LMFDB - Embedded newform 1386.2.r.d.1277.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, 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("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1277.8
Character	$\chi$	$=$	1386.1277
Dual form			1386.2.r.d.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.474393 + 0.821673i) q^{5} +(1.41034 - 2.23851i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.474393 + 0.821673i) q^{5} +(1.41034 - 2.23851i) q^{7} -1.00000i q^{8} +(0.821673 + 0.474393i) q^{10} +(-0.866025 - 0.500000i) q^{11} +7.03063i q^{13} +(0.102135 - 2.64378i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.29971 - 3.98321i) q^{17} +(1.93280 - 1.11590i) q^{19} +0.948786 q^{20} -1.00000 q^{22} +(7.17812 - 4.14429i) q^{23} +(2.04990 - 3.55054i) q^{25} +(3.51532 + 6.08871i) q^{26} +(-1.23344 - 2.34065i) q^{28} -0.930621i q^{29} +(-2.80537 - 1.61968i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.59942i q^{34} +(2.50838 + 0.0969044i) q^{35} +(4.57553 + 7.92505i) q^{37} +(1.11590 - 1.93280i) q^{38} +(0.821673 - 0.474393i) q^{40} -8.54500 q^{41} +12.7269 q^{43} +(-0.866025 + 0.500000i) q^{44} +(4.14429 - 7.17812i) q^{46} +(-0.251245 - 0.435168i) q^{47} +(-3.02187 - 6.31413i) q^{49} -4.09981i q^{50} +(6.08871 + 3.51532i) q^{52} +(-8.22868 - 4.75083i) q^{53} -0.948786i q^{55} +(-2.23851 - 1.41034i) q^{56} +(-0.465310 - 0.805941i) q^{58} +(-3.94585 + 6.83441i) q^{59} +(-2.02250 + 1.16769i) q^{61} -3.23936 q^{62} -1.00000 q^{64} +(-5.77688 + 3.33528i) q^{65} +(-2.94653 + 5.10354i) q^{67} +(-2.29971 - 3.98321i) q^{68} +(2.22077 - 1.17027i) q^{70} -12.7563i q^{71} +(4.85471 + 2.80287i) q^{73} +(7.92505 + 4.57553i) q^{74} -2.23181i q^{76} +(-2.34065 + 1.23344i) q^{77} +(-4.16723 - 7.21785i) q^{79} +(0.474393 - 0.821673i) q^{80} +(-7.40019 + 4.27250i) q^{82} +12.0026 q^{83} +4.36386 q^{85} +(11.0218 - 6.36346i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(0.441480 + 0.764665i) q^{89} +(15.7382 + 9.91559i) q^{91} -8.28858i q^{92} +(-0.435168 - 0.251245i) q^{94} +(1.83381 + 1.05875i) q^{95} +12.6315i q^{97} +(-5.77409 - 3.95726i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 8 * q^7	$ 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.474393	+	0.821673i	0.212155	+	0.367463i	0.952389	−	0.304886i	$-0.0986185\pi$
$5$	0.474393	+	0.821673i	0.212155	+	0.367463i	−0.740234	+	0.672350i	$0.765285\pi$
$6$		0			0
$7$	1.41034	−	2.23851i	0.533059	−	0.846078i
$7$	1.41034	−	2.23851i	0.533059	−	0.846078i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.821673	+	0.474393i	0.259836	+	0.150016i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$		0			0
$13$			7.03063i			1.94995i	0.222322	+	0.974973i	$0.428636\pi$
$13$			7.03063i			1.94995i	−0.222322	+	0.974973i	$0.571364\pi$
$14$	0.102135	−	2.64378i	0.0272968	−	0.706580i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.29971	−	3.98321i	0.557761	−	0.966071i	−0.439922	−	0.898036i	$-0.644994\pi$
$17$	2.29971	−	3.98321i	0.557761	−	0.966071i	0.997683	−	0.0680349i	$-0.0216729\pi$
$18$		0			0
$19$	1.93280	−	1.11590i	0.443415	−	0.256006i	−0.261630	−	0.965168i	$-0.584260\pi$
$19$	1.93280	−	1.11590i	0.443415	−	0.256006i	0.705045	+	0.709163i	$0.250927\pi$
$20$	0.948786			0.212155
$21$		0			0
$22$	−1.00000			−0.213201
$23$	7.17812	−	4.14429i	1.49674	−	0.864144i	0.496748	−	0.867895i	$-0.334527\pi$
$23$	7.17812	−	4.14429i	1.49674	−	0.864144i	0.999993	+	0.00375054i	$0.00119384\pi$
$24$		0			0
$25$	2.04990	−	3.55054i	0.409981	−	0.710107i
$26$	3.51532	+	6.08871i	0.689410	+	1.19409i
$27$		0			0
$28$	−1.23344	−	2.34065i	−0.233098	−	0.442341i
$29$		−	0.930621i		−	0.172812i	−0.996260	−	0.0864060i	$-0.972462\pi$
$29$		−	0.930621i		−	0.172812i	0.996260	−	0.0864060i	$-0.0275382\pi$
$30$		0			0
$31$	−2.80537	−	1.61968i	−0.503859	−	0.290903i	0.226447	−	0.974023i	$-0.427289\pi$
$31$	−2.80537	−	1.61968i	−0.503859	−	0.290903i	−0.730306	+	0.683121i	$0.760622\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	4.59942i		−	0.788794i
$35$	2.50838	+	0.0969044i	0.423994	+	0.0163798i
$36$		0			0
$37$	4.57553	+	7.92505i	0.752213	+	1.30287i	0.946748	+	0.321975i	$0.104347\pi$
$37$	4.57553	+	7.92505i	0.752213	+	1.30287i	−0.194535	+	0.980895i	$0.562320\pi$
$38$	1.11590	−	1.93280i	0.181023	−	0.313542i
$39$		0			0
$40$	0.821673	−	0.474393i	0.129918	−	0.0750081i
$41$	−8.54500			−1.33450			−0.667252	−	0.744832i	$-0.732530\pi$
$41$	−8.54500			−1.33450			−0.667252	+	0.744832i	$0.732530\pi$
$42$		0			0
$43$	12.7269			1.94084			0.970418	−	0.241430i	$-0.0776164\pi$
$43$	12.7269			1.94084			0.970418	+	0.241430i	$0.0776164\pi$
$44$	−0.866025	+	0.500000i	−0.130558	+	0.0753778i
$45$		0			0
$46$	4.14429	−	7.17812i	0.611042	−	1.05836i
$47$	−0.251245	−	0.435168i	−0.0366478	−	0.0634758i	0.847120	−	0.531402i	$-0.178335\pi$
$47$	−0.251245	−	0.435168i	−0.0366478	−	0.0634758i	−0.883768	+	0.467926i	$0.845001\pi$
$48$		0			0
$49$	−3.02187	−	6.31413i	−0.431696	−	0.902019i
$50$		−	4.09981i		−	0.579800i
$51$		0			0
$52$	6.08871	+	3.51532i	0.844352	+	0.487487i
$53$	−8.22868	−	4.75083i	−1.13030	−	0.652577i	−0.186287	−	0.982495i	$-0.559645\pi$
$53$	−8.22868	−	4.75083i	−1.13030	−	0.652577i	−0.944009	+	0.329919i	$0.892979\pi$
$54$		0			0
$55$		−	0.948786i		−	0.127934i
$56$	−2.23851	−	1.41034i	−0.299134	−	0.188465i
$57$		0			0
$58$	−0.465310	−	0.805941i	−0.0610982	−	0.105825i
$59$	−3.94585	+	6.83441i	−0.513706	+	0.889764i	0.486168	+	0.873865i	$0.338394\pi$
$59$	−3.94585	+	6.83441i	−0.513706	+	0.889764i	−0.999874	+	0.0158990i	$0.994939\pi$
$60$		0			0
$61$	−2.02250	+	1.16769i	−0.258955	+	0.149508i	−0.623858	−	0.781538i	$-0.714436\pi$
$61$	−2.02250	+	1.16769i	−0.258955	+	0.149508i	0.364903	+	0.931046i	$0.381102\pi$
$62$	−3.23936			−0.411399
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.77688	+	3.33528i	−0.716533	+	0.413691i
$66$		0			0
$67$	−2.94653	+	5.10354i	−0.359976	+	0.623497i	−0.987956	−	0.154732i	$-0.950548\pi$
$67$	−2.94653	+	5.10354i	−0.359976	+	0.623497i	0.627980	+	0.778229i	$0.283882\pi$
$68$	−2.29971	−	3.98321i	−0.278881	−	0.483036i
$69$		0			0
$70$	2.22077	−	1.17027i	0.265433	−	0.139874i
$71$		−	12.7563i		−	1.51390i	−0.653475	−	0.756948i	$-0.726689\pi$
$71$		−	12.7563i		−	1.51390i	0.653475	−	0.756948i	$-0.273311\pi$
$72$		0			0
$73$	4.85471	+	2.80287i	0.568201	+	0.328051i	0.756431	−	0.654074i	$-0.226942\pi$
$73$	4.85471	+	2.80287i	0.568201	+	0.328051i	−0.188229	+	0.982125i	$0.560275\pi$
$74$	7.92505	+	4.57553i	0.921269	+	0.531895i
$75$		0			0
$76$		−	2.23181i		−	0.256006i
$77$	−2.34065	+	1.23344i	−0.266742	+	0.140563i
$78$		0			0
$79$	−4.16723	−	7.21785i	−0.468850	−	0.812072i	0.530516	−	0.847675i	$-0.321998\pi$
$79$	−4.16723	−	7.21785i	−0.468850	−	0.812072i	−0.999366	+	0.0356031i	$0.988665\pi$
$80$	0.474393	−	0.821673i	0.0530387	−	0.0918658i
$81$		0			0
$82$	−7.40019	+	4.27250i	−0.817214	+	0.471819i
$83$	12.0026			1.31745			0.658727	−	0.752382i	$-0.271095\pi$
$83$	12.0026			1.31745			0.658727	+	0.752382i	$0.271095\pi$
$84$		0			0
$85$	4.36386			0.473327
$86$	11.0218	−	6.36346i	1.18851	−	0.686189i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	0.441480	+	0.764665i	0.0467968	+	0.0810544i	0.888475	−	0.458925i	$-0.151765\pi$
$89$	0.441480	+	0.764665i	0.0467968	+	0.0810544i	−0.841678	+	0.539979i	$0.818432\pi$
$90$		0			0
$91$	15.7382	+	9.91559i	1.64981	+	1.03944i
$92$		−	8.28858i		−	0.864144i
$93$		0			0
$94$	−0.435168	−	0.251245i	−0.0448842	−	0.0259139i
$95$	1.83381	+	1.05875i	0.188145	+	0.108626i
$96$		0			0
$97$			12.6315i			1.28253i	0.767319	+	0.641265i	$0.221590\pi$
$97$			12.6315i			1.28253i	−0.767319	+	0.641265i	$0.778410\pi$
$98$	−5.77409	−	3.95726i	−0.583271	−	0.399744i
$99$		0			0
$100$	−2.04990	−	3.55054i	−0.204990	−	0.355054i
$101$	8.03742	−	13.9212i	0.799754	−	1.38521i	−0.120023	−	0.992771i	$-0.538297\pi$
$101$	8.03742	−	13.9212i	0.799754	−	1.38521i	0.919776	−	0.392443i	$-0.128370\pi$
$102$		0			0
$103$	7.42570	−	4.28723i	0.731676	−	0.422433i	−0.0873588	−	0.996177i	$-0.527843\pi$
$103$	7.42570	−	4.28723i	0.731676	−	0.422433i	0.819035	+	0.573743i	$0.194509\pi$
$104$	7.03063			0.689410
$105$		0			0
$106$	−9.50166			−0.922883
$107$	−12.2507	+	7.07294i	−1.18432	+	0.683767i	−0.957010	−	0.290056i	$-0.906326\pi$
$107$	−12.2507	+	7.07294i	−1.18432	+	0.683767i	−0.227309	+	0.973823i	$0.572993\pi$
$108$		0			0
$109$	3.35840	−	5.81692i	0.321676	−	0.557160i	−0.659158	−	0.752005i	$-0.729087\pi$
$109$	3.35840	−	5.81692i	0.321676	−	0.557160i	0.980834	+	0.194845i	$0.0624203\pi$
$110$	−0.474393	−	0.821673i	−0.0452316	−	0.0783434i
$111$		0			0
$112$	−2.64378	−	0.102135i	−0.249814	−	0.00965087i
$113$			8.39880i			0.790093i	0.918661	+	0.395046i	$0.129271\pi$
$113$			8.39880i			0.790093i	−0.918661	+	0.395046i	$0.870729\pi$
$114$		0			0
$115$	6.81050	+	3.93204i	0.635082	+	0.366665i
$116$	−0.805941	−	0.465310i	−0.0748298	−	0.0432030i
$117$		0			0
$118$			7.89170i			0.726490i
$119$	−5.67310	−	10.7656i	−0.520052	−	0.986882i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	−1.16769	+	2.02250i	−0.105718	+	0.183109i
$123$		0			0
$124$	−2.80537	+	1.61968i	−0.251929	+	0.145451i
$125$	8.63377			0.772227
$126$		0			0
$127$	−7.99819			−0.709724			−0.354862	−	0.934919i	$-0.615472\pi$
$127$	−7.99819			−0.709724			−0.354862	+	0.934919i	$0.615472\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.33528	+	5.77688i	−0.292524	+	0.506666i
$131$	4.37253	+	7.57344i	0.382030	+	0.661695i	0.991352	−	0.131228i	$-0.0418919\pi$
$131$	4.37253	+	7.57344i	0.382030	+	0.661695i	−0.609323	+	0.792922i	$0.708559\pi$
$132$		0			0
$133$	0.227946	−	5.90040i	0.0197654	−	0.511630i
$134$			5.89306i			0.509083i
$135$		0			0
$136$	−3.98321	−	2.29971i	−0.341558	−	0.197198i
$137$	−0.350664	−	0.202456i	−0.0299592	−	0.0172970i	0.484946	−	0.874544i	$-0.338839\pi$
$137$	−0.350664	−	0.202456i	−0.0299592	−	0.0172970i	−0.514905	+	0.857247i	$0.672173\pi$
$138$		0			0
$139$			17.5997i			1.49278i	0.665506	+	0.746392i	$0.268216\pi$
$139$			17.5997i			1.49278i	−0.665506	+	0.746392i	$0.731784\pi$
$140$	1.33811	−	2.12387i	0.113091	−	0.179500i
$141$		0			0
$142$	−6.37816	−	11.0473i	−0.535243	−	0.927069i
$143$	3.51532	−	6.08871i	0.293966	−	0.509163i
$144$		0			0
$145$	0.764665	−	0.441480i	0.0635020	−	0.0366629i
$146$	5.60574			0.463934
$147$		0			0
$148$	9.15106			0.752213
$149$	−17.5141	+	10.1118i	−1.43481	+	0.828390i	−0.997483	−	0.0709110i	$-0.977409\pi$
$149$	−17.5141	+	10.1118i	−1.43481	+	0.828390i	−0.437331	+	0.899301i	$0.644076\pi$
$150$		0			0
$151$	−3.93283	+	6.81186i	−0.320049	+	0.554341i	−0.980498	−	0.196530i	$-0.937033\pi$
$151$	−3.93283	+	6.81186i	−0.320049	+	0.554341i	0.660449	+	0.750871i	$0.270366\pi$
$152$	−1.11590	−	1.93280i	−0.0905117	−	0.156771i
$153$		0			0
$154$	−1.41034	+	2.23851i	−0.113649	+	0.180384i
$155$		−	3.07346i		−	0.246866i
$156$		0			0
$157$	−0.300234	−	0.173340i	−0.0239613	−	0.0138340i	0.487972	−	0.872860i	$-0.337737\pi$
$157$	−0.300234	−	0.173340i	−0.0239613	−	0.0138340i	−0.511933	+	0.859026i	$0.671070\pi$
$158$	−7.21785	−	4.16723i	−0.574221	−	0.331527i
$159$		0			0
$160$		−	0.948786i		−	0.0750081i
$161$	0.846556	−	21.9132i	0.0667179	−	1.72700i
$162$		0			0
$163$	−4.00467	−	6.93629i	−0.313670	−	0.543292i	0.665484	−	0.746412i	$-0.268225\pi$
$163$	−4.00467	−	6.93629i	−0.313670	−	0.543292i	−0.979154	+	0.203120i	$0.934892\pi$
$164$	−4.27250	+	7.40019i	−0.333626	+	0.577857i
$165$		0			0
$166$	10.3945	−	6.00129i	0.806772	−	0.465790i
$167$	−23.3784			−1.80907			−0.904537	−	0.426395i	$-0.859783\pi$
$167$	−23.3784			−1.80907			−0.904537	+	0.426395i	$0.859783\pi$
$168$		0			0
$169$	−36.4298			−2.80229
$170$	3.77922	−	2.18193i	0.289853	−	0.167346i
$171$		0			0
$172$	6.36346	−	11.0218i	0.485209	−	0.840407i
$173$	−3.94270	−	6.82895i	−0.299758	−	0.519196i	0.676323	−	0.736605i	$-0.263573\pi$
$173$	−3.94270	−	6.82895i	−0.299758	−	0.519196i	−0.976080	+	0.217410i	$0.930239\pi$
$174$		0			0
$175$	−5.05686	−	9.59620i	−0.382262	−	0.725405i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$	0.764665	+	0.441480i	0.0573141	+	0.0330903i
$179$	3.03581	+	1.75273i	0.226907	+	0.131005i	0.609145	−	0.793059i	$-0.291513\pi$
$179$	3.03581	+	1.75273i	0.226907	+	0.131005i	−0.382237	+	0.924064i	$0.624846\pi$
$180$		0			0
$181$			18.4507i			1.37143i	0.727871	+	0.685714i	$0.240510\pi$
$181$			18.4507i			1.37143i	−0.727871	+	0.685714i	$0.759490\pi$
$182$	18.5874	+	0.718075i	1.37779	+	0.0532273i
$183$		0			0
$184$	−4.14429	−	7.17812i	−0.305521	−	0.529178i
$185$	−4.34120	+	7.51918i	−0.319171	+	0.552821i
$186$		0			0
$187$	−3.98321	+	2.29971i	−0.291281	+	0.168171i
$188$	−0.502489			−0.0366478
$189$		0			0
$190$	2.11750			0.153620
$191$	−22.4364	+	12.9536i	−1.62344	+	0.937293i	−0.637449	+	0.770493i	$0.720010\pi$
$191$	−22.4364	+	12.9536i	−1.62344	+	0.937293i	−0.985991	+	0.166800i	$0.946656\pi$
$192$		0			0
$193$	−0.304714	+	0.527780i	−0.0219338	+	0.0379904i	−0.876784	−	0.480884i	$-0.840316\pi$
$193$	−0.304714	+	0.527780i	−0.0219338	+	0.0379904i	0.854850	+	0.518875i	$0.173649\pi$
$194$	6.31573	+	10.9392i	0.453443	+	0.785386i
$195$		0			0
$196$	−6.97914	−	0.540046i	−0.498510	−	0.0385747i
$197$			2.19657i			0.156499i	0.996934	+	0.0782494i	$0.0249330\pi$
$197$			2.19657i			0.156499i	−0.996934	+	0.0782494i	$0.975067\pi$
$198$		0			0
$199$	22.9865	+	13.2713i	1.62947	+	0.940775i	0.984251	+	0.176778i	$0.0565675\pi$
$199$	22.9865	+	13.2713i	1.62947	+	0.940775i	0.645220	+	0.763997i	$0.276766\pi$
$200$	−3.55054	−	2.04990i	−0.251061	−	0.144950i
$201$		0			0
$202$		−	16.0748i		−	1.13102i
$203$	−2.08321	−	1.31249i	−0.146212	−	0.0921189i
$204$		0			0
$205$	−4.05369	−	7.02119i	−0.283122	−	0.490381i
$206$	4.28723	−	7.42570i	0.298706	−	0.517373i
$207$		0			0
$208$	6.08871	−	3.51532i	0.422176	−	0.243743i
$209$	−2.23181			−0.154377
$210$		0			0
$211$	6.72897			0.463242			0.231621	−	0.972806i	$-0.425597\pi$
$211$	6.72897			0.463242			0.231621	+	0.972806i	$0.425597\pi$
$212$	−8.22868	+	4.75083i	−0.565148	+	0.326288i
$213$		0			0
$214$	−7.07294	+	12.2507i	−0.483496	+	0.837440i
$215$	6.03756	+	10.4574i	0.411758	+	0.713186i
$216$		0			0
$217$	−7.58219	+	3.99555i	−0.514713	+	0.271235i
$218$		−	6.71680i		−	0.454919i
$219$		0			0
$220$	−0.821673	−	0.474393i	−0.0553971	−	0.0319836i
$221$	28.0045	+	16.1684i	1.88379	+	1.08760i
$222$		0			0
$223$			24.1105i			1.61456i	0.590168	+	0.807280i	$0.299061\pi$
$223$			24.1105i			1.61456i	−0.590168	+	0.807280i	$0.700939\pi$
$224$	−2.34065	+	1.23344i	−0.156391	+	0.0824125i
$225$		0			0
$226$	4.19940	+	7.27357i	0.279340	+	0.483831i
$227$	−4.95825	+	8.58794i	−0.329091	+	0.570002i	−0.982332	−	0.187148i	$-0.940075\pi$
$227$	−4.95825	+	8.58794i	−0.329091	+	0.570002i	0.653241	+	0.757150i	$0.273409\pi$
$228$		0			0
$229$	−19.6700	+	11.3565i	−1.29983	+	0.750458i	−0.980375	−	0.197144i	$-0.936833\pi$
$229$	−19.6700	+	11.3565i	−1.29983	+	0.750458i	−0.319456	+	0.947601i	$0.603500\pi$
$230$	7.86408			0.518542
$231$		0			0
$232$	−0.930621			−0.0610982
$233$	10.6634	−	6.15652i	0.698583	−	0.403327i	−0.108237	−	0.994125i	$-0.534520\pi$
$233$	10.6634	−	6.15652i	0.698583	−	0.403327i	0.806819	+	0.590798i	$0.201187\pi$
$234$		0			0
$235$	0.238377	−	0.412882i	0.0155500	−	0.0269334i
$236$	3.94585	+	6.83441i	0.256853	+	0.444882i
$237$		0			0
$238$	−10.2959	−	6.48675i	−0.667381	−	0.420474i
$239$			0.355903i			0.0230215i	0.999934	+	0.0115107i	$0.00366406\pi$
$239$			0.355903i			0.0230215i	−0.999934	+	0.0115107i	$0.996336\pi$
$240$		0			0
$241$	−19.3413	−	11.1667i	−1.24588	−	0.719311i	−0.275597	−	0.961273i	$-0.588876\pi$
$241$	−19.3413	−	11.1667i	−1.24588	−	0.719311i	−0.970286	+	0.241962i	$0.922209\pi$
$242$	0.866025	+	0.500000i	0.0556702	+	0.0321412i
$243$		0			0
$244$			2.33539i			0.149508i
$245$	3.75459	−	5.47837i	0.239872	−	0.350000i
$246$		0			0
$247$	7.84550	+	13.5888i	0.499197	+	0.864635i
$248$	−1.61968	+	2.80537i	−0.102850	+	0.178141i
$249$		0			0
$250$	7.47706	−	4.31688i	0.472891	−	0.273024i
$251$	−10.8938			−0.687612			−0.343806	−	0.939041i	$-0.611716\pi$
$251$	−10.8938			−0.687612			−0.343806	+	0.939041i	$0.611716\pi$
$252$		0			0
$253$	−8.28858			−0.521098
$254$	−6.92663	+	3.99909i	−0.434616	+	0.250925i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.48335	+	7.76538i	0.279663	+	0.484391i	0.971301	−	0.237853i	$-0.0764438\pi$
$257$	4.48335	+	7.76538i	0.279663	+	0.484391i	−0.691638	+	0.722245i	$0.743110\pi$
$258$		0			0
$259$	24.1934	+	0.934646i	1.50330	+	0.0580761i
$260$			6.67056i			0.413691i
$261$		0			0
$262$	7.57344	+	4.37253i	0.467889	+	0.270136i
$263$	7.32723	+	4.23038i	0.451817	+	0.260856i	0.708597	−	0.705613i	$-0.249328\pi$
$263$	7.32723	+	4.23038i	0.451817	+	0.260856i	−0.256781	+	0.966470i	$0.582662\pi$
$264$		0			0
$265$		−	9.01504i		−	0.553790i
$266$	−2.75279	−	5.22387i	−0.168785	−	0.320296i
$267$		0			0
$268$	2.94653	+	5.10354i	0.179988	+	0.311748i
$269$	−1.61227	+	2.79253i	−0.0983017	+	0.170264i	−0.910982	−	0.412447i	$-0.864674\pi$
$269$	−1.61227	+	2.79253i	−0.0983017	+	0.170264i	0.812680	+	0.582710i	$0.198008\pi$
$270$		0			0
$271$	0.662223	−	0.382335i	0.0402272	−	0.0232252i	−0.479752	−	0.877404i	$-0.659273\pi$
$271$	0.662223	−	0.382335i	0.0402272	−	0.0232252i	0.519979	+	0.854179i	$0.325940\pi$
$272$	−4.59942			−0.278881
$273$		0			0
$274$	−0.404912			−0.0244616
$275$	−3.55054	+	2.04990i	−0.214105	+	0.123614i
$276$		0			0
$277$	13.6448	−	23.6334i	0.819834	−	1.41999i	−0.0859699	−	0.996298i	$-0.527399\pi$
$277$	13.6448	−	23.6334i	0.819834	−	1.41999i	0.905804	−	0.423697i	$-0.139268\pi$
$278$	8.79984	+	15.2418i	0.527779	+	0.914140i
$279$		0			0
$280$	0.0969044	−	2.50838i	0.00579115	−	0.149904i
$281$		−	4.36625i		−	0.260468i	−0.991483	−	0.130234i	$-0.958427\pi$
$281$		−	4.36625i		−	0.260468i	0.991483	−	0.130234i	$-0.0415729\pi$
$282$		0			0
$283$	−16.5596	−	9.56067i	−0.984364	−	0.568323i	−0.0807792	−	0.996732i	$-0.525741\pi$
$283$	−16.5596	−	9.56067i	−0.984364	−	0.568323i	−0.903585	+	0.428409i	$0.859074\pi$
$284$	−11.0473	−	6.37816i	−0.655537	−	0.378474i
$285$		0			0
$286$		−	7.03063i		−	0.415730i
$287$	−12.0514	+	19.1281i	−0.711370	+	1.12910i
$288$		0			0
$289$	−2.07732	−	3.59803i	−0.122196	−	0.211649i
$290$	0.441480	−	0.764665i	0.0259246	−	0.0449027i
$291$		0			0
$292$	4.85471	−	2.80287i	0.284101	−	0.164026i
$293$	9.23974			0.539791			0.269896	−	0.962890i	$-0.413011\pi$
$293$	9.23974			0.539791			0.269896	+	0.962890i	$0.413011\pi$
$294$		0			0
$295$	−7.48753			−0.435941
$296$	7.92505	−	4.57553i	0.460634	−	0.265947i
$297$		0			0
$298$	−10.1118	+	17.5141i	−0.585760	+	1.01457i
$299$	29.1370	+	50.4667i	1.68503	+	2.91857i
$300$		0			0
$301$	17.9493	−	28.4894i	1.03458	−	1.64210i
$302$			7.86566i			0.452618i
$303$		0			0
$304$	−1.93280	−	1.11590i	−0.110854	−	0.0640014i
$305$	−1.91892	−	1.10789i	−0.109877	−	0.0634377i
$306$		0			0
$307$		−	7.06021i		−	0.402947i	−0.979494	−	0.201474i	$-0.935427\pi$
$307$		−	7.06021i		−	0.402947i	0.979494	−	0.201474i	$-0.0645730\pi$
$308$	−0.102135	+	2.64378i	−0.00581969	+	0.150643i
$309$		0			0
$310$	−1.53673	−	2.66169i	−0.0872803	−	0.151174i
$311$	4.32056	−	7.48343i	0.244997	−	0.424346i	−0.717134	−	0.696935i	$-0.754547\pi$
$311$	4.32056	−	7.48343i	0.244997	−	0.424346i	0.962131	+	0.272589i	$0.0878798\pi$
$312$		0			0
$313$	−20.6329	+	11.9124i	−1.16624	+	0.673330i	−0.952792	−	0.303624i	$-0.901803\pi$
$313$	−20.6329	+	11.9124i	−1.16624	+	0.673330i	−0.213450	+	0.976954i	$0.568470\pi$
$314$	−0.346680			−0.0195643
$315$		0			0
$316$	−8.33446			−0.468850
$317$	−21.9545	+	12.6754i	−1.23309	+	0.711923i	−0.967672	−	0.252212i	$-0.918842\pi$
$317$	−21.9545	+	12.6754i	−1.23309	+	0.711923i	−0.265414	+	0.964134i	$0.585509\pi$
$318$		0			0
$319$	−0.465310	+	0.805941i	−0.0260524	+	0.0451240i
$320$	−0.474393	−	0.821673i	−0.0265194	−	0.0459329i
$321$		0			0
$322$	−10.2234	−	19.4006i	−0.569730	−	1.08116i
$323$		−	10.2650i		−	0.571160i
$324$		0			0
$325$	24.9625	+	14.4121i	1.38467	+	0.799440i
$326$	−6.93629	−	4.00467i	−0.384166	−	0.221798i
$327$		0			0
$328$			8.54500i			0.471819i
$329$	−1.32847	−	0.0513218i	−0.0732410	−	0.00282946i
$330$		0			0
$331$	−3.86378	−	6.69226i	−0.212372	−	0.367840i	0.740084	−	0.672514i	$-0.234786\pi$
$331$	−3.86378	−	6.69226i	−0.212372	−	0.367840i	−0.952457	+	0.304674i	$0.901452\pi$
$332$	6.00129	−	10.3945i	0.329363	−	0.570474i
$333$		0			0
$334$	−20.2463	+	11.6892i	−1.10783	+	0.639604i
$335$	−5.59125			−0.305483
$336$		0			0
$337$	24.9208			1.35752			0.678761	−	0.734359i	$-0.262517\pi$
$337$	24.9208			1.35752			0.678761	+	0.734359i	$0.262517\pi$
$338$	−31.5491	+	18.2149i	−1.71605	+	0.990760i
$339$		0			0
$340$	2.18193	−	3.77922i	0.118332	−	0.204957i
$341$	1.61968	+	2.80537i	0.0877105	+	0.151919i
$342$		0			0
$343$	−18.3961	−	2.14058i	−0.993298	−	0.115580i
$344$		−	12.7269i		−	0.686189i
$345$		0			0
$346$	−6.82895	−	3.94270i	−0.367127	−	0.211961i
$347$	11.0204	+	6.36264i	0.591607	+	0.341564i	0.765733	−	0.643159i	$-0.222377\pi$
$347$	11.0204	+	6.36264i	0.591607	+	0.341564i	−0.174126	+	0.984723i	$0.555710\pi$
$348$		0			0
$349$		−	6.72324i		−	0.359887i	−0.983677	−	0.179943i	$-0.942409\pi$
$349$		−	6.72324i		−	0.359887i	0.983677	−	0.179943i	$-0.0575914\pi$
$350$	−9.17747	−	5.78213i	−0.490556	−	0.309068i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	9.54247	−	16.5280i	0.507895	−	0.879699i	−0.492064	−	0.870559i	$-0.663757\pi$
$353$	9.54247	−	16.5280i	0.507895	−	0.879699i	0.999958	−	0.00914007i	$-0.00290941\pi$
$354$		0			0
$355$	10.4815	−	6.05151i	0.556301	−	0.321181i
$356$	0.882960			0.0467968
$357$		0			0
$358$	3.50545			0.185269
$359$	−11.1639	+	6.44550i	−0.589210	+	0.340181i	−0.764785	−	0.644285i	$-0.777155\pi$
$359$	−11.1639	+	6.44550i	−0.589210	+	0.340181i	0.175575	+	0.984466i	$0.443822\pi$
$360$		0			0
$361$	−7.00952	+	12.1408i	−0.368922	+	0.638992i
$362$	9.22534	+	15.9788i	0.484873	+	0.839825i
$363$		0			0
$364$	16.4562	−	8.67185i	0.862541	−	0.454528i
$365$			5.31865i			0.278391i
$366$		0			0
$367$	−2.21459	−	1.27860i	−0.115601	−	0.0667422i	0.441085	−	0.897465i	$-0.354594\pi$
$367$	−2.21459	−	1.27860i	−0.115601	−	0.0667422i	−0.556686	+	0.830723i	$0.687927\pi$
$368$	−7.17812	−	4.14429i	−0.374185	−	0.216036i
$369$		0			0
$370$			8.68240i			0.451376i
$371$	−22.2400	+	11.7197i	−1.15465	+	0.608457i
$372$		0			0
$373$	−15.1993	−	26.3259i	−0.786989	−	1.36310i	−0.927804	−	0.373069i	$-0.878306\pi$
$373$	−15.1993	−	26.3259i	−0.786989	−	1.36310i	0.140815	−	0.990036i	$-0.455028\pi$
$374$	−2.29971	+	3.98321i	−0.118915	+	0.205967i
$375$		0			0
$376$	−0.435168	+	0.251245i	−0.0224421	+	0.0129570i
$377$	6.54285			0.336974
$378$		0			0
$379$	−13.6206			−0.699642			−0.349821	−	0.936817i	$-0.613758\pi$
$379$	−13.6206			−0.699642			−0.349821	+	0.936817i	$0.613758\pi$
$380$	1.83381	−	1.05875i	0.0940726	−	0.0543129i
$381$		0			0
$382$	−12.9536	+	22.4364i	−0.662766	+	1.14795i
$383$	11.4051	+	19.7542i	0.582774	+	1.00939i	0.995149	+	0.0983803i	$0.0313661\pi$
$383$	11.4051	+	19.7542i	0.582774	+	1.00939i	−0.412375	+	0.911014i	$0.635301\pi$
$384$		0			0
$385$	−2.12387	−	1.33811i	−0.108242	−	0.0681965i
$386$			0.609428i			0.0310191i
$387$		0			0
$388$	10.9392	+	6.31573i	0.555352	+	0.320633i
$389$	1.46953	+	0.848435i	0.0745083	+	0.0430174i	0.536791	−	0.843715i	$-0.319636\pi$
$389$	1.46953	+	0.848435i	0.0745083	+	0.0430174i	−0.462283	+	0.886732i	$0.652970\pi$
$390$		0			0
$391$		−	38.1226i		−	1.92794i
$392$	−6.31413	+	3.02187i	−0.318912	+	0.152628i
$393$		0			0
$394$	1.09828	+	1.90228i	0.0553307	+	0.0958356i
$395$	3.95381	−	6.84819i	0.198938	−	0.344570i
$396$		0			0
$397$	−21.7326	+	12.5473i	−1.09073	+	0.629733i	−0.933770	−	0.357873i	$-0.883502\pi$
$397$	−21.7326	+	12.5473i	−1.09073	+	0.629733i	−0.156958	+	0.987605i	$0.550169\pi$
$398$	26.5425			1.33046
$399$		0			0
$400$	−4.09981			−0.204990
$401$	18.8176	−	10.8643i	0.939705	−	0.542539i	0.0498372	−	0.998757i	$-0.484130\pi$
$401$	18.8176	−	10.8643i	0.939705	−	0.542539i	0.889868	+	0.456218i	$0.150796\pi$
$402$		0			0
$403$	11.3874	−	19.7235i	0.567245	−	0.982497i
$404$	−8.03742	−	13.9212i	−0.399877	−	0.692607i
$405$		0			0
$406$	−2.46036	−	0.0950491i	−0.122105	−	0.00471721i
$407$		−	9.15106i		−	0.453601i
$408$		0			0
$409$	−4.03930	−	2.33209i	−0.199730	−	0.115314i	0.396799	−	0.917905i	$-0.370121\pi$
$409$	−4.03930	−	2.33209i	−0.199730	−	0.115314i	−0.596530	+	0.802591i	$0.703454\pi$
$410$	−7.02119	−	4.05369i	−0.346752	−	0.200197i
$411$		0			0
$412$		−	8.57446i		−	0.422433i
$413$	9.73392	+	18.4717i	0.478975	+	0.908932i
$414$		0			0
$415$	5.69394	+	9.86219i	0.279504	+	0.484116i
$416$	3.51532	−	6.08871i	0.172353	−	0.298523i
$417$		0			0
$418$	−1.93280	+	1.11590i	−0.0945363	+	0.0545806i
$419$	36.6109			1.78856			0.894281	−	0.447506i	$-0.147688\pi$
$419$	36.6109			1.78856			0.894281	+	0.447506i	$0.147688\pi$
$420$		0			0
$421$	−30.4576			−1.48441			−0.742206	−	0.670172i	$-0.766220\pi$
$421$	−30.4576			−1.48441			−0.742206	+	0.670172i	$0.766220\pi$
$422$	5.82746	−	3.36449i	0.283676	−	0.163781i
$423$		0			0
$424$	−4.75083	+	8.22868i	−0.230721	+	0.399620i
$425$	−9.42836	−	16.3304i	−0.457343	−	0.792141i
$426$		0			0
$427$	−0.238525	+	6.17425i	−0.0115430	+	0.298793i
$428$			14.1459i			0.683767i
$429$		0			0
$430$	10.4574	+	6.03756i	0.504299	+	0.291157i
$431$	16.1392	+	9.31798i	0.777399	+	0.448832i	0.835508	−	0.549479i	$-0.185174\pi$
$431$	16.1392	+	9.31798i	0.777399	+	0.448832i	−0.0581087	+	0.998310i	$0.518507\pi$
$432$		0			0
$433$		−	9.69502i		−	0.465913i	−0.972487	−	0.232956i	$-0.925160\pi$
$433$		−	9.69502i		−	0.465913i	0.972487	−	0.232956i	$-0.0748400\pi$
$434$	−4.56860	+	7.25134i	−0.219300	+	0.348075i
$435$		0			0
$436$	−3.35840	−	5.81692i	−0.160838	−	0.278580i
$437$	9.24925	−	16.0202i	0.442451	−	0.766348i
$438$		0			0
$439$	29.0710	−	16.7841i	1.38748	−	0.801063i	0.394450	−	0.918917i	$-0.370935\pi$
$439$	29.0710	−	16.7841i	1.38748	−	0.801063i	0.993031	+	0.117854i	$0.0376016\pi$
$440$	−0.948786			−0.0452316
$441$		0			0
$442$	32.3368			1.53811
$443$	−2.64582	+	1.52756i	−0.125707	+	0.0725767i	−0.561535	−	0.827453i	$-0.689789\pi$
$443$	−2.64582	+	1.52756i	−0.125707	+	0.0725767i	0.435828	+	0.900030i	$0.356456\pi$
$444$		0			0
$445$	−0.418870	+	0.725504i	−0.0198563	+	0.0343922i
$446$	12.0553	+	20.8803i	0.570833	+	0.988713i
$447$		0			0
$448$	−1.41034	+	2.23851i	−0.0666324	+	0.105760i
$449$			0.355204i			0.0167631i	0.999965	+	0.00838157i	$0.00266797\pi$
$449$			0.355204i			0.0167631i	−0.999965	+	0.00838157i	$0.997332\pi$
$450$		0			0
$451$	7.40019	+	4.27250i	0.348461	+	0.201184i
$452$	7.27357	+	4.19940i	0.342120	+	0.197523i
$453$		0			0
$454$			9.91650i			0.465404i
$455$	−0.681299	+	17.6355i	−0.0319398	+	0.826765i
$456$		0			0
$457$	−4.80324	−	8.31946i	−0.224686	−	0.389168i	0.731539	−	0.681800i	$-0.238802\pi$
$457$	−4.80324	−	8.31946i	−0.224686	−	0.389168i	−0.956225	+	0.292632i	$0.905469\pi$
$458$	−11.3565	+	19.6700i	−0.530654	+	0.919119i
$459$		0			0
$460$	6.81050	−	3.93204i	0.317541	−	0.183332i
$461$	−38.6120			−1.79834			−0.899169	−	0.437602i	$-0.855828\pi$
$461$	−38.6120			−1.79834			−0.899169	+	0.437602i	$0.855828\pi$
$462$		0			0
$463$	3.61880			0.168180			0.0840899	−	0.996458i	$-0.473202\pi$
$463$	3.61880			0.168180			0.0840899	+	0.996458i	$0.473202\pi$
$464$	−0.805941	+	0.465310i	−0.0374149	+	0.0216015i
$465$		0			0
$466$	6.15652	−	10.6634i	0.285195	−	0.493972i
$467$	−4.07804	−	7.06337i	−0.188709	−	0.326854i	0.756111	−	0.654443i	$-0.227097\pi$
$467$	−4.07804	−	7.06337i	−0.188709	−	0.326854i	−0.944820	+	0.327590i	$0.893764\pi$
$468$		0			0
$469$	7.26873	+	13.7936i	0.335639	+	0.636928i
$470$		−	0.476755i		−	0.0219910i
$471$		0			0
$472$	6.83441	+	3.94585i	0.314579	+	0.181622i
$473$	−11.0218	−	6.36346i	−0.506784	−	0.292592i
$474$		0			0
$475$		−	9.14997i		−	0.419829i
$476$	−12.1598	−	0.469763i	−0.557346	−	0.0215315i
$477$		0			0
$478$	0.177951	+	0.308221i	0.00813931	+	0.0140977i
$479$	12.9635	−	22.4534i	0.592316	−	1.02592i	−0.401604	−	0.915814i	$-0.631547\pi$
$479$	12.9635	−	22.4534i	0.592316	−	1.02592i	0.993920	−	0.110108i	$-0.0351196\pi$
$480$		0			0
$481$	−55.7181	+	32.1689i	−2.54053	+	1.46677i
$482$	−22.3334			−1.01726
$483$		0			0
$484$	1.00000			0.0454545
$485$	−10.3789	+	5.99227i	−0.471283	+	0.272095i
$486$		0			0
$487$	−1.93103	+	3.34464i	−0.0875032	+	0.151560i	−0.906455	−	0.422302i	$-0.861222\pi$
$487$	−1.93103	+	3.34464i	−0.0875032	+	0.151560i	0.818952	+	0.573862i	$0.194555\pi$
$488$	1.16769	+	2.02250i	0.0528590	+	0.0915545i
$489$		0			0
$490$	0.512388	−	6.62171i	0.0231473	−	0.299138i
$491$			13.5459i			0.611317i	0.952141	+	0.305658i	$0.0988766\pi$
$491$			13.5459i			0.611317i	−0.952141	+	0.305658i	$0.901123\pi$
$492$		0			0
$493$	−3.70686	−	2.14016i	−0.166949	−	0.0963878i
$494$	13.5888	+	7.84550i	0.611389	+	0.352986i
$495$		0			0
$496$			3.23936i			0.145451i
$497$	−28.5552	−	17.9908i	−1.28088	−	0.806996i
$498$		0			0
$499$	−5.02599	−	8.70526i	−0.224994	−	0.389701i	0.731324	−	0.682031i	$-0.238903\pi$
$499$	−5.02599	−	8.70526i	−0.224994	−	0.389701i	−0.956318	+	0.292329i	$0.905570\pi$
$500$	4.31688	−	7.47706i	0.193057	−	0.334384i
$501$		0			0
$502$	−9.43433	+	5.44691i	−0.421075	+	0.243108i
$503$	10.4299			0.465048			0.232524	−	0.972591i	$-0.425302\pi$
$503$	10.4299			0.465048			0.232524	+	0.972591i	$0.425302\pi$
$504$		0			0
$505$	15.2516			0.678687
$506$	−7.17812	+	4.14429i	−0.319106	+	0.184236i
$507$		0			0
$508$	−3.99909	+	6.92663i	−0.177431	+	0.307320i
$509$	−5.46543	−	9.46640i	−0.242251	−	0.419591i	0.719104	−	0.694902i	$-0.244552\pi$
$509$	−5.46543	−	9.46640i	−0.242251	−	0.419591i	−0.961355	+	0.275311i	$0.911219\pi$
$510$		0			0
$511$	13.1211	−	6.91433i	0.580441	−	0.305872i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	7.76538	+	4.48335i	0.342516	+	0.197752i
$515$	7.04540	+	4.06766i	0.310457	+	0.179243i
$516$		0			0
$517$			0.502489i			0.0220995i
$518$	21.4194	−	11.2873i	0.941115	−	0.495934i
$519$		0			0
$520$	3.33528	+	5.77688i	0.146262	+	0.253333i
$521$	0.801194	−	1.38771i	0.0351010	−	0.0607966i	−0.847941	−	0.530090i	$-0.822158\pi$
$521$	0.801194	−	1.38771i	0.0351010	−	0.0607966i	0.883042	+	0.469294i	$0.155491\pi$
$522$		0			0
$523$	18.6963	−	10.7943i	0.817533	−	0.472003i	−0.0320322	−	0.999487i	$-0.510198\pi$
$523$	18.6963	−	10.7943i	0.817533	−	0.472003i	0.849565	+	0.527484i	$0.176865\pi$
$524$	8.74506			0.382030
$525$		0			0
$526$	8.46076			0.368907
$527$	−12.9030	+	7.44958i	−0.562066	+	0.324509i
$528$		0			0
$529$	22.8503	−	39.5778i	0.993490	−	1.72077i
$530$	−4.50752	−	7.80725i	−0.195794	−	0.339125i
$531$		0			0
$532$	−4.99592	−	3.14761i	−0.216601	−	0.136466i
$533$		−	60.0767i		−	2.60221i
$534$		0			0
$535$	−11.6233	−	6.71070i	−0.502518	−	0.290129i
$536$	5.10354	+	2.94653i	0.220439	+	0.127271i
$537$		0			0
$538$			3.22454i			0.139020i
$539$	−0.540046	+	6.97914i	−0.0232614	+	0.300613i
$540$		0			0
$541$	−1.76339	−	3.05429i	−0.0758142	−	0.131314i	0.825626	−	0.564218i	$-0.190822\pi$
$541$	−1.76339	−	3.05429i	−0.0758142	−	0.131314i	−0.901440	+	0.432904i	$0.857489\pi$
$542$	0.382335	−	0.662223i	0.0164227	−	0.0284449i
$543$		0			0
$544$	−3.98321	+	2.29971i	−0.170779	+	0.0985992i
$545$	6.37280			0.272981
$546$		0			0
$547$	0.548636			0.0234580			0.0117290	−	0.999931i	$-0.496266\pi$
$547$	0.548636			0.0234580			0.0117290	+	0.999931i	$0.496266\pi$
$548$	−0.350664	+	0.202456i	−0.0149796	+	0.00864848i
$549$		0			0
$550$	−2.04990	+	3.55054i	−0.0874082	+	0.151395i
$551$	−1.03848	−	1.79870i	−0.0442408	−	0.0766274i
$552$		0			0
$553$	−22.0345	−	0.851241i	−0.937001	−	0.0361985i
$554$		−	27.2895i		−	1.15942i
$555$		0			0
$556$	15.2418	+	8.79984i	0.646395	+	0.373196i
$557$	6.28514	+	3.62873i	0.266310	+	0.153754i	0.627209	−	0.778851i	$-0.284197\pi$
$557$	6.28514	+	3.62873i	0.266310	+	0.153754i	−0.360900	+	0.932605i	$0.617530\pi$
$558$		0			0
$559$			89.4783i			3.78453i
$560$	−1.17027	−	2.22077i	−0.0494529	−	0.0938448i
$561$		0			0
$562$	−2.18312	−	3.78128i	−0.0920895	−	0.159504i
$563$	−4.89429	+	8.47715i	−0.206270	+	0.357269i	−0.950537	−	0.310613i	$-0.899466\pi$
$563$	−4.89429	+	8.47715i	−0.206270	+	0.357269i	0.744267	+	0.667882i	$0.232799\pi$
$564$		0			0
$565$	−6.90106	+	3.98433i	−0.290330	+	0.167622i
$566$	−19.1213			−0.803730
$567$		0			0
$568$	−12.7563			−0.535243
$569$	25.5726	−	14.7644i	1.07206	−	0.618954i	0.143316	−	0.989677i	$-0.454223\pi$
$569$	25.5726	−	14.7644i	1.07206	−	0.618954i	0.928743	+	0.370723i	$0.120890\pi$
$570$		0			0
$571$	16.4562	−	28.5031i	0.688673	−	1.19282i	−0.283595	−	0.958944i	$-0.591527\pi$
$571$	16.4562	−	28.5031i	0.688673	−	1.19282i	0.972267	−	0.233872i	$-0.0751396\pi$
$572$	−3.51532	−	6.08871i	−0.146983	−	0.254582i
$573$		0			0
$574$	−0.872745	+	22.5911i	−0.0364277	+	0.942934i
$575$		−	33.9816i		−	1.41713i
$576$		0			0
$577$	14.0259	+	8.09787i	0.583907	+	0.337119i	0.762685	−	0.646771i	$-0.223881\pi$
$577$	14.0259	+	8.09787i	0.583907	+	0.337119i	−0.178777	+	0.983890i	$0.557214\pi$
$578$	−3.59803	−	2.07732i	−0.149658	−	0.0864053i
$579$		0			0
$580$		−	0.882960i		−	0.0366629i
$581$	16.9277	−	26.8679i	0.702281	−	1.11467i
$582$		0			0
$583$	4.75083	+	8.22868i	0.196759	+	0.340797i
$584$	2.80287	−	4.85471i	0.115984	−	0.200889i
$585$		0			0
$586$	8.00185	−	4.61987i	0.330553	−	0.190845i
$587$	−13.5685			−0.560031			−0.280016	−	0.959995i	$-0.590340\pi$
$587$	−13.5685			−0.560031			−0.280016	+	0.959995i	$0.590340\pi$
$588$		0			0
$589$	−7.22961			−0.297891
$590$	−6.48439	+	3.74376i	−0.266958	+	0.154128i
$591$		0			0
$592$	4.57553	−	7.92505i	0.188053	−	0.325718i
$593$	12.5012	+	21.6528i	0.513365	+	0.889174i	0.999880	+	0.0155014i	$0.00493446\pi$
$593$	12.5012	+	21.6528i	0.513365	+	0.889174i	−0.486515	+	0.873672i	$0.661732\pi$
$594$		0			0
$595$	6.15454	−	9.76856i	0.252311	−	0.400472i
$596$			20.2236i			0.828390i
$597$		0			0
$598$	50.4667	+	29.1370i	2.06374	+	1.19150i
$599$	12.1564	+	7.01849i	0.496696	+	0.286768i	0.727348	−	0.686269i	$-0.240753\pi$
$599$	12.1564	+	7.01849i	0.496696	+	0.286768i	−0.230652	+	0.973036i	$0.574086\pi$
$600$		0			0
$601$			15.3598i			0.626540i	0.949664	+	0.313270i	$0.101424\pi$
$601$			15.3598i			0.626540i	−0.949664	+	0.313270i	$0.898576\pi$
$602$	1.29987	−	33.6472i	0.0529786	−	1.37136i
$603$		0			0
$604$	3.93283	+	6.81186i	0.160025	+	0.277171i
$605$	−0.474393	+	0.821673i	−0.0192868	+	0.0334057i
$606$		0			0
$607$	3.15436	−	1.82117i	0.128032	−	0.0739190i	−0.434616	−	0.900616i	$-0.643116\pi$
$607$	3.15436	−	1.82117i	0.128032	−	0.0739190i	0.562648	+	0.826697i	$0.309783\pi$
$608$	−2.23181			−0.0905117
$609$		0			0
$610$	−2.21578			−0.0897144
$611$	3.05951	−	1.76641i	0.123774	−	0.0714612i
$612$		0			0
$613$	−21.4436	+	37.1414i	−0.866099	+	1.50013i	−0.000146529		1.00000i	$0.500047\pi$
$613$	−21.4436	+	37.1414i	−0.866099	+	1.50013i	−0.865952	+	0.500127i	$0.833287\pi$
$614$	−3.53010	−	6.11432i	−0.142463	−	0.246754i
$615$		0			0
$616$	1.23344	+	2.34065i	0.0496966	+	0.0943074i
$617$		−	2.97864i		−	0.119915i	−0.998201	−	0.0599577i	$-0.980903\pi$
$617$		−	2.97864i		−	0.119915i	0.998201	−	0.0599577i	$-0.0190966\pi$
$618$		0			0
$619$	−14.6085	−	8.43422i	−0.587165	−	0.339000i	0.176810	−	0.984245i	$-0.443422\pi$
$619$	−14.6085	−	8.43422i	−0.587165	−	0.339000i	−0.763976	+	0.645245i	$0.776755\pi$
$620$	−2.66169	−	1.53673i	−0.106896	−	0.0617165i
$621$		0			0
$622$		−	8.64112i		−	0.346477i
$623$	2.33435	+	0.0901812i	0.0935238	+	0.00361304i
$624$		0			0
$625$	−6.15372	−	10.6586i	−0.246149	−	0.426342i
$626$	−11.9124	+	20.6329i	−0.476116	+	0.824657i
$627$		0			0
$628$	−0.300234	+	0.173340i	−0.0119806	+	0.00691702i
$629$	42.0896			1.67822
$630$		0			0
$631$	26.6847			1.06230			0.531150	−	0.847278i	$-0.321760\pi$
$631$	26.6847			1.06230			0.531150	+	0.847278i	$0.321760\pi$
$632$	−7.21785	+	4.16723i	−0.287111	+	0.165763i
$633$		0			0
$634$	−12.6754	+	21.9545i	−0.503405	+	0.871924i
$635$	−3.79428	−	6.57189i	−0.150572	−	0.260798i
$636$		0			0
$637$	44.3923	−	21.2457i	1.75889	−	0.841785i
$638$			0.930621i			0.0368436i
$639$		0			0
$640$	−0.821673	−	0.474393i	−0.0324795	−	0.0187520i
$641$	26.1562	+	15.1013i	1.03311	+	0.596464i	0.917873	−	0.396874i	$-0.129905\pi$
$641$	26.1562	+	15.1013i	1.03311	+	0.596464i	0.115234	+	0.993338i	$0.463238\pi$
$642$		0			0
$643$			10.8154i			0.426517i	0.976996	+	0.213259i	$0.0684077\pi$
$643$			10.8154i			0.426517i	−0.976996	+	0.213259i	$0.931592\pi$
$644$	−18.5541	−	11.6897i	−0.731133	−	0.460640i
$645$		0			0
$646$	−5.13250	−	8.88976i	−0.201936	−	0.349763i
$647$	7.24060	−	12.5411i	0.284657	−	0.493041i	−0.687869	−	0.725835i	$-0.741453\pi$
$647$	7.24060	−	12.5411i	0.284657	−	0.493041i	0.972526	+	0.232794i	$0.0747868\pi$
$648$		0			0
$649$	6.83441	−	3.94585i	0.268274	−	0.154888i
$650$	28.8242			1.13058
$651$		0			0
$652$	−8.00934			−0.313670
$653$	−37.4800	+	21.6391i	−1.46671	+	0.846804i	−0.999306	−	0.0372417i	$-0.988143\pi$
$653$	−37.4800	+	21.6391i	−1.46671	+	0.846804i	−0.467401	+	0.884045i	$0.654810\pi$
$654$		0			0
$655$	−4.14859	+	7.18557i	−0.162099	+	0.280764i
$656$	4.27250	+	7.40019i	0.166813	+	0.288929i
$657$		0			0
$658$	−1.17615	+	0.619789i	−0.0458511	+	0.0241619i
$659$			9.95936i			0.387962i	0.981005	+	0.193981i	$0.0621400\pi$
$659$			9.95936i			0.387962i	−0.981005	+	0.193981i	$0.937860\pi$
$660$		0			0
$661$	−22.1474	−	12.7868i	−0.861434	−	0.497349i	0.00305800	−	0.999995i	$-0.499027\pi$
$661$	−22.1474	−	12.7868i	−0.861434	−	0.497349i	−0.864492	+	0.502646i	$0.832360\pi$
$662$	−6.69226	−	3.86378i	−0.260102	−	0.150170i
$663$		0			0
$664$		−	12.0026i		−	0.465790i
$665$	4.95633	−	2.61181i	0.192198	−	0.101282i
$666$		0			0
$667$	−3.85676	−	6.68011i	−0.149334	−	0.258655i
$668$	−11.6892	+	20.2463i	−0.452269	+	0.783352i
$669$		0			0
$670$	−4.84217	+	2.79563i	−0.187069	+	0.108004i
$671$	2.33539			0.0901566
$672$		0			0
$673$	22.7065			0.875269			0.437635	−	0.899153i	$-0.355816\pi$
$673$	22.7065			0.875269			0.437635	+	0.899153i	$0.355816\pi$
$674$	21.5820	−	12.4604i	0.831309	−	0.479957i
$675$		0			0
$676$	−18.2149	+	31.5491i	−0.700573	+	1.21343i
$677$	−13.1278	−	22.7380i	−0.504542	−	0.873893i	−0.999986	−	0.00525286i	$-0.998328\pi$
$677$	−13.1278	−	22.7380i	−0.504542	−	0.873893i	0.495444	−	0.868640i	$-0.335005\pi$
$678$		0			0
$679$	28.2757	+	17.8147i	1.08512	+	0.683664i
$680$		−	4.36386i		−	0.167346i
$681$		0			0
$682$	2.80537	+	1.61968i	0.107423	+	0.0620207i
$683$	−27.1231	−	15.6595i	−1.03784	−	0.599194i	−0.118616	−	0.992940i	$-0.537846\pi$
$683$	−27.1231	−	15.6595i	−1.03784	−	0.599194i	−0.919219	+	0.393746i	$0.871179\pi$
$684$		0			0
$685$		−	0.384174i		−	0.0146785i
$686$	−17.0018	+	7.34427i	−0.649132	+	0.280406i
$687$		0			0
$688$	−6.36346	−	11.0218i	−0.242605	−	0.420203i
$689$	33.4013	−	57.8528i	1.27249	−	2.20402i
$690$		0			0
$691$	−22.5041	+	12.9927i	−0.856096	+	0.494267i	−0.862703	−	0.505711i	$-0.831230\pi$
$691$	−22.5041	+	12.9927i	−0.856096	+	0.494267i	0.00660716	+	0.999978i	$0.497897\pi$
$692$	−7.88540			−0.299758
$693$		0			0
$694$	12.7253			0.483045
$695$	−14.4612	+	8.34916i	−0.548543	+	0.316702i
$696$		0			0
$697$	−19.6510	+	34.0366i	−0.744335	+	1.28923i
$698$	−3.36162	−	5.82250i	−0.127239	−	0.220385i
$699$		0			0
$700$	−10.8390	−	0.418734i	−0.409675	−	0.0158267i
$701$		−	1.46095i		−	0.0551793i	−0.999619	−	0.0275897i	$-0.991217\pi$
$701$		−	1.46095i		−	0.0551793i	0.999619	−	0.0275897i	$-0.00878318\pi$
$702$		0			0
$703$	17.6872	+	10.2117i	0.667084	+	0.385141i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$		0			0
$706$		−	19.0849i		−	0.718271i
$707$	−19.8273	−	37.6256i	−0.745683	−	1.41505i
$708$		0			0
$709$	−7.35318	−	12.7361i	−0.276155	−	0.478314i	0.694271	−	0.719714i	$-0.255727\pi$
$709$	−7.35318	−	12.7361i	−0.276155	−	0.478314i	−0.970426	+	0.241400i	$0.922394\pi$
$710$	6.05151	−	10.4815i	0.227109	−	0.393364i
$711$		0			0
$712$	0.764665	−	0.441480i	0.0286570	−	0.0165452i
$713$	−26.8497			−1.00553
$714$		0			0
$715$	6.67056			0.249465
$716$	3.03581	−	1.75273i	0.113454	−	0.0655025i
$717$		0			0
$718$	−6.44550	+	11.1639i	−0.240544	+	0.416634i
$719$	−15.2799	−	26.4656i	−0.569844	−	0.986999i	−0.996581	−	0.0826233i	$-0.973670\pi$
$719$	−15.2799	−	26.4656i	−0.569844	−	0.986999i	0.426737	−	0.904376i	$-0.359663\pi$
$720$		0			0
$721$	0.875755	−	22.6690i	0.0326148	−	0.844237i
$722$			14.0190i			0.521735i
$723$		0			0
$724$	15.9788	+	9.22534i	0.593846	+	0.342857i
$725$	−3.30420	−	1.90768i	−0.122715	−	0.0708495i
$726$		0			0
$727$		−	23.9985i		−	0.890056i	−0.895517	−	0.445028i	$-0.853194\pi$
$727$		−	23.9985i		−	0.890056i	0.895517	−	0.445028i	$-0.146806\pi$
$728$	9.91559	−	15.7382i	0.367496	−	0.583295i
$729$		0			0
$730$	2.65932	+	4.60608i	0.0984259	+	0.170479i
$731$	29.2682	−	50.6940i	1.08252	−	1.87499i
$732$		0			0
$733$	21.1549	−	12.2138i	0.781373	−	0.451126i	−0.0555434	−	0.998456i	$-0.517689\pi$
$733$	21.1549	−	12.2138i	0.781373	−	0.451126i	0.836917	+	0.547330i	$0.184356\pi$
$734$	−2.55719			−0.0943877
$735$		0			0
$736$	−8.28858			−0.305521
$737$	5.10354	−	2.94653i	0.187991	−	0.108537i
$738$		0			0
$739$	11.6718	−	20.2161i	0.429354	−	0.743663i	−0.567462	−	0.823399i	$-0.692075\pi$
$739$	11.6718	−	20.2161i	0.429354	−	0.743663i	0.996816	+	0.0797369i	$0.0254080\pi$
$740$	4.34120	+	7.51918i	0.159586	+	0.276410i
$741$		0			0
$742$	−13.4006	+	21.2696i	−0.491951	+	0.780831i
$743$		−	7.04913i		−	0.258608i	−0.991605	−	0.129304i	$-0.958726\pi$
$743$		−	7.04913i		−	0.258608i	0.991605	−	0.129304i	$-0.0412742\pi$
$744$		0			0
$745$	−16.6172	−	9.59392i	−0.608805	−	0.351494i
$746$	−26.3259	−	15.1993i	−0.963860	−	0.556485i
$747$		0			0
$748$			4.59942i			0.168171i
$749$	−1.44479	+	37.3986i	−0.0527915	+	1.36651i
$750$		0			0
$751$	−0.999206	−	1.73068i	−0.0364615	−	0.0631533i	0.847219	−	0.531244i	$-0.178275\pi$
$751$	−0.999206	−	1.73068i	−0.0364615	−	0.0631533i	−0.883680	+	0.468091i	$0.844942\pi$
$752$	−0.251245	+	0.435168i	−0.00916195	+	0.0158690i
$753$		0			0
$754$	5.66628	−	3.27143i	0.206354	−	0.119138i
$755$	−7.46283			−0.271600
$756$		0			0
$757$	−39.3860			−1.43151			−0.715753	−	0.698353i	$-0.753917\pi$
$757$	−39.3860			−1.43151			−0.715753	+	0.698353i	$0.753917\pi$
$758$	−11.7958	+	6.81029i	−0.428442	+	0.247361i
$759$		0			0
$760$	1.05875	−	1.83381i	0.0384050	−	0.0665194i
$761$	4.01747	+	6.95846i	0.145633	+	0.252244i	0.929609	−	0.368547i	$-0.120145\pi$
$761$	4.01747	+	6.95846i	0.145633	+	0.252244i	−0.783976	+	0.620791i	$0.786811\pi$
$762$		0			0
$763$	−8.28476	−	15.7217i	−0.299928	−	0.569162i
$764$			25.9073i			0.937293i
$765$		0			0
$766$	19.7542	+	11.4051i	0.713750	+	0.412084i
$767$	−48.0502	−	27.7418i	−1.73499	−	1.00170i
$768$		0			0
$769$			1.71938i			0.0620025i	0.999519	+	0.0310013i	$0.00986959\pi$
$769$			1.71938i			0.0620025i	−0.999519	+	0.0310013i	$0.990130\pi$
$770$	−2.50838	−	0.0969044i	−0.0903957	−	0.00349219i
$771$		0			0
$772$	0.304714	+	0.527780i	0.0109669	+	0.0189952i
$773$	−5.05536	+	8.75614i	−0.181829	+	0.314936i	−0.942503	−	0.334197i	$-0.891535\pi$
$773$	−5.05536	+	8.75614i	−0.181829	+	0.314936i	0.760675	+	0.649133i	$0.224868\pi$
$774$		0			0
$775$	−11.5015	+	6.64037i	−0.413144	+	0.238529i
$776$	12.6315			0.453443
$777$		0			0
$778$	1.69687			0.0608357
$779$	−16.5158	+	9.53539i	−0.591739	+	0.341641i
$780$		0			0
$781$	−6.37816	+	11.0473i	−0.228229	+	0.395303i
$782$	−19.0613	−	33.0152i	−0.681631	−	1.18062i
$783$		0			0
$784$	−3.95726	+	5.77409i	−0.141331	+	0.206217i
$785$		−	0.328925i		−	0.0117398i
$786$		0			0
$787$	9.25705	+	5.34456i	0.329978	+	0.190513i	0.655831	−	0.754907i	$-0.272318\pi$
$787$	9.25705	+	5.34456i	0.329978	+	0.190513i	−0.325853	+	0.945420i	$0.605652\pi$
$788$	1.90228	+	1.09828i	0.0677660	+	0.0391247i
$789$		0			0
$790$		−	7.90761i		−	0.281340i
$791$	18.8008	+	11.8452i	0.668480	+	0.421166i
$792$		0			0
$793$	−8.20962	−	14.2195i	−0.291532	−	0.504949i
$794$	−12.5473	+	21.7326i	−0.445288	+	0.771262i
$795$		0			0
$796$	22.9865	−	13.2713i	0.814735	−	0.470388i
$797$	8.76241			0.310380			0.155190	−	0.987885i	$-0.450401\pi$
$797$	8.76241			0.310380			0.155190	+	0.987885i	$0.450401\pi$
$798$		0			0
$799$	−2.31116			−0.0817629
$800$	−3.55054	+	2.04990i	−0.125530	+	0.0724750i
$801$		0			0
$802$	10.8643	−	18.8176i	0.383633	−	0.664472i
$803$	−2.80287	−	4.85471i	−0.0989111	−	0.171319i
$804$		0			0
$805$	18.4071	−	9.69986i	0.648763	−	0.341875i
$806$		−	22.7747i		−	0.802206i
$807$		0			0
$808$	−13.9212	−	8.03742i	−0.489747	−	0.282756i
$809$	24.4799	+	14.1335i	0.860669	+	0.496908i	0.864236	−	0.503086i	$-0.167802\pi$
$809$	24.4799	+	14.1335i	0.860669	+	0.496908i	−0.00356720	+	0.999994i	$0.501135\pi$
$810$		0			0
$811$		−	19.6593i		−	0.690331i	−0.938542	−	0.345166i	$-0.887823\pi$
$811$		−	19.6593i		−	0.690331i	0.938542	−	0.345166i	$-0.112177\pi$
$812$	−2.17825	+	1.14786i	−0.0764418	+	0.0402821i
$813$		0			0
$814$	−4.57553	−	7.92505i	−0.160372	−	0.277773i
$815$	3.79957	−	6.58105i	0.133093	−	0.230524i
$816$		0			0
$817$	24.5986	−	14.2020i	0.860596	−	0.496865i
$818$	−4.66418			−0.163079
$819$		0			0
$820$	−8.10737			−0.283122
$821$	8.92687	−	5.15393i	0.311550	−	0.179873i	−0.336070	−	0.941837i	$-0.609098\pi$
$821$	8.92687	−	5.15393i	0.311550	−	0.179873i	0.647620	+	0.761964i	$0.275765\pi$
$822$		0			0
$823$	−0.561944	+	0.973316i	−0.0195881	+	0.0339277i	−0.875653	−	0.482940i	$-0.839569\pi$
$823$	−0.561944	+	0.973316i	−0.0195881	+	0.0339277i	0.856065	+	0.516868i	$0.172902\pi$
$824$	−4.28723	−	7.42570i	−0.149353	−	0.258687i
$825$		0			0
$826$	17.6657	+	11.1300i	0.614667	+	0.387262i
$827$			23.9832i			0.833976i	0.908912	+	0.416988i	$0.136914\pi$
$827$			23.9832i			0.833976i	−0.908912	+	0.416988i	$0.863086\pi$
$828$		0			0
$829$	5.07807	+	2.93182i	0.176369	+	0.101826i	0.585585	−	0.810611i	$-0.300865\pi$
$829$	5.07807	+	2.93182i	0.176369	+	0.101826i	−0.409217	+	0.912437i	$0.634198\pi$
$830$	9.86219	+	5.69394i	0.342322	+	0.197639i
$831$		0			0
$832$		−	7.03063i		−	0.243743i
$833$	−32.1000	−	2.48390i	−1.11220	−	0.0860619i
$834$		0			0
$835$	−11.0905	−	19.2094i	−0.383804	−	0.664768i
$836$	−1.11590	+	1.93280i	−0.0385943	+	0.0668473i
$837$		0			0
$838$	31.7060	−	18.3055i	1.09527	−	0.632352i
$839$	−14.4962			−0.500464			−0.250232	−	0.968186i	$-0.580507\pi$
$839$	−14.4962			−0.500464			−0.250232	+	0.968186i	$0.580507\pi$
$840$		0			0
$841$	28.1339			0.970136
$842$	−26.3771	+	15.2288i	−0.909013	+	0.524819i
$843$		0			0
$844$	3.36449	−	5.82746i	0.115810	−	0.200590i
$845$	−17.2820	−	29.9334i	−0.594520	−	1.02974i
$846$		0			0
$847$	2.64378	+	0.102135i	0.0908413	+	0.00350941i
$848$			9.50166i			0.326288i
$849$		0			0
$850$	−16.3304	−	9.42836i	−0.560128	−	0.323390i
$851$	65.6874	+	37.9246i	2.25174	+	1.30004i
$852$		0			0
$853$		−	22.1687i		−	0.759042i	−0.925183	−	0.379521i	$-0.876089\pi$
$853$		−	22.1687i		−	0.759042i	0.925183	−	0.379521i	$-0.123911\pi$
$854$	2.88056	+	5.46632i	0.0985706	+	0.187054i
$855$		0			0
$856$	7.07294	+	12.2507i	0.241748	+	0.418720i
$857$	8.89302	−	15.4032i	0.303780	−	0.526162i	−0.673209	−	0.739452i	$-0.735085\pi$
$857$	8.89302	−	15.4032i	0.303780	−	0.526162i	0.976989	+	0.213290i	$0.0684180\pi$
$858$		0			0
$859$	−5.96846	+	3.44589i	−0.203641	+	0.117572i	−0.598353	−	0.801233i	$-0.704178\pi$
$859$	−5.96846	+	3.44589i	−0.203641	+	0.117572i	0.394712	+	0.918805i	$0.370845\pi$
$860$	12.0751			0.411758
$861$		0			0
$862$	18.6360			0.634744
$863$	−30.7013	+	17.7254i	−1.04508	+	0.603380i	−0.921269	−	0.388926i	$-0.872846\pi$
$863$	−30.7013	+	17.7254i	−1.04508	+	0.603380i	−0.123815	+	0.992305i	$0.539513\pi$
$864$		0			0
$865$	3.74078	−	6.47921i	0.127190	−	0.220300i
$866$	−4.84751	−	8.39613i	−0.164725	−	0.285312i
$867$		0			0
$868$	−0.330852	+	8.56414i	−0.0112299	+	0.290686i
$869$			8.33446i			0.282727i
$870$		0			0
$871$	−35.8811	−	20.7160i	−1.21579	−	0.701934i
$872$	−5.81692	−	3.35840i	−0.196986	−	0.113730i
$873$		0			0
$874$		−	18.4985i		−	0.625721i
$875$	12.1766	−	19.3268i	0.411643	−	0.653365i
$876$		0			0
$877$	11.5495	+	20.0042i	0.389997	+	0.675495i	0.992449	−	0.122660i	$-0.0391425\pi$
$877$	11.5495	+	20.0042i	0.389997	+	0.675495i	−0.602451	+	0.798156i	$0.705809\pi$
$878$	16.7841	−	29.0710i	0.566437	−	0.981097i
$879$		0			0
$880$	−0.821673	+	0.474393i	−0.0276986	+	0.0159918i
$881$	−10.9038			−0.367360			−0.183680	−	0.982986i	$-0.558801\pi$
$881$	−10.9038			−0.367360			−0.183680	+	0.982986i	$0.558801\pi$
$882$		0			0
$883$	35.5478			1.19628			0.598140	−	0.801392i	$-0.295907\pi$
$883$	35.5478			1.19628			0.598140	+	0.801392i	$0.295907\pi$
$884$	28.0045	−	16.1684i	0.941893	−	0.543802i
$885$		0			0
$886$	−1.52756	+	2.64582i	−0.0513195	+	0.0888880i
$887$	−5.61786	−	9.73042i	−0.188629	−	0.326716i	0.756164	−	0.654382i	$-0.227071\pi$
$887$	−5.61786	−	9.73042i	−0.188629	−	0.326716i	−0.944793	+	0.327666i	$0.893738\pi$
$888$		0			0
$889$	−11.2802	+	17.9040i	−0.378325	+	0.600482i
$890$			0.837739i			0.0280811i
$891$		0			0
$892$	20.8803	+	12.0553i	0.699125	+	0.403640i
$893$	−0.971211	−	0.560729i	−0.0325003	−	0.0187641i
$894$		0			0
$895$			3.32593i			0.111173i
$896$	−0.102135	+	2.64378i	−0.00341210	+	0.0883225i
$897$		0			0
$898$	0.177602	+	0.307616i	0.00592666	+	0.0102653i
$899$	−1.50731	+	2.61073i	−0.0502715	+	0.0870728i
$900$		0			0
$901$	−37.8471	+	21.8511i	−1.26087	+	0.727964i
$902$	8.54500			0.284517
$903$		0			0
$904$	8.39880			0.279340
$905$	−15.1604	+	8.75287i	−0.503949	+	0.290955i
$906$		0			0
$907$	9.85180	−	17.0638i	0.327124	−	0.566595i	−0.654816	−	0.755788i	$-0.727254\pi$
$907$	9.85180	−	17.0638i	0.327124	−	0.566595i	0.981940	+	0.189193i	$0.0605873\pi$
$908$	4.95825	+	8.58794i	0.164545	+	0.285001i
$909$		0			0
$910$	8.22773	+	15.6134i	0.272746	+	0.517580i
$911$			35.0219i			1.16033i	0.814500	+	0.580164i	$0.197011\pi$
$911$			35.0219i			1.16033i	−0.814500	+	0.580164i	$0.802989\pi$
$912$		0			0
$913$	−10.3945	−	6.00129i	−0.344009	−	0.198614i
$914$	−8.31946	−	4.80324i	−0.275183	−	0.158877i
$915$		0			0
$916$			22.7130i			0.750458i
$917$	23.1200	+	0.893178i	0.763490	+	0.0294953i
$918$		0			0
$919$	18.8411	+	32.6337i	0.621510	+	1.07649i	0.989205	+	0.146541i	$0.0468139\pi$
$919$	18.8411	+	32.6337i	0.621510	+	1.07649i	−0.367694	+	0.929947i	$0.619853\pi$
$920$	3.93204	−	6.81050i	0.129636	−	0.224535i
$921$		0			0
$922$	−33.4389	+	19.3060i	−1.10125	+	0.635808i
$923$	89.6850			2.95202
$924$		0			0
$925$	37.5176			1.23357
$926$	3.13397	−	1.80940i	0.102989	−	0.0594605i
$927$		0			0
$928$	−0.465310	+	0.805941i	−0.0152746	+	0.0264563i
$929$	17.5570	+	30.4096i	0.576027	+	0.997707i	0.995929	+	0.0901382i	$0.0287309\pi$
$929$	17.5570	+	30.4096i	0.576027	+	0.997707i	−0.419903	+	0.907569i	$0.637936\pi$
$930$		0			0
$931$	−12.8866	−	8.83184i	−0.422342	−	0.289452i
$932$		−	12.3130i		−	0.403327i
$933$		0			0
$934$	−7.06337	−	4.07804i	−0.231120	−	0.133437i
$935$	−3.77922	−	2.18193i	−0.123594	−	0.0713568i
$936$		0			0
$937$			9.17435i			0.299713i	0.988708	+	0.149857i	$0.0478812\pi$
$937$			9.17435i			0.299713i	−0.988708	+	0.149857i	$0.952119\pi$
$938$	13.1917	+	8.31123i	0.430724	+	0.271371i
$939$		0			0
$940$	−0.238377	−	0.412882i	−0.00777501	−	0.0134667i
$941$	13.1537	−	22.7828i	0.428798	−	0.742699i	−0.567969	−	0.823050i	$-0.692271\pi$
$941$	13.1537	−	22.7828i	0.428798	−	0.742699i	0.996767	+	0.0803507i	$0.0256040\pi$
$942$		0			0
$943$	−61.3370	+	35.4129i	−1.99741	+	1.15320i
$944$	7.89170			0.256853
$945$		0			0
$946$	−12.7269			−0.413788
$947$	29.2145	−	16.8670i	0.949343	−	0.548103i	0.0564662	−	0.998405i	$-0.482017\pi$
$947$	29.2145	−	16.8670i	0.949343	−	0.548103i	0.892877	+	0.450301i	$0.148683\pi$
$948$		0			0
$949$	−19.7059	+	34.1317i	−0.639682	+	1.10796i
$950$	−4.57498	−	7.92410i	−0.148432	−	0.257092i
$951$		0			0
$952$	−10.7656	+	5.67310i	−0.348916	+	0.183866i
$953$		−	26.6703i		−	0.863937i	−0.901889	−	0.431968i	$-0.857819\pi$
$953$		−	26.6703i		−	0.863937i	0.901889	−	0.431968i	$-0.142181\pi$
$954$		0			0
$955$	−21.2873	−	12.2902i	−0.688841	−	0.397703i
$956$	0.308221	+	0.177951i	0.00996858	+	0.00575536i
$957$		0			0
$958$		−	25.9269i		−	0.837661i
$959$	−0.947755	+	0.499433i	−0.0306046	+	0.0161275i
$960$		0			0
$961$	−10.2533	−	17.7592i	−0.330751	−	0.572878i
$962$	−32.1689	+	55.7181i	−1.03717	+	1.79642i
$963$		0			0
$964$	−19.3413	+	11.1667i	−0.622942	+	0.359655i
$965$	−0.578217			−0.0186135
$966$		0			0
$967$	36.1827			1.16356			0.581779	−	0.813347i	$-0.302357\pi$
$967$	36.1827			1.16356			0.581779	+	0.813347i	$0.302357\pi$
$968$	0.866025	−	0.500000i	0.0278351	−	0.0160706i
$969$		0			0
$970$	−5.99227	+	10.3789i	−0.192400	+	0.333247i
$971$	14.3469	+	24.8495i	0.460413	+	0.797459i	0.998981	−	0.0451229i	$-0.0143679\pi$
$971$	14.3469	+	24.8495i	0.460413	+	0.797459i	−0.538568	+	0.842582i	$0.681035\pi$
$972$		0			0
$973$	39.3971	+	24.8215i	1.26301	+	0.795742i
$974$			3.86205i			0.123748i
$975$		0			0
$976$	2.02250	+	1.16769i	0.0647388	+	0.0373770i
$977$	−40.1239	−	23.1656i	−1.28368	−	0.741132i	−0.306160	−	0.951980i	$-0.599044\pi$
$977$	−40.1239	−	23.1656i	−1.28368	−	0.741132i	−0.977519	+	0.210848i	$0.932377\pi$
$978$		0			0
$979$		−	0.882960i		−	0.0282195i
$980$	−2.86711	−	5.99076i	−0.0915865	−	0.191368i
$981$		0			0
$982$	6.77294	+	11.7311i	0.216133	+	0.374354i
$983$	25.0199	−	43.3357i	0.798009	−	1.38219i	−0.122901	−	0.992419i	$-0.539220\pi$
$983$	25.0199	−	43.3357i	0.798009	−	1.38219i	0.920911	−	0.389774i	$-0.127447\pi$
$984$		0			0
$985$	−1.80486	+	1.04203i	−0.0575075	+	0.0332020i
$986$	−4.28031			−0.136313
$987$		0			0
$988$	15.6910			0.499197
$989$	91.3553	−	52.7440i	2.90493	−	1.67716i
$990$		0			0
$991$	8.38422	−	14.5219i	0.266334	−	0.461303i	−0.701579	−	0.712592i	$-0.747521\pi$
$991$	8.38422	−	14.5219i	0.266334	−	0.461303i	0.967912	+	0.251289i	$0.0808544\pi$
$992$	1.61968	+	2.80537i	0.0514248	+	0.0890704i
$993$		0			0
$994$	−33.7249	−	1.30287i	−1.06969	−	0.0413245i
$995$			25.1832i			0.798360i
$996$		0			0
$997$	4.51546	+	2.60700i	0.143006	+	0.0825645i	0.569796	−	0.821786i	$-0.307022\pi$
$997$	4.51546	+	2.60700i	0.143006	+	0.0825645i	−0.426790	+	0.904351i	$0.640356\pi$
$998$	−8.70526	−	5.02599i	−0.275560	−	0.159095i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.d.1277.8	yes	24
3.2	odd	2	inner	1386.2.r.d.1277.5	yes	24
7.5	odd	6	inner	1386.2.r.d.89.5	✓	24
21.5	even	6	inner	1386.2.r.d.89.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.5	✓	24	7.5	odd	6	inner
1386.2.r.d.89.8	yes	24	21.5	even	6	inner
1386.2.r.d.1277.5	yes	24	3.2	odd	2	inner
1386.2.r.d.1277.8	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.474393 + 0.821673i) q^{5} +(1.41034 - 2.23851i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.474393 + 0.821673i) q^{5} +(1.41034 - 2.23851i) q^{7} -1.00000i q^{8} +(0.821673 + 0.474393i) q^{10} +(-0.866025 - 0.500000i) q^{11} +7.03063i q^{13} +(0.102135 - 2.64378i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.29971 - 3.98321i) q^{17} +(1.93280 - 1.11590i) q^{19} +0.948786 q^{20} -1.00000 q^{22} +(7.17812 - 4.14429i) q^{23} +(2.04990 - 3.55054i) q^{25} +(3.51532 + 6.08871i) q^{26} +(-1.23344 - 2.34065i) q^{28} -0.930621i q^{29} +(-2.80537 - 1.61968i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.59942i q^{34} +(2.50838 + 0.0969044i) q^{35} +(4.57553 + 7.92505i) q^{37} +(1.11590 - 1.93280i) q^{38} +(0.821673 - 0.474393i) q^{40} -8.54500 q^{41} +12.7269 q^{43} +(-0.866025 + 0.500000i) q^{44} +(4.14429 - 7.17812i) q^{46} +(-0.251245 - 0.435168i) q^{47} +(-3.02187 - 6.31413i) q^{49} -4.09981i q^{50} +(6.08871 + 3.51532i) q^{52} +(-8.22868 - 4.75083i) q^{53} -0.948786i q^{55} +(-2.23851 - 1.41034i) q^{56} +(-0.465310 - 0.805941i) q^{58} +(-3.94585 + 6.83441i) q^{59} +(-2.02250 + 1.16769i) q^{61} -3.23936 q^{62} -1.00000 q^{64} +(-5.77688 + 3.33528i) q^{65} +(-2.94653 + 5.10354i) q^{67} +(-2.29971 - 3.98321i) q^{68} +(2.22077 - 1.17027i) q^{70} -12.7563i q^{71} +(4.85471 + 2.80287i) q^{73} +(7.92505 + 4.57553i) q^{74} -2.23181i q^{76} +(-2.34065 + 1.23344i) q^{77} +(-4.16723 - 7.21785i) q^{79} +(0.474393 - 0.821673i) q^{80} +(-7.40019 + 4.27250i) q^{82} +12.0026 q^{83} +4.36386 q^{85} +(11.0218 - 6.36346i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(0.441480 + 0.764665i) q^{89} +(15.7382 + 9.91559i) q^{91} -8.28858i q^{92} +(-0.435168 - 0.251245i) q^{94} +(1.83381 + 1.05875i) q^{95} +12.6315i q^{97} +(-5.77409 - 3.95726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 8 * q^7	\( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

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