LMFDB - Embedded newform 4020.2.q.k.841.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			841.6
Root			$-1.36264 + 2.36015i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.k.3781.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 - 2.19041i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 - 2.19041i) q^{7} +1.00000 q^{9} +(0.0636774 - 0.110293i) q^{11} +(-2.22527 - 3.85428i) q^{13} -1.00000 q^{15} +(0.129720 + 0.224682i) q^{17} +(3.21355 + 5.56603i) q^{19} +(-1.26463 + 2.19041i) q^{21} +(3.09212 + 5.35572i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-0.920164 + 1.59377i) q^{29} +(-2.61911 + 4.53644i) q^{31} +(-0.0636774 + 0.110293i) q^{33} +(1.26463 - 2.19041i) q^{35} +(4.92280 + 8.52654i) q^{37} +(2.22527 + 3.85428i) q^{39} +(0.579529 - 1.00377i) q^{41} +2.35137 q^{43} +1.00000 q^{45} +(5.48732 - 9.50432i) q^{47} +(0.301411 + 0.522059i) q^{49} +(-0.129720 - 0.224682i) q^{51} -2.37847 q^{53} +(0.0636774 - 0.110293i) q^{55} +(-3.21355 - 5.56603i) q^{57} -0.400614 q^{59} +(2.78302 + 4.82033i) q^{61} +(1.26463 - 2.19041i) q^{63} +(-2.22527 - 3.85428i) q^{65} +(7.76655 - 2.58469i) q^{67} +(-3.09212 - 5.35572i) q^{69} +(3.62714 - 6.28239i) q^{71} +(1.00399 + 1.73897i) q^{73} -1.00000 q^{75} +(-0.161057 - 0.278959i) q^{77} +(0.753802 - 1.30562i) q^{79} +1.00000 q^{81} +(-3.21009 - 5.56004i) q^{83} +(0.129720 + 0.224682i) q^{85} +(0.920164 - 1.59377i) q^{87} -1.27157 q^{89} -11.2566 q^{91} +(2.61911 - 4.53644i) q^{93} +(3.21355 + 5.56603i) q^{95} +(-2.93224 - 5.07880i) q^{97} +(0.0636774 - 0.110293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	1.26463	−	2.19041i	0.477986	−	0.827896i	−0.521695	−	0.853132i	$-0.674700\pi$
$7$	1.26463	−	2.19041i	0.477986	−	0.827896i	0.999682	+	0.0252357i	$0.00803361\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.0636774	−	0.110293i	0.0191995	−	0.0332544i	−0.856266	−	0.516535i	$-0.827222\pi$
$11$	0.0636774	−	0.110293i	0.0191995	−	0.0332544i	0.875466	+	0.483281i	$0.160555\pi$
$12$		0			0
$13$	−2.22527	−	3.85428i	−0.617179	−	1.06899i	−0.989998	−	0.141081i	$-0.954942\pi$
$13$	−2.22527	−	3.85428i	−0.617179	−	1.06899i	0.372819	−	0.927904i	$-0.378391\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	0.129720	+	0.224682i	0.0314618	+	0.0544935i	0.881328	−	0.472506i	$-0.156650\pi$
$17$	0.129720	+	0.224682i	0.0314618	+	0.0544935i	−0.849866	+	0.526999i	$0.823317\pi$
$18$		0			0
$19$	3.21355	+	5.56603i	0.737239	+	1.27694i	0.953734	+	0.300652i	$0.0972041\pi$
$19$	3.21355	+	5.56603i	0.737239	+	1.27694i	−0.216495	+	0.976284i	$0.569463\pi$
$20$		0			0
$21$	−1.26463	+	2.19041i	−0.275965	+	0.477986i
$22$		0			0
$23$	3.09212	+	5.35572i	0.644753	+	1.11674i	0.984359	+	0.176176i	$0.0563729\pi$
$23$	3.09212	+	5.35572i	0.644753	+	1.11674i	−0.339606	+	0.940568i	$0.610294\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.920164	+	1.59377i	−0.170870	+	0.295956i	−0.938724	−	0.344669i	$-0.887991\pi$
$29$	−0.920164	+	1.59377i	−0.170870	+	0.295956i	0.767854	+	0.640625i	$0.221325\pi$
$30$		0			0
$31$	−2.61911	+	4.53644i	−0.470407	+	0.814768i	−0.999427	−	0.0338409i	$-0.989226\pi$
$31$	−2.61911	+	4.53644i	−0.470407	+	0.814768i	0.529021	+	0.848609i	$0.322559\pi$
$32$		0			0
$33$	−0.0636774	+	0.110293i	−0.0110848	+	0.0191995i
$34$		0			0
$35$	1.26463	−	2.19041i	0.213762	−	0.370246i
$36$		0			0
$37$	4.92280	+	8.52654i	0.809303	+	1.40175i	0.913347	+	0.407182i	$0.133488\pi$
$37$	4.92280	+	8.52654i	0.809303	+	1.40175i	−0.104044	+	0.994573i	$0.533178\pi$
$38$		0			0
$39$	2.22527	+	3.85428i	0.356328	+	0.617179i
$40$		0			0
$41$	0.579529	−	1.00377i	0.0905072	−	0.156763i	−0.817217	−	0.576329i	$-0.804485\pi$
$41$	0.579529	−	1.00377i	0.0905072	−	0.156763i	0.907725	+	0.419566i	$0.137818\pi$
$42$		0			0
$43$	2.35137			0.358580			0.179290	−	0.983796i	$-0.442620\pi$
$43$	2.35137			0.358580			0.179290	+	0.983796i	$0.442620\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	5.48732	−	9.50432i	0.800408	−	1.38635i	−0.118940	−	0.992901i	$-0.537950\pi$
$47$	5.48732	−	9.50432i	0.800408	−	1.38635i	0.919348	−	0.393446i	$-0.128717\pi$
$48$		0			0
$49$	0.301411	+	0.522059i	0.0430587	+	0.0745798i
$50$		0			0
$51$	−0.129720	−	0.224682i	−0.0181645	−	0.0314618i
$52$		0			0
$53$	−2.37847			−0.326708			−0.163354	−	0.986568i	$-0.552231\pi$
$53$	−2.37847			−0.326708			−0.163354	+	0.986568i	$0.552231\pi$
$54$		0			0
$55$	0.0636774	−	0.110293i	0.00858626	−	0.0148718i
$56$		0			0
$57$	−3.21355	−	5.56603i	−0.425645	−	0.737239i
$58$		0			0
$59$	−0.400614			−0.0521555			−0.0260777	−	0.999660i	$-0.508302\pi$
$59$	−0.400614			−0.0521555			−0.0260777	+	0.999660i	$0.508302\pi$
$60$		0			0
$61$	2.78302	+	4.82033i	0.356329	+	0.617180i	0.987344	−	0.158590i	$-0.0506949\pi$
$61$	2.78302	+	4.82033i	0.356329	+	0.617180i	−0.631015	+	0.775770i	$0.717362\pi$
$62$		0			0
$63$	1.26463	−	2.19041i	0.159329	−	0.275965i
$64$		0			0
$65$	−2.22527	−	3.85428i	−0.276011	−	0.478065i
$66$		0			0
$67$	7.76655	−	2.58469i	0.948836	−	0.315771i
$67$	7.76655	−	2.58469i	0.948836	−	0.315771i
$68$		0			0
$69$	−3.09212	−	5.35572i	−0.372248	−	0.644753i
$70$		0			0
$71$	3.62714	−	6.28239i	0.430462	−	0.745582i	−0.566451	−	0.824095i	$-0.691684\pi$
$71$	3.62714	−	6.28239i	0.430462	−	0.745582i	0.996913	+	0.0785133i	$0.0250173\pi$
$72$		0			0
$73$	1.00399	+	1.73897i	0.117509	+	0.203531i	0.918780	−	0.394770i	$-0.129176\pi$
$73$	1.00399	+	1.73897i	0.117509	+	0.203531i	−0.801271	+	0.598301i	$0.795843\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−0.161057	−	0.278959i	−0.0183542	−	0.0317903i
$78$		0			0
$79$	0.753802	−	1.30562i	0.0848094	−	0.146894i	−0.820501	−	0.571646i	$-0.806305\pi$
$79$	0.753802	−	1.30562i	0.0848094	−	0.146894i	0.905310	+	0.424752i	$0.139639\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−3.21009	−	5.56004i	−0.352353	−	0.610294i	0.634308	−	0.773081i	$-0.281285\pi$
$83$	−3.21009	−	5.56004i	−0.352353	−	0.610294i	−0.986661	+	0.162786i	$0.947952\pi$
$84$		0			0
$85$	0.129720	+	0.224682i	0.0140702	+	0.0243702i
$86$		0			0
$87$	0.920164	−	1.59377i	0.0986520	−	0.170870i
$88$		0			0
$89$	−1.27157			−0.134786			−0.0673932	−	0.997726i	$-0.521468\pi$
$89$	−1.27157			−0.134786			−0.0673932	+	0.997726i	$0.521468\pi$
$90$		0			0
$91$	−11.2566			−1.18001
$92$		0			0
$93$	2.61911	−	4.53644i	0.271589	−	0.470407i
$94$		0			0
$95$	3.21355	+	5.56603i	0.329703	+	0.571063i
$96$		0			0
$97$	−2.93224	−	5.07880i	−0.297724	−	0.515674i	0.677891	−	0.735163i	$-0.262894\pi$
$97$	−2.93224	−	5.07880i	−0.297724	−	0.515674i	−0.975615	+	0.219489i	$0.929561\pi$
$98$		0			0
$99$	0.0636774	−	0.110293i	0.00639982	−	0.0110848i
$100$		0			0
$101$	1.52837	−	2.64722i	0.152079	−	0.263408i	−0.779913	−	0.625888i	$-0.784737\pi$
$101$	1.52837	−	2.64722i	0.152079	−	0.263408i	0.931992	+	0.362480i	$0.118070\pi$
$102$		0			0
$103$	6.62209	−	11.4698i	0.652494	−	1.13015i	−0.330021	−	0.943973i	$-0.607056\pi$
$103$	6.62209	−	11.4698i	0.652494	−	1.13015i	0.982516	−	0.186180i	$-0.0596107\pi$
$104$		0			0
$105$	−1.26463	+	2.19041i	−0.123415	+	0.213762i
$106$		0			0
$107$	9.51097			0.919460			0.459730	−	0.888059i	$-0.347946\pi$
$107$	9.51097			0.919460			0.459730	+	0.888059i	$0.347946\pi$
$108$		0			0
$109$	6.74556			0.646107			0.323054	−	0.946381i	$-0.395291\pi$
$109$	6.74556			0.646107			0.323054	+	0.946381i	$0.395291\pi$
$110$		0			0
$111$	−4.92280	−	8.52654i	−0.467251	−	0.809303i
$112$		0			0
$113$	−4.56883	+	7.91345i	−0.429800	+	0.744435i	−0.996855	−	0.0792448i	$-0.974749\pi$
$113$	−4.56883	+	7.91345i	−0.429800	+	0.744435i	0.567056	+	0.823679i	$0.308082\pi$
$114$		0			0
$115$	3.09212	+	5.35572i	0.288342	+	0.499423i
$116$		0			0
$117$	−2.22527	−	3.85428i	−0.205726	−	0.356328i
$118$		0			0
$119$	0.656194			0.0601532
$120$		0			0
$121$	5.49189	+	9.51223i	0.499263	+	0.864748i
$122$		0			0
$123$	−0.579529	+	1.00377i	−0.0522544	+	0.0905072i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.10991	+	1.92242i	−0.0984887	+	0.170587i	−0.911059	−	0.412275i	$-0.864734\pi$
$127$	−1.10991	+	1.92242i	−0.0984887	+	0.170587i	0.812571	+	0.582863i	$0.198067\pi$
$128$		0			0
$129$	−2.35137			−0.207026
$130$		0			0
$131$	−21.0542			−1.83952			−0.919758	−	0.392487i	$-0.871615\pi$
$131$	−21.0542			−1.83952			−0.919758	+	0.392487i	$0.871615\pi$
$132$		0			0
$133$	16.2558			1.40956
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	7.65782			0.654252			0.327126	−	0.944981i	$-0.393920\pi$
$137$	7.65782			0.654252			0.327126	+	0.944981i	$0.393920\pi$
$138$		0			0
$139$	13.0649			1.10815			0.554074	−	0.832467i	$-0.313072\pi$
$139$	13.0649			1.10815			0.554074	+	0.832467i	$0.313072\pi$
$140$		0			0
$141$	−5.48732	+	9.50432i	−0.462116	+	0.800408i
$142$		0			0
$143$	−0.566798			−0.0473980
$144$		0			0
$145$	−0.920164	+	1.59377i	−0.0764155	+	0.132355i
$146$		0			0
$147$	−0.301411	−	0.522059i	−0.0248599	−	0.0430587i
$148$		0			0
$149$	−1.39911			−0.114619			−0.0573096	−	0.998356i	$-0.518252\pi$
$149$	−1.39911			−0.114619			−0.0573096	+	0.998356i	$0.518252\pi$
$150$		0			0
$151$	−8.77578	−	15.2001i	−0.714163	−	1.23697i	−0.963281	−	0.268494i	$-0.913474\pi$
$151$	−8.77578	−	15.2001i	−0.714163	−	1.23697i	0.249118	−	0.968473i	$-0.419859\pi$
$152$		0			0
$153$	0.129720	+	0.224682i	0.0104873	+	0.0181645i
$154$		0			0
$155$	−2.61911	+	4.53644i	−0.210372	+	0.364375i
$156$		0			0
$157$	−2.24823	−	3.89404i	−0.179428	−	0.310779i	0.762257	−	0.647275i	$-0.224091\pi$
$157$	−2.24823	−	3.89404i	−0.179428	−	0.310779i	−0.941685	+	0.336496i	$0.890758\pi$
$158$		0			0
$159$	2.37847			0.188625
$160$		0			0
$161$	15.6416			1.23273
$162$		0			0
$163$	10.4296	−	18.0645i	0.816907	−	1.41492i	−0.0910440	−	0.995847i	$-0.529020\pi$
$163$	10.4296	−	18.0645i	0.816907	−	1.41492i	0.907951	−	0.419077i	$-0.137646\pi$
$164$		0			0
$165$	−0.0636774	+	0.110293i	−0.00495728	+	0.00858626i
$166$		0			0
$167$	−6.14610	+	10.6454i	−0.475600	+	0.823763i	−0.999609	−	0.0279497i	$-0.991102\pi$
$167$	−6.14610	+	10.6454i	−0.475600	+	0.823763i	0.524010	+	0.851712i	$0.324436\pi$
$168$		0			0
$169$	−3.40366	+	5.89531i	−0.261820	+	0.453485i
$170$		0			0
$171$	3.21355	+	5.56603i	0.245746	+	0.425645i
$172$		0			0
$173$	3.90299	+	6.76018i	0.296739	+	0.513967i	0.975388	−	0.220496i	$-0.0707676\pi$
$173$	3.90299	+	6.76018i	0.296739	+	0.513967i	−0.678649	+	0.734463i	$0.737434\pi$
$174$		0			0
$175$	1.26463	−	2.19041i	0.0955972	−	0.165579i
$176$		0			0
$177$	0.400614			0.0301120
$178$		0			0
$179$	15.9995			1.19586			0.597929	−	0.801549i	$-0.295990\pi$
$179$	15.9995			1.19586			0.597929	+	0.801549i	$0.295990\pi$
$180$		0			0
$181$	−10.8380	+	18.7720i	−0.805583	+	1.39531i	0.110314	+	0.993897i	$0.464814\pi$
$181$	−10.8380	+	18.7720i	−0.805583	+	1.39531i	−0.915897	+	0.401414i	$0.868519\pi$
$182$		0			0
$183$	−2.78302	−	4.82033i	−0.205727	−	0.356329i
$184$		0			0
$185$	4.92280	+	8.52654i	0.361931	+	0.626884i
$186$		0			0
$187$	0.0330410			0.00241620
$188$		0			0
$189$	−1.26463	+	2.19041i	−0.0919885	+	0.159329i
$190$		0			0
$191$	−12.8281	−	22.2189i	−0.928207	−	1.60770i	−0.786320	−	0.617820i	$-0.788016\pi$
$191$	−12.8281	−	22.2189i	−0.928207	−	1.60770i	−0.141888	−	0.989883i	$-0.545317\pi$
$192$		0			0
$193$	17.9337			1.29090			0.645449	−	0.763804i	$-0.276670\pi$
$193$	17.9337			1.29090			0.645449	+	0.763804i	$0.276670\pi$
$194$		0			0
$195$	2.22527	+	3.85428i	0.159355	+	0.276011i
$196$		0			0
$197$	−3.49225	+	6.04876i	−0.248813	+	0.430956i	−0.963197	−	0.268798i	$-0.913374\pi$
$197$	−3.49225	+	6.04876i	−0.248813	+	0.430956i	0.714384	+	0.699754i	$0.246707\pi$
$198$		0			0
$199$	−1.19684	−	2.07299i	−0.0848417	−	0.146950i	0.820482	−	0.571672i	$-0.193705\pi$
$199$	−1.19684	−	2.07299i	−0.0848417	−	0.146950i	−0.905324	+	0.424722i	$0.860372\pi$
$200$		0			0
$201$	−7.76655	+	2.58469i	−0.547810	+	0.182310i
$202$		0			0
$203$	2.32734	+	4.03107i	0.163347	+	0.282926i
$204$		0			0
$205$	0.579529	−	1.00377i	0.0404761	−	0.0701066i
$206$		0			0
$207$	3.09212	+	5.35572i	0.214918	+	0.372248i
$208$		0			0
$209$	0.818522			0.0566184
$210$		0			0
$211$	1.40604	+	2.43533i	0.0967959	+	0.167655i	0.910357	−	0.413824i	$-0.135807\pi$
$211$	1.40604	+	2.43533i	0.0967959	+	0.167655i	−0.813561	+	0.581480i	$0.802474\pi$
$212$		0			0
$213$	−3.62714	+	6.28239i	−0.248527	+	0.430462i
$214$		0			0
$215$	2.35137			0.160362
$216$		0			0
$217$	6.62443	+	11.4738i	0.449695	+	0.778895i
$218$		0			0
$219$	−1.00399	−	1.73897i	−0.0678436	−	0.117509i
$220$		0			0
$221$	0.577326	−	0.999958i	0.0388352	−	0.0672645i
$222$		0			0
$223$	−12.8891			−0.863117			−0.431558	−	0.902085i	$-0.642036\pi$
$223$	−12.8891			−0.863117			−0.431558	+	0.902085i	$0.642036\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	4.67253	−	8.09306i	0.310127	−	0.537155i	−0.668263	−	0.743925i	$-0.732962\pi$
$227$	4.67253	−	8.09306i	0.310127	−	0.537155i	0.978390	+	0.206770i	$0.0662952\pi$
$228$		0			0
$229$	1.60442	+	2.77893i	0.106023	+	0.183637i	0.914156	−	0.405363i	$-0.132855\pi$
$229$	1.60442	+	2.77893i	0.106023	+	0.183637i	−0.808133	+	0.589000i	$0.799522\pi$
$230$		0			0
$231$	0.161057	+	0.278959i	0.0105968	+	0.0183542i
$232$		0			0
$233$	5.73530	−	9.93383i	0.375732	−	0.650787i	−0.614704	−	0.788758i	$-0.710725\pi$
$233$	5.73530	−	9.93383i	0.375732	−	0.650787i	0.990436	+	0.137971i	$0.0440580\pi$
$234$		0			0
$235$	5.48732	−	9.50432i	0.357953	−	0.619993i
$236$		0			0
$237$	−0.753802	+	1.30562i	−0.0489647	+	0.0848094i
$238$		0			0
$239$	−2.95082	+	5.11096i	−0.190872	+	0.330601i	−0.945540	−	0.325507i	$-0.894465\pi$
$239$	−2.95082	+	5.11096i	−0.190872	+	0.330601i	0.754667	+	0.656108i	$0.227798\pi$
$240$		0			0
$241$	9.02817			0.581556			0.290778	−	0.956791i	$-0.406086\pi$
$241$	9.02817			0.581556			0.290778	+	0.956791i	$0.406086\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.301411	+	0.522059i	0.0192564	+	0.0333531i
$246$		0			0
$247$	14.3020	−	24.7719i	0.910017	−	1.57620i
$248$		0			0
$249$	3.21009	+	5.56004i	0.203431	+	0.352353i
$250$		0			0
$251$	−2.88177	−	4.99137i	−0.181896	−	0.315052i	0.760630	−	0.649185i	$-0.224890\pi$
$251$	−2.88177	−	4.99137i	−0.181896	−	0.315052i	−0.942526	+	0.334133i	$0.891557\pi$
$252$		0			0
$253$	0.787594			0.0495156
$254$		0			0
$255$	−0.129720	−	0.224682i	−0.00812341	−	0.0140702i
$256$		0			0
$257$	−14.0716	+	24.3727i	−0.877761	+	1.52033i	−0.0239683	+	0.999713i	$0.507630\pi$
$257$	−14.0716	+	24.3727i	−0.877761	+	1.52033i	−0.853792	+	0.520614i	$0.825703\pi$
$258$		0			0
$259$	24.9021			1.54734
$260$		0			0
$261$	−0.920164	+	1.59377i	−0.0569567	+	0.0986520i
$262$		0			0
$263$	14.3621			0.885607			0.442803	−	0.896619i	$-0.353984\pi$
$263$	14.3621			0.885607			0.442803	+	0.896619i	$0.353984\pi$
$264$		0			0
$265$	−2.37847			−0.146108
$266$		0			0
$267$	1.27157			0.0778190
$268$		0			0
$269$	21.7111			1.32375			0.661873	−	0.749616i	$-0.269762\pi$
$269$	21.7111			1.32375			0.661873	+	0.749616i	$0.269762\pi$
$270$		0			0
$271$	10.7458			0.652758			0.326379	−	0.945239i	$-0.394171\pi$
$271$	10.7458			0.652758			0.326379	+	0.945239i	$0.394171\pi$
$272$		0			0
$273$	11.2566			0.681280
$274$		0			0
$275$	0.0636774	−	0.110293i	0.00383989	−	0.00665089i
$276$		0			0
$277$	27.2641			1.63814			0.819070	−	0.573693i	$-0.194490\pi$
$277$	27.2641			1.63814			0.819070	+	0.573693i	$0.194490\pi$
$278$		0			0
$279$	−2.61911	+	4.53644i	−0.156802	+	0.271589i
$280$		0			0
$281$	−6.30782	−	10.9255i	−0.376293	−	0.651758i	0.614227	−	0.789130i	$-0.289468\pi$
$281$	−6.30782	−	10.9255i	−0.376293	−	0.651758i	−0.990520	+	0.137371i	$0.956135\pi$
$282$		0			0
$283$	22.7031			1.34956			0.674780	−	0.738019i	$-0.264239\pi$
$283$	22.7031			1.34956			0.674780	+	0.738019i	$0.264239\pi$
$284$		0			0
$285$	−3.21355	−	5.56603i	−0.190354	−	0.329703i
$286$		0			0
$287$	−1.46578	−	2.53881i	−0.0865224	−	0.149861i
$288$		0			0
$289$	8.46635	−	14.6641i	0.498020	−	0.862596i
$290$		0			0
$291$	2.93224	+	5.07880i	0.171891	+	0.297724i
$292$		0			0
$293$	−10.2730			−0.600156			−0.300078	−	0.953915i	$-0.597013\pi$
$293$	−10.2730			−0.600156			−0.300078	+	0.953915i	$0.597013\pi$
$294$		0			0
$295$	−0.400614			−0.0233246
$296$		0			0
$297$	−0.0636774	+	0.110293i	−0.00369494	+	0.00639982i
$298$		0			0
$299$	13.7616	−	23.8358i	0.795855	−	1.37846i
$300$		0			0
$301$	2.97362	−	5.15045i	0.171396	−	0.296867i
$302$		0			0
$303$	−1.52837	+	2.64722i	−0.0878028	+	0.152079i
$304$		0			0
$305$	2.78302	+	4.82033i	0.159355	+	0.276011i
$306$		0			0
$307$	−5.66618	−	9.81412i	−0.323386	−	0.560121i	0.657798	−	0.753194i	$-0.271488\pi$
$307$	−5.66618	−	9.81412i	−0.323386	−	0.560121i	−0.981184	+	0.193073i	$0.938155\pi$
$308$		0			0
$309$	−6.62209	+	11.4698i	−0.376718	+	0.652494i
$310$		0			0
$311$	13.3637			0.757784			0.378892	−	0.925441i	$-0.376305\pi$
$311$	13.3637			0.757784			0.378892	+	0.925441i	$0.376305\pi$
$312$		0			0
$313$	22.3998			1.26611			0.633057	−	0.774105i	$-0.281800\pi$
$313$	22.3998			1.26611			0.633057	+	0.774105i	$0.281800\pi$
$314$		0			0
$315$	1.26463	−	2.19041i	0.0712540	−	0.123415i
$316$		0			0
$317$	13.0809	+	22.6568i	0.734699	+	1.27254i	0.954855	+	0.297071i	$0.0960097\pi$
$317$	13.0809	+	22.6568i	0.734699	+	1.27254i	−0.220157	+	0.975464i	$0.570657\pi$
$318$		0			0
$319$	0.117187	+	0.202974i	0.00656123	+	0.0113644i
$320$		0			0
$321$	−9.51097			−0.530850
$322$		0			0
$323$	−0.833726	+	1.44406i	−0.0463898	+	0.0803494i
$324$		0			0
$325$	−2.22527	−	3.85428i	−0.123436	−	0.213797i
$326$		0			0
$327$	−6.74556			−0.373030
$328$		0			0
$329$	−13.8789	−	24.0389i	−0.765168	−	1.32531i
$330$		0			0
$331$	11.5888	−	20.0723i	0.636975	−	1.10327i	−0.349117	−	0.937079i	$-0.613519\pi$
$331$	11.5888	−	20.0723i	0.636975	−	1.10327i	0.986093	−	0.166195i	$-0.0531481\pi$
$332$		0			0
$333$	4.92280	+	8.52654i	0.269768	+	0.467251i
$334$		0			0
$335$	7.76655	−	2.58469i	0.424332	−	0.141217i
$336$		0			0
$337$	−10.8157	−	18.7333i	−0.589168	−	1.02047i	−0.994342	−	0.106230i	$-0.966122\pi$
$337$	−10.8157	−	18.7333i	−0.589168	−	1.02047i	0.405173	−	0.914240i	$-0.367211\pi$
$338$		0			0
$339$	4.56883	−	7.91345i	0.248145	−	0.429800i
$340$		0			0
$341$	0.333557	+	0.577737i	0.0180631	+	0.0312862i
$342$		0			0
$343$	19.2295			1.03830
$344$		0			0
$345$	−3.09212	−	5.35572i	−0.166474	−	0.288342i
$346$		0			0
$347$	0.804179	−	1.39288i	0.0431706	−	0.0747736i	−0.843633	−	0.536921i	$-0.819587\pi$
$347$	0.804179	−	1.39288i	0.0431706	−	0.0747736i	0.886803	+	0.462147i	$0.152921\pi$
$348$		0			0
$349$	−14.7156			−0.787710			−0.393855	−	0.919173i	$-0.628859\pi$
$349$	−14.7156			−0.787710			−0.393855	+	0.919173i	$0.628859\pi$
$350$		0			0
$351$	2.22527	+	3.85428i	0.118776	+	0.205726i
$352$		0			0
$353$	−10.3424	−	17.9136i	−0.550473	−	0.953447i	−0.998240	−	0.0592968i	$-0.981114\pi$
$353$	−10.3424	−	17.9136i	−0.550473	−	0.953447i	0.447768	−	0.894150i	$-0.352219\pi$
$354$		0			0
$355$	3.62714	−	6.28239i	0.192508	−	0.333434i
$356$		0			0
$357$	−0.656194			−0.0347295
$358$		0			0
$359$	−14.3344			−0.756539			−0.378269	−	0.925696i	$-0.623481\pi$
$359$	−14.3344			−0.756539			−0.378269	+	0.925696i	$0.623481\pi$
$360$		0			0
$361$	−11.1538	+	19.3190i	−0.587043	+	1.01679i
$362$		0			0
$363$	−5.49189	−	9.51223i	−0.288249	−	0.499263i
$364$		0			0
$365$	1.00399	+	1.73897i	0.0525514	+	0.0910218i
$366$		0			0
$367$	−13.2343	+	22.9225i	−0.690825	+	1.19654i	0.280744	+	0.959783i	$0.409419\pi$
$367$	−13.2343	+	22.9225i	−0.690825	+	1.19654i	−0.971568	+	0.236760i	$0.923914\pi$
$368$		0			0
$369$	0.579529	−	1.00377i	0.0301691	−	0.0522544i
$370$		0			0
$371$	−3.00789	+	5.20981i	−0.156162	+	0.270480i
$372$		0			0
$373$	−19.0974	+	33.0776i	−0.988824	+	1.71269i	−0.365298	+	0.930891i	$0.619033\pi$
$373$	−19.0974	+	33.0776i	−0.988824	+	1.71269i	−0.623526	+	0.781803i	$0.714300\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	8.19046			0.421830
$378$		0			0
$379$	11.6683	+	20.2101i	0.599361	+	1.03812i	0.992916	+	0.118822i	$0.0379119\pi$
$379$	11.6683	+	20.2101i	0.599361	+	1.03812i	−0.393555	+	0.919301i	$0.628755\pi$
$380$		0			0
$381$	1.10991	−	1.92242i	0.0568625	−	0.0984887i
$382$		0			0
$383$	6.37068	+	11.0343i	0.325526	+	0.563828i	0.981619	−	0.190852i	$-0.0611251\pi$
$383$	6.37068	+	11.0343i	0.325526	+	0.563828i	−0.656092	+	0.754681i	$0.727792\pi$
$384$		0			0
$385$	−0.161057	−	0.278959i	−0.00820823	−	0.0142171i
$386$		0			0
$387$	2.35137			0.119527
$388$		0			0
$389$	3.79864	+	6.57944i	0.192599	+	0.333591i	0.946111	−	0.323843i	$-0.104975\pi$
$389$	3.79864	+	6.57944i	0.192599	+	0.333591i	−0.753512	+	0.657434i	$0.771642\pi$
$390$		0			0
$391$	−0.802223	+	1.38949i	−0.0405702	+	0.0702696i
$392$		0			0
$393$	21.0542			1.06204
$394$		0			0
$395$	0.753802	−	1.30562i	0.0379279	−	0.0656931i
$396$		0			0
$397$	−9.30752			−0.467131			−0.233565	−	0.972341i	$-0.575039\pi$
$397$	−9.30752			−0.467131			−0.233565	+	0.972341i	$0.575039\pi$
$398$		0			0
$399$	−16.2558			−0.813810
$400$		0			0
$401$	−1.38966			−0.0693961			−0.0346980	−	0.999398i	$-0.511047\pi$
$401$	−1.38966			−0.0693961			−0.0346980	+	0.999398i	$0.511047\pi$
$402$		0			0
$403$	23.3129			1.16130
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	1.25388			0.0621528
$408$		0			0
$409$	−4.77429	+	8.26931i	−0.236073	+	0.408891i	−0.959584	−	0.281422i	$-0.909194\pi$
$409$	−4.77429	+	8.26931i	−0.236073	+	0.408891i	0.723511	+	0.690313i	$0.242527\pi$
$410$		0			0
$411$	−7.65782			−0.377732
$412$		0			0
$413$	−0.506629	+	0.877508i	−0.0249296	+	0.0431793i
$414$		0			0
$415$	−3.21009	−	5.56004i	−0.157577	−	0.272932i
$416$		0			0
$417$	−13.0649			−0.639790
$418$		0			0
$419$	7.84344	+	13.5852i	0.383177	+	0.663683i	0.991515	−	0.129996i	$-0.0414965\pi$
$419$	7.84344	+	13.5852i	0.383177	+	0.663683i	−0.608337	+	0.793679i	$0.708163\pi$
$420$		0			0
$421$	−9.83514	−	17.0350i	−0.479336	−	0.830233i	0.520384	−	0.853933i	$-0.325789\pi$
$421$	−9.83514	−	17.0350i	−0.479336	−	0.830233i	−0.999719	+	0.0236991i	$0.992456\pi$
$422$		0			0
$423$	5.48732	−	9.50432i	0.266803	−	0.462116i
$424$		0			0
$425$	0.129720	+	0.224682i	0.00629236	+	0.0108987i
$426$		0			0
$427$	14.0780			0.681281
$428$		0			0
$429$	0.566798			0.0273653
$430$		0			0
$431$	−16.2820	+	28.2012i	−0.784275	+	1.35840i	0.145156	+	0.989409i	$0.453632\pi$
$431$	−16.2820	+	28.2012i	−0.784275	+	1.35840i	−0.929431	+	0.368996i	$0.879702\pi$
$432$		0			0
$433$	12.6446	−	21.9010i	0.607659	−	1.05250i	−0.383966	−	0.923347i	$-0.625442\pi$
$433$	12.6446	−	21.9010i	0.607659	−	1.05250i	0.991625	−	0.129149i	$-0.0412246\pi$
$434$		0			0
$435$	0.920164	−	1.59377i	0.0441185	−	0.0764155i
$436$		0			0
$437$	−19.8734	+	34.4217i	−0.950673	+	1.64661i
$438$		0			0
$439$	1.23674	+	2.14209i	0.0590263	+	0.102237i	0.894029	−	0.448010i	$-0.147867\pi$
$439$	1.23674	+	2.14209i	0.0590263	+	0.102237i	−0.835002	+	0.550247i	$0.814534\pi$
$440$		0			0
$441$	0.301411	+	0.522059i	0.0143529	+	0.0248599i
$442$		0			0
$443$	−11.3001	+	19.5724i	−0.536885	+	0.929913i	0.462184	+	0.886784i	$0.347066\pi$
$443$	−11.3001	+	19.5724i	−0.536885	+	0.929913i	−0.999070	+	0.0431289i	$0.986267\pi$
$444$		0			0
$445$	−1.27157			−0.0602783
$446$		0			0
$447$	1.39911			0.0661755
$448$		0			0
$449$	−4.22258	+	7.31373i	−0.199276	+	0.345156i	−0.948294	−	0.317394i	$-0.897192\pi$
$449$	−4.22258	+	7.31373i	−0.199276	+	0.345156i	0.749018	+	0.662550i	$0.230526\pi$
$450$		0			0
$451$	−0.0738058	−	0.127835i	−0.00347538	−	0.00601954i
$452$		0			0
$453$	8.77578	+	15.2001i	0.412322	+	0.714163i
$454$		0			0
$455$	−11.2566			−0.527717
$456$		0			0
$457$	−12.9230	+	22.3833i	−0.604512	+	1.04705i	0.387616	+	0.921821i	$0.373299\pi$
$457$	−12.9230	+	22.3833i	−0.604512	+	1.04705i	−0.992128	+	0.125225i	$0.960035\pi$
$458$		0			0
$459$	−0.129720	−	0.224682i	−0.00605483	−	0.0104873i
$460$		0			0
$461$	−18.0486			−0.840605			−0.420302	−	0.907384i	$-0.638076\pi$
$461$	−18.0486			−0.840605			−0.420302	+	0.907384i	$0.638076\pi$
$462$		0			0
$463$	4.34724	+	7.52964i	0.202033	+	0.349932i	0.949183	−	0.314723i	$-0.101912\pi$
$463$	4.34724	+	7.52964i	0.202033	+	0.349932i	−0.747150	+	0.664655i	$0.768578\pi$
$464$		0			0
$465$	2.61911	−	4.53644i	0.121458	−	0.210372i
$466$		0			0
$467$	15.0554	+	26.0767i	0.696681	+	1.20669i	0.969611	+	0.244653i	$0.0786741\pi$
$467$	15.0554	+	26.0767i	0.696681	+	1.20669i	−0.272929	+	0.962034i	$0.587993\pi$
$468$		0			0
$469$	4.16030	−	20.2806i	0.192105	−	0.936471i
$470$		0			0
$471$	2.24823	+	3.89404i	0.103593	+	0.179428i
$472$		0			0
$473$	0.149729	−	0.259338i	0.00688455	−	0.0119244i
$474$		0			0
$475$	3.21355	+	5.56603i	0.147448	+	0.255387i
$476$		0			0
$477$	−2.37847			−0.108903
$478$		0			0
$479$	−8.45632	−	14.6468i	−0.386379	−	0.669228i	0.605580	−	0.795784i	$-0.292941\pi$
$479$	−8.45632	−	14.6468i	−0.386379	−	0.669228i	−0.991959	+	0.126556i	$0.959608\pi$
$480$		0			0
$481$	21.9091	−	37.9477i	0.998970	−	1.73027i
$482$		0			0
$483$	−15.6416			−0.711717
$484$		0			0
$485$	−2.93224	−	5.07880i	−0.133146	−	0.230616i
$486$		0			0
$487$	−8.89964	−	15.4146i	−0.403281	−	0.698503i	0.590839	−	0.806790i	$-0.298797\pi$
$487$	−8.89964	−	15.4146i	−0.403281	−	0.698503i	−0.994120	+	0.108286i	$0.965464\pi$
$488$		0			0
$489$	−10.4296	+	18.0645i	−0.471641	+	0.816907i
$490$		0			0
$491$	−30.3667			−1.37043			−0.685216	−	0.728340i	$-0.740292\pi$
$491$	−30.3667			−1.37043			−0.685216	+	0.728340i	$0.740292\pi$
$492$		0			0
$493$	−0.477456			−0.0215036
$494$		0			0
$495$	0.0636774	−	0.110293i	0.00286209	−	0.00495728i
$496$		0			0
$497$	−9.17399	−	15.8898i	−0.411510	−	0.712756i
$498$		0			0
$499$	5.87126	+	10.1693i	0.262834	+	0.455242i	0.966994	−	0.254800i	$-0.0820096\pi$
$499$	5.87126	+	10.1693i	0.262834	+	0.455242i	−0.704160	+	0.710041i	$0.748676\pi$
$500$		0			0
$501$	6.14610	−	10.6454i	0.274588	−	0.475600i
$502$		0			0
$503$	18.0945	−	31.3406i	0.806793	−	1.39741i	−0.108280	−	0.994120i	$-0.534534\pi$
$503$	18.0945	−	31.3406i	0.806793	−	1.39741i	0.915074	−	0.403287i	$-0.132132\pi$
$504$		0			0
$505$	1.52837	−	2.64722i	0.0680117	−	0.117800i
$506$		0			0
$507$	3.40366	−	5.89531i	0.151162	−	0.261820i
$508$		0			0
$509$	−16.6125			−0.736335			−0.368167	−	0.929759i	$-0.620015\pi$
$509$	−16.6125			−0.736335			−0.368167	+	0.929759i	$0.620015\pi$
$510$		0			0
$511$	5.07873			0.224670
$512$		0			0
$513$	−3.21355	−	5.56603i	−0.141882	−	0.245746i
$514$		0			0
$515$	6.62209	−	11.4698i	0.291804	−	0.505420i
$516$		0			0
$517$	−0.698837	−	1.21042i	−0.0307348	−	0.0532342i
$518$		0			0
$519$	−3.90299	−	6.76018i	−0.171322	−	0.296739i
$520$		0			0
$521$	1.82684			0.0800353			0.0400176	−	0.999199i	$-0.487259\pi$
$521$	1.82684			0.0800353			0.0400176	+	0.999199i	$0.487259\pi$
$522$		0			0
$523$	2.41000	+	4.17424i	0.105382	+	0.182527i	0.913894	−	0.405953i	$-0.133060\pi$
$523$	2.41000	+	4.17424i	0.105382	+	0.182527i	−0.808512	+	0.588479i	$0.799727\pi$
$524$		0			0
$525$	−1.26463	+	2.19041i	−0.0551931	+	0.0955972i
$526$		0			0
$527$	−1.35901			−0.0591994
$528$		0			0
$529$	−7.62247	+	13.2025i	−0.331412	+	0.574022i
$530$		0			0
$531$	−0.400614			−0.0173852
$532$		0			0
$533$	−5.15844			−0.223437
$534$		0			0
$535$	9.51097			0.411195
$536$		0			0
$537$	−15.9995			−0.690429
$538$		0			0
$539$	0.0767722			0.00330681
$540$		0			0
$541$	−13.4880			−0.579895			−0.289948	−	0.957043i	$-0.593638\pi$
$541$	−13.4880			−0.579895			−0.289948	+	0.957043i	$0.593638\pi$
$542$		0			0
$543$	10.8380	−	18.7720i	0.465104	−	0.805583i
$544$		0			0
$545$	6.74556			0.288948
$546$		0			0
$547$	9.28593	−	16.0837i	0.397038	−	0.687690i	−0.596321	−	0.802746i	$-0.703372\pi$
$547$	9.28593	−	16.0837i	0.397038	−	0.687690i	0.993359	+	0.115056i	$0.0367048\pi$
$548$		0			0
$549$	2.78302	+	4.82033i	0.118776	+	0.205727i
$550$		0			0
$551$	−11.8280			−0.503889
$552$		0			0
$553$	−1.90657	−	3.30227i	−0.0810754	−	0.140427i
$554$		0			0
$555$	−4.92280	−	8.52654i	−0.208961	−	0.361931i
$556$		0			0
$557$	10.3068	−	17.8518i	0.436711	−	0.756406i	−0.560722	−	0.828004i	$-0.689476\pi$
$557$	10.3068	−	17.8518i	0.436711	−	0.756406i	0.997434	+	0.0715977i	$0.0228098\pi$
$558$		0			0
$559$	−5.23243	−	9.06284i	−0.221308	−	0.383317i
$560$		0			0
$561$	−0.0330410			−0.00139499
$562$		0			0
$563$	22.6923			0.956365			0.478182	−	0.878261i	$-0.341296\pi$
$563$	22.6923			0.956365			0.478182	+	0.878261i	$0.341296\pi$
$564$		0			0
$565$	−4.56883	+	7.91345i	−0.192212	+	0.332921i
$566$		0			0
$567$	1.26463	−	2.19041i	0.0531096	−	0.0919885i
$568$		0			0
$569$	−16.4285	+	28.4550i	−0.688720	+	1.19290i	0.283532	+	0.958963i	$0.408494\pi$
$569$	−16.4285	+	28.4550i	−0.688720	+	1.19290i	−0.972252	+	0.233935i	$0.924840\pi$
$570$		0			0
$571$	−10.7995	+	18.7053i	−0.451944	+	0.782791i	−0.998507	−	0.0546277i	$-0.982603\pi$
$571$	−10.7995	+	18.7053i	−0.451944	+	0.782791i	0.546562	+	0.837418i	$0.315936\pi$
$572$		0			0
$573$	12.8281	+	22.2189i	0.535901	+	0.928207i
$574$		0			0
$575$	3.09212	+	5.35572i	0.128951	+	0.223349i
$576$		0			0
$577$	1.03957	−	1.80059i	0.0432780	−	0.0749596i	−0.843575	−	0.537011i	$-0.819553\pi$
$577$	1.03957	−	1.80059i	0.0432780	−	0.0749596i	0.886853	+	0.462052i	$0.152887\pi$
$578$		0			0
$579$	−17.9337			−0.745300
$580$		0			0
$581$	−16.2383			−0.673680
$582$		0			0
$583$	−0.151455	+	0.262327i	−0.00627261	+	0.0108645i
$584$		0			0
$585$	−2.22527	−	3.85428i	−0.0920036	−	0.159355i
$586$		0			0
$587$	−16.6645	−	28.8637i	−0.687817	−	1.19133i	−0.972543	−	0.232725i	$-0.925236\pi$
$587$	−16.6645	−	28.8637i	−0.687817	−	1.19133i	0.284726	−	0.958609i	$-0.408097\pi$
$588$		0			0
$589$	−33.6666			−1.38721
$590$		0			0
$591$	3.49225	−	6.04876i	0.143652	−	0.248813i
$592$		0			0
$593$	−15.1056	−	26.1636i	−0.620311	−	1.07441i	−0.989428	−	0.145027i	$-0.953673\pi$
$593$	−15.1056	−	26.1636i	−0.620311	−	1.07441i	0.369117	−	0.929383i	$-0.379660\pi$
$594$		0			0
$595$	0.656194			0.0269013
$596$		0			0
$597$	1.19684	+	2.07299i	0.0489834	+	0.0848417i
$598$		0			0
$599$	21.0034	−	36.3789i	0.858175	−	1.48640i	−0.0154922	−	0.999880i	$-0.504932\pi$
$599$	21.0034	−	36.3789i	0.858175	−	1.48640i	0.873668	−	0.486523i	$-0.161735\pi$
$600$		0			0
$601$	−6.98941	−	12.1060i	−0.285104	−	0.493815i	0.687530	−	0.726156i	$-0.258695\pi$
$601$	−6.98941	−	12.1060i	−0.285104	−	0.493815i	−0.972634	+	0.232341i	$0.925361\pi$
$602$		0			0
$603$	7.76655	−	2.58469i	0.316279	−	0.105257i
$604$		0			0
$605$	5.49189	+	9.51223i	0.223277	+	0.386727i
$606$		0			0
$607$	4.38323	−	7.59197i	0.177910	−	0.308149i	−0.763255	−	0.646098i	$-0.776400\pi$
$607$	4.38323	−	7.59197i	0.177910	−	0.308149i	0.941164	+	0.337949i	$0.109733\pi$
$608$		0			0
$609$	−2.32734	−	4.03107i	−0.0943085	−	0.163347i
$610$		0			0
$611$	−48.8431			−1.97598
$612$		0			0
$613$	10.8529	+	18.7977i	0.438343	+	0.759233i	0.997562	−	0.0697873i	$-0.0222321\pi$
$613$	10.8529	+	18.7977i	0.438343	+	0.759233i	−0.559219	+	0.829020i	$0.688899\pi$
$614$		0			0
$615$	−0.579529	+	1.00377i	−0.0233689	+	0.0404761i
$616$		0			0
$617$	−13.0856			−0.526805			−0.263403	−	0.964686i	$-0.584845\pi$
$617$	−13.0856			−0.526805			−0.263403	+	0.964686i	$0.584845\pi$
$618$		0			0
$619$	2.59657	+	4.49739i	0.104365	+	0.180766i	0.913479	−	0.406887i	$-0.133386\pi$
$619$	2.59657	+	4.49739i	0.104365	+	0.180766i	−0.809114	+	0.587652i	$0.800052\pi$
$620$		0			0
$621$	−3.09212	−	5.35572i	−0.124083	−	0.214918i
$622$		0			0
$623$	−1.60807	+	2.78526i	−0.0644261	+	0.111589i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−0.818522			−0.0326886
$628$		0			0
$629$	−1.27718	+	2.21213i	−0.0509243	+	0.0882035i
$630$		0			0
$631$	19.6639	+	34.0589i	0.782807	+	1.35586i	0.930300	+	0.366799i	$0.119546\pi$
$631$	19.6639	+	34.0589i	0.782807	+	1.35586i	−0.147493	+	0.989063i	$0.547120\pi$
$632$		0			0
$633$	−1.40604	−	2.43533i	−0.0558851	−	0.0967959i
$634$		0			0
$635$	−1.10991	+	1.92242i	−0.0440455	+	0.0762890i
$636$		0			0
$637$	1.34144	−	2.32344i	0.0531498	−	0.0920582i
$638$		0			0
$639$	3.62714	−	6.28239i	0.143487	−	0.248527i
$640$		0			0
$641$	−10.2916	+	17.8256i	−0.406495	+	0.704071i	−0.994494	−	0.104791i	$-0.966583\pi$
$641$	−10.2916	+	17.8256i	−0.406495	+	0.704071i	0.587999	+	0.808862i	$0.299916\pi$
$642$		0			0
$643$	13.1661			0.519221			0.259611	−	0.965713i	$-0.416406\pi$
$643$	13.1661			0.519221			0.259611	+	0.965713i	$0.416406\pi$
$644$		0			0
$645$	−2.35137			−0.0925851
$646$		0			0
$647$	−21.8290	−	37.8089i	−0.858185	−	1.48642i	−0.873658	−	0.486540i	$-0.838259\pi$
$647$	−21.8290	−	37.8089i	−0.858185	−	1.48642i	0.0154731	−	0.999880i	$-0.495075\pi$
$648$		0			0
$649$	−0.0255101	+	0.0441847i	−0.00100136	+	0.00173440i
$650$		0			0
$651$	−6.62443	−	11.4738i	−0.259632	−	0.449695i
$652$		0			0
$653$	−6.06309	−	10.5016i	−0.237267	−	0.410959i	0.722662	−	0.691202i	$-0.242918\pi$
$653$	−6.06309	−	10.5016i	−0.237267	−	0.410959i	−0.959929	+	0.280243i	$0.909585\pi$
$654$		0			0
$655$	−21.0542			−0.822656
$656$		0			0
$657$	1.00399	+	1.73897i	0.0391695	+	0.0678436i
$658$		0			0
$659$	−5.16250	+	8.94172i	−0.201103	+	0.348320i	−0.948884	−	0.315625i	$-0.897786\pi$
$659$	−5.16250	+	8.94172i	−0.201103	+	0.348320i	0.747781	+	0.663945i	$0.231119\pi$
$660$		0			0
$661$	−7.49081			−0.291359			−0.145679	−	0.989332i	$-0.546537\pi$
$661$	−7.49081			−0.291359			−0.145679	+	0.989332i	$0.546537\pi$
$662$		0			0
$663$	−0.577326	+	0.999958i	−0.0224215	+	0.0388352i
$664$		0			0
$665$	16.2558			0.630374
$666$		0			0
$667$	−11.3810			−0.440676
$668$		0			0
$669$	12.8891			0.498321
$670$		0			0
$671$	0.708862			0.0273653
$672$		0			0
$673$	36.6286			1.41193			0.705964	−	0.708248i	$-0.250514\pi$
$673$	36.6286			1.41193			0.705964	+	0.708248i	$0.250514\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	0.846703	−	1.46653i	0.0325415	−	0.0563634i	−0.849296	−	0.527917i	$-0.822973\pi$
$677$	0.846703	−	1.46653i	0.0325415	−	0.0563634i	0.881837	+	0.471553i	$0.156307\pi$
$678$		0			0
$679$	−14.8328			−0.569232
$680$		0			0
$681$	−4.67253	+	8.09306i	−0.179052	+	0.310127i
$682$		0			0
$683$	1.70767	+	2.95778i	0.0653423	+	0.113176i	0.896846	−	0.442343i	$-0.145853\pi$
$683$	1.70767	+	2.95778i	0.0653423	+	0.113176i	−0.831503	+	0.555520i	$0.812519\pi$
$684$		0			0
$685$	7.65782			0.292590
$686$		0			0
$687$	−1.60442	−	2.77893i	−0.0612123	−	0.106023i
$688$		0			0
$689$	5.29274	+	9.16729i	0.201637	+	0.349246i
$690$		0			0
$691$	−0.242076	+	0.419288i	−0.00920901	+	0.0159505i	−0.870593	−	0.492004i	$-0.836265\pi$
$691$	−0.242076	+	0.419288i	−0.00920901	+	0.0159505i	0.861384	+	0.507954i	$0.169598\pi$
$692$		0			0
$693$	−0.161057	−	0.278959i	−0.00611805	−	0.0105968i
$694$		0			0
$695$	13.0649			0.495579
$696$		0			0
$697$	0.300707			0.0113901
$698$		0			0
$699$	−5.73530	+	9.93383i	−0.216929	+	0.375732i
$700$		0			0
$701$	−20.4531	+	35.4258i	−0.772503	+	1.33801i	0.163684	+	0.986513i	$0.447662\pi$
$701$	−20.4531	+	35.4258i	−0.772503	+	1.33801i	−0.936187	+	0.351502i	$0.885671\pi$
$702$		0			0
$703$	−31.6393	+	54.8009i	−1.19330	+	2.06686i
$704$		0			0
$705$	−5.48732	+	9.50432i	−0.206664	+	0.357953i
$706$		0			0
$707$	−3.86566	−	6.69552i	−0.145383	−	0.251811i
$708$		0			0
$709$	−10.0717	−	17.4447i	−0.378250	−	0.655148i	0.612558	−	0.790426i	$-0.290141\pi$
$709$	−10.0717	−	17.4447i	−0.378250	−	0.655148i	−0.990808	+	0.135278i	$0.956807\pi$
$710$		0			0
$711$	0.753802	−	1.30562i	0.0282698	−	0.0489647i
$712$		0			0
$713$	−32.3945			−1.21318
$714$		0			0
$715$	−0.566798			−0.0211970
$716$		0			0
$717$	2.95082	−	5.11096i	0.110200	−	0.190872i
$718$		0			0
$719$	−14.2608	−	24.7005i	−0.531839	−	0.921173i	−0.999309	−	0.0371636i	$-0.988168\pi$
$719$	−14.2608	−	24.7005i	−0.531839	−	0.921173i	0.467470	−	0.884009i	$-0.345166\pi$
$720$		0			0
$721$	−16.7490	−	29.0102i	−0.623766	−	1.08040i
$722$		0			0
$723$	−9.02817			−0.335761
$724$		0			0
$725$	−0.920164	+	1.59377i	−0.0341740	+	0.0591912i
$726$		0			0
$727$	3.10936	+	5.38557i	0.115320	+	0.199740i	0.917908	−	0.396794i	$-0.129877\pi$
$727$	3.10936	+	5.38557i	0.115320	+	0.199740i	−0.802588	+	0.596534i	$0.796544\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.305021	+	0.528311i	0.0112816	+	0.0195403i
$732$		0			0
$733$	3.23190	−	5.59782i	0.119373	−	0.206760i	−0.800146	−	0.599805i	$-0.795245\pi$
$733$	3.23190	−	5.59782i	0.119373	−	0.206760i	0.919519	+	0.393045i	$0.128578\pi$
$734$		0			0
$735$	−0.301411	−	0.522059i	−0.0111177	−	0.0192564i
$736$		0			0
$737$	0.209482	−	1.02118i	0.00771636	−	0.0376156i
$738$		0			0
$739$	−16.6691	−	28.8717i	−0.613183	−	1.06206i	−0.990700	−	0.136061i	$-0.956556\pi$
$739$	−16.6691	−	28.8717i	−0.613183	−	1.06206i	0.377518	−	0.926002i	$-0.376778\pi$
$740$		0			0
$741$	−14.3020	+	24.7719i	−0.525398	+	0.910017i
$742$		0			0
$743$	4.72772	+	8.18865i	0.173443	+	0.300412i	0.939621	−	0.342216i	$-0.111177\pi$
$743$	4.72772	+	8.18865i	0.173443	+	0.300412i	−0.766178	+	0.642628i	$0.777844\pi$
$744$		0			0
$745$	−1.39911			−0.0512593
$746$		0			0
$747$	−3.21009	−	5.56004i	−0.117451	−	0.203431i
$748$		0			0
$749$	12.0279	−	20.8329i	0.439489	−	0.761217i
$750$		0			0
$751$	3.14643			0.114815			0.0574074	−	0.998351i	$-0.481717\pi$
$751$	3.14643			0.114815			0.0574074	+	0.998351i	$0.481717\pi$
$752$		0			0
$753$	2.88177	+	4.99137i	0.105017	+	0.181896i
$754$		0			0
$755$	−8.77578	−	15.2001i	−0.319383	−	0.553188i
$756$		0			0
$757$	−9.64743	+	16.7098i	−0.350642	+	0.607329i	−0.986362	−	0.164590i	$-0.947370\pi$
$757$	−9.64743	+	16.7098i	−0.350642	+	0.607329i	0.635720	+	0.771919i	$0.280703\pi$
$758$		0			0
$759$	−0.787594			−0.0285879
$760$		0			0
$761$	−40.2180			−1.45790			−0.728951	−	0.684566i	$-0.759992\pi$
$761$	−40.2180			−1.45790			−0.728951	+	0.684566i	$0.759992\pi$
$762$		0			0
$763$	8.53065	−	14.7755i	0.308830	−	0.534910i
$764$		0			0
$765$	0.129720	+	0.224682i	0.00469005	+	0.00812341i
$766$		0			0
$767$	0.891474	+	1.54408i	0.0321893	+	0.0557535i
$768$		0			0
$769$	3.67851	−	6.37137i	0.132650	−	0.229757i	−0.792047	−	0.610460i	$-0.790985\pi$
$769$	3.67851	−	6.37137i	0.132650	−	0.229757i	0.924697	+	0.380703i	$0.124318\pi$
$770$		0			0
$771$	14.0716	−	24.3727i	0.506775	−	0.877761i
$772$		0			0
$773$	−23.8282	+	41.2717i	−0.857042	+	1.48444i	0.0176957	+	0.999843i	$0.494367\pi$
$773$	−23.8282	+	41.2717i	−0.857042	+	1.48444i	−0.874738	+	0.484597i	$0.838966\pi$
$774$		0			0
$775$	−2.61911	+	4.53644i	−0.0940813	+	0.162954i
$776$		0			0
$777$	−24.9021			−0.893359
$778$		0			0
$779$	7.44938			0.266902
$780$		0			0
$781$	−0.461933	−	0.800092i	−0.0165293	−	0.0286296i
$782$		0			0
$783$	0.920164	−	1.59377i	0.0328840	−	0.0569567i
$784$		0			0
$785$	−2.24823	−	3.89404i	−0.0802427	−	0.138984i
$786$		0			0
$787$	24.3590	+	42.1911i	0.868305	+	1.50395i	0.863727	+	0.503959i	$0.168124\pi$
$787$	24.3590	+	42.1911i	0.868305	+	1.50395i	0.00457767	+	0.999990i	$0.498543\pi$
$788$		0			0
$789$	−14.3621			−0.511305
$790$		0			0
$791$	11.5558	+	20.0152i	0.410876	+	0.711659i
$792$		0			0
$793$	12.3859	−	21.4531i	0.439838	−	0.761821i
$794$		0			0
$795$	2.37847			0.0843556
$796$		0			0
$797$	2.99411	−	5.18595i	0.106057	−	0.183696i	−0.808113	−	0.589028i	$-0.799511\pi$
$797$	2.99411	−	5.18595i	0.106057	−	0.183696i	0.914169	+	0.405332i	$0.132844\pi$
$798$		0			0
$799$	2.84727			0.100729
$800$		0			0
$801$	−1.27157			−0.0449288
$802$		0			0
$803$	0.255727			0.00902441
$804$		0			0
$805$	15.6416			0.551294
$806$		0			0
$807$	−21.7111			−0.764265
$808$		0			0
$809$	4.20123			0.147707			0.0738537	−	0.997269i	$-0.476470\pi$
$809$	4.20123			0.147707			0.0738537	+	0.997269i	$0.476470\pi$
$810$		0			0
$811$	−21.5830	+	37.3828i	−0.757880	+	1.31269i	0.186049	+	0.982540i	$0.440432\pi$
$811$	−21.5830	+	37.3828i	−0.757880	+	1.31269i	−0.943930	+	0.330147i	$0.892902\pi$
$812$		0			0
$813$	−10.7458			−0.376870
$814$		0			0
$815$	10.4296	−	18.0645i	0.365332	−	0.632773i
$816$		0			0
$817$	7.55624	+	13.0878i	0.264359	+	0.457884i
$818$		0			0
$819$	−11.2566			−0.393337
$820$		0			0
$821$	12.5317	+	21.7055i	0.437359	+	0.757527i	0.997485	−	0.0708800i	$-0.0225807\pi$
$821$	12.5317	+	21.7055i	0.437359	+	0.757527i	−0.560126	+	0.828407i	$0.689247\pi$
$822$		0			0
$823$	15.5534	+	26.9393i	0.542158	+	0.939046i	0.998780	+	0.0493847i	$0.0157260\pi$
$823$	15.5534	+	26.9393i	0.542158	+	0.939046i	−0.456622	+	0.889661i	$0.650941\pi$
$824$		0			0
$825$	−0.0636774	+	0.110293i	−0.00221696	+	0.00383989i
$826$		0			0
$827$	−17.4403	−	30.2076i	−0.606460	−	1.05042i	−0.991819	−	0.127653i	$-0.959256\pi$
$827$	−17.4403	−	30.2076i	−0.606460	−	1.05042i	0.385359	−	0.922767i	$-0.374078\pi$
$828$		0			0
$829$	−18.6255			−0.646890			−0.323445	−	0.946247i	$-0.604841\pi$
$829$	−18.6255			−0.646890			−0.323445	+	0.946247i	$0.604841\pi$
$830$		0			0
$831$	−27.2641			−0.945781
$832$		0			0
$833$	−0.0781983	+	0.135443i	−0.00270941	+	0.00469283i
$834$		0			0
$835$	−6.14610	+	10.6454i	−0.212695	+	0.368398i
$836$		0			0
$837$	2.61911	−	4.53644i	0.0905298	−	0.156802i
$838$		0			0
$839$	−0.964584	+	1.67071i	−0.0333011	+	0.0576792i	−0.882196	−	0.470883i	$-0.843935\pi$
$839$	−0.964584	+	1.67071i	−0.0333011	+	0.0576792i	0.848895	+	0.528562i	$0.177269\pi$
$840$		0			0
$841$	12.8066	+	22.1817i	0.441607	+	0.764885i
$842$		0			0
$843$	6.30782	+	10.9255i	0.217253	+	0.376293i
$844$		0			0
$845$	−3.40366	+	5.89531i	−0.117089	+	0.202805i
$846$		0			0
$847$	27.7809			0.954563
$848$		0			0
$849$	−22.7031			−0.779168
$850$		0			0
$851$	−30.4438	+	52.7302i	−1.04360	+	1.80757i
$852$		0			0
$853$	16.9753	+	29.4021i	0.581224	+	1.00671i	0.995335	+	0.0964828i	$0.0307593\pi$
$853$	16.9753	+	29.4021i	0.581224	+	1.00671i	−0.414111	+	0.910226i	$0.635907\pi$
$854$		0			0
$855$	3.21355	+	5.56603i	0.109901	+	0.190354i
$856$		0			0
$857$	−48.6154			−1.66067			−0.830334	−	0.557265i	$-0.811851\pi$
$857$	−48.6154			−1.66067			−0.830334	+	0.557265i	$0.811851\pi$
$858$		0			0
$859$	10.1749	−	17.6234i	0.347162	−	0.601302i	−0.638582	−	0.769554i	$-0.720479\pi$
$859$	10.1749	−	17.6234i	0.347162	−	0.601302i	0.985744	+	0.168251i	$0.0538120\pi$
$860$		0			0
$861$	1.46578	+	2.53881i	0.0499537	+	0.0865224i
$862$		0			0
$863$	19.5329			0.664907			0.332454	−	0.943120i	$-0.392123\pi$
$863$	19.5329			0.664907			0.332454	+	0.943120i	$0.392123\pi$
$864$		0			0
$865$	3.90299	+	6.76018i	0.132706	+	0.229853i
$866$		0			0
$867$	−8.46635	+	14.6641i	−0.287532	+	0.498020i
$868$		0			0
$869$	−0.0960004	−	0.166278i	−0.00325659	−	0.00564058i
$870$		0			0
$871$	−27.2448	−	24.1828i	−0.923156	−	0.819404i
$872$		0			0
$873$	−2.93224	−	5.07880i	−0.0992414	−	0.171891i
$874$		0			0
$875$	1.26463	−	2.19041i	0.0427524	−	0.0740493i
$876$		0			0
$877$	−11.3691	−	19.6918i	−0.383906	−	0.664945i	0.607711	−	0.794159i	$-0.292088\pi$
$877$	−11.3691	−	19.6918i	−0.383906	−	0.664945i	−0.991617	+	0.129214i	$0.958755\pi$
$878$		0			0
$879$	10.2730			0.346500
$880$		0			0
$881$	−1.97368	−	3.41852i	−0.0664950	−	0.115173i	0.830861	−	0.556480i	$-0.187848\pi$
$881$	−1.97368	−	3.41852i	−0.0664950	−	0.115173i	−0.897356	+	0.441307i	$0.854515\pi$
$882$		0			0
$883$	12.8940	−	22.3331i	0.433918	−	0.751568i	−0.563288	−	0.826260i	$-0.690464\pi$
$883$	12.8940	−	22.3331i	0.433918	−	0.751568i	0.997207	+	0.0746919i	$0.0237973\pi$
$884$		0			0
$885$	0.400614			0.0134665
$886$		0			0
$887$	3.63446	+	6.29508i	0.122033	+	0.211368i	0.920569	−	0.390579i	$-0.127725\pi$
$887$	3.63446	+	6.29508i	0.122033	+	0.211368i	−0.798536	+	0.601947i	$0.794392\pi$
$888$		0			0
$889$	2.80726	+	4.86231i	0.0941524	+	0.163077i
$890$		0			0
$891$	0.0636774	−	0.110293i	0.00213327	−	0.00369494i
$892$		0			0
$893$	70.5351			2.36037
$894$		0			0
$895$	15.9995			0.534804
$896$		0			0
$897$	−13.7616	+	23.8358i	−0.459487	+	0.795855i
$898$		0			0
$899$	−4.82003	−	8.34853i	−0.160757	−	0.278439i
$900$		0			0
$901$	−0.308536	−	0.534400i	−0.0102788	−	0.0178034i
$902$		0			0
$903$	−2.97362	+	5.15045i	−0.0989558	+	0.171396i
$904$		0			0
$905$	−10.8380	+	18.7720i	−0.360268	+	0.624002i
$906$		0			0
$907$	12.9180	−	22.3746i	0.428934	−	0.742936i	−0.567845	−	0.823136i	$-0.692223\pi$
$907$	12.9180	−	22.3746i	0.428934	−	0.742936i	0.996779	+	0.0801999i	$0.0255559\pi$
$908$		0			0
$909$	1.52837	−	2.64722i	0.0506930	−	0.0878028i
$910$		0			0
$911$	−52.4490			−1.73771			−0.868857	−	0.495064i	$-0.835145\pi$
$911$	−52.4490			−1.73771			−0.868857	+	0.495064i	$0.835145\pi$
$912$		0			0
$913$	−0.817642			−0.0270600
$914$		0			0
$915$	−2.78302	−	4.82033i	−0.0920038	−	0.159355i
$916$		0			0
$917$	−26.6258	+	46.1173i	−0.879263	+	1.52293i
$918$		0			0
$919$	1.72068	+	2.98031i	0.0567600	+	0.0983112i	0.893009	−	0.450038i	$-0.148590\pi$
$919$	1.72068	+	2.98031i	0.0567600	+	0.0983112i	−0.836249	+	0.548350i	$0.815256\pi$
$920$		0			0
$921$	5.66618	+	9.81412i	0.186707	+	0.323386i
$922$		0			0
$923$	−32.2855			−1.06269
$924$		0			0
$925$	4.92280	+	8.52654i	0.161861	+	0.280351i
$926$		0			0
$927$	6.62209	−	11.4698i	0.217498	−	0.376718i
$928$		0			0
$929$	8.69058			0.285129			0.142564	−	0.989786i	$-0.454465\pi$
$929$	8.69058			0.285129			0.142564	+	0.989786i	$0.454465\pi$
$930$		0			0
$931$	−1.93720	+	3.35532i	−0.0634891	+	0.109966i
$932$		0			0
$933$	−13.3637			−0.437507
$934$		0			0
$935$	0.0330410			0.00108056
$936$		0			0
$937$	−35.0064			−1.14361			−0.571805	−	0.820390i	$-0.693757\pi$
$937$	−35.0064			−1.14361			−0.571805	+	0.820390i	$0.693757\pi$
$938$		0			0
$939$	−22.3998			−0.730991
$940$		0			0
$941$	−38.2468			−1.24681			−0.623404	−	0.781900i	$-0.714251\pi$
$941$	−38.2468			−1.24681			−0.623404	+	0.781900i	$0.714251\pi$
$942$		0			0
$943$	7.16790			0.233419
$944$		0			0
$945$	−1.26463	+	2.19041i	−0.0411385	+	0.0712540i
$946$		0			0
$947$	8.23043			0.267453			0.133726	−	0.991018i	$-0.457306\pi$
$947$	8.23043			0.267453			0.133726	+	0.991018i	$0.457306\pi$
$948$		0			0
$949$	4.46832	−	7.73935i	0.145048	−	0.251230i
$950$		0			0
$951$	−13.0809	−	22.6568i	−0.424178	−	0.734699i
$952$		0			0
$953$	4.94687			0.160245			0.0801224	−	0.996785i	$-0.474469\pi$
$953$	4.94687			0.160245			0.0801224	+	0.996785i	$0.474469\pi$
$954$		0			0
$955$	−12.8281	−	22.2189i	−0.415107	−	0.718986i
$956$		0			0
$957$	−0.117187	−	0.202974i	−0.00378813	−	0.00656123i
$958$		0			0
$959$	9.68433	−	16.7737i	0.312723	−	0.541652i
$960$		0			0
$961$	1.78050	+	3.08391i	0.0574354	+	0.0994811i
$962$		0			0
$963$	9.51097			0.306487
$964$		0			0
$965$	17.9337			0.577307
$966$		0			0
$967$	0.598311	−	1.03631i	0.0192404	−	0.0333254i	−0.856245	−	0.516570i	$-0.827209\pi$
$967$	0.598311	−	1.03631i	0.0192404	−	0.0333254i	0.875485	+	0.483245i	$0.160542\pi$
$968$		0			0
$969$	0.833726	−	1.44406i	0.0267831	−	0.0463898i
$970$		0			0
$971$	−20.0105	+	34.6592i	−0.642167	+	1.11227i	0.342781	+	0.939415i	$0.388631\pi$
$971$	−20.0105	+	34.6592i	−0.642167	+	1.11227i	−0.984948	+	0.172851i	$0.944702\pi$
$972$		0			0
$973$	16.5223	−	28.6174i	0.529680	−	0.917432i
$974$		0			0
$975$	2.22527	+	3.85428i	0.0712657	+	0.123436i
$976$		0			0
$977$	−5.18689	−	8.98396i	−0.165943	−	0.287422i	0.771047	−	0.636779i	$-0.219734\pi$
$977$	−5.18689	−	8.98396i	−0.165943	−	0.287422i	−0.936990	+	0.349357i	$0.886400\pi$
$978$		0			0
$979$	−0.0809705	+	0.140245i	−0.00258783	+	0.00448225i
$980$		0			0
$981$	6.74556			0.215369
$982$		0			0
$983$	−2.64691			−0.0844233			−0.0422117	−	0.999109i	$-0.513440\pi$
$983$	−2.64691			−0.0844233			−0.0422117	+	0.999109i	$0.513440\pi$
$984$		0			0
$985$	−3.49225	+	6.04876i	−0.111272	+	0.192729i
$986$		0			0
$987$	13.8789	+	24.0389i	0.441770	+	0.765168i
$988$		0			0
$989$	7.27072	+	12.5933i	0.231196	+	0.400442i
$990$		0			0
$991$	0.365907			0.0116234			0.00581172	−	0.999983i	$-0.498150\pi$
$991$	0.365907			0.0116234			0.00581172	+	0.999983i	$0.498150\pi$
$992$		0			0
$993$	−11.5888	+	20.0723i	−0.367758	+	0.636975i
$994$		0			0
$995$	−1.19684	−	2.07299i	−0.0379424	−	0.0657181i
$996$		0			0
$997$	−19.2282			−0.608964			−0.304482	−	0.952518i	$-0.598483\pi$
$997$	−19.2282			−0.608964			−0.304482	+	0.952518i	$0.598483\pi$
$998$		0			0
$999$	−4.92280	−	8.52654i	−0.155750	−	0.269768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.841.6	✓	14
67.29	even	3	inner	4020.2.q.k.3781.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.6	✓	14	1.1	even	1	trivial
4020.2.q.k.3781.6	yes	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 - 2.19041i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 - 2.19041i) q^{7} +1.00000 q^{9} +(0.0636774 - 0.110293i) q^{11} +(-2.22527 - 3.85428i) q^{13} -1.00000 q^{15} +(0.129720 + 0.224682i) q^{17} +(3.21355 + 5.56603i) q^{19} +(-1.26463 + 2.19041i) q^{21} +(3.09212 + 5.35572i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-0.920164 + 1.59377i) q^{29} +(-2.61911 + 4.53644i) q^{31} +(-0.0636774 + 0.110293i) q^{33} +(1.26463 - 2.19041i) q^{35} +(4.92280 + 8.52654i) q^{37} +(2.22527 + 3.85428i) q^{39} +(0.579529 - 1.00377i) q^{41} +2.35137 q^{43} +1.00000 q^{45} +(5.48732 - 9.50432i) q^{47} +(0.301411 + 0.522059i) q^{49} +(-0.129720 - 0.224682i) q^{51} -2.37847 q^{53} +(0.0636774 - 0.110293i) q^{55} +(-3.21355 - 5.56603i) q^{57} -0.400614 q^{59} +(2.78302 + 4.82033i) q^{61} +(1.26463 - 2.19041i) q^{63} +(-2.22527 - 3.85428i) q^{65} +(7.76655 - 2.58469i) q^{67} +(-3.09212 - 5.35572i) q^{69} +(3.62714 - 6.28239i) q^{71} +(1.00399 + 1.73897i) q^{73} -1.00000 q^{75} +(-0.161057 - 0.278959i) q^{77} +(0.753802 - 1.30562i) q^{79} +1.00000 q^{81} +(-3.21009 - 5.56004i) q^{83} +(0.129720 + 0.224682i) q^{85} +(0.920164 - 1.59377i) q^{87} -1.27157 q^{89} -11.2566 q^{91} +(2.61911 - 4.53644i) q^{93} +(3.21355 + 5.56603i) q^{95} +(-2.93224 - 5.07880i) q^{97} +(0.0636774 - 0.110293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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