LMFDB - Embedded newform 220.3.x.a.37.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(37,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	220.37
Dual form			220.3.x.a.113.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.509699 + 1.00034i) q^{3} +(4.99414 + 0.242016i) q^{5} +(3.01016 - 5.90777i) q^{7} +(4.54918 - 6.26141i) q^{9} +(-10.5242 + 3.20004i) q^{11} +(5.53236 - 0.876240i) q^{13} +(2.30341 + 5.11919i) q^{15} +(2.21197 + 0.350342i) q^{17} +(23.9751 + 7.78999i) q^{19} +7.44406 q^{21} +(-5.60384 + 5.60384i) q^{23} +(24.8829 + 2.41733i) q^{25} +(18.5622 + 2.93997i) q^{27} +(20.1705 - 6.55380i) q^{29} +(-27.3004 - 19.8349i) q^{31} +(-8.56532 - 8.89677i) q^{33} +(16.4629 - 28.7757i) q^{35} +(-24.0612 + 47.2228i) q^{37} +(3.69638 + 5.08763i) q^{39} +(7.19251 - 22.1363i) q^{41} +(-6.66866 + 6.66866i) q^{43} +(24.2346 - 30.1694i) q^{45} +(-46.7321 + 23.8112i) q^{47} +(2.96077 + 4.07516i) q^{49} +(0.776979 + 2.39129i) q^{51} +(-12.2514 + 1.94043i) q^{53} +(-53.3340 + 13.4344i) q^{55} +(4.42745 + 27.9538i) q^{57} +(-68.0175 + 22.1002i) q^{59} +(26.6184 - 19.3394i) q^{61} +(-23.2972 - 45.7234i) q^{63} +(27.8415 - 3.03714i) q^{65} +(-15.4175 - 15.4175i) q^{67} +(-8.46202 - 2.74948i) q^{69} +(-51.3604 + 37.3155i) q^{71} +(-94.7847 - 48.2952i) q^{73} +(10.2646 + 26.1234i) q^{75} +(-12.7746 + 71.8075i) q^{77} +(33.9037 - 46.6645i) q^{79} +(-15.0046 - 46.1795i) q^{81} +(-16.1752 + 102.127i) q^{83} +(10.9621 + 2.28499i) q^{85} +(16.8369 + 16.8369i) q^{87} -83.4051i q^{89} +(11.4767 - 35.3216i) q^{91} +(5.92667 - 37.4196i) q^{93} +(117.850 + 44.7067i) q^{95} +(24.4577 + 154.420i) q^{97} +(-27.8399 + 80.4542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.509699	+	1.00034i	0.169900	+	0.333447i	0.960219	−	0.279248i	$-0.0900853\pi$
$3$	0.509699	+	1.00034i	0.169900	+	0.333447i	−0.790319	+	0.612695i	$0.790085\pi$
$4$		0			0
$5$	4.99414	+	0.242016i	0.998828	+	0.0484032i
$5$	4.99414	+	0.242016i	0.998828	+	0.0484032i
$6$		0			0
$7$	3.01016	−	5.90777i	0.430023	−	0.843967i	−0.569732	−	0.821830i	$-0.692953\pi$
$7$	3.01016	−	5.90777i	0.430023	−	0.843967i	0.999755	−	0.0221369i	$-0.00704697\pi$
$8$		0			0
$9$	4.54918	−	6.26141i	0.505464	−	0.695712i
$10$		0			0
$11$	−10.5242	+	3.20004i	−0.956750	+	0.290913i
$11$	−10.5242	+	3.20004i	−0.956750	+	0.290913i
$12$		0			0
$13$	5.53236	−	0.876240i	0.425566	−	0.0674031i	0.0600221	−	0.998197i	$-0.480883\pi$
$13$	5.53236	−	0.876240i	0.425566	−	0.0674031i	0.365544	+	0.930794i	$0.380883\pi$
$14$		0			0
$15$	2.30341	+	5.11919i	0.153561	+	0.341280i
$16$		0			0
$17$	2.21197	+	0.350342i	0.130116	+	0.0206084i	0.221153	−	0.975239i	$-0.429018\pi$
$17$	2.21197	+	0.350342i	0.130116	+	0.0206084i	−0.0910367	+	0.995848i	$0.529018\pi$
$18$		0			0
$19$	23.9751	+	7.78999i	1.26185	+	0.409999i	0.862153	−	0.506649i	$-0.169116\pi$
$19$	23.9751	+	7.78999i	1.26185	+	0.409999i	0.399696	+	0.916648i	$0.369116\pi$
$20$		0			0
$21$	7.44406			0.354479
$22$		0			0
$23$	−5.60384	+	5.60384i	−0.243645	+	0.243645i	−0.818356	−	0.574711i	$-0.805114\pi$
$23$	−5.60384	+	5.60384i	−0.243645	+	0.243645i	0.574711	+	0.818356i	$0.305114\pi$
$24$		0			0
$25$	24.8829	+	2.41733i	0.995314	+	0.0966930i
$26$		0			0
$27$	18.5622	+	2.93997i	0.687490	+	0.108888i
$28$		0			0
$29$	20.1705	−	6.55380i	0.695536	−	0.225993i	0.0601513	−	0.998189i	$-0.480842\pi$
$29$	20.1705	−	6.55380i	0.695536	−	0.225993i	0.635384	+	0.772196i	$0.280842\pi$
$30$		0			0
$31$	−27.3004	−	19.8349i	−0.880659	−	0.639836i	0.0527668	−	0.998607i	$-0.483196\pi$
$31$	−27.3004	−	19.8349i	−0.880659	−	0.639836i	−0.933426	+	0.358771i	$0.883196\pi$
$32$		0			0
$33$	−8.56532	−	8.89677i	−0.259555	−	0.269599i
$34$		0			0
$35$	16.4629	−	28.7757i	0.470370	−	0.822164i
$36$		0			0
$37$	−24.0612	+	47.2228i	−0.650303	+	1.27629i	0.296670	+	0.954980i	$0.404124\pi$
$37$	−24.0612	+	47.2228i	−0.650303	+	1.27629i	−0.946973	+	0.321312i	$0.895876\pi$
$38$		0			0
$39$	3.69638	+	5.08763i	0.0947789	+	0.130452i
$40$		0			0
$41$	7.19251	−	22.1363i	0.175427	−	0.539909i	−0.824226	−	0.566261i	$-0.808389\pi$
$41$	7.19251	−	22.1363i	0.175427	−	0.539909i	0.999653	+	0.0263526i	$0.00838927\pi$
$42$		0			0
$43$	−6.66866	+	6.66866i	−0.155085	+	0.155085i	−0.780385	−	0.625300i	$-0.784977\pi$
$43$	−6.66866	+	6.66866i	−0.155085	+	0.155085i	0.625300	+	0.780385i	$0.284977\pi$
$44$		0			0
$45$	24.2346	−	30.1694i	0.538547	−	0.670430i
$46$		0			0
$47$	−46.7321	+	23.8112i	−0.994301	+	0.506622i	−0.873901	−	0.486104i	$-0.838418\pi$
$47$	−46.7321	+	23.8112i	−0.994301	+	0.506622i	−0.120400	+	0.992725i	$0.538418\pi$
$48$		0			0
$49$	2.96077	+	4.07516i	0.0604240	+	0.0831665i
$50$		0			0
$51$	0.776979	+	2.39129i	0.0152349	+	0.0468881i
$52$		0			0
$53$	−12.2514	+	1.94043i	−0.231158	+	0.0366119i	−0.270939	−	0.962597i	$-0.587334\pi$
$53$	−12.2514	+	1.94043i	−0.231158	+	0.0366119i	0.0397805	+	0.999208i	$0.487334\pi$
$54$		0			0
$55$	−53.3340	+	13.4344i	−0.969709	+	0.244262i
$56$		0			0
$57$	4.42745	+	27.9538i	0.0776746	+	0.490418i
$58$		0			0
$59$	−68.0175	+	22.1002i	−1.15284	+	0.374580i	−0.822212	−	0.569181i	$-0.807260\pi$
$59$	−68.0175	+	22.1002i	−1.15284	+	0.374580i	−0.330627	+	0.943762i	$0.607260\pi$
$60$		0			0
$61$	26.6184	−	19.3394i	0.436367	−	0.317039i	−0.347823	−	0.937560i	$-0.613079\pi$
$61$	26.6184	−	19.3394i	0.436367	−	0.317039i	0.784190	+	0.620521i	$0.213079\pi$
$62$		0			0
$63$	−23.2972	−	45.7234i	−0.369797	−	0.725768i
$64$		0			0
$65$	27.8415	−	3.03714i	0.428330	−	0.0467253i
$66$		0			0
$67$	−15.4175	−	15.4175i	−0.230111	−	0.230111i	0.582628	−	0.812739i	$-0.302025\pi$
$67$	−15.4175	−	15.4175i	−0.230111	−	0.230111i	−0.812739	+	0.582628i	$0.802025\pi$
$68$		0			0
$69$	−8.46202	−	2.74948i	−0.122638	−	0.0398475i
$70$		0			0
$71$	−51.3604	+	37.3155i	−0.723386	+	0.525571i	−0.887464	−	0.460876i	$-0.847535\pi$
$71$	−51.3604	+	37.3155i	−0.723386	+	0.525571i	0.164078	+	0.986447i	$0.447535\pi$
$72$		0			0
$73$	−94.7847	−	48.2952i	−1.29842	−	0.661578i	−0.338267	−	0.941050i	$-0.609841\pi$
$73$	−94.7847	−	48.2952i	−1.29842	−	0.661578i	−0.960154	+	0.279472i	$0.909841\pi$
$74$		0			0
$75$	10.2646	+	26.1234i	0.136862	+	0.348312i
$76$		0			0
$77$	−12.7746	+	71.8075i	−0.165903	+	0.932565i
$78$		0			0
$79$	33.9037	−	46.6645i	0.429161	−	0.590690i	−0.538599	−	0.842562i	$-0.681046\pi$
$79$	33.9037	−	46.6645i	0.429161	−	0.590690i	0.967760	+	0.251872i	$0.0810463\pi$
$80$		0			0
$81$	−15.0046	−	46.1795i	−0.185242	−	0.570117i
$82$		0			0
$83$	−16.1752	+	102.127i	−0.194883	+	1.23044i	0.675238	+	0.737600i	$0.264041\pi$
$83$	−16.1752	+	102.127i	−0.194883	+	1.23044i	−0.870120	+	0.492840i	$0.835959\pi$
$84$		0			0
$85$	10.9621	+	2.28499i	0.128966	+	0.0268822i
$86$		0			0
$87$	16.8369	+	16.8369i	0.193528	+	0.193528i
$88$		0			0
$89$		−	83.4051i		−	0.937136i	−0.883428	−	0.468568i	$-0.844770\pi$
$89$		−	83.4051i		−	0.937136i	0.883428	−	0.468568i	$-0.155230\pi$
$90$		0			0
$91$	11.4767	−	35.3216i	0.126117	−	0.388149i
$92$		0			0
$93$	5.92667	−	37.4196i	0.0637277	−	0.402361i
$94$		0			0
$95$	117.850	+	44.7067i	1.24052	+	0.470596i
$96$		0			0
$97$	24.4577	+	154.420i	0.252141	+	1.59196i	0.710833	+	0.703361i	$0.248318\pi$
$97$	24.4577	+	154.420i	0.252141	+	1.59196i	−0.458692	+	0.888596i	$0.651682\pi$
$98$		0			0
$99$	−27.8399	+	80.4542i	−0.281211	+	0.812668i
$100$		0			0
$101$	−71.9859	−	52.3009i	−0.712732	−	0.517830i	0.171322	−	0.985215i	$-0.445196\pi$
$101$	−71.9859	−	52.3009i	−0.712732	−	0.517830i	−0.884054	+	0.467385i	$0.845196\pi$
$102$		0			0
$103$	−143.379	−	73.0552i	−1.39203	−	0.709273i	−0.412570	−	0.910926i	$-0.635369\pi$
$103$	−143.379	−	73.0552i	−1.39203	−	0.709273i	−0.979457	+	0.201652i	$0.935369\pi$
$104$		0			0
$105$	37.1767	+	1.80158i	0.354063	+	0.0171579i
$106$		0			0
$107$	−134.634	+	68.5994i	−1.25826	+	0.641116i	−0.950611	−	0.310384i	$-0.899543\pi$
$107$	−134.634	+	68.5994i	−1.25826	+	0.641116i	−0.307650	+	0.951500i	$0.599543\pi$
$108$		0			0
$109$		−	155.283i		−	1.42462i	−0.701866	−	0.712309i	$-0.747649\pi$
$109$		−	155.283i		−	1.42462i	0.701866	−	0.712309i	$-0.252351\pi$
$110$		0			0
$111$	−59.5028			−0.536062
$112$		0			0
$113$	51.1289	+	100.346i	0.452468	+	0.888019i	0.998729	+	0.0504035i	$0.0160507\pi$
$113$	51.1289	+	100.346i	0.452468	+	0.888019i	−0.546261	+	0.837615i	$0.683949\pi$
$114$		0			0
$115$	−29.3426	+	26.6301i	−0.255153	+	0.231566i
$116$		0			0
$117$	19.6812	−	38.6266i	0.168216	−	0.330142i
$118$		0			0
$119$	8.72813	−	12.0132i	0.0733457	−	0.100952i
$120$		0			0
$121$	100.519	−	67.3560i	0.830740	−	0.556661i
$122$		0			0
$123$	25.8098	−	4.08787i	0.209836	−	0.0332347i
$124$		0			0
$125$	123.683	+	18.0945i	0.989467	+	0.144756i
$126$		0			0
$127$	162.636	+	25.7590i	1.28060	+	0.202827i	0.759408	−	0.650615i	$-0.225489\pi$
$127$	162.636	+	25.7590i	1.28060	+	0.202827i	0.521189	+	0.853441i	$0.325489\pi$
$128$		0			0
$129$	−10.0699	−	3.27192i	−0.0780615	−	0.0253637i
$130$		0			0
$131$	−140.811			−1.07489			−0.537445	−	0.843299i	$-0.680611\pi$
$131$	−140.811			−1.07489			−0.537445	+	0.843299i	$0.680611\pi$
$132$		0			0
$133$	118.190	−	118.190i	0.888650	−	0.888650i
$134$		0			0
$135$	91.9908	+	19.1750i	0.681413	+	0.142037i
$136$		0			0
$137$	2.14658	+	0.339984i	0.0156684	+	0.00248164i	0.164264	−	0.986416i	$-0.447475\pi$
$137$	2.14658	+	0.339984i	0.0156684	+	0.00248164i	−0.148595	+	0.988898i	$0.547475\pi$
$138$		0			0
$139$	207.621	−	67.4601i	1.49367	−	0.485324i	0.555508	−	0.831511i	$-0.312524\pi$
$139$	207.621	−	67.4601i	1.49367	−	0.485324i	0.938166	+	0.346187i	$0.112524\pi$
$140$		0			0
$141$	−47.6386	−	34.6115i	−0.337863	−	0.245472i
$142$		0			0
$143$	−55.4199	+	26.9256i	−0.387552	+	0.188291i
$144$		0			0
$145$	102.321	−	27.8490i	0.705659	−	0.192062i
$146$		0			0
$147$	−2.56744	+	5.03888i	−0.0174656	+	0.0342781i
$148$		0			0
$149$	155.402	+	213.892i	1.04297	+	1.43552i	0.894752	+	0.446564i	$0.147353\pi$
$149$	155.402	+	213.892i	1.04297	+	1.43552i	0.148214	+	0.988955i	$0.452647\pi$
$150$		0			0
$151$	26.7145	−	82.2188i	0.176917	−	0.544496i	−0.822798	−	0.568333i	$-0.807588\pi$
$151$	26.7145	−	82.2188i	0.176917	−	0.544496i	0.999716	+	0.0238376i	$0.00758845\pi$
$152$		0			0
$153$	12.2563	−	12.2563i	0.0801065	−	0.0801065i
$154$		0			0
$155$	−131.542	−	105.666i	−0.848657	−	0.681713i
$156$		0			0
$157$	178.849	−	91.1283i	1.13917	−	0.580435i	0.220469	−	0.975394i	$-0.429241\pi$
$157$	178.849	−	91.1283i	1.13917	−	0.580435i	0.918699	+	0.394959i	$0.129241\pi$
$158$		0			0
$159$	−8.18561	−	11.2665i	−0.0514818	−	0.0708587i
$160$		0			0
$161$	16.2377	+	49.9747i	0.100856	+	0.310402i
$162$		0			0
$163$	−61.8370	+	9.79401i	−0.379368	+	0.0600860i	−0.343206	−	0.939260i	$-0.611513\pi$
$163$	−61.8370	+	9.79401i	−0.379368	+	0.0600860i	−0.0361614	+	0.999346i	$0.511513\pi$
$164$		0			0
$165$	−40.6233	−	46.5047i	−0.246202	−	0.281846i
$166$		0			0
$167$	16.5358	+	104.403i	0.0990168	+	0.625168i	0.986429	+	0.164190i	$0.0525011\pi$
$167$	16.5358	+	104.403i	0.0990168	+	0.625168i	−0.887412	+	0.460977i	$0.847499\pi$
$168$		0			0
$169$	−130.889	+	42.5285i	−0.774493	+	0.251648i
$170$		0			0
$171$	157.843	−	114.680i	0.923061	−	0.670643i
$172$		0			0
$173$	92.9790	+	182.482i	0.537451	+	1.05481i	0.986875	+	0.161488i	$0.0516294\pi$
$173$	92.9790	+	182.482i	0.537451	+	1.05481i	−0.449424	+	0.893319i	$0.648371\pi$
$174$		0			0
$175$	89.1824	−	139.726i	0.509614	−	0.798433i
$176$		0			0
$177$	−56.7762	−	56.7762i	−0.320769	−	0.320769i
$178$		0			0
$179$	125.948	+	40.9230i	0.703621	+	0.228620i	0.638907	−	0.769284i	$-0.279387\pi$
$179$	125.948	+	40.9230i	0.703621	+	0.228620i	0.0647133	+	0.997904i	$0.479387\pi$
$180$		0			0
$181$	−73.4455	+	53.3613i	−0.405776	+	0.294814i	−0.771890	−	0.635757i	$-0.780688\pi$
$181$	−73.4455	+	53.3613i	−0.405776	+	0.294814i	0.366113	+	0.930570i	$0.380688\pi$
$182$		0			0
$183$	32.9133	+	16.7702i	0.179854	+	0.0916404i
$184$		0			0
$185$	−131.594	+	230.014i	−0.711318	+	1.24332i
$186$		0			0
$187$	−24.4005	+	3.39132i	−0.130484	+	0.0181354i
$188$		0			0
$189$	73.2439	−	100.812i	0.387534	−	0.533395i
$190$		0			0
$191$	31.2967	+	96.3213i	0.163857	+	0.504300i	0.998950	−	0.0458084i	$-0.0145864\pi$
$191$	31.2967	+	96.3213i	0.163857	+	0.504300i	−0.835093	+	0.550108i	$0.814586\pi$
$192$		0			0
$193$	−46.6808	+	294.731i	−0.241869	+	1.52710i	0.505577	+	0.862781i	$0.331280\pi$
$193$	−46.6808	+	294.731i	−0.241869	+	1.52710i	−0.747446	+	0.664322i	$0.768720\pi$
$194$		0			0
$195$	17.2289	+	26.3029i	0.0883535	+	0.134887i
$196$		0			0
$197$	−207.731	−	207.731i	−1.05447	−	1.05447i	−0.998428	−	0.0560431i	$-0.982152\pi$
$197$	−207.731	−	207.731i	−1.05447	−	1.05447i	−0.0560431	−	0.998428i	$-0.517848\pi$
$198$		0			0
$199$			6.13609i			0.0308346i	0.999881	+	0.0154173i	$0.00490767\pi$
$199$			6.13609i			0.0308346i	−0.999881	+	0.0154173i	$0.995092\pi$
$200$		0			0
$201$	7.56444	−	23.2810i	0.0376340	−	0.115826i
$202$		0			0
$203$	21.9982	−	138.891i	0.108365	−	0.684192i
$204$		0			0
$205$	41.2777	−	108.811i	0.201355	−	0.530785i
$206$		0			0
$207$	9.59506	+	60.5808i	0.0463529	+	0.292661i
$208$		0			0
$209$	−277.248	−	5.26240i	−1.32655	−	0.0251789i
$210$		0			0
$211$	127.347	+	92.5228i	0.603539	+	0.438497i	0.847133	−	0.531380i	$-0.178326\pi$
$211$	127.347	+	92.5228i	0.603539	+	0.438497i	−0.243594	+	0.969877i	$0.578326\pi$
$212$		0			0
$213$	−63.5066	−	32.3582i	−0.298153	−	0.151917i
$214$		0			0
$215$	−34.9181	+	31.6903i	−0.162410	+	0.147397i
$216$		0			0
$217$	−199.359	+	101.578i	−0.918704	+	0.468103i
$218$		0			0
$219$		−	119.433i		−	0.545356i
$220$		0			0
$221$	12.5444			0.0567621
$222$		0			0
$223$	−87.5124	−	171.753i	−0.392432	−	0.770191i	0.607273	−	0.794494i	$-0.292264\pi$
$223$	−87.5124	−	171.753i	−0.392432	−	0.770191i	−0.999705	+	0.0243022i	$0.992264\pi$
$224$		0			0
$225$	128.332	−	144.805i	0.570366	−	0.643577i
$226$		0			0
$227$	88.0771	−	172.861i	0.388005	−	0.761502i	−0.611554	−	0.791203i	$-0.709455\pi$
$227$	88.0771	−	172.861i	0.388005	−	0.761502i	0.999559	+	0.0297004i	$0.00945533\pi$
$228$		0			0
$229$	−34.6959	+	47.7547i	−0.151510	+	0.208536i	−0.878025	−	0.478615i	$-0.841139\pi$
$229$	−34.6959	+	47.7547i	−0.151510	+	0.208536i	0.726515	+	0.687151i	$0.241139\pi$
$230$		0			0
$231$	−78.3431	+	23.8213i	−0.339148	+	0.103122i
$232$		0			0
$233$	−331.313	+	52.4748i	−1.42194	+	0.225214i	−0.819560	−	0.572993i	$-0.805782\pi$
$233$	−331.313	+	52.4748i	−1.42194	+	0.225214i	−0.602383	+	0.798207i	$0.705782\pi$
$234$		0			0
$235$	−239.150	+	107.607i	−1.01766	+	0.457900i
$236$		0			0
$237$	63.9610	+	10.1304i	0.269878	+	0.0427444i
$238$		0			0
$239$	32.6802	+	10.6184i	0.136737	+	0.0444286i	0.376586	−	0.926382i	$-0.377098\pi$
$239$	32.6802	+	10.6184i	0.136737	+	0.0444286i	−0.239849	+	0.970810i	$0.577098\pi$
$240$		0			0
$241$	−87.2263			−0.361935			−0.180967	−	0.983489i	$-0.557923\pi$
$241$	−87.2263			−0.361935			−0.180967	+	0.983489i	$0.557923\pi$
$242$		0			0
$243$	158.149	−	158.149i	0.650819	−	0.650819i
$244$		0			0
$245$	13.8003	+	21.0685i	0.0563276	+	0.0859937i
$246$		0			0
$247$	139.465	+	22.0891i	0.564636	+	0.0894295i
$248$		0			0
$249$	−110.406	+	35.8730i	−0.443397	+	0.144068i
$250$		0			0
$251$	156.857	+	113.963i	0.624929	+	0.454037i	0.854640	−	0.519221i	$-0.173778\pi$
$251$	156.857	+	113.963i	0.624929	+	0.454037i	−0.229711	+	0.973259i	$0.573778\pi$
$252$		0			0
$253$	41.0437	−	76.9087i	0.162228	−	0.303987i
$254$		0			0
$255$	3.30161	+	12.1305i	0.0129475	+	0.0475706i
$256$		0			0
$257$	−219.415	+	430.625i	−0.853753	+	1.67559i	−0.123568	+	0.992336i	$0.539434\pi$
$257$	−219.415	+	430.625i	−0.853753	+	1.67559i	−0.730185	+	0.683249i	$0.760566\pi$
$258$		0			0
$259$	206.553	+	284.296i	0.797503	+	1.09767i
$260$		0			0
$261$	50.7233	−	156.110i	0.194342	−	0.598124i
$262$		0			0
$263$	196.149	−	196.149i	0.745813	−	0.745813i	−0.227877	−	0.973690i	$-0.573178\pi$
$263$	196.149	−	196.149i	0.745813	−	0.745813i	0.973690	+	0.227877i	$0.0731783\pi$
$264$		0			0
$265$	−61.6548	+	6.72574i	−0.232660	+	0.0253802i
$266$		0			0
$267$	83.4334	−	42.5115i	0.312485	−	0.159219i
$268$		0			0
$269$	−141.708	−	195.045i	−0.526797	−	0.725074i	0.459841	−	0.888001i	$-0.347906\pi$
$269$	−141.708	−	195.045i	−0.526797	−	0.725074i	−0.986638	+	0.162928i	$0.947906\pi$
$270$		0			0
$271$	39.5152	+	121.615i	0.145813	+	0.448765i	0.997115	−	0.0759111i	$-0.0241865\pi$
$271$	39.5152	+	121.615i	0.145813	+	0.448765i	−0.851302	+	0.524676i	$0.824187\pi$
$272$		0			0
$273$	41.1832	−	6.52278i	0.150854	−	0.0238930i
$274$		0			0
$275$	−269.609	+	54.1856i	−0.980396	+	0.197039i
$276$		0			0
$277$	−33.7282	−	212.951i	−0.121762	−	0.768777i	−0.970702	−	0.240287i	$-0.922758\pi$
$277$	−33.7282	−	212.951i	−0.121762	−	0.768777i	0.848939	−	0.528490i	$-0.177242\pi$
$278$		0			0
$279$	−248.389	+	80.7065i	−0.890283	+	0.289271i
$280$		0			0
$281$	−297.274	+	215.982i	−1.05791	+	0.768619i	−0.973701	−	0.227829i	$-0.926837\pi$
$281$	−297.274	+	215.982i	−1.05791	+	0.768619i	−0.0842124	+	0.996448i	$0.526837\pi$
$282$		0			0
$283$	−174.015	−	341.524i	−0.614895	−	1.20680i	−0.963040	−	0.269358i	$-0.913188\pi$
$283$	−174.015	−	341.524i	−0.614895	−	1.20680i	0.348145	−	0.937441i	$-0.386812\pi$
$284$		0			0
$285$	15.3460	+	140.677i	0.0538457	+	0.493603i
$286$		0			0
$287$	−109.125	−	109.125i	−0.380228	−	0.380228i
$288$		0			0
$289$	−270.085	−	87.7560i	−0.934551	−	0.303654i
$290$		0			0
$291$	−142.006	+	103.174i	−0.487994	+	0.354548i
$292$		0			0
$293$	445.679	+	227.085i	1.52109	+	0.775034i	0.997057	−	0.0766637i	$-0.0244268\pi$
$293$	445.679	+	227.085i	1.52109	+	0.775034i	0.524033	+	0.851698i	$0.324427\pi$
$294$		0			0
$295$	−345.037	+	93.9103i	−1.16962	+	0.318340i
$296$		0			0
$297$	−204.761	+	28.4589i	−0.689432	+	0.0958213i
$298$		0			0
$299$	−26.0922	+	35.9128i	−0.0872648	+	0.120110i
$300$		0			0
$301$	19.3232	+	59.4706i	0.0641966	+	0.197577i
$302$		0			0
$303$	15.6275	−	98.6681i	0.0515759	−	0.325637i
$304$		0			0
$305$	137.616	−	90.1416i	0.451201	−	0.295546i
$306$		0			0
$307$	−31.9464	−	31.9464i	−0.104060	−	0.104060i	0.653160	−	0.757220i	$-0.273443\pi$
$307$	−31.9464	−	31.9464i	−0.104060	−	0.104060i	−0.757220	+	0.653160i	$0.773443\pi$
$308$		0			0
$309$		−	180.664i		−	0.584672i
$310$		0			0
$311$	−45.1098	+	138.834i	−0.145048	+	0.446411i	−0.997017	−	0.0771806i	$-0.975408\pi$
$311$	−45.1098	+	138.834i	−0.145048	+	0.446411i	0.851969	+	0.523592i	$0.175408\pi$
$312$		0			0
$313$	−38.7572	+	244.704i	−0.123825	+	0.781800i	0.845130	+	0.534562i	$0.179523\pi$
$313$	−38.7572	+	244.704i	−0.123825	+	0.781800i	−0.968955	+	0.247239i	$0.920477\pi$
$314$		0			0
$315$	−105.284	−	233.987i	−0.334234	−	0.742816i
$316$		0			0
$317$	−68.0249	−	429.492i	−0.214590	−	1.35487i	−0.826053	−	0.563593i	$-0.809419\pi$
$317$	−68.0249	−	429.492i	−0.214590	−	1.35487i	0.611463	−	0.791273i	$-0.290581\pi$
$318$		0			0
$319$	−191.307	+	133.520i	−0.599709	+	0.418559i
$320$		0			0
$321$	−137.246	−	99.7147i	−0.427556	−	0.310638i
$322$		0			0
$323$	50.3031	+	25.6307i	0.155737	+	0.0793521i
$324$		0			0
$325$	139.779	−	8.42984i	0.430090	−	0.0259380i
$326$		0			0
$327$	155.336	−	79.1478i	0.475034	−	0.242042i
$328$		0			0
$329$			347.758i			1.05702i
$330$		0			0
$331$	299.212			0.903962			0.451981	−	0.892027i	$-0.350717\pi$
$331$	299.212			0.903962			0.451981	+	0.892027i	$0.350717\pi$
$332$		0			0
$333$	186.222	+	365.482i	0.559226	+	1.09754i
$334$		0			0
$335$	−73.2656	−	80.7282i	−0.218703	−	0.240980i
$336$		0			0
$337$	169.163	−	332.000i	0.501966	−	0.985165i	−0.491482	−	0.870887i	$-0.663545\pi$
$337$	169.163	−	332.000i	0.501966	−	0.985165i	0.993449	−	0.114277i	$-0.0364552\pi$
$338$		0			0
$339$	−74.3199	+	102.293i	−0.219233	+	0.301748i
$340$		0			0
$341$	350.789	+	121.385i	1.02871	+	0.355968i
$342$		0			0
$343$	353.879	−	56.0490i	1.03172	−	0.163408i
$344$		0			0
$345$	−41.5951	−	15.7792i	−0.120565	−	0.0457368i
$346$		0			0
$347$	591.180	+	93.6337i	1.70369	+	0.269838i	0.931019	−	0.364972i	$-0.118921\pi$
$347$	591.180	+	93.6337i	1.70369	+	0.269838i	0.772669	+	0.634809i	$0.218921\pi$
$348$		0			0
$349$	371.277	+	120.635i	1.06383	+	0.345659i	0.788082	−	0.615571i	$-0.211074\pi$
$349$	371.277	+	120.635i	1.06383	+	0.345659i	0.275748	+	0.961230i	$0.411074\pi$
$350$		0			0
$351$	105.269			0.299912
$352$		0			0
$353$	−137.609	+	137.609i	−0.389829	+	0.389829i	−0.874626	−	0.484798i	$-0.838893\pi$
$353$	−137.609	+	137.609i	−0.389829	+	0.389829i	0.484798	+	0.874626i	$0.338893\pi$
$354$		0			0
$355$	−265.532	+	173.929i	−0.747978	+	0.489941i
$356$		0			0
$357$	16.4661	+	2.60797i	0.0461234	+	0.00730523i
$358$		0			0
$359$	199.543	−	64.8354i	0.555830	−	0.180600i	−0.0176141	−	0.999845i	$-0.505607\pi$
$359$	199.543	−	64.8354i	0.555830	−	0.180600i	0.573444	+	0.819245i	$0.305607\pi$
$360$		0			0
$361$	222.067	+	161.341i	0.615145	+	0.446929i
$362$		0			0
$363$	118.614	+	66.2224i	0.326759	+	0.182431i
$364$		0			0
$365$	−461.680	−	264.132i	−1.26488	−	0.723651i
$366$		0			0
$367$	247.625	−	485.992i	0.674728	−	1.32423i	−0.258873	−	0.965911i	$-0.583351\pi$
$367$	247.625	−	485.992i	0.674728	−	1.32423i	0.933600	−	0.358316i	$-0.116649\pi$
$368$		0			0
$369$	−105.884	−	145.737i	−0.286949	−	0.394951i
$370$		0			0
$371$	−25.4150	+	78.2195i	−0.0685042	+	0.210834i
$372$		0			0
$373$	48.5219	−	48.5219i	0.130085	−	0.130085i	−0.639066	−	0.769152i	$-0.720679\pi$
$373$	48.5219	−	48.5219i	0.130085	−	0.130085i	0.769152	+	0.639066i	$0.220679\pi$
$374$		0			0
$375$	44.9406	+	132.948i	0.119842	+	0.354529i
$376$		0			0
$377$	105.848	−	53.9323i	0.280764	−	0.143056i
$378$		0			0
$379$	97.7032	+	134.477i	0.257792	+	0.354820i	0.918221	−	0.396068i	$-0.129626\pi$
$379$	97.7032	+	134.477i	0.257792	+	0.354820i	−0.660429	+	0.750888i	$0.729626\pi$
$380$		0			0
$381$	57.1275	+	175.820i	0.149941	+	0.461471i
$382$		0			0
$383$	380.185	−	60.2154i	0.992651	−	0.157220i	0.361077	−	0.932536i	$-0.382409\pi$
$383$	380.185	−	60.2154i	0.992651	−	0.157220i	0.631574	+	0.775316i	$0.282409\pi$
$384$		0			0
$385$	−81.1765	+	355.525i	−0.210848	+	0.923441i
$386$		0			0
$387$	11.4183	+	72.0921i	0.0295046	+	0.186284i
$388$		0			0
$389$	80.4695	−	26.1461i	0.206863	−	0.0672137i	−0.203753	−	0.979022i	$-0.565314\pi$
$389$	80.4695	−	26.1461i	0.206863	−	0.0672137i	0.410615	+	0.911809i	$0.365314\pi$
$390$		0			0
$391$	−14.3588	+	10.4323i	−0.0367233	+	0.0266810i
$392$		0			0
$393$	−71.7710	−	140.859i	−0.182623	−	0.358419i
$394$		0			0
$395$	180.613	−	224.844i	0.457249	−	0.569224i
$396$		0			0
$397$	−515.176	−	515.176i	−1.29767	−	1.29767i	−0.929926	−	0.367747i	$-0.880129\pi$
$397$	−515.176	−	515.176i	−1.29767	−	1.29767i	−0.367747	−	0.929926i	$-0.619871\pi$
$398$		0			0
$399$	178.472	+	57.9891i	0.447299	+	0.145336i
$400$		0			0
$401$	350.951	−	254.981i	0.875190	−	0.635863i	−0.0567845	−	0.998386i	$-0.518085\pi$
$401$	350.951	−	254.981i	0.875190	−	0.635863i	0.931975	+	0.362524i	$0.118085\pi$
$402$		0			0
$403$	−168.416	−	85.8123i	−0.417906	−	0.212934i
$404$		0			0
$405$	−63.7590	−	234.258i	−0.157430	−	0.578415i
$406$		0			0
$407$	102.111	−	573.981i	0.250888	−	1.41027i
$408$		0			0
$409$	248.996	−	342.713i	0.608792	−	0.837930i	−0.387686	−	0.921792i	$-0.626725\pi$
$409$	248.996	−	342.713i	0.608792	−	0.837930i	0.996477	+	0.0838616i	$0.0267254\pi$
$410$		0			0
$411$	0.754007	+	2.32060i	0.00183457	+	0.00564622i
$412$		0			0
$413$	−74.1805	+	468.357i	−0.179614	+	1.13404i
$414$		0			0
$415$	−105.498	+	506.119i	−0.254211	+	1.21956i
$416$		0			0
$417$	173.307	+	173.307i	0.415604	+	0.415604i
$418$		0			0
$419$		−	321.729i		−	0.767851i	−0.923364	−	0.383925i	$-0.874572\pi$
$419$		−	321.729i		−	0.767851i	0.923364	−	0.383925i	$-0.125428\pi$
$420$		0			0
$421$	77.5213	−	238.586i	0.184136	−	0.566712i	−0.815796	−	0.578339i	$-0.803701\pi$
$421$	77.5213	−	238.586i	0.184136	−	0.566712i	0.999932	+	0.0116268i	$0.00370100\pi$
$422$		0			0
$423$	−63.5012	+	400.931i	−0.150121	+	0.947826i
$424$		0			0
$425$	54.1933	+	14.0646i	0.127514	+	0.0330931i
$426$		0			0
$427$	−34.1271	−	215.470i	−0.0799230	−	0.504614i
$428$		0			0
$429$	−55.1822	−	41.7149i	−0.128630	−	0.0972375i
$430$		0			0
$431$	−90.4105	−	65.6870i	−0.209769	−	0.152406i	0.477940	−	0.878392i	$-0.341384\pi$
$431$	−90.4105	−	65.6870i	−0.209769	−	0.152406i	−0.687709	+	0.725986i	$0.741384\pi$
$432$		0			0
$433$	36.6991	+	18.6991i	0.0847554	+	0.0431850i	0.495854	−	0.868406i	$-0.334855\pi$
$433$	36.6991	+	18.6991i	0.0847554	+	0.0431850i	−0.411099	+	0.911591i	$0.634855\pi$
$434$		0			0
$435$	80.0112	+	88.1608i	0.183934	+	0.202668i
$436$		0			0
$437$	−178.007	+	90.6989i	−0.407338	+	0.207549i
$438$		0			0
$439$			301.109i			0.685897i	0.939354	+	0.342949i	$0.111426\pi$
$439$			301.109i			0.685897i	−0.939354	+	0.342949i	$0.888574\pi$
$440$		0			0
$441$	38.9853			0.0884021
$442$		0			0
$443$	29.5026	+	57.9021i	0.0665973	+	0.130705i	0.921905	−	0.387415i	$-0.126632\pi$
$443$	29.5026	+	57.9021i	0.0665973	+	0.130705i	−0.855308	+	0.518120i	$0.826632\pi$
$444$		0			0
$445$	20.1854	−	416.537i	0.0453604	−	0.936037i
$446$		0			0
$447$	−134.757	+	264.475i	−0.301470	+	0.591668i
$448$		0			0
$449$	−303.000	+	417.044i	−0.674833	+	0.928828i	−0.999858	−	0.0168774i	$-0.994628\pi$
$449$	−303.000	+	417.044i	−0.674833	+	0.928828i	0.325024	+	0.945706i	$0.394628\pi$
$450$		0			0
$451$	−4.85878	+	255.984i	−0.0107733	+	0.567591i
$452$		0			0
$453$	95.8632	−	15.1832i	0.211618	−	0.0335171i
$454$		0			0
$455$	65.8645	−	173.623i	0.144757	−	0.381590i
$456$		0			0
$457$	80.1608	+	12.6962i	0.175407	+	0.0277817i	0.243520	−	0.969896i	$-0.421698\pi$
$457$	80.1608	+	12.6962i	0.175407	+	0.0277817i	−0.0681132	+	0.997678i	$0.521698\pi$
$458$		0			0
$459$	40.0291	+	13.0063i	0.0872094	+	0.0283361i
$460$		0			0
$461$	220.986			0.479363			0.239682	−	0.970852i	$-0.422957\pi$
$461$	220.986			0.479363			0.239682	+	0.970852i	$0.422957\pi$
$462$		0			0
$463$	0.0481113	−	0.0481113i	0.000103912	−	0.000103912i	−0.707055	−	0.707159i	$-0.749977\pi$
$463$	0.0481113	−	0.0481113i	0.000103912	−	0.000103912i	0.707159	+	0.707055i	$0.249977\pi$
$464$		0			0
$465$	38.6548	−	185.444i	0.0831286	−	0.398805i
$466$		0			0
$467$	200.014	+	31.6790i	0.428294	+	0.0678352i	0.366861	−	0.930276i	$-0.380433\pi$
$467$	200.014	+	31.6790i	0.428294	+	0.0678352i	0.0614340	+	0.998111i	$0.480433\pi$
$468$		0			0
$469$	−137.492	+	44.6738i	−0.293159	+	0.0952533i
$470$		0			0
$471$	182.319	+	132.462i	0.387088	+	0.281236i
$472$		0			0
$473$	48.8426	−	91.5225i	0.103261	−	0.193494i
$474$		0			0
$475$	577.739	+	251.793i	1.21629	+	0.530090i
$476$		0			0
$477$	−43.5840	+	85.5384i	−0.0913710	+	0.179326i
$478$		0			0
$479$	−235.710	−	324.427i	−0.492088	−	0.677301i	0.488683	−	0.872461i	$-0.337477\pi$
$479$	−235.710	−	324.427i	−0.492088	−	0.677301i	−0.980771	+	0.195160i	$0.937477\pi$
$480$		0			0
$481$	−91.7369	+	282.337i	−0.190721	+	0.586979i
$482$		0			0
$483$	−41.7153	+	41.7153i	−0.0863671	+	0.0863671i
$484$		0			0
$485$	84.7730	+	777.113i	0.174790	+	1.60230i
$486$		0			0
$487$	199.120	−	101.457i	0.408870	−	0.208330i	−0.237444	−	0.971401i	$-0.576310\pi$
$487$	199.120	−	101.457i	0.408870	−	0.208330i	0.646314	+	0.763071i	$0.276310\pi$
$488$		0			0
$489$	−41.3156	−	56.8660i	−0.0844899	−	0.116290i
$490$		0			0
$491$	−258.045	−	794.182i	−0.525551	−	1.61748i	−0.763225	−	0.646133i	$-0.776385\pi$
$491$	−258.045	−	794.182i	−0.525551	−	1.61748i	0.237674	−	0.971345i	$-0.423615\pi$
$492$		0			0
$493$	46.9127	−	7.43025i	0.0951577	−	0.0150715i
$494$		0			0
$495$	−158.508	+	395.062i	−0.320217	+	0.798104i
$496$		0			0
$497$	65.8486	+	415.751i	0.132492	+	0.836522i
$498$		0			0
$499$	84.5286	−	27.4650i	0.169396	−	0.0550401i	−0.223091	−	0.974798i	$-0.571615\pi$
$499$	84.5286	−	27.4650i	0.169396	−	0.0550401i	0.392487	+	0.919757i	$0.371615\pi$
$500$		0			0
$501$	−96.0103	+	69.7555i	−0.191637	+	0.139233i
$502$		0			0
$503$	−169.370	−	332.408i	−0.336720	−	0.660851i	0.659113	−	0.752044i	$-0.270932\pi$
$503$	−169.370	−	332.408i	−0.336720	−	0.660851i	−0.995833	+	0.0911933i	$0.970932\pi$
$504$		0			0
$505$	−346.850	−	278.620i	−0.686832	−	0.551722i
$506$		0			0
$507$	−109.257	−	109.257i	−0.215497	−	0.215497i
$508$		0			0
$509$	−469.777	−	152.640i	−0.922942	−	0.299882i	−0.191269	−	0.981538i	$-0.561260\pi$
$509$	−469.777	−	152.640i	−0.922942	−	0.299882i	−0.731673	+	0.681656i	$0.761260\pi$
$510$		0			0
$511$	−570.634	+	414.590i	−1.11670	+	0.811331i
$512$		0			0
$513$	422.129	+	215.086i	0.822864	+	0.419270i
$514$		0			0
$515$	−698.373	−	399.548i	−1.35606	−	0.775821i
$516$		0			0
$517$	415.624	−	400.140i	0.803914	−	0.773965i
$518$		0			0
$519$	−135.152	+	186.021i	−0.260409	+	0.358423i
$520$		0			0
$521$	−120.242	−	370.068i	−0.230791	−	0.710303i	−0.997652	−	0.0684889i	$-0.978182\pi$
$521$	−120.242	−	370.068i	−0.230791	−	0.710303i	0.766861	−	0.641814i	$-0.221818\pi$
$522$		0			0
$523$	109.458	−	691.091i	0.209289	−	1.32140i	−0.629526	−	0.776980i	$-0.716751\pi$
$523$	109.458	−	691.091i	0.209289	−	1.32140i	0.838814	−	0.544418i	$-0.183249\pi$
$524$		0			0
$525$	185.229	+	17.9947i	0.352818	+	0.0342756i
$526$		0			0
$527$	−53.4388	−	53.4388i	−0.101402	−	0.101402i
$528$		0			0
$529$			466.194i			0.881274i
$530$		0			0
$531$	−171.045	+	526.423i	−0.322119	+	0.991381i
$532$		0			0
$533$	20.3949	−	128.768i	0.0382643	−	0.241591i
$534$		0			0
$535$	−688.983	+	310.011i	−1.28782	+	0.579461i
$536$		0			0
$537$	23.2587	+	146.849i	0.0433122	+	0.273462i
$538$		0			0
$539$	−44.2006	−	33.4134i	−0.0820048	−	0.0619914i
$540$		0			0
$541$	145.137	+	105.448i	0.268276	+	0.194914i	0.713787	−	0.700362i	$-0.246978\pi$
$541$	145.137	+	105.448i	0.268276	+	0.194914i	−0.445512	+	0.895276i	$0.646978\pi$
$542$		0			0
$543$	−90.8145	−	46.2723i	−0.167246	−	0.0852160i
$544$		0			0
$545$	37.5811	−	775.507i	0.0689562	−	1.42295i
$546$		0			0
$547$	−619.797	+	315.803i	−1.13308	+	0.577336i	−0.916940	−	0.399026i	$-0.869348\pi$
$547$	−619.797	+	315.803i	−1.13308	+	0.577336i	−0.216145	+	0.976361i	$0.569348\pi$
$548$		0			0
$549$		−	254.647i		−	0.463838i
$550$		0			0
$551$	534.645			0.970318
$552$		0			0
$553$	−173.627	−	340.763i	−0.313974	−	0.616208i
$554$		0			0
$555$	−297.165	−	14.4007i	−0.535433	−	0.0259471i
$556$		0			0
$557$	−314.140	+	616.534i	−0.563986	+	1.10688i	0.416287	+	0.909233i	$0.363331\pi$
$557$	−314.140	+	616.534i	−0.563986	+	1.10688i	−0.980272	+	0.197651i	$0.936669\pi$
$558$		0			0
$559$	−31.0501	+	42.7368i	−0.0555458	+	0.0764522i
$560$		0			0
$561$	−15.8294	−	22.6802i	−0.0282163	−	0.0404282i
$562$		0			0
$563$	−273.725	+	43.3538i	−0.486190	+	0.0770050i	−0.394717	−	0.918803i	$-0.629157\pi$
$563$	−273.725	+	43.3538i	−0.486190	+	0.0770050i	−0.0914729	+	0.995808i	$0.529157\pi$
$564$		0			0
$565$	231.059	+	513.516i	0.408955	+	0.908879i
$566$		0			0
$567$	−317.984	−	50.3638i	−0.560819	−	0.0888250i
$568$		0			0
$569$	−189.539	−	61.5851i	−0.333110	−	0.108234i	0.137687	−	0.990476i	$-0.456033\pi$
$569$	−189.539	−	61.5851i	−0.333110	−	0.108234i	−0.470796	+	0.882242i	$0.656033\pi$
$570$		0			0
$571$	−1103.78			−1.93307			−0.966535	−	0.256534i	$-0.917419\pi$
$571$	−1103.78			−1.93307			−0.966535	+	0.256534i	$0.917419\pi$
$572$		0			0
$573$	−80.4022	+	80.4022i	−0.140318	+	0.140318i
$574$		0			0
$575$	−152.986	+	125.893i	−0.266062	+	0.218945i
$576$		0			0
$577$	275.287	+	43.6011i	0.477100	+	0.0755652i	0.390353	−	0.920665i	$-0.372353\pi$
$577$	275.287	+	43.6011i	0.477100	+	0.0755652i	0.0867466	+	0.996230i	$0.472353\pi$
$578$		0			0
$579$	−318.624	+	103.527i	−0.550301	+	0.178804i
$580$		0			0
$581$	554.650	+	402.977i	0.954647	+	0.693592i
$582$		0			0
$583$	122.727	−	59.6265i	0.210510	−	0.102275i
$584$		0			0
$585$	107.639	−	188.143i	0.183998	−	0.321612i
$586$		0			0
$587$	−190.051	+	372.996i	−0.323767	+	0.635428i	−0.994320	−	0.106433i	$-0.966057\pi$
$587$	−190.051	+	372.996i	−0.323767	+	0.635428i	0.670553	+	0.741862i	$0.266057\pi$
$588$		0			0
$589$	−500.017	−	688.215i	−0.848926	−	1.16845i
$590$		0			0
$591$	101.921	−	313.682i	0.172456	−	0.530764i
$592$		0			0
$593$	−1.62737	+	1.62737i	−0.00274429	+	0.00274429i	−0.708478	−	0.705733i	$-0.750618\pi$
$593$	−1.62737	+	1.62737i	−0.00274429	+	0.00274429i	0.705733	+	0.708478i	$0.250618\pi$
$594$		0			0
$595$	46.4969	−	57.8835i	0.0781461	−	0.0972831i
$596$		0			0
$597$	−6.13817	+	3.12756i	−0.0102817	+	0.00523879i
$598$		0			0
$599$	−146.637	−	201.829i	−0.244803	−	0.336943i	0.668880	−	0.743371i	$-0.266774\pi$
$599$	−146.637	−	201.829i	−0.244803	−	0.336943i	−0.913683	+	0.406428i	$0.866774\pi$
$600$		0			0
$601$	132.774	+	408.636i	0.220922	+	0.679927i	0.998680	+	0.0513635i	$0.0163567\pi$
$601$	132.774	+	408.636i	0.220922	+	0.679927i	−0.777758	+	0.628563i	$0.783643\pi$
$602$		0			0
$603$	−166.672	+	26.3982i	−0.276404	+	0.0437781i
$604$		0			0
$605$	518.310	−	312.058i	0.856710	−	0.515798i
$606$		0			0
$607$	163.364	+	1031.44i	0.269133	+	1.69924i	0.638230	+	0.769846i	$0.279667\pi$
$607$	163.364	+	1031.44i	0.269133	+	1.69924i	−0.369097	+	0.929391i	$0.620333\pi$
$608$		0			0
$609$	150.151	−	48.7869i	0.246553	−	0.0801098i
$610$		0			0
$611$	−237.675	+	172.681i	−0.388993	+	0.282620i
$612$		0			0
$613$	−394.158	−	773.579i	−0.642999	−	1.26196i	−0.950593	−	0.310439i	$-0.899524\pi$
$613$	−394.158	−	773.579i	−0.642999	−	1.26196i	0.307595	−	0.951517i	$-0.400476\pi$
$614$		0			0
$615$	129.887	−	14.1690i	0.211199	−	0.0230390i
$616$		0			0
$617$	270.551	+	270.551i	0.438494	+	0.438494i	0.891505	−	0.453011i	$-0.149650\pi$
$617$	270.551	+	270.551i	0.438494	+	0.438494i	−0.453011	+	0.891505i	$0.649650\pi$
$618$		0			0
$619$	841.122	+	273.297i	1.35884	+	0.441514i	0.895656	−	0.444748i	$-0.146707\pi$
$619$	841.122	+	273.297i	1.35884	+	0.441514i	0.463184	+	0.886262i	$0.346707\pi$
$620$		0			0
$621$	−120.495	+	87.5446i	−0.194034	+	0.140974i
$622$		0			0
$623$	−492.738	−	251.063i	−0.790912	−	0.402990i
$624$		0			0
$625$	613.313	+	120.300i	0.981301	+	0.192480i
$626$		0			0
$627$	−136.049	−	280.025i	−0.216984	−	0.446611i
$628$		0			0
$629$	−69.7669	+	96.0259i	−0.110917	+	0.152664i
$630$		0			0
$631$	−334.438	−	1029.29i	−0.530013	−	1.63121i	−0.754185	−	0.656661i	$-0.771968\pi$
$631$	−334.438	−	1029.29i	−0.530013	−	1.63121i	0.224173	−	0.974549i	$-0.428032\pi$
$632$		0			0
$633$	−27.6458	+	174.549i	−0.0436743	+	0.275749i
$634$		0			0
$635$	805.992	+	168.004i	1.26928	+	0.264574i
$636$		0			0
$637$	19.9509	+	19.9509i	0.0313201	+	0.0313201i
$638$		0			0
$639$			491.344i			0.768926i
$640$		0			0
$641$	376.713	−	1159.40i	0.587696	−	1.80874i	−0.000468558	−	1.00000i	$-0.500149\pi$
$641$	376.713	−	1159.40i	0.587696	−	1.80874i	0.588164	−	0.808741i	$-0.299851\pi$
$642$		0			0
$643$	−124.751	+	787.649i	−0.194015	+	1.22496i	0.677845	+	0.735205i	$0.262914\pi$
$643$	−124.751	+	787.649i	−0.194015	+	1.22496i	−0.871860	+	0.489755i	$0.837086\pi$
$644$		0			0
$645$	−49.4988	−	18.7775i	−0.0767423	−	0.0291124i
$646$		0			0
$647$	−128.898	−	813.833i	−0.199225	−	1.25786i	−0.861175	−	0.508308i	$-0.830271\pi$
$647$	−128.898	−	813.833i	−0.199225	−	1.25786i	0.661951	−	0.749548i	$-0.269729\pi$
$648$		0			0
$649$	645.111	−	450.247i	0.994008	−	0.693755i
$650$		0			0
$651$	−203.226	−	147.652i	−0.312175	−	0.226808i
$652$		0			0
$653$	531.508	+	270.817i	0.813949	+	0.414728i	0.810840	−	0.585268i	$-0.199011\pi$
$653$	531.508	+	270.817i	0.813949	+	0.414728i	0.00310841	+	0.999995i	$0.499011\pi$
$654$		0			0
$655$	−703.228	−	34.0785i	−1.07363	−	0.0520282i
$656$		0			0
$657$	−733.589	+	373.782i	−1.11657	+	0.568923i
$658$		0			0
$659$			194.554i			0.295226i	0.989045	+	0.147613i	$0.0471591\pi$
$659$			194.554i			0.295226i	−0.989045	+	0.147613i	$0.952841\pi$
$660$		0			0
$661$	−24.2160			−0.0366355			−0.0183177	−	0.999832i	$-0.505831\pi$
$661$	−24.2160			−0.0366355			−0.0183177	+	0.999832i	$0.505831\pi$
$662$		0			0
$663$	6.39388	+	12.5487i	0.00964386	+	0.0189271i
$664$		0			0
$665$	618.863	−	561.655i	0.930622	−	0.844595i
$666$		0			0
$667$	−76.3060	+	149.759i	−0.114402	+	0.224526i
$668$		0			0
$669$	127.206	−	175.084i	0.190144	−	0.261710i
$670$		0			0
$671$	−218.252	+	288.713i	−0.325263	+	0.430272i
$672$		0			0
$673$	−1275.62	+	202.038i	−1.89542	+	0.300205i	−0.991766	−	0.128064i	$-0.959124\pi$
$673$	−1275.62	+	202.038i	−1.89542	+	0.300205i	−0.903652	+	0.428268i	$0.859124\pi$
$674$		0			0
$675$	454.774	+	118.026i	0.673740	+	0.174853i
$676$		0			0
$677$	−207.381	−	32.8459i	−0.306323	−	0.0485168i	0.00138070	−	0.999999i	$-0.499561\pi$
$677$	−207.381	−	32.8459i	−0.306323	−	0.0485168i	−0.307704	+	0.951482i	$0.599561\pi$
$678$		0			0
$679$	985.898	+	320.338i	1.45199	+	0.471779i
$680$		0			0
$681$	217.813			0.319842
$682$		0			0
$683$	209.108	−	209.108i	0.306162	−	0.306162i	−0.537257	−	0.843419i	$-0.680539\pi$
$683$	209.108	−	209.108i	0.306162	−	0.306162i	0.843419	+	0.537257i	$0.180539\pi$
$684$		0			0
$685$	10.6380	+	2.21744i	0.0155300	+	0.00323713i
$686$		0			0
$687$	−65.4554	−	10.3671i	−0.0952772	−	0.0150904i
$688$		0			0
$689$	−66.0789	+	21.4703i	−0.0959055	+	0.0311616i
$690$		0			0
$691$	745.702	+	541.784i	1.07916	+	0.784059i	0.977537	−	0.210764i	$-0.0675952\pi$
$691$	745.702	+	541.784i	1.07916	+	0.784059i	0.101627	+	0.994823i	$0.467595\pi$
$692$		0			0
$693$	391.502	+	406.652i	0.564938	+	0.586799i
$694$		0			0
$695$	1053.21	−	286.657i	1.51541	−	0.412457i
$696$		0			0
$697$	23.6649	−	46.4450i	0.0339525	−	0.0666355i
$698$		0			0
$699$	−221.362	−	304.679i	−0.316684	−	0.435879i
$700$		0			0
$701$	426.238	−	1311.83i	0.608043	−	1.87137i	0.133709	−	0.991021i	$-0.457311\pi$
$701$	426.238	−	1311.83i	0.608043	−	1.87137i	0.474335	−	0.880345i	$-0.342689\pi$
$702$		0			0
$703$	−944.735	+	944.735i	−1.34386	+	1.34386i
$704$		0			0
$705$	−229.537	−	184.384i	−0.325585	−	0.261538i
$706$		0			0
$707$	−525.671	+	267.843i	−0.743523	+	0.378844i
$708$		0			0
$709$	346.214	+	476.523i	0.488313	+	0.672105i	0.980076	−	0.198624i	$-0.0636472\pi$
$709$	346.214	+	476.523i	0.488313	+	0.672105i	−0.491763	+	0.870729i	$0.663647\pi$
$710$		0			0
$711$	−137.951	−	424.570i	−0.194024	−	0.597145i
$712$		0			0
$713$	264.139	−	41.8355i	0.370461	−	0.0586753i
$714$		0			0
$715$	−283.291	+	121.057i	−0.396212	+	0.169311i
$716$		0			0
$717$	6.03501	+	38.1035i	0.00841702	+	0.0531430i
$718$		0			0
$719$	1312.82	−	426.560i	1.82589	−	0.593268i	0.826345	−	0.563164i	$-0.190416\pi$
$719$	1312.82	−	426.560i	1.82589	−	0.593268i	0.999547	−	0.0301044i	$-0.00958398\pi$
$720$		0			0
$721$	−863.186	+	627.142i	−1.19721	+	0.869822i
$722$		0			0
$723$	−44.4591	−	87.2559i	−0.0614926	−	0.120686i
$724$		0			0
$725$	517.743	−	114.319i	0.714129	−	0.157681i
$726$		0			0
$727$	908.087	+	908.087i	1.24909	+	1.24909i	0.956123	+	0.292965i	$0.0946419\pi$
$727$	908.087	+	908.087i	1.24909	+	1.24909i	0.292965	+	0.956123i	$0.405358\pi$
$728$		0			0
$729$	−176.804	−	57.4472i	−0.242530	−	0.0788027i
$730$		0			0
$731$	−17.0872	+	12.4146i	−0.0233751	+	0.0169830i
$732$		0			0
$733$	−23.3848	−	11.9152i	−0.0319029	−	0.0162553i	0.437966	−	0.898991i	$-0.355699\pi$
$733$	−23.3848	−	11.9152i	−0.0319029	−	0.0162553i	−0.469869	+	0.882736i	$0.655699\pi$
$734$		0			0
$735$	−14.0416	+	24.5435i	−0.0191043	+	0.0333926i
$736$		0			0
$737$	211.594	+	112.921i	0.287101	+	0.153217i
$738$		0			0
$739$	385.682	−	530.845i	0.521897	−	0.718329i	−0.463972	−	0.885850i	$-0.653576\pi$
$739$	385.682	−	530.845i	0.521897	−	0.718329i	0.985869	+	0.167521i	$0.0535762\pi$
$740$		0			0
$741$	48.9885	+	150.771i	0.0661114	+	0.203470i
$742$		0			0
$743$	136.550	−	862.140i	0.183781	−	1.16035i	−0.707437	−	0.706776i	$-0.750149\pi$
$743$	136.550	−	862.140i	0.183781	−	1.16035i	0.891219	−	0.453574i	$-0.149851\pi$
$744$		0			0
$745$	724.333	+	1105.82i	0.972260	+	1.48432i
$746$		0			0
$747$	565.872	+	565.872i	0.757526	+	0.757526i
$748$		0			0
$749$			1001.88i			1.33763i
$750$		0			0
$751$	−300.253	+	924.085i	−0.399805	+	1.23047i	0.525351	+	0.850885i	$0.323934\pi$
$751$	−300.253	+	924.085i	−0.399805	+	1.23047i	−0.925156	+	0.379587i	$0.876066\pi$
$752$		0			0
$753$	−34.0523	+	214.998i	−0.0452221	+	0.285521i
$754$		0			0
$755$	153.314	−	404.147i	0.203065	−	0.535294i
$756$		0			0
$757$	−187.347	−	1182.86i	−0.247486	−	1.56256i	−0.728000	−	0.685578i	$-0.759550\pi$
$757$	−187.347	−	1182.86i	−0.247486	−	1.56256i	0.480514	−	0.876987i	$-0.340450\pi$
$758$		0			0
$759$	97.8548	+	1.85736i	0.128926	+	0.00244712i
$760$		0			0
$761$	−1013.08	−	736.044i	−1.33125	−	0.967206i	−0.999718	−	0.0237608i	$-0.992436\pi$
$761$	−1013.08	−	736.044i	−1.33125	−	0.967206i	−0.331528	−	0.943446i	$-0.607564\pi$
$762$		0			0
$763$	−917.379	−	467.428i	−1.20233	−	0.612619i
$764$		0			0
$765$	64.1759	−	58.2434i	0.0838900	−	0.0761352i
$766$		0			0
$767$	−356.932	+	181.866i	−0.465362	+	0.237114i
$768$		0			0
$769$			17.1904i			0.0223543i	0.999938	+	0.0111771i	$0.00355786\pi$
$769$			17.1904i			0.0223543i	−0.999938	+	0.0111771i	$0.996442\pi$
$770$		0			0
$771$	−542.607			−0.703771
$772$		0			0
$773$	58.4029	+	114.622i	0.0755535	+	0.148282i	0.925693	−	0.378275i	$-0.123483\pi$
$773$	58.4029	+	114.622i	0.0755535	+	0.148282i	−0.850140	+	0.526557i	$0.823483\pi$
$774$		0			0
$775$	−631.365	−	559.544i	−0.814665	−	0.721992i
$776$		0			0
$777$	−179.113	+	351.529i	−0.230519	+	0.452418i
$778$		0			0
$779$	344.882	−	474.690i	0.442725	−	0.609358i
$780$		0			0
$781$	421.119	−	557.073i	0.539204	−	0.713282i
$782$		0			0
$783$	393.678	−	62.3525i	0.502782	−	0.0796328i
$784$		0			0
$785$	915.253	−	411.823i	1.16593	−	0.524615i
$786$		0			0
$787$	482.146	+	76.3645i	0.612638	+	0.0970323i	0.455040	−	0.890471i	$-0.349625\pi$
$787$	482.146	+	76.3645i	0.612638	+	0.0970323i	0.157598	+	0.987503i	$0.449625\pi$
$788$		0			0
$789$	296.192	+	96.2388i	0.375402	+	0.121976i
$790$		0			0
$791$	746.728			0.944030
$792$		0			0
$793$	130.317	−	130.317i	0.164334	−	0.164334i
$794$		0			0
$795$	−38.1534	−	58.2477i	−0.0479917	−	0.0732675i
$796$		0			0
$797$	937.206	+	148.439i	1.17592	+	0.186247i	0.713656	−	0.700497i	$-0.247038\pi$
$797$	937.206	+	148.439i	1.17592	+	0.186247i	0.462261	+	0.886744i	$0.347038\pi$
$798$		0			0
$799$	−111.712	+	36.2975i	−0.139815	+	0.0454287i
$800$		0			0
$801$	−522.233	−	379.425i	−0.651977	−	0.473689i
$802$		0			0
$803$	1152.08	+	204.956i	1.43472	+	0.255238i
$804$		0			0
$805$	68.9989	+	253.510i	0.0857129	+	0.314919i
$806$		0			0
$807$	122.883	−	241.171i	0.152271	−	0.298848i
$808$		0			0
$809$	−393.296	−	541.326i	−0.486151	−	0.669130i	0.493521	−	0.869734i	$-0.335710\pi$
$809$	−393.296	−	541.326i	−0.486151	−	0.669130i	−0.979672	+	0.200604i	$0.935710\pi$
$810$		0			0
$811$	103.251	−	317.774i	0.127313	−	0.391830i	−0.867002	−	0.498304i	$-0.833956\pi$
$811$	103.251	−	317.774i	0.127313	−	0.391830i	0.994315	+	0.106475i	$0.0339563\pi$
$812$		0			0
$813$	−101.516	+	101.516i	−0.124866	+	0.124866i
$814$		0			0
$815$	−311.193	+	33.9471i	−0.381832	+	0.0416529i
$816$		0			0
$817$	−211.831	+	107.933i	−0.259279	+	0.132109i
$818$		0			0
$819$	−168.953	−	232.544i	−0.206292	−	0.283937i
$820$		0			0
$821$	78.1775	+	240.606i	0.0952223	+	0.293064i	0.987312	−	0.158795i	$-0.0507609\pi$
$821$	78.1775	+	240.606i	0.0952223	+	0.293064i	−0.892089	+	0.451859i	$0.850761\pi$
$822$		0			0
$823$	275.737	−	43.6724i	0.335038	−	0.0530649i	0.0133511	−	0.999911i	$-0.495750\pi$
$823$	275.737	−	43.6724i	0.335038	−	0.0530649i	0.321687	+	0.946846i	$0.395750\pi$
$824$		0			0
$825$	−191.623	−	242.082i	−0.232271	−	0.293433i
$826$		0			0
$827$	136.077	+	859.154i	0.164542	+	1.03888i	0.922337	+	0.386387i	$0.126277\pi$
$827$	136.077	+	859.154i	0.164542	+	1.03888i	−0.757795	+	0.652493i	$0.773723\pi$
$828$		0			0
$829$	706.905	−	229.687i	0.852720	−	0.277065i	0.150135	−	0.988666i	$-0.452029\pi$
$829$	706.905	−	229.687i	0.852720	−	0.277065i	0.702585	+	0.711600i	$0.252029\pi$
$830$		0			0
$831$	195.833	−	142.281i	0.235659	−	0.171216i
$832$		0			0
$833$	5.12145	+	10.0514i	0.00614820	+	0.0120665i
$834$		0			0
$835$	57.3149	+	525.405i	0.0686406	+	0.629228i
$836$		0			0
$837$	−448.443	−	448.443i	−0.535774	−	0.535774i
$838$		0			0
$839$	−1101.10	−	357.771i	−1.31240	−	0.426425i	−0.432522	−	0.901623i	$-0.642376\pi$
$839$	−1101.10	−	357.771i	−1.31240	−	0.426425i	−0.879879	+	0.475198i	$0.842376\pi$
$840$		0			0
$841$	−316.485	+	229.940i	−0.376320	+	0.273412i
$842$		0			0
$843$	−367.576	−	187.289i	−0.436033	−	0.222170i
$844$		0			0
$845$	−663.972	+	180.716i	−0.785766	+	0.213865i
$846$		0			0
$847$	−95.3443	−	796.599i	−0.112567	−	0.940494i
$848$		0			0
$849$	252.945	−	348.149i	0.297933	−	0.410069i
$850$		0			0
$851$	−129.794	−	399.464i	−0.152519	−	0.469406i
$852$		0			0
$853$	46.8265	−	295.651i	0.0548962	−	0.346601i	−0.944918	−	0.327308i	$-0.893858\pi$
$853$	46.8265	−	295.651i	0.0548962	−	0.346601i	0.999814	−	0.0192929i	$-0.00614151\pi$
$854$		0			0
$855$	816.046	−	534.527i	0.954440	−	0.625178i
$856$		0			0
$857$	1198.76	+	1198.76i	1.39878	+	1.39878i	0.803563	+	0.595219i	$0.202935\pi$
$857$	1198.76	+	1198.76i	1.39878	+	1.39878i	0.595219	+	0.803563i	$0.297065\pi$
$858$		0			0
$859$			659.409i			0.767647i	0.923406	+	0.383823i	$0.125393\pi$
$859$			659.409i			0.767647i	−0.923406	+	0.383823i	$0.874607\pi$
$860$		0			0
$861$	53.5414	−	164.784i	0.0621852	−	0.191386i
$862$		0			0
$863$	−102.652	+	648.118i	−0.118948	+	0.751006i	0.854050	+	0.520191i	$0.174139\pi$
$863$	−102.652	+	648.118i	−0.118948	+	0.751006i	−0.972998	+	0.230815i	$0.925861\pi$
$864$		0			0
$865$	420.187	+	933.841i	0.485765	+	1.07958i
$866$		0			0
$867$	−49.8763	−	314.906i	−0.0575274	−	0.363214i
$868$		0			0
$869$	−207.483	+	599.602i	−0.238761	+	0.689990i
$870$		0			0
$871$	−98.8043	−	71.7856i	−0.113438	−	0.0824174i
$872$		0			0
$873$	1078.15	+	549.344i	1.23499	+	0.629260i
$874$		0			0
$875$	479.205	−	676.226i	0.547663	−	0.772830i
$876$		0			0
$877$	−1422.87	+	724.989i	−1.62243	+	0.826669i	−0.623433	+	0.781877i	$0.714263\pi$
$877$	−1422.87	+	724.989i	−1.62243	+	0.826669i	−0.998996	+	0.0447920i	$0.985737\pi$
$878$		0			0
$879$			561.576i			0.638881i
$880$		0			0
$881$	−188.287			−0.213720			−0.106860	−	0.994274i	$-0.534080\pi$
$881$	−188.287			−0.213720			−0.106860	+	0.994274i	$0.534080\pi$
$882$		0			0
$883$	−467.194	−	916.920i	−0.529099	−	1.03841i	−0.988646	−	0.150261i	$-0.951988\pi$
$883$	−467.194	−	916.920i	−0.529099	−	1.03841i	0.459548	−	0.888153i	$-0.348012\pi$
$884$		0			0
$885$	−269.807	−	297.289i	−0.304867	−	0.335920i
$886$		0			0
$887$	−122.385	+	240.193i	−0.137976	+	0.270793i	−0.949647	−	0.313322i	$-0.898558\pi$
$887$	−122.385	+	240.193i	−0.137976	+	0.270793i	0.811671	+	0.584115i	$0.198558\pi$
$888$		0			0
$889$	641.738	−	883.276i	0.721865	−	0.993562i
$890$		0			0
$891$	305.689	+	437.989i	0.343085	+	0.491570i
$892$		0			0
$893$	−1305.90	+	206.834i	−1.46237	+	0.231617i
$894$		0			0
$895$	619.098	+	234.857i	0.691730	+	0.262410i
$896$		0			0
$897$	−49.2241	−	7.79634i	−0.0548764	−	0.00869157i
$898$		0			0
$899$	−680.658	−	221.159i	−0.757128	−	0.246006i
$900$		0			0
$901$	−27.7796			−0.0308319
$902$		0			0
$903$	−49.6419	+	49.6419i	−0.0549744	+	0.0549744i
$904$		0			0
$905$	−379.711	+	248.719i	−0.419571	+	0.274827i
$906$		0			0
$907$	1017.11	+	161.095i	1.12140	+	0.177613i	0.689484	−	0.724301i	$-0.257837\pi$
$907$	1017.11	+	161.095i	1.12140	+	0.177613i	0.431917	+	0.901913i	$0.357837\pi$
$908$		0			0
$909$	−654.954	+	212.807i	−0.720521	+	0.234112i
$910$		0			0
$911$	−862.561	−	626.687i	−0.946829	−	0.687911i	0.00322608	−	0.999995i	$-0.498973\pi$
$911$	−862.561	−	626.687i	−0.946829	−	0.687911i	−0.950055	+	0.312084i	$0.898973\pi$
$912$		0			0
$913$	−156.577	−	1126.57i	−0.171497	−	1.23392i
$914$		0			0
$915$	160.315	+	91.7182i	0.175208	+	0.100238i
$916$		0			0
$917$	−423.863	+	831.877i	−0.462227	+	0.907173i
$918$		0			0
$919$	−874.863	−	1204.15i	−0.951973	−	1.31028i	−0.950646	−	0.310279i	$-0.899578\pi$
$919$	−874.863	−	1204.15i	−0.951973	−	1.31028i	−0.00132702	−	0.999999i	$-0.500422\pi$
$920$		0			0
$921$	15.6742	−	48.2404i	0.0170187	−	0.0523782i
$922$		0			0
$923$	−251.447	+	251.447i	−0.272424	+	0.272424i
$924$		0			0
$925$	−712.865	+	1116.87i	−0.770664	+	1.20743i
$926$		0			0
$927$	−1109.68	+	565.412i	−1.19707	+	0.609938i
$928$		0			0
$929$	−264.904	−	364.609i	−0.285149	−	0.392474i	0.642282	−	0.766469i	$-0.277988\pi$
$929$	−264.904	−	364.609i	−0.285149	−	0.392474i	−0.927431	+	0.373994i	$0.877988\pi$
$930$		0			0
$931$	39.2395	+	120.767i	0.0421477	+	0.129717i
$932$		0			0
$933$	−161.873	+	25.6382i	−0.173498	+	0.0274794i
$934$		0			0
$935$	−122.680	+	11.0314i	−0.131209	+	0.0117983i
$936$		0			0
$937$	110.039	+	694.757i	0.117437	+	0.741470i	0.974188	+	0.225739i	$0.0724796\pi$
$937$	110.039	+	694.757i	0.117437	+	0.741470i	−0.856751	+	0.515731i	$0.827520\pi$
$938$		0			0
$939$	−264.541	+	85.9547i	−0.281727	+	0.0915385i
$940$		0			0
$941$	−756.838	+	549.875i	−0.804292	+	0.584352i	−0.912170	−	0.409812i	$-0.865594\pi$
$941$	−756.838	+	549.875i	−0.804292	+	0.584352i	0.107878	+	0.994164i	$0.465594\pi$
$942$		0			0
$943$	83.7424	+	164.354i	0.0888042	+	0.174288i
$944$		0			0
$945$	390.188	−	485.741i	0.412898	−	0.514012i
$946$		0			0
$947$	−289.989	−	289.989i	−0.306219	−	0.306219i	0.537222	−	0.843441i	$-0.319474\pi$
$947$	−289.989	−	289.989i	−0.306219	−	0.306219i	−0.843441	+	0.537222i	$0.819474\pi$
$948$		0			0
$949$	−566.702	−	184.133i	−0.597157	−	0.194028i
$950$		0			0
$951$	394.966	−	286.960i	0.415317	−	0.301745i
$952$		0			0
$953$	−1256.56	−	640.252i	−1.31854	−	0.671828i	−0.353868	−	0.935295i	$-0.615134\pi$
$953$	−1256.56	−	640.252i	−1.31854	−	0.671828i	−0.964668	+	0.263468i	$0.915134\pi$
$954$		0			0
$955$	132.989	+	488.616i	0.139255	+	0.511640i
$956$		0			0
$957$	−231.075	−	123.317i	−0.241458	−	0.128858i
$958$		0			0
$959$	8.47009	−	11.6581i	0.00883221	−	0.0121565i
$960$		0			0
$961$	54.9239	+	169.038i	0.0571528	+	0.175898i
$962$		0			0
$963$	−182.945	+	1155.07i	−0.189974	+	1.19945i
$964$		0			0
$965$	−304.460	+	1460.63i	−0.315503	+	1.51361i
$966$		0			0
$967$	−10.0460	−	10.0460i	−0.0103888	−	0.0103888i	0.701893	−	0.712282i	$-0.252338\pi$
$967$	−10.0460	−	10.0460i	−0.0103888	−	0.0103888i	−0.712282	+	0.701893i	$0.752338\pi$
$968$		0			0
$969$			63.3842i			0.0654120i
$970$		0			0
$971$	−161.947	+	498.420i	−0.166783	+	0.513306i	−0.999163	−	0.0408991i	$-0.986978\pi$
$971$	−161.947	+	498.420i	−0.166783	+	0.513306i	0.832380	+	0.554205i	$0.186978\pi$
$972$		0			0
$973$	226.433	−	1429.64i	0.232716	−	1.46931i
$974$		0			0
$975$	79.6780	+	135.530i	0.0817210	+	0.139005i
$976$		0			0
$977$	−114.998	−	726.068i	−0.117705	−	0.743161i	−0.973979	−	0.226639i	$-0.927226\pi$
$977$	−114.998	−	726.068i	−0.117705	−	0.743161i	0.856274	−	0.516522i	$-0.172774\pi$
$978$		0			0
$979$	266.900	+	877.775i	0.272625	+	0.896604i
$980$		0			0
$981$	−972.293	−	706.412i	−0.991124	−	0.720094i
$982$		0			0
$983$	−650.118	−	331.252i	−0.661361	−	0.336980i	0.0908859	−	0.995861i	$-0.471030\pi$
$983$	−650.118	−	331.252i	−0.661361	−	0.336980i	−0.752247	+	0.658881i	$0.771030\pi$
$984$		0			0
$985$	−987.163	−	1087.71i	−1.00220	−	1.10428i
$986$		0			0
$987$	−347.877	+	177.252i	−0.352459	+	0.179587i
$988$		0			0
$989$		−	74.7402i		−	0.0755714i
$990$		0			0
$991$	1112.27			1.12237			0.561187	−	0.827689i	$-0.310345\pi$
$991$	1112.27			1.12237			0.561187	+	0.827689i	$0.310345\pi$
$992$		0			0
$993$	152.508	+	299.313i	0.153583	+	0.301423i
$994$		0			0
$995$	−1.48503	+	30.6445i	−0.00149250	+	0.0307985i
$996$		0			0
$997$	224.907	−	441.404i	0.225583	−	0.442732i	−0.750278	−	0.661122i	$-0.770080\pi$
$997$	224.907	−	441.404i	0.225583	−	0.442732i	0.975862	+	0.218390i	$0.0700805\pi$
$998$		0			0
$999$	−585.463	+	805.821i	−0.586049	+	0.806627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.37.8	✓	96
5.3	odd	4	inner	220.3.x.a.213.5	yes	96
11.3	even	5	inner	220.3.x.a.157.5	yes	96
55.3	odd	20	inner	220.3.x.a.113.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.8	✓	96	1.1	even	1	trivial
220.3.x.a.113.8	yes	96	55.3	odd	20	inner
220.3.x.a.157.5	yes	96	11.3	even	5	inner
220.3.x.a.213.5	yes	96	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.509699 + 1.00034i) q^{3} +(4.99414 + 0.242016i) q^{5} +(3.01016 - 5.90777i) q^{7} +(4.54918 - 6.26141i) q^{9} +(-10.5242 + 3.20004i) q^{11} +(5.53236 - 0.876240i) q^{13} +(2.30341 + 5.11919i) q^{15} +(2.21197 + 0.350342i) q^{17} +(23.9751 + 7.78999i) q^{19} +7.44406 q^{21} +(-5.60384 + 5.60384i) q^{23} +(24.8829 + 2.41733i) q^{25} +(18.5622 + 2.93997i) q^{27} +(20.1705 - 6.55380i) q^{29} +(-27.3004 - 19.8349i) q^{31} +(-8.56532 - 8.89677i) q^{33} +(16.4629 - 28.7757i) q^{35} +(-24.0612 + 47.2228i) q^{37} +(3.69638 + 5.08763i) q^{39} +(7.19251 - 22.1363i) q^{41} +(-6.66866 + 6.66866i) q^{43} +(24.2346 - 30.1694i) q^{45} +(-46.7321 + 23.8112i) q^{47} +(2.96077 + 4.07516i) q^{49} +(0.776979 + 2.39129i) q^{51} +(-12.2514 + 1.94043i) q^{53} +(-53.3340 + 13.4344i) q^{55} +(4.42745 + 27.9538i) q^{57} +(-68.0175 + 22.1002i) q^{59} +(26.6184 - 19.3394i) q^{61} +(-23.2972 - 45.7234i) q^{63} +(27.8415 - 3.03714i) q^{65} +(-15.4175 - 15.4175i) q^{67} +(-8.46202 - 2.74948i) q^{69} +(-51.3604 + 37.3155i) q^{71} +(-94.7847 - 48.2952i) q^{73} +(10.2646 + 26.1234i) q^{75} +(-12.7746 + 71.8075i) q^{77} +(33.9037 - 46.6645i) q^{79} +(-15.0046 - 46.1795i) q^{81} +(-16.1752 + 102.127i) q^{83} +(10.9621 + 2.28499i) q^{85} +(16.8369 + 16.8369i) q^{87} -83.4051i q^{89} +(11.4767 - 35.3216i) q^{91} +(5.92667 - 37.4196i) q^{93} +(117.850 + 44.7067i) q^{95} +(24.4577 + 154.420i) q^{97} +(-27.8399 + 80.4542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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