LMFDB - Embedded newform 693.2.be.a.89.14

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			89.14
Character	$\chi$	$=$	693.89
Dual form			693.2.be.a.584.14

$q$-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	0.453048	−	0.891486i	$-0.350337\pi$
$2$	−0.130783	−	0.0755078i	−0.0924778	−	0.0533921i	−0.545526	+	0.838094i	$0.683670\pi$
$3$		0			0
$3$		0			0
$4$	−0.988597	−	1.71230i	−0.494299	−	0.856150i
$5$	0.0122719	−	0.0212556i	0.00548817	−	0.00950579i	−0.863268	−	0.504745i	$-0.831586\pi$
$5$	0.0122719	−	0.0212556i	0.00548817	−	0.00950579i	0.868756	+	0.495240i	$0.164920\pi$
$6$		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	0.994991	−	0.0999620i	$-0.0318721\pi$
$17$	1.69429	+	2.93460i	0.410926	+	0.711745i	−0.584065	+	0.811707i	$0.698539\pi$
$18$		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	0.989806	−	0.142426i	$-0.0454902\pi$
$23$	6.52887	+	3.76945i	1.36136	+	0.785984i	0.371559	+	0.928410i	$0.378824\pi$
$24$		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	$-0.814259\pi$
$29$		−	5.93410i		−	1.10193i	0.834527	−	0.550967i	$-0.185741\pi$
$30$		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	$-0.200736\pi$
$41$	10.3430			1.61531			0.807655	+	0.589655i	$0.200736\pi$
$42$		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	$0.531098\pi$
$47$	−6.24322	+	10.8136i	−0.910667	+	1.57732i	−0.813125	+	0.582089i	$0.802235\pi$
$48$		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	−0.662840	−	0.748761i	$-0.730649\pi$
$53$	−2.51756	+	1.45352i	−0.345814	+	0.199656i	0.317026	+	0.948417i	$0.397316\pi$
$54$		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	$-0.903775\pi$
$59$	−5.64685	−	9.78064i	−0.735158	−	1.27333i	0.219497	−	0.975613i	$-0.429559\pi$
$60$		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	$0.241739\pi$
$71$			11.6031i			1.37704i	−0.725219	+	0.688518i	$0.758261\pi$
$72$		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	$-0.576214\pi$
$83$	−4.32112			−0.474304			−0.237152	+	0.971472i	$0.576214\pi$
$84$		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	$0.537480\pi$
$89$	−8.66763	+	15.0128i	−0.918766	+	1.59135i	−0.801291	+	0.598274i	$0.795853\pi$
$90$		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	$0.0964560\pi$
$101$	7.39318	+	12.8054i	0.735649	+	1.27418i	−0.218789	+	0.975772i	$0.570211\pi$
$102$		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	0.153701	−	0.988117i	$-0.450881\pi$
$107$	−6.46695	−	3.73369i	−0.625183	−	0.360950i	−0.778884	+	0.627168i	$0.784214\pi$
$108$		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	$-0.832478\pi$
$113$		−	10.6796i		−	1.00465i	0.864679	−	0.502326i	$-0.167522\pi$
$114$		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	−0.578569	−	0.815634i	$-0.696389\pi$
$131$	4.77364	−	8.26819i	0.417075	−	0.722395i	0.995644	+	0.0932385i	$0.0297219\pi$
$132$		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	−0.329343	−	0.944210i	$-0.606827\pi$
$137$	3.78876	−	2.18744i	0.323696	−	0.186886i	0.653039	+	0.757324i	$0.273494\pi$
$138$		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	0.846976	−	0.531632i	$-0.178421\pi$
$149$	9.88801	+	5.70884i	0.810057	+	0.467687i	−0.0369186	+	0.999318i	$0.511754\pi$
$150$		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	$-0.473895\pi$
$167$	2.11725			0.163837			0.0819187	+	0.996639i	$0.473895\pi$
$168$		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	−0.846743	−	0.532002i	$-0.821440\pi$
$173$	0.491331	−	0.851009i	0.0373552	−	0.0647010i	0.884099	+	0.467301i	$0.154773\pi$
$174$		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	−0.853074	−	0.521790i	$-0.825264\pi$
$179$	−11.0742	+	6.39371i	−0.827727	+	0.477888i	0.0253469	+	0.999679i	$0.491931\pi$
$180$		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	0.357182	−	0.934035i	$-0.383738\pi$
$191$	−3.77467	−	2.17931i	−0.273125	−	0.157689i	−0.630307	+	0.776346i	$0.717071\pi$
$192$		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	$-0.730612\pi$
$197$		−	21.0209i		−	1.49768i	0.662754	−	0.748838i	$-0.269388\pi$
$198$		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	$0.0712632\pi$
$227$	10.2421	+	17.7398i	0.679792	+	1.17743i	−0.295252	+	0.955420i	$0.595403\pi$
$228$		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	−0.120370	−	0.992729i	$-0.538408\pi$
$233$	−15.8792	−	9.16788i	−1.04028	−	0.600608i	−0.919914	+	0.392121i	$0.871741\pi$
$234$		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	$-0.923136\pi$
$239$		−	7.39387i		−	0.478270i	0.970986	−	0.239135i	$-0.0768638\pi$
$240$		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	$-0.575905\pi$
$251$	−7.48450			−0.472417			−0.236209	+	0.971702i	$0.575905\pi$
$252$		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	$-0.633497\pi$
$257$	9.41623	−	16.3094i	0.587368	−	1.01735i	0.994576	−	0.104016i	$-0.0331694\pi$
$258$		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	0.409009	−	0.912531i	$-0.365875\pi$
$263$	22.7656	−	13.1437i	1.40379	−	0.810477i	0.994779	+	0.102053i	$0.0325413\pi$
$264$		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	0.967131	−	0.254278i	$-0.0818378\pi$
$269$	4.31934	+	7.48131i	0.263355	+	0.456143i	−0.703777	+	0.710421i	$0.748504\pi$
$270$		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	$0.297731\pi$
$281$			26.9821i			1.60961i	−0.593536	+	0.804807i	$0.702269\pi$
$282$		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	$-0.262274\pi$
$293$	23.2562			1.35864			0.679322	+	0.733840i	$0.262274\pi$
$294$		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	$0.131526\pi$
$311$	14.2081	+	24.6091i	0.805666	+	1.39546i	−0.110174	+	0.993912i	$0.535141\pi$
$312$		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	0.779618	−	0.626256i	$-0.215413\pi$
$317$	11.1647	+	6.44596i	0.627073	+	0.362041i	−0.152544	+	0.988297i	$0.548747\pi$
$318$		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	−0.598891	−	0.800830i	$-0.704392\pi$
$347$	−3.81495	+	2.20256i	−0.204797	+	0.118240i	0.394094	+	0.919070i	$0.371058\pi$
$348$		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	0.979120	−	0.203284i	$-0.0651613\pi$
$353$	5.89034	+	10.2024i	0.313511	+	0.543017i	−0.665609	+	0.746301i	$0.731828\pi$
$354$		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	0.611175	−	0.791495i	$-0.290697\pi$
$359$	4.38266	+	2.53033i	0.231308	+	0.133546i	−0.379867	+	0.925041i	$0.624030\pi$
$360$		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	$0.334267\pi$
$383$	−9.83486	+	17.0345i	−0.502538	+	0.870421i	−0.999996	+	0.00293288i	$0.999066\pi$
$384$		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	−0.593734	−	0.804661i	$-0.702347\pi$
$389$	−3.82123	+	2.20619i	−0.193744	+	0.111858i	0.399990	+	0.916520i	$0.369014\pi$
$390$		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	0.902634	−	0.430409i	$-0.141631\pi$
$401$	19.6486	+	11.3441i	0.981206	+	0.566499i	0.0785718	+	0.996908i	$0.474964\pi$
$402$		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	$-0.461120\pi$
$419$	4.98807			0.243683			0.121842	+	0.992550i	$0.461120\pi$
$420$		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	−0.150837	−	0.988559i	$-0.548197\pi$
$431$	13.0763	−	7.54959i	0.629862	−	0.363651i	0.780699	+	0.624908i	$0.214863\pi$
$432$		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	0.593416	−	0.804896i	$-0.297779\pi$
$443$	4.06354	+	2.34608i	0.193065	+	0.111466i	−0.400352	+	0.916361i	$0.631112\pi$
$444$		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	$-0.962394\pi$
$449$		−	4.99512i		−	0.235735i	0.993029	−	0.117867i	$-0.0376057\pi$
$450$		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	$-0.703666\pi$
$461$	−25.6390			−1.19413			−0.597064	+	0.802193i	$0.703666\pi$
$462$		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	−0.696198	−	0.717850i	$-0.745126\pi$
$467$	5.91205	−	10.2400i	0.273577	−	0.473849i	0.969775	+	0.244000i	$0.0784598\pi$
$468$		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	0.673336	−	0.739337i	$-0.264861\pi$
$479$	−6.64497	−	11.5094i	−0.303617	−	0.525879i	−0.976952	+	0.213457i	$0.931528\pi$
$480$		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	$-0.751282\pi$
$491$		−	31.2104i		−	1.40851i	0.709949	−	0.704253i	$-0.248718\pi$
$492$		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	$-0.727674\pi$
$503$	−29.4167			−1.31163			−0.655813	+	0.754924i	$0.727674\pi$
$504$		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	−0.974179	−	0.225778i	$-0.927508\pi$
$509$	−6.57790	+	11.3933i	−0.291560	+	0.504997i	0.682619	+	0.730775i	$0.260841\pi$
$510$		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	0.641232	−	0.767347i	$-0.278424\pi$
$521$	−7.85027	−	13.5971i	−0.343927	−	0.595698i	−0.985158	+	0.171649i	$0.945090\pi$
$522$		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	0.482692	−	0.875790i	$-0.339659\pi$
$557$	34.9881	−	20.2004i	1.48249	−	0.855918i	0.999803	+	0.0198719i	$0.00632583\pi$
$558$		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	0.867771	−	0.496965i	$-0.165552\pi$
$563$	0.0830765	+	0.143893i	0.00350126	+	0.00606436i	−0.864269	+	0.503029i	$0.832219\pi$
$564$		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	0.436987	−	0.899468i	$-0.356046\pi$
$569$	−2.94549	−	1.70058i	−0.123481	−	0.0712920i	−0.560468	+	0.828176i	$0.689379\pi$
$570$		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	$-0.427249\pi$
$587$	10.9786			0.453136			0.226568	+	0.973995i	$0.427249\pi$
$588$		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	$-0.634508\pi$
$593$	14.2407	−	24.6656i	0.584796	−	1.01290i	0.994901	−	0.100858i	$-0.0321588\pi$
$594$		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	−0.471133	−	0.882062i	$-0.656155\pi$
$599$	1.39965	−	0.808088i	0.0571881	−	0.0330176i	0.528321	+	0.849044i	$0.322822\pi$
$600$		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	$-0.737184\pi$
$617$		−	36.5139i		−	1.46999i	0.678071	−	0.734997i	$-0.262816\pi$
$618$		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	−0.585386	−	0.810755i	$-0.699057\pi$
$641$	−4.45456	+	2.57184i	−0.175944	+	0.101582i	0.409441	+	0.912336i	$0.365724\pi$
$642$		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	0.999576	−	0.0291134i	$-0.00926841\pi$
$647$	12.0714	+	20.9083i	0.474575	+	0.821988i	−0.525001	+	0.851102i	$0.675935\pi$
$648$		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	0.670332	−	0.742062i	$-0.266152\pi$
$653$	9.27230	+	5.35337i	0.362853	+	0.209493i	−0.307478	+	0.951555i	$0.599485\pi$
$654$		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	$-0.987533\pi$
$659$		−	2.01031i		−	0.0783106i	0.999233	−	0.0391553i	$-0.0124667\pi$
$660$		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	−0.605546	−	0.795810i	$-0.707045\pi$
$677$	10.0543	−	17.4146i	0.386419	−	0.669297i	0.991965	+	0.126513i	$0.0403786\pi$
$678$		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	−0.731567	−	0.681770i	$-0.761211\pi$
$683$	−13.2480	+	7.64873i	−0.506920	+	0.292670i	0.224647	+	0.974440i	$0.427877\pi$
$684$		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	$0.0147317\pi$
$701$			2.44984i			0.0925291i	−0.998929	+	0.0462645i	$0.985268\pi$
$702$		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	$-0.662761\pi$
$719$	13.6910	−	23.7135i	0.510588	−	0.884364i	0.999925	−	0.0122691i	$-0.00390547\pi$
$720$		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	$0.0496178\pi$
$743$			8.46353i			0.310497i	−0.987875	+	0.155248i	$0.950382\pi$
$744$		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	−0.997905	−	0.0646925i	$-0.979393\pi$
$761$	−12.2187	+	21.1634i	−0.442927	+	0.767173i	0.554978	+	0.831865i	$0.312727\pi$
$762$		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	0.633724	−	0.773559i	$-0.281525\pi$
$773$	−9.81608	−	17.0019i	−0.353060	−	0.611517i	−0.986784	+	0.162042i	$0.948192\pi$
$774$		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	$-0.686593\pi$
$797$	−31.2349			−1.10640			−0.553198	+	0.833049i	$0.686593\pi$
$798$		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	−0.577523	−	0.816374i	$-0.695981\pi$
$809$	−4.53051	+	2.61569i	−0.159284	+	0.0919628i	0.418239	+	0.908337i	$0.362647\pi$
$810$		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	0.872465	−	0.488677i	$-0.162520\pi$
$821$	25.3721	+	14.6486i	0.885491	+	0.511239i	0.0130262	+	0.999915i	$0.495854\pi$
$822$		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	$0.383645\pi$
$827$			53.7152i			1.86786i	−0.357454	+	0.933931i	$0.616355\pi$
$828$		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	$-0.421888\pi$
$839$	14.0737			0.485879			0.242940	+	0.970041i	$0.421888\pi$
$840$		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	$0.000168809\pi$
$857$	14.6507	+	25.3758i	0.500459	+	0.866821i	−0.499541	+	0.866290i	$0.666498\pi$
$858$		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	0.0228443	−	0.999739i	$-0.492728\pi$
$863$	−24.4278	−	14.1034i	−0.831533	−	0.480086i	−0.854377	+	0.519653i	$0.826061\pi$
$864$		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	$-0.331846\pi$
$881$	29.9215			1.00808			0.504041	+	0.863680i	$0.331846\pi$
$882$		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	−0.915109	−	0.403206i	$-0.867896\pi$
$887$	−3.22746	+	5.59013i	−0.108368	+	0.187698i	0.806742	+	0.590904i	$0.201229\pi$
$888$		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	$0.145832\pi$
$911$			26.6987i			0.884568i	−0.896875	+	0.442284i	$0.854168\pi$
$912$		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	$-0.641928\pi$
$929$	17.2432	−	29.8660i	0.565729	−	0.979872i	0.996981	−	0.0776407i	$-0.0247387\pi$
$930$		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	$-0.932420\pi$
$941$	−20.5914	−	35.6654i	−0.671261	−	1.16266i	0.306286	−	0.951939i	$-0.400914\pi$
$942$		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	0.707712	−	0.706501i	$-0.249728\pi$
$947$	13.8394	+	7.99017i	0.449719	+	0.259646i	−0.257992	+	0.966147i	$0.583061\pi$
$948$		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	$0.0287600\pi$
$953$			5.57089i			0.180459i	−0.995921	+	0.0902294i	$0.971240\pi$
$954$		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	$-0.581370\pi$
$971$	22.1696	−	38.3988i	0.711456	−	1.23228i	0.964311	−	0.264773i	$-0.0852971\pi$
$972$		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	−0.260918	−	0.965361i	$-0.584025\pi$
$977$	13.8984	−	8.02425i	0.444650	−	0.256719i	0.705568	+	0.708642i	$0.250692\pi$
$978$		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	$-0.974585\pi$
$983$	−17.7921	−	30.8169i	−0.567480	−	0.982905i	0.429334	−	0.903146i	$-0.358748\pi$
$984$		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.89.14	✓	56
3.2	odd	2	inner	693.2.be.a.89.15	yes	56
7.3	odd	6	inner	693.2.be.a.584.15	yes	56
21.17	even	6	inner	693.2.be.a.584.14	yes	56

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