LMFDB - Embedded newform 927.2.f.f.262.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(46,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("927.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.f (of order $3$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			262.2
Character	$\chi$	$=$	927.262
Dual form			927.2.f.f.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24321 + 2.15331i) q^{2} +(-2.09117 - 3.62201i) q^{4} +(-1.45965 - 2.52819i) q^{5} +(1.35416 + 2.34547i) q^{7} +5.42622 q^{8} +O(q^{10})$	\(q+(-1.24321 + 2.15331i) q^{2} +(-2.09117 - 3.62201i) q^{4} +(-1.45965 - 2.52819i) q^{5} +(1.35416 + 2.34547i) q^{7} +5.42622 q^{8} +7.25864 q^{10} +(0.0639416 + 0.110750i) q^{11} +1.64811 q^{13} -6.73404 q^{14} +(-2.56362 + 4.44032i) q^{16} +(-0.975790 - 1.69012i) q^{17} +(0.0327746 - 0.0567672i) q^{19} +(-6.10475 + 10.5737i) q^{20} -0.317973 q^{22} -7.84025 q^{23} +(-1.76116 + 3.05043i) q^{25} +(-2.04895 + 3.54889i) q^{26} +(5.66355 - 9.80955i) q^{28} +(-3.64157 + 6.30738i) q^{29} -3.83700 q^{31} +(-0.948049 - 1.64207i) q^{32} +4.85247 q^{34} +(3.95320 - 6.84714i) q^{35} -7.28984 q^{37} +(0.0814917 + 0.141148i) q^{38} +(-7.92039 - 13.7185i) q^{40} +(1.66590 - 2.88543i) q^{41} +(2.11532 - 3.66385i) q^{43} +(0.267425 - 0.463194i) q^{44} +(9.74711 - 16.8825i) q^{46} +(-2.05987 - 3.56779i) q^{47} +(-0.167494 + 0.290109i) q^{49} +(-4.37901 - 7.58467i) q^{50} +(-3.44647 - 5.96946i) q^{52} +(-4.46793 - 7.73868i) q^{53} +(0.186665 - 0.323313i) q^{55} +(7.34796 + 12.7270i) q^{56} +(-9.05450 - 15.6829i) q^{58} +(4.62319 - 8.00760i) q^{59} +7.99282 q^{61} +(4.77021 - 8.26225i) q^{62} -5.53998 q^{64} +(-2.40566 - 4.16673i) q^{65} +(-3.93499 - 6.81560i) q^{67} +(-4.08108 + 7.06863i) q^{68} +(9.82936 + 17.0249i) q^{70} +(4.59233 + 7.95414i) q^{71} -14.1779 q^{73} +(9.06284 - 15.6973i) q^{74} -0.274148 q^{76} +(-0.173174 + 0.299947i) q^{77} -11.7918 q^{79} +14.9680 q^{80} +(4.14215 + 7.17442i) q^{82} +(5.96249 - 10.3273i) q^{83} +(-2.84863 + 4.93396i) q^{85} +(5.25960 + 9.10990i) q^{86} +(0.346961 + 0.600954i) q^{88} +2.09140 q^{89} +(2.23180 + 3.86559i) q^{91} +(16.3953 + 28.3974i) q^{92} +10.2434 q^{94} -0.191358 q^{95} +(-7.43871 + 12.8842i) q^{97} +(-0.416463 - 0.721335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q - 18 * q^4 + 8 * q^7	$ 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) $ 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.24321	+	2.15331i	−0.879086	+	1.52262i	−0.0267399	+	0.999642i	$0.508513\pi$
$2$	−1.24321	+	2.15331i	−0.879086	+	1.52262i	−0.852346	+	0.522979i	$0.824821\pi$
$3$		0			0
$3$		0			0
$4$	−2.09117	−	3.62201i	−1.04558	−	1.81100i
$5$	−1.45965	−	2.52819i	−0.652776	−	1.13064i	−0.982446	−	0.186545i	$-0.940271\pi$
$5$	−1.45965	−	2.52819i	−0.652776	−	1.13064i	0.329670	−	0.944096i	$-0.393062\pi$
$6$		0			0
$7$	1.35416	+	2.34547i	0.511824	+	0.886505i	0.999906	+	0.0137075i	$0.00436337\pi$
$7$	1.35416	+	2.34547i	0.511824	+	0.886505i	−0.488082	+	0.872798i	$0.662303\pi$
$8$	5.42622			1.91846
$9$		0			0
$10$	7.25864			2.29538
$11$	0.0639416	+	0.110750i	0.0192791	+	0.0333924i	0.875504	−	0.483211i	$-0.160530\pi$
$11$	0.0639416	+	0.110750i	0.0192791	+	0.0333924i	−0.856225	+	0.516603i	$0.827196\pi$
$12$		0			0
$13$	1.64811			0.457103			0.228552	−	0.973532i	$-0.426601\pi$
$13$	1.64811			0.457103			0.228552	+	0.973532i	$0.426601\pi$
$14$	−6.73404			−1.79975
$15$		0			0
$16$	−2.56362	+	4.44032i	−0.640906	+	1.11008i
$17$	−0.975790	−	1.69012i	−0.236664	−	0.409914i	0.723091	−	0.690753i	$-0.242721\pi$
$17$	−0.975790	−	1.69012i	−0.236664	−	0.409914i	−0.959755	+	0.280839i	$0.909387\pi$
$18$		0			0
$19$	0.0327746	−	0.0567672i	0.00751900	−	0.0130233i	−0.862241	−	0.506498i	$-0.830940\pi$
$19$	0.0327746	−	0.0567672i	0.00751900	−	0.0130233i	0.869760	+	0.493474i	$0.164273\pi$
$20$	−6.10475	+	10.5737i	−1.36506	+	2.36436i
$21$		0			0
$22$	−0.317973			−0.0677920
$23$	−7.84025			−1.63480			−0.817402	−	0.576067i	$-0.804587\pi$
$23$	−7.84025			−1.63480			−0.817402	+	0.576067i	$0.804587\pi$
$24$		0			0
$25$	−1.76116	+	3.05043i	−0.352233	+	0.610085i
$26$	−2.04895	+	3.54889i	−0.401833	+	0.695995i
$27$		0			0
$28$	5.66355	−	9.80955i	1.07031	−	1.85383i
$29$	−3.64157	+	6.30738i	−0.676222	+	1.17125i	0.299888	+	0.953974i	$0.403051\pi$
$29$	−3.64157	+	6.30738i	−0.676222	+	1.17125i	−0.976110	+	0.217276i	$0.930283\pi$
$30$		0			0
$31$	−3.83700			−0.689145			−0.344573	−	0.938760i	$-0.611976\pi$
$31$	−3.83700			−0.689145			−0.344573	+	0.938760i	$0.611976\pi$
$32$	−0.948049	−	1.64207i	−0.167593	−	0.290279i
$33$		0			0
$34$	4.85247			0.832191
$35$	3.95320	−	6.84714i	0.668213	−	1.15738i
$36$		0			0
$37$	−7.28984			−1.19844			−0.599221	−	0.800583i	$-0.704523\pi$
$37$	−7.28984			−1.19844			−0.599221	+	0.800583i	$0.704523\pi$
$38$	0.0814917	+	0.141148i	0.0132197	+	0.0228972i
$39$		0			0
$40$	−7.92039	−	13.7185i	−1.25232	−	2.16909i
$41$	1.66590	−	2.88543i	0.260170	−	0.450628i	−0.706117	−	0.708095i	$-0.749555\pi$
$41$	1.66590	−	2.88543i	0.260170	−	0.450628i	0.966287	+	0.257467i	$0.0828879\pi$
$42$		0			0
$43$	2.11532	−	3.66385i	0.322584	−	0.558732i	−0.658437	−	0.752636i	$-0.728782\pi$
$43$	2.11532	−	3.66385i	0.322584	−	0.558732i	0.981020	+	0.193905i	$0.0621152\pi$
$44$	0.267425	−	0.463194i	0.0403159	−	0.0698291i
$45$		0			0
$46$	9.74711	−	16.8825i	1.43713	−	2.48919i
$47$	−2.05987	−	3.56779i	−0.300462	−	0.520416i	0.675778	−	0.737105i	$-0.263808\pi$
$47$	−2.05987	−	3.56779i	−0.300462	−	0.520416i	−0.976241	+	0.216689i	$0.930474\pi$
$48$		0			0
$49$	−0.167494	+	0.290109i	−0.0239278	+	0.0414441i
$50$	−4.37901	−	7.58467i	−0.619286	−	1.07263i
$51$		0			0
$52$	−3.44647	−	5.96946i	−0.477939	−	0.827815i
$53$	−4.46793	−	7.73868i	−0.613717	−	1.06299i	−0.990608	−	0.136731i	$-0.956340\pi$
$53$	−4.46793	−	7.73868i	−0.613717	−	1.06299i	0.376891	−	0.926258i	$-0.376993\pi$
$54$		0			0
$55$	0.186665	−	0.323313i	0.0251699	−	0.0435955i
$56$	7.34796	+	12.7270i	0.981913	+	1.70072i
$57$		0			0
$58$	−9.05450	−	15.6829i	−1.18891	−	2.05926i
$59$	4.62319	−	8.00760i	0.601888	−	1.04250i	−0.390647	−	0.920541i	$-0.627749\pi$
$59$	4.62319	−	8.00760i	0.601888	−	1.04250i	0.992535	−	0.121960i	$-0.0389180\pi$
$60$		0			0
$61$	7.99282			1.02338			0.511688	−	0.859171i	$-0.329020\pi$
$61$	7.99282			1.02338			0.511688	+	0.859171i	$0.329020\pi$
$62$	4.77021	−	8.26225i	0.605818	−	1.04931i
$63$		0			0
$64$	−5.53998			−0.692497
$65$	−2.40566	−	4.16673i	−0.298386	−	0.516820i
$66$		0			0
$67$	−3.93499	−	6.81560i	−0.480735	−	0.832658i	0.519020	−	0.854762i	$-0.326297\pi$
$67$	−3.93499	−	6.81560i	−0.480735	−	0.832658i	−0.999756	+	0.0221038i	$0.992964\pi$
$68$	−4.08108	+	7.06863i	−0.494903	+	0.857198i
$69$		0			0
$70$	9.82936	+	17.0249i	1.17483	+	2.03487i
$71$	4.59233	+	7.95414i	0.545009	+	0.943983i	0.998606	+	0.0527763i	$0.0168070\pi$
$71$	4.59233	+	7.95414i	0.545009	+	0.943983i	−0.453598	+	0.891207i	$0.649860\pi$
$72$		0			0
$73$	−14.1779			−1.65939			−0.829697	−	0.558214i	$-0.811487\pi$
$73$	−14.1779			−1.65939			−0.829697	+	0.558214i	$0.811487\pi$
$74$	9.06284	−	15.6973i	1.05353	−	1.82477i
$75$		0			0
$76$	−0.274148			−0.0314470
$77$	−0.173174	+	0.299947i	−0.0197350	+	0.0341821i
$78$		0			0
$79$	−11.7918			−1.32668			−0.663342	−	0.748316i	$-0.730863\pi$
$79$	−11.7918			−1.32668			−0.663342	+	0.748316i	$0.730863\pi$
$80$	14.9680			1.67347
$81$		0			0
$82$	4.14215	+	7.17442i	0.457424	+	0.792282i
$83$	5.96249	−	10.3273i	0.654468	−	1.13357i	−0.327558	−	0.944831i	$-0.606226\pi$
$83$	5.96249	−	10.3273i	0.654468	−	1.13357i	0.982027	−	0.188742i	$-0.0604408\pi$
$84$		0			0
$85$	−2.84863	+	4.93396i	−0.308977	+	0.535164i
$86$	5.25960	+	9.10990i	0.567158	+	0.982346i
$87$		0			0
$88$	0.346961	+	0.600954i	0.0369862	+	0.0640619i
$89$	2.09140			0.221688			0.110844	−	0.993838i	$-0.464645\pi$
$89$	2.09140			0.221688			0.110844	+	0.993838i	$0.464645\pi$
$90$		0			0
$91$	2.23180	+	3.86559i	0.233956	+	0.405224i
$92$	16.3953	+	28.3974i	1.70932	+	2.96064i
$93$		0			0
$94$	10.2434			1.05653
$95$	−0.191358			−0.0196329
$96$		0			0
$97$	−7.43871	+	12.8842i	−0.755286	+	1.30819i	0.189946	+	0.981795i	$0.439169\pi$
$97$	−7.43871	+	12.8842i	−0.755286	+	1.30819i	−0.945232	+	0.326400i	$0.894165\pi$
$98$	−0.416463	−	0.721335i	−0.0420691	−	0.0728658i
$99$		0			0
$100$	14.7316			1.47316
$101$	−6.55451	+	11.3527i	−0.652198	+	1.12964i	0.330390	+	0.943844i	$0.392820\pi$
$101$	−6.55451	+	11.3527i	−0.652198	+	1.12964i	−0.982588	+	0.185796i	$0.940514\pi$
$102$		0			0
$103$	0.340970	−	10.1432i	0.0335968	−	0.999435i
$103$	0.340970	−	10.1432i	0.0335968	−	0.999435i
$104$	8.94300			0.876933
$105$		0			0
$106$	22.2184			2.15804
$107$	0.0842018	+	0.145842i	0.00814009	+	0.0140991i	0.870067	−	0.492934i	$-0.164076\pi$
$107$	0.0842018	+	0.145842i	0.00814009	+	0.0140991i	−0.861927	+	0.507033i	$0.830742\pi$
$108$		0			0
$109$	−2.74059	+	4.74683i	−0.262500	+	0.454664i	−0.966906	−	0.255134i	$-0.917880\pi$
$109$	−2.74059	+	4.74683i	−0.262500	+	0.454664i	0.704405	+	0.709798i	$0.251214\pi$
$110$	0.464129	+	0.803895i	0.0442530	+	0.0766484i
$111$		0			0
$112$	−13.8862			−1.31212
$113$	−9.45318			−0.889280			−0.444640	−	0.895709i	$-0.646668\pi$
$113$	−9.45318			−0.889280			−0.444640	+	0.895709i	$0.646668\pi$
$114$		0			0
$115$	11.4440	+	19.8216i	1.06716	+	1.84838i
$116$	30.4605			2.82819
$117$		0			0
$118$	11.4952	+	19.9103i	1.05822	+	1.83289i
$119$	2.64275	−	4.57738i	0.242260	−	0.419607i
$120$		0			0
$121$	5.49182	−	9.51212i	0.499257	−	0.864738i
$122$	−9.93679	+	17.2110i	−0.899635	+	1.55821i
$123$		0			0
$124$	8.02380	+	13.8976i	0.720559	+	1.24804i
$125$	−4.31377			−0.385835
$126$		0			0
$127$	−12.3754			−1.09814			−0.549070	−	0.835777i	$-0.685018\pi$
$127$	−12.3754			−1.09814			−0.549070	+	0.835777i	$0.685018\pi$
$128$	8.78348	−	15.2134i	0.776357	−	1.34469i
$129$		0			0
$130$	11.9630			1.04923
$131$	0.769538	−	1.33288i	0.0672349	−	0.116454i	−0.830448	−	0.557096i	$-0.811916\pi$
$131$	0.769538	−	1.33288i	0.0672349	−	0.116454i	0.897683	+	0.440641i	$0.145249\pi$
$132$		0			0
$133$	0.177528			0.0153936
$134$	19.5681			1.69043
$135$		0			0
$136$	−5.29485	−	9.17095i	−0.454030	−	0.786402i
$137$	−15.8111			−1.35083			−0.675415	−	0.737438i	$-0.736035\pi$
$137$	−15.8111			−1.35083			−0.675415	+	0.737438i	$0.736035\pi$
$138$		0			0
$139$	−7.78100	−	13.4771i	−0.659976	−	1.14311i	−0.980621	−	0.195912i	$-0.937233\pi$
$139$	−7.78100	−	13.4771i	−0.659976	−	1.14311i	0.320646	−	0.947199i	$-0.396100\pi$
$140$	−33.0672			−2.79469
$141$		0			0
$142$	−22.8370			−1.91644
$143$	0.105383	+	0.182528i	0.00881255	+	0.0152638i
$144$		0			0
$145$	21.2617			1.76569
$146$	17.6261	−	30.5294i	1.45875	−	2.52663i
$147$		0			0
$148$	15.2443	+	26.4039i	1.25307	+	2.17038i
$149$	−6.63527	+	11.4926i	−0.543583	+	0.941513i	0.455112	+	0.890434i	$0.349599\pi$
$149$	−6.63527	+	11.4926i	−0.543583	+	0.941513i	−0.998695	+	0.0510788i	$0.983734\pi$
$150$		0			0
$151$	10.0844	−	17.4667i	0.820658	−	1.42142i	−0.0845347	−	0.996421i	$-0.526940\pi$
$151$	10.0844	−	17.4667i	0.820658	−	1.42142i	0.905193	−	0.425001i	$-0.139726\pi$
$152$	0.177842	−	0.308031i	0.0144249	−	0.0249846i
$153$		0			0
$154$	−0.430586	−	0.745796i	−0.0346976	−	0.0600980i
$155$	5.60068	+	9.70066i	0.449857	+	0.779176i
$156$		0			0
$157$	0.542544	−	0.939713i	0.0432997	−	0.0749973i	−0.843563	−	0.537030i	$-0.819546\pi$
$157$	0.542544	−	0.939713i	0.0432997	−	0.0749973i	0.886863	+	0.462032i	$0.152880\pi$
$158$	14.6598	−	25.3915i	1.16627	−	2.02004i
$159$		0			0
$160$	−2.76764	+	4.79370i	−0.218801	+	0.378975i
$161$	−10.6169	−	18.3891i	−0.836732	−	1.44926i
$162$		0			0
$163$	1.19683	−	2.07296i	0.0937426	−	0.162367i	−0.815341	−	0.578982i	$-0.803450\pi$
$163$	1.19683	−	2.07296i	0.0937426	−	0.162367i	0.909083	+	0.416615i	$0.136784\pi$
$164$	−13.9347			−1.08812
$165$		0			0
$166$	14.8253	+	25.6782i	1.15067	+	1.99301i
$167$	5.60156			0.433462			0.216731	−	0.976231i	$-0.430461\pi$
$167$	5.60156			0.433462			0.216731	+	0.976231i	$0.430461\pi$
$168$		0			0
$169$	−10.2837			−0.791057
$170$	−7.08291	−	12.2680i	−0.543234	−	0.940909i
$171$		0			0
$172$	−17.6940			−1.34915
$173$	−7.54832	−	13.0741i	−0.573888	−	0.994004i	−0.996161	−	0.0875352i	$-0.972101\pi$
$173$	−7.54832	−	13.0741i	−0.573888	−	0.994004i	0.422273	−	0.906469i	$-0.361232\pi$
$174$		0			0
$175$	−9.53959			−0.721125
$176$	−0.655689			−0.0494244
$177$		0			0
$178$	−2.60006	+	4.50343i	−0.194882	+	0.337546i
$179$	−2.59009			−0.193593			−0.0967963	−	0.995304i	$-0.530860\pi$
$179$	−2.59009			−0.193593			−0.0967963	+	0.995304i	$0.530860\pi$
$180$		0			0
$181$	−11.3854	+	19.7201i	−0.846270	+	1.46578i	0.0382445	+	0.999268i	$0.487823\pi$
$181$	−11.3854	+	19.7201i	−0.846270	+	1.46578i	−0.884514	+	0.466513i	$0.845510\pi$
$182$	−11.0984			−0.822671
$183$		0			0
$184$	−42.5429			−3.13630
$185$	10.6406	+	18.4301i	0.782315	+	1.35501i
$186$		0			0
$187$	0.124787	−	0.216138i	0.00912534	−	0.0158056i
$188$	−8.61504	+	14.9217i	−0.628317	+	1.08828i
$189$		0			0
$190$	0.237899	−	0.412053i	0.0172590	−	0.0298935i
$191$	7.86071	+	13.6152i	0.568781	+	0.985158i	0.996687	+	0.0813345i	$0.0259182\pi$
$191$	7.86071	+	13.6152i	0.568781	+	0.985158i	−0.427906	+	0.903823i	$0.640748\pi$
$192$		0			0
$193$	−5.78173			−0.416178			−0.208089	−	0.978110i	$-0.566724\pi$
$193$	−5.78173			−0.416178			−0.208089	+	0.978110i	$0.566724\pi$
$194$	−18.4958	−	32.0357i	−1.32792	−	2.30003i
$195$		0			0
$196$	1.40103			0.100074
$197$	22.2283			1.58370			0.791852	−	0.610713i	$-0.209117\pi$
$197$	22.2283			1.58370			0.791852	+	0.610713i	$0.209117\pi$
$198$		0			0
$199$	2.24281	+	3.88467i	0.158989	+	0.275377i	0.934504	−	0.355952i	$-0.115843\pi$
$199$	2.24281	+	3.88467i	0.158989	+	0.275377i	−0.775516	+	0.631329i	$0.782510\pi$
$200$	−9.55646	+	16.5523i	−0.675744	+	1.17042i
$201$		0			0
$202$	−16.2973	−	28.2278i	−1.14668	−	1.98610i
$203$	−19.7250			−1.38443
$204$		0			0
$205$	−9.72655			−0.679332
$206$	21.4175	+	13.3443i	1.49223	+	0.929745i
$207$		0			0
$208$	−4.22513	+	7.31814i	−0.292960	+	0.507422i
$209$	0.00838263			0.000579839
$210$		0			0
$211$	0.536086	+	0.928528i	0.0369057	+	0.0639225i	0.883888	−	0.467698i	$-0.154917\pi$
$211$	0.536086	+	0.928528i	0.0369057	+	0.0639225i	−0.846983	+	0.531621i	$0.821583\pi$
$212$	−18.6864	+	32.3657i	−1.28338	+	2.22289i
$213$		0			0
$214$	−0.418724			−0.0286234
$215$	−12.3505			−0.842300
$216$		0			0
$217$	−5.19591	−	8.99957i	−0.352721	−	0.610931i
$218$	−6.81427	−	11.8027i	−0.461521	−	0.799378i
$219$		0			0
$220$	−1.56139			−0.105269
$221$	−1.60821	−	2.78550i	−0.108180	−	0.187373i
$222$		0			0
$223$	6.97340	+	12.0783i	0.466973	+	0.808822i	0.999288	−	0.0377248i	$-0.0120110\pi$
$223$	6.97340	+	12.0783i	0.466973	+	0.808822i	−0.532315	+	0.846547i	$0.678678\pi$
$224$	2.56762	−	4.44724i	0.171556	−	0.297144i
$225$		0			0
$226$	11.7523	−	20.3556i	0.781753	−	1.35404i
$227$	−6.93243	−	12.0073i	−0.460121	−	0.796954i	0.538845	−	0.842405i	$-0.318861\pi$
$227$	−6.93243	−	12.0073i	−0.460121	−	0.796954i	−0.998967	+	0.0454511i	$0.985527\pi$
$228$		0			0
$229$	16.1086			1.06449			0.532243	−	0.846592i	$-0.321349\pi$
$229$	16.1086			1.06449			0.532243	+	0.846592i	$0.321349\pi$
$230$	−56.9095			−3.75250
$231$		0			0
$232$	−19.7599	+	34.2252i	−1.29730	+	2.24700i
$233$	−0.462461			−0.0302969			−0.0151484	−	0.999885i	$-0.504822\pi$
$233$	−0.462461			−0.0302969			−0.0151484	+	0.999885i	$0.504822\pi$
$234$		0			0
$235$	−6.01337	+	10.4155i	−0.392269	+	0.679430i
$236$	−38.6714			−2.51730
$237$		0			0
$238$	6.57101	+	11.3813i	0.425935	+	0.737742i
$239$	11.5164	+	19.9470i	0.744933	+	1.29026i	0.950226	+	0.311561i	$0.100852\pi$
$239$	11.5164	+	19.9470i	0.744933	+	1.29026i	−0.205294	+	0.978700i	$0.565815\pi$
$240$		0			0
$241$	13.3992	−	23.2081i	0.863118	−	1.49496i	−0.00578506	−	0.999983i	$-0.501841\pi$
$241$	13.3992	−	23.2081i	0.863118	−	1.49496i	0.868903	−	0.494982i	$-0.164825\pi$
$242$	13.6550	+	23.6512i	0.877779	+	1.52036i
$243$		0			0
$244$	−16.7143	−	28.9501i	−1.07002	−	1.85334i
$245$	0.977933			0.0624778
$246$		0			0
$247$	0.0540161	−	0.0935585i	0.00343696	−	0.00595299i
$248$	−20.8204			−1.32210
$249$		0			0
$250$	5.36294	−	9.28889i	0.339182	−	0.587481i
$251$	9.54377	+	16.5303i	0.602398	+	1.04338i	0.992457	+	0.122594i	$0.0391211\pi$
$251$	9.54377	+	16.5303i	0.602398	+	1.04338i	−0.390059	+	0.920790i	$0.627546\pi$
$252$		0			0
$253$	−0.501318	−	0.868308i	−0.0315176	−	0.0545901i
$254$	15.3853	−	26.6481i	0.965359	−	1.67205i
$255$		0			0
$256$	16.2995	+	28.2316i	1.01872	+	1.76448i
$257$	10.6555	+	18.4558i	0.664669	+	1.15124i	0.979375	+	0.202051i	$0.0647607\pi$
$257$	10.6555	+	18.4558i	0.664669	+	1.15124i	−0.314706	+	0.949189i	$0.601906\pi$
$258$		0			0
$259$	−9.87161	−	17.0981i	−0.613392	−	1.06243i
$260$	−10.0613	+	17.4267i	−0.623975	+	1.08076i
$261$		0			0
$262$	1.91340	+	3.31411i	0.118210	+	0.204746i
$263$	3.64597	−	6.31501i	0.224820	−	0.389400i	−0.731445	−	0.681900i	$-0.761154\pi$
$263$	3.64597	−	6.31501i	0.224820	−	0.389400i	0.956265	+	0.292500i	$0.0944872\pi$
$264$		0			0
$265$	−13.0432	+	22.5915i	−0.801239	+	1.38779i
$266$	−0.220705	+	0.382273i	−0.0135323	+	0.0234387i
$267$		0			0
$268$	−16.4574	+	28.5051i	−1.00530	+	1.74123i
$269$	2.11418	+	3.66186i	0.128904	+	0.223268i	0.923252	−	0.384195i	$-0.125521\pi$
$269$	2.11418	+	3.66186i	0.128904	+	0.223268i	−0.794348	+	0.607462i	$0.792188\pi$
$270$		0			0
$271$	−7.79017	−	13.4930i	−0.473219	−	0.819639i	0.526311	−	0.850292i	$-0.323575\pi$
$271$	−7.79017	−	13.4930i	−0.473219	−	0.819639i	−0.999530	+	0.0306528i	$0.990241\pi$
$272$	10.0062			0.606717
$273$		0			0
$274$	19.6565	−	34.0461i	1.18750	−	2.05680i
$275$	−0.450447			−0.0271630
$276$		0			0
$277$	0.147097	+	0.254779i	0.00883820	+	0.0153082i	0.870411	−	0.492326i	$-0.163853\pi$
$277$	0.147097	+	0.254779i	0.00883820	+	0.0153082i	−0.861572	+	0.507635i	$0.830520\pi$
$278$	38.6938			2.32070
$279$		0			0
$280$	21.4509	−	37.1541i	1.28194	−	2.22038i
$281$	5.83718	−	10.1103i	0.348217	−	0.603130i	−0.637716	−	0.770272i	$-0.720121\pi$
$281$	5.83718	−	10.1103i	0.348217	−	0.603130i	0.985933	+	0.167142i	$0.0534538\pi$
$282$		0			0
$283$	−9.46960	+	16.4018i	−0.562910	+	0.974988i	0.434331	+	0.900753i	$0.356985\pi$
$283$	−9.46960	+	16.4018i	−0.562910	+	0.974988i	−0.997241	+	0.0742347i	$0.976349\pi$
$284$	19.2066	−	33.2669i	1.13970	−	1.97403i
$285$		0			0
$286$	−0.524054			−0.0309879
$287$	9.02359			0.532646
$288$		0			0
$289$	6.59567	−	11.4240i	0.387981	−	0.672002i
$290$	−26.4328	+	45.7830i	−1.55219	+	2.68847i
$291$		0			0
$292$	29.6483	+	51.3524i	1.73504	+	3.00517i
$293$	−1.61462	+	2.79661i	−0.0943274	+	0.163380i	−0.909328	−	0.416081i	$-0.863403\pi$
$293$	−1.61462	+	2.79661i	−0.0943274	+	0.163380i	0.815000	+	0.579461i	$0.196737\pi$
$294$		0			0
$295$	−26.9930			−1.57159
$296$	−39.5563			−2.29916
$297$		0			0
$298$	−16.4981	−	28.5756i	−0.955712	−	1.65534i
$299$	−12.9216			−0.747274
$300$		0			0
$301$	11.4579			0.660425
$302$	25.0742	+	43.4298i	1.44286	+	2.49910i
$303$		0			0
$304$	0.168043	+	0.291059i	0.00963794	+	0.0166934i
$305$	−11.6667	−	20.2074i	−0.668035	−	1.15707i
$306$		0			0
$307$	−3.21504	+	5.56862i	−0.183492	+	0.317818i	−0.943067	−	0.332602i	$-0.892074\pi$
$307$	−3.21504	+	5.56862i	−0.183492	+	0.317818i	0.759575	+	0.650419i	$0.225407\pi$
$308$	1.44854			0.0825385
$309$		0			0
$310$	−27.8514			−1.58185
$311$	13.6324	−	23.6120i	0.773022	−	1.33891i	−0.162878	−	0.986646i	$-0.552078\pi$
$311$	13.6324	−	23.6120i	0.773022	−	1.33891i	0.935900	−	0.352267i	$-0.114589\pi$
$312$		0			0
$313$	15.5263	+	26.8924i	0.877600	+	1.52005i	0.853967	+	0.520328i	$0.174190\pi$
$313$	15.5263	+	26.8924i	0.877600	+	1.52005i	0.0236338	+	0.999721i	$0.492476\pi$
$314$	1.34900	+	2.33653i	0.0761283	+	0.131858i
$315$		0			0
$316$	24.6587	+	42.7101i	1.38716	+	2.40263i
$317$	7.81872			0.439143			0.219571	−	0.975596i	$-0.429534\pi$
$317$	7.81872			0.439143			0.219571	+	0.975596i	$0.429534\pi$
$318$		0			0
$319$	−0.931391			−0.0521479
$320$	8.08643	+	14.0061i	0.452045	+	0.782966i
$321$		0			0
$322$	52.7966			2.94224
$323$	−0.127924			−0.00711790
$324$		0			0
$325$	−2.90259	+	5.02744i	−0.161007	+	0.278872i
$326$	2.97582	+	5.15427i	0.164816	+	0.285469i
$327$		0			0
$328$	9.03955	−	15.6570i	0.499126	−	0.864511i
$329$	5.57877	−	9.66271i	0.307568	−	0.532723i
$330$		0			0
$331$	−30.3275			−1.66695			−0.833474	−	0.552559i	$-0.813651\pi$
$331$	−30.3275			−1.66695			−0.833474	+	0.552559i	$0.813651\pi$
$332$	−49.8742			−2.73720
$333$		0			0
$334$	−6.96394	+	12.0619i	−0.381050	+	0.659998i
$335$	−11.4874	+	19.8968i	−0.627625	+	1.08708i
$336$		0			0
$337$	−10.0364	+	17.3836i	−0.546719	+	0.946946i	0.451777	+	0.892131i	$0.350790\pi$
$337$	−10.0364	+	17.3836i	−0.546719	+	0.946946i	−0.998497	+	0.0548148i	$0.982543\pi$
$338$	12.7849	−	22.1441i	0.695407	−	1.20448i
$339$		0			0
$340$	23.8278			1.29224
$341$	−0.245344	−	0.424948i	−0.0132861	−	0.0230122i
$342$		0			0
$343$	18.0510			0.974661
$344$	11.4782	−	19.8808i	0.618864	−	1.07190i
$345$		0			0
$346$	37.5368			2.01799
$347$	8.10915	+	14.0455i	0.435322	+	0.754000i	0.997322	−	0.0731374i	$-0.0233012\pi$
$347$	8.10915	+	14.0455i	0.435322	+	0.754000i	−0.562000	+	0.827137i	$0.689968\pi$
$348$		0			0
$349$	10.4086	+	18.0282i	0.557160	+	0.965030i	0.997732	+	0.0673123i	$0.0214424\pi$
$349$	10.4086	+	18.0282i	0.557160	+	0.965030i	−0.440572	+	0.897717i	$0.645224\pi$
$350$	11.8598	−	20.5417i	0.633931	−	1.09800i
$351$		0			0
$352$	0.121240	−	0.209993i	0.00646209	−	0.0111927i
$353$	−8.31368	+	14.3997i	−0.442492	+	0.766419i	−0.997874	−	0.0651764i	$-0.979239\pi$
$353$	−8.31368	+	14.3997i	−0.442492	+	0.766419i	0.555381	+	0.831596i	$0.312572\pi$
$354$		0			0
$355$	13.4064	−	23.2205i	0.711537	−	1.23242i
$356$	−4.37346	−	7.57505i	−0.231793	−	0.401477i
$357$		0			0
$358$	3.22004	−	5.57727i	0.170184	−	0.294768i
$359$	−17.2537	−	29.8843i	−0.910615	−	1.57723i	−0.813197	−	0.581989i	$-0.802275\pi$
$359$	−17.2537	−	29.8843i	−0.910615	−	1.57723i	−0.0974183	−	0.995244i	$-0.531058\pi$
$360$		0			0
$361$	9.49785	+	16.4508i	0.499887	+	0.865830i
$362$	−28.3090	−	49.0326i	−1.48789	−	2.57710i
$363$		0			0
$364$	9.33414	−	16.1672i	0.489242	−	0.847392i
$365$	20.6948	+	35.8444i	1.08321	+	1.87618i
$366$		0			0
$367$	−11.2381	−	19.4650i	−0.586624	−	1.01606i	−0.994671	−	0.103102i	$-0.967123\pi$
$367$	−11.2381	−	19.4650i	−0.586624	−	1.01606i	0.408047	−	0.912961i	$-0.366210\pi$
$368$	20.0994	−	34.8132i	1.04776	−	1.81477i
$369$		0			0
$370$	−52.9144			−2.75089
$371$	12.1006	−	20.9588i	0.628230	−	1.08813i
$372$		0			0
$373$	10.7263			0.555389			0.277695	−	0.960669i	$-0.410430\pi$
$373$	10.7263			0.555389			0.277695	+	0.960669i	$0.410430\pi$
$374$	0.310274	+	0.537411i	0.0160439	+	0.0277889i
$375$		0			0
$376$	−11.1773	−	19.3596i	−0.576424	−	0.998396i
$377$	−6.00170	+	10.3952i	−0.309103	+	0.535382i
$378$		0			0
$379$	4.01833	+	6.95995i	0.206408	+	0.357508i	0.950580	−	0.310479i	$-0.100489\pi$
$379$	4.01833	+	6.95995i	0.206408	+	0.357508i	−0.744173	+	0.667987i	$0.767156\pi$
$380$	0.400161	+	0.693099i	0.0205278	+	0.0355552i
$381$		0			0
$382$	−39.0902			−2.00003
$383$	7.82805	−	13.5586i	0.399995	−	0.692811i	−0.593730	−	0.804664i	$-0.702345\pi$
$383$	7.82805	−	13.5586i	0.399995	−	0.692811i	0.993725	+	0.111853i	$0.0356786\pi$
$384$		0			0
$385$	1.01110			0.0515302
$386$	7.18793	−	12.4499i	0.365856	−	0.633681i
$387$		0			0
$388$	62.2223			3.15886
$389$	29.1292			1.47691			0.738455	−	0.674303i	$-0.235556\pi$
$389$	29.1292			1.47691			0.738455	+	0.674303i	$0.235556\pi$
$390$		0			0
$391$	7.65043	+	13.2509i	0.386899	+	0.670129i
$392$	−0.908861	+	1.57419i	−0.0459044	+	0.0795087i
$393$		0			0
$394$	−27.6346	+	47.8645i	−1.39221	+	2.41138i
$395$	17.2120	+	29.8120i	0.866028	+	1.50000i
$396$		0			0
$397$	−10.3208	−	17.8762i	−0.517986	−	0.897178i	−0.999782	−	0.0208947i	$-0.993349\pi$
$397$	−10.3208	−	17.8762i	−0.517986	−	0.897178i	0.481796	−	0.876284i	$-0.339985\pi$
$398$	−11.1532			−0.559059
$399$		0			0
$400$	−9.02992	−	15.6403i	−0.451496	−	0.782014i
$401$	−8.33604	−	14.4385i	−0.416282	−	0.721022i	0.579280	−	0.815129i	$-0.303334\pi$
$401$	−8.33604	−	14.4385i	−0.416282	−	0.721022i	−0.995562	+	0.0941069i	$0.970000\pi$
$402$		0			0
$403$	−6.32379			−0.315010
$404$	54.8263			2.72771
$405$		0			0
$406$	24.5225	−	42.4742i	1.21703	−	2.10796i
$407$	−0.466124	−	0.807351i	−0.0231049	−	0.0400189i
$408$		0			0
$409$	18.8344			0.931300			0.465650	−	0.884969i	$-0.345821\pi$
$409$	18.8344			0.931300			0.465650	+	0.884969i	$0.345821\pi$
$410$	12.0922	−	20.9443i	0.597191	−	1.03436i
$411$		0			0
$412$	−37.4516	+	19.9760i	−1.84511	+	0.984149i
$413$	25.0421			1.23224
$414$		0			0
$415$	−34.8126			−1.70888
$416$	−1.56249	−	2.70631i	−0.0766073	−	0.132688i
$417$		0			0
$418$	−0.0104214	+	0.0180504i	−0.000509728	+	0.000882875i
$419$	7.35614	+	12.7412i	0.359371	+	0.622449i	0.987856	−	0.155373i	$-0.0496580\pi$
$419$	7.35614	+	12.7412i	0.359371	+	0.622449i	−0.628485	+	0.777822i	$0.716325\pi$
$420$		0			0
$421$	4.51982			0.220283			0.110141	−	0.993916i	$-0.464870\pi$
$421$	4.51982			0.220283			0.110141	+	0.993916i	$0.464870\pi$
$422$	−2.66588			−0.129773
$423$		0			0
$424$	−24.2439	−	41.9917i	−1.17739	−	2.03930i
$425$	6.87411			0.333443
$426$		0			0
$427$	10.8236	+	18.7469i	0.523788	+	0.907228i
$428$	0.352160	−	0.609959i	0.0170223	−	0.0294835i
$429$		0			0
$430$	15.3544	−	26.5946i	0.740454	−	1.28250i
$431$	−5.62164	+	9.73697i	−0.270785	+	0.469013i	−0.969063	−	0.246813i	$-0.920617\pi$
$431$	−5.62164	+	9.73697i	−0.270785	+	0.469013i	0.698278	+	0.715827i	$0.253950\pi$
$432$		0			0
$433$	−10.0559	−	17.4173i	−0.483255	−	0.837023i	0.516560	−	0.856251i	$-0.327212\pi$
$433$	−10.0559	−	17.4173i	−0.483255	−	0.837023i	−0.999815	+	0.0192285i	$0.993879\pi$
$434$	25.8385			1.24029
$435$		0			0
$436$	22.9241			1.09786
$437$	−0.256961	+	0.445069i	−0.0122921	+	0.0212905i
$438$		0			0
$439$	−32.9335			−1.57183			−0.785914	−	0.618335i	$-0.787807\pi$
$439$	−32.9335			−1.57183			−0.785914	+	0.618335i	$0.787807\pi$
$440$	1.01288	−	1.75437i	0.0482874	−	0.0836362i
$441$		0			0
$442$	7.99739			0.380397
$443$	−17.2369			−0.818950			−0.409475	−	0.912321i	$-0.634288\pi$
$443$	−17.2369			−0.818950			−0.409475	+	0.912321i	$0.634288\pi$
$444$		0			0
$445$	−3.05271	−	5.28745i	−0.144712	−	0.250649i
$446$	−34.6777			−1.64204
$447$		0			0
$448$	−7.50201	−	12.9939i	−0.354437	−	0.613902i
$449$	−24.2580			−1.14481			−0.572403	−	0.819973i	$-0.693989\pi$
$449$	−24.2580			−1.14481			−0.572403	+	0.819973i	$0.693989\pi$
$450$		0			0
$451$	0.426082			0.0200634
$452$	19.7682	+	34.2395i	0.929817	+	1.61049i
$453$		0			0
$454$	34.4740			1.61794
$455$	6.51531	−	11.2848i	0.305442	−	0.529042i
$456$		0			0
$457$	9.55748	+	16.5540i	0.447080	+	0.774365i	0.998195	−	0.0600644i	$-0.0191306\pi$
$457$	9.55748	+	16.5540i	0.447080	+	0.774365i	−0.551115	+	0.834430i	$0.685797\pi$
$458$	−20.0265	+	34.6868i	−0.935775	+	1.62081i
$459$		0			0
$460$	47.8627	−	82.9007i	2.23161	−	3.86526i
$461$	−7.89875	+	13.6810i	−0.367882	+	0.637190i	−0.989234	−	0.146341i	$-0.953250\pi$
$461$	−7.89875	+	13.6810i	−0.367882	+	0.637190i	0.621352	+	0.783531i	$0.286584\pi$
$462$		0			0
$463$	−11.2577	−	19.4989i	−0.523191	−	0.906193i	−0.999636	−	0.0269886i	$-0.991408\pi$
$463$	−11.2577	−	19.4989i	−0.523191	−	0.906193i	0.476445	−	0.879204i	$-0.341925\pi$
$464$	−18.6712	−	32.3395i	−0.866789	−	1.50132i
$465$		0			0
$466$	0.574939	−	0.995823i	0.0266335	−	0.0461306i
$467$	12.2269	−	21.1776i	0.565792	−	0.979981i	−0.431183	−	0.902264i	$-0.641904\pi$
$467$	12.2269	−	21.1776i	0.565792	−	0.979981i	0.996975	−	0.0777166i	$-0.0247629\pi$
$468$		0			0
$469$	10.6572	−	18.4588i	0.492104	−	0.852349i
$470$	−14.9518	−	25.8973i	−0.689676	−	1.19455i
$471$		0			0
$472$	25.0864	−	43.4510i	1.15470	−	1.99999i
$473$	0.541029			0.0248765
$474$		0			0
$475$	0.115443	+	0.199953i	0.00529688	+	0.00917446i
$476$	−22.1057			−1.01321
$477$		0			0
$478$	−57.2693			−2.61944
$479$	2.22804	+	3.85908i	0.101802	+	0.176326i	0.912427	−	0.409239i	$-0.134206\pi$
$479$	2.22804	+	3.85908i	0.101802	+	0.176326i	−0.810625	+	0.585565i	$0.800873\pi$
$480$		0			0
$481$	−12.0145			−0.547812
$482$	33.3162	+	57.7053i	1.51751	+	2.62840i
$483$		0			0
$484$	−45.9373			−2.08806
$485$	43.4317			1.97213
$486$		0			0
$487$	17.9138	−	31.0277i	0.811753	−	1.40600i	−0.0998832	−	0.994999i	$-0.531847\pi$
$487$	17.9138	−	31.0277i	0.811753	−	1.40600i	0.911636	−	0.410998i	$-0.134820\pi$
$488$	43.3708			1.96330
$489$		0			0
$490$	−1.21578	+	2.10579i	−0.0549234	+	0.0951301i
$491$	21.8085			0.984202			0.492101	−	0.870538i	$-0.336229\pi$
$491$	21.8085			0.984202			0.492101	+	0.870538i	$0.336229\pi$
$492$		0			0
$493$	14.2136			0.640149
$494$	0.134307	+	0.232627i	0.00604276	+	0.0104664i
$495$		0			0
$496$	9.83661	−	17.0375i	0.441677	−	0.765007i
$497$	−12.4375	+	21.5423i	−0.557897	+	0.966306i
$498$		0			0
$499$	−1.56884	+	2.71731i	−0.0702308	+	0.121643i	−0.899002	−	0.437944i	$-0.855707\pi$
$499$	−1.56884	+	2.71731i	−0.0702308	+	0.121643i	0.828772	+	0.559587i	$0.189040\pi$
$500$	9.02081	+	15.6245i	0.403423	+	0.698749i
$501$		0			0
$502$	−47.4598			−2.11824
$503$	−0.0734840	−	0.127278i	−0.00327649	−	0.00567505i	0.864383	−	0.502835i	$-0.167710\pi$
$503$	−0.0734840	−	0.127278i	−0.00327649	−	0.00567505i	−0.867659	+	0.497160i	$0.834376\pi$
$504$		0			0
$505$	38.2692			1.70296
$506$	2.49298			0.110827
$507$		0			0
$508$	25.8790	+	44.8238i	1.14820	+	1.98873i
$509$	−5.53388	+	9.58496i	−0.245285	+	0.424846i	−0.962212	−	0.272303i	$-0.912215\pi$
$509$	−5.53388	+	9.58496i	−0.245285	+	0.424846i	0.716927	+	0.697148i	$0.245548\pi$
$510$		0			0
$511$	−19.1991	−	33.2538i	−0.849318	−	1.47106i
$512$	−45.9213			−2.02946
$513$		0			0
$514$	−52.9881			−2.33720
$515$	−26.1415	+	13.9434i	−1.15193	+	0.614422i
$516$		0			0
$517$	0.263422	−	0.456261i	0.0115853	−	0.0200663i
$518$	49.0901			2.15690
$519$		0			0
$520$	−13.0537	−	22.6096i	−0.572441	−	0.991497i
$521$	12.1298	−	21.0094i	0.531414	−	0.920437i	−0.467913	−	0.883774i	$-0.654994\pi$
$521$	12.1298	−	21.0094i	0.531414	−	0.920437i	0.999328	−	0.0366623i	$-0.0116726\pi$
$522$		0			0
$523$	33.3716			1.45924			0.729620	−	0.683853i	$-0.239697\pi$
$523$	33.3716			1.45924			0.729620	+	0.683853i	$0.239697\pi$
$524$	−6.43693			−0.281199
$525$		0			0
$526$	9.06545	+	15.7018i	0.395272	+	0.684632i
$527$	3.74410	+	6.48498i	0.163096	+	0.282490i
$528$		0			0
$529$	38.4695			1.67259
$530$	−32.4311	−	56.1723i	−1.40872	−	2.43997i
$531$		0			0
$532$	−0.371240	−	0.643007i	−0.0160953	−	0.0278779i
$533$	2.74559	−	4.75550i	0.118925	−	0.205984i
$534$		0			0
$535$	0.245811	−	0.425756i	0.0106273	−	0.0184071i
$536$	−21.3521	−	36.9829i	−0.922271	−	1.59742i
$537$		0			0
$538$	−10.5135			−0.453270
$539$	−0.0428394			−0.00184522
$540$		0			0
$541$	−7.97792	+	13.8182i	−0.342998	+	0.594089i	−0.984988	−	0.172623i	$-0.944776\pi$
$541$	−7.97792	+	13.8182i	−0.342998	+	0.594089i	0.641990	+	0.766713i	$0.278109\pi$
$542$	38.7394			1.66400
$543$		0			0
$544$	−1.85019	+	3.20463i	−0.0793264	+	0.137397i
$545$	16.0012			0.685416
$546$		0			0
$547$	−7.96313	−	13.7925i	−0.340479	−	0.589727i	0.644043	−	0.764989i	$-0.277256\pi$
$547$	−7.96313	−	13.7925i	−0.340479	−	0.589727i	−0.984522	+	0.175263i	$0.943922\pi$
$548$	33.0636	+	57.2678i	1.41241	+	2.44636i
$549$		0			0
$550$	0.560002	−	0.969952i	0.0238786	−	0.0413589i
$551$	0.238702	+	0.413443i	0.0101690	+	0.0176133i
$552$		0			0
$553$	−15.9680	−	27.6574i	−0.679029	−	1.17611i
$554$	−0.731492			−0.0310781
$555$		0			0
$556$	−32.5427	+	56.3657i	−1.38012	+	2.39044i
$557$	18.2419			0.772935			0.386467	−	0.922303i	$-0.373695\pi$
$557$	18.2419			0.772935			0.386467	+	0.922303i	$0.373695\pi$
$558$		0			0
$559$	3.48628	−	6.03842i	0.147454	−	0.255398i
$560$	20.2690	+	35.1070i	0.856523	+	1.48354i
$561$		0			0
$562$	14.5137	+	25.1385i	0.612225	+	1.06041i
$563$	−15.8339	+	27.4251i	−0.667319	+	1.15583i	0.311332	+	0.950301i	$0.399225\pi$
$563$	−15.8339	+	27.4251i	−0.667319	+	1.15583i	−0.978651	+	0.205529i	$0.934109\pi$
$564$		0			0
$565$	13.7983	+	23.8994i	0.580501	+	1.00546i
$566$	−23.5455	−	40.7820i	−0.989691	−	1.71420i
$567$		0			0
$568$	24.9190	+	43.1609i	1.04558	+	1.81099i
$569$	11.6294	−	20.1428i	0.487531	−	0.844429i	−0.512366	−	0.858767i	$-0.671231\pi$
$569$	11.6294	−	20.1428i	0.487531	−	0.844429i	0.999897	+	0.0143382i	$0.00456413\pi$
$570$		0			0
$571$	5.55253	+	9.61726i	0.232366	+	0.402470i	0.958504	−	0.285079i	$-0.0920200\pi$
$571$	5.55253	+	9.61726i	0.232366	+	0.402470i	−0.726138	+	0.687549i	$0.758687\pi$
$572$	0.440746	−	0.763394i	0.0184285	−	0.0319191i
$573$		0			0
$574$	−11.2183	+	19.4306i	−0.468241	+	0.811018i
$575$	13.8080	−	23.9161i	0.575832	−	0.997370i
$576$		0			0
$577$	14.0121	−	24.2697i	0.583333	−	1.01036i	−0.411748	−	0.911298i	$-0.635082\pi$
$577$	14.0121	−	24.2697i	0.583333	−	1.01036i	0.995081	−	0.0990643i	$-0.0315849\pi$
$578$	16.3997	+	28.4051i	0.682136	+	1.18149i
$579$		0			0
$580$	−44.4617	−	77.0099i	−1.84617	−	3.19766i
$581$	32.2966			1.33989
$582$		0			0
$583$	0.571373	−	0.989647i	0.0236638	−	0.0409870i
$584$	−76.9322			−3.18348
$585$		0			0
$586$	−4.01465	−	6.95358i	−0.165844	−	0.287250i
$587$	−17.8798			−0.737976			−0.368988	−	0.929434i	$-0.620296\pi$
$587$	−17.8798			−0.737976			−0.368988	+	0.929434i	$0.620296\pi$
$588$		0			0
$589$	−0.125756	+	0.217816i	−0.00518168	+	0.00897494i
$590$	33.5581	−	58.1243i	1.38156	−	2.39294i
$591$		0			0
$592$	18.6884	−	32.3693i	0.768089	−	1.33037i
$593$	12.2931	−	21.2922i	0.504815	−	0.874366i	−0.495169	−	0.868797i	$-0.664894\pi$
$593$	12.2931	−	21.2922i	0.504815	−	0.874366i	0.999984	−	0.00556931i	$-0.00177277\pi$
$594$		0			0
$595$	−15.4300			−0.632567
$596$	55.5019			2.27344
$597$		0			0
$598$	16.0643	−	27.8242i	0.656918	−	1.13782i
$599$	6.11892	−	10.5983i	0.250012	−	0.433034i	−0.713516	−	0.700638i	$-0.752899\pi$
$599$	6.11892	−	10.5983i	0.250012	−	0.433034i	0.963529	+	0.267604i	$0.0862320\pi$
$600$		0			0
$601$	−5.90442	−	10.2268i	−0.240846	−	0.417158i	0.720109	−	0.693861i	$-0.244092\pi$
$601$	−5.90442	−	10.2268i	−0.240846	−	0.417158i	−0.960956	+	0.276703i	$0.910758\pi$
$602$	−14.2447	+	24.6725i	−0.580570	+	1.00558i
$603$		0			0
$604$	−84.3528			−3.43227
$605$	−32.0646			−1.30361
$606$		0			0
$607$	1.15776	+	2.00529i	0.0469918	+	0.0813922i	0.888565	−	0.458752i	$-0.151703\pi$
$607$	1.15776	+	2.00529i	0.0469918	+	0.0813922i	−0.841573	+	0.540144i	$0.818370\pi$
$608$	−0.124288			−0.00504053
$609$		0			0
$610$	58.0170			2.34904
$611$	−3.39488	−	5.88011i	−0.137342	−	0.237884i
$612$		0			0
$613$	21.9150	+	37.9579i	0.885138	+	1.53310i	0.845555	+	0.533889i	$0.179270\pi$
$613$	21.9150	+	37.9579i	0.885138	+	1.53310i	0.0395836	+	0.999216i	$0.487397\pi$
$614$	−7.99398	−	13.8460i	−0.322611	−	0.558778i
$615$		0			0
$616$	−0.939681	+	1.62758i	−0.0378608	+	0.0655769i
$617$	−34.4543			−1.38708			−0.693538	−	0.720420i	$-0.743949\pi$
$617$	−34.4543			−1.38708			−0.693538	+	0.720420i	$0.743949\pi$
$618$		0			0
$619$	−3.11128			−0.125053			−0.0625265	−	0.998043i	$-0.519916\pi$
$619$	−3.11128			−0.125053			−0.0625265	+	0.998043i	$0.519916\pi$
$620$	23.4239	−	40.5714i	0.940727	−	1.62939i
$621$		0			0
$622$	33.8960	+	58.7096i	1.35910	+	2.35404i
$623$	2.83208	+	4.90531i	0.113465	+	0.196527i
$624$		0			0
$625$	15.1024	+	26.1582i	0.604097	+	1.04633i
$626$	−77.2103			−3.08594
$627$		0			0
$628$	−4.53820			−0.181094
$629$	7.11335	+	12.3207i	0.283628	+	0.491258i
$630$		0			0
$631$	43.9134			1.74816			0.874082	−	0.485778i	$-0.161464\pi$
$631$	43.9134			1.74816			0.874082	+	0.485778i	$0.161464\pi$
$632$	−63.9850			−2.54519
$633$		0			0
$634$	−9.72035	+	16.8361i	−0.386044	+	0.668648i
$635$	18.0638	+	31.2874i	0.716839	+	1.24160i
$636$		0			0
$637$	−0.276049	+	0.478131i	−0.0109375	+	0.0189442i
$638$	1.15792	−	2.00557i	0.0458424	−	0.0794014i
$639$		0			0
$640$	−51.2833			−2.02715
$641$	−45.5644			−1.79969			−0.899843	−	0.436213i	$-0.856319\pi$
$641$	−45.5644			−1.79969			−0.899843	+	0.436213i	$0.856319\pi$
$642$		0			0
$643$	−5.12847	+	8.88277i	−0.202247	+	0.350302i	−0.949252	−	0.314516i	$-0.898158\pi$
$643$	−5.12847	+	8.88277i	−0.202247	+	0.350302i	0.747005	+	0.664818i	$0.231491\pi$
$644$	−44.4036	+	76.9093i	−1.74975	+	3.03065i
$645$		0			0
$646$	0.159037	−	0.275461i	0.00625724	−	0.0108379i
$647$	−20.1300	+	34.8662i	−0.791392	+	1.37073i	0.133713	+	0.991020i	$0.457310\pi$
$647$	−20.1300	+	34.8662i	−0.791392	+	1.37073i	−0.925105	+	0.379711i	$0.876024\pi$
$648$		0			0
$649$	1.18246			0.0464155
$650$	−7.21709	−	12.5004i	−0.283078	−	0.490305i
$651$		0			0
$652$	−10.0110			−0.392063
$653$	−7.23997	+	12.5400i	−0.283322	+	0.490728i	−0.972201	−	0.234149i	$-0.924770\pi$
$653$	−7.23997	+	12.5400i	−0.283322	+	0.490728i	0.688879	+	0.724876i	$0.258103\pi$
$654$		0			0
$655$	−4.49303			−0.175557
$656$	8.54149	+	14.7943i	0.333489	+	0.577620i
$657$		0			0
$658$	13.8712	+	24.0257i	0.540757	+	0.936618i
$659$	3.77403	−	6.53682i	0.147015	−	0.254638i	−0.783108	−	0.621886i	$-0.786367\pi$
$659$	3.77403	−	6.53682i	0.147015	−	0.254638i	0.930123	+	0.367248i	$0.119700\pi$
$660$		0			0
$661$	−14.2263	+	24.6407i	−0.553340	+	0.958413i	0.444691	+	0.895684i	$0.353314\pi$
$661$	−14.2263	+	24.6407i	−0.553340	+	0.958413i	−0.998031	+	0.0627288i	$0.980020\pi$
$662$	37.7035	−	65.3044i	1.46539	−	2.53813i
$663$		0			0
$664$	32.3538	−	56.0384i	1.25557	−	2.17471i
$665$	−0.259129	−	0.448824i	−0.0100486	−	0.0174047i
$666$		0			0
$667$	28.5508	−	49.4514i	1.10549	−	1.91477i
$668$	−11.7138	−	20.2889i	−0.453220	−	0.785001i
$669$		0			0
$670$	−28.5627	−	49.4720i	−1.10347	−	1.91127i
$671$	0.511074	+	0.885206i	0.0197298	+	0.0341730i
$672$		0			0
$673$	8.08550	−	14.0045i	0.311673	−	0.539833i	−0.667052	−	0.745011i	$-0.732444\pi$
$673$	8.08550	−	14.0045i	0.311673	−	0.539833i	0.978725	+	0.205178i	$0.0657773\pi$
$674$	−24.9549	−	43.2231i	−0.961226	−	1.66489i
$675$		0			0
$676$	21.5050	+	37.2478i	0.827116	+	1.43261i
$677$	−4.82017	+	8.34877i	−0.185254	+	0.320869i	−0.943662	−	0.330911i	$-0.892644\pi$
$677$	−4.82017	+	8.34877i	−0.185254	+	0.320869i	0.758408	+	0.651780i	$0.225977\pi$
$678$		0			0
$679$	−40.2928			−1.54629
$680$	−15.4573	+	26.7728i	−0.592759	+	1.02669i
$681$		0			0
$682$	1.22006			0.0467185
$683$	5.24616	+	9.08661i	0.200739	+	0.347689i	0.948767	−	0.315978i	$-0.102332\pi$
$683$	5.24616	+	9.08661i	0.200739	+	0.347689i	−0.748028	+	0.663667i	$0.768999\pi$
$684$		0			0
$685$	23.0786	+	39.9734i	0.881789	+	1.52730i
$686$	−22.4412	+	38.8694i	−0.856810	+	1.48404i
$687$		0			0
$688$	10.8458	+	18.7854i	0.413492	+	0.716188i
$689$	−7.36363	−	12.7542i	−0.280532	−	0.485896i
$690$		0			0
$691$	12.5488			0.477379			0.238690	−	0.971096i	$-0.423282\pi$
$691$	12.5488			0.477379			0.238690	+	0.971096i	$0.423282\pi$
$692$	−31.5696	+	54.6802i	−1.20010	+	2.07863i
$693$		0			0
$694$	−40.3257			−1.53074
$695$	−22.7151	+	39.3437i	−0.861632	+	1.49239i
$696$		0			0
$697$	−6.50228			−0.246292
$698$	−51.7606			−1.95917
$699$		0			0
$700$	19.9489	+	34.5525i	0.753996	+	1.30596i
$701$	7.00043	−	12.1251i	0.264403	−	0.457959i	−0.703004	−	0.711186i	$-0.748159\pi$
$701$	7.00043	−	12.1251i	0.264403	−	0.457959i	0.967407	+	0.253227i	$0.0814919\pi$
$702$		0			0
$703$	−0.238921	+	0.413824i	−0.00901109	+	0.0156077i
$704$	−0.354235	−	0.613553i	−0.0133507	−	0.0231241i
$705$		0			0
$706$	−20.6714	−	35.8039i	−0.777978	−	1.34750i
$707$	−35.5034			−1.33524
$708$		0			0
$709$	−4.21374	−	7.29840i	−0.158250	−	0.274097i	0.775988	−	0.630748i	$-0.217252\pi$
$709$	−4.21374	−	7.29840i	−0.158250	−	0.274097i	−0.934238	+	0.356651i	$0.883919\pi$
$710$	33.3340	+	57.7363i	1.25100	+	2.16680i
$711$		0			0
$712$	11.3484			0.425298
$713$	30.0830			1.12662
$714$		0			0
$715$	0.307644	−	0.532855i	0.0115052	−	0.0199277i
$716$	5.41631	+	9.38133i	0.202417	+	0.350597i
$717$		0			0
$718$	85.8002			3.20204
$719$	−12.5978	+	21.8200i	−0.469818	+	0.813749i	−0.999404	−	0.0345069i	$-0.989014\pi$
$719$	−12.5978	+	21.8200i	−0.469818	+	0.813749i	0.529586	+	0.848256i	$0.322347\pi$
$720$		0			0
$721$	24.2522	−	12.9357i	0.903200	−	0.481751i
$722$	−47.2315			−1.75777
$723$		0			0
$724$	95.2350			3.53938
$725$	−12.8268	−	22.2167i	−0.476375	−	0.825106i
$726$		0			0
$727$	−3.74479	+	6.48616i	−0.138886	+	0.240558i	−0.927075	−	0.374875i	$-0.877686\pi$
$727$	−3.74479	+	6.48616i	−0.138886	+	0.240558i	0.788189	+	0.615433i	$0.211019\pi$
$728$	12.1102	+	20.9756i	0.448836	+	0.777406i
$729$		0			0
$730$	−102.912			−3.80895
$731$	−8.25645			−0.305376
$732$		0			0
$733$	−4.50629	−	7.80512i	−0.166444	−	0.288289i	0.770723	−	0.637170i	$-0.219895\pi$
$733$	−4.50629	−	7.80512i	−0.166444	−	0.288289i	−0.937167	+	0.348881i	$0.886562\pi$
$734$	55.8855			2.06277
$735$		0			0
$736$	7.43294	+	12.8742i	0.273982	+	0.474550i
$737$	0.503219	−	0.871601i	0.0185363	−	0.0321058i
$738$		0			0
$739$	−14.9568	+	25.9060i	−0.550196	+	0.952967i	0.448064	+	0.894001i	$0.352113\pi$
$739$	−14.9568	+	25.9060i	−0.550196	+	0.952967i	−0.998260	+	0.0589654i	$0.981220\pi$
$740$	44.5027	−	77.0809i	1.63595	−	2.83355i
$741$		0			0
$742$	30.0872	+	52.1126i	1.10454	+	1.91311i
$743$	9.45046			0.346704			0.173352	−	0.984860i	$-0.444540\pi$
$743$	9.45046			0.346704			0.173352	+	0.984860i	$0.444540\pi$
$744$		0			0
$745$	38.7408			1.41935
$746$	−13.3352	+	23.0972i	−0.488235	+	0.845647i
$747$		0			0
$748$	−1.04380			−0.0381652
$749$	−0.228045	+	0.394986i	−0.00833259	+	0.0144325i
$750$		0			0
$751$	3.64418			0.132978			0.0664890	−	0.997787i	$-0.478820\pi$
$751$	3.64418			0.132978			0.0664890	+	0.997787i	$0.478820\pi$
$752$	21.1229			0.770272
$753$		0			0
$754$	−14.9228	−	25.8471i	−0.543456	−	0.941294i
$755$	−58.8789			−2.14282
$756$		0			0
$757$	9.32551	+	16.1523i	0.338941	+	0.587064i	0.984234	−	0.176872i	$-0.0565979\pi$
$757$	9.32551	+	16.1523i	0.338941	+	0.587064i	−0.645293	+	0.763936i	$0.723265\pi$
$758$	−19.9826			−0.725800
$759$		0			0
$760$	−1.03835			−0.0376649
$761$	−2.41111	−	4.17616i	−0.0874025	−	0.151386i	0.819010	−	0.573779i	$-0.194523\pi$
$761$	−2.41111	−	4.17616i	−0.0874025	−	0.151386i	−0.906412	+	0.422394i	$0.861190\pi$
$762$		0			0
$763$	−14.8448			−0.537416
$764$	32.8761	−	56.9431i	1.18942	−	2.06013i
$765$		0			0
$766$	19.4639	+	33.7125i	0.703259	+	1.21808i
$767$	7.61952	−	13.1974i	0.275125	−	0.476530i
$768$		0			0
$769$	18.8081	−	32.5766i	0.678237	−	1.17474i	−0.297275	−	0.954792i	$-0.596078\pi$
$769$	18.8081	−	32.5766i	0.678237	−	1.17474i	0.975511	−	0.219949i	$-0.0705890\pi$
$770$	−1.25701	+	2.17720i	−0.0452995	+	0.0784610i
$771$		0			0
$772$	12.0906	+	20.9415i	0.435149	+	0.753700i
$773$	−2.00709	−	3.47638i	−0.0721899	−	0.125037i	0.827671	−	0.561214i	$-0.189665\pi$
$773$	−2.00709	−	3.47638i	−0.0721899	−	0.125037i	−0.899861	+	0.436177i	$0.856332\pi$
$774$		0			0
$775$	6.75758	−	11.7045i	0.242740	−	0.420437i
$776$	−40.3640	+	69.9126i	−1.44898	+	2.50972i
$777$		0			0
$778$	−36.2139	+	62.7243i	−1.29833	+	2.24877i
$779$	−0.109198	−	0.189137i	−0.00391244	−	0.00677655i
$780$		0			0
$781$	−0.587281	+	1.01720i	−0.0210146	+	0.0363983i
$782$	−38.0445			−1.36047
$783$		0			0
$784$	−0.858784	−	1.48746i	−0.0306709	−	0.0531235i
$785$	−3.16770			−0.113060
$786$		0			0
$787$	−3.02818			−0.107943			−0.0539715	−	0.998542i	$-0.517188\pi$
$787$	−3.02818			−0.107943			−0.0539715	+	0.998542i	$0.517188\pi$
$788$	−46.4832	−	80.5112i	−1.65589	−	2.86809i
$789$		0			0
$790$	−85.5927			−3.04525
$791$	−12.8011	−	22.1722i	−0.455155	−	0.788352i
$792$		0			0
$793$	13.1730			0.467788
$794$	51.3239			1.82142
$795$		0			0
$796$	9.38019	−	16.2470i	0.332472	−	0.575858i
$797$	25.8473			0.915558			0.457779	−	0.889066i	$-0.348645\pi$
$797$	25.8473			0.915558			0.457779	+	0.889066i	$0.348645\pi$
$798$		0			0
$799$	−4.01999	+	6.96283i	−0.142217	+	0.246327i
$800$	6.67868			0.236127
$801$		0			0
$802$	41.4540			1.46379
$803$	−0.906556	−	1.57020i	−0.0319917	−	0.0554112i
$804$		0			0
$805$	−30.9941	+	53.6833i	−1.09240	+	1.89209i
$806$	7.86183	−	13.6171i	0.276921	−	0.479642i
$807$		0			0
$808$	−35.5662	+	61.6025i	−1.25121	+	2.16717i
$809$	−12.5176	−	21.6811i	−0.440095	−	0.762267i	0.557601	−	0.830109i	$-0.311722\pi$
$809$	−12.5176	−	21.6811i	−0.440095	−	0.762267i	−0.997696	+	0.0678423i	$0.978389\pi$
$810$		0			0
$811$	−49.5535			−1.74006			−0.870030	−	0.493000i	$-0.835900\pi$
$811$	−49.5535			−1.74006			−0.870030	+	0.493000i	$0.835900\pi$
$812$	41.2484	+	71.4442i	1.44753	+	2.50720i
$813$		0			0
$814$	2.31797			0.0812448
$815$	−6.98779			−0.244772
$816$		0			0
$817$	−0.138658	−	0.240162i	−0.00485102	−	0.00840221i
$818$	−23.4152	+	40.5563i	−0.818692	+	1.41802i
$819$		0			0
$820$	20.3398	+	35.2296i	0.710298	+	1.23027i
$821$	−6.12377			−0.213721			−0.106861	−	0.994274i	$-0.534080\pi$
$821$	−6.12377			−0.213721			−0.106861	+	0.994274i	$0.534080\pi$
$822$		0			0
$823$	−42.5514			−1.48325			−0.741624	−	0.670816i	$-0.765944\pi$
$823$	−42.5514			−1.48325			−0.741624	+	0.670816i	$0.765944\pi$
$824$	1.85018	−	55.0390i	0.0644540	−	1.91737i
$825$		0			0
$826$	−31.1328	+	53.9235i	−1.08325	+	1.87624i
$827$	−40.4801			−1.40763			−0.703816	−	0.710382i	$-0.748522\pi$
$827$	−40.4801			−1.40763			−0.703816	+	0.710382i	$0.748522\pi$
$828$		0			0
$829$	12.0587	+	20.8863i	0.418816	+	0.725410i	0.995821	−	0.0913305i	$-0.0291120\pi$
$829$	12.0587	+	20.8863i	0.418816	+	0.725410i	−0.577005	+	0.816741i	$0.695779\pi$
$830$	43.2796	−	74.9624i	1.50226	−	2.60198i
$831$		0			0
$832$	−9.13048			−0.316543
$833$	0.653757			0.0226513
$834$		0			0
$835$	−8.17632	−	14.1618i	−0.282953	−	0.490090i
$836$	−0.0175295	−	0.0303620i	−0.000606270	−	0.00105009i
$837$		0			0
$838$	−36.5811			−1.26367
$839$	−17.8268	−	30.8769i	−0.615450	−	1.06599i	−0.990305	−	0.138907i	$-0.955641\pi$
$839$	−17.8268	−	30.8769i	−0.615450	−	1.06599i	0.374856	−	0.927083i	$-0.377692\pi$
$840$		0			0
$841$	−12.0220	−	20.8227i	−0.414552	−	0.718025i
$842$	−5.61911	+	9.73259i	−0.193647	+	0.335407i
$843$		0			0
$844$	2.24209	−	3.88342i	0.0771759	−	0.133673i
$845$	15.0107	+	25.9992i	0.516383	+	0.894401i
$846$		0			0
$847$	29.7472			1.02213
$848$	45.8163			1.57334
$849$		0			0
$850$	−8.54599	+	14.8021i	−0.293125	+	0.507708i
$851$	57.1542			1.95922
$852$		0			0
$853$	−12.3035	+	21.3102i	−0.421263	+	0.729649i	−0.996063	−	0.0886448i	$-0.971746\pi$
$853$	−12.3035	+	21.3102i	−0.421263	+	0.729649i	0.574800	+	0.818294i	$0.305080\pi$
$854$	−53.8240			−1.84182
$855$		0			0
$856$	0.456897	+	0.791369i	0.0156164	+	0.0270484i
$857$	−25.8800	−	44.8254i	−0.884043	−	1.53121i	−0.846806	−	0.531901i	$-0.821478\pi$
$857$	−25.8800	−	44.8254i	−0.884043	−	1.53121i	−0.0372369	−	0.999306i	$-0.511856\pi$
$858$		0			0
$859$	−2.93127	+	5.07710i	−0.100014	+	0.173228i	−0.911690	−	0.410879i	$-0.865222\pi$
$859$	−2.93127	+	5.07710i	−0.100014	+	0.173228i	0.811676	+	0.584107i	$0.198555\pi$
$860$	25.8270	+	44.7337i	0.880695	+	1.52541i
$861$		0			0
$862$	−13.9778	−	24.2103i	−0.476086	−	0.824606i
$863$	−54.9254			−1.86968			−0.934841	−	0.355066i	$-0.884459\pi$
$863$	−54.9254			−1.86968			−0.934841	+	0.355066i	$0.884459\pi$
$864$		0			0
$865$	−22.0358	+	38.1672i	−0.749241	+	1.29772i
$866$	50.0065			1.69929
$867$		0			0
$868$	−21.7310	+	37.6392i	−0.737598	+	1.27756i
$869$	−0.753989	−	1.30595i	−0.0255773	−	0.0443012i
$870$		0			0
$871$	−6.48529	−	11.2329i	−0.219746	−	0.380611i
$872$	−14.8710	+	25.7574i	−0.503596	+	0.872254i
$873$		0			0
$874$	−0.638915	−	1.10663i	−0.0216116	−	0.0374324i
$875$	−5.84153	−	10.1178i	−0.197480	−	0.342045i
$876$		0			0
$877$	11.4350	+	19.8061i	0.386134	+	0.668804i	0.991926	−	0.126819i	$-0.0404769\pi$
$877$	11.4350	+	19.8061i	0.386134	+	0.668804i	−0.605792	+	0.795623i	$0.707144\pi$
$878$	40.9434	−	70.9160i	1.38177	−	2.39330i
$879$		0			0
$880$	0.957077	+	1.65771i	0.0322631	+	0.0558812i
$881$	−1.26187	+	2.18562i	−0.0425135	+	0.0736355i	−0.886499	−	0.462730i	$-0.846870\pi$
$881$	−1.26187	+	2.18562i	−0.0425135	+	0.0736355i	0.843986	+	0.536366i	$0.180203\pi$
$882$		0			0
$883$	27.5422	−	47.7045i	0.926869	−	1.60538i	0.138342	−	0.990385i	$-0.455823\pi$
$883$	27.5422	−	47.7045i	0.926869	−	1.60538i	0.788527	−	0.615000i	$-0.210844\pi$
$884$	−6.72606	+	11.6499i	−0.226222	+	0.391828i
$885$		0			0
$886$	21.4292	−	37.1164i	0.719927	−	1.24695i
$887$	21.8777	+	37.8933i	0.734582	+	1.27233i	0.954906	+	0.296907i	$0.0959551\pi$
$887$	21.8777	+	37.8933i	0.734582	+	1.27233i	−0.220324	+	0.975427i	$0.570712\pi$
$888$		0			0
$889$	−16.7583	−	29.0262i	−0.562054	−	0.973507i
$890$	15.1807			0.508858
$891$		0			0
$892$	29.1651	−	50.5154i	0.976519	−	1.69138i
$893$	−0.270045			−0.00903670
$894$		0			0
$895$	3.78063	+	6.54825i	0.126373	+	0.218884i
$896$	47.5769			1.58943
$897$		0			0
$898$	30.1579	−	52.2350i	1.00638	−	1.74311i
$899$	13.9727	−	24.2014i	0.466015	−	0.807162i
$900$		0			0
$901$	−8.71951	+	15.1026i	−0.290489	+	0.503142i
$902$	−0.529712	+	0.917487i	−0.0176375	+	0.0305490i
$903$		0			0
$904$	−51.2950			−1.70605
$905$	66.4748			2.20970
$906$		0			0
$907$	13.3869	−	23.1867i	0.444504	−	0.769903i	−0.553514	−	0.832840i	$-0.686713\pi$
$907$	13.3869	−	23.1867i	0.444504	−	0.769903i	0.998018	+	0.0629368i	$0.0200467\pi$
$908$	−28.9937	+	50.2186i	−0.962191	+	1.66656i
$909$		0			0
$910$	16.1999	+	28.0590i	0.537020	+	0.930146i
$911$	8.47219	−	14.6743i	0.280696	−	0.486180i	−0.690860	−	0.722988i	$-0.742768\pi$
$911$	8.47219	−	14.6743i	0.280696	−	0.486180i	0.971556	+	0.236808i	$0.0761014\pi$
$912$		0			0
$913$	1.52501			0.0504703
$914$	−47.5280			−1.57209
$915$		0			0
$916$	−33.6858	−	58.3455i	−1.11301	−	1.92779i
$917$	4.16831			0.137650
$918$		0			0
$919$	41.9566			1.38402			0.692010	−	0.721888i	$-0.256726\pi$
$919$	41.9566			1.38402			0.692010	+	0.721888i	$0.256726\pi$
$920$	62.0978	+	107.557i	2.04730	+	3.54603i
$921$		0			0
$922$	−19.6397	−	34.0170i	−0.646799	−	1.12029i
$923$	7.56865	+	13.1093i	0.249125	+	0.431498i
$924$		0			0
$925$	12.8386	−	22.2371i	0.422131	−	0.731152i
$926$	55.9831			1.83972
$927$		0			0
$928$	13.8095			0.453320
$929$	14.4791	−	25.0785i	0.475044	−	0.822800i	−0.524548	−	0.851381i	$-0.675765\pi$
$929$	14.4791	−	25.0785i	0.475044	−	0.822800i	0.999591	+	0.0285809i	$0.00909883\pi$
$930$		0			0
$931$	0.0109791	+	0.0190164i	0.000359826	+	0.000623236i
$932$	0.967084	+	1.67504i	0.0316779	+	0.0548677i
$933$		0			0
$934$	30.4013	+	52.6565i	0.994760	+	1.72297i
$935$	−0.728583			−0.0238272
$936$		0			0
$937$	12.2488			0.400149			0.200075	−	0.979781i	$-0.435881\pi$
$937$	12.2488			0.400149			0.200075	+	0.979781i	$0.435881\pi$
$938$	26.4984	+	45.8966i	0.865203	+	1.49858i
$939$		0			0
$940$	50.2998			1.64060
$941$	−21.0006			−0.684598			−0.342299	−	0.939591i	$-0.611206\pi$
$941$	−21.0006			−0.684598			−0.342299	+	0.939591i	$0.611206\pi$
$942$		0			0
$943$	−13.0611	+	22.6225i	−0.425328	+	0.736689i
$944$	23.7042	+	41.0569i	0.771507	+	1.33629i
$945$		0			0
$946$	−0.672615	+	1.16500i	−0.0218686	+	0.0378775i
$947$	26.8871	−	46.5698i	0.873714	−	1.51332i	0.0155870	−	0.999879i	$-0.495038\pi$
$947$	26.8871	−	46.5698i	0.873714	−	1.51332i	0.858127	−	0.513438i	$-0.171628\pi$
$948$		0			0
$949$	−23.3667			−0.758515
$950$	−0.574081			−0.0186256
$951$		0			0
$952$	14.3401	−	24.8378i	0.464766	−	0.804999i
$953$	−27.8702	+	48.2726i	−0.902805	+	1.56370i	−0.0789679	+	0.996877i	$0.525162\pi$
$953$	−27.8702	+	48.2726i	−0.902805	+	1.56370i	−0.823837	+	0.566827i	$0.808171\pi$
$954$		0			0
$955$	22.9478	−	39.7468i	0.742573	−	1.28617i
$956$	48.1653	−	83.4248i	1.55778	−	2.69815i
$957$		0			0
$958$	−11.0797			−0.357970
$959$	−21.4107	−	37.0844i	−0.691387	−	1.19752i
$960$		0			0
$961$	−16.2775			−0.525079
$962$	14.9365	−	25.8709i	0.481574	−	0.834110i
$963$		0			0
$964$	−112.080			−3.60985
$965$	8.43931	+	14.6173i	0.271671	+	0.470548i
$966$		0			0
$967$	−20.0275	−	34.6886i	−0.644039	−	1.11551i	−0.984522	−	0.175258i	$-0.943924\pi$
$967$	−20.0275	−	34.6886i	−0.644039	−	1.11551i	0.340483	−	0.940251i	$-0.389409\pi$
$968$	29.7998	−	51.6148i	0.957803	−	1.65896i
$969$		0			0
$970$	−53.9949	+	93.5219i	−1.73367	+	3.00281i
$971$	−9.27354	+	16.0622i	−0.297602	+	0.515462i	−0.975587	−	0.219614i	$-0.929520\pi$
$971$	−9.27354	+	16.0622i	−0.297602	+	0.515462i	0.677985	+	0.735076i	$0.262854\pi$
$972$		0			0
$973$	21.0734	−	36.5002i	0.675583	−	1.17014i
$974$	44.5415	+	77.1481i	1.42720	+	2.47198i
$975$		0			0
$976$	−20.4906	+	35.4907i	−0.655887	+	1.13603i
$977$	10.4060	+	18.0237i	0.332918	+	0.576630i	0.983083	−	0.183163i	$-0.0586335\pi$
$977$	10.4060	+	18.0237i	0.332918	+	0.576630i	−0.650165	+	0.759793i	$0.725300\pi$
$978$		0			0
$979$	0.133727	+	0.231622i	0.00427394	+	0.00740269i
$980$	−2.04502	−	3.54208i	−0.0653258	−	0.113148i
$981$		0			0
$982$	−27.1126	+	46.9604i	−0.865198	+	1.49857i
$983$	−22.5912	−	39.1291i	−0.720547	−	1.24802i	−0.960781	−	0.277309i	$-0.910558\pi$
$983$	−22.5912	−	39.1291i	−0.720547	−	1.24802i	0.240234	−	0.970715i	$-0.422776\pi$
$984$		0			0
$985$	−32.4456	−	56.1975i	−1.03380	−	1.79060i
$986$	−17.6706	+	30.6063i	−0.562746	+	0.974704i
$987$		0			0
$988$	−0.451826			−0.0143745
$989$	−16.5847	+	28.7255i	−0.527362	+	0.913417i
$990$		0			0
$991$	23.6824			0.752297			0.376148	−	0.926559i	$-0.377248\pi$
$991$	23.6824			0.752297			0.376148	+	0.926559i	$0.377248\pi$
$992$	3.63766	+	6.30061i	0.115496	+	0.200045i
$993$		0			0
$994$	−30.9249	−	53.5635i	−0.980879	−	1.69893i
$995$	6.54745	−	11.3405i	0.207568	−	0.359518i
$996$		0			0
$997$	5.46936	+	9.47321i	0.173216	+	0.300020i	0.939543	−	0.342432i	$-0.111251\pi$
$997$	5.46936	+	9.47321i	0.173216	+	0.300020i	−0.766326	+	0.642452i	$0.777917\pi$
$998$	−3.90081	−	6.75639i	−0.123478	−	0.213870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.f.f.262.2	yes	32
3.2	odd	2	inner	927.2.f.f.262.15	yes	32
103.46	even	3	inner	927.2.f.f.46.2	✓	32
309.149	odd	6	inner	927.2.f.f.46.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.f.f.46.2	✓	32	103.46	even	3	inner
927.2.f.f.46.15	yes	32	309.149	odd	6	inner
927.2.f.f.262.2	yes	32	1.1	even	1	trivial
927.2.f.f.262.15	yes	32	3.2	odd	2	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24321 + 2.15331i) q^{2} +(-2.09117 - 3.62201i) q^{4} +(-1.45965 - 2.52819i) q^{5} +(1.35416 + 2.34547i) q^{7} +5.42622 q^{8} +O(q^{10})\)	\(q+(-1.24321 + 2.15331i) q^{2} +(-2.09117 - 3.62201i) q^{4} +(-1.45965 - 2.52819i) q^{5} +(1.35416 + 2.34547i) q^{7} +5.42622 q^{8} +7.25864 q^{10} +(0.0639416 + 0.110750i) q^{11} +1.64811 q^{13} -6.73404 q^{14} +(-2.56362 + 4.44032i) q^{16} +(-0.975790 - 1.69012i) q^{17} +(0.0327746 - 0.0567672i) q^{19} +(-6.10475 + 10.5737i) q^{20} -0.317973 q^{22} -7.84025 q^{23} +(-1.76116 + 3.05043i) q^{25} +(-2.04895 + 3.54889i) q^{26} +(5.66355 - 9.80955i) q^{28} +(-3.64157 + 6.30738i) q^{29} -3.83700 q^{31} +(-0.948049 - 1.64207i) q^{32} +4.85247 q^{34} +(3.95320 - 6.84714i) q^{35} -7.28984 q^{37} +(0.0814917 + 0.141148i) q^{38} +(-7.92039 - 13.7185i) q^{40} +(1.66590 - 2.88543i) q^{41} +(2.11532 - 3.66385i) q^{43} +(0.267425 - 0.463194i) q^{44} +(9.74711 - 16.8825i) q^{46} +(-2.05987 - 3.56779i) q^{47} +(-0.167494 + 0.290109i) q^{49} +(-4.37901 - 7.58467i) q^{50} +(-3.44647 - 5.96946i) q^{52} +(-4.46793 - 7.73868i) q^{53} +(0.186665 - 0.323313i) q^{55} +(7.34796 + 12.7270i) q^{56} +(-9.05450 - 15.6829i) q^{58} +(4.62319 - 8.00760i) q^{59} +7.99282 q^{61} +(4.77021 - 8.26225i) q^{62} -5.53998 q^{64} +(-2.40566 - 4.16673i) q^{65} +(-3.93499 - 6.81560i) q^{67} +(-4.08108 + 7.06863i) q^{68} +(9.82936 + 17.0249i) q^{70} +(4.59233 + 7.95414i) q^{71} -14.1779 q^{73} +(9.06284 - 15.6973i) q^{74} -0.274148 q^{76} +(-0.173174 + 0.299947i) q^{77} -11.7918 q^{79} +14.9680 q^{80} +(4.14215 + 7.17442i) q^{82} +(5.96249 - 10.3273i) q^{83} +(-2.84863 + 4.93396i) q^{85} +(5.25960 + 9.10990i) q^{86} +(0.346961 + 0.600954i) q^{88} +2.09140 q^{89} +(2.23180 + 3.86559i) q^{91} +(16.3953 + 28.3974i) q^{92} +10.2434 q^{94} -0.191358 q^{95} +(-7.43871 + 12.8842i) q^{97} +(-0.416463 - 0.721335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q - 18 * q^4 + 8 * q^7	\( 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) \) 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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