LMFDB - Embedded newform 560.2.q.k.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.k.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(2.41421 - 4.18154i) q^{11} +0.828427 q^{13} -2.41421 q^{15} +(0.414214 - 0.717439i) q^{17} +(-1.41421 - 2.44949i) q^{19} +(6.32843 - 0.866025i) q^{21} +(-1.20711 - 2.09077i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.414214 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(-5.82843 - 10.0951i) q^{33} +(1.00000 - 2.44949i) q^{35} +(1.00000 - 1.73205i) q^{39} -2.17157 q^{41} -6.41421 q^{43} +(-1.41421 + 2.44949i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(3.41421 - 5.91359i) q^{53} -4.82843 q^{55} -6.82843 q^{57} +(-6.24264 + 10.8126i) q^{59} +(5.74264 + 9.94655i) q^{61} +(2.82843 - 6.92820i) q^{63} +(-0.414214 - 0.717439i) q^{65} +(6.20711 - 10.7510i) q^{67} -5.82843 q^{69} +12.4853 q^{71} +(-2.41421 + 4.18154i) q^{73} +(1.20711 + 2.09077i) q^{75} +(12.6569 - 1.73205i) q^{77} +(4.58579 + 7.94282i) q^{79} +(4.74264 - 8.21449i) q^{81} +11.7279 q^{83} -0.828427 q^{85} +(-1.20711 + 2.09077i) q^{87} +(-1.32843 - 2.30090i) q^{89} +(1.34315 + 1.73205i) q^{91} +(7.24264 + 12.5446i) q^{93} +(-1.41421 + 2.44949i) q^{95} +0.343146 q^{97} -13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{21} - 2 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{29} - 12 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} - 20 q^{41} - 20 q^{43} + 4 q^{47} + 10 q^{49} - 4 q^{51} + 8 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} + 6 q^{61} + 4 q^{65} + 22 q^{67} - 12 q^{69} + 16 q^{71} - 4 q^{73} + 2 q^{75} + 28 q^{77} + 24 q^{79} + 2 q^{81} - 4 q^{83} + 8 q^{85} - 2 q^{87} + 6 q^{89} + 28 q^{91} + 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^21 - 2 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^29 - 12 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 - 20 * q^41 - 20 * q^43 + 4 * q^47 + 10 * q^49 - 4 * q^51 + 8 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 + 6 * q^61 + 4 * q^65 + 22 * q^67 - 12 * q^69 + 16 * q^71 - 4 * q^73 + 2 * q^75 + 28 * q^77 + 24 * q^79 + 2 * q^81 - 4 * q^83 + 8 * q^85 - 2 * q^87 + 6 * q^89 + 28 * q^91 + 12 * q^93 + 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.20711	−	2.09077i	0.696923	−	1.20711i	−0.272605	−	0.962126i	$-0.587885\pi$
$3$	1.20711	−	2.09077i	0.696923	−	1.20711i	0.969528	−	0.244981i	$-0.0787816\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	2.41421	−	4.18154i	0.727913	−	1.26078i	−0.229851	−	0.973226i	$-0.573824\pi$
$11$	2.41421	−	4.18154i	0.727913	−	1.26078i	0.957764	−	0.287556i	$-0.0928428\pi$
$12$		0			0
$13$	0.828427			0.229764			0.114882	−	0.993379i	$-0.463351\pi$
$13$	0.828427			0.229764			0.114882	+	0.993379i	$0.463351\pi$
$14$		0			0
$15$	−2.41421			−0.623347
$16$		0			0
$17$	0.414214	−	0.717439i	0.100462	−	0.174005i	−0.811413	−	0.584473i	$-0.801301\pi$
$17$	0.414214	−	0.717439i	0.100462	−	0.174005i	0.911875	+	0.410468i	$0.134635\pi$
$18$		0			0
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$		0			0
$21$	6.32843	−	0.866025i	1.38098	−	0.188982i
$22$		0			0
$23$	−1.20711	−	2.09077i	−0.251699	−	0.435956i	0.712295	−	0.701881i	$-0.247656\pi$
$23$	−1.20711	−	2.09077i	−0.251699	−	0.435956i	−0.963994	+	0.265925i	$0.914323\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	0.414214			0.0797154
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$		0			0
$33$	−5.82843	−	10.0951i	−1.01460	−	1.75734i
$34$		0			0
$35$	1.00000	−	2.44949i	0.169031	−	0.414039i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		0			0
$41$	−2.17157			−0.339143			−0.169571	−	0.985518i	$-0.554238\pi$
$41$	−2.17157			−0.339143			−0.169571	+	0.985518i	$0.554238\pi$
$42$		0			0
$43$	−6.41421			−0.978158			−0.489079	−	0.872239i	$-0.662667\pi$
$43$	−6.41421			−0.978158			−0.489079	+	0.872239i	$0.662667\pi$
$44$		0			0
$45$	−1.41421	+	2.44949i	−0.210819	+	0.365148i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$		0			0
$53$	3.41421	−	5.91359i	0.468978	−	0.812294i	−0.530393	−	0.847752i	$-0.677956\pi$
$53$	3.41421	−	5.91359i	0.468978	−	0.812294i	0.999371	+	0.0354577i	$0.0112889\pi$
$54$		0			0
$55$	−4.82843			−0.651065
$56$		0			0
$57$	−6.82843			−0.904447
$58$		0			0
$59$	−6.24264	+	10.8126i	−0.812723	+	1.40768i	0.0982291	+	0.995164i	$0.468682\pi$
$59$	−6.24264	+	10.8126i	−0.812723	+	1.40768i	−0.910952	+	0.412513i	$0.864651\pi$
$60$		0			0
$61$	5.74264	+	9.94655i	0.735270	+	1.27352i	0.954605	+	0.297875i	$0.0962779\pi$
$61$	5.74264	+	9.94655i	0.735270	+	1.27352i	−0.219335	+	0.975650i	$0.570389\pi$
$62$		0			0
$63$	2.82843	−	6.92820i	0.356348	−	0.872872i
$64$		0			0
$65$	−0.414214	−	0.717439i	−0.0513769	−	0.0889873i
$66$		0			0
$67$	6.20711	−	10.7510i	0.758319	−	1.31345i	−0.185389	−	0.982665i	$-0.559354\pi$
$67$	6.20711	−	10.7510i	0.758319	−	1.31345i	0.943707	−	0.330781i	$-0.107312\pi$
$68$		0			0
$69$	−5.82843			−0.701660
$70$		0			0
$71$	12.4853			1.48173			0.740865	−	0.671654i	$-0.234416\pi$
$71$	12.4853			1.48173			0.740865	+	0.671654i	$0.234416\pi$
$72$		0			0
$73$	−2.41421	+	4.18154i	−0.282562	+	0.489412i	−0.972015	−	0.234918i	$-0.924518\pi$
$73$	−2.41421	+	4.18154i	−0.282562	+	0.489412i	0.689453	+	0.724331i	$0.257851\pi$
$74$		0			0
$75$	1.20711	+	2.09077i	0.139385	+	0.241421i
$76$		0			0
$77$	12.6569	−	1.73205i	1.44238	−	0.197386i
$78$		0			0
$79$	4.58579	+	7.94282i	0.515941	+	0.893637i	0.999829	+	0.0185063i	$0.00589107\pi$
$79$	4.58579	+	7.94282i	0.515941	+	0.893637i	−0.483887	+	0.875130i	$0.660776\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$		0			0
$83$	11.7279			1.28731			0.643653	−	0.765317i	$-0.277418\pi$
$83$	11.7279			1.28731			0.643653	+	0.765317i	$0.277418\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$		0			0
$87$	−1.20711	+	2.09077i	−0.129415	+	0.224154i
$88$		0			0
$89$	−1.32843	−	2.30090i	−0.140813	−	0.243895i	0.786990	−	0.616966i	$-0.211638\pi$
$89$	−1.32843	−	2.30090i	−0.140813	−	0.243895i	−0.927803	+	0.373070i	$0.878305\pi$
$90$		0			0
$91$	1.34315	+	1.73205i	0.140800	+	0.181568i
$92$		0			0
$93$	7.24264	+	12.5446i	0.751027	+	1.30082i
$94$		0			0
$95$	−1.41421	+	2.44949i	−0.145095	+	0.251312i
$96$		0			0
$97$	0.343146			0.0348412			0.0174206	−	0.999848i	$-0.494455\pi$
$97$	0.343146			0.0348412			0.0174206	+	0.999848i	$0.494455\pi$
$98$		0			0
$99$	−13.6569			−1.37257
$100$		0			0
$101$	−6.15685	+	10.6640i	−0.612630	+	1.06111i	0.378165	+	0.925738i	$0.376555\pi$
$101$	−6.15685	+	10.6640i	−0.612630	+	1.06111i	−0.990795	+	0.135368i	$0.956778\pi$
$102$		0			0
$103$	0.207107	+	0.358719i	0.0204068	+	0.0353457i	0.876048	−	0.482223i	$-0.160171\pi$
$103$	0.207107	+	0.358719i	0.0204068	+	0.0353457i	−0.855642	+	0.517569i	$0.826837\pi$
$104$		0			0
$105$	−3.91421	−	5.04757i	−0.381988	−	0.492592i
$106$		0			0
$107$	1.37868	+	2.38794i	0.133282	+	0.230851i	0.924940	−	0.380113i	$-0.124115\pi$
$107$	1.37868	+	2.38794i	0.133282	+	0.230851i	−0.791658	+	0.610965i	$0.790782\pi$
$108$		0			0
$109$	−1.74264	+	3.01834i	−0.166915	+	0.289105i	−0.937334	−	0.348433i	$-0.886714\pi$
$109$	−1.74264	+	3.01834i	−0.166915	+	0.289105i	0.770419	+	0.637538i	$0.220047\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.4853			1.17452			0.587258	−	0.809400i	$-0.300207\pi$
$113$	12.4853			1.17452			0.587258	+	0.809400i	$0.300207\pi$
$114$		0			0
$115$	−1.20711	+	2.09077i	−0.112563	+	0.194965i
$116$		0			0
$117$	−1.17157	−	2.02922i	−0.108312	−	0.187602i
$118$		0			0
$119$	2.17157	−	0.297173i	0.199068	−	0.0272418i
$120$		0			0
$121$	−6.15685	−	10.6640i	−0.559714	−	0.969453i
$122$		0			0
$123$	−2.62132	+	4.54026i	−0.236356	+	0.409381i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.3137			−1.18140			−0.590700	−	0.806891i	$-0.701148\pi$
$127$	−13.3137			−1.18140			−0.590700	+	0.806891i	$0.701148\pi$
$128$		0			0
$129$	−7.74264	+	13.4106i	−0.681702	+	1.18074i
$130$		0			0
$131$	1.65685	+	2.86976i	0.144760	+	0.250732i	0.929283	−	0.369368i	$-0.120426\pi$
$131$	1.65685	+	2.86976i	0.144760	+	0.250732i	−0.784523	+	0.620099i	$0.787092\pi$
$132$		0			0
$133$	2.82843	−	6.92820i	0.245256	−	0.600751i
$134$		0			0
$135$	−0.207107	−	0.358719i	−0.0178249	−	0.0308737i
$136$		0			0
$137$	−0.828427	+	1.43488i	−0.0707773	+	0.122590i	−0.899242	−	0.437451i	$-0.855881\pi$
$137$	−0.828427	+	1.43488i	−0.0707773	+	0.122590i	0.828465	+	0.560041i	$0.189215\pi$
$138$		0			0
$139$	−12.1421			−1.02988			−0.514941	−	0.857225i	$-0.672186\pi$
$139$	−12.1421			−1.02988			−0.514941	+	0.857225i	$0.672186\pi$
$140$		0			0
$141$	4.82843			0.406627
$142$		0			0
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$		0			0
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$		0			0
$147$	12.0711	+	11.8272i	0.995605	+	0.975490i
$148$		0			0
$149$	3.91421	+	6.77962i	0.320665	+	0.555408i	0.980625	−	0.195892i	$-0.0627603\pi$
$149$	3.91421	+	6.77962i	0.320665	+	0.555408i	−0.659961	+	0.751300i	$0.729427\pi$
$150$		0			0
$151$	0.171573	−	0.297173i	0.0139624	−	0.0241836i	−0.858960	−	0.512043i	$-0.828889\pi$
$151$	0.171573	−	0.297173i	0.0139624	−	0.0241836i	0.872922	+	0.487859i	$0.162222\pi$
$152$		0			0
$153$	−2.34315			−0.189432
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	2.65685	−	4.60181i	0.212040	−	0.367264i	−0.740313	−	0.672263i	$-0.765323\pi$
$157$	2.65685	−	4.60181i	0.212040	−	0.367264i	0.952353	+	0.304998i	$0.0986559\pi$
$158$		0			0
$159$	−8.24264	−	14.2767i	−0.653684	−	1.13221i
$160$		0			0
$161$	2.41421	−	5.91359i	0.190267	−	0.466056i
$162$		0			0
$163$	11.8284	+	20.4874i	0.926474	+	1.60470i	0.789173	+	0.614170i	$0.210509\pi$
$163$	11.8284	+	20.4874i	0.926474	+	1.60470i	0.137301	+	0.990529i	$0.456157\pi$
$164$		0			0
$165$	−5.82843	+	10.0951i	−0.453742	+	0.785905i
$166$		0			0
$167$	−19.5858			−1.51559			−0.757797	−	0.652491i	$-0.773724\pi$
$167$	−19.5858			−1.51559			−0.757797	+	0.652491i	$0.773724\pi$
$168$		0			0
$169$	−12.3137			−0.947208
$170$		0			0
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$		0			0
$173$	9.65685	+	16.7262i	0.734197	+	1.27167i	0.955075	+	0.296365i	$0.0957745\pi$
$173$	9.65685	+	16.7262i	0.734197	+	1.27167i	−0.220878	+	0.975302i	$0.570892\pi$
$174$		0			0
$175$	−2.62132	+	0.358719i	−0.198153	+	0.0271166i
$176$		0			0
$177$	15.0711	+	26.1039i	1.13281	+	1.96209i
$178$		0			0
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	−0.990134	−	0.140122i	$-0.955250\pi$
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	0.616417	+	0.787420i	$0.288584\pi$
$180$		0			0
$181$	−8.65685			−0.643459			−0.321729	−	0.946832i	$-0.604264\pi$
$181$	−8.65685			−0.643459			−0.321729	+	0.946832i	$0.604264\pi$
$182$		0			0
$183$	27.7279			2.04971
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$		0			0
$189$	0.671573	+	0.866025i	0.0488497	+	0.0629941i
$190$		0			0
$191$	−3.58579	−	6.21076i	−0.259458	−	0.449395i	0.706639	−	0.707575i	$-0.250211\pi$
$191$	−3.58579	−	6.21076i	−0.259458	−	0.449395i	−0.966097	+	0.258180i	$0.916877\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$	−2.00000			−0.143223
$196$		0			0
$197$	−23.6569			−1.68548			−0.842741	−	0.538320i	$-0.819059\pi$
$197$	−23.6569			−1.68548			−0.842741	+	0.538320i	$0.819059\pi$
$198$		0			0
$199$	0.828427	−	1.43488i	0.0587256	−	0.101716i	−0.835168	−	0.549995i	$-0.814630\pi$
$199$	0.828427	−	1.43488i	0.0587256	−	0.101716i	0.893894	+	0.448279i	$0.147963\pi$
$200$		0			0
$201$	−14.9853	−	25.9553i	−1.05698	−	1.83074i
$202$		0			0
$203$	−1.62132	−	2.09077i	−0.113794	−	0.146743i
$204$		0			0
$205$	1.08579	+	1.88064i	0.0758346	+	0.131349i
$206$		0			0
$207$	−3.41421	+	5.91359i	−0.237304	+	0.411023i
$208$		0			0
$209$	−13.6569			−0.944664
$210$		0			0
$211$	−3.51472			−0.241963			−0.120982	−	0.992655i	$-0.538604\pi$
$211$	−3.51472			−0.241963			−0.120982	+	0.992655i	$0.538604\pi$
$212$		0			0
$213$	15.0711	−	26.1039i	1.03265	−	1.78861i
$214$		0			0
$215$	3.20711	+	5.55487i	0.218723	+	0.378839i
$216$		0			0
$217$	−15.7279	+	2.15232i	−1.06768	+	0.146109i
$218$		0			0
$219$	5.82843	+	10.0951i	0.393849	+	0.682166i
$220$		0			0
$221$	0.343146	−	0.594346i	0.0230825	−	0.0399800i
$222$		0			0
$223$	−11.6569			−0.780601			−0.390300	−	0.920688i	$-0.627629\pi$
$223$	−11.6569			−0.780601			−0.390300	+	0.920688i	$0.627629\pi$
$224$		0			0
$225$	2.82843			0.188562
$226$		0			0
$227$	13.4853	−	23.3572i	0.895050	−	1.55027i	0.0613063	−	0.998119i	$-0.480473\pi$
$227$	13.4853	−	23.3572i	0.895050	−	1.55027i	0.833743	−	0.552152i	$-0.186193\pi$
$228$		0			0
$229$	0.171573	+	0.297173i	0.0113379	+	0.0196377i	0.871639	−	0.490149i	$-0.163058\pi$
$229$	0.171573	+	0.297173i	0.0113379	+	0.0196377i	−0.860301	+	0.509787i	$0.829724\pi$
$230$		0			0
$231$	11.6569	−	28.5533i	0.766965	−	1.87867i
$232$		0			0
$233$	5.58579	+	9.67487i	0.365937	+	0.633822i	0.988926	−	0.148409i	$-0.0474152\pi$
$233$	5.58579	+	9.67487i	0.365937	+	0.633822i	−0.622989	+	0.782231i	$0.714082\pi$
$234$		0			0
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$		0			0
$237$	22.1421			1.43829
$238$		0			0
$239$	−1.31371			−0.0849767			−0.0424884	−	0.999097i	$-0.513529\pi$
$239$	−1.31371			−0.0849767			−0.0424884	+	0.999097i	$0.513529\pi$
$240$		0			0
$241$	−8.17157	+	14.1536i	−0.526377	+	0.911712i	0.473150	+	0.880982i	$0.343117\pi$
$241$	−8.17157	+	14.1536i	−0.526377	+	0.911712i	−0.999528	+	0.0307305i	$0.990217\pi$
$242$		0			0
$243$	−10.8284	−	18.7554i	−0.694644	−	1.20316i
$244$		0			0
$245$	6.74264	−	1.88064i	0.430772	−	0.120150i
$246$		0			0
$247$	−1.17157	−	2.02922i	−0.0745454	−	0.129116i
$248$		0			0
$249$	14.1569	−	24.5204i	0.897154	−	1.55392i
$250$		0			0
$251$	−13.3137			−0.840354			−0.420177	−	0.907442i	$-0.638032\pi$
$251$	−13.3137			−0.840354			−0.420177	+	0.907442i	$0.638032\pi$
$252$		0			0
$253$	−11.6569			−0.732860
$254$		0			0
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$		0			0
$257$	−8.82843	−	15.2913i	−0.550702	−	0.953844i	−0.998224	−	0.0595711i	$-0.981027\pi$
$257$	−8.82843	−	15.2913i	−0.550702	−	0.953844i	0.447522	−	0.894273i	$-0.352307\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.41421	+	2.44949i	0.0875376	+	0.151620i
$262$		0			0
$263$	9.52082	−	16.4905i	0.587079	−	1.01685i	−0.407534	−	0.913190i	$-0.633611\pi$
$263$	9.52082	−	16.4905i	0.587079	−	1.01685i	0.994613	−	0.103660i	$-0.0330554\pi$
$264$		0			0
$265$	−6.82843			−0.419467
$266$		0			0
$267$	−6.41421			−0.392543
$268$		0			0
$269$	15.2279	−	26.3755i	0.928463	−	1.60814i	0.142568	−	0.989785i	$-0.454464\pi$
$269$	15.2279	−	26.3755i	0.928463	−	1.60814i	0.785895	−	0.618360i	$-0.212202\pi$
$270$		0			0
$271$	−0.242641	−	0.420266i	−0.0147394	−	0.0255293i	0.858562	−	0.512710i	$-0.171359\pi$
$271$	−0.242641	−	0.420266i	−0.0147394	−	0.0255293i	−0.873301	+	0.487181i	$0.838025\pi$
$272$		0			0
$273$	5.24264	−	0.717439i	0.317299	−	0.0434214i
$274$		0			0
$275$	2.41421	+	4.18154i	0.145583	+	0.252156i
$276$		0			0
$277$	6.07107	−	10.5154i	0.364775	−	0.631809i	−0.623965	−	0.781452i	$-0.714479\pi$
$277$	6.07107	−	10.5154i	0.364775	−	0.631809i	0.988740	+	0.149643i	$0.0478125\pi$
$278$		0			0
$279$	16.9706			1.01600
$280$		0			0
$281$	26.2843			1.56799			0.783994	−	0.620768i	$-0.213179\pi$
$281$	26.2843			1.56799			0.783994	+	0.620768i	$0.213179\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	3.41421	+	5.91359i	0.202241	+	0.350291i
$286$		0			0
$287$	−3.52082	−	4.54026i	−0.207827	−	0.268003i
$288$		0			0
$289$	8.15685	+	14.1281i	0.479815	+	0.831064i
$290$		0			0
$291$	0.414214	−	0.717439i	0.0242816	−	0.0420570i
$292$		0			0
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$		0			0
$295$	12.4853			0.726921
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	−10.3995	−	13.4106i	−0.599417	−	0.772977i
$302$		0			0
$303$	14.8640	+	25.7451i	0.853912	+	1.47902i
$304$		0			0
$305$	5.74264	−	9.94655i	0.328823	−	0.569538i
$306$		0			0
$307$	13.2426			0.755797			0.377899	−	0.925847i	$-0.376647\pi$
$307$	13.2426			0.755797			0.377899	+	0.925847i	$0.376647\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$	−9.41421	+	16.3059i	−0.533831	+	0.924623i	0.465388	+	0.885107i	$0.345915\pi$
$311$	−9.41421	+	16.3059i	−0.533831	+	0.924623i	−0.999219	+	0.0395157i	$0.987418\pi$
$312$		0			0
$313$	8.82843	+	15.2913i	0.499012	+	0.864314i	0.999999	−	0.00114023i	$-0.000362947\pi$
$313$	8.82843	+	15.2913i	0.499012	+	0.864314i	−0.500987	+	0.865455i	$0.667030\pi$
$314$		0			0
$315$	−7.41421	+	1.01461i	−0.417744	+	0.0571669i
$316$		0			0
$317$	−12.8995	−	22.3426i	−0.724508	−	1.25488i	−0.959176	−	0.282809i	$-0.908734\pi$
$317$	−12.8995	−	22.3426i	−0.724508	−	1.25488i	0.234668	−	0.972075i	$-0.424600\pi$
$318$		0			0
$319$	−2.41421	+	4.18154i	−0.135170	+	0.234121i
$320$		0			0
$321$	6.65685			0.371549
$322$		0			0
$323$	−2.34315			−0.130376
$324$		0			0
$325$	−0.414214	+	0.717439i	−0.0229764	+	0.0397964i
$326$		0			0
$327$	4.20711	+	7.28692i	0.232654	+	0.402968i
$328$		0			0
$329$	−2.00000	+	4.89898i	−0.110264	+	0.270089i
$330$		0			0
$331$	−5.48528	−	9.50079i	−0.301498	−	0.522210i	0.674977	−	0.737839i	$-0.264153\pi$
$331$	−5.48528	−	9.50079i	−0.301498	−	0.522210i	−0.976476	+	0.215628i	$0.930820\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.4142			−0.678261
$336$		0			0
$337$	14.8284			0.807756			0.403878	−	0.914813i	$-0.367662\pi$
$337$	14.8284			0.807756			0.403878	+	0.914813i	$0.367662\pi$
$338$		0			0
$339$	15.0711	−	26.1039i	0.818548	−	1.41777i
$340$		0			0
$341$	14.4853	+	25.0892i	0.784422	+	1.35866i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$	2.91421	+	5.04757i	0.156896	+	0.271752i
$346$		0			0
$347$	11.0355	−	19.1141i	0.592418	−	1.02610i	−0.401487	−	0.915865i	$-0.631507\pi$
$347$	11.0355	−	19.1141i	0.592418	−	1.02610i	0.993906	−	0.110234i	$-0.0351601\pi$
$348$		0			0
$349$	−26.6569			−1.42691			−0.713454	−	0.700702i	$-0.752870\pi$
$349$	−26.6569			−1.42691			−0.713454	+	0.700702i	$0.752870\pi$
$350$		0			0
$351$	0.343146			0.0183158
$352$		0			0
$353$	10.5858	−	18.3351i	0.563425	−	0.975880i	−0.433770	−	0.901024i	$-0.642817\pi$
$353$	10.5858	−	18.3351i	0.563425	−	0.975880i	0.997194	−	0.0748562i	$-0.0238498\pi$
$354$		0			0
$355$	−6.24264	−	10.8126i	−0.331325	−	0.573872i
$356$		0			0
$357$	2.00000	−	4.89898i	0.105851	−	0.259281i
$358$		0			0
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$		0			0
$363$	−29.7279			−1.56031
$364$		0			0
$365$	4.82843			0.252731
$366$		0			0
$367$	−5.62132	+	9.73641i	−0.293431	+	0.508237i	−0.974619	−	0.223872i	$-0.928130\pi$
$367$	−5.62132	+	9.73641i	−0.293431	+	0.508237i	0.681188	+	0.732108i	$0.261464\pi$
$368$		0			0
$369$	3.07107	+	5.31925i	0.159873	+	0.276909i
$370$		0			0
$371$	17.8995	−	2.44949i	0.929295	−	0.127171i
$372$		0			0
$373$	−6.48528	−	11.2328i	−0.335795	−	0.581614i	0.647842	−	0.761775i	$-0.275672\pi$
$373$	−6.48528	−	11.2328i	−0.335795	−	0.581614i	−0.983637	+	0.180160i	$0.942338\pi$
$374$		0			0
$375$	1.20711	−	2.09077i	0.0623347	−	0.107967i
$376$		0			0
$377$	−0.828427			−0.0426662
$378$		0			0
$379$	−21.1716			−1.08751			−0.543755	−	0.839244i	$-0.682998\pi$
$379$	−21.1716			−1.08751			−0.543755	+	0.839244i	$0.682998\pi$
$380$		0			0
$381$	−16.0711	+	27.8359i	−0.823346	+	1.42608i
$382$		0			0
$383$	8.44975	+	14.6354i	0.431762	+	0.747834i	0.997025	−	0.0770770i	$-0.0245587\pi$
$383$	8.44975	+	14.6354i	0.431762	+	0.747834i	−0.565263	+	0.824911i	$0.691225\pi$
$384$		0			0
$385$	−7.82843	−	10.0951i	−0.398974	−	0.514496i
$386$		0			0
$387$	9.07107	+	15.7116i	0.461108	+	0.798663i
$388$		0			0
$389$	−6.17157	+	10.6895i	−0.312911	+	0.541978i	−0.978991	−	0.203902i	$-0.934638\pi$
$389$	−6.17157	+	10.6895i	−0.312911	+	0.541978i	0.666080	+	0.745880i	$0.267971\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		0			0
$393$	8.00000			0.403547
$394$		0			0
$395$	4.58579	−	7.94282i	0.230736	−	0.399646i
$396$		0			0
$397$	−14.3137	−	24.7921i	−0.718384	−	1.24428i	−0.961640	−	0.274316i	$-0.911549\pi$
$397$	−14.3137	−	24.7921i	−0.718384	−	1.24428i	0.243255	−	0.969962i	$-0.421785\pi$
$398$		0			0
$399$	−11.0711	−	14.2767i	−0.554247	−	0.714728i
$400$		0			0
$401$	−3.84315	−	6.65652i	−0.191918	−	0.332411i	0.753968	−	0.656911i	$-0.228137\pi$
$401$	−3.84315	−	6.65652i	−0.191918	−	0.332411i	−0.945886	+	0.324500i	$0.894804\pi$
$402$		0			0
$403$	−2.48528	+	4.30463i	−0.123801	+	0.214429i
$404$		0			0
$405$	−9.48528			−0.471327
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−12.3995	+	21.4766i	−0.613116	+	1.06195i	0.377596	+	0.925970i	$0.376751\pi$
$409$	−12.3995	+	21.4766i	−0.613116	+	1.06195i	−0.990712	+	0.135977i	$0.956583\pi$
$410$		0			0
$411$	2.00000	+	3.46410i	0.0986527	+	0.170872i
$412$		0			0
$413$	−32.7279	+	4.47871i	−1.61044	+	0.220383i
$414$		0			0
$415$	−5.86396	−	10.1567i	−0.287851	−	0.498572i
$416$		0			0
$417$	−14.6569	+	25.3864i	−0.717749	+	1.24318i
$418$		0			0
$419$	23.3137			1.13895			0.569475	−	0.822009i	$-0.307147\pi$
$419$	23.3137			1.13895			0.569475	+	0.822009i	$0.307147\pi$
$420$		0			0
$421$	−3.48528			−0.169862			−0.0849311	−	0.996387i	$-0.527067\pi$
$421$	−3.48528			−0.169862			−0.0849311	+	0.996387i	$0.527067\pi$
$422$		0			0
$423$	2.82843	−	4.89898i	0.137523	−	0.238197i
$424$		0			0
$425$	0.414214	+	0.717439i	0.0200923	+	0.0348009i
$426$		0			0
$427$	−11.4853	+	28.1331i	−0.555812	+	1.36146i
$428$		0			0
$429$	−4.82843	−	8.36308i	−0.233119	−	0.403773i
$430$		0			0
$431$	−10.8995	+	18.8785i	−0.525010	+	0.909344i	0.474566	+	0.880220i	$0.342605\pi$
$431$	−10.8995	+	18.8785i	−0.525010	+	0.909344i	−0.999576	+	0.0291242i	$0.990728\pi$
$432$		0			0
$433$	−31.7990			−1.52816			−0.764081	−	0.645120i	$-0.776807\pi$
$433$	−31.7990			−1.52816			−0.764081	+	0.645120i	$0.776807\pi$
$434$		0			0
$435$	2.41421			0.115753
$436$		0			0
$437$	−3.41421	+	5.91359i	−0.163324	+	0.282885i
$438$		0			0
$439$	16.9706	+	29.3939i	0.809961	+	1.40289i	0.912890	+	0.408205i	$0.133845\pi$
$439$	16.9706	+	29.3939i	0.809961	+	1.40289i	−0.102930	+	0.994689i	$0.532822\pi$
$440$		0			0
$441$	19.0711	−	5.31925i	0.908146	−	0.253297i
$442$		0			0
$443$	−6.10660	−	10.5769i	−0.290133	−	0.502526i	0.683708	−	0.729756i	$-0.260366\pi$
$443$	−6.10660	−	10.5769i	−0.290133	−	0.502526i	−0.973841	+	0.227230i	$0.927033\pi$
$444$		0			0
$445$	−1.32843	+	2.30090i	−0.0629735	+	0.109073i
$446$		0			0
$447$	18.8995			0.893915
$448$		0			0
$449$	−1.82843			−0.0862888			−0.0431444	−	0.999069i	$-0.513738\pi$
$449$	−1.82843			−0.0862888			−0.0431444	+	0.999069i	$0.513738\pi$
$450$		0			0
$451$	−5.24264	+	9.08052i	−0.246866	+	0.427585i
$452$		0			0
$453$	−0.414214	−	0.717439i	−0.0194615	−	0.0337082i
$454$		0			0
$455$	0.828427	−	2.02922i	0.0388373	−	0.0951315i
$456$		0			0
$457$	16.1421	+	27.9590i	0.755097	+	1.30787i	0.945326	+	0.326127i	$0.105744\pi$
$457$	16.1421	+	27.9590i	0.755097	+	1.30787i	−0.190229	+	0.981740i	$0.560923\pi$
$458$		0			0
$459$	0.171573	−	0.297173i	0.00800834	−	0.0138708i
$460$		0			0
$461$	18.6863			0.870307			0.435154	−	0.900356i	$-0.356694\pi$
$461$	18.6863			0.870307			0.435154	+	0.900356i	$0.356694\pi$
$462$		0			0
$463$	−11.0416			−0.513148			−0.256574	−	0.966525i	$-0.582594\pi$
$463$	−11.0416			−0.513148			−0.256574	+	0.966525i	$0.582594\pi$
$464$		0			0
$465$	7.24264	−	12.5446i	0.335869	−	0.581743i
$466$		0			0
$467$	−11.4497	−	19.8315i	−0.529831	−	0.917694i	−0.999394	−	0.0347956i	$-0.988922\pi$
$467$	−11.4497	−	19.8315i	−0.529831	−	0.917694i	0.469563	−	0.882899i	$-0.344411\pi$
$468$		0			0
$469$	32.5416	−	4.45322i	1.50263	−	0.205631i
$470$		0			0
$471$	−6.41421	−	11.1097i	−0.295551	−	0.511910i
$472$		0			0
$473$	−15.4853	+	26.8213i	−0.712014	+	1.23324i
$474$		0			0
$475$	2.82843			0.129777
$476$		0			0
$477$	−19.3137			−0.884314
$478$		0			0
$479$	−12.1716	+	21.0818i	−0.556133	+	0.963251i	0.441681	+	0.897172i	$0.354382\pi$
$479$	−12.1716	+	21.0818i	−0.556133	+	0.963251i	−0.997814	+	0.0660791i	$0.978951\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−9.44975	−	12.1859i	−0.429978	−	0.554478i
$484$		0			0
$485$	−0.171573	−	0.297173i	−0.00779072	−	0.0134939i
$486$		0			0
$487$	7.82843	−	13.5592i	0.354740	−	0.614428i	−0.632334	−	0.774696i	$-0.717903\pi$
$487$	7.82843	−	13.5592i	0.354740	−	0.614428i	0.987073	+	0.160269i	$0.0512361\pi$
$488$		0			0
$489$	57.1127			2.58273
$490$		0			0
$491$	13.3137			0.600839			0.300420	−	0.953807i	$-0.402873\pi$
$491$	13.3137			0.600839			0.300420	+	0.953807i	$0.402873\pi$
$492$		0			0
$493$	−0.414214	+	0.717439i	−0.0186552	+	0.0323118i
$494$		0			0
$495$	6.82843	+	11.8272i	0.306915	+	0.531592i
$496$		0			0
$497$	20.2426	+	26.1039i	0.908007	+	1.17092i
$498$		0			0
$499$	2.41421	+	4.18154i	0.108075	+	0.187191i	0.914990	−	0.403476i	$-0.132198\pi$
$499$	2.41421	+	4.18154i	0.108075	+	0.187191i	−0.806915	+	0.590667i	$0.798865\pi$
$500$		0			0
$501$	−23.6421	+	40.9494i	−1.05625	+	1.82948i
$502$		0			0
$503$	−37.8701			−1.68854			−0.844271	−	0.535916i	$-0.819966\pi$
$503$	−37.8701			−1.68854			−0.844271	+	0.535916i	$0.819966\pi$
$504$		0			0
$505$	12.3137			0.547953
$506$		0			0
$507$	−14.8640	+	25.7451i	−0.660132	+	1.14338i
$508$		0			0
$509$	−12.3284	−	21.3535i	−0.546448	−	0.946476i	−0.998514	−	0.0544912i	$-0.982646\pi$
$509$	−12.3284	−	21.3535i	−0.546448	−	0.946476i	0.452066	−	0.891984i	$-0.350687\pi$
$510$		0			0
$511$	−12.6569	+	1.73205i	−0.559906	+	0.0766214i
$512$		0			0
$513$	−0.585786	−	1.01461i	−0.0258631	−	0.0447962i
$514$		0			0
$515$	0.207107	−	0.358719i	0.00912622	−	0.0158071i
$516$		0			0
$517$	9.65685			0.424708
$518$		0			0
$519$	46.6274			2.04672
$520$		0			0
$521$	9.48528	−	16.4290i	0.415558	−	0.719767i	−0.579929	−	0.814667i	$-0.696920\pi$
$521$	9.48528	−	16.4290i	0.415558	−	0.719767i	0.995487	+	0.0948999i	$0.0302531\pi$
$522$		0			0
$523$	12.1716	+	21.0818i	0.532226	+	0.921842i	0.999292	+	0.0376197i	$0.0119776\pi$
$523$	12.1716	+	21.0818i	0.532226	+	0.921842i	−0.467066	+	0.884222i	$0.654689\pi$
$524$		0			0
$525$	−2.41421	+	5.91359i	−0.105365	+	0.258090i
$526$		0			0
$527$	2.48528	+	4.30463i	0.108261	+	0.187513i
$528$		0			0
$529$	8.58579	−	14.8710i	0.373295	−	0.646566i
$530$		0			0
$531$	35.3137			1.53248
$532$		0			0
$533$	−1.79899			−0.0779229
$534$		0			0
$535$	1.37868	−	2.38794i	0.0596055	−	0.103240i
$536$		0			0
$537$	12.0711	+	20.9077i	0.520905	+	0.902234i
$538$		0			0
$539$	24.1421	+	23.6544i	1.03988	+	1.01887i
$540$		0			0
$541$	−9.32843	−	16.1573i	−0.401060	−	0.694657i	0.592794	−	0.805354i	$-0.298025\pi$
$541$	−9.32843	−	16.1573i	−0.401060	−	0.694657i	−0.993854	+	0.110697i	$0.964692\pi$
$542$		0			0
$543$	−10.4497	+	18.0995i	−0.448442	+	0.776724i
$544$		0			0
$545$	3.48528			0.149293
$546$		0			0
$547$	−5.10051			−0.218082			−0.109041	−	0.994037i	$-0.534778\pi$
$547$	−5.10051			−0.218082			−0.109041	+	0.994037i	$0.534778\pi$
$548$		0			0
$549$	16.2426	−	28.1331i	0.693219	−	1.20069i
$550$		0			0
$551$	1.41421	+	2.44949i	0.0602475	+	0.104352i
$552$		0			0
$553$	−9.17157	+	22.4657i	−0.390015	+	0.955338i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.1421	−	29.6910i	0.726336	−	1.25805i	−0.232086	−	0.972695i	$-0.574555\pi$
$557$	17.1421	−	29.6910i	0.726336	−	1.25805i	0.958422	−	0.285355i	$-0.0921115\pi$
$558$		0			0
$559$	−5.31371			−0.224746
$560$		0			0
$561$	−9.65685			−0.407713
$562$		0			0
$563$	8.13604	−	14.0920i	0.342893	−	0.593908i	−0.642076	−	0.766641i	$-0.721926\pi$
$563$	8.13604	−	14.0920i	0.342893	−	0.593908i	0.984969	+	0.172733i	$0.0552598\pi$
$564$		0			0
$565$	−6.24264	−	10.8126i	−0.262630	−	0.454888i
$566$		0			0
$567$	24.8640	−	3.40256i	1.04419	−	0.142894i
$568$		0			0
$569$	1.82843	+	3.16693i	0.0766517	+	0.132765i	0.901803	−	0.432147i	$-0.142244\pi$
$569$	1.82843	+	3.16693i	0.0766517	+	0.132765i	−0.825152	+	0.564911i	$0.808910\pi$
$570$		0			0
$571$	7.41421	−	12.8418i	0.310275	−	0.537412i	−0.668147	−	0.744030i	$-0.732912\pi$
$571$	7.41421	−	12.8418i	0.310275	−	0.537412i	0.978422	+	0.206617i	$0.0662455\pi$
$572$		0			0
$573$	−17.3137			−0.723291
$574$		0			0
$575$	2.41421			0.100680
$576$		0			0
$577$	−11.9706	+	20.7336i	−0.498341	+	0.863152i	−0.999998	−	0.00191453i	$-0.999391\pi$
$577$	−11.9706	+	20.7336i	−0.498341	+	0.863152i	0.501657	+	0.865067i	$0.332724\pi$
$578$		0			0
$579$	−2.41421	−	4.18154i	−0.100331	−	0.173779i
$580$		0			0
$581$	19.0147	+	24.5204i	0.788863	+	1.01728i
$582$		0			0
$583$	−16.4853	−	28.5533i	−0.682751	−	1.18256i
$584$		0			0
$585$	−1.17157	+	2.02922i	−0.0484386	+	0.0838981i
$586$		0			0
$587$	−22.2843			−0.919770			−0.459885	−	0.887978i	$-0.652109\pi$
$587$	−22.2843			−0.919770			−0.459885	+	0.887978i	$0.652109\pi$
$588$		0			0
$589$	16.9706			0.699260
$590$		0			0
$591$	−28.5563	+	49.4610i	−1.17465	+	2.03456i
$592$		0			0
$593$	−21.8995	−	37.9310i	−0.899304	−	1.55764i	−0.828385	−	0.560159i	$-0.810740\pi$
$593$	−21.8995	−	37.9310i	−0.899304	−	1.55764i	−0.0709193	−	0.997482i	$-0.522593\pi$
$594$		0			0
$595$	−1.34315	−	1.73205i	−0.0550636	−	0.0710072i
$596$		0			0
$597$	−2.00000	−	3.46410i	−0.0818546	−	0.141776i
$598$		0			0
$599$	8.82843	−	15.2913i	0.360720	−	0.624785i	−0.627360	−	0.778730i	$-0.715864\pi$
$599$	8.82843	−	15.2913i	0.360720	−	0.624785i	0.988079	+	0.153945i	$0.0491977\pi$
$600$		0			0
$601$	8.34315			0.340324			0.170162	−	0.985416i	$-0.445571\pi$
$601$	8.34315			0.340324			0.170162	+	0.985416i	$0.445571\pi$
$602$		0			0
$603$	−35.1127			−1.42990
$604$		0			0
$605$	−6.15685	+	10.6640i	−0.250312	+	0.433553i
$606$		0			0
$607$	−2.10660	−	3.64874i	−0.0855043	−	0.148098i	0.820102	−	0.572218i	$-0.193917\pi$
$607$	−2.10660	−	3.64874i	−0.0855043	−	0.148098i	−0.905606	+	0.424120i	$0.860583\pi$
$608$		0			0
$609$	−6.32843	+	0.866025i	−0.256441	+	0.0350931i
$610$		0			0
$611$	0.828427	+	1.43488i	0.0335146	+	0.0580489i
$612$		0			0
$613$	7.72792	−	13.3852i	0.312128	−	0.540621i	−0.666695	−	0.745331i	$-0.732292\pi$
$613$	7.72792	−	13.3852i	0.312128	−	0.540621i	0.978823	+	0.204709i	$0.0656249\pi$
$614$		0			0
$615$	5.24264			0.211404
$616$		0			0
$617$	−11.3137			−0.455473			−0.227736	−	0.973723i	$-0.573132\pi$
$617$	−11.3137			−0.455473			−0.227736	+	0.973723i	$0.573132\pi$
$618$		0			0
$619$	21.2426	−	36.7933i	0.853814	−	1.47885i	−0.0239273	−	0.999714i	$-0.507617\pi$
$619$	21.2426	−	36.7933i	0.853814	−	1.47885i	0.877741	−	0.479135i	$-0.159050\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$		0			0
$623$	2.65685	−	6.50794i	0.106445	−	0.260735i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−16.4853	+	28.5533i	−0.658359	+	1.14031i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−8.14214			−0.324133			−0.162067	−	0.986780i	$-0.551816\pi$
$631$	−8.14214			−0.324133			−0.162067	+	0.986780i	$0.551816\pi$
$632$		0			0
$633$	−4.24264	+	7.34847i	−0.168630	+	0.292075i
$634$		0			0
$635$	6.65685	+	11.5300i	0.264169	+	0.457554i
$636$		0			0
$637$	−1.44365	+	5.61642i	−0.0571995	+	0.222531i
$638$		0			0
$639$	−17.6569	−	30.5826i	−0.698494	−	1.20983i
$640$		0			0
$641$	−7.25736	+	12.5701i	−0.286648	+	0.496490i	−0.973008	−	0.230773i	$-0.925875\pi$
$641$	−7.25736	+	12.5701i	−0.286648	+	0.496490i	0.686359	+	0.727263i	$0.259208\pi$
$642$		0			0
$643$	30.2843			1.19430			0.597148	−	0.802131i	$-0.296301\pi$
$643$	30.2843			1.19430			0.597148	+	0.802131i	$0.296301\pi$
$644$		0			0
$645$	15.4853			0.609732
$646$		0			0
$647$	8.52082	−	14.7585i	0.334988	−	0.580216i	−0.648495	−	0.761219i	$-0.724601\pi$
$647$	8.52082	−	14.7585i	0.334988	−	0.580216i	0.983482	+	0.181003i	$0.0579345\pi$
$648$		0			0
$649$	30.1421	+	52.2077i	1.18318	+	2.04933i
$650$		0			0
$651$	−14.4853	+	35.4815i	−0.567723	+	1.39063i
$652$		0			0
$653$	12.4142	+	21.5020i	0.485806	+	0.841440i	0.999867	−	0.0163133i	$-0.00519292\pi$
$653$	12.4142	+	21.5020i	0.485806	+	0.841440i	−0.514061	+	0.857754i	$0.671860\pi$
$654$		0			0
$655$	1.65685	−	2.86976i	0.0647387	−	0.112131i
$656$		0			0
$657$	13.6569			0.532805
$658$		0			0
$659$	−26.8284			−1.04509			−0.522544	−	0.852613i	$-0.675017\pi$
$659$	−26.8284			−1.04509			−0.522544	+	0.852613i	$0.675017\pi$
$660$		0			0
$661$	−13.0858	+	22.6652i	−0.508978	+	0.881576i	0.490968	+	0.871178i	$0.336643\pi$
$661$	−13.0858	+	22.6652i	−0.508978	+	0.881576i	−0.999946	+	0.0103982i	$0.996690\pi$
$662$		0			0
$663$	−0.828427	−	1.43488i	−0.0321734	−	0.0557260i
$664$		0			0
$665$	−7.41421	+	1.01461i	−0.287511	+	0.0393450i
$666$		0			0
$667$	1.20711	+	2.09077i	0.0467394	+	0.0809549i
$668$		0			0
$669$	−14.0711	+	24.3718i	−0.544019	+	0.942268i
$670$		0			0
$671$	55.4558			2.14085
$672$		0			0
$673$	18.3431			0.707076			0.353538	−	0.935420i	$-0.384978\pi$
$673$	18.3431			0.707076			0.353538	+	0.935420i	$0.384978\pi$
$674$		0			0
$675$	−0.207107	+	0.358719i	−0.00797154	+	0.0138071i
$676$		0			0
$677$	−0.0710678	−	0.123093i	−0.00273136	−	0.00473085i	0.864656	−	0.502364i	$-0.167536\pi$
$677$	−0.0710678	−	0.123093i	−0.00273136	−	0.00473085i	−0.867388	+	0.497633i	$0.834203\pi$
$678$		0			0
$679$	0.556349	+	0.717439i	0.0213507	+	0.0275328i
$680$		0			0
$681$	−32.5563	−	56.3893i	−1.24756	−	2.16084i
$682$		0			0
$683$	−21.6213	+	37.4492i	−0.827317	+	1.43295i	0.0728189	+	0.997345i	$0.476801\pi$
$683$	−21.6213	+	37.4492i	−0.827317	+	1.43295i	−0.900136	+	0.435610i	$0.856533\pi$
$684$		0			0
$685$	1.65685			0.0633051
$686$		0			0
$687$	0.828427			0.0316065
$688$		0			0
$689$	2.82843	−	4.89898i	0.107754	−	0.186636i
$690$		0			0
$691$	−2.41421	−	4.18154i	−0.0918410	−	0.159073i	0.816445	−	0.577423i	$-0.195942\pi$
$691$	−2.41421	−	4.18154i	−0.0918410	−	0.159073i	−0.908286	+	0.418350i	$0.862608\pi$
$692$		0			0
$693$	−22.1421	−	28.5533i	−0.841110	−	1.08465i
$694$		0			0
$695$	6.07107	+	10.5154i	0.230289	+	0.398872i
$696$		0			0
$697$	−0.899495	+	1.55797i	−0.0340708	+	0.0590124i
$698$		0			0
$699$	26.9706			1.02012
$700$		0			0
$701$	−42.7990			−1.61650			−0.808248	−	0.588843i	$-0.799584\pi$
$701$	−42.7990			−1.61650			−0.808248	+	0.588843i	$0.799584\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−2.41421	−	4.18154i	−0.0909245	−	0.157486i
$706$		0			0
$707$	−32.2782	+	4.41717i	−1.21395	+	0.166125i
$708$		0			0
$709$	−19.1569	−	33.1806i	−0.719451	−	1.24613i	−0.961218	−	0.275791i	$-0.911060\pi$
$709$	−19.1569	−	33.1806i	−0.719451	−	1.24613i	0.241767	−	0.970334i	$-0.422273\pi$
$710$		0			0
$711$	12.9706	−	22.4657i	0.486434	−	0.842529i
$712$		0			0
$713$	14.4853			0.542478
$714$		0			0
$715$	−4.00000			−0.149592
$716$		0			0
$717$	−1.58579	+	2.74666i	−0.0592223	+	0.102576i
$718$		0			0
$719$	−20.5563	−	35.6046i	−0.766622	−	1.32783i	−0.939385	−	0.342865i	$-0.888602\pi$
$719$	−20.5563	−	35.6046i	−0.766622	−	1.32783i	0.172762	−	0.984964i	$-0.444731\pi$
$720$		0			0
$721$	−0.414214	+	1.01461i	−0.0154261	+	0.0377861i
$722$		0			0
$723$	19.7279	+	34.1698i	0.733689	+	1.27079i
$724$		0			0
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$		0			0
$727$	40.4142			1.49888			0.749440	−	0.662072i	$-0.230323\pi$
$727$	40.4142			1.49888			0.749440	+	0.662072i	$0.230323\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−2.65685	+	4.60181i	−0.0982673	+	0.170204i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$		0			0
$735$	4.20711	−	16.3674i	0.155181	−	0.603722i
$736$		0			0
$737$	−29.9706	−	51.9105i	−1.10398	−	1.91215i
$738$		0			0
$739$	20.5563	−	35.6046i	0.756178	−	1.30974i	−0.188609	−	0.982052i	$-0.560398\pi$
$739$	20.5563	−	35.6046i	0.756178	−	1.30974i	0.944787	−	0.327686i	$-0.106269\pi$
$740$		0			0
$741$	−5.65685			−0.207810
$742$		0			0
$743$	1.92893			0.0707657			0.0353828	−	0.999374i	$-0.488735\pi$
$743$	1.92893			0.0707657			0.0353828	+	0.999374i	$0.488735\pi$
$744$		0			0
$745$	3.91421	−	6.77962i	0.143406	−	0.248386i
$746$		0			0
$747$	−16.5858	−	28.7274i	−0.606842	−	1.05108i
$748$		0			0
$749$	−2.75736	+	6.75412i	−0.100752	+	0.246790i
$750$		0			0
$751$	−20.8284	−	36.0759i	−0.760040	−	1.31643i	−0.942829	−	0.333276i	$-0.891846\pi$
$751$	−20.8284	−	36.0759i	−0.760040	−	1.31643i	0.182789	−	0.983152i	$-0.441487\pi$
$752$		0			0
$753$	−16.0711	+	27.8359i	−0.585662	+	1.01440i
$754$		0			0
$755$	−0.343146			−0.0124884
$756$		0			0
$757$	19.4558			0.707135			0.353567	−	0.935409i	$-0.384969\pi$
$757$	19.4558			0.707135			0.353567	+	0.935409i	$0.384969\pi$
$758$		0			0
$759$	−14.0711	+	24.3718i	−0.510747	+	0.884640i
$760$		0			0
$761$	6.65685	+	11.5300i	0.241311	+	0.417963i	0.961088	−	0.276243i	$-0.0890894\pi$
$761$	6.65685	+	11.5300i	0.241311	+	0.417963i	−0.719777	+	0.694205i	$0.755756\pi$
$762$		0			0
$763$	−9.13604	+	1.25024i	−0.330747	+	0.0452617i
$764$		0			0
$765$	1.17157	+	2.02922i	0.0423583	+	0.0733667i
$766$		0			0
$767$	−5.17157	+	8.95743i	−0.186735	+	0.323434i
$768$		0			0
$769$	44.6274			1.60931			0.804653	−	0.593745i	$-0.202351\pi$
$769$	44.6274			1.60931			0.804653	+	0.593745i	$0.202351\pi$
$770$		0			0
$771$	−42.6274			−1.53519
$772$		0			0
$773$	−12.5563	+	21.7482i	−0.451620	+	0.782230i	−0.998487	−	0.0549903i	$-0.982487\pi$
$773$	−12.5563	+	21.7482i	−0.451620	+	0.782230i	0.546866	+	0.837220i	$0.315821\pi$
$774$		0			0
$775$	−3.00000	−	5.19615i	−0.107763	−	0.186651i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.07107	+	5.31925i	0.110032	+	0.190582i
$780$		0			0
$781$	30.1421	−	52.2077i	1.07857	−	1.86814i
$782$		0			0
$783$	−0.414214			−0.0148028
$784$		0			0
$785$	−5.31371			−0.189654
$786$		0			0
$787$	−14.2782	+	24.7305i	−0.508962	+	0.881548i	0.490984	+	0.871168i	$0.336637\pi$
$787$	−14.2782	+	24.7305i	−0.508962	+	0.881548i	−0.999946	+	0.0103795i	$0.996696\pi$
$788$		0			0
$789$	−22.9853	−	39.8117i	−0.818298	−	1.41733i
$790$		0			0
$791$	20.2426	+	26.1039i	0.719745	+	0.928146i
$792$		0			0
$793$	4.75736	+	8.23999i	0.168939	+	0.292611i
$794$		0			0
$795$	−8.24264	+	14.2767i	−0.292336	+	0.506341i
$796$		0			0
$797$	−8.00000			−0.283375			−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000			−0.283375			−0.141687	+	0.989911i	$0.545253\pi$
$798$		0			0
$799$	1.65685			0.0586153
$800$		0			0
$801$	−3.75736	+	6.50794i	−0.132760	+	0.229947i
$802$		0			0
$803$	11.6569	+	20.1903i	0.411361	+	0.712499i
$804$		0			0
$805$	−6.32843	+	0.866025i	−0.223048	+	0.0305234i
$806$		0			0
$807$	−36.7635	−	63.6762i	−1.29413	−	2.24151i
$808$		0			0
$809$	4.81371	−	8.33759i	0.169241	−	0.293134i	−0.768912	−	0.639354i	$-0.779202\pi$
$809$	4.81371	−	8.33759i	0.169241	−	0.293134i	0.938153	+	0.346220i	$0.112535\pi$
$810$		0			0
$811$	−24.6274			−0.864786			−0.432393	−	0.901685i	$-0.642331\pi$
$811$	−24.6274			−0.864786			−0.432393	+	0.901685i	$0.642331\pi$
$812$		0			0
$813$	−1.17157			−0.0410889
$814$		0			0
$815$	11.8284	−	20.4874i	0.414332	−	0.717644i
$816$		0			0
$817$	9.07107	+	15.7116i	0.317356	+	0.549678i
$818$		0			0
$819$	2.34315	−	5.73951i	0.0818761	−	0.200555i
$820$		0			0
$821$	9.97056	+	17.2695i	0.347975	+	0.602710i	0.985890	−	0.167397i	$-0.0535361\pi$
$821$	9.97056	+	17.2695i	0.347975	+	0.602710i	−0.637915	+	0.770107i	$0.720203\pi$
$822$		0			0
$823$	−6.03553	+	10.4539i	−0.210385	+	0.364398i	−0.951835	−	0.306610i	$-0.900805\pi$
$823$	−6.03553	+	10.4539i	−0.210385	+	0.364398i	0.741450	+	0.671008i	$0.234139\pi$
$824$		0			0
$825$	11.6569			0.405840
$826$		0			0
$827$	−16.2132			−0.563788			−0.281894	−	0.959446i	$-0.590963\pi$
$827$	−16.2132			−0.563788			−0.281894	+	0.959446i	$0.590963\pi$
$828$		0			0
$829$	−3.34315	+	5.79050i	−0.116112	+	0.201112i	−0.918224	−	0.396062i	$-0.870377\pi$
$829$	−3.34315	+	5.79050i	−0.116112	+	0.201112i	0.802112	+	0.597174i	$0.203710\pi$
$830$		0			0
$831$	−14.6569	−	25.3864i	−0.508441	−	0.880645i
$832$		0			0
$833$	4.14214	+	4.05845i	0.143516	+	0.140617i
$834$		0			0
$835$	9.79289	+	16.9618i	0.338897	+	0.586987i
$836$		0			0
$837$	−1.24264	+	2.15232i	−0.0429519	+	0.0743950i
$838$		0			0
$839$	−20.8284			−0.719077			−0.359539	−	0.933130i	$-0.617066\pi$
$839$	−20.8284			−0.719077			−0.359539	+	0.933130i	$0.617066\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	31.7279	−	54.9544i	1.09277	−	1.89273i
$844$		0			0
$845$	6.15685	+	10.6640i	0.211802	+	0.366852i
$846$		0			0
$847$	12.3137	−	30.1623i	0.423104	−	1.03639i
$848$		0			0
$849$	−16.8995	−	29.2708i	−0.579989	−	1.00457i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	53.4558			1.83029			0.915147	−	0.403121i	$-0.132075\pi$
$853$	53.4558			1.83029			0.915147	+	0.403121i	$0.132075\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$		0			0
$857$	11.1421	−	19.2987i	0.380608	−	0.659233i	−0.610541	−	0.791985i	$-0.709048\pi$
$857$	11.1421	−	19.2987i	0.380608	−	0.659233i	0.991149	+	0.132752i	$0.0423814\pi$
$858$		0			0
$859$	23.3137	+	40.3805i	0.795453	+	1.37777i	0.922551	+	0.385876i	$0.126101\pi$
$859$	23.3137	+	40.3805i	0.795453	+	1.37777i	−0.127097	+	0.991890i	$0.540566\pi$
$860$		0			0
$861$	−13.7426	+	1.88064i	−0.468348	+	0.0640919i
$862$		0			0
$863$	−8.27817	−	14.3382i	−0.281792	−	0.488079i	0.690034	−	0.723777i	$-0.257596\pi$
$863$	−8.27817	−	14.3382i	−0.281792	−	0.488079i	−0.971826	+	0.235698i	$0.924262\pi$
$864$		0			0
$865$	9.65685	−	16.7262i	0.328343	−	0.568707i
$866$		0			0
$867$	39.3848			1.33758
$868$		0			0
$869$	44.2843			1.50224
$870$		0			0
$871$	5.14214	−	8.90644i	0.174235	−	0.301783i
$872$		0			0
$873$	−0.485281	−	0.840532i	−0.0164243	−	0.0284477i
$874$		0			0
$875$	1.62132	+	2.09077i	0.0548106	+	0.0706809i
$876$		0			0
$877$	−15.4142	−	26.6982i	−0.520501	−	0.901534i	−0.999716	−	0.0238366i	$-0.992412\pi$
$877$	−15.4142	−	26.6982i	−0.520501	−	0.901534i	0.479215	−	0.877698i	$-0.340921\pi$
$878$		0			0
$879$	−19.3137	+	33.4523i	−0.651435	+	1.12832i
$880$		0			0
$881$	−3.82843			−0.128983			−0.0644915	−	0.997918i	$-0.520543\pi$
$881$	−3.82843			−0.128983			−0.0644915	+	0.997918i	$0.520543\pi$
$882$		0			0
$883$	38.2843			1.28837			0.644184	−	0.764870i	$-0.277197\pi$
$883$	38.2843			1.28837			0.644184	+	0.764870i	$0.277197\pi$
$884$		0			0
$885$	15.0711	−	26.1039i	0.506608	−	0.877471i
$886$		0			0
$887$	22.0355	+	38.1667i	0.739881	+	1.28151i	0.952549	+	0.304387i	$0.0984515\pi$
$887$	22.0355	+	38.1667i	0.739881	+	1.28151i	−0.212668	+	0.977125i	$0.568215\pi$
$888$		0			0
$889$	−21.5858	−	27.8359i	−0.723964	−	0.933586i
$890$		0			0
$891$	−22.8995	−	39.6631i	−0.767162	−	1.32876i
$892$		0			0
$893$	2.82843	−	4.89898i	0.0946497	−	0.163938i
$894$		0			0
$895$	10.0000			0.334263
$896$		0			0
$897$	−4.82843			−0.161216
$898$		0			0
$899$	3.00000	−	5.19615i	0.100056	−	0.173301i
$900$		0			0
$901$	−2.82843	−	4.89898i	−0.0942286	−	0.163209i
$902$		0			0
$903$	−40.5919	+	5.55487i	−1.35081	+	0.184855i
$904$		0			0
$905$	4.32843	+	7.49706i	0.143882	+	0.249211i
$906$		0			0
$907$	14.1066	−	24.4334i	0.468402	−	0.811296i	−0.530946	−	0.847406i	$-0.678163\pi$
$907$	14.1066	−	24.4334i	0.468402	−	0.811296i	0.999348	+	0.0361097i	$0.0114966\pi$
$908$		0			0
$909$	34.8284			1.15519
$910$		0			0
$911$	49.7990			1.64991			0.824957	−	0.565195i	$-0.191199\pi$
$911$	49.7990			1.64991			0.824957	+	0.565195i	$0.191199\pi$
$912$		0			0
$913$	28.3137	−	49.0408i	0.937047	−	1.62301i
$914$		0			0
$915$	−13.8640	−	24.0131i	−0.458328	−	0.793848i
$916$		0			0
$917$	−3.31371	+	8.11689i	−0.109428	+	0.268043i
$918$		0			0
$919$	9.55635	+	16.5521i	0.315235	+	0.546003i	0.979487	−	0.201505i	$-0.0645834\pi$
$919$	9.55635	+	16.5521i	0.315235	+	0.546003i	−0.664253	+	0.747508i	$0.731250\pi$
$920$		0			0
$921$	15.9853	−	27.6873i	0.526733	−	0.912328i
$922$		0			0
$923$	10.3431			0.340449
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.585786	−	1.01461i	0.0192398	−	0.0333242i
$928$		0			0
$929$	5.74264	+	9.94655i	0.188410	+	0.326336i	0.944720	−	0.327877i	$-0.106333\pi$
$929$	5.74264	+	9.94655i	0.188410	+	0.326336i	−0.756310	+	0.654213i	$0.773000\pi$
$930$		0			0
$931$	19.0711	−	5.31925i	0.625029	−	0.174331i
$932$		0			0
$933$	22.7279	+	39.3659i	0.744079	+	1.28878i
$934$		0			0
$935$	−2.00000	+	3.46410i	−0.0654070	+	0.113288i
$936$		0			0
$937$	−10.6274			−0.347183			−0.173591	−	0.984818i	$-0.555537\pi$
$937$	−10.6274			−0.347183			−0.173591	+	0.984818i	$0.555537\pi$
$938$		0			0
$939$	42.6274			1.39109
$940$		0			0
$941$	−5.14214	+	8.90644i	−0.167629	+	0.290342i	−0.937586	−	0.347754i	$-0.886944\pi$
$941$	−5.14214	+	8.90644i	−0.167629	+	0.290342i	0.769957	+	0.638096i	$0.220278\pi$
$942$		0			0
$943$	2.62132	+	4.54026i	0.0853619	+	0.147851i
$944$		0			0
$945$	0.414214	−	1.01461i	0.0134744	−	0.0330053i
$946$		0			0
$947$	−21.5919	−	37.3982i	−0.701642	−	1.21528i	−0.967890	−	0.251375i	$-0.919117\pi$
$947$	−21.5919	−	37.3982i	−0.701642	−	1.21528i	0.266248	−	0.963905i	$-0.414216\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	−62.2843			−2.01971
$952$		0			0
$953$	−2.34315			−0.0759019			−0.0379510	−	0.999280i	$-0.512083\pi$
$953$	−2.34315			−0.0759019			−0.0379510	+	0.999280i	$0.512083\pi$
$954$		0			0
$955$	−3.58579	+	6.21076i	−0.116033	+	0.200976i
$956$		0			0
$957$	5.82843	+	10.0951i	0.188406	+	0.326329i
$958$		0			0
$959$	−4.34315	+	0.594346i	−0.140247	+	0.0191924i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	3.89949	−	6.75412i	0.125659	−	0.217649i
$964$		0			0
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	27.5269			0.885206			0.442603	−	0.896718i	$-0.354055\pi$
$967$	27.5269			0.885206			0.442603	+	0.896718i	$0.354055\pi$
$968$		0			0
$969$	−2.82843	+	4.89898i	−0.0908622	+	0.157378i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	−19.6863	−	25.3864i	−0.631114	−	0.813851i
$974$		0			0
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$		0			0
$977$	−10.6569	+	18.4582i	−0.340943	+	0.590531i	−0.984608	−	0.174777i	$-0.944080\pi$
$977$	−10.6569	+	18.4582i	−0.340943	+	0.590531i	0.643665	+	0.765307i	$0.277413\pi$
$978$		0			0
$979$	−12.8284			−0.409998
$980$		0			0
$981$	9.85786			0.314737
$982$		0			0
$983$	−7.10660	+	12.3090i	−0.226665	+	0.392596i	−0.956818	−	0.290688i	$-0.906116\pi$
$983$	−7.10660	+	12.3090i	−0.226665	+	0.392596i	0.730152	+	0.683284i	$0.239449\pi$
$984$		0			0
$985$	11.8284	+	20.4874i	0.376885	+	0.652784i
$986$		0			0
$987$	7.82843	+	10.0951i	0.249182	+	0.321332i
$988$		0			0
$989$	7.74264	+	13.4106i	0.246202	+	0.426434i
$990$		0			0
$991$	−7.82843	+	13.5592i	−0.248678	+	0.430723i	−0.963159	−	0.268931i	$-0.913329\pi$
$991$	−7.82843	+	13.5592i	−0.248678	+	0.430723i	0.714481	+	0.699655i	$0.246663\pi$
$992$		0			0
$993$	−26.4853			−0.840485
$994$		0			0
$995$	−1.65685			−0.0525258
$996$		0			0
$997$	8.72792	−	15.1172i	0.276416	−	0.478767i	−0.694075	−	0.719902i	$-0.744187\pi$
$997$	8.72792	−	15.1172i	0.276416	−	0.478767i	0.970491	+	0.241136i	$0.0775199\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.k.81.2		4
4.3	odd	2		35.2.e.a.11.2	✓	4
7.2	even	3	inner	560.2.q.k.401.2		4
7.3	odd	6		3920.2.a.bv.1.2		2
7.4	even	3		3920.2.a.bq.1.1		2
12.11	even	2		315.2.j.e.46.1		4
20.3	even	4		175.2.k.a.74.3		8
20.7	even	4		175.2.k.a.74.2		8
20.19	odd	2		175.2.e.c.151.1		4
28.3	even	6		245.2.a.g.1.1		2
28.11	odd	6		245.2.a.h.1.1		2
28.19	even	6		245.2.e.e.226.2		4
28.23	odd	6		35.2.e.a.16.2	yes	4
28.27	even	2		245.2.e.e.116.2		4
84.11	even	6		2205.2.a.n.1.2		2
84.23	even	6		315.2.j.e.226.1		4
84.59	odd	6		2205.2.a.q.1.2		2
140.3	odd	12		1225.2.b.h.99.3		4
140.23	even	12		175.2.k.a.149.2		8
140.39	odd	6		1225.2.a.k.1.2		2
140.59	even	6		1225.2.a.m.1.2		2
140.67	even	12		1225.2.b.g.99.2		4
140.79	odd	6		175.2.e.c.51.1		4
140.87	odd	12		1225.2.b.h.99.2		4
140.107	even	12		175.2.k.a.149.3		8
140.123	even	12		1225.2.b.g.99.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.2	✓	4	4.3	odd	2
35.2.e.a.16.2	yes	4	28.23	odd	6
175.2.e.c.51.1		4	140.79	odd	6
175.2.e.c.151.1		4	20.19	odd	2
175.2.k.a.74.2		8	20.7	even	4
175.2.k.a.74.3		8	20.3	even	4
175.2.k.a.149.2		8	140.23	even	12
175.2.k.a.149.3		8	140.107	even	12
245.2.a.g.1.1		2	28.3	even	6
245.2.a.h.1.1		2	28.11	odd	6
245.2.e.e.116.2		4	28.27	even	2
245.2.e.e.226.2		4	28.19	even	6
315.2.j.e.46.1		4	12.11	even	2
315.2.j.e.226.1		4	84.23	even	6
560.2.q.k.81.2		4	1.1	even	1	trivial
560.2.q.k.401.2		4	7.2	even	3	inner
1225.2.a.k.1.2		2	140.39	odd	6
1225.2.a.m.1.2		2	140.59	even	6
1225.2.b.g.99.2		4	140.67	even	12
1225.2.b.g.99.3		4	140.123	even	12
1225.2.b.h.99.2		4	140.87	odd	12
1225.2.b.h.99.3		4	140.3	odd	12
2205.2.a.n.1.2		2	84.11	even	6
2205.2.a.q.1.2		2	84.59	odd	6
3920.2.a.bq.1.1		2	7.4	even	3
3920.2.a.bv.1.2		2	7.3	odd	6

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(2.41421 - 4.18154i) q^{11} +0.828427 q^{13} -2.41421 q^{15} +(0.414214 - 0.717439i) q^{17} +(-1.41421 - 2.44949i) q^{19} +(6.32843 - 0.866025i) q^{21} +(-1.20711 - 2.09077i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.414214 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(-5.82843 - 10.0951i) q^{33} +(1.00000 - 2.44949i) q^{35} +(1.00000 - 1.73205i) q^{39} -2.17157 q^{41} -6.41421 q^{43} +(-1.41421 + 2.44949i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(3.41421 - 5.91359i) q^{53} -4.82843 q^{55} -6.82843 q^{57} +(-6.24264 + 10.8126i) q^{59} +(5.74264 + 9.94655i) q^{61} +(2.82843 - 6.92820i) q^{63} +(-0.414214 - 0.717439i) q^{65} +(6.20711 - 10.7510i) q^{67} -5.82843 q^{69} +12.4853 q^{71} +(-2.41421 + 4.18154i) q^{73} +(1.20711 + 2.09077i) q^{75} +(12.6569 - 1.73205i) q^{77} +(4.58579 + 7.94282i) q^{79} +(4.74264 - 8.21449i) q^{81} +11.7279 q^{83} -0.828427 q^{85} +(-1.20711 + 2.09077i) q^{87} +(-1.32843 - 2.30090i) q^{89} +(1.34315 + 1.73205i) q^{91} +(7.24264 + 12.5446i) q^{93} +(-1.41421 + 2.44949i) q^{95} +0.343146 q^{97} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{21} - 2 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{29} - 12 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} - 20 q^{41} - 20 q^{43} + 4 q^{47} + 10 q^{49} - 4 q^{51} + 8 q^{53} - 8 q^{55} - 16 q^{57} - 8 q^{59} + 6 q^{61} + 4 q^{65} + 22 q^{67} - 12 q^{69} + 16 q^{71} - 4 q^{73} + 2 q^{75} + 28 q^{77} + 24 q^{79} + 2 q^{81} - 4 q^{83} + 8 q^{85} - 2 q^{87} + 6 q^{89} + 28 q^{91} + 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^21 - 2 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^29 - 12 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 - 20 * q^41 - 20 * q^43 + 4 * q^47 + 10 * q^49 - 4 * q^51 + 8 * q^53 - 8 * q^55 - 16 * q^57 - 8 * q^59 + 6 * q^61 + 4 * q^65 + 22 * q^67 - 12 * q^69 + 16 * q^71 - 4 * q^73 + 2 * q^75 + 28 * q^77 + 24 * q^79 + 2 * q^81 - 4 * q^83 + 8 * q^85 - 2 * q^87 + 6 * q^89 + 28 * q^91 + 12 * q^93 + 24 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more