LMFDB - Embedded newform 572.2.b.c.571.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(571,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("572.571");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.b (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			571.20
Character	$\chi$	$=$	572.571
Dual form			572.2.b.c.571.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.883550 + 1.10424i) q^{2} +2.47596i q^{3} +(-0.438678 - 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 - 2.18764i) q^{6} -0.534510i q^{7} +(2.54229 + 1.23966i) q^{8} -3.13038 q^{9} +O(q^{10})$	\(q+(-0.883550 + 1.10424i) q^{2} +2.47596i q^{3} +(-0.438678 - 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 - 2.18764i) q^{6} -0.534510i q^{7} +(2.54229 + 1.23966i) q^{8} -3.13038 q^{9} +(-3.05794 - 2.44680i) q^{10} +(-3.29596 - 0.369696i) q^{11} +(4.83134 - 1.08615i) q^{12} +(-3.35334 - 1.32481i) q^{13} +(0.590226 + 0.472267i) q^{14} -6.85664 q^{15} +(-3.61512 + 1.71198i) q^{16} -5.90649i q^{17} +(2.76585 - 3.45669i) q^{18} +5.54527i q^{19} +(5.40369 - 1.21482i) q^{20} +1.32343 q^{21} +(3.32037 - 3.31287i) q^{22} +4.48555i q^{23} +(-3.06936 + 6.29461i) q^{24} -2.66893 q^{25} +(4.42574 - 2.53235i) q^{26} -0.322828i q^{27} +(-1.04299 + 0.234478i) q^{28} -0.677674i q^{29} +(6.05818 - 7.57135i) q^{30} -9.20526 q^{31} +(1.30371 - 5.50458i) q^{32} +(0.915354 - 8.16066i) q^{33} +(6.52216 + 5.21868i) q^{34} +1.48021 q^{35} +(1.37323 + 6.10831i) q^{36} -1.55230i q^{37} +(-6.12329 - 4.89953i) q^{38} +(3.28017 - 8.30274i) q^{39} +(-3.43298 + 7.04032i) q^{40} +2.50658 q^{41} +(-1.16931 + 1.46138i) q^{42} -8.49046 q^{43} +(0.724477 + 6.59357i) q^{44} -8.66892i q^{45} +(-4.95311 - 3.96321i) q^{46} +10.0993 q^{47} +(-4.23881 - 8.95090i) q^{48} +6.71430 q^{49} +(2.35813 - 2.94713i) q^{50} +14.6242 q^{51} +(-1.11405 + 7.12453i) q^{52} +4.38869 q^{53} +(0.356479 + 0.285235i) q^{54} +(1.02379 - 9.12743i) q^{55} +(0.662613 - 1.35888i) q^{56} -13.7299 q^{57} +(0.748313 + 0.598759i) q^{58} +5.47956 q^{59} +(3.00786 + 13.3793i) q^{60} +10.3154i q^{61} +(8.13331 - 10.1648i) q^{62} +1.67322i q^{63} +(4.92647 + 6.30317i) q^{64} +(3.66876 - 9.28634i) q^{65} +(8.20254 + 8.22112i) q^{66} -2.88040 q^{67} +(-11.5253 + 2.59105i) q^{68} -11.1060 q^{69} +(-1.30784 + 1.63450i) q^{70} +3.09875 q^{71} +(-7.95834 - 3.88063i) q^{72} -9.44310 q^{73} +(1.71411 + 1.37154i) q^{74} -6.60816i q^{75} +(10.8205 - 2.43259i) q^{76} +(-0.197607 + 1.76172i) q^{77} +(6.27000 + 10.9580i) q^{78} -8.42639 q^{79} +(-4.74097 - 10.0113i) q^{80} -8.59184 q^{81} +(-2.21469 + 2.76786i) q^{82} +2.83221i q^{83} +(-0.580559 - 2.58240i) q^{84} +16.3567 q^{85} +(7.50175 - 9.37548i) q^{86} +1.67789 q^{87} +(-7.92097 - 5.02575i) q^{88} -6.95222i q^{89} +(9.57254 + 7.65943i) q^{90} +(-0.708123 + 1.79239i) q^{91} +(8.75264 - 1.96771i) q^{92} -22.7919i q^{93} +(-8.92321 + 11.1520i) q^{94} -15.3564 q^{95} +(13.6291 + 3.22792i) q^{96} -2.27247i q^{97} +(-5.93242 + 7.41418i) q^{98} +(10.3176 + 1.15729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^4 - 32 * q^9	$ 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) $ 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.883550	+	1.10424i	−0.624764	+	0.780813i
$2$	−0.883550	+	1.10424i	−0.624764	+	0.780813i
$3$			2.47596i			1.42950i	0.699382	+	0.714748i	$0.253459\pi$
$3$			2.47596i			1.42950i	−0.699382	+	0.714748i	$0.746541\pi$
$4$	−0.438678	−	1.95130i	−0.219339	−	0.975649i
$5$			2.76928i			1.23846i	0.785209	+	0.619230i	$0.212555\pi$
$5$			2.76928i			1.23846i	−0.785209	+	0.619230i	$0.787445\pi$
$6$	−2.73405	−	2.18764i	−1.11617	−	0.893099i
$7$		−	0.534510i		−	0.202026i	−0.994885	−	0.101013i	$-0.967792\pi$
$7$		−	0.534510i		−	0.202026i	0.994885	−	0.101013i	$-0.0322083\pi$
$8$	2.54229	+	1.23966i	0.898835	+	0.438287i
$9$	−3.13038			−1.04346
$10$	−3.05794	−	2.44680i	−0.967007	−	0.773746i
$11$	−3.29596	−	0.369696i	−0.993768	−	0.111468i
$11$	−3.29596	−	0.369696i	−0.993768	−	0.111468i
$12$	4.83134	−	1.08615i	1.39469	−	0.313545i
$13$	−3.35334	−	1.32481i	−0.930049	−	0.367435i
$13$	−3.35334	−	1.32481i	−0.930049	−	0.367435i
$14$	0.590226	+	0.472267i	0.157745	+	0.126219i
$15$	−6.85664			−1.77038
$16$	−3.61512	+	1.71198i	−0.903781	+	0.427996i
$17$		−	5.90649i		−	1.43253i	−0.697827	−	0.716267i	$-0.745849\pi$
$17$		−	5.90649i		−	1.43253i	0.697827	−	0.716267i	$-0.254151\pi$
$18$	2.76585	−	3.45669i	0.651918	−	0.814749i
$19$			5.54527i			1.27217i	0.771618	+	0.636086i	$0.219448\pi$
$19$			5.54527i			1.27217i	−0.771618	+	0.636086i	$0.780552\pi$
$20$	5.40369	−	1.21482i	1.20830	−	0.271643i
$21$	1.32343			0.288795
$22$	3.32037	−	3.31287i	0.707906	−	0.706306i
$23$			4.48555i			0.935301i	0.883913	+	0.467651i	$0.154899\pi$
$23$			4.48555i			0.935301i	−0.883913	+	0.467651i	$0.845101\pi$
$24$	−3.06936	+	6.29461i	−0.626531	+	1.28488i
$25$	−2.66893			−0.533785
$26$	4.42574	−	2.53235i	0.867960	−	0.496634i
$27$		−	0.322828i		−	0.0621283i
$28$	−1.04299	+	0.234478i	−0.197106	+	0.0443122i
$29$		−	0.677674i		−	0.125841i	−0.998019	−	0.0629204i	$-0.979959\pi$
$29$		−	0.677674i		−	0.125841i	0.998019	−	0.0629204i	$-0.0200414\pi$
$30$	6.05818	−	7.57135i	1.10607	−	1.38233i
$31$	−9.20526			−1.65331			−0.826657	−	0.562706i	$-0.809760\pi$
$31$	−9.20526			−1.65331			−0.826657	+	0.562706i	$0.809760\pi$
$32$	1.30371	−	5.50458i	0.230465	−	0.973081i
$33$	0.915354	−	8.16066i	0.159343	−	1.42059i
$34$	6.52216	+	5.21868i	1.11854	+	0.894996i
$35$	1.48021			0.250201
$36$	1.37323	+	6.10831i	0.228872	+	1.01805i
$37$		−	1.55230i		−	0.255197i	−0.991826	−	0.127598i	$-0.959273\pi$
$37$		−	1.55230i		−	0.255197i	0.991826	−	0.127598i	$-0.0407268\pi$
$38$	−6.12329	−	4.89953i	−0.993329	−	0.794808i
$39$	3.28017	−	8.30274i	0.525248	−	1.32950i
$40$	−3.43298	+	7.04032i	−0.542802	+	1.11317i
$41$	2.50658			0.391462			0.195731	−	0.980658i	$-0.437292\pi$
$41$	2.50658			0.391462			0.195731	+	0.980658i	$0.437292\pi$
$42$	−1.16931	+	1.46138i	−0.180429	+	0.225495i
$43$	−8.49046			−1.29478			−0.647392	−	0.762157i	$-0.724140\pi$
$43$	−8.49046			−1.29478			−0.647392	+	0.762157i	$0.724140\pi$
$44$	0.724477	+	6.59357i	0.109219	+	0.994018i
$45$		−	8.66892i		−	1.29229i
$46$	−4.95311	−	3.96321i	−0.730296	−	0.584343i
$47$	10.0993			1.47313			0.736565	−	0.676367i	$-0.236447\pi$
$47$	10.0993			1.47313			0.736565	+	0.676367i	$0.236447\pi$
$48$	−4.23881	−	8.95090i	−0.611819	−	1.29195i
$49$	6.71430			0.959186
$50$	2.35813	−	2.94713i	0.333490	−	0.416787i
$51$	14.6242			2.04780
$52$	−1.11405	+	7.12453i	−0.154491	+	0.987994i
$53$	4.38869			0.602834			0.301417	−	0.953492i	$-0.402540\pi$
$53$	4.38869			0.602834			0.301417	+	0.953492i	$0.402540\pi$
$54$	0.356479	+	0.285235i	0.0485106	+	0.0388156i
$55$	1.02379	−	9.12743i	0.138048	−	1.23074i
$56$	0.662613	−	1.35888i	0.0885454	−	0.181588i
$57$	−13.7299			−1.81857
$58$	0.748313	+	0.598759i	0.0982583	+	0.0786209i
$59$	5.47956			0.713378			0.356689	−	0.934223i	$-0.383906\pi$
$59$	5.47956			0.713378			0.356689	+	0.934223i	$0.383906\pi$
$60$	3.00786	+	13.3793i	0.388313	+	1.72726i
$61$			10.3154i			1.32076i	0.750933	+	0.660378i	$0.229604\pi$
$61$			10.3154i			1.32076i	−0.750933	+	0.660378i	$0.770396\pi$
$62$	8.13331	−	10.1648i	1.03293	−	1.29093i
$63$			1.67322i			0.210806i
$64$	4.92647	+	6.30317i	0.615808	+	0.787896i
$65$	3.66876	−	9.28634i	0.455054	−	1.15183i
$66$	8.20254	+	8.22112i	1.00966	+	1.01195i
$67$	−2.88040			−0.351897			−0.175949	−	0.984399i	$-0.556299\pi$
$67$	−2.88040			−0.351897			−0.175949	+	0.984399i	$0.556299\pi$
$68$	−11.5253	+	2.59105i	−1.39765	+	0.314211i
$69$	−11.1060			−1.33701
$70$	−1.30784	+	1.63450i	−0.156317	+	0.195360i
$71$	3.09875			0.367754			0.183877	−	0.982949i	$-0.441135\pi$
$71$	3.09875			0.367754			0.183877	+	0.982949i	$0.441135\pi$
$72$	−7.95834	−	3.88063i	−0.937900	−	0.457336i
$73$	−9.44310			−1.10523			−0.552616	−	0.833436i	$-0.686370\pi$
$73$	−9.44310			−1.10523			−0.552616	+	0.833436i	$0.686370\pi$
$74$	1.71411	+	1.37154i	0.199261	+	0.159438i
$75$		−	6.60816i		−	0.763044i
$76$	10.8205	−	2.43259i	1.24119	−	0.279037i
$77$	−0.197607	+	1.76172i	−0.0225194	+	0.200767i
$78$	6.27000	+	10.9580i	0.709937	+	1.24075i
$79$	−8.42639			−0.948043			−0.474021	−	0.880513i	$-0.657198\pi$
$79$	−8.42639			−0.948043			−0.474021	+	0.880513i	$0.657198\pi$
$80$	−4.74097	−	10.0113i	−0.530056	−	1.11930i
$81$	−8.59184			−0.954649
$82$	−2.21469	+	2.76786i	−0.244572	+	0.305659i
$83$			2.83221i			0.310875i	0.987846	+	0.155438i	$0.0496788\pi$
$83$			2.83221i			0.310875i	−0.987846	+	0.155438i	$0.950321\pi$
$84$	−0.580559	−	2.58240i	−0.0633442	−	0.281763i
$85$	16.3567			1.77414
$86$	7.50175	−	9.37548i	0.808935	−	1.01098i
$87$	1.67789			0.179889
$88$	−7.92097	−	5.02575i	−0.844379	−	0.535747i
$89$		−	6.95222i		−	0.736933i	−0.929641	−	0.368467i	$-0.879883\pi$
$89$		−	6.95222i		−	0.736933i	0.929641	−	0.368467i	$-0.120117\pi$
$90$	9.57254	+	7.65943i	1.00903	+	0.807374i
$91$	−0.708123	+	1.79239i	−0.0742314	+	0.187894i
$92$	8.75264	−	1.96771i	0.912526	−	0.205148i
$93$		−	22.7919i		−	2.36341i
$94$	−8.92321	+	11.1520i	−0.920358	+	1.15024i
$95$	−15.3564			−1.57554
$96$	13.6291	+	3.22792i	1.39102	+	0.329449i
$97$		−	2.27247i		−	0.230734i	−0.993323	−	0.115367i	$-0.963196\pi$
$97$		−	2.27247i		−	0.230734i	0.993323	−	0.115367i	$-0.0368045\pi$
$98$	−5.93242	+	7.41418i	−0.599265	+	0.748945i
$99$	10.3176	+	1.15729i	1.03696	+	0.116312i
$100$	1.17080	+	5.20787i	0.117080	+	0.520787i
$101$			17.2908i			1.72050i	0.509874	+	0.860249i	$0.329692\pi$
$101$			17.2908i			1.72050i	−0.509874	+	0.860249i	$0.670308\pi$
$102$	−12.9212	+	16.1486i	−1.27939	+	1.59895i
$103$			16.1107i			1.58744i	0.608285	+	0.793718i	$0.291858\pi$
$103$			16.1107i			1.58744i	−0.608285	+	0.793718i	$0.708142\pi$
$104$	−6.88284	−	7.52506i	−0.674918	−	0.737892i
$105$			3.66494i			0.357662i
$106$	−3.87763	+	4.84616i	−0.376629	+	0.470701i
$107$	−2.42591			−0.234522			−0.117261	−	0.993101i	$-0.537411\pi$
$107$	−2.42591			−0.234522			−0.117261	+	0.993101i	$0.537411\pi$
$108$	−0.629934	+	0.141618i	−0.0606154	+	0.0136272i
$109$	3.59775			0.344602			0.172301	−	0.985044i	$-0.444880\pi$
$109$	3.59775			0.344602			0.172301	+	0.985044i	$0.444880\pi$
$110$	9.17428	+	9.19505i	0.874733	+	0.876714i
$111$	3.84344			0.364803
$112$	0.915073	+	1.93232i	0.0864663	+	0.182587i
$113$	−16.3185			−1.53511			−0.767556	−	0.640982i	$-0.778527\pi$
$113$	−16.3185			−1.53511			−0.767556	+	0.640982i	$0.778527\pi$
$114$	12.1310	−	15.1610i	1.13618	−	1.41996i
$115$	−12.4217			−1.15833
$116$	−1.32234	+	0.297281i	−0.122776	+	0.0276018i
$117$	10.4972	+	4.14715i	0.970471	+	0.383405i
$118$	−4.84147	+	6.05074i	−0.445693	+	0.557015i
$119$	−3.15708			−0.289409
$120$	−17.4316	−	8.49993i	−1.59128	−	0.775933i
$121$	10.7266	+	2.43701i	0.975150	+	0.221546i
$122$	−11.3907	−	9.11420i	−1.03126	−	0.825161i
$123$			6.20620i			0.559594i
$124$	4.03815	+	17.9622i	0.362637	+	1.61305i
$125$			6.45540i			0.577389i
$126$	−1.84763	−	1.47838i	−0.164600	−	0.131704i
$127$	−13.6785			−1.21377			−0.606887	−	0.794788i	$-0.707582\pi$
$127$	−13.6785			−1.21377			−0.606887	+	0.794788i	$0.707582\pi$
$128$	−11.3130	−	0.129179i	−0.999935	−	0.0114179i
$129$		−	21.0221i		−	1.85089i
$130$	7.01279	+	12.2561i	0.615062	+	1.07493i
$131$	5.26829			0.460292			0.230146	−	0.973156i	$-0.426080\pi$
$131$	5.26829			0.460292			0.230146	+	0.973156i	$0.426080\pi$
$132$	−16.3254	+	1.79378i	−1.42095	+	0.156128i
$133$	2.96400			0.257012
$134$	2.54498	−	3.18065i	0.219853	−	0.274766i
$135$	0.894002			0.0769435
$136$	7.32206	−	15.0160i	0.627861	−	1.28761i
$137$			14.4042i			1.23063i	0.788281	+	0.615315i	$0.210971\pi$
$137$			14.4042i			1.23063i	−0.788281	+	0.615315i	$0.789029\pi$
$138$	9.81275	−	12.2637i	0.835316	−	1.04396i
$139$	10.9164			0.925915			0.462958	−	0.886380i	$-0.346788\pi$
$139$	10.9164			0.925915			0.462958	+	0.886380i	$0.346788\pi$
$140$	−0.649336	−	2.88833i	−0.0548789	−	0.244108i
$141$			25.0054i			2.10583i
$142$	−2.73790	+	3.42175i	−0.229760	+	0.287147i
$143$	10.5627	+	5.60622i	0.883296	+	0.468816i
$144$	11.3167	−	5.35917i	0.943060	−	0.446597i
$145$	1.87667			0.155849
$146$	8.34345	−	10.4274i	0.690509	−	0.862980i
$147$			16.6243i			1.37115i
$148$	−3.02900	+	0.680961i	−0.248982	+	0.0559746i
$149$	−17.4380			−1.42857			−0.714287	−	0.699853i	$-0.753249\pi$
$149$	−17.4380			−1.42857			−0.714287	+	0.699853i	$0.753249\pi$
$150$	7.29697	+	5.83864i	0.595795	+	0.476723i
$151$		−	11.6811i		−	0.950595i	−0.879825	−	0.475298i	$-0.842340\pi$
$151$		−	11.6811i		−	0.950595i	0.879825	−	0.475298i	$-0.157660\pi$
$152$	−6.87427	+	14.0977i	−0.557577	+	1.14347i
$153$			18.4896i			1.49479i
$154$	−1.77076	−	1.77477i	−0.142692	−	0.143015i
$155$		−	25.4920i		−	2.04756i
$156$	−17.6401	−	2.75835i	−1.41233	−	0.220845i
$157$	−8.98086			−0.716750			−0.358375	−	0.933578i	$-0.616669\pi$
$157$	−8.98086			−0.716750			−0.358375	+	0.933578i	$0.616669\pi$
$158$	7.44514	−	9.30473i	0.592303	−	0.740245i
$159$			10.8662i			0.861749i
$160$	15.2437	+	3.61033i	1.20512	+	0.285422i
$161$	2.39757			0.188955
$162$	7.59133	−	9.48743i	0.596431	−	0.745403i
$163$	−11.2972			−0.884862			−0.442431	−	0.896803i	$-0.645884\pi$
$163$	−11.2972			−0.884862			−0.442431	+	0.896803i	$0.645884\pi$
$164$	−1.09958	−	4.89108i	−0.0858630	−	0.381929i
$165$	22.5992	+	2.53487i	1.75934	+	0.197340i
$166$	−3.12743	−	2.50240i	−0.242736	−	0.194224i
$167$			8.52950i			0.660032i	0.943975	+	0.330016i	$0.107054\pi$
$167$			8.52950i			0.660032i	−0.943975	+	0.330016i	$0.892946\pi$
$168$	3.36453	+	1.64060i	0.259579	+	0.126575i
$169$	9.48977	+	8.88505i	0.729983	+	0.683466i
$170$	−14.4520	+	18.0617i	−1.10842	+	1.38527i
$171$		−	17.3588i		−	1.32746i
$172$	3.72458	+	16.5674i	0.283997	+	1.26325i
$173$			13.0482i			0.992033i	0.868313	+	0.496017i	$0.165204\pi$
$173$			13.0482i			0.992033i	−0.868313	+	0.496017i	$0.834796\pi$
$174$	−1.48250	+	1.85279i	−0.112388	+	0.140460i
$175$			1.42657i			0.107838i
$176$	12.5482	−	4.30613i	0.945856	−	0.324586i
$177$			13.5672i			1.01977i
$178$	7.67689	+	6.14263i	0.575408	+	0.460410i
$179$			7.19411i			0.537713i	0.963180	+	0.268857i	$0.0866458\pi$
$179$			7.19411i			0.537713i	−0.963180	+	0.268857i	$0.913354\pi$
$180$	−16.9156	+	3.80287i	−1.26082	+	0.283449i
$181$	6.78219			0.504116			0.252058	−	0.967712i	$-0.418893\pi$
$181$	6.78219			0.504116			0.252058	+	0.967712i	$0.418893\pi$
$182$	−1.35357	−	2.36561i	−0.100333	−	0.175350i
$183$	−25.5406			−1.88802
$184$	−5.56057	+	11.4036i	−0.409931	+	0.840682i
$185$	4.29876			0.316051
$186$	25.1676	+	20.1378i	1.84538	+	1.47657i
$187$	−2.18361	+	19.4675i	−0.159681	+	1.42361i
$188$	−4.43033	−	19.7067i	−0.323115	−	1.43726i
$189$	−0.172555			−0.0125515
$190$	13.5682	−	16.9571i	0.984338	−	1.23020i
$191$			2.12348i			0.153650i	0.997045	+	0.0768248i	$0.0244782\pi$
$191$			2.12348i			0.153650i	−0.997045	+	0.0768248i	$0.975522\pi$
$192$	−15.6064	+	12.1977i	−1.12629	+	0.880296i
$193$	13.1530			0.946770			0.473385	−	0.880856i	$-0.343032\pi$
$193$	13.1530			0.946770			0.473385	+	0.880856i	$0.343032\pi$
$194$	2.50935	+	2.00784i	0.180161	+	0.144155i
$195$	22.9926	+	9.08372i	1.64654	+	0.650499i
$196$	−2.94542	−	13.1016i	−0.210387	−	0.935828i
$197$	2.47118			0.176064			0.0880321	−	0.996118i	$-0.471942\pi$
$197$	2.47118			0.176064			0.0880321	+	0.996118i	$0.471942\pi$
$198$	−10.3941	+	10.3706i	−0.738673	+	0.737004i
$199$		−	17.6493i		−	1.25113i	−0.780174	−	0.625563i	$-0.784869\pi$
$199$		−	17.6493i		−	1.25113i	0.780174	−	0.625563i	$-0.215131\pi$
$200$	−6.78518	−	3.30857i	−0.479785	−	0.233951i
$201$		−	7.13177i		−	0.503036i
$202$	−19.0931	−	15.2773i	−1.34339	−	1.07491i
$203$	−0.362224			−0.0254231
$204$	−6.41534	−	28.5362i	−0.449163	−	1.99794i
$205$			6.94143i			0.484810i
$206$	−17.7901	−	14.2346i	−1.23949	−	0.991774i
$207$		−	14.0415i		−	0.975951i
$208$	14.3908	−	0.951526i	0.997821	−	0.0659765i
$209$	2.05007	−	18.2770i	0.141806	−	1.26424i
$210$	−4.04696	−	3.23816i	−0.279267	−	0.223454i
$211$	25.0448			1.72416			0.862078	−	0.506775i	$-0.169163\pi$
$211$	25.0448			1.72416			0.862078	+	0.506775i	$0.169163\pi$
$212$	−1.92523	−	8.56365i	−0.132225	−	0.588154i
$213$			7.67239i			0.525703i
$214$	2.14342	−	2.67878i	0.146521	−	0.183118i
$215$		−	23.5125i		−	1.60354i
$216$	0.400199	−	0.820723i	0.0272301	−	0.0558431i
$217$			4.92031i			0.334012i
$218$	−3.17879	+	3.97276i	−0.215295	+	0.269070i
$219$		−	23.3808i		−	1.57993i
$220$	−18.2595	+	2.00628i	−1.23105	+	0.135264i
$221$	−7.82495	+	19.8065i	−0.526363	+	1.33233i
$222$	−3.39587	+	4.24406i	−0.227916	+	0.284843i
$223$	−1.33070			−0.0891100			−0.0445550	−	0.999007i	$-0.514187\pi$
$223$	−1.33070			−0.0891100			−0.0445550	+	0.999007i	$0.514187\pi$
$224$	−2.94225	−	0.696844i	−0.196587	−	0.0465598i
$225$	8.35476			0.556984
$226$	14.4182	−	18.0195i	0.959083	−	1.19864i
$227$		−	18.9517i		−	1.25787i	−0.777458	−	0.628935i	$-0.783491\pi$
$227$		−	18.9517i		−	1.25787i	0.777458	−	0.628935i	$-0.216509\pi$
$228$	6.02300	+	26.7911i	0.398883	+	1.77428i
$229$		−	11.3147i		−	0.747697i	−0.927490	−	0.373848i	$-0.878038\pi$
$229$		−	11.3147i		−	0.747697i	0.927490	−	0.373848i	$-0.121962\pi$
$230$	10.9752	−	13.7166i	0.723686	−	0.904443i
$231$	−4.36196	−	0.489266i	−0.286996	−	0.0321913i
$232$	0.840088	−	1.72284i	0.0551545	−	0.113110i
$233$		−	27.0748i		−	1.77373i	−0.462028	−	0.886865i	$-0.652878\pi$
$233$		−	27.0748i		−	1.77373i	0.462028	−	0.886865i	$-0.347122\pi$
$234$	−13.8543	+	7.92723i	−0.905683	+	0.518219i
$235$			27.9677i			1.82441i
$236$	−2.40377	−	10.6923i	−0.156472	−	0.696007i
$237$		−	20.8634i		−	1.35522i
$238$	2.78944	−	3.48616i	0.180812	−	0.225974i
$239$			14.6552i			0.947969i	0.880533	+	0.473984i	$0.157185\pi$
$239$			14.6552i			0.947969i	−0.880533	+	0.473984i	$0.842815\pi$
$240$	24.7876	−	11.7385i	1.60003	−	0.757714i
$241$	−7.37547			−0.475096			−0.237548	−	0.971376i	$-0.576344\pi$
$241$	−7.37547			−0.475096			−0.237548	+	0.971376i	$0.576344\pi$
$242$	−12.1686	+	9.69155i	−0.782225	+	0.622996i
$243$		−	22.2416i		−	1.42680i
$244$	20.1285	−	4.52516i	1.28859	−	0.289694i
$245$			18.5938i			1.18791i
$246$	−6.85311	−	5.48349i	−0.436938	−	0.349614i
$247$	7.34641	−	18.5952i	0.467441	−	1.18318i
$248$	−23.4024	−	11.4114i	−1.48606	−	0.724627i
$249$	−7.01244			−0.444395
$250$	−7.12830	−	5.70367i	−0.450833	−	0.360732i
$251$		−	2.77747i		−	0.175312i	−0.996151	−	0.0876562i	$-0.972062\pi$
$251$		−	2.77747i		−	0.175312i	0.996151	−	0.0876562i	$-0.0279377\pi$
$252$	3.26496	−	0.734007i	0.205673	−	0.0462381i
$253$	1.65829	−	14.7842i	0.104256	−	0.929473i
$254$	12.0857	−	15.1043i	0.758322	−	0.947730i
$255$			40.4986i			2.53612i
$256$	10.1382	−	12.3781i	0.633639	−	0.773629i
$257$	15.1479			0.944903			0.472452	−	0.881357i	$-0.343369\pi$
$257$	15.1479			0.944903			0.472452	+	0.881357i	$0.343369\pi$
$258$	23.2133	+	18.5740i	1.44520	+	1.15637i
$259$	−0.829720			−0.0515563
$260$	−19.7298	−	3.08513i	−1.22359	−	0.191332i
$261$			2.12138i			0.131310i
$262$	−4.65479	+	5.81744i	−0.287574	+	0.359402i
$263$	−3.46372			−0.213582			−0.106791	−	0.994281i	$-0.534058\pi$
$263$	−3.46372			−0.213582			−0.106791	+	0.994281i	$0.534058\pi$
$264$	12.4436	−	19.6120i	0.765849	−	1.20704i
$265$			12.1535i			0.746586i
$266$	−2.61885	+	3.27296i	−0.160572	+	0.200678i
$267$	17.2134			1.05344
$268$	1.26357	+	5.62052i	0.0771849	+	0.343328i
$269$	20.6283			1.25773			0.628863	−	0.777516i	$-0.283520\pi$
$269$	20.6283			1.25773			0.628863	+	0.777516i	$0.283520\pi$
$270$	−0.789896	+	0.987191i	−0.0480715	+	0.0600785i
$271$			14.0761i			0.855065i	0.904000	+	0.427532i	$0.140617\pi$
$271$			14.0761i			0.855065i	−0.904000	+	0.427532i	$0.859383\pi$
$272$	10.1118	+	21.3527i	0.613119	+	1.29470i
$273$	−4.43790	−	1.75328i	−0.268594	−	0.106114i
$274$	−15.9056	−	12.7268i	−0.960892	−	0.768854i
$275$	8.79666	+	0.986692i	0.530459	+	0.0594998i
$276$	4.87198	+	21.6712i	0.293259	+	1.30445i
$277$			26.1430i			1.57078i	0.619000	+	0.785391i	$0.287538\pi$
$277$			26.1430i			1.57078i	−0.619000	+	0.785391i	$0.712462\pi$
$278$	−9.64517	+	12.0543i	−0.578479	+	0.722967i
$279$	28.8160			1.72517
$280$	3.76312	+	1.83496i	0.224889	+	0.109660i
$281$	22.8496			1.36309			0.681545	−	0.731776i	$-0.261308\pi$
$281$	22.8496			1.36309			0.681545	+	0.731776i	$0.261308\pi$
$282$	−27.6119	−	22.0935i	−1.64426	−	1.31565i
$283$	−13.1440			−0.781331			−0.390666	−	0.920533i	$-0.627755\pi$
$283$	−13.1440			−0.781331			−0.390666	+	0.920533i	$0.627755\pi$
$284$	−1.35936	−	6.04658i	−0.0806629	−	0.358799i
$285$		−	38.0219i		−	2.25222i
$286$	−15.5233	+	6.71033i	−0.917909	+	0.396790i
$287$		−	1.33979i		−	0.0790855i
$288$	−4.08110	+	17.2314i	−0.240481	+	1.01537i
$289$	−17.8866			−1.05215
$290$	−1.65813	+	2.07229i	−0.0973689	+	0.121689i
$291$	5.62655			0.329834
$292$	4.14249	+	18.4263i	0.242421	+	1.07832i
$293$	−11.1419			−0.650917			−0.325459	−	0.945556i	$-0.605519\pi$
$293$	−11.1419			−0.650917			−0.325459	+	0.945556i	$0.605519\pi$
$294$	−18.3572	−	14.6884i	−1.07061	−	0.856647i
$295$			15.1745i			0.883491i
$296$	1.92433	−	3.94640i	0.111849	−	0.229380i
$297$	−0.119348	+	1.06403i	−0.00692530	+	0.0617411i
$298$	15.4073	−	19.2556i	0.892521	−	1.11545i
$299$	5.94248	−	15.0416i	0.343663	−	0.869876i
$300$	−12.8945	+	2.89886i	−0.744463	+	0.167366i
$301$			4.53824i			0.261580i
$302$	12.8987	+	10.3208i	0.742238	+	0.593898i
$303$	−42.8113			−2.45945
$304$	−9.49342	−	20.0468i	−0.544485	−	1.14976i
$305$	−28.5663			−1.63570
$306$	−20.4169	−	16.3365i	−1.16716	−	0.933894i
$307$		−	28.8175i		−	1.64470i	−0.568980	−	0.822351i	$-0.692662\pi$
$307$		−	28.8175i		−	1.64470i	0.568980	−	0.822351i	$-0.307338\pi$
$308$	3.52433	−	0.387240i	0.200817	−	0.0220651i
$309$	−39.8895			−2.26924
$310$	28.1492	+	22.5234i	1.59877	+	1.27924i
$311$			14.7627i			0.837114i	0.908190	+	0.418557i	$0.137464\pi$
$311$			14.7627i			0.837114i	−0.908190	+	0.418557i	$0.862536\pi$
$312$	18.6317	−	17.0417i	1.05482	−	0.964794i
$313$	−12.4148			−0.701726			−0.350863	−	0.936427i	$-0.614112\pi$
$313$	−12.4148			−0.701726			−0.350863	+	0.936427i	$0.614112\pi$
$314$	7.93504	−	9.91699i	0.447800	−	0.559648i
$315$	−4.63363			−0.261075
$316$	3.69648	+	16.4424i	0.207943	+	0.924957i
$317$			8.15212i			0.457869i	0.973442	+	0.228934i	$0.0735241\pi$
$317$			8.15212i			0.457869i	−0.973442	+	0.228934i	$0.926476\pi$
$318$	−11.9989	−	9.60087i	−0.672865	−	0.538390i
$319$	−0.250534	+	2.23358i	−0.0140272	+	0.125057i
$320$	−17.4553	+	13.6428i	−0.975778	+	0.762654i
$321$		−	6.00647i		−	0.335248i
$322$	−2.11837	+	2.64749i	−0.118052	+	0.147539i
$323$	32.7531			1.82243
$324$	3.76906	+	16.7652i	0.209392	+	0.931402i
$325$	8.94981	+	3.53581i	0.496446	+	0.196131i
$326$	9.98161	−	12.4747i	0.552830	−	0.690912i
$327$			8.90788i			0.492607i
$328$	6.37245	+	3.10732i	0.351860	+	0.171573i
$329$		−	5.39816i		−	0.297610i
$330$	−22.7666	+	22.7152i	−1.25326	+	1.25043i
$331$	−10.6108			−0.583223			−0.291611	−	0.956537i	$-0.594191\pi$
$331$	−10.6108			−0.583223			−0.291611	+	0.956537i	$0.594191\pi$
$332$	5.52648	−	1.24243i	0.303305	−	0.0681871i
$333$			4.85930i			0.266288i
$334$	−9.41859	−	7.53624i	−0.515362	−	0.412365i
$335$		−	7.97665i		−	0.435811i
$336$	−4.78435	+	2.26569i	−0.261008	+	0.123603i
$337$		−	9.58696i		−	0.522235i	−0.965307	−	0.261117i	$-0.915909\pi$
$337$		−	9.58696i		−	0.522235i	0.965307	−	0.261117i	$-0.0840910\pi$
$338$	−18.1959	+	2.62857i	−0.989726	+	0.142975i
$339$		−	40.4039i		−	2.19444i
$340$	−7.17534	−	31.9168i	−0.389138	−	1.73093i
$341$	30.3401	+	3.40315i	1.64301	+	0.184291i
$342$	19.1683	+	15.3374i	1.03650	+	0.829352i
$343$		−	7.33043i		−	0.395806i
$344$	−21.5852	−	10.5253i	−1.16380	−	0.567487i
$345$		−	30.7558i		−	1.65584i
$346$	−14.4083	−	11.5287i	−0.774593	−	0.619787i
$347$	15.7991			0.848142			0.424071	−	0.905629i	$-0.360601\pi$
$347$	15.7991			0.848142			0.424071	+	0.905629i	$0.360601\pi$
$348$	−0.736056	−	3.27407i	−0.0394568	−	0.175509i
$349$	−18.7254			−1.00235			−0.501174	−	0.865346i	$-0.667098\pi$
$349$	−18.7254			−1.00235			−0.501174	+	0.865346i	$0.667098\pi$
$350$	−1.57527	−	1.26044i	−0.0842017	−	0.0673736i
$351$	−0.427685	+	1.08255i	−0.0228281	+	0.0577824i
$352$	−6.33198	+	17.6609i	−0.337496	+	0.941327i
$353$			4.16295i			0.221571i	0.993844	+	0.110786i	$0.0353367\pi$
$353$			4.16295i			0.221571i	−0.993844	+	0.110786i	$0.964663\pi$
$354$	−14.9814	−	11.9873i	−0.796252	−	0.637117i
$355$			8.58132i			0.455449i
$356$	−13.5658	+	3.04979i	−0.718988	+	0.161638i
$357$		−	7.81680i		−	0.413709i
$358$	−7.94401	−	6.35636i	−0.419854	−	0.335944i
$359$			9.90104i			0.522557i	0.965264	+	0.261278i	$0.0841440\pi$
$359$			9.90104i			0.522557i	−0.965264	+	0.261278i	$0.915856\pi$
$360$	10.7465	−	22.0389i	0.566393	−	1.16155i
$361$	−11.7500			−0.618423
$362$	−5.99240	+	7.48914i	−0.314954	+	0.393621i
$363$	−6.03393	+	26.5588i	−0.316699	+	1.39397i
$364$	3.80813	+	0.595473i	0.199600	+	0.0312113i
$365$		−	26.1506i		−	1.36879i
$366$	22.5664	−	28.2029i	1.17957	−	1.47419i
$367$			4.13130i			0.215652i	0.994170	+	0.107826i	$0.0343890\pi$
$367$			4.13130i			0.215652i	−0.994170	+	0.107826i	$0.965611\pi$
$368$	−7.67919	−	16.2158i	−0.400305	−	0.845307i
$369$	−7.84656			−0.408476
$370$	−3.79817	+	4.74685i	−0.197457	+	0.246777i
$371$		−	2.34580i		−	0.121788i
$372$	−44.4737	+	9.99830i	−2.30585	+	0.518388i
$373$			34.4449i			1.78349i	0.452538	+	0.891745i	$0.350519\pi$
$373$			34.4449i			1.78349i	−0.452538	+	0.891745i	$0.649481\pi$
$374$	−19.5674	−	19.6117i	−1.01181	−	1.01410i
$375$	−15.9833			−0.825376
$376$	25.6752	+	12.5197i	1.32410	+	0.645654i
$377$	−0.897787	+	2.27247i	−0.0462384	+	0.117038i
$378$	0.152461	−	0.190542i	0.00784175	−	0.00980040i
$379$	29.3313			1.50665			0.753323	−	0.657651i	$-0.228450\pi$
$379$	29.3313			1.50665			0.753323	+	0.657651i	$0.228450\pi$
$380$	6.73653	+	29.9649i	0.345577	+	1.53717i
$381$		−	33.8675i		−	1.73509i
$382$	−2.34482	−	1.87620i	−0.119972	−	0.0959948i
$383$	23.6902			1.21051			0.605255	−	0.796032i	$-0.293071\pi$
$383$	23.6902			1.21051			0.605255	+	0.796032i	$0.293071\pi$
$384$	0.319842	−	28.0105i	0.0163218	−	1.42940i
$385$	−4.87871	−	0.547228i	−0.248642	−	0.0278893i
$386$	−11.6213	+	14.5240i	−0.591508	+	0.739251i
$387$	26.5784			1.35106
$388$	−4.43427	+	0.996884i	−0.225116	+	0.0506091i
$389$	−18.0886			−0.917130			−0.458565	−	0.888661i	$-0.651636\pi$
$389$	−18.0886			−0.917130			−0.458565	+	0.888661i	$0.651636\pi$
$390$	−30.3457	+	17.3634i	−1.53662	+	0.879230i
$391$	26.4938			1.33985
$392$	17.0697	+	8.32347i	0.862149	+	0.420399i
$393$			13.0441i			0.657986i
$394$	−2.18341	+	2.72877i	−0.109999	+	0.137473i
$395$		−	23.3351i		−	1.17411i
$396$	−2.26789	−	20.6404i	−0.113966	−	1.03722i
$397$		−	27.1183i		−	1.36103i	−0.732735	−	0.680514i	$-0.761757\pi$
$397$		−	27.1183i		−	1.36103i	0.732735	−	0.680514i	$-0.238243\pi$
$398$	19.4890	+	15.5940i	0.976896	+	0.781659i
$399$			7.33876i			0.367398i
$400$	9.64849	−	4.56916i	0.482425	−	0.228458i
$401$			30.7606i			1.53611i	0.640383	+	0.768056i	$0.278776\pi$
$401$			30.7606i			1.53611i	−0.640383	+	0.768056i	$0.721224\pi$
$402$	7.87516	+	6.30128i	0.392777	+	0.314279i
$403$	30.8684	+	12.1952i	1.53766	+	0.607486i
$404$	33.7395	−	7.58510i	1.67860	−	0.377373i
$405$		−	23.7932i		−	1.18230i
$406$	0.320043	−	0.399981i	0.0158835	−	0.0198507i
$407$	−0.573880	+	5.11631i	−0.0284462	+	0.253606i
$408$	37.1790	+	18.1291i	1.84064	+	0.897526i
$409$	30.4703			1.50666			0.753331	−	0.657642i	$-0.228446\pi$
$409$	30.4703			1.50666			0.753331	+	0.657642i	$0.228446\pi$
$410$	−7.66498	−	6.13310i	−0.378546	−	0.302892i
$411$	−35.6641			−1.75918
$412$	31.4368	−	7.06743i	1.54878	−	0.348187i
$413$		−	2.92888i		−	0.144121i
$414$	15.5051	+	12.4064i	0.762036	+	0.609739i
$415$	−7.84318			−0.385007
$416$	−11.6643	+	16.7316i	−0.571888	+	0.820332i
$417$			27.0285i			1.32359i
$418$	18.3708	+	18.4124i	0.898544	+	0.900579i
$419$		−	3.97053i		−	0.193973i	−0.995286	−	0.0969866i	$-0.969080\pi$
$419$		−	3.97053i		−	0.193973i	0.995286	−	0.0969866i	$-0.0309204\pi$
$420$	7.15139	−	1.60773i	0.348952	−	0.0784493i
$421$			20.6838i			1.00807i	0.863684	+	0.504033i	$0.168151\pi$
$421$			20.6838i			1.00807i	−0.863684	+	0.504033i	$0.831849\pi$
$422$	−22.1284	+	27.6554i	−1.07719	+	1.34624i
$423$	−31.6146			−1.53715
$424$	11.1573	+	5.44051i	0.541848	+	0.264214i
$425$			15.7640i			0.764665i
$426$	−8.47213	−	6.77894i	−0.410476	−	0.328441i
$427$	5.51370			0.266827
$428$	1.06420	+	4.73368i	0.0514399	+	0.228811i
$429$	−13.8808	+	26.1528i	−0.670171	+	1.26267i
$430$	25.9634	+	20.7745i	1.25206	+	1.00183i
$431$			28.8707i			1.39065i	0.718693	+	0.695327i	$0.244740\pi$
$431$			28.8707i			1.39065i	−0.718693	+	0.695327i	$0.755260\pi$
$432$	0.552677	+	1.16706i	0.0265907	+	0.0561504i
$433$	0.958185			0.0460474			0.0230237	−	0.999735i	$-0.492671\pi$
$433$	0.958185			0.0460474			0.0230237	+	0.999735i	$0.492671\pi$
$434$	−5.43318	−	4.34734i	−0.260801	−	0.208679i
$435$			4.64656i			0.222786i
$436$	−1.57825	−	7.02027i	−0.0755846	−	0.336210i
$437$	−24.8736			−1.18986
$438$	25.8179	+	20.6581i	1.23363	+	0.987081i
$439$	1.22798			0.0586083			0.0293042	−	0.999571i	$-0.490671\pi$
$439$	1.22798			0.0586083			0.0293042	+	0.999571i	$0.490671\pi$
$440$	13.9177	−	21.9354i	0.663502	−	1.04573i
$441$	−21.0183			−1.00087
$442$	−14.9573	−	26.1406i	−0.711445	−	1.24338i
$443$		−	31.4487i		−	1.49417i	−0.664727	−	0.747086i	$-0.731452\pi$
$443$		−	31.4487i		−	1.49417i	0.664727	−	0.747086i	$-0.268548\pi$
$444$	−1.68603	−	7.49969i	−0.0800156	−	0.355919i
$445$	19.2526			0.912663
$446$	1.17574	−	1.46940i	0.0556727	−	0.0695783i
$447$		−	43.1757i		−	2.04214i
$448$	3.36911	−	2.63325i	0.159175	−	0.124409i
$449$			4.36055i			0.205787i	0.994692	+	0.102894i	$0.0328101\pi$
$449$			4.36055i			0.205787i	−0.994692	+	0.102894i	$0.967190\pi$
$450$	−7.38185	+	9.22564i	−0.347984	+	0.434901i
$451$	−8.26158	−	0.926674i	−0.389023	−	0.0436354i
$452$	7.15856	+	31.8422i	0.336710	+	1.49773i
$453$	28.9220			1.35887
$454$	20.9272	+	16.7448i	0.982161	+	0.785872i
$455$	−4.96365	−	1.96099i	−0.232699	−	0.0919327i
$456$	−34.9053	−	17.0204i	−1.63459	−	0.797055i
$457$	30.1840			1.41195			0.705974	−	0.708237i	$-0.250509\pi$
$457$	30.1840			1.41195			0.705974	+	0.708237i	$0.250509\pi$
$458$	12.4941	+	9.99711i	0.583812	+	0.467134i
$459$	−1.90678			−0.0890009
$460$	5.44915	+	24.2385i	0.254068	+	1.13013i
$461$	32.5822			1.51751			0.758753	−	0.651378i	$-0.225809\pi$
$461$	32.5822			1.51751			0.758753	+	0.651378i	$0.225809\pi$
$462$	4.39427	−	4.38434i	0.204440	−	0.203978i
$463$	−4.03113			−0.187343			−0.0936713	−	0.995603i	$-0.529860\pi$
$463$	−4.03113			−0.187343			−0.0936713	+	0.995603i	$0.529860\pi$
$464$	1.16017	+	2.44987i	0.0538594	+	0.113733i
$465$	63.1171			2.92699
$466$	29.8970	+	23.9220i	1.38495	+	1.10816i
$467$		−	3.41015i		−	0.157803i	−0.996882	−	0.0789014i	$-0.974859\pi$
$467$		−	3.41015i		−	0.157803i	0.996882	−	0.0789014i	$-0.0251412\pi$
$468$	3.48742	−	22.3025i	0.161206	−	1.03093i
$469$			1.53961i			0.0710924i
$470$	−30.8830	−	24.7109i	−1.42453	−	1.13983i
$471$		−	22.2363i		−	1.02459i
$472$	13.9306	+	6.79282i	0.641209	+	0.312665i
$473$	27.9842	+	3.13889i	1.28671	+	0.144326i
$474$	23.0382	+	18.4339i	1.05818	+	0.846696i
$475$		−	14.7999i		−	0.679067i
$476$	1.38494	+	6.16040i	0.0634787	+	0.282361i
$477$	−13.7383			−0.629034
$478$	−16.1829	−	12.9486i	−0.740187	−	0.592257i
$479$			7.23882i			0.330750i	0.986231	+	0.165375i	$0.0528834\pi$
$479$			7.23882i			0.330750i	−0.986231	+	0.165375i	$0.947117\pi$
$480$	−8.93904	+	37.7429i	−0.408009	+	1.72272i
$481$	−2.05650	+	5.20539i	−0.0937682	+	0.237345i
$482$	6.51660	−	8.14427i	0.296823	−	0.370961i
$483$			5.93629i			0.270111i
$484$	0.0497733	−	21.9999i	0.00226242	−	0.999997i
$485$	6.29311			0.285756
$486$	24.5600	+	19.6515i	1.11406	+	0.891412i
$487$	−22.4374			−1.01674			−0.508368	−	0.861140i	$-0.669751\pi$
$487$	−22.4374			−1.01674			−0.508368	+	0.861140i	$0.669751\pi$
$488$	−12.7877	+	26.2248i	−0.578871	+	1.18714i
$489$		−	27.9713i		−	1.26491i
$490$	−20.5319	−	16.4285i	−0.927539	−	0.742166i
$491$	−21.1277			−0.953480			−0.476740	−	0.879044i	$-0.658182\pi$
$491$	−21.1277			−0.953480			−0.476740	+	0.879044i	$0.658182\pi$
$492$	12.1101	−	2.72252i	0.545967	−	0.122741i
$493$	−4.00267			−0.180271
$494$	14.0426	+	24.5420i	0.631805	+	1.10419i
$495$	−3.20487	+	28.5724i	−0.144048	+	1.28423i
$496$	33.2781	−	15.7593i	1.49423	−	0.707612i
$497$		−	1.65631i		−	0.0742958i
$498$	6.19584	−	7.74339i	0.277642	−	0.346990i
$499$	−8.39062			−0.375616			−0.187808	−	0.982206i	$-0.560138\pi$
$499$	−8.39062			−0.375616			−0.187808	+	0.982206i	$0.560138\pi$
$500$	12.5964	−	2.83185i	0.563329	−	0.126644i
$501$	−21.1187			−0.943514
$502$	3.06699	+	2.45403i	0.136886	+	0.109529i
$503$	20.0923			0.895870			0.447935	−	0.894066i	$-0.352160\pi$
$503$	20.0923			0.895870			0.447935	+	0.894066i	$0.352160\pi$
$504$	−2.07423	+	4.25382i	−0.0923937	+	0.189480i
$505$	−47.8831			−2.13077
$506$	14.8600	+	14.8937i	0.660609	+	0.662106i
$507$	−21.9990	+	23.4963i	−0.977012	+	1.04351i
$508$	6.00048	+	26.6909i	0.266228	+	1.18422i
$509$		−	19.2550i		−	0.853463i	−0.904378	−	0.426732i	$-0.859665\pi$
$509$		−	19.2550i		−	0.853463i	0.904378	−	0.426732i	$-0.140335\pi$
$510$	−44.7201	−	35.7826i	−1.98024	−	1.58448i
$511$			5.04743i			0.223285i
$512$	4.71069	+	22.1316i	0.208185	+	0.978089i
$513$	1.79017			0.0790379
$514$	−13.3840	+	16.7269i	−0.590342	+	0.737793i
$515$	−44.6151			−1.96598
$516$	−41.0203	+	9.22193i	−1.80582	+	0.405973i
$517$	−33.2867	−	3.73366i	−1.46395	−	0.164206i
$518$	0.733100	−	0.916208i	0.0322105	−	0.0402559i
$519$	−32.3067			−1.41811
$520$	20.8390	−	19.0605i	0.913851	−	0.835860i
$521$	37.4309			1.63988			0.819939	−	0.572451i	$-0.194007\pi$
$521$	37.4309			1.63988			0.819939	+	0.572451i	$0.194007\pi$
$522$	−2.34251	−	1.87435i	−0.102529	−	0.0820379i
$523$	7.29447			0.318965			0.159482	−	0.987201i	$-0.449017\pi$
$523$	7.29447			0.318965			0.159482	+	0.987201i	$0.449017\pi$
$524$	−2.31108	−	10.2800i	−0.100960	−	0.449084i
$525$	−3.53213			−0.154155
$526$	3.06037	−	3.82477i	0.133439	−	0.166768i
$527$			54.3708i			2.36843i
$528$	10.6618	+	31.0689i	0.463995	+	1.35210i
$529$	2.87986			0.125211
$530$	−13.4204	−	10.7383i	−0.582944	−	0.466440i
$531$	−17.1531			−0.744383
$532$	−1.30024	−	5.78365i	−0.0563728	−	0.250753i
$533$	−8.40542	−	3.32073i	−0.364079	−	0.143837i
$534$	−15.2089	+	19.0077i	−0.658154	+	0.822543i
$535$		−	6.71804i		−	0.290446i
$536$	−7.32282	−	3.57073i	−0.316298	−	0.154232i
$537$	−17.8124			−0.768660
$538$	−18.2261	+	22.7785i	−0.785783	+	0.982050i
$539$	−22.1300	−	2.48225i	−0.953208	−	0.106918i
$540$	−0.392180	−	1.74446i	−0.0168767	−	0.0750698i
$541$	−4.63441			−0.199249			−0.0996243	−	0.995025i	$-0.531764\pi$
$541$	−4.63441			−0.199249			−0.0996243	+	0.995025i	$0.531764\pi$
$542$	−15.5434	−	12.4370i	−0.667646	−	0.534214i
$543$			16.7924i			0.720632i
$544$	−32.5127	−	7.70032i	−1.39397	−	0.330149i
$545$			9.96318i			0.426776i
$546$	5.85715	−	3.35138i	0.250663	−	0.143426i
$547$	−17.5177			−0.749002			−0.374501	−	0.927226i	$-0.622186\pi$
$547$	−17.5177			−0.749002			−0.374501	+	0.927226i	$0.622186\pi$
$548$	28.1068	−	6.31879i	1.20066	−	0.269925i
$549$		−	32.2913i		−	1.37816i
$550$	−8.86183	+	8.84180i	−0.377870	+	0.377016i
$551$	3.75789			0.160091
$552$	−28.2348	−	13.7678i	−1.20175	−	0.585995i
$553$			4.50399i			0.191529i
$554$	−28.8681	−	23.0987i	−1.22649	−	0.981369i
$555$			10.6436i			0.451794i
$556$	−4.78878	−	21.3011i	−0.203090	−	0.903368i
$557$	34.5051			1.46203			0.731014	−	0.682363i	$-0.239048\pi$
$557$	34.5051			1.46203			0.731014	+	0.682363i	$0.239048\pi$
$558$	−25.4604	+	31.8197i	−1.07782	+	1.34704i
$559$	28.4714	+	11.2482i	1.20421	+	0.475749i
$560$	−5.35114	+	2.53410i	−0.226127	+	0.107085i
$561$	−48.2008	−	5.40653i	−2.03504	−	0.228264i
$562$	−20.1887	+	25.2313i	−0.851610	+	1.06432i
$563$	−3.29489			−0.138863			−0.0694314	−	0.997587i	$-0.522119\pi$
$563$	−3.29489			−0.138863			−0.0694314	+	0.997587i	$0.522119\pi$
$564$	48.7929	−	10.9693i	2.05455	−	0.461892i
$565$		−	45.1904i		−	1.90118i
$566$	11.6134	−	14.5141i	0.488148	−	0.610074i
$567$			4.59243i			0.192864i
$568$	7.87792	+	3.84141i	0.330550	+	0.161182i
$569$			36.4540i			1.52823i	0.645080	+	0.764115i	$0.276824\pi$
$569$			36.4540i			1.52823i	−0.645080	+	0.764115i	$0.723176\pi$
$570$	41.9852	+	33.5943i	1.75857	+	1.40711i
$571$	−35.0455			−1.46661			−0.733305	−	0.679900i	$-0.762023\pi$
$571$	−35.0455			−1.46661			−0.733305	+	0.679900i	$0.762023\pi$
$572$	6.30578	−	23.0703i	0.263658	−	0.964616i
$573$	−5.25765			−0.219642
$574$	1.47945	+	1.18377i	0.0617510	+	0.0494098i
$575$		−	11.9716i		−	0.499250i
$576$	−15.4217	−	19.7313i	−0.642572	−	0.822139i
$577$		−	22.6920i		−	0.944681i	−0.881416	−	0.472340i	$-0.843409\pi$
$577$		−	22.6920i		−	0.944681i	0.881416	−	0.472340i	$-0.156591\pi$
$578$	15.8037	−	19.7510i	0.657347	−	0.821535i
$579$			32.5662i			1.35341i
$580$	−0.823255	−	3.66194i	−0.0341838	−	0.152054i
$581$	1.51384			0.0628048
$582$	−4.97134	+	6.21304i	−0.206069	+	0.257539i
$583$	−14.4649	−	1.62248i	−0.599077	−	0.0671964i
$584$	−24.0071	−	11.7063i	−0.993421	−	0.484409i
$585$	−11.4846	+	29.0698i	−0.474832	+	1.20189i
$586$	9.84443	−	12.3033i	0.406670	−	0.508245i
$587$	23.1795			0.956722			0.478361	−	0.878163i	$-0.341231\pi$
$587$	23.1795			0.956722			0.478361	+	0.878163i	$0.341231\pi$
$588$	32.4390	−	7.29274i	1.33776	−	0.300748i
$589$		−	51.0457i		−	2.10330i
$590$	−16.7562	−	13.4074i	−0.689842	−	0.551974i
$591$			6.11855i			0.251683i
$592$	2.65751	+	5.61176i	0.109223	+	0.230642i
$593$	−1.34031			−0.0550399			−0.0275200	−	0.999621i	$-0.508761\pi$
$593$	−1.34031			−0.0550399			−0.0275200	+	0.999621i	$0.508761\pi$
$594$	−1.06949	−	1.07191i	−0.0438816	−	0.0439810i
$595$		−	8.74284i		−	0.358421i
$596$	7.64966	+	34.0266i	0.313342	+	1.39379i
$597$	43.6990			1.78848
$598$	11.3590	+	19.8519i	0.464503	+	0.811804i
$599$			34.7876i			1.42138i	0.703504	+	0.710691i	$0.251618\pi$
$599$			34.7876i			1.42138i	−0.703504	+	0.710691i	$0.748382\pi$
$600$	8.19189	−	16.7998i	0.334433	−	0.685851i
$601$			34.3990i			1.40317i	0.712588	+	0.701583i	$0.247523\pi$
$601$			34.3990i			1.40317i	−0.712588	+	0.701583i	$0.752477\pi$
$602$	−5.01129	−	4.00976i	−0.204245	−	0.163426i
$603$	9.01677			0.367191
$604$	−22.7933	+	5.12425i	−0.927447	+	0.208503i
$605$	−6.74876	+	29.7051i	−0.274376	+	1.20768i
$606$	37.8260	−	47.2739i	1.53657	−	1.92037i
$607$	−14.0802			−0.571498			−0.285749	−	0.958305i	$-0.592242\pi$
$607$	−14.0802			−0.571498			−0.285749	+	0.958305i	$0.592242\pi$
$608$	30.5244	+	7.22940i	1.23793	+	0.293191i
$609$		−	0.896852i		−	0.0363423i
$610$	25.2398	−	31.5440i	1.02193	−	1.27718i
$611$	−33.8663	−	13.3796i	−1.37008	−	0.541280i
$612$	36.0787	−	8.11098i	1.45839	−	0.327867i
$613$	10.9545			0.442447			0.221224	−	0.975223i	$-0.428995\pi$
$613$	10.9545			0.442447			0.221224	+	0.975223i	$0.428995\pi$
$614$	31.8214	+	25.4617i	1.28421	+	1.02755i
$615$	−17.1867			−0.693035
$616$	−2.68632	+	4.23384i	−0.108235	+	0.170586i
$617$			6.00315i			0.241678i	0.992672	+	0.120839i	$0.0385584\pi$
$617$			6.00315i			0.241678i	−0.992672	+	0.120839i	$0.961442\pi$
$618$	35.2444	−	44.0475i	1.41774	−	1.77185i
$619$	−13.0392			−0.524088			−0.262044	−	0.965056i	$-0.584397\pi$
$619$	−13.0392			−0.524088			−0.262044	+	0.965056i	$0.584397\pi$
$620$	−49.7424	+	11.1828i	−1.99770	+	0.449111i
$621$	1.44806			0.0581087
$622$	−16.3015	−	13.0436i	−0.653630	−	0.522999i
$623$	−3.71603			−0.148880
$624$	2.35594	+	35.6310i	0.0943132	+	1.42638i
$625$	−31.2215			−1.24886
$626$	10.9691	−	13.7089i	0.438413	−	0.547917i
$627$	45.2531	+	5.07589i	1.80723	+	0.202711i
$628$	3.93971	+	17.5243i	0.157211	+	0.699297i
$629$	−9.16864			−0.365578
$630$	4.09404	−	5.11662i	0.163111	−	0.203851i
$631$	19.0168			0.757046			0.378523	−	0.925592i	$-0.376432\pi$
$631$	19.0168			0.757046			0.378523	+	0.925592i	$0.376432\pi$
$632$	−21.4223	−	10.4459i	−0.852134	−	0.415515i
$633$			62.0100i			2.46468i
$634$	−9.00187	−	7.20281i	−0.357510	−	0.286060i
$635$		−	37.8797i		−	1.50321i
$636$	21.2033	−	4.76678i	0.840764	−	0.189015i
$637$	−22.5153	−	8.89515i	−0.892090	−	0.352439i
$638$	−2.24505	−	2.25013i	−0.0888822	−	0.0890835i
$639$	−9.70028			−0.383737
$640$	0.357732	−	31.3288i	0.0141406	−	1.23838i
$641$	−18.2023			−0.718949			−0.359475	−	0.933155i	$-0.617044\pi$
$641$	−18.2023			−0.718949			−0.359475	+	0.933155i	$0.617044\pi$
$642$	6.63257	+	5.30702i	0.261767	+	0.209451i
$643$	−18.4562			−0.727840			−0.363920	−	0.931430i	$-0.618562\pi$
$643$	−18.4562			−0.727840			−0.363920	+	0.931430i	$0.618562\pi$
$644$	−1.05176	−	4.67837i	−0.0414453	−	0.184354i
$645$	58.2160			2.29225
$646$	−28.9390	+	36.1672i	−1.13859	+	1.42298i
$647$		−	16.4584i		−	0.647047i	−0.946220	−	0.323524i	$-0.895132\pi$
$647$		−	16.4584i		−	0.647047i	0.946220	−	0.323524i	$-0.104868\pi$
$648$	−21.8430	−	10.6510i	−0.858072	−	0.418411i
$649$	−18.0604	−	2.02577i	−0.708933	−	0.0795186i
$650$	−11.8120	+	6.75865i	−0.463304	+	0.265096i
$651$	−12.1825			−0.477469
$652$	4.95582	+	22.0441i	0.194085	+	0.863315i
$653$	−2.39687			−0.0937967			−0.0468983	−	0.998900i	$-0.514934\pi$
$653$	−2.39687			−0.0937967			−0.0468983	+	0.998900i	$0.514934\pi$
$654$	−9.83641	−	7.87056i	−0.384634	−	0.307763i
$655$			14.5894i			0.570054i
$656$	−9.06159	+	4.29123i	−0.353796	+	0.167544i
$657$	29.5605			1.15327
$658$	5.96085	+	4.76954i	0.232378	+	0.185936i
$659$	37.1638			1.44770			0.723848	−	0.689959i	$-0.242371\pi$
$659$	37.1638			1.44770			0.723848	+	0.689959i	$0.242371\pi$
$660$	−4.96748	−	45.2097i	−0.193359	−	1.75979i
$661$			47.4011i			1.84369i	0.387562	+	0.921844i	$0.373317\pi$
$661$			47.4011i			1.84369i	−0.387562	+	0.921844i	$0.626683\pi$
$662$	9.37518	−	11.7168i	0.364377	−	0.455388i
$663$	−49.0400	−	19.3743i	−1.90456	−	0.752435i
$664$	−3.51099	+	7.20029i	−0.136253	+	0.279425i
$665$			8.20817i			0.318299i
$666$	−5.36582	−	4.29343i	−0.207921	−	0.166367i
$667$	3.03974			0.117699
$668$	16.6436	−	3.74171i	0.643960	−	0.144771i
$669$		−	3.29475i		−	0.127382i
$670$	8.80811	+	7.04777i	0.340287	+	0.272279i
$671$	3.81358	−	33.9992i	0.147222	−	1.31252i
$672$	1.72536	−	7.28490i	0.0665572	−	0.281021i
$673$		−	5.26521i		−	0.202959i	−0.994838	−	0.101479i	$-0.967642\pi$
$673$		−	5.26521i		−	0.202959i	0.994838	−	0.101479i	$-0.0323576\pi$
$674$	10.5863	+	8.47056i	0.407768	+	0.326274i
$675$			0.861604i			0.0331632i
$676$	13.1744	−	22.4151i	0.506709	−	0.862117i
$677$		−	0.333277i		−	0.0128089i	−0.999979	−	0.00640444i	$-0.997961\pi$
$677$		−	0.333277i		−	0.0128089i	0.999979	−	0.00640444i	$-0.00203861\pi$
$678$	44.6155	+	35.6989i	1.71345	+	1.37101i
$679$	−1.21466			−0.0466143
$680$	41.5835	+	20.2768i	1.59466	+	0.777582i
$681$	46.9237			1.79812
$682$	−30.5649	+	30.4958i	−1.17039	+	1.16775i
$683$	2.49175			0.0953442			0.0476721	−	0.998863i	$-0.484820\pi$
$683$	2.49175			0.0953442			0.0476721	+	0.998863i	$0.484820\pi$
$684$	−33.8722	+	7.61495i	−1.29514	+	0.291165i
$685$	−39.8892			−1.52409
$686$	8.09453	+	6.47680i	0.309051	+	0.247286i
$687$	28.0148			1.06883
$688$	30.6941	−	14.5355i	1.17020	−	0.554162i
$689$	−14.7168	−	5.81417i	−0.560665	−	0.221502i
$690$	33.9617	+	27.1743i	1.29290	+	1.03451i
$691$	39.4033			1.49897			0.749486	−	0.662020i	$-0.230301\pi$
$691$	39.4033			1.49897			0.749486	+	0.662020i	$0.230301\pi$
$692$	25.4608	−	5.72395i	0.967876	−	0.217592i
$693$	0.618584	−	5.51487i	0.0234981	−	0.209493i
$694$	−13.9593	+	17.4460i	−0.529889	+	0.662241i
$695$			30.2305i			1.14671i
$696$	4.26569	+	2.08003i	0.161691	+	0.0788432i
$697$		−	14.8051i		−	0.560783i
$698$	16.5448	−	20.6773i	0.626232	−	0.782647i
$699$	67.0362			2.53554
$700$	2.78366	−	0.625805i	0.105212	−	0.0236532i
$701$		−	14.3122i		−	0.540565i	−0.962781	−	0.270283i	$-0.912883\pi$
$701$		−	14.3122i		−	0.540565i	0.962781	−	0.270283i	$-0.0871171\pi$
$702$	−0.817514	−	1.42876i	−0.0308551	−	0.0539249i
$703$	8.60793			0.324654
$704$	−13.9072	−	22.5963i	−0.524146	−	0.851629i
$705$	−69.2470			−2.60799
$706$	−4.59688	−	3.67817i	−0.173006	−	0.138430i
$707$	9.24210			0.347585
$708$	26.4736	−	5.95163i	0.994939	−	0.223676i
$709$		−	26.4836i		−	0.994612i	−0.867575	−	0.497306i	$-0.834323\pi$
$709$		−	26.4836i		−	0.994612i	0.867575	−	0.497306i	$-0.165677\pi$
$710$	−9.47581	−	7.58202i	−0.355621	−	0.284548i
$711$	26.3778			0.989246
$712$	8.61841	−	17.6745i	0.322989	−	0.662381i
$713$		−	41.2906i		−	1.54635i
$714$	8.63160	+	6.90654i	0.323030	+	0.258471i
$715$	−15.5252	+	29.2511i	−0.580610	+	1.09393i
$716$	14.0379	−	3.15590i	0.524619	−	0.117942i
$717$	−36.2858			−1.35512
$718$	−10.9331	−	8.74806i	−0.408019	−	0.326475i
$719$		−	28.7663i		−	1.07280i	−0.843963	−	0.536401i	$-0.819783\pi$
$719$		−	28.7663i		−	1.07280i	0.843963	−	0.536401i	$-0.180217\pi$
$720$	14.8411	+	31.3392i	0.553093	+	1.16794i
$721$	8.61135			0.320703
$722$	10.3817	−	12.9748i	0.386369	−	0.482873i
$723$		−	18.2614i		−	0.679148i
$724$	−2.97520	−	13.2341i	−0.110572	−	0.491840i
$725$			1.80866i			0.0671720i
$726$	−23.9959	−	30.1289i	−0.890571	−	1.11819i
$727$		−	23.8682i		−	0.885221i	−0.896714	−	0.442610i	$-0.854052\pi$
$727$		−	23.8682i		−	0.885221i	0.896714	−	0.442610i	$-0.145948\pi$
$728$	−4.02222	+	3.67895i	−0.149073	+	0.136351i
$729$	29.2937			1.08495
$730$	28.8765	+	23.1054i	1.06877	+	0.855168i
$731$			50.1488i			1.85482i
$732$	11.2041	+	49.8373i	0.414116	+	1.84204i
$733$	0.489259			0.0180712			0.00903560	−	0.999959i	$-0.497124\pi$
$733$	0.489259			0.0180712			0.00903560	+	0.999959i	$0.497124\pi$
$734$	−4.56193	−	3.65021i	−0.168384	−	0.134732i
$735$	−46.0375			−1.69812
$736$	24.6910	+	5.84783i	0.910124	+	0.215554i
$737$	9.49368	+	1.06487i	0.349704	+	0.0392252i
$738$	6.93283	−	8.66446i	0.255201	−	0.318943i
$739$		−	4.59628i		−	0.169077i	−0.996420	−	0.0845384i	$-0.973058\pi$
$739$		−	4.59628i		−	0.169077i	0.996420	−	0.0845384i	$-0.0269416\pi$
$740$	−1.88577	−	8.38816i	−0.0693224	−	0.308355i
$741$	46.0409	+	18.1894i	1.69136	+	0.668206i
$742$	2.59032	+	2.07263i	0.0950937	+	0.0760888i
$743$		−	38.4847i		−	1.41187i	−0.708278	−	0.705934i	$-0.750528\pi$
$743$		−	38.4847i		−	1.41187i	0.708278	−	0.705934i	$-0.249472\pi$
$744$	28.2543	−	57.9435i	1.03585	−	2.12431i
$745$		−	48.2906i		−	1.76923i
$746$	−38.0354	−	30.4338i	−1.39257	−	1.11426i
$747$		−	8.86590i		−	0.324386i
$748$	38.9448	−	4.27911i	1.42396	−	0.156460i
$749$			1.29668i			0.0473795i
$750$	14.1221	−	17.6494i	0.515665	−	0.644464i
$751$		−	2.60106i		−	0.0949141i	−0.998873	−	0.0474571i	$-0.984888\pi$
$751$		−	2.60106i		−	0.0949141i	0.998873	−	0.0474571i	$-0.0151117\pi$
$752$	−36.5101	+	17.2898i	−1.33139	+	0.630493i
$753$	6.87691			0.250609
$754$	−1.71611	−	2.99921i	−0.0624969	−	0.109225i
$755$	32.3483			1.17727
$756$	0.0756962	+	0.336706i	0.00275304	+	0.0122459i
$757$	−15.6223			−0.567802			−0.283901	−	0.958854i	$-0.591629\pi$
$757$	−15.6223			−0.567802			−0.283901	+	0.958854i	$0.591629\pi$
$758$	−25.9156	+	32.3887i	−0.941299	+	1.17641i
$759$	36.6050	+	4.10586i	1.32868	+	0.149033i
$760$	−39.0405	−	19.0368i	−1.41615	−	0.690537i
$761$	16.2114			0.587662			0.293831	−	0.955857i	$-0.405070\pi$
$761$	16.2114			0.587662			0.293831	+	0.955857i	$0.405070\pi$
$762$	37.3978	+	29.9236i	1.35478	+	1.08402i
$763$		−	1.92303i		−	0.0696184i
$764$	4.14354	−	0.931525i	0.149908	−	0.0337014i
$765$	−51.2029			−1.85124
$766$	−20.9314	+	26.1595i	−0.756284	+	0.945183i
$767$	−18.3748	−	7.25936i	−0.663477	−	0.262120i
$768$	30.6476	+	25.1018i	1.10590	+	0.905785i
$769$	12.0546			0.434700			0.217350	−	0.976094i	$-0.430259\pi$
$769$	12.0546			0.434700			0.217350	+	0.976094i	$0.430259\pi$
$770$	4.91485	−	4.90374i	0.177119	−	0.176719i
$771$			37.5057i			1.35074i
$772$	−5.76992	−	25.6653i	−0.207664	−	0.923715i
$773$		−	29.6851i		−	1.06770i	−0.845579	−	0.533850i	$-0.820745\pi$
$773$		−	29.6851i		−	1.06770i	0.845579	−	0.533850i	$-0.179255\pi$
$774$	−23.4834	+	29.3489i	−0.844092	+	1.05492i
$775$	24.5682			0.882514
$776$	2.81710	−	5.77728i	0.101128	−	0.207392i
$777$		−	2.05436i		−	0.0736996i
$778$	15.9822	−	19.9741i	0.572990	−	0.716107i
$779$			13.8997i			0.498007i
$780$	7.63866	−	48.8503i	0.273508	−	1.74912i
$781$	−10.2133	−	1.14560i	−0.365462	−	0.0409927i
$782$	−23.4086	+	29.2555i	−0.837091	+	1.04617i
$783$	−0.218772			−0.00781828
$784$	−24.2730	+	11.4948i	−0.866893	+	0.410528i
$785$		−	24.8705i		−	0.887667i
$786$	−14.4037	−	11.5251i	−0.513765	−	0.411086i
$787$		−	6.17918i		−	0.220264i	−0.993917	−	0.110132i	$-0.964873\pi$
$787$		−	6.17918i		−	0.220264i	0.993917	−	0.110132i	$-0.0351274\pi$
$788$	−1.08405	−	4.82201i	−0.0386178	−	0.171777i
$789$		−	8.57605i		−	0.305315i
$790$	25.7674	+	20.6177i	0.916764	+	0.733544i
$791$			8.72239i			0.310132i
$792$	24.7957	+	15.7325i	0.881077	+	0.559032i
$793$	13.6660	−	34.5911i	0.485292	−	1.22837i
$794$	29.9450	+	23.9604i	1.06271	+	0.850322i
$795$	−30.0917			−1.06724
$796$	−34.4390	+	7.74237i	−1.22066	+	0.274421i
$797$	−10.8368			−0.383861			−0.191930	−	0.981409i	$-0.561475\pi$
$797$	−10.8368			−0.383861			−0.191930	+	0.981409i	$0.561475\pi$
$798$	−8.10373	−	6.48416i	−0.286869	−	0.229537i
$799$		−	59.6512i		−	2.11031i
$800$	−3.47949	+	14.6913i	−0.123019	+	0.519416i
$801$			21.7631i			0.768962i
$802$	−33.9670	−	27.1785i	−1.19942	−	0.959708i
$803$	31.1240	+	3.49108i	1.09834	+	0.123198i
$804$	−13.9162	+	3.12855i	−0.490787	+	0.110336i
$805$			6.63955i			0.234013i
$806$	−40.7401	+	23.3109i	−1.43501	+	0.821093i
$807$			51.0748i			1.79792i
$808$	−21.4348	+	43.9582i	−0.754073	+	1.54644i
$809$		−	17.7739i		−	0.624897i	−0.949935	−	0.312448i	$-0.898851\pi$
$809$		−	17.7739i		−	0.624897i	0.949935	−	0.312448i	$-0.101149\pi$
$810$	26.2734	+	21.0225i	0.923152	+	0.738656i
$811$			49.2510i			1.72944i	0.502256	+	0.864719i	$0.332503\pi$
$811$			49.2510i			1.72944i	−0.502256	+	0.864719i	$0.667497\pi$
$812$	0.158900	+	0.706806i	0.00557629	+	0.0248040i
$813$	−34.8520			−1.22231
$814$	−5.14257	−	5.15422i	−0.180247	−	0.180655i
$815$		−	31.2850i		−	1.09587i
$816$	−52.8684	+	25.0365i	−1.85076	+	0.876451i
$817$		−	47.0819i		−	1.64719i
$818$	−26.9221	+	33.6465i	−0.941308	+	1.17642i
$819$	2.21670	−	5.61088i	0.0774577	−	0.196060i
$820$	13.5448	−	3.04506i	0.473005	−	0.106338i
$821$	−30.7585			−1.07348			−0.536739	−	0.843748i	$-0.680344\pi$
$821$	−30.7585			−1.07348			−0.536739	+	0.843748i	$0.680344\pi$
$822$	31.5110	−	39.3816i	1.09907	−	1.37359i
$823$			12.7499i			0.444433i	0.974997	+	0.222217i	$0.0713292\pi$
$823$			12.7499i			0.444433i	−0.974997	+	0.222217i	$0.928671\pi$
$824$	−19.9719	+	40.9581i	−0.695753	+	1.42684i
$825$	−2.44301	+	21.7802i	−0.0850547	+	0.758289i
$826$	3.23418	+	2.58781i	0.112532	+	0.0900416i
$827$			15.8622i			0.551584i	0.961217	+	0.275792i	$0.0889400\pi$
$827$			15.8622i			0.551584i	−0.961217	+	0.275792i	$0.911060\pi$
$828$	−27.3991	+	6.15970i	−0.952185	+	0.214064i
$829$	48.1345			1.67178			0.835890	−	0.548897i	$-0.184952\pi$
$829$	48.1345			1.67178			0.835890	+	0.548897i	$0.184952\pi$
$830$	6.92984	−	8.66073i	0.240538	−	0.300618i
$831$	−64.7291			−2.24543
$832$	−8.16964	−	27.6633i	−0.283231	−	0.959052i
$833$		−	39.6579i		−	1.37407i
$834$	−29.8459	−	23.8811i	−1.03348	−	0.826934i
$835$	−23.6206			−0.817424
$836$	−36.5631	+	4.01742i	−1.26456	+	0.138945i
$837$			2.97172i			0.102718i
$838$	4.38441	+	3.50816i	0.151457	+	0.121188i
$839$	31.6487			1.09264			0.546318	−	0.837578i	$-0.316029\pi$
$839$	31.6487			1.09264			0.546318	+	0.837578i	$0.316029\pi$
$840$	−4.54330	+	9.31734i	−0.156759	+	0.321479i
$841$	28.5408			0.984164
$842$	−22.8398	−	18.2752i	−0.787112	−	0.629804i
$843$			56.5746i			1.94853i
$844$	−10.9866	−	48.8699i	−0.378175	−	1.68217i
$845$	−24.6052	+	26.2799i	−0.846445	+	0.904055i
$846$	27.9331	−	34.9100i	0.960359	−	1.20023i
$847$	1.30260	−	5.73350i	0.0447580	−	0.197006i
$848$	−15.8657	+	7.51338i	−0.544829	+	0.258010i
$849$		−	32.5441i		−	1.11691i
$850$	−17.4072	−	13.9283i	−0.597061	−	0.477735i
$851$	6.96292			0.238686
$852$	14.9711	−	3.36571i	0.512902	−	0.115307i
$853$	−42.8801			−1.46819			−0.734094	−	0.679048i	$-0.762393\pi$
$853$	−42.8801			−1.46819			−0.734094	+	0.679048i	$0.762393\pi$
$854$	−4.87163	+	6.08844i	−0.166704	+	0.208342i
$855$	48.0715			1.64401
$856$	−6.16738	−	3.00732i	−0.210797	−	0.102788i
$857$			37.0942i			1.26711i	0.773696	+	0.633557i	$0.218406\pi$
$857$			37.0942i			1.26711i	−0.773696	+	0.633557i	$0.781594\pi$
$858$	−16.6145	−	38.4350i	−0.567210	−	1.31215i
$859$		−	53.4127i		−	1.82242i	−0.411944	−	0.911209i	$-0.635150\pi$
$859$		−	53.4127i		−	1.82242i	0.411944	−	0.911209i	$-0.364850\pi$
$860$	−45.8799	+	10.3144i	−1.56449	+	0.351719i
$861$	3.31728			0.113052
$862$	−31.8801	−	25.5087i	−1.08584	−	0.868831i
$863$	−13.3427			−0.454190			−0.227095	−	0.973873i	$-0.572923\pi$
$863$	−13.3427			−0.454190			−0.227095	+	0.973873i	$0.572923\pi$
$864$	−1.77703	−	0.420873i	−0.0604559	−	0.0143184i
$865$	−36.1340			−1.22859
$866$	−0.846605	+	1.05806i	−0.0287688	+	0.0359545i
$867$		−	44.2865i		−	1.50405i
$868$	9.60098	−	2.15843i	0.325879	−	0.0732620i
$869$	27.7730	+	3.11521i	0.942135	+	0.105676i
$870$	−5.13091	−	4.10547i	−0.173954	−	0.139189i
$871$	9.65897	+	3.81598i	0.327282	+	0.129299i
$872$	9.14651	+	4.46000i	0.309740	+	0.151035i
$873$			7.11371i			0.240763i
$874$	21.9771	−	27.4663i	0.743385	−	0.929062i
$875$	3.45048			0.116648
$876$	−45.6228	+	10.2566i	−1.54145	+	0.346540i
$877$	−7.39316			−0.249649			−0.124825	−	0.992179i	$-0.539837\pi$
$877$	−7.39316			−0.249649			−0.124825	+	0.992179i	$0.539837\pi$
$878$	−1.08498	+	1.35598i	−0.0366164	+	0.0457622i
$879$		−	27.5869i		−	0.930484i
$880$	11.9249	+	34.7495i	0.401988	+	1.17141i
$881$	1.04846			0.0353235			0.0176618	−	0.999844i	$-0.494378\pi$
$881$	1.04846			0.0353235			0.0176618	+	0.999844i	$0.494378\pi$
$882$	18.5708	−	23.2092i	0.625310	−	0.781495i
$883$		−	16.7074i		−	0.562249i	−0.959671	−	0.281124i	$-0.909293\pi$
$883$		−	16.7074i		−	0.562249i	0.959671	−	0.281124i	$-0.0907073\pi$
$884$	42.0809	+	6.58014i	1.41533	+	0.221314i
$885$	−37.5714			−1.26295
$886$	34.7268	+	27.7865i	1.16667	+	0.933505i
$887$	−53.5161			−1.79690			−0.898448	−	0.439080i	$-0.855304\pi$
$887$	−53.5161			−1.79690			−0.898448	+	0.439080i	$0.855304\pi$
$888$	9.77113	+	4.76457i	0.327897	+	0.159888i
$889$			7.31131i			0.245214i
$890$	−17.0107	+	21.2595i	−0.570199	+	0.712620i
$891$	28.3183	+	3.17637i	0.948700	+	0.106413i
$892$	0.583747	+	2.59658i	0.0195453	+	0.0869400i
$893$			56.0032i			1.87407i
$894$	47.6762	+	38.1479i	1.59453	+	1.27586i
$895$	−19.9225			−0.665937
$896$	−0.0690473	+	6.04690i	−0.00230671	+	0.202013i
$897$	37.2423	+	14.7134i	1.24349	+	0.491265i
$898$	−4.81508	−	3.85276i	−0.160681	−	0.128568i
$899$			6.23817i			0.208054i
$900$	−3.66505	−	16.3026i	−0.122168	−	0.543421i
$901$		−	25.9218i		−	0.863579i
$902$	8.32279	−	8.30398i	0.277118	−	0.276492i
$903$	−11.2365			−0.373928
$904$	−41.4863	−	20.2294i	−1.37981	−	0.672820i
$905$			18.7818i			0.624328i
$906$	−25.5540	+	31.9367i	−0.848975	+	1.06103i
$907$			20.6013i			0.684054i	0.939690	+	0.342027i	$0.111113\pi$
$907$			20.6013i			0.684054i	−0.939690	+	0.342027i	$0.888887\pi$
$908$	−36.9804	+	8.31371i	−1.22724	+	0.275900i
$909$		−	54.1268i		−	1.79527i
$910$	6.55103	−	3.74841i	0.217165	−	0.124258i
$911$		−	16.0253i		−	0.530941i	−0.964119	−	0.265470i	$-0.914473\pi$
$911$		−	16.0253i		−	0.530941i	0.964119	−	0.265470i	$-0.0855272\pi$
$912$	49.6352	−	23.5053i	1.64359	−	0.778339i
$913$	1.04706	−	9.33483i	0.0346525	−	0.308938i
$914$	−26.6691	+	33.3303i	−0.882135	+	1.10247i
$915$		−	70.7292i		−	2.33823i
$916$	−22.0783	+	4.96352i	−0.729489	+	0.163999i
$917$		−	2.81595i		−	0.0929910i
$918$	1.68474	−	2.10554i	0.0556046	−	0.0694931i
$919$	−15.6755			−0.517088			−0.258544	−	0.966000i	$-0.583243\pi$
$919$	−15.6755			−0.517088			−0.258544	+	0.966000i	$0.583243\pi$
$920$	−31.5797	−	15.3988i	−1.04115	−	0.507683i
$921$	71.3511			2.35110
$922$	−28.7880	+	35.9785i	−0.948084	+	1.18489i
$923$	−10.3912	−	4.10525i	−0.342029	−	0.135126i
$924$	0.958792	+	8.72610i	0.0315420	+	0.287068i
$925$			4.14297i			0.136220i
$926$	3.56171	−	4.45132i	0.117045	−	0.146280i
$927$		−	50.4328i		−	1.65643i
$928$	−3.73031	−	0.883487i	−0.122453	−	0.0290019i
$929$			17.5641i			0.576258i	0.957592	+	0.288129i	$0.0930332\pi$
$929$			17.5641i			0.576258i	−0.957592	+	0.288129i	$0.906967\pi$
$930$	−55.7671	+	69.6963i	−1.82868	+	2.28543i
$931$			37.2326i			1.22025i
$932$	−52.8310	+	11.8771i	−1.73054	+	0.389049i
$933$	−36.5518			−1.19665
$934$	3.76561	+	3.01303i	0.123214	+	0.0985895i
$935$	−53.9111	−	6.04702i	−1.76308	−	0.197759i
$936$	21.5460	+	23.5563i	0.704251	+	0.769962i
$937$		−	51.2539i		−	1.67439i	−0.546904	−	0.837195i	$-0.684194\pi$
$937$		−	51.2539i		−	1.67439i	0.546904	−	0.837195i	$-0.315806\pi$
$938$	−1.70009	−	1.36032i	−0.0555099	−	0.0444160i
$939$		−	30.7386i		−	1.00312i
$940$	54.5733	−	12.2688i	1.77999	−	0.400165i
$941$	−5.44008			−0.177342			−0.0886708	−	0.996061i	$-0.528262\pi$
$941$	−5.44008			−0.177342			−0.0886708	+	0.996061i	$0.528262\pi$
$942$	24.5541	+	19.6468i	0.800016	+	0.640129i
$943$			11.2434i			0.366135i
$944$	−19.8093	+	9.38092i	−0.644737	+	0.305323i
$945$		−	0.477853i		−	0.0155446i
$946$	−28.1915	+	28.1278i	−0.916585	+	0.914514i
$947$	21.5672			0.700841			0.350420	−	0.936593i	$-0.386039\pi$
$947$	21.5672			0.700841			0.350420	+	0.936593i	$0.386039\pi$
$948$	−40.7107	+	9.15233i	−1.32222	+	0.297254i
$949$	31.6659	+	12.5103i	1.02792	+	0.406101i
$950$	16.3426	+	13.0765i	0.530224	+	0.424257i
$951$	−20.1843			−0.654522
$952$	−8.02620	−	3.91372i	−0.260131	−	0.126844i
$953$			7.87118i			0.254972i	0.991840	+	0.127486i	$0.0406909\pi$
$953$			7.87118i			0.254972i	−0.991840	+	0.127486i	$0.959309\pi$
$954$	12.1385	−	15.1703i	0.392998	−	0.491158i
$955$	−5.88051			−0.190289
$956$	28.5967	−	6.42894i	0.924885	−	0.207927i
$957$	−5.53027	−	0.620312i	−0.178768	−	0.0200518i
$958$	−7.99337	−	6.39586i	−0.258254	−	0.206641i
$959$	7.69917			0.248619
$960$	−33.7790	−	43.2185i	−1.09021	−	1.39487i
$961$	53.7368			1.73345
$962$	−3.93097	−	6.87008i	−0.126739	−	0.221500i
$963$	7.59405			0.244715
$964$	3.23546	+	14.3917i	0.104207	+	0.463527i
$965$			36.4242i			1.17254i
$966$	−6.55508	−	5.24501i	−0.210906	−	0.168756i
$967$		−	2.04860i		−	0.0658785i	−0.999457	−	0.0329392i	$-0.989513\pi$
$967$		−	2.04860i		−	0.0658785i	0.999457	−	0.0329392i	$-0.0104868\pi$
$968$	24.2492	+	19.4930i	0.779398	+	0.626529i
$969$			81.0953i			2.60516i
$970$	−5.56028	+	6.94909i	−0.178530	+	0.223122i
$971$		−	24.7936i		−	0.795663i	−0.917458	−	0.397832i	$-0.869763\pi$
$971$		−	24.7936i		−	0.795663i	0.917458	−	0.397832i	$-0.130237\pi$
$972$	−43.3999	+	9.75689i	−1.39205	+	0.312953i
$973$		−	5.83492i		−	0.187059i
$974$	19.8246	−	24.7762i	0.635221	−	0.793881i
$975$	−8.75453	+	22.1594i	−0.280369	+	0.709668i
$976$	−17.6599	−	37.2915i	−0.565278	−	1.19367i
$977$			41.2555i			1.31988i	0.751318	+	0.659940i	$0.229418\pi$
$977$			41.2555i			1.31988i	−0.751318	+	0.659940i	$0.770582\pi$
$978$	30.8870	+	24.7141i	0.987657	+	0.790269i
$979$	−2.57021	+	22.9142i	−0.0821442	+	0.732341i
$980$	36.2820	−	8.15669i	1.15899	−	0.260556i
$981$	−11.2623			−0.359579
$982$	18.6674	−	23.3300i	0.595700	−	0.744490i
$983$	27.3410			0.872042			0.436021	−	0.899936i	$-0.356387\pi$
$983$	27.3410			0.872042			0.436021	+	0.899936i	$0.356387\pi$
$984$	−7.69360	+	15.7779i	−0.245263	+	0.502982i
$985$			6.84340i			0.218049i
$986$	3.53656	−	4.41990i	0.112627	−	0.140758i
$987$	13.3656			0.425433
$988$	−39.5074	−	6.17773i	−1.25690	−	0.196540i
$989$		−	38.0844i		−	1.21101i
$990$	−28.7190	−	28.7841i	−0.912750	−	0.914818i
$991$		−	10.0759i		−	0.320072i	−0.987111	−	0.160036i	$-0.948839\pi$
$991$		−	10.0759i		−	0.320072i	0.987111	−	0.160036i	$-0.0511611\pi$
$992$	−12.0010	+	50.6711i	−0.381031	+	1.60881i
$993$		−	26.2719i		−	0.833715i
$994$	1.82896	+	1.46344i	0.0580112	+	0.0464174i
$995$	48.8759			1.54947
$996$	3.07620	+	13.6833i	0.0974733	+	0.433573i
$997$		−	33.7038i		−	1.06741i	−0.845670	−	0.533706i	$-0.820799\pi$
$997$		−	33.7038i		−	1.06741i	0.845670	−	0.533706i	$-0.179201\pi$
$998$	7.41353	−	9.26523i	0.234671	−	0.293286i
$999$	−0.501126			−0.0158549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.b.c.571.20	yes	56
4.3	odd	2	inner	572.2.b.c.571.18	yes	56
11.10	odd	2	inner	572.2.b.c.571.38	yes	56
13.12	even	2	inner	572.2.b.c.571.37	yes	56
44.43	even	2	inner	572.2.b.c.571.40	yes	56
52.51	odd	2	inner	572.2.b.c.571.39	yes	56
143.142	odd	2	inner	572.2.b.c.571.19	yes	56
572.571	even	2	inner	572.2.b.c.571.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.b.c.571.17	✓	56	572.571	even	2	inner
572.2.b.c.571.18	yes	56	4.3	odd	2	inner
572.2.b.c.571.19	yes	56	143.142	odd	2	inner
572.2.b.c.571.20	yes	56	1.1	even	1	trivial
572.2.b.c.571.37	yes	56	13.12	even	2	inner
572.2.b.c.571.38	yes	56	11.10	odd	2	inner
572.2.b.c.571.39	yes	56	52.51	odd	2	inner
572.2.b.c.571.40	yes	56	44.43	even	2	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883550 + 1.10424i) q^{2} +2.47596i q^{3} +(-0.438678 - 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 - 2.18764i) q^{6} -0.534510i q^{7} +(2.54229 + 1.23966i) q^{8} -3.13038 q^{9} +O(q^{10})\)	\(q+(-0.883550 + 1.10424i) q^{2} +2.47596i q^{3} +(-0.438678 - 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 - 2.18764i) q^{6} -0.534510i q^{7} +(2.54229 + 1.23966i) q^{8} -3.13038 q^{9} +(-3.05794 - 2.44680i) q^{10} +(-3.29596 - 0.369696i) q^{11} +(4.83134 - 1.08615i) q^{12} +(-3.35334 - 1.32481i) q^{13} +(0.590226 + 0.472267i) q^{14} -6.85664 q^{15} +(-3.61512 + 1.71198i) q^{16} -5.90649i q^{17} +(2.76585 - 3.45669i) q^{18} +5.54527i q^{19} +(5.40369 - 1.21482i) q^{20} +1.32343 q^{21} +(3.32037 - 3.31287i) q^{22} +4.48555i q^{23} +(-3.06936 + 6.29461i) q^{24} -2.66893 q^{25} +(4.42574 - 2.53235i) q^{26} -0.322828i q^{27} +(-1.04299 + 0.234478i) q^{28} -0.677674i q^{29} +(6.05818 - 7.57135i) q^{30} -9.20526 q^{31} +(1.30371 - 5.50458i) q^{32} +(0.915354 - 8.16066i) q^{33} +(6.52216 + 5.21868i) q^{34} +1.48021 q^{35} +(1.37323 + 6.10831i) q^{36} -1.55230i q^{37} +(-6.12329 - 4.89953i) q^{38} +(3.28017 - 8.30274i) q^{39} +(-3.43298 + 7.04032i) q^{40} +2.50658 q^{41} +(-1.16931 + 1.46138i) q^{42} -8.49046 q^{43} +(0.724477 + 6.59357i) q^{44} -8.66892i q^{45} +(-4.95311 - 3.96321i) q^{46} +10.0993 q^{47} +(-4.23881 - 8.95090i) q^{48} +6.71430 q^{49} +(2.35813 - 2.94713i) q^{50} +14.6242 q^{51} +(-1.11405 + 7.12453i) q^{52} +4.38869 q^{53} +(0.356479 + 0.285235i) q^{54} +(1.02379 - 9.12743i) q^{55} +(0.662613 - 1.35888i) q^{56} -13.7299 q^{57} +(0.748313 + 0.598759i) q^{58} +5.47956 q^{59} +(3.00786 + 13.3793i) q^{60} +10.3154i q^{61} +(8.13331 - 10.1648i) q^{62} +1.67322i q^{63} +(4.92647 + 6.30317i) q^{64} +(3.66876 - 9.28634i) q^{65} +(8.20254 + 8.22112i) q^{66} -2.88040 q^{67} +(-11.5253 + 2.59105i) q^{68} -11.1060 q^{69} +(-1.30784 + 1.63450i) q^{70} +3.09875 q^{71} +(-7.95834 - 3.88063i) q^{72} -9.44310 q^{73} +(1.71411 + 1.37154i) q^{74} -6.60816i q^{75} +(10.8205 - 2.43259i) q^{76} +(-0.197607 + 1.76172i) q^{77} +(6.27000 + 10.9580i) q^{78} -8.42639 q^{79} +(-4.74097 - 10.0113i) q^{80} -8.59184 q^{81} +(-2.21469 + 2.76786i) q^{82} +2.83221i q^{83} +(-0.580559 - 2.58240i) q^{84} +16.3567 q^{85} +(7.50175 - 9.37548i) q^{86} +1.67789 q^{87} +(-7.92097 - 5.02575i) q^{88} -6.95222i q^{89} +(9.57254 + 7.65943i) q^{90} +(-0.708123 + 1.79239i) q^{91} +(8.75264 - 1.96771i) q^{92} -22.7919i q^{93} +(-8.92321 + 11.1520i) q^{94} -15.3564 q^{95} +(13.6291 + 3.22792i) q^{96} -2.27247i q^{97} +(-5.93242 + 7.41418i) q^{98} +(10.3176 + 1.15729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^4 - 32 * q^9	\( 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) \) 56 * q + 4 * q^4 - 32 * q^9 - 12 * q^14 - 4 * q^16 - 4 * q^22 - 192 * q^25 + 4 * q^26 + 28 * q^36 + 24 * q^38 + 88 * q^42 + 56 * q^48 + 40 * q^49 - 8 * q^53 - 68 * q^56 + 28 * q^64 - 76 * q^66 - 16 * q^69 + 32 * q^77 + 108 * q^78 - 152 * q^81 - 60 * q^82 + 52 * q^88 + 132 * q^92

Introduction

L-functions

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