i	−0.0186223	−	0.0322547i
$459$		0			0
$460$	−0.316833	−	0.182923i	−0.0147724	−	0.00852885i
$461$	25.6390			1.19413			0.597064	−	0.802193i	$-0.296334\pi$
$461$	25.6390			1.19413			0.597064	+	0.802193i	$0.296334\pi$
$462$		0			0
$463$	−5.36147			−0.249169			−0.124584	−	0.992209i	$-0.539760\pi$
$463$	−5.36147			−0.249169			−0.124584	+	0.992209i	$0.539760\pi$
$464$	−19.8558	−	11.4637i	−0.921782	−	0.532191i
$465$		0			0
$466$	1.38449	+	2.39801i	0.0641354	+	0.111086i
$467$	−5.91205	+	10.2400i	−0.273577	+	0.473849i	−0.969775	−	0.244000i	$-0.921540\pi$
$467$	−5.91205	+	10.2400i	−0.273577	+	0.473849i	0.696198	+	0.717850i	$0.254874\pi$
$468$		0			0
$469$	−0.0571090	−	0.0630097i	−0.00263705	−	0.00290952i
$470$			0.0462810i			0.00213478i
$471$		0			0
$472$	5.87443	−	3.39160i	0.270393	−	0.156111i
$473$	−0.823094	+	0.475214i	−0.0378459	+	0.0218503i
$474$		0			0
$475$		−	22.2783i		−	1.02220i
$476$	5.42246	−	16.8765i	0.248538	−	0.773533i
$477$		0			0
$478$	−0.558295	+	0.966995i	−0.0255358	+	0.0442293i
$479$	6.64497	+	11.5094i	0.303617	+	0.525879i	0.976952	−	0.213457i	$-0.0684725\pi$
$479$	6.64497	+	11.5094i	0.303617	+	0.525879i	−0.673336	+	0.739337i	$0.735139\pi$
$480$		0			0
$481$	−27.2953	−	15.7589i	−1.24456	−	0.718546i
$482$	−4.59349			−0.209228
$483$		0			0
$484$	−1.97719			−0.0898725
$485$	−0.0941493	−	0.0543571i	−0.00427510	−	0.00246823i
$486$		0			0
$487$	10.1754	+	17.6243i	0.461092	+	0.798635i	0.999016	−	0.0443589i	$-0.0141245\pi$
$487$	10.1754	+	17.6243i	0.461092	+	0.798635i	−0.537924	+	0.842993i	$0.680791\pi$
$488$	−3.16953	+	5.48979i	−0.143478	+	0.248511i
$489$		0			0
$490$	−0.0151126	+	0.0210898i	−0.000682716	+	0.000952740i
$491$			31.2104i			1.40851i	0.709949	+	0.704253i	$0.248718\pi$
$491$			31.2104i			1.40851i	−0.709949	+	0.704253i	$0.751282\pi$
$492$		0			0
$493$	17.4142	−	10.0541i	0.784296	−	0.452813i
$494$	1.64173	−	0.947852i	0.0738649	−	0.0426459i
$495$		0			0
$496$		−	20.6754i		−	0.928351i
$497$	6.48099	+	30.0071i	0.290712	+	1.34600i
$498$		0			0
$499$	17.6171	−	30.5137i	0.788650	−	1.36598i	−0.138144	−	0.990412i	$-0.544114\pi$
$499$	17.6171	−	30.5137i	0.788650	−	1.36598i	0.926794	−	0.375570i	$-0.122553\pi$
$500$	0.242625	+	0.420239i	0.0108505	+	0.0187937i
$501$		0			0
$502$	0.978847	+	0.565138i	0.0436881	+	0.0252233i
$503$	29.4167			1.31163			0.655813	−	0.754924i	$-0.272326\pi$
$503$	29.4167			1.31163			0.655813	+	0.754924i	$0.272326\pi$
$504$		0			0
$505$	0.362914			0.0161495
$506$	−0.985962	−	0.569245i	−0.0438313	−	0.0253060i
$507$		0			0
$508$	−14.7296	−	25.5124i	−0.653519	−	1.13193i
$509$	6.57790	−	11.3933i	0.291560	−	0.504997i	−0.682619	−	0.730775i	$-0.739159\pi$
$509$	6.57790	−	11.3933i	0.291560	−	0.504997i	0.974179	+	0.225778i	$0.0724923\pi$
$510$		0			0
$511$	8.13379	−	7.37208i	0.359818	−	0.326121i
$512$		−	11.5368i		−	0.509858i
$513$		0			0
$514$	−2.46297	+	1.42200i	−0.108637	+	0.0627216i
$515$	0.305512	−	0.176387i	0.0134624	−	0.00777255i
$516$		0			0
$517$		−	12.4864i		−	0.549153i
$518$	3.31232	−	3.00213i	0.145535	−	0.131906i
$519$		0			0
$520$	−0.0207633	+	0.0359630i	−0.000910529	+	0.00157708i
$521$	7.85027	+	13.5971i	0.343927	+	0.595698i	0.985158	−	0.171649i	$-0.0549095\pi$
$521$	7.85027	+	13.5971i	0.343927	+	0.595698i	−0.641232	+	0.767347i	$0.721576\pi$
$522$		0			0
$523$	−3.96327	−	2.28820i	−0.173302	−	0.100056i	0.410840	−	0.911707i	$-0.365235\pi$
$523$	−3.96327	−	2.28820i	−0.173302	−	0.100056i	−0.584142	+	0.811652i	$0.698569\pi$
$524$	18.8768			0.824638
$525$		0			0
$526$	−3.96982			−0.173092
$527$	15.7036	+	9.06649i	0.684061	+	0.394943i
$528$		0			0
$529$	16.9175	+	29.3019i	0.735541	+	1.27400i
$530$	−0.00538746	+	0.00933135i	−0.000234016	+	0.000405328i
$531$		0			0
$532$	−4.92130	−	22.7857i	−0.213366	−	0.987885i
$533$		−	29.1362i		−	1.26203i
$534$		0			0
$535$	−0.158724	+	0.0916392i	−0.00686222	+	0.00396191i
$536$	0.0167186	−	0.00965248i	0.000722133	−	0.000416923i
$537$		0			0
$538$		−	1.30457i		−	0.0562442i
$539$	4.07731	−	5.68995i	0.175622	−	0.245083i
$540$		0			0
$541$	−19.1164	+	33.1106i	−0.821880	+	1.42354i	0.0824011	+	0.996599i	$0.473741\pi$
$541$	−19.1164	+	33.1106i	−0.821880	+	1.42354i	−0.904281	+	0.426938i	$0.859592\pi$
$542$	−0.239837	−	0.415410i	−0.0103019	−	0.0178434i
$543$		0			0
$544$	5.23742	+	3.02382i	0.224552	+	0.129645i
$545$	0.316834			0.0135717
$546$		0			0
$547$	22.8244			0.975902			0.487951	−	0.872871i	$-0.337745\pi$
$547$	22.8244			0.975902			0.487951	+	0.872871i	$0.337745\pi$
$548$	7.49112	+	4.32500i	0.320005	+	0.184755i
$549$		0			0
$550$	0.377494	+	0.653838i	0.0160964	+	0.0278797i
$551$	13.2218	−	22.9007i	0.563266	−	0.975605i
$552$		0			0
$553$	−2.08880	+	6.50104i	−0.0888249	+	0.276452i
$554$			1.34522i			0.0571531i
$555$		0			0
$556$	−3.06443	+	1.76925i	−0.129961	+	0.0750330i
$557$	−34.9881	+	20.2004i	−1.48249	+	0.855918i	−0.999803	−	0.0198719i	$-0.993674\pi$
$557$	−34.9881	+	20.2004i	−1.48249	+	0.855918i	−0.482692	+	0.875790i	$0.660341\pi$
$558$		0			0
$559$		−	2.67734i		−	0.113239i
$560$	0.168492	+	0.185901i	0.00712008	+	0.00785575i
$561$		0			0
$562$	2.03736	−	3.52880i	0.0859407	−	0.148854i
$563$	−0.0830765	−	0.143893i	−0.00350126	−	0.00606436i	0.864269	−	0.503029i	$-0.167781\pi$
$563$	−0.0830765	−	0.143893i	−0.00350126	−	0.00606436i	−0.867771	+	0.496965i	$0.834448\pi$
$564$		0			0
$565$	−0.227001	−	0.131059i	−0.00955000	−	0.00551369i
$566$	−3.58491			−0.150685
$567$		0			0
$568$	−6.96905			−0.292415
$569$	2.94549	+	1.70058i	0.123481	+	0.0712920i	0.560468	−	0.828176i	$-0.310621\pi$
$569$	2.94549	+	1.70058i	0.123481	+	0.0712920i	−0.436987	+	0.899468i	$0.643954\pi$
$570$		0			0
$571$	−8.60933	−	14.9118i	−0.360289	−	0.624040i	0.627719	−	0.778440i	$-0.283989\pi$
$571$	−8.60933	−	14.9118i	−0.360289	−	0.624040i	−0.988008	+	0.154400i	$0.950655\pi$
$572$	2.78486	−	4.82353i	0.116441	−	0.201682i
$573$		0			0
$574$	3.93446	+	1.26415i	0.164221	+	0.0527646i
$575$		−	37.6899i		−	1.57178i
$576$		0			0
$577$	24.0560	−	13.8888i	1.00147	−	0.578197i	0.0927843	−	0.995686i	$-0.470423\pi$
$577$	24.0560	−	13.8888i	1.00147	−	0.578197i	0.908682	+	0.417490i	$0.137090\pi$
$578$	0.721598	−	0.416615i	0.0300145	−	0.0173289i
$579$		0			0
$580$			0.287969i			0.0119573i
$581$	−11.1749	+	2.41359i	−0.463614	+	0.100132i
$582$		0			0
$583$	1.45352	−	2.51756i	0.0601985	−	0.104267i
$584$	1.24602	+	2.15816i	0.0515606	+	0.0893055i
$585$		0			0
$586$	−3.04153	−	1.75603i	−0.125644	−	0.0725408i
$587$	−10.9786			−0.453136			−0.226568	−	0.973995i	$-0.572751\pi$
$587$	−10.9786			−0.453136			−0.226568	+	0.973995i	$0.572751\pi$
$588$		0			0
$589$	23.8460			0.982557
$590$	−0.0362520	−	0.0209301i	−0.00149247	−	0.000861677i
$591$		0			0
$592$	−21.6145	−	37.4373i	−0.888349	−	1.53866i
$593$	−14.2407	+	24.6656i	−0.584796	+	1.01290i	0.410105	+	0.912038i	$0.365492\pi$
$593$	−14.2407	+	24.6656i	−0.584796	+	1.01290i	−0.994901	+	0.100858i	$0.967841\pi$
$594$		0			0
$595$	−0.215085	+	0.0464544i	−0.00881761	+	0.00190445i
$596$			22.5750i			0.924707i
$597$		0			0
$598$	2.77744	−	1.60356i	0.113578	−	0.0655743i
$599$	−1.39965	+	0.808088i	−0.0571881	+	0.0330176i	−0.528321	−	0.849044i	$-0.677178\pi$
$599$	−1.39965	+	0.808088i	−0.0571881	+	0.0330176i	0.471133	+	0.882062i	$0.343845\pi$
$600$		0			0
$601$		−	16.0944i		−	0.656506i	−0.944590	−	0.328253i	$-0.893540\pi$
$601$		−	16.0944i		−	0.656506i	0.944590	−	0.328253i	$-0.106460\pi$
$602$	0.361539	+	0.116164i	0.0147352	+	0.00473447i
$603$		0			0
$604$	−12.9637	+	22.4537i	−0.527484	+	0.913629i
$605$	0.0122719	+	0.0212556i	0.000498924	+	0.000864162i
$606$		0			0
$607$	27.6215	+	15.9473i	1.12112	+	0.647279i	0.941687	−	0.336491i	$-0.109240\pi$
$607$	27.6215	+	15.9473i	1.12112	+	0.647279i	0.179434	+	0.983770i	$0.442574\pi$
$608$	7.95303			0.322538
$609$		0			0
$610$	0.0391193			0.00158389
$611$	30.4617	+	17.5870i	1.23235	+	0.711496i
$612$		0			0
$613$	11.0310	+	19.1063i	0.445540	+	0.771697i	0.998090	−	0.0617824i	$-0.0196785\pi$
$613$	11.0310	+	19.1063i	0.445540	+	0.771697i	−0.552550	+	0.833480i	$0.686345\pi$
$614$	−0.342695	+	0.593565i	−0.0138300	+	0.0239543i
$615$		0			0
$616$	1.06717	+	1.17743i	0.0429975	+	0.0474401i
$617$			36.5139i			1.46999i	0.678071	+	0.734997i	$0.262816\pi$
$617$			36.5139i			1.46999i	−0.678071	+	0.734997i	$0.737184\pi$
$618$		0			0
$619$	31.4362	−	18.1497i	1.26353	−	0.729498i	0.289772	−	0.957096i	$-0.406421\pi$
$619$	31.4362	−	18.1497i	1.26353	−	0.729498i	0.973755	+	0.227598i	$0.0730872\pi$
$620$	−0.224892	+	0.129841i	−0.00903187	+	0.00521455i
$621$		0			0
$622$		−	4.29128i		−	0.172065i
$623$	−14.0301	+	43.6662i	−0.562102	+	1.74945i
$624$		0			0
$625$	−12.4955	+	21.6428i	−0.499819	+	0.865712i
$626$	0.721931	+	1.25042i	0.0288542	+	0.0499769i
$627$		0			0
$628$	0.291144	+	0.168092i	0.0116179	+	0.00670761i
$629$	37.9132			1.51170
$630$		0			0
$631$	−30.8272			−1.22721			−0.613606	−	0.789613i	$-0.710282\pi$
$631$	−30.8272			−1.22721			−0.613606	+	0.789613i	$0.710282\pi$
$632$	−1.34245	−	0.775063i	−0.0533997	−	0.0308303i
$633$		0			0
$634$	−0.973440	−	1.68605i	−0.0386602	−	0.0669615i
$635$	−0.182845	+	0.316697i	−0.00725598	+	0.0125677i
$636$		0			0
$637$	8.13823	+	17.9612i	0.322448	+	0.711648i
$638$			0.896141i			0.0354786i
$639$		0			0
$640$	−0.0998094	+	0.0576250i	−0.00394531	+	0.00227783i
$641$	4.45456	−	2.57184i	0.175944	−	0.101582i	−0.409441	−	0.912336i	$-0.634276\pi$
$641$	4.45456	−	2.57184i	0.175944	−	0.101582i	0.585386	+	0.810755i	$0.300943\pi$
$642$		0			0
$643$		−	41.4351i		−	1.63404i	−0.576610	−	0.817020i	$-0.695625\pi$
$643$		−	41.4351i		−	1.63404i	0.576610	−	0.817020i	$-0.304375\pi$
$644$	−8.32575	−	38.5483i	−0.328081	−	1.51902i
$645$		0			0
$646$	−1.14018	+	1.97485i	−0.0448599	+	0.0776996i
$647$	−12.0714	−	20.9083i	−0.474575	−	0.821988i	0.525001	−	0.851102i	$-0.324065\pi$
$647$	−12.0714	−	20.9083i	−0.474575	−	0.821988i	−0.999576	+	0.0291134i	$0.990732\pi$
$648$		0			0
$649$	9.78064	+	5.64685i	0.383924	+	0.221658i
$650$	−2.12679			−0.0834195
$651$		0			0
$652$	−7.66580			−0.300216
$653$	−9.27230	−	5.35337i	−0.362853	−	0.209493i	0.307478	−	0.951555i	$-0.400515\pi$
$653$	−9.27230	−	5.35337i	−0.362853	−	0.209493i	−0.670332	+	0.742062i	$0.733848\pi$
$654$		0			0
$655$	−0.117163	−	0.202933i	−0.00457796	−	0.00792925i
$656$	19.9811	−	34.6083i	0.780132	−	1.35123i
$657$		0			0
$658$	−3.69656	+	3.35038i	−0.144107	+	0.130612i
$659$			2.01031i			0.0783106i	0.999233	+	0.0391553i	$0.0124667\pi$
$659$			2.01031i			0.0783106i	−0.999233	+	0.0391553i	$0.987533\pi$
$660$		0			0
$661$	2.21895	−	1.28111i	0.0863070	−	0.0498294i	−0.456225	−	0.889864i	$-0.650799\pi$
$661$	2.21895	−	1.28111i	0.0863070	−	0.0498294i	0.542532	+	0.840035i	$0.317466\pi$
$662$	−1.79485	+	1.03626i	−0.0697587	+	0.0402752i
$663$		0			0
$664$		−	2.59534i		−	0.100719i
$665$	−0.214410	+	0.194331i	−0.00831445	+	0.00753582i
$666$		0			0
$667$	22.3683	−	38.7430i	0.866103	−	1.50013i
$668$	2.09310	+	3.62536i	0.0809846	+	0.140269i
$669$		0			0
$670$	−0.000103173	0	5.95668e-5i	−3.98591e−6	0	2.30127e-6i
$671$	−10.5542			−0.407442
$672$		0			0
$673$	−2.93560			−0.113159			−0.0565795	−	0.998398i	$-0.518019\pi$
$673$	−2.93560			−0.113159			−0.0565795	+	0.998398i	$0.518019\pi$
$674$	0.0412674	+	0.0238258i	0.00158956	+	0.000917734i
$675$		0			0
$676$	−5.00684	−	8.67211i	−0.192571	−	0.333543i
$677$	−10.0543	+	17.4146i	−0.386419	+	0.669297i	−0.991965	−	0.126513i	$-0.959621\pi$
$677$	−10.0543	+	17.4146i	−0.386419	+	0.669297i	0.605546	+	0.795810i	$0.292955\pi$
$678$		0			0
$679$	−2.47406	−	11.4549i	−0.0949458	−	0.439600i
$680$		−	0.0499527i		−	0.00191560i
$681$		0			0
$682$	−0.699848	+	0.404057i	−0.0267986	+	0.0154722i
$683$	13.2480	−	7.64873i	0.506920	−	0.292670i	−0.224647	−	0.974440i	$-0.572123\pi$
$683$	13.2480	−	7.64873i	0.506920	−	0.292670i	0.731567	+	0.681770i	$0.238789\pi$
$684$		0			0
$685$		−	0.107377i		−	0.00410265i
$686$	−2.77852	+	0.319666i	−0.106084	+	0.0122049i
$687$		0			0
$688$	1.83608	−	3.18018i	0.0699997	−	0.121243i
$689$	4.09453	+	7.09194i	0.155989	+	0.270181i
$690$		0			0
$691$	−1.30032	−	0.750738i	−0.0494664	−	0.0285594i	0.475063	−	0.879952i	$-0.342425\pi$
$691$	−1.30032	−	0.750738i	−0.0494664	−	0.0285594i	−0.524529	+	0.851392i	$0.675759\pi$
$692$	1.94291			0.0738584
$693$		0			0
$694$	0.665242			0.0252522
$695$	0.0380402	+	0.0219625i	0.00144295	+	0.000833087i
$696$		0			0
$697$	17.5241	+	30.3527i	0.663773	+	1.14969i
$698$	−1.96861	+	3.40972i	−0.0745128	+	0.129060i
$699$		0			0
$700$	−8.00011	+	24.8990i	−0.302376	+	0.941094i
$701$		−	2.44984i		−	0.0925291i	−0.998929	−	0.0462645i	$-0.985268\pi$
$701$		−	2.44984i		−	0.0925291i	0.998929	−	0.0462645i	$-0.0147317\pi$
$702$		0			0
$703$	43.1785	−	24.9291i	1.62851	−	0.940219i
$704$	6.45869	−	3.72893i	0.243421	−	0.140539i
$705$		0			0
$706$		−	1.77907i		−	0.0669561i
$707$	26.2722	+	28.9867i	0.988066	+	1.09016i
$708$		0			0
$709$	−7.57434	+	13.1191i	−0.284460	+	0.492700i	−0.972478	−	0.232994i	$-0.925148\pi$
$709$	−7.57434	+	13.1191i	−0.284460	+	0.492700i	0.688018	+	0.725694i	$0.258481\pi$
$710$	0.0215035	+	0.0372451i	0.000807012	+	0.00139779i
$711$		0			0
$712$	−9.01694	−	5.20594i	−0.337924	−	0.195101i
$713$	40.3421			1.51082
$714$		0			0
$715$	−0.0691396			−0.00258568
$716$	−21.8959	−	12.6416i	−0.818288	−	0.472439i
$717$		0			0
$718$	−0.382119	−	0.661850i	−0.0142606	−	0.0247000i
$719$	−13.6910	+	23.7135i	−0.510588	+	0.884364i	0.489337	+	0.872095i	$0.337239\pi$
$719$	−13.6910	+	23.7135i	−0.510588	+	0.884364i	−0.999925	+	0.0122691i	$0.996095\pi$
$720$		0			0
$721$	36.2051	+	11.6328i	1.34835	+	0.433227i
$722$			0.129524i			0.00482039i
$723$		0			0
$724$	13.7752	−	7.95310i	0.511950	−	0.295575i
$725$	−25.6923	+	14.8335i	−0.954188	+	0.550901i
$726$		0			0
$727$		−	27.5126i		−	1.02039i	−0.860060	−	0.510193i	$-0.829574\pi$
$727$		−	27.5126i		−	1.02039i	0.860060	−	0.510193i	$-0.170426\pi$
$728$	−4.37554	+	0.945039i	−0.162168	+	0.0350255i
$729$		0			0
$730$	0.00768935	−	0.0133183i	0.000284596	−	0.000492934i
$731$	1.61030	+	2.78912i	0.0595591	+	0.103159i
$732$		0			0
$733$	16.0549	+	9.26927i	0.593000	+	0.342368i	0.766283	−	0.642504i	$-0.222104\pi$
$733$	16.0549	+	9.26927i	0.593000	+	0.342368i	−0.173283	+	0.984872i	$0.555438\pi$
$734$	−5.40633			−0.199551
$735$		0			0
$736$	13.4548			0.495949
$737$	0.0278356	+	0.0160709i	0.00102534	+	0.000591979i
$738$		0			0
$739$	−7.51515	−	13.0166i	−0.276449	−	0.478824i	0.694050	−	0.719926i	$-0.255824\pi$
$739$	−7.51515	−	13.0166i	−0.276449	−	0.478824i	−0.970500	+	0.241102i	$0.922491\pi$
$740$	−0.271478	+	0.470213i	−0.00997972	+	0.0172854i
$741$		0			0
$742$	−1.13532	+	0.245210i	−0.0416791	+	0.00900194i
$743$		−	8.46353i		−	0.310497i	−0.987875	−	0.155248i	$-0.950382\pi$
$743$		−	8.46353i		−	0.310497i	0.987875	−	0.155248i	$-0.0496178\pi$
$744$		0			0
$745$	0.242690	−	0.140117i	0.00889146	−	0.00513349i
$746$	−1.64784	+	0.951381i	−0.0603317	+	0.0348325i
$747$		0			0
$748$			6.69989i			0.244972i
$749$	−18.8098	−	6.04363i	−0.687294	−	0.220829i
$750$		0			0
$751$	7.20133	−	12.4731i	0.262780	−	0.455148i	−0.704200	−	0.710002i	$-0.748694\pi$
$751$	7.20133	−	12.4731i	0.262780	−	0.455148i	0.966980	+	0.254854i	$0.0820273\pi$
$752$	24.1218	+	41.7802i	0.879632	+	1.52357i
$753$		0			0
$754$	−2.18621	−	1.26221i	−0.0796170	−	0.0459669i
$755$	0.321848			0.0117133
$756$		0			0
$757$	16.2604			0.590994			0.295497	−	0.955344i	$-0.404515\pi$
$757$	16.2604			0.590994			0.295497	+	0.955344i	$0.404515\pi$
$758$	1.17493	+	0.678344i	0.0426753	+	0.0246386i
$759$		0			0
$760$	−0.0328455	−	0.0568900i	−0.00119143	−	0.00206362i
$761$	12.2187	−	21.1634i	0.442927	−	0.767173i	−0.554978	−	0.831865i	$-0.687273\pi$
$761$	12.2187	−	21.1634i	0.442927	−	0.767173i	0.997905	+	0.0646925i	$0.0206066\pi$
$762$		0			0
$763$	22.9363	+	25.3062i	0.830351	+	0.916146i
$764$		−	8.61782i		−	0.311782i
$765$		0			0
$766$	2.57247	−	1.48522i	0.0929472	−	0.0536631i
$767$	−27.5519	+	15.9071i	−0.994842	+	0.574372i
$768$		0			0
$769$			8.60701i			0.310377i	0.987885	+	0.155188i	$0.0495984\pi$
$769$			8.60701i			0.310377i	−0.987885	+	0.155188i	$0.950402\pi$
$770$	0.00299981	−	0.00933639i	0.000108106	−	0.000336460i
$771$		0			0
$772$	14.4930	−	25.1026i	0.521615	−	0.903464i
$773$	9.81608	+	17.0019i	0.353060	+	0.611517i	0.986784	−	0.162042i	$-0.0518079\pi$
$773$	9.81608	+	17.0019i	0.353060	+	0.611517i	−0.633724	+	0.773559i	$0.718475\pi$
$774$		0			0
$775$	−23.1686	−	13.3764i	−0.832240	−	0.480494i
$776$	2.66037			0.0955019
$777$		0			0
$778$	0.666338			0.0238894
$779$	39.9156	+	23.0453i	1.43013	+	0.825684i
$780$		0			0
$781$	−5.80156	−	10.0486i	−0.207596	−	0.359567i
$782$	−1.92893	+	3.34101i	−0.0689786	+	0.119474i
$783$		0			0
$784$	−2.65081	+	26.9156i	−0.0946716	+	0.961271i
$785$		−	0.00417321i		−	0.000148948i
$786$		0			0
$787$	−36.6104	+	21.1370i	−1.30502	+	0.753453i	−0.981260	−	0.192686i	$-0.938280\pi$
$787$	−36.6104	+	21.1370i	−1.30502	+	0.753453i	−0.323759	+	0.946140i	$0.604947\pi$
$788$	35.9941	−	20.7812i	1.28223	−	0.740299i
$789$		0			0
$790$			0.00956604i			0.000340345i
$791$	−5.96515	−	27.6187i	−0.212096	−	0.982008i
$792$		0			0
$793$	14.8656	−	25.7479i	0.527891	−	0.914335i
$794$	1.56943	+	2.71833i	0.0556969	+	0.0964698i
$795$		0			0
$796$	−7.82343	−	4.51686i	−0.277294	−	0.160096i
$797$	31.2349			1.10640			0.553198	−	0.833049i	$-0.313407\pi$
$797$	31.2349			1.10640			0.553198	+	0.833049i	$0.313407\pi$
$798$		0			0
$799$	−42.3113			−1.49687
$800$	−7.72711	−	4.46125i	−0.273194	−	0.157729i
$801$		0			0
$802$	−1.71314	−	2.96725i	−0.0604932	−	0.104777i
$803$	−2.07456	+	3.59324i	−0.0732095	+	0.126803i
$804$		0			0
$805$	−0.362733	+	0.328764i	−0.0127847	+	0.0115874i
$806$		−	2.27645i		−	0.0801844i
$807$		0			0
$808$	−7.69114	+	4.44048i	−0.270573	+	0.156216i
$809$	4.53051	−	2.61569i	0.159284	−	0.0919628i	−0.418239	−	0.908337i	$-0.637353\pi$
$809$	4.53051	−	2.61569i	0.159284	−	0.0919628i	0.577523	+	0.816374i	$0.304019\pi$
$810$		0			0
$811$		−	44.4357i		−	1.56035i	−0.625563	−	0.780174i	$-0.715131\pi$
$811$		−	44.4357i		−	1.56035i	0.625563	−	0.780174i	$-0.284869\pi$
$812$	−23.0007	+	20.8468i	−0.807167	+	0.731578i
$813$		0			0
$814$	−0.844820	+	1.46327i	−0.0296109	+	0.0512876i
$815$	0.0475796	+	0.0824102i	0.00166664	+	0.00288670i
$816$		0			0
$817$	3.66787	+	2.11765i	0.128322	+	0.0740870i
$818$	2.85227			0.0997274
$819$		0			0
$820$	−0.501926			−0.0175280
$821$	−25.3721	−	14.6486i	−0.885491	−	0.511239i	−0.0130262	−	0.999915i	$-0.504146\pi$
$821$	−25.3721	−	14.6486i	−0.885491	−	0.511239i	−0.872465	+	0.488677i	$0.837480\pi$
$822$		0			0
$823$	10.6610	+	18.4655i	0.371620	+	0.643665i	0.989815	−	0.142360i	$-0.0454690\pi$
$823$	10.6610	+	18.4655i	0.371620	+	0.643665i	−0.618195	+	0.786025i	$0.712136\pi$
$824$	−4.31641	+	7.47625i	−0.150369	+	0.260447i
$825$		0			0
$826$	−0.952631	−	4.41069i	−0.0331463	−	0.153468i
$827$		−	53.7152i		−	1.86786i	−0.357454	−	0.933931i	$-0.616355\pi$
$827$		−	53.7152i		−	1.86786i	0.357454	−	0.933931i	$-0.383645\pi$
$828$		0			0
$829$	−13.5991	+	7.85143i	−0.472315	+	0.272691i	−0.717209	−	0.696859i	$-0.754580\pi$
$829$	−13.5991	+	7.85143i	−0.472315	+	0.272691i	0.244893	+	0.969550i	$0.421247\pi$
$830$	−0.0138705	+	0.00800812i	−0.000481451	+	0.000277966i
$831$		0			0
$832$			21.0087i			0.728344i
$833$	−19.2809	−	13.8163i	−0.668042	−	0.478707i
$834$		0			0
$835$	0.0259827	−	0.0450033i	0.000899167	−	0.00155740i
$836$	4.40538	+	7.63035i	0.152363	+	0.263901i
$837$		0			0
$838$	−0.652357	−	0.376638i	−0.0225353	−	0.0130108i
$839$	−14.0737			−0.485879			−0.242940	−	0.970041i	$-0.578112\pi$
$839$	−14.0737			−0.485879			−0.242940	+	0.970041i	$0.578112\pi$
$840$		0			0
$841$	−6.21352			−0.214259
$842$	2.95039	+	1.70341i	0.101677	+	0.0587034i
$843$		0			0
$844$	−5.41819	−	9.38458i	−0.186502	−	0.323031i
$845$	−0.0621523	+	0.107651i	−0.00213810	+	0.00370330i
$846$		0			0
$847$	−0.809336	+	2.51892i	−0.0278091	+	0.0865512i
$848$			11.2319i			0.385703i
$849$		0			0
$850$	2.21558	−	1.27917i	0.0759939	−	0.0438751i
$851$	73.0484	−	42.1745i	2.50407	−	1.44572i
$852$		0			0
$853$		−	50.7094i		−	1.73626i	−0.496341	−	0.868128i	$-0.665323\pi$
$853$		−	50.7094i		−	1.73626i	0.496341	−	0.868128i	$-0.334677\pi$
$854$	2.83193	+	3.12454i	0.0969067	+	0.106920i
$855$		0			0
$856$	2.24253	−	3.88417i	0.0766479	−	0.132758i
$857$	−14.6507	−	25.3758i	−0.500459	−	0.866821i	−1.00000		0.000530328i	$-0.999831\pi$
$857$	−14.6507	−	25.3758i	−0.500459	−	0.866821i	0.499541	−	0.866290i	$-0.333502\pi$
$858$		0			0
$859$	12.1447	+	7.01173i	0.414371	+	0.239237i	0.692666	−	0.721259i	$-0.256436\pi$
$859$	12.1447	+	7.01173i	0.414371	+	0.239237i	−0.278295	+	0.960496i	$0.589769\pi$
$860$	−0.0461223			−0.00157276
$861$		0			0
$862$	−2.28021			−0.0776644
$863$	24.4278	+	14.1034i	0.831533	+	0.480086i	0.854377	−	0.519653i	$-0.173939\pi$
$863$	24.4278	+	14.1034i	0.831533	+	0.480086i	−0.0228443	+	0.999739i	$0.507272\pi$
$864$		0			0
$865$	−0.0120591	−	0.0208870i	−0.000410023	−	0.000710180i
$866$	1.07170	−	1.85624i	0.0364180	−	0.0630778i
$867$		0			0
$868$	−26.6511	−	8.56307i	−0.904598	−	0.290650i
$869$		−	2.58088i		−	0.0875504i
$870$		0			0
$871$	−0.0784125	+	0.0452715i	−0.00265691	+	0.00153397i
$872$	−6.71458	+	3.87666i	−0.227384	+	0.131280i
$873$		0			0
$874$			5.07334i			0.171608i
$875$	0.634695	−	0.137083i	0.0214566	−	0.00463424i
$876$		0			0
$877$	−7.26766	+	12.5880i	−0.245411	+	0.425065i	−0.962247	−	0.272177i	$-0.912256\pi$
$877$	−7.26766	+	12.5880i	−0.245411	+	0.425065i	0.716836	+	0.697242i	$0.245590\pi$
$878$	−2.13875	−	3.70442i	−0.0721793	−	0.125018i
$879$		0			0
$880$	−0.0821249	−	0.0474148i	−0.00276843	−	0.00159835i
$881$	−29.9215			−1.00808			−0.504041	−	0.863680i	$-0.668154\pi$
$881$	−29.9215			−1.00808			−0.504041	+	0.863680i	$0.668154\pi$
$882$		0			0
$883$	−45.7763			−1.54049			−0.770247	−	0.637746i	$-0.779867\pi$
$883$	−45.7763			−1.54049			−0.770247	+	0.637746i	$0.779867\pi$
$884$	−16.3449	−	9.43674i	−0.549739	−	0.317392i
$885$		0			0
$886$	−0.354295	−	0.613658i	−0.0119028	−	0.0206162i
$887$	3.22746	−	5.59013i	0.108368	−	0.187698i	−0.806742	−	0.590904i	$-0.798771\pi$
$887$	3.22746	−	5.59013i	0.108368	−	0.187698i	0.915109	+	0.403206i	$0.132104\pi$
$888$		0			0
$889$	−38.5318	+	8.32218i	−1.29232	+	0.279117i
$890$			0.0642531i			0.00215377i
$891$		0			0
$892$	10.1849	−	5.88026i	0.341016	−	0.196886i
$893$	−48.1874	+	27.8210i	−1.61253	+	0.930994i
$894$		0			0
$895$			0.313852i			0.0104909i
$896$	−11.8281	−	3.80038i	−0.395148	−	0.126962i
$897$		0			0
$898$	−0.377171	+	0.653279i	−0.0125864	+	0.0218002i
$899$	−15.8773	−	27.5002i	−0.529537	−	0.917185i
$900$		0			0
$901$	−8.53097	−	4.92536i	−0.284208	−	0.164087i
$902$	−1.56196			−0.0520076
$903$		0			0
$904$	6.41436			0.213338
$905$	−0.170998	−	0.0987256i	−0.00568416	−	0.00328175i
$906$		0			0
$907$	26.6528	+	46.1640i	0.884991	+	1.53285i	0.845724	+	0.533621i	$0.179169\pi$
$907$	26.6528	+	46.1640i	0.884991	+	1.53285i	0.0392674	+	0.999229i	$0.487498\pi$
$908$	−20.2506	+	35.0751i	−0.672040	+	1.16401i
$909$		0			0
$910$	0.0185517	+	0.0204685i	0.000614982	+	0.000678525i
$911$		−	26.6987i		−	0.884568i	−0.896875	−	0.442284i	$-0.854168\pi$
$911$		−	26.6987i		−	0.884568i	0.896875	−	0.442284i	$-0.145832\pi$
$912$		0			0
$913$	3.74220	−	2.16056i	0.123849	−	0.0715041i
$914$	2.67680	−	1.54545i	0.0885406	−	0.0511189i
$915$		0			0
$916$			10.4357i			0.344806i
$917$	7.72696	−	24.0489i	0.255167	−	0.794164i
$918$		0			0
$919$	−18.4699	+	31.9908i	−0.609266	+	1.05528i	0.382095	+	0.924123i	$0.375203\pi$
$919$	−18.4699	+	31.9908i	−0.609266	+	1.05528i	−0.991362	+	0.131157i	$0.958131\pi$
$920$	−0.0555672	−	0.0962452i	−0.00183200	−	0.00317311i
$921$		0			0
$922$	3.35316	+	1.93595i	0.110430	+	0.0637570i
$923$	32.6858			1.07587
$924$		0			0
$925$	−55.9358			−1.83916
$926$	−0.701191	−	0.404833i	−0.0230426	−	0.0133036i
$927$		0			0
$928$	−5.29533	−	9.17179i	−0.173828	−	0.301079i
$929$	−17.2432	+	29.8660i	−0.565729	+	0.979872i	0.431252	+	0.902232i	$0.358072\pi$
$929$	−17.2432	+	29.8660i	−0.565729	+	0.979872i	−0.996981	+	0.0776407i	$0.975261\pi$
$930$		0			0
$931$	−31.0432	−	3.05732i	−1.01740	−	0.100199i
$932$		−	36.2534i		−	1.18752i
$933$		0			0
$934$	−1.54640	+	0.892812i	−0.0505996	+	0.0292137i
$935$	0.0720263	−	0.0415844i	0.00235551	−	0.00135996i
$936$		0			0
$937$			39.5642i			1.29251i	0.763123	+	0.646254i	$0.223665\pi$
$937$			39.5642i			1.29251i	−0.763123	+	0.646254i	$0.776335\pi$
$938$	−0.00271118	−	0.0125528i	−8.85232e−5	−	0.000409863i
$939$		0			0
$940$	0.302970	−	0.524760i	0.00988180	−	0.0171158i
$941$	20.5914	+	35.6654i	0.671261	+	1.16266i	0.977547	+	0.210718i	$0.0675802\pi$
$941$	20.5914	+	35.6654i	0.671261	+	1.16266i	−0.306286	+	0.951939i	$0.599086\pi$
$942$		0			0
$943$	67.5284	+	38.9875i	2.19903	+	1.26961i
$944$	−43.6353			−1.42021
$945$		0			0
$946$	−0.143529			−0.00466654
$947$	−13.8394	−	7.99017i	−0.449719	−	0.259646i	0.257992	−	0.966147i	$-0.416939\pi$
$947$	−13.8394	−	7.99017i	−0.449719	−	0.259646i	−0.707712	+	0.706501i	$0.750272\pi$
$948$		0			0
$949$	−5.84400	−	10.1221i	−0.189704	−	0.328577i
$950$	1.68219	−	2.91363i	0.0545773	−	0.0945307i
$951$		0			0
$952$	3.98983	−	3.61619i	0.129311	−	0.117201i
$953$		−	5.57089i		−	0.180459i	−0.995921	−	0.0902294i	$-0.971240\pi$
$953$		−	5.57089i		−	0.180459i	0.995921	−	0.0902294i	$-0.0287600\pi$
$954$		0			0
$955$	−0.0926448	+	0.0534885i	−0.00299792	+	0.00173085i
$956$	12.6605	−	7.30956i	0.409471	−	0.236408i
$957$		0			0
$958$			2.00699i			0.0648429i
$959$	8.57639	−	7.77323i	0.276946	−	0.251011i
$960$		0			0
$961$	−1.18233	+	2.04785i	−0.0381396	+	0.0660597i
$962$	−2.37985	−	4.12201i	−0.0767293	−	0.132899i
$963$		0			0
$964$	52.0836	+	30.0705i	1.67750	+	0.968505i
$965$	−0.359817			−0.0115829
$966$		0			0
$967$	−21.0889			−0.678173			−0.339087	−	0.940755i	$-0.610118\pi$
$967$	−21.0889			−0.678173			−0.339087	+	0.940755i	$0.610118\pi$
$968$	−0.520151	−	0.300309i	−0.0167183	−	0.00965230i
$969$		0			0
$970$	−0.00820878	−	0.0142180i	−0.000263568	−	0.000456513i
$971$	−22.1696	+	38.3988i	−0.711456	+	1.23228i	0.252855	+	0.967504i	$0.418630\pi$
$971$	−22.1696	+	38.3988i	−0.711456	+	1.23228i	−0.964311	+	0.264773i	$0.914703\pi$
$972$		0			0
$973$	0.999624	+	4.62827i	0.0320465	+	0.148376i
$974$			3.07329i			0.0984746i
$975$		0			0
$976$	35.3150	−	20.3891i	1.13041	−	0.652640i
$977$	−13.8984	+	8.02425i	−0.444650	+	0.256719i	−0.705568	−	0.708642i	$-0.749308\pi$
$977$	−13.8984	+	8.02425i	−0.444650	+	0.256719i	0.260918	+	0.965361i	$0.415975\pi$
$978$		0			0
$979$		−	17.3353i		−	0.554037i
$980$	0.309416	−	0.140196i	0.00988392	−	0.00447841i
$981$		0			0
$982$	−2.35663	+	4.08180i	−0.0752031	+	0.130256i
$983$	17.7921	+	30.8169i	0.567480	+	0.982905i	0.996814	+	0.0797590i	$0.0254151\pi$
$983$	17.7921	+	30.8169i	0.567480	+	0.982905i	−0.429334	+	0.903146i	$0.641252\pi$
$984$		0			0
$985$	−0.446811	−	0.257966i	−0.0142366	−	0.00821949i
$986$	3.03665			0.0967066
$987$		0			0
$988$	−24.8198			−0.789623
$989$	6.20522	+	3.58258i	0.197314	+	0.113920i
$990$		0			0
$991$	8.22417	+	14.2447i	0.261249	+	0.452497i	0.966574	−	0.256387i	$-0.0825322\pi$
$991$	8.22417	+	14.2447i	0.261249	+	0.452497i	−0.705325	+	0.708884i	$0.749199\pi$
$992$	4.77518	−	8.27085i	0.151612	−	0.262600i
$993$		0			0
$994$	−1.41816	+	4.41379i	−0.0449813	+	0.139997i
$995$			0.112140i			0.00355507i
$996$		0			0
$997$	21.5684	−	12.4525i	0.683078	−	0.394375i	−0.117936	−	0.993021i	$-0.537628\pi$
$997$	21.5684	−	12.4525i	0.683078	−	0.394375i	0.801014	+	0.598646i	$0.204294\pi$
$998$	4.60805	−	2.66046i	0.145865	−	0.0842154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.be.a.89.15	yes	56
3.2	odd	2	inner	693.2.be.a.89.14	✓	56
7.3	odd	6	inner	693.2.be.a.584.14	yes	56
21.17	even	6	inner	693.2.be.a.584.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.be.a.89.14	✓	56	3.2	odd	2	inner
693.2.be.a.89.15	yes	56	1.1	even	1	trivial
693.2.be.a.584.14	yes	56	7.3	odd	6	inner
693.2.be.a.584.15	yes	56	21.17	even	6	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.130783 + 0.0755078i) q^{2} +(-0.988597 - 1.71230i) q^{4} +(-0.0122719 + 0.0212556i) q^{5} +(-2.58612 + 0.558556i) q^{7} -0.600618i q^{8} +O(q^{10})\)	\(q+(0.130783 + 0.0755078i) q^{2} +(-0.988597 - 1.71230i) q^{4} +(-0.0122719 + 0.0212556i) q^{5} +(-2.58612 + 0.558556i) q^{7} -0.600618i q^{8} +(-0.00320993 + 0.00185325i) q^{10} +(0.866025 - 0.500000i) q^{11} +2.81699i q^{13} +(-0.380397 - 0.122222i) q^{14} +(-1.93184 + 3.34605i) q^{16} +(-1.69429 - 2.93460i) q^{17} +(-3.85918 - 2.22810i) q^{19} +0.0485279 q^{20} +0.151016 q^{22} +(-6.52887 - 3.76945i) q^{23} +(2.49970 + 4.32961i) q^{25} +(-0.212704 + 0.368415i) q^{26} +(3.51305 + 3.87603i) q^{28} +5.93410i q^{29} +(-4.63428 + 2.67560i) q^{31} +(-1.54561 + 0.892357i) q^{32} -0.511729i q^{34} +(0.0198642 - 0.0618240i) q^{35} +(-5.59426 + 9.68954i) q^{37} +(-0.336478 - 0.582796i) q^{38} +(0.0127665 + 0.00737074i) q^{40} -10.3430 q^{41} -0.950427 q^{43} +(-1.71230 - 0.988597i) q^{44} +(-0.569245 - 0.985962i) q^{46} +(6.24322 - 10.8136i) q^{47} +(6.37603 - 2.88898i) q^{49} +0.754987i q^{50} +(4.82353 - 2.78486i) q^{52} +(2.51756 - 1.45352i) q^{53} +0.0245438i q^{55} +(0.335479 + 1.55327i) q^{56} +(-0.448071 + 0.776081i) q^{58} +(5.64685 + 9.78064i) q^{59} +(-9.14023 - 5.27712i) q^{61} -0.808115 q^{62} +7.45785 q^{64} +(-0.0598767 - 0.0345698i) q^{65} +(0.0160709 + 0.0278356i) q^{67} +(-3.34994 + 5.80227i) q^{68} +(0.00726611 - 0.00658565i) q^{70} -11.6031i q^{71} +(-3.59324 + 2.07456i) q^{73} +(-1.46327 + 0.844820i) q^{74} +8.81077i q^{76} +(-1.96037 + 1.77678i) q^{77} +(1.29044 - 2.23511i) q^{79} +(-0.0474148 - 0.0821249i) q^{80} +(-1.35270 - 0.780980i) q^{82} +4.32112 q^{83} +0.0831688 q^{85} +(-0.124300 - 0.0717647i) q^{86} +(-0.300309 - 0.520151i) q^{88} +(8.66763 - 15.0128i) q^{89} +(-1.57344 - 7.28506i) q^{91} +14.9059i q^{92} +(1.63302 - 0.942823i) q^{94} +(0.0947191 - 0.0546861i) q^{95} +4.42939i q^{97} +(1.05202 + 0.103609i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 32 q^{4} - 4 q^{7}+O(q^{10}) \) 56 * q + 32 * q^4 - 4 * q^7	\( 56 q + 32 q^{4} - 4 q^{7} - 40 q^{16} - 12 q^{19} - 36 q^{25} + 48 q^{28} + 12 q^{31} - 12 q^{37} - 120 q^{40} - 8 q^{43} - 56 q^{46} + 20 q^{49} + 72 q^{52} + 32 q^{58} + 24 q^{61} - 64 q^{64} + 44 q^{67} + 40 q^{70} + 12 q^{73} - 20 q^{79} + 168 q^{82} - 16 q^{85} + 24 q^{88} - 92 q^{91} - 96 q^{94}+O(q^{100}) \) 56 * q + 32 * q^4 - 4 * q^7 - 40 * q^16 - 12 * q^19 - 36 * q^25 + 48 * q^28 + 12 * q^31 - 12 * q^37 - 120 * q^40 - 8 * q^43 - 56 * q^46 + 20 * q^49 + 72 * q^52 + 32 * q^58 + 24 * q^61 - 64 * q^64 + 44 * q^67 + 40 * q^70 + 12 * q^73 - 20 * q^79 + 168 * q^82 - 16 * q^85 + 24 * q^88 - 92 * q^91 - 96 * q^94

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