LMFDB - Embedded newform 544.2.bb.e.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [544,2,Mod(161,544)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(544, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("544.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bb (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 36 x^{18} + 460 x^{16} + 2762 x^{14} + 8608 x^{12} + 14244 x^{10} + 12257 x^{8} + 5436 x^{6} + \cdots + 4 $ x^20 + 36x^18 + 460x^16 + 2762x^14 + 8608x^12 + 14244x^10 + 12257x^8 + 5436x^6 + 1200x^4 + 120*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			321.2
Root			$-2.85946i$ of defining polynomial
Character	$\chi$	$=$	544.321
Dual form			544.2.bb.e.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.856942 - 2.06884i) q^{3} +(3.04112 - 1.25967i) q^{5} +(-2.54908 - 1.05586i) q^{7} +(-1.42443 + 1.42443i) q^{9} +(0.405492 - 0.978945i) q^{11} -1.68352i q^{13} +(-5.21213 - 5.21213i) q^{15} +(-0.295654 - 4.11249i) q^{17} +(3.89152 + 3.89152i) q^{19} +6.17845i q^{21} +(-0.188717 + 0.455603i) q^{23} +(4.12610 - 4.12610i) q^{25} +(-2.03895 - 0.844559i) q^{27} +(-9.06866 + 3.75636i) q^{29} +(0.827163 + 1.99695i) q^{31} -2.37276 q^{33} -9.08209 q^{35} +(1.31624 + 3.17768i) q^{37} +(-3.48294 + 1.44268i) q^{39} +(-6.54925 - 2.71279i) q^{41} +(7.14546 - 7.14546i) q^{43} +(-2.53755 + 6.12618i) q^{45} -9.02539i q^{47} +(0.433201 + 0.433201i) q^{49} +(-8.25473 + 4.13583i) q^{51} +(9.88305 + 9.88305i) q^{53} -3.48788i q^{55} +(4.71612 - 11.3857i) q^{57} +(7.92018 - 7.92018i) q^{59} +(-6.19471 - 2.56593i) q^{61} +(5.13499 - 2.12698i) q^{63} +(-2.12069 - 5.11979i) q^{65} -4.89023 q^{67} +1.10429 q^{69} +(2.22270 + 5.36608i) q^{71} +(-0.0120368 + 0.00498579i) q^{73} +(-12.0721 - 5.00042i) q^{75} +(-2.06726 + 2.06726i) q^{77} +(-4.15294 + 10.0261i) q^{79} +10.9853i q^{81} +(10.4006 + 10.4006i) q^{83} +(-6.07952 - 12.1342i) q^{85} +(15.5426 + 15.5426i) q^{87} -10.8032i q^{89} +(-1.77757 + 4.29142i) q^{91} +(3.42254 - 3.42254i) q^{93} +(16.7366 + 6.93253i) q^{95} +(7.83754 - 3.24642i) q^{97} +(0.816844 + 1.97204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{9} - 12 q^{11} + 24 q^{15} - 8 q^{17} + 16 q^{23} - 16 q^{25} + 12 q^{27} - 8 q^{29} - 24 q^{31} - 32 q^{35} - 32 q^{37} - 16 q^{41} + 44 q^{43} - 8 q^{49} + 16 q^{53} + 16 q^{57} - 12 q^{59}+ \cdots - 32 q^{99}+O(q^{100}) $ 20 * q + 4 * q^9 - 12 * q^11 + 24 * q^15 - 8 * q^17 + 16 * q^23 - 16 * q^25 + 12 * q^27 - 8 * q^29 - 24 * q^31 - 32 * q^35 - 32 * q^37 - 16 * q^41 + 44 * q^43 - 8 * q^49 + 16 * q^53 + 16 * q^57 - 12 * q^59 - 8 * q^61 - 48 * q^63 + 8 * q^65 + 72 * q^67 - 48 * q^69 + 16 * q^71 + 16 * q^73 - 84 * q^75 - 32 * q^77 - 32 * q^79 + 36 * q^83 + 48 * q^85 + 32 * q^87 + 16 * q^91 + 48 * q^93 + 32 * q^95 + 28 * q^97 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	−0.856942	−	2.06884i	−0.494756	−	1.19445i	−0.952274	−	0.305245i	$-0.901262\pi$
$3$	−0.856942	−	2.06884i	−0.494756	−	1.19445i	0.457518	−	0.889200i	$-0.348738\pi$
$4$		0			0
$5$	3.04112	−	1.25967i	1.36003	−	0.563343i	0.420964	−	0.907078i	$-0.361692\pi$
$5$	3.04112	−	1.25967i	1.36003	−	0.563343i	0.939067	+	0.343734i	$0.111692\pi$
$6$		0			0
$7$	−2.54908	−	1.05586i	−0.963461	−	0.399078i	−0.155187	−	0.987885i	$-0.549598\pi$
$7$	−2.54908	−	1.05586i	−0.963461	−	0.399078i	−0.808274	+	0.588807i	$0.799598\pi$
$8$		0			0
$9$	−1.42443	+	1.42443i	−0.474810	+	0.474810i
$10$		0			0
$11$	0.405492	−	0.978945i	0.122261	−	0.295163i	−0.850886	−	0.525351i	$-0.823934\pi$
$11$	0.405492	−	0.978945i	0.122261	−	0.295163i	0.973146	+	0.230188i	$0.0739341\pi$
$12$		0			0
$13$		−	1.68352i		−	0.466925i	−0.972366	−	0.233462i	$-0.924994\pi$
$13$		−	1.68352i		−	0.466925i	0.972366	−	0.233462i	$-0.0750056\pi$
$14$		0			0
$15$	−5.21213	−	5.21213i	−1.34577	−	1.34577i
$16$		0			0
$17$	−0.295654	−	4.11249i	−0.0717066	−	0.997426i
$17$	−0.295654	−	4.11249i	−0.0717066	−	0.997426i
$18$		0			0
$19$	3.89152	+	3.89152i	0.892775	+	0.892775i	0.994784	−	0.102009i	$-0.0325269\pi$
$19$	3.89152	+	3.89152i	0.892775	+	0.892775i	−0.102009	+	0.994784i	$0.532527\pi$
$20$		0			0
$21$			6.17845i			1.34825i
$22$		0			0
$23$	−0.188717	+	0.455603i	−0.0393502	+	0.0949997i	−0.942333	−	0.334677i	$-0.891373\pi$
$23$	−0.188717	+	0.455603i	−0.0393502	+	0.0949997i	0.902983	+	0.429677i	$0.141373\pi$
$24$		0			0
$25$	4.12610	−	4.12610i	0.825221	−	0.825221i
$26$		0			0
$27$	−2.03895	−	0.844559i	−0.392395	−	0.162535i
$28$		0			0
$29$	−9.06866	+	3.75636i	−1.68401	+	0.697539i	−0.999505	−	0.0314699i	$-0.989981\pi$
$29$	−9.06866	+	3.75636i	−1.68401	+	0.697539i	−0.684504	+	0.729009i	$0.739981\pi$
$30$		0			0
$31$	0.827163	+	1.99695i	0.148563	+	0.358662i	0.980589	−	0.196074i	$-0.0628192\pi$
$31$	0.827163	+	1.99695i	0.148563	+	0.358662i	−0.832026	+	0.554736i	$0.812819\pi$
$32$		0			0
$33$	−2.37276			−0.413045
$34$		0			0
$35$	−9.08209			−1.53515
$36$		0			0
$37$	1.31624	+	3.17768i	0.216388	+	0.522407i	0.994380	−	0.105867i	$-0.0337618\pi$
$37$	1.31624	+	3.17768i	0.216388	+	0.522407i	−0.777992	+	0.628274i	$0.783762\pi$
$38$		0			0
$39$	−3.48294	+	1.44268i	−0.557716	+	0.231014i
$40$		0			0
$41$	−6.54925	−	2.71279i	−1.02282	−	0.423666i	−0.192704	−	0.981257i	$-0.561726\pi$
$41$	−6.54925	−	2.71279i	−1.02282	−	0.423666i	−0.830116	+	0.557591i	$0.811726\pi$
$42$		0			0
$43$	7.14546	−	7.14546i	1.08967	−	1.08967i	0.0941105	−	0.995562i	$-0.469999\pi$
$43$	7.14546	−	7.14546i	1.08967	−	1.08967i	0.995562	−	0.0941105i	$-0.0300007\pi$
$44$		0			0
$45$	−2.53755	+	6.12618i	−0.378275	+	0.913238i
$46$		0			0
$47$		−	9.02539i		−	1.31649i	−0.752805	−	0.658244i	$-0.771300\pi$
$47$		−	9.02539i		−	1.31649i	0.752805	−	0.658244i	$-0.228700\pi$
$48$		0			0
$49$	0.433201	+	0.433201i	0.0618859	+	0.0618859i
$50$		0			0
$51$	−8.25473	+	4.13583i	−1.15589	+	0.579132i
$52$		0			0
$53$	9.88305	+	9.88305i	1.35754	+	1.35754i	0.876938	+	0.480603i	$0.159582\pi$
$53$	9.88305	+	9.88305i	1.35754	+	1.35754i	0.480603	+	0.876938i	$0.340418\pi$
$54$		0			0
$55$		−	3.48788i		−	0.470305i
$56$		0			0
$57$	4.71612	−	11.3857i	0.624666	−	1.50808i
$58$		0			0
$59$	7.92018	−	7.92018i	1.03112	−	1.03112i	0.0316200	−	0.999500i	$-0.489933\pi$
$59$	7.92018	−	7.92018i	1.03112	−	1.03112i	0.999500	−	0.0316200i	$-0.0100667\pi$
$60$		0			0
$61$	−6.19471	−	2.56593i	−0.793152	−	0.328534i	−0.0509419	−	0.998702i	$-0.516222\pi$
$61$	−6.19471	−	2.56593i	−0.793152	−	0.328534i	−0.742210	+	0.670167i	$0.766222\pi$
$62$		0			0
$63$	5.13499	−	2.12698i	0.646948	−	0.267974i
$64$		0			0
$65$	−2.12069	−	5.11979i	−0.263039	−	0.635032i
$66$		0			0
$67$	−4.89023			−0.597437			−0.298719	−	0.954341i	$-0.596559\pi$
$67$	−4.89023			−0.597437			−0.298719	+	0.954341i	$0.596559\pi$
$68$		0			0
$69$	1.10429			0.132941
$70$		0			0
$71$	2.22270	+	5.36608i	0.263786	+	0.636837i	0.999167	−	0.0408180i	$-0.0129964\pi$
$71$	2.22270	+	5.36608i	0.263786	+	0.636837i	−0.735380	+	0.677655i	$0.762996\pi$
$72$		0			0
$73$	−0.0120368	+	0.00498579i	−0.00140880	+	0.000583543i	−0.383388	−	0.923587i	$-0.625243\pi$
$73$	−0.0120368	+	0.00498579i	−0.00140880	+	0.000583543i	0.381979	+	0.924171i	$0.375243\pi$
$74$		0			0
$75$	−12.0721	−	5.00042i	−1.39396	−	0.577399i
$76$		0			0
$77$	−2.06726	+	2.06726i	−0.235586	+	0.235586i
$78$		0			0
$79$	−4.15294	+	10.0261i	−0.467242	+	1.12802i	0.498120	+	0.867108i	$0.334024\pi$
$79$	−4.15294	+	10.0261i	−0.467242	+	1.12802i	−0.965362	+	0.260914i	$0.915976\pi$
$80$		0			0
$81$			10.9853i			1.22059i
$82$		0			0
$83$	10.4006	+	10.4006i	1.14161	+	1.14161i	0.988155	+	0.153459i	$0.0490412\pi$
$83$	10.4006	+	10.4006i	1.14161	+	1.14161i	0.153459	+	0.988155i	$0.450959\pi$
$84$		0			0
$85$	−6.07952	−	12.1342i	−0.659416	−	1.31613i
$86$		0			0
$87$	15.5426	+	15.5426i	1.66635	+	1.66635i
$88$		0			0
$89$		−	10.8032i		−	1.14514i	−0.819857	−	0.572568i	$-0.805947\pi$
$89$		−	10.8032i		−	1.14514i	0.819857	−	0.572568i	$-0.194053\pi$
$90$		0			0
$91$	−1.77757	+	4.29142i	−0.186340	+	0.449864i
$92$		0			0
$93$	3.42254	−	3.42254i	0.354900	−	0.354900i
$94$		0			0
$95$	16.7366	+	6.93253i	1.71714	+	0.711263i
$96$		0			0
$97$	7.83754	−	3.24642i	0.795782	−	0.329624i	0.0525161	−	0.998620i	$-0.483276\pi$
$97$	7.83754	−	3.24642i	0.795782	−	0.329624i	0.743266	+	0.668997i	$0.233276\pi$
$98$		0			0
$99$	0.816844	+	1.97204i	0.0820959	+	0.198197i
$100$		0			0
$101$	15.9634			1.58841			0.794207	−	0.607647i	$-0.207887\pi$
$101$	15.9634			1.58841			0.794207	+	0.607647i	$0.207887\pi$
$102$		0			0
$103$	1.74089			0.171535			0.0857676	−	0.996315i	$-0.472666\pi$
$103$	1.74089			0.171535			0.0857676	+	0.996315i	$0.472666\pi$
$104$		0			0
$105$	7.78282	+	18.7894i	0.759526	+	1.83366i
$106$		0			0
$107$	0.679143	−	0.281310i	0.0656552	−	0.0271953i	−0.349614	−	0.936894i	$-0.613687\pi$
$107$	0.679143	−	0.281310i	0.0656552	−	0.0271953i	0.415269	+	0.909698i	$0.363687\pi$
$108$		0			0
$109$	11.6545	+	4.82743i	1.11629	+	0.462384i	0.863101	−	0.505031i	$-0.168519\pi$
$109$	11.6545	+	4.82743i	1.11629	+	0.462384i	0.253193	+	0.967416i	$0.418519\pi$
$110$		0			0
$111$	5.44617	−	5.44617i	0.516927	−	0.516927i
$112$		0			0
$113$	3.52351	−	8.50651i	0.331464	−	0.800226i	−0.667012	−	0.745047i	$-0.732427\pi$
$113$	3.52351	−	8.50651i	0.331464	−	0.800226i	0.998476	−	0.0551787i	$-0.0175729\pi$
$114$		0			0
$115$			1.62326i			0.151370i
$116$		0			0
$117$	2.39806	+	2.39806i	0.221701	+	0.221701i
$118$		0			0
$119$	−3.58858	+	10.7952i	−0.328965	+	0.989597i
$120$		0			0
$121$	6.98427	+	6.98427i	0.634933	+	0.634933i
$122$		0			0
$123$			15.8740i			1.43131i
$124$		0			0
$125$	1.05207	−	2.53992i	0.0940999	−	0.227177i
$126$		0			0
$127$	−1.46741	+	1.46741i	−0.130211	+	0.130211i	−0.769209	−	0.638998i	$-0.779349\pi$
$127$	−1.46741	+	1.46741i	−0.130211	+	0.130211i	0.638998	+	0.769209i	$0.279349\pi$
$128$		0			0
$129$	−20.9061	−	8.65957i	−1.84068	−	0.762433i
$130$		0			0
$131$	20.4019	−	8.45075i	1.78252	−	0.738346i	0.790475	−	0.612495i	$-0.209834\pi$
$131$	20.4019	−	8.45075i	1.78252	−	0.738346i	0.992049	−	0.125851i	$-0.0401661\pi$
$132$		0			0
$133$	−5.81087	−	14.0287i	−0.503866	−	1.21644i
$134$		0			0
$135$	−7.26455			−0.625233
$136$		0			0
$137$	2.94219			0.251368			0.125684	−	0.992070i	$-0.459887\pi$
$137$	2.94219			0.251368			0.125684	+	0.992070i	$0.459887\pi$
$138$		0			0
$139$	3.15912	+	7.62679i	0.267953	+	0.646896i	0.999387	−	0.0350165i	$-0.0111484\pi$
$139$	3.15912	+	7.62679i	0.267953	+	0.646896i	−0.731434	+	0.681913i	$0.761148\pi$
$140$		0			0
$141$	−18.6721	+	7.73423i	−1.57247	+	0.651340i
$142$		0			0
$143$	−1.64807	−	0.682655i	−0.137819	−	0.0570865i
$144$		0			0
$145$	−22.8471	+	22.8471i	−1.89735	+	1.89735i
$146$		0			0
$147$	0.524996	−	1.26745i	0.0433009	−	0.104538i
$148$		0			0
$149$		−	1.87441i		−	0.153558i	−0.997048	−	0.0767788i	$-0.975536\pi$
$149$		−	1.87441i		−	0.153558i	0.997048	−	0.0767788i	$-0.0244635\pi$
$150$		0			0
$151$	−13.5689	−	13.5689i	−1.10422	−	1.10422i	−0.993895	−	0.110329i	$-0.964810\pi$
$151$	−13.5689	−	13.5689i	−1.10422	−	1.10422i	−0.110329	−	0.993895i	$-0.535190\pi$
$152$		0			0
$153$	6.27910	+	5.43682i	0.507635	+	0.439541i
$154$		0			0
$155$	5.03100	+	5.03100i	0.404100	+	0.404100i
$156$		0			0
$157$		−	15.8204i		−	1.26261i	−0.775537	−	0.631303i	$-0.782521\pi$
$157$		−	15.8204i		−	1.26261i	0.775537	−	0.631303i	$-0.217479\pi$
$158$		0			0
$159$	11.9773	−	28.9157i	0.949858	−	2.29316i
$160$		0			0
$161$	0.962107	−	0.962107i	0.0758247	−	0.0758247i
$162$		0			0
$163$	8.45516	+	3.50224i	0.662259	+	0.274317i	0.688389	−	0.725342i	$-0.258318\pi$
$163$	8.45516	+	3.50224i	0.662259	+	0.274317i	−0.0261297	+	0.999659i	$0.508318\pi$
$164$		0			0
$165$	−7.21586	+	2.98891i	−0.561754	+	0.232686i
$166$		0			0
$167$	−2.75273	−	6.64567i	−0.213013	−	0.514258i	0.780871	−	0.624693i	$-0.214776\pi$
$167$	−2.75273	−	6.64567i	−0.213013	−	0.514258i	−0.993883	+	0.110435i	$0.964776\pi$
$168$		0			0
$169$	10.1658			0.781981
$170$		0			0
$171$	−11.0864			−0.847798
$172$		0			0
$173$	−1.01910	−	2.46032i	−0.0774806	−	0.187055i	0.880393	−	0.474245i	$-0.157279\pi$
$173$	−1.01910	−	2.46032i	−0.0774806	−	0.187055i	−0.957874	+	0.287190i	$0.907279\pi$
$174$		0			0
$175$	−14.8744	+	6.16116i	−1.12440	+	0.465740i
$176$		0			0
$177$	−23.1727	−	9.59846i	−1.74177	−	0.721464i
$178$		0			0
$179$	10.3427	−	10.3427i	0.773052	−	0.773052i	−0.205587	−	0.978639i	$-0.565910\pi$
$179$	10.3427	−	10.3427i	0.773052	−	0.773052i	0.978639	+	0.205587i	$0.0659103\pi$
$180$		0			0
$181$	−4.46735	+	10.7851i	−0.332056	+	0.801653i	0.666373	+	0.745618i	$0.267846\pi$
$181$	−4.46735	+	10.7851i	−0.332056	+	0.801653i	−0.998429	+	0.0560350i	$0.982154\pi$
$182$		0			0
$183$			15.0147i			1.10992i
$184$		0			0
$185$	8.00567	+	8.00567i	0.588589	+	0.588589i
$186$		0			0
$187$	−4.14579	−	1.37815i	−0.303170	−	0.100781i
$188$		0			0
$189$	4.30569	+	4.30569i	0.313193	+	0.313193i
$190$		0			0
$191$			18.0751i			1.30787i	0.756552	+	0.653933i	$0.226882\pi$
$191$			18.0751i			1.30787i	−0.756552	+	0.653933i	$0.773118\pi$
$192$		0			0
$193$	0.540968	−	1.30601i	0.0389397	−	0.0940088i	−0.903213	−	0.429192i	$-0.858798\pi$
$193$	0.540968	−	1.30601i	0.0389397	−	0.0940088i	0.942153	+	0.335183i	$0.108798\pi$
$194$		0			0
$195$	−8.77472	+	8.77472i	−0.628371	+	0.628371i
$196$		0			0
$197$	−1.08112	−	0.447816i	−0.0770268	−	0.0319055i	0.343837	−	0.939029i	$-0.388273\pi$
$197$	−1.08112	−	0.447816i	−0.0770268	−	0.0319055i	−0.420864	+	0.907124i	$0.638273\pi$
$198$		0			0
$199$	−16.8615	+	6.98424i	−1.19528	+	0.495100i	−0.889470	−	0.456994i	$-0.848926\pi$
$199$	−16.8615	+	6.98424i	−1.19528	+	0.495100i	−0.305807	+	0.952094i	$0.598926\pi$
$200$		0			0
$201$	4.19065	+	10.1171i	0.295585	+	0.713606i
$202$		0			0
$203$	27.0829			1.90085
$204$		0			0
$205$	−23.3343			−1.62974
$206$		0			0
$207$	−0.380160	−	0.917788i	−0.0264230	−	0.0637907i
$208$		0			0
$209$	5.38756	−	2.23160i	0.372665	−	0.154363i
$210$		0			0
$211$	−22.0103	−	9.11698i	−1.51525	−	0.627639i	−0.538620	−	0.842549i	$-0.681054\pi$
$211$	−22.0103	−	9.11698i	−1.51525	−	0.627639i	−0.976634	+	0.214910i	$0.931054\pi$
$212$		0			0
$213$	9.19684	−	9.19684i	0.630157	−	0.630157i
$214$		0			0
$215$	12.7293	−	30.7311i	0.868128	−	2.09585i
$216$		0			0
$217$		−	5.96374i		−	0.404845i
$218$		0			0
$219$	0.0206296	+	0.0206296i	0.00139402	+	0.00139402i
$220$		0			0
$221$	−6.92347	+	0.497739i	−0.465723	+	0.0334816i
$222$		0			0
$223$	−0.285633	−	0.285633i	−0.0191274	−	0.0191274i	0.697478	−	0.716606i	$-0.254305\pi$
$223$	−0.285633	−	0.285633i	−0.0191274	−	0.0191274i	−0.716606	+	0.697478i	$0.754305\pi$
$224$		0			0
$225$			11.7547i			0.783647i
$226$		0			0
$227$	−4.65203	+	11.2310i	−0.308766	+	0.745427i	0.690980	+	0.722874i	$0.257179\pi$
$227$	−4.65203	+	11.2310i	−0.308766	+	0.745427i	−0.999746	+	0.0225527i	$0.992821\pi$
$228$		0			0
$229$	9.14708	−	9.14708i	0.604456	−	0.604456i	−0.337036	−	0.941492i	$-0.609424\pi$
$229$	9.14708	−	9.14708i	0.604456	−	0.604456i	0.941492	+	0.337036i	$0.109424\pi$
$230$		0			0
$231$	6.04836	+	2.50531i	0.397953	+	0.164837i
$232$		0			0
$233$	−10.8316	+	4.48660i	−0.709602	+	0.293927i	−0.708140	−	0.706072i	$-0.750465\pi$
$233$	−10.8316	+	4.48660i	−0.709602	+	0.293927i	−0.00146198	+	0.999999i	$0.500465\pi$
$234$		0			0
$235$	−11.3690	−	27.4473i	−0.741634	−	1.79046i
$236$		0			0
$237$	24.3012			1.57853
$238$		0			0
$239$	3.82714			0.247557			0.123779	−	0.992310i	$-0.460499\pi$
$239$	3.82714			0.247557			0.123779	+	0.992310i	$0.460499\pi$
$240$		0			0
$241$	5.74869	+	13.8786i	0.370306	+	0.893997i	0.993698	+	0.112088i	$0.0357539\pi$
$241$	5.74869	+	13.8786i	0.370306	+	0.893997i	−0.623392	+	0.781909i	$0.714246\pi$
$242$		0			0
$243$	16.6101	−	6.88012i	1.06554	−	0.441360i
$244$		0			0
$245$	1.86311	+	0.771725i	0.119030	+	0.0493037i
$246$		0			0
$247$	6.55145	−	6.55145i	0.416859	−	0.416859i
$248$		0			0
$249$	12.6045	−	30.4299i	0.798776	−	1.92842i
$250$		0			0
$251$			17.9018i			1.12995i	0.825108	+	0.564975i	$0.191114\pi$
$251$			17.9018i			1.12995i	−0.825108	+	0.564975i	$0.808886\pi$
$252$		0			0
$253$	0.369487	+	0.369487i	0.0232294	+	0.0232294i
$254$		0			0
$255$	−19.8938	+	22.9758i	−1.24580	+	1.43880i
$256$		0			0
$257$	−2.49552	−	2.49552i	−0.155666	−	0.155666i	0.624977	−	0.780643i	$-0.285108\pi$
$257$	−2.49552	−	2.49552i	−0.155666	−	0.155666i	−0.780643	+	0.624977i	$0.785108\pi$
$258$		0			0
$259$		−	9.48991i		−	0.589674i
$260$		0			0
$261$	7.56701	−	18.2684i	0.468386	−	1.13078i
$262$		0			0
$263$	−2.26587	+	2.26587i	−0.139720	+	0.139720i	−0.773507	−	0.633788i	$-0.781499\pi$
$263$	−2.26587	+	2.26587i	−0.139720	+	0.139720i	0.633788	+	0.773507i	$0.281499\pi$
$264$		0			0
$265$	42.5050	+	17.6061i	2.61106	+	1.08154i
$266$		0			0
$267$	−22.3501	+	9.25770i	−1.36780	+	0.566562i
$268$		0			0
$269$	4.17362	+	10.0760i	0.254470	+	0.614346i	0.998555	−	0.0537396i	$-0.0171141\pi$
$269$	4.17362	+	10.0760i	0.254470	+	0.614346i	−0.744085	+	0.668085i	$0.767114\pi$
$270$		0			0
$271$	−31.2682			−1.89941			−0.949703	−	0.313153i	$-0.898615\pi$
$271$	−31.2682			−1.89941			−0.949703	+	0.313153i	$0.898615\pi$
$272$		0			0
$273$	10.4015			0.629530
$274$		0			0
$275$	−2.36613	−	5.71233i	−0.142683	−	0.344467i
$276$		0			0
$277$	11.7163	−	4.85303i	0.703962	−	0.291590i	−0.00184167	−	0.999998i	$-0.500586\pi$
$277$	11.7163	−	4.85303i	0.703962	−	0.291590i	0.705803	+	0.708408i	$0.250586\pi$
$278$		0			0
$279$	−4.02275	−	1.66628i	−0.240836	−	0.0997574i
$280$		0			0
$281$	−11.2781	+	11.2781i	−0.672794	+	0.672794i	−0.958359	−	0.285565i	$-0.907819\pi$
$281$	−11.2781	+	11.2781i	−0.672794	+	0.672794i	0.285565	+	0.958359i	$0.407819\pi$
$282$		0			0
$283$	2.70550	−	6.53165i	0.160825	−	0.388266i	−0.822840	−	0.568273i	$-0.807612\pi$
$283$	2.70550	−	6.53165i	0.160825	−	0.388266i	0.983665	+	0.180007i	$0.0576119\pi$
$284$		0			0
$285$		−	40.5661i		−	2.40293i
$286$		0			0
$287$	13.8302	+	13.8302i	0.816371	+	0.816371i
$288$		0			0
$289$	−16.8252	+	2.43175i	−0.989716	+	0.143044i
$290$		0			0
$291$	−13.4326	−	13.4326i	−0.787435	−	0.787435i
$292$		0			0
$293$			6.41620i			0.374838i	0.982280	+	0.187419i	$0.0600123\pi$
$293$			6.41620i			0.374838i	−0.982280	+	0.187419i	$0.939988\pi$
$294$		0			0
$295$	14.1094	−	34.0631i	0.821480	−	1.98323i
$296$		0			0
$297$	−1.65355	+	1.65355i	−0.0959489	+	0.0959489i
$298$		0			0
$299$	0.767016	+	0.317709i	0.0443577	+	0.0183736i
$300$		0			0
$301$	−25.7589	+	10.6697i	−1.48472	+	0.614992i
$302$		0			0
$303$	−13.6797	−	33.0256i	−0.785876	−	1.89727i
$304$		0			0
$305$	−22.0711			−1.26379
$306$		0			0
$307$	−30.6680			−1.75031			−0.875157	−	0.483839i	$-0.839242\pi$
$307$	−30.6680			−1.75031			−0.875157	+	0.483839i	$0.839242\pi$
$308$		0			0
$309$	−1.49184	−	3.60163i	−0.0848680	−	0.204890i
$310$		0			0
$311$	14.0406	−	5.81579i	0.796167	−	0.329783i	0.0527468	−	0.998608i	$-0.483202\pi$
$311$	14.0406	−	5.81579i	0.796167	−	0.329783i	0.743420	+	0.668825i	$0.233202\pi$
$312$		0			0
$313$	2.39329	+	0.991333i	0.135277	+	0.0560335i	0.449295	−	0.893384i	$-0.351675\pi$
$313$	2.39329	+	0.991333i	0.135277	+	0.0560335i	−0.314018	+	0.949417i	$0.601675\pi$
$314$		0			0
$315$	12.9368	−	12.9368i	0.728907	−	0.728907i
$316$		0			0
$317$	5.40627	−	13.0519i	0.303646	−	0.733067i	−0.696237	−	0.717812i	$-0.745144\pi$
$317$	5.40627	−	13.0519i	0.303646	−	0.733067i	0.999884	−	0.0152556i	$-0.00485621\pi$
$318$		0			0
$319$			10.4009i			0.582339i
$320$		0			0
$321$	−1.16397	−	1.16397i	−0.0649666	−	0.0649666i
$322$		0			0
$323$	14.8533	−	17.1544i	0.826459	−	0.954495i
$324$		0			0
$325$	−6.94638	−	6.94638i	−0.385316	−	0.385316i
$326$		0			0
$327$		−	28.2480i		−	1.56212i
$328$		0			0
$329$	−9.52956	+	23.0064i	−0.525382	+	1.26838i
$330$		0			0
$331$	−14.4317	+	14.4317i	−0.793239	+	0.793239i	−0.982019	−	0.188781i	$-0.939546\pi$
$331$	−14.4317	+	14.4317i	−0.793239	+	0.793239i	0.188781	+	0.982019i	$0.439546\pi$
$332$		0			0
$333$	−6.40127	−	2.65149i	−0.350787	−	0.145301i
$334$		0			0
$335$	−14.8718	+	6.16010i	−0.812533	+	0.336562i
$336$		0			0
$337$	−1.67449	−	4.04257i	−0.0912152	−	0.220213i	0.871687	−	0.490063i	$-0.163026\pi$
$337$	−1.67449	−	4.04257i	−0.0912152	−	0.220213i	−0.962903	+	0.269849i	$0.913026\pi$
$338$		0			0
$339$	−20.6181			−1.11982
$340$		0			0
$341$	2.29031			0.124027
$342$		0			0
$343$	6.74417	+	16.2819i	0.364151	+	0.879139i
$344$		0			0
$345$	3.35827	−	1.39104i	0.180803	−	0.0748912i
$346$		0			0
$347$	−11.3597	−	4.70533i	−0.609820	−	0.252596i	0.0563318	−	0.998412i	$-0.482060\pi$
$347$	−11.3597	−	4.70533i	−0.609820	−	0.252596i	−0.666151	+	0.745817i	$0.732060\pi$
$348$		0			0
$349$	3.23178	−	3.23178i	0.172993	−	0.172993i	−0.615300	−	0.788293i	$-0.710965\pi$
$349$	3.23178	−	3.23178i	0.172993	−	0.172993i	0.788293	+	0.615300i	$0.210965\pi$
$350$		0			0
$351$	−1.42183	+	3.43261i	−0.0758918	+	0.183219i
$352$		0			0
$353$			16.3984i			0.872797i	0.899754	+	0.436398i	$0.143746\pi$
$353$			16.3984i			0.872797i	−0.899754	+	0.436398i	$0.856254\pi$
$354$		0			0
$355$	13.5190	+	13.5190i	0.717515	+	0.717515i
$356$		0			0
$357$	25.4088	−	1.82668i	1.34478	−	0.0966782i
$358$		0			0
$359$	2.33907	+	2.33907i	0.123452	+	0.123452i	0.766133	−	0.642682i	$-0.222178\pi$
$359$	2.33907	+	2.33907i	0.123452	+	0.123452i	−0.642682	+	0.766133i	$0.722178\pi$
$360$		0			0
$361$			11.2878i			0.594094i
$362$		0			0
$363$	8.46422	−	20.4344i	0.444256	−	1.07253i
$364$		0			0
$365$	−0.0303248	+	0.0303248i	−0.00158727	+	0.00158727i
$366$		0			0
$367$	17.4631	+	7.23347i	0.911568	+	0.377584i	0.788657	−	0.614834i	$-0.210777\pi$
$367$	17.4631	+	7.23347i	0.911568	+	0.377584i	0.122911	+	0.992418i	$0.460777\pi$
$368$		0			0
$369$	13.1931	−	5.46477i	0.686807	−	0.284485i
$370$		0			0
$371$	−14.7575	−	35.6278i	−0.766172	−	1.84970i
$372$		0			0
$373$	−7.12337			−0.368834			−0.184417	−	0.982848i	$-0.559040\pi$
$373$	−7.12337			−0.368834			−0.184417	+	0.982848i	$0.559040\pi$
$374$		0			0
$375$	−6.15625			−0.317907
$376$		0			0
$377$	6.32392	+	15.2673i	0.325698	+	0.786305i
$378$		0			0
$379$	−16.6843	+	6.91086i	−0.857015	+	0.354987i	−0.767539	−	0.641002i	$-0.778519\pi$
$379$	−16.6843	+	6.91086i	−0.857015	+	0.354987i	−0.0894754	+	0.995989i	$0.528519\pi$
$380$		0			0
$381$	4.29331	+	1.77835i	0.219953	+	0.0911074i
$382$		0			0
$383$	16.4285	−	16.4285i	0.839458	−	0.839458i	−0.149329	−	0.988788i	$-0.547711\pi$
$383$	16.4285	−	16.4285i	0.839458	−	0.839458i	0.988788	+	0.149329i	$0.0477115\pi$
$384$		0			0
$385$	−3.68272	+	8.89087i	−0.187689	+	0.453121i
$386$		0			0
$387$			20.3564i			1.03478i
$388$		0			0
$389$	−8.09228	−	8.09228i	−0.410295	−	0.410295i	0.471546	−	0.881841i	$-0.343696\pi$
$389$	−8.09228	−	8.09228i	−0.410295	−	0.410295i	−0.881841	+	0.471546i	$0.843696\pi$
$390$		0			0
$391$	1.92946	+	0.641395i	0.0975768	+	0.0324368i
$392$		0			0
$393$	−34.9665	−	34.9665i	−1.76383	−	1.76383i
$394$		0			0
$395$			35.7219i			1.79736i
$396$		0			0
$397$	−6.60415	+	15.9438i	−0.331453	+	0.800197i	0.667025	+	0.745035i	$0.267567\pi$
$397$	−6.60415	+	15.9438i	−0.331453	+	0.800197i	−0.998477	+	0.0551618i	$0.982433\pi$
$398$		0			0
$399$	−24.0435	+	24.0435i	−1.20368	+	1.20368i
$400$		0			0
$401$	−3.79088	−	1.57023i	−0.189307	−	0.0784137i	0.286016	−	0.958225i	$-0.407669\pi$
$401$	−3.79088	−	1.57023i	−0.189307	−	0.0784137i	−0.475323	+	0.879811i	$0.657669\pi$
$402$		0			0
$403$	3.36190	−	1.39255i	0.167468	−	0.0693676i
$404$		0			0
$405$	13.8379	+	33.4077i	0.687613	+	1.66004i
$406$		0			0
$407$	3.64450			0.180651
$408$		0			0
$409$	−7.26084			−0.359025			−0.179513	−	0.983756i	$-0.557452\pi$
$409$	−7.26084			−0.359025			−0.179513	+	0.983756i	$0.557452\pi$
$410$		0			0
$411$	−2.52128	−	6.08692i	−0.124366	−	0.300246i
$412$		0			0
$413$	−28.5518	+	11.8265i	−1.40494	+	0.581946i
$414$		0			0
$415$	44.7308	+	18.5281i	2.19575	+	0.909509i
$416$		0			0
$417$	13.0714	−	13.0714i	0.640111	−	0.640111i
$418$		0			0
$419$	4.41187	−	10.6512i	0.215534	−	0.520345i	−0.778723	−	0.627368i	$-0.784132\pi$
$419$	4.41187	−	10.6512i	0.215534	−	0.520345i	0.994256	+	0.107024i	$0.0341320\pi$
$420$		0			0
$421$			19.0719i			0.929509i	0.885439	+	0.464755i	$0.153857\pi$
$421$			19.0719i			0.929509i	−0.885439	+	0.464755i	$0.846143\pi$
$422$		0			0
$423$	12.8560	+	12.8560i	0.625082	+	0.625082i
$424$		0			0
$425$	−18.1885	−	15.7487i	−0.882270	−	0.763923i
$426$		0			0
$427$	13.0815	+	13.0815i	0.633060	+	0.633060i
$428$		0			0
$429$			3.99460i			0.192861i
$430$		0			0
$431$	−0.379306	+	0.915725i	−0.0182705	+	0.0441089i	−0.932752	−	0.360520i	$-0.882599\pi$
$431$	−0.379306	+	0.915725i	−0.0182705	+	0.0441089i	0.914481	+	0.404629i	$0.132599\pi$
$432$		0			0
$433$	1.21635	−	1.21635i	0.0584542	−	0.0584542i	−0.677275	−	0.735730i	$-0.736839\pi$
$433$	1.21635	−	1.21635i	0.0584542	−	0.0584542i	0.735730	+	0.677275i	$0.236839\pi$
$434$		0			0
$435$	66.8457	+	27.6884i	3.20500	+	1.32756i
$436$		0			0
$437$	−2.50738	+	1.03859i	−0.119944	+	0.0496825i
$438$		0			0
$439$	4.34180	+	10.4820i	0.207223	+	0.500280i	0.992984	−	0.118250i	$-0.0377284\pi$
$439$	4.34180	+	10.4820i	0.207223	+	0.500280i	−0.785761	+	0.618530i	$0.787728\pi$
$440$		0			0
$441$	−1.23413			−0.0587681
$442$		0			0
$443$	−19.3737			−0.920473			−0.460236	−	0.887796i	$-0.652235\pi$
$443$	−19.3737			−0.920473			−0.460236	+	0.887796i	$0.652235\pi$
$444$		0			0
$445$	−13.6085	−	32.8538i	−0.645104	−	1.55742i
$446$		0			0
$447$	−3.87785	+	1.60626i	−0.183416	+	0.0759735i
$448$		0			0
$449$	31.8505	+	13.1929i	1.50312	+	0.622612i	0.974124	−	0.226013i	$-0.0725693\pi$
$449$	31.8505	+	13.1929i	1.50312	+	0.622612i	0.528994	+	0.848625i	$0.322569\pi$
$450$		0			0
$451$	−5.31134	+	5.31134i	−0.250101	+	0.250101i
$452$		0			0
$453$	−16.4442	+	39.6997i	−0.772615	+	1.86526i
$454$		0			0
$455$			15.2899i			0.716801i
$456$		0			0
$457$	−19.7453	−	19.7453i	−0.923647	−	0.923647i	0.0736385	−	0.997285i	$-0.476539\pi$
$457$	−19.7453	−	19.7453i	−0.923647	−	0.923647i	−0.997285	+	0.0736385i	$0.976539\pi$
$458$		0			0
$459$	−2.87042	+	8.63485i	−0.133980	+	0.403040i
$460$		0			0
$461$	2.22594	+	2.22594i	0.103672	+	0.103672i	0.757040	−	0.653368i	$-0.226645\pi$
$461$	2.22594	+	2.22594i	0.103672	+	0.103672i	−0.653368	+	0.757040i	$0.726645\pi$
$462$		0			0
$463$		−	8.05071i		−	0.374148i	−0.982346	−	0.187074i	$-0.940100\pi$
$463$		−	8.05071i		−	0.374148i	0.982346	−	0.187074i	$-0.0599005\pi$
$464$		0			0
$465$	6.09707	−	14.7196i	0.282745	−	0.682606i
$466$		0			0
$467$	−9.60145	+	9.60145i	−0.444302	+	0.444302i	−0.893455	−	0.449153i	$-0.851726\pi$
$467$	−9.60145	+	9.60145i	−0.444302	+	0.444302i	0.449153	+	0.893455i	$0.351726\pi$
$468$		0			0
$469$	12.4656	+	5.16341i	0.575607	+	0.238424i
$470$		0			0
$471$	−32.7299	+	13.5572i	−1.50811	+	0.624681i
$472$		0			0
$473$	−4.09758	−	9.89244i	−0.188407	−	0.454855i
$474$		0			0
$475$	32.1136			1.47347
$476$		0			0
$477$	−28.1554			−1.28915
$478$		0			0
$479$	−9.75660	−	23.5545i	−0.445791	−	1.07623i	−0.973884	−	0.227047i	$-0.927093\pi$
$479$	−9.75660	−	23.5545i	−0.445791	−	1.07623i	0.528093	−	0.849186i	$-0.322907\pi$
$480$		0			0
$481$	5.34969	−	2.21591i	0.243925	−	0.101037i
$482$		0			0
$483$	−2.81492	−	1.16598i	−0.128083	−	0.0530538i
$484$		0			0
$485$	19.7455	−	19.7455i	0.896596	−	0.896596i
$486$		0			0
$487$	−4.67614	+	11.2892i	−0.211896	+	0.511562i	−0.993715	−	0.111944i	$-0.964292\pi$
$487$	−4.67614	+	11.2892i	−0.211896	+	0.511562i	0.781819	+	0.623506i	$0.214292\pi$
$488$		0			0
$489$		−	20.4936i		−	0.926752i
$490$		0			0
$491$	20.5776	+	20.5776i	0.928653	+	0.928653i	0.997619	−	0.0689658i	$-0.0219700\pi$
$491$	20.5776	+	20.5776i	0.928653	+	0.928653i	−0.0689658	+	0.997619i	$0.521970\pi$
$492$		0			0
$493$	18.1292	+	36.1842i	0.816498	+	1.62966i
$494$		0			0
$495$	4.96824	+	4.96824i	0.223306	+	0.223306i
$496$		0			0
$497$		−	16.0254i		−	0.718839i
$498$		0			0
$499$	14.8029	−	35.7374i	0.662669	−	1.59983i	−0.130935	−	0.991391i	$-0.541798\pi$
$499$	14.8029	−	35.7374i	0.662669	−	1.59983i	0.793604	−	0.608434i	$-0.208202\pi$
$500$		0			0
$501$	−11.3899	+	11.3899i	−0.508864	+	0.508864i
$502$		0			0
$503$	18.4457	+	7.64044i	0.822451	+	0.340670i	0.753910	−	0.656978i	$-0.228165\pi$
$503$	18.4457	+	7.64044i	0.822451	+	0.340670i	0.0685414	+	0.997648i	$0.478165\pi$
$504$		0			0
$505$	48.5465	−	20.1086i	2.16029	−	0.894822i
$506$		0			0
$507$	−8.71146	−	21.0313i	−0.386890	−	0.934034i
$508$		0			0
$509$	6.53333			0.289585			0.144792	−	0.989462i	$-0.453749\pi$
$509$	6.53333			0.289585			0.144792	+	0.989462i	$0.453749\pi$
$510$		0			0
$511$	0.0359469			0.00159020
$512$		0			0
$513$	−4.64798	−	11.2212i	−0.205213	−	0.495428i
$514$		0			0
$515$	5.29426	−	2.19296i	0.233293	−	0.0966332i
$516$		0			0
$517$	−8.83536	−	3.65972i	−0.388578	−	0.160954i
$518$		0			0
$519$	−4.21670	+	4.21670i	−0.185093	+	0.185093i
$520$		0			0
$521$	8.41129	−	20.3067i	0.368505	−	0.889651i	−0.625490	−	0.780232i	$-0.715101\pi$
$521$	8.41129	−	20.3067i	0.368505	−	0.889651i	0.993996	−	0.109419i	$-0.0348990\pi$
$522$		0			0
$523$			20.3613i			0.890336i	0.895447	+	0.445168i	$0.146856\pi$
$523$			20.3613i			0.890336i	−0.895447	+	0.445168i	$0.853144\pi$
$524$		0			0
$525$	25.4929	+	25.4929i	1.11260	+	1.11260i
$526$		0			0
$527$	7.96788	−	3.99211i	0.347086	−	0.173899i
$528$		0			0
$529$	16.0915	+	16.0915i	0.699630	+	0.699630i
$530$		0			0
$531$			22.5635i			0.979173i
$532$		0			0
$533$	−4.56703	+	11.0258i	−0.197820	+	0.477580i
$534$		0			0
$535$	1.71100	−	1.71100i	0.0739729	−	0.0739729i
$536$		0			0
$537$	−30.2606	−	12.5343i	−1.30584	−	0.540897i
$538$		0			0
$539$	0.599740	−	0.248420i	0.0258326	−	0.0107002i
$540$		0			0
$541$	−7.06544	−	17.0575i	−0.303767	−	0.733358i	−0.999881	−	0.0154270i	$-0.995089\pi$
$541$	−7.06544	−	17.0575i	−0.303767	−	0.733358i	0.696114	−	0.717931i	$-0.254911\pi$
$542$		0			0
$543$	26.1410			1.12182
$544$		0			0
$545$	41.5236			1.77868
$546$		0			0
$547$	−4.44540	−	10.7322i	−0.190072	−	0.458874i	0.799901	−	0.600132i	$-0.204885\pi$
$547$	−4.44540	−	10.7322i	−0.190072	−	0.458874i	−0.989973	+	0.141258i	$0.954885\pi$
$548$		0			0
$549$	12.4789	−	5.16895i	0.532588	−	0.220605i
$550$		0			0
$551$	−49.9088	−	20.6729i	−2.12619	−	0.880695i
$552$		0			0
$553$	21.1723	−	21.1723i	0.900338	−	0.900338i
$554$		0			0
$555$	9.70206	−	23.4228i	0.411830	−	0.994245i
$556$		0			0
$557$			42.1765i			1.78708i	0.448986	+	0.893539i	$0.351785\pi$
$557$			42.1765i			1.78708i	−0.448986	+	0.893539i	$0.648215\pi$
$558$		0			0
$559$	−12.0295	−	12.0295i	−0.508795	−	0.508795i
$560$		0			0
$561$	0.701517	+	9.75797i	0.0296181	+	0.411982i
$562$		0			0
$563$	23.4910	+	23.4910i	0.990026	+	0.990026i	0.999951	−	0.00992515i	$-0.00315933\pi$
$563$	23.4910	+	23.4910i	0.990026	+	0.990026i	−0.00992515	+	0.999951i	$0.503159\pi$
$564$		0			0
$565$		−	30.3078i		−	1.27506i
$566$		0			0
$567$	11.5990	−	28.0025i	0.487113	−	1.17599i
$568$		0			0
$569$	−30.8907	+	30.8907i	−1.29501	+	1.29501i	−0.363356	+	0.931650i	$0.618369\pi$
$569$	−30.8907	+	30.8907i	−1.29501	+	1.29501i	−0.931650	+	0.363356i	$0.881631\pi$
$570$		0			0
$571$	−5.75444	−	2.38357i	−0.240816	−	0.0997491i	0.259012	−	0.965874i	$-0.416603\pi$
$571$	−5.75444	−	2.38357i	−0.240816	−	0.0997491i	−0.499827	+	0.866125i	$0.666603\pi$
$572$		0			0
$573$	37.3944	−	15.4893i	1.56218	−	0.647074i
$574$		0			0
$575$	1.10120	+	2.65853i	0.0459231	+	0.110868i
$576$		0			0
$577$	−19.1580			−0.797559			−0.398779	−	0.917047i	$-0.630566\pi$
$577$	−19.1580			−0.797559			−0.398779	+	0.917047i	$0.630566\pi$
$578$		0			0
$579$	−3.16551			−0.131554
$580$		0			0
$581$	−15.5303	−	37.4935i	−0.644306	−	1.55549i
$582$		0			0
$583$	13.6825	−	5.66746i	0.566670	−	0.234722i
$584$		0			0
$585$	10.3136	+	4.27202i	0.426413	+	0.176626i
$586$		0			0
$587$	7.98915	−	7.98915i	0.329748	−	0.329748i	−0.522743	−	0.852490i	$-0.675091\pi$
$587$	7.98915	−	7.98915i	0.329748	−	0.329748i	0.852490	+	0.522743i	$0.175091\pi$
$588$		0			0
$589$	−4.55224	+	10.9901i	−0.187572	+	0.452838i
$590$		0			0
$591$			2.62042i			0.107790i
$592$		0			0
$593$	−6.37675	−	6.37675i	−0.261862	−	0.261862i	0.563948	−	0.825810i	$-0.309282\pi$
$593$	−6.37675	−	6.37675i	−0.261862	−	0.261862i	−0.825810	+	0.563948i	$0.809282\pi$
$594$		0			0
$595$	2.68516	+	37.3500i	0.110081	+	1.53120i
$596$		0			0
$597$	28.8986	+	28.8986i	1.18274	+	1.18274i
$598$		0			0
$599$		−	3.04853i		−	0.124560i	−0.998059	−	0.0622799i	$-0.980163\pi$
$599$		−	3.04853i		−	0.124560i	0.998059	−	0.0622799i	$-0.0198371\pi$
$600$		0			0
$601$	−12.3244	+	29.7538i	−0.502723	+	1.21368i	0.445272	+	0.895396i	$0.353107\pi$
$601$	−12.3244	+	29.7538i	−0.502723	+	1.21368i	−0.947995	+	0.318286i	$0.896893\pi$
$602$		0			0
$603$	6.96580	−	6.96580i	0.283669	−	0.283669i
$604$		0			0
$605$	30.0379	+	12.4421i	1.22121	+	0.505843i
$606$		0			0
$607$	−9.49541	+	3.93313i	−0.385407	+	0.159641i	−0.566970	−	0.823739i	$-0.691884\pi$
$607$	−9.49541	+	3.93313i	−0.385407	+	0.159641i	0.181563	+	0.983379i	$0.441884\pi$
$608$		0			0
$609$	−23.2085	−	56.0303i	−0.940455	−	2.27046i
$610$		0			0
$611$	−15.1944			−0.614701
$612$		0			0
$613$	11.9951			0.484479			0.242239	−	0.970216i	$-0.422118\pi$
$613$	11.9951			0.484479			0.242239	+	0.970216i	$0.422118\pi$
$614$		0			0
$615$	19.9961	+	48.2749i	0.806321	+	1.94663i
$616$		0			0
$617$	−0.334925	+	0.138730i	−0.0134836	+	0.00558508i	−0.389415	−	0.921062i	$-0.627323\pi$
$617$	−0.334925	+	0.138730i	−0.0134836	+	0.00558508i	0.375931	+	0.926647i	$0.377323\pi$
$618$		0			0
$619$	38.5560	+	15.9704i	1.54970	+	0.641905i	0.983261	−	0.182201i	$-0.0583223\pi$
$619$	38.5560	+	15.9704i	1.54970	+	0.641905i	0.566435	+	0.824107i	$0.308322\pi$
$620$		0			0
$621$	0.769567	−	0.769567i	0.0308816	−	0.0308816i
$622$		0			0
$623$	−11.4067	+	27.5382i	−0.456999	+	1.10329i
$624$		0			0
$625$			20.1265i			0.805060i
$626$		0			0
$627$	−9.23365	−	9.23365i	−0.368756	−	0.368756i
$628$		0			0
$629$	12.6790	−	6.35251i	0.505546	−	0.253291i
$630$		0			0
$631$	−9.09510	−	9.09510i	−0.362070	−	0.362070i	0.502504	−	0.864575i	$-0.332412\pi$
$631$	−9.09510	−	9.09510i	−0.362070	−	0.362070i	−0.864575	+	0.502504i	$0.832412\pi$
$632$		0			0
$633$			53.3486i			2.12042i
$634$		0			0
$635$	−2.61411	+	6.31101i	−0.103738	+	0.250445i
$636$		0			0
$637$	0.729303	−	0.729303i	0.0288960	−	0.0288960i
$638$		0			0
$639$	−10.8097	−	4.47753i	−0.427625	−	0.177128i
$640$		0			0
$641$	23.2938	−	9.64861i	0.920050	−	0.381097i	0.128155	−	0.991754i	$-0.459095\pi$
$641$	23.2938	−	9.64861i	0.920050	−	0.381097i	0.791895	+	0.610657i	$0.209095\pi$
$642$		0			0
$643$	14.0034	+	33.8071i	0.552239	+	1.33322i	0.915793	+	0.401650i	$0.131563\pi$
$643$	14.0034	+	33.8071i	0.552239	+	1.33322i	−0.363554	+	0.931573i	$0.618437\pi$
$644$		0			0
$645$	−74.4861			−2.93289
$646$		0			0
$647$	−29.8075			−1.17185			−0.585926	−	0.810364i	$-0.699269\pi$
$647$	−29.8075			−1.17185			−0.585926	+	0.810364i	$0.699269\pi$
$648$		0			0
$649$	−4.54185	−	10.9650i	−0.178283	−	0.430414i
$650$		0			0
$651$	−12.3380	+	5.11058i	−0.483566	+	0.200299i
$652$		0			0
$653$	−16.2966	−	6.75027i	−0.637735	−	0.264159i	0.0403004	−	0.999188i	$-0.487169\pi$
$653$	−16.2966	−	6.75027i	−0.637735	−	0.264159i	−0.678036	+	0.735029i	$0.737169\pi$
$654$		0			0
$655$	51.3995	−	51.3995i	2.00835	−	2.00835i
$656$		0			0
$657$	0.0100436	−	0.0242475i	0.000391839	−	0.000945983i
$658$		0			0
$659$			39.1712i			1.52589i	0.646462	+	0.762946i	$0.276248\pi$
$659$			39.1712i			1.52589i	−0.646462	+	0.762946i	$0.723752\pi$
$660$		0			0
$661$	−11.1803	−	11.1803i	−0.434864	−	0.434864i	0.455415	−	0.890279i	$-0.349491\pi$
$661$	−11.1803	−	11.1803i	−0.434864	−	0.434864i	−0.890279	+	0.455415i	$0.849491\pi$
$662$		0			0
$663$	6.96275	+	13.8970i	0.270411	+	0.539715i
$664$		0			0
$665$	−35.3431	−	35.3431i	−1.37055	−	1.37055i
$666$		0			0
$667$		−	4.84060i		−	0.187429i
$668$		0			0
$669$	−0.346158	+	0.835699i	−0.0133832	+	0.0323100i
$670$		0			0
$671$	−5.02382	+	5.02382i	−0.193942	+	0.193942i
$672$		0			0
$673$	−23.2518	−	9.63121i	−0.896291	−	0.371256i	−0.113498	−	0.993538i	$-0.536206\pi$
$673$	−23.2518	−	9.63121i	−0.896291	−	0.371256i	−0.782793	+	0.622282i	$0.786206\pi$
$674$		0			0
$675$	−11.8976	+	4.92816i	−0.457940	+	0.189685i
$676$		0			0
$677$	15.8286	+	38.2137i	0.608344	+	1.46867i	0.864800	+	0.502116i	$0.167445\pi$
$677$	15.8286	+	38.2137i	0.608344	+	1.46867i	−0.256456	+	0.966556i	$0.582555\pi$
$678$		0			0
$679$	−23.4063			−0.898250
$680$		0			0
$681$	27.2216			1.04314
$682$		0			0
$683$	−8.16716	−	19.7173i	−0.312508	−	0.754460i	−0.999611	−	0.0279002i	$-0.991118\pi$
$683$	−8.16716	−	19.7173i	−0.312508	−	0.754460i	0.687103	−	0.726560i	$-0.258882\pi$
$684$		0			0
$685$	8.94755	−	3.70620i	0.341868	−	0.141606i
$686$		0			0
$687$	−26.7624	−	11.0853i	−1.02105	−	0.422932i
$688$		0			0
$689$	16.6383	−	16.6383i	0.633870	−	0.633870i
$690$		0			0
$691$	10.4108	−	25.1338i	0.396044	−	0.956135i	−0.592551	−	0.805533i	$-0.701879\pi$
$691$	10.4108	−	25.1338i	0.396044	−	0.956135i	0.988595	−	0.150602i	$-0.0481210\pi$
$692$		0			0
$693$		−	5.88934i		−	0.223718i
$694$		0			0
$695$	19.2145	+	19.2145i	0.728849	+	0.728849i
$696$		0			0
$697$	−9.22000	+	27.7358i	−0.349232	+	1.05057i
$698$		0			0
$699$	18.5641	+	18.5641i	0.702159	+	0.702159i
$700$		0			0
$701$		−	36.8975i		−	1.39360i	−0.717265	−	0.696800i	$-0.754606\pi$
$701$		−	36.8975i		−	1.39360i	0.717265	−	0.696800i	$-0.245394\pi$
$702$		0			0
$703$	−7.24382	+	17.4881i	−0.273206	+	0.659578i
$704$		0			0
$705$	−47.0414	+	47.0414i	−1.77168	+	1.77168i
$706$		0			0
$707$	−40.6918	−	16.8551i	−1.53037	−	0.633902i
$708$		0			0
$709$	−32.8820	+	13.6202i	−1.23491	+	0.511516i	−0.902120	−	0.431485i	$-0.857990\pi$
$709$	−32.8820	+	13.6202i	−1.23491	+	0.511516i	−0.332789	+	0.943001i	$0.607990\pi$
$710$		0			0
$711$	−8.36588	−	20.1970i	−0.313745	−	0.757448i
$712$		0			0
$713$	−1.06591			−0.0399188
$714$		0			0
$715$	−5.87191			−0.219597
$716$		0			0
$717$	−3.27964	−	7.91775i	−0.122480	−	0.295694i
$718$		0			0
$719$	23.7670	−	9.84462i	0.886360	−	0.367143i	0.107400	−	0.994216i	$-0.465747\pi$
$719$	23.7670	−	9.84462i	0.886360	−	0.367143i	0.778960	+	0.627073i	$0.215747\pi$
$720$		0			0
$721$	−4.43767	−	1.83814i	−0.165267	−	0.0684560i
$722$		0			0
$723$	23.7863	−	23.7863i	0.884620	−	0.884620i
$724$		0			0
$725$	−21.9191	+	52.9174i	−0.814055	+	1.96530i
$726$		0			0
$727$			15.3016i			0.567505i	0.958897	+	0.283753i	$0.0915795\pi$
$727$			15.3016i			0.567505i	−0.958897	+	0.283753i	$0.908421\pi$
$728$		0			0
$729$	−5.16431	−	5.16431i	−0.191271	−	0.191271i
$730$		0			0
$731$	−31.4982	−	27.2731i	−1.16500	−	1.00873i
$732$		0			0
$733$	−26.8539	−	26.8539i	−0.991871	−	0.991871i	0.00809624	−	0.999967i	$-0.497423\pi$
$733$	−26.8539	−	26.8539i	−0.991871	−	0.991871i	−0.999967	+	0.00809624i	$0.997423\pi$
$734$		0			0
$735$		−	4.51580i		−	0.166568i
$736$		0			0
$737$	−1.98295	+	4.78727i	−0.0730430	+	0.176341i
$738$		0			0
$739$	24.8605	−	24.8605i	0.914508	−	0.914508i	−0.0821146	−	0.996623i	$-0.526167\pi$
$739$	24.8605	−	24.8605i	0.914508	−	0.914508i	0.996623	+	0.0821146i	$0.0261673\pi$
$740$		0			0
$741$	−19.1681	−	7.93969i	−0.704158	−	0.291672i
$742$		0			0
$743$	39.6688	−	16.4313i	1.45531	−	0.602808i	0.491852	−	0.870679i	$-0.336320\pi$
$743$	39.6688	−	16.4313i	1.45531	−	0.602808i	0.963455	+	0.267871i	$0.0863202\pi$
$744$		0			0
$745$	−2.36114	−	5.70030i	−0.0865056	−	0.208843i
$746$		0			0
$747$	−29.6299			−1.08410
$748$		0			0
$749$	−2.02821			−0.0741093
$750$		0			0
$751$	7.59323	+	18.3317i	0.277081	+	0.668933i	0.999752	−	0.0222592i	$-0.00708591\pi$
$751$	7.59323	+	18.3317i	0.277081	+	0.668933i	−0.722671	+	0.691192i	$0.757086\pi$
$752$		0			0
$753$	37.0359	−	15.3408i	1.34966	−	0.559049i
$754$		0			0
$755$	−58.3572	−	24.1723i	−2.12384	−	0.879721i
$756$		0			0
$757$	−18.8153	+	18.8153i	−0.683855	+	0.683855i	−0.960867	−	0.277012i	$-0.910656\pi$
$757$	−18.8153	+	18.8153i	−0.683855	+	0.683855i	0.277012	+	0.960867i	$0.410656\pi$
$758$		0			0
$759$	0.447780	−	1.08104i	0.0162534	−	0.0392392i
$760$		0			0
$761$		−	24.9243i		−	0.903505i	−0.892143	−	0.451753i	$-0.850799\pi$
$761$		−	24.9243i		−	0.903505i	0.892143	−	0.451753i	$-0.149201\pi$
$762$		0			0
$763$	−24.6110	−	24.6110i	−0.890978	−	0.890978i
$764$		0			0
$765$	25.9441	+	8.62442i	0.938012	+	0.311817i
$766$		0			0
$767$	−13.3338	−	13.3338i	−0.481455	−	0.481455i
$768$		0			0
$769$			32.9062i			1.18663i	0.804971	+	0.593314i	$0.202181\pi$
$769$			32.9062i			1.18663i	−0.804971	+	0.593314i	$0.797819\pi$
$770$		0			0
$771$	−3.02432	+	7.30135i	−0.108918	+	0.262952i
$772$		0			0
$773$	18.8632	−	18.8632i	0.678463	−	0.678463i	−0.281189	−	0.959652i	$-0.590729\pi$
$773$	18.8632	−	18.8632i	0.678463	−	0.678463i	0.959652	+	0.281189i	$0.0907289\pi$
$774$		0			0
$775$	11.6526	+	4.82665i	0.418573	+	0.173378i
$776$		0			0
$777$	−19.6331	+	8.13230i	−0.704334	+	0.291745i
$778$		0			0
$779$	−14.9296	−	36.0433i	−0.534910	−	1.29139i
$780$		0			0
$781$	6.15439			0.220221
$782$		0			0
$783$	21.6630			0.774172
$784$		0			0
$785$	−19.9285	−	48.1117i	−0.711280	−	1.71718i
$786$		0			0
$787$	−42.2183	+	17.4874i	−1.50492	+	0.623359i	−0.974502	−	0.224378i	$-0.927965\pi$
$787$	−42.2183	+	17.4874i	−1.50492	+	0.623359i	−0.530418	+	0.847736i	$0.677965\pi$
$788$		0			0
$789$	6.62945	+	2.74601i	0.236015	+	0.0977604i
$790$		0			0
$791$	−17.9634	+	17.9634i	−0.638705	+	0.638705i
$792$		0			0
$793$	−4.31980	+	10.4289i	−0.153401	+	0.370342i
$794$		0			0
$795$		−	103.023i		−	3.65386i
$796$		0			0
$797$	9.59546	+	9.59546i	0.339889	+	0.339889i	0.856325	−	0.516437i	$-0.172742\pi$
$797$	9.59546	+	9.59546i	0.339889	+	0.339889i	−0.516437	+	0.856325i	$0.672742\pi$
$798$		0			0
$799$	−37.1168	+	2.66839i	−1.31310	+	0.0944008i
$800$		0			0
$801$	15.3884	+	15.3884i	0.543722	+	0.543722i
$802$		0			0
$803$			0.0138050i			0.000487169i
$804$		0			0
$805$	1.71394	−	4.13782i	0.0604086	−	0.145839i
$806$		0			0
$807$	17.2691	−	17.2691i	0.607902	−	0.607902i
$808$		0			0
$809$	33.0522	+	13.6907i	1.16205	+	0.481339i	0.878558	−	0.477635i	$-0.158506\pi$
$809$	33.0522	+	13.6907i	1.16205	+	0.481339i	0.283496	+	0.958973i	$0.408506\pi$
$810$		0			0
$811$	−3.08402	+	1.27744i	−0.108295	+	0.0448572i	−0.436173	−	0.899863i	$-0.643666\pi$
$811$	−3.08402	+	1.27744i	−0.108295	+	0.0448572i	0.327878	+	0.944720i	$0.393666\pi$
$812$		0			0
$813$	26.7950	+	64.6888i	0.939741	+	2.26874i
$814$		0			0
$815$	30.1248			1.05523
$816$		0			0
$817$	55.6133			1.94566
$818$		0			0
$819$	−3.58082	−	8.64486i	−0.125124	−	0.302076i
$820$		0			0
$821$	12.4758	−	5.16763i	0.435407	−	0.180351i	−0.154204	−	0.988039i	$-0.549281\pi$
$821$	12.4758	−	5.16763i	0.435407	−	0.180351i	0.589611	+	0.807688i	$0.299281\pi$
$822$		0			0
$823$	−22.3841	−	9.27180i	−0.780261	−	0.323195i	−0.0432400	−	0.999065i	$-0.513768\pi$
$823$	−22.3841	−	9.27180i	−0.780261	−	0.323195i	−0.737021	+	0.675870i	$0.763768\pi$
$824$		0			0
$825$	−9.79027	+	9.79027i	−0.340853	+	0.340853i
$826$		0			0
$827$	−18.5777	+	44.8506i	−0.646011	+	1.55961i	0.172431	+	0.985022i	$0.444838\pi$
$827$	−18.5777	+	44.8506i	−0.646011	+	1.55961i	−0.818443	+	0.574588i	$0.805162\pi$
$828$		0			0
$829$			12.5026i			0.434235i	0.976145	+	0.217117i	$0.0696655\pi$
$829$			12.5026i			0.434235i	−0.976145	+	0.217117i	$0.930335\pi$
$830$		0			0
$831$	−20.0803	−	20.0803i	−0.696578	−	0.696578i
$832$		0			0
$833$	1.65346	−	1.90961i	0.0572889	−	0.0661642i
$834$		0			0
$835$	−16.7428	−	16.7428i	−0.579407	−	0.579407i
$836$		0			0
$837$		−	4.77026i		−	0.164884i
$838$		0			0
$839$	−10.5986	+	25.5872i	−0.365903	+	0.883367i	0.628510	+	0.777802i	$0.283665\pi$
$839$	−10.5986	+	25.5872i	−0.365903	+	0.883367i	−0.994412	+	0.105566i	$0.966335\pi$
$840$		0			0
$841$	47.6243	−	47.6243i	1.64222	−	1.64222i
$842$		0			0
$843$	32.9972	+	13.6679i	1.13648	+	0.470747i
$844$		0			0
$845$	30.9153	−	12.8055i	1.06352	−	0.440524i
$846$		0			0
$847$	−10.4290	−	25.1779i	−0.358345	−	0.865121i
$848$		0			0
$849$	−15.8314			−0.543332
$850$		0			0
$851$	−1.69615			−0.0581434
$852$		0			0
$853$	−14.6995	−	35.4876i	−0.503300	−	1.21507i	−0.947676	−	0.319233i	$-0.896575\pi$
$853$	−14.6995	−	35.4876i	−0.503300	−	1.21507i	0.444376	−	0.895840i	$-0.353425\pi$
$854$		0			0
$855$	−33.7151	+	13.9652i	−1.15303	+	0.477601i
$856$		0			0
$857$	−17.3797	−	7.19892i	−0.593681	−	0.245911i	0.0655526	−	0.997849i	$-0.479119\pi$
$857$	−17.3797	−	7.19892i	−0.593681	−	0.245911i	−0.659233	+	0.751939i	$0.729119\pi$
$858$		0			0
$859$	−9.60321	+	9.60321i	−0.327657	+	0.327657i	−0.851695	−	0.524038i	$-0.824425\pi$
$859$	−9.60321	+	9.60321i	−0.327657	+	0.327657i	0.524038	+	0.851695i	$0.324425\pi$
$860$		0			0
$861$	16.7608	−	40.4642i	0.571207	−	1.37901i
$862$		0			0
$863$		−	47.9451i		−	1.63207i	−0.578002	−	0.816035i	$-0.696167\pi$
$863$		−	47.9451i		−	1.63207i	0.578002	−	0.816035i	$-0.303833\pi$
$864$		0			0
$865$	−6.19840	−	6.19840i	−0.210752	−	0.210752i
$866$		0			0
$867$	19.4491	+	32.7247i	0.660526	+	1.11139i
$868$		0			0
$869$	8.13099	+	8.13099i	0.275825	+	0.275825i
$870$		0			0
$871$			8.23281i			0.278958i
$872$		0			0
$873$	−6.53974	+	15.7883i	−0.221337	+	0.534354i
$874$		0			0
$875$	−5.36361	+	5.36361i	−0.181323	+	0.181323i
$876$		0			0
$877$	29.4723	+	12.2078i	0.995207	+	0.412228i	0.820037	−	0.572310i	$-0.193953\pi$
$877$	29.4723	+	12.2078i	0.995207	+	0.412228i	0.175170	+	0.984538i	$0.443953\pi$
$878$		0			0
$879$	13.2741	−	5.49831i	0.447724	−	0.185453i
$880$		0			0
$881$	−6.02818	−	14.5533i	−0.203095	−	0.490314i	0.789212	−	0.614121i	$-0.210489\pi$
$881$	−6.02818	−	14.5533i	−0.203095	−	0.490314i	−0.992306	+	0.123807i	$0.960489\pi$
$882$		0			0
$883$	−26.4467			−0.890001			−0.445000	−	0.895530i	$-0.646796\pi$
$883$	−26.4467			−0.890001			−0.445000	+	0.895530i	$0.646796\pi$
$884$		0			0
$885$	−82.5620			−2.77529
$886$		0			0
$887$	−14.1126	−	34.0707i	−0.473853	−	1.14398i	−0.962447	−	0.271471i	$-0.912490\pi$
$887$	−14.1126	−	34.0707i	−0.473853	−	1.14398i	0.488593	−	0.872512i	$-0.337510\pi$
$888$		0			0
$889$	5.28991	−	2.19115i	0.177418	−	0.0734889i
$890$		0			0
$891$	10.7540	+	4.45447i	0.360274	+	0.149230i
$892$		0			0
$893$	35.1224	−	35.1224i	1.17533	−	1.17533i
$894$		0			0
$895$	18.4250	−	44.4820i	0.615881	−	1.48687i
$896$		0			0
$897$		−	1.85909i		−	0.0620733i
$898$		0			0
$899$	−15.0025	−	15.0025i	−0.500362	−	0.500362i
$900$		0			0
$901$	37.7220	−	43.5659i	1.25670	−	1.45139i
$902$		0			0
$903$	44.1478	+	44.1478i	1.46915	+	1.46915i
$904$		0			0
$905$			38.4263i			1.27733i
$906$		0			0
$907$	12.3557	−	29.8292i	0.410263	−	0.990462i	−0.574804	−	0.818291i	$-0.694922\pi$
$907$	12.3557	−	29.8292i	0.410263	−	0.990462i	0.985067	−	0.172171i	$-0.0550781\pi$
$908$		0			0
$909$	−22.7387	+	22.7387i	−0.754195	+	0.754195i
$910$		0			0
$911$	3.07875	+	1.27526i	0.102004	+	0.0422513i	0.433102	−	0.901345i	$-0.357419\pi$
$911$	3.07875	+	1.27526i	0.102004	+	0.0422513i	−0.331098	+	0.943596i	$0.607419\pi$
$912$		0			0
$913$	14.3990	−	5.96425i	0.476536	−	0.197388i
$914$		0			0
$915$	18.9137	+	45.6616i	0.625266	+	1.50953i
$916$		0			0
$917$	−60.9289			−2.01205
$918$		0			0
$919$	−26.5711			−0.876501			−0.438250	−	0.898853i	$-0.644402\pi$
$919$	−26.5711			−0.876501			−0.438250	+	0.898853i	$0.644402\pi$
$920$		0			0
$921$	26.2807	+	63.4471i	0.865978	+	2.09065i
$922$		0			0
$923$	9.03391	−	3.74197i	0.297355	−	0.123168i
$924$		0			0
$925$	18.5424	+	7.68050i	0.609669	+	0.252533i
$926$		0			0
$927$	−2.47978	+	2.47978i	−0.0814467	+	0.0814467i
$928$		0			0
$929$	−13.6323	+	32.9113i	−0.447262	+	1.07979i	0.526082	+	0.850434i	$0.323661\pi$
$929$	−13.6323	+	32.9113i	−0.447262	+	1.07979i	−0.973344	+	0.229352i	$0.926339\pi$
$930$		0			0
$931$			3.37162i			0.110500i
$932$		0			0
$933$	−24.0639	−	24.0639i	−0.787816	−	0.787816i
$934$		0			0
$935$	−14.3439	+	1.03120i	−0.469095	+	0.0337240i
$936$		0			0
$937$	−37.3294	−	37.3294i	−1.21950	−	1.21950i	−0.967807	−	0.251693i	$-0.919013\pi$
$937$	−37.3294	−	37.3294i	−1.21950	−	1.21950i	−0.251693	−	0.967807i	$-0.580987\pi$
$938$		0			0
$939$		−	5.80085i		−	0.189304i
$940$		0			0
$941$	7.21644	−	17.4220i	0.235249	−	0.567942i	−0.761531	−	0.648129i	$-0.775552\pi$
$941$	7.21644	−	17.4220i	0.235249	−	0.567942i	0.996780	+	0.0801870i	$0.0255518\pi$
$942$		0			0
$943$	2.47190	−	2.47190i	0.0804963	−	0.0804963i
$944$		0			0
$945$	18.5179	+	7.67036i	0.602387	+	0.249517i
$946$		0			0
$947$	38.1862	−	15.8172i	1.24088	−	0.513991i	0.336894	−	0.941543i	$-0.390624\pi$
$947$	38.1862	−	15.8172i	1.24088	−	0.513991i	0.903991	+	0.427551i	$0.140624\pi$
$948$		0			0
$949$	0.00839368	+	0.0202641i	0.000272470	+	0.000657802i
$950$		0			0
$951$	−31.6351			−1.02584
$952$		0			0
$953$	12.3861			0.401227			0.200613	−	0.979671i	$-0.435707\pi$
$953$	12.3861			0.401227			0.200613	+	0.979671i	$0.435707\pi$
$954$		0			0
$955$	22.7687	+	54.9685i	0.736778	+	1.77874i
$956$		0			0
$957$	21.5178	−	8.91297i	0.695572	−	0.288115i
$958$		0			0
$959$	−7.49987	−	3.10655i	−0.242183	−	0.100316i
$960$		0			0
$961$	18.6167	−	18.6167i	0.600539	−	0.600539i
$962$		0			0
$963$	−0.566685	+	1.36810i	−0.0182612	+	0.0440864i
$964$		0			0
$965$		−	4.65318i		−	0.149791i
$966$		0			0
$967$	−1.24879	−	1.24879i	−0.0401584	−	0.0401584i	0.686742	−	0.726901i	$-0.259040\pi$
$967$	−1.24879	−	1.24879i	−0.0401584	−	0.0401584i	−0.726901	+	0.686742i	$0.759040\pi$
$968$		0			0
$969$	−48.2180	−	16.0288i	−1.54899	−	0.514919i
$970$		0			0
$971$	5.74228	+	5.74228i	0.184278	+	0.184278i	0.793217	−	0.608939i	$-0.208405\pi$
$971$	5.74228	+	5.74228i	0.184278	+	0.184278i	−0.608939	+	0.793217i	$0.708405\pi$
$972$		0			0
$973$		−	22.7769i		−	0.730193i
$974$		0			0
$975$	−8.41831	+	20.3236i	−0.269602	+	0.650876i
$976$		0			0
$977$	18.9242	−	18.9242i	0.605439	−	0.605439i	−0.336311	−	0.941751i	$-0.609179\pi$
$977$	18.9242	−	18.9242i	0.605439	−	0.605439i	0.941751	+	0.336311i	$0.109179\pi$
$978$		0			0
$979$	−10.5757	−	4.38061i	−0.338002	−	0.140005i
$980$		0			0
$981$	−23.4773	+	9.72462i	−0.749573	+	0.310483i
$982$		0			0
$983$	5.72176	+	13.8136i	0.182496	+	0.440584i	0.988480	−	0.151354i	$-0.0483632\pi$
$983$	5.72176	+	13.8136i	0.182496	+	0.440584i	−0.805984	+	0.591938i	$0.798363\pi$
$984$		0			0
$985$	−3.85192			−0.122733
$986$		0			0
$987$	55.7629			1.77495
$988$		0			0
$989$	1.90702	+	4.60396i	0.0606398	+	0.146397i
$990$		0			0
$991$	−9.33374	+	3.86616i	−0.296496	+	0.122813i	−0.525973	−	0.850501i	$-0.676299\pi$
$991$	−9.33374	+	3.86616i	−0.296496	+	0.122813i	0.229477	+	0.973314i	$0.426299\pi$
$992$		0			0
$993$	42.2240	+	17.4898i	1.33994	+	0.555021i
$994$		0			0
$995$	−42.4798	+	42.4798i	−1.34670	+	1.34670i
$996$		0			0
$997$	18.0136	−	43.4886i	0.570496	−	1.37730i	−0.330638	−	0.943758i	$-0.607264\pi$
$997$	18.0136	−	43.4886i	0.570496	−	1.37730i	0.901134	−	0.433541i	$-0.142736\pi$
$998$		0			0
$999$		−	7.59075i		−	0.240161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bb.e.321.2	yes	20
4.3	odd	2		544.2.bb.f.321.4	yes	20
17.5	odd	16		9248.2.a.by.1.17		20
17.8	even	8	inner	544.2.bb.e.161.2	✓	20
17.12	odd	16		9248.2.a.by.1.4		20
68.39	even	16		9248.2.a.bz.1.4		20
68.59	odd	8		544.2.bb.f.161.4	yes	20
68.63	even	16		9248.2.a.bz.1.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bb.e.161.2	✓	20	17.8	even	8	inner
544.2.bb.e.321.2	yes	20	1.1	even	1	trivial
544.2.bb.f.161.4	yes	20	68.59	odd	8
544.2.bb.f.321.4	yes	20	4.3	odd	2
9248.2.a.by.1.4		20	17.12	odd	16
9248.2.a.by.1.17		20	17.5	odd	16
9248.2.a.bz.1.4		20	68.39	even	16
9248.2.a.bz.1.17		20	68.63	even	16

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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bb (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.856942 - 2.06884i) q^{3} +(3.04112 - 1.25967i) q^{5} +(-2.54908 - 1.05586i) q^{7} +(-1.42443 + 1.42443i) q^{9} +(0.405492 - 0.978945i) q^{11} -1.68352i q^{13} +(-5.21213 - 5.21213i) q^{15} +(-0.295654 - 4.11249i) q^{17} +(3.89152 + 3.89152i) q^{19} +6.17845i q^{21} +(-0.188717 + 0.455603i) q^{23} +(4.12610 - 4.12610i) q^{25} +(-2.03895 - 0.844559i) q^{27} +(-9.06866 + 3.75636i) q^{29} +(0.827163 + 1.99695i) q^{31} -2.37276 q^{33} -9.08209 q^{35} +(1.31624 + 3.17768i) q^{37} +(-3.48294 + 1.44268i) q^{39} +(-6.54925 - 2.71279i) q^{41} +(7.14546 - 7.14546i) q^{43} +(-2.53755 + 6.12618i) q^{45} -9.02539i q^{47} +(0.433201 + 0.433201i) q^{49} +(-8.25473 + 4.13583i) q^{51} +(9.88305 + 9.88305i) q^{53} -3.48788i q^{55} +(4.71612 - 11.3857i) q^{57} +(7.92018 - 7.92018i) q^{59} +(-6.19471 - 2.56593i) q^{61} +(5.13499 - 2.12698i) q^{63} +(-2.12069 - 5.11979i) q^{65} -4.89023 q^{67} +1.10429 q^{69} +(2.22270 + 5.36608i) q^{71} +(-0.0120368 + 0.00498579i) q^{73} +(-12.0721 - 5.00042i) q^{75} +(-2.06726 + 2.06726i) q^{77} +(-4.15294 + 10.0261i) q^{79} +10.9853i q^{81} +(10.4006 + 10.4006i) q^{83} +(-6.07952 - 12.1342i) q^{85} +(15.5426 + 15.5426i) q^{87} -10.8032i q^{89} +(-1.77757 + 4.29142i) q^{91} +(3.42254 - 3.42254i) q^{93} +(16.7366 + 6.93253i) q^{95} +(7.83754 - 3.24642i) q^{97} +(0.816844 + 1.97204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{9} - 12 q^{11} + 24 q^{15} - 8 q^{17} + 16 q^{23} - 16 q^{25} + 12 q^{27} - 8 q^{29} - 24 q^{31} - 32 q^{35} - 32 q^{37} - 16 q^{41} + 44 q^{43} - 8 q^{49} + 16 q^{53} + 16 q^{57} - 12 q^{59}+ \cdots - 32 q^{99}+O(q^{100}) \) 20 * q + 4 * q^9 - 12 * q^11 + 24 * q^15 - 8 * q^17 + 16 * q^23 - 16 * q^25 + 12 * q^27 - 8 * q^29 - 24 * q^31 - 32 * q^35 - 32 * q^37 - 16 * q^41 + 44 * q^43 - 8 * q^49 + 16 * q^53 + 16 * q^57 - 12 * q^59 - 8 * q^61 - 48 * q^63 + 8 * q^65 + 72 * q^67 - 48 * q^69 + 16 * q^71 + 16 * q^73 - 84 * q^75 - 32 * q^77 - 32 * q^79 + 36 * q^83 + 48 * q^85 + 32 * q^87 + 16 * q^91 + 48 * q^93 + 32 * q^95 + 28 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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