LMFDB - Embedded newform 4020.2.q.j.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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 $ x^12 - x^11 + 30x^10 - 53x^9 + 798x^8 - 1096x^7 + 4060x^6 - 915x^5 + 10392x^4 - 7038x^3 + 4869x^2 - 675x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.4
Root			$-0.818190 - 1.41715i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.j.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(1.22030 + 2.11362i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(1.22030 + 2.11362i) q^{7} +1.00000 q^{9} +(-1.39089 - 2.40909i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(3.87422 - 6.71035i) q^{17} +(-3.64240 + 6.30882i) q^{19} +(1.22030 + 2.11362i) q^{21} +(0.334853 - 0.579982i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-4.34001 - 7.51712i) q^{29} +(2.47181 + 4.28129i) q^{31} +(-1.39089 - 2.40909i) q^{33} +(-1.22030 - 2.11362i) q^{35} +(4.86878 - 8.43298i) q^{37} +(0.500000 - 0.866025i) q^{39} +(-2.30666 - 3.99525i) q^{41} +4.28479 q^{43} -1.00000 q^{45} +(2.96028 + 5.12735i) q^{47} +(0.521754 - 0.903704i) q^{49} +(3.87422 - 6.71035i) q^{51} +3.94361 q^{53} +(1.39089 + 2.40909i) q^{55} +(-3.64240 + 6.30882i) q^{57} -0.583616 q^{59} +(0.949983 - 1.64542i) q^{61} +(1.22030 + 2.11362i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(3.58812 + 7.35700i) q^{67} +(0.334853 - 0.579982i) q^{69} +(-1.74756 - 3.02687i) q^{71} +(2.24155 - 3.88247i) q^{73} +1.00000 q^{75} +(3.39459 - 5.87960i) q^{77} +(-2.89911 - 5.02141i) q^{79} +1.00000 q^{81} +(4.02703 - 6.97501i) q^{83} +(-3.87422 + 6.71035i) q^{85} +(-4.34001 - 7.51712i) q^{87} +0.596874 q^{89} +2.44059 q^{91} +(2.47181 + 4.28129i) q^{93} +(3.64240 - 6.30882i) q^{95} +(0.689324 - 1.19394i) q^{97} +(-1.39089 - 2.40909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * 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
$7$	1.22030	+	2.11362i	0.461229	+	0.798871i	0.999022	−	0.0442049i	$-0.0140755\pi$
$7$	1.22030	+	2.11362i	0.461229	+	0.798871i	−0.537794	+	0.843076i	$0.680742\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.39089	−	2.40909i	−0.419368	−	0.726367i	0.576508	−	0.817092i	$-0.304415\pi$
$11$	−1.39089	−	2.40909i	−0.419368	−	0.726367i	−0.995876	+	0.0907246i	$0.971082\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.87422	−	6.71035i	0.939637	−	1.62750i	0.173489	−	0.984836i	$-0.444496\pi$
$17$	3.87422	−	6.71035i	0.939637	−	1.62750i	0.766148	−	0.642664i	$-0.222171\pi$
$18$		0			0
$19$	−3.64240	+	6.30882i	−0.835623	+	1.44734i	0.0578987	+	0.998322i	$0.481560\pi$
$19$	−3.64240	+	6.30882i	−0.835623	+	1.44734i	−0.893522	+	0.449019i	$0.851773\pi$
$20$		0			0
$21$	1.22030	+	2.11362i	0.266290	+	0.461229i
$22$		0			0
$23$	0.334853	−	0.579982i	0.0698216	−	0.120935i	−0.829001	−	0.559247i	$-0.811090\pi$
$23$	0.334853	−	0.579982i	0.0698216	−	0.120935i	0.898823	+	0.438312i	$0.144424\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−4.34001	−	7.51712i	−0.805920	−	1.39589i	−0.915668	−	0.401935i	$-0.868338\pi$
$29$	−4.34001	−	7.51712i	−0.805920	−	1.39589i	0.109748	−	0.993959i	$-0.464996\pi$
$30$		0			0
$31$	2.47181	+	4.28129i	0.443950	+	0.768943i	0.997978	−	0.0635543i	$-0.0202436\pi$
$31$	2.47181	+	4.28129i	0.443950	+	0.768943i	−0.554029	+	0.832498i	$0.686910\pi$
$32$		0			0
$33$	−1.39089	−	2.40909i	−0.242122	−	0.419368i
$34$		0			0
$35$	−1.22030	−	2.11362i	−0.206268	−	0.357266i
$36$		0			0
$37$	4.86878	−	8.43298i	0.800423	−	1.38637i	−0.118916	−	0.992904i	$-0.537942\pi$
$37$	4.86878	−	8.43298i	0.800423	−	1.38637i	0.919338	−	0.393468i	$-0.128725\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	−2.30666	−	3.99525i	−0.360240	−	0.623953i	0.627760	−	0.778407i	$-0.283972\pi$
$41$	−2.30666	−	3.99525i	−0.360240	−	0.623953i	−0.988000	+	0.154453i	$0.950638\pi$
$42$		0			0
$43$	4.28479			0.653425			0.326713	−	0.945124i	$-0.394059\pi$
$43$	4.28479			0.653425			0.326713	+	0.945124i	$0.394059\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	2.96028	+	5.12735i	0.431801	+	0.747901i	0.997028	−	0.0770342i	$-0.0245451\pi$
$47$	2.96028	+	5.12735i	0.431801	+	0.747901i	−0.565228	+	0.824935i	$0.691212\pi$
$48$		0			0
$49$	0.521754	−	0.903704i	0.0745363	−	0.129101i
$50$		0			0
$51$	3.87422	−	6.71035i	0.542500	−	0.939637i
$52$		0			0
$53$	3.94361			0.541697			0.270848	−	0.962622i	$-0.412696\pi$
$53$	3.94361			0.541697			0.270848	+	0.962622i	$0.412696\pi$
$54$		0			0
$55$	1.39089	+	2.40909i	0.187547	+	0.324841i
$56$		0			0
$57$	−3.64240	+	6.30882i	−0.482447	+	0.835623i
$58$		0			0
$59$	−0.583616			−0.0759804			−0.0379902	−	0.999278i	$-0.512096\pi$
$59$	−0.583616			−0.0759804			−0.0379902	+	0.999278i	$0.512096\pi$
$60$		0			0
$61$	0.949983	−	1.64542i	0.121633	−	0.210674i	−0.798779	−	0.601625i	$-0.794520\pi$
$61$	0.949983	−	1.64542i	0.121633	−	0.210674i	0.920412	+	0.390950i	$0.127854\pi$
$62$		0			0
$63$	1.22030	+	2.11362i	0.153743	+	0.266290i
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	3.58812	+	7.35700i	0.438359	+	0.898800i
$67$	3.58812	+	7.35700i	0.438359	+	0.898800i
$68$		0			0
$69$	0.334853	−	0.579982i	0.0403115	−	0.0698216i
$70$		0			0
$71$	−1.74756	−	3.02687i	−0.207398	−	0.359223i	0.743496	−	0.668740i	$-0.233166\pi$
$71$	−1.74756	−	3.02687i	−0.207398	−	0.359223i	−0.950894	+	0.309517i	$0.899833\pi$
$72$		0			0
$73$	2.24155	−	3.88247i	0.262353	−	0.454409i	−0.704514	−	0.709690i	$-0.748835\pi$
$73$	2.24155	−	3.88247i	0.262353	−	0.454409i	0.966867	+	0.255282i	$0.0821682\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	3.39459	−	5.87960i	0.386849	−	0.670043i
$78$		0			0
$79$	−2.89911	−	5.02141i	−0.326175	−	0.564952i	0.655574	−	0.755131i	$-0.272427\pi$
$79$	−2.89911	−	5.02141i	−0.326175	−	0.564952i	−0.981750	+	0.190179i	$0.939093\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	4.02703	−	6.97501i	0.442023	−	0.765607i	−0.555816	−	0.831305i	$-0.687594\pi$
$83$	4.02703	−	6.97501i	0.442023	−	0.765607i	0.997840	+	0.0656982i	$0.0209275\pi$
$84$		0			0
$85$	−3.87422	+	6.71035i	−0.420219	+	0.727840i
$86$		0			0
$87$	−4.34001	−	7.51712i	−0.465298	−	0.805920i
$88$		0			0
$89$	0.596874			0.0632685			0.0316342	−	0.999500i	$-0.489929\pi$
$89$	0.596874			0.0632685			0.0316342	+	0.999500i	$0.489929\pi$
$90$		0			0
$91$	2.44059			0.255844
$92$		0			0
$93$	2.47181	+	4.28129i	0.256314	+	0.443950i
$94$		0			0
$95$	3.64240	−	6.30882i	0.373702	−	0.647271i
$96$		0			0
$97$	0.689324	−	1.19394i	0.0699902	−	0.121227i	−0.828907	−	0.559387i	$-0.811037\pi$
$97$	0.689324	−	1.19394i	0.0699902	−	0.121227i	0.898897	+	0.438161i	$0.144370\pi$
$98$		0			0
$99$	−1.39089	−	2.40909i	−0.139789	−	0.242122i
$100$		0			0
$101$	1.79513	+	3.10925i	0.178622	+	0.309382i	0.941409	−	0.337268i	$-0.109503\pi$
$101$	1.79513	+	3.10925i	0.178622	+	0.309382i	−0.762787	+	0.646650i	$0.776169\pi$
$102$		0			0
$103$	−5.89146	−	10.2043i	−0.580503	−	1.00546i	−0.995420	−	0.0956012i	$-0.969523\pi$
$103$	−5.89146	−	10.2043i	−0.580503	−	1.00546i	0.414917	−	0.909859i	$-0.363811\pi$
$104$		0			0
$105$	−1.22030	−	2.11362i	−0.119089	−	0.206268i
$106$		0			0
$107$	2.20720			0.213378			0.106689	−	0.994292i	$-0.465975\pi$
$107$	2.20720			0.213378			0.106689	+	0.994292i	$0.465975\pi$
$108$		0			0
$109$	−14.5691			−1.39547			−0.697734	−	0.716357i	$-0.745808\pi$
$109$	−14.5691			−1.39547			−0.697734	+	0.716357i	$0.745808\pi$
$110$		0			0
$111$	4.86878	−	8.43298i	0.462124	−	0.800423i
$112$		0			0
$113$	3.47181	+	6.01335i	0.326600	+	0.565688i	0.981835	−	0.189737i	$-0.0607636\pi$
$113$	3.47181	+	6.01335i	0.326600	+	0.565688i	−0.655235	+	0.755425i	$0.727430\pi$
$114$		0			0
$115$	−0.334853	+	0.579982i	−0.0312252	+	0.0540836i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	18.9108			1.73355
$120$		0			0
$121$	1.63087	−	2.82474i	0.148261	−	0.256795i
$122$		0			0
$123$	−2.30666	−	3.99525i	−0.207984	−	0.360240i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.83179	+	4.90481i	0.251281	+	0.435231i	0.963879	−	0.266342i	$-0.0858149\pi$
$127$	2.83179	+	4.90481i	0.251281	+	0.435231i	−0.712598	+	0.701573i	$0.752482\pi$
$128$		0			0
$129$	4.28479			0.377255
$130$		0			0
$131$	3.69628			0.322946			0.161473	−	0.986877i	$-0.448376\pi$
$131$	3.69628			0.322946			0.161473	+	0.986877i	$0.448376\pi$
$132$		0			0
$133$	−17.7792			−1.54165
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	16.7025			1.42699			0.713494	−	0.700661i	$-0.247112\pi$
$137$	16.7025			1.42699			0.713494	+	0.700661i	$0.247112\pi$
$138$		0			0
$139$	15.7732			1.33786			0.668932	−	0.743324i	$-0.266752\pi$
$139$	15.7732			1.33786			0.668932	+	0.743324i	$0.266752\pi$
$140$		0			0
$141$	2.96028	+	5.12735i	0.249300	+	0.431801i
$142$		0			0
$143$	−2.78177			−0.232624
$144$		0			0
$145$	4.34001	+	7.51712i	0.360418	+	0.624263i
$146$		0			0
$147$	0.521754	−	0.903704i	0.0430335	−	0.0745363i
$148$		0			0
$149$	22.6059			1.85194			0.925972	−	0.377591i	$-0.123248\pi$
$149$	22.6059			1.85194			0.925972	+	0.377591i	$0.123248\pi$
$150$		0			0
$151$	−11.9860	+	20.7603i	−0.975405	+	1.68945i	−0.296814	+	0.954935i	$0.595924\pi$
$151$	−11.9860	+	20.7603i	−0.975405	+	1.68945i	−0.678591	+	0.734516i	$0.737409\pi$
$152$		0			0
$153$	3.87422	−	6.71035i	0.313212	−	0.542500i
$154$		0			0
$155$	−2.47181	−	4.28129i	−0.198540	−	0.343882i
$156$		0			0
$157$	10.2026	−	17.6715i	0.814259	−	1.41034i	−0.0955996	−	0.995420i	$-0.530477\pi$
$157$	10.2026	−	17.6715i	0.814259	−	1.41034i	0.909859	−	0.414918i	$-0.136190\pi$
$158$		0			0
$159$	3.94361			0.312749
$160$		0			0
$161$	1.63448			0.128815
$162$		0			0
$163$	−6.34522	−	10.9902i	−0.496996	−	0.860822i	0.502998	−	0.864287i	$-0.332230\pi$
$163$	−6.34522	−	10.9902i	−0.496996	−	0.860822i	−0.999994	+	0.00346570i	$0.998897\pi$
$164$		0			0
$165$	1.39089	+	2.40909i	0.108280	+	0.187547i
$166$		0			0
$167$	11.5026	+	19.9231i	0.890098	+	1.54170i	0.839757	+	0.542963i	$0.182698\pi$
$167$	11.5026	+	19.9231i	0.890098	+	1.54170i	0.0503416	+	0.998732i	$0.483969\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−3.64240	+	6.30882i	−0.278541	+	0.482447i
$172$		0			0
$173$	−0.0548381	+	0.0949824i	−0.00416927	+	0.00722138i	−0.868103	−	0.496385i	$-0.834660\pi$
$173$	−0.0548381	+	0.0949824i	−0.00416927	+	0.00722138i	0.863933	+	0.503606i	$0.167994\pi$
$174$		0			0
$175$	1.22030	+	2.11362i	0.0922457	+	0.159774i
$176$		0			0
$177$	−0.583616			−0.0438673
$178$		0			0
$179$	−1.76914			−0.132232			−0.0661158	−	0.997812i	$-0.521061\pi$
$179$	−1.76914			−0.132232			−0.0661158	+	0.997812i	$0.521061\pi$
$180$		0			0
$181$	−1.11125	−	1.92475i	−0.0825988	−	0.143065i	0.821767	−	0.569824i	$-0.192989\pi$
$181$	−1.11125	−	1.92475i	−0.0825988	−	0.143065i	−0.904365	+	0.426759i	$0.859655\pi$
$182$		0			0
$183$	0.949983	−	1.64542i	0.0702248	−	0.121633i
$184$		0			0
$185$	−4.86878	+	8.43298i	−0.357960	+	0.620005i
$186$		0			0
$187$	−21.5544			−1.57622
$188$		0			0
$189$	1.22030	+	2.11362i	0.0887635	+	0.153743i
$190$		0			0
$191$	6.43628	−	11.1480i	0.465713	−	0.806638i	−0.533521	−	0.845787i	$-0.679131\pi$
$191$	6.43628	−	11.1480i	0.465713	−	0.806638i	0.999233	+	0.0391491i	$0.0124647\pi$
$192$		0			0
$193$	14.1758			1.02040			0.510198	−	0.860057i	$-0.329572\pi$
$193$	14.1758			1.02040			0.510198	+	0.860057i	$0.329572\pi$
$194$		0			0
$195$	−0.500000	+	0.866025i	−0.0358057	+	0.0620174i
$196$		0			0
$197$	−2.97300	−	5.14939i	−0.211818	−	0.366879i	0.740466	−	0.672094i	$-0.234605\pi$
$197$	−2.97300	−	5.14939i	−0.211818	−	0.366879i	−0.952283	+	0.305215i	$0.901272\pi$
$198$		0			0
$199$	−3.54607	+	6.14197i	−0.251374	+	0.435392i	−0.963904	−	0.266249i	$-0.914216\pi$
$199$	−3.54607	+	6.14197i	−0.251374	+	0.435392i	0.712530	+	0.701641i	$0.247549\pi$
$200$		0			0
$201$	3.58812	+	7.35700i	0.253087	+	0.518922i
$202$		0			0
$203$	10.5922	−	18.3462i	0.743427	−	1.28765i
$204$		0			0
$205$	2.30666	+	3.99525i	0.161104	+	0.279040i
$206$		0			0
$207$	0.334853	−	0.579982i	0.0232739	−	0.0403115i
$208$		0			0
$209$	20.2647			1.40174
$210$		0			0
$211$	8.71424	−	15.0935i	0.599913	−	1.03908i	−0.392921	−	0.919572i	$-0.628535\pi$
$211$	8.71424	−	15.0935i	0.599913	−	1.03908i	0.992833	−	0.119507i	$-0.0381314\pi$
$212$		0			0
$213$	−1.74756	−	3.02687i	−0.119741	−	0.207398i
$214$		0			0
$215$	−4.28479			−0.292221
$216$		0			0
$217$	−6.03267	+	10.4489i	−0.409525	+	0.709317i
$218$		0			0
$219$	2.24155	−	3.88247i	0.151470	−	0.262353i
$220$		0			0
$221$	−3.87422	−	6.71035i	−0.260609	−	0.451387i
$222$		0			0
$223$	−27.1265			−1.81653			−0.908263	−	0.418399i	$-0.862591\pi$
$223$	−27.1265			−1.81653			−0.908263	+	0.418399i	$0.862591\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−11.3924	−	19.7322i	−0.756141	−	1.30967i	−0.944805	−	0.327633i	$-0.893749\pi$
$227$	−11.3924	−	19.7322i	−0.756141	−	1.30967i	0.188664	−	0.982042i	$-0.439584\pi$
$228$		0			0
$229$	−4.63810	+	8.03342i	−0.306494	+	0.530863i	−0.977593	−	0.210505i	$-0.932489\pi$
$229$	−4.63810	+	8.03342i	−0.306494	+	0.530863i	0.671099	+	0.741368i	$0.265823\pi$
$230$		0			0
$231$	3.39459	−	5.87960i	0.223348	−	0.386849i
$232$		0			0
$233$	4.23603	+	7.33702i	0.277512	+	0.480664i	0.970766	−	0.240029i	$-0.0771569\pi$
$233$	4.23603	+	7.33702i	0.277512	+	0.480664i	−0.693254	+	0.720693i	$0.743824\pi$
$234$		0			0
$235$	−2.96028	−	5.12735i	−0.193107	−	0.334471i
$236$		0			0
$237$	−2.89911	−	5.02141i	−0.188317	−	0.326175i
$238$		0			0
$239$	0.874507	+	1.51469i	0.0565672	+	0.0979772i	0.892922	−	0.450211i	$-0.148651\pi$
$239$	0.874507	+	1.51469i	0.0565672	+	0.0979772i	−0.836355	+	0.548188i	$0.815318\pi$
$240$		0			0
$241$	9.12424			0.587744			0.293872	−	0.955845i	$-0.405056\pi$
$241$	9.12424			0.587744			0.293872	+	0.955845i	$0.405056\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−0.521754	+	0.903704i	−0.0333336	+	0.0577355i
$246$		0			0
$247$	3.64240	+	6.30882i	0.231760	+	0.401420i
$248$		0			0
$249$	4.02703	−	6.97501i	0.255202	−	0.442023i
$250$		0			0
$251$	3.55127	−	6.15098i	0.224154	−	0.388246i	−0.731911	−	0.681400i	$-0.761371\pi$
$251$	3.55127	−	6.15098i	0.224154	−	0.388246i	0.956065	+	0.293154i	$0.0947048\pi$
$252$		0			0
$253$	−1.86297			−0.117124
$254$		0			0
$255$	−3.87422	+	6.71035i	−0.242613	+	0.420219i
$256$		0			0
$257$	−12.8699	−	22.2912i	−0.802799	−	1.39049i	−0.917767	−	0.397120i	$-0.870010\pi$
$257$	−12.8699	−	22.2912i	−0.802799	−	1.39049i	0.114967	−	0.993369i	$-0.463324\pi$
$258$		0			0
$259$	23.7654			1.47671
$260$		0			0
$261$	−4.34001	−	7.51712i	−0.268640	−	0.465298i
$262$		0			0
$263$	−16.0417			−0.989171			−0.494585	−	0.869129i	$-0.664680\pi$
$263$	−16.0417			−0.989171			−0.494585	+	0.869129i	$0.664680\pi$
$264$		0			0
$265$	−3.94361			−0.242254
$266$		0			0
$267$	0.596874			0.0365281
$268$		0			0
$269$	9.59445			0.584984			0.292492	−	0.956268i	$-0.405515\pi$
$269$	9.59445			0.584984			0.292492	+	0.956268i	$0.405515\pi$
$270$		0			0
$271$	12.5032			0.759513			0.379756	−	0.925087i	$-0.376008\pi$
$271$	12.5032			0.759513			0.379756	+	0.925087i	$0.376008\pi$
$272$		0			0
$273$	2.44059			0.147711
$274$		0			0
$275$	−1.39089	−	2.40909i	−0.0838736	−	0.145273i
$276$		0			0
$277$	24.8143			1.49095			0.745474	−	0.666535i	$-0.232223\pi$
$277$	24.8143			1.49095			0.745474	+	0.666535i	$0.232223\pi$
$278$		0			0
$279$	2.47181	+	4.28129i	0.147983	+	0.256314i
$280$		0			0
$281$	−7.54113	+	13.0616i	−0.449866	+	0.779191i	−0.998377	−	0.0569525i	$-0.981862\pi$
$281$	−7.54113	+	13.0616i	−0.449866	+	0.779191i	0.548511	+	0.836143i	$0.315195\pi$
$282$		0			0
$283$	−9.28294			−0.551814			−0.275907	−	0.961184i	$-0.588978\pi$
$283$	−9.28294			−0.551814			−0.275907	+	0.961184i	$0.588978\pi$
$284$		0			0
$285$	3.64240	−	6.30882i	0.215757	−	0.373702i
$286$		0			0
$287$	5.62962	−	9.75078i	0.332306	−	0.575570i
$288$		0			0
$289$	−21.5192	−	37.2724i	−1.26584	−	2.19249i
$290$		0			0
$291$	0.689324	−	1.19394i	0.0404089	−	0.0699902i
$292$		0			0
$293$	−27.1448			−1.58582			−0.792909	−	0.609340i	$-0.791434\pi$
$293$	−27.1448			−1.58582			−0.792909	+	0.609340i	$0.791434\pi$
$294$		0			0
$295$	0.583616			0.0339795
$296$		0			0
$297$	−1.39089	−	2.40909i	−0.0807074	−	0.139789i
$298$		0			0
$299$	−0.334853	−	0.579982i	−0.0193650	−	0.0335412i
$300$		0			0
$301$	5.22872	+	9.05641i	0.301378	+	0.522003i
$302$		0			0
$303$	1.79513	+	3.10925i	0.103127	+	0.178622i
$304$		0			0
$305$	−0.949983	+	1.64542i	−0.0543959	+	0.0942164i
$306$		0			0
$307$	5.08212	−	8.80248i	0.290052	−	0.502384i	−0.683770	−	0.729698i	$-0.739661\pi$
$307$	5.08212	−	8.80248i	0.290052	−	0.502384i	0.973822	+	0.227313i	$0.0729942\pi$
$308$		0			0
$309$	−5.89146	−	10.2043i	−0.335154	−	0.580503i
$310$		0			0
$311$	−19.6823			−1.11608			−0.558041	−	0.829813i	$-0.688447\pi$
$311$	−19.6823			−1.11608			−0.558041	+	0.829813i	$0.688447\pi$
$312$		0			0
$313$	−10.5586			−0.596805			−0.298403	−	0.954440i	$-0.596454\pi$
$313$	−10.5586			−0.596805			−0.298403	+	0.954440i	$0.596454\pi$
$314$		0			0
$315$	−1.22030	−	2.11362i	−0.0687559	−	0.119089i
$316$		0			0
$317$	14.5394	−	25.1830i	0.816613	−	1.41442i	−0.0915502	−	0.995800i	$-0.529182\pi$
$317$	14.5394	−	25.1830i	0.816613	−	1.41442i	0.908164	−	0.418615i	$-0.137484\pi$
$318$		0			0
$319$	−12.0729	+	20.9109i	−0.675955	+	1.17079i
$320$		0			0
$321$	2.20720			0.123194
$322$		0			0
$323$	28.2229	+	48.8835i	1.57037	+	2.71995i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	−14.5691			−0.805673
$328$		0			0
$329$	−7.22483	+	12.5138i	−0.398318	+	0.689906i
$330$		0			0
$331$	−14.5362	−	25.1775i	−0.798984	−	1.38388i	−0.920278	−	0.391264i	$-0.872038\pi$
$331$	−14.5362	−	25.1775i	−0.798984	−	1.38388i	0.121294	−	0.992617i	$-0.461295\pi$
$332$		0			0
$333$	4.86878	−	8.43298i	0.266808	−	0.462124i
$334$		0			0
$335$	−3.58812	−	7.35700i	−0.196040	−	0.401956i
$336$		0			0
$337$	4.80364	−	8.32015i	0.261671	−	0.453227i	−0.705015	−	0.709192i	$-0.749060\pi$
$337$	4.80364	−	8.32015i	0.261671	−	0.453227i	0.966686	+	0.255965i	$0.0823932\pi$
$338$		0			0
$339$	3.47181	+	6.01335i	0.188563	+	0.326600i
$340$		0			0
$341$	6.87601	−	11.9096i	0.372357	−	0.644941i
$342$		0			0
$343$	19.6309			1.05997
$344$		0			0
$345$	−0.334853	+	0.579982i	−0.0180279	+	0.0312252i
$346$		0			0
$347$	−16.0651	−	27.8256i	−0.862419	−	1.49375i	−0.869587	−	0.493780i	$-0.835615\pi$
$347$	−16.0651	−	27.8256i	−0.862419	−	1.49375i	0.00716792	−	0.999974i	$-0.497718\pi$
$348$		0			0
$349$	−13.8362			−0.740635			−0.370317	−	0.928905i	$-0.620751\pi$
$349$	−13.8362			−0.740635			−0.370317	+	0.928905i	$0.620751\pi$
$350$		0			0
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$		0			0
$353$	−16.6118	+	28.7724i	−0.884156	+	1.53140i	−0.0374778	+	0.999297i	$0.511932\pi$
$353$	−16.6118	+	28.7724i	−0.884156	+	1.53140i	−0.846678	+	0.532105i	$0.821401\pi$
$354$		0			0
$355$	1.74756	+	3.02687i	0.0927510	+	0.160649i
$356$		0			0
$357$	18.9108			1.00087
$358$		0			0
$359$	29.5139			1.55768			0.778841	−	0.627221i	$-0.215808\pi$
$359$	29.5139			1.55768			0.778841	+	0.627221i	$0.215808\pi$
$360$		0			0
$361$	−17.0341	−	29.5040i	−0.896532	−	1.55284i
$362$		0			0
$363$	1.63087	−	2.82474i	0.0855983	−	0.148261i
$364$		0			0
$365$	−2.24155	+	3.88247i	−0.117328	+	0.203218i
$366$		0			0
$367$	17.3563	+	30.0619i	0.905989	+	1.56922i	0.819584	+	0.572959i	$0.194205\pi$
$367$	17.3563	+	30.0619i	0.905989	+	1.56922i	0.0864056	+	0.996260i	$0.472462\pi$
$368$		0			0
$369$	−2.30666	−	3.99525i	−0.120080	−	0.207984i
$370$		0			0
$371$	4.81238	+	8.33528i	0.249846	+	0.432746i
$372$		0			0
$373$	17.8739	+	30.9585i	0.925475	+	1.60297i	0.790795	+	0.612081i	$0.209668\pi$
$373$	17.8739	+	30.9585i	0.925475	+	1.60297i	0.134681	+	0.990889i	$0.456999\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−8.68003			−0.447044
$378$		0			0
$379$	6.30785	−	10.9255i	0.324013	−	0.561206i	−0.657299	−	0.753630i	$-0.728301\pi$
$379$	6.30785	−	10.9255i	0.324013	−	0.561206i	0.981312	+	0.192423i	$0.0616346\pi$
$380$		0			0
$381$	2.83179	+	4.90481i	0.145077	+	0.251281i
$382$		0			0
$383$	−8.75633	+	15.1664i	−0.447427	+	0.774967i	−0.998218	−	0.0596766i	$-0.980993\pi$
$383$	−8.75633	+	15.1664i	−0.447427	+	0.774967i	0.550790	+	0.834644i	$0.314326\pi$
$384$		0			0
$385$	−3.39459	+	5.87960i	−0.173004	+	0.299652i
$386$		0			0
$387$	4.28479			0.217808
$388$		0			0
$389$	−8.46758	+	14.6663i	−0.429323	+	0.743610i	−0.996813	−	0.0797707i	$-0.974581\pi$
$389$	−8.46758	+	14.6663i	−0.429323	+	0.743610i	0.567490	+	0.823380i	$0.307915\pi$
$390$		0			0
$391$	−2.59459	−	4.49396i	−0.131214	−	0.227269i
$392$		0			0
$393$	3.69628			0.186453
$394$		0			0
$395$	2.89911	+	5.02141i	0.145870	+	0.252654i
$396$		0			0
$397$	−26.4197			−1.32597			−0.662984	−	0.748633i	$-0.730710\pi$
$397$	−26.4197			−1.32597			−0.662984	+	0.748633i	$0.730710\pi$
$398$		0			0
$399$	−17.7792			−0.890074
$400$		0			0
$401$	6.12171			0.305704			0.152852	−	0.988249i	$-0.451154\pi$
$401$	6.12171			0.305704			0.152852	+	0.988249i	$0.451154\pi$
$402$		0			0
$403$	4.94361			0.246259
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−27.0877			−1.34269
$408$		0			0
$409$	−6.62655	−	11.4775i	−0.327662	−	0.567527i	0.654386	−	0.756161i	$-0.272927\pi$
$409$	−6.62655	−	11.4775i	−0.327662	−	0.567527i	−0.982047	+	0.188634i	$0.939594\pi$
$410$		0			0
$411$	16.7025			0.823872
$412$		0			0
$413$	−0.712185	−	1.23354i	−0.0350443	−	0.0606985i
$414$		0			0
$415$	−4.02703	+	6.97501i	−0.197679	+	0.342390i
$416$		0			0
$417$	15.7732			0.772416
$418$		0			0
$419$	5.15432	−	8.92755i	0.251805	−	0.436139i	−0.712218	−	0.701959i	$-0.752309\pi$
$419$	5.15432	−	8.92755i	0.251805	−	0.436139i	0.964023	+	0.265819i	$0.0856425\pi$
$420$		0			0
$421$	2.37700	−	4.11709i	0.115848	−	0.200655i	−0.802270	−	0.596961i	$-0.796375\pi$
$421$	2.37700	−	4.11709i	0.115848	−	0.200655i	0.918118	+	0.396306i	$0.129708\pi$
$422$		0			0
$423$	2.96028	+	5.12735i	0.143934	+	0.249300i
$424$		0			0
$425$	3.87422	−	6.71035i	0.187927	−	0.325500i
$426$		0			0
$427$	4.63704			0.224402
$428$		0			0
$429$	−2.78177			−0.134305
$430$		0			0
$431$	4.47031	+	7.74280i	0.215327	+	0.372957i	0.953374	−	0.301792i	$-0.0975849\pi$
$431$	4.47031	+	7.74280i	0.215327	+	0.372957i	−0.738047	+	0.674750i	$0.764252\pi$
$432$		0			0
$433$	5.91121	+	10.2385i	0.284075	+	0.492032i	0.972384	−	0.233385i	$-0.0749803\pi$
$433$	5.91121	+	10.2385i	0.284075	+	0.492032i	−0.688310	+	0.725417i	$0.741647\pi$
$434$		0			0
$435$	4.34001	+	7.51712i	0.208088	+	0.360418i
$436$		0			0
$437$	2.43933	+	4.22505i	0.116689	+	0.202112i
$438$		0			0
$439$	−1.68006	+	2.90996i	−0.0801851	+	0.138885i	−0.903329	−	0.428948i	$-0.858884\pi$
$439$	−1.68006	+	2.90996i	−0.0801851	+	0.138885i	0.823144	+	0.567832i	$0.192218\pi$
$440$		0			0
$441$	0.521754	−	0.903704i	0.0248454	−	0.0430335i
$442$		0			0
$443$	−11.0105	−	19.0707i	−0.523124	−	0.906077i	−0.999638	−	0.0269101i	$-0.991433\pi$
$443$	−11.0105	−	19.0707i	−0.523124	−	0.906077i	0.476514	−	0.879167i	$-0.341900\pi$
$444$		0			0
$445$	−0.596874			−0.0282945
$446$		0			0
$447$	22.6059			1.06922
$448$		0			0
$449$	2.64777	+	4.58607i	0.124956	+	0.216430i	0.921716	−	0.387866i	$-0.126788\pi$
$449$	2.64777	+	4.58607i	0.124956	+	0.216430i	−0.796760	+	0.604296i	$0.793454\pi$
$450$		0			0
$451$	−6.41661	+	11.1139i	−0.302146	+	0.523332i
$452$		0			0
$453$	−11.9860	+	20.7603i	−0.563151	+	0.975405i
$454$		0			0
$455$	−2.44059			−0.114417
$456$		0			0
$457$	2.96596	+	5.13720i	0.138742	+	0.240308i	0.927021	−	0.375010i	$-0.122361\pi$
$457$	2.96596	+	5.13720i	0.138742	+	0.240308i	−0.788279	+	0.615318i	$0.789028\pi$
$458$		0			0
$459$	3.87422	−	6.71035i	0.180833	−	0.313212i
$460$		0			0
$461$	1.68430			0.0784456			0.0392228	−	0.999230i	$-0.487512\pi$
$461$	1.68430			0.0784456			0.0392228	+	0.999230i	$0.487512\pi$
$462$		0			0
$463$	−11.2082	+	19.4131i	−0.520887	+	0.902203i	0.478818	+	0.877914i	$0.341065\pi$
$463$	−11.2082	+	19.4131i	−0.520887	+	0.902203i	−0.999705	+	0.0242885i	$0.992268\pi$
$464$		0			0
$465$	−2.47181	−	4.28129i	−0.114627	−	0.198540i
$466$		0			0
$467$	0.282154	−	0.488706i	0.0130565	−	0.0226146i	−0.859423	−	0.511265i	$-0.829177\pi$
$467$	0.282154	−	0.488706i	0.0130565	−	0.0226146i	0.872480	+	0.488650i	$0.162511\pi$
$468$		0			0
$469$	−11.1713	+	16.5616i	−0.515842	+	0.764745i
$470$		0			0
$471$	10.2026	−	17.6715i	0.470113	−	0.814259i
$472$		0			0
$473$	−5.95967	−	10.3224i	−0.274026	−	0.474626i
$474$		0			0
$475$	−3.64240	+	6.30882i	−0.167125	+	0.289468i
$476$		0			0
$477$	3.94361			0.180566
$478$		0			0
$479$	4.72662	−	8.18675i	0.215965	−	0.374062i	−0.737606	−	0.675232i	$-0.764044\pi$
$479$	4.72662	−	8.18675i	0.215965	−	0.374062i	0.953571	+	0.301169i	$0.0973770\pi$
$480$		0			0
$481$	−4.86878	−	8.43298i	−0.221997	−	0.384511i
$482$		0			0
$483$	1.63448			0.0743714
$484$		0			0
$485$	−0.689324	+	1.19394i	−0.0313006	+	0.0542142i
$486$		0			0
$487$	−1.52143	+	2.63519i	−0.0689424	+	0.119412i	−0.898436	−	0.439104i	$-0.855296\pi$
$487$	−1.52143	+	2.63519i	−0.0689424	+	0.119412i	0.829494	+	0.558516i	$0.188629\pi$
$488$		0			0
$489$	−6.34522	−	10.9902i	−0.286941	−	0.496996i
$490$		0			0
$491$	16.3197			0.736496			0.368248	−	0.929728i	$-0.379958\pi$
$491$	16.3197			0.736496			0.368248	+	0.929728i	$0.379958\pi$
$492$		0			0
$493$	−67.2567			−3.02909
$494$		0			0
$495$	1.39089	+	2.40909i	0.0625157	+	0.108280i
$496$		0			0
$497$	4.26509	−	7.38735i	0.191315	−	0.331368i
$498$		0			0
$499$	−0.173542	+	0.300584i	−0.00776881	+	0.0134560i	−0.869884	−	0.493257i	$-0.835806\pi$
$499$	−0.173542	+	0.300584i	−0.00776881	+	0.0134560i	0.862115	+	0.506713i	$0.169140\pi$
$500$		0			0
$501$	11.5026	+	19.9231i	0.513898	+	0.890098i
$502$		0			0
$503$	15.3851	+	26.6478i	0.685987	+	1.18816i	0.973125	+	0.230275i	$0.0739627\pi$
$503$	15.3851	+	26.6478i	0.685987	+	1.18816i	−0.287138	+	0.957889i	$0.592704\pi$
$504$		0			0
$505$	−1.79513	−	3.10925i	−0.0798822	−	0.138360i
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	−14.3865			−0.637669			−0.318834	−	0.947810i	$-0.603291\pi$
$509$	−14.3865			−0.637669			−0.318834	+	0.947810i	$0.603291\pi$
$510$		0			0
$511$	10.9414			0.484019
$512$		0			0
$513$	−3.64240	+	6.30882i	−0.160816	+	0.278541i
$514$		0			0
$515$	5.89146	+	10.2043i	0.259609	+	0.449656i
$516$		0			0
$517$	8.23482	−	14.2631i	0.362167	−	0.627292i
$518$		0			0
$519$	−0.0548381	+	0.0949824i	−0.00240713	+	0.00416927i
$520$		0			0
$521$	−43.5339			−1.90726			−0.953628	−	0.300987i	$-0.902684\pi$
$521$	−43.5339			−1.90726			−0.953628	+	0.300987i	$0.902684\pi$
$522$		0			0
$523$	−12.5682	+	21.7688i	−0.549569	+	0.951882i	0.448735	+	0.893665i	$0.351875\pi$
$523$	−12.5682	+	21.7688i	−0.549569	+	0.951882i	−0.998304	+	0.0582168i	$0.981459\pi$
$524$		0			0
$525$	1.22030	+	2.11362i	0.0532581	+	0.0922457i
$526$		0			0
$527$	38.3053			1.66861
$528$		0			0
$529$	11.2757	+	19.5302i	0.490250	+	0.849138i
$530$		0			0
$531$	−0.583616			−0.0253268
$532$		0			0
$533$	−4.61332			−0.199825
$534$		0			0
$535$	−2.20720			−0.0954256
$536$		0			0
$537$	−1.76914			−0.0763440
$538$		0			0
$539$	−2.90280			−0.125033
$540$		0			0
$541$	−36.5488			−1.57136			−0.785679	−	0.618635i	$-0.787686\pi$
$541$	−36.5488			−1.57136			−0.785679	+	0.618635i	$0.787686\pi$
$542$		0			0
$543$	−1.11125	−	1.92475i	−0.0476884	−	0.0825988i
$544$		0			0
$545$	14.5691			0.624072
$546$		0			0
$547$	−2.81993	−	4.88427i	−0.120572	−	0.208836i	0.799422	−	0.600770i	$-0.205139\pi$
$547$	−2.81993	−	4.88427i	−0.120572	−	0.208836i	−0.919993	+	0.391934i	$0.871806\pi$
$548$		0			0
$549$	0.949983	−	1.64542i	0.0405443	−	0.0702248i
$550$		0			0
$551$	63.2322			2.69378
$552$		0			0
$553$	7.07555	−	12.2552i	0.300883	−	0.521144i
$554$		0			0
$555$	−4.86878	+	8.43298i	−0.206668	+	0.357960i
$556$		0			0
$557$	2.31325	+	4.00666i	0.0980154	+	0.169768i	0.910863	−	0.412709i	$-0.135417\pi$
$557$	2.31325	+	4.00666i	0.0980154	+	0.169768i	−0.812848	+	0.582476i	$0.802084\pi$
$558$		0			0
$559$	2.14240	−	3.71074i	0.0906138	−	0.156948i
$560$		0			0
$561$	−21.5544			−0.910029
$562$		0			0
$563$	−32.2239			−1.35808			−0.679039	−	0.734103i	$-0.737603\pi$
$563$	−32.2239			−1.35808			−0.679039	+	0.734103i	$0.737603\pi$
$564$		0			0
$565$	−3.47181	−	6.01335i	−0.146060	−	0.252983i
$566$		0			0
$567$	1.22030	+	2.11362i	0.0512476	+	0.0887635i
$568$		0			0
$569$	−1.66605	−	2.88568i	−0.0698444	−	0.120974i	0.828988	−	0.559266i	$-0.188917\pi$
$569$	−1.66605	−	2.88568i	−0.0698444	−	0.120974i	−0.898833	+	0.438292i	$0.855584\pi$
$570$		0			0
$571$	15.3842	+	26.6462i	0.643809	+	1.11511i	0.984575	+	0.174962i	$0.0559804\pi$
$571$	15.3842	+	26.6462i	0.643809	+	1.11511i	−0.340766	+	0.940148i	$0.610686\pi$
$572$		0			0
$573$	6.43628	−	11.1480i	0.268879	−	0.465713i
$574$		0			0
$575$	0.334853	−	0.579982i	0.0139643	−	0.0241869i
$576$		0			0
$577$	11.4490	+	19.8303i	0.476629	+	0.825545i	0.999641	−	0.0267797i	$-0.00852527\pi$
$577$	11.4490	+	19.8303i	0.476629	+	0.825545i	−0.523013	+	0.852325i	$0.675192\pi$
$578$		0			0
$579$	14.1758			0.589125
$580$		0			0
$581$	19.6567			0.815496
$582$		0			0
$583$	−5.48512	−	9.50051i	−0.227170	−	0.393471i
$584$		0			0
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$		0			0
$587$	2.84220	−	4.92284i	0.117310	−	0.203187i	−0.801391	−	0.598141i	$-0.795906\pi$
$587$	2.84220	−	4.92284i	0.117310	−	0.203187i	0.918701	+	0.394954i	$0.129239\pi$
$588$		0			0
$589$	−36.0132			−1.48390
$590$		0			0
$591$	−2.97300	−	5.14939i	−0.122293	−	0.211818i
$592$		0			0
$593$	−8.86947	+	15.3624i	−0.364226	+	0.630857i	−0.988652	−	0.150227i	$-0.952000\pi$
$593$	−8.86947	+	15.3624i	−0.364226	+	0.630857i	0.624426	+	0.781084i	$0.285333\pi$
$594$		0			0
$595$	−18.9108			−0.775267
$596$		0			0
$597$	−3.54607	+	6.14197i	−0.145131	+	0.251374i
$598$		0			0
$599$	−15.1500	−	26.2406i	−0.619013	−	1.07216i	−0.989666	−	0.143390i	$-0.954200\pi$
$599$	−15.1500	−	26.2406i	−0.619013	−	1.07216i	0.370654	−	0.928771i	$-0.379134\pi$
$600$		0			0
$601$	0.112939	−	0.195615i	0.00460686	−	0.00797932i	−0.863713	−	0.503984i	$-0.831867\pi$
$601$	0.112939	−	0.195615i	0.00460686	−	0.00797932i	0.868320	+	0.496005i	$0.165200\pi$
$602$		0			0
$603$	3.58812	+	7.35700i	0.146120	+	0.299600i
$604$		0			0
$605$	−1.63087	+	2.82474i	−0.0663042	+	0.114842i
$606$		0			0
$607$	−0.976639	−	1.69159i	−0.0396406	−	0.0686595i	0.845524	−	0.533937i	$-0.179288\pi$
$607$	−0.976639	−	1.69159i	−0.0396406	−	0.0686595i	−0.885165	+	0.465277i	$0.845955\pi$
$608$		0			0
$609$	10.5922	−	18.3462i	0.429218	−	0.743427i
$610$		0			0
$611$	5.92055			0.239520
$612$		0			0
$613$	−16.1722	+	28.0111i	−0.653189	+	1.13136i	0.329155	+	0.944276i	$0.393236\pi$
$613$	−16.1722	+	28.0111i	−0.653189	+	1.13136i	−0.982345	+	0.187081i	$0.940097\pi$
$614$		0			0
$615$	2.30666	+	3.99525i	0.0930135	+	0.161104i
$616$		0			0
$617$	16.4424			0.661945			0.330972	−	0.943640i	$-0.392623\pi$
$617$	16.4424			0.661945			0.330972	+	0.943640i	$0.392623\pi$
$618$		0			0
$619$	−7.29238	+	12.6308i	−0.293105	+	0.507673i	−0.974542	−	0.224203i	$-0.928022\pi$
$619$	−7.29238	+	12.6308i	−0.293105	+	0.507673i	0.681437	+	0.731877i	$0.261355\pi$
$620$		0			0
$621$	0.334853	−	0.579982i	0.0134372	−	0.0232739i
$622$		0			0
$623$	0.728363	+	1.26156i	0.0291812	+	0.0505434i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	20.2647			0.809292
$628$		0			0
$629$	−37.7255	−	65.3425i	−1.50421	−	2.60537i
$630$		0			0
$631$	4.41419	−	7.64560i	0.175726	−	0.304367i	−0.764686	−	0.644403i	$-0.777106\pi$
$631$	4.41419	−	7.64560i	0.175726	−	0.304367i	0.940412	+	0.340036i	$0.110439\pi$
$632$		0			0
$633$	8.71424	−	15.0935i	0.346360	−	0.599913i
$634$		0			0
$635$	−2.83179	−	4.90481i	−0.112376	−	0.194641i
$636$		0			0
$637$	−0.521754	−	0.903704i	−0.0206726	−	0.0358061i
$638$		0			0
$639$	−1.74756	−	3.02687i	−0.0691325	−	0.119741i
$640$		0			0
$641$	−0.596262	−	1.03276i	−0.0235509	−	0.0407914i	0.854010	−	0.520257i	$-0.174164\pi$
$641$	−0.596262	−	1.03276i	−0.0235509	−	0.0407914i	−0.877561	+	0.479466i	$0.840831\pi$
$642$		0			0
$643$	−1.75194			−0.0690898			−0.0345449	−	0.999403i	$-0.510998\pi$
$643$	−1.75194			−0.0690898			−0.0345449	+	0.999403i	$0.510998\pi$
$644$		0			0
$645$	−4.28479			−0.168714
$646$		0			0
$647$	2.66307	−	4.61257i	0.104696	−	0.181339i	−0.808918	−	0.587922i	$-0.799946\pi$
$647$	2.66307	−	4.61257i	0.104696	−	0.181339i	0.913614	+	0.406583i	$0.133280\pi$
$648$		0			0
$649$	0.811744	+	1.40598i	0.0318637	+	0.0551896i
$650$		0			0
$651$	−6.03267	+	10.4489i	−0.236439	+	0.409525i
$652$		0			0
$653$	8.32354	−	14.4168i	0.325725	−	0.564173i	−0.655933	−	0.754819i	$-0.727725\pi$
$653$	8.32354	−	14.4168i	0.325725	−	0.564173i	0.981659	+	0.190646i	$0.0610582\pi$
$654$		0			0
$655$	−3.69628			−0.144426
$656$		0			0
$657$	2.24155	−	3.88247i	0.0874510	−	0.151470i
$658$		0			0
$659$	−8.14489	−	14.1074i	−0.317280	−	0.549545i	0.662640	−	0.748938i	$-0.269436\pi$
$659$	−8.14489	−	14.1074i	−0.317280	−	0.549545i	−0.979919	+	0.199394i	$0.936103\pi$
$660$		0			0
$661$	−26.7204			−1.03930			−0.519652	−	0.854378i	$-0.673938\pi$
$661$	−26.7204			−1.03930			−0.519652	+	0.854378i	$0.673938\pi$
$662$		0			0
$663$	−3.87422	−	6.71035i	−0.150462	−	0.260609i
$664$		0			0
$665$	17.7792			0.689448
$666$		0			0
$667$	−5.81306			−0.225083
$668$		0			0
$669$	−27.1265			−1.04877
$670$		0			0
$671$	−5.28528			−0.204036
$672$		0			0
$673$	28.7222			1.10716			0.553579	−	0.832796i	$-0.313262\pi$
$673$	28.7222			1.10716			0.553579	+	0.832796i	$0.313262\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	19.4324	+	33.6579i	0.746848	+	1.29358i	0.949327	+	0.314292i	$0.101767\pi$
$677$	19.4324	+	33.6579i	0.746848	+	1.29358i	−0.202479	+	0.979287i	$0.564900\pi$
$678$		0			0
$679$	3.36472			0.129126
$680$		0			0
$681$	−11.3924	−	19.7322i	−0.436558	−	0.756141i
$682$		0			0
$683$	−24.7268	+	42.8281i	−0.946144	+	1.63877i	−0.192701	+	0.981257i	$0.561725\pi$
$683$	−24.7268	+	42.8281i	−0.946144	+	1.63877i	−0.753443	+	0.657513i	$0.771609\pi$
$684$		0			0
$685$	−16.7025			−0.638168
$686$		0			0
$687$	−4.63810	+	8.03342i	−0.176954	+	0.306494i
$688$		0			0
$689$	1.97181	−	3.41527i	0.0751199	−	0.130111i
$690$		0			0
$691$	11.2305	+	19.4519i	0.427230	+	0.739984i	0.996626	−	0.0820796i	$-0.0261562\pi$
$691$	11.2305	+	19.4519i	0.427230	+	0.739984i	−0.569396	+	0.822063i	$0.692823\pi$
$692$		0			0
$693$	3.39459	−	5.87960i	0.128950	−	0.223348i
$694$		0			0
$695$	−15.7732			−0.598311
$696$		0			0
$697$	−35.7461			−1.35398
$698$		0			0
$699$	4.23603	+	7.33702i	0.160221	+	0.277512i
$700$		0			0
$701$	21.9923	+	38.0917i	0.830636	+	1.43870i	0.897534	+	0.440945i	$0.145356\pi$
$701$	21.9923	+	38.0917i	0.830636	+	1.43870i	−0.0668980	+	0.997760i	$0.521310\pi$
$702$		0			0
$703$	35.4681	+	61.4325i	1.33770	+	2.31697i
$704$		0			0
$705$	−2.96028	−	5.12735i	−0.111490	−	0.193107i
$706$		0			0
$707$	−4.38118	+	7.58842i	−0.164771	+	0.285392i
$708$		0			0
$709$	−9.44843	+	16.3652i	−0.354843	+	0.614607i	−0.987091	−	0.160160i	$-0.948799\pi$
$709$	−9.44843	+	16.3652i	−0.354843	+	0.614607i	0.632248	+	0.774766i	$0.282132\pi$
$710$		0			0
$711$	−2.89911	−	5.02141i	−0.108725	−	0.188317i
$712$		0			0
$713$	3.31077			0.123989
$714$		0			0
$715$	2.78177			0.104032
$716$		0			0
$717$	0.874507	+	1.51469i	0.0326591	+	0.0565672i
$718$		0			0
$719$	−6.80093	+	11.7795i	−0.253632	+	0.439303i	−0.964523	−	0.263999i	$-0.914958\pi$
$719$	−6.80093	+	11.7795i	−0.253632	+	0.439303i	0.710891	+	0.703302i	$0.248292\pi$
$720$		0			0
$721$	14.3787	−	24.9046i	0.535489	−	0.927494i
$722$		0			0
$723$	9.12424			0.339334
$724$		0			0
$725$	−4.34001	−	7.51712i	−0.161184	−	0.279179i
$726$		0			0
$727$	−8.45300	+	14.6410i	−0.313505	+	0.543006i	−0.979118	−	0.203290i	$-0.934836\pi$
$727$	−8.45300	+	14.6410i	−0.313505	+	0.543006i	0.665614	+	0.746296i	$0.268170\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	16.6003	−	28.7525i	0.613983	−	1.06345i
$732$		0			0
$733$	−2.78996	−	4.83236i	−0.103050	−	0.178487i	0.809890	−	0.586582i	$-0.199527\pi$
$733$	−2.78996	−	4.83236i	−0.103050	−	0.178487i	−0.912940	+	0.408094i	$0.866193\pi$
$734$		0			0
$735$	−0.521754	+	0.903704i	−0.0192452	+	0.0333336i
$736$		0			0
$737$	12.7330	−	18.8768i	0.469025	−	0.695338i
$738$		0			0
$739$	17.0394	−	29.5131i	0.626804	−	1.08566i	−0.361385	−	0.932417i	$-0.617696\pi$
$739$	17.0394	−	29.5131i	0.626804	−	1.08566i	0.988189	−	0.153240i	$-0.0489708\pi$
$740$		0			0
$741$	3.64240	+	6.30882i	0.133807	+	0.231760i
$742$		0			0
$743$	1.41801	−	2.45606i	0.0520216	−	0.0901040i	−0.838842	−	0.544375i	$-0.816767\pi$
$743$	1.41801	−	2.45606i	0.0520216	−	0.0901040i	0.890864	+	0.454271i	$0.150100\pi$
$744$		0			0
$745$	−22.6059			−0.828215
$746$		0			0
$747$	4.02703	−	6.97501i	0.147341	−	0.255202i
$748$		0			0
$749$	2.69344	+	4.66517i	0.0984161	+	0.170462i
$750$		0			0
$751$	51.3321			1.87314			0.936568	−	0.350487i	$-0.113984\pi$
$751$	51.3321			1.87314			0.936568	+	0.350487i	$0.113984\pi$
$752$		0			0
$753$	3.55127	−	6.15098i	0.129415	−	0.224154i
$754$		0			0
$755$	11.9860	−	20.7603i	0.436215	−	0.755546i
$756$		0			0
$757$	2.68615	+	4.65256i	0.0976300	+	0.169100i	0.910703	−	0.413061i	$-0.135541\pi$
$757$	2.68615	+	4.65256i	0.0976300	+	0.169100i	−0.813073	+	0.582161i	$0.802207\pi$
$758$		0			0
$759$	−1.86297			−0.0676215
$760$		0			0
$761$	21.1411			0.766365			0.383183	−	0.923673i	$-0.374828\pi$
$761$	21.1411			0.766365			0.383183	+	0.923673i	$0.374828\pi$
$762$		0			0
$763$	−17.7786	−	30.7935i	−0.643629	−	1.11480i
$764$		0			0
$765$	−3.87422	+	6.71035i	−0.140073	+	0.242613i
$766$		0			0
$767$	−0.291808	+	0.505426i	−0.0105366	+	0.0182499i
$768$		0			0
$769$	−13.0729	−	22.6429i	−0.471421	−	0.816525i	0.528044	−	0.849217i	$-0.322925\pi$
$769$	−13.0729	−	22.6429i	−0.471421	−	0.816525i	−0.999465	+	0.0326914i	$0.989592\pi$
$770$		0			0
$771$	−12.8699	−	22.2912i	−0.463497	−	0.802799i
$772$		0			0
$773$	6.81636	+	11.8063i	0.245168	+	0.424643i	0.962179	−	0.272419i	$-0.0878237\pi$
$773$	6.81636	+	11.8063i	0.245168	+	0.424643i	−0.717011	+	0.697062i	$0.754490\pi$
$774$		0			0
$775$	2.47181	+	4.28129i	0.0887899	+	0.153789i
$776$		0			0
$777$	23.7654			0.852580
$778$		0			0
$779$	33.6071			1.20410
$780$		0			0
$781$	−4.86133	+	8.42006i	−0.173952	+	0.301294i
$782$		0			0
$783$	−4.34001	−	7.51712i	−0.155099	−	0.268640i
$784$		0			0
$785$	−10.2026	+	17.6715i	−0.364148	+	0.630722i
$786$		0			0
$787$	−1.31724	+	2.28152i	−0.0469544	+	0.0813274i	−0.888547	−	0.458785i	$-0.848285\pi$
$787$	−1.31724	+	2.28152i	−0.0469544	+	0.0813274i	0.841593	+	0.540112i	$0.181618\pi$
$788$		0			0
$789$	−16.0417			−0.571098
$790$		0			0
$791$	−8.47327	+	14.6761i	−0.301275	+	0.521823i
$792$		0			0
$793$	−0.949983	−	1.64542i	−0.0337349	−	0.0584306i
$794$		0			0
$795$	−3.94361			−0.139866
$796$		0			0
$797$	−6.24567	−	10.8178i	−0.221233	−	0.383186i	0.733950	−	0.679204i	$-0.237675\pi$
$797$	−6.24567	−	10.8178i	−0.221233	−	0.383186i	−0.955183	+	0.296017i	$0.904341\pi$
$798$		0			0
$799$	45.8751			1.62294
$800$		0			0
$801$	0.596874			0.0210895
$802$		0			0
$803$	−12.4709			−0.440090
$804$		0			0
$805$	−1.63448			−0.0576078
$806$		0			0
$807$	9.59445			0.337741
$808$		0			0
$809$	6.30833			0.221789			0.110894	−	0.993832i	$-0.464628\pi$
$809$	6.30833			0.221789			0.110894	+	0.993832i	$0.464628\pi$
$810$		0			0
$811$	−1.06701	−	1.84811i	−0.0374677	−	0.0648960i	0.846683	−	0.532097i	$-0.178596\pi$
$811$	−1.06701	−	1.84811i	−0.0374677	−	0.0648960i	−0.884151	+	0.467201i	$0.845262\pi$
$812$		0			0
$813$	12.5032			0.438505
$814$		0			0
$815$	6.34522	+	10.9902i	0.222263	+	0.384971i
$816$		0			0
$817$	−15.6069	+	27.0320i	−0.546017	+	0.945730i
$818$		0			0
$819$	2.44059			0.0852812
$820$		0			0
$821$	−9.53897	+	16.5220i	−0.332912	+	0.576621i	−0.983082	−	0.183168i	$-0.941365\pi$
$821$	−9.53897	+	16.5220i	−0.332912	+	0.576621i	0.650169	+	0.759789i	$0.274698\pi$
$822$		0			0
$823$	4.44047	−	7.69112i	0.154785	−	0.268095i	−0.778196	−	0.628022i	$-0.783865\pi$
$823$	4.44047	−	7.69112i	0.154785	−	0.268095i	0.932981	+	0.359926i	$0.117198\pi$
$824$		0			0
$825$	−1.39089	−	2.40909i	−0.0484245	−	0.0838736i
$826$		0			0
$827$	−15.4919	+	26.8328i	−0.538706	+	0.933066i	0.460268	+	0.887780i	$0.347753\pi$
$827$	−15.4919	+	26.8328i	−0.538706	+	0.933066i	−0.998974	+	0.0452863i	$0.985580\pi$
$828$		0			0
$829$	−32.7142			−1.13621			−0.568105	−	0.822956i	$-0.692323\pi$
$829$	−32.7142			−1.13621			−0.568105	+	0.822956i	$0.692323\pi$
$830$		0			0
$831$	24.8143			0.860799
$832$		0			0
$833$	−4.04278	−	7.00231i	−0.140074	−	0.242616i
$834$		0			0
$835$	−11.5026	−	19.9231i	−0.398064	−	0.689467i
$836$		0			0
$837$	2.47181	+	4.28129i	0.0854381	+	0.147983i
$838$		0			0
$839$	−15.4014	−	26.6761i	−0.531717	−	0.920961i	−0.999315	−	0.0370195i	$-0.988214\pi$
$839$	−15.4014	−	26.6761i	−0.531717	−	0.920961i	0.467597	−	0.883942i	$-0.345120\pi$
$840$		0			0
$841$	−23.1714	+	40.1341i	−0.799015	+	1.38393i
$842$		0			0
$843$	−7.54113	+	13.0616i	−0.259730	+	0.449866i
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	7.96056			0.273528
$848$		0			0
$849$	−9.28294			−0.318590
$850$		0			0
$851$	−3.26065	−	5.64761i	−0.111774	−	0.193598i
$852$		0			0
$853$	−1.63151	+	2.82586i	−0.0558619	+	0.0967556i	−0.892604	−	0.450841i	$-0.851124\pi$
$853$	−1.63151	+	2.82586i	−0.0558619	+	0.0967556i	0.836742	+	0.547597i	$0.184457\pi$
$854$		0			0
$855$	3.64240	−	6.30882i	0.124567	−	0.215757i
$856$		0			0
$857$	17.2395			0.588889			0.294444	−	0.955669i	$-0.404865\pi$
$857$	17.2395			0.588889			0.294444	+	0.955669i	$0.404865\pi$
$858$		0			0
$859$	15.2000	+	26.3272i	0.518618	+	0.898272i	0.999766	+	0.0216329i	$0.00688651\pi$
$859$	15.2000	+	26.3272i	0.518618	+	0.898272i	−0.481148	+	0.876639i	$0.659780\pi$
$860$		0			0
$861$	5.62962	−	9.75078i	0.191857	−	0.332306i
$862$		0			0
$863$	−21.1827			−0.721068			−0.360534	−	0.932746i	$-0.617406\pi$
$863$	−21.1827			−0.721068			−0.360534	+	0.932746i	$0.617406\pi$
$864$		0			0
$865$	0.0548381	−	0.0949824i	0.00186455	−	0.00322950i
$866$		0			0
$867$	−21.5192	−	37.2724i	−0.730831	−	1.26584i
$868$		0			0
$869$	−8.06467	+	13.9684i	−0.273575	+	0.473846i
$870$		0			0
$871$	8.16541	+	0.571092i	0.276674	+	0.0193507i
$872$		0			0
$873$	0.689324	−	1.19394i	0.0233301	−	0.0404089i
$874$		0			0
$875$	−1.22030	−	2.11362i	−0.0412535	−	0.0714532i
$876$		0			0
$877$	2.25138	−	3.89950i	0.0760237	−	0.131677i	−0.825507	−	0.564391i	$-0.809111\pi$
$877$	2.25138	−	3.89950i	0.0760237	−	0.131677i	0.901531	+	0.432715i	$0.142444\pi$
$878$		0			0
$879$	−27.1448			−0.915572
$880$		0			0
$881$	11.6781	−	20.2271i	0.393446	−	0.681469i	−0.599455	−	0.800408i	$-0.704616\pi$
$881$	11.6781	−	20.2271i	0.393446	−	0.681469i	0.992902	+	0.118939i	$0.0379494\pi$
$882$		0			0
$883$	6.52174	+	11.2960i	0.219474	+	0.380140i	0.954647	−	0.297739i	$-0.0962325\pi$
$883$	6.52174	+	11.2960i	0.219474	+	0.380140i	−0.735173	+	0.677879i	$0.762899\pi$
$884$		0			0
$885$	0.583616			0.0196180
$886$		0			0
$887$	18.0844	−	31.3232i	0.607216	−	1.05173i	−0.384481	−	0.923133i	$-0.625619\pi$
$887$	18.0844	−	31.3232i	0.607216	−	1.05173i	0.991697	−	0.128597i	$-0.0410472\pi$
$888$		0			0
$889$	−6.91125	+	11.9706i	−0.231796	+	0.401482i
$890$		0			0
$891$	−1.39089	−	2.40909i	−0.0465965	−	0.0807074i
$892$		0			0
$893$	−43.1300			−1.44329
$894$		0			0
$895$	1.76914			0.0591358
$896$		0			0
$897$	−0.334853	−	0.579982i	−0.0111804	−	0.0193650i
$898$		0			0
$899$	21.4553	−	37.1618i	0.715576	−	1.23941i
$900$		0			0
$901$	15.2784	−	26.4630i	0.508999	−	0.881612i
$902$		0			0
$903$	5.22872	+	9.05641i	0.174001	+	0.301378i
$904$		0			0
$905$	1.11125	+	1.92475i	0.0369393	+	0.0639807i
$906$		0			0
$907$	−22.4403	−	38.8678i	−0.745119	−	1.29058i	−0.950139	−	0.311826i	$-0.899059\pi$
$907$	−22.4403	−	38.8678i	−0.745119	−	1.29058i	0.205020	−	0.978758i	$-0.434274\pi$
$908$		0			0
$909$	1.79513	+	3.10925i	0.0595407	+	0.103127i
$910$		0			0
$911$	−32.5285			−1.07772			−0.538859	−	0.842396i	$-0.681144\pi$
$911$	−32.5285			−1.07772			−0.538859	+	0.842396i	$0.681144\pi$
$912$		0			0
$913$	−22.4045			−0.741482
$914$		0			0
$915$	−0.949983	+	1.64542i	−0.0314055	+	0.0543959i
$916$		0			0
$917$	4.51056	+	7.81252i	0.148952	+	0.257992i
$918$		0			0
$919$	−24.0584	+	41.6703i	−0.793612	+	1.37458i	0.130104	+	0.991500i	$0.458469\pi$
$919$	−24.0584	+	41.6703i	−0.793612	+	1.37458i	−0.923717	+	0.383076i	$0.874865\pi$
$920$		0			0
$921$	5.08212	−	8.80248i	0.167461	−	0.290052i
$922$		0			0
$923$	−3.49513			−0.115043
$924$		0			0
$925$	4.86878	−	8.43298i	0.160085	−	0.277275i
$926$		0			0
$927$	−5.89146	−	10.2043i	−0.193501	−	0.335154i
$928$		0			0
$929$	12.7251			0.417496			0.208748	−	0.977969i	$-0.433061\pi$
$929$	12.7251			0.417496			0.208748	+	0.977969i	$0.433061\pi$
$930$		0			0
$931$	3.80087	+	6.58330i	0.124568	+	0.215759i
$932$		0			0
$933$	−19.6823			−0.644370
$934$		0			0
$935$	21.5544			0.704905
$936$		0			0
$937$	−52.3990			−1.71180			−0.855900	−	0.517142i	$-0.826996\pi$
$937$	−52.3990			−1.71180			−0.855900	+	0.517142i	$0.826996\pi$
$938$		0			0
$939$	−10.5586			−0.344566
$940$		0			0
$941$	−0.413413			−0.0134769			−0.00673844	−	0.999977i	$-0.502145\pi$
$941$	−0.413413			−0.0134769			−0.00673844	+	0.999977i	$0.502145\pi$
$942$		0			0
$943$	−3.08957			−0.100610
$944$		0			0
$945$	−1.22030	−	2.11362i	−0.0396962	−	0.0687559i
$946$		0			0
$947$	−31.9156			−1.03712			−0.518559	−	0.855042i	$-0.673531\pi$
$947$	−31.9156			−1.03712			−0.518559	+	0.855042i	$0.673531\pi$
$948$		0			0
$949$	−2.24155	−	3.88247i	−0.0727637	−	0.126030i
$950$		0			0
$951$	14.5394	−	25.1830i	0.471472	−	0.816613i
$952$		0			0
$953$	−27.8755			−0.902975			−0.451487	−	0.892278i	$-0.649106\pi$
$953$	−27.8755			−0.902975			−0.451487	+	0.892278i	$0.649106\pi$
$954$		0			0
$955$	−6.43628	+	11.1480i	−0.208273	+	0.360739i
$956$		0			0
$957$	−12.0729	+	20.9109i	−0.390263	+	0.675955i
$958$		0			0
$959$	20.3820	+	35.3026i	0.658168	+	1.13998i
$960$		0			0
$961$	3.28034	−	5.68172i	0.105818	−	0.183281i
$962$		0			0
$963$	2.20720			0.0711260
$964$		0			0
$965$	−14.1758			−0.456335
$966$		0			0
$967$	−25.0919	−	43.4604i	−0.806900	−	1.39759i	−0.915001	−	0.403452i	$-0.867810\pi$
$967$	−25.0919	−	43.4604i	−0.806900	−	1.39759i	0.108100	−	0.994140i	$-0.465523\pi$
$968$		0			0
$969$	28.2229	+	48.8835i	0.906651	+	1.57037i
$970$		0			0
$971$	−28.8290	−	49.9333i	−0.925166	−	1.60244i	−0.791293	−	0.611437i	$-0.790592\pi$
$971$	−28.8290	−	49.9333i	−0.925166	−	1.60244i	−0.133873	−	0.990999i	$-0.542741\pi$
$972$		0			0
$973$	19.2479	+	33.3384i	0.617061	+	1.06878i
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	−22.3630	+	38.7339i	−0.715456	+	1.23921i	0.247328	+	0.968932i	$0.420448\pi$
$977$	−22.3630	+	38.7339i	−0.715456	+	1.23921i	−0.962783	+	0.270274i	$0.912886\pi$
$978$		0			0
$979$	−0.830184	−	1.43792i	−0.0265328	−	0.0459561i
$980$		0			0
$981$	−14.5691			−0.465156
$982$		0			0
$983$	−3.04840			−0.0972287			−0.0486144	−	0.998818i	$-0.515481\pi$
$983$	−3.04840			−0.0972287			−0.0486144	+	0.998818i	$0.515481\pi$
$984$		0			0
$985$	2.97300	+	5.14939i	0.0947277	+	0.164073i
$986$		0			0
$987$	−7.22483	+	12.5138i	−0.229969	+	0.398318i
$988$		0			0
$989$	1.43478	−	2.48510i	0.0456232	−	0.0790217i
$990$		0			0
$991$	−12.2961			−0.390599			−0.195299	−	0.980744i	$-0.562568\pi$
$991$	−12.2961			−0.390599			−0.195299	+	0.980744i	$0.562568\pi$
$992$		0			0
$993$	−14.5362	−	25.1775i	−0.461294	−	0.798984i
$994$		0			0
$995$	3.54607	−	6.14197i	0.112418	−	0.194713i
$996$		0			0
$997$	15.9271			0.504417			0.252209	−	0.967673i	$-0.418843\pi$
$997$	15.9271			0.504417			0.252209	+	0.967673i	$0.418843\pi$
$998$		0			0
$999$	4.86878	−	8.43298i	0.154041	−	0.266808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.j.3781.4	yes	12
67.37	even	3	inner	4020.2.q.j.841.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.j.841.4	✓	12	67.37	even	3	inner
4020.2.q.j.3781.4	yes	12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(1.22030 + 2.11362i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(1.22030 + 2.11362i) q^{7} +1.00000 q^{9} +(-1.39089 - 2.40909i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(3.87422 - 6.71035i) q^{17} +(-3.64240 + 6.30882i) q^{19} +(1.22030 + 2.11362i) q^{21} +(0.334853 - 0.579982i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-4.34001 - 7.51712i) q^{29} +(2.47181 + 4.28129i) q^{31} +(-1.39089 - 2.40909i) q^{33} +(-1.22030 - 2.11362i) q^{35} +(4.86878 - 8.43298i) q^{37} +(0.500000 - 0.866025i) q^{39} +(-2.30666 - 3.99525i) q^{41} +4.28479 q^{43} -1.00000 q^{45} +(2.96028 + 5.12735i) q^{47} +(0.521754 - 0.903704i) q^{49} +(3.87422 - 6.71035i) q^{51} +3.94361 q^{53} +(1.39089 + 2.40909i) q^{55} +(-3.64240 + 6.30882i) q^{57} -0.583616 q^{59} +(0.949983 - 1.64542i) q^{61} +(1.22030 + 2.11362i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(3.58812 + 7.35700i) q^{67} +(0.334853 - 0.579982i) q^{69} +(-1.74756 - 3.02687i) q^{71} +(2.24155 - 3.88247i) q^{73} +1.00000 q^{75} +(3.39459 - 5.87960i) q^{77} +(-2.89911 - 5.02141i) q^{79} +1.00000 q^{81} +(4.02703 - 6.97501i) q^{83} +(-3.87422 + 6.71035i) q^{85} +(-4.34001 - 7.51712i) q^{87} +0.596874 q^{89} +2.44059 q^{91} +(2.47181 + 4.28129i) q^{93} +(3.64240 - 6.30882i) q^{95} +(0.689324 - 1.19394i) q^{97} +(-1.39089 - 2.40909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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