LMFDB - Embedded newform 1323.2.g.g.361.3

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			361.3
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.g.667.3

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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	−0.820653	−	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
$5$	−2.59179			−1.15908			−0.579542	−	0.814943i	$-0.696768\pi$
$5$	−2.59179			−1.15908			−0.579542	+	0.814943i	$0.696768\pi$
$6$		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	−0.489168	−	0.872190i	$-0.662699\pi$
$13$	1.84155	−	3.18966i	0.510755	−	0.884653i	0.999922	−	0.0124633i	$-0.00396730\pi$
$14$		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	$-0.899865\pi$
$17$	−0.855536	+	1.48183i	−0.207498	+	0.359397i	0.743428	+	0.668816i	$0.233199\pi$
$18$		0			0
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	−0.905084	−	0.425233i	$-0.860192\pi$
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	0.0842790	−	0.996442i	$-0.473141\pi$
$20$	−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	0.750366	−	0.661023i	$-0.229877\pi$
$29$	−1.06238	−	1.84010i	−0.197279	−	0.341698i	−0.947645	+	0.319325i	$0.896544\pi$
$30$		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
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	0.789690	−	0.613506i	$-0.210241\pi$
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	−0.926157	+	0.377139i	$0.876908\pi$
$38$	−1.71107			−0.277573
$39$		0			0
$40$	−2.44359			−0.386366
$41$	5.10948	−	8.84988i	0.797967	−	1.38212i	−0.122972	−	0.992410i	$-0.539242\pi$
$41$	5.10948	−	8.84988i	0.797967	−	1.38212i	0.920938	−	0.389708i	$-0.127424\pi$
$42$		0			0
$43$	0.830095	+	1.43777i	0.126588	+	0.219257i	0.922353	−	0.386349i	$-0.126264\pi$
$43$	0.830095	+	1.43777i	0.126588	+	0.219257i	−0.795764	+	0.605606i	$0.792931\pi$
$44$	−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	0.293596	+	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
$52$	7.15561			0.992305
$53$	5.32326	−	9.22015i	0.731206	−	1.26649i	−0.225162	−	0.974321i	$-0.572291\pi$
$53$	5.32326	−	9.22015i	0.731206	−	1.26649i	0.956368	−	0.292164i	$-0.0943754\pi$
$54$		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	$-0.295836\pi$
$59$	−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	$-0.335084\pi$
$68$	−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	$-0.695802\pi$
$73$	3.57780	−	6.19694i	0.418750	−	0.725297i	0.995814	+	0.0914022i	$0.0291349\pi$
$74$	−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	−0.445170	−	0.895446i	$-0.646857\pi$
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	0.998064	−	0.0621945i	$-0.0198099\pi$
$80$	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	$-0.290190\pi$
$83$	−3.44733	−	5.97094i	−0.378393	−	0.655396i	−0.990829	+	0.135124i	$0.956857\pi$
$84$		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	$-0.0806757\pi$
$89$	2.51769	+	4.36077i	0.266875	+	0.462240i	−0.701178	+	0.712986i	$0.747342\pi$
$90$		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	$-0.116962\pi$
$97$	1.53167	+	2.65294i	0.155518	+	0.269365i	−0.777730	+	0.628599i	$0.783629\pi$
$98$		0			0
$99$		0			0
$100$	1.66827	+	2.88953i	0.166827	+	0.288953i
$101$	−11.0997			−1.10446			−0.552229	−	0.833692i	$-0.686223\pi$
$101$	−11.0997			−1.10446			−0.552229	+	0.833692i	$0.686223\pi$
$102$		0			0
$103$	−7.98597			−0.786881			−0.393440	−	0.919350i	$-0.628715\pi$
$103$	−7.98597			−0.786881			−0.393440	+	0.919350i	$0.628715\pi$
$104$	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	0.945663	−	0.325149i	$-0.105414\pi$
$107$	1.97825	+	3.42642i	0.191244	+	0.331245i	−0.754419	+	0.656394i	$0.772081\pi$
$108$		0			0
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	−0.985866	−	0.167534i	$-0.946420\pi$
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	0.638022	+	0.770018i	$0.279753\pi$
$110$	1.29589	−	2.24456i	0.123559	−	0.214010i
$111$		0			0
$112$		0			0
$113$	3.46457	−	6.00082i	0.325920	−	0.564509i	−0.655778	−	0.754953i	$-0.727659\pi$
$113$	3.46457	−	6.00082i	0.325920	−	0.564509i	0.981698	+	0.190444i	$0.0609928\pi$
$114$		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	$-0.560191\pi$
$131$	−4.30286			−0.375943			−0.187971	+	0.982175i	$0.560191\pi$
$132$		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	0.309914	+	0.950765i	$0.399700\pi$
$139$	−7.88067	+	13.6497i	−0.668429	+	1.15775i	−0.978343	+	0.206989i	$0.933634\pi$
$140$		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	$-0.153594\pi$
$157$	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
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	0.700772	−	0.713385i	$-0.252839\pi$
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	−0.968196	+	0.250194i	$0.919505\pi$
$164$	19.8536			1.55031
$165$		0			0
$166$	−1.64867			−0.127962
$167$	−8.99716	+	15.5835i	−0.696221	+	1.20589i	0.273546	+	0.961859i	$0.411803\pi$
$167$	−8.99716	+	15.5835i	−0.696221	+	1.20589i	−0.969767	+	0.244032i	$0.921530\pi$
$168$		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	$-0.823284\pi$
$173$	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
$178$	1.20408			0.0902493
$179$	3.78947	−	6.56355i	0.283238	−	0.490583i	−0.688942	−	0.724816i	$-0.741925\pi$
$179$	3.78947	−	6.56355i	0.283238	−	0.490583i	0.972180	+	0.234233i	$0.0752580\pi$
$180$		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
$184$	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	−0.415779	−	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	$0.686409\pi$
$194$	0.732518			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	$-0.910193\pi$
$199$	−3.37323	+	5.84260i	−0.239122	+	0.414171i	0.721341	+	0.692580i	$0.243526\pi$
$200$	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	0.414106	+	0.910228i	$0.364094\pi$
$211$	−8.44282	+	14.6234i	−0.581228	+	1.00672i	−0.995334	+	0.0964875i	$0.969239\pi$
$212$	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	$-0.214825\pi$
$223$	−2.25071	−	3.89834i	−0.150719	−	0.261052i	−0.931492	+	0.363762i	$0.881492\pi$
$224$		0			0
$225$		0			0
$226$	−0.828460	−	1.43494i	−0.0551084	−	0.0954505i
$227$	−6.06429			−0.402501			−0.201251	−	0.979540i	$-0.564501\pi$
$227$	−6.06429			−0.402501			−0.201251	+	0.979540i	$0.564501\pi$
$228$		0			0
$229$	11.0493			0.730159			0.365080	−	0.930976i	$-0.381042\pi$
$229$	11.0493			0.730159			0.365080	+	0.930976i	$0.381042\pi$
$230$	−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	0.701394	−	0.712774i	$-0.252561\pi$
$233$	−4.06922	−	7.04809i	−0.266583	−	0.461736i	−0.967977	+	0.251038i	$0.919228\pi$
$234$		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	−0.289166	−	0.957279i	$-0.593378\pi$
$239$	10.5813	−	18.3273i	0.684445	−	1.18549i	0.973611	−	0.228214i	$-0.0732886\pi$
$240$		0			0
$241$	−13.6915			−0.881945			−0.440972	−	0.897521i	$-0.645366\pi$
$241$	−13.6915			−0.881945			−0.440972	+	0.897521i	$0.645366\pi$
$242$	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	$-0.340697\pi$
$251$	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
$257$	25.6215			1.59822			0.799112	−	0.601182i	$-0.205303\pi$
$257$	25.6215			1.59822			0.799112	+	0.601182i	$0.205303\pi$
$258$		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	−0.499078	−	0.866557i	$-0.666328\pi$
$269$	8.21572	−	14.2301i	0.500922	−	0.867622i	0.999999	−	0.00106448i	$-0.000338834\pi$
$270$		0			0
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	0.991862	−	0.127314i	$-0.0406357\pi$
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	−0.606189	+	0.795321i	$0.707302\pi$
$272$	−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	0.933310	−	0.359071i	$-0.116906\pi$
$281$	2.60985	+	4.52039i	0.155690	+	0.269664i	−0.777620	+	0.628735i	$0.783573\pi$
$282$		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
$289$	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	$-0.906745\pi$
$293$	−3.91286	+	6.77728i	−0.228592	+	0.395933i	0.728799	+	0.684728i	$0.240079\pi$
$294$		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	$-0.723955\pi$
$307$	−22.6709			−1.29390			−0.646948	+	0.762534i	$0.723955\pi$
$308$		0			0
$309$		0			0
$310$	4.05064			0.230061
$311$	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
$320$	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	−0.659307	−	0.751874i	$-0.729150\pi$
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	0.980795	+	0.195040i	$0.0624835\pi$
$332$	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	0.114883	−	0.993379i	$-0.463351\pi$
$337$	16.8473	−	29.1804i	0.917733	−	1.58956i	0.802850	−	0.596181i	$-0.203316\pi$
$338$	−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	0.955563	+	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	0.990670	+	0.136281i	$0.0435150\pi$
$349$	11.4585	+	19.8467i	0.613358	+	1.06237i	−0.377312	+	0.926086i	$0.623152\pi$
$350$		0			0
$351$		0			0
$352$	−5.77292	−	9.99898i	−0.307697	−	0.532948i
$353$	10.2693			0.546581			0.273290	−	0.961932i	$-0.411888\pi$
$353$	10.2693			0.546581			0.273290	+	0.961932i	$0.411888\pi$
$354$		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	0.967968	−	0.251075i	$-0.0807839\pi$
$359$	5.05034	+	8.74745i	0.266547	+	0.461673i	−0.701421	+	0.712747i	$0.747451\pi$
$360$		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	$-0.434952\pi$
$367$	7.77537			0.405871			0.202935	+	0.979192i	$0.434952\pi$
$368$	−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	$-0.575863\pi$
$383$	−9.24040			−0.472162			−0.236081	+	0.971733i	$0.575863\pi$
$384$		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	$-0.169935\pi$
$397$	−0.204579	−	0.354341i	−0.0102675	−	0.0177838i	−0.871114	+	0.491082i	$0.836602\pi$
$398$	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	$-0.215068\pi$
$409$	−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
$415$	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	$-0.845488\pi$
$419$	−0.781437	+	1.35349i	−0.0381757	+	0.0661223i	0.846306	+	0.532697i	$0.178821\pi$
$420$		0			0
$421$	−11.6316	−	20.1465i	−0.566889	−	0.981881i	−0.996871	−	0.0790438i	$-0.974813\pi$
$421$	−11.6316	−	20.1465i	−0.566889	−	0.981881i	0.429982	−	0.902838i	$-0.358520\pi$
$422$	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	−0.853660	−	0.520831i	$-0.825622\pi$
$431$	0.502879	−	0.871011i	0.0242228	−	0.0419551i	0.877883	+	0.478876i	$0.158956\pi$
$432$		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
$436$	−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	$-0.686821\pi$
$439$	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
$446$	−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	−0.118205	−	0.992989i	$-0.537714\pi$
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	0.919056	−	0.394126i	$-0.128953\pi$
$458$	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	$-0.324136\pi$
$461$	−10.1938	−	17.6561i	−0.474772	−	0.822328i	−0.999583	+	0.0288903i	$0.990803\pi$
$462$		0			0
$463$	−3.40451	+	5.89679i	−0.158221	+	0.274047i	−0.934227	−	0.356678i	$-0.883909\pi$
$463$	−3.40451	+	5.89679i	−0.158221	+	0.274047i	0.776006	+	0.630725i	$0.217243\pi$
$464$	7.77704			0.361040
$465$		0			0
$466$	−1.94609			−0.0901509
$467$	−12.3956	−	21.4698i	−0.573598	−	0.993502i	−0.996192	−	0.0871825i	$-0.972214\pi$
$467$	−12.3956	−	21.4698i	−0.573598	−	0.993502i	0.422594	−	0.906319i	$-0.361120\pi$
$468$		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	$-0.581608\pi$
$479$	−11.0997			−0.507157			−0.253579	+	0.967315i	$0.581608\pi$
$480$		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	−0.729618	−	0.683855i	$-0.760302\pi$
$487$	5.01887	−	8.69295i	0.227427	−	0.393915i	0.957045	+	0.289940i	$0.0936354\pi$
$488$	−3.76466	+	6.52059i	−0.170418	+	0.295173i
$489$		0			0
$490$		0			0
$491$	−6.19398	+	10.7283i	−0.279530	+	0.484161i	−0.971268	−	0.237988i	$-0.923512\pi$
$491$	−6.19398	+	10.7283i	−0.279530	+	0.484161i	0.691738	+	0.722149i	$0.256845\pi$
$492$		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	$-0.560379\pi$
$503$	−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
$509$	−10.5657			−0.468317			−0.234159	−	0.972198i	$-0.575233\pi$
$509$	−10.5657			−0.468317			−0.234159	+	0.972198i	$0.575233\pi$
$510$		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	$-0.975793\pi$
$521$	−9.87788	+	17.1090i	−0.432758	+	0.749558i	0.564352	+	0.825534i	$0.309126\pi$
$522$		0			0
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	−0.964415	−	0.264394i	$-0.914828\pi$
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	0.253236	−	0.967405i	$-0.418505\pi$
$524$	−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	0.654734	−	0.755859i	$-0.272781\pi$
$541$	−7.61109	−	13.1828i	−0.327226	−	0.566773i	−0.981960	+	0.189087i	$0.939447\pi$
$542$	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	0.500294	−	0.865856i	$-0.333225\pi$
$547$	−11.6871	−	20.2427i	−0.499706	−	0.865517i	−1.00000		0.000339172i	$0.999892\pi$
$548$	−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	−0.408580	−	0.912723i	$-0.633976\pi$
$557$	13.8337	−	23.9606i	0.586151	−	1.01524i	0.994731	−	0.102521i	$-0.0326908\pi$
$558$		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	$-0.108946\pi$
$563$	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	$0.905328\pi$
$572$	−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	0.204307	−	0.978907i	$-0.434506\pi$
$577$	22.8177	−	39.5214i	0.949912	−	1.64530i	0.745605	−	0.666389i	$-0.232161\pi$
$578$	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	$-0.234303\pi$
$587$	−5.10948	−	8.84988i	−0.210891	−	0.365274i	−0.951994	+	0.306118i	$0.900970\pi$
$588$		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	$-0.0914883\pi$
$593$	5.69804	+	9.86929i	0.233990	+	0.405283i	−0.724988	+	0.688761i	$0.758155\pi$
$594$		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	0.924610	+	0.380915i	$0.124391\pi$
$601$	19.4207	+	33.6376i	0.792187	+	1.37211i	−0.132423	+	0.991193i	$0.542276\pi$
$602$		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	$-0.816752\pi$
$607$	−41.3325			−1.67763			−0.838817	+	0.544414i	$0.816752\pi$
$608$	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	−0.416905	−	0.908950i	$-0.636885\pi$
$613$	14.3285	−	24.8176i	0.578721	−	1.00237i	0.995626	−	0.0934244i	$-0.0297813\pi$
$614$	−2.71057	+	4.69485i	−0.109390	+	0.189469i
$615$		0			0
$616$		0			0
$617$	−16.8518	+	29.1883i	−0.678430	+	1.17508i	0.297024	+	0.954870i	$0.404006\pi$
$617$	−16.8518	+	29.1883i	−0.678430	+	1.17508i	−0.975454	+	0.220205i	$0.929327\pi$
$618$		0			0
$619$	1.43807			0.0578010			0.0289005	−	0.999582i	$-0.490799\pi$
$619$	1.43807			0.0578010			0.0289005	+	0.999582i	$0.490799\pi$
$620$	−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	−0.496013	−	0.868315i	$-0.665203\pi$
$643$	12.7795	−	22.1348i	0.503976	−	0.872912i	0.999989	−	0.00459728i	$-0.00146337\pi$
$644$		0			0
$645$		0			0
$646$	1.46389	−	2.53552i	0.0575958	−	0.0997588i
$647$	14.1556	−	24.5181i	0.556512	−	0.963908i	−0.441272	−	0.897374i	$-0.645472\pi$
$647$	14.1556	−	24.5181i	0.556512	−	0.963908i	0.997784	−	0.0665343i	$-0.0211942\pi$
$648$		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	−0.982169	−	0.188000i	$-0.939799\pi$
$659$	−16.7862	−	29.0745i	−0.653897	−	1.13258i	0.328272	−	0.944583i	$-0.393534\pi$
$660$		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
$667$	−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	0.875384	+	0.483429i	$0.160609\pi$
$673$	22.2157	+	38.4788i	0.856354	+	1.48325i	−0.0190299	+	0.999819i	$0.506058\pi$
$674$	−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	$-0.922412\pi$
$677$	−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
$682$	6.53585			0.250271
$683$	−16.1546	+	27.9806i	−0.618138	+	1.07065i	0.371687	+	0.928358i	$0.378780\pi$
$683$	−16.1546	+	27.9806i	−0.618138	+	1.07065i	−0.989825	+	0.142289i	$0.954554\pi$
$684$		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	−0.446631	−	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
$698$	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	−0.782441	−	0.622725i	$-0.786025\pi$
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	0.930516	+	0.366251i	$0.119359\pi$
$710$	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	−0.989822	−	0.142314i	$-0.954546\pi$
$719$	−16.5754	−	28.7095i	−0.618159	−	1.07068i	0.371663	−	0.928368i	$-0.378788\pi$
$720$		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	−0.990591	−	0.136853i	$-0.956301\pi$
$727$	−16.5502	−	28.6658i	−0.613814	−	1.06316i	0.376777	−	0.926304i	$-0.377032\pi$
$728$		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	$-0.807651\pi$
$733$	−44.5589			−1.64582			−0.822911	+	0.568170i	$0.807651\pi$
$734$	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	0.223742	+	0.974648i	$0.428173\pi$
$739$	−19.9045	+	34.4756i	−0.732199	+	1.26821i	−0.955941	+	0.293558i	$0.905161\pi$
$740$	−4.17984	+	7.23970i	−0.153654	+	0.266137i
$741$		0			0
$742$		0			0
$743$	5.37072	−	9.30237i	0.197033	−	0.341271i	−0.750532	−	0.660834i	$-0.770203\pi$
$743$	5.37072	−	9.30237i	0.197033	−	0.341271i	0.947565	+	0.319563i	$0.103536\pi$
$744$		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	$-0.249170\pi$
$761$	39.1144			1.41790			0.708948	+	0.705261i	$0.249170\pi$
$762$		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	−0.291826	−	0.956471i	$-0.594263\pi$
$769$	18.9240	−	32.7773i	0.682415	−	1.18198i	0.974242	−	0.225507i	$-0.0724038\pi$
$770$		0			0
$771$		0			0
$772$	−12.0205	+	20.8201i	−0.432628	+	0.749333i
$773$	14.9133	−	25.8305i	0.536393	−	0.929059i	−0.462702	−	0.886514i	$-0.653120\pi$
$773$	14.9133	−	25.8305i	0.536393	−	0.929059i	0.999095	−	0.0425453i	$-0.0135467\pi$
$774$		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	$-0.268354\pi$
$787$	−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
$793$	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	$-0.775965\pi$
$797$	5.06056	−	8.76515i	0.179254	−	0.310477i	0.941625	+	0.336663i	$0.109298\pi$
$798$		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	0.0701816	+	0.997534i	$0.477642\pi$
$809$	−23.5735	+	40.8305i	−0.828799	+	1.43552i	−0.898981	+	0.437988i	$0.855691\pi$
$810$		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
$814$	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	−0.752069	−	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	$0.885914\pi$
$824$	−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	−0.0472838	−	0.998881i	$-0.515057\pi$
$829$	24.2263	−	41.9612i	0.841415	−	1.45737i	0.888699	−	0.458492i	$-0.151610\pi$
$830$	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	$-0.249289\pi$
$839$	−7.43429	−	12.8766i	−0.256660	−	0.444548i	−0.965345	+	0.260977i	$0.915955\pi$
$840$		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	$-0.210388\pi$
$853$	−3.99900	−	6.92648i	−0.136923	−	0.237158i	−0.926331	+	0.376712i	$0.877055\pi$
$854$		0			0
$855$		0			0
$856$	1.86513	+	3.23050i	0.0637488	+	0.110416i
$857$	43.1322			1.47337			0.736684	−	0.676237i	$-0.236390\pi$
$857$	43.1322			1.47337			0.736684	+	0.676237i	$0.236390\pi$
$858$		0			0
$859$	−2.44359			−0.0833742			−0.0416871	−	0.999131i	$-0.513273\pi$
$859$	−2.44359			−0.0833742			−0.0416871	+	0.999131i	$0.513273\pi$
$860$	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	0.997515	−	0.0704589i	$-0.0224464\pi$
$863$	12.8594	+	22.2731i	0.437738	+	0.758185i	−0.559777	+	0.828644i	$0.689113\pi$
$864$		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	$-0.298907\pi$
$881$	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
$887$	−47.8180			−1.60557			−0.802785	−	0.596269i	$-0.796649\pi$
$887$	−47.8180			−1.60557			−0.802785	+	0.596269i	$0.796649\pi$
$888$		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	0.676789	−	0.736177i	$-0.263371\pi$
$911$	−9.02928	−	15.6392i	−0.299153	−	0.518149i	−0.975942	+	0.218028i	$0.930038\pi$
$912$		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	0.700828	−	0.713330i	$-0.252814\pi$
$919$	−8.10464	−	14.0377i	−0.267348	−	0.463060i	−0.968176	+	0.250270i	$0.919481\pi$
$920$	−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	$-0.711971\pi$
$929$	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
$934$	−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	$-0.816182\pi$
$937$	−51.2933			−1.67568			−0.837840	+	0.545915i	$0.816182\pi$
$938$		0			0
$939$		0			0
$940$	47.0216			1.53368
$941$	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
$950$	−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	0.123295	+	0.992370i	$0.460654\pi$
$967$	−24.8080	+	42.9686i	−0.797770	+	1.38178i	−0.921065	+	0.389408i	$0.872680\pi$
$968$	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	$-0.140419\pi$
$971$	2.56661	+	4.44550i	0.0823664	+	0.142663i	−0.821900	+	0.569632i	$0.807086\pi$
$972$		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
$982$	1.48113	+	2.56538i	0.0472646	+	0.0818647i
$983$	20.3401			0.648748			0.324374	−	0.945929i	$-0.394846\pi$
$983$	20.3401			0.648748			0.324374	+	0.945929i	$0.394846\pi$
$984$		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	−0.744498	−	0.667625i	$-0.767311\pi$
$991$	6.48276	−	11.2285i	0.205932	−	0.356684i	0.950429	+	0.310941i	$0.100644\pi$
$992$	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	$-0.213408\pi$
$997$	49.4816			1.56710			0.783548	+	0.621331i	$0.213408\pi$
$998$	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.361.3		12
3.2	odd	2		441.2.g.g.67.4		12
7.2	even	3		1323.2.h.g.226.4		12
7.3	odd	6		1323.2.f.g.442.3		12
7.4	even	3		1323.2.f.g.442.4		12
7.5	odd	6		1323.2.h.g.226.3		12
7.6	odd	2	inner	1323.2.g.g.361.4		12
9.2	odd	6		441.2.h.g.214.3		12
9.7	even	3		1323.2.h.g.802.4		12
21.2	odd	6		441.2.h.g.373.3		12
21.5	even	6		441.2.h.g.373.4		12
21.11	odd	6		441.2.f.g.148.4	yes	12
21.17	even	6		441.2.f.g.148.3	✓	12
21.20	even	2		441.2.g.g.67.3		12
63.2	odd	6		441.2.g.g.79.4		12
63.4	even	3		3969.2.a.bd.1.3		6
63.11	odd	6		441.2.f.g.295.4	yes	12
63.16	even	3	inner	1323.2.g.g.667.3		12
63.20	even	6		441.2.h.g.214.4		12
63.25	even	3		1323.2.f.g.883.4		12
63.31	odd	6		3969.2.a.bd.1.4		6
63.32	odd	6		3969.2.a.be.1.4		6
63.34	odd	6		1323.2.h.g.802.3		12
63.38	even	6		441.2.f.g.295.3	yes	12
63.47	even	6		441.2.g.g.79.3		12
63.52	odd	6		1323.2.f.g.883.3		12
63.59	even	6		3969.2.a.be.1.3		6
63.61	odd	6	inner	1323.2.g.g.667.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	21.17	even	6
441.2.f.g.148.4	yes	12	21.11	odd	6
441.2.f.g.295.3	yes	12	63.38	even	6
441.2.f.g.295.4	yes	12	63.11	odd	6
441.2.g.g.67.3		12	21.20	even	2
441.2.g.g.67.4		12	3.2	odd	2
441.2.g.g.79.3		12	63.47	even	6
441.2.g.g.79.4		12	63.2	odd	6
441.2.h.g.214.3		12	9.2	odd	6
441.2.h.g.214.4		12	63.20	even	6
441.2.h.g.373.3		12	21.2	odd	6
441.2.h.g.373.4		12	21.5	even	6
1323.2.f.g.442.3		12	7.3	odd	6
1323.2.f.g.442.4		12	7.4	even	3
1323.2.f.g.883.3		12	63.52	odd	6
1323.2.f.g.883.4		12	63.25	even	3
1323.2.g.g.361.3		12	1.1	even	1	trivial
1323.2.g.g.361.4		12	7.6	odd	2	inner
1323.2.g.g.667.3		12	63.16	even	3	inner
1323.2.g.g.667.4		12	63.61	odd	6	inner
1323.2.h.g.226.3		12	7.5	odd	6
1323.2.h.g.226.4		12	7.2	even	3
1323.2.h.g.802.3		12	63.34	odd	6
1323.2.h.g.802.4		12	9.7	even	3
3969.2.a.bd.1.3		6	63.4	even	3
3969.2.a.bd.1.4		6	63.31	odd	6
3969.2.a.be.1.3		6	63.59	even	6
3969.2.a.be.1.4		6	63.32	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.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