LMFDB - Embedded newform 1120.2.bz.e.271.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 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("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.8
Character	$\chi$	$=$	1120.271
Dual form			1120.2.bz.e.591.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.219454 - 0.126702i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.978876 + 2.45801i) q^{7} +(-1.46789 + 2.54247i) q^{9} +O(q^{10})$	\(q+(0.219454 - 0.126702i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.978876 + 2.45801i) q^{7} +(-1.46789 + 2.54247i) q^{9} +(-1.81455 - 3.14289i) q^{11} +5.36097 q^{13} +0.253404i q^{15} +(-4.46956 + 2.58050i) q^{17} +(-5.49220 - 3.17092i) q^{19} +(0.0966157 + 0.663445i) q^{21} +(-0.231195 - 0.133481i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.50415i q^{27} +2.99647i q^{29} +(-2.72336 - 4.71700i) q^{31} +(-0.796419 - 0.459813i) q^{33} +(-1.63926 - 2.07674i) q^{35} +(-7.48336 - 4.32052i) q^{37} +(1.17649 - 0.679245i) q^{39} +3.46796i q^{41} -5.33960 q^{43} +(-1.46789 - 2.54247i) q^{45} +(-2.26364 + 3.92073i) q^{47} +(-5.08360 - 4.81217i) q^{49} +(-0.653908 + 1.13260i) q^{51} +(3.09705 - 1.78808i) q^{53} +3.62909 q^{55} -1.60705 q^{57} +(-6.83489 + 3.94613i) q^{59} +(-2.63069 + 4.55649i) q^{61} +(-4.81251 - 6.09685i) q^{63} +(-2.68049 + 4.64274i) q^{65} +(-0.963653 - 1.66910i) q^{67} -0.0676490 q^{69} +15.9319i q^{71} +(7.12385 - 4.11296i) q^{73} +(-0.219454 - 0.126702i) q^{75} +(9.50145 - 1.38367i) q^{77} +(9.94273 + 5.74044i) q^{79} +(-4.21310 - 7.29731i) q^{81} +5.75814i q^{83} -5.16100i q^{85} +(0.379658 + 0.657587i) q^{87} +(4.77496 + 2.75683i) q^{89} +(-5.24773 + 13.1773i) q^{91} +(-1.19531 - 0.690110i) q^{93} +(5.49220 - 3.17092i) q^{95} -7.98474i q^{97} +10.6542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.219454	−	0.126702i	0.126702	−	0.0731514i	−0.435309	−	0.900281i	$-0.643361\pi$
$3$	0.219454	−	0.126702i	0.126702	−	0.0731514i	0.562011	+	0.827130i	$0.310028\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.978876	+	2.45801i	−0.369980	+	0.929040i
$7$	−0.978876	+	2.45801i	−0.369980	+	0.929040i
$8$		0			0
$9$	−1.46789	+	2.54247i	−0.489298	+	0.847489i
$10$		0			0
$11$	−1.81455	−	3.14289i	−0.547106	−	0.947616i	−0.998471	−	0.0552761i	$-0.982396\pi$
$11$	−1.81455	−	3.14289i	−0.547106	−	0.947616i	0.451365	−	0.892339i	$-0.350937\pi$
$12$		0			0
$13$	5.36097			1.48687			0.743433	−	0.668810i	$-0.233196\pi$
$13$	5.36097			1.48687			0.743433	+	0.668810i	$0.233196\pi$
$14$		0			0
$15$			0.253404i			0.0654286i
$16$		0			0
$17$	−4.46956	+	2.58050i	−1.08403	+	0.625863i	−0.931980	−	0.362510i	$-0.881920\pi$
$17$	−4.46956	+	2.58050i	−1.08403	+	0.625863i	−0.152047	+	0.988373i	$0.548586\pi$
$18$		0			0
$19$	−5.49220	−	3.17092i	−1.26000	−	0.727460i	−0.286924	−	0.957953i	$-0.592633\pi$
$19$	−5.49220	−	3.17092i	−1.26000	−	0.727460i	−0.973074	+	0.230494i	$0.925966\pi$
$20$		0			0
$21$	0.0966157	+	0.663445i	0.0210833	+	0.144776i
$22$		0			0
$23$	−0.231195	−	0.133481i	−0.0482076	−	0.0278326i	0.475703	−	0.879606i	$-0.342194\pi$
$23$	−0.231195	−	0.133481i	−0.0482076	−	0.0278326i	−0.523910	+	0.851774i	$0.675527\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$			1.50415i			0.289474i
$28$		0			0
$29$			2.99647i			0.556430i	0.960519	+	0.278215i	$0.0897428\pi$
$29$			2.99647i			0.556430i	−0.960519	+	0.278215i	$0.910257\pi$
$30$		0			0
$31$	−2.72336	−	4.71700i	−0.489130	−	0.847199i	0.510791	−	0.859705i	$-0.329352\pi$
$31$	−2.72336	−	4.71700i	−0.489130	−	0.847199i	−0.999922	+	0.0125059i	$0.996019\pi$
$32$		0			0
$33$	−0.796419	−	0.459813i	−0.138639	−	0.0800431i
$34$		0			0
$35$	−1.63926	−	2.07674i	−0.277085	−	0.351032i
$36$		0			0
$37$	−7.48336	−	4.32052i	−1.23026	−	0.710289i	−0.263173	−	0.964749i	$-0.584769\pi$
$37$	−7.48336	−	4.32052i	−1.23026	−	0.710289i	−0.967083	+	0.254460i	$0.918102\pi$
$38$		0			0
$39$	1.17649	−	0.679245i	0.188389	−	0.108766i
$40$		0			0
$41$			3.46796i			0.541604i	0.962635	+	0.270802i	$0.0872889\pi$
$41$			3.46796i			0.541604i	−0.962635	+	0.270802i	$0.912711\pi$
$42$		0			0
$43$	−5.33960			−0.814281			−0.407140	−	0.913366i	$-0.633474\pi$
$43$	−5.33960			−0.814281			−0.407140	+	0.913366i	$0.633474\pi$
$44$		0			0
$45$	−1.46789	−	2.54247i	−0.218821	−	0.379008i
$46$		0			0
$47$	−2.26364	+	3.92073i	−0.330185	+	0.571898i	−0.982548	−	0.186009i	$-0.940445\pi$
$47$	−2.26364	+	3.92073i	−0.330185	+	0.571898i	0.652363	+	0.757907i	$0.273778\pi$
$48$		0			0
$49$	−5.08360	−	4.81217i	−0.726229	−	0.687453i
$50$		0			0
$51$	−0.653908	+	1.13260i	−0.0915655	+	0.158596i
$52$		0			0
$53$	3.09705	−	1.78808i	0.425413	−	0.245612i	−0.271978	−	0.962304i	$-0.587678\pi$
$53$	3.09705	−	1.78808i	0.425413	−	0.245612i	0.697391	+	0.716691i	$0.254344\pi$
$54$		0			0
$55$	3.62909			0.489347
$56$		0			0
$57$	−1.60705			−0.212859
$58$		0			0
$59$	−6.83489	+	3.94613i	−0.889827	+	0.513742i	−0.873886	−	0.486131i	$-0.838408\pi$
$59$	−6.83489	+	3.94613i	−0.889827	+	0.513742i	−0.0159410	+	0.999873i	$0.505074\pi$
$60$		0			0
$61$	−2.63069	+	4.55649i	−0.336825	+	0.583398i	−0.983834	−	0.179084i	$-0.942686\pi$
$61$	−2.63069	+	4.55649i	−0.336825	+	0.583398i	0.647009	+	0.762483i	$0.276020\pi$
$62$		0			0
$63$	−4.81251	−	6.09685i	−0.606320	−	0.768131i
$64$		0			0
$65$	−2.68049	+	4.64274i	−0.332473	+	0.575861i
$66$		0			0
$67$	−0.963653	−	1.66910i	−0.117729	−	0.203913i	0.801138	−	0.598479i	$-0.204228\pi$
$67$	−0.963653	−	1.66910i	−0.117729	−	0.203913i	−0.918867	+	0.394567i	$0.870895\pi$
$68$		0			0
$69$	−0.0676490			−0.00814398
$70$		0			0
$71$			15.9319i			1.89077i	0.325956	+	0.945385i	$0.394314\pi$
$71$			15.9319i			1.89077i	−0.325956	+	0.945385i	$0.605686\pi$
$72$		0			0
$73$	7.12385	−	4.11296i	0.833783	−	0.481385i	−0.0213629	−	0.999772i	$-0.506801\pi$
$73$	7.12385	−	4.11296i	0.833783	−	0.481385i	0.855146	+	0.518387i	$0.173467\pi$
$74$		0			0
$75$	−0.219454	−	0.126702i	−0.0253404	−	0.0146303i
$76$		0			0
$77$	9.50145	−	1.38367i	1.08279	−	0.157684i
$78$		0			0
$79$	9.94273	+	5.74044i	1.11864	+	0.645849i	0.941054	−	0.338255i	$-0.109837\pi$
$79$	9.94273	+	5.74044i	1.11864	+	0.645849i	0.177590	+	0.984105i	$0.443170\pi$
$80$		0			0
$81$	−4.21310	−	7.29731i	−0.468122	−	0.810812i
$82$		0			0
$83$			5.75814i			0.632039i	0.948753	+	0.316019i	$0.102346\pi$
$83$			5.75814i			0.632039i	−0.948753	+	0.316019i	$0.897654\pi$
$84$		0			0
$85$		−	5.16100i		−	0.559789i
$86$		0			0
$87$	0.379658	+	0.657587i	0.0407036	+	0.0705007i
$88$		0			0
$89$	4.77496	+	2.75683i	0.506145	+	0.292223i	0.731248	−	0.682112i	$-0.238938\pi$
$89$	4.77496	+	2.75683i	0.506145	+	0.292223i	−0.225103	+	0.974335i	$0.572272\pi$
$90$		0			0
$91$	−5.24773	+	13.1773i	−0.550111	+	1.38136i
$92$		0			0
$93$	−1.19531	−	0.690110i	−0.123947	−	0.0715611i
$94$		0			0
$95$	5.49220	−	3.17092i	0.563488	−	0.325330i
$96$		0			0
$97$		−	7.98474i		−	0.810727i	−0.914156	−	0.405364i	$-0.867145\pi$
$97$		−	7.98474i		−	0.810727i	0.914156	−	0.405364i	$-0.132855\pi$
$98$		0			0
$99$	10.6542			1.07079
$100$		0			0
$101$	4.74975	+	8.22681i	0.472618	+	0.818598i	0.999509	−	0.0313347i	$-0.00997577\pi$
$101$	4.74975	+	8.22681i	0.472618	+	0.818598i	−0.526891	+	0.849933i	$0.676642\pi$
$102$		0			0
$103$	3.75103	−	6.49697i	0.369600	−	0.640166i	−0.619903	−	0.784678i	$-0.712828\pi$
$103$	3.75103	−	6.49697i	0.369600	−	0.640166i	0.989503	+	0.144513i	$0.0461615\pi$
$104$		0			0
$105$	−0.622868	−	0.248051i	−0.0607857	−	0.0242073i
$106$		0			0
$107$	3.73750	−	6.47354i	0.361318	−	0.625821i	−0.626860	−	0.779132i	$-0.715660\pi$
$107$	3.73750	−	6.47354i	0.361318	−	0.625821i	0.988178	+	0.153311i	$0.0489936\pi$
$108$		0			0
$109$	−16.8873	+	9.74989i	−1.61751	+	0.933870i	−0.629949	+	0.776636i	$0.716924\pi$
$109$	−16.8873	+	9.74989i	−1.61751	+	0.933870i	−0.987561	+	0.157234i	$0.949742\pi$
$110$		0			0
$111$	−2.18967			−0.207834
$112$		0			0
$113$	−20.8176			−1.95836			−0.979179	−	0.202997i	$-0.934932\pi$
$113$	−20.8176			−1.95836			−0.979179	+	0.202997i	$0.934932\pi$
$114$		0			0
$115$	0.231195	−	0.133481i	0.0215591	−	0.0124471i
$116$		0			0
$117$	−7.86933	+	13.6301i	−0.727520	+	1.26010i
$118$		0			0
$119$	−1.96774	−	13.5122i	−0.180383	−	1.23866i
$120$		0			0
$121$	−1.08515	+	1.87954i	−0.0986502	+	0.170867i
$122$		0			0
$123$	0.439397	+	0.761058i	0.0396191	+	0.0686223i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$			8.44123i			0.749038i	0.927219	+	0.374519i	$0.122192\pi$
$127$			8.44123i			0.749038i	−0.927219	+	0.374519i	$0.877808\pi$
$128$		0			0
$129$	−1.17180	+	0.676537i	−0.103171	+	0.0595657i
$130$		0			0
$131$	4.74957	+	2.74216i	0.414972	+	0.239584i	0.692924	−	0.721011i	$-0.256322\pi$
$131$	4.74957	+	2.74216i	0.414972	+	0.239584i	−0.277952	+	0.960595i	$0.589656\pi$
$132$		0			0
$133$	13.1703	−	10.3959i	1.14201	−	0.901441i
$134$		0			0
$135$	−1.30263	−	0.752075i	−0.112113	−	0.0647283i
$136$		0			0
$137$	4.21281	+	7.29680i	0.359925	+	0.623408i	0.987948	−	0.154787i	$-0.0494691\pi$
$137$	4.21281	+	7.29680i	0.359925	+	0.623408i	−0.628023	+	0.778195i	$0.716136\pi$
$138$		0			0
$139$		−	11.5832i		−	0.982472i	−0.871027	−	0.491236i	$-0.836545\pi$
$139$		−	11.5832i		−	0.982472i	0.871027	−	0.491236i	$-0.163455\pi$
$140$		0			0
$141$			1.14723i			0.0966140i
$142$		0			0
$143$	−9.72773	−	16.8489i	−0.813473	−	1.40898i
$144$		0			0
$145$	−2.59502	−	1.49823i	−0.215504	−	0.124422i
$146$		0			0
$147$	−1.72533	−	0.411949i	−0.142303	−	0.0339769i
$148$		0			0
$149$	−10.0102	−	5.77937i	−0.820065	−	0.473465i	0.0303740	−	0.999539i	$-0.490330\pi$
$149$	−10.0102	−	5.77937i	−0.820065	−	0.473465i	−0.850439	+	0.526074i	$0.823664\pi$
$150$		0			0
$151$	−13.9344	+	8.04501i	−1.13396	+	0.654694i	−0.944929	−	0.327276i	$-0.893869\pi$
$151$	−13.9344	+	8.04501i	−1.13396	+	0.654694i	−0.189035	+	0.981970i	$0.560536\pi$
$152$		0			0
$153$		−	15.1516i		−	1.22493i
$154$		0			0
$155$	5.44673			0.437492
$156$		0			0
$157$	1.07894	+	1.86877i	0.0861086	+	0.149144i	0.905863	−	0.423571i	$-0.139223\pi$
$157$	1.07894	+	1.86877i	0.0861086	+	0.149144i	−0.819754	+	0.572715i	$0.805890\pi$
$158$		0			0
$159$	0.453107	−	0.784805i	0.0359337	−	0.0622391i
$160$		0			0
$161$	0.554408	−	0.437619i	0.0436935	−	0.0344892i
$162$		0			0
$163$	−0.598474	+	1.03659i	−0.0468761	+	0.0811918i	−0.888511	−	0.458854i	$-0.848260\pi$
$163$	−0.598474	+	1.03659i	−0.0468761	+	0.0811918i	0.841635	+	0.540046i	$0.181593\pi$
$164$		0			0
$165$	0.796419	−	0.459813i	0.0620011	−	0.0357964i
$166$		0			0
$167$	13.0622			1.01079			0.505393	−	0.862889i	$-0.331347\pi$
$167$	13.0622			1.01079			0.505393	+	0.862889i	$0.331347\pi$
$168$		0			0
$169$	15.7400			1.21077
$170$		0			0
$171$	16.1239	−	9.30916i	1.23303	−	0.711889i
$172$		0			0
$173$	12.3607	−	21.4093i	0.939764	−	1.62772i	0.173854	−	0.984771i	$-0.444378\pi$
$173$	12.3607	−	21.4093i	0.939764	−	1.62772i	0.765910	−	0.642948i	$-0.222289\pi$
$174$		0			0
$175$	2.61814	−	0.381272i	0.197912	−	0.0288215i
$176$		0			0
$177$	−0.999963	+	1.73199i	−0.0751618	+	0.130184i
$178$		0			0
$179$	6.48006	+	11.2238i	0.484342	+	0.838905i	0.999838	−	0.0179868i	$-0.00572569\pi$
$179$	6.48006	+	11.2238i	0.484342	+	0.838905i	−0.515496	+	0.856892i	$0.672392\pi$
$180$		0			0
$181$	10.5665			0.785403			0.392702	−	0.919666i	$-0.371541\pi$
$181$	10.5665			0.785403			0.392702	+	0.919666i	$0.371541\pi$
$182$		0			0
$183$			1.33325i			0.0985569i
$184$		0			0
$185$	7.48336	−	4.32052i	0.550187	−	0.317651i
$186$		0			0
$187$	16.2204	+	9.36487i	1.18616	+	0.684827i
$188$		0			0
$189$	−3.69721	−	1.47238i	−0.268933	−	0.107100i
$190$		0			0
$191$	−3.42981	−	1.98020i	−0.248173	−	0.143282i	0.370755	−	0.928731i	$-0.379099\pi$
$191$	−3.42981	−	1.98020i	−0.248173	−	0.143282i	−0.618927	+	0.785448i	$0.712432\pi$
$192$		0			0
$193$	7.14531	+	12.3760i	0.514330	+	0.890846i	0.999862	+	0.0166270i	$0.00529279\pi$
$193$	7.14531	+	12.3760i	0.514330	+	0.890846i	−0.485531	+	0.874219i	$0.661374\pi$
$194$		0			0
$195$			1.35849i			0.0972835i
$196$		0			0
$197$			4.05223i			0.288709i	0.989526	+	0.144355i	$0.0461106\pi$
$197$			4.05223i			0.288709i	−0.989526	+	0.144355i	$0.953889\pi$
$198$		0			0
$199$	1.37120	+	2.37499i	0.0972020	+	0.168359i	0.910525	−	0.413453i	$-0.135677\pi$
$199$	1.37120	+	2.37499i	0.0972020	+	0.168359i	−0.813324	+	0.581812i	$0.802344\pi$
$200$		0			0
$201$	−0.422955	−	0.244193i	−0.0298330	−	0.0172241i
$202$		0			0
$203$	−7.36534	−	2.93317i	−0.516946	−	0.205868i
$204$		0			0
$205$	−3.00334	−	1.73398i	−0.209762	−	0.121106i
$206$		0			0
$207$	0.678740	−	0.391871i	0.0471757	−	0.0272369i
$208$		0			0
$209$			23.0151i			1.59199i
$210$		0			0
$211$	2.41112			0.165988			0.0829942	−	0.996550i	$-0.473552\pi$
$211$	2.41112			0.165988			0.0829942	+	0.996550i	$0.473552\pi$
$212$		0			0
$213$	2.01860	+	3.49632i	0.138312	+	0.239564i
$214$		0			0
$215$	2.66980	−	4.62422i	0.182079	−	0.315370i
$216$		0			0
$217$	14.2603	−	2.07668i	0.968050	−	0.140975i
$218$		0			0
$219$	1.04224	−	1.80521i	0.0704279	−	0.121985i
$220$		0			0
$221$	−23.9612	+	13.8340i	−1.61180	+	0.930575i
$222$		0			0
$223$	19.8843			1.33155			0.665774	−	0.746153i	$-0.268101\pi$
$223$	19.8843			1.33155			0.665774	+	0.746153i	$0.268101\pi$
$224$		0			0
$225$	2.93579			0.195719
$226$		0			0
$227$	−21.4464	+	12.3821i	−1.42345	+	0.821827i	−0.996592	−	0.0824926i	$-0.973712\pi$
$227$	−21.4464	+	12.3821i	−1.42345	+	0.821827i	−0.426855	+	0.904320i	$0.640379\pi$
$228$		0			0
$229$	5.98187	−	10.3609i	0.395293	−	0.684668i	−0.597845	−	0.801612i	$-0.703976\pi$
$229$	5.98187	−	10.3609i	0.395293	−	0.684668i	0.993139	+	0.116943i	$0.0373096\pi$
$230$		0			0
$231$	1.90982	−	1.50750i	0.125657	−	0.0991865i
$232$		0			0
$233$	5.54956	−	9.61212i	0.363564	−	0.629711i	−0.624981	−	0.780640i	$-0.714893\pi$
$233$	5.54956	−	9.61212i	0.363564	−	0.629711i	0.988545	+	0.150929i	$0.0482265\pi$
$234$		0			0
$235$	−2.26364	−	3.92073i	−0.147663	−	0.255760i
$236$		0			0
$237$	2.90930			0.188979
$238$		0			0
$239$			24.8172i			1.60529i	0.596455	+	0.802646i	$0.296575\pi$
$239$			24.8172i			1.60529i	−0.596455	+	0.802646i	$0.703425\pi$
$240$		0			0
$241$	9.84971	−	5.68673i	0.634475	−	0.366315i	−0.148008	−	0.988986i	$-0.547286\pi$
$241$	9.84971	−	5.68673i	0.634475	−	0.366315i	0.782483	+	0.622672i	$0.213953\pi$
$242$		0			0
$243$	−5.75706	−	3.32384i	−0.369316	−	0.213225i
$244$		0			0
$245$	6.70926	−	1.99644i	0.428639	−	0.127548i
$246$		0			0
$247$	−29.4435	−	16.9992i	−1.87345	−	1.08164i
$248$		0			0
$249$	0.729568	+	1.26365i	0.0462345	+	0.0800805i
$250$		0			0
$251$		−	8.98434i		−	0.567087i	−0.958959	−	0.283543i	$-0.908490\pi$
$251$		−	8.98434i		−	0.567087i	0.958959	−	0.283543i	$-0.0915100\pi$
$252$		0			0
$253$			0.968827i			0.0609096i
$254$		0			0
$255$	−0.653908	−	1.13260i	−0.0409493	−	0.0709263i
$256$		0			0
$257$	−2.10401	−	1.21475i	−0.131244	−	0.0757740i	0.432940	−	0.901423i	$-0.357476\pi$
$257$	−2.10401	−	1.21475i	−0.131244	−	0.0757740i	−0.564185	+	0.825649i	$0.690809\pi$
$258$		0			0
$259$	17.9451	−	14.1649i	1.11506	−	0.880164i
$260$		0			0
$261$	−7.61842	−	4.39850i	−0.471568	−	0.272260i
$262$		0			0
$263$	1.99243	−	1.15033i	0.122858	−	0.0709323i	−0.437311	−	0.899310i	$-0.644069\pi$
$263$	1.99243	−	1.15033i	0.122858	−	0.0709323i	0.560170	+	0.828378i	$0.310736\pi$
$264$		0			0
$265$			3.57617i			0.219682i
$266$		0			0
$267$	1.39718			0.0855060
$268$		0			0
$269$	0.609154	+	1.05509i	0.0371408	+	0.0643297i	0.883998	−	0.467490i	$-0.154842\pi$
$269$	0.609154	+	1.05509i	0.0371408	+	0.0643297i	−0.846857	+	0.531820i	$0.821508\pi$
$270$		0			0
$271$	−12.1092	+	20.9738i	−0.735582	+	1.27406i	0.218886	+	0.975750i	$0.429758\pi$
$271$	−12.1092	+	20.9738i	−0.735582	+	1.27406i	−0.954468	+	0.298314i	$0.903576\pi$
$272$		0			0
$273$	0.517954	+	3.55671i	0.0313480	+	0.215262i
$274$		0			0
$275$	−1.81455	+	3.14289i	−0.109421	+	0.189523i
$276$		0			0
$277$	−7.22720	+	4.17263i	−0.434240	+	0.250709i	−0.701151	−	0.713012i	$-0.747330\pi$
$277$	−7.22720	+	4.17263i	−0.434240	+	0.250709i	0.266911	+	0.963721i	$0.413997\pi$
$278$		0			0
$279$	15.9904			0.957322
$280$		0			0
$281$	19.8252			1.18267			0.591337	−	0.806425i	$-0.298600\pi$
$281$	19.8252			1.18267			0.591337	+	0.806425i	$0.298600\pi$
$282$		0			0
$283$	8.33705	−	4.81340i	0.495586	−	0.286127i	−0.231303	−	0.972882i	$-0.574299\pi$
$283$	8.33705	−	4.81340i	0.495586	−	0.286127i	0.726889	+	0.686755i	$0.240965\pi$
$284$		0			0
$285$	0.803524	−	1.39174i	0.0475966	−	0.0824398i
$286$		0			0
$287$	−8.52427	−	3.39470i	−0.503172	−	0.200383i
$288$		0			0
$289$	4.81796	−	8.34495i	0.283409	−	0.490879i
$290$		0			0
$291$	−1.01168	−	1.75228i	−0.0593058	−	0.102721i
$292$		0			0
$293$	0.487956			0.0285067			0.0142534	−	0.999898i	$-0.495463\pi$
$293$	0.487956			0.0285067			0.0142534	+	0.999898i	$0.495463\pi$
$294$		0			0
$295$		−	7.89225i		−	0.459505i
$296$		0			0
$297$	4.72737	−	2.72935i	0.274310	−	0.158373i
$298$		0			0
$299$	−1.23943	−	0.715586i	−0.0716782	−	0.0413834i
$300$		0			0
$301$	5.22680	−	13.1248i	0.301268	−	0.756499i
$302$		0			0
$303$	2.08470	+	1.20360i	0.119763	+	0.0691453i
$304$		0			0
$305$	−2.63069	−	4.55649i	−0.150633	−	0.260904i
$306$		0			0
$307$		−	11.8335i		−	0.675376i	−0.941258	−	0.337688i	$-0.890355\pi$
$307$		−	11.8335i		−	0.675376i	0.941258	−	0.337688i	$-0.109645\pi$
$308$		0			0
$309$		−	1.90105i		−	0.108147i
$310$		0			0
$311$	−2.29486	−	3.97481i	−0.130129	−	0.225391i	0.793597	−	0.608444i	$-0.208206\pi$
$311$	−2.29486	−	3.97481i	−0.130129	−	0.225391i	−0.923726	+	0.383053i	$0.874873\pi$
$312$		0			0
$313$	17.7907	+	10.2714i	1.00559	+	0.580577i	0.909897	−	0.414834i	$-0.136160\pi$
$313$	17.7907	+	10.2714i	1.00559	+	0.580577i	0.0956913	+	0.995411i	$0.469494\pi$
$314$		0			0
$315$	7.68629	−	1.11933i	0.433073	−	0.0630673i
$316$		0			0
$317$	6.76332	+	3.90481i	0.379866	+	0.219316i	0.677760	−	0.735283i	$-0.262951\pi$
$317$	6.76332	+	3.90481i	0.379866	+	0.219316i	−0.297894	+	0.954599i	$0.596284\pi$
$318$		0			0
$319$	9.41755	−	5.43723i	0.527282	−	0.304426i
$320$		0			0
$321$		−	1.89419i		−	0.105724i
$322$		0			0
$323$	32.7303			1.82116
$324$		0			0
$325$	−2.68049	−	4.64274i	−0.148687	−	0.257533i
$326$		0			0
$327$	−2.47066	+	4.27931i	−0.136628	+	0.236646i
$328$		0			0
$329$	−7.42137	−	9.40195i	−0.409153	−	0.518346i
$330$		0			0
$331$	−6.35126	+	11.0007i	−0.349097	+	0.604654i	−0.986089	−	0.166216i	$-0.946845\pi$
$331$	−6.35126	+	11.0007i	−0.349097	+	0.604654i	0.636992	+	0.770870i	$0.280178\pi$
$332$		0			0
$333$	21.9695	−	12.6841i	1.20392	−	0.695085i
$334$		0			0
$335$	1.92731			0.105300
$336$		0			0
$337$	13.8789			0.756033			0.378016	−	0.925799i	$-0.376606\pi$
$337$	13.8789			0.756033			0.378016	+	0.925799i	$0.376606\pi$
$338$		0			0
$339$	−4.56852	+	2.63763i	−0.248128	+	0.143257i
$340$		0			0
$341$	−9.88333	+	17.1184i	−0.535213	+	0.927015i
$342$		0			0
$343$	16.8046	−	7.78501i	0.907362	−	0.420351i
$344$		0			0
$345$	0.0338245	−	0.0585857i	0.00182105	−	0.00315415i
$346$		0			0
$347$	6.43516	+	11.1460i	0.345457	+	0.598350i	0.985437	−	0.170042i	$-0.0543905\pi$
$347$	6.43516	+	11.1460i	0.345457	+	0.598350i	−0.639979	+	0.768392i	$0.721057\pi$
$348$		0			0
$349$	21.0526			1.12692			0.563460	−	0.826143i	$-0.309470\pi$
$349$	21.0526			1.12692			0.563460	+	0.826143i	$0.309470\pi$
$350$		0			0
$351$			8.06371i			0.430409i
$352$		0			0
$353$	−25.8483	+	14.9235i	−1.37577	+	0.794298i	−0.991647	−	0.128985i	$-0.958828\pi$
$353$	−25.8483	+	14.9235i	−1.37577	+	0.794298i	−0.384119	+	0.923284i	$0.625495\pi$
$354$		0			0
$355$	−13.7974	−	7.96595i	−0.732292	−	0.422789i
$356$		0			0
$357$	−2.14385	−	2.71599i	−0.113465	−	0.143745i
$358$		0			0
$359$	−16.5346	−	9.54628i	−0.872665	−	0.503833i	−0.00443178	−	0.999990i	$-0.501411\pi$
$359$	−16.5346	−	9.54628i	−0.872665	−	0.503833i	−0.868233	+	0.496157i	$0.834744\pi$
$360$		0			0
$361$	10.6095	+	18.3762i	0.558396	+	0.967169i
$362$		0			0
$363$			0.549963i			0.0288656i
$364$		0			0
$365$			8.22591i			0.430564i
$366$		0			0
$367$	−4.90832	−	8.50146i	−0.256212	−	0.443773i	0.709012	−	0.705197i	$-0.249141\pi$
$367$	−4.90832	−	8.50146i	−0.256212	−	0.443773i	−0.965224	+	0.261424i	$0.915808\pi$
$368$		0			0
$369$	−8.81717	−	5.09059i	−0.459003	−	0.265006i
$370$		0			0
$371$	1.36349	+	9.36290i	0.0707890	+	0.486097i
$372$		0			0
$373$	−20.2929	−	11.7161i	−1.05072	−	0.606636i	−0.127873	−	0.991791i	$-0.540815\pi$
$373$	−20.2929	−	11.7161i	−1.05072	−	0.606636i	−0.922852	+	0.385154i	$0.874148\pi$
$374$		0			0
$375$	0.219454	−	0.126702i	0.0113326	−	0.00654286i
$376$		0			0
$377$			16.0640i			0.827337i
$378$		0			0
$379$	−10.7259			−0.550954			−0.275477	−	0.961308i	$-0.588836\pi$
$379$	−10.7259			−0.550954			−0.275477	+	0.961308i	$0.588836\pi$
$380$		0			0
$381$	1.06952	+	1.85246i	0.0547932	+	0.0949046i
$382$		0			0
$383$	−0.700673	+	1.21360i	−0.0358027	+	0.0620122i	−0.883372	−	0.468673i	$-0.844732\pi$
$383$	−0.700673	+	1.21360i	−0.0358027	+	0.0620122i	0.847569	+	0.530686i	$0.178065\pi$
$384$		0			0
$385$	−3.55243	+	8.92033i	−0.181049	+	0.454622i
$386$		0			0
$387$	7.83796	−	13.5757i	0.398426	−	0.690094i
$388$		0			0
$389$	2.49049	−	1.43789i	0.126273	−	0.0729037i	−0.435533	−	0.900173i	$-0.643440\pi$
$389$	2.49049	−	1.43789i	0.126273	−	0.0729037i	0.561806	+	0.827269i	$0.310107\pi$
$390$		0			0
$391$	1.37779			0.0696777
$392$		0			0
$393$	1.38975			0.0701036
$394$		0			0
$395$	−9.94273	+	5.74044i	−0.500273	+	0.288833i
$396$		0			0
$397$	−1.26251	+	2.18672i	−0.0633633	+	0.109749i	−0.895967	−	0.444121i	$-0.853516\pi$
$397$	−1.26251	+	2.18672i	−0.0633633	+	0.109749i	0.832603	+	0.553870i	$0.186849\pi$
$398$		0			0
$399$	1.57310	−	3.95014i	0.0787536	−	0.197754i
$400$		0			0
$401$	−19.3792	+	33.5657i	−0.967749	+	1.67619i	−0.265707	+	0.964054i	$0.585606\pi$
$401$	−19.3792	+	33.5657i	−0.967749	+	1.67619i	−0.702041	+	0.712136i	$0.747728\pi$
$402$		0			0
$403$	−14.5999	−	25.2877i	−0.727271	−	1.25967i
$404$		0			0
$405$	8.42620			0.418701
$406$		0			0
$407$			31.3591i			1.55441i
$408$		0			0
$409$	2.68850	−	1.55221i	0.132938	−	0.0767518i	−0.432056	−	0.901847i	$-0.642212\pi$
$409$	2.68850	−	1.55221i	0.132938	−	0.0767518i	0.564994	+	0.825095i	$0.308878\pi$
$410$		0			0
$411$	1.84904	+	1.06754i	0.0912062	+	0.0526579i
$412$		0			0
$413$	−3.00909	−	20.6630i	−0.148068	−	1.01676i
$414$		0			0
$415$	−4.98670	−	2.87907i	−0.244787	−	0.141328i
$416$		0			0
$417$	−1.46761	−	2.54197i	−0.0718691	−	0.124481i
$418$		0			0
$419$			11.1649i			0.545441i	0.962093	+	0.272720i	$0.0879234\pi$
$419$			11.1649i			0.545441i	−0.962093	+	0.272720i	$0.912077\pi$
$420$		0			0
$421$			35.1106i			1.71119i	0.517648	+	0.855594i	$0.326808\pi$
$421$			35.1106i			1.71119i	−0.517648	+	0.855594i	$0.673192\pi$
$422$		0			0
$423$	−6.64555	−	11.5104i	−0.323118	−	0.559656i
$424$		0			0
$425$	4.46956	+	2.58050i	0.216805	+	0.125173i
$426$		0			0
$427$	−8.62476	−	10.9265i	−0.417381	−	0.528770i
$428$		0			0
$429$	−4.26958	−	2.46504i	−0.206137	−	0.119013i
$430$		0			0
$431$	12.4675	−	7.19809i	0.600536	−	0.346720i	−0.168716	−	0.985665i	$-0.553962\pi$
$431$	12.4675	−	7.19809i	0.600536	−	0.346720i	0.769253	+	0.638945i	$0.220629\pi$
$432$		0			0
$433$		−	36.8668i		−	1.77171i	−0.463967	−	0.885853i	$-0.653574\pi$
$433$		−	36.8668i		−	1.77171i	0.463967	−	0.885853i	$-0.346426\pi$
$434$		0			0
$435$	−0.759316			−0.0364064
$436$		0			0
$437$	0.846514	+	1.46621i	0.0404943	+	0.0701381i
$438$		0			0
$439$	−18.4785	+	32.0057i	−0.881930	+	1.52755i	−0.0327369	+	0.999464i	$0.510422\pi$
$439$	−18.4785	+	32.0057i	−0.881930	+	1.52755i	−0.849193	+	0.528083i	$0.822911\pi$
$440$		0			0
$441$	19.6970	−	5.86113i	0.937951	−	0.279101i
$442$		0			0
$443$	−10.7895	+	18.6880i	−0.512626	+	0.887895i	0.487267	+	0.873253i	$0.337994\pi$
$443$	−10.7895	+	18.6880i	−0.512626	+	0.887895i	−0.999893	+	0.0146414i	$0.995339\pi$
$444$		0			0
$445$	−4.77496	+	2.75683i	−0.226355	+	0.130686i
$446$		0			0
$447$	−2.92903			−0.138538
$448$		0			0
$449$	−31.7876			−1.50015			−0.750075	−	0.661353i	$-0.769983\pi$
$449$	−31.7876			−1.50015			−0.750075	+	0.661353i	$0.769983\pi$
$450$		0			0
$451$	10.8994	−	6.29277i	0.513233	−	0.296315i
$452$		0			0
$453$	−2.03864	+	3.53102i	−0.0957835	+	0.165902i
$454$		0			0
$455$	−8.78802	−	11.1333i	−0.411989	−	0.521938i
$456$		0			0
$457$	11.5642	−	20.0298i	0.540950	−	0.936954i	−0.457899	−	0.889004i	$-0.651398\pi$
$457$	11.5642	−	20.0298i	0.540950	−	0.936954i	0.998850	−	0.0479496i	$-0.0152687\pi$
$458$		0			0
$459$	−3.88146	−	6.72289i	−0.181171	−	0.313797i
$460$		0			0
$461$	−9.98126			−0.464874			−0.232437	−	0.972611i	$-0.574670\pi$
$461$	−9.98126			−0.464874			−0.232437	+	0.972611i	$0.574670\pi$
$462$		0			0
$463$		−	24.3501i		−	1.13165i	−0.824527	−	0.565823i	$-0.808558\pi$
$463$		−	24.3501i		−	1.13165i	0.824527	−	0.565823i	$-0.191442\pi$
$464$		0			0
$465$	1.19531	−	0.690110i	0.0554310	−	0.0320031i
$466$		0			0
$467$	22.6077	+	13.0525i	1.04616	+	0.604000i	0.921571	−	0.388209i	$-0.126906\pi$
$467$	22.6077	+	13.0525i	1.04616	+	0.604000i	0.124587	+	0.992209i	$0.460239\pi$
$468$		0			0
$469$	5.04595	−	0.734828i	0.233000	−	0.0339312i
$470$		0			0
$471$	0.473554	+	0.273407i	0.0218202	+	0.0125979i
$472$		0			0
$473$	9.68894	+	16.7817i	0.445498	+	0.771625i
$474$		0			0
$475$			6.34185i			0.290984i
$476$		0			0
$477$			10.4989i			0.480710i
$478$		0			0
$479$	−3.24704	−	5.62403i	−0.148361	−	0.256969i	0.782261	−	0.622951i	$-0.214066\pi$
$479$	−3.24704	−	5.62403i	−0.148361	−	0.256969i	−0.930622	+	0.365982i	$0.880733\pi$
$480$		0			0
$481$	−40.1181	−	23.1622i	−1.82923	−	1.05610i
$482$		0			0
$483$	0.0662200	−	0.166282i	0.00301311	−	0.00756608i
$484$		0			0
$485$	6.91499	+	3.99237i	0.313993	+	0.181284i
$486$		0			0
$487$	0.244780	−	0.141324i	0.0110921	−	0.00640400i	−0.494444	−	0.869210i	$-0.664628\pi$
$487$	0.244780	−	0.141324i	0.0110921	−	0.00640400i	0.505536	+	0.862806i	$0.331295\pi$
$488$		0			0
$489$			0.303311i			0.0137162i
$490$		0			0
$491$	−18.1902			−0.820912			−0.410456	−	0.911880i	$-0.634630\pi$
$491$	−18.1902			−0.820912			−0.410456	+	0.911880i	$0.634630\pi$
$492$		0			0
$493$	−7.73239	−	13.3929i	−0.348249	−	0.603185i
$494$		0			0
$495$	−5.32712	+	9.22684i	−0.239436	+	0.414716i
$496$		0			0
$497$	−39.1607	−	15.5954i	−1.75660	−	0.699548i
$498$		0			0
$499$	0.608016	−	1.05312i	0.0272185	−	0.0471439i	−0.852095	−	0.523387i	$-0.824668\pi$
$499$	0.608016	−	1.05312i	0.0272185	−	0.0471439i	0.879314	+	0.476243i	$0.158002\pi$
$500$		0			0
$501$	2.86656	−	1.65501i	0.128069	−	0.0739404i
$502$		0			0
$503$	37.9355			1.69146			0.845729	−	0.533612i	$-0.179166\pi$
$503$	37.9355			1.69146			0.845729	+	0.533612i	$0.179166\pi$
$504$		0			0
$505$	−9.49950			−0.422722
$506$		0			0
$507$	3.45421	−	1.99429i	0.153407	−	0.0885695i
$508$		0			0
$509$	−5.30256	+	9.18430i	−0.235032	+	0.407087i	−0.959282	−	0.282450i	$-0.908853\pi$
$509$	−5.30256	+	9.18430i	−0.235032	+	0.407087i	0.724250	+	0.689537i	$0.242186\pi$
$510$		0			0
$511$	3.13631	+	21.5365i	0.138742	+	0.952721i
$512$		0			0
$513$	4.76955	−	8.26110i	0.210581	−	0.364736i
$514$		0			0
$515$	3.75103	+	6.49697i	0.165290	+	0.286291i
$516$		0			0
$517$	16.4299			0.722585
$518$		0			0
$519$		−	6.26448i		−	0.274980i
$520$		0			0
$521$	−1.18563	+	0.684522i	−0.0519432	+	0.0299894i	−0.525747	−	0.850641i	$-0.676214\pi$
$521$	−1.18563	+	0.684522i	−0.0519432	+	0.0299894i	0.473803	+	0.880631i	$0.342881\pi$
$522$		0			0
$523$	1.24052	+	0.716212i	0.0542439	+	0.0313178i	0.526877	−	0.849942i	$-0.323363\pi$
$523$	1.24052	+	0.716212i	0.0542439	+	0.0313178i	−0.472633	+	0.881259i	$0.656696\pi$
$524$		0			0
$525$	0.526253	−	0.415394i	0.0229675	−	0.0181293i
$526$		0			0
$527$	24.3445	+	14.0553i	1.06046	+	0.612257i
$528$		0			0
$529$	−11.4644	−	19.8569i	−0.498451	−	0.863342i
$530$		0			0
$531$		−	23.1700i		−	1.00549i
$532$		0			0
$533$			18.5916i			0.805293i
$534$		0			0
$535$	3.73750	+	6.47354i	0.161586	+	0.279876i
$536$		0			0
$537$	2.84415	+	1.64207i	0.122734	+	0.0708606i
$538$		0			0
$539$	−5.89967	+	24.7091i	−0.254117	+	1.06430i
$540$		0			0
$541$	−1.20272	−	0.694390i	−0.0517089	−	0.0298542i	0.473923	−	0.880566i	$-0.342838\pi$
$541$	−1.20272	−	0.694390i	−0.0517089	−	0.0298542i	−0.525632	+	0.850712i	$0.676171\pi$
$542$		0			0
$543$	2.31887	−	1.33880i	0.0995120	−	0.0574533i
$544$		0			0
$545$		−	19.4998i		−	0.835279i
$546$		0			0
$547$	−43.0700			−1.84154			−0.920770	−	0.390106i	$-0.872438\pi$
$547$	−43.0700			−1.84154			−0.920770	+	0.390106i	$0.872438\pi$
$548$		0			0
$549$	−7.72314	−	13.3769i	−0.329616	−	0.570911i
$550$		0			0
$551$	9.50157	−	16.4572i	0.404781	−	0.701100i
$552$		0			0
$553$	−23.8427	+	18.8201i	−1.01390	+	0.800313i
$554$		0			0
$555$	1.09484	−	1.89631i	0.0464732	−	0.0804939i
$556$		0			0
$557$	−20.0779	+	11.5920i	−0.850727	+	0.491167i	−0.860896	−	0.508781i	$-0.830096\pi$
$557$	−20.0779	+	11.5920i	−0.850727	+	0.491167i	0.0101693	+	0.999948i	$0.496763\pi$
$558$		0			0
$559$	−28.6254			−1.21073
$560$		0			0
$561$	4.74619			0.200384
$562$		0			0
$563$	−20.3256	+	11.7350i	−0.856620	+	0.494570i	−0.862879	−	0.505410i	$-0.831341\pi$
$563$	−20.3256	+	11.7350i	−0.856620	+	0.494570i	0.00625865	+	0.999980i	$0.498008\pi$
$564$		0			0
$565$	10.4088	−	18.0286i	0.437902	−	0.758469i
$566$		0			0
$567$	22.0609	−	3.21268i	0.926472	−	0.134920i
$568$		0			0
$569$	1.75158	−	3.03382i	0.0734300	−	0.127185i	−0.826972	−	0.562242i	$-0.809939\pi$
$569$	1.75158	−	3.03382i	0.0734300	−	0.127185i	0.900402	+	0.435058i	$0.143272\pi$
$570$		0			0
$571$	6.67971	+	11.5696i	0.279537	+	0.484172i	0.971270	−	0.237981i	$-0.0764857\pi$
$571$	6.67971	+	11.5696i	0.279537	+	0.484172i	−0.691733	+	0.722154i	$0.743152\pi$
$572$		0			0
$573$	−1.00358			−0.0419252
$574$		0			0
$575$			0.266961i			0.0111331i
$576$		0			0
$577$	−29.5233	+	17.0453i	−1.22907	+	0.709604i	−0.966835	−	0.255401i	$-0.917793\pi$
$577$	−29.5233	+	17.0453i	−1.22907	+	0.709604i	−0.262234	+	0.965004i	$0.584459\pi$
$578$		0			0
$579$	3.13613	+	1.81065i	0.130333	+	0.0752479i
$580$		0			0
$581$	−14.1536	−	5.63651i	−0.587189	−	0.233842i
$582$		0			0
$583$	−11.2395	−	6.48912i	−0.465492	−	0.268752i
$584$		0			0
$585$	−7.86933	−	13.6301i	−0.325357	−	0.563535i
$586$		0			0
$587$			8.77581i			0.362216i	0.983463	+	0.181108i	$0.0579684\pi$
$587$			8.77581i			0.362216i	−0.983463	+	0.181108i	$0.942032\pi$
$588$		0			0
$589$			34.5423i			1.42329i
$590$		0			0
$591$	0.513425	+	0.889277i	0.0211195	+	0.0365800i
$592$		0			0
$593$	−5.54851	−	3.20343i	−0.227850	−	0.131549i	0.381730	−	0.924274i	$-0.375328\pi$
$593$	−5.54851	−	3.20343i	−0.227850	−	0.131549i	−0.609580	+	0.792725i	$0.708662\pi$
$594$		0			0
$595$	12.6858	+	5.05198i	0.520066	+	0.207111i
$596$		0			0
$597$	0.601832	+	0.347468i	0.0246313	+	0.0142209i
$598$		0			0
$599$	−13.6488	+	7.88017i	−0.557677	+	0.321975i	−0.752213	−	0.658921i	$-0.771013\pi$
$599$	−13.6488	+	7.88017i	−0.557677	+	0.321975i	0.194536	+	0.980895i	$0.437680\pi$
$600$		0			0
$601$		−	23.5644i		−	0.961213i	−0.876936	−	0.480606i	$-0.840417\pi$
$601$		−	23.5644i		−	0.961213i	0.876936	−	0.480606i	$-0.159583\pi$
$602$		0			0
$603$	5.65816			0.230418
$604$		0			0
$605$	−1.08515	−	1.87954i	−0.0441177	−	0.0764141i
$606$		0			0
$607$	23.5467	−	40.7841i	0.955733	−	1.65538i	0.223050	−	0.974807i	$-0.428399\pi$
$607$	23.5467	−	40.7841i	0.955733	−	1.65538i	0.732683	−	0.680570i	$-0.238268\pi$
$608$		0			0
$609$	−1.98799	+	0.289506i	−0.0805575	+	0.0117314i
$610$		0			0
$611$	−12.1353	+	21.0189i	−0.490941	+	0.850335i
$612$		0			0
$613$	−28.4900	+	16.4487i	−1.15070	+	0.664357i	−0.949058	−	0.315102i	$-0.897961\pi$
$613$	−28.4900	+	16.4487i	−1.15070	+	0.664357i	−0.201642	+	0.979459i	$0.564628\pi$
$614$		0			0
$615$	−0.878794			−0.0354364
$616$		0			0
$617$	6.76738			0.272444			0.136222	−	0.990678i	$-0.456504\pi$
$617$	6.76738			0.272444			0.136222	+	0.990678i	$0.456504\pi$
$618$		0			0
$619$	−13.7468	+	7.93673i	−0.552531	+	0.319004i	−0.750142	−	0.661276i	$-0.770015\pi$
$619$	−13.7468	+	7.93673i	−0.552531	+	0.319004i	0.197611	+	0.980281i	$0.436682\pi$
$620$		0			0
$621$	0.200775	−	0.347752i	0.00805682	−	0.0139548i
$622$		0			0
$623$	−11.4504	+	9.03830i	−0.458750	+	0.362112i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	2.91606	+	5.05077i	0.116456	+	0.201708i
$628$		0			0
$629$	44.5964			1.77817
$630$		0			0
$631$			18.6006i			0.740479i	0.928936	+	0.370240i	$0.120724\pi$
$631$			18.6006i			0.740479i	−0.928936	+	0.370240i	$0.879276\pi$
$632$		0			0
$633$	0.529130	−	0.305493i	0.0210310	−	0.0121423i
$634$		0			0
$635$	−7.31032	−	4.22062i	−0.290101	−	0.167490i
$636$		0			0
$637$	−27.2530	−	25.7979i	−1.07980	−	1.02215i
$638$		0			0
$639$	−40.5063	−	23.3863i	−1.60241	−	0.925149i
$640$		0			0
$641$	−3.77857	−	6.54468i	−0.149245	−	0.258499i	0.781704	−	0.623650i	$-0.214351\pi$
$641$	−3.77857	−	6.54468i	−0.149245	−	0.258499i	−0.930948	+	0.365151i	$0.881018\pi$
$642$		0			0
$643$			21.9243i			0.864609i	0.901728	+	0.432305i	$0.142299\pi$
$643$			21.9243i			0.864609i	−0.901728	+	0.432305i	$0.857701\pi$
$644$		0			0
$645$		−	1.35307i		−	0.0532772i
$646$		0			0
$647$	11.3244	+	19.6144i	0.445207	+	0.771120i	0.998067	−	0.0621538i	$-0.0197969\pi$
$647$	11.3244	+	19.6144i	0.445207	+	0.771120i	−0.552860	+	0.833274i	$0.686464\pi$
$648$		0			0
$649$	24.8044	+	14.3208i	0.973659	+	0.562143i
$650$		0			0
$651$	2.86635	−	2.26254i	0.112341	−	0.0886759i
$652$		0			0
$653$	−3.05556	−	1.76413i	−0.119573	−	0.0690357i	0.439020	−	0.898477i	$-0.355326\pi$
$653$	−3.05556	−	1.76413i	−0.119573	−	0.0690357i	−0.558594	+	0.829441i	$0.688659\pi$
$654$		0			0
$655$	−4.74957	+	2.74216i	−0.185581	+	0.107145i
$656$		0			0
$657$			24.1495i			0.942162i
$658$		0			0
$659$	−37.5143			−1.46135			−0.730676	−	0.682725i	$-0.760795\pi$
$659$	−37.5143			−1.46135			−0.730676	+	0.682725i	$0.760795\pi$
$660$		0			0
$661$	−14.6573	−	25.3871i	−0.570102	−	0.987445i	−0.996555	−	0.0829357i	$-0.973570\pi$
$661$	−14.6573	−	25.3871i	−0.570102	−	0.987445i	0.426453	−	0.904510i	$-0.359763\pi$
$662$		0			0
$663$	−3.50558	+	6.07185i	−0.136146	+	0.235811i
$664$		0			0
$665$	2.41797	+	16.6038i	0.0937648	+	0.643868i
$666$		0			0
$667$	0.399971	−	0.692769i	0.0154869	−	0.0268241i
$668$		0			0
$669$	4.36368	−	2.51937i	0.168710	−	0.0974046i
$670$		0			0
$671$	19.0940			0.737116
$672$		0			0
$673$	−16.3062			−0.628558			−0.314279	−	0.949331i	$-0.601763\pi$
$673$	−16.3062			−0.628558			−0.314279	+	0.949331i	$0.601763\pi$
$674$		0			0
$675$	1.30263	−	0.752075i	0.0501383	−	0.0289474i
$676$		0			0
$677$	17.9655	−	31.1171i	0.690469	−	1.19593i	−0.281216	−	0.959645i	$-0.590738\pi$
$677$	17.9655	−	31.1171i	0.690469	−	1.19593i	0.971684	−	0.236282i	$-0.0759290\pi$
$678$		0			0
$679$	19.6265	+	7.81607i	0.753198	+	0.299953i
$680$		0			0
$681$	−3.13766	+	5.43459i	−0.120236	+	0.208254i
$682$		0			0
$683$	−13.9429	−	24.1497i	−0.533509	−	0.924064i	−0.999234	−	0.0391349i	$-0.987540\pi$
$683$	−13.9429	−	24.1497i	−0.533509	−	0.924064i	0.465725	−	0.884929i	$-0.345794\pi$
$684$		0			0
$685$	−8.42562			−0.321926
$686$		0			0
$687$		−	3.03166i		−	0.115665i
$688$		0			0
$689$	16.6032	−	9.58587i	0.632532	−	0.365193i
$690$		0			0
$691$	−20.9094	−	12.0721i	−0.795432	−	0.459243i	0.0464394	−	0.998921i	$-0.485213\pi$
$691$	−20.9094	−	12.0721i	−0.795432	−	0.459243i	−0.841871	+	0.539678i	$0.818546\pi$
$692$		0			0
$693$	−10.4292	+	26.1882i	−0.396172	+	0.994807i
$694$		0			0
$695$	10.0313	+	5.79158i	0.380510	+	0.219687i
$696$		0			0
$697$	−8.94907	−	15.5002i	−0.338970	−	0.587113i
$698$		0			0
$699$		−	2.81256i		−	0.106381i
$700$		0			0
$701$		−	14.4688i		−	0.546481i	−0.961946	−	0.273240i	$-0.911905\pi$
$701$		−	14.4688i		−	0.546481i	0.961946	−	0.273240i	$-0.0880954\pi$
$702$		0			0
$703$	27.4001	+	47.4583i	1.03341	+	1.78992i
$704$		0			0
$705$	−0.993528	−	0.573614i	−0.0374184	−	0.0216035i
$706$		0			0
$707$	−24.8710	+	3.62189i	−0.935369	+	0.136215i
$708$		0			0
$709$	16.2208	+	9.36506i	0.609183	+	0.351712i	0.772646	−	0.634837i	$-0.218933\pi$
$709$	16.2208	+	9.36506i	0.609183	+	0.351712i	−0.163462	+	0.986550i	$0.552266\pi$
$710$		0			0
$711$	−29.1897	+	16.8527i	−1.09470	+	0.632025i
$712$		0			0
$713$			1.45407i			0.0544552i
$714$		0			0
$715$	19.4555			0.727593
$716$		0			0
$717$	3.14439	+	5.44624i	0.117429	+	0.203394i
$718$		0			0
$719$	14.8589	−	25.7364i	0.554145	−	0.959807i	−0.443824	−	0.896114i	$-0.646379\pi$
$719$	14.8589	−	25.7364i	0.554145	−	0.959807i	0.997970	−	0.0636936i	$-0.0202880\pi$
$720$		0			0
$721$	12.2978	+	15.5798i	0.457994	+	0.580221i
$722$		0			0
$723$	1.44104	−	2.49595i	0.0535928	−	0.0928255i
$724$		0			0
$725$	2.59502	−	1.49823i	0.0963765	−	0.0556430i
$726$		0			0
$727$	−7.23594			−0.268366			−0.134183	−	0.990957i	$-0.542841\pi$
$727$	−7.23594			−0.268366			−0.134183	+	0.990957i	$0.542841\pi$
$728$		0			0
$729$	23.5941			0.873854
$730$		0			0
$731$	23.8656	−	13.7788i	0.882702	−	0.509628i
$732$		0			0
$733$	−11.4471	+	19.8270i	−0.422810	+	0.732328i	−0.996213	−	0.0869452i	$-0.972289\pi$
$733$	−11.4471	+	19.8270i	−0.422810	+	0.732328i	0.573403	+	0.819273i	$0.305623\pi$
$734$		0			0
$735$	1.21942	−	1.28820i	0.0449791	−	0.0475161i
$736$		0			0
$737$	−3.49719	+	6.05730i	−0.128821	+	0.223124i
$738$		0			0
$739$	19.9700	+	34.5891i	0.734610	+	1.27238i	0.954894	+	0.296946i	$0.0959682\pi$
$739$	19.9700	+	34.5891i	0.734610	+	1.27238i	−0.220284	+	0.975436i	$0.570699\pi$
$740$		0			0
$741$	−8.61534			−0.316492
$742$		0			0
$743$			7.99702i			0.293382i	0.989182	+	0.146691i	$0.0468623\pi$
$743$			7.99702i			0.293382i	−0.989182	+	0.146691i	$0.953138\pi$
$744$		0			0
$745$	10.0102	−	5.77937i	0.366744	−	0.211740i
$746$		0			0
$747$	−14.6399	−	8.45234i	−0.535645	−	0.309255i
$748$		0			0
$749$	12.2535	+	15.5236i	0.447732	+	0.567220i
$750$		0			0
$751$	−11.9662	−	6.90868i	−0.436652	−	0.252101i	0.265524	−	0.964104i	$-0.414455\pi$
$751$	−11.9662	−	6.90868i	−0.436652	−	0.252101i	−0.702177	+	0.712003i	$0.747788\pi$
$752$		0			0
$753$	−1.13833	−	1.97165i	−0.0414832	−	0.0718509i
$754$		0			0
$755$		−	16.0900i		−	0.585576i
$756$		0			0
$757$			10.8579i			0.394636i	0.980340	+	0.197318i	$0.0632232\pi$
$757$			10.8579i			0.394636i	−0.980340	+	0.197318i	$0.936777\pi$
$758$		0			0
$759$	0.122752	+	0.212613i	0.00445562	+	0.00771736i
$760$		0			0
$761$	−39.6101	−	22.8689i	−1.43586	−	0.828996i	−0.438305	−	0.898826i	$-0.644421\pi$
$761$	−39.6101	−	22.8689i	−1.43586	−	0.828996i	−0.997559	+	0.0698299i	$0.977754\pi$
$762$		0			0
$763$	−7.43472	−	51.0531i	−0.269155	−	1.84825i
$764$		0			0
$765$	13.1217	+	7.57580i	0.474415	+	0.273904i
$766$		0			0
$767$	−36.6416	+	21.1551i	−1.32305	+	0.763865i
$768$		0			0
$769$			5.29591i			0.190976i	0.995431	+	0.0954878i	$0.0304411\pi$
$769$			5.29591i			0.190976i	−0.995431	+	0.0954878i	$0.969559\pi$
$770$		0			0
$771$	−0.615644			−0.0221719
$772$		0			0
$773$	8.85880	+	15.3439i	0.318629	+	0.551882i	0.980202	−	0.197999i	$-0.0634443\pi$
$773$	8.85880	+	15.3439i	0.318629	+	0.551882i	−0.661573	+	0.749881i	$0.730111\pi$
$774$		0			0
$775$	−2.72336	+	4.71700i	−0.0978261	+	0.169440i
$776$		0			0
$777$	2.14342	−	5.38223i	0.0768947	−	0.193086i
$778$		0			0
$779$	10.9966	−	19.0467i	0.393995	−	0.682420i
$780$		0			0
$781$	50.0722	−	28.9092i	1.79172	−	1.03445i
$782$		0			0
$783$	−4.50714			−0.161072
$784$		0			0
$785$	−2.15787			−0.0770179
$786$		0			0
$787$	27.1625	−	15.6823i	0.968240	−	0.559013i	0.0695406	−	0.997579i	$-0.477847\pi$
$787$	27.1625	−	15.6823i	0.968240	−	0.559013i	0.898699	+	0.438566i	$0.144513\pi$
$788$		0			0
$789$	0.291498	−	0.504889i	0.0103776	−	0.0179745i
$790$		0			0
$791$	20.3779	−	51.1699i	0.724554	−	1.81939i
$792$		0			0
$793$	−14.1030	+	24.4272i	−0.500814	+	0.867435i
$794$		0			0
$795$	0.453107	+	0.784805i	0.0160701	+	0.0278342i
$796$		0			0
$797$	12.8746			0.456040			0.228020	−	0.973656i	$-0.426775\pi$
$797$	12.8746			0.456040			0.228020	+	0.973656i	$0.426775\pi$
$798$		0			0
$799$		−	23.3652i		−	0.826603i
$800$		0			0
$801$	−14.0183	+	8.09345i	−0.495311	+	0.285968i
$802$		0			0
$803$	−25.8531	−	14.9263i	−0.912336	−	0.526737i
$804$		0			0
$805$	0.101785	+	0.698941i	0.00358745	+	0.0246344i
$806$		0			0
$807$	0.267363	+	0.154362i	0.00941162	+	0.00543380i
$808$		0			0
$809$	−3.22687	−	5.58910i	−0.113451	−	0.196502i	0.803709	−	0.595023i	$-0.202857\pi$
$809$	−3.22687	−	5.58910i	−0.113451	−	0.196502i	−0.917159	+	0.398521i	$0.869524\pi$
$810$		0			0
$811$		−	24.3882i		−	0.856385i	−0.903688	−	0.428192i	$-0.859151\pi$
$811$		−	24.3882i		−	0.856385i	0.903688	−	0.428192i	$-0.140849\pi$
$812$		0			0
$813$			6.13703i			0.215235i
$814$		0			0
$815$	−0.598474	−	1.03659i	−0.0209636	−	0.0363101i
$816$		0			0
$817$	29.3261	+	16.9314i	1.02599	+	0.592356i
$818$		0			0
$819$	−25.7997	−	32.6850i	−0.901516	−	1.14211i
$820$		0			0
$821$	15.5027	+	8.95047i	0.541047	+	0.312373i	0.745503	−	0.666502i	$-0.232209\pi$
$821$	15.5027	+	8.95047i	0.541047	+	0.312373i	−0.204456	+	0.978876i	$0.565543\pi$
$822$		0			0
$823$	−23.0780	+	13.3241i	−0.804449	+	0.464449i	−0.845024	−	0.534728i	$-0.820414\pi$
$823$	−23.0780	+	13.3241i	−0.804449	+	0.464449i	0.0405758	+	0.999176i	$0.487081\pi$
$824$		0			0
$825$			0.919625i			0.0320172i
$826$		0			0
$827$	38.2259			1.32924			0.664622	−	0.747179i	$-0.268592\pi$
$827$	38.2259			1.32924			0.664622	+	0.747179i	$0.268592\pi$
$828$		0			0
$829$	3.10978	+	5.38630i	0.108007	+	0.187074i	0.914963	−	0.403538i	$-0.132220\pi$
$829$	3.10978	+	5.38630i	0.108007	+	0.187074i	−0.806956	+	0.590612i	$0.798886\pi$
$830$		0			0
$831$	−1.05736	+	1.83140i	−0.0366794	+	0.0635305i
$832$		0			0
$833$	35.1393	+	8.39004i	1.21750	+	0.290698i
$834$		0			0
$835$	−6.53112	+	11.3122i	−0.226019	+	0.391476i
$836$		0			0
$837$	7.09508	−	4.09635i	0.245242	−	0.141590i
$838$		0			0
$839$	−0.919692			−0.0317513			−0.0158757	−	0.999874i	$-0.505054\pi$
$839$	−0.919692			−0.0317513			−0.0158757	+	0.999874i	$0.505054\pi$
$840$		0			0
$841$	20.0212			0.690386
$842$		0			0
$843$	4.35073	−	2.51189i	0.149847	−	0.0865142i
$844$		0			0
$845$	−7.87001	+	13.6312i	−0.270736	+	0.468929i
$846$		0			0
$847$	−3.55769	−	4.50715i	−0.122244	−	0.154867i
$848$		0			0
$849$	1.21973	−	2.11264i	0.0418611	−	0.0725056i
$850$		0			0
$851$	1.15341	+	1.99777i	0.0395384	+	0.0684826i
$852$		0			0
$853$	−32.0382			−1.09697			−0.548484	−	0.836161i	$-0.684795\pi$
$853$	−32.0382			−1.09697			−0.548484	+	0.836161i	$0.684795\pi$
$854$		0			0
$855$			18.6183i			0.636733i
$856$		0			0
$857$	−14.8577	+	8.57808i	−0.507529	+	0.293022i	−0.731817	−	0.681501i	$-0.761327\pi$
$857$	−14.8577	+	8.57808i	−0.507529	+	0.293022i	0.224289	+	0.974523i	$0.427994\pi$
$858$		0			0
$859$	45.5226	+	26.2825i	1.55321	+	0.896747i	0.997878	+	0.0651185i	$0.0207425\pi$
$859$	45.5226	+	26.2825i	1.55321	+	0.896747i	0.555333	+	0.831628i	$0.312591\pi$
$860$		0			0
$861$	−2.30080	+	0.335059i	−0.0784111	+	0.0114188i
$862$		0			0
$863$	8.80096	+	5.08124i	0.299588	+	0.172967i	0.642258	−	0.766489i	$-0.277998\pi$
$863$	8.80096	+	5.08124i	0.299588	+	0.172967i	−0.342670	+	0.939456i	$0.611331\pi$
$864$		0			0
$865$	12.3607	+	21.4093i	0.420275	+	0.727938i
$866$		0			0
$867$		−	2.44178i		−	0.0829271i
$868$		0			0
$869$		−	41.6651i		−	1.41339i
$870$		0			0
$871$	−5.16612	−	8.94798i	−0.175047	−	0.303191i
$872$		0			0
$873$	20.3009	+	11.7207i	0.687082	+	0.396687i
$874$		0			0
$875$	−0.978876	+	2.45801i	−0.0330921	+	0.0830958i
$876$		0			0
$877$	−32.0621	−	18.5111i	−1.08266	−	0.625074i	−0.151047	−	0.988527i	$-0.548264\pi$
$877$	−32.0621	−	18.5111i	−1.08266	−	0.625074i	−0.931613	+	0.363453i	$0.881598\pi$
$878$		0			0
$879$	0.107084	−	0.0618250i	0.00361185	−	0.00208531i
$880$		0			0
$881$			46.4428i			1.56470i	0.622841	+	0.782348i	$0.285978\pi$
$881$			46.4428i			1.56470i	−0.622841	+	0.782348i	$0.714022\pi$
$882$		0			0
$883$	26.4744			0.890935			0.445468	−	0.895298i	$-0.353037\pi$
$883$	26.4744			0.890935			0.445468	+	0.895298i	$0.353037\pi$
$884$		0			0
$885$	−0.999963	−	1.73199i	−0.0336134	−	0.0582201i
$886$		0			0
$887$	−5.77822	+	10.0082i	−0.194014	+	0.336041i	−0.946577	−	0.322479i	$-0.895484\pi$
$887$	−5.77822	+	10.0082i	−0.194014	+	0.336041i	0.752563	+	0.658520i	$0.228817\pi$
$888$		0			0
$889$	−20.7486	−	8.26293i	−0.695886	−	0.277130i
$890$		0			0
$891$	−15.2897	+	26.4826i	−0.512225	+	0.887200i
$892$		0			0
$893$	24.8647	−	14.3556i	0.832065	−	0.480393i
$894$		0			0
$895$	−12.9601			−0.433209
$896$		0			0
$897$	−0.362664			−0.0121090
$898$		0			0
$899$	14.1343	−	8.16047i	0.471407	−	0.272167i
$900$		0			0
$901$	−9.22831	+	15.9839i	−0.307439	+	0.532501i
$902$		0			0
$903$	−0.515889	−	3.54253i	−0.0171677	−	0.117888i
$904$		0			0
$905$	−5.28326	+	9.15087i	−0.175621	+	0.304185i
$906$		0			0
$907$	−19.9712	−	34.5911i	−0.663131	−	1.14858i	−0.979788	−	0.200037i	$-0.935894\pi$
$907$	−19.9712	−	34.5911i	−0.663131	−	1.14858i	0.316657	−	0.948540i	$-0.397440\pi$
$908$		0			0
$909$	−27.8885			−0.925003
$910$		0			0
$911$		−	46.6862i		−	1.54678i	−0.633929	−	0.773391i	$-0.718559\pi$
$911$		−	46.6862i		−	1.54678i	0.633929	−	0.773391i	$-0.281441\pi$
$912$		0			0
$913$	18.0972	−	10.4484i	0.598930	−	0.345792i
$914$		0			0
$915$	−1.15463	−	0.666626i	−0.0381709	−	0.0220380i
$916$		0			0
$917$	−11.3895	+	8.99023i	−0.376114	+	0.296884i
$918$		0			0
$919$	−7.20385	−	4.15914i	−0.237633	−	0.137198i	0.376455	−	0.926435i	$-0.377143\pi$
$919$	−7.20385	−	4.15914i	−0.237633	−	0.137198i	−0.614088	+	0.789237i	$0.710476\pi$
$920$		0			0
$921$	−1.49933	−	2.59692i	−0.0494046	−	0.0855714i
$922$		0			0
$923$			85.4105i			2.81132i
$924$		0			0
$925$			8.64104i			0.284116i
$926$		0			0
$927$	11.0122	+	19.0737i	0.361689	+	0.626463i
$928$		0			0
$929$	23.5169	+	13.5775i	0.771565	+	0.445463i	0.833433	−	0.552621i	$-0.186372\pi$
$929$	23.5169	+	13.5775i	0.771565	+	0.445463i	−0.0618674	+	0.998084i	$0.519706\pi$
$930$		0			0
$931$	12.6611	+	42.5491i	0.414952	+	1.39449i
$932$		0			0
$933$	−1.00723	−	0.581525i	−0.0329753	−	0.0190383i
$934$		0			0
$935$	−16.2204	+	9.36487i	−0.530465	+	0.306264i
$936$		0			0
$937$			36.9312i			1.20649i	0.797556	+	0.603245i	$0.206126\pi$
$937$			36.9312i			1.20649i	−0.797556	+	0.603245i	$0.793874\pi$
$938$		0			0
$939$	5.20565			0.169880
$940$		0			0
$941$	7.58723	+	13.1415i	0.247336	+	0.428399i	0.962786	−	0.270265i	$-0.0871114\pi$
$941$	7.58723	+	13.1415i	0.247336	+	0.428399i	−0.715449	+	0.698664i	$0.753778\pi$
$942$		0			0
$943$	0.462905	−	0.801776i	0.0150743	−	0.0261094i
$944$		0			0
$945$	3.12372	−	2.46569i	0.101615	−	0.0802090i
$946$		0			0
$947$	16.7591	−	29.0275i	0.544596	−	0.943268i	−0.454036	−	0.890983i	$-0.650016\pi$
$947$	16.7591	−	29.0275i	0.544596	−	0.943268i	0.998632	−	0.0522848i	$-0.0166503\pi$
$948$		0			0
$949$	38.1907	−	22.0494i	1.23972	−	0.715755i
$950$		0			0
$951$	1.97899			0.0641730
$952$		0			0
$953$	−2.60332			−0.0843298			−0.0421649	−	0.999111i	$-0.513425\pi$
$953$	−2.60332			−0.0843298			−0.0421649	+	0.999111i	$0.513425\pi$
$954$		0			0
$955$	3.42981	−	1.98020i	0.110986	−	0.0640779i
$956$		0			0
$957$	1.37781	−	2.38644i	0.0445384	−	0.0771428i
$958$		0			0
$959$	−22.0594	+	3.21245i	−0.712335	+	0.103736i
$960$		0			0
$961$	0.666587	−	1.15456i	0.0215028	−	0.0372439i
$962$		0			0
$963$	10.9725	+	19.0049i	0.353584	+	0.612426i
$964$		0			0
$965$	−14.2906			−0.460031
$966$		0			0
$967$		−	43.0328i		−	1.38384i	−0.721973	−	0.691921i	$-0.756764\pi$
$967$		−	43.0328i		−	1.38384i	0.721973	−	0.691921i	$-0.243236\pi$
$968$		0			0
$969$	7.18279	−	4.14699i	0.230744	−	0.133220i
$970$		0			0
$971$	−50.5453	−	29.1823i	−1.62208	−	0.936506i	−0.986364	−	0.164579i	$-0.947373\pi$
$971$	−50.5453	−	29.1823i	−1.62208	−	0.936506i	−0.635712	−	0.771927i	$-0.719293\pi$
$972$		0			0
$973$	28.4715	+	11.3385i	0.912755	+	0.363495i
$974$		0			0
$975$	−1.17649	−	0.679245i	−0.0376777	−	0.0217532i
$976$		0			0
$977$	0.680919	+	1.17939i	0.0217845	+	0.0377319i	0.876712	−	0.481015i	$-0.159732\pi$
$977$	0.680919	+	1.17939i	0.0217845	+	0.0377319i	−0.854928	+	0.518747i	$0.826399\pi$
$978$		0			0
$979$		−	20.0095i		−	0.639508i
$980$		0			0
$981$		−	57.2472i		−	1.82776i
$982$		0			0
$983$	−5.32160	−	9.21728i	−0.169733	−	0.293986i	0.768593	−	0.639738i	$-0.220957\pi$
$983$	−5.32160	−	9.21728i	−0.169733	−	0.293986i	−0.938326	+	0.345752i	$0.887624\pi$
$984$		0			0
$985$	−3.50933	−	2.02611i	−0.111817	−	0.0645573i
$986$		0			0
$987$	−2.81989	−	1.12299i	−0.0897582	−	0.0357453i
$988$		0			0
$989$	1.23449	+	0.712733i	0.0392545	+	0.0226636i
$990$		0			0
$991$	34.2678	−	19.7845i	1.08855	−	0.628476i	0.155361	−	0.987858i	$-0.450346\pi$
$991$	34.2678	−	19.7845i	1.08855	−	0.628476i	0.933191	+	0.359382i	$0.117013\pi$
$992$		0			0
$993$			3.21887i			0.102148i
$994$		0			0
$995$	−2.74240			−0.0869401
$996$		0			0
$997$	−10.3520	−	17.9301i	−0.327850	−	0.567852i	0.654235	−	0.756291i	$-0.272991\pi$
$997$	−10.3520	−	17.9301i	−0.327850	−	0.567852i	−0.982085	+	0.188439i	$0.939657\pi$
$998$		0			0
$999$	6.49871	−	11.2561i	0.205610	−	0.356127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.271.8		24
4.3	odd	2		280.2.bj.f.131.3	yes	24
7.3	odd	6		1120.2.bz.f.591.8		24
8.3	odd	2		1120.2.bz.f.271.8		24
8.5	even	2		280.2.bj.e.131.6	✓	24
28.3	even	6		280.2.bj.e.171.6	yes	24
56.3	even	6	inner	1120.2.bz.e.591.8		24
56.45	odd	6		280.2.bj.f.171.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.6	✓	24	8.5	even	2
280.2.bj.e.171.6	yes	24	28.3	even	6
280.2.bj.f.131.3	yes	24	4.3	odd	2
280.2.bj.f.171.3	yes	24	56.45	odd	6
1120.2.bz.e.271.8		24	1.1	even	1	trivial
1120.2.bz.e.591.8		24	56.3	even	6	inner
1120.2.bz.f.271.8		24	8.3	odd	2
1120.2.bz.f.591.8		24	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.219454 - 0.126702i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.978876 + 2.45801i) q^{7} +(-1.46789 + 2.54247i) q^{9} +O(q^{10})\)	\(q+(0.219454 - 0.126702i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.978876 + 2.45801i) q^{7} +(-1.46789 + 2.54247i) q^{9} +(-1.81455 - 3.14289i) q^{11} +5.36097 q^{13} +0.253404i q^{15} +(-4.46956 + 2.58050i) q^{17} +(-5.49220 - 3.17092i) q^{19} +(0.0966157 + 0.663445i) q^{21} +(-0.231195 - 0.133481i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.50415i q^{27} +2.99647i q^{29} +(-2.72336 - 4.71700i) q^{31} +(-0.796419 - 0.459813i) q^{33} +(-1.63926 - 2.07674i) q^{35} +(-7.48336 - 4.32052i) q^{37} +(1.17649 - 0.679245i) q^{39} +3.46796i q^{41} -5.33960 q^{43} +(-1.46789 - 2.54247i) q^{45} +(-2.26364 + 3.92073i) q^{47} +(-5.08360 - 4.81217i) q^{49} +(-0.653908 + 1.13260i) q^{51} +(3.09705 - 1.78808i) q^{53} +3.62909 q^{55} -1.60705 q^{57} +(-6.83489 + 3.94613i) q^{59} +(-2.63069 + 4.55649i) q^{61} +(-4.81251 - 6.09685i) q^{63} +(-2.68049 + 4.64274i) q^{65} +(-0.963653 - 1.66910i) q^{67} -0.0676490 q^{69} +15.9319i q^{71} +(7.12385 - 4.11296i) q^{73} +(-0.219454 - 0.126702i) q^{75} +(9.50145 - 1.38367i) q^{77} +(9.94273 + 5.74044i) q^{79} +(-4.21310 - 7.29731i) q^{81} +5.75814i q^{83} -5.16100i q^{85} +(0.379658 + 0.657587i) q^{87} +(4.77496 + 2.75683i) q^{89} +(-5.24773 + 13.1773i) q^{91} +(-1.19531 - 0.690110i) q^{93} +(5.49220 - 3.17092i) q^{95} -7.98474i q^{97} +10.6542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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