LMFDB - Embedded newform 1323.2.f.g.883.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.4
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.g.442.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})$	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +0.619757 q^{10} +(2.09097 - 3.62167i) q^{11} +(1.84155 + 3.18966i) q^{13} +(-1.83009 + 3.16982i) q^{16} +1.71107 q^{17} +7.15561 q^{19} +(-2.51769 + 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 - 4.43818i) q^{23} +(-0.858685 + 1.48729i) q^{25} +0.880716 q^{26} +(-1.06238 + 1.84010i) q^{29} +(-3.26793 - 5.66021i) q^{31} +(1.38044 + 2.39099i) q^{32} +(0.204579 - 0.354341i) q^{34} +1.66019 q^{37} +(0.855536 - 1.48183i) q^{38} +(1.22180 + 2.11621i) q^{40} +(5.10948 + 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +8.12476 q^{44} -1.22545 q^{46} +(-4.66912 + 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} +(-3.57780 + 6.19694i) q^{52} -10.6465 q^{53} +10.8387 q^{55} +(0.254040 + 0.440011i) q^{58} +(-3.03215 - 5.25183i) q^{59} +(-3.99298 + 6.91605i) q^{61} -1.56287 q^{62} -6.66019 q^{64} +(-4.77292 + 8.26693i) q^{65} +(-4.13160 - 7.15614i) q^{67} +(1.66215 + 2.87893i) q^{68} -6.23912 q^{71} -7.15561 q^{73} +(0.198495 - 0.343803i) q^{74} +(6.95103 + 12.0395i) q^{76} +(4.91423 - 8.51170i) q^{79} -9.48644 q^{80} +2.44359 q^{82} +(-3.44733 + 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 - 0.343803i) q^{86} +(1.97141 - 3.41458i) q^{88} -5.03538 q^{89} +(4.97825 - 8.62258i) q^{92} +(1.11650 + 1.93383i) q^{94} +(9.27292 + 16.0612i) q^{95} +(1.53167 - 2.65294i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	−0.820653	−	0.571426i	$-0.806390\pi$
$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	0.905196	+	0.424994i	$0.139724\pi$
$3$		0			0
$3$		0			0
$4$	0.971410	+	1.68253i	0.485705	+	0.841266i
$5$	1.29589	+	2.24456i	0.579542	+	1.00380i	0.995532	+	0.0944264i	$0.0301017\pi$
$5$	1.29589	+	2.24456i	0.579542	+	1.00380i	−0.415990	+	0.909369i	$0.636565\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$		0			0
$10$	0.619757			0.195984
$11$	2.09097	−	3.62167i	0.630452	−	1.09197i	−0.357008	−	0.934101i	$-0.616203\pi$
$11$	2.09097	−	3.62167i	0.630452	−	1.09197i	0.987459	−	0.157873i	$-0.0504636\pi$
$12$		0			0
$13$	1.84155	+	3.18966i	0.510755	+	0.884653i	0.999922	+	0.0124633i	$0.00396730\pi$
$13$	1.84155	+	3.18966i	0.510755	+	0.884653i	−0.489168	+	0.872190i	$0.662699\pi$
$14$		0			0
$15$		0			0
$16$	−1.83009	+	3.16982i	−0.457524	+	0.792454i
$17$	1.71107			0.414996			0.207498	−	0.978235i	$-0.433468\pi$
$17$	1.71107			0.414996			0.207498	+	0.978235i	$0.433468\pi$
$18$		0			0
$19$	7.15561			1.64161			0.820805	−	0.571209i	$-0.193525\pi$
$19$	7.15561			1.64161			0.820805	+	0.571209i	$0.193525\pi$
$20$	−2.51769	+	4.36077i	−0.562973	+	0.975097i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.56238	−	4.43818i	−0.534294	−	0.925424i	−0.999197	−	0.0400622i	$-0.987244\pi$
$23$	−2.56238	−	4.43818i	−0.534294	−	0.925424i	0.464904	−	0.885361i	$-0.346089\pi$
$24$		0			0
$25$	−0.858685	+	1.48729i	−0.171737	+	0.297457i
$26$	0.880716			0.172723
$27$		0			0
$28$		0			0
$29$	−1.06238	+	1.84010i	−0.197279	+	0.341698i	−0.947645	−	0.319325i	$-0.896544\pi$
$29$	−1.06238	+	1.84010i	−0.197279	+	0.341698i	0.750366	+	0.661023i	$0.229877\pi$
$30$		0			0
$31$	−3.26793	−	5.66021i	−0.586937	−	1.01660i	−0.994631	−	0.103486i	$-0.967000\pi$
$31$	−3.26793	−	5.66021i	−0.586937	−	1.01660i	0.407694	−	0.913119i	$-0.366333\pi$
$32$	1.38044	+	2.39099i	0.244029	+	0.422671i
$33$		0			0
$34$	0.204579	−	0.354341i	0.0350850	−	0.0607689i
$35$		0			0
$36$		0			0
$37$	1.66019			0.272934			0.136467	−	0.990645i	$-0.456425\pi$
$37$	1.66019			0.272934			0.136467	+	0.990645i	$0.456425\pi$
$38$	0.855536	−	1.48183i	0.138786	−	0.240385i
$39$		0			0
$40$	1.22180	+	2.11621i	0.193183	+	0.334602i
$41$	5.10948	+	8.84988i	0.797967	+	1.38212i	0.920938	+	0.389708i	$0.127424\pi$
$41$	5.10948	+	8.84988i	0.797967	+	1.38212i	−0.122972	+	0.992410i	$0.539242\pi$
$42$		0			0
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	−0.795764	−	0.605606i	$-0.792931\pi$
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	0.922353	+	0.386349i	$0.126264\pi$
$44$	8.12476			1.22485
$45$		0			0
$46$	−1.22545			−0.180683
$47$	−4.66912	+	8.08715i	−0.681061	+	1.17963i	0.293596	+	0.955930i	$0.405148\pi$
$47$	−4.66912	+	8.08715i	−0.681061	+	1.17963i	−0.974657	+	0.223703i	$0.928185\pi$
$48$		0			0
$49$		0			0
$50$	0.205332	+	0.355645i	0.0290383	+	0.0502958i
$51$		0			0
$52$	−3.57780	+	6.19694i	−0.496152	+	0.859361i
$53$	−10.6465			−1.46241			−0.731206	−	0.682157i	$-0.761042\pi$
$53$	−10.6465			−1.46241			−0.731206	+	0.682157i	$0.761042\pi$
$54$		0			0
$55$	10.8387			1.46149
$56$		0			0
$57$		0			0
$58$	0.254040	+	0.440011i	0.0333571	+	0.0577762i
$59$	−3.03215	−	5.25183i	−0.394752	−	0.683730i	0.598318	−	0.801259i	$-0.295836\pi$
$59$	−3.03215	−	5.25183i	−0.394752	−	0.683730i	−0.993069	+	0.117529i	$0.962503\pi$
$60$		0			0
$61$	−3.99298	+	6.91605i	−0.511249	+	0.885509i	0.488666	+	0.872471i	$0.337484\pi$
$61$	−3.99298	+	6.91605i	−0.511249	+	0.885509i	−0.999915	+	0.0130384i	$0.995850\pi$
$62$	−1.56287			−0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−4.77292	+	8.26693i	−0.592007	+	1.02539i
$66$		0			0
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	−0.999985	−	0.00549964i	$-0.998249\pi$
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	0.495230	−	0.868762i	$-0.335084\pi$
$68$	1.66215	+	2.87893i	0.201566	+	0.349122i
$69$		0			0
$70$		0			0
$71$	−6.23912			−0.740448			−0.370224	−	0.928943i	$-0.620719\pi$
$71$	−6.23912			−0.740448			−0.370224	+	0.928943i	$0.620719\pi$
$72$		0			0
$73$	−7.15561			−0.837501			−0.418750	−	0.908101i	$-0.637532\pi$
$73$	−7.15561			−0.837501			−0.418750	+	0.908101i	$0.637532\pi$
$74$	0.198495	−	0.343803i	0.0230746	−	0.0399663i
$75$		0			0
$76$	6.95103	+	12.0395i	0.797338	+	1.38103i
$77$		0			0
$78$		0			0
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	−0.445170	−	0.895446i	$-0.646857\pi$
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	0.998064	−	0.0621945i	$-0.0198099\pi$
$80$	−9.48644			−1.06062
$81$		0			0
$82$	2.44359			0.269849
$83$	−3.44733	+	5.97094i	−0.378393	+	0.655396i	−0.990829	−	0.135124i	$-0.956857\pi$
$83$	−3.44733	+	5.97094i	−0.378393	+	0.655396i	0.612436	+	0.790521i	$0.290190\pi$
$84$		0			0
$85$	2.21737	+	3.84060i	0.240508	+	0.416571i
$86$	−0.198495	−	0.343803i	−0.0214043	−	0.0370733i
$87$		0			0
$88$	1.97141	−	3.41458i	0.210153	−	0.363996i
$89$	−5.03538			−0.533749			−0.266875	−	0.963731i	$-0.585991\pi$
$89$	−5.03538			−0.533749			−0.266875	+	0.963731i	$0.585991\pi$
$90$		0			0
$91$		0			0
$92$	4.97825	−	8.62258i	0.519018	−	0.898966i
$93$		0			0
$94$	1.11650	+	1.93383i	0.115158	+	0.199459i
$95$	9.27292	+	16.0612i	0.951381	+	1.64784i
$96$		0			0
$97$	1.53167	−	2.65294i	0.155518	−	0.269365i	−0.777730	−	0.628599i	$-0.783629\pi$
$97$	1.53167	−	2.65294i	0.155518	−	0.269365i	0.933247	+	0.359234i	$0.116962\pi$
$98$		0			0
$99$		0			0
$100$	−3.33654			−0.333654
$101$	5.54984	−	9.61260i	0.552229	−	0.956489i	−0.445884	−	0.895091i	$-0.647111\pi$
$101$	5.54984	−	9.61260i	0.552229	−	0.956489i	0.998113	−	0.0613986i	$-0.0195561\pi$
$102$		0			0
$103$	3.99298	+	6.91605i	0.393440	+	0.681459i	0.992901	−	0.118946i	$-0.0379515\pi$
$103$	3.99298	+	6.91605i	0.393440	+	0.681459i	−0.599460	+	0.800404i	$0.704618\pi$
$104$	1.73625	+	3.00728i	0.170254	+	0.294888i
$105$		0			0
$106$	−1.27292	+	2.20475i	−0.123636	+	0.214145i
$107$	−3.95649			−0.382489			−0.191244	−	0.981542i	$-0.561252\pi$
$107$	−3.95649			−0.382489			−0.191244	+	0.981542i	$0.561252\pi$
$108$		0			0
$109$	7.26320			0.695688			0.347844	−	0.937552i	$-0.386914\pi$
$109$	7.26320			0.695688			0.347844	+	0.937552i	$0.386914\pi$
$110$	1.29589	−	2.24456i	0.123559	−	0.214010i
$111$		0			0
$112$		0			0
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	0.981698	−	0.190444i	$-0.0609928\pi$
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	−0.655778	+	0.754953i	$0.727659\pi$
$114$		0			0
$115$	6.64115	−	11.5028i	0.619291	−	1.07264i
$116$	−4.12803			−0.383278
$117$		0			0
$118$	−1.45011			−0.133494
$119$		0			0
$120$		0			0
$121$	−3.24433	−	5.61934i	−0.294939	−	0.510849i
$122$	0.954815	+	1.65379i	0.0864449	+	0.149727i
$123$		0			0
$124$	6.34899	−	10.9968i	0.570156	−	0.987540i
$125$	8.50788			0.760968
$126$		0			0
$127$	9.11109			0.808479			0.404239	−	0.914653i	$-0.367536\pi$
$127$	9.11109			0.808479			0.404239	+	0.914653i	$0.367536\pi$
$128$	−3.55718	+	6.16122i	−0.314413	+	0.544580i
$129$		0			0
$130$	1.14132	+	1.97682i	0.100100	+	0.173378i
$131$	2.15143	+	3.72639i	0.187971	+	0.325576i	0.944574	−	0.328299i	$-0.106475\pi$
$131$	2.15143	+	3.72639i	0.187971	+	0.325576i	−0.756602	+	0.653875i	$0.773142\pi$
$132$		0			0
$133$		0			0
$134$	−1.97592			−0.170694
$135$		0			0
$136$	1.61323			0.138334
$137$	10.2947	−	17.8309i	0.879533	−	1.52340i	0.0276785	−	0.999617i	$-0.491189\pi$
$137$	10.2947	−	17.8309i	0.879533	−	1.52340i	0.851854	−	0.523779i	$-0.175478\pi$
$138$		0			0
$139$	−7.88067	−	13.6497i	−0.668429	−	1.15775i	−0.978343	−	0.206989i	$-0.933634\pi$
$139$	−7.88067	−	13.6497i	−0.668429	−	1.15775i	0.309914	−	0.950765i	$-0.399700\pi$
$140$		0			0
$141$		0			0
$142$	−0.745960	+	1.29204i	−0.0625996	+	0.108426i
$143$	15.4025			1.28802
$144$		0			0
$145$	−5.50694			−0.457326
$146$	−0.855536	+	1.48183i	−0.0708047	+	0.122637i
$147$		0			0
$148$	1.61273	+	2.79332i	0.132565	+	0.229610i
$149$	3.03379	+	5.25468i	0.248538	+	0.430480i	0.963120	−	0.269071i	$-0.0867166\pi$
$149$	3.03379	+	5.25468i	0.248538	+	0.430480i	−0.714582	+	0.699551i	$0.753383\pi$
$150$		0			0
$151$	−2.24433	+	3.88728i	−0.182641	+	0.316343i	−0.942779	−	0.333418i	$-0.891798\pi$
$151$	−2.24433	+	3.88728i	−0.182641	+	0.316343i	0.760138	+	0.649761i	$0.225131\pi$
$152$	6.74645			0.547210
$153$		0			0
$154$		0			0
$155$	8.46978	−	14.6701i	0.680309	−	1.17833i
$156$		0			0
$157$	0.514457	+	0.891066i	0.0410582	+	0.0711148i	0.885824	−	0.464021i	$-0.153594\pi$
$157$	0.514457	+	0.891066i	0.0410582	+	0.0711148i	−0.844766	+	0.535136i	$0.820260\pi$
$158$	−1.17511	−	2.03534i	−0.0934865	−	0.161923i
$159$		0			0
$160$	−3.57780	+	6.19694i	−0.282850	+	0.489911i
$161$		0			0
$162$		0			0
$163$	6.82846			0.534846			0.267423	−	0.963579i	$-0.413828\pi$
$163$	6.82846			0.534846			0.267423	+	0.963579i	$0.413828\pi$
$164$	−9.92680	+	17.1937i	−0.775153	+	1.34260i
$165$		0			0
$166$	0.824336	+	1.42779i	0.0639809	+	0.110818i
$167$	−8.99716	−	15.5835i	−0.696221	−	1.20589i	−0.969767	−	0.244032i	$-0.921530\pi$
$167$	−8.99716	−	15.5835i	−0.696221	−	1.20589i	0.273546	−	0.961859i	$-0.411803\pi$
$168$		0			0
$169$	−0.282630	+	0.489530i	−0.0217408	+	0.0376561i
$170$	1.06045			0.0813328
$171$		0			0
$172$	3.22545			0.245938
$173$	0.415178	−	0.719110i	0.0315654	−	0.0546729i	−0.849811	−	0.527087i	$-0.823284\pi$
$173$	0.415178	−	0.719110i	0.0315654	−	0.0546729i	0.881377	+	0.472414i	$0.156617\pi$
$174$		0			0
$175$		0			0
$176$	7.65335	+	13.2560i	0.576893	+	0.999208i
$177$		0			0
$178$	−0.602038	+	1.04276i	−0.0451247	+	0.0781582i
$179$	−7.57893			−0.566476			−0.283238	−	0.959050i	$-0.591409\pi$
$179$	−7.57893			−0.566476			−0.283238	+	0.959050i	$0.591409\pi$
$180$		0			0
$181$	−0.409157			−0.0304124			−0.0152062	−	0.999884i	$-0.504840\pi$
$181$	−0.409157			−0.0304124			−0.0152062	+	0.999884i	$0.504840\pi$
$182$		0			0
$183$		0			0
$184$	−2.41586	−	4.18440i	−0.178100	−	0.308478i
$185$	2.15143	+	3.72639i	0.158176	+	0.273969i
$186$		0			0
$187$	3.57780	−	6.19694i	0.261635	−	0.453165i
$188$	−18.1425			−1.32318
$189$		0			0
$190$	4.43474			0.321730
$191$	8.01204	−	13.8773i	0.579731	−	1.00412i	−0.415779	−	0.909466i	$-0.636491\pi$
$191$	8.01204	−	13.8773i	0.579731	−	1.00412i	0.995510	−	0.0946575i	$-0.0301756\pi$
$192$		0			0
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	0.998077	−	0.0619822i	$-0.0197422\pi$
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	−0.552717	+	0.833369i	$0.686409\pi$
$194$	−0.366259	−	0.634379i	−0.0262959	−	0.0455458i
$195$		0			0
$196$		0			0
$197$	−23.1021			−1.64595			−0.822977	−	0.568075i	$-0.807688\pi$
$197$	−23.1021			−1.64595			−0.822977	+	0.568075i	$0.807688\pi$
$198$		0			0
$199$	6.74645			0.478243			0.239122	−	0.970990i	$-0.423141\pi$
$199$	6.74645			0.478243			0.239122	+	0.970990i	$0.423141\pi$
$200$	−0.809585	+	1.40224i	−0.0572463	+	0.0991536i
$201$		0			0
$202$	−1.32710	−	2.29860i	−0.0933741	−	0.161729i
$203$		0			0
$204$		0			0
$205$	−13.2427	+	22.9370i	−0.924910	+	1.60199i
$206$	1.90963			0.133050
$207$		0			0
$208$	−13.4809			−0.934730
$209$	14.9622	−	25.9153i	1.03496	−	1.79260i
$210$		0			0
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	−0.995334	−	0.0964875i	$-0.969239\pi$
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	0.414106	−	0.910228i	$-0.364094\pi$
$212$	−10.3421	−	17.9131i	−0.710301	−	1.23028i
$213$		0			0
$214$	−0.473045	+	0.819338i	−0.0323367	+	0.0560088i
$215$	4.30286			0.293453
$216$		0			0
$217$		0			0
$218$	0.868400	−	1.50411i	0.0588155	−	0.101871i
$219$		0			0
$220$	10.5288	+	18.2365i	0.709854	+	1.22950i
$221$	3.15103	+	5.45774i	0.211961	+	0.367128i
$222$		0			0
$223$	−2.25071	+	3.89834i	−0.150719	+	0.261052i	−0.931492	−	0.363762i	$-0.881492\pi$
$223$	−2.25071	+	3.89834i	−0.150719	+	0.261052i	0.780773	+	0.624815i	$0.214825\pi$
$224$		0			0
$225$		0			0
$226$	1.65692			0.110217
$227$	3.03215	−	5.25183i	0.201251	−	0.348576i	−0.747681	−	0.664058i	$-0.768833\pi$
$227$	3.03215	−	5.25183i	0.201251	−	0.348576i	0.948932	+	0.315482i	$0.102166\pi$
$228$		0			0
$229$	−5.52466	−	9.56899i	−0.365080	−	0.632336i	0.623709	−	0.781656i	$-0.285625\pi$
$229$	−5.52466	−	9.56899i	−0.365080	−	0.632336i	−0.988789	+	0.149320i	$0.952292\pi$
$230$	−1.58805	−	2.75059i	−0.104713	−	0.181369i
$231$		0			0
$232$	−1.00163	+	1.73488i	−0.0657605	+	0.113901i
$233$	8.13844			0.533167			0.266583	−	0.963812i	$-0.414105\pi$
$233$	8.13844			0.533167			0.266583	+	0.963812i	$0.414105\pi$
$234$		0			0
$235$	−24.2028			−1.57881
$236$	5.89092	−	10.2034i	0.383466	−	0.664183i
$237$		0			0
$238$		0			0
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	0.973611	+	0.228214i	$0.0732886\pi$
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	−0.289166	+	0.957279i	$0.593378\pi$
$240$		0			0
$241$	6.84573	−	11.8572i	0.440972	−	0.763786i	−0.556790	−	0.830654i	$-0.687967\pi$
$241$	6.84573	−	11.8572i	0.440972	−	0.763786i	0.997762	+	0.0668671i	$0.0213004\pi$
$242$	−1.55159			−0.0997398
$243$		0			0
$244$	−15.5153			−0.993265
$245$		0			0
$246$		0			0
$247$	13.1774	+	22.8240i	0.838460	+	1.45225i
$248$	−3.08107	−	5.33656i	−0.195648	−	0.338872i
$249$		0			0
$250$	1.01722	−	1.76187i	0.0643344	−	0.111430i
$251$	15.2040			0.959667			0.479833	−	0.877360i	$-0.340697\pi$
$251$	15.2040			0.959667			0.479833	+	0.877360i	$0.340697\pi$
$252$		0			0
$253$	−21.4315			−1.34738
$254$	1.08934	−	1.88679i	0.0683511	−	0.118388i
$255$		0			0
$256$	−5.80959	−	10.0625i	−0.363099	−	0.628906i
$257$	−12.8107	−	22.1889i	−0.799112	−	1.38410i	−0.920195	−	0.391461i	$-0.871970\pi$
$257$	−12.8107	−	22.1889i	−0.799112	−	1.38410i	0.121082	−	0.992642i	$-0.461363\pi$
$258$		0			0
$259$		0			0
$260$	−18.5458			−1.15016
$261$		0			0
$262$	1.02891			0.0635665
$263$	3.55034	−	6.14938i	0.218924	−	0.379187i	−0.735556	−	0.677464i	$-0.763079\pi$
$263$	3.55034	−	6.14938i	0.218924	−	0.379187i	0.954479	+	0.298278i	$0.0964121\pi$
$264$		0			0
$265$	−13.7968	−	23.8967i	−0.847528	−	1.46796i
$266$		0			0
$267$		0			0
$268$	8.02696	−	13.9031i	0.490324	−	0.849267i
$269$	−16.4314			−1.00184			−0.500922	−	0.865493i	$-0.667006\pi$
$269$	−16.4314			−1.00184			−0.500922	+	0.865493i	$0.667006\pi$
$270$		0			0
$271$	−12.6980			−0.771348			−0.385674	−	0.922635i	$-0.626031\pi$
$271$	−12.6980			−0.771348			−0.385674	+	0.922635i	$0.626031\pi$
$272$	−3.13143	+	5.42379i	−0.189871	+	0.328865i
$273$		0			0
$274$	−2.46169	−	4.26378i	−0.148716	−	0.257584i
$275$	3.59097	+	6.21975i	0.216544	+	0.375065i
$276$		0			0
$277$	0.414230	−	0.717468i	0.0248887	−	0.0431084i	−0.853313	−	0.521399i	$-0.825410\pi$
$277$	0.414230	−	0.717468i	0.0248887	−	0.0431084i	0.878201	+	0.478291i	$0.158744\pi$
$278$	−3.76890			−0.226044
$279$		0			0
$280$		0			0
$281$	2.60985	−	4.52039i	0.155690	−	0.269664i	−0.777620	−	0.628735i	$-0.783573\pi$
$281$	2.60985	−	4.52039i	0.155690	−	0.269664i	0.933310	+	0.359071i	$0.116906\pi$
$282$		0			0
$283$	−3.67708	−	6.36890i	−0.218580	−	0.378592i	0.735794	−	0.677205i	$-0.236809\pi$
$283$	−3.67708	−	6.36890i	−0.218580	−	0.378592i	−0.954374	+	0.298614i	$0.903476\pi$
$284$	−6.06075	−	10.4975i	−0.359639	−	0.622913i
$285$		0			0
$286$	1.84155	−	3.18966i	0.108893	−	0.188609i
$287$		0			0
$288$		0			0
$289$	−14.0722			−0.827778
$290$	−0.658419	+	1.14041i	−0.0386637	+	0.0669674i
$291$		0			0
$292$	−6.95103	−	12.0395i	−0.406778	−	0.704561i
$293$	−3.91286	−	6.77728i	−0.228592	−	0.395933i	0.728799	−	0.684728i	$-0.240079\pi$
$293$	−3.91286	−	6.77728i	−0.228592	−	0.395933i	−0.957391	+	0.288795i	$0.906745\pi$
$294$		0			0
$295$	7.85868	−	13.6116i	0.457550	−	0.792500i
$296$	1.56526			0.0909789
$297$		0			0
$298$	1.45090			0.0840484
$299$	9.43752	−	16.3463i	0.545786	−	0.945329i
$300$		0			0
$301$		0			0
$302$	0.536670	+	0.929540i	0.0308819	+	0.0534890i
$303$		0			0
$304$	−13.0954	+	22.6820i	−0.751075	+	1.30090i
$305$	−20.6979			−1.18516
$306$		0			0
$307$	−22.6709			−1.29390			−0.646948	−	0.762534i	$-0.723955\pi$
$307$	−22.6709			−1.29390			−0.646948	+	0.762534i	$0.723955\pi$
$308$		0			0
$309$		0			0
$310$	−2.02532	−	3.50796i	−0.115030	−	0.199239i
$311$	16.1588	+	27.9879i	0.916281	+	1.58705i	0.805015	+	0.593255i	$0.202157\pi$
$311$	16.1588	+	27.9879i	0.916281	+	1.58705i	0.111266	+	0.993791i	$0.464509\pi$
$312$		0			0
$313$	−12.1598	+	21.0614i	−0.687312	+	1.19046i	0.285392	+	0.958411i	$0.407876\pi$
$313$	−12.1598	+	21.0614i	−0.687312	+	1.19046i	−0.972704	+	0.232048i	$0.925457\pi$
$314$	0.246037			0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	2.56922	−	4.45002i	0.144302	−	0.249938i	−0.784811	−	0.619736i	$-0.787240\pi$
$317$	2.56922	−	4.45002i	0.144302	−	0.249938i	0.929112	+	0.369798i	$0.120573\pi$
$318$		0			0
$319$	4.44282	+	7.69519i	0.248750	+	0.430848i
$320$	−8.63090	−	14.9492i	−0.482482	−	0.835684i
$321$		0			0
$322$		0			0
$323$	12.2438			0.681262
$324$		0			0
$325$	−6.32525			−0.350862
$326$	0.816422	−	1.41408i	0.0452174	−	0.0783189i
$327$		0			0
$328$	4.81732	+	8.34384i	0.265992	+	0.460712i
$329$		0			0
$330$		0			0
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	−0.659307	−	0.751874i	$-0.729150\pi$
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	0.980795	+	0.195040i	$0.0624835\pi$
$332$	−13.3951			−0.735150
$333$		0			0
$334$	−4.30286			−0.235442
$335$	10.7082	−	18.5472i	0.585053	−	1.01334i
$336$		0			0
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.802850	+	0.596181i	$0.203316\pi$
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.114883	+	0.993379i	$0.463351\pi$
$338$	0.0675835	+	0.117058i	0.00367606	+	0.00636711i
$339$		0			0
$340$	−4.30795	+	7.46159i	−0.233631	+	0.404661i
$341$	−27.3326			−1.48014
$342$		0			0
$343$		0			0
$344$	0.782630	−	1.35556i	0.0421966	−	0.0730866i
$345$		0			0
$346$	−0.0992788	−	0.171956i	−0.00533726	−	0.00924441i
$347$	13.6557	+	23.6523i	0.733075	+	1.26972i	0.955563	+	0.294788i	$0.0952490\pi$
$347$	13.6557	+	23.6523i	0.733075	+	1.26972i	−0.222488	+	0.974936i	$0.571418\pi$
$348$		0			0
$349$	11.4585	−	19.8467i	0.613358	−	1.06237i	−0.377312	−	0.926086i	$-0.623152\pi$
$349$	11.4585	−	19.8467i	0.613358	−	1.06237i	0.990670	−	0.136281i	$-0.0435150\pi$
$350$		0			0
$351$		0			0
$352$	11.5458			0.615395
$353$	−5.13466	+	8.89349i	−0.273290	+	0.473353i	−0.969702	−	0.244289i	$-0.921445\pi$
$353$	−5.13466	+	8.89349i	−0.273290	+	0.473353i	0.696412	+	0.717642i	$0.254779\pi$
$354$		0			0
$355$	−8.08525	−	14.0041i	−0.429120	−	0.743258i
$356$	−4.89142	−	8.47218i	−0.259245	−	0.449025i
$357$		0			0
$358$	−0.906150	+	1.56950i	−0.0478915	+	0.0829505i
$359$	−10.1007			−0.533094			−0.266547	−	0.963822i	$-0.585883\pi$
$359$	−10.1007			−0.533094			−0.266547	+	0.963822i	$0.585883\pi$
$360$		0			0
$361$	32.2028			1.69488
$362$	−0.0489195	+	0.0847311i	−0.00257115	+	0.00445337i
$363$		0			0
$364$		0			0
$365$	−9.27292	−	16.0612i	−0.485367	−	0.840680i
$366$		0			0
$367$	−3.88768	+	6.73367i	−0.202935	+	0.351494i	−0.949473	−	0.313849i	$-0.898381\pi$
$367$	−3.88768	+	6.73367i	−0.202935	+	0.351494i	0.746538	+	0.665343i	$0.231715\pi$
$368$	18.7576			0.977808
$369$		0			0
$370$	1.02891			0.0534907
$371$		0			0
$372$		0			0
$373$	−12.0555	−	20.8808i	−0.624212	−	1.08117i	−0.988693	−	0.149957i	$-0.952087\pi$
$373$	−12.0555	−	20.8808i	−0.624212	−	1.08117i	0.364480	−	0.931211i	$-0.381247\pi$
$374$	−0.855536	−	1.48183i	−0.0442387	−	0.0766237i
$375$		0			0
$376$	−4.40214	+	7.62473i	−0.227023	+	0.393215i
$377$	−7.82573			−0.403045
$378$		0			0
$379$	−13.3581			−0.686161			−0.343081	−	0.939306i	$-0.611470\pi$
$379$	−13.3581			−0.686161			−0.343081	+	0.939306i	$0.611470\pi$
$380$	−18.0156	+	31.2039i	−0.924181	+	1.60073i
$381$		0			0
$382$	−1.91586	−	3.31838i	−0.0980242	−	0.169783i
$383$	4.62020	+	8.00242i	0.236081	+	0.408905i	0.959586	−	0.281414i	$-0.0908035\pi$
$383$	4.62020	+	8.00242i	0.236081	+	0.408905i	−0.723505	+	0.690319i	$0.757470\pi$
$384$		0			0
$385$		0			0
$386$	2.95898			0.150608
$387$		0			0
$388$	5.95153			0.302143
$389$	5.22421	−	9.04859i	0.264878	−	0.458782i	−0.702654	−	0.711532i	$-0.748002\pi$
$389$	5.22421	−	9.04859i	0.264878	−	0.458782i	0.967532	+	0.252750i	$0.0813351\pi$
$390$		0			0
$391$	−4.38442	−	7.59404i	−0.221730	−	0.384047i
$392$		0			0
$393$		0			0
$394$	−2.76212	+	4.78413i	−0.139154	+	0.241021i
$395$	25.4733			1.28170
$396$		0			0
$397$	0.409157			0.0205350			0.0102675	−	0.999947i	$-0.496732\pi$
$397$	0.409157			0.0205350			0.0102675	+	0.999947i	$0.496732\pi$
$398$	0.806617	−	1.39710i	0.0404321	−	0.0700304i
$399$		0			0
$400$	−3.14295	−	5.44375i	−0.157147	−	0.272187i
$401$	7.62640	+	13.2093i	0.380844	+	0.659641i	0.991183	−	0.132499i	$-0.0423001\pi$
$401$	7.62640	+	13.2093i	0.380844	+	0.659641i	−0.610339	+	0.792140i	$0.708967\pi$
$402$		0			0
$403$	12.0361	−	20.8472i	0.599562	−	1.03847i
$404$	21.5647			1.07288
$405$		0			0
$406$		0			0
$407$	3.47141	−	6.01266i	0.172071	−	0.298036i
$408$		0			0
$409$	−3.06335	−	5.30587i	−0.151473	−	0.262359i	0.780296	−	0.625410i	$-0.215068\pi$
$409$	−3.06335	−	5.30587i	−0.151473	−	0.262359i	−0.931769	+	0.363051i	$0.881735\pi$
$410$	3.16664	+	5.48477i	0.156389	+	0.270874i
$411$		0			0
$412$	−7.75765	+	13.4366i	−0.382192	+	0.661976i
$413$		0			0
$414$		0			0
$415$	−17.8695			−0.877178
$416$	−5.08430	+	8.80626i	−0.249278	+	0.431763i
$417$		0			0
$418$	−3.57780	−	6.19694i	−0.174996	−	0.303102i
$419$	−0.781437	−	1.35349i	−0.0381757	−	0.0661223i	0.846306	−	0.532697i	$-0.178821\pi$
$419$	−0.781437	−	1.35349i	−0.0381757	−	0.0661223i	−0.884482	+	0.466574i	$0.845488\pi$
$420$		0			0
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	0.429982	+	0.902838i	$0.358520\pi$
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	−0.996871	+	0.0790438i	$0.974813\pi$
$422$	−4.03775			−0.196555
$423$		0			0
$424$	−10.0377			−0.487476
$425$	−1.46927	+	2.54485i	−0.0712702	+	0.123444i
$426$		0			0
$427$		0			0
$428$	−3.84338	−	6.65692i	−0.185777	−	0.321775i
$429$		0			0
$430$	0.514457	−	0.891066i	0.0248093	−	0.0429710i
$431$	−1.00576			−0.0484456			−0.0242228	−	0.999707i	$-0.507711\pi$
$431$	−1.00576			−0.0484456			−0.0242228	+	0.999707i	$0.507711\pi$
$432$		0			0
$433$	−13.1071			−0.629889			−0.314945	−	0.949110i	$-0.601986\pi$
$433$	−13.1071			−0.629889			−0.314945	+	0.949110i	$0.601986\pi$
$434$		0			0
$435$		0			0
$436$	7.05555	+	12.2206i	0.337899	+	0.585259i
$437$	−18.3354	−	31.7579i	−0.877101	−	1.51918i
$438$		0			0
$439$	9.30704	−	16.1203i	0.444201	−	0.769378i	−0.553795	−	0.832653i	$-0.686821\pi$
$439$	9.30704	−	16.1203i	0.444201	−	0.769378i	0.997996	+	0.0632744i	$0.0201543\pi$
$440$	10.2190			0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	−0.559503	+	0.969088i	−0.0265828	+	0.0460427i	−0.879011	−	0.476802i	$-0.841796\pi$
$443$	−0.559503	+	0.969088i	−0.0265828	+	0.0460427i	0.852428	+	0.522845i	$0.175129\pi$
$444$		0			0
$445$	−6.52532	−	11.3022i	−0.309330	−	0.535775i
$446$	0.538197	+	0.932185i	0.0254844	+	0.0441402i
$447$		0			0
$448$		0			0
$449$	39.4419			1.86138			0.930689	−	0.365813i	$-0.119209\pi$
$449$	39.4419			1.86138			0.930689	+	0.365813i	$0.119209\pi$
$450$		0			0
$451$	42.7351			2.01232
$452$	−6.73104	+	11.6585i	−0.316602	+	0.548370i
$453$		0			0
$454$	−0.725057	−	1.25584i	−0.0340286	−	0.0589393i
$455$		0			0
$456$		0			0
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	−0.118205	−	0.992989i	$-0.537714\pi$
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	0.919056	−	0.394126i	$-0.128953\pi$
$458$	−2.64215			−0.123459
$459$		0			0
$460$	25.8051			1.20317
$461$	−10.1938	+	17.6561i	−0.474772	+	0.822328i	−0.999583	−	0.0288903i	$-0.990803\pi$
$461$	−10.1938	+	17.6561i	−0.474772	+	0.822328i	0.524811	+	0.851219i	$0.324136\pi$
$462$		0			0
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	0.776006	−	0.630725i	$-0.217243\pi$
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	−0.934227	+	0.356678i	$0.883909\pi$
$464$	−3.88852	−	6.73511i	−0.180520	−	0.312670i
$465$		0			0
$466$	0.973045	−	1.68536i	0.0450754	−	0.0780729i
$467$	24.7911			1.14720			0.573598	−	0.819137i	$-0.305547\pi$
$467$	24.7911			1.14720			0.573598	+	0.819137i	$0.305547\pi$
$468$		0			0
$469$		0			0
$470$	−2.89372	+	5.01207i	−0.133477	+	0.231190i
$471$		0			0
$472$	−2.85877	−	4.95153i	−0.131586	−	0.227913i
$473$	−3.47141	−	6.01266i	−0.159616	−	0.276462i
$474$		0			0
$475$	−6.14441	+	10.6424i	−0.281925	+	0.488309i
$476$		0			0
$477$		0			0
$478$	5.06045			0.231460
$479$	5.54984	−	9.61260i	0.253579	−	0.439211i	−0.710930	−	0.703263i	$-0.751726\pi$
$479$	5.54984	−	9.61260i	0.253579	−	0.439211i	0.964508	+	0.264052i	$0.0850590\pi$
$480$		0			0
$481$	3.05733	+	5.29545i	0.139402	+	0.241452i
$482$	−1.63697	−	2.83532i	−0.0745621	−	0.129145i
$483$		0			0
$484$	6.30314	−	10.9174i	0.286506	−	0.496244i
$485$	7.93955			0.360516
$486$		0			0
$487$	−10.0377			−0.454854			−0.227427	−	0.973795i	$-0.573031\pi$
$487$	−10.0377			−0.454854			−0.227427	+	0.973795i	$0.573031\pi$
$488$	−3.76466	+	6.52059i	−0.170418	+	0.295173i
$489$		0			0
$490$		0			0
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	0.691738	−	0.722149i	$-0.256845\pi$
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	−0.971268	+	0.237988i	$0.923512\pi$
$492$		0			0
$493$	−1.81781	+	3.14854i	−0.0818702	+	0.141803i
$494$	6.30206			0.283543
$495$		0			0
$496$	23.9225			1.07415
$497$		0			0
$498$		0			0
$499$	−5.11109	−	8.85267i	−0.228804	−	0.396300i	0.728650	−	0.684886i	$-0.240148\pi$
$499$	−5.11109	−	8.85267i	−0.228804	−	0.396300i	−0.957454	+	0.288586i	$0.906815\pi$
$500$	8.26464	+	14.3148i	0.369606	+	0.640177i
$501$		0			0
$502$	1.81781	−	3.14854i	0.0811329	−	0.140526i
$503$	−8.45753			−0.377102			−0.188551	−	0.982063i	$-0.560379\pi$
$503$	−8.45753			−0.377102			−0.188551	+	0.982063i	$0.560379\pi$
$504$		0			0
$505$	28.7680			1.28016
$506$	−2.56238	+	4.43818i	−0.113912	+	0.197301i
$507$		0			0
$508$	8.85060	+	15.3297i	0.392682	+	0.680145i
$509$	5.28286	+	9.15018i	0.234159	+	0.405574i	0.959028	−	0.283312i	$-0.0914332\pi$
$509$	5.28286	+	9.15018i	0.234159	+	0.405574i	−0.724869	+	0.688886i	$0.758100\pi$
$510$		0			0
$511$		0			0
$512$	−17.0071			−0.751616
$513$		0			0
$514$	−6.12670			−0.270237
$515$	−10.3490	+	17.9249i	−0.456030	+	0.789867i
$516$		0			0
$517$	19.5260	+	33.8200i	0.858752	+	1.48740i
$518$		0			0
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	19.7558			0.865515			0.432758	−	0.901510i	$-0.357541\pi$
$521$	19.7558			0.865515			0.432758	+	0.901510i	$0.357541\pi$
$522$		0			0
$523$	32.5282			1.42236			0.711179	−	0.703011i	$-0.248161\pi$
$523$	32.5282			1.42236			0.711179	+	0.703011i	$0.248161\pi$
$524$	−4.17984	+	7.23970i	−0.182597	+	0.316268i
$525$		0			0
$526$	−0.848970	−	1.47046i	−0.0370168	−	0.0641150i
$527$	−5.59166	−	9.68504i	−0.243577	−	0.421887i
$528$		0			0
$529$	−1.63160	+	2.82601i	−0.0709391	+	0.122870i
$530$	−6.59825			−0.286610
$531$		0			0
$532$		0			0
$533$	−18.8187	+	32.5950i	−0.815130	+	1.41185i
$534$		0			0
$535$	−5.12720	−	8.88057i	−0.221668	−	0.383940i
$536$	−3.89536	−	6.74695i	−0.168254	−	0.291424i
$537$		0			0
$538$	−1.96457	+	3.40274i	−0.0846987	+	0.146702i
$539$		0			0
$540$		0			0
$541$	15.2222			0.654453			0.327226	−	0.944946i	$-0.393886\pi$
$541$	15.2222			0.654453			0.327226	+	0.944946i	$0.393886\pi$
$542$	−1.51819	+	2.62959i	−0.0652119	+	0.112950i
$543$		0			0
$544$	2.36203	+	4.09116i	0.101271	+	0.175407i
$545$	9.41234	+	16.3027i	0.403180	+	0.698329i
$546$		0			0
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	−1.00000		0.000339172i	$-0.999892\pi$
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	0.500294	+	0.865856i	$0.333225\pi$
$548$	40.0014			1.70877
$549$		0			0
$550$	1.71737			0.0732289
$551$	−7.60199	+	13.1670i	−0.323856	+	0.560934i
$552$		0			0
$553$		0			0
$554$	−0.0990521	−	0.171563i	−0.00420832	−	0.00728902i
$555$		0			0
$556$	15.3107	−	26.5189i	0.649319	−	1.12465i
$557$	−27.6673			−1.17230			−0.586151	−	0.810202i	$-0.699357\pi$
$557$	−27.6673			−1.17230			−0.586151	+	0.810202i	$0.699357\pi$
$558$		0			0
$559$	6.11465			0.258622
$560$		0			0
$561$		0			0
$562$	−0.624075	−	1.08093i	−0.0263250	−	0.0455963i
$563$	4.27912	+	7.41166i	0.180343	+	0.312364i	0.941998	−	0.335620i	$-0.108946\pi$
$563$	4.27912	+	7.41166i	0.180343	+	0.312364i	−0.761654	+	0.647984i	$0.775612\pi$
$564$		0			0
$565$	−8.97944	+	15.5529i	−0.377768	+	0.654313i
$566$	−1.75855			−0.0739175
$567$		0			0
$568$	−5.88237			−0.246819
$569$	6.86389	−	11.8886i	0.287749	−	0.498396i	−0.685523	−	0.728051i	$-0.740426\pi$
$569$	6.86389	−	11.8886i	0.287749	−	0.498396i	0.973272	+	0.229655i	$0.0737597\pi$
$570$		0			0
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	0.731841	−	0.681475i	$-0.238661\pi$
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	−0.956095	+	0.293056i	$0.905328\pi$
$572$	14.9622	+	25.9153i	0.625600	+	1.08357i
$573$		0			0
$574$		0			0
$575$	8.80111			0.367032
$576$		0			0
$577$	−45.6353			−1.89982			−0.949912	−	0.312518i	$-0.898827\pi$
$577$	−45.6353			−1.89982			−0.949912	+	0.312518i	$0.898827\pi$
$578$	−1.68250	+	2.91417i	−0.0699827	+	0.121214i
$579$		0			0
$580$	−5.34950	−	9.26560i	−0.222126	−	0.384733i
$581$		0			0
$582$		0			0
$583$	−22.2616	+	38.5582i	−0.921980	+	1.59692i
$584$	−6.74645			−0.279170
$585$		0			0
$586$	−1.87131			−0.0773032
$587$	−5.10948	+	8.84988i	−0.210891	+	0.365274i	−0.951994	−	0.306118i	$-0.900970\pi$
$587$	−5.10948	+	8.84988i	−0.210891	+	0.365274i	0.741103	+	0.671392i	$0.234303\pi$
$588$		0			0
$589$	−23.3840	−	40.5023i	−0.963521	−	1.66887i
$590$	−1.87919	−	3.25486i	−0.0773652	−	0.134000i
$591$		0			0
$592$	−3.03831	+	5.26250i	−0.124874	+	0.216287i
$593$	−11.3961			−0.467981			−0.233990	−	0.972239i	$-0.575178\pi$
$593$	−11.3961			−0.467981			−0.233990	+	0.972239i	$0.575178\pi$
$594$		0			0
$595$		0			0
$596$	−5.89411	+	10.2089i	−0.241432	+	0.418173i
$597$		0			0
$598$	−2.25673	−	3.90877i	−0.0922846	−	0.159842i
$599$	−17.2873	−	29.9424i	−0.706339	−	1.22341i	−0.966206	−	0.257771i	$-0.917012\pi$
$599$	−17.2873	−	29.9424i	−0.706339	−	1.22341i	0.259867	−	0.965644i	$-0.416321\pi$
$600$		0			0
$601$	19.4207	−	33.6376i	0.792187	−	1.37211i	−0.132423	−	0.991193i	$-0.542276\pi$
$601$	19.4207	−	33.6376i	0.792187	−	1.37211i	0.924610	−	0.380915i	$-0.124391\pi$
$602$		0			0
$603$		0			0
$604$	−8.72064			−0.354838
$605$	8.40861	−	14.5641i	0.341858	−	0.592116i
$606$		0			0
$607$	20.6662	+	35.7950i	0.838817	+	1.45287i	0.890885	+	0.454229i	$0.150085\pi$
$607$	20.6662	+	35.7950i	0.838817	+	1.45287i	−0.0520683	+	0.998644i	$0.516581\pi$
$608$	9.87788	+	17.1090i	0.400601	+	0.693861i
$609$		0			0
$610$	−2.47468	+	4.28627i	−0.100197	+	0.173546i
$611$	−34.3937			−1.39142
$612$		0			0
$613$	−28.6569			−1.15744			−0.578721	−	0.815526i	$-0.696448\pi$
$613$	−28.6569			−1.15744			−0.578721	+	0.815526i	$0.696448\pi$
$614$	−2.71057	+	4.69485i	−0.109390	+	0.189469i
$615$		0			0
$616$		0			0
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	−0.975454	−	0.220205i	$-0.929327\pi$
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	0.297024	−	0.954870i	$-0.404006\pi$
$618$		0			0
$619$	−0.719036	+	1.24541i	−0.0289005	+	0.0500571i	−0.880114	−	0.474763i	$-0.842534\pi$
$619$	−0.719036	+	1.24541i	−0.0289005	+	0.0500571i	0.851213	+	0.524820i	$0.175867\pi$
$620$	32.9105			1.32172
$621$		0			0
$622$	7.72789			0.309860
$623$		0			0
$624$		0			0
$625$	15.3187	+	26.5328i	0.612750	+	1.06131i
$626$	2.90769	+	5.03626i	0.116215	+	0.201290i
$627$		0			0
$628$	−0.999498	+	1.73118i	−0.0398843	+	0.0690816i
$629$	2.84071			0.113266
$630$		0			0
$631$	−30.7680			−1.22486			−0.612428	−	0.790527i	$-0.709807\pi$
$631$	−30.7680			−1.22486			−0.612428	+	0.790527i	$0.709807\pi$
$632$	4.63323	−	8.02500i	0.184300	−	0.319217i
$633$		0			0
$634$	−0.614360	−	1.06410i	−0.0243993	−	0.0422609i
$635$	11.8070	+	20.4503i	0.468547	+	0.811547i
$636$		0			0
$637$		0			0
$638$	2.12476			0.0841202
$639$		0			0
$640$	−18.4389			−0.728862
$641$	4.61956	−	8.00132i	0.182462	−	0.316033i	−0.760257	−	0.649623i	$-0.774927\pi$
$641$	4.61956	−	8.00132i	0.182462	−	0.316033i	0.942718	+	0.333590i	$0.108260\pi$
$642$		0			0
$643$	12.7795	+	22.1348i	0.503976	+	0.872912i	0.999989	+	0.00459728i	$0.00146337\pi$
$643$	12.7795	+	22.1348i	0.503976	+	0.872912i	−0.496013	+	0.868315i	$0.665203\pi$
$644$		0			0
$645$		0			0
$646$	1.46389	−	2.53552i	0.0575958	−	0.0997588i
$647$	−28.3111			−1.11302			−0.556512	−	0.830839i	$-0.687861\pi$
$647$	−28.3111			−1.11302			−0.556512	+	0.830839i	$0.687861\pi$
$648$		0			0
$649$	−25.3605			−0.995488
$650$	−0.756258	+	1.30988i	−0.0296629	+	0.0513776i
$651$		0			0
$652$	6.63323	+	11.4891i	0.259778	+	0.449948i
$653$	−4.17511	−	7.23150i	−0.163385	−	0.282990i	0.772696	−	0.634776i	$-0.218908\pi$
$653$	−4.17511	−	7.23150i	−0.163385	−	0.282990i	−0.936080	+	0.351786i	$0.885574\pi$
$654$		0			0
$655$	−5.57605	+	9.65801i	−0.217874	+	0.377370i
$656$	−37.4033			−1.46035
$657$		0			0
$658$		0			0
$659$	−16.7862	+	29.0745i	−0.653897	+	1.13258i	0.328272	+	0.944583i	$0.393534\pi$
$659$	−16.7862	+	29.0745i	−0.653897	+	1.13258i	−0.982169	+	0.188000i	$0.939799\pi$
$660$		0			0
$661$	8.47668	+	14.6820i	0.329705	+	0.571065i	0.982453	−	0.186509i	$-0.0597175\pi$
$661$	8.47668	+	14.6820i	0.329705	+	0.571065i	−0.652748	+	0.757575i	$0.726384\pi$
$662$	−1.39862	−	2.42249i	−0.0543591	−	0.0941527i
$663$		0			0
$664$	−3.25021	+	5.62952i	−0.126133	+	0.218468i
$665$		0			0
$666$		0			0
$667$	10.8889			0.421620
$668$	17.4799	−	30.2760i	0.676316	−	1.17141i
$669$		0			0
$670$	−2.56059	−	4.43507i	−0.0989242	−	0.171342i
$671$	16.6984	+	28.9225i	0.644636	+	1.11654i
$672$		0			0
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	−0.0190299	−	0.999819i	$-0.506058\pi$
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	0.875384	−	0.483429i	$-0.160609\pi$
$674$	8.05718			0.310351
$675$		0			0
$676$	−1.09820			−0.0422384
$677$	−7.18681	+	12.4479i	−0.276212	+	0.478412i	−0.970440	−	0.241342i	$-0.922412\pi$
$677$	−7.18681	+	12.4479i	−0.276212	+	0.478412i	0.694229	+	0.719755i	$0.255746\pi$
$678$		0			0
$679$		0			0
$680$	2.09058	+	3.62099i	0.0801701	+	0.138859i
$681$		0			0
$682$	−3.26793	+	5.66021i	−0.125135	+	0.216741i
$683$	32.3092			1.23628			0.618138	−	0.786069i	$-0.287887\pi$
$683$	32.3092			1.23628			0.618138	+	0.786069i	$0.287887\pi$
$684$		0			0
$685$	53.3632			2.03890
$686$		0			0
$687$		0			0
$688$	3.03831	+	5.26250i	0.115834	+	0.200631i
$689$	−19.6061	−	33.9588i	−0.746934	−	1.29373i
$690$		0			0
$691$	14.4981	−	25.1114i	0.551533	−	0.955283i	−0.446631	−	0.894718i	$-0.647376\pi$
$691$	14.4981	−	25.1114i	0.551533	−	0.955283i	0.998164	−	0.0605650i	$-0.0192902\pi$
$692$	1.61323			0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	20.4250	−	35.3772i	0.774765	−	1.34193i
$696$		0			0
$697$	8.74269	+	15.1428i	0.331153	+	0.573574i
$698$	−2.73999	−	4.74580i	−0.103710	−	0.179631i
$699$		0			0
$700$		0			0
$701$	26.3912			0.996783			0.498392	−	0.866952i	$-0.333924\pi$
$701$	26.3912			0.996783			0.498392	+	0.866952i	$0.333924\pi$
$702$		0			0
$703$	11.8797			0.448050
$704$	−13.9263	+	24.1210i	−0.524866	+	0.909095i
$705$		0			0
$706$	1.22782	+	2.12664i	0.0462095	+	0.0800372i
$707$		0			0
$708$		0			0
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	−0.782441	−	0.622725i	$-0.786025\pi$
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	0.930516	+	0.366251i	$0.119359\pi$
$710$	−3.86674			−0.145116
$711$		0			0
$712$	−4.74746			−0.177918
$713$	−16.7473	+	29.0073i	−0.627193	+	1.08633i
$714$		0			0
$715$	19.9601	+	34.5718i	0.746464	+	1.29291i
$716$	−7.36225	−	12.7518i	−0.275140	−	0.476557i
$717$		0			0
$718$	−1.20765	+	2.09172i	−0.0450693	+	0.0780623i
$719$	33.1508			1.23632			0.618159	−	0.786053i	$-0.287879\pi$
$719$	33.1508			1.23632			0.618159	+	0.786053i	$0.287879\pi$
$720$		0			0
$721$		0			0
$722$	3.85021	−	6.66877i	0.143290	−	0.248186i
$723$		0			0
$724$	−0.397460	−	0.688420i	−0.0147715	−	0.0255849i
$725$	−1.82450	−	3.16013i	−0.0677603	−	0.117364i
$726$		0			0
$727$	−16.5502	+	28.6658i	−0.613814	+	1.06316i	0.376777	+	0.926304i	$0.377032\pi$
$727$	−16.5502	+	28.6658i	−0.613814	+	1.06316i	−0.990591	+	0.136853i	$0.956301\pi$
$728$		0			0
$729$		0			0
$730$	−4.43474			−0.164137
$731$	1.42035	−	2.46012i	0.0525337	−	0.0909910i
$732$		0			0
$733$	22.2795	+	38.5892i	0.822911	+	1.42532i	0.903505	+	0.428577i	$0.140985\pi$
$733$	22.2795	+	38.5892i	0.822911	+	1.42532i	−0.0805946	+	0.996747i	$0.525682\pi$
$734$	0.929636	+	1.61018i	0.0343135	+	0.0594327i
$735$		0			0
$736$	7.07442	−	12.2533i	0.260767	−	0.451661i
$737$	−34.5562			−1.27290
$738$		0			0
$739$	39.8090			1.46440			0.732199	−	0.681090i	$-0.238494\pi$
$739$	39.8090			1.46440			0.732199	+	0.681090i	$0.238494\pi$
$740$	−4.17984	+	7.23970i	−0.153654	+	0.266137i
$741$		0			0
$742$		0			0
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	0.947565	−	0.319563i	$-0.103536\pi$
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	−0.750532	+	0.660834i	$0.770203\pi$
$744$		0			0
$745$	−7.86295	+	13.6190i	−0.288076	+	0.498962i
$746$	−5.76552			−0.211091
$747$		0			0
$748$	13.9021			0.508310
$749$		0			0
$750$		0			0
$751$	−9.85705	−	17.0729i	−0.359689	−	0.622999i	0.628220	−	0.778036i	$-0.283784\pi$
$751$	−9.85705	−	17.0729i	−0.359689	−	0.622999i	−0.987909	+	0.155036i	$0.950450\pi$
$752$	−17.0899	−	29.6005i	−0.623203	−	1.07942i
$753$		0			0
$754$	−0.935657	+	1.62060i	−0.0340746	+	0.0590189i
$755$	−11.6336			−0.423391
$756$		0			0
$757$	35.3549			1.28499			0.642497	−	0.766288i	$-0.277898\pi$
$757$	35.3549			1.28499			0.642497	+	0.766288i	$0.277898\pi$
$758$	−1.59712	+	2.76629i	−0.0580100	+	0.100476i
$759$		0			0
$760$	8.74269	+	15.1428i	0.317131	+	0.549286i
$761$	−19.5572	−	33.8741i	−0.708948	−	1.22793i	−0.965248	−	0.261336i	$-0.915837\pi$
$761$	−19.5572	−	33.8741i	−0.708948	−	1.22793i	0.256300	−	0.966597i	$-0.417497\pi$
$762$		0			0
$763$		0			0
$764$	31.1319			1.12631
$765$		0			0
$766$	2.20960			0.0798359
$767$	11.1677	−	19.3430i	0.403243	−	0.698437i
$768$		0			0
$769$	18.9240	+	32.7773i	0.682415	+	1.18198i	0.974242	+	0.225507i	$0.0724038\pi$
$769$	18.9240	+	32.7773i	0.682415	+	1.18198i	−0.291826	+	0.956471i	$0.594263\pi$
$770$		0			0
$771$		0			0
$772$	−12.0205	+	20.8201i	−0.432628	+	0.749333i
$773$	−29.8265			−1.07279			−0.536393	−	0.843969i	$-0.680213\pi$
$773$	−29.8265			−1.07279			−0.536393	+	0.843969i	$0.680213\pi$
$774$		0			0
$775$	11.2245			0.403195
$776$	1.44409	−	2.50124i	0.0518399	−	0.0897894i
$777$		0			0
$778$	−1.24923	−	2.16373i	−0.0447870	−	0.0775734i
$779$	36.5614	+	63.3263i	1.30995	+	2.26890i
$780$		0			0
$781$	−13.0458	+	22.5960i	−0.466817	+	0.808550i
$782$	−2.09683			−0.0749827
$783$		0			0
$784$		0			0
$785$	−1.33336	+	2.30946i	−0.0475898	+	0.0824280i
$786$		0			0
$787$	−8.81030	−	15.2599i	−0.314053	−	0.543956i	0.665182	−	0.746681i	$-0.268354\pi$
$787$	−8.81030	−	15.2599i	−0.314053	−	0.543956i	−0.979236	+	0.202724i	$0.935020\pi$
$788$	−22.4416	−	38.8700i	−0.799448	−	1.38468i
$789$		0			0
$790$	3.04563	−	5.27518i	0.108359	−	0.187683i
$791$		0			0
$792$		0			0
$793$	−29.4132			−1.04449
$794$	0.0489195	−	0.0847311i	0.00173609	−	0.00300699i
$795$		0			0
$796$	6.55357	+	11.3511i	0.232285	+	0.402330i
$797$	5.06056	+	8.76515i	0.179254	+	0.310477i	0.941625	−	0.336663i	$-0.109298\pi$
$797$	5.06056	+	8.76515i	0.179254	+	0.310477i	−0.762371	+	0.647140i	$0.775965\pi$
$798$		0			0
$799$	−7.98921	+	13.8377i	−0.282638	+	0.489543i
$800$	−4.74145			−0.167635
$801$		0			0
$802$	3.64730			0.128791
$803$	−14.9622	+	25.9153i	−0.528004	+	0.914529i
$804$		0			0
$805$		0			0
$806$	−2.87812	−	4.98504i	−0.101377	−	0.175591i
$807$		0			0
$808$	5.23250	−	9.06295i	0.184079	−	0.318834i
$809$	47.1469			1.65760			0.828799	−	0.559546i	$-0.189025\pi$
$809$	47.1469			1.65760			0.828799	+	0.559546i	$0.189025\pi$
$810$		0			0
$811$	21.0577			0.739435			0.369717	−	0.929144i	$-0.379454\pi$
$811$	21.0577			0.739435			0.369717	+	0.929144i	$0.379454\pi$
$812$		0			0
$813$		0			0
$814$	−0.830095	−	1.43777i	−0.0290948	−	0.0503937i
$815$	8.84896	+	15.3269i	0.309966	+	0.536876i
$816$		0			0
$817$	5.93984	−	10.2881i	0.207809	−	0.359935i
$818$	−1.46504			−0.0512238
$819$		0			0
$820$	−51.4563			−1.79693
$821$	5.58018	−	9.66515i	0.194750	−	0.337316i	−0.752069	−	0.659085i	$-0.770944\pi$
$821$	5.58018	−	9.66515i	0.194750	−	0.337316i	0.946818	+	0.321768i	$0.104277\pi$
$822$		0			0
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	0.772018	−	0.635601i	$-0.219247\pi$
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	−0.936455	+	0.350787i	$0.885914\pi$
$824$	3.76466	+	6.52059i	0.131148	+	0.227156i
$825$		0			0
$826$		0			0
$827$	−17.2646			−0.600348			−0.300174	−	0.953884i	$-0.597045\pi$
$827$	−17.2646			−0.600348			−0.300174	+	0.953884i	$0.597045\pi$
$828$		0			0
$829$	−48.4526			−1.68283			−0.841415	−	0.540390i	$-0.818277\pi$
$829$	−48.4526			−1.68283			−0.841415	+	0.540390i	$0.818277\pi$
$830$	−2.13650	+	3.70053i	−0.0741591	+	0.128447i
$831$		0			0
$832$	−12.2651	−	21.2438i	−0.425215	−	0.736495i
$833$		0			0
$834$		0			0
$835$	23.3187	−	40.3893i	0.806978	−	1.39773i
$836$	58.1376			2.01073
$837$		0			0
$838$	−0.373720			−0.0129099
$839$	−7.43429	+	12.8766i	−0.256660	+	0.444548i	−0.965345	−	0.260977i	$-0.915955\pi$
$839$	−7.43429	+	12.8766i	−0.256660	+	0.444548i	0.708685	+	0.705525i	$0.249289\pi$
$840$		0			0
$841$	12.2427	+	21.2050i	0.422162	+	0.731206i
$842$	2.78139	+	4.81750i	0.0958529	+	0.166022i
$843$		0			0
$844$	16.4029	−	28.4106i	0.564610	−	0.977934i
$845$	−1.46504			−0.0503988
$846$		0			0
$847$		0			0
$848$	19.4841	−	33.7475i	0.669088	−	1.15889i
$849$		0			0
$850$	0.351337	+	0.608534i	0.0120508	+	0.0208725i
$851$	−4.25404	−	7.36821i	−0.145827	−	0.252579i
$852$		0			0
$853$	−3.99900	+	6.92648i	−0.136923	+	0.237158i	−0.926331	−	0.376712i	$-0.877055\pi$
$853$	−3.99900	+	6.92648i	−0.136923	+	0.237158i	0.789407	+	0.613870i	$0.210388\pi$
$854$		0			0
$855$		0			0
$856$	−3.73026			−0.127498
$857$	−21.5661	+	37.3536i	−0.736684	+	1.27597i	0.217296	+	0.976106i	$0.430276\pi$
$857$	−21.5661	+	37.3536i	−0.736684	+	1.27597i	−0.953980	+	0.299869i	$0.903057\pi$
$858$		0			0
$859$	1.22180	+	2.11621i	0.0416871	+	0.0722042i	0.886116	−	0.463463i	$-0.153393\pi$
$859$	1.22180	+	2.11621i	0.0416871	+	0.0722042i	−0.844429	+	0.535667i	$0.820060\pi$
$860$	4.17984	+	7.23970i	0.142531	+	0.246872i
$861$		0			0
$862$	−0.120250	+	0.208279i	−0.00409573	+	0.00709401i
$863$	−25.7187			−0.875476			−0.437738	−	0.899103i	$-0.644220\pi$
$863$	−25.7187			−0.875476			−0.437738	+	0.899103i	$0.644220\pi$
$864$		0			0
$865$	2.15211			0.0731739
$866$	−1.56711	+	2.71432i	−0.0532526	+	0.0922362i
$867$		0			0
$868$		0			0
$869$	−20.5510	−	35.5954i	−0.697146	−	1.20749i
$870$		0			0
$871$	15.2171	−	26.3568i	0.515612	−	0.893067i
$872$	6.84789			0.231899
$873$		0			0
$874$	−8.76884			−0.296611
$875$		0			0
$876$		0			0
$877$	10.9795	+	19.0170i	0.370751	+	0.642160i	0.989681	−	0.143286i	$-0.0457670\pi$
$877$	10.9795	+	19.0170i	0.370751	+	0.642160i	−0.618930	+	0.785446i	$0.712434\pi$
$878$	−2.22553	−	3.85473i	−0.0751080	−	0.130091i
$879$		0			0
$880$	−19.8359	+	34.3567i	−0.668667	+	1.15817i
$881$	35.0576			1.18112			0.590560	−	0.806994i	$-0.298907\pi$
$881$	35.0576			1.18112			0.590560	+	0.806994i	$0.298907\pi$
$882$		0			0
$883$	26.3009			0.885097			0.442549	−	0.896744i	$-0.354074\pi$
$883$	26.3009			0.885097			0.442549	+	0.896744i	$0.354074\pi$
$884$	−6.12188	+	10.6034i	−0.205901	+	0.356631i
$885$		0			0
$886$	0.133790	+	0.231731i	0.00449477	+	0.00778517i
$887$	23.9090	+	41.4116i	0.802785	+	1.39046i	0.917776	+	0.397098i	$0.129983\pi$
$887$	23.9090	+	41.4116i	0.802785	+	1.39046i	−0.114991	+	0.993366i	$0.536684\pi$
$888$		0			0
$889$		0			0
$890$	−3.12071			−0.104607
$891$		0			0
$892$	−8.74545			−0.292819
$893$	−33.4104	+	57.8685i	−1.11804	+	1.93650i
$894$		0			0
$895$	−9.82150	−	17.0113i	−0.328296	−	0.568626i
$896$		0			0
$897$		0			0
$898$	4.71574	−	8.16789i	0.157366	−	0.272566i
$899$	13.8871			0.463162
$900$		0			0
$901$	−18.2170			−0.606895
$902$	5.10948	−	8.84988i	0.170127	−	0.294669i
$903$		0			0
$904$	3.26647	+	5.65769i	0.108641	+	0.188172i
$905$	−0.530225	−	0.918376i	−0.0176253	−	0.0305279i
$906$		0			0
$907$	9.55718	−	16.5535i	0.317341	−	0.549651i	−0.662591	−	0.748981i	$-0.730543\pi$
$907$	9.55718	−	16.5535i	0.317341	−	0.549651i	0.979932	+	0.199330i	$0.0638767\pi$
$908$	11.7818			0.390994
$909$		0			0
$910$		0			0
$911$	−9.02928	+	15.6392i	−0.299153	+	0.518149i	−0.975942	−	0.218028i	$-0.930038\pi$
$911$	−9.02928	+	15.6392i	−0.299153	+	0.518149i	0.676789	+	0.736177i	$0.263371\pi$
$912$		0			0
$913$	14.4165	+	24.9701i	0.477117	+	0.826391i
$914$	−4.09385	−	7.09076i	−0.135413	−	0.234541i
$915$		0			0
$916$	10.7334	−	18.5908i	0.354642	−	0.614258i
$917$		0			0
$918$		0			0
$919$	16.2093			0.534695			0.267348	−	0.963600i	$-0.413853\pi$
$919$	16.2093			0.534695			0.267348	+	0.963600i	$0.413853\pi$
$920$	6.26141	−	10.8451i	0.206433	−	0.357552i
$921$		0			0
$922$	2.43757	+	4.22199i	0.0802771	+	0.139044i
$923$	−11.4897	−	19.9007i	−0.378187	−	0.655039i
$924$		0			0
$925$	−1.42558	+	2.46918i	−0.0468728	+	0.0811860i
$926$	−1.62820			−0.0535059
$927$		0			0
$928$	−5.86621			−0.192568
$929$	11.3415	−	19.6440i	0.372102	−	0.644499i	−0.617787	−	0.786345i	$-0.711971\pi$
$929$	11.3415	−	19.6440i	0.372102	−	0.644499i	0.989889	+	0.141846i	$0.0453039\pi$
$930$		0			0
$931$		0			0
$932$	7.90576	+	13.6932i	0.258962	+	0.448535i
$933$		0			0
$934$	2.96407	−	5.13392i	0.0969873	−	0.167987i
$935$	18.5458			0.606513
$936$		0			0
$937$	−51.2933			−1.67568			−0.837840	−	0.545915i	$-0.816182\pi$
$937$	−51.2933			−1.67568			−0.837840	+	0.545915i	$0.816182\pi$
$938$		0			0
$939$		0			0
$940$	−23.5108	−	40.7219i	−0.766838	−	1.32820i
$941$	15.9659	+	27.6538i	0.520474	+	0.901487i	0.999717	+	0.0238048i	$0.00757801\pi$
$941$	15.9659	+	27.6538i	0.520474	+	0.901487i	−0.479243	+	0.877682i	$0.659089\pi$
$942$		0			0
$943$	26.1849	−	45.3535i	0.852697	−	1.47691i
$944$	22.1965			0.722433
$945$		0			0
$946$	−1.66019			−0.0539774
$947$	−2.24665	+	3.89131i	−0.0730063	+	0.126451i	−0.900218	−	0.435440i	$-0.856593\pi$
$947$	−2.24665	+	3.89131i	−0.0730063	+	0.126451i	0.827211	+	0.561891i	$0.189926\pi$
$948$		0			0
$949$	−13.1774	−	22.8240i	−0.427757	−	0.740898i
$950$	1.46927	+	2.54485i	0.0476695	+	0.0825660i
$951$		0			0
$952$		0			0
$953$	−1.14635			−0.0371340			−0.0185670	−	0.999828i	$-0.505910\pi$
$953$	−1.14635			−0.0371340			−0.0185670	+	0.999828i	$0.505910\pi$
$954$		0			0
$955$	41.5310			1.34391
$956$	−20.5575	+	35.6066i	−0.664876	+	1.15160i
$957$		0			0
$958$	−1.32710	−	2.29860i	−0.0428765	−	0.0742643i
$959$		0			0
$960$		0			0
$961$	−5.85868	+	10.1475i	−0.188990	+	0.327340i
$962$	1.46216			0.0471418
$963$		0			0
$964$	26.6000			0.856730
$965$	−16.0358	+	27.7748i	−0.516210	+	0.894102i
$966$		0			0
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	−0.921065	−	0.389408i	$-0.872680\pi$
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	0.123295	−	0.992370i	$-0.460654\pi$
$968$	−3.05881	−	5.29802i	−0.0983140	−	0.170285i
$969$		0			0
$970$	0.949266	−	1.64418i	0.0304791	−	0.0527913i
$971$	−5.13322			−0.164733			−0.0823664	−	0.996602i	$-0.526248\pi$
$971$	−5.13322			−0.164733			−0.0823664	+	0.996602i	$0.526248\pi$
$972$		0			0
$973$		0			0
$974$	−1.20013	+	2.07869i	−0.0384546	+	0.0666054i
$975$		0			0
$976$	−14.6151	−	25.3141i	−0.467817	−	0.810283i
$977$	15.5974	+	27.0155i	0.499006	+	0.864303i	0.999999	−	0.00114787i	$-0.000365378\pi$
$977$	15.5974	+	27.0155i	0.499006	+	0.864303i	−0.500994	+	0.865451i	$0.667032\pi$
$978$		0			0
$979$	−10.5288	+	18.2365i	−0.336503	+	0.582840i
$980$		0			0
$981$		0			0
$982$	−2.96225			−0.0945292
$983$	−10.1700	+	17.6150i	−0.324374	+	0.561832i	−0.981385	−	0.192049i	$-0.938487\pi$
$983$	−10.1700	+	17.6150i	−0.324374	+	0.561832i	0.657012	+	0.753880i	$0.271820\pi$
$984$		0			0
$985$	−29.9378	−	51.8539i	−0.953899	−	1.65220i
$986$	0.434681	+	0.752890i	0.0138431	+	0.0239769i
$987$		0			0
$988$	−25.6014	+	44.3429i	−0.814488	+	1.41074i
$989$	−8.50808			−0.270541
$990$		0			0
$991$	−12.9655			−0.411863			−0.205932	−	0.978566i	$-0.566022\pi$
$991$	−12.9655			−0.411863			−0.205932	+	0.978566i	$0.566022\pi$
$992$	9.02234	−	15.6272i	0.286460	−	0.496163i
$993$		0			0
$994$		0			0
$995$	8.74269	+	15.1428i	0.277162	+	0.480059i
$996$		0			0
$997$	−24.7408	+	42.8523i	−0.783548	+	1.35715i	0.146314	+	0.989238i	$0.453259\pi$
$997$	−24.7408	+	42.8523i	−0.783548	+	1.35715i	−0.929863	+	0.367907i	$0.880074\pi$
$998$	−2.44436			−0.0773749
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.g.883.4		12
3.2	odd	2		441.2.f.g.295.4	yes	12
7.2	even	3		1323.2.h.g.802.4		12
7.3	odd	6		1323.2.g.g.667.4		12
7.4	even	3		1323.2.g.g.667.3		12
7.5	odd	6		1323.2.h.g.802.3		12
7.6	odd	2	inner	1323.2.f.g.883.3		12
9.2	odd	6		3969.2.a.be.1.4		6
9.4	even	3	inner	1323.2.f.g.442.4		12
9.5	odd	6		441.2.f.g.148.4	yes	12
9.7	even	3		3969.2.a.bd.1.3		6
21.2	odd	6		441.2.h.g.214.3		12
21.5	even	6		441.2.h.g.214.4		12
21.11	odd	6		441.2.g.g.79.4		12
21.17	even	6		441.2.g.g.79.3		12
21.20	even	2		441.2.f.g.295.3	yes	12
63.4	even	3		1323.2.h.g.226.4		12
63.5	even	6		441.2.g.g.67.3		12
63.13	odd	6	inner	1323.2.f.g.442.3		12
63.20	even	6		3969.2.a.be.1.3		6
63.23	odd	6		441.2.g.g.67.4		12
63.31	odd	6		1323.2.h.g.226.3		12
63.32	odd	6		441.2.h.g.373.3		12
63.34	odd	6		3969.2.a.bd.1.4		6
63.40	odd	6		1323.2.g.g.361.4		12
63.41	even	6		441.2.f.g.148.3	✓	12
63.58	even	3		1323.2.g.g.361.3		12
63.59	even	6		441.2.h.g.373.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	63.41	even	6
441.2.f.g.148.4	yes	12	9.5	odd	6
441.2.f.g.295.3	yes	12	21.20	even	2
441.2.f.g.295.4	yes	12	3.2	odd	2
441.2.g.g.67.3		12	63.5	even	6
441.2.g.g.67.4		12	63.23	odd	6
441.2.g.g.79.3		12	21.17	even	6
441.2.g.g.79.4		12	21.11	odd	6
441.2.h.g.214.3		12	21.2	odd	6
441.2.h.g.214.4		12	21.5	even	6
441.2.h.g.373.3		12	63.32	odd	6
441.2.h.g.373.4		12	63.59	even	6
1323.2.f.g.442.3		12	63.13	odd	6	inner
1323.2.f.g.442.4		12	9.4	even	3	inner
1323.2.f.g.883.3		12	7.6	odd	2	inner
1323.2.f.g.883.4		12	1.1	even	1	trivial
1323.2.g.g.361.3		12	63.58	even	3
1323.2.g.g.361.4		12	63.40	odd	6
1323.2.g.g.667.3		12	7.4	even	3
1323.2.g.g.667.4		12	7.3	odd	6
1323.2.h.g.226.3		12	63.31	odd	6
1323.2.h.g.226.4		12	63.4	even	3
1323.2.h.g.802.3		12	7.5	odd	6
1323.2.h.g.802.4		12	7.2	even	3
3969.2.a.bd.1.3		6	9.7	even	3
3969.2.a.bd.1.4		6	63.34	odd	6
3969.2.a.be.1.3		6	63.20	even	6
3969.2.a.be.1.4		6	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})\)	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +0.619757 q^{10} +(2.09097 - 3.62167i) q^{11} +(1.84155 + 3.18966i) q^{13} +(-1.83009 + 3.16982i) q^{16} +1.71107 q^{17} +7.15561 q^{19} +(-2.51769 + 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 - 4.43818i) q^{23} +(-0.858685 + 1.48729i) q^{25} +0.880716 q^{26} +(-1.06238 + 1.84010i) q^{29} +(-3.26793 - 5.66021i) q^{31} +(1.38044 + 2.39099i) q^{32} +(0.204579 - 0.354341i) q^{34} +1.66019 q^{37} +(0.855536 - 1.48183i) q^{38} +(1.22180 + 2.11621i) q^{40} +(5.10948 + 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +8.12476 q^{44} -1.22545 q^{46} +(-4.66912 + 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} +(-3.57780 + 6.19694i) q^{52} -10.6465 q^{53} +10.8387 q^{55} +(0.254040 + 0.440011i) q^{58} +(-3.03215 - 5.25183i) q^{59} +(-3.99298 + 6.91605i) q^{61} -1.56287 q^{62} -6.66019 q^{64} +(-4.77292 + 8.26693i) q^{65} +(-4.13160 - 7.15614i) q^{67} +(1.66215 + 2.87893i) q^{68} -6.23912 q^{71} -7.15561 q^{73} +(0.198495 - 0.343803i) q^{74} +(6.95103 + 12.0395i) q^{76} +(4.91423 - 8.51170i) q^{79} -9.48644 q^{80} +2.44359 q^{82} +(-3.44733 + 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 - 0.343803i) q^{86} +(1.97141 - 3.41458i) q^{88} -5.03538 q^{89} +(4.97825 - 8.62258i) q^{92} +(1.11650 + 1.93383i) q^{94} +(9.27292 + 16.0612i) q^{95} +(1.53167 - 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more