LMFDB - Embedded newform 280.2.bg.a.249.4

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			249.4
Character	$\chi$	$=$	280.249
Dual form			280.2.bg.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76528 - 1.01918i) q^{3} +(2.04540 - 0.903506i) q^{5} +(-2.27974 - 1.34267i) q^{7} +(0.577473 + 1.00021i) q^{9} +O(q^{10})$	\(q+(-1.76528 - 1.01918i) q^{3} +(2.04540 - 0.903506i) q^{5} +(-2.27974 - 1.34267i) q^{7} +(0.577473 + 1.00021i) q^{9} +(-0.524037 + 0.907658i) q^{11} -1.15495i q^{13} +(-4.53155 - 0.489703i) q^{15} +(-5.90617 - 3.40993i) q^{17} +(-2.37560 - 4.11466i) q^{19} +(2.65595 + 4.69367i) q^{21} +(2.76549 - 1.59666i) q^{23} +(3.36735 - 3.69607i) q^{25} +3.76090i q^{27} -5.14130 q^{29} +(2.78686 - 4.82698i) q^{31} +(1.85014 - 1.06818i) q^{33} +(-5.87611 - 0.686550i) q^{35} +(-4.25885 + 2.45885i) q^{37} +(-1.17710 + 2.03880i) q^{39} +9.68948 q^{41} +7.44559i q^{43} +(2.08486 + 1.52409i) q^{45} +(8.04651 - 4.64565i) q^{47} +(3.39445 + 6.12190i) q^{49} +(6.95070 + 12.0390i) q^{51} +(4.85078 + 2.80060i) q^{53} +(-0.251792 + 2.33000i) q^{55} +9.68469i q^{57} +(5.43118 - 9.40708i) q^{59} +(1.66722 + 2.88770i) q^{61} +(0.0264698 - 3.05558i) q^{63} +(-1.04350 - 2.36233i) q^{65} +(4.72071 + 2.72551i) q^{67} -6.50915 q^{69} -4.10916 q^{71} +(5.60213 + 3.23439i) q^{73} +(-9.71129 + 3.09264i) q^{75} +(2.41336 - 1.36562i) q^{77} +(0.306372 + 0.530652i) q^{79} +(5.56547 - 9.63967i) q^{81} -0.275623i q^{83} +(-15.1614 - 1.63842i) q^{85} +(9.07583 + 5.23993i) q^{87} +(-8.63232 - 14.9516i) q^{89} +(-1.55072 + 2.63298i) q^{91} +(-9.83916 + 5.68064i) q^{93} +(-8.57667 - 6.26977i) q^{95} -7.59854i q^{97} -1.21047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.76528	−	1.01918i	−1.01918	−	0.588426i	−0.105317	−	0.994439i	$-0.533586\pi$
$3$	−1.76528	−	1.01918i	−1.01918	−	0.588426i	−0.913868	+	0.406012i	$0.866919\pi$
$4$		0			0
$5$	2.04540	−	0.903506i	0.914732	−	0.404060i
$5$	2.04540	−	0.903506i	0.914732	−	0.404060i
$6$		0			0
$7$	−2.27974	−	1.34267i	−0.861662	−	0.507483i
$7$	−2.27974	−	1.34267i	−0.861662	−	0.507483i
$8$		0			0
$9$	0.577473	+	1.00021i	0.192491	+	0.333404i
$10$		0			0
$11$	−0.524037	+	0.907658i	−0.158003	+	0.273669i	−0.934148	−	0.356885i	$-0.883839\pi$
$11$	−0.524037	+	0.907658i	−0.158003	+	0.273669i	0.776145	+	0.630554i	$0.217172\pi$
$12$		0			0
$13$		−	1.15495i		−	0.320324i	−0.987091	−	0.160162i	$-0.948798\pi$
$13$		−	1.15495i		−	0.320324i	0.987091	−	0.160162i	$-0.0512017\pi$
$14$		0			0
$15$	−4.53155	−	0.489703i	−1.17004	−	0.126441i
$16$		0			0
$17$	−5.90617	−	3.40993i	−1.43246	−	0.827030i	−0.435150	−	0.900358i	$-0.643305\pi$
$17$	−5.90617	−	3.40993i	−1.43246	−	0.827030i	−0.997308	+	0.0733282i	$0.976638\pi$
$18$		0			0
$19$	−2.37560	−	4.11466i	−0.545000	−	0.943967i	−0.998607	−	0.0527653i	$-0.983196\pi$
$19$	−2.37560	−	4.11466i	−0.545000	−	0.943967i	0.453607	−	0.891202i	$-0.350137\pi$
$20$		0			0
$21$	2.65595	+	4.69367i	0.579576	+	1.02424i
$22$		0			0
$23$	2.76549	−	1.59666i	0.576645	−	0.332926i	−0.183154	−	0.983084i	$-0.558631\pi$
$23$	2.76549	−	1.59666i	0.576645	−	0.332926i	0.759799	+	0.650158i	$0.225297\pi$
$24$		0			0
$25$	3.36735	−	3.69607i	0.673471	−	0.739214i
$26$		0			0
$27$			3.76090i			0.723786i
$28$		0			0
$29$	−5.14130			−0.954716			−0.477358	−	0.878709i	$-0.658405\pi$
$29$	−5.14130			−0.954716			−0.477358	+	0.878709i	$0.658405\pi$
$30$		0			0
$31$	2.78686	−	4.82698i	0.500534	−	0.866951i	−0.499465	−	0.866334i	$-0.666470\pi$
$31$	2.78686	−	4.82698i	0.500534	−	0.866951i	1.00000		0.000617170i	$-0.000196451\pi$
$32$		0			0
$33$	1.85014	−	1.06818i	0.322068	−	0.185946i
$34$		0			0
$35$	−5.87611	−	0.686550i	−0.993244	−	0.116048i
$36$		0			0
$37$	−4.25885	+	2.45885i	−0.700150	+	0.404232i	−0.807403	−	0.590000i	$-0.799128\pi$
$37$	−4.25885	+	2.45885i	−0.700150	+	0.404232i	0.107253	+	0.994232i	$0.465794\pi$
$38$		0			0
$39$	−1.17710	+	2.03880i	−0.188487	+	0.326469i
$40$		0			0
$41$	9.68948			1.51324			0.756621	−	0.653853i	$-0.226849\pi$
$41$	9.68948			1.51324			0.756621	+	0.653853i	$0.226849\pi$
$42$		0			0
$43$			7.44559i			1.13544i	0.823221	+	0.567721i	$0.192175\pi$
$43$			7.44559i			1.13544i	−0.823221	+	0.567721i	$0.807825\pi$
$44$		0			0
$45$	2.08486	+	1.52409i	0.310793	+	0.227198i
$46$		0			0
$47$	8.04651	−	4.64565i	1.17370	−	0.677638i	0.219154	−	0.975690i	$-0.429670\pi$
$47$	8.04651	−	4.64565i	1.17370	−	0.677638i	0.954550	+	0.298052i	$0.0963370\pi$
$48$		0			0
$49$	3.39445	+	6.12190i	0.484922	+	0.874558i
$50$		0			0
$51$	6.95070	+	12.0390i	0.973292	+	1.68579i
$52$		0			0
$53$	4.85078	+	2.80060i	0.666305	+	0.384692i	0.794675	−	0.607035i	$-0.207641\pi$
$53$	4.85078	+	2.80060i	0.666305	+	0.384692i	−0.128370	+	0.991726i	$0.540974\pi$
$54$		0			0
$55$	−0.251792	+	2.33000i	−0.0339516	+	0.314177i
$56$		0			0
$57$			9.68469i			1.28277i
$58$		0			0
$59$	5.43118	−	9.40708i	0.707080	−	1.22470i	−0.258856	−	0.965916i	$-0.583346\pi$
$59$	5.43118	−	9.40708i	0.707080	−	1.22470i	0.965936	−	0.258782i	$-0.0833211\pi$
$60$		0			0
$61$	1.66722	+	2.88770i	0.213465	+	0.369733i	0.952797	−	0.303609i	$-0.0981917\pi$
$61$	1.66722	+	2.88770i	0.213465	+	0.369733i	−0.739331	+	0.673342i	$0.764858\pi$
$62$		0			0
$63$	0.0264698	−	3.05558i	0.00333489	−	0.384967i
$64$		0			0
$65$	−1.04350	−	2.36233i	−0.129430	−	0.293011i
$66$		0			0
$67$	4.72071	+	2.72551i	0.576727	+	0.332973i	0.759832	−	0.650120i	$-0.225281\pi$
$67$	4.72071	+	2.72551i	0.576727	+	0.332973i	−0.183105	+	0.983093i	$0.558615\pi$
$68$		0			0
$69$	−6.50915			−0.783609
$70$		0			0
$71$	−4.10916			−0.487668			−0.243834	−	0.969817i	$-0.578405\pi$
$71$	−4.10916			−0.487668			−0.243834	+	0.969817i	$0.578405\pi$
$72$		0			0
$73$	5.60213	+	3.23439i	0.655680	+	0.378557i	0.790629	−	0.612296i	$-0.209754\pi$
$73$	5.60213	+	3.23439i	0.655680	+	0.378557i	−0.134949	+	0.990853i	$0.543087\pi$
$74$		0			0
$75$	−9.71129	+	3.09264i	−1.12136	+	0.357107i
$76$		0			0
$77$	2.41336	−	1.36562i	0.275028	−	0.155626i
$78$		0			0
$79$	0.306372	+	0.530652i	0.0344695	+	0.0597030i	0.882746	−	0.469851i	$-0.155692\pi$
$79$	0.306372	+	0.530652i	0.0344695	+	0.0597030i	−0.848276	+	0.529554i	$0.822359\pi$
$80$		0			0
$81$	5.56547	−	9.63967i	0.618385	−	1.07107i
$82$		0			0
$83$		−	0.275623i		−	0.0302535i	−0.999886	−	0.0151268i	$-0.995185\pi$
$83$		−	0.275623i		−	0.0302535i	0.999886	−	0.0151268i	$-0.00481518\pi$
$84$		0			0
$85$	−15.1614	−	1.63842i	−1.64449	−	0.177712i
$86$		0			0
$87$	9.07583	+	5.23993i	0.973031	+	0.561780i
$88$		0			0
$89$	−8.63232	−	14.9516i	−0.915024	−	1.58487i	−0.806866	−	0.590735i	$-0.798838\pi$
$89$	−8.63232	−	14.9516i	−0.915024	−	1.58487i	−0.108158	−	0.994134i	$-0.534495\pi$
$90$		0			0
$91$	−1.55072	+	2.63298i	−0.162559	+	0.276011i
$92$		0			0
$93$	−9.83916	+	5.68064i	−1.02027	+	0.589055i
$94$		0			0
$95$	−8.57667	−	6.26977i	−0.879948	−	0.643265i
$96$		0			0
$97$		−	7.59854i		−	0.771515i	−0.922600	−	0.385757i	$-0.873940\pi$
$97$		−	7.59854i		−	0.771515i	0.922600	−	0.385757i	$-0.126060\pi$
$98$		0			0
$99$	−1.21047			−0.121657
$100$		0			0
$101$	0.282335	−	0.489019i	0.0280934	−	0.0486592i	−0.851637	−	0.524132i	$-0.824390\pi$
$101$	0.282335	−	0.489019i	0.0280934	−	0.0486592i	0.879730	+	0.475473i	$0.157723\pi$
$102$		0			0
$103$	−13.4944	+	7.79097i	−1.32964	+	0.767667i	−0.985244	−	0.171157i	$-0.945249\pi$
$103$	−13.4944	+	7.79097i	−1.32964	+	0.767667i	−0.344395	+	0.938825i	$0.611916\pi$
$104$		0			0
$105$	9.67325	+	7.20079i	0.944012	+	0.702725i
$106$		0			0
$107$	12.1452	−	7.01205i	1.17412	−	0.677880i	0.219475	−	0.975618i	$-0.429565\pi$
$107$	12.1452	−	7.01205i	1.17412	−	0.677880i	0.954648	+	0.297738i	$0.0962321\pi$
$108$		0			0
$109$	−7.89890	+	13.6813i	−0.756577	+	1.31043i	0.188009	+	0.982167i	$0.439797\pi$
$109$	−7.89890	+	13.6813i	−0.756577	+	1.31043i	−0.944586	+	0.328263i	$0.893537\pi$
$110$		0			0
$111$	10.0241			0.951442
$112$		0			0
$113$		−	20.3625i		−	1.91554i	−0.287536	−	0.957770i	$-0.592836\pi$
$113$		−	20.3625i		−	1.91554i	0.287536	−	0.957770i	$-0.407164\pi$
$114$		0			0
$115$	4.21396	−	5.76445i	0.392953	−	0.537537i
$116$		0			0
$117$	1.15519	−	0.666949i	0.106797	−	0.0616595i
$118$		0			0
$119$	8.88613	+	15.7038i	0.814590	+	1.43957i
$120$		0			0
$121$	4.95077	+	8.57499i	0.450070	+	0.779544i
$122$		0			0
$123$	−17.1046	−	9.87536i	−1.54227	−	0.890432i
$124$		0			0
$125$	3.54818	−	10.6024i	0.317359	−	0.948306i
$126$		0			0
$127$			0.358593i			0.0318199i	0.999873	+	0.0159100i	$0.00506451\pi$
$127$			0.358593i			0.0318199i	−0.999873	+	0.0159100i	$0.994935\pi$
$128$		0			0
$129$	7.58843	−	13.1435i	0.668124	−	1.15722i
$130$		0			0
$131$	7.75572	+	13.4333i	0.677620	+	1.17367i	0.975696	+	0.219130i	$0.0703220\pi$
$131$	7.75572	+	13.4333i	0.677620	+	1.17367i	−0.298075	+	0.954542i	$0.596345\pi$
$132$		0			0
$133$	−0.108891	+	12.5700i	−0.00944206	+	1.08996i
$134$		0			0
$135$	3.39800	+	7.69256i	0.292453	+	0.662070i
$136$		0			0
$137$	−0.729539	−	0.421199i	−0.0623287	−	0.0359855i	0.468512	−	0.883457i	$-0.344790\pi$
$137$	−0.729539	−	0.421199i	−0.0623287	−	0.0359855i	−0.530841	+	0.847472i	$0.678124\pi$
$138$		0			0
$139$	−2.97876			−0.252655			−0.126327	−	0.991989i	$-0.540319\pi$
$139$	−2.97876			−0.252655			−0.126327	+	0.991989i	$0.540319\pi$
$140$		0			0
$141$	−18.9391			−1.59496
$142$		0			0
$143$	1.04830	+	0.605233i	0.0876628	+	0.0506122i
$144$		0			0
$145$	−10.5160	+	4.64520i	−0.873310	+	0.385763i
$146$		0			0
$147$	0.247192	−	14.2664i	0.0203881	−	1.17668i
$148$		0			0
$149$	0.551451	+	0.955142i	0.0451767	+	0.0782483i	0.887730	−	0.460365i	$-0.152282\pi$
$149$	0.551451	+	0.955142i	0.0451767	+	0.0782483i	−0.842553	+	0.538614i	$0.818948\pi$
$150$		0			0
$151$	6.27624	−	10.8708i	0.510753	−	0.884650i	−0.489169	−	0.872189i	$-0.662700\pi$
$151$	6.27624	−	10.8708i	0.510753	−	0.884650i	0.999922	−	0.0124612i	$-0.00396661\pi$
$152$		0			0
$153$		−	7.87657i		−	0.636783i
$154$		0			0
$155$	1.33904	−	12.3911i	0.107555	−	0.995274i
$156$		0			0
$157$	−18.2482	−	10.5356i	−1.45636	−	0.840831i	−0.457532	−	0.889193i	$-0.651267\pi$
$157$	−18.2482	−	10.5356i	−1.45636	−	0.840831i	−0.998830	+	0.0483621i	$0.984600\pi$
$158$		0			0
$159$	−5.70865	−	9.88767i	−0.452725	−	0.784143i
$160$		0			0
$161$	−8.44840	−	0.0731866i	−0.665827	−	0.00576791i
$162$		0			0
$163$	18.9364	−	10.9329i	1.48321	−	0.856332i	0.483393	−	0.875404i	$-0.339404\pi$
$163$	18.9364	−	10.9329i	1.48321	−	0.856332i	0.999818	+	0.0190714i	$0.00607100\pi$
$164$		0			0
$165$	2.81918	−	3.85647i	0.219473	−	0.300226i
$166$		0			0
$167$			10.1680i			0.786821i	0.919363	+	0.393411i	$0.128705\pi$
$167$			10.1680i			0.786821i	−0.919363	+	0.393411i	$0.871295\pi$
$168$		0			0
$169$	11.6661			0.897392
$170$		0			0
$171$	2.74369	−	4.75220i	0.209815	−	0.363410i
$172$		0			0
$173$	0.691475	−	0.399223i	0.0525719	−	0.0303524i	−0.473484	−	0.880803i	$-0.657004\pi$
$173$	0.691475	−	0.399223i	0.0525719	−	0.0303524i	0.526056	+	0.850450i	$0.323670\pi$
$174$		0			0
$175$	−12.6393	+	3.90483i	−0.955443	+	0.295177i
$176$		0			0
$177$	−19.1751	+	11.0707i	−1.44129	+	0.832128i
$178$		0			0
$179$	−6.08777	+	10.5443i	−0.455021	+	0.788119i	−0.998689	−	0.0511806i	$-0.983702\pi$
$179$	−6.08777	+	10.5443i	−0.455021	+	0.788119i	0.543668	+	0.839300i	$0.317035\pi$
$180$		0			0
$181$	−4.00613			−0.297773			−0.148887	−	0.988854i	$-0.547569\pi$
$181$	−4.00613			−0.297773			−0.148887	+	0.988854i	$0.547569\pi$
$182$		0			0
$183$		−	6.79680i		−	0.502434i
$184$		0			0
$185$	−6.48948	+	8.87722i	−0.477116	+	0.652666i
$186$		0			0
$187$	6.19010	−	3.57386i	0.452665	−	0.261346i
$188$		0			0
$189$	5.04966	−	8.57389i	0.367309	−	0.623658i
$190$		0			0
$191$	−8.33082	−	14.4294i	−0.602797	−	1.04407i	−0.992396	−	0.123090i	$-0.960720\pi$
$191$	−8.33082	−	14.4294i	−0.602797	−	1.04407i	0.389599	−	0.920985i	$-0.372614\pi$
$192$		0			0
$193$	6.43024	+	3.71250i	0.462859	+	0.267232i	0.713246	−	0.700914i	$-0.247224\pi$
$193$	6.43024	+	3.71250i	0.462859	+	0.267232i	−0.250387	+	0.968146i	$0.580558\pi$
$194$		0			0
$195$	−0.565581	+	5.23369i	−0.0405021	+	0.374792i
$196$		0			0
$197$			1.88883i			0.134574i	0.997734	+	0.0672869i	$0.0214343\pi$
$197$			1.88883i			0.134574i	−0.997734	+	0.0672869i	$0.978566\pi$
$198$		0			0
$199$	−8.61865	+	14.9279i	−0.610960	+	1.05821i	0.380119	+	0.924938i	$0.375883\pi$
$199$	−8.61865	+	14.9279i	−0.610960	+	1.05821i	−0.991079	+	0.133276i	$0.957450\pi$
$200$		0			0
$201$	−5.55558	−	9.62255i	−0.391861	−	0.678723i
$202$		0			0
$203$	11.7208	+	6.90309i	0.822642	+	0.484502i
$204$		0			0
$205$	19.8189	−	8.75450i	1.38421	−	0.611441i
$206$		0			0
$207$	3.19399	+	1.84405i	0.221998	+	0.128170i
$208$		0			0
$209$	4.97960			0.344446
$210$		0			0
$211$	−5.25478			−0.361754			−0.180877	−	0.983506i	$-0.557894\pi$
$211$	−5.25478			−0.361754			−0.180877	+	0.983506i	$0.557894\pi$
$212$		0			0
$213$	7.25381	+	4.18799i	0.497023	+	0.286956i
$214$		0			0
$215$	6.72713	+	15.2292i	0.458787	+	1.03863i
$216$		0			0
$217$	−12.8344	+	7.26243i	−0.871254	+	0.493006i
$218$		0			0
$219$	−6.59288	−	11.4192i	−0.445506	−	0.771639i
$220$		0			0
$221$	−3.93828	+	6.82131i	−0.264918	+	0.458851i
$222$		0			0
$223$			13.2760i			0.889027i	0.895772	+	0.444513i	$0.146623\pi$
$223$			13.2760i			0.889027i	−0.895772	+	0.444513i	$0.853377\pi$
$224$		0			0
$225$	5.64141	+	1.23369i	0.376094	+	0.0822459i
$226$		0			0
$227$	−10.2225	−	5.90197i	−0.678492	−	0.391727i	0.120795	−	0.992677i	$-0.461456\pi$
$227$	−10.2225	−	5.90197i	−0.678492	−	0.391727i	−0.799286	+	0.600950i	$0.794789\pi$
$228$		0			0
$229$	6.74611	+	11.6846i	0.445796	+	0.772141i	0.998107	−	0.0614969i	$-0.0195874\pi$
$229$	6.74611	+	11.6846i	0.445796	+	0.772141i	−0.552311	+	0.833638i	$0.686254\pi$
$230$		0			0
$231$	−5.65206	−	0.0489625i	−0.371878	−	0.00322150i
$232$		0			0
$233$	0.987785	−	0.570298i	0.0647120	−	0.0373615i	−0.467295	−	0.884101i	$-0.654771\pi$
$233$	0.987785	−	0.570298i	0.0647120	−	0.0373615i	0.532007	+	0.846740i	$0.321438\pi$
$234$		0			0
$235$	12.2610	−	16.7723i	0.799818	−	1.09410i
$236$		0			0
$237$		−	1.24900i		−	0.0811311i
$238$		0			0
$239$	−2.94796			−0.190688			−0.0953438	−	0.995444i	$-0.530395\pi$
$239$	−2.94796			−0.190688			−0.0953438	+	0.995444i	$0.530395\pi$
$240$		0			0
$241$	−5.30655	+	9.19122i	−0.341825	+	0.592058i	−0.984772	−	0.173853i	$-0.944378\pi$
$241$	−5.30655	+	9.19122i	−0.341825	+	0.592058i	0.642947	+	0.765911i	$0.277712\pi$
$242$		0			0
$243$	−9.87810	+	5.70312i	−0.633680	+	0.365856i
$244$		0			0
$245$	12.4742	+	9.45486i	0.796947	+	0.604049i
$246$		0			0
$247$	−4.75220	+	2.74369i	−0.302375	+	0.174577i
$248$		0			0
$249$	−0.280910	+	0.486551i	−0.0178020	+	0.0308339i
$250$		0			0
$251$	−12.3119			−0.777120			−0.388560	−	0.921423i	$-0.627027\pi$
$251$	−12.3119			−0.777120			−0.388560	+	0.921423i	$0.627027\pi$
$252$		0			0
$253$			3.34683i			0.210413i
$254$		0			0
$255$	25.0943	+	18.3445i	1.57146	+	1.14878i
$256$		0			0
$257$	15.3706	−	8.87421i	0.958790	−	0.553558i	0.0629896	−	0.998014i	$-0.479936\pi$
$257$	15.3706	−	8.87421i	0.958790	−	0.553558i	0.895800	+	0.444456i	$0.146603\pi$
$258$		0			0
$259$	13.0105	+	0.112707i	0.808433	+	0.00700327i
$260$		0			0
$261$	−2.96896	−	5.14239i	−0.183774	−	0.318306i
$262$		0			0
$263$	3.61626	+	2.08785i	0.222988	+	0.128742i	0.607333	−	0.794447i	$-0.292239\pi$
$263$	3.61626	+	2.08785i	0.222988	+	0.128742i	−0.384345	+	0.923190i	$0.625573\pi$
$264$		0			0
$265$	12.4522	+	1.34565i	0.764930	+	0.0826624i
$266$		0			0
$267$			35.1917i			2.15370i
$268$		0			0
$269$	13.1341	−	22.7489i	0.800798	−	1.38702i	−0.118294	−	0.992979i	$-0.537743\pi$
$269$	13.1341	−	22.7489i	0.800798	−	1.38702i	0.919092	−	0.394044i	$-0.128924\pi$
$270$		0			0
$271$	−13.1537	−	22.7829i	−0.799031	−	1.38396i	−0.920248	−	0.391337i	$-0.872013\pi$
$271$	−13.1537	−	22.7829i	−0.799031	−	1.38396i	0.121216	−	0.992626i	$-0.461321\pi$
$272$		0			0
$273$	5.42093	−	3.06748i	0.328090	−	0.185652i
$274$		0			0
$275$	1.59015	+	4.99328i	0.0958896	+	0.301106i
$276$		0			0
$277$	18.1278	+	10.4661i	1.08919	+	0.628845i	0.933361	−	0.358938i	$-0.116861\pi$
$277$	18.1278	+	10.4661i	1.08919	+	0.628845i	0.155831	+	0.987784i	$0.450194\pi$
$278$		0			0
$279$	6.43734			0.385393
$280$		0			0
$281$	15.7097			0.937162			0.468581	−	0.883420i	$-0.344765\pi$
$281$	15.7097			0.937162			0.468581	+	0.883420i	$0.344765\pi$
$282$		0			0
$283$	−9.36062	−	5.40436i	−0.556431	−	0.321256i	0.195281	−	0.980747i	$-0.437438\pi$
$283$	−9.36062	−	5.40436i	−0.556431	−	0.321256i	−0.751712	+	0.659492i	$0.770772\pi$
$284$		0			0
$285$	8.75017	+	19.8091i	0.518316	+	1.17339i
$286$		0			0
$287$	−22.0895	−	13.0098i	−1.30390	−	0.767945i
$288$		0			0
$289$	14.7553	+	25.5569i	0.867957	+	1.50335i
$290$		0			0
$291$	−7.74431	+	13.4135i	−0.453979	+	0.786316i
$292$		0			0
$293$			9.91887i			0.579467i	0.957107	+	0.289733i	$0.0935667\pi$
$293$			9.91887i			0.579467i	−0.957107	+	0.289733i	$0.906433\pi$
$294$		0			0
$295$	2.60960	−	24.1484i	0.151937	−	1.40597i
$296$		0			0
$297$	−3.41361	−	1.97085i	−0.198078	−	0.114360i
$298$		0			0
$299$	−1.84405	−	3.19399i	−0.106644	−	0.184713i
$300$		0			0
$301$	9.99700	−	16.9740i	0.576218	−	0.978367i
$302$		0			0
$303$	−0.996801	+	0.575504i	−0.0572647	+	0.0330618i
$304$		0			0
$305$	6.01919	+	4.40018i	0.344658	+	0.251954i
$306$		0			0
$307$			5.64632i			0.322252i	0.986934	+	0.161126i	$0.0515126\pi$
$307$			5.64632i			0.322252i	−0.986934	+	0.161126i	$0.948487\pi$
$308$		0			0
$309$	31.7617			1.80686
$310$		0			0
$311$	−6.00950	+	10.4088i	−0.340767	+	0.590226i	−0.984575	−	0.174961i	$-0.944020\pi$
$311$	−6.00950	+	10.4088i	−0.340767	+	0.590226i	0.643808	+	0.765187i	$0.277353\pi$
$312$		0			0
$313$	16.4358	−	9.48924i	0.929009	−	0.536363i	0.0425107	−	0.999096i	$-0.486464\pi$
$313$	16.4358	−	9.48924i	0.929009	−	0.536363i	0.886498	+	0.462733i	$0.153131\pi$
$314$		0			0
$315$	−2.70660	−	6.27382i	−0.152499	−	0.353490i
$316$		0			0
$317$	−11.0347	+	6.37090i	−0.619772	+	0.357826i	−0.776780	−	0.629772i	$-0.783148\pi$
$317$	−11.0347	+	6.37090i	−0.619772	+	0.357826i	0.157008	+	0.987597i	$0.449815\pi$
$318$		0			0
$319$	2.69423	−	4.66654i	0.150848	−	0.261276i
$320$		0			0
$321$	−28.5863			−1.59553
$322$		0			0
$323$			32.4025i			1.80292i
$324$		0			0
$325$	−4.26876	−	3.88911i	−0.236788	−	0.215729i
$326$		0			0
$327$	27.8875	−	16.1009i	1.54218	−	0.890380i
$328$		0			0
$329$	−24.5816	−	0.212945i	−1.35523	−	0.0117400i
$330$		0			0
$331$	−11.9192	−	20.6446i	−0.655137	−	1.13473i	−0.981859	−	0.189611i	$-0.939277\pi$
$331$	−11.9192	−	20.6446i	−0.655137	−	1.13473i	0.326722	−	0.945120i	$-0.394056\pi$
$332$		0			0
$333$	−4.91873	−	2.83983i	−0.269545	−	0.155622i
$334$		0			0
$335$	12.1183	+	1.30957i	0.662092	+	0.0715492i
$336$		0			0
$337$			23.7427i			1.29335i	0.762767	+	0.646673i	$0.223840\pi$
$337$			23.7427i			1.29335i	−0.762767	+	0.646673i	$0.776160\pi$
$338$		0			0
$339$	−20.7531	+	35.9454i	−1.12715	+	1.95229i
$340$		0			0
$341$	2.92083	+	5.05903i	0.158172	+	0.273962i
$342$		0			0
$343$	0.481244	−	18.5140i	0.0259848	−	0.999662i
$344$		0			0
$345$	−13.3138	+	5.88106i	−0.716793	+	0.316625i
$346$		0			0
$347$	−2.19579	−	1.26774i	−0.117876	−	0.0680558i	0.439903	−	0.898045i	$-0.355013\pi$
$347$	−2.19579	−	1.26774i	−0.117876	−	0.0680558i	−0.557779	+	0.829990i	$0.688346\pi$
$348$		0			0
$349$	−24.9321			−1.33459			−0.667293	−	0.744795i	$-0.732547\pi$
$349$	−24.9321			−1.33459			−0.667293	+	0.744795i	$0.732547\pi$
$350$		0			0
$351$	4.34363			0.231846
$352$		0			0
$353$	−2.03574	−	1.17533i	−0.108351	−	0.0625567i	0.444845	−	0.895608i	$-0.353259\pi$
$353$	−2.03574	−	1.17533i	−0.108351	−	0.0625567i	−0.553196	+	0.833051i	$0.686592\pi$
$354$		0			0
$355$	−8.40489	+	3.71265i	−0.446085	+	0.197047i
$356$		0			0
$357$	0.318602	−	36.7782i	0.0168622	−	1.94651i
$358$		0			0
$359$	−16.1508	−	27.9740i	−0.852407	−	1.47641i	−0.879030	−	0.476766i	$-0.841809\pi$
$359$	−16.1508	−	27.9740i	−0.852407	−	1.47641i	0.0266238	−	0.999646i	$-0.491524\pi$
$360$		0			0
$361$	−1.78693	+	3.09506i	−0.0940491	+	0.162898i
$362$		0			0
$363$		−	20.1830i		−	1.05933i
$364$		0			0
$365$	14.3809	+	1.55408i	0.752732	+	0.0813442i
$366$		0			0
$367$	−6.54302	−	3.77762i	−0.341543	−	0.197190i	0.319411	−	0.947616i	$-0.396515\pi$
$367$	−6.54302	−	3.77762i	−0.341543	−	0.197190i	−0.660954	+	0.750426i	$0.729848\pi$
$368$		0			0
$369$	5.59541	+	9.69153i	0.291285	+	0.504521i
$370$		0			0
$371$	−7.29823	−	12.8977i	−0.378905	−	0.669613i
$372$		0			0
$373$	−25.1708	+	14.5324i	−1.30329	+	0.752457i	−0.980968	−	0.194171i	$-0.937798\pi$
$373$	−25.1708	+	14.5324i	−1.30329	+	0.752457i	−0.322327	+	0.946628i	$0.604465\pi$
$374$		0			0
$375$	−17.0693	+	15.0999i	−0.881455	+	0.779756i
$376$		0			0
$377$			5.93792i			0.305819i
$378$		0			0
$379$	9.36318			0.480954			0.240477	−	0.970655i	$-0.422696\pi$
$379$	9.36318			0.480954			0.240477	+	0.970655i	$0.422696\pi$
$380$		0			0
$381$	0.365472	−	0.633016i	0.0187237	−	0.0324304i
$382$		0			0
$383$	1.67551	−	0.967354i	0.0856143	−	0.0494295i	−0.456582	−	0.889682i	$-0.650926\pi$
$383$	1.67551	−	0.967354i	0.0856143	−	0.0494295i	0.542196	+	0.840252i	$0.317593\pi$
$384$		0			0
$385$	3.70245	−	4.97372i	0.188694	−	0.253484i
$386$		0			0
$387$	−7.44717	+	4.29962i	−0.378561	+	0.218562i
$388$		0			0
$389$	0.378695	−	0.655919i	0.0192006	−	0.0332564i	−0.856265	−	0.516536i	$-0.827221\pi$
$389$	0.378695	−	0.655919i	0.0192006	−	0.0332564i	0.875466	+	0.483280i	$0.160555\pi$
$390$		0			0
$391$	−21.7780			−1.10136
$392$		0			0
$393$		−	31.6180i		−	1.59492i
$394$		0			0
$395$	1.10610	+	0.808588i	0.0556540	+	0.0406845i
$396$		0			0
$397$	28.9755	−	16.7290i	1.45424	−	0.839604i	0.455519	−	0.890226i	$-0.349454\pi$
$397$	28.9755	−	16.7290i	1.45424	−	0.839604i	0.998718	+	0.0506216i	$0.0161203\pi$
$398$		0			0
$399$	13.0034	−	22.0786i	0.650983	−	1.10531i
$400$		0			0
$401$	−15.2506	−	26.4148i	−0.761577	−	1.31909i	−0.942037	−	0.335508i	$-0.891092\pi$
$401$	−15.2506	−	26.4148i	−0.761577	−	1.31909i	0.180460	−	0.983582i	$-0.442241\pi$
$402$		0			0
$403$	−5.57490	−	3.21867i	−0.277705	−	0.160333i
$404$		0			0
$405$	2.67413	−	24.7455i	0.132878	−	1.22961i
$406$		0			0
$407$		−	5.15410i		−	0.255479i
$408$		0			0
$409$	−9.33683	+	16.1719i	−0.461676	+	0.799647i	−0.999045	−	0.0437007i	$-0.986085\pi$
$409$	−9.33683	+	16.1719i	−0.461676	+	0.799647i	0.537368	+	0.843348i	$0.319419\pi$
$410$		0			0
$411$	0.858559	+	1.48707i	0.0423496	+	0.0733517i
$412$		0			0
$413$	−25.0123	+	14.1534i	−1.23078	+	0.696444i
$414$		0			0
$415$	−0.249027	−	0.563760i	−0.0122242	−	0.0276739i
$416$		0			0
$417$	5.25834	+	3.03590i	0.257502	+	0.148669i
$418$		0			0
$419$	34.8449			1.70228			0.851142	−	0.524936i	$-0.175911\pi$
$419$	34.8449			1.70228			0.851142	+	0.524936i	$0.175911\pi$
$420$		0			0
$421$	5.53106			0.269567			0.134784	−	0.990875i	$-0.456966\pi$
$421$	5.53106			0.269567			0.134784	+	0.990875i	$0.456966\pi$
$422$		0			0
$423$	9.29327	+	5.36547i	0.451854	+	0.260878i
$424$		0			0
$425$	−32.4915	+	10.3472i	−1.57607	+	0.501912i
$426$		0			0
$427$	0.0764209	−	8.82175i	0.00369826	−	0.426914i
$428$		0			0
$429$	−1.23369	−	2.13681i	−0.0595631	−	0.103166i
$430$		0			0
$431$	−5.28274	+	9.14998i	−0.254461	+	0.440739i	−0.964749	−	0.263172i	$-0.915231\pi$
$431$	−5.28274	+	9.14998i	−0.254461	+	0.440739i	0.710288	+	0.703911i	$0.248565\pi$
$432$		0			0
$433$		−	14.3654i		−	0.690358i	−0.938537	−	0.345179i	$-0.887818\pi$
$433$		−	14.3654i		−	0.690358i	0.938537	−	0.345179i	$-0.112182\pi$
$434$		0			0
$435$	23.2981	+	2.51771i	1.11706	+	0.120715i
$436$		0			0
$437$	−13.1394	−	7.58603i	−0.628542	−	0.362889i
$438$		0			0
$439$	15.8084	+	27.3809i	0.754493	+	1.30682i	0.945626	+	0.325256i	$0.105451\pi$
$439$	15.8084	+	27.3809i	0.754493	+	1.30682i	−0.191133	+	0.981564i	$0.561216\pi$
$440$		0			0
$441$	−4.16300	+	6.93040i	−0.198238	+	0.330019i
$442$		0			0
$443$	10.3862	−	5.99650i	0.493465	−	0.284902i	−0.232546	−	0.972585i	$-0.574706\pi$
$443$	10.3862	−	5.99650i	0.493465	−	0.284902i	0.726011	+	0.687683i	$0.241372\pi$
$444$		0			0
$445$	−31.1655	−	22.7827i	−1.47738	−	1.08001i
$446$		0			0
$447$		−	2.24812i		−	0.106333i
$448$		0			0
$449$	4.98107			0.235071			0.117536	−	0.993069i	$-0.462501\pi$
$449$	4.98107			0.235071			0.117536	+	0.993069i	$0.462501\pi$
$450$		0			0
$451$	−5.07764	+	8.79473i	−0.239097	+	0.414128i
$452$		0			0
$453$	−22.1586	+	12.7933i	−1.04110	+	0.601081i
$454$		0			0
$455$	−0.792928	+	6.78658i	−0.0371730	+	0.318160i
$456$		0			0
$457$	23.3640	−	13.4892i	1.09292	−	0.631000i	0.158570	−	0.987348i	$-0.449311\pi$
$457$	23.3640	−	13.4892i	1.09292	−	0.631000i	0.934353	+	0.356348i	$0.115978\pi$
$458$		0			0
$459$	12.8244	−	22.2125i	0.598592	−	1.03679i
$460$		0			0
$461$	22.6886			1.05672			0.528358	−	0.849022i	$-0.322808\pi$
$461$	22.6886			1.05672			0.528358	+	0.849022i	$0.322808\pi$
$462$		0			0
$463$		−	27.0921i		−	1.25908i	−0.776969	−	0.629539i	$-0.783244\pi$
$463$		−	27.0921i		−	1.25908i	0.776969	−	0.629539i	$-0.216756\pi$
$464$		0			0
$465$	−14.9926	+	20.5089i	−0.695263	+	0.951080i
$466$		0			0
$467$	3.94459	−	2.27741i	0.182534	−	0.105386i	−0.405949	−	0.913896i	$-0.633059\pi$
$467$	3.94459	−	2.27741i	0.182534	−	0.105386i	0.588483	+	0.808510i	$0.299726\pi$
$468$		0			0
$469$	−7.10255	−	12.5518i	−0.327965	−	0.579590i
$470$		0			0
$471$	21.4754	+	37.1965i	0.989534	+	1.71392i
$472$		0			0
$473$	−6.75805	−	3.90176i	−0.310735	−	0.179403i
$474$		0			0
$475$	−23.2075	−	5.07513i	−1.06483	−	0.232863i
$476$		0			0
$477$			6.46907i			0.296199i
$478$		0			0
$479$	4.11469	−	7.12684i	0.188005	−	0.325634i	−0.756580	−	0.653901i	$-0.773131\pi$
$479$	4.11469	−	7.12684i	0.188005	−	0.325634i	0.944585	+	0.328267i	$0.106465\pi$
$480$		0			0
$481$	2.83983	+	4.91873i	0.129485	+	0.224275i
$482$		0			0
$483$	14.8392	+	8.73967i	0.675206	+	0.397669i
$484$		0			0
$485$	−6.86533	−	15.5421i	−0.311738	−	0.705730i
$486$		0			0
$487$	16.4600	+	9.50316i	0.745872	+	0.430629i	0.824200	−	0.566298i	$-0.191625\pi$
$487$	16.4600	+	9.50316i	0.745872	+	0.430629i	−0.0783285	+	0.996928i	$0.524958\pi$
$488$		0			0
$489$	−44.5706			−2.01555
$490$		0			0
$491$	19.2359			0.868102			0.434051	−	0.900888i	$-0.357084\pi$
$491$	19.2359			0.868102			0.434051	+	0.900888i	$0.357084\pi$
$492$		0			0
$493$	30.3654	+	17.5315i	1.36759	+	0.789579i
$494$		0			0
$495$	−2.47589	+	1.09366i	−0.111283	+	0.0491565i
$496$		0			0
$497$	9.36783	+	5.51726i	0.420204	+	0.247483i
$498$		0			0
$499$	6.10526	+	10.5746i	0.273309	+	0.473385i	0.969707	−	0.244271i	$-0.0785485\pi$
$499$	6.10526	+	10.5746i	0.273309	+	0.473385i	−0.696398	+	0.717656i	$0.745215\pi$
$500$		0			0
$501$	10.3630	−	17.9493i	0.462986	−	0.801916i
$502$		0			0
$503$			2.17917i			0.0971646i	0.998819	+	0.0485823i	$0.0154703\pi$
$503$			2.17917i			0.0971646i	−0.998819	+	0.0485823i	$0.984530\pi$
$504$		0			0
$505$	0.135658	−	1.25533i	0.00603671	−	0.0558616i
$506$		0			0
$507$	−20.5939	−	11.8899i	−0.914608	−	0.528049i
$508$		0			0
$509$	6.22006	+	10.7735i	0.275699	+	0.477525i	0.970311	−	0.241859i	$-0.0777573\pi$
$509$	6.22006	+	10.7735i	0.275699	+	0.477525i	−0.694612	+	0.719384i	$0.744424\pi$
$510$		0			0
$511$	−8.42868	−	14.8954i	−0.372863	−	0.658935i
$512$		0			0
$513$	15.4748	−	8.93439i	0.683230	−	0.394463i
$514$		0			0
$515$	−20.5622	+	28.1279i	−0.906080	+	1.23946i
$516$		0			0
$517$			9.73797i			0.428275i
$518$		0			0
$519$	−1.62753			−0.0714405
$520$		0			0
$521$	−9.42724	+	16.3285i	−0.413015	+	0.715363i	−0.995218	−	0.0976807i	$-0.968858\pi$
$521$	−9.42724	+	16.3285i	−0.413015	+	0.715363i	0.582203	+	0.813044i	$0.302191\pi$
$522$		0			0
$523$	−16.4600	+	9.50316i	−0.719744	+	0.415544i	−0.814658	−	0.579941i	$-0.803076\pi$
$523$	−16.4600	+	9.50316i	−0.719744	+	0.415544i	0.0949146	+	0.995485i	$0.469742\pi$
$524$		0			0
$525$	26.2917	+	5.98868i	1.14746	+	0.261368i
$526$		0			0
$527$	−32.9193	+	19.0060i	−1.43399	+	0.827914i
$528$		0			0
$529$	−6.40137	+	11.0875i	−0.278321	+	0.482065i
$530$		0			0
$531$	12.5454			0.544426
$532$		0			0
$533$		−	11.1908i		−	0.484728i
$534$		0			0
$535$	18.5065	−	25.3158i	0.800104	−	1.09450i
$536$		0			0
$537$	21.4932	−	12.4091i	0.927500	−	0.535493i
$538$		0			0
$539$	−7.33541	−	0.127100i	−0.315958	−	0.00547457i
$540$		0			0
$541$	−12.1810	−	21.0982i	−0.523703	−	0.907081i	−0.999619	−	0.0275900i	$-0.991217\pi$
$541$	−12.1810	−	21.0982i	−0.523703	−	0.907081i	0.475916	−	0.879491i	$-0.342117\pi$
$542$		0			0
$543$	7.07193	+	4.08298i	0.303486	+	0.175218i
$544$		0			0
$545$	−3.79531	+	35.1205i	−0.162573	+	1.50440i
$546$		0			0
$547$		−	3.44667i		−	0.147369i	−0.997282	−	0.0736845i	$-0.976524\pi$
$547$		−	3.44667i		−	0.147369i	0.997282	−	0.0736845i	$-0.0234758\pi$
$548$		0			0
$549$	−1.92554	+	3.33514i	−0.0821802	+	0.142340i
$550$		0			0
$551$	12.2137	+	21.1547i	0.520320	+	0.901220i
$552$		0			0
$553$	0.0140433	−	1.62111i	0.000597181	−	0.0689365i
$554$		0			0
$555$	20.5033	−	9.05680i	0.870315	−	0.384440i
$556$		0			0
$557$	33.3606	+	19.2607i	1.41353	+	0.816104i	0.995719	−	0.0924287i	$-0.0294630\pi$
$557$	33.3606	+	19.2607i	1.41353	+	0.816104i	0.417814	+	0.908533i	$0.362796\pi$
$558$		0			0
$559$	8.59925			0.363709
$560$		0			0
$561$	−14.5697			−0.615132
$562$		0			0
$563$	−9.32476	−	5.38365i	−0.392992	−	0.226894i	0.290464	−	0.956886i	$-0.406190\pi$
$563$	−9.32476	−	5.38365i	−0.392992	−	0.226894i	−0.683456	+	0.729992i	$0.739524\pi$
$564$		0			0
$565$	−18.3976	−	41.6495i	−0.773993	−	1.75221i
$566$		0			0
$567$	−25.6308	+	14.5034i	−1.07639	+	0.609084i
$568$		0			0
$569$	−11.6853	−	20.2395i	−0.489873	−	0.848486i	0.510059	−	0.860140i	$-0.329624\pi$
$569$	−11.6853	−	20.2395i	−0.489873	−	0.848486i	−0.999932	+	0.0116540i	$0.996290\pi$
$570$		0			0
$571$	5.78226	−	10.0152i	0.241980	−	0.419122i	−0.719298	−	0.694701i	$-0.755536\pi$
$571$	5.78226	−	10.0152i	0.241980	−	0.419122i	0.961278	+	0.275580i	$0.0888698\pi$
$572$		0			0
$573$			33.9625i			1.41881i
$574$		0			0
$575$	3.41103	−	15.5980i	0.142250	−	0.650480i
$576$		0			0
$577$	1.87268	+	1.08119i	0.0779608	+	0.0450107i	0.538474	−	0.842642i	$-0.319001\pi$
$577$	1.87268	+	1.08119i	0.0779608	+	0.0450107i	−0.460513	+	0.887653i	$0.652334\pi$
$578$		0			0
$579$	−7.56745	−	13.1072i	−0.314492	−	0.544717i
$580$		0			0
$581$	−0.370072	+	0.628349i	−0.0153532	+	0.0260683i
$582$		0			0
$583$	−5.08397	+	2.93523i	−0.210556	+	0.121565i
$584$		0			0
$585$	1.76024	−	2.40790i	0.0727769	−	0.0995545i
$586$		0			0
$587$			1.65367i			0.0682544i	0.999417	+	0.0341272i	$0.0108651\pi$
$587$			1.65367i			0.0682544i	−0.999417	+	0.0341272i	$0.989135\pi$
$588$		0			0
$589$	−26.4818			−1.09116
$590$		0			0
$591$	1.92507	−	3.33432i	0.0791868	−	0.137155i
$592$		0			0
$593$	−22.1592	+	12.7936i	−0.909971	+	0.525372i	−0.880422	−	0.474191i	$-0.842740\pi$
$593$	−22.1592	+	12.7936i	−0.909971	+	0.525372i	−0.0295491	+	0.999563i	$0.509407\pi$
$594$		0			0
$595$	32.3642	+	24.0920i	1.32680	+	0.987676i
$596$		0			0
$597$	30.4286	−	17.5680i	1.24536	−	0.719010i
$598$		0			0
$599$	5.88867	−	10.1995i	0.240604	−	0.416739i	−0.720282	−	0.693681i	$-0.755988\pi$
$599$	5.88867	−	10.1995i	0.240604	−	0.416739i	0.960887	+	0.276942i	$0.0893210\pi$
$600$		0			0
$601$	18.5454			0.756484			0.378242	−	0.925707i	$-0.376529\pi$
$601$	18.5454			0.756484			0.378242	+	0.925707i	$0.376529\pi$
$602$		0			0
$603$			6.29562i			0.256377i
$604$		0			0
$605$	17.8739	+	13.0663i	0.726677	+	0.531219i
$606$		0			0
$607$	−6.18915	+	3.57331i	−0.251210	+	0.145036i	−0.620318	−	0.784350i	$-0.712997\pi$
$607$	−6.18915	+	3.57331i	−0.251210	+	0.145036i	0.369108	+	0.929386i	$0.379663\pi$
$608$		0			0
$609$	−13.6550	−	24.1316i	−0.553330	−	0.977861i
$610$		0			0
$611$	−5.36547	−	9.29327i	−0.217064	−	0.375966i
$612$		0			0
$613$	−17.8182	−	10.2873i	−0.719669	−	0.415501i	0.0949620	−	0.995481i	$-0.469727\pi$
$613$	−17.8182	−	10.2873i	−0.719669	−	0.415501i	−0.814631	+	0.579980i	$0.803060\pi$
$614$		0			0
$615$	−43.9083	−	4.74497i	−1.77055	−	0.191336i
$616$		0			0
$617$			44.4857i			1.79093i	0.445134	+	0.895464i	$0.353156\pi$
$617$			44.4857i			1.79093i	−0.445134	+	0.895464i	$0.646844\pi$
$618$		0			0
$619$	−14.4068	+	24.9533i	−0.579058	+	1.00296i	0.416530	+	0.909122i	$0.363246\pi$
$619$	−14.4068	+	24.9533i	−0.579058	+	1.00296i	−0.995588	+	0.0938359i	$0.970087\pi$
$620$		0			0
$621$	6.00487	+	10.4007i	0.240967	+	0.417367i
$622$		0			0
$623$	−0.395683	+	45.6762i	−0.0158527	+	1.82998i
$624$		0			0
$625$	−2.32186	−	24.8919i	−0.0928742	−	0.995678i
$626$		0			0
$627$	−8.79038	−	5.07513i	−0.351054	−	0.202681i
$628$		0			0
$629$	33.5380			1.33725
$630$		0			0
$631$	48.6854			1.93813			0.969067	−	0.246796i	$-0.0793777\pi$
$631$	48.6854			1.93813			0.969067	+	0.246796i	$0.0793777\pi$
$632$		0			0
$633$	9.27615	+	5.35559i	0.368694	+	0.212866i
$634$		0			0
$635$	0.323991	+	0.733467i	0.0128572	+	0.0291067i
$636$		0			0
$637$	7.07046	−	3.92041i	0.280142	−	0.155332i
$638$		0			0
$639$	−2.37293	−	4.11003i	−0.0938716	−	0.162590i
$640$		0			0
$641$	−18.1248	+	31.3931i	−0.715888	+	1.23995i	0.246729	+	0.969085i	$0.420644\pi$
$641$	−18.1248	+	31.3931i	−0.715888	+	1.23995i	−0.962616	+	0.270869i	$0.912689\pi$
$642$		0			0
$643$		−	17.4717i		−	0.689015i	−0.938784	−	0.344507i	$-0.888046\pi$
$643$		−	17.4717i		−	0.689015i	0.938784	−	0.344507i	$-0.111954\pi$
$644$		0			0
$645$	3.64613	−	33.7400i	0.143566	−	1.32851i
$646$		0			0
$647$	5.77643	+	3.33502i	0.227095	+	0.131113i	0.609231	−	0.792993i	$-0.291478\pi$
$647$	5.77643	+	3.33502i	0.227095	+	0.131113i	−0.382136	+	0.924106i	$0.624812\pi$
$648$		0			0
$649$	5.69227	+	9.85931i	0.223441	+	0.387012i
$650$		0			0
$651$	30.0580	+	0.260386i	1.17807	+	0.0102053i
$652$		0			0
$653$	13.8781	−	8.01251i	0.543091	−	0.313554i	−0.203240	−	0.979129i	$-0.565147\pi$
$653$	13.8781	−	8.01251i	0.543091	−	0.313554i	0.746331	+	0.665575i	$0.231814\pi$
$654$		0			0
$655$	28.0006	+	20.4692i	1.09408	+	0.799797i
$656$		0			0
$657$			7.47109i			0.291475i
$658$		0			0
$659$	−12.3934			−0.482780			−0.241390	−	0.970428i	$-0.577603\pi$
$659$	−12.3934			−0.482780			−0.241390	+	0.970428i	$0.577603\pi$
$660$		0			0
$661$	−6.15660	+	10.6635i	−0.239464	+	0.414763i	−0.960561	−	0.278071i	$-0.910305\pi$
$661$	−6.15660	+	10.6635i	−0.239464	+	0.414763i	0.721097	+	0.692834i	$0.243638\pi$
$662$		0			0
$663$	13.9043	−	8.02767i	0.540000	−	0.311769i
$664$		0			0
$665$	11.1344	+	25.8091i	0.431772	+	1.00084i
$666$		0			0
$667$	−14.2182	+	8.20890i	−0.550532	+	0.317850i
$668$		0			0
$669$	13.5307	−	23.4358i	0.523127	−	0.906082i
$670$		0			0
$671$	−3.49473			−0.134913
$672$		0			0
$673$		−	10.3139i		−	0.397572i	−0.980043	−	0.198786i	$-0.936300\pi$
$673$		−	10.3139i		−	0.397572i	0.980043	−	0.198786i	$-0.0636998\pi$
$674$		0			0
$675$	13.9006	+	12.6643i	0.535032	+	0.487449i
$676$		0			0
$677$	−26.3265	+	15.1996i	−1.01181	+	0.584168i	−0.911721	−	0.410811i	$-0.865246\pi$
$677$	−26.3265	+	15.1996i	−1.01181	+	0.584168i	−0.100088	+	0.994979i	$0.531912\pi$
$678$		0			0
$679$	−10.2024	+	17.3227i	−0.391531	+	0.664785i
$680$		0			0
$681$	12.0304	+	20.8372i	0.461005	+	0.798484i
$682$		0			0
$683$	22.3400	+	12.8980i	0.854817	+	0.493529i	0.862273	−	0.506444i	$-0.169040\pi$
$683$	22.3400	+	12.8980i	0.854817	+	0.493529i	−0.00745650	+	0.999972i	$0.502374\pi$
$684$		0			0
$685$	−1.87276	−	0.202380i	−0.0715544	−	0.00773255i
$686$		0			0
$687$		−	27.5021i		−	1.04927i
$688$		0			0
$689$	3.23454	−	5.60238i	0.123226	−	0.213434i
$690$		0			0
$691$	7.82266	+	13.5492i	0.297588	+	0.515437i	0.975584	−	0.219629i	$-0.0704845\pi$
$691$	7.82266	+	13.5492i	0.297588	+	0.515437i	−0.677996	+	0.735066i	$0.737151\pi$
$692$		0			0
$693$	2.75955	+	1.62526i	0.104827	+	0.0617386i
$694$		0			0
$695$	−6.09276	+	2.69133i	−0.231112	+	0.102088i
$696$		0			0
$697$	−57.2278	−	33.0405i	−2.16766	−	1.25150i
$698$		0			0
$699$	−2.32496			−0.0879379
$700$		0			0
$701$	30.3083			1.14473			0.572365	−	0.819999i	$-0.306026\pi$
$701$	30.3083			1.14473			0.572365	+	0.819999i	$0.306026\pi$
$702$		0			0
$703$	20.2346	+	11.6825i	0.763163	+	0.440612i
$704$		0			0
$705$	−38.7381	+	17.1116i	−1.45896	+	0.644460i
$706$		0			0
$707$	−1.30025	+	0.735754i	−0.0489008	+	0.0276709i
$708$		0			0
$709$	20.3543	+	35.2547i	0.764423	+	1.32402i	0.940551	+	0.339652i	$0.110309\pi$
$709$	20.3543	+	35.2547i	0.764423	+	1.32402i	−0.176129	+	0.984367i	$0.556357\pi$
$710$		0			0
$711$	−0.353843	+	0.612874i	−0.0132701	+	0.0229846i
$712$		0			0
$713$		−	17.7986i		−	0.666564i
$714$		0			0
$715$	2.69102	+	0.290806i	0.100638	+	0.0108755i
$716$		0			0
$717$	5.20397	+	3.00451i	0.194346	+	0.112206i
$718$		0			0
$719$	5.63458	+	9.75938i	0.210134	+	0.363963i	0.951756	−	0.306855i	$-0.0992765\pi$
$719$	5.63458	+	9.75938i	0.210134	+	0.363963i	−0.741622	+	0.670818i	$0.765943\pi$
$720$		0			0
$721$	41.2244	+	0.357118i	1.53528	+	0.0132998i
$722$		0			0
$723$	18.7351	−	10.8167i	0.696765	−	0.402278i
$724$		0			0
$725$	−17.3126	+	19.0026i	−0.642973	+	0.705739i
$726$		0			0
$727$			25.5742i			0.948495i	0.880392	+	0.474248i	$0.157280\pi$
$727$			25.5742i			0.948495i	−0.880392	+	0.474248i	$0.842720\pi$
$728$		0			0
$729$	−10.1427			−0.375655
$730$		0			0
$731$	25.3889	−	43.9749i	0.939044	−	1.62647i
$732$		0			0
$733$	−6.81251	+	3.93320i	−0.251626	+	0.145276i	−0.620508	−	0.784200i	$-0.713074\pi$
$733$	−6.81251	+	3.93320i	−0.251626	+	0.145276i	0.368883	+	0.929476i	$0.379740\pi$
$734$		0			0
$735$	−12.3842	−	29.4040i	−0.456798	−	1.08458i
$736$		0			0
$737$	−4.94765	+	2.85653i	−0.182249	+	0.105222i
$738$		0			0
$739$	7.02574	−	12.1689i	0.258446	−	0.447641i	−0.707380	−	0.706834i	$-0.750123\pi$
$739$	7.02574	−	12.1689i	0.258446	−	0.447641i	0.965826	+	0.259192i	$0.0834563\pi$
$740$		0			0
$741$	11.1853			0.410902
$742$		0			0
$743$		−	11.3464i		−	0.416258i	−0.978101	−	0.208129i	$-0.933263\pi$
$743$		−	11.3464i		−	0.416258i	0.978101	−	0.208129i	$-0.0667374\pi$
$744$		0			0
$745$	1.99092	+	1.45541i	0.0729415	+	0.0533221i
$746$		0			0
$747$	0.275681	−	0.159165i	0.0100866	−	0.00582353i
$748$		0			0
$749$	−37.1029	−	0.321414i	−1.35571	−	0.0117442i
$750$		0			0
$751$	24.0968	+	41.7369i	0.879306	+	1.52300i	0.852104	+	0.523372i	$0.175326\pi$
$751$	24.0968	+	41.7369i	0.879306	+	1.52300i	0.0272012	+	0.999630i	$0.491341\pi$
$752$		0			0
$753$	21.7339	+	12.5481i	0.792028	+	0.457278i
$754$		0			0
$755$	3.01564	−	27.9057i	0.109750	−	1.01559i
$756$		0			0
$757$		−	20.3236i		−	0.738676i	−0.929295	−	0.369338i	$-0.879585\pi$
$757$		−	20.3236i		−	0.738676i	0.929295	−	0.369338i	$-0.120415\pi$
$758$		0			0
$759$	3.41103	−	5.90808i	0.123813	−	0.214450i
$760$		0			0
$761$	−3.46441	−	6.00054i	−0.125585	−	0.217519i	0.796377	−	0.604801i	$-0.206747\pi$
$761$	−3.46441	−	6.00054i	−0.125585	−	0.217519i	−0.921961	+	0.387282i	$0.873414\pi$
$762$		0			0
$763$	36.3770	−	20.5842i	1.31693	−	0.745197i
$764$		0			0
$765$	−7.11653	−	16.1108i	−0.257299	−	0.582486i
$766$		0			0
$767$	−10.8647	−	6.27272i	−0.392300	−	0.226495i
$768$		0			0
$769$	32.5653			1.17434			0.587168	−	0.809465i	$-0.300243\pi$
$769$	32.5653			1.17434			0.587168	+	0.809465i	$0.300243\pi$
$770$		0			0
$771$	−36.1778			−1.30291
$772$		0			0
$773$	−27.2562	−	15.7364i	−0.980338	−	0.565998i	−0.0779655	−	0.996956i	$-0.524842\pi$
$773$	−27.2562	−	15.7364i	−0.980338	−	0.565998i	−0.902372	+	0.430958i	$0.858176\pi$
$774$		0			0
$775$	−8.45651	−	26.5546i	−0.303767	−	0.953868i
$776$		0			0
$777$	−22.8523	−	13.4591i	−0.819821	−	0.482841i
$778$		0			0
$779$	−23.0183	−	39.8689i	−0.824717	−	1.42845i
$780$		0			0
$781$	2.15335	−	3.72971i	0.0770529	−	0.133460i
$782$		0			0
$783$		−	19.3359i		−	0.691010i
$784$		0			0
$785$	−46.8438	−	5.06220i	−1.67193	−	0.180678i
$786$		0			0
$787$	−39.7737	−	22.9633i	−1.41778	−	0.818555i	−0.421675	−	0.906747i	$-0.638558\pi$
$787$	−39.7737	−	22.9633i	−1.41778	−	0.818555i	−0.996103	+	0.0881921i	$0.971891\pi$
$788$		0			0
$789$	−4.25581	−	7.37128i	−0.151511	−	0.262424i
$790$		0			0
$791$	−27.3402	+	46.4212i	−0.972104	+	1.65055i
$792$		0			0
$793$	3.33514	−	1.92554i	0.118434	−	0.0683781i
$794$		0			0
$795$	−20.6101	−	15.0665i	−0.730964	−	0.534353i
$796$		0			0
$797$		−	13.5988i		−	0.481696i	−0.970563	−	0.240848i	$-0.922575\pi$
$797$		−	13.5988i		−	0.481696i	0.970563	−	0.240848i	$-0.0774255\pi$
$798$		0			0
$799$	−63.3654			−2.24171
$800$		0			0
$801$	9.96986	−	17.2683i	0.352268	−	0.610145i
$802$		0			0
$803$	−5.87144	+	3.38988i	−0.207199	+	0.119626i
$804$		0			0
$805$	−17.3465	+	7.48348i	−0.611384	+	0.263758i
$806$		0			0
$807$	−46.3706	+	26.7721i	−1.63232	+	0.942421i
$808$		0			0
$809$	8.53756	−	14.7875i	0.300165	−	0.519900i	−0.676009	−	0.736894i	$-0.736292\pi$
$809$	8.53756	−	14.7875i	0.300165	−	0.519900i	0.976173	+	0.216994i	$0.0696251\pi$
$810$		0			0
$811$	−35.7020			−1.25367			−0.626833	−	0.779153i	$-0.715649\pi$
$811$	−35.7020			−1.25367			−0.626833	+	0.779153i	$0.715649\pi$
$812$		0			0
$813$			53.6242i			1.88068i
$814$		0			0
$815$	28.8546	−	39.4714i	1.01073	−	1.38262i
$816$		0			0
$817$	30.6360	−	17.6877i	1.07182	−	0.618815i
$818$		0			0
$819$	−3.52903	−	0.0305712i	−0.123314	−	0.00106824i
$820$		0			0
$821$	8.23349	+	14.2608i	0.287351	+	0.497706i	0.973177	−	0.230060i	$-0.0738922\pi$
$821$	8.23349	+	14.2608i	0.287351	+	0.497706i	−0.685826	+	0.727766i	$0.740559\pi$
$822$		0			0
$823$	−25.1493	−	14.5200i	−0.876651	−	0.506135i	−0.00709835	−	0.999975i	$-0.502259\pi$
$823$	−25.1493	−	14.5200i	−0.876651	−	0.506135i	−0.869553	+	0.493840i	$0.835593\pi$
$824$		0			0
$825$	2.28201	−	10.4352i	0.0794495	−	0.363307i
$826$		0			0
$827$			47.8903i			1.66531i	0.553794	+	0.832654i	$0.313179\pi$
$827$			47.8903i			1.66531i	−0.553794	+	0.832654i	$0.686821\pi$
$828$		0			0
$829$	12.0593	−	20.8873i	0.418836	−	0.725446i	−0.576986	−	0.816754i	$-0.695771\pi$
$829$	12.0593	−	20.8873i	0.418836	−	0.725446i	0.995823	+	0.0913081i	$0.0291048\pi$
$830$		0			0
$831$	−21.3337	−	36.9511i	−0.740058	−	1.28182i
$832$		0			0
$833$	0.827043	−	47.7319i	0.0286553	−	1.65381i
$834$		0			0
$835$	9.18682	+	20.7976i	0.317923	+	0.719731i
$836$		0			0
$837$	18.1538	+	10.4811i	0.627487	+	0.362280i
$838$		0			0
$839$	−25.1230			−0.867343			−0.433672	−	0.901071i	$-0.642782\pi$
$839$	−25.1230			−0.867343			−0.433672	+	0.901071i	$0.642782\pi$
$840$		0			0
$841$	−2.56701			−0.0885175
$842$		0			0
$843$	−27.7320	−	16.0111i	−0.955141	−	0.551451i
$844$		0			0
$845$	23.8619	−	10.5404i	0.820874	−	0.362601i
$846$		0			0
$847$	0.226930	−	26.1960i	0.00779742	−	0.900106i
$848$		0			0
$849$	11.0161	+	19.0804i	0.378071	+	0.654838i
$850$		0			0
$851$	−7.85186	+	13.5998i	−0.269158	+	0.466196i
$852$		0			0
$853$			2.78647i			0.0954069i	0.998862	+	0.0477035i	$0.0151902\pi$
$853$			2.78647i			0.0954069i	−0.998862	+	0.0477035i	$0.984810\pi$
$854$		0			0
$855$	1.31830	−	12.1991i	0.0450850	−	0.417201i
$856$		0			0
$857$	29.2071	+	16.8627i	0.997694	+	0.576019i	0.907565	−	0.419911i	$-0.137939\pi$
$857$	29.2071	+	16.8627i	0.997694	+	0.576019i	0.0901287	+	0.995930i	$0.471272\pi$
$858$		0			0
$859$	9.55853	+	16.5559i	0.326133	+	0.564879i	0.981741	−	0.190223i	$-0.0609210\pi$
$859$	9.55853	+	16.5559i	0.326133	+	0.564879i	−0.655608	+	0.755101i	$0.727588\pi$
$860$		0			0
$861$	25.7348	+	45.4792i	0.877038	+	1.54993i
$862$		0			0
$863$	−28.6167	+	16.5218i	−0.974122	+	0.562410i	−0.900490	−	0.434876i	$-0.856792\pi$
$863$	−28.6167	+	16.5218i	−0.974122	+	0.562410i	−0.0736318	+	0.997285i	$0.523459\pi$
$864$		0			0
$865$	1.05364	−	1.44132i	0.0358250	−	0.0490065i
$866$		0			0
$867$		−	60.1533i		−	2.04291i
$868$		0			0
$869$	−0.642200			−0.0217852
$870$		0			0
$871$	3.14781	−	5.45217i	0.106659	−	0.184740i
$872$		0			0
$873$	7.60015	−	4.38795i	0.257226	−	0.148510i
$874$		0			0
$875$	−22.3245	+	19.4066i	−0.754705	+	0.656064i
$876$		0			0
$877$	0.160302	−	0.0925506i	0.00541303	−	0.00312521i	−0.497291	−	0.867584i	$-0.665672\pi$
$877$	0.160302	−	0.0925506i	0.00541303	−	0.00312521i	0.502704	+	0.864459i	$0.332339\pi$
$878$		0			0
$879$	10.1092	−	17.5096i	0.340974	−	0.590583i
$880$		0			0
$881$	43.7063			1.47250			0.736252	−	0.676708i	$-0.236594\pi$
$881$	43.7063			1.47250			0.736252	+	0.676708i	$0.236594\pi$
$882$		0			0
$883$		−	4.70129i		−	0.158211i	−0.996866	−	0.0791055i	$-0.974794\pi$
$883$		−	4.70129i		−	0.158211i	0.996866	−	0.0791055i	$-0.0252064\pi$
$884$		0			0
$885$	−29.2183	+	39.9690i	−0.982164	+	1.34354i
$886$		0			0
$887$	25.0933	−	14.4876i	0.842550	−	0.486447i	−0.0155799	−	0.999879i	$-0.504959\pi$
$887$	25.0933	−	14.4876i	0.842550	−	0.486447i	0.858130	+	0.513432i	$0.171626\pi$
$888$		0			0
$889$	0.481473	−	0.817499i	0.0161481	−	0.0274180i
$890$		0			0
$891$	5.83302	+	10.1031i	0.195413	+	0.338466i
$892$		0			0
$893$	−38.2305	−	22.0724i	−1.27934	−	0.738625i
$894$		0			0
$895$	−2.92508	+	27.0677i	−0.0977748	+	0.904774i
$896$		0			0
$897$			7.51771i			0.251009i
$898$		0			0
$899$	−14.3281	+	24.8170i	−0.477868	+	0.827692i
$900$		0			0
$901$	−19.0997	−	33.0816i	−0.636303	−	1.10211i
$902$		0			0
$903$	−34.9471	+	19.7751i	−1.16297	+	0.658074i
$904$		0			0
$905$	−8.19415	+	3.61956i	−0.272383	+	0.120318i
$906$		0			0
$907$	31.1475	+	17.9830i	1.03424	+	0.597117i	0.918196	−	0.396127i	$-0.129646\pi$
$907$	31.1475	+	17.9830i	1.03424	+	0.597117i	0.116041	+	0.993244i	$0.462979\pi$
$908$		0			0
$909$	0.652164			0.0216309
$910$		0			0
$911$	29.1414			0.965499			0.482749	−	0.875759i	$-0.339638\pi$
$911$	29.1414			0.965499			0.482749	+	0.875759i	$0.339638\pi$
$912$		0			0
$913$	0.250171	+	0.144436i	0.00827946	+	0.00478015i
$914$		0			0
$915$	−6.14095	−	13.9022i	−0.203014	−	0.459593i
$916$		0			0
$917$	0.355502	−	41.0379i	0.0117397	−	1.35519i
$918$		0			0
$919$	13.8007	+	23.9035i	0.455243	+	0.788503i	0.998702	−	0.0509320i	$-0.0162192\pi$
$919$	13.8007	+	23.9035i	0.455243	+	0.788503i	−0.543459	+	0.839435i	$0.682886\pi$
$920$		0			0
$921$	5.75464	−	9.96733i	0.189622	−	0.328435i
$922$		0			0
$923$			4.74585i			0.156212i
$924$		0			0
$925$	−5.25298	+	24.0208i	−0.172717	+	0.789799i
$926$		0			0
$927$	−15.5853	−	8.99815i	−0.511887	−	0.295538i
$928$		0			0
$929$	20.7143	+	35.8783i	0.679616	+	1.17713i	0.975097	+	0.221780i	$0.0711867\pi$
$929$	20.7143	+	35.8783i	0.679616	+	1.17713i	−0.295481	+	0.955349i	$0.595480\pi$
$930$		0			0
$931$	17.1257	−	28.5102i	0.561271	−	0.934384i
$932$		0			0
$933$	21.2169	−	12.2496i	0.694609	−	0.401033i
$934$		0			0
$935$	9.43226	−	12.9028i	0.308468	−	0.421966i
$936$		0			0
$937$			17.6450i			0.576438i	0.957564	+	0.288219i	$0.0930632\pi$
$937$			17.6450i			0.576438i	−0.957564	+	0.288219i	$0.906937\pi$
$938$		0			0
$939$	−38.6851			−1.26244
$940$		0			0
$941$	−12.0502	+	20.8716i	−0.392827	+	0.680396i	−0.992821	−	0.119609i	$-0.961836\pi$
$941$	−12.0502	+	20.8716i	−0.392827	+	0.680396i	0.599995	+	0.800004i	$0.295169\pi$
$942$		0			0
$943$	26.7962	−	15.4708i	0.872603	−	0.503798i
$944$		0			0
$945$	2.58205	−	22.0995i	0.0839940	−	0.718896i
$946$		0			0
$947$	8.34994	−	4.82084i	0.271337	−	0.156656i	−0.358158	−	0.933661i	$-0.616595\pi$
$947$	8.34994	−	4.82084i	0.271337	−	0.156656i	0.629495	+	0.777005i	$0.283262\pi$
$948$		0			0
$949$	3.73555	−	6.47016i	0.121261	−	0.210030i
$950$		0			0
$951$	25.9725			0.842216
$952$		0			0
$953$		−	12.3033i		−	0.398544i	−0.979944	−	0.199272i	$-0.936142\pi$
$953$		−	12.3033i		−	0.398544i	0.979944	−	0.199272i	$-0.0638577\pi$
$954$		0			0
$955$	−30.0769	−	21.9870i	−0.973267	−	0.711483i
$956$		0			0
$957$	−9.51213	+	5.49183i	−0.307484	+	0.177526i
$958$		0			0
$959$	1.09763	+	1.93976i	0.0354442	+	0.0626381i
$960$		0			0
$961$	−0.0331498	−	0.0574172i	−0.00106935	−	0.00185217i
$962$		0			0
$963$	14.0271	+	8.09853i	0.452016	+	0.260972i
$964$		0			0
$965$	16.5067	+	1.78380i	0.531370	+	0.0574227i
$966$		0			0
$967$			15.7098i			0.505193i	0.967572	+	0.252597i	$0.0812846\pi$
$967$			15.7098i			0.505193i	−0.967572	+	0.252597i	$0.918715\pi$
$968$		0			0
$969$	33.0241	−	57.1995i	1.06089	−	1.83751i
$970$		0			0
$971$	2.35791	+	4.08402i	0.0756689	+	0.131062i	0.901377	−	0.433035i	$-0.142557\pi$
$971$	2.35791	+	4.08402i	0.0756689	+	0.131062i	−0.825708	+	0.564098i	$0.809224\pi$
$972$		0			0
$973$	6.79080	+	3.99950i	0.217703	+	0.128218i
$974$		0			0
$975$	3.57183	+	11.2160i	0.114390	+	0.359200i
$976$		0			0
$977$	25.1247	+	14.5057i	0.803809	+	0.464079i	0.844801	−	0.535080i	$-0.179719\pi$
$977$	25.1247	+	14.5057i	0.803809	+	0.464079i	−0.0409922	+	0.999159i	$0.513052\pi$
$978$		0			0
$979$	18.0946			0.578306
$980$		0			0
$981$	−18.2456			−0.582537
$982$		0			0
$983$	25.6697	+	14.8204i	0.818735	+	0.472697i	0.849980	−	0.526815i	$-0.176614\pi$
$983$	25.6697	+	14.8204i	0.818735	+	0.472697i	−0.0312448	+	0.999512i	$0.509947\pi$
$984$		0			0
$985$	1.70657	+	3.86343i	0.0543759	+	0.123099i
$986$		0			0
$987$	43.1763	+	25.4290i	1.37432	+	0.809415i
$988$		0			0
$989$	11.8881	+	20.5907i	0.378018	+	0.654746i
$990$		0			0
$991$	−19.5139	+	33.7991i	−0.619879	+	1.07366i	0.369628	+	0.929180i	$0.379485\pi$
$991$	−19.5139	+	33.7991i	−0.619879	+	1.07366i	−0.989507	+	0.144483i	$0.953848\pi$
$992$		0			0
$993$			48.5913i			1.54200i
$994$		0			0
$995$	−4.14114	+	38.3207i	−0.131283	+	1.21485i
$996$		0			0
$997$	10.7136	+	6.18548i	0.339302	+	0.195896i	0.659963	−	0.751298i	$-0.270572\pi$
$997$	10.7136	+	6.18548i	0.339302	+	0.195896i	−0.320661	+	0.947194i	$0.603905\pi$
$998$		0			0
$999$	−9.24747	−	16.0171i	−0.292577	−	0.506758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bg.a.249.4	yes	24
4.3	odd	2		560.2.bw.f.529.9		24
5.2	odd	4		1400.2.q.o.1201.2		12
5.3	odd	4		1400.2.q.n.1201.5		12
5.4	even	2	inner	280.2.bg.a.249.9	yes	24
7.2	even	3	inner	280.2.bg.a.9.9	yes	24
7.3	odd	6		1960.2.g.e.1569.4		12
7.4	even	3		1960.2.g.f.1569.9		12
20.19	odd	2		560.2.bw.f.529.4		24
28.23	odd	6		560.2.bw.f.289.4		24
35.2	odd	12		1400.2.q.o.401.2		12
35.3	even	12		9800.2.a.cw.1.5		6
35.4	even	6		1960.2.g.f.1569.4		12
35.9	even	6	inner	280.2.bg.a.9.4	✓	24
35.17	even	12		9800.2.a.cy.1.2		6
35.18	odd	12		9800.2.a.cx.1.2		6
35.23	odd	12		1400.2.q.n.401.5		12
35.24	odd	6		1960.2.g.e.1569.9		12
35.32	odd	12		9800.2.a.cv.1.5		6
140.79	odd	6		560.2.bw.f.289.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.4	✓	24	35.9	even	6	inner
280.2.bg.a.9.9	yes	24	7.2	even	3	inner
280.2.bg.a.249.4	yes	24	1.1	even	1	trivial
280.2.bg.a.249.9	yes	24	5.4	even	2	inner
560.2.bw.f.289.4		24	28.23	odd	6
560.2.bw.f.289.9		24	140.79	odd	6
560.2.bw.f.529.4		24	20.19	odd	2
560.2.bw.f.529.9		24	4.3	odd	2
1400.2.q.n.401.5		12	35.23	odd	12
1400.2.q.n.1201.5		12	5.3	odd	4
1400.2.q.o.401.2		12	35.2	odd	12
1400.2.q.o.1201.2		12	5.2	odd	4
1960.2.g.e.1569.4		12	7.3	odd	6
1960.2.g.e.1569.9		12	35.24	odd	6
1960.2.g.f.1569.4		12	35.4	even	6
1960.2.g.f.1569.9		12	7.4	even	3
9800.2.a.cv.1.5		6	35.32	odd	12
9800.2.a.cw.1.5		6	35.3	even	12
9800.2.a.cx.1.2		6	35.18	odd	12
9800.2.a.cy.1.2		6	35.17	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)

\(f(q)\)	\(=\)	\(q+(-1.76528 - 1.01918i) q^{3} +(2.04540 - 0.903506i) q^{5} +(-2.27974 - 1.34267i) q^{7} +(0.577473 + 1.00021i) q^{9} +O(q^{10})\)	\(q+(-1.76528 - 1.01918i) q^{3} +(2.04540 - 0.903506i) q^{5} +(-2.27974 - 1.34267i) q^{7} +(0.577473 + 1.00021i) q^{9} +(-0.524037 + 0.907658i) q^{11} -1.15495i q^{13} +(-4.53155 - 0.489703i) q^{15} +(-5.90617 - 3.40993i) q^{17} +(-2.37560 - 4.11466i) q^{19} +(2.65595 + 4.69367i) q^{21} +(2.76549 - 1.59666i) q^{23} +(3.36735 - 3.69607i) q^{25} +3.76090i q^{27} -5.14130 q^{29} +(2.78686 - 4.82698i) q^{31} +(1.85014 - 1.06818i) q^{33} +(-5.87611 - 0.686550i) q^{35} +(-4.25885 + 2.45885i) q^{37} +(-1.17710 + 2.03880i) q^{39} +9.68948 q^{41} +7.44559i q^{43} +(2.08486 + 1.52409i) q^{45} +(8.04651 - 4.64565i) q^{47} +(3.39445 + 6.12190i) q^{49} +(6.95070 + 12.0390i) q^{51} +(4.85078 + 2.80060i) q^{53} +(-0.251792 + 2.33000i) q^{55} +9.68469i q^{57} +(5.43118 - 9.40708i) q^{59} +(1.66722 + 2.88770i) q^{61} +(0.0264698 - 3.05558i) q^{63} +(-1.04350 - 2.36233i) q^{65} +(4.72071 + 2.72551i) q^{67} -6.50915 q^{69} -4.10916 q^{71} +(5.60213 + 3.23439i) q^{73} +(-9.71129 + 3.09264i) q^{75} +(2.41336 - 1.36562i) q^{77} +(0.306372 + 0.530652i) q^{79} +(5.56547 - 9.63967i) q^{81} -0.275623i q^{83} +(-15.1614 - 1.63842i) q^{85} +(9.07583 + 5.23993i) q^{87} +(-8.63232 - 14.9516i) q^{89} +(-1.55072 + 2.63298i) q^{91} +(-9.83916 + 5.68064i) q^{93} +(-8.57667 - 6.26977i) q^{95} -7.59854i q^{97} -1.21047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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