LMFDB - Embedded newform 4020.2.q.k.3781.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.4
Root			$0.150493 + 0.260662i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.k.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +(-2.81310 - 4.87244i) q^{11} +(0.800986 - 1.38735i) q^{13} -1.00000 q^{15} +(-1.35601 + 2.34868i) q^{17} +(-0.454704 + 0.787570i) q^{19} +(-0.827889 - 1.43395i) q^{21} +(-3.02247 + 5.23507i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.34683 - 2.33278i) q^{29} +(5.11431 + 8.85825i) q^{31} +(2.81310 + 4.87244i) q^{33} +(0.827889 + 1.43395i) q^{35} +(-0.237490 + 0.411344i) q^{37} +(-0.800986 + 1.38735i) q^{39} +(0.573228 + 0.992859i) q^{41} +5.46671 q^{43} +1.00000 q^{45} +(1.69934 + 2.94334i) q^{47} +(2.12920 - 3.68788i) q^{49} +(1.35601 - 2.34868i) q^{51} -5.97455 q^{53} +(-2.81310 - 4.87244i) q^{55} +(0.454704 - 0.787570i) q^{57} +8.25736 q^{59} +(5.07988 - 8.79861i) q^{61} +(0.827889 + 1.43395i) q^{63} +(0.800986 - 1.38735i) q^{65} +(8.03367 - 1.56851i) q^{67} +(3.02247 - 5.23507i) q^{69} +(1.81642 + 3.14614i) q^{71} +(-0.751860 + 1.30226i) q^{73} -1.00000 q^{75} +(4.65787 - 8.06767i) q^{77} +(4.38601 + 7.59678i) q^{79} +1.00000 q^{81} +(-5.96714 + 10.3354i) q^{83} +(-1.35601 + 2.34868i) q^{85} +(1.34683 + 2.33278i) q^{87} +10.1310 q^{89} +2.65251 q^{91} +(-5.11431 - 8.85825i) q^{93} +(-0.454704 + 0.787570i) q^{95} +(2.33139 - 4.03809i) q^{97} +(-2.81310 - 4.87244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.827889	+	1.43395i	0.312913	+	0.541981i	0.978992	−	0.203901i	$-0.0653620\pi$
$7$	0.827889	+	1.43395i	0.312913	+	0.541981i	−0.666079	+	0.745881i	$0.732029\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.81310	−	4.87244i	−0.848182	−	1.46909i	−0.882829	−	0.469695i	$-0.844364\pi$
$11$	−2.81310	−	4.87244i	−0.848182	−	1.46909i	0.0346464	−	0.999400i	$-0.488970\pi$
$12$		0			0
$13$	0.800986	−	1.38735i	0.222154	−	0.384781i	−0.733308	−	0.679897i	$-0.762025\pi$
$13$	0.800986	−	1.38735i	0.222154	−	0.384781i	0.955462	+	0.295115i	$0.0953580\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−1.35601	+	2.34868i	−0.328882	+	0.569640i	−0.982290	−	0.187366i	$-0.940005\pi$
$17$	−1.35601	+	2.34868i	−0.328882	+	0.569640i	0.653409	+	0.757005i	$0.273338\pi$
$18$		0			0
$19$	−0.454704	+	0.787570i	−0.104316	+	0.180681i	−0.913459	−	0.406932i	$-0.866599\pi$
$19$	−0.454704	+	0.787570i	−0.104316	+	0.180681i	0.809142	+	0.587613i	$0.199932\pi$
$20$		0			0
$21$	−0.827889	−	1.43395i	−0.180660	−	0.312913i
$22$		0			0
$23$	−3.02247	+	5.23507i	−0.630228	+	1.09159i	0.357277	+	0.933999i	$0.383705\pi$
$23$	−3.02247	+	5.23507i	−0.630228	+	1.09159i	−0.987505	+	0.157588i	$0.949628\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.34683	−	2.33278i	−0.250100	−	0.433186i	0.713453	−	0.700703i	$-0.247130\pi$
$29$	−1.34683	−	2.33278i	−0.250100	−	0.433186i	−0.963553	+	0.267517i	$0.913797\pi$
$30$		0			0
$31$	5.11431	+	8.85825i	0.918558	+	1.59099i	0.801608	+	0.597850i	$0.203978\pi$
$31$	5.11431	+	8.85825i	0.918558	+	1.59099i	0.116950	+	0.993138i	$0.462688\pi$
$32$		0			0
$33$	2.81310	+	4.87244i	0.489698	+	0.848182i
$34$		0			0
$35$	0.827889	+	1.43395i	0.139939	+	0.242381i
$36$		0			0
$37$	−0.237490	+	0.411344i	−0.0390430	+	0.0676245i	−0.884887	−	0.465806i	$-0.845764\pi$
$37$	−0.237490	+	0.411344i	−0.0390430	+	0.0676245i	0.845844	+	0.533431i	$0.179098\pi$
$38$		0			0
$39$	−0.800986	+	1.38735i	−0.128260	+	0.222154i
$40$		0			0
$41$	0.573228	+	0.992859i	0.0895231	+	0.155059i	0.907310	−	0.420463i	$-0.138132\pi$
$41$	0.573228	+	0.992859i	0.0895231	+	0.155059i	−0.817787	+	0.575522i	$0.804799\pi$
$42$		0			0
$43$	5.46671			0.833665			0.416833	−	0.908983i	$-0.363140\pi$
$43$	5.46671			0.833665			0.416833	+	0.908983i	$0.363140\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	1.69934	+	2.94334i	0.247874	+	0.429330i	0.962936	−	0.269731i	$-0.0869348\pi$
$47$	1.69934	+	2.94334i	0.247874	+	0.429330i	−0.715062	+	0.699061i	$0.753601\pi$
$48$		0			0
$49$	2.12920	−	3.68788i	0.304171	−	0.526840i
$50$		0			0
$51$	1.35601	−	2.34868i	0.189880	−	0.328882i
$52$		0			0
$53$	−5.97455			−0.820667			−0.410334	−	0.911935i	$-0.634588\pi$
$53$	−5.97455			−0.820667			−0.410334	+	0.911935i	$0.634588\pi$
$54$		0			0
$55$	−2.81310	−	4.87244i	−0.379319	−	0.656999i
$56$		0			0
$57$	0.454704	−	0.787570i	0.0602270	−	0.104316i
$58$		0			0
$59$	8.25736			1.07502			0.537509	−	0.843258i	$-0.319366\pi$
$59$	8.25736			1.07502			0.537509	+	0.843258i	$0.319366\pi$
$60$		0			0
$61$	5.07988	−	8.79861i	0.650412	−	1.12655i	−0.332611	−	0.943064i	$-0.607930\pi$
$61$	5.07988	−	8.79861i	0.650412	−	1.12655i	0.983023	−	0.183482i	$-0.0587371\pi$
$62$		0			0
$63$	0.827889	+	1.43395i	0.104304	+	0.180660i
$64$		0			0
$65$	0.800986	−	1.38735i	0.0993501	−	0.172079i
$66$		0			0
$67$	8.03367	−	1.56851i	0.981469	−	0.191623i
$67$	8.03367	−	1.56851i	0.981469	−	0.191623i
$68$		0			0
$69$	3.02247	−	5.23507i	0.363862	−	0.630228i
$70$		0			0
$71$	1.81642	+	3.14614i	0.215570	+	0.373378i	0.953449	−	0.301555i	$-0.0975058\pi$
$71$	1.81642	+	3.14614i	0.215570	+	0.373378i	−0.737879	+	0.674933i	$0.764172\pi$
$72$		0			0
$73$	−0.751860	+	1.30226i	−0.0879985	+	0.152418i	−0.906665	−	0.421851i	$-0.861380\pi$
$73$	−0.751860	+	1.30226i	−0.0879985	+	0.152418i	0.818667	+	0.574269i	$0.194714\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	4.65787	−	8.06767i	0.530814	−	0.919397i
$78$		0			0
$79$	4.38601	+	7.59678i	0.493464	+	0.854705i	0.999972	−	0.00753058i	$-0.00239708\pi$
$79$	4.38601	+	7.59678i	0.493464	+	0.854705i	−0.506507	+	0.862236i	$0.669064\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.96714	+	10.3354i	−0.654979	+	1.13446i	0.326920	+	0.945052i	$0.393989\pi$
$83$	−5.96714	+	10.3354i	−0.654979	+	1.13446i	−0.981899	+	0.189405i	$0.939344\pi$
$84$		0			0
$85$	−1.35601	+	2.34868i	−0.147080	+	0.254751i
$86$		0			0
$87$	1.34683	+	2.33278i	0.144395	+	0.250100i
$88$		0			0
$89$	10.1310			1.07389			0.536943	−	0.843619i	$-0.319579\pi$
$89$	10.1310			1.07389			0.536943	+	0.843619i	$0.319579\pi$
$90$		0			0
$91$	2.65251			0.278059
$92$		0			0
$93$	−5.11431	−	8.85825i	−0.530329	−	0.918558i
$94$		0			0
$95$	−0.454704	+	0.787570i	−0.0466516	+	0.0808030i
$96$		0			0
$97$	2.33139	−	4.03809i	0.236717	−	0.410006i	−0.723053	−	0.690792i	$-0.757262\pi$
$97$	2.33139	−	4.03809i	0.236717	−	0.410006i	0.959770	+	0.280786i	$0.0905952\pi$
$98$		0			0
$99$	−2.81310	−	4.87244i	−0.282727	−	0.489698i
$100$		0			0
$101$	−4.05606	−	7.02530i	−0.403593	−	0.699043i	0.590564	−	0.806991i	$-0.298905\pi$
$101$	−4.05606	−	7.02530i	−0.403593	−	0.699043i	−0.994157	+	0.107948i	$0.965572\pi$
$102$		0			0
$103$	−0.101231	−	0.175338i	−0.00997461	−	0.0172765i	0.860995	−	0.508613i	$-0.169842\pi$
$103$	−0.101231	−	0.175338i	−0.00997461	−	0.0172765i	−0.870970	+	0.491337i	$0.836508\pi$
$104$		0			0
$105$	−0.827889	−	1.43395i	−0.0807937	−	0.139939i
$106$		0			0
$107$	−7.09586			−0.685983			−0.342991	−	0.939339i	$-0.611440\pi$
$107$	−7.09586			−0.685983			−0.342991	+	0.939339i	$0.611440\pi$
$108$		0			0
$109$	−9.42556			−0.902805			−0.451402	−	0.892321i	$-0.649076\pi$
$109$	−9.42556			−0.902805			−0.451402	+	0.892321i	$0.649076\pi$
$110$		0			0
$111$	0.237490	−	0.411344i	0.0225415	−	0.0390430i
$112$		0			0
$113$	5.20764	+	9.01990i	0.489894	+	0.848520i	0.999932	−	0.0116309i	$-0.00370232\pi$
$113$	5.20764	+	9.01990i	0.489894	+	0.848520i	−0.510039	+	0.860151i	$0.670369\pi$
$114$		0			0
$115$	−3.02247	+	5.23507i	−0.281847	+	0.488173i
$116$		0			0
$117$	0.800986	−	1.38735i	0.0740512	−	0.128260i
$118$		0			0
$119$	−4.49051			−0.411645
$120$		0			0
$121$	−10.3271	+	17.8870i	−0.938826	+	1.62610i
$122$		0			0
$123$	−0.573228	−	0.992859i	−0.0516862	−	0.0895231i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.57825	+	14.8580i	0.761196	+	1.31843i	0.942234	+	0.334955i	$0.108721\pi$
$127$	8.57825	+	14.8580i	0.761196	+	1.31843i	−0.181038	+	0.983476i	$0.557946\pi$
$128$		0			0
$129$	−5.46671			−0.481317
$130$		0			0
$131$	−4.43412			−0.387411			−0.193705	−	0.981060i	$-0.562051\pi$
$131$	−4.43412			−0.387411			−0.193705	+	0.981060i	$0.562051\pi$
$132$		0			0
$133$	−1.50578			−0.130567
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	13.6451			1.16578			0.582890	−	0.812551i	$-0.301922\pi$
$137$	13.6451			1.16578			0.582890	+	0.812551i	$0.301922\pi$
$138$		0			0
$139$	3.07755			0.261034			0.130517	−	0.991446i	$-0.458336\pi$
$139$	3.07755			0.261034			0.130517	+	0.991446i	$0.458336\pi$
$140$		0			0
$141$	−1.69934	−	2.94334i	−0.143110	−	0.247874i
$142$		0			0
$143$	−9.01303			−0.753707
$144$		0			0
$145$	−1.34683	−	2.33278i	−0.111848	−	0.193727i
$146$		0			0
$147$	−2.12920	+	3.68788i	−0.175613	+	0.304171i
$148$		0			0
$149$	8.71209			0.713722			0.356861	−	0.934158i	$-0.383847\pi$
$149$	8.71209			0.713722			0.356861	+	0.934158i	$0.383847\pi$
$150$		0			0
$151$	11.4966	−	19.9127i	0.935582	−	1.62048i	0.161989	−	0.986793i	$-0.448209\pi$
$151$	11.4966	−	19.9127i	0.935582	−	1.62048i	0.773593	−	0.633683i	$-0.218458\pi$
$152$		0			0
$153$	−1.35601	+	2.34868i	−0.109627	+	0.189880i
$154$		0			0
$155$	5.11431	+	8.85825i	0.410791	+	0.711512i
$156$		0			0
$157$	10.0754	−	17.4511i	0.804106	−	1.39275i	−0.112786	−	0.993619i	$-0.535978\pi$
$157$	10.0754	−	17.4511i	0.804106	−	1.39275i	0.916893	−	0.399134i	$-0.130689\pi$
$158$		0			0
$159$	5.97455			0.473812
$160$		0			0
$161$	−10.0091			−0.788825
$162$		0			0
$163$	4.52114	+	7.83085i	0.354123	+	0.613359i	0.986968	−	0.160920i	$-0.0514460\pi$
$163$	4.52114	+	7.83085i	0.354123	+	0.613359i	−0.632844	+	0.774279i	$0.718113\pi$
$164$		0			0
$165$	2.81310	+	4.87244i	0.219000	+	0.379319i
$166$		0			0
$167$	3.20616	+	5.55323i	0.248100	+	0.429722i	0.962999	−	0.269506i	$-0.0868606\pi$
$167$	3.20616	+	5.55323i	0.248100	+	0.429722i	−0.714899	+	0.699228i	$0.753527\pi$
$168$		0			0
$169$	5.21684	+	9.03584i	0.401296	+	0.695064i
$170$		0			0
$171$	−0.454704	+	0.787570i	−0.0347721	+	0.0602270i
$172$		0			0
$173$	−9.45972	+	16.3847i	−0.719209	+	1.24571i	0.242104	+	0.970250i	$0.422162\pi$
$173$	−9.45972	+	16.3847i	−0.719209	+	1.24571i	−0.961313	+	0.275457i	$0.911171\pi$
$174$		0			0
$175$	0.827889	+	1.43395i	0.0625825	+	0.108396i
$176$		0			0
$177$	−8.25736			−0.620661
$178$		0			0
$179$	5.01635			0.374939			0.187470	−	0.982270i	$-0.439971\pi$
$179$	5.01635			0.374939			0.187470	+	0.982270i	$0.439971\pi$
$180$		0			0
$181$	−4.71426	−	8.16533i	−0.350408	−	0.606924i	0.635913	−	0.771761i	$-0.280624\pi$
$181$	−4.71426	−	8.16533i	−0.350408	−	0.606924i	−0.986321	+	0.164836i	$0.947290\pi$
$182$		0			0
$183$	−5.07988	+	8.79861i	−0.375516	+	0.650412i
$184$		0			0
$185$	−0.237490	+	0.411344i	−0.0174606	+	0.0302426i
$186$		0			0
$187$	15.2584			1.11581
$188$		0			0
$189$	−0.827889	−	1.43395i	−0.0602201	−	0.104304i
$190$		0			0
$191$	3.77371	−	6.53626i	0.273056	−	0.472947i	−0.696587	−	0.717473i	$-0.745299\pi$
$191$	3.77371	−	6.53626i	0.273056	−	0.472947i	0.969643	+	0.244525i	$0.0786322\pi$
$192$		0			0
$193$	9.80997			0.706137			0.353068	−	0.935597i	$-0.385138\pi$
$193$	9.80997			0.706137			0.353068	+	0.935597i	$0.385138\pi$
$194$		0			0
$195$	−0.800986	+	1.38735i	−0.0573598	+	0.0993501i
$196$		0			0
$197$	7.16415	+	12.4087i	0.510425	+	0.884082i	0.999927	+	0.0120795i	$0.00384513\pi$
$197$	7.16415	+	12.4087i	0.510425	+	0.884082i	−0.489502	+	0.872002i	$0.662822\pi$
$198$		0			0
$199$	−12.8696	+	22.2908i	−0.912304	+	1.58016i	−0.101502	+	0.994835i	$0.532365\pi$
$199$	−12.8696	+	22.2908i	−0.912304	+	1.58016i	−0.810802	+	0.585321i	$0.800969\pi$
$200$		0			0
$201$	−8.03367	+	1.56851i	−0.566651	+	0.110634i
$202$		0			0
$203$	2.23005	−	3.86256i	0.156519	−	0.271099i
$204$		0			0
$205$	0.573228	+	0.992859i	0.0400360	+	0.0693443i
$206$		0			0
$207$	−3.02247	+	5.23507i	−0.210076	+	0.363862i
$208$		0			0
$209$	5.11651			0.353917
$210$		0			0
$211$	−12.5115	+	21.6706i	−0.861329	+	1.49187i	0.00931696	+	0.999957i	$0.497034\pi$
$211$	−12.5115	+	21.6706i	−0.861329	+	1.49187i	−0.870646	+	0.491910i	$0.836299\pi$
$212$		0			0
$213$	−1.81642	−	3.14614i	−0.124459	−	0.215570i
$214$		0			0
$215$	5.46671			0.372826
$216$		0			0
$217$	−8.46816	+	14.6673i	−0.574856	+	0.995681i
$218$		0			0
$219$	0.751860	−	1.30226i	0.0508060	−	0.0879985i
$220$		0			0
$221$	2.17230	+	3.76253i	0.146124	+	0.253095i
$222$		0			0
$223$	16.9045			1.13201			0.566004	−	0.824402i	$-0.308489\pi$
$223$	16.9045			1.13201			0.566004	+	0.824402i	$0.308489\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−5.58831	−	9.67924i	−0.370909	−	0.642434i	0.618796	−	0.785551i	$-0.287621\pi$
$227$	−5.58831	−	9.67924i	−0.370909	−	0.642434i	−0.989706	+	0.143118i	$0.954287\pi$
$228$		0			0
$229$	7.62535	−	13.2075i	0.503897	−	0.872776i	−0.496092	−	0.868270i	$-0.665232\pi$
$229$	7.62535	−	13.2075i	0.503897	−	0.872776i	0.999990	−	0.00450622i	$-0.00143438\pi$
$230$		0			0
$231$	−4.65787	+	8.06767i	−0.306466	+	0.530814i
$232$		0			0
$233$	−1.94446	−	3.36790i	−0.127386	−	0.220639i	0.795277	−	0.606246i	$-0.207325\pi$
$233$	−1.94446	−	3.36790i	−0.127386	−	0.220639i	−0.922663	+	0.385607i	$0.873992\pi$
$234$		0			0
$235$	1.69934	+	2.94334i	0.110853	+	0.192002i
$236$		0			0
$237$	−4.38601	−	7.59678i	−0.284902	−	0.493464i
$238$		0			0
$239$	−4.86697	−	8.42984i	−0.314818	−	0.545281i	0.664581	−	0.747217i	$-0.268610\pi$
$239$	−4.86697	−	8.42984i	−0.314818	−	0.545281i	−0.979399	+	0.201935i	$0.935277\pi$
$240$		0			0
$241$	18.8478			1.21409			0.607047	−	0.794666i	$-0.292354\pi$
$241$	18.8478			1.21409			0.607047	+	0.794666i	$0.292354\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.12920	−	3.68788i	0.136030	−	0.235610i
$246$		0			0
$247$	0.728423	+	1.26167i	0.0463484	+	0.0802778i
$248$		0			0
$249$	5.96714	−	10.3354i	0.378152	−	0.654979i
$250$		0			0
$251$	2.50889	−	4.34552i	0.158360	−	0.274287i	−0.775918	−	0.630834i	$-0.782713\pi$
$251$	2.50889	−	4.34552i	0.158360	−	0.274287i	0.934277	+	0.356547i	$0.116046\pi$
$252$		0			0
$253$	34.0100			2.13819
$254$		0			0
$255$	1.35601	−	2.34868i	0.0849169	−	0.147080i
$256$		0			0
$257$	−0.989493	−	1.71385i	−0.0617229	−	0.106907i	0.833513	−	0.552500i	$-0.186326\pi$
$257$	−0.989493	−	1.71385i	−0.0617229	−	0.106907i	−0.895236	+	0.445593i	$0.852993\pi$
$258$		0			0
$259$	−0.786460			−0.0488682
$260$		0			0
$261$	−1.34683	−	2.33278i	−0.0833667	−	0.144395i
$262$		0			0
$263$	6.03457			0.372107			0.186054	−	0.982540i	$-0.440430\pi$
$263$	6.03457			0.372107			0.186054	+	0.982540i	$0.440430\pi$
$264$		0			0
$265$	−5.97455			−0.367014
$266$		0			0
$267$	−10.1310			−0.620008
$268$		0			0
$269$	22.0260			1.34295			0.671474	−	0.741028i	$-0.265662\pi$
$269$	22.0260			1.34295			0.671474	+	0.741028i	$0.265662\pi$
$270$		0			0
$271$	−16.3255			−0.991705			−0.495852	−	0.868407i	$-0.665144\pi$
$271$	−16.3255			−0.991705			−0.495852	+	0.868407i	$0.665144\pi$
$272$		0			0
$273$	−2.65251			−0.160537
$274$		0			0
$275$	−2.81310	−	4.87244i	−0.169636	−	0.293819i
$276$		0			0
$277$	−21.6875			−1.30307			−0.651537	−	0.758617i	$-0.725875\pi$
$277$	−21.6875			−1.30307			−0.651537	+	0.758617i	$0.725875\pi$
$278$		0			0
$279$	5.11431	+	8.85825i	0.306186	+	0.530329i
$280$		0			0
$281$	−11.1094	+	19.2421i	−0.662733	+	1.14789i	0.317161	+	0.948372i	$0.397270\pi$
$281$	−11.1094	+	19.2421i	−0.662733	+	1.14789i	−0.979895	+	0.199516i	$0.936063\pi$
$282$		0			0
$283$	18.8268			1.11914			0.559568	−	0.828784i	$-0.310967\pi$
$283$	18.8268			1.11914			0.559568	+	0.828784i	$0.310967\pi$
$284$		0			0
$285$	0.454704	−	0.787570i	0.0269343	−	0.0466516i
$286$		0			0
$287$	−0.949138	+	1.64395i	−0.0560258	+	0.0970396i
$288$		0			0
$289$	4.82245	+	8.35274i	0.283674	+	0.491337i
$290$		0			0
$291$	−2.33139	+	4.03809i	−0.136669	+	0.236717i
$292$		0			0
$293$	31.2928			1.82814			0.914072	−	0.405552i	$-0.132921\pi$
$293$	31.2928			1.82814			0.914072	+	0.405552i	$0.132921\pi$
$294$		0			0
$295$	8.25736			0.480762
$296$		0			0
$297$	2.81310	+	4.87244i	0.163233	+	0.282727i
$298$		0			0
$299$	4.84191	+	8.38643i	0.280015	+	0.485000i
$300$		0			0
$301$	4.52583	+	7.83896i	0.260864	+	0.451830i
$302$		0			0
$303$	4.05606	+	7.02530i	0.233014	+	0.403593i
$304$		0			0
$305$	5.07988	−	8.79861i	0.290873	−	0.503807i
$306$		0			0
$307$	−1.74426	+	3.02115i	−0.0995503	+	0.172426i	−0.911499	−	0.411303i	$-0.865074\pi$
$307$	−1.74426	+	3.02115i	−0.0995503	+	0.172426i	0.811948	+	0.583729i	$0.198407\pi$
$308$		0			0
$309$	0.101231	+	0.175338i	0.00575884	+	0.00997461i
$310$		0			0
$311$	−14.1487			−0.802300			−0.401150	−	0.916012i	$-0.631389\pi$
$311$	−14.1487			−0.802300			−0.401150	+	0.916012i	$0.631389\pi$
$312$		0			0
$313$	11.0740			0.625941			0.312971	−	0.949763i	$-0.398676\pi$
$313$	11.0740			0.625941			0.312971	+	0.949763i	$0.398676\pi$
$314$		0			0
$315$	0.827889	+	1.43395i	0.0466463	+	0.0807937i
$316$		0			0
$317$	14.1965	−	24.5890i	0.797353	−	1.38106i	−0.123981	−	0.992285i	$-0.539566\pi$
$317$	14.1965	−	24.5890i	0.797353	−	1.38106i	0.921334	−	0.388772i	$-0.127101\pi$
$318$		0			0
$319$	−7.57754	+	13.1247i	−0.424261	+	0.734842i
$320$		0			0
$321$	7.09586			0.396052
$322$		0			0
$323$	−1.23317	−	2.13591i	−0.0686153	−	0.118845i
$324$		0			0
$325$	0.800986	−	1.38735i	0.0444307	−	0.0769563i
$326$		0			0
$327$	9.42556			0.521235
$328$		0			0
$329$	−2.81373	+	4.87352i	−0.155126	+	0.268686i
$330$		0			0
$331$	−12.0830	−	20.9283i	−0.664140	−	1.15032i	−0.979518	−	0.201358i	$-0.935465\pi$
$331$	−12.0830	−	20.9283i	−0.664140	−	1.15032i	0.315378	−	0.948966i	$-0.397869\pi$
$332$		0			0
$333$	−0.237490	+	0.411344i	−0.0130143	+	0.0225415i
$334$		0			0
$335$	8.03367	−	1.56851i	0.438926	−	0.0856966i
$336$		0			0
$337$	−5.35191	+	9.26977i	−0.291537	+	0.504957i	−0.974173	−	0.225801i	$-0.927500\pi$
$337$	−5.35191	+	9.26977i	−0.291537	+	0.504957i	0.682636	+	0.730758i	$0.260833\pi$
$338$		0			0
$339$	−5.20764	−	9.01990i	−0.282840	−	0.489894i
$340$		0			0
$341$	28.7742	−	49.8383i	1.55821	−	2.69890i
$342$		0			0
$343$	18.6414			1.00654
$344$		0			0
$345$	3.02247	−	5.23507i	0.162724	−	0.281847i
$346$		0			0
$347$	7.40314	+	12.8226i	0.397421	+	0.688354i	0.993407	−	0.114641i	$-0.0365718\pi$
$347$	7.40314	+	12.8226i	0.397421	+	0.688354i	−0.595986	+	0.802995i	$0.703238\pi$
$348$		0			0
$349$	10.5221			0.563236			0.281618	−	0.959527i	$-0.409129\pi$
$349$	10.5221			0.563236			0.281618	+	0.959527i	$0.409129\pi$
$350$		0			0
$351$	−0.800986	+	1.38735i	−0.0427535	+	0.0740512i
$352$		0			0
$353$	11.7966	−	20.4324i	0.627872	−	1.08751i	−0.360106	−	0.932911i	$-0.617259\pi$
$353$	11.7966	−	20.4324i	0.627872	−	1.08751i	0.987978	−	0.154595i	$-0.0494072\pi$
$354$		0			0
$355$	1.81642	+	3.14614i	0.0964057	+	0.166980i
$356$		0			0
$357$	4.49051			0.237663
$358$		0			0
$359$	−20.4751			−1.08063			−0.540317	−	0.841461i	$-0.681696\pi$
$359$	−20.4751			−1.08063			−0.540317	+	0.841461i	$0.681696\pi$
$360$		0			0
$361$	9.08649	+	15.7383i	0.478236	+	0.828330i
$362$		0			0
$363$	10.3271	−	17.8870i	0.542032	−	0.938826i
$364$		0			0
$365$	−0.751860	+	1.30226i	−0.0393541	+	0.0681633i
$366$		0			0
$367$	15.3612	+	26.6064i	0.801848	+	1.38884i	0.918398	+	0.395657i	$0.129483\pi$
$367$	15.3612	+	26.6064i	0.801848	+	1.38884i	−0.116550	+	0.993185i	$0.537184\pi$
$368$		0			0
$369$	0.573228	+	0.992859i	0.0298410	+	0.0516862i
$370$		0			0
$371$	−4.94626	−	8.56718i	−0.256797	−	0.444786i
$372$		0			0
$373$	13.9993	+	24.2476i	0.724859	+	1.25549i	0.959032	+	0.283297i	$0.0914283\pi$
$373$	13.9993	+	24.2476i	0.724859	+	1.25549i	−0.234173	+	0.972195i	$0.575238\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−4.31517			−0.222243
$378$		0			0
$379$	−13.3276	+	23.0841i	−0.684594	+	1.18575i	0.288970	+	0.957338i	$0.406687\pi$
$379$	−13.3276	+	23.0841i	−0.684594	+	1.18575i	−0.973564	+	0.228413i	$0.926646\pi$
$380$		0			0
$381$	−8.57825	−	14.8580i	−0.439477	−	0.761196i
$382$		0			0
$383$	8.54153	−	14.7944i	0.436452	−	0.755957i	−0.560961	−	0.827842i	$-0.689568\pi$
$383$	8.54153	−	14.7944i	0.436452	−	0.755957i	0.997413	+	0.0718855i	$0.0229016\pi$
$384$		0			0
$385$	4.65787	−	8.06767i	0.237387	−	0.411167i
$386$		0			0
$387$	5.46671			0.277888
$388$		0			0
$389$	1.45917	−	2.52735i	0.0739828	−	0.128142i	−0.826661	−	0.562701i	$-0.809762\pi$
$389$	1.45917	−	2.52735i	0.0739828	−	0.128142i	0.900643	+	0.434559i	$0.143096\pi$
$390$		0			0
$391$	−8.19701	−	14.1976i	−0.414541	−	0.718006i
$392$		0			0
$393$	4.43412			0.223672
$394$		0			0
$395$	4.38601	+	7.59678i	0.220684	+	0.382236i
$396$		0			0
$397$	−35.6606			−1.78976			−0.894878	−	0.446312i	$-0.852737\pi$
$397$	−35.6606			−1.78976			−0.894878	+	0.446312i	$0.852737\pi$
$398$		0			0
$399$	1.50578			0.0753831
$400$		0			0
$401$	−34.4152			−1.71861			−0.859306	−	0.511462i	$-0.829104\pi$
$401$	−34.4152			−1.71861			−0.859306	+	0.511462i	$0.829104\pi$
$402$		0			0
$403$	16.3860			0.816243
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	2.67233			0.132462
$408$		0			0
$409$	−0.883687	−	1.53059i	−0.0436955	−	0.0756829i	0.843350	−	0.537364i	$-0.180580\pi$
$409$	−0.883687	−	1.53059i	−0.0436955	−	0.0756829i	−0.887046	+	0.461681i	$0.847246\pi$
$410$		0			0
$411$	−13.6451			−0.673064
$412$		0			0
$413$	6.83618	+	11.8406i	0.336386	+	0.582638i
$414$		0			0
$415$	−5.96714	+	10.3354i	−0.292916	+	0.507345i
$416$		0			0
$417$	−3.07755			−0.150708
$418$		0			0
$419$	−0.414007	+	0.717081i	−0.0202256	+	0.0350317i	−0.875961	−	0.482382i	$-0.839772\pi$
$419$	−0.414007	+	0.717081i	−0.0202256	+	0.0350317i	0.855735	+	0.517414i	$0.173105\pi$
$420$		0			0
$421$	−2.38387	+	4.12898i	−0.116183	+	0.201234i	−0.918252	−	0.395997i	$-0.870399\pi$
$421$	−2.38387	+	4.12898i	−0.116183	+	0.201234i	0.802069	+	0.597231i	$0.203732\pi$
$422$		0			0
$423$	1.69934	+	2.94334i	0.0826247	+	0.143110i
$424$		0			0
$425$	−1.35601	+	2.34868i	−0.0657763	+	0.113928i
$426$		0			0
$427$	16.8223			0.814088
$428$		0			0
$429$	9.01303			0.435153
$430$		0			0
$431$	−5.53658	−	9.58964i	−0.266688	−	0.461917i	0.701317	−	0.712850i	$-0.252596\pi$
$431$	−5.53658	−	9.58964i	−0.266688	−	0.461917i	−0.968004	+	0.250933i	$0.919263\pi$
$432$		0			0
$433$	0.740009	+	1.28173i	0.0355626	+	0.0615962i	0.883259	−	0.468886i	$-0.155344\pi$
$433$	0.740009	+	1.28173i	0.0355626	+	0.0615962i	−0.847696	+	0.530482i	$0.822011\pi$
$434$		0			0
$435$	1.34683	+	2.33278i	0.0645756	+	0.111848i
$436$		0			0
$437$	−2.74865	−	4.76081i	−0.131486	−	0.227740i
$438$		0			0
$439$	10.4870	−	18.1641i	0.500519	−	0.866924i	−0.499481	−	0.866325i	$-0.666476\pi$
$439$	10.4870	−	18.1641i	0.500519	−	0.866924i	1.00000		0.000598899i	$-0.000190636\pi$
$440$		0			0
$441$	2.12920	−	3.68788i	0.101390	−	0.175613i
$442$		0			0
$443$	15.1526	+	26.2450i	0.719921	+	1.24694i	0.961031	+	0.276441i	$0.0891551\pi$
$443$	15.1526	+	26.2450i	0.719921	+	1.24694i	−0.241110	+	0.970498i	$0.577512\pi$
$444$		0			0
$445$	10.1310			0.480256
$446$		0			0
$447$	−8.71209			−0.412068
$448$		0			0
$449$	14.1124	+	24.4433i	0.666004	+	1.15355i	0.979012	+	0.203802i	$0.0653298\pi$
$449$	14.1124	+	24.4433i	0.666004	+	1.15355i	−0.313008	+	0.949750i	$0.601337\pi$
$450$		0			0
$451$	3.22510	−	5.58603i	0.151864	−	0.263036i
$452$		0			0
$453$	−11.4966	+	19.9127i	−0.540158	+	0.935582i
$454$		0			0
$455$	2.65251			0.124352
$456$		0			0
$457$	0.527111	+	0.912983i	0.0246572	+	0.0427076i	0.878091	−	0.478494i	$-0.158817\pi$
$457$	0.527111	+	0.912983i	0.0246572	+	0.0427076i	−0.853433	+	0.521202i	$0.825484\pi$
$458$		0			0
$459$	1.35601	−	2.34868i	0.0632933	−	0.109627i
$460$		0			0
$461$	−37.0052			−1.72350			−0.861751	−	0.507331i	$-0.830632\pi$
$461$	−37.0052			−1.72350			−0.861751	+	0.507331i	$0.830632\pi$
$462$		0			0
$463$	2.62376	−	4.54448i	0.121936	−	0.211200i	−0.798595	−	0.601869i	$-0.794423\pi$
$463$	2.62376	−	4.54448i	0.121936	−	0.211200i	0.920531	+	0.390669i	$0.127756\pi$
$464$		0			0
$465$	−5.11431	−	8.85825i	−0.237171	−	0.410791i
$466$		0			0
$467$	−15.8832	+	27.5106i	−0.734989	+	1.27304i	0.219740	+	0.975559i	$0.429479\pi$
$467$	−15.8832	+	27.5106i	−0.734989	+	1.27304i	−0.954728	+	0.297479i	$0.903854\pi$
$468$		0			0
$469$	8.90013	+	10.2213i	0.410970	+	0.471975i
$470$		0			0
$471$	−10.0754	+	17.4511i	−0.464251	+	0.804106i
$472$		0			0
$473$	−15.3784	−	26.6362i	−0.707100	−	1.22473i
$474$		0			0
$475$	−0.454704	+	0.787570i	−0.0208632	+	0.0361362i
$476$		0			0
$477$	−5.97455			−0.273556
$478$		0			0
$479$	−17.6079	+	30.4978i	−0.804527	+	1.39348i	0.112084	+	0.993699i	$0.464248\pi$
$479$	−17.6079	+	30.4978i	−0.804527	+	1.39348i	−0.916610	+	0.399782i	$0.869086\pi$
$480$		0			0
$481$	0.380452	+	0.658962i	0.0173471	+	0.0300461i
$482$		0			0
$483$	10.0091			0.455428
$484$		0			0
$485$	2.33139	−	4.03809i	0.105863	−	0.183360i
$486$		0			0
$487$	−0.935906	+	1.62104i	−0.0424100	+	0.0734562i	−0.886451	−	0.462822i	$-0.846837\pi$
$487$	−0.935906	+	1.62104i	−0.0424100	+	0.0734562i	0.844041	+	0.536278i	$0.180170\pi$
$488$		0			0
$489$	−4.52114	−	7.83085i	−0.204453	−	0.354123i
$490$		0			0
$491$	4.81111			0.217122			0.108561	−	0.994090i	$-0.465376\pi$
$491$	4.81111			0.217122			0.108561	+	0.994090i	$0.465376\pi$
$492$		0			0
$493$	7.30528			0.329013
$494$		0			0
$495$	−2.81310	−	4.87244i	−0.126440	−	0.219000i
$496$		0			0
$497$	−3.00759	+	5.20930i	−0.134909	+	0.233669i
$498$		0			0
$499$	2.88805	−	5.00226i	0.129287	−	0.223932i	−0.794114	−	0.607769i	$-0.792064\pi$
$499$	2.88805	−	5.00226i	0.129287	−	0.223932i	0.923401	+	0.383838i	$0.125398\pi$
$500$		0			0
$501$	−3.20616	−	5.55323i	−0.143241	−	0.248100i
$502$		0			0
$503$	−7.34561	−	12.7230i	−0.327525	−	0.567289i	0.654495	−	0.756066i	$-0.272881\pi$
$503$	−7.34561	−	12.7230i	−0.327525	−	0.567289i	−0.982020	+	0.188777i	$0.939548\pi$
$504$		0			0
$505$	−4.05606	−	7.02530i	−0.180492	−	0.312622i
$506$		0			0
$507$	−5.21684	−	9.03584i	−0.231688	−	0.401296i
$508$		0			0
$509$	−39.1868			−1.73692			−0.868462	−	0.495756i	$-0.834891\pi$
$509$	−39.1868			−1.73692			−0.868462	+	0.495756i	$0.834891\pi$
$510$		0			0
$511$	−2.48982			−0.110143
$512$		0			0
$513$	0.454704	−	0.787570i	0.0200757	−	0.0347721i
$514$		0			0
$515$	−0.101231	−	0.175338i	−0.00446078	−	0.00772630i
$516$		0			0
$517$	9.56083	−	16.5598i	0.420485	−	0.728301i
$518$		0			0
$519$	9.45972	−	16.3847i	0.415236	−	0.719209i
$520$		0			0
$521$	−15.0438			−0.659080			−0.329540	−	0.944142i	$-0.606894\pi$
$521$	−15.0438			−0.659080			−0.329540	+	0.944142i	$0.606894\pi$
$522$		0			0
$523$	−17.6705	+	30.6062i	−0.772677	+	1.33832i	0.163413	+	0.986558i	$0.447750\pi$
$523$	−17.6705	+	30.6062i	−0.772677	+	1.33832i	−0.936091	+	0.351759i	$0.885584\pi$
$524$		0			0
$525$	−0.827889	−	1.43395i	−0.0361320	−	0.0625825i
$526$		0			0
$527$	−27.7403			−1.20839
$528$		0			0
$529$	−6.77062	−	11.7271i	−0.294375	−	0.509872i
$530$		0			0
$531$	8.25736			0.358339
$532$		0			0
$533$	1.83659			0.0795515
$534$		0			0
$535$	−7.09586			−0.306781
$536$		0			0
$537$	−5.01635			−0.216471
$538$		0			0
$539$	−23.9586			−1.03197
$540$		0			0
$541$	6.01368			0.258548			0.129274	−	0.991609i	$-0.458735\pi$
$541$	6.01368			0.258548			0.129274	+	0.991609i	$0.458735\pi$
$542$		0			0
$543$	4.71426	+	8.16533i	0.202308	+	0.350408i
$544$		0			0
$545$	−9.42556			−0.403747
$546$		0			0
$547$	7.04360	+	12.1999i	0.301163	+	0.521629i	0.976400	−	0.215972i	$-0.0692920\pi$
$547$	7.04360	+	12.1999i	0.301163	+	0.521629i	−0.675237	+	0.737601i	$0.735959\pi$
$548$		0			0
$549$	5.07988	−	8.79861i	0.216804	−	0.375516i
$550$		0			0
$551$	2.44963			0.104358
$552$		0			0
$553$	−7.26225	+	12.5786i	−0.308822	+	0.534896i
$554$		0			0
$555$	0.237490	−	0.411344i	0.0100809	−	0.0174606i
$556$		0			0
$557$	−18.4614	−	31.9761i	−0.782235	−	1.35487i	−0.930637	−	0.365944i	$-0.880746\pi$
$557$	−18.4614	−	31.9761i	−0.782235	−	1.35487i	0.148401	−	0.988927i	$-0.452587\pi$
$558$		0			0
$559$	4.37876	−	7.58423i	0.185202	−	0.320779i
$560$		0			0
$561$	−15.2584			−0.644211
$562$		0			0
$563$	−19.4229			−0.818578			−0.409289	−	0.912405i	$-0.634223\pi$
$563$	−19.4229			−0.818578			−0.409289	+	0.912405i	$0.634223\pi$
$564$		0			0
$565$	5.20764	+	9.01990i	0.219087	+	0.379470i
$566$		0			0
$567$	0.827889	+	1.43395i	0.0347681	+	0.0602201i
$568$		0			0
$569$	5.90660	+	10.2305i	0.247617	+	0.428886i	0.962864	−	0.269986i	$-0.0870191\pi$
$569$	5.90660	+	10.2305i	0.247617	+	0.428886i	−0.715247	+	0.698872i	$0.753686\pi$
$570$		0			0
$571$	−10.0988	−	17.4916i	−0.422620	−	0.731999i	0.573575	−	0.819153i	$-0.305556\pi$
$571$	−10.0988	−	17.4916i	−0.422620	−	0.731999i	−0.996195	+	0.0871539i	$0.972223\pi$
$572$		0			0
$573$	−3.77371	+	6.53626i	−0.157649	+	0.273056i
$574$		0			0
$575$	−3.02247	+	5.23507i	−0.126046	+	0.218317i
$576$		0			0
$577$	−14.2372	−	24.6596i	−0.592703	−	1.02659i	−0.993867	−	0.110585i	$-0.964728\pi$
$577$	−14.2372	−	24.6596i	−0.592703	−	1.02659i	0.401164	−	0.916006i	$-0.368606\pi$
$578$		0			0
$579$	−9.80997			−0.407688
$580$		0			0
$581$	−19.7605			−0.819805
$582$		0			0
$583$	16.8070	+	29.1106i	0.696075	+	1.20564i
$584$		0			0
$585$	0.800986	−	1.38735i	0.0331167	−	0.0573598i
$586$		0			0
$587$	−8.22117	+	14.2395i	−0.339324	+	0.587726i	−0.984306	−	0.176472i	$-0.943532\pi$
$587$	−8.22117	+	14.2395i	−0.339324	+	0.587726i	0.644982	+	0.764198i	$0.276865\pi$
$588$		0			0
$589$	−9.30198			−0.383282
$590$		0			0
$591$	−7.16415	−	12.4087i	−0.294694	−	0.510425i
$592$		0			0
$593$	0.417897	−	0.723819i	0.0171610	−	0.0297237i	−0.857317	−	0.514788i	$-0.827871\pi$
$593$	0.417897	−	0.723819i	0.0171610	−	0.0297237i	0.874478	+	0.485065i	$0.161204\pi$
$594$		0			0
$595$	−4.49051			−0.184093
$596$		0			0
$597$	12.8696	−	22.2908i	0.526719	−	0.912304i
$598$		0			0
$599$	−13.8672	−	24.0187i	−0.566599	−	0.981378i	−0.996899	−	0.0786922i	$-0.974926\pi$
$599$	−13.8672	−	24.0187i	−0.566599	−	0.981378i	0.430300	−	0.902686i	$-0.358408\pi$
$600$		0			0
$601$	3.10975	−	5.38625i	0.126850	−	0.219710i	−0.795605	−	0.605816i	$-0.792847\pi$
$601$	3.10975	−	5.38625i	0.126850	−	0.219710i	0.922454	+	0.386106i	$0.126180\pi$
$602$		0			0
$603$	8.03367	−	1.56851i	0.327156	−	0.0638745i
$604$		0			0
$605$	−10.3271	+	17.8870i	−0.419856	+	0.727212i
$606$		0			0
$607$	18.3997	+	31.8692i	0.746822	+	1.29353i	0.949339	+	0.314254i	$0.101754\pi$
$607$	18.3997	+	31.8692i	0.746822	+	1.29353i	−0.202517	+	0.979279i	$0.564912\pi$
$608$		0			0
$609$	−2.23005	+	3.86256i	−0.0903663	+	0.156519i
$610$		0			0
$611$	5.44459			0.220264
$612$		0			0
$613$	−15.2977	+	26.4965i	−0.617870	+	1.07018i	0.372004	+	0.928231i	$0.378671\pi$
$613$	−15.2977	+	26.4965i	−0.617870	+	1.07018i	−0.989874	+	0.141951i	$0.954663\pi$
$614$		0			0
$615$	−0.573228	−	0.992859i	−0.0231148	−	0.0400360i
$616$		0			0
$617$	19.4967			0.784906			0.392453	−	0.919772i	$-0.371627\pi$
$617$	19.4967			0.784906			0.392453	+	0.919772i	$0.371627\pi$
$618$		0			0
$619$	6.62543	−	11.4756i	0.266298	−	0.461242i	−0.701605	−	0.712567i	$-0.747533\pi$
$619$	6.62543	−	11.4756i	0.266298	−	0.461242i	0.967903	+	0.251324i	$0.0808660\pi$
$620$		0			0
$621$	3.02247	−	5.23507i	0.121287	−	0.210076i
$622$		0			0
$623$	8.38736	+	14.5273i	0.336032	+	0.582025i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−5.11651			−0.204334
$628$		0			0
$629$	−0.644078	−	1.11558i	−0.0256811	−	0.0444809i
$630$		0			0
$631$	18.9734	−	32.8629i	0.755320	−	1.30825i	−0.189896	−	0.981804i	$-0.560815\pi$
$631$	18.9734	−	32.8629i	0.755320	−	1.30825i	0.945215	−	0.326448i	$-0.105852\pi$
$632$		0			0
$633$	12.5115	−	21.6706i	0.497289	−	0.861329i
$634$		0			0
$635$	8.57825	+	14.8580i	0.340417	+	0.589620i
$636$		0			0
$637$	−3.41092	−	5.90789i	−0.135146	−	0.234079i
$638$		0			0
$639$	1.81642	+	3.14614i	0.0718566	+	0.124459i
$640$		0			0
$641$	−17.2803	−	29.9304i	−0.682531	−	1.18218i	−0.974206	−	0.225660i	$-0.927546\pi$
$641$	−17.2803	−	29.9304i	−0.682531	−	1.18218i	0.291675	−	0.956517i	$-0.405787\pi$
$642$		0			0
$643$	−14.3668			−0.566570			−0.283285	−	0.959036i	$-0.591424\pi$
$643$	−14.3668			−0.566570			−0.283285	+	0.959036i	$0.591424\pi$
$644$		0			0
$645$	−5.46671			−0.215251
$646$		0			0
$647$	14.3641	−	24.8794i	0.564712	−	0.978110i	−0.432364	−	0.901699i	$-0.642321\pi$
$647$	14.3641	−	24.8794i	0.564712	−	0.978110i	0.997076	−	0.0764108i	$-0.0243461\pi$
$648$		0			0
$649$	−23.2288	−	40.2335i	−0.911811	−	1.57930i
$650$		0			0
$651$	8.46816	−	14.6673i	0.331894	−	0.574856i
$652$		0			0
$653$	3.76966	−	6.52924i	0.147518	−	0.255509i	−0.782791	−	0.622284i	$-0.786205\pi$
$653$	3.76966	−	6.52924i	0.147518	−	0.255509i	0.930310	+	0.366775i	$0.119538\pi$
$654$		0			0
$655$	−4.43412			−0.173255
$656$		0			0
$657$	−0.751860	+	1.30226i	−0.0293328	+	0.0508060i
$658$		0			0
$659$	8.82506	+	15.2854i	0.343775	+	0.595437i	0.985131	−	0.171808i	$-0.0549608\pi$
$659$	8.82506	+	15.2854i	0.343775	+	0.595437i	−0.641355	+	0.767244i	$0.721627\pi$
$660$		0			0
$661$	0.732720			0.0284995			0.0142498	−	0.999898i	$-0.495464\pi$
$661$	0.732720			0.0284995			0.0142498	+	0.999898i	$0.495464\pi$
$662$		0			0
$663$	−2.17230	−	3.76253i	−0.0843650	−	0.146124i
$664$		0			0
$665$	−1.50578			−0.0583915
$666$		0			0
$667$	16.2830			0.630480
$668$		0			0
$669$	−16.9045			−0.653565
$670$		0			0
$671$	−57.1609			−2.20667
$672$		0			0
$673$	44.2787			1.70682			0.853409	−	0.521242i	$-0.174531\pi$
$673$	44.2787			1.70682			0.853409	+	0.521242i	$0.174531\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−17.6334	−	30.5420i	−0.677708	−	1.17383i	−0.975669	−	0.219247i	$-0.929640\pi$
$677$	−17.6334	−	30.5420i	−0.677708	−	1.17383i	0.297961	−	0.954578i	$-0.403693\pi$
$678$		0			0
$679$	7.72054			0.296287
$680$		0			0
$681$	5.58831	+	9.67924i	0.214145	+	0.370909i
$682$		0			0
$683$	2.93772	−	5.08828i	0.112409	−	0.194698i	−0.804332	−	0.594180i	$-0.797477\pi$
$683$	2.93772	−	5.08828i	0.112409	−	0.194698i	0.916741	+	0.399482i	$0.130810\pi$
$684$		0			0
$685$	13.6451			0.521353
$686$		0			0
$687$	−7.62535	+	13.2075i	−0.290925	+	0.503897i
$688$		0			0
$689$	−4.78553	+	8.28878i	−0.182314	+	0.315777i
$690$		0			0
$691$	15.1951	+	26.3186i	0.578048	+	1.00121i	0.995703	+	0.0926028i	$0.0295187\pi$
$691$	15.1951	+	26.3186i	0.578048	+	1.00121i	−0.417655	+	0.908606i	$0.637148\pi$
$692$		0			0
$693$	4.65787	−	8.06767i	0.176938	−	0.306466i
$694$		0			0
$695$	3.07755			0.116738
$696$		0			0
$697$	−3.10922			−0.117770
$698$		0			0
$699$	1.94446	+	3.36790i	0.0735462	+	0.127386i
$700$		0			0
$701$	17.7302	+	30.7097i	0.669661	+	1.15989i	0.977999	+	0.208611i	$0.0668941\pi$
$701$	17.7302	+	30.7097i	0.669661	+	1.15989i	−0.308337	+	0.951277i	$0.599773\pi$
$702$		0			0
$703$	−0.215975	−	0.374079i	−0.00814564	−	0.0141087i
$704$		0			0
$705$	−1.69934	−	2.94334i	−0.0640008	−	0.110853i
$706$		0			0
$707$	6.71593	−	11.6323i	0.252578	−	0.437479i
$708$		0			0
$709$	−12.5341	+	21.7097i	−0.470727	+	0.815324i	−0.999439	−	0.0334774i	$-0.989342\pi$
$709$	−12.5341	+	21.7097i	−0.470727	+	0.815324i	0.528712	+	0.848801i	$0.322675\pi$
$710$		0			0
$711$	4.38601	+	7.59678i	0.164488	+	0.284902i
$712$		0			0
$713$	−61.8314			−2.31560
$714$		0			0
$715$	−9.01303			−0.337068
$716$		0			0
$717$	4.86697	+	8.42984i	0.181760	+	0.314818i
$718$		0			0
$719$	12.9619	−	22.4507i	0.483397	−	0.837269i	−0.516421	−	0.856335i	$-0.672736\pi$
$719$	12.9619	−	22.4507i	0.483397	−	0.837269i	0.999818	+	0.0190661i	$0.00606931\pi$
$720$		0			0
$721$	0.167616	−	0.290320i	0.00624236	−	0.0108121i
$722$		0			0
$723$	−18.8478			−0.700958
$724$		0			0
$725$	−1.34683	−	2.33278i	−0.0500200	−	0.0866372i
$726$		0			0
$727$	19.5361	−	33.8375i	0.724555	−	1.25497i	−0.234603	−	0.972091i	$-0.575379\pi$
$727$	19.5361	−	33.8375i	0.724555	−	1.25497i	0.959157	−	0.282874i	$-0.0912878\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−7.41293	+	12.8396i	−0.274177	+	0.474889i
$732$		0			0
$733$	4.97287	+	8.61326i	0.183677	+	0.318138i	0.943130	−	0.332424i	$-0.107867\pi$
$733$	4.97287	+	8.61326i	0.183677	+	0.318138i	−0.759453	+	0.650562i	$0.774533\pi$
$734$		0			0
$735$	−2.12920	+	3.68788i	−0.0785367	+	0.136030i
$736$		0			0
$737$	−30.2420	−	34.7312i	−1.11398	−	1.27934i
$738$		0			0
$739$	18.5996	−	32.2155i	0.684197	−	1.18506i	−0.289491	−	0.957181i	$-0.593486\pi$
$739$	18.5996	−	32.2155i	0.684197	−	1.18506i	0.973688	−	0.227884i	$-0.0731807\pi$
$740$		0			0
$741$	−0.728423	−	1.26167i	−0.0267593	−	0.0463484i
$742$		0			0
$743$	4.37068	−	7.57024i	0.160345	−	0.277725i	−0.774648	−	0.632393i	$-0.782073\pi$
$743$	4.37068	−	7.57024i	0.160345	−	0.277725i	0.934992	+	0.354668i	$0.115406\pi$
$744$		0			0
$745$	8.71209			0.319186
$746$		0			0
$747$	−5.96714	+	10.3354i	−0.218326	+	0.378152i
$748$		0			0
$749$	−5.87458	−	10.1751i	−0.214653	−	0.371789i
$750$		0			0
$751$	−44.5269			−1.62481			−0.812405	−	0.583094i	$-0.801842\pi$
$751$	−44.5269			−1.62481			−0.812405	+	0.583094i	$0.801842\pi$
$752$		0			0
$753$	−2.50889	+	4.34552i	−0.0914290	+	0.158360i
$754$		0			0
$755$	11.4966	−	19.9127i	0.418405	−	0.724699i
$756$		0			0
$757$	−20.1417	−	34.8865i	−0.732064	−	1.26797i	−0.956000	−	0.293368i	$-0.905224\pi$
$757$	−20.1417	−	34.8865i	−0.732064	−	1.26797i	0.223936	−	0.974604i	$-0.428109\pi$
$758$		0			0
$759$	−34.0100			−1.23449
$760$		0			0
$761$	−20.5812			−0.746068			−0.373034	−	0.927818i	$-0.621682\pi$
$761$	−20.5812			−0.746068			−0.373034	+	0.927818i	$0.621682\pi$
$762$		0			0
$763$	−7.80331	−	13.5157i	−0.282499	−	0.489303i
$764$		0			0
$765$	−1.35601	+	2.34868i	−0.0490268	+	0.0849169i
$766$		0			0
$767$	6.61403	−	11.4558i	0.238819	−	0.413647i
$768$		0			0
$769$	0.892739	+	1.54627i	0.0321930	+	0.0557599i	0.881673	−	0.471861i	$-0.156418\pi$
$769$	0.892739	+	1.54627i	0.0321930	+	0.0557599i	−0.849480	+	0.527621i	$0.823084\pi$
$770$		0			0
$771$	0.989493	+	1.71385i	0.0356357	+	0.0617229i
$772$		0			0
$773$	−1.82765	−	3.16558i	−0.0657359	−	0.113858i	0.831284	−	0.555848i	$-0.187606\pi$
$773$	−1.82765	−	3.16558i	−0.0657359	−	0.113858i	−0.897020	+	0.441990i	$0.854273\pi$
$774$		0			0
$775$	5.11431	+	8.85825i	0.183712	+	0.318198i
$776$		0			0
$777$	0.786460			0.0282141
$778$		0			0
$779$	−1.04259			−0.0373548
$780$		0			0
$781$	10.2196	−	17.7008i	0.365685	−	0.633385i
$782$		0			0
$783$	1.34683	+	2.33278i	0.0481318	+	0.0833667i
$784$		0			0
$785$	10.0754	−	17.4511i	0.359607	−	0.622858i
$786$		0			0
$787$	−9.99119	+	17.3053i	−0.356148	+	0.616866i	−0.987314	−	0.158782i	$-0.949243\pi$
$787$	−9.99119	+	17.3053i	−0.356148	+	0.616866i	0.631166	+	0.775648i	$0.282577\pi$
$788$		0			0
$789$	−6.03457			−0.214836
$790$		0			0
$791$	−8.62269	+	14.9349i	−0.306588	+	0.531025i
$792$		0			0
$793$	−8.13783	−	14.0951i	−0.288983	−	0.500533i
$794$		0			0
$795$	5.97455			0.211895
$796$		0			0
$797$	−6.17916	−	10.7026i	−0.218877	−	0.379106i	0.735588	−	0.677429i	$-0.236906\pi$
$797$	−6.17916	−	10.7026i	−0.218877	−	0.379106i	−0.954465	+	0.298323i	$0.903573\pi$
$798$		0			0
$799$	−9.21730			−0.326085
$800$		0			0
$801$	10.1310			0.357962
$802$		0			0
$803$	8.46023			0.298555
$804$		0			0
$805$	−10.0091			−0.352773
$806$		0			0
$807$	−22.0260			−0.775351
$808$		0			0
$809$	8.09959			0.284767			0.142383	−	0.989812i	$-0.454523\pi$
$809$	8.09959			0.284767			0.142383	+	0.989812i	$0.454523\pi$
$810$		0			0
$811$	−4.32560	−	7.49215i	−0.151892	−	0.263085i	0.780031	−	0.625741i	$-0.215203\pi$
$811$	−4.32560	−	7.49215i	−0.151892	−	0.263085i	−0.931923	+	0.362656i	$0.881870\pi$
$812$		0			0
$813$	16.3255			0.572561
$814$		0			0
$815$	4.52114	+	7.83085i	0.158369	+	0.274303i
$816$		0			0
$817$	−2.48573	+	4.30541i	−0.0869648	+	0.150627i
$818$		0			0
$819$	2.65251			0.0926862
$820$		0			0
$821$	13.2168	−	22.8921i	0.461268	−	0.798940i	−0.537756	−	0.843100i	$-0.680728\pi$
$821$	13.2168	−	22.8921i	0.461268	−	0.798940i	0.999024	+	0.0441607i	$0.0140614\pi$
$822$		0			0
$823$	−2.33192	+	4.03900i	−0.0812855	+	0.140791i	−0.903802	−	0.427950i	$-0.859236\pi$
$823$	−2.33192	+	4.03900i	−0.0812855	+	0.140791i	0.822517	+	0.568741i	$0.192569\pi$
$824$		0			0
$825$	2.81310	+	4.87244i	0.0979397	+	0.169636i
$826$		0			0
$827$	16.6353	−	28.8133i	0.578468	−	1.00194i	−0.417188	−	0.908820i	$-0.636984\pi$
$827$	16.6353	−	28.8133i	0.578468	−	1.00194i	0.995655	−	0.0931149i	$-0.0296824\pi$
$828$		0			0
$829$	6.92652			0.240568			0.120284	−	0.992740i	$-0.461619\pi$
$829$	6.92652			0.240568			0.120284	+	0.992740i	$0.461619\pi$
$830$		0			0
$831$	21.6875			0.752330
$832$		0			0
$833$	5.77445	+	10.0016i	0.200073	+	0.346536i
$834$		0			0
$835$	3.20616	+	5.55323i	0.110954	+	0.192177i
$836$		0			0
$837$	−5.11431	−	8.85825i	−0.176776	−	0.306186i
$838$		0			0
$839$	−1.78860	−	3.09795i	−0.0617495	−	0.106953i	0.833498	−	0.552522i	$-0.186335\pi$
$839$	−1.78860	−	3.09795i	−0.0617495	−	0.106953i	−0.895247	+	0.445569i	$0.853001\pi$
$840$		0			0
$841$	10.8721	−	18.8310i	0.374900	−	0.649346i
$842$		0			0
$843$	11.1094	−	19.2421i	0.382629	−	0.662733i
$844$		0			0
$845$	5.21684	+	9.03584i	0.179465	+	0.310842i
$846$		0			0
$847$	−34.1987			−1.17508
$848$		0			0
$849$	−18.8268			−0.646134
$850$		0			0
$851$	−1.43561	−	2.48655i	−0.0492120	−	0.0852377i
$852$		0			0
$853$	2.55867	−	4.43174i	0.0876071	−	0.151740i	−0.818892	−	0.573948i	$-0.805411\pi$
$853$	2.55867	−	4.43174i	0.0876071	−	0.151740i	0.906499	+	0.422208i	$0.138745\pi$
$854$		0			0
$855$	−0.454704	+	0.787570i	−0.0155505	+	0.0269343i
$856$		0			0
$857$	−40.2584			−1.37520			−0.687600	−	0.726090i	$-0.741336\pi$
$857$	−40.2584			−1.37520			−0.687600	+	0.726090i	$0.741336\pi$
$858$		0			0
$859$	18.2959	+	31.6894i	0.624247	+	1.08123i	0.988686	+	0.150001i	$0.0479277\pi$
$859$	18.2959	+	31.6894i	0.624247	+	1.08123i	−0.364438	+	0.931228i	$0.618739\pi$
$860$		0			0
$861$	0.949138	−	1.64395i	0.0323465	−	0.0560258i
$862$		0			0
$863$	9.16219			0.311885			0.155942	−	0.987766i	$-0.450159\pi$
$863$	9.16219			0.311885			0.155942	+	0.987766i	$0.450159\pi$
$864$		0			0
$865$	−9.45972	+	16.3847i	−0.321640	+	0.557097i
$866$		0			0
$867$	−4.82245	−	8.35274i	−0.163779	−	0.283674i
$868$		0			0
$869$	24.6766	−	42.7411i	0.837095	−	1.44989i
$870$		0			0
$871$	4.25879	−	12.4018i	0.144304	−	0.420221i
$872$		0			0
$873$	2.33139	−	4.03809i	0.0789057	−	0.136669i
$874$		0			0
$875$	0.827889	+	1.43395i	0.0279878	+	0.0484762i
$876$		0			0
$877$	5.46422	−	9.46430i	0.184513	−	0.319587i	−0.758899	−	0.651208i	$-0.774262\pi$
$877$	5.46422	−	9.46430i	0.184513	−	0.319587i	0.943412	+	0.331622i	$0.107596\pi$
$878$		0			0
$879$	−31.2928			−1.05548
$880$		0			0
$881$	12.0875	−	20.9362i	0.407238	−	0.705357i	−0.587341	−	0.809339i	$-0.699825\pi$
$881$	12.0875	−	20.9362i	0.407238	−	0.705357i	0.994579	+	0.103983i	$0.0331586\pi$
$882$		0			0
$883$	−2.54851	−	4.41415i	−0.0857642	−	0.148548i	0.819952	−	0.572432i	$-0.194000\pi$
$883$	−2.54851	−	4.41415i	−0.0857642	−	0.148548i	−0.905717	+	0.423884i	$0.860667\pi$
$884$		0			0
$885$	−8.25736			−0.277568
$886$		0			0
$887$	−15.0295	+	26.0319i	−0.504642	+	0.874065i	0.495344	+	0.868697i	$0.335042\pi$
$887$	−15.0295	+	26.0319i	−0.504642	+	0.874065i	−0.999986	+	0.00536822i	$0.998291\pi$
$888$		0			0
$889$	−14.2037	+	24.6015i	−0.476376	+	0.825107i
$890$		0			0
$891$	−2.81310	−	4.87244i	−0.0942425	−	0.163233i
$892$		0			0
$893$	−3.09078			−0.103429
$894$		0			0
$895$	5.01635			0.167678
$896$		0			0
$897$	−4.84191	−	8.38643i	−0.161667	−	0.280015i
$898$		0			0
$899$	13.7762	−	23.8611i	0.459463	−	0.795813i
$900$		0			0
$901$	8.10157	−	14.0323i	0.269902	−	0.467485i
$902$		0			0
$903$	−4.52583	−	7.83896i	−0.150610	−	0.260864i
$904$		0			0
$905$	−4.71426	−	8.16533i	−0.156707	−	0.271425i
$906$		0			0
$907$	2.80223	+	4.85361i	0.0930466	+	0.161161i	0.908792	−	0.417250i	$-0.137006\pi$
$907$	2.80223	+	4.85361i	0.0930466	+	0.161161i	−0.815745	+	0.578412i	$0.803673\pi$
$908$		0			0
$909$	−4.05606	−	7.02530i	−0.134531	−	0.233014i
$910$		0			0
$911$	−19.8524			−0.657740			−0.328870	−	0.944375i	$-0.606668\pi$
$911$	−19.8524			−0.657740			−0.328870	+	0.944375i	$0.606668\pi$
$912$		0			0
$913$	67.1448			2.22217
$914$		0			0
$915$	−5.07988	+	8.79861i	−0.167936	+	0.290873i
$916$		0			0
$917$	−3.67096	−	6.35828i	−0.121226	−	0.209969i
$918$		0			0
$919$	−6.59944	+	11.4306i	−0.217695	+	0.377060i	−0.954103	−	0.299479i	$-0.903187\pi$
$919$	−6.59944	+	11.4306i	−0.217695	+	0.377060i	0.736408	+	0.676538i	$0.236521\pi$
$920$		0			0
$921$	1.74426	−	3.02115i	0.0574754	−	0.0995503i
$922$		0			0
$923$	5.81972			0.191558
$924$		0			0
$925$	−0.237490	+	0.411344i	−0.00780861	+	0.0135249i
$926$		0			0
$927$	−0.101231	−	0.175338i	−0.00332487	−	0.00575884i
$928$		0			0
$929$	−27.7574			−0.910690			−0.455345	−	0.890315i	$-0.650484\pi$
$929$	−27.7574			−0.910690			−0.455345	+	0.890315i	$0.650484\pi$
$930$		0			0
$931$	1.93631	+	3.35379i	0.0634600	+	0.109916i
$932$		0			0
$933$	14.1487			0.463208
$934$		0			0
$935$	15.2584			0.499004
$936$		0			0
$937$	14.5093			0.474000			0.237000	−	0.971510i	$-0.423836\pi$
$937$	14.5093			0.474000			0.237000	+	0.971510i	$0.423836\pi$
$938$		0			0
$939$	−11.0740			−0.361387
$940$		0			0
$941$	55.2412			1.80081			0.900406	−	0.435051i	$-0.143270\pi$
$941$	55.2412			1.80081			0.900406	+	0.435051i	$0.143270\pi$
$942$		0			0
$943$	−6.93025			−0.225680
$944$		0			0
$945$	−0.827889	−	1.43395i	−0.0269312	−	0.0466463i
$946$		0			0
$947$	21.4760			0.697876			0.348938	−	0.937146i	$-0.386542\pi$
$947$	21.4760			0.697876			0.348938	+	0.937146i	$0.386542\pi$
$948$		0			0
$949$	1.20446	+	2.08618i	0.0390984	+	0.0677204i
$950$		0			0
$951$	−14.1965	+	24.5890i	−0.460352	+	0.797353i
$952$		0			0
$953$	−1.20463			−0.0390219			−0.0195110	−	0.999810i	$-0.506211\pi$
$953$	−1.20463			−0.0390219			−0.0195110	+	0.999810i	$0.506211\pi$
$954$		0			0
$955$	3.77371	−	6.53626i	0.122114	−	0.211508i
$956$		0			0
$957$	7.57754	−	13.1247i	0.244947	−	0.424261i
$958$		0			0
$959$	11.2966	+	19.5663i	0.364787	+	0.631830i
$960$		0			0
$961$	−36.8124	+	63.7609i	−1.18750	+	2.05680i
$962$		0			0
$963$	−7.09586			−0.228661
$964$		0			0
$965$	9.80997			0.315794
$966$		0			0
$967$	−6.92337	−	11.9916i	−0.222641	−	0.385625i	0.732968	−	0.680263i	$-0.238134\pi$
$967$	−6.92337	−	11.9916i	−0.222641	−	0.385625i	−0.955609	+	0.294638i	$0.904801\pi$
$968$		0			0
$969$	1.23317	+	2.13591i	0.0396151	+	0.0686153i
$970$		0			0
$971$	4.56739	+	7.91096i	0.146575	+	0.253875i	0.929959	−	0.367662i	$-0.119842\pi$
$971$	4.56739	+	7.91096i	0.146575	+	0.253875i	−0.783385	+	0.621537i	$0.786508\pi$
$972$		0			0
$973$	2.54787	+	4.41304i	0.0816810	+	0.141476i
$974$		0			0
$975$	−0.800986	+	1.38735i	−0.0256521	+	0.0444307i
$976$		0			0
$977$	−2.73407	+	4.73556i	−0.0874708	+	0.151504i	−0.906441	−	0.422332i	$-0.861212\pi$
$977$	−2.73407	+	4.73556i	−0.0874708	+	0.151504i	0.818971	+	0.573835i	$0.194545\pi$
$978$		0			0
$979$	−28.4996	−	49.3627i	−0.910851	−	1.57764i
$980$		0			0
$981$	−9.42556			−0.300935
$982$		0			0
$983$	12.5261			0.399522			0.199761	−	0.979845i	$-0.435983\pi$
$983$	12.5261			0.399522			0.199761	+	0.979845i	$0.435983\pi$
$984$		0			0
$985$	7.16415	+	12.4087i	0.228269	+	0.395373i
$986$		0			0
$987$	2.81373	−	4.87352i	0.0895619	−	0.155126i
$988$		0			0
$989$	−16.5229	+	28.6186i	−0.525399	+	0.910018i
$990$		0			0
$991$	−7.90849			−0.251222			−0.125611	−	0.992080i	$-0.540089\pi$
$991$	−7.90849			−0.251222			−0.125611	+	0.992080i	$0.540089\pi$
$992$		0			0
$993$	12.0830	+	20.9283i	0.383441	+	0.664140i
$994$		0			0
$995$	−12.8696	+	22.2908i	−0.407995	+	0.706667i
$996$		0			0
$997$	−44.8026			−1.41891			−0.709456	−	0.704750i	$-0.751059\pi$
$997$	−44.8026			−1.41891			−0.709456	+	0.704750i	$0.751059\pi$
$998$		0			0
$999$	0.237490	−	0.411344i	0.00751384	−	0.0130143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.3781.4	yes	14
67.37	even	3	inner	4020.2.q.k.841.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.4	✓	14	67.37	even	3	inner
4020.2.q.k.3781.4	yes	14	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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(0.827889 + 1.43395i) q^{7} +1.00000 q^{9} +(-2.81310 - 4.87244i) q^{11} +(0.800986 - 1.38735i) q^{13} -1.00000 q^{15} +(-1.35601 + 2.34868i) q^{17} +(-0.454704 + 0.787570i) q^{19} +(-0.827889 - 1.43395i) q^{21} +(-3.02247 + 5.23507i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.34683 - 2.33278i) q^{29} +(5.11431 + 8.85825i) q^{31} +(2.81310 + 4.87244i) q^{33} +(0.827889 + 1.43395i) q^{35} +(-0.237490 + 0.411344i) q^{37} +(-0.800986 + 1.38735i) q^{39} +(0.573228 + 0.992859i) q^{41} +5.46671 q^{43} +1.00000 q^{45} +(1.69934 + 2.94334i) q^{47} +(2.12920 - 3.68788i) q^{49} +(1.35601 - 2.34868i) q^{51} -5.97455 q^{53} +(-2.81310 - 4.87244i) q^{55} +(0.454704 - 0.787570i) q^{57} +8.25736 q^{59} +(5.07988 - 8.79861i) q^{61} +(0.827889 + 1.43395i) q^{63} +(0.800986 - 1.38735i) q^{65} +(8.03367 - 1.56851i) q^{67} +(3.02247 - 5.23507i) q^{69} +(1.81642 + 3.14614i) q^{71} +(-0.751860 + 1.30226i) q^{73} -1.00000 q^{75} +(4.65787 - 8.06767i) q^{77} +(4.38601 + 7.59678i) q^{79} +1.00000 q^{81} +(-5.96714 + 10.3354i) q^{83} +(-1.35601 + 2.34868i) q^{85} +(1.34683 + 2.33278i) q^{87} +10.1310 q^{89} +2.65251 q^{91} +(-5.11431 - 8.85825i) q^{93} +(-0.454704 + 0.787570i) q^{95} +(2.33139 - 4.03809i) q^{97} +(-2.81310 - 4.87244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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