LMFDB - Embedded newform 280.2.bg.a.9.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(9,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bg (of order $6$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.11
Character	$\chi$	$=$	280.9
Dual form			280.2.bg.a.249.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20343 - 1.27215i) q^{3} +(2.12965 - 0.681602i) q^{5} +(-2.64391 - 0.0988222i) q^{7} +(1.73675 - 3.00813i) q^{9} +O(q^{10})$	\(q+(2.20343 - 1.27215i) q^{3} +(2.12965 - 0.681602i) q^{5} +(-2.64391 - 0.0988222i) q^{7} +(1.73675 - 3.00813i) q^{9} +(1.95614 + 3.38814i) q^{11} -3.47349i q^{13} +(3.82544 - 4.21111i) q^{15} +(-4.40168 + 2.54131i) q^{17} +(-2.62594 + 4.54826i) q^{19} +(-5.95139 + 3.14570i) q^{21} +(-5.21157 - 3.00890i) q^{23} +(4.07084 - 2.90315i) q^{25} -1.20471i q^{27} +10.2660 q^{29} +(-1.02175 - 1.76973i) q^{31} +(8.62046 + 4.97702i) q^{33} +(-5.69796 + 1.59163i) q^{35} +(-0.350741 - 0.202501i) q^{37} +(-4.41881 - 7.65361i) q^{39} -2.57534 q^{41} +6.15769i q^{43} +(1.64832 - 7.59005i) q^{45} +(0.416173 + 0.240278i) q^{47} +(6.98047 + 0.522553i) q^{49} +(-6.46587 + 11.1992i) q^{51} +(-0.403939 + 0.233214i) q^{53} +(6.47526 + 5.88224i) q^{55} +13.3624i q^{57} +(-5.15565 - 8.92984i) q^{59} +(-4.04044 + 6.99825i) q^{61} +(-4.88906 + 7.78159i) q^{63} +(-2.36754 - 7.39733i) q^{65} +(3.59547 - 2.07585i) q^{67} -15.3111 q^{69} -4.28658 q^{71} +(-4.16976 + 2.40741i) q^{73} +(5.27657 - 11.5756i) q^{75} +(-4.83703 - 9.15122i) q^{77} +(-6.33197 + 10.9673i) q^{79} +(3.67766 + 6.36990i) q^{81} -8.42280i q^{83} +(-7.64188 + 8.41230i) q^{85} +(22.6205 - 13.0599i) q^{87} +(1.19298 - 2.06629i) q^{89} +(-0.343258 + 9.18358i) q^{91} +(-4.50272 - 2.59965i) q^{93} +(-2.49224 + 11.4761i) q^{95} +1.32080i q^{97} +13.5893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{9}+O(q^{10}) $ 24 * q + 14 * q^9	$ 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) $ 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	2.20343	−	1.27215i	1.27215	−	0.734478i	0.296760	−	0.954952i	$-0.404094\pi$
$3$	2.20343	−	1.27215i	1.27215	−	0.734478i	0.975393	+	0.220474i	$0.0707605\pi$
$4$		0			0
$5$	2.12965	−	0.681602i	0.952409	−	0.304822i
$5$	2.12965	−	0.681602i	0.952409	−	0.304822i
$6$		0			0
$7$	−2.64391	−	0.0988222i	−0.999302	−	0.0373513i
$7$	−2.64391	−	0.0988222i	−0.999302	−	0.0373513i
$8$		0			0
$9$	1.73675	−	3.00813i	0.578915	−	1.00271i
$10$		0			0
$11$	1.95614	+	3.38814i	0.589799	+	1.02156i	0.994258	+	0.107006i	$0.0341264\pi$
$11$	1.95614	+	3.38814i	0.589799	+	1.02156i	−0.404459	+	0.914556i	$0.632540\pi$
$12$		0			0
$13$		−	3.47349i		−	0.963373i	−0.876344	−	0.481687i	$-0.840024\pi$
$13$		−	3.47349i		−	0.963373i	0.876344	−	0.481687i	$-0.159976\pi$
$14$		0			0
$15$	3.82544	−	4.21111i	0.987726	−	1.08730i
$16$		0			0
$17$	−4.40168	+	2.54131i	−1.06756	+	0.616358i	−0.927515	−	0.373787i	$-0.878059\pi$
$17$	−4.40168	+	2.54131i	−1.06756	+	0.616358i	−0.140049	+	0.990145i	$0.544726\pi$
$18$		0			0
$19$	−2.62594	+	4.54826i	−0.602432	+	1.04344i	0.390019	+	0.920807i	$0.372468\pi$
$19$	−2.62594	+	4.54826i	−0.602432	+	1.04344i	−0.992452	+	0.122637i	$0.960865\pi$
$20$		0			0
$21$	−5.95139	+	3.14570i	−1.29870	+	0.686449i
$22$		0			0
$23$	−5.21157	−	3.00890i	−1.08669	−	0.627399i	−0.153994	−	0.988072i	$-0.549214\pi$
$23$	−5.21157	−	3.00890i	−1.08669	−	0.627399i	−0.932692	+	0.360673i	$0.882547\pi$
$24$		0			0
$25$	4.07084	−	2.90315i	0.814167	−	0.580630i
$26$		0			0
$27$		−	1.20471i		−	0.231846i
$28$		0			0
$29$	10.2660			1.90635			0.953175	−	0.302419i	$-0.0977942\pi$
$29$	10.2660			1.90635			0.953175	+	0.302419i	$0.0977942\pi$
$30$		0			0
$31$	−1.02175	−	1.76973i	−0.183512	−	0.317852i	0.759562	−	0.650435i	$-0.225413\pi$
$31$	−1.02175	−	1.76973i	−0.183512	−	0.317852i	−0.943074	+	0.332583i	$0.892080\pi$
$32$		0			0
$33$	8.62046	+	4.97702i	1.50063	+	0.866389i
$34$		0			0
$35$	−5.69796	+	1.59163i	−0.963130	+	0.269035i
$36$		0			0
$37$	−0.350741	−	0.202501i	−0.0576615	−	0.0332909i	0.470892	−	0.882191i	$-0.343932\pi$
$37$	−0.350741	−	0.202501i	−0.0576615	−	0.0332909i	−0.528554	+	0.848900i	$0.677265\pi$
$38$		0			0
$39$	−4.41881	−	7.65361i	−0.707576	−	1.22556i
$40$		0			0
$41$	−2.57534			−0.402200			−0.201100	−	0.979571i	$-0.564452\pi$
$41$	−2.57534			−0.402200			−0.201100	+	0.979571i	$0.564452\pi$
$42$		0			0
$43$			6.15769i			0.939038i	0.882922	+	0.469519i	$0.155573\pi$
$43$			6.15769i			0.939038i	−0.882922	+	0.469519i	$0.844427\pi$
$44$		0			0
$45$	1.64832	−	7.59005i	0.245716	−	1.13146i
$46$		0			0
$47$	0.416173	+	0.240278i	0.0607051	+	0.0350481i	0.530045	−	0.847969i	$-0.322175\pi$
$47$	0.416173	+	0.240278i	0.0607051	+	0.0350481i	−0.469340	+	0.883017i	$0.655508\pi$
$48$		0			0
$49$	6.98047	+	0.522553i	0.997210	+	0.0746504i
$50$		0			0
$51$	−6.46587	+	11.1992i	−0.905403	+	1.56820i
$52$		0			0
$53$	−0.403939	+	0.233214i	−0.0554852	+	0.0320344i	−0.527486	−	0.849564i	$-0.676865\pi$
$53$	−0.403939	+	0.233214i	−0.0554852	+	0.0320344i	0.472001	+	0.881598i	$0.343532\pi$
$54$		0			0
$55$	6.47526	+	5.88224i	0.873124	+	0.793162i
$56$		0			0
$57$			13.3624i			1.76989i
$58$		0			0
$59$	−5.15565	−	8.92984i	−0.671208	−	1.16257i	−0.977562	−	0.210649i	$-0.932442\pi$
$59$	−5.15565	−	8.92984i	−0.671208	−	1.16257i	0.306354	−	0.951918i	$-0.400891\pi$
$60$		0			0
$61$	−4.04044	+	6.99825i	−0.517325	+	0.896034i	0.482472	+	0.875911i	$0.339739\pi$
$61$	−4.04044	+	6.99825i	−0.517325	+	0.896034i	−0.999798	+	0.0201223i	$0.993594\pi$
$62$		0			0
$63$	−4.88906	+	7.78159i	−0.615964	+	0.980388i
$64$		0			0
$65$	−2.36754	−	7.39733i	−0.293657	−	0.917526i
$66$		0			0
$67$	3.59547	−	2.07585i	0.439257	−	0.253605i	−0.264026	−	0.964516i	$-0.585050\pi$
$67$	3.59547	−	2.07585i	0.439257	−	0.253605i	0.703282	+	0.710911i	$0.251717\pi$
$68$		0			0
$69$	−15.3111			−1.84324
$70$		0			0
$71$	−4.28658			−0.508724			−0.254362	−	0.967109i	$-0.581865\pi$
$71$	−4.28658			−0.508724			−0.254362	+	0.967109i	$0.581865\pi$
$72$		0			0
$73$	−4.16976	+	2.40741i	−0.488034	+	0.281767i	−0.723759	−	0.690053i	$-0.757587\pi$
$73$	−4.16976	+	2.40741i	−0.488034	+	0.281767i	0.235724	+	0.971820i	$0.424254\pi$
$74$		0			0
$75$	5.27657	−	11.5756i	0.609286	−	1.33664i
$76$		0			0
$77$	−4.83703	−	9.15122i	−0.551231	−	1.04288i
$78$		0			0
$79$	−6.33197	+	10.9673i	−0.712403	+	1.23392i	0.251550	+	0.967844i	$0.419060\pi$
$79$	−6.33197	+	10.9673i	−0.712403	+	1.23392i	−0.963953	+	0.266073i	$0.914274\pi$
$80$		0			0
$81$	3.67766	+	6.36990i	0.408629	+	0.707767i
$82$		0			0
$83$		−	8.42280i		−	0.924522i	−0.886744	−	0.462261i	$-0.847038\pi$
$83$		−	8.42280i		−	0.924522i	0.886744	−	0.462261i	$-0.152962\pi$
$84$		0			0
$85$	−7.64188	+	8.41230i	−0.828878	+	0.912442i
$86$		0			0
$87$	22.6205	−	13.0599i	2.42517	−	1.40017i
$88$		0			0
$89$	1.19298	−	2.06629i	0.126455	−	0.219027i	−0.795846	−	0.605500i	$-0.792973\pi$
$89$	1.19298	−	2.06629i	0.126455	−	0.219027i	0.922301	+	0.386473i	$0.126307\pi$
$90$		0			0
$91$	−0.343258	+	9.18358i	−0.0359832	+	0.962701i
$92$		0			0
$93$	−4.50272	−	2.59965i	−0.466911	−	0.269571i
$94$		0			0
$95$	−2.49224	+	11.4761i	−0.255698	+	1.17742i
$96$		0			0
$97$			1.32080i			0.134107i	0.997749	+	0.0670537i	$0.0213599\pi$
$97$			1.32080i			0.134107i	−0.997749	+	0.0670537i	$0.978640\pi$
$98$		0			0
$99$	13.5893			1.36577
$100$		0			0
$101$	−3.87583	−	6.71314i	−0.385660	−	0.667982i	0.606201	−	0.795312i	$-0.292693\pi$
$101$	−3.87583	−	6.71314i	−0.385660	−	0.667982i	−0.991860	+	0.127330i	$0.959359\pi$
$102$		0			0
$103$	1.90841	+	1.10182i	0.188041	+	0.108565i	0.591065	−	0.806624i	$-0.298708\pi$
$103$	1.90841	+	1.10182i	0.188041	+	0.108565i	−0.403024	+	0.915189i	$0.632041\pi$
$104$		0			0
$105$	−10.5303	+	10.7557i	−1.02765	+	1.04965i
$106$		0			0
$107$	9.37347	+	5.41177i	0.906167	+	0.523176i	0.879196	−	0.476460i	$-0.158080\pi$
$107$	9.37347	+	5.41177i	0.906167	+	0.523176i	0.0269713	+	0.999636i	$0.491414\pi$
$108$		0			0
$109$	−5.52166	−	9.56380i	−0.528880	−	0.916046i	−0.999433	−	0.0336747i	$-0.989279\pi$
$109$	−5.52166	−	9.56380i	−0.528880	−	0.916046i	0.470553	−	0.882372i	$-0.344054\pi$
$110$		0			0
$111$	−1.03045			−0.0978057
$112$		0			0
$113$		−	7.29167i		−	0.685942i	−0.939346	−	0.342971i	$-0.888567\pi$
$113$		−	7.29167i		−	0.685942i	0.939346	−	0.342971i	$-0.111433\pi$
$114$		0			0
$115$	−13.1497	−	2.85569i	−1.22622	−	0.266295i
$116$		0			0
$117$	−10.4487	−	6.03257i	−0.965985	−	0.557712i
$118$		0			0
$119$	11.8888	−	6.28400i	1.08984	−	0.576053i
$120$		0			0
$121$	−2.15298	+	3.72908i	−0.195726	+	0.339007i
$122$		0			0
$123$	−5.67458	+	3.27622i	−0.511660	+	0.295407i
$124$		0			0
$125$	6.69067	−	8.95739i	0.598432	−	0.801174i
$126$		0			0
$127$			7.66305i			0.679986i	0.940428	+	0.339993i	$0.110425\pi$
$127$			7.66305i			0.679986i	−0.940428	+	0.339993i	$0.889575\pi$
$128$		0			0
$129$	7.83352	+	13.5680i	0.689703	+	1.19460i
$130$		0			0
$131$	8.60596	−	14.9060i	0.751906	−	1.30234i	−0.194991	−	0.980805i	$-0.562468\pi$
$131$	8.60596	−	14.9060i	0.751906	−	1.30234i	0.946898	−	0.321535i	$-0.104199\pi$
$132$		0			0
$133$	7.39221	−	11.7657i	0.640986	−	1.02021i
$134$		0			0
$135$	−0.821132	−	2.56561i	−0.0706718	−	0.220813i
$136$		0			0
$137$	−4.55592	+	2.63036i	−0.389239	+	0.224727i	−0.681830	−	0.731510i	$-0.738816\pi$
$137$	−4.55592	+	2.63036i	−0.389239	+	0.224727i	0.292592	+	0.956238i	$0.405482\pi$
$138$		0			0
$139$	15.2148			1.29050			0.645250	−	0.763971i	$-0.276753\pi$
$139$	15.2148			1.29050			0.645250	+	0.763971i	$0.276753\pi$
$140$		0			0
$141$	1.22268			0.102968
$142$		0			0
$143$	11.7687	−	6.79464i	0.984146	−	0.568197i
$144$		0			0
$145$	21.8630	−	6.99733i	1.81563	−	0.581097i
$146$		0			0
$147$	16.0458	−	7.72881i	1.32343	−	0.637462i
$148$		0			0
$149$	−0.508607	+	0.880934i	−0.0416667	+	0.0721689i	−0.886107	−	0.463481i	$-0.846600\pi$
$149$	−0.508607	+	0.880934i	−0.0416667	+	0.0721689i	0.844440	+	0.535650i	$0.179933\pi$
$150$		0			0
$151$	−6.62914	−	11.4820i	−0.539472	−	0.934392i	−0.998932	−	0.0461942i	$-0.985291\pi$
$151$	−6.62914	−	11.4820i	−0.539472	−	0.934392i	0.459461	−	0.888198i	$-0.348043\pi$
$152$		0			0
$153$			17.6544i			1.42728i
$154$		0			0
$155$	−3.38222	−	3.07247i	−0.271667	−	0.246787i
$156$		0			0
$157$	15.3912	−	8.88611i	1.22835	−	0.709189i	0.261666	−	0.965158i	$-0.415728\pi$
$157$	15.3912	−	8.88611i	1.22835	−	0.709189i	0.966685	+	0.255970i	$0.0823947\pi$
$158$		0			0
$159$	−0.593368	+	1.02774i	−0.0470571	+	0.0815053i
$160$		0			0
$161$	13.4815	+	8.47026i	1.06249	+	0.667550i
$162$		0			0
$163$	2.52838	+	1.45976i	0.198038	+	0.114337i	0.595740	−	0.803177i	$-0.296859\pi$
$163$	2.52838	+	1.45976i	0.198038	+	0.114337i	−0.397702	+	0.917515i	$0.630192\pi$
$164$		0			0
$165$	21.7509	+	4.72361i	1.69331	+	0.367732i
$166$		0			0
$167$		−	9.21710i		−	0.713240i	−0.934249	−	0.356620i	$-0.883929\pi$
$167$		−	9.21710i		−	0.713240i	0.934249	−	0.356620i	$-0.116071\pi$
$168$		0			0
$169$	0.934854			0.0719118
$170$		0			0
$171$	9.12118	+	15.7984i	0.697514	+	1.20813i
$172$		0			0
$173$	−18.7757	−	10.8402i	−1.42749	−	0.824162i	−0.430568	−	0.902558i	$-0.641687\pi$
$173$	−18.7757	−	10.8402i	−1.42749	−	0.824162i	−0.996922	+	0.0783961i	$0.975020\pi$
$174$		0			0
$175$	−11.0498	+	7.27337i	−0.835287	+	0.549815i
$176$		0			0
$177$	−22.7202	−	13.1175i	−1.70776	−	0.985975i
$178$		0			0
$179$	−12.4983	−	21.6476i	−0.934164	−	1.61802i	−0.776117	−	0.630588i	$-0.782814\pi$
$179$	−12.4983	−	21.6476i	−0.934164	−	1.61802i	−0.158047	−	0.987432i	$-0.550520\pi$
$180$		0			0
$181$	−4.17900			−0.310623			−0.155311	−	0.987866i	$-0.549638\pi$
$181$	−4.17900			−0.310623			−0.155311	+	0.987866i	$0.549638\pi$
$182$		0			0
$183$			20.5602i			1.51986i
$184$		0			0
$185$	−0.884982	−	0.192190i	−0.0650651	−	0.0141301i
$186$		0			0
$187$	−17.2206	−	9.94232i	−1.25930	−	0.727055i
$188$		0			0
$189$	−0.119052	+	3.18513i	−0.00865975	+	0.231684i
$190$		0			0
$191$	4.48585	−	7.76972i	0.324585	−	0.562197i	−0.656844	−	0.754027i	$-0.728109\pi$
$191$	4.48585	−	7.76972i	0.324585	−	0.562197i	0.981428	+	0.191830i	$0.0614422\pi$
$192$		0			0
$193$	15.7806	−	9.11092i	1.13591	−	0.655818i	0.190496	−	0.981688i	$-0.438990\pi$
$193$	15.7806	−	9.11092i	1.13591	−	0.655818i	0.945415	+	0.325870i	$0.105657\pi$
$194$		0			0
$195$	−14.6272	−	13.2877i	−1.04748	−	0.951549i
$196$		0			0
$197$			23.5632i			1.67881i	0.543509	+	0.839403i	$0.317095\pi$
$197$			23.5632i			1.67881i	−0.543509	+	0.839403i	$0.682905\pi$
$198$		0			0
$199$	10.3582	+	17.9409i	0.734271	+	1.27180i	0.955042	+	0.296470i	$0.0958094\pi$
$199$	10.3582	+	17.9409i	0.734271	+	1.27180i	−0.220771	+	0.975326i	$0.570857\pi$
$200$		0			0
$201$	5.28159	−	9.14798i	0.372534	−	0.645249i
$202$		0			0
$203$	−27.1424	−	1.01451i	−1.90502	−	0.0712046i
$204$		0			0
$205$	−5.48457	+	1.75535i	−0.383059	+	0.122599i
$206$		0			0
$207$	−18.1023	+	10.4514i	−1.25820	+	0.726422i
$208$		0			0
$209$	−20.5469			−1.42126
$210$		0			0
$211$	7.69865			0.529997			0.264998	−	0.964249i	$-0.414629\pi$
$211$	7.69865			0.529997			0.264998	+	0.964249i	$0.414629\pi$
$212$		0			0
$213$	−9.44520	+	5.45319i	−0.647174	+	0.373646i
$214$		0			0
$215$	4.19709	+	13.1137i	0.286239	+	0.894349i
$216$		0			0
$217$	2.52653	+	4.77996i	0.171512	+	0.324485i
$218$		0			0
$219$	−6.12520	+	10.6092i	−0.413903	+	0.716900i
$220$		0			0
$221$	8.82722	+	15.2892i	0.593783	+	1.02846i
$222$		0			0
$223$		−	12.7136i		−	0.851366i	−0.904872	−	0.425683i	$-0.860034\pi$
$223$		−	12.7136i		−	0.851366i	0.904872	−	0.425683i	$-0.139966\pi$
$224$		0			0
$225$	−1.66305	−	17.2877i	−0.110870	−	1.15251i
$226$		0			0
$227$	−9.28633	+	5.36146i	−0.616355	+	0.355853i	−0.775449	−	0.631411i	$-0.782476\pi$
$227$	−9.28633	+	5.36146i	−0.616355	+	0.355853i	0.159093	+	0.987264i	$0.449143\pi$
$228$		0			0
$229$	−12.3946	+	21.4681i	−0.819059	+	1.41865i	0.0873173	+	0.996181i	$0.472171\pi$
$229$	−12.3946	+	21.4681i	−0.819059	+	1.41865i	−0.906376	+	0.422471i	$0.861163\pi$
$230$		0			0
$231$	−22.2998	−	14.0107i	−1.46722	−	0.921835i
$232$		0			0
$233$	19.7059	+	11.3772i	1.29098	+	0.745345i	0.978827	−	0.204689i	$-0.0656182\pi$
$233$	19.7059	+	11.3772i	1.29098	+	0.745345i	0.312148	+	0.950034i	$0.398952\pi$
$234$		0			0
$235$	1.05008	+	0.228044i	0.0684996	+	0.0148759i
$236$		0			0
$237$			32.2210i			2.09298i
$238$		0			0
$239$	1.49071			0.0964258			0.0482129	−	0.998837i	$-0.484647\pi$
$239$	1.49071			0.0964258			0.0482129	+	0.998837i	$0.484647\pi$
$240$		0			0
$241$	−13.0839	−	22.6619i	−0.842806	−	1.45978i	−0.887513	−	0.460783i	$-0.847569\pi$
$241$	−13.0839	−	22.6619i	−0.842806	−	1.45978i	0.0447069	−	0.999000i	$-0.485765\pi$
$242$		0			0
$243$	19.3369	+	11.1642i	1.24046	+	0.716182i
$244$		0			0
$245$	15.2221	−	3.64505i	0.972507	−	0.232873i
$246$		0			0
$247$	15.7984	+	9.12118i	1.00523	+	0.580367i
$248$		0			0
$249$	−10.7151	−	18.5591i	−0.679041	−	1.17613i
$250$		0			0
$251$	4.90277			0.309460			0.154730	−	0.987957i	$-0.450549\pi$
$251$	4.90277			0.309460			0.154730	+	0.987957i	$0.450549\pi$
$252$		0			0
$253$		−	23.5433i		−	1.48016i
$254$		0			0
$255$	−6.13664	+	28.2576i	−0.384292	+	1.76956i
$256$		0			0
$257$	−10.6866	−	6.16993i	−0.666614	−	0.384870i	0.128179	−	0.991751i	$-0.459087\pi$
$257$	−10.6866	−	6.16993i	−0.666614	−	0.384870i	−0.794792	+	0.606882i	$0.792420\pi$
$258$		0			0
$259$	0.907315	+	0.570053i	0.0563778	+	0.0354214i
$260$		0			0
$261$	17.8295	−	30.8815i	1.10362	−	1.91152i
$262$		0			0
$263$	17.4285	−	10.0623i	1.07469	−	0.620471i	0.145229	−	0.989398i	$-0.453608\pi$
$263$	17.4285	−	10.0623i	1.07469	−	0.620471i	0.929458	+	0.368927i	$0.120275\pi$
$264$		0			0
$265$	−0.701290	+	0.771990i	−0.0430799	+	0.0474230i
$266$		0			0
$267$		−	6.07059i		−	0.371514i
$268$		0			0
$269$	−7.46972	−	12.9379i	−0.455437	−	0.788840i	0.543276	−	0.839554i	$-0.317184\pi$
$269$	−7.46972	−	12.9379i	−0.455437	−	0.788840i	−0.998713	+	0.0507142i	$0.983850\pi$
$270$		0			0
$271$	2.90466	−	5.03102i	0.176446	−	0.305613i	−0.764215	−	0.644962i	$-0.776873\pi$
$271$	2.90466	−	5.03102i	0.176446	−	0.305613i	0.940661	+	0.339349i	$0.110207\pi$
$272$		0			0
$273$	10.9266	+	20.6721i	0.661306	+	1.25113i
$274$		0			0
$275$	17.7994	+	8.11358i	1.07334	+	0.489267i
$276$		0			0
$277$	−22.4639	+	12.9695i	−1.34972	+	0.779263i	−0.988210	−	0.153104i	$-0.951073\pi$
$277$	−22.4639	+	12.9695i	−1.34972	+	0.779263i	−0.361513	+	0.932367i	$0.617740\pi$
$278$		0			0
$279$	−7.09809			−0.424952
$280$		0			0
$281$	−14.8840			−0.887904			−0.443952	−	0.896051i	$-0.646424\pi$
$281$	−14.8840			−0.887904			−0.443952	+	0.896051i	$0.646424\pi$
$282$		0			0
$283$	−8.41378	+	4.85770i	−0.500147	+	0.288760i	−0.728774	−	0.684754i	$-0.759910\pi$
$283$	−8.41378	+	4.85770i	−0.500147	+	0.288760i	0.228627	+	0.973514i	$0.426576\pi$
$284$		0			0
$285$	9.10783	+	28.4573i	0.539502	+	1.68566i
$286$		0			0
$287$	6.80894	+	0.254500i	0.401919	+	0.0150227i
$288$		0			0
$289$	4.41651	−	7.64961i	0.259794	−	0.449977i
$290$		0			0
$291$	1.68027	+	2.91031i	0.0984989	+	0.170605i
$292$		0			0
$293$			8.08596i			0.472387i	0.971706	+	0.236194i	$0.0758999\pi$
$293$			8.08596i			0.472387i	−0.971706	+	0.236194i	$0.924100\pi$
$294$		0			0
$295$	−17.0663	−	15.5034i	−0.993640	−	0.902640i
$296$		0			0
$297$	4.08172	−	2.35658i	0.236845	−	0.136743i
$298$		0			0
$299$	−10.4514	+	18.1023i	−0.604419	+	1.04688i
$300$		0			0
$301$	0.608516	−	16.2803i	0.0350743	−	0.938383i
$302$		0			0
$303$	−17.0803	−	9.86130i	−0.981236	−	0.566517i
$304$		0			0
$305$	−3.83471	+	17.6578i	−0.219575	+	1.01108i
$306$		0			0
$307$			8.81809i			0.503275i	0.967822	+	0.251637i	$0.0809690\pi$
$307$			8.81809i			0.503275i	−0.967822	+	0.251637i	$0.919031\pi$
$308$		0			0
$309$	5.60673			0.318956
$310$		0			0
$311$	−4.83219	−	8.36960i	−0.274009	−	0.474597i	0.695876	−	0.718162i	$-0.255016\pi$
$311$	−4.83219	−	8.36960i	−0.274009	−	0.474597i	−0.969885	+	0.243565i	$0.921683\pi$
$312$		0			0
$313$	23.5441	+	13.5932i	1.33079	+	0.768334i	0.985421	−	0.170132i	$-0.0544194\pi$
$313$	23.5441	+	13.5932i	1.33079	+	0.768334i	0.345372	+	0.938466i	$0.387753\pi$
$314$		0			0
$315$	−5.10806	+	19.9045i	−0.287806	+	1.12149i
$316$		0			0
$317$	10.5294	+	6.07913i	0.591388	+	0.341438i	0.765646	−	0.643262i	$-0.222419\pi$
$317$	10.5294	+	6.07913i	0.591388	+	0.341438i	−0.174258	+	0.984700i	$0.555753\pi$
$318$		0			0
$319$	20.0818	+	34.7827i	1.12436	+	1.94745i
$320$		0			0
$321$	27.5384			1.53704
$322$		0			0
$323$		−	26.6933i		−	1.48526i
$324$		0			0
$325$	−10.0841	−	14.1400i	−0.559364	−	0.784347i
$326$		0			0
$327$	−24.3332	−	14.0488i	−1.34563	−	0.776901i
$328$		0			0
$329$	−1.07658	−	0.676399i	−0.0593537	−	0.0372911i
$330$		0			0
$331$	1.71473	−	2.96999i	0.0942499	−	0.163246i	−0.815045	−	0.579397i	$-0.803288\pi$
$331$	1.71473	−	2.96999i	0.0942499	−	0.163246i	0.909295	+	0.416151i	$0.136621\pi$
$332$		0			0
$333$	−1.21830	+	0.703384i	−0.0667623	+	0.0385452i
$334$		0			0
$335$	6.24220	−	6.87151i	0.341048	−	0.375431i
$336$		0			0
$337$			1.39770i			0.0761375i	0.999275	+	0.0380687i	$0.0121206\pi$
$337$			1.39770i			0.0761375i	−0.999275	+	0.0380687i	$0.987879\pi$
$338$		0			0
$339$	−9.27611	−	16.0667i	−0.503809	−	0.872623i
$340$		0			0
$341$	3.99738	−	6.92367i	0.216470	−	0.374938i
$342$		0			0
$343$	−18.4041	−	2.07141i	−0.993726	−	0.111845i
$344$		0			0
$345$	−32.6074	+	10.4361i	−1.75552	+	0.561860i
$346$		0			0
$347$	−2.99906	+	1.73151i	−0.160998	+	0.0929522i	−0.578334	−	0.815800i	$-0.696297\pi$
$347$	−2.99906	+	1.73151i	−0.160998	+	0.0929522i	0.417336	+	0.908752i	$0.362964\pi$
$348$		0			0
$349$	19.2360			1.02968			0.514838	−	0.857287i	$-0.327852\pi$
$349$	19.2360			1.02968			0.514838	+	0.857287i	$0.327852\pi$
$350$		0			0
$351$	−4.18454			−0.223354
$352$		0			0
$353$	−14.9520	+	8.63257i	−0.795817	+	0.459465i	−0.842006	−	0.539467i	$-0.818626\pi$
$353$	−14.9520	+	8.63257i	−0.795817	+	0.459465i	0.0461892	+	0.998933i	$0.485292\pi$
$354$		0			0
$355$	−9.12893	+	2.92174i	−0.484513	+	0.155070i
$356$		0			0
$357$	18.2019	−	28.9707i	0.963345	−	1.53329i
$358$		0			0
$359$	0.433817	−	0.751393i	0.0228960	−	0.0396570i	−0.854350	−	0.519697i	$-0.826045\pi$
$359$	0.433817	−	0.751393i	0.0228960	−	0.0396570i	0.877246	+	0.480040i	$0.159378\pi$
$360$		0			0
$361$	−4.29113	−	7.43246i	−0.225849	−	0.391182i
$362$		0			0
$363$			10.9557i			0.575025i
$364$		0			0
$365$	−7.23925	+	7.96908i	−0.378920	+	0.417121i
$366$		0			0
$367$	−14.2880	+	8.24920i	−0.745830	+	0.430605i	−0.824185	−	0.566321i	$-0.808366\pi$
$367$	−14.2880	+	8.24920i	−0.745830	+	0.430605i	0.0783555	+	0.996925i	$0.475033\pi$
$368$		0			0
$369$	−4.47270	+	7.74695i	−0.232840	+	0.403290i
$370$		0			0
$371$	1.09102	−	0.576678i	0.0566430	−	0.0299396i
$372$		0			0
$373$	−17.6557	−	10.1935i	−0.914179	−	0.527801i	−0.0324054	−	0.999475i	$-0.510317\pi$
$373$	−17.6557	−	10.1935i	−0.914179	−	0.527801i	−0.881773	+	0.471673i	$0.843650\pi$
$374$		0			0
$375$	3.34728	−	28.2486i	0.172853	−	1.45875i
$376$		0			0
$377$		−	35.6589i		−	1.83653i
$378$		0			0
$379$	−13.1652			−0.676251			−0.338126	−	0.941101i	$-0.609793\pi$
$379$	−13.1652			−0.676251			−0.338126	+	0.941101i	$0.609793\pi$
$380$		0			0
$381$	9.74857	+	16.8850i	0.499434	+	0.865046i
$382$		0			0
$383$	4.49608	+	2.59581i	0.229739	+	0.132640i	0.610452	−	0.792054i	$-0.290988\pi$
$383$	4.49608	+	2.59581i	0.229739	+	0.132640i	−0.380713	+	0.924693i	$0.624321\pi$
$384$		0			0
$385$	−16.5387	−	16.1920i	−0.842890	−	0.825221i
$386$		0			0
$387$	18.5231	+	10.6943i	0.941584	+	0.543624i
$388$		0			0
$389$	15.5709	+	26.9697i	0.789478	+	1.36742i	0.926287	+	0.376819i	$0.122982\pi$
$389$	15.5709	+	26.9697i	0.789478	+	1.36742i	−0.136809	+	0.990597i	$0.543685\pi$
$390$		0			0
$391$	30.5862			1.54681
$392$		0			0
$393$		−	43.7924i		−	2.20903i
$394$		0			0
$395$	−6.00957	+	27.6724i	−0.302374	+	1.39235i
$396$		0			0
$397$	13.0826	+	7.55325i	0.656598	+	0.379087i	0.790979	−	0.611843i	$-0.209571\pi$
$397$	13.0826	+	7.55325i	0.656598	+	0.379087i	−0.134382	+	0.990930i	$0.542905\pi$
$398$		0			0
$399$	1.32050	−	35.3289i	0.0661077	−	1.76866i
$400$		0			0
$401$	−8.12353	+	14.0704i	−0.405670	+	0.702641i	−0.994399	−	0.105690i	$-0.966295\pi$
$401$	−8.12353	+	14.0704i	−0.405670	+	0.702641i	0.588729	+	0.808330i	$0.299628\pi$
$402$		0			0
$403$	−6.14713	+	3.54905i	−0.306210	+	0.176791i
$404$		0			0
$405$	12.1739	+	11.0590i	0.604925	+	0.549525i
$406$		0			0
$407$		−	1.58448i		−	0.0785397i
$408$		0			0
$409$	16.6603	+	28.8565i	0.823798	+	1.42686i	0.902834	+	0.429989i	$0.141482\pi$
$409$	16.6603	+	28.8565i	0.823798	+	1.42686i	−0.0790359	+	0.996872i	$0.525184\pi$
$410$		0			0
$411$	−6.69245	+	11.5917i	−0.330114	+	0.571774i
$412$		0			0
$413$	12.7486	+	24.1191i	0.627316	+	1.18683i
$414$		0			0
$415$	−5.74100	−	17.9376i	−0.281814	−	0.880524i
$416$		0			0
$417$	33.5247	−	19.3555i	1.64171	−	0.947844i
$418$		0			0
$419$	−11.3290			−0.553457			−0.276729	−	0.960948i	$-0.589250\pi$
$419$	−11.3290			−0.553457			−0.276729	+	0.960948i	$0.589250\pi$
$420$		0			0
$421$	12.5047			0.609440			0.304720	−	0.952442i	$-0.401437\pi$
$421$	12.5047			0.609440			0.304720	+	0.952442i	$0.401437\pi$
$422$		0			0
$423$	1.44558	−	0.834603i	0.0702863	−	0.0405798i
$424$		0			0
$425$	−10.5407	+	23.1240i	−0.511299	+	1.12168i
$426$		0			0
$427$	11.3741	−	18.1034i	0.550432	−	0.876086i
$428$		0			0
$429$	17.2877	−	29.9431i	0.834656	−	1.44567i
$430$		0			0
$431$	2.57356	+	4.45754i	0.123964	+	0.214712i	0.921328	−	0.388787i	$-0.127106\pi$
$431$	2.57356	+	4.45754i	0.123964	+	0.214712i	−0.797363	+	0.603499i	$0.793773\pi$
$432$		0			0
$433$		−	1.88420i		−	0.0905491i	−0.998975	−	0.0452745i	$-0.985584\pi$
$433$		−	1.88420i		−	0.0905491i	0.998975	−	0.0452745i	$-0.0144163\pi$
$434$		0			0
$435$	39.2721	−	43.2313i	1.88295	−	2.07278i
$436$		0			0
$437$	27.3705	−	15.8024i	1.30931	−	0.755930i
$438$		0			0
$439$	5.29522	−	9.17159i	0.252727	−	0.437736i	−0.711549	−	0.702637i	$-0.752006\pi$
$439$	5.29522	−	9.17159i	0.252727	−	0.437736i	0.964276	+	0.264901i	$0.0853392\pi$
$440$		0			0
$441$	13.6952	−	20.0906i	0.652153	−	0.956697i
$442$		0			0
$443$	21.0886	+	12.1755i	1.00195	+	0.578476i	0.908825	−	0.417179i	$-0.136981\pi$
$443$	21.0886	+	12.1755i	1.00195	+	0.578476i	0.0931250	+	0.995654i	$0.470314\pi$
$444$		0			0
$445$	1.13223	−	5.21362i	0.0536730	−	0.247149i
$446$		0			0
$447$			2.58811i			0.122413i
$448$		0			0
$449$	−20.2506			−0.955684			−0.477842	−	0.878446i	$-0.658581\pi$
$449$	−20.2506			−0.955684			−0.477842	+	0.878446i	$0.658581\pi$
$450$		0			0
$451$	−5.03772	−	8.72559i	−0.237217	−	0.410872i
$452$		0			0
$453$	−29.2137	−	16.8666i	−1.37258	−	0.792460i
$454$		0			0
$455$	5.52853	+	19.7918i	0.259181	+	0.927854i
$456$		0			0
$457$	16.6159	+	9.59321i	0.777261	+	0.448752i	0.835459	−	0.549553i	$-0.185202\pi$
$457$	16.6159	+	9.59321i	0.777261	+	0.448752i	−0.0581979	+	0.998305i	$0.518535\pi$
$458$		0			0
$459$	3.06154	+	5.30274i	0.142900	+	0.247511i
$460$		0			0
$461$	−13.4096			−0.624548			−0.312274	−	0.949992i	$-0.601091\pi$
$461$	−13.4096			−0.624548			−0.312274	+	0.949992i	$0.601091\pi$
$462$		0			0
$463$			17.7864i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$463$			17.7864i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$464$		0			0
$465$	−11.3612	−	2.46728i	−0.526861	−	0.114417i
$466$		0			0
$467$	−13.1723	−	7.60500i	−0.609539	−	0.351918i	0.163246	−	0.986585i	$-0.447804\pi$
$467$	−13.1723	−	7.60500i	−0.609539	−	0.351918i	−0.772785	+	0.634668i	$0.781137\pi$
$468$		0			0
$469$	−9.71122	+	5.13303i	−0.448423	+	0.237021i
$470$		0			0
$471$	22.6090	−	39.1599i	1.04177	−	1.80439i
$472$		0			0
$473$	−20.8631	+	12.0453i	−0.959286	+	0.553844i
$474$		0			0
$475$	2.51451	+	26.1387i	0.115374	+	1.19933i
$476$		0			0
$477$			1.62013i			0.0741809i
$478$		0			0
$479$	−6.28422	−	10.8846i	−0.287133	−	0.497329i	0.685991	−	0.727610i	$-0.259369\pi$
$479$	−6.28422	−	10.8846i	−0.287133	−	0.497329i	−0.973124	+	0.230281i	$0.926036\pi$
$480$		0			0
$481$	−0.703384	+	1.21830i	−0.0320716	+	0.0555496i
$482$		0			0
$483$	40.4811	+	1.51308i	1.84196	+	0.0688475i
$484$		0			0
$485$	0.900263	+	2.81286i	0.0408789	+	0.127725i
$486$		0			0
$487$	11.9425	−	6.89503i	0.541169	−	0.312444i	−0.204384	−	0.978891i	$-0.565519\pi$
$487$	11.9425	−	6.89503i	0.541169	−	0.312444i	0.745552	+	0.666447i	$0.232186\pi$
$488$		0			0
$489$	7.42816			0.335913
$490$		0			0
$491$	27.4423			1.23845			0.619226	−	0.785213i	$-0.287447\pi$
$491$	27.4423			1.23845			0.619226	+	0.785213i	$0.287447\pi$
$492$		0			0
$493$	−45.1877	+	26.0891i	−2.03515	+	1.17499i
$494$		0			0
$495$	28.9405	−	9.26249i	1.30078	−	0.416318i
$496$		0			0
$497$	11.3333	+	0.423609i	0.508369	+	0.0190015i
$498$		0			0
$499$	−9.86895	+	17.0935i	−0.441795	+	0.765211i	−0.997823	−	0.0659525i	$-0.978991\pi$
$499$	−9.86895	+	17.0935i	−0.441795	+	0.765211i	0.556028	+	0.831164i	$0.312325\pi$
$500$		0			0
$501$	−11.7256	−	20.3093i	−0.523859	−	0.907351i
$502$		0			0
$503$		−	5.00417i		−	0.223125i	−0.993757	−	0.111562i	$-0.964415\pi$
$503$		−	5.00417i		−	0.223125i	0.993757	−	0.111562i	$-0.0355855\pi$
$504$		0			0
$505$	−12.8299	−	11.6549i	−0.570921	−	0.518635i
$506$		0			0
$507$	2.05989	−	1.18928i	0.0914828	−	0.0528176i
$508$		0			0
$509$	11.3796	−	19.7100i	0.504392	−	0.873632i	−0.495595	−	0.868553i	$-0.665050\pi$
$509$	11.3796	−	19.7100i	0.504392	−	0.873632i	0.999987	−	0.00507852i	$-0.00161655\pi$
$510$		0			0
$511$	11.2624	−	5.95291i	0.498218	−	0.263341i
$512$		0			0
$513$	5.47933	+	3.16349i	0.241918	+	0.139672i
$514$		0			0
$515$	4.81524	+	1.04572i	0.212185	+	0.0460798i
$516$		0			0
$517$			1.88007i			0.0826854i
$518$		0			0
$519$	−55.1614			−2.42131
$520$		0			0
$521$	8.76856	+	15.1876i	0.384158	+	0.665381i	0.991652	−	0.128943i	$-0.0411586\pi$
$521$	8.76856	+	15.1876i	0.384158	+	0.665381i	−0.607494	+	0.794324i	$0.707825\pi$
$522$		0			0
$523$	−11.9425	−	6.89503i	−0.522211	−	0.301499i	0.215628	−	0.976476i	$-0.430820\pi$
$523$	−11.9425	−	6.89503i	−0.522211	−	0.301499i	−0.737839	+	0.674977i	$0.764154\pi$
$524$		0			0
$525$	−15.0947	+	30.0834i	−0.658786	+	1.31295i
$526$		0			0
$527$	8.99484	+	5.19317i	0.391821	+	0.226218i
$528$		0			0
$529$	6.60694	+	11.4436i	0.287258	+	0.497546i
$530$		0			0
$531$	−35.8162			−1.55429
$532$		0			0
$533$			8.94541i			0.387469i
$534$		0			0
$535$	23.6509	+	5.13622i	1.02252	+	0.222058i
$536$		0			0
$537$	−55.0782	−	31.7994i	−2.37680	−	1.37225i
$538$		0			0
$539$	11.8843	+	24.6730i	0.511893	+	1.06274i
$540$		0			0
$541$	−23.0000	+	39.8372i	−0.988849	+	1.71274i	−0.365454	+	0.930829i	$0.619086\pi$
$541$	−23.0000	+	39.8372i	−0.988849	+	1.71274i	−0.623395	+	0.781907i	$0.714247\pi$
$542$		0			0
$543$	−9.20815	+	5.31633i	−0.395160	+	0.228146i
$544$		0			0
$545$	−18.2779	−	16.6040i	−0.782941	−	0.711237i
$546$		0			0
$547$			26.4411i			1.13054i	0.824906	+	0.565270i	$0.191228\pi$
$547$			26.4411i			1.13054i	−0.824906	+	0.565270i	$0.808772\pi$
$548$		0			0
$549$	14.0344	+	24.3084i	0.598975	+	1.03746i
$550$		0			0
$551$	−26.9579	+	46.6925i	−1.14845	+	1.98917i
$552$		0			0
$553$	17.8249	−	28.3708i	0.757994	−	1.20645i
$554$		0			0
$555$	−2.19449	+	0.702355i	−0.0931510	+	0.0298133i
$556$		0			0
$557$	−27.4720	+	15.8609i	−1.16402	+	0.672050i	−0.952265	−	0.305272i	$-0.901253\pi$
$557$	−27.4720	+	15.8609i	−1.16402	+	0.672050i	−0.211759	+	0.977322i	$0.567919\pi$
$558$		0			0
$559$	21.3887			0.904644
$560$		0			0
$561$	−50.5926			−2.13602
$562$		0			0
$563$	17.9483	−	10.3624i	0.756429	−	0.436724i	−0.0715834	−	0.997435i	$-0.522805\pi$
$563$	17.9483	−	10.3624i	0.756429	−	0.436724i	0.828012	+	0.560710i	$0.189472\pi$
$564$		0			0
$565$	−4.97001	−	15.5287i	−0.209090	−	0.653298i
$566$		0			0
$567$	−9.09391	−	17.2049i	−0.381908	−	0.722536i
$568$		0			0
$569$	21.2727	−	36.8454i	0.891799	−	1.54464i	0.0540816	−	0.998537i	$-0.482777\pi$
$569$	21.2727	−	36.8454i	0.891799	−	1.54464i	0.837717	−	0.546104i	$-0.183890\pi$
$570$		0			0
$571$	−15.0531	−	26.0727i	−0.629952	−	1.09111i	−0.987561	−	0.157238i	$-0.949741\pi$
$571$	−15.0531	−	26.0727i	−0.629952	−	1.09111i	0.357608	−	0.933872i	$-0.383592\pi$
$572$		0			0
$573$		−	22.8267i		−	0.953601i
$574$		0			0
$575$	−29.9507	+	2.88122i	−1.24903	+	0.120155i
$576$		0			0
$577$	−8.89257	+	5.13413i	−0.370202	+	0.213736i	−0.673547	−	0.739144i	$-0.735230\pi$
$577$	−8.89257	+	5.13413i	−0.370202	+	0.213736i	0.303344	+	0.952881i	$0.401897\pi$
$578$		0			0
$579$	23.1810	−	40.1506i	0.963368	−	1.66860i
$580$		0			0
$581$	−0.832360	+	22.2691i	−0.0345321	+	0.923877i
$582$		0			0
$583$	−1.58032	−	0.912400i	−0.0654503	−	0.0377877i
$584$		0			0
$585$	−26.3640	−	5.72541i	−1.09002	−	0.236717i
$586$		0			0
$587$			41.5546i			1.71514i	0.514367	+	0.857570i	$0.328027\pi$
$587$			41.5546i			1.71514i	−0.514367	+	0.857570i	$0.671973\pi$
$588$		0			0
$589$	10.7322			0.442214
$590$		0			0
$591$	29.9760	+	51.9199i	1.23305	+	2.13570i
$592$		0			0
$593$	20.7242	+	11.9651i	0.851041	+	0.491349i	0.861002	−	0.508601i	$-0.169837\pi$
$593$	20.7242	+	11.9651i	0.851041	+	0.491349i	−0.00996069	+	0.999950i	$0.503171\pi$
$594$		0			0
$595$	21.0357	−	21.4861i	0.862381	−	0.880845i
$596$		0			0
$597$	45.6471	+	26.3544i	1.86821	+	1.07861i
$598$		0			0
$599$	4.54134	+	7.86583i	0.185554	+	0.321389i	0.943763	−	0.330623i	$-0.107259\pi$
$599$	4.54134	+	7.86583i	0.185554	+	0.321389i	−0.758209	+	0.652012i	$0.773925\pi$
$600$		0			0
$601$	−29.8162			−1.21623			−0.608114	−	0.793850i	$-0.708074\pi$
$601$	−29.8162			−1.21623			−0.608114	+	0.793850i	$0.708074\pi$
$602$		0			0
$603$		−	14.4209i		−	0.587263i
$604$		0			0
$605$	−2.04336	+	9.40912i	−0.0830744	+	0.382535i
$606$		0			0
$607$	−12.5990	−	7.27401i	−0.511376	−	0.295243i	0.222023	−	0.975041i	$-0.428734\pi$
$607$	−12.5990	−	7.27401i	−0.511376	−	0.295243i	−0.733399	+	0.679798i	$0.762067\pi$
$608$		0			0
$609$	−61.0970	+	32.2938i	−2.47577	+	1.30861i
$610$		0			0
$611$	0.834603	−	1.44558i	0.0337644	−	0.0584817i
$612$		0			0
$613$	−8.93982	+	5.16141i	−0.361076	+	0.208467i	−0.669553	−	0.742765i	$-0.733514\pi$
$613$	−8.93982	+	5.16141i	−0.361076	+	0.208467i	0.308477	+	0.951232i	$0.400181\pi$
$614$		0			0
$615$	−9.85180	+	10.8450i	−0.397263	+	0.437313i
$616$		0			0
$617$			13.0906i			0.527008i	0.964658	+	0.263504i	$0.0848782\pi$
$617$			13.0906i			0.527008i	−0.964658	+	0.263504i	$0.915122\pi$
$618$		0			0
$619$	−16.2794	−	28.1968i	−0.654325	−	1.13332i	−0.982063	−	0.188556i	$-0.939619\pi$
$619$	−16.2794	−	28.1968i	−0.654325	−	1.13332i	0.327737	−	0.944769i	$-0.393714\pi$
$620$		0			0
$621$	−3.62485	+	6.27842i	−0.145460	+	0.251944i
$622$		0			0
$623$	−3.35831	+	5.34519i	−0.134548	+	0.214151i
$624$		0			0
$625$	8.14343	−	23.6365i	0.325737	−	0.945460i
$626$		0			0
$627$	−45.2736	+	26.1387i	−1.80805	+	1.04388i
$628$		0			0
$629$	2.05847			0.0820764
$630$		0			0
$631$	−13.2537			−0.527620			−0.263810	−	0.964575i	$-0.584979\pi$
$631$	−13.2537			−0.527620			−0.263810	+	0.964575i	$0.584979\pi$
$632$		0			0
$633$	16.9635	−	9.79386i	0.674237	−	0.389271i
$634$		0			0
$635$	5.22315	+	16.3196i	0.207274	+	0.647625i
$636$		0			0
$637$	1.81508	−	24.2466i	0.0719162	−	0.960685i
$638$		0			0
$639$	−7.44470	+	12.8946i	−0.294508	+	0.510103i
$640$		0			0
$641$	−0.351536	−	0.608879i	−0.0138848	−	0.0240493i	0.858999	−	0.511976i	$-0.171086\pi$
$641$	−0.351536	−	0.608879i	−0.0138848	−	0.0240493i	−0.872884	+	0.487927i	$0.837753\pi$
$642$		0			0
$643$		−	4.64163i		−	0.183048i	−0.995803	−	0.0915240i	$-0.970826\pi$
$643$		−	4.64163i		−	0.183048i	0.995803	−	0.0915240i	$-0.0291738\pi$
$644$		0			0
$645$	25.9307	+	23.5559i	1.02102	+	0.927512i
$646$		0			0
$647$	10.4230	−	6.01770i	0.409769	−	0.236580i	−0.280921	−	0.959731i	$-0.590640\pi$
$647$	10.4230	−	6.01770i	0.409769	−	0.236580i	0.690691	+	0.723150i	$0.257307\pi$
$648$		0			0
$649$	20.1704	−	34.9361i	0.791756	−	1.37136i
$650$		0			0
$651$	11.6479	+	7.31819i	0.456516	+	0.286823i
$652$		0			0
$653$	15.8018	+	9.12319i	0.618373	+	0.357018i	0.776235	−	0.630443i	$-0.217127\pi$
$653$	15.8018	+	9.12319i	0.618373	+	0.357018i	−0.157862	+	0.987461i	$0.550460\pi$
$654$		0			0
$655$	8.16777	−	37.6104i	0.319141	−	1.46956i
$656$		0			0
$657$			16.7243i			0.652476i
$658$		0			0
$659$	−29.4231			−1.14616			−0.573081	−	0.819499i	$-0.694252\pi$
$659$	−29.4231			−1.14616			−0.573081	+	0.819499i	$0.694252\pi$
$660$		0			0
$661$	8.64783	+	14.9785i	0.336361	+	0.582595i	0.983745	−	0.179569i	$-0.0574703\pi$
$661$	8.64783	+	14.9785i	0.336361	+	0.582595i	−0.647384	+	0.762164i	$0.724137\pi$
$662$		0			0
$663$	38.9004	+	22.4591i	1.51077	+	0.872241i
$664$		0			0
$665$	7.72332	−	30.0953i	0.299498	−	1.16705i
$666$		0			0
$667$	−53.5020	−	30.8894i	−2.07161	−	1.19604i
$668$		0			0
$669$	−16.1737	−	28.0136i	−0.625309	−	1.08307i
$670$		0			0
$671$	−31.6147			−1.22047
$672$		0			0
$673$			28.7525i			1.10833i	0.832407	+	0.554164i	$0.186962\pi$
$673$			28.7525i			1.10833i	−0.832407	+	0.554164i	$0.813038\pi$
$674$		0			0
$675$	−3.49745	−	4.90417i	−0.134617	−	0.188762i
$676$		0			0
$677$	4.75096	+	2.74297i	0.182594	+	0.105421i	0.588511	−	0.808489i	$-0.299714\pi$
$677$	4.75096	+	2.74297i	0.182594	+	0.105421i	−0.405917	+	0.913910i	$0.633048\pi$
$678$		0			0
$679$	0.130525	−	3.49208i	0.00500908	−	0.134014i
$680$		0			0
$681$	−13.6412	+	23.6273i	−0.522732	+	0.905398i
$682$		0			0
$683$	9.85256	−	5.68838i	0.376998	−	0.217660i	−0.299514	−	0.954092i	$-0.596824\pi$
$683$	9.85256	−	5.68838i	0.376998	−	0.217660i	0.676511	+	0.736432i	$0.263491\pi$
$684$		0			0
$685$	−7.90967	+	8.70708i	−0.302213	+	0.332681i
$686$		0			0
$687$			63.0714i			2.40632i
$688$		0			0
$689$	0.810067	+	1.40308i	0.0308611	+	0.0534530i
$690$		0			0
$691$	22.6631	−	39.2536i	0.862144	−	1.49328i	−0.00771164	−	0.999970i	$-0.502455\pi$
$691$	22.6631	−	39.2536i	0.862144	−	1.49328i	0.869855	−	0.493307i	$-0.164212\pi$
$692$		0			0
$693$	−35.9288	−	1.34292i	−1.36482	−	0.0510134i
$694$		0			0
$695$	32.4022	−	10.3704i	1.22908	−	0.393372i
$696$		0			0
$697$	11.3358	−	6.54472i	0.429374	−	0.247899i
$698$		0			0
$699$	57.8941			2.18976
$700$		0			0
$701$	4.87634			0.184177			0.0920884	−	0.995751i	$-0.470646\pi$
$701$	4.87634			0.184177			0.0920884	+	0.995751i	$0.470646\pi$
$702$		0			0
$703$	1.84205	−	1.06351i	0.0694743	−	0.0401110i
$704$		0			0
$705$	2.60388	−	0.833382i	0.0980680	−	0.0313870i
$706$		0			0
$707$	9.58392	+	18.1319i	0.360441	+	0.681921i
$708$		0			0
$709$	−12.4443	+	21.5542i	−0.467357	+	0.809485i	−0.999304	−	0.0372918i	$-0.988127\pi$
$709$	−12.4443	+	21.5542i	−0.467357	+	0.809485i	0.531948	+	0.846777i	$0.321460\pi$
$710$		0			0
$711$	21.9941	+	38.0948i	0.824842	+	1.42867i
$712$		0			0
$713$			12.2974i			0.460541i
$714$		0			0
$715$	20.4319	−	22.4918i	0.764111	−	0.841145i
$716$		0			0
$717$	3.28467	−	1.89641i	0.122668	−	0.0708226i
$718$		0			0
$719$	−2.71787	+	4.70748i	−0.101359	+	0.175559i	−0.912245	−	0.409645i	$-0.865653\pi$
$719$	−2.71787	+	4.70748i	−0.101359	+	0.175559i	0.810886	+	0.585205i	$0.198986\pi$
$720$		0			0
$721$	−4.93676	−	3.10170i	−0.183855	−	0.115513i
$722$		0			0
$723$	−57.6589	−	33.2894i	−2.14436	−	1.23804i
$724$		0			0
$725$	41.7913	−	29.8038i	1.55209	−	1.10688i
$726$		0			0
$727$			17.1112i			0.634621i	0.948322	+	0.317310i	$0.102780\pi$
$727$			17.1112i			0.634621i	−0.948322	+	0.317310i	$0.897220\pi$
$728$		0			0
$729$	34.7441			1.28682
$730$		0			0
$731$	−15.6486	−	27.1041i	−0.578784	−	1.00248i
$732$		0			0
$733$	6.80474	+	3.92872i	0.251339	+	0.145111i	0.620377	−	0.784304i	$-0.286980\pi$
$733$	6.80474	+	3.92872i	0.251339	+	0.145111i	−0.369038	+	0.929414i	$0.620313\pi$
$734$		0			0
$735$	28.9039	−	27.3965i	1.06614	−	1.01054i
$736$		0			0
$737$	14.0665	+	8.12130i	0.518146	+	0.299152i
$738$		0			0
$739$	25.5055	+	44.1768i	0.938234	+	1.62507i	0.768763	+	0.639534i	$0.220873\pi$
$739$	25.5055	+	44.1768i	0.938234	+	1.62507i	0.169471	+	0.985535i	$0.445794\pi$
$740$		0			0
$741$	46.4142			1.70507
$742$		0			0
$743$		−	6.82733i		−	0.250470i	−0.992127	−	0.125235i	$-0.960031\pi$
$743$		−	6.82733i		−	0.250470i	0.992127	−	0.125235i	$-0.0399686\pi$
$744$		0			0
$745$	−0.482711	+	2.22275i	−0.0176851	+	0.0814353i
$746$		0			0
$747$	−25.3369	−	14.6283i	−0.927028	−	0.535220i
$748$		0			0
$749$	−24.2478	−	15.2345i	−0.885994	−	0.556657i
$750$		0			0
$751$	−16.1785	+	28.0220i	−0.590361	+	1.02254i	0.403822	+	0.914837i	$0.367681\pi$
$751$	−16.1785	+	28.0220i	−0.590361	+	1.02254i	−0.994184	+	0.107698i	$0.965652\pi$
$752$		0			0
$753$	10.8029	−	6.23708i	0.393681	−	0.227292i
$754$		0			0
$755$	−21.9439	−	19.9342i	−0.798621	−	0.725481i
$756$		0			0
$757$		−	29.1180i		−	1.05831i	−0.848524	−	0.529156i	$-0.822509\pi$
$757$		−	29.1180i		−	1.05831i	0.848524	−	0.529156i	$-0.177491\pi$
$758$		0			0
$759$	−29.9507	−	51.8762i	−1.08714	−	1.88299i
$760$		0			0
$761$	−14.0865	+	24.3986i	−0.510636	+	0.884447i	0.489288	+	0.872122i	$0.337257\pi$
$761$	−14.0865	+	24.3986i	−0.510636	+	0.884447i	−0.999924	+	0.0123251i	$0.996077\pi$
$762$		0			0
$763$	13.6536	+	25.8315i	0.494295	+	0.935161i
$764$		0			0
$765$	12.0333	+	37.5978i	0.435065	+	1.35935i
$766$		0			0
$767$	−31.0177	+	17.9081i	−1.11999	+	0.646624i
$768$		0			0
$769$	−16.5017			−0.595065			−0.297532	−	0.954712i	$-0.596164\pi$
$769$	−16.5017			−0.595065			−0.297532	+	0.954712i	$0.596164\pi$
$770$		0			0
$771$	−31.3964			−1.13071
$772$		0			0
$773$	16.0120	−	9.24453i	0.575912	−	0.332503i	−0.183595	−	0.983002i	$-0.558774\pi$
$773$	16.0120	−	9.24453i	0.575912	−	0.332503i	0.759507	+	0.650499i	$0.225440\pi$
$774$		0			0
$775$	−9.29717	−	4.23797i	−0.333964	−	0.152232i
$776$		0			0
$777$	2.72440	+	0.101831i	0.0977374	+	0.00365317i
$778$		0			0
$779$	6.76268	−	11.7133i	0.242298	−	0.419673i
$780$		0			0
$781$	−8.38516	−	14.5235i	−0.300045	−	0.519693i
$782$		0			0
$783$		−	12.3675i		−	0.441980i
$784$		0			0
$785$	26.7211	−	29.4150i	0.953717	−	1.04987i
$786$		0			0
$787$	13.6350	−	7.87216i	0.486035	−	0.280612i	−0.236893	−	0.971536i	$-0.576129\pi$
$787$	13.6350	−	7.87216i	0.486035	−	0.280612i	0.722928	+	0.690923i	$0.242796\pi$
$788$		0			0
$789$	25.6017	−	44.3434i	0.911444	−	1.57867i
$790$		0			0
$791$	−0.720579	+	19.2785i	−0.0256208	+	0.685464i
$792$		0			0
$793$	24.3084	+	14.0344i	0.863215	+	0.498377i
$794$		0			0
$795$	−0.563155	+	2.59318i	−0.0199731	+	0.0919705i
$796$		0			0
$797$		−	29.9307i		−	1.06020i	−0.847935	−	0.530100i	$-0.822154\pi$
$797$		−	29.9307i		−	1.06020i	0.847935	−	0.530100i	$-0.177846\pi$
$798$		0			0
$799$	−2.44248			−0.0864088
$800$		0			0
$801$	−4.14379	−	7.17726i	−0.146414	−	0.253596i
$802$		0			0
$803$	−16.3133	−	9.41849i	−0.575684	−	0.332371i
$804$		0			0
$805$	34.4843	+	8.84967i	1.21541	+	0.311910i
$806$		0			0
$807$	−32.9181	−	19.0052i	−1.15877	−	0.669016i
$808$		0			0
$809$	2.58329	+	4.47439i	0.0908236	+	0.157311i	0.907858	−	0.419278i	$-0.137717\pi$
$809$	2.58329	+	4.47439i	0.0908236	+	0.157311i	−0.817034	+	0.576589i	$0.804383\pi$
$810$		0			0
$811$	−38.4698			−1.35086			−0.675430	−	0.737425i	$-0.736042\pi$
$811$	−38.4698			−1.35086			−0.675430	+	0.737425i	$0.736042\pi$
$812$		0			0
$813$		−	14.7807i		−	0.518381i
$814$		0			0
$815$	6.37955	+	1.38543i	0.223466	+	0.0485297i
$816$		0			0
$817$	−28.0068	−	16.1697i	−0.979833	−	0.565707i
$818$		0			0
$819$	27.0293	+	16.9821i	0.944479	+	0.593403i
$820$		0			0
$821$	1.84776	−	3.20041i	0.0644872	−	0.111695i	−0.831979	−	0.554807i	$-0.812792\pi$
$821$	1.84776	−	3.20041i	0.0644872	−	0.111695i	0.896466	+	0.443112i	$0.146126\pi$
$822$		0			0
$823$	36.7220	−	21.2015i	1.28005	−	0.739037i	0.303193	−	0.952929i	$-0.401947\pi$
$823$	36.7220	−	21.2015i	1.28005	−	0.739037i	0.976857	+	0.213892i	$0.0686141\pi$
$824$		0			0
$825$	49.5415	−	4.76583i	1.72481	−	0.165925i
$826$		0			0
$827$		−	40.0950i		−	1.39424i	−0.716954	−	0.697120i	$-0.754464\pi$
$827$		−	40.0950i		−	1.39424i	0.716954	−	0.697120i	$-0.245536\pi$
$828$		0			0
$829$	26.9132	+	46.6151i	0.934734	+	1.61901i	0.775107	+	0.631830i	$0.217696\pi$
$829$	26.9132	+	46.6151i	0.934734	+	1.61901i	0.159628	+	0.987177i	$0.448971\pi$
$830$		0			0
$831$	−32.9984	+	57.1549i	−1.14470	+	1.98268i
$832$		0			0
$833$	−32.0537	+	15.4394i	−1.11060	+	0.534944i
$834$		0			0
$835$	−6.28239	−	19.6292i	−0.217411	−	0.679297i
$836$		0			0
$837$	−2.13200	+	1.23091i	−0.0736928	+	0.0425466i
$838$		0			0
$839$	25.1002			0.866556			0.433278	−	0.901260i	$-0.357357\pi$
$839$	25.1002			0.866556			0.433278	+	0.901260i	$0.357357\pi$
$840$		0			0
$841$	76.3910			2.63417
$842$		0			0
$843$	−32.7959	+	18.9347i	−1.12955	+	0.652146i
$844$		0			0
$845$	1.99091	−	0.637198i	0.0684895	−	0.0219203i
$846$		0			0
$847$	6.06080	−	9.64657i	0.208252	−	0.331460i
$848$		0			0
$849$	−12.3595	+	21.4072i	−0.424176	+	0.734694i
$850$		0			0
$851$	1.21861	+	2.11069i	0.0417733	+	0.0723535i
$852$		0			0
$853$		−	26.7320i		−	0.915286i	−0.889136	−	0.457643i	$-0.848694\pi$
$853$		−	26.7320i		−	0.915286i	0.889136	−	0.457643i	$-0.151306\pi$
$854$		0			0
$855$	30.1931	+	27.4280i	1.03258	+	0.938017i
$856$		0			0
$857$	40.3473	−	23.2945i	1.37824	−	0.795726i	0.386291	−	0.922377i	$-0.373756\pi$
$857$	40.3473	−	23.2945i	1.37824	−	0.795726i	0.991947	+	0.126651i	$0.0404228\pi$
$858$		0			0
$859$	−9.32674	+	16.1544i	−0.318224	+	0.551180i	−0.980118	−	0.198418i	$-0.936420\pi$
$859$	−9.32674	+	16.1544i	−0.318224	+	0.551180i	0.661893	+	0.749598i	$0.269753\pi$
$860$		0			0
$861$	15.3268	−	8.10124i	0.522336	−	0.276090i
$862$		0			0
$863$	−15.4360	−	8.91196i	−0.525447	−	0.303367i	0.213714	−	0.976896i	$-0.431444\pi$
$863$	−15.4360	−	8.91196i	−0.525447	−	0.303367i	−0.739160	+	0.673530i	$0.764777\pi$
$864$		0			0
$865$	−47.3744	−	10.2882i	−1.61078	−	0.349810i
$866$		0			0
$867$		−	22.4739i		−	0.763253i
$868$		0			0
$869$	−49.5450			−1.68070
$870$		0			0
$871$	−7.21043	−	12.4888i	−0.244316	−	0.423168i
$872$		0			0
$873$	3.97316	+	2.29390i	0.134471	+	0.0776368i
$874$		0			0
$875$	−18.5747	+	23.0213i	−0.627939	+	0.778262i
$876$		0			0
$877$	−23.1915	−	13.3896i	−0.783123	−	0.452136i	0.0544130	−	0.998519i	$-0.482671\pi$
$877$	−23.1915	−	13.3896i	−0.783123	−	0.452136i	−0.837536	+	0.546382i	$0.816005\pi$
$878$		0			0
$879$	10.2866	+	17.8169i	0.346958	+	0.600949i
$880$		0			0
$881$	17.5843			0.592429			0.296215	−	0.955121i	$-0.404276\pi$
$881$	17.5843			0.592429			0.296215	+	0.955121i	$0.404276\pi$
$882$		0			0
$883$			18.9638i			0.638182i	0.947724	+	0.319091i	$0.103378\pi$
$883$			18.9638i			0.638182i	−0.947724	+	0.319091i	$0.896622\pi$
$884$		0			0
$885$	−57.3272	−	12.4496i	−1.92703	−	0.418490i
$886$		0			0
$887$	9.66950	+	5.58269i	0.324670	+	0.187448i	0.653472	−	0.756950i	$-0.273312\pi$
$887$	9.66950	+	5.58269i	0.324670	+	0.187448i	−0.328802	+	0.944399i	$0.606645\pi$
$888$		0			0
$889$	0.757280	−	20.2604i	0.0253983	−	0.679511i
$890$		0			0
$891$	−14.3881	+	24.9209i	−0.482018	+	0.834881i
$892$		0			0
$893$	−2.18569	+	1.26191i	−0.0731415	+	0.0422282i
$894$		0			0
$895$	−41.3720	−	37.5831i	−1.38291	−	1.25626i
$896$		0			0
$897$			53.1830i			1.77573i
$898$		0			0
$899$	−10.4893	−	18.1680i	−0.349838	−	0.605938i
$900$		0			0
$901$	1.18534	−	2.05307i	0.0394893	−	0.0683975i
$902$		0			0
$903$	−19.3703	−	36.6468i	−0.644602	−	1.21953i
$904$		0			0
$905$	−8.89982	+	2.84842i	−0.295840	+	0.0946846i
$906$		0			0
$907$	33.0516	−	19.0823i	1.09746	−	0.633619i	0.161907	−	0.986806i	$-0.448235\pi$
$907$	33.0516	−	19.0823i	1.09746	−	0.633619i	0.935553	+	0.353187i	$0.114902\pi$
$908$		0			0
$909$	−26.9253			−0.893057
$910$		0			0
$911$	47.0251			1.55801			0.779006	−	0.627016i	$-0.215724\pi$
$911$	47.0251			1.55801			0.779006	+	0.627016i	$0.215724\pi$
$912$		0			0
$913$	28.5376	−	16.4762i	0.944457	−	0.545282i
$914$		0			0
$915$	14.0139	+	43.7861i	0.463285	+	1.44752i
$916$		0			0
$917$	−24.2264	+	38.5595i	−0.800026	+	1.27335i
$918$		0			0
$919$	12.6939	−	21.9865i	0.418734	−	0.725269i	−0.577078	−	0.816689i	$-0.695807\pi$
$919$	12.6939	−	21.9865i	0.418734	−	0.725269i	0.995812	+	0.0914199i	$0.0291405\pi$
$920$		0			0
$921$	11.2180	+	19.4301i	0.369644	+	0.640243i
$922$		0			0
$923$			14.8894i			0.490091i
$924$		0			0
$925$	−2.01570	+	0.193908i	−0.0662758	+	0.00637565i
$926$		0			0
$927$	6.62883	−	3.82716i	0.217719	−	0.125700i
$928$		0			0
$929$	3.82355	−	6.62257i	0.125446	−	0.217280i	−0.796461	−	0.604690i	$-0.793297\pi$
$929$	3.82355	−	6.62257i	0.125446	−	0.217280i	0.921907	+	0.387410i	$0.126630\pi$
$930$		0			0
$931$	−20.7070	+	30.3768i	−0.678645	+	0.995560i
$932$		0			0
$933$	−21.2948	−	12.2946i	−0.697161	−	0.402506i
$934$		0			0
$935$	−43.4506	−	9.43609i	−1.42099	−	0.308593i
$936$		0			0
$937$			1.40923i			0.0460375i	0.999735	+	0.0230188i	$0.00732774\pi$
$937$			1.40923i			0.0460375i	−0.999735	+	0.0230188i	$0.992672\pi$
$938$		0			0
$939$	69.1706			2.25730
$940$		0			0
$941$	−26.2051	−	45.3885i	−0.854260	−	1.47962i	−0.877330	−	0.479888i	$-0.840677\pi$
$941$	−26.2051	−	45.3885i	−0.854260	−	1.47962i	0.0230692	−	0.999734i	$-0.492656\pi$
$942$		0			0
$943$	13.4215	+	7.74892i	0.437065	+	0.252340i
$944$		0			0
$945$	1.91745	+	6.86437i	0.0623748	+	0.223298i
$946$		0			0
$947$	28.3388	+	16.3614i	0.920888	+	0.531675i	0.883918	−	0.467641i	$-0.154896\pi$
$947$	28.3388	+	16.3614i	0.920888	+	0.531675i	0.0369700	+	0.999316i	$0.488229\pi$
$948$		0			0
$949$	8.36214	+	14.4836i	0.271446	+	0.470159i
$950$		0			0
$951$	30.9344			1.00312
$952$		0			0
$953$			41.7747i			1.35322i	0.736344	+	0.676608i	$0.236551\pi$
$953$			41.7747i			1.35322i	−0.736344	+	0.676608i	$0.763449\pi$
$954$		0			0
$955$	4.25744	−	19.6044i	0.137768	−	0.634382i
$956$		0			0
$957$	88.4977	+	51.0942i	2.86072	+	1.65164i
$958$		0			0
$959$	12.3054	−	6.50420i	0.397361	−	0.210032i
$960$		0			0
$961$	13.4120	−	23.2303i	0.432647	−	0.749366i
$962$		0			0
$963$	32.5587	−	18.7978i	1.04919	−	0.605749i
$964$		0			0
$965$	27.3971	−	30.1592i	0.881944	−	0.970858i
$966$		0			0
$967$		−	6.47375i		−	0.208182i	−0.994568	−	0.104091i	$-0.966807\pi$
$967$		−	6.47375i		−	0.208182i	0.994568	−	0.104091i	$-0.0331933\pi$
$968$		0			0
$969$	−33.9580	−	58.8169i	−1.09089	−	1.88947i
$970$		0			0
$971$	16.5872	−	28.7298i	0.532308	−	0.921984i	−0.466981	−	0.884267i	$-0.654658\pi$
$971$	16.5872	−	28.7298i	0.532308	−	0.921984i	0.999288	−	0.0377164i	$-0.0120083\pi$
$972$		0			0
$973$	−40.2264	−	1.50356i	−1.28960	−	0.0482018i
$974$		0			0
$975$	−40.2078	−	18.3281i	−1.28768	−	0.586969i
$976$		0			0
$977$	34.7026	−	20.0356i	1.11023	−	0.640994i	0.171344	−	0.985211i	$-0.445189\pi$
$977$	34.7026	−	20.0356i	1.11023	−	0.640994i	0.938890	+	0.344217i	$0.111856\pi$
$978$		0			0
$979$	9.33452			0.298333
$980$		0			0
$981$	−38.3589			−1.22471
$982$		0			0
$983$	−0.737954	+	0.426058i	−0.0235371	+	0.0135891i	−0.511722	−	0.859151i	$-0.670992\pi$
$983$	−0.737954	+	0.426058i	−0.0235371	+	0.0135891i	0.488185	+	0.872740i	$0.337659\pi$
$984$		0			0
$985$	16.0607	+	50.1814i	0.511737	+	1.59891i
$986$		0			0
$987$	−3.23265	−	0.120828i	−0.102896	−	0.00384600i
$988$		0			0
$989$	18.5279	−	32.0912i	0.589151	−	1.02044i
$990$		0			0
$991$	2.51380	+	4.35403i	0.0798535	+	0.138310i	0.903187	−	0.429248i	$-0.141221\pi$
$991$	2.51380	+	4.35403i	0.0798535	+	0.138310i	−0.823333	+	0.567558i	$0.807888\pi$
$992$		0			0
$993$		−	8.72558i		−	0.276898i
$994$		0			0
$995$	34.2878	+	31.1477i	1.08700	+	0.987448i
$996$		0			0
$997$	23.4079	−	13.5146i	0.741336	−	0.428011i	−0.0812187	−	0.996696i	$-0.525881\pi$
$997$	23.4079	−	13.5146i	0.741336	−	0.428011i	0.822555	+	0.568686i	$0.192548\pi$
$998$		0			0
$999$	−0.243954	+	0.422541i	−0.00771837	+	0.0133686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bg.a.9.11	yes	24
4.3	odd	2		560.2.bw.f.289.2		24
5.2	odd	4		1400.2.q.o.401.1		12
5.3	odd	4		1400.2.q.n.401.6		12
5.4	even	2	inner	280.2.bg.a.9.2	✓	24
7.2	even	3		1960.2.g.f.1569.11		12
7.4	even	3	inner	280.2.bg.a.249.2	yes	24
7.5	odd	6		1960.2.g.e.1569.2		12
20.19	odd	2		560.2.bw.f.289.11		24
28.11	odd	6		560.2.bw.f.529.11		24
35.2	odd	12		9800.2.a.cv.1.6		6
35.4	even	6	inner	280.2.bg.a.249.11	yes	24
35.9	even	6		1960.2.g.f.1569.2		12
35.12	even	12		9800.2.a.cy.1.1		6
35.18	odd	12		1400.2.q.n.1201.6		12
35.19	odd	6		1960.2.g.e.1569.11		12
35.23	odd	12		9800.2.a.cx.1.1		6
35.32	odd	12		1400.2.q.o.1201.1		12
35.33	even	12		9800.2.a.cw.1.6		6
140.39	odd	6		560.2.bw.f.529.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.2	✓	24	5.4	even	2	inner
280.2.bg.a.9.11	yes	24	1.1	even	1	trivial
280.2.bg.a.249.2	yes	24	7.4	even	3	inner
280.2.bg.a.249.11	yes	24	35.4	even	6	inner
560.2.bw.f.289.2		24	4.3	odd	2
560.2.bw.f.289.11		24	20.19	odd	2
560.2.bw.f.529.2		24	140.39	odd	6
560.2.bw.f.529.11		24	28.11	odd	6
1400.2.q.n.401.6		12	5.3	odd	4
1400.2.q.n.1201.6		12	35.18	odd	12
1400.2.q.o.401.1		12	5.2	odd	4
1400.2.q.o.1201.1		12	35.32	odd	12
1960.2.g.e.1569.2		12	7.5	odd	6
1960.2.g.e.1569.11		12	35.19	odd	6
1960.2.g.f.1569.2		12	35.9	even	6
1960.2.g.f.1569.11		12	7.2	even	3
9800.2.a.cv.1.6		6	35.2	odd	12
9800.2.a.cw.1.6		6	35.33	even	12
9800.2.a.cx.1.1		6	35.23	odd	12
9800.2.a.cy.1.1		6	35.12	even	12

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.20343 - 1.27215i) q^{3} +(2.12965 - 0.681602i) q^{5} +(-2.64391 - 0.0988222i) q^{7} +(1.73675 - 3.00813i) q^{9} +O(q^{10})\)	\(q+(2.20343 - 1.27215i) q^{3} +(2.12965 - 0.681602i) q^{5} +(-2.64391 - 0.0988222i) q^{7} +(1.73675 - 3.00813i) q^{9} +(1.95614 + 3.38814i) q^{11} -3.47349i q^{13} +(3.82544 - 4.21111i) q^{15} +(-4.40168 + 2.54131i) q^{17} +(-2.62594 + 4.54826i) q^{19} +(-5.95139 + 3.14570i) q^{21} +(-5.21157 - 3.00890i) q^{23} +(4.07084 - 2.90315i) q^{25} -1.20471i q^{27} +10.2660 q^{29} +(-1.02175 - 1.76973i) q^{31} +(8.62046 + 4.97702i) q^{33} +(-5.69796 + 1.59163i) q^{35} +(-0.350741 - 0.202501i) q^{37} +(-4.41881 - 7.65361i) q^{39} -2.57534 q^{41} +6.15769i q^{43} +(1.64832 - 7.59005i) q^{45} +(0.416173 + 0.240278i) q^{47} +(6.98047 + 0.522553i) q^{49} +(-6.46587 + 11.1992i) q^{51} +(-0.403939 + 0.233214i) q^{53} +(6.47526 + 5.88224i) q^{55} +13.3624i q^{57} +(-5.15565 - 8.92984i) q^{59} +(-4.04044 + 6.99825i) q^{61} +(-4.88906 + 7.78159i) q^{63} +(-2.36754 - 7.39733i) q^{65} +(3.59547 - 2.07585i) q^{67} -15.3111 q^{69} -4.28658 q^{71} +(-4.16976 + 2.40741i) q^{73} +(5.27657 - 11.5756i) q^{75} +(-4.83703 - 9.15122i) q^{77} +(-6.33197 + 10.9673i) q^{79} +(3.67766 + 6.36990i) q^{81} -8.42280i q^{83} +(-7.64188 + 8.41230i) q^{85} +(22.6205 - 13.0599i) q^{87} +(1.19298 - 2.06629i) q^{89} +(-0.343258 + 9.18358i) q^{91} +(-4.50272 - 2.59965i) q^{93} +(-2.49224 + 11.4761i) q^{95} +1.32080i q^{97} +13.5893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{9}+O(q^{10}) \) 24 * q + 14 * q^9	\( 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) \) 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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