LMFDB - Embedded newform 1323.2.g.g.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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			667.4
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.g.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 + 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +O(q^{10})$	\(q+(0.119562 + 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +(0.309879 + 0.536725i) q^{10} -4.18194 q^{11} +(-1.84155 - 3.18966i) q^{13} +(-1.83009 - 3.16982i) q^{16} +(0.855536 + 1.48183i) q^{17} +(3.57780 - 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +5.12476 q^{23} +1.71737 q^{25} +(0.440358 - 0.762722i) q^{26} +(-1.06238 + 1.84010i) q^{29} +(3.26793 - 5.66021i) q^{31} +(1.38044 - 2.39099i) q^{32} +(-0.204579 + 0.354341i) q^{34} +(-0.830095 + 1.43777i) q^{37} +1.71107 q^{38} +2.44359 q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(-4.06238 + 7.03625i) q^{44} +(0.612725 + 1.06127i) q^{46} +(4.66912 + 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} -7.15561 q^{52} +(5.32326 + 9.22015i) q^{53} -10.8387 q^{55} -0.508080 q^{58} +(3.03215 - 5.25183i) q^{59} +(3.99298 + 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(-4.77292 - 8.26693i) q^{65} +(-4.13160 + 7.15614i) q^{67} +3.32431 q^{68} -6.23912 q^{71} +(-3.57780 - 6.19694i) q^{73} -0.396990 q^{74} +(-6.95103 - 12.0395i) q^{76} +(4.91423 + 8.51170i) q^{79} +(-4.74322 - 8.21550i) q^{80} +(1.22180 - 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +0.396990 q^{86} -3.94282 q^{88} +(-2.51769 + 4.36077i) q^{89} +(4.97825 - 8.62258i) q^{92} +(-1.11650 + 1.93383i) q^{94} +(9.27292 - 16.0612i) q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 16 q^{11} - 6 q^{16} - 6 q^{22} - 8 q^{23} + 24 q^{25} + 22 q^{29} + 16 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} + 36 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} - 72 q^{74} + 6 q^{79} + 30 q^{85} + 72 q^{86} - 12 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 - 16 * q^11 - 6 * q^16 - 6 * q^22 - 8 * q^23 + 24 * q^25 + 22 * q^29 + 16 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 + 36 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 - 72 * q^74 + 6 * q^79 + 30 * q^85 + 72 * q^86 - 12 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.119562	+	0.207087i	0.0845428	+	0.146433i	0.905196	−	0.424994i	$-0.139724\pi$
$2$	0.119562	+	0.207087i	0.0845428	+	0.146433i	−0.820653	+	0.571426i	$0.806390\pi$
$3$		0			0
$3$		0			0
$4$	0.971410	−	1.68253i	0.485705	−	0.841266i
$5$	2.59179			1.15908			0.579542	−	0.814943i	$-0.303232\pi$
$5$	2.59179			1.15908			0.579542	+	0.814943i	$0.303232\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$		0			0
$10$	0.309879	+	0.536725i	0.0979922	+	0.169727i
$11$	−4.18194			−1.26090			−0.630452	−	0.776228i	$-0.717130\pi$
$11$	−4.18194			−1.26090			−0.630452	+	0.776228i	$0.717130\pi$
$12$		0			0
$13$	−1.84155	−	3.18966i	−0.510755	−	0.884653i	−0.999922	−	0.0124633i	$-0.996033\pi$
$13$	−1.84155	−	3.18966i	−0.510755	−	0.884653i	0.489168	−	0.872190i	$-0.337301\pi$
$14$		0			0
$15$		0			0
$16$	−1.83009	−	3.16982i	−0.457524	−	0.792454i
$17$	0.855536	+	1.48183i	0.207498	+	0.359397i	0.950926	−	0.309419i	$-0.100135\pi$
$17$	0.855536	+	1.48183i	0.207498	+	0.359397i	−0.743428	+	0.668816i	$0.766801\pi$
$18$		0			0
$19$	3.57780	−	6.19694i	0.820805	−	1.42168i	−0.0842790	−	0.996442i	$-0.526859\pi$
$19$	3.57780	−	6.19694i	0.820805	−	1.42168i	0.905084	−	0.425233i	$-0.139808\pi$
$20$	2.51769	−	4.36077i	0.562973	−	0.975097i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	5.12476			1.06859			0.534294	−	0.845299i	$-0.320578\pi$
$23$	5.12476			1.06859			0.534294	+	0.845299i	$0.320578\pi$
$24$		0			0
$25$	1.71737			0.343474
$26$	0.440358	−	0.762722i	0.0863613	−	0.149582i
$27$		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	−0.407694	−	0.913119i	$-0.633667\pi$
$31$	3.26793	−	5.66021i	0.586937	−	1.01660i	0.994631	−	0.103486i	$-0.0329997\pi$
$32$	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
$37$	−0.830095	+	1.43777i	−0.136467	+	0.236367i	−0.926157	−	0.377139i	$-0.876908\pi$
$37$	−0.830095	+	1.43777i	−0.136467	+	0.236367i	0.789690	+	0.613506i	$0.210241\pi$
$38$	1.71107			0.277573
$39$		0			0
$40$	2.44359			0.386366
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	−0.920938	−	0.389708i	$-0.872576\pi$
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	0.122972	−	0.992410i	$-0.460758\pi$
$42$		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	$0.126264\pi$
$44$	−4.06238	+	7.03625i	−0.612427	+	1.06075i
$45$		0			0
$46$	0.612725	+	1.06127i	0.0903414	+	0.156476i
$47$	4.66912	+	8.08715i	0.681061	+	1.17963i	0.974657	+	0.223703i	$0.0718146\pi$
$47$	4.66912	+	8.08715i	0.681061	+	1.17963i	−0.293596	+	0.955930i	$0.594852\pi$
$48$		0			0
$49$		0			0
$50$	0.205332	+	0.355645i	0.0290383	+	0.0502958i
$51$		0			0
$52$	−7.15561			−0.992305
$53$	5.32326	+	9.22015i	0.731206	+	1.26649i	0.956368	+	0.292164i	$0.0943754\pi$
$53$	5.32326	+	9.22015i	0.731206	+	1.26649i	−0.225162	+	0.974321i	$0.572291\pi$
$54$		0			0
$55$	−10.8387			−1.46149
$56$		0			0
$57$		0			0
$58$	−0.508080			−0.0667142
$59$	3.03215	−	5.25183i	0.394752	−	0.683730i	−0.598318	−	0.801259i	$-0.704164\pi$
$59$	3.03215	−	5.25183i	0.394752	−	0.683730i	0.993069	+	0.117529i	$0.0374972\pi$
$60$		0			0
$61$	3.99298	+	6.91605i	0.511249	+	0.885509i	0.999915	+	0.0130384i	$0.00415038\pi$
$61$	3.99298	+	6.91605i	0.511249	+	0.885509i	−0.488666	+	0.872471i	$0.662516\pi$
$62$	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	0.495230	+	0.868762i	$0.335084\pi$
$67$	−4.13160	+	7.15614i	−0.504755	+	0.874262i	−0.999985	+	0.00549964i	$0.998249\pi$
$68$	3.32431			0.403131
$69$		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
$73$	−3.57780	−	6.19694i	−0.418750	−	0.725297i	0.577064	−	0.816699i	$-0.304198\pi$
$73$	−3.57780	−	6.19694i	−0.418750	−	0.725297i	−0.995814	+	0.0914022i	$0.970865\pi$
$74$	−0.396990			−0.0461492
$75$		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	0.998064	+	0.0621945i	$0.0198099\pi$
$79$	4.91423	+	8.51170i	0.552894	+	0.957641i	−0.445170	+	0.895446i	$0.646857\pi$
$80$	−4.74322	−	8.21550i	−0.530308	−	0.918521i
$81$		0			0
$82$	1.22180	−	2.11621i	0.134925	−	0.233696i
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	−0.612436	−	0.790521i	$-0.709810\pi$
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	0.990829	+	0.135124i	$0.0431434\pi$
$84$		0			0
$85$	2.21737	+	3.84060i	0.240508	+	0.416571i
$86$	0.396990			0.0428085
$87$		0			0
$88$	−3.94282			−0.420306
$89$	−2.51769	+	4.36077i	−0.266875	+	0.462240i	−0.968053	−	0.250745i	$-0.919324\pi$
$89$	−2.51769	+	4.36077i	−0.266875	+	0.462240i	0.701178	+	0.712986i	$0.252658\pi$
$90$		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	−0.933247	−	0.359234i	$-0.883038\pi$
$97$	−1.53167	+	2.65294i	−0.155518	+	0.269365i	0.777730	+	0.628599i	$0.216371\pi$
$98$		0			0
$99$		0			0
$100$	1.66827	−	2.88953i	0.166827	−	0.288953i
$101$	11.0997			1.10446			0.552229	−	0.833692i	$-0.313777\pi$
$101$	11.0997			1.10446			0.552229	+	0.833692i	$0.313777\pi$
$102$		0			0
$103$	7.98597			0.786881			0.393440	−	0.919350i	$-0.371285\pi$
$103$	7.98597			0.786881			0.393440	+	0.919350i	$0.371285\pi$
$104$	−1.73625	−	3.00728i	−0.170254	−	0.294888i
$105$		0			0
$106$	−1.27292	+	2.20475i	−0.123636	+	0.214145i
$107$	1.97825	−	3.42642i	0.191244	−	0.331245i	−0.754419	−	0.656394i	$-0.772081\pi$
$107$	1.97825	−	3.42642i	0.191244	−	0.331245i	0.945663	+	0.325149i	$0.105414\pi$
$108$		0			0
$109$	−3.63160	−	6.29012i	−0.347844	−	0.602484i	0.638022	−	0.770018i	$-0.279753\pi$
$109$	−3.63160	−	6.29012i	−0.347844	−	0.602484i	−0.985866	+	0.167534i	$0.946420\pi$
$110$	−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
$115$	13.2823			1.23858
$116$	2.06402	+	3.57498i	0.191639	+	0.331929i
$117$		0			0
$118$	1.45011			0.133494
$119$		0			0
$120$		0			0
$121$	6.48865			0.589877
$122$	−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
$131$	4.30286			0.375943			0.187971	−	0.982175i	$-0.439809\pi$
$131$	4.30286			0.375943			0.187971	+	0.982175i	$0.439809\pi$
$132$		0			0
$133$		0			0
$134$	−1.97592			−0.170694
$135$		0			0
$136$	0.806617	+	1.39710i	0.0691668	+	0.119800i
$137$	−20.5893			−1.75907			−0.879533	−	0.475838i	$-0.842145\pi$
$137$	−20.5893			−1.75907			−0.879533	+	0.475838i	$0.842145\pi$
$138$		0			0
$139$	7.88067	+	13.6497i	0.668429	+	1.15775i	0.978343	+	0.206989i	$0.0663665\pi$
$139$	7.88067	+	13.6497i	0.668429	+	1.15775i	−0.309914	+	0.950765i	$0.600300\pi$
$140$		0			0
$141$		0			0
$142$	−0.745960	−	1.29204i	−0.0625996	−	0.108426i
$143$	7.70127	+	13.3390i	0.644012	+	1.11546i
$144$		0			0
$145$	−2.75347	+	4.76915i	−0.228663	+	0.396056i
$146$	0.855536	−	1.48183i	0.0708047	−	0.122637i
$147$		0			0
$148$	1.61273	+	2.79332i	0.132565	+	0.229610i
$149$	−6.06758			−0.497076			−0.248538	−	0.968622i	$-0.579950\pi$
$149$	−6.06758			−0.497076			−0.248538	+	0.968622i	$0.579950\pi$
$150$		0			0
$151$	4.48865			0.365281			0.182641	−	0.983180i	$-0.441536\pi$
$151$	4.48865			0.365281			0.182641	+	0.983180i	$0.441536\pi$
$152$	3.37323	−	5.84260i	0.273605	−	0.473897i
$153$		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	$-0.846406\pi$
$157$	−0.514457	+	0.891066i	−0.0410582	+	0.0711148i	0.844766	+	0.535136i	$0.179740\pi$
$158$	−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
$163$	−3.41423	+	5.91362i	−0.267423	+	0.463190i	−0.968196	−	0.250194i	$-0.919505\pi$
$163$	−3.41423	+	5.91362i	−0.267423	+	0.463190i	0.700772	+	0.713385i	$0.252839\pi$
$164$	−19.8536			−1.55031
$165$		0			0
$166$	1.64867			0.127962
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	0.969767	+	0.244032i	$0.0784701\pi$
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	−0.273546	+	0.961859i	$0.588197\pi$
$168$		0			0
$169$	−0.282630	+	0.489530i	−0.0217408	+	0.0376561i
$170$	−0.530225	+	0.918376i	−0.0406664	+	0.0704362i
$171$		0			0
$172$	−1.61273	−	2.79332i	−0.122969	−	0.212989i
$173$	−0.415178	−	0.719110i	−0.0315654	−	0.0546729i	0.849811	−	0.527087i	$-0.176716\pi$
$173$	−0.415178	−	0.719110i	−0.0315654	−	0.0546729i	−0.881377	+	0.472414i	$0.843383\pi$
$174$		0			0
$175$		0			0
$176$	7.65335	+	13.2560i	0.576893	+	0.999208i
$177$		0			0
$178$	−1.20408			−0.0902493
$179$	3.78947	+	6.56355i	0.283238	+	0.490583i	0.972180	−	0.234233i	$-0.0752580\pi$
$179$	3.78947	+	6.56355i	0.283238	+	0.490583i	−0.688942	+	0.724816i	$0.741925\pi$
$180$		0			0
$181$	0.409157			0.0304124			0.0152062	−	0.999884i	$-0.495160\pi$
$181$	0.409157			0.0304124			0.0152062	+	0.999884i	$0.495160\pi$
$182$		0			0
$183$		0			0
$184$	4.83173			0.356200
$185$	−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	0.995510	+	0.0946575i	$0.0301756\pi$
$191$	8.01204	+	13.8773i	0.579731	+	1.00412i	−0.415779	+	0.909466i	$0.636491\pi$
$192$		0			0
$193$	6.18715	−	10.7164i	0.445360	−	0.771387i	−0.552717	−	0.833369i	$-0.686409\pi$
$193$	6.18715	−	10.7164i	0.445360	−	0.771387i	0.998077	+	0.0619822i	$0.0197422\pi$
$194$	−0.732518			−0.0525917
$195$		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
$199$	3.37323	+	5.84260i	0.239122	+	0.414171i	0.960463	−	0.278409i	$-0.0898072\pi$
$199$	3.37323	+	5.84260i	0.239122	+	0.414171i	−0.721341	+	0.692580i	$0.756474\pi$
$200$	1.61917			0.114493
$201$		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
$206$	0.954815	+	1.65379i	0.0665251	+	0.115225i
$207$		0			0
$208$	−6.74043	+	11.6748i	−0.467365	+	0.809500i
$209$	−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	$-0.364094\pi$
$212$	20.6843			1.42060
$213$		0			0
$214$	0.946090			0.0646734
$215$	2.15143	−	3.72639i	0.146726	−	0.254138i
$216$		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	−0.780773	−	0.624815i	$-0.785175\pi$
$223$	2.25071	−	3.89834i	0.150719	−	0.261052i	0.931492	+	0.363762i	$0.118508\pi$
$224$		0			0
$225$		0			0
$226$	−0.828460	+	1.43494i	−0.0551084	+	0.0954505i
$227$	6.06429			0.402501			0.201251	−	0.979540i	$-0.435499\pi$
$227$	6.06429			0.402501			0.201251	+	0.979540i	$0.435499\pi$
$228$		0			0
$229$	−11.0493			−0.730159			−0.365080	−	0.930976i	$-0.618958\pi$
$229$	−11.0493			−0.730159			−0.365080	+	0.930976i	$0.618958\pi$
$230$	1.58805	+	2.75059i	0.104713	+	0.181369i
$231$		0			0
$232$	−1.00163	+	1.73488i	−0.0657605	+	0.113901i
$233$	−4.06922	+	7.04809i	−0.266583	+	0.461736i	−0.967977	−	0.251038i	$-0.919228\pi$
$233$	−4.06922	+	7.04809i	−0.266583	+	0.461736i	0.701394	+	0.712774i	$0.252561\pi$
$234$		0			0
$235$	12.1014	+	20.9602i	0.789407	+	1.36729i
$236$	−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
$241$	13.6915			0.881945			0.440972	−	0.897521i	$-0.354634\pi$
$241$	13.6915			0.881945			0.440972	+	0.897521i	$0.354634\pi$
$242$	0.775794	+	1.34371i	0.0498699	+	0.0863772i
$243$		0			0
$244$	15.5153			0.993265
$245$		0			0
$246$		0			0
$247$	−26.3549			−1.67692
$248$	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	$-0.659303\pi$
$251$	−15.2040			−0.959667			−0.479833	+	0.877360i	$0.659303\pi$
$252$		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
$257$	−25.6215			−1.59822			−0.799112	−	0.601182i	$-0.794697\pi$
$257$	−25.6215			−1.59822			−0.799112	+	0.601182i	$0.794697\pi$
$258$		0			0
$259$		0			0
$260$	−18.5458			−1.15016
$261$		0			0
$262$	0.514457	+	0.891066i	0.0317833	+	0.0550502i
$263$	−7.10069			−0.437847			−0.218924	−	0.975742i	$-0.570255\pi$
$263$	−7.10069			−0.437847			−0.218924	+	0.975742i	$0.570255\pi$
$264$		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
$269$	−8.21572	−	14.2301i	−0.500922	−	0.867622i	−0.999999	−	0.00106448i	$-0.999661\pi$
$269$	−8.21572	−	14.2301i	−0.500922	−	0.867622i	0.499078	−	0.866557i	$-0.333672\pi$
$270$		0			0
$271$	−6.34899	+	10.9968i	−0.385674	+	0.668007i	−0.991862	−	0.127314i	$-0.959364\pi$
$271$	−6.34899	+	10.9968i	−0.385674	+	0.668007i	0.606189	+	0.795321i	$0.292698\pi$
$272$	3.13143	−	5.42379i	0.189871	−	0.328865i
$273$		0			0
$274$	−2.46169	−	4.26378i	−0.148716	−	0.257584i
$275$	−7.18194			−0.433087
$276$		0			0
$277$	−0.828460			−0.0497773			−0.0248887	−	0.999690i	$-0.507923\pi$
$277$	−0.828460			−0.0497773			−0.0248887	+	0.999690i	$0.507923\pi$
$278$	−1.88445	+	3.26396i	−0.113022	+	0.195760i
$279$		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	$-0.763191\pi$
$283$	3.67708	−	6.36890i	0.218580	−	0.378592i	0.954374	+	0.298614i	$0.0965242\pi$
$284$	−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
$289$	7.03611	−	12.1869i	0.413889	−	0.716877i
$290$	−1.31684			−0.0773273
$291$		0			0
$292$	−13.9021			−0.813557
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	0.957391	−	0.288795i	$-0.0932545\pi$
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	−0.728799	+	0.684728i	$0.759921\pi$
$294$		0			0
$295$	7.85868	−	13.6116i	0.457550	−	0.792500i
$296$	−0.782630	+	1.35556i	−0.0454895	+	0.0787900i
$297$		0			0
$298$	−0.725450	−	1.25652i	−0.0420242	−	0.0727881i
$299$	−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
$304$	−26.1909			−1.50215
$305$	10.3490	+	17.9249i	0.592580	+	1.02638i
$306$		0			0
$307$	22.6709			1.29390			0.646948	−	0.762534i	$-0.276045\pi$
$307$	22.6709			1.29390			0.646948	+	0.762534i	$0.276045\pi$
$308$		0			0
$309$		0			0
$310$	4.05064			0.230061
$311$	−16.1588	+	27.9879i	−0.916281	+	1.58705i	−0.111266	+	0.993791i	$0.535491\pi$
$311$	−16.1588	+	27.9879i	−0.916281	+	1.58705i	−0.805015	+	0.593255i	$0.797843\pi$
$312$		0			0
$313$	12.1598	+	21.0614i	0.687312	+	1.19046i	0.972704	+	0.232048i	$0.0745428\pi$
$313$	12.1598	+	21.0614i	0.687312	+	1.19046i	−0.285392	+	0.958411i	$0.592124\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	2.56922	+	4.45002i	0.144302	+	0.249938i	0.929112	−	0.369798i	$-0.120573\pi$
$317$	2.56922	+	4.45002i	0.144302	+	0.249938i	−0.784811	+	0.619736i	$0.787240\pi$
$318$		0			0
$319$	4.44282	−	7.69519i	0.248750	−	0.430848i
$320$	−17.2618			−0.964964
$321$		0			0
$322$		0			0
$323$	12.2438			0.681262
$324$		0			0
$325$	−3.16263	−	5.47783i	−0.175431	−	0.303855i
$326$	−1.63284			−0.0904349
$327$		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	0.980795	−	0.195040i	$-0.0624835\pi$
$331$	5.84897	+	10.1307i	0.321488	+	0.556834i	−0.659307	+	0.751874i	$0.729150\pi$
$332$	−6.69753	−	11.6005i	−0.367575	−	0.636658i
$333$		0			0
$334$	−2.15143	+	3.72639i	−0.117721	+	0.203899i
$335$	−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	$0.463351\pi$
$338$	−0.135167			−0.00735211
$339$		0			0
$340$	8.61590			0.467263
$341$	−13.6663	+	23.6707i	−0.740071	+	1.28184i
$342$		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	−0.222488	−	0.974936i	$-0.571418\pi$
$347$	13.6557	−	23.6523i	0.733075	−	1.26972i	0.955563	−	0.294788i	$-0.0952490\pi$
$348$		0			0
$349$	−11.4585	+	19.8467i	−0.613358	+	1.06237i	0.377312	+	0.926086i	$0.376848\pi$
$349$	−11.4585	+	19.8467i	−0.613358	+	1.06237i	−0.990670	+	0.136281i	$0.956485\pi$
$350$		0			0
$351$		0			0
$352$	−5.77292	+	9.99898i	−0.307697	+	0.532948i
$353$	−10.2693			−0.546581			−0.273290	−	0.961932i	$-0.588112\pi$
$353$	−10.2693			−0.546581			−0.273290	+	0.961932i	$0.588112\pi$
$354$		0			0
$355$	−16.1705			−0.858241
$356$	4.89142	+	8.47218i	0.259245	+	0.449025i
$357$		0			0
$358$	−0.906150	+	1.56950i	−0.0478915	+	0.0829505i
$359$	5.05034	−	8.74745i	0.266547	−	0.461673i	−0.701421	−	0.712747i	$-0.747451\pi$
$359$	5.05034	−	8.74745i	0.266547	−	0.461673i	0.967968	+	0.251075i	$0.0807839\pi$
$360$		0			0
$361$	−16.1014	−	27.8884i	−0.847441	−	1.46781i
$362$	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
$367$	−7.77537			−0.405871			−0.202935	−	0.979192i	$-0.565048\pi$
$367$	−7.77537			−0.405871			−0.202935	+	0.979192i	$0.565048\pi$
$368$	−9.37880	−	16.2446i	−0.488904	−	0.846806i
$369$		0			0
$370$	−1.02891			−0.0534907
$371$		0			0
$372$		0			0
$373$	24.1111			1.24842			0.624212	−	0.781255i	$-0.285420\pi$
$373$	24.1111			1.24842			0.624212	+	0.781255i	$0.285420\pi$
$374$	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
$383$	9.24040			0.472162			0.236081	−	0.971733i	$-0.424137\pi$
$383$	9.24040			0.472162			0.236081	+	0.971733i	$0.424137\pi$
$384$		0			0
$385$		0			0
$386$	2.95898			0.150608
$387$		0			0
$388$	2.97577	+	5.15418i	0.151072	+	0.261664i
$389$	−10.4484			−0.529756			−0.264878	−	0.964282i	$-0.585332\pi$
$389$	−10.4484			−0.529756			−0.264878	+	0.964282i	$0.585332\pi$
$390$		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
$395$	12.7366	+	22.0605i	0.640850	+	1.10999i
$396$		0			0
$397$	0.204579	−	0.354341i	0.0102675	−	0.0177838i	−0.860846	−	0.508866i	$-0.830065\pi$
$397$	0.204579	−	0.354341i	0.0102675	−	0.0177838i	0.871114	+	0.491082i	$0.163398\pi$
$398$	−0.806617	+	1.39710i	−0.0404321	+	0.0700304i
$399$		0			0
$400$	−3.14295	−	5.44375i	−0.157147	−	0.272187i
$401$	−15.2528			−0.761688			−0.380844	−	0.924639i	$-0.624367\pi$
$401$	−15.2528			−0.761688			−0.380844	+	0.924639i	$0.624367\pi$
$402$		0			0
$403$	−24.0722			−1.19912
$404$	10.7823	−	18.6756i	0.536441	−	0.929143i
$405$		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	$-0.784932\pi$
$409$	3.06335	−	5.30587i	0.151473	−	0.262359i	0.931769	+	0.363051i	$0.118265\pi$
$410$	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
$415$	8.93474	−	15.4754i	0.438589	−	0.759659i
$416$	−10.1686			−0.498557
$417$		0			0
$418$	−7.15561			−0.349992
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	0.884482	−	0.466574i	$-0.154512\pi$
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	−0.846306	+	0.532697i	$0.821179\pi$
$420$		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	$0.974813\pi$
$422$	2.01887	−	3.49679i	0.0982773	−	0.170221i
$423$		0			0
$424$	5.01887	+	8.69295i	0.243738	+	0.422167i
$425$	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
$430$	1.02891			0.0496187
$431$	0.502879	+	0.871011i	0.0242228	+	0.0419551i	0.877883	−	0.478876i	$-0.158956\pi$
$431$	0.502879	+	0.871011i	0.0242228	+	0.0419551i	−0.853660	+	0.520831i	$0.825622\pi$
$432$		0			0
$433$	13.1071			0.629889			0.314945	−	0.949110i	$-0.398014\pi$
$433$	13.1071			0.629889			0.314945	+	0.949110i	$0.398014\pi$
$434$		0			0
$435$		0			0
$436$	−14.1111			−0.675799
$437$	18.3354	−	31.7579i	0.877101	−	1.51918i
$438$		0			0
$439$	−9.30704	−	16.1203i	−0.444201	−	0.769378i	0.553795	−	0.832653i	$-0.313179\pi$
$439$	−9.30704	−	16.1203i	−0.444201	−	0.769378i	−0.997996	+	0.0632744i	$0.979846\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	−0.559503	−	0.969088i	−0.0265828	−	0.0460427i	0.852428	−	0.522845i	$-0.175129\pi$
$443$	−0.559503	−	0.969088i	−0.0265828	−	0.0460427i	−0.879011	+	0.476802i	$0.841796\pi$
$444$		0			0
$445$	−6.52532	+	11.3022i	−0.309330	+	0.535775i
$446$	1.07639			0.0509687
$447$		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
$451$	21.3676	+	37.0097i	1.00616	+	1.74272i
$452$	13.4621			0.633203
$453$		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	0.919056	+	0.394126i	$0.128953\pi$
$457$	17.1202	+	29.6531i	0.800852	+	1.38712i	−0.118205	+	0.992989i	$0.537714\pi$
$458$	−1.32107	−	2.28817i	−0.0617297	−	0.106919i
$459$		0			0
$460$	12.9026	−	22.3479i	0.601585	−	1.04198i
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	−0.524811	−	0.851219i	$-0.675864\pi$
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	0.999583	+	0.0288903i	$0.00919735\pi$
$462$		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	$0.883909\pi$
$464$	7.77704			0.361040
$465$		0			0
$466$	−1.94609			−0.0901509
$467$	12.3956	−	21.4698i	0.573598	−	0.993502i	−0.422594	−	0.906319i	$-0.638880\pi$
$467$	12.3956	−	21.4698i	0.573598	−	0.993502i	0.996192	−	0.0871825i	$-0.0277863\pi$
$468$		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
$478$	−2.53022	+	4.38248i	−0.115730	+	0.200450i
$479$	11.0997			0.507157			0.253579	−	0.967315i	$-0.418392\pi$
$479$	11.0997			0.507157			0.253579	+	0.967315i	$0.418392\pi$
$480$		0			0
$481$	6.11465			0.278804
$482$	1.63697	+	2.83532i	0.0745621	+	0.129145i
$483$		0			0
$484$	6.30314	−	10.9174i	0.286506	−	0.496244i
$485$	−3.96978	+	6.87585i	−0.180258	+	0.312216i
$486$		0			0
$487$	5.01887	+	8.69295i	0.227427	+	0.393915i	0.957045	−	0.289940i	$-0.0936354\pi$
$487$	5.01887	+	8.69295i	0.227427	+	0.393915i	−0.729618	+	0.683855i	$0.760302\pi$
$488$	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
$493$	−3.63562			−0.163740
$494$	−3.15103	−	5.45774i	−0.141772	−	0.245556i
$495$		0			0
$496$	−23.9225			−1.07415
$497$		0			0
$498$		0			0
$499$	10.2222			0.457608			0.228804	−	0.973473i	$-0.426519\pi$
$499$	10.2222			0.457608			0.228804	+	0.973473i	$0.426519\pi$
$500$	−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	$-0.439621\pi$
$503$	8.45753			0.377102			0.188551	+	0.982063i	$0.439621\pi$
$504$		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
$509$	10.5657			0.468317			0.234159	−	0.972198i	$-0.424767\pi$
$509$	10.5657			0.468317			0.234159	+	0.972198i	$0.424767\pi$
$510$		0			0
$511$		0			0
$512$	−17.0071			−0.751616
$513$		0			0
$514$	−3.06335	−	5.30587i	−0.135118	−	0.234032i
$515$	20.6979			0.912060
$516$		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
$521$	9.87788	+	17.1090i	0.432758	+	0.749558i	0.997110	−	0.0759760i	$-0.0242072\pi$
$521$	9.87788	+	17.1090i	0.432758	+	0.749558i	−0.564352	+	0.825534i	$0.690874\pi$
$522$		0			0
$523$	16.2641	−	28.1702i	0.711179	−	1.23180i	−0.253236	−	0.967405i	$-0.581495\pi$
$523$	16.2641	−	28.1702i	0.711179	−	1.23180i	0.964415	−	0.264394i	$-0.0851718\pi$
$524$	4.17984	−	7.23970i	0.182597	−	0.316268i
$525$		0			0
$526$	−0.848970	−	1.47046i	−0.0370168	−	0.0641150i
$527$	11.1833			0.487153
$528$		0			0
$529$	3.26320			0.141878
$530$	−3.29913	+	5.71426i	−0.143305	+	0.248211i
$531$		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
$541$	−7.61109	+	13.1828i	−0.327226	+	0.566773i	−0.981960	−	0.189087i	$-0.939447\pi$
$541$	−7.61109	+	13.1828i	−0.327226	+	0.566773i	0.654734	+	0.755859i	$0.272781\pi$
$542$	−3.03638			−0.130424
$543$		0			0
$544$	4.72406			0.202542
$545$	−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	$0.333225\pi$
$548$	−20.0007	+	34.6422i	−0.854387	+	1.47984i
$549$		0			0
$550$	−0.858685	−	1.48729i	−0.0366144	−	0.0634181i
$551$	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
$556$	30.6214			1.29864
$557$	13.8337	+	23.9606i	0.586151	+	1.01524i	0.994731	+	0.102521i	$0.0326908\pi$
$557$	13.8337	+	23.9606i	0.586151	+	1.01524i	−0.408580	+	0.912723i	$0.633976\pi$
$558$		0			0
$559$	−6.11465			−0.258622
$560$		0			0
$561$		0			0
$562$	1.24815			0.0526500
$563$	−4.27912	+	7.41166i	−0.180343	+	0.312364i	−0.941998	−	0.335620i	$-0.891054\pi$
$563$	−4.27912	+	7.41166i	−0.180343	+	0.312364i	0.761654	+	0.647984i	$0.224388\pi$
$564$		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	0.973272	−	0.229655i	$-0.0737597\pi$
$569$	6.86389	+	11.8886i	0.287749	+	0.498396i	−0.685523	+	0.728051i	$0.740426\pi$
$570$		0			0
$571$	−5.35868	+	9.28151i	−0.224254	+	0.388419i	−0.956095	−	0.293056i	$-0.905328\pi$
$571$	−5.35868	+	9.28151i	−0.224254	+	0.388419i	0.731841	+	0.681475i	$0.238661\pi$
$572$	29.9244			1.25120
$573$		0			0
$574$		0			0
$575$	8.80111			0.367032
$576$		0			0
$577$	−22.8177	−	39.5214i	−0.949912	−	1.64530i	−0.745605	−	0.666389i	$-0.767839\pi$
$577$	−22.8177	−	39.5214i	−0.949912	−	1.64530i	−0.204307	−	0.978907i	$-0.565494\pi$
$578$	3.36500			0.139965
$579$		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
$584$	−3.37323	−	5.84260i	−0.139585	−	0.241768i
$585$		0			0
$586$	−0.935657	+	1.62060i	−0.0386516	+	0.0669466i
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	−0.741103	−	0.671392i	$-0.765697\pi$
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	0.951994	+	0.306118i	$0.0990302\pi$
$588$		0			0
$589$	−23.3840	−	40.5023i	−0.963521	−	1.66887i
$590$	3.75839			0.154730
$591$		0			0
$592$	6.07661			0.249747
$593$	−5.69804	+	9.86929i	−0.233990	+	0.405283i	−0.958979	−	0.283478i	$-0.908512\pi$
$593$	−5.69804	+	9.86929i	−0.233990	+	0.405283i	0.724988	+	0.688761i	$0.241845\pi$
$594$		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	0.259867	+	0.965644i	$0.416321\pi$
$599$	−17.2873	+	29.9424i	−0.706339	+	1.22341i	−0.966206	+	0.257771i	$0.917012\pi$
$600$		0			0
$601$	−19.4207	+	33.6376i	−0.792187	+	1.37211i	0.132423	+	0.991193i	$0.457724\pi$
$601$	−19.4207	+	33.6376i	−0.792187	+	1.37211i	−0.924610	+	0.380915i	$0.875609\pi$
$602$		0			0
$603$		0			0
$604$	4.36032	−	7.55230i	0.177419	−	0.307299i
$605$	16.8172			0.683717
$606$		0			0
$607$	41.3325			1.67763			0.838817	−	0.544414i	$-0.183248\pi$
$607$	41.3325			1.67763			0.838817	+	0.544414i	$0.183248\pi$
$608$	−9.87788	−	17.1090i	−0.400601	−	0.693861i
$609$		0			0
$610$	−2.47468	+	4.28627i	−0.100197	+	0.173546i
$611$	17.1969	−	29.7858i	0.695710	−	1.20501i
$612$		0			0
$613$	14.3285	+	24.8176i	0.578721	+	1.00237i	0.995626	+	0.0934244i	$0.0297813\pi$
$613$	14.3285	+	24.8176i	0.578721	+	1.00237i	−0.416905	+	0.908950i	$0.636885\pi$
$614$	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
$619$	−1.43807			−0.0578010			−0.0289005	−	0.999582i	$-0.509201\pi$
$619$	−1.43807			−0.0578010			−0.0289005	+	0.999582i	$0.509201\pi$
$620$	−16.4552	−	28.5013i	−0.660859	−	1.14464i
$621$		0			0
$622$	−7.72789			−0.309860
$623$		0			0
$624$		0			0
$625$	−30.6375			−1.22550
$626$	−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
$635$	23.6140			0.937094
$636$		0			0
$637$		0			0
$638$	2.12476			0.0841202
$639$		0			0
$640$	−9.21946	−	15.9686i	−0.364431	−	0.631213i
$641$	−9.23912			−0.364923			−0.182462	−	0.983213i	$-0.558407\pi$
$641$	−9.23912			−0.364923			−0.182462	+	0.983213i	$0.558407\pi$
$642$		0			0
$643$	−12.7795	−	22.1348i	−0.503976	−	0.872912i	−0.999989	−	0.00459728i	$-0.998537\pi$
$643$	−12.7795	−	22.1348i	−0.503976	−	0.872912i	0.496013	−	0.868315i	$-0.334797\pi$
$644$		0			0
$645$		0			0
$646$	1.46389	+	2.53552i	0.0575958	+	0.0997588i
$647$	−14.1556	−	24.5181i	−0.556512	−	0.963908i	−0.997784	−	0.0665343i	$-0.978806\pi$
$647$	−14.1556	−	24.5181i	−0.556512	−	0.963908i	0.441272	−	0.897374i	$-0.354528\pi$
$648$		0			0
$649$	−12.6803	+	21.9629i	−0.497744	+	0.862118i
$650$	0.756258	−	1.30988i	0.0296629	−	0.0513776i
$651$		0			0
$652$	6.63323	+	11.4891i	0.259778	+	0.449948i
$653$	8.35021			0.326769			0.163385	−	0.986562i	$-0.447759\pi$
$653$	8.35021			0.326769			0.163385	+	0.986562i	$0.447759\pi$
$654$		0			0
$655$	11.1521			0.435749
$656$	−18.7017	+	32.3922i	−0.730177	+	1.26470i
$657$		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	$-0.940283\pi$
$661$	−8.47668	+	14.6820i	−0.329705	+	0.571065i	0.652748	+	0.757575i	$0.273616\pi$
$662$	−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
$667$	−5.44445	+	9.43007i	−0.210810	+	0.365134i
$668$	34.9597			1.35263
$669$		0			0
$670$	−5.12118			−0.197848
$671$	−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	$-0.160609\pi$
$674$	−4.02859	+	6.97772i	−0.155175	+	0.268772i
$675$		0			0
$676$	0.549100	+	0.951068i	0.0211192	+	0.0365796i
$677$	7.18681	+	12.4479i	0.276212	+	0.478412i	0.970440	−	0.241342i	$-0.0775876\pi$
$677$	7.18681	+	12.4479i	0.276212	+	0.478412i	−0.694229	+	0.719755i	$0.744254\pi$
$678$		0			0
$679$		0			0
$680$	2.09058	+	3.62099i	0.0801701	+	0.138859i
$681$		0			0
$682$	−6.53585			−0.250271
$683$	−16.1546	−	27.9806i	−0.618138	−	1.07065i	−0.989825	−	0.142289i	$-0.954554\pi$
$683$	−16.1546	−	27.9806i	−0.618138	−	1.07065i	0.371687	−	0.928358i	$-0.378780\pi$
$684$		0			0
$685$	−53.3632			−2.03890
$686$		0			0
$687$		0			0
$688$	−6.07661			−0.231669
$689$	19.6061	−	33.9588i	0.746934	−	1.29373i
$690$		0			0
$691$	−14.4981	−	25.1114i	−0.551533	−	0.955283i	−0.998164	−	0.0605650i	$-0.980710\pi$
$691$	−14.4981	−	25.1114i	−0.551533	−	0.955283i	0.446631	−	0.894718i	$-0.352624\pi$
$692$	−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
$698$	−5.47997			−0.207420
$699$		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
$703$	5.93984	+	10.2881i	0.224025	+	0.388023i
$704$	27.8525			1.04973
$705$		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	0.930516	−	0.366251i	$-0.119359\pi$
$709$	3.94282	+	6.82916i	0.148076	+	0.256475i	−0.782441	+	0.622725i	$0.786025\pi$
$710$	−1.93337	−	3.34870i	−0.0725581	−	0.125674i
$711$		0			0
$712$	−2.37373	+	4.11142i	−0.0889592	+	0.154082i
$713$	16.7473	−	29.0073i	0.627193	−	1.08633i
$714$		0			0
$715$	19.9601	+	34.5718i	0.746464	+	1.29291i
$716$	14.7245			0.550281
$717$		0			0
$718$	2.41531			0.0901385
$719$	16.5754	−	28.7095i	0.618159	−	1.07068i	−0.371663	−	0.928368i	$-0.621212\pi$
$719$	16.5754	−	28.7095i	0.618159	−	1.07068i	0.989822	−	0.142314i	$-0.0454544\pi$
$720$		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	$-0.622968\pi$
$727$	16.5502	−	28.6658i	0.613814	−	1.06316i	0.990591	−	0.136853i	$-0.0436989\pi$
$728$		0			0
$729$		0			0
$730$	2.21737	−	3.84060i	0.0820685	−	0.142147i
$731$	2.84071			0.105067
$732$		0			0
$733$	44.5589			1.64582			0.822911	−	0.568170i	$-0.192349\pi$
$733$	44.5589			1.64582			0.822911	+	0.568170i	$0.192349\pi$
$734$	−0.929636	−	1.61018i	−0.0343135	−	0.0594327i
$735$		0			0
$736$	7.07442	−	12.2533i	0.260767	−	0.451661i
$737$	17.2781	−	29.9266i	0.636448	−	1.10236i
$738$		0			0
$739$	−19.9045	−	34.4756i	−0.732199	−	1.26821i	−0.955941	−	0.293558i	$-0.905161\pi$
$739$	−19.9045	−	34.4756i	−0.732199	−	1.26821i	0.223742	−	0.974648i	$-0.428173\pi$
$740$	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
$745$	−15.7259			−0.576152
$746$	2.88276	+	4.99309i	0.105545	+	0.182810i
$747$		0			0
$748$	−13.9021			−0.508310
$749$		0			0
$750$		0			0
$751$	19.7141			0.719378			0.359689	−	0.933072i	$-0.382883\pi$
$751$	19.7141			0.719378			0.359689	+	0.933072i	$0.382883\pi$
$752$	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
$761$	−39.1144			−1.41790			−0.708948	−	0.705261i	$-0.750830\pi$
$761$	−39.1144			−1.41790			−0.708948	+	0.705261i	$0.750830\pi$
$762$		0			0
$763$		0			0
$764$	31.1319			1.12631
$765$		0			0
$766$	1.10480	+	1.91357i	0.0399180	+	0.0691399i
$767$	−22.3354			−0.806486
$768$		0			0
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	−0.974242	−	0.225507i	$-0.927596\pi$
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	0.291826	−	0.956471i	$-0.405737\pi$
$770$		0			0
$771$		0			0
$772$	−12.0205	−	20.8201i	−0.432628	−	0.749333i
$773$	−14.9133	−	25.8305i	−0.536393	−	0.929059i	−0.999095	−	0.0425453i	$-0.986453\pi$
$773$	−14.9133	−	25.8305i	−0.536393	−	0.929059i	0.462702	−	0.886514i	$-0.346880\pi$
$774$		0			0
$775$	5.61224	−	9.72068i	0.201598	−	0.349177i
$776$	−1.44409	+	2.50124i	−0.0518399	+	0.0897894i
$777$		0			0
$778$	−1.24923	−	2.16373i	−0.0447870	−	0.0775734i
$779$	−73.1229			−2.61990
$780$		0			0
$781$	26.0917			0.933633
$782$	−1.04842	+	1.81591i	−0.0374913	+	0.0649369i
$783$		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	$-0.731646\pi$
$787$	8.81030	−	15.2599i	0.314053	−	0.543956i	0.979236	+	0.202724i	$0.0649796\pi$
$788$	−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
$793$	14.7066	−	25.4725i	0.522246	−	0.904556i
$794$	0.0978390			0.00347218
$795$		0			0
$796$	13.1071			0.464570
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	0.762371	−	0.647140i	$-0.224035\pi$
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	−0.941625	+	0.336663i	$0.890702\pi$
$798$		0			0
$799$	−7.98921	+	13.8377i	−0.282638	+	0.489543i
$800$	2.37072	−	4.10621i	0.0838177	−	0.145177i
$801$		0			0
$802$	−1.82365	−	3.15865i	−0.0643953	−	0.111536i
$803$	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
$808$	10.4650			0.368157
$809$	−23.5735	−	40.8305i	−0.828799	−	1.43552i	−0.898981	−	0.437988i	$-0.855691\pi$
$809$	−23.5735	−	40.8305i	−0.828799	−	1.43552i	0.0701816	−	0.997534i	$-0.477642\pi$
$810$		0			0
$811$	−21.0577			−0.739435			−0.369717	−	0.929144i	$-0.620546\pi$
$811$	−21.0577			−0.739435			−0.369717	+	0.929144i	$0.620546\pi$
$812$		0			0
$813$		0			0
$814$	1.66019			0.0581896
$815$	−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	0.946818	−	0.321768i	$-0.104277\pi$
$821$	5.58018	+	9.66515i	0.194750	+	0.337316i	−0.752069	+	0.659085i	$0.770944\pi$
$822$		0			0
$823$	−4.71737	+	8.17072i	−0.164437	+	0.284814i	−0.936455	−	0.350787i	$-0.885914\pi$
$823$	−4.71737	+	8.17072i	−0.164437	+	0.284814i	0.772018	+	0.635601i	$0.219247\pi$
$824$	7.52933			0.262297
$825$		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
$829$	−24.2263	−	41.9612i	−0.841415	−	1.45737i	−0.888699	−	0.458492i	$-0.848390\pi$
$829$	−24.2263	−	41.9612i	−0.841415	−	1.45737i	0.0472838	−	0.998881i	$-0.484943\pi$
$830$	4.27301			0.148318
$831$		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
$836$	29.0688	+	50.3487i	1.00537	+	1.74135i
$837$		0			0
$838$	−0.186860	+	0.323651i	−0.00645497	+	0.0111803i
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	−0.708685	−	0.705525i	$-0.750711\pi$
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	0.965345	+	0.260977i	$0.0840446\pi$
$840$		0			0
$841$	12.2427	+	21.2050i	0.422162	+	0.731206i
$842$	−5.56277			−0.191706
$843$		0			0
$844$	−32.8058			−1.12922
$845$	−0.732518	+	1.26876i	−0.0251994	+	0.0436466i
$846$		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	−0.789407	−	0.613870i	$-0.789612\pi$
$853$	3.99900	−	6.92648i	0.136923	−	0.237158i	0.926331	+	0.376712i	$0.122945\pi$
$854$		0			0
$855$		0			0
$856$	1.86513	−	3.23050i	0.0637488	−	0.110416i
$857$	−43.1322			−1.47337			−0.736684	−	0.676237i	$-0.763610\pi$
$857$	−43.1322			−1.47337			−0.736684	+	0.676237i	$0.763610\pi$
$858$		0			0
$859$	2.44359			0.0833742			0.0416871	−	0.999131i	$-0.486727\pi$
$859$	2.44359			0.0833742			0.0416871	+	0.999131i	$0.486727\pi$
$860$	−4.17984	−	7.23970i	−0.142531	−	0.246872i
$861$		0			0
$862$	−0.120250	+	0.208279i	−0.00409573	+	0.00709401i
$863$	12.8594	−	22.2731i	0.437738	−	0.758185i	−0.559777	−	0.828644i	$-0.689113\pi$
$863$	12.8594	−	22.2731i	0.437738	−	0.758185i	0.997515	+	0.0704589i	$0.0224464\pi$
$864$		0			0
$865$	−1.07605	−	1.86378i	−0.0365870	−	0.0633705i
$866$	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
$871$	30.4342			1.03122
$872$	−3.42395	−	5.93045i	−0.115949	−	0.200830i
$873$		0			0
$874$	8.76884			0.296611
$875$		0			0
$876$		0			0
$877$	−21.9590			−0.741502			−0.370751	−	0.928732i	$-0.620900\pi$
$877$	−21.9590			−0.741502			−0.370751	+	0.928732i	$0.620900\pi$
$878$	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	$-0.701093\pi$
$881$	−35.0576			−1.18112			−0.590560	+	0.806994i	$0.701093\pi$
$882$		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
$887$	47.8180			1.60557			0.802785	−	0.596269i	$-0.203351\pi$
$887$	47.8180			1.60557			0.802785	+	0.596269i	$0.203351\pi$
$888$		0			0
$889$		0			0
$890$	−3.12071			−0.104607
$891$		0			0
$892$	−4.37272	−	7.57378i	−0.146410	−	0.253589i
$893$	66.8208			2.23607
$894$		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
$899$	6.94357	+	12.0266i	0.231581	+	0.401110i
$900$		0			0
$901$	−9.10848	+	15.7764i	−0.303448	+	0.525587i
$902$	−5.10948	+	8.84988i	−0.170127	+	0.294669i
$903$		0			0
$904$	3.26647	+	5.65769i	0.108641	+	0.188172i
$905$	1.06045			0.0352505
$906$		0			0
$907$	−19.1144			−0.634682			−0.317341	−	0.948312i	$-0.602790\pi$
$907$	−19.1144			−0.634682			−0.317341	+	0.948312i	$0.602790\pi$
$908$	5.89092	−	10.2034i	0.195497	−	0.338611i
$909$		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
$919$	−8.10464	+	14.0377i	−0.267348	+	0.463060i	−0.968176	−	0.250270i	$-0.919481\pi$
$919$	−8.10464	+	14.0377i	−0.267348	+	0.463060i	0.700828	+	0.713330i	$0.252814\pi$
$920$	12.5228			0.412865
$921$		0			0
$922$	4.87514			0.160554
$923$	11.4897	+	19.9007i	0.378187	+	0.655039i
$924$		0			0
$925$	−1.42558	+	2.46918i	−0.0468728	+	0.0811860i
$926$	0.814099	−	1.41006i	0.0267529	−	0.0463375i
$927$		0			0
$928$	2.93310	+	5.08029i	0.0962839	+	0.166769i
$929$	−11.3415	−	19.6440i	−0.372102	−	0.644499i	0.617787	−	0.786345i	$-0.288029\pi$
$929$	−11.3415	−	19.6440i	−0.372102	−	0.644499i	−0.989889	+	0.141846i	$0.954696\pi$
$930$		0			0
$931$		0			0
$932$	7.90576	+	13.6932i	0.258962	+	0.448535i
$933$		0			0
$934$	5.92814			0.193975
$935$	−9.27292	−	16.0612i	−0.303257	−	0.525256i
$936$		0			0
$937$	51.2933			1.67568			0.837840	−	0.545915i	$-0.183818\pi$
$937$	51.2933			1.67568			0.837840	+	0.545915i	$0.183818\pi$
$938$		0			0
$939$		0			0
$940$	47.0216			1.53368
$941$	−15.9659	+	27.6538i	−0.520474	+	0.901487i	0.479243	+	0.877682i	$0.340911\pi$
$941$	−15.9659	+	27.6538i	−0.520474	+	0.901487i	−0.999717	+	0.0238048i	$0.992422\pi$
$942$		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	0.827211	−	0.561891i	$-0.189926\pi$
$947$	−2.24665	−	3.89131i	−0.0730063	−	0.126451i	−0.900218	+	0.435440i	$0.856593\pi$
$948$		0			0
$949$	−13.1774	+	22.8240i	−0.427757	+	0.740898i
$950$	2.93854			0.0953390
$951$		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
$955$	20.7655	+	35.9669i	0.671956	+	1.16386i
$956$	41.1150			1.32975
$957$		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
$962$	0.731078	+	1.26626i	0.0235709	+	0.0408260i
$963$		0			0
$964$	13.3000	−	23.0363i	0.428365	−	0.741950i
$965$	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	$-0.460654\pi$
$968$	6.11763			0.196628
$969$		0			0
$970$	−1.89853			−0.0609582
$971$	−2.56661	+	4.44550i	−0.0823664	+	0.142663i	−0.904266	−	0.426970i	$-0.859581\pi$
$971$	−2.56661	+	4.44550i	−0.0823664	+	0.142663i	0.821900	+	0.569632i	$0.192914\pi$
$972$		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	−0.500994	−	0.865451i	$-0.667032\pi$
$977$	15.5974	−	27.0155i	0.499006	−	0.864303i	0.999999	+	0.00114787i	$0.000365378\pi$
$978$		0			0
$979$	10.5288	−	18.2365i	0.336503	−	0.582840i
$980$		0			0
$981$		0			0
$982$	1.48113	−	2.56538i	0.0472646	−	0.0818647i
$983$	−20.3401			−0.648748			−0.324374	−	0.945929i	$-0.605154\pi$
$983$	−20.3401			−0.648748			−0.324374	+	0.945929i	$0.605154\pi$
$984$		0			0
$985$	−59.8757			−1.90780
$986$	−0.434681	−	0.752890i	−0.0138431	−	0.0239769i
$987$		0			0
$988$	−25.6014	+	44.3429i	−0.814488	+	1.41074i
$989$	4.25404	−	7.36821i	0.135271	−	0.234296i
$990$		0			0
$991$	6.48276	+	11.2285i	0.205932	+	0.356684i	0.950429	−	0.310941i	$-0.100644\pi$
$991$	6.48276	+	11.2285i	0.205932	+	0.356684i	−0.744498	+	0.667625i	$0.767311\pi$
$992$	−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
$997$	−49.4816			−1.56710			−0.783548	−	0.621331i	$-0.786592\pi$
$997$	−49.4816			−1.56710			−0.783548	+	0.621331i	$0.786592\pi$
$998$	1.22218	+	2.11688i	0.0386875	+	0.0670086i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	63.23	odd	6
441.2.f.g.148.4	yes	12	63.5	even	6
441.2.f.g.295.3	yes	12	21.2	odd	6
441.2.f.g.295.4	yes	12	21.5	even	6
441.2.g.g.67.3		12	63.32	odd	6
441.2.g.g.67.4		12	63.59	even	6
441.2.g.g.79.3		12	3.2	odd	2
441.2.g.g.79.4		12	21.20	even	2
441.2.h.g.214.3		12	21.17	even	6
441.2.h.g.214.4		12	21.11	odd	6
441.2.h.g.373.3		12	63.41	even	6
441.2.h.g.373.4		12	9.5	odd	6
1323.2.f.g.442.3		12	63.58	even	3
1323.2.f.g.442.4		12	63.40	odd	6
1323.2.f.g.883.3		12	7.2	even	3
1323.2.f.g.883.4		12	7.5	odd	6
1323.2.g.g.361.3		12	63.31	odd	6	inner
1323.2.g.g.361.4		12	63.4	even	3	inner
1323.2.g.g.667.3		12	7.6	odd	2	inner
1323.2.g.g.667.4		12	1.1	even	1	trivial
1323.2.h.g.226.3		12	9.4	even	3
1323.2.h.g.226.4		12	63.13	odd	6
1323.2.h.g.802.3		12	7.4	even	3
1323.2.h.g.802.4		12	7.3	odd	6
3969.2.a.bd.1.3		6	63.61	odd	6
3969.2.a.bd.1.4		6	63.16	even	3
3969.2.a.be.1.3		6	63.2	odd	6
3969.2.a.be.1.4		6	63.47	even	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 + 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +O(q^{10})\)	\(q+(0.119562 + 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +(0.309879 + 0.536725i) q^{10} -4.18194 q^{11} +(-1.84155 - 3.18966i) q^{13} +(-1.83009 - 3.16982i) q^{16} +(0.855536 + 1.48183i) q^{17} +(3.57780 - 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +5.12476 q^{23} +1.71737 q^{25} +(0.440358 - 0.762722i) q^{26} +(-1.06238 + 1.84010i) q^{29} +(3.26793 - 5.66021i) q^{31} +(1.38044 - 2.39099i) q^{32} +(-0.204579 + 0.354341i) q^{34} +(-0.830095 + 1.43777i) q^{37} +1.71107 q^{38} +2.44359 q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(-4.06238 + 7.03625i) q^{44} +(0.612725 + 1.06127i) q^{46} +(4.66912 + 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} -7.15561 q^{52} +(5.32326 + 9.22015i) q^{53} -10.8387 q^{55} -0.508080 q^{58} +(3.03215 - 5.25183i) q^{59} +(3.99298 + 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(-4.77292 - 8.26693i) q^{65} +(-4.13160 + 7.15614i) q^{67} +3.32431 q^{68} -6.23912 q^{71} +(-3.57780 - 6.19694i) q^{73} -0.396990 q^{74} +(-6.95103 - 12.0395i) q^{76} +(4.91423 + 8.51170i) q^{79} +(-4.74322 - 8.21550i) q^{80} +(1.22180 - 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +0.396990 q^{86} -3.94282 q^{88} +(-2.51769 + 4.36077i) q^{89} +(4.97825 - 8.62258i) q^{92} +(-1.11650 + 1.93383i) q^{94} +(9.27292 - 16.0612i) q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} - 16 q^{11} - 6 q^{16} - 6 q^{22} - 8 q^{23} + 24 q^{25} + 22 q^{29} + 16 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} + 36 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} - 72 q^{74} + 6 q^{79} + 30 q^{85} + 72 q^{86} - 12 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 - 16 * q^11 - 6 * q^16 - 6 * q^22 - 8 * q^23 + 24 * q^25 + 22 * q^29 + 16 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 + 36 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 - 72 * q^74 + 6 * q^79 + 30 * q^85 + 72 * q^86 - 12 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more