LMFDB - Embedded newform 4020.2.q.m.841.9

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.9
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(0.983461 - 1.70340i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.983461 - 1.70340i) q^{7} +1.00000 q^{9} +(-0.830677 + 1.43877i) q^{11} +(1.04456 + 1.80922i) q^{13} +1.00000 q^{15} +(3.67662 + 6.36809i) q^{17} +(2.16912 + 3.75702i) q^{19} +(0.983461 - 1.70340i) q^{21} +(-0.0409499 - 0.0709273i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-4.86971 + 8.43459i) q^{29} +(-2.11641 + 3.66574i) q^{31} +(-0.830677 + 1.43877i) q^{33} +(0.983461 - 1.70340i) q^{35} +(-4.24467 - 7.35199i) q^{37} +(1.04456 + 1.80922i) q^{39} +(-2.62332 + 4.54373i) q^{41} +0.536623 q^{43} +1.00000 q^{45} +(2.27990 - 3.94890i) q^{47} +(1.56561 + 2.71171i) q^{49} +(3.67662 + 6.36809i) q^{51} -6.41766 q^{53} +(-0.830677 + 1.43877i) q^{55} +(2.16912 + 3.75702i) q^{57} -12.6477 q^{59} +(0.416747 + 0.721828i) q^{61} +(0.983461 - 1.70340i) q^{63} +(1.04456 + 1.80922i) q^{65} +(-1.23403 + 8.09180i) q^{67} +(-0.0409499 - 0.0709273i) q^{69} +(5.10094 - 8.83508i) q^{71} +(-0.703227 - 1.21802i) q^{73} +1.00000 q^{75} +(1.63388 + 2.82996i) q^{77} +(4.45578 - 7.71764i) q^{79} +1.00000 q^{81} +(3.88070 + 6.72157i) q^{83} +(3.67662 + 6.36809i) q^{85} +(-4.86971 + 8.43459i) q^{87} +13.3312 q^{89} +4.10912 q^{91} +(-2.11641 + 3.66574i) q^{93} +(2.16912 + 3.75702i) q^{95} +(-5.51786 - 9.55722i) q^{97} +(-0.830677 + 1.43877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	0.983461	−	1.70340i	0.371713	−	0.643826i	−0.618116	−	0.786087i	$-0.712104\pi$
$7$	0.983461	−	1.70340i	0.371713	−	0.643826i	0.989829	+	0.142261i	$0.0454371\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.830677	+	1.43877i	−0.250458	+	0.433807i	−0.963652	−	0.267160i	$-0.913915\pi$
$11$	−0.830677	+	1.43877i	−0.250458	+	0.433807i	0.713194	+	0.700967i	$0.247248\pi$
$12$		0			0
$13$	1.04456	+	1.80922i	0.289708	+	0.501788i	0.973740	−	0.227663i	$-0.0731086\pi$
$13$	1.04456	+	1.80922i	0.289708	+	0.501788i	−0.684032	+	0.729452i	$0.739775\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	3.67662	+	6.36809i	0.891711	+	1.54449i	0.837823	+	0.545942i	$0.183828\pi$
$17$	3.67662	+	6.36809i	0.891711	+	1.54449i	0.0538876	+	0.998547i	$0.482839\pi$
$18$		0			0
$19$	2.16912	+	3.75702i	0.497630	+	0.861920i	0.999996	−	0.00273457i	$-0.000870440\pi$
$19$	2.16912	+	3.75702i	0.497630	+	0.861920i	−0.502366	+	0.864655i	$0.667537\pi$
$20$		0			0
$21$	0.983461	−	1.70340i	0.214609	−	0.371713i
$22$		0			0
$23$	−0.0409499	−	0.0709273i	−0.00853864	−	0.0147894i	0.861725	−	0.507376i	$-0.169385\pi$
$23$	−0.0409499	−	0.0709273i	−0.00853864	−	0.0147894i	−0.870263	+	0.492587i	$0.836051\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−4.86971	+	8.43459i	−0.904283	+	1.56626i	−0.0824057	+	0.996599i	$0.526260\pi$
$29$	−4.86971	+	8.43459i	−0.904283	+	1.56626i	−0.821877	+	0.569665i	$0.807073\pi$
$30$		0			0
$31$	−2.11641	+	3.66574i	−0.380119	+	0.658386i	−0.991079	−	0.133276i	$-0.957450\pi$
$31$	−2.11641	+	3.66574i	−0.380119	+	0.658386i	0.610960	+	0.791662i	$0.290784\pi$
$32$		0			0
$33$	−0.830677	+	1.43877i	−0.144602	+	0.250458i
$34$		0			0
$35$	0.983461	−	1.70340i	0.166235	−	0.287928i
$36$		0			0
$37$	−4.24467	−	7.35199i	−0.697820	−	1.20866i	−0.969221	−	0.246193i	$-0.920820\pi$
$37$	−4.24467	−	7.35199i	−0.697820	−	1.20866i	0.271401	−	0.962466i	$-0.412513\pi$
$38$		0			0
$39$	1.04456	+	1.80922i	0.167263	+	0.289708i
$40$		0			0
$41$	−2.62332	+	4.54373i	−0.409694	+	0.709612i	−0.994855	−	0.101306i	$-0.967698\pi$
$41$	−2.62332	+	4.54373i	−0.409694	+	0.709612i	0.585161	+	0.810917i	$0.301031\pi$
$42$		0			0
$43$	0.536623			0.0818342			0.0409171	−	0.999163i	$-0.486972\pi$
$43$	0.536623			0.0818342			0.0409171	+	0.999163i	$0.486972\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	2.27990	−	3.94890i	0.332558	−	0.576007i	−0.650455	−	0.759545i	$-0.725422\pi$
$47$	2.27990	−	3.94890i	0.332558	−	0.576007i	0.983013	+	0.183538i	$0.0587550\pi$
$48$		0			0
$49$	1.56561	+	2.71171i	0.223658	+	0.387388i
$50$		0			0
$51$	3.67662	+	6.36809i	0.514830	+	0.891711i
$52$		0			0
$53$	−6.41766			−0.881533			−0.440767	−	0.897622i	$-0.645293\pi$
$53$	−6.41766			−0.881533			−0.440767	+	0.897622i	$0.645293\pi$
$54$		0			0
$55$	−0.830677	+	1.43877i	−0.112008	+	0.194004i
$56$		0			0
$57$	2.16912	+	3.75702i	0.287307	+	0.497630i
$58$		0			0
$59$	−12.6477			−1.64659			−0.823295	−	0.567614i	$-0.807867\pi$
$59$	−12.6477			−1.64659			−0.823295	+	0.567614i	$0.807867\pi$
$60$		0			0
$61$	0.416747	+	0.721828i	0.0533590	+	0.0924206i	0.891471	−	0.453077i	$-0.149674\pi$
$61$	0.416747	+	0.721828i	0.0533590	+	0.0924206i	−0.838112	+	0.545498i	$0.816341\pi$
$62$		0			0
$63$	0.983461	−	1.70340i	0.123904	−	0.214609i
$64$		0			0
$65$	1.04456	+	1.80922i	0.129561	+	0.224407i
$66$		0			0
$67$	−1.23403	+	8.09180i	−0.150760	+	0.988570i
$67$	−1.23403	+	8.09180i	−0.150760	+	0.988570i
$68$		0			0
$69$	−0.0409499	−	0.0709273i	−0.00492979	−	0.00853864i
$70$		0			0
$71$	5.10094	−	8.83508i	0.605370	−	1.04853i	−0.386623	−	0.922238i	$-0.626359\pi$
$71$	5.10094	−	8.83508i	0.605370	−	1.04853i	0.991993	−	0.126293i	$-0.0403080\pi$
$72$		0			0
$73$	−0.703227	−	1.21802i	−0.0823065	−	0.142559i	0.821934	−	0.569583i	$-0.192895\pi$
$73$	−0.703227	−	1.21802i	−0.0823065	−	0.142559i	−0.904240	+	0.427024i	$0.859562\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	1.63388	+	2.82996i	0.186198	+	0.322504i
$78$		0			0
$79$	4.45578	−	7.71764i	0.501315	−	0.868303i	−0.498684	−	0.866784i	$-0.666183\pi$
$79$	4.45578	−	7.71764i	0.501315	−	0.868303i	0.999999	−	0.00151873i	$-0.000483428\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	3.88070	+	6.72157i	0.425962	+	0.737788i	0.996510	−	0.0834765i	$-0.0266023\pi$
$83$	3.88070	+	6.72157i	0.425962	+	0.737788i	−0.570548	+	0.821265i	$0.693269\pi$
$84$		0			0
$85$	3.67662	+	6.36809i	0.398785	+	0.690716i
$86$		0			0
$87$	−4.86971	+	8.43459i	−0.522088	+	0.904283i
$88$		0			0
$89$	13.3312			1.41310			0.706550	−	0.707663i	$-0.250250\pi$
$89$	13.3312			1.41310			0.706550	+	0.707663i	$0.250250\pi$
$90$		0			0
$91$	4.10912			0.430753
$92$		0			0
$93$	−2.11641	+	3.66574i	−0.219462	+	0.380119i
$94$		0			0
$95$	2.16912	+	3.75702i	0.222547	+	0.385462i
$96$		0			0
$97$	−5.51786	−	9.55722i	−0.560254	−	0.970388i	−0.997474	−	0.0710337i	$-0.977370\pi$
$97$	−5.51786	−	9.55722i	−0.560254	−	0.970388i	0.437220	−	0.899355i	$-0.355963\pi$
$98$		0			0
$99$	−0.830677	+	1.43877i	−0.0834862	+	0.144602i
$100$		0			0
$101$	−4.08350	+	7.07283i	−0.406323	+	0.703773i	−0.994475	−	0.104978i	$-0.966523\pi$
$101$	−4.08350	+	7.07283i	−0.406323	+	0.703773i	0.588151	+	0.808751i	$0.299856\pi$
$102$		0			0
$103$	4.38112	−	7.58832i	0.431685	−	0.747700i	−0.565334	−	0.824862i	$-0.691253\pi$
$103$	4.38112	−	7.58832i	0.431685	−	0.747700i	0.997019	+	0.0771624i	$0.0245860\pi$
$104$		0			0
$105$	0.983461	−	1.70340i	0.0959760	−	0.166235i
$106$		0			0
$107$	18.8592			1.82319			0.911594	−	0.411091i	$-0.134852\pi$
$107$	18.8592			1.82319			0.911594	+	0.411091i	$0.134852\pi$
$108$		0			0
$109$	−6.17731			−0.591679			−0.295839	−	0.955238i	$-0.595599\pi$
$109$	−6.17731			−0.591679			−0.295839	+	0.955238i	$0.595599\pi$
$110$		0			0
$111$	−4.24467	−	7.35199i	−0.402887	−	0.697820i
$112$		0			0
$113$	−1.84983	+	3.20400i	−0.174017	+	0.301407i	−0.939821	−	0.341668i	$-0.889008\pi$
$113$	−1.84983	+	3.20400i	−0.174017	+	0.301407i	0.765803	+	0.643075i	$0.222342\pi$
$114$		0			0
$115$	−0.0409499	−	0.0709273i	−0.00381860	−	0.00661400i
$116$		0			0
$117$	1.04456	+	1.80922i	0.0965692	+	0.167263i
$118$		0			0
$119$	14.4632			1.32584
$120$		0			0
$121$	4.11995	+	7.13597i	0.374541	+	0.648724i
$122$		0			0
$123$	−2.62332	+	4.54373i	−0.236537	+	0.409694i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.45037	+	7.70826i	−0.394906	+	0.683998i	−0.993089	−	0.117362i	$-0.962556\pi$
$127$	−4.45037	+	7.70826i	−0.394906	+	0.683998i	0.598183	+	0.801360i	$0.295890\pi$
$128$		0			0
$129$	0.536623			0.0472470
$130$		0			0
$131$	12.9882			1.13479			0.567393	−	0.823447i	$-0.307952\pi$
$131$	12.9882			1.13479			0.567393	+	0.823447i	$0.307952\pi$
$132$		0			0
$133$	8.53298			0.739903
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−6.22145			−0.531534			−0.265767	−	0.964037i	$-0.585625\pi$
$137$	−6.22145			−0.531534			−0.265767	+	0.964037i	$0.585625\pi$
$138$		0			0
$139$	14.9130			1.26490			0.632452	−	0.774599i	$-0.282048\pi$
$139$	14.9130			1.26490			0.632452	+	0.774599i	$0.282048\pi$
$140$		0			0
$141$	2.27990	−	3.94890i	0.192002	−	0.332558i
$142$		0			0
$143$	−3.47075			−0.290239
$144$		0			0
$145$	−4.86971	+	8.43459i	−0.404408	+	0.700454i
$146$		0			0
$147$	1.56561	+	2.71171i	0.129129	+	0.223658i
$148$		0			0
$149$	5.60207			0.458940			0.229470	−	0.973316i	$-0.426301\pi$
$149$	5.60207			0.458940			0.229470	+	0.973316i	$0.426301\pi$
$150$		0			0
$151$	4.61529	+	7.99391i	0.375587	+	0.650535i	0.990415	−	0.138126i	$-0.0441079\pi$
$151$	4.61529	+	7.99391i	0.375587	+	0.650535i	−0.614828	+	0.788661i	$0.710775\pi$
$152$		0			0
$153$	3.67662	+	6.36809i	0.297237	+	0.514830i
$154$		0			0
$155$	−2.11641	+	3.66574i	−0.169994	+	0.294439i
$156$		0			0
$157$	−6.86337	−	11.8877i	−0.547757	−	0.948743i	−0.998428	−	0.0560526i	$-0.982149\pi$
$157$	−6.86337	−	11.8877i	−0.547757	−	0.948743i	0.450671	−	0.892690i	$-0.351185\pi$
$158$		0			0
$159$	−6.41766			−0.508954
$160$		0			0
$161$	−0.161090			−0.0126957
$162$		0			0
$163$	3.55321	−	6.15435i	0.278309	−	0.482046i	−0.692656	−	0.721269i	$-0.743559\pi$
$163$	3.55321	−	6.15435i	0.278309	−	0.482046i	0.970965	+	0.239223i	$0.0768927\pi$
$164$		0			0
$165$	−0.830677	+	1.43877i	−0.0646681	+	0.112008i
$166$		0			0
$167$	−1.68966	+	2.92657i	−0.130750	+	0.226465i	−0.923966	−	0.382475i	$-0.875072\pi$
$167$	−1.68966	+	2.92657i	−0.130750	+	0.226465i	0.793216	+	0.608940i	$0.208405\pi$
$168$		0			0
$169$	4.31781	−	7.47866i	0.332139	−	0.575282i
$170$		0			0
$171$	2.16912	+	3.75702i	0.165877	+	0.287307i
$172$		0			0
$173$	5.09706	+	8.82836i	0.387522	+	0.671208i	0.992116	−	0.125326i	$-0.0399978\pi$
$173$	5.09706	+	8.82836i	0.387522	+	0.671208i	−0.604594	+	0.796534i	$0.706664\pi$
$174$		0			0
$175$	0.983461	−	1.70340i	0.0743427	−	0.128765i
$176$		0			0
$177$	−12.6477			−0.950659
$178$		0			0
$179$	−20.2547			−1.51391			−0.756954	−	0.653469i	$-0.773313\pi$
$179$	−20.2547			−1.51391			−0.756954	+	0.653469i	$0.773313\pi$
$180$		0			0
$181$	4.59855	−	7.96493i	0.341808	−	0.592028i	−0.642961	−	0.765899i	$-0.722294\pi$
$181$	4.59855	−	7.96493i	0.341808	−	0.592028i	0.984768	+	0.173871i	$0.0556275\pi$
$182$		0			0
$183$	0.416747	+	0.721828i	0.0308069	+	0.0533590i
$184$		0			0
$185$	−4.24467	−	7.35199i	−0.312075	−	0.540529i
$186$		0			0
$187$	−12.2163			−0.893346
$188$		0			0
$189$	0.983461	−	1.70340i	0.0715363	−	0.123904i
$190$		0			0
$191$	−10.1457	−	17.5729i	−0.734117	−	1.27153i	−0.955110	−	0.296252i	$-0.904263\pi$
$191$	−10.1457	−	17.5729i	−0.734117	−	1.27153i	0.220993	−	0.975275i	$-0.429070\pi$
$192$		0			0
$193$	18.7315			1.34832			0.674161	−	0.738585i	$-0.264506\pi$
$193$	18.7315			1.34832			0.674161	+	0.738585i	$0.264506\pi$
$194$		0			0
$195$	1.04456	+	1.80922i	0.0748022	+	0.129561i
$196$		0			0
$197$	8.19912	−	14.2013i	0.584163	−	1.01180i	−0.410816	−	0.911718i	$-0.634756\pi$
$197$	8.19912	−	14.2013i	0.584163	−	1.01180i	0.994979	−	0.100082i	$-0.0319105\pi$
$198$		0			0
$199$	−1.58998	−	2.75393i	−0.112711	−	0.195221i	0.804151	−	0.594424i	$-0.202620\pi$
$199$	−1.58998	−	2.75393i	−0.112711	−	0.195221i	−0.916862	+	0.399203i	$0.869287\pi$
$200$		0			0
$201$	−1.23403	+	8.09180i	−0.0870415	+	0.570751i
$202$		0			0
$203$	9.57834	+	16.5902i	0.672268	+	1.16440i
$204$		0			0
$205$	−2.62332	+	4.54373i	−0.183221	+	0.317348i
$206$		0			0
$207$	−0.0409499	−	0.0709273i	−0.00284621	−	0.00492979i
$208$		0			0
$209$	−7.20735			−0.498543
$210$		0			0
$211$	−14.3503	−	24.8554i	−0.987912	−	1.71111i	−0.628202	−	0.778050i	$-0.716209\pi$
$211$	−14.3503	−	24.8554i	−0.987912	−	1.71111i	−0.359711	−	0.933064i	$-0.617125\pi$
$212$		0			0
$213$	5.10094	−	8.83508i	0.349510	−	0.605370i
$214$		0			0
$215$	0.536623			0.0365974
$216$		0			0
$217$	4.16282	+	7.21022i	0.282591	+	0.489461i
$218$		0			0
$219$	−0.703227	−	1.21802i	−0.0475197	−	0.0823065i
$220$		0			0
$221$	−7.68087	+	13.3036i	−0.516671	+	0.894900i
$222$		0			0
$223$	5.60262			0.375179			0.187590	−	0.982248i	$-0.439933\pi$
$223$	5.60262			0.375179			0.187590	+	0.982248i	$0.439933\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	2.10172	−	3.64029i	0.139496	−	0.241614i	−0.787810	−	0.615918i	$-0.788785\pi$
$227$	2.10172	−	3.64029i	0.139496	−	0.241614i	0.927306	+	0.374304i	$0.122118\pi$
$228$		0			0
$229$	5.98088	+	10.3592i	0.395227	+	0.684554i	0.993130	−	0.117015i	$-0.0373324\pi$
$229$	5.98088	+	10.3592i	0.395227	+	0.684554i	−0.597903	+	0.801569i	$0.703999\pi$
$230$		0			0
$231$	1.63388	+	2.82996i	0.107501	+	0.186198i
$232$		0			0
$233$	9.27899	−	16.0717i	0.607887	−	1.05289i	−0.383701	−	0.923457i	$-0.625351\pi$
$233$	9.27899	−	16.0717i	0.607887	−	1.05289i	0.991588	−	0.129434i	$-0.0413160\pi$
$234$		0			0
$235$	2.27990	−	3.94890i	0.148724	−	0.257598i
$236$		0			0
$237$	4.45578	−	7.71764i	0.289434	−	0.501315i
$238$		0			0
$239$	−8.08282	+	13.9999i	−0.522834	+	0.905575i	0.476813	+	0.879005i	$0.341792\pi$
$239$	−8.08282	+	13.9999i	−0.522834	+	0.905575i	−0.999647	+	0.0265706i	$0.991541\pi$
$240$		0			0
$241$	−8.79588			−0.566592			−0.283296	−	0.959032i	$-0.591428\pi$
$241$	−8.79588			−0.566592			−0.283296	+	0.959032i	$0.591428\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.56561	+	2.71171i	0.100023	+	0.173245i
$246$		0			0
$247$	−4.53153	+	7.84884i	−0.288334	+	0.499410i
$248$		0			0
$249$	3.88070	+	6.72157i	0.245929	+	0.425962i
$250$		0			0
$251$	13.9297	+	24.1270i	0.879236	+	1.52288i	0.852180	+	0.523248i	$0.175280\pi$
$251$	13.9297	+	24.1270i	0.879236	+	1.52288i	0.0270561	+	0.999634i	$0.491387\pi$
$252$		0			0
$253$	0.136064			0.00855430
$254$		0			0
$255$	3.67662	+	6.36809i	0.230239	+	0.398785i
$256$		0			0
$257$	0.658891	−	1.14123i	0.0411005	−	0.0711882i	−0.844743	−	0.535172i	$-0.820247\pi$
$257$	0.658891	−	1.14123i	0.0411005	−	0.0711882i	0.885844	+	0.463983i	$0.153580\pi$
$258$		0			0
$259$	−16.6979			−1.03756
$260$		0			0
$261$	−4.86971	+	8.43459i	−0.301428	+	0.522088i
$262$		0			0
$263$	7.85254			0.484208			0.242104	−	0.970250i	$-0.422162\pi$
$263$	7.85254			0.484208			0.242104	+	0.970250i	$0.422162\pi$
$264$		0			0
$265$	−6.41766			−0.394234
$266$		0			0
$267$	13.3312			0.815854
$268$		0			0
$269$	−22.3481			−1.36259			−0.681294	−	0.732010i	$-0.738582\pi$
$269$	−22.3481			−1.36259			−0.681294	+	0.732010i	$0.738582\pi$
$270$		0			0
$271$	−6.47928			−0.393588			−0.196794	−	0.980445i	$-0.563053\pi$
$271$	−6.47928			−0.393588			−0.196794	+	0.980445i	$0.563053\pi$
$272$		0			0
$273$	4.10912			0.248695
$274$		0			0
$275$	−0.830677	+	1.43877i	−0.0500917	+	0.0867614i
$276$		0			0
$277$	−20.4013			−1.22580			−0.612898	−	0.790162i	$-0.709996\pi$
$277$	−20.4013			−1.22580			−0.612898	+	0.790162i	$0.709996\pi$
$278$		0			0
$279$	−2.11641	+	3.66574i	−0.126706	+	0.219462i
$280$		0			0
$281$	5.98618	+	10.3684i	0.357106	+	0.618525i	0.987476	−	0.157769i	$-0.0504303\pi$
$281$	5.98618	+	10.3684i	0.357106	+	0.618525i	−0.630370	+	0.776295i	$0.717097\pi$
$282$		0			0
$283$	−6.90775			−0.410623			−0.205312	−	0.978697i	$-0.565821\pi$
$283$	−6.90775			−0.410623			−0.205312	+	0.978697i	$0.565821\pi$
$284$		0			0
$285$	2.16912	+	3.75702i	0.128487	+	0.222547i
$286$		0			0
$287$	5.15988	+	8.93717i	0.304578	+	0.527544i
$288$		0			0
$289$	−18.5350	+	32.1036i	−1.09030	+	1.88845i
$290$		0			0
$291$	−5.51786	−	9.55722i	−0.323463	−	0.560254i
$292$		0			0
$293$	22.6227			1.32163			0.660817	−	0.750547i	$-0.270210\pi$
$293$	22.6227			1.32163			0.660817	+	0.750547i	$0.270210\pi$
$294$		0			0
$295$	−12.6477			−0.736377
$296$		0			0
$297$	−0.830677	+	1.43877i	−0.0482008	+	0.0834862i
$298$		0			0
$299$	0.0855489	−	0.148175i	0.00494742	−	0.00856918i
$300$		0			0
$301$	0.527747	−	0.914085i	0.0304189	−	0.0526870i
$302$		0			0
$303$	−4.08350	+	7.07283i	−0.234591	+	0.406323i
$304$		0			0
$305$	0.416747	+	0.721828i	0.0238629	+	0.0413317i
$306$		0			0
$307$	7.85073	+	13.5979i	0.448065	+	0.776071i	0.998260	−	0.0589651i	$-0.0187801\pi$
$307$	7.85073	+	13.5979i	0.448065	+	0.776071i	−0.550195	+	0.835036i	$0.685447\pi$
$308$		0			0
$309$	4.38112	−	7.58832i	0.249233	−	0.431685i
$310$		0			0
$311$	15.0215			0.851793			0.425896	−	0.904772i	$-0.359959\pi$
$311$	15.0215			0.851793			0.425896	+	0.904772i	$0.359959\pi$
$312$		0			0
$313$	−2.57311			−0.145441			−0.0727204	−	0.997352i	$-0.523168\pi$
$313$	−2.57311			−0.145441			−0.0727204	+	0.997352i	$0.523168\pi$
$314$		0			0
$315$	0.983461	−	1.70340i	0.0554118	−	0.0959760i
$316$		0			0
$317$	−10.9274	−	18.9269i	−0.613747	−	1.06304i	−0.990603	−	0.136769i	$-0.956328\pi$
$317$	−10.9274	−	18.9269i	−0.613747	−	1.06304i	0.376856	−	0.926272i	$-0.377005\pi$
$318$		0			0
$319$	−8.09031	−	14.0128i	−0.452971	−	0.784568i
$320$		0			0
$321$	18.8592			1.05262
$322$		0			0
$323$	−15.9500	+	27.6263i	−0.887484	+	1.53717i
$324$		0			0
$325$	1.04456	+	1.80922i	0.0579415	+	0.100358i
$326$		0			0
$327$	−6.17731			−0.341606
$328$		0			0
$329$	−4.48439	−	7.76719i	−0.247232	−	0.428219i
$330$		0			0
$331$	7.12866	−	12.3472i	0.391826	−	0.678663i	−0.600864	−	0.799351i	$-0.705177\pi$
$331$	7.12866	−	12.3472i	0.391826	−	0.678663i	0.992690	+	0.120688i	$0.0385100\pi$
$332$		0			0
$333$	−4.24467	−	7.35199i	−0.232607	−	0.402887i
$334$		0			0
$335$	−1.23403	+	8.09180i	−0.0674220	+	0.442102i
$336$		0			0
$337$	−2.51918	−	4.36334i	−0.137228	−	0.237686i	0.789218	−	0.614113i	$-0.210486\pi$
$337$	−2.51918	−	4.36334i	−0.137228	−	0.237686i	−0.926446	+	0.376427i	$0.877153\pi$
$338$		0			0
$339$	−1.84983	+	3.20400i	−0.100469	+	0.174017i
$340$		0			0
$341$	−3.51611	−	6.09008i	−0.190408	−	0.329797i
$342$		0			0
$343$	19.9273			1.07597
$344$		0			0
$345$	−0.0409499	−	0.0709273i	−0.00220467	−	0.00381860i
$346$		0			0
$347$	10.1405	−	17.5638i	0.544369	−	0.942875i	−0.454277	−	0.890860i	$-0.650103\pi$
$347$	10.1405	−	17.5638i	0.544369	−	0.942875i	0.998646	−	0.0520143i	$-0.0165641\pi$
$348$		0			0
$349$	0.996854			0.0533604			0.0266802	−	0.999644i	$-0.491506\pi$
$349$	0.996854			0.0533604			0.0266802	+	0.999644i	$0.491506\pi$
$350$		0			0
$351$	1.04456	+	1.80922i	0.0557543	+	0.0965692i
$352$		0			0
$353$	9.07234	+	15.7138i	0.482872	+	0.836359i	0.999807	−	0.0196661i	$-0.00626031\pi$
$353$	9.07234	+	15.7138i	0.482872	+	0.836359i	−0.516935	+	0.856025i	$0.672927\pi$
$354$		0			0
$355$	5.10094	−	8.83508i	0.270730	−	0.468917i
$356$		0			0
$357$	14.4632			0.765476
$358$		0			0
$359$	27.0942			1.42998			0.714988	−	0.699137i	$-0.246432\pi$
$359$	27.0942			1.42998			0.714988	+	0.699137i	$0.246432\pi$
$360$		0			0
$361$	0.0898493	−	0.155624i	0.00472891	−	0.00819072i
$362$		0			0
$363$	4.11995	+	7.13597i	0.216241	+	0.374541i
$364$		0			0
$365$	−0.703227	−	1.21802i	−0.0368086	−	0.0637543i
$366$		0			0
$367$	11.2572	−	19.4980i	0.587619	−	1.01779i	−0.406924	−	0.913462i	$-0.633399\pi$
$367$	11.2572	−	19.4980i	0.587619	−	1.01779i	0.994543	−	0.104324i	$-0.0332679\pi$
$368$		0			0
$369$	−2.62332	+	4.54373i	−0.136565	+	0.236537i
$370$		0			0
$371$	−6.31152	+	10.9319i	−0.327678	+	0.567555i
$372$		0			0
$373$	−2.10703	+	3.64948i	−0.109098	+	0.188963i	−0.915405	−	0.402534i	$-0.868130\pi$
$373$	−2.10703	+	3.64948i	−0.109098	+	0.188963i	0.806307	+	0.591497i	$0.201463\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−20.3467			−1.04791
$378$		0			0
$379$	−8.63858	−	14.9625i	−0.443734	−	0.768570i	0.554229	−	0.832364i	$-0.313013\pi$
$379$	−8.63858	−	14.9625i	−0.443734	−	0.768570i	−0.997963	+	0.0637944i	$0.979680\pi$
$380$		0			0
$381$	−4.45037	+	7.70826i	−0.227999	+	0.394906i
$382$		0			0
$383$	8.17816	+	14.1650i	0.417884	+	0.723797i	0.995726	−	0.0923515i	$-0.0294383\pi$
$383$	8.17816	+	14.1650i	0.417884	+	0.723797i	−0.577842	+	0.816149i	$0.696105\pi$
$384$		0			0
$385$	1.63388	+	2.82996i	0.0832701	+	0.144228i
$386$		0			0
$387$	0.536623			0.0272781
$388$		0			0
$389$	−2.75812	−	4.77720i	−0.139842	−	0.242214i	0.787595	−	0.616194i	$-0.211326\pi$
$389$	−2.75812	−	4.77720i	−0.139842	−	0.242214i	−0.927437	+	0.373980i	$0.877993\pi$
$390$		0			0
$391$	0.301114	−	0.521545i	0.0152280	−	0.0263757i
$392$		0			0
$393$	12.9882			0.655169
$394$		0			0
$395$	4.45578	−	7.71764i	0.224195	−	0.388317i
$396$		0			0
$397$	−19.2472			−0.965989			−0.482995	−	0.875623i	$-0.660451\pi$
$397$	−19.2472			−0.965989			−0.482995	+	0.875623i	$0.660451\pi$
$398$		0			0
$399$	8.53298			0.427183
$400$		0			0
$401$	−4.23057			−0.211265			−0.105632	−	0.994405i	$-0.533687\pi$
$401$	−4.23057			−0.211265			−0.105632	+	0.994405i	$0.533687\pi$
$402$		0			0
$403$	−8.84285			−0.440494
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	14.1038			0.699100
$408$		0			0
$409$	11.1361	−	19.2883i	0.550646	−	0.953747i	−0.447582	−	0.894243i	$-0.647715\pi$
$409$	11.1361	−	19.2883i	0.550646	−	0.953747i	0.998228	−	0.0595041i	$-0.0189519\pi$
$410$		0			0
$411$	−6.22145			−0.306881
$412$		0			0
$413$	−12.4385	+	21.5441i	−0.612059	+	1.06012i
$414$		0			0
$415$	3.88070	+	6.72157i	0.190496	+	0.329949i
$416$		0			0
$417$	14.9130			0.730293
$418$		0			0
$419$	−7.74113	−	13.4080i	−0.378179	−	0.655025i	0.612618	−	0.790379i	$-0.290116\pi$
$419$	−7.74113	−	13.4080i	−0.378179	−	0.655025i	−0.990797	+	0.135354i	$0.956783\pi$
$420$		0			0
$421$	−8.54533	−	14.8009i	−0.416474	−	0.721354i	0.579108	−	0.815251i	$-0.303401\pi$
$421$	−8.54533	−	14.8009i	−0.416474	−	0.721354i	−0.995582	+	0.0938971i	$0.970068\pi$
$422$		0			0
$423$	2.27990	−	3.94890i	0.110853	−	0.192002i
$424$		0			0
$425$	3.67662	+	6.36809i	0.178342	+	0.308898i
$426$		0			0
$427$	1.63942			0.0793371
$428$		0			0
$429$	−3.47075			−0.167570
$430$		0			0
$431$	15.0993	−	26.1528i	0.727308	−	1.25974i	−0.230708	−	0.973023i	$-0.574104\pi$
$431$	15.0993	−	26.1528i	0.727308	−	1.25974i	0.958017	−	0.286712i	$-0.0925623\pi$
$432$		0			0
$433$	−16.0116	+	27.7330i	−0.769471	+	1.33276i	0.168380	+	0.985722i	$0.446147\pi$
$433$	−16.0116	+	27.7330i	−0.769471	+	1.33276i	−0.937850	+	0.347040i	$0.887187\pi$
$434$		0			0
$435$	−4.86971	+	8.43459i	−0.233485	+	0.404408i
$436$		0			0
$437$	0.177650	−	0.307699i	0.00849817	−	0.0147193i
$438$		0			0
$439$	11.1434	+	19.3010i	0.531847	+	0.921185i	0.999309	+	0.0371722i	$0.0118350\pi$
$439$	11.1434	+	19.3010i	0.531847	+	0.921185i	−0.467462	+	0.884013i	$0.654832\pi$
$440$		0			0
$441$	1.56561	+	2.71171i	0.0745528	+	0.129129i
$442$		0			0
$443$	−3.61891	+	6.26814i	−0.171940	+	0.297808i	−0.939098	−	0.343649i	$-0.888337\pi$
$443$	−3.61891	+	6.26814i	−0.171940	+	0.297808i	0.767158	+	0.641458i	$0.221670\pi$
$444$		0			0
$445$	13.3312			0.631958
$446$		0			0
$447$	5.60207			0.264969
$448$		0			0
$449$	18.6007	−	32.2174i	0.877822	−	1.52043i	0.0240957	−	0.999710i	$-0.492329\pi$
$449$	18.6007	−	32.2174i	0.877822	−	1.52043i	0.853726	−	0.520722i	$-0.174337\pi$
$450$		0			0
$451$	−4.35827	−	7.54874i	−0.205223	−	0.355457i
$452$		0			0
$453$	4.61529	+	7.99391i	0.216845	+	0.375587i
$454$		0			0
$455$	4.10912			0.192639
$456$		0			0
$457$	13.0651	−	22.6294i	0.611158	−	1.05856i	−0.379888	−	0.925033i	$-0.624037\pi$
$457$	13.0651	−	22.6294i	0.611158	−	1.05856i	0.991046	−	0.133524i	$-0.0426294\pi$
$458$		0			0
$459$	3.67662	+	6.36809i	0.171610	+	0.297237i
$460$		0			0
$461$	−33.4982			−1.56017			−0.780083	−	0.625677i	$-0.784823\pi$
$461$	−33.4982			−1.56017			−0.780083	+	0.625677i	$0.784823\pi$
$462$		0			0
$463$	−2.63871	−	4.57039i	−0.122631	−	0.212404i	0.798173	−	0.602428i	$-0.205800\pi$
$463$	−2.63871	−	4.57039i	−0.122631	−	0.212404i	−0.920805	+	0.390024i	$0.872467\pi$
$464$		0			0
$465$	−2.11641	+	3.66574i	−0.0981463	+	0.169994i
$466$		0			0
$467$	0.233202	+	0.403918i	0.0107913	+	0.0186911i	0.871371	−	0.490625i	$-0.163232\pi$
$467$	0.233202	+	0.403918i	0.0107913	+	0.0186911i	−0.860579	+	0.509316i	$0.829898\pi$
$468$		0			0
$469$	12.5700	+	10.0600i	0.580428	+	0.464528i
$470$		0			0
$471$	−6.86337	−	11.8877i	−0.316248	−	0.547757i
$472$		0			0
$473$	−0.445760	+	0.772079i	−0.0204961	+	0.0355002i
$474$		0			0
$475$	2.16912	+	3.75702i	0.0995260	+	0.172384i
$476$		0			0
$477$	−6.41766			−0.293844
$478$		0			0
$479$	12.6904	+	21.9804i	0.579837	+	1.00431i	0.995497	+	0.0947879i	$0.0302173\pi$
$479$	12.6904	+	21.9804i	0.579837	+	1.00431i	−0.415660	+	0.909520i	$0.636449\pi$
$480$		0			0
$481$	8.86760	−	15.3591i	0.404328	−	0.700316i
$482$		0			0
$483$	−0.161090			−0.00732987
$484$		0			0
$485$	−5.51786	−	9.55722i	−0.250553	−	0.433971i
$486$		0			0
$487$	−17.3344	−	30.0241i	−0.785497	−	1.36052i	−0.928702	−	0.370827i	$-0.879074\pi$
$487$	−17.3344	−	30.0241i	−0.785497	−	1.36052i	0.143205	−	0.989693i	$-0.454259\pi$
$488$		0			0
$489$	3.55321	−	6.15435i	0.160682	−	0.278309i
$490$		0			0
$491$	12.4903			0.563680			0.281840	−	0.959461i	$-0.409055\pi$
$491$	12.4903			0.563680			0.281840	+	0.959461i	$0.409055\pi$
$492$		0			0
$493$	−71.6163			−3.22544
$494$		0			0
$495$	−0.830677	+	1.43877i	−0.0373361	+	0.0646681i
$496$		0			0
$497$	−10.0331	−	17.3779i	−0.450048	−	0.779506i
$498$		0			0
$499$	−10.2257	−	17.7114i	−0.457765	−	0.792871i	0.541078	−	0.840972i	$-0.318016\pi$
$499$	−10.2257	−	17.7114i	−0.457765	−	0.792871i	−0.998842	+	0.0481011i	$0.984683\pi$
$500$		0			0
$501$	−1.68966	+	2.92657i	−0.0754883	+	0.130750i
$502$		0			0
$503$	−18.8047	+	32.5708i	−0.838462	+	1.45226i	0.0527181	+	0.998609i	$0.483212\pi$
$503$	−18.8047	+	32.5708i	−0.838462	+	1.45226i	−0.891180	+	0.453649i	$0.850122\pi$
$504$		0			0
$505$	−4.08350	+	7.07283i	−0.181713	+	0.314737i
$506$		0			0
$507$	4.31781	−	7.47866i	0.191761	−	0.332139i
$508$		0			0
$509$	26.6388			1.18074			0.590371	−	0.807132i	$-0.298981\pi$
$509$	26.6388			1.18074			0.590371	+	0.807132i	$0.298981\pi$
$510$		0			0
$511$	−2.76638			−0.122378
$512$		0			0
$513$	2.16912	+	3.75702i	0.0957689	+	0.165877i
$514$		0			0
$515$	4.38112	−	7.58832i	0.193055	−	0.334382i
$516$		0			0
$517$	3.78772	+	6.56053i	0.166584	+	0.288532i
$518$		0			0
$519$	5.09706	+	8.82836i	0.223736	+	0.387522i
$520$		0			0
$521$	15.3598			0.672925			0.336463	−	0.941697i	$-0.390769\pi$
$521$	15.3598			0.672925			0.336463	+	0.941697i	$0.390769\pi$
$522$		0			0
$523$	20.2663	+	35.1022i	0.886182	+	1.53491i	0.844353	+	0.535787i	$0.179985\pi$
$523$	20.2663	+	35.1022i	0.886182	+	1.53491i	0.0418291	+	0.999125i	$0.486682\pi$
$524$		0			0
$525$	0.983461	−	1.70340i	0.0429218	−	0.0743427i
$526$		0			0
$527$	−31.1250			−1.35583
$528$		0			0
$529$	11.4966	−	19.9128i	0.499854	−	0.865773i
$530$		0			0
$531$	−12.6477			−0.548863
$532$		0			0
$533$	−10.9608			−0.474766
$534$		0			0
$535$	18.8592			0.815355
$536$		0			0
$537$	−20.2547			−0.874055
$538$		0			0
$539$	−5.20206			−0.224069
$540$		0			0
$541$	−25.8086			−1.10960			−0.554798	−	0.831985i	$-0.687205\pi$
$541$	−25.8086			−1.10960			−0.554798	+	0.831985i	$0.687205\pi$
$542$		0			0
$543$	4.59855	−	7.96493i	0.197343	−	0.341808i
$544$		0			0
$545$	−6.17731			−0.264607
$546$		0			0
$547$	4.72488	−	8.18373i	0.202021	−	0.349911i	−0.747158	−	0.664646i	$-0.768582\pi$
$547$	4.72488	−	8.18373i	0.202021	−	0.349911i	0.949180	+	0.314735i	$0.101916\pi$
$548$		0			0
$549$	0.416747	+	0.721828i	0.0177863	+	0.0308069i
$550$		0			0
$551$	−42.2519			−1.79999
$552$		0			0
$553$	−8.76418	−	15.1800i	−0.372691	−	0.645519i
$554$		0			0
$555$	−4.24467	−	7.35199i	−0.180176	−	0.312075i
$556$		0			0
$557$	−4.75332	+	8.23299i	−0.201405	+	0.348843i	−0.948981	−	0.315332i	$-0.897884\pi$
$557$	−4.75332	+	8.23299i	−0.201405	+	0.348843i	0.747577	+	0.664176i	$0.231217\pi$
$558$		0			0
$559$	0.560532	+	0.970870i	0.0237080	+	0.0410634i
$560$		0			0
$561$	−12.2163			−0.515774
$562$		0			0
$563$	30.1328			1.26995			0.634974	−	0.772534i	$-0.281011\pi$
$563$	30.1328			1.26995			0.634974	+	0.772534i	$0.281011\pi$
$564$		0			0
$565$	−1.84983	+	3.20400i	−0.0778229	+	0.134793i
$566$		0			0
$567$	0.983461	−	1.70340i	0.0413015	−	0.0715363i
$568$		0			0
$569$	−19.5112	+	33.7944i	−0.817952	+	1.41673i	0.0892368	+	0.996010i	$0.471557\pi$
$569$	−19.5112	+	33.7944i	−0.817952	+	1.41673i	−0.907189	+	0.420724i	$0.861776\pi$
$570$		0			0
$571$	−2.76037	+	4.78110i	−0.115518	+	0.200083i	−0.917987	−	0.396611i	$-0.870186\pi$
$571$	−2.76037	+	4.78110i	−0.115518	+	0.200083i	0.802469	+	0.596694i	$0.203519\pi$
$572$		0			0
$573$	−10.1457	−	17.5729i	−0.423843	−	0.734117i
$574$		0			0
$575$	−0.0409499	−	0.0709273i	−0.00170773	−	0.00295787i
$576$		0			0
$577$	3.04983	−	5.28246i	0.126966	−	0.219912i	−0.795534	−	0.605909i	$-0.792809\pi$
$577$	3.04983	−	5.28246i	0.126966	−	0.219912i	0.922500	+	0.385998i	$0.126143\pi$
$578$		0			0
$579$	18.7315			0.778454
$580$		0			0
$581$	15.2661			0.633343
$582$		0			0
$583$	5.33100	−	9.23357i	0.220788	−	0.382415i
$584$		0			0
$585$	1.04456	+	1.80922i	0.0431871	+	0.0748022i
$586$		0			0
$587$	−7.63754	−	13.2286i	−0.315235	−	0.546003i	0.664252	−	0.747508i	$-0.268750\pi$
$587$	−7.63754	−	13.2286i	−0.315235	−	0.546003i	−0.979487	+	0.201505i	$0.935417\pi$
$588$		0			0
$589$	−18.3630			−0.756635
$590$		0			0
$591$	8.19912	−	14.2013i	0.337267	−	0.584163i
$592$		0			0
$593$	16.5277	+	28.6268i	0.678711	+	1.17556i	0.975369	+	0.220578i	$0.0707943\pi$
$593$	16.5277	+	28.6268i	0.678711	+	1.17556i	−0.296659	+	0.954984i	$0.595872\pi$
$594$		0			0
$595$	14.4632			0.592935
$596$		0			0
$597$	−1.58998	−	2.75393i	−0.0650737	−	0.112711i
$598$		0			0
$599$	−6.82542	+	11.8220i	−0.278879	+	0.483033i	−0.971106	−	0.238647i	$-0.923296\pi$
$599$	−6.82542	+	11.8220i	−0.278879	+	0.483033i	0.692227	+	0.721680i	$0.256630\pi$
$600$		0			0
$601$	−10.5423	−	18.2598i	−0.430029	−	0.744833i	0.566846	−	0.823824i	$-0.308163\pi$
$601$	−10.5423	−	18.2598i	−0.430029	−	0.744833i	−0.996875	+	0.0789912i	$0.974830\pi$
$602$		0			0
$603$	−1.23403	+	8.09180i	−0.0502534	+	0.329523i
$604$		0			0
$605$	4.11995	+	7.13597i	0.167500	+	0.290118i
$606$		0			0
$607$	3.50847	−	6.07684i	0.142404	−	0.246651i	−0.785997	−	0.618230i	$-0.787850\pi$
$607$	3.50847	−	6.07684i	0.142404	−	0.246651i	0.928402	+	0.371579i	$0.121183\pi$
$608$		0			0
$609$	9.57834	+	16.5902i	0.388134	+	0.672268i
$610$		0			0
$611$	9.52593			0.385378
$612$		0			0
$613$	−4.20464	−	7.28265i	−0.169824	−	0.294144i	0.768534	−	0.639809i	$-0.220987\pi$
$613$	−4.20464	−	7.28265i	−0.169824	−	0.294144i	−0.938358	+	0.345665i	$0.887653\pi$
$614$		0			0
$615$	−2.62332	+	4.54373i	−0.105783	+	0.183221i
$616$		0			0
$617$	41.3006			1.66270			0.831349	−	0.555750i	$-0.187569\pi$
$617$	41.3006			1.66270			0.831349	+	0.555750i	$0.187569\pi$
$618$		0			0
$619$	−10.5134	−	18.2097i	−0.422568	−	0.731909i	0.573622	−	0.819120i	$-0.305538\pi$
$619$	−10.5134	−	18.2097i	−0.422568	−	0.731909i	−0.996190	+	0.0872111i	$0.972205\pi$
$620$		0			0
$621$	−0.0409499	−	0.0709273i	−0.00164326	−	0.00284621i
$622$		0			0
$623$	13.1107	−	22.7084i	0.525268	−	0.909791i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.20735			−0.287834
$628$		0			0
$629$	31.2121	−	54.0609i	1.24451	−	2.15555i
$630$		0			0
$631$	−18.3443	−	31.7732i	−0.730274	−	1.26487i	−0.956766	−	0.290859i	$-0.906059\pi$
$631$	−18.3443	−	31.7732i	−0.730274	−	1.26487i	0.226492	−	0.974013i	$-0.427274\pi$
$632$		0			0
$633$	−14.3503	−	24.8554i	−0.570371	−	0.987912i
$634$		0			0
$635$	−4.45037	+	7.70826i	−0.176607	+	0.305893i
$636$		0			0
$637$	−3.27073	+	5.66507i	−0.129591	+	0.224458i
$638$		0			0
$639$	5.10094	−	8.83508i	0.201790	−	0.349510i
$640$		0			0
$641$	−10.7749	+	18.6626i	−0.425582	+	0.737130i	−0.996475	−	0.0838949i	$-0.973264\pi$
$641$	−10.7749	+	18.6626i	−0.425582	+	0.737130i	0.570892	+	0.821025i	$0.306597\pi$
$642$		0			0
$643$	44.4790			1.75408			0.877041	−	0.480416i	$-0.159514\pi$
$643$	44.4790			1.75408			0.877041	+	0.480416i	$0.159514\pi$
$644$		0			0
$645$	0.536623			0.0211295
$646$		0			0
$647$	15.0867	+	26.1309i	0.593120	+	1.02731i	0.993809	+	0.111100i	$0.0354372\pi$
$647$	15.0867	+	26.1309i	0.593120	+	1.02731i	−0.400690	+	0.916214i	$0.631229\pi$
$648$		0			0
$649$	10.5061	−	18.1972i	0.412402	−	0.714302i
$650$		0			0
$651$	4.16282	+	7.21022i	0.163154	+	0.282591i
$652$		0			0
$653$	16.1428	+	27.9602i	0.631718	+	1.09417i	0.987200	+	0.159485i	$0.0509832\pi$
$653$	16.1428	+	27.9602i	0.631718	+	1.09417i	−0.355483	+	0.934683i	$0.615683\pi$
$654$		0			0
$655$	12.9882			0.507492
$656$		0			0
$657$	−0.703227	−	1.21802i	−0.0274355	−	0.0475197i
$658$		0			0
$659$	−1.89517	+	3.28252i	−0.0738252	+	0.127869i	−0.900575	−	0.434701i	$-0.856854\pi$
$659$	−1.89517	+	3.28252i	−0.0738252	+	0.127869i	0.826750	+	0.562570i	$0.190187\pi$
$660$		0			0
$661$	6.52997			0.253986			0.126993	−	0.991904i	$-0.459467\pi$
$661$	6.52997			0.253986			0.126993	+	0.991904i	$0.459467\pi$
$662$		0			0
$663$	−7.68087	+	13.3036i	−0.298300	+	0.516671i
$664$		0			0
$665$	8.53298			0.330895
$666$		0			0
$667$	0.797656			0.0308854
$668$		0			0
$669$	5.60262			0.216610
$670$		0			0
$671$	−1.38473			−0.0534569
$672$		0			0
$673$	−27.2904			−1.05197			−0.525983	−	0.850495i	$-0.676303\pi$
$673$	−27.2904			−1.05197			−0.525983	+	0.850495i	$0.676303\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−5.05251	+	8.75121i	−0.194184	+	0.336336i	−0.946633	−	0.322315i	$-0.895539\pi$
$677$	−5.05251	+	8.75121i	−0.194184	+	0.336336i	0.752449	+	0.658651i	$0.228872\pi$
$678$		0			0
$679$	−21.7064			−0.833016
$680$		0			0
$681$	2.10172	−	3.64029i	0.0805381	−	0.139496i
$682$		0			0
$683$	9.50575	+	16.4644i	0.363727	+	0.629994i	0.988571	−	0.150756i	$-0.0481706\pi$
$683$	9.50575	+	16.4644i	0.363727	+	0.629994i	−0.624844	+	0.780750i	$0.714837\pi$
$684$		0			0
$685$	−6.22145			−0.237709
$686$		0			0
$687$	5.98088	+	10.3592i	0.228185	+	0.395227i
$688$		0			0
$689$	−6.70360	−	11.6110i	−0.255387	−	0.442343i
$690$		0			0
$691$	9.80603	−	16.9845i	0.373039	−	0.646122i	−0.616993	−	0.786969i	$-0.711649\pi$
$691$	9.80603	−	16.9845i	0.373039	−	0.646122i	0.990031	+	0.140847i	$0.0449825\pi$
$692$		0			0
$693$	1.63388	+	2.82996i	0.0620658	+	0.107501i
$694$		0			0
$695$	14.9130			0.565683
$696$		0			0
$697$	−38.5799			−1.46132
$698$		0			0
$699$	9.27899	−	16.0717i	0.350964	−	0.607887i
$700$		0			0
$701$	15.0700	−	26.1019i	0.569184	−	0.985856i	−0.427462	−	0.904033i	$-0.640592\pi$
$701$	15.0700	−	26.1019i	0.569184	−	0.985856i	0.996647	−	0.0818232i	$-0.0260743\pi$
$702$		0			0
$703$	18.4144	−	31.8947i	0.694512	−	1.20293i
$704$		0			0
$705$	2.27990	−	3.94890i	0.0858660	−	0.148724i
$706$		0			0
$707$	8.03193	+	13.9117i	0.302072	+	0.523203i
$708$		0			0
$709$	−13.6877	−	23.7077i	−0.514051	−	0.890363i	−0.999867	−	0.0163019i	$-0.994811\pi$
$709$	−13.6877	−	23.7077i	−0.514051	−	0.890363i	0.485816	−	0.874061i	$-0.338523\pi$
$710$		0			0
$711$	4.45578	−	7.71764i	0.167105	−	0.289434i
$712$		0			0
$713$	0.346668			0.0129828
$714$		0			0
$715$	−3.47075			−0.129799
$716$		0			0
$717$	−8.08282	+	13.9999i	−0.301858	+	0.522834i
$718$		0			0
$719$	−8.91602	−	15.4430i	−0.332511	−	0.575927i	0.650492	−	0.759513i	$-0.274563\pi$
$719$	−8.91602	−	15.4430i	−0.332511	−	0.575927i	−0.983004	+	0.183586i	$0.941229\pi$
$720$		0			0
$721$	−8.61732	−	14.9256i	−0.320926	−	0.555860i
$722$		0			0
$723$	−8.79588			−0.327122
$724$		0			0
$725$	−4.86971	+	8.43459i	−0.180857	+	0.313253i
$726$		0			0
$727$	5.63567	+	9.76127i	0.209016	+	0.362026i	0.951405	−	0.307943i	$-0.0996407\pi$
$727$	5.63567	+	9.76127i	0.209016	+	0.362026i	−0.742389	+	0.669969i	$0.766307\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.97296	+	3.41726i	0.0729724	+	0.126392i
$732$		0			0
$733$	2.05010	−	3.55087i	0.0757220	−	0.131154i	−0.825678	−	0.564142i	$-0.809207\pi$
$733$	2.05010	−	3.55087i	0.0757220	−	0.131154i	0.901400	+	0.432987i	$0.142541\pi$
$734$		0			0
$735$	1.56561	+	2.71171i	0.0577483	+	0.100023i
$736$		0			0
$737$	−10.6172	−	8.49715i	−0.391089	−	0.312997i
$738$		0			0
$739$	−22.3444	−	38.7017i	−0.821954	−	1.42367i	−0.904225	−	0.427056i	$-0.859551\pi$
$739$	−22.3444	−	38.7017i	−0.821954	−	1.42367i	0.0822718	−	0.996610i	$-0.473782\pi$
$740$		0			0
$741$	−4.53153	+	7.84884i	−0.166470	+	0.288334i
$742$		0			0
$743$	−13.3223	−	23.0748i	−0.488746	−	0.846533i	0.511170	−	0.859480i	$-0.329212\pi$
$743$	−13.3223	−	23.0748i	−0.488746	−	0.846533i	−0.999916	+	0.0129464i	$0.995879\pi$
$744$		0			0
$745$	5.60207			0.205244
$746$		0			0
$747$	3.88070	+	6.72157i	0.141987	+	0.245929i
$748$		0			0
$749$	18.5473	−	32.1249i	0.677704	−	1.17382i
$750$		0			0
$751$	−16.9796			−0.619596			−0.309798	−	0.950802i	$-0.600261\pi$
$751$	−16.9796			−0.619596			−0.309798	+	0.950802i	$0.600261\pi$
$752$		0			0
$753$	13.9297	+	24.1270i	0.507627	+	0.879236i
$754$		0			0
$755$	4.61529	+	7.99391i	0.167968	+	0.290928i
$756$		0			0
$757$	17.1463	−	29.6982i	0.623191	−	1.07940i	−0.365696	−	0.930734i	$-0.619169\pi$
$757$	17.1463	−	29.6982i	0.623191	−	1.07940i	0.988888	−	0.148665i	$-0.0474976\pi$
$758$		0			0
$759$	0.136064			0.00493883
$760$		0			0
$761$	6.09505			0.220946			0.110473	−	0.993879i	$-0.464764\pi$
$761$	6.09505			0.220946			0.110473	+	0.993879i	$0.464764\pi$
$762$		0			0
$763$	−6.07514	+	10.5225i	−0.219935	+	0.380938i
$764$		0			0
$765$	3.67662	+	6.36809i	0.132928	+	0.230239i
$766$		0			0
$767$	−13.2112	−	22.8825i	−0.477030	−	0.826240i
$768$		0			0
$769$	−27.3260	+	47.3300i	−0.985399	+	1.70676i	−0.345251	+	0.938510i	$0.612206\pi$
$769$	−27.3260	+	47.3300i	−0.985399	+	1.70676i	−0.640148	+	0.768251i	$0.721127\pi$
$770$		0			0
$771$	0.658891	−	1.14123i	0.0237294	−	0.0411005i
$772$		0			0
$773$	−15.0405	+	26.0508i	−0.540968	+	0.936983i	0.457881	+	0.889013i	$0.348609\pi$
$773$	−15.0405	+	26.0508i	−0.540968	+	0.936983i	−0.998849	+	0.0479700i	$0.984725\pi$
$774$		0			0
$775$	−2.11641	+	3.66574i	−0.0760238	+	0.131677i
$776$		0			0
$777$	−16.6979			−0.599033
$778$		0			0
$779$	−22.7612			−0.815505
$780$		0			0
$781$	8.47446	+	14.6782i	0.303240	+	0.525227i
$782$		0			0
$783$	−4.86971	+	8.43459i	−0.174029	+	0.301428i
$784$		0			0
$785$	−6.86337	−	11.8877i	−0.244964	−	0.424291i
$786$		0			0
$787$	3.84862	+	6.66601i	0.137189	+	0.237618i	0.926431	−	0.376464i	$-0.122860\pi$
$787$	3.84862	+	6.66601i	0.137189	+	0.237618i	−0.789243	+	0.614081i	$0.789527\pi$
$788$		0			0
$789$	7.85254			0.279558
$790$		0			0
$791$	3.63847	+	6.30201i	0.129369	+	0.224074i
$792$		0			0
$793$	−0.870632	+	1.50798i	−0.0309170	+	0.0535499i
$794$		0			0
$795$	−6.41766			−0.227611
$796$		0			0
$797$	−20.1021	+	34.8179i	−0.712053	+	1.23331i	0.252032	+	0.967719i	$0.418901\pi$
$797$	−20.1021	+	34.8179i	−0.712053	+	1.23331i	−0.964085	+	0.265593i	$0.914432\pi$
$798$		0			0
$799$	33.5293			1.18618
$800$		0			0
$801$	13.3312			0.471033
$802$		0			0
$803$	2.33662			0.0824574
$804$		0			0
$805$	−0.161090			−0.00567769
$806$		0			0
$807$	−22.3481			−0.786691
$808$		0			0
$809$	−34.1277			−1.19986			−0.599932	−	0.800051i	$-0.704806\pi$
$809$	−34.1277			−1.19986			−0.599932	+	0.800051i	$0.704806\pi$
$810$		0			0
$811$	−5.27739	+	9.14070i	−0.185314	+	0.320973i	−0.943682	−	0.330853i	$-0.892664\pi$
$811$	−5.27739	+	9.14070i	−0.185314	+	0.320973i	0.758368	+	0.651826i	$0.225997\pi$
$812$		0			0
$813$	−6.47928			−0.227238
$814$		0			0
$815$	3.55321	−	6.15435i	0.124464	−	0.215577i
$816$		0			0
$817$	1.16400	+	2.01610i	0.0407231	+	0.0705345i
$818$		0			0
$819$	4.10912			0.143584
$820$		0			0
$821$	9.57780	+	16.5892i	0.334268	+	0.578969i	0.983344	−	0.181755i	$-0.0581777\pi$
$821$	9.57780	+	16.5892i	0.334268	+	0.578969i	−0.649076	+	0.760723i	$0.724844\pi$
$822$		0			0
$823$	13.7121	+	23.7500i	0.477973	+	0.827873i	0.999681	−	0.0252508i	$-0.00803842\pi$
$823$	13.7121	+	23.7500i	0.477973	+	0.827873i	−0.521708	+	0.853124i	$0.674705\pi$
$824$		0			0
$825$	−0.830677	+	1.43877i	−0.0289205	+	0.0500917i
$826$		0			0
$827$	−9.12927	−	15.8124i	−0.317456	−	0.549850i	0.662501	−	0.749061i	$-0.269495\pi$
$827$	−9.12927	−	15.8124i	−0.317456	−	0.549850i	−0.979956	+	0.199212i	$0.936162\pi$
$828$		0			0
$829$	−8.42685			−0.292677			−0.146338	−	0.989235i	$-0.546749\pi$
$829$	−8.42685			−0.292677			−0.146338	+	0.989235i	$0.546749\pi$
$830$		0			0
$831$	−20.4013			−0.707714
$832$		0			0
$833$	−11.5123	+	19.9399i	−0.398877	+	0.690875i
$834$		0			0
$835$	−1.68966	+	2.92657i	−0.0584730	+	0.101278i
$836$		0			0
$837$	−2.11641	+	3.66574i	−0.0731540	+	0.126706i
$838$		0			0
$839$	1.90256	−	3.29533i	0.0656837	−	0.113768i	−0.831313	−	0.555804i	$-0.812410\pi$
$839$	1.90256	−	3.29533i	0.0656837	−	0.113768i	0.896997	+	0.442036i	$0.145744\pi$
$840$		0			0
$841$	−32.9282	−	57.0333i	−1.13545	−	1.96667i
$842$		0			0
$843$	5.98618	+	10.3684i	0.206175	+	0.357106i
$844$		0			0
$845$	4.31781	−	7.47866i	0.148537	−	0.257274i
$846$		0			0
$847$	16.2073			0.556888
$848$		0			0
$849$	−6.90775			−0.237074
$850$		0			0
$851$	−0.347638	+	0.602126i	−0.0119169	+	0.0206406i
$852$		0			0
$853$	−15.1735	−	26.2813i	−0.519531	−	0.899853i	−0.999742	−	0.0227008i	$-0.992773\pi$
$853$	−15.1735	−	26.2813i	−0.519531	−	0.899853i	0.480212	−	0.877153i	$-0.340560\pi$
$854$		0			0
$855$	2.16912	+	3.75702i	0.0741823	+	0.128487i
$856$		0			0
$857$	−53.3187			−1.82133			−0.910667	−	0.413142i	$-0.864431\pi$
$857$	−53.3187			−1.82133			−0.910667	+	0.413142i	$0.864431\pi$
$858$		0			0
$859$	−4.23798	+	7.34039i	−0.144598	+	0.250451i	−0.929223	−	0.369520i	$-0.879522\pi$
$859$	−4.23798	+	7.34039i	−0.144598	+	0.250451i	0.784625	+	0.619971i	$0.212856\pi$
$860$		0			0
$861$	5.15988	+	8.93717i	0.175848	+	0.304578i
$862$		0			0
$863$	36.1453			1.23040			0.615200	−	0.788371i	$-0.289075\pi$
$863$	36.1453			1.23040			0.615200	+	0.788371i	$0.289075\pi$
$864$		0			0
$865$	5.09706	+	8.82836i	0.173305	+	0.300173i
$866$		0			0
$867$	−18.5350	+	32.1036i	−0.629483	+	1.09030i
$868$		0			0
$869$	7.40263	+	12.8217i	0.251117	+	0.434947i
$870$		0			0
$871$	−15.9289	+	6.21970i	−0.539730	+	0.210747i
$872$		0			0
$873$	−5.51786	−	9.55722i	−0.186751	−	0.323463i
$874$		0			0
$875$	0.983461	−	1.70340i	0.0332471	−	0.0575856i
$876$		0			0
$877$	−9.79087	−	16.9583i	−0.330614	−	0.572640i	0.652018	−	0.758203i	$-0.273923\pi$
$877$	−9.79087	−	16.9583i	−0.330614	−	0.572640i	−0.982632	+	0.185563i	$0.940589\pi$
$878$		0			0
$879$	22.6227			0.763046
$880$		0			0
$881$	−3.08842	−	5.34930i	−0.104051	−	0.180222i	0.809299	−	0.587397i	$-0.199847\pi$
$881$	−3.08842	−	5.34930i	−0.104051	−	0.180222i	−0.913350	+	0.407175i	$0.866514\pi$
$882$		0			0
$883$	−15.1964	+	26.3210i	−0.511400	+	0.885771i	0.488512	+	0.872557i	$0.337540\pi$
$883$	−15.1964	+	26.3210i	−0.511400	+	0.885771i	−0.999913	+	0.0132144i	$0.995794\pi$
$884$		0			0
$885$	−12.6477			−0.425148
$886$		0			0
$887$	−3.15086	−	5.45744i	−0.105795	−	0.183243i	0.808267	−	0.588815i	$-0.200406\pi$
$887$	−3.15086	−	5.45744i	−0.105795	−	0.183243i	−0.914063	+	0.405572i	$0.867072\pi$
$888$		0			0
$889$	8.75353	+	15.1616i	0.293584	+	0.508502i
$890$		0			0
$891$	−0.830677	+	1.43877i	−0.0278287	+	0.0482008i
$892$		0			0
$893$	19.7815			0.661963
$894$		0			0
$895$	−20.2547			−0.677040
$896$		0			0
$897$	0.0855489	−	0.148175i	0.00285639	−	0.00494742i
$898$		0			0
$899$	−20.6126	−	35.7022i	−0.687470	−	1.19073i
$900$		0			0
$901$	−23.5953	−	40.8682i	−0.786073	−	1.36152i
$902$		0			0
$903$	0.527747	−	0.914085i	0.0175623	−	0.0304189i
$904$		0			0
$905$	4.59855	−	7.96493i	0.152861	−	0.264763i
$906$		0			0
$907$	10.5491	−	18.2716i	0.350277	−	0.606697i	−0.636021	−	0.771672i	$-0.719421\pi$
$907$	10.5491	−	18.2716i	0.350277	−	0.606697i	0.986298	+	0.164974i	$0.0527541\pi$
$908$		0			0
$909$	−4.08350	+	7.07283i	−0.135441	+	0.234591i
$910$		0			0
$911$	−5.13412			−0.170101			−0.0850505	−	0.996377i	$-0.527105\pi$
$911$	−5.13412			−0.170101			−0.0850505	+	0.996377i	$0.527105\pi$
$912$		0			0
$913$	−12.8944			−0.426743
$914$		0			0
$915$	0.416747	+	0.721828i	0.0137772	+	0.0238629i
$916$		0			0
$917$	12.7734	−	22.1242i	0.421815	−	0.730605i
$918$		0			0
$919$	22.8502	+	39.5778i	0.753760	+	1.30555i	0.945988	+	0.324201i	$0.105095\pi$
$919$	22.8502	+	39.5778i	0.753760	+	1.30555i	−0.192228	+	0.981350i	$0.561571\pi$
$920$		0			0
$921$	7.85073	+	13.5979i	0.258690	+	0.448065i
$922$		0			0
$923$	21.3128			0.701521
$924$		0			0
$925$	−4.24467	−	7.35199i	−0.139564	−	0.241732i
$926$		0			0
$927$	4.38112	−	7.58832i	0.143895	−	0.249233i
$928$		0			0
$929$	−42.5393			−1.39567			−0.697834	−	0.716260i	$-0.745853\pi$
$929$	−42.5393			−1.39567			−0.697834	+	0.716260i	$0.745853\pi$
$930$		0			0
$931$	−6.79198	+	11.7641i	−0.222598	+	0.385551i
$932$		0			0
$933$	15.0215			0.491783
$934$		0			0
$935$	−12.2163			−0.399517
$936$		0			0
$937$	−23.1247			−0.755452			−0.377726	−	0.925917i	$-0.623294\pi$
$937$	−23.1247			−0.755452			−0.377726	+	0.925917i	$0.623294\pi$
$938$		0			0
$939$	−2.57311			−0.0839703
$940$		0			0
$941$	−40.0146			−1.30444			−0.652219	−	0.758031i	$-0.726162\pi$
$941$	−40.0146			−1.30444			−0.652219	+	0.758031i	$0.726162\pi$
$942$		0			0
$943$	0.429699			0.0139929
$944$		0			0
$945$	0.983461	−	1.70340i	0.0319920	−	0.0554118i
$946$		0			0
$947$	23.3560			0.758967			0.379483	−	0.925199i	$-0.376102\pi$
$947$	23.3560			0.758967			0.379483	+	0.925199i	$0.376102\pi$
$948$		0			0
$949$	1.46912	−	2.54459i	0.0476896	−	0.0826009i
$950$		0			0
$951$	−10.9274	−	18.9269i	−0.354347	−	0.613747i
$952$		0			0
$953$	−41.0361			−1.32929			−0.664645	−	0.747159i	$-0.731417\pi$
$953$	−41.0361			−1.32929			−0.664645	+	0.747159i	$0.731417\pi$
$954$		0			0
$955$	−10.1457	−	17.5729i	−0.328307	−	0.568644i
$956$		0			0
$957$	−8.09031	−	14.0128i	−0.261523	−	0.452971i
$958$		0			0
$959$	−6.11855	+	10.5976i	−0.197578	+	0.342216i
$960$		0			0
$961$	6.54159	+	11.3304i	0.211019	+	0.365496i
$962$		0			0
$963$	18.8592			0.607730
$964$		0			0
$965$	18.7315			0.602987
$966$		0			0
$967$	30.4130	−	52.6769i	0.978016	−	1.69397i	0.308416	−	0.951252i	$-0.400201\pi$
$967$	30.4130	−	52.6769i	0.978016	−	1.69397i	0.669600	−	0.742722i	$-0.266465\pi$
$968$		0			0
$969$	−15.9500	+	27.6263i	−0.512389	+	0.887484i
$970$		0			0
$971$	−6.86575	+	11.8918i	−0.220333	+	0.381627i	−0.954909	−	0.296899i	$-0.904048\pi$
$971$	−6.86575	+	11.8918i	−0.220333	+	0.381627i	0.734576	+	0.678526i	$0.237381\pi$
$972$		0			0
$973$	14.6664	−	25.4029i	0.470182	−	0.814379i
$974$		0			0
$975$	1.04456	+	1.80922i	0.0334526	+	0.0579415i
$976$		0			0
$977$	−10.3186	−	17.8723i	−0.330121	−	0.571786i	0.652414	−	0.757862i	$-0.273756\pi$
$977$	−10.3186	−	17.8723i	−0.330121	−	0.571786i	−0.982535	+	0.186076i	$0.940423\pi$
$978$		0			0
$979$	−11.0739	+	19.1805i	−0.353923	+	0.613013i
$980$		0			0
$981$	−6.17731			−0.197226
$982$		0			0
$983$	−2.79196			−0.0890496			−0.0445248	−	0.999008i	$-0.514177\pi$
$983$	−2.79196			−0.0890496			−0.0445248	+	0.999008i	$0.514177\pi$
$984$		0			0
$985$	8.19912	−	14.2013i	0.261246	−	0.452491i
$986$		0			0
$987$	−4.48439	−	7.76719i	−0.142740	−	0.247232i
$988$		0			0
$989$	−0.0219746	−	0.0380612i	−0.000698753	−	0.00121027i
$990$		0			0
$991$	37.3799			1.18741			0.593706	−	0.804682i	$-0.297664\pi$
$991$	37.3799			1.18741			0.593706	+	0.804682i	$0.297664\pi$
$992$		0			0
$993$	7.12866	−	12.3472i	0.226221	−	0.391826i
$994$		0			0
$995$	−1.58998	−	2.75393i	−0.0504058	−	0.0873055i
$996$		0			0
$997$	−22.6970			−0.718822			−0.359411	−	0.933179i	$-0.617022\pi$
$997$	−22.6970			−0.718822			−0.359411	+	0.933179i	$0.617022\pi$
$998$		0			0
$999$	−4.24467	−	7.35199i	−0.134296	−	0.232607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.9	✓	24
67.29	even	3	inner	4020.2.q.m.3781.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.9	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.9	yes	24	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.983461 - 1.70340i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(0.983461 - 1.70340i) q^{7} +1.00000 q^{9} +(-0.830677 + 1.43877i) q^{11} +(1.04456 + 1.80922i) q^{13} +1.00000 q^{15} +(3.67662 + 6.36809i) q^{17} +(2.16912 + 3.75702i) q^{19} +(0.983461 - 1.70340i) q^{21} +(-0.0409499 - 0.0709273i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-4.86971 + 8.43459i) q^{29} +(-2.11641 + 3.66574i) q^{31} +(-0.830677 + 1.43877i) q^{33} +(0.983461 - 1.70340i) q^{35} +(-4.24467 - 7.35199i) q^{37} +(1.04456 + 1.80922i) q^{39} +(-2.62332 + 4.54373i) q^{41} +0.536623 q^{43} +1.00000 q^{45} +(2.27990 - 3.94890i) q^{47} +(1.56561 + 2.71171i) q^{49} +(3.67662 + 6.36809i) q^{51} -6.41766 q^{53} +(-0.830677 + 1.43877i) q^{55} +(2.16912 + 3.75702i) q^{57} -12.6477 q^{59} +(0.416747 + 0.721828i) q^{61} +(0.983461 - 1.70340i) q^{63} +(1.04456 + 1.80922i) q^{65} +(-1.23403 + 8.09180i) q^{67} +(-0.0409499 - 0.0709273i) q^{69} +(5.10094 - 8.83508i) q^{71} +(-0.703227 - 1.21802i) q^{73} +1.00000 q^{75} +(1.63388 + 2.82996i) q^{77} +(4.45578 - 7.71764i) q^{79} +1.00000 q^{81} +(3.88070 + 6.72157i) q^{83} +(3.67662 + 6.36809i) q^{85} +(-4.86971 + 8.43459i) q^{87} +13.3312 q^{89} +4.10912 q^{91} +(-2.11641 + 3.66574i) q^{93} +(2.16912 + 3.75702i) q^{95} +(-5.51786 - 9.55722i) q^{97} +(-0.830677 + 1.43877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more