LMFDB - Embedded newform 1456.2.cc.g.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.1
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64970 - 2.85736i) q^{3} +0.585323i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.94299 + 6.82946i) q^{9} +O(q^{10})$	\(q+(-1.64970 - 2.85736i) q^{3} +0.585323i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.94299 + 6.82946i) q^{9} +(2.18937 - 1.26403i) q^{11} +(1.94161 - 3.03812i) q^{13} +(1.67248 - 0.965606i) q^{15} +(-3.75538 + 6.50450i) q^{17} +(1.63478 + 0.943840i) q^{19} -3.29939i q^{21} +(1.62263 + 2.81048i) q^{23} +4.65740 q^{25} +16.1208 q^{27} +(3.51324 + 6.08510i) q^{29} -9.37426i q^{31} +(-7.22358 - 4.17054i) q^{33} +(-0.292662 + 0.506905i) q^{35} +(9.17423 - 5.29675i) q^{37} +(-11.8840 - 0.535894i) q^{39} +(4.38794 - 2.53338i) q^{41} +(-2.82059 + 4.88541i) q^{43} +(-3.99744 - 2.30793i) q^{45} +4.57145i q^{47} +(0.500000 + 0.866025i) q^{49} +24.7809 q^{51} -1.36120 q^{53} +(0.739868 + 1.28149i) q^{55} -6.22820i q^{57} +(-3.16353 - 1.82647i) q^{59} +(-4.38685 + 7.59824i) q^{61} +(-6.82946 + 3.94299i) q^{63} +(1.77828 + 1.13647i) q^{65} +(-1.03813 + 0.599365i) q^{67} +(5.35370 - 9.27289i) q^{69} +(2.22017 + 1.28181i) q^{71} -6.75730i q^{73} +(-7.68329 - 13.3078i) q^{75} +2.52807 q^{77} +3.16871 q^{79} +(-14.7654 - 25.5744i) q^{81} -9.05649i q^{83} +(-3.80724 - 2.19811i) q^{85} +(11.5915 - 20.0771i) q^{87} +(14.9056 - 8.60576i) q^{89} +(3.20054 - 1.66028i) q^{91} +(-26.7856 + 15.4647i) q^{93} +(-0.552452 + 0.956874i) q^{95} +(-2.57685 - 1.48774i) q^{97} +19.9363i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 - 18 * q^9	$ 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) $ 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.64970	−	2.85736i	−0.952452	−	1.64970i	−0.740093	−	0.672504i	$-0.765219\pi$
$3$	−1.64970	−	2.85736i	−0.952452	−	1.64970i	−0.212359	−	0.977192i	$-0.568115\pi$
$4$		0			0
$5$			0.585323i			0.261765i	0.991398	+	0.130882i	$0.0417810\pi$
$5$			0.585323i			0.261765i	−0.991398	+	0.130882i	$0.958219\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	−3.94299	+	6.82946i	−1.31433	+	2.27649i
$10$		0			0
$11$	2.18937	−	1.26403i	0.660119	−	0.381120i	−0.132203	−	0.991223i	$-0.542205\pi$
$11$	2.18937	−	1.26403i	0.660119	−	0.381120i	0.792322	+	0.610103i	$0.208872\pi$
$12$		0			0
$13$	1.94161	−	3.03812i	0.538505	−	0.842622i
$13$	1.94161	−	3.03812i	0.538505	−	0.842622i
$14$		0			0
$15$	1.67248	−	0.965606i	0.431832	−	0.249318i
$16$		0			0
$17$	−3.75538	+	6.50450i	−0.910813	+	1.57757i	−0.0978939	+	0.995197i	$0.531211\pi$
$17$	−3.75538	+	6.50450i	−0.910813	+	1.57757i	−0.812919	+	0.582377i	$0.802123\pi$
$18$		0			0
$19$	1.63478	+	0.943840i	0.375044	+	0.216532i	0.675660	−	0.737214i	$-0.263859\pi$
$19$	1.63478	+	0.943840i	0.375044	+	0.216532i	−0.300616	+	0.953745i	$0.597192\pi$
$20$		0			0
$21$		−	3.29939i		−	0.719986i
$22$		0			0
$23$	1.62263	+	2.81048i	0.338343	+	0.586026i	0.984121	−	0.177498i	$-0.0568004\pi$
$23$	1.62263	+	2.81048i	0.338343	+	0.586026i	−0.645779	+	0.763525i	$0.723467\pi$
$24$		0			0
$25$	4.65740			0.931479
$26$		0			0
$27$	16.1208			3.10245
$28$		0			0
$29$	3.51324	+	6.08510i	0.652392	+	1.12998i	0.982541	+	0.186047i	$0.0595676\pi$
$29$	3.51324	+	6.08510i	0.652392	+	1.12998i	−0.330149	+	0.943929i	$0.607099\pi$
$30$		0			0
$31$		−	9.37426i		−	1.68367i	−0.539738	−	0.841833i	$-0.681477\pi$
$31$		−	9.37426i		−	1.68367i	0.539738	−	0.841833i	$-0.318523\pi$
$32$		0			0
$33$	−7.22358	−	4.17054i	−1.25746	−	0.725998i
$34$		0			0
$35$	−0.292662	+	0.506905i	−0.0494689	+	0.0856826i
$36$		0			0
$37$	9.17423	−	5.29675i	1.50823	−	0.870780i	0.508281	−	0.861191i	$-0.330281\pi$
$37$	9.17423	−	5.29675i	1.50823	−	0.870780i	0.999954	−	0.00958820i	$-0.00305207\pi$
$38$		0			0
$39$	−11.8840	−	0.535894i	−1.90297	−	0.0858117i
$40$		0			0
$41$	4.38794	−	2.53338i	0.685282	−	0.395647i	−0.116560	−	0.993184i	$-0.537187\pi$
$41$	4.38794	−	2.53338i	0.685282	−	0.395647i	0.801842	+	0.597536i	$0.203854\pi$
$42$		0			0
$43$	−2.82059	+	4.88541i	−0.430136	+	0.745017i	−0.996885	−	0.0788734i	$-0.974868\pi$
$43$	−2.82059	+	4.88541i	−0.430136	+	0.745017i	0.566749	+	0.823891i	$0.308201\pi$
$44$		0			0
$45$	−3.99744	−	2.30793i	−0.595904	−	0.344045i
$46$		0			0
$47$			4.57145i			0.666815i	0.942783	+	0.333408i	$0.108199\pi$
$47$			4.57145i			0.666815i	−0.942783	+	0.333408i	$0.891801\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	24.7809			3.47002
$52$		0			0
$53$	−1.36120			−0.186975			−0.0934877	−	0.995620i	$-0.529802\pi$
$53$	−1.36120			−0.186975			−0.0934877	+	0.995620i	$0.529802\pi$
$54$		0			0
$55$	0.739868	+	1.28149i	0.0997638	+	0.172796i
$56$		0			0
$57$		−	6.22820i		−	0.824945i
$58$		0			0
$59$	−3.16353	−	1.82647i	−0.411857	−	0.237786i	0.279730	−	0.960079i	$-0.409755\pi$
$59$	−3.16353	−	1.82647i	−0.411857	−	0.237786i	−0.691587	+	0.722293i	$0.743088\pi$
$60$		0			0
$61$	−4.38685	+	7.59824i	−0.561678	+	0.972855i	0.435672	+	0.900105i	$0.356511\pi$
$61$	−4.38685	+	7.59824i	−0.561678	+	0.972855i	−0.997350	+	0.0727496i	$0.976823\pi$
$62$		0			0
$63$	−6.82946	+	3.94299i	−0.860432	+	0.496770i
$64$		0			0
$65$	1.77828	+	1.13647i	0.220569	+	0.140962i
$66$		0			0
$67$	−1.03813	+	0.599365i	−0.126828	+	0.0732241i	−0.562072	−	0.827089i	$-0.689995\pi$
$67$	−1.03813	+	0.599365i	−0.126828	+	0.0732241i	0.435244	+	0.900313i	$0.356662\pi$
$68$		0			0
$69$	5.35370	−	9.27289i	0.644510	−	1.11632i
$70$		0			0
$71$	2.22017	+	1.28181i	0.263485	+	0.152123i	0.625923	−	0.779885i	$-0.284722\pi$
$71$	2.22017	+	1.28181i	0.263485	+	0.152123i	−0.362438	+	0.932008i	$0.618056\pi$
$72$		0			0
$73$		−	6.75730i		−	0.790882i	−0.918491	−	0.395441i	$-0.870592\pi$
$73$		−	6.75730i		−	0.790882i	0.918491	−	0.395441i	$-0.129408\pi$
$74$		0			0
$75$	−7.68329	−	13.3078i	−0.887190	−	1.53666i
$76$		0			0
$77$	2.52807			0.288100
$78$		0			0
$79$	3.16871			0.356508			0.178254	−	0.983985i	$-0.442955\pi$
$79$	3.16871			0.356508			0.178254	+	0.983985i	$0.442955\pi$
$80$		0			0
$81$	−14.7654	−	25.5744i	−1.64060	−	2.84160i
$82$		0			0
$83$		−	9.05649i		−	0.994079i	−0.867728	−	0.497039i	$-0.834420\pi$
$83$		−	9.05649i		−	0.994079i	0.867728	−	0.497039i	$-0.165580\pi$
$84$		0			0
$85$	−3.80724	−	2.19811i	−0.412953	−	0.238419i
$86$		0			0
$87$	11.5915	−	20.0771i	1.24274	−	2.15250i
$88$		0			0
$89$	14.9056	−	8.60576i	1.57999	−	0.912209i	0.585134	−	0.810937i	$-0.301042\pi$
$89$	14.9056	−	8.60576i	1.57999	−	0.912209i	0.994859	−	0.101273i	$-0.0322914\pi$
$90$		0			0
$91$	3.20054	−	1.66028i	0.335508	−	0.174045i
$92$		0			0
$93$	−26.7856	+	15.4647i	−2.77754	+	1.60361i
$94$		0			0
$95$	−0.552452	+	0.956874i	−0.0566803	+	0.0981732i
$96$		0			0
$97$	−2.57685	−	1.48774i	−0.261639	−	0.151058i	0.363443	−	0.931616i	$-0.381601\pi$
$97$	−2.57685	−	1.48774i	−0.261639	−	0.151058i	−0.625082	+	0.780559i	$0.714935\pi$
$98$		0			0
$99$			19.9363i			2.00367i
$100$		0			0
$101$	−0.789475	−	1.36741i	−0.0785557	−	0.136063i	0.824071	−	0.566486i	$-0.191698\pi$
$101$	−0.789475	−	1.36741i	−0.0785557	−	0.136063i	−0.902627	+	0.430424i	$0.858364\pi$
$102$		0			0
$103$	−18.0946			−1.78291			−0.891455	−	0.453110i	$-0.850314\pi$
$103$	−18.0946			−1.78291			−0.891455	+	0.453110i	$0.850314\pi$
$104$		0			0
$105$	1.93121			0.188467
$106$		0			0
$107$	−7.43254	−	12.8735i	−0.718531	−	1.24453i	−0.961582	−	0.274518i	$-0.911482\pi$
$107$	−7.43254	−	12.8735i	−0.718531	−	1.24453i	0.243051	−	0.970013i	$-0.421852\pi$
$108$		0			0
$109$		−	3.64426i		−	0.349057i	−0.984652	−	0.174528i	$-0.944160\pi$
$109$		−	3.64426i		−	0.349057i	0.984652	−	0.174528i	$-0.0558401\pi$
$110$		0			0
$111$	−30.2694	−	17.4760i	−2.87304	−	1.65875i
$112$		0			0
$113$	2.63423	−	4.56262i	0.247808	−	0.429215i	−0.715110	−	0.699012i	$-0.753623\pi$
$113$	2.63423	−	4.56262i	0.247808	−	0.429215i	0.962917	+	0.269797i	$0.0869566\pi$
$114$		0			0
$115$	−1.64504	+	0.949766i	−0.153401	+	0.0885661i
$116$		0			0
$117$	13.0930	+	25.2394i	1.21045	+	2.33338i
$118$		0			0
$119$	−6.50450	+	3.75538i	−0.596267	+	0.344255i
$120$		0			0
$121$	−2.30444	+	3.99141i	−0.209495	+	0.362856i
$122$		0			0
$123$	−14.4775	−	8.35861i	−1.30540	−	0.753671i
$124$		0			0
$125$			5.65270i			0.505593i
$126$		0			0
$127$	0.227565	+	0.394154i	0.0201931	+	0.0349755i	0.875945	−	0.482410i	$-0.160239\pi$
$127$	0.227565	+	0.394154i	0.0201931	+	0.0349755i	−0.855752	+	0.517386i	$0.826905\pi$
$128$		0			0
$129$	18.6125			1.63874
$130$		0			0
$131$	12.0924			1.05652			0.528258	−	0.849084i	$-0.322845\pi$
$131$	12.0924			1.05652			0.528258	+	0.849084i	$0.322845\pi$
$132$		0			0
$133$	0.943840	+	1.63478i	0.0818413	+	0.141753i
$134$		0			0
$135$			9.43587i			0.812110i
$136$		0			0
$137$	8.09475	+	4.67351i	0.691581	+	0.399285i	0.804204	−	0.594353i	$-0.202592\pi$
$137$	8.09475	+	4.67351i	0.691581	+	0.399285i	−0.112623	+	0.993638i	$0.535925\pi$
$138$		0			0
$139$	9.41833	−	16.3130i	0.798853	−	1.38365i	−0.121511	−	0.992590i	$-0.538774\pi$
$139$	9.41833	−	16.3130i	0.798853	−	1.38365i	0.920364	−	0.391063i	$-0.127893\pi$
$140$		0			0
$141$	13.0623	−	7.54151i	1.10004	−	0.635110i
$142$		0			0
$143$	0.410614	−	9.10581i	0.0343372	−	0.761466i
$144$		0			0
$145$	−3.56175	+	2.05638i	−0.295788	+	0.170773i
$146$		0			0
$147$	1.64970	−	2.85736i	0.136065	−	0.235671i
$148$		0			0
$149$	8.57164	+	4.94884i	0.702216	+	0.405425i	0.808172	−	0.588946i	$-0.200457\pi$
$149$	8.57164	+	4.94884i	0.702216	+	0.405425i	−0.105956	+	0.994371i	$0.533790\pi$
$150$		0			0
$151$			9.56475i			0.778368i	0.921160	+	0.389184i	$0.127243\pi$
$151$			9.56475i			0.778368i	−0.921160	+	0.389184i	$0.872757\pi$
$152$		0			0
$153$	−29.6148	−	51.2944i	−2.39422	−	4.14691i
$154$		0			0
$155$	5.48697			0.440724
$156$		0			0
$157$	6.16478			0.492003			0.246002	−	0.969269i	$-0.420883\pi$
$157$	6.16478			0.492003			0.246002	+	0.969269i	$0.420883\pi$
$158$		0			0
$159$	2.24557	+	3.88944i	0.178085	+	0.308453i
$160$		0			0
$161$			3.24527i			0.255763i
$162$		0			0
$163$	9.43020	+	5.44453i	0.738630	+	0.426449i	0.821571	−	0.570106i	$-0.193098\pi$
$163$	9.43020	+	5.44453i	0.738630	+	0.426449i	−0.0829407	+	0.996554i	$0.526431\pi$
$164$		0			0
$165$	2.44111	−	4.22813i	0.190040	−	0.329160i
$166$		0			0
$167$	10.8189	−	6.24631i	0.837193	−	0.483354i	−0.0191158	−	0.999817i	$-0.506085\pi$
$167$	10.8189	−	6.24631i	0.837193	−	0.483354i	0.856309	+	0.516463i	$0.172752\pi$
$168$		0			0
$169$	−5.46032	−	11.7977i	−0.420025	−	0.907513i
$170$		0			0
$171$	−12.8918	+	7.44311i	−0.985864	+	0.569189i
$172$		0			0
$173$	−1.86521	+	3.23063i	−0.141809	+	0.245620i	−0.928178	−	0.372137i	$-0.878625\pi$
$173$	−1.86521	+	3.23063i	−0.141809	+	0.245620i	0.786369	+	0.617757i	$0.211959\pi$
$174$		0			0
$175$	4.03342	+	2.32870i	0.304898	+	0.176033i
$176$		0			0
$177$			12.0525i			0.905918i
$178$		0			0
$179$	6.07746	+	10.5265i	0.454250	+	0.786785i	0.998645	−	0.0520447i	$-0.0165738\pi$
$179$	6.07746	+	10.5265i	0.454250	+	0.786785i	−0.544394	+	0.838829i	$0.683241\pi$
$180$		0			0
$181$	13.4670			1.00100			0.500498	−	0.865738i	$-0.333150\pi$
$181$	13.4670			1.00100			0.500498	+	0.865738i	$0.333150\pi$
$182$		0			0
$183$	28.9478			2.13989
$184$		0			0
$185$	3.10031	+	5.36989i	0.227939	+	0.394802i
$186$		0			0
$187$			18.9877i			1.38852i
$188$		0			0
$189$	13.9610	+	8.06039i	1.01551	+	0.586307i
$190$		0			0
$191$	−7.25019	+	12.5577i	−0.524605	+	0.908643i	0.474984	+	0.879994i	$0.342454\pi$
$191$	−7.25019	+	12.5577i	−0.524605	+	0.908643i	−0.999590	+	0.0286489i	$0.990880\pi$
$192$		0			0
$193$	4.18561	−	2.41656i	0.301287	−	0.173948i	−0.341734	−	0.939797i	$-0.611014\pi$
$193$	4.18561	−	2.41656i	0.301287	−	0.173948i	0.643021	+	0.765849i	$0.277681\pi$
$194$		0			0
$195$	0.313671	−	6.95601i	0.0224625	−	0.498130i
$196$		0			0
$197$	−1.89034	+	1.09139i	−0.134681	+	0.0777582i	−0.565827	−	0.824524i	$-0.691443\pi$
$197$	−1.89034	+	1.09139i	−0.134681	+	0.0777582i	0.431146	+	0.902282i	$0.358110\pi$
$198$		0			0
$199$	−9.39703	+	16.2761i	−0.666138	+	1.15378i	0.312838	+	0.949807i	$0.398720\pi$
$199$	−9.39703	+	16.2761i	−0.666138	+	1.15378i	−0.978976	+	0.203978i	$0.934613\pi$
$200$		0			0
$201$	3.42520	+	1.97754i	0.241595	+	0.139485i
$202$		0			0
$203$			7.02647i			0.493162i
$204$		0			0
$205$	1.48285	+	2.56837i	0.103567	+	0.179382i
$206$		0			0
$207$	−25.5921			−1.77878
$208$		0			0
$209$	4.77218			0.330098
$210$		0			0
$211$	3.19286	+	5.53020i	0.219806	+	0.380715i	0.954748	−	0.297415i	$-0.0961244\pi$
$211$	3.19286	+	5.53020i	0.219806	+	0.380715i	−0.734943	+	0.678129i	$0.762791\pi$
$212$		0			0
$213$		−	8.45841i		−	0.579560i
$214$		0			0
$215$	−2.85954	−	1.65096i	−0.195019	−	0.112594i
$216$		0			0
$217$	4.68713	−	8.11835i	0.318183	−	0.551109i
$218$		0			0
$219$	−19.3080	+	11.1475i	−1.30471	+	0.753277i
$220$		0			0
$221$	12.4700	+	24.0385i	0.838822	+	1.61700i
$222$		0			0
$223$	−10.5181	+	6.07263i	−0.704344	+	0.406653i	−0.808963	−	0.587859i	$-0.799971\pi$
$223$	−10.5181	+	6.07263i	−0.704344	+	0.406653i	0.104619	+	0.994512i	$0.466638\pi$
$224$		0			0
$225$	−18.3641	+	31.8075i	−1.22427	+	2.12050i
$226$		0			0
$227$	10.5678	+	6.10130i	0.701407	+	0.404957i	0.807871	−	0.589359i	$-0.200620\pi$
$227$	10.5678	+	6.10130i	0.701407	+	0.404957i	−0.106465	+	0.994316i	$0.533953\pi$
$228$		0			0
$229$		−	16.3341i		−	1.07938i	−0.841862	−	0.539692i	$-0.818541\pi$
$229$		−	16.3341i		−	1.07938i	0.841862	−	0.539692i	$-0.181459\pi$
$230$		0			0
$231$	−4.17054	−	7.22358i	−0.274401	−	0.475277i
$232$		0			0
$233$	−15.2583			−0.999606			−0.499803	−	0.866139i	$-0.666594\pi$
$233$	−15.2583			−0.999606			−0.499803	+	0.866139i	$0.666594\pi$
$234$		0			0
$235$	−2.67578			−0.174549
$236$		0			0
$237$	−5.22741	−	9.05414i	−0.339557	−	0.588130i
$238$		0			0
$239$			9.74398i			0.630286i	0.949044	+	0.315143i	$0.102052\pi$
$239$			9.74398i			0.630286i	−0.949044	+	0.315143i	$0.897948\pi$
$240$		0			0
$241$	20.0787	+	11.5925i	1.29338	+	0.746736i	0.979253	−	0.202643i	$-0.0649532\pi$
$241$	20.0787	+	11.5925i	1.29338	+	0.746736i	0.314132	+	0.949379i	$0.398287\pi$
$242$		0			0
$243$	−24.5357	+	42.4971i	−1.57396	+	2.72619i
$244$		0			0
$245$	−0.506905	+	0.292662i	−0.0323850	+	0.0186975i
$246$		0			0
$247$	6.04160	−	3.13408i	0.384418	−	0.199417i
$248$		0			0
$249$	−25.8776	+	14.9404i	−1.63993	+	0.946812i
$250$		0			0
$251$	0.536680	−	0.929556i	0.0338749	−	0.0586731i	−0.848591	−	0.529050i	$-0.822549\pi$
$251$	0.536680	−	0.929556i	0.0338749	−	0.0586731i	0.882466	+	0.470377i	$0.155882\pi$
$252$		0			0
$253$	7.10509	+	4.10212i	0.446693	+	0.257898i
$254$		0			0
$255$			14.5049i			0.908329i
$256$		0			0
$257$	9.95641	+	17.2450i	0.621064	+	1.07571i	0.989288	+	0.145977i	$0.0466326\pi$
$257$	9.95641	+	17.2450i	0.621064	+	1.07571i	−0.368224	+	0.929737i	$0.620034\pi$
$258$		0			0
$259$	10.5935			0.658248
$260$		0			0
$261$	−55.4107			−3.42983
$262$		0			0
$263$	−8.82917	−	15.2926i	−0.544430	−	0.942981i	−0.998643	−	0.0520873i	$-0.983413\pi$
$263$	−8.82917	−	15.2926i	−0.544430	−	0.942981i	0.454212	−	0.890893i	$-0.349921\pi$
$264$		0			0
$265$		−	0.796743i		−	0.0489435i
$266$		0			0
$267$	−49.1795	−	28.3938i	−3.00974	−	1.73767i
$268$		0			0
$269$	0.217802	−	0.377244i	0.0132796	−	0.0230010i	−0.859309	−	0.511456i	$-0.829106\pi$
$269$	0.217802	−	0.377244i	0.0132796	−	0.0230010i	0.872589	+	0.488455i	$0.162440\pi$
$270$		0			0
$271$	−0.0345513	+	0.0199482i	−0.00209884	+	0.00121177i	−0.501049	−	0.865419i	$-0.667052\pi$
$271$	−0.0345513	+	0.0199482i	−0.00209884	+	0.00121177i	0.498950	+	0.866631i	$0.333719\pi$
$272$		0			0
$273$	−10.0239	−	6.40612i	−0.606677	−	0.387716i
$274$		0			0
$275$	10.1968	−	5.88710i	0.614888	−	0.355006i
$276$		0			0
$277$	9.63076	−	16.6810i	0.578656	−	1.00226i	−0.416977	−	0.908917i	$-0.636911\pi$
$277$	9.63076	−	16.6810i	0.578656	−	1.00226i	0.995634	−	0.0933454i	$-0.0297561\pi$
$278$		0			0
$279$	64.0212	+	36.9626i	3.83285	+	2.21290i
$280$		0			0
$281$			14.3098i			0.853653i	0.904334	+	0.426826i	$0.140368\pi$
$281$			14.3098i			0.853653i	−0.904334	+	0.426826i	$0.859632\pi$
$282$		0			0
$283$	5.43032	+	9.40560i	0.322799	+	0.559105i	0.981064	−	0.193681i	$-0.0620428\pi$
$283$	5.43032	+	9.40560i	0.322799	+	0.559105i	−0.658265	+	0.752786i	$0.728709\pi$
$284$		0			0
$285$	3.64551			0.215941
$286$		0			0
$287$	5.06676			0.299081
$288$		0			0
$289$	−19.7057	−	34.1313i	−1.15916	−	2.00772i
$290$		0			0
$291$			9.81730i			0.575500i
$292$		0			0
$293$	0.753925	+	0.435279i	0.0440447	+	0.0254292i	0.521861	−	0.853031i	$-0.325238\pi$
$293$	0.753925	+	0.435279i	0.0440447	+	0.0254292i	−0.477816	+	0.878460i	$0.658571\pi$
$294$		0			0
$295$	1.06907	−	1.85169i	0.0622439	−	0.107810i
$296$		0			0
$297$	35.2943	−	20.3772i	2.04798	−	1.18240i
$298$		0			0
$299$	11.6891	+	0.527103i	0.675998	+	0.0304832i
$300$		0			0
$301$	−4.88541	+	2.82059i	−0.281590	+	0.162576i
$302$		0			0
$303$	−2.60479	+	4.51163i	−0.149641	+	0.259186i
$304$		0			0
$305$	−4.44743	−	2.56772i	−0.254659	−	0.147027i
$306$		0			0
$307$		−	31.5607i		−	1.80127i	−0.434580	−	0.900633i	$-0.643103\pi$
$307$		−	31.5607i		−	1.80127i	0.434580	−	0.900633i	$-0.356897\pi$
$308$		0			0
$309$	29.8505	+	51.7026i	1.69814	+	2.94126i
$310$		0			0
$311$	25.1782			1.42772			0.713861	−	0.700287i	$-0.246945\pi$
$311$	25.1782			1.42772			0.713861	+	0.700287i	$0.246945\pi$
$312$		0			0
$313$	−0.499674			−0.0282432			−0.0141216	−	0.999900i	$-0.504495\pi$
$313$	−0.499674			−0.0282432			−0.0141216	+	0.999900i	$0.504495\pi$
$314$		0			0
$315$	−2.30793	−	3.99744i	−0.130037	−	0.225231i
$316$		0			0
$317$			3.83012i			0.215121i	0.994199	+	0.107560i	$0.0343039\pi$
$317$			3.83012i			0.215121i	−0.994199	+	0.107560i	$0.965696\pi$
$318$		0			0
$319$	15.3835	+	8.88169i	0.861313	+	0.497279i
$320$		0			0
$321$	−24.5229	+	42.4748i	−1.36873	+	2.37071i
$322$		0			0
$323$	−12.2784	+	7.08895i	−0.683190	+	0.394440i
$324$		0			0
$325$	9.04283	−	14.1497i	0.501606	−	0.784885i
$326$		0			0
$327$	−10.4130	+	6.01192i	−0.575838	+	0.332460i
$328$		0			0
$329$	−2.28573	+	3.95900i	−0.126016	+	0.218267i
$330$		0			0
$331$	17.6477	+	10.1889i	0.970005	+	0.560033i	0.899238	−	0.437460i	$-0.144122\pi$
$331$	17.6477	+	10.1889i	0.970005	+	0.560033i	0.0707674	+	0.997493i	$0.477455\pi$
$332$		0			0
$333$			83.5401i			4.57797i
$334$		0			0
$335$	−0.350822	−	0.607642i	−0.0191675	−	0.0331990i
$336$		0			0
$337$	−27.7240			−1.51022			−0.755111	−	0.655597i	$-0.772417\pi$
$337$	−27.7240			−1.51022			−0.755111	+	0.655597i	$0.772417\pi$
$338$		0			0
$339$	−17.3827			−0.944100
$340$		0			0
$341$	−11.8494	−	20.5237i	−0.641679	−	1.11142i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	5.42764	+	3.13365i	0.292214	+	0.168710i
$346$		0			0
$347$	7.77404	−	13.4650i	0.417332	−	0.722841i	−0.578338	−	0.815797i	$-0.696298\pi$
$347$	7.77404	−	13.4650i	0.417332	−	0.722841i	0.995670	+	0.0929566i	$0.0296318\pi$
$348$		0			0
$349$	−9.27468	+	5.35474i	−0.496462	+	0.286633i	−0.727251	−	0.686371i	$-0.759203\pi$
$349$	−9.27468	+	5.35474i	−0.496462	+	0.286633i	0.230789	+	0.973004i	$0.425869\pi$
$350$		0			0
$351$	31.3002	−	48.9768i	1.67068	−	2.61419i
$352$		0			0
$353$	24.2023	−	13.9732i	1.28816	−	0.743718i	0.309832	−	0.950791i	$-0.399727\pi$
$353$	24.2023	−	13.9732i	1.28816	−	0.743718i	0.978325	+	0.207074i	$0.0663940\pi$
$354$		0			0
$355$	−0.750275	+	1.29951i	−0.0398205	+	0.0689711i
$356$		0			0
$357$	21.4609	+	12.3905i	1.13583	+	0.655773i
$358$		0			0
$359$			34.8499i			1.83931i	0.392733	+	0.919653i	$0.371530\pi$
$359$			34.8499i			1.83931i	−0.392733	+	0.919653i	$0.628470\pi$
$360$		0			0
$361$	−7.71833	−	13.3685i	−0.406228	−	0.703608i
$362$		0			0
$363$	15.2065			0.798136
$364$		0			0
$365$	3.95520			0.207025
$366$		0			0
$367$	0.0561008	+	0.0971695i	0.00292844	+	0.00507221i	0.867486	−	0.497462i	$-0.165735\pi$
$367$	0.0561008	+	0.0971695i	0.00292844	+	0.00507221i	−0.864557	+	0.502534i	$0.832401\pi$
$368$		0			0
$369$			39.9564i			2.08005i
$370$		0			0
$371$	−1.17884	−	0.680601i	−0.0612021	−	0.0353350i
$372$		0			0
$373$	10.5775	−	18.3207i	0.547682	−	0.948612i	−0.450751	−	0.892650i	$-0.648844\pi$
$373$	10.5775	−	18.3207i	0.547682	−	0.948612i	0.998433	−	0.0559628i	$-0.0178228\pi$
$374$		0			0
$375$	16.1518	−	9.32524i	0.834074	−	0.481553i
$376$		0			0
$377$	25.3086	+	1.14125i	1.30346	+	0.0587776i
$378$		0			0
$379$	18.3416	−	10.5895i	0.942144	−	0.543947i	0.0515124	−	0.998672i	$-0.483596\pi$
$379$	18.3416	−	10.5895i	0.942144	−	0.543947i	0.890632	+	0.454725i	$0.150263\pi$
$380$		0			0
$381$	0.750826	−	1.30047i	0.0384660	−	0.0666251i
$382$		0			0
$383$	−14.0337	−	8.10235i	−0.717088	−	0.414011i	0.0965920	−	0.995324i	$-0.469206\pi$
$383$	−14.0337	−	8.10235i	−0.717088	−	0.414011i	−0.813680	+	0.581313i	$0.802539\pi$
$384$		0			0
$385$			1.47974i			0.0754143i
$386$		0			0
$387$	−22.2431	−	38.5262i	−1.13068	−	1.95840i
$388$		0			0
$389$	9.72438			0.493046			0.246523	−	0.969137i	$-0.420712\pi$
$389$	9.72438			0.493046			0.246523	+	0.969137i	$0.420712\pi$
$390$		0			0
$391$	−24.3744			−1.23267
$392$		0			0
$393$	−19.9487	−	34.5522i	−1.00628	−	1.74293i
$394$		0			0
$395$			1.85472i			0.0933211i
$396$		0			0
$397$	−30.2997	−	17.4935i	−1.52070	−	0.877976i	−0.999702	−	0.0244166i	$-0.992227\pi$
$397$	−30.2997	−	17.4935i	−1.52070	−	0.877976i	−0.520996	−	0.853559i	$-0.674439\pi$
$398$		0			0
$399$	3.11410	−	5.39378i	0.155900	−	0.270027i
$400$		0			0
$401$	−7.67955	+	4.43379i	−0.383498	+	0.221413i	−0.679339	−	0.733824i	$-0.737733\pi$
$401$	−7.67955	+	4.43379i	−0.383498	+	0.221413i	0.295841	+	0.955237i	$0.404400\pi$
$402$		0			0
$403$	−28.4801	−	18.2011i	−1.41870	−	0.906663i
$404$		0			0
$405$	14.9693	−	8.64254i	0.743831	−	0.429451i
$406$		0			0
$407$	13.3905	−	23.1931i	0.663743	−	1.14964i
$408$		0			0
$409$	−0.543638	−	0.313869i	−0.0268811	−	0.0155198i	0.486499	−	0.873681i	$-0.338274\pi$
$409$	−0.543638	−	0.313869i	−0.0268811	−	0.0155198i	−0.513380	+	0.858161i	$0.671607\pi$
$410$		0			0
$411$		−	30.8395i		−	1.52120i
$412$		0			0
$413$	−1.82647	−	3.16353i	−0.0898746	−	0.155667i
$414$		0			0
$415$	5.30097			0.260215
$416$		0			0
$417$	−62.1495			−3.04348
$418$		0			0
$419$	2.43213	+	4.21258i	0.118817	+	0.205798i	0.919299	−	0.393559i	$-0.128756\pi$
$419$	2.43213	+	4.21258i	0.118817	+	0.205798i	−0.800482	+	0.599357i	$0.795423\pi$
$420$		0			0
$421$			8.51783i			0.415133i	0.978221	+	0.207567i	$0.0665544\pi$
$421$			8.51783i			0.415133i	−0.978221	+	0.207567i	$0.933446\pi$
$422$		0			0
$423$	−31.2206	−	18.0252i	−1.51800	−	0.876416i
$424$		0			0
$425$	−17.4903	+	30.2941i	−0.848403	+	1.46948i
$426$		0			0
$427$	−7.59824	+	4.38685i	−0.367705	+	0.212294i
$428$		0			0
$429$	−26.6960	+	13.8486i	−1.28889	+	0.668615i
$430$		0			0
$431$	9.91454	−	5.72416i	0.477567	−	0.275723i	−0.241835	−	0.970317i	$-0.577749\pi$
$431$	9.91454	−	5.72416i	0.477567	−	0.275723i	0.719402	+	0.694594i	$0.244416\pi$
$432$		0			0
$433$	−15.8045	+	27.3742i	−0.759516	+	1.31552i	0.183581	+	0.983005i	$0.441231\pi$
$433$	−15.8045	+	27.3742i	−0.759516	+	1.31552i	−0.943098	+	0.332516i	$0.892102\pi$
$434$		0			0
$435$	11.7516	+	6.78480i	0.563447	+	0.325306i
$436$		0			0
$437$			6.12603i			0.293048i
$438$		0			0
$439$	1.38800	+	2.40408i	0.0662456	+	0.114741i	0.897246	−	0.441531i	$-0.145565\pi$
$439$	1.38800	+	2.40408i	0.0662456	+	0.114741i	−0.831000	+	0.556272i	$0.812231\pi$
$440$		0			0
$441$	−7.88599			−0.375523
$442$		0			0
$443$	−17.0948			−0.812199			−0.406099	−	0.913829i	$-0.633111\pi$
$443$	−17.0948			−0.812199			−0.406099	+	0.913829i	$0.633111\pi$
$444$		0			0
$445$	5.03716	+	8.72461i	0.238784	+	0.413586i
$446$		0			0
$447$		−	32.6563i		−	1.54459i
$448$		0			0
$449$	−28.4358	−	16.4174i	−1.34197	−	0.774787i	−0.354874	−	0.934914i	$-0.615476\pi$
$449$	−28.4358	−	16.4174i	−1.34197	−	0.774787i	−0.987096	+	0.160128i	$0.948809\pi$
$450$		0			0
$451$	6.40455	−	11.0930i	0.301578	−	0.522349i
$452$		0			0
$453$	27.3299	−	15.7789i	1.28407	−	0.741359i
$454$		0			0
$455$	0.971803	+	1.87335i	0.0455588	+	0.0878241i
$456$		0			0
$457$	20.9275	−	12.0825i	0.978947	−	0.565196i	0.0769952	−	0.997031i	$-0.475467\pi$
$457$	20.9275	−	12.0825i	0.978947	−	0.565196i	0.901952	+	0.431836i	$0.142134\pi$
$458$		0			0
$459$	−60.5396	+	104.858i	−2.82575	+	4.89434i
$460$		0			0
$461$	0.126087	+	0.0727962i	0.00587245	+	0.00339046i	0.502933	−	0.864325i	$-0.332254\pi$
$461$	0.126087	+	0.0727962i	0.00587245	+	0.00339046i	−0.497061	+	0.867716i	$0.665587\pi$
$462$		0			0
$463$			21.9805i			1.02152i	0.859724	+	0.510759i	$0.170636\pi$
$463$			21.9805i			1.02152i	−0.859724	+	0.510759i	$0.829364\pi$
$464$		0			0
$465$	−9.05184	−	15.6782i	−0.419769	−	0.727061i
$466$		0			0
$467$	−8.81976			−0.408130			−0.204065	−	0.978957i	$-0.565415\pi$
$467$	−8.81976			−0.408130			−0.204065	+	0.978957i	$0.565415\pi$
$468$		0			0
$469$	−1.19873			−0.0553522
$470$		0			0
$471$	−10.1700	−	17.6150i	−0.468609	−	0.811655i
$472$		0			0
$473$			14.2613i			0.655734i
$474$		0			0
$475$	7.61381	+	4.39584i	0.349346	+	0.201695i
$476$		0			0
$477$	5.36721	−	9.29628i	0.245748	−	0.425647i
$478$		0			0
$479$	−19.8624	+	11.4676i	−0.907536	+	0.523966i	−0.879638	−	0.475645i	$-0.842215\pi$
$479$	−19.8624	+	11.4676i	−0.907536	+	0.523966i	−0.0278984	+	0.999611i	$0.508881\pi$
$480$		0			0
$481$	1.72062	−	38.1566i	0.0784534	−	1.73979i
$482$		0			0
$483$	9.27289	−	5.35370i	0.421931	−	0.243602i
$484$		0			0
$485$	0.870811	−	1.50829i	0.0395415	−	0.0684879i
$486$		0			0
$487$	11.4857	+	6.63130i	0.520469	+	0.300493i	0.737126	−	0.675755i	$-0.236182\pi$
$487$	11.4857	+	6.63130i	0.520469	+	0.300493i	−0.216658	+	0.976248i	$0.569516\pi$
$488$		0			0
$489$		−	35.9273i		−	1.62469i
$490$		0			0
$491$	11.4044	+	19.7530i	0.514674	+	0.891442i	0.999855	+	0.0170278i	$0.00542038\pi$
$491$	11.4044	+	19.7530i	0.514674	+	0.891442i	−0.485181	+	0.874414i	$0.661246\pi$
$492$		0			0
$493$	−52.7741			−2.37683
$494$		0			0
$495$	−11.6692			−0.524490
$496$		0			0
$497$	1.28181	+	2.22017i	0.0574972	+	0.0995880i
$498$		0			0
$499$			2.60213i			0.116487i	0.998302	+	0.0582437i	$0.0185500\pi$
$499$			2.60213i			0.116487i	−0.998302	+	0.0582437i	$0.981450\pi$
$500$		0			0
$501$	−35.6959	−	20.6090i	−1.59477	−	0.920743i
$502$		0			0
$503$	5.81082	−	10.0646i	0.259092	−	0.448760i	−0.706907	−	0.707306i	$-0.749910\pi$
$503$	5.81082	−	10.0646i	0.259092	−	0.448760i	0.965999	+	0.258546i	$0.0832434\pi$
$504$		0			0
$505$	0.800378	−	0.462098i	0.0356163	−	0.0205631i
$506$		0			0
$507$	−24.7023	+	35.0646i	−1.09707	+	1.55728i
$508$		0			0
$509$	−21.5515	+	12.4428i	−0.955255	+	0.551517i	−0.894709	−	0.446649i	$-0.852617\pi$
$509$	−21.5515	+	12.4428i	−0.955255	+	0.551517i	−0.0605454	+	0.998165i	$0.519284\pi$
$510$		0			0
$511$	3.37865	−	5.85199i	0.149463	−	0.258877i
$512$		0			0
$513$	26.3539	+	15.2154i	1.16355	+	0.671778i
$514$		0			0
$515$		−	10.5912i		−	0.466702i
$516$		0			0
$517$	5.77847	+	10.0086i	0.254137	+	0.440178i
$518$		0			0
$519$	12.3081			0.540265
$520$		0			0
$521$	20.2180			0.885768			0.442884	−	0.896579i	$-0.353955\pi$
$521$	20.2180			0.885768			0.442884	+	0.896579i	$0.353955\pi$
$522$		0			0
$523$	−11.6131	−	20.1145i	−0.507806	−	0.879547i	−0.999959	−	0.00903773i	$-0.997123\pi$
$523$	−11.6131	−	20.1145i	−0.507806	−	0.879547i	0.492153	−	0.870509i	$-0.336210\pi$
$524$		0			0
$525$		−	15.3666i		−	0.670652i
$526$		0			0
$527$	60.9749	+	35.2039i	2.65611	+	1.53351i
$528$		0			0
$529$	6.23412	−	10.7978i	0.271049	−	0.469470i
$530$		0			0
$531$	24.9476	−	14.4035i	1.08263	−	0.625058i
$532$		0			0
$533$	0.822954	−	18.2499i	0.0356461	−	0.790492i
$534$		0			0
$535$	7.53518	−	4.35044i	0.325774	−	0.188086i
$536$		0			0
$537$	20.0519	−	34.7309i	0.865304	−	1.49875i
$538$		0			0
$539$	2.18937	+	1.26403i	0.0943028	+	0.0544457i
$540$		0			0
$541$		−	4.74987i		−	0.204213i	−0.994773	−	0.102107i	$-0.967442\pi$
$541$		−	4.74987i		−	0.204213i	0.994773	−	0.102107i	$-0.0325583\pi$
$542$		0			0
$543$	−22.2165	−	38.4801i	−0.953400	−	1.65134i
$544$		0			0
$545$	2.13307			0.0913707
$546$		0			0
$547$	−19.9348			−0.852350			−0.426175	−	0.904641i	$-0.640139\pi$
$547$	−19.9348			−0.852350			−0.426175	+	0.904641i	$0.640139\pi$
$548$		0			0
$549$	−34.5946	−	59.9196i	−1.47646	−	2.55731i
$550$		0			0
$551$			13.2637i			0.565054i
$552$		0			0
$553$	2.74418	+	1.58436i	0.116695	+	0.0673737i
$554$		0			0
$555$	10.2291	−	17.7174i	0.434203	−	0.752061i
$556$		0			0
$557$	−25.1098	+	14.4971i	−1.06393	+	0.614263i	−0.926518	−	0.376250i	$-0.877213\pi$
$557$	−25.1098	+	14.4971i	−1.06393	+	0.614263i	−0.137417	+	0.990513i	$0.543880\pi$
$558$		0			0
$559$	9.36596	+	18.0548i	0.396138	+	0.763638i
$560$		0			0
$561$	54.2546	−	31.3239i	2.29063	−	1.32250i
$562$		0			0
$563$	−8.40607	+	14.5597i	−0.354274	+	0.613620i	−0.986993	−	0.160761i	$-0.948605\pi$
$563$	−8.40607	+	14.5597i	−0.354274	+	0.613620i	0.632720	+	0.774381i	$0.281938\pi$
$564$		0			0
$565$	2.67061	+	1.54188i	0.112353	+	0.0648672i
$566$		0			0
$567$		−	29.5308i		−	1.24018i
$568$		0			0
$569$	15.4299	+	26.7253i	0.646853	+	1.12038i	0.983870	+	0.178884i	$0.0572486\pi$
$569$	15.4299	+	26.7253i	0.646853	+	1.12038i	−0.337017	+	0.941498i	$0.609418\pi$
$570$		0			0
$571$	29.4285			1.23155			0.615773	−	0.787924i	$-0.288844\pi$
$571$	29.4285			1.23155			0.615773	+	0.787924i	$0.288844\pi$
$572$		0			0
$573$	47.8424			1.99865
$574$		0			0
$575$	7.55725	+	13.0895i	0.315159	+	0.545872i
$576$		0			0
$577$			42.6627i			1.77607i	0.459776	+	0.888035i	$0.347930\pi$
$577$			42.6627i			1.77607i	−0.459776	+	0.888035i	$0.652070\pi$
$578$		0			0
$579$	−13.8100	−	7.97318i	−0.573922	−	0.331354i
$580$		0			0
$581$	4.52824	−	7.84315i	0.187863	−	0.325389i
$582$		0			0
$583$	−2.98017	+	1.72060i	−0.123426	+	0.0712601i
$584$		0			0
$585$	−14.7732	+	7.66362i	−0.610797	+	0.316852i
$586$		0			0
$587$	−37.3134	+	21.5429i	−1.54009	+	0.889170i	−0.541256	+	0.840858i	$0.682051\pi$
$587$	−37.3134	+	21.5429i	−1.54009	+	0.889170i	−0.998832	+	0.0483120i	$0.984616\pi$
$588$		0			0
$589$	8.84780	−	15.3248i	0.364567	−	0.631449i
$590$		0			0
$591$	6.23697	+	3.60092i	0.256555	+	0.148122i
$592$		0			0
$593$		−	28.4634i		−	1.16885i	−0.811447	−	0.584426i	$-0.801320\pi$
$593$		−	28.4634i		−	1.16885i	0.811447	−	0.584426i	$-0.198680\pi$
$594$		0			0
$595$	−2.19811	−	3.80724i	−0.0901137	−	0.156082i
$596$		0			0
$597$	62.0090			2.53786
$598$		0			0
$599$	−2.12689			−0.0869025			−0.0434513	−	0.999056i	$-0.513835\pi$
$599$	−2.12689			−0.0869025			−0.0434513	+	0.999056i	$0.513835\pi$
$600$		0			0
$601$	−8.28457	−	14.3493i	−0.337935	−	0.585320i	0.646109	−	0.763245i	$-0.276395\pi$
$601$	−8.28457	−	14.3493i	−0.337935	−	0.585320i	−0.984044	+	0.177925i	$0.943062\pi$
$602$		0			0
$603$		−	9.45317i		−	0.384963i
$604$		0			0
$605$	−2.33627	−	1.34884i	−0.0949828	−	0.0548383i
$606$		0			0
$607$	−19.0553	+	33.0048i	−0.773432	+	1.33962i	0.162239	+	0.986751i	$0.448128\pi$
$607$	−19.0553	+	33.0048i	−0.773432	+	1.33962i	−0.935671	+	0.352872i	$0.885205\pi$
$608$		0			0
$609$	20.0771	−	11.5915i	0.813567	−	0.469713i
$610$		0			0
$611$	13.8886	+	8.87597i	0.561873	+	0.359083i
$612$		0			0
$613$	8.54900	−	4.93577i	0.345291	−	0.199354i	−0.317318	−	0.948319i	$-0.602782\pi$
$613$	8.54900	−	4.93577i	0.345291	−	0.199354i	0.662609	+	0.748965i	$0.269449\pi$
$614$		0			0
$615$	4.89249	−	8.47404i	0.197284	−	0.341706i
$616$		0			0
$617$	−41.0736	−	23.7139i	−1.65356	−	0.954684i	−0.975591	−	0.219595i	$-0.929526\pi$
$617$	−41.0736	−	23.7139i	−1.65356	−	0.954684i	−0.677970	−	0.735089i	$-0.737140\pi$
$618$		0			0
$619$		−	12.1183i		−	0.487076i	−0.969891	−	0.243538i	$-0.921692\pi$
$619$		−	12.1183i		−	0.487076i	0.969891	−	0.243538i	$-0.0783080\pi$
$620$		0			0
$621$	26.1581	+	45.3072i	1.04969	+	1.81812i
$622$		0			0
$623$	17.2115			0.689565
$624$		0			0
$625$	19.9783			0.799133
$626$		0			0
$627$	−7.87264	−	13.6358i	−0.314403	−	0.544562i
$628$		0			0
$629$			79.5651i			3.17247i
$630$		0			0
$631$	9.39978	+	5.42697i	0.374199	+	0.216044i	0.675291	−	0.737551i	$-0.264018\pi$
$631$	9.39978	+	5.42697i	0.374199	+	0.216044i	−0.301092	+	0.953595i	$0.597351\pi$
$632$		0			0
$633$	10.5345	−	18.2463i	0.418709	−	0.725225i
$634$		0			0
$635$	−0.230708	+	0.133199i	−0.00915536	+	0.00528585i
$636$		0			0
$637$	3.60189	+	0.162422i	0.142712	+	0.00643540i
$638$		0			0
$639$	−17.5082	+	10.1084i	−0.692613	+	0.399881i
$640$		0			0
$641$	18.5825	−	32.1858i	0.733965	−	1.27126i	−0.221211	−	0.975226i	$-0.571001\pi$
$641$	18.5825	−	32.1858i	0.733965	−	1.27126i	0.955176	−	0.296038i	$-0.0956657\pi$
$642$		0			0
$643$	−8.43885	−	4.87217i	−0.332796	−	0.192140i	0.324286	−	0.945959i	$-0.394876\pi$
$643$	−8.43885	−	4.87217i	−0.332796	−	0.192140i	−0.657082	+	0.753819i	$0.728209\pi$
$644$		0			0
$645$			10.8943i			0.428963i
$646$		0			0
$647$	−6.55650	−	11.3562i	−0.257763	−	0.446458i	0.707880	−	0.706333i	$-0.249652\pi$
$647$	−6.55650	−	11.3562i	−0.257763	−	0.446458i	−0.965642	+	0.259875i	$0.916319\pi$
$648$		0			0
$649$	−9.23485			−0.362500
$650$		0			0
$651$	−30.9294			−1.21222
$652$		0			0
$653$	−0.810078	−	1.40310i	−0.0317008	−	0.0549074i	0.849740	−	0.527202i	$-0.176759\pi$
$653$	−0.810078	−	1.40310i	−0.0317008	−	0.0549074i	−0.881441	+	0.472295i	$0.843426\pi$
$654$		0			0
$655$			7.07795i			0.276558i
$656$		0			0
$657$	46.1487	+	26.6440i	1.80043	+	1.03948i
$658$		0			0
$659$	19.2587	−	33.3570i	0.750211	−	1.29940i	−0.197509	−	0.980301i	$-0.563285\pi$
$659$	19.2587	−	33.3570i	0.750211	−	1.29940i	0.947720	−	0.319103i	$-0.103381\pi$
$660$		0			0
$661$	−19.1051	+	11.0303i	−0.743102	+	0.429030i	−0.823196	−	0.567757i	$-0.807811\pi$
$661$	−19.1051	+	11.0303i	−0.743102	+	0.429030i	0.0800942	+	0.996787i	$0.474478\pi$
$662$		0			0
$663$	48.1148	−	75.2874i	1.86862	−	2.92392i
$664$		0			0
$665$	−0.956874	+	0.552452i	−0.0371060	+	0.0214232i
$666$		0			0
$667$	−11.4014	+	19.7478i	−0.441464	+	0.764638i
$668$		0			0
$669$	34.7033	+	20.0360i	1.34171	+	0.774635i
$670$		0			0
$671$			22.1805i			0.856267i
$672$		0			0
$673$	−0.460408	−	0.797449i	−0.0177474	−	0.0307394i	0.857015	−	0.515291i	$-0.172316\pi$
$673$	−0.460408	−	0.797449i	−0.0177474	−	0.0307394i	−0.874763	+	0.484552i	$0.838983\pi$
$674$		0			0
$675$	75.0809			2.88986
$676$		0			0
$677$	−34.4678			−1.32470			−0.662352	−	0.749193i	$-0.730442\pi$
$677$	−34.4678			−1.32470			−0.662352	+	0.749193i	$0.730442\pi$
$678$		0			0
$679$	−1.48774	−	2.57685i	−0.0570944	−	0.0988904i
$680$		0			0
$681$		−	40.2611i		−	1.54281i
$682$		0			0
$683$	4.33833	+	2.50474i	0.166002	+	0.0958410i	0.580699	−	0.814118i	$-0.302779\pi$
$683$	4.33833	+	2.50474i	0.166002	+	0.0958410i	−0.414698	+	0.909959i	$0.636113\pi$
$684$		0			0
$685$	−2.73551	+	4.73805i	−0.104519	+	0.181031i
$686$		0			0
$687$	−46.6722	+	26.9462i	−1.78066	+	1.02806i
$688$		0			0
$689$	−2.64292	+	4.13549i	−0.100687	+	0.157550i
$690$		0			0
$691$	−13.6764	+	7.89606i	−0.520274	+	0.300380i	−0.737047	−	0.675842i	$-0.763780\pi$
$691$	−13.6764	+	7.89606i	−0.520274	+	0.300380i	0.216773	+	0.976222i	$0.430447\pi$
$692$		0			0
$693$	−9.96814	+	17.2653i	−0.378658	+	0.655856i
$694$		0			0
$695$	9.54840	+	5.51277i	0.362191	+	0.209111i
$696$		0			0
$697$			38.0552i			1.44144i
$698$		0			0
$699$	25.1716	+	43.5985i	0.952077	+	1.64905i
$700$		0			0
$701$	14.6605			0.553718			0.276859	−	0.960911i	$-0.410707\pi$
$701$	14.6605			0.553718			0.276859	+	0.960911i	$0.410707\pi$
$702$		0			0
$703$	19.9971			0.754206
$704$		0			0
$705$	4.41422	+	7.64566i	0.166249	+	0.287952i
$706$		0			0
$707$		−	1.57895i		−	0.0593825i
$708$		0			0
$709$	−13.3762	−	7.72273i	−0.502353	−	0.290033i	0.227332	−	0.973817i	$-0.427000\pi$
$709$	−13.3762	−	7.72273i	−0.502353	−	0.290033i	−0.729685	+	0.683784i	$0.760333\pi$
$710$		0			0
$711$	−12.4942	+	21.6406i	−0.468569	+	0.811586i
$712$		0			0
$713$	26.3462	−	15.2110i	0.986673	−	0.569656i
$714$		0			0
$715$	5.32985	+	0.240342i	0.199325	+	0.00898827i
$716$		0			0
$717$	27.8420	−	16.0746i	1.03978	−	0.600317i
$718$		0			0
$719$	−5.03616	+	8.72288i	−0.187817	+	0.325309i	−0.944522	−	0.328448i	$-0.893475\pi$
$719$	−5.03616	+	8.72288i	−0.187817	+	0.325309i	0.756705	+	0.653756i	$0.226808\pi$
$720$		0			0
$721$	−15.6703	−	9.04728i	−0.583594	−	0.336938i
$722$		0			0
$723$		−	76.4961i		−	2.84492i
$724$		0			0
$725$	16.3625	+	28.3407i	0.607689	+	1.05255i
$726$		0			0
$727$	−4.62399			−0.171494			−0.0857472	−	0.996317i	$-0.527328\pi$
$727$	−4.62399			−0.171494			−0.0857472	+	0.996317i	$0.527328\pi$
$728$		0			0
$729$	73.3132			2.71530
$730$		0			0
$731$	−21.1848	−	36.6931i	−0.783547	−	1.35714i
$732$		0			0
$733$		−	32.4005i		−	1.19674i	−0.801219	−	0.598371i	$-0.795815\pi$
$733$		−	32.4005i		−	1.19674i	0.801219	−	0.598371i	$-0.204185\pi$
$734$		0			0
$735$	1.67248	+	0.965606i	0.0616903	+	0.0356169i
$736$		0			0
$737$	−1.51523	+	2.62446i	−0.0558144	+	0.0966733i
$738$		0			0
$739$	−39.0930	+	22.5704i	−1.43806	+	0.830264i	−0.997715	−	0.0675652i	$-0.978477\pi$
$739$	−39.0930	+	22.5704i	−1.43806	+	0.830264i	−0.440344	+	0.897829i	$0.645144\pi$
$740$		0			0
$741$	−18.9220	−	12.0927i	−0.695117	−	0.444237i
$742$		0			0
$743$	−25.1291	+	14.5083i	−0.921898	+	0.532258i	−0.884240	−	0.467033i	$-0.845323\pi$
$743$	−25.1291	+	14.5083i	−0.921898	+	0.532258i	−0.0376577	+	0.999291i	$0.511990\pi$
$744$		0			0
$745$	−2.89667	+	5.01718i	−0.106126	+	0.183815i
$746$		0			0
$747$	61.8509	+	35.7097i	2.26301	+	1.30655i
$748$		0			0
$749$		−	14.8651i		−	0.543158i
$750$		0			0
$751$	−18.0850	−	31.3242i	−0.659933	−	1.14304i	−0.980633	−	0.195856i	$-0.937251\pi$
$751$	−18.0850	−	31.3242i	−0.659933	−	1.14304i	0.320700	−	0.947181i	$-0.396082\pi$
$752$		0			0
$753$	−3.54143			−0.129057
$754$		0			0
$755$	−5.59847			−0.203749
$756$		0			0
$757$	−5.68024	−	9.83846i	−0.206452	−	0.357585i	0.744143	−	0.668021i	$-0.232858\pi$
$757$	−5.68024	−	9.83846i	−0.206452	−	0.357585i	−0.950594	+	0.310436i	$0.899525\pi$
$758$		0			0
$759$		−	27.0690i		−	0.982543i
$760$		0			0
$761$	−39.2057	−	22.6354i	−1.42121	−	0.820533i	−0.424803	−	0.905286i	$-0.639657\pi$
$761$	−39.2057	−	22.6354i	−1.42121	−	0.820533i	−0.996402	+	0.0847524i	$0.972990\pi$
$762$		0			0
$763$	1.82213	−	3.15602i	0.0659656	−	0.114256i
$764$		0			0
$765$	30.0238	−	17.3343i	1.08551	−	0.626722i
$766$		0			0
$767$	−11.6914	+	6.06491i	−0.422151	+	0.218991i
$768$		0			0
$769$	6.11442	−	3.53016i	0.220492	−	0.127301i	−0.385686	−	0.922630i	$-0.626035\pi$
$769$	6.11442	−	3.53016i	0.220492	−	0.127301i	0.606178	+	0.795329i	$0.292702\pi$
$770$		0			0
$771$	32.8501	−	56.8980i	1.18307	−	2.04913i
$772$		0			0
$773$	10.5780	+	6.10722i	0.380465	+	0.219662i	0.678021	−	0.735043i	$-0.262838\pi$
$773$	10.5780	+	6.10722i	0.380465	+	0.219662i	−0.297556	+	0.954705i	$0.596171\pi$
$774$		0			0
$775$		−	43.6596i		−	1.56830i
$776$		0			0
$777$	−17.4760	−	30.2694i	−0.626949	−	1.08591i
$778$		0			0
$779$	9.56442			0.342681
$780$		0			0
$781$	6.48101			0.231909
$782$		0			0
$783$	56.6361	+	98.0966i	2.02401	+	3.50569i
$784$		0			0
$785$			3.60839i			0.128789i
$786$		0			0
$787$	15.6804	+	9.05306i	0.558944	+	0.322707i	0.752722	−	0.658339i	$-0.228741\pi$
$787$	15.6804	+	9.05306i	0.558944	+	0.322707i	−0.193777	+	0.981046i	$0.562074\pi$
$788$		0			0
$789$	−29.1309	+	50.4562i	−1.03709	+	1.79629i
$790$		0			0
$791$	4.56262	−	2.63423i	0.162228	−	0.0936625i
$792$		0			0
$793$	14.5668	+	28.0806i	0.517283	+	0.997170i
$794$		0			0
$795$	−2.27658	+	1.31438i	−0.0807420	+	0.0466164i
$796$		0			0
$797$	7.20159	−	12.4735i	0.255094	−	0.441835i	−0.709827	−	0.704376i	$-0.751227\pi$
$797$	7.20159	−	12.4735i	0.255094	−	0.441835i	0.964921	+	0.262541i	$0.0845604\pi$
$798$		0			0
$799$	−29.7350	−	17.1675i	−1.05195	−	0.607344i
$800$		0			0
$801$			135.730i			4.79578i
$802$		0			0
$803$	−8.54144	−	14.7942i	−0.301421	−	0.522077i
$804$		0			0
$805$	−1.89953			−0.0669497
$806$		0			0
$807$	−1.43723			−0.0505928
$808$		0			0
$809$	20.6173	+	35.7102i	0.724866	+	1.25550i	0.959029	+	0.283308i	$0.0914317\pi$
$809$	20.6173	+	35.7102i	0.724866	+	1.25550i	−0.234163	+	0.972197i	$0.575235\pi$
$810$		0			0
$811$		−	21.6479i		−	0.760159i	−0.924954	−	0.380080i	$-0.875897\pi$
$811$		−	21.6479i		−	0.760159i	0.924954	−	0.380080i	$-0.124103\pi$
$812$		0			0
$813$	0.113998	+	0.0658170i	0.00399810	+	0.00230830i
$814$		0			0
$815$	−3.18681	+	5.51972i	−0.111629	+	0.193347i
$816$		0			0
$817$	−9.22208	+	5.32437i	−0.322640	+	0.186276i
$818$		0			0
$819$	−1.28086	+	28.4045i	−0.0447568	+	0.992532i
$820$		0			0
$821$	−20.1432	+	11.6297i	−0.703001	+	0.405878i	−0.808464	−	0.588545i	$-0.799701\pi$
$821$	−20.1432	+	11.6297i	−0.703001	+	0.405878i	0.105463	+	0.994423i	$0.466367\pi$
$822$		0			0
$823$	−25.9735	+	44.9875i	−0.905380	+	1.56816i	−0.0849736	+	0.996383i	$0.527081\pi$
$823$	−25.9735	+	44.9875i	−0.905380	+	1.56816i	−0.820406	+	0.571781i	$0.806253\pi$
$824$		0			0
$825$	−33.6431	−	19.4239i	−1.17130	−	0.676252i
$826$		0			0
$827$		−	8.56814i		−	0.297944i	−0.988841	−	0.148972i	$-0.952404\pi$
$827$		−	8.56814i		−	0.297944i	0.988841	−	0.148972i	$-0.0475963\pi$
$828$		0			0
$829$	9.04823	+	15.6720i	0.314258	+	0.544311i	0.979280	−	0.202513i	$-0.0649109\pi$
$829$	9.04823	+	15.6720i	0.314258	+	0.544311i	−0.665021	+	0.746824i	$0.731578\pi$
$830$		0			0
$831$	−63.5513			−2.20457
$832$		0			0
$833$	−7.51075			−0.260232
$834$		0			0
$835$	3.65611	+	6.33257i	0.126525	+	0.219148i
$836$		0			0
$837$		−	151.120i		−	5.22348i
$838$		0			0
$839$	−41.4439	−	23.9277i	−1.43080	−	0.826075i	−0.433622	−	0.901095i	$-0.642765\pi$
$839$	−41.4439	−	23.9277i	−1.43080	−	0.826075i	−0.997182	+	0.0750200i	$0.976098\pi$
$840$		0			0
$841$	−10.1857	+	17.6421i	−0.351230	+	0.608348i
$842$		0			0
$843$	40.8883	−	23.6069i	1.40827	−	0.813063i
$844$		0			0
$845$	6.90545	−	3.19605i	0.237555	−	0.109948i
$846$		0			0
$847$	−3.99141	+	2.30444i	−0.137147	+	0.0791816i
$848$		0			0
$849$	17.9168	−	31.0327i	0.614902	−	1.06504i
$850$		0			0
$851$	29.7728	+	17.1894i	1.02060	+	0.589244i
$852$		0			0
$853$			23.9983i			0.821687i	0.911706	+	0.410843i	$0.134766\pi$
$853$			23.9983i			0.821687i	−0.911706	+	0.410843i	$0.865234\pi$
$854$		0			0
$855$	−4.35663	−	7.54590i	−0.148993	−	0.258064i
$856$		0			0
$857$	36.7162			1.25420			0.627101	−	0.778938i	$-0.284241\pi$
$857$	36.7162			1.25420			0.627101	+	0.778938i	$0.284241\pi$
$858$		0			0
$859$	−11.0247			−0.376157			−0.188079	−	0.982154i	$-0.560226\pi$
$859$	−11.0247			−0.376157			−0.188079	+	0.982154i	$0.560226\pi$
$860$		0			0
$861$	−8.35861	−	14.4775i	−0.284861	−	0.493393i
$862$		0			0
$863$		−	32.0149i		−	1.08980i	−0.838501	−	0.544900i	$-0.816568\pi$
$863$		−	32.0149i		−	1.08980i	0.838501	−	0.544900i	$-0.183432\pi$
$864$		0			0
$865$	−1.89096	−	1.09175i	−0.0642947	−	0.0371206i
$866$		0			0
$867$	−65.0169	+	112.613i	−2.20809	+	3.82452i
$868$		0			0
$869$	6.93748	−	4.00535i	0.235338	−	0.135872i
$870$		0			0
$871$	−0.194700	+	4.31769i	−0.00659717	+	0.146300i
$872$		0			0
$873$	20.3210	−	11.7323i	0.687761	−	0.397079i
$874$		0			0
$875$	−2.82635	+	4.89538i	−0.0955481	+	0.165494i
$876$		0			0
$877$	−31.0099	−	17.9036i	−1.04713	−	0.604561i	−0.125286	−	0.992121i	$-0.539985\pi$
$877$	−31.0099	−	17.9036i	−1.04713	−	0.604561i	−0.921845	+	0.387560i	$0.873318\pi$
$878$		0			0
$879$		−	2.87231i		−	0.0968806i
$880$		0			0
$881$	9.48732	+	16.4325i	0.319636	+	0.553625i	0.980412	−	0.196958i	$-0.0631061\pi$
$881$	9.48732	+	16.4325i	0.319636	+	0.553625i	−0.660776	+	0.750583i	$0.729773\pi$
$882$		0			0
$883$	−7.52168			−0.253125			−0.126562	−	0.991959i	$-0.540394\pi$
$883$	−7.52168			−0.253125			−0.126562	+	0.991959i	$0.540394\pi$
$884$		0			0
$885$	−7.05459			−0.237137
$886$		0			0
$887$	21.1477	+	36.6288i	0.710069	+	1.22988i	0.964831	+	0.262872i	$0.0846697\pi$
$887$	21.1477	+	36.6288i	0.710069	+	1.22988i	−0.254761	+	0.967004i	$0.581997\pi$
$888$		0			0
$889$			0.455130i			0.0152646i
$890$		0			0
$891$	−64.6538	−	37.3279i	−2.16598	−	1.25053i
$892$		0			0
$893$	−4.31472	+	7.47332i	−0.144387	+	0.250085i
$894$		0			0
$895$	−6.16138	+	3.55728i	−0.205952	+	0.118907i
$896$		0			0
$897$	−17.7773	−	34.2695i	−0.593568	−	1.14423i
$898$		0			0
$899$	57.0433	−	32.9340i	1.90250	−	1.09841i
$900$		0			0
$901$	5.11183	−	8.85394i	0.170300	−	0.294968i
$902$		0			0
$903$	16.1189	+	9.30623i	0.536402	+	0.309692i
$904$		0			0
$905$			7.88256i			0.262025i
$906$		0			0
$907$	−8.47904	−	14.6861i	−0.281542	−	0.487645i	0.690223	−	0.723597i	$-0.257512\pi$
$907$	−8.47904	−	14.6861i	−0.281542	−	0.487645i	−0.971765	+	0.235952i	$0.924179\pi$
$908$		0			0
$909$	12.4516			0.412993
$910$		0			0
$911$	−45.7607			−1.51612			−0.758060	−	0.652185i	$-0.773853\pi$
$911$	−45.7607			−1.51612			−0.758060	+	0.652185i	$0.773853\pi$
$912$		0			0
$913$	−11.4477	−	19.8280i	−0.378863	−	0.656211i
$914$		0			0
$915$			16.9439i			0.560146i
$916$		0			0
$917$	10.4723	+	6.04619i	0.345826	+	0.199663i
$918$		0			0
$919$	−12.7996	+	22.1695i	−0.422219	+	0.731305i	−0.996156	−	0.0875945i	$-0.972082\pi$
$919$	−12.7996	+	22.1695i	−0.422219	+	0.731305i	0.573937	+	0.818899i	$0.305415\pi$
$920$		0			0
$921$	−90.1803	+	52.0656i	−2.97154	+	1.71562i
$922$		0			0
$923$	8.20499	−	4.25635i	0.270070	−	0.140099i
$924$		0			0
$925$	42.7280	−	24.6690i	1.40489	−	0.811113i
$926$		0			0
$927$	71.3467	−	123.576i	2.34333	−	4.05877i
$928$		0			0
$929$	22.6286	+	13.0646i	0.742419	+	0.428636i	0.822948	−	0.568117i	$-0.192328\pi$
$929$	22.6286	+	13.0646i	0.742419	+	0.428636i	−0.0805293	+	0.996752i	$0.525661\pi$
$930$		0			0
$931$			1.88768i			0.0618662i
$932$		0			0
$933$	−41.5363	−	71.9430i	−1.35984	−	2.35531i
$934$		0			0
$935$	−11.1139			−0.363464
$936$		0			0
$937$	0.603992			0.0197315			0.00986577	−	0.999951i	$-0.496860\pi$
$937$	0.603992			0.0197315			0.00986577	+	0.999951i	$0.496860\pi$
$938$		0			0
$939$	0.824310	+	1.42775i	0.0269003	+	0.0465928i
$940$		0			0
$941$		−	35.5175i		−	1.15784i	−0.815385	−	0.578919i	$-0.803475\pi$
$941$		−	35.5175i		−	1.15784i	0.815385	−	0.578919i	$-0.196525\pi$
$942$		0			0
$943$	14.2400	+	8.22150i	0.463720	+	0.267729i
$944$		0			0
$945$	−4.71793	+	8.17170i	−0.153474	+	0.265826i
$946$		0			0
$947$	7.74967	−	4.47428i	0.251831	−	0.145394i	−0.368772	−	0.929520i	$-0.620222\pi$
$947$	7.74967	−	4.47428i	0.251831	−	0.145394i	0.620602	+	0.784126i	$0.286888\pi$
$948$		0			0
$949$	−20.5295	−	13.1200i	−0.666415	−	0.425894i
$950$		0			0
$951$	10.9440	−	6.31853i	0.354884	−	0.204892i
$952$		0			0
$953$	16.8494	−	29.1840i	0.545805	−	0.945363i	−0.452750	−	0.891637i	$-0.649557\pi$
$953$	16.8494	−	29.1840i	0.545805	−	0.945363i	0.998556	−	0.0537254i	$-0.0171095\pi$
$954$		0			0
$955$	−7.35032	−	4.24371i	−0.237851	−	0.137323i
$956$		0			0
$957$		−	58.6084i		−	1.89454i
$958$		0			0
$959$	4.67351	+	8.09475i	0.150915	+	0.261393i
$960$		0			0
$961$	−56.8767			−1.83473
$962$		0			0
$963$	117.226			3.77755
$964$		0			0
$965$	1.41447	+	2.44993i	0.0455334	+	0.0788662i
$966$		0			0
$967$		−	17.6070i		−	0.566203i	−0.959090	−	0.283102i	$-0.908637\pi$
$967$		−	17.6070i		−	0.566203i	0.959090	−	0.283102i	$-0.0913633\pi$
$968$		0			0
$969$	40.5113	+	23.3892i	1.30141	+	0.751370i
$970$		0			0
$971$	−0.444682	+	0.770212i	−0.0142705	+	0.0247173i	−0.873072	−	0.487590i	$-0.837876\pi$
$971$	−0.444682	+	0.770212i	−0.0142705	+	0.0247173i	0.858802	+	0.512308i	$0.171209\pi$
$972$		0			0
$973$	16.3130	−	9.41833i	0.522972	−	0.301938i
$974$		0			0
$975$	−55.3487	−	2.49587i	−1.77258	−	0.0799319i
$976$		0			0
$977$	−10.5022	+	6.06342i	−0.335994	+	0.193986i	−0.658499	−	0.752582i	$-0.728808\pi$
$977$	−10.5022	+	6.06342i	−0.335994	+	0.193986i	0.322505	+	0.946568i	$0.395475\pi$
$978$		0			0
$979$	21.7559	−	37.6824i	0.695323	−	1.20433i
$980$		0			0
$981$	24.8883	+	14.3693i	0.794624	+	0.458776i
$982$		0			0
$983$			59.4878i			1.89737i	0.316226	+	0.948684i	$0.397584\pi$
$983$			59.4878i			1.89737i	−0.316226	+	0.948684i	$0.602416\pi$
$984$		0			0
$985$	−0.638815	−	1.10646i	−0.0203543	−	0.0352548i
$986$		0			0
$987$	15.0830			0.480098
$988$		0			0
$989$	−18.3071			−0.582133
$990$		0			0
$991$	13.5333	+	23.4404i	0.429900	+	0.744609i	0.996864	−	0.0791336i	$-0.0252154\pi$
$991$	13.5333	+	23.4404i	0.429900	+	0.744609i	−0.566964	+	0.823743i	$0.691882\pi$
$992$		0			0
$993$		−	67.2344i		−	2.13362i
$994$		0			0
$995$	−9.52680	−	5.50030i	−0.302020	−	0.174371i
$996$		0			0
$997$	−22.1640	+	38.3891i	−0.701940	+	1.21580i	0.265844	+	0.964016i	$0.414349\pi$
$997$	−22.1640	+	38.3891i	−0.701940	+	1.21580i	−0.967785	+	0.251780i	$0.918984\pi$
$998$		0			0
$999$	147.896	−	85.3877i	4.67922	−	2.70155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.673.1		24
4.3	odd	2		728.2.bm.c.673.12	yes	24
13.4	even	6	inner	1456.2.cc.g.225.1		24
52.11	even	12		9464.2.a.bm.1.1		12
52.15	even	12		9464.2.a.bl.1.1		12
52.43	odd	6		728.2.bm.c.225.12	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.12	✓	24	52.43	odd	6
728.2.bm.c.673.12	yes	24	4.3	odd	2
1456.2.cc.g.225.1		24	13.4	even	6	inner
1456.2.cc.g.673.1		24	1.1	even	1	trivial
9464.2.a.bl.1.1		12	52.15	even	12
9464.2.a.bm.1.1		12	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.64970 - 2.85736i) q^{3} +0.585323i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.94299 + 6.82946i) q^{9} +O(q^{10})\)	\(q+(-1.64970 - 2.85736i) q^{3} +0.585323i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.94299 + 6.82946i) q^{9} +(2.18937 - 1.26403i) q^{11} +(1.94161 - 3.03812i) q^{13} +(1.67248 - 0.965606i) q^{15} +(-3.75538 + 6.50450i) q^{17} +(1.63478 + 0.943840i) q^{19} -3.29939i q^{21} +(1.62263 + 2.81048i) q^{23} +4.65740 q^{25} +16.1208 q^{27} +(3.51324 + 6.08510i) q^{29} -9.37426i q^{31} +(-7.22358 - 4.17054i) q^{33} +(-0.292662 + 0.506905i) q^{35} +(9.17423 - 5.29675i) q^{37} +(-11.8840 - 0.535894i) q^{39} +(4.38794 - 2.53338i) q^{41} +(-2.82059 + 4.88541i) q^{43} +(-3.99744 - 2.30793i) q^{45} +4.57145i q^{47} +(0.500000 + 0.866025i) q^{49} +24.7809 q^{51} -1.36120 q^{53} +(0.739868 + 1.28149i) q^{55} -6.22820i q^{57} +(-3.16353 - 1.82647i) q^{59} +(-4.38685 + 7.59824i) q^{61} +(-6.82946 + 3.94299i) q^{63} +(1.77828 + 1.13647i) q^{65} +(-1.03813 + 0.599365i) q^{67} +(5.35370 - 9.27289i) q^{69} +(2.22017 + 1.28181i) q^{71} -6.75730i q^{73} +(-7.68329 - 13.3078i) q^{75} +2.52807 q^{77} +3.16871 q^{79} +(-14.7654 - 25.5744i) q^{81} -9.05649i q^{83} +(-3.80724 - 2.19811i) q^{85} +(11.5915 - 20.0771i) q^{87} +(14.9056 - 8.60576i) q^{89} +(3.20054 - 1.66028i) q^{91} +(-26.7856 + 15.4647i) q^{93} +(-0.552452 + 0.956874i) q^{95} +(-2.57685 - 1.48774i) q^{97} +19.9363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 - 18 * q^9	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) \) 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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